:T« V, '•-♦■ Digitized by the Internet Archive in 2010 with funding from Boston Library Consortium IVIember Libraries http://www.archive.org/details/economicsofbridgOOwadd / Gl- /. 9}cUJuJl. ECONOMICS OF BRIDGEWORK A SEQUEL TO BEIDGE ENGINEERING BY J. A. L. WADDELL ?..Q C.E. (Rens. Poly. Inst.); B.A.Sc, Ma.E., D.Sc. (McGill Univ.); D.E. (Univ. of Neb.); LL.D. (Univ. of Mo.); Kogakuhukushi (Doctor of Eng., Imp. Univ. of Japan) Correspondant de I'lnstltut de France dans I'Academle des Sciences; Corresponsal de la Socledad de Ingenleroa del Peru; Knight Commander of the Japanese Order of the Rising Sun; Membre de la Soclete de Blenfalsance de la Grande Duchesse OlgadeRussle; Consulting Engineer, New York City; Member of the American Society of Civil Engineers; of the American Institute of Consulting Engineers; of the Franklin Institute; of the Institution of Civil Engineers, London; of La Soclete des Ingenleurs CIvlls, Paris; of the En- gineering Institute ot Canada; of the Western Society of Engineers; of the Rensselaer Society of Engineers; of the Society for the Promotion of Englqeerlng Education; of the American Association for the Advancement of Science; of the American Society for Testing Materials; of the International Society for Testing Materials; of the American Railway Engineering Association; of La Soclete de Geographic de France; ot the Phi Beta Kappa Society; of the Tau Beta Pi Society; of the Sigma XI Society; of the National Conservation Association; of The National Economic League; and Hon- orary Member of the Engineers' Club of Kansas City; and of the Soclete Internationale d'Etudes de Correspondance et d'Echangea " Concordia," Paris BOSTOK COLLEGE LIBRART CHESTJSUT HILL, MASS» NEW YORK JOHN WILEY & SONS, Inc London: CHAPMAN & HALL, Limited 1921 Copyright. 1921. by J. A. L. WADDELL ^ ^ PRESS or ORAUNWOHTH I. CO. •OOK MANUFACTUHIRS ■ROOKLVN, N. V. TO THE OF f Ittatitttt U Jlrante THE UNIVERSALLY ACKNOWLEDGED LEADER OF THE WORLD IN ALL LINES OP SCIENTIFIC THOUGHT AS A MARK OP THE AUTHOR'S GRATEFUL APPRECIATION OP THE PROUD DISTINCTION CONFERRED UPON HIM BY FRANCE THROUGH ADMISSION TO ITS RANKS ON DECEMBER 16. 1918. AND AS AN EVIDENCE OP HIS PROPOUIvD ADMIRATION AND REGARD FOR THE ENTIRE FRENCH NATION THIS TREATISE HIS FINAL CONTRIBUTION IN BOOK FORM TO ENGINEERING LITERATURE WITH THE academy's KIND PERMISSION IS MOST RESPECTFULLY . DEDICATED PREFACE The author's object in foisting still another bridge book upon his long- suffering brother engineers is twofold, viz.: First. A desire to leave behind him for the benefit of the next generation of bridge speciahsts, in shape readily available for use, a solution of all the major economic problems in bridge work and an extensive treatment of most of the minor ones. He has endeavored to cover every possible economic question of importance; and, if any such be omitted, it is because he did not recognize their existence. To what extent he has succeeded in this endeavor can be determined only by the reception which the book meets from the engineering profession. Second. To show to specialists in all branches of the engineering profession the type of book on economics which, in his opinion, each specialty needs and how broad and thorough, if possible, should be the treatment of the subject. The author feels that he is the logical person to write a book upon the economics of bridgework, because he has been investigating the matter for thirty-seven years, and has dealt at length, upon more than twenty different occasions, in books, pamphlets, and memoirs, with various economic topics on the subject of bridge designing, as can be seen by referring to the list of the said writings given in the Appendix. An explanation but not an apology is needed for the fact that certain portions of "Bridge Engineering" have been copied in a few of the chap- ters. As that work from start to finish is impregnated with the funda- mental idea of economy, and as this book is intended to cover the entire field of bridge economics, it was necessary to include herein the gist of all that appears on the matter in that work, as well as the substance of all the author's economic writings that are subsequent to its publication. Wher- ever an3^hing previously written on the subject could advantageously be modified or enlarged, this has been done; but where it could not be im- proved upon or augmented, the only thing to do was to copy it verbatim. Hence, should any reader see any portion of "Economics of Bridgework," which appears familiar to him, if he has read this preface he will under- stand the reason therefor and will, the author trusts, excuse the occurrence. V VI PREFACE In proof of the previous statement that the treatment throughout "Bridge Engineering" is based on the conception of economics, there is offered the following extract from a review of that work written by Albert Reichmann, Mem. Am. Soc. C.E., and pubHshed in the October, 1916, issue of the Journal of the Western Society of Engineers. "In a larger sense, this work is a treatise on the subject of 'Economics of Bridge Engineering.' This train of thought can be traced throughout the entire work, all subjects being treated fully and in a broad way, and with the idea of value constantly brought out." There is a salient feature of the present book to which attention should be called, and that is the scarcity of treatment of economic problems by pure mathematics, nearly all the form_ulse given being semi-rational, semi- empirical. The reason for this is that the conditions affecting most of the economic questions in bridge designing are far too complicated to lend themselves to solution by mathematical manipulations. This fact has not always been recognized by engineering writers; for, during the last three or four decades, numerous attempts have been made to settle important eco- nomic bridge-problems mathematically, with the result that the conclusions thus drawn have proved to be erroneous and generally totally useless. It is prognosticated that, in the future, there will be no such fundamental changes in methods of bridge design and construction as to render really incorrect the numerous economic conclusions reached herein; because bridge building has now become fairly well systematized. About the only important change in sight is the adoption of high-alloy steel for long-span superstructures; and the effects of this have been duly anticipated. The reasons for this belief are that the investigations upon which the book is based were in general predicated upon fundamental engineering principles that do not vary; and that the effects of possible changes in unit prices of materials in place and in other general conditions affecting design have been indicated. While it is true that an abnormal variation of a temporary nature in the unit price of some important material of bridge construction, some pecuhar feature of structure-location affecting erection, or possibly some other cause, may change somewhat the findings stated herein, it must be remembered that, as pointed out in several places, up to a certain limit a considerable divergence from the exact economic condition will usually cause no serious augmentation of total cost. This is the saving clause which Hinders the author's economic conclusions sufficiently dependable for th(; future as well as for the present. The story of the writing of this treatise is as follows: In the summer of 1916, when "Bridge Engineering" was issued, the author recognized that there was one very important bridge subject that he had not completely covered, viz., economics; and he thereupon listed ten major e(;onomic pro])loms at tliat time unsolved, and came to the deter- mination that they should no longer be left in that condition, if he could prevent it. After repeatedly failing to interest any other investigator in PREFACE Vll the matter, he himself undertook the task and accomphshed it, at least to his own satisfaction, in four years of hard work. The following is a hst of the said economic questions arranged in the order of their final solution: 1. Economics of Steel Arch-Bridges. 2. Comparative Economics of Cantilever and Suspension Bridges. 3. Economic Span-Lengths for Simple-Truss Bridges on Various Types of Foundation. 4. Possibilities and Economics of the Transbordeur. 5. Comparative Economics of Continuous and Non-Continuous Trusses. 6. Comparative Economics of Wire Cables and High-Alloy-Steel Eye-bar-Cables for Long-Span Suspension-Bridges. 7. Economics of Reinforced-Concrete, Steam-Railway Bridges. 8. De VEmploi Economique des Alliages d.Acier dans la Construction des Fonts. 9. Bridge Versus Tunnel for the Proposed Hudson River Crossing at New York City. 10. Economics of Movable Spans. As fast as these economic investigations were finished, they were separately incorporated in chapters of this book, occasionally in toto but generally with slight modifications or omissions. In the preparation of a few portions of the manuscript, the author has received valuable assistance from the following engineers, to whom he herewith tenders his hearty thanks: Messrs. Thomas E. Brown, Leon L. Clarke, Watson Vredenburgh, Thomas Earle, C. M. Canady, Harry K. Seltzer, Joseph J. Yates, Frank W. Skinner, Charles F. Loweth, Carl S. Heritage, J. G. Chalfant, Vernon R. Covell, Edward A. Byrne, J. B. W. Gardiner, L. H. Beach, P. S. Bond, A. H. Sabin, and Shortridge Hardesty. The special portions of the book whereon these gentlemen have aided are indicated throughout the text, excepting in the case of the author's assistant engineer, Mr. Hardesty, who helped with certain of the cal- culations and gave the entire treatise a general check. It may be of interest to some readers to learn how Chapter XLIV on "Economics of Military Bridging" happened to be included in the book; for it is a subject concerning which, before the said chapter was written, the author knew practically nothing. Incidentally it came to the atten- tion of Major R. W. Lewis — a young engineer who served with distinction in the American Army on the battle fields of France, and a son of Col. I. N. Lewis, the famous inventor of the machine gun which bears his name, and which so greatly aided the Allies in winning the war — that this book was in course of preparation. He thereupon called on the author and asked if he would consider favorably a suggestion to insert in the treatise a chapter prepared officially by the Engineer Corps of the Army on the subject of VIU PREFACE economics of military bridgework. Upon receiving an acquiescent reply, Major Lewis proceeded to the Capital, consulted Major General Beach, the Chief of Engineers, and made a Uke suggestion to him. The result was that the General agreed to write a "Foreword" for the chapter, and detailed Col. P. S. Bond, in consultation with some of his brother officers, to do the writing. The author deems the outcome an exceedingly valuable addition to his book; and he hopes that many of his readers, in consequence of its perusal, will be induced to take such an interest in mihtary bridge engineering as to ensure that they shall be better prepared to serve our country in case of war than were most of the civilian engineers when the call to arms came in 1917. It is intended that this shall be the last technical book which the author will ever write, for reasons explained in the concluding chapter; and he hopes that it and its immediate predecessor, "Bridge Engineering," wiU, for many a year to come, prove of real service to the engineers of his specialty, in the advancement of which, almost ever since graduation forty-five years ago, he has taken an intense and absorbing interest. CONTENTS PAGE Preface • v Table op Contents . ix List of Illustkations xxvii List of Tables xxxi CHAPTER I INTRODUCTION Necessity for general application of principles of economics. — Labor a blessing — not a curse. — Love for one's work a requisite. — ^Business opportunity of U. S. A. being lost. — Necessity for Americans to work harder and more efficiently. — Increasing national efficiency through application of economic principles. — Importance of the work of the engineer and increasing his efficiency. — Teaching economics in technical schools. — Report of Committee of S.P.E.E. on "The Study of Economics in Technical Schools." — Sug- gested treatise on "Economics of Engineering." — Author's lectures on "Engineering Economics" at University of Kansas. — -Author's failure to in- terest others in proposed treatise on "Economics of Engineering." — Presen- tation of this book as a sample of what is needed in all engineering specialties. CHAPTER II GENERAL ECONOMIC PRINCIPLES Literature on Engineering Economics very meagre. — Definition of "Economics." — General economic principle. — Economics of proposed enterprises. — Experi- ence requisite for making economic investigations. — -Complication of economic investigations. — Example of economic study for proposed bridge across San Francisco Harbor. — Short-sightedness of promoters. — ^Glaring example of failure for want of economic study. — ^Economic study for proposed bridge over Mississippi River near New Orleans. — Economic study for replacement of a bridge over the Mississippi River. — Method for comparing the economics of several methods of accomplishing the same result. — Method of contrasting several differing types of construction. — ^Mathematical treatment of economic comparison. — Special conditions precluding adoption of most economic method of procedure. — Anticipating the future. — First cost. — Systemization. — Time versus materials. — Labor versus materials. — Compensating factors in economic comparisons and frequent wide range of economic limits. — Economic variation with live loads. — Recording diagrams. — Economics of mental effort. — Labor 6 X CONTENTS CHAPTER III ECONOMICS OF THE PROMOTION OF BRIDGE PROJECTS PAGE Promoter's inflated ideas. — Keeping down first cost. — -Traffic investigation. — Revenue investigation. — Maintenance and repairs. — Determination re undertaking the proposed venture. — Pedestrian traffic. — Initial temporary economic expedients. — Constructions part permanent part temporary. —East Omaha Bridge, — Growing scarcity of timber 20 CHAPTER IV EFFECT ON ECONOMICS FROM VARIATIONS IN MARIvET PRICES OF LABOR AND MATERIALS Comparative unimportance of market price variations. — Structural metal price variations. — Cement price variations. — Monograph on "Economic Span- lengths for Simple-truss Bridges on Various Types of Foundation." — Sus- pension-bridge price- variations. — Location affecting economic layout. . . 23 CHAPTER V ECONOMICS OF ALLOY STEELS Three fundamental conditions affecting economic question. — Economic criterion for rods or bars. — Economic criterion for plate-girder spans. — Economic cri- terion for long spans. — Examples computed. — How economic curves were established. — Extension of economic curves into "speculative zone." — Cutting out carbon steel entirely in very-long-span bridges. — Accuracy of the curves. — General applicability of curves for all cases. — Use of alloy steel for bridgework in its infancy. — ^Author's investigation on "Nickel Steel for Bridges." — -Present great demand for nickel prohibits use in bridges. — Other alloys of steel for bridgework. — High-carbon steel not advisable for bridges. — Mayarl Steel. — Vanadium steel. — Silicon steel. — "Purffied steel." — Aluminum steel. — Molybdenum steel. — Nichromol steel. — Improvement by French scientists on Bessemer process. — Study on economics of molyb- denum steel for bridgework. — Catalogue re " Molybdenum Commercial Steels." — Proposed nomenclature for various molybdenum-steel alloys. — Legitimate working intensities for molybdenum steel alloys. — Moa^reness of data. — Heat-treated chrome steel with and without molybdenum. — Heat- treated chrome-nickel steel with and without molybdenum. — Ileat-troated chrome-vanadium steel with and without molybdenum. — Heat-treated nickel steel with and without molybdenum. — Heat-treated carbon steel with molybdenum. — Untreated and treated chrome steel with molybdenum. — Assumed unit prices erected for alloy steels. — Best drawing temperature for alloy steels in bridgework. — Carmol steel versus carbon steel. — Chromol steel versus vhromo, steel. Nicmol steel versus nickel steel. — Nichromol steel versus nichro steel. — Chrovanmol steel versus chrovan steel. Best per- centage of molybdenum for alloy steels in bridgework. — Comi)ilation of results. — Most i)romisiiig molybdenum alloy for bridge steel 26 CONTENTS XI CHAPTER VI COMPARATIVE ECONOMICS OF BRIDGES AND TUNNELS PAGE Difficulty of comparison. — Must be between one bridge and several tunnels. — ■ Traffic in tunnels. — Ventilation of traffic tunnels. — Comparative agreeable- ness of passage by bridge and tunnel. — Comparative extents of climbing ia bridges and tunnels. — Comparative costs. — Bridge versus Tunnel for the Pro- posed Hudson River Crossing at New York City. — Desirability of methods of handUng traffic across the river. — Cost of operation. — Time expenditures. — ^Agreeableness. — Sanitation. — Ventilation. — Carbon monoxide danger.— Approach grades used in the comparison. — Tunnel estimates. — Variation of cost of tubes with diameter. — Comparative cost of a double- track tube and two single-track tubes. — Unit prices for bridge materials in place. — Limi- tation of cost by efficiency instead of aesthetics. — Cost diagram for bridges and tunnels. — Description of contrasted structures. — Fairness of com- parison. — Cost of right-of-way and property damages. — Spiral approaches. — Table of total costs of bridges and tunnels. — Conclusion as to the compara- tive economics. — Temporary combination of bridge and tunnels. — Sugges- tion for further study of proposed crossing before committing the pubUc to the present policy 53 CHAPTER VII COMPARATIVE ECONOMICS OF HIGH-LEVEL AND LOW-LEVEL CROSSINGS Definition of terms. — Comparison generally a matter of expediency instead of one of economics. — Using one through span over channel and making all other spans deck structures. — Advantages and disadvantages of the two types. — Approximate average figures of comparative costs. — Capitalization of various aimual expenditures. — Power-cost capitaHzation unnecessary 61 CHAPTER VIII COMPARATIVE ECONOMICS OF STEEL AND REINFORCED- CONCRETE STRUCTURES Difficulty in making comparison. — Variation in market prices an important factor. — Must consider factors of maintenance and repairs. — Greater popularity of concrete structures among non-technical, iminitiated people. — -Comparative limits of life. — Personal equation. — Science of reinforced-concrete-bridge designing not yet so highly developed as that of steel-bridge designing. — ^Esthetics affects costs of reinforced-concrete bridges. — Live load affects the economic comparison. — Designing by inexperienced computers. — Variation in costs of excavation for foundations. — Quick method of settling this eco- nomic question. — Practicable limit of span-length for reinforced-concrete bridges. — Settlement of arches during construction. — Effect of height of crossing upon the economic comparison. — Unavoidable generality of treat- ment of subject and reasons therefor. — Impracticable to reach any fixed or reliable conclusion 64 XIV CONTENTS PAGE emment requirements. — Rules somewhat elastic. — Location of movable span. — Grade and alignment. — Curvature on approaches. — Skew crossings. — Geo- graphical conditions. — Commercial influences. — Proposed bridge at Second Narrows, Vancouver, B, C. — ^Property considerations. — General features of structure. — Character of movable span. — Shore protection.— Future enlarge- ment. — Time considerations. — Stream conditions. — Passing drift and ice. — Clear waterway for probable maximum flood. — Shifting of channel. — Foundation considerations. — Navigation influences. — Construction facilities. — ^Erection considerations. — ^Esthetics. — Maintenance and repairs. — Theo- retical economics. — Conclusion .,,,.. 116 CHAPTER XVI ECONOMICS OF LOADS AND UNIT STRESSES Importance of economic determination of live load. — Occasional excess live load- ings. — Modern truck loadings. — ^Decrease of live load with span-length. — Electric-railway car loads. — Standard steam-railway loadings. — Electric-rail- way loadings. — Highway loadings. — Loadings for cantilevers. — Impact load- ings. — Widths for roadways. — Three-line-travel decks are unsatisfactory. — Footwalk widths. — Pedestrian trafiic. — Gauntleted tracks. — Economic arrangement of decks to accommodate several kinds of traffic. — Combined- railway-and-highway-bridge traffic. — Screens. — Division of combined bridges into six classes and dissertation concerning economics of each class. — Author's Sioux City Bridge. — Author's East Omaha Bridge. — Author's Eraser River Bridge at New Westminster, B. C. — Design for Second Narrows Bridge over Burrard Inlet at Vancouver, B. C. — Author's Fratt Bridge at Kansas City. — Keeping live loads down to least legitimate limits. — ^Extreme and illegitimate reduction of live loads. — Determination of unit stresses. — High-carbon steel not good for reinforcing bars. — In frequent loadings permit live-load reduction. — Fallacy of abnormally high live loads and correspondingly greater unit stresses. — Selection of live load important for very-long- span bridges. — Forced increase in unit stresses. — Skimping of details. — Combination of stresses in trestles. — Increments of intensities for various combinations of stresses, and dissertation on the economics involved. — Impracticability of eliminating entirely the personal equation in trestle designing. — Combination of stresses in cantilever bridges and arches. — Caution against inadvertently adding stresses of opposite kinds. — Com- bination of stresses of opposite kinds. — Conclusion re best policy for combining reversing stresses. — Combinations of live and dead-load stresses with secondary stresses. — Proper relation between intensities of working stresses in tension and compression. — Report of the Committee on Column Tests of the A.S.C.E. and author's comment thereon in Engineering News Record. — Suggested tests of members when actually in full-size bridges. . . 125 CHAPTER XVII ECONOMICS OF TIME AND MONEY IN MAKING COST ESTIMATES FOR BRIDGES Value of data in "Bridge Engineering" for making bridge estimates expeditiously. — Four problems in economic estimating set for solution in a competition CONTENTS XV PAGE between students of technical schools. — Tests made by the author of the "B. E. " methods of making quick cost-computations in bridgework. — Eleven examples solved in the making of quick estimates. — Quick estimates for suspension bridges. — Statement of the student problems 141 CHAPTER XVIII ECONOMIC SPAN-LENGTHS FOR SIMPLE-TRUSS BRIDGES ON VARIOUS TYPES OF FOUNDATION But little known previously concerning true economic span-lengths for varying substructure conditions. — Author's mathematical solution of three decades ago and its limitations. — Special investigation made by actual estimates of cost of over two hundred piers with their spans. — -Instigation of the inves- tigation was the series of studies for the proposed New Orleans bridge. — ■ Assumptions and conditions for investigation. — -Character of structures. — ■ Methods of pier sinking. — ^Specifications for designing. — -Loads. — Per- missible pressures on soil and piles. — Unit prices of materials in place. — Method of determining the economic span-length. — Recording-diagrams and table. — Resume of results of computations. — Deductions. — Check on old method of determining economic span-lengths. — -Relative weights of metal in equal-truss, three-span bridges and structures of the same kind, same total length, and same loading, but having the central span lengthened and the other two equally shortened , 150 CHAPTER XIX ECONOMICS OF SUBSTRUCTURES Old method of designing masonry piers. — Author's experience in designing piers for Red Rock Cantilever bridge. — Day of cut-stone-masonry piers is past. — ■ Copings. — Economics of reinforcing for traction effects. — Dumb-bell piers. — Hollow shafts to reduce load on foundations. — Piers composed of two cyl- inders. — Mattresses. — Temporary piers. — Cocked hat. — -Cutting down and rebuilding of main piers of the Fratt Bridge at Kansas City. — Ice-breakers. — Reinforced-concrete versus timber for cribs and caissons of bridge piers. — Steel versus timber for concrete forms. — Best depth to carry pier-shaft below low-water mark. — Reduction of pier size to avoid lessening the area of Avater- way. — Clearance in crib around base of shaft. — Pneumatic process versus open-dredging. — Coffer-dam method versus open-dredging. — Comparative economics of open-dredging caisson and pile-filled crib. — Economics of employing both the pneumatic and the open-dredging processes on the piers for same bridge. — Economics of hastening pier sinking. — -Comparative economics of stepping off plain-concrete bases or spreading suddenly by using reinforcing bars. — Reinforced concrete piles versus wooden ones. . 167 CHAPTER XX ECONOMICS OF TRUSSES AND GIRDERS This problem cannot be solved by complicated mathematics, but only by making actual competitive designs and estimates of cost. — Mathematical solution of economic truss-depths. — Economic depths of plate-girder spans and XVI CONTENTS beams. — True economic investigation for plate-girders. — Considerations tending to offset the advantage of employing economic web-depth. — Old rule of making weight of flanges equal to that of web and its stiffening is just about right. — Economic panel-lengths. — Comparative economics of Warren with Pratt and Petit trusses. — Economic limiting span-lengths for polygonal chords 175 CHAPTER XXI ECONOMICS OF DECKS AND FLOOR-SYSTEMS Possible types of deck for railway bridges. — -Open-floor. — Trough floor. — Bal- lasted decks. — Ballast resting directly on steel plate. — Ballast resting on reinforced-con Crete slab. — Resting ties on bottom-flange angles or on special shelf-angles. — Depth and number of beams and stringers. — Encasing the said beams in concrete. — Floor systems. — Standard floor system. — Jack- stringers versus fom- lines of carrying stringers per track. — Economic panel length. — Cut-away ends of floor-beams. — Economic depths for stringers. — Economic depths for floor-beams. — -Effect on economics of under-clearance requirements. — Floors for half-through, plate-girder spans. — -Economic spac- ing of deck trusses for double-track bridges. — Electric-raU^^ay bridges. — Highway-bridge decks. — Timber deck versus concrete deck. — Danger to timber deck from fire. — Deck for bascule bridges. — Pavings for roadways. — Plank floors. — Creosoted planks. — ^Concrete base. — Wooden block pave- ment. — Brick pavement. — Asphalt and bituminous pavements. — Concrete wearing surface. — -Sidewalks. — ^Sub-paving or base. — Curbs. — Handrails. — • Electric-railway tracks. — Floor systems. — Spaqing of I-beams. — Omission of floor-system in deck spans.— Economic number of girders in deck, plate- girder spans. — Standard floor-system in deck, plate-girder spans. — Stringer spacing. — Sidewalk slabs. — Number of girders in half-through spans. — Stringerless floor vers^ls floor with stringers. — Cantilever brackets. — Floor of minimum weight. — Stiffened-buckle-plate floor. — Haydite concrete. . 182 CHAPTER XXn GENERAL ECONOMICS OF DESIGNING AND DETAILING Simple details are economic. — Carry stresses by shortest route. — Reduction of number of rivet holes in a section to a minimum. — Largest practicable radii of gyration for compression members. — H sections for posts. — Compression members carrying shear. — Non-use of cover plates in railway, deck, plate- girder spans. — Batten plates. — Turning flanges of post channels in. — Must consider all panels of compression chord simultaneously when designing any length thereof. — Use metal to best advantage in detailing. — False economy to skimp details. — Details and joints frequently defy exact analysis. — Consider i)ossiblc rusting when detailing. — All parts to be easily accessible to paint brush. 199 CHAPTER XXni ECONOMICS IN DESIGN FOR SHOP CONSIDERATIONS Designs to be made so as to facilitate shopwork. — Sub-i)imcliiiig ;\ii(l reaming versus imiiching full size. — Drilling solid. — Sheared edges. — End stiffencrs CONTENTS XVll PAGE must not be omitted. — Turning in flanges of channels. — Batten plates inside of the gussets. — Girders of constant or varying depths for viaducts. — Location of pedestal pins. — Non-omission of end floor-beams. — Single angles not to be used in tension.— Exact location of top-chord pins. — Cast iron in bridges. — Insertion of casting between foot of column and the masonry. — Variation in pound prices for different sections of metal. — Avoid special material. — Adhere to standard sizes. — Design to avoid all unnecessary shopwork. — ^Reaming to templates. — Avoid side plates and doubling of web plates. — Cheaper to use heavy flange angles in stringers rather than lighter angles with cover-plates. — Avoid beveled cuts. — Design so as to use multiple punches. — -Do not crimp stiffeners for ordinary work. — Solid web versus lacing. — Avoid hand-riveting. — Duplication in skew spans. — Use very few sizes of pins in same bridge. — In riveted tension members use tie plates instead of lacing. — ^AUow ample clearance. — When metal is drilled from the solid use as few pieces as possible in make-up of sections. Mr. Canady's contribution to chapter: Duplicate spans. — Avoidance of light and heavj^ trusses in same span. — Long panels. — Symmeliry. — Squaring small skews. — -Treatment of skewed spaiis. — Unnecessary completeness of many engineers' drawings. — Freedom to be allowed shops in rivet spacing. — • Duties of shop designing-engineer. — Full-punched work. — Sub-punching. — •' Forge and machine-shop work to be a minimum. — Curving ends of girders. — Staggering rivets. — Variety of rivet diameters. — Web-plate versus lacing for I-shaped sections of struts. — -Thickening of stringer webs. — Allowing suffi- cient difference between gross and net sectional areas. — Fitting of fillers beneath stiffeners. — -Avoiding bevel cuts. — ^Thickening of base plates to avoid shop-work. — Coordination of different parts of a design 202 CHAPTER XXIV ECONOMICS IN DESIGN FOR ERECTION CONSIDERATIONS Design so that metal will go together easily in field. — Furnish sufficient clearance. — Wolf el's general instructions. — Allow one-half inch clearance for sheared ends. — Allow for "growth of steel." — Allow ample space in pockets. — Allow ample width for packing. — Begin erection at center panel. — Arrange for putting floor in place either before or after trusses are erected. — Detail through plate-girders so as to avoid spreading them in field. — Half pin-holes undesirable. — Entering connections to be avoided. — Clearance for packing.— Avoid necessity for notching timber ties to clear rivet-heads. — ^Minimize number of field rivets. — Most important points to facilitate and cheapen erection. — Viaducts. — Make two bents of tower alike. — Proper lengths for sections of columns. — Swinging-in of cross-frames 214 CHAPTER XXV ECONOMICS OF REINFORCED-CONCRETE BRIDGES Economics of this type not yet so highly developed as that of older types. — Intensity of stress for reinforcing bars. — Objections to high-carbon steel therefor. — Intensity of working stress for concrete. — Pavings. — Hand rails. — Designs. — Economics of design rather difficult to determine. — Slabs. — Girders. — Simple-span girders versus continuous girders. — Character of foundations. — Balanced-cantilever type of girder. — Columns. — Footings. — XVIU CONTENTS Highway girder-bridges. — Panel length. — Girder spacing. — Best number of columns per bent. — Economic span-lengths. — Pile foundations. — Arch bridges. — -Ratio of rise to span. — Abutment reaction affects ratio of rise to span. — Economic span-length with rise unchanged. — Factors to be con- sidered. — Distance from springing to bottom of base. — Substructure effects. — Massiveness of piers. — Ratio of live load to dead load. — Type of arch- ring. — Equality or inequality of adjacent spans. — Arbitrary requirements. — Other special conditions. — Solid spandrel versus open-spandrel. — Solid barrel versus ribbed structures. — Hingeless and three-hinged arches. — Arch with steel bottom chords. — Reinforced-concrete trestles for steam-railways. — Slabs therefor. — Special economic investigation. — Retaining walls. . . 218 CHAPTER XXVI ECONOMICS OF STEEL ARCH-BRIDGES Great lack of reliable information thereon prior to 1918. — Failure to build many steel arch-bridges in America. — Author's appeal to the profession for inves- tigation on arches.— Relation between metal weights in arch bridges and corresponding truss bridges. — Paper on "Economics of Steel Arch Bridges" for A. S. C. E. — Invitation to discuss same. — Effect of discussion. — Fowler's arch-dimension compilation. — Economic ratio of rise to span-length. — Eco- nomic rib-depths. — Percentage effects of using uneconomic rib-depths. — Location for crown hinge. — Solid-rib versus braced-rib versus spandrel-braced arches. — Three-hinged versus two-hinged versus hingeless arches. — Com- bination of three hinges for dead load and two hinges for live load. — Can- tilever arches. — Ratio of metal weights in arch-bridges and corresponding truss-bridges. — Other 'economic factors than weight of metal. — Side issues of investigation. — Percentage equations for metal weights in arches and trusses. — Arches more economic for highway than for railway bridges. — Formulaj for weights of metal in arches alone. — Limiting span-length for three-hinged arches of carbon steel. — Economic or practicable limit of arch spans. — Influence of substructure on economics — Suitable foundations for arch bridges. — Conclusion 232 CHAPTER XXVn ECONOMICS OF STEEL TRESTLES, VIADUCTS, AND ELEVATED RAILROADS Economic factors for high steel-railway-trestles. — Distance from center to center of towers. — Modifications necessary for three diagrams of "Bridge Engi- neering." — Economic span-lengths for low railway-trestles. — Double-track- railway trestles. — Pedestal costs to be included. — Highway trestles. — Column spacing for h(!nts when cantilevers are employed. — Elevated railroads. — Best span lengths therefor. — Plate-girders versus open-webbed girders. — Best sections for columns. — Paper by Mr. Grcist 250 CHAPTER XXVni ECONOMICS OF CANTILEVER BRIDGES Division of cantilevers into types. — Comparison of Types A and B. — Comparison of Types A and C. — Comparison of Type D with other types. — Economic CONTENTS XIX PAGE division of span-lengths. — Economic truss depths. — Legitimate economies in cantilever designing. — Wind stresses during erection. — Splaying the trusses. —Reducing weight during erection. — Solitary piers or pedestals are economic. — Adoption of intermediate trusses. — Division of stress on members meeting over main pier. — Choice between riveted and pin-connected construction. — Box-section chords. — Merriman and Jacoby's treatment of cantilevers. — Truss-depth constant for cantilevers: the practice is absurd. — Simple trusses and cantilevers compared 257 CHAPTER XXIX ECONOMICS OF SUSPENSION BRIDGES Much still to be learned about designing suspension bridges. — Suitable mostly for highway structures. — Paper on "Comparative Economics of Wire Cables and High- Alloy-Steel Eye-bar-Cables for Long-Span Suspension Bridges." — ■ Best floor to adopt. — Advantages and disadvantages of adopting many lines of cables. — Economics of stiffening trusses. — Best panel length. — Single-intersection versus double-intersection. — Ends free versus ends anchored. — Versed sine of cable. — Best type of approaches. — Suspending floor from backstays. — Design for anchorages. — Economics of cables. — Unsuitability of suspension bridges for steam railways. — Effect of anchoring ends of trusses upon the economics. — Comparative advantages and disad- vantages of two types of cables. — Layout for proposed suspension bridge between Philadelphia and Camden and description of structure. — Outline of first economic investigation. — Live loads and intensities therefor. — Stress theory adopted for stiffening trusses. — Second set of computations. — Ratios of quantities of materials in eye-bar-cable bridges to those in wire- cable bridges. — Formulae for quantities of materials in suspension bridges. — Diagrams of quantities of materials. — Unit prices of materials. — Examples for illustration. — Mayari steel comparison. — Heat-treated, carbon-steel-eye- bar comparison. — High-grade-nickel-steel comparison. — Heat-treated, chrome-molybdenum-steel comparison. — Resume of findings. .... 263 CHAPTER XXX ECONOMICS OF MOVABLE SPANS Types considered. — Swing-span versus either bascule or vertical lift. — One open- ing versus two openings. — Shifting channel. — Vertical-lift versus bascule. — Future raising or lowering of grade-line. — Skew-crossings. — Carrying pipes and wires over movable spans. — Simplicity of vertical lift. — Economics of swing spans. — Rim-bearing versus center-bearing spans. — Bob-tailed swing versus ordinary swing. — Economics of bascule spans. — Single-leaf bas- cule versus double-leaf bascule. — Double-leaf bascule unfit for railway bridges. — Heel trunnion bascule. — Thomas Ellis Brown, Jr., type of bascule. — Rolling-lift bascule. — Trunnion type of bascule. — Waddell and Harring- ton axle details.— Roller-bearing type of bascule. — Brown-balance-beam type versus Strauss type of bascule. — Economics of vertical-lift spans. — Con- ditions favorable to the vertical lift. — Flanking spans for vertical lifts. — Skew layouts. — Wind-pressure on movable spans. — Widening of decks of movable spans. — Quickness of operation. — Economics in detailing of ver- tical lifts. — Best material for counterweights. — Balancing-chains. — Buffers. XX CONTENTS — Pavement base. — Location of machinery house. — Best number of ropes. — Combination of vertical Uft and cantilevers. — Design for Hoogly Eiver Bridge, Calcutta. — Comparative costs of vario'is types of movable spans. — Records of quantities of materials in vertical-lift and bascule bridges. — Percentage weight-curves for vertical lifts and bascules. — Housatonic River Bascule Bridge. — Unit prices used in comparison of total costs. — Diagrams of vertical clearances for movable spans of equal cost. — Application of dia- grams to skew layouts. — Effect of substructure conditions on comparative economics of vertical lifts and bascules. — Comparative costs of swing-span bridges with vertical lifts and bascules. — Mystic River, Brown-Balance- Beam, Bascule Bridge. — Housatonic River, Bascule Bridge. — General ratio of clear height to clear horizontal opening for vertical-lift bridges and bas- cules of equal cost. — Extension of investigation for economics of very short spans is unnecessary, and why. 284 CHAPTER XXXT ECONOMICS OF OPERATING MACHINERY AND POWER Data furnished by Mr. Thomas E. Brown and Major Leon L. Clarke. — Kind of power and type of machinery depend greatly on local conditions. — Location near a city. — Steam power very objectionable. — ^Hydraulic pressure or com- pressed air. — Electric power. — Internal-combustion-engine power and its advantages. — Efficiency definition. — Probable time of operation. — Direct versus alternating current. — ^Accumulators. — Storage batteries. — Hydraulic power. — ^Conveyance of power on span. Gear reduction. — Worm gearing. — Multi-cylinder, gasoline engines for bridge operation. — Ideal apparatus. — Division of parts of movable spans into three groups. — Carrying structure. — Supporting machinery parts. — Operating machinery. — Breakdowns. — Power required for swings, lifts, and bascules. — Amount of wind pressure for bas- cule designing. — Brake power for bascules. — Holding power. — Economics in using standard machinery. — Tendency to cramp machinery space. . . 310 CHAPTER XXXII POSSIBILITIES AND ECONOMICS OF THE TRANSBORDEUR Various names for this type of structure. — ^Legitimate function of transbordeur. — Transbordcur versus bridge. — Descrij^tion of transbordeur. — Author's development of tyi)e. — ^Types of bridge suitable for supporting transbordeur cages. — Transbordcur design for New Orleans. — Tabulation of (•onii)arativc costs of four transhordeurs, a low-level bridge, nnd a high-level bridge for New Orleans. — Deductions from table. — Comparative economics of long cages and short cages.— Best number of cages to adopt. — Cost of operating transhordeurs. — Character of construction and general modus operarnii of transbordeur. — Details of structure. — Operation of New Orleans trans- bordeur. — Conditions necessitating a "corral." — Method of caring for ped(!strians. — -Time sdjedules. — Evolution of author's transbordeur type. — C'()m()arison of cai)a('iti(^s of transl)ordeur and low-level bridge. — O])])ortuiii- tioH for buihhiig transhordeurs are S(Uirce. — Fixed-span bridge iircferablc (o traiisbordeur. — 'I'nuisbonk'ur design for Havana Harbor. — Phila(l('li)liia- Carnden transbordeur design. — Cotidusion and recapitulation. . . 318 CONTENTS XXI CHAPTER XXXIII ECONOMICS IN CONTRACT-LETTING PAGE Proper contract letting is a matter of real economics. — Author's discussion of paper by Mr. Ernest Wilder Clarke. — Importance of subject. — Business opportunity of the U. S. A. — Prevention of progress. — Labor and capital. — Men who do the work must share in the profits, but preferably not in the management of business. — Quieting popular unrest. — Various methods of contract letting listed. — Description of each method. — Injustice of straight- lump-sum contracts. — Advantages of unit-price method. — Cost-plus method. — Hospital jobs. — Conscientiousness of contractors and workmen. — ^Paying by the job. — Cost-plus methods cut out competition. — All ordinary methods are faulty. — Salient features of an ideal system. — Description of the ideal method. — -Method of profit-sharing contract. — Application of corrective ratio. — Employee's percentage of total profits. — Method of anticipating rise or fall of prices. — Exemplification of ideal method. — ^Advantages of ideal method. — Objections that have been raised thereto. — Adoption of method. — Addendum re profit-sharing in manufactories. ..,..,... 337 CHAPTER XXXIV ECONOMICS OF BRIDGE-ENGINEERING OFFICEWORK Scheme of management expounded in Chapter LVIII of "Bridge Engineering." — • General principles for office management. — Employees should reach office on time. — No talking in office. — No visitors should be allowed in office. — No smoking in office. — Employees should attend strictly to their own business. — • Collecting full data before starting computations. — Limits of accuracy in cal- culations. — ^Checking calculations. — Filing and indexing. — Drawings. — ■ Standards. — Lettering. — No issuing of unchecked drawings. — Blank forms. —Cost records. — Card indices 358 CHAPTER XXXV ECONOMICS OF INSPECTION Subject somewhat intangible. — To what extent will it pay owner to inspect? — ■ Compensation for inspection. — Quality of inspection. — Methods of pay- ment for inspection. — Omission of inspection. — Supervision by direct employ- ees of the Engineer. — Inspection by established bureaus. — Economy in per- formance. — Start shop inspection at beginning of work. — Ground to be covered by shop inspection. — Economics of mental effort for shop inspectors. —Field inspection. — General question of the Economics of Inspection. . 361 CHAPTER XXXVI ECONOMICS OF SHOPWORK Necessity for aid of shop expert in preparing notes for this chapter. — Importance of systemization of one's knowledge. — Assistance of Mr. Earle. — General XXU CONTENTS PAGE economic problem stated. — Design of shop for special class of work or for general work. — Keeping shop force occupied. — Transportation of materials in shop. — Principal economic factors in shopwork. — Scrapping tools and apparatus for betterment. — Light. — Interior painting of shop. — Heat. — Ventilation. — Space. — Handling of work. — Management of men. — Safety considerations and their importance. — Prevention of accidents and how to accomplish it. — Smoking on premises. — Anticipating troubles. — Standardi- zation. — Stock materials and storing thereof. — Supply of labor. — Tool equip- ment. — Shop floors. — Straightening metal. — Marking metal. — Trimming and cutting. — Punching. — Drilling. — Storage of punched metal. — Assem- bUng. — Reaming. — Riveting. — MUling and planing. — Boring. — Special space. — Machine shop. — Foimdry. — Blacksmith shop. — Match marking. — Painting. — Tracks. — Templet shop. — Recapitulation 365 CHAPTER XXXVII ECONOMICS OF BRIDGE-ENGINEERING FIELDWORK Instructions to Resident Engineer. — Starting work ahead of contractor. — Employ- ing smallest force consistent with efficiency. — Keeping force busy. — Laying out on paper an economic system for carrying on fieldwork. — Prevention of dropping behind on work — Supplying home office with information. — Testing cement. — Checking receipt of materials. — Unloading materials quickly. — Aiding contractor. — Prompt monthly estimates. — Extras. — Progress reports. — Resident Engineer is a confidential agent and not a principal. — Insuring field property. — Copying survey notes. — Diary. — Resident Engineer must act in a semi-judicial capacity. — Care of instrimaents. — Non-abuse of power. — Storing materials. — No damage to reinforcing bars. — Care of paving blocks. — Protecting cement against weather. — Care of explosives. — Falsework and forms. — Sinking cribs and caissons. — Building up cribs and caissons. — Depositing concrete under water 380 CHAPTER XXXVIII ECONOMICS OF BRIDGE-CONTRACTOR'S GENERAL FIELDWORK Data furnished by Mr. H. K. Seltzer. — Contractor's guiding principle in perform- ance of work. — List of main subjects requiring Contractor's attention at outset. — Field organization. — Plant. — Yards, wharves, and tracks. — Plans of buildings and plant. — Materials and supplies. — General notes. . . . 383 CHAPTER XXXIX ECONOMICS OF CONCRETE MIXING Two main points of view for consideration of problem. — Contractor's viewpoint. — Duty of the Engineer. — How to j)r()ducc strongest concrete. — Legitimate major ways for a contractor to economize in concrete-mixing. — Minor ways for economizing. — List of economic problems. — Best proportions of materials. — Reduction of voids in the aggregate. — Using a mixture of gravel and sand without screening. — Water-proofing. — Increasing fluidity of mixture. — CONTENTS Xxiii PAQE Manner and time of mixing. — Using of large stones in mass. — ^Vibration and jigging of freshly-made concrete. — Age of cment. — Protection of fresh concrete. — General remarks. — Indebtedness for suggestions to Mr. J. J. Yates 386 CHAPTER XL ECONOMICS OF ERECTION Indebtedness for data to Mr. Frank W. Skinner. — Bridge erection is a function of design, location, and available equipment. — Specialization of bridge erection. — Division of subject. — Steel bridges. — Completion of fabrication at bridge shops. — Use of standard plant and equipment. — Skilful and experienced labor necessary. — Complication of problem by artificial condi- tions. — Girder spans. — Limits in dimensions. — Derrick cars, derricks, gin- poles, and other erection apparatus. — Viaduct erection. — Ideal method is by derrick traveler or mule. — Cantilever travelers. — Strident gantry traveler. — Medium spans. — Pile foundations. — Supplementary gantry traveler. — Alternative methods. — Cantilever erection. — Erection on eccentric false- work. — Method of protrusion. — Erection on moving suspending platform. — Distribution of steel on ground. — rMethod of flotation.- — Erection from tem- porary suspension span. — Long spans. — Framed-timber falsework. — Canti- lever method. — Limiting lengths for cantilever spans. — Assisted cantilever method of erection. — Erection of suspended spans by flotation and hoisting. — Suspension bridges. — Methods of erection. — Arch spans. — Methods of erection. — Cantilevering arches. — Erection plant.— Steel travelers. — Struc- tural-steel falsework. — Yokes, clamps, etc. — Replacing steel bridges. — Main- tenance of traffic. — Diversion of traffic. — Replacing short spans on old sub- .:jtructure. — Use of barges therefor. — Replacing by transverse displacement. —Replacing long spans. — Erection of concrete-girder bridges and concrete- arch spans 396 CHAPTER XLI ECONOMICS OF MAINTENANCE^ AND REPAIRS Data furnished for chapter. — Old rule of author's for- passing upon over-stressed structures. — Converting two old bridges into one. — Repairing bridges that should be relegated to the discard. — Criterion for determining whether to repair or to discard. — But little repair work now done by consulting engi- neers. — Mr. Loweth's letter and contribution. — Shifting light structures to branch lines. — Necessity in war times for repairing structures thai at other times would have been removed. — "Carrying Bridges Over." — Shifting overloaded bridges to branch lines. — Strengthening bridges in place. — Example of problem in repairing or replacing. — General considerations. — Classification of bridges. — Determination of safe unit stresses for actual maximum loading. — List of factors affecting such determination. — Standard loadings. — General method of investigating a bridge. — Classification of load- ings. — Speed restrictions. — Where low classification usually occurs in bridges. — Timber trestles. — Safe unit stresses for timber. — Effect of brine drippings. — Effect of locomotive smoke. — Fatigue of metal in bridges is a fallacy. — Strengthening of light steel bridges. — Strengthening timber bridges. — Strengthening versus renewal and examples thereof. — Conditions shaping the general policy concerning the keeping of light bridges in service. XXIV CONTENTS PAGE Mr. Heritage's contribution to this chapter: Definition of most economical structure. — Periodical inspection. — Inspection departments. — Repairs to timber bridges and pile-driven trestles. — Tools for bridge-repairing gangs. — Preservation of timber. — Fire- protection. — Planks no longer fit for highway bridge-floors. — Old masonry piers and abutments. — Repointing. — Concrete piers. — Steel cylinder piers. — Protection against corrosion of steel. — Paint and painting. — Cleaning of metalwork. — Application of paint. — Spraying of paint. — Signs of deterioration in connections. — Wear on pins. — Wear at intersection of diagonals. — Overstress on counters. — Joint contribution of Mr. Chalfant and Mr. Covell. — Division of subject. — Masonry. — Scouring . of bed and cutting of banks. — Turning of stream. — Rip-rapping. — System- atic soundings. — Floors. — Best type of pavement and base. — Concrete slab. — Buckle-plate floors. — Plank floors are antiquated. — Weight of trucks too great for timber floors. — Nailing-pieces for stringers. — Stringer-spacing. — Laying of planks. — RaU supporting. — Laying of wood-blocks. — Hillside blocks. — Crowning of roadway. — Sidewalks. — Adjusting old back-wall to new grade. — Replacing of floors. — Itemized record of repairs. — Detection of decay in timber. — Painting. — Division of territory for painting. — Colors for bridge paints. — Cleaning and repainting of metal below flooring. — Paint formulae 407 CHAPTER XLII ECONOMICS OF METAL PROTECTION Importance of proper protection of metalwork. — Duration of life of metallic structures. — Subjects included in the economics of metal protection. — Best kinds of paint for shop and field. — Author's experience with paints. — Ideal paint for shop coat. — Finishing coats. — Havre de Grace test of paints. — Houston Lowe's conclusions concerning the characteristics of good bridge paints. — Objections to the old-fashioned, red-lead paints. — Amount of red- lead pigment per gallon of vehicle. — Varying elasticity of paint coats. — Functions of an anti-corrosive metal-coating. — Best vehicle for paint. — Author's experiments on paints in Mexico. — Use of driers. — Best colors for paints. — Covering and spreading powers of paints. — Cement paints. — Lin- seed oil alone for shop coat. — Climatic influences on paints. — Salt-water-proof paint. — A special paint for the hot climate of Brazil. — Spraying of paint. — Spraying on metalwork for" shop coat. — Cleansing paint. — Pickling. — Paint- ing newly-erected steelwork. — Concrete encasement. — Gunite. — Treat- ment of st^el that has to be encased in concrete or gunite. — Protection against brine drippings. — Protection against locomotive gases. — Causes of paint deterioration. — How to care for incipient failure of paint. — Deter- mination of time for repainting. — Cleansing of metalwork preparatory to apf)lying now field coats. — Application of paint after cleaning. — Factors that affect resulls in painting. — E(!onomic observations concerning jxiinting in general. — Price of paint. — Thickness of coats. — Character ,of brush. — liest temperature for paintingf — Special kinds of paint for special conditions. — Summary 430 CHAPTER XLIII ECONOMICS OF WATER-PROOFING Aid from Mr. J. B. W. Gardiner. — Definition of cc^ononiics of water-])roofing. — Profitablen(!SS of wat(!r-{)ro()fing. — Factors affecting cost of water-|)r()ofiiig. — CONTENTS XXV Relative cost of water-proofing to that of total cost of structure. — Interest on investment may be ignored.— Probable life of water-proofing. — Qual- ities of materials for water-proofing. — Deterioration of water-proofing and causes therefor. — Damage due to lack of water-proofing. — Water-proofing in steel bridges. — Brine drip. — Water-proofing of concrete viaducts. — Water-proofing of flat slabs. — Water-proofing of concrete roads. — Disin- tegrating effects of water-penetration on concrete. — Leaching of alkalies. — Erosive action of water percolating concrete. — Effect of freezing on rein- forced concrete. — Cracks in floor slabs. — Electrolysis. — -Softening of con- crete and expansion thus induced. — Appearance deteriorated by water per- colation. — Excrescence of magnesia and other salts. — .Esthetics and eco- nomics. — Water-proofing is a form of insurance. — ^Effect of this disserta- tion on author's future policy in the designing and construction of bridges. — Mr. Rhett's conclusions re water-proofing 449 CHAPTER XLIV ECONOMICS OF MILITARY BRIDGES Fundamental Economics of Military Engineering. — Time factor substituted for cost factor. — Principle of "Bare Necessities Only." — Safety and perma- nence. — Waste not justifiable. — Classes of Military Bridges. — -Types of Military Bridges. — -The typical military bridge. — Framed trestles. — Economic span for military trestle bridges. — ^Spar bridges. — Pile trestles. — Trusses. — Sectional trusses and girders. — Cribs. — Suspension bridges. — Ponton or floating bridges. — New type of ponton equipage. — Raflroad bridges. — Foot-bridges. — -Deck or flooring of military bridges. — Width of roadway. — Side-rails and hand-rails.— Materials employed in Military Bridging. — Timber. — Piling. — Steel. — ■ Concrete. — Stone. — Paint. — Joints and fastenings. — Sizes of individual members. — Plant and tools. — Class of labor available. — Improvisation and standardization. — Utilization of existing bridges. — Utilization of Iccal resources. — -Loading of military bridges. — -Transportation of materials. — Selection of site. — Protection against flood and drift. — Inspection of mflitary bridges 459 CHAPTER XLV CONCLUSION Explanation of innovation in technical literature. — Reasons why this is to be author's last technical treatise. — Great expense involved in technical-book writing. — Great amount of valuable time involved. — Subject of bridges about exhausted by author's various writings. — Probable economic investi- gation on "Molybdenum Steel for Bridges." — This treatise is mainly author's own personal work. — Suggested method of utilizing "Bridge Engineering " and "Economics of Bridgework " by young engineers desirous of becoming "Bridge Experts." 486 APPENDIX Chronologically arranged list of author's various investigations and writings on the subject of "Bridge Economics." 489 LIST OF ILLUSTRATIONS CHAPTER V ECONOMICS OF ALLOY STEELS PAGE Fig. 5a. Economic Limiting-Values of rr' for Simple-Span, Steam-Railway Bridges 28 Fig. 56. Economic Limiting-Values of rr' for Cantilever, Steam-Railway Bridges 29 Fig. 5c. Total Weights of Metal per Lineal Foot of Span for Double-Track, Steam-Railway, Cantilever Bridges of Carbon Steel and Alloy-Steels of Various Elastic Limits 31 Fig. 5d. Diagram Showing Comparative Economics of All Procurable, or Prac- tically-Possible, High-Alloy Steels for Long-Span, Cantilever Bridges 32 CHAPTER VI COMPARATIVE ECONOMICS OF BRIDGES AND TUNNELS Fig. 6a. Diagram of Total Costs of Highway and Electric-Railway Bridges and Tunnels, with their Approaches, for Crossings Similar to that of the North River at New York City 58 CHAPTER XI COMPARATIVE ECONOMICS OF CONTINUOUS AND NON- CONTINUOUS TRUSSES Fig. 11a. Layout of Petit-Truss, Continuous Spans 76 Fig. 116. liayout of Petit-Truss, Non-Continuous Spans 76 Fig. lie. Layout of Subdivided-Triangular-Truss, Continuous Spans ... 79 Fig. lid. Layout of Subdivided-Triangular-Truss, Non-Continuous Spans , . 79 CHAPTER XII COMPARATIVE ECONOMICS OF SIMPLE-TRUSS AND CANTILEVER BRIDGES Fig. 12a. Typical Layouts for Double-Track-Railway, Cantilever Bridges . 85 Fig. 126. Comparative Weights of Metal for Double-Track, Simple-Truss Bridges and Type-C-Cantilever Bridges 86 Fig. 12c. Comparative Weights of Metal for Double-Track, Simple-Truss Bridges and Type-A-Cantilever Bridges 87 xxvii XXVm LIST OF ILLUSTRATIONS CHAPTER XIII COMPARATIVE ECONOMICS OF CANTILEVER AND SUSPENSION BRIDGES PAGE 95 95 96 97 Fig. 13a. Layout for 1,700-root-Span, Cantilever, Railway Bridge Fig. 136. Layout for 1,700-Foot-Span, Suspension, Railway Bridge Fig. 13c. Cost-Curves for Double-Track-Railway Bridges . . Fig. 13d. Layout for 2,400-Foot-Span, Cantilever, Railway Bridge Fig. 13e. Layout for 2,400-Foot-Span, Suspension, Raih\'ay Bridge Fig. 13/. Modified Cost-Curves for Double-Track-Railway Bridges .... 99 Fig. 13^. Dr. Steinman's Layouts for Cantilever Bridges 101 Fig. 13/i. Dr. Steinman's Layouts for Suspension Bridges . . ' . . . . 101 Fig. ISi. Cost-Curves for Combined Railway and Highway Bridges ot the Gen- eral Type Computed by Dr. Steinman 105 Fig. 13/. Cost-Curves for Highway Bridges of Carbon Steel 107 Fig. ISJfc. Diagram of Main-Span Lengths of Equal Cost for Combined-Railway- and-Highway, Cantilever and Suspension Bridges . . . . . . 109 CHAPTER XVII ECONOMICS OF TIME AND MONEY IN MAKING COST- ESTIMATES FOR BRIDGES Fig. 17o. Profile for Student Problem No. 1 148 Fig. 176. Profile for Student Problem No. 2 148 Fig. 17c. Profile for Student Problem No. 3 148 Fig. 17d. Profile for Student Problem No. 4 . . 148 1 CHAPTER XVIII ECONOMIC SPAN-LENGTHS FOB SIMPLE-TRUSS BRIDGES ON VARIOUS TYPES OF FOUNDATION Fig. 18a. Live-Plus-Impact Loads 153 Fig. 186. Live Loads without Impact 154 Fig. 18c. Total Weights of Metal in Superstructures 155 Fig. 18f/. Costs per Lineal Foot of Structure for Low-Level, Combined Bridges on Sand Foundations 100 Feet Deep 159 Fig. 18e. Costs per Lineal Foot of Structure for Low-Level, Combined Bridges on Sand Foundations 150 Feet Deep 101 Fig. 18/. Costs per Lineal Foot of Structure for Low-Level, Combined Bridges on Sand Foundations 200 Feet Deep 162 Fig. 18f/. Costs per Lineal Foot of Structure for Low-Level, Combined Bridges on Sand Foundations 2.50 Feet Deep Ili3 Fig. 18/i. Economic Span-Lengths for Simple-Truss Bridges on ^'ari 156 Table 186. Unit Prices of Materials in Place 156 Table 18c. Resume of Results of Computations 160 CHAPTER XXrX ECONOMICS OF SUSPENSION BRIDGES Table 29a. Ratios of Quantities of Materials in Eye-bar-Cable Bridges to those in Wire-Cable Bridges 273 CHAPTER XXXII POSSIBILITIES AND ECONOMICS OF THE TRANSBORDEUR Table 32a. Estimated Costs of Various Proposed Structures for Crossing the Mississippi River at New Orleans 320 CHAPTER XXXIX ECONOMICS OF CONCRETE MIXING Table 39a. Proportions of Materials in Concrete 387 Table 396. Moduli of Rupture in Plain Concrete Beams 389 CHAPTER XLI ECONOMICS OF MAINTENANCE AND REPAIRS Table 41a. Amounts that can Economically be Spent on Strengthening Old Bridges 418 ECONOMICS OF BRIDGEWORK CHAPTER I INTRODUCTION Upon the scientific application of the principles of true economy in all lines of activity will depend the success of every one of the great nations in the world-struggle for business-supremacy which is about to follow the final close of the Great War. This statement is peculiarly applicable to the United States of America, which is always unavoidably handicapped by the high cost of labor, and at present is unnecessarily and stupidly ham- pered by an epidemic of strikes and a wide-spread insane desire to shorten working hours far below the minimum limit requisite for adequate produc- tion of the necessities of life for our own country alone. Until mankind recognizes that labor is a blessing — not a curse — prog- ress will be slow, and the development of the world in all fines will be seriously impeded. No healthy man or woman, or even a child of school age, is injured by eight hours per day of fairly-strenuous physical or mental exercise, provided that its character be suited to the individual's age, capacity, and taste. When one is healthily tired upon the expiration of his daily task, he is in condition, after a very short rest, to enjoy his food and recreation; but any person having no settled occupation nor any regular duties to perform is an unhappy, discontented individual who not only spoils his own life but also interferes with the enjoyment and well- being of all persons with whom he comes in contact. A real love for work per se should be inculcated in every child by its parents and teachers; and extra work should never be given as a punish- ment, because so doing would engender a distaste for labor. All work should bo made as pleasant and interesting as possible, not only for chil- dren but also for adults ; and if anyone cannot learn to fike the occupation to which he has been assigned, the character of his employment should be changed from time to time until he finds a niche into which he fits com- fortably. This development of a love for work in the young is specially important in relation to study; because, when an individual once becomes truly interested in his occupation, be it either mental or physical, his life's battle is already more than half-won. 2 ECONOMICS OF BRIDGEWOEK Chapter I For several years the U, S. A. has had a unique opportunity to become in all hnes the leading nation of the world; but alas! it has not recognized the existence of this important privilege or taken the steps necessary for its utHization. Latin-America is knocking at our door asking us to do business; the nations of Asia, Africa, and Australasia are eager to enter into commercial relations with us; and the peoples of war-afflicted Europe need both our manufactures and our raw materials. But what foreign business can we do when Americans in general are wiUing to work only six hours per day and five days per week — and even then with lessened effi- ciency? That amount of effort is insufficient to provide for home necessi- ties; and, therefore, it is entirely inadequate for the development of foreign trade. The beaten Huns and their deluded aUies will have to work long hours for many a year to come, in order to pay the principal and interest of the immense debts which are a just punishment for their iniquitous endeavor to conquer the rest of the world and impose upon it their vicious system of "kultur"; the innocent nations whom they have despoiled will have to labor just as strenuously, in order to repair their damages and repay the money they were forced to borrow in their dire struggle to main- tain national existence; and even the people of Great Britain and her colonies will be compelled to work overtime to reduce their enormous in- debtedness. While all these peoples are laboring year in and year out early and late for six and even seven days per week, what will eventually happen to this country if its inhabitants cut down the hours of labor and insist notwithstanding upon maintaining an extravagant style of living? There is but one answer to this question, and that is Dire Disaster! Even should the American populace awaken to the fact that it is neces- sary for them to work full time, the difficulty will still not be overcome; because the average personal efficiency of Americans in all hnes is decidedly lower than it was in ante helium days. This inexcusable evil will certainly have to be corrected; but even then our country will be handicapped, for it must not be forgotten that, notwithstanding our being the one great creditor nation of the world, the war has run us deeply into debt, and that it will require hard work and plenty of it to pay the interest and hquidate the principal. What then can be done to increase our national efficiency to the extent which is necessary for the maintenance of the improved general style of living of the so-called working classes and at the same time outstrip our competitors for the business supremacy of the world? The answer to this momentous question is not difficult, although the accomphshment of the desideratum may prove to be far from easy. It is to develop throughout the entire country to the utmost limit both the theory and the practice of true economy in every line of endeavor. By the expression "true econ- omy" is not meant depriving people of either the necessities or even the hixuries of lift! (although, truth to tell, a curtailment of the latter would gniatly aid in expediting the desired result), but a universal increase in INTRODUCTION 3 personal efficiency — an elimination of useless effort — a systematic, scien- tific study of how best to accomplish all important desiderata — and keep- ing usefully and efficiently occupied all members of society. As almost all the material progress of mankind is either directly or indirectly due to the work of the engineer, the importance of increasing his efficiency is paramount; and, hence, the study and development of the science of engineering economics is of prime importance. Notwithstanding this incontrovertible truth, it is a fact that in times past our universities and technical schools have almost entirely ignored this fundamental and vitally-important requirement of the engineering profession. Only a few of them provided in the curriculum any instruction at all in technical economics; and even these did not attach to the course anything like the importance which is its due. A few years ago, the Society for the Promotion of Engineering Educa- tion, awakening to a realization of its shortcoming in this vital matter, appointed a committee of four, of which the author was chairman, to inves- tigate and report upon the subject of "The Study of Economics in Tech- nical Schools." After working upon the question for two years, the com- mittee reported unanimously in favor of the subject being taught in all technical courses, and indicated the ground that ought to be covered and the minimum amount of time that should be allotted to it in the curriculum. This was as far as the other three members of the committee at that time were willing to go; but the author went farther by submitting a supplementary report advocating the preparation of an elaborate treatise on "The Economics of Engineering" by a large number of carefully- chosen specialists under the auspices of the Society. As, in the author's opinion, this suggestion of his is of national importance, he herewith repro- duces verbatim the said supplementary report. "This is by no means a minority report, for the writer thereof agrees heartily with all the conclusions of the committee, the members of which are now in entire accord on all matters considered, after having discussed at great length many mooted points; but it is a supplementary report, or something in the nature of a corollary. It is true that the fundamental suggestion it contains was made to the committee, but it was not deemed advisable to include it in the formal report; hence the writer makes it upon his own responsibility. "Briefly stated, it is that the Society undertake the .compilation into book form of a large number of monographs to be prepared by the most eminent American or Canadian specialists, one in each division or subdivision of engineering, all of the said mono- graphs being edited and introduced by a special committee of the Society, and treating, in as complete a manner as practicable, of the economics of design and construction in the various Unes. The book (which might very properly be called 'The Economics of Engineering') should begin with a full 'Introduction' explaining the raison d'etre of the work, giving a history of its compilation, and offering suggestions as to how best it may be utilized, both in its own form and in smaller derived books. "This chapter should be followed by one which treats fully of the fundamental economic problem underlying every important engineering enterprise, viz., its financial probabilities and possibilities — in other words, whether the project under consideration would prove to be a profitable investment. 4 ECONOMICS OF BRIDGEWORK Chapter I "Following this should come, preferably in their alphabetical order, the before- mentioned treatments of the economics of design and construction in the various engi- neering specialties. "Such a treixtise would constitute an encj^clopiedia of practical information on one of the most important features of modern teclmics. It would be invaluable to both the practicing engineers and the teachers of engineering; also to the better class of engineering students, or those of them who are not afraid of hard work — especially ]io.st-graduate students. But in order to make its contents of use to the average stu- dent, it would be necessary to jirepare from it text-books of a simple character. Should the Society favor having such a treatise issued imder its auspices, a publisher of estab- lished reputation could undoubtedly be found to finance the imdertaking and issue the work at his own expense — preferably A\'ithout paying any royalty, in order to keep the selUng price down to a minimum. "A short time ago, by the request of the Dean of the Engineering Department of the University of Kansas, the writer prepared and delivered a course on 'Engineering Economics' in three lectures to the engineering fa cult j^ and students of that institu- tion. The University has lately published these lectures in pamphlet form; and the writer has placed a few copies thereof at the disposal of tliis meeting. The first lecture deals with the fundamental economic problem of finance before-mentioned; the second treats in general detail of the economics of bridge design and construction; and the third is a compilation of certain data furnished by the courtesy of a number of prominent specialists, outlining in a general way the economics of design and construction in their specialties. The writer would be willing to rewrite and expand the first lectiu-e so as to make it serve for the second chapter of the proposed treatise; and the second lec- ture could be sent to each of the chosen specialists in order to indicate the extent of the desired thoroughness of treatment of his subject, and to serve otherwise as a guide to him in the ]ire])aration of the manuscript. If it were expanded by the writer so as to include the 'Economics of Steel Arch Bridges,' it might serve for the chapter devoted to the specialty of bridge engineering. "The third lecture, wlaich nowhere aims at completeness, would prove useful in suggesting some of the sahent topics which should be covered in the \\ritings of a few of the specialists. "The preceding proposal is made with all due deference to the distinguished tech- nical educators and practicing engineers of which tliis Society is so largely comjiosed, in the hojie that it will meet with a favorable reception and will prove to be the means of materially augmenting the amount of available teclmical knowledge in a line of thought which has not received, up to the present time, the consideration which is its due. "Respectfully submitted, "J. A. L. Waddell, "Chairman." This report was read by the author at an amiual nipotin«r of the Society; and, in response to his suggestion, a connnittee of three members was a{>- pointed to consider and report upon the jiroposal. At the next annual meeting that connnittee reconnnended against the Society's fathering the suggested enter]irise. FaiUng in this endeavor, the author, over a year ago, made to the National Economic League, of which he is a member, the suggestion that it undertake the work which the S.P.E.E. had refused; but the fii-st- mentioned organization has not j'^et taken any action. Assuming that the long delay indicates that this society also intends to "pass the buck," INTRODUCTION 5 the author has given up the attempt to inthicc his brother speciaUsts to collaborate with him in the production of the proposed treatise on "The Economics of Engineering." Instead he presents to the profession as a possible starter for such a joint work this treatise on bridge economics, in the hope that some day American engineers will awaken to the importance of having available either a number of small books on the economics of the various specialties or else a joint work similar to the one which he has advo- cated, and which appears at present to be too much in advance of the times. CHAPTER II GENERAL ECONOMIC PRINCIPLES The subject of economics in engineering may properly be termed a new one, in spite of the facts that for several decades the leading specialists, in a more or less desultory way, have given the matter some attention in their designing, and that there have been several small treatises written upon the mathematical theory of engineering economics, notably Prof. J. C. L. Fish's excellent little book which bears that title, and which eveiy progress- ive engineer ought to read. Besides bridgework, the only engineering specialty that has received any attention worth mentioning in respect to the important question of economics is railroading — and that field still needs a vast amount of investigation. It is a branch of engineering which, like bridgework, readily lends itseK to economic study; and it is to be hoped that ere many years the economics of railroading in all its branches will be thoroughly solved by a number of America's most able railroad men, and that they wiU give to the engineering profession the benefit of their experience and investigations. As far as relates to engineering, the term "Economics" has been thus defined by the author in the ''Glossary of Terms" given in "Bridge Engi- neering" — "The science of obtaining a desired result with the ultimate minimum expenditure of effort, money, or material." It is upon the basis of that definition that this treatise is predicated. When determining, from the standpoint of economy, which one is the best of a number of proposed constructions or machines, there should be computed for each case the four following quantities, and then- sums : A. The annual expense for operation. B. The average annual cost of repairs. C. The average annual cost of renewals. D. The annual interest on the money invested. That one for which the sum of these items is least is the most economic of all the proposed constructions or machines; but this statement is ti'uly correct only when the costs of operation, repairs, and renewals are averaged over a long term of years; or else for a comparatively short period of time, when the conditions in respect to wear and deterioration at the end of that period are practically the same for all cases. The principal economic investigation which occurs in engineering practice is that of determining the financial excellence of a proposed enter- GENERAL ECONOMIC PRINCIPLES 7 prise. It consists in showing by proper calculations its first cost, the probable total annual expense of maintenance, repairs, operation, and interest, the advisable allowance for deterioration or ultimate replacement, the probable gross income, and the resulting net income that can be used in paying dividends on the stock or other profits to the promoters. Whether any proposed enterprise, after being thus figured, will prove profitable will depend greatly on the state of the money market, the size of the proj- ect, the probabilities of future changes in governing conditions, and the personal equation of the investor. Generally speaking, if the computed net annual profits on the total cost of the investment (over and above all expenses of every kind, including maintenance, repairs, operation, sinking fund, and interest on all borrowed capital) do not exceed five (5) per cent of the said total cost, the project is not attractive; if it be as high as ten (10) per cent, the enterprise is deemed ordinarily good; and if it be fifteen (15) per cent or more, the scheme is termed "gilt-edged." Small projects necessitate greater probable percentages of net earnings than do large ones; and any possibility of a future reduction of income will call for a high estimate of net earning capacity. Finally, the measure of individual greed on the part of the investor will be found to be an important factor in the determination of the attractiveness of any suggested enterprise. Such investigations as the economics of an important project should generally be entrusted only to engineers experienced in the line of activity to which the said project properly belongs; for if they be left to inexperi- enced investigators, it is more than likely that mistakes will be made and money lost in consequence. The professional men who generally do such work are the independent consulting engineers; certain speciahsts retained on salary solely for this purpose by important organizations, such as rail- road companies; and engineers who are regularly in the employ of large banking houses. The work involved is of such importance that it usually commands large compensation — as, indeed, it should; because to do it effectively demands not only long experience but also good judgment and a vast amount of mental labor, both in order to make oneself capable in general and so as to consider thoroughly all the points embraced by the special problem in hand. How short sighted most promoters of important projects can be! They imagine they can obtain expert opinion of real value without paying for it; consequently they collect a mass of scattered and divergent infor- mation, which, in most cases, is of no earthly use. Any project of impor-' tance is, of necessity, a great economic problem, and ought to be solved at the very outset by special engineering talent of the highest order. A glaring example of the utter folly of a community in proceeding with important engineering construction without first having a thorough eco- nomic study of the problem made by a competent specialist is given in Engineering News of November 30, 1916. It relates to the municipal water- power enterprise on which the city of Montreal has been busy for some 8 ECONOMICS OF BRIDGEWORK Chapter II years. Feeling that the work was being sadly mismanaged, certain prom- inent Canadian engineers ''butted in," investigated, and reported upon the incomplete project. They showed that the $12,000,000 enterprise, which the city had about half finished, will faU so far short of returning a profit on its cost, and that it has so many serious defects, that it will be far better for the community to lose aU it has thus far expended than to incur the additional outlay necessary to complete the work. A thorough investigation to determine beforehand whether the scheme would be profitable would certainly have indicated the futility of constructing on the lines adopted. This fundamental economic problem of whether the proposed construc- tion will prove to be a paying enterprise is often one of extreme complica- tion, involving, perhaps, a determination of the character of the pro- posed improvement, a choice of sites or routes, a selection of uses, a consideration of aesthetics, an opinion on type or style of construction, a question of ultimate durability, a study of greatest possible convenience, a prevision of serious opposition, a prognostication of future conditions, an anticipation of prospective structural modifications, and a safe estimate of cost. The best way to illustrate such complication is by presenting a few examples of actual cases, either pending or already solved.* Case I There is in contemplation a project for building a long, high, and exceedingly expensive bridge across San Francisco Harbor so as to connect the city of San Francisco with the cities of Oakland, Berkeley, and its other suburbs. This project has been a dream for at least a decade; but it is not an idle dream, because some day in some manner or other it is certain to be realized. Some ten years ago the author prepared a report for a banker on the feasibility of the project, the necessity for the structure, the possible revenue from its use, and its approximate cost; and since then several other engineers have made independent studies of the problem. * These examples are copied verbatim from Lecture No. 1 of the author's series of lectures on "Engineering Economics" delivered early in 1917 to the Engineering Alumni Association of the University of Kansas. Three only of the five illustrative cases, viz., those pertaining to bridges, have been reproduced. In respect to Case 2, it is of interest to note that the suggested economic study has since been made by a Board of Advisory Engineers consisting of Col. Bion J. Arnold as terminal expert, Mr. J. Vipond Davies as tunnel expert, and the author-as bridge expert. Their joint report was finished and presented early in 1919; but its contents have not yet been made public. All of the items mentioned were given full consideration; and the difficult question of how to tunnel through soft material at an unprecedented depth was solved in a masterly manner by Mr. Davies. It is hoped by the writers of the report, which consists of some 600 tyf)e-written pages and a large volume of folded blueprints, that it will be iniblished ere long by the city of New Orleans; because it would provide the engineering profession with a good example of how to prepare a complicated economics study of a (H)miilex sub- ject ui)on an unusually large scale, and how to solve several new and difficult engineering problems. GENERAL ECONOMIC PRINCIPLES 9 The communities interested, however, have taken as yet no sensible step towards making a thorough study of the question. Practically none of the governing conditions are satisfactorily known; and, judging by present indications, it is likely to be a long time before they will be, unless, perchance, the leading citizens of the various communities concerned bestir themselves and prevail on their ruling bodies to join forces, raise the requisite funds, choose an engineer of national reputation (or, preferably, a board of three such engineers), arrange to allow him or them adequate compensation for expert services and all the money necessary for borings and other investigations, accord ample time for the entire work, and thus obtain a report that will settle finally all the important economic and technical points involved in the proposition. The main features to determine are as follows, the hsting being done according to relative importance: First. The probable gross incomes from all practicable combinations of the various sources, year by year for a long term of years, and the pro- portion thereof that is likely to prove net in each combination. Second. Based upon the result of this investigation, the determination of the extreme superior limit of cost for the structure for each combination of the different kinds of traffic. Third. In view of the great depths of water in the harbor, what one or more of the various proposed or possible sites might be utilized for building a bridge within the several ascertained limits of cost. Fourth. Of what kind of traffic it is advisable that the proposed bridge should take care. Fifth. The character of the foundation soil as determined beyond all doubt by making proper borings, and the settlement of best depths for all pier foundations. Sixth. The various requirements of the U. S. Government in respect to minimum span-lengths, vertical clearances, and temporary obstruction of waterway for each proposed crossing. Seventh. The minimum clear-headway which, for a combination of all reasons, it is expedient to adopt for each proposed crossing; and the choice between a bridge with and a bridge without an opening span or opening spans. Eighth. A safe estimate of total cost of structure for each layout that proves to be feasible, and the corresponding estimates of cost of operation, maintenance, repairs, etc. Ninth. The time required for completion of construction of the structure for each feasible layout. After all these points have been settled and embodied in a report, it will be easy to determine finally whether, either at the present time or within a certain number of years, it will be practicable or advisable to build the proposed structure; where it should be located; what traffic it should carry; how long it will take to build it; what it will cost for construction, 10 ECONOMICS OF BRIDGEWORK Chapter II maintenance, and operation; and how the necessary funds are to be pro- vided. The actual conditions for the proposed San Francisco Harbor bridge, as well as they can be stated at present, are as follows : A. There is a large possible income from passenger traffic, mainly from commutors who now use the ferry, most of which traffic would soon be diverted to the structure, provided that truly-rapid transit thereon be furnished at all times; and the said income, under present conditions, would be large enough to warrant the building of an open-decked, double- track, electric-railway bridge that would carr}^ no other kind of traffic. B. There is a rapidly increasing amount of automobile traffic now cared for by the ferry; and this, undoubtedly, would be augmented materially by the superior and, possibly, cheaper service of the bridge; nevertheless it is doubtful whether it would be large enough to warrant the building of separate passageways with paved floor and the necessarily-greater carry- ing capacity of the trusses.* It would be out of the question to let the automobiles use the same space as the electric trains; for such an arrange- ment would prevent the rapid transit of the latter. C. There is an immense amount of freight crossing the water; but, for two reasons, it does not appear probable that it would ever be economical to transport it over a bridge. The first reason is the great height to which both it and its containing vehicles would have to be hfted, and the con- sequent expense of such hfting. The second is the greatly augmented cost of structure, due to the far larger five loads for both the floor system and the truoses, which the carrying of such freight would necessitate. It would probably be more economical either to transfer the freight by ferry, as is done at present, or to carry it by rail around the south end of the Bay. D. There is at certain seasons a large amount of passenger traffic to and from San Francisco by certain trans-continental raih'oads; hence the question arises whether the passengers should be carried across in the steam-railway cars on which they travel or whether they should go over in the electric-railway cars. The objection to the latter method is the indi- vidual trouble, inconvenience, and loss of time for each passenger; while the objection to the former is the increased cost of structure due to the difference in the live loads between steam-railway cars and electric-railway cars. Of course, the former cars would have to be hauled in short trains by electric motors, so as to avoid the excessive concentrated loading from the heavy steam-locomotives. E. The most direct route for the crossing is from Telegraph Hill to the outer end of Goat Island, and thence to near the Oakland Pier; and this k the one to which, until quite lately, most attention has been paid. Th main objections to it arc as follows: * Sinnc this was written, the immense development of automobile travel and motor- truck trafric throughout the entire country might reverse (his economic conclusion. GENERAL ECONOMIC PRINCIPLES 11 First. The depth of water between the city and Goat Island is excess- ive, thus making the pier foundations very expensive. Second. A large proportion of the steamers using the harbor would have to pass under the structure. Third. The War-Department requirements in respect to both hori- zontal and vertical clearances would be excessive for this location, because of the large number of vessels passing; and, in consequence, the cost of structure would be greatly augmented. F. By locating further inside the Bay, the depth of water would be reduced to a reasonable amount, and the number of vessels passing the structure would be comparatively small. In fact, the farther back from the harbor-entrance the structure is located, the smaller will be the depth of water and the fewer will be the passing vessels. On the other hand, though, the greater will be the total length of structure, the farther from the center of population will be its city end, and the greater will be the distance which the passengers will have to travel. G. Practically nothing is known about the characters of founda- tions that would be encountered at the various proposed locations; and no provision has been made for money to make the necessary borings. H. It is impracticable to obtain a final decision concerning required span-lengths until a bona fide design, properly backed, has been presented to the War Department for approval. I. In regard to minimum clear-headway, it is probable that the farther inside the harbor the location the less the requirement, because the smaller and less important would be the passing craft, and the fewer the number thereof. Some of them might be forced to lower topgallant masts in order to pass beneath the structure. J. There would be a serious objection to any opening span, because of the delay which would be involved by its operation. The real raison d'etre of the structure is rapid transit, hence to interfere with that in any way would be highly objectionable. K. The total cost of structure would decrease to a certain point as the location is moved up the harbor, because of cheaper foundations and the consequently shorter spans; but beyond the said point it would increase because of the greater length of bridge. L. The more expensive the structure the longer will be the time re- quired to build it; hence it may be concluded that one of the inner-harbor locations would need much less time for completion of bridge than the Goat-Island layout. This matter of time for completion of structure possesses a double importance, because any delay increases the item of cost due to interest during construction; and by postponing the inception of operation it involves a loss of income from use. From the preceding it is evident that the solution of the initial economic problem in connection with the proposed San Francisco Harbor bridge is one of considerable complication. 12 ECONOMICS OF BRIDGEWORK Chapter II Case II The City of New Orleans for many years has had under consideration the building of a combined railway and highway bridge across the Miss- issippi River; and within the last few years the project has been seriously contemplated. Some two decades ago the late CoUis P. Huntington, President of the Southern Pacific Railway Company, and his consulting engineer, the late Dr. Elmer L. Corthell, made an investigation of the scheme of building at that place a double-track railway bridge; and they called in as advisory engineers the author and his brother, Montgomery, to estimate upon the cost of a low bridge. The death of Mr. Huntington, which occurred shortly afterwards, caused the project to be dropped; and it was never revived. The author's joint study was made with considerable thoroughness. It involved the solution of two or three problems of great magnitude that were new to the engineering profession, the principal economic one being a comparison of costs of a high bridge and a low bridge. The result was decidedly in favor of the latter. The problem now facing the city, however, is much more complicated, involving, as it does, a combination of steam-railway, electric-railway, vehicular, and pedestrian traffics. There is a choice between two loca- tions, one near the center of the city and the other several miles further up- stream — in fact, some intermediate locations might have to be considered. There is a sentiment among certain prominent citizens favoring a tunnel rather than a bridge; and, on that account, the question of bridge versus tunnel will have to be considered, notwithstanding the fact that the difficulties presented by the tunnel proposition are almost insurmountable in view of the present status of engineering knowledge and experience. The question of high-bridge versus low-bridge will have to be thoroughly thrashed out in order to please the public, although any truly-experienced engineer would determine very quickly in favor of the latter, irrespective of the possible opposition of the river interests and even that of the War Department. The economic method of handling the combination of the various kinds of traffic would require some study to determine; and the best m(>ilu;(l might vary with the location of the structure. The style and dimensions of the moving span— whether swing, bascule, or vertical lift — and the sizes of the clear opening or openings are mooted points involving a consideration of economics and other important matters. This (}uestion is complicated by the fact that the requirements ought to be dependent on the location; because at the upper one there would be very few vessels passing, while at the lower one there would be many. The unpre(xxlented depth for the pier foundations involves an economic study in order to ascertain the best method of sinking and founding. The facilities for freight, passenger, and vehicular traffic afforded by . GENEEAL ECONOMIC PRINCIPLES 13 the several proposed crossings would affect the total earnings of the struc- ture; hence this feature should receive special attention. The grade and alignment for any proposed crossing are factors that must be included in the economic study, because they affect the cost of handling the traffic; and the matter of right-of-way may prove an impor- tant consideration. The property damages involved by the approaches to the structure and by the shifting of existing tracks would differ materially in cost at the various possible crossings, hence this feature is one involving eco- nomics. The choice between single-deck and double-deck entails a consideration of economics that may prove to be of some importance. After determining the various kinds of traffic to take care of, there remains the economic problem of deciding upon the live loads for the various parts of the structure. If these are made too high, there is a waste of material involved, and the bridge enterprise will forever after be bur- dened with an unnecessarily large annual interest to be paid on that account; but if they are made much too low, the life of the structure will be curtailed. The saving clause, however, in respect to this adjustment is that, ordinarily, a steel bridge does not have to be removed because of overloading until the metal thereof is actually stressed at least fifty (50) per cent more than the permissible intensities of working stresses given in standard specifications for design. This general problem of the proposed New Orleans bridge, while not so complicated as that of the proposed San Francisco-Harbor structure, is of an intricate nature, and will demand for its solution engineering ability and experience of the highest order. Case III There is given in "Bridge Engineering" in the chapter on "Reports" on pp. 1575 to 1581, inclusive, an economic study for the replacement of a bridge over the Mississippi River, which illustrates some of the economic questions that arise in a consulting bridge engineer's practice. In that case the point at issue was whether it would be best to build a single-track or a double-track bridge or to arrange for the conversion at some future time of a single-track structure into a double-track one. Five methods of doing the latter were suggested, and the estimates of their total first costs were made ; then, at an assumed rate of interest, a table was prepared show- ing the total cost of each structure plus compound interest thereon for periods of five years, up to the limit of forty years. That table indicates at a glance the comparative economics of all five methods at any of the five- year periods. A diagram prepared from the said table, of course, would be preferable, as it would show more readily the comparison at any inter- mediate period. 14 ECONOMICS OF BRIDGEWORK Chapter II In comparing the economics of several methods of accomplishing the same result, the author has advocated the method of computing and con- trasting the total annual costs, including interest on first cost, upon the assumption that all the money needed for the construction had been bor- rowed; and this is the most logical method, although in his practice he has sometimes adopted other methods — mainly to please his chents. Some chents want to see figures of total cost instead of estimates of annual ex- pense; and, under such a condition, it is necessary to sum up for each case all annual expenses except interest, ascertain what amount of money would produce this sum by simple interest at current rates; and add that amount to the total first cost. The case giving the least grand total would be the economic one. An effective method of contrasting several differing types of construc- tion for their economics is that used in Case III, viz., to assume a number of future dates, preferably those at which certain large expenditures would probably have to be made for renewals or repairs of perishable portions, and compute the grand total cost to each date for each proposed structure under the assumption that it is then put into perfect condition, and allow- ing standard compound interest not only on the first cost but also on all annual expenditures. A comparison of these grand total costs at the several dates adopted will indicate clearly which is the most economic of all the types of construction compared. To those who have a penchant for using mathematical formulsB, the following economic treatment will appeal. It was evolved some forty years ago by Ashbel Welsh, past-president of the American Society of Civil Engineers. To Find the Comparative Economy of Two Bridges of Different Cost and Durability, that will Answer the Same Purpose Equally Well While They Last "Let C be the cost and assumed real value of one of them, T the time it will last, a the compound interest on one dollar for that time, at whatever rate money is worth to the party pa3'ing for the bridge, and L the loss on the bridge at the end of the time T, or the amount which it would take to make it as good as new. Let R be the real value of the other bridge, C its cost, T' its duration, a' the compound interest on one dollar for that time, and L' the loss on the bridge at the end of the time T' , or the amount required to make it as good as new. And let V be the real value of the bridge that would last forever, if all circumstances should remain constant. "Now, supposing that the money required for building had been borrowed for an indefinite time, the actual expense at the end of the time T to the party paying for the bridge which would last forever would be aV; and the actual expense at the end of the same time for the first bridge, after making it as good as new, would be aC-\-L. These two quantities arc eciual : therefore the hitherto unknown value of V is . "Similarly, at the end of the time T", the expense for the bridge which would last forever would be a'V; and that for the second bridge, after making it as good as new, GENEKAL ECONOMIC PRINCIPLES 15 if the cost had been the real value R, would be a'R+L'. As before, these two values are equal; and, therefore, F = /?+^. Equating the two values of V gives L U a a and a a " Now, if the value thus found for R be greater than the cost C, the second bridge is more economical than the first; while, if it be less, the first bridge will be the more economical." It will be noted that the foregoing method does not mention costs of operation and maintenance. They can be taken into account by adding their capitalized costs to the costs C and C. Conditions sometimes arise which render it inadvisable to adopt the most economic of the several compared types of construction — for instance, when the promoters cannot possibly raise the money required to build the kind of structure which they desire, and, consequently, must content themselves, for a time at least, with one that is inferior. An example of this is a proposed railroad through virgin country, where the cheapest kind of a line will serve to develop business, and will suffice for many years to take care of the traffic, although uneconomically as compared with first- class railroads. Under such conditions an engineer possessed of sound financial judgment would advocate building the line at first as cheaply as practicable; adopting comparatively heavy grades, sharp curves, cheap ties, light rails, temporary structures, earth ballast, low-power locomotives, etc. ; but paying strict attention to the vital matter of thorough drainage, and studying in advance of construction the question of how the line can be improved later at least expense and without materially interfering with traffic. As another illustration of this economic consideration, there might be taken the case of a bridge for a crossing where there is danger from washout of falsework. Here it would be advisable to adopt a cantilever structure instead of a layout of simple-truss spans, notwithstanding the fact that it might require considerably more metal and might involve a higher pound price for erection. Such problems as these may be deemed by some people to be questions of expediency rather than of economics; but the author prefers to treat them as pertaining to the latter, which means that, in the case first men- tioned, he would consider it truly economic to build the cheap fine and operate it for a while uneconomically rather than to spend at the outset large sums of money in order, later on, to handle economically traffic that possibly might fail ever to materialize; and that in the second case it would 16 ECONOMICS OF BRIDGEWORK Ch.m>ter II be in the line of true economy to be somewhat extravagant in the cost of superstructure so as to avoid all possibihty of disaster during erection. In this connection it should be noted that it will sometimes be more economic to build a hght structure at the outset and later remove it and replace it by a heavier one, rather than to build the heavier one at first, provided that the hght structure will serve the purpose adequately for a number of years, and that the replacement can be done without too serious an interruption of traffic. For instance, it might be cheaper to build a $50,000 bridge now and replace it in fifteen years by a bridge costing $100,- 000 than to build the $100,000 structure at first; for the compound interest on the $50,000 additional investment for fifteen years at six per- cent amounts to $70,000. It will rarely pay to anticipate traffic require- ments by more than twenty or thirty years, in case that thus anticipating them involves a large additional expenditure. In respect to the economics of design and construction of bridges, the following general suggestions are pertinent: Anticipating the Future In all engineering work of both designing and construction, true econ- omy necessitates a thorough consideration of future requirements and pos- sible eventualities, also a provision for meeting the same. For instance, in designing a structure one should consider possible future additions of loading and how to accommodate them; and in construction one should anticipate delays, floods, storms, and other possible difficulties, and should prepare his programme so as to meet them effectively and without any un- necessary expenditure of time, labor, or money. Foresight of this kind is an important element of success in the career of every engineer. First Cost It must not be forgotten that under the item "First Cost" must be considered all items of expense, of every kind whatsoever, that may be incurred before the structure is ready for operation. It should include not merely the ordinary estimated cost of construction, oi' the amount of money to be paid to the contractor, but also promotion expenses, discount due to sale of bonds below par, commissions or other considerations for services rendered, interest on money during construction, right-of-way, rents and minor incidental expenses during construction, administration, legal expenses, engineering, and a proper contingency allowance. Compensating Factors in Economic Comparisons and Frequent Wide Range of Economic Limits In (he making of economic studies, assumed variations in proportions or types will nearly always increase the cost of certain factors and reduce that GENERAL ECONOMIC PRINCIPLES 17 of others, while the vakies of some factors may remain unchanged. The costs of these various factors tend to balance, so that considerable modifi- cations rarely produce great changes in total cost. This principle is true for all kinds of factors. For instance, in determining the economic span lengths for a truss bridge, increasing the span-length augments the cost per lineal foot for the superstructure and generally, but not always, reduces that of the substructure. Again, in contrasting carbon steel and alloy steel for bridgework, the latter gives smaller weights but greater costs per pound. Also, in comparing railway decks of the ordinary wooden type with ballasted floors, the first cost of the latter is greater, but the expense for its maintenance is less ; and this last condition is generally found when pitting steel bridges against reinforced concrete ones. The effects of variations in factors can be well comprehended by a study of the various diagrams for Chapter XVIII, which treats of the economic span-lengths for simple-truss bridges on various types of founda- tions at different depths below the elevation of Low Water. The plotted curves show costs per lineal foot for superstructure, substructure, and the total. It will be noted that all substructure curves are concave upward, that the superstructure records are either right lines or easy curves also concave upward, and that the lines for totals are generally very flat curves, concave upward. The economic span-length occurs where the steepness of the substructure curve is just the same as that of the superstructure curve, but it will be noted from the upper of the three curves (the one for total costs per lineal foot) that varying twenty-five feet either way from the absolute minimum augments very slightly, indeed, the total cost per foot, and that a variation therefrom of fifty feet seldom increases the said cost more than two per cent. Furthermore, the exact minimum is dependent somewhat upon the personal equation of the designer; for such matters as sizes of pier bases must be determined largely by judgment, and a slight variation in unit prices of materials in place will move the lowest point of curve some distance horizontally. From the foregoing it is evidently a waste of time to split hairs when one knows he is near the economic point; but, on the other hand, adopting a span-length of 450 feet when 300 feet is the economic limit may sometimes add ten or fifteen per cent to the total cost of structure, consequent^ one must make sure that his adopted span-lengths do not differ too seriously from those for truly greatest economy. There is another economic fact that is well worth noting, viz., that whenever in reducing the span-length, some important part reaches mini- mum size, so that further diminution in length will not reduce that part, it is practically certain that a shorter length will not be economic. In nearly all economic studies for bridges, the lighter the superimposed load the greater will be the economic length, whether it be span, panel, stringer-spacing, or what-not. This is largely due to the fact that, in case of any design, as the distance in question is reduced, if the loading were 18 ECONOMICS OF BRIDGEWORK Chapter II light, certain parts would more quickly reach minimum size than they would if the loading were heavier; and any further material reduction would prove uneconomic. Systemization Quoting from "Bridge Engineering/' "The systemization of all that one does in connection with his professional work is one of the most impor- tant steps that can be taken towards the attainment of success." More- over, it is one of the fundamental elements of economics in all lines of work. Time Versus Material Some designers in their endeavor to save a small amount of material expend a large amount of time, not only of their own but also of other people's, which time when properly evaluated is often greatly in excess of the cost of the material saved. Such economy as this is false; and its practice is unscientific. Labor Versus Material Similarly, some designers in an endeavor to cut down quantities in their structures increase the labor thereon to such an extent that the material saved is worth only a small portion of the value of the extra labor ex- pended. For instance, if one were to make a smaU pier hollow, the con- crete thus saved would not be worth anything like as much as the cost of the forms needed to construct the hollow space and that of the reinforce- ment which would be required in the thin pier walls. Recording Diagrams The study of economics is greatly facilitated by the use of diagrams that record quantities of materials, costs of construction, times of operation, etc., for varying conditions. In general, it may be stated that American engineers do not use graphics for studying economics to the extent which is advisable; and that in this they might learn something from their European brethren. Economics of Mental Effort Almost nothing concerning this important subject is taught in our technical schools; and but little is known about it by practicing engineers. To be a truly-successful engineer, one has need to study deeply the matter of how best and most economically to utilize his mental forces; how to ac- complish the greatest amount of work with the smallest expenditure of effort; how many hours of woi'k pvv day for k)ng-continued labor will effect the largest acconipUshiiKUit; to what extent men in various lines of GENERAL ECONOMIC PRINCIPLES 19 activity should take vacations, and how these should be spent; what are the effects upon one's working capacity from the use of liquor and tobacco in both small and large quantities; etc. All these are economic questions of great importance; and they need to be given proper attention by every engineer who aspires to efficiency in both himself and his employees. Again, the development of the faculty of concentration is an economic consideration of the greatest value. Labor The scientific handling of labor is an economic problem of the utmost importance, and a treatise could well be written on the subject. The principal desideratum is to keep the workmen well, happy, and contented; and the best ways to do this are to treat them kindly, make them com- fortable, feed and house them well, amuse them in their spare time, avoid working them too long hours, pay them by piece-work when practicable, listen patiently to their complaints, right their wrongs, see that they are well taken care of when they are ill or injured, and evolve, if possible, some feasible method of sharing profits with them. On the other hand, though, drive them hard and continuously during working hours, insist upon their putting in overtime when the conditions truly require it, dis- charge instantly all insubordinate or otherwise troublesome men, dispense quietly with the services of all shirkers, and insist that everybody put forth his best and most intelligent effort to effect the maximum of accomplish- ment in the minimum of time. CHAPTER III ECONOMICS OF THE PROMOTION OF BRIDGE PROJECTS In most cases the promoter of a bridge project at the outset is possessed of rather inflated ideas as to the possibilities for gain by the materiahzation of his proposed enterprise, and, in consequence, is inclined to be uneconom- ical in his layout of structure and of the money expenditure therefor. If he is to make a success of his venture, he should begin withojit delay an economic study of his problem; and in this he will require the aid of a bridge specialist of wide experience. It will nearly always be found advisable to keep the first cost of structure down to an absolute minimum, but arrang- ing to increase its capacity from time to time as the augmenting business warrants. Generally this is a necessity, because bankers will not furnish money for an extravagantly conceived proposition; but even if the money be available, it would be bad policy to spend any of it unavoidably at the outset, for the reason that the interest on the extra expenditure, up to the time when the facihty in question is really needed, might amount to a large sum of money. The promoter should investigate thoroughly the possibility for traffic of all kinds, keeping his own counsel about what he is doing, in order to protect himself from hold-up by property owners or the malevolent opposi- tion of possible rival promoters. After finishing this investigation of con- ditions, he should, if possible, determine the kind or kinds of traffic for which the proposed structure should provide and the probable amounts thereof that there will be, both at the outset and for a long series of years, also the net income it will produce. The preliminary investigations concerning the probable traffic and other sources of revenue should be made with great care and conservatism. One who is optimistic by nature is prone to overestimate, and no promoter is of any account at all unless he is optimivstic; hence he should consider very carefully all unceitain matters connec^ted with the revenue estimates, and should endeavor always to err upon the side of safety. Similarly, in com- puting the annual cost for maintenance, repairs, and otlicr like ex]ienses, he should be (;areful to omit no items and to figure; each item high enough to be beyond criticism. After his l)i-idge specialist has reported upon the best type of structure to build, the first (^ost for the minimum amount of construction at the outset, and ( h(> subsequent increased costs for enlargements or betterments, the pi-onioioj- should complete the economic study of the enterprise and 20 ECONOMICS OF THE PROMOTION OF BRIDGE PROJECTS 21 decide whether it is advisable to undertake the venture. If he experiences any difficulty in making up his mind as to the kinds of traffic for which he ought to provide, his engineer should be able to tell him approximately the cost of structure to carry any kind or combination of kinds thereof; and, knowing the probable receipts therefrom, he should then be able to come to a proper decision. The question often arises as to whether it will pay to accommodate pedestrian travel; and, in the case of a long structure carrying street cars, it will not. In some cases, however, in order to procure a franchise for building the bridge, it may be necessary to agree to provide footwalks for pedestrians, even if there be very few of them. In the old days of horse- propelled vehicles, it was practicable for pedestrians to cross on the main roadway, but to-day the rapid passage of automobiles would render such a procedure exceedingly hazardous. In the case of a proposed combined-railway-and-highway bridge, it is often good policy to floor over the railway deck so as to carry temporarily both trains and vehicles, and to provide for attaching brackets in the future to support the latter. Such an arrangement gives very poor service; but it often will suffice for a number of years. In the building of a railway bridge only, the approaches may be timber trestles, which have a life of ten years, more or less; and at the end of that time they can be replaced either with new timber or by permanent con- struction. If the bridge be built to carry a double track, and if one track will take care of the traffic for a few years, a single track can be laid on the two inner lines of stringers, and the approaches may be single-track wooden- trestles; or, if preferred, one side only of the double-track structure can be used, and the temporary approaches can be built off-center. In case of a great scarcity of funds, a double-track bridge can be designed with trusses for half live load and partial dead load, and an arrangement made in advance for the future doubhng of trusses. The author evolved and patented this detail many years ago, but has never since had occasion to utilize it in actual construction, although he has estimated upon its employment. Occasionally it is feasible to build a portion of the main bridge of perma- nent construction and the remainder of cheap, perishable materials; and this expedient may be in the line of true economy. A quarter of a century ago the author built a bridge across the Missouri River between Council Bluffs, Iowa, and East Omaha, Nebraska, on the basis of part permanent and part temporary construction; and later he replaced the temporary portion with permanent spans. In the original structure the cheapening of everything was carried to the utmost legitimate limit, in order to come within the bankers' appropriation. The pivot pier of the swing span (the largest in the world at that time, viz., 520 feet) was made permanent; but the span itself was stripped of its cantilever brackets for roadways and sidewalks, a portion of the deck was floored over for teams, a single track 22 ECONOMICS OF BRIDGEWORK Chapter III was placed at the middle of the double-track space, and pedestrians had to use the roadway. Of course, there could not be railway and highway vehicles simultaneously on the structure, but the roadway was wide enough for teams to pass and for a line of pedestrians on each side of a railroad train. The end piers of the swing span and aU the other piers were built of piles and other timbers, the flanking spans were of the combination t3^pe, viz., tension members of steel and compression members of timber, and the approaches were single-track timber-trestles for the railway and wooden approaches with fairty-steep grades for the highway. This temporary work was constructed so as to last at least eight years, and it was used for ten, when it was taken out by the author and replaced with permanent construction for the lUinois Central Railroad Company, which had bought the structure for its main-line entrance into the city of Omaha. The temporary work here described was aU so well and thoroughly done that, when it was removed, there were no evidences whatsoever of decay or failure. The author is of the opinion that it could have been used for six or eight years longer without the slightest danger of any kind. The evolution of a design such as above described involves economics of the highest type; and the author considers it to be by no means one of his minor achievements in bridge designing and construction. There is a matter of economic importance which no promoter should ever forget; and that is the growing scarcity of timber, and, consequently, its greater future price. While it may prove, temporarily advantageous to use it in his bridge, he should make sure that the metalwork of his super- structure is strong enough and that the foundations of his substructure are sufficiently substantial to carry properly the increased dead load of the spans due to the future substitution of heavy concrete for hght timber. CHAPTER IV EFFECT ON ECONOMICS FROM VARIATIONS IN MARKET PRICES OF LABOR AND MATERIALS The economics of bridge design are not so greatly affected by variations in prices of labor and materials as is commonly supposed, because there is a tendency for all prices to rise and fall more or less uniformly. If they were to do so exactly, the effect on the economics would be absolutely nil. It is only when the variations in unit prices for the component materials are irregular that the economics of design are affected, and then in most cases but shghtly. It is true that when there is a sudden rise or drop in the cost of superstructure metal erected, the proportionate change in substructure prices wiU lag behind; but it is generally not long before a state of com- parative equilibrium is reached, and the variations in prices become more nearly uniform as compared with those that existed before the change occurred. So far as economic span-lengths for simple-span bridges are concerned, the practical effect is small indeed ; for, even though the theoretic economic length be considerably changed, there is always a rather wide range on either side of the minimum where the costs are but little higher. Of more importance than this is the effect upon the relative economics of different types of structures, especially those of different materials such as steel and reinforced concrete. In normal times the base price of structural metal fluctuates from about 1.15 cents per pound to about 1.75 cents — it even ran up to 2.25 cents in 1899 and 1900. The cost of fabricated struc- tural metal is subject to still greater changes. Freight rates in different portions of the country vary from about 0.1 cent a pound to over one cent. Local conditions may affect transportation and erection costs materially. For the foregoing reasons the price of structural metal erected is subject to a variation of about two cents a pound, entirely apart from causes influencing the prices of other materials. For instance, in January of 1920, the price of cement was $2.80 a barrel in New York and $2.43 a barrel in San Fran- cisco, while the freight rate on structural metal was 0.27 cent a pound to the former point and 1.25 cents to the latter. At the same time, heavy construc- tion timber cost nearly twice as much in New York as in San Francisco; and while structural iron workers received only 8 per cent more in the for- mer than in the latter, common labor was paid nearly 50 per cent more. Sand, stone, and gravel were considerably cheaper in San Francisco than in New York. At that period, therefore, structural metal was about one cent 23 ,24 ECONOMICS OF BRIDGEWORK Chapter IV a pound cheaper in New York than in San Francisco, whereas concrete and timber were about 40 per cent more expensive in New York. Again, early in 1915 structural metal erected was let in a few cases as low as three cents a pound, with prices of other materials correspondinglj^ small; while about two years later the said metal erected was for a short time as expensive as ten cents a pound, the prices of other materials show- ing an increase of less than 50 per cent. In January of 1920, structural metal erected was quoted as low as 7 cents a pound, while other prices were much higher than in 1917. Economic comparisons in 1920 are, there- fore, quite similar to those in the pre-war period, while those of 1917 were decidedly different from those of either of the other dates. The foregoing examples are sufficient to indicate the fact that, when close economic comparisons are to be made, carefully selected unit prices must be used. The statement at the beginning of this chapter to the effect that such variations will seldom radically affect economic comparisons, is nevertheless correct. The result of an economic study made with nor- mally-balanced unit prices will rarely be in error by any serious amount. This question will be discussed further in the various chapters deahng with comparative economics. In connection with the elaborate series of computations made by the author in the preparation of his monograph on "Economic Span-Lengths for Simple-Truss Bridges on Various Types of Foundations/' he took occa- sion to figure three sets of economic curves for low-level, double-track, steam-railroad bridges on sand foundations, one with normal unit prices for all materials in place, another for extremely high prices, and the third for extremely low prices. The various unit prices for each case were ad- justed according to the author's best judgment, based upon an experience in bridge estimating extending continuously over a longer period of years than he likes to acknowledge. The results of this comparison are given in the following table: TABLE 4a Economic Span-Lengths for Double-Track, Steam-Railway Bridges on Sand Foundations at Various Depths below Extreaie Low-Water Depth of Foundation below Low- Water Condition of Material Market Low Normal Hi-h 100' 150' 200' 250' 290' 330' 375' 425' 275' 310' 3G0' 430' 275' 325' 375' 425' The slightnoss in the variations of these economic 8]iaii-l(Migths with the different coiiditions of the material market is suflicienlly c^vidcMit to warrant ECONOMICS FROM VARIATIONS IN MARKET PRICES 25 the conclusion that ordinary differences of unit prices will not affect the economic layouts for simple-truss spans having piers on sand foundations. Similarly it might be shown that the conclusion holds good for any other type of pier foundation. There is, however, a case in the late practice of the author which indi- cates that abnormally high variations (for the different component mate- rials of bridges) in the changes in unit prices do sometimes affect materially the economics. At the present time the following pound prices for metal erected in suspension bridges prevail: Wire Cables 23^ per lb. Carbon Steel S^ per lb. Nickel Steel 10^ per lb. A fair average for the ante-bellum unit prices of these materials is re- spectively 13^, 5, and 7 cents. Using the averages for the two kinds of structural steel as representative market prices, and applying their ratio to the pre-war price of wire cables indicates that a proper present price for the latter in place would be 20 cents. This shows that these cables are about 15 per cent too expensive. As explained in Chapter XIII, the use of existing unit prices instead of ante helium ones raised the span-length of equal cost for highway cantilever and suspension bridges from 1,000 ft. to 1,200 ft., that length for like structures which carry a certain combina- tion of highway and railway loadings from 2,190 ft. to 2,360 ft., and that length for similar bridges subjected to only steam-railway loading from 2,570 ft. to 2,630 ft. These changes are of some importance, hence one must conclude that the economics of certain types of bridges are materially affected by abnormally great variations in the ratios of rise or faU in the unit prices of their component constituents. The location of a bridge may affect to a certain extent its economic lay- out, especially for American constructions in foreign countries. For in- stance, the freight and customs duties on superstructure metal might be very high and the importation of skilled erection-workmen might be a necessity, while the prices of substructure materials and of i^nskilled labor therefor might be exceedingly low; and with such a combination of conditions the economic span-lengths would be considerably shorter than those governing in the United States. CHAPTER V ECONOMICS OF ALLOY STEELS* Whether it be economical or the reverse to use for bridge construction any particular alloy of steel instead of standard carbon steel will depend upon three fundamental conditions, viz., A. The ratio of costs per pound erected of carbon steel and the alloy steel under consideration. B. The ratio of the elastic Umits of these two steels. C. The type and the span length, or span lengths, of the structure contemplated. If r (greater than unity) is the ratio of costs per pound erected of the alloy steel and carbon steel, and r' (less than unity) is the ratio of elastic limits of the two metals, then for primary truss members of rods or bars the economy in using the alloy will depend upon whether the product of r and r' is less than unity, or mathematically rr'e('tive alloy of nickel, chro- mium, and molybdenum, with an excess of manganese above the amount ECONOMICS OF ALLOY STEELS 35 ordinarily used in steel-making, as being the ultimate solution of the said problem. He is endeavoring to make the dream come true by trying to induce a combination of miners, metallurgists, and steel manufacturers to furnish the requisite money for an elaborate series of experiments' to find an ideal high-alloy of steel for long-span bridges; and, perhaps, if he lives long enough, he will be successful. He feels confident that within three years after actually starting the investigation, with ordinarily good luck in respect to governing conditions, and with a reasonable expenditure of money, he could find how to manufacture the material desired at a fairly- moderate pound-price. A successful solution of this problem would be epoch-making in respect to the economics of bridgework. There appeared in the New York Times of February 18th, 1920, a notice concerning some experiments that are being made in France upon the production of high-grade steels by a modification of the Bessemer process. If these experiments prove to be successful, the manufacture of the author's proposed ''Nichromol Steel" may be readily materialized. The following is the notice referred to : Paris, Feb. 16. — A revolution in the steel industry is promised by four inventors who are working here. Final tests of their process are now being made. Their claim is that hard steel — nickel, chromium, manganese and the other kinds — can be manu- factured at roughly the same cost as ordinary Bessemer steel, with the sole added expense of the alloys involved. In a mill on the northern outskirts of Paris to-day five experiments were made each involving the production of a ton and a half of high-class steel. There was little in appearance to distinguish the new from the ordinary Bessemer process. There was an ordinary furnace, packed with coal and iron. The metal was fused at a rela- tively low temperature and then passed to a furnace, where the temperature was raised to 1500^ C. and the impurities burned out. By the Bessemer process a relatively small percentage of impurities, chiefly phosphorus and sulphur, is eliminated. The result is that Bessemer steel is suitable for only ordinary work and cannot be employed as raw material for the high grade steel necessary for many phases of industry. The essential feature of these experiments is that by the addition of certain secret substances and by means of a certain undivulged process the ordinary Bessemer steel process can be applied to produce steel as pure as that derived electrically. These results are predicted by the inventors: First, France will be in a position to produce high-grade steel at the same cost, or approximately the same cost, as ordinary steel plus the expense of the alloys, while special steel containing no alloys can be produced at the same price as ordinary steel. Second, high-grade steel, which hitherto could not be employed for such ordinary purposes as railway rails, etc., now becomes available for the everyday purposes of commerce. The four inventors have been working for more than six months and have satisfied themselves that the high-grade steel they produce answers to every test, whether of chemical analysis or of physical properties, such as hardness, tensile stress, malleabil ity, etc. One of the inventors is Jules Lambrecht of Herstal, Belgium, who worked as a steel expert for France during the war. Another is Marc Antoine, also a Belgian, known as an authority on railroad steel. The other two, whose names may not now be men- tioned, are Frenchmen. To-day's tests were attended by a number of steel experts and scientists who took 36 ECONOMICS OF BKIDGEWORK Chapter V away samples of the inventors' product. The presence of these men attested the seri- ousness of the experiments, and it is reported that the inventors may have discovered a process as valuable as that of Sir Robert Hadfield, which is reserved for Government use in England, despite the demand on the part of private enterprise. The French inventors have no connection with the Government. They caU attention to the fact that ordinary Bessemer steel, because of the impurities of the metal, wears badly and irregularly. Hard steel having a much longer life can be made to bear the same strains with very much less content of material, and thus the country that is able to produce high-grade steel at the cost of ordinary steel will benefit by the immensely increased output and will be able, because of superior methods, to compete on very favorable terms with Great Britain, the United States and other steel- manufacturmg countries. At a time when the whole world is in need of steel of every sort, the cheapening of the highest grades and the reduction in the amount of labor required to produce it are factors of capital importance in the general work of reconstruction. It is pointed out that, while the electrical process for producing pure steel is excellent, it requires an enormous expenditure of energy and labor, and is consequent Ij' extremely costly. The Bessemer process, on the other hand, \vhile relatively cheap, has hitherto failed to remove impurities. What the inventors say they can do is to obtain pure steel by the use of the Bessemer process with slight alterations. Since the preceding was written the author has secured some informa- tion concerning molybdenum steel for which he has been searching during the last year or two, and which had been refused him by a high authority in the employ of an automobile manufacturing compam' — possibly with the thought that, if molybdenum were adopted for bridgework, there would not be a large enough supply left for the use of the automobile industry. Some six months ago, however, the author was so fortunate as to secure from the president of the Climax Molybdenum Company of New York and Colorado certain interesting general information concern- ing the alloying properties of molybdenum, with the promise of detailed data as soon as they could be collected and formulated for publication in pamphlet form. In accordance with that promise, there came to hand a short time ago an advance copy of a booklet entitled, "Molybdenum Com- mercial Steels," issued as a trade catalogue by the before-mentioned com- pany. The work contains a mass of detailed information about the alloy; and, although the data apply directly to steel for automobiles, it has proved practicable to make from the tabular matter deductions indicating how the said alloy might be applied to bridge construction. It certainly contains sufficient statistics to enable an investigator to draft a programme of studies and tests for determining the best practicable combination or combinations of molybdenum and other alloying elements with iron in order to produce the high alloy of steel for bridgework for which the author has been search- ing these many years. While it is true that the publication is unijuestionably a trade cata- logue for the promotion of the sale of molybdeiuim, it is i)ointed out therein that, in order to avoid any undue rose-coloiing caused by the natural tendency in writing such a work to "])ui one's best foot foremost," the MS. was submitted for connnent to the officials and metallurgists of some ECONOMICS OF ALLOY STEELS "37 of the largest alloy-steel manufacturers and consumers in the United States, with the result that it met with their approval — their experience with the various molybdenum-steel types described conforming to the statements, facts, and figures set forth. Moreover, the general treatment of the subject gives 'prima facie evidence of a spirit of fairness; and the style of work is that of a technical scientist and not that of a promoter. Unfortunately, the records all deal with heat-treated steel, which, while applicable for eye-bars, is not suitable for built members of bridges; but by inquiry from the writer of the pamphlet the author obtained a small amount of data concerning tests of one of the steels untreated, as well as some results of tests of carbon-molybdenum steel that were made on an accidental melt from which chromium had unintentionally been omitted. From the same source it was learned that the proportionate increase in ultimate strength and elastic limit due to the addition of molybdenum is practically the same for untreated as for treated steels. From the contents of the pamphlet, the additional information just mentioned, and the author's previous experience with nickel steel, the deductions which follow have been drawn. For simplification of the discussion, and in order to distinguish readily between the various combinations of alloying materials, the author has taken the liberty of evolving and using the following nomenclature: Carmol = Carbon-Molybdenum. Chromol = Chromium-Molybdenum. Nichromol = Nickel-Chromium-Molybdenum. Nicmol = Nickel-Molybdenum. Chrovanmol = Chromium- Vanadium-Molybdenum. Nichro = Chrome-Nickel. Chrovan = Chrome- Vanadium. In order to utilize the diagrams of this chapter for finding the economics of molybdenum as an alloying material for bridge steel, an understanding will have to be arrived at, in order to determine properly the values of r' ; because, while a high intensity of working stress may be employed for heat- treated eye-bars, a[much lower one will have to be adopted for the untreated built-members; and, again, it would never be legitimate to use a working stress greater than one third of the ultimate strength. In heat-treated steels the elastic limit generally falls but little below the ultimate strength, hence it would not do to use one half of its amount for the working tensile stress as is done in the case of untreated steel. As the data concerning the untreated molybdenum steel are rather meagre, it will be necessary to make a few approximate assumptions in determining the elastic limits and intensities of working stresses. For instance, one is that the proportion of untreated and treated steel in a pin-connected bridge will be about as two is to one. This is fairly accurate, , and will suffice for a preliminary study of which the sole purpose is to indi- 38 ECONOMICS OF BRIDGEWORK Chapter V cate in outline the final investigation it will be necessary to make, in order to establish the suitability of molybdenum steel for bridgework, determine the best proportions for the alloying elements, and demonstrate the economics of the alloy in comparison with other bridge steels, both plain and alloyed. From "Molybdenum Commercial Steels" and the before-mentioned supplementary data furnished to the author the following tables have been copied or prepared: Heat-Treated Chrome Steel with and without Molybdenum TABLE 5o Tensile Test on Chrome Steel Analysis Carbon Manganese Chromium Molybdenum 0,27 0.63 0.99 None Physical Properties. (1 inch round) Elastic Limit Tensile Strength Elongation Per Cent Red. of Area Per Cent 130,000 139,000 16.5 58 TABLE 56 Tensile Test on Chromol Steel Analysis Carbon 0.26 Manganese 0.64 Chromium 0.76 Molybdenum 0.31 Physical Properties. (1 inch round) Elastic Limit 142,000 Tensile Strength 151,000 Elongation Per Cent 18.5 Red. of Area Per Cent 62 ECONOMICS OF ALLOY STEELS 39 Heat-Treated Chrome Nickel Steel with and without Molyb- denum TABLE 5c Tensile and Dynamic Tests on Nichro Steel Analysis Carbon Manganese Silicon Chromium Nickel Molybdenum . 33 av. 0.5 av. 0.18 av. 1.0 av. 3.27 av. None Physical Properties. (Rolled Bars 1" to 2") Elastic Limit 116,700 Tensile Strength 135,200 Elongation Per Cent. 19.6 Red. of Area Per Cent 57.1 Izod Ft.-Lbs. 61 Brinell Hardness 270 TABLE 5d Tensile and Dynamic Tests on Nichromol Steel Analysis Carbon Manganese Silicon Chromium Nickel Molybdenum 0.27 av. 0.6 av. 0.3 av. . 86 av. 2.95 av. 0.43 av. Physical Properties. (On finished shaft) Elastic Limit Tensile Strength Elongation Per Cent Red. of Area Per Cent Izod Ft.-Lbs. Brinell Hardness 130,000 142,000 20.5 65 67 303 40 ECONOMICS OF BRIDGEWORK Chapter V Heat-Treated Chrome- Vanadium Steel with and without Molyb- denum TABLE 5e Tensile Tests on Chrovan Steel Analysis Carbon Manganese Chromium Vanadium Molybdenum 0.36 av. 0.5 av. 0.9 av. over . 16 None Physical Properties. (1" round) Elastic Limit Tensile Strength Elongation Per Cent Red. of Area Per Cent Brinell Hardness 146,500 167,500 16 54.5 340 TABLE 5/ Tensile Tests on Chrovanmol Steel Analysis Carbon Manganese Chromium Vanadium Molybdenum 0.39 • 0.4S 1.06 0.17 0.85 Physi( •al Prop(n'ties. (1 i" round) Elastic ; Limit ! Tensile Strength Elongation Per Cent Kod. of Area Per Cent Brinell Hardness 170,000 KIO.OOO 19 (10 392 ECONOMICS OF ALLOY STEELS 41 Heat-Tkeated Nickel Steel with and without Molybdenum TABLE 5^ Tensile Tests on Nickel Steel Analysis Carbon Manganese Nickel Molybdenum 0.30 0.25 4.00 None Physical Properties Elastic Limit Tensile Strength Elongation Per Cent Red. of Area Per Cent 108,000 120,000 16 55 TABLE 5h Tensile Tests on Nicmol Steel Analysis Carbon Manganese Silicon Nickel Molybdenum 0.33 0.25 0.18 4.50 0.58 Physical Properties. (1|" round) Oil Quench Elastic Limit Tensile Strength Elongation Per Cent Red. of Area Per Cent 1450° F. 1500° F. 1550° F. 1600° F. 1650° F. 164,600 166,500 165,100 164,900 166,000 173,800 176,000 175,000 173,300 174,400 16.0 15.5 15.5 15.5 15.0 53.4 55.3 54.0 55.6 55.0 165,000 av. 175,000 av. 15.5 av. 54.7 av. 42 ECONOMICS OF BKIDGEWORK Chapter V Heat-Treated Carbon Steel with Molybdenum TABLE 5i Tensile Tests on Carmol Steel Test No. 1 Analysis Carbon Manganese Molybdenum 0.24 0.69 0.32 Physical Properties Elastic Limit TensUe Strength Elongation Per Cent Red. of Area Per Cent 92,000 114,000 20 66.5 TABLE 5j Test No. 2 Analysis Carbon Manganese Molybdenum 0.17 0.49 0.96 Physical Properties Elastic Limit Tensile Strength Elongation Per Cent Red. of Area Per Cent 102,000 135,300 19.5 01 ECONOMICS OF ALLOY STEELS 43 Untreated and Treated Chrome Steel with Molybdenum TABLE 5k Tensile Tests on Chromol Steel (Untreated) Analysis Carbon Manganese Chromium Molybdenum 0.26 0.65 0.95 0.32 Physical Properties Diam. of Test Piece Elastic Limit Tensile Strength Elongation Per Cent Red. of Area Per Cent 1" 89J00 116,900 18.5 55 U" 104,000 115,000 17.5 54 2" 75,000 100,000 20.5 60 TABLE 51 Tensile Tests on Chromol Steel (Treated) Analysis Diam. of Test Piece Carbon Manganese Chromium Molybdenum 8 0.26 0.65 0.95 0.32 Physical Properties Drawing Temperature Elastic Limit Tensile Strength Elongation Per Cent Red. of Area Per Cent 500° F. 220,000 232,000 12 48 1100° F. 130,000 142,000 20 63 44 ECONOMICS OF BRTDGEWORK Chapter V In making cost estimates for alloy-steel bridges, the following unit prices have been assumed. They are based upon the market conditions govern- ing in March, 1920. Ordinary carbon-steel work, erected 8^ per lb. Nickel 40^ per lb. Chromium 22^ per lb. Vanadium residue in steel (to include wastage) $10 . 00 per lb. . Molybdenum $ 2 . 50 per lb. Heat-treatment of eye-bars 1^ per lb. There will first be determined from the various diagrams in "Molyb- denum Commercial Steels" the best drawing temperature for the heat treat- ment of alloy steels to be used in bridgework. In modern alloy-steel prac- tice there has come into vogue the term "Quality Number," meaning the product of the elastic limit in pounds per square inch by the reduction of area expressed in ratio to unity. This is considered the criterion of excel- lence, because the maximum values of these two quantities are desirable. As the drawing temperature is increased, the elastic limit drops and the reduction of area augments, consequently that temperature which makes the product of the two values a maximum probably gives the best result for combined strength and toughness. An analysis of fifteen diagrams in "Molybdenum Commercial Steels" shows that the average best drawing temperature is 800° F., it being a trifle greater for oil quenching than for water quenching. A higher draw- ing temperature than this seems to be preferable for automobile steel, in order to secure great toughness for resisting shock; but it gives very good results with steel having main characteristics suita])le for bridge building, the average percentage of elongation for small test pieces being 15.5. As the principal standard bridge specifications call for an elongation of 15 per cent in specimen tests of nickel steel, it may be concluded that the molybdenum-steel alloys above considered are satisfactory in respect to this criterion. There will next be determined, as accurately as the rather meagre data available will permit, for all of the usual kinds of alloy steels, the economic benefit to l)e derived by adding molybdenum to the other ingredients of the steel. Cakmol Steel versus Carbon Steel From a reliable source the author has learned that the heat-treatment of carbon-steel eye-bars raises the elastic limit from 30,000 lbs. per square inch to at least 50, 000 lbs. per square inch, and that the present-day cost of the lieat -treatment tis aboiit one cent per pound. Let us assume that in a pin-connected bridge the average value in place ECONOMICS OF ALLOY STEELS 45 for carbon steel, both treated and untreated, is 8.5^ per pound, then refer- ring to Table 5i, w(! shall have the following: CArtMOL STEEL 99.68 lbs. steel @ 8.5^ = $8.47 0.32 lb. molybdenum @ $2.53 = .81 100.00 lbs. alloy @ 9.28^= $9.28 Excess cost in manufacture and erection, say @ 1.00^5= 1.00 Total =$10.28 ^=fF-- Working tensile stress for heat-treated steel . . . . = 38,000 lbs. Ditto untreated (assumed) = 30,000 lbs. Average = I (2X30,000+38,000) =32,700 lbs. ' ■ - •- :.tSi . ■■?■ 'lev ' CARBON STEEL Working tensile stress for heat-treated steel = 26,700 lbs. Ditto untreated = 16,000 lbs. Average = ^ (2X16,000+26,700) =19,600 lbs. . / 19,600 „ „ ' • .. r= — = 0.0 32,700 ,rm '■ . uh and r/ = l. 21X0. 6 = 0. 726 As this is far lower than any values of r r' given in Figs. 5a and 56, it is evident that the addition of molybdenum to carbon steel will always effect a large economy. ChroMol Steel versus Chrome Steel ■'h&r.i. Referring to Tables 5a and 56, we have the following: CHROMOL steel 98.93 lbs. Steel '. @ 8.5c^ ^$8.41 0.76 lb. Chromium @ 25?^ ^ . 19 0.31 lb. Molybdenum @ $2.53 = .78 IflO.OOlbs. Alloy. @ 9.38cf = $9..38 46 ECONOMICS OF BRIDGEWORK Chapter V CHROME STEEL 99 lbs. Steel @ 8.5ff =$8.42 1 lb. Chromium. @ 25^ = .25 100 lbs. AUoy @ 8.67^ = $8.67 ....=-S.x.0S2 CHROMOL STEEL Working tensile stress for heat-treated steel = 50,300 lbs. Ditto untreated (approximately) = 39,000 lbs. Average = ^ (2X39,000+50,300) =42,800 lbs. CHROME STEEL Working tensile stress for heat-treated steel = 46,300 lbs. Ditto untreated (assumed) = 33,000 lbs. Average = i (2X33,000+46,300) =37,400 lbs. . ,_37\400_ and rr' = l. 082X0. 87 = 0. 94 As this is lower than nearly all the values of r r' in Figs. 5a and 56, it may be concluded that it is almost always economic to add molybdenum to chrome steel; or, in other words, chromol steel is preferable to chrome steel for bridgework on account of both cost and toughness. NiCMOL Steel versus Nickel Steel Unfortunately, the records in "Molybdenum Commercial Steels" do not give any tests for the untreated Nickel Steel; but as the author once made some tests on a 4 j% nickel steel for eye-bars, he will use the results thereof in this crude investigation. Referring to Table 5/i, and employing averages, we have the following: NICMOL steel 94.92 lbs. Steel @ 8.5^ = $8.07 4.50 lbs. Nickel @ 43^ = 1.94 0.58 lb. Molybdenum @ $2.53 = 1.47 100.00 lbs. Alloy @ 11.48^ = $11.48 ECONOMICS OF ALLOY STEELS 47 Referring to Table 5g, we have NICKEL STEEL 96.00 lbs. Steel @ 8.5^ = $8.16 4.00 lbs. Nickel @ 43^ = 1.72 100.00 lbs. Alloy @ 9.88^ = $9.88 . . r-1^-^^-1 162 NICMOL STEEL Working tensile stress for heat-treated steel = 58,300 lbs. Ditto untreated (approximately) = 45,000 lbs. Average = i (2X45,000+58,300) =49,400 lbs NICKEL STEEL Working tensile stress for heat-treated steel . . , . = 40,000 lbs Ditto untreated =28,000 lbs. Average = | (2X28,000+40,000) =32,000 lbs. ... r' = ^^^ = 0.m 49,400 and rr'=l. 162X0. 647 = 0. 752 As this is lower than any of the values of r r' given in Figs. 5a and 56, it is evident that the addition of molybdenum to nickel steel will always effect a large economy. NicHROMOL Steel versus Nichro Steel Referring to Tables 5c and 5d, we have the following: NICHROMOL steel 95.76 lbs. Steel @ 8.5^ = $8.14 0.86 1b. Chromium @ 25^ = 0.22 2.95 lbs. Nickel (^43^ = 1.27 .43 lbs. Molybdenum @ $2 . 53 = 1 . 09 100.00 lbs. Alloy @ 10. 72)25 = $10. 72 48 ECONOMICS or BRIDGEWORK Chapter \' NICHRO STEEL 95.7 lbs. Steel @ 8.5^ = S8.13 1.0 1b. Chromium @ 25^ = 0.25 3.3 lbs. Nickel. @ 43^ = 1 .42 100.0 lbs. Alloy @ 9.8^ = $9.80 NICHROMOL STEEL Working tensile stress for heat-treated steel .... =47,300 lbs. Ditto untreated (approximately) = 37,500 lbs. Average = i (2X37,500+47,300) =40,800 lbs. NICHRO STEEL Working tensile stress for heat-treated steel — = 45,000 lbs. Ditto untreated (approximately) =35,500 lbs. Average = i (2X35,500+45,000) =38,700 lbs. 38,700^ 40,800 and rr' = 1.094X0. 949= 1.038 Referring to Figs. 5a and 56, it is seen that the simple-span length cor- responding to this product is about 600 feet and the main opening for a Type A cantilever is about 1,600 feet; and as most spans are below this limit, it appears probable that there is seldom any economy in adding molybdenum to chrome-nickel steel for the manufacture of bridges; but the^data used for this investigation are so crudely approximate that this conclusion requires corroboration. It would need some elaborate and expensive experimenting to determine this economic point with accuracy. The addition of the molybdenum, though, would undoubtedly improve the quality of the alloy by increasing its resistance to shock. Chrovanmol Steel versus Chrovan Steel Referring to Tables 5e and 5/, we have the following: chrovanmol steel 97.92 lbs. Steel @ 8.5^ = $8.32 1 .06 lbs. Chromium (g). 25^ = . 27 0.17 lb. Vanadium (a;, $10.00= 1.70 0.85 lb. Molybdenum @ $2.53 = 2.15 100. 00 lbs. Alloy.... ■.;.......•. @ 12.44^ = $12.44 J ECONOMICS OF ALLOY STEELS 49 CHROVAN STEEL 98.94 lbs. Steel @ 8.5^ = $8.41 0.90 1b. Chromium @ 25^ = 0.23 0.16 1b. Vanadium #$10.00= 1.60 100.00 lbs. Alloy % 10.24j^ = $10.24 • r-^^^^-1215 ••'^"io:24-^-^^^ CHROVANMOL STEEL Working tensile stress for heat-treated steel — =63,300 lbs. Ditto untreated (entirely assumed) =47,000 lbs. Average = I (2X47,000+63,300) = 52,400 lbs. CHROVAN STEEL Working tensile stress for heat-treated steel . . . . = 56,000 lbs. Ditto untreated (entirely assumed) =41,500 lbs, Average = | (2X41,500+56,000) =46,300 lbs. and rr' = 1.215X0. 884 = 1.074 From Figs. 5a and 56 we find that this product corresponds to a simple- span length of about 750 feet and to a main cantilever opening of about 2000 feet; and, as these are excessive, it may be concluded, for bridgework, that there is no advantage in adding molybdenum to chrovan steel. The next economic question to solve is that of the gain involved by in- creasing the percentage of molybdenum in an alloy of steel. From cer- tain diagrams in "Molybdenum Commercial Steels" the following data for comparison of chromol steel of Classes A and C have been excerpted, the treatment-temperature being 800° F, CLASS A Average analysis, Carb. 0.15, Mang. 0.38, Chrom. 0.72, Moly. 0.28 E. L. = 105,000 lbs., Ult. = 130,000 lbs., Elong. = 20%, Red. = 65%. 50 ECONOMICS OF BRIDGEWORK Chapteb V CLASS C Average analysis, Carb. 0.18, Mang. 0.37, Chrom. 1.05, Moly., 0.73, E. L. = 150,000 lbs., Ult. = 170,000 lbs., Elong. = 18%, Red. = 58%. CLASS A 99:00 lbs. Steel @ 8.5jz^ = S8.42 0.72 1b. Chromium @ 25^ = 0.18 0.28 lb. Molybdenum @ $2.53 = 0.71 100.00 lbs. Alloy @ 9.31^ = $9.31 CLASS C 98.22 lbs. Steel @ 8.5^^ = $8.35 1.05 lbs. Chromium @, 2H = 0.26 0.73 lb. Molybdenum @ $2.53 = 1.85 100.00 lbs. Alloy @ 10.46^ = 110.46 10.46 . .„. CLASS A Working tensile stress for heat-treated steel — =43,300 lbs. Ditto untreated (assumed) =37,000 lbs. Average = i (2X37,000+43,300) =39,100 lbs. CLASS C Working tensile stress for heat-treated steel — = 56,700 lbs. Ditto untreated (assumed) '. =48,500 lbs. Average = ^ (2X48,500+56,700) = 51,200 lbs. 39,100^Q^g3 51,200 and r/ = 1.124X0. 763 = 0. 858 From Figs. 5a and 56 we find that this is lower than those recorded there for very short spans, from which it is evident that increasing the molybdenum content up to three quarters of one per cent is in the line of economy, provided that the resulting alloy be not too brittle. The writer of "Molybdenum Commercial Steels" states that there is an advantage in using molybdenum up to a limit of one per cent; but whether this can ECONOMICS OF ALLOY STEELS 51 be done with impunity in the case of bridge metal can only be proved by actual experiments with the high alloy thus produced. COMFILATION The following table gives a resume of the findings and deductions herein evolved : TABLE 5m Kind of Steel Cost per Lb. in Place Average Intensity for Tension Carmol 9.28«f 9.38^ 11.48^ 10.72^ 12.44«f 32,700 lbs. 42,800 lbs. 49,400 lbs. 40,800 lbs. 52,400 lbs. Chromol Nicmol Nichromol Chrovanmol An inspection of Table 5m shows that the Carmol and Nichromol steels are out of the running; hence it will be necessary to test the three others. Comparing Chromoland Nicmol, we have: 11.48 42,800 _ '^'^~ 9.38^49:400 ^"'^ From Figs. 5a and 56 we find that this product corresponds to a simple- span length of about 700 feet and to a main cantilever opening of about 1,900 feet, hence it may be concluded that, except for unusually long spans, Nicmol Steel is not as economic as Chromol steel. Comparing Chromol and Chrovanmol, we have: 12^ 42^800^ 9.38 52,400 As in the last case, this is so great as to show that Chromol steel is more economic than Chrovanmol steel. From all that precedes it is evident that the most promising combina- tion of alloying materials for a high-grade bridge-steel is one of chromium and molybdenum; and a good analysis to test as a starter would be as follows: Carbon 0.25 Manganese . 75 Chromium . 75 Molybdenum 0.75 52 ECONOMICS OF BRIDGEWORK Chapter V It would not do, however, to confine one's attention solely to Chromol steel in making a systematic study of the question of the best high-alloy of steel for bridgework, because the preceding study has been made upon data some of which, of necessity, are so roughly approximate that the findings therefrom have to be taken cum grano salts. All that can properly be claimed for this tentative investigation is that it will sei've as an indi- cation that an exhaustive series of tests on molybdenum steel for bridges woidd be well worth while, and that it suggests about what might be expected as a result thereof. • C Jvii D'iL'-' CHAPTER VI COMPARATIVE ECONOMICS OF BRIDGES AND TUNNELS The contrasting of a bridge with a tunnel or a combination of tunnels for any proposed crossing, in respect to the question of economics, is by no means easy; because, in order to make a perfectly just comparison, the facilities afforded by the two structures should be alike. Generally, lay- men make the mistake of pitting a single-track tunnel against either a double-track bridge or a purely railway tunnel against a combined-rail- way-and-highway bridge. As it is usually uneconomic to make the interior diameter of a tunnel tube much greater than twenty feet, because the cost of such a tube increases very rapidly with the diameter, and as any pro- jected bridge that is in competition with a tunnel is necessarily a structure of some importance, and, therefore, wide of deck, it is evident that the comparison will probably always be made between one bridge and two or more tunnels. Again, as the travel in a tube of twenty-foot internal diameter must either be in one direction only or else very slow, two tubes will be required in order to obtain rapid transit. The reason for this is that, in a tube just large enough for two lines of traffic in opposite direc- tions, the speed is absolutely limited to that of the most-slowly-moving vehicle; because it would be impracticable for a rapidly-moving automobile to turn out so as to pass a slow vehicle without facing the Hne of traffic coming in the opposite direction; and a single breakdown would quickly block all motion. Anyone who gives the subject any thought must quickly arrive at the conclusion that the motion of traffic in any highway-tunnel tube must be restricted to one direction only. ' Another obstacle to the satisfactory comparison of these fundamentally- different types of transportation structures is the as-yet-unsolved problem of ventilation. Many engineers contend that it is absolutely unsafe to run automobiles through a long tunnel because of the exceedingly-poison- ous carbon-monoxide given forth during combustion; while others say they are certain that such traffic can be maintained without danger. Probably this question will be settled finally during the next five years, and in the only convincing manner possible, viz., by building a long tunnel for automobile travel and operating it. As it is stated by medical men of high authority that the action of carbon-monoxide upon the human system is cumulative, it may prove difficult, expensive, or even totally impracticable to dilute the poison to such an extent as to make the atmos- 53 54 ECONOMICS OF BRIDGEWORK Chapter VI phere in the tube perfectly safe for breathing, especially by people of feeble constitution. There is another factor that is likely to have considerable influence in deciding between bridge and tunnel, viz., that driving over the former is much more agreeable than driving through the latter. Again, walking through a long tunnel is so unpleasant that it would seldom be worth while to make any provision whatsoever for pedestrian travel therein. Then, too, the difference between the height of climb over a bridge and the depth of descent into a tunnel will have some effect upon the choice of structure. In general, it may be stated that the dip of a tunnel is greater than the rise of a low-level bridge, about equal to that of an ordinary high-' level bridge, and less than that of a structure below which pass ocean-going vessels. Supposing, however, that all the pros and cons of the two types, barring cost only, about balance each other, the question for settlement would be one of economics; and then the decision would favor the bridge, because for equal facilities the cost of the tunnel almost always greatly exceeds that 'of the bridge. Of course, the conditions affecting the latter might be so onerous as to increase the cost of the structure beyond any reasonable limit — for instance a span of unprecedented length; but, in general, the bridge costs less than the tunnel. In the author's practice he has twice had occasion to pit bridge against tunnel. In the first case a highway suspension bridge with a span of 1,750 feet and a total clear roadway, including sidewalks, of 96 feet was con- trasted with two tubes which together gave a clear roadway of 56 feet. The result was that the tubes, in spite of their smaller carrying capacity, cost about fifty per cent more than the bridge. In the other case, a single-track-railway tube cost considerably^ more than a double-track, low-level bridge — and even a little more than a low- level, combined-railway-and-highway, double-deck structure. Comparing the tunnel and a high-level bridge with a clearance above high water of 150 feet, the ratio of costs of a two-tul)e, railway tunnel and a double-track, railway bridge was 1.1; and comparing a three-tube tunnel for both railway and highway traffic with a combined-railway-and-highway, high-level bridge, in which comparison the facilities afforded were neai'ly equal, the ratio of costs was 1.12 — both of these results being in favor of the bridge. There is one advantage which, theoretically, the tunnel possesses over the bridge; and under certain conditions it might become i)racticall,y opera- tive, viz., that, while a wide-decked bridge has to be built all at once, several tunnels of the same aggregate width can be constructed from time to time as the traffic necessitates, thus saving for some years the interest on the difference between first costs. A claim has been made that any bridge having more than about forty feet of deck-width will congest the ti'affic to sucli an extent that there is no advantage to be obtained from the extra width above the said forty feet; COMPARATIVE ECONOMICS OF BRIDGES AND TUNNELS 55 but such an idea is a fallacy, because the incoming and the outgoing vehicles could enter and leave the bridge at points two blocks apart, and a double-track, electric-railway line could enter and leave by the street between. If this arrangement would not separate the incoming and the outgoing traffic sufficiently, the entrances and exits might be located four, six, or eight blocks apart — in fact there need be no restriction as to the total width of deck in case that this method of traffic separation be adopted. By employing a spiral approach of large diameter, the traffic could leave the periphery thereof at three, or even more, points, thus making the approaches to the said spiral of different lengths, but all comparatively short. Some months after the preceding was written with the intention of considering the treatment of the subject as closed, the author had occasion to prepare for the American Society of Civil Engineers a paper entitled "Bridge versus Tunnel for the Proposed Hudson River Crossing at New York City"; and as it gives much additional information upon the general economic question involved in this chapter, it is here reproduced practically verbatim: Whilst making lately some extensive calculations concerning the costs and economics of long-span suspension-bridges for his forthcoming treatise on "Economics of Bridgework," the author has had occasion to figure weights of metal for a number of such spans; and by means of the result- ing data he was able to undertake an investigation of the comparative costs and efficiencies of bridges and tunnels for the long-talked-of crossing of the North River at New York City. Thinking that the present is an auspicious time for a thorough discussion of the subject, he has collected and condensed the results of his labors and incorporated them in this memoir for the Society. For some years he has been of the opinion that the best and most economic solution of the problem under consideration is to carry all street cars and subway cars beneath the water and the strictly-highway traffic above it. As far as the question of desirability is concerned, this arrange- ment would be the best practicable for the following reasons : First. In respect to cost of operation, the tunnel would require a dip of ninety feet below high-water, and the bridge a rise of one hundred and eighty feet above it; consequently it is evident that, as far as the matter of expenditure of energy is concerned, the tunnel would be decidedly pref- erable. The difference in cost of power would be very apparent to the management of the electric railways, and possibly also to the operators of heavy trucks, but it would not be noticed at aU by the owners of automo- biles used mainly for pleasure traffic. When an automobilist is about to climb a long, heavy grade, he seldom thinks anything concerning how much extra his gasoline is going to cost him ; but the officers of an electric railway line generally figure with the greatest of care on the item of power expense, and aim to reduce it to a minimum. 56 ECONOMICS OF BRIDGEWORK Chapter VI Second. In regard to the difference in the expenditures of time in climb- ing up and down the approaches of the two crossings under comparison, the gravity of this matter would be duly appreciated b}^ the railroad com- panj^ and more or less by the operators of ti-ucks, but it would not be recog- nized by automobile owners and users. Third. As to the agreeableness of the two kinds of crossing, while people do not particularly fancy going under ground before they are ulti- mately compelled to, they soon become accustomed to passing beneath the water in electric cars, as is evidenced by the many New York business men and women who reside on Long Island or in New Jersey. Perhaps in time the drivers of trucks would become so used to traversing tunnels as not to object to the gloom that is inherent in such passage; but the general pub- lic, almost to a man (and certainly to a woman), would always greatly prefer driving over a structure that provides good air and light, and usually a fine view of the harbor and the surrounding country, in comparison with traversing a long, cramped, and dingy tube. Fourth. In relation to the question of sanitation, there is practically no greater danger to health in passing through a tunnel in which the power used is always electrical than there is in traversing a bridge; but the safe ventilation of a tube carrying automobile traffic is as yet an unsolved problem. Figures show that such ventilation, if feasible, would be exceed- ingly expensive, and the velocity of the passing air would be excessive. Again, as carbon monoxide, like arsenic, is a cumulative poison, there exists a possibility that the regular daily passage through a tube where the gas remains constantly, even in minute quantities, would eventually under- mine one's health. Besides, there is always the chance of a blockade of traffic with the tunnel full of automobiles, and these may be counted upon to discharge more or less products of combustion even when standing still. Such a blockade might result in a holocaust. The author sees no serious objection, however, to building the contem- plated highway tunnels under the North River; because if, after comple- tion, they prove to be unsafe, or otherwise unsatisfactory for automobile traffic, they can either be used by electric railway cars or else a moving platform can be put in to carry vehicles through A\'ithout letting them use their own power. The experiment of automobile transportation through long tunnels might be worth making, for the results in any event would prove of great interest and value to the engineering profession, as well as to the general public. In making the comparative estimates of cost of bridges and tunnels for this crossing, the author adopted four (4) per cent grades on the approaches of both structures and clear roadways of twenty-two feet, with sidewalks eleven feet wide. He utilized as a basis for his comparison the cost esti- mates for tunnels given in the report of Clifford M. Holland, M. Am. Soc. C. K., Chief Kiigineer of the New York State Bridge and Tinui(>l Commis- sion and the New Jersey Interstate Bridge and Tunnel Conmiission; but COMPARATIVE ECONOMICS OF BRIDGES AND TUNNELS 57 it was necessary to modify some of the items for the increased diameter of tube and the steeper approach grades, also to omit the costs of equipment and administration, as these are not included in the bridge estimates. For the modification of cost due to a changed diameter of tube, it was assumed that the cost per lineal foot increases and decreases as the square of the exterior diameter. This assumption is almost exactly correct, because the thickness of the shell varies directly with the diameter, as does also the length of the periphery, consequently, the volume of the shell is approxi- mately proportional to the square of the diameter. Again, the volume of excavation for any shield-driven, circular tunnel varies as the square of the diameter; and as almost the entire cost per lineal foot is that of the shell plus that of the excavation, it is evident that the assumption mentioned is justified. Increasing the exterior diameter of the tube to thirty-one (31) feet makes the interior diameter twenty-seven (27) feet. This is just enough to provide a clear roadway of twenty-two (22) feet in the highway tunnel and allows just enough space for two lines of the widest subway cars in the electric-railway tunnel. In the latter type it is feasible to contrast the cost of a double-track tube with that of two single-track tubes; but in a highway tunnel it is not, because a breakdown of a single vehicle would block all traffic until it is hauled out by sending a double-ender wrecking-car into the tube in a reverse direction to that of the traffic. With such an occurrence in a double-track tunnel, the automobiles could pass by the wrecked vehicle. If there were an accidental stoppage of an electric railway car in a single-track tube, it would cause no more obstruction to rail traffic than it would if the accident had taken place in a double-track tube that operates in both directions. The author computed all the quantities of materials in substructure, superstructure, and approaches of six structures, in order to plot the two cost curves for bridges shown in Fig. 6a. On that diagram are given the total costs for bridges with their approaches and for timnels with their approaches based upon the unit prices which governed at the time the tunnel estimates were prepared. The principal ones of these are as follows: Wire cables in place 23^ per lb. Nickel steel in place 11^ per lb. Plain concrete in shafts and anchorages $16.00 per cu. yd. Mass of pneumatic bases $35 . 00 per cu. yd. In proportioning the substructures the author made the dimensions as small as considerations of true efficiency would permit, and did not attempt any beautification of structure by an unnecessary enlargement of piers. If these are properly built to meet all possible conditions of loading and so as to provide against future deterioration caused by the elements, that ought to suffice; and so doing should be deemed good engineering practice. 58 ECONOMICS OF BRIDGEWORK Chapter VI In order to make the investigation general instead of particular, so as to apply to all other similar river crossings by verj'-high-level suspension- bridges, the span-lengths were assumed to be 1,500, 2,300, and 3,000 feet, to permit the plotting of curves of total costs for both bridges and tunnels with their approaches for various widths of river. In this special case the span length would have to be about 2,900 feet; and in all cases the length 1800 2000 2200 2400 Mm Spa/? Len^f/> ji) feef. Fig. 6a. Diagram of Total Costs of Highway and Electric-Railway Bridges and Tunnels, with their Approaches, for Crossings Similar to that of the North River at New York City. of the horizontal portion of the tunnel has been assumed to be exactly equal to that of the main span of the competing bridge. In the highway-structure comparison there were adopted for the bridge three clear roadways of twenty-two feet each, and two sidewalks of eleven feet each, corresponding to four double-track tubes each of twenty-two feet clear roadway. The driveways were assumed to consist of creosotcd- COMPARATIVE ECONOMICS OP BRIDGES AND TUNNELS 59 wooden-block pavement supported by reinforced-concrete slab, and the sidewalks to be of reinforced granitoid. In the electric-railway-structure comparison, the floors were assumed to be of the open type, having wooden ties and guardrails and the usual steel rails; and eight lines of track were adopted so as to compare with four lines of double-track tubes and with eight hues of single-track tubes. In every possible manner the comparison was made fair and equitable, excepting that the costs of right-of-way and property damages for the approaches, for obvious reasons, had to be ignored. This militated against the tunnel; hence in any actual case of comparison an allowance would have to be made for the difference in costs of right-of-way and property damages for the approaches to the two structures. In the case of the bridge, by purchasing a large city-block close to the water and building a spiral approach thereon, the cost of the said right-of-way and propertj^ damages would be reduced to a minimum; and even that cost might be offset by constructing a high office building above the spiral. Such a building, owing to its location, ought to possess a high rental value. Fig. 6a shows the total costs of main span, piers, and approaches for both highway and electric railway bridges and those of the corresponding tunnels. As before indicated, the shortest span-length that can be used for the proposed North River bridge is about 2,900 feet, for which length the diagram gives approximately the following costs: Highway Bridge $32,500,000 Four Highway Tunnels $49,000,000 Electric-Railway Bridge $34,500,000 Four Double-Track, Electric-Railway Tunnels. . $48,000,000 Eight Single-Track, Electric Railway Tunnels . . $30,000,000 This indicates that there is a saving of cost in favor of the highway bridge amounting to $16,500,000, and one of $4,500,000, in favor of single- track, electric-railway tunnels. The former saving is far greater than the difference in costs of right-of-way and property damages for bridge and tunnel is ever likely to be; hence the conclusion is reached that, for the proposed North River crossing, it is not only better from every point of view, but also more economic to carry automobile traffic by a bridge and electric trains by single-track tunnels. The question arises as to how cheaply there could be built at present prices a combination of bridge and tunnels to care for both kinds of traffic. For a number of years two single-track tubes would take care of the electric-railway trains, hence the cost would be as follows: Highway Bridge $32,500,000 Two Single-Track Tunnels 7,500,000 Total $40,000,000 60 ECONOMICS OF BRIDGEWORK Chapter VI If it were decided that a bridge having a total width of roadways of forty-fom- (44) feet and two eleven-foot sidewalks inside the trusses, would suffice for possible future conditions of traffic, the amount of money re- quired for the combination would reduce to about ^33,500,000. It must not be forgotten that these totals do not include any allowance for right-of-way, property damages, equipment, or administration. In conclusion the author offers the suggestion that, in view of the facts presented in this memoir, it might be advisable to give the economics of the proposed crossing of the North River some further study before finally committing the community to the policy that is now contemplated. The preceding paper was delivered to the American Society of Civil Engineers in May, 1920, was accepted by the Publication Committee, and was printed immediately, advance copies of it being distributed for discussion. It was slated for delivery at the meeting of September third; but, upon very short notice, its reading was indefinitely postponed. The author hopes that, in the interests of engineering economics, this injunc- tion against a thorough discussion of an important engineering problem of great magnitude will not prove to be permanent. For about thirty years there has been discussed in the public press the proposed construction of an immense bridge across the North River to carry all kinds of traffic, including steam-railway trains; and to-day there is serious talk of materiahzing the project by building for that purpose a structure to cost two hundred millions of dollars. In the author's opinion, the construction of a high bridge over the Hudson at New York City for the purpose of transferring freight and passenger trains would involve a serious economic blunder from the engineering standpoint. His reasons for this rather drastic and sweeping statement are as follows: First. It would cost more to build at this location a standard rail- way bridge carrying n tracks than it would to construct /) single-track tunnels. Second. The right-of-way and property damages would be much greater for a railway bridge than for the corresponding tvmnels. Third. The cost of operation to cover rise and fall is twice as great for the bridge as for the tunnels. While the unnecessary expenditure of a large sum of money for the construction of the proposed bridge might bo ]xirdoncd, it would be exceedingly uneconomic to saddle for centuiies to come u]ion posterity a financial burden that will involve needlessly lifting and lowering ninety feet a load of two tons for each ton of freight carried across the river. CHAPTER VII COMPARATIVE ECONOMICS OF HIGH-LEVEL AND LOW-LEVEL CROSSINGS The term high-level is applied to a structure having all its spans fixed and its deck at a considerable elevation above high-water level; but the term low-level is generally interpreted as applying to structures having one or more movable spans, although, strictly speaking, a bridge over a non-navigable stream may be a low-level one without having any movable span. The comparison between a proposed high-level and a proposed low- level crossing for any stream is generally more dependent upon the condition of expediency than it is upon that of economy. The convenience of the passengers is often the criterion that will settle the question; but sometimes convenience has to be ignored because of the paramount con- dition of first cost. Again, the comparison will depend largely upon how much higher the high-level bridge must be than the low-level one, and upon the height and slope of the banks. The clear channel required will also be of some importance, the wider the channel the greater the advantage for the high-level bridge. Sometimes in a long, high-level structure with only one channel span required, it is practicable to build all the others on grade and as deck spans, economizing on substructure and shortening the approaches, thus lowering materially the total cost of the high-level bridge. The advantages and disadvantages of a low-level bridge over a high- level one are as follows : Advantages a. The first cost is almost always less. b. The costs of maintenance and repairs are less. c. The entrance and exit are closer to the river. d. The chmb is less, and, therefore, the total amount of power of all kinds required for the climb is less. e. The time spent in crossing is less. Disadvantages /. Increased annual expense due to the several items of cost in connection with operating the movable span. 61 62 ECONOMICS OF BRIDGEWORK Chapter VII g. Interruptions to travel over the structure from opening the movable span. h. A somewhat greater obstruction of the thoroughfare in respect to vessel traffic as well as to the passage of the water, in case of the adoption of a swing span with its protection. A thorough consideration of all these criteria will have to be made before a logical conclusion can be reached as to which type of layout is preferable. The correct ratio of first costs for a low-level bridge and a high-level one of the same capacity and strength at any proposed crossing must, of course, be determined from layouts, computations of quantities of materials, and estimates based upon current prices of the said materials and of labor. It is sometimes necessary, however, to make a hurried economic compari- son; and as an aid in so doing the author has estabhshed the following results, based upon assumed conditions that may properly be deemed aver- age or normal. Let us assume a double-track-railway crossing of a river like the Mis- souri, requiring 1,500 feet of main spans with a vertical clearance of 50-feet above high water for passing vessels, a variation of twenty-five feet be- tween extreme stages of water, a horizontal bed-rock 75 feet below high- water elevation, one bank high and sloping back from high-water line at a ratio of three horizontal to one vertical and the other bank level and very low; and let the approach grades be one per cent. Under such condi- tions the deepest water will nearly always be found comparatively close to the higher bank, and the position of channel will be permanent; conse- quently it would be legitimate to employ a single through span over the second opening from the high-bank end. With certain assumed medium unit prices for materials in place, the minimum costs of these two structures proved to be as follows : Low-Level Bridge $1,204,000 High-Level Bridge $1,530,000 The ratio of these costs is 1.27 With a low, flat approach on each side, and the other conditions un- changed, it would be necessary in the case of the high-level bridge to adopt a level grade over the entire river so as to provide against any drastic shift- ing of channel; and in the case of the low-level bridge to figure on being able to take down the towers, machinery, and house and shift them to any one of the other openings. Under these conditions the costs of the two structures proved to be as follows: Low-Level Bridge $1 ,256,000 High-Level Bridge $2,004,000 The ratio of these costs is 2.08 ECONOMICS OF HIGH-LEVEL AND LOW-LEVEL CROSSINGS 63 For one of the author's standard-type highway-bridges, having four per cent grades on the approaches and sand foundations at a depth of 125 feet below high water, the other conditions being as previously indicated for the crossing with one high and one low bank, the estimated costs of structure were as follows: Low-Level Bridge $1,386,000 High-Level Bridge $1,371,000 The ratio of these costs is 0.99. For the layout with two low banks the costs of the two structures were as follows: Low-Level Bridge $1,426,000 j High-Level Bridge $1,623,000 The ratio of these costs is 1.14. The main reason for high-level structures costing more than low-level ones is the greater lengths and costs of the approaches; and as in highway bridges the grades thereon are much steeper than on railway bridges, their ratios of costs of high-level and low-level structures are less. It will be necessary to compute carefully for each type the total annual costs of maintenance, repairs, sinking fund, and operation, capitalize these totals, and add the results to the estimates of first cost. A comparison of these sums will determine the financial economics of the two types com- pared. To be strictly accurate, however, in determining these comparing figures, one should estimate the total annual costs of all kinds of power expended in climbing the approaches, capitalize these, and add them to the previous sums before making the comparison; but, as considerable guess-work would be involved in making such a computation, it might be exact enough for all practical purposes to assume that the total annual costs of power are the same for the two types of structure. CHAPTER VIII COMPARATIVE ECONOMICS OF STEEL AND REINFORCED-CONCRETE STRUCTURES The settlement of the question as to which costs more, a steel bridge or a reinforced-concrete one of the same capacity, is a difficult task. For structures of ordinary span-lengths, under normal conditions of the material market, the first cost of the steel bridge is the smaller, but when the price of that metal takes a sudden jump the reverse is true. However, in a short time either the prices of concrete materials rise to correspond or else the cost of the metal gradually drops back until a normal ratio of unit prices for bridge materials once more exists. But the question of the economics of the two types is not settled by a comparison of first costs alone, because the elements of maintenance and repairs must be considered; and these are much greater for the steel structure than for the reinforced-concrete one. The latter requires no painting, and there should be no renewal of parts called for, excepting only the pavements, while in the former these items are often large, especially that of painting, if the upkeep be properly performed. It is necessary, therefore, to capitalize the said items and add the results to the first costs, in which case under normal conditions there is generally but little differ- ence; and as the painting of steel structures is very hkely to be neglected and the metal, in consequence, to lose its normal areas, it will often pay to adopt the reinforced-concrete construction, even when the economic com- parison indicates a slight disadvantage by so doing. The fact that the annual cost of maintenance and repairs is less for reinforced-concrete bridges than for steel ones tends to render the former the more popular, especially amongst those persons who do not make a practice of comparing values strictly upon the basis of the principles of true economy. Such persons, too, are prone to say that the reinforced- concrete structure is superior to the steel one because of its longer life, not recognizing the facts that a properly designed, built, and cared-for steel bridge will do its work for a very long term of years, and that the longevity of reinforced-concrete structures as yet is a matter of surmise, in view of the uncertainty about the efficiency of the concrete in protect- ing the reinforcing steel perpetually against rusting — which, if allowed to continue, will c|uickly and inevitably disintegrate the said concrete and destroy the structure. 64 ECONOMICS OF STEEL AND REINPORCED-CONCRETE STRUCTURES 65 The comparison of the types is complicated also by the matter of personal equation in designing; for, with the most elaborate and rigid specifications ever written, two computers working independently on the same job would be likely to vary in their final results far more in reinforced- concrete work than they would in steelwork. This is due partially to the fact that the science of reinforced-concrete bridge designing is newer and less highly developed than that of proportioning steel bridges, and also because in the former type equal strength can be secured with varying proportions of concrete and steel. As the most econqmical proportions are frequently not known, it is evident that the combined costs of the two materials in place may differ appreciably. Again, in arch bridges there is often a choice of ratio of rise to span or even of span-lengths; and as the effect on economics by variations in these features is not yet determined with accuracy, the final estimates of cost made by the two computers are liable to be still more widely divergent on this account. The amount of attention paid to aesthetics when making the design generally affects the cost of a concrete bridge more than it does that of a steel one; hence this factor has to be given consideration when contrasting the two types in respect to the matter of economics. The size of the live load, too, is likely to affect the comparison, because a diminution thereof cuts down the cost of a steel structure much more than it does that of a concrete one. For short-span bridges, reinforced-concrete has an advantage over steel in respect to rigidity of structure; and under certain conditions such an advantage may be of importance, but ordinarily it is not. There is another complication of the question, which, however, ought not to be allowed to exist, viz., the fact that many small reinforced-concrete bridges are designed by inexperienced and incompetent computers, who are hired by municipalities on account of the low compensation they are wilHng to accept. Still another cause for divergence is the great variation in costs of exca- vation for foundations at different localities. This affects the substructure costs for reinforced-concrete arch-bridges far more than it does those for the corresponding steel structures, because of the larger footings and shafts of the former. Is it then impracticable for a bridge engineer to settle quickly the com- parative economics of the two types of construction for a proposed bridge? Not at all — only it will take more time than that required for the deter- mination of most of the economic problems dealt with in this treatise. The method to be followed is this: Having obtained in advance all the unit prices for materials, figure the cost of the steel structure by means of the diagrams of quantities given in Chapters LV and LVI of "Bridge Engineer- ing," then find that for the reinforced-concrete bridge by employing the rules, tables, and diagrams given for that purpose in the latter chapter, fixing by judgment, whenever necessary, an allowance for difference in 66 ECONOMICS OF BRIDGEWORK Chapter VIII costs of excavation. As explained in Chapter XVII of this work, the labor involved in making such computations as the above-mentioned is by no means onerous. The greater the span-lengths which are necessitated as minimum by the conditions of the crossing, the more favorable is it to the steel structure in the economic comparison; and when a certain span-length has been reached, the reinforced-concrete structure becomes impracticable. What this limiting span-length is, designers have not yet determined with gen- eral satisfaction; but the author is of the opinion that it is not very far from seventy (70) feet for girders and three hundred (300) feet for arches. While it is practicable to build reinforced-concrete arch-spans of greater length than the latter figure, much trouble would be involved during their erection by the unequal and abnormally great settlement of the falsework, which settlement tends to distort the arch rings and, in consequence, to give the structure an unsightly appearance. Such settlement can be reduced, if sufficient care be taken; but an excessive amount of the latter adds to the time required for fieldwork and, consequently, to the first cost. In general, it may be stated that a high-level crossing is usually more favorable to a steel structure than to one of reinforced-concrete, as are likewise deep foundations and perilous erection conditions; also that, other things being equal, a great width of deck generally militates in favor of the reinforced-concrete type of construction; as do, too, the remoteness of the site from the source of the structural-steel supply and the cheapness of common labor available for fieldwork. It may be that some reader of this chapter wiU claim that it is rather indefinite in its conclusions and deals mainly with glittering generalities. Possibly there may be some justice in such a claim; but it must not be forgotten that the economics of the two contrasted types of bridges is primarily dependent upon such arbitrary and uncertain conditions as the relative prices of steel and cement, the availability of concrete aggregate, the comparative costs of high-grade and low-grade labor, and the distances of the bridge site from the various sources of supplies. This fact makes it impossible to come to any fixed or reliable conclusion concerning the relative economics of steel and reinforced-concrete bridges. CHAPTER IX COMPARATIVE ECONOMICS OF DIFFERENT TYPES OF ORDINARY STEEL STRUCTURES Under the term ordinary steel structures will be included only girder or simple-truss fixed spans of the following types: Deck, rolled-T-beam spans. Deck, plate-girder spans. Half-through, plate-girder spans. Deck, open-webbed, riveted spans. Through, riveted spans. Deck, pin-connected spans. Through, pin-connected spans. The economics of all other types of steel bridges will be treated in other chapters. ROLLED-I-BEAM SPANS These are always deck structures because of the shortness of their limiting lengths. They are preferable to plate-girder bridges up to the limit which due consideration for the question of deflection sets, even if the economic Hmit for weight of metal be exceeded. This is because of their extreme simpUcity for both manufacture and erection, and also at most times because the base prices for rolled I-beams are lower than those for plates and light shapes — besides the cost of shopwork is less, owing to the small amount of detaihng and the comparatively few rivets that have to be driven. In respect to the economics of erection, they are generally built of standard lengths and sizes, thus permitting the larger railroad systems to keep a supply of them in stock to be used for emergencies. Moreover, they are put in place very readily, and there are but few rivets to drive. Of course, plate-girder spans could be standardized and employed in the same manner, but not quite so conveniently. For ordinary I-beams the longest steam-railway spans are about twenty (20) feet when four lines of stringers per track are adopted, but by employ- ing the thirty (30) inch special sections of the Bethlehem Steel Company the hmit can be increased to about thirty (30) feet for fairly-heavy engine- loads. By using six lines of beams per track the limit can be increased to about thirty-five (35) feet, for which span the depth is only one-four- teenth (1/14) of the length, a ratio common enough in England, but ob- 67 68 ECONOMICS OF BRIDGEWORK Chapter IX jected to by most American railway engineers on account of the great de- flection that it permits. Deck Plate-Girder Spans Although plate-girders are of necessity as unscientific structures as a bridge specialist ever has to design, they are without doubt the most satis- factory type of construction possible for short spans. Their superiority over articulated trusses is due to the following reasons: First. OAving to their compactness they better resist shock and check vibration. Second. They have fewer critical points where overstress is hkely to exist because of faults of either designing or workmanship. Third. A number of loose rivets lying close together will do far less harm in a plate-girder than in an open-webbed one. Fourth. The cost of manufacture per pound of metal is a little less. Fifth. Owing to the steady demand for plate-girder structures and the comparatively small number of the sections of metal used in their manufacture, it is easy to obtain quickly the materials required; and the work on the metal is of a simple character. For these reasons plate-girder spans can generally be purchased with less delay than open- webbed girders. Sixth. The cost per pound for erection is decidedly less, excepting where the conditions are unusual, and the cost of painting is comparatively small. Seventh. They can be overstressed without danger much higher than open-webbed girders. Eighth. They are less liable to injury by accident than articulated trusses. Ninth. They are more easily painted, and are more accessible to examination for rust. Tenth. The cost of maintenance is less, owing to the absence of small parts and details that might work loose under traffic. The ordinary limit of length of plate-girder spans is about one hundred (100) feet, but that limit has often l)een surpassed by twenty-five (25) or thirty (30) per cent for simple spans and by much more for swing spans. Usually it is the difficulty in shipping very long plate-girders from bridge shop to site that determines the superior limit of such spans. The loading of long girders on cars for shipment is quite an art, and it should be en- trusted only to men experienced in such loadings; for, otherwise, the metal is liable to be injured in transit or the cars to break down, or some other trouble is likely to happen befoi-e they reach their destination. Some en- gineers believe that the liability to injury of long plate-girders in shop, transit, and field should limit their loiigtli to one Innidred (100) feet; but the author is not of this opinion, foi- he thinks that by taking jiroper pre- ECONOMICS OF DIFFERENT TYPES OF ORDINARY STEEL STRUCTURES 69 cautions the danger can be pretty nearly eliminated. About as long a plate-girder as has ever been shipped in one piece was one of one hundred and thirty-two (132) feet. It required four flat-cars to transport it. Longer plate-girder spans than this have been built, notably tubular bridges and swing spans, but they were shipped in parts and assembled at site. This expedient for simple spans is really permissible only in case of bridges to be sent to foreign countries, and it is to be avoided if possible even then, because it is sometimes difficult to obtain a satisfactory job of field-riveting when making the splices, although the use of pneumatic riveters tends to reduce materially the force of this objection. As far as economics is concerned, it may be stated that, if deck plate- girders are feasible for any opening, they are more economical than truss spans up to a length that is prohibitory for shipment. As the depth of a very long plate-girder is generally from one-tenth (1/10) to one- twelfth (1/12) of the span, the requirements of underneath clearance often bar out deck plate-girders and necessitate either half -through plate-girders or through trusses. Again, the great depth required for very long plate-girder spans often sets the limit for span-length because of shipping requirements. Some railroads have tunnels and overhead crossings which are lower than cus- tom is now requiring; and very deep girders loaded on flat-cars might not be able to pass — nor could such girders be placed flat, because then the horizontal clearance would be encroached upon. Half-Through Plate Girder-Spans The economic limit of length for this type of structure is materially less than that of the type just treated, because of the necessity for using a steel floor. On this account it has not the advantage over the through- truss bridge which the deck-plate girder structure possesses. For a length of one hundred (100) feet the weight of metal in the latter type exceeds that in the former, by from five (5) to fifteen (15) per cent, the smaller figure being for the lightest live-loads and the larger for the heaviest. Of course, the cheaper metal of the plate-girder type would tend to offset its greater weight, but, in order to make the costs of the two 100-ft. steam-railway- bridge spans the same, the ratio of pound prices for metal erected in the girders and trusses themselves would have to be from 1.1 to 1.3 — a condi- tion of market that is unusual. But as, for various good reasons, it hardly seems advisable to build through, steam-railway spans shorter than one hundred (100) feet, it is well to adopt this length as the superior limit for half-through plate-girders and deck plate-girders in standard railway bridges. For electric-railway bridges and highway bridges, this limit might advantageously be reduced to about seventy-five (75) feet. 70 ECONOMICS OF BRIDGEWORK Chapter IX Deck, Open-Webbed, Riveted Spans Some engineers entertain the notion that for short deck-spans an econ- omy can be effected by using open-webbed girders instead of plate-girders. If there be no objection to increasing the depth considerably, some metal can be saved in this way; but, if the same depth must be employed for both types, there is but httle, if any, saving in weight, provided that the detaihng be done properly — besides the pound price of the manufactured steel is a trifle greater for the open-webbed structure. Some years ago there were designed for a transcontinental Une a number of plate-lattice-girder spans. Their raison d'etre was supposed to be primarily their ability to pass water through them when submerged, but secondarily, economy. The designer claimed that they effected a saving of metal amounting to about fifteen hundred (1500) pounds for an eighty (80) foot, single-track span, and that the pound price for their manufac- ture was no greater than that for ordinary plate-girder work. The author once used plate-lattice girders for the cross-girders of the Union Loop Elevated Railroad of Chicago, but his object was simply to evade a trouble- some clause in the city ordinance. The webs of these cross-girders were solid near mid-span and at the ends, and were open near the quarter points, while those of the railroad girders previously mentioned were sohd at the ends and open over more than the middle half of the total length. As far as the author's experience goes, it takes just as much metal to build the webs open, and the pound price for the finished metal is a trifle greater than it is for ordinary plate-girder construction. The fact that this same railroad, when drawing up a set of standard plans a few years later, dis- carded the plate-lattice girders is a pretty sure indication that the advan- tages claimed for them were more imaginary than real. It is true, of course, that in case of submergence they would pass a certain amount of water through their webs; but it is seldom that a railroad company will build a bridge of any kind so close to the high-water mark as to run any risk of its being submerged. In respect to the economics of deck and through riveted spans, it may be stated as a general proposition that, although the former sometimes require more metal than the latter, they effect a great saving in the cost of the piers, and hence are to be adopted whenever permissible. Deck spans are cheaper per se when the ties can rest on the chords. This arrangement works well with double-track bridges having trusses spaced about twenty feet centers with two lines of stringers. The question of the comparative economics of pin-connected and riveted spans is treated at length in the next chapter. In respect to the comparative economics of the various kinds of trusses, it might be stated that a very few of them have stood the test of time, all freak and expensive styles having been discarded, the only types used ECONOMICS OF DIFFERENT TYPES OF ORDINARY STEEL STRUCTURES 71 today being the Pratt, Petit, Triangular (both simple and sub-divided and including the Warren), and K trusses. Comparing Pratt and Petit truss-spans, for which there is no difference worth mentioning in the pound prices of the metal, the weights per foot (and therefore the costs) are alike for single-track spans of three hundred (300) feet, and for double-track spans of three hundred and fifty (350) feet; but both constructive and aesthetic reasons generally necessitate limiting the lengths of Pratt trusses to about three hundred and twenty-five (325) feet. In respect to the comparative economics of the Pratt and Triangular trusses, there seems to be a difference of opinion amongst bridge engineers. The author has found very little variation in their total weights of metal, with occasionally a slight economy in favor of the Triangular truss. That truss has the practical advantage that changes in chord stresses occur at only every other panel point. This often makes it possible to section the chords more economically. As explained at length in Chapter XI, for continuous trusses of very long span, the Triangular truss has quite an advantage over the Petit truss. The K truss is appUcable for long spans only, and, therefore, is in com- petition with the Petit truss and not with the Pratt. Its principal claim for economy lies in ease and simplicity of erection, but it also has a tendency to reduce the high secondary stresses inherent in the Petit type. It was employed to advantage in the design of the great Quebec cantilever bridge. The statements made in this chapter apply mainly to railway bridges and heavy highway structures. For light highway bridges some of them might require a slight modification. CHAPTER X COMPARATIVE ECONOMICS OF RIVETED AND PIN-CONNECTED BRIDGES For at least a dozen years near the close of the last century there was waged in the technical press and orally when bridge engineers met (espe- cially if there were both Europeans and Americans present) a war of words concerning the relative merits of riveted and pin-connected bridges; but all arguments that were advanced failed to solve the disputed question. Time and the steady development of the real science of bridge designing, however, gradually brought about changes of opinion among the leaders in that specialty; and the matter was finally settled upon a compromise basis. The advocates of riveted structures used to claim greater rigidity and an increased chance for safe passage by a derailed train, while the endorsers of pin-connected construction used to rest their case mainly upon the theo- retically-correct distribution of stresses by articulated joints and the smaller amount of metal needed for building. It is true that there was then a wide divergence in the weights of metal required for constructing riveted and pin-connected bridges to carry the same Uve loads; and for this there were two saUent reasons. First, the riveted structures were of the lattice- girder type, having two, three, or even four systems of triangulation, thus involving much idle or superfluous metal in the main members of the web and even more in the numerous connecting plates and fillers; and, second, the pin-connected structures were proportioned essentially for the theo- retical stress-requirements, irrespective of proper minimum sections, thus cutting the weight of metal down to an absolute minimum. Gradually, though, these two types approached each other in weight, the lattice-trusses being abandoned for the riveted single-intersection types, such as the Warren and the Pratt, and experience in operation showing in pin-connected trusses the necessity for stiffening the abnormally-light members so as to increase the rigidity and check the vibration. Today good designers of riveted structures intersect all the axial lines of main members at panel points just as carefully as do the designers of pin-con- nected structures; and, hence, the prime objection to the former type, viz., its unscientific intersection of symmetry lines, vanishes in ioto. It is true, though, that there remain the unavoidable secondary stresses, but these exist also to a small degree in pin-connected bridges because of the friction of the pins in their holes and the consequent failure of the joints to function as actual articulations. The employment of eye-bars certainly, 72 ECONOMICS OF RIVETED AND PIN-CONNECTED BRIDGES 73 cuts down the quantity of metal, because, in the members where they are used, the weight of steel for both main sections and details is an absolute minimum; and, in general, pins weigh less than connecting plates. Whether secondary stresses receive proper consideration or not, a pin-connected bridge is somewhat lighter than the corresponding riveted one, and there- fore ought to be less expensive. It is true that the fine shopwork requisite for the proper manufacture of pins and for the drilling of pin-holes makes the pound price for fabrication greater in the pin-connected structure; but this is offset more or less by its lower pound cost for erection, owing to the smaller number of field rivets to be driven, the shorter time required to make safe against loss of span by washout of falsework, and the reduction in overhead expense effected by minimizing the time for field operations. From a study of the diagrams of weights of metal per lineal foot of span for pin-connected and riveted-truss bridges given in Chapter LV of " Bridge Engineering," it is found that the weights of the latter exceed those of the former by the following percentages: Simple Spans Span Lengths 200' Percentage of Increase 4 300' 5 400' 6 500' 8 600' 11 700' 14 Cantilever Spans Main Openings 600' Percentage of Increase 6 1000' 9 1400' 13 It is seen from these tables that the percentage of saving by using pin- connections increases gradually with the span-length. This is because of the effect of the reduced dead-loads. Notwithstanding the fact that pin-connected-truss bridges are some- what fighter, and possibly somewhat cheaper, than the corresponding riveted-truss bridges, the latter are decidedly preferable for all short or medium-length spans of railway structures (both steam and electric); because in short, pin-connected spans the vibration from rapidly-passing loads is so great that the motion of the eyes on the pins causes such a grind- ing of both that eventually the structure has to be replaced on that account. This was shown long ago to be the case in pin-connected elevated railroads; and lately it has been found necessary to replace pins in a number of rail- 74 ECONOMICS OF BKIDGEWORK Chapter X road bridges. The author saw an elevated raUroad in Kansas City re- moved practically for this cause alone, the pins having been cut into and the eyes elongated as much as an eighth of an inch. In the author's opinion, a steam-railroad-bridge span should be pretty long before pin- connections are resorted to — say 500 feet for simple spans and 900 feet for the main openings of cantilevers; but for highway and electric-railway bridges these lengths may be cut down from twenty-five to thirty-five per cent. The point is one to be settled by individual judgment based upon experience — not prejudice. The size of the appropriation available for construction may quite legitimately be a ruhng factor in making the deci- sion, because a pin-connected highway span of five hundred, or even four hundred feet, does not make a bad bridge; although, if the traffic be great, such a structure certainly is inferior to a riveted one, in that it will vibrate more and will possibly be shorter hved. But if the Uve load assumed for the designing be never greatly exceeded, and if the structure be always kept properly painted, it would probably require more than a century of use to wear the pins and pin holes to any dangerous extent. The discovery of a high-alloy of steel that can be manufactured at rea- sonable cost, and the development of a satisfactory and absolutely-rehable method of heat treatment thereof for eye-bars may bring the pin-connected structure once more into vogue; but it will be for long spans only, and preferably for highway structures. CHAPTER XI COMPARATIVE ECONOMICS OF CONTESTUOUS AND NON-CONTINUOUS TRUSSES This chapter is mainly a reproduction of a joint paper by Mr. H. Mal- colm Priest and the author, lately presented to the Engineers' Society of Western Pennsylvania. For many years past bridge engineers have held differing opinions con- cerning the advantages of continuous trusses as compared with the cor- responding non-continuous ones. Some claimed a great saving in weight of metal from continuity while others felt sure there was none. The author had been under the impression that the advantage claimed for the contin- uous truss was mainly due to the ignoring of the effect of reversing stresses; and, as will be seen later, in this opinion he was partly right and partly wrong. Under certain conditions it is not bad practice to use continuous trusses, and under others it is, irrespective of the question of economics. When the foundations of the piers are solid rock or other very hard material, continuity is permissible; but when they are piles or comparatively soft material without piles, it is better to forego any possible saving of metal rather than to run the risk of unequal settlement of piers and the conse- quent upsetting of stress distribution throughout the trusses from end to end of structure. The most notable example of continuous trusses in America, or, as far as the author knows, anywhere else in the world, is the Sciotoville Bridge over the Ohio River on the Hne of the Chesapeake and Ohio Northern Rail- road. At this location continuous trusses were permissible, for the reason that the pier foundations are sohd rock at no great distance below the bed of the stream. That structure consists of two continuous, double-track- railway spans of 775 feet each. It was designed and engineered by Dr. Gustav Lindenthal, Consulting Engineer, and was completed in 1917. Desiring to have this comparison of weights of metal for continuous trusses conform as closely as possible with actual conditions, the author assumed the outhnes of the Sciotoville structure, and contrasted it with a bridge of two simple spans, each made five (5) feet shorter, so as to allow for the dist9,nce between centers of pedestals on the middle pier, using prac- tically the same panel-lengths as those of the Sciotoville Bridge and eco- nomic truss-depths for the simple spans based upon the information given in "Bridge Engineering." 75 76 ECONOMICS OF BRIDGEWORK These two layouts are shown in Figs. 11a and 116. 9ZJ, ^Q o ^^ -^ m o §1 03 It is unnecessary to consider the comparative economics of simple- spans and cantilevers for electric-railway bridges pure and simple. Nobody 86 ECONOMICS OF BRIDGEWORK Chapter XII is ever going to build any of them of long-enough span to bring up the question, because such expensive structures would surely be constructed to accommodate highway traffic also. The type of cantilever under discussion (Type C of Fig. 12a) is not well adapted to crossings where falsework cannot be emploj^ed; and the use of the simple-span layout, in which the central span can be cantilevered out from the side ones, is frequently preferable on this account. Also the adoption of the three duplicate spans or even the duphcate side spans will .0 100 200 300 400 500 600 700 600 900 1000 40.000 35000 30000 25000 20.000 15000 \ 10 000 5000 900 1000 m 200 200 400 500 600 700 SOi Length of 5/mp/e Span in reef Fig. 126. Comparative Weights of Metal for Double-Track, Simple-Truss Bridges and Type-C-Cantilever Bridges. usually cause a small reduction in the pound price of the manufactured metal, as compared with that for the cantilever. The cantilever layout denominated Type A in Fig. 12a is the most common of the four types illustrated. It is generally used for a long- span structure where the length of the central openings is fixed, while the lengths of the end spans can be made much shorter. Also, it is more likely to be adopted where the central span cannot be erected on falsework. For these reasons it cannot fairly be contrasted with a siniplc-truss, equal- span layout, nor with the Type-C cantilever. It may very properly, though, be pitted against a simple-truss layout with imequal sixms— in fact the same spans as the cantilever layout has. Fig. 12c gives curves of weights for such layouts, for pin-connected, double-track, steam-railway ECONOMICS OF SIMPLE-TRUSS AND CANTILEVER BRIDGES 87 bridges. It will be noted that the span-length for equal weights is about 620 feet. If the central span must be erected by cantilevering, extra metal will be required for the simple-truss layout, amounting to about 8 per cent of the truss-weight. The span-length for equal weights will then be a little over 500 feet. If the side-spans in the simple-truss layout be replaced by steel trestle, the span length for equality of weights will be about 700 feet when the central span is erected on falsework. This layout, evidently, cannot be used when the central span must be cantilevered out. The Type-A cantilever of the proportions shown in Fig. 12a is usually an uneconomic layout to adopt when the distance between the end piers is a 100 ZOO 300 400 500 600 700 300 900 1000 mooo 30.000 25.000 20.000 15.000 10.000 5.000 Fig. 12c. 100 200 300 400 500 600 Lentjth of Cenfral Span in Feet Comparative Weights of Metal for Double-Track, Simple-Truss Bridges and Type-A-Cantilever Bridges. fixed quantity, while the two intermediate piers can be placed where desired. For such a location there should generally be used three simple- truss spans, a Type-C cantilever, or a cantilever with the end spans nearly as long as the central span. As before stated, this latter layout is discussed subsequently in this chapter. In many cases, however, the piers of the Type-A cantilever with a long central span will be much cheaper than those of the simple-span bridge, on account of their being nearer to the banks of the river. For such a crossing, the total cost of the simple-span struc- ture can sometimes be reduced by lengthening the center span and shorten- ing the side-spans; and the most economic layout for the simple-span bridge should first be found, and its total cost then compared with that of the cantilever structure. There is an economic consideration of some importance in the compari- son of simple-truss and cantilever bridges which, as far as the author knows, 88 ECONOMICS OF BEIDGEWORK Chapter XII has never yet been given any attention — at least none in print. It indi- cates within rather narrow hmits a sHght economy for the cantilever type, but the amount thereof and the location of the said limits are dependent upon several considerations, among which the most important are the fol- lowing: A. Average length of spans considered. B. Ratio of live load plus impact to total load. C. Method adopted for combining reversing stresses, when proportioning sections of members. The best conception of this matter of economics can be obtained from a dissertation based upon an assumed layout of simple-truss spans, all of equal length, — for instance, a long succession of like spans of two hundred feet each, the panel-lengths being twenty feet. If now we extend the trusses of every other span one panel beyond each of its piers and sus- pend from the cantilevered ends thus formed the shortened intermediate spans, we shall have a cantilever bridge that will effect a saving in weight of metal in every span. It is evident without any figuring at all that the spans which contain the suspended trusses will weigh less than the simple- truss spans, because the suspended portion is decidedly lighter and the cantilever arms, being so short, cannot be very heav3^ Again, the dead load stresses in the chords of the other spans are somewhat reduced, but probably not enough to permit of any reversion of stress when the span is empty with the adjoining spans loaded. The total stresses in chords are, therefore, materially smaller than those for the simple-truss spans, resulting in an economy of metal, notwithstanding the fact that there are two extra panel-lengths of top chord involved by the change from simple-span type to cantilever type, and that the vertical posts over the piers combined with the end main diagonals are somewhat heavier than the inclined end posts of the simple-truss span. On the other hand, though, the canti- lever structure, having only one pair of pedestals per pier, involves a slight economy of "metal on piers" and permits the width of pier-top to be reduced a little below that required for the two pedestals of consecutive trusses in the simple-truss layout, which saving in some cases will extend from coping to bottom of caisson. Next, let us assume that there are cantilever extensions of two panel lengths instead of one. There may or may not be a material saving of metal in those spans containing the suspended trusses in comparison with simple-truss spans, although there will be some reduction ; for, while there is a decided lessening in the weight of metal per lineal foot in the sus- pended portion, the cantilever arms tend to become heav}^ In the chords of the other spans, the dead-load stresses are made very small, permitting some reversion therein from the live loads on the adjoining spans; and the result will probably involve an increase in woiglit of truss metal. The net effect of the change in layout upon the struciuie as a whole is uncertain; but it is probably slightly uneconomic of metal. ECONOMICS OF SIMPLE-TRUSS AND CANTILEVER BRIDGES 89 If the assumption be made that three panel-lengths be cantilevered, it is almost certain that the total weight of metal in the structure will be augmented. It is evident that the proportionate effect of the cantilevering under consideration is dependent upon whether the bridge is a railroad structure or a highway one with a paved roadway supported on a reinforced-concrete base, because the relative effect of reversion is far greater in the former case than in the latter; hence an amount of cantilevering of this kind that would be uneconomic in a railroad bridge might be truly economic in the cor- responding highway structure. As the span-length increases, the ratio of live load to total load decreases, and hence the proportionate effect on weight of metal due to reversing stresses diminishes. For this reason one can anticipate that the longer the average span the greater will be the relative importance of the economic feature of design under consideration. Finally, the saving in metal (or the reverse) by this method of cantilever- ing is fundamentally dependent upon the manner in which the designing specifications take care of reversing stresses. If these be entirely ignored, as some engineers advocate doing, the cantilevering will effect a large economy of metal, even when the cantilever arms are comparatively long; whereas, if these stresses of opposite sign are cared for by adding to the larger three-quarters of the smaller and proportioning for the sum, the saving will be but little, if any. The most approved and up-to-date prac- tice is to add to the larger stress only one-half of the smaller; and in that event some economy may be anticipated, provided that the length of the cantilever arms be not too great. If, with a layout such as is being considered, there be found for openings of equal size an economy in a certain amount of cantilevering, the question arises "would there not be a further saving of metal, if the lengths of the continuous spans were to remain fixed and those of the other spans were to be moderately increased? " The answer to this question, in all probability, is affirmative, although the economy involved would not be important. In view of the preceding dissertation, it is evident that it is entirely impracticable to give any quantitative solution to this economic question, but that it must be solved for each case as it arises. In railroad bridge designing the matter is not important; because it is highly improbable that the value of the metal saved would offset the disadvantage of the reduction in rigidity that is unavoidable when changing from the fixed-span type to that of the cantilever. But in the case of a highway bridge with a heavj' floor, it is an altogether different matter, because, as previously pointed out, rigidity is not so fundamentally important in highway structures as it is in railway bridges; and, moreover, the stiff concrete slab itself increases so greatly the rigidity of the steel construction that the detrimental looseness caused by the hinged attachments of the suspended span loses most of its importance. CHAPTER XIII COMPARATIVE ECONOMICS OF CANTILEVER AND SUSPENSION BRIDGES This chapter is essentially a reproduction of a paper delivered by the author to the Western Society of Engineers at Chicago on September 15th, 1919. It is reproduced here practically in full for two reasons: First. Outside of the membership of that society, the paper has been read very httle, and it did not receive any written discussion; consequently, its contents, as far as this treatise and the engineering profession in general are concerned, are practically new material. Second. Unless it be shown herein that most of the information which had been published about the subject prior to September, 1919, was wrong, there would not be much use in the author's stating that such is the fact and claiming correctness for the data thereon which he presents; because in engineering, as in all other walks of life, any man's word is as good as another's on a disputed point until one has given absolute proof of the correctness of his claim. Moreover, from the strictly-professional point of view, the demonstration of the author's findings and the record of the various steps which he took in his investigation ought to prove fairly interesting reading— at least to structural engineers and students of the specialty of bridge design and construction. But if any reader should feel averse to wading through this long chapter, he can easily arrive at the results of the somewhat-elaborate study by skipping to near the end of it, where he will find a resume of conclusions. The calculations for the suspension bridges were prepared upon the basis that the stiffening trusses were free at their ends; but later some more computations were made in order to determine the effect upon the economic deductions, under the assumption that the said ends were anchored, but not fixed, to the masonry. The results showed for both the longer and the shorter spans a decrease of nearly one hundred feet in the span-length for equal cost. This is not a serious difference, nevertheless it is well to remem- ber that it exists. The following is a reproduction of the previously-mentioned paper: The Comparative Economics of Cantilever and Suspension Bridges Under the title "Suspension Bridges and Cantilevers — Their Economic Proportions and Limiting Spans," Dr. D. B. Steinman in 1911 issued a little ' 90 ECONOMICS OF CANTILEVER AND SUSPENSION BiRIDGES 91 book in the Van Nostrand Science Series; and in 1913 he produced a second edition of it with a few revisions and the addition of four folding plates. In that treatise he draws the conclusion that "the critical span at which the suspension bridge becomes economically superior to the canti- lever bridge is 1,670 feet." His calculations were made for a structure carrying four steam railway tracks between trusses and two exterior side- walks on the lower deck, and a roadway with electric railway tracks between trusses on the upper deck, the total live load for the trusses being 18,000 pounds per linear foot, of which 12,000 pounds were for the steam railways. His profile shows bare bed rock, which, under the approaches, is approximately horizontal and a few feet above extreme high-water level. He figured his cantilever structures for main openings of 1,000 feet, 1,500 feet, and 2,000 feet, and his suspension bridges for main openings of 1,500 feet, 2,250 feet, and 3,000 feet. While recognizing the value of Dr. Steinman's work and giving him due credit for his laudable energy and ambition, the author doubted the cor- rectness of the main conclusion just mentioned, and in "Bridge Engineer- ing" he wrote concerning it as follows: "In order to evolve a mathematical demonstration of the problem, he (Dr. Stein- man) had to make numerous assumptions more or less approximately correct. Without checking all of his mathematical work, it is evident that the professor has made as fair a comparison as he could; but his assumptions were so numerous and approximate that his conclusions must be taken with a liberal allowance for variation. . . . "All these facts affect materially the question at issue, and it is probable that, if the changes implied were incorporated, the span length for equal cost found by the inves- tigator would be considerably greater." For a number of years the author has had the desire to settle this economic question; but the amount of labor involved had always appeared appalling. In truth, it was so, because Dr. Steinman spent most of his spare time for two years in making the computations for his investigation. It is true that the author could easily have figured the weights of metal and the costs thereof for cantilever bridges by employing the diagrams which he prepared for his papers on "Nickel Steel for Bridges,"* and "The PossibiKties in Bridge Construction by the Use of High- Alloy Steels/'* most of which diagrams were published in these papers; but not until after he had written Chapter XXVII of "Bridge Engineering" did he possess any quick method of computing the weights of metal and the costs of suspension bridges. In that chapter are presented for the first time a number of formulae, from which, in conjunction with the numerous dia- grams in Chapter LV of the same treatise, can be found quite readily the approximate weights of metal for all portions of suspension bridges. In April, 1918, for the first time since the issuing of his book, the author found leisure to make the contemplated economic investigations. They * Published in the Transactions of the American Society of Civil Engineers. 02 ECONOMICS OF BRIDGEWORK Chapter XIII occupied all of his spare time for a month and a haK, representing alto- gether some 300 hours of steady figuring. As in the case of his paper on "The Possibihties in Bridge Construction by the Use of High-Alloj" Steels," he did all of the computation work entirely unaided, checking the results himself, but relying for their correctness mainly upon the regularity of the platted curves. As his data on weights of metal in cantilever bridges were primarily for double-track-railway structures, his first investigation was made for that class of bridges, using the Uve loads, impact, and specifications indi- cated in the two previously-mentioned papers. For convenience of com- parison, he assumed Dr. Steinman's unit prices for metal in place, but for substructure estimating he adopted the method which he has employed for many years, viz., using a unit price for concrete above low water, another for the mass of the pneumatic caissons with their superimposed cribs below low water, auQther for the corresponding mass below the same in box cribs filled with concrete resting on piles, and a price per lineal foot for those portions of the said piles projecting below the bases of the cribs. These unit prices are as follows: Shafts and walls S15 . 00 per cu. yd. Mass of pneumatic caissons with their cribs 25 . 00 per cu. yd. Mass of box cribs, including enclosed por- tions of piles 20 . 00 per cu. yd. Piles projecting below base of crib 1 . 50 per lin. ft. The unit prices for metal in place were as follows : Wire cables , 12 . 5)!f per lb. Nickel steel 8.0^ per lb. Carbon steel in spans 5.6^ per lb. Carbon steel in trestle approaches 5.0^ per lb. The costs of the railway tracks, the roadway pavements with their rein- forced-concrete bases, and the reinforced-concrete sidewalks have been ignored when computing the total costs of structures, because they are common to the two classes of bridges compared. In making the computations for this investigation, the avithor took the liberty of adopting several short cuts, such as assuming squared instead of rounded ends for all piers, using generally the method of "end areas" instead of that of the "prismoidal formula" when calculating volumes of masonry, carrying out quantities of materials and total costs to rather large limiting units, and estimating costs of certain parts by proportion from the previously-computed costs of similar parts of other structui-es. All these and many other short cuts for avoiding labor are perfectly legitimate when making comparative estimates, provided that they affect alike the com- pared types of construction, as they do in this case. In the plotted curves of the accompanying diagrams no curve was ECONOMICS OF CANTILEVER AND SUSPENSION BRIDGES 93 drawn through less than three located points, and in many cases the num- ber was four or more. The regularity of all the curves proves that there was no error of any magnitude in the figuring which located the points thereof. It does not mean, however, that the author's calculations con- tained no errors. Unfortunately, several mistakes crept into the work, but the plotting invariably pointed them out and led quickly to their satisfactory correction. In the diagrams the abscissae represent main-span lengths in feet, and the ordinates show the total costs of structures in dollars, the recorded units being milhons. In figuring the weights of stiffening trusses for suspension bridges, the author made an important modification in one of the formulae given in Chapter XXVII of "Bridge Engineering."* Equation 15 thereof has been employed without change, when wind stresses are ignored; but the follow- ing formula for the weight 'per foot of both trusses has been added to cover the case wliere the effect of the wind load is considered: The corresponding equation when the wind stresses are ignored is : 7^ = 2.8 5.06 Mm . 3.26F™/p2+2d2\ ds s \ dp / The greater of the two values of T given by these equations is, of course, the one to use in the estimate of total weight of metal. The division of total metal weight between carbon steel and nickel steel was made by the author's judgment, based upon the curves in his two before-mentioned papers and upon the assumptions of material distribution adopted when preparing the suspension -bridge computations. No error of any magnitude exists because of this assumed distribution, although, of course, the method employed is only approximately correct. Whenever a proper weight curve for cantilever structures was not available, the author fell back upon the general curves for weights of metal in trusses and laterals that record the various double-panel weights in can- tilever arms and anchor arms as multiples of the corresponding double- panel weight of the suspended span, which general curves were first given on Plate X of "De Pontibus," and afterwards were reproduced in Fig. 25j of "Bridge Engineering." In establishing the general assumptions for the layouts of both canti- lever and suspension bridges, with one exception they were made as favor- able as possible for each type, that exception being that, for the sake of appearance, the anchor arms of each cantilever structure were made of the * This modification has lately been incorporated in the third thousand of that treatise, now on sale. 04 ECONOMICS OF BRIDGEWORK Chapter XIII same length as that of the cantilever arms, viz. : 0.3125 of the main opening, instead of the more economic value of 0.2 thereof. Concerning the cor- rectness of the last claim for economy there is some dispute in the profes- sion; but of this matter, more anon. In the suspension-bridge layout the backstays were not used to support side spans, but were run by approximately right hnes to the anchorages. This is the most economic layout possible, because a steel-trestle approach is always cheaper than any layout of truss spans that can be made, not only because it requires less metal, but also because the unit prices thereof erected are somewhat smaller. The main piers of all the cantilever bridges and most of those for the suspension structures were designed as two pedestals with a reinforced- concrete wall between, this wall extending a short distance below extreme- low-water mark. It was found, however, in the case of the combined four-track-railway-and-highway suspension-bridges, that it was just as economic to use a continuous pier, because of the four points of support required by the tower columns, hence that feature of construction was adopted. The method employed for finding the quantity of concrete in the anchor pier for a cantilever bridge was to compute the maximum uplift, multiply it by two, and divide the product by the weight of one cubic foot of concrete, taking due cognizance, of course, of the buoyant effort of the water on all submerged portions thereof. If the volume thus found would work up into a properly-shaped pier, well and good; but if not, an addi- tional amount was provided. The method of proportioning the anchorages for suspension bridges, when the foundations were solid rock, was to make each one quite long and narrow, high in the rear and low in the front, and to let the line of pressure reach the base exactly on the edge of the middle third thereof. In case the foundation were piles, a similar shape was used, but it was necessary to keep the load on each pile of the front row down to forty tons. When piles were employed to support the main piers, the Hmiting load per pile was taken also at forty tons, exclusive of the effect of wind pressure. The piles used were all assumed to be one hundred feet long. The limiting widths of structure were as follows: In cantilever bridges one twenty-fifth of the main opening; in suspension bridges one-twentieth thereof, measuring between central planes of exterior columns over main piers; and between central planes of stiffening trusses one-thirtieth of the main opening. As a matter of economj^, in some of the cantilever struc- tures the distance between truss planes was made as small as practicable for the suspended span, and was gradually widened out to a maximum over the main ])ier, and then gi'adually re(hiced to a mininuun over the anchor pier. The economic lengths for the cantilever structui-c^s were taken as estab- lished tw(!iity years or more ago by the autlu)r wIumi preparing the MS. of ECONOMICS OF CANTILEVER AND SUSPENSION BRIDGES 95 "De Pontibus," viz.: For the suspended span, three-eighths of the main opening; for each cantilever arm, five-sixteenths of the main opening. As before stated, the length of the anchor arm, for the sake of appearance, was made the same as that of .the cantilever arm, although some metal would have been saved by assuming it shorter. In the suspension span, also, economic dimensions were used, viz.: one-fortieth of the length for the truss depth, and one-ninth thereof for the deflection of the cables. In order to provide proper splay for the latter (when splay was required), the tower width, as before indicated, was made one-twentieth of the main opening. This militated but slightly against the suspension bridge, because, in the substructure, it generally increased the cost of only the walls between the pedestals of the main piers, the increase being a bagatelle in comparison with the total cost of the said substructure. The first estimates prepared by the author were for double-track-rail- way bridges; and he assumed, to begin with, an opening of 1,700 feet, which is approximately Dr. Steinman's span-length for equal cost. The profile adopted for this crossing is shown in Fig. 13a and Fig. 136. It will be seen Fig. 13a. Layout for 1,700-foot Span Cantilever Railway Bridge. Fig. 136. Layout for 1,700-foot Span Suspension Railway Bridge. that there is a difference of twenty-five feet between high water and low water, that the river bed is some fifty feet below the latter, and that the bed rock is one hundred feet below the same for condition No. 1. In con- dition No. 2 there is no bed rock, hence the piers and anchorages are sup- ported on piles. As the author had anticipated, the result of the calcula- tions showed a large difference in favor of the cantilever structure, the 96 ECONOMICS OF BRIDGEWORK Chapter XIII total costs being $4,120,000 and 87,980,000. These figures are for condi- tion No. 1, in wliich all piers and anchorages were assiuned to be sunk by the pneimiatic process to bed rock. 1700 1800 1900 2000 2100 ZZOO 2300 2m 2500 2600 270Q Afa/n 5pan-Leput in Dr. Steinman's study it is th(! iriuin piers that are fixeil in location, licncic the assumption made for economic leiiKlli of aiiclior-arma is unwarranted. ECONOMICS OF CANTILEVER AND SUSPENSION BRIDGES 101 of Fig. 13(7, and for a corresponding layout in which the exterior half thereof is replaced by steel trestle ; but as this would involve considerable trouble IT T" ^ oi *0 t Suspension 3,017,000 6,995,000 Of the preceding nine cases there are only three which can be directly compared, viz., the 1,500-foot cantilcvcM-, llio 1,500-foot suspension, and the 2,000-r()()t cantilever, although ollu-r coniiKU'isons miglit be made ai)iii"oxi- malely by inter])()lation. It will \)v iH)(i('(>d (hat Dr. Steinman's main piers cost two or three times as much as those of [\\v author, his anchor piers for ECONOMICS OF CANTILEVER AND SUSPENSION BRIDGES 105 cantilevers from three and a half to six times as nnich, and his anchorages for suspension bridges about twice as much. This gives further proof of the statement previously made to the effect that his entire economic investiga- /4a> /sao /£>M Z2PO ?9M ;3Vft» Fig. 13i. nao /e^ /m> zaoo z/oo /^m S/x3/?-l&^^ iff f^'f^ Cost Curves for Combined Railway and Highway Bridges of the General Type Computed by Dr. Steinman. tion is incorrect and that the deduction which he makes therefrom concern- ing the span length for equal cost is wrong. In thus criticizing Dr. Steinman's little book, the author does so merely because he feels that the profession should not be left in error on such an 106 ECONOMICS OF BRIDGEWORK Chapter XIII important point as the comparative economics of cantilever and suspension bridges. Some time in the not very distant future there are going to be built in this country many long-span bridges; and it behooves engineers to know in advance the economics of the different types of structures appli- cable thereto. Dr. Steinman deserv^es great credit for his energ;^^ and courage in attacking such a stupendous problem at such an early date in his professional career, without -any records of weights at his disposal, and before he had had any actual experience in bridgework. In undertaking such an immense task he set a splendid example to other young engineers; and the incorrectness of his conclusion is no blot whatsoever upon his pro- fessional record. It would be well for engineering if there were in its ranks many more young men possessing the attributes of energy, ambition, and love for hard work to the same extent that he does. Such men will be badly needed in every branch of technics, if our profession is to take the high position in the community to which it is entitled by its importance to mankind. Dr. Steinman can console himseK with the reflection that he is not the only engineer who has devoted an entire treatise to the production of a wrong conclusion, for several decades ago an eminent French professor of engineering published a large book deahng with the economics of truss bridges, basing his calculations upon such incorrect premises that the result of his work was of no real value to the profession. Comparing the results of the preceding calculations, as shown in Fig. 13c and Fig. 13i, it will be noticed that the span length for equal cost is much less for the combined railway and highway type of structure than for the strictly railway type. The reason for this is that in a modern highway bridge the proportion of dead load to live load is much greater than it is in a railway bridge, because of the large weight of the pavement, the supporting slabs, and the concrete footwalks. In the stiffening trusses of a suspension bridge it is generally the live load only which causes stresses that influence the sectional areas of the members, the dead load having no effect thereon whatsoever, but in a cantilever bridge it is the total live load plus the dead load which does so, with sometimes a little assistance from the wind load; hence it is evident that the smaller the i)roportion of live load to total load the more favorable it is for the susp(;nsion bridge. On this account, in strictly highway structures, the span length for equal cost will be much shoi'ler than those thus far determined. Not knowing what the length would probably be, the author hgured the costs of the two types for 1,500- foot, 1,200-foot, and 1,000-foot main openings, using carbon steel only; and fi-()rn the i-esults of the computations lie plotted the curves in Fig. 13^. From this diagram it will be seen that the span length for equal cost is about 1,000 feet. Recognizing that this investigatioTi would not l)e comiilete without pr(!paring a set of coinj^iitalions for slrictly-highway structures of nickel steel, the necessary calculations were made for a 1,000-foot span of each ECONOMICS OF CANTILEVER AND SUSPENSION BRIDGES 107 type, the result showing ahnost exactly equnl costs. This indicates that the strength of the steel used does not modify the span length for equal cost in highway structures, although changing the totals of the estimates. //a:? /Jtv /3aff Fig. 13j. Cost Curves for Highway Bridges of Carbon Steel. These highway bridges are of the same kind as that adopted as standard by the author in his late paper on "The Economics of Steel Arch Bridges," viz., a deck about 60 feet wide, out to out, composed of a paved roadway 42 feet wide, resting on a reinforced-concrete base, and having a double- track street-railway at the middle, and two 8-foot-wide, reinforced-concrete 108 ECONOMICS OF BRIDGE WORK Chapter XIII sidewalks. The live loads for the floor sj^stem are Class 25 for the electric railway, Class B for the rest of the roadway, and Class C for the side- walks. Class A over the full width of the deck was employed for the trusses. RESUME OF INVESTIGATION First. For exclusively railroad bridges, the economic limit for the cantilever type of structure, or, m other words, the mam span length for a cost equal to that of the corresponding suspension bridge is that length which requhes 4| pounds of metal to carry 1 pound of live load. Second. For modern highway structures, carrying also incidentally electric railway tracks, this span' length for equal cost is 1,000 feet. Third. For combined-railway-and-highway structures the hmit is intermediate between the limit for railway structures and that for high- way .structures, the interpolation being done in direct proportion to the ratio of railway-truss-live-load to total-truss-live-load. This may be expressed by formula thus: If G is the span length of equal cost for strictly-railway bridges, and R is the ratio of railway-tiuss- hve-load to total-truss-live-load, then, for combined-railway-and-highway structures the span length for equal cost will be given approximately by the equation: ,S,= 1,000+ (G- 1, 000) /? For instance, if (7=2,700 feet for nickel steel railway bridges and i2 = |, S,= 1,000+1,700x1 = 2,133 This checks fairly well with the value shown in Fig. 13t, where 12,000 _ 2 "18,000 "3* Fig. 13/i is a diagram from which can be found at a glance the span length for ofjual cost for any proportionate combination of railway and highway live loads, under the assumption that nickel steel is employed for the principal portions of the structure. In case, though, that carbon steel alone be used, which is unlikely, the limiting span length for canti- lever construction is to be taken at about 2,000 feet. Whil(>, it was not intended to do any figuring concerning the com- pai-ativ(! economics of cantilever and suspension bridges when alloy steels having higher elastic limits than 60,000 pounds per square inch are cm- ploy (m1, it was surmised that the span Icngtli for equal cost for strictly- railway bridges will not differ essentially from the limiting lengths for cantilever main spans determined by the author in "The Possibilities in liiidg(! (Construction })y the Use of High Alloy Steels," viz.: For E= 70,000 pounds per square inch 2,780 feet For Fj= 8(),(K)() i)oun(ls ])er square inch 2,910 feet For Fj= 0(),0()() i)oun(ls per square inch 3,030 feet For ^=100,000 pounds per square inch 3,140 feet ECONOMICS OF CANTILEVER AND SUSPENSION BRIDGES 109 It is possible that the author is not entirely justified in making this surmise, because computations might show that the span length for equal cost does not exceed 2,700 feet, no matter how high may be the alloy of steel used. It seemed hardly worth while to spend much time in figuring f£iT//i^S!]yL'y&l^>a^/^rL/hea//w^^lSij/LV£loaaf/i^ Fig. IS/b. Diagram of Main Span Lengths of Equal Cost for Combined Railway and Highway Cantilever and Suspension Bridges. upon this question before a high alloy of steel satisfactory for long-span- bridge building is found; nevertheless, as a matter of curiosity, it was decided to test a main span length of 2,900 feet, for steel having an elastic limit of 80,000 pounds per square inch, and assuming that the cost of that metal in place is 9 cents per pound. 110 ECONOMICS OF BEIDGEWORK Chapter XIII The comparative figures of cost for the two structures proved to be as follows: Cantilever bridge $15,720,000 Suspension bridge 15,233,000 However, had the price of the alloy steel been taken at 8 cents per pound the same as for nickel steel, the cost estimates would have been as follows: Cantilever bridge $14,448,000 Suspension bridge 14,856,000 As these last figures reverse the previously found economics of the two types, it is evident that for bridges of high-alloy steels the span length for equal cost is vitally dependent upon the pound price of the said aUoy steel, the lower it is the more favorable is it to the cantilever structure. In view of the fact that at present no one has any idea of what the cost per pound wiU be for high-alloy steels used in future long-span-bridge construction, it will be well to adopt temporarily as correct the author's before-mentioned surmise, viz., that in alloy steel bridges carrying railway loads only, the span length for equal cost is that for which, in the can- tilever bridge, there are required 4| pounds of metal to sustain 1 pound of live load. The author recognizes that a change in the assumed conditions would modify somewhat all the previously found span-lengths of equal cost for both carbon-steel and nickel-steel bridges; but he does not believe that the variation will be material — say not to exceed 2 or 3 per cent in any case for any one fundamental change, or 5 per cent for any probable com- bination of changes. For instance, if the main piers rest on piles instead of going to bed rock, this will mihtate a little against the suspension struc- ture, increasing slightly the span length for equal cost. The same effect occurs if the pound price for steel cables be increased without changing the pound prices for the other metals, and vice versa. If the unit prices for substructure be decreased, the result will be favorable to the suspension bridge, because, while the main piers will be affected about alike, there will be a greater saving in the anchorages of the suspension bridge than in the anchor piers of the cantilever structure. Let us see what effect it would have to reduce the prices of all concrete work five dollars per cubic yard, thus bringing them close to the lowest limits for truly-first-class construction that have existed in periods of national depression. In the railroad bridges of 2,700 feet span, the reduction in total cost of substructure would be $473,000 for the cantilever bridge and $928,000 for the suspension bridge, making the total costs, respectively, $14,796,000 and $14,330,000. Performing the corresponding reduction in prices of substructure for the 2,400-foot spans gives, for the total costs, respectively, $9,877,000 and $11,196,000. Plotting these points on a cross-section ECONOMICS OF CANTILEVER AND SUSPENSION BRIDGES 111 diagram and joining them properly by very slightly curved lines shows that the span length of equal cost is reduced from 2,700 feet to 2,640 feet. This is no material amount, indicating, as it does, a variation of only 2.2 per cent. Addendum The preceding was written in the summer of 1918. A year later the author was called in by some prominent citizens of Detroit to make a study of the governing conditions for a proposed highway-and-street- railway bridge over the Detroit River, practically on a line joining the business centers of the cities of Detroit and Windsor, and to determine upon the best type of structure to adopt. A few days of investigation led to the conclusion that a single span of 2,500 feet, crossing the entire river in the clear between harbor lines, would be obligatory; and, accord- ingly, the layout and the approximate cost-calculations were made for a suspension bridge. It became necessary to obtain pound prices for structural metal (both nickel steel and carbon steel) and wire cables in place; and the following values were found: Carbon steel erected 7.0^ per lb. Nickel steel erected . . . 9.0^ per lb. Cables erected 23.0^ per lb. The last figure was simply staggering! Surely, such an enormous price can be only temporary, for the great difference between it and the other two figures is altogether illogical. Nevertheless, it shows the pos- sibility of an abnormal price-condition existing long enough to affect tem- porarily the economics of cantilever and suspension bridges. It is not likely that there can ever be a worse condition than the one at present governing; consequently, the author has recast for existing unit prices the estimates of cost made for the preceding investigation, and has found the following results: The span of equal cost for highway bridges has been advanced from 1,000 feet to exactly 1,200 feet; that for the particular combined bridges investigated has been increased by 170 feet; but that for the steam railway bridges has been augmented only 60 feet. The reason for the smaller increase in the last case is that, in cantilever structures the weight curves, and consequently the cost curves, rise very rapidly at a span of 2,700 feet, because such a length is really a little beyond the truly prac- ticable limit for that style of bridge. These variations are somewhat greater than the maximum which the author anticipated when writing his paper; but at that time he never would have deemed it possible that such a great variation in unit prices of struc- tural steel and wire cables could hold as that which exists to-day; nor does he now consider it possible that it can be made to last for any great length of time. 112 ECONOMICS OF BRIDGE WORK Chapter XIII In making the Detroit-Windsor Bridge study, a practical proof was given of the usefulness of the paper. No copy of "Bridge Engineering" was available for making an estimate of the cost of the suspension bridge and its approaches, but a copy of the paper was at hand ; and, as a rough estimate was required immediately, the following procedure was adopted, it being recognized at the outset that all the assumptions made therein were upon the side of safety, and that, consequently, the resulting figures of cost would be somewhat too great: Referring to Fig. 13 j, the curve for costs of suspension bridges was extended on an enlarged cross-section sheet to a span of 1,700 feet, at which length the spans on Fig. 13c begin. Ths cost thus found was mul- tiplied by the ratio of the total combined clear widths of roadway and side- walks for the two structures considered, and the product was multiplied by the average of the ratios of the unit costs of all substructure and superstructure materials in place for present conditions and the condi- tions assumed in the paper. Then, referring to Fig. 13c, it was noted that the cost of a 2,500 foot-span suspension-bridge and its approaches is almost exactly double that for a similar 1,700-foot span with its approaches; hence the cost just found was doubled, and to the result were added the cost of the entire flooring from entrance to exit of structure, an allowance for the greater length of the approaches involved, and the approximate cost of either elevators or an escalator and a stanway at the Detroit approach. Later, a more exact estimate of cost was made from the various data in "Bridge Engineering," the result being some 5 per cent less than that of the first approximation. This more-exact estimate was computed in a single working day. Without the aid of the book mentioned, it would probably have required as many weeks of figuring as it actual^ took hours thereof, in order to obtain results of equal accuracy. In the Appendix to the original paper there are given five pages of estimates of cost, covering fourteen structures out of the twenty-five that were computed. It has not been deemed worth while to reproduce them in this treatise; for probably they would not be of much interest to any reader. If, though, anyone desires to see them, he can do so by consulting the Transactions of the Western Society of Engineers. CHAPTER XIV ECONOMICS OF BRIDGE APPROACHES The economics of approaches to bridges will involve the question whether it is best and cheapest to build earth embankments, timber trestles, steel viaducts, reinforced-concrete viaducts, or any combination of these, and at what heights it would pay to change from one type of construction to another. In determining the economics of the different kinds of structure it does not suffice to compare merely their first costs; for it is necessary to take into account the items of depreciation, maintenance, and repairs by computing the annual expenses for these, finding the sums of money which, at the governing rate for simple interest, would produce these annual amounts, and adding the results to the first costs. In certain cases it might not be best to adopt the theoretically-economic kind of structure, because the requisite funds for building it may not be available; and in such cases the cost of renewals should receive due con- sideration by taking cognizance of the probable increase in the future prices of perishable materials, such as timber, as well as of the special danger to the structure from fire or washout due to the employment, either permanently or temporarily, of such inferior construction. As indicated in a previous chapter, the danger from fire to a structure built either wholly or partially of timber is a serious matter. It may be permissible under certain conditions to risk losing an approach to a bridge by either fire or flood; but if the danger extends also to the main structure, the cheapening expedient is not permissible. Again, due consideration should be given to the question of the expense caused by the interruption of traffic by putting out of commission either one or both of the approaches. Generally speaking, it does not pay to take any chance of even temporary disaster to the structure; but, as before pointed out, it sometimes appears to be unavoidable. In the case of embankments when earth is expensive at the outset and can be brought to the site much more cheaply after the bridge is finished and the railroad line that it carries is in operation, it will generally pay to build, as inexpensively as possible, a timber trestle; and later, just before it begins to need expensive repairs, fill around it and construct an embankment by dumping earth from above by means of a construction train. 113 114 ECONOMICS OF BRIDGEWORK Chapter XIV There is an economic question concerning embankments, not at all difficult to settle, which exists when the right-of-way is expensive; and that is whether it is preferable to use wide banks with the natural side- slopes or to build concrete side-walls and thus diminish the area to be occupied. The only proper way to detennine the economics in this case is to make a complete estimate of cost for each layout, based upon current prices of materials, labor, and right-of-way. Occasionally in an engineer's practice there arises the economic ques- tion whether it will be better to build an expensive abutment with wing- walls, and possibly also toe-walls, or an inexpensive buried pier with longer superstructure and with rip-rap protection along the end and sides of the embankment. In most cases the latter will prove the more economic, but that such is the case should never be assumed without making accurate comparative estimates. With substantial bank protection that no flood is hkely to wash out, the expedient of the buried pier is a perfectly legiti- mate one, and the construction invol ^ed by its use can properly be deemed first-class. The choice between a steel trestle and a reinforced-concrete trestle for an approach should always be determined by including in the comparing estimates of cost the equivalents for depreciation, maintenance and repairs, giving a substantial preference to the concrete layout because of the possibility of future deterioration of the steel due to neglect of painting. As indicated on page 1193 of "Bridge Engineering" there are given in Chapters 53, 55, and 56 of that treatise a large number of tables and dia- grams, by means of which can be quickly computed the costs of the em- bankments, timber trestles, steel viaducts, reinforced-concrete viaducts, retaining walls, abutments, and culverts which may be needed in esti- mating the cost of approaches to bridges. From these data there can also be found very easily the comparative economics of plain and reinforced concrete for building retaining walls and abutments. It is sometimes the case that in the approaches to a proposed bridge there would be a variation in the total cost of right-of-way and property damages by adopting different kinds of construction therefor, hence this matter should always receive due consideration. One of the most effective methods of economizing on these items is to substitute a spiral approach, such as mentioned on page 1076 of "Bridge Engineering," for the usual straight trestle. While the construction costs of the two types do not differ materially, if the property occupied or damaged be very valuable, a great saving can sometimes be secured because of the comparatively small and compact area required for the spiral. Moreover, it is some- times practicable to construct a building in connection with the latter, that will bring in such large rentals as more than to wipe out all costs for right-of-way and property damages. In gcnei-al. it may be stated that timber trestle is the cheapest kind of approach, as far as first cost is concei'ned, excepting for small heights, but ECONOMICS OF BRIDGE APPROACHES 115 that its upkeep and replacement are expensive. If funds for the con- struction are hmited, it may be best to adopt timber trestle-work in spite of its being ultimately uneconomic, with the expectation of saving from the traffic receipts enough money to substitute later on, when replacement becomes necessary, the most desirable type of construction. Of the permanent types of approach, the embankment is the cheapest where the property-cost is little or nothing, excepting when the grade line is very high or the earth difficult to obtain and, therefore, expensive. When property is costly or side slopes are not permitted, it is economic for comparatively-low grade-levels to adopt earth embankment between retaining walls. As the height increases, it becomes cheaper to pass from embankment to trestlework ; and the point of division is not difficult to determine when there are no side walls, but when these are requisite, it will be necessary, as previously mentioned, to make the determination by actual cost- estimates. The wider the approach is at grade surface, the greater, for economy, will be the limiting height of embankment. For low trestles of permanent construction, reinforced-concrete wiU generally prove economic, but for high ones it will, be found necessary to employ steel. CHAPTER XV DETERMINATION OF LAYOUTS The determination of the best possible layout for any proposed structure is truly an economic problem, notwithstanding the fact that many of the considerations which influence it may not bear directly on the question of cost. It is one of the most important responsibihties in the province of the bridge engineer, and to do the work in the most effective manner possible demands a wide experience, coupled with good judgment and the ability to foresee eventuahties over a long period of years. The general idea that the best possible layout is the one which makes the first cost of structure -a minunum is a fallacy; for there are many other considerations besides economy in initial expenditure that are of great importance. The follow- ing is a fairly complete list of the various items which should be carefulty considered before settling finally upon the layout of grades, clearances, span-lengths, character of substructure, and type of superstructure to adopt. This is a long list, but it must be remembered that it is intended to cover all the considerations for all cases, and that, probably, only a few of the items will apply to any particular case. List of Factors and Conditions Affecting the Layouts of Bridges A. Government Requirements. L Stream Conditions. B. Grade and Alignment. J. Foundation Considerations. C. Geographical Conditions. K. Navigation Lifluences. D. Commercial Influences. L. Construction Facilities. E. Property Considerations. M. Erection Considerations. F. General Featvires of Structure. N. ^Esthetics. G. Future Enlargement. O. Maintenance and Repairs. H. Time Considerations. P. Economics. While there is an attempt at logic in the arrangement of the preceding list on the combined hues of natural sequence and comparative im])ortance, it is impossible to state in advance for an}^ particular case or class of cases which are the items that should receive the most consideration. Each item will be taken up and discussed in the order adopted in the list. Government Recjiiirements In Cliaplcir L of "l')ridge Engin(MM-ing" the re(|uirenients of tlie United States Government icgulating th(> bridging of navigable streams are treated 116 DETERMINATION OF LAYOUTS 117 at length. Neither the Federal GoverniDent nor any of the State Govern- ments, however, concern themselves with the bridging of streams that are not navigable, unless it happen that suit against the builder or the pio- posed builder of the bridge be instituted in either a State or a Federal Court, when, of course, the law will be concerned. The War Department nearly always confines its attention to a few salient features of any proposed crossing of a navigable stream, viz., the span-lengths, the clear waterway for navigation, the angle of skew (if the crossing be not square) , the position of the movable span or spans (if there be any), the clear headway above high water for both the movable and the fixed spans, the character and the dimensions of the draw protection, and the amount of obstruction to the flow of water caused by the piers — espe- cially those parts thereof below low-water mark. In spite of the fact that the War Department has certain rules for deter- mining the span-lengths for crossing various navigable rivers, the said rules are more or less elastic; hence it will generally pay any consulting bridge engineer, or other engineer who intends to bridge navigable water, to con- sult first with the local engineer of the Government who has charge of the district in which the proposed structure is located, and later, if necessary, with headquarters at Washington, in order to settle as to what the exact requirements of the Government will be. Often by stating one's case clearly and logically one can persuade the authorities to ease up on some regulation that appears to be unnecessarily strenuous or severe. For instance, the relation between the widths of clear openings required for swing spans and bascules or vertical-lift spans is a matter that has never been finally determined by the Department, each case as it arises being solved on its own merits. Again, if the limiting length of span set by the Government does not exactly fit a crossing, one has to put in a shorter span at one end of the bridge, or to increase equally all the span-lengths, or else to obtain permis- sion to decrease them equally. If the decrease be small, it is sometimes practicable to obtain the consent of the Department to the adoption of the shortened span-length. In the case that the grade of a bridge is so low as to bring the clearance line too close to the elevation of high water to meet the Government requirements, it is sometimes possible to persuade the Department to per- mit an encroachment; but to do so would certainly be bad policy, for the limit set by the United States Engineers is adjusted about right to provide safety from passing drift. In respect to the position of the movable span, the broad statement can be made that its mid-length should coincide with the deepest part of the channel, but there are occasional exceptions to the rule, notably when the channel is not permanent, or where it can advantageously be shifted by a little dyking. Permission to do such shifting and to locate the movable span accordingly would have to be obtained from the War Department. 118 ECONOMICS OF BRIDGEWORK Chapter XV The latter may have something to say about the angle of skew, as the United States Engineer Corps always advocates a square crossing, if it be practicable; hence the bridge engineer who deskes to obtain approval for a bridge on a skew of any magnitude must be prepared to show good reason for his request; and even then it may not be granted, because, like the author, the Govermnent engineers look upon a skew bridge as an abom- ination. While the Department does not pay much attention to the character of the draw protection, it is likely to insist that it be not omitted and that its dimensions be satisfactory. Ordinarily, also, it does not concern itself with the dimensions of the substructure; but sometimes, especially in case of a skew bridge, objection is raised to placing too much rip-rap around the piers and thus obstructing the flow of water in the channel. Grade and Alignment In most cases the grade and the alignment of the railroad or travelway are determined before the bridge engineer is called in, but sometimes it is otherwise; and there arise occasionally conditions which compel a con- scientious bridge specialist to insist upon a change in either the grade or the alignment — or in both. The ideal way to adjust the grade on a structure is to carry it over unbroken and, preferably, level in the case of railroad bridges, thus avoiding either a sag or a hump, as either of these objectionable conditions involves loss of power due to the climbing of unnecessary grades. Again, any great sag causes traction stresses and a shock that might better be avoided, if practicable. In a highway bridge this is not so important, and a rise from ends to centre of structure is permissible, especially as it facilitates drainage and improves appearance, notably in long-span suspension- bridges. The ideal alignment for a structure is not only to have it on tangent throughout its entire length, but also to continue the said tangent quite a distance away from the bridge at each end. Sharp curves constitute an invitation for derailment; and a derailment on a bridge, or near the end of one, is liable to prove disastrous. A reverse curve on a structure, or on an approach thereto, is not permissible, if it can possibly be avoided. Where two curves in opposite directions come close together, there should be a stretch of tangent b(;tween them; and when this tangent is on a bridge, it should be made as long as possible. Sometimes it is entirely impracticable to avoid curvature on bridges and their approaches, as in the case of a rail- road following the course of a river that runs between high banks and having to cross it from time to time in order to avoid heavy excavations and tun- neling. In su(;h cases curves on the approaches are unavoidable, and often it is necessary to put a part of even the whole of the structure itself on curve. DETERMINATION OF LAYOUTS 119 Such a general condition existed on the Hne of the Canadian Northern Pacific Railway as it followed up the Fraser and the Thompson rivers, crossing them nine times with only one structure entirely on the square. In some skew crossings, especially when the obliquity is small, it is permissible to square the piers to the structure, thus saving considerable masomy; but this practice is not always advisable because of the damming of the water by the large area of the substructure that is opposed to the current The layout of any bridge on a curve, or which has its approaches on curve, is greatly affected by the curvature, in that it has a tendency to shorten the span-lengths in the effort to avoid excessive width of superstruc- ture and undue increase in length of piers. The determination of the best grade to use for the approaches to a bridge is an economic problem of major import. It is of much more con- sequence in railroad bridges than in highway structures, because of the far steeper grades which are permissible in the latter; for, of course, the steeper the grade the shorter the approach and the less its cost. It is sometimes practicable to put a grade on the river spans of a bridge, leading up to a movable span or to a single, high-level channel-span; and this should always be done when practicable, notwithstanding the fact that the grade may have to be less than that allowable for the approaches, because even inches in elevation on the land construction often count materially in determining the length and cost thereof. In railroad bridges the fixing of the approach grades sometimes involves the economic solution of the question of a steep grade with pusher engines versus an easy grade without them. In this case it is necessary to add to the first cost of the former, the first cost of all the pusher engines needed, plus the capitalized value of the annual cost of their operation and deterio- ration, and compare the sum with the first cost of the latter. Moreover when figuring the annual cost of operation, it is necessary to include therein the annual expense due to delay of trains caused by stopping, attaching the pushers, and regaining speed. Geographical Conditions The layout of a bridge is sometimes influenced to a certain extent by its geographical location, because a structure suitable for the heart of a city might not be appropriate in a country district, and vice versa. Generally the variation involved would be a question of aesthetics, or possibly one of flooring, for sometimes it is necessary to cover over the deck of a railroad bridge so as to permit it to take care also of highway traffic. In mountain- ous districts where the transportation of large, heavy pieces is either very expensive or altogether impracticable, the layout would be governed by this condition. 120 ECONOMICS OF BRIDGE WORK Chapter XV Commercial Influences The principal commercial consideration that will affect the layout of a bridge is the amount and character of the traffic of which it will have to take care. If there is a variety of traffic, such as steam railwaj', electric railway, wagon, and pedestrian, considerable attention must be paid to the question of how best to take care of all probable combinations of the different kinds. Much money can be saved for a chent by a bridge engineer W'ho knows how to handle the question; and much can be wasted by one who is not properly posted on this important subject. An indisputable proof of the correctness of the latter statement is furnished by the notorious case of a proposed bridge to cross the Second Narrows at Vancouver, B. C. In that layout three railway tracks were adopted where two would have served the pur- pose equally well, with the result that the estimated cost of the structure was increased about seven hundred and fifty thousand dollars, and the project, in consequence, was either killed or relegated for consummation to the dim and distant future. Property Considerations Property considerations sometimes have a far greater effect on the lay- out of a structure than is at all legitimate. For instance, in the case of the Northwestern Elevated Railroad of Chicago, engineered by the author in the early nineties, certain high prices for land caused the company to lay out such a crooked line as to interfere materially with the attainment of a satisfactory train velocity. Refusal of property owners to allow the con- struction of piers or pedestals on their land will often oblige an engineer to adopt an unduly long span, or even an entirely different type of construc- tion from the ordinary. Again, the necessity for occupying a certain city street will sometimes change entirely the character and layout of an approach to a bridge, and it might affect even the layout of the bridge itself. The method of crossing a railroad track at the entrance to a bridge might alter fundamentally the type of structure, a low bridge with an opening span being adopted if the crossing be at grade, and a high bridge with fixed spans if it be overhead. Public improvements sometimes cause material modifications of plans for proposed bridges; and even projected improve- ments with prior rights are liable to cause troublesome interference. The author has lately encountered obstructive opposition of this nature on a big bridge project. General Features of Structure The question of wh(>ther tluougli, deck, or half-through truss spans or girders are adoptt^d is one that will radically affect the layout, but mainly in tin; line of economics, because^ d(H;k structures in most cases involve a saving of expense in both substructure and superstructure, in that the DETERMINATION OF LAYOUTS 121 piers are shorter than those for through or half-through spans, and, gen- erally, the spans are narrower, thus causing a saving of metal in both the cross-girders and the lateral bracing. The clear headway required, especially for short spans, is likely to influence the layout more or less. The possibility of using buried piers and protecting the feet of the embanlonents near them by rip-rap will not only affect the physical appearance of the bridge, but also it will modify the economics of the crossing. . In case a bridge is to cross a navigable stream, the layout of spans will depend primarily upon whether a swing, bascule, or vertical-lift span is adopted for the opening. If a swing is employed, it will generally require an expensive draw protection, while for a bascule or a vertical lift some comparatively inexpensive dolphins, either with or without cheap fender- walls of sheathed piles, will suffice. The possibility of building an arch, a cantilever, or a suspension bridge instead of a simple-span structure would affect the layout in many ways — physically, aesthetically, and economically. Again, the material adopted for construction — whether masonry, con- crete, steel, or timber — will have a similar influence. The matter of shore protection is not likely to affect directly the layout for a bridge, although its use certainly does increase the total cost; but it might be the reason for shifting the crossing to a location where the bank is better protected by nature against scour. Finally, the layout is affected by the character of the approaches; for they may be of earth embankment, timber or pile trestle, steel viaduct, or reinforced-concrete girders or arches. Future Enlargement The possibility of future enlargement of structure ought to receive consideration; and if it be decided that it is at all probable, a study of the layout should be made so as to determine how best to accomplish such enlargement when the time comes for so doing. The points to consider are whether it will be best to build an entirely separate new bridge close alongside, or to put a double-track superstructure on the old, single-track piers by enlarging them or expanding their tops, or, at the outset, to put in large piers and build thQ superstructure in such a manner that the trusses can be doubled in the future. Again, it would frequently be good engineering to provide at first only the floor systems necessary to suffice for traffic requirements at the outset, but to design the trusses and substructure so that additional roadways and tracks can be added in the future when needed. Time Considerations The time allowed for completing the substructure or the superstructure or the whole bridge may affect the layout, for it is understandable that a 122 ECONOMICS OF BRIDGEWORK Chapter XV certain type of structure could be built in a certain limited time while another type of structure could not. Again, the length or shortness of the working season that is entirely free from danger of washout of false- work could be a sufficient reason for changing materially the layout — for instance, by necessitating pin-connected spans instead of riveted ones, or steel truss-spans instead of concrete-arch ones, or semi-cantilevering of certain spans instead of falsework erection throughout. Stream Conditions The various influences of the stream that is to be crossed are more potent than most other factors in affecting the layout. The high-water- and the low-water-elevations are important features in the designing of the piers; the amount and character of the drift determine the minimum vertical distance between high water and the bottom of the superstructure, and, therefore, aid in settling the pier height; and the amount and con- sistency of the passing ice constitute an important factor in the design of the piers, especially in respect to their length and the character of their end finish; and any increasing of the cost of the piers tends, for economic reasons, to lengthen the spans. The clear waterway required to pass the probable maximum flood will often settle the total length of structure; and it may result in raising the high-water mark that was determined in some other manner. The profile of the river-bed and the probable scour of the materials of which it is composed are likely to affect the layout, especially if the piers require expensive protection of mattress work and rip-rap to check the said scour. The frequency and extent of the floods will influence the cost of building the piers — hence also the determination of the layout — as will also the questions of rise and fall of tides, velocities of the passing water, reversal of current, and the existence or possible future building of levees. A most important factor is the possibility of the permanent shifting of the channel from one side of the river to the other. If this possibilitj'' exist, one of three things must be done, viz. : first, two movable spans must be provided; second, some effective method of retaining the channel in one position must be arranged for; or, third, the design must be so made that any fixed span of the structure may at any time be converted into a vertical-lift span. Foundation Considerations Important also in the determination of layout are the character and the depth of the substructure foimdation. The deeper the piers have to go the longer will be the economic lengths of the spans. Again, the more difficult it is to penetrate the materials overlying the bed-rock or final foundation, the greater the cost of the piers, and the longer the economic spans. The ultimate depths to foundation and the materials to be penc- DETERMINATION OF LAYOUTS 123 trated determine what process of sinking to adopt; and as the cost of the substructure depends upon the said process, so also will the layout. Navigation Influences The influences of navigation that are likely to prevail during the time of the contractor's operations may be of such moment as to affect more or less the design and the layout of the structure; although this is not very likely. Again, the possibility in the future of greatly augmented river- traffic may influence the type of movable span adopted. Construction Facilities The availability or otherwise at the bridge site of sand, gravel, concrete- stone, a machine shop for repairs, and a reliable source of supplies for the work and workmen, the accessibility or the contrary of the site from the nearest railroad depot or siding, the length and difficulty of wagon-haul or other means of transportation of materials and supplies, the facilities for securing and retaining labor, and the availabihty of supplies of timber and pihng all affect greatly the cost of the substructure and to possibly a somewhat less degree that of the superstructure — hence also the layout of spans and piers. Erection Considerations The difficulties that may be anticipated for erection, and the method thereof finally adopted, whether by falsework, cantilevering, semi-canti- levering, or flotation, are important factors affecting the layout of the structure, as are also the questions of the maintenance of traffic and the replacement of an existing bridge. J^sthetics Too often the question of aesthetics is totally ignored; but when it is given proper consideration, it may cause modifications in span lengths, truss dimensions, and shapes of piers. How much extra money it is legitimate for a bridge engineer to spend for the purpose of beautifying a structure is a mooted point. It depends greatly upon the designer's appreciation of the beautiful in nature and in art, as well as upon the elasticity of the client's purse and the extent of the influence upon him exerted by his consulting engineer, also upon the location and surroundings. Generally speaking, the best layout for aU the other ruHng causes is the best also for aesthetic reasons; but there are cases when a little extra expenditure of money, time, and brains will secure great improvement in appearance; and in such cases the beautifying of the construction should, if possible, be accomplished. 124 ECONOMICS OF BRIDGEWOEK Chapter XV Maixtexaxce and Repairs The cost of maintenance and repairs as well as that of operation may sometimes be a vital consideration affecting the layout of a structure. For instance, when the Jefferson City highway bridge over the Missouri River was about to be built, the bridge company, in spite of the author's forcible remonstrance, let the contract for the structure on the basis of a high bridge with a long and expensive timber trestle approach. Later they were convinced that the annual expense of maintaining the said trestle would be so great as to consume more than the total net income from traffic receipts; hence they had to change to a low bridge design. Theoretical Economics From time to time an engineer encounters a bridge problem in which the controlling factor in the layout determination is really that of economics, and then he is happy; for, comparatively speaking, the case is a smiple one. A case of this kind occurred in the author's Canadian Northern Pacific Railway bridge across the North Thompson River, near Kamloops, B. C. The structure consists of a number of deck, plate-girder spans, one of which is lifted so as to permit of the passage of small river steamers at certain high stages of water. The requirements of aesthetics often conflict with those of economics; for it would not look well to let the span lengths change backward and forward, perhaps, to suit the vagaries of an unusual bed-rock profile; hence it is best in many cases to compute the economic span length for average conditions of pier cost and to use one length instead of several. It will generally be found that such an arrangement does not involve any extra expenditure worth mentioning when the cost of structure for that layout is compared with that for the truly economic one. The question of economics, however, cannot be finally settled by adopting simply that structure for which the initial cost is a minimum; because, as pointed out previously, the truly economic bridge is the one for which the sum of the first cost and the capitalized annual cost of operation, maintenance, and repairs is a minimum. As a conclusion to the general subject under discussion, in order not to discourage young (engineers, it might be well t(i state that any designer who, when deterniiiiing the layout for any largo and impoi-fant ])i'idge, can and does giv(^ full and (lu(> consideration to all the fai'tors treated in this chapter, is truly worthy to be ternuxl an ex])ert bridge engin(H>i'. CHAPTER XVI ECONOMICS OF LOADS AND UNIT STRESSES The determination of the live loading for any proposed structure is an economic problem of prime importance; and it often involves the employ- ment of engineering talent of the highest order. As a rule, that loading should be made large enough to take care of the greatest moving loads that may reasonably be expected to come often upon the structure during its lifetime; and as the latter for a well-designed, modern bridge is of indefinitely great length, the problem is by no means an easy one to solve. It must be recognized that the occasional application of a load exceeding by 25 per cent, or even more, the one used in making the design, will do no harm to the structure, but that when the excess reaches 50 per cent and is applied often the condition begins to become serious. While it is right and proper for an engineer to act with precaution by assuming the live load great enough to meet all likely contingencies, it would be uneconomic to attempt to provide for improbable or impossible loadings. Again, while it is feasible to subject a short span to a very heavy loading, it is not so in the case of a long one; and the longer the span the smaller is the chance of its ever having to carry an abnormally great live load. This remark applies more forcibly to highway bridges than to steam-railway structures; although it undoubtedly holds good to a certain extent for the latter, because it is very seldom that long trains are composed entirely of the heaviest kinds of loaded cars. About the only exception to this rule is in the case of a structure on a railroad carrying long trains of fully-loaded ore-cars or coal-cars. There is one point in connection with highway live loadings that is of importance, viz., that all new highway bridges should be proportioned to carry heavy trucks. The concentrated loads caused by these are so great that the old-fashioned wooden-joist floors will not be able to carry them. There is no telling how far from home these exceedingly heavy auto- trucks will travel, so that no out-of-the-way highway bridge will be safe from their invasion. Again, it must be remembered that auto-truck loads are rapidly on the increase; hence one should be hberal in his assumptions for this feature of the live loading. In respect to live loading in general, it seems almost unnecessary to mention that the amount thereof decreases slowly with the span-length. In steam-railway structures this is primarily because the effect on the total span-length of the greater weight per foot of the coupled standard locomo- 125 126 ECONOMICS OF BRIDGEWORK Cilipter XVI tives, as compared with that assiuned for the loaded cars, diminishes as the span-length increases; but in highway bridges the lessening is due to an application of the theory of probabilities. For the electric-railway loading the diminution in the equivalent hve load per lineal foot exists only when the length of span is greater than the assumed total length of train, and the greater the difference in length the greater the said diminution of load- ing per lineal foot of span. On pages 110 to 116, inclusive, of "Bridge Engineering" are given curves of equivalent uniform loads for trains of two, three, four, five, and six electric-railway cars and for aU the classes of loading from 15 to 40. These are carried out to a length of only 600 feet; and in case of longer spans it would become necessary to lengthen them either accurately by computation or approximately by visual extension. For ordinary railroad bridges the determination of the proper hve load to adopt is generally a simple affair, because the company is likely to have a standard of its own; but sometimes it may be advisable to depart from this, in order to provide for some unusual condition or complication. For highway bridges, though, it is a different matter, because the amount and character of the traffic will depend greatly on local conditions; and, consequently, the size of the loading is a question of judgment. In exercising it, one should look to the possibility of a material increase in the weights to be transported; and should be governed accordingly. The standard steam-railway loadings given in Chapter VI of "Bridge Engineering" are still sufficient for maximum requirements, and it is not likely that the greatest (Class 70) will ever be materially exceeded, unless some fundamental improvement be made in the character of railway roadbeds. The distribution of weight on the axles of the locomotives is gradually being changed, but the weight thereof per lineal foot of track does not appear to be augmenting to any great extent. The heaviest live loads for electric railways given in the aforesaid chapter have not yet been reached, except in the case of electrified steam- railroads; and these are not treated as real electric railways, as far as bridge loadings are concerned. Ordinarily, Class 25 is heavy enough for the street-railway live-loads on highway bridges; but sometimes it is advisable to proportion for Class 30, in order to provide for future heavy suburban cars. Classes A, B, and C for highway loadings are sufficiently heavy, even if it be possible to crowd vehicles and pedestrians so close together as to cause the actual loadings to exceed them; because, when much crowding occurs, the speed of travel is materially reduced, and then the effect of impact may practically be ignored. Class A loading is so great that, for comparatively long spans and wide decks, it may be used to cover the average loading over the full width of deck from electric-cars, vehicles, and pedestrians — and this applies in nearly all cases to suspension bridges. But in that type of bi-idge it nmst be remembered that for the stiffening trusses the equivalent uniform live load per lineal foot of structure must ECONOMICS OF LOADS AND UNIT STRESSES 127 be taken for about four-tenths of the span-length and not for the full length, as is the case for shnple spans. In cantilever bridges judgment must be used in determining the lengths for equivalent uniform loads for the different portions of structure. For instance, in Type-A cantilever, shown in Fig. 12a, for the suspended span its total length is to be used; for the cantilever arms the sum of the length of the suspended span and that of the portion of the cantilever arm that is loaded for maximum stress on the member considered; and for the anchor arms the total length of the loaded portion of one such arm for direct loading and that of one cantilever arm plus suspended span for reverse loading. A skilful bridge designer can often legitimately economize in his work by making a careful study of the live-load question and cut- ting down the loading as hereinbefore indicated. Similarly a study of the question of impact allowance and the utilization of the very latest information thereon will result in a certain amount of economy. For instance, since "Bridge Engineering" was written, the author has found it advisable to modify the impact allowances recom- mended in Chapter VII thereof in the following particulars: First. For electric-railway loads use the same impact as for highway loads. This modification is based upon some late experiments by Prof. Turneaure. Second. When a reinforced-concrete base is used for the pavement of a highway bridge with similar slabs for the footwalks, the impacts given may be reduced twenty-five (25) per cent. Third. For reinforced-concrete arches and girders, without earth filling, the impacts may be reduced fifty (50) per cent. Fourth. For earth-filled, concrete arches, they may be reduced seventy- five (75) per cent. The determination of the width of deck that it is best to employ is an economic question of salient importance. A narrow roadway tends to induce slow travel, owing to the necessity for reducing the speed of automo- biles in narrow places so as to avoid collision. For two lines of travel at high speed a width of twenty-two feet is advisable, although one of twenty feet is often considered sufficient because it is practicable to pass most auto-vehicles on a width that is two or three feet less. There are many bridges in country districts that are only eighteen feet wide and some as narrow as sixteen feet ; but these do not meet with the approval of automo- bile drivers, because a load of hay will almost block the structure — besides, when one is driving at high speed, he does not like to be compelled to slow down when he is approaching a bridge upon which there is another vehicle. A thirty or thirty-two-foot width of main roadway is better than one of twenty or twenty-two feet, in that it will permit a fast vehicle to turn out and pass a slowly-moving one; but there is always the danger of run- ning into an automobile of the other Hne that is trying to accomplish the same purpose. A roadway of forty or, preferably, forty-two or even forty- 128 ECONOMICS OF BRIDGEWORK Chapter XVI four feet in the clear between curbs will take care nicely of four lines of automobiles, and the middle twenty feet thereof may carry a double track for an electric railway. From the viewpoints of both economy and pubHc convenience it is better to pass at once from a two-line-travel deck to a four-line-travel deck, because a width great enough for only three hues is unsatisfactory in that, as before indicated, it offers to reckless drivers a fine opportunity for head- on colhsion — and, again, it is not as suitable for high speed as a wider struc- ture. It is true that in the case of a total break-down it has a decided advantage over the two-line-travel deck, permitting vehicles to pass around the obstruction, but that is not sufficient reason to warrant its adoption. Footwalks are often made much wider than necessary, but sometimes too narrow. The minunum width should be five (5) feet, which will just permit two people to wallc abreast and to carry umbrellas. Any smaller width would be uncomfortable, and one a foot wider would be better. A width of eight (8) feet is generally sufficient for all requirements, but some- times ten (10) or even twelve (12) feet are called for. If travel in both directions is permittted on the same footwalk, it should not be made less than seven (7) feet wide, and preferably nine (9) or ten (10), but it is seldom good poUcy to allow such traffic, because the pedestrian travel will be faster if it is always kept to the right-hand side of the structure. If a bridge is very long, it is not hkely that there will be much pedestrian travel over it, unless there be some special inducement such as beautiful scenery or cool breezes in hot weather, consequently the omission of side- walks, either entirely or temporarily, becomes an economic question of some importance. Sometimes, however, the obtaining of a charter for building the bridge is conditioned upon putting on sidewalks; and in that case the only economy practicable would be to obtain from the authorities per- mission to provide for their future addition and to omit them temporarily until the development of traffic indicates their necessity. In very long bridges it is economical to reduce the sidewalk width to the absolute mini- mum of five (5) feet, owing to the small number of people that are likely to pass over the structure on foot. When a steam-railway bridge has to carry electric-railway cars as well, it is often economic to adopt the expedient of gauntleted tracks, i.e., sepa- rate lines of rails for the electric railway lying quite close to the steam- railway rails and with no connection thereto, switches being omitted and the steam-railway rails being cut so as to permit the wheels of the elec- tric-railway cars to cross them on a frog. This expedient obviates the necessity for increasing the railway live loads in order to provide for the electric-railway traffic. The cjuestion of what arrangement of decks to adopt for the acconmio- dation of several kinds of traffic is an economic problem that sometimes arises in a bridge engineer's practice. It has lately come up in the author's ECONOMICS OF LOADS AND UNIT STRESSES 129 in a case where a double-track, steam-railway bridge had to carry in addi- tion a double-track electric-railway, wagon-ways, and footwalks. The choice lay between a double-deck structure with the steam railways below, a combined double-track electric-railway and wagon-way above between trusses, and footwalks outside of the wagon-way; and a single-deck struc- ture with the double-track steam-railway between trusses as before, a combined single-track electric-railway and wagon-way on cantilever brack- ets outside of each truss, and a footwalk outside of each wagon-way. For reasons unnecessary to state, the gauntleted tracks between trusses for the electric railway were barred. The comparison was hardly a fair one, because the single-deck layout provided facilities superior to those afforded by the other layout in relation to rapid transit, — there being two roadways of twenty-two feet each instead of one roadway of thirty feet — besides avoiding a climb of some twenty-five feet. Wliile the cost of the main spans was greater for the single-deck structure than for the double-deck one, on the other hand there was a saving in the lengths and costs. of the approaches. It is impracticable to make any general statement of com- parative costs or advantages of these two types; and each case as it arises, will have to be worked out by itself as a special economic problem. More- over, one layout or the other, irrespective of cost, will be preferable from the point of view of service or accommodation, hence this feature will have to be given serious consideration. As a rule, bridges for carrying both railway and highway traffic are located in or near large cities, although an occasional structure of this kind is found in country districts. The principal advantage of this type of bridge is the saving in first cost, and its principal disadvantage is a reluc- tance to cross over it on the part of timid drivers, whose horses may be frightened by the trains. The saving in first cost of a combined railway and highway bridge, as compared with two separate bridges for railway and highway traffic, is considerable, because the piers for the combined bridge are but little, if any, more expensive than those for the railway bridge, and because the extra metal for the super-structure of the former in comparison with that of the latter is very much less in weight than the metal required for a separate highway bridge. The prejudice against combined bridges on account of danger is almost wholly unfounded, for horses soon become accustomed to railway trains, and, when screens are employed to hide the latter, but little trouble is experienced on account of frightened animals. These screens may be made either slatted or solid, the former offering less resistance to the wind, and the latter being the cheaper. Moreover, auto- mobiles have almost entirely displaced horses in highway traffic. The advent of the electric railway has somewhat complicated the ques- tion of designing combined bridges, for now it is often necessary to accom- modate all kinds of traffic on the same structure. Combined bridges may be divided into the following classes : 1. Structures having a single deck for all kinds of traffic, the railway 130 ECONOMICS OF BRIDGEWOEK Chapter XVI occupying the center of the bridge, and the electric railway lying close to one truss. 2. Structures having a single-track railway at the middle, a narrow foot- walk on each side thereof inside of the trusses, and cantilever brackets out- side of the latter to carry roadways and electric hues. This arrangement may be varied by running the electric cars over the main railway track, thus leaving the wings free for vehicular traffic. 3. Structures having a double-track railway inside of the trusses, with long cantilever brackets outside carrying wagons and electric lines next to the trusses and pedestrians outside. This arrangement may be varied, as in Case 2, by carrying the electric trains on either one or both of the main railway tracks. 4. Structures having a double-track railway inside of the trusses, with short, cantilever brackets for wagon and electric-railway traffic outside, and either a single passageway overhead at the middle for pedestrians, or two passageways therefor on overhead brackets outside of the trusses. As before, this arrangement may be modified by running the electric trains over the main railway tracks. 5. Double-deck, single-track structures carrying a railway train on one deck and vehicles and pedestrians on the other. If electric cars also are carried, they should generally use the railway track on account of the nar- rowness of the bridge; but by putting the railway below and using canti- lever brackets above, the electric cars may share the wagon-way and run over either one or two tracks. When the electric cars and the vehicles occupy jointly the upper deck, it is generally best to carry the pedestrians by cantilever brackets on the lower deck, as the structure might be too narrow to warrant caring for them above by footwalks outside of the joint wagon and electric car roadway and because permitting them to use the said joint roadway would be too hazardous. 6. Double-deck, double-track structures carrying railway trains on one deck and vehicles, electric trains, and pedestrians on the other, or with the electric trains using the steam railway tracks. The vehicles and electric trains may either occupy the same roadwaj^, or the former may be carried on cantilever brackets, leaving the middle portion of the deck for the latter. In such a bridge the footwalks should be on cantilever brackets, either above or below, outside of the other roadways. In double-deck structures where the steam railroad is below, it is neces- sary to use every precaution for keeping the locomotive fumes away from the upper deck, as smoke rising through the floor frightens horses even more than does the train itself. Moreover, smoke is exceedingly disagree- able to everybody passing over the structure. Again, the question of protecting the highway floor from being set on fire by sparks from locomo- tives must be satisfactorily solved in this (•om])inati()n. Class No. 1 is the cheapest possible kind of combined bi-idge, and at the same time the most unsatisfactory, for a\ hen a railroad train is about ECONOMICS OF LOADS AND UNIT STRESSES 131 to pass over the structure all vehicular and electric-railway travel must be kept off, and because pedestrians must look out sharply for their safety when on the deck with a railway train crossing. Their danger is really greater, though, when an electric train is passing a team or teams. The least allowable clear width of bridge for this class of structure is twenty feet, the electric cars running on a third rail and on one of the rails of the main railway. Class No. 2 is a very satisfactory type of structure. The author has designed and built several bridges of this kind, the largest of which is the Combination Bridge Company's bridge over the Missouri River at Sioux City, Iowa. It consists of two draw-spans of 470 feet each and two fixed spans of 500 feet each, besides the deck approach spans, the distance between central planes of trusses being twenty-five (25) feet. Class No. 3 is also a satisfactory type of structure. The author once built a large bridge of this type, viz., the one across the Missouri River at East Omaha, Nebraska. This class of structure involves very heavy metal- work; but it is not uneconomical. Class No. 4 is an unusual type, and is not likely to be called for very often, although the author has had occasion to figure on bridges of this kind. Class No. 5 gives a satisfactory distribution of traffic, as was proved by the author's bridge over the Fraser River at New Westminster, British Columbia. In this the steam railway and the electric cars occupy a single track on the lower deck; and vehicles and pedestrians use in common a sixteen (16) -foot clear roadway on the upper deck. Early in 1908 in preparing a design for a combined bridge to carry a rail- way, a street-railway, wagons, and pedestrians over the Second Narrows of Burrard Inlet at Vancouver, British Columbia, the author evolved a rather novel method of dividing the traffic. The bridge was to be built at first to carry only the railway and the street-railway, but provision was to be made to take care of wagon and pedestrian traffic in the future. The distance between central planes of trusses being restricted from motives of economy to the least consistent with the Dominion Government's requirements for clear roadway — in this case nineteen (19) feet — it would have been improper construction to put twelve (12) foot roadways outside of the trusses and six (6) foot sidewalks outside of these;' for such an arrangement would make each cantilevered portion of the deck wider than the distance between trusses, while good practice does not permit it to exceed two-thirds thereof. As the clearance above high water was ample on account of there being an overhead crossing of the Canadian Pacific Railway tracks at the south end of the structure, it was suggested to suspend the footwalks from the canti- lever brackets that carry the roadways. This would necessitate small roofs to protect pedestrians from the roadway drippings. The arrange- ment described was shown by cost estimates to be exceedingly economical, but it was objected to on account of its interfering with the running of certain small craft under the swing span. 132 ECONOMICS OF BRIDGEWORK Chapter XVI Class No. 6 represents a veiy good arrangement which can be modified to suit nearly any conditions of combined traffic. A good example of this type is the author's bridge over the Missouri River at Kansas City, Mo., owned by the Union Depot, Bridge, and Terminal Railroad Company, and known as the Fratt Bridge. In designing combined bridges of all classes except No. 1, a considerable economy of metal may be effected legitimately by keeping the total live load for trusses as low as is proper with reference to the theory of probabili- ties. For instance, in Class No. 2 or Class No. 5 the live load for trusses may be determined by adding to the equivalent uniform live load for the steam-railway tracks, given by the diagram in Fig. 6e of "Bridge Fngineer- ing," a much lighter highway floor load per lineal foot of span than that pre- scribed in the specifications; because when the greatest train load is on the bridge, the chance of having simultaneous^ a heavy highway live load is very small. The longer the span the smaller may the live load per square foot of floor be taken when finding the total live load for the trusses. Again , in Classes No. 3 and No. 4 it would be legitimate to take the truss live load per Kneal foot for the railway equal to twice the car load per lineal foot, and add thereto a small highway live load as in the last case. Finally, in Class No. 6 in case of a four-track bridge with cantilevered highways and foot- walks, it would be proper to assume the live load for the trusses equal to the sum of the car loads per lineal foot on the four tracks and ignore entirely the vehicular and pedestrian loadings; for the greatest probable live load from all classes of loading would never exceed the said four car loads. This reduction of live load, however, can readily be carried to extremes, as was the case in the jBrst accepted design of the great cantilever bridge over the St. Lawrence River near Quebec, and as is likely to be the case whenever the preparation of the specifications for a bridge is left either directly or indirectly to the contractor who is to build the structure. Good judgment, uninfluenced in any way by considerations of personal gain or by motives of false economy, should rule in the estabUsliment of the hve loads for the trusses of "combined" bridges. It is very seldom that the designing engineer of a bridge has an oppor- tunity to economize by the manipulation of unit stresses, because ordinarily he employes standard bridge specifications; and truly it is better for him to do so, for the reason that this question has already been very thoroughly threshed out; but, as will be explained presently, in certain structures, such as trestles, he may have an opportunity to employ his judgment in the determination of unit stresses for certain unusual but possible combina- tions of loads. In modern specifications the aim is to liavo a fixed unit stiess for each kind of matei-ial for all l)ut oxtraoi-dina-ry ('()m1)iiuitions of loads. In metals it is generally proper to place the ordinary intensity of working stress at one-half of the elastic limit of the material; but with high-alloy steels it ECONOMICS OF LOADS AND UNIT STRESSES 133 should not exceed one-third of the ultimate strength. This restriction applies mainly to heat-treated eye-bars. Some engineers deem it good practice on the score of economy to use high-carbon steel for reinforcing-bars; but the author is opposed to this for two reasons; first, such metal is liable to crack when being bent cold in the field; and, second, a high intensity of working stress on the bars tends to permit the formation of cracks in the concrete in their vicinity. Very infrequent loads will permit overstresses, or, in other words, en- croachment on the factor of safety. A future increase of live loads will affect differently different portions of a bridge. This is sometimes allowed for by reducing the unit stresses on certain members; but it is better to design the structure so that an increase of loading of fifty per cent will not overstress any member more than fifty per cent. Some designers specify abnormally heavy loadings and correspondingly greater unit stresses. This gives well balanced structures; but the method is illogical, and it has a tendency to deceive. If such a practice were to become established, there would be a liability on the part of inexperienced engineers to employ high unit stresses with normal loads, which would be dangerous or at least ultimately uneconomic. In very-long-span bridges the selection of live loads and unit stresses is of extreme importance ; because a small legitimate increase in unit stresses or a small reduction of loading may result in a comparatively large saving in cost, due to decrease of dead load. If, for the sake of either a real or an imaginary economy, an increase in unit stresses must be adopted, it is better to make it frankly in the main members, where the danger from overstress is least ; and then the fact of the existence of this condition will be apparent. But if skimping were done in the detailing, there might easily be developed weaknesses of such a serious nature as eventually to cause disaster. Again, more money can be saved by reducing the sectional areas of main members than by trimming the details. In the designing of ordinarj^ truss bridges, the computer has practically no choice as to how the various stresses which he figures are to be com- bined, because the standard specifications by which he is governed indicate the method very clearly; but in structures unusual as to either tj^pe or magnitude and in trestles the designer should have some option in making the combinations. No hard-and-fast rule can well be given to cover all cases of spans of unusual size and character; except to state that the engineer should employ his best judgment in relation to possibilities and probabilities, stressing the standard amount for combinations that are likely to occur and increasing the intensities of working stresses as the combinations considered become more and more improbable of realization, up to the limit of an excess of fifty (50) per cent. In bridges proper, with the exception of arches having less than three hinges, the only unusual combination is that of the ordinary stresses and the 134 ECONOMICS OF BRIDGEWORK Chapter XVI wind stresses, to allow for which standard bridge specifications permit an increase of thirty (30) per cent over the regular intensities of working stresses; but in trestles there may be combinations of Hve-load, impact, dead-load, centrifugal-load, wind-load, traction-load, and temperature stresses; hence the computing of some of the sections for these structures is a complicated matter. As stated in the specij&cations for designing given in Chapter LXXVIII of "Bridge Engineering," the columns of steel trestles are to be propor- tioned thus: First. For Hve load, unpact, centrifugal load, and dead load, with the usual intensities. Second. For Hve load, impact, centrifugal load, dead load, and wind load or traction load, with an excess of thirty (30) per cent over the usual intensities. Third. For live load, impact, centrifugal load, dead load, wind load or traction load, and temperature, with an excess of forty (40) per cent over the usual intensities. Fourth. For hve load, impact, centrifugal load, dead load, traction load, and wind load, with an excess of forty (40) per cent over the usual intensities. Fifth. For hve load, impact, centrifugal load, dead load, traction load, wind load, and temperature, with an excess of fifty (50) per cent over the usual intensities. The preceding combinations and excess percentages of intensities were adjusted after much deliberation; and their pubhcation in "Bridge Engi- neering" was the first complete exposition of the matter ever made in print. In the preparation of specifications theretofore, the question had been deemed too comphcated for written treatment and had been left for settle- ment entirely to the judgment of each individual designer. A study of the preceding adjustment will show that the greater the improbability of any combination the greater the intensity of the working stress adopted. The worst combination (which, really, never could occur) would stress the metal up to three-quarters of its elastic-lhnit, which is perfectly safe for an occasional loading. It is much better to take into account all possible combinations and to stress the metal high for the worst summation than to ignore such combinations entirely and trust to luck that they will never occur, as is too generally done in trestle designing. On the other hand, though, it would be extiavagant practice to combine all the possible stresses and use either the ordinary intensities or even these increased by the usual thirty per cent allowance for the inclusion of wind. Trestle proportioning hith(M-to has been rather unscientific, and it is to be hoped that it will soon b(; improved. When all is said and done, however, it is impi;i(rti(';il)](' to eliminate entirely individual judgnK^it in the designing of high steel trestles, because in some cases local considerations will i)ermit of the retluction or even the ignoiing of certain stresses. For instance, ECONOMICS OF LOADS AND UNIT STRESSES 135 when a trestle is situated near the middle of a sharp curve or near the apex of two heavy, rising grades, it would be bad judgment to assume a high velocity of train when finding the stresses due to centrifugal loading. The combination of stresses in cantilever bridges and in arches is not so compHcated as it is in trestles; but it is to be noted that the sections of members do not need to be increased because of erection stresses, unless such total stresses (including those from wind under an assumed probable pressure of ten (10) or fifteen (15) pounds per square foot) raise the inten- sities on the computed sections above those specified for a combination of the usual loads with wind. In summing up stresses care must be taken to add only those that can act simultaneously, because some stresses can never occur together; for instance, live load and erection stresses in cantilevers and in arches erected by cantilevering, and hve load and wind stresses in highway bridges. This word of warning seems almost unnecessary; nevertheless a careless computer is liable to smn up stresses that cannot act together, as the author knows from personal experience. At the present time there is a division of opinion among bridge specialists concerning the combination of stresses of opposite kinds, some of them going so far as to ignore altogether the effect of reversing stresses. Until good reason is offered for making a change, the author intends to adhere to the method which he advocates in "Bridge Engineering." It is as follows: If the cause of the reversal be wind, the effect of reversion is ignored, because not only is there generally a long interval between reversals, but also the maximum wind stress on any piece is of infrequent occurrence. Reversals due to live loads combined with impact are divided into two classes; first, those which occur in succession during the passage of a live load over the structure, and, second, those which are caused by different loadings. In the first case, each of the two kinds of stress is to be increased by seventy-five (75) per cent of the other, then the section required for each combination is to be computed and the larger of the two adopted. In the second case the procedure is similar to that just described, except that the percentage to be added is fifty (50) instead of seventy-five (75) . The author does not deny that it might be perfectly safe to reduce these per- centages to fifty (50) and twenty-five (25), respectively, but he is decidedly averse to ignoring altogether the effect of reversion. In any case it would require some exceedingly strong evidence to induce him to change his method of computing the number of rivets for connecting main members, viz., to add together without any reduction the two stresses of opposite kinds and proportion for the sum. Stress reversal is certainly harder upon the connecting rivets than upon the members themselves which they join. After all, this controversy about the proper allowance for reversal of stress may amount to much ado about nothing, because, as pointed out in Chapter XI, the difference in the weights of metal in two continuous-truss 136 ECONOMICS OF BRIDGEWORK Chapter XVI spans of 775 feet each, when for all reversals an addition of seventy-five (75) per cent of each stress to the other stress was made, and when the effect of reversion was entirely ignored, was only two and a half (2|) per cent. Of this one and a half (H) per cent were due directly to the increase in the sections of the pieces in which reversion occurred, and one (1) per cent to the augmented dead load. Such being the case, and in view of our Imiited knowledge concerning the wearing effects of stress reversal, it seems hardly worth while at present to make any change in the practice prescribed in ''Bridge Engineering." On the other hand, though, to be perfectly fair, it should be pointed out that reversal of stress may have a greater effect on some other kinds of bridges, such as arches, than it does on continuous- truss structures. Until the appearance of the January, 1920, issue of the Bulletin of the American Railway Engineering Association, no writer of bridge specifica- tions, as far as the author knows, had ever attempted to specify intensities of working stresses for combinations of Hve and dead load stresses with secondary stresses. In the Report of "Committee XV — on Iron and Steel Structures" (of which, by the way, the author is a member), published in that issue, there appears the following clause, numbered 47 : Secondary Stresses: Designing and detailing shall be done so as to avoid secondary stresses as far as possible. In ordinary trusses without subpaneling, no account usually need be taken of the secondary stresses in any meml^er whose width, measured in the plane of the truss, is less than one-tenth of its length. Where this ratio is exceeded, or where subpaneling is used, secondary stresses due to deflection of the truss shall be computed. The unit stresses specified in Article 38 may be increased one-third for a combination of the secondary stresses with the axial stresses. This allowance of thirty-three and a third per cent applies only to com- binations of live load, centrifugal load, impact, and dead load with second- ary stresses; but if other loadings, such as wind loads, traction loads, and temperature effects, are added to the combination, the increment of inten- sity ought to be increased, according to the designer's judgment, up to a limit of fifty per cent. Th('i(! is an important (question now before the engineering profession for s(!ttlement, which, strictly speaking, is one of economics, viz.: the proper relation between intensities of working stresses for bridge members in tension and coin])ression. In the author's opinion, there is no valid r(;as(>n for the drastic cut in compression intensities made of late in bridge specifications hy seveial of 1 \\v leading technical societies. Concerning this question h(; wrote b)r tlie Jan. IG, 1919, issue of Engineering Neivs Record the fcjllowing communication: Tlio report of the Committee on Column Tests of the American Society of Civil EngiiKMTH aiipoMTs to hav(i caused som(^ fright among ])ridgo designee's; for I notice th;i,t the Engineering Tnstifute of Cnnada has lately puhlisluHi a "Ceiiernl Siiecification for Stcicl Rail\v;iy Bridges" in which the unit stress for columns is given by the formula, 7> = 12,000 -n.3 (//r)2, ECONOMICS OF LOADS AND UNIT STRESSES 137 in which Z = the unsupported length of the column in inches and r = its least radius of gyration in inches. This is quite a sudden jump from the old standard formula, p = m,000- 60 l/r The -change indicates one of two things : Either that hitherto we have been over- stressing compression members 15 to 25 per cent, or that there is going to be wasted a vast quantity of metal in the future. Moreover, in making such a sweeping change in the compression formula, the writers of the Canadian specifications were not consistent, because in Clause 47 they allow for the compression flanges of beams an intensity of 16,000-200 i/&. In the case of railway stringers l/b is generally in the neighborhood of 10; hence the intensity of working stress is about 14,000 lbs. As b is equal to about 4.5 r, for l/b = 10 we shall have ^/r = 45. Substituting this in the Canadian column formula gives p = 12,000'-0.3 (45)2 = 11,400 lbs. In the case of one compression member of a bridge, it appears to be legitimate to stress the metal up to 14,000 lbs. per square inch, and in another up to only 11,400 lbs. per square inch, a difference of 23 per cent. And there is no valid reason for stressing differently a strut which forms a part of the top chord, of a truss and a strut which forms a part of the top flange of a beam. ' 'Consistency, thou art a jewel!" If the correctness of the formula for compression flanges of beams be conceded — a formula which, for a dozen years or more, has been one of the clauses of the American Railway Engineering Association's standard bridge-specifications, and which the Engi- neering Institute of Canada has appropriated without change — and if it be granted that b is generally equal to about 4.5 r — why should not the equivalent formula, p = 16,000- 45 Z/r, apply in general to struts with fixed ends? Be it noticed that this formula gives higher results than does my old formula, 73 = 16,000-60 Z/r. The American R,ailway Engineering Association is getting ready to trim down materially its old intensities for steel struts, although not to the extent that the Engi- neering Institute of Canada has done.* What aggravates the effect of this proposed decrease of compression intensities is that, simultaneously therewith, the American Railway Engineering Association is contemplating increasing its tensile intensity of working stress from 16,000 lbs. to 18,000 lbs.; and other specification writers are advising that it be made as high as 20,000 lbs. * The 1920 A. R. E. A. bridge specifications permit the following intensities of working compressive stresses : I Struts 15,000-50 - but not to exceed 12,500 lbs. r I Flanges of girders 14,000-200 -. b The previous strut formula of the A. R. E. A. was 16,000—70 — ; hence the new r I formula gives lower results when — is less than 50 and higher results when it is greater. 138 ECONOMICS OF BRIDGEWORK Chapter XVI To an outsider it must look as if the bridge engineers of this country were losing their heads! The compression tests that started the present wave of apprehension did not have governing conditions corresponding properly to those of actual truss-members; hence I would suggest that, before the bridge engineers of America take the drastic step of assuming steel in compression to be only 60 or 70% as strong as the same material in tension, some really practical tests of struts be made under conditions corresponding to those in actual structures. Such a series of tests would cost considerable money; but, if the Bin-eau of Standards at Washington were to indorse the suggestion to make them, it ought not to be at all difficult to obtain from Congress an ample appropriation for the purpose. The method of conducting these tests that I have in mind is this: Let there be built a five-panel, riveted-truss bridge of about 100-ft. 3pan; let the middle panel-lengths of the top chords thereof be made decidedly weaker than all the other portions of the structure; and let a uniformly-distributed live-load be applied at the panel-points by hydraulic pistons. All portions of the structure, including the two weak members, should be scientifically detailed, so that failure will inevitably take place in the main portions of the weak struts and not in the details thereof, and so that the bridge can be used for a long series of tests to destruction of the said mid- panel lengths of the top chords. The weak members should be attached to the con- necting plates with an ample number of rivets to develop the full strength of the test pieces; and these rivets should be removed carefully after each test to destruction is completed. Of course it would be entirely practicable to vary the value of Z/r in the different tests, provided that the attachment of the test-strut be not made eccentric. There should be a supporting platform beneath the span to prevent its falling any material distance when failure occurs. By adopting a weak vertical post instead of a weak panel-length of top chord, and by loading (at the elevation of the latter) three panel-points only, a series of tests could be made on vertical posts. A similar series could be carried out on the inclined end posts. A cheaper method than that just described, but not quite as satisfactory, would be to build a single truss, instead of the complete span, and steady it laterally but not vertically, and then to apply the test loadings directly above the top chord at the panel- points. A great advantage of the span tests as compared with the truss tests is that duplicate tests could be Tnade simultaneously on similar members. Moreover, the span tests would be in practically exact accord with actual conditions of loading, while the truss tests would not. By removing occasionally the test loading, the elastic limits of the struts could be ascertained through noting the absence or otherwise of permanent set. Experiments similar to those described could be made on a pin-connected span or a pin-connected truss so as to determine the strength of struts with hinged ends. In view of the immense amount of bridge manufacture and construction that is likely to be done in the United States within the next five or ten years, the making of this proposed series of tests is worthy of being considered a matter of national impor- tance. In order to elaborate the preceding communication, the author had his associate engineer, F. H. Frankland, Member American Society Civil Engineers, write another letter to Engineering News-Record embodying certain subsequent thoughts upon the details of the proposed series of experiments, which letter was published in the issue of March 6, 1919. It reads as follows: ECONOMICS OF LOADS AND UNIT STRESSES 139 With reference to the matter of formulae for steel columns, dealt with in recent articles and letters appearing in Engineering News-Record, the writer wishes to take this opportunity of drawing attention to the fact that existing column formulae are not founded on really proper tests, and that, therefore, engineers should not rest satisfied until such proper tests have been made, and, from the empirical rules deduced there- from, a really sound column formula has been evolved. No column experiments have yet been made which conform to actual conditions existing in modern bridges, as very few columns nowadays have hinged ends, and flat- end tests are likely to be very deceptive, because of corner bearing. The opinion expressed by Mr. Charles E. Fowler in his letter on page 343 of your issue of Feb. 13, 1919, to the effect that a straight-line formula is to be desired on account of its simplicity, is to be commended, as there is every probability that a satisfactory straight-line formula can be derived from proper tests. It is to be noted that some of the formula) given by Mr; Fowler in his letter use the {l/rY, this being a holdover from the old Euler formula, which was established for greater values of l/r than are used in practice. With reference to Dr. Waddell's scheme for testing top-chord members by means of experiments conducted on a specially-built, full-size bridge, the writer begs to make the following suggestions for a practical method for maJcing such tests: Build a single- track. Class 70, through -truss bridge, with the weak member designed for, say, Class 40 loading, so that the destruction of the weak member could be accomplished without injury to the rest of the structure, thus facilitating repairs for repeated tests. The connection plates for the weak members should be extra strong. After the compression tests are completed, a series of corresponding tests on tension members should be made, so as to determine the real efficiencies of both tension and compression members and their comparative strengths. Unless this kind of a test be carried out, we shall never have any really reliable test data, as the existing data are, to a great extent, mis- leading. It is advisable that more than one value of l/r should be tested for. It should not be overlooked, in making up a design for a test structure, that there is a necessity for thorough detailing throughout, especially in connection with the weak members, so that failure will be in the form of a square break instead of being due to any insufficient detail, thus removing ambiguity. It would be advisable to build the permanent members of the trusses of the test bridge of nickel steel, so that the permanent and the weak sections would be somewhat alike, if the weak section were of the ordinary structural grade of carbon steel. . The most satisfactory method of applying the load would be by means of hydraulic presses or jacks, to be applied at panel points, and all connected so that the load would be uniform. Pressure records should be automatically made. Control of the applied load by this means would be very simple and positive. It would be desirable to make tests for low values of l/r, so as to establish the necessity or otherwise for limiting inten- sities of working i^tress. Many of the tests we are relying on at the present time for our formulae were made on badly designed struts; and I venture to say that tests on properly designed struts would show up stronger than the present tendency of the profession in strut design indicates. If the series of tests above suggested were thoroughly carried out, the engineering profession would possess some authentic knowledge concerning the actual strengths of both tension and compression members in bridges, and a large amount of guess work would be avoided in future constructions. As yet no steps have been taken to materialize this suggestion of the author's. Probably the profession will say that it is up to him to see that his proposed tests are made; and, possibly, after this treatise is com- pleted and launched, he will find time to make an attempt to induce the 140 ECONOMICS OF BRTDGEWOKK Chapter XVI Federal Government to undertake the said tests through the Bureau of Standards. The matter of allowmg higher intensities of working stresses for old bridges in service than those specified for the designing of new structures is treated at length in Chapter XLI on "Economics of Maintenance and Repairs." There is an economic question concerning loads to which but little attention has hitherto been paid, viz., the best way to compute the total loading for a foundation pile. Most engineers ignore impact altogether in estimating the load on piles supporting piers of bridges and trestles, and the author has often done so; but there are cases in which such practice might be unsafe. An instance of this kind occurred in a competitive study made by the author in relation to the rebuilding of the Galveston Causeway after a large portion of it had been destroyed during a hurricane accom- panied by a tidal wave. There the piles were comparatively short; and they passed through a thick layer of very soft material before reaching a somewhat firmer one. The layout under consideration was one of rein- forced-concrete girders; hence the spans had to be short and the piers small. Under such conditions the vibration from passing trains certainly would have reached the piles from the spans with comparatively little diminution in effectiveness; hence it was essential to allow for impact on the said piles. They had to be proportioned also for effect of thrust of braked trains; but, as the thrust would have been exerted when the train speed was slowing down, it would not have been logical to combine the thrust- effect with the full value of impact. That was an instance where the con- sulting engineer's judgment had to be relied upon to determine the proper combination of loads, and where a familiarity • with the principles of true economics would be of great value to the owners. The reason why the impact on foundation piles may either be assumed comparatively small, or possibly ignored altogether, are as follows: First. If allowed for at all, the impact should be assumed for a span- length equal to the sum of the lengths of the two spans which the pier under consideration helps to support. Second. The impacts given by formula for any span are the greatest that can come upon any main truss-member thereof, and are much larger than those for the span as a whole, as indicated by the ratio of mid- span d(!fl(;ctions under the same load when moving and when quiescent. Third. The critical speed which produces the impact given liy foinuila is likely to Ix; d(^v(!loped very seldom, if at all, on any ])articular bridge. Fourth. Th(! massiv(Miess of the pier will absorb some of the shock that reaches its top befor(> the said shock i)asses to th(> base. Fifth. As the to]is of the ])iles are (Micased in \\\v mass of concrete, they will act together as a unit and thus k^ssen somewhat the impact ])er pile. CHAPTER XVII ECONOMICS OF TIME AND MONEY IN MAKING COST-ESTIMATES FOR BRIDGES One of the author's fundamental motives in writing "Bridg3 Engineer- ing" was to provide bridge speciaHsts with a means of estimating quite accurately, and at the same time very quickly, the costs of substructure, superstructure, and approaches for any kind of bridge upon which they are ever likely to have to figure. Rather to his surprise, the numerous review- ers of the work almost entirely overlooked this important characteristic of the treatise. As it is one of the most valuable features thereof, the author, in order to make known this special usefulness, drafted a set of four prob- lems for solution, solely by means of the curves of quantities, tables, for- mulae, and other information scattered throughout the book; and arranged for a series of competitions among the senior students in a number of tech- nical schools, and afterwards, by a comparison of the marks resulting from a pre-arranged system of grading, effecting a competition among the said schools themselves by comparing in the columns of the technical press the sums of the marks of the three prize winners in each school. The judges were appointed, and the system of marking was fixed, all ready for the comparison of the unsigned competitive papers ; but the entering of Amer- ica into the Great War so upset the technical students all over the country that the competition had to be abandoned. The author is ready to provide the promised prizes (books of no great financial worth, but valuable as souvenirs of success in competition), in case that any of the teachers of engineering show a desire to have the offer renewed for a new set of prob- lems. As a matter of possible interest, the original list of questions is reproduced at the end of this chapter; and the author suggests that, for the sake of practice in quick computation, engineering students try their wits on the solution of them. In the author's practice during the last three or four years he has made very quickly many cost estimates on steam-railway, electric-railway, high- way, and combined bridges by means of the diagrams, tables, and formulae of "Bridge Engineering" for rolled I-beam spans, plate-girder spans (both deck and half -through) , riveted-truss simple-spans, pin-connected simple- spans, swing spans, cantilevers, suspension bridges, and reinforced-con- crete structures; and the results when tested have been found to be exceed- ingly accurate. The estimating of costs of structures in this manner is a very easy task compared with the job of making similar computations 141 142 ECONOMICS OF BRIDGEWORK Chapteh XVII before these records were compiled; consequently it is to be hoped that bridge engineers will soon learn to utilize properly the vast amount of information collected by the author in his many years of practice as a bridge specialist and presented to the engineering profession in his magnum opus. The following examples and-their solutions will illustrate how the dia- grams are to be used and how quickly they give results: Example No. 1 What is the weight of structural steel in a single-track, steam-railway, Class 60, riveted-truss bridge built of carbon steel and consisting of one 420' through span, two 265', two 215', and two 165' deck spans for a proposed crossing of the Missouri River? Solution From Fig. 55t on p. 1228, and Fig. 55/ on p. 1231 of B.E., we have the following : 1 420' Thro, span @ 5,450 lbs. = 2,289,000 lbs. 2 265' Deck spans @ 2,675 lbs. = 1,418,000 lbs. 2 215' " '' @ 2,060 lbs. = 886,000 lbs. 2 165' " '' @ 1,620 lbs. = 535,000 lbs. Total metal in superstructure = 5, 128,000 lbs. Example No. 2 A double-track, steam-railway. Class 55 bridge, having a total length of 820' from end to end of superstructure, is to be built so close to high water that half -through plate-girders will be required. Assuming that there will be 10, 11, 12, or 13 spans of equal length, what will be the total weight of metal for each case? Solution Ignoring the small spaces over piers between ends of girders, the various span-lengths will be 82, 74.5, 68.3, and 63.1 feet. Referring to Fig. 55r, on p. 1237 of B.E., we find the following weights of metal per lineal foot of structure; 3,860, 3,700, 3,550, and 3,420. The total weights of metal will, therefore be, 3,860 Ibs.X 820 = 3,165,000 lbs. 3,690 lbs. X 820 = 3,026,000 lbs. 3,550 lbs. X 820 = 2,91 1,000 lbs. 3,460 Ibs.X 820 = 2,837,000 lbs. Example No. S What is the weight of metal in a double-track, steam-railway, Class 65, pin-connected, Pratt-truss bridge, ))ui]t of ('ar])on stool and consisting of five 330' through spans? TIME AND MONEY IN MAKING COST-ESTIMATES FOR BRIDGES 143 Solution From Fig. 5566, on p. 1246 of B.E., we find the weight of superstructure metal to be 7,350 lbs. per Uneal foot of span; hence the total weight of metal will be, 5X330X7,350= 12,127,000 lbs. Example No. 4 What is the total weight of metal in a double-track, steam-railway, center-bearing swing-span, 350' long between centres of end supports, having riveted trusses, and carrying a Class 50 live load? Solution From Fig. 5566, on p. 1246 of B.E., we find the weight of structural steel per lineal foot of a 350' fixed span to be 6,450 lbs.; and in Fig. 55ee on p. 1249 thereof is given 83 as the percentage to apply for a swing span of that length and the type stated ; hence the total weight of metal will be, 6,450 X 0.83 X 350 = 1,874,000 lbs. Example No. 5 A 540', riveted, Petit-truss, highway span with paved roadway on rein- forced concrete base and with reinforced-granitoid sidewalks, for which the total live load per Hneal foot of span for trusses is 3,200 lbs., has a dead load, exclusive of weight of trusses, equal to 7,200 lbs. per lineal foot, the total clear width of deck from out to out being 60'. What is the weight of carbon steel in the two trusses required to carry this loading? Solution From Fig. 7e, on p. 131 of B.E., we find the coefficient for impact with ^ = fo^ = 3 to be 0.05; hence each truss load per lineal foot, exclusive of its own weight, will be as follows: Live load = |X3,200 lbs = 1,600 lbs. Impact = 0.05X1,600 lbs = 80 lbs. Flooring and metal in floor and lateral sys- tems = iX7,200 lbs =3,600 lbs. Summation = 5,280 lbs. Assume weight per foot of one truss to be = 3,000 lbs. Tentative total load per lineal foot per truss. ... = 8,280 lbs. Referring to Fig. 55/i/i, on p. 1252 of B.E., for a 540' span the 8,000 lbs. curve gives 3,100 lbs. and the 10,000 lbs. curve gives 3,700 lbs.; hence, by 144 ECONOMICS OF BRIDGEWORK Chapter XVII interpolation, 8,280 lbs. would give 3,184 lbs., showing that the assumed truss weight of 3,000 lbs. per foot was too light. Let us try 3,260 lbs. mak- ing the total load 8,540 lbs. Interpolating as before gives 3,262 lbs. As this agrees with the assumed 3,260 lbs., it is correct; and, therefore, the total weight of steel in the two trusses is 2X3,262X540-3,523,000 lbs. Example No. 6 What is the weight of metal in the four shoes of a 380' span, double- track, steam-railway, riveted-truss bridge for Class 60 live load? Solution From Fig. 6e, on p. 106 of B.E., we find the equivalent uniform hve load to be, 2X6,830 lbs = 13,660 lbs. From Fig. 7c, on p. 129 thereof, we find the impact to be 18% or 2,460 lbs. From Fig. 55y, on p. 1243 of same, we find the weight of metal per lineal foot of span to be 8,000 lbs. Flooring for two tracks, say 1,000 lbs. Total load per lineal foot of span =25,120 lbs. Weight of span = 25,120X380 . . =9,546,000 lbs. Load on one shoe = iX9,546,000 lbs =2,386,000 lbs. From Fig. 55mm, on p. 1257 of B.E., we find the average weight of one shoe to be 18,400 lbs., hence the weight of the four shoes is, 4X18,400 = 73,600 lbs. Example No. 7 What is the weight of metal per lineal foot of structure in a single-track, steam-railway, steel trestle, 170' high, to carry Class 55 live load? Solution From Fig. 55rr, on p. 1262 of B.E., we find the required weight to be 3,140 lbs. Example No. 8 What is the average weight of carbon steel per lineal foot of structure in a double-track, steam-railway, riveted-truss. Type A, cantilever- ])iidge to carry C'lass 70 live loading, the length of main span, mcasunnl from center to center of piers, being 1140 feet? TIME AND MONEY IN MAKING COST-ESTIMATES FOR BRIDGES 145 Solution From Fig. 55ccc, on p. 1273 of B.E., we find the required weight to be 20,500 lbs. Example No. 9 What is the yardage in a concrete pier with rounded ends and a half- inch batter, having no coping, the extreme top dimensions being 8' and 28' and the height 52'? Solution From Fig. 566, on p. 1302 of B.E., we find the yardage of the two half-truncated cones to be 160; and from Fig. 56d, on p. 1304 thereof, we find the yardage of a strip one foot wide to be 19.5; hence the total volume will be 160+ (28- 8) X 19.5 = 550 cu. yds. Example No. 10 ' What is the yardage in a column-pedestal 4.5' square on top, 14' high, and having a batter of two inches to one foot? Solution From Fig. 56/c, on p. 1311 of B.E., we find the volume to be 25.2 cu. yds Example No. 11 What is the yardage in a wing abutment for a single-track-railway embankment having side slopes of one and a half to one, the vertical dis- tance from foundation to base of rail being 28', the height of parapet 7', that of base 2', that of coping 1', and that of wing walls at ends 14'? Solution The height from bottom of coping to top of base will be about 17', the greatest height of wing wall above top of base 25', and the least height thereof above same 12'. From Figs. 56o and 56p, on pp. 1315 and 1316 of B.E., we find the fol- lowing Volume of Parapet, Coping, Shaft, and Walls to end of Parapet 185 cu. yds. Volume of Portions of Wing Walls extending beyond Parapet, and above elevation of top of Base = 190-35 =155 cu. yds. Volume of base to end of Parapet = 2X 17 = 34 cu. yds. Volume of base beyond Parapet = 2(14.2 — 7.2) = 14 cu. yds. Total volume of abutment = 388 cu. yds. 146 ECONOMICS OF BRIDGEWORK Chapter XVII These examples might be continued so as to include the finding of quantities in retaining walls, both plain and reinforced, reinforced-concrete trestles, and reinforced-concrete arch bridges, but space wiU not permit; hence the reader is referred for examples of the estimates for such structures to pages 1317-1347 of ''Bridge Engineering." Again, by employing the various formulae given in Chapter XXVII of that treatise, the cost of any highway or electric railway suspension bridge can be quickly estimated. As stated elsewhere herein, the author in a single working day made thereby a close estimate of cost for a 2,500'- span, highway bridge, including substructure, superstructure, approaches, and accessory works, for a proposed crossing of the Detroit River at the City of Detroit. The eleven simple examples given should suffice to illustrate the faciUty with which one who is famihar with ''Bridge Engineering" can figure the quantities of materials for all ordinary bridges. Those for other structures can be obtained in a similar manner by the expenditure of somewhat more time, but still very readily. The following are the four student problems referred to near the begin- ning of this chapter; and the author again suggests that they be solved by any young engineer who desires to perfect himself in the art of making quick computations for costs of bridges: Problem A The following data for a river crossing are supposed to be furnished by a survey for a double-track, steam railway in the northwest corner of the state of Arkansas: Width of watershed at crossing 36 miles. Width of same at a distance of forty (40) miles up-stream 44 miles. Ditto eighty (80) miles up-stream 28 miles. Ditto one hundred and ten (110) miles up-stream 16 miles. Intermediate widths are to be directly interpolated. Extreme length of watershed above crossing 125 miles. Width of river at a fairly low stage of water when the •survey was made 520 feet. Maximum depth of water at the same time at a point about one hundred and ten (110) feet from the water's edge on the left bank 5 feet. Average depth of water 3.3 feet. Greatest observed surface velocity at crossing when sur- vey was made, being the average of four observa- tions 2.55 ft. per sec. [ three (3) vertical Side slope on left bank where the rock is exposed j to one (I) horizon- [ tal. Height of top of left bank al)ove water at time of survey . 15 feet. TIME AND MONEY IN MAKING COST-ESTIMATES FOR BRIDGES 147 Side slope on the right bank of the stream, from water's edge to break of bank (a distance of thirty-five (35) feet) one (1) vertical in five (5) horizontal. Height of top of right bank above surface of water when survey was made 7 feet. Width of level portion of top of right bank 80 feet. Falling slope back of right bank for a distance of eight hundred (800) feet averages four-tenths (0.4) of one per cent. Then comes a dry, level slough, three hundred (300) feet wide; and, finally, there is a rising grade of seven- tenths (0.7) of one per cent for a distance of some eighteen hundred (1,800) feet. A profile of the crossing is shown in Fig. 17a. Average slope of river for first ten (10) miles up-stream is 1.37 feet per mile; and in each ten-mile stretch beyond it increases regularly by one and one-tenth (1.1) feet per mile. The stream at times carries considerable drift, but there is no proba- bility of the channel changing. Borings near the water's edge on the right side, at time of survey, showed five (5) feet of silt, sixteen (16) feet of sand, running from fine at top to coarse at bottom, then gravel very fine at first but increasing in coarseness gradually with the depth, the vertical measurements being made from the elevation of the water. Material of the low bank and of the flat is sandy loam covered with vegetation that would offer considerable resistance to scour. Across the slough the material is harder. The crossing is near the middle of a long, easy bend in the stream ; and the current at high water impinges against the rocky bank. Highest water-mark found was about eight feet above the water level at time of survey. No reliable records of floods were obtainable. Rainfall on watershed averages about fortj^-five (45) inches per annum. Grade line on structure, twelve (12) feet above the extreme future high- water. Clearance line for superstructure, at least four (4) feet above same. Crossing is entirely on tangent and, as nearly as may be, at right angles to the current. Superstructure is to be of steel, and substructure of concrete. Piles may or may not be used for foundations. The channel pier foundations must go to a depth of twelve (12) feet below greatest probable scour in case piles are employed, or twenty (20) feet below same in case that they are not. Approaches are to be of earth embankment, but it is permissible to put in some wooden pile trestle across the slough, if investigation should indi- cate it to be necessary. 148 ECONOMICS OF BRIDGEWORK Chapter XVII There are no restrictions as to span-lengths or locations of piers, because the river is not navigable. The type of floor is the ordinary one of untreated wooden ties and guards with eighty (80) pound rails. The live load is Waddell's Class 60. The following are the costs of -the various materials delivered at site: Cement two dollars ($2.00) per bbl. Broken stone and gravel, one dollar and fifty cents ($1.50) per cubic yard. Sand (clean and ready for use), one dollar ($1.00) per cubic yard. Timber, twenty-two dollars ($22.00) per M. feet B. M. Piles, twenty (20) cents per lineal foot. Structural steel, 4.5 cents per pound for truss spans and 4.2 cents per pound for plate-girder spans. Rails, forty-two dollars ($42.00) per long ton. The following are the schedule costs of the erection work: Sinking of pneumatic caissons, five dollars ($5.00) per cubic yard. Sinking by open-dredging, three dollars and fifty cents ($3.50) per cubic yard. Driving piles for trestle, twenty (20) cents per lineal foot. Driving piles for foundations, forty (40) cents per lineal foot. Erection of metal, including cost of falsework and painting, 1.2 cents per pound for truss spans and 0.8 cent per pound for plate-girder spans. The problem is to determine the extreme high-water profiles both before and after the structure is completed, to make an economic layout of spans, piers, and abutments for the proposed bridge, knd to prepare an estimate of cost of the finished structure, exclusive of the earth embankments. Problem B Given the profile for a dry-gulch crossing, as shown in Fig. 176, to determine, for a combined highway-and-electric-railway, reinforced-con- crete arch bridge, having a clear roadway of forty-four (44) feet and two sidewalks each eight (8) feet wide in the clear, the quantities of all the materials in tho structure and an estimate of its cost excluding the earth fills. The live loads ai'(! to l)c taken as follows: For the electric railway, Class 25. For the wagonways, Class B For the sidewalks. Class C. Permissible pressures on foundations, five and a half (5.5) tons per square foot. Arches ai'c (o he of I lie lihbcd tyi)e witli two (2) liiu^s of ribs. Av(!rag(^ d(^pth of excavation for foundations is to be six (()) feet. For unit prices of materials in place, the average costs given in Tables riq /7 -3 l5 iZoooii 400 Lodded Lengrh in Fcah Fig. 186. Live Loads Without Impact. study. It consists of allowing four tons per square foot plus the intensity of i)rcssurc on the adjacent soil at the elevation of the base, due to thewe^ weight of the overlying solid material, after having deducted from the net weight of the caisson and its superimposed load for side friction at the rate of 400 pounds per square foot of lateral sinfacc in contact with solid material. The not weight of the water-soaked timber in the caisson is taken as zero ECONOMIC SPAN-LENGTHS FOR SIMPLE-TRUSS BRIDGES 155 and that of the concrete at eighty pounds per cubic foot. The partially-filled caissons when complete weigh about fifty-six pounds net per cubic foot. As a matter of precaution, the caissons have to be figured for side- frictional resistance of 600 pounds per square foot during sinking, or some- o ^oo 200 200 Aoo SCO aoa^EL rroiSeR SOQcw^ioaf. no)qobi. Sp<3n '\n Feef- FiG. 18c. Total Weights of Metal in Superstructures. times (in extreme cases) 500 pounds per square foot. Of course, it is prac- ticable to load temporarily the caisson as it reaches the neighborhood of its final position; but such an expedient is sometimes costly and troublesome, hence it is better to design it large enough to avoid the probabihty of holdup. Some engineers have objected to relying upon side friction in supporting the load, but their contention is wrong, because it certainly does exist, and it has to be overcome before any settlement of the finished pier can 156 ECONOMICS OF BRIDGEWORK Chapter XVIII occur. In the case of long piles driven into soft material, it is almost entirely the side friction which gives them supporting power. Again, someone may question the correctness of loading sand apparently as high as nine tons per square foot at a depth of 250 feet below low water level, when the depth of water is eighty feet; but it must be remembered that the net weight of 170 feet of earth loads the soil some five tons per square foot, and that before any settlement can occur, the material adjacent to the caisson has to be raised. The reason for this is that the sand at such a great depth is practically incompressible, so that for any settlement to occur it must flow. It cannot flow downward or laterally, because there is no vacant space for it to fill; consequently, if flow it must, it will have to pass upward; and, in order to do so, it must lift a large column of the adja- cent solid material. In the author's opinion, it would take an excessively large unit loading on the base of a filled caisson resting on coarse sand at a depth of two hundred and fifty feet to cause the slightest settlement. TABLE 18a Character of structure Weight per Lineal Foot for Flooring Exclusive of all Steel but Reinforcing Bars Low level combined bridges 5,800 pounds High level combined bridges 6,900 pounds Double-track-railway bridges 900 pounds Single-track-railway bridges. 450 pounds Standard highway bridges 6,100 pounds The permissible loading for long piles has been taken at forty tons per pile, this being in accordance with the author's practice for a quarter of a century ; and he has never yet found any settlement to occur under such loading. Unit Prices of Materials in Place The following table gives the unit prices for materials in place assumed for the purpose of this investigation: TABLE 186 Materials Structural steel, per pound Concrete shafts of 20' average thickness, per cubic yard Mass of caissons, including all materials, for a width of 30' and a height of 150', sunk by open-dredging, per cubic yard Mass of cribs, including enclosed pile-heads, per cubic yard Portion of long piles projecting below base of crib, per lineal fool Condition of Market Low 4p $9.00 15.00 15.00 .75 Medium 6^ $12.00 20.00 20.00 1.00 High |;i5.oo 25.00 25 . 00 1.25 ECONOMIC SPAN-LENGTHS FOE SIMPLE-TEUSS BEIDGES 157 For the "Medium Condition of Market/' the price per cubic yard of the shafts is to be modified by the addition or subtraction of fifteen cents for each foot of variation from the assumed average of twenty, the greater the thickness the smaller the unit price. For instance, if a shaft were 12 feet wide under coping and 18 feet wide at the bottom, the average width would be 15 feet and the unit price for medium market $12.75. For the same market condition the unit price for mass of caissons is to be modified by the addition or subtraction of ten cents for each foot of variation from the assumed average of thirty, the wider the caisson the smaller the price per cubic yard. Again, for the said market condition, the unit price for mass of caissons is to be modified by the addition or sub- traction of two cents for each foot of variation from the assumed average height of one hundred and fifty feet, the deeper the caisson the smaller the unit price. For instance, with medium condition of market, the unit price for a caisson twenty-six feet wide and two hundred and forty feet high would be 20.00+4X0.10-90X0.02 = $18.60. For the other two assumed conditions of the market, these figures of modification would have to be multiplied by the ratios indicated in the table, viz., 0.75 and 1.25. Without these modifications of unit prices for substructure, the investi- gation would be not only illogical, but incorrect. The variation in cost of shafts per cubic yard is due primarily to the lower unit cost of forms for thick piers, but also somewhat to the economy effected by manufacturing and handling larger masses of concrete. The latter reason applies also to the two variations in the cost of mass of caissons; but the main cause there- of is that the total cost of cutting edge, shelter against current, and flota- tion to final location are the same for a shallow base as for a deep one. The prices per cubic yard for caissons sunk by the pneumatic process, under medium-market conditions, have been made two dollars greater than those for caissons sunk by open-dredging. This is in conformity with the author's bridge experience of nearly four decades. It is due primarily to the more rapid sinking by open dredging and the greater cost of the pneu- matic outfit, but also to the fact that the pneumatic caissons are generally filled solid, while the open-dredging caissons often have their excavating wells only partially filled. , The price used for nickel steel superstructure in place for medium market conditions has been taken as eight and a half cents per pound; for the reason that the last ante-bellum figures quoted to the author made :the price of nickel-steel two and a half cents per pound higher than that of (B^rbon-steeL The weights of metal in nickel-steel superstructures were qojnjpujbed by means of ratios determined from diagrams given in the a^tlvor's-. paper "Nickel Steel for Bridges."* -ryi'y '3/;.- -M * See Trans. Am. Soc. Civ. Engrs. for 1909. 158 ECONOMICS OF BRIDGEWORK Chapter XVIII Method of Determining the Economic Span-Lengths In determining the economic span-lengths, computations were made for the volumes of concrete in shafts, volumes of caissons, volumes of cribs, total lengths of piles below crib bases, and weights of metal in spans, but no notice was taken of the cost of flooring, as that is a constant for any type of bridge. It might be well to mention that while the abscissae of the diagrams give the span lengths measured from center to center of end pins, the costs of structure per lineal foot were computed by using the distance from center to center of piers. In making each of these cost estimates there was assumed a structure of indefinitely great length and unvarying profile, so that the sum of the cost of the steel work in a span and the cost of a complete pier divided by the horizontal distance between adjacent-pier centers gives the comparing cost per lineal foot of structure, although, as before indicated, not the complete cost thereof. The results of all calculations made were plotted on cross-section dia- grams, but only a few thereof have been reproduced herein. However, the important deductions from all the estnuates hav^e been tabulated. The plotting was done with the utmost care, and due consideration was given to a proper determination of the economic span-length. As previously indi- cated, a number of arithmetical errors were located and corrected by reason of irregularities in the curves, thus maldng the latter truly reliable. In almost all cases, at least four points were plotted from computations, in order to locate the curves of cost for substructure and for the steelwork of superstructure; and a combination of these was used for locating a few intermediate points on the curve which gives the combined cost of sub- structure and steelwork. In a few instances, though, three points for the lower curves were found to be sufficient for a correct plotting of the upper curve. Recording Diagrams and Table On Figs. IM to 18g, inclusive, are graphically recorded specimen dia- grams of the results of the special calculations. Each diagram contains three curves, one for substructure, one for steelwork in superstructure, and the other for a combination of these two. The computed cost points there- for are marked on the three curves, respectively, by circles, squares, and diamonds. The abscissse of these diagrams give the span-lengths in feet, measuring from center to center of bearings; and the ordinates record the cost per lineal foot, measuring from center to center of piers. On each diagram is clearly indicated the span-length for greatest economy ; and it is to be noticed by the flatness of the upper curves that a variation of twenty- five feet or more, either aljove or below the economic length, will make very ECONOMIC SPAN-LENGTHS FOR SIMPLE-TRUSS BRIDGES 159 little difference in the cost per foot of structure. Each diagram is provided with a title which indicates clearly the type of structure and depth of foundation to which it refers. Unless otherwise shown thereon, these YTOOf 200 2S0 450 BX) 300 350 400 Spxan in Feef Fig. ISd. Costs per Lineal Foot of Structure for Low-Level, Combined Bridges on Sand Foundations 100 Feet Deep. diagrams relate to normal or medium conditions of the material market. In the following table is given a resume of the results of most of the cost computations that were prepared: 160 ECONOMICS OF BRIDGEWORK Chapter XVIII TABLE ISc Resume of Results op Computations Character of Structure Character of Foun- dations Low-Level Combined Low-Level Combined Low-Level Combined. ... Low-Level Combined .... Low-Level D. T. R. R. . . . Low-Level D. T. R. R. .. Low-Level D. T. R. R Low-Level D. T. R. R. .. High-Level Combined. . . . High-Level Combined. . . . High-Level Combined. . . . High-Level Combined. ... Low-Level Combined .... Low-Level Combined .... Low-Level D. T. R. R. . . . Low-Level D. T. R. R. .. High-Level Combined. ... High-Level Combined. . . . Low-Level S. T. R. R. . . . Low-Level S. T. R. R. . . . High-Level Combined. . . . Low-Level Highway Low-Level Highway Low-Level Highway Low-Level Highway High-Level Highway High-Level Highway High-Level Highway High-Level Highway Low-Level D. T. R. R. . . Low-Level D. T. R. R. . . Low-Level D. T. R. R. . . Low-Level D. T. R. R. . . Low-Level D. T. R. R . . . Low-Level D. T. R. R. . . Low-Level D. T. R. R. . . Low-Level D. T. R. R. .. Low-Level D. T. R. R. . . Low-Level D. T. R. R. .. Low-Level D. T. R. R.. . . Low-Level D. T. R. R. .. Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Rock Rock Rock Rock Rock Rock Rock Rock Piles Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Depth of Caisson Footings 100' 150' 200' 250' 100' 150' 200' 250' 100' 150' 200' 250' 50' 100' 50' 100' 50' 100' 50' 100' 20' 100' 150' 200' 250' 100' 150' 200' 2.50' 100' 150' 200' 250' 100' 1-50' 200' 250' 100' 150' 200' 250' Economic Span Lengths 275' 300' 325' 350' 275' 310' 360' 430' 275' 300' 325' 350' 250' 300' 275' 325' 300' 350' 250' 300' 175' 300' 350' 400' 450' 325' 350' 375' 400' 350' 385' 425' 470' 290' 330' 375' 425' 275' 325' 375' 425' Remarks Shaft Batter l"to 1' Shaft Batter 1" to 1' Shaft Batter f " to 1' Pneumatic Caissons Pneumatic Caissons Pneumatic Caissons Pneumatic Caissons Pile Piers Shaft Batter ¥' to 1' Shaft Batter ¥' to 1' Nickel-Steel Super- Structure Ijow-Market Unit-Prices High-Market Unit-Prices These results are recorded graphically in Fig- 18/i. ECONOMIC SPAN-LENGTHS FOR SIMPLE-TRUSS BRIDGES 161 From a study of the preceding table there can be drawn the following deductions : A. For all types of bridges the economic span-length increases with the depth of foundation, though not necessarily in the same proportion. 1700 1600 I50C ZOOtriliiill ffiffll SPffi [Cost pen ; hn.{i\c(i'5frod\Jrei J — 1-' — I ' f ^1 — I — til' — 1~ — ^ -t- m^m mm m m 250 300 450 500 350 ^0 5pan In Yeel Fig. 18e. Costs per Lineal Foot of Structure for Low-Level, Combined Bridges on Sand Foundations 150 Feet Deep. B. The lighter the superstructure and the live load it carries, the greater generally is the economic span-length, and the greater the variation of the latter with the depth of foundation. 162 ECONOMICS OF BRIDGEWORK Chapter XVIII C. For sand foundations there is not much difference in the economic span-lengths for low-level and liigh-level bridges of the same type. D. Structures with piers founded on bed rock generally have economic 250 450 500 300 350 400 Span In Feef- FiG. 18/. Costs per Lineal Foot of Structure for Low-Level, Combined Bridges on Sand Foundations 200 Feet Deep. span-longths somewhat greater than tliose of ihc e()i-rcs])on(Ung structures founded upon sand at the same depth. E. Single-track railroad-biidges have economic span-lengths a little less than those of the corresponding double-track structures. ECONOMIC SPAN-LENGTHS FOR SIMPLE-TRUSS BRIDGES 163 F. Pile piers for high-level bridges involve, for economic considera- tions, rather short spans; and for low-level structures they usually neces- 4O0tt±t 250 300 400 450 SCO 350 Span in Feeh FiG. 18^. Costs per Lineal Foot of Structure for Low-Level, Combined Bridges on Sand Foundations 250 Feet Deep. sitate such short ones as to require the adoption of plate-girder super- structures. G. In highway bridges having very deep foundations on sand, increas- ing the batter of the shaft augments the economic span-length. 164 ECONOMICS OF BRIDGEWORK Chapter XVIII H. Using nickel steel instead of carbon steel in the superstructure increases materially the economic span-length. I. The assumed variations in unit prices with changing market condi- tions make very httle difference in the economic span-lengths. There would have been no difference at all had the prices of all the materials used been assumed to vary in the same proportion ; but the superstructure steel, 60 220 240 Fig. 18/i. 80 m 120 MO 160 180 200 Depfh of rou/jdafion be/s^- low Wafer le\/el in Feef Economic .SiJan-Lcngths for Siinplc-Truss Bridges on Various TyiJe'S of Foundation. erected, ordinarily changes in value somewhat more rapidly than docs the substructure of the ])ri(lge. J. There arc not many irregularities to be found in comparing the diagrams or the tal)ulatc(l results of the calculations; and what few exist arc small. They arc generally due to the adoption of a mininuun weight limit for sinking to grcuit depths instead of figuring upon employing tem- porary loading. Certain of tlio cost curves in fh(> dingi-anis, in combination with oIIum- diagrams giving weights of steel (list ril)ut('(l Ix-lwccn trusses, laterals, and ECONOMIC SPAN-LENGTHS FOR SIMPLE-TKUSS BlilDCES 166 floor systems, will provide a check on the correctness of the old method of determining economic span-lengths. Let us take the case of a low-level, double-track-railway bridge founded on rock, find the cost per lineal foot of the trusses and laterals in the span of economic length, and check it against the cost per lineal foot for the substructure thereof. For a 50-foot depth of bed rock the economic span-length is 275 feet; and for that span (see "Bridge Engineering," pages 1239 and 1240) the weight of metal per lineal foot for trusses and laterals with Class 60 live load is 4,600 pounds, which at six cents per pound would be worth $276, while the cost per foot for the substructure given by the diagram is $270. This is not a bad check. For a depth of 100 feet, the economic span-length is 325 feet, for which the weight of trusses and laterals is 5,860 pounds, which at six cents per pound would be worth $352. The diagram makes the cost per foot for the substructure $420 — quite a discrepancy. For low-level, single-track-railroad bridges with a foundation depth of 50 feet, the economic span-length given by diagram is 250 feet, for which the weight of trusses and laterals is 2,480 pounds, which at six cents per pound would be worth $149, while the said diagram gives the cost per foot for substructure at $175 — not a close check. For a depth of 100 feet, the economic span-length is 300 feet, for which the weight of trusses and laterals is 3,050 pounds, which at six cents per pound would be worth $183. The diagram makes the cost per foot for substructure $275 — another large variation. It is evident from the preceding comparisons of cost that the former rule for determining the economic span-length is not reliable, especially for foundations at great depths; hence its use should be discontinued. There is a little economic, or more strictly speaking uneconomic, investi- gation concerning simple-truss spans the results of which are worth know- ing and may sometimes, prove valuable, especially in answering questions propounded by laymen, viz., "what are the relative weights of metal in equal- truss, three-span bridges and structures of the same kind, same total length, and same loading, but having the central span lengthened and the other two equally shortened? " The answer to this question is that the weight-ratios for the unequal-span layouts, as compared with those for equal spans, are greater for long structures than for short ones, and increase with the ratio of middle-span length to average-span length. The values of such ratios for three-span structures, varying in average span-length by one hundred feet from 200 feet to 500 feet, are given in Fig. 18i. The curves for cost ratios are almost coincident with those for w^eight- ratios, because the pound prices erected for the metal in the various lay- outs are nearly alike. On the one hand, those for the equal-span layouts should be less because of a saving in cost of making working drawings and templets; but, on the other hand, the erection costs per pound are a trifle less for the layouts of unequal-span length because of their greater total weights of metal. C. W, Bryan, Esq., Chief Engineer of the American 166 ECONOMICS OF BRIDGEWORK Chapter XVIII Bridge Company, has ver}" kindly investigated this question for the author; and in a letter dated January 29th, 1920, he reports as follows concerning a double-track, steam-railway bridge, 1,200 feet long, for which the metal erected is assumed to cost 1 .^i per lb.: After careful study I feel that the three equal spans and the two spans of 350 feet with one of 500 feet should take the same pound price. For the two spans of 300 feet // 7 J 14 15 /.6 1.7 1.8 1.9 J^af/os of Len^f/) ofAf/dd/e Span fo fhahf (fi^era(je Jpan Fig. 18i. Diagram of Weight-Ratios showing Effect of Lengthening the Central Span of any Simple-Truss, Three-Span Layout, Keeping the Total Length Unchanged. and one of 600 feet I would reduce the price $1.00 per ton or to 6.95^5 per pound; and for the two 250-foot spans and one 700-foot span, I would reduce the price $2.00 per ton, or to 6.90c. per pound. As the extreme variation in pound price is only one-and-a-half per cent, evidently, as before stated, it is not worth while tt) make a special diagram recording total cost-ratios for uneconomic, three-span, simple-truss lay- outs; because those for the weight-ratios thereof will suffice. CHAPTER XIX ECONOMICS OF SUBSTRUCTURES In the old days of cut-stone-masonry piers, the method of proportion- ing the shafts was to make them as small as possible on top, keeping the pedestals of the spans just within the periphery hmits of the first sub-coping course, putting on a batter of half an inch to the foot, and carrying this down as low as the governing conditions would permit, thus ignoring entirely the effect of thrust from trains or wind. For the small structures of those times, with their short spans, this arrangement generally answered the purpose well enough, because the maximum theoretical thrusts assumed in modern bridge practice seldom, if ever, came upon the structures; but occasionally there would arise a case for which this rule-of-thumb method of pier-shaft proportioning would not suffice. The author recalls an experience of the late eighties when at Albuquer- que, New Mexico, he was making the preliminary calculations for the Red Rock cantilever bridge over the Colorado River. The Chief Engineer of the railroad company had undertaken the designing of the piers, and after learning the area required for the main pedestals, he proportioned the coping, then laid out the rest of the shaft with a batter of one-half inch to the foot, and submitted the design to the author for comment. A glance brought the instant conclusion that something was wrong, and upon this being stated the job of pier-designing was turned over to him, whereupon he proceeded to figure the overturning effect on the pier by combined trac- tion and wind loads, with the result that a batter of one and a quarter inches to the foot was found necessary; and this batter gave the layout a decidedly-pleasing appearance. The day of cut-stone-masonry piers is past — or, at any rate, ought to be; for compared with concrete piers they are always uneconomical. Some- times, as a defence against the grinding effect of ice, or the disintegrating effects of sea-water between high-water and low-water levels, it is necessary to protect the concrete thus exposed with a facing of granite or other hard rock; and occasionally someone desires to adhere to cut-stone work for the sake of retaining the old-fashioned appearance which it gives to struc- tures; but no engineer who is a student of true economy in design and con- struction will continue to use coursed masonry in his bridge piers. There is an economic problem in concrete-pier designing which comes up occasionally — whether it is better to reinforce for bending due to traction and wind loads or to omit the rods and use more concrete. There is no 167 168 ECONOMICS OF BRIDGEWORK Chapter XIX means of settling this except to design the shaft in both ways and com- pute the costs. Even then it may not be economics but aesthetics which will govern the decision, because the reinforced-concrete piers are liable to lack the massive appearance which is necessary for a pleasing effect. Un- less there be some really-material advantage in reinforcing the shafts, it is generally better to build them of plain concrete. There is an economic expedient in pier designing that is very often perfectly legitimate, especially in small structures and occasionally in very large ones, viz., the use of the "dumb-bell" cross-section, or, in other words, adopting two pedestals with a diaphragm wall betv/een. This wall may either rest on a continuous base or may be entirely unsupported between the pedestal bases, thus acting as both a strut and a beam. The appearance of a structure having piers of this type is not unpleasing, and the effect of massiveness is obtained by the expenditure of very little extra material. In a wide, two-truss bridge, solitary pedestals without a connecting wall may be employed, reliance being placed upon the end floor-beams of the spans to divide the wind load about equally between the two supports. In case that the deck is fairly close to the water, the great width will par- tially hide the substructure, and the lack of the connecting wall will not be noticed ; but in a high-level bridge, especially when carrying railroad trains, pedestal shafts not only produce a flimsy appearance but also fail to resist properly the rack from the live load. The Missouri River bridge at Glas- gow was originally built in that manner; and the experience with its piers was so unsatisfactory that the twin pedestals had to be remoued. and replaced by a solid shaft. '. ■ In some cases it" is essential that the load on the foundations be reduced to an absolute minimum, and to this end hollow shafts, or pedestals' con- nected by two thin walls, may be employed; and the excavating shafts in the bases need' not be filled, excepting only sufficiently at the bottom to transfer properly the upward thrust of the foundation into the solid por- tions of the base. Tall steel cylinders filled with concrete and well braced between make an economical substructure for light highway bridges; and this type of con- struction is proper, provided that the cylinders be carried far enough down into fairly-hard material to hold firmly the lower ends, so as to enable the cylinders to act as beams with fixed ends for resisting the bending effects of wind loads and traction loads. Generally in such cases it will be foimd necessary to build a substantial mattress around each pier, so as to prevent the scouring out of the material upon which reliance is being placed for fixing the ends. Temporary piers of timber, such as those built by the author in the middle nineties for the Missouri Iliver bridge between Council Bluff's, Iowa, and l^^ast Omaha, Nel^raska, are a k^gitimate economic expedient,, provided that (hw. arrangement be made for replacing them later l)y ])er- manent piers without involving any unnecessary expense or inteiiupting ECONOMICS OF SUBSTRUCTURES 169 traffic. In building a new railroad through timber country it is in the line of true economy to put steel spans temporarily on pile piers in order to avoid the excessive cost of hauling in substructure materials before the track reaches the site. In such cases the temporary piers should be located far enough from the positions of the permanent piers to allow the latter to be constructed without interfering with traffic. The employment of the cocked hat in pier shafts is generally an archi- tectural extravagance that should be avoided whenever its use is not demanded by the necessity for spreading the base over a wide pile founda- tion. It certainly relieves the monotony of appearance in a tall shaft, but the principles of economy generally bar it out. Only once in the author's career has he ever been guilty of adopting the cocked hat, viz., in the late eighties when he made the design for what was then termed the Winner Bridge over the Missouri River at Kansas City, the spans of which were proportioned to carry between the trusses a single-track railway with a narrow foot-walk on each side and a single-track roadway outside of each truss, thus making the perpendicular distance between central planes of trusses twenty-five (25) feet. It proved to be a fortunate thing that the cocked hat was employed, for the superstructure of the Winner Bridge was never erected, because of lack of funds ; and when the double-deck, double- track, Fratt Bridge was built on the old piers, after cutting down the shafts to an elevation of ten feet above high-water mark, the extra length of pier afforded by the said cocked hat provided just the necessary extra size for permitting the superstructure to be widened sufficiently to carry the double track. Ice breakers are sometimes used where there is no real need for them, because it takes an enormous amount of thick ice to damage any well- founded pier having a shaft with rounded ends; nor, as a rule, does a con- crete pier require special protection against the grinding of ice. If real granitoid of one-two-three composition with ten per cent of hydrated lime added to the cement were substituted for the ordinary concrete between high-water and low-water marks and extending into the mass about twelve inches, the protection thus afforded would almost always be ample and would involve very little additional expense. Moreover, the repairing of an abraded pier-surface by means of granitoid is not a difficult matter. Unless a pier rest on bed rock, the placing of an unbalanced ice-break upon it is going to upset the equality of load distribution over the foundations and thus, possibly, cause trouble. In case of a pier on piles, it would be better to put another ice-break on the down-stream end of the pier for the sake of symmetry, although it would serve no useful purpose as an ice- break per se. All violations of the precept of symmetry are to be avoided whenever this is practicable; for, by so doing, trouble also is often avoided. The economic question of reinforced-concrete versus timber for cribs and caissons is beginning to loom up. At the same total first cost, timber is preferable, owing to the ease and rapidity with which it may be put in place; 170 ECONOMICS OF BRIDGEWORK Chapter XIX but its growing scarcity will certainly make the reinforced-concrete shells of such constructions more and more popular among bridge builders as the years go by. In using it, the time required to let the concrete set and harden is Hable to cause delay in the sinking; and the removal of the forms is often troublesome. This last statement leads to the thought that there is coming up soon the economic question of steel versus timber for concrete forms. At present the former material is not much employed for this purpose, but its adoption therefor is on the increase, especially when the forms have to be used a number of times. After timber has been utilized for this purpose three or four times it becomes badly broken up and unfit for further service, while the steel forms with care can be used an indefinitely great number of times. A combination of the two materials might be employed to advantage, the steel being interposed between the concrete and the timber girders, thus avoiding injury to the latter and permitting them to be used over and over again. In respect to the depth below extreme low water to which it is economic to carry the shaft of a pier, there is great difference of opinion amongst engineers. The author generally locates the plane of division between shaft and base at an elevation of two feet below the lowest-recorded water- level, thus providing against exposure to the air of water-soaked timber, even in seasons of abnormal drought. Such treatment for a short time would probably do no harm, but the exposure of the crib to vision is not pleasing. Those who claim economy for locating this division plane far below the water's surface do so on the plea that it requires less material. This is true enough, but the unit price of the portion of the shaft below low- water is far higher than that above the same, and generally somewhat greater than that of the top of the crib itself. For tliis there are several reasons, viz.: First. In order to build it, a fairly-water-tight, removable cofferdam has to be constructed, which is certainly more expensive than the simple crib-top. Second. This cofferdam has to be kept pumped clear of water until after the shaft is built. Third. The form-work below low-water is expensive and adds mate- rially to the unit cost of the shaft-concrete. Fourth. Where the shafts are carried down deep, more allowance has to be made for possible error of position; and to do this would involve the enlarging of the area of the base, thus increasing the total cost. The (condition sometimes exists which calls for the least possible obstruction of the waterway, and then it often becomes neccssarj^ to carry the shaft down to the bottom of the channel, irrespective of the extra cost of the piers. In such cases it will be found that the unit value of the shaft-concrete will be high, and that, as far as mere cost is conccirned, it would have been better to carry the cribs up to near low-water mark. ECONOMICS OF SUBSTRUCTURES 171 The determination of the proper clearance to allow between the bottom of the shaft and the inside of the timber or reinforced-concrete shell is an economic problem of importance. If it be made unnecessarily large, the volume of the base will be too great and the construction too costly. On the other hand, if it be made too small and an error in location should occur because of unanticipated trouble in sinking, it would be difficult to shift the shaft the right amount on top of the crib in order to get it into correct position; and this would involve delay, than which there is nothing more expensive in substructure construction. It is evident that one must endeavor to strike a happy mean in designing his cribs and caissons — but what is that mean? The author's practice is to allow as a minimum a foot clear all around the base of the shaft for easy conditions of sinking, and to increase this gradually as the said conditions become more and more unfavorable, up to a hmit of about twice that amount. It would certainly be a case of either gross carelessness or extremely hard luck which would prevent the correct location of a pier-shaft when the larger allowance-limit for shifting was provided. With due care in sinking, the error of position of a crib-top should seldom exceed a few inches; consequently, when a bridge engineer, in order to be surely on the safe side, makes an abnormally- great allowance for error of crib position, he does so at the expense of the work, and therefore imperils his reputation as a true economist. Whether to use the pneumatic process instead of either open-dredging or cofferdam excavation is fundamentally an economic problem based upon the theory of probabilities. Comparing the open-dredging and the pneumatic methods of sinking, while the former generally figures out to be the cheaper, its cost is rather uncertain, because of the possibility of encoun- tering large logs or boulders; and, while the cost of installation of a pneu- matic plant adds some two or three dollars to the cost per cubic yard of the bases, one can count almost with certainty upon the total expense involved in the sinking. If bed rock be within reach by the pneumatic process, that method of sinking should always be adopted, unless it be decided not to go that far down for a foundation, in which case the open-dredging process is likely to be the more economic. One should never sink a caisson to bed rock by open-dredging for fear that it will rest on one edge or one corner only and thus provide an unequal bearing. It would be far better to stop short of it a small distance and rest on sand, gravel, or boulders overlying the rock. Comparing the cofferdam method with that of open-dredging into a clay or other fairly-hard foundation-material, unless the depth below the working stage of water be less than eighteen (18) or twenty (20) feet, the latter usually is preferable, because the former is likely to give trouble and nearly always involves a greater expenditure of money than that allowed in the preliminary estimate. The economics of steel sheet piling for cofferdams is still an unsettled question among bridge engineers. Some of the old-time substructure con- 172 ECONOMICS OF BRIDGEWORK Chapter XIX tractors contend that cofferdam piers sunk by their use are more expensive than those placed by the pneumatic process; whilst other contractors, equally experienced, declare the contrary, all however agreeing that the difference in cost by the two methods is small. The author is inclined to believe that, if a thorough set of borings has failed to indicate any sunken logs, beds of large boulders, quicksand, or other serious impediment to driving or excavating, the steel sheet-piling will involve a moderate saving in first cost for depths of foundation below ordinary low water as great as forty feet. To effect such a saving, however, requires an experienced and energetic contractor or superintendent; piling of ample size, thickness, and length; sufficient of it for three, four, or even five piers (according to the size of the job), with extra pieces to provide for damage in driving; heavy pile-driving hammers; ample pumping capacity; and a full supply of derricks, engines, and other outfit. Generally, it is the small-fry contractor who prefers the cofferdam method to the pneumatic ; and he is tha one who is most likely to get into trouble from failure to anticipate and provide against difficulties in driving and excavating. His pseudo-economic dis- position leads hi n into purchasing small, thin, and short piles; for he does not recognize that large ones will withstand battering at both top and bot- tom much better than small ones, that thin webs are liable to be split and bent by striking large, hard boulders, and that short lengths are almost sure to involve not only flooding the dams but also filling them with sand or silt— possibly several times during the progress of the work. Steel-pile cofferdams have been successfully used for depths as great as fifty feet below ordinary-low-water elevation; but the conditions were unu- sually favorable, the material penetrated being mostly soft clay that shut out the water almost completely, thus enabling bed rock to be reached at moderate expense. Large, strong sheet-piles, in addition to the security against injury in driving which they provide, effect an economy by permitting the waling frames to be placed farther apart, thus lessening the amount of timber to be bought and the expense of both its placement and its removal ; besides the metal often, has more than merely scrap value at the end of the job, which is seldom the case when small, light sections are employed. Sunken logs or wrecks give endless trouble when encountered in coffer- darn work, as usually they have to be shattered to splinters by dynamite before the piling can penetrate them; and under such conditions the steel sh{;ct-piling is decidedly superior to the wooden Wakefield-piling. The lattei- is advantageous for shallow excavations and for cases where the bed roclc is too hard to penetrate; because the ends of the piles broom, and the l)att(!re(l wood, by absorbing water, expands and seals the bottom of the pit. T'lu! cofferdam method is spocinlly applicable where clay overlies the IxmI rof'k; for it will seal the bottom of the l)ox. Where there is no such scaling lay(!r, it is oft(;n necessary to place clay, manure, or some other ECONOMICS OF SUBSTRUCTURES 173 material on the outside, or else to employ a double-wall cofferdam filled with clay. In relation to the comparative economics of a caisson, put down by open-dredging to a depth that is absolutely great enough to insure against disaster from scour, and a crib sunk to a reasonable depth and filled with long piles, the latter generally will be found to be much less expensive; but cases will occasionally occur when the reverse is true, hence it is well always to make complete comparative estimates of cost. These require only a few minutes' work for an experienced bridge computer. Once in a while it occurs that the pneumatic process has to be employed for one or more piers of a long bridge, the others being sunk by open- dredging. The question then arises as to how many to put down by the more expensive process ; and it should be solved more with reference to the expediting of the construction than to using pneumatics only where actu- ally required. For instance, if all the piers but one could be handled by open-dredging, it would be found that the unit price for the base of that one would run extravagantly high, because it would have to take care of a large overhead charge for use and transportation both to and fro of the pneumatic machinery and other outfit. In that case one should figure how much it would actually cost to put down another pier by pneumatics when everything necessary is on the ground and ready to move over to the site of the next pier, then compare the result with the cost of that pier sunk by open-dredging. Generally but httle difference will be found, and, therefore, it might prove truly economic to keep both outfits occupied. The sooner any piece of bridge construction is finished, the sooner will the erection contractor be ready to undertake another contract — besides it is often the case that an expeditious handhng of the work will avoid a rise of river or the advent of other unfavorable working conditions. It is, therefore, logical to conclude as a general proposition that the harder a contractor drives his work the more money will he net from his operations, even if it appear to the casual observer that he is spending cash rather recklessly for the purpose of finishing the work quickly. Of course, if the contractor is absolutely sure that he will have no work at all to keep his force occupied after a certain job that he is on is completed, it will not pay him to spend any extra money to rush it; but, on the other hand, there is nothing to be gained by dragging it out unnecessarily. It would be better to finish it and trust to luck about getting another contract. In foundations for trestles there sometimes arises the economic question whether, in order to obtain the requisite bearing area, it would be better to use plain concrete and go rather deep by stepping off the base in the old- fashioned way, or to spread out quickly by adopting reinforcem.ent. The surest way to settle the question is to proportion a pedestal or two by each method and compare results. If for any reason the cost of the excavation should run high, the reinforcement method will have a decided advantage. Again, as the volume of the concrete is much smaller for that type of base 174 ECONOMICS OF BRIDGEWORK Chapter XIX than for the other, the total load on the foundation is less, and, conse- quently, the area of base required is smaller. Whether the excavation is wet or dry will make considerable difference, the former condition favoring reinforcing and the latter militating for plain concrete. Where the footing cannot be pumped out, it is rarely permissible to use reinforcement. Sometimes in a long trestle it is doubtful whether to adopt reinforced- concrete piles with quite-shallow bases for the pedestals or to employ the cheaper wooden piles and sink the said bases to extreme-low-water eleva- tion, in order to ensure that the wood shall always be saturated and never exposed to the air. In such a case, one or two pedestals should be designed by each method and their costs determined for comparison. CHAPTER XX ECONOMICS OF TRUSSES AND GIRDERS During the last half century several treatises have been written upon the subject of economy in superstructure design, but unfortunately the result is simply a waste of good mental energy; for the writers tiiereof invariably attack the problem by means of complicated mathematical investigations, not recognizing the fact that the questions they endeavor to solve are altogether too intricate to be undertaken by mathematics. The object of each investigation appears to have been to establish an equation for the economic depth of truss, or that depth which corresponds to the minimum amount of metal required for the said truss; and, to start the investigation, it seems to have been customary to make certain assumptions which are not even approximately correct. For instance, the principal assumption of several treatises in French and English is that the sectional area and the weight of each member of a truss are directly proportional to its greatest stress; or, in other words, that in proportioning all members of trusses a constant intensity of working stress is to be used, while in reality for modern steel bridges the intensities often vary considerably in the same specifications. Again, no distinction is made between tension and com- pression members, and no account is taken of the greatly varying amounts of their percentages of weights of details. There is, however, one mathematical investigation concerning economic truss depths which is approximately correct, and which is based on assump- tions that are very nearly true ; but it holds good only for trusses with par- allel chords. It is this: Let A = weight of the chords, 5 = weight of the web, C = weight of the truss, and D = depth of the truss. Then C = A-\-B. [Eq. 1] But the weight of the chords varies inversely as the depth, or A=j:, and the weight of the web varies directly as the depth, or B = bD, where a and h are constants; and, therefore, C = j:-\-bD. 175 176 ECONOMICS OF BRIDGEWORK Chapter XX If C is to be made a mimmum, we shall have, by dLfferentiation, ^■=-^ + " = 0. [Eq.2] or -^+^-=0, or A=B. [Eq.3] As the second differential coefficient, after substitution according to the usual method of maxima and minima, comes out positive, the result obtained corresponds to a minimum. From this it is evident that, for trusses with parallel chords, the greatest economy of material wiU prevail when the weight of the chords is equal to the weight of the web. The author has verified this conclusion by checking the weights of chords and webs in a number of finished designs, finding it to be absolutely reliable. However, it is not of much practical value, because the economic depths of trusses with parallel chords are pretty well known; and, again, when spans are in excess of 175 or 200 feet, the chords of through-bridges are seldom made parallel. Moreover, the best depth to use is not often the one which gives the least weight of metal in the trusses. It has been found by experience that, for trusses with polygonal top chords, the economic depths, as far as weight of metal is concerned, are generally much greater than certain important conditions wiU permit to be used. For instance, especially in single-track, pin-connected bridges, after a certain truss depth is exceeded, the overturning effect of the wind- pressure is so great as to reduce the dead-load tension on the windward bottom chord to such an extent that the compression from the wind load carried by the lower lateral system causes reversion of stress, and such reversion eye-bars are not adapted to withstand. A very deep truss reciuires an expensive traveler, and decreasing the theoretically economic depth increases the weight but sHghtly; hence it is really economical to reduce the depth of both truss and traveler. Again, the total cost of a structure does not vary directly as the total weight of metal, for the reason that an increase in the sectional area of a piece adds nothing to the cost of its manufacture, and but little to the cost of erection; consequently it is only for raw material and freight that the expense is reaUy augmented. Hence it is generally best to use truss depths considerably less than those which would require the minimum amount of metal. For parallel chords, the theoretically economic truss-depths vary from one-fifth of the span for spans of 100 feet to about one-sixth of the sjxxn for spans of 200 feet; but for modern single-track-railway through-bridges the least allowable truss- depth is about 30 feet, unless suspended floor-lieams be used, a detail which very properly has gone out of fashion. In two fivc-hund red-foot spans of a combined railway and highway l)ri(lg(! the author employed a truss depth of seventy-two feet; Imt this was determined by the reversal of stress in bottom chords through wind- ECONOMICS OF TRUSSES AND GIRDERS 177 pressure. A greater depth, if permissible, would have caused a saving in total weight of metal. In another of his designs for a five-hundred-and sixty-foot span a truss depth of ninety feet was adopted, but in this case the live load was very great, varying fi'om ten thousand pounds per lineal foot for short spans to eight thousand pounds per lineal foot for long ones; and the bridge is twenty per cent wider than in the case of the two five- hundred-foot spans just mentioned. The greater the live load and the wider the bridge, the greater generally can the truss depth be made advan- tageously. The little mathematical investigation given in this chapter can be applied with fair accuracy to plate-girder bridges and to the floor systems of truss-bridges. If, for ordinary cases, in designing plate girders, one will adopt such a depth as will make the total weight of the web with its splice- plates and stiffening angles about equal to the weight of the flanges, he will obtain an economically designed girder, and a deep and stiff one. For long spans, however, this arrangement would make the girders so deep as to become clumsy and expensive to handle; consequently, when a span exceeds about forty feet, the amount of metal in the flanges should be a little greater than that in the web ; and the more the span exceeds forty feet the greater should be the relative amount of metal in the flanges. The true economic investigation for plate-girders is as follows, when the web is assumed to resist its share of the bending moment : Let M = bending moment at mid-span, h = depth of web, t = thickness of web, S = intensity of working stress for tension, I = length of span, and c = ratio of weight of details of web (i.e., end stiff eners, inter- mediate stiffeners, splice plates, and fillers) to weight of the web plate itself. The sum of the two flange areas at mid-span, including an allowance of fifteen per cent for rivet holes, will be given by the equation, F=1.15(^^-lhty, [Eq.4] and the total weight of metal in the flanges, taking into account the fact that the cover plates do not run the full length of the girder, will be given approximately by the equation. /2Af 1 \ Wf=3AXl.l5ij^-^ht] X0.8 l. 1 84 M = 3.4 Z ( -^^ 0.23 ht ) . [Eq. 5] hS The weight of the web and its details will be W^ = 3.4:l(ht-\-cht). [Eq. 6] 178 ECONOMICS OF BRIDGEWORK Chapter XX Therefore the total weight of girder will be = 3.4 //^-^^^+0.77 U+cht\. [Eq. 7] Differeritiating with respect to h and placing the differential coefficient equal to zero gives / 1 84 M \ = 3.4 ?( -^^^p+0.77 t+ct\ -0. [Eq. 8] = 0.77 ht-{-cht; [Eq. 9] dW o . _/ 1.84 M dh Hence 1.84 U hS from which we find 1 84 M Vl -0.23 ht^OM ht^cht, [Eq. 10] and 3.4 l0^^^-0.23 hi) =3.4 Z(0.54 ht-\-cht). [Eq. 11] But the value of c is generally about 0.3. Substituting this gives 3.4 ^("-^^-0.23 /iA =3.4 Z(0.84/i0. [Eq. 12] But the first member of this equation represents the weight of the flanges for the most economic condition, and the second member is eighty-four per cent of the total weight of the web plate without its details. Dividing both sides of the last equation by 0.8 and canceling the 3.4 I gives /O Q /If \ (^1^-0.29 ht) = 1.05 ht, [Eq. 13] or 1.15(^^-0.25 ht\ = 1.05 ht. [Eq. 14] Evidently the first member of this equation represents the gross area of the flanges and the second member differs only a little from the gross area of the w(^b and may without any great error be called such. Hence it may be stated that the theoretical maximum of economy exists when the gross areas of flanges and of web at mid-span are equal — a condition readily remembered. If the depth of web be selected on this basis, rather than by the old criterion which makes the total weight of flanges equal to the total weight of web with all its details, it will be found to give a greater web depth. This increased depth is likely to augment the cost from one or more of the following practical considerations which the formula cannot take into account: ECONOMICS OF TRUSSES AND GIRDERS 179 A. An additional splice or two in the web, or else a slightly increased pound price for the large plates. B. Larger outstanding legs for all stiffening angles. C. Reduction in the number of cover plates. D. Narrowing of flange angles and necessitating thereby either an additional bracing frame or an increase in sectional area of the compression flange, in order to compensate for the greater ratio of unsupported length to width. E. Possible thickening of web because of its greater depth. F. Possible encroachment on under-clearance in deck spans, or raising of grade to avoid the same. G. Possible difficulty in fabrication or shipment in case of long or heavy girders because of excessive depth. Any one of these changes would be likely so to upset the economics of the case as to cause material decrease in the theoretical depth found by the preceding investigation. One will not often make an error in economy by following the old established rule in " De Pontibus " to the effect that the best practicable arrangement is generally to make the weight of the flanges equal to the weight of the web and its details; and there are occasionally cases where a saving of metal can be effected by making the web depth even smaller than that given by this old criterion, when by so doing a web splice may be avoided or smaller stiffening angles may be adopted. It should be borne in mind that there is quite a range in web depths over which the theoretic minimum weight is about constant, unless the thickness of the shallower web must be increased on account of the shear; hence one may often vary the dimensions of a plate-girder materially without affecting greatly the matter of economics. In Fig. 20a is given a diagram of eco- nomic depths of plate-girders with riveted end connections. Concerning economic panel lengths for truss bridges, it is safe to make the foflowing statement: Within the limit set by good judgment and one's inherent sense of fitness, the longer the panel the greater the economy of material in the superstructure. Of course, when one goes to such an extent as to use a thirty-foot panel in an ordinary single-track-railway bridge he exceeds the limits referred to, because the lateral diagonals become too long, and their inclination to the chords becomes too flat for rigidity. Again, an extremely long panel might sometimes cause the truss diagonals to have an unsightly appearance on account of their small inclination to the horizontal. In plate-girder structures with floor-system of cross-girders and string- ers, there is generally no economy in adopting long panels — in fact they are certain to involve an increase of total weight of metal; but, on the other hand, the cost of erection is probably lessened by reducing the number of field-driven rivets. Warren trusses are cheaper than Pratt or Petit trusses for parallel chords, but not for those with a polygonal chord. The first-mentioned type 180 ECONOMICS OF BRIDGEWORK Ch.^pter XX changes sectional areas of chords onlj^ one-half as often as do the others, which feature tends to save metal in spUce plates and expense in field riveting. The length of span at which it pays to change from parallel chords to curved or, more properlj' speaking, polygonal chords, will vary with the class of bridge; but it is seldom advisable to adopt the latter for spans under two hundred feet. The greater the panel length the greater the Hmit of span for parallel chords, consequently it will generally be found shorter for highway bridges than for railway bridges. This curving of the tcp chords of long through-spans has sometimes been carried to such excess /oooo /5G00 J50 Fig, O 5000 /OOOO /SOOO Jb/a/l. oej<^ /n /^oancfs perjL/nea/ /vofofG/rc^er 20a. Economic Depths of Plate-Girders witli Kiveted End-Connections. as to approach very closely the old pai-abolic trusses, in which the curve extends from end-pin to end-pin. In a large and in'portant bridge over the Mississippi River the top chords of the main spans, which exceed five hun- dred feet in lengtli, are so curved as to involve the use of a very shallow portal, allowing but the ordinary clear headway beneath. Such excessive curvature causes the top chord to do most of the work of the web and makes the lattei- too light and vibratory. It also necessitates the use of counters or stiff main diagonals almost up to the ends of the span. A proper curva- ture of the chords is not only economical of both metal and money, but also is iT'sthotic, adding greatly to the appearance of most bridges, consequently this featui-e should be encouraged, but not, of course, to excess. The best curvature of chords for any span can only be determined by experience, ECONOMICS OF TRUSSES AND GIRDERS 181 the controlling factor being reversion of web stresses. In general, it may be said that the greater the arching the more artistic the effect. For highway bridges it can be made greater than for railway bridges, because the effect of impact is less in the former than in the latter; nevertheless, even in high- way bridges the curvature must not be carried to excess on account of the tendency of light web members to set up vibration from insignificant moving loads. CHAPTER XXI economics of decks and floor-systems Steam-Railway Bridges Decks Railway-bridge decks may be of timber ties, either plain or treated, spaced from twelve to fifteen inches from center to center, with either two or four rows of wooden guard-rails bolted thereto; trough floors with or without ballast; ballasted road-bed resting on a solid floor of treated planking, steel plate, or reinforced-concrete slab; or rails resting directly on the steelwork. The most common type, and the cheapest, as far as fii'st cost is con- cerned, is the open, untreated-timber deck; but it maj^ be more expensive than some of the other types when the item of maintenance is considered. It affords easy riding, but is not so safe against derailment or burning. as decks that are closed. These advantages and disadvantages, however, cannot be evaluated in money. Treated ties, of .course, cost more than the plain ones; but they generally last so much longer that they are more economical in the end. They can be of a cheaper grade of tmiber than the untreated ones, but this saving is offset by the necessity for using tie plates between the timber and the rails. Without these the hfe of the soft timber would be very short under heavy traffic. However, first-class con- struction calls for tie plates on all timber ties. Trough floors with ballast and ties therein are uncommon. This was one of the first kinds of shallow floor to be built, but it has gone out' of fashion. There was one tie per trough, and it generally rested directly on the steel; but sometimes a few inches of ballast were interposed. This type is noisy and expensive, and the replacement of ties in the trough is both difficult and costly. Ballasted decks are more expensive in respect to first cost than the open ones, especially in long-span structures, on account of the augmented dead load. They provide easier riding; and for short-span bridges on first- class lines they are almost exclusively adopted as standard. One incidental advantage that they possess is that they permit the use of skew nbutments, which are not compatible with the open-timber type of deck. Again, they are more conducive to maintenance of alignment; and they protect the steelwork fairly well from bi-ine di-ippings. 182 ECONOMICS OF DECKS AND FLOOR-SYSTEMS 183 The cheapest good type of ballasted floor is that in which the ballast rests on a solid base of creosoted planks; and a high authority on railroad bridge building and operation claims that, considering the cost of mainte- nance, this deck is cheaper than the open-timber one for spans of ordinary length. It would be very uneconomical to omit the treatment of the timber; because, in replacing the base, it is necessary to remove and store the ballast and later to put it back. Ballast resting directly on steel plate is not much used, although it produces a shallow deck, which is sometimes a sine qua non. It is expen- sive, and the steel plate is hable to rust. Ballast resting on a reinforced-concrete slab represents \he highest grade of construction, but it is too heavy for long spans. In short spans, weight is desirable for high speed so as to check vibration, notwithstanding the fact that the cost of the steelwork is increased thereby. It is the best type for overhead crossings for the following reasons — the noise is reduced to a minimum, it can be built waterproof to exclude drippings, the depth can be made comparatively small, and the maintenance cost is the least practicable. This style of deck requires a specially-good drainage system; and, if the steel is encased, the deck must be waterproofed, which adds to the expense. True economy calls for a two-ply, three-ply, or even four- ply membrane of cotton drilling or burlap covered with asphalt of the proper consistency. The cotton has proved to be more durable than the burlap ; and, therefore, it is the more economic. It is advisable for the sake of durabihty (and, consequently, for that of economy) to cover the waterproofing with either protection-bricks or thin concrete, the latter being the lighter and cheaper. An important portion of the work is the joint of the flashing with the web of the girder. This requires very care- ful attention in both design and construction, if leakage is to be prevented. Rails laid directly on the steelwork give a minimum depth for the floor, but they require a rather expensive floor-system; and there being no cushion between rails and steel supports, the riding is not easy and the noise involved is excessive. For these reasons the type is not desirable ; and the only excuse for using it is a compulsory call for an exceedingly shallow floor. Spans without Floor- Systems The floor-system proper may be omitted in I-beam spans, most deck plate-girder spans, those half-through plate-girder spans in which the wooden ties rest on either the bottom flanges of the main girders or on spe- cial shelf-angles, and short deck truss-spans in which the ties are sup- ported directly by the top chords. This omission of the floor-system is entirely proper from the points of view of both economy and expediency, as far as I-beam and deck plate-girder spans are concerned, and even in the case of deck truss-spans when the truss-spacing is not too wide. Beyond the limit of ten feet from center to center of trusses the size required for ties 184 ECONOMICS OF BRIDGE WORK Chapter XXI becomes too great for heavy loadings. It is true that this hmit is some- times made as high as thirteen feet; but then the ties are difficult to secure, and the maintenance cost thereof is large. Resting ties on the bottom flanges or on special sheK-angles in half- through, plate-girder spans, although economic in first cost, is not good construction; because the removal and replacement of the said ties is abnormally troublesome and expensive. This practice, which was quite common two or three decades ago, is pseudo-economical, especially in view of the rapidly-augmenting prices of timber. Moreover, this detail has a tendency to distort the webs of the girders; and the depth available for cross-struts is small. These are needed for a proper staying of the top flanges of the main girders, and they have to be stiff in order to be effective. Open timber decks can be used on I-beam spans, on deck, plate-girder spans, and on deck truss-spans without floor-systems, as can also ballasted decks supported by treated timber or reinforced-concrete slabs. In short I-beam spans the beams can be spaced closely and a thin slab can be employed, or the beams can be embedded in the slab, or there can be used longitudinal, reinforced-concrete troughs resting on the bottom flanges of the I-beams with the latter encased in concrete. For I-beam spans with either timber or ballasted deck, it is cheapest to adopt the minimum number of beams that will carry the load; but with limited headroom it will be found necessary to employ shallow beams and space them closely. If it be desirable for the sake of protection to encase the said beams in con- crete, it is usually most economic to rest the slab on the beams and encase them separately; but for very thin floors it is cheapest either to embed the beams in the solid slab, or to use reinforced-concrete troughs. Floor-Systems The standard floor-system consists of two stringers per track riveted to the cross-girders, with the latter riveted in turn to the trusses or main girders. In general, this construction is by far the most economic type of floor-system; and it provides substantial floor-beams at panel points to serve as lateral struts. It can be used with any of the ordinary types of deck previously described. Auxiliary stringers, often termed "jack- stringers," are sometimes added so as to take care of derailed trains. Four carrying-stringers per track are occasionally employed, cither because it is the policy of the road to do so or in order to permit the adoption of a shallow floor, especially in half-through, plate-girder spans. It is more economic to adopt four lines of carrying-stringers per track than to have only two of them and two lines of jack-stringers, for the reason that, except in the case of derailment, the latter are idlers. Four carrying-stringers, of course, re(iuii'e more metal than do two, especially with long paiK>ls; but with hallastcd dc^cks on concrete slabs they ])(Miuit a reduction in the slab- tlii(;kn(\ss; and in sjjans of considerable length I he reduction in dead load involved will nearly compensate for the extra stringer metal. ECONOMICS OF DECKS AND FLOOR-SYSTEMS 185 The economic panel length for this type of floor-system, as far as that floor-s,ystem alone is concerned, is always smaller than can be employed for single-track truss-bridges, whether through or deck, as can be seen by referring to the curves on pages 1224, 1229, and 1233 of "Bridge Engineer- ing." This is also true for double-track, riveted-truss biidges, as shown by the curves on page 1239 of that treatise, although there is no great reduction below 25 feet. For double-track, pin-connected bridges, 25 feet is the economic length (see " Bridge Engineering," page 1244). This is due to the extra metal required for the cut-away ends of the floor-beams, making pin-span cross-girders much heavier than riveted-span ones. Where jack-stringers or four lines of carrying-stringers per track are employed, the economic panel lengths would be still shorter. It will be found, however, that variation in panel length will not affect greatly the total weight of metal in span, since lengthening the panels generally reduces the truss weight. For long, deep trusses, longer panels than usual give smaller total weights of truss metal. In respect to the economic depths of stringers for two lines per track, they vary from 4 feet for 20-foot panels to 5 feet for 35-foot panels with light live loads, and from 5 feet for 20-foot panels to 6 feet for 35-foot panels for heavy live loads. The economic depths for four lines of stringers per track are about one foot less than the preceding. The economic depths for floor-beams vary from 5 feet to 6 feet, accord- ing to panel length, in single-track bridges with light live loads, and from 6 feet to, 7 feet with heavy live loads. The corresponding figures for double-track bridges are respectively, from 6 feet to 8 feet, and from 8 feet to 10 feet. Under-clearance requirements often call for shallower floor-beams than those of economic depth, especially for double-track bridges. Very shallow, double-track, railway-bridge floor-beams are quite expensive. Any decrease in depth of floor-system below the economic one will increase the cost of main structure; but this is partially ofi^set by the slightly- reduced lengths of approaches; consequently, when comparing the costs of floor-systems of different depths, this fact must not be forgotten. Half-through, plate-girder spans are used only where the headroom is Umited; hence the floor-systems for these structures are almost always shallow and uneconomic of metal. With open-timber decks, four lines of carrying-stringers per track are employed in order to provide a shallow floor; and the panels can be short and of economic length. Sohd floors are quite common with through-plate-girder construction. The trough floor-system is very thin, and hence is appHcable thereto; but it is expensive and otherwise objectionable, as hereinbefore explained. When a ballasted deck on creosoted timber is adopted, four stringers per track can be used, but it is more common to employ closely-spaced, transverse rolled I-beams, especially when the headroom beneath is small. The latter construction is also usually employed with a ballasted deck carried on a steel plate. 186 ECONOMICS OF BRIDGEWOKK Ch.\pter XXI Ballasted decks on reinforced-concrete slabs are much used for half- through, plate-girder spans. The floor-system can be of the usual stringer- and-fioor-beam type, generally with four lines of stringers per track, on account of restricted headroom; or the slabs can rest on rather- closely-spaced, transverse beams. With the latter arrangement it is economic of metal to adopt spacings of 5 feet or more; but, on account of restricted head room, it is frequently necessary to space much more closely, in order to permit the use of shallower beams. If the available depth is very small, these cross-beams can be embedded in the sohd slab; or reinforced-concrete troughs resting on the bottom flanges of the beams can be employed, the tops of the beams being encased in concrete. The relative economics of the last three types depend on whether the steel needs to be encased so as to protect it from locomotive blast or other attack from below. If no encasement be required, the first type is the cheapest; but otherwise there is not much difference in the costs of the three. As before mentioned, in all cases where beams are embedded in concrete, the top surface of the slab must be water- proofed. Rails resting directly on the steel require floor-systems of closely-spaced, transverse beams — an expensive construction and not good in case of derailment. In respect to encasement, it is generally economic to put it on by cement-gun, because it is cheaper than the poured covering, and being thinner it saves in the dead load to be carried by the steelwork. For double-track, deck truss-spans it is most economical for the floor- system to space the trusses 20 feet or 21 feet centers, and to use two lines of stringers about 7 feet centers, resting the ties on the stringers and top chords. Such a floor-system weighs but little more than that for a single- track through-bridge. It may take so much extra metal in the strength- ened chords as to absorb most of the saving from the omission of the two lines of stringers, but the floor beams are much lighter than those ordi- narily required for double-track bridges. There is also considerable economy involved in the lateral system and vertical sway bracing. In this layout of floor-system any of the three ordinary types of deck can be utilized. In general it may be stated that for any span-length the floor-system of a deck span will be cheaper than that of a through span. Stringers are usually plate-girders, except for through, plate-girder spans; and in these rolled I-beams are more applicable. Floor-beams are nearly always plate-girders, although occasionally in narrow structures it may pay to use deep rolled I-beams. Cross-beams in through, plate- girder spans having no stringers arc nearly always rolled I-bcams, unless the span be unusually wide. In making economic comparisons between plate-girder and rolled I-beam constructions, it is necessary to take into account the difference in ECONOMICS OF DECKS AND FLOOR-SYSTEMS 187 the pound prices of the two types, the said difference usually, but not always, being in favor of the latter. Electric Railway B^iiidges This type of structure is found on interurban roads and elevated railways. The economic problems of the deck and floor-system are sim- ilar to those in steam-railway structures, except that the construction is much lighter. The economic lengths are somewhat greater because the loads are smaller, but the economic principles involved are identical. Highway Bridges Decks For highway bridges there are two general types of deck, viz., timber and concrete. In respect to first cost of both the deck itself and the material required to support its weight, the timber type is always the cheaper, the saving increasing with the span length. In times past the timber deck per se was very much less costly than the concrete deck, but to-day it is otherwise, because the price of timber has risen more rapidly than that of any other material employed in bridge construction. Whether at the present time in any particular case timber or concrete per se for decks is the cheaper will depend somewhat upon the locahty and the availability of supply for the various materials. The solution of the question has to be determined specially for each case, as it arises, but the difference in first cost for the two types will seldom be found great. The real economic question involved is one of comparative weights and costs of the materials required to carry the deck. When, however, maintenance and renewals are taken into considera- tion, the concrete deck will nearly always be found to be the more econom- ical for short spans and those of moderate length. There is, though, one factor of vital importance that cannot well be considered in the economic comparison, viz., the danger from fire. This is so important as to rule out the use of timber in bridge decks for aU cases in which it is practicable to raise the money required for the concrete construction, excepting only that creosoted wooden blocks on a reinforced concrete base are permis- sible on account of being almost fireproof, or at any rate very slow-burning. An exception might be made for the movable span in a bascule bridge because the tipping of the floor to a vertical, or nearly vertical, position is somewhat objectionable, although it is not impracticable to design a concrete floor with a concrete pavement thereon in such a manner as to withstand effectively the said tipping. In case the timber floor be adopted, it would be necessary to take the utmost precaution against injury by fire. Pavings for Roadways The type of paving to adopt depends upon whether any timber is to be used in the deck. Planks make the cheapest kind of flooring, but 188 ECONOMICS OF BRIDGEWOKK Chapter XXI they afford a poor riding surface and are short-lived. Transverse planks are objectionable on account of rough riding, and diagonal ones are better for high-speed traffic, although they splinter and are primarily somewhat more expensive — due to a waste in cutting them to proper lengths. Longi- tudinal planks afford the easiest-riding, but they do not wear at all uniformly because of the tendency of the travel to run in certain lines. Planks can be either untreated or creosoted. Creosoting delays the process of decay but lowers the resistance to abrasion; hence, for the wearing floor, untreated planks are the more economical. A hard- wood tunber that does not warp or twist excessively is the best for the said wearing floor. A double-plank floor with the lower laj^er creosoted and the upper layer placed diagonally is ultimately the most economical of all plank floors. With the creosoted planks it is practicable to use a pavement of cre- osoted pine blocks, but the combination is very inflammable, and hence, is not truly economic. A similar pavement can be used to advantage for bascule spans by adopting instead of the blocks maple planks on edge bolted into groups and attached firmly to the steelwork. With a concrete base any desired type of paving can be employed — wood blocks, brick, asphalt, bitulithic concrete or any other kind of bituminous paving, plain concrete, or granitoid. Wood block is the most expensive as far as first cost is concerned, but it makes a much better showing in the comparison when maintenance and renewal are considered. Brick per se is less expensive, but it is heavy and, in consequence, requires more metal to carry it. This is not a serious handicap on short-span bridges, but on long-span ones it is almost prohibitory. Asphalt and bituminous pavements in general are good; and usually they are no heavier than the wooden-block ones. Unfortunately, they require an extensive plant to lay them; and, as the total area of paved surface on most bridges is comparatively small, the charge per square yard for use of plant will be excessive, unless there be a nearby plant available. To adopt an asphalt or bitulithic paving on a bridge in a small town is, for that reason, rarely economic practice. This difficulty, however, can be overcome by adopting an asphalt block pavement, which requires no plant for its construction. A concrete wearing-surface in many cases is both satisfactory and com- paratively inexpensive, for it requires no special plant to lay it; neverthe- less an extra hard and durable aggregate is obligatory, and the concrete must be very carefully mixed, placed, and finished, and must be kept properly wet while curing, especially in hot, dry weather. Unless these prectautions be observed, the concrete pavement will not prove economic b(H'ause of short life and the expense of repairs and replacement. It will b(> found advisable to design with an allowance in dead load for an extra two inches of concr(>te, so that a thick(M- W(vu'iiig surface may b(^ ]Mit on, if ever desired, without overloading the floor-syst(un or the trusses. ECONOMICS or DECKS AND FLOOR-SYSTEMS 189 Sidewalks Sidewalks are usually reinforced slabs of granitoid or specially-hard concrete, or else untreated planks. The latter are the cheapest, even when the cost of maintenance is considered, for they last fairly well; but, like all other timberwork, they are subject to destruction by fire, involving also injury to the metallic portion of the structure. Sub-Paving or Base As previously stated, the reinforced-concrete slab makes the best and most economic base for pavement. The reinforcing must be arranged to suit the steel floor-system, which will be described later. A timber base, either plain or creosoted is not truly economic construction because of the fire risk, nevertheless it is frequently used because of limited funds, or for lack of appreciation of true economy in design. Comparing creosoted and plain planking, the former is more expensive and heavier, but the plain plank as a base rots so rapidly that its use is uneconomic. Modern con- centrated loads require that the distances between supports for the planks be small — say two feet for 3-inch planks and two and a half feet for 4-inch ones. The former thickness is totally unfit to support heavy traffic, espe- cially after either abrasion or decay has started. With the live loads adopted in the standard bridge-specifications of today, timber joists .or stringers are not truly economic; for very heavy members would be required for panels of any length, even down to the shortest ever likely to be considered. The cheapest timber floor is obtained by plank carried on ties supported by widely-spaced steel stringers. Common practice, however, spaces the stringers closer and puts nailing-strips thereon. This increases materially the cost of the stringers. Curbs The best kind of curb to adopt depends essentially upon the style of deck. With a concrete deck or a pavement on a reinforced concrete base, a concrete curb properly faced with a steel angle is the appropriate con- struction; but for timber decks, wooden guards are the proper thing. True economj^ demands that the drainage of the deck be correctly taken care of, either by openings beneath the curbs or by an effective grade on the roadway. Waterprooji'nn When the steelwork is encased in concrete, or when no dripping of water on the space below the deck is allowable, it becomes necessary to provide waterproofing between the paving and the sub-base. The mem- brane type of waterproofing, previously described for railroad bridges, is the best and most economical. 190 ECONOMICS OF BRIDGEWORK Chapter XXI Handrails Handrails are made of concrete, structural steel, gaspipe, or timber. The concrete rails are the best looking, but are also the most expensive. Contrary to the general ideas -of engineers, they wiU require repairs from time to time, in order to replace chips broken off from the sharp edges of columns by blows, or, by spaUing in the case of concrete placed in cold weather and not thoroughly protected against freezing. • Steel handrails are expensive, when substantial; and they require paint- ing from time to time. Gas-pipe handrails are flimsy in appearance and ineffective besides. Timber handrails are the cheapest, but like all other timber construc- tion in bridges they are objectionable because of fire — besides, the ordinary ones are inherently ugly. Electric-Railway Tracks With timber decks the problem of caring for the electric-railwa}'^ tracks is a simple one, but with a permanent deck it is somewhat difficult, involv- ing, as it does, some economic considerations. In the first place, the rails must be of a height to suit the pavement adopted, and their heads must be flush with the top thereof. Next, the best method of support is a knotty point to solve. For a concrete deck there can be employed timber ties surrounded with either ballast or concrete, or steel ties embedded in con- crete, or steel ties embedded in the reinforced-concrete slab and resting directly on the steel stringers, or steel rail-chairs supported in a similar manner. When the roadway and the railway are separated so that the two kinds of traffic cannot mingle, any of the types of floor previously described for steam railways can be used. The wooden ties are generally the least expensive type of track, and steel ties in a concrete base are costly. Steel ties in the reinforcing slab and resting directh^ on the steel stringers make good construction, especially for long-span bridges. Steel chairs are cheaper and fairly good, but they do not ensure a perfect spacing of the rails. Wooden ties in ballast are cheap per se, but the construction is heavy, and, therefore, expensive for all but very short spans. Floor-Systems The arrangement of the floor-system, i.e., stringers, joists, floor-beams, and cross-girders, with their bracing, depends upon both the t>'i)c of deck adopted and the kind of span employed. In I-beam spans there is no need for a floor-system, because they are so short that a concrete deck is all they require; and its extra weight, as com- pared with that of the open dock of timber ties, does not add appreciably to the cost, because of the large ratio in any case of live load to dead load. The o(!onomical spacing of the I-beams varies from six to ten feet, increasing gradually with the span length. The undcM'-ckvirance, however, may be ECONOMICS OF DECKS AND FLOOR-SYSTEMS 191 limited, requiring close spacing, so as to permit the adoption of shallower sections than the economic ones. The beams are frequently encased in concrete in order to protect the metal from the fumes of locomotives passing below. If a timber deck should be adopted with planks resting either directly on the stringers or on nailing-shims bolted thereto, the spacing should be some two and a half feet, more or less, depending upon the size of the concentrated wheel-loading; but, if the planks are carried on wooden ties, the spacing may be made about five feet. In deck, plate-girder spans also, the floor-system can sometimes be omitted, especially in short spans, with either concrete deck or planks on ties; but in long spans of this type the steel floor-system will generally be found more economical. The limiting span-length for omission of floor- system is sixty or seventy feet, as far as the economics of the superstructure alone are concerned ; but such extreme lengths may increase too greatly the cost of the supporting parts. For instance, with only two lines of main girders and a floor-system there will be required only two columns per bent and two pedestals to support them; whereas with several lines of girders there must be several columns and pedestals per bent, or else a heavy cross- girder or a continuous concrete pier, either of which is more expensive than a pair of columns with their pedestals and bracing. If for any reason it be decided to use continuous shafts in the piers, there may be no extra expense due to supporting several lines of girders ; in fact, there may be a reduction in cost, because it might be possible to employ narrower piers or seats. In deck, plate-girder spans with floor-systems it is economic to use only two lines of main girders up to a fifty-foot total width of deck or in some cases even sixty feet. The girders for economy should generally be placed at the quarter widths, so as to obtain, in both substructure and super- structure, the full economic benefit of the cantilevering. In narrow struc- tures the spacing should be proportionately greater for the sake of rigidity and stability. With three lines of main girders, the spacing should be about one-third of the total width of che deck. The standard floor-system in deck, plate-girder construction has stringers carried on floor-beams. The portions of the latter outside of the outer girders are cantilever beams with a strap-plate over the top of the main girder and some kind of properly designed detail below to carry the compression from the bottom flange of the cantilever to the bottom flange of the floor-beam. The stringers are generally rolled I-beams and the cross-girders built beams, although occasionally it will be found economic to employ a deep rolled-I-beam. With planks resting on stringers, either directly or by interposed naihng strips, the stringer spacing will, of course, be determined by the size of the specified concentrated live loads and the assumed thickness and kind of material of plank. It is generally about two feet for three-inch plank and two and a half feet for four-inch plank. Closer spacings than these involve an extravagant amount of metal for stringers. 192 ECONOMICS OF BEIDGEWORK Chapter XXI With planks resting on ties, a spacing of five feet, or even more, can be used, depending, of course, on the size and strength of tie and the assumed concentrated live load. This wide spacing reduces materially the weight of metal in the stringers, thus saving more than enough to com- pensate for the cost of the ties. With a concrete deck it is economical to space the stringers from six to ten feet, there being very little difference in total cost for variations between this range. It is better, as a rule, to adopt the smaller limit so as to reduce the cost of the slab-forms. The economic panel-length is small, running from ten or twelve feet for a twenty-foot spacing of main girders to fifteen feet for a thirty-foot spacing, and to eighteen feet for a fifty-foot spacing. It is specially short for closely-spaced stringers with plank floor. In general it may be said that the greatest economy obtains when one of the standard beams just barely figures as a stringer. For instance, if in choosing between a six-foot and a seven-foot stringer-spacing, the 20" 65 lb. I just figures for the latter and must also be used for the former because the 18" 60 lb. I is not strong enough, it will be found economical to adopt the greater spacing. On the other hand, if the 18" 55 lb. I just figures for the six-foot spacing, and the 20" 65 lb. I is required for the seven-foot spacing, the former will prove the more economic. The question of extra metal in girders or trusses to carry heavier slabs is not important with short spans, but is very much so with long spans. With concrete deck on plate-girder spans it will sometimes be found cheaper to use no stringers, but to employ -rather-closely-spaced cross- girders on which the slab rests directly. The economic spacing of these girders figures out twelve feet or more, so far as quantities of materials are concerned; but it is better to use ten feet or even less, because the supporting of the slab-forms for the long panels is expensive. This type of floor is specially adapted to through, plate-girder spans and will be dis- cussed further in connection therewith. It does not save quite so much with deck plate-girders, as the girders themselves form two or more lines of stringers; hence the total weight of stringer metal which can be saved is less with deck plate-girders than with through plate-girders. Again, an outside stringer may, in any case, be required to support the hand- railing. When the structure carries electric railway tracks, a stringer must be placed under each rail. The addition of such stringers would practically eliminate the saving above discussed; and, therefore, the standard type of floor-system with stringers and floor-beams should be employed. Sidewalk slabs should be carried on longitudinal stringei-s, even if the cross-girders are spaced closely. The outside stringer should generally be a channel so as to provide a flush surface for the attachment of the hand- railing; and with short panels the inner stringers may be of the same sec- tion. Vov five-foot walks two stringers will give the cheapest construc- tion, the curb stringer of the roadway sometimes being utilized as one of ECONOMICS OF DECKS AND FLOOR-SYSTEMS 193 them. For eight-foot or ten-foot sidewalks three stringers are economic. Sidewalks on deck, plate-girder bridges reduce, or even eliminate, the economy of the stringerless type of floor-system. With half-through, plate-girder spans, the positions and numbers of girders are generally fixed, two being just outside of the curb-hnes; but in wide roadways it is economic to use three hues of girders, although the splitting of the traffic by the middle girder is not a desirable feature. In the case of a very shallow floor, though, such splitting cannot be avoided. The stringerless type of floor-system is nearly always cheaper in half- through, plate-girder, spans than the standard type with its stringers and floor-beams. With electric-railway tracks the advantage is smaller than where there are none. With no such tracks the saving of metal amounts to some 200 lbs. per lineal foot of span for a structure of any ordinary width; and the excess cost of the thicker slab is small. Again, the stringer- less type is shallower than the other — which is often very important. By spacing the beams closely a very shallow floor can be obtained at moderate cost; but too shallow sections are not desirable, as they do not afford sufficient lateral support for the top flanges of the main girders. The floor-systems of half -through, plate-girder bridges very often must be encased in concrete. This is to the advantage of the stringerless type, which has smaller area to cover and involves more simple work. When a concrete slab is employed, it should be carried over to the webs of the girders and supported on shelf angles. If the floor is encased, the detail at the girder web needs careful attention, in order to prevent water from entering and thus causing rusting of metal and splitting off of encase- ment. Sidewalks on half- through, plate-girder spans are carried on cantilever brackets, but outer steel stringers will be needed. The inner edge is supported on a shelf angle. A close spacing of these brackets is advan- tageous, as generally there is difficulty in properly taking care of large top-flange tension. With truss spans, the standard floor-system of stringers and floor-beams is nearly always adopted, because it would usually be uneconomic to sup- port the cross-girders by the chords between panel points. As previously indicated, the economic panel length for the floor-system per se is from fifteen to seventeen feet, which is too short for the economics of the trusses, hence longer panels than that limit generally have to be adopted. For a bridge of practically any width of roadway, the metal in the floor-system with 25-foot panels weighs about 70 pounds per lineal foot more than that required for the economic panel length, and for 30-foot panels about 150 pounds per lineal foot more. Divided panels in spans of moderate length permit the use of the economic panel length, but the secondary truss- members increase the weight of metal in trusses enough, or more than enough, to offset the saving in the floor-system. With long spans, how- ever, this uneconomic feature disappears. 194 ECONOMICS OF BRIDGEWORK Chapter XXI In timber decks the economic stringer spacing is about the same as it is in plate-girder spans; and in concrete decks it is five or six feet for spans of 200 feet or under, and less for longer spans. For instance, in spans of 400 feet with 25-foot panels it is four feet, and with 35-foot panels it is four and a half feet. The stringerless type of floor system with concrete deck for very short panels — say 12 feet — shows the same economy in truss spans as it does in haK-through, plate-girder spans. With truss-spans of moderate length, the panels are so long that the chords would have to be built as girders in order to carry cross-girders between panel points. The floor-system itseK, as compared with that of the stringer type, when the panels are 25 or 30 feet long may show for standard deck-widths a saving of from 250 lbs. to 350 lbs., per lineal foot, while the extra metal in the chords required to make them serve as girders would amount to 250 or 300 lbs.; besides which there must be taken into consideration the increase in weight of truss-metal due to the augmented dead load by reason of the thicker slab. On this account the stringer type wiU nearly always be found cheaper, especially when electric railways are carried. With encasement there may be an economic advantage in the stringerless type, especiallj' if a very shallow floor be called for. With extremely long panels it will be found cheaper to use stringers close to the trusses rather than to stiffen the chords of the latter enough to make them able properly to carry the transverse loading. For very long spans with concrete slabs it is desirable to reduce the weight of deck to a minimum. In such cases it will be most economic to support the slab on closely-spaced cross-beams carried on stringers rather widely spaced — say 10 or 12 feet centers. Considering both the weight of metal in the floor-system and that in the trusses, it is found that the economic spacing of the small beams is about three feet. Comparing this with the ordinary type having stringers spaced four and a half or five feet, it will be found that the metal in the cross-beam type weighs about three pounds more per square foot for 25-foot panels and about one pound more per square foot for 35-foot panels, while the slab weighs eight pounds per square foot less. The total deck, therefore, weighs some five pounds per square foot less for 25-foot panels and seven pounds per square foot less for 35-foot panels. Considering the extra weight of truss-metal needed to support this excess of dead load, and remembering that the pound cost for the cross beams is a little less than that for the remainder of the floor-system, it has been figured that the cross-beam type is cheaper with 35-foot panels for spans in excess of 200 feet, cheaper with 30-foot panels for spans of 350 feet, and cheaper with 25-foot panels for spans of 600 feet. Evidently, therefore, there is no economy in adopting this type for spans shortcM- than 250 or 300 feet; but for all long spans it is quite economical. This type of floor affords a good support for the rails, which must, ECONOMICS OF DECKS AND TLOOR-SYSTEMS 195 however, be made quite deep. The reinforced slab must be cut back from the rail in order to permit of the latter being removed. This detail requires careful watching. Sidewalks on through-truss bridges are usually placed outside of the trusses and carried on longitudinal stringers supported by cantilever brackets. In very-long-span bridges, such as cantilever or suspension structures, the matter of economy from deck and floor-system should be very closely studied, in order to eliminate every unnecessary pound of dead load. Preliminary designs should be made for various types and for different spacings of beams and stringers, in order to determine the most economic arrangement. The question of total weight of deck may be far more important for such long-span structures than the total weight of metal in the floor. Timber decks, of course, will be much cheaper than concrete decks; and the decision between the two types must be made by judgment, considering the nature of the traffic, the money available, the possible revenues, the first cost, the cost of maintenance, and especially the danger from fire. In general it may be said that the concrete deck should be adopted if sufficient money can be secured, and, for a toll bridge, if the estimated revenue justifies the expenditure. There is a Hght type of floor recommended for long spans by Edward A. Byrne, Esq., Member American Society Civil Engineers, Chief Engineer of the Department of Plant and Structures of the City of New York. It ' consists of stiffened buckle plate, having the buckle down, covered with plain concrete, and supporting a thin block pavement. Concerning this type Mr. Byrne on June 8, 1920, wrote the author as follows : Where buckle plates are used to support the roadway pavement the following detail of construction is suggested. The ends of all buckle plates should rest on supports and be properly spliced. The fillets of the buckle plates should be reinforced by angles — 3"X3"X|" angles have proven effective in buckle plates supported on stringers five feet on centers. The plates should be laid with the buckle down and filled with Port- land cement concrete to a depth of at least three inches above the top of the plate. Longitudinal angles, 3"X3"Xf", should be riveted to the buckle plates along the line of the supporting stringers to restrain the concrete foundation and act as a template for laying the concrete. Each buckle plate should have a drain hole; and a hole in the concrete, extending from the top thereof to the buckle plate, should be provided. On top of the concrete foundation a wood block pavement, three inches in depth, should be laid without any cushion, sand to be spread over the pavement and brushed into the joints. The Portland cement concrete should be one part cement, two parts sand, and four parts broken stone or gravel — the top to be rubbed to a smooth finish. . . . It is highly important that, in using a buckle plate floor, all deflections of plates be eliminated, otherwise the concrete foundation will crack and disintegrate. Tests made by Mr. Byrne on the floor of the Queensboro Bridge, where the stringers were spaced five feet on centers and where the buckles were about four feet long, showed deflections of buckle plates as great as three- eighths of an inch before the stiffening angles were attached, but no appreciable amount after they were put on. 196 ECONOMICS OF BRIDGEWORK Chaptek XXI The cost of the pavement-support -per se is about twice as great for the buckle-plate type as for the orchnary type with reinforced-concrete slab, 100 200 300 400 300 600 700 dOO POO WOO 200 300 400 300 600 700 600 $00 1000 ■ Span leoqfd /o feef Ficj. 2lr;. Diugnim of Iruiretiw! in Wcif^hl, of Metal for Each Excess Pound of Extrane- ous, Uiiiforinly-l)is(ril)ul(>(l Tioad in Siniijle-Truss Spans. the (li(TcM(Mic(> ;il cmrcnt i)iiccs of nuitcrials and labor being about eighty cents pc;f' s(ju:uc loot of fkjor; but there is a saving effected in the dead ECONOMICS OF DECKS AND FLOOR-SYSTEMS 197 load by the former, amounting to about eighteen pounds per square foot. For a simple truss span of 600 feet, it requires about 0.58 lb. of steel to m 600 2000 2m 2m 3.0 1000 m 1400 ^ 1600 /©7^/6, of Ma/n Opepi/?q //? fee/- Fig. 216. Diagram of Increase in Weight of Metal for Each Excess Pound of Extrane- ous, Uniformly-Distributed Load in Type-A-Cantilever Bridges. carry an extra pound of extraneous load ; hence, for such a span, the extra metal to support the eighteen pounds of excess dead load of the floor would 198 ECONOMICS OF BRIDGEWORK Chapter XXI be about ten and a half pounds, which, at the present unit prices of mate- rial and labor, are worth in place about 84 cents, showing that to-day for simple-truss spans exceeding 600 feet in length it would be economic to adopt the buckle-plate floor. As this economic question is likely to arise at any time, and as its solu- tion is largely dependent upon the relative unit prices of concrete and structural steel in place, the author has prepared the diagrams shown in Figs. 21a and 216, which indicate for simple-truss and cantilever spans, respectively, and for both carbon steel and nickel steel, the amount of extra metal that will be required to support one excess pound of extraneous load uniformly distributed. Just as the MS. of this book was about to go to press, the author's attention was called to a Hght aggregate for concrete, termed Haydite, being named after its discoverer, Mr. Stephen Hayde, a well-known citizen of Kansas City, Mo. He claims that concrete made of it weighs only 108 lbs. per cubic foot, as against 150 lbs. per cubic foot for ordinary 1:2:4 concrete of small broken stone or gravel, and that the hghter concrete not only is practically impervious to water, but also that it gives some 25% greater resistance to compression than its heavier competitor. If these claims are correct, there should be quite a demand for Haydite for the bases of highway-bridge floors, especially as the extra cost of the aggregate is moderate. Mr. Hayde and his business associates contemplate retaining the author to make a thorough investigation of, the suitability of Haydite for pavement bases in bridge construction and to show by diagrams and otherwise the economics involved thereby. Until some engineer of standing tests the new aggregate and vouches in print for its characteristics, the profession will have to take the discoverer's claim cum grano salts; nevertheless, the author has great hope of its being proved to be all that is claimed. If such be the case, its use will result in a real boon to the builders of modern, first-class, highway bridges, especially those of long span. CHAPTER XXII GENERAL ECONOMICS OF DESIGNING AND DETAILING In this chapter will be treated only the salient economic features of ordinary designing and detailing, because to attempt to do more would lengthen this portion of the book beyond all reason. In all cases it is economic to choose the most simple types of structures and details, and especially those that lend themselves best to stress analysis. One should select members which by form and location are best adapted to resist forces economically and to carry stresses by shortest routes. For instance, in a long-span truss with parallel chords, shear is transferred entirely by the web members; and the path of the web stresses is much shorter by the divided-triangular truss than by the Pratt truss, hence the use of the former is economical. But in short-span trusses the verticals are nearly all of minimum section, hence there is but Httle, if any, difference in the economics of the two types. Similarly, with polygonal top chords, the shear on the webs being comparatively small, there is not much to choose between the said two types. In riveted tension members the riveting should be arranged so as to reduce to a minimum the number of rivet-holes to be taken out of a section; but if the number assumed be too small, material will be wasted at splices in developing the net section, because extra holes above the number that would normally be employed cannot be used at joints unless extra section is first developed into the splice-plates or gussets. Furthermore, the section will very Hkely be reduced in detaihng, without the fact being noted. This will overstress the metal at such sections. In compression members the metal of the section should be arranged to secure the largest practicable radii of gyration without involving the use of metal that by its thinness would transgress the rules of standard speci- fications, viz., minimum limits of one thirty-second of unsupported width for webs, and one fortieth thereof for cover-plates. It is economic to employ fairly heavy angles, as thereby the radii of gyration are increased and, in consequence, also the strength of the strut. If the unbraced length of the piece is greater in one direction than in the other, the section should be so arranged that the values of the ratios of length to radius of gyration are approximately equal. For instance, in the case of intersecting diago- nals of lower lateral bracing, the unbraced length in one direction is twice as great as that in the other. Then for 2-angle sections unequal-legged 199 200 ECONOMICS OF BRIDGEWORK Chapter XXII angles should be employed with the longer legs vertical; but for 4-angle sections it is economic to make the longer legs horizontal and connect the shorter legs by a single line of lacing placed between them. For vevy long struts it is economic to employ four angles in box section, connected by four lines of lacing. In Ught bridges the posts can be made either of H section or of four angles with either a web or lacing between, rather than of two channels laced. This arrangement saves considerably in weight of details, but some of that saving is lost because of the greater sectional area required to allow for the reduced radii of gyration. For compression members which carry shear, there should be one or more webs in planes parallel to the said shear. Such webs can be employed to advantage also in simple struts of large cross-section. If lacing can be omitted thereby, a saving of metal may result. On the other hand, the radius of gyration may be reduced by using such diaphragms, thus, lowering the unit stresses. In railway, deck plate-girders, as far as weight of metal is concerned, it is economical to use cover plates for top flanges, but this requires rivets and the variable dapping of the ties. Rivets increase the work of placing and maintaining the ties, and deep dapping is undesirable. The best railroad practice forbids the use of rivets through the upper horizontal legs of the flange angles of stringers when timber deck is employed. Batten plates for large compression members must be excessivety thick, unless they be properly stiffened by angles; and it will generally be found less expensive to adopt thin plates and stiffen them. Unless considerable metal be saved by that expedient, however, it is better not to do this, because the addition of stiffening angles increases materially the amount and cost of the shopwork^ — besides it may involve some difficulty in han- dhng the members. In compression members consisting of two built or rolled channels, it is usually economical of metal to turn the said channels in. However, this increases the cost of the shop work, because lacing-rivets when the channels are turned in usually cannot well be machine driven. In designing a built chord for a bridge, the sections must be determined by considering all panels of the chord simultaneously. It is well to adopt as few differing thicknesses of metal as practicable, and to arrange the various sections so as to avoid, to as great an extent as possible, the use of filling plates at the splices. In field splicing the loss of loose filling plates is a cause of serious troul)le and expense; hence they should be avoided. For the sake of simplicity, it is frequently best to waste metal in some of the panels; but such waste should always be reduced to a mininunn. When cover plates arc employed, it is advisable to avoid changes in the location of the center of gravity of the section. In detailing onc^ should always endeavor to use metal to best advantage; and the strength of each detail or connection should be figured whenever GENEKAL ECONOMICS OF DESIGNING AND DETAILING 201 this is practicable. When exact analysis is impossible, an ample amount of metal should be used so as to avoid any possible weakness due to such uncertainty; but this does not mean that it is well to be recklessly extrava- gant of metal in order to save the trouble of figuring the sti'ength. It is false economy of the worst type to skimp details; because the saving in metal is comparatively small, and the loss of strength may be very great. It is worse than useless to adopt low unit stresses for the main members and put in weak details; for the stress sheet then gives a false sense of security. It would be much better to have strong details and high working stresses in the main members. Details and joints frequently defy exact analysis; and in such cases the designer should not fail to make approximate analyses to determine the character and magnitude of stress in every part so as to avoid all possibility of the existence of weak spots. It is not unusual to see metal placed at a joint where it could not possibly do any good, while an important com- ponent part of a member is left unspliced. A ten per cent error in strength on the side of danger will rarely do any harm ; but the complete omission of a vital part of a detail may be very serious. For instance, in the lateral systems of highway bridges, it is not uncommon to see a diagonal of strong section connected by details so flimsy that they could not possibly transmit one-quarter of the stress which the said diagonal is capable of withstand- ing. The m'etal in such a lateral system is nearly all wasted. As an important matter of economy, rusting and other kinds of deterio- ration should be carefully considered when making designs. It is very un- economical to use parts which will rust out or wear out in a small fraction of the possible life of the structure. Repairs are not only expensive 'per se, but also they generally interfere seriously with the traffic. Some mipor- tant railroads use ys ii^ch or even ^ inch as the minimum thickness of metal in steel superstructures; because they find thin metal to be one of the most fruitful causes of replacement. The author, however, is of the opin- ion that, if the said companies were to adhere to the f inch minimum thickness and keep the metal always properly painted, they would obtain more satisfactory results. All parts should be easily accessible to the paint brush; for otherwise the painters wiU fail to cover some metal that is difficult to reach, thus curtailing the fife of the structure. A horizontal plate in a bottom chord will frequently save metal; but it invites rusting, and therefore is sure ultimately to prove uneconomical. When there is a choice of plates and shapes that can be used in the malce- up of a member, it is sometimes practicable to economize a little by adopting the most inexpensive ones; but too often it will be found that the more expensive shapes are also the ones which are the more appropriate and serviceable. CHAPTER XXIII ECONOMICS IN DESIGN FOR SHOP CONSIDERATIONS While the consulting bridge engineers of America do not yet agree entirely with the engineers of the bridge manufacturing companies concern- ing all points of design, the ideas of both have of late been gradually getting closer together. The differences of opinion are generally in the line of economics, the shopmen desiring to cheapen work in ways of which the consulting engineers disapprove. Designs should be made so as to afford the bridge shops every facility possible for using their machinery to advantage. For instance, details should be arranged for multiple-punch spacing, and to suit the requirements for bending, machining, and the various other operations which are gov- erned by the shop equipment. One great bone of contention in times past was the matter of sub-punch- ing and reaming as against punching full-size and running a loose reamer through the holes in the assembled component parts, so as to ensure the possibility of the passage of the hot rivets. Even today much work is done by the latter method, but it is generally confined to parts of so-called minor importance. The object of sub-punching and reaming is two-fold: first, to make the holes in the component parts match properly after the passage through them of rigid-drill reamers, and, second, to cut away the metal around the peripheries of the holes which was injured by the brutal process of punching. The author, if he could always have his way in this matter, would bar entirely the punching of holes full-size; and he believes the day is coming when even the sub-punching and reaming will be prohil^ited by adopting the method of solid drilling. He has asked some of the })rominent bridge manufacturers how much extra it would cost to employ the latter method, and has been told that, if the shops were propo-ly outfitted for the work, the excess cost as compared with sub-punching and reaming would be practically nil. For nickel steel and other high-alloy steels solid drilling should be exclusively employed. In the case of sheared edges, if the metal near the shear is to be depended on for strength, the said edges should be planed, but otherwise the planing should ])(\ omitted, unless the raw edges would be too much in evidence to th(! b(!hold(;r of the finished structure. It is more than probable that the shearing of edges is just as destructive as the punching; for the brutality of the treatment of the metal in the two cases is of the same character and apparently of the same severity. 202 ECONOMICS IN DESIGN FOR SHOP CONSIDERATIONS 203 While it is undoubtedly difficult to procure a tight fit for stiffeners on rolled I-beams, it does not appear to the author safe to omit them at the ends of railway girders that are supported from beneath, or even from those used for carrying heavy highway loads to the masonry, because the unsupported webs are not of a shape satisfactorily to resist severe pounding. Although it is true that turning the flanges of channels in makes the riveting somewhat more difficult, it need not prevent the use of power riveters, except in the case of a few rivets; while it facilitates greatly the detailing by bringing all the webs of main truss members in the same plane for the attachment of the gusset plates. Most of the author's riveted bridges are built in this way. Again, it is important to have the batten plates inside of the gussets, and to carry them to near the ends of the members, both of which condi- tions the turned-in channels permit. Moreover, they generally involve an economy of weight of metal for lacing and battens. But one of the most important advantages of turned-in channels is that they permit the ends of the floor-beams to fit closely to the bottom chords without cutting either the chord or the beam, which is not practicable if the flanges of the bottom chords turn out. In viaduct construction some manufacturers use their influence to have the girder-depth the same from end to end of structure, which is uneconomic of material, because the tower spans and the intermediate spans are nearly always of different lengths, which arrangement would call for different depths unless metal is to be wasted. The manufacturers' claim has appar- ently some justification if the tops of the columns are cut off so as to let the main girders be supported directly thereon; but, in the author's prac- tice, the columns are carried up to the level of the deck, and both the longi- tudinal girders and the tower cross-girders abut into them; hence there is no valid objection to making the comparatively-short longitudinal-girders over the towers shallower than the long, intermediate longitudinal-girders. This layout certainly looks much better; and the corner brackets afford an excellent connection for the diagonals of the longitudinal bracing. If the designing of details be left to the manufacturers of the metalwork, they often place the end or pedestal pin of a riveted-truss span below the bottom chord, forgetting that the thrust of a braked train, acting with a lever arm equal to the vertical distance between the center of the chord and the center of the pin, produces a large bending moment that has to be resisted by the stiffness of the bottom chord and that of the inclined end post. When bridge superstructures are let to the manufacturers by the lump sum and they have the designing to do, they like to omit the end floor beams of through bridges, substitute instead inexpensive struts, and rest the stringers on the masonry; but the author beheves that invariably end 204 ECONOMICS OF BRIDGEWORK Chapter XXIII floor-beams should be employed and be riveted to the end posts of the trusses so as to make the lower lateral system a harmonious whole; and it matters not if the end posts be inchned. Manufacturers are willing to use single angles in tension, but this is objectionable because of the violation of the rules of symmetiy and the con- sequent causing of secondaiy stresses. A mooted point in designing is the exact location of top-chord pins. The author believes they should always be placed either on or a very little below the gravity lines of the sections, for it takes an exceedingl3r small eccentricity to produce a high intensity of bending stress on the chord. It is not right to assume that the reverse bending moment due to the weight of the member between panel-points will entirely counteract the bending moment due to the eccentricity; because the form taken under loading by the center line of the long strut will be a waved line passing through the centers of the chord pins, being concave upward in one panel and convex upward in the adjoining one. The amount to lower the chord pins below the centers of gravity of the sections is to be determined by making the compressive intensity due to eccentricity equal to the tensional intensit}'' due to bending from weight of member. In any case this adjustment is a matter of compromise on account of the shifting of centers of gravit}^ from centers of figure by reason of the variation in make-up of section from pangl to panel, the amount ordinarily varying from zero to a quarter or three- eighths of an inch. In large bridges, of course, the variation will be greater than this. Manufacturers hke to use cast iron in bridges on account of its com- parative cheapness per pound; but on general principles the author tries to bar out all cast iron from his bridges, fearing that, if it be permitted in one place, the contractor will insist upon putting it into another. Cast iron is nearly always inferior to cast steel for any purpose. There is an uneconomic detail which is too often employed in both trestles and elevated railroads, viz., the insertion of a heavj^ casting between the lower end of a column and the masonry. The author has never been able to i^erceive the philosophj^ of this detail; for it involves the planing of a large amount of extra surface as well as a considerable increase in the weight of metal. Moreover, the additional surfaces in contact do not militate towards rigidity, for perfect contact is not always attained. The object is evidently the spreading of the load over the masonry; but this could be accomplished just as effectively and at less cost by using a rolled base-plate of the proper size and carrying the load to it from the colunui section by means of vertical plates, horizontal connecting angles, and verti- cal stiffening angles. The necessity for giving the latter a tight fit at tlieir lower ends i-ecjuires some troublesome shojiwork, but the additional cost thei'(!of will not offset the expense of the extra amount of planing involved by tlic (iasting detail. In respect to the general and detail principles of the economics of shop- ECONOMICS IN DESIGN FOR SHOP CONSIDERATIONS 205 work advocated by the highest authorities on the manufacture of structural steel and concurred in by the author, the following may be stated.* Attention should be paid by designers to the different pound prices for the various sections, and they should remember that these variations are lilvely to change from time to time. For instance, all angles over 6" and all beams over 15" deep cost a small amount above the base price; and for large plates the extras increase with the widths by a rapidly augmenting scale, starting generally from 100" with a trifling amount and reaching as much as one cent per pound extra for a width of 130". It is, therefore, often more economic to adopt the shallower of two widths and use a little more metal, especially when the variation of an inch or two of girder-depth would change the pound price of the raw material in the web plates as much as a quarter of a cent. Large differences have existed at times during the past few years, plates sometimes being very expensive and almost unprocurable. In the design for structural work for all purposes, more consideration should be given by the designer to the sections which are employed. Spe- cial material should be avoided, if possible; sections varying by xe inch should be so combined as to use one section as far as practicable; and spe- cial sections in small quantities should be eliminated entirely. Very often the delivery on the contract is delayed because the shop has to wait for a small quantity of a special section which is not rolled on time. Compli- ance with the above will insure better deliveries from the mill and quicker fabrication in the shop ; and all parties concerned will be benefited thereby. When ordering plates, the designer should adhere to standard dimen- sions as far as possible. This can always be done in the case of lateral and gusset plates, but a special depth may be necessary at times for the webs of stringers or girders. Standard widths for plates are 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 24, 30, 36, and 48 inches. Eye-bars, adjustable members, turnbuckles, screw-threads, segmental rollers, devices, upsets, etc., should be designed according to the standards of the bridge manufacturers, because quicker deliveries and better fabrica- tion are obtained by the use of standards. Designs should be made so that all extra or unnecessary operations in the shop are avoided. This should apply particularly to large and heavy members and to small members used in large nmnbers. The work on these pieces should be kept as simple as possible. When there is an extensive duplication of any piece, it will pay in its designing to save every pound of metal that can legitimately be omitted. Reaming to templets is useless unless the templets can be set from finished surfaces, as in chord splices, ends of stringers, floor-beam connec- tions, etc. Reaming of laterals to templets is liable to do more harm * The data for most of the remainder of this chapter were furnished to the author in 1915 for Chapter XVII of "Bridge Engineering" through the courtesy of Messrs. Paul L. Wolfel and Albert F. Reichmann. 206 ECONOMICS OF BRIDGEWORK Chapter XXIII than good, as no finished surfaces are available. The same apphes to diag- onals in trusswork. While in a punched connection a few holes may be slightly out, which can be corrected in the field, if a connection is reamed to templet and the templet is not properly set, all holes wiU be equally out. Riveted trusses should be reamed and match-marked in the maker's shop when assembled. In aU plate girders and truss-bridge stringers the lateral system should be dropped so that the rivet heads thereof will clear the ties. Wherever possible in heavy work, avoid, in the construction of the chords or web members, side plates or doubhng up of the web plates. It will often pay to use heavier web plates without side plates^ even if they have to be drilled from the solid. If, however, webs have to be doubled up or side plates used, the stitch rivets made necessary by this construc- tion should be reduced to a reasonable amount. If a plate is used as a cover plate in a chord, it is good practice to hmit its thickness to ^oth of the distance between rivets. If the same plate were used as a side plate in a chord, in most designs two or three times as many lines of rivets would be called for as would be necessary by the above limits. It is cheaper and better to use heavy flange angles in stringers than lighter angles with cover plates, even if the said angles should have to be drilled from the solid. Beveled cuts are to be avoided whenever possible, especially beveled cuts for angles that cannot be obtained by cutting multiple pieces from a long piece; also beveled cuts in all beams and channels, as these have to be sawed. One of the greatest savings in recent years in bridge shops has been made by the use of multiple punches. These not only reduce the cost of the punching proper, but also save the cost of making templets and the laying out of the material. They further give far superior work; as the effect of the stretch of the material during punching on the accuracy of the work is eliminated, if these multiple punches are property constructed. Their use, therefore, should be encouraged in every way. In order to do this, it is necessary to: (a) Keep all rivets in line longitudinally. (6) Keep as many rivets in line transversely as possible and do not use any more combinations of rivets transversely than necessary. (c) Never have the longitudinal fines of rivets less than 21" apart, nor the transverse lines less than 1|". Do not crimp stifTeners if it can be helped, especially do not crimp stiffeners of short lengths, say up to about three feet. If stiffencrs are crimped |" or more, the crimp is unsightly; and better and more sightly work win be ol^tained by using a thin filler with a smaller crimp. Do not call for fillers or s])lice plates to have a tight fit, as this is impracticable in the shop. The stiffeners, of course, should have a close bearing. Do not call for planing ot the base, cap, sole, or masonry plates, as the mills can roll the same closer than they can be planed. ECONOMICS IN DESIGN FOR SHOP CONSIDERATIONS 207 The old rule of sixty degrees for single lacing should be abolished, because this makes the lacing entirely too close for narrow members, and it is quite expensive and unsightly. Lacing bars should generally be lapped, as this detail will save about half the rivets. Instead of lacing it is often advisable to employ a solid web. This will sometimes permit the use of lighter main angles by counting the web as part of the section, although it reduces the radius of gyration and consequently increases the sectional area of a compression member — besides, it greatly facilitates the painting. All hand riveting should be avoided wherever possible, also all odd riveting that has to be done either before the work is assembled or after a piece is otherwise finished. In short plate-girder-spans it is economic to omit the bottom lateral system. Lug angles on laterals are expensive — it is better to use larger connecting plates in order to get the requisite number of connecting rivets. In laying out viaducts, as many towers as possible should be made alike by varying the heights of the pedestals. In square-girder spans, the number of panels of bracing should be even, but in skew-girder spans it should be odd. The greatest amount of duplication in any skew-span will be obtained if the floor is laid out so that the entire span can be revolved around a central point. In pin-connected work the sizes of the pins should not be varied more than is strictly necessary, two or three sizes being generally sufficient for one span. It is not altogether a waste of material to use larger pins than necessary, as the bearing plates can be reduced in thickness and often in length. It is economic of shopwork to avoid running the top flanges of stringers over the tops of the cross-girders. In riveted tension members it is well to use tie plates instead of lacing. The former have the advantage of getting better shop rivets. It is not necessary that the web-plate of a plate girder should be in con- tact with the sole plate, and to make it so is expensive. In deep girders the web thickness should not be less than ywo oi the depth thereof, as otherwise buckling is liable to occur. Where webs are spliced, ample clearance should be allowed, and the depth of the web should be one-half inch less than the distance from out to out of flange angles. Rounded corners in plate girders are expensive, but sometimes they are required for the sake of appearance. Cambering of plate-girders is useless and quite expensive. Information should be furnished to the fabricating shop, specifying the end of the structure which is to be erected first, it being very desirable to fabricate the work in the order of erection and also to note the direction of long plate-girders, so as to save turning them during shipment, at the shop, or in the field. 208 ECONOMICS OF BRIDGEWORK Chapter XXIII On chord or column sections extending over two panels with the same depth of section, but with smaller area required, the increased weight of the shop spHces will tend to offset the increase in weight due to making both sections the same, the big advantage in the latter construction, of course, being that the material is continuous without the splice. Frequently, on stringers and hght girders, the webs are designed very light, which necessitates the use of many stiff eners to prevent buckhng. It is often a big advantage to thicken the web and omit the stiff eners. The weight in either case is about the same, as the omission of the stiffeners will partially offset the increased weight of the thicker web. For chord sections, the employment of reinforcing plates between angles should be avoided by using additional web-plates the full depth of the chord. This design has the advantage of connecting more of the main material to the flange angles direct, and avoids the use of a great many rivets which are necessary to connect the reinforcing plates to webs. When two webs are riveted together, the rivets should be about 12" from center to center, the edges of the webs, of course, being held together by the rivets through the flange angles. When the specifications call for material drilled from the soHd on account of the use of either alloy steel or very thick ordinary steel, the members should be designed with as few pieces as possible. Instead of using f " or I" plates, which generally are of the right thickness for. punched work, the material should be ordered as thick as permissible within the mill requirements, provided that the strength of the plates does not drop below the specification stipulations on account of insufficient rolhng. The preceding portion of this chapter applies specially to the practice of the consulting engineer, although it records the opinions of experts in the line of steel manufacture; but the following pertains specially to the drafting work in the office of a bridge manufacturing company. Its inclusion is in the nature of an afterthought; and the explanation thereof is as follows: Long after the supposed finishing of the chapter, the author was being shown through the shops of the American Bridge Company at Ambridge by an old friend of his, Mr. C. M. Canady, one of the principal engineers of that Company; and needing additional data for the chapter on "Eco- nomics of Shop work" he persuaded that gentleman to promise to furnish some. Wlien the notes came to hand, it appeared that Mr. Canady had confined his remarks entirely to the economics of design as practiced in the Company's drafting office. As the said notes are of great value, and as they supplement and, in many ways, endorse the statements herein which precede, the author decided at once to include them in this place; and they are, consequently, given practically verbatim. ECONOMICS IN DESIGN FOR SHOP CONSIDERATIONS 209 Principles of Economics in Bridge Design for Shop Considerations '' In the following notes relative to the Economics in the Design of Bridges for Shop Considerations, the Drawing Room attached to the Fabricating Shop has been considered as a component and closely related part of the said shop ; and points that facilitate the execution of shop draw- ings have been included. "In the preparations of a bridge design for a given location, making spans duplicate instead of different lengths has not, in the writer's opinion, been given quite the attention it deserves. Such duplication always means decreased cost of drawings and shop work, and may mean also the adop- tion of a special fabrication programme for that contract, which would further reduce costs. " For the same reason the design should lend itself to the maximum amount of duplication in the details. To this end small differences in the cross-section of main members should be shunned. The avoidance of light and heavy trusses, on account of a sidewalk on one side only, is a case in point. This, however, is more applicable to hght work and to where the sidewalk load is comparatively small. Otherwise, where there is a mate- rial saving in weight by using Kght and heavy trusses, the difference can generally be accomplished by increasing the thickness of component parts of the various sections without changing the dimensions of the sections themselves, thus preserving the duplication of spacing and the details for the two trusses, as well as those for the lateral-system connections. " Under modern mill and shop conditions it is economical to build bridges with longer panels than formerly used. Longer panels mean fewer joints and fewer separate pa.rts, with consequent decrease in shop and drawing-room costs. '' If members can be made symmetrical about a point midway between the ends, it counts for economy in the preparation of drawings and templets. " Often spans have been designed with a small skew where a nominal increase in length, due to making the span square, vv^ould have meant a decided saving in the cost of the structure as a whole. '' In the design of a deck-girder bridge, if the span is square, it is econom- ical to arrange the lateral system with an even number of panels, so that the girder can be made symmetrical about the center. " If the span is skewed, use an odd Aumber of panels, so that the girders can be made alike and their position in the span reversed. Stringers with- out cover plates should have an odd number of panels of laterals. They will then have the same punching in the top flanges and be made alike for turning end for end, instead of different, as they would be if an even number of panels were used. " Some Consulting Engineers and occasionally even the designing offlces of the Bridge Companies are prone to make their designs so complete as to be almost shop drawings. This does not make for economy, either in 210 ECONOMICS OF BRIDGEWORK: Chapter XXIII the preparation of the design or in the work of the drawing room. Even where considerable freedom is allowed in the way of modifications to suit the standard methods, details, and equipment of the particular shop doing the work, the fact that such modifications must be arranged for with the Engineer, as well as their actual accomphshment, involves a certain delay and slowing down in getting the work under way in the drawing room. The engineers thereof must necessarily make complete investigation of the geometry, fits, etc., including the requisite number of large-scale lay- outs, independent of the completeness of the design. The manufacturer is always (and properly so) held responsible for the coiTCct fit of the steelwork. The Engineer's preference for certain types of details, or details that are required by the conditions of erection, should, of course, be indicated as a part of the design. " The spacing and arrangement of rivets should not be fixed; for the limitations of the specifications as to the maximum and minimum spacing ought to be sufficient. The designer should always keep in mind that modern bridge shops are equipped with multiple punches and various spacing devices, and that contract prices are based upon the largest possible use of such machines. Erection difficulties and impossibihties are often incorporated in such complete designs, which objectionable features must be 'ironed out' by the engineer responsible for the shop drawings before the detailing can go ahead. He has as his particular field the following duties : "1. To make details for carrying out the specifications and properly developing the strength of the parts connected. "2. To detail so that the shop can fabricate most economically. "3. To detail so that the erection methods and the equipment determined upon for the particular bridge shall be not only possible but economical as well. The sequence in the placing of the different members must be taken account of throughout the entire detaihng. " The engineer at the plant, versed in the preparation of shop drawings, is both by experience and environment the best qualified man to meet these three necessities. In fact, the last two are never possible of final solution until after the contract has been signed and the work is being developed in the shop drawing room. " It is, of course, conceded that, for unusual or monumental structures, the makeup of the details is so interwoven with the general design that the development of the two must proceed together. Even in such cases it is nearly always necessary for the best results that modifications be made as the work progresses in the drawing room. " The corre(^tness of the foregoing statements has been proved by the actual experience of our Shop Engineers covering their work reaching over a period of the past twenty years. We are now so wcH fortified with examples ECONOMICS IN DESIGN FOR SHOP CONSIDERATIONS 211 of the boet practice for different types of bridges that there is no great difficulty in reahzing the true intent of the design in the study of the structure that must be made in the shop drawing room. It would seem to be wise economy on the part of the designing engineer to take full advantage of these facts. '' For full-punched work,* with splices in chords reamed to fit, it is im- portant that the design should provide for the next larger sized rivet in the reamed splices. This saves in the shop one handling of all the main parts, because one size of punched holes wiU answer for both reamed and unreamed holes. If, for instance, |" rivets are being generally used, and allowance is not made in the des'gn for larger punching than yf", it is necessary to punch xf" holes in the body of the member and rehandle all the long main parts in order to punch a smaller -sized hole (say yf " diameter) at the ends where the splice is to be reamed for fit. If allowance is made in the design for Ire" holes, the punching throughout will be jf " and the splices will then be reamed out to 1]^", thus saving the extra handling at the punch. " In heavy, reamed girder- work where several cover plates, side plates, and heavy flange-angles are used, the size of the sub-punched holes should be not less than jf " diameter. It is difficult and expensive to fit up such work where, because of the size of sub-punched holes, smaller fitting-up bolts are necessary. This is because of the great difficulty in properly pulling together such heavy parts and so many of them with f " fitting-up bolts. For work not properly brought together in fitting, the riveting is expensive and apt to be imperfect. " It almost goes without saying that Forge and Machine Shop work should be kept at a minimum. Bending of long pieces is particularly undesirable, because, when a long angle, for instance, is to be bent, the operation of heating and bending disorganizes and interferes with all the adjacent operations in the shop. Making a bend at each end of a long angle, channel, or beam is not only quite expensive, but next to impossible to do, because of the extreme difficulty in maintaining the correct measurement between bends. " Curving ends of girders is a considerable item of extra shop expense. It adds to the cost of drawings, templets, laying out, punching, assem- bling, and riveting, in addition to the extra cost of bending the end angles. In fact, it is doubtful if the aesthetic value is enhanced at all in proportion to the increased price which the buyer must pay. However, where it is decided to use 'round ends,' the exact radius of the curve should be left to the shop detailer, so that standard bending forms may be used. '■ Staggered riveting invites shop errors and slows down the work. Pref- erence should be given to rivets placed opposite or in single rows, where the necessities of design do not require that they be staggered. The different members of a span should be designed, as far as possible, to allow The author is opposed, on general principles, to punching any rivet holes full size. 212 ECONOMICS OF BRIDGEWORK Chapter XXIII the use of power riveters. This is especially applicable to box sections with the flanges of channels turned in. In general, the clear distance in such cases should be not less than 5^" or 6". " Avoid sections calh.ng for the use of a variety of sizes of shop and field rivets in the same span or structure. ''For narrow, ' I '-shaped sections, preference should be given to four angles with a web plate instead of four angles laced. Often for such narrow sections the latticed type accomplishes very httle or no saving in weight, and the shop expense is greater and the result is less desirable from a maintenance standpoint, as compared with the plate-and-four-angle section. " Quite often a small increase in the thickness of stringer webs will eliminate the necessity for the use of stiff eners. " Designers very often do not make enough allowance between gross and net section for the proper maintenance of the latter and at the same time for the preservation of rational details at the critical points. For instance, according to the 1920 specifications of the American Railway Engineering Association, if only one |" rivet hole is allowed out of an angle, the stagger must be four inches; and other specifications have been more stringent. If the piece happens to be a Q"X4:" angle with two rows of rivets in the six-inch leg, the detailer is in trouble at once with the loca- tion of rivets in the four-inch leg adjacent to the critical section. He is often compelled to give it up and encroach on net section after he has wasted a lot of valuable time in trying to meet the conditions. Any angle with punching in both legs, used in tension, should have two rivet holes deducted from the gross section. "In plate-girder work, fillers under stiff ener angles should not be required to fit tight against flanges. The overrun in width of flange angles, often varying for the different angles on a single girder, means the re-cutting and fitting of fillers to suit. This results in a slowing down and an increased cost in the work of fitting uj) the girder for riveting. A clearance of at least I" should be permitted at each end of filler. " All unnecessary bevel cuts on the ends of long angles, plates, or other shapes should be dispensed with. These are mu(;h more cxi:)ensive to make on long i)icceK than on small detail parts. It seems somewhat absurd carefully to cut the end of an angle to bevel, for the sake of apjieaiance, when it is not exposed to view in the finished structure. IndeiHl, the sesthetic value of such bevel cuts is very much in ({uestion, excejit where a projecting corner is exposed to the skyline. " The ends of columns for viaducts or other structures resting on masonry can often ])e made less expensive in hoih wcnght and workman- ship by using thicker base plates and omitting vertical stiffening angles with their extrmsive arrangement of wing-i^lates that are intended to help in the distribtition of the load. " Finally, and in general, the designer should give the most careful atten- ECONOMICS IN DESIGN FOR SHOP CONSIDERATIONS 213 tion to tho coordination of the different parts of his design, so that it can be detailed in the simplest and most natural manner with the elimination, as far as possible, of cumbersome or complicated joints and connections. In determining the makeup of the different sections, the detailing possibili- ties should be given much weight, for quite frequently they are the deter- mining factor." CHAPTER XXIV ECONOMICS IN DESIGN FOR ERECTION CONSIDERATIONS The tyro in bridge designing, no matter how profound may be his theoretical knowledge, often falls down very hard untU he has learned through sad experience that the erectors of structural steelwork have cer- tain standard requirements which must be observed. If they be ignored, the work is often seriously delayed; and, as delays in the field are exceed- ingly expensive, the matter of making the designs so that aU the metal wiU go together easily and expeditiously involves engineering economics of great importance. The failure to furnish sufficient clearance is generally the tj^ro's first offense — and it certainly is a serious one. If the designer who commits this blunder could hear what the bridge erectors say about him, his ears would certainly tingle. Mr. Wolfel's general instructions concerning designing to meet field requirements are as follows: (1) Allow ample clearance for aU entering connections. (2) Provide erection shelves for girders and beams, particularly when they frame opposite each other. (3) Have all riveting arranged in such a way that it can follow the erection of the work. Riveting should never be allowed to interfere with the raising and placing of the steel. (4) Be sure that cross frames in deck bridges can be swung in place without spread- ing the girders. (5) Be careful in through plate-girders to arrange the stiffeners so that the floor- beams and stringers can be put in place with the girders in their final position. (6) Arrange the riveting around the ends of the spans so that the rivets can be driven with the steel in the final posi- tion. It should never be necessary to jack up spans to drive rivets. (7) In trough floorwork, especially where the under clearance is small, arrange the design so that all field rivets can be driven from the top, as in Fig. 24a. (8) While it has been customary to call for 25 per cent excess for all field rivets, 10 per cent excess should be Fig. 24o. Trough-Floor Construction for Easy Field Riveting. sufficient, if the rivets are driven with air hammers. On this subject Mr, Reichmann has written thus: The designer should always remember to allow plenty of clearance at the ends of sheared members so as to take up variations of shopwork. One-half inc^h clearance is considered a minimum for sheared ends. l'\)r enteruig connections, plenty of clearance 214 ECONOMICS IN DESIGN FOR ERECTION CONSIDERATIONS 215 should be allowed, as a great many of the difficulties in erection are due to lack of clearance; besides, giving reasonable clearance will permit of more rapid shopwork and the avoidance of many errors in the field due to inaccuracies thereof. It is often advisable to provide, in addition to the usual allowance for expansion, a small amount for erecting the metal, due to what is called the "growth of steel." For viaducts such adjustment should be provided about every 400 feet; and similarly for mill-building work it is necessary to consider effects of adjustment, even if it is decided not to take care of expansion, while in other structures the joints for expansion wUl also serve the purpose of adjustment. The expansion points for stringers or elevated raUroad-girders, where pockets are used, sometimes have not enough space behind the end stiffeners of the expansion girders to allow for the insertion of rivets through the end connections of the fixed girders. It should be remembered that the expansion stringers and the fixed-end stringers are erected before the rivets in the connection of the fixed stringers are driven. When columns are set to stone bolts, which have been imbedded in masonry, the holes should be |" or 1" larger than the diameter of the bolt, so as to provide adjustment to take care of the inaccuracies in setting the bolts in the concrete. A common mistake in design is to proportion the members with too small a width, causing considerable trouble in packing the pins and in making room for the verticals, pin plates, etc. Another bad feature of narrow chords is that practically all rivets around the connections must be countersunk because of close space, and the ends of the posts must be cut away for clearance, thereby weakening the said ends. By adopting chords of larger widths much better details can be used around the pins at panel-points. When two or more truss spans are identical, or when they are similar and have the same field connections, the field holes should be reamed to an iron templet, in place of reaming them while the members are assembled. This will facilitate the delivery of the work, and wUl make identical members throughout the structure interchangeable. The advantages in the field are evident, less time being spent in sorting and finding material. In the designing of details extreme care shoiild be exercised in arranging all joints and connections, so that the work cannot only be buUt at the shop for the least cost in labor and material, but also that it may be erected most economically and with a minimum of risk. In the case of bridgework, all connections should be so detailed that spans can be connected and made self-sustaining and safe in the shortest possible time. Unless for special reasons, it is usually customary to begin the erection of pin- connected spans at the center panel, as this panel has adjustable members and the trusses can be squared up there before proceeding. The details should, therefore, be so arranged that the center panel can be completed and made self-sustaining before the traveler is moved to the next panel. It is the usual custom for the erection to pro- ceed from the center panel toward the fixed end, and after this half of the span is erected, to proceed toward the roller end. Top chord sections in any particular panel are put in place after the posts and bars are erected; and it is especially desirable in heavy work that the details be so arranged that these chord sections can be lifted above the posts and set directly in place without being moved on end or sideways. Therefore, plates connecting two adjoining chord sections in heavy work should always be shipped loose. Wherever possible, in all truss spans the floor connections should be so arranged that the floor system can be put in place either before or after the trusses have been erected in their final position. It is usually customary, where local conditions will permit, to put the floor system in place first and erect the trusses afterward. This method of procedure has a great many advantages over that of raising the trusses first, viz.: there is a large saving in falsework, as longer panels can be used, putting bents 216 ECONOMICS OF BRIDGEWORK Chapter XXIV directly under the panel-points and using the new floor system for carrying traffic and for running out material for the trusses; it permits the posts to be bolted to the floor- beams and released from the tackles on the travelers; it fixes the exact position of the shoes on the piers so that we can proceed with the erection from the center either toward the fixed or the roller end, as we may prefer; it has the advantage of giving more opportunity for jacking up the spans in order to secure proper camber; and it requiers a minimum amount of blocking. There are other featm-es which render it desirable, where possible, to erect the floor system in advance of the trusses. Over dangerous streams, however, where there is a possibility of loss during the erection, it is some- times desirable to erect the trusses first, so as to have as little material on the false- work as practicable and thus minimize the amount endangered. There are also some- times certain local conditions which make it imperative that the trusses be erected first; and, therefore, it is important, wherever possible, that details be so arranged that either method can be used. In the erection of through, riveted, lattice spans, it is customary to place the floor system first, then to put the lower chords in position, set up the web members, and put the top chords on last. Therefore, it is more advan- tageous to have the gusset-plates connecting the web members with top chord riveted to the top chord sections rather than to posts or diagonals, as the rivets in gusset- plates connecting top chords with web members are more easily driven in the web members than in the top chord sections. In the case of through plate-girders, the details of the floor system should be so arranged that the stringers and floor-beams can be put in place, panel by panel, without the necessity of spreading the main girders. Particularly is this the case in "Rolling Lift Bridges," which, in the majority of cases, have to be erected in an upright position, and where it is extremely dangerous and practically an impossible operation to spread the trusses in order to put in place the floor system. Top chord sections with half pin-holes, having a hinge-plate on each section, are undesirable. When half pin-holes are -used, if possible put a hinge-plate on one sec- tion only and make it long enough to rivet or bolt to the adjoining section when in place. Hinge-plates should be arranged so as to give two full pin-holes in center chord sections, and should be put on the ends farthest from the center on the other sections, except in special cases when it is necessary to commence raising spans from the end instead of the center. Entering connections are usually the most difficult and expensive to make; and v/here at all possible, entering connections of any character should be avoided, but where they must be used, particular attention should be given to insure necessary clearances. An entering connection is not only an expensive and dangerous operation, but in a great many cases it cannot be accomplished on account of the interference with back walls, adjoining spans, etc. It is of the ^-^reatest importance to allow ample clearance where members are packed inside of chords, posts, etc., as lack of proper clearance causes much trouble and expense, not only augmenting the cost of erection by increasing the time required for making the span safe, but adding materially to the risk. In putting in tie-bars and diagonals, it is customary to connect them on the bottom chord pins first, and then swing them into the chords and posts around the lower pins as a center. All rivet heads coming in the path of bars swung in this way should be cleared. Too much attention cannot be given to this matter of proper clearance. Particularly is this the case in through and deck riveted lattice spans, which are being erected now more than ever Ix^fore with the use of a derrick car with one boom; and the ai)pliances for pull- ing tight-fitting members into place are not always present, as was the case formerly when these spans were erected by a gantry traveler. For adjustable rods packed close together, the sleeve nuts should be staggered. Attention .should be given to the field connections so that enough space is allowed around all field rivets to enable them to be driven, ECONOMICS IN DESIGN FOR ERECTION CONSIDERATIONS 217 All lateral bracing, hitch plates, rivet heads in laterals, etc., should be kept enough below the level of the top chords of girders, stringers, etc., so that the ties when in place will not foul them, it being an expensive operation to notch ties to clear such obstructions. Where laterals and hitch plates do not interfere with the loading of girders, and are not of such character as wiU allow them to be easUy broken off, they should be riveted to the said girders; otherwise they should be shipped loose or riveted to the braces. Particular attention should be given to the question of field riveting. Details should be closely examined with a view of minimizing the number of field rivets. It is not advisable to put two shoes on one bed-plate; but if this cannot be avoided, the bed-plate should be made longer and the anchor holes should be slotted to allow for variations in masonry. The following are the most important points to be observed in detaUing, Ib order to facilitate and cheapen erection. (a) Avoid as far as possible entering connections. (b) See that proper clearances are given. (c) Minimize the number of field rivets. Viaducts When the track is on a grade and the grade is not very steep, make the two bents of one tower alike by adding filler plates on the tops of the up-grade columns. For steep grades make the two bents of one tower the same length, but square the longi- tudinal bracing. A good detailer will then make the punching the same on all four columns of the tower, but the gusset plates which connect to the longitudinal bracing will be different for the two bents. When designing colunms for the towers, the splices should be indicated so that the column sections should, preferably, be imder 40' long, but should not under any cir- cumstances exceed 60'. Where two deck girder spans are adjacent, the end cross-frames are placed close to the ends of the girders. The cross-frames cannot be set by swinging in from the end of the span. They must be erected by swinging in from the center of the span. The stiffener angles carrying the cross girders should be built with the back of the angles toward the center of the span. CHAPTER XXV ECONOMICS OF REINFORCED-CONCEETE BRIDGES Reinforced-concrete structures being the most modern of all the general types of bridge construction, it is not to be expected that the economics of their designing should be so highly developed as in the case of any of the older types. Nevertheless much has been learned about the subject through the numerous investigations made for the author's firms by a number of young computers during the last twelve or fifteen years. Practically all that was known concerning it in 1915 was stated in Chapter LIII of "Bridge Engineering"; and an elaboration of that treatment will be given herein, supplemented by the results of a series of investiga- tions made specially for this book. The first topic for economic discussion is that of Reinforcing Steel At the present time one of the mooted points in the designing specifica- tions for reinforced-concrete bridges is the proper intensity of working stress for the reinforcing bars. It is generally conceded that it should not exceed one-half of the elastic limit of the metal; and, in consequence, engineering practice in the past has Umited it to 16,000 lbs. per square inch, but a number of manufacturers now desire to raise it to 18,000 lbs. per square inch by using a higher-carbon steel — notably re-roUed steel. Of course, the higher intensity saves in \he quantity of steel, but generally increases the amount of concrete required ; because the higher stress in the steel reduces the moment of resistance of the concrete about six per cent. If the amount of concrete is increased, the net saving is about two (2) per cent in slabs and three (3) per cent in beams; but if the section of the concrete is determined by shear or other considerations, so that no increase is necessary, those percentages will be increased by unity. There are two grave objections to usmg the higher steel, \'iz. : First. When bent cold it is liable to crack on account of its increased hardness, and Second. It tends to open up cracks m the concrete. For these reasons the author is not willing to use such steel in his prac- tice; and, on general principles, he is opposed to the employment of any re-rolled metal, because of the temptation for the mnnufactm-er thereof to run in all kinds of old materials — even wornout Bessemer rails. 218 ECONOMICS OF REINFORCED-CONCRETE BRIDGES 219 Intensity of Working Stress for Concrete For many years the author's practice has been to stress the concrete in compression only six hundred (600) pounds per square inch; but lately the Joint Committee of the Technical Societies has reported in favor of adopting six hundred and fifty (650) pounds. When a good aggregate is procurable, the author has no objection to this increase of eight per cent; but otherwise he prefers to adhere to his old custom, especially as by so doing he adds only two per cent to the cost of the concrete in those cases where the section can be reduced by using the higher intensity. Very often, though, no such reduction is practicable, and the saving on the entire job reduces to only one per cent. The actual reduction in the amount of concrete in a beam due to this difference of intensity of working stress is about six per cent, but this is partially offset by an increase in the amount of steel required. The com- bination of the intensities of 600 for concrete and 16,000 for steel requires a percentage of 0.68 for reinforcing steel, while with 650 and 16,000 that figure is increased to 0.77. Moreover, construction work is simplified by using more concrete and less steel, also better concrete is secured; hence the author does not think that there is much real advantage in adopting the higher intensity. The general complaint from contractors on his work has been "too much steel"; and adopting the higher intensity for concrete would make matters worse. Moreover, the use of heavier concrete sections tends to keep down the shear intensity, which is always' desirable. Frequently there is a choice between a heavy concrete section with no shear reinforcement, and a lighter section with such reinforcement. In superstructure it is generally preferable to adopt the latter and in sub- structure the former. Pavings The subject of the economics of pavings is treated fully in Chapter XXI. The economy lies in the cost of the pavement itself, excepting that brick is heavier than the other paving materials; and, consequently, 'it adds to the cost of a concrete structure, the amount being from two to three per cent. It is poor economy to neglect the expansion joints in block pavements; because expansion is sometimes quite destructive, not only causing waves in the pavement but sometimes actually pushing off the curbs. Handrails Handrails for reinforced-concrete bridges should always be made of concrete, in order to harmonize with the rest of the structure. A steel railing on a concrete bridge is ruinous to the general appearance, and, therefore, should not be tolerated. The first costs of the two types of railing are about alike; but the concrete one, being heavier, requires more 220 ECONOMICS OF BRIDGEWORK Chapter XXV material for its support. Artistic rails are more expensive than plain ones; hence the selection of the design will often involve a compromise between economics and sesthetics, and wlU depend greatlj- upon the amount of money available for the work. Rails can be built entirely in place, or they may be either partly or wholly cast in sections and set in position. The jointing will require care- ful attention; for, otherwise, the railing will have a bad appearance and even may go to pieces. A better character of construction can be secured with separately-moulded work; but unsightly joints would offset this advantage. Separately-moulded rails generally interfere much less than other types of rails with the progress of construction ; besides, the moulding of the parts can be carried on at odd times in the intervals of other work. Both of these features are money savers. Designs The economics of design are rather difficult to determine, as the quanti- ties involved are influenced quite largely by the individual tastes of the designer. The problem is also complicated by the facts that the unit costs of the various portions of a structure may be more or less different, and that the unit costs of different types of construction may be decidedly unHke. In general, it may be said that the unit costs are lower for those struc- tures which have the smiplest form-work; and a reduction will also be effected by decreasing the area of form-surface per cubic yard of concrete. For instance, in the case of a wall or slab, the fojm-cost per cubic yard will vary practically inversely as the thickness of the said wall or slab. Evi- dently, therefore, it is desirable to concentrate the concrete into a few large members, rather than to employ a great number of small ones. It should be noted that reinforcing bars less than f " in diameter com- mand higher pound prices than do the larger bars. The extras for these small bars may be found in Engineering News-Record in the first issue of each month. The economics of the designing of the different parts of reinforced- concrete structures will now be discussed in logical order. Slabs A primary economic problem in slab designing is that of two-way versus one-way reinforcing. Two-way reinforcing involves less concrete but more steel than does one-way reinforcing; hence it has but little advantage, unless the reduction of dead-load to a minimum be of prime hnportance. Different arrangements of slab steel are discussed on pages 918 to 921, inclusive, of "Bridge Engineering"; and it will be noted therefrom that there is very little difference in the weights of the various types. Lighter ECONOMICS OF REINPORCED-CONCRETE BRIDGES 221 arrangements of steel are generally used in buildings; but roadway slabs, in view of the heavy concentrated-live-loads that they have to carry, and which produce large shears throughout and positive moments over almost the entire span, require carefully and liberally designed reinforcement. Barring most of those in railway bridges, slabs are usually continuous over panel points, excepting at the expansion joints. There is but little difference in the actual costs of continuous and non-continuous slabs; but continuity is desirable from the standpoints of paving and drainage; also with continuous slabs T-beam construction can be employed — involv- ing the saving of much material in girders. The continuity of slabs and girders complicates construction problems — sometimes very seriously. The various processes of the construction of a proposed design should be studied through completely in order to make certain that no impracticable or unnecessarily expensive work is involved. Frequently important savings can thus be effected ; and sometimes it is found cheaper in the long run to use more concrete than the minimum practicable amount. For instance, a sidev/alk slab usually rests upon the curb, which in turn rests on the roadway slab; and in the designing it is advisable to provide for a construction joint at the top of the roadway slab, because it would b3 both difficult and expensive to pour the curb and the sidewalk slab simulta- neously with the roadway slab. Such construction joints can be arranged for by the designer without involving much extra expense, provided that he gives the matter proper consideration at the outset. Girders Girders are of two main types, single or continuous; and there is no great difference in their costs, there being more concrete but less steel in the simple-span type. The two-span-continuous type is nearly always a little more expensive than the simple-span type. The simple-span girder can be moulded separately and set in place. This is not a paramount feature in highway bridges, but it is often all-important in railway structures. Comparing simple girders and continuous ones of three or more spans, the following general observations may be made: If there is no T-beam action, the simple spans will be the more expen- sive; because the section will be determined by the moment at mid-span in the simple girder, and this is greater than any of the moments of the con- tinuous girders. Again, higher unit stresses than ordinary are allowed over the supports of continuous girders. For the T-section, if the bottoms are straight, the continuous type will be the more expensive, having more concrete and more steel than the simple type. But if the bottoms of all girders are cur-ved, the continuous girders will be the cheaper, there being decidedly less concrete required for them. When the bottoms are straight for simple-span girders and are cui^ed for continuous girders, the curves on page 1323 of "Bridge Engineering" indicate the relationships. It will be 222 ECONOMICS OF BRIDGEWOEK Chapter XXV noted therefrom that for hght loads the simple spans have less concrete, and that for heavy girders there is but little difference in the concrete quantities, excepting that for exceedinglj^-heavj^, long-span girders the continuous type is the lighter. There is always more steel required for the continuous type than for the non-continuous one. From the foregoing remarks it is evident that shnple-span girders are generally cheaper than the continuous ones. It will be found, however, that the bents or other supports are cheaper for continuous girders than for simple ones, and that floor joints in simple spans are expensive, also that the continuous girders give a solid, monolithic structure. The continuous- girder construction is very generally used in highway bridges; but the railway companies have adopted as standard the simple-girder type. How- ever, nearly all railway concrete-bridges up to the present have been of soUd-slab construction, rather than of that of the slab-girder. The foregoing comparisons are based upon girders in which the rein- forcement was liberally proportioned for positive moments, negative moments, and shears, making full provision for impact and a small allow- ance for uncertainties of stress distribution in continuous girders. It is possible to skimp the reinforcing of concrete girders considerably, and this practice in highway bridgework is altogether too common. It is an evil that should be stamped out, if not by the engineering profession, then by the laws of the land ; for while it is most reprehensible to skin a steel bridge in which the skinning cannot be hidden from the expert eye, it is criminal to trim down to dangerous limits of strength a reinforced- concrete structure in which the flaws and weaknesses are buried out of sight. The character of the foundations should be duly considered in deciding between simple and continuous girders; for, if there is danger of settle- ment, the simple-girder type is far preferable — in fact, it is obhgatory. The balanced-cantilever type of girder is beginning to be used, each monolithic unit consisting of a pier and two half-spans. In this the foundation pressure is centric for dead load and for hve load over the two arms; but with the latter loading on one arm only, the pressure en the base is decidedly eccentric, subjecting the pier shaft to bending. This type of layout permits of a very shallow depth at the center of the span, and is thus specially applicable to long spans, where the weight of the concrete in the central portion of either simi)le or continuous girders is an important factor. The balanced-cantilever girder usuall.v shows for the superstructure a small economy over either the simple oi- the con- tinuous girder for short spans and a larger saving for long ones. The substru(;tui-e, though, is always more expensive, as it has to be designed for the unbalanced load on one arm. If the live load is small in com- parison with the dead load, this increase in sub-structure cost is not great; but otherwise it is so large as to outweigh the economy in the girders themselves. This type of layout should not be used on soft foundations ECONOMICS OF KEINFORCED-CONCRETE BRIDGES 223 or with pile bearings when the Hve load is comparatively great, on account of the tendency to rock the piers. Where the ends of the arms come together it is necessary to insert a detail that will take up shear but not moment; for, otherwise, there would be a sudden break in the grade that might give serious trouble. In the author's opinion this type is never suitable for carrying steam-railwg^y loadings and is none too good for electric-railway structures, although satisfactory enough for highway bridges. In order to determine for any case the relative economy of cantilever and ordinary types, estimates for both superstructure and sub- structure will have to be made. Columns Columns are generally square or rectangular in cross-section for con- structive and aesthetic reasons. A round or octagonal column is really a better structural member; and, if the lines of the bridge are worked out in accordance with it, there should seldom be any difficulty about the matter of appearance. A round column can be hooped or banded better than any other type. Frequently, for the sake of appearance, the size of a column must be made greater than that necessitated by theoretical require- ments. Footings Footings may be either plain or reinforced; and the question as to which style to adopt is one solely of economics, because, as they are buried out of sight, the consideration of aesthetics will not apply. If the area of the footing is but little larger than that of the column supported, plain concrete wiU be the cheaper; while for a spread foundation the reinforced type will nearly always be found more economical. If a footing has to be poured under water, plain concrete should invariably be employed; and in wet-excavation work in general it is preferable, because it is often difficult to prepare the bottom of the pit properly, and to stop absolutely the flow of water from below. Such a flow is liable to wash out the cement from the lower part of the footing; and thus it would destroy most of the value of the reinforcing. Plain footings are made of 1:3:5 concrete or sometimes 1:3:6; but the latter, in the author's opinion, is too weak. The use of 1 : 2 : 4 concrete permits thinner footings, but this is not of much importance when plain-concrete bases are used. Highway Girder Bridges In respect to the economics of girder bridges resting on columns, the following points must be considered: First. The panel length, when cross-girders are employed. Second. The number and spacing of the longitudinal girders. Third. The number of columns per bent. 224 ECONOMICS or BRIDGEWORK Chapter XXV Fourth. The span length. Fifth. The use of reinforced concrete piles to carry the footings. The panel length adopted is usually not of great unportance from the standpoint of economy. Lengths of from eight to ten feet are generally employed; but a considerable variation from these values will cause httle change in the combined cost of the slabs and cross-girders. A reduction in concrete quantities can frequently be effected by using long panels, and by carrying the slabs on short stringers supported by the floor- beams; but the extra form work required will generally overbalance this saving in volume. The number and spacing of the longitudinal girders will depend upon the width and the height of the structure, the span-length, and the load to be carried. For a high structure in which the economic span-length is fairly great, it will nearly always be found best to employ two lines of girders, the spacing thereof being equal to about five-eighths of the total width of the structure; but for bridges much over sixty (60) feet wide the use of three or even four lines may be preferable. The slab in such struc- tures is carried on cross-girders and cantilever-beams. For a low bridge in which the economic span length is short, it will generally be the cheapest to omit the cross-girders, except at the bents, and to employ several lines of longitudinal girders. The wider the structure, the more hkely will this arrangement prove to be economical; and very heavy" loads also favor its adoption. For a structure in which the span-length is from one- half to two-thirds of the width, it will usually make httle difference which of the two types is adopted, unless the height is rather large; and even in extreme cases the variation between the two is not likely to exceed ten per cent. Ordinarily, it will be found more desirable to use two lines of girders, with cross-girders and cantilevers about eight or ten feet centers. The proper number of columns per bent depends on the number of longitudinal girders. When there are only two Hues, two columns will, of course, be employed. Wlien there are several lines of girders, there should generally be one column per girder in low structures, and two columns per bent in higher ones. In this latter case a heavy cross-girder will be required at each bent to carry the longitudinal girders. The economic span-length is affected by the height and the load, being larger for greater heights and smaller for heavier loads. An approxunate value thereof is given by the formula, in which i = economic span length in feet, measured from center to center of supports, w = load in pounds per lineal foot of girder (excluding its own weight) , and h = fixed height of structure in feet. ECONOMICS OF REINFORCED-CONCEETE BRIDGES 225 The quantity h represents in any given case the height which is fixed, such as the height from grade to top of footing, height from grade to bottom of footing, height from underside of girder to top of footing, or height from underside of girder to bottom of footing, as the case may be. There is always a considerable range of lengths for which the quantities remain nearly constant. The formula gives values a trifle greater than those for which the quantities are a minimum, since the use of heavier sections will reduce slightly the unit costs of the concrete. Reinforced-concrete piles should be used under footings when a suitable foundation is to be found only at a considerable depth, or v/hen a very large footing-area would be required in order to reduce the pressures to a proper amount. A comparison must be made for each case as it arises, allowing properly for the costs of the column shaft, the footing, the piles, and the excavation. This latter item must not be overlooked. The curves of Figs. 5Qt to 5Qy, inclusive, of ''Bridge Engineering," will be found of great value in studying the questions of economy of rein- forced-concrete-girder bridges, as most of the points involved can be settled directly thereby. Arch Bridges Economic Rise with Span -Length Unchanged The economics of arch bridges are much more complicated than those of girder bridges. The important factors are the costs of the arch ribs and those of the piers or abutments ; and the main economic point to determine is that of ratio of rise to span-length. For any fixed span-length, the greater the rise, up to a limit of one-third of the opening, the smaller will be the cost of both arch-ribs and piers. By increasing it further, up to the limit of one-half of the opening, the cost of the rib will be but little aug- mented, and the cost of the pier above the springing will be increased, while that of the portion thereof below the same will be reduced. If the increase in rise is secured by lowering the springings, the greater the rise the greater the economy of material and cost; but if the increase must be secured by raising the grade, the springing remaining at a fixed elevation, it will rarely be economical to increase the rise above the Kmit of one- third of the opening. The exact limit in any case will depend upon the distance from the springing to the bottom of the base, and upon the mass- iveness of the pier-shafts above the springing; also upon the spans of the arch-ribs resting on the pier, and upon the character of the substructure employed. If the springing is but little above the top of the base, a comparatively-low rise will be economic. If the pier carries two arch-spans of the same length, and if the live loads are small as compared with the dead loads, a low ratio of rise to span-length will be economic. On the other hand, if the distance from the springing to the bottom of the base be great, the live load large as compared with the 226 ECONOMICS OF BRTDGEWORK: Chapter XXV dead load, the two adjacent arch spans of different lengths (or, still more important, if there be only one arch), and the substructure work expensive or the foundation of low bearing-value, the ratio of rise to span length should be large. Frequently an arch abutment retains a fill, in which case a veiy low rise is likely to be economic, in order that the larger thrust of the rib may oppose the earth-thrust on the abutment. In such an event it may be economic to make the springing higher. This is the only exception to the general rule that, for maximum economy, the springing should be placed as low as clearances, waterway requirements, or due consideration of aesthetics will permit. Economic Span-Length with Rise Unchanged In most instances there is Httle chance to vary either the grade or the elevations of the springings to any great extent; hence the principal eco- nomic problem is the determination of the best span-length. The prin- cipal factors to be considered are the following: A. The rise of the arch. B. The distance from springing to bottom of base. C. The character of the substructure work. D. The massiveness or hghtness of the piers, determined from the aesthetic viewpoint. E. The ratio of Uve load to dead load. , F. The type of arch-ring — whether solid-barrel or two or more separate ribs. G. The equality or inequaUty of lengths of adjacent spans. H. Arbitrary requirements fixing clearances of ribs or positions of piers. I. Other special conditions. The rise of the arch is evidently of paramount importance; because the greater it is the greater will be the economic length of span. The distance from springing to bottom of base is another very impor- tant factor. In general, it may be stated that, for ribbed arches, when the adjoining spans are of equal length and when the springings are but a short distance above the bottom of the base, a ratio of rise to span-length of one- third or even le:3s will be quite economic; while, if the said springings are a considerable distance above the said bottom, a ratio of one-half wiU be better. Generally speaking, it may be said that low ratios of rise to span are more pleasing to the eye than higiier ones, so that the adoption of longer spans is preferable from the aesthetic standpoint. Also longer spans involve larger members, and consequently lower unit costs, so that the economic span-length is somewhat greater than that which gives mini- mum quantities of materials. ECONOMICS OF REINFORCED-CONCRETE BRIDGES 227 Difficult foundations favor long spans, not only because of the reduc- tion in the number of piers but also because the unit costs for small piers are much higher than those for large ones. On the other hand, if the foundations are very deep, the effect of unbalanced thrusts becomes of great importance; and this favors shorter spans. Poor foundation con- ditions also mihtate for shorter spans, as do invariably pile foundations. If it be decided for the sake of appearance to make the piers heavy and massive, this will tend towards greater span-length; because, in that case, up to a certain limit, an increase of span will augment the size of each individual pier but little, if any. It will rarely pay to reduce the span-length, if such reduction will not decrease the size of the pier or piers. Light live loads in proportion to the dead loads tend, for economy, towards the adoption of longer spans, especially when the adjoining spans are of the same length. With such light live loads the economic span- length is not greatly affected by the distance from springing to bottom of base. When a pier carries one arch span only, the ratio of hve load to dead load is of much smaller importance than it is in the case where there is a succession of spans. The type of arch ring, whether it be of one solid-barrel or of two or more arch ribs, often affects materially the economic span-length, but to what extent it is difficult to predict in advance of designing and esti- mating. The piers of the solid-barrel type are generally more expensive than those of the ribbed type, as are also the arches; but in most cases the piers are comparatively the more expensive; and this favors the employment of longer spans. Also, it wiU frequently be found that increasing the span-length will augment but slightly the quantities in the arch rings of the solid-barrel type — which also favors longer spans. The economic ratio of rise to span-length for solid-barrel arches may generally be taken at 0.25, varying, of course, with the other factors previously dis- cussed. The foregoing conclusion may seem to be in contradiction to the well-known fact that long spans are nearly always of the ribbed type. This, however, is because the solid-barreled arch is generally used for low rises, which necessarily means comparatively short spans, while the open- ribbed arches are employed for nearly all arch structures of high rise. The comparative economics of these two types will be discussed later in this chapter. When adjoining spans must be unequal, the inequality, for economy's sake, should be made as small as practicable. This is very important if the springings are far above the base; but is of small consequence if they are not. If the springing of the smaller arch can be located well above that of the larger one, it may be possible so to adjust the spans and rises that there shall be very little eccentricity of pressure on the base, in which case the pier will not be much more expensive than it would have been had the adjacent spans been of equal length. The appearance of the piers 228 ECONOMICS OF BRIDGEWORK Chapter XXV will demand special study, if the springings are located at different ele- vations; otherwise, the principles of aesthetics are likely to be violated. The influence of earth-thrust on an arch abutment has already been mentioned. Where such thrust exists, it will favor the use of longer spans, in order that the larger arch-thrust may counterbalance the said earth- thrust. In a long bridge of many spans, the abutments will not cut much figure; but if only two or three spans are to be adopted, they may be of more importance than the intermediate piers. If there is no earth- thrust on the abutment, its cost will augment as the span-length increases; but if there is such a thrust, the cost may reduce when the span-length is made greater. In many layouts the positions and even the sizes of certain piers are fixed, and specified clearances (both horizontal and vertical) must be maintained under certain of the spans. These conditions, of course, must be taken as a basis, and the layout adapted to suit them. Special govern- ing conditions must often be observed, such as the character of the sur- roundings, the relative importance of aesthetics and cost, or the adoption of some special architectural treatment. In a discussion of economic span-lengths of arch bridges it is imprac- ticable to give exact figures, for there are too many variables concerned. Whenever there is any choice, it wiU be necessary to make preliminary designs for at least two span-lengths; and, if one of these proves to be somewhat cheaper than the other, a third length should be figured. There is no other way to ensure that the truly economic length has been selected, unless it happens that the figures can be compared with those for a very similar structure. Comparison of Solid-Spandrel versus Open-Spandrel and Solid- Barrel versus Ribbed Structures Arch-spans can be divided into two general classes, solid-spandrel and open-spandrel. In the first form the arch-rib must be solid, while in the second it may be either solid or ribbed. Considering the two solid-barrel types, the filled-spandrel has no floor-system or cross walls, but instead an earth fill between the spandrel-walls. For very low rises the walls and filling are cheaper than the floor-system and columns; but for high rises the reverse is true. The great weight of the filling makes the piers expen- sive in the cases of pile foundations and bearings upon comparatively soft soil. The spandrel-filled arch is often used on railroads when it is not the most economic type, in order thnt the weight and inertia of the filling may absorb the impact of moving trains. In highway structures, the open-spandrel type is generally preferred to the filled type, for various good and economic reasons, among which may be mentioned the fact that, with the latter type, it will be found desirable, for the sake of appearance, to make the ring the full width of the ECONOMICS OF REINFORCED-CONCRETE BRIDGES 229 deck; whereas for the former type it will be satisfactory to carry a part of the deck on cantilevers. The consequent narrowing of the arch-rings and shortening of the piers involve quite a saving in cost. Comparing, in open-spandrel structures, the solid-barrel type and the ribbed type, it will be found that the latter is cheaper, except in the case of very low ratios of rise to span-length. In the solid-barrel type there is one wide, rather-thin ring carried on a wide, comparatively-thin pier; while in the ribbed type there are two or more thicker and rather-narrow ribs, carried on piers which must be somewhat wide as seen in side elevation, there usually being a separate shaft for each hne of ribs. For arches of considerable rise in which the Uve load moments are the only ones of impor- tance, the thick, narrow rib is much the cheaper; but, as the rise is reduced, temperature and arch-shortening stresses increase in importance, and it becomes more economical to reduce the thickness and make each rib wider, until eventually the sohd-barrel rib is reached. For any special case, com- parison can be made by means of the curves on pages 1332 and 1333 of "Bridge Engineering." It must not be forgotten that, with the ribbed type, cross-braces between the ribs are generally necessary. The type of pier required is also important. If a separate shaft can be used for each line of ribs, the ribbed type will usually be the more economical; but in many cases, as in most rivers, solid pier-shafts must be employed in any event. Frequently, in river crossings, the springings are located below the high-water line; and the adoption of solid barrels then becomes almost imperative. Hingeless and Three-Hinged Arches Comparing the hingeless and the three-hinged types for reinforced- concrete arch-bridges, it will be found that the latter is cheaper for low rises, and the former for high ones. The principal objection to the three- hinged type is its awkward appearance, due to the fact that it is thicker in the haunch than at the springing line; and since the concrete-arch bridge is often selected from aesthetic considerations, this is an important matter. If the three-hinged rib be thickened at the springing, in order to make its appearance satisfactory, it will rarely, if ever, prove to be cheaper than the hingeless type. Arch with Steel Bottom Chords An unusual economic problem arose in the design of the author's Twelfth Street Trafficway Viaduct in Kansas City, Mo. This is a double- deck, reinforced-concrete-girder structure; but there was one portion of it where a 134-foot span was required over some railroad tracks. An arch span was adopted; but the springings were high above the foundations, which were on piles; and the area allowable for the piers was restricted by other tracks. The question of what to do was finally solved by putting in 230 ECONOMICS OF BRIDGEWOEK Chapter XXV encased bottom chords of eye-bars at the elevation of the lower deck, so as to take up the arch thrusts. The available clearance was very small; so that the floor-beams of the lower deck had to be made of steel I-beams encased in concrete and riveted to steel hangers, also encased. Reinforced-Concrete Trestles for Steam Railways A number of reinf orced-concrete trestles have been built of late years for steam-railways. The usual type for river crossings has been sohd-concrete slabs on concrete piles. The economic span-lengths for such trestles are very short, usually from ten (10) to fifteen (15) feet; but most of the structures have had spans of fifteen (15) or twenty (20) feet on account of waterway requirements. Solid slabs have also been used extensively for grade-crossing-elimination work in cities, the substructure generally con- sisting of either soUd cross-walls or cross-girders resting on a row of small columns carried on a continuous footing. The economic span-lengths for such structures are a little greater than those for the slab-pile-trestles; but this economic question is of very small importance, since the span-lengths are generally fixed definitely by other considerations. The slabs for most of these trestles have been separately moulded and afterwards set into place by derrick cars or locomotive cranes. In some cases this was the cheapest possible method of construction; but in others the need for maintenance of traffic demanded it. In many cases also the headroom was limited, and falsework beneath was not permissible. For the purpose of determining the economics involved, the author has had made in his offices during the last three or four years a large number of estimates for steam-railway, reinf orced-concrete trestles of the slab-girder type, for span-lengths varying from twenty (20) to fifty (50) feet, and for heights varying from twenty (20) to sixty (60) feet, measuring from base of rail to bottoms of footings. Both sunple and continuous girders have been computed, the former proving somewhat the cheaper. The substruc- ture considered consists of bents composed of two battered columns with a cross-girder at the top, the columns being supported by either one con- tinuous footing or two separate footings. For the higher trestles it proved to be economical to use longitudinal struts between columns in alternate spans, thus making a succession of towers with a single span between each of them. The economic span-length for such trestles varies from one-half to six-tenths of the height. In the second edition of "Bridge Engineering" (fourth thousand), which will probably be issued in 1922, there will be a lengthy Appendix for the purpose of recording the results of all of the author's studies (excepting the economic ones reproduced in this treatise) on the subject of bridges made since July, 1916, when the first edition of that work appeared. The said Appendix will contain an extensive series of diagrams giving curves of quantities for diffei-ent types of steam-railway, reinforced-concrctc trestles. ECONOMICS OF REINFORCED-CONCEETE BRIDGES 231 Comparing such structures with those composed of steel girders carrying ballasted decks on concrete slabs, there is very little difference in cost, the reinforced-concrete trestles, pure-and-simple, being a trifle cheaper for twenty-foot spans and a little more expensive for fifty-foot spans. But if the steel girders are encased in concrete, the reinforced-concrete trestle will always be found the cheaper. Retaining Walls Reinforced-concrete retaining walls show a small saving over plain-con- crete ones for even small heights. However, it is better to use plain con- crete up to heights of ten (10) feet, measuring from bottom of footing to grade, as the section of a low reinforced-concrete retaining wall is too small, for the reason that a certain amount of massiveness is necessary in such constructions. In respect to the economics of cantilevered and counterforted walls, the former type is the cheaper up to about twenty or twenty-five-foot heights, above which limit the latter type is the more economic. The dis- cussion of ''Footings" previously given in this chapter will apply to the footings of retaining walls. CHAPTER XXVI ECONOMICS OF STEEL ARCH-BRIDGES For some twenty-five or thirty years American bridge engineers have been sadly in need of reUable information concerning certain fundamental economic functions of steel arch-bridges, and especially the relative costs of such structures in comparison with the corresponding truss bridges. The want of such information has resulted in the failure of American engineers to develop the steel arch and to use it in places where it would be both m-ore economic and more aesthetic than the simple-truss bridge. Wherever the governing conditions of crossing are suitable for an arch structure, that type of bridge is to be preferred; for, as we now know, the arch, in all places where its use is really justified, is less expensive than the truss bridge. For two decades or more, the author had been urging the engineering profession to make certain investigations which would settle for all time every uncertainty concerning the economics of designing steel-arch bridges, as well as the relative costs of these structures in comparison with the cor- responding truss bridges. As long ago as 1897, when he wrote "De Pontibus," he appealed to the engineering profession as follows: In concluding this chapter, the author desires to call attention to the fact that there is still a great deal to be learned about the designing of arches; and to suggest that some professor of civil engineering, who is well posted on bridge designing and who has time to spare, could spend several months to the great advantage of the engineering profession in determining the proper relations of span-lengths, rise, arch depth, width between exterior arches, etc., for the varous styles of arch, and in ascertaining the relative economies of the latter. During the eighteen years which elapsed between the issuing of ''De Pontibus" and its successor, "Bridge Engineering," the author made repeated attempts to find some bridge engineer who would be willing to undertake the task' which he had suggested — but all to no avail; and in the last-mentioned treatise he made another forcible appeal to the pro- fession to undertake the requisite investigations, speaking as follows: " For many years the author has been endeavoring to establish some approximate relation between the weights of metal per lineal foot for trusses and laterals of arch bridges and those for the corresponding simple truss bridges; but has met with very little success. He once submitted the (nuisiion to his brotlier bridge specialists of America, but tlioy were unable to throw any light upon the subject, because their opportunities to 232 ECONOMICS OF STEEL ARCH-BKIDGES 233 design and build arch bridges had been few and far between, and because the ratio of rise to span has a great effect upon the weight of metal in an arch. Of course, there is for any span length some economic value of that ratio ; but it is not yet known, and it probably varies more or less not only with the span but also with the type of construction. The only practicable method of determining the original question would be to settle first that of the economic ratios of rise to span, design a few arch bridges with the said ratios, and make the comparison. This would have to be done for the solid-rib, the braced-rib, and the spandrel-braced types to make the job complete, adopting for the first set of curves the three-hinged type, and afterward modifying the results for the other three types of hinging. It is evident that the amount of work involved in such an investigation would be immense. It should be clone by an experienced bridge designer, as the results would be worthless if obtained by any other investigator. The author suggests that one of his younger brother-specialists undertake the investigation." The result of this appeal, as in all previous attempts, was absolutely nil; and in 1917, despairing of ever being able to induce anyone to assume the obKgation, the author himself shouldered the burden by making, with the aid of one of his assistants, all the calculations needed to determine every desired point, and from the results thereof prepared a paper on ''The Economics of Steel Arch Bridges," which he presented to the American Society, of Civil Engineers. As soon as he learned of its acceptance by the Publication Committee, he sent a circular letter to all the bridge engineers in America whose addresses he could obtain, as well as to a number of prominent engineers abroad, inviting them to discuss the paper, and enclosing the following synopsis: Up to the present time, nothing at all certain has been known concerning the economics of steel arch-bridges, the weights of metal required to build them, or how they compare in cost with the corresponding steel truss-bridges. The objects of this paper and its anticipated discussions are to settle finally every important economic question that can arise in the designing of steel arches; to give formulae and diagrams for determining, with a fair amount of accuracy, the weights of metal in both arch-bridges as a whole and the arches themselves; and to indicate the relations between the weights and costs of arch-bridges in comparison with those of the corresponding truss-bridges. There are eight economic problems set for solution; and all of them have been solved — the first two by employing certain formulaj given in "Bridge Engineering," and the other six by means of a large number of special arch-designs and the resulting estimates of weights of metal. Incidentally, during the investigation there have arisen and been solved a few minor questions which may properly be termed side-issues. The computations have been made for both railway and highway arch-bridges; and the weights of -metal are plotted for both carbon-steel and nickel-steel structures. Several diagrams are given to show the percentage effects of weight-increase due to departure from economic conditions. The need for the special knowledge concerning arch-bridges presented in this paper has been recognized during the last three decades by American structural-steel- engineers; but the authors of books on bridges (this author included) have hitherto 234 ECONOMICS OF BRIDGEWORK Chapter XXVI avoided the issue because of the immense amount of work involved in the solution of the various problems. The author has tried of late years on several occasions to per- suade some of his brother engineers to undertake the task; but not meeting with any success, he finally decided to do the work himself. The results of his efforts are here- with presented to the members of the Society with a most earnest request for a thor- ough discussion, particularly by those who specialize in bridgework. The principal economic problems concerning the design of steel arch-bridges which have been solved for this paper are the following : First. The economic ratio of rise to span-length. Second. The economic depths for the ribs. Third. The economic location for the crown-hinge in three-hinged, spandrel-braced arches. Fourth. The ratios of weights of metal required for the solid-rib, th3 braced-rib, and the spandrel-braced types. Fifth. The ratios of weights of metal required for the hingeless, the two-hinged, and the three-hinged types. Sixth. The economics involved by making arches three-hinged for the dead load and two-hinged for the live load. Seventh. The economy of the cantilever-arch with suspended end-spans, as com- pared with an ordinary arch and two flanking simple-truss-spans. Eighth. The ratios of weights of metal required for certain portions of arch bridges as compared with the corresponding portions of simple-truss bridges of the same span and same Uve-load-carrying-capacity. In answer to this request, a number of engineers, both at home and abroad, discussed the paper; and their discussions have been printed in several copies of the Society's "Proceedings." These discussions have been thoroughly analyzed and replied to in the closure of the memoir. With one exception, the discussions did not result in the modification of any of the author's findings — and in that one the change was not serious. It was pointed out by him that the first two problems were solved by the use of certain semi-rational, semi-empirical formulae for weights of metal in arches established in Chapter XXVI of "Bridge Engineering," but that the other six were settled by means of actual computations of weights of metal determined from specially-prepared diagrams of stresses and sec- tional areas of main members. Mr. Charles Evan Fowler in his thorough and elaborate discussion, including a tabulation of the salient features and dimensions of one hundred of the world's largest steel-arch-bridges, showed that the author's finding for economic ratios of rise to span-length agreed fairly well with the averages computed from existing structures, but that his deduced economic ratio of depth of arch-ring to span-length did not; whereupon the author agreed to settle this question beyond a doubt by submitting it to the incontrovertible test of making actual designs and estimates of weights for arches of 500-feet span, of economic ratio of rise to span-length, and having regularly-varying depths of arch ribs, so as to determine the depth producing the least weight of metal. This was done; and the results of the special calculations were given in the resume, which showed that, for short-span railroad arch-bridges, the previous finding was correct, but that, ECONOMICS OF STEEL ARCH-BRTDGES 235 for the corresponding long-span structures, it was somewhat too great — • also that the conclusion to the effect that the economic depth for arch ribs is the same for both railway and highway bridges is wrong. The reason for the variation in the two findings is that the weight formulae, upon which the first investigation was made, were of too empirical a nature to warrant their use for an exact determination of economic depth of arch rib. From the original paper, the discussions, and the resume, the following answers to the set questions have been reached : First. For three-hinged arches with the grade Une approximately tan- gent to the top chord of the arch at the crown, the average economic ratios of rise to span-length are as follows : Solid-rib structures 0.2 Braced-rib structures . 225 Spandrel-braced structures (with hinge above) . 25 These values may be either increased or decreased by 0.025 without making any material difference in the economics. For three-hinged, half -through arch-bridges, the average economic ratios for rise to span-length are as follows: Solid-rib structures . 225 Braced-rib structures 0.3 For three-hinged, high-deck arch-bridges, they are as follows : SoKd-rib structures . 25 to . 28 Braced-rib structures . 33 to . 38 For two-hinged arches and combined two-hinged and three-hinged arches, the economic ratios of rise to span will be practically the same as for three-hinged structures. For the hingeless arch, a somewhat greater ratio of rise to span than that for the three-hinged arch is economical. The single test of this made for the 500-ft. span indicates that the best ratio is about 0.28 with low- grade deck, 0.33 for half-through arches, and 0.38 with high-grade deck. Second. In respect to solid-rib arches, the question of economic rib-depth does not arise; for the depth should always be made as great as a proper consideration of the section for resisting compression will permit, and with due regard to shipping restrictions concerning limiting sizes of single pieces. For braced-rib, three-hinged arches in steam-railroad bridges, the economic rib-depth varies from 7.8% of the span-length for 100-ft. spans to 5.3% thereof for 1000-ft. spans; and for highway bridges the corresponding variation is from 5.8% to 4.2%, as shown in Fig. 26a. The effects on rib weights from using uneconomic rib-depths in braced- rib arches for both railway and highway bridges are given in Fig. 266. Third. It was found for all cases that the most economic location for the crown-hinge in a spandrel-braced arch is in the top chord. In braced^ 236 ECONOMICS OF BRIDGEWOEK Chapter XXVI 0.03 . ,100 200 300 400 500 600 700 800 900 3^00 Span- length, in Feet, Fig. 26a. Economic Ratios of Depth of Arch-Rib to Span Length. GS Q6 df 0.8 .. 0.9 ._; 1.0 U f.2 15 1.4 . 'S V5 06 . aj^ m 0.9 1.0 // // /? M 15 ^^ahos of ffdaaf Fid Vepfds fo rco/jcmic Eib Depf/js Fig. 20/;. Effects on Rib-"Weights from Using Uneconomic Rib-Depths in Braced-Rib Arches. ECONOMICS OF STEEL ARCH-BRIDGES 237 rib and solid-rib arches, however, the hinge should always be placed at mid- depth, so as to distribute properly the thrust over the two chords. Fourth. Comparing the economics of solid-rib, braced-rib, and span- drel-braced arches, it was found that the first mentioned is always con- siderably heavier than either of the others; and, under normal conditions of the metal market, it is also more expensive. The spandrel-braced-arch requires for long spans a little more metal than the braced-rib arch; but, 500 600 Sran. in Feet U09 Fig. 26c. Ratio of Weights of Metal in Hingeless Arches as Compared with Three- Hinged Arches for both Railway and Highway Bridges. in case of cantilevering, this would generally be offset by the extra quan- tity of erection metal needed for the braced-rib structure. In short spans, the spandrel-braced arch is a trifle the lighter. Fifth. Comparing three-hinged, two-hinged, and hingeless arches, it was found that the three-hinged is a little heavier than the two-hinged, but nearly always lighter than the hingeless. The variations in weight among the three types, however, are never great. In Fig. 26c are given ratios of weights of metal in hingeless arches as compared with three- hinged arches for both railway and highway bridges. 238 ECONOMICS OF bridgework: Chapter XXVI Sixth. The combination of three liinges for dead load and two hinges for Hve load produces very httle sa\dng over the three-hinged type; but it adds materially to the rigidity. In the writer's opinion, the combined type is preferable to any of the others. Seventh. ^Vhen an arch is flanked by other spans than arches, there is generally quite a httle economy involved by cantilevering the ends of the arch and shortening the lengths of the smiple spans. The best proportions for lengths of cantilever arm and suspended span to total length of flanking span are, respectively, 0.4 and 0.6. Eighth. The ratios of weights of arches to the weights of the corre- sponding simple spans for both railway and highway bridges have been determined and plotted. As was anticipated, the arch usually effects a greater relative economy in highway structures than in railway structures of the same span length; and the longer the span the greater alwaj^s is the proportionate saving of metal. The results of this investigation are shown in Fig. 2Qd. 100 1 1 1 N I M 1 1 1 1 11 1 1 1 1 M 1 1 1 1 1 1 1 n II I I iT i TTi I rn 1 1 1 1 1 1 1 1 ii 1 1 1 1 1 1 n n i n 1 1 1 1 1 1 1 1 1 n 1 1 rrm-nlOO i 60 600 600 Span, in Feet. Fig. 26fZ. Percentages to Apply to Weights of Metal in Trusses of Simple-Truss Spans in Order to Find the Weights for Arch-Ribs and the Superimposed Colunms, with their Bracing, to Carry the Same Live Loads. In concluding his paper, the author quoted as follows from "Bridge Engineering": In dealing with the comparative economics of arches and simple trusses, it must not ])('. forgotten that there are other factors than mere weight of metal involved; for the l)ouMd i)rice of the manufactun^d material is generally somewhat greater for the former, a:i(l sometimes the cost of erection also is larger. Again, the comparison of the costs of arch superstructures and truss supetstructurcs alone is not of much importance, for ECONOMICS OF STEEL ARCH-BRIDGES 239 an economic investigation, to be of any value, must include both substructure and superstructure; and the costs of the former are likely to be very different in arch designs and simple-truss designs for any crossing. Some of the solutions of the ^'side issues" referred to in the preceding "Synopsis" are the following: First. The percentages to apply to weights of metal in simple-truss spans, in order to find the weights for arch ribs and the superimposed col- umns with their bracing to carry the same live loads, are given by the following equations: For steam-railway structures: P-106-0.08.S [Eq. 1] For electric-railway structures: P = 93-0.07/Sf [Eq. 2] For highway structures p^80-0.056*S [Eq. 3] In these equations S is the span-length in feet, and P is the percentage to apply to the weight of metal in the trusses of any simple-truss bridge, in order to ascertain the weight of metal in the corresponding arches and the superimposed columns with their bracing. It must not be forgotten that the superior limit of S in these equations is about 1000-ft., which is as far as the recorded weights of simple-truss spans are carried, and that the inferior limit is 100-ft. In Fig. 26d are plotted curves giving the same information as that presented in the three preceding equations. Second. It is evident from the computations and the resultant diagrams that the arch is more economical for highway bridges and for combined highway and electric-railway bridges than for steam-railway structures. This is because of the smaller ratio of live load plus impact to total load in the former. The larger the dead load of the flooring and floor-system, the more advantageous is it for the arch structure in comparison with the truss bridge. Third. Based on the numerous weight computations made specially for the preparation of the paper, the following formulae for weights of metal in the arches alone, per lineal foot of span, in arch bridges of the several types, have been established: For Three-Hinged Arches: IFa = (0 . 000282D^-0 . 000426L)Z [Eq. 4] For Two-Hinged Arches: PTa = (0 . 000248Z)-l-0 . 000416L)Z [Eq. 5] For Combined Two-Hinged and Three-Hinged Arches: Wc: - (0 . 000282D-I-0 . 000416L)^ [Eq. 6] 240 ECONOMICS OF BRIDGE WORK Chapter XXVI For Hingeless Arches: Fa=(0.000272D+0.000460L)i lEq. 7] These four formulae are based on the author's pubhshed designing speci- fications, which treat reversing -stresses by adding one-haK of the smaller stress to the larger stress and proportioning for the sum ; but if the effect of reversion is entirely ignored, as some engineers deem proper, the;'e formulae will reduce to the following: For Three-Hinged Ai'ches: W'a = (0 . 000292Z)+0 . 000396L)Z [Eq. 8] For Two-Hinged Arches W'a = (0 . 000258Z) + . 000380L) I [Eq. 9] For Combined Two-Hinged and Three-Hinged Arches F'a= (0. 0002921) +0.000380L)Z [Eq. 10] For Hingeless Arches Tf'a=(0.000270D+0.000398L)^ [Eq. 11] In Equations (4) to (11) inclusive, Wa, or W'a, is the weight of metal, in pounds per lineal foot of span, in the arches of the structure; D is the dead load, in pounds per hneal foot of span; L is the five load plus impact, in pounds per lineal foot, used in making the calculations; and I is the span length, in feet. These eight equations will give fairly accurate results (slightly on the side of safety) for ordinary conditions which do not vary greatly from the theoretically economic ones. In computing the value of L for insertion in Equations (4) to (11), inclu- sive, the equivalent uniform live load and the impact should be determined for the half-span-length. Fourth. From the formulae given above for weights of arch ribs, some interesting deductions may be drawn. For instance, in Equation (4), viz., Wa=^(0. 000282Z)-f . 000426L)Z, the dead load, D, is composed of the rib weight, Wa, plus the weight of floor, columns, lateral system, etc., all of which may be grouped under the symbol, W', making the equation Wa = (0 . 000282IFa+0 . 000282Tr'+0 . 000426L)Z Solving this gives _ (0 . 000282F'-F0 . 000426L)? ^° ~ 1-0.000^82] In order that Wa may be infinitely great, the divisor of the second term must be equal to zero, or ECONOMICS OF STEEL ARCH-BRIDGES 241 This is the theoretical Hmiting span-length for three-hinged arches of carbon steel, or the span at which such an arch could carry nothing but its own weight without being over-stressed. It will be noted that this limiting length is the reciprocal of the dead-load coefficient in Equation (4), and that a vertical line on the diagram of arch-rib weights per lineal foot of span, drawn through the abscissa point which represents this value of Z, will be asymptotic to the weight curve. Fifth. From the curves in the diagrams it is possible to determine the economic or practicable limit of arch spans, by assuming, as the author did years ago in his economic investigations for cantilevers, that the said 80000 9000O 70 00O 30 000' 10 000> 1100 1300 1500 1700 1900 2100 2300 2600 Span, in Feet. Fig. 26e. Weights of Metal in Double-Track, Steam-Railway, Long-Span Arch- Bridges of Carbon Steel for Class-60 Live-Load. limit is reached when it takes 4| lbs. of metal to carry 1 lb. of live load. On that basis, and assuming that the equivalent uniform live load per lineal foot for a long span is equal to the car load per lineal foot, the limiting weight of metal per foot for carbon-steel, double-track, steam-railway bridges of Class 60 would be 4.5X12,000 = 54,000 lbs. Referring to Fig. 26e, it is found that the span for that weight is nearly 2,100 ft.; consequently, gen- erally speaking, it may be stated that, for steam-railway arch-bridges of carbon steel, the limiting length of span is about 2,000 ft., or the same as the limiting length of main opening in cantilever bridges built of the same material. Judging by analogy, the corresponding practicable limiting length of nickel-steel arch-spans is about 2,600 ft. Sixth. It is impracticable to take the substructure into account when 242 ECONOMICS OF BRIDGEWORK Chapter XXVI making general economic investigations for arch bridges, because no two examples thereof are alike. In case of a succession of long spans in which there is a choice of rise, a tentative layout should be made using the antici- pated economic ratio of rise to span-length when both substructure and superstructure costs are considered, then the costs of piers and spans should 1.13^ 0.15 0.20 0.25 0.30 O.i Ratios of Rise to Span Lengrth. 0.60 Fig. 26/. Economics of Solid-Rib Arches, with Columns and Bracing, for Steam- Railway Structures, in Relation to Ratios of Rise to Span-Length. be computed, the uneconomic effect of departing from the established economic ratio of rise to span-length, given in Figs. 26/ to 26f , inclusive, being employed to calculate the weights of metal from those shown in certain other fliagrams. Next, this work should be repeated for a slightly greater ratio of rise to span-l(>ngth, and then for a slightly smaller ratio thereof. These three sets of computations would probably determine the best ratio to adopt; ECONOMICS OF STEEL ARCH-BRIDGES 243 but, if not, still another set of calculations would be necessary. The com- putation work involved in this investigation is not as great as a perusal of the preceding directions might lead one to surmise, especially after the computer has become accustomed to utilizing the diagrams of the paper and to estimating quickly the approximate quantities of masonry in arch piers. O.Oi) 0,15 0.20 0.25 0.30 0.35 Ratios of Rise to Span Length. 0.45 1.13 l.OS 1.02 0.60 Fig. 26g. Economics of Solid-Rib Arches for Steam-Railway Structures (Ribs Alone Considered), in Relation to Ratios of Rise to Span-Length. Seventh. In the cantilever arch the reduction of the horizontal thrusts at the tops of the piers, as compared with simple or non-cantilevered arches, effects a decided saving in the cost of the said piers; and the greater the proportionate lengths of the flanking spans to the arch span, the larger the economy in pier material. Eighth. Some engineers who adhere to old-fashioned notions contend that both masonry and steel arch-bridges are applicable to bed-rock foun- 244 ECONOMICS OF BRIDGEWORK Chapter XXVI dations only, and that the piers and abutments therefor should never rest on piles. While it is true that bed-rock is the ideal foundation for such structures, pile foundations can be made entirely satisfactory, provided that the masonry of the bases is carried well down into firm material which is capable of resisting properly the horizontal thrusts. It is not legitimate to count upon the horizontal resistance of the piles; and it would be criminal practice to rest the piers and abutments of an arch bridge on piles the tops of which below the pier bases act like stilts because of passing through soft material before reaching a hard bearing. 0.05 0.15 0.20 0.25 0.30 0.35 Ratios of Rise to Span Length Fig. 26/i. Economics of Braced-Rib Arches, with Columns and Bracing, for Steam- Railway Structures, in Relation to Ratios of Rise to Span-Length. Ninth. As stated by Mr. F. H. Frankland in his discussion, "in respect to arch designing, the proper determination of the true economics calls for more judgment on the part of the designing engineer than with any other type of bridge." The paper and the resume combined contain twenty-six diagrams, of which only ten have been reproduccnl in this cliapter; hence the reader who desires to utilize the I'esults of that inv(>stigation, is referred to the paper itself, which, with all the discussions and the resume, is soon to be pubhshed in the "Transactions" of the American Society of Civil Engi- neers. As previously indicated, the comparative economics of steel arch-bridges ECONOMICS OF STEEL ARCH-BRIDGES 245 and the corresponding bridges of simple-truss or cantilever type depend greatly upon the governing conditions for the substructure, and that, as these almost invariably differ essentially at proposed crossings, it is imprac- ticable to determine in general the economics of substructure for such com- 0.15 0,20 0.25 0,30 Ratios of Rise to Span Length. Fig. 26i. Economics of Braced-Rib Arches for Steam-Railway Structures (Ribs Alone Considered), in Relation to Ratios of Rise to Span-Length. parisons, each case having to be treated upon its own merits. While this is certainly true, it is practicable, nevertheless, to outline some general principles that will enable a bridge designer to determine readily the suit- ability of any proposed crossing for an arch layout, as affected by sub- structure conditions; and the author offers the following: 246 ECONOMICS OF BRIDGEWORK Chapter XXVI First. Where there is a gorge with steep, rocky sides to be crossed hy a single span, the arch is eminently suitable; for not only does it reduce the Fig. 2Q/. Canadian Northern Pacific Railway Bridge over the Fraser River at Lytton, B. C Fif!. 2U:. Arch Bridge over llic ^^';lik,■ll() IJivor at Hamilton, N. Z. required volume of masonry to a minimum but also it bi'ings the pressure on the rock foundations practically normal to the surface — a coiisi(l(>jatioii ECONOMICS OF STEEL ARCH-BRIDGES 247 often of great importance when the rock would be subject to shp under vertical loading. A good illustration of such a condition is the author's Fraser River Bridge at Lytton, British Columbia, shown in Fig. 2Qj. Second. Where there is a navigable stream to be crossed by a single span, and where the material near the water's edge is either rock or some fairly-hard material, such as shale or stiff clay, a deck truss-bridge would be inadmissible on account of navigation, and a through truss-bridge would involve high, expensive piers; hence, under these circumstances, an arch structure would be economic. Two of the author's bridges over the Waikato River in New Zealand, shown in Figs. 26A; and 2QI, illustrate such conditions. h L Fig. 2GL Arch Bridge over the Waikato River at Cambridge, N. Z. Third. Where the foundations of a wide crossing are either solid rock or some other hard material lying close to the bed of the stream or to the sur- face of the banks thereof, and where the grade line is much above the high- water line, a layout consisting of a succession of arch spans will frequently be economic. The springings of the arches can be brought down close to the high-water line or to the ground, as the case may be, giving small piers ; whereas, for a deck simple-truss layout, much higher piers would be required. An excellent illustration of such conditions is given by the author's highway bridge over the Arroyo Seco at Pasadena, Calif., shown in Fig. 26w. 248 ECONOMICS OF BRIDGEWORK Chapter XXVI e3 O Another illustration of the said conditions, in which the economic advan- tage of the arch is not so marked, is the author's combined-high- waj^-and-electric-railway bridge over the Colorado River at Austin, Texas, shown in Fig. 26n. Here the vertical distance from high-water to pier-base is con- siderable, thus rendering the piers much more expensive than those of the Pasadena structure. Where the foundation-level is much below the river-bed, the conditions are not favorable to the arch; because, in order properly to resist the horizontal thrust, the piers have to be made much wider ^than those for simple-truss spans. Before concluding, it might be well to quote the following caution given by the author to those intending to utilize the information furnished in his memoir : The various formulse and dia- grams in this paper are to be con- sidered as merely approximate; and though they are sufficiently accurate for preliminary estimates and for ob- taining trial dead loads, they should not be used by contractors in tender- ing on work. The reason for this uncertainty is that the varying physi- cal conditions at different crossings affect the arch layouts to such an extent as materially to influence the weight of metal required. As the formulae were based on economic functions, the weights given by their use might very properly be considered as the minima possible; and any un- economic conditions which may exist will involve an increase thereof, the ainontit being a matter to be deter- iniiicd by the computer's judgment. ECONOMICS OF STEEL ARCH-BRIDGES 249 CHAPTER XXVII ECONOMICS OF STEEL TRESTLES, VIADUCTS, AXD ELEVATED RAILROADS The usual railway steel trestle consists of alternate towers and inter- mediate spans. In determining the economic span-lengths for such a structure, there are two separate factors to be studied : 1. The ratio of length of intermediate span to that of tower-span. 2. The cUstance from center to center of towers. Investigation of the fu'st of these factors for a single-track-railwaj' trestle shows that, for Class 40 loacUng, the length of tower-span should vary from 44 per cent of the distance between centers of towers for a trestle 60 feet high, to 35 per cent thereof for one 240 feet high, the length of inter- mediate span for these limits being from 1.27 to 1.86 times that of the tower- span. For a Class 70 loading the corresponding percentages for tower-spans vary from 46 to 38, and the corresponding span-ratios from 1.18 to 1.63. After the fii-st factor has been investigated the second one can be deter- mined. Fig. 27a gives the economic distances from center to center of towers and the economic lengths of intermediate and tower-spans for single-track railway trestles, varying in height from 60 feet to 240 feet, and for Classes 40 to 70. Considerable variation from these economic relations will affect the total weights but slightly. It will be noted that the economic lengths are considerably greater for Hght loadings than for hea\'A' ones. Fig. 55oo on page 1259 of "Bridge Engineering" covers the same data as Fig. 27a, but the lengths there given are incorrect. In the investigation for Fig. 55oo no attempt was made to ascertain the economic ratio of intermediate span-length to tower span-lengih, it being assumed that it would be sufficiently accurate, in determining the economic distance from center to center of towers, to consider the length of the tower-span fixed, and to vary the length of the intermediate span only. The weights of longitudinal bracing given in Fig. oopp on page 1260 of "Bridge Engineering" are also incorrect. The weights should vary from 450 pounds per vertical foot for 30-foot tower-spans to 580 pounds for 60- foot tower-spans, being independent of the height. The total weights of metal given by Fig. D5rr on page 1262 of "Bridge Engineering" are but slightly in error, being about 2 per cent too great for a 60-foot height, and about 6 per cent too small for a 240-foot height. In Fig. 276 are given the economic span-lengths for various heights of low, single-track-railway trestles consisting of towers with two rocker 250 STEEL TRESTLES, VIADUCTS, AND ELEVATED RAILROADS 251 bents between, as shown in a corner of the diagram. It will be noted that, as in the previous type, the lighter the live load the greater the economic 60 60 100 120 140 160 ISO 200 220 240 260 ao 100 IZO /fe/^hf of lower m feef. 240 260 Fig. 27a. 140 160 JdO ZOO 220 Top of Masonry fo Base of 2a}/. Economic Span-Lengths for High, Single-Track-Railway Trestles. span-length. It has been assumed that the length of tower-span would in all cases be 30 feet. Actually, this length should vary somewhat, increas- 252 ECONOMICS OF BRIDGEWORK Chapter XXVII ing slightly with the height; but the resulting error in the total weights of metal will be negligible. For double-track-railway trestles consisting of alternate tower-spans and intermediate-spans, and having two planes of longitudinal bracing, the ratio of intermediate-spanrlength to tower-span-length is a trifle less than for the single-track trestle, the values for Class 40 being about 1.08 for a 60-foot height, and 1.55 for a 240-foot height. The corresponding values for Class 70 are 1.05 and 1.34. The economic distances from center to center of towers are 85 or 90 per cent of those for a single-track trestle. The lengths of tower-spans are about the same as for the single-track trestles, but the lengths of intermediate-spans are only about 80 per cent as great. 10 iO 70 60 90 100, 1 90 m Fig. 276. Economic Span-Lengths for Low, Single-Track-Railway Trestles. ■JO iO 30 40 30 60 70 Hei0 in /ie/, I>p of Mason j to ^se of 2a/f The economics for low, double-track-railway trestles of the type shown in Fig. 276 are as follows: The lengths of the tower-spans will be identical with those for like single-track-railway trestles, and those of the intermediate spans about ninety per cent of the corresponding lengths for same. Strictly speaking, the costs of the pedestals should be figured in comput- ing the economic span-lengths, but for bare rock foundations they are insignificant and, therefore, negligil)le; for pile foundations and spread foundations on soft soil they are almost constant \)q\' lineal foot of stmcture, irrespective of the span-lengths, and consequently also negligible; and it is only when the pedestals have to penetrate dee]:)l>' into the ground and rest on fairly hard soil that their cost boc^omes influential. TluMr c^lTcct is to increase the economic lengths of both the intern unliate and Ilu> tower spans, although probably not more than a few feet. The economic span-knigths for highway trestles with two lines of main girders will generally be a trifle greater than those for Class 40, single- track-railway trestles; and for like structuix^s with several lines of main girders they will be somewhat larger than those for C^lass 40, double-track- STEEL TRESTLES, VIADUCTS, AND ELEVATED RAILROADS 253 railway trestles. The economic lengths will be greater for hght live loads and timber decks than for heavy live loads and concrete decks. The economics of column spacing for bents when cantilever brackets are employed is an interesting little problem, but the final determination must be in accordance with good judgment as well as economy; for if the spacing be too small, rigidity is Ukely to be sacrificed. Upon certain assumptions of approximate correctness the mathematical solution of this problem is a possibility; but the equations involved would be so complicated that it is much better for any particular case to assume two or three spacings, com- pute the total weight of metal in the bent for each, and find the one which will give approxi^nately the least weight of metal. If the columns are placed at the quarter points of the beam, the dead-load bending-moment at the middle will be approximately zero; and if the effect of stress rever- sion is ignored, the direct and the reverse bending moments for the central portion of the beam will be equal, and this arrangement would be about the most economical possible. But if reversion is considered, the sectional area of the middle-portion of the beam must be greater than that of the outside portions, hence for economy its length should be somewhat less than one-half of the total, and the columns would then be spaced somewhat closer than when they are located at the quarter points. The fact that the brackets are usually lighter near the outer ends than at the inner ones would, for economy, tend to draw the columns together; but, on the other hand, this would increase the weight of the splices and connecting details. The proper column spacing to adopt will depend upon the length of the columns; for it is easily conceivable that the structure could be so high and so narrow that the quarter-point spacing would be too close for proper resistance to wind pressure. Again, in such a case the wind load might be so great as to necessitate an increase in column section above that required to care for the live and dead load stresses only; and thus the effect of wind pressure would enter the economic study. It will be found in most cases that it is inadvisable to space the columns much less than one-half of the total length of the beam. Elevated Railroads In respect to the economics for Elevated Railroads, as long ago as 1896 the author, when designing the Northwestern Elevated and the Union Loop Elevated Railroads of Chicago, determined certain economic functions for such structures and published the results in a paper entitled "A Study in Designing and Construction of Elevated Railroads, with Special Refer- ence to the Northwestern Elevated Railroad and the Union Loop Elevated Railroad of Chicago, III," which paper was presented to the American Society of Civil Engineers and published in its "Transactions" for 1897. From it the following statements concerning the economics of elevated- railroads have been excerpted: 254 ECONOMICS OF BEIDGEWORK Chapter XXVII Best and Most Economical Span-Lengths This question was investigated very exhaustively, considering every item of expense, including not only the cost of metal in place, but also that of concrete, excavation, back-filUng, and pavement; also the possibihty of expense for the moving of water pipes and other conduits. The investiga- tion showed that, for plate-girder construction through private property, the econoinic span-length is about 40 ft. for intermediate spans and 23 ft. for tower spans; while for construction in the street, where towers are inad- missible, it varies from 47 to 50 ft., or even 3 or 4 ft. more, in case of cross- girders spanning wide streets from curb to curb. The theory of true economy in elevated railroad designing, as far as length of bays is concerned, is simply this: "The cost of the longitudinal girders should be, as nearly as may be, equal to the cost of the bents and their supporting pedestals, in cases of doubt adopting the longer span." Four-Column versus Two-Column Structures Detailed estimates of cost show that, as far as economy is concerned, there is but little, if any, difference between these two styles of bent. Whether the total cost of the four-column bent will exceed that of the two- column one for a four-track structure depends upon the various schedule prices for metal, concrete, excavation, paving, etc., as well as upon the character of the soil. As there is no great difference in the cost of these two types of structure, and as the four-column bent is decidedly the more rigid of the two, it was adopted wherever practicable. Cantilevering an entire train load beyond the exterior column of a two-column bent is not conducive to rigidity, but this is the only method that will bring the cost as low as that of the four-column bent. Braced Towers versus Solitary Columns Where an elevated railroad occupies private property and crosses the streets by spanning from curb to curb, it is practicable to use braced towers and thus stiffen the structure and check vibration; and, moreover, this arrangement is very economical. For the Northwestern Elevated, upon which it is proposed to rim trains at a speed of 40 miles per hour on the inner tracks between the inter-track stations, situated about a mile apart, the consideration of the extra rigidity afforded by the braced towers is quite important. It was therefore, decided to use both longitudinal and transverse sway bracing, forming braced towers spaced about 150 ft. apart (or two towers per block), and to use the transverse sway bracing in all bents on curves, wherever practicable. Two only of the three spaces between columns have transvci'se sway STEEL TRESTLES, VIADUCTS, AND ELEVATED RAILROADS 255 bracing, thus leaving a longitudinal passageway for wagons at the center of the structure. The saving in weight of metal per lineal foot of four-track structure on tangents by adopting braced towers instead of solitary columns was found to be about 140 lbs., or nearly 9 per cent of the total weight. Plate Girders versus Open-Webbed Girders In designing these elevated railroads for Chicago, many estimates were made for both plate-girders and open-webbed girders, which demonstrate that there is practically no difference in the weight when both girders are properly designed. As the open-webbed girders cost a trifle more per pound to manufacture, there is no economy in their use; nevertheless they were adopted for all structures running longitudinally in the streets, in order to comply with certain city ordinances. The observance of these ordinances was sometimes carried to extremes, producing ridiculous com- binations of solid and open web in the same girder, and an evident waste of material and labor. For this the engineers are not to blame, because they did not frame the ordinances. Best Sections for Columns Investigations concerning strength, capacity to resist impact, facility of erection, economy of metal, etc., determined that the section for columns located in the street should be two 15-in. rolled channels with the flanges turned inward and a 15-in. rolled I-beam riveted between to act as a cen- tral web or diaphragm, the flanges of the channels being held in place by interior stay plates spaced about 3-feet centers. In most cases the column feet pass below the pavement and are embedded in the concrete, to which, of course, they are bolted, but in some cases they rest on pedestals a little above the level of the sidewalk. The main object in turning the flanges inward is to enable the column better to resist impact from heavily loaded vehicles. Just above the pavement there is a curved casting filled with concrete and surrounding the column to act as a fender. This type of column is very satisfactory after it is erected, although it gives some little difficulty in the shops and involves slightly more field riveting than usual. One complaint made was that the planes of the top and bottom flanges of I-beams are never exactly parallel to each other, hence some straightening was necessitated. For columns located on private property or on sidewalks where the structure is transverse to the street, four Z-bars and a web plate were adopted as the most satisfactory section. At the top of the column a wide, curved web-plate and curved angles were used. This design makes a most satisfactory column, which goes through the shops readil}^, and which is well adapted for quick erection. It is true that it necessitated a 256 ECONOMICS OF BRIDGEWORK Chapter XXVII special tool for cutting the webs to a circular curve, but after this was made, the manufacture was easy and comparatively inexpensive. In Engineering News of May 20, 1915, there appeared an excellent article by Mr. Maurice E. Griest, Assistant Designing Engineer of the Public Service Commission of New York City, entitled "Design of Steel Elevated Railways, New York Rapid Transit System," in which he gives a diagram showing that for structures located in the street the economic span-length is fifty feet, but that for lengths from forty-five feet to fifty- five feet there is not much difference in the cost. This not only confirms the author's findings of two decades earlier, but also is in accordance with a general deduction made by him of late from several economic investi- gations, viz., that, up to a certain limit, a material variation from abso- lutely economic conditions can generally be made without seriously increasing the total cost, but when the said limit is passed the uneconomics involved increases rapidly. For further information concerning the details of elevated railroads, the reader is referred to the before-mentioned "Transactions" of the American Society of Civil Engineers. CHAPTER XXVIII ECONOMICS OF CANTILEVER BRIDGES Cantilever bridges inay be divided into four types, which cover all the layouts that are used by good designers. These are shown as Types A, B, C, and D, in Fig. 12a. Type A is the one ordinarily adopted — probably as often as three times out of four. It is applicable to the case of a fairly-wide crossing, where, for some reason or other, it is not permissible or advisable to put piers in the deep water. Type B really amounts to the doubling up of two Type-A structures by omitting the anchorages at the junction and forming the anchor arms into one continuous span. It is applicable to very wide rivers. Type C, which' is the most economic of the four, is used occasionally instead of three simple-truss spans, either for reasons connected with the navigation of the stream or because of economic motives that are some- times based on reahty but too often upon unwarranted assumption. This question is discussed at length in Chapter XII . Type D is a combination of Types B and C, as can be seen by an inspec- tion of the layout in Fig. 12a. Comparing Types A and B, a glance at the two layouts of the diagram shows that there can be but little difference in the weights of metal per lineal foot of entire bridge; because, while the weight per foot for the anchor span is generally somewhat greater than that of the anchor arms, the entire weight of two anchorages is saved, whatever net difference there is constituting generally an excess for Type B. There can, however, be no real comparison between these two types for any particular case, as one is for a comparatively narrow crossing and the other for a very wide one. Comparing Types A and C for a crossing in which the over-all length is fixed, but where the intermediate piers can be placed as desired, the ratio of the weight of Type C to that of Type A varies from about 0.8 for structures under two thousand feet in length to about 0.65 for structures three thousand feet long. The method of determining this may best be illustrated by an example. Given Class 70 live load and a total length of structure of 2500', we have from Fig. 12a for Type A. 3^L+i|L+3^L = f|L = 2500'.-. L=1538' and for Type C, H^+if ^+liL = f|L = 2500'.-. L=1250'. 257 258 ECONOMICS OF BRIDGEWORK Chapter XXVIII From Fig. 55ddd on page 1274 of "Bridge Engineering" we find, for Class 70 and L = 1538', a weight of metal per foot of 28,000 lbs. ; and from Fig. 55jjj on page 1282 thereof, for that loading and L = 1,250', a weight of 21,000 lbs. The ratio of these weights is fi = 0.75. Comparing Type D with the other types in Fig. 12a, it is evident that, for the same value of the hypothetical opening, L, its weight of metal is intermediate in amount; but, as before, there is really no necessity for contrasting this type with the others, because, for any crossing where it would be suitable, the other types would be whoUy unsuitable. Recapitulating, there is never any necessity for a discussion as to which of the four types should be adopted for any proposed crossing, because the profile thereof with its governing conditions will indicate clearly which is the only type appHcable; but there is occasionally an economic question to determine as to whether a simple-truss layout or a cantilever layout should be adopted. This question is treated at length in Chapter XII. In respect to the economic division of span-lengths for any proposed layout, the author determined this question for Type A nearly a quarter of a century ago when writing ''DePontibus,"his findings being as follows: First. The economic length of the suspended span is about three- eighths (I) of the length of the main opening, but a considerable increase or decrease of this proportion does not greatly change the total weight of metal. Second. The most economic length of anchor arms, where the total length between centers of anchorages is given, and when the main piers can be placed wherever desired, is one-fifth (|) of the said total length, or one-third (|) of the m^ain opening. By keeping the anchor arms short, the top chords may be built of eye-bars, provided that, with the usual allowance for impact, there is no reversion of chord stress ; and this effects quite an economy of metal. But it is conceivable that cases might arise where, from danger of washout of falsework, eye-bar top chords would be objectionable; hence this method of economizing must be used with caution. It must not be forgotten that for every dollar saved by reducing the total weight of metal through the shortening of the anchor arm, it will be necessary to spend about twenty cents for extra concrete in the anchorages. On that account, for the conditions assumed, the truly economic length of each anchor arm of a three-span. Type A, cantilever bridge may be a trifle greater than twenty per cent of the total distance between centers of anchorages. Dr. Steinman in his "Suspension Bridges and Cantilevers," by a theoretical investigation and by using certain constants determined from computed structures, shows that for this case the length of anchor arm for economy should be four-tenths of the main opening, or four-eighteenths (0.22) of th(^ total length of structure. This checks quite closely with the author's long-previous determination of "two-tenths or slightly more." ECONOMICS OF CANTILEVER BRIDGES 259 Third. When, however, the problem is to determine the economic length of anchor arm for a fixed distance between main piers, the result will be quite different; because, within reasonable limits, the shorter the anchor arm the smaller will be its total weight of metal, and because trestle approach is much less expensive than anchor arm. It would not, for evident reasons, be advisable to make the length of anchor arm less than twenty per cent of that of the main opening, or say fifteen per cent of the total distance between centers of anchorages. With this length there would probably be no reversion of stress in the chords of the anchor arm, even when impact is considered. Generally, though, the appearance of the structure would be improved by using longer anchor arms than the inferior Hmit just suggested. Fourth. In respect to the economic length of anchor-span in a suc- cession of cantilever spans, it may be stated that, within reasonable limits, the shorter such anchor-spans are the greater will be the economy involved ; but, generally, navigation interests wiU prevent their being built as short as might be desired. If permissible, they may be made so short that, as in the case of anchor arms, eye-bars may be used for the top chords, thus effecting a decided economy of metal, although shortening the anchor- span increases proportionately the stresses on the web members and the weights thereof. In regard to truss-depths for cantilever bridges, the author's practice is to make that for the suspended span, when the chords are parallel, from one-fifth of its length for short spans to one-seventh of its length for very long ones, interpolating between these limits for intermediate lengths. If one of the chords be polygonal, a greater proportionate truss depth at mid-span and a smaller one at the ends would logically be employed. The height of the vertical posts over the main piers can be made about fifteen (15) per cent of the length of the main opening, or not to exceed three and a half (3.5) times the perpendicular distance between central planes of trusses over the main piers. In the new design for the Quebec bridge these posts were made 310 feet high for the sake of appearance, although the economic length was found to be only 290 feet. These figures correspond to percentages of main openings of about seventeen (17) and sixteen (16) respectively. There are certain legitimate economies that may be employed in the designing of cantilever bridges, among which may be mentioned the fol- lowing: A. The wind pressure assumed in computing the erection stresses may be taken lower than that given in the specifications for the finished structure, provided that the full wind pressure would not overstress any of the metal seriously or involve any risk of disaster during erection. A stress of three-quarters of the elastic limit of the metal applied a few times during erection would do no harm; and the chance of there being in such limited time any wind pressure at all approaching in magnitude that 260 ECONOMICS OF BRIDGEWORK Cil4lPTEr XXVIII specified is very small. This lowering of the intensity of wind pressure may be the means of avoiding, in a perfectly legitimate manner, the increasing of the sections of a nmnber of truss members because of erection stresses; but such economizing should be done with caution after a thor- ough consideration of its greatest poss-ible effects. B. A certain amount of metal can sometimes be saved by splaying the trusses between the main piers and the ends of the cantilever and anchor arms ; but unless the amount thereof be fairly large, the extra pound price of the metalwork in the cantilever and anchor arms due to the said splay- ing may more than offset the value of the reduction. C. A small economy may sometimes be accompHshed by omitting dur- ing erection from the cantilevered portion of the structure all parts that are not essential to its strength before the coupHng of the cantilevered ends is effected, thus reducing the erection stresses a httle. D. Solitary piers or large pedestals under the main vertical posts are sometimes just as satisfactory in every way as long, continuous shafts, especially if a connecting wall of reinforced concrete between them be employed. Generally they will be found to involve a large saving in the cost of the substructure. E. In very wide cantilever bridges it might sometunes be advisable to adopt intermediate trusses so as to economize materially in the weight of the floor-beams and sometimes a trifle in that of the trusses, also because of the consequent reduction in dead load, but mainly so as to keep within rea- sonable limits the sizes and weights of the pieces to be handled and thus decrease the size of the traveler and the cost of the erecting machinery. On the other hand, though, increasing the number of trusses is likely to augment a little the percentage of weight of truss details; but, where the sections of members are large, this increase would be small. In case the wind stresses are an important factor in the proportioning of the truss members, the employment of an interior truss or interior trusses might, by the reduction in areas of chord sections, cause such relatively-large wind-stresses on the chords of the exterior trusses that the additional metal required to take care of them would offset all the saving obtained in the ways just mentioned. F. In long-span cantilever bridges the stresses on the truss members that rest upon the piers should be divided among as many such members as possible by using an inclined strut on each side as well as a vertical post, instead of carrying all the loads to the top of the latter by tension members, as was done in the original design of the ill-fated Quebec bridge. Again, if a lowering of the inner ends of the cantilever arms be permissible, the inclin- ing of the end sections of the bottom chords to the horizontal will take up a portion of the load that is carried to the pier, and thus will rcnhu'e the stresses on the vertical and inclined posts assembling there. This last feature reduces also the total cost of the masoniy l)y diminishing the height ECONOMICS OF CANTILEVER BRIDGES 261 of the main piers, and saves placing the tops of the trusses at an abnormal height above the water. G. If there be any choice between the riveted and the pin-connected types of construction for any cantilever bridge, it is generally better to adopt the latter; because, as cantilever bridges are usually employed for long spans only, pin-connected work is the more suitable. Again, it is a little lighter than riveted work; and, therefore, the dead load on the struc- ture would be somewhat less. On the other hand, the riveted construc- tion is so much more rigid than the pin-connected that it is preferable to adopt it whenever the conditions permit; besides, in the riveted work it is not necessary to stiffen any truss members for erection, although it might be obligatory to increase a few of their sectional areas. H. Very large compression members should be made of box section so as to do away with latticing. This not only effects an improvement in the design, but also saves some metal, although the details required afc the panel points to distribute the stresses from the cut cover-plates tend to offset the saving in weight of lattice bars and stay plates. Professors Merriman and Jacoby present in their ''Roofs and Bridges," Part IV, an excellent treatment of the subject of cantilever bridges, dis- cussed mainly from the theoretical point of view. Their economic investi- gations, which are based upon chord weights only, show that for a three- span cantilever of Type A, each anchor arm should be about twenty-one and two-tenths (21.2) per cent of the total length of structure. This is quite a close agreement with the twenty (20) per cent minimum found by the more accurate and practical investigation that was made for "De Ponti- bus." The professors find, though, thirty-nine and four-tenths (39.4) per cent of the total length of structure for the economic length of the suspended span, corresponding to about sixty-eight per cent of that of the main open- ing, while the "De Pontibus" investigation made it only thirty-seven and a half (37.5) per cent thereof. Actual experience has repeatedly shown that the economic length of the suspended span is from three-eighths (|) to one- half (^) of the main opening, hence the professors' figures for this portion of their work have the appearance of being incorrect; but Prof. Merriman has explained to the author by letter that he assumed the truss depth to be the same throughout the entire structure. This assumption, combined with that of ignoring the effect of the weight of the web, will account for the large d.^screpancy; because the professors' mathematics have been checked and found to be faultless. As a matter of fact, though, no Ameri- can engineer would think for an instant of making the truss depth constant throughout the structure, because for economic reasons it should gen- erally be about twice as great over the main piers as in the suspended span. European engineers, however, often fail to make the truss depths, espe- cially in the cantilever and anchor arms, great enough for economy.. 262 ECONOMICS OF BRIDGEWORK Chapter XXVIII The professors make also from their economic investigations the fol- lowing deduction: "The cantilever system hence has no theoretic economy over simple trusses when the piers can be located in any position; moreover, when the influence of the alternating stresses in the anchor arm and the material required for anchor rods are taken into account, it is at a marked disadvantage." This is true for Type A, which is the layout employed by the professors; but it is not correct in general. The professors are right in their surmise that "probably the common three-span-cantilever bridge has a lower degree of economy than the arrangement where the simple trusses are in the end spans, as in the Ken- tucky River bridge"; for, as previously stated, Type-C layout requires only from eighty to sixty-five per cent as much metal as does that of Type A, for the same total length of structure. It must be remembered, how- ever, that, as previously indicated, the comparison is hardly fair to the common three-span-cantilever, because the latter provides a greater main opening than that of the alternative layout. CHAPTER XXIX ECONOMICS OF SUSPENSION BRIDGES In the designing of suspension bridges there is still much to be learned, because so few of them have been built ; and this is as it should be, because they are not an economic type of structure, excepting for exceedingly long spans, or in the case of a very -light highway bridge at the crossing of a gorge or a river of great depth and swift current where it would be too expensive to build piers in the stream. As shown in Chapter XIII, for steam-railway structures suspension bridges are more expensive than can- tilever bridges up to the practicable limiting length of the latter; and, moreover, in respect to the important element of rigidity the former are certainly inferior. But the suspension bridge has its legitimate place in engineering construction, and that is for long-span highway bridges pure and simple, and sometimes when they carry also electric railways. There are crossings, hke that of the North River at New York City, where the conditions are such as to make the use of the suspension bridge obligatory. It is, therefore, well worth while to study the economics of the type, even to the extent of making an exceedingly elaborate investigation, as the author did lately in his memoir on "Comparative Economics of Wire Cables and High-Alloy-Steel Eye-bar-Cables for Long-Span Suspension Bridges," presented in May, 1920, to the Engineers' Society of Western Pennsylvania, of which memoir more anon. In designing a highway suspension bridge, the first economic point to consider is that of the deck and floor-system, both of which should always be made as light as the ruling conditions wiU allow, because the heavier the floor the £;reater the load on the cables. This general question of economics in deck and floor-system has been treated in Chapter XXI, to which the reader is referred. While it is certainly advisable to cut down the dead load to a minimum, it would be anything but economic to adopt a plank base for the pavement, on account of the great danger from fire which that type of construction involves. Modern highway bridges call for a reinforced-concrete base for pavement, and there is no dodging this issue; but in suspension bridges it should be made as hght as practicable by using closely-spaced stringers and thus reducing the thickness of slab to a minimum. It is true that a buckled-plate floor is lighter than a rein- forced-concrete slab, but, until quite lately, as indicated in Chapter XXI, experience has shown it to be so lacking in rigidity that under the passage 263 264 ECONOMICS OF BETDGEWORK Chapter XXEX of modern wheel-loads it has permitted the pavement to crack and eventu- ally to break up. It is probable, though, that Mr. Byrne's correction of the defect will permit in future, with perfect safety, the emplojnnent of tliis type of flooring. When the electric railway tracks are entirely separated from the road- ways, it is economic to use the ordinary open floor of wooden ties with proper guard-rails, because the danger from fire with such a floor is not great; and even if some of the ties were to burn, no injury of any impor- tance would be done to the metalwork. Such fires do not spread rapidly and are readily extinguished ; but when a plank base with a wooden block pavement thereon catches fire on a windy day, disaster is almost sure to ensue. There are two legitimate ways of trimming down the weight of metal in the floor-system to a minimum, viz., employing nickel steel or some other alloy for the metalwork, and supporting the cross-girders at intervals by means of intermediate trusses and cables. In adopting the first expedient, care should be taken not to reduce the depths of the joists and stringers below the limit set by good practice — otherwise their deflections would be great enough to injure the pavement. In respect to the second expedient there are both pros and cons concerning the advisability of adopting many lines of trusses and cables. The advantages are as follows : First. The saving in weight of metal in the cross-girders. Second. The reduction in cable cross-section due to the lightening of the cross-girders. Third. The better distribution of load on the piers with its conse- quent saving of both shaft masonry and base. Fourth. The lowering of the grade line of the structure (due to the shallowing of the cross-girders), with its consequent reduction in cost of climb for everything that crosses on the structure. Fifth. The shortening and consequent cheapening of the approaches due to the smaller height to be surmounted. The disadvantages are as follows: First. The somewhat greater weight of metal due to the larger number of parts in trusses, cables, and steel towers. In long, heavy spans this really is not a disadvantage; because, on account of ease of erection, it often pays to employ comparatively light members Second. The somewhat greater total width of deck called for to allow space for the extra trusses and cables; but this is often not disadvan- tageous, because great width of structure is necessitated by great span- length. Third. In accordance with the theory of probabilities, the more numerous the trusses and cables the greater should be the total live load per lineal foot assumed for the design; for witli only two lines of cables, practically the entire width of deck must be loacUnl in order to produce the maximum stresses in either cable, while with sevei-al lines of cables, ECONOMICS OF SUSPENSION BRIDGES 265 the loading of a much smaller width of deck will produce maximum stresses in any one cable. The next economic consideration is the design of the stiffening trusses. It must be remembered that the weight of these is a direct function of the live load and entirely independent of the dead load, which passes immediately from the floor to the suspenders and cables without causing either moment or shear on the trusses. It is, consequently, expedient to keep the live load down to the lowest legitimate limit consistent with the probable loads from future traffic. Custom has decreed that the truss depth should be about one-fortieth of the span length, but a greater depth would reduce the weight of metal in the chords without increasing materially that in the web. It is claimed that a greater depth than this established limit would not be aesthetic, but this can be determined only by careful study for each case as it arises. The choice of panel length may be determined from the standpoint of aesthetics or by an economic adjustment between floor-system and trusses. This question also will require careful study. The system of cancellation adopted for the trusses will have quite a little to do with their weights of metal, but the consideration of appear- ance should govern in this matter. If a single-intersection truss be adopted, it will have the advantage of avoidance of ambiguity in stress dis- tribution, but it will not provide as pleasing an appearance as will the double system of cancellation. In the latter the vertical posts, as far as the ques- tion of statics is concerned, are superfluous; but without them the second- ary stresses would run high, the connection of the floor-beams to trusses would be awkward, and the proper attachment of the trusses to the cables would be difficult. It is better, therefore, to adhere to the use of the verti- cal posts when the double-intersection type of truss is selected. These posts, though, may be made of minimum section consistent with their appearance and with the function which some of them perform in distribu- ting the load to the cables. An economic point of importance is that of having the ends of stiffening trusses free or anchored. The latter condition is more economic of metal in chords, but there is little or no difference for the web ; however, it neces- sitates extra metal and expense for the anchoring, but the resultant effect invariably is a reduction in the total weight of metal, and hence the expe- dient should generally be adopted. The selection of the versed sine for the cables is a matter of economic importance. Increasing it reduces the sectional area of cables and back- stays, but augments sHghtly their lengths; and it adds to the height and weight of the tower columns and their bracing. On the other hand, it effects a slight saving in mass and cost of anchor- ages due to the reduction of overturning moment that is caused by the diminution of stress in the backstays. Experience has shown that a depth of catenary equal to one-ninth of the span will usually give the most satis- 266 ECONOMICS OF BRIDGEWORK Chapter XXIX factory results; but there is no hard-and-fast rule about this, and it is per- missible to use any depth between the limits of one-eighth and one-tenth of the span. In the past the author had never tested the economics of this feature, having been content to accept the dictum of experience as recorded in engineering text books and hand books; but in connection with the special investigations prepared for this treatise and the late economic studies upon which it is so largely based, a number of estimates have been made which have enabled him to obtain some rough figures upon the effect of increasing the depth of catenary. The result of these computations appears to indicate that the economic depth for cables was originally adjusted upon the basis of cariying the masonry piers all the way up to the cable carriages, as in the case of the first East River bridge known as the Brooklyn Bridge; because an assumed increase in the height for this type effected no economy. But in the case of a bridge with steel towers the result was quite different; for a saving of total cost was indicated when the depth was made one-seventh of the span- length. That is probably as great a depth as a proper consideration of appearance would permit. The question of the best type of approaches to adopt is one that has to be settled at the outset. It is an economic one in most cases, but occa- sionally the local conditions or the matter of aesthetics will necessitate a departure from the economic layout. Briefly, it may be stated that the type of approach which costs the least is an ordinary trestle or viaduct entirely independent of the main structure. This may be either straight or built in spiral form, as there is but little difference in the construction costs of the two, the latter generally having the advantage of saving in expense for right-of-way and property damages. Suspending the floor- system or stiffening trusses from the backstays is not economic, if it be practicable to build a trestle approach; and even if it is not, it may be better to substitute short spans for the trestle, supporting them at intervals on either piers or rocker bents, the depth of the said spans, if through ones, being made the same as that of the stiffening trusses in the case of a wire cable structure, or of any convenient or economic depth in the case of an eye-bar-cable bridge. The uneconomics of suspending the floor of the approaches from the backstays are as follows: First. The far greater weight of metal required for stiffening trusses and hangers as compared with that for the trestle approach, the item of pedestals for the latter being generally a bagatelle. Second. The far greater cost of the anchorages due to the large lever arm for the overturning moment, the cable pull being horizontal and applied near the elevation of the floor. The only case in which it is economic to suspend the floor of the ap- |)roachcs from the backstays is when there is deep water beneath that is required for navigation purposes. If there be fairly deep water that is ECONOMICS OF SUSPENSION BRIDGES 267 not needed for navigation, the best type of approach to adopt is a suc- cession of deck spans of, as nearly as may be, economic length. In the design for the anchorages there is a fine opportunity for bene- fiting from economic study. There are three general cases of governing conditions to consider, viz., foundations on bed rock, foundations on piles, and foundations on clay or similar material without piling. If the bed rock is fairly close to the surface, it will be advisable to found upon it; but otherwise it will be cheaper to put in shallow foundations, obtaining the necessary supporting power either by piling or by spreading the base. The maximum of economy will be obtained by making both the weight of ma- sonry in the rear of the anchorage and the foundation area in the front thereof proportionately as large as practicable. The first expedient tends to increase the resisting moment against overturning, and the second to reduce the intensity of bearing at the toe of the face; where, of course, it is greatest. It is economic, therefore, to make the anchorages long and narrow, low in the front and high in the rear. If there be several of these in the form of walls — one for each cable, or pair of cables, — instead of one solid mass of concrete, they can be advantageously connected in front below the ground so as to spread the base, and joined in the rear by a great wall above the ground, in order to increase the weight there. If piles be employed, they should be driven as closely together as practicable near the front of the anchorage, and, if it be found advisable, spread somewhat near the rear thereof — in other words their spacing should be adjusted to the intensity of the foundation loading. That intensity should be made as nearly uniform as possible over the entire base by the expedient just explained, thus avoiding the call for varied spacing. With a single exception, the preceding considerations cover all the important economic features in the designing of suspension bridges. That exception is the question of the comparative economics of wire cables and high-alloy-steel eye-bar-cables, concerning which hitherto absolutely noth- ing definite has been known. It is one of the series of ten major economic problems in bridgework that in 1916 the author undertook to solve. Its investigation was completed in March, 1920; and the results thereof, as herein previously stated, were presented two months later, in the form of a memoir to the Engineers' Society of Western Pennsylvania. In view of the fact that the said memoir is very complete, it is here reproduced verbatim as follows: Comparative Economics of Wire-Cables and High-Alloy-Steel Eye-bar-Cables for Long-Span Suspension Bridges The economic comparison of wire cables and eye-bar cables for sus- pension bridges has never before been brought to the attention of American engineers, for the reason that comparatively few structures of the sus- pension type have been built in this country. Their unsuitability for 268 ECONOMICS OF BRIDGEWORK Chapter XXIX railway bridges, excepting those of exceedingly long span — far longer than any that have been constructed — and the slow development of the Amer- ican highway system have combined to keep the type in the background; but the time is approaching when it will be necessary to carry our rapidly developing network of highways across some of the largest of our rivers, and then the suspension bridge may have an opportunity to come into its own. It must not be forgotten, however, that the conditions warranting the building of a suspension bridge are not likely to be often encountered; because it is nearly always the fiat of the War Department which neces- sitates a span-length so great as to render economical the building of a structure of that type. By means of a long and elaborate economic investigation made in 1918 and published in 1919 by the Western Society of Engineers under the caption "Comparative Economics of Cantilever and Suspension Bridges," the author has shown the span-lengths of equal cost for these two classes of structure. The said lengths usually vary from 1,000 feet for liighway bridges to about 2,600 feet for steam-railway bridges, the lengths for com- bined steam-railway and highway structures being intermediate and directly interpolated in accordance with the division of total hve load, including impact allowances, between railways and highways. Later it was found that the irregularity of the abnormal unit prices of materials at present governing has lengthened the spans of equal cost some two hundred feet for highway bridges and sixty feet for steam-railway bridges; but a return to normal market conditions will assuredly bring them back to about the Umits first found. Had the original investigation been based upon the assumption of anchored ends instead of free ends for the stiffening trusses, the span- lengths for equal cost would have been found about one hundred feet shorter, or 900 ft. for highway bridges and 2,500 ft. for railway bridges at ante-bellum unit prices, and 1,100 ft. for highway bridges and 2,560 ft. for railway bridges at the unit prices prevailing early in 1920. As that investigation proved that the suspension bridge is less econom- ical for steams-railway traffic than the cantilever structure up to the extreme practicable main-span-length of the latter, and as it is well known that the cantilever is always the superior of the two in respect to the important matter of rigidity, the present investigation has been limited to the consideration of highway bridges carrying also electric railway trains, such as those that cross the East River in New York City. The comparative advantages and disadvantages of the two types of cables are as follows: First. The wires for the cables have higher clastic limit and ultimate strength than can proljably ever be dc^velojiod in eye-bars. Second. The percentage of weight of details is far lower for wire cables than for eye-bar cables. Third. The cost of erection is inevitably less for wire cables than ECONOMICS OF SUSPENSION BRIDGES 269 for eye-bar cables, because with the former, the process, while tedious, is not at all complicated. Before the erection of the eye-bar chains is begun, it is necessary to string across from anchorage to anchorage and over the tower tops several lines of small wire cables. These have to be used in order to carry the first few lines of bars until the latter can be made seK- supporting; and although there will, of course, be some salvage on such erecting cables, their use will be quite expensive. Again, as the eye-bars will have to be placed on the pins by heating and shrinking, it is evident that the process is necessarily a slow one, requiring considerable apparatus; hence the erection cost will run high. The total cost of erection, therefore, is larger for the eye-bar cables not only because of the higher unit cost of manipulation but also on account of the greater weight of metal to be put in place. Fourth. The lowest point in the catenary of the wire cables can be located very close to the top surface of the deck, thus making the height and the cost of the tower columns a minimum. Owing to the necessity for keeping the bottom chords of the crescent trusses above the elevation of the floor, and because, for a fair comparison, the center lines of the pairs of eye-bar cables must coincide with those of the wire cables, it is necessary to raise the tops of the towers several feet, thus increasing not only the cost of the latter but also the length and cost of the backstays. Fifth. Wire-cable bridges do not call for special wind chords for the lateral system; but in eye-bar-cable bridges, owing to the omission of special stiffening trusses, it is necessary to provide such chords; and this item is likely to be quite expensive. Sixth. The pound price of the wire cables is comparatively high, being at present about twice as great as that for eye-bar cables of nickel steel. Seve7ith. The attachment of the wires at the anchorages is both tedious and expensive, whilst that of the eye-bars is simple and expeditious. Eighth. The wire cables require stiffening trusses; but the two tiers of eye-bar cables are in tension under all conditions of loading; and hence they can serve, without stiffening, as the compression chords of the cres- cent trusses which are formed by the addition to them of vertical posts and adjustable diagonals. Ninth. There is an uncertainty in respect to stress distribution in the stiffening trusses of the wire-cable bridge that does not exist in the eye-bar- cable structure, although, strictly speaking, the adjustable diagonals in the latter involve a small amount of ambiguity in the division of the shear. All stresses in the eye-bar-cable bridges can be determined with accuracy by the established principles of statics, v/hilst those in the stif- fening trusses of wire-cable bridges are found approximately by several dif- ferent theories based upon assumptions which are sometimes of more than doubtful accuracy; and, consequently, considerable uncertainty concerning the maximum stresses to be provided for is involved. To as great an extent as practicable, all of these governing conditions 270 ECONOMICS OF BRIDGEWORK Chapter XXIX have been duly considered in making the economic studies for the prep- aration of this memoir. When the layout of the investigation for the solution of the economic problem herein discussed was first considered, it was intended to make the said investigation comparatively short by confining it to spans of only one length and having but one live load. That span-length was 1,750 feet, — selected because it was used by the author in his preliminary study of the proposed crossing of the Delaware River between Philadelphia, Pa., and Camden, N. J., made for the Camden Bridge Commissioners. The proposed structure consisted of a single suspension span with backstays, the approaches to it being either steel or reinforced-concrete trestlework, entirely independent of the main span. The deck, in a later modification, was laid out for a double-track electric railway at the middle, a paved roadway supported by a reinforced-concrete base twenty-two feet wide in the clear on each side thereof, and two sidewalks, each ten feet wide, cantilevered beyond the trusses, of which there were four lines. In the first design each of these trusses consisted of two eye-bar cables forming two crescents, each with a web system between composed of vertical posts and adjustable tension diagonals, but later there was also figured a wire-cable structure with stiffening trusses. In each case the towers consisted of braced steel columns with segmental-roller pedestals resting on concrete shafts supported by pneumatic caissons sunk to bed rock at a depth of about one hundred feet below low water. The anchor- ages were to be of plain concrete either supported by piles driven to bed rock or else resting directly on a foundation of satisfactorily-hard material, should such be encountered when making the borings. Fig. 29a gives the layout for the wire-cable type, and Fig. 296 that for the eye-bar-cable structure. The first set of calculations prepared for this paper was based on the preceding data and consisted of five designs and estimates of cost of fin- ished bridge upon the following lines : First. Wire cables of very high elastic limit and ultimate strength. Second. Mayarl-steel eye-bar-cables having an elastic limit of 50,000 lbs. per square 'nch and an ultimate strength of 85,000 lbs. per square inch. Third. High-grade, nickel-steel eye-bar-cables having an elastic limit of 60,000 lbs. per square inch and an ultimate strength of 100,000 lbs. per square inch. Fourth. Heat-treated, alloy-steel eye-bar-cables having an elastic limit of at least 75,000 lbs. per square inch and an ultimate strength of 115,000 lbs. per square inch. Fifth. Heat-treated, alloy-steel cye-bar-cablcs having an elastic limit of at least 100,000 lbs. per square inch and an ultimate strength of 150,000 lbs. per square inch. The specifications used for the designing, as far as they would apply, were those given in Chapter LXXVIIl of "Bridge Engineering," and the ECONOMICS OF SUSPENSION BRIDGES 271 intensities of working stresses for the wire cables were 60,000 lbs. per square inch for wire, and either one-half of the elastic limit or one-third of the ultimate strength for eye-bars, the lower of the two values being adopted. The material for stiffening trusses, webs of crescent trusses, floor-systems, lateral systems, towers, and anchorages was assumed to be commercial 272 ECONOMICS OF BRIDGEWORK Chapter XXIX nickel steel, having an elastic Hmit of 55,000 lbs. per square inch and an ultimate strength of 90,000 lbs. per square inch. The hve loads employed were as follows: For the floor-system, Class 25 for the electric railway, Class B for the roadways, Class C for the sidewalks. For the trusses a logical combination of these loads was adopted; and a ten-car subway train was assumed on each track when figuring the stiffening trusses of the wire-cable structure and the crescent trusses of the eye-bar-cable structure. When finding the moments and shears for the former, in order to give the wire-cable bridge the best possible chance to compete, the ends of its stiffening trusses were assumed to be anchored down, although, of course, not fixed, and the theory of stress determina- tion adopted was the approximate method given in Johnson, Bryan, and Turneaure's "Modern Framed Structures," Part II, instead of the older method of Dr. Wm. H. Burr, which, for convenience and simphcity, was taken as standard by the author in writing Chapter XXVII of "Bridge Engineering." The results of the two theories do not differ greatly, espe- cially for ends of trusses anchored, but the latter theory requires a Kttle less metal. In order to ascertain the weights of metal in the crescent trusses, there was assumed for each panel point a load of unity; and its effect was com- puted for every web member and every chord member thereof, thus rendering it easy to find all the Hve load stresses and dead load stresses by means of the sUde-rule. These index stresses were checked by an inde- pendent computer. After the first set of computations was completed, the question arose as to whether the assumption of a double-deck structure carrying a much greater proportion of electric-railway live load would have caused any material changes in the results; and it was decided to repeat the calcu- lations for a set of five double-deck structures. The result indicated no serious disagreement, as is shown in Table 29a. An analysis of this table shows how very little variation there is between single-deck and double-deck bridges in respect to the proportions of the various materials in wire-cable structures and the corresponding eye-bar- cable structures. For this reason in what follows the author, with a clear conscience, has drawn his general conclusions from computations on single- deck structures only, thus saving considerable time and expense. His so doing is a good illustration of the appHcation of the "economics of bridgework" which he is endeavoring to expound. The investigations made up to this point permitted the estabhshment of a number of formulse for quantities of materials involving variations in span length and loading, thus permitting of an extension of the study ECONOMICS OF SUSPENSION BRIDGES 273 without a seriously great augmentation of labor and expense. These formulae are strictly logical in form. They were derived on a theoretical basis, the coefficients thus determined being changed a few per cent, where necessary, to agree with the computed weights for the various structures which had been worked out completely. It was, therefore, decided to compute and record quantities for shorter and longer spans in order to prepare curves giving, for all practicable span-lengths,, the quan- tities of all materials per lineal foot of main span. TABLE 29a Ratio of Quantities of Materials in Eye-bar-cable Bridges to those in Wire-cable Bridges. Ratios Elastic Limits of Eye-bars Cables Nickel Steel Anchorages and Pier Shafts Pier Bases Single Deck Double Deck Single Deck Double Deck Single Deck Double Deck Single Deck Double Deck 50,000 60,000 75,000 100,000 3.76 2.. 82 2.05 1.42 3.75 2.82 2.05 1.41 0.73 0.68 0.65 0.63 0.69 0.66 0.62 0.60 1.09 1.03 0.99 0.94 1.08 1.02 0.98 0.93 1.16 1.06 1.00 1.00 1.15 1.08 0.96 0.88 The formulae referred to are the following: Wire Cable Bridges. Stiffening Trusses. Weight of One Chord: Effect of Live Load Reversal Neglected, Wc=O.Q9^(o.8^4:~), but not<0.09^^ sd\ Lt J sd Fifty Per Cent of Reversal Stress Added to Main Stress, TFc=0.12^fo.9+1.5^Vbutnot<0.12^. sd \ Lt J sd Seventy Five Per Cent of Reversal Stress Added to Main Stress, Tfc = 0. 132^(0. 92+1.1^), but not<0. 132=^. sd\ Lt J sd ■ Weight of Web Members : Pratt System. Effect of Live Load Reversal Neglected, TF^ = 0.83 — - — z =2.5 — for p = d. s \ dp / s 274 ECONOMICS OF BRIDGEWORK Chapter XXIX Fifty Per Cent of Reversal Stress Added to Main Stress. ,^„=1.25^(?^)=3.75^forp = d s \ dp / s Seventy-five Per Cent of Reversal Stress Added to Main Stress. Tr„ = 1.46^(?^) =4.38^' for , = d. Warren System, Single or Double-Cancellation, with Verticals. Effect of Live Load Reversal Neglected, Tf „ = 0.83 ^'(?^ii^) =2. 1 ^ for p=d. Fifty Per Cent of Reversal Stress Added to Main Stress. Tr„=1.25^(P^±l^) =3.12^' for p=d. Seventy-five Per Cent of Reversal Stress Added to Main Stress. H.„=1.46W?!^±^) =3.65^ for p = d. Notation. i = Main span length in feet; d = Depth of stiffening truss in feet; p = Panel length of stiffening truss in feet; i = Transverse distance between chords carrying wind stresses; L = Live load in pounds per lineal foot of truss; i/; = Transverse wind load in pounds per lineal foot of bridge; s = Working stress in tension, in pounds per square inch; Trc = Weight of one chord in pounds per hneal foot; Wto = Weight of web members in pounds per lineal foot of truss. Main Cables. Weights : rs—QAoL-^ sec B j V „ 0.45^2 sec 5 Y _ ._„, _, rs— 0.45i^ sec 5-j- For r/l = i sec B = 1 .094, r/l = 1 . 032; ECONOMICS OF SUSPENSION BRIDGES 275 Notation. I = Main span length in feet. V = Length of cable of central span in feet, r = Rise of cable in feet. B = Angle of inclination of cable at tower. Ds = Superimposed dead load in pounds per Kneal foot of bridge (exclusive of weight of cable). L = Live load in pounds per lineal foot of bridge, s = Working tensile stress in cable in pounds per square inch. TF = Weight of cable in pounds per foot of cable. V . TF -T= Weight of cable in pounds per lineal foot of bridge. r 1 Eye-bar Cable Bridges, for t^k- Weight of Eye-bars in Main Span. TF.= '■'' s-5.21 A+L(0.44 ^^ lOOd )]• Weight of Web Members of Cable. T7^=1.7— fo. 8+0.2 ^V but not <1.7— . Notation. I = Length of main span in feet, r = Rise of cable in feet. d = Maximum depth of crescent truss in feet. p = Panel length of crescent truss in feet. Ds = Superimposed dead load in pounds per lineal foot of bridge (exclusive of weight of eye-bars, but including weight of web members of cable). L = Live load in pounds per lineal foot of bridge. s = Working stress in tension in pounds per square inch. We = Weight of eye-bars in pounds per lineal foot of bridge. TFjo= Weight of web members of crescent truss, in pounds per lineal foot of bridge. The span-length selected for the low limit of the computations was 1,200 feet, and that for the high limit thereof was 2,300 feet, thus giving for all diagrams three points through which to pass each curve. Ordinarily, it is not safe to plot a curve through three points only; but in this case there were at hand several similar curves for suspension bridges estab- lished previously by the author for another economic investigation, hence no mistake was made in the plotting. The results of the computations are shown in Figs. 29c, 29d, and 29e. In Fig. 29c are recorded on four separate diagrams the quantities of the various materials for wire-cable bridges of span-lengths varying from 276 ECONOMICS OF BEIDGEWORK Chapte.r XXIX 1,000 feet to 3,000 feet. The curves are for single-deck structures; but the quantities found for the double-deck structures of 1,750 feet span are shown by short dotted lines. In Fig. 29d are indicated in a similar manner the weights of metal per lineal foot of main span for alloy-steel eye-bars in bridges of that type; and in Fig. 29e are recorded correspondingly the /ZC /?00 AW /SOO /8a) 20(y} 2200 2400 dSCO ^(O 306O StXO /tXOJ ajoo 6000 ?0(XO &X0 -/eooa i^OOOi /aoo /600 jax> 2CW 2ax> zaoo ia/y^ of Cenf-ra/ Span rn fief- Z600 2303 JOOO Pig. 29c. Quantities for Wire-Cable Suspension-Bridges. quantities of nickel steel, concrete in shafts and anchorages, and mass of materials in pier bases for such structures. In order to illustrate the manner of using these diagrams and at the same time to draw therefrom conclusions conceniing the ]-)resent status of the economics of the two types of cable under discussion, it will be wcU to ECONOMICS OF SUSPENSION BRIDGES 277 solve several examples based on current unit prices of the materials in place. These may be taken as follows: Wire Cables 23^ per lb Mayan steel 10^ " Commercial nickel steel 11^ " High-grade nickel steel 12^ ' ' Concrete in pier shafts and anchorages . . $16.00 per cu. yd. Mass of pneumatic bases $35.00 " " ^'^ /-^^ . -^^ /«!? /av jaxi 2ZX) sw 3500 zsoo Jtm /ceo /2X) AW /SCO J&OO 3XX> 2200 2W 2500 2900 ' 30tX) Ljsnffff} a^ Cenfraf 3pan rn Feef Fig. 29d. Weights of Alloy-Steel Eye-bars in Eye-bar-Cable Suspension-Bridges. In pitting the eye-bar-cables of the various alloy-steels against wire cables it will suffice to figure for three spans, viz., those of 1,000, 2,000, and 278 ECONOMICS OF BRIDGEWORK Chapter IQOX 3,000 feet. Attention is called to the fact that the costs found per foot of main span are not total for the structures; because the items of costs of deck and floor-system, being the same for both types, have been omitted for the sake of simphcity. The lateral system, though, has been taken sm SSCOJ =^mo JQW 3X0 1000 JZOO /6C0 /800 ZOOO Z20Q ZW Length of Csnfra/ ^san /n Feet- 2S00 2dX) 3000 Fig. 29e. Quantities of Various Materials in Eye-bar-Cable Suspension- Bridges, into account, because the weights of metal thereof in the two types of structure differ materially. The principal reason for this is that, in the eye-bar type, special wind chords will be obhgatory; whilst, in the wire- cable type, the chords of the Htiffciiing trusses serve as wind chords, only a small increase in sections above those needed for live loads being required. ECONOMICS OF SUSPENSION BRIDGES 279 MAYARf Steel Comparison. 1,000-Foot Span. From Fig. 29c we can make for the wire-cable structm-e the follow- ing estimate: Wire cables ........ 4,300 lbs. @ 23^ = $989 . 00 Nickel steel. ...... . 12,200 " @ lU = 1,342.00 Plain concrete 94 cu. yd. @ $16.00= 1,504.00 Mass of bases 28 " @ $35.00= 980.00 Total . = $4,815.00 From Figs. 29d! and 29e we have for the Mayari steel the following estimate. Mayari steel. ...... 14,400 lbs. @ 10^ = $1,440.00 Nickel steel 8,600 '' @ lU = 946.00 Plain concrete 98 cu. yds. @ $16 . 00 = 1,568 . 00 Mass of bases 28 " @ $35.00= 980.00 Total .....,......= $4,934.00 2,000-Foot Span. wire-cable structure Wire cables. . 8,500 lbs. @ 23^ = $1,955.00 Nickel steel 18,000 '' @ lU = 1,980.00 Plain concrete 89 cu. yds. @ $16 . 00 = 1,424 . 00 Mass of bases 17 " @ $35.00= 595.00 Total = $5,954.00 EYE-BAR-CABLE STRUCTURE Mayan' steel 33,600 lbs. @ 10(2^ = $3,360 . 00 Nickel steel 13,800 " @ 11^ = 1,518.00 Plain concrete 100 cu. yds. @ $16 . 00 = 1,600 . 00 Mass of bases 22 '' @ $35.00= 770.00 Total =$7,248.00 From these four estimates it is evident that at present prices untreated Mayari-steel eye-bar-cables cannot compete with wire cables in suspension bridges. With the shortest economic span-length for highway suspension bridges, viz., 1,000 feet, in order to compete with wire, the untreated Mayari steel would have to be put in place at a pound price of less than 9.2 cents. While this could probably be done without actual loss, it can readily be seen that, in general, untreated Mayari-steel eye-bars cannot be employed economically for suspension-bridge cables. 280 ECONOMICS OF BKIDGEWORK Chapter XXIX As heat-treated, carbon-steel eye-bars have an elastic limit of 50,000 lbs. per square inch, the same as that for untreated Mayari-steel eye-bars, and as the unit price erected is also about the same, the conclusions reached concerning the latter will apply also to the former. As for heat-treated, Mayari-steel eye-bars, the author has no data regarding their strength, nor is he conviflced that the irregularity in the elastic limit of that alloy would not militate too strongly against using it in bridgework after heat treatment. Judging, though, from the com- putations which follow concerning heat-treated nickel-steel eye-bars, one would surmise that suspension bridges of heat-treated, Mayari-steel eye- bars might be economical up to spans of 2,000 feet, High-Grade Nickel-Steel Comparison. 1,000-Foot Span. EYE-BAR-CABLE STRUCTURE Eye-bar cables 11,400 lbs. @ 12^ = Sl,368.00 Nickel steel 8,300" @ 11^ = 913.00 Plain concrete. ..... 94 cu. yds. @ $16 . 00 = 1,504 . 00 Mass of bases 27 " @ $35.00= 945.00 Total = $4,730.00 2,000-Foot Span. Eye-bar cables 24,600 lbs. @ 12^ = $2,952.00 Nickel steel 12,800" @ lU = 1,408.00 Plain concrete 94 cu. yds. @ $16.00= 1,504.00 Mass of bases 20 " @ $35.00= 700.00 Total .,.,.,.. = $6,564.00 A comparison of these figures with those previously made for wire- cable structures shows that the high-grade, untreated, nickel-steel is economic .for 1,000-ft. spans but not for those of 2,000 feet, hence let us test for an intermediate length. 1,500-Foot Span. WIRE-CABLE STRUCTURE Wire cables 6,400 lbs. @ 23^^ = $1,472 . 00 Nickel steel 15,000 " @ 11^ = 1,650.00 Plain concrete 88 cu. yds. @ $16.00= 1,408.00 Mass of bases 20 '' @ $35.00= 700.00 Total = $5,230.00 ECONOMICS OF SUSPENSION BRIDGES 281 EYE-BAR-CABLE STRUCTURE Eye-bar cables 17,300 lbs. @ 12^ = $2,076.00 Nickel steel 10,100 " @ lU = 1,111.00 Plain concrete 90 cu. yds. (a) $16 . 00 = 1,440 . 00 Mass of bases 20 " @ $35.00= 700.00 Total = $5,327 .00 From these figures it is seen that untreated, high-grade, nickel-steel eye-bars can compete today with wire cables for span-lengths below about 1,400 feet. If they were heat-treated, their intensities of working stress could probably be made as high as 40,000 lbs. per square inch, correspond- ing to an elastic limit of 80,000 lbs. or an ultimate strength of 120,000 lbs. The value of these eye-bars in place would be 13 cents per lb. Heat-Treated Nickel-Steel Comparison 2000-Foot Span. eye-bar-cable structure Eye-bar cables ...... 16,100 lbs. @ 13^ = $2,093 .00 Nickel steel. 11,900 " @ 11^ = 1,309.00 Plain concrete. . . 87 cu. yds. @ $16.00= 1,392.00 Mass of bases....... 18 " @ $35.00= 630.00 Total. =$5,424.00 This is considerably less than the cost previously found for a wire-cable structure, consequently let us test for a 2,500-ft. span. 2500-Foot Span. WIRE-CABLE STRUCTURE Wire cables ......... 10,800 lbs. @ 23^ = $2,484 . 00 Nickel steel 21,400 " @ 11^ =2,354.00 Plain concrete. 97 cu. yds. @ $16.00= 1,552.00 Mass of bases 19 '' @ $35.00= 665.00 Total =$7,055.00 EYE-BAR-CABLE STRUCTURE Eye-bar cables 21,000 lbs. @ 13^ =$2,730.00 Nickel steel 14,800 " @ 11^ = 1,628.00 Plain concrete 98 cu. yds. @ $16 . 00 = 1,568 . 00 Massofbases ...20 '* @ $35.00= 700.00 Total =$6,626.00 ' 282 ECONOMICS or BRIDGEWORK Chapter XXIX From these assumed figures it appears that heat-treated, high-grade, nickel-steel eye-bars could probably be used economically for suspension- bridge spans up to at least 3,000 feet. It is within the realm of possibility that in a few years there will be manufactured heat-treated, chrome-molybdenum-steel eye-bars having an ultima,te strength of 150,000 lbs. per square inch, for which the intensity of working stress may be taken at 50,000 lbs. per square inch, corresponding to a minimum elastic limit of 100,000 lbs.; and that the metal in place will be worth not to exceed 15 cents per lb. Let us test this for a 3,000-ft. span, Heat-Treated Chrome-Molybdenum-Steel Comparison dOOO-Foot Span. WIRE-CABLE STRUCTURE Wire cables 13,400 lbs. @ 23^^ = $3,082 . GO Nickel steel 25,000 " @ llj!^ =2,750.00 Plain concrete 112 cu. yds. @ $16.00= 1,792.00 Mass of bases 25 " @ $35.00= 875.00 Total =$8,499.00 EYE-BAR-CABLE STRUCTURE Ey^^bar cables 19,000 lbs. @ 15cf = $2,850 . 00 Nickel steel 17,200 " @ nj r>^ f leva fed P/afK>rm /or Pedes/nan. ■ Pocke/B ;^ 73'-0' m'O" 73'-0 Fig. 32c, Third Preliminary Study for Proposed New Orleans Transbordeur. /O3'0'' //O'-O" 75'-0" /OO'O' . Z^'o' 45f.Py S/<7/nvay far /^^ Wder /n Fesf Ratios of Costs of Fixed-Span Bridges and their Approaches for Various Clearances Above High Water. transbordeur and fixed-span bridge, and of the facts that a climb of 65 feet above the water is by no means prohibitory for any class of vehicle, even the horse-drawn, — that the carrying capacity of the bridge is generally greater than that of the transbordeur for both pedestrians and street-cars and always much greater for automobiles, — and that horse-drawn vehicles are fast becoming obsolete, — the deduction may be made that, for crossings with moderately-high vertical-clearance, the fixed-span bridge is decidedly preferable to the transbordeur. It is true that this general inference has been drawn from a single case, and on that account may not be satis- factory to some engineers; but the author is of the opinion that, were similar reasoning applied to any other practical case, a like conclusion would be reached. 332 ' ECONOMICS OF BEIDGEWORK; Chapter XXXII Before closing this chapter the author has decided that it will be well to take two pending cases from his own practice and indicate how they should be solved. One is that of the crossing of Havana Harbor, Cuba, so as to develop a tract of beautifully-situated and almost-entirely unoccupied land about five miles long and one mile wide parallehng the coast line. Some seven years ago the author spent considerable time and money on the development of the project to build a high-level, cantilever, highway-and- street-railway bridge over the entrance channel near the inner end of Cabana Castle at a location quite close to the place where the said channel expands into the body of the gourd-shaped bay forming the anchorage- ground of the harbor. Just as the project was about to materialize, the war in Europe began;' and ever since then it has been impracticable to raise money for any large enterprise not directly connected with war work. However, the time is probably close at hand when it will be advisable to try to revive the scheme, because sooner or later a bridge of some kind will certainly be built across the channel so as to permit the city to expand in the one possible direction that will permit of the building of fine residences within quick reach of the business center. The old layout, shown in Fig. 32/, necessitated the carrying of all traffic from an elevation of five feet above water level on the city side by means of a spiral approach and passenger elevators to an elevation of two hundred and four feet above the same, and then down to an elevation of about one hundred and fifty feet at the entrance to the North approach. About a year ago, it struck the author that it might be better to build a double-track transbordeur quite close to the mouth of the harbor and to carry the traffic across at an elevation of about eighty feet above the water. Near La Punta, the outermost land on the City side of the channel, there is a large area of open ground which rises gradually to an elevation of twenty- five or thirty feet some four or five blocks back from the water; and at the other side of the harbor, between Morro and Cabana Castles, the elevation of the land is much lower than it is farther in. By starting with a trestle approach near the South end of the said open ground and rising on a four per cent grade, more or less, to within about five hundred feet of mid-chan- nel, it would be practicable to attain the elevation just mentioned for the cage deck; and on the other side a short trestle with an easy up-grade would lead to the general surface of the ground back of the two castles. The length of span over the channel would not be more than 800 feet; and, possibly, it might be a hundred feet shorter, thus making the travel of the cages only 800 or 900 feet. On that account it would not be economical to adopt the transverse travelers, because the time required for crossing is so short. It would pay better to widen the structure and put in another track or two, should the prospective traffic warrant it, especially as, on account of the great height of the overhead span, a large width of structure is necessary for resisting properly the overturning effect of the wind pres- sure, which during tropical storms is likely to be excessive. In order to POSSIBILITIES AND ECONOMICS OF THE TRANSBORDEUE 333 334 ECONOMICS OF BRIDGEWORK Chapter XXXII secure a large capacity, it would be advisable to make the cages three- decked, and possibly longer than fifty feet. Again, ui order to save tune in unloading and reloading, the street-cars leaving the city side could take the lower deck and the automobiles and other vehicles leaving the same could occupy the middle deck, the pedestrians, of course, always using the upper deck. Starting from the other side, the automobiles could occupy the lower deck, and the street-cars the middle deck. By this arrangement the climb- ing of the comparatively steep grade at the North end from the lower-deck level would be done by street-cars only, and time would be saved by holding the automobiles and horse-drawn vehicles in a corral until after the street- car has left clear both the cage and the portion of the approach close thereto. Similarly, the street-car would be held in a corral until after aU the other vehicles have gotten out of the way. Barring interference from navigation, each cage could make a round trip in about 3| minutes, which would give 17 round trips per hour, or 34 trips per hour in each direction by the two cages. A 60 ft. -cage would carry two street-cars, eight auto-vehicles, and 300 pedestrians, making 68 cars, 272 auto-vehicles, and 10,200 pedestrians per hour in each direction. Allowing for interruptions from navigation, which would not be serious, because of the great clearance beneath the cages that would permit a large proportion of passing craft to go by with- out stopping operation, it would be legitimate to count upon a maximum limit of 60 street-cars, 240 automobiles, and 9,000 pedestrians per hour in each direction. Deducting liberally for service to outlying towns, the remaining capacity would be great enough to provide for a population of at least 75,000 persons, or 15,000 per square mile, which is fairly dense for a residence district. Fig. 32gr shows in skeleton outline the elevation of this transbordeur span with a short portion of each of the adjacent approaches, also a cross- section of the structure at mid-span. From this drawing it will be seen that, in reality, there are two distinct, parallel, cantilever bridges located a short distance apart and connected to each other by cross-girders and bracing, leaving ample space between for the safe passage of the two cages; that the latter pass shoreward beyond each main pier a distance equal to one panel-length of the anchor arm, connecting to an approach deck that is suspended from the other two panel points of the said anchor arm; that all the panels of the entire structure are of equal length, there being three of the n in each anchor arm, five in each cantilever arm, and six in the sus- pended span; and that the outlines of all chords are parabolic curves. Each main pier consists of four pneun^atic cylinders sunk to bed rock, each cylinder being surmounted by a truncated concrete cone, and the three spaces between the four cones being filled with thin, reinforced-concrete walls. Each anchor-pier shaft consists of a mass of concrete supported upon a coiicreto liase that rests on piles. Tho niithor believes that the bold, (Mirved oiitlinos of the tniss(^s, in spite of tlio liorizontal line of girders between the twin spans, would make an a^stlietic structure that would be fieVdT/ON _ Sca/e /'=SO'o' Fig. 32j?. General Layout fur a Prupust-d Traiisljordcur to Cruss Havana Harbor, Cuba. 3ECTioNffT Af/D-cmmn To face page 3S4- POSSIBILITIES AND ECONOMICS OF THE TRANSBORDEUR 335 in keeping with the cominantling position which it would occupy at the entrance to one of the most beautiful harbors in the world. The other case, as indicated at the beginning of this chapter, is that of a proposed suspension bridge, having a single span of 1,750 feet which clears the entire width of river between the established harbor lines, to join the cities of Philadelphia and Camden. Quite lately the author was struck with the idea that a transbordeur might serve all the traffic at the crossing and save considerable money as compared with a bridge, consequently he had his office prepare a layout, using a three-deck cage to carry street-cars, automobiles, and pedestrians; but a short preliminary economic study showed that the expense involved would be too great, consequently he prepared a two-deck layout that does not carry street-cars. These would run around a loop on each approach and would discharge and take on passengers close to the loading places of the cages. An estimate of cost was made for this layout based on the then- ruling prices of materials and labor, the grand total, excluding right-of-way, property damages, and interest during construction, amounting to $12,- 000,000. Then a layout was made for a bridge and its approaches, and a similar estimate of cost was prepared, amounting to $13,400,000. As these two amounts differ so little, it was at once concluded that for this crossing there would be no real economy in adopting a transbordeur. The ratio of the said amounts is about 0.9, while the corresponding ratio for the New Orleans study was only 0.58. From these figures it may be concluded that a long-span-suspension layout does not accommodate itself to the carrying of transbordeur cages as economically as does a layout of several shorter continuous spans. The explanation of this fact is that the piers for the two cases are about alike, that the approaches of the transbordeur are nearly but not quite as expensive as those of the bridge, and that while there is a large saving in the combined costs of superstructure and anchorages, it is largely offset by the cost of the cages, travelers, and pockets. In the New Orleans investigation the substructure of the transbordeyr would cost but little more than one-half of that for the corresponding bridge, and the cost of the approaches to the former is a bagatelle when compared with that of those to the latter; but the total steelwork for the river spans, towers, bents, cages, travelers, and pockets of the transbordeur exceeds in value that of the river spans of the bridge. Conclusion and Recapitulation The title of this chapter indicates that it is intended to show both the possibilities and the economics of what in slang parlance might be termed the ''glorified" transbordeur, i.e., the existing type of transporter bridge expanded and enlarged many fold so as to accommodate it to wide rivers, high carrying capacity, and rapid transit. Some of its possibilities have 336 ECONOMICS OF BRIDGEV/ORK Chapter XXXII been shown, but probably not all of them; and as for the economics, it has been proved to cost less, even in extreme cases, than a very-high-level structure, and about the same as a low-level structure; but that, strictly speaking, it cannot be said to be in economic competition with either type; because when the conditions really call for the consideration of a transbordeur, a very-high-level bridge would generally necessitate too great a climb for the traffic, and a low-level bridge would be barred because of its interfering too much with the paramount interest of navigation. .The Philadelphia-Camden case is apparently an exception to this rule, but it must be remembered that its vertical clearance is only 135 feet, while that for the proposed crossing at New Orleans is 175 feet, and that the extra forty feet of height make a great difference in the costs of the approaches. CHAPTER XXXIII ECONOMICS IN CONTRACT-LETTING At first thought one might be incHned to claim that contract-letting is not a matter of economics, but a little reflection will soon convince him that it certainly is, because if contracts be badly drawn, or if the modus operandi of compensating the contractor and his workmen be faulty, the work of construction will assuredly cost more than it would under ideally perfect conditions. During the last few months the author has been writing a series of papers on contract-letting and profit-sharing, culminating in a lengthy discussion of a paper by Mr. Ernest Wilder Clarke, published in the August, 1919, Proceedings of the American Society of Civil Engineers, the said discussion appearing in the October-November-December Pro- ceedings. As this discussion is in reality a complete treatment of the subject, and was intended as such (although for good and sufficient reasons presented as an adjunct to another paper instead of being offered as a separate memoir), it is here reproduced practically verbatim. The importance of the subject of this paper, to owners, contractors, and the entire American nation, cannot well be exaggerated; for, until there is reached a satisfactory compromise between owners on the one hand and contractors on the other concerning the vital questions of contract-letting and profit-sharing, the business of the country will fail to recuperate to the extent that it should at this critical period in the readjustment of all constructional activities — which activities were so fundamentally upset throughout the whole world more than five years ago by the advent of the World War. The opportunity now within easy reach of the American people to secure the bulk of the world's trade is unique; but, apparently, our leaders in diplomacy, manufacture, shipping, business, and finance are either unaware ot its existence or indifferent about taking advantage of their good fortune. The Latin-American nations are now knocking at our door asking to do business with us and begging us to lend them money for the development of their as-yet-almost-virgin lands, mines, and water powers, and their other more or less embryonic resources; and the leading peoples of Asia, Africa, Australasia, and even Europe are to-day much more willing to enter into business relations with this country than they have ever been before. They all recognize that, for the present at least, the European countries are in no condition to lend money, being 337 338 ECONOMICS OF BRIDGEWORK Chaptek XXXIII themselves borrowers and having so many demands at home for their time, attention, and capital that they are unable to give consideration to the needs of any nation but their own; and the entire civihzed world is well aware of the fact that, in spite of our vast war debt, we are today the most wealthy of all peoples. These conditions — unfortunately, as far as we are concerned — will not last indefinitely; and if we are so short-sighted as to neglect to seize the golden opportunity which is not only easily within our reach, but which is actually being tendered to us and almost forced on our acceptance, it will not be long before both England and Germany will re-secure the grip on the world's trade which they possessed in ante-bellum days. Prevention of Progress. One of the greatest stumbhng blocks in the pathway of our nation's advancement is the conflict between labor and capital; and until it is removed the wheels of progress will be clogged, and the present paralyzation of all great peace industries will continue to exist — possibly in even worse form than it does today. Again, the main issues between labor and capital are these questions of contract-letting and profit- sharing. If they were once settled to the satisfaction of all concerned — bankers, manufacturers, contractors, and workmen — all other minor dif- ferences would quickly be adjusted. Such a settlement is perfectly feasible; and the possibility of its speedy accomphshment is neither a Utopian conception nor an idle dream. Primarily, the men who do the work must have a substantial share in all net profits of manufacture and construction; but the way for them to obtain it is not by the organization of strikes nor by seizing the plant and running the business of the manufacturer or the contractor. The uneducated workman is no more fit to manage business and to handle industry than the sedentary office man is to undertake the physical labor of the workman — in fact, much less so; because it would generally be totally impracticable to educate the illiterate workman up to a state of efficiency which would enable him to undertake business management and finance, while, in most cases, in a comparatively short time, the office man's muscles could be developed sufficiently to enable him to endure the physical stress of the workman's job. Nothing of value can be accom- plished by mob rule, as the pending subsidence of the present wave of Bolshevism will soon prove. Labor and Capital. Although it is certainly true that the laborer cannot succeed independently of the business man, it is equally true that the lattci' cannot accomplish much without the aid of the capitalist, hence it behooves business men and financiers to f^ome quickly to a friendly under- standing and agreement. In times past, the capitalist secured and exer- cised a strangle hold on the promoter, the manufacturer, and the con- tractor, often forcing them to turn over the lion's share of their profits as compensation for the use of. money in the development of their under- takings; and these men in their turn endeavored to even up matters by ECONOMICS IN CONTRACT LETTING 339 getting their pound of flesh out of the workman by compeHing him to labor long hours for meager compensation. Today, the laboring man is beginning to come into his own; but if he unwisely takes too great advan- tage of his growing power, he will "kill the goose that lays the golden eggs," and this will ruin his chance of securing comfort and happiness for himself and his family. The first step requisite for quieting the existing widely spread popular unrest and returning to normally prosperous conditions is to bring together, so that they may operate in harmony, the financier, the employer, and the laborer; and this must be accomphshed primarily by establishing some method of contract-letting and profit-sharing which will be just and equitable to all parties interested. For some time, the author has been endeavoring to formulate and develop, through communications to the technical press, an ideal method of accomplishing this desideratum; and later herein he will indicate clearly of what it consists. First, however, he will discuss in detail not only the suggestions offered by Mr. Clarke in his timely paper, but also those of various engineers and political economists who have of late been treating the matter in print. Various Methods of Contract-Letting. The common ways of contract- letting are the following: A. Lump smn for complete construction. B. Schedule rates for all materials in place. C. Actual cost plus a percentage, with some kind of allowance for overhead expenses. D. Actual cost of labor and materials plus a percentage, with no allowance for overhead expenses. E. Actual cost plus a lump sum, with some kind of allowance for over- head expenses. F. Actual cost of labor and materials plus a lump sum, with no allow- ance for overhead expenses. G. Actual cost plus a profit based on small unit prices agreed upon in the contract, as advocated of late by Mr. G. H. Hailey. H. Various methods of profit sharing between the client and the contractor. Method A generally appeals best of all to the client, because it fixes in advance what the construction is going to cost him, unless, perchance, there are important variations in the estimated total quantities of materials, due to lack of sufficient preliminary information or to the encountering of conditions that could not well have been foreseen. It is by no means as satisfactory to the contractor, however, who has to run the risk of being actually out of pocket on the job, in addition to the loss of personal time and effort. Method B is quite an improvement on Method A, in that the contractor does not have to guarantee the correctness of the estimated quantities of materials; but the prime objection to Method A holds good for Method B, 340 ECONOMICS OF BRIDGEWORK Chapter XXXIII as the latter does not prevent the contractor from losing monej- heavily on the venture. In the days of hard times, when contractors are wilhng to take work at low figures, and even below cost, in order to keep their force together, the public, in general, especially as represented by companies and munici- palities, is prone to take advantage of them by insisting that work be let by the lump sum, and by throv\^ing on the unfortunate "successful biddpr" not only the risk of loss from rising prices of materials and labor and from unforeseen contingencies, but, also, in many cases, from excess of quan- tities above those given in the specifications. This is accomplished by inserting in the latter a most unjust clause compelling each bidi.!er to verify for himself both the quantities stated and the character of the conditions described. The bidders, hungry for work, accept this clause without comment, but with the mental reservation that, in case of hard luck, they will, by some means or other, obtain extra compensation, even if they have to carry the controversy into the Courts. In nineteen cases out of twenty, it is unjust to bidders to ask them to name a lump-sum compensation for doing work, unless provision is made for a variation in the quantities of materials on which they tender. If provision is arranged for such variation, the method of letting is no longer that of the "lump sum," but reduces to a modification of that of "unit prices." As before indicated, the latter method is certainly the more logical, and yet it is far from being entirely fair to the contractor; because, although it provides against loss through excess above the estimated quantities of materials, it leaves him open to the possibility of still greater loss through changing prices, onerous unanticipated conditions, and disastrous hap- penings beyond his control. Up to a certain point, the client is the proper party to assume the principal risks inherent to the work, provided that the adverse happenings are really unavoidable by the contractor, and that the latter takes every reasonable precaution against disaster or loss. And yet the contractor should not be altogether relieved from the possibility of loss due to hard luck, because such misfortune is often caused by his dilatoriness, which carries the work into an unfavora])le season for field operations. The idea, promulgated of late by certain writers, that it is unjust ever to penalize a contractor, is wrong; because he, like eveiybody else in this world, should bear the burden resulting from his own careless- ness, negligence, or incompetence. The owner surely has some rights — and this is one of them. A liberal limit of total cost which can be increased or reduced properly, in order to provide for an increase or decrease in the estimated total quantities of materials, will prevent the owner from being excessively overcharged, and still will give the contractor every oppor- tunity to come out whole in any case except that of extraordinary hard luck. M(ithod C is wholly objectionable to the client, in that it places him entirely at the mercy of the contractor and his men. The allowanc ECONOMICS IN CONTRACT LETTING 341 for overhead may be either an assumed percentage, or the actually com- puted amount in complete detail, the former being generally the less objec- tionable. Even if the contractor is perfectly honest and has the best will in the world to keep down the cost for the benefit of the client, his employees will not have that desire. In effect, they say to themselves and to each other, "What is the use in my exerting myself unduly? The more the work costs, the more money the 'old man' makes." The author knows this to be the case, for some years ago he had to let a large contract for foreign work at cost plus a percentage; and although the contractors themselves tried to do the honest thing at all times, their men "loafed" to such an extent that the final cost of the construction was atrociously high; and he had occasionally, on his own responsibility, to discharge some of the con- tractor's employees, including once the field superintendent. This method of letting work involves asking too much of frail human nature. Method D involves less labor in cost-keeping than Method C; but, otherwise, it is open to the same general objection. Method E is almost as unsatisfactory to the client as Methods C and D, except that the contractor's reward for his own iniquity is a fixed quantity and not in direct proportion to the extent of that iniquity. Method F involves a slight improvement on Method E, but only to the extent of a little simphfication in bookkeeping and perhaps a reduced opportunity for "squeezing" the chent. The author readily acknowledges that during war times, when the trend of the market for both materials and labor was rapidly upward, no con- tractor could have afforded to take work either for a lump sum or by unit prices. Unfortunately, in order to bring the war to a successful conclusion, a vast amount of public work had to be done with the utmost despatch, irrespective of what the cost might be ; hence the Government had no choice at all in the matter, and, consequently, it let many millions of dollars, worth of contracts at "cost plus a percentage" or "cost plus a lump sum." If the true history of all such contracts was ever written and made public, the nation would stand aghast at the extravagance they involved; and those two methods of contract-letting would receive the universal condem- nation of all intelligent, disinterested persons. As was stated in the oral discussion of Mr. Clarke's paper, when a contractor has simultaneously two or more contracts, one of which is on the "cost plus" basis and the other or others on either the "lump-sum" or the "unit-price" basis, he will naturally put his best and most ener- getic men on the latter, and will shift the lazy and incompetent ones to the former. This practice has become so well established by custom that the "cost plus" contracts have been dubbed "hospital jobs"; and it appears that the nickname has stuck. Is it not obvious that anyone who lets a contract on the "cost plus" basis places himself absolutely at the mercy of the contractor and the contractor's employees? It is true that the specifications often contain 342 ECONOMICS OF BEIDGEWORK Ch.\i'ter XXXIII restri'^tions which tend to lessen the contractor's power to take advantage of the cHent ; but their enforcement would be very troublesome, and would generall}' involve Utigation with its attendant delay and expense. Most people will acknowledge that the percentage of truly conscientious contractors is not overwhelming^ large, but how much smaller is that of truty conscientious workmen! The author does not deny that there are worlonen who always give a quid pro quo and who are upright and honor- able in all their dealings; but, alas, they are sadly in the minority. Their number is so small that they are unable to induce their co-laborers to exert themselves any more than they are compelled to, unless they are paid bj- the job instead of by the day or hour. By the way, when it is practicable, such a scheme of paj'ing the work- men is an improvement on that of time compensation, because it provides a great incentive to effort; but, at the same time, it also serves as a strong temptation to scamp the work. "With close supervision, however, and a strict enforcement of the clause in the specifications relating to the taking out and replacing of defectively built work, the employees soon learn, through the fines and penalties enforced by the contractor, that scamping does not pay, and that the old adage of honesty being the best policy is just as apphcable now as it was when first enunciated. Method G involves only a very shght modification of that of ''cost plus a lump sum," the said lump sum being replaced by another sum obtained by adding together the products of the actual quantities of all the materials by certain small unit prices agreed on in the contract. Although the author concedes that this method is undoubtedly the best of all the straight "cost-plus" methods, it possesses all the serious objections inherent thereto. In addition to those previously indicated, there might be mentioned the fact that any straight ''cost-plus" basis effectively cuts out competition, and advantages a favored few of the larger and more experienced con- tractors, rendering it difficult for the smaller and less experienced ones to secure any work, except through some other method of letting. It ought to be evident to anyone possessed of ordinary vision that such a method will militate toward cutting the "small fry" contractors out of bidding; for when an owner is wilhng to let a piece of work on any straight "cost-plus" basis, he naturally will want to award it to a large contractor of means, who has an esta,blished reputation for fairness and efficiency. That would practically mean letting all contract work without competition, and American contractors, as ai body, would object seriously to any such procedure. It is true that the owner might call for competitive bids on the basis of having each bidder name a lump-sum as a fixed net fee, and award- ing the contract to the competitor who quotes the lowest figure; but the adoption of such a method would often result in serious trouble, delay, and expense, and would not ensure that the work would go to the most desirable bidder. ECONOMICS IN CONTRACT LETTING 343 Under the heading TI, a number of profit-sharing methods have been tried and have proved to be more or less satisfactory. All of them neces- sarily presuppose a careful accounting of cost from start to finish. Unless the contract between the two parties clearly indicates how every main detail of cost is to be computed, there will be trouble before the work is finished. For instance, in respect to plant — does the contractor furnish it free of charge, or does he receive rental for it, with the rental charged as one of the items of cost of the work? How about paying for repairs and renewals to plant? Who stands the expense of these items — does the con- tractor, or is it charged as an item of cost of doing the work? Again, if extra work is done under the contract, how is it to be counted when making the final settlement? It requires the service of an expert consulting engineer or that of an experienced contractor to draft a contract and specifications which will provide, in a manner satisfactory to both parties, for all possible contingen- cies. With such papers, however, and with a close system of cost-account- ing, this general method of profit-sharing is the most satisfactory scheme for contract-letting which can be evolved. None of the modified methods of the "cost-plus" system, involving some means or other of profit-sharing, which have yet been tried in practice, can be said to be entirely satisfactory to the owner, though possibly so to the contractor, in that they all fail to put a limit on the total cost of the construction or to penalize a contractor who, through either wilfulness or carelessness, allows the cost of construction to pass the bounds of reason. It does not suffice to stipulate in the contract that, when the total cost passes a certain amount, the allowance for profit is gradually to be reduced until a certain minimum limit, however small it may be, is reached. The setting of that limit leaves the contractor in a position to take fife easily and to avoid personal worry after his hard luck has attained to a certain magnitude; for, subsequently to that, he will lose nothing but his time and the possible use of his plant on some remunerative contract, while the owner will have to pay whatever additional amount the job may cost. On this point the writer knows whereof he speaks; because one of the war-time contracts engineered by his firm was, of necessity, let on that basis, and the results thereof are siriply sickening. The chent was left at the mercy of the con- tractor, and the totil cost proved to be excessive. From the preceding it is evident that the ''cost-plus," the "lump sum," and the "unit-price" methods of letting contracts are not only faulty, but also unjust to one or other of the two parties to the agreement; conse- quently, the question arises: "Is there not some method which will be just and fair to both? That question, the writer claims, can truly be answered in the affirmative; but before proceeding to explain such a method in complete detail there will be presented a statement of the main require- ments of an ideal system. Salient Features of an Ideal System, of Contract-Letting and Profit-Shar- 344 ECONOMICS OF BRIDGEWORK Ch.^ter XXXIII ing. The essential requirements of an ideal tj'pe of contract are as fol- lows: First. It must provide a means of sharing with the workmen on an equitable basis the total net profit on the job. Second. It must set some kind of a limit to the total cost of the work, so as to prevent a careless, incompetent, or conscienceless contractor from running up the expense to an outrageously great amount. Third. It must reduce to a minimum the chance of the contractor's being out of pocket on the completion of the work, unless such con- dition is due to his own carelessness or lack of push. Fourth. It must retain all the advantages of competitive bidding, so as to give every capable and worthy contractor who is desirous of figuring on the work an even chance of securing the contract. Fifth. It must provide an incentive for the contractor and all his assistants and workmen to use every legitimate effort to make the work as inexpensive as possible, without violating in any manner the requirements of the specifications. Sixth. It must provide a just and equitable basis of payment for a possible increase in the estimate of total quantities and for adjusting satisfactorily to all concerned the reduction of payment due to a possible diminution thereof. Seventh. It must ensure that the owner will be acting for his own best interests by aiding the contractor in every possible way to com- plete his work quickly and inexpensively, provided, of course, that it is done in such a manner as to guarantee the attainment of the owner's ultimate purpose, as expressed in the specifications. Eighth. Its provisions must be such as to keep constantly in good humor every one connected with the construction. Ninth. Its method of final settlement of accounts must be clear, simple, ?nd easy of application; and the keeping of them during the prog- ress of the work must be no more complicated or expensive than it would be in the case of any ordinary " cost-plus " contract. Description of the Ideal Method. Let the specifications, which should invariably be drafted by an engineer who is acknowledged to be an expert in the class of work covered in the proposed contract, be complete and thorough in every detail, recording all that is known concerning the govern- ing conditions; pointing out all featm-es about which there is any uncer- tainty; tabulating as accurately as possible the estimated quantities of all the materials that will probably enter the construction; providing a justly- drawn clause for unclassified work and the payment theix^for; calling for each bidder to submit in full detail his estimate of actual cost of doing the work by applying to all quantities of materials given in the s]i(H'ifi(';vtions, unit-(;ost prices (termed Schedule A), each price containing a projiortionate share of any contingency allowance that may have been made, totaling the products so as to form ''Sum A," and adding thereto the amount of profit ECONOMICS IN CONTRACT LETTING 345 which he has decided to ask, thus making "Sum B." This last amount will, in reality, represent the bidder's tender; but to it there will be added a profit for the owner, exactly equal to that asked for by the successful bidder, and another profit or bonus for the employees, amounting to a previously fixed percentage (say, 20 or 25) of the sum of the aforesaid prof- its of the contractor and the owner, thus making "Sum C." This last sum is the temporary limit of total expenditure on the part of the owner, pred- icated upon the assumption that the approximate quantities of materials given in the specifications are correct; and it is on the basis of these "Sums C" that bids will be compared and the award of the contract made. The ratio r of "Sum C" to "Sum A" is to be applied to each of the unit prices used in the preparation of the cost estimate, in order to obtain the list of unit prices (termed "Schedule B") to apply temporarily to the actual quantities of materials in the completed construction, when making the final adjustment of accounts. If there are any items of expense of construction not covered by the list given in the specifications, the clause of the latter relating to "Unclassified Work" will take care of them. That clause should stipulate that, for aU such unlisted items, the actual cost of labor and materials therefor, without any allowance for superintendence or overhead, is to be recorded ; and to it is to be added later 30% of its amount to allow for superintendence, over- head, and the various profits. This sum is to be added to the total value of the actual quantities of all the materials listed in the specifications figured at the proportionately increased unit prices as given in "Schedule B"; and the result, "Sum D" (with a single modification explained hereinafter), will be the final limiting cost to the owner and the basis for computing the net profits to be divided between the contractor, the owner, and the work- men. The specifications, of course, will contain a clause providing a surety company bond for the faithful performance of the work and for guarantee- ing the client against having to pay more than the limiting sum agreed on (as finally modified). Method of Profit-Sharing Contract. The following method of profit-shar- ing between the contractor, the owner, and the employees is to be adopted: An accurate estimate of cost of every detail of the work from start to finish is to be kept by the contractor and verified by an accountant in the employ of the cKent, so that the total profit on the job may be ascertained by deducting this total cost from the maximum figure named in the con- tractor's tender and afterward embodied in the contract (modified, how- ever, as hereinafter described). This profit, less the amount of the employ- ees' bonus, is to be shared between the contractor and the client as indicated in the profit diagram, Fig. 33a*. It should be clearly understood that every * Mr. Hardesty has pointed out the fact that on large contracts the curves cannot be read with sufficient accuracy for a proper final settlement of the account, and that much trouble might be engendered thereby between the accountants of the two parties. 346 ECONOMICS OF BRIDGEWORK Chapter XXXIII direct and indirect expense to which the contractor is put in doing the work, after the contract is signed, is to be included in the cost — all overhead expenses of every kind, plant deterioration, travehng expenses, supervision, and salaries, excepting only that the contractor hmiself is not entitled to any salary. In the case of a firm being the contractor, the head of that firm should receive no salary; but if any of the juniors devote their time exclusively to the job, it would be legitunate to allow them reasonable salaries, equivalent to what would have to be paid to regular assistants. All such matters, of course, should be stipulated in the contract. In order to determine, after the entire job is finished, the amount due the contractor, "Sum C" is to be subtracted from "Sum D," and the ratio which this difference (either a positive or a negative quantity) bears to 20 19 'l8 27 16 15 14 13 S 12 ^ 11 1 10 s' 4 S 2 1 n — ~ ~ — ~ — ~ ~ P p P ~ ~ ~ ~ p — "■ ■" ^" y^' DIAGRAM FOR PROFIT SHARING y ^ ..^v< ^^ <^- Jt ^. o 1 ^'^ t ^N^ m^ •'■ -s '< -> 11 '^^ -s itv g ^. ' t .. ~i?S ^-: /s ^% > / (O* ^ y / a' ■0 f ? / .^ / 5 C} t y i _e^ / / y \\ / / X ^e■C 1> / ^ ^ I ^ -- ^ 1 J _ 012345678 9 10 U 12 1314 15 1617 IS 19 20 2122 23 24 25 26 27 28 29 30 3U2 33 3'H35 36 37 Total Percentage of Saving on Limiting Cost to Client Fig. 33a. Total Percentage of Saving on Limiting Cost to Client. "Sum C" is to be figured and adopted in the use of the diagram of "cor- rective ratios" (Fig. 336*) for the said difference. Application of Corrective Ratio. There are two reasons for applying this corrective ratio: First. In the case where the actual quantities of materials exceed the The solution of the difficulty is to substitute a broken line for each curve, passing through the known points at zero, five, ten, fifteen, and twenty percentages. The readings for these points on the upper line are zero, four, seven, nine, and ten; and on the lower line they are zero, one, three, six, and ten. Such an arrangement removes every possibiUty of dispute concerning the reading of the diagram, because all per- centages intermediate to the above-mentioned ones can be directly interpolated. * The curve in this diagram is intended to be the quadrant of a circle; hence, if in reading it there be any dispute between the accountants of the two parties, it can be settled by drawing the cvn-ve on cross-section paj^er using a large scale, or by employing exact mathematical formulae. ECONOMICS IN CONTRACT LETTING 347 estimated ones of the specifications, it would be hardly fair to the owner to apply to the excess those unit prices which produce his tentative Hmiting expenditure. Second. In the case where the actual quantities of materials are less than the estimated ones, it would be unjust to the contractor to use the high unit prices on the diminution quantities, not only because of the great difference between these and the unit actual costs, but, also, for the reason that the total overhead charges would be about the same for the dimin- ished amounts as for the estimated total quantities. 1.00 0.99 — \ \ \ \ \ \ \ i \ DIAGRAM OF CORRECTIVE RATIOS \ V \ \ \ \ \ N s. N. ^ ■~~ — ___ ,00..01 .02 .02 .04 .05 .06 .07 .08 .09 .10 .11 .12 .13 .14 .15 .16 .17 .18 .19 .20 .21 .22 .23 .24 .25 Ratios of Value Difference Fig. 336. Diagram of Corrective Ratios. In the corrective ratio diagram (Fig. 336) it will be noticed, that, after the ratio of value difference (due to increase or diminution of quantities of materials) reaches 0.2, the "corrective ratio" remains constant at 0.8, which corresponds approximately to actual cost conditions. The object of this is to provide that the contractor shall not be too much benefited by an abnormal increase in quantities, nor, on the other hand, shall he be at too much disadvantage because of an abnormal diminution thereof. To utiHze the corrective ratio diagram (Fig. 336) look on the line of abscissae for the ratio of cost difference, pass vertically upward to the curve (or right line, as the- case may be), then horizontally to the extreme 348 ECONOMICS OF BRIDGEWORK Ch.a.pter XXXIII left vertical, which will indicate the corrective ratio reqmred. Next, mul- tiply the previously computed difference by this corrective ratio, and add the result to or subtract it from "Sum C." The result, ''Sum E," will be the finally corrected limit, from which must be subtracted the total actual cost so as to determine the amount of profit to be divided. The first step in such division is to set aside the employees' share on the basis of percentage agreed on; and the next is to divide the remaining profit between the contractor and the owner, as per the profit diagram (Fig. 33a). The size of the percentage of the declared profit to allow the employees will depend on the character of the work covered in the contract in respect to the proportionate division of the cost between materials and labor. Under ordinary conditions, the division is about half and half, in which case the employees' percentage should be from 20 to 25; but where the labor cost preponderates these figures should be increased, and where the materials cost is the greater they should be diminished. In respect to the division of this bonus among the employees, the fol- lowing method is suggested : Only those workmen or assistants of any class who have stayed on the job, either until its completion or until their services were no longer needed, should participate in the profits; and the amount of the share of each such workman and assistant should be in the proportion which his total earning on the work bears to the grand total of the earnings of all those employees who so participate. As, in any good business organization, a record is always kept of the amount of salary or wages paid to each employee on any contract, it would require only a few hours of extra work for the book- keeper, after the job is finished, to compute each man's proportionate share of the bonus. There is an additional protection against possible loss which might be given to the contractor under certain conditions, especially on work to be done in a foreign country. If it be anticipated that during construction any large general rise in the price of labor is likely to occur, thus greatly augmenting the total cost of the work, the hmiting total expenditure of the owner, as hereinbefore finally adjusted, should be increased by an amount figured thus: Determine the average current wages for common labor at the time of letting the contract, and the average paid therefor during the entire tune occupied by the construction, and call the ratio of these two averages r'; then figure the total amount of salaries and wages paid to employees from start to finish and call it W. Then, Tf(/-l)Xl.2 will be the amount required, the factor, 1.2, covering a fair allowance for overhead and profits. It has been suggested of late in the technical press that the contractor himself should be paid a salary by the owner, in addition to whatever ECONOMICS IN CONTRACT LETTING S49 profit he may make on the job. Such a pohcy would be simply suicidal on the part of the owner, for if the work were to be handled badly, the contractor might continue to earn money while the owner would be losing heavily. The writer has met with just such a case; hence, in this particu- lar, he certainly knows whereof he speaks. Such a practice should never, under any conditions, be countenanced by either the owner or his engineer. Exemplification. In order to illustrate the modus operandi of this method of profit-sharing, let us assmiie the following case, in which the estimated quantities are exceeded. For the purpose of simplification in figuring, round numbers have been assumed for both the quantities of materials and the unit costs thereof. The job is one of railroad construction and the number of items is intentionally limited for the sake of convenience. The following are the quantities of materials supposed to be stated in the specifications: Earthwork, measured in cutting 1,000,000 cu. yds. Loose rock, " " " ......... 100,000 " SoHdrock, " " " 40,000 " Concrete in structures. . 10,000 " Wooden trestle. 2,000 Hn. ft. Structural steelwork, erected. ........... 500,000 lbs. The tender of the successful bidder was as follows : Quantities. Schedule A. Totals. Earthwork 1,000,000 cu. yds. @ $0 . 50 = $500,000 Loose rock 100,000 '' @ 1.00 = 100,000 Solid rock 40,000 " @ 1.50= 60,000 Concrete. 10,000 " @ 20 . 00 = 200,000 Wooden trestle 2,000 Un. ft. @ 50.00 = 100,000 Steelwork..... 500,000 lbs. @ 0.08 = 40,000 Total estimated cost ("Sum A") • = • • • = $1,000,000 Profit required, 10%. = 100,000 Tender C'Sum B") = $1,100,000 Allowance for owner's profit — 100,000 Employees' profit, 25% of $200,000. = 50,000 Temporary limit ("Sum. C"). = $1,250,000 SumC $1,250,000 Katio, r-Q^^ ^ ~ $1,000,000 ^'"^^^ The proportionately increased unit prices, therefore, will be as follows: 350 ECONOMICS OF BRIDGEWORK Chapter XXXIII Schedule B. Earthwork $0.50X1.25 = $0.625 Loose rock 1.00X1.25= 1.25 Solid rock 1.50X1.25= 1.875 Concrete 20.00X1.25 = 25.00 Wooden trestle 50.00X1.25 = 62.50 Steelwork 0.08X1.25= 0.10 The actual quantities of the materials in the completed job were, as follows : Earthwork 980,000 cu. yds. Loose rock 110,000 " Solid rock 50,000 " Concrete 10,500 " Wooden trestle 2,100 lin. ft. Steelwork 480,000 lbs. In addition, there was done by the contractor certain "unclassified work " which actually cost him for labor and materials $20,000. The revised estimate is, therefore, as follows: Earthwork 980,000 cu. yds. @ SO . 625 = $612,500 Loose rock 110,000 " @ 1.25 = 137,500 SoHdrock 50,000 " @ 1.875= 93,750 Concrete 10,500 " @ 25 .00 = 262,500 Wooden trestle 2,100 lin. ft. @ 62.50= 131,250 Steelwork 480,000 lbs. @ . 10 = 48,000 Unclassified work $20,000X 1 . 3 = 26,000 Summation, or "Sum D" =$1,311,500 The difference between "Sum D" and "Sum C" equals $1,311,500-$1,250,000 = $61,500. $61,500 Ratio of difference = ^ .. ^ ^„ ^^^ = . 0492 ; say, 0.05. For this ratio, the diagram. Fig. 33fo, gives a corrective ratio of 0.865, which multiplied by $61,500 gives $53,198, say, $53,200, making the cor- rected limit, or "Sum E," = $l,250,000+$53,200 = $1,303,200. If the total actual cost of the work, including that of the imclassified work without allowance for superintendence or overhead, amounted to $1,100,000, the total profit would be: $1,303,200- $1,100,000 = $203,200. Of this, the joint share of the contractor and the owner would be: $203,200-^1. 25 = $162,560; ECONOMICS IN CONTRACT LETTING 351 and the employees' bonus would be: $203,200 - $162,560 = $40,640. which is exactly 25% of $162,560. In respect to the division of this last amount between the contractor and the owner, its ratio to total cost is: $162,560^ $1,100,000 = 0.148, or 14.8%. From the diagram for profit division (Fig. 33a) we find the division of this percentage to be: Contractor 8.9% Owner 5.9% This makes the total payment by the owner to the contractor: $1,100,000X 108 . 9 = $1,197,900. Let us now take a case where there is a diminution in the estimated quantities of materials. Using the same case as before in respect to estimated quantities and tender, we shall assume the following actual quantities of materials: Earthwork 1,050,000 cu. yds. Loose rock 50,000 " Solid rock 20,000 '' Concrete 8,000 '' Wooden trestle 1,800 Hn. ft. Steel work 450,000 lb. The cost of the unclassified work was $20,000, as in the preceding case. The revised estimate is, therefore, as follows: Earthwork 1,050,000 cu. yds. @ $0 . 625 = $656,250 Loose rock 50,000 '' @ 1.25 = 62,500 Solid rock 20,000 " @ 1.875= 37,500 Concrete 8,000 '' @ 25.00= 200,000 Wooden trestle 1,800 lin. ft. @ 62.50 = 112,500 Steelwork 450,000 lb. @ . 10 = 45,000 Unclassified work $20,000X1 .3= 26,000 , Summation, or "Sum D" = $1,139,750 The difference between "Sum D" and "Sum C" equals $1,139,750-$1,250,000= -$110,250. $110,250 Ratio of difference = ^rr?7?7r7^7^ = 0-0882. !t)l,^oU,000 352 ECONOMICS OF BRIDGEWORK Chapter XXXIII For this ratio, the diagram gives a corrective ratio of 0.835, which, multipUed by $110,250, gives $92,059, say, $92,100, making the corrected limit. '' Sum E " = $1,250,000- $92,100 = $1,157,900. If the total actual cost of the construction, including that of the unclassi- fied work without allowance for superintendence or overhead, amounted to $880,000, the total profit would be: $1,157,900 - $880,000 = $277,900. Of this, the joint share of the contractor and the owner would be: $277,900 -^ 1 .25 = $222,320, and the employees' bonus would be: $277,900 - $222,320 = $55,580, which is exactly 25% of $222,320. In respect to the division of this last amount between the contractor and the owner, its ratio to total cost is: $222,320 -^ $880,000 = 0.253, or 25.3%. From the diagram for profit division, (Fig. 33a) , we find the division of this percentage to be on the "fifty-fifty" basis, making the total payment by the owner to the contractor = $880,000 X 1.1265 = $991,320. Advantages. The advantages of this method of contract-letting are as f pUows : First. While it is true that the client at the outset does not know exactly what the work is going to cost him, he is positive that it will not cost him materially more than a certain amount, provided his engineer's estimate of quantities is about right, as, generally speaking, it certainly ought to be. Second. The client has the satisfaction of feeling that even if, in his opinion, the limit determined by the contractor's bid is excessive, and that the final net profit on the job, in consequence, will be too large, the said net profit will be shared between them on a ''fifty-fifty" basis. Third. While the client is bound to pay a certain percentage of the joint profit as a bonus to the contractor's employees, generally he will not be out of pocket thereby, but, on the contrary, he will gain; because the incen- tive that the prospective bonus gives to all hands to labor energetically will save in the total cost much more than the amount of the bonus. Fourth. All the advantages of competitive bidding are retained by this method, because the fully-capable competitor who tenders the lowest amount for "Sum C" should be awarded the contract. All bids will be on exactly the same basis, no modification of the stipulated method of tender- ing being permitted. It is understood, of course, that the contract will not ECONOMICS IN CONTRACT LETTING 353 be awarded to any competitor who docs not possess the necessary experi- ence, capital, and plant, and who has not an established reputation for doing good and satisfactory work. Fifth. The contractor, if he was not too keen in bidding, knows that there is almost no chance whatsoever of his losing money on the job; because before doing so he would have to use up his allowance for contin- gencies, his own estimated profit, a profit of like amount allowed for the owner, and a substantial sum representing the employees' bonus. If he ever does use up all these safeguards, the chances are many to one that the fault therefor is entirely his own, being due to his negligence, lack of fore- thought, or deficiency in energy and push; and in that event he certainly would deserve to be penahzed. Sixth. All the workmen and salaried employees of the contractor will be satisfied with their job because of the excellent opportunity offered for extra compensation; and they will, of their own accord, work diligently, and occasionally even overtime, in order to expedite the construction. Of their own accord, too, they will run off the job any employee who is a chronic shirker, and they will make it their business to keep everybody busy; because the more cheaply the construction is done the greater will be the bonus to divide among the faithful employees who stick by the work to the finish. Seventh. The method of profit-sharing given by the diagram for profit division (Fig. 33a) is eminently equitable, in that when the net amount is small, nearly all of it goes to the contractor, and, as it augments, a con- tinually increasing proportion of it goes to the owner, up to the point where the total joint profit amounts to 20%, after which the partition is on a "fifty-fifty" basis. It will be seen that for a total net joint profit of less than 20%, the fol- lowing divisions will prevail : With 5% net, 4% goes to the contractor and 1% to the owner With 10% net, 7% "" " " "3% " '' " With 15% net, 9% "" " '' " Q% "" '' The 20% point was selected for equal division as being the one above which a contract is generally deemed by contractors to be good, slightly below which it is only fair, and much below which it is bad ; for it corresponds to a net profit of 10 per cent. That is as small a margin as is generally deemed safe for any bidder to tender upon, and yet it constitutes a satisfactory profit on a finished job. As for limiting the client's share of the profit to one-half — that is reasonable and just, because he would have no moral right to receive more than his partner, the contractor. If the client's share were allowed to increase indefinitely, it is conceivable that, with a very large prospective total profit, the contractor could save money for himself by making the work more expensive. Any bidder who tenders on the basis of a profit less than 10% should 354 ECONOMICS OF BRIDGEWORK Chapter XXXIII be looked on askance by the owner and his engineer; and such a competitor should not be awarded the contract, unless he possesses an exceptionally fine reputation for doing good work and for not quitting liis job before finishing it. It is true that during very hard times many worthy contract- ors are willing to work almost for actual cost, in order to keep their work- men employed; and in such cases the good intention should be recognized in making the award. Nevertheless, it nearly always proves to be unsatis- factory to both the owner and his engineer to let a contract for anj^ piece of construction at a figure below its real value. Eighth. The contractor will feel during the progress of the construc- tion that the chent is a partner on the job, and that, therefore, he and his engineers will not be likely to be unnecessarily severe in their requirements, also that they will permit the adoption of all legitimate expense-saving expedients, and will not demand too many frills on the finishing. Ninth. Owing to the justice and equity involved by this method of contract-letting and profit-sharing, all concerned in the execution of the work will labor whole-heartedly and good-naturedly, avoiding petty squabbles and disagreements; and the result will be earnest, honest effort, a satisfactory piece of construction, and the general contentment of both parties to the agreement. Tenth. While this method may at first glance have the appearance of being complicated, it is quite simple; and because of the clear manner in which it is explained herein, it is easily utilized in any actual case by follow- ing one step at a time the directions given. The nomenclature of "sums" and "schedules" renders the appUcation of the method very easy. More- over, it must be remembered that it is to be used only once for each con- tract, and then only after all the work is completed and the accounts are in proper form. Again, the keeping of the accounts is in no way any more compHcated than it would be in case any of the "cost-plus" methods were used. Objections That Have Been Raised to This Method. A few objections, both orally and in print, have been raised to this proposed method of contract-letting and profit-sharing; but they could not have been well considered, for they are not valid. It will be well before closing this dis- cussion to mention them and show wherein they are untenable. They are as follows: A. It has been asserted that there would be special difficulty in keeping the accounts; but there would be required therefor exactly the same woi-k which would be necessitated by any of the "cost-plus" methods. They all involve a correct record of the amount of every legitimate item of expense to which the contractor is put; and the book- keeping in any case would certainly re(|uirc an account with each employee, so as to show how much money had been paid him from start to finish. B. It has been claimed that the method is too complicated to be use- ful. On the contrary, as explained previously, it is simple; and the pecul- ECONOMICS IN CONTKACT LETTING 355 iar manner of its presentation herein is such as to render its use merely a matter of following step by step certain clearly written instructions. More- over, as before indicated, this method of settlement of accounts is used only once, viz., after the completion of the job. C. It has been stated that uneducated contractors would have diffi- culty in understanding the method ; but the man who made this claim did the average American contractor a grave injustice. The construction contractors in this country are as bright a body of men as one can find any- where; and certainly they may be trusted to understand anything in reason that affects their interests. D. It has been claimed that most contractors have a general inherent objection to sharing profits with the owner; but a little consideration wiU show that there is no sharing of the requested profit until after the estimated cost of the work (under the assumption of unchanged quantities of mate- rials) has been exceeded. It was to clarify this situation that the writer changed his original idea of having each bidder name a lump-sum (corre- sponding to "Sum C") as a provisional limit of the owner's total expendi- ture, and a fist of unit prices (corresponding to "Schedule B") which, when appHed to the estimated quantities of the specifications, would make the sum of the products exactly equal to the said lump-sum, and substituted therefor the method herein described, viz., that of having each bidder sub- mit in detail his estimate of cost and his desired profit, and arranging the method of determining the Hmiting cost to the owner by two additions to the bidder's tender. This change is simply a concession to prejudice, and does not modify the method proposed by the writer in his letter pubhshed in Contracting in its issue of September 15th, 1919. The only fundamental change between that presentation of the matter and this one is the inclusion herein of a bonus for the employees. E. It has been claimed that this method would tend to deceive the owner. He would certainly be stupid if he could not see clearly how its tendency is to cut down the amount that he will pay for the entire work, and that it will set a just limit beyond which, under the worst possible conditions, he cannot be compelled to pay any more. F. It has been stated, as a reason for favoring the "cost-plus" system, that bonding companies favor it and oppose all other methods of contract- letting. Naturally, they would do so; because, with the "cost-plus" method, their obligation reduces almost to zero, the risk being placed solely on the owner. In truth, with that method adopted, there does not appear to be any valid reason for having a bond at all. When the contractor runs no risk of loss whatsoever, why a surety company bond? Possibly, if the surety companies would consider it from this point of view, they would not oppose the writer's suggested method of contract-letting; for, while it reduces very greatly the possibility of loss to the surety company, it does not destroy that organization's function by removing entirely its raison d'etre. 356 ECONOMICS OF BRIDGEWORK Chapter XXXIII G. The claim has been made that this method is not apphcable to cases where no estimate of quantities has been made or for which no specifications have been prepared, and when it is necessary to let the work without delay. The correctness of this claim is granted, but its apphca- bihty should be confined to war work, in which the element of time is the principal consideration. In civil life, if a projector of an enterprise is in such haste to start his work that he has to omit the preparation of specifi- cations and estimates of quantities before letting the contract, he certainly deserves what is coming to him in case it proves that he has placed himself in the hands of an unscrupulous contractor on the "cost-plus" basis. H. It has been pointed out that the law will prevent certain public bodies from letting contracts on a "cost-plus" basis, and that such a ruling might apply to the writer's proposed method also. If such really is the case, the remedy would evidently be to modify the law so as to permit of its adoption; but would not the fact of its containing a clause which sets a limit to the contractor's total compensation always render the method legal? This, however, is a question for the lawyers to settle. I. A prominent writer on economics has lately issued a tirade against gambling, especially as it applies to contractors guaranteeing owners against the cost of work exceeding the amount of the tender. The writer concurs in this theory to the extent that there should be no gambling on the amounts of assumed quantities of materials, or, in certain cases, on there not being any great rise in the average price of labor, or on possible loss through any reasonably great amount of hard luck; but there is cer- tainly nothing unmoral or oppressive in insisting on his gambling to the extent of guaranteeing against his own incompetency, carelessness, or lack of forethought. The writer is of the opinion that a margin against actual money loss to the contractor, consisting of his estimated amount for con- tingencies, plus his requested profit, plus an equal profit for the owner, plus a substantial bonus for the employees, is amply large to guarantee liim against all loss through ordinarily unfavorable eventualities; and that, in ninety-nine cases out of a hundred, if such a margin were exceeded, it would be because of the contractor's own fault. Adoption of Method. If this proposed method of contract-letting antl profit sharing is received with favor by engineers, architects, contractors, and builders in general, it could easily be adopted as a standard for the country by calling a small convention with a single representative from each of the leading technical and railroad societies, contracting oiganizations, bankers' associations, and labor guilds, to discuss the advisability of adopt- ing it (or else some modification of it) and to report the decision of the meeting to the said })0(lies for their approval. If any large group of clients, such as the railroad companies, were to adopt the method as standard and use it, very soon everybody having construction contracts to let would follow their (;xample, thus making it the universal standard of contract- letting for the countiy — nor would it be long before other American coun- ECONOMICS IN CONTRACT LETTING 357 tries would follow our lead, thus greatly simplifying our business relations with the various American Commonwealths. Addendum. In all lines of manufacture the employees should share in the net annual profits of the company; but, in figuring the yearly cost of running the establishment and doing the work, there should be included fair salaries for all the working officers, 6% on the actual amount of cash invested in the plant and business (but not on the total capital stock), an annual allowance for a sinking fund to redeem the bonds or other indebted- ness of the organization, and taxes of every kind. The net profit estimated in this way should generally be divided on the basis of one-third to the employees and two-thirds to the company, but sometimes, perhaps, on that of one-fourth and three-fourths. The reason why it should not be split on a "fifty-fifty" basis is that the company has to run the risk of standing a loss in bad years, while the employees do not. Only those employees who are still connected with the company at the end of the year, or who have been discharged in good standing, should share in the bonus; and their propor- tionate amounts should be computed as previously indicated for the case of construction contracts. CHAPTER XXXIV ECONOMICS OF BRIDGE-ENGINEERING OFFICEWORK Concerning economics in the management of a bridge engineer's office, it will suffice to offer a few general principles and refer the reader to Chapter LVIII of "Bridge Engineering." It has been claimed by some engineers that the scheme of management therein expounded is far too elaborate and costly, some going so far as to state that, if it were followed out exactly, the expense involved would eat up all the profits. Such, though, is not the case, for while it is true that it is too expensive for an office with a small force, it is not so for one handhng simultaneously many millions of dollars' worth of bridgework, as did the author's in ante-bellum days. It represents an ideal system worked out with great care and in complete detail; and if it were utihzed with proper discretion by bridge engineers, bearing in mind that one should "cut his coat according to his cloth," much benefit would result. In any case, though, the following principles should be observed: First. All employees should arrive promptly in the morning, preferably a few minutes ahead of time, should get to work immediately, should work diUgently, and should put in full time. If, for any unavoidable reason, an employee loses some time from his work, it should be a point of honor with him to make it up by working overtime. Second. Talking among the employees during office hours should be reduced to an absolute minimum consistent with a proper exchange of ideas as to the development of the work of designing and detailing. No general conversation in the office should be allowed under any circum- stances whatsoever. Third. No visitors should be permitted to enter the drafting or com- puting rooms, and callers upon employees should be made to understand that they are not welcome and that visiting is against the rules. Fourth. No smoking should be allowed during office hours. It takes valuable time from the work; and hot cigarette ashes are very destructive to tracings. Fifth. Each employee should be made to attend strictly to his own business, and no one should be allowed to pry into matters in relation to which he has no legitimate concern. Sixth. Before any computations on a design are made, full data should be collected therefor; and a complete list of the conditions precedent should be sent to the client for approval in writing before any serious work is done. 358 ECONOMICS OF BRIDGE-ENGINEERING OFFICEWORK 859 Then, if later any changes are called for by the client, they would be made at his expense, and he could raise no vaUd objection to standing the cost thereof. In order to systematize the collection of data, each office should have a printed Hst of questions or memoranda to send to cUents, agents, or field men; and these should be filled in as fully as practicable for each job. Such a list is given in Chapter XLVI of "Bridge Engineering," but lately the author, for the benefit of his future practice (especially in foreign countries) has materially elaborated this. He feels that it cannot well be made too full or complete, because the more one knows in advance about the govern- ing conditions the better will he make his design. Seventh. There should be estabhshed certain Kmits to the accuracy of all calculations, and these should be adhered to. The list of limits adopted in the author's practice is given on page 1377 of "Bridge Engineering." Eighth. After each page of calculations is finished, it should be checked by the same computer so that, if he has made any error thereon, it may be corrected; and thus its effect will not be carried into any succeeding pages. Ninth. All results should be roughly checked by the computer, using old records or diagrams, so as to ensure that no egregious blunder has been made. Tenth. All calculations should be checked by an independent com- puter before being turned over to the drafting room. Eleventh. Every record, book, pamphlet, and similar office possession should be filed and indexed so that it can be found at any time without delay. Twelfth. Enough drawings should be made to enable the contractor to prepare properly and readily his shop drawings or other working drawings — but no more; and the preparation of shop drawings in the engineer's office should be strictly avoided. If they are made there so as to suit the style of one shop, they would probably not satisfy the idiosyncrasies of another — hence it is better to let each shop prepare its own shop drawings. Thirteenth. It is truly economic to use standard parts whenever this is practicable. It saves time in the office and money in manufacture. Special sections of metal should be avoided, even if they apparently be economical; for generally time is far more valuable than a little extra metal. It is only in case of a large amount of dupUcation that special sections are legitimate. Fourteenth. A simple style of lettering is both neat and economic, and the use of stencils and the printing press involves the saving of time and money. Fifteenth. No unchecked drawing should ever be allowed to go out of the office — no matter how pressing the call for it may be. The method of checking all drawings should be thorough and systematic, and it should invariably be followed. Sixteenth. When changes on drawings become necessary, they should, 360 ECONOMICS OF BRIDGE WOEK! CnAPTEa XXXIV of course, be made; but their effects on all parts should invariably be fol- lowed out to the utmost hmit of their influence. Seventeenth. Handling of the office work should be done by a thorough and approved system, such as that given on page 1387 et seq. of "Bridge Engineering." Eighteenth. Proper blank f onus facihtate office work and therefore economize on cost. Nineteenth. Cost records for the various jobs should be kept so as to be able to figure properly on the probable expense that wiU be involved in doing prospective work. Twentieth. Card indices should be kept for all possessions as well as for records; and this apphes to the engineer's library. No books should be taken from the office without special permission, and a record of all such loans should be kept and utilized for compelung the return of all books thus borrowed. CHAPTER XXXV ECONOMICS OE INSPECTION* The economics of inspection is a subject that is rather intangible, and yet is a branch of economics which really exists and is of great importance; hence it has a proper place in this general study, because it involves a desired result to be accomplished with a mimmum expenditure of effort, money, and (to a slight degree) material. The first point to treat is this important question — To what extent will it pay the owner or promoter to have his work inspected, and how much money should be spent therefor? To this query the answer is clear and unequivocal, viz., that, within the realm of reason, the manufacture and construction of bridgework cannot well receive too thorough inspection, and the owner should be wiUing to pay for it a reasonable compensation to high- class men. A few dollars saved by employing cheap inspectors may mean very many dollars lost through their blundering and from lowering the value of the finished product. Like all service functions, there should be a strong distinction between professional service at reasonable rates and simply commercial service rendered on low competitive terms. The quality of inspection is evidently dependent, as is all professional work, upon the character of the men employed, and this is unavoidably dependent upon the compensation allowed. From the above it will be appreciated that the quality of inspection must, according to the same rule as applies to all business, be in direct pro- portion to its financial reward. To be of genuine value, inspection must be constant, intelligent, and complete. A final inspection may determine the satisfactory comphance with the contract, but cannot, generally, secure an adequate correction of errors; and certainly it cannot prevent them or tend to the improvement of the work. The criteria of quality of inspection are the experience of the men directly on the job, the time spent on it, and the quaUty of the final record. The engineer or person having the respon- sibility of engaging Inspecting Engineers should decide upon the experience and reputation of the firm with which he purposes dealing, should know the * For a large portion of the data from which this chapter was prepared, the author is indebted to his friend, Mr. Watson Vredenburgh, C. E., of Hildreth & Co., one of the best-known and most successful inspecting bureaus of this country. The first part of the chapter, which is his work, relates to superstructure, while the latter portion from where the treatment of substructure begins represents the author's opinions. 361 362 ECONOMICS OF BRIDGEWORK Chapter XXXV experience of the men to be employed upon the work, and should critically examine the character of both progress and final reports furnished him. He may also properly demand information as to the time of the men employed upon the job. The method of payment by tons inspected is satisfactory, with a knowl- edge as to the quahty of inspection; but if the Engineer is doubtful as to the character of the work that is to be done, he may arrange his terms on a basis of cost of the actual time of the men employed on the work, plus a percentage or a fixed allowance per ton to the Inspecting Engineers for organization and supervision. It is difficult to fix a proper charge per ton to cover all sizes, kinds, and locations of work which would be economical to the chent and fair to the Inspecting Engineer. The latter may properly make a profit from the favorable combination of his work at rolling mills and manufacturing shops, and from the saving of time and traveling expenses, and at the same time, under proper arrangement and knowledge of these conditions, give the cHent the benefit of any economy arising from these propitious circumstances. Some Engineers, solely with the false thought of economy in the cost of a structure, omit to specify inspection, or bow to the wish of an owner who may consider the inspection an unnecessary expense, without having any conception of either the details of the service or its benefits. It is not inconceivable that an owner or Engineer who fails to provide for the super- vision of manufacture may be held responsible for damage or loss of life resulting from any failure during erection or thereafter. The question may weU be asked— What is the use of drawing plans, specifications, and con- tracts, unless steps are taken to determine that their requirements are being carried out? Supervision of the manufacture of bridgework may be made by the direct employees of an Engineer or of a Railroad Company; and where this method may be considered, the question of economy as compared with the employment of Inspecting Engineers who make a specialty of such work becomes a factor. The reasons for the existence of the latter class are primarily that the manufacture of structural metalwork is conducted at various rolling mills and at one or more fabricating plants, is in progress at several points at the same time, and is frequently intermittent. If an Engineer uses his own forces for this work, it is essential that a number of men be employed; and there is, consequently, much waste of time and of traveling expenses. To meet this situation, the independent Inspecting Engineer establishes an organization of experienced men who are per- manently located at the various manufacturing centers, and, by competent supervision of their work, makes use of their time simultancviusly over a num})cr of contracts, thereby tending to efficiency and economy. The overhead expense necessary in the operation and supeivision of inspection for any single contract is less with the Inspecting Engineers, as their normal expense of this nature is distributed over a volume of work. The efficiency ECONOMICS OP INSPECTION 863 of their service can be made at least equal tc that of any other Inspectors, if the principles of selection referred to previously in this chapter are care- fully followed. The Inspection Company, presumably, has a wide knowl- edge of shop methods and an intimate contact with many shop managers, and from experience is able to handle the defects arising during manufacture with some advantage of practical famiharity, as compared with the Design- ing Engineer; and the former has personal acquaintance and constant business relations with the shop management which the latter does not possess. Economy in Performance The Inspecting Engineers entrusted with the mill and shop inspection of the steel work of any project have directly the solution of the problem of accomplishing the desired result with the least expenditure of effort and money consistent with first-class service. I The systematizing of the service for economical performance involves the selection of inspectors-in-charge having proper experience in the class of work under contract, as well as training in the handling of the relations with the manufacturers, making correct reports, etc. Where the work is of sufficient size and character to warrant more than one inspector at the shop, it can be so arranged that the assistants may be men of lesser experience, with corresponding saving in remuneration, and duties assigned to them accordingly. The assistants can supervise the routine work of assembling, punching, and riveting before completion of the finished members, and cleaning, painting, weighing, and loading before shipment, besides estimat- ing weights and making proper reports, while the chief inspector can be made responsible for the relations with the shop, the planning of the work to meet the field conditions, the delivery of material from the mills, the actual inspection of finished members for measurements and character of workmanship, the shipment of material in the order and manner desired at the building site, and the making of final reports to his headquarters, in accordance with instructions, so that the client can be furnished with a complete descriptive report which will serve as a valuable record of the manufacture. Under a proper system of organization there are a number of considera- tions in connection with the method of inspection which should have atten- tion, in order that the service may be economical and successful. The inspectors at both mills and shops should be placed on the work as soon as it starts; their instructions as to specifications and plans should be prompt and complete; their co-operation with the mills should be such as to secure the rolhng and shipment of material to the shop, in accordance with the order of manufacture there, so as to prevent errors or discover defects as early as possible in the work, and thereby save time in manufacture and delay in shipment, with the additional advantage of avoiding being com- pelled to allow the work to be patched by corrections; and the co-operation 364 ECONOMICS OF BRIDGEWORK Chapter XXXV should be extended so as to secure the cleaning and painting at the proper time, and under correct conditions, in order to save cost in labor, time, and materials of repainting, either at the shop or in the field. The inspection should cover such co-operation with the management as to secure good work with the least expense to the manufacturer, and the shipment of the finished product at the time and in the order necessary for expeditious and economical erection. Much that is stated in Chapter II, under the heading "Economics of Mental Effort," is important to apply to the service of inspectors as well as to that of the Designing Engineers. It would be well for the Inspection Firms and the Supervising Inspectors to study and practice the considera- tions referred to therein, and apply the knowledge gained to the selection and direction of their inspectors actually performing the duties. The inspectors should be selected not only for their experience but for tempera- ment to fit them for the very important duty of co-operation with manu- facturers; also with regard to their health and habits. In all cases where inspectors have demonstrated their fitness and loyalty to the employer's interests, the direction of the work should be handled with every considera- tion for the employee that is consistent with the nature of the work and with other conditions affecting the cUents' interests. This relation between Inspecting Engineers and their employees in charge of work affects directly the character of the service and, therefore, the economics of inspection. The inspection in the field of the placing of foundations, the building of masonry, and the erection of metalwork needs, from an economic view- point, the same consideration as does the manufacture of the bridge super- structure. The inspectors should be men of experience; their duties should be so laid out as to promote the progress of the fieldwork, and prevent the rejection and rebuilding of portions of the work; their idle time should be appUed to other features of the project when the actual fieldwork does not demand their attention; and they should be subject to the same considera- tions of the ''Economics of Mental Effort." In general, it can very properly be considered poor economy to have given attention to the economics of promotion and secured competent design and specifications, and not to have provided for inspection to make sure of the entire manufacture and erection being performed in strict com- pliance with them; or to have had incompetent inspection by persons inexperienced and without proper organization; or to have failed to secure a fair and reasonable compensation for Inspecting Engineers fully qualified by experience and organization to perform the required service in a manner commensurate with its importance. CHAPTER XXXVI ECONOMICS OF SHOPWORK Without the aid of a thoroughly posted bridge-shop engineer, it would be entirely impracticable for anyone who is not truly experienced in struc- tural-steel manufacture to write at all intelligently upon the economics of that branch of bridgework. The author encountered great difficulty in securing the needed aid, partially because the work involved in the prepara- tion of the notes called for many hours of a busy man's time, but mainly because those who are best posted on such characteristically practical matters are not accustomed to express their thoughts on paper. Failure so to collect one's knowledge is a serious drawback to any man; for he never can determine wherein that knowledge is hazy or lacking until after he has attempted to collect, correlate, and systematize all that he knows upon the subject at issue. Many engineers and others, who in times past have done the author the honor of supplying him with special informa- tion, have afterwards assured him that they felt well repaid for the time and effort which they had devoted to the work, through their increase in knowl- edge obtained in making the investigation. Many a time and oft in his professional career has the author personally proved the correctness of this principle; and he earnestly recommends its serious consideration to the younger members of the engineering profession. Fortunately in this case, from his old friend, Mr. Thomas Earle, C.E., Vice-President of the Bethlehem Steel Bridge Corporation, the author succeeded in securing the information of which he was in search; and he feels very thankful for the aid rendered, because it is certainly a great concession and a real favor, in the case of an exceedingly busy man, to take the trouble to collect and systematize the special knowledge which he obtained by many years of hard work. The most of what follows in this chapter is essentially the substance of the data so courteously furnished by Mr. Earle. The economics of design to meet shop conditions has been discussed at length in Chapter XXIII; and Mr. Canady's contribution thereto covers very thoroughly the ground of economics in the drafting-room of a bridge shop ; hence there is left for treatment only the economics of doing the work in the shops themselves, together with certain allied economic subjects. The general economic problem in shopwork is to attain a certain result with the minimum expenditure of effort, time, and money. Each piece of 365 366 ECONOMICS OF BRIDGEWORK Chapter XXXVI material, therefore, must be taken up as few times as possible and carried the shortest practicable distance in securing the desired results. A por- tion of the problem must be solved before any phj^sical work is performed, because the design of the shop will have a large bearing upon it. The Con- tracting Department of the organization is also an economic factor of con- siderable importance in shopwork. A shop that is designed to handle all classes of fabricated steelwork will not handle any one particular class to the greatest advantage; hence, before the shop layout is made, this matter will have to receive careful consideration. If a general miscellaneous class of fabricated work is expected, the shop should be designed to suit such mixed fabrication ; but if the circumstances are such that it is probable that the bulk of the manu- facture will be of a particular character, it will be advisable to design the shop so as to handle that type of work to best advantage. If that is done, and if the Contracting Department of the organization keeps the shop filled most of the time with fabrication of a different class, the results will be unsatisfactory, thus proving the modus operandi to be uneconomic. It is true that at certain times it is impracticable to secure work of the character best suited to the shop, and then the results will inevitably be uneconomic; but it is better to keep the force occupied and everything moving, even at a disadvantage, rather than either to close down entirely or to let a portion of the men be idle. In that case it might eventually prove truly economical to operate temporarily at a small pecuniary loss. Nothing in shop or office is so disheartening or so disorganizing as idleness of employees; and when there is not enough work on hand to keep everybody on the qui vive, the general effort slackens and the efficiency of the entire organization is low- ered. For this reason, in bad times it really pays to do work at actual cost or even a trifle below, so that, when the revival of business comes, all in the organization wiU be ready to tackle the new work with energy and efficiency. If, during the larger part of the time, work of the proper character is going through the shop, and if the results are particularly favorable, this will more than offset the uneconomics due to unsuitable operation for short periods. The primary economic feature of any shop-layout is the elimination of unnecessary transportation and the provision for rapid passage there- through of all the materials which are being fabricated. The usual arrange- ment is to transport the metal longitudinally through on surface tracks and to carry it transversely by traveling cranes, thus reaching expeditiously every portion of the floor space. In some shops the cars are pushed along the tracks by man power, while in others electric or gasoline energy is employed. In these days of almost universal power operation and of high- priced-labor, it certainly is economic to use power for traction purposes. Of (;ourse, the cranes are operated electrically. Sonictinies thoy are handled by special operators who ride on them, but often by the workmen on the floor by means of hanging ropes arranged in a very ingenious ECONOMICS OF SHOPWOKK 367 manner, so as perfectly to control all the operations of the moving apparatus. Assuming that the work to be fabricated is miscellaneous bridgework, including movable spans, there are certain factors relating to major opera- tions and numerous others that pertain to specific parts of the work; and all of them, according to their effectiveness, influence more or less the general economics of the shopwork. Principal Economic Factors The most important factors covering all operations are light, heat, ven- tilation, space, handling of work, and management of men. The first four are, of course, dependent upon shop design; but if they did not receive proper consideration at the time the shop was planned, a study should be made in relation thereto; and any resulting proposed changes that promise to provide more economic fabrication should be inaugurated with the least possible delay. A relatively small amount of money saved every day will warrant the expenditure of a considerable sum. Similarly, it is truly an economic policy to scrap any tool, machine, or apparatus which can be replaced by one of decidedly greater efficiency, even if the one condemned be practically new. Economic results are what should be striven for, regardless of the difficulties and expenses that are inevitably inherent in the making of changes. It is this willingness of the American manufacturer to scrap all apparatus that can advantageously be replaced by something more effective, which has often given him the supremacy over his foreign competitors. It is the truly-up-to-date operator who proves most successful in his business. Light A well-lighted shop is necessary to enable the men to read the drawings readily, to decipher the marks on the metal, to find the material expedi- tiously, and to assemble it properly. Good light makes it possible to handle the metal rapidly, to inspect the work effectively, and to detect errors. It makes the shop safer and more pleasant to work in ; and it has a beneficial psychological effect upon the spirits of the men, because, when everything about the place is bright and cheerful, they not only operate to greater advantage but their brains function better, with the ultimate result of a largely increased output. By painting the interior of the shop throughout in white and keeping the paint comparatively clean through frequent washings and occasional renewal, the visibility of everything which it contains is greatly aug- mented, both in daylight and after dark, provided that a proper system of electric lighting is installed and maintained. It does not pay to retain old, dim lamps; hence a supply of fresh ones should be constantly on hand and installed whenever necessary. Moreover, powerful lamps should always 368 ECONOMICS OF BRIDGEWORK Chapter XXXVI be used, because the small amount of electric cm-rent saved by employing weak ones is a bagatelle in comparison with the benefits obtained through ample Hghting capacity. Heat While in the past some bridge shops have been run during the winter months without heat, the furnishing of a reasonable amount of it then will assuredly result in a sufficient increase of tonnage in a given period to pay for several times its cost. No man who is uncomfortably cold when housed can work to advantage, although it is true that out-of-doors laborers in winter often have to keep busy in order to maintain the necessary blood circulation. So much attention has been paid in late years to the condi- tions under which labor operates that it is probable that at the present time in most of the northern states it would be impossible to induce men to work during the winter months in an unheated shop. It is certain that such a shop would not attract the best character of labor; and efficient workmen are essential to the production of economic results. Ventilation In most bridge shops certain operations involve the production of considerable quantities of smoke and gas; and it is essential to arrange for their removal as rapidly as generated. The men cannot do satisfactory work unless they have a sufficient supply of fresh air; and the atmosphere they breathe should be free from gases and odors. Even though these be not actually harmful, their existence militates against economy; because, when such odors are perceptible, the workmen seem to get the impression that all of their ordinary ills and discomforts result therefrom. The importance of ventilation is greater where the design of the shop is such that overhead traveling cranes are operated by men located near the roof, as the heat, smoke, and gases accumulate there and make it impossible for these men to handle their work properly. Space The shop should be so designed that all of the work of any particular character can be done in a space by itself; and sufficient area should be provided for handling the maximum output of material for each oj^eration throughout the shop. For instance, if the space devoted to reaming be insufficient, the shop up to that point will become over-crowded with material ready for reaming, the shop beyond will not contain sufficient material, and the tonnage of the work going through will be limited because of the lack of space in this particular area. It is just as important to have enough space for each operation as it is to have sufficient total space. If it be found that there is a lack of space in certain areas, and if more space cannot be secured at these points, the trouble will have to be overcome as ECONOMICS OF SHOPWORK 369 much as possible by placing particularly efficient men in these areas and by making special efforts to prevent their work from being delayed by the other operations. Material must be ready for them as soon as they can handle it, and it must be taken away from them as soon as they have finished with it. This, of course, involves some increase in expense, but the additional tonnage secured in a given time will amply warrant the extra cost. Handling of Work The four factors of light, heat, ventilation, and space, all dependent upon shop design, have a direct bearing upon the proper planning of the passage of the work through the shop. A proper planning system is one of the most important factors in shop economics; and certainly it would not work out satisfactorily, unless there were sufficient hght, heat, ventila- tion, and space. Such a system should provide for the location and move- ment of the material from the time it is delivered at the shop until the time it is shipped therefrom. The Shop Manager should always be able to ascertain immediately in exactly what portion of the shop any particular material is located. Special stress should be laid upon the importance of having ample space for the raw materials as they are received from the mills. Some years ago this was neglected, resulting, in the case of large shops, in unsatisfactory operation, as it was impossible to locate and bring into the shop any particular material on short notice. There is an ideal -feature of economics in shop practice that should be adhered to when it is possible, viz., the continuous passage of all material in one direction through the shop. This is not always feasible; but it is the general experience that, whenever the principle is violated by carrying material backward, progress is interfered with, output is lessened, and unit cost of. production is increased. Management of Men The efficient management of the workmen is one of the most important factors in shop economics; because the maximum of output can only be attained by having each man in the shop labor to his limit of efficiency, all work together harmoniously, and all act in concert under a scientifically- laid-out programme. If workmen are to develop one hundred per cent of efficiency, or any- thing like that amount, they must be well fed, properly housed, com- fortable in their surroundings, happy, interested in their occupation, con- tented with their recompense, and amused in their leisure hours. Some of the broad-gauge managers of bridge shops are recognizing these require- ments, and are endeavoring to fulfil them in various ways. For instance, cafeterias are being established for the employees, where good, plain, whole- some food is served at actual cost; Hbraries and reading rooms are being 370 ECONOMICS OF BRIDGEWORK Chapter XXXVI provided; comfortable cottages with all modern improvements are being built and rented to the men at low rates; playgrounds are being inaugu- rated; and opportunities for large earnings are being afforded by the adoption of the system of piece-work. If a method of annual profit-sharing hke that advocated by the author and expounded in Chapter XXXIII were adopted, in addition to the other welfare methods just mentioned, most of the labor troubles in bridge shops would disappear. Great care should, however, be exercised in giving the employees unusual privileges or rewards, as these may do more harm than good if the employee does not feel that they are due to special effort and that he is receiving them as a payment for work that he has performed. There has recently been too much talk for rights without consideration of duties. Rights result only from the performance of duties. It is most important in the interest of true economy that the amount of each workman's compensation shaU be proportionate to the efficiency of his accomphshment. A flat scale of wages is absolutely destructive to progress, output, initiative, and economy. Safety Considerations Every effort made by both the management and the employees to increase the safety of the workmen is a step in the line of true economy. Each accident in the shop, no matter how trivial, causes immediately more or less delay, and often incapacitates one or more men for some time. Notwithstanding the fact that such men may be replaced quickly, their successors naturally, for a while at least, are not as efficient; hence progress is impeded by the failure of the new men to function effectively. Again, many of the injured men return to their work out of condition — some of them permanently so, for instance with the loss of a finger or an eye. Then there must be considered living expenses and doctor's bills during the enforced absence from work. Somebody has to pay these; and while in the end they are borne by society, they are carried primarily by the shop ; and that shop which is freest from accidents has the least expense on that account. Other things being equal, it can, therefore, secure the largest percentage of profit. Generally, too, the workman has to be com- pensated for his injury, which is another economic factor of importance. Possibly, insurance will cover this; but often the company has to pay it. Much might be said from the humanitarian point of view concerning the prevention of accidents; but this is a treatise on economics, not ethics. Viewed from every possible angle, it is in the line of true economy for the company to take every precaution to prevent accidents in the shop; for safety and efficiency are inseparable. To this end the responsibility should be laid upon one of its officers whose duty it would be to anticipate all possible accidents in the shop and take measures to prevent their occur- rence. This could b(^ accomplished in various ways, among which might be mentioned the following: ECONOMICS OF SHOPWORK 371 A. Properly guarding the running parts of all machinery. B. Frequent inspection of all machines of which the failure could injure anybody. C. Modification of machinery that is essentially dangerous in any particular. D. Posting of efficient warnings around the buildings, calling attention to possible dangers. E. Keeping the floors clean so that they will not become slippery. F. Prevention of excessive or injurious dust in the atmosphere of the shop. G. Occasional lectures to the workmen instructing them as to what they should do to avoid accidents. H. Distribution of pamphlets treating of important matters of safety, sanitation, hygiene, and like subjects. I. Having available at all times a surgeon to care for anyone who, in spite of all precautions, may be injured. Smoking* Smoking in the shop, for several good reasons, is an uneconomic practice and should never be permitted. In the first place, it causes danger from fire; in the second, it occupies a quite-considerable portion of employees' time that should be devoted to work; and in the third, no man's mind can act as keenly when his system is under the soporific influence of nicotine as it can when free from the effects of that narcotic. Very few first-class shops nowadays permit smoking on the premises. The restrictions against smoking apply with even more force in the drafting-room than they do in the shop; for, in addition to the objections just noted, it might pertinently be stated that the dropping of hot ashes from cigarettes onto tracing cloth is not specially conducive to economy. If a man must smoke, let him do it out of working hours and not upon the company's premises, unless there be provided a smoking room for use during the luncheon hour and after one's day's work is done. Anticipating Troubles All officials of the company should make it their business to try in every possible manner to anticipate and forestall accidents or occurrences of any kind tending to interfere with shop operations or to reduce efficiency, quality of workmanship, or output. Conferences of officials should be held from time to time for the purpose of discussing this and other matters relating to the general welfare of the works and the workmen. * Mr. Earle deems the author to be a bit drastic in his views on the uneconomics of smoking. 372 ECONOMICS OF BRIDGEWOKK Chapter XXXVI Standardization * There are few matters of such importance for efficiency and economics as that of standardization ; and it should apply not only to tools and prod- uct but also to the operations of the workmen. The motion-stud}^ expert has proved conclusively that everybody wastes a certain portion of his time and energy in all of his operations; hence it would be economic to make a study of all workmen's motions and indicate to them what they should do in order to correct at least the most glaring of such faults. This has alread}^ been tried; and the good results effected have been surprising. Probably the motion-study expert who secures the best results is the foreman who sees that the men learn how to do their work without loss of motion, and then treats them in such a manner as will make them wish to stay where they are. Stock Materials The amount of stock material that is kept on hand is one of the deter- mining factors in the size of space required. It is influenced by the char- acter of the work done, and is dependent upon whether a warehouse supply of material is promptly available. If quick shipments are to be made and high prices obtained for them, a considerable amount of stock material will have to be kept on hand ; and it should be stored under shelter so as to be protected from rusting. A day is coming, and it may not be far distant, when the purchaser of a bridge will insist that the structure shall be manu- factured of metal which has never been attacked seriously by rust or has * Concerning this clause and the next succeeding one, Mr. Earle has commented by letter as follows: I wish to comment somewhat on what you say under the above heading, in connec- tion with what 3'ou say under the heading of Stock Materials. The question of Standard- ization as relating to economy of shopwork is, of course, the smaller portion of the economy of Standardization ; for, so long as each engineer wishes his bridges built to his own specification and design, it would be uneconomical for the Shop to store steel under cover. It is, to my mind, absolutely undefensiblc for standard bridges of standard lengths to be built in accordance with the various specifications, as is now being done. Deck plate-girder spans, through [)Iatc-girdcr spans, and truss spans of two or three types can be built to standard specifications and standard loading and will give absolutely as good service on the New York Central R.R. as they will on the Pennsylvania R.R. or on the Chicago & Northwestern R.R., or any other railroad; and, as far as wc can tell at the present time, the life of a bridge under one good specification is the same as the life of a similar bridge under another good specification. If all such bridges were built in accord- ance with a standard design and sf)ecification, it might then be economical for the Bridge Shop to keej) material for su(!h structures under cover. The manufacturers would then know that it would be safe to do this; for, if they did not sell to one cus- tomer, they could sell to another. Incidentally, this would lie a great advantage to customers; because, if they should, want a bridge in a great hurry on account of a flood or other accident, it could undoubtedly be secured without delay from a shop having such a bridge in process of manufacture. ECONOMICS OF SHOPWORK 373 been stored or kept for any length of time in any place unprotected from the weather. Stock material should be ordered to such specifications as will permit of its employment in connection with the usual class of work going through the shop. Each metal section should be kept by itself; and the various lengths thereof should be stored in separate piles. The storage ground should be divided into various areas; and records should be kept of the location of the materials in these areas. It is only in this way that the Con- tracting Department would be warranted in promising early shipment, in order to secure orders at favorable prices. It is essential for the satis- factory and economical running of the shop that both stock materials and contract materials can be deHvered promptly to the machines as soon as it is decided to call for them. In the case of special material for contracts, just as soon as it is received from the mills it should be stored in the units in which it is later to be brought into the shop, the said units being the metal called for by a bill of material, or shown on a drawing, or indicated by some combination of these methods. A record should be kept of its location, so that, when the templets are completed and the shop is ready to take up the work, it can be delivered in complete units; and it should then be carried through the shop in such units. Too much stress can hardly be laid upon the desirabUity of bringing in material complete in units, as the lack of any portion thereof would hold up in the shop a large part of the balance of the material of this particular unit; and this material would clog up the shop and either pre- vent other material from going through or allow it to pass only at additional cost. Supply of Labor For several years past the supply of suitable labor for fabricating shops has been limited; and there is no reason to assume that there will soon be any improvement in this respect — in fact the evidence at the present time is to the effect that the difficulties will be aggravated rather than ameliorated; and this condition must receive due thought in considering shop economics. The character of the shop and the way in which the work goes through it have an important bearing upon the securing of a sufficient force of capable employees. It is of the utmost importance that a permanent force of well-trained workmen be estabhshed. Every legitimate effort should be made to retain the services of capable and efficient workmen, because the breaking in of each new man costs, in various ways, considerable money. There is an immense difference between both the quality and the quantity of the daily accomphshment of the trained workman and that of one who is not experi- enced. As one walks through a bridge shop, even on a short visit, by watching for a few minutes the men at work he can readily distin^ish between those who are experienced and those who are not; and when a new 374 ECONOMICS OF BRIDGEWORK shop is opened with imtraiQed workmen, it takes many months to bring it into any condition at all approaching the ideal. Tool Equipment A comparatively large expenditure is warranted for securing labor-sav- ing tools. Labor is a very undependable element; but the tools, if given proper attention, wiU take care of the work at all times. In the case of shops of equal capacity, the difficulties of running them successfully seem to increase about in proportion to the square of the number of men employed. Shop Floors The character of the shop floors has an influence on production, because it has an effect on the character of the labor that can be secured and also upon the amount of work that can be performed in a given time. The floors should be level, clean, in good repair, and not too hard. A wood- block floor seems to meet these conditions, as it can be kept clean and level, is not too hard, is long lived, and can be repaired quickly and economically. It is not cold, and, when kept clean, it is not shppery. Straightening Metal A certain amount of material as it comes from the mills is not sufficiently straight to be used in the condition in which it is received, if the result is to be a first-class product. Straightening by hammers is unsatisfactoiy and expensive, and it is prohibited by many specifications. The best results can be secured by the installation of straightening roUs for plates and angles and roUs or presses for channels and I-beams. Marking Metal The marking-off of the material is largely done by hand; and efficient appliances should, therefore, be provided for handling and holding the individual pieces. Jib-cranes or traveling wall-cranes are suitable for such manipulation. They should have either electric or quick air hoists, and should be operated from the floor. Overhead cranes should be pro- vided for delivering materials to the proper zone and for removing them therefrom. Proper skids should be furnished on which the material can be marked off and stored. Trimming and Cutting As trimming and cutting of metal in the condition in which it comes from the mill aie always required, the necessary space and tools should be provided for doing this work either before the material is marked off or before it is punched. Among the tools that might be mentioned are ECONOMICS OF SHOPWORK 375 angle, beam, and plate shears; coping machines for coping I-beams and channels; planers for trimming the edges of plates; planing or milling machines; and machines for ending stiff eners and chamfering them so as to fit the flange angles. Planing or chamfering machines can be designed with one head fixed and one movable, so as to permit the setting of the heads a given distance apart, whereby both ends of a nmnber of stiffeners can be chamfered at one setting, and all the duplicate pieces chamfered while the heads are a given distance apart. Punching In punching, the material has to be handled in individual pieces. Jib- cranes or traveling wall-cranes should, therefore, cover the tool area; and overhead cranes should be provided for transferring the material to and from the punches in quantities. As an alternative, facilities for trucking the said material in quantities might be provided. Punches, to as great an extent as possible, should be equipped with spacing-tables of some of the various standard designs; and, where practicable, the punching should be done by spacing machines. The cost of punching a given number of holes is reduced thereby, the marking-off of the material is eliminated, and, in most cases, the cost of templet-making is diminished. It is also possible to punch a larger number of holes within a given time; and the increase in capacity of the Punch Shop would make spacing-punches economical, even if the actual cost of doing the work were the same. In addition to this, as a rule, the work is more accurate, which condition militates for economy, in that the fitting-up is facilitated. It is probable that more small, labor-saving devices have been intro- duced in Punch Shops than in any other part of the fabricating plant — such, for instance, as electrically-operated gags, ball tables, punching through wooden or pasteboard templets, using a model and applying the principle of the pantagraph, etc. Drilling Many bridge specifications require metal of over a certain thickness to be drilled instead of punched; and often such drilling really proves to be more economical than the punching. The shop, therefore, that is going to handle heavy bridge work has to have, in addition to its punching equip- ment, a sufficient number of power drills to permit the drilling from the solid of a considerable tonnage of metal. If the shop is designed especially for this class of work, sufficient drills should be provided to handle from fifty to seventy-five per cent of the normal output of the shop.* * The author predicts that it will not be many years before all important steel bridgework will be drilled solid, and that the increased cost of so doing will amount practically to zero. 376 ECONOMICS or BRIDGEWORK Chapter XXXVI Storage of Punched Metal As it is not possible in a shop handling a large tonnage to punch or drill all of the material for a particular unit at the same time, sufficient space should be provided in the Punch Shop, or the Assembling Shop, or between them, for the storage of punched or drilled material, so that when the Assembling Shop is ready to start on the assembUng of a given unit, or any part thereof, the metal can be located and delivered to the assemblers as wanted. Assembling The planning system should also provide for the performance of second- ary operations, if necessary, before the dehvery of the material to the Assemblers. Angles, plates, etc., frequently have to be bent before or after punching, and sheared edges of plates have to be planed; and the assem- bUng work should not be held up by any of these operations. As the assemblers handle the material in mill sizes, they require cranes for the rapid manipulation and holding of same while assembling. These cranes should, preferably, be operated from the floor. Overhead cranes should be provided for handling the finished pieces. The assembling area should be equipped with level skids at such a height above the floor as to permit of accurate and rapid assembling. It is important that the skids be truly level, so that the material assembled thereon will be straight and out of wind. If girders are assembled in a vertical position, cast-iron bases, or some- thing similar, should be provided for holding them during the assembling. These bases should be of such a character that the bottom flanges of the girders can be readily clamped thereto, in order to prevent the girders from falling over. The tops of the bases should be at the same elevation ; and, if the girders are to be cambered, steel filling-pieces can be placed above the bases, so as to provide the camber desired.* Reaming Present-day specifications for bridgework provide, in the case of a large portion of the work, that the rivet holes shall be reamed after assembling. This requirement renders necessary the furnishing of a complete reaming equipment; and, in the end, economy will result if the reaming capacity is sufficient to take care of the entire output of the shop. Even though the specifications do not require it, economy will result from the reaming of all rivet holes after assembling. The reamers should be power-driven and capable of being forced up to the capacity of the drills. Level skids should be furnished in the reaming area on which the * The author dooms the cainberiiiff of phdo-girders to bo absohitcly unnecessary and, conscfjuently, uneconomic. ECONOMICS OF SHOPWORK 377 material can be reamed, and on which it can be stored so as to remain straight and out of wind. Overhead travehng cranes should be provided for conveying the material to and from the reamers. Riveting Rivets should be driven as much as possible by power machines; and machines of different types should be provided, in order to be able to drive the greatest number of rivets practicable. These machines should have ample power, because tight rivets should be secured throughout the work the first time they are driven, the expense of cutting out and redriving rivets being thereby reduced to a minimum. Portable riveting machines probably give the best results, as it is more economical to move a compara- tively light riveting machine than it is to shift a heavy piece of bridgework. Machines can be quickly handled and the rivets can be rapidly driven, if the machine is suspended from a wall-crane or a jib-crane. These cranes can be operated from the floor by one of the riveting gang. The bridge members can be transferred by travehng wall-cranes, overhead cranes, or trucks. Milling and Planing Certain members of trusses, columns, and sometimes even girders have to have their ends planed; and various machines have been built for this work, a rotary planer being generally the most economical. Milling machines, however, have been used. No matter which type of machine is employed, economy will result by having it furnished with two heads, one of which travels on the ways of the apparatus. This permits the heads to be set at a given distance apart, and both ends of the piece to be planed or milled at the same time, duplicate pieces being finished without re-setting the movable head. Boring Double-headed horizontal or vertical boring machines should be pro- vided with one head traveling on the ways of the machine, so that the pin holes can be bored at an exact distance apart. For duphcate parts there wUl be no need of re-setting the heads. Special Space All bridge members do not need to go through the same number of opera- tions in order to be completed ; and some provision should, consequently, be made for keeping material that requires only one or two operations (or special operations) out of the Main Shop. To this end a special space should be provided for the fabrication of shoes, cross-frames, laterals, small struts, and other miscellaneous pieces. 378 ECONOMICS OF BRIDGEWORK Chapter XXXVI Machine Shop For the fabrication of fixed spans not many machinB tools are required, the turning of pins, the planing of main members, shoes, and base plates, and the boring and drilling of holes being about the only machine opera- tions required. If, however, movable spans are to be manufactured, a small machine shop will effect an economy of operation. Such, a machine shop should be equipped with the following tools: Boring Mill, Grinding Machine, Lathe, Screw Cutter, Planing Machine, Slotting Machine. Foundry It is probable that an iron or steel foundry cannot be added to the equipment of the fabricating plant with economy, unless there is a market for general commercial work; because there are not enough castings required in bridgework to keep a foundry busy more than a very small portion of the time. Blacksmith Sho'p A Blacksmith Shop should be installed with hammers, presses, heating furnaces, etc. If the Shop is one of large capacity, there should be added a rivet-and-bolt-making plant with the necessary heating furnaces, continu- ous rivet-making machines, bolt machines, screw-cutting machines, and bins for the storage of rivets and bolts. Shop Assembling Bridge specifications in many cases provide that the members of riveted trusses shall be assembled at the shop, that the field holes shall be reamed while the trusses are so assembled, and that the members shall be match- marked before they arc taken apart. This ensures the proper matching of the holes when the work is subsequently erected. The shop, therefore, should have the necessary space and equipment for assembling such trusses. Generally, it is economical rather than the reverse to do such assembling and reaming; but, if there be a large number of duplicate spans, it is uneconomical. In such a case the field connections should be reamed to iron templets, so that the members will be interchangeable. The woi-k can •be done mu(;h more quickly in this way; and, if it be carefully performed, the results will always be satisfactory. If desired, one or two of the trusses can be assembled before any of them are shipped, in order to check the accuracy of the work. ECONOMICS OF SHOPWORK 379 If possible, the space for such assembling of trusses should be com- manded by overhead traveling cranes, and should be equipped with port- able power drills, both horizontal and vertical. These portable drills will be found of great value in the shop as a supplement to the regular drilling and reaming equipment. The top and bottom chords of the trusses, after planing, should be assembled in the shop, and the holes on one side of the sphce drilled from the soHd whilst the chords are thus assembled, using these portable drills. Painting For finishing and painting, ample space and proper handling facilities should be provided. At least a portion of the space (and the larger the better) should be covered, as all of this work cannot be done out of doors during the winter. While spraying machines have been used for painting, doing the work by hand seems to give more satisfactory results. Tracks Ample track facilities should be provided both for the bringing in of material to the shop and for shipping it out. Templet Shop For economy, the templet shop should be light, well heated, and furnished with benches at one level, and with tools for planing, cutting, and boring the templet lumber and for boring and shearing pasteboard for templets. The use of the latter material instead of lumber is in the line of true economy. Recapitulation To summarize — the main factors are light, heat, ventilation, space, and tools; and the Planning System should result in: Availability of material when desired. Short and continuous travel. Handling as few times as possible. Keeping of men busy. Tools of such character as to permit the securing of the proper grade of workmanship. Competent employees to maintain such a grade of work. CHAPTER XXXVII ECONOMICS OF BRIDGE ENGINEERING FIELDWORK The economics of fieldwork in bridge building may be summed up in the following instructions to the Resident Engineer: First. Start work ahead of the contractor so as to have all the triangu- lation finished and bench-marks estabhshed before he is ready to begin actual operations. Second. Employ as small a force as practicable for attending properly to all work, especially the inspection of materials and workmanship, and retain only truly competent, energetic men. If low-grade helpers are required occasionally, obtain them from the contractor, and be sure to pay him for their time, unless the specifications or contract provide that such labor shall be furnished free of charge, as is often the case. Third. See that the entire force is kept really busy at all times. This can be accomplished by laying out for each member thereof routine work for his spare moments. Fourth. Before any construction work is begun, lay out on paper an economic system for carrying on the field work from start to finish, and see thereafter that it is strictly followed. Should at any time any develop- ment occur that would render advisable a modification of the working schedule, the necessary changes therein should at once be made; and all interested parties should be notified in writing accordingly. Fifth. Never let any portion of the work drop behind, even for a single day; because field engineers are assumed to work longer hours than the staff of the designing office. Field engineers should live on the job, so as to be ready at aU hours to do unexpected work and to meet emergencies, consequently they have no cause for complaint when instructed to work overtime. Sixth. See that the home office is supplied strictly on time with the regular field reports, and send in special ones whenever such seem necessary or advisable. Seventh. Do the testing of cement far enough in advance of its use to make sure of its having the requisite strength; and if therc^ be any other materials to be inspected, keep the work of inspection well in advance of the demand. Eighth. As soon as materials are received at the site, see that they are che(;ked by the contractor at once, and report immediately to tlie home office any shortage discovcncnl, in oider that it may be made good before it can cause delay in the construction. See also that all material is unloaded 380 ECONOMICS OF BRIDGE-ENGINEERING FIELDWORK 381 quickly, even if the onus of paying for demurrage be upon the contractor, because it is economic to keep the railroad officials in good humor by return- ing their cars quickly, and because it does not take many unloaded cars to clutter up the small, temporary yards built specially for the job. Ninth. Give the contractor and his employees every aid that you can legitimately, short of assuming duties that are not your own — such as prep- aration of bills of materials, designs for plant, etc. By keeping the force in a good humor the work will be expedited, and economy for all concerned wiU result. Tenth. Make all monthly estimates promptly, starting in two or three days before the end of the month, if that be necessary to accomplish the purpose. Eleventh. For all unclassified work or so-called ''extras," be sure to give the contractor in advance written instructions to do the same, and keep on file copies of ail letters containing such directions. Twelfth. Keep your progress reports and charts up to date so that you may know at a glance what proportion of each class of work on the job is finished and what proportion remains to be done. Thirteenth. Remember at all times that the Resident Engineer is a confidential agent and not a principal, and be governed accordingly. While he has the right to discharge at any time any of his employees for just cause, he should keep the home office au courant with the character of the work of his assistants, in order that, if changes in the staff are to be made, the field work will not be disorganized thereby. Fourteenth. If practicable, the field property of the Engineers, such as instruments, tapes, testing apparatus, etc., should be insured against loss • by fire, theft, or the action of the elements. Sometimes this is impossible; but whether it is or not, every precaution should be taken to prevent such occurrences, not merely because of the pecuniary loss to the principals but also because of the delay to the fieldwork that would be likely to result. Fifteenth. Copy all important surveys from the field books into a survey-record as soon as made; and never let that record be taken into the field, for its loss might cause great inconvenience and expense. When loose- leaf books are used for records that might be called into a court of law, each page must be signed and dated by the writer thereof at the time he makes the record; and each such page must have a heading or title which will show beyond any doubt just what is recorded thereon and the source of the information. Sixteenth. Log books or diaries must be written up each day, whether there was any work done or not. Seventeenth. As a great many of the Resident Engineer's duties are of a semi-judicial character, all of his acts may at any time come under the review or inspection of a court of law ; hence he must always keep this in mind when making decisions or compiling records. The latter must be full, concise, and so made as to be admissible as evidence in a suit at law. 382 ECONOMICS OF BRIDGEWORK Chaptee XXXVII Eighteenth. All instruments for surveying or for testing materials, when not in use, must be kept in their cases or boxes in the Resident Engi- neer's office. No transits or levels should be left set up around derricks or machinery where there is danger of their being struck by the said machinery or by teams, unless someone is left to guard them. Nineteenth. The Resident Engineer must be careful not to abuse in any way the rather arbitrary power that is placed in his hands; but, on the other hand, he must not fail to act promptly in exercising the authority conferred on him, if it be necessary to do so in order to protect the interests of his client or those of his superiors. Twentieth. See that all materials are properly stored and kept in good condition until used in the construction; and make sure that the contractor takes every precaution to prevent injury to them from fire or flood, no matter whose property they may be. If practicable, they should be insured. Twenty-first. Make sure that no damage is done to structural steel or reinforcing bars through carelessness in handling or unloading. Twenty-second. See that all wooden paving-blocks are ricked up in compact piles and covered so as to prevent checking; and, as all creosoted timber is very inflammable, take every precaution against its being injured by fire. Twenty-third. Make sure that all cement is properly protected against the weather; and that no injured cement is allowed to remain on the job. Twenty-fourth. Take great care to avoid accident in the storage or use of explosives; and see that the proper charges are used. Twenty-fifth. Make sure that all falsework and forms — in respect to both design and quality of materials — are fit for the purpose to be served; and take the necessary steps to prevent unsightly bulges and offsets in concrete surfaces due to the yielding of forms. Twenty-sixth. In sinking cribs or caissons do not permit the contractor to allow them to get materially out of position or tipped; but check con- stantly for line, elevation, and verticality until all danger of the occurrence of such errors of any magnitude is past. Twenty-seventh. Look carefully to the building up of cribs and caissons; because, if they become badly warped or twisted, much needless expense and delay will be involved. Twenty-eighth. Watch carefully the depositing under water of all con- crete so as to make sure that it is not injured in the process of placing. The preceding instructions, of course, could readily be extended by entering more into detail, and it is true that the Resident Engineer should study and follow closely many other directions, both written and oral, given him by his superiors; but enough has already been said in this chapter to indicate the necessity for a proper application to fieldwork of the principles of economics, what the said principles are, and how they should be utilized. CHAPTER XXXVIII ECONOMICS OF BRIDGE-CONTRACTOr's GENERAL FIELDWORK The data for this chapter were furnished by Mr. H. K. Seltzer, C.E., of the Union Bridge and Construction Company, and, in years long gone by, one of the author's principal assistant engineers. As that Company is one of the most experienced and successful bridge-contracting firms in America, what Mr. Seltzer has to say about the economics of his specialty ought to be authoritative. The Contractor who has been awarded a contract naturally says to him- self — "I must do this work as quickly and as economically as practicable." He, therefore, gives thorough consideration to the problem of how this result can be brought about; and, while so doing, he should think not only of the profit he expects to make, but also of the fact that he must maintain his good reputation, and improve it, if possible. In order to complete the work promptly and economically, he should devote careful thought to the following subjects: 1. The Field Organization. 2. Plant. 3. Yards, Wharves, and Tracks. 4. Plans of Buildings and Plant. 5. Materials and Supplies. 6. General. 1. The Field Organization The man in active charge should have had previous experience, either as a superintendent or engineer of construction, in charge of similar work. It is not absolutely necessary that he should have managed work equally large or important; but he should certainly be a man of character and force. He may be known as Chief Engineer, Manager, General Superin- tendent, or Engineer of Construction. We shall assume that he is an engineer and that his company has designated him as "Engineer of Con- struction." He should have the following general assistants, if the size of the work warrant it, — these men to report to him directly: Assistant Engineer of Construction. General assistant to Engineer of Construction. In charge of field and office engineering work. Superintendent. In charge of all foremen, including the master me- chanic. The superintendent should have complete charge of work in field and should be a capable and reliable man. 383 384 ECONOMICS OF BRIDGEWORK Chapter XXXVIII Purchasing Agent. The making of all purchases should be placed in the hands of a competent man. Schedules of materials and supplies should be furnished to him by the office engineers, specifying when they will be required; and he should arrange his deUveries as nearly as possible in that order. Accountant or Auditor. In charge of all office work outside of the engineering department. He should have charge of bookkeepers, pay- masters, timekeepers, cost accountants, material checkers, storehouse men, and any other clerical help required. 2. Plant. The best plant obtainable should be provided in sufficient qaantity to permit of the rapid execution of the work with the smallest possible number of men. Hand, air, or electrical tools should be liberally provided. There should also be furnished spare equipment, such as an extra hoisting engine, an extra derrick, and an extra dredge-bucket. On large jobs of work these extra pieces of equipment are always needed because of breakdowns. A liberal supply of repair parts for engines, pumps, pneumatic tools, etc., should always be kept on hand. 3. Yards, Wharves, and Tracks. Sufficient ground should be obtained to provide storage room and space for the necessary operations. Existing wharves should be secured, when they can be had, and new ones built when necessary. A plan should be prepared showing the exact location of railroad tracks, storage grounds, buildings, and wharves. The arrangement, of course, will depend to a great degree on the ground and the river front available; and the cost and progress of the work will vary largely with the care and attention given to this subject. 4. Plans of Buildings and Plant. After it is known just what yard-room can be secured, and after a general ground-layout has been drafted, detailed plans of buildings, der- ricks, and other material-handling devices should be prepared; then the necessary bills of material should be made therefrom. These plans should include drawings of barges, pile-drivers, falsework, etc. — in fact of every- thing that must be built at the bridge site. While planning buildings and barges, it is well to give consideration to the fact that, after the completion of the job, buyers may be obtained in the vicinity, provided such constructions are so designed as to meet local con- ditions and requirements. 5. Materials and Supplies. Schedules of materials for both construction and permanent work should be made as quickly as possible, even though the contractor may have contracted for his materials bofoic bidcUng. It is important that no time be lost, in order that early shipments may be made; and, again, BRIDGE-CONTRACTORS GENERAL FIELDWORK 385 prices change so rapidly that those used in bidding may not hold in every case, especially if there be considerable delay. Materials should be ordered for shipment as nearly as possible in the order required. It frequently occurs that no special attention is given to this point; and, as a result, delay and unnecessary cost are involved. Contracts for fuel, oil, water, electricity, and supplies should be made immediately, whenever it appears to the contractor's advantage so to do. 6. General It pays well to have satisfied and loyal employees; and every effort should be made to provide and maintain such a force. Special care should be used in the selection of the skeleton organization, including the foreman; and these men and all other employees should be well paid, and given the best treatment possible. Where camps are necessary, they should be sani- tary; and good food should be provided at actual cost. It is well to prepare in advance a schedule of the progress of the work that it is intended to follow; and plans should be made accordingly so as to carry it out. Daily unit costs should be kept, when possible, in addition to the usual cost system; and the foremen and all others interested should be advised how well they are found to be doing, comparisons being drawn with other work of a similar nature. Nothing should be done by hand that can be accomplished with ma- chinery or power tools. In concluding this chapter, the author begs to make, for the benefit of progressive contractors, the following additional suggestion, based upon extended experience and close observation of bridge builders and their methods of operation: It is almost always consistent with true economy to push every piece of work to completion as rapidly as practicable, even if by so doing there should be involved additional expense (of course within the bounds of reason) for outfit and labor; because the time thus saved can generally be more advantageously devoted to another Job. CHAPTER XXXIX ECONOMICS OF CONCEETE MIXING In the mixing of concrete there arise many economic problems, most of which are apparently of such minor importance as not to be worthy of consideration. For small jobs of work this may be true enough, but on large ones, involving great yardage of concrete, every httle item of economy is well worth while. There are two main points of view from which this question may be considered — that of the contractor and that of the engineer — the latter, of course, acting for the best interests of his client. The contractor gen- erally is paid for concrete in place at so much per cubic yard; but there are often several unit prices arranged to cover varying conditions. Sometimes these conditions are variations in the composition of the mixture, but often they relate to the differing costs of placing and form work. Be this as it may, though, in ordinary specifications there is nothing to induce the con- tractor to try to produce the strongest and best concrete practicable. This is the duty of the engineer; and he accomplishes it by stating clearly in his specifications the qualities of all the materials employed, the compositions of the different classes of concrete, how the components thereof are to be mixed, how the fresh concrete is to be placed, and how the finished work is to be protected until the mass hardens and dries — also by carefully inspecting the materials for quality, the mixing, the placing, and the protection, so as to ensure that the specifications are fully comphed with. Ordinarily there are not many legitunate major ways in which the contractor may economize in his concrete-work, as he is confined mainly to purchasing the materials as cheaply as possible, doing the mixing economic- ally, and placing the mixture expeditiously ; but occasionally he is given an opportunity to economize on the quantity of cement by the engineer's having made it proportional to the volume of voids in the aggregate, and by being permitted to use one-man stones in the mass. There are, however, many minor ways in which the contractor may legitimately economize in the making of concrete, principally by the appli- cation of forethought in the receiving and storing of materials promptly; locating the bins in the most favorable places for expediting the work; csta))lishing the best practicable scheme for transportation from bins to mixers and from mixers to points of deposit; substituting machinery for man-power wherever it will facilitate the work and reduce cost; designing and building forms that are not too expensive, that can be placed and removed expeditiously, and that have some salvage value; and installing 3SG ECONOMICS OF CONCRETE MIXING 387 efficient and not-too-expensive apparatus for protecting the finished con- crete from injury by frost or heat. Doing all these things scientifically and systematically will often enable a contractor to make money out of a job on which otherwise there would have been a loss. Amongst the economic problems that arise in the manufacture of con- crete, the principal ones are the following: A. Best proportions of materials. B. Reduction of voids in the aggregate. C. Using a mixture of gravel and sand without screening. > D. Waterproofing. E. Increasing fluidity of mixture. F. Manner and time of mixing. G. Amount of mixing water. H. Use of large stones in mass. I. Vibration and jigging of newly placed concrete. J. Age of cement. K. Protection of fresh concrete. Each of these economic questions will be taken up in the above order and discussed in detail. Best Proportions of Materials Without knowing in advance the kinds and characteristics of the aggre- gates which the successful bidder will employ, it is impracticable for an engineer to specify the best possible proportions for concrete, hence he is. either compelled to name three or four standard mixtures or else to specify certain maximum limits of the materials in the aggregate and an amount of cement proportionate to the volume of voids therein. The principle to be adopted in specifying the proportions for concrete is to use a little more than enough cement to fill the voids in the sand and a little more than enough of the resulting mortar to fill the voids in the broken stone or gravel. If the mixing were perfect, there might not be good reason for these excesses of cement and mortar; but, of course, it never is. The author is satisfied with an excess of ten per cent for each case, or with an excess of ten per cent of cement above the volume of voids in the aggregate. The most common proportions specified are those given in the following table: TABLE 39a Ingredients Proportions Cement 1 2 3 1 2 4 1 21 5 1 3 5 1 3 6 Sand. Broken stone or gravel. . . 388 ECONOMICS OF BRIDGEWORK Chapter XXXIX The mixture of 1 : 3 : 5 used to be the standard for concrete in large masses placed in the dry, but there are certain sands of such uniform grain- size that one portion of cement to three of sand will not fill all the voids therein; and, although the mortar produced will be ample in amount to fill all the voids in the stone or gravel, the mass resulting will be permeable by water, and, therefore, not first-class concrete. The proportion of 1 : 2| : 5 is better than that of 1:3:5, because the amount of cement is always more than enough to fill the voids in the sand, and that of the mortar is more than enough to fill the voids in the stone or gravel. It is a perfectly safe mixture but not an economic one. It is being rather widely specified today for mass concrete placed in the dry; and for small jobs it is a good one to adopt therefor. The proportion of 1 : 2 : 4 is the common one for reinforced-concrete; and the stone or gravel should not be very coarse, because otherwise the concrete would not flow properly between the reinforcing bars, and voids might result. In view of the importance of having reinforced-concrete as perfect as possible, and of the fact that the mortar should take a firm grip on the reinforcing bars, it is not advisable to use for this purpose any concrete less rich in cement than this mixture. The proportion of 1:2:3 with fine broken stone or gravel is the author's standard for concrete to be deposited through water by tremie or trip-bucket. It contains an excess of cement to provide for the contin- gency that, in spite of all precautions, there may be a slight flow of water through some portion of the concrete. The author has often had occasion to examine concrete of this mixture placed through water, and has invariably found it to be perfectly satisfactory, in fact, just as good as the less-rich concrete placed in the dry. It has been stated by good authority that this proportion makes much better concrete for reinforced work than does the standard proportion of 1 : 2 : 4; hence it might prove economic to adopt the richer mixture therefor, but it would first be necessary to educate the profession to the advisability of the innovation. The only excuse for adopting in a specification a general clause for a 1:3:6 mixture is to save expense in a structure where the total cost has to be hold down to an absolute minimum, in order to meet a limited appro- priation ; and then it should usually be confined to locations below ground where no frost can reach. It would be legitimate to adopt it for large anchorages where great mass is required, in which case it might have to be faced with richer concrete and employed only in locahties where the climate is mild. But when special care is taken in the grading of the aggregate, a 1:3:0 proportion can safely 1)0 employed, because in gradini santl the 1 to 3 proportion will fill all voids in the mortar, and the latter will fill all voids in the stone, thus producing satisfactory concrete, providing, of course, that the mixing be thoroughly done. The 1:3:6 mixture does not always make good concrete, and the author would hesitate a long time before deciding to adopt it on any of ECONOMICS OF CONCRETE MIXING 389 his constructions. He did once use it for some below-ground work on a bridge in Southern CaHfornia, in which every legitimate effort had to be made to keep the total cost of structure within a limit of $200,000. There proved to be a margin of less than $500 when the bridge was finally com- pleted and turned over to the owners. Concretes as poor as 1 : 4 : 8 or even 1 : 6 : 10 have been used in times past in large mass-work, in order to reduce the cost of construction; but, in the author's opinion, such mixtures are not legitimate. Some tests on plain concrete beams by Wm. B. Fuller, Esq., gave on the average the moduli of rupture indicated in the following table: TABLE 396 Proportions by Proportions by Modulus of Weights of Cement, Volume of Cement, Rupture. (Lbs. Sand, and Stone Sand, and Stone per Sq. In.) Average 1:2:4 1 : 2.34 : 4.12 439 2 5 2.34 5.17 380 3 5 3.51 5.17 285 3 6 3.51 6.21 226 4 8 4.68 8.25 157 6 10 7.02 10.34 89 This table gives a very clear idea of the relative strengths of concrete of varying richnesses; and it is evident therefrom that the last two mixtures are too poor to warrant use in any first-class construction, also that 1 : 2| : 5 concrete is better than 1 : 3| : 5 concrete in the ratio of 1.33. By interpolation it may be concluded that it is probably better than 1:3:5 concrete in the ratio of about 1.2. Comparing the 1 : 2| : 5 mixture with the 1:3:6 one, the ratio of strengths would be about 1.5. Reduction of Voids in the Aggregate Whenevesr there is a large amount of concreting to be done on a job, it will prove to be economical to study carefully the percentage of voids in the aggregate of broken stone and sand (or of gravel and sand), and to experi- ment in order to determine what mixture of broken stone and gravel, or of several sizes of broken stone, with the proper amount of sand in each case, will reduce the said percentage of voids to a minimum. If then this mixed aggregate be adopted, and if the amount of cement is never less than one and a tenth times the volume of voids, the resulting product will be first- class and satisfactory to all concerned, provided, of course, that only proper materials be employed and that the mixing be thorough. As a matter of precaution, however, against carelessness or error on the part of the tester of voids, the author's specifications require that, for aggre- gates in which all the materials are measured separately before mixing, 390 ECONOMICS OF BEIDGEWORK Chapter XXXIX there shall be used not less than 420 lbs. of cement per cubic yard of finished concrete, excluding, of course, the space occupied by any one-man stones that it may contain. Using a Mixture of Gravel and Sand without Screening. If there be available and located convenient!}^ for the work a large body of clean, mixed gravel and sand, it may prove economical to use it without screening in one of two ways, viz. : First. By constantly making tests and finding what amount of sand or of gravel should be added to the natural mixture in order to secure the correct proportions, sifting out a supply of the material required, stoi'ing it close at hand for use, and combining it with the said natural mixture ; and Second. By using the natural mixture directly as it comes from the pit. In either case the rule previously given for a volume of cement equal to at least one and one-tenth times that of the voids should be followed; and as a matter of precaution, the amount per cubic yard of finished concrete (excluding all embedded one-man stones) should be 460 lbs. for the first- mentioned of these two methods and 500 lbs. for the second. This is in accordance with the author's standard specifications. Whether it is most economic to separate all the ingredients of the natural mixture and re-mix in the desired proportions, to add sand or gravel to the natural mixture, or to use the pit run, can-only be determined for each case as it arises by some very careful computing, based upon the governing prices of labor and materials. In fact it might be necessary to make some actual experiments. If labor were very high and the price of cement dehvered at site were reasonably low, it would probably be most economical to use 80 lbs. extra of cement per cubic yard of concrete and employ the pit run; but if cement were very expensive and labor cheap, it would be most economical to sift the natural mixture and remix. Whether adding either sand or gravel to the natural mixture, in order to bring it to best proportions is economical, will depend upon whether the screening out and incorporating of the additional material and the occa- sional testing of the pit run will cost less than the 40 lbs. of cement saved per cubic yard of finished concrete. Waterproofing In certain places it is necessary that the construction should be abso- lutely waterproof; and whether accomplishing this is to be done by adding some foreign ingredient to the cement or by inserting a layer of burlaj:) or other similar material covered with pitch or asphaltum applied hot is a pi()})l('ni in economics that has to be solved for each case by some close figuring. There are on the market several patented materials to add to concrete for waterproofing, the manufacturer of each of which claims it to be the best possible for the purpose; but, as far as the author knows, there ECONOMICS or CONCRETE MIXING 391 is nothing better than the addition of hydrated lime to the cement to the amount of about ten per cent of its volume. In any case where the condi- tion of impermeability is paramount, it would be well to adopt both of these expedients, irrespective of cost; and the combined expedients, if success- ful, would effect a true economy. The question of the economics of water- proofing concrete is treated at length in Chapter XLIII. Increasing Fluidity of Mixture The addition to the cement of not more than ten per cent of its volume of hydrated lime not only tends to make the finished work waterproof, but also adds greatly to the fluidity of the mixture, thus facihtating the placing of it around the reinforcing bars. Certain reliable tests have shown that the addition of lime up to fifteen per cent of the volume of cement really slightly increases the tensile strength after some three weeks; and as the addition of lime does not add materially to the expense of the concrete, it is a matter of true economy to employ it. The beneficial effect of hydrated lime is partly due to the fact that it permits a reduction in the amount of mixing water without lessening the plasticity of the mixture. Manner and Time of Mixing Almost all concrete nowadays is mixed by machinery, and preferably in batch mixers, although .some continuous mixers have been known to give good results. The strength of the concrete is augmented as the time of mixing is increased; hence it is an economic problem for the engineer, hut not for the contractor, to determine what is the best time to adopt for mixing each batch. If the time be made too short, the attainable strength and quality of the concrete are not developed; while if it be made too long, the output per mixer is reduced and the cost per cubic yard of the finished work is increased. As the contractor is paid so much per cubic yard for concrete in place, it is evident that he always loses instead of gains by increasing the time of mixing, and that the owner, up to a certain point, is a gainer by such an increase, after which he is a loser. In respect to what that Umit is, most engineers differ. Contractors would like to make it thirty seconds, but are willing to concede a fuU minute. The author, how- ever, would set a minimum of two minutes. As loading and unloading the mixer require for the two operations, on an average, about 45 seconds, and as the time given to actual mixing is about the same, the total time needed per batch is one and a half minutes, but when the time of rotating the mixer is increased to two minutes, the total time per batch is two minutes and forty-five seconds, hence the output per mixer would be nearly halved. Nevertheless, the author beheves that doubhng the ordinary time of mixing will result in true economy for the owner. The authorities recog- nize that it is far better, when a truly-first-class job is required, to employ more mkers, even at a higher first-cost for equipment, and work them on a 392 ECONOMICS OF BRIDGE WORK Chapter XXXIX longer schedule, than it is to try with each single mixer to produce the greatest possible yardage in the least practicable time. Greater care and increased expense in mixing and placing are in the hne of true economy; for they produce a stronger concrete and, therefore, justify the use of higher unit stresses and a consequent reduction in the concrete sections. This question is of especial importance for concrete slabs on long-span steel-bridges, and in long-span concrete-bridges. Amount of Mixing Water It has been the general practice to use very wet mixes, especially for reinforced-concrete. From the construction standpoint this is economical, as it reduces considerably the cost of handling and placing. Recent investi- gation, however, has shown that an excess of water reduces the strength of the concrete very materially, and makes the concrete porous; it also tends to cause segregation of the materials. The use of an excess of water is, therefore, false economy. The new American Railway Engineering Asso- ciation Specification for Plain and Reinforced-Concrete contains the following requirement: The quantity of water used in mLxing shall be the least amount that will produce a plastic or workable mixture which can be worked into the forms and around the rein- forcement. Under no circumstances shall the consistencj'^ of the concrete be such as to permit a separation of the coarse aggregate from the mortar in handling. An excess of water will not be permitted, as it seriously affects the strength of the concrete; and any batch containing such an excess will be rejected. Use of Large Stones in the Mass When the contractor is permitted, under certain restrictions, to place one-man stones in the concrete in order to save mortar, he usually thinks he has a "soft snap," but sometimes this is not the case; because, in addition to their having to be carried to the site, they must be thoroughly cleaned and wetted before being placed. This placing when properly performed takes time, and is done by man power — not by machinery. Again, such one- man stones are generally boulders taken from the river bed, where they are often found covered with moss and slime, all of which has to be carefully removed. In the old days when labor was cheap and cement expensive, these one-man stones were looked upon as plums in the pudding, but today the same volume of straight, machine-made concrete will often prove less costly than the said "plums." In case, however, there is old stone masonry to disposer of, it will generally be found cheaper to use it as one-man stone in the concrete rather than to haul it away. Vibration and Jigging of Freshly-made Concrete During the past year there has been considerable talk about the bene- fits to be derived by fresh concrete through vibration and jigging; but the ECONOMICS OF CONCRETE MIXING 393 truth is that, while such treatment sometimes augments the strength, it often has the opposite effect. From the resume of an able paper by Prof. Duff A. Abrams entitled ' 'Effect of Vibration, Jigging, and Pressure on Fresh Concrete" the author extracts the following: The indications of the vibration and jigging tests should not be misinterpreted. The tests show that, after the concrete is properhj placed, these methods of treatment do no good, and may be harmful, if too severe or too long continued. However, there can be no doubt of the value of such methods for getting concrete into place in intricate forms and around reinforcing bars. The tests are of value in showing that this is the only desirable function of such treatments. The tests show that, with jigging, high strength may be secured with drier mixes .than would otherwise be feasible. It is a matter of common experience that concrete of drier consistency (and consequently higher strength) can be placed by means of jig- ging or vibration than would be possible by the usual methods. It is clear from these tests that if tamping, vibration, or pressure on fresh concrete is to be effective in increasing its strength three factors must be kept in mind. (1) We must take advantage of the fact that with these methods the concrete can be placed and finished drier than with ordinary methods. (2) Excess water which is brought to the surface must be removed. (3) We must take advantage of the fact that aggregate of a coarser grading may be used when such methods are employed than would be practicable otherwise. The advantages to be gained under (3) are due to the fact that, up to a certain point, a plastic mix can be secured with a smaller quantity of water, if the aggregate is as coarse as practicable. Unless these precautions are taken, tamping and vibration are of doubtful value. Age of Cement Prof. Abrams ha,s lately proved that the ultimate strength of concrete in compression is a function of the age of the cement at time of mixing, the fresher it is the greater the strength. This is at variance with the idea which governed previously, viz., that cement is better for a httle aging; but we are learning these days that many of our old ideas about cement and concrete were incorrect. In Bulletin No. 6 of the Structural Materials Research Laboratory of Lewis Institute, Prof. Abrams presents a number of diagrams showing the percentages of loss of strength in compression for concrete by using cement that had been stored from two to twenty-four months, as compared with that manufactured with perfectly fresh cement; and the amounts thereof are surprising. They average fifteen per cent for two months and fifty-five per cent for twenty-four months, with almost proportionate percentages for intermediate periods. However, the loss is not quite as bad as these figures would show, because the experiments prove that the concrete tends to recover its strength with age. For instance, when two-months-old cement is employed, the loss is nineteen per cent at one month and only eleven per cent at two years; and when two-year-old cement is used the loss is fifty-six per cent at one month and only forty-two per cent at one year. 394 ECONOMICS OF BRIDGEWOKK Chapter XXXIX The large amounts of these losses indicate clearly the desirability (from the standpoint of the strength of the finished product) of using cement as soon after grinding as is practicable. It must not be forgotten, however, that cement which has had no aging is hkely to be deficient in regard to soundness; so that its testing in respect to this requirement should be extremely thorough. The author for many years has insisted upon twenty- eight day tests on cement whenever that arrangement would not delay the progress of the work; but on the strength of Prof. Abrams' findings, he would now be willing to accept on seven-day tests any standard cement with which he is acquainted. Again, the author has sometimes made arrangements for testing and storing large quantities of cement at the manufactory, so as to have it available when needed ; but he may now be obliged to forego this practice. Prof. Abrams' experiments were made on sacked cement; and he intends dupHcating them upon cement shipped in bulk. Possibly the result of the new tests will show that keeping the cement in large masses will postpone somewhat the sudden drop in strength of concrete which occurs with cement two months old. It would be interesting to learn what the loss is on cement one month old; and it is to be hoped that Prof. Abrams will add to the value of his very useful experiments by settling this point. Protection of Fresh Concrete The protection of fresh concrete is an economic matter, as far as the con- tractor is concerned, because, according to all properly drawn specifications, he will have to make good at his own expense all damage done to the concrete through excessive cold or heat, or any other cause, before the final acceptance of the finished construction. It is also a matter of economy to the owner, because if the concrete is at all damaged, all the repairing that the contractor may do, short of entire removal and rebuilding, will fail to make the job as good and satisfactory as it would have been, had no such misfortune occurred. General Remarks From the point of view of both the engineer and his client, it is truly economic invariably to obtain concrete that is first-class in ever}'^ particu- lar — strong, solid, smooth, and hard — no matter how much it may cost; because failure of any kind in a reinforced-concrcte structure is likely to be both serious and expensive. Many large bridges of that type, which were constructed under contracts secured through competitive bidding, show after a few years signs of disintegration. The ultimate result of such work is that the structure sooner or later will require cither extensive repairs or entire rebuilding. The causes of such failures may be attributed to objec- tionable methods used by contractors in order to cheapen the cost of han- ECONOMICS OF CONCRETE MIXING 395 dling and depositing the concrete — such as chuting it long distances, using gravity mixers, allowing insufficient time for mixing, putting too much water in the mixture so as to avoid most of the expense of tamping and working the aggregate back from the face of the forms, permitting the employment of too large pieces of broken stone which fail to pass between the reinforcing bars, laying concrete in freezing weather, and placing concrete under water when there are available other methods which would permit depositing it in the air at a httle greater cost. At the time when the " Final Report of the Joint Committee on Concrete and Reinforced-Concrete" was presented, the above condition prevailed, but since then much important research work on concrete manufacture has been done, and there are now several publications which give valuable data and point the way to better concrete structures — notably the records of the elaborate series of experiments made by Prof. Duff A. Abrams. But as this treatise is intended to cover solely the field of economics and not that of general engineering practice, the reader is referred for further data on the manufacture of proper concrete to the well-known "Report" before mentioned; the "Transactions" of the American Railway Engineering Asso- ciation, the American Society for Testing Materials, and the American Society of Civil Engineers; and the ''Bulletin" of the Structural-Materials Research-Laboratory of the Lewis Institute. The author is indebted for a number of valuable suggestions on concrete manufacture to his friend, J. J. Yates, Mem. Am. Soc. C. E., Bridge Engi- neer of the Central Railroad Company of New Jersey, and Chairman of the Committee on Masonry of the American Railway Engineering Asso- ciation. CHAPTER XL ECONOMICS OF ERECTION The data for this chapter were furnished by the author's old friend, Frank W. Skinner, Mem. Am. Soc. C.E., who, for a number of years, made a special study of bridge erection in all its details, and gave the results of his findings in numerous lectures to engineering students of the leading uni- versities and technical schools of this country. Much of the valuable material that he collected was published in Engineering Record, of which paper for a long time he was the chief editor and leading spirit. The author feels that he is exceedingly fortunate in obtaining for the writing of this chapter the assistance of an eminent engineer who has made such a thorough study of bridge erection in aU its ramifications. There are very few engineers who are fitted by both experience and temperament to dis- course scientifically and practically concerning the essentially specialized subject of the economics of erection; and of these there is probably not one who possesses such a grasp thereof as does Mr. Skinner. What follows is given as closely as practicable in his own diction. The erection of an important bridge is a function first of the design, second of the location, and third of the available equipment; and its eco- nomics are directly related to these fundamentals, variations in which materially influence the total cost of erection of spans of the same length, the same carrying capacity, and the same type. The recognition of these facts has been such that, in this country, the art of bridge erection, particu- larly of steel spans, has been highly specialized — to an amount comparable with that of the fabrication of bridge superstructures in great shops fitted with costly tools and used almost exclusively for this single purpose. It has resulted in the development of a clearly-defined, standard practice and the perfection of a number of methods for securing essentially the same effects under different conditions and with different appliances arranged to secure the maximum safety and rapidity with the mininunn total cost. These methods, and the special equipments that have been devised for them, make it possible for a given structure to be handled in several radically-different ways, which may either show in some cases compara- tively-uniform 'results, or, generally, will indicate a decided advantage for one method over all the rest. The physical and mechanical combinations can be readily analyzed so as to give a limited number of principal cases that will here be classified 396 ECONOMICS OF ERECTION 397 for the general and comparative economics, so that, by inteUigent develop- ment and modification, they will cover the field within the limits of justi- fiable construction. The subjects considered are divided on broad lines into steel and concrete; long, medium, and short spans; and high and low structures. Steel Bridges As far as possible all items of fabrication should be completed at the bridge shop, so as to reduce the amount of assembling, fitting, and riveting in the field to a minimum. No work should be done at the site which can be performed at the shop; and no v/ork should be done on the structure itself that can be performed ashore upon the separate or combined pieces before erection. Standard plant and equipment should be used ; the largest possible proportion of work should be done by machinery and power; and the most skilful and experienced labor available should be employed in conformity with the equation of the different costs to a minimum for the completed work, including salvage, rental of plant, cost of transportation, installation and removal of plant, and the greater or less importance of extra speed (as in case of danger from floods), always considering the fun- damental requirements for absolute safety and the excellence of the fin- ished work. It is assumed that the methods, plant, equipment, and service best adapted to the type of structure and the given conditions are available, and erection with them wiU be considered the economic method; but this decision, of course, is subject to modification when the problem is compli- cated by artificial conditions or by sudden emergencies that make changes of details, methods, or equipment safer or more practicable, as, for instance, when labor troubles, difficult transportation, scarcity of materials, or acci- dental physical developments make the original preparation susceptible to delays and to important changes of conditions that may have a vital influence on erection operations; and radical changes in the original programme are sometimes necessary, in order to prevent large increases over the proper estiiiated cost. Girder Spans These are plate girders or riveted trusses of such dimensions that they can be erected complete as units, usually not exceeding 50 or 60 tons in weight, 100 feet in length, and 15 feet in depth. Even these Hmits are likely to be excessive for transportation by rail from the fabricating shop, the size generally being limited by bridge and tunnel clearances and track curvature, and the weight by twice the capacity of each of the available cars. If the girders can be shipped entirely by water, the limits for trans- portation are very greatly increased ; and under special circumstances they 398 ECONOMICS OF BRIDGEWORK CkAPTER XL may be equally extended for erection. Ordinarily the latter is a very simple process, effected by one or by two derrick cars or wrecking cars that unload, transport, and erect the girders in position in single or successive operations at a direct cost of as httle in pre-war times as $1.00 per ton. Derrick cars or their equivalent are not always available in remote locahties, and are not generally possessed, except by raih-oad companies, bridge companies, and important contractors. In their absence the girders can be handled, usually less advantageously, by derricks, gin-poles, and various combinations of jacking, blocking, rolling, and other operations that may be devised, modified, and combined according to the experience and ingenuity of the erector; and although theoretically they are more expensive and less efficient, they may often be more advantageous than the provision of high-class equipment under disadvantageous conditions. Viaduct Erection Viaducts generally consist of two or more lines of plate or lattice girders from 30 to 100 feet long on towers up to 100 feet high, although these dimen- sions have been considerably exceeded in infrequent cases. The ideal method of erection is by means of a derrick traveler, sometimes called a mule, installed at grade at one end of the viaduct and having a reach long enough to erect one tower and one connecting span in advance; after which it moves forward on the completed portion of the structure, erecting panel after panel as it proceeds. Such travelers have at least two main booms of great length and one or more auxiliary booms for hoisting, swinging, and placing the steel that may be delivered either at grade or on the surface of the ground. With a large number of duplicate heavy spans, such as occur in elevated railroad construction, this class of metalwork can be erected with great rapidity, a record of 1,000 lineal feet of double-track structure per day having been made in Brooklyn with one traveler and crew, independent of the preliminary distribution of steel and the subsequent field riveting. Where the girders have been too long or too heavy, or the towers too far apart for erection with a boom of practicable length, cantilever travelers have been successfully employed. They have been of different types, usually having an elevated horizontal boom overhanging the wheel base by the length of one tower span and one connecting span, and equipped with trolley hoists for unloading material from cars on the tracks in the rear and transferring it to the required position in advance for assembHng in the structure. In a few cases where there has been a great length of viaduct of sub- stantially uniform height above the surface of the levi^l gromid, the struc- ture has been erected by a strident gantry traveller, moving on a surface track and provided with several sets of hoisting tackles to handle from the ground (where they were distributed) tlu^ span and tower members. ECONOMICS OF ERECTION 399 Medium Spans Medium spans up to 300 or 400 feet long, and including some short spans, when for any reason it is impracticable to handle the trusses as com- plete units, are generally, in the case of new work, best erected on ordinary framed wooden falsework by means of one or two derrick cars. When there are pile foundations which can be placed in advance, the derrick car can rapidly put in the framed-falsework bents; after which two derrick cars, one at each end of the span, if two are available, can place the floor system, assemble the lower chords, erect the web members on them, and finish the erection by placing the top chords, top laterals, and sway bracing as the cars retreat from the center to the ends of the span. For heavy structures where the top chords involve too great a load for a pair of derrick cars, or where locomotive cranes are used instead, they can be supplemented advantageously by a simple gantry traveler to handle the heaviest members. It is entirely practicable to execute the erection wholly with the gantry traveler; but that traveler is costly to construct, difficult to transport from job to job, and rot as rapid or economical as derrick cars when the latter are available. Alternative Methods If the elevation of the span is exceedingly high above the water; if there is great danger from ice or floods; if the bottom is very treacherous or difficult; if the current is too fierce; or if the space underneath the span must not be obstructed by falsework (as when it is required to be left open for navigation or for heavy city or railroad traffic beneath), falsework becomes too dangerous or expensive or is wholly inadmissible, and some other system of erection must be devised. The most common method is by cantilever erection from each end of the- span, the truss members being made heavier or temporarily reinforced until the center-panel connections are made and the structure is trans- formed into a simple, self-supporting span. This method involves either the provision of special anchorages and counterweights or the erection of alternate spans in advance so that they may serve as anchorages. Canti- lever erection is always objectionable when it can be avoided, because it is much slower and more costly than falsework erection, and as there is greater danger of injury to the uncompleted structure by sudden storms or from various accidents than there is when falsework is used. Sometimes falsework of various types can be provided eccentric from the alignment of the bridge, and the permanent span may be erected on it by the ordinary method — then, when complete, moved transversely to the required position and permanently seated on the substructure. The method of protrusion is occasionally employed abroad and has infre- quently been adopted in America. When it is used, the span is erected 400 ECONOMICS OF BRIDGEWORK Chapter XL complete at one end of the bridge and as nearly as possible at the requu-ed level, the rear end is counterweighted, and (especially if there is. only a single span) the forward end is extended by a temporary pilot truss, when such extension is necessary. Each span is pushed forward longitudinally on roUers until the forward end or extension takes roller bearing on the next pier, so as to support it during the farther advance until the span comes to position and is lowered to bearing. If several spans are erected in the same way, they are temporarily connected to form a continuous-girder structure during protrusion. Where a nmnber of spans of substantially uniform and moderate lengths are constructed in one bridge, they have, under certain circumstances, been erected on a platform suspended from a temporary, overhead, movable span that travels from pier to pier as the work progresses. Where the ground under the bridge is accessible, unobstructed, and com- paratively level, and when materials can be delivered there, it may be possible, as has occurred in some cases, to distribute the steel in advance at low level, erect the spans there complete in the proper alignment, and raise them to required position and elevation as the piers are built up. Considerable use has been made of the floating method whereby the spans, having been erected in the usual manner on shore or on falsework built in comparatively shallow and sheltered waters, have been transferred to the decks of scows, towed to position between the piers, and aligned with their seats on the latter, usually at low-level elevation, and lowered to place by the use of water ballast or tidal fluctuations or both. In very difficult and unusual conditions, as in some mountain railroads, temporary suspension spans have been built, the permanent spans erected on them,. and the suspension spans removed. The above methods and their combinations, variations, and -modifica- tions have all been successfully used on different occasions; and together they cover the principal features of ordinary erection for medium, long, and short spans. Any one of them under special conditions may become the economic method for erection in that case ; but where it is practicable, the method of erection on ordinary falsework with a derrick car or traveler is likely to be most desirable and economic. Long Spans Up to about 700 feet in length and 150 feet in clear height, spans have been erected on framcd-timber falsework, which, of course, for such extreme dimensions becomes very costly, but permits more rapid and satisfactory assembling of the span than do the other methods, thus making presump- tion of economic desirability for this method when it can be used. The very fact that conditions require spans of more than 400 feet is quite likely to indicate deep water, bad bottom, swift current, great height, or wide, unobstructed openings between the piers that will make falsework impracticable. ECONOMICS OF ERECTION 401 In such cases, as in medium spans, the most common solution is erec- tion by the cantilever method, generally counterbalancing the cantilever arms from previously-completed portions of the permanent structure, building both cantilevers of the same spans simultaneously, and connecting their extremities by an independent suspended span designed to resist cantilever stresses developed by erection and to function subsequently as a simple span. Cantilever spans have been erected up to a length of 1,800 feet with results which indicate that the same method can be extended to lengths several hundred feet greater. Serious consideration has been given to the practicability of constructing cantilever spans up to 3,000 foet in length, which length approaches the present limit set by the strength of materials; and such a detailed design would, of course, involve the development of complete cantilever-erection plant. In this case it is probable that the assisted cantilever method or some modification of it, such as has already been adopted in some large cantilever spans, would be employed, whereby temporary supports would be placed under the cantilevers between the permanent piers, thus greatly reducing the erection stresses. The length and weight of the members of the suspended trusses in a cantilever span necessitate their erection by a heavy traveler, and, if accomplished by the cantilever method, produce a great increase of the stresses developed by the erection of the cantilever arms proper. In order to avoid these stresses, and for other reasons, the suspended span has in some instances been erected complete at a low level, towed to position under the ends of the finished cantilever arms, hoisted up, and connected. In another case of a long-span cantilever, the ends of the cantilever arms were connected by a light, temporary suspension bridge on which the permanent suspended span was erected. The difference in local conditions, type, and other features may make any one of these methods the most economic one for the given case, so that for an extremely large structure, all of them wiU probably have to be analyzed for the final comparative determination. Suspension Beidges Short-span and temporary suspension bridges may be designed with main cables, each composed of one or more twisted wire ropes extending continuously from anchorage to anchorage, that can be dehvered complete at the site, and, with ordinary appliances, pulled across the river from tower to tower and from tower to anchorage, secured in place, and adjusted, after which the erection fron^ them of the remainder of the superstructure is comparatively simple and easy. Generally this is the most economic method. For all long-span suspension bridges, the universal method of erection has been the preliminary construction of falsework suspension bridges, 402 ECONOMICS OF BRIDGEWORK Chapter XL erected as described for short-span and medium suspension bridges, and their use as suspended falsework for the construction of the main cables built up from straight wires spliced to form continuous lines reaching around and around the anchorage pins and adjusted to the proper catenary curve and elevation as they are successively laid. These are grouped first into strands and then into the main cables; and the stiffening trusses and the roadways are erected on them by means of simple travelers. Suspension bridges having eye-bar chains could be erected in a similar manner from a temporary, suspension-falsework platform. Arch Spans Very short arch-spans should be erected like girder spans, and handled as units by any convenient apparatus. Medium and long spans are gen- erally erected on falsework or by the cantilever method. As in the case of ordinary truss spans, erection on falsework is economic when practicable; and for arches of the plate-girder or solid-rib type this method can hardly be replaced by any other, when the spans are of any considerable length. Care must be taken, however, to brace the falsework thoroughly so as to resist the oblique stresses and thrusts that are produced by unequal loading as the inclined sections of girders are assembled, unless particular pains are taken to arrange them so as to maintain balanced reactions throughout the erection. Plate-girder arch-spans up to 510 feet long have been erected on falsework. Truss arch-spans may be erected by the cantilever method, which has been employed successfully for most of the large spans and up to the greatest present maximum of about 1,000 feet clear opening. 'By this method the top chords of the semi-spans which are built simultaneously are tied back to sufficient anchorages with adjustable connections so that the spans may be revolved around their skewback hinges in order to make the center connection at the crown. Erection Plant A very important feature in the economics of bridge erection is the design and operation of the special plant provided for handling the heavy members in the field. It has been found good, economic practice to expend large sums in the construction of plant for the erection of a single structure, and for the equipment of the field force with special machinery and ]iower appliances of great capacity. This apparatus is so costly that none but the most important construction-companies keep it in stock; and the existence of available plant of this nature is often an important factor in the design of the stnu^turc and in the award of the construction contract. Among the important standard appliances for bridge erection are derrick cars, derricks, hoisting engines, and riveting machinery that, in general, are applicable for ECONOMICS OF ERECTION 403 all very large jobs, and may, therefore, constitute a part of the regular equipment, the same as do the tools in the fabricating shop. The cost of their transportation, installation, and removal is, however, a special feature that must be considered in the determination of the eco- nomics of each structure. For very-long-span trusses there are necessary- enormous steel travelers that, with their equipment, may sometimes weigh 1,000 tons; and, when the job is finished, they are hkely to be unsuit- able for future work and of comparatively small value for salvage. For very heavy work it is also necessary in some cases to provide structural-steel falsework and to employ considerable ingenuity in its con- struction from portions of the permanent structure afterwards to be erected. The repeated use of special erection-metal and its availability for other purposes after the finishing of the job are important elements in the economics of the problem. As the principal members of long spans have attained a maximum weight of more than 100 tons each, it has been necessary to provide special methods of handling them and of securing them to the hoisting apparatus; and considerable sums have been spent in the construction of steel yokes, clamps, beams, and other special devices intended solely to provide rapid and effective connections to these pieces and to enable them to be accurately and safely handled. Such appliances greatly reduce the amount of hand labor and justify considerable preliminary expenditure. Replacing Steel Bridges The replacement of steel bridges almost always involves the mainte- nance of traffic on the bridge and often of navigation below the structure during the process of reconstruction. In most cases the new structure is on the same alignment and nearly or quite at the same elevation as the old one; and frequently the old substructure is satisfactory with minor modi- fications to receive the new superstructure. It is often difficult, and some- times very expensive, to divert the traffic from the old structure while the new one is being erected; hence the problem of reconstruction, especially of long and high spans, thus becomes one of the most difficult and expensive that are likely to be encountered, and the economics vary so greatly that no general determination can be made, necessitating that they be investi- gated independently for each structure. For short spans where the whole span or its single complete girders or trusses can be handled as units by travelers, derrick cars, or other apparatus traveUng on the ground alongside, or on the structure itself, and especially where the bridge is a double-track railroad structure, it is usually compara- tively easy to divert traffic to one track, and to remove the old structure piecemeal, putting in the new parts as fast as the old ones are taken out and gradually rebuilding the entire superstructure. For viaducts this may frequently be done with two derrick cars handUng 404 ECONOMICS OF BRIDGEWORK Chapter XL the girders together, one at each end, provided the towers do not need removal ; but in the latter case, particularly if the viaduct is very high and the connecting spans are long, the problem becomes one of great difficulty and expense. This replacement can be, and has been, accompUshed by supporting the structure on falsework; by suspending it from overhead spans long enough to reach from tower to tower, and carrying successively both old and new structures; and by providing new towers, or portions of new towers, before the old towers are wholly or partly removed. All of these methods are hkely to be slow, hazardous, and expensive; and they must be very carefully plaimed in detail for each structure con- sidered. When the old and the new structures can successively support each other during the construction, or when it is possible to by-pass the traffic, or to transpose old and new structures transversely in sections, or when it is possible to build new towers intermediate between the old ones or adja- cent to them, the difficulties are likely to be considerably diminished, but such favorable conditions do not frequently prevail. As the economics of design necessitate a rapid increase of span-lengths and weight with increasing height of track, the units handled in recon- structing a high viaduct become very large, and the derrick-car method and the translation of the structure as a whole are likely to be impracticable. Replacing Short Spans on Old Substructure Several methods of replacement of short and medium-length spans have been devised and repeatedly executed until they are to a certain degree standardized; and under ordinary conditions they may frequently be selected by inspection and modified, if necessary, to suit the special condi- tions and requirements of the case. Under such circumstances the method that provides the most simple and rapid operations with the least temporary construction is likely to be the most economic. Where the spans are over water that is not too swift nor too much obstructed, and where navigation permits, it is frequently possible to place both the old and the new span on barges or theh equivalents, and, at the given time, disconnect the old span from its original support and carry it immediately transversely out of position, and sinuiltaneously or succes- sively move the new span into the former position of the old one, seating it on its permanent foundations, the old span being removed to any suitable location. This system is frequently used for drawbridges; and under favorable circumstances the entire operation can be concluded with only a very short interruption to traffic on the structure. The spans are usually raised and lowered by regulating the amount of water ballast in the barges. Replacing by transverse displacement has been successfully accom- plished for spans up to 200 feet or more in length. By this method the ECONOMICS OF ERECTION 405 new span is completely erected as close alongside the old span as possible, and the floor is placed on it ready for traffic. Upper and lower sets of track- rails, transverse to the bridge axis and extending completely under and beyond both the old and the new span, are placed beneath the ends of both spans, and are separated by live rollers. Both the old and the new span are seated on the upper track-rails and are moved, usually simultaneously, transversely until the old span is carried clear of the alignment, the new span following it up until it occupies the required permanent position, when it is lowered to its masonry seat and the old span is dismembered and removed. The operations are accomplished with hydraulic jacks and power tackles; and the work can sometimes be done so rapidly as to involve only a few minutes' interruption to traffic. The rapidity of the work is often an important economic consideration that may outweigh considerable extra expense in the way of labor, material, and equipment. For spans of more than 100 feet, it is often desirable to support the old span on falsework that is designed also to carry the new span during erec- tion, and, after the removal of the old trusses, to erect the new span on the falsework, frequently while the traffic is carried on the old floor that is still supported by the said falsework. If the old span is strong enough to sustain the new span during con- struction, plus the weight of the minimum traffic necessary, the new span may be so designed as to permit its construction by this method; and, after ■ completion, it may, if necessary, be moved a short distance either horizon- tally or vertically, in order to bring it into the exact ahgnment after the old structure has been removed. In other cases the new span may be designed with transverse dimensions, greater than those of the old structure, that enable it to be built outside of the latter and practically independent of it, so that the new construction may be substantially completed while traffic is maintained on the old structure; after which it will receive traffic and will support it and the weight of the old structure whilst the latter is removed piece-meal. Replacing Long Spans Comparatively few very-long spans have been replaced by new ones in the same alignment. The principles governing the operation are sub- stantially those developed for moderate-length spans, with the exception, perhaps, of the application of the cantilever method, by which the trusses of new long spans have been built out as cantilever arms which clear the old structure and are self-supporting during erection. If traffic can be diverted from the old structure during its replacement, the old trusses will be likely to be found strong enough to support the new span during erection; and, if there are more than two lines of trusses, the old ones may be successively replaced by the new ones. In the case of a suspension bridge, the factor of safety of the cables is 406 ECONOMICS OF BRIDGEWORK Chapter XL such that, if well designed, they are likely to outlast the roadwaj^ and trusses, consequently the latter can easily be replaced without other support than that afforded by the cables themselves. For spans approaching the present limits of lengths, the necessary practice is for such efficient construction, capacity, and maintenance that there is little prospect of any need for replacement of the superstructures; and, should it become necessary, there would probably be little choice of methods. Any scheme that would be possible, however, should be entitled to favorable consideration. Erection of Concrete-Girder Bridges Concrete-girder bridges are usually concreted in situ by ordinary meth- ods and with standard equipment involving regular operations that do not present any special economic features. There may, however, be a decided economic consideration in the question of using pre-cast members for such structures. The large capacity of derrick cars and of other equipment that is available makes it possible in some cases to cast long girders and heavy floor slabs in multiple, in the Contractor's yard, remote from the bridge site and under conditions more favorable to good work and eco- nomical operation than those existing at the latter, and afterwards to transport the well-seasoned units to position and set them in place ready for service. This method is especially applicable to railway structures. The economic considerations are likely to involve not only freight cost but also quality of structure and rapidity of operations as affecting the interruption of traffic. Concrete Arch Spans Arch spans must be concreted in situ on forms rigidly supported against settlement and provided with devices for striking the center so as to swing the arch free of its construction support when the concrete has sufficiently hardened. For short spans, low heights, and where obstructions under- neath are permissible, the forms can usually be most economically sup- ported on ordinary falsework-bents. Where the height is great, or where passage must be maintained under- neath for stream flow, navigation, or traffic, it is often necessary to carry these forms on arch-center trusses. For short spans these may be of cither timber or steel; but for medium and long spans they are almost always constructed of riveted st(H^lwork, usually arranged in sets braced together and often moved transversely from side to side of a wide bridge and longi- tudinally from span to span as the work progresses, thus making one set suffice for many places. CHAPTER XLI Economics of Maintenance and Repairs Although in years long gone by the author did considerable work in the line of examination and repairs of old bridges, he feels that he can no longer consider himself an expert therein. It is a case of tempora mutantur; for the methods employed today in bridge repairing are essentially different from those that were in vogue some two or three decades ago. For this reason the author appealed to several old friends in his specialty, who are authorities in this class of work, to furnish him data for the writing of this chapter. Several of them generously complied with his request, viz., Mr. Chas. F Loweth, Chief Engineer and formerly Bridge Engineer of the Chicago, Milwaukee, and St. Paul Railway System, Mr. Carl S. Heritage, Bridge Engineer of the Kansas City Southern Railway Company, of which line the author is, and for some two decades has been, the Consulting Engineer, and Messrs. J. G. Chalfant and V. R. Covell, respectively County Engineer and Deputy County Engineer of the County of Allegheny, Penna. For their truly valuable aid the author desires to extend to these gentlemen his hearty thanks and his deep appreciation of their kindness and courtesy. A rule of practice which the author established for his own guidance fully a quarter of a century ago seems to have found favor with the pro- fession, viz., that any old bridge, which, in either main members or details, would be overstressed by the actual live loads passing across it, or likely soon to traverse it, not more than fifty per cent in excess of the standard intensities of working stresses employed in designing new struc- tures, may safely be allowed to remain in use. If overstressed much more than this, it should be removed and employed at some other location where the traffic is light, or else scrapped. Exception was made in the case of plate-girder spans; for these could be relied upon to give ample warning of failing strength by rivets working loose. A plate-girder span when greatly overloaded will not collapse suddenly as will a pin-connected or even an open-webbed-riveted span. A favorite economic expedient of the author's used to be to convert two old duplicate bridges into one and put in a new one at the crossing left vacant. This scheme was specially applicable on long lines of railway where standard I-beam and deck-plate-girder spans were used. The more crudely a bridge was designed the more difficult it is to rein- 407 408 ECONOMICS OF BRIDGE WORK Chapter XLI force it so as to make it carry satisfactorily heavier loads than those for which it was proportioned. In fact, the character of detaihng employed previous to the nineties, in which decade the science of bridge design began to be estabhshed, was so outrageously unscientific as to lead the author to suggest the axiom that "the best way to repair an old bridge is to throw it into the scrap heap and build a new one." Quite often bridges are repaired, which, from the standpoint of true economy, should be relegated to the discard. One such case of some importance occurred in the author's practice in the late eighties. It was an old Post Truss bridge across the Missouri River at Fort Leavenworth, Kansas, which had been seriously injured by the burning of a large portion of the wooden floor. The total cost of the repairs was somewhat in excess of one hundred thousand dollars — an amount greater than the sum total of all the subsequent incomes from both railway and highway traffic. In extenuation of his action in repairing this structure, the author might mention the fact that he was not consulted about the economics of the case or the advisability of repairing, but was simply given the job of engi- neering the reconstruction of the damaged structure. However, he is not sure that, at that stage of his career and in those days of primitive bridge design and construction, his judgment was far enough developed to enable him to come to a truly economic decision, had the problem of the economics of the case been submitted to him. The method of solving such a problem is to estimate upon a liberal basis the probable cost of the repairs, and upon a conservative basis the probable duration of life of the repaired structure, also the probable costs of an entirely' new bridge both at the date of consideration and at the expiration of the said life. If the latter cost, plus the cost of the repairs with compound interest thereon up to the time of the renewal, plus the net cost of removal of old structure (i.e., cost of the work less scrap value) is smaller than the net cost of immediate removal, plus the cost of a new structure, built imme- diately, plus compound interest on the sum of these two costs at the assumed later date, plus the small value of the deterioration of the new structure in the interval between the said two dates, then the repairs will be warranted. It is evident that the correct determination of the answer to any such economic question demands wide experience, sound judgment, correct vision, and a practical acquaintance with the theory of economics. In the old days a large portion of the work of bridge examination and repairing fell to the lot of the consulting engineers; but such now is far from being the case, because it is only for very large and important struc- tures, or those having moval)lc spans of a complicated character, that the independent specialists arc retained on repairs and roconstruc^tion. Such work is ordinarily done by the bridge engineers regularly employed by the raih'oads, the states, and the municipalities; and these men have become exceedingly expert therein. ECONOMICS OF MAINTENANCE AND REPAIRS 409 So much for the author's views upon the subject under consideration; and now for those of his before-mentioned friends. In respect to Mr. Loweth's contribution to this symposium, on Feb. 6, 1920, he wrote as follows: My Dear Dr. Waddell, Replying to your inquiry regarding "Bridge Maintenance and Repairs," I would refer you to a paper which was somewhat hurriedly written in the fall of 1918 for the annual convention of the American Railway Bridge and Building Association, entitled "Carrying Bridges Over," and which covers in general the matters referred to in your letter. This paper was written during the stress of war times when steelwork was very difficult to get and the need of economies was urgent; hence it was necessarily quite hastily prepared, and I feel that for usual conditions the views expressed therein should in some respects be modified. My experience on this road * has been generally one in which it was comparatively easy to take care of the replacement of the lighter bridges. We have a great many branch lines on which the traffic is necessarily light and where in many cases it will always remain so. There was little loss, therefore, in taking a light bridge out from a first-class line and placing it in a second-class or third-class line where it would serve just as useful a purpose, at least for many years, as a bridge of the heaviest classification. To do this involved charges to Capital Account on the lighter lines. During wai times we were not in a position to assume the charges to Capital for improvement of the said lighter lines; and the difficulties of getting new steelwork, to say nothing of the very-rapidly-increasing cost, resulted in a new condition, hence we looked into the matter of strengthening bridges in place more fully than we had done previously, with the result that we did more of that work than we had even thought of doing before that time. All of this work was not uniformly satisfactory, as you can readily see, because some structures did not easily lend themselves to strengthening in a manner at all suit- able from the designer's standpoint; but by the exercise of judgment and some courage, and at the same time by ignoring some of the refinements of calculation, we arrived at results that produced economies, or what may be equally important, the deferring of major expense even at the loss of ultimate economy. The curse of the poor is their poverty, and the railroads have sometimes been, and to a large extent are now, in the position where present economy is perhaps more to be considered than ultimate economy. Just as an illustration of what we are up against, we have on one of our second or third-class lines four rather large bridges which have been carried to their limit. The substructures are very old and small, and the superstructures also are quite old. It is an exceedingly difficult matter to strengthen them — in fact, we can only hope to remove the most glaring defects; and anything we can do in that line will permit of using only sUghtly heavier power than the quite-Hght power now being operated over that division. Our program for strengthening would involve a cost of about $74,000. To replace the bridges with new structures would require probably more than $600,000. It seems too bad to spend so large a sum on these old structures; but assuming that we could carry them along safely for only four years, that would make an annual cost of only $18,500, exclusive of interest, and we should have saved an expenditure of over $500,000, the interest on which would amount to at least $30 000 a year. In this instance a new structure could be credited with a considerable amount for the greater safety and other considerations incident to the better bridge, but I think we shall have to decide favorably on the extraordinary repairs for what will probably be but a short period of usefulness. * Chicago, Milwaukee, & St. Paul Railway System. 410 ECONOMICS OF BRIDGEWORK Chapter XLI We are now aiming to restrict fiber stresses ia all structures to the lower limit indicated in the paper, with the understanding that some features of the design or other conditions may make even this lower Umit inadmissible and vice-versa. The more important parts of the paper mentioned are as follows: General Considerations In the maintenance of bridges there are two general considerations to be observed: 1. Safety in carrying the necessary traffic. 2. Economy — i.e., obtaining the maximmn hfe from the structure at reasonable maintenance cost. On all railroads which are twenty-five or more years old, there are usurHy a number of light-capacity bridges which impose more or less restrictions on the train loadings that can be handled over the lines. This is a very serious problem on railroads which have many bridges that were built during the eighties and early nineties. New bridges are generally designed for the heaviest engine and car loadings in existence at the time. In proportioning them there is, however, a certain margin between the unit stresses which are used and the maximum unit stresses which the material can safely carry. This margin provides an allowance for some future increased engine and train loadings, in addition to the contingencies which are usually embraced by the term " factor of safety." Classification of Bridges The term "Classification of Bridges " is used to describe the systematic investigation of fight-capacity bridges, with the view to determining the maximum loads which can safely be carried. Formerly, the common practice, when a new engine loading was up for consider- ation, was to investigate aU of the light bridges on the lines where the use of the heavy loading was contemplated. Stresses throughout the structures for this loading were figured, and decision then made by the one responsible for the said structures as to whether the load could be safely handled. Each time a new loading came up for con- sideration the process was repeated; and Uttle or no use was made of the previous com- putations. The present practice on the C. M. & St. P. Ry. is to make an investigation or "classification" of each structure. Its carrying capacity is determined in terms of a standard series of train loadings. New engine and car loadings that come up for con- sideration are classified in the same series of standard loadings, and it is then a matter of direct comparison to tell whether such proposed loadings can be safely handled over the various bridges. Every bridge whose date of construction indicates that it is of light design, or which is known to be, or suspected of being, overloaded, is thus classified. Every part of the structure is figured or taken into consideration. In making these classifications it is necessary first of all to establish the maximum unit stresses to which the various materials can safely be subjected. For the different materials these maximum safe stresses are taken as near the limit of strength of the material as is considered safe. The maximum safe stresses must be assumed low enough so that there is no danger of the material yielding, altering its character, or reducing its strength for carrying loads after being subjected to this limiting stress for any number of times. As an illustration of what may be considered as safe limiting unit stresses, the following are given, and may be taken to api)ly where the design and physical condi- tion of the structure arc known to be first-class: ECONOMICS OF MAINTENANCE AND REPAIRS 411 Poimds per Square Inch Wrought Iron Steel Beams and girders, fiber stress in bending 22,000 20,000 2,000 26,000 Truss members, tension on net section 24,000 Timber stringers, fiber stress in bending (with suitable reduction for age in the case of exposed timber over six or eight years old) In fixing upon limiting unit stresses for loading old bridges, it is necessary to take into account the following: Character of design; that the details are well proportioned and direct in action, and that there is no ambiguity or uncertainty as to how the members act. Character of the workmanship entering into the structure as indicated by the reputation of the makers and by any material-test data that may be available. Deterioration. Action under load, such as rigidity and freedom from excessive vibration. Speeds likely to obtain over the structure, and confidence as to the observance of any speed restrictions that may be imposed. Element of certainty as to the assmned loading being the. maximum to which the bridge will be subjected. Importance of traffic, and the hardship which might result thereto from temporary disablement of the structure. Probability of early renewal on account of change of line, etc. A higher limit might be allowed for a short time to meet an emergency than would be proper for a structure to be kept in service indefinitely. General reliability of the data upon which the investigation of the structure is based. Generally, judgment founded upon all of the factors surrounding the bridge, its location, service, and condition. It must be recognized that there is danger in setting down a hard-and-fast rule for the limits to which structures might be stressed. In all cases it is necessary to exercise care, knowledge, and good judgment, in order to be always on the safe side and at the same time conserve the maximum life of the structure. Standard Loadings In the systematic investigation of a large number of bridges, it is necessary to have a unit loading as a basis of comparison. The familiar Cooper's Series of Standard Train Loadings furnishes a convenient and well-known basis. This series consists of two consohdation-type engines, followed by a train load having a fixed spacing of wheels and a fixed relation between the weights on the various wheels. These weights, however, are directly proportionable to the classes; i.e., the drivers for Class E-40 Loading have 40,000 lbs. on each axle; for Class E-50 Loading, 50,000 lbs. on each axle; etc. The imit loading in this Series is taken as Class E-1 Loading. On account of the fixed wheel rearrangement for all classes and the proportion- ality of wheel loads, it follows that the stresses in all parts of bridges due to these loadings are directly proportionable to the classes; that is, the stresses in every part of the structure from Class E-50 Loading will be just fifty times the stresses from Class E-1 Loading, 412 ECONOMICS OF BRIDGEWORK Chapter XLI In connection with the Hve-load, it is necessary to make proper allowance for "impact," "centrifugal force," and "traction." The general method of investigating any part of a bridge and of making a classification is as f oUows ; 1. The maximum allowable stress is determined, which, in the simpler cases, is the cross-sectional area of ttie member multiplied by the limiting unit stress allowed. 2. Deduct from this the total amoimt of stress in the part due to both "Dead Load" and "Wind Load." The remainder gives the allowable stress for the "Live Load" effect. 3. Dividing this by the stress for unit "Live Load" (Class E-1) gives the classi- fication for allowed " Live Load," if at rest. 4. Divide this classification by the term which takes into account the extra effects of the "Live Load," due to Impact and Centrifugal Force, and the result wiU be the classification of the allowed " Live Load " at fuU speed. Classification of Loadings The "Class E" loading above described is an assumed typical loading. Actual engine and car loadings vary a great deal as to spacing of the wheels and the distribution of the weight on the various axles. The effects of different loadings on bridges are not in direct proportion to the weight of the engine or cars, but depend on the number of wheels, spacing of wheels, distribution of weight, etc. Actual engine loadings can, however, be reduced to equivalents in the standard train loadings, corresponding to the different span lengths. This is done by computing the maximum bending moments and end shears for the given train loadings for each different span length. These are divided by the maximum bending moments and end shears for the Unit Class "E-1 " loading, for the corresponding span, the result being the "Classification" of the loading. As an illustration of classification of various engine loadings. Fig. 41o is given. This shows the classification of several types of the new standard locomotives which have been purchased by the Government and are now being assigned to the various railroads. Fig. 41& shows similar classifications for typical car loadings. In placing restrictions on the use of car loadings over bridges, it is not practicable to take into account all of the variations in car lengths which occur. An equivalent for the various car loadings can be arrived at by considering typical hopper cars about 33 ft. long, as shown in Fig. 416, for which the wheel spacing given is a fair average. For bridges under 50-ft. span, the trucks of two adjacent cars produce the maximum effects, and, for like axle loads, are independent of the lengths of the cars. The approximately parallel curves on the diagram represent the classification of these typical car loadings for different weights of cars, where the total weight repre- sents the weight of the car and contents. The said diagram shows by dotted line the classification of a typical ore-car loading, which, on account of the extremely short length of the car, produces a high classification on the long sjians; and it records also the classification of a heavy wrecking crane of 120 tons capacity. Speed Restrictions In the foregoing the classification has been determined with an allowance for the effect of the maximum speed over bridges. Where speed is reduced, the effects of the live k)ad are much less; and the allow- ance for impact and centrifugal force, if any, may be correspondingly reduced. This will, of cour.se, permit heavier loadings to be oiierated at reduced speed as compared with those permissible for full speed. ECONOMICS OF MAINTENANCE AND REPAIRS 413 10 20 30 40 50 60 70 80_90 100 110 110 130 140 150 f65 10 ZO 30 40 30 60 70 80 90 100 110 llO IdO 140 150 Spon in Feef Fig. 41a. Diagram Showing Classification of U. S. Government, Standard Locomotives. %^.5iiMtw^^}sr-i'fxks •S3C. u. '/4&::: $■6 ;lt 31 IS ■5P?5 T^.-- ZZ-ff t ii ^Wti's 20 40 60 80 100 JZO 140 160 Span Jo Feef Fig. 416. Diagram Showing Classification of Typical Loadings 180 200 414 ECONOMICS OF BRIDGEWORK Chapter XLI From the tests conducted by the American Railway Engineering Association, it is found that the maximum impact which will be obtained at reduced speed is : Less than 30% for speed of 10 miles per hour. Less than 40% for speed of 15 miles per hour. Less than 50% for speed of 20 miles per hour. Less than 55% for speed of 25 miles per hour. An inspection of the diagrams indicates that the effective span of the bridges and the characteristics of the engine loadings determine to a great extent whether a given loading can be run over the bridge, and shows that it is unsafe to attempt to decide whether any engine loading can be handled over a structure simply by knowing its total weight. There is, unfortunately, a misunderstanding, among some railroad operating officials, as to the effect on bridge structures of such complex loadings as locomotives and cars. In these cases it is assumed that the effect is the same for all locomotives of the same total weight; and bridges are classified as being safe, or otherwise, for all locomotives of given total weights. If this practice must be resorted to, the limits set should be on a very conservative basis ; for otherwise there would be danger of certain types of locomotives having a serious effect on some bridges, producing unsafe condi- tions. The practice would not be economical, because it would either lead to the premature renewal of some bridges or to an unnecessary ruling off of certain types of engines. Where Low Classification Usually Occurs in Bridges In older bridges there are certain parts where low classifications can usually be expected. These have been found to occur most often in the lightest members of the structure and in members which carry the smallest dead-load stresses. In propor- tioning a member, a part of the sectional area thereof can be taken as carrying dead- load stress and the remainder live-load stress. As the dead-load stress is constant, a smaller area would be required where a higher unit stress is used. This, therefore, leaves a portion of the area originally provided for dead-load stress available to carry live-load stress. It .is found that the floor systems of bridges have generally a lower classification than the girders or chords of the trusses. The low classification of stringers is generally in the section of the flanges near the center, in the riveting of flanges near the ends (par- ticularly if they are shallow), and in the riveting connecting the stringers to the floor beams. Floor beams, if of shallow depth, frequently show a low classification in flanges near the stringer connections, also in the riveting of flanges near the ends, and in splices connecting the wtbs of the floor beams to the gusset plates, particularly in types where the lower part of the floor beam is cut out to fit around the ends of the trusses or over pins. In plate girders, the flanges frequently show low classification at points whei-e the web is not fully spliced near the center and at points near the ends of cover i)lates. The flange riveting near the ends of girders frequently has a k)w classification, par- ticularly where the girders are shallower at the ends. Webs of plate girders show low classification near the ends of the girders where there is a relatively large expanse of web, unsupported by stiffeners. The web splices near the ends of the span have a low classification where only one line of rivets is used on each side of the splice. In trusses, the i)osts and diagonals near the center of the span usually show a low classification. This is particularly true of the diagonals and counter-diagonals of light eye-bars or loop rods. Suspenders, or hip-vertical members, frequently have a low classification. The ECONOMICS OF MAINTENANCE AND REPAIRS 415 classification of end posts and top chords of truss bridges is frequently low on account of the eccentricity of the member with respect to the location of the pin. The pins of old truss bridges frequently show a startUngly low classification where computations are made in accordance with the usual methods; hence it is necessary to take advantage of certain conditions which are more favorable than the usual assump- tion, in order to help out the classification. Where eye-bar members consisting of more than two pairs of eye-bars meet on a pin, a slight redistribution of stress in the several eye-bars wiU frequently increase the classification of the pin; and this is justifiable as being in line with the way the structure actually works. Where certain members have wide bearing surfaces on the pins, the center of pressure can be taken near one edge of the bearing surface, thus increasing the classification of the pin and, at the same time, approximating more nearly to the actual behavior of the detail. It is also permissible to use higher unit stress for figuring pins than for the other members of the structure. The following illustrates what might be considered permissible, providing there is assurance that the material is of good quality and that the computations take account of all the forces acting: Wrought iron 40,000 lbs. per sq, in. in bending Softsteel (.1%C) 45,000 " " " Structural steel (.2 %C) 48,000 " " " *♦ Mild " (.25%C) 52,000 " " ** tt Medium " (.35%C) 56,000 " " «* tt Hard " (.45%C) 64,000 " " *t ti It is to be noted that, In bridges built in the late 80's and early 90's, hard grades of steel were frequently used for the pins. In timber-trestle bridges, the stringers in bending usually show low classification. On account of there being three or more sticks acting together, it is permissible to use a higher unit stress for trestle stringers than for a single stick, as the average strength for the several pieces exceeds that of the poorest one. On account of the exposure to the weather and the deterioration which gradually takes place, the allowed xmit stress in timber stringers should be reduced as the age of the bridge increases. Where timber bridges are thoroughly inspected and defective material is promptly replaced, and where they are subject to the same general consideration as given above for metal bridges, the following unit stresses might be taken as a safe practice for maximum fiber stress in stringer bridges without allowance for impact: For stringer bridges six years old, 2,000 lbs. per sq. in., and reduced about 100 lbs. per sq. in. for each year following. The above figures are based on Douglas Fir or dense yellow pine and for climatic conditions prevailing in the North Central States. In more arid regions where longer life of timber may be expected, the reduction in stress for age need not be so rapid. On account of the comparatively short life of timber bridges and the ease with which they can be renewed, there is not generally the same urgency in establishing maximum- safe-stress limits as in the case of the more permanent metal bridges. In timber truss- bridges the lowest classification usually occurs in the floor beams, truss rods, and diag- onal braces. It has been foimd that metal bridges suffer frequently from corrosion in the top flanges of stringers and floor beams, on account of the action of brine drippings from refrigerator cars. In bridges where the ties are supported on shelf-angles riveted to the webs of the girders, the shelf-angles frequently show considerable corrosion and tend to break in the root of the angle. In pin-connected trusses, excessive wear sometimes takes place in the pin bearings, particularly in draw bridges. 416 ECONOMICS OF BRIDGE WORK Chapter XLI Metal bridges and viaducts over railroad tracks frequently show excessive corrosion in the floor system and laterals, due to smoke and gas from locomotives, also because of the fact that the sohd floors of such bridges do not permit the steel work beneath to dry out quickly. MetaUic overhead bridges having a scant clearance, so that the stacks of the loco- motives come close to the steelwork, frequently show excessive wear from the sand- blasting effect of cinders issuing from the engine exhaust, particularly when the loca- tion is on an ascending grade where the locomotive is worked hard under the bridge. Possible deterioration of the structure of the metal itseh, by fatigue, has in some quarters been a matter of apprehension ; but it now seems to be recognized that no such interna] deteriorating action takes place where the bridge has not been subjected to excessively high stress. If crystallization is found in the metal of a structure, it prob- ably was there at the time the structure was built, and is due to improper methods of manufacture of the material. It may, therefore, be taken as a certainty that iron and steel bridges, if not reduced in section by rust, etc., and if not shaky on account of inadequate bracing, are fuUy capable of carrying the figured loads at reasonable limiting unit stresses, provided they are carcfuUy inspected and properly maintained. Strengthening of Light BniDGEa Strengthening of light bridges may be either a matter of reinforcing minor details which are found to hmit the carrying capacity of the structures, or may consist of heavy reinforcing in an attempt to increase the strength thereof throughout. The minor strengthening can usually be done at small expense; and it is an economical method of getting considerably greater life out of bridges. Heavy reinforcing may or may not be an economical proposition, as it involves work being done in the field, which is costly, and the maintenance of traffic during the time the work is in progress, which involves some risk to traffic and is usuafly expensive. On very large bridges where the cost of replacing is great, some extensive strengthening operations have been carried out economically. In making plans for reinforcing bridges, it is usually preferable to add new material to the structure so that the present structure is not temporarily weakened, rather than to remove parts and substitute heavier ones, though the latter expedient has some- times to be resorted to. The descriptions of the points at which low classification usually occurs suggest in themselves how these might be strengthened. In plate girders the top and bottom flanges may be reinforced by additional cover plates, particularly at points where the web is spliced and not effective for carrying its proportion of the bending stress. Where there are no cover plates on the girders, cover plates of desired length can be added. On plate girders where there are two or more cover plates, additional cover plates would be nearly the full length of the girder and expensive to apply. Plate girders can be doubled up to make deck si)ans, using three or more girders per span at small expense, thereby using up light girders and jiro- viding bridges of large carrying capacity. Where waterways or other under-crossing conditions permit, timber bents can be placed under spans to strengthen them. Where the rivets in the flanges of girders show low classification, larger rivets can be substituted for existing rivets, or, where the rivet spacing permits, additional rivets can be driven. Where the web plates give a low classification, additional stiffeners can be placed in the panels near the ends of the girders to provide extra support for the web and thereby increase its classification. Sh(^lf-anf!;l('s can bo strengthened by placing short vertical stiffeners beneath them. Where web splices with low classific^ation o(!cur, these can be replaced with wider splice plates having additional rows of rivets in the splice. ECONOMICS OF MAINTENANCE AND REPAIRS 4l7 In through bridges the stringers can be reinforced by additional riveting, by the placing of additional stringers, either timber or steel, and by shifting existing stringers to secure better distribution of the load. Where str;':>ger3 are spaced so that some of them do not carry their full proportion of load, it is possible to introduce cross bracing so that all the stringers in the panel shall act together to carry the total load and thus relieve the excessive burden on certain stringers. Floor beams can be reinforced by cover plates or angles added to the flanges, by additional riveting, or by shifting the stringers toward the trusses so as to reduce the bending in the beams. In very old bridges the floor beams are frequently of much lower classification than the remainder of the bridge; and they can sometimes be replaced with entirely new beams at a reasonable expense so as to get additional life out of the rest of the structure. In trusses, diagonals and counters can usually be reinforced with additional bars or rods having loops over the truss pins and being connected by turn-buckles to provide adjustment. Similarly, bottom chords of eye-bars can be reinforced with additional bars having yokes bearing on the heads of the original eye-bars. End posts of through bridges, whose low classification is due to eccentricity of members, can be strengthened by placing angles or plates on the sides of the said mem- bers, so as to make the cross-sections better balanced, thus reducing eccentricity. The bottom chords of truss spans may be reinforced by adding an auxiliary bottom chord above the present chord and sloping the end panels to meet as nearly concentric with the end pins as conditions will permit. Auxiliary web members may be con- nected to the new auxiliary bottom chord and the top chord. This is the method employed on the North Halsted Street Viaduct over the C. M. & St. P. Ry. Co.'s tracks in Chicago. This method has also been employed by the City of Chicago on several bridges in that city. Where pins have low classification, it is sometimes possible to move the members on the pin and reduce the bending. In some cases, diaphragms placed in built-up members will reUeve the bending on the pins. The pins themselves can be strengthened by replacing them with high-carbon or special-alloy steel pins of the same size; or, if still more strength is required, by boring out the pin holes and putting in larger pins. This operation has been done a number of times; but it requires rather elaborate arrange- ments for holding the members in position while the pins are removed. Timber truss-bridges can be strengthened by placmg floor beams, diagonal braces, or truss rods where needed. Where timber trusses are old and have commenced to open slightly in the joints or to show other signs of diminished strength, they can be temporarily strengthened and carried for a few more years by placing timber bents under the panels points at two or three panels from the end of the span. This has the effect of reducing the span- length and stiffening the structure. Timber-trestle bridges can be readily strengthened by additional stringers. The cost of strengthening bridges varies with the size of the job, the amount of staging required, the amount of moving the same about so as to reach different portions of the work, the size of the crew available, the distance traveled by the crew, the tools at hand, etc. In a general way, it has been found that the cutting out and replacing of rivets on ordinary strengthening jobs costs from 25c. to 75c. each. DriUing new holes and driving new rivets therein cost from 50c. to $1.00 each; i.e., the cost of such work will be given by the total number of rivets driven at these imit prices, plus the cost of the additional material required. With the maintenance of old and hght-capacity bridges, the question continually arises whether it is more economical to strengthen the structure or to renew it. As a general proposition, it would be permissible to spend each year for strengthening an amount equal to the interest on the investment in a new bridge, less the cost of addi- 418 ECONOMICS OF BRIDGEWORK Chapter XLI tional maintenance required by the old bridge on account of the greater attention it receives. For illustration, let us consider a few lengths of through spans designed for E-55 loading, replacing similar spans designed in the early 90's. New steel work taken at 5c. per pound erected; falsework at $10.00 per lineal foot; removing old structure at $10.00 per ton; salvage on old spans at 22-c. per pound; additional cost of main- tenance of the old span on account of additional inspection, classification, and super- vision required, $1.00 per foot of span per year. The last column of the following table shows the amount which we could afford to spend per year in strengthening old spans rather than to renew them. The costs shown in this table are for illustration only. As they fluctuate from time to time, the resulting economics will vary accord- ingly: TABLE 41a Available Interest on for Span New Steel Weight Cost Erected Salvage Net Net Cost at 5% Strengthen- ing Each Year 50' 66,000 lbs. $ 4,330 $ 1,130 $ 3,200 $ 160 $ 110 100' 218,000 13,390 3,700 9,690 485 385 200' 800,000 46,000 12,500 34,500 1,725 1,525 300' 1,600,000 92,200 25,000 67,200 3,360 3,060 The writer has in mind a bridge having three 400 ft. spans which, if renewed about ten years ago, as some Railroad Managements might have done, would have cost about $370,000 after deducting the salvage value of old spans recovered. The interest on this investment for the ten years would have amounted to about $185,000. Instead, however, of replacing these spans, they have been carefully maintained and inspected and the details strengthened wherever the classification showed that it was necessary to carry the heavier traffic. The actual cost of strengthening, together with the addi- tional maintenance expense, has amounted to not over $20,000 during tliis period, showing a saving for this bridge of about $165,000; because of the policy of getting the longest practicable life out of structures. This illustration is intended to show only one way in which the problem may be considered. With old and light bridges a limit is reached beyond which it is not econom- ical to strengthen them ; and replacement then becomes necessary. It must be recog- nized, of course, that a newly designed and heavy structure is preferable to a lighter one. It is possibly true that, in case of a serious derailment on a bridge, a light structure might be destroyed while a heavy new structure might withstand the same treatment without being seriously disabled. Such considerations must be taken into account in shaping the general policy concerning the keeping of light bridges in service. From tho data furnished by Mr. Heritage, tlic following has been excer[)ted : Strictly speaking, the economics of nia.iiitonaiu'o iiud r(^pairs starts with the design of the bridge. The most (H'ononiical structure is that on which the total fixed annual charges are a mininmni — these charges to include ECONOMICS OF MAINTENANCE AND REPAIRS 419 interest on the original investment, annuity to provide for the replacement of the structure when the time comes for its renewal, insurance when neces- sary, and charges for maintenance and repairs. It is evident that, by increasing the original investment, we can usually provide a structure that will have a longer life and will require less annual expenditure for maintenance and repairs. However, we are considering here only the subject of maintenance and repairs, and shall take into account only such structures as are actually built, the economics of design and the types of structure best suited for various purposes and conditions having been covered in other chapters. All structures should have periodical and careful inspection; and when anything is found requiring attention, it should be done promptly. The neglect of attending quickly to minor repairs needed will usually result in much more extensive and costly repairs later on; for, according to an old and well known proverb, "a stitch in time saves nine." When an organization, such as a Railway Company or a City, has a large number of bridges to maintain, it is customary to have a department to look after the work, with the requisite force of men and the necessary equipment; and these should be continually engaged in making repairs to bridges and like structures. Repairs to timber bridges are more frequent than those on permanent structures, on account of the liability of timber to decay. Wood preserva- tion, especially by the process of creosoting, has taken wonderful strides in the last few years. With the growing scarcity of timber and the rise in its price, such preservation will increase until it will be the exception rather than the rule to have untreated timbers in exposed structures. The majority of wooden bridges now in service on railways are trestles; although, in some parts of the country, timber or combination-timber-and-steel truss- spans are still used. Timber structures can be kept up almost indefinitely by replacing members shortly before they become dangerously decayed; however, when a bridge is so old that a large portion of the timber shows more or less decay, it is more economical to renew the whole structure, salvaging such second-hand material as possible, after which the bridge will be serviceable without further repairs for a period of years. In case of pile-driven trestles, it is cheaper under some conditions to replace the piles with frame bents than it would be to renew the structure as a pile-driven trestle. In this case the old piles are cut off under the ground until sound timber is reached, usually about two or three feet; and the new frame bents are supported on these old piles. The latter usually rot off close to the ground line; but in good soil they will remain sound at a depth of two or three feet for a long period of years. The objections to this procedure are that the sill, being underground, is difficult to inspect and that a frame bent structure is not as stiff as a pile structure; conse- quently, if a pile driver is available, it is preferable to drive pile bents rather than to construct frame ones. 420 ECONOMICS OF BKIDGEWORK Chapter XLI In making repairs and renewals to timber bridges — and, in fact, all bridges — the bridge gangs formerly were usually equipped with only hand tools; but, now that the cost of labor is so much greater, it is economical to replace manual labor as far as possible with machines. A hght^derrick car equipped with a hoisting engine or a locomotive crane will save the work of many men in handling heavy bridge material. On timber struc- tures a large part of the labor consists of boring holes for bolts and fasten- ings. Repair gangs should be equipped with boring machines operated by either air or electricity, in order to do this work economically. The magnitude of the task will determine whether machinery or hand labor is the more economical. On very small jobs it will be more costly to set up the equipment than it would be to do the work with hand tools; however, the tendency is to make more and more use of machines instead of manual labor. The preservation of timber, in order to increase its hfe and reduce the necessary maintenance, has been mentioned. Formerly timber highway bridges were commonly covered by roofs and siding to protect the frame work from the weather; and such structures lasted for a long period of years, several notable wooden bridges in this country having reached an age of nearly 100 years. This sort of bridge accumulated a great deal of dirt and was very dark at night, and the roof, housing, and floor naturally required considerable maintenance. The question of fire protection should also receive proper attention in connection with timber bridges. The expense caused by a burned bridge in some cases far exceeds the value of the structure itself, as, for instance, on a railway where the traffic is stopped on this account. On railways, timber trestles are frequently partially protected from fire by covering the deck with sheet metal or with stone or gravel, so that sparks from a defec- tive engine will not set it ablaze. Sometimes fire-proof paints are used. Some of these paints are very effective for several years, and at the same time are good timber preservers; hence, if properly selected, they will be economical from a maintenance standpoint as well as in respect to protec- tion from lire. The timber floors on highway bridges and the ties on rail- way bridges are subject to wear, and are usually worn out before they rot out; In cases of very heavy traffic, bridge floors should be constructed of more permanent material than planks; and the ties on railroad bridges should be protected with tic plates. Old stone piers and abutments often show open seams where the mortar has fallen out of the joints. If these receive attention in time, it will usually be sufficient to dig the old mortar out of the seams and repoint them, thus protecting the interior of the structure from moisture; but in some cases more work than that is necessary. On high structures, especially over rivers, it is very costly to put, the spans on falsework in order to repair or rebuild pi(!rs, hence other expedients arc resorted to, in order to avoid this ECONOMICS OF MAINTENANCE AND REPAIRS 421 expense. Sometimes a jacket of reinforced-concrete can be built around an old pier and the top protected with a water-proof coating. Concrete has largely displaced stonework for the material of sub- structures in bridges. Piers made of iron or steel cylinders and filled with concrete provide a cheap construction where conditions are suitable. They were formerly largely used for railroad bridges, but their employment is now confined mostly to a light class of highway bridges or to railroad bridges carrying only light loading. If this type of pier is very high, it is subject to vibration under traffic; and this vibration will produce an injurious effect on the superstructure as well as on the piers. Many piers of this class are kept in service by encasing them in concrete, thus increas- ing their weight and stability ; and this can usually be done without putting the bridge on falsework and removing the old piers, because the spans will be supported upon the old cylinders while the new work is in progress. Steel-frame structures are subject to deterioration by corrosion; and to prevent this the surface must be always covered by a protective coating, usually paint. Since corrosion will gradually eat away metal which cannot be replaced, it is evident that this protection is of the utmost importance. In many cases it does not receive the attention it deserves. Many bridges have been seriously damaged by rust, even to the extent of having to replace them, all of which expense could have been prevented by keeping the structures properly painted. Railroads usually recognize the importance of painting, and seldom allow the rust to accumulate to the extent of weak ening the structure. However, even on railroads, bridges are found thai have been materially damaged by corrosion. There are parts speciallj subject to rust, such as the top flanges of deck girders and of stringers thai are more or less hidden by the ties, and which sometimes become badly corroded while the paint on the main body of the structure is still in a good state of preservation. Also parts of highway bridges underneath the floor are frequently in bad condition, owing to the fact that they cannot be noticed by anyone crossing the bridge. However, if proper provision for inspection at regular intervals is made, there is no excuse for this condi- tion resulting in damage to the structure. There are many varieties of paint recommended for steel bridges. The best are usually the most expensive but will be the most economical in the end. The application of paint being about twice as costly as the material, a saving of a considerable percentage in cost of paint will result in only a small percentage of economy on the entire job. The result is that the cheaper paints will last probably two or three years less than will the more expensive ones. The subject of bridge paints is highly technical and cannot be gone into in detail here; however, it is important to note that different paints should be used for different conditions. For instance, a paint that would give satisfactory results in a dry climate would not be suited for a structure subject to acid fumes or engine blasts, as on bridges 422 ECONOMICS OF BRIDGEWOEK Chapter XLI that are over railroad tracks, or for a moist climate, especially near salt water. Some paints are a good protection against corrosion but do not stand the weather, while others have exactly the opposite properties. Therefore, the first or priming coat should be of the first-mentioned variety and the finishing coats of a paint that is not readily affected by exposure to the weather. The most commonly used and satisfactory paint for the priming coat is pure red lead ground in linseed oil. Sometimes linseed oil alone is used and sometimes paint with a Portland cement base. For the finishing coats, graphite paints, graphite and silica paints, or paints of other carbon pigments, such as lamp black with oxide of iron, or oxide of iron paints are most frequently employed. The latter are not suitable for the priming coat, owing to the fact that these pigments promote oxidation, a condition that is often ignored in practical work. As to the appHcation of the paint — this must be well done, if satisfactory results are expected. Metal should never be painted when it is damp, in freezing weather, or over rust. In repainting old structures probably the most important consideration is the cleaning of the metal. Paint apphed over rusted surfaces will not be durable. Further, there is likehhood of corrosion spreading underneath the paint, and then the protection will soon break down. As previously noted, some parts of the structure are subject to faster deterioration of the paint than other parts. This is true of the tops of stringers, floor beams, and compression chords, and of flat surfaces exposed to weather, especially surfaces beneath the floor, such as lateral plates, battens, etc., which give lodging to cinders and other materials that will hold moisture. For this reason a very satisfactory method to use in painting an old bridge, where the paint is bad on certain parts and fair on others, is to clean thoroughly the metalwork and paint over the parts where it is exposed with a coat of red lead or some other good priming paint, and then give the whole structure a good finishing coat. As to the method of cleaning rust from the metal — this is done by cut- ting with chisels and hammers and by scrubbing off with wire brushes, or with a sand blast. The latter method is most effective; however, it is expensive and is not recommended unless the bridges are in a bad state of corrosion. Also it must be used with a great deal of caution so that in removing the rust an excessive amount of the surrounding metal will not be cut away at the same time. To obtain satisfactory results, a great deal of care must be taken in apply- ing the paint; it should be brushed out thoroughly on the metal. Recently painting by air-spraying machines has come into extensive use, but the employment of these machines on bi'idgework is not connnon. It is doubtless a labor saver and, if properly handknl, is not very wasteful of paint. The manufacturers of these devices claim that the work they do is superior to hand painting; and, when skilfully used, it is certain that good results can be obtained. Howevei-, for durability, it is ]irobable that such coatings arc not as good as paint well brushed on ])y hand; still it might be ECONOMICS OF MAINTENANCE AND REPAIRS 423 economical to use spraying machines on bridges, if the labor cost saved will more than offset the decreased life of the paint. Painting by spraying machines would be satisfactory on large vertical surfaces, such as the sides of girders and beams and the faces of large posts and columns; but it is not recommended for lattice work and other small parts, on account of the wasting of paint. One advantage derived from the use of these machines is the application of paint in places that are difficult to reach with a brush. On flat surfaces like walls, recent experiments indicate that the air spray will decrease the labor cost by more than one-half, with a slight increase in amount of paint used, about 5%; but similar data for bridgework are not available. Deterioration of steel structures due to wear will be apparent in the loosening of rivets and in the increased vibration caused by cutting in pins and other parts. When loose rivets appear in the structure, they should be cut out and replaced. They are generally most frequent in lateral bracing of stringers and girders and where single-angle bottom-laterals are attached to the stringers. Also stringer and floor-beam connections are likely to develop loose rivets when the structure is overloaded. In old and heavy bridges the pins will often show considerable wear. This is an expensive matter to repair, as it involves putting the structure on falsework and the use of considerable machinery to re-drill the holes. If pins are replaced, the new pins should be slightly larger than the original ones. This class of repair work is not often done, because a bridge in this condition is usually very much overloaded and should be replaced with a heavier structure. Another location for wear is at the intersection of diag- onal bars that are in contact. In order to prevent these bars from cutting away, a buffer should be placed between them and clamped thereto. On old bridges it is frequently found that the eye-bars making up one member are not pulling evenly. If the member consists of two bars, a satisfactory repair can be made by cutting out a piece of the loose bar, inserting a turn-buckle, and drawing it up to the same tension as that of the tight bar. This can be done without falsework, but traffic must be kept off the bridge while work is in progress. The same procedure can also be adopted for the outside bar of members composed of more than two bars, but on the inside bars it is impracticable, because rivets cannot be driven. When truss bridges are more heavily loaded than was originally con- templated, the overstress is likely to be greatest on the counters. Also on a long span the overstress on the floor system is liable to be considerably greater than it is on the main truss members. For this reason it is often possible to make the structure safe for considerably heavier loading by reinforcing these parts and keeping it in service instead of replacing with a heavier bridge. Also in some cases it is possible to improve the struc- ture without strengthening it; that is, on a very light bridge, subject to large vibrations under trainloads, it is practicable to improve the action by 424 ECONOMICS OF BRIDGEWORK Chapter XLI putting in suitable bracing that will decrease the vibrations and the wear, although, strictly speaking, it will not strengthen the main trusa members. This dissertation does not aim to describe all the details of repairs neces- sary for bridges, because usually special problems in each case are devel- oped; but the underlying principle of economics of maintenance of bridges and similar structures is to keep a close watch on them by frequent and thorough inspection, and to repair promptly any damage that is found. The neglect of prompt attention on a structure often leads to much unnec- essarily expensive work and sometimes to the development of dangerous conditions. The joint data of Mr. Chalfant and Mr. Covell were contained in two letters from which the following extracts have been made : The subject will be divided for convenience into three parts, viz: A. Masonry. B. Floors. C. Painting. (A) Masonry The constant tendency of small streams to change their courses necessi- tates regular inspection to prevent undue scouring and cutting of the banks and approaches. Where the nature of the foundation and depth of masonry are a matter of record, the soundings and measurements can be inter- preted with comparative ease, but where this knowledge is lacking, as is true in many cases, chances should not be taken. Sometimes barriers of a more or less permanent nature can be erected above the bridge in such a manner as to turn the stream back into its natural channel, or the channel itself may be changed. When this cannot be done, heavy rip-rap should be placed around the masonry in such a manner as to fill the hole and prevent further erosion. This rip-rap may be formed of rough stones from the quarry or of blocks of concrete made at the site. When concrete is used for protection, it should be in loose blocks which are free to settle, rather than in a solid mass which, in turn, may be under-scoured. When the stream is of sufficient size to require piers in the channel, with other than rock foundations, there should be a systematic program of sound- ings so that the conditions of the stream-bed around the piers may be known, and so that changes may be noted. This is essential when the masonry rests on piles, but is of even greater importance when the founda- tion consists of a timber grillage on gravel or other hard stratum. Heavy rip-rap is a most excellent protection to piers against scouring of the bed of the stream; but, when once pla(;ed, there can be no assurance of future security. The rip-rap may be moved by ice so that the bed around the pier is again ex])osed to erosion. ECONOMICS OF MAINTENANCE AND REPAIKS 425 (B) Floors When the strength of the superstructure will admit of such loading, the roadway floor should be reconstructed with a reinforced-concrete slab and brick wearing surface, and the sidewalk should be of reinforced-concrete. In some cases, where new steel stringers are required, buckle plates may be used with some form of comparatively-permanent wearing-surface. Where the foot traffic is heavy, the sidewalk can be given an asphalt wearing-sur- face. Few of the older bridges are heavy enough for the loading indicated, having been originally floored with plank. The time for use of a timber floor with the side of the grain exposed to wear has passed in most places. The spikes work up and cut automobile tires, and the floor soon requires renewal. Lumber is now so costly that it is not usually economical to employ untreated timber in so exposed a place as a bridge floor, and the use of treated lumber only, with wood-block wearing-surface, is recom- mended. We have scores of iron and steel bridges over rivers and small streams, which structures are too light to carry a concrete and brick roadway floor or a concrete sidewalk. The weight of trucks now traversing these bridges makes the use of wooden stringers very undesirable because of the presence of knots and other defects, hence steel stringers are employed. The prac- tice in some places is to lay planks directly on the steel stringers with only occasional fastenings, but this does not seem to be satisfactory. Bolting at each bearing point is expensive, hence our practice is to bolt a surfaced 2f"X5" naihng piece on top of each stringer, nailing the planks with two nails at each intersection, as in the case of wooden stringers. It has been found that such solid nailing distributes the load so that a wheel load is carried by at least two stringers. On such bridges the stringers should be from 24" to 28" center to center; and planks of uniform width, at least 10 inches wide and surfaced to 2f inches, should be laid parallel with the back- walls, even though the skew necessitates extra-long planks. This prevents pointed ends, which are hard to support. In extreme cases the planks may be in more than one length across the floor, but the joints in adjacent planks should not come over the same stringer or adjacent stringers, but should lap for a distance equal to at least two spaces between stringers. In case the bridge carries street-car traffic, there seems to be no better construction than to employ ties to support the rails and planks. Seven- inch grooved rails and half-inch tie plates are used. Planks at least 10 inches wide and surfaced to 3f inches give good results. The blocks should then have sufficient depth to come flush with the rail. A shaped wood-filler on each side of the rail is much lighter and more permanent than concrete filling. It is very important, however, that each tie shall have but two bearings and that the rails be as nearly over the stringers as possible, other- wise the springing and warping of the ties wiU give an irregular bearing for the rails, resulting in future trouble. In this connection it might be sug- gested that all street-car rails be painfed, when laid, like all other struc- 426 ECONOMICS OF BRIDGEWORK Chapter XLI tural steel, omitting paint from the head if desired. The rails, in many installations where the traffic is comparatively fight, rust out in the web and base, rather than wear out. Wood blocks may be laid directly on the planks, but the usual practice is to place a single layer of tar paper between, so as to prevent loss of the hot joint-fiUer. A very convenient depth for the wood blocks is 3| inches, but, whatever depth is selected, there should be at least one-fourth inch difference between the depth and the width, so that they wOl not be laid accidentaUy with the side of the grain up. On long bridges, especiaUy where there is a grade, angles should be fastened to the floor with lag screws at intervals varying from 10 feet to 30 feet, according to conditions, in order to prevent the blocks from creeping. On grades greater than two per cent, "hniside" blocks, made like hillside brick, can be used to good advan- tage. We have had a short section of such floor in place on an eight per cent grade for several years with good success. Where there are no street- car rails to prevent side drainage, it is well to give the roadway a crown of two or three inches in order to assist in draining. While it is true that the floors described are heavier than the plank floors which they replace, this is offset by the comparative smoothness of the surface, which reduces the vibration caused by passing vehicles. The sidewalks on our lighter bridges have been constructed with either treated or untreated lumber laid in the usual manner, but this is not very satisfactory. Such floors wear out rapidly, if the traffic is heavy, and are rough and irregular. Treated lumber exposed to wear on the side of the grain does not last well and does not make a good sidewalk. We have recently laid a sidewalk on a river bridge with tongued-and-grooved lumber surfaced to If inches, and with wood blocks 2 inches deep, 3 inches wide, and averaging 6 inches long, laid thereon. Each block in every fifth row was nailed with a lOd wire finishing nail to prevent movement or dis- placement, and the joints were filled with dry sand. It was found, while the work was in progress, that blocks of this depth, on a surface where there was no wheel traffic, remained loose so that mischief -loving boys lifted them out of the walk and threw them into the river. The joints were then filled with hot bituminous filler, as was done on the roadway, but care was taken to cover the surface immediately with dry sand before the filler had time to cool. The resulting surface is very satisfactory. When the old plank floors on the smaller bridges are replaced with the wood-block floor as described, the grade is usually raised a few inches. This necessitates an increased height in the back-wall. At first this was accom- plished by taking up the sand-stone back-walls and resetting them at suffi- cient height to dress to the new floor-level. This is expensive and not wholly satisfactory; and for three years the same result has been reached by cutting the old ba(;k-wall r had Ix^en finished for some time it was submitted for criticism to the veteran paint speciaUst, Dr. A. 11. Sabin, Consviltinp Chemist to the National Lead Company, and the a('knowl(>d.u;(Ml dean nf Aineriean i)aint men. Dr. Sabin very i\indly prepared some memoranda on (■ertain points; and, in order not to necessitate a re-writing of the entire chapter, his .suggestions have been incorporated as foot-notes. 430 ECONOMICS OF METAL PROTECTION 431 4. What colors for paint are best suited to different conditions. 5. Elasticity of paint coats. 6. Covering and spreading powers of paints. 7. Cement paints. 8. Linseed oil alone for the shop coat. 9. Climatic influences on paints. 10. Application of paint by spraying. 11. How best to prepare new metalwork to receive the shop coat. 12. Pickling. 13. How best to paint newly-erected metal. 14. Concrete encasement. 15. Gunite. 16. Proper treatment of steel that is to be encased in concrete or gunite. 17. 'Water-proofing. 18. Protection of metal against brine drippings. 19. Protection of metal against locomotive gases. 20. Causes of paint deterioration. 21. How to care for incipient failure of paint. 22. How to determine when repainting is necessary. 23. How to clean the metalwork preparatory to applying a new coat of paint. 24. Application of paint after field cleaning. 25. Factors that affect results in painting. 26. Economic observations concerning painting in general. The topics in the above list will be taken one at a time and discussed from the economic view-point. Best Kinds of Paint for Shop and Field Concerning the best kinds of paint for bridges there has been waged a lively war of competitors during half a century or longer, each one claiming that his product is the best. Independent engineers, too, have varied in their views thereon, for each one has been rather prone to be influenced by his own personal experience; but of late years a general consensus of opinions has been reached, the decision being that the priming or shop coat should be red-lead paint, the first field coat a mixture of red-lead and some so-called inert material, and the third coat a carbon or graphite paint. The term "inert" as applied to paint constituents was originated some thirty years ago by the late Dr. Dudley. It reflects his idea that lead and zinc pigments are chemically active towards linseed oil, while barytes, silica, etc., are not. As a matter of fact, the most important, if not the only, relations between the pigment and the vehicle are physical, and in that sense there are no inert pigments. Nothing can be less chem- 432 ECONOMICS OF BRIDGEWORK Chapter XLII ically active than powdered quartz, yet it will bleach oil as thoroughly as is possible in any way. Some valuable suggestions concerning the composition of shop and field coats are given at the end of Chapter XLI in the data supplied by Messrs. Chalfant and Covell. There seems to exist among engineers a notion that it is unprofessional for a technical writer to recommend in print any special make of paint. Such a tenet, however, is fundamentally wrong, as is also the idea that one should not call for any particular material of any kind in his specifications. If an engineer is confident that a certain material will suit his proposed construction better than any other, he should have the courage of his con- viction and should call for its use, even if he has to run the risk of evil- minded persons insinuating that he was illegitimately influenced so to do. Similarly, when a technical writer has learned from long experience that certain materials are best for certain purposes, he should be- sufficiently brave and independent to give to his brother engineers the benefit of his accrued knowledge. For many years the author has favored red lead for the shop coat, provided that it were honestly manufactured, honestly mixed, honestly applied, and honestly dried before being either covered or subjected to possible abrasion. Again, experience has taught him that the pigment should not be delivered at the shops as a powder or even as a paste, but that the paint should be previously mixed and ready for use; because the cahber of the men employed for shop-painting is generally so small that they can- not be trusted properly to mix the paint, hence it has usually occurred that the mixture was lumpy, that thinners were illegitimately added, and that the coating was daubed on the steel irregularly, being too thick in some places and too attenuated in others. Year after year the author has continued his search for an ideal shop coat; and it was not until a short time ago that he found it in Dutch Boy Red Lead. At first he could obtain this only in either powder or paste form, with which it was impracticable to obtain perfect results; but finally he persuaded the manufacturers to furnish it ready mixed, using to one American gallon of pure raw linseed oil twenty-eight pounds of the pigment thoroughly incorporated by grinding with the oil. He is now satisfied that he has discovered what he has been searching for during more than three decades. For the field coat he has had the most satisfactory results with Gohccn's Carbonizing Coating, Nobrac, and Detroit Graphite, although at one time long ago, as will be explained further on, the latter paint failed him. ()th(M- engineers have had good luck with other finishing coats — for instance, those recommended by Cheesnian & Elliot, Lowe Brothers' "Metalcote," and Toch Brothers' "Tockohth." Lowe Brothers' "Red Lead Lute" has giv(m good satisfaction as a slio]") coat; and for tlmt ]inrpose many users pin their faith on Cheesman & Elliot's No. 31 Red Oxide. A ECONOMICS OF METAL PROTECTION 433 quarter of a century ago the author used to employ the last-mentioned paint as a finishing coat, and found it excellent; but for a shop coat he believes that nothing is as good as truly-first-class, red-lead paints. Between 1906 and 1912 there was made, on the Havre de Grace, Md., bridge of the Pennsylvania Railroad Company, an elaborate and exceed- ingly valuable series of tests of nineteen different kinds of paint under the direction of certain expert engineers. The results, as reported, emphasize the fact that red-lead paints and those having a considerable amount of red lead in their composition are the most durable, and that a paint in which the top coat is strictly a preservative cover over the red-lead coat gives the best results of all, and justifies the well-known philosophy of the late Mr. Houston Lowe regarding protective paints for steel. To quote the exact words of Mr. Geo. S. Rice, one of the engineers who reported on the said tests, "this philosophy prescribes the production of a solid and sufficiently-elastic foundation with rust-restraining properties by a priming coat of red lead, followed by a transition coat intermediate between the primer and the top coat, the office of the latter being essen- tially protective of the undercoats." It was noticeable in the test that the paints which withstood best had in all instances a very large percentage of pigment in their composition. The winning paint in the competition was a combination of the kind just described, submitted by the Lowe Brothers Company.* In his book "Paint for Steel Structures" Mr. Lowe expresses these conclusions: 1. That the priming, or first coat of paint, upon any surface is the most important one; and that it should form an inhibitive, firm, unyield- ing, and receptive foundation for those to follow it. 2. That under-coats should dry harder and more quickly than those above them, and that the difference in drying between adjoining coats should not be very great. 3. That the quality of the binder is equally as important as the quality of the pigment. 4. That the quantity or weight of pigment used is equally as impor- tant as its quaUty or volume. 5. That the time and method of application are equally as impor- tant as the quality of the paint. There used to be some well-founded objections to red-lead paints in general, and these still hold good against the cheap varieties thereof. The principal ones were a tendency to sag and run on vertical surfaces, and * This statement is on the authority of Lowe Brothers' written claim, but it has been contradicted by Dr. Sabin, who says that the winning paint was a pure red lead man- ufactured by the National Lead Company. Dr. Sabin prefers to use red-lead paint for all three coats instead of for the shop coat only, in spite of the very prevalent idea that red lead, for efficiency, should be covered by a more elastic pigment. 434 ECONOMICS OF BRIDGEWORK Chapter XLII to settle into a hard mass in the bottom of the container. These faults were due to an excessive amount of Utharge in the pigment, sometimes as much as thirty per cent. Within a few years certain lead-paint manufacturers have reduced the Utharge to as low as two per cent, the remaining ninety- eight per cent being true red lead, Pb304. This makes an ideal paint for the priming coat; for, being extremely fine, it fills aU pores, and brushes out in a smooth, even film free from voids. Moreover, it stays in place on vertical surfaces, does not act ropy under the brush, and does not settle to the bottom of the container. It is sold generally in paste form; but, until it can be regularly furnished ready-mixed for apphcation, it v-ill not have attained its acme of excellence. The amount of red lead to be used per American gallon of vehicle is stni a disputed point among engineers. In some cases the amoimt actually employed has been as high as thirty-seven pounds; but such an unusually great quantity cannot be made to give satisfactory results, unless all the conditions are ideal. If the paint be appHed under contract, which is by no means the best way but sometimes is unavoidable, it is well to limit the amount of pigment to twenty-eight, or possibly thirty, pounds per gallon of oil. The theory one should adopt when applying the coats which follow the priming coat, as well as at any time thereafter when the bridge is to be repainted, is to have each coat more elastic than the one preceding it, so as to insure against checking and alligatoring — a term very aptly apphed to what occurs when paint dries in lumps or ridges or when it shows wide, irregular cracks, giving the surface an appearance of alligator hide. Some authorities advise adding a little non-drying oil to the final coat of paint, in order to enable it better to shed water; and the author agrees with this practice, provided that the amount used be not great enough to prevent the paint from drying thoroughly by the time an additional coat is required. Summing up the matter of the best kinds of paint for bridgework, the author feels that he cannot do better than to quote the following from Mr. Houston Lowe's ''Paints for Steel Structures" concerning the desirable features of an anti-corrosive metal coating: 1. It should hide the surface. 2. Should cement itself together, and also cement itself to either damp or dry metallic surfaces. 3. Should expand and contract without breaking its own body. 4. Should present a hard, yet tough, outer surface. 5. Should be impervious to water, carbonic acid, or other gases. 6. Should be unaffected by sunshine, heat, frost, dew, or climatic changes. 7. Should be unaffected by ordinary mechanical abrasion. 8. Should wear evenly. ECONOMICS OF METAL PROTECTION 435 9. Should fail by gradual wear, not by disintegration. 10. Should leave a good surface for repainting, 11. Should not require an unreasonable amount of skill or muscle in I application. 12. Should be homogeneous. 13. Should dry fast enough. 14. Should not be readily ignited. 15. Should have power to absorb and remove moisture or dampness from the metal. 16. Should have properties that will prevent corrosive action of traces of water in contact with the metal. Best Vehicle for Paint Durability of paint depends just as much upon the vehicle as it does upon the pigment. Up to the present time no vehicle has proved to be anything hke as good as pure, raw, linseed oil, notwithstanding the fact that many substitutes have been tried. Some of these substitutes are valuable as thinners of linseed oil, if used in moderate quantity, because they often improve somewhat both its drying and its working properties. The usual reason, however, for the adoption of such thinners or adulterants is to reduce the cost of the paint; and too often this is done at the expense of its quality. It is generally conceded that ''the base of the best substi- tutes for linseed oil is linseed oil itself." The author once had great hope of Leucol Oil as a vehicle; and, as a test of it, he used Leucol Red-Lead Paint on one of his Mexican bridges in com- petition with a number of other paints on several nearby structures; but it failed to give satisfactory results, the surface quickly assuming a whitish tinge, and the protection failing much sooner than it should have. It should be stated, though, that the climatic conditions in the tierra caliente where these structures were located were unusually severe for bridge paints. All but one of the paints then tested failed unequivocally — but of that exception, more anon. Boiled linsesd oil was much used for bridge paint in times long past; but experience has shown that the boiUng is a detriment to the vehicle instead of an improvement thereto. Use of Driers ■ Some engineers consider all driers merely as adulterants, employed solely for the purpose of cheapening the product; but the author is of the opinion that they occupy a legitimate place in paint manufacture, provided they be used in moderation — especially for priming and intermediate coats, which often need to dry fairly quickly in order not to delay the application of the succeeding coat. As far as he knows, the best drier to employ is 436 ECONOMICS OF BRIDGEWORK Chapter XLII Sipe's Japan oil, most of the other driers being a detriment rather than a help, especially to red-lead paints.* Best Colors for Paints Practice seems to have decreed that dark paints are more suitable for bridges than light ones, notwithstanding the well-known facts that they absorb much heat, and that excessive heat is one of the most active agencies in paint deterioration. The main reason for the reluctance to use light paints is their tendency to fade and to show the dirt that inevitably accu- mulates on all bridge metal; but the fading is avoidable by a proper study of the finishing coat, and it cannot be denied that dirt shows more or less on dark paints as well as on light ones. It must not be forgotten that the selection of paint color for any bridge is a matter of aesthetics as well as of expediency; for in some structures dark colors give the finer effect, and in others light ones provide a better appearance. An old favorite color of the author's is olive green; and he has employed it on a number of occasions with satisfaction to all concerned. Canary yellow and pearl gray are often suitable colors for the finishing coat. There is one important point about paint colors that should never be ignored, viz., that, no matter how many coats are given to any steel- work, all of them should be of essentially different shades or colors, in order to make sure that all the coats called for are really applied. In one of his early bridges, the author caught the erection superintendent trying to palm off on him a single coat of rather thick paint instead of two field coats of the same color. Ever since then his bridge-erection specifications have called for distinctly different shades or colors of paint coats. Elasticity of Paint Coats The matter of elasticity in paint coats is one of extreme importance; because, if neglected, the paint is liable to crack and permit moisture to reach the metal, thus starting rust. As before indicated, there should be a gradual increase in the elasticity of the different coats from the priming one outward. Covering and Spreading Powers of Paints One of the most effective claims of paint-selling agents is that the special paint which they handle has a very lai-ge spreading power; and this *Concerning driers Dr. Sabin writes as follows: Three or four years ago I sent a circular letter, asking confidential opinions as to driers, to about a dozen of the chemists of the really big mixed-paint companies. >\'ith- out exception they agreed that if price is left out of account the best drier is free from rosin, and contains lead and manganese, from three lo tw only-five times as nnich lead as manganese, but must contain both. 1 myself would not object to a drier made by a r(>s)ionsible concern, whic^h con- tained a little rosin, as most commercial driers do. The trouble is to draw the line. ECONOMICS OF METAL PROTECTION 437 appeals strongly to most of their buyers — usually erection contractors — who recognize that the greater the spreading power the smaller the quantity of paint required, and, consequently, the less the cost. The bridge owner, on the contrary, is not interested in having his contractor use paint of the greatest possible spreading capacity, because the greater the said capacity the thinner the coating — and the thinner the coating the sooner will it become disintegrated by moisture, gases, etc. Of course, one can go to the other extreme by laying on the coat too thick, in which case it will run on vertical surfaces and will be too slow in drying on horizontal ones. Ordinarily, single coats of dried paint vary in thickness between one five- hundredth and one one-thousandth of an inch; and to produce this the spreading capacity is from eight-hundred to sixteen-hundred square feet per American gallon of paint.* The inspector of painting on bridgework, acting solely in the interests of the owner, should endeavor to have all paint apphed just as thickly as it can be used without flowing on vertical surfaces. It should be daubed on thick at first, then gradually worked out by careful brushing so that it will flow into all the pores of the metal. Distinction should be drawn between covering capacity and spreading capacity of paints. The former refers to the hiding capacity of the coating in relation to the surface on which it is apphed, and is measured by certain standard tests on white surfaces, while the spreading capacity refers to the number of square feet of surface that can be covered by an American gallon of the paint. Cement Paints Portland cement as a pigment in bridge paints has begun to come into vogue of late years, the principal manufacturers of it being the well-known firm of Toch Brothers, and their product being designated "Tockolith." The author has not yet tried this brand of paint on any of his bridges, hence cannot speak from personal experience concerning its efficacy; but the fact that such a prominent bridge engineer as Dr. Gustav Lindenthal has used it on some of his largest structures is a guarantee that it is a first-class protective agent. However, Dr. Lindenthal is not willing to go so far as to state that Tockolith is superior to red-lead paints of best quaHty; for the author asked him the direct question and he would not reply affirma- tively. Toch Brothers have issued a very interesting little pamphlet "R.I.W. Steel Preservative Paints" (R.I.W. meaning "Remember It's Waterproof) ; and the reader is referred to that publication for further infor- * Dr. Sabin prefers to adopt an area of 700 square feet per gallon of paint for red lead coatings, and states that graphite paints are supposed to cover from 350 to 600 square feet per gallon. He claims that red lead makes a stronger and more impervious film than anything else, hence can be safely put on thinner, and that three red lead coats, covering 700 square feet per gallon, make a final film seven one-thousandths of an inch thick. 438 ECONOMICS OF BRIDGEWORK Chapter XLII mation on the subject. If the claims made by its writer are correct, Tockohth has all other paints beaten for bridgework. Speaking of the claims of paint manufacturers and agents concerning the excellence of their products, reminds the author of an amusing storj^ once told him by Dr. Sabin; and, as it has never yet appeared in print, it is here put on record. The late Mr. D. D. Carrothers, of the Baltimore and Ohio Railway, used to tell of a well-known paint manufacturer, a most accomplished and adroit salesman, who persuaded him to buy a considerable quantity of bridge-paint, which did not turn out well. When he came around the next year, the engineer told him to get out; his paint was worthless. "I tnow that," was the unexpected reply; ''don't you suppose I know all about my own paint? We tested that paint thoroughly, as I' thought; but, when it came to practical use, it developed unforeseen defects, and I have had trouble — the utmost trouble — in finding their cause. But we have found and corrected it, and now I have a paint that is absolutely all right; but I had a dreadful time with it last year." He was so plausible, convincing, and persistent that he went away with another good order; which, however, turned out no better than the first lot. "But," said Mr. Carrothers, "I expect he will sell me some more this year! " Linseed Oil alone for Shop Coat A quarter of a century ago it was quite usiial to employ boiled linseed oil without any pigment therein for the shop coat on structural steelwork; and, in conformity with the fashion, the author followed the custom when building the Union Loop and the Northwestern Elevated Railroads of Chicago. In so doing he learned by sad experience the fallacy of the practice; for, owing to a sudden shortage of funds, the Company had to close down all work instanter, leaving a mile or more of metalwork erected and unpainted. When construction was resumed a year or two later the steel was in an awful mess, and required an immense amount of labor to clean it. In all probability, that portion of the structure actually lost a portion of its vitality through this unfortunate circumstance. Thereafter, of course, the author refused to allow linseed oil alone to be used for a shop coat; and eventually the custom went out of fashion. Climatic Influences on Paints Two decades ago very few persons recognized that climate had anything to do with the durability of ])ridge paint, and that a brand which was effective in one locality might fail uttei-ly in another, even if the material were taken from the same Ijarrcl. During the Into nineties the author secured very good results from the Detroit Superior Ca-aphite paint, finding that it could be relied upon for five years before a new coat was needed. All the bridges where he em))loyed it, however, were located in the north ECONOMICS OF METAL PROTECTION 439 until he built one across the Red River at Alexandria, La. About the same time he was constructing over two hundred bridges on the line of a certain Mexican railway; and, although he experimented there with a number of paints, he used at first the Detroit product on most of the metalwork, for i?he reason that it had given him such satisfaction previously. It had not been applied in the field on these Mexican bridges more than a year before it began to fail and to go to pieces rapidly ; and about the same time the paint on the Alexandria bridge showed rapid deterioration. Of course, other paints were immediately adopted for the remaining Mexican bridges; and the manufacturers of the Detroit paint were noti- fied of the trouble. In consultation it was decided that the paint fur- nished by the company, while excellent for dry climates, was unsuited for very damp ones, especially where the dampness was combined with heat. Thereupon the Company instituted an elaborate and extensive series of practical tests, and learned therefrom how to manufacture paints suited to all kinds of climates, thus regaining for their product the high reputation for excellence which it had previously enjoyed. Today it is one of the best finishing coats for bridges that the market affords; but the Company's agents are now very careful to enquire where any paint is going to be used before they sell it. Of all the paints tested on the Mexican bridges previously referred to, there was only one that proved satisfactory for the damp climate of the tierra caliente; and, strange to say, that one was located in the worst pos- sible place for paint endurance, viz., close to the elevation of the salt water of the Gulf of Mexico at the very mouth of a river and not far from the city of Vera Cruz— a place noted for its disagreeable, muggy climate. The paint referred to was Z. P. Leiter's "Air-Drying, Salt- Water-Proof Paint." It had proved to be the best of some twenty standard paints tested at Tampico, Mex., for a large wharf there by the late A. J. Tullock, a noted bridge contractor and the founder of the present Missouri Valley Bridge Company of Leavenworth, Kan. It was because of Mr. TuUock's recom- mendation that the author tried it at Boca del Rio. Some six years or more after the bridge was built and finally painted, the author received a letter from the General Manager of the railroad company asking the name of the brand of the paint, and stating that, in spite of its being often drenched with salt spray, it appeared to be in as good condi- tion as new paint.* Soon after that the author was engaged on the building of an important bridge, having the bottom chords quite close to the salt water, at Vancou- ver, B. C. ; and, naturally, he arranged to use the Leiter paint. The metal- work was being manufactured in the shops of the Dominion Bridge Com- * It has been stated that, since the death of Mr. Leiter, the formula for his Air- Drying, Salt- Water-Proof Paint has been lost. If such be the case, it is truly regret- table, for it certainly was a most effective protection to steel against the attacks of salt- water. 440 ECONOMICS OF BRIDGEWORK Chapter XLII pany near Montreal, during the winter; and, when the paint was applied to the cold steel, it would not adhere, consequently another brand had to be employed. Mr. Howard P. Quick, Consulting Engineer, formerly Mechanical Engineer and Designer for the Pearson Engineering Corporation and Asso- ciated Companies in Brazil, Mexico, Canada, Spain, and the United States, has very kindly furnished the author with the following information con- cerning the developing of a suitable paint for steelwork of all kinds to meet the abnormal climatic conditions of Brazil at a place where no paint of any kind imported from either America or Europe could endure the tropical humidity. Various American engineers on Brazilian Constructions, recog- nizing the gravity of the situation, combined forces, and had the chemists of the Rio Janeiro Gas Company experiment for them in their search for a paint that would meet the conditions. That company possessed an up- to-date, by-products, coke-retort system, and produced therefrom plenty of tar and other residues; consequently its chemists set to work investi- gating the question on the basis of utilizing these by-products, and finally developed a tough, adhesive, elastic, and glossy-surfaced paint which had all the qualities desired, barring appearance. The composition as reported to Mr. Quick by the American Chemist, Dr. Harrop, General Manager of the Sodete Anonyme du Gaz, was as follows: 1 part of Portland cement. 1 part of kerosene, and 4 parts of gas-works tar. The cement was first mixed with the kerosene, and then tar was added to develop the consistency required. This produced a glossy, quick-drying paint of a dark, greenish-black color which dried as hard as rock and was unaffected by weather or temperature changes. Such a paint ought to be quite inexpensive; and it should be tried in other tropical climates than that of Brazil and also in the Gulf States of the U. S. A. The author surmises that it might not withstand well the cold winters of our northern states; but it would be well to give it a trial there. To-day all first-class paint-manufacturers recognize that it is absolutely essential to know about the peculiarities of the climate where any structure is to be erected before starting to manufacture the field coats of paint therefor. Spraying of Paint Spraying paint on bridge metal is a lately-developed custom; and con- cerning the satisfactoriness of the process there are both pros and cons. It involv(!S a wastage of paint that is unavoidable^ but which may be kept down to r(!asona])le limits by constant care and attention; and it is claimed by some painters that it does not work the paint into the pores of the metal ECONOMICS OF METAL PROTECTION 441 as well as does first-class brushwork. Again, spraying is a messy process, and much paint is likely to go to places for which it was not intended. One great advantage which it has is that it will reach locations difficult of access by the brush, and which, in consequence, are often improperly protected. As far as ultimate total cost is concerned, it is probable that the saving in labor will about offset the wastage of paint. Cleaning of Metalwork for Shop Coat Unless metalwork is thoroughly cleaned before the shop coat of paint is appHed, the endurance of the protection will be short; hence it is truly economic to ensure that the cleaning is effectively done, so as to remove all dirt, rust, scale, and grease. The time elapsing between cleaning and painting should be made as short as possible; because it does not take long to start fresh rusting on cleaned metal. As to the methods for shop-clean- ing, hand-work ought to suffice; for sand-blasting should be unnecessary. If the metal is very badly rusted, it generally establishes sound evidence of carelessness on the part of somebody who ought to be held responsible for its injured condition. Strictly speaking, all rolled material for bridgework should be taken from the mill to the shops with the least possible delay, and should be stored under proper shelter from the elements, in order to avoid rusting; and it would be in the line of true ultimate economy to give it a coat of linseed oil soon after it comes from the rolls. Most steel manufacturers and users will claim that these precautions are unnecessary, that the coat of oil would be troublesome to put on, and that the storage sheds would cost a lot of money. These objections, of course, are important; but the author is of the opinion that, in the interest of true economy, they will ultimately be overcome, and that sometime in the future all proper precautions will be taken on important steel structures to protect effectively against rust the metal that is to be employed in their manufacture. The torch should first be used freely in cleaning metal in the shops, for the double purpose of burning any grease that there may be on it and to remove all moisture; after which should follow scraping with steel brushes, file scrapers, and putty knives. Any heavy seed rust which has formed cups in the metal should be chipped out by hammer, care being taken to avoid all unnecessary cutting of the steel. This cleaning should be most carefully watched by a competent and reliable inspector whose compen- sation comes wholly from the owner; but too often it is done in a careless or perfunctory manner by ignorant foreigners who take no interest in per- forming their work well. It used to be the custom in some bridge shops to turn over the painting to newly-imported Hungarians, who were the cheapest laborers on the pay-roll; and, as a result, the author has seen metal delivered at site with the shop coat of paint overlying in large areas half an inch of frozen mud. Conditions in this respect today are undoubt- 442 ECONOMICS OF BEIDGEWORK Ch.\pter XLII edly much better than they were twenty-five or thu-ty j^ears ago, but there is still much room for improvement. Pickling Pickling is an effective way to clean steel; and it is much used in electro- plating and enameling, but not for bridgework. The reason is the trouble and expense which it involves. In applying the method, it must be remembered that when metal is immersed in a hot bath of either sulphuric acid or muriatic acid, it will be necessary, immediately after removal there- from, to neutralize any portion of the Kquid which adheres to the steel. Painting Newly-erected Steelwork As soon as practicable after a span is erected, provided the weather is propitious for painting, the metal should be thoroughly cleansed from any dirt, grease, rust, or other impurity which it has taken on since leaving the shop; and if, for any reason, any serious rusting has started, all traces of it should be removed. Next, all spots abraded either by accident or during cleaning should be touched up with some of the red-lead paint used in the shop (with, perhaps, the addition of a little Japan drier in order to hasten the job) ; and, after this spotting has dried sufficiently, the first field coat should be applied. This should be allowed ample time to dry before the next coat is put on. Concrete Encasement The encasing of bridge metal in concrete is an expedient which has come into vogue of late years. It is employed in most cases for protecting all metal below the level of the deck against locomotive gases, and is not often used above that elevation. The expedient, though, in one sense is quite old; because, for several decades, column feet of trestles and elevated railroads have been protected by enclosure in the concrete of pedestal tops. In order to make such protection truly effective, the concrete should be water-proof. This result can be accompUshed in a number of ways. A water-proofing membrane gives the most certain results; but in niany instances it will be best to adopt a rich mixture and to add to the cement some five or ten per cent of its volume of hydrated hme. This matter of water-proofing is treated at length in Chapter XLIII. As concrete is heavy, its use for a metal protector adds materially to the dead load of structure, thus necessitating the employment of more steel to sustain it; hence it behooves one to make ihc coating as thin as practi(;ablc— and yet not too thin, because very thin concrete may not afford the requisite protection, unless it be placed by pneumatic gun, in which case it is termed gunite. ECONOMICS OF METAL PROTECTION 443 GUNITE There is an economic question involved in choosing between ordinary concrete and gunite for metal protection, the former being cheaper per cubic unit but requiring a larger volume and, consequently, more metal to sustain its greater weight. The gunite is much more dense than ordinary concrete, and hence affords better protection against moisture. In order to prevent its cracking under changes of temperature, it generally requires coarse wire mesh or expanded metal to hold it together. It adheres so closely to structural steel that, in order to remove it after it has fully set and hardened, chiseling is necessary. Gunite should be at least one inch in thickness. When shot horizontal^ or vertically upward the covering is strong and uniform; but, when shot vertically downward, sand-pockets are likely to form, unless the operation be carefully watched and all improp- erly-cemented material instantly removed. Treatment of Steel that is to be Encased in Concrete OR Gunite In most cases, sufficient attention is not paid to the covering of metal which is to be buried in concrete; because, if it is given a coat or two or ordinary paint, the concrete may adhere to the said paint all right, but the latter may eventually separate from the metal, thus loosening the whole protection and either lessening or destroying its efficiency. In the old days, when the question was much more simple than it is now (involving, as it did, only the burying of anchor bolts or anchor metal in the concrete), the author solved it for his work by giving the metal a coat of boiled hnseed oil at the shops, and by scrubbing it off at site just before placement. That method would be impracticable today on account of the large amounts of steel to be protected; hence one might put on the ordinary shop coat of red-lead paint and take it off after erection by means of a sand blast, thus leaving the clean metal exposed to the concrete or gunite. Toch Brothers, however, claim that their No. 1087A "R.I.W. " paint, which contains no saponifiable oil and, therefore, avoids all chemical action between the concrete and the paint, will make a permanent bond between the steel and the concrete. Some other manufacturers make similar claims for special products of their own. Protection Against Brine Drippings One of the most destructive agencies in respect to bridge metal is brine drippings from refrigerator cars; and, as yet, no satisfactory protection against it has been found. The metal most injured is that in the top flanges of stringers and cross-girders; but the webs and bottom flanges thereof and the buck braces suffer also more or less. Of course, the ideal method of pro- tection would be to catch the drippings in receptacles on the cars and thus 444 ECONOMICS OF BRIDGEWORK Chapter XLII prevent their ever reaching the bridges; but this has not yet been done. It is a matter which should be investigated promptly ; and, if an effective remedy for the trouble be found, it should be utiHzed without delaj^ by aU railroads, because the damage done by the drippings is not confined to the floor-systems, but in deck truss-bridges extends also to the upper chords. The total value of the annual damage to all the steel bridges of North Amer- ica by brine drippings must amount to a goodly sum. The railroads are now struggling with the owners of the refrigerator- car lines in an endeavor to force them to lead the brine to one side so far that it will not drip on the track rails and their fastenings; but nothing of any account is being done to protect steel bridges with open timber decks, excepting sometimes to cover each stringer and each floor-beam with a wide plank or to daub thickly, the top surface of the endangered metal with some paint or other compound that has no chemical affinity for the brine. Protection Against Locomotive Gases Another deadly agent of destruction to steel bridges is the gas from steam locomotives, especially when they pass beneath the structure, in which case the gas collects in semi-enclosed spaces where it remains and steadily attacks first the paint and then the steel beneath. As before mentioned, the surest method of protection against such attack is to enclose the entire metalwork below the elevation of track- rails in concrete or gunite. Another method is to use special paint beneath the floor and to hang wooden or sheet-iron protecting platforms close to the deck. If the tops of the smoke-stacks of the locomotives come very near to the floor of the bridge above, especially where there is a heavy up-grade, cinders are driven out of the stacks at high velocity, combined with smoke and steam, thus forming the most effective possible kind of blast for cutting first the protection and then the steelwork itself. Causes of Paint Deterioration The main causes for deterioration of bridge paint, as stated by the late Mr. Houston Lowe, are as follows: L Water. (Dissolution.) 2. Action of light and heat. . (Chemical and physical change.) 3. Chemical action between pigment and binder. (Disintegration.) 4. Abrasion or mechanical injury. (Motion.) 5. Action of deleterious gases. (Foul air.) It is impracticable to keep water away from a bridge, but the design can be so made that there are no pockets to hold it, in which case it quickly runs off and (evaporates. The deleterious action of light and heat can best be combated by a proper choice of color for the finishing coat. ECONOMICS OF METAL PROTECTION 445 Disintegration by reason of chemical action between pigment and binder is a matter for the paint-manufacturers' chemists to take care of; and this has already been done by all of the first-class companies with more or less success. Abrasion of bridge paint, except by the before-mentioned cinder blast from steam locomotives, is something which should seldom occur, because nothing should be allowed to strike the metalwork of a bridge hard enough to disturb the paint thereon. In respect to the action of deleterious gases, that question has already been discussed at some length herein. How TO Care for Incipient Failure of Paint As all bridges should be submitted to careful inspection at short intervals of time, any incipient failure of paint should be quickly dis- covered. If the failure pertains to the field coats only, it will suffice to cover the defective parts with a layer or two of the final coating; but, if it extends into the shop coat, the spot affected should be covered with red- lead paint of best quality, and afterwards, for the sake of appearance, re- covered with some of the finishing-coat paint. If the metal is exposed and rusted, which will not occur if the structure is properly examined at inter- vals of time not too great, some scraping will be necessary before the red- lead paint is applied. By careful attention of this kind the life of the paint can readily be extended from twenty-five to fifty per cent, as compared with what it would be without such attention. Determination of Time for Repainting When the partial failures begin to come so rapidly that the retouching process is expensive and troublesome, and especially when the attacks appear to be liable to reach the metal through the shop coat, it is about time to give the structure a thorough cleaning and one or (better) two coats of paint. The psychological time for doing this can only be determined by an experienced bridge man — preferably the Superintendent of Structures of the railroad, state, county, or municipality. Cleaning ob' Metalwork Preparatory to Applying New Field Coats The cleaning of the metalwork, if it has been properly cared for, will not prove to be a serious business; but, otherwise, it will involve a rather drastic operation. If possible, the shop coat of red lead should not be disturbed, but should be effectively re-covered. In places the torch may have to be used; but, as it cuts to the quick, its use should be avoided whenever practicable. Similarly, the sand-blast should not be adopted, 446 ECONOMICS OF BRIDGEWORK Chapter XLII unless actual rusting has started, for it eats into the metal; and some good authorities claim that where it is employed the paint will not adhere as long as it will where hand cleaning alone has been adopted. The use of the sand blast deposits a lot of sand in numerous corners and pockets of the metalwork; and it should all be carefully brushed therefrom before any painting is done. Application of Paint after Cleaning The following suggestions concerning field painting, if followed, should lead to economic results in maintenance of bridges: First. Avoid both cleaning and painting in wet or very cold weather. A few months' delay will seldom do any real harm to the metal or even to the priming coat, unless, perchance, the bridge has been neglected to the extent of actually permitting rusting to start. Second. Never do much cleaning ahead of the painting, because a spell of bad weather may come on and last so long that such cleaning wiU have to be repeated. It is not only the extra expense of doing the cleaning twice which is uneconomic, but also the possible injury to the exposed metal from rusting and pitting. Third. Provide large and safe platforms for both cleaners and painters. It is true that these may be expensive in both first-cost and handhng, but their use will enable the workmen to do a much greater amount of work per diem — and better work — than if they were not effectively, safely, and com- fortably supported. Again, there is to be considered the reduced danger to the lives of the workmen; and as a killed employee generally costs the company $5,000, and an injured one whatever amount he can persuade the company to give him or the court to award, it is certainly economical as well as humanitarian to reduce the danger to a minimum. Fourth. Give the first field coat a chance to dry thoroughly before applying the next one. In a long structure or a large one, requiring weeks to clean and paint, this restriction will work no economic hardship; but in a short bridge it will, often necessitating the moving of the painting gang to another structure and returning later to apply the second coat. Fifth. When the amount of cleaning and painting is large, it will be economic to , divide the gang permanently into groups of cleaners and painters; but when the bridges are small, or when the total amount of work is not large, ah the workmen should be trained so as to become proficient in both of these kinds of labor. Factors that Affect Results in Painting As stated by Mr. Houston Lowe;, the ])rin('ipal factors that affect results in painting an^ as follows: 1. Lo(tation of the structure, for example, seaboard or inland. 2. Kind and condition of the surface. ECONOMICS OF METAL PROTECTION 447 3. Quality of the paint and its temperature. 4. Workmanship of the painter. 5. Number of coats appHed and their sequence. 6. Time allowed to elapse between coats. 7. Atmospheric conditions when painting is done. By giving all these factors due consideration when handling a job of bridge painting, and by striving in every way to accommodate the work in the best manner possible to the governing conditions, one can often effect a decided economy. Economic Observations Concerning Painting in General The price of paint is a matter which seldom needs much consideration from the economic standpoint, unless when debating on the choice of two or three kinds of nearly equal quality; because painting is so much more expensive than the paint itself that a very little extra hfe of the coatings will out-weigh in economic importance a large difference in the cost of the material. Generally, one should determine what kinds of paint would probably be the best for any job, then pay for them whatever is necessary, unless it should occur that the seller is extortionate in his demands, which is not likely to be the case when dealing with first-class business men. It does not pay to dicker about the price of paint, because the manu- facturer is accustomed to ''cutting his coat according to his cloth." The author remembers a glaring case of this reprehensible trick that occurred in the nineties. He had been using very satisfactorily a certain magnetic- iron-oxide paint that was not expensive, and recommended it to a contract- or-friend of his for an elevated railroad line. Some three years later the paint agent dropped into the author's office and asked him to specify the brand in question for a large piece of work then about to be let. The request was refused — much to the surprise of the agent, who exclaimed ''is not our paint that you used on the Blank City train-shed giving good service after four years of use? " The reply was: "Yes; but how about the con- dition of your paint on the elevated railroad in the same locality — is it not already going to pieces with only two years' service?" In answer to this question the agent had to explain that the Contractor had jewed down the price and, therefore, the paint had to be adulterated in order to meet the cut. Thereupon the author refused to have any more dealings with such a dishonest manufacturing company, and never again adopted the said paint on any of his metalwork. A layer of good paint is about three times as thick as a layer of the lin- seed oil in which it is mixed, and the increase in thickness cf the former is in direct proportion to the fineness of the pigment; hence it is economic to have the said pigment ground as fine as possible, for it is a fact that, with the same weight of oil and the same weight of pigment, the greater the 448 ECONOMICS OF BRIDGEWORK Chapter XLII volume of the latter — i.e., the finer it is ground — the more slowly will the paint dry and the longer will it endure. The correct and economic theory of metal painting is that the paint used for the priming coat should be of a preservative nature, i.e., of such a character that it will not only possess the power of inhibiting the corrosion of the metal but also that of absolutely excluding air and moisture there- from, and that the other coats should be of a protective nature, i.e., that they will protect the priming coat from the deleterious action of rain, sun- shine, and all other deteriorating agents. In respect to the character of the pigments for the finishing coats, it is important that they be both chemically and physically inert, that they be ground very fine, and that they have an affinity for linseed oil. It is a matter of minor importance whether the pigment be graphite, lampblack, charcoal, oxide of iron, or what not, as far as durability is concerned. Where only three coats of paint are to be used, it is often advantageous to employ for the middle one a direct mixture of the priming and the finishing paints. The character of the brush used is an important element in painting; for it is possible to ruin a coat of good paint by applying it with a broad, thin, flat brush. Instead, the paint should be well rubbed into the surface with a stout, full, round, bristle brush. "Less paint and more painting" should be the slogan for every painter who desires to do good work. A temperature of about 70° F., combined with an atmosphere free from moisture, makes the ideal condition for both the applying and the drying of paint. The matter of humidity is of even greater importance than that of temperature; because nothing retards drying more than dampness and darkness. For places that are badly ventilated, where sunshine does not reach, and that are damp or at times filled with steam or locomotive gases, it is economic to use a special kind of coating, preferably a varnish or resin paint so composed that it will dry rapidly. This dissertation on paint and painting could be carried on almost indef- initely; but, if it were, the author might properly be open to criticism for departing from his subject of economics. It is possible that, even as it is, some of the readers of this chapter will accuse him of that fault. If so, he would reply that anything which treats of how to prolong the life of bridge paint or to protect the metal effectively against corrosion is directly in the line of true economics. Summarizing in a very few words all that has been said herein upon the subject of "Economics of Metal Protection," it may be stated that it is always truly economic to use the best protective agencies procurable, irrespective of their cost, and to spend without hesitation all the money requisite for taking the very best of care of the metalwoi-k in all first-class railway and highway bridges — or, for that matter, in any other bridges that arc worth saving from speedy destruction. CHAPTER XLIII Economics of Water-proofing The economics of water-proofing solid-floor bridges might properly be considered in the chapter on "Economics of Maintenance and Repairs," or in that of "Economics of Metal Protection"; but the subject is one of such importance that it truly merits special treatment in an independent chapter. Very few engineers are sufficiently conversant with the water-proofing of bridges to permit of their writing authoritatively upon the subject of its economics, and the author's experience therein certainly has not been very extensive; hence he deems himself exceedingly fortunate in having secured the aid of Mr. J. B. W. Gardiner, President of Gardiner and Lewis, Inc., of New York City, who has made a special study of the subject, extending over several years, and who has very kindly prepared for him the substance of the following dissertation: The economics of water-proofing means this: Is or is not water-proof- ing worth while financially? does the effect produced or the protection afforded the structure by water-proofing the floor justify the expenditure involved? It must be assumed at the outset that the same care has been taken with the water-proofing as is taken ordinarily with the steel or other structural material, i.e., that the bridge was designed to be water-proofed, that a careful selection of materials was made, and that those materials were installed by men skilled in that particular trade, or at least were placed under careful supervision. These conditions are no more stringent or unreasonable than those which apply to the design, fabrication, and placing of other materials that go into the structure. The initiatory pre- sumption is, therefore, entirely proper. Whether water-proofing as applied to bridge floors is a profitable invest- ment depends on several factors. These are : a. The proportionate original cost of the water-proofed bridge as compared with the total cost of the bridge without water- proofing. 6. The probable life of the water-proofing and the probable cost of its renewal. c. Its effect on the life of the structure itself and on the cost of maintenance and repairs. d49 450 ECONOMICS OF BRIDGEWORK Chapter XLIII The original cost of water-proofing is a function of a number of different factors. The cost of the material itself delivered at site, that of the direct labor involved in placing it, the cost of such provisions as are made for flashing along the hnes of tenniiiation of the water-proofing, the cost of the protective or armor coat, the additional depth of flooring and the greater strength that must be provided in steel bridges to carry the dead load of the water-proofing and its protection, and the accessibihtj' of the site of the work, are all considerations that influence the solution of this question of economics. It is readily seen that the cost of water-proofing must be a fundamentally variable factor, as weU as one which fluctuates with the building-material market. Moreover, the cost per square foot is usually greater in the case of steel bridges than when the protection is appHed to concrete viaducts; because, in the latter, the increase in the dead load does not materially affect the design, and also because in con- crete bridges the protection coat is usually a part of the paving-floor system (except in bridges of the sohd-spandrel, earth-filled type), and hence involves no additional cost. At present-day prices, however, a cost of 40 cents per square foot for water-proofing steel bridges or 35 cents per square foot for water-proofing concrete bridges is a fair average. The relative cost, i.e., the cost of the water-proofing as compared with the total cost of the structure, is also variable. In the case of unique steel bridges, such as the Hell Gate Arch or the Quebec Cantilever Bridge over the St. Lawrence River, or in unusual concrete bridges, such as the Tunk- hannock Creek Viaduct on the D. L. & W. R. R., this percentage cost is abnormally low, because of the extremely high cost of those structures per square foot of floor area. But such structures as those are so unusual that we may ignore them in our cost considerations, and base our results on the more common types of bridges. Data gathered from several eastern railroads show that, of the total cost of a steel bridge, four per cent is properly chai-geable to water-proofing. In computing this figure various standard types of bridges were considered i.e., concrete-filled trough-floors, plate-girders wdth transverse I-beam floors, longitudinal I-beam floors with steel-plate, and deck-girder bridges. Cost data were also gathered for different periods — before, during, and after the war — and the results were averaged. It might be remarked in passing that the advance in water-proofing costs has not kept pace with the advance in other elements of construction. For example, in 1914 the steel in a certain bridge cost S73 per ton erected and the water-proofing 28 cents per square foot. In 1917-1918 the steel in a bridge of exactly the same type cost $143 per ton erected, while the water-proofing cost but 35^ cents per scjuarc foot. Thus, although the steel increased in cost ninety-six per cent, the water- proofing inci-eased only twenty-seven per cent. When it is stated, there- fore, that the cost of water-pi'oofing averages four per cent of the cost of the structure, we are takirig a figui'(» which is really extreme and which we may safely assume will not be exceeded, except in isolated and very ECONOMICS OF WATER-PROOFING 451 extreme cases. To look at this percentage in another Hght, the interest on the cost of a bridge for one year at four per cent will pay for the water- proofing. In concrete bridges the relation between water-proofing costs and total costs is apparently a variable with wide limits, because the character of the pier-work exercises such a great influence on the latter figure. As a matter of fact, however, for certain types of bridges this relation is surprisingly uniform; but distinction must be made between two classes of concrete bridges, in order to arrive at the proper ratio. This is because of the cost of the protection or armor coat placed on the water-proofing. Such pro- tection is always adopted for concrete railroad bridges of whatever type, and for earth-filled, solid-spandrel highway-bridges. These two then may be considered together. On flat-slab highway bridges, the protection coat is frequently omitted; and, if used, it is little more than a grouting course under the paving, which might be required even if the bridge were not water-proofed. This type of bridge constitutes the second class. In the first class the cost of water-proofing bears about the same relation to the total cost as was found in the case of steel bridges — i.e., an average of four per cent. Isolated cases were encountered in railroad viaducts where the cost of water-proofing ran up to eight per cent; but this was exceptional, the usual cost being well under five per cent. On flat-slab highway-bridges remarkable uniformity in relative costs was found. Ninety per cent of the cost figures which were analyzed showed the expense of water-proofing to be between one and a half and two per cent, and only a single bridge showed a greater cost. This last figure, therefore, may safely be taken as a fair average. Thus in all bridges, steel or concrete, except flat-slab-floor highway-bridges, the water-proofing cost is four per cent of the total, while in flat-slab-floor structures it is two per cent thereof. The only element of cost which has not been considered is that of the interest on the investment; but this will not change the ratios which have already been arrived at, since the rate of increase in the cost of water- proofing through the addition of interest charges is, of course, identical with the rate of increase in the value of what the water-proofing is to protect, hence this element of cost may be ignored. Probable Life of Water-proofing By the probable fife of water-proofing is meant, of course, its effective hfe, — the length of time it will continue to exercise its water-excluding function. If a bridge has been properly designed with respect to water- proofing details, and if the water-proofing has been properly placed it will fail, if at all, from one or both of two causes, — a break in the continuity of the water-proofing envelope by rupture or otherwise, and the deterioration of the water-proofing material itself by oxidation or rotting. The shock of 452 ECONOMICS OF BRIDGEWORK Chapter XLIII impact when a locomotive first passes on a bridge, the grinding wrench when brakes are appHed while it is on the structure, the vibration of any steel construction caused by the moving load, the deflection and reverse bending on continuous-span steel-bridges, the changes in volume incident to tem- perature variations — all' these place very severe but indefinite stresses on the water-proofing blanket. At the same time, an engineer, knowing these conditions, can select a material, the physical properties of which will generally meet them. Materials which are brittle at low temperatures should receive scant consideration, because of the probabihty of their being fractured by vibration in cold weather. Materials which are very soft at high temperatures should likewise be regarded with suspicion, because they cannot be held on vertical or steeply-inclined surfaces. Finall}^, a material should be selected all parts of which are flexible and elastic, so that they will yield rather than break under the conditions mentioned. To put it briefly, the water-proofing, in so far as physical requirements are concerned, should be selected on the basis of its plasticity or flexibility at all tempera- tures and its small factor of susceptibihty to temperature changes. As to the deterioration of water-proofing, that is almost entirely a chemical matter. The exclusion of all materials that are affected by water, whether or not the water carries acids or alkahes, such as the hgno-cellulose com- pounds (jute or burlap) and the felts in which tapioca is the binding medium (asbestos felt), the non-employment of those that are physically unstable, such as most of the artificially compounded asphalts and asphalts contain- ing organic matter, and the selection of a material which has to a large degree been pre-aged or pre-oxidized will assure long fife for the protection. Indeed, water-proofing materials (asphaltic) placed in 2500 b.c. have lately been found to be still in good serviceable condition. A discussion of the various materials sold for bridge water-proofing is a compKcated one and very technical. It is relevant to the subject of this chapter only in so far as it may point out the answer to the questions that have been raised. It is sufficient to say, however, that if a selection of materials is made with regard to the known conditions which must be met, rather than on the basis of initial cost, a life of at least 25 years may reasonably be antici- pated, with the probability that this figure will be greatly increased. It is obvious that, if water-proofing a bridge floor is economically wise, the resultant value of the protection afforded to the structure thereby must exceed the cost thereof. That the said value does exceed the cost may be a difficult proposition to establish by definite figures. As far as is known, no data exist concerning the amount of the damage caused by lack of water- proofing. All that can be done with this question is to indicate the agents which attack l)ridge floors and tlu^ effcn-t of water-jiroofing in warding off such attacks, leaving it to the judgment of the intlividual to decide whether the probabilities in the case justify the expense which water-proofing involves. For convenience in treatment, the effect of water on steel alone will be ECONOMICS OF WATEK-PROOFING 453 considered in connection with steel bridges, the effect thereof on the con- crete floor of such structures being discussed in connection with concrete viaducts. The primary function of water-proofing on steel bridges is to furnish protection to those steel members which, because of the very exist- ence of the sohd floor, are not accessible for ordinary maintenance. They cannot be painted or otherwise guarded from moisture — as they are, so must they remain. On railroad structures the flow of water to the drains is seriously interfered with by the ballast, which, to some extent, acts as a dam to hold the water on the surface of the concrete floor. The said concrete floor may thus become saturated, because of the moisture being held for a considerable time against the steel — an ideal condition for destructive cor- rosion. Brine-drip from refrigerator cars is a singularly active corrosive which is a cause of trouble and annoyance to bridge engineers everywhere, its effect being very frequently seen on the top flanges of stringers and floor beams, where it is extremely destructive. Not only are these affected, but also in half-through, plate-girder bridges those portions of the webs of the girders which are covered by the concrete are also subject to corrosion, as the joints where the concrete meets the steel invariably open sufficiently to allow water to enter. It is unnecessary, though, to dilate further on the action of either atmos- pheric water or brine-drip on steel. The facts are well known and univer- sally recognized, and it is conceded that many bridges have been seriously damaged by rust, even to the extent of having to be replaced. This deteri- oration can be prevented on the exposed metal by painting; but the only protection that can be given to those members which are not exposed is water-proofing. The actual money damage resulting from failure to water- proof cannot, for lack of dependable data, be definitely stated. Certain it is, however, that, if a steel bridge is left unpainted long enough, the sectional areas of the metal will be so reduced that the structure will become unfit for use and ready for the scrap heap. And if this is true of the exposed members from which the water dries out quickly, how much more true is it of those members which are subjected to a greatly aggra- vated condition! At just what period inaccessible and unprotected steel will become unsafe no one can say; but the fact that so many and such important members cannot be inspected so as to determine their condi- tion would appear to impose upon an engineer, from the standpoints of both public safety and economy to his client, the duty of protecting the metal by efficient water-proofing. With increasing live loads, it is all the more necessary to maintain the full strength of the steelwork, and not to allow of its weakening by preventable deterioration. From the foregoing it is evident that water-proofing is a necessity for bridges which contain structural steel embedded in the concrete of the floor, and for those having members encased in concrete or gunite. Failure to follow this practise has caused loss in some instances, the encased 454 ECONOMICS OF BRIDGEWORK Ch.^pter XLIII members being seriously weakened, and the encasement being split off by rust. It is not so important when the concrete slab merely rests on the tops of the stringers without encasing them; for the destructive effects are then hmited almost entirely to the slab itself and to the tops of the stringer flanges. The question as to whether reinforced-concrete viaducts should be water-proofed is somewhat more complicated than that for steel bridges, owing to the fact that there is not the same concurrence of opinion as to the injurious effect of water on the structure. It may be stated, though, that the water-proofing of concrete viaducts has lately become a conmion practice with the railroads of this country and with many of the private consulting engineers, as well as with a number of state, countj^, and muni- cipal officials. Certainly, those engineers who include water-proofing in their specifications are actuated by the same desire to produce creditable work, the same loyalty to the interest of their chents, as those who do not. This being the case, on what theory and for what reasons do they consider it justifiable to make this addition to the cost of the structure? Just lohy should a reinforced-concrete viaduct be water-proofed? That there is virtue in water-proofing a flat slab, even though weU pitched for drainage, is shown by the experience of the country with con- crete roads. It cannot be denied that such roads, well blanketed with asphalt, give longer and better service, with less cracking and other evi- dence of disintegration, than those not so blanketed. While this is partly due to the fact that mechanical wear is eliminated, the protection of the concrete from the action of frost and freezing water is an important factor. The drainage problem on a road is much more simple than that on a bridge floor. The standard width of road is generally but 18', so that the area to be drained is only 9' wide — the distance from the crown to the curb. The areas on a bridge floor are generally much larger; and since the water must be conducted to small down spouts, instead of to an open trench, as is the case with a road, the problem in bridgework exists in a much more aggravated form. If, therefore, it is found that water-proofing a concrete road by means of an impervious blanket of asphalt protects the road, prevents its disintegration, and prolongs its life, how much more urgent is the need for water-proofing a bridge floor? A brief analysis of the more important of the disintegrating effects of water penetrations on concrete will serve to bring out the reasons why from an economic standpoint — i.e., from the standpoint of preservation and consequent reduction in both annual-replacement reserves and main- tenance charges, — the water-proofing of concrete bridges is profitable. Water is a universal solvent, affecting, of course, some materials more than others. Th(u-e is in concrete sonic solulile matter; and, if water be permitted to pass completely through, such soluble n\atter is gradually removed by a lea(^hiiig process. This is shown by the fact that water, after it has passed through concrcite, will invariably give alkaline reaction, ECONOMICS OF WATER-PROOFING 455 indicating that it has carried away some of the hme or other alkali content of the cement. Coupled with this is an erosive action which, while shght, is nevertheless present. Particularly are both solvent and erosive actions aggressive at the construction joints, as is evidenced by the excrescence of magnesia and other salts on the under surface at these places. This is because at the joints there is almost always found a film or deposit of laitance, which is loose in texture, non-coherent, chalky, and very porous. Water, if allowed to pass through the concrete at the said joints, will both leach and erode the joint walls very rapidly, thus exposing the reinforcing steel to the air with consequent corrosion, and opening the way in temper- ate and cold climates to the disruptive effect of frost. The result of these combined actions on concrete is certainly the weakening of the structure, as well as the making ready for further and more drastic effects of water dis- integration. In climates where freezing temperatures prevail in winter, there are peculiarly forceful reasons for water-proofing bridge floors. The dis- ruptive force of freezing water is one of the most destructive agencies operating against masonry of whatever nature, whether its mass be mainly natural or artificial. It is particularly harmful where the masonry con- tains cracks, however small or shallow they may be, into which water can penetrate freely. This again has a most direct bearing on concrete bridge floors. In common with most fiat-slab constructions, whether the slab rest on arches or beams, bridge floors are almost certain to develop cracks. They may be merely shrinkage cracks incident to the setting of the con- crete, and hence more or less superficial, or they may be expansion cracks extending through the full depth of the slab ; but the ultimate results will be practically the same. If only surface cracks exist, these will fill with water, which, on freezing, will break down the surrounding walls, causing the concrete to spall. It will thus be weakened along the line of the crack, which must inevitably be deepened with each repetition of the process, until the injury has extended through the entire thickness of the slab. Further- more, since the concrete has been weakened along this line, any unusual stresses incident to expansion, or other force, are apt to spht the slab at the weakened section. ?■: ■ Where the crack extends completely through the slab, the action is still more serious. In such a case, the same frost action may force the walls of the crack apart a material distance, exposing the reinforcing metal to unin- rupted and unavoidable corrosion, thus weakening the entire structure. If electricity be present, the condition will be aggravated by electrolysis, which will not only accelerate the corrosion of the steel but also will soften the concrete, providing it be moist or wet. (See Tech. Paper, No. 19, U. S. Bureau of Standards.) If electrolytic action does occur, the concrete is certain to be split away from the reinforcing material by the mechanical pressure of the forming rust scale, which pressure has been recorded as high as 4,700 pounds to the square inch. 456 ECONOMICS OF BRIDGEWORK Chapter XLIII Efficient, well-planned water-proofing is the only sure preventive of these evils. As provocative of cracks in concrete, the effect of moisture-changes merits attention. It has been fully demonstrated by some most-carefully- conducted tests that concrete expands in volume on becoming wet. This fact may well produce cross stresses in the slab, which will result in the cracking of the surface. If, for example, we have a floor slab 10 inches thick, and if sufficient water falls upon it to wet it to a depth of two inches, the upper two inches will have a tendency to swell or expand, while the lower 8 inches will remain fixed. Along the planes separating these two, therefore, there will be produced a stress which no amount of provision could guard against. Should this cross stress produce surface fissures or cracks, the way is opened for the ultimate disintegration which has been mentioned. On this point, Hool & Johnson, in their "Concrete Engineers' Hand Book" made the following statement: "The expansion and contraction of mortars and concretes, subjected to variations of temperature and moisture conditions, are responsible for practically all failures of these materials under conditions of exposure to the weather. Either temperature effects or moisture effects may be alone operative, or both effects may be combined. ... In the average situation the introduction of dangerous stresses caused by a tendency to expand or contract is more apt to be due to moisture changes than to temperature changes, because the volumetric variations in the latter cases are less marked." There is still another factor entering into the subject, to which engineers generally are not inclined to pay sufficient consideration, largely because it is one which is not directly or immediately measurable in dollars and cents, viz., the matter of appearance. There is no concrete structure which is designed for a greater degree of permanency than a reinforced-concrete viaduct. It is almost invariably an important, indeed a vital, link in a railway or a national or state high- way, the line of which does not change in a generation; and it is usualty designed to carry many times the load which present conditions render requisite, thus making improbable the necessity for renewal by reason of changes in transportation methods. It stands, therefore, through many years a monument to the man who designed it, as well as an indication of the progressive spirit of the community; consequently, both from the stand- point of the designing engineer and fi-om that of the community, every reasonable precaution should be taken to preserve the appearance of what is naturally a beautiful structure. If water is permitted to flow freely through a bridge floor, the result will invariably be the excrescence of magnesia and other salts, which appear on the surface in the form of a white "bloom." This is particularly in evi- dence at the constnu^tion joints, and notably at the joints between suc- cessive arch ribs. Notliing is more disfiguring to a concrete bridge, nothing is more indicative of careless or incomplete work, than the discoloration of ECONOMICS OF WATER-PROOFING 457 a structure due to the action of water. It is readily guarded against at small cost; hence, for aesthetic as well as preservative reasons, water- proofing is well worth while. This consideration, apparently purely aesthetic, has, paradoxical as it may seem, a distinct place in a discussion of the economics of bridge water- proofing. Cities and towns are in constant competition with each other for new industries. Large sums of money are spent annually by these municipalities or their 3oards of Trade in advertising their advantages as loci for manufacturing enterprises. Visible evidences of a spirit of progress in the community, obvious care in attention to details of appearances of public structures, are impressive and cannot fail to attract the notice of prospective residents. This makes for the wealth and progress of all con- cerned. When a visitor's first impression of a city is produced by seeing what should be a beautiful monumental construction covered with the disfiguring surface-blemishes which water-penetration produces, he is apt to turn to a competitor whose neglect of detail is not so marked ; for to the layman — this term being used to differentiate from the engineer — such blemishes mean more than mere surface disfiguration, because they convey the impression of general disintegration and eventual failure, and reflect unfavorably upon the community or the owner of the structure. It is not contended that the neglect to water-proof a concrete bridge will always result in its ultimate destruction. Many bridges which are not water-proofed are still intact; few have completely failed. But water-proofing certainly does provide a measure of protection. It is, in fact, a form of insurance. The cost is small — not more than two per cent of the total — so that if it extends the life of a bridge only a year or two, it is worth while, since the prolonged use of the structure is almost always of greater value than the extra cost plus compound interest thereon. When, however, the protection afforded is not merely for a year or two, but for a great many years, the life of the water-proofing being the only limit, and even that being capable of extension by renewals, it is obvious that the additional cost incident tJiereto is a wise investment. Although, of late years, the author has been specifying the addition of a small percentage of hydrated lime to the cement used for making concrete in bridgework, with the dual purpose in view of increasing fluidity and reducing porosity, he has not called for blanket water-proofing and flash- ing, excepting where there was special reason for preventing drip; but, because of the convincing character of the preceding dissertation, he has decided that in future, if his clients can be persuaded to stand for the additional expense, he will adopt every available effective means in order to water-proof his structures thoroughly. Since the preceding was written, the author's attention has been called to an important paper delivered to the Brooklyn Engineers' Club in May, 458 ECONOMICS OF BRIDGEWORK Chapter XLIII 1916, by Mr. Albert H. Rhett, C. E., entitled "The Water-Proofing of Structiires Subject to Stress from Moving Loads and Temperature Varia- tions." In it Mr. Rhett gives a short, chronological record of the various unsuccessful endeavors to produce an effective water-proofing for bridge floors, leading up to a successful one of his own. In concluding his inter- esting and valuable memoir he makes the following statement : To recapitulate, then : The theory evolved, and which it was attempted to prove, is that, if a structure subject to moving load and temperature variation is to be water- proofed, it can be effected only through the medium of a membrane, incorporated in the floor, which fulfills these two conditions: (1) The compound element of this membrane must, of necessity, be the eventual factor upon which reliance is to be placed. (2) The compound, to fulfill its true function, must remain water-proof, non- hardening, elastic, coherent, and adherent at low temperatures as well as high. CHAPTER XLIV ECONOMICS OF MILITARY BRIDGING FOREWORD By Major General Lansing H. Beach, Chief of Engineers, U. S. Army. The work of our Engineers in France during the World War was some- thing of which the whole American people have good reason to be proud. In this work the members of the engineering profession showed their great versatihty and their ability to attack successfully problems previously unknown to those without military training. There were many things to be learned and some to be unlearned. The Civil Engineer, in general, was forced to revise much that had been incul- cated in him during his earhest studies in engineering, and confirmed during the course of his professional practice. Possibly the most important new lessons were that, in a military construction, time is of more importance than any other feature involved; that a structure, especially a bridge, does not have to be of uniform strength throughout, but that, Hke a chain, it will answer its purpose if its weakest link is just strong enough to stand the strain which will be put upon it ; that architectural beauty for its own sake has no place in field operations; and that permanence is a consideration of such slight importance that frequently it does not enter the calculations at all. The appearaiice and the lack of strength occasionally gave the new officers of Engineers a shock, inducing a feeling that much of their study and practice had been in vain and that much of their previous experience could help them but little in the construction of emergency bridges. It is, how- ever, the Engineer best trained in civil practice who can build the best emergency structure, if he will but properly evaluate the conditions imposed by military exigencies. The Engineers in the War were adaptable, but we are all the results of our education and training; ; and it is, therefore, not amiss to bring to the attention of the members of the profession at large certain principles which they may learn in time of peace and be prepared to apply in time of war, and thus avoid having to acquire this knowledge in the face of the enemy, when the lives of thousands of their fellow citizen-soldiers are at stake. Victory and defeat, the rise and the fall of nations, have often depended upon seeming trifles. It is conceivable that an engineering failure in war may involve the extinction of a state. 459 460 ECONOMICS OF BRIDGEWORK Chapter XLIV The eminent author of this book has made a profound study of the economics that apply to many of the problems which the Civil Engineer is called upon to solve, and it will be widely read by all engineers who are determined to be in the forefront of their profession. It, therefore, seems most fitting that in this book there should appear a chapter deahng with the principles which must apply to a phase of the work of the Military Engineer, work which any one of the many readers may be called upon at some time to carry on. Colonel P. S. Bond, Corps of Engineers, U. S. Army, was selected to prepare this chapter because of his intimate knowledge of the subject, acquired by study and by practice. He has presented it clearly and logically, pointing out the essential differences which must prevail between the principles that govern the building of bridges, according as they are intended for military use or to serve peaceful purposes. He has stressed particularly the all important time element in war enterprises, and has shown that what in civil practice might be wilful waste, in war may be the greatest of all economic measures. In fact, so tre- mendous is the cost of conducting a modern war, it is hardly too much to say that any expenditure of money or of material which will shorten its duration is easily justified. A careful reading of this chapter is, therefore, earnestly recommended to all of those to whom the Army must look for help when next we are called upon to take up arms in the defense of our rights and the rights of humanity. , Economics of Military Bridging Streams constitute one of the greatest obstacles to military operations, and bridge building is, accordingly, one of the chief duties of the military engineer. Fundamental Economics of Military Engineering Military bridge engineering is an adaptation, in a simple and frequently crude and makeshift form, of civil practice to military needs. The finida- mental difference between civil and military practice is in their economic aspects. The technical details of military bridges are characterized by extreme simplicity, which is demanded by the conditions under which they must be Ijuilt. They will present little difficulty to the engineer having a good general knowledge of civil practice. But the successful practice of military engineering, including bridging, doinands a knowledge of the economic principles which are specially appli- cable to warfare. Mistakes in economic judgment will have more far- reaching and disastrous consequences in war tiian in peace — there will be greater opporl unities for tremendous i)rofits or ruinous losses. A practical ECONOMICS OP MILITARY BRIDGES 461 knowledge of economic principles is, accordingly, of greater importance than a knowledge of technical details. It will, therefore, be of interest to consider these principles m their application to warfare. In war the highest economy is victory, and the greatest waste is defeat; consequently, anything which contributes to victory and evades defeat is justifiable, however great its cost or the incidental waste involved — of course within the hmits of reason and common sense. A free and rapid expenditure of available resources m war is not waste, but the highest form of economy when it contributes to early victory. The march of events is rapid in modern war. A few days, even a few hours, have decided the issue of battle. The Commander does not ask his Engineer, "How much will your bridge cost? " but, " How soon will it be ready? " In civil bridge construction the essential requirements, in their usual order of importance, are. initial cost, safety, durability or permanence, time required for construction, and aesthetics. The time required for construction is of importance chiefly in so far as it affects the financial returns on the investment. A considerable time spent in design and other preliminaries to construction, and on the work itself, will usually be amply justified by a material saving in cost. The Time Factor Substituted for the Cost Factor In military construction some of these desiderata entirely disappear, and the order of importance of others is reversed. In particular, the time of construction becomes of paramount importance — the time factor is substituted for the cost factor as the principal consideration. In sharp contrast to civil practice, we find that any cost will be justified, if it results in saving of valuable time at a critical juncture. As a consequence of this, the construction of military bridges is conducted with feverish rapidity. The highest achievement of the military bridge builder is a structure just sufficient for its immediate purpose, erected in the minimum time, without undue regard for cost, appearance, or durability. Time is always the chief — often the only — consideration; delay is always inadmissible; and suc- cess is the only criterion by which the engineer will be judged. In civil construction time is of importance; but it is seldom necessary to sacrifice cost, safety, and all other considerations to gain time. A delay for a moderate period will usually not be hurtful. In military operations, on the contrary, a delay of a few days, or even a few hours, may mean failure instead of success. A similar situation sometimes arises in civil bridge practice, as, for example, when it is necessary to restore traffic on an important main-line railroad after a bridge has been destroyed by fire or flood. In such a situation the economics are similar to those of warfare; and military methods of procedure would there be appropriate. The Principle of "Bare Necessities Only " Military bridges are always required in the least possible time, and there will very often, perhaps usually, be a dearth of building material. 462 ECONOMICS OF BRIDGEWORK Chapter XLIV It is, accordingly, a fundamental economic principle of military construc- tion that bare necessities alone should be provided for. An engineer who wastes valuable time and material constructing a bridge wide enough and strong enough to carry heavy motor trucks, when the need of the instant is a simple foot-bridge over which a body of infantry may pass at once to a critical point of the field, has manifestly failed to grasp this fundamental economic principle. Safety and Permanence The civil engineer "builds for posterity." Whatever the type of bridge adopted, it is usually constructed in as enduring a faslnon as the funds available and the material employed will permit. The useful life of the bridge is ordinarily a measure of the skill of its builder. The military engineer builds to meet the exigency of the moment. He is lacking in skill if he expends time in order that his bridge may endure unduly long beyond the period it is needed, which in no case exceeds the duration of the war, and is often limited to that of a single action. The thoroughness of his work should be sufficient unto the immediate needs — and no more than sufficient. Nicety, finish, refinement, and permanency, for their own sake, are to be avoided. The military bridge should have no beauty except that which is inherent in utilitarianism. In civil construction great weight is properly given to the factor of safety and to the durability or permanence of the structure. In military procedure these considerations have far less weight. The factor of safety need seldom be as great, although this will depend to some extent on the situation. Where a military force is entirely dependent on a single line of supply, the bridges on this line should have a factor of safety as great or nearly as great, as would be employed in civil practice. But ordinarily, in the combat zone at least, the saving in time and material which results from using a factor of safety of 2 instead of 4 or 5 will more than compen- sate the risk involved in the possible collapse of structures. The risks attendant upon military operations are so numerous and so great that the slight additional risk of a small factor of safety is of minor significance. Permanence is of negligible importance in military construction, inas- much as the structures will never be required beyond the duration of the war, and frequently for much shorter periods. It is generally good economy first to meet the exigency of the moment, and later to repair, strengthen, or even replace the structure, should this be necessary by reason of continued need. The time for which any military structure will be required is usually short, and always uncertain, so that it is not good economy to look too far into the future. Warfare is an economic art, no less than any of the pursuits of peace.' In war we have a mission to perform, which is the achievement of victory; and this mission sliould ])e acconiplislied with the least ])ossible expenditure of blood and treasure — in oilier words, in the most economical fashion. ECONOMICS OF MILITARY BRIDGES 463 This demands that victory be won in the shortest possible time, since the cost of war is nearly proportional to the duration of the conflict. More- over, in the prosecution of the conflict itself, victory comes to the com- batant who can most rapidly mass his resources of men and materials at the critical points. It is for these reasons that time is so important an element in all military operations, including construction. Waste not Justifiable The achievement of our purpose in war calls for a rapid expenditure of both life and material. It is the duty of the Commander, however, to expend in the most economical manner possible the resources which the nation by painful sacrifice has placed at his disposal; and the same obhga- tion rests upon all his subordinates. But great expenditures to accom- plish great results are not wasteful. The engineer must thoroughly disabuse his mind of any belief that military necessity ever calls for or justifies waste of the nation's resources; but he must not allow a penny-wise inclination toward economy of material or money to cause him to overlook the greater necessity for economy of time. Material should be freely expended to save time, but it should never be wasted. However great the resources of the nation, there is always a dearth of construction material in war, due not alone to lack of material but also to lack of transportation facilities for dehvering it at the places where it is required. A reckless use of material in one locality may mean the failure of important operations in some other place where the material thus wasted is needed. A small saving of material must not be made at the expense of a great waste of time; but the soldier who deliber- ately or carelessly wastes any useful material is guilty of highly unpatriotic, not to say criminal, conduct. Classes of Military Bridges There are two general classes of military bridges; (o) Those constructed in rear of the battle lines, in the zone of com- munications, not in the immediate presence of the enemy. (6) Those constructed at the front, within the combat zone or the area subject to hostile fire and raids. Structures of the first class are erected for purposes and under conditions approximating those of civil construction in time of peace. The need for such bridges is determined mainly from strategical considerations, and they seldom have any intimate relation to the tactical operations of the com- batant forces. As compared to bridges within the zone of tactical activi- ties, they are usually needed for a relatively long period — from several months to the duration of the war. They are required to carry heavy loads. They may be constructed by non-combatant troops, by hired civilian labor, or even by contract. Construction plant, similar to that employed in civil works, will be utilized whenever it is available. With the exception 464 ECONOMICS OF BRIDGEWOEK: Chapter XLIV of the facts that they are less permanent in their nature, and that no con- sideration is given to the appearance of the finished structures, these bridges are built in accordance with the recognized rules of good civil practice. Structures of the second class, those at the front, are erected to meet the immediate tactical requirements of the combatant forces. They are usu- ally in the form of hasty makeshifts of a crude character, and are built by combatant troops in accordance with the economic principles of warfare heretofore enunciated. There are no sharp lines of demarcation between civil practice and mili- tary bridges of the first class, nor between military bridges on the lines of communication and those at the battle front. Mihtary economics are occasionally applicable to civil practice, and vice versa. Types of Military Bridges The particular type of bridge to be employed in any situation depends on the nature of the stream — its width, depth, swiftness of current, and liability to flood; the character of the approaches; the labor, plant, and materials available; and the loads to be carried. Every type of bridge known to civil practice has been employed for military purposes, including pile and framed trestles, and cantilever, truss, girder, suspension, floating, and arch bridges. The last mentioned, either of steel or masonry, are very rarely used, and only on the fines of communication. Military bridges are, in general, crude, impermanent, and makeshift forms of their civil prototypes. Any bridge for which the erection requires a long time and an elaborate and heavy plant will usually be avoided in military practice, and is out of the question for any tactical purpose. The considerations calHng for such bridges in civil practice will usually have much less weight in time of war. For example, a long-span-truss or cantilever bridge may be adopted in order to avoid the expense of very deep foundations, to evade danger from floods, or to meet the requireinents of navigation. Deep foundations are out of the question in emergency military bridging, and are evaded by the use of the floating equipage, by portable (sectional) trusses, by long-span suspension-bridges for very light loads, or by ferries for occasional traffic too heavy for the bridges. Danger from flood is avoided in a similar man- ner; but, as the period for which a military bridge will be required is always relatively short, it will frequently be bettor to run the rechicod risk of flood damage, rather than spend nuich time in guarding against it. If the flo(Kl risk be really great and imminent, it is best avoided by using the floating equipage, \mless a clear span of moderate length will meet the situation. In war the rights of (uvil navigation must give way to military necessity. Military traffic, both over the ])ri(lge and along the stream, may be regulated so as to intcn'fere with each oi hei- as fit! h^ as possible, draw spans being provided, if necessary, for the i)assage of vessels. ECONOMICS OF MILITARY BRIDGES 465 The Typical Military Bridge The typical military bridge, therefore, since it must be erected in a short time and without elaborate plant, will be characterized, as a rule, by shallow foundations, by a relatively large number of piers or supports with correspondingly short spans, and by structural members of small size, light weight, and great simplicity. If we add that timber is the material most frequently employed, this dehneation of the typical military structure wiU be recognized as a description of the short span, framed-trestle-and-stringer, timber bridge; and, in fact, this is the type employed in the majority of cases in military practice. If we now permit the occasional use of pile trestles instead of framed trestles, I-beams in place of wooden stringers, and simple wooden or sectional steel trusses for greater spans, and include the standard floating equipage, we shall have enabled the military bridge builder to meet nearly all situations with which he will be confronted. Some of the economic features of the more usual types of military bridges will now be considered. Framed Trestles The framed trestle requires no plant, other than simple tackle, for its erection. It is readily constructed from a great variety of materials, and by unskilled labor; and it meets the majority of emergency situations. The framed trestle, as we have seen, is accordingly the favorite type of support in hasty military bridging in the combat zone. The usual form of bent is the simple, one-plane type with cap, sill, two or more posts or legs, and diagonal sway-bracing. The trestle will be stiff er against lateral stresses, if the outer posts be inclined or battered; but with unskilled labor it is easier to make all the posts vertical. If pieces of sufficient length are available, the stiffness may be greatly increased by extending both the cap and the sill a foot or more beyond the outer posts and attaching the sway braces to the ends of the cap and sill as well as to each post. If the depth of water is such that the trestles tend to float up, the bot- toms of the posts may be boxed in and the compartments filled with stone. If the river bottom be of low bearing power, a sill of greater width than that of the posts may be employed. The bearing power of the bottom may be increased by brush mattresses or fascines, wooden mud-sills (where the water is shallow), or rip-rap. It is usually well worth while to resort to such measures, in order to avoid the use of piles. Economic Span of Trestles The proper economic span of pile or framed trestles is determined by balancing the time and material required for the bents against that required for the stringers. The problem cannot be solved with mathematical pre- cision. It depends upon the height of the trestles, the difficulty of placing 466 ECONOMICS OF BRIDGEWORK Chapter XLIV the bents, the load to be carried, the materials available which are suitable for bents or stringers, respectively, etc. Crooked stringers are an unmiti- gated nuisance; and in a hasty bridge, when only a scrubby growth of timber is available, it may be impossible to secure reasonably straight pieces, except in very short lengths. In such a case the spans must be short. On the other hand, if bents must be built of round timber, and if good dimensioned material is available for stringers, the number of trestle bents may be reduced and the span-length increased. If the loads to be carried are moderate, longer spans will, of course, be permissible. The engineer must scan the situation and come to a decision based on his experi- ence and common sense. However, it is possible to state the usual limits of good practice. Under average conditions the proper economic span of hasty, mihtaiy trestle- bridges is from 10 to 15 ft., averaging about 12 ft. For heavy standard bridges, designed to carry the greatest loads of the army, the maximum practicable span, when wooden stringers are employed, is 16 ft., which length requires 16-inch stringers. If I-beams be employed, this span may be increased to 22 ft. For any length over this, either strutted beams or some form of truss should be adopted. When very tall trestles are required, it will often be good economy to increase the span by using simple trusses, or by strutting. In practice, the number of bents and the span of trestles are frequently determined by the material actually available for stringers. These must be able to carry the required loads; and, whenever possible, they are furnished in standard sizes and lengths for this purpose. Where the material for stringers has been cut to a given length, the span of the trestles is, of course, thereby fixed. For moderate loads, tall trestles may be built in single stories, if material of suitable length is available. For the standard heavy trestles the follow- ing rules have been adopted: Up to 16 ft., one-story bents with one-story bracing. From 16 to 24 ft., one-story bents with two-story bracing. Over 24 ft., two or more stories. The need for longitudinal bracing between bents depends on the height, the span, and the nature of the traffic. If the height of the trestle exceeds 7 ft. and the span is greater than 10 ft., longitudinal bracing should be placed in each alternate bay. For considerable heights it is well to brace all bays, if practicable. In multiple-story bents each story should be separately braced. Spar-Bridges The term spar-bridge is a general designation for a military structure of rough (round) timber. Such bridges ai-e built from necessity when better material is not available. They will continue, as in the past, to be a characteristic type in the operations of relatively small and poorly equipped ECONOMICS OF MILITARY BRIDGES 467 forces, especially in sparsely settled countries under bad conditions as to transportation. Because of lack of other fastening materials, spar-bridges are often assembled by lashing the trestles. In such cases it is impossible to use "rider" sills and caps, placed on the tops and bottoms of the posts; hence "ledgers," attached a short distance below the tops and above the bottoms of the posts, are employed. Stringers are also lashed, and decking is secured by means of side-rails placed over and lashed down to the outer stringers. The term "spar-bridge" is generally used to describe such a characteristically military structure. Whenever possible, however, even bridges of round timber should be roughly framed, have rider caps and sills, and be fastened with bolts, spikes, or dogs. A special form of spar-bridge, known as the lock-spar, is a structure in which the trestle bents are tilted towards each other and locked together or to a frame placed between two bents (double lock). These are of very limited application, but may occasionally be used to advantage in spanning a deep gorge. With the double lock the bridge is practicable in spans up to 50 ft. for moderate loads. Spar-bridges, especially when lashed, if of necessity employed in the first instance for a hasty crossing, should be replaced promptly by a better type of bridge, as they are unsuitable for continued heavy traffic. Pile Trestles Framed bents, as they are so easily erected without plant, will be gen- erally employed when the bottom is firm enough to support them, and when scour can be prevented. When the bottom is of very low bearing- power, or subject to scour, as in the case of soft mud or shifting sand, piles will be required. Pile bents have the disadvantage of necessitating longer pieces, more time, and the use of a pile driver for their erection. How- ever, they are required in many situations, especially for railroad bridges, where even a slight settlement, such as might result from the use of framed bents, would be dangerous. Accordingly, a number of efficient portable pile-drivers should form part of the equipment of an army; and, when such are available, pile trestles will often be preferred to framed ones. Pile-trestle bents are subject to the same economic considerations as framed-trestle bents, except that, being stiffer, they require less bracing. Trusses For military purposes the truss has all the economic advantages it pos- sesses in civil use. It is employed to reduce the number of trestle bents, or other type of piers, when the construction of the said piers is, for any reason, particularly difficult. Trusses are also used to give greater clear- ance as a measure of flood protection, or to span deep chasms or streams without intermediate supports. Military trusses must usually be erected without falsework, and with 468 ECONOMICS OF BRIDGEWORK Chapter XLIV the aid of only animals, simple tackle, and gin-poles or A-frames. There will be difficulty in transporting long pieces for such trusses. Where they must be constructed in the combat zone, the span, consequently, is limited to 40 or 50 ft. in the usual case. Larger trusses may occasionally be built in place; and when plant is available, as in the rear areas, much greater spans will be practicable. Improvised trusses must be constructed of wood, preferably sawed material, and steel tie-rods or, in exceptional cases, cables. Accordingly, simple triangular (King post), Howe, and Pratt trusses (generallj- erect or through) will be the usual types. Where only hght material is available, lattice or bow-string trusses may be employed. These types should be built as nearly as possible in accordance with civil practice in similar structures. Joints should be as simple as practicable, requiring a mini- mum of expert carpentering. Round timbers may be used in the simpler forms of trusses, if dimensioned stuff is not available. Deck spans may be employed for reasons similar to those which would dictate their adop- tion in civil practice. Sectional Trusses and Girders Sectional, portable, or "knock-down" trusses and girders, in wood and especially in steel, were the principal development in military bridging during the World War. They were demanded by the augmented density of traffic, and especially by the tremendous increase in mihtaiy loads, which now include heavy motor-trucks, artillery of great caHbers, tractors, and 30-ton tanks. The improvised bridges, long characteristic of mihtary operations on a smaller scale, were, alone, inadequate to meet the unprec- edented situation. It was recognized that there was needed some form of standardized superstructure, easily transported, rapidly erected, adapt- able to varying spans, and capable of carrying the heaviest loads. This demand was best met by portable, sectional, steel girders and trusses; and various types of such structures were developed by the British, French, and American Armies. As usual in such cases, a great variety of types was evolved; but, in the interests of efficiency, the number of such should be limited, and each should be made adaptable to varying conditions. For the American Army, sectional steel girders (I-beams) for spans up to 30 ft., and sectional steel trusses, for spans from 33 to 90 ft., were designed. The British employed sectional trusses in spans up to 180 ft. In order to permit transportation in motor trucks, the truss sections (panels or bays) were limited to 11 ft. 3 ins. Spans from 33 to 90 ft., in increments, could be erected with this equipage. The sections were con- nected for erection by bolts, no field rivets being used. These trusses can be (unployed with any ty])(^ of sujiport or \V\cr. The truss is erected with- out falsework, being bolted together on one bank, and placed by launch- ECONOMICS OF MILITARY BRIDGES 469 ing with the aid of tackle and an A-frame derrick, or by a counter-poise of additional sections of truss. It is certain that sectional steel girders and trusses will be used on a vast scale in future wars of any grea.t magnitude. Portable girder-spans, usually of timber, complete with flooring, in one or two sections, are provided for the passage of foot troops and artillery- over trenches, ditches, and small shell-holes, in following up an attack. These bridges are transported on combat wagons or artillery caissons. Cribs Cribs may be usefully employed for piers on very unstable bottoms, especially when there is a swift current, and for abutments. They have the advantages that they require no plant, and can be built of short pieces of almost any material. Cribs have greater power of resistance to floods, ice, and drift than have simple trestles, provided they are solidly con- structed and filled with stone. Cribs are often employed as foundations for framed trestles, the crib-work being carried above ordinary flood level. Trenches, ditches, shell-holes, and small ravines can be made passable by filUng them with any debris that may be at hand. An interesting development of the World War was a small cube oi crib of structural steel, any number of which could be bolted together to form a bridge abutment. Suspension Bridges Suspension bridges are occasionally employed in military operations. For spans exceeding 50 ft., when no. plant and no sectional trusses are avail- able, they will sometimes meet the situation. For military purposes they have the advantage that the only essential parts are the cables, which are easily transported. If these are at hand, the remaining portions, being small and light, can usually be obtained in any locality. Light suspen- sion bridges are easily erected without plant. When materials for a fixed bridge must be carried with a rapidly-moving column, the suspension type has the advantage of requiring the least material, for a given span and capacity, of any kind of bridge. Moreover, its parts, being small, are easily transported and handled. The suspension bridge is specially applicable to long spans combined with light loads, but even in such situations the ponton equipage or ferries will usually be preferred for stream crossings. Hasty suspension bridges may be built to carry wagons, but for motor traffic they are unsuitable. In general, they are used only for foot bridges of relatively long span. Their ideal function is for foot traffic and pack transportation over wide and deep ravines in mountainous country, where the ponton equipage or sectional trusses are not applicable. Because of the difficulty of handling in the field, cables are generally 470 ECONOMICS or BRIDGEWORK Chapter XLIV limited to one inch diameter, as many as necessary being employed. Standing trees are utilized as towers and anchorages when this is feasible. It will usually be impracticable to insure vertical reactions on the towers; and as roller bearings are not employed, the said towers should be of the sawhorse-trestle type and well braced, in order effectively to resist the overturning moment. The sag of cables usuallj' employed for mihtarj'' bridges is from ^^ to y of the span. Oscillation and undulation are limited by the usual methods, such as lateral bracing of the roadway, trussing the handrails, drawing the cables together at the center, gujdng, etc. While materials for light suspension bridges, excepting only the cables, may usually be obtained locally, erection will be greatly facilitated if adjustable suspension rods (slings or hangers) are provided in advance. Ponton or Floating Bridges The construction of any type of fixed bridge is at best a slow process. Indeed, in the case where an army with heavy artillery and trains is con- fronted by a wide and deep crossing, the construction of a fixed bridge might require weeks, even months, of time — in fact it might prove utterly impossible under some field conditions, for instance, in the absence of heavy and elaborate construction plant. Tactical requirements cannot brook such delays; and, to meet situations of this kind, some form of portable bridge, with floating supports and capable of extremely rapid installation, is abso- lutely indispensable. Accordingly, all modern armies are equipped with such bridges, which are known as ponton or floating equipage. The floating equipage which up to the present has been used in our own army (except the foot-bridge) was devised prior to the Civil War, and has been employed with conspicuous success since that time. It is a tribute to the wisdom of those who designed it that, in over 60 years, no radical changes in the equipage have had to be made. This standard equipage is of the utmost simplicity, consisting merely of any number of boats, called pontons, which are anchored in position and connected by stringers or "balk," resting on the gimwales of the boats, on which stringers the deck planks or "chess" are laid, the whole being secured by lashings. For shallow portions of the stream, near the banks, portable, collapsible trestles take the place of the boats. There are three forms of ponton equipage, a heavy wagon bridge, a light wagon bridge, and a foot-bridge, the latter devised during the World War. The heavy pontons are of wood, having an available su]^poi-ting power of 9| tons each. The hght pontons are collapsible wooden frames, covered with water-proof canvas, and have a supporting power of 6 tons each. The portable foot-l)ridge employs miniature canvas pontons and provides a path 2 ft. wide. Th(! advantages of this type of bridge are its portability and the extreme rapidity with which it can ])e installed. The ajiproximate wcMghts of the material per running foot of bridge are as follows: heavy equij^age, 170 lbs; ECONOMICS OF MILITARY BRIDGES 471 light equipage, 130 lbs.; foot-bridge, 16 lbs. One "division" (225 ft. of bridge) of the heavy equipage requires 16 wagons to transport it, and covers a road space of about 300 yards. One division (186 ft. of bridge) of the light equipage requires 14 wagons and a road space of about 250 yds. One division (285 ft. of bridge) of the foot-bridge can be transported in one three-ton truck. Lacking the standard equipage, almost any kind of boats, rafts, casks, or in fact anything that will float, may be utilized as supports for an impro- vised bridge. The heavy equipage has the advantages of greater strength and capac- ity, and less vulnerability to hostile fire. The light (canvas) equipage has the advantage of greater mobility in transport. The heavy train is required when heavy loads are to be carried, when very swift streams are to be crossed, or when the bridge must resist ice and drift, or stand up under hostile fire. The erection of the ponton bridge takes the form of a drill, and is accom- plished in an incredibly short period of time by men who have been properly instructed. The equipage, moreover, is so simple that average soldiers may be quickly trained to install it. There is no stream too wide, too deep, or too swift for the ponton equip- age, when handled by trained men. As an indication of its capacity, adaptability, and speed of erection, the following historical examples will be of interest. On June 15th, 1864, Gen. Grant, in his attack on Richmond, had need of a crossing of the James River. The stream was deep, and so swift that the pontons could not be held by their own anchors, it being necessary to attach their cables to schooners placed in the stream. The crossing was over 2,000 ft. wide, 101 heavy pontons being employed, and was com- pleted in 5^ hours, or at an average speed of 6 ft. per minute. In February, 1862, a bridge of 60 boats was thrown across the Potomac at Harper's Ferry. The river was in flood — a perfect torrent — carrying great quantities of ice and drift. In spite of all these difficulties, the struc- ture was successfully completed in 8 hours — average speed of erection, 2| ft. per minute. In the winter of 1919 a ponton bridge was built across the Chattahoo- chee River at West Point, Ga., by a detachment of the 7th Engineers with civilian assistants. The bridge was reinforced to carry heavy traffic, and the flooring was spiked in place. It was installed during a flood, the current varying from 5 to 10 miles per hour, and the water level rising 4 ft. during construction. The length was 440 ft.; and the bridge was com- pleted in 10 hours' working time. These performances under service conditions, remarkable as they be, are quite eclipsed by the exhibition bridge constructed across the Rhine (near Honningen) by the 1st Engineers, American Expeditionary Forces, during the military occupation of Germany (1919). The river at this 472 ECONOMICS OF BRIDGEWORK Chapter XLIV point is 1,450 ft. wide, with a maximum depth of 25 ft. and a current of 3 to 4 miles per hour. The bridge was built from both ends, 400 trained men being employed, and 93 pontons (of the German equipage) being used. The structure was completed in the astonishing time of 41 minutes 8 sec- onds, or at an average rate of more than thirty-five feet per minute, the world's record for speed in bridge construction. No other type of bridge ever devised is capable of anything approach- ing such speed in erection. By contrast with the time required in the cases mentioned, one of the best examples of the construction of a heavy, miU- tary trestle-bridge was a structure built over the Little Pedee River in the Civil War, in which a length of 100 ft. was completed in about 9 hours. The ponton bridge is designed to meet emergencies; and if the crossing is to be required for any considerable period, the ponton equipage should be released by the construction of a fixed bridge, in order that it may be available for fresh emergencies. For the requirements of a moving column in a theatre where stream crossings are encountered, the ponton equipage is indispensable. In addition to its use for bridging, the equipage may also be employed for ferrying, as in the passage of a stream by force in the face of the enemy. If it be necessary to employ the ponton bridge for a considerable period, the chess (floor plank) should be protected by a sheathing of thin lumber or by hay or brush. These chess are very thin (1| in.), and, if unprotected, would soon be worn through and ruined by continued traffic. As just stated, the floating equipage, if available, will often be the first solution for an important emergency crossing. Subsequently, and as soon as possible, it should be replaced by a trestle bridge, which in turn may later be used as falsework for a more elaborate structure. The adaptability of the ponton equipage is very great; it is ideally fitted to meet military emergencies; and its value as a saver of time cannot be over-estimated. New Types of Ponton Equipage The old types of ponton bridge, which have so long served military needs, and which are of generally similar design in all armies, like other former types of military bridges are inadequate to the needs of modern traffic. In future wars a heavier equipage will be required, and even this must be capable of "reinforced" construction to carry the augmented loads. Such an equipage has been designed for the American Army. The pontons have an available buoyancy of 10 tons, the span has been decreased to 15 ft. and heavier balk are used. An alLmetal boat, or one of metal sheathing on a wooden frame, will be employed. The adjustable trestles for end spans will be of steel. This bridge will normally cai-ry a concen- trated load of 13,500 lbs. on one axle, and may be reinforced to carry an axle load of 20,000 lbs. This will take all the loads of a corps or army, except- ing only heavy tanks and the guns and tractors of the artillery weighing ECONOMICS OF MILITARY BRIDGES 473 more than twenty tons. The reinforcement consists of an intermediate roadway-bearer supported by the heavy side rails. The wagons used to transport the new equipage will be such that they can be hauled by animals, truck, or tractor. Railroad Bridges In the construction of railroad bridges, military practice follows civil practice more closely than in highway bridges. As they must usually carry heavier loads, and as variations in either horizontal or vertical align- ment are much more serious, greater attention should be paid to the solidity of the structure, including its foundations. Pile trestles, girders, and trusses on piers of pile clusters are the usual types of military-railroad bridge. Most of them, except for light, narrow-gauge railways, will be in rear of the combat zone, though often bridges for standard gauge must be constructed close to the front. Foot-Bridges Foot-bridges, employed usually to meet tactical emergencies, exhibit a greater variety of forms, and have heretofore been less subject to standardi- zation than either vehicle or railroad bridges. In a crisis, any design and any material that will serve, or even partially serve, the purpose must be employed. Trees, cut near the bank and allowed to fall across the stream, often have enabled a combatant force to meet a grave emergency. As traffic accidents thereon will be less serious than in the case of other bridges, less attention is usually paid to the factor of safety. If this be very uncertain, the bridge should be tested by sending a few men across, and the traffic should be regulated to prevent crowding. The demands for the rapid passage of foot troops over streams are so frequent and insistent in modern warfare, that it is certain that in future, even more than in the past, standardized, portable foot-bridges will form part of the equipment of combatant organizations. A number of such standardized foot-bridges, including the light ponton type heretofore de- scribed, were devised during the World War. Floating types will be the ones most commonly employed, these being supplemented by light sectional trusses and, in some instances, by suspension bridges. The floats which have been successfully used include light canvas pontons, casks of wood or steel, rafts of wood or cork, and Kapok Rafts. The latter have the advantage that they are unsinkable by rifle or machine-gun fire. The width of the roadway or path of foot-bridges is from 2 to 2| ft. A greater width is unnecessary for the passage of men, and unduly decreases the mobility of the equipage, which is an essential requirement. Such a width (2 ft.) does not permit the passage of machine gun carts, which must seek other means of crossing. Machine guns, light mortars, and one-pound cannon accompanying the infantry, with their ammunition, may be carried across by hand. 474 ECONOMICS OF BRIDGEWOEK Chapter XLIV Deck or Flooring of Military Bridges Dimensioned lumber, never less than 2 inches thick and preferably 4 to 5 inches (except for foot-bridges), is most desirable for decking. The construction of a deck of poles is a slow process; because it is a tedious task to collect and prepare sufficient material for a bridge of considerable length. Poles for decking should be at least 3^ inches in diameter. They should be well spiked so that they will not rattle. As a pole deck is usually very rough, it will generally be advisable to chink the openings and cover first with brush and leaves and then with a layer of earth. The addi- tional dead load thus brought upon the structure should not be overlooked. Woven-brush mattresses, supported on deck poles at relatively wide intervals and covered with earth, make a satisfactory deck for foot-bridges. The wear on decking resulting from military traffic is very great, hence light material is unsatisfactory. For heavy bridges on important routes a deck 5 inches thick, preferably of hardwood, is now regarded as standard. If only 2-inch material is available, a double thickness should be used. The distance between stringers in feet should not be more than the thickness of the decking in inches. Width of Roadway As the amount of material and the time required for construction increase with the width of the roadway, military bridges are made no wider than necessary, and are generally limited to a single line of traffic, with clearance for the passage of footmen, horsemen, or motor-cycles. As mih- tary traffic usually moves in trains and can be closely regulated, it requires a less width of roadway than unregulated civil traffic. For the standard bridges, a roadway of 10 or 11 feet is employed. If it be necessary to pro- vide for the continuous movement of traffic in both directions, two bridges side by side may be adopted; or, if the traffic be very dense, three or four parallel bridges may be built. Two-way bridges are, of course, also employed. A 15 ft. roadway will pass two lines of traffic, but can hardly be called ample for the purpose, a width of 18 or 20 feet being better. The maximum capacity of military bridges in service should be devel- oped by efficient traffic control. Side-Rails and Hand-Rails Side-rails or wheel-guards of ample strength should never be omitted from any vehicle bridge. Hub-guards and hand-rails are generally pro- vided for through-truss spans, including suspension bridges, largely for the protection of the bridge itself; l:)ut they ai'c generally omitted in the case of deck spans. On the other hand, side-rails are unnecessary for foot bridges, except to secure the flooring; but hand-rails are generally provided. Materials Em-ployed, in Military Bridging Any available material must be utilized in the construction of military ECONOMICS OF MILITARY BRIDGES 475 bridges. Even bamboo has been successfully employed to carry heavy loads. Timber Timber can be adapted to the requirements of bridge construction more easily and rapidly than any other material. It is also the most generally available of all bridge materials. For civil constructions it has the dis- advantage of lack of permanence — a consideration having little or no weight in military operations. Timber, accordingly, is the favorite material of the military bridge builder. Dimensioned (sawed) timber is greatly preferable to round timber (unsawed logs and poles) ; first, because it can be much more quickly incor- porated in the bridge; second, because it makes a stronger and better struc- ture; and third, because it lends itself better to standardized designs and methods of construction. A few standard sizes of lumber (sawed timber), sufficient to meet the requirements of the standardized designs, are prefer- able to a great number of miscellaneous sizes that are difficult to adapt to any design. Military bridges must be and are frequently constructed of round timber, but this is from necessity and not from choice. Round timber is seldom used (except for piles or posts of framed trestles), if dimensioned material is available. Piling Piles are frequently employed for abutments, trestles, and piers in situations where the nature of the bottom does not permit the use of framed trestles. The use of piles necessitates a pile-driver, and consequently at the front should be avoided if possible, although frequently necessary there. Framed trestles, which require no plant for their erection, are preferable, even if it be obligatory to rip-rap the bottom in order to increase its bearing power, or to prevent scour. Nevertheless there will be situations, even at the front, where piles must be used ; and portable pile-drivers will be a part of the engineer equipment of every army. Steel Any steelwork which involves field riveting will find little application in mihtary bridging, even on the lines of communication, for the reason that its erection demands special plant and skilled labor. Rolled sections (I-Beams) are frequently employed as stringers in trestle bridges on the lines of communication, and even at the front, when it is necessary to carry very heavy loads, such as tanks. Portable, demountable, steel truss-bridges, capable of very rapid erection, and designed for both light and heavy traffic, were employed in the World War. The designs were very ingenious, and such structures will undoubtedly be used to a great extent in future. Special fabricated-steel girders are frequently employed for long stringer- 476 ECONOMICS OF BRIDGEWORK Chapter XLIV spans, mainly for railroad bridges on the Knes of communication. Their purpose, of course, is to reduce the time required for pier construction. They differ in no essential from civil structures for similar situations. Concrete Concrete is utihzed for culverts, for foundations of framed trestles, occasionally for abutments of bridges on important routes of communica- tion, and in the repair of old masonry bridges. For piers, piHng or crib- work is almost invariably preferable, even in the case of large and important bridges. Arches and girder spans of concrete will seldom be used. In the battle zone concrete finds very little application in bridgework. Stone Stone is employed as rip-rap for the protection of piers and abutments, and as crib-filling. Stone masonry will only exceptionally be used for abutments or wing and retaining walls; for there will be but few situations in which either concrete or rubble-concrete would not be preferable. If no cement is available, lime-mortar or dry-stone walls are sometimes employed. Paint Paint and other protective materials are sparingly used in military bridging. Ordinarily the time for which the structures will be required does not justify the employment of these preservatives. Steelwork should always receive a shop coat, but field coats will usually be omitted. Joints and Fastenings As military bridges must be constructed in the least possible time and usually by unskilled labor, intricate joints, involving expert carpentering, are to be avoided. Generally a plain butt joint, requiring no carpentering, other than squaring the end of a timber, should be used. The fastenings ordinarily employed for hasty bridges include lashings of rope, marline, or wire; dogs; fish-plates or " scabbing " ; drift bolts; through (screw) bolts; and spikes. Lashings are employed in the absence of other materials, or, as in the floating equipage (which is generally lashed throughout), when the bridge is to be later dismantled and the material salvaged. They are not a very secure form of attachment, especially when they actually carry the load, as in the case of the cap of a spar trestle. In such structures it is advisable to dap or notch the timbers together. Marline gives a tighter lashing than rope, but not such a strong one; and small rope is profoiable to large. Lashings do not stand racking well, and often are not sufficiently durable even for military uses. Dogs are easily made of any iron available. They should not ho em- ployed to carry a load, but only to hold timber in position. Drift bolts are commonly employed as fastenings for all ])arts of a bridge except the deck. They are readily made up in any desii-ed length, and are ECONOMICS OF MILITARY BRIDGES 477 quickly driven. A variation in the length of the bolt makes no difference, provided it is long enough. It is not necessary to point the ends. Lag screws may be used, if available. Through bolts, with nuts and washers, are the most secure form of fastenings; and, if procurable, they should be used for all important joints, except sills and caps which are usually "riders" (butted on the trestle legs), and for which drift bolts, dogs, or scabbing, are employed. For round timbers, through bolts have the disadvantage that they are generally either too long or too short, requiring the use of wooden washers in one case, or dapping out the timber in the other — in either instance involving a loss of time. Turned bolts are invariably used in lieu of field rivets in the assem- bly of sectional steel trusses. A full supply of nails and spikes of assorted sizes should, of course, be provided. Sizes of Individual Members For bridges at the front, the sizes of individual members must gen- erally be such that they can be readily handled and placed by unskilled labor, with the aid of animals and ordinary tackle, gin-poles, or shears. In the cases when plant is available, heavier pieces may be used to advan- tage. The principal considerations limiting the size of individual pieces are the requirements of transportation, by motor truck as well as by rail. Plant and Tools The mihtary bridge builder in the past has made comparatively little use of heavy construction plant in his operations, but this resulted from necessity rather than choice. Construction plant is utilized whenever practicable; and in view of the great capacity now required of military bridges, portable plant is necessary even in the combat zone. However, in the tactical operations of the combat troops the opportunities for the emplo3Tiient of plant will be relatively few. The work of the military bridge builder is spread over a considerable area; he moves rapidly from place to place; and he cannot be unduly hampered in his movements by the necessity of transporting heavy construction plant. Usually the plant is not at hand when needed, and it can seldom be depended upon. More- over, one of the principal uses of plant is to save manual labor, and this consideration has less weight in military than in civil constructions. There are, however, a number of pieces of light, portable construction- plant that may often be advantageously employed, even at localities quite close to the front. These include small hoists, pile-drivers, com- pressors, pneumatic tools, concrete mixers, and rock crushers. Gasoline is the best motive power, because of the compactness of both machine and fuel. For works on the lines of communication; heavy, standard construc- tion-plant is frequently adopted. For the future, portable hoists and pile-driving outfits will be provided for corps and army engineer-troops. 478 ECONOMICS OF BRIDGEWORK Ch.\pter XLIV The tools used in military bridge work, like the structures built there- with, should be of the utmost simpUcity. There should be an ample supply of the common tools, such as picks, mattocks, axes, saws, hammers, wrenches, shovels, cant-hooks, etc., with a few of the less usual tools that will occasionally be required. AU should preferably be of commercial sizes; but, to meet emergencies, miniature ■ tools, easily transported on a pack mule or on the person of the soldier, should also be available in case of need. There will arise situations in which the entire equipment of the bridge builder must be carried on pack mules. Class of Labor Available Mihtary bridges must usually be built chiefly by unskilled labor. In every engineer organization there wiU be a number of skilled artisans of every class; but the majority of the men in the ranks of these organiza- tions, as well as those from labor battalions and working parties from the infantry, wiU be of the class known as "unskilled labor." This fact has an important bearing on the design and methods of construction of mihtary bridges. Improvisation and Standardization. The difficult situations encountered, the varied circumstances under which work must be performed, the emergencies constantly arising, and the necessity of adapting to his purposes whatever materials are available, will require the military bridge builder to be skilled in improvising struc- tures to meet these conditions. Improvisation, in fact, is characteristic of all the operations of military engineering. It is a valuable means of developing ingenuity and resourcefulness; nevertheless it is a practice which results only from necessity, and it has the disadvantages that it consumes valuable time and that it tends towards lack of uniformity both in training and in actual construction. Standardization, including standard designs, standard materials, and standard methods of construction and of training, is at least as useful and economical in military practice as in civil practice. It has the follow- ing important military advantages: (a) A standardized structure can always be erected in less time than one in which extensive improvisation is necessary, especially by troops who have been trained in standardized construction. The saving of time results from both the fact that it is possible to use standard plans, and that loss of time from improvisation is eliminated. (6) A further saving of time is effected by the fact that standardized materials may be prepared beforehand at the engineer depots, and sent to the front as needed. Lumber can be cut to exactly the required dimensions, bolts will be of exactly the i-ight length, and special pieces of all kinds can b(; made up in rear, so that it will not be necessary to spend time in pre- paring them under difficult conditions at the front. ECONOMICS OF MILITARY BRIDGES 479 (c) Standardized structures require less skilled labor than improvised structures. (r/) Standardization promotes imiformity in training and practice. (e) A standardized structure is nearly always superior to an improvised structure in every item of utility. (/) In a hasty, improvised bridge constructed of random materials, the actual strength of the structure is usually a matter of uncertainty and guess-work. In standardized designs the safe loading is accurately known, and the chance of accident from overloading the structure is correspond- ingly reduced. The benefits of standardization being so manifest, standardized-type plans have been prepared for all forms of military bridges, even for those constructed of local materials. Standardized material for these structures is prepared in the engineer shops, so as to reduce as far as possible the amount of labor required in the field. Standardized designs are, or should be, of the utmost simplicity and flexibility. They should be simple, because only the simplest structures can be successfully and promptly erected under the difficult conditions incident to warfare, involving lack of time, adequate tools and plant, skilled labor, etc. They should be flexible, because no two situations are exactly alike; and the type plans must be modified in practice to meet the actual conditions. It should be possible, with a few minor variations, to adapt the type plans and the standard materials to any situation, with a minimum of improvisation. The best example of standardization in military bridging is the sectional steel truss heretofore described. It has been said that standardization has a tendency to discourage invention, and hence is inimical to progress. While it must be admitted that there is some truth in this contention, the tremendous results that have been achieved through standardization, in both civil and military practice, are a sufficient justification for its adoption. There will be an ample field for the inventive talents and resourcefulness of the engineer, both within and without the limitations imposed by standardization. Moreover, for every inventive genius who has been discouraged by stand- ardization there are thousands of average men who have profited by it; and it is the average man with whom we invariably reckon in military oper- ations of all kinds. Standards should be- revised and improved in the light of experience; and this was frequently done during the World War. Because of the density of traffic and the heavy loads incident to modern military operations, standardized bridge designs will be employed more frequently in the future than they have been in the past. There were times during the World War when the regular daily traffic on a single road was 5000 motor trucks (in both directions), and during troop movements this reached a maximum of more than 17,000. Rough, improvised struc- tures would not be adequate to the needs of such a traffic. 480 ECONOMICS OF BRIDGEWORK Chapter XLIV Utilization of Existing Bridges To save time, material, and labor and to obtain quicker results, existing bridges should always be utilized as far as possible. Unless the bridge is a complete wreck, it will nearly always be easier to repair or strengthen it than to build a new structure. Existing bridges should be examined by an engineer who is familiar with bridge construction in the particular locality. Any bridge built on approved standard design, and the parts of which are in good condition, may be regarded as safe for its rated loading. Any bridge that exhibits a radical departure from standard design should, of course, be looked upon with suspicion. The horizontal and vertical ahgnments of the structure should be noted, after which all its parts should be examined for weakness or deterioration. The conduct of the bridge as loads pass over it should be carefully observed. A weak bridge of any type may be strengthened by placing additional trestle bents between its supports, or by strutting its stringers. All bracing should be thoroughly reinforced. Even in the case of a demolished bridge, it will generally be possible to utihze at least its abutments and piers, or what remains of them. A fallen truss may often be raised to position and its undamaged portion made available by introducing a new pier. A few hours' work will often render a weak bridge sufficiently strong to carry military loads; whereas, if it be allowed to break down, extensive recon- struction or even a new bridge may be needed. It certainly is a very poor bridge indeed that cannot be strengthened sufficiently to carry the desired loads, with less labor than would be required to build a new structure; and, in the interests of economy, such strengthening should always be undertaken. Utilization of Local Resources To save transportation, to promote mobility, and to meet the frequent emergencies in which no standard materials will be available, the military engineer will often have occasion to build his bridges of any local materials that may be available. Structures built of such materials are generally known as hasty or improvised bridges. While the utilization of local resources may save transportation, it will not economize time in construc- tion. A great deal of time and effort must usually be expended in finding and collecting the available material, and in transporting it to the site of the work; and when it is there, further difficulty will be encountered in adapting the heterogeneous collection to the standard clesigns, oi- indecnl to any design In a wooded area, round timber will be available, and will jirove io bo very satisfactoi-y for the (construction of bridges, though by no moans equal to sawed lumber of standard sizes. As before stated, the military engineer does not use round timber from choice, although it may be remarked that bridges constru(ctod of such niatcM'ial hav(^ a characteristically military ap- pearance, and sometimes a certain rustic beauty quite jik^asing to the ECONOMICS OF MILITARY BRIDGES 481 eye. But it is also to be remarked that it was to ayoid the loss of time involved in laboriously collecting the material for and constructing such bridges, that the ponton equipage and the standard types of fixed bridges were devised. The construction of a bridge of round timber is a rather entertaining recreation, and engineers occasionally overlook the loss of time thus involved; hence it should be avoided whenever possible. The collection of the material and the laying of a pole deck, in particular, con- stitute a time-consuming operation. In building a bridge of mixed mate- rial, the round timber may be employed for trestle posts, sills, and caps, and, if necessary, also for stringers and side rails, leaving the dimensioned stuff for bracing, stringers, and deck — especially the deck. In almost every town, unless it has been previously overrun by the military, a small stock of lumber can be found; and frame buildings may be wrecked, if necessary. This, in combination with standing timber, will often meet the needs of the situation. Local materials are, in general, decidedly inferior in all respects to standardized materials from the engineer depots. They must, however, frequently be employed; and the engineers should be skilful in collecting them and in adapting them to their needs. Loading of Military Bridges The military bridge builder should be familiar with the usual loads that bridges in various situations and for various purposes will be called upon to bear. Usually these loads are quite definite, and the standardized designs are based upon them. As the factor of safety employed in military bridging is almost always low, especially at the front, vehicles heavier than those for which the structure was designed should not be permitted to cross it. Nevertheless, it is generally unpossible to foresee the extent to which any bridge may be used. Bridges on important routes of trans- port are almost certain to be called upon to carry the heaviest loads. Drivers of heavy trucks wiU proceed across any bridge they come to, what- ever warning signs may be posted, unless a guard is placed at the structure. Accordingly, it is desirable that, on any main route, or any road apt to become an important route, the bridges, whatever their immediate purpose, should be built to carry the heaviest mihtary loads. The supports, at least, should be made of ample strength, which will allow the bridge later to be reinforced to carry heavy loads by introducing additional supports or otherwise strengthening the superstructure. In general, the first crossing will be a hasty improvisation, or a light foot-bridge of some standard design. If the need for the crossing continues, this bridge may be replaced by the ponton equipage, and subsequently by an improvised or standardized fixed bridge. By this time the probable future needs of the route will be known with some certainty, and future steps can be taken accordingly. There should be an ample number of through routes having bridges capable of carrying the greatest loads, including tanks and heavy artillery. 482 ECONOMICS OF BRIDGEWORK Chapter XLIV These routes for heavy traffic should be properly sign-posted ; and informa- tion concerning them should be circulated throughout the command. It will evidently be impossible to. provide all routes with the heaviest bridges; hence a rigid traffic supervision should be exercised to prevent heavy vehicles from wandering into the minor routes where the bridges have not sufficient strength to carry the loads that would thus be imposed upon them. The foregoing requirements conflict to some extent with the previous statement that a hasty bridge should be built with a low factor of safety and to meet the exigency of the moment only. • Most bridges constructed for tactical uses will be off the main routes of transport. In any case, the engineer must decide whether the probable future service justifies the expenditure of more time in initial construction. In the operations of the large, fuUy-equipped, modern army, stand- ardized steel superstructures, capable of carrying its heaviest loads, will hereafter be characteristic of aU important routes of transport, even quite close to the front. In the operations of small, detached, rapidly-moving, and lightly-equipped forces in a sparsely settled country, the fighter forms of floating bridge, and various kinds of improvised structures to carry moderate loads, will in the future, as in the past, be typical of bridging activities. In any campaign, miprovised structures will always be required in the combat zone. Transportation of Materials There is always a shortage of transportation for every purpose in time of war. Such important supplies as ammunition, weapons, and food must naturally take precedence over construction materials. When the neces- sity for a bridge can be foreseen for a reasonable time, it may be practicable to assemble in advance the plant and material requisite for its erection. This will often be possible on the lines of communication; but at the front it will be absolutely impracticable to have on hand, at every locality where an emergency may demand a bridge, all the materials required for the standardized design. The engineer is thus compelled to improvise and adapt to his needs such miscellaneous material as he can secure on short notice, locally or otherwise. Where military activities can be foreseen, depots or "dumps" of construction material are assembled in the vicinit}', so that only local transport will be required. Large, heavy, awkwardly-shaped pieces will always be delayed in transport. They are difficult to load and ship; moreover, they arouse the hostility of the transport personnel, who have a natural tendency to push them towards the bottom, of the "priority list"; hence, all bridge material should ])o of a siz(> and weight that will insure reasonable pi'om])tness in transportation. While it will s(^klom be possible to supply \ho engiiuHM' with everything that he needs, it will often be jiracticable to provide certain materials that ECONOMICS OF MILITARY BRIDGES 483 will greatly reduce the time required for construction. For example, the building of a pole floor is the slowest item of an improvised bridge. If dimensioned flooring material (decking) alone can be sent up from the rear, a material loss of time is elmiinated, and the engineer will be able to improvise the rest of the structure. Bolts, spikes, wire, cordage, etc., form a very small part of the weight of the bridge — they come in small packages and are easily transported. Without them the time and difficulty involved in building the structure would be greatly increased; hence, these fasten- ings, at least, should be made available wherever needed. Selection of Site In many cases there will be little room for choice in the selection of a site. New bridges must frequently be built at locahties where former bridges have been destroyed. In any case accessibility to adjacent roads on both sides will be a controlling factor in fixing the site, except for foot- bridges. The location must fulfill the tactical requirements; but, as a rule, the chief tactical requirement is rapid construction, and, accordingly, the site is selected with this in view. Where there is room for choice, the following conditions, affecting the time required for construction, wiU be given consideration. (a) Width of Stream. This, of course, directly affects the length of the bridge and the time required for its construction. Other things being equal, the narrowest point is preferred. (6) Depth of Water. The time and effort required for the construction of any type of fixed bridge increases rapidly with the depth of water, unless the stream can be crossed with a single span (truss or suspension). For the ponton bridge there should be sufficient depth to float the boats. Any greater depth does not increase the time required, except that very great depths make the anchorage of the pontons somewhat more difficult. Its independence of the depth of water is one of the principal advantages of the floating equipage. (c) Swiftness of Current. A swift current greatly increases the diffi- culty of constructing and maintaining any type of bridge, except one with a single span from bank to bank. The slowest current is found in wide, straight reaches of the stream. (d) Nature of Bottom. A very soft, yielding bottom will demand pile or crib construction, whereas a hard bottom will support framed trestles, which can be more rapidly placed. A ponton bridge, or a fixed bridge of a single span, is, of course, independent of the nature of the bottom, as it is of the depth. (e) Nature of Banks and Approaches. A low, flat, and marshy ap- proach, or one subject to overflow, will demand either a very long bridge, or a causeway, the construction of which is apt to require much more time than the bridge itself. . On the other hand, high banks will necessitate tail 484 ECONOMICS OF BRIDGEWORK Chapter XLIV trestles; or else they must be cut down to provide approaches with a prac- ticable grade — an operation usually involving much labor. The ponton bridge demands low approaches, as its height above the water surface can- not be increased. For crossings of small or moderate width that can be cleared with a single span or by using a small number of intermediate supports, high banks will be no great disadvantage; consequently, for any type of bridge, the most favorable crossing is one having low, firm banks of equal height, but above the level of any flood likely to occur during the time that the bridge is in use. (/) Materials Available. If the bridge is to be constructed in whole or in part of materials obtained at the site, the availability of such local materials, without an excessive amount of transportation, is important. There are certain other considerations, of a tactical nature, that have a bearing on the selection of a bridge site. Amongst these may be men- tioned : (g) Defensibility. It is desirable that the bridge be located where its construction cannot be interfered with by the enemy, and where it and the troops crossing it will not be subject to artillery or rifle flre after its com- pletion. If built in the near presence of the enemy, it will be advisable, before beginning construction, to ferry some troops across, in order to pre- vent the enemy's snipers from interfering with the work. It is desirable to locate the bridge in a position where it is sheltered by woods or hills from hostile flre, and where it cannot be seen for any great distance either up or down stream. (h) Secrecy. If the crossing is to be made secretly as a surprise, it is desirable that there be a sheltered locality on the near bank, at or close to the bridge site, where the material can be assembled without the enemy's knowledge. To sum up then, the desirable requisites for a bridge site are: accessi- bility to adjacent roads; narrow width of crossing; moderate depth and swiftness of current; solid bottom; favorable approaches; usually low, firm banks of equal height; materials, as needed, available near at hand; and a sheltered, concealed, and defensible locality. In making a reconnaissance for the selection of a site, these various desid- erata must be balanced against each other in coming to a decision; for it will seldom be practicable to find a location that combines all the advan- tages mentioned. In the selection of a site for a railroad bridge there will, of course, be less latitude than in the case of a highway structure. It is to be remembered that the thing sought is not a site for a n(nv l)ritlgo, but a practicable crossing of the stream. A bridge should not be built if a suitable ford, or an existing bridge which meets (or may b(^ mad(^ to nuH't) recjuire- ments, can be found. In anticipation of their probable future use, all existing bridges within range of the army's operations should be promptly siezed and guai'ded, in order to prevent their destruction by either the enemy or his sympathizers. ECONOMICS OF MILITARY BRIDGES 485 Protection against Flood and Drift Military bridges are protected against flood, ice, and drift by the usual methods of civil practice. Trestles may be strengthened against lateral thrust by guying upstream or strutting downstream. One or more wide spans, with booms or guide walls, may be provided for the passage of ice and drift. Cribs or clumps of piles are used as fenders and ice breakers. Ponton bridges should have a draw span that may be removed for the passage of drift, with booms to guide the latter into the opening. Inspection of Bridges All the important bridges in the area occupied by an army should be inspected at suitable intervals by specially qualified engineer-officers. This should be done at least once a month, and the results of the inspection reported to the Chief Engineer. At such inspections, any change in the nature or density of the traffic should be ascertained. It is quite as impor- tant to note the change in the condition of the bridge since the last inspec- tion, as it is to determine its present condition. CHAPTER XLV CONCLUSION The devotion of an entire chapter specifically to the conclusion of an engineering treatise is somewhat of an innovation in technical literature, and, therefore, demands an explanation for its intrusion. The essential reason is that this is to be the author's last technical book, excepting only that after the third thousand of his "Bridge Engineering," now on sale, is exhausted, he intends to write for the second edition thereof an "Appendix" to cover the results of all bridge investigations, other than economic, which he has made (or shall have made) since that work was first issued in the summer of 1916. The reasons why, after thirty-seven years of rather desultory book- writing, he is about to desert the field of technical literature, or, strictly speaking, that portion of it which pertains to the preparation of formal treatises, are the following: First. In many cases the writing of technical works is an extrava- gant indulgence that very few engineers can afford; for not only does it necessitate the expenditure of a large amount of cold cash to prepare the manuscript of any book worthy of being considered real engineering literature, but, even after it is finished, an author sometimes has to pro- vide all the money required for publication; the publisher deeming the many years spent and the great outlay of money used in building up the means for placing such works on the market a fair equivalent for that spent in preparing the manuscript. This is specially true in scien- tific books which require special means and careful study to put them properly before those they are written for. Second. The amount of personal time that one nuist devote to the preparation of the MS. of any engineering work which aims to offer mainly original material, and is not, like many engineering books, a mere com- pilation of data gathered from standard treatises and the technical press, is simply appalling; and the diversion of such time from his professional practice is often a serious menace to the success of an engineer's business. Third. The author feels that in presenting this treatise on bridge economics to the profession, in addition to his seven preceding books and numerous technical memoirs, he shall have almost exhausted all that he has to say in print on the subject of his chosen specialty. In other words, his message to the younger generation of engineers shall have been deliv- ered; and he should then, with a clear conscience about having "done 486 CONCLUSION 487 his bit" towards the development of engineering science, be able to devote his remaining working years principally to serving the public in an advisory capacity on important engineering projects — provided that, before the time arrives for him to pass on, the profession shall have extricated itself from the disastrous slump into which it was plunged in 1914 by the advent of the World War. The reader must not deduce from the preceding that the author desires to convey the impression that his labors in the field of engineering economics are over — far from it! — for he has good reason to expect that he shall be retained some day to investigate the great economic problem of "Molyb- denum Steel for Bridges" in the same manner in which years ago he investigated that of "Nickel Steel for Bridges." The economic studies of the last four years, upon which this treatise is mainly based, have been intensely interesting; but the work involved, which (somewhat unlike that of the writing of the author's magnum opus) has been chiefly personal, and, in spite of steady application and long work- ing hours, exceedingly long-drawn-out, has become rather overpowering; so that, it must be confessed, the ultimate completion of the undertaking, which will not occur until the book is actually issued, will be decidedly in the nature of a relief. In another particular the preparation of this treatise has differed from that of its predecessor, which (as a side issue, it is true,) necessitated a thorough search of engineering literature; because in this case no search- ing has been done, the reason being that the subject is ahiiost entirely a new one, and, consequently, essentially independent of past records. The author hopes that this book will prove of real service to several generations of engineers, notwithstanding the fact that, on account of changes in practice due to the rapid development of the profession, nearly all engineering books are short-lived. Such a hope is not entirely without foundation, because his little "De Pontibus," pubhshed nearly a quarter of a century ago, in spite of its contents having been absorbed by its suc- cessor, "Bridge Engineering," had a steady sale until about the end of 1920, when the publishers let it go out of print because of its low price combined with the exceedingly high cost of paper, press-work, and binding. In conclusion, there is a suggestion which the author would like to make concerning a possible utility for this work in combination with its immediate predecessor; but he has long debated as to the advisability of offering it, fearing that some of his readers may either misconstrue his motive or charge him with undue conceit concerning the value of his technical pro- ductions. However, he has decided to run the risk; because he greatly desires that the results of the long and arduous labor which he has put upon their preparation shall be utilized to the utmost for the benefit of all future young engineers who have the ambition to specialize in bridgework. The suggestion is this: " 488 ECONOMICS OF BRIDGEWORK Chapter XLV If a young engineer of fine intelligence, great energj^ , unceasing persevre- ance, and high ambition, who has had during his technical-school course a thorough training in the theoretical portion of bridge designing and has systematically continued to read and study concerning bridgework during a practice of five or six years, devoted mainly to the various ramifications of that specialty in computation room, drafting office, manufacturing shops, and field, wishes to become a bridge expert and carry on an independent consulting practice, he can do so by adopting the following procedure: Let him devote all of his time for an entire year to the reading and re-read- ing of "Bridge Engineering" and "Economics of Bridgework" and to solv- ing, by the use of these books, numerous examples of all kinds upon assumed data, so as to obtain actual experience in the computation of secondary stresses and deflections, in the designing of the various types of bridges, in the determination of economic layouts for all kinds of assumed conditions, in the expeditious making of cost estimates, in the writing of specifications for manufacture and erection of substructure, superstructure, and ap- proaches, and in the drafting of sound engineering contracts. Such work could best be done as a post-graduate course in one of the leading technical schools; but this is not really essential, because such a young man as the one described should certainly be able to carry on his studies unaided. Again, it could be carried out well, by taking longer time, were the young man in the employ of a consulting engineer, a bridge manufacturing com- pany, or a bridge erector. The author feels confident that, upon the com- pletion of the training above recommended, the young man under con- sideration would be truly entitled to term himself a Consulting Bridge Engineer, and his success in that capacity would practically be assured. APPENDIX The following is a chronologically arranged list of the author's various investigations and writings on the subject of bridge economics, extending over a period of thirty-seven years: In 1883, a paper on ''Economy in Struts and Ties." In 1884, a chapter on "Economy" in " The Designing of Ordinary Iron Highway Bridges." In 1891, a paper in "Indian Engineering" on "Economic Span- Lengths." In 1897, a chapter on "True Economy in Design" in "De Pontibus." In 1897, an elaborate investigation of the economics of cantilever bridges, published in the last-mentioned work. In 1906, a complete investigation of the economics of steel trestles, which was later incorporated in "Bridge Engineering." In 1907, an extensive paper on "Nickel Steel for Bridges," published by the American Society of Civil Engineers and awarded its Norman Medal. In 1909, a paper written in French for Le Genie Civil and entitled " Une Etude Economique de VEmploi de I'Acier au Carbone a Grande Resist- ance pour la Construction des Fonts." In 1913, a paper on "The Possibilities in Bridge Construction by the Use of High-Alloy Steels," published by the American Society of Civil Engineers, and awarded its Norman Medal. In 1914, a paper on "Alloy Steels for Bridgework," presented to the International Engineering Congress of the San Francisco World's Fair. In 1916, a chapter on "True Economy in Design," in "Bridge Engineer- ing," being an expansion of a similar chapter in "De Pontibus." In 1917, a series of three lectures on "Engineering Economics," deliv- ered to the Engineering Alumni Association of the University of Kansas. In 1917, a paper on "The Economics of Steel Arch Bridges," presented to the American Society of Civil Engineers, published in its " Proceedings," and awarded its Norman Medal. In 1918, a paper entitled "Comparative Economics of Cantilever and Suspension Bridges," presented to the Western Society of Engineers and published in its "Proceedings." In 1919, a paper on "Economic Span-Lengths for Simple Truss Bridges on Various Types of Foundation," presented to the last-mentioned society and published in its "Proceedings." 489 490 APPENDIX In 1919, a paper entitled "Possibilities and Economics of the Trans- bordeur/' presented to the Institution of Civil Engineers of Great Britain, and published as the basis of two editorials in Le Genie Civil. In 1920, a joint paper with Mr. H. Malcolm Priest on "Comparative Economics of Continuous and Non-Continuous Trusses," presented to the Engineers' Society of Western Pennsylvania and published in its "Pro- ceedings," In 1920, a paper for the same society on "Comparative Economics of Wire Cables and High-Alloy-Steel Eyebar-Cables for Long-Span Suspen- sion-Bridges," and pubhshed in its "Proceedings." In 1920, a rnemoir entitled "De VEynyloi Econoviigue cles AlUages d'Acier dans la Construction des Fonts," published in condensed form by the Academic des Sciences on July 12, 1920, and in full by Le Genie Civil on July 24, 1920. In 1920, a paper entitled "Bridge versus Tunnel for the Proposed Hud- son River Crossing at New York City," presented to the American Society of Civil Engineers and published in its "Proceedings." In 1920, an as-yet-unpublished paper on "Economics of Reinforced- Concrete, Steam-Railway Bridges." In 1920, a paper on "Economics of Movable Spans," presented to the American Railway Engineering Association, but not yet published. INDEX Abrams, Prof. Duff A., 395 Abrasion of bridge paint, 445 Abutments for arches with filling, 226 Abutments with wing-walls versus buried piers, 114 Academic des Sciences, 26 Accessibility to paint brush, 201 Accidents in shops, 370, 371 Accumulators, 312 Accuracy in calculations, limits of, 359 Additions to future loadings, 16 Advantages of ideal method of contract- letting, 352-354 Aerial ferry, 318 Aesthetics, 123 pier-shafts, 168 Age of cement, 393, 394 Aggregate for concrete, light, 198 prices of, 23 reduction of voids in, 389 volume of voids in, 386 Agreeableness of traversing bridges and tunnels, 54, 56 Air-spraying of paint, 422 Algiers, 319 Alignment and grade, 119 Alligatoring of paint, 434 Allowance for clearance, 214 Allowance for expansion, 215 Alloy steels, carbon steel, comparison with, 32, 33 criterion for plate-girders of, 27 economic comparisons of, 44—51 economics of, 26-52 prices of, 44 tests of, 38-43 use in bridgework, 33 Alternating versus direct current, 312 Alternative methods of erection, 399 Aluminum steel, 33, 34 Analysis of details and joints sometimes im- practicable, 201 Anchor arms, economic lengths of, 100, 258 Anchor piers for cantilever bridges, compu- tations of, 94 Anchor span, economic length of, 259 491 Anchorages for suspension bridges, 94, 267 Anchored ends versus free ends for stiffening trusses, 268 Angles, single, in tension, 204 Annual costs, total, contrasting of, 14 Annual expenses, 14 Anticipating accidents in shop, 370, 371 Anticipating the future, 16 Anticipating troubles, 371 Antoine, Marc, 35 Appearance of reinforced concrete bridges, 456 Appendix, 489 Application of paint, 422 after cleaning, 446 Approaches, bridges and tunnels, time expended in climbing up and down, 56 economics of, 113 nature of, 483 spiral, 59 suspension bridges, 266 timber trestle, 21 Arbitrary power of resident engineer, 382 Arches, combination of stresses in, 135 Fraser River Bridge at Lytton, B. C, 246 reinforced-concrete, 225-230 abutment, 226 erection of, 406 inequality in length of, 227 ribs, types of, 227 rise of, 226 steel bottom chords, 229 steel, cantilever, 238 economics of, 232-249 erection of, 402 formulae for weights of metal in, 239, 240, 248 limiting span-length for, 241 pile foundations for, 244 tabulation of salient features of, 234 weights of, compared to trusses, 238, 239 Waikato River Bridge at Cambridge, N. Z., 247 492 INDEX Arches, Waikato River Bridge at Hamilton, N. Z., 246 Arnold, Col. Bion J., 8 Arrangement of deck, 128 Arrangement of riveting, 199 Arroyo Seco Bridge at Pasadena, Calif., 248 Asphalt, Ufe of, 452 Asphalt pavements, 188 Assembling, 376 Assembling in shops, 378, 379 Assistant Engineer of Construction, 383 Auditor, 384 Austin, Texas, bridge over Colorado River, 248, 249 Author's report to S. P. E. E., 3 Automatic brakes on Uft bridges, 295 Automobile travel in tunnels, 53 Auto-truck loadings, 125 Availability of supplies, 123 Avoidance of special material, 205 B Backstays, 94 suspending floor from, 266 Balance-beam bascule bridge. Brown, for Mystic River, 297, 308 Balanced-cantilever type of girder, 222 Balancing chains in lift bridges, 294 Ballasted decks, 182, 183, 185, 186 Ballast resting directly on steel plate, 183 Ballast resting on reinforced-concrete slab, 183 Banks, nature of, 483 "Bare necessities only," principle of, 461 Bascules, Brown balance-beam, 298 economics of, 289 heel-counterbalanced-trunnion type, 290 heel-trunnion, 297 Housatonic River Bridge, 298, 308, 309 Mystic River Bridge, 298 quantities for, 299 singlo-lcaf versus double-leaf, 289 swing-span, comparison with, 284, 285 vertical-lift, comparison with 285-287, 302 wind pressure on, 316 Base for pavement on lift bridges, 295 ' Bases of pedestals, plain concrete versus reinforced, 173 Batten plates, 200, 203 Beach, Major General Lansing H., 459 Beams, intensities for compression flanges of, 137 Mending of long pieces undosiral )1(\ '_' I I J{(!Hsotii('r process, modification of, for high grade steel, 35 Beveled cuts, 206, 212 Bitulithic pavements, 188 Bituminous concrete floors, unsatisfactory, 427 Bituminous pavements, 188 Blacksmith shop, 378 Blank forms, 360 Blockade of tunnel traffic, 56 Block pavements, 426 "Bloom," 456 Bob-taUed swing versus ordinary swing, 288 Boca del Rio Bridge painting, 439 Boiled linseed oU, 435 Bond, Colonel P. S., 460 Bonus, method of division of among em- ployees, 348 Boring, 377 Bottom, nature of, 483 Box sections for compression members, 261 Braced towers versus solitary columns, 254 Braked trains, thrust of, 140 Brake power for bascules, 316 Brake resistance, 315 Brakes, automatic, on lift bridges, 295 Brazil, paint for, 440 Breakdown of machinery, 315 vehicles in tunnels, 57 Bridges, agreeableness of crossing, 54, 56 approaches, data concerning, in "Bridge Engineer- ing," 114 economics of, 113 arch, steel, economics of, 232-249 combined, 129, 131 comparative economy of, 14 contractors, general fieldwork of, 383 economics, list of author's writings on, 489, 490 entrances and exits, separation of, 55 height of climb over, 54 manufacturers' standards, 205 movable, 284-309 cost of operation of, 55 operated by combustion engine, 311 operated by electricity, 311 operation by hydraulic pressure or compressed air, 311 power for operating, cost of, 55 projects, promotion of, 20 reinforced-concrete, 218-231 comparison with steel bridges, 64-66 small cost of maintenance and repairs for, 64 replacing of, 403, 404 riveted versus pin-conno<'teact on, 140 Foundry, 378 Four-angle columns, 212 INDEX 499 l'"our-column versus two-column structures for elevated raDroads, 254 Fowler, Charles Evan, 139, 234 Frame trestles for military bridges, 465 Fraser River Arch Bridge at Lytton, B. C, 249 Fraser River Bridge at New Westminster, B. C, 131 Fratt Bridge at Kansas City, 132, 169 Free ends versus anchored ends for stiffening trusses, 268 Freezing water, disruptive force of, 455 Freight rates, 23 Friction, caisson, 156 long piles, 156 Fuller, William B., 389 Full-punched work, 211 Full time work, necessity for, 2 Function of operating machinery, 315 Future, anticipating the, 16 Future enlargement, 121 G Galveston Causeway, 140 Gardiner, J. B. W., 449 Gardiner and Lewis, Inc., 449 Gas, effects of, on steel, 416 Gases, locomotive, protection against, 444 Gasoline engine, multi-cylinder, 313 Gauntleted tracks, 128 Gearing, elimination of noise of, 313 spur, 312, 313 worm, 313 General economic principles, 6 General features of structure, 120 Geographical conditions, 119 Girders, depths in viaducts, 203 economics of, 175-181 erection of, 397 reinforced-concrete, 221, 223-225 spacing of, 191 Glasgow, Missouri River, Bridge, 168 Goheen's Carbonizing Coating, 432 Gorge crossings are specially suitable for arches, 246 Government requirements, 116, 117 Grade and alignment, 118, 119 Grant, General, crossing of the James River by, 471 Gratis expert opinion, 7 Gravel and sand used without screening, 390 Great Miami River Bridge, 84 Griest, Maurice E., 256 Growth of steel, 215 Gunite, 443 H Hadfield, Sir Robert, 36 Half pin holes, 216 Half-through, plate-girder spans, 185 economics of, 69 Halsted-Street Lift-Bridge, 294 Hamilton Arch Bridge over the Waikato River, 246 Handling of work in shops, 368, 369 Handrails, 190, 219 military bridges, 474 Hand riveting, 207 Harbor of refuge, 318 Hardesty, Shortridge, 297 Harper's Ferry crossing of the Potomac, 471 Harrop, Dr. H. B., 440 Havana Harbor bridge, proposed, 332 transbordeur, proposed, 332-334 Havre de Grace, Md., paint experiments, 433 Hayde, Stephen, 198 Haydite, 198 Heat for shops, 367, 368 Heat-treated steel, 37 intensities of working stresses for, 37 Heel-counterbalanced-trunnion type of bas- cule, 290 Heel-trunnion bascule, 297 Height from springing to bottom of base, 226 Height of climb over a bridge, 54 Helpers, low-grade, 380 Heritage, Carl S., 407, 418 High bridge versus low bridge, 12 High-carbon steel, objections to, 33 reinforcing bars, 133 High-level bridge versus transbordeur, 330 High level versus low level crossings, 61, 62, 63 High steel, 34 reinforcing, objections to, 218 High unit stresses, 133 High water, clearances above, 122 Highway, girder-bridges, 223-225 live loads for, 126 trestles, economic span-lengths of, 252 Highway bridges, decks of, 187 timber versus concrete for, 187 economics of cantilever and suspension, 106 econoinics of continuous spans for, 78 floors, ties in, 192 floor-systems of, 190-200 Hildreth & Company, 361 "Hillside" blocks, 426 Hingeless arches, 237 three-hinged arches comparison, 229 Hinge plates, 216 Holding power for bascules, 316 Holland, Chfford M., 56 500 INDEX Hollow shafts, 168 Home office, reports for, 380 Honningen crossing of the Rhine, 471 Hoogly River bridge at Calcutta, proposed, 296 Horse-propelled vehicles, 21 "Hospital jobs," 341 Housa tonic River bascule bridge, 298, 308, 309 H-section for posts, 200 Hudson River crossing at New York City, 58 railway bridge, uneconomics of, 60 Hudson River Tunnels, 56 Huntington, ColHs P., 12 Hydrated lime, 391, 457 Hydraulic power for bridge operation, 311, 312 Hydraulic reducing-gear, 313 Ice-breakers, 169 Ice drift, 122 Ideal, method of contract-letting, 344; 345 operating apparatus, 313 shop coat of paint, 432 system of contract-letting, 343, 344 Idleness, 366 Ignoring of impact on foundation piles, 140 Illinois Central Railroad Bridge at East Omaha, 22 Impact, allowances, latest modifications of, 127 foundation piles, 140 old bridges, 412 Improvisation in military bridging, 47!S, 479 Inclination of lacing bars, 207 Increasing fluidity of mixture of concrete, 391 Increasing national efficiency, 2 Indices, card, 360 Infrequent loadings, 133 Inspecting Bureaus and Engineers, 362 Inspection, compensation for, 361, 362 damages for faulty, 362 economics of, 361-363 economics of mental effort as applied lo, 364 field, 364 force, 363 importance of having it properly done, 304 methods of payment for, 362 military bridges, 4S5 omission of is uneconomic, 362 periodical, 419 quality of, 361 Inspectors, fitness of, 363, 364 Instnictions to resident engineer, 380 Instruments, surveying, 382 Intensities of working stresses concrete, 219 heat-treated steel, 37 tension and compression, relation of, 136 Intermediate trusses and cables for suspen- sion bridges, 264 Intermediate trusses for cantilever bridges, 260 Investigation, principle of economic, 6 Jack-stringers, 184, 185 James River crossing by General Grant, 471 Japan oil, Sipe's, 436 Jigging of freshly made concrete, 392, 393 Joints and fastenings of military bridges, 476 K-truss, 71 Kansas City bridge over Missouri River, 132 Kansas City elevated railroad, defective, 74 Kansas University, lectures on engineering economics, 4 Keeping employees busy, 380 Knowledge, collection of, 365 Labor, a blessing, 1 facilities, 123 handling of, 19 material versus, 18 military bridges, 478 rise in price of, 348 supply of, 373 Labor and capital, 338 Lacing bars, inclination of, 207 Lacing versus tie plates in riveted tension members, 207 Lambrecht, Jules, 35 Lamps, electric, in shops, 367 Large stones in mass of concrete, 392 Lashings, 476 Lateness of starting work, 358 Lateral system, dropping of, for clearance, 206 Latin America asking for business, 2 Layouts, determination of, 116-124 factors and conditions affecting, 116 fieldwork, 380 Leaching of concrete by iiercolation of wat(>r, 454 Le Genie Civil, 26 Leiter's Air-Drying, Salt-Water-Proof paint, 439 Lengths of panels for rcinforccd-concrete girders, 224 Lettering, 359 Lcucol oil, 435 INDEX 501 Levees, 122 Life, metal bridge, 430 reinforced-concrete bridges, 64 steel bridges, 64 water-proofing, probable, 451 Lift bridges, automatic brakes, 295 balancing chains, 294 base for pavement, 295 buffers, 295 location of machinery house, 295 quantities, 299 records, 297 Light, beneficial effects of, 367 shops, 367 Light bridges, strengthening of, 416, 417 Light structure at outset, economics of, 16 Lime, hydrated, 391, 457 Limiting span-length, inferior for pin-connected bridges, 74 reinforced-concrete bridges, 66 steel arches, 241 Limits, economic, wide range of, 16 Lindenthal, Dr. Gustav, 75, 437 Linseed oil, alone for shop coat, 438 boiled, 435 List of author's writings on bridge economics, 489, 490 Litharge, 434 Little Pedee River crossing, 472 Live loads, 125-127 cantilever bridges, 127 combined bridges, 132 decreasing with span-length, 125 determination of, 13, 125 excessive, 125 highway, 126 steam railway, 126 Loadings, abnormally heavy, 133 auto-truck, 125 classification of, 412 deep foundations, 156 electric railway, 126 future additions to, 16 highway, 126 infrequent, 133 military bridges, 481 standard, for old bridges, 411 steam railway, 126 Train, Classification of, 413 Loads and unit stresses, economics of, 125- 140 Local resources, utilization of, 480 Location, bridge, effect of, on economics, 25 machinery house for lift bridges, 295 Location, sidewalks, 195 top-chord pins, 204 Locomotive gases, protection against, 444 Log books, 381 Logs, sunken, 172 Longitudinal girders, spacing of, 224 Loose plates to be avoided, 217 Loose rivets, 423 Love for work, 1 Lowe, Houston, 433, 444, 446 conclusions concerning paint, 433 opinion of concerning the desirable fea- tures of an anti-corrosive metal coating, 434 Loweth, Charles F., 407, 409 Low bridge versus high bridge, 12 Low classification for old bridges, 414 Low level versus high level crossings, 61, 62, 63 Lubrication, 314, 315 Lumber, treated, unsatisfactory for floor, 426 Lump sum contracts, 340 objections to, 340, 341 suitable only for war times, 341 Lytton arch bridge over the Fraser River, 246 M Machinery, breakdowns of, 315 definition of, 314 house for lift bridges, location of, 295 operating, economics of, 310-317 function of, 315 power operation versus operation by hand, 386 shops, 378 steel, 34 utilization in shopwork, 202 Machine shop, 378 work to be minimized, 211 Machines, scrapping of old, 367 Magnesia, excrescence of, 456 Maintenance, floors, 425 masonry, 424 operation, capitalization of, 15 repairs, 124 economics of, 407-429 Maintenance of bridges, economic consideration, 410 safety consideration, 410 Management of men in shops, 368, 369 Manner and time of mixing concrete, 391 Man-power, 366, 386 Manufacture of concrete, economic problems in, 387 Manufacturers' standards, 205 Market price variations, effect of, 23 Marking metal, 374 502 INDEX Masonrj^ maintenance, 424 Masonry piers, 167 Masonry, stone, repairs to, 420 Materials and supplies, 384 available, 484 best proportions of, for concrete, 387-389 checking of, 380 counterweights, 294 employed in miHtary bridging, 474 purchasing cheaply, 386 quick ordering of, 385 special, for contracts, 373 stock, 372 storage of, 382, 386 unloading of, 380, 381 versus labor, 18 versus time, 18 Mathematics in bridge-economics investiga- tions, 175 Mattress work, 122 woven brush, 474 Mayari steel, 33, 34 cables, 279 Medium spans, erection of, 399 Members in military bridges, sizes of, 477 Men, management of, 368, 369 treatment of, 385 Mental effort, economics of, 18 as applied to inspection, 364 Merriman and Jacoby's treatment of canti- lever bridges, 261 Metal, cleaning of, 422, 445 for shop coat, 441 life of, 430 marking of, 374 minimum thickness of, 201 protection, economics of, 430-448 storage of, 376, 441 straightening of, 374 structural, prices of, 23 trimming and cutting of, 374 "Metalcote, " 432 Methods, comparison, 14 contract-letting, 339, 340 erection, 123 profit-sharing contract, 345, 346 Military bridges, bolts, 477 classes of, 463 concrete, 476 deck or flooring, 474 economics of, 459-485 improvisation in, 478, 479 inspection, 485 joints and fastenings, 476 labor, 478 lack of strength, 459 Military' bridges, loading, 481 paint, 476 piling, 475 plant and tools, 464, 477 standardization, 478, 479 steel, 475 stone, 476 timber, 475 transportation of materials, 482 types, 464 typical, 465 waste not justified, 462 Mill inspection, 363 Milling and planing, 377 Minimum thickness of metal, 201 Mississippi River Bridge, economic study for replacement of, 13 Mississippi River bridge or tunnel at or near New Orleans, 296, 319 Missouri River Bridges, East Omaha, 131 Fort Leavenworth, repairs to, 408 Sioux City, 131 Missouri Valley Bridge Company, 439 Mixed carbon and alloy-steel bridges, 30 Mixing concrete, economics of, 386 increasing fluidity of mixture, 391 manper and time of, 391 water, amount of, 392 Moisture changes, provocative of cracks in concrete, 456 Molybdenum, as an alloy, 34 economic benefit from, in steels, 44 gain involved by increasing percentage of, 49 Molybdenum steel, 36 bridges, use in, 487 Commercial Steels (catalogue) , 36 economic comparisons of, 44-51 tests of, 38-43 Monthly estimates to be made promi)lly, 3M Montreal enterprise, 7 Motive power dependent on location of structure, 310 Movalile bridges, comparative costs of various typos of, 297 economics of, 284-309 effect of wind pressure on, 293 examples illustrating use of economic curves for, 304-30S main elements in, 314 pavements for, 293 quickness of operation in, 293 skew layouts for, 303 Multi-cylinder gasoline engine, 313 Mulfiple punches, 375 effect of, 206 INDEX 503 Mystic River, Brown balance-beam bascule bridge, 291, 298, 308 N National Economic League, 4 National efficiency, increasing, 2 Nature of banks and approaches, 483 Nature of bottom, 483 Navigation influences, 123 Necessity for economic studies, 7 New Orleans, bridge project, 12 bridge studies, 151, 155 proposed bridge, 296 report, 8, 319 transbordeur, description of, 321-323 New types of ponton equipage, 472 New Westminster, B. C, bridge over Fraser River, 131 Nichro steel, 37, 48 Nichromol steel comparison, 47 tests of, 39 Nichromol steel, 34, 37, 48 Nichro steel comparison, 47 tests of, 39 Nickel- chromium-molybdenum steel, 37 Nickel-molybdenum steel, 37 Nickel price, as affected by Great War, 33 "Nickel Steel for Bridges," 91 Nickel steel, 26, 47 bridges, use in, 33 cables, 280, 281 floor-systems, 31 Nicmol steel comparison, 46 tests of, 41 Nicmol steel, 37, 47 Chromol steel comparison, 51 nickel steel comparison, 46 tests of, 41 Nobrac, 432 Noise of gearing, elimination of, 313 Non-continuous versus continuous trusses, 75-82 North River crossing at New York City, 58 highway tunnels, 56 proposed bridge for railway and highway traffic, 60 Northwestern Elevated Railroad, 253 Number of columns per bent, best, 224 O Objections raised to proposed ideal method of contract-letting, 354-356 Obstruction of waterway by pier shafts, 170 Office work, economics of, 358-360 Old bridges, doubling-up of, 407 pins in, 415 rule for condemnation of, 407 strengthening of, 409 Omission of end floor beams, 203 Omissions, avoidance of, 20 One-man stones in concrete, 386 One-way versus two-way reinforcing in slabs, 220 Open-dredging and pneumatic methods on same job, 173 Open-dredging versus cofferdam method, 171 Open-dredging versus pneumatic i^rocess, 171 Open spandrel versus solid spandrel, 228 Open timber decks, 184 Open-web girders versus plate-girders, 255 Open-web riveted spans, economics of, 70 Operating apparatus, ideal, 313 Operating bridges by hydraulic pressure or compressed air, 311 Operating machinery and power, economics of, 310-317 function of, 315 power of, 315 strength of, 315 Operation and maintenance, capitalization of, 15 Operation costs of tunnels and bridges, 55 Opinion, expert, gratis, 7 Opposition of rival promoters, 20 Optimism, 20 Ordering quickly of materials, 385 Ordinary swing versus bob-tailed swing, 288 Organization, field, 383 Overestimating, 20 Overloading of bridges, 13 Over-stressing counters, 423 Paints and Painting, 379 abrasion, 445 accessibility for, 201 application, 422 after cleaning, 446 best colors, 436 best kind, 430, 431 cement, 437 climatic influences, 421, 438, 440 colors, 428 comparative cost of application, 421 correct and economic theory of, 448 covering power, 436 deterioration, causes of, 444 economics of, 430-448 elasticity, 436 experiments at Havre de Grace, 433 factors that affect results in, 446 fire-proof, 420 for steel bridges, 421 general economic observations concern- ing, 447 highway bridges, 427 importance, 421 incipient failure, 445 504 INDEX Paints and painting, interior of shop white, 367 layers, thickness, 447 Leiter's Air-Drying, Salt- Water-Proof, 4.39 Lowe's conclusions concerning, 433 military bridges, 476 mixing, 432 newly-erected steelwork, 442 paste form, 432 powder form, 432 price, 447 priming coats, 422 program, 428 recommendation of, by engineers, 431 spraying, 422, 440 spreading power, 436 summary of author's conclusions concern- ing, 448 temperatures suitable for, 448 Panel lengths, economic, 179, 209 for suspension bridges, 265 reinforced-concrete girders, 224 Parallel chords, economic truss depths for, 176 Parallel chords versus polygonal chords, 180 Pasadena, Calif., bridge over Arroyo Seco, 248 Pavements, 187, 188, 219 asphalt, 188 base on lift bridges, 295 bitulithic, 188 bituminous, 188 concrete, 188 expansion joints for, 219 movable spans, 293 Paving blocks, storage of, 382 Paying enterprises, 8 Pedestals, bases, plain concrete versus reinforced, 173 cantilever bridges, 260 costs affecting economic layouts for trestles, 252 Pedestrian traffic on transbordeur, 323 Pedestrian travel, 21, 128 Penalizing a contractor, 340 Percentage of profit for employees, 348 Percolation of water through concrete, 454 Permanence negligible in military bridges, 462 Permissible pressures on soil and piles, 155 Personal equation in designing, 05 Petit trus.ses for continuous spans, 78, 81 Petit versus Pratt trussing, 71 Philadelphia-Camden Suspension Bridge, proposed, 270, 318 ( riuisbordour, fn'oposod, .335 PickMng f)f metalwork, 442 Piers, minimum expense for, 57 temporary, in Missouri River, 168 two-pedestal, 94 Pier-shafts, aesthetics, 168 cocked-hat, 169 depth below water, 170 reinforcing of concrete, 167 ' Pigments, character of, 448 Piles, buUt, 296 cribs versus caissons, 173 foundations for arches, 244 friction, 156 impact, 140 loading, permissible, 155 military bridges, 475 piers under steel spans, 169 reinforced-concrete, 225 steel sheet, 171, 172 trestles for military bridges, 467 trestles, replacing of, 419 wooden versus reinforced, 174 Pin bearings, wear in, 415 Pin-connected bridges, inferior span-length for, 74 Pin-connected elevated railroads, 73 Pin-connected versus riveted bridges, 72 Pin holes, half, 216 Pins, cost of shopwork on, 73 old bridges, 415 sizes, 207 top chords, location of, 204 wear, 423 Plain concrete versus reinforced-concrete for pedestal bases, 173 Planing and milling, 377 sheared edges, 202 Plank floors, undesirable, 425 Planning system for shops, 379 Plant, 384 erection, 402, 403 military bridges, 464 tools for militarj^ bridges, 477 Plate-girders, cambering, 207 criterion for alloy steels, 27 deck, economics of, 68 economic depths of, 178-180 half-through, 185 economics of, 09 open-web girder comparison, 255 round corners in, 207 Plate-lattice-girder spans, 70 Plates, loose, to bo avoided, 217 standard dimensions for, 205 Platforms for cleaners and painters, 446 INDEX 505 Pneumatic and open-dredging methods on same job, 173 Pneumatic process versus open-dredging, 171 Polygonal chords versus parallel chords, 180 economic depths of trusses with, 176, 177 Ponton equipage, new types of, 472 Ponton or floating bridges, 470 Portable drills, 379 Possibilities and economics of the trans- bordeur, 318-336 "Possibilities in Bridge Construction by the Use of High-Alloy Steels, "91 Posts, H-section for, 200 Potomac River crossing at Harper's Ferry, 471 Pound prices for various sections, 205 Power, arbitrary, of resident engineer, 382 conveyance of, 312 cost of, 55 crossing bridges and tunnels, 54, 55 economics of, 310-317 efficiency, definition of, 311 hydraulic, 311, 312 operating machinery, 315 shop operation, 366 steam, for bridge operation, 311 type of, dependent on location of struc- ture, 310 Pratt versus Petit trussing, 71 Pratt versus triangular trussing, 71 Pre-moulded slabs, 230 Preservation of timber, 419 Prevention of progress, 338 Prices, alloy steels, 44 alloy steel constituents, 44 structural metal, erected, 23 suspension bridges, 25 unit, for bridges, 57 variations, effect of, 23, 24 Priest, H. Malcolm, 75 Primary truss members, criterion for econom- ics of, 26 Priming coats of paint, 422 Principles, economic investigation of engineering practice, 6 general economic, 6 of true economy, importance of, 1 Probable life of water-proofing, 451 Probable traffic, 20 Problems, economic, in manufacture of con- crete, 387 Profit, percentage of for employees, 348 Profit sharing, 338, 343, 370 employees of manufacturers, 357 method of, 345, 346 Progress, prevention of, 338 Progress, reports and charts of, 381 Promotion of bridge projects, 20 Property considerations, 120 Property (field) of the engineers, 381 Proportions for concrete, 387 Proposed, enterprise, economics of, 7 railroad economics, 15 Protection, against brine drippings, 443 against flood and drift, 485 against locomotive gases, 444 cement, 382 fresh concrete, 394 Protrusion method of erection, 399 Public Belt Railroad Commission of New Orleans, 320 Punch Shops, 375 Punched metal, storage of, 376 Punching, 375 full size, 202 Purchasing Agent, 384 Purchasing of materials cheaply, 386 Purified steel, 33, 34 "Quality Number," 44 Quantities, vertical lifts and bascules, 299 wire-cable suspension-bridges, 276 Quebec cantilever bridge, 30, 71, 132 Queensboro Bridge, 195 Quick, Howard P., 440 R Railroads, bridges, electric, 187 economics of, 6, 15 elevated, 253 economics of, 250-256 miUtary bridges, 473 trestles, economics of, 250-256 Rails laid directly on steel work, 183 Rails resting on steel floor, 186 Range of economic limits, 16 Ratios, cost of fixed-span bridges and their ap- proaches for various clearances above high water, 331 rise to span, 225, 233-235 Reaming, 376 subpunching-versMs punching full size, 202 templets, 205, 215 Recommendation of paints by engineers, 431 Recording diagrams, 18 Records, cost, 360 floors, 427 506 INDEX Records, unit costs, 385 weights of lift bridges, 297 " Red Lead Lute, " 432 Red lead, paint for shop coat, 431 proportion of, in paint, 434 Red Oxide No. 31, 432 Red Rock Cantilever Bridge, designing of piers for, 167 Reduced live loads for combined bridges, 132 Reducing-gear, hydraulic, 313 Reduction of voids in the aggregate, 389 Reichmann, Albert, 214 Reinforced-concrete, bridges, arch bridges, 225-230 economics of, 218 Hfe of, 64 limiting span-length of, 66 small cost of maintenance and repairs for, 64 caissons, 169 columns, 223 girders, 221, 223-225 pier-shafts, 167 piles, 225 piles versus wooden piles, 174 steel structures, 64 trestles for steam railways, 230 trestle versus steel trestle, 114 versus plain concrete for pedestal bases, 173 viaducts, water-proofing for, 454 Reinforcing bars, high-carbon steel for, 133 Reinforcing steel, 218 Repainting, determination of time for, 445 Repairs, 124 economics of, 407-429 renewals, equipment for, 420 stone masonry, 420 timber bridges, 419 Replacing, long spans, 405 short spans on old substructure, 404 steel bridges, 403, 404 Report, author to S. P. E. E., 3 home office, 380 progress, 381 Requirements of U. S. Government, 116 Resident engineer, arbitrary power of, 382 decisions by, 381 instructions to, 380 Resistance of brakes, 315 Restrictions of speed, 412 Retaining walls, 231 Revenue, sources of, 20 Reversal of current, 122 Reversing stresses, 135 effect of, on continuous trusses, 77 Rhett, Albert H., 458 Rhine crossing near Honningen, 471 Ribbed structure versus solid barrel, 228, 229 Rib depths, economic, 235, 236 Rice, Geo. S., 433 Right-of-way, cost of, 114 Rim-bearing versus center-bearing swing- spans, 287 Rip-rap, 122, 424 Rise, arch, 226 economic, of suspension bridge cables, 265, 266 ratio of, to span, 233-235 with span-length unchanged, 225 Rise in price of labor, 348 Risk, assumption of, 340 Rivalry in bridge projects, 20 River traffic, 123 Riveted spans, economics of, 70 Riveted tension members, 199 Riveted versus pin-connected bridges, 72 Riveting, arrangement of, 199 machines, 377 sequence of, 214 staggered, 211 Rivets, . loose, 423 spacing, 210 Roads, drainage of, 454 Roadwaj^s, crowning of, 426 widths, 127 widths for military bridges, 473, 474 Rolled I-beam spans, economics of, 67 Roller-bearing bascules, 290 Rolling-lift bascules, 290 Roof protection for timber bridges, 420 Round corners in plate-girders, 207 Rusting as affecting detailing, 201 S Sabin, Dr. A. H., 433, 436-438 Safety and permanence in military l)ridges, 462 Safety considerations, 370 Safety factor small in military bridges, 462 Salary for contractor, objoctional)lp, 348, 349 Sand and gravel used without screening, 390 San Francisco Harlior Bridge, proposed, 8, 10 Sanitation of liridges and tininels, 56 Scamping work, 342 Scarcity of timl)er, growing, 22 Schedule pric^os for various sections, 205 Schneider, C. C., 287 Sciotoville bridge, 75, 77 Scour, 122. 424 INDEX 507 Scrapping old machines, 367 Screens between railway and highway traffic, 129 Sealing cofferdams, 172 Secondary stresses, 72, 73 intensities of working stresses for, 136 Second Narrows proposed bridge, Vancouver, B. C, 131 Secrecy, 484 Sectional trusses and girders for military bridging, 468 Sections, columns, best, 255 floor beams, 186 stringers, 186, 206 Selection of site for military bridges, 483 Seltzer, Harry K., 383 Semi-cantilevers, 83 Semi-can tilevering of continuous trusses, 81 Separation of entrances and exits, 55 Shafts, depth below water, 170 hollow, 168 proportioning, 167 Sharing of profits with workmen, 370 Sheared edges, planing of, 202 Sheet piling, steel, 171, 172 Shelf angles, 184 Shelves, 214 Shifting of channel, 122, 293 Shop, accidents, 370, 371 assembling, 378, 379 blacksmith, 378 coat, cleaning of metalwork for, 441 coat, red lead paint for, 431 considerations, 209 economics in designing for, 202—213 designing to suit fabrication, 366 drawings, 210 should not be prepared in Consulting Engineer's office, 359 electric lamps, 367 floors, 374 handling of work, 368, 369 heat, 367, 368 inspection, 363 light, 367 machinery, 378 management of men, 368, 369 operation, power for, 366 painting interior white, 367 size of force, 380 smoking, 371 space, 367, 368 special space, 377 standardization, 372 storage ground, 373 tracks, 379 ventilation, 367, 368 Shopwork, cost on pins and holes, 73 economics, 365-379 general economic problem, 365, 366 Short cuts in computing, 92 Side friction on caisson, 156 Side plates, avoidance of, 206 Side rails of military bridges, 474 Sidewalks, 189, 195 Silicon steel, 33, 34 Simple-truss bridges, cantilever bridge comparison, 83-89 economic limit of length for, 84 economic span-lengths for, 17, 150-165 Simple versus continuous reinforced-concrete girders, 221, 222 Single angles in tension, 204 Single-leaf versus double-leaf bascule, 289 Sioux City Bridge over Missouri River, 131 Sipe's Japan oil, 436 Site selection for military bridges, 483 Sizes of individual members in military bridges, 477 Skew layouts for movable spans, 303 Skewed crossings for vertical lifts, 293 Skewed spans, 209 Skids, 376, 377 Skimping details, 133, 201 Skimping reinforcing of girders, 222 Skinner, Frank W., 396 Slabs, continuity, 221 designing, 220 pre-moulded, 230 steel, arrangement of, 220, 221 supporting, 193 water-proofing, 454 Smoke effects on steel, 416 Smoking in office, 358 Smoking in shops, 371 Society for the Promotion of Engineering Education, 3 author's report to, on study of econom- ics, 3 Soil pressure, permissible, 155 Solid-barrel arches, 227 ribbed arch comparison, 228, 229 Solid drilling, 208 Solid-slab trestles, 230 Solid spandrel versus open spandrel, 228 Solitary columns versus braced towers, 254 Solitary piers for cantilever bridges, 260 Soundings around piers, 424 Space in shops, 367, 368 Spacing, columns in bents, 253 longitudinal girders, 224 rivets, 210 stringers and cross girders, 192, 194 trusses, 186 508 INDEX Spacing-tables, 375 Spandrel-braced arch, 237 Span-lengths, arches, inequality in length of, 227 economic, cantilever bridges, 258 determination of, 17, 158 elevated railroads, 254, 256 for trestles, 250-256 rise unchanged, 226 simple-truss bridges, 17, 150-165 tabulation of, 160 effect on comparative economics of steel and reinforced-concrete struc- tures, 66 limiting, for steel arches, 241 Spans without floor systems, 183 Spar bridges, 466, 467 Special material for contracts, 373 Special material to be avoided, 205 Special space in shops, 377 Specifications, standardization of, 372 Speculative zone, 30 Speed restrictions, 412 Speeds for maximum impact, 414 Spiral approaches, 59, 114 Splaying of trusses in cantilever bridges, 260 Splices in webs, 207 Spraying of paint, 422, 440 Spreading power of paint, 436 Springings, arch, 226 Spur gearing, 312, 313 Staggered riveting, 211 Standard, apparatus, use of, 316 dimensions for plates, 205 loadings for old bridges, 411 parts, importance of using, 359 Standards of bridge manufacturers, 205 Standardization, bridges, 372 military bridging, 478, 479 shops, 372 specifications, 372 Stay plates inside of gussets, 203 Steam power for bridge operation, 311 Steam railways, electrified, 126 loadings, 126 reinforced-concrete trestles for, 230 Steel, arches, economics of, 232-249 limiting span-length for, 241 tabulation of salient features of, 234 bottom chords in reinforced-concrete arches, 229 bridges, comparative (■(•nnoniics of different types of, 67 Steel, Ufe of, 64 replacing of, 403, 404 cylinder piers, 168 forms for concrete compared with timber, 170 growth of, 215 military bridges, 475 sheet pihng, 171, 172 structures, prevention of corrosion in, 421 treatment of, for encasement, 443 trestles, columns, method of proportioning of, 134 economics of, 250-256 reinforced-concrete trestle compari- son, 114 Steel versus reinforced-concrete structures, 64 Steinman, Dr. D. B., 90, 91, 95-106 Stiffened buckle-plate, 195 Stiffening angles, fitting of, 203, 212 Stiffening trusses, anchored versiis free ends, 265, 268 Stiffening trusses for suspension bridges, 265 formula for weights of, 93 Stitch rivets, 208 Stock materials, 372 Stone in military bridges, 476 Stone masonry, repairs to, 420 Stone masonry versus concrete for piers, 167 Stoppage of traffic in tunnels, 57 Storage, batteries, 312 explosives, 382 ground, divided, for shops, 373 materials, 382, 386 metal, 441 punched metal, 376 Straightening metal, 374 Strauss bascule, 291 Stream conditions, 122 velocity, 122 width, 483 Street car traffic, method of supporting, 425 Strength, alloy steels, 38-43 operating machinery, 315 Strengthening old bridges, 409 light bridges, 416, 417 Stresses, (combination of, 133 cantilever l)ridges and arches, 136 old bridges, 415 reversing, 135 summitig up, 135 Stringerless tyije of floor-system, 193, 194 Stringers, crooked, 466 depths, economic:, 185 INDEX 509 Stringers, sections, 186, 206 spacing, 192, 194 "Structural" defined, 314 Structural metal, price of, 23 Structure, general features of, 120 Student competition on cost estimating, 141, 146-149 Study of engineering economics, importance of, 3 Subpaving or base, 189 Subpunching, 211 Subpunching and reaming versus punching full size, 202 Substructure, economics, 167—174 influence on arch economics, 238-243, 245 Sunken logs, 172 Superintendent, 383 Supplies, 384 availability of, 123 Supply of labor, 373 Supporting, cables for vertical-lift bridges, 295 machinery parts, 314 structure, 314 Surveying instruments, 382 Surveys, copying of, from field books, 381 Suspended span in cantilever bridges, eco- nomic lengths of, 258 . Suspending floor from backstays, 266 Suspension bridges, 25 anchorages, 94, 267 approaches, 266 best system of cancellation for stiffening trusses, 265 buckle-plate floor, 263 cantilever bridge comparison, 90-112 decks, 263 economic dimensions, 95 economics, 263-283 panel lengths in, 265 rise of cables, 265, 266 truss depths, 265 ends of stiffening trusses free or anchored, 265 erection, 401 eye-bar cable, quantities of various materials in, 278 floor-system, 263 formulae for weights, 273-275 intermediate trusses and cables, 264 legitimate function, 263 limiting -widths of structure, 94 military bridging, 469 nickel steel floors, 264 prices, 25 quantities for wire cables, 276 stiffening trusses, 265 weights of alloy-steel eye-bars, 277 "Suspension Bridges and Cantilevers — Their Economic Proportions and Lim- iting Spans," 90 Swiftness of current, 483 Swing spans, 298 bascule or vertical-lift comparison, 284, 285 combined rim-bearing and center-bearing type of, 288 comparative economics of, 308 economics of, 287 Symmetry, 209 System of contract-letting, ideal, 343, 344 Systemization, 18 Tabulation of economic span-lengths, 160 Tallcing among employees, 358 Technical book writing an extravagance, 486 Technical schools, study of economics in, 3 Temperatures suitable for painting, 448 Templet shop, 379 Templets, reaming to, 205, 215 Temporary bridges, 21 Temporary economic expedients, 15 Temporary piers in Missouri River, 168 Tests, alloy steels, 38-43 cement, 380 members in full-size bridges, 138, 139 Thickness of web, 207 Three-hinged versus hingeless arches, 229 Three-hinged versus two-hinged arches, 238 Three-span structure, economic investiga- tion of, 165 Through bolts in military bridges, 477 Thrust of braked trains, 140 Thrust of earth, influence of, 228 Tides, 122 Tie-plates a necessity, 182 Tie-plates versus lacing in riveted tension members, 207 Ties, highway bridge floors, 192 street car traffic, 425 treated, economics of, 182 Timber, bridges, fire protection, 420 repairs, 419 roof-protection for, 420 decks, 184-195 concrete for highway bridges, com- parison with, 187 gromng scarcity of, 22 military bridges, 475 prices, 23 steel for concrete forms, comparison with, 170 treatment, 183, 188 510 INDEX Timber, trestles, 113-115 approaches, 21 filling up, 113 low classification of, 415 military bridges, 465 Time, considerations, 121 element in war, 460 expenditure on approach grades to bridges and tunnels, 56 factor substituted for cost factor, 461 mixing concrete, 391 repainting, determination of, 445 required for solution of economic prob- lems, 33 schedule of fieldwork, 380 versus material, 18 Toch Bros., 437 "TockoUth," 432, 437 Tool equipment, 374 Tools for military bridges, 477 Top-chord, pins, location of, 204 polygonal, economic depths of trusses with, 176, 177 Top flanges, cover-plates for, 200 Torch, use of, for cleaning metal, 441 Towers for vertical lifts, 294 Tracks, 384 electric-railway, 190 gauntleted, 128 shops, 379 Traction loadings for old bridges, 412 Traffic, 20 congestion at entrance and exit, 54 diversion of, during replacement, 405 investigations, 20 pedestrians on transbordeur, 323 probable, 20 several kinds on one deck, 128 tunnels, stoppage of, 57 Trains, thrust of braked, 140 Transbordeur, author's improvements on, 320 comparative operating capacity, 328- 330 conditions favorable for, 330 description, 318 efficiency, 330 general conclusions concerning the eco- nomics of, 335, 336 Havana Harbor, proposed, 332-334 high-level bridge comparison, 330 improvements on present type of, 319, 325-328 inferior features of, 318 New Orleans, description' of , 321-323 ordinary, description of, 319 Philadelphia and Camden, proposed, 335 Transbordeur, possibiHties and economics of, 318-336 summary of conclusions on economics of, 320, 321 time schedule, 324 tji^es of truss suitable for, 319 velocity of cages, 323 Transformers, 312 Transportation, materials for miUtary bridging, 482 unnecessary, elimination of, 366 Transporter bridge, 318 Travel, automobiles in tunnels, 53 Travelers, expensive for deep trusses, 176 Treated lumber unsatisfactorj' for sidewalks, 426 Treated ties, economics of, 182 Treatment of men, 385 Treatment of steel to be encased, 443 Treatment of timber, 183, l<5l8 Trestles, approaches, timber, 21 double-track railway, 252 economic span-lengths, 250-256 highway, economic span-lengths of, 252 military bridges, 467 pedestal costs affecting economic layouts. 252 reinforced-concrete for steam railways, 230 span-iength, economic, for military, 465 steel, economics of, 250-256 versus reinforced-concrete, 114 Triangular trusses, divided, for continuous spans, 78, SO Triangular versus Pratt trussing, 71 Trimming and cutting metal, 374 Troubles, anticipating, 371 Trough floors, 182, 214 Truck loadings, 125 Trucks, great weight of, 425 True economy, development of, 2 Trunnion bascules, 290 Trusses, bridges, economic span lengths for, 150— 165 crescent, 272 criterion for alloy steels, 27, 28 depths, economic, for parallel chords, 176 'depths, economic, for suspension bridges, 265 depths for cantilever bridges, 259 doubling of, 21 economics of, 175-181 spacing, 186 Tullock, A. J., 439 Tunnels, almost always more expensive than bridge, 54 iiuiinui>l)ilo travel in, 53 INDEX 511 Tunnels, breakdown of vehicles in, 57 bridge costs compared, 54 bridges, comparative cost curves for, 57 bridges, comparative economics, 12, 53 building one pair of tubes at a time, ad- vantage of, 54 carbon-monoxide gas in, 53 cost of operation, 55 cost of power, 55 ■ depth of descent into, 54 diameters, 53 disagreeableness of traversing, 54, 56 Hudson River, 56 sanitation, 56 separation of entrances and exits, 55 stoppage of traffic, 57 traffic, blockade of, 56 travel in, 53 variation of cost, with diameters, 53, 57 ventilation, 53 Turning flanges of channels in, 200, 203 Twelfth Street Trafficway Viaduct in Kansas City, 229 Two-column versus four-column structures for elevated railroads, 254 Two-pedestal piers, 94 Two-way versus one-way reinforcing in slabs, 220 Type A cantilevers. 86 Types of military bridges, 464 Typical military bridges, 465 U Unbalanced wind pressure, 315 Unchecked drawings, 359 Unclassified work, 381 Union Loop Elevated Railroad, 253 Unit-cost records, 385 Unit prices, alloy steel constituents, 44 bridges, 57 method of contract-letting, 340 various sections, 205 Unit stresses, determination, 132 economics, 125-140 old bridges, 415 limiting, 410, 411 Unit wind loads, 316 University of Kansas, lectures on engineering economics, 4 Unloading of materials, 380, 381 Unnecessary transportation, elimination of, 366 Utilization, existing bridges, 480 local resources, 480 machinery in shopwork, 202 Vanadium steel, 33, 34 Vancouver, B. C, bridge painting, 439 Variation of cost of tunnels with diameters, 57 Variations in market price, effect of, 23 Vehicle for paint, best, 435 Velocity of stream, 122 Ventilation for shops, 367, 368 Ventilation of tunnels, 53 Versed sine for cables, 265, 266 Vertical-lift bridges, bascule comparison, 285-287 bascules, comparative economics of, 302 base for pavement of, 295 cantilever combination, 295 Duluth, proposed, 310 economics, 291-293 economics of detailing, 294 quantities, 299 records, 297 skewed crossings, 293 supporting cables, 295 swing-span comparison, 284, 285 towers, 294 Viaducts, 217 economics, 250-256 erection, 398 girder depths, 203 reinforced concrete, water-proofing for, 454 Vibration and jigging of freshly made con- crete, 392, 393 Victory a criterion in military bridge eco- nomics, 462 Visitors to drafting room, 358 Voids, volume of, in aggregate, 386 reduction of, 389 Vredenburgh, Watson, 361 W Waddell and Harrington axle, 291 Waddell, Montgomery, 12 Wages, flat scale of, 370 Waikato River arch bridge at Cambridge, N. Z., 247 Waikato River arch bridge at Hamilton, N. Z., 246 Wakefield piling, 172 Waling frames, spacing of, 172 War, effect of, on nickel price, 33 engineers in, 459 time element, 460 Warren trusses, economics of, 179 Washout of falsework, 15 Waste not justified in military bridging; 463 Water, amount of, for mixing concrete, 392 512 INDEX Water, depth, 483 disruptive force of, freezing, 455 Water-proofing, 189, 390 concrete bridges, 451 cost of, 450 definition, 449 deterioration, 452 economics, 449-458 material for decks, 183 material must be elastic, 452 original cost, 450 probable life, 451 slabs, 454 value of, 452 Waterway, clear, 122 obstruction of, by pier shafts, 170 Weakness in old bridges, 414 Wearing of pins, 415, 423 Wearing out of steel structures, 423 Web splices, 207 Web thickness, 207 Weights, alloy-steel eye-bars in suspension-bridges, 277 arch bridges, approximate formulee for, 248 arches compared to weights of trusses, 238, 239 deck reduced to minimum, 194 metal in arches, formulte for, 239, 240 metal in cantilever bridges, 31 metal to carry one pound of load, 196, 197 stiffening trusses, 93 Welsh, Ashbel, 14 economic comparison, 14 West Point, Ga., crossing of the Chattahoo- chee River, 471 Western Society of Engineers, 90, 112, 268 paper presented to, 150 Wharves, 384 Wide range of economic limits, 16 Widths, decks, 126-128 footwalks, 128 roadway for militarj- bridges, 473, 474 stream, 4S3 structure in cantilever and suspension bridges, 94 Wind loads, unit, 316 Wind pressure, bascules, 316 effect on mo^dng spans, 293 unbalanced, 315 Winner Bridge, 169 Wolfel, Paul L., 214 Wood preservation, 419 Wooden, block pavements, 426 piles versus reinforced-concrete pUes, 174 stringers undesirable, 425 ties for street car traffic, 425 Work of Engineer, importance of, 3 Work, unclassified, 381 Working full time, necessity for, 2 Working stresses, concrete, intensities of, 219 determination of, 132 heat-treated steel, 37 old bridges, limiting, 410, 411 tension and compression, lelation of, 136 Workmen, force of, 373 sharing profits with, 338, 370 Worm gearing, 313 Wrecks encountered in sinking, 172 Writings, author's, on bridge economics, 489 Yards, 384 Yates, J. J., 395 Date Due M/^r'> ^ f\ iQQ'i WK 1 lyy^ ^ ^1 BOSTON COLLEGE 3 9031 01513706