ENGINEERS' POCKETBOOK OF REINFORCED CONCRETE By E. LEE HEIDENREICH M. Am. Soc. Test. Mat., M. W. S. E., M. Am. Inst. Min. Eng. SECOND EDITION CHICAGO THE MYRON C. CLARK PUBLISHING CO. LONDON E. & F. N. SPON, Ltd.. 57 Haymarket 1915 Copyright, 1908. Copyright, 1915. By The Myron C. Clark Publishing Co. PREFACE TO FIRST EDITION. For the past fifteen years the author has been largely occu- pied with the study, exploitation and construction qf reinforced concrete, and during this time has collected a very considerable amount of literature as well as personal experience in the sub- ject, some of which in a more or less concise manner is laid be- fore his engineering colleagues in this "Engineers' Pocketbook of Reinforced Concrete." For a person occupied and making his living as an engineer it is at best a thankless task to write a pocketbook in his spare moments, but when the subject is so comparatively new and where such wonderful possibilities for additions and amend- ments are confronting one it is almost impossible to find a proper moment when the book may be considered temporarily finished. From 1899 when the author wrote his first booklet, "Monier Constructions" (published 1900), reinforced concrete has made such gigantic strides forward, that it has entered every branch of civil engineering, and the American Society for Testing Ma- terials in conjunction with the American Society of Civil Engi- neers through a Joint Committee for Concrete and Reinforced Concrete, of which the author is a member, is endeavoring to standardize specifications and to recommend factors and formu- las "required in the design of structures in which this material is used." As yet this committee has not attained results further than "a knowledge of the work such a report demands." Meanwhile the author has been writing, changing, substitut- ing and improving the book for upwards of eight years and finally lets go of it for his own peace of mind, trusting to future opportunities for further changes and amendments. A pocket- book is needed, and the author presents this one for what as- sistance it may render to constructors in reinforced concrete. The author wishes to express his appreciation to the many engineers and authors, from whose treatises quotations have been made. 1H 314622 iv PREFACE TO FIRST EDITION. "Le Beton Arme," by Paul Christophe; "Ciment Arme," by M. M. C. Berger and V. Guillerme; "Beton und Eisen," by Dr. F. von Emperger; "Concrete, Plain and Reinforced," by Taylor & Thompson; "Concrete and Reinforced Concrete Construc- tion," by Homer A. Reid; "Reinforced Concrete," by Buel & Hill; "Walls-, Bins and Grain Elevators," by Prof. Milo S. Ket- chum ; "Reinforced Concrete Bridges and Viaducts," by John Po- dolsky, besides works by Prof. Arthur N. Talbot, Prof. Edwin Thacher, Walter W. Colpitts, C. E., and many others, have been referred to, whose names have been acknowledged in footnotes without intentionally missing any one. A number of manufacturing establishments have courteously furnished much information as to their specialties and their ad- dress or place of business has been given for reference. In the compilation of the different data, in calculations or checking of the many tables, in the research for information from current literature on the subject, both in Europe and in America, the author has been most ably and loyally assisted by Miss Alice Law, Chicago, for whose untiring efforts he hereby expresses his thankful appreciation. E. LEE HEIDENREICH. New York, December 1, 1908. PREFACE TO SECOND EDITION As suggested in the preface to first edition, the author has trusted to future opportunities for further changes and amendments, and will probably continue to do so. While the intention at first was to adopt the new nota- tions proposed in the Progress Report of the Joint Com- mittee of the International Society for Testing Materials, the author has decided to await the results of conferences between the Joint Committee and the Committee on Nota- tion's appointed by that body. The changes and additions in the second edition have been prompted by the development of the art and by the de- ficiencies discovered in the first issue. Several tables have been added, such as are in daily use in the author's office. Under "Bridges" some valuable information has been added, adapted from "Designing Methods," by permission of Mr. Alfred Lindau, M. Am. Soc. C. E., of the Corrugated Bar Company of Buffalo, New York, and as in the first edition the author has acknowledged the sources of information in footnotes and otherwise. The author begs to express his gratitude to his col- leagues and to the public for their kind reception of his earlier endeavors and hopes that the new edition wfll be accepted in the spirit in which it is given an attempt to produce a pocketbook which, in a measure, follows the improvements in the art. E. LEE HEIDENREICH. Kansas City, Mo., January 1, 1915. TABLE OF CONTENTS. Page CHAPTER I. MATERIALS AND MACHINES USED IN RE- INFORCED CONCRETE CONSTRUCTION 1 Definition of Reinforced Concrete Cement: Portland Ce- ment Barrels and Sacks Storage Standard Specifica- tions Necessity for Tests on the Work Sampling Cement for Testing Other Tests Aggregates: Choice of Aggre- gates Determination of Voids in Aggregates Table of Voids Sand Selection of Sand Sand for Mortar Sand for Concrete Table of Sand Cleanness of Sand Washing of Sand Voids in Sand Weight of Sand Standard Sand Screenings Gravel Choice of Crushed Stone Size of Crushed Stone Crusher Run Rock Crushers Table of Rock Crushers Voids in Graded Mixtures Voids in Loose Broken Stone Cinders Mortar: Strength of Mortar Vol- ume of Mortar with Varying Proportions of Sand Weight of Mortar Mortar Tests Retempered Mortar Concrete: Proportioning Concrete Usual Methods of Proportioning Concrete Fuller's Rule Thacher's Table Proportioning Concrete for Maximum Strength For Maximum Density Concrete in Different Classes of Work Mixing Mixtures, Wet or Dry Mixtures for Plain Concrete For Reinforced Concrete The Proper Consistency Hand or Machine Mix- ing Batch or Continuous Mixers Classification of Batch Mixers Table of Batch Mixers Classification of Con- tinuous Mixers Table of Continuous Mixers Hains Grav- ity Mixer Steel: High or Low Carbon Medium Steel Percentage of Reinforcement Mechanical Bond Rein- forcing Steel Loose Rods for Reinforcing Square Bars and Round Rods Twisted Bars Corrugated Bars Dia- mond Bars Thacher Bars Cup Bars Collings Corru- gated Bars Wire Fabric Triangle Mesh Reinforcement Lock-Woven Fabric American Wire Fabric Welded Wire Fabric Expanded Metal Kahn Rib Metal Beam and Girder Units Cummings Girder Frame Pittsburgh Steel Products Co.'s Beam Reinforcement Xpantrus Bar "Unit" Frame Kahn Trussed Bar Luten Truss Hooped Column Reinforcement Cummings Hooped Column American Hooped Column Smith Hooped Column Structural Steel I-Beams Channels Angles Table of Area and Circum- ference of Circles Table of Properties of Sections. vii viii CONTENTS. Page CHAPTER II. DESIGN AND CONSTRUCTION OF BUILD- INGS 67 General Discussion: General Assumptions Made in De- sign Percentage of Steel Reinforcement Basis of Calcu- lations Dead Loads Live Loads Allowable Stresses Bending Moments for Beams Bending Moments for Slabs Cross Reinforcement in Slabs Shearing Pro- visions Location of Stirrups in Beams Adhesion of Con- crete to Steel Modulus of Elasticity Summary of Tal- bot's Tests on Tee Beams Foundations: Types of Founda- tions Bearing Power of Soils Pile Foundations The Raymond Pile The Simplex Pile The Corrugated Pile The Pedestal Pile The Chenoweth Pile Other Forms of Piles Pile Driving Slab Foundations Raft Foundations Portable Foundations Floors: Floor Loads Factor of Safety Classification Slab Floors Beam Floors Beam and Tile Floors Arch Floors Manufactured Floors Floors Without Beams or Girders Umbrella Flat Slab System Heidenreich Flat Slab System Calculation of Slabs Straight-Line Formula Tables Parabolic Line Formula Tables Maximum Bending Moment in Slabs Beams and Girders: Loose Rod Systems Frame Systems Tables of Safe Loads and Steel Areas for Beams Tables of Safe Loads and Steel Areas for Slabs Formulas Giving Ultimate Strength of Beams: Class No. 1 Class No. 2 Class No. 3 Tables Columns: Classification Rectangular or Polygonal Columns Hooped Columns Design of Hooped Columns Tables Considfire's Formula Tables Euler's Formula Structural Details: Roofs Stairs Structural * Steel or Cast Iron Columns Bracket Connections Example of Building Designed According to the Foregoing Prin- ciples: Assumptions Slabs Beams Girders Location of Stirrups Wall Girders Roof Slab Roof Beams and Roof Girders Columns Foundations Raft 2-7 Quadrilateral Raft 4-5-9-10 Square Footings 12, 13, 17 and 18 Conclu- sion Sequence of Operations in Construction: Clearing the Site Lumber and Reinforcing Materials Placing the Re- inforcement Making Concrete Delivering Concrete Depositing Concrete Concreting Columns Concreting. Walls Joining Successive Days' Work Protection of Con- crete in Setting Protection Against Freezing Forms, Molds, Centering and Falsework: Kind of Lumber Table of Working Stresses in Lumber Points to Consider in the Design of Forms Assumptions Made in the Design of Forms Fastening of Forms Joints in Forms Spacing of Studs Thickness of Lagging Rotation in the Use of CONTENTS. ix Forms Alignment and Setting of Forms Adhesion of Concrete to Forms Time to Remove Forms Column and Floor Forms Forms in Combined Steel and Concrete Construction Separately Molded Members Eliminating the Use of Forms Small Tools for Mixing, Conveying and Ramming Finishing Concrete Surfaces: Types of Finish Hair Cracks Mortar Facing Using Special Dry Mixture Bringing Aggregates into Relief Tooling Plastering Concrete Painting and Varnishing Waterproofing: Waterproofing Cracked Walks or Joints Between Steel and Concrete Protection of Steel to Be Ineased in Con- crete Coloring Cement Mortar. CHAPTER III. THE DESIGN AND CONSTRUCTION OF BRIDGES ............................................... 211 Flat Slab and Girder Bridges Classification by Load- ings: Class No. 1 Class No. 2 Class N.o. 3 Load Dia- grams: Live Loads: Wheel Loads on Roadway Wheel Loads on Tracks Impact Treatment of Loads for Girder Bridges Abutments and Side Walls Weights and Di- mensions of Electric Cars Detailed Design of a Flat Slab Bridge: Problem Dead Load: Live Loads: Road Roller: Electric Car Transverse Reinforcement Shear- ing Investigation Side Walls for Retaining Fill Water- proofing Bearing on Abutments Girder Bridges: Problem Floor Slab Design of Slab Girders Girder Gl Shearing Provisions Girder G2 Girder G3 Live Loads Shearing Provisions Stirrups Bent Up Bars Girder G2 Bearing of Bridge on Abutment Tables Girder Bridges: Reinforcing Steel Tables Current Meth- ods: Parabolic Arch without Hinges Parabolic Arch with Two Hinges Flat Parabolic Arch with Two Hinges For 3-Center 'Arch For 5-Center Arch For 7-Center Arch Classification of Arch Bridges The Elastic Theory of Arches Simplified: Introduction Reactions Caused by Concentrated Load Successive Steps in the Design of an Arch Line of Pressure Due to Dead Load Line of Pressure for the Critical Condition of Loading Critical Condition of Loading for a Given Section Proof of the Correctness of Locating Points A and B Approximate An- alysis of Dead Load Thickness of Arch Ring at Crown and Springing Thickness of Arch Ring on Both Sides of Crown Down to the Skewback Location of Neutral Axis Thermal Stresses Example of an Arch Designed Accord- ing to the Elastic Theory: Assumptions Constructing the A,rch Ring Dead Load Diagram Live Load Diagram x CONTENTS. Page Maximum Fiber Stresses Table of Dead and Live Loads at Joints of Arch Moments, Stresses, etc., at the Crown Moments, Stresses, etc., at the Springing Moments, Stresses, etc., at Joint 4 Construction of Arch Center- ing Examples of Centering for Two 50-Ft. Arches Cen- tering for the Pollasky Bridge Concreting the Arch Re- moval of Arch-Centering Grand River Bridge, Grand Rapids, Mich. The Santa Monica Viaduct. CHAPTER IV. ABUTMENTS AND RETAINING WALLS... 296 Theories for Pressure of the Filling: Rankine's Theory Weyrauch's Theory Coulomb's Theory Cain's Theory Trautwine's Theory Rankine's Formulas Caine's Formu- las General Discussion: Thrust Back Filling Drain- age Expansion Joints Temperature Cracks Masonry Retaining Wall: Calculation of Resultant Pressure Stability Against Overturning Stability Against Sliding Stability Against Crushing Reinforced Concrete Re- taining Wall of Beam Type: The Vertical Beam Foun- dation Reinforced Concrete Retaining Wall With Count- erforts: Calculation of Pressure P Vertical Walls Counterforts Foundation Conclusion Retaining Wall Forms: Setting the Forms Removing the Forms Ex- pansion Joints Wall Form Tie Examples of Construc- tion: Retaining Walls, Paris, France Retaining Wall, Great Northern Ry., Wash. Specifications for Reinforced Concrete Retaining Wall: General Workmanship Re- inforcement Loading and Risks Measurement and Pay- ment. CHAPTER V. CULVERTS, CONDUITS, SEWERS, PIPES, AND DAMS 320 Arch Culverts: Box Culverts: Assumptions Design, of Covers for Box Culverts Diagram for the Design of Covers for Box Culverts Design of Sides of Box Cul- verts Diagram for the Design of Sides of Box Culverts Cost of Concrete Culverts Examples of Arch Culverts: Standard Arch Culverts, C., B. & Q. R. R. Arch Culvert, Kalamazoo, Mich. Arch Culvert, Great Northern Ry. Examples of Box Culverts: Standard Box Culverts, C., B. & Q. R. R. Conduits, Sewers and Pipes: Erosive and Transporting Powers of Water Resistance of Soil to Erosion by Water Kutter's Formula Table of Flow of Water in Circular Pipes Grade of Sewers Calculations Calculation for Internal Pressure Calculation for Ex- ternal Pressure Myer's Formula Talbot's Formula Rankine's Rule Reinforcement for Sewers Thickness CONT-ENTS. xi , Page and Weight of Reinforced Concrete Pipe Stresses In Pipes and Rings According to Talbot's Researches Con- centrated Load Distributed Vertical Load Distributed Vertical and Horizontal Load Summary of Tests Made on Concrete Pipes Forms for Sewers Dams: Classification Comparative Features Pressure on the Immersed Sur- face Conclusion Types of Construction The Open Front Dam The Half Apron Dam The Curtain Dam. CHAPTER VI. TANKS, RESERVOIRS, BINS AND GRAIN ELEVATORS 357 Tanks and Reservoirs: General Discussion Shape or Form of Tanks and Reservoirs Calculations Table Giv- ing Capacity of Tanks Foundations Tightness of Tanks Reinforcement Cost Tank for Montgomery Ward & Co., Chicago Heights, 111. Tank for American Steel & Wire Co., Cleveland, O. Forms for an Intake Tank Bat- tery Tanks Bins and Grain Elevators: Action of Grain Flowing From a Bin Bridging Action of Grain in a Bin Table of Grain Pressure Ratio of Grain to Liquid Bressure Vertical Pressure Ratio Between Lateral and Vertical Pressure The Coefficient of Friction Pressure of Coal in Bins Tables of Pressure for Bituminous and Anthracite Coal Weight, Angle of Repose and Angle of Friction of Various Materials Capacity of Bins Conclu- sions Classification of Grain Elevators Comparative Cost of Timber and Reinforced Concrete Elevators Ce- ment Storage Tanks, Illinois Steel Co., South Chicago, 111. Canadian Pacific Grain Elevator, Port Arthur, Ont. CHAPTER VII. CHIMNEYS, MISCELLANEOUS DATA, COST OF KEEPING, ESTIMATING, SPECIFICATONS, ETC 390 Chimneys: Calculation The Core Theory Wind Press- ure and Velocity Approximate Method of Calculation- Example Summary of Points in Design of Chimneys Construction Concrete Chimneys Horsepower of Chim- neys Construction of Molds The Wiederholt Concrete Steel Chimney Manufactured Articles: Inspection: Prog- ress Reporting and Keeping of Costs: Blank Forms Notes on Estimating: Plant Expense Percentage to Al- low for Profits Accident Insurance Blank Form for Estimate of Building General Specifications for Rein- forced Concrete: In General Cement Sand Gravel or Stone Proportion Mixing Placing Reinforcement Ex- pansion Centering Removal of Forms Freezing Weath- er Protecting Work Fireproofing Structural Steel Ce- xii CONTENTS. Page ment Finish Stresses Tests Finally Standard Specifi- cations for Cement: Natural Cement Portland Cement Specific Gravity Fineness- Time of Setting Tensile Strength Constancy of Volume Sulphuric Acid and Mag- nesia Uniform Tests of Cement: Sampling Chemical Analysis Specific Gravity Fineness Normal Consistency Standard Sand Mixing Storage of Test Pieces Tensile Strength Constancy of Volume Miscellaneous Informa- tion Glossary of Terms Used in Plain and Reinforced Concrete Useful Information. INDEX 433-439 CHAPTER I. MATERIALS AND MACHINES USED IN REIN- FORCED CONCRETE CONSTRUCTION. Definition of Reinforced Concrete. This material is a combination of concrete and steel, so united that the con- crete takes the compression, while the steel takes the tension and assists in the resistance to shear. When reinforced concrete first appeared in America it was known as armored concrete; subsequent names applied to it have been ferro- concrete, ferro-cement, steel-concrete, and concrete-steel. At the present time, however, the term preferred by the majority of engineers and designers is reinforced concrete. CEMENT. Cement used in construction is either natural cement or Portland cement. Natural cement being manufactured in much less quantity, and being of inferior strength to Portland, is used so little in comparison with Portland cement that its use .will be disregarded in this book. Portland Cement. The definition of Portland cement, recommended by the committee on standard specifications for cement of the American Society for Testing Materials, is "the finely pulverized product resulting from the calcination to in- cipient fusion of an intimate mixture of properly proportioned argillaceous and calcareous materials. It has a definite chemical composition varying within comparatively nar- row limits." This definition is supported by the American Association of Portland Cement Manufacturers, so that we may consider Portland cement to be nominally a definite, uniform product. Barrels and Sacks. Cement is sent from the mills in barrels or sacks. For long shipments or when there is risk of dampness, barrels are used, but the general mode of 1 .REINFORCED' CONCRETE. transportation is in sacks. Portland cement barrels of dif- ferent manufacturers vary in weight and capacity. If tightly packed, a barrel of Portland cement may contain only 3.5 cu. ft. and if very loosely measured the volume may be 4.2 cu. ft. or more. The generally accepted standard is that a barrel of Portland cement shall weigh 380 Ibs. net, the barrel weigh- ing 20 Ibs. more, and that' it shall contain 4 cu. ft. of cement measured loose. Four bags of cement are always assumed to be equivalent to a barrel; a sack of cement is then gen- erally assumed to weigh 95 Ibs., and to contain 1 cu. ft. of cement measured loose. Cement sacks are made of either cloth or paper, cloth being preferred, as paper bags are easily torn in handling, causing waste of cement. Cloth bags may be returned, and will be re-purchased by the manufacturer; paper bags cannot be returned. Storage. Cement should be stored in a dry place. It is insufficient that it be stored out of the rain; storage in a damp basement will soon ruin cement by caking it, and it should not be stored upon the ground in wet weather. Cement should be rejected which has been wet, and caked into hard lumps. On large works, enough cement should be stored to last a month, in order that tests may be made, un- less tests are made in the warehouse of the manufacturer. Cement several weeks old is better seasoned than that which is fresh from the mill. Well seasoned cement may be lumpy but the lumps are easily broken with the fingers, in which case the cement is entirely satisfactory. Standard Specifications. The recommendations of the committee on standard specifications for cement, of the American Society for Testing Materials, have been adopted by so many societies and companies that they may be re- garded as practically the standard throughout the country. These requirements for Portland cement are set forth in the recommendations on the opposite page. Necessity for Tests on the Work. The manufacture of Portland cement has reached such uniformity that fairly MATERIALS AND MACHINES. 3 identical results may be attained by using any one of a number of well known brands, so that the choice of any particular brand is ruled largely by other considerations than its own intrinsic qualities. Though cement direct from the mill is uniform and reliable, it may not remain so, and tests on the work are therefore necessary to determine its genuineness, and whether it is reasonably sound, the sound- ness of a cement being a quality that can be readily affected by improper storage, etc. The fact that cement is satisfactory when tested is no indication that it will continue to be, hence cement which is not used for some time after test, should be tested again, if there is any possibility that damp weather or other factors have affected its soundness. AMERICAN SOCIETY FOR TESTING MATERIALS' REQUIRE- MENTS FOR CEMENT. SPECIFIC GRAVITY. Dried at 100 C ..not less than 3.1 FINENESS. Passing No. 100 sieve not less than 92% by weight Passing No. 200 sieve not less than 75% by weight TIME OF SETTING. Initial set in not less than 30 minutes Hard set In not less than 1 hour nor more than 10 hours TENSILE STRENGTH, NEAT. Age. Strength. 24 hours in moist air 175 Ibs. per sq. in. 7 days (1 day in moist air, 6 days in water) . . .500 Ibs. per sq. in. 28 days (1 day in moist air, 27 days in water). .600 Ibs. per sq. in. TENSILE STRENGTH, ONE PART CEMENT, THREE PARTS SAND. 7 days (1 day in moist air, 6 days in water) 200 Ibs. 28 days (1 day in moist air, 27 days in water) 275 Ibs. CONSTANCY OF VOLUME. Pats, neat, about 3 inches in diameter, one-half inch thick at the center, tapering to a thin edge, kept in moist air for 24 hours. (a) A pat is then kept in air at normal temperature and ob- served at intervals for at least 28 days. (b) Another pat is kept in water maintained as near 70 F. as practicable, and observed at intervals for at least 28 days. (c) A third pat is exposed in any convenient way in an atmos- phere of steam, above boiling water, in a loosely closed vessel for five hours. These pats .shall remain firm and hard and show no signs of distortion, checking, cracking or disintegrating. SULPHURIC ACID AND MAGNESIA. Anhydrous Sulphuric Acid (SO 3 ) not over 1.75 per cent Magnesia (MgO) not over 4 per cent I REINFORCED CONCRETE. Sampling Cement for Testing. The best sampler to use is one similar to a sugar-sampler, which takes a small cylinder of the material from the surface to the center of the bag. Small samples should be taken from a great number of bags and mixed. This gives a better average indication of the cement. On large works it is customary to sample every tenth bag. The cement so taken for testing purposes should be kept away from the air and dampness till made into paste, as otherwise it may not be in the same condition as the cement in the bags. Other Tests. Setting and hardening qualities should be noted by estimating the time required before a pressure of the thumb-nail is resisted by a cement pat. This point is where initial set ends and final set begins. Such tests should agree with the standard tests above. The color and weight of dry Portland cement are no indication of quality. Mr. W. Purves Taylor, in "Practical Cement Testing," states that cement balls made for tests should be soft, pliable, and damp on the surface, and should not feel warm at the end of 20 minutes. Cement failing in this is quick-setting. Such cement often becomes slow-setting on being stored a month or two. Good cement should have a uniform color when drying. Yellowish spots indicate poor cement. The color of cement hardening in air is a better indication than when hard- ening under water. The quantity of cement paste obtained by using different percentages of water is the same, per given weight of cement, provided the compacting is the same. Neat cement tests afford more information as regards the properties of the cement itself, than as regards how it will behave in the work; to get practical information regarding this, mortar and concrete tests are necessary as the testing of the aggregates to be used is of more practical value. AGGREGATES. The aggregates used with cement in the formation of concrete are generally sand or stone screenings and gravel or crushed stone. MATERIALS AND MACHINES. 5 Choice of Aggregates. In general it may be said that concrete aggregates should be chosen which will undergo no future alterations, either disintegration due to chemical changes, or breaking of particles under the rammer, due to the presence of cracks or bruises received at the crusher. Other things being equal, rounded aggregates give greater density and a lower percentage of voids, since the compact- ness increases as the particles become more rounded. In all cases a well graded aggregate gives the best results; this means, not a mixture of two sizes of aggregate only, but a uniform gradation from the finest material up to the coarsest to be used. This will be further discussed under Concrete. An excess of medium sized particles of the aggre- gate decreases the density and also the strength of mortar or concrete. The shape of the particles of aggregate has little effect on mortar, except as to density, but concrete is affected by the shape of the particles, especially of coarse aggregate. Determination of Voids in Aggregates. While not suit- able for laboratory practice, the following method of meas- uring voids in the field has been found adequate:- Fill a vessel of known capacity with the material, then pour in all the water it will contain; measure the volume of the water and divide by the volume of the vessel. The quotient expresses the percentage of voids. Some experi- menters start with the material wet; others begin with it dry. The dry method allows a little larger factor of safety. Table of Voids. Table I gives the specific gravity, weight solid, and weight loose, of aggregates varying from a specific gravity of 1.0 to 3.5. To use the table, suppose an aggre- gate, for instance, limestone of specific gravity 2.6, con- tains 52 per cent of voids, its weight per cubic yard is seen to be 2,101 Ibs. Or suppose an aggregate weighing 162 Ibs. REINFORCED CONCRETE. per cubic foot solid is found to weigh 2,625 Ibs. per cubic yard when crushed, the voids are seen to be 40 per cent. TABLE I. PERCENTAGES OF VOIDS. Specific Solid Weight Loose weight in Ibs. per cubic yard when voids are: Gravity In Ibs. per cubic foot In Ibs. pel- cubic yard 30% 32% 34% 36% 38% 40% 1.0 62.35 1684 1179 1145 1111 1077 1044 1010 2.0 124.7 3367 2357 2289 2222 2155 2088 2 020 2.1 130.9 3536 2475 2404 2333 2263 2192 212] 2.2 137.2 3704 2593 2519 2445 2370 2296 2222 2.25 140.3 3788 2652 2576 2500 2424 2349 2273 2.3 143.4 3872 2711 2633 2556 2478 2401 2323 2.35 146.5 3956 2769 2690 2611 2532 2453 2374 2.4 149.7 4041 2828 2748 2667 25SH6 2505 2424 2.45 152.8 4125 288V 2805 2722 2640 2557 2475 2.5 155.9 4209 2946 2862 2778 2694 2610 2525 2.55 159.0 4293 3005 2919 2833 2748 2662 2576 2.6 162.1 4377 3064 2977 2889 2801 2714 2626 2.65 165.2 4462 3123 3034 2945 2855 2766 2677 2.7 168.4 4546 3182 3091 3000 2909 2818 2727 2.75 171.5 4630 3241 3148 3056 2963 2871 2778 2.8 174.6 4714 3300 3206 3111 3017 2933 2828 2.85 177.7 4798 3359 3263 3167 3071 2975 2879 2.9 180.9 4882 3418 3320 3222 3125 3027 2929 2.95 183.9 4967 3477 3377 3278 3179 3079 2980 3.0 187.1 5051 3536 3434 3333 3232 3131 3030 8.1 193.3 ' 6219 3653 3549 3445 3340 3236 3131 3.2 199.5 5387 3771 3663 3556 3448 3340 3232 3.3 205.8 5556 3889 3778 3667 3556 3445 3333 3.4 212.0 5724 4007 3892 3778 3663 3549 3435 3.5 218.3 5893 4125 4007 3889 3771 3653 3536 Sand. In order to distinguish between sand and gravel, an arbitrary line must be drawn between the two. In this work sand, except when referring to standard sand, will refer to all particles of gravel passing a No. 5 sieve (having open- ings 0.16 in. wide). This is sand about 1/6 in. in diameter and under, and is practically identical with the French limit suggested by Mr. Feret. Selection of Sand. The proper selection of sand as one of the aggregates for concrete is largely a matter of judg- MATERIALS AND MACHINES. ment, as often, sands differing very materially in phys- ical characteristics will make equally good concrete. Coarse TABLE I. (Continued.) PERCENTAGES OF VOIDS. Loose weight in Ibs. per cubic yard when voids are: Specific Gravity 42% 44% 46% 48% 50% 52% 54% 56% 976 943 909 875 842 808 774 741 1.0 1953 1886 1818 1751 1684 1616 1549 1482 2.0 2051 1980 1909 1838 1768 1097 1626 1556 2.1 2148 2074 2000 1926 1852 1778 1704 1630 2.2 2197 2121 2046 1970 1894 1818 1742 1667 2.25 2246 2 1 08 2091 2014 1936 1859 1781 1704 2.3 2295 2216 2136 2057 1978 1899 1820 1741 2.35 2344 2203 2182 2101 2021 1939 1859 1778 2.4 2392 2310 2227 2145 2063 1980 1897 1815 2.45 2441 2357 2273 2189 2105 2020 1936 1852, 2.5 2490 2404 2318 2232 2147 2061 1975 1889 2.55 2539 ' 2451 2364 2276 2189 2101 2014 1926 2.6 2588 2498 2409 2320 2231 2142 2052 1963 2.C5 2636 2546 2455 2364 2273 2182 2091 2000 2.7 2685 2593 2500 2408 2315 2222 2030 2037 2.75 2734 2G40 2546 2451 2357 2263 2168 2074 2.8 2783 2687 2591 2495 2399 2303 2207 2111 2.85 2832 2734 2636 2539 2441 2344 2246 2148 2.9 2881 2781 2682 2583 2483 2384 2285 2185 2.95 2929 2828 2727 2626 2525 2424 2323 2222 3.0 3027 2923 2818 2714 2609 2505 2401 2296 3.1 3125 3017 2909 2801 2694 2586 2478 2371 3.2 3222 3111 3000 2889 2778 2667 2556 2445 3.3 3320 3206 3091 2977 2862 2748 2633 2519 3.4 3418 3300 3182 3064 2946 2828 2710 2593 3.5 sand is generally better than fine sand; a coarse grain will have a smaller surface area than a number of fine grains of equivalent volume, so that coarse sand will be better coated than fine, with the same quantity of cement. For general work, a mixed sand is better than either, because of a better gradation of particles and a consequent lower percentage of voids. Sand for Mortar. Coarse sand is better for rich mortars, and fine sand is better for lean mortars. Fine sand makes a mortar of lower density; to remedy this a richer mixture 8 REINFORCED CONCRETE. must be used. Mr. Feret's rule is that the coarse graina should be double the fine grains, including the cement. Fine sand may produce a mortar only one-third as strong as spe- cially graded sand mixed with cement in the same propor- tions. Sand for Concrete. Sand for concrete requires more fine material than mortar sand, and tests indicate that the best percentages passing a No. 40 sieve may range from about 18 per cent for a 1-2-4 concrete up to 27 per cent for a 1-4-8 concrete. For water-tight concrete, even a larger percent- age of fine grains appears to be beneficial.* Table of Sand. Table II from Gillette's "Handbook of Cost Data" gives the voids in sand from various localities. Cleanness of Sand. The phrase, "clean, sharp sand," for so many years a stereotyped form in specifications, is now obsolete. Sharpness of sand is of little value except when it indicates the presence of silica. Cleanness of sand is also disregarded by many engineers, who permit the presence of loam or clay; the quantity allowed is from 2 to 10 per cent, some authorities allowing even 15 per cent.f The author would prefer that all specifications should state that not over 5 per cent of loam or clay should be permitted in mortar or concrete for reinforced concrete work, as these impurities have a tendency to fill the small voids, preventing the cement from flowing in, and thereby reducing the adhesion between the cement and the aggregates, or the cement and the rein- forcement. The permission to use sand with a small per- centage of impurities is apt to be taken advantage of in a dangerous manner, for, except where silica is present, loam consists largely of vegetable mold, which should be guarded against. Washing of Sand. When sand containing loam or clay must be used, the impurities should be washed out. This Sand for Mortar and Concrete, Sanford E. Thompson, Bulletin No. 3, American Assoc. Portland Cement Mfrs., Philadelphia. fFor tests with sand containing loam and clay see Report, Chief of Engineers, U. S. A., 1896, p. 2826 et seq., and 1905, p. 3001; also C. J. Griesenauer, Engineering News, April, 1904; also Chas. E. Mills, Proc. Engineers' Club of Philadelphia, Pa., April, 1904. MATERIALS AND MACHINES. < TABLE II. VOIDS IN SAND. Locality. Authority. Voids. Remarks. Ohio River W. H. Hall 31% Washed Sandusky, O C. E. Sherman 40% Lake Franklin Co., O C. E. Sherman.. . . 40% Bank Sandusky Bay, O S. B. Newberry. . . 32.3% St. Louis, Mo H. H. Henby 34 . 3% Miss. Rivei Sault Ste. Marie H. von Schon 41 . 7% River Chicago, 111 H. P. Boardman. . 34 to 40% Philadelphia, Pa 39% Del. River Mass. Coast 31 to 34% Boston, Mass .... Geo. A. Kimball. . 33% Clean Cow Bay, L. I Myron S. Falk.. . . 40*% Little Falls, N, t. . W. B. Fuller 45 . 6% Canton, 111 G. W. Chandler. . . 30% Clean can be done by pouring the sand into the upper end of an in- clined tank filled with water and having a small gate at the lower end, which permits the escape of the clean sand, the overflow of the water carrying away the dirt. Sand can also be washed in a concrete mixer. Voids in Sand. The more rounded the grains of a mixed granular material, the lower the percentage of voids. Nat- ural sand, therefore, with rounded grains, gives the lowest percentage of voids of any material used as an aggregate. Ground quartz (with angular grains) comes next, then crushed shells (with flat grains) and finally crushed quartzite (with laminated grains).* In all aggregates except sand the moistening of the material decreases the percentage of voids. This is because the addition of water destroys in part, the arching or frictional effect, permitting the finer material to enter the voids of the larger material. With sand, however, dampness holds the particles apart and increases the per- centage of voids, the maximum occurring when the per- centage of water varies from 5 to 8 per cent. The addition of more water, however, decreases the voids again, to practically the same as contained in dry sand. The following tests by Mr. Wm. B. Fullerf bear out the above statement, whether the sand be tested loose or compact: *Mr. Feret. tReid, "Concrete and Reinforced Concrete Construction." 10 REINFORCED CONCRETE. Percentage of voids. Loose. Compact. Dry 34 6 per cent water 44 Saturated 33 26.5 Weight of Sand. From dealers' catalogs, bank sand is given as weighing 2,500 Ibs. per cu. yd., and Torpedo sand, 3,000 Ibs. per cu. yd. Standard Sand. As recommended by the American So- ciety for Testing Materials, standard sand is the natural sand from Ottawa, 111., screened to pass a sieve having 20 meshes per linear inch and retained on a sieve having 30 meshes per linear inch; the wires to have diameters of 0.0165 and 0.112 in., respectively, i. e., half the width of the opening in each case. Sand having passed the No. 20 sieve shall be consid- ered standard when not more than 1 per cent passes a No. 30 sieve after one minute continuous sifting of a 500 gram sample. Screenings. Screenings are often used as a fine aggregate in place of sand. In using screenings, the aggregates should be carefully mixed dry, as otherwise the fine material will collect in lumps and impair the uniformity of the concrete. Under similar conditions, sand produces a denser concrete than screenings.* Gravel. Many engineers have a decided preference for gravel over crushed stone as an aggregate. Gravel is thought by many to be superior to crushed stone in that the well rounded pebbles, worn down as found in nature are the survival of the best parts of the stone, the weaker por- tions having been worn away, also that round fragments offer less surface to be coated, thus insuring better union with the mortar and giving under similar conditions, a denser concrete than broken stone. The exponents of crushed stone, however, maintain that the rough surfaces and the angularity of broken fragments insure better bonding of the concrete. Practice in all lines of work has demon- strated that equally good concrete can be made with either. *Fuller and Thompson, Trans. Am. Soc. C. E, 1907. MATERIALS AND MACHINES. 11 In using gravel, that containing mud or gravel cemented in- to lumps with mud, should be avoided. Choice of Crushed Stone. The best stone for crushing purposes is that which is hard and tough, breaking into angular fragments, with rather rough surfaces. Stone which breaks more easily in some directions than others, or exhibits cleavage, is hard to tamp compactly. Mica schist is of this class, and should be avoided for reinforced con- crete, though it is allowable for massive construction. All things considered, trap rock makes the best aggregate, as it is tough, hard, bonds well, and furnishes a concrete of great strength. Crushed granite is also very good, unless the fragments are bruised in the crushing. Limestone is by far the most used, though when subjected to great heat, limestone will calcine and crumble. Some sandstones are used with excellent results, though, as a rule, sandstones are not considered strong enough. Stone which yields a great deal of fine material in crushing should be avoided as such stone is not strong. Size of Crushed Stone. The size to which an aggregate should be reduced by crushing depends upon the class of structure in which the stone is to be used. Since the largest stone makes the densest, and also the strongest concrete, the largest stone should be used that is consistent with proper placing, taking into account the dimensions of the mold, and the size and disposition of the reinforcing rods or wires. In using large stone, care must be taken to prevent it from separating from the concrete, and to prevent it from moving the reinforcement out of place. Stone for reinforced concrete varies from l / 2 in. to V/ 2 ins., that passing a ^-in. ring or mesh being most common. The following tests show that the size of the stone influ- ences the density:* *Fuller and Thompson, Trans. Am. Soc. C. E., 1907. 12 REINFORCED CONCRETE. Stone. Density. Ratio. 2% ins. .847 1.00 1 in. .814 .96 V 2 in. .788 .93 Crusher Run. When limestone is selected, the run of the crusher is often used for the entire aggregate. Unless care is exercised, however, the true run of the crusher will not be obtained, for, if the crushed stone is poured into a heap, a separation of the different sizes is sure to occur, in a greater or a less degree. To prevent this, the crushed stone should fall directly into the gage-box from the crusher. Even when the true run of the crusher is obtained, it is evi- dent that the product may not be uniform. Slight variations in the hardness or texture of the stone may produce great variations in the size of the crushed material, the percentage of fine particles, etc. A more accurate method is to screen out the fine material and then mix in the required propor- tions. Rock Crushers. A great number of rock crushers are on the market. In general, it may be said that the same crusher will crush different aggregates to different percentages of voids, and that the capacity of the machine varies with many conditions. It is well known that the efficiency of a crusher is higher on a short time test than on a long time test, and while a crusher may be used up to its rated capacity for an hour or for a day, the average efficiency for a month will be found much less than this, usually about SO per cent of the rated capacity. On one well-known work, a machine that puts out 175 cu. yds. per day of 10 hours, averaged 65 cu. yds. per day, when the monthly output was taken as a basis for calculation, this variation being due, not to the machine, but to the feeding and operating, which are difficult to maintain uniformly on long time tests. Table of Rock Crushers. The favorite crusher for use in concrete work is the gyratory crusher. Table III gives di- mensions and other data regarding a well known make. MATERIALS AND MACHINES. 13 TABLE III. GATES ROCK CRUSHERS, STYLE K. Allis-Chalmers Co., Milwaukee. Dimen- sions of Each Re- ceiving Opening, About Weight of Breaker. Capacity per hour, According to Character of Rock, in Tons of 2,0001bs., to Pass Through a Ring of Small- est size Prod- uct Driving Pulley. IN ii o& W 14 to 21 22 to 80 28 to 45 50 to 75 Dimen- sions in inches. Rev. per Min. Inches Lbs. H H 2 2i 3 3} 4 120 Inches Sx 30 10 x 38 12x44 14x52 20900 31200 45500 64800 15 20 30 25 40 50 30 50 70 80 40 60 80 90 70 90 100 H if 2 2} 32x12 36 x 14 40 x 16 44 x 18 400 375 350 350 Voids in Graded Mixtures. It is well known that differ- ent aggregates, screened so that the same proportions are retained on the same screens, will contain different percent- ages of voids. This is due to the fact that different kinds of rock crush into fragments of different degrees of regu- larity some breaking cubically, others in sharp, angular frag- ments, etc. It is to be noted that, other things being equal, gravel contains a smaller percentage of voids, and weighs more per unit volume than crushed stone, which is equiva- lent to saying that the compactness increases as the particles become more rounded. Voids in Loose Broken Stone. For practical work, Table IV, from Gillette's "Handbook of Cost Data," gives percent- ages of voids for various kinds of stone from a number of localities. Cinders. Cinders are used for concrete in fireproonng work, such as floors. Such concrete is porous, and therefore a poor conductor of heat or sound, and is much lighter than stone concrete, as it weighs about 112 to 120 Ibs. per cu. ft., while stone concrete weighs about 150 Ibs. per cu. ft. Cinders for fireproofing work should be chosen carefully, as the presence of unburned coal will render such concrete the 14 REINFORCED CONCRETE. TABLE IV. VOIDS IN LOOSE BROKEN STONE. Authority. Voids. % Remarks. Sabin 49.0 44.0 Limestone, crusher run after screening out i-in. and under. Limestone ( 1 part screenings mixed with 6 Wm. M. Black J. J. R. Croes S. B. Newberry 46.5 47.5 47.0 parts broken stone). Screened and washed, 2 ins. and under. Gneiss, after screening out -in. and under. Chiefly about egg size. H. P. Boardman Wm. H. Hall... '.'.'.'.'.'. Wm. H. Hall Wm. B. Fuller.. . Geo. A. Kimball Myron -S. Falk W H Henby 39 to 42 48 to 52 48.0 50.0 47.6 49.5 48.0 43 Chicago limestone, crusher run. screened into sizes. Green River limestone, 2| ins. and smaller, dust screened out. Hudson River trap, 2 ins. and smaller, dust screened out. New Jersey trap, crusher run, J to 2.1 in. Roxbury conglomerate, \ to 2% ins. Limestone, ^ to 3 ins. 2 -in. size. Feret 46.0 53.4 51.7 52.1 " 1^-in. size. Stone, 1 .6 to 2.4 ins. . 8 to 1 . 6 in. " 0.4 to 0.8 in. A.W.Dow Taylor and ( Thompson G W Chandler 45.3 45.3 54.5 54.5 45.0 51.2 40 Bluestone, 89% being 1 to 2J ins. 90% being J to H in. Trap, hard, 1 to 2i ins. " i to 1 in. to 2J ins. " soft, | to 2 ins. Canton 111 Emile Low C M Saville . 39.0 46 Buffalo limestone, crusher run, dust in. Crushed cobblestone, screened into sizes. least fireproof, whereas it is supposed to be the most fire- proof. Good boiler furnace cinders make the best cinder concrete. Cinders should be well wet before being used in concrete, and should not be heavily rammed, as the cinders will crush. Being porous and light in weight, cinders are not as strong as gravel or stone, and should not be used where strength is required, nor should cinder concrete be subjected to load before one month old. When slag is to be used as an aggregate it should be allowed at least a year for aeration to get rid of the sulphur, which would disintegrate the concrete. Many failures have occurred from using slag not sufficiently aerated, as other- wise it is a satisfactory aggregate.* "Thomas Potter, Builders' Journal, London, Dec. 5, 1906. MATERIALS AND MACHINES. 15 MORTAR, Mortar is a mixture of cement, sand or screenings, and water. In European practice, mortar is often used in rein- forced concrete construction. American practice limits the use of mortar to facing, finishing, etc., except in certain constructions, such as chimneys and water-tight receptacles. Strength of Mortar. The strength of mortar depends upon its density and the percentage of cement it contains. Evidently a change of density must be accomplished by the sand, since there is practically no variation in different ce- ments. -It has been found that sands with rounded grains contain the lowest percentage of voids, and therefore produce mortars of the least volume, which are the densest and strongest mortars. Apparent exceptions, where greater strength is obtained by using broken stone screenings, may be caused by the fine particles of the screenings uniting chem- ically with the cement. Coarse sand gives higher strength than fine sand. Mica, when laminated, may be injurious, having more effect upon the compressive than upon the ten-* sile strength of mortar. Mica to 2 per cent is unimportant. Volume of Mortar, with Varying Proportions of Sand. Table V is compiled from experiments made by Mr. Edwin Thacher. All materials were measured loose, and gently shaken down. One barrel of cement contained 4.12 cu. ft. loose, thus requiring 6.56 barrels per cu. yd. One volume of Portland cement yielded 0.78 volumes of stiff cement paste on the addition of 0.35 volumes of water. The sand used was moist, ordinary coarse and fine mixed, containing 38 per cent of voids. TABLE V. VOLUME OP MORTAR. Parts of sand mixed with 1 part of cement 1.0 1.5 2.0 2.5 3.0 3.5 4.0 5.0 Volume of slush mortar.. 1.40 1.78 2.17 2.55 2.98 3.39 3.82 4.65 Required for 1 cu. yd. Cement, bbls 4.70 3.70 3.04 2.58 2.21 1.94 1.72 141 Sand, cu. yds 0.71 0.84 0.92 0.98 1.01 1.03 1.05 1.08 Volume of dry facing mortar (rammed) 1.22 1.57 1.93 2.28 2.64 2.99 3.35 4.08 Required for 1 cu. yd. Cement, bbls 5.40 4.18 3.41 2.88 2.49 2.20 1.96 1.61 Sand, cu. yds 0.82 0.95 1.04 1.10 1.14 1.17 1.20 1.23 16 REINFORCED CONCRETE. Weight of Mortar. From experiments by Mr. Feret, it is found that 1-3 mortars with sand of fine, medium and coarse grains respectively, weigh approximately the same, 122 Ibs. per cu. ft. If the three sands be mixed in the best propor- tions, the weight of the mortar reaches 141 Ibs. per cu. ft., as shown in Table VI. Mortar Tests. Mortar tests on the work are receiving more attention than formerly, since it is found that tests in- volving the aggregates are of more value than tests of the cement alone. Cement is generally uniform when its sound- ness has been established, and steel for reinforcement is also uniform and reliable, but concrete aggregates vary consider- ably in different parts of the country, so that statements made regarding a sand in one locality may not apply to that of another. Tests of cement were formerly the only tests made. Mortar and concrete -tests are now assuming import- ance, and in all municipal work the tendency is to secure a maximum density of the aggregates by actual tests on the building premises, whereby a maximum economy may be reached simultaneously with maximum strength. Retempered Mortar. Generally speaking, mortar should not be used after it has attained a certain set, but there are instances where such mortar after being thoroughly re- worked, preferably without adding any water, can be used to great advantage as a binder between old and new work for instance, in repairing concrete sidewalks where the finish has scaled off, or for finishing rough surfaces. TABLE VI. WEIGHT OP MORTAR. 1-3 Mortar by Weight Wt. in Ibs. per cu. ft. Density Voids Ratio compressive strength after one year In fresh water In air Coarse Sand 122 .665 .335 .68 .60 Medium Sand 123 .640 .360 .45 .50 Fine Sand 123 .575 .425 .34 .34 Mixed in best pro- portions 141 . .734 .266 1.00 1.00 MATERIALS AND MACHINES. 17 CONCRETE. Concrete is an artificial stone composed of cement with suitable aggregates, which may be sand and gravel, sand and crushed stone, screenings and crushed stone, or any other combination of these materials, before described. Proportioning Concrete. Many of the usual methods of proportioning concrete are unsatisfactory, owing to the fact that the laws governing the mixing and setting of concrete are net definitely understood. A number of formulas and rules have been devised to regulate the quantity of cement and aggregates to use per cubic yard of concrete. The usual field practice in America is to take cement and aggregates by volume; in France, the cement is measured by weight, the aggregates by volume; in Germany both are measured by weight. In American testing laboratories, the practice is to measure cement and aggregates by weight. Usual Methods of Proportioning Concrete. Hitherto, 'the practice has been to mix concrete by taking 1 part cement with certain parts of sand and crushed stone or gravel. This practice is gradually changing, however, in view of the fact that the best concrete is that in which the aggregate is uniformly graded from coarse to fine. Another point in favor of abandoning the former method is that the 1-2-3 mixture of one contractor may be identical with the 1-3-5 mixture of another, owing to differences in the sizes of sand and stone. In view of this, it is preferable to abandon speci- fying mixtures as 1-2-3, 1-2-4, 1-3-5, but as 1-5, 1-6, 1-8, re- spectively, in which case the 5, the 6 or the 8 parts of aggre- gate are mixed up, reducing the voids to whatever figure is necessary for maximum density, and then the cement added. Both methods of proportioning will be considered, since both methods are in use at the present time. The best rules gov- erning former practice are given below. Fuller's Rule. An approximate rule for ready calculation is the one originated by Mr. Wm. B. Fuller, and is as fol- lows: Divide 11 by the sum of the parts (by volume) of all the ingredients; the quotient is the number of barrels of 18 REINFORCED CONCRETE. Portland cement required per cubic yard of concrete. Mul- tiplying this by the number of parts of sand and of stone will give the number of barrels of each. To reduce barrels to cubic yards, multiply by 0.14 (since a barrel contains 3.8 cu. ft. and there are 27 cu. ft. in a cubic yard). For example, suppose we wish to mix a concrete in the proportion 1-3-6. Then 11' H- 10 =1.1 barrels of cement required per cubic yard of concrete. 3 X 1-1 X 0.14 = 0.462 cu. yds. of sand required per cubic yard of concrete. 6 X 1-1 X 0.14 = 0.924 cu. yds. of crushed stone required per cubic yard of concrete. Fuller's rule gives slightly more cement per cubic yard than is given in Table VII. Thacher's Table. Table VII is compiled from experi- ments conducted by Mr. Edwin Thacher. In these experi- ments, the volumes of all materials were measured loose, but gently shaken down. A barrel of cement was taken at 4.1 cu. ft. Proportioning Concrete for Maximum Strength. It is well known that with any given sand and stone, with a fixed quantity of cement, the mixture that gives the least volume will furnish a cement of maximum strength. Such a mixture MATERIALS AND MACHINES. 19 TABLE VII. PROPORTIONS OF MATERIALS FOR CONCRETE. Mir.tures. Required for one cubic yard rammed concrete. Stone, 1 in. and und., dust screened out. (46% voids.) Stone, 2 in and und., dust screened out. (41% voids.) Stone, 2 2 in. with most small stone scr'n'd out (45% voids.) Gravel, f in. and under. rrt ** 1 1.0 2.C 1 .026 1 .0 3.0 1 .0 3.6 !i u! ft M W g^ .> a, >> g2 *g 3 g 3 |l iM ^ 4 -o 2.30 0.35 0.74 2.10 0.32 0.80 .89 0.29 0.86 .71 0.26 0.91 CJ CO 02 2.57 0.39 0.78 2.29 0.35 0.70 2.06 0.31 0.94 1.84 0.28 0.98 O 02 CO 2.63 0.40 0.80 2 34 0.36 0.89 2.10 0.32 0.96 1.88 0.29 1.00 O CO 02 2.72 0.41 0.83 2.41 0.37 0.92 2.16 0.33 0.98 1.88 0.29 1.05 1 .5 2.5 1 .5 3.0 1 .5 3.5 1 .5 4.0 1 .5 4.5 2.05 0.47 0.78 1.85 0.42 0.84 1.72 0.39 0.91 1.57 0.36 0.96 1.43 0.33 0.98 2.09 0.48 0.80 1.90 0.43 0.87 1.74 0.40 0.93 1.61 0.37 0.98 1.46 0.33 1.00 2.16 0.49 0.82 1.96 0.45 0.89 1.79 0.41 0.96 1.64 0.38 1.00 0.51 0.35 1.06 .83 0.42 0.73 .71 0.39 0.78 .57 0.36 0.83 .46 0.33 0,88 1.34 0.31 0.91 1 2.0 3.0 1 2.0 3.5 1 2.0 4.0 1 2.0 4.5 1 2.0 5.0 1.70 0.52 0.77 1.57 0.48 0.83 1.46 0.44 0.89 1.36 0.42 0.93 1.27 0.39 0.97 1.73 0.53 0.79 1.61 0.49 0.85 1.48 0.45 0.90 1.38 0.42 0.95 1.29 0.39 0.98 1.78 0.54 0.81 1.66 0.50 0.88 1.53 0.47 0.93 1.43 0.43 0.98 1.33 0.39 1.03 1.54 0.47 0.73 1.44 0.44 0.77 1.34 0.41 0.81 1.26 0.38 0.86 1.17 0.36 0.89 1 2.5 3.5 1 2.5 4.0 1 2.5 4.5 1 2.5 5.0 1 2.5 5.5 1 2.5 6.0 1.45 0.55 0.77 1.35 0.52 0.82 1.27 0.48 0.87 1.19 0.46 0.91 1.13 0.43 0.94 1.07 0.41 0.97 1.48 0.56 0.79 1.38 0.53 0.84 1.29 0.49 0.88 1.21 0.46 0.92 1.15 0.44 0.96 1.07 0.41 0.98 1.51 0.58 0.81 1.42 0.54 0.87 1.33 0.51 0.91 1.26 0.48 0.96 1.18 0.44 0.99 1.10 0.41 1.03 1.32 0.50 0.70 1.24 0.47 0.75 1.16 0.44 0.80 1.10 0.42 0.83 1.03 0.39 0.86 0.98 0.37 0.89 1 3.0 4.0 1 3.0 4.5 1 3.0 5.0 1 3.0 5.5 1 3.0 6.0 -1 3.0 6.5 1 3.0 7.0 1.26 0.58 0.77 1.18 0.54 0.81 1.11 0.51 0.85 1.06 0.48 0.89 1.01 0.46 0.92 0.96 44 0.95 0.91 0.42 0.97 1.28 0.58 0.78 1.20 0.55 0.82 1.14 0.52 0.87 1.07 0.49 0.90 1.02 0.47 0.93 0.98 0.44 0.98 0.92 0.42 0.98 1.32 0.60 0.80 1.24 0.57 0.85 1.17 0.54 0.89 1.11 0.51 0.93 1.06 0.48 0.97 1.00 0.45 1.01 0.94 0.42 1.05 1.15 0.52 0.72 1.09 0.50 0.75 1.03 0.47 0.78 0.97 0.44 0.81 0.92 0.42 0.84 0.88 0.40 0.87 0.84 0.38 0.89 1 3.5 5.0 1 3.5 5.5 1 3.5 6.0 1 3.5 6.5 1 3.5 7.0 1 3.5 7.5 1 3.5 8.0 1.05 0.56 0.80 1.00 0.53 0.84 0.95 0.50 0.87 0.92 0.49 0.91 0.87 0.47 0.93 0.84 0.45 0.96 0.80 0.42 0.97 1.07 0.57 0.82 1.02 0.54 0.85 0.97 0.51 0.89 O.S3 0.49 0.92 0.89 0.47 0.95 0.86 0.45 0.98 0.82 0.43 1.01 1.11 0.59 0.85 1.06 0.56 0.89 1.00 0.53 0.92 0.96 0.51 0.95 0.91 0.49 0.98 0.86 0.47 1.01 0.81 0.45 1.04 0.96 0.50 0.76 0.92 0.48 78 0.88 0.46 0.80 0.83 0.44 0.82 0.80 0.43 0.85 0.76 0.41 0.87 0.73 0.39 0.89 1 4.0 6.0 1 4.0 6.5 1 4.0 7.0 1 4.0 7.5 1 4.0 8.0 1 4.0 8.5 1 4.0 9.0 0.90 0.55 0.82 0.87 0.53 0.85 0.83 0.51 0.89 0.80 0.49 0.91 0.77 0.47 0.93 0.74 0.45 0.95 71 0.43 0.97 0.92 0.56 0.84 0.88 0.53 0.87 0.84 0.51 0.90 0.81 0.50 0.93 0.78 0.48 0.95 0.76 0.46 0.98 0.73 0.44 1.01 0.95 0.58 0.87 0.91 0.55 0.90 0.87 0.53 0.93 0.84 0.51 0.96 0.81 0.49 0.98 0.78 0.47 1.01 0.75 0.45 1.04 0.83 0.51 0.77 0.80 0.49 0.79 0.77 0.47 0.81 0.73 0.44 0.83 0.71 0.43 0.86 0.68 0.42 0.88 0.65 0.40 0.89 1 5.0 9.0 1 5.0 10.0 66 0.50 0.90 0.62 0.47 0.95 0.67 0.52 0.93 0.63 0.48 0.96 0.70 0.53 0.96 0.65 0.50 1.00 0.61 0.46 0.83 0.57 0.43 0.87 20 REINFORCED CONCRETE. is the densest obtainable under the given conditions, and is obtained when the volume of cement, sand and water just fills the voids in the stone. The density of concrete has been found to vary considerably by varying the proportions of the aggregates. Proportioning Concrete for Maximum Density. In this connection may be cited the field method devised by Mr. Wm. B. Fuller, which is to determine the maximum density by trial. His method is as follows: "Procure a piece of steel pipe 8 to 12 ins. in diameter and about a foot long and close off one end, also obtain an accurate weighing scale. Weigh out any proportions selected at random, of cement, sand and stone, and of such quantity as will fill the pipe about three-quarters full, and mix thoroughly with water on an im- pervious platform, such as a sheet of iron; then, standing the pipe on end, put all the concrete in the pipe, tamping it thoroughly, and when all is in measure and record the depth of the concrete in the pipe. Now throw this concrete away, clean the pipe and tools and make up another batch with the total weight of cement, sand and stone the same as before, but with the proportions of the sand to the stone slightly different. Mix and place as before and meas- ure and record the depth in the pipe, and if the depth in the pipe is less and the concrete still looks nice and works well, this is a better mixture than the first. Continue trying in this way until the proportion has been found which will give the least depth in the pipe. This simply shows that the same amount of material is being compacted into a smaller space and that consequently the concrete is more dense. Of course, exactly similar material must be used as is to be used en the work, and after having in this way decided on the proportions to be used on the work it is de- sirable to make such trials several times while the work is in progress, to be sure there is no great change in materials, or, if there is any change, to determine the corresponding change in the proportions. "The above described method of obtaining proportions does not take very much time, is not difficult, and a little trouble taken in this way will often be productive of very important results over the guess method of deciding proportions so universally prevalent. "A person interested in this method of proportioning will find on trial that other sands and stones available in the vicinity will give other depths in the pipe, and it is probable that by looking around and obtaining the best available materials the strength of the concrete obtainable will be very materially increased. "As a guide to obtaining the best concrete, the proportion of cement remaining the same, the following are the results of exten- sive tests: "The stone should all be of one size or should be evenly graded from fine to coarse, as an excessive amount of the fine or middle sizes is very harmful to strength. "All of the fine material smaller in diameter than one-tenth of the diameter of the largest stone should be screened out from the stone. "The diameter of the largest grains of sand should not exceed one-tenth of the diameter of the largest stone. MATERIALS AND MACHINES. 21 "The coarser the stone used the coarser the sand must be, and the stronger, more dense and watertight the properly proportioned work becomes. "When small stones only are used the sand must be fine and a larger proportion of cement must be used to obtain equal strength." A set of test beams has shown the following decrease in strength, due to decrease in density: Modulus of Rupture. Proportions. Lbs. Sq. In. 1:2:6 319 1:3:5 285 1:4:4 209 1:5:3 151 1:6:2 102 1:8:0 41 By inspecting the above figures it is seen that although the amount of cement in each of the above beams was the same (namely, 1-9 of the total material), some of the beams were over 700 per cent stronger than others.* Concrete in Different Classes of Work. By properly pro- portioning concrete, a great saving in materials can be effect- ed. Lean mixtures can be used in heavy construction where the concrete is stressed only in compression. Also the rich- ness of the mixture can be varied in different parts of the same structure, according to the nature of the stress, rein- forcement, etc. Mixing. The mixing of concrete is as important as the choice of the aggregates. In general, it may be said that mixing for a long time retards setting and increases strength and bond capacity. Thorough mixing is essential in order to produce a coherent and uniform concrete; the leaner and dryer the mixture the more mixing is required. Some con- structors mix the materials dry till a uniform color and ap- pearance are secured before the water is added. Others put in the material and the water at once. Either way will produce good results except for hand mixing, where the mixing of the materials in the dry state is the general practice. Mixtures, Wet or Dry. Dry mixtures are of advantage because the forms need not be as tight, but more mixing of the dry materials and more tamping are required. Wet mix- *William B. Fuller. 22 REINFORCED CONCRETE. tures require less tamping, but the forms must be tighter. With dry mixtures the forms may be removed sooner, and they are used where quick set and quick strength are re- quired. Mixtures too wet will separate and the cement will go to the bottom. Dry mixtures require more wetting sub- sequent to placing than wet mixtures, because, to set prop- erly requires a certain amount of water; if this is not all supplied in the mixing, it should be supplied afterward. Whether wet or dry mixtures are used depends chiefly upon the temperature and the class of work. Mixtures for Plain Concrete. For plain concrete, the author agrees with Mr. H. W. Parkhurst,* who summarizes as follows: A medium concrete or one that has not enough surplus water to produce quaking, while having enough to permit easy and thorough ramming, is the most desirable. To specify that the concrete should not quake in the barrow nor in handling, but when heavily rammed, would seem about right for regulating the amount of water. It is probably safer to have an excess of water than a deficiency. Above all, it is of the utmost importance that concrete shall be thoroughly consolidated by ramming. If too wet, ramming will tend to separate the ingredients, and if too dry, no reasonable amount of ramming will fill the voids with mortar. Mixtures for Reinforced Concrete. Wet mixtures for reinforced work are preferred in America, though no hard and fast rule can be laid down to gage the proportion of water. The quantity of water varies, first, with the temperature. During hot weather, a so-called wet mixture is used to best advantage, so as to allow for evaporation. In cold weather, although heated water and heated sand may be used, there are more chances for freezing with wet than with dry mixtures, therefore a dry mixture is preferable. The quantity of water varies also with the form and size of the mold. For molds of small dimensions, more water is required in order that the concrete may properly enter into all corners and surround the reinforcement. In molds of larger dimensions, the concrete can be more readily tamped. Journal of the Western Society of Engineers, Vol. VII, No. 3. MATERIALS AND MACHINES. 23 Other considerations influence the amount of water used: rich mixtures require more water than lean ones; fine sand requires more water than coarse; some crushed stone ab- sorbs more water than others and again, for water tanks, chimneys or manufactured articles, where a mixture of 1-4 Fig. 1. McKelvey Mixer. is used and the aggregate generally consists of a very coarse sand, usually a very dry, hard rammed mixture is used. A wet mix, in place of being tamped, is spaded or stirred by continuous working with a suitable tool. A dry mix is spaded only around the edges of the mold, but otherwise Fig. 2. Smith Mixer. tamped until a moisture appears on top of the concrete. European engineers are very successful with dry mixtures, but their success is due to the fact that the mixing and the placing are very carefully done. Their rule is to mix con- crete moist enough to flow between the reinforcing members 24 REINFORCED CONCRETE. and coat them with cement, but which will at the same time stand heavy ramming. The Proper Consistency for Concrete. This important factor is a matter of judgment and experience on the part of the engineer and contractor in charge and changes during a day's work according to local circumstances, dimensions of forms, shape of reinforcement, etc. The behavior of plastic concrete as it comes from the mixer, and especially while being tamped into place, will with a little practice enable one to judge if the amount of water is correct. Hand or Machine Mixing. Machine mixed concrete is superior in quality and generally less expensive than hand Fig. 3. Chicago Improved Cube Mixer. mixed. Mixing by hand is employed only when the quantity is small or when machinery is unobtainable. Batch or Continuous Mixers. For reinforced concrete, it has been conceded that batch mixing is preferable. In cases of very heavy construction, such as sea walls and break- waters, locks, dams, etc., continuous mixers are used to ad- vantage. Continuous mixing is cheaper and more rapid than batch mixing. Classification of Batch Mixers. The following classifica- tion of batch mixers is made by Mr. Clarence Coleman:* (1) Revolving drum or cylinder with horizontal axis, with deflectors, receiving and discharging without stopping, concrete visible. *Engineering News, Aug. 27, 1903. MATERIALS AND MACHINES. 25 (2) Revolving drum formed with two cones, with hori- zontal axis, deflectors, receiving and discharging without stopping, concrete visible. (3) Revolving circular pan or trough, vertical axis, frame with radial arms, receiving and discharging without stopping, concrete visible. (4) Horizontal revolving cylinder, mixes by revolving about axis, stops to receive and discharge, concrete invisible. (5) Horizontal trough, semi-cylindrical cross-section, longitudinal shaft carrying blades, which mix the material and feed it toward the discharge end, receiving and dis- charging without stopping, concrete visible. Fig. 4. Ransome Mixer. (6) Cubical box revolving about horizontal axis passing through two diagonally opposite corners, door at one side, stops to receive and discharge, concrete not visible. (7) Same as above, except with corners through which axis passes cut away, tilts to discharge, receives and dis- charges without stopping, concrete visible. Table of Batch Mixers. Table VIII gives comparative sizes and capacities, and Figs. 1 to 4 illustrate several well known batch mixers. As in the case of rock crushers, how- ever, the actual output which may be relied upon in long- time runs will average much lower than the rated capacity. 26 REINFORCED CONCRETE. TABLE VIII. BATCH MIXERS. McKelvey Concrete Machinery Co., Cleveland, O. Koehring Mixer Koehring Machine Co., M Wis. ilwaukee, Catalog No. Size of Batch in cu. ft. Capacity, yds. per hr. Catalog No. Size of Batch in cu. ft. Capacity, yds, per hr. ? 7 8 9 27 21 m 9 4* 3 25 18 12 7* 4 3* B 1 B 2 B 3 B 7 11 22 27 7 14 25 30 Chicago Cube Mixer. Municipal Engineering & Contracting Co., Chicago. Polygon Mixer. Waterloo Cement Machinery Waterloo, la. Co., "Handy" 6 11 17 22 33 64 6 11 17 22 33 64 5} 13 24 40 50 70 120 4 5 6 7 6 10 12 16 Per day of lOhrs. 60 100 130 180 Ransome Concrete Machinery Co., New York. Smith Mixer. The T. L. Smith Co., Chicago. 1 2 3 4 10 20 30 40 10 20 30 40 Catalog No. Mixed dry. Volume unmixed. Yds. 1 per hr. R. Z. Snell Manufacturing Co., South Bend, Ind. 1 2 \ l 5 6 9 m 16} 22 30 8| 13 20 24* 34i 46 9 20 30 39 46 62 1 2 3 3 7 11 24 I 1 8 20 Cropp Mixer. A-. J. Cropp, Chicago. Chicago Concrete Machinery Co., Chicago. 1 2 3 7 to 8 10 13 16 20 15 20 25 30 40 00 1 2 3J 6 9 18 5 8} 13 26 8 14 21 42 MATERIALS AND MACHINES. 27 Classification of Continuous Mixers. They are classified as follows by Mr. Clarence Coleman:* (1) Inclined chute fitted with pins, material slides down by gravity, concrete visible. (2) Series of funnels placed one above another, contain- ing baffles, concrete falls by gravity, invisible for most part. TABLE IX. CONTINUOUS MIXERS. Scheiffler Mixer. The Hartwick Machinery Co., Jackson, Mich. Drake Mixer. Drake Standard Machine Works, Chicago. Catalog No. Capacity per hour in cu. yds. Catalog No. Capacity per hour in cu. yds. 2 I* 12 to 15 1 2 3 4 4 Special P 40 20 15 7.5 10 2.5 Eureka Mixer. Eureka Machine Co., Lansing, Mich. Foote Mixer. W. H. Wilcox Co., Binghamton, N. \ '. 81 82 83 84 25 23 10 to 12 10 to 18 10 to 18 10 to 18 10 to 18 2 to 4 1 2 I 6 7 12 16 U5 Advance Mixer. Cement Machinery Co., Jackson, Mich. 25 to 75 on (3) Long inclined box of square section, revolving horizontal axis, concrete practically invisible. (4) Like (3), except being cylindrical, with deflectors. Practically invisible. *Engineering- News, Aug. 27, 1903. 28 REINFORCED CONCRETE, (5) Open trough or closed cylinder, fitted with shaft on which are paddles or blades which mix and feed concrete toward discharge end, concrete visible. Table of Continuous Mixers. Table IX gives compara- tive outputs of several well known continuous mixers. Hains Gravity Mixer. The Hains Concrete Mixer Co. of Washington, D. C, manufacture the mixer shown in Fig. 5. The charge passes successively through the hoppers. Fig. 5. Hains Gravity Mixer, Fixed Hopper Form. The four hoppers at the top have a combined capacity of one of the lower hoppers. Each top hopper is charged with cement, sand and stone in the order named and in the proper proportions. Water is then dashed over the tops of the rilled hoppers and they are dumped simultaneously into the hopper next below. This hopper is then discharged into the next and so on to the bottom. Meanwhile the four top hop- pers have been charged with materials for another batch. It MATERIALS AND MACHINES. 29 will be observed that (1) the concrete is mixed in separate batches, and (2) the ingredients making a batch are accurate- ly proportioned and begin to be mixed at once for the whole batch. The best arrangement is to have the top of the hopper tower carry sand and stone bins which chute directly into the top hoppers. STEEL. While in Europe wrought iron is preferred for reinforce- ment, steel is used exclusively in the United States, both on account of lesser cost and on account of having more suitable qualities. High or Low Carbon. Engineers differ as to the qualities of steel desirable for reinforcement, some apprehension be- ing entertained as to the brittleness of certain kinds of high carbon steel. Open-hearth steel is decidedly preferable. High steel should have an ultimate strength of about 85,000 Ibs. per sq. in., with an elastic limit averaging 54,000 Ibs.,. with not more than 0.067 per cent of phosphorus, 0.06 per cent of sulphur and between 0.4 and 0.8 per cent of manganese, with 0.5 to 0.6 per cent of carbon, and showing 10 per cent elongation in 8 ins. for a test piece ^ to 34 m - m diameter, and a l / 2 in. test piece should bend cold 110 around twice its diameter without fracture. Low carbon steel or soft steel should have an ultimate strength of from 54,000 to 62,000 Ibs. per sq. in., with an elastic limit not less than one-half the ultimate 'strength. It should elongate 25 per cent in 8 ins. and bend cold 180 double without fracture on outside of bend. Drawn steel wire of an ultimate strength of 156,000 Ibs. per sq. in. has been used, with an elastic limit of from 90,000 to 126,000 Ibs. in wire fabric and has shown many remarka- ble results. For a medium steel of 32,000 to 35,000 Ibs. elastic limit it is customary to specify a. safe strength of 16,000 Ibs. How- ever, for steel wire of 90..000 to 126,000 Ibs. the author has 30 REINFORCED CONCRETE. never specified more than 30,000 Ibs. as safe strength, owing to accidental defects by indentation in handling. Owing to the fact that the coefficients of elasticity of high and low steel are very nearly equal, and hence the limit stretch only varies as 0.001 of the length for soft steel to 0.00167 of the length for high steel and furthermore since, according to Prof. A. N. Talbot, the maximum allowable stretch of concrete lies near the point 0.001, it would appear that nothing could be gained by using a high carbon steel.* However, the author has since found that by using a high class concrete, of proportions such as 1 cement to 3 or 4 of aggregates proportioned for maximum density, far better results were obtained using high carbon steel than low car- bon, and owing to lesser dimensions, a lower dead weight of floor slabs and girders has resulted, showing economy in spite of the fact that more expensive mixtures of the con- crete were used, while taking advantage of the properties of high carbon steel. Medium Steel. When medium steel is used it should have an ultimate strength of from 60,000 to 68,000 Ibs. per sq. in., with an elastic limit of not less than one-half the ultimate strength. It should elongate 22 per cent in 8 ins., and bend cold 180 around a diameter equal to the thickness of the test piece without fracture on outside of bend. In the above bending tests for soft and medium steel the quality of metal should be such that it will stand the above described tests upon a test piece at least 5/16 in. in diame- ter, after being heated to a cherry red and cooled in water to a temperature of 70 F. In reinforced concrete permissible working stresses are not based upon the ultimate strength of the steel, but upon the elastic limit, owing to the necessary adhesion between the concrete and the steel, which is apt to be destroyed by any reduction in the sectional area of the steel, such as oc- curs during the rapid elongation beyond the elastic limit. *These conclusions were based upon extensive experiments made by Profs. Talbot, Hatt and Turneaure with concrete mix- tures of 1-2-4 and 1-3-6. MATERIALS AND MACHINES. 31 Percentage of Reinforcement. With low carbon steel the percentage of reinforcement is from 1 to 1.4 per cent. With high carbon steel, the figures vary from 0.7 to 0.9 per cent TABLE X. WEIGHTS OF SQUARE AND ROUND RODS. Calculated for steel, weighing 489.6 Ibs. per cu. ft. For iron, weighing 480 Ibs. per cu. ft., substract 2%. Thickness or diameter in ins. Wt. of Bar in Ibs. per ft. Wt. of Rod in Ibs. per foot. Area of Bar in sq. ins. Area of Rod in sq. ins. Circumfer- ence of ORod in ins. A .003 .003 .001 .0008 .0982 ft .013 .010 .0039 .0031 .1964 s .030 .023 .0088 .0069 .2945 1 .053 .042 .0156 .0123 .3927 & .083 .065 .0244 .0192 .4909 I .119 .163 .094 .128 .0352 .0479 .0276 .0376 .5891 .6872 1 .212 .167 .0625 .0491 .7854 i .269 .211 .0791 .0621 .8836 T 5 B .333 .261 .0977 .0767 .9818 II .402 .316 .1182 .0928 1.0799 .478 .376 .1406 .1104 1.1781 a .561 .441 .1650 .1296 1.2763 ?B .651 .511 .1914 .1503 1.3745 II .747 .587 .2197 .1726 1.4726 * .850 .668 .2500 .1963 1.5708 ft .960 .754 .2822 .2217 1.6690 A .076 .199 .845 .941 .3164 .3525 .2485 .2769 1.7672 1.8653 f .328 .043 .3906 .3068 1.9635 it .464 .150 .4307 .3382 2.0617 if .607 .262 .4727 .3712 2.1599 y 1.756 .380 .5166 . .4057 2.2580 i 1.913 .502 .5625 .4418 2.3562 it 2.075 .630 .6103 .4794 2.4544 T8 2.245 1.763 .6602 .5185 2.5526 B 2.420 1.901 .7119 .5591 2.6507 i 2.603 2.044 .7656 .6013 2.7489 it 2.793 2.193 .8213 .6450 2.8471 H 2.988 2.347 .8789 .6903 2.9453 B 3.1-91 2.506 .9385 .7371 3.0434 of the cross section; thus it is seen that by using high car- bon steel, there is only required from 0.64 to 0.7 as much re- inforcing steel. 32 REINFORCED CONCRETE. Mechanical Bond. Mechanical bond is obtained by de- formed rods, supplementary rods, stirrups or anchors. Such bond is absolutely necessary where a lean concrete is used, in which the adhesion between steel and concrete has a low TABLE X. (Continued). WEIGHTS OF SQUARE AND ROUND RODS. Thickness or diameter in ins. Wt. of Bar in Ibs. per ft. Wt. of Rod in Ibs. per foot. Area of Bar in sq. ins. Area of Rod in sq. ins. Circumfer- ence of ORod in ins. 1 3.400 2.670 .0000 .7854 3.1416 1C 3.838 3.015 .1289 .8866 3.3380 t 4.303 3.380 .2656 .9940 3.5343 4.795 3.766 .4102 1.1075 3.7306 1 5.312 4.172 .5625 1.2272 3.9270 4 5.857 4.600 .7227 1.3530 4.1234 t 6.428 5.049 .8906 1.4849 4.3197 7 n 7.026 5.518 2.0664 1.6230 4.5161 i 7.650 6.008 2.2500 1.7671 4.7124 A 8.301 6.519 2.4414 - 1.9175 4.9088 T 8.978 7.051 2.6406 2.0739 5.1051 9.682 7.604 2.8477 2.2365 5.3015 1 10.404 8.178 3.0625 2.4053 5.4978 Vs 11.169 8.773 3.2852 2.5802 5.6942 l 11.953 9.388 3.5156 2.7612 5.8905 n 12.763 10.024 3.7539 2.9483 6.0869 2 13.60 10.68 4.0000 3.1416 6.2832 TB 14.46 11.36 4.2539 3.3410 6.4796 ? 15.35 12.06 4.5156 3.5466 6.6759 A 16.27 12.78 4.7852 3.7583 6.8723 i ' 17.21 13.52 5.0625 3.9761 7.0686 18.18 14.28 5.3477 4.2000 7.2650 19.18 15.06 5.6406 4.4301 7.4613 20.20 15.87 5.9414 4.6664 7.6577 1 21.25 16.69 6.2500 4.9087 7.8540 TR 22.33 17.53 6.5664 5.1573 8.0504 I 23.43 18.40 6.8906 5.4119 8.2467 tt 24.56 19.29 7.2227 5.6727 8.4431 i 25.71 20.19 7.5625 5.9396 8.6394 y 26.90 21.12 7.9102 6.2126 8.8358 i 28.10 22.07 8.2656 6.4918 9.0321 *i 29.34 23.04 8.6289 6.7771 9.2285 3 30.60 24.03 9.0000 7.0686 9.4248 value. Mechanical bond caused by deforming the bars, is always preferable; besides, plain and deformed bars may now be ob- tained in the market at the same*price. See page 35. MATERIALS AND MACHINES. 33 Reinforcing Steel. There are a great many styles and TABLE XI. AREAS OF FLAT ROLLED STEEL. For thicknesses, from T ' g in. co 1 in., and widths from 1 in. to 4 in. Thickness in Ins. \" \" r 1" H" ir 1|" 2" A .016 .031 .047 .063 .078 .094 .109 .125 f .031 .063 .094 .125 .156 .188 .219 .250 j 3 B .047 .091 .141 .188 .234 .281 .328 .375 i .063 .125 .188 .250 .313 .375 .438 .500 T 8 3 .078 .156 .234 .313 .391 .469 .547 .625 i .094 .188 .281 .375 .469 .563 .656 .750 T 7 5 .109 .219 .328 .438 .547 .656 .766 .875 i .125 .250 .375 .500 .625 .750 .875 1.00 A .141 ,281 .422 .563 .703 .844 .984 .13 1 .156 .313 .469 .625 .781 .938 1.09 .25 u .172 .344 .516 .688 .859 .03 1.20 .38 i .188 .375 .563 .750 .938 .13 1.31 .60 b .203 .406 .609 .813 1.02 .22 1.42 .63 i .219 .438 .656 .875 1.09 .31 1.53 .75 $ .234 .469 .703 .938 1.17 .41 1.64 1.88 1 .250 .500 .750 1.000 1.25 .50 1.75 2.00 TABLE XII. WEIGHTS OF FLAT ROLLED STEEL, PER LINEAL FOOT. One cubic foot weighing 489.6 pounds. Thickness in Ins. Y r f" 1" H" li" If 2" rV .053 .106 .159 .213 .266 .319 .372 .425 | .106 .213 .319 .425 .531 .638 .744 .850 I 3 B .159 .319 .478 .638 .797 .956 1.12 1.28 i .213 .425 .638 .850 1.06 1.28 1.49 1.70 .266 .531 .797 1.06 1.33 1.59 1.86 2.12 .319 .638 .956 1.28 1.59 1.91 2.23 2.55 . . .372 .744 1.12 1.49 1.86 2.23 2.60 2.98 i .425 .850 1.28 1.70 2.13 2.55 2.98 3.40 .478 .956 1.43 1.91 2.39 2.87 3.35 3.83 1 .531 1.06 1.59 2.13 2.66 3.19 3.72 4.25 1.1 .584 1.17 1.75 2.34 2.92 3.51 4.09 4.68 1 .638 1.28 1.91 2.55 3.19 3.83 4.46 5.10 H .691 1.38 2.07 2.76 3.45 4.14 4.83 5.53 Ks .744 1.49 2.23 2.98 3.72 4.46 5.21 5.95 H .797 1.59 2.39 3.19 3.98 4.78 5.58 G.38 l .850 1.70 2.55 3.40 4.25 5.10 5.95 6.80 34 REINFORCED CONCRETE. kinds of steel in use for reinforcing concrete, which may be classified as loose rods, expanded metal, fabrics, beam and girder units, column reinforcements, and structural steel. TABLE XI. (Continued). AREAS OP FLAT ROLLED STEEL. For thicknesses, from T * ff in. to 1 in., and widths from { in. to 4 in. Thickness in Ins. 21" 21" 2J" 3" 3J" 3J" 3}" 4* A .141 .156 .172 .188 .203 .219 .234 .250 i .281 .313 .344 .375 .406 .438 .469 .500 n .422 .469 .516 .563 .609 .656 .703 .750 J .563 .625 .688 .750 .813 .875 .938 1.00 6 a .703 .781 .859 .938 1.02 1.09 1.17 1.25 1 .844 .938 1.03 1.13 1.22 1.31 1.41 1.50 1 .984 1.09 1.20 1.31 1.42 1.53 1.64 1.75 i . 1.13 1.25 1.38 1.50 1.63 1.75 1.88 2.00 I 9 5 1.27 1.41 1.55 1.69 1.83 1.97 2.11 2.25 f 1.41 1.56 1.72 1.88 2.03 2.19 2.34 2.50 y 1.55 1.72 1.89 2.06 2.23 2.41 2.58 2.75 1.69 1.88 2.06 2.25 2.44 2.63 2.81 3.00 la 1.83 2.03 2.23 2.44 2.64 2.84 3.05 3 25 v 1.97 2.19 2.41 2.63 2.84 3.06 3.28 3.50 2.11 2.34 2.58 2.81 3.05 3.28 3.52 3.75 I 3 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00- TABLE XII. (Continued). WEIGHTS OP FLAT ROLLED STEEL. One cubic foot weighing 489.6 pounds. Thickness in Ins. 21" 21" 2f 3" 31" 31" 3J" 4" A .478 .531 .584 .638 .691 .744 .797 .850 X .956 1.06 1.17 1.28 1.38 1.49 1.59 1.70 fit 1.43 1.59 1.75 1.91 2.07 2.23 2.39 2.55 i 1.91 2.13 2.34 2.56 2.76 2.98 3.19 3.40 T*B 2.39 2.66 2.92 3.19 3.45 3.72 3.98 4.25 I 2.87 3.35 3.19 3.72 3.51 4.09 3.83 4.46 4.14 4.83 4.46 5.21 4.78 5.58 5.10 5.95 J 3.83 4.25 4.68 5.10 5.53 5.95 6.38 6.80 X 4.30 4.78 5.26 5.74 6.22 6.69 7.17 7.65 I 4.78 5.31 5.84 6.38 6.91 7.44 7.97 8.50 tt 5.26 5.84 6.43 7.02 7.60 8.18 8.76 9.35 5.74 6.38 7.02 7.65 8.29 8.93 9.57 10.20 6.22 6.91 7.60 8.29 8.98 9.67 10.36 11.05 6.69 7.44 8.18 8.93 9.67 10.41 11.16 11.90 7.17 7.97 8.76 9.57 10.36 11.16 11.95 12.75 i 5 7.65 8.50 9.35 10.20 11.05 11.90 12.75 13.60 MATERIALS AND MACHINES. 35 Loose Rods for Reinforcing. These comprise round rods, square and flat bars, and the various patented deformed bars. Owing to the fact that in the United States nearly all the building regulations or ordinances require a mechanical bond, and specify or permit such concrete mixtures as will require it, tables are here inserted showing the properties of several of the most popular forms of reinforcement based upon the principle of mechanical bond. There are a number of prominent systems of construc- tion that are built up of loose rods, the assembling being done in the field. Practically all reinforced concrete work abroad comes under this classification, and formerly, loose rod systems were the only ones used in America. If loose rods are used for reinforcing instead of built up units, great- er freedom is allowed in adapting the reinforcing material to the part of the structure in which it is located. A number of prominent systems of reinforcement which are built of loose rods, will be given further on. Square Bars and Round Rods. The first form of rein- forcing steel to be used was plain round rods, and these at first found favor among engineers on account of being more easily obtained and cheaper. However, with the rapid increase in the demand for efficient reinforcement the manufacture of so-called de- formed bars developed as a specialty and today such bars may be obtained as easily and as cheaply as the plain product and should therefore always be preferred. Weights and Areas of Twisted Bars. Twisted bars, Fig. 6, are not covered by patent and can be obtained in open market. These bars are square in section, so that, for a given thickness, the weights and areas correspond with those for plain square bars. Table XIII, for twisted bars, is based upon steel weighing 489.6 Ibs. per cu. ft. 36 REINFORCED CONCRETE. Fig. 6. Twisted Bar. TABLE XIII. WEIGHTS AND AREAS OF TWISTED BARS. Thickness of section in ins. Weight in Ibs. per ft. Area of section in sq. ins. H 0.212 0.063 3 A 0.478 0.141 H 0.85 0.25 H 1.32 0.391 U 1.91 0.563 y* 2.60 0.765 i 3.4 1.000 IK 4.3 1.266 IM 5.3 1.563 Weights and Areas of Corrugated Bars. Xew style cor- rugated bars, Figs. 7 and 7-A are patented, and can be ob- Fig. 7. Corrugated Rounds Type C. TABLE XIV. SIZES AND WEIGHTS FOR TYPE C. Size. Net Section. Weight per Ft. %" .110" .38 lb. 7" .190" .66 lb. % .250" .86 lb. % .300" 1 05 Ibs. .440" 1.52 Ibs. % .600" 2.06 Ibs. 1 .780" 2.69 Ibs. iH .990" 3.41 Ibs. iS 1.220" 4.21 Ibs. MATERIALS AND MACHINES. 37 tained from the Corrugated Bar Company, Buffalo, N. Y. The universal corrugated bar shown by Fig. 8 is made by the same firm, its dimensions, area, etc., are shown by Table XV. Figr. 7 -A. Corrugated Squares Type D. TABLE XIV-A. AREAS AND WEIGHTS FOR TYPE D. Size. Net Section. Weight per Ft. l /4" .060" .22 Ib. H* .140" .49 Ib. W .250" .86 Ib. w .390" 1.35 Ibs. \" .56c" 1.941bs. y& .76Q" 2.64 Ibs. i " l.OOa" 3.43 Ibs, 1/8" 1.250" 4.34 Ibs. IX* 1.550" 5.35 Ibs. 38 REINFORCED CONCRETE. Fig. 8. Universal Corrugated Bar. TABLE XV. WEIGHTS AND AREAS OF UNIVERSAL CORRUGATED BARS. No. Size. Net section Wt. in Ibs. in sq. ins. per ft. 1 Jx 1 0.19 0.73 2 3 4 5 6 fell 11 J 1 1 x2 0.32 0.41 0.54 0.65 0.80 1.18 1.35 1.97 2.27 2.85 Weights and Areas of Diamond Bars. Diamond bars, Fig, 9, are patented and can be obtained from the Concrete Fig. 9. Diamond Bar. TABLE XVI. WEIGHTS AND AREAS OF DIAMOND BARS. Size in ins. Weight in Ibs. per ft. Area of section in sq. ins. 1 li .85 1.33 1.91 2.60 3.40 5.31 .25 .39 .56 .76 1.00 1.56 MATERIALS AND MACHINES. 39 Steel Engineering Company, New York City, Their sectional areas and weights correspond with standard sizes of square bars, and are shown in Table XVI. However, according to Bulletin No. 71, "Tests of Bond Be- tween Concrete and Steel," compiled by Prof. A. N. Talbot of the University of Illinois and his assistant, Prof. Duff A. Abrams, the more ideal deformed bar is described as follows : (page 212, Sec. 21) : "In a deformed bar of good design, the projections should present bearing faces as nearly as possible at right angles to the axis of the bar. "The areas of the projections should be such as to preserve the proper ratio between the bearing stress against the concrete ahead of projections and the shearing stress over the surround- ing envelope of concrete." Regarding the twisted bar, Bulletin 71 says : "The tests here recorded show conclusively that the bond resistance of twisted square bars is inferior in characteristics to that of plain round bars of similar surface, and that these bars have little or no advantage in bond resistance within limits of slip which would be useful in structures. " It seems strange that the twisted bar has gained such a wide popularity as a reinforcing material." Further (page 76), "It has been frequently stated that cold twisting is effective in raising the yield point of the bar by over- stressing a portion of the metal, and at the same time it furnishes a very severe test on the quality of the steel itself. "However, it has been shown by tests that the elastic limit has been raised on only a portion of the section (the outside) and that for stresses above the original yield point the modulus of elasticity of the whole section is considerably smaller than the normal value for steel within the elastic limit. In other words, for stresses above the original yield point the metal in the interior of the section will be stressed beyond its elastic limit and the rate of change in tensile deformation in the bar as a whole will be larger than at the lower stresses." The corrugated bars, pages 36 and 37, and the rib bars and corrugated bar described on next page come nearer to the specifications suggested in Bulletin 71 than any other bars in the market. 40 REINFORCED CONCRETE. Rib Bars. The rib bar shown by Fig. 11 is made by the Trussed Concrete Steel Co., Detroit, Mich. The projections Fig. 11. Rib Bar. on the bar are for the purpose of furnishing a mechanical bond. Table XIX gives sizes and weights. TABLE XIX. SIZES AND WEIGHTS OF RIB BARS. Size, ins Weight, Ibs. per ft. Size, ins. Weight, Ibs. per ft. j 0.48 0.86 1.35 1.95 i 2.65 3.46 4.38 4.51 The American Deformed Bar comes round or square and is rolled by several mills at Chicago and St. Louis. These bars have same areas and weights as plain rounds or squares and are preferable to twisted rods or to bars with closely spaced deformations or corrugations and appear to have a maximum bond value with a minimum of corru- gations. TESTS MADE BY R. W. HUNT & Co., ON HIGH CARBON DEFORMED ROUND BARS. AUGUST 22, 1911. Rods used for the Dallas-Oakcliffe Reinforced Concrete "Viaduct: DU. TENSILE ELAST. LIMIT ELONG. 1/8 in. 107,370 64,140 12.1% 64,090 15 % 62,000 13.7% 8 in. Y* in. 104,000 120,660 100,520 68.940 15.6% MATERIALS AND MACHINES. 41 Table XX shows results of experiments made by Prof. A. N. Talbot at Urbana, 111., showing the remarkable bond- ing strength of the Collings Bar, which is similar to the American Deformed Bar, but wifh deformations like those on the Rib Bars, page 40. Fig. 12. American Deformed Bar. TABLE XX. DATA OF TESTS OP BOND BETWEEN CONCRETE AND STEEL. 1, 1M, 2H Concrete; 62 days old. All specimens from same batch. Length Maximum Stress in Speci- men No. Kind and Size of Bar. of Embed- ment, Bond Area, So, Maximum Load, Lbs. Bond Stress, Lbs. per Steel at Maximum Load, Method of Failure. Ins. Ins. Sq. In. Lbs. per Sq. In. 1 H'Rd. Collings Bar 8.3 13.05 13,350 1,020 68,000 Block Split 2 H'Rd. Collings Bar 8.2 12.87 20,200 1,570 104,200 Block Split 3 H"Rd. Collings Bar 8.1 12.70 17,900 1,410 91,500 Block Split 4 y 2 "Rd. Collings Bar 8.2 12.87 16,800 1,300 85,800 Block Split 5 6 H*Rd. Collings Bar ^"Rd. Collings Bar 8.0 8.3 12.54 19.50 18,100 17,100 1,440 878 92,300 38,700 Block Split Block Split 7 ^"Rd. Collings Bar 8.1 19.05 19,700 1,030 44,700 Block Split 8 ^"Rd. Collings Bar 8.1 19.05 19,700 1,030 44,700 Block Split 9 3 /T'Rd. Collings Bar 8.1 19.05 18,600 978 42,200 Block Split 10 %*Rd. Collings Bar 8.2 19.30 16,100 836 36,400 Block Split 11 1" Rd. Collings Bar 8.2 25.7 18,800 732 23,900 Block Split 12 l"Rd. Collings Bar 8.0 25.1 17,700 706 22,500 Block Split 13 1* Rd. Collings Bar 8.1 25.4 17,500 690 22,300 Block Split 14 TRd. Collings Bar 8.1 25.4 17,700 696 22,500 Block Split 15 l"Rd Collings Bar 8.2 25.7 16,950 660 21,600 Block Split 16 M' Plain Round 8.1 19.05 12,200 640 27,600 Rod pulled out 17 %" Plain Round 8.2 19.30 11,900 617 26,900 Rod pulled out 18 %' Plain Round 8.2 19.3 13,100 678 29,600 Rod pulled out 19 % " Plain Round 8.1 19.05 13,500 708 -30,600 Rod pulled out 20 % * Plain Round 8.0 18.80 13,700 730 31,000 Rod pulled out Tests made May 5, 1910, at Urbana, 111. (Signed). A. N. TALBOT. 42 REINFORCED CONCRETE. Wire Fabric. This material has come into almost uni- versal use and has been found to possess many valuable, even indispensable qualities. Its advantages are that it pre- vents temperature cracks and also prevents cracks from shocks. A building having fabric in walls, floors, girders, beams, columns, and resting on a mat foundation can with- stand unequal loading, treacherous subsoil, excessive wind pressure, fire and even seismic disturbances much better than any other structure known to the technical world. Wire fabric is made of steel wires crossing at right or oblique angles and secured at the intersections. The heavier wires run lengthwise and are called carrying wires; the lighter ones cross these and are called distributing or tie wires. The manner of securing the intersections has given TABLE XXI. AREA IN SQ.'!NS. PER ONE FT. IN WIDTH. 02 American Steel & Wire Co. Wire Gage. Gage 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Dia. .283' .263" .244* .225* .207' .192' .177* 162* .148* .135* 0143 .121* .0114 .106* .092* .080" .072' Area .0629 .0541 .0466 .0399 .0337 .0290 .0246 0206 .0173 .0087 .0066 .0050 .0041 i* 1H* .7538 .6492 .5592 .4797 .3944 .3480 .2952 .2472 .2076J.1722 .1368 .1044 .0696 .0792 .0548 .0396 .0600 .0400 .0300 .0492 .0328 .0246 .5032 .4328 .3728 .3192 .2696 .2320 .1968 .1648 .1384 .1144 .0912 2" .3774 .3246 .2796 .2394 .2022 .1740 .1476 .1236 .1038 .0858 .0684 .0522 VA" .3015 .2597 .2237 .1917 .1577 .1392 .1181 .0989 .0828 .0689 .0544 .0417 .0397 .0160 .0197 3* .2516 .2164 .1864 .1596 .1348 .1160^.0984 0824 .0692 .0572 .0456 .0348 .0264 .0200 .0164 4* .1887 .1623 .1398 .1197 .1011 .0870 .058p .0497 .0738 .0618 .0519 .0429 .0342 .0261 .0198 .0150 .0123 5* .1507 .1258 .1118 .0959 .0759 .0590 0494 .0415 .0344 .0273 .0209 .0158 .0120 .0098 6* .1258 .1082 .0932 .0798 .0674 .0492 0412 .0346 .0286 .0228 .0174 .0132 .0100 .0082 7' .1077 .0924 .0799 .0685 .0535 .0422 0353 .0287 .0246 .0196 .0149 .0113 .0086 .0073 8' .0943 .0821 .0689 .0598 .0505 .0435 .0369 0309 .0259'.0214 .0171 .0130 .0099 .0075 .0066 .0050 .0061 .0055 9" .0837 .0721 .0691 .0533 .0439 .0387 .0328 0275 .023l|.0169 .0152 .0115 .0088 12' .0629 .0541 0466 .0399 0337 .0290 .0246 0206 .0173 .0143 .0114 .0087 .0066 .0041 MATERIALS AND MACHINES. 43 rise to a number of different types of wire fabric, several of the principal ones of which are given below. The manu- facturers of each of these forms will furnish fabric in special size of wire and mesh if desired. Triangle Mesh Steel Woven Wire Reinforcement is made with both single and stranded longitudinal, or tension mem- bers. That with the single wire longitudinal is made with one wire varying in size from a No. 12 gage up to and including a ^-inch diameter, and that with the stranded longitudinal is composed of two or three wires varying from No. 12 gage up to and including No. 4 wires stranded or twisted together with a long lay. These longitudinals either solid or stranded are invariably spaced 4-inch centers, the sizes being varied in order to obtain the desired cross sec- tional area of steel per foot of width. The transverse or diagonal cross wires are so woven be- \/\ i3. 4-Inch Triangle Mesh Reinforcement. 44 REINFORCED CONCRETE. TABLE XXII. LONGITUDINALS SPACED 4-iNcn CENTERS. CROSS WIRES SPACED 2-iNCH CENTERS. Number and Gage of Wires, Areas per Foot Width and Weights per 100 Square Feet. Styles Marked * Usually Carried in Stock. Style Number No. of Wires Each Long. Gage of Wire Each Long. Gage of Cross Wires Sectional Area Long Sq. In. Sectional Area Cross Wires Sq. In. Cross Sectional Area per Ft. Width Approxi- mate Weight per 100 Sq. Ft. 4-A 6 14 .087 .050 .102 53 5-A 8 14 .062 .050 .077 44 6-A 10 14 .043 .050 .058 37 * 7-A 12 14 .026 .050 .041 31 23-A /4" 12H .147 .076 .170 86 24-A 4 12H .119 .076 .142 76 25-A ( 5 12^ .101 .076 .124 70 26-A 12H .087 .076 .110 64 27-A 8 mi .062 .076 .085 55 *28-A 10 WA .043 .076 .066 48 29-A 12 U 1 A .026 .076 .049 42 31-A 2 4 WA .238 .076 .261 120 32-A 2 5 i2H .202 .076 .225 107 33-A 2 6 12H .174 076 .196 97 34-A 2 8 WA .124 .076 .146 78 35-A 2 10 12 1 A .086 .076 .109 64 36-A 2 12 l^A .052 .076 .075 52 38-A 3 4 12^ .358 .076 .380 165 39-A 3 5 12H .303 .076 .325 145 40-A 3 6 12H .260 .076 .283 129 41-A 3 8 12H .185 .076 .208 101 42-A 3 10 12^ .129 .076 .151 81 43-A 3 12 12H .078 .076 .101 C2 Special Sizes on Application. Length of Rolls: 150-ft., 300-ft. and 600-ft. Widths: 18-in., 22-in., 26-in., 30-in., 34-iu., 38-in., 42-in., 46-in., 50-in., 54-in. and 58-in. MATERIALS AND MACHINES. 45 TABLE XXII-A. AREAS IN SQUARE FEET PER ROLL OF TRIANGLE MESH REINFORCEMENT Width of Roll in Inches Square Feet of Reinforcement in Roll 150-ft. Roll 300-ft. Roll 600-ft. Roll 18 225 450 900 22. ......... 275 550 1100 2G.'.'.. '.'.'.'.'.'.'.'........'..'..........'. 325 650 1300 375 750 1500 34... 425 850 1700 00 475 950 1900 12...'..'.'..'.'.'.'.'.'.'.'.'.'.'.'....'.'.'....... 525 1050 2100 575 1150 2300 50... 625 1250 2500 54 675 1350 2700 58 725 1450 2900 As indicated in the above table, Triangle Mesh Reinforcement is made up in the following widths: 18, 22, 26, 30, 34, 38, 42, 46, 50, 54 and 58 inches, and in standards lengths of rolls of 150, 300 and 600 feet. For the lighter styles, rolls of any of the above lengths may be used. Material of medium weights is recommended to be used in 150 or 300 foot lengths, while with the heaviest styles it is more conveniently handled in rolls containing 150-foot lengths. TABLE XXII-B. LONGITUDINALS SPACED 4-iNCH CENTERS. CROSS WIRES SPACED 4-iNcn CENTERS. Number and Gage of Wires, Areas per Foot Width and Weights per 100 Square Feet. Styles Marked * Usually Carried in Stock. Style Number No. of Wires Each Long. Gage of Wire Each Long. Gage of Cross Wires Sectional Area Long Sq. In. Sectional Area Cross Wires Cross Sectional Area per Ft. Width Approxi- mate Weight per 100 Sq. Ft. * 4 6 14 .087 .025 .102 43 5 8 14 .062 .025 .077 34 6 10 14 .043 .025 .058 27 * 7 12 14 .026 .025 .041 21 *23 M* 12H .147' .038 .170 72 24 4 12^2 .119 .038 .142 62 25 5 12H .101 .038 .124 55 *26 1 6 12J4 .087 .038 .110 50 *27 1 8 12^ .062 .038 .085 41 28 1 10 12/^ .043 .038 .066 34 29 1 12 12^2 .026 .038 .049 28 31 2 4 12}/jj .238 .038 .261 106 32 2 5 12H .202 .038 .225 92 33 2 6 12}^ .174 .038 .196 82 34 2 8 12V6 .124 .038 .146 63 35 2 10 12|i .086 .038 .109 50 36 2 12 .052 .038 .075 37 *38 3 4 12 1 A .358 .038 .380 151 39 3 5 l2}/2 .303 .038 .325 130 40 3 6 12 1 A .260 .038 .283 114 41 3 8 12/^ .185 .038 .208 87 *42 3 10 12H .129 .038 .151 66 43 3 ; 12 i|y .078 .038 .101 47 Special Sizes on Application. Length of Rolls: 150-ft., 300-ft. and 600-ft. Widths: 18-in., 22-in., 26-in., 30-in., 34-in., 38-in., 42-in., 46-in., 50-in., 54-in. and 58-in. 46 REINFORCED CONCRETE. tween the longitudinals that perfect triangles are formed by their arrangement, thereby not only lending additional carry- ing strength to the longitudinal or tension members, but positively spacing them and providing a most perfect dis- tribution of the steel. These diagonal cross or transverse wires are woven either 2 or 4 inches apart, as is desired. It is the most perfect reinforcement for concentrated loads, distributing the stress imposed by the load throughout the floor slab. A hinge joint is provided on each longitudinal, which enables this reinforcement to be folded longitudinally in any desired shape, making it adaptable to all kinds of con- crete construction. Its design provides a most perfect me- chanical bond between the steel and the concrete, and from the fact that it is not galvanized (unless specially ordered) the maximum adhesive bond is developed. A sufficient area of steel is provided in the cross wires of Triangle Mesh Reinforcement to prevent temperature cracks, thereby eliminating the necessity of laying additional re- inforcement at right angles to the longitudinal or tension members. Lock-Woven Fabric. Lock-woven fabric, Fig. 15, is man- ufactured by W. N. Wight & Co., New York. The wires are from No. 3 to No. 12 gage, commonly woven in 4x6-in. mesh, 56 ins. wide and 300 ft. long. -$==t Fig 15 Lock-woven Fabric. Fig. 16. American Wire Fabric. American Wire Fabric. American wire fabric, Fig. 16, is of high carbon steel wires, secured at the intersections by No. 14 wire, and manufactured by the American Wire Fence Co., Chicago. Standard sizes are shown by Table XXIII. MATERIALS AND MACHINES. 47 TABLE XXIII. GAGE AND MESH OF AMERICAN WIRE FABRIC. Gage of Carrying Wires. Gage of Distributing Wires. Mesh in Inches. 9 9 9 7 7 11 11 11 11 11 11 4x 12 4x6 6x6 4x12 4x6 6x6 Welded Wire Fabric. Welded wire fabric, Fig. 17, has the intersections electrically welded and is manufactured by the Clinton Wire Cloth Co., Clinton, Mass., in a variety of meshes the longitudinals spaced in steps of l /z in. and the transverse wires in steps of 1 in. TABLE XXIV. WEIGHT AND STRENGTH OP WELDED WIRE FABRIC. Fig. 17. Welded Wire Fabric. Gage W. &M. Diameter of One Wire Wt. per Lineal Foot of One Wire Tensile Strength of One Wire No. in ins. in Ibs. in Ibs. .3065 .2506 4,427 1 .2830 .2136 3,774 2 .2625 .1838 3,247 3 .2437 .1584 2,799 4 .2253 .1354 2,392 5 .2070 .1143 2,019 6 .1920 .0983 1,737 7 .1770 .0835 1,476 8 .1620 .0700 1,237 9 .1483 .0586 1,036 10 .1350 .0486 859 11 .1205 .0387 684 12 .1055 .0296 524 The following figures* show a comparison between two kinds of wire as to breaking loads: *By Lorin E. Hunt, C. E., Berkeley, Cal. 48 REINFORCED CONCRETE. Diameter in inches. Breaking loaa in Ibs. Load per sq. in. Welded Fabric No 8 163 1 510 72 300 Welded Fabric No. 6. 191 1 860 64 900 146 2 292 136 900 American System No. 7 0.175 3,060 127,100 I "7 J Fig. 18. Expanded Metal. Expanded Metal. Expanded metal, Fig. 18, is a mesh formed from a sheet of soft steel by slitting and opening or expanding the metal with meshes in direction normal to the axis of the sheet. Table XXV is compiled from information furnished by the Associated Expanded Metal Companies, New York. Fig. 19. Kahn Rib Metal. Kahn Rib Metal. This material, Fig. 19, is made from a sheet of metal, flat on one side and corrugated on the other. Strips of the metal adjacent to the ribs are stamped out, and the sheet is drawn out into square meshes. The illustration shows these points and Table XXVI gives the properties of MATERIALS AND MACHINES. 49 this material. It is manufactured by the Trussed Concrete Steel Co., Detroit, Mich. TABLE XXV. EXPANDED METAL MESHES. Designation Size of Mesh d ^ Secti'n Size of S rQ M I 1 in standard w .si 5 1 Thick- Width center Leng'h center Strand sq. in. per Wt. in Ibs sheets, in feet II e t/5 ness to to foot per w 3 o-oo '~ in center center of sq. ft. Width by t o' D Wn_, , 4 t Q 1 bo ctf ins. in in width length O o I ins. ins. ; d'Q w j S5 18 0.049 0.43 1.2 Standard .209 .74 3 or 6x8 5 120 13 0.095 0.95 2.0 " .225 .80 6x8 or 12 5 240 12 0.109 1.36 3.0 " .207 .70 4x8 or 12 5 160 2 12 0.109 1.82 4.0 " .166 .56 5x8 or 12 5 200 3 16 0.065 3.00 8.0 " .083 .28 6x8 or 12 10 480 3 10 0.134 3.0 8.0 Light .148 .50 Six 8 or 12 5 210 3 10 0.134 3.0 8.0 Standard .178 .60 6x 8 or 12 .5 240 3 10 0.134 3.0 8.0 Heavy .267 .90 4x8 or 12 5 160 3 10 0.134 3.0 8.0 Ex. Heavy .356 1.20 6x8 or 12 3 144 3 6 0.203 3.0 8.0 Standard .400 1.38 5x8 or 12 3 120 3 6 0.203 3.0 8.0 Heavy .600 2.07 5x8 or 12 3 120 4 16 0.065 3.86 6.85 Old Style .093 .42 4|x8or 9 6 206 6 4 0.238 6.0 16.0 Standard .245 .84 5x8 or 12 5 200 6 4 0.238 6.0 16.0 Heavy .368 1.26 5x8 or 12 3 120 LATHING. Size of Mesh Designation Width center to center in inches w Leng'h center to center in inches / Gage U.S. Stand- ard Thick- ness inches Size of sheets in feet Sheets in a bundle Sq. yds. in a bundle Wt. in Ibs. per sq. yd. A B BB Diamond, Ho. 24 Diamond, No. 26 *0.40 *0 . 40 -0.60 0.41 0.41 *2.0 *2.0 62.0 1.2 1.2 24 27 27 24 26 .025 .0171875 .0171875 .025 .01875 18x96 18x96 22x96 18x96 24x96 9 15 15 15 9 12. 20. 24.44 20. 16. 4.00 2.90 2.33 3.75 2.66 *The meshes of "A" and "B" lath are parallelograms, the sides being 0.6x1.5 ins. on centers, and the perpendicular distance between centers of long sides is about 0.4 in. "BB" lath is practi- cally the same as "B" except meshes are wider. The tensile strength of the uncut sheet is 16,000 Ibs. per sq. in. 50 REINFORCED CONCRETE. TABLE XXVI. PROPERTIES OF KAHN RIB METAL. Distance Sect, area Size No. center to center in sq. ins. per ft. in Width of sheets ins. Sq. ft. in sheet 12ft. Safe tensile stress, Ultimate strength Weight, Ibs. per sq. ft. of bars, width long Ibs. in ins. 2 2 0.54 17 17 9,700 38,800 2.13 3 3 0.36 25 25 6,480 25,920 1.43 4 4 0.27 33 33 4,860 19,440 1.08 5 5 0.22 41 41 3,960 15,840 0.87 6 6 0.18 49 49 3,240 12,960 0.72 7 7 0.15 57 57 2,700 10,800 0.62 8 8 0.14 65 65 2,520 10,080 0.55 NOTE. Area of each rib is 0.08 sq. in. Standard lengths of sheets are 12, 14 and 16 ft. Beam and Girder Units. There are several forms of beam or girder reinforcement which are either in one piece or assembled together as one unit, the steel being placed along the planes of greatest stress. A number of the best known forms are given below. In nearly all of these built- up forms, deformed bars can be used instead of plain rods, according to the choice of the engineer. Fig. 20. Cummings Girder Frame. Cummings Girder Frame. The Cummings trussed girder reinforcement is arranged as a framed system by the intro- duction of hoop iron chair-clamps around all rods where one of them is bent up. The rods are shipped flat to the build- ing for the sake of convenience, as shown at C, D and E, Fig. 20. The prongs are bent up at 45 degrees (as at A) on the floor before the frame is set in the mold, the chairs MATERIALS AND MACHINES. 51 further serving to keep the bars at proper distance from the molds. Pittsburgh Steel Products Co.'s Beam Reinforcement con- sists of electrically welded frames with shear bars inclined 45 with the horizontal and spaced at the theoretically cor- rect points. The bottom horizontals consist of two members placed one above the other with a clearance of ^ inch, the upper of the two being cut off at the correct theoretical point so as to prevent a waste of material, which results when the same cross section of metal extends for the full length of the beam or girder. The top bars at supports extend a sufficient distance be- yond the support to develop the full strength of the bars so as to protect the stresses of negative moments, causing cracks over supports. The shear bars are spaced from 4 inches on centers to not exceeding the depth of the beam. The Xpantrus Bar is of similar appearance to the Pitts- burgh Steel Products Co.'s bar, but is manufactured by slit- ting and expanding both ends. Continuity over supports is produced by pin connection as of course the top bar cannot extend beyond the bottom bar, being sheared from the same metal. "Unit" Frame. The Unit concrete-steel frame, Fig. 21, has the reinforcing rods and stirrups rigidly held together by a unit socket support, which latter also serves the pur- pose of receiving hanger bolts or other appliances that are Fig. 21. Unit Frame. to be suspended to the girder afterwards. Kami Trussed Bar. The Kahn trussed bar, Fig. 22, named for its inventor, is a form of beam, girder or column re- 52 REINFORCED CONCRETE. inforcement, consisting of a special rolled section of steel with' diagonal members sheared up at 45 on both sides of the main body. For continuous beams, inverted bars are placed over the supports in the upper part of the beam, ex- tending over the region of tension. These bars are of two forms of section, as shown by Fig. 22, and either form may be sheared alternately or opposite with varying lengths of diagonal. They are manufactured by the Trussed Concrete Steel Co., Detroit, Mich. Fig. 22. Kahn Trussed Bar. TABLE XXVII. PROPERTIES OP KAHN TRUSSED BARS. Size Weight Area of un- Area of Shear value Tensile strength of bar Length of Diagonals in in sheared sheared of one in Ibs. per sq. in. in ins. ins. Ibs. bar in bar in diagon'l per ft. sq. ins sq. ins. in Ibs. a x b per Un- Stand- Gross. Net. sq. in. sheared. Sheared . ard. Special. Square Section Bars. JxU 1.4 .41 .25 900 6,600 4,000 6 Ix2f 2.7 .79 .56 1,300 12,600 9,000 12 8 1 x3 4.8 1.41 1.00 2,300 22,600 16,000 24 18 Hx3f 6.8 2.00 1.60 2,300 32,000 25,600 24 / 18 I 30 C X d New Section Bars. Ifx2f 6.8 2.00 1.60 2,300 32,000 25,600 24 / 30 2 x 3i 10.2 3.00 2.40 3,400 48,000 38.400 24 I 18 30 NOTE. 6, 8 and 12 in. diagonals are sheared opposite. 18, 24 and 30 in. diagonals are sheared alternately. MATERIALS AND MACHINES. S3 Luten Truss. The Luten truss is clamped and locked in a rigid unit by means of a clamp with a wedge that is self- locking when tightly driven in. The truss and one of the clamps in position are shown by Fig. 23. This truss is to be obtained from the National Concrete Co., Indianapolis, Ind. Fig. 23. Luten Truss. Hooped Column Reinforcement. While there are several types of reinforced concrete column constructed, almost the only assembled units on the market are those for hooped col- umns, since the other types of column reinforcement are assembled in the field from loose rods. As with wire fab- rics and girder units, the main points of difference in hooped column reinforcements are the methods of fastening. The hoops may be arranged either as a spiral or as annular rings, and the hooping material may be either flat band steel or wires. The longitudinal reinforcement may be part of the hooping unit or separate rods may be inserted. The supe- rior advantages of hooped columns over other forms are re- ferred to under Design. Cummings Hooped Column. The Cummings hooped col- umn, invented by Mr. Robert A. Cummings, is shown by Fig. 26. Table XXVIII gives the safe loads. This -column reinforcement is built up of annular hoops made of flat steel bent to a circle with the ends riveted or welded together in such a manner that the ends of the hoops protrude at right angles to keep them the proper distance from the mold. The vertical reinforcement is often made of angles with holes punched at intervals for staples to fasten them to the hoops. 54 REINFORCED CONCRETE. TABLE XXVIII. HOOPED COLUMNS, CUMMINGS SYSTEM. (Factor of Safety = 4.) Size of Column, inches. Diameter of Hoops, inches. Breadth and Gage of Hooping Steel. Distance c.c.of hoops inches. No. and Size of Verticals. Wt. of Steel per lin. ft. Safe load for Col., in Ibs. 12 10 - 18 2 _ 7.5 99,500 14 12 - 16 2 _ 9.27 143,000 16 13 * - 16 3 _ 11.88 166,400 18 15 t - 14 3 _ 14.44 223,500 20 17 i - 14 3 _ 17.52 277,000 22 19 i - 14 3 _ I 20.93 336,200 24 21 J - 12 3 6- i 26.84 430,500 26 28 30 32 23 25 27 29 1 - 12 i -12 i - 10 i - 10 3 3 3 3 6 - 6 - 8 - 8 - 31.74 32.88 43.55 45.05 505,700 575,000 704.500 786,500 34 31 ! - 10 3 6 - i 50.15 884,200 36 33 * - 8 3 6 - 1 57.69 1.036 ,200 38 35 1 - 8 3 6 - H 59.45 1,136,200 American Hooped Column. The American system of col- umn reinforcement is illustrated by Fig. 27. The spiral is made of high carbon steel. Table LVIII, page 157, compiled from Considered formula, gives the ultimate loads for this form of column reinforcement. The manufacturers are the American Wire Fence Co., Chicago. JnL Fig. 26. Cummings Figr. 27. American Hooped Hooped Column. Column. Smith Hooped Column. Fig. 29 shows an assembled view and Fig. 30 a detail of a hooped reinforcement for con- crete columns made by the F. P. Smith Wire & Iron Works, Chicago, 111., and used for some 4,000 columns in the large MATERIALS AND MACHINES. 55 new warehouse of reinforced concrete built for Mont- gomery Ward & Co., at Chicago, 111. The reinforcement, as shown, is made up in units of any length and diameter and of any shape bar and size of hooping specified. Ordinarily the bars used are plain flats with rounded edges, as shown, and four bars are used. The bars are fixed to rotating heads and the hooping wire wound into the rounded holes, which are then closed by a hammer blow on the projecting fin or point. The pitch of the hooping can be made as desired. These spirals are shipped knocked down or in collapsed form, whereby a much lower freight rate is obtained. Fig. 29. Smith Hooped Column. Fig. 30. Connection of Hoops to Verticals, Smith Column. Structural Steel. The following tables include those forms of structural steel which may be used for reinforcing purposes. Standard Carnegie I-beams and channels are giv- en by Tables XXIX and XXX. These are often used in beams and columns, which are afterward encased in con- crete. Tables XXXI to XXXIV show corresponding data for angles. Table XXXV is inserted as being useful in de- termining the areas and numbers of steel rods required for a given percentage of reinforcement. The properties of sections are given in Table XXXVI. 56 REINFORCED CONCRETE. TABLE XXIX. PROPERTIES OF STANDARD CARNEGIE I-BEAMS. 1 2 3 4 5 6 7 8 9 ~~ W . g . .52 d -3 <2d 1 s-s 5-S S-t *- || P la +-* (T> t> .*3-g Iplll 111 iff J'ihf-p! 1 la Q i f S "o w |.S H -3% M PH ill III SB** I !' r B5 ~15~ 60.00 17.67 0.590 6.000 609.0 25.96 5 87 B7 15 42.00 12.48 0.410 5.500 441.7 14.62 5.95 B8 12 40.00 11.84 0.460 5.250 268.9 13.81 4.77 B9 12 31.50 9.26 0.350 5.000 215.8 9.50 4 83 Bll 10 25.00 7.37 0.310 4.660 122.1 6.89 4.07 B13 9 21.00 6.31 0.290 4.330 84.9 5.16 3.67 B15 8 18.00 5.33 0.270 4.000 56.9 3.78 3.27 B17 7 15.00 4.42 0.250 3.660 36.2 2.67 2.36 B19 6 12.25 3.61 0.230 3.330 21.8 1.85 2.46 B21 5 9.75 2.87 0.210 3.000 12.1 1.23 2 05 B23 4 7.50 2.21 0.190 2.660 6.0 0.77 1.64 B77 3 5.50 1.63 0.170 2.330 2.5 0.46 1.23 TABLE XXX. PROPERTIES OF STANDARD CARNEGIE CHANNELS. 1 2 3 4 5 6 7 8 9 K O c d "o tn 3 fl|- as. a Section Ind S Si! P. C l o f Area of Section in sq. ins Thickness Web in in Width oi Flange in i -J2 ^ rt 40 rt< o vj mm o? o * ir SI i J/ r 01 15 33.00 9.90 0.400 3.400 312.6 8.23 5.62 C2 12 20.50 6.03 0.280 2.940 128.1 3.91 4.61 03 10 15.00 4.46 0.240 2.600 66.9 2.30 3.87 04 9 13.25 3.89 0.230 2.430 47.3 1.77 3.49 05 8 11.25 3.35 0.220 2.260 32.3 1.33 3.11 C6 7 9.75 2.85 0.210 2.090 21.1 0.98 2.72 07 6 8.00 2.38 0.200 1.920 13.0 0.70 2.34 08 5 6.50 1.95 0.190 1.750 7.40 0.48 1.95 C9 4 5.25 1.55 0.180 1.580 3.80 0.32 1.56 072 3 4.00 1.19 0.170 1.410 1.60 0.20 1.17 For each of the above tables: L = Safe load in pounds uniformly distributed; 7=span in feet. M = Moment of forces in foot pounds ; C and C' = coefficients given on oppo- site page. MATERIALS AND MACHINES. 57 TABLE XXIX. (Continued). PROPERTIES OF STANDARD CARNEGIE I-BEAMS 10 11 12 13 14 15 C* S eJ'Sl J_, c 9*3 g 2 ^ * ^!y . J$a*! 9 < r . IHJ.1 rt >> g o -^ o||g *u iiifi! co,| 3 P, O O ** s C 5t3'0 lllPl Ifiill T3 c i i r' S o^ c ^C' 1.21 81.2 866100 876600 . 11.49 B5 1.08 58.9 628300 490800 11.70 B7 1 08 44.8 478100 373500 9.29 B8 1 01 36.0 383700 299700 9.45 B9 0.97 24.4 260500 203500 7.91 Bll 0.90 18.9 201300 157300 7.12 B13 0.84 14.2 151700 118500 6.32 B15 0.78 10.4 110400 86300 5.53 B17 0.72 7.3 77500 60500 4.70 B19 0.65 4.8 51600 40300 B21 59 3 31800 24900 ' B23 0.53 1.7 17600 13800 B77 TABLE XXX. (Continued). PROPERTIES OF STANDARD CARNEGIE CHANNELS. 10 11 12 13 14 15 16 Radius of Gyration, Neutral Axis Parallel with Center line of web. Section Modulus, Neutral Axis Perpendicular to web at Center. Coefficient of Strength for Fibre Stress of 16,0001bs. per sq. in. used for Buildings. -A* . C -t~> -*J ' C tn o MCOo"*,8 % iJllfif o^E-H 3PQ l Distance Between Channels Required to make Radii of Gyration equal Distance of Center of Gravity from Outside of web. Section Index. r' S C C' X .912 41.7 444500 347300 9.50 0.794 Cl .805 21.4 227800 178000 7.67 0.704 C2 .718 13.4 142700 111500 6.33 . 0.639 C3 .674 10.5 112200 87600 5.63 0.607 C4 .630 8.1 86100 67300 4.94 0.576 C5 .586 6.0 66800 52200 4.22 0.546 C6 .542 4.3 46200 36100 3.52 0.517 C7 .498 3.0 31600 24700 2.79 C.489 C8 .453 1.9 20200 15800 2.06 0.464 C9 .409 1.1 11600 9100 1.31 0.443 C72 For each of the above tables: 58 REINFORCED CONCRETE. TABLE XXXI. PROPERTIES OF STANDARD CARNEGIE ANGLES. Angles with unequal legs. 1 2 3 4 5 6 7 Weight Area of Perpendicular Distance from Center of Gravity Section Size in Thickness in per Foot Section in to Back of Flange. Index. Inches. Inches. in. Pounds Square Inches. To Back of Longer To Back o Shorter Flange. Flange. A 89 6 x 1 30.6 9.00 1.17 2.17 A 91 6 x T! 28.9 8.50 1.14 2.14 A160 6 x I 27.2 7.99 1.12 2.12 A161 6 x a 25.4 7.47 1.10 2.10 A162 6 x i 23.6 6.94 1.08 2.08 A163 6 x 21.8 6.41 1.06 2.06 A164 6 x i 20.0 5.86 1.03 2.03 A165 6 x 9 18.1 5.31 1.01 2.01 A166 6 x I 16.2 4.75 0.99 1.99 A167 6x4 ? 7 14.3 4.18 0.96 1.96 A168 6x4 12.3 3.61 0.94 1.94 A 92 6 x 3J 1 28.9 8.50 1 01 2.26 A 93 6 x l| 27.3 8.03 0.99 2.24 A169 6x3 1*3 25.7 7.55 0.97 2.22 A170 6x3 24.0 7.06 0.95 2.20 A171 6 x & | 22.4 6.56 0.93 2.18 A172 6x3 11 20.6 6.06 0.90 2.15 A173 6x3 | 18.9 5.55 0.88 2.13 A174 6 x 3J 9 17.1 5.03 0.86 2.11 A175 6x3 I 15.3 4.50 0.83 2.08 A176 6x3 yg 13.5 3.97 0.81 2.06 A177 6 x # f 11.7 3.42 0.79 2.04 A187 5 x 3J i 22.7 6.67 1.04 1.79 A 188 5 x 3J TS 21.3 6.25 1.02 1.77 A189 5 x 3= I 19.8 5.81 1.00 1.75 A190 5x3 18.3 5.37 0.97 1.72 A191 5x3 jj 16.8 4.92 0.95 1.70 A192 5x3 9 15.2 4.47 0.93 1.68 A193 5x3 X 13.6 4.00 0.91 1.66 A 194 5x3' r 12.0 3.53 0.88 1.63 A195 5x3; | 10.4 3.05 0.86 1.-61 A 96 5 x 3J I 6 8 8.7 2.56 0.84 1.59 A196 5 x 3 11 19.9 5.84 0.86 1.86 A197 5x3 1 18.5 5.44 0.84 .84 A198 5x3 18 17.1 5.03 0.82 .82 A199 5x3 f 15.7 4.61 0.80 .80 A200 5x3 ft 14.3 4.18 0.77 .77 A201 A202 5x3 5x3 f 12.8 11.3 3.75 3.31 0.75 0.73 75 .73 A203 5x3 f 9.8 2.86 0.70 .70 A280 5x3 A 8.2 2.40 0.68 .68 MATERIALS AND MACHINES. 59 TABLE XXXi. (Continued). PROPERTIES OP STANDARD CARNEGIE ANGLES. Angles with unequal lees. 8 9 10 11 12 13 14 15 Moment D Inertia. Section Modulus. Radii of Gyratic >n. I S r Neutral Neutral Neutral Neutral Neutral Neutral Sec- Axis Axis Axis Axis Axis Axis Least tion Parallel to Parallel to Parallel to Parallel to Paral'l to Paral'l to Radi- Index Longer Shorter Longer Shorter Longer Shorter us. Flange. Flange. Flange. Flange. Flange. Flange. 10.75 30.75 3.79 8.02 1.09 1.85 0.85 A 89 10.26 29.26 3.59 7.59 1.10 1.86 0.85 A 91 9.75 27.73 3.39 7.15 1.11 1.86 0.86 A160 9.23 26.15 3.18 6.70 1.11 1.87 0.86 A161 8.68 24.51 2.97 6.25 1.12 1.88 0.86 A 162 8.11 22.82 2.76 5.78 1.13 1.89 0.86 A 163 7.52 21.07 2.54 5.31 1.13 1.90 0.86 A 164 6.91 19.26 2.31 4.83 1.14 1.90 0.87 A165 6.27 17.40 2.08 4.33 1.15 1.91 0.87 A 166 5.60 15.46 1.85 3.83 1.16 1.92 0.87 A 167 4.90 13.47 1.60 3.32 1.17 1.93 0.88 A168 7.21 29.24 2.90 7.83 0.92 1.85 0.74 A 92 6.88 27.84 2.74 7.41 0.93 1.86 0.74 A 93 6.55 26.38 2.59 6.98 0.93 1.87 0.75 A169 6.20 24.89 2.43 6.55 0.94 1.88 0.75 A170 5.84 23.34 2.27 6.10 0.94 1.89 0.75 A171 5.47 21.74 2.11 5.65 0.95 1.89 0.75 A172 5.08 20.08 .94 5.19 0.96 1.90 0.75 A 173 4.67 18.37 .77 4.72 0.96 1.91 0.75 A 174 4.25 16.59 .59 4.24 0.97 1.92 0.76 A175 3.81 14,76 .41 3.75 0.98 1.93 0.76 A176 3.34 12.86 .23 3.25 0.99 1.94 0.77 A177 6.21 15.67 2.52 4.88 0.96 1.53 0.75 A187 5.89 14.81 2.37 4.58 0.97 1.54 0.75 A 188 5.55 13.92 2.22 4.28 0.98 1.55 0.75 A 189 5.20 12.99 2.06 3.97 0.98 1.56 0.75 A 190 4.83 12.03 1.90 3.65 0.99 1.56 0.75 A191 4.45 11.03 1.73 3.32 1.00 1.57 0.75 A 192 4.05 9.99 1.56 2.99 1.01 1.58 0.75 A193 3.63 8.90 1.39 2.64 1.01 1.59 0.76 A 194 3.18 7.78 1.21 2.29 1.02 1.60 0.76 A 195 2 72 6.60 1.02 1.94 1.03 1.61 0.76 A 96 3.'71 13.98 .74 4.45 0.80 1.55 0.64 A196 3.51 13.15 .63 4.16 0.80 1.55 0.64 A 197 3.29 12.28 .51 3.86 0.81 1.56 0.64 A 198 3.06 11.37 .39 3.55 0.82 1.57 0.64 A 199 2.83 10.43 .27 3.23 0.82 1.58 0.65 A200 2.58 9.45 .15 2.91 0.83 1.59 0.65 A201 2.32 8.43 .02 2.58 0.84 1.60 0.65 A202 2.04 7.37 0.89 2.24 0.84 1.61 0.65 A203 1.75 6.26 0.75 1.89 0.85 1.61 0.66 A280 60 REINFORCED CONCRETE. TABLE XXXII. PROPERTIES OF STANDARD CARNEGIE ANGLES. Angles with unequal legs. 1 2 3 4 5 6 7 Perpendicular Distance Section Size in Thickness in Weight Foot Area of Section in from Center of Gravity to Back of Flange. Index. Inches Inches. in Pounds. Square Inches. To Back of Longer To Back cl Shorter Flange. Flange. A220 4x3 u 17.1 5.03 0.94 .44 A221 4x3 I 16.0 4.69 0.92 .42 A222 4x3 IB 14.8 4.34 0.89 .39 A223 4x3 f 13.6 3.98 0.87 .37 A224 4x3 I 9 3 12.4 3.62 0.85 .35 A225 4x3 ^ 11.1 3.25 0.83 .33 A226 4x3 /3 9.8 2.87 0.80 .30 A227 4x3 1 8.5 2.48 0.78 . 28 A228 4x3 1 IS 7.2 2.09 0.76 .26 A229 33 x 3 u 15.8 4.62 0.98 .23 A230 3 x 3 i 14.7 4.31 0.96 .21 A231 3 x 3 18 13.6 4.00 0.94 .19 A232 x 3 I 12.5 3.67 0.92 .17 A233 si x 3 11.4 3.34 0.90 .15 A234 3: x 3 X 10.2 3.00 0.88 .13 A235 ft x 3 TR 9.1 2.65 0.85 .10 A236 x 3 7.9 2.30 0.83 .08 A237 3: x 3 13 6.6 1.93 0.81 .06 A238 3; x 2j 11 12.5 3.65 0.77 .27 A239 i x 2- | 11.5 3.36 0.75 .25 A240 3 x 2< IB 10.4 3.06 0.73 .23 A241 i x 2i I 9.4 2.75 0.70 .20 A242 8i x 2i T ? 8 8.3 2.43 0.68 .18 A243 8j X 2; | 7 2 2.11 0.66 .16 A244 3 x 2\ JL 6.1 1.78 0.64 .14 A245 3; i 4.9 1.44 0.61 .11 A252 3 x 23 I 9 8 9.5 2.78 0.77 .02 A253 3 x 2> i 8.5 2.50 0.75 .00 A254 3 x 2> A 7.6 2.22 0.73 0.98 A255 A256 A257 3 x % 3 x % 3x2; 1 6.6 5.6 4.5 1.92 1.62 1.31 0.71 0.68 0.66 0.96 0.93 0.91 A264 2* x 2 1 6.8 2.00 0.63 0.88 A265 2 x 2 6.1 1.78 0.60 0.85 A266 2J r x 2 1* 5.3 1.55 0.58 0.83 A267 2J x 2 T3 4.5 1.31 0.56 0.81 A268 2 r x 2 3.7 1.06 0.54 0.79 A269 r x 2 _ 2.8 0.81 0.51 0.76 MATERIALS AND MACHINES. 61 TABLE XXXII. (Continued). PROPERTIES OF STANDARD CARNEGIE ANGLES. Angles with unequal legs. 8 9 ^ 10 11 12 13 14 15 Moment c )f Inertia. Section Modulus. Radii of Gyratic n. I S r Neutral Neutral Neutral Neutral Neutral Neutral Sec- Axis Axis Axis Axis Axis Axis Least tion Parallel to Parallel to Parallel to Parallel to Paral'l to Paral'l to Radi- Index Longer Shorter Longer Shorter Longer Shorter us. Flange. Flange. Flange. Flange. Flange. - Flange. 3.47 7.34 1.68 2.87 0.83 .21 0.64 A220 3.28 6.93 1.57 2.68 0.84 .22 0.64 A221 3.08 6.49 1.46 2.49 0.84 .22 0.64 A222 2.87 6.03 1.35 2.30 0.85 .23 0.64 A223 2.66 5.55 1.23 2.09 0.86 .24 0.64 A224 2.42 5.02 1.12 1.89 0.86 .25 0.64 A225 2.18 4.52 0.99 1.68 0.87 .25 0.64 A226 1.92 3.96 0.87 1.46 1.88 .26 0.64 A227 1.65 3.38 0.74 1.23 0.89 .27 0.65 A228 3.33 4.98 1.65 2.20 0.85 1.04 0.62 A229 3.15 4.70 1.54 2.05 0.85 1.04 0.62 A230 2.96 4.41 1.44 1.91 0.86 1.05 0.62 A231 2.76 4.11 1.33 1.76 0.87 1.06 0.62 A232 2.55 3.79 1.21 1.61 0.87 1.07 0.62 A233 2.33 3.45 1.10 1.45 0.88 1.07 0.62 A234 2.09 3.10 0.98 1.29 0.89 1.08 0.62 A235 1.85 2.72 0.85 1.13 0.90 1.09 0.62 A236 1.58 2.33 0.72 96 0.90 1.10 0.63 A237 1.72 4.13 0.99 1.85 0.67 .06 0.53 A233 1.61 3.85 0.92 1.71 0.69 .07 0.53 A239 1.49 3.55 0.84 1.56 0.70 .08 0.53 A240 1.36 3.24 0.76 1.41 0.70 .09 0.53 A241 1.23 2.91 0.68 1.26 0.71 .09 0.54 A242 1.09 2.56 0.59 1.09 0.72 .10 0.54 A243 0.94 2.19 0.50 0.93 0.73 .11 0.54 A244 0.78 1.80 0.41 0.75 0.74 .12 0.54 A245 1.42 2.28 0.82 1.15 0.72 0.91 0.52 A252 1.30 2.08 0.74 1.04 0.72 0.91 0.52 A253 1.18 1.88 0.66 0.93 0.73 0.92 0.52 A254 1.04 1.66 0.58 0.81 0.74 0.93 0.52 A255 0.90 1.42 0.49 0.69 0.74 0.94 0.53 A256 0.74 1.17 0.40 0.56 0.75 0.95 0.53 A257 0.64 1.14 0.46 0.70 0.56 0.75 0.42 A264 0.58 1.03 0.41 0.62 0.57 0.76 0.42 A265 0.51 0.91 0.36 0.55 0.58 0.77 0.42 A266 0.45 0.79 0.31 0.47 0.58 0.78 0.42 A267 037 0.65 0.25 0.38 0.59 0.78 0.42 A268 0.29 0.51 0.20 0.29 0.60 0.79 0.43 A269 62 REINFORCED CONCRETE. TABLE XXXIII. PROPERTIES OF STANDARD CARNEGIE ANGLES. Angles with equal legs. 1 2 3 4 5 6 7 8 9 10 "o 60 & B - o "rtM 8 J3 c S3 3 j. .3 1*2 .1 .p >>>>- O i 1 | C I 'J3 5 * Jjjlig .33 l! |.al| *o o C H RT 33 l ^*j I ox2 $i 5.3 1.56 0.66 0.54 0.40 0.59 0.39 A57 x2 4.7 1.36 0.64 0.48 0.35 0.59 0.39 A58 i >x2 4.0 1.15 0.61 0.42 0.30 0.60 0.39 A59 \ 'x2 3.2 0.94 0.59 0.35 0.25 0.61 0.39 AGO ( x2 T8 2.5 0.72 0.57 0.28 0.19 0.62 0.40 A61 xl 7 4.6 1.30 0.59 0.35 0.30 0.51 0.33 AG2 xl V 4.0 1.17 0.57 0.31 0.26 0.51 0.34 A63 xl 6 3.4 1.00 0.55 0.27 0.23 0.52 0.34 A64 xl 1 2.8 0.81 0.53 0.23 0.19 0.53 0.34 A65 xl A 2.2 0.62 0.51 0.18 0.14 0.54 0.35 A66 xl 1 3.4 0.99 0.51 0.19 0.19 0.44 0.29 A67 xl ft 2.9 0.84 0.49 0.16 0.162 0.44 0.29 ACS xl I 2.4 0.69 0.47 0.14 0.134 0.45 0.29 AG9 xl 1.8 0.53 0.44 0.11 0.104 0.46 0.29 A 102 xl Y 1.3 0.36 0.42 0.08 0.070 0.46 0.30 A70 i xl T B B 2.4 0.69 0.42 0.09 0.109 0.36 0.23 A71 xl 1 2.0 0.56 0.40 0.077 0.091 0.37 0.24 A72 xl 1.5 0.43 0.38 0.061 0.071 0.38 0.24 A73 xl 1.1 0.30 0.35 0.044 0.049 0.38 0.25 A78 ] xl J 1.5 0.44 0.34 0.037 0.056 0.29 0.19 A79 ] xl A 1.2 0.34 0.32 0.030 0.044 0.30 0.19 A80 ] xl T 0.8 0.24 0.30 0.022 0.031 0.31 0.20 A83 X 0.9 0.25 0.26 0.012 0.024 0.22 0.16 A84 X 0.6 0.17 0.23 0.009 0.017 0.23 0.17 64 REINFORCED CONCRETE. TABLE XXXV. AREA AND CIRCUMFERENCE OF CIRCLES. Diameter, Area. Circumference Decimals of a foot. Ins. and fract'ns Ins and decimals. Decimals of a sq. ft. Sq. ins. decimals. Decimals of a foot. Ins. and decimals. .00260 .. .03125 .000005 .00077 .0082 .09818 .00521 i .0625 .000021 .00307 .0164 . 19635 .00781 & .09375 .000048 .00690 .0245 .29452 .01042 i .125 .000085 .01227 .0327 .39270 .01302 !5 6 Z .15625 .000133 .01917 .0409 .49087 .01562 .1875 .000192 .02761 .0491 .58905 .01823 A .21875 .000261 .03758 .0573 .68722 .02083 | .25 .000341 .04909 .0654 .78540 .02344 .28125 .000431 .06213 .0736 .88357 .02604 6 .3125 .000533 .07670 .0818 .98175 .02865 si .34375 .000644 .09281 .0900 1.0799 .03125 1 .375 .000767 .11045 .0982 1.1781 .03385 3 .40625 .000900 .12962 .1064 1.2763 .03646 TB .4375 .001044 .15033 .1145 1.3744 .03906 II .46875 .001198 .17257 .1227 1.4726 .04167 I .50 .001363 .19635 .1309 .5708 .04427 hi .53125 .001539 .22166 .1391 .6690 .04688 .5625 .001726 .24850 .1473 .7671 .04948 .59375 .001923 .27688 .1554 .8653 .05208 .625 .002130 .30680 .1636 .9635 .05469 H .65625 .002349 .33824 .1718 2.0617 .05729 || .6875 .002578 .37122 .1800 2.1598 .05990 .71875 .002817 .40574 .1882 2.2580 .06250 f .75 .003068 .44179 .1963 2.3562 .06510 .78125 .003329 .47937 2045 2.4544 .06771 13 .8125 .003604 .51849 .2127 2.5525 .07031 li .84375 .003883 .55914 .2209 2.6507 .07292 1 .875 .004176 .60132 .2291 2.7489 .07552 1 .90625 .004479 .64504 .2373 2.8471 .07813 TB .9375 .004793 .69029 .2454 2.9452 .08073 ii .96875 .005118 .73708 .2536 3.0434 .0833 1 .0000 .005454 .7854 .2618 3.1416 .0,859 A .03125 .005800 .8353 .2700 3.2398 . 0*885 X .0625 .006157 .8866 .2782 3.3379 .0911 .09375 .006524 .9396 .2863 3.4361 .0938 i .125 .006902 .9940 .2945 3.5343 .0964 /i .15625 .007291 .0500 .3027 3.6325 .0990 IB .1875 .007691 .1075 .3109 3.7306 .1016 g .21875 .008101 .1666 .3191 3.8288 .1042 1 .25 .008522 .2272 .3272 3.9270 .1068 3 9 Z .28125 .008953 .2893 .3354 4.0252 .1094 i 6 g .3125 .009395 .3530 .3436 4.1233 .1120 y .34375 .009848 .4182 .3518 4.2215 .1146 f .375 .010311 1.4849 .3600 4.3197 .1172 a .40625 .010785 1.5532 .3682 4.4179 .1198 .1224 a .4375 .46875 .011270 .012197 1.6230 1.6943 .3763 .3845 4.5160 4.6142 MATERIALS AND MACHINES. 65 TABLE XXXV. (Continued). AREA AND CIRCUMFERENCE OF CIRCLES. Diameter. Area. Circumference Decimals of a foot. Ins. and fract'ns In. and decimals. Decimals of a sq. ft. Sq. ins. decimals. Decimals of a foot. Ins. and decimals. .1250 n 1.50 .01227 1.7671 .3927 4.7124 .1276 ii 1.53125 .01279 1.8415 .4009 4.8106 .1302 T 9 B 1.5625 .01331 1.9175 .4091 4.9087 .1328 H 1.59375 .01385 1.9949 .4172 5.0069 .1354 f 1.625 .01440 2.0739 .4254 5.1051 .1380 H 1.G5625 .01493 2.1545 .4336 5.2033 .1406 \ l s 1.6875 .01553 2.2365 .4418 5.3014 .1432 ii 1.71875 .01611 2.3201 .4500 5.3996 .1458 1 1.75 .01670 2.4053 .4581 5.4978 .1484 1.78125 .01730 2.4920 .4663 5.5960 .1510 IB 1.8125 .01792 2.5802 .4745 5.6941 .1536 32 1.84375 .01854 2.9699 .4827 5.7923 .1563 J 1.875 .01917 2.7612 .4909 5.8905 .1589 HI 1.90625 .01982 2.8540 4991 5.9887 .1615 T8 1.9375 .02047 2.9483 .5072 6.0868 .1642 Ii 1.96875 .02114 3.0442 .5154 6.1850 .1667 2 2.00 .02182 3.1416 .5236 6.2832 .1719 TO 2.0625 .02320 3.3410 .5400 6.4795 .1771 2.125 .02463 3.5466 .5563 6.6759 .1823 1 3 B 2.1875 .02610 3.7583 .5727 6.8722 .1875 2.25 .02761 3.9761 .5890 7.0686 .1927 T B 3 2.3125 .02917 4.2000 .6054 7.2649 .1979 | 2.375 .03076 4.4301 .6218 7.4613 .2031 T ? 8 2.4375 .03240 4.6664 .6381 7.6576 .2083 i 2.50 .03409 4.9087 .6545 7.8540 .2135 T 9 B 2.5625 .03581 5.1572 .6709 8.0503 .2187 ? 2.625 .03758 5.4119 .6872 8.2467 .2240 2.6875 .03939 5.6727 .7036 8.4430 .2292 2.75 .04124 5.9396 .7199 8.6394 .2344 13 2.8125 .04314 6.2126 .7363 8.8357 .2396 J 2.875 .0^508 6.4918 .7527 9.0321 .2448 il 2.9375 .04706 6.7771 .7690 9.2284 .2503 3^ 3.00 .04908 7.0686 '.7854 9.4248 .2552 3.0625 .05115 7.3662 .8018 9.6211 .2o04 X 3.125 .05326 7.6699 .8181 .8175 .2856 3 3.1875 .0*541 7.9798 .8345 10.014 .2708 | 3.25 .05761 8.2958 .8508 10.210 .2760 fa 3.3125 .05984 8.6179 .8672 10.407 .2812 3.375 .06212 8.9462 .8836 10.603 .2865 T8 3.4375 .06444 9.2806 .8999 10.799 .2917 * 3.50 .06681 9.6211 .9163 10.996 .2969 3.5625 .06922 9.9678 .9327 11.192 .3021 3.625 .07167 10.321 .9490 11.388 .3073 u 3.6875 .07416 10.680 .9654 11.585 .3125 i 3.75 .07669 10.045 .9817 11.781 .3177 9 3.8125 .07927 11.416 .9981 11.977 .3229 1 3.875 .08189 11.793 1.0145 12.174 .3281 il 3.9375 .08456 12.177 1.0308 12.370 .3333 4 4.00 .08726 12.566 1.0472 12.566 66 REINFORCED CONCRETE. TABLE XXXVI. PROPERTIES OF VARIOUS SECTIONS. SECTION. Moment of Inertia. I Section Modulus _ 12 36 __ 12 ^ 0.0491J* 12 12 24 32 0.098 xx is the position of neutral axis. n and n' are the distances from the neutral axis to most remote fibers of the section; n being the greater. CHAPTER II. DESIGN AND CONSTRUCTION OF BUILDINGS. GENERAL DISCUSSION. Reinforced concrete is used for nearly every type of build- ing. The variety of designs employed is so great that the subject will be considered here in only a general way. In all designing it is necessary to figure on the strength at- tained by the concrete at the time the molds are removed. For instance, when molds must be removed in 48 hours, it is necessary to design a section that will have the requisite strength in 48 hours; where molds may remain for 28 days, early strength is not required. General Assumptions Made in Design. Before designing, certain assumptions must be made in order to eliminate some of the variables entering into reinforced concrete construc- tion. The assumptions usually made in the United States to date are as follows: (1) Sections plane before bending remain plane after bending, at least within the limit of elasticity of the steel. (2) Stresses in sections subjected to bending are com- puted assuming that elongations vary with the distance from the neutral axis. (3) The union between the steel and the concrete is suf- ficient to cause the two materials to act as one material, the unit value of adhesion being at least equal to the unit shear of concrete. (4) No initial strains are considered in either the con- crete or the steel due to change of volume of the concrete in setting. (5) The concrete takes up the compression, while the steel takes up the tension and assists in the resistance to shear. 67 68 REINFORCED CONCRETE. (6) The form of stress-strain curve of concrete in com- pression is, as a rule, assumed as a straight line. (7) Columns are designed for flexure, if the height ex- ceeds 18 times the least diameter. (8) The ratio of the modulus of elasticity of steel to that of concrete, which varies with the quality and bulk of the concrete, is generally assumed to be 10. Percentage of Steel Reinforcement. This varies accord- ing to construction, design, proportion in mixtures and is different in girders, floor slabs and columns, as will appear as each detail is treated. As a rule, p is a function of the ratio between the moduli of elasticity, the ratio of the actual stresses in the steel and in the concrete, and of the ratio between the unit costs of steel and concrete. A writer in Engineering News, June 20, 1907, sums up, in part, as fol- lows: (1) When a beam is strictly limited as to depth an over- reinforced beam is the cheapest. (2) When beams or slabs are not limited in dimensions by local conditions, the cheapest construction is that which is reinforced for the full utilization of both concrete and steel. These conditions are easily shown graphically in curves, giving the most economical percentage under dif- ferent assumptions. Thus, for the city of New York, with ~- = 12, f s = 16,000 and f c = 625, it is found that the most . ^ rt o -eS 1 -B I 5 + .il 72 'REINFORCED CONCRETE. inforced with steel wire, found that the steel, if calculated by the usual theories, attained in one case an apparent ten- sion of 250,000 Ibs. per sq. in. before rupture, thus showing the evident inaccuracies of present theories for continuous slabs. Hennebique* found by tests of floor slabs at the Paris Exposition that the bending moment at the middle of a slab continuous in both directions was less than s? 36' Meanwhile the building laws of New York permit the calculation of the bending moment of square floor plates, re- inforced in both directions and supported on four sides by the formula Wl . M B = ^it. Ibs. If the length of the slab exceeds 1.5 times its width the entire load should be carried by transverse reinforcement. Square slabs may well be reinforced in both directions. The following method is recognized to be faulty, but it is offered *s a tentative method which will give results on the safe side. The distribution of load is first to be determined by the formula r _ " in which r = proportion of load carried by the transverse reinforcement. / = length of slab b = breadth of slab For various ratios of the values of r are as follows: o 0.5 0.59 0.67 0.75 0.80 0.83 *Beton & Eisen, 1903, Heft I. BUILDING DESIGN AND CONSTRUCTION. 73 Using the values above specified each set of reinforce. ment is to be calculated in the same manner as slabs having supports on two sides only, but the total amount of rein- forcement thus determined may be reduced 25 per cent by gradually increasing the rod-spacing from the third point to the edge of the slab. Cross Reinforcement in Slabs. The author finds that steel rods parallel to the principal supports greatly increase the strength of the slab and render expansion joints unnec- essary. In fact, by using a wire fabric a "lateral continuity" is gained which causes the author to use these formulas when building codes will permit: wl 2 , M = -it. Ibs., and lo respectively, for slabs continuous over two supports and over four supports, for uniformly distributed loads, in calculating the middle of the slab, and tests have invariably proved that the dimensions resulting have been ample and safe. Shearing Provisions. There are two general methods of reinforcing against diagonal and shearing stresses which may be used singly or in combination. One of these consists in bending all, or part, of the longitudinal bars up toward the supports at various points. The other method involves the use of stirrups, either vertical or inclined, which should be attached to the main reinforcement. It is desirable, and, in fact, essential, in all beam work that some provision be made for web stresses; otherwise, if failure should occur, it would be sudden and without warn- ing. When the two systems of web reinforcement are used in combination the analysis becomes uncertain, and it is impossible to predicate the distribution of the stresses. We will, accordingly, consider ihe two methods separately. 74 REINFORCED CONCRETE. When bars are bent up at intervals near the supports, the inclined portions act as the diagonals of a truss, taking tension, and the stress carried is a function of the inclination. Adjacent diagonals should overlap sufficiently to insure "truss" action. It is necessary that the inclined bars have sufficient length of imbedment above the neutral axis to develop the requisite stress. Since the length of imbedment is necessarily limited, a bar with a strong mechanical bond is especially useful for such purposes. In this conception of the action occurring in the beam, all the bars are considered to act as a unit, owing to their rigid connection through the concrete, the bent-up bars acting as attached diagonals to the main member. Stirrups are generally used vertically, and we will consider only the case of vertical stirrups carried under the longi- tudinal bars and extending to the top of the beam. Assum- ing no tension in the concrete, or that this discussion applies only after the concrete is itself unable to resist the diagonal tensile stresses developed, we may say that the stress in any stirrup is equal to the variation in the total stress in the longitudinal reinforcement in the distance tributary to that stirrup. It is assumed that the stirrups carry only vertical stresses, all horizontal stresses being transferred to the lon- gitudinal bars through bond with the concrete. Vertical stirrups should be investigated for sufficiency of bond above the neutral axis of the beam, and owing to the short length of imbedment available, it will be desirable to use a me- chanical bond bar, if no form of anchorage is provided. Location of Stirrups in Beams. The newest theory re- garding diagonal cracks in beams attributes them to internal tension caused by a stretching and slipping of the rods em- ployed in the reinforcement. Theoretically, the stirrups should slope 45 away from the center of the beam, although for practical reasons they are frequently set vertically. BUILDING DESIGN AND CONSTRUCTION. 75 Mr. E. L. Ransome's empirical rule for spacing stirrups is to place the first a distance from the end of a beam cor- responding to one-quarter the depth of the beam, the second a distance of one-half the depth of the beam, beyond the first, the third a distance of three-quarters the depth of the beam beyond the second, and the fourth a distance of the depth of the beam beyond the third. Having found this rule very simple, practical and corresponding with calculations the author generally employs it. Total area of stirrups at one end of a beam b inches wide and / inches long (total span) is in square inches: a = 0.00074 bl if stirrups are inclined 45, and a = 0.00104 bl if stirrups are placed vertically. If one-half of the beam tension rods are bent up at the quarter point as is usual, sufficient stirrup area at each end of beam is found by using the first formula. These formulas are based upon a total shear at sup- port of A= 150 Ibs. per sq, in. bjd and a unit shear in concrete of not to exceed 50 Ibs. per sq. in. For concentrated loads the stirrups can be figured as for shear, the horizontal shear s being constant and approxi- n/ mately equal to the vertical shear divided by the depth d. 76 REINFORCED CONCRETE. In locating stirrups as in a plate girder* the simplest method is to draw the shear diagrams for concentrated and distributed loads. To determine the spacing, an area equal to the adhesion is subtracted from the shear diagram and the remaining area is divided into panels, giving each an area to correspond with the maximum shear allowed for each stirrup. As the height of the panels decreases, their length increases, giving a series of spaces representing graphically the spacing of the stirrup. Thus Fig. 31 represents the shear diagram of a beam with a uniform and a concentrated load- ing. The area above the line A B represents the shear due to the concentrated load P, and that below the line A B the shear due to the uniformly distributed load only consider- ing the portion of the shear diagram to the right of the cen- Fig. 31. Diagram for Locating Stirrups. ter line of the beam. Then if the area above the dotted line kl represents the allowable stress cared for by the adhesion of the rods, the portion of stress in the diagram below this line must be provided for by stirrups. If this be divided in equal areas, a, one for each stirrup, the horizontal dimen- sions of the trapezoids, a, will give graphically the desired stirrup spacing. Also see Shear, p. 227. Adhesion of Concrete to Steel. The adhesion of concrete to steel depends upon the richness of the concrete and has been found to reach 700 Ibs. per sq. in. Where the yield point of the steel is not exceeded, the minimum ultimate ad- hesion for first-class concrete may be placed at 275 Ibs. per sq. in., according to Mr. Paul Christophe, and for a shear- ing strength of concrete equal to 400 Ibs. per sq. in. this cor- *Reid, Concrete and Reinforced Concrete Construction, p. 311, BUILDING DESIGN AND CONSTRUCTION. 77 responds to a minimum clear distance between rods of about \ l /4 times the diameters of rods. Modulus of Elasticity. The modulus of elasticity or "the ratio between stress and strain" of steel varies from 28,000,000 to 31,000,000 Ibs. per sq. in., and 30,000,000 Ibs. is usually taken as an average value. The modulus of elas- ticity of concrete varies considerably, from 1,500,000 Ibs. per sq. in. to 5,000,000 Ibs. The following tabulation gives an idea of the variation as compared with different proportions: Broken stone or gravel concrete Proportions Modulus of Blast. Ibs. per sq. in. 1 li 3 12 4 12* 5 136 14 8 4,000,000 3,000,000 2,500,000 2,000,000 1.500,000 Cinder concrete 1 25 850,000 However, for graded mixtures considerably higher values may be found. The higher the modulus of elasticity of the concrete the lower should be the percentage of steel and the greater the depth of the beam for symmetrical design, maintaining fixed relations of pull in steel to pressure of concrete. Summary of Talbot's Tests on Tee Beams. From the summary of the discussion* referring to the theory of re- inforced concrete tee beams, the following is of particular in- terest to the designer: (1) Beams of flange width of 2, 3 and 4 times the width of stem or web and reinforced in each case with steel equal to 1 per cent of the inclosing rectangle (an imaginary rectan- gle as wide as the flange and as deep as the distance from the centroid of longitudinal metal reinforcement to most strained fiber in compression) exhibited in a common way the characteristics of rectangular beams, and the critical failure in every case came through the longitudinal reinforce- ment becoming stressed beyond its yield point. *Prof. A. N. Talbot, Bulletin Univ. of 111., Feb. 1, 1907. 78 REINFORCED CONCRETE. (2) The full compressive strength of the concrete at the most remote fiber was not developed at the yield point of the beam, even in the beams which were reinforced with steel of 54,000 Ibs. pr sqare inch yield point. (3) The vertical stirrups used proved to be very effective web reinforcement. The diagonal tension cracks appeared at or above loads at which failure by diagonal tension may be expected in beams without web reinforcement. A high resistance to diagonal tensile stresses was developed, as measured by the calculated maximum vertical shearing unit stress, which in one beam was 605 Ibs. per sq. in. Since no beam failed by diagonal tension, the limit of strength of the web reinforcement was not determined. (4) The maximum strength of tee beams to resist hori- zontal tension and compression (flange stresses) may well be calculated by using the ordinary methods and formulas in use for rectangular beams and considering the inclosing rectangle of the tee beam to. be the equivalent rectangular beam. This approximation is at least applicable for rein- forcement not exceeding 1 per cent of the inclosing rectan- gle. The effective width of a Tee beam should not exceed Y\ of span length of beam and its overhanging width on either side of the web should not exceed 4 times the thickness of the slab. FOUNDATIONS. Types of Foundations. The type of foundation for a building depends upon the weight of the proposed building and the character of the underlying soil. When the weight of the building has been estimated, the character of the soil will determine the form of foundation. Careful borings should be taken showing location of hard pan or the condi- tion of the different strata, their thickness and water-bearing qualities, which will determine whether piling, caissons, floats or rafts be required. The location and condition of adja- cent buildings must be considered, as their maintenance gen- erally devolves upon the contractor for the new structure. BUILDING DESIGN AND CONSTRUCTION. 79 As, however, these conditions and the selection of the foundations required must be met at any event, we shall only describe the most usual methods used in connection with reinforced concrete structures. Reinforced concrete foundations may be classified as pile, slab, raft, mat, and portable foundations. Bearing Power of Soils. The following tabulations, which are self-explanatory, are useful in connection with the designing of foundations; they show the bearing power of soils in tons per square foot: (From Baker's Masonry Construction.) Rock, the hardest, thick layers, in native bed 200 tons Rock, equal to the best ashlar masonry 25 to 30 tons Rock, equal to the best brick masonry 15 to 20 tons Rock, equal to poor brick masonry 5 to 10 tons Clay on thick beds, always dry 4 to 6 tons Clay on thick beds, moderately dry 2 to 4 tons Clay, soft 1 to 2 tons Gravel and coarse sand, well cemented 8 to 10 tons Sand, compact and well cemented 4 to 6 tons Sand, clean and dry 2 to 4 tons Quicksand, alluvial soils, etc 0.5 to 1 ton (From Building Code, National Board of Fire Underwriters.) Soft clay 1 ton per sq. ft. Clay and sand together, wet and springy 2 tons per sq. ft. Loam, clay, or fine sand, firm and dry 3 tons per sq. ft. Very firm coarse sand, stiff gravel or hard clay.. 4 tons per sq. ft Pile Foundations. Concrete piling offers many advan- tages which are not obtained with timber piling. Concrete piles of the same strength and bearing capacity need not be so long as those of wood, and they need not be so numer- ous. Timber piles, to prevent decay, must be cut off at mean low water, and the footings must be started from this point. With concrete piling, the tops can be left just far enough below the bottoms of the columns to allow for a footing thick enough to carry the superimposed building. Concrete piles are of two classes: (1) Piles molded in place, and (2) piles molded on the surface and driven after having become hard, as a timber pile is driven. The Ray- mond and Simplex piles, described here, belong to the first class and the Corrugated and Chenoweth piles belong to the second class. 80 REINFORCED CONCRETE. The Raymond Pile. This pile, controlled by the Ray- mond Concrete Pile Co., Chicago, is placed in the ground by the pile core method, which is as follows: A collapsible steel core, encased in a thin, closely fitting sheet steel shell, is driven by a pile driver to the required depth. Fig. 32. Raymond Collapsible Steel Core. Fig. 32 shows two views of this core, the view to the left showing the shell driver and the core expanded. The view to the right shows the pile core collapsed and ready to be drawn from BUILDING DESIGN AND CONSTRUCTION. 81 the shell. This shell, which is left in the ground, acts as a mold for the concrete, protecting it from back pressure, which would distort the pile, and from the admixture of foreign mat- ter, which would impair the bond of the concrete. An electric light can be lowered at intervals during the placing of the concrete, to enable the operator to see just what condition prevails. When reinforcement is desired, the reinforcing material is inserted in the shell before the placing of the concrete. The piles are tapered to obtain greater bearing value, since the load on a tapered pile is more uniformly distributed along the entire length. Fig. 32-A shows a comparison between wooden piles and concrete piles, where 22 wooden piles and an 8-ft. deep solid concrete pier were replaced by 8 concrete piles and two piers 5 ft. deep connected by an arch construction, An excellent example of the economy of concrete piles is given in the following extract of a report by Mr. Walter R. Harper, showing a comparison in cost of foundation with wooden piles and with Raymond piles in the Academic building at Annapolis : The difference in thickness of concrete footings is well illus- trated by a section of the footings of the academic building with wood piles and the same section as redesigned and built with concrete piles. This saving in excavation and footings depends upon the height of the building above mean low water. At the Naval Academy the rise and fall of the tide in the Severn river is very slight, consequently the buildings have been placed only a few feet above mean low water. Notwithstand- ing that the cost per linear foot for concrete piles far exceeds that of wood piles, being about four times as much, the saving in the entire foundation by their use will surprise the uninitiated, as will be seen by a glance at the cuts shown here. In the diagram, Fig. 32-B, the section E-F shows the footing of the connection between the library and academic building as designed by Mr. Flagg for wood piles. Another sketch shows the same section, G-H in the diagram as built with concrete piles. The depth of footing on this section was re- 82 REINFORCED CONCRETE. I BUILDING DESIGN AND CONSTRUCTION. 83 duced from 7 ft. to 2 ft. 8 ins., and the width on the bottom from 12 ft. 1 in. to 5 ft. 2 ins. The area of the cross-section was reduced from 58 to 12 sq. ft. In the plan of the wood piles under the library tower there are 202 piles in a rectangle 38 ft. 5% ins, square. The plan of the same tower foundation with 84 concrete piles has footings 8 ft. 2 ins. wide. ' < Tfmbtr Piles, With wood piles it will be noticed that the piles and foot- ings extend over the entire rectangle, while with concrete piles the piles and footings are only 8 ft. 2 ins. wide and directly under the walls of the tower. The depth of the footing was reduced by the use of concrete piles from 10 ft. 1% ins. to 4 ft. 1% ins. Twenty-seven 12-ins. 31^-lb. I-beams were done away with. The following reductions on the foundations of the two buildings were by the use of concrete piles: 2,193 wood piles were replaced by 885 concrete piles ; 4,542 yds. of .excavation were reduced to 1,038 yds., saving 3,504 yds., and 3,250 yds. of concrete footings were reduced to 986 yds., saving 2,264 yds. With wood piles, after excavating to mean low water, shor- ing and pumping would have been necessary in all trenches, and this saving was estimated at $4,000. A schedule of changes showing the saving by the use of concrete piles is given in the accompanying tabulation . The saving in the cost of foundations by the use of concrete piles was $27,458.18, or more than half of the original cost of the foundations, as designed with wood piles. 84 REINFORCED CONCRETE. COMPARATIVE COST OF WOOD AND CONCRETE PILES. Wood Piles. 2,193 piles at $9.50 $20,835.50 4,542 cu. yds. excavation at .40 1,816.80 3,250 cu. yds. concrete at 8.00 26,000.00 5,222 Ibs. I-beams at .04 208.88 Shoring and pumping 4,000.00 Total cost $52,861.18 Concrete Piles. 855 piles at $20.00 $17,100.00 1,038 cu. yds. excavation at .40 415.00 986 cu. yds. concrete at 8.00 7,888.00 Shoring and pumping Total cost $25,403.00 Difference in cost $27,458.18 The estimate of length of wood piles was taken from the length of wood piles driven in the marine engineering build- ing, a structure about 200 ft. from the library site. Wood piles would have been required 40 ft. in length at a cost of 20 cts. a foot, and would have been on an average driven 30 ft. below mean low water, which at 5 cts. a foot would mean an average cost of $9.50 per pile. For the estimate of excavations it was assumed that the en- tire site was at an elevation of 7 ft. above mean low water, which is an average of the existing conditions. The longest concrete pile driven was 29.7 ft., but owing to the solid nature of the soil at the southerly end of the library building, where shorter piles were used, the average length was 1C ft., and the cost of the concrete piles was taken at $20 per pile. The concrete pile selected was that of the Raymond Con- crete Pile Co., of Chicago. It is conical in shape, running from 6 ins. in diameter at the bottom to 20 ins. at the top. Owing to this conical shape the ground is compacted and a mucl: shorter pile can be used with this style than with a cylindrical pile. The difference in bearing power between a conical and a cylindrical pile was shown by an experiment tried on this work at the Naval Academy. A Raymond pile core tapered from 6 ins. at the point to 20 ins. at the head, was driven 19 ft. until the penetration under two blows from a 2,100-lb. hammer fall- ing 20 ft. was % in. A wood pile 9 1 / ins. at the point and 11 ins. at the head and having the same length, 19 ft., as the con- BUILDING DESIGN AND CONSTRUCTION. 85 ical pile, had a penetration of 5 5-16 ins. under two blows of the same hammer, falling 20 ft. This pile was driven after the concrete pile and about 2 ft. from it, thus showing the com- parative bearing power between a conical and a cylindrical pile of the same length. These piles of the Raymond style are driven by the use of a hollow steel core 6 ins. in diameter at the point and 20 ins. at the head. The cores used on this work were 20 and 30 ft. in length. The exterior pieces of the core are spread and held in place during the driving by a wedge device. The core is held in the leads of the pile driver by steel plates, fastened to its top, which form guides to slide in the leads. The top of the steel core is protected by a hardwood cap block, which sets in a cavity made for it. This block receives, the blow of the ham- mer and has to be renewed from time to time. The sheet-steel shells are formed on the work in an extra heavy cornice brake machine, and are made in 8-ft. sections with locked seams. The sections are telescoped, the point of the core is raised about 8 ft. and inserted in the smallest section, then the other sections are drawn up around the core by a line from the hoisting engine on the driver. Two drivers were used on the work at the Naval Academy, one with a 2,240-lb. drop hammer and the other a steam hammer of the Vulcan make, weighing 3,000 Ibs. The steam hammer was found more sat- isfactory, working much more rapidly. This was partly due to the fact that the steam hammer was mounted on a turn-table, and was able to turn in a circle by its own power. It was also provided with an extension top by which the core could be raised or lowered, if necessary, in a trench below the driver. The Simplex Pile. The Simplex pile, controlled by the Sim- plex Concrete Piling Co., Philadelphia, is constructed as follows : A wrought iron driving pipe of the diameter and length of the intended pile, and of sufficient strength to withstand driving, with a point made of cast iron or steel and a hardwood driving head which protects the pipe from injury during driving, is driven to a firm bearing, and the pipe is withdrawn and the hole filled with concrete. Fig. 33. 86 REINFORCED CONCRETE. A BUILDING DESIGN AND CONSTRUCTION. 87 The Corrugated Pile. The Corrugated Concrete Pile Co. of New York manufactures piles which are polygonal in section and are corrugated longitudinally like a fluted col- umn. Fig. 34. There is a hole extending the length of the pile, so that it can be driven by water jet, the water being forced down through the hole and returning along the cor- rugated sides. The Pedestal Pile is made by MacArthur Concrete Pile & Foundation Co., of New York, which claims a large carrying capacity for this pile on account of the fact, that, in addition to the fractional adhesion, there is a direct bearing power of a broad base resting in firm and compacted soil. The apparatus necessary to form the Pedestal Pile con- sists of a casing and a core. The casing is a steel pipe 16 ins. in diameter and ^ in. thick, with outside reinforcing bands top and bottom. The core is a smaller and longer pipe, with a cast steel point and an enlarged cast steel head. The core fits inside the casing, its enlarged head engaging the top of the casing and its lower pointed end projecting some 4 or 5 ft. below the casing. In the head of the core there is an oak driving block which receives the blows of the hammer. The core is fitted into the casing and both are driven into the ground to the desired depth. The core is then pulled out and a charge of concrete is dropped to the bottom of the casing. The rammer is now lowered into the casing and driven down through this con- crete, which thereby is driven into the soil below forming a bulb 3 ft. in diameter. 88 REINFORCED CONCRETE. The casing is then filled with concrete to the top and withdrawn. The Chenoweth Pile. This pile, shown in section by Fig. 35, is manufactured by Mr. A. C. Chenoweth, Brooklyn, N. Y., by spreading a layer of concrete on wire mesk and rolling both together by a special machine into a solid pile with a gas pipe core or center. Other Forms of Piles. Various patented forms of con- crete piles besides those mentioned above are on the mar- 'Reinfyrcement Fig. 34. Section of Corrugated Pile. Fig. 35. Chenoweth Pile. ket. In addition the builder is free to mold square, round or polygonal piles reinforced by longitudinal bars, hooping, etc., in practically any way desired, and such piles have been used in great numbers. Pile Driving. Concrete piles may be driven by jetting like timber piles, using exactly the same methods and ap- paratus. Concrete piles may also be driven by hammers, using pile drivers of the ordinary type, but equipped to handle the heavier concrete pile. Care is required in ham- mer driving. The pile must be maintained exactly in line with the direction of the hammer blow, a heavy hammer and a short drop must be employed, and the head of the pile BUILDING DESIGN AND CONSTRUCTION. 89 must be protected by a special cap to cushion the hammer blow. For a full discussion of the methods of molding and driv- ing concrete piles and for detailed costs of pile foundation work the reader is referred to "Concrete Construction Methods and Costs," by Gillette and Hill. Slab Foundations. Slab foundations are of two kinds, self-contained, rectangular slabs, and rafts, where two or more columns are supported on one slab so constructed that the center of gravity of the slab coincides with that of the superimposed loads in a manner to have the weight of the superstructure practically a constant on the underlying soil. Such foundations were designed by the author for the new Battle House, Mobile, Ala., the architects being Frank H. Andrews Co., Cincinnati, O. The advantages of connecting all separate footings by a reinforced concrete grillage are illustrated under Example of Building, page 141. For rectangular slabs, such as column foundations, the simplest construction is to run the reinforcement by diago- nals and squares, and after deducting the area of the col- umn base, to consider the remainder of the slab as eight cantilevers, four running parallel to the sides and four on the diagonals, assuming one-eighth of the load for each sec- tion, and calculating the reinforcement for each overhang as a uniformly loaded cantilever. A close approximation is found by selecting the size of rods and dividing the four outsides of the base into equal parts, as many as are re- quired to meet the steel area calculated, and draw in the rods accordingly. The diagonal rods will in this manner come closer together to compensate for their longer lever- age. The thickness of the slab is calculated to meet the compressive stresses, the same as in any beam, and the hori- zontal shear likewise. In most cases the horizontal shear will be taken care of by the concrete except for very heavy structures. As a rule, it is advisable to step off a column footing rather than to batter it, the steps conforming to the theoretical parabola, as shown 90 REINFORCED CONCRETE. by Fig. 36, owing to the saving in labor and the convenience in tamping, and the layers can be arranged to follow one another directly. Another method for piers is to stiffen the slabs by brackets on top, as was done in the foundations at the terminal station, Atlanta, Ga. Raft Foundations. To show the value of a raft founda- tion for treacherous soil, a brief description is here given of the foundation for the Co-operative Wholesale Society, Ltd., at Newcastle-on-Tyne, England. The building rises above the quay-level on which it abuts, and consists of base- ment, ground-floor and six upper fc-^j floors. The frontage is 92 ft. and the depth 125 ft. The subsoil was of the poorest quality for founda- tions, consisting of 18 ft. of made ground, principally clay, 18 ft. of silt and quicksand, 10 ft. of soft clay, 5 ft. of hard clay, 10 ft. of silty sand and finally gravel. The above stratification had a decided dip toward the river Tyne. To carry the enormous weight of the building, several plans for founda- tions were proposed. It was at first intended to construct the building of brick on a foundation of cylinders 6 ft. 6 ins. in diam- eter, sunk from 20 to 62 ft. below the ground level, carrying a sill of concrete 4 ft. thick reinforced with rails. Another alternative consid- ered was the driving of piles to the same depth, but the liability of injuring the adjoining property proved this method in- advisable. Finally, both these projects were abandoned and it was decided to construct a raft of reinforced concrete over the whole area of the ground. This raft, as constructed, measures 2 ft. 6 ins. in its thickest part and only 7 ins. in the \\\ XXxx 3 XXX \\ Fig. 36. Plan and Section of Column Footing. BUILDING DESIGN AND CONSTRUCTION. 91 thinnest part, as shown by Fig. 37. The entire site is di- vided up into rectangles measuring generally 14 ft. 8 ins. by 14 ft. 6 ins. Each side of these rectangles is a reinforced concrete beam 6 ft. 6 ins. deep by 2 ft. 5 ins. wide at the bottom, the reinforcement being according to the Henne- biqtie system. The steel reinforcement along the bottom of the mid- spans consists of ten 1^2-in. round rods. At the end of each beam half of the bars are carried up to the upper surface, this arrangement being a characteristic feature of the Hen- nebique system. Light steel stirrups also extend from around the bottom bars up to the upper surface, in the or- dinary manner, thus tying the concrete together in a ver- Fig. 37. Raft Foundation for Warehouse, Newcastle-on-Tyne, England. tical direction. The concrete floor filling in each rectangle is constructed on practically the same system; but the bars used are of much lighter section, being in some cases J^-in. and in others 24-in. in diameter. The columns which sup- port the upper floors are also of reinforced concrete. .They are placed at the corners of the foundation "squares." The reinforcement here is of 2-in. bars, which are carried right into the foundation. At higher levels, where the total load to be carried is naturally less, the reinforcement is, of course, much lighter, the weight of steel used and the size of the 92 REINFORCED CONCRETE. columns being accurately proportioned to the load to be carried. At the foundation level the columns measure 29 ins. square, and diminish to 8 ins. at the sixth floor. Thus, if settlement takes place, the entire building settles as a solid block, and therefore cannot suffer any deterioration from unequal settlement. In the particular case of this warehouse, there has been a settlement of 3 l /2 ins. at the front and of 3 ins. at the rear, which took place between the date of construction of the foundations and of the first floor. Since then no further settlement has taken place, nor is any anticipated. Mat Foundations. In this construction the building may be considered as turned upside down and the bearing power of the soil be considered as an evenly distributed load rest- ing on the columns, in a manner similar to that used by the author for the Cement Storage Elevator at South Chicago, 111., described on ' page 382 and following ; at the Battle House Hotel, Mobile, Ala. ; the brokers' office and ware- house building, in Kansas City, Mo.; and in the mushroom system of Mr. C. A. P. Turner, Minneapolis, illustrated by Fig. 55, p. 103. The mat should first be laid down, preferably a wire fabric, near the top of a 4-or 6-in. layer of concrete, and the regular slab foundation supported on and connected to it. This will tie all foundations together in a most effect- ive manner, will facilitate damp-proofing and, as a rule, prove an economical construction. Portable Foundations. Incidental to railroad construc- tion, a number of similar buildings are often erected along the line, such as small depots, water stations, tool sheds, corn cribs, coal trestles, semaphores, switch and signal struc- tures, etc., which require concrete foundations and where cement and aggregates must be shipped in by the railroad in too small quantities for economy and proper care-taking. In such cases portable foundations of reinforced concrete can be manufactured at a location on the line where sand and gravel are plentiful and where there can be a good cem- ent warehouse. These portable foundations are built of BUILDING DESIGN AND CONSTRUCTION. 93 one small top plate and one larger bottom plate, connected by diagonal ribs into the form of a truncated square pyramid and provided with holes and sockets for holding down bolts. The hole for the pier is dug as usual, the foundation lowered into position and steadied at the proper level, then the backfilling is washed in and tamped. Sand, being practically of the same weight as the concrete, will serve the same pur- pose, with the difference that only a small fraction of the material has been hauled from a distance. These plates and ribs should be made of a rich concrete about 1-4, with aggregates of maximum density, and reinforced with two layers of wire fabric in each plate or rib, with all vertical fabric tied to the horizontal where they join. Such structures can be moved without destroying the foundation or leaving TABLE XXXVII. FLOOR LOADS FOR BUILDINGS, IN POUNDS PER SQUARE FOOT. Bldg. Code CLASS OF BUILDINGS Nat'l Board of Fire New York 1906 Chicago 1905 Phila- delphia 1904 St. Louis San Fran- cisco Under- 1906 writers 1905 Dwellings, tenements, apart- ments fiats . ... 60 60 40 70 60 60 Hotels, lodging houses 60 60 50 70 60 Offices, all floors except first floor 75 75 50 100 70 75 Offices first floor 150 15 150 150 Schools 75 75 75 100 75 Stables and carriage houses 75 75 75 Public assembly ... . 90 90 100 120 100 125 Stores .... .... 120 120 100 120 120 Light manufacturing and 120 120 100 120 250 Heavy storage, warehouses. 150 150 100 150 150 250 or or Factories, manufacturing, more more 150 150 100 150 150 250 or or or or more more more more 94 REINFORCED CONCRETE. them, and in the author's opinion portable foundations will with the increase of manufactured articles in reinforced con- crete form a very considerable item. FLOORS. Floor Loads. The construction of reinforced concrete floors depends upon their purpose and the live loads that are to be supported, whether quiescent, moving or with im- pact. Different cities specify different loads for the several classes of buildings, as may be seen from Table XXXVII. All specifications should contain a condition or clause, stipulating, that the floor should be tested within a period of 90 days or more, for an actual load equal to twice the speci- fied floor load without any permanent deflection. This should be considered a very liberal condition and be insisted upon. Table XXXVIII shows the weight per cubic foot of va- rious substances, which are stored in warehouses. TABLE XXXVIli. WEIGHT* OF' VARIOUS SUBSTANCES STORED IN WAREHOUSES. Lbs. per cu. ft. Wheat 50 Beans, peas, etc 58 Flour in bulk 36 Preserved meats 35 Loose hay . 5 Baled hay 20 Loose straw 5 Paper in layers 80 Books in layers 58 Clothing in layers 43 Hardwood in layers 29 Coke 23 Coal 100 Loose snow 14 Tamped snow 58 Brick, Pressed ,,,.,,,,,,,.,,,.,,, 150 Brick, Common 125 Earth, Rammed 90-100 Granite 170 Granite Rubble Masonry 140 Granite Masonry, Well Dressed 165 Limestone 160-170 Limestone Rubble Masonry 165 Marble 170 Sandstone 145-150 BUILDING DESIGN AND CONSTRUCTION. 95 TABLE XXXVIII (Continued). Lbs. per cu. ft. Slate 175 Water (1 cu. ft. 7.48 U. S. gals.) 62 Vz Gravel 120 Sand, Dry 90-105 Mortar 100 Rock Concrete 150 Cinder Concrete 90 Plaster 140 Cast Iron 450 Steel 480 Paving Asphaltum 100 WEIGHT OF BRICK WALLS, PER SUPERFICIAL FOOT. 9-inch wall 84 Ibs. 13-inch wall. . ..121 Ibs. 22-inch wall 205 Ibs. 26-inch wall. . . .243 Ibs. 18-inch wall 168 Ibs. A bar of steel 1-inch square and 1 foot long weighs 3.40 Ibs. Factor of Safety. As a rule for floors, the factor of safety is taken as the dead load plus four times the live load, di- vided by the actual total floor load. Classification. A great number of floor constructions have developed both in Europe and in the United States. In general they belong to the following classes: (1) Slab Floors, running from girder to girder. (2) Beam Floors, with short span slabs. (3) Beam and Tile Floors with tiles between beams, making a flat ceiling. (4) Arched Floors, with or without cinder rilling. (5) Manufactured Floors, not made in situ. (6) Floors without Beams or Girders. Slab Floors. This is the simplest type of reinforced con- crete floor, and consists of a slab resting on I-beams, which may or may not be encased in concrete, and the slabs may be carried on either the top or the bottom flange of the beam, or -on both. In the second case, the space to the top of the beams may be filled with cinder concrete, and in the latter case, a cinder filling may be employed or the space left as an air space. The reinforcement may consist of wire fabric, expanded metal, or loose rods or wires inserted singly and tied. The first two are most used in America. The reinforcement may be placed along the lower part of 96 REINFORCED CONCRETE. the slab, may curve from the bottom of the slab at mid- spans to the top over the support, or two sets of reinforce- ment may be used, one in the upper and one in the lower part of the slab. Expanded metal floors are very extensively used in the United States, as they are easy to construct and are emi- nently satisfactory. Fig. 39 shows a common type of ex- Fig. 39. Expanded Metal Floor Slab. panded metal floor, with one of the beams left exposed, and the other protected by being encased in three reinforced slabs. The Columbian slab floor, illustrated by Fig. 40, is re- inforced with bars resembling a double cross in section, which are suspended from the top flange of the I-beam either Fig. 40. Columbian Slab Floor. by a hanger, which is shown by Fig. 41, or are riveted to the web of the beam, as shown by Fig. 40. Monier reinforcement, Fig. 42, is much used in Europe. It consists of carrying rods in the direction of the span and distributing rods of lighter weight crossing same, often with an additional trellis near the top surface of the slab. The BUILDING DESIGN AND CONSTRUCTION. 97 rods in each netting are tied together at intervals, usually with No. 18 annealed wire. The Cottancin system is similar to the Monier, bat the carry- ing and distributing rods are of the same size and are in- terlaced, as shown by Fig. 43. Fig. 41. Hanger for Columbian Bars. Fig. 42. Monier Slab Floor. Fig. 43. Cottancin Reinforcement. The Roebling slab floor is of many types, a common form being that illustrated by Fig. 44. The reinforcement is flat bars, which are bent at the beams so as to connect with the flange, as shown. Spacers supply the place of dis- BS "-Z * Flat Bar \'.t in Conerete\ ^ZxIShiptr Part Longitudinal Section. F/crf/ror? ' PaH- Plan. Fig. 44. Roebling Flat Slab Floor. tributing rods, and are fitted into slots in the bars. Spans may be constructed up to 16 ft. The Matrai system, Fig. 45, has wires suspended from fixed points and allowed to assume the form of catenary 98 REINFORCED CONCRETE. curves, the wires crossing diagonally as well as in series par- allel to both sides of the frame work. X si Fig. 45. Matrai Floor. In either of the above fabric systems, additional carry- ing rods and distributing rods are usually laid in to make BUILDING DESIGN AND CONSTRUCTION. 99 up for such steel areas as may be required over and above the section furnished by the manufactured article. Beam Floors. Beam floors are those in which the beams as well as the slabs are of reinforced concrete and are built in one piece with the slab. Constructions vary, but gener- ally the floor system consists of main girders carried by columns, intermediate beams or joists carried by the main girders and the covering floor slab in one piece with both beams and girders. Figure 46 shows a fairly typical beam floor. Fig. 46. Hennebique Floor with Single Reinforcement. The slab reinforcement may be of any of the forms de- scribed in the preceding section, and the girder reinforce- ment may be either loose rods or framed units. Several forms of unit frames for girder reinforcement are described in Chapter I. When loose rods are used the arrangement consists of straight and bent rods in some form of alterna- tion with, in many types of construction, vertical or inclined stirrups anchoring the straight rods up into the concrete above. 100 REINFORCED CONCRETE. Examples of beam floors showing variations without end are available, but only two are given here. Fig. 46 shows a beam floor of Hennebique construction, much used in Europe. Fig. 47 shows a Ransome floor reinforced with twisted square rods. The drawing shows a section of the floor built in the addition to the Pacific Coast Borax Fac- tory, Bayonne, N. J. The designed load is 100 Ibs. dead zb"-> *-J ____ $*-* X~~ '----M- ?$"* z u ~ Bars , a c K-fi?"* faW U^-L--J---!--! V Rods,!? Centers 8,-% Vertical Rods Intermediate Girder Typical Transverse , Floor Section net 'Walls ,, jU-Bar Section C-C. Fig. 47. Ransome Floor, Pacific Coast Borax Factory. load and 400 Ibs. uniformly distributed live load per square foot. It will be seen that two girders are used at the col- umns. These are separated by a plane of cleavage to allow for expansion. Beam and Tile Floors. In beam and tile floors the tiles act primarily as forms or scaffold and are placed from on "'* &.*??' Fig. 48. Beam and Tile Floor with Kahn Bars. 3 to 5 ins. apart, the reinforced concrete beams occupying the space between the tiles, a 2 to 4-in. slab being laid on top connecting the beams laterally. The reinforcement of the beams between the tiles may be any that is employed for beam floors. Such a floor is light in weight, the air spaces serving to deaden sound. Fig. 48 shows this type of floor BUILDING DESIGN 4ND CONSTRUCTION 101 using the Kahn bar as reinforcement, and Fig. 49 shows a combination type employed by the National Fireproofing Co. of Chicago. Arch Floors. In arched floors the different fabrics are em- ployed as for slab floors and are usually laid between struc- tural steel girders or beams. A flat ceiling is obtained by sus- pending metal lathing from beam to beam and plastering. A Roebling arch floor, with both flat and curved ceilings, is shown by Fig. 50. a\ X> II Fig. 49 Beam and Tile Floor, National Fireproofing Co. The Wuensch arch floor, Fig. 51, is reinforced with angle or tee-iron riveted to the I-beams. This gives a very strong floor. Oak Flooring^ y Spruce Flooring .5*4 Steepens, l?"C,ti?C. Fig. 50. Roebling Arch Floor. The Monier arch Ho or is reinforced with Mor.ier netting, either one or two sets of netting being employed. A very heavy floor is obtained by placing the upper netting in an Fig. 51. Wuensch Arch Floor. arch, and filling to a flat top with lean concrete. Fig. 52 shows both the single and the double arch construction. 102 REINFORCED CONCRETE. Manufactured Floors. Among manufactured floors a great number of varieties have appeared abroad and are gradually gaming ground in the United States. The Siegiwri system, Fig. 53, consists of a hollow beam reinforced by round rods, its top face forming the floor slab, and its bottom face the ceiling. The sections are 10 ins. wide with corrugated sides and the spaces are filled with Fig-. 52. Single and Double Arch Monier Floor. mortar. These floors cost from 15 to 20 cts. per square foot, according to span and load. The Visintini system, Fig. 54, is also used in the con- struction of floors and roofs and consists of shallow beams molded in advance. Floors are made up of a series of these beams placed side by side, usually 6 to 12 ins. wide and 6 Fig. 53. Siegwart Hollow Beam. Fig-. 54. Visintini Beams. to 8 ins. in depth. In appearance they are Warren trusses with no reinforcement for the web members which are stressed in compression. For deep trusses spanning from column to column and supporting the floor slabs usually Pratt trusses are used, where the verticals are in compres- sion and not reinforced. The fact that a manufactured floor can be dismantled without complete destruction, and besides can be manufac- BUILDING DESIGN AND CONSTRUCTION. 103 tured under roof at any time and erected rapidly with a great saving in scaffolding and labor, will doubtless before long bring this construction prominently before owners and con- tractors. Floors Without Beams or Girders. Floors without beams or girders are illustrated by the "mushroom" system, which Fig. 55. Floor Slab Reinforcement, Mushroom System. is an adaptation of the Matrai system, excluding beams or girders, the reinforcing elbow rod of the head of the col- umns being curved out to receive a large floor area directly. This system is patented by Mr. C. A. P. Turner, Minneapo- lis, Minn. The columns are octagonal or cylindrical, and the floor panels are built up to 24x24 ft., or 26x26 ft. The floor 104 REINFORCED CONCRETE. loads sustained are from 200 to 1,000 Ibs. per sq. ft. Fig. 55 shows the floor and column reinforcement. Fig. 55-A. Head Reinforcement and Plan of Basket. The Umbrella Flat-Slab System is a style of reinforcement for concrete columns and building floors recently devised by Mr. W. P. Cowles, of Minneapolis, Minn. As indicated in the accompanying drawing, it consists essentially of a con- ical-shaped column cap, enclosing a system of reinforce- ment which extends' partly into the floor slab. The latter is without beams or girders and is reinforced with rods running from each column to each of the eight on the sides of the square of which it forms the center. The columns are continuous and have a telescope splice in the umbrella head, which has triple-hooping reinforce- ment, insuring, it is claimed, that the load from the column above is transmitted to the center of the column below, thus preventing eccentric loading. In addition to the tension or slab rods, cantilever compression rods are provided and are distributed so as to strengthen the concrete in compression BUILDING DESIGN AND CONSTRUCTION. 105 at the perimeter of the umbrella head. Incidentally they tend to reinforce the slab at this point in shear, and to re- strain the concrete at the bottom of that portion of the slab forming the top of the umbrella head. They lie directly be- neath the tension or slab rods. The umbrella basket is designed to reinforce the head in shear and also to restrain the concrete forming the column cap. This basket can be assembled and spirally wound at the shop by machine. Fig. 55-B. Fig. 55-C. Elevation of Column and Plan of Slab Reinforcement. 106 REINFORCED CONCRETE. The Heidenreich Flat-Slab System employs metal fabric exclusively instead of loose rods, the compression and shear above the supports being met with double reinforcing, the compression reinforcement at the underside of the slab above supports being tied to the tension reinforcement in the top of the slab. These reinforcing bands of fabric run rectangularly and diagonally over the columns and in one length from end to end or side to side of the building, thus obviating splices, and the use of fabric insures a greater lateral continuity than does the use of loose rods, and also greater safety in the correct placing of the steel. When we add, that the combined thickness of the four unspliced bands above the columns, is approximately one- eighth of the jcombined thickness of the spliced loose rods, the added value of / d more than makes up for the higher pound cost of the fabric reinforcement. Calculation of Slabs. The tables for calculation of floors and beams closely conform to the theory developed by Prof. A. N. Talbot*, and have been adapted to such ratio of moduli of elasticity and permissible stresses as have been adopted by New York building regulations. Other tables show results for richer concrete and other unit stresses, also other ratio of moduli permissible under such conditions. The table based upon the parabolic stress-line deformation is given for comparison. f "Test of Reinforced Concrete Tee Beams, Univ. of 111. Bul- letin, Feb. 1, 1907. tSee also Taylor & Thompson, "Concrete, Plain and Re- inforced." BUILDING DESIGN AND CONSTRUCTION. 107 Notation: b = breadth of flange or tee-beam in inches d = distance from the compressive face to the center of the metal reinforcement h = thickness of beam or slab p = ratio of area of metal reinforcement to area of in- closing rectangle above center of reinforcement ."3 = modulus of elasticity of the steel EC. initial modulus of elasticity of concrete in compres- sion n = jr"** ratio of moduli of elasticity of steel and con- crete f s = tensile stress per sq. in. in metal reinforcement f c compressive stress per sq. in. in compression face of concrete at most remote fiber v horizontal shearing stress per sq. in. in concrete fc= ratio of distanced between compressive face and neu- tral axis to distance d M c = resisting moment of concrete M resisting moment of metal reinforcement A" c , A" s and A" v are constants, varying in direct proportion with y^., fs, and v 138 REW FORCED CONCRETE. K = the smaller of the two values A" c and A" s V = safe vertical shear at a given section in Ibs. M - safe bending moment at a given section in inch Ibs. M = Kbd? (6) F= KJd (7) K v = v(\ Y 3 k} (8) Straight Line Formula. (See Fig. 56.) I. Rectangular Beams. Fig. 56. Rectangular Line Diagram. k 7 = 13- _ M fs ~ pjbd* 2M jkbd* P = P = Area of steel bd np -f) (l 3") fc (9) (11) BUILDING DESIGN AND CONSTRUCTION. 109 K c = f c k l (12) (13) (14) K = the smaller of the two values K c and K s Table XXXIX gives values of K for various proportions of steel used in designing concrete beams, slabs, etc. TABLE XXXIX. VALUES OF K FOR VARIOUS PROPORTIONS OF STEEL USED, WHEN ft = 500 ; AND rt=16,000. = 12. p * -1 Kc K, K k '-I Kc #8 K .001 .143 .952 35.8 15.2 15.2 .158 .947 37.6 15.2 15.2 .002 .196 .935 45.8 29.9 29.9 .215 .928 50.0 29.6 29.6 .003 .235 .922 54.2 44.3 44.3 .258 .914 58.9 43.8 43.8 .004 .266 .911 60.2 58.4 58.4 .291 .903 65.8 57.8 57.8 .005 .291 .903 65.8 72.2 65.8 .319 .894 71.2 71.4 71.2 .006 .314 .896 70.3 86.0 70.3 .343 .885 76.2 84.8 76.2 .007 .334 .889 74.2 99.5 74.2 .366 .878 80.3 98.6 80.3 .008 .352 .883 77.7 113.0 77.7 .384 .872 83.8 111.7 83.8 .009 .370 .877 81.1 126.1 81.1 .401 .866 86.9 124.7 86.9 .010 .384 .872 83.8 139.8 83.8 .417 .861 90.0 137.8 90.0 .011 .398 .867 86.4 152.5 86.4 .432 .856 92.4 150.6 92.4 .012 .411 .863 88.8 166. 88.8 .444 .852 94.8 163.8 94.8 .014 .435 .855 93.0 192. 93.0 .470 .843 99.1 188.5 99.1 .016 .456 .848 96.7 217. 96.7 .492 .836 103.0 214.0 103.0 .018 .476 .841 100.0 243. 100. .513 .829 106.0 238.3 106.0 .020 .493 .836 103. 267. 103. .530 .823 108.8 263.2 108.8 .030 .561 .813 114. 390. 114. .600 .800 120.0 384. 120.0 .040 .610 .796 122. 510. 122. .650 .784 127.6 502. 127.6 .050 .650 .783 127. 628. 127. .680 .774 131.8 620. 128.2 n=15. 110 REINFORCED CONCRETE. When high carbon steel is used as a reinforcement with a rich concrete, we may assume/ s = 20,000 and/ c =750. Table XL uses these values. The selection of the vaiue of n depends upon the bulk of the concrete as E c assumes a higher value for light constructions than for heavy ones. TABLE XL. VALUES OF K FOR VARIOUS PROPORTIONS OF STEEL USED WHEN /c = 750, AND / = 20,000. =12 n=15 P k '-i K 9 K s K k . * 3 k K s K .001 .145 92.5 53.7 19.1 19.1 .158 94.7 56.4 19.1 19.1 .002 .196 93.5 88.6 37.4 37.4 .215 92.8 75.0 37.1 37.1 .003 .235 92.2 8L2 55.3 55.3 .258 91.4 88.4 54.8 54.8 .004 .266 91.1 90.3 72.9 72.9 .291 90.3 98.7 72.2 72.2 .005 .291 90.3 98.7 90.3 90.3 .319 89.4 106.8 89.4 89.4 .006 .314 89.6 105.4 107.5 105.4 .343 88.5 114.3 106.2 106.2 .007 .334 88.9 111.3 124.5 111.3 .366 87.8 120.4 122.9 120.4 .008 .352 88.3 116.5 141.2 116.5 .384 87.2 125.7 139.5 125.7 .009 .370 87.7 121.6 157.9 121.6 .401 86.6 130.3 155.9 130.3 .010 .384 87.2 125.7 174.4 125.7 .417 86.1 135.0 172.2 135.0 .011 .398 86.7 129.6 190.7 129.6 .432 85.6 138.6 188.3 138.6 .012 .411 86.3 133.2 207.1 133.2 .444 85.2 142.2 204.5 142.2 .014 .435 85.5 139.5 239.4 139.5 .470 84.3 148.6 235.6 148.6 .016 .456 84.8 145.0 271.4 145.0 .492 83.6 154.5 267.6 154.5 .018 .476 84.1 150.0 302.8 150.0 .413 82.9 159.0 298.4 159.0 .020 .493 83.6 154.5 334.4 154.5 .530 82.3 163.2 329.2 163.2 .030 .561 81.3 171. 487.8 171. .600 80.0 180.0 480. 180.0 .040 .610 79.6 183. 636.8 183. .650 78.4 191.4 627. 191.4 .050 .650 78.3 190. 783.0 190. .680 77.4 197.7 774. 197.7 For bulky concrete constructions, such as bridge abutments or very heavy slab floors, E G has a lower value and in such cases we make n = 20 or even more. Table XLI is calculated for these conditions. BUILDING DESIGN AND CONSTRUCTION. Ill TABLE XLI. VALUES OF K FOR VARIOUS PROPORTIONS OF STEEL USED WHERE C=700, AND /= 16,000. =10 =20 p k "4 K c K s K k '-f K c K s K .001 .132 .956 44.2 15.3 15.3 .181 .879 55.7 14.06 14.06 .002 .190 .937 62.3 30.0 30.0 .246 .836 72.0 26.8 26.8 .003 .217 .928 70.5 44.6 44.6 .292 .805 82.3 38.6 38,6 .004 .246 .918 79.0 58.8 58.8 .328 .781 89.7 50.0 50.0 .005 .270 .910 86.0 72.8 72.8 .358 .761 95.4 60.9 60.9 .006 .292 .903 92.3 86.7 86.7 .384 .744 100.0 71.4 71.4 .007 .311 .896 97.5 100.4 97.5 .407 .729 103.8 81.6 81.6 .008 .328 .890 102.2 113.9 102.2 428 .715 108.1 91.5 91.5 .009 .344 .885 106.6 127.4 106.6 .447 .702 109.8 101.1 101.1 .010 .358 .881 110.4 140.9 110.4 .463 .691 112.0 110.6 110.6 .011 .372 .876 114.1 154.2 114.1 .479 .681 114.2 119.9 114.2 .012 .384 .872 117.2 167.4 117.2 .493 .671 115.8 128.8 115.8 .014 .389 .870 118.5 194.9 118.5 .519 .654 118.8 146.5 11-8.8 .016 .428 .857 128.4 219.4 128.4 .542 .639 121.2 163.6 121.2 .018 .446 .851 132.8 245.1 132.8 .562 .625 122.9 180.0 122.9 .020 .463 .846 137.1 270.7 137.1 .580 .613 124.4 196.2 124.4 .030 .531 .823 153.0 395.0 153.0 .65 .567 129.0 272.2 129.0 .040 .580 .807 163.8 516.5 163.8 .70 .534 130.8 341.8 130.8 .050 .618 .794 171.7 635.2 171.7 .73 .514 131.3 411.2 131.3 56-A. T-Beams. 56-B. T-Beams. 112 REINFORCED CONCRETE. AS = total net area of reinforcement. Case I. When the neutral axis lies in the flange: use the formulas for rectangular beams. Case II. When the neutral axis lies in the stem: the fol- lowing formulas neglect the compression in the stem: Position of neutral axis: 2ndAs -f bt* Position of resultant compression Zkd 2, = 2kd-t ~ 3 Arm of resisting couple id = dz Fibre stresses M Mkd f* k fc ~ bt(kdy*f)jd ~ n k\ (For approximate results the formulas for rectangular beams may be used.) BUILDING DESIGN AND CONSTRUCTION. 113 The following formulas take into account the compres- sion in the stem; they are recommended where the flange is small compared with the stem. Position of neutral axis kd-- V + (b-b'} nA & +(b b'} A 2 nA s + (bb'} t Position of resultant compression Arm of resisting couple jd = dz Fibre stresses M 2Mkd J * ~ AJd ~ [ (2kdt III. Beams Reinforced for Compression. Fig. 56-C. Beams Reinforced for Compression. Position of neutral axis k- 114 REINFORCED CONCRETE. where p'= steel ratio for compressive steel d ' = depth to center of compressive steel f a = compressive unit in steel C= total compressive stress in concrete C'= total compressive stress in steel z= depth to resultant of C and C' A' s = area of compressive steel Position of resultant compression 2 = Arm of resisting couple Fibre stresses 6M Ic = M k-* f s ' = nf c * d IV. Shear Bond and Web Reinforcement. In the follow- ing, 2 refers only to the bars constituting the tension re- inforcement at the section in question and jd is the lever arm of the resisting couple at the section. For rectangular beam V bjd V BUILDING DESIGN AND CONSTRUCTION. 115 where F = total shear v = shearing unit stress u = bond stress per unit area of bar o = circumference or perimeter of bar 28+. 02320 6X149200+32500 I) .0906,^ 6,/2 8" 34 6X.1646+. 02320 &/U93300+34800 .0886,Z6,/2 36 6X.1928+. 02320 &,(243000+37200 I) .0876,Z 6,/2 38 6,(. 2224+. 02320 6X299000+39500 .0866,? 6,/2 40 b,(. 2526+. 02320 6X361000+41800 .0866,Z 6,/2 42 6X.2820+. 02320 6X426500+44200 .0856,Z6,/2 44 6X.3130+. 02320 6, (500000+46500 .0856,Z 6,/2 46 6X.3430+.0232Z) 6X578000+48750 I) .0846,Z 6,72 48 6X.3760+. 02320 6X664000+51100 .0846,i-6,/2 Parabolic Line Formula. Assumptions for New York. (See Fig. 57.) Fig. 57. Parabolic Line Diagram. BUILDING DESIGN AND CONSTRUCTION. 119 500 Ibs. per sq. in. 50 Ibs. per sq. in. 16,000 Ibs. per sq. in. 10 K A v pn) (15) (16) (17) (18) (19) Pft (1 f^) (20) the smaller of the two values A"c and AS z/(l f) (21) TABLE XLII VALUES OF K FOR VARIOUS PROPORTIONS OF STEEL USED WHEN /c=500 AND /=16,000. p k H* K c K s K ** .001 .115 .954 36.6 15.3 15.3 47.7 .002 .159 .936 49.6 30.0 30.0 46.8 .003 .191 .924 58.7 44.3 44.3 46.2 .004 .217 .913 66.0 58.3 58.3 45.6 .005 .239 .904 72.0 72.4 72.0 45.2 .006 .258 .897 77.2 86. 77.2 44.8 .007 .276 .890 81.8 99. 81.8 44.5 .008 .292 .883 85.9 113. 85.9 44.2 .009 .306 .878 89.5 126. 89.5 43.9 .010 .320 .872 92.9 139. 92.9 43.6 .012 .344 .862 98.8 165.6 98.8 43. * .014 .365 .854 103.9 191.3 103.9 42.7 .016 .384 .846 108.4 216.6 108.4 42.3 .018 .402 .839 112.4 241.7 112.4 42.0 .020 .418 .833 116.0 266.5 116.0 41.6 .030 .483 .807 129.8 387.4 129.8 40 4 .040 .631 .788 139.3 504.2 139.3 39.4 .060 .669 .772 146.4 618.0 146.4 38.6 120 REINFORCED CONCRETE. TABLE XLIII. VALUES OP K FOR VARIOUS PROPORTIONS OP STEEL USED WHEN f*=750. a=75, /-aO.OOO. n=12 M=15 P k '-!* K c K a K *v k -I* K c K 3 K ^v .001 .125 .950 57.2 19.0 19.0 71.2 .137 .945 64.7 18.9 18.9 70.9 .002 .173 .931 80.5 37.2 37.2 69.8 .161 .936 75.3 37.4 37.4 70.2 .003 .207 .917 94.5 55.0 55.0 68.8 .228 .909 103.6 54.5 54.5 68.2 .004 .235 .906 106.0 72.5 72.5 67.9 .258 .897 115.7 71.8 71.8 67.3 .005 .258 .897 115.7 89.7 89.7 67.3 .284 .886 125.8 88.6 88.6 66.4 .006 .279 .888 123.4 106.6 106.6 66.6 .308 .877 135.0 105.2 105.2 65.8 .007 .297 .881 130.4 123.3 123.3 66.1 .326 .870 141.8 121.8 121.8 65.2 .008 .314 .874 137.2 139.8 137.2 65.5 .342 .863 147.6 138.1 138.1 64.7 .009 .329 .868 142.4 156.2 142.4 65.1 .360 .856 154.1 154.1 154.1 64.2 .010 .344 .862 148.3 172.4 148.3 64.6 .375 .850 159.4 170.0 159.4 63.7 .012 .369 .852 156.8 204.5 156.8 63.9 .402 .839 168.7 201.4 168.7 62.9 .014 .392 .843 165.2 236.0 165.2 J63.2 .425 .830 176.4 232.4 176.4 62.2 .016 .412 .835 172.0 267.2 172.0 62.6 .446 .822 183.3 253.0 183.3 61.6 .018 .430 .828 178.0 298.1 178.0 62.1 .465 .814 189.3 293.0 189.3 61.0 .020 .446 .822 183.3 328.8 183.3 61.6 .482 .807 194.5 322.8 194.5 60.5 .030 .513 .795 203.5 477.0 203.5 59.6 .551 .780 214.5 468. 214.5 58.5 .040 .562 .775 217.8 620.0 217.8 58.1 .600 .760 228.0 608. 228.0 57.0 .050 .599 .760 228.0 760.0 228.0 57.0 .638 .745 237.6 745. 237.6 55.8 Maximum Bending Moment in Slabs. In Table XLIV, giving maximum bending moment in slabs according to straight line formula, the assumptions are: / c =500 Ibs. per sq. in. n = 12. Fireproofing 1 in. in thousands of in. Ibs. BUILDING DESIGN AND CONSTRUCTION. 121 TABLE XLIV. MAXIMUM BENDING MOMENTS IN SLABS ACCORDING TO STRAIGHT LINE FORMULA. Steel Sizes. Slab Sizes in inches. Diameter in ins. Spacing in ins. 3 3* 4 41 5 5i 6 H 1 1 1 1 1 6 5 4 6 5 4 3 2J 5 4 3 n 6 5 4 3 M 6 5 4 3 6 5 4 6 5 4 2.8 3.2 3.4 3.4 3.8 4.0 4.3 4.6 3.9 4.2 4.4 3.6 4.4 5.0 5.0 5.4 5.8 6.3 6.8 5.6 6.1 6.5 7.0 7.5 6.3 6.7 7.2 7.7 4.3 5.4 6.2 6.3 7.3 8.0 8.7 9.2 7.7 8.3 8.8 9.6 10.2 8.6 9.1 9.6 10.6 5.2 6.2 7.3 7.4 9.0 10.2 11.2 11.9. 10.0 10.6 11.4 12.7 13.4 10.9 11.9 12.6 13.7 14.7 9.0 11.1 12.4 13.8 14.9 12.4 13.3 14.1 15.5 16.5 13.7 14.8 15.8 17.2 18.4 15.0 16.1 17.1 9.7 12.5 14.7 16.8 18.0 14.4 15.6 17.3 18.9 20.4 16.9 18.0 19.2 21.0 22.4 18.1 19.6 21.0 22.9 16.9 20.2 21.2 15.5 18.4 20.7 22.6 24.5 20.0 21.2 22.8 25.1 26.8 21.7 23.4 25.0 27.2 23.5 25.5 26.8 18.0 21.8 24.4 26.2 28.0 23.1 24.6 26.7 29.5 31.7 25.4 27.2 29.0 31.8 27.3 30.5 31.7 39.2 31.8 33.3 The American Wire Fence Co., Chicago, who control the Ameri- can system of reinforcing, have designed and executed a large number of buildings, basing their floor slab dimensions on Table XLTV, in which the following assumptions are made: (1) One layer of 4xl2-in. mesh high-carbon fabric of No. 5 carrying wires and No. 11 distributing wires. (2) High carbon steel rods in addition to the fabric where shown. (3) A 1 to 6 graded mixture of Portland cement, sand and peb- bles or hard stone crushed to pass through a %-in. mesh screen, proportioned to give a maximum density (see page 21.) (4) All spans continuous in one direction. Example. For a 9-ft. span with a live load of 150 Ibs. per sq. ft. over and above the dead load we require one layer of fabric and a /4-in. rods spaced G 1 ^ ins. on centers in a 4-in. slab. 122 REINFORCED CONCRETE. g *^7 00 CO 0510 1 05UT3 o? 1 ^ Sj. 00 s* 2l s i 7 ? > 05^5 cT 1 """ 27 OCO T-l 1 oo H CO? Hn "1 "1 w ! *- > * 05 J 07 * 05 H 1-H "=7 J. ^Jw ffl 1 ^'i 1-1 *e to s i CO>O 1 **! t^oo ^Jc, *i' oo i HN 0500 "*-J^ s 05 >O I 1 Hn -? -I ^i -1 CO OO I 1 . 2 He* oo "3 1 i 5l *i .* t^J^ w^. g, Hn <* .s H ^7 ""J. "'nL CO , I S CO 1 1005 njo> s? 5? mjoo *z *1 1 2 eo^ 1 "I HM*** 1 mfoo >o ,*4c* CO-H J. 1 s? H> Hn H^T 05 "3 1 f 00 who -^S 1 CO CO 1 05 "I oo COr-H 1 eo'J' ? ,s S? ^7 1OOO -*.'** 00 O "1 o -1 W 7 CO^ x ^ "I -? IOC35* 1 u s ^ "1 - 03 CCCj, 7 co ! 5 ^V to _o 45 "1 "1 -i "1 ro i CO(M -7 O5 h ^ II 11 spacing of rods. Slab thickness. Reinforcement Slab thickness Reinforcement Slab thickness Reinforcement Slab thickness Reinforcement Slab thickness Reinforcement Slab thickness Reinforcement Slab thickness Reinforcement Slab thickness Reinforcement Slab thickness Reinforcement |l-s &1 o 3 US >o o CO BUILDING DESIGN AND CONSTRUCTION. 123 TABLE XLV A. Spacing. Spacing of Round Rods for Given Area per 1 Ft. Wide. Dia. Rods y %> H /& y% % % % 3' f .196 .307 .441 .601 .785 .994 1.227 1.485 1.767 2.405 3.142 .168 .263 .378 .515 .673 .852 1.052 1.272 1.514 2.061 2.692 4' 2 .147 .230 .331 .451 .589 .745 .920 1.113 1.325 1.804 2.356 4H* .131 .204 .294 .401 .523 .663 .818 .990 1.178 1.603 2.094 5' f .118 .184 .265 .361 .471 .596 .736 .891 1.060 .443 .885 .107 .167 .240 .327 .428 .542 .669 .809 .963 .311 .712 6 2 .098 .153 .221 .300 .392 .497 .613 .742 .883 .202 .571 6H* .090 .141 .204 .277 .362 .458 .566 .685 .815 .110 .450 7' .084 .131 .189 .257 .336 .426 .526 .636 .757 .030 .346 7}^ .078 .123 .176 .240 .314 .397 .441 .594 .707 .962 .256 8* .073 .115 .165 .225 .294 .373 .460 .557 .663 .902 .178 9' .066 .102 .146 .200 .262 .330 .405 .495 .590 .800 .050 10* .058 .091 .132 .180 .235 .297 .365 .445 .530 .720 .940 12' .049 .076 .110 .150 .196 .248 .306 .371 .442 .601 .785 14' .042 .065 .094 .128 .167 .212 .263 .318 .376 .515 .665 16' .037 .057 .082 .112 .146 .185 .230 .277 .330 .450 .585 TABLE XLV B. Spacing. Weight of Round Rods per 1 Ft. Width for Given Spacing. dia. * V H' H* V | K- %" *' H* r 3' .666 1.044 1.50 2.044 2.667 3.38 4.172 5.048 6.008 8.176 10.68 3^* .568 .895 1.287 .755 2.287 2.897 3.576 4.327 5.15 7.008 9.154 4' .500 .783 1.125 .533 2.000 2.535 3.193 3.786 4.506 6.132 8.000 4M* .444 .696 1.000 .362 .778 2.254 2.782 3.366 4.006 5.450 7.120 5 .400 .626 .900 .226 .600 2.028 2.500 3.029 3.605 4.906 6.400 5^* .364 .570 .818 .115 .455 1.825 2.275 2.753 3.277 4.412 5.827 6' .333 .522 .750 .022 .333 .690 2.086 2.524 3.004 4.088 5.340 6J-4' .307 .482 .693 .944 .231 .561 .925 2.330 2.780 3.732 4.929 7' .285 .447 .643 .876 .143 .448 .788 2.163 2.575 3.465 4.577 7V6* .266 .418 .600 .818 1.067 .352 .669 2.019 2.403 3.234 4.272 8* .250 .392 .563 .767 1.000 .268 .565 .893 2.253 3.066 4.000 9' .222 .348 .500 .681 .889 1.127 .391 .683 2.003 2.725 3.560 10' .200 .313 .450 .613 .800 1.014 .251 .519 1.803 2.453 3.200 12' .167 .261 .375 .511 .667 .845 .043 .262 1.502 2.044 2.670 14' .143 .224 .332 .438 .572 .724 .894 .082 1.288 1.733 2.289 16' .126 .196 .282 .384 .500 .634 .783 .947 1.127 1.533 2.000 1 124 REINFORCED CONCRETE. TABLE XLV-C. (New Style Bar) Spacing. Spacing of Corrugated Square Bars for Given Area per 1 Foot Width. Size of Bar. %* 1-3* W %" %" %" 1" IH' 2" .360 .66 1.50 2.34 3.36 4.62 6.00 9.37 2H" .29 .53 1.20 1.87 2.69 3.70 4.80 7.50 3" .24 .44 1.00 1.56 2.24 3.08 4.00 6.24 3^" .21 .38 .86 1.34 .92 2.64 3.43 5.36 4" .18 .33 .75 1.17 .68 2.31 3.00 4.68 4H" .16 .29 .67 1.04 .49 2.05 2.67 4.16 5" .14 .26 .60 .94 .34 1.85 2.40 3.75 5M" .13 .24 .55 .85 .22 1.68 2.18 3.41 6" .12 .22 .50 .78 .11 1.53 2.00 3.12 6H" .11 .20 .46 .72 1.03 1.42 1.85 2.88 7* .10 .19 .43 .67 .96 1.32 1.72 2.68 7 1 A" .10 .18 .40 .62 .89 1.23 1.60 2.50 8" .09 .17 .38 .59 .84 1.15 1.50 2.34 8^" .08 .16 .35 .55 .79 1.09 1.42 2.20 9* .08 .15 .33 .52 .75 1.02 1.33 2.08 9K" .08 .14 .32 .49 .71 .97 1.26 1.97 10' .07 .13 .30 .47 .67 .92 1.20 1.87 11" .07 .12 .27 .43 .61 .84 1.09 1.70 12" .06 .11 .25 .39 .56 .77 1.00 1.56 TABLE XLV-D. Size. Weight in Lbs. per Foot. Peri- meter. Areas of Square Bars. Number of Rods. 1 2 3 4 5 6 7 8 9 H' .212 1.00 .063 .125 .187 .250 .313 .375 .438 .500 .565 %," .332 1.25 .098 .195 .293 .391 .489 .586 .684 .782 .879 %' .478 1.50 .141 .282 .422 .562 .703 .844 .984 1.125 1.265 %,' .651 1.75 .191 .383 .574 .766 .957 1.148 1.340 1.531 1.723 y* .850 2.00 .250 .500 .750 1.000 1.250 1.500 1.750 2.000 2.250 %' 1.076 2.25 .316 .632 .949 1.266 1.583 1.898 2.215 2.532 2.848 5 A" 1.328 2.50 .391 .781 1.172 1.562 1.953 2.344 2.734 3.125 3.515 %' . 1.C07 2.75 .473 .945 1.418 1.892 2.364 2.836 3.309 3.782 4.254 %' 1.913 3.00 .563 1.125 1.618 2.250 2.813 3.375 3.938 4.500 5.053 %* 2.245 3.25 .660 1.320 1.981 2.641 3.301 3.961 4.621 5.282 5.942 y&' 2.603 3.50 .766 1 531 2.297 3.062 3.828 4.594 5.359 6.125 6.890 %" 2.988 3.75 .879 1.758 2.637 3.516 4.395 5.273 6.152 7.031 7.910 r 3.400 4.00 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 \%," 3.838 4.25 1.129 2.258 3.387 4.516 5.645 6.773 7.903 9.031 10.160 VA" 4.303 4.50 1.266 2.531 3.797 5.062 6.328 7.594 8.859 10.125 11.390 ifc' 4.795 4.75 1.410 2.820 4.231 5.641 7.051 8.461 9.871 11.281 12.692 IK* 5.313 5.00 1.563 3.125 4.688 6.250 7.813 9.375 10.938 12.500 14.063 i 5.857 5.25 1.723 3.445 5.168 6.891 8.614 10.336 12.059 13.782 15.504 W 6.428 5.50 1.891 3.781 5.672 7.562 9.453 11.344 13.234 15.125 17.015 1%' 7.026 5.75 2.067 4.133 6.199 8.266 10.332 12.398 14.465 16.531 18.598 VA' 7.650 6.00 2.250 4.500 6.750 9.000 11.250 13.500 15.750 18.000 20.250 BUILDING DESIGN AND CONSTRUCTION. 125 BEAMS AND GIRDERS. Whenever a slab floor construction becomes too heavy owing to large span and load, beams are introduced and in most cases built monolithic with the floor slabs, so that for calculation purposes the beams may be considered as tee- beams. The area above the neutral axis is then relied upon to take care of the compressive stresses, while the tension is taken up by the steel reinforcement placed below the neutral axis in the web. There is as great a number of beam systems as floor slab systems, and before entering upon the calculation of typical floors and beams a number of the better known systems will be described. Beams are classed as loose rod systems or frame systems. Loose Rod Systems. Loose rods for reinforcing beams were formerly employed exclusively, but more recent prac- tice has shown the advisability of tying the reinforcing mem- bers rigidly together before placing them in the mold. This latter method is used very extensively in American prac- tice, while the loose rod method is preferred abroad. This difference between American and foreign practice is tracea- ble directly to the difference in conditions governing the work. In America, where labor is higher, rapidity in erec- tion becomes an important feature, and the time cannot be spent in the field for careful placing of reinforcement, hence the utility of having the reinforcement arrive in the field in an assembled state. The following are some of the more important loose rod systems: The Hennebique system uses two round rods with split ends, one rod being straight and the other bent upward at a point about one-third of the span from the supports for the purpose of resisting the shearing stresses at the ends. Another feature is the use of hoop iron stir- rups (Fig. 58) at intervals to strengthen the beam against horizontal shear or diagonal ten- sion. Both bars are included within the same stirrup, but in some forms of construction the bique System. bent and straight bars are used alternately. 126 REINFORCED CONCRETE. For heavy construction, compression reinforcement is also re- sorted to, and in this case stirrups are placed outside of these rods and extend downward into the concrete. 'The Coularou system, Fig. 59, has stirrups inclined at 45 and their spacing increases from the supports toward the middle of the span. Each stirrup is hooked around upper and lower reinforcement, and near the middle of the beam Fig. 59. Coularou Beam Reinforcement. the upper reinforcement is bent down at an angle of 45 and joins the lower bar, parallel to the same over the central portion of the beam. The Locher beam consists of a number of round or flat bars of different length, having their middle portion straight and being curved up at the ends, with the intention of being as nearly as possible normal to the direction of the maximum tensile stresses, thereby decreasing the tendency toward slid- ing or slipping along the length of the reinforcement. The Coignet system, Fig. 60, has upper and lower bars connected by a light hoop iron web fastened alternately to the upper and lower bars, thus forming a light truss. Fig. 60. Coignet Beam Reinforcement. BUILDING DESIGN AND CONSTRUCTION. 127 Frame Systems. Various styles of reinforcement for frame systems are illustrated by Figs. 20 to 25. In addition to having the beam and girder reinforcement tied rigidly together, it is customary with most of these systems, to tie the columns and slabs reinforcement to that in the beams and girders, thus having all the steel reinforcement in the building tied together. As much as possible of the fastening together is done before insertion in the forms, thus reduc- ing to a minimum the liability of wrongly placing the steel. Tables of Safe Loads and Steel Areas for Beams. From formulas evolved by Prof. Talbot, given on p. 94, from Univ. of 111. Bulletin, Feb. 1, 1907, the following rules are deduced : (1) For area of cross-section of steel reinforcement for other widths of beam multiply by the width in inches. (2) Total loads for other spans and the same depth of steel are inversely proportional to the spans. (3) Total loads for other depths of steel and the same span are directly proportional to the squares of the depths. By using the above mentioned formulas, Tables XLVI to LI, similar to those given in Concrete, Plain and Reinforced, by Taylor and Thompson, have been calculated, using different values for K % p, f c and f s . Some writers prefer to use ultimate loads and ultimate moments. Considerable economy in construction is often found by using 4LL -f- 2DL, where LL = live load, and DL dead load. For instance, for a roof 4 X 40 = 160 Ibs. per sq. ft. LL 2 X 50 = 100 Ibs. per sq. ft. DL Total 260 Ibs. per sq. ft. Then the elastic limits of steel and concrete are used in- stead of the values given for f s and f c . 128 REINFORCED CONCRETE. TABLE XLVI. SAFE LOADS AND STEEL AREAS FOR BEAMS. a 1 +-* Sal e loac in Ib 3. per linear ft. of beam 1 inc i wide A & 0) Span i n feet Q ft ins. 5 6 7 8 9 10 11 12 13 14 15 16 5 44 30 22 17 13 11 9 8 ...... 6 68 47 35 27 21 17 15 12 "16" ..... 7 98 68 50 38 30 25 20 17 15 13 "io" 8 134 93 68 52 41 33 28 23 20 17 15 13 9 164 114 84 64 51 41 34 28 24 21 19 16 10 209 145 106 82 64 52 43 36 31 27 23 20 11 259 180 132 101 80 65 54 45 38 33 29 25 12 315 219 161 123 97 79 65 55 47 40 35 31 13 360 250 184 141 111 90 74 63 53 46 40 35 14 426 296 217 166 131 106 88 74 63 54 47 42 15 497 345 253 194 153 124 103 86 73 63 55 48 16 573 398 292 224 177 143 118 99 85 73 64 56 17 655 455 334 256 202 164 135 114 97 84 73 64 18 742 515 379 290 229 185 153 129 110 95 82 72 19 788 547 402 308 243 197 163 137 116 100 88 77 20 613 451 345 272 221 182 153 131 113 98 86 22 757 556 426 336 273 225 189 161 139 121 106 24 673 515 407 330 272 229 195 168 147 129 26 613 484 392 324 272 232 200 174 153 28 720 569 461 381 320 272 235 205 180 30 660 534 441 371 316 273 237 209 36 765 632 531 452 390 340 300 42 738 629 542 472 415 48 720 627 551 Proportions, 1:6: steel reinforcement, 0.8 percent; K= 102.2; =3,000,000. /t = depth of beam; n=-10; /, - 700 ;/,=- 14,000; 6=1; d=* depth of steel from top of beam. BUILDING DESIGN AND CONSTRUCTION. 129 TABLE XLVI (Continued). SAFE LOADS AND STEEL AREAS FOR BEAMS. Safe load in Ibs. per linear ft. of beam 1 inch wide. ll 43 ! 3 . ^3 T 3 | J3 H CTiTJ . PI loment stance. *+< . i^H ~O-*J *% H-a o ..s % Q W a- !fv4H % ^3 Span in ft. ~* B Q "V $"3 O. Q d sq. h 17 18 19 20 25 30 35 Ibs. ins. ins. ins. M ms. 5.3 4.0 .0 .032 1,635 5 6.3 5.0 .0 .040 2,555 6 7 4 6 o 048 3 679 7 12 8.5 7.0 .0 .056 5,008 8 14 9.5 7.75 .25 .062 6,138 9 18 16 14 13 10 6 8.75 25 070 7 825 10 22 20 18 16 11.6 9.75 .25 .078 9J15 11 27 24 22 20 12 7 10 75 .25 086 11 810 31 28 25 23 13.8 11.5 .5 .092 13,516 13 37 33 29 27 14.8 12.5 .5 .10 15 ,969 14 43 38 34 31 20 15.9 13.5 .5 .108 18 ,626 15 50 44 40 36 23 16 9 14 5 5 116 21 487 16 57 51 45 41 26 18 15^5 .5 '.124 24 !513 17 64 57 51 46 30 "2i" 19.1 16.5 .5 .132 27 ,824 18 68 61 55 49 31 22 20.1 17.0 2.0 .136 29 ,536 19 76 68 61 55 35 25 21.2 18.0 2.0 .144 33,113 20 94 84 75 68 44 30 "22" 23.3 20.0 2.0 .160 40,880 22 114 102 91 82 53 37 27 25.4 22.0 2.0 .176 49 ,465 24 136 121 109 98 63 44 32 27.6 24.0 2.0 .192 58,867 26 159 142 128 115 74 51 38 29.7 26.0 2.0 .208 69 ,087 28 185 165 148 133 85 59 44 31.8 28.0 2.0 .224 80,125 30 264 236 212 191 122 85 62 38.1 33.5 2.5 .268 114 ,694 36 368 328 294 266 170 118 87 44.5 39.5 2.5 .316 159 ,457 42 488 435 391 353 220 157 115 50.9 45.5 2.5 .364 211 ,579 48 M-- wl n - X 12 Kbd*. 130 REINFORCED CONCRETE. TABLE XLVII. SAFE LOADS AND STEEL AREAS FOR BEAMS. B 1 Safe : load in Ibs . per linear ft. of beam 1 incl i wide o ,c a & s pan in feet. h ins. 5 6 7 8 9 10 11 12 13 14 15 16 5 37 26 19 14 11 9 g 6 58 40 29 22 18 14 12 10 9 ...... 7 83 58 42 32 26 21 17 14 12 '"9" 8 113 79 58 43 35 28 23 20 17 14 13 ii 9 139 97 71 54 43 35 29 24 20 18 15 14 10 177 123 91 69 54 44 37 31 26 23 20 17 11 220 153 112 86 68 55 45 38 32 28 24 21 12 267 186 136 104 82 67 55 46 39 34 30 26 13 305 212 156 119 94 76 63 53 45 39 34 30 14 361 255 184 141 111 90 74 63 53 46 40" 35 15 421 292 214 165 130 105 87 73 62 54 47 41 16 485 338 248 189 150 121 100 84 72 62 54 47 17 555 385 284 216 171 139 115 96 82 71 62 54 18 630 437 321 246 194 157 130 109 93 80 70 61 19 667 465 341 261 206 167 138 116 99 85 74 65 20 748 521 382 293 231 187 155 130 111 95 83 73 22 924 644 472 361 285 231 191 161 137 118 103 90 24 1119 780 571 437 345 280 231 194 166 143 125 110 26 1330 927 680 520 410 332 275 230 197 170 148 130 28 1560 1083 797 610 481 390 322 271 231 199 174 153 30 1810 1260 925 708 558 454 374 314 268 231 202 177 36 2586 1808 1322 1010 800 648 532 450 384 331 288 254 42 3600 2516 1840 1410 1114 903 745 626 534 460 401 353 48 4782 3340 2442 1869 1475 1192 988 830 708 610 532 468 Proportions, 1:6; steel reinforcement, 0.4 per cent; K=74; =3,000,000; h - depth of beam; n = 7.5; /.-750;A =20,000; b=l; d = depth of steel from top of beam. BUILDING DESIGN AND CONSTRUCTION. 131 TABLE XLVII (Continued). SAFE LOADS AND STEEL AREAS FOR BEAMS. Safe load in Ibs. per linear ft. of beam . g J3 *j 6 1 inch wide. Ifl 3 . 3-3 P o +* J Span in feet. 1*1 F 4> Q 3.S.8 *? 1! o Q 17 18 19 20 25 30 35 Ibs. d ins. ins. sq. ins. M h ins. 5.3 4 1 .016 1,392 5 6.3 5. | .020 2 175 6 7 7.3 6. i! .024 3,132 7 10 9 78 9 8 4 7 i 028 4 262 g 12 11 9.6 9 9.4 7.75 1.25 .031 5J225 9 15 14 12.2 11 7 ....... 10.5 8.75 .25 .035 6,661 10 19 17 15.2 14 10 4 5 11.5 9.75 .25 .039 8,270 11 23 21 18.5 17 11 7 5.4 12.6 10.75 .25 .043 10,054 12 26 23 21.2 19 12 8 6.2 13.7 11.5 .5 .046 11,506 13 31 28 25 23 14 10 7.3 14.7 12.5 .5 .05 13,594 14 36 32 29 26 17 12 8.6 15.8 13.5 .5 .054 15,856 15 42 37 33.6 30 19 13 9.9 16.8 14.5 .5 .058 18 ,292 16 48 43 38.4 35 22 15 11.3 17.9 15.5 .5 .062 20,903 17 54 48 43.5 39 25 17 12.8 18.9 16.5 .5 .066 23,686 18 58 51 46.2 42 27 19 13.6 20.0 17 .068 25,143 19 65 57 51.9 47 30 20.8 15.2 21.0 18 2 .072 28 ,188 20 80 71 64 58 37 25.7 18.8 23.1 20 2 .080 34,800 22 97 86 77.5 70 45 31.1 22.8 25.2 22 2 .088 42 ,108 24 115 100 92.1 83 53 37 27 27.3 24 2 .096 50,012 26 135 120 108 98 62 43.5 31.8 29.4 26 2 .104 55,712 28 157 140 125 114 72 50.4 37 31.5 28 2 .112 68,208 30 224 200 180 163 103 72.2 52.8 37.8 33.5 2.5 .134 106,357 36 312 278 250 226 144 100 73.4 44.1 39.5 2.5 .158 135,742 42 414 368 331 300 191 133 97.2 50.4 45.5 2.5 .182 180,112 48 M a;/ 3 X 12 132 REINFORCED CONCRETE. TABLE XLVIII. SAFE LOADS AND STEEL AREAS FOR BEAMS. a i Saf 2 load in Ibs >. per linear ft. of beam 1 inc i wide * o "o. S pan in feet. * ins. 5 6 7 8 9 10 11 12 13 14 15 16 5 32 22 16 12 10 8 g 49 34 25 19 15 12 10 9 7 71 50 36 28 22 18 15 12 10 9 8 8 97 67 49 38 30 24 20 17 14 12 11 '"9" 9 119 82 61 46 37 30 25 21 17 15 13 11 10 151 105 77 59 42 38 31 26 22 19 17 15 11 188 131 97 73 58 47 39 33 28 24 21 18 12 228 158 117 89 70 56 47 40 34 29 25 22 13 262 181 134 102 80 65 54 42 39 33 29 25 14 309 214 158 120 95 77 64 53 45 39 34 23 15 360 250 184 140 111 90 75 62 53 46 40 35 16 415 288 212 162 128 103 86 72 61 53 46 40 17 475 331 243 185 146 119 99 82 70 60 53 43 18 542 378 275 216 167 135 112 94 80 69 60 52 19 573 396 291 222 176 143 116 99 84 73 63 55 20 642 445 327 250 198 160 133 111 94 81 71 62 22 792 550 404 308 244 197 164 137 117 101 88 77 24 956 665 489 372 295 248 198 166 142 124 106 93 26 1138 793 582 443 352 284 236 197 168 145 127 111 28 1336 925 683 520 412 333 276 232 197 170 148 130 30 1550 1078 792 605 478 386 320 269 229 197 172 151 36 2220 1540 1134 865 685 553 459 385 328 282 246 217 42 3085 2140 1576 1204 952 770 638 535 455 393 344 299 48 4090 2838 2090 1595 1264 1020 845 710 605 521 455 396 Proportions, 1:6; steel reinforcement, 0.6 per cent; K=87; E= 3,000,000; /t = depth of beam; n=10; /-=750;/t = 16,000; &=!; d=depth of steel from top of beam. BUILDING DESIGN AND CONSTRUCTION. 133 TABLE XLVIII. (Continued). SAFE LOADS AND STEEL AREAS FOR BEAMS. Safe load in Ibs. per linear ft. of beam fl . 1 fc *" a> B 1 inch wide. S-S* to " d iW *F Safe moment of resistance. Thickness. Span in feet. 13 14 | 15 Ibs. | dins. | ins. | sq.ins. | in.lbs. | fcins. = 0.004; / c =460. 36 30 26 23 37.8 2i .108 3,070 3 53 45 39 34 44.2 2f .132 4,590 31 74 63 54 48 50.4 31 .156 6,410 4 86 73 63 55 56.7 31 1 .168 7,440 112 96 83 72 63.0 4 1 .192 9,720 5 176 150 129 112 75.6 5 1 .240 15,180 6 253 216 186 162 88.2 6 1 .288 21,860 7 344 293 253 220 100.8 7 1 .336 29,750 8 p = 0.006; / c =580. 52 78 109 126 165 258 372 506 45 66 93 108 141 220 316 431 38 57 80 93 121 190 273 371 33 50 70 81 106 165 238 324 37.9 44.3 50.5 56.8 63.2 75.8 88.6 101.2 5 5 ,1 ! .162 .192 .234 .252 .288 .360 .432 .504 4,510 6,740 9,420 10 ,920 14 ,270 22,290 32,100 43 ,690 3 3* ! J 6 7 8 = 0.008; / 8 =680. 69 103 143 166 217 339 488 664 58 87 122 141 185 288 416 566 50 75 105 122 159 249 359 488 44 66 92 106 139 217 312 425 38.0 44.4 50.7 57.0 63 4 76.1 88.9 101.6 4 5 6 7 ' .216 .264 .312 .336 .384 .480 .576 .672 5,930 8,860 12 ,370 14,350 18 ,740 29 ,280 42,160 57 ,390 3 3} 4* 5 6 7 8 = 0.010; /c=700. 85 126 177 205 268 418 602 820 72 107 151 175 228 356 513 698 62 93 130 151 196 307 442 602 54 81 113 131 171 268 385 524 38.1 44 5 50.9 57.2 63.6 76.4 89.2 102.0 2f 5 6 7 1 1 1 1 1 .270 .330 .390 .420 .480 .600 .720 .840 7,320 10,930 15,260 17,700 23 ,120 36 ,120 52 ,020 70,800 3 7 \ = 0.012; /=700. 94 140 195 226 295 462 665 905 80 119 166 193 252 393 565 771 69 103 143 166 217 339 489 665 60 90 125 145 190 296 426 580 38.3 44.6 51.1 57.3 63.9 76.7 89.5 102.4 4 5 6 7 ' .324 .396 .468 .504 .576 .720 .864 1.008 8,080 12 ,070 16,860 19,550 25,540 39,900 57,460 78,200 3 7 US- M n=15; M = X 12 140 REINFORCED CONCRETE. The following tables are taken by permission from Lin- dau's "Designing Methods" and are based upon ultimate bending moments of 3 LL -f 2 DL or 4 LL + 2 DL as the case may be. The following formulas are used in preparing the tables: FORMULAS GIVING THE ULTIMATE STRENGTH OF BEAMS A TAKEN AS 50,000 LBS. Class No. 1, Average Rock Concrete. This class is meant tc include all concretes having a compressive strength of 2000 Ibs. per square inch; f c then = 2000 and taking E K = 2,600,000 we get for the ultimate resisting moment: M Q = 370 bd^ for A* = 0.0085 bd (1) Class No. 2, Good Rock Concrete. By using a 1 :2:4 mix and good rock or gravel we get a concrete of much greater compressive strength, but with a higher modulus of elasticity. For such a concrete we may assume E c = 2,800,000 and fc 2700, and we get: M = 570 bcl^ for A s = 0.013 bd (2) Class No. 3, Cinder Concrete. For a 1 : 2 : 5 mix of cinder concrete we may assume c = 750,000 and f< ~ 750; then we have: Mo = 207 bd* for A s = 0.0047 bd.... .(3) BUILDING DESIGN AND CONSTRUCTION. 141 f > 5 O 1C Cfl O eo to to to t^ t>i i>.' t^ od od oo 000000. OiOOOOOOOOO tOt>-OOOiCO4CO^C OO OO 09 CQ oo n eo << ^ ^* <4> ^f >o >o to >e ooooooooo- e* ^ o gfl i 5<-lCqiOt^( 8 142 REINFORCED CONCRETE. " 3 I ? o 8 1 &4 H rS II II O 9 O i! fe -a | "o 5 2 1001 OS CO t '' - SSS:S!|^ : : ggssg^iiss : "r^^ J'"" CNIT:} ^^ s'S.S S 18-Sl '053>S \N\N\N\N X^l \C* * pJSp-K^.lX.-iX* ft *4\fc rH\ c nnDDGnnnnnnnnnn CMOOCMt^-COOOC<]t^-COCO-Ht^i-HCDi f O O O O O O O O O O O O O O O * 1 BUILDING DESIGN AND CONSTRUCTION. 6 - II g g^ l S.I .s 'j ttfd Co ze an pacng of Corrugated Rounds 8 1 :;;;;;;: i-c CO CD O5 O iO *O O *O iO O i O CO *O O5 C^ CC i i I i-i-ii-Hi-H CO O5COt^-C<|CX}COOiCOcO~'O< oocokc O US O O 10 O O O 5O >OO C (N cq CO <*< tti t t--T4t>. O5 ^ (M rt rt rt r-l of the C. & N. W. railway at Chicago and to the company's Pintch gas plant. The plates were made waterproof, of a mixture of 1 cement to 3 torpedo sand, 2 ft. wide, 5 ft. long and only % in. thick. They are self-locking and removable, similar to corrugated iron sheets. The reinforcement consisted of a wire fabric, which in this case was electrically welded. Roofs for saw- tooth factories are also often built of a tile concrete con- struction laid on top of steel rafters. For flat roofs the concrete slabs must be covered by some composition, while for inclined roofs, roofing plates may be put on without cov- ering. Stairs. Reinforced concrete stairs are easily constructed and are rapidly coming into use, even on existing brick build- ings where wooden porches and stairs have been employed. There are five kinds of stair construction in reinforced con- crete: (1) Concrete steps manufactured in shops and fitted on top of inclined concrete slabs. BUILDING DESIGN AND CONSTRUCTION. 161 (2) Similar steps fitted to iron stringers. (3) Plain inclined slab with top side toothed to form risers and treads. (4) Soffit and top molded in connection with the string- ers and cast in' one piece. In this case the top is toothed for risers and the soffit may be either flat or toothed to conform with the profile of the top. (5) Stairs attached to concrete wall on one side and overhanging. The general construction of stairs is based upon the same calculations as have been presented under floor beams and girders and need not be further detailed. A wire fabric forms a very satisfactory reinforcement between the string- ers for continuous stairs, and one layer is generally sufficient, adding to the cheapness and rapidity of the construction. At the Lakeside Hospital in Chicago the author con- structed porches along the rear of the hospital so as to make verandas on each floor for the patients and have the con- struction absolutely fireproof. The porches were 10 ft. wide and 40 ft. long and rested on 8x8-in. reinforced concrete columns extending down to the foundation in the basement of the building. There were four verandas and the inner edges rested on angle irons extending 4 ins. into the brick building, being anchored thereto. The stairs were 4 ft. wide and molded in place, each with two stringers supporting a flat soffit slab with the top toothed for risers and treads. The railings were made of 2-in. wrought iron pipe in the usual manner, the posts being inserted and wedged to wrought iron sleeves previously molded into the concrete stringers and beams and the railings then fastened to same and into the brick wall of the building at both ends of the veranda. Concrete porches and stairs are rapidly replacing the common wooden constructions in the rear of tenement houses and apartment buildings of large cities. Structural Steel or Cast Iron Columns. Structural steel or cast iron columns are frequently employed in reinforced 162 REINFORCED CONCRETE. concrete structures on account of rapidity in erection after they have been delivered on the premises. If structural steel columns, owing to their smaller floor area, are em- ployed, Fig. 61, gives a typical view of the attachment of girder and floor beams, and Fig. 62 shows a view of the Fig. 62. Cast Iron Base for Steel Cores. Fig. 61. Steel Core Column Footing and Bracket for Beam and Girder Con- nection. base for same. Fig. 63 indicates the reinforcing of a heavy steel floor girder and a method of running the slab beams into same. This construction was used in the Eagle Ware- house & Storage Company's building on Fulton St., Brook- lyn, N. Y. BUILDING DESIGN AND CONSTRUCTION. 163 The steel columns are proportioned for working stresses of 16,000 Ibs. per sq. in., the hollow columns being filled with concrete (Fig. 64). The cast iron columns in this build- ing are generally 12 ins. in diameter down to the fourth floor and 15 ins. to the second floor with thicknesses varying "3 -** __^~^ Fig. 63. Fireproofing of Box Girder and Twin Girder. from \}/4 ins. to 1^4 ins. and lengths of from 12 ft. 6 ins. to 13 ft. They are of standard construction. Fig. 65 shows flange connections faced and drilled for 24-in. connection bolts. The upper ends of the columns are special in that, above the beams and girder seats, they are made square out- side with rectangular openings 5 or 6 ins. wide and 14 ins. deep in the face, to permit the re- inforcement rods in beams and girders to pass through for pur- poses of continuity. The fire- proofing concrete is extended 2 ins. beyond the flanges and care- fully finished with beveled fillets. The brick walls are carried at every story by reinforced concrete girders (Fig. 66) with their outer face 4 l /2 ins. clear of the outer face of the brick work. The concrete walls are 12 ins. thick for the first three stories, 10 ins. for the next two, 9 ins. for the next two, and 8 ins. for the upper story, reinforced with %-in. rods 2% ft. on centers running hori- zontally and %-in. rods 3 ft. on centers running vertically. Fig. 64. Fireproofing and Filling for Columns. 164 REINFORCED CONCRETE. The author invariably uses wire fabric for walls, running it through the reinforced concrete columns and connecting with floor and ceiling, both to prevent temperature cracks and to guard against cracks resulting from uneven settling of the building foundation. L i p-.z-.v.-.-j j : _*.r N* , ..:, :ff ; o ^n\ '% ii ! V *T V T ri ; \ Fig. 65. Special Top for Cast Iron Column; Column and Girder Connections. The author also has advocated a construction in which the struc- tural steel, correctly located, should be calculated to assume the dead loads of the building as well as the loads incidental to the build- ing erection and wind pressure and afterwards incased in con- crete in a manner to support the additional live load. Such a building could be erected with the rapidity inherent in the traditional skyscraper and sev- eral floors put in simultaneously without waiting for the setting of the column concrete from floor to floor. This construction has been adopted by several well known engi- Fig. 66. Concrete Girders Supporting Brick Walls. BUILDING DESIGN AND CONSTRUCTION. 165 neers. As an example, the construction employed by Mr. Guy B. Waite, New York City, is here illustrated. Fig. 67 shows details of the general construction. The original beams and girders consist of small I-beams usually from 4 to 5 ins. deep, entering into the columns and con- nected to them by bent plates and angles. The column itself consists of four angles latticed together, so designed as to form when filled with concrete a reinforcement with a maximum radius of gyration. The column details, of course, may be changed. In such construction it hardly needs to Fig. 67. General Structural Details. be added that the support of molds and scaffolding is simply a matter of hooks, no floor supports being required. Bracket Connections. Figure 68 shows a typical beam floor slab construction with hooped column supports and Fig. 69 the construction of the connection. The brackets are reinforced by one or more corner rods from f to 1 in. in diameter hooked at the ends to withstand eccentric loads and wind pressure. Fig. 70 shows a typical footing for such a column on rock. Sometimes the bearing plate consists of 166 REINFORCED CONCRETE. Fig. 68. Typical Beam Floor Slab Construction. BUILDING DESIGN AND CONSTRUCTION. : V one plate the same as before quoted. Sometimes economy is gained by using short flat bars, as here shown. Fig. 71 shows a typical wall beam and its connection to a girder and bracket to the column. The wall beams usually represent the entire panel between the lintel of one floor opening and the sill of the opening on floor above. Fig. 69. Typical Beam, Girder and Column Connection. Fig-. 70. Typical Footing for Column on Rock. EXAMPLE OF BUILDING DESIGNED ACCORDING TO THE FOREGOING PRINCIPLES. In order to illustrate the use of the tables given under Building Design, and to illustrate further the principles un- derlying the design of raft foundations, the following exam- ple is given: Assumptions. -It is required to design a warehouse, 60 by 60 ft. square, 6 stories in height, with basement. (Fig. 72.) In the southeast corner, above the roof, is a garner, weighing with contents 200,000 Ibs. The live lond on floors is 182 Ibs. per sq ft., and on the roof the live load is 78 Ibs. per 168 REINFORCED CONCRETE. sq. ft. The property on the north is not occupied, but must not be encroached upon. On the east stands a heavy ware- house without basement, hence its foundations are compara- tively shallow, so that the basement of the new building is 2 ft. below the bottom of foundations of this property. Soil is stratified, sustaining a pres- sure of 5,000 Ibs. per sq. ft. Time prevents the driving of piling, which also would endanger the adjoining building. A reinforced concrete mat and raft foundation is decided upon. The calculations, based upon a 1-6 mixture of Portland cement, sand and crushed stone passing a %-in. ring, are as follows, for the first to the sixth floors inclusive, assuming that beams are spaced 7 ft. 6 ins. on centers, and that girders are spaced 15 ft. on centers: Slabs. Assuming a span of 7 ft. and a dead load of 64 Ibs. per sq. ft., 182 + 64 = 246 Ibs. per sq. ft. Referring to Table L, and taking p = 0.006 and fc 580, h = 5 ins. The steel area per foot is .288 sq. in., from same table. Assuming ^-in. rods as reinforcement, by Table XXXV Fig. 71. Typical Bracket and Ties at Walls. The spacing accord- their area is seen to be 0.196 sq. ins. ingly is 288 * 12 = 8% ins. on centers where no fabric is used. Beams. We approximate: W = S X 246 = 1,968 Ibs. per ft. of beam, including the weight of the beam, and assuming a beam 12 ins. wide. For 1-in. width of beam, w= i- = 164 Ibs. BUILDING DESIGN AND CONSTRUCTION. 169 n^t^c Garner weighing 2.00,000 Ibs. 4-* --- /S'O" 6" /S'O" ' - - /S'O" Fig. 72. Section Through Building. 170 REINFORCED CONCRETE. Table XLVI, for span of 15 ft, gives a depth of 26 ins. for a load of 174 Ibs. For 164 Ibs. the depth is' 25 ins., giv- ing a beam 12x25 ins., or 12x20 ins. below the slab. The same table gives steel area for 1 in. width between 0.192 and 0.176; assuming 0.190 sq. ins., 0.190 X 12 = 2.28 sq. ins. Assuming 8 rods, 228-^8 = .285 sq. ins., which corresponds to a diameter of 5i ins. Later will be shown that two extra rods are laid in such beams as support the columns on a cantilever. All rods are to be carefully fastened in a frame before being placed. Girders. 1,968 X 15 = 29,520 Ibs. concentrated load. 20 520 x 15 Hence M = : | - X 12 = 1,328,400 in. Ibs. Selecting a width of 16 ins., the moment for 1 in. width be- comes In Table XLVI we interpolate between a 36-in. depth at 114,694 in. Ibs., and a 30-in. depth at 80,125, and find a depth of slightly over 30 ins. for 83,025 in. Ibs., leaving the girder practically 16x25 ins. below the slab. The steel area for 30 ins. depth is 0.224 sq. ins. 16X0.224 = 3.584 sq. ins. Assuming 8 rods, and consulting Table XXXV, 'g = 0.448 sq. in. or 8 rods, 24 m - m diameter. Eight 24-in. rods are accepted, as no attention has been paid to the fact that the girder is continuous. Location of Stirrups. The net span of the beam is seen to be 13 ft. 8 ins., the depth being 25 ins. Using Mr. Ran- some's empirical rule for spacing stirrups, Formula 5, Fig. 31, BUILDING DESIGN AND CONSTRUCTION. 171 they would be located 6% ins., \2 l / 2 ins., 18^4 ins., and 25 ins. apart, from the end of the beam. This leaves a space of 39^ ins. in the center of the span, which is too great. To eliminate this, the spacing adopted is 6 ins., 14 ins., 20 ins., and 26 ins., thus making the central space 32 ins., and employing 8 stirrups, the material used being y 2 -\n. square bars. Stirrups for girders are calculated and located in the same manner as for beams. Wall Girders. The load is one-half the regular girder load, or 14,760 Ibs., plus the weight of the curtain wall be- tween pilasters, which is 13,500 Ibs. Formula for M, with uniform and concentrated load is 15x12 = 967,950 in. Ibs. Assuming the same depth as for the other girders, their breadth will be 967,950 80,125 = The steel area is 24 that of the other girders, or 24 of 3.584 sq. ins., or 2.688 sq. ins. Choosing six rods, their diameter is found to be ^4 ins. The stirrups and their spacing are calculated as before. Roof Slab. We will make the slabs continuous in both directions and omit the center beams. The live and dead load is 78 + 64=142 Ibs. per sq. ft. Since a more carefully graded concrete will be used in the roof to increase its impermeability to water, the value for C can be higher, and p will be higher. Taking p = 0.008, and /c = 680, Table LI gives for 142 Ibs. load and 15 ft. span, a depth of 5 ins., and a steel area of 0.384 sq. in., or, by Table XXXV, using 5^-in. rods, their spacing is 0.3068 Q og 4 X 12 = 9f ms. on centers. 172 REINFORCED CONCRETE. Roof Beams and Roof Girders. These are calculated alike. Approximately PF = 142 X 8.5 = 1,207 Ibs. per linear foot, including weight of beam. Selecting a width of 10 ins., W--- 121 Ibs. By Table XLVI, this corresponds to a depth of 22 ins. The steel area is 10 X .160 = 1.60 sq. ins. Assuming 6 rods, their diameter is found, by Table XXXV, to be $/& in. Columns. We first make a column schedule (see pp. 174 and 175), which explains itself. For tall buildings, it is customary to deduct 5 per cent of the live load for the top floor, 10 per cent for the floor below, and 5 per cent more for each floor except the first floor, until 50 per cent of the live load has been deducted. This, however, we will omit in the example, as it amounts to very little, and might tend to complicate the problem. We will use a column with high carbon wire hooping, and employ different percentages of vertical reinforcement, according to Conside're's formula, and Table LVIII. The values in this table being ultimate, are divided by 4 to get the working stress. The 90,000 Ibs. for No. 7 gage represents the elastic limit of the wire employed. The other tables for column loads could be used see Table XXVIII, and Tables LII to LVII. The calculations are made, bearing in mind that the roof load is 142 Ibs. per sq. ft., the floor loads 246 Ibs. per sq. ft. The weight of the column is approximate, allowing for not having included brackets, etc. The spiral in each case is 2 ins. less in diameter than the column for same, and all spirals used are on 1-in. pitch, as shown in Table LVIII. Foundations. From tests, the bearing power of the soil is found to be 5,000 Ibs. per sq. ft. Fig. 73 shows the founda- tion lay-out. As we cannot encroach upon the adjacent BUILDING DESIGN AND CONSTRUCTION. 173 property, rafts must be resorted to on the north and east sides. Rafts 2-7, 3-8 and 15-14 are calculated alike. Raft 2-7. The principle consists in constructing a base, the center of gravity of which coincides with the center of Fig. 73. Foundation Plan Showing Position of Rafts. gravity of the two unequal loads. The calculation becomes approximate as we move in the outside column 1 ft., on account of sheet piling, etc., and add 18 ins. at the other end of the raft beyond the centers calculated. See Fig. 74. 174 REINFORCED CONCRETE. COLUMN SCHEDULE. Floor. Loads in Ibs. per sq. ft. Columns 1, 5, 21, supporting panel 7ix7ift. Columr 12, 13, support 15x s 7, 8. 9, 14, 17, 18, Columns 2, 3. 4, 10, 6, 11, 15, 16. 22, 23, ing panel 15 ft. supporting panel 7ix 15ft. 6th. . . 5th... 4th... 3rd... 2nd.. 1: t.. . Base- ment. Foun- da- tion. . Panel load . . . Column wt.. . Panel load . . . Column wt.. . Curtain wall.. Panel load . . . Column wt.. . Curtain wall.. Panel load . . . Column wt.. . Curtain wall.. Panel load.. . Column wt.. . Curtain wall.. Panel load . . . Column wt.. . Curtain wall.. Panel load.. . Column wt.. . Curtain wall. . At 5,000 Ibs. per sq. ft., or 2.5 tons. 7,988 1,250 10" sq. 1-V rd. % " ties 6" ctrs. 4-%"rd. 10" sq. 4-5"rd. 10* spiral y^"\\ l /2" i 1% 4 \/A " rH 31,950 1,250 Same as col. 1, 6th floor. Same as col. 1, 3rd floor. 12" spiral ^"xlH" P. 1% A Z/" r( \ 15.975 1,250 Same as col. 1, 6th floor." Same as col. 1, 6th floor. Same as col. 7, 4th floor. Same as col. 7. 4th floor. Same as col. 1, basement . 14" spiral H"*l l A" p. 3% 8-1^" rd. 16' spiral K"xlH" P. 3% 8 1^1$ rd 9,238 13,837 1,250 13,500 33,200 55,350 3,200 17,225 27,675 3,200 13,500 37,825 13,837 1,250 13,500 91,750 55,350 3,200 59,650 27,675 3,200 13,500 66,412 13,837 2,450 13,500 150,300 55,350 3,200 14* spiral K"xlH" P. 1% 4-5T rd. 16" spiral M"xl>i" p. 1% 4 M'rd. 4-y*' rd. 18" spiral K"xlM" P. 1% ,/ 4 %*rd. 1%" rd. 18" spiral W-a\ l A" p. 3% 8 lYs" rd 77.3 sq. ft. 104,025 27,675 3.200 13,500 96,199 13,837 2,450 13,500 10" spiral ^"xl^" P. 2% 4% rd. 12* spiral Wji\Vi" P. 1% 43/ff j 208,850 55,350 3,600 148,400 27,675 3,200 13,500 125,986 13,837 3,200 15,750 267,800 55,350 4,050 192,775 27,675 3,600 15,750 158,773 13,837 3,600 13,500 14' spiral #"xlH" p. 1% 4-M" rd. 37.94 sq. ft. 327,200 55,350 4,050 239,800 27,675 3,600 13,500 189,710 94.86 tons. 386,600 193.3 tons. 284,575 142.3 tons. 56.9 sq. ft. BUILDING DESIGN AND CONSTRUCTION. 175 COLUMN SCHEDULE. (Continued). Floor. Loads in Ibs. per sq. ft. Columns 20, 24. Supporting panel 7J x 15 ft. Column 19. Supporting panel 15x15 ft. Column 25. Supporting panel fj x 7i ft. 6th... 5th... 4th. . . 3rd... 2nd.. 1st.. . Base- ment. Foun- da- tion. . Wt. of garner Panel load.. . Column wt.. . Panel load . . . Column wt.. . Curtain wall.. Panel load . . . Column wt.. . Curtain wall.. Panel load.. . Column wt.. . Curtain wall.. Panel load . . . Column wt.. . Curtain wall.. Panel load . . . Column wt.. . Curtain wall.. Panel load... Column wt.. . Curtain wall.. At 5.000 Ibs. per sq. ft., or 2.5 tons. 50,000 15,975 3,600 12" sq. 4 M" rd. 10" spiral K"xlM" p. 1% A 3/" T A 50,000 31,950 3,600 Same as col. 20, 6th floor. Same as col. 20, 5th floor. Same as col. 20. 3d floor. Same as col. 7, 2d floor. Same as col. 20, 1st floor. Same as col. 7, bast. 20" spiral ,* 8 \W rd. 88.2 q. ft. 50,000 7,988 2,450 Same as col. 1. 6th floor. Same as col. 20. 6th floor. Same as col. 1. 2d floor. Same as col. 7. 4th floor. Same as col. 20, 3d floor. Same as col. 7, 3d floor. 16" spiral J'xlX 2 " p. I/O 4 W rd 69,575 27,675 3,600 13,500 85,550 55,350 3,600 60,438 13,837 2,450 13,500 114,350 27,675 3,600 13,500 12" spiral , 4 3/" T A 144,500 55,350 3,600 90,225 13,837 3,200 13,500 159.125 27,675 3,600 13.500 14" spiral M"xlX 2 " p 1%, 4 W rd. 16" spiral W*\W P 1% 4 %, rd. 4%" rd. 16" spiral M"xlM" P. 3% 81" rd. 18" spiral M"xlM" P. 2% 203,450 55,350 3,600 120,762 13,837 3,200 13,500 203,900 27,675 3,600 13,500 262,400 55,350 4,000 151,299 13,837 3,600 13,500 248,675 27,675 4,000 15,750 321,750 55,350 4,800 182,236 13,837 4.000 15,750 296,100 27,675 4,000 13,500 381,900 55,350 4,000 215,823 13,837 3,600 13,500 341,275 170.6 tons. 68.25 sq. ft. 441,250 220.6 tons. 246,760 123.4 tons. 49.4 sq. ft. 17,6 REINFORCED CONCRETE. Fig. 74. Diagram for Raft 2-7. Load column 2 = 284,575 Ibs. Load column 7 = 386,600 Ibs. Sum =671,175 Ibs. Dividing by 5,000 = 134.23 sq. ft. Area of raft X 14 = 134.23. 19.18. ll ~ 284575 671175 X 14 5.94. 26 2 o A i J-. o -into O."4. 3 b t + b a 3 19.18 Solving, b 2 = 5.22, and bi = 13.95. To find the cross-section of raft, we must find the center of gravity of one-half the trapezoid, which gives the leverage for the bending moment, as follows: b 1 b, = 13.95 - 5.22 = 8.73. 6 3 b 2 _ l^ _ 8.06 ~1T7T == 14 = T4 ' 6 3 _ & 2 = 5.03. 5.03 + 5.22 = 10.25. 10.25 + 2x5.22 10.25 + 5.22 = 3.59. BUILDING DESIGN AND CONSTRUCTION. 177 In like manner, solving for 1 5 Z 5 = 3.12. Let A = area of entire trapezoid, and a = the area of that part to the left of the center of gravity, CG, then M =Wk-(W + W l )k= W l h - (W + W l ) k - 2,294,800 1,120,750 = 1,174,050 ft. Ibs.* This is 1,174,050 x 12 = 14,088,600 in. Ibs. Per inch of width this is 14088600 1025 1<12 = 114 >540in.lbs. We will choose n = 15, as E for concrete in a comparatively large mass is nearer 2,000,000. Choosing p = 0.01, we find, from Table XXXIX, 1 j =0.861. Substituting in Formula (11), M,= /; I < 8 J I $.s Jo O- 1 * ^g el s II ooo OG>0 - -O -O :gggg : OOO 'OOO 'OOOOOOOO OOO 'OOO 'OOOOOOOO 0000 '000 '00000000 : : : : Section of Door Frame Tile Partition. Section of Base Boards for "Tile Partition. Section of Bass Boards and Cap-for Picture Mould at Celling. Fig. 86. Separately Molded Details for Doors, Windows and Partitions. Spiral reinforcement was adopted for the columns and was molded into the shell, so that the placing of the column form also placed the column reinforcement. There was gained at once by this scheme of form work, a fireproofing for the col- umn, the placing of the form and reinforcement in one opera- tion by unskilled laborers and the elimination of labor for re- moval of forms. As for the shells themselves, their cost was certainly not greater and was probably less than would have been for cylindrical molds in wood. In the Wiederholdt system of reinforced concrete con- struction, no forms whatever are used. Fig. 87 shows the 202 REINFORCED CONCRETE. system as applied to wall construction. By the use of hollow tile blocks of special shape, thin shells of fire clay or cement tile are used as molds and form the exterior surface. The vertical steel bars are embedded in the foundation in the usual way, and the tiles are laid between them with horizontal bars at suitable intervals, after which the concrete is placed, the tiling and concrete being carried up as the work pro- gresses. This system is also adapted to the construction of grain and other storage buildings, and especially for smoke stacks. Small Tools for Mixing, Conveying and Ramming. As reinforced concrete construction has developed, the tools used have changed considerably. They are becoming standardized as the importance of this phase of the work is being recog- Vert.&Hor.Rods i' Bars -to Lap Zat Fig. 87. Wall Construction, Wiederholdt System. nized. While formerly the same tools that were used for brick and mortar were used for concrete work, now special tools, adapted to the peculiarities of concrete work, are a great advantage. Instead of the old-fashioned wooden brick and mortar barrows formerly in use / most contractors are now using iron wheel barrows, Fig. 88, or, for larger work, a Ransome concrete cart, Fig. 89. The latter is built entirely of steel, and as it has large wheels is very easy to move about, en- abling one man to move several times as much material as he can handle with a wheel barrow. This form of cart is easy to dump and the concrete is not readily spilled over the side of the bowl. This saves time and material. It is stated BUILDING DESIGN AND CONSTRUCTION. 203 by the manufacturers that the cost of moving concrete with an iron push cart is \ 1 /^ cts. per cu. yd. per 100 ft. of haul. Square pointed shovels are generally employed and for mixing and handling the materials size No. 3 is considered the best. Fig. 88. Iron Wheelbarrow for Handling Concrete. Fig. j. Ransome Concrete Cart. A simple measuring box is shown by Fig. 90. It is bot- tomless and 8 to 10 ins. high, and of a size to suit the mix- ture. Thus, if in a 1-6 mixture the proportions 1-2-4 give Fig. 90. Measuring Box for Aggregates. Fig. 91. Cast Iron Rammer for Dry Concrete. the greatest density, the box would be 8 ins. deep and 2 ft. 7 l / 2 ins. x4 ft. This box should be filled once with sand and twice with broken stone, each time being struck off level 204 REINFORCED CONCRETE. Sometimes hoes are used for mixing material and give good results, particularly if one of the men is a regular mor- tar mixer. Rammers are used for compacting the materials. For dry mixtures a flat rammer, usually cast iron with 7x7 ins. base, as shown by Fig. 91, is used. These generally weigh from 6 to 8 Ibs., while for wet concrete a wooden rammer, Fig. 92, is used to cut and compact the material. For thin walls a tool having a long flat steel plate mounted on a handle will be found of use. For large work pneumatic ram- mers built on the principle of pneumatic riveting machines have been used. Other tools, such as mixers and crushers, have been referred to before and the different contracting equipment companies issue very complete catalogs from which selections can be made. Fig. 92. Wooden Rammer for Wet Concrete. FINISHING CONCRETE SURFACES. Since the character of a concrete structure is judged largely by the appearance of the exterior, the finishing of such surfaces becomes very important. In the first place, concrete is a comparatively new building material, different from iron, wood, or tile, and should be recognized as such by giving it a distinct concrete appearance. To the author's mind, imitation of other materials is out of place in concrete structures. The manner of finishing must be governed by the size and class of the structure and the style of architec- tural decoration. The facility with which concrete lends itself to ornamentation enables the choice of a style of ar- chitecture with features that otherwise might be considered very expensive. On the whole, simplicity and plainness in general outlines should mark concrete construction. BUILDING DESIGN AND CONSTRUCTION. 205 Types of Finish. There are five main types of finish for concrete: (1) Leaving the concrete as it is when the forms are re- moved. (2) Hammer dressing or tooling. (3) Using a mortar facing or plastering. (4) Using special concrete mixtures. (5) Washing away the cement to expose the aggregates. Hair Cracks. Smooth concrete surfaces often show cracks generally caused by using a wet concrete, in which the ex- cess of water carries to the surface and deposits a coating of very fine cement which sets and contracts at a different rate from the underlying concrete. These cracks can be eliminated by covering the concrete with wet sand or saw- dust, which is kept well sprinkled for some time after the placing of the concrete. Too rich a mixture, or a surface mixture richer than the body concrete, will also cause hair cracks. If impracticable to cover with sawdust, the surface showing cracks may be scrubbed thoroughly with a wire brush or a cement brick to remove the cement film. Mortar Facing. To produce a smooth surface finish on concrete a mortar facing is often used, varying in thickness from 1 in. to 3 ins. To place this facing a steel plate is in- serted in the form and held away from it by means of angle irons from 1 in. to \ l / 2 ins. wide, depending upon the thick- ness of facing required. The concrete is put into the form back of the plate and the mortar into the narrow space be- tween the form and the plate, and the plate is carefully with- drawn. Another method of obtaining a smooth surface is to use a very wet concrete and throw it violently against the mold, so that the aggregates rebound leaving in effect a mortar facing. This is, however, not to be recommended for fine work, as the molds are apt to be indented and the alignment impaired. 206 REINFORCED CONCRETE. Using Special Dry Mixture. This method has been used extensively for park buildings in Chicago and is described by Mr. Linn White as follows: "The method consists in using for the exposed surfaces the walls of concrete composed of one part of cement and three parts of fine limestone screenings and three parts of crushed limestone known as the ^-in. size. This was then mixed quite dry, so no mortar was flushed to the surface, and well rammed in wooden forms. It was not spaded next the form, and was too dry to cause any flushing of mortar. The imprints of joints between the boards were hardly no- ticed, and no efflorescence can appear on the surface on ac- count of the dryness of the mix and the porosity of the sur- face. The same finis'h has been successfully used for retain- ing walls, arch bridges, fence posts, walls enclosing service yards, etc. A dry, rich mix with finely crushed stone has been found especially suited to another condition where a sound, smooth surface was particularly difficult to secure, namely, for the under-water portion of a sea wall on Lake Michigan. It was mixed very dry and dumped in sunken boxes, joined end to end, made fairly water-tight, but from which water was not excluded. With a finely crushed stone, a sound, smooth surface was obtained when the sides of the boxes were removed where it was manifestly impossible to plaster or grout the surface and where spading a mix of coarser stone would obviously wash away the cement." Bringing Aggregates Into Relief. This gives a finish which, to the author's mind, is superior to a smooth surface, since with it variations in color, efflorescence, hair cracks, and other superficial blemishes are practically removed. The simplest method of bringing out this rough effect is to scrub the concrete with brushes while it is green, as soon as the forms are removed. In cases where the forms must be left until concrete is hard, the cement may be removed by the application of a weak acid solution, which afterwards should be neutralized with an alkaline solution and then well washed with water. Rubbing with a small block of wood or sand- BUILDING DESIGN AND CONSTRUCTION. 207 stone or scrubbing with a stiff wire brush also removes a hard cement coating. When the forms are removed at the right time, three or four passages of an ordinary scrubbing brush with plenty of water is all that is required and a la- borer can wash about 100 sq. ft. in an hour where the work is easily accessible. Tooling. Tooled surfaces are obtained on concrete simi- larly as for stone. When the concrete is hardened, the sur- face may be bush-hammered or treated in any other man- ner. In these cases the forms may be of rough lumber. Tooling the surface generally costs from 3 to 10 cts. per sq. ft., according to quantity and outfit. The Citizens' National Bank of Los Angeles, Cal., was finished with bush-hammer- ing at a cost of l l / 2 cts. per sq. ft., common laborers at $2 a day doing the work. Plastering Concrete. When plaster is to be applied to concrete the concrete should be left quite rough, so as to form a clinch. There should be no difficulty in causing the layers to adhere to each other if properly applied. The con- crete should be well sprinkled before the plaster is laid, as the interior concrete, being dry, will otherwise absorb moist- ure and prevent adhesion. In every case the plaster must be rubbed and tooled hard against the concrete, and while surfacing more water should be applied by means of a sprink- ling brush. Painting and Varnishing. Cement floors can be -painted and varnished like wood if first the surface is primed with a solution that will fill the pores and stop capillary action. A solution of hydrofluoric acid has been used for this purpose to good advantage. WATERPROOFING. With the increased use of concrete and reinforced con- crete, waterproofing is daily becoming of greater importance. A number of patented preparations have been invented and put on the market to serve the purpose of making a struc tnre waterproof, either by application on the outside of the wall or on the inside, and in some instances by adding chem- 208 REINFORCED CONCRETE. ical substances to the cement, so as to form a gelatinous sub- stance, which prevents the absorption of water and still have no harmful effect on the crystallizing of the cement. In the author's opinion, waterproofing is as yet in its infancy, and owing to the increasing demand, great attention is now being given to the matter by chemists and waterproofing engineers. At present we must realize that the simplest means of re- ducing permeability in concrete is to increase its density, both in the selection and application of aggregates and in compressing the surface after finishing by vigorous tooling or rubbing. Impurities in water through seepage assist in making tanks water-tight by filling the pores, and numerous tanks and pipes have been made water-tight without the ad- dition of any particular preparation to the material or on the surface. When, however, we notice the leaking or dripping from subways, tunnels, or concrete coverings, or suffer from wet or damp cellars or basements, we must realize that lack of proper waterproofing is a menace to public health. To reduce the personal equation to a minimum it is the safest to apply a waterproofing layer of felt, tar, asphalt or pitch, as the case may be, and where it will do the most good. In- asmuch as waterproofing is a specialty and requires skilled mechanics for its proper application, and, furthermore, in- asmuch as the different waterproofing companies generally provide their own waterproofing compounds, it is hardly within the province of this book to go further into details than to offer the following advice in the specifications: (1) Design the structure so as not to make application of waterproofing impossible for lack of space of operation. (2) No waterproofing must be done under a lower tem- perature than 25 F. (3) Waterproofing must be done only by experienced and skilled laborers. (4) Watch the waterproofing during and after the ap- plication, and inspect the work during progress. (5) Do not depend upon guarantees. (6) Do not stick to a standard specification, but make a specification to suit local circumstances. BUILDING DESIGN AND CONSTRUCTION. 209 Waterproofing Cracked Walks or Joints Between Steel and Concrete. Here an elastic putty is required and the author after much experimenting finally obtained satisfactory results as follows: 1. With a cold chisel cut a groove 2 ins. to 2 l / 2 ins. deep, ^ in. wide, along the crack or adjoining the steel. 2. Tightly caulk one-half this depth with oakum. 3. Paint the top of oakum and the sides of groove above oakum with No. 110 R. I. W. (a preparation manufactured by Toch Bros., 520 Fifth Ave., New York City). 4. Make a putty by kneading one-half volume dry Port- land cement with one-half volume No. 110 R. I. W. until the putty does not stick to the hand. 5. Stuff this putty in on top of the oakum, entirely filling the groove and sprinkle dry cement on top of finished joint. 6. Absolutely no water must be used and the grooves must be dry. Experiments indicate that concrete can also be 'rendered impervious to water through the addition of at least 5 per cent and not more than 10 per cent of the weight of cement of petroleum residuum oil, without impairing the strength of the concrete. Oil-mixed mortar containing 10 per cent of oil is abso- lutely watertight under pressure as high as 40 Ibs. per sq. in. Such mortar may also effectively be painted or plastered on either side of porous concrete. The crushing strength of concrete with oil is reduced to 75 per cent at 28 days, but 1 : 3 mortar suffers practically no harm at the age of one year. (L. W. Page. Proc. Am. Soc. C. E., Vol. XXXVII, p. 994.) Protection of Steel Which Is to Be Incased in Concrete. Usually reinforcements are not painted but structural steel, which may remain exposed in shop, transit or during erec- tion previous to being incased in concrete, should have a shop coat of a cement paint, such as Tockolith, manufactured by Toch Bros, of 520 Fifth Ave., New York, and, if delayed in erection, a second coat of the same material will effectively 210 REINFORCED CONCRETE. protect the steel without injuring its adhesion to the con- crete. Toxement. Two pounds of Toxement (Toch Bros., New York), added to each bag of Portland cement used in the concrete will make the latter impervious to water. This mixture has proved very satisfactory in all instances which have come under the author's personal supervision. TABLE LIX-A. COLORING OF CEMENT MORTAR. 1 part of Portland cement to 2 parts sand. Weight of Dry Coloring Matter to 100 Lbs. Cement. P Dry "o Material 2 ^ Used. *o S; Yi lb. lib. 21bs. 41bs. J^ls g So Lampblack Light Slate Light Gray Blue Gray Dark Blue 15 t Slate Prussian Blue Light Green Light Blue Blue Slate Bright Blue 50 Slate Slate Slate Ultramarine Blue Light Bluf Blue Slate Bright Blue 20 Slate Slate Yellow Ocher Light Green Pinkish Slite Light Buff 3 Burnt Umber Light Pinkish Slate Dull Lavender Pink Chocolate 10 Venetian Red Slate, Pink Bright Pinkish Light Dull Dull Pink 2J^ Chattanooga Iron Tinge Light Pinkish Slate Dull Pink Pink Light Terra Light Brick 2 Ore Slate Cotta Red Red Iron Ore Pinkish Slate Dull Pink Terra Cotta Light Brick Red 2H CHAPTER III. THE DESIGN AND CONSTRUCTION OF BRIDGES. The methods employed in bridge construction vary with the design and the type of the bridge. Bridges are classified as Flat Slab, Girder Spans and Arches. The two first classes are similar in design to floor slabs and girders for buildings and are used for short spans and light traffic. FLAT SLAB AND GIRDER BRIDGES. (After "Designing Methods," by Lindau.) A flat slab design will in general be found more desirable and economical for spans up to twenty feet; for longer spans a girder type bridge should be used. By a "girder bridge" is meant a comparatively thin reinforced concrete decking carried by girders extending from abutment to abutment; these girders should preferably be entirely below the deck- ing. In some cases, however, the side girders may be carried up above the slab to form the side rail. Girder bridges are economical under the usual conditions for spans of from eighteen to thirty-five feet; for longer spans an arch bridge will probably be more desirable. Girder bridges have been built for spans as great as sixty or seventy feet; these larger structures, however, should be specially designed, and we have made no attempt to include such unusual structures in the standard tables given. CLASSIFICATION BY LOADINGS. Highway bridges must be designed to safely carry the heaviest load likely to come upon them, and as this maximum load varies with the locality we have arbitrarily adopted three standard classifications by loadings, which should cover all usual conditions. 211 212 REINFORCED CONCRETE. In short span bridges, such as we are now considering, the concentrated loads are the determining factors in the design the uniformly distributed loads usually specified (100 to 150 pounds per square foot) causing smaller stresses. Class No. 1. Light highway specification answering the purposes of ordinary country traffic where the heaviest load may be taken as a 12-ton road roller. Uniformly distributing load, 100 pounds per square foot. Class No. 2. Heavy highway specification, designed for localities where heavy road rollers, up to 20 tons, and electric cars of a maximum weight of 40 tons must be provided for. Uniformly distributed load, 125 pounds per square foot. Class No. 3. City highway specification, designed for heavy concentrated loads and large interurban cars. This classification should be adopted for all city work; the weight of the maximum car has been taken as 60 tons. Uniformly distributed load, 150 pounds per square foot. LOAD DIAGRAMS. The following diagrams represent the loadings adopted in the above classifications and used in the design of the cul- verts and bridges shown herein: .47-0'- -8'6- 71? .. W H 24-0" Ul fcSfc* kftTJ Fig. 92-A. Standard Car, Class No. 2 40 tons on eight wheels. BRIDGE DESIGN AND CONSTRUCTION. 213 Fig. 92-B. Standard Car, Class No. 3 60 tons on eight wheels. The concentrations due to a steam roller will be taken as indicated by Fig. 92-C; two-thirds of the total load being as- sumed on the rear wheels. /t-O o Fig. 92-C. Road Roller Loading Diagram, Class 2. Note. Reinforced concrete slab bridges are very stiff and that part of the slab directly under the concentrated load is materially assisted by the adjoining sections. To assist this lateral distribution of load transverse reinforcement should be used in all slab bridges. 214 REINFORCED CONCRETE. LIVE LOADS. A uniformly distributed load shall be considered as caus- ing the specified pressure per square foot on the bridge re- gardless of depth of fill. A minimum fill of twelve inches is required on all bridges. Wheel or road roller concentrations shall be considered as acting on a line whose length equals the out to out tread of the wheels. Loads on car tracks shall be considered as uniformly dis- tributed over a width of roadway equal to the length of the ties and in the direction of the track for a distance of two feet on both sides of single wheels and for a distance of the wheel base plus two feet for trucks. The above distribution of load is at the level of the road- way. The following methods of findiag the loads on the bridge itself are. suggested: Wheel Loads on Roadway. Assume distribution of load by fill to be only in the direction of the roadway and to be carried down on a slope of l / 2 to 1. The following diagram, Fig. 92-D, showing the distribution of road roller concentrations, illustrates our method. //-O' Fig. 92-D. Showing Distribution of Loads Due to Road Roller. With this arbitrary distribution of loading it will be noted that for a strip, the width of the front wheel, the loaded areas overlap when the depth of fill is greater than the distance be- tween axles. In this case, consider the load as. uniformly distributed over an area of slab 7'6" wide by (d+ll'O") long. BRIDGE DESIGN AND CONSTRUCTION. 215 Wheel Loads on Tracks. See distribution by track sys- tem, page 211. These loads will be considered as distributed in a manner similar to that adopted for wheel, loads on the roadway, excepting that the distribution will be assumed to be in both directions. It should, however, be borne in mind that on double track slab bridges the width of slab considered as supporting one track can not be taken as greater than the distance c. to c. of tracks. Impact. When the fill is less than five feet add 25% for impact for rapidly moving loads. The following diagram (Fig. 92-E) shows the assumed dis- tribution of standard truck load, 40- ton car. "*--"<"<-l ~"~'fa m ,w,.m,>*>iJr" 'UJ\ >> /l-*-tfJ\ r,* L*fffc Fig. 92-E. Load Distribution, 40-Ton Car. Treatment of Loads for Girder Bridges. The distribu- tion of loads through the fill will be as above outlined; in this type of bridge, however, the girders must be so located as to properly take care of the track loads. The girders under the tracks being assumed to carry the full load. Abutments and Side Walls. For the design of abutments and side walls take the horizontal component of the earth pressure as one-third of the vertical pressure at that depth, assuming the resultant to act at a distance one-third the 216 REINFORCED CONCRETE. height above the base. The intensity of the horizontal pres- sure due to live load may also be taken equal to one-third of the vertical intensity at any depth; assuming that the planes of zero pressure, bounding the supporting prism of earth to have a slope of one-half to one. Weights and Dimensions of Electric Cars. The weights assumed for the electric cars in the preceding classification may seem rather large, but it should be remembered that the stresses in the bridge depend not only on the weight of the car, but also on the wheel base, distance between trucks, etc. The dimensions vary with the locality and the weights and dimensions chosen are, in our opinion, justified. It it is desired to make a special design the following data on electric cars may be of use. The values given must be taken as approximate averages. The weights given are for the loaded car and include the weight of the trucks. Small cars, such as are used in small towns, four wheels on two axles, seating twenty-eight persons. Car body, 20'0"x8'3"; over all length, 29'0"; distance c. to c. axles, 8'0"; weight, 11 tons. City car for heavy service, seating fifty-two persons. Car body, 34'0"x8'6"; over all length, 47'0"; wheel base, 4'0" to 6'0"; c. to c. trucks, 24'0"; weight, 15 tons. Large interurban cars, seating 72 persons. Car body, 50'0"- x8'6"; over all length, 56'0"; wheel base, 6'3"; c. to c. trucks, 30'0"; weight, 42 tons. DETAILED DESIGN OF A FLAT SLAB BRIDGE. The following example illustrates the application of the methods above outlined: Problem. Design a flat slab bridge, resting on abut- ments, clear span 16'0", with an earth fill 2'0" deep. Road- way to be 16'0" wide in the clear, Class 2 loading. See Fig. 92-F. BRIDGE DESIGN AND CONSTRUCTION. 217 EAflTH FIU, Fig. 92-F. In the design we will consider only a strip of bridge 12" wide as this simplifies matters. The section will be made constant across the width. DEAD LOAD. Weight of fill = 50 d(2s+d) = 100(36) =3,600 Ibs. Weight of slab (assuming thickness =16") = 1 1 A X 150 X 16 = 3,200 Ibs. Total 6,800 Ibs. Bending moment = 1 /&WI= >^X6,800Xl6 = 13,600 ft. Ibs. Actual dead-load moment = 163,200 inch Ibs. LIVE LOADS. For this span maximum stresses will be caused by the concentrated loads; the uniform load will not be considered. We will determine the bending moments due to the 20-ton roller and to the 40-ton car, using the larger in the design. Road Roller. Maximum moment occurs with rear wheels at center of span. Load on rear wheels equals two-thirds of 40,000 pounds=26,700 pounds. This load as previously explained (see Fig. 92-D) acts on a line 7'6" long; the distribu- tion on the slab is shown by the following diagram (Fig. 92-G) ; 218 REINFORCED CONCRETE. the broken lines indicate the area of slab over which the load is distributed. e'o"- Fig. 92-H. The load per square foot on area 2'0" X 7'6" = ' = 1,780 Ibs. On a strip of bridge 12" wide, the load would be as shown by Fig. 92-H. Maximum moment at center of span, on strip 12" wide, = ^/=(l,780x8) (1,780X^) = 13,400 ft. Ibs. =161,000 inch Ibs. Electric Car. The maximum moment occurs with one truck on center of span. Distribution of load on slab is as shown by diagram (Fig. 92-1) ; assuming ties to be 8 feet long. BRIDGE DESIGN AND CONSTRUCTION. 219 \ 'A * s "I 7-0 \ The full line shows area over which truck load is distributed by track system; the brok- en lines indicate loaded area of slab. Load per square foot of loaded area = 40,000-^90=445 Ibs. Fig. 92-1. The load on a strip 12" wide would be as shown by the following diagram, Fig. 92-J. .9-0' /6~0' Fig. 92-J. Moment at center=yJ/=(2,OOOX8) (2,OOOX2X)-=1 1,500 ft. Ibs. =138,000 in. Ibs. Adding 25% for impact, moment^ 172,000 in. pounds. This moment is larger than that due to the road roller and we will use it in the design. 220 REINFORCED CONCRETE. Using a factor of safety of two on the dead load and four on the live load we have Ultimate moment, dead load=2Xl61,000= 322,000 in. Ibs. Ultimate moment, live load=4X 172,000= 688,000 in. Ibs. Designing moment = /J/o = l, 010,000 in. Ibs. We can determine the depth of slab and the amount of reinforcement required by the formula: 71/0 = 370 fid*, for A s = 0.0085 bd. from which d=15" ^8 = 0.0085X12X15 = 1.53 sq. in. d= distance from top of slab to the center of the rein- forcing bars, we will add \ l / 2 " of concrete, giving 1" on un- derside of bars. Make slab 16J4" thick; 1" corrugated rounds spaced 6" centers. Bend up every third bar at the sixth point, say 2'6" from the abutments. Transverse Reinforcement. To properly distribute con- centrated loads and to tie the bridge in the transverse direc- tion y 2 " corrugated rounds will be placed (over the main re- inforcing bars) crosswise of the bridge, and 12" on centers. Shearing Investigation. The dead-load shear on a strip 12" wide is 3,400 pounds. The maximum live-load shear occurs when the rear wheels of the road roller are 12" inside the abutment, and is equal to 3.S60X1S. s 16 Total shear = 3,400+3,340 = 6,740 Ibs. At the allowed stress of fifty pounds the concrete alone is capable of carrying 12X15X50=9,000 pounds of vertical shear. This would indicate that no provision for shear need be made; every third bar will be bent up, however, as stated. Side Walls for Retaining Fill. It will not be necessary to figure these. They will be made 12" thick and reinforced as shown. BRIDGE DESIGN AND CONSTRUCTION. 221 Waterproofing. Some form of waterproofing should be used and the top surface of the slab arranged for drainage. The top surface of the slab will be as shown on the draw- ings. Bearing on Abutments. All concrete bridges resting on abutments shall have at least 12" bearing; a maximum pres- sure of fifty pounds per square inch will be allowed for slab bridges. DETAILED DESIGN OF A GIRDER BRIDGE. The following detailed design will illustrate the applica- tion of the methods advocated to the design of a girder bridge: Problem. Design a girder bridge, resting on abutm'ents; clear span 32'0"; earth fill 15" deep. Bridge to be 24'0" wide in the clear, with two 4'0" sidewalks and car track on center line. Class 2 loading. The cross-section of the bridge will be as shown on Fi- 92-K. #ir#/rA7 xcr/on Fig. 92-K. 222 REINFORCED CONCRETE. Floor Slab. The minimum thickness of floor slabs will be taken as 5". This thickness of slab should take care of extraordinary concentrated loads such as might be caused should a car be derailed on the bridge. To provide for such contingencies all slabs for girder bridges will be designed for a live load of 500 pounds per square foot, in addition to weight of slab and fill, using a factor of two on the dead and four on the live load. Moments will be figured by the formula M= r 2 zul 2 , since the slabs are continuous over three or more supports; /=dis- tance c. to c. of beams. Design of Slab. Dead load per square foot: . Slab, -&X150= 621bs. Fill, jfXlOO=125 Ibs. Total, 18? Ibs. Dead load moment= A/ 2=3S AXl87X25=390 ft. Ibs. Live load moment= A X 500X25 = 1,040 ft. Ibs. Designing moment = ^0= (2X1 2X 390) + (4 X 12 X 1,040) = 59,350 in. Ibs. Taking a strip of slab 12" wide, we can find the thickness of slab and the amount of reinforcement required from the formula Mo = 370 6d 2 , in which ^ s = 0.0085 bd. Inserting the values for M and b in this formula, we find that d=3.7 inches, and ^ s = 0.38 square inches, where A s is the section of reinforcing steel required in a 12-inch width of slab. Since we have made the thickness of the slab 5", d will be 4", which is greater than required by the formula. The amount of steel required may accordingly be decreased, and is equal to ' X0.38 sq. in. = 0.35 sq. in. Slab will be 5" thick, reinforced with l / 2 " corrugated rounds placed 7" on centers. In the design we have considered the slab as partially fixed on the beams and to provide for the reverse bending moment developed, reinforcing bars will be placed in the top of the slab over the beams; the amount used will be BRIDGE DESIGN AND CONSTRUCTION. 223 one-half that required in the bottom of the slab and we will use l / 2 " corrugated rounds, 3'0" long, spaced 14" on centers. Note. That part of the slab under the sidewalks will be the same as that under the roadway. Girders. In all girder bridge designs the length center to center of bearings will be taken equal to the clear span plus one foot. This length, c. to c. of bearings, will be used in computing the stresses developed. It is desirable to have, brackets at the ends of the girders when conditions permit, so as to reduce the unit vertical shearing stresses and gradu- ally unload the reaction at the abutment into the girder. In all girder designs special provisions for taking care of shear- ing and diagonal tensile stresses should be made. Some of the main reinforcing bars should be bent up near the ends of the girder and stirrups used throughout the length. Girder Gl. This girder will be figured for the dead load and a live load of 125 pounds per square foot on the walk. Dead load on girder: Sidewalk, AXl50X2#X32= 4,000 Ibs. Fill, -HX100X2^X32= 7,350 Ibs. Slab, AX150X2^X32 = 5,000 Ibs. Girder (assumed 12"X36") = 14,400 ibs. Total =30,750 Ibs. Dead load moment = >6 0Y=HX30,750X33 = 127,000 ft. Ibs. Live load, 125 Ibs. per square foot. Live load on girder = 125X2^X33 = 10,000 Ibs. Live load moment =*/& #7=^X 10,000X33 = 41,200 ft. Ibs. To get the designing moment, use a factor of 2 on dead load and 4 on live load, minimum to be, however, 3 (DL-f- LL.) ^/ = 3 (127,000+41,200) X12 = 6,050,000 in. Ibs. Applying the formula Af = 37Q dd 2 , and taking b=\2", we find that d=37"; ^ s = 0.0085 &/=3.76 square inches. We will make girder 12" wide and 40" deep, using five 1" corrugated rounds and bending up two bars as shown, at a point 4'0" from each abutment. 224 REINFORCED CONCRETE. Shearing Provisions. The maximum external vertical shear at the end of the girder, due to full live and dead loads equals 20,375 pounds. In all girder designs the concrete will be assumed as capable of carrying 50 pounds of vertical shear over the cross section bd. Accordingly, if l/ c = total shearing value of the concrete, we have: F c =12x37x50=22,2001bs. This would indicate that no special shearing provisions are necessary. It is advisable, however, in all cases to make some shearing provisions, and we will use U-shaped stirrups of l /2" corrugated rounds, spaced 18" throughout the length of the girder. Girder G2. This will be designed for the average of the stresses in girders Gl and G3, so we will accordingly figure girder G3 first. Girder G3. Class 2 loading requires that the design be based on the maximum stresses produced by either a 20- ton road roller or a 40-ton electric car/ (The alternative live load of 125 pounds per square foot causes much smaller stresses than the concentrated loads.) The two girders G3 will be designed to carry the total car load. Each girder may, however, carry two-thirds of the road roller concentrations; the full load on the front wheel and one-half of the load on the two rear wheels. All interior girders on single span bridges should be fig- ured as T-beams. .Dead load on girder: Fill, HxlOOX5x32 = 20,0001bs. Slab, AX150X5X32 = 10,000 Ibs. Girder (assume 450 Ibs. per ft.) = 14,400 Ibs. Total =44,400 Ibs. Dead load bending moment: J/=}fJF/=^X44,400x33 = 183,000 ft. Ibs. BRIDGE DESIGN AND CONSTRUCTION. Live Loads. Maximum moment due to road roller. 225 We will assume that only one road roller will be on the bridge at any one time. The maximum load on one girder then may be represented by two concentrated loads of 13,300 pounds each, 11 '0" on centers. The maximum moment will occur with one of the loads 2'9" off center of span, as shown Fig. 92-L. Fig. 92-L. Since the fill is but 15" deep, the effect of the fill in distri- buting the loads will be neglected in determining the mo- ment on the girder. 13,300X8.25^13,300X19.25 = 11,100 Ibs. 33 33 M= 13.75X11,100= 153,000 ft. Ibs. Maximum moment due to electric car. For assumed distribution of load by track system, see Fig. 92-E, p. 215. The maximum moment will occur with one truck at the middle of the span, the other truck being off the bridge. (Two cars following each other will, for this span, produce practically the same moment as one car. See sketch of standard forty-ton car, Fig. 92-A.) 226 REINFORCED CONCRETE. Fig. 92-M. The loading for maximum moment will be as shown by Fig. 92-M ; where the load given is that on one girder. #=(10,OOOX16K) (10,000X1.75) =147,500 ft. Ibs. To this static moment add 25% for impact for rapidly moving loads, giving a moment of 184,000 foot-pounds. The maximum moment then due to the specified live loads is 184,000 foot pounds. Designing moment: M =( (2X183,000)+(4X 184,000) \ 12 = 13,224,000 in. Ibs. For the design of T-beams we will use the formula M =O.S6 Fp ^ 2 = 43,000^ dd 2 , using high elastic limit cor- rugated bars. Assume dZ2" and =14", we then have M = 13,224, 000= 43, OOOX14X32 2 X/> from which /> = .0215 AS = . 0215X14X32 = 9.65 square inches. We will make the girder 36" deep over all and use eight 1/4" corrugated rounds. For this length of beam there is no danger of failure by horizontal shear along the horizontal or vertical planes of attachment of the stem to the flange. The distance between beams is S'O", and the amount of reinforcement used = 0.0215 bd, where b = 14"; corresponding to an average percentage of reinforcement for the full width of slab of one-half of 1 BRIDGE DESIGN AND CONSTRUCTION. 227 per cent. This indicates that there is ample width of slab be- tween beams for T-beam action. Shearing Provisions. The vertical external shear at the end of the beam, due to dead load is 22,200 pounds, the load per foot of girder being 1,380 pounds. The shear at the end of the girder due to the car would be practically a maximum when the center of one truck is 3'6" from the abutment; this total vertical shear may be taken equal to 20,000 pounds. The total maximum shear at end of girder = 42,200pounds. In providing for vertical shear we will assume that the concrete carries fifty pounds per square inch on the section dd, and put in steel to carry the excess. Steel for reinforcing against diagonal tensile and shear- ing stresses will consist of bent up main reinforcing bars and loose stirrups. In the design we will neglect the effect of the bent up bars. (If bent up bars are figured to carry the diagonal compon- ent of the vertical shear in the "panel" in which they occur, limit the direct tensile stress to 12,000 Ibs. per sq. inch.) Loose vertical stirrups will be figured by the formula 0.86 dP_ 0.86 dP y ~ V Fc ~ V SOXfid Where y=spacing of stirrups required at any section, F=total stress in one stirrup=total cross section- al area of the vertical legs of the stirrup times the allowed unit stress (16,000 Ibs.). F=external vertical shear at any section. F c =total vertical shearing stress that the concrete is assumed to be capable of taking=F c X bd. If the stirrups are to be figured to carry all the vertical shear without assistance from the concrete, use the formula 228 REINFORCED CONCRETE. Should it be desired to include that part of the vertical shear assumed to be carried by the bent up bars the for- mula becomes 0.86 dP whlch y& = amount of vertical shearing stress carried by bent up bars. The following table gives the data necessary to deter- mine the required stirrup spacing, neglecting the effect of the bent up bars: Stirrups U-shaped, y 2 " Corrugated Rounds, P=6,080. TABLE LIX-B. Distance from Abutment. Vert. Ext. Shear, V. Vc V Vc Required Spacing, y. 42,200 22,400 19,800 8.4' 2 38,400 22,400 16,000 10.4' 4 33,200 22,400 10,800 15.5' 6 28,400 22,400 6,000 27.9' 8 24,200 22,400 1,800 12 16,100 22,400 We will make spacing nine inches for a distance of six feet from the abutment, increasing the spacing to eighteen inches beyond this point. Bent-Up Bars Bend up two reinforcing bars at a point 6'6* from abutment, and two additional bars 3'3" from abut- ment. Girder G2 In designing this girder we will take the average of the moments in girders Gl and G3. J!fothen= */ 2 (6,050,000+13,224,000)^9,637,000 in. Ibs. BRIDGE DESIGN AND CONSTRUCTION. 229 This girder will be made the same size as G3; the amount of reinforcing steel required may be determined by the formula 9,637,000=50,000 ^ 8 X0.86X32 from which A s =7.0 square inches. Make girder 36"xl4" as before, using seven \ l /%" corru- gated rounds. Bend up one bar 6'6" from end and two bars 3'3" from abutment. Stirrups: use l /2" corrugated rounds same spacing as in G3. Bearing of Bridge on Abutment In order to properly distribute the load and provide for sufficient bearing area the bridge will be made solid for the full depth of the gird- ers, where it rests on the abutment. This construction is desirable on all girder bridges, owing to the rigidity and general stiffness given by the solid end. -4 ^ \ k 3 Vi i \ "iit-.-- i kf '" *l \! i^-1 ii ' " i 1 . * li i 4 "TM v " V * :' V 11 H fj 1 J :'; tj Tl : *""***2 ^ -A! % 7 ?-/4 7 ^1 R- /-1 *ces&9'~ : o" /fMfOUCCMtMr [ (. J it. J 1 .".' v v;!|) * is BRIDGE DESIGN AND CONSTRUCTION. 233 TABLE LIX-C. STANDARD DESIGNS FLAT SLAB BRIDGES. LIGHT HIGHWAY SPECIFICATION. Class No. 1 Loading. 12-ton Road Roller. d= depth of fill. t=thickness of con- crete. f=bearing on abut- ment. Main Reinforcement Corr. Rounds. Every third bar bent up as shown. Bars A. llff i is i Illlf S fc; gj> *~ Np< .t "23 .f. _2,-\ . 3-3 Hill 11 d. t. f. Size. Spa. No. L'gth. Number Required. Number Required. No. Length. No. Length. CLEAR SPAN, 6'-0*. 2' 4' 6' 8' 8" 8" 9" 10" 12" 12" 12" 12" W- 35 38 38 30 7'-6" 7'-6" 7'-6" 9 9 9 9 None. 9 9 9 18 18 '18 18 2'-9" 4'-9* 6'-9* 8'-9" 10 14 20 26 7'-6" 7'-6" 7'-6" 7'-6* CLEAR SPAN, 8'-0*. 2' 4' 6' 8' 10" 10" 11" 12" 12" 12" 12" 12" 1 7 " 6 ' 5 * 30 35 38 42 9'-6" 9'-6" 9'-6" 9'-6" 11 11 11 11 None. 11 11 11 22 22 22 22 2'-9" 4'-9* 7'-0* 9'-0" 10 14 20 26 9'-6" 9'-6" 9'-6" 9'-6* CLEAR SPAN, lO'-O*. 2' 4' 6' 8' 11"| 12" 12" 12" 13" 12" 15"| 12" w* 35 38 32 35 iii 13 13 13 13 None. 13 13 13 26 26 26 26 3'-0" 5'-0* 7'-0* 9'-3" 10 14 20 26 j| CLEAR SPAN, 12'-0". 2' 4' 6' 8' 12" 14" 15" 17" 12" 12" 12" 12" S|| 38 32 38 32 13'-6]| 15 15 15 15 None. 15 15 15 30 30 30 30 3'-0" 5'-3" 7'-3* 9'-6" 10 14 20 26 13'1" CLEAR SPAN, 14'-0". 2' 4' 6' 8' 14'i 12" 151 12" 17"i 15* 19" 15" \<> 6H'| 32 6 2 " 35 5^1 38 K 17 17 17 17 None. 17 17 17 34 34 34 34 3'-3* 5'-3" 7'-6" 9'-6" 10 14 20 26 16'-0* CLEAR SPAN, 16 -0. V 15" 12* 7 ^* 5V4" 38 17'-6" 19 None. 38 3'-3" 10 17'-6* 4' 17" 12" 6 * 35 17'-6" 19 19 38 5'-6* 14 17'-6* r/ 19" 15" 1 ' W" 38 18'-0" 19 19 38 7'-6* 20 18'-0* 8' 21" 15" 1 " 4X2" 46 18'-0" 19 19 38 9'-9" 26 18'-0" CLEAR SPAN, 18'-0". V 16" 15" y s "\5 "\ 42 20'-0" 21 None. 42 3'-3* 10 20'-0" 4' 19" 15" 1 "5^*1 38 20'-0" 21 21 42 5'-6" 14 20'-0" V 21" 18" 1 J4HJ 46 20'-6" 22 22 44 7'-9" 20 20'-6" 8' 23" 20" I^ISH'I 38 20'-9" 22 22 44 lO'-O" 26 20'-9" CLEAR SPAN, 20'-0". 2' 18" 15" 1 "16 '1 35 |22'-0" 23 None. 46 3'-6" 10 22'-0" 4' 21" 15" 1 ",5 "| 42 22'-0" 23 23 4fi 5'-9" 14 22'-0" 6' 23" 18" l^'SM"! 38 22'-6" 24 24 48 8'-0" 20 22'-6" 8' 26"| 20" 1H'5 "1 42 |22'-9" 24 24 48 10'-3" 26 22'-9* 234 REINFORCED CONCRETE. TABLE LIX-D. STANDARD DESIGNS FLAT SLAB BRIDGES. HEAVY HIGHWAY SPECIFICATION. Loading. 20-ton Roller or 40-ton Car. d = depth of fill. t=thickness of con- crete. f = bearing on abut- ment. Main Reinforcement Corr. Rounds. Every third bar bent up as shown. Bars A. I* !!' s-sslt WSo!z: d. t. f. Size. Spa No. L'gth Number Number Required. Required. No Length. No. Length. CLEAR SPAN, 6'-0*. 2' 4' (i' 8' OOCOCC to to to to ^"5 * 42 %*<5 "l 42 %"\7 1 A"\ 28 3 4*|6 "| 35 7M5" 7'-6" 7'-6" 9 9 9 9 None. 9 9 9 18 18 18 18 2'-9" 4'-9" 6'-9* 8'-9" 10 14 20 26 7'-6" 7'-6" 7'-6" 7'-G" CLEAR SPAN, 8'-0". 2' 4' 6' 8' 11" 11" 12" 13" 12" 12" 12" 12" W- 38 38 38 30 2222 11 11 11 11 None. 11 11 11 22 22 22 22 3'-0" 5'-0* 7'-0" 9'-0* 10 14 20 26 9'-6" 9'-6" 9'-6* 9'-6" CLEAR SPAN, lO'-O*. 2' 4' 6' 8' 12" 13* 14" 15" 12" 12" 12" 12" H' 5 ' s 2 " 42 32 35 38 !!$ 13 13 13 13 None. 13 13 13 26 26 26 26 3'-0" 5'-0" 7'-3* 9'-3" 10' 14 20 26 11:? CLEAR SPAN, 12'-0*. 2' 4' (i' 8' 14" 15" 16" 17" 12" 12" 12* 12* 7*' 6" 6" 5* 6" 35 35 42 35 CO CO CO CO O2 O2 O2 O5 15 15 15 15 None. 15 15 15 30 30 30 30 3'-3" 5'-3" 7'-3" 9'-6" 10 14 20 26 || CLEAR SPA N, 14'-0". 2' 4' (i' 8' 17" 18" 20" 12" 12* 15" 15" K " 5 * 5 " 42 38 38 42 15'-6" 15'-6" 16'-0" 16'-0* 17 17 17 17 None. 17 17 17 34 34 34 34 3'-3" 5'-6" 7'-6* 9'-9" 10 14 20 26 15^-6" CLEAR SPAN, 16'-0". 2' 4' 6' 8' 18" 18" 20" 22" 12" 12" 15" 15" H" 6 " 5 2 " 6 " 35 38 42 35 ll'Io' 19 19 19 19 None. 19 19 19 38 38 38 38 3'-6" 5'-6" 7'-9" 9'-9" 10 14 20 26 F rt * pQ 1st? i.sc3s Tranverse Rein- forcement in top of slab. H"Corr. Rounds. 17 '0' Long. Bars C. sga.2 aP^-S .0 SN .fc.2 a, 3 jil 5 SrflfS*" Illil : Horizontals in Side Walls. H* Corr. Rounds. Number required for both walla. Bars E. d. t. f. Size. Spa. No. L'gth. Number Required. Number Required. No. Length. No. Length. CLEAR SPAN 6'-0'. 2' 11' 12' 3 4' &/<>' 32 7'-6' 9 None. 18 3'-0' 10 7'-6' 4' 11' 12" Z 4' VM* 32 7'-6" 9 9 18 5'-0' 14 7'-6' 6' 11' 12" */*' W/o" 32 7'-fi' 9 9 18 7'-0' 20 7'-6' 8' 11' 12" %" 6 ' 35 7 '-6' 9 9 18 9'-0' 26 7 '-6' CLEAR SPAN, 2' 4' 6' 8' 12'j 12' 12' 12' 12" 12' 13"| 12' K 5 ' 5 ' 6H* 42 42 42 32 9'-6' 9 '-6' 9'-6' 9'-6' 11 11 11 11 None. 11 11 11 22 22 22 22 3'-0' 5'-0' 7'-0' 9'-0' 10 14 20 26 SP-6* 9'-6' 9'-6' 9'-6' CLEAR SPAN, lO'-O". 2' 14" 121 V*" w 32 ir-6' 13 None. 26 3 '-3" 10 11 '-6' 4' 14" 12" W VM' 32 ll'-6" 13 13 26 5'-3" 14 ir-6* 6' 14" 12" %' 6 ' 35 ll'-6" 13 13 26 7'-3" 20 ll'-6' 8' 15" 121 y 8 " 5W 38 ll'-6" 13 13 26 9 '-3" 26 ll'-6' CLEAR SPAN, 12'-0'. 2' 16" 12* t/' 5' 42 13-6' 15 None. 30 3 '-3" 10 13 '-6' 4' 16" 12" ' 5' 42 13'-6' 15 15 30 5'-3" 14 13'-6* 6' 16" 12' %' 5' 42 13 '-6' 15 15 30 7 '-3" 20 13'-6' S' 17' 12" 1 " 6' 35 13 '-6" 15 15 30 9'-6" 26 13'-6' CLEAR SPAN, 14'-0' 2' 19" 12" 1" 5V*" 38 15'-6" 17 None. 34 3 '-6* 10 15'-6' 4' 19" 12' 1' WA 1 38 15 '-6' 17 17 34 5 '-6' 14 15'-6* 6' 19" 15" r VA' 38 16'-0' 17 17 34 7'-6' 20 16'-0' 8' 20" 151 i" 5 " 42 16'-0" 17 17 34 9'-9' 26 16'-0' CLEAR SPAN, 16'-0*. >' 21' 12" 1 " 5" 42 17'-6" 19 None. 38 3 '-9" 10 17'-6' 4' 21" 12" 1 " 5* 42 17'-6" 19 19 38 5'-9" 14 17'-6' 6' 21" 15" 1 " 5* 42 18'-0" 19 19 38 7'-9" 20 18'-0" 8' 22' 15" \%" 6" 35 18'-0" 19 19 38 9'-9* 26 18'-0* CLEAR SPAN, 18'-0". 2' 22" 15" m" 6* 35 20'-0" 21 None. 42 3 '-9" 10 20'-0' 4' 22' 15" m' 6" 35 20'-0" 21 21 42 5'-9* 14 20'-0' 6' 22" 18" m r 6' 35 20'-6" 22 22 44 7 '-9' 20 20'-6' 8' 24" 20" \w "5" 42 20'-9" 22 22 44 lO'-O" 26 20'-9' CLEAR SPAN, 20'-0'. 2' 24" 15" 11/" WA' 38 22 '-0" 23 None. 46 4'-0" 10 22'-0' 4' 24" T5" m" WA* 38 22 '-0" 23 23 46 6'-0' 14 22'-0' 6' 24" 18" m" 5 " 42 22 '-6" 24 24 48 8'-0' 20 22'-6" S' 27" 20" w 4J/2" 46 22 '-9" 24 24 48 10'-3" 26 22"9* 236 REINFORCED CONCRETE. COMPLETE DESIGNS OF GIRDER BRIDGES FOR SPANS FROM TWENTY TO FORTY FEET. Reference drawings: Figs. 92-Q, 92-R and 92-S. (See also Detail Sheets for Girders Gl, G2 and G3.) Reinforcing Steel. Mechanical bond bars, elastic limit, 50,000 Ibs. The following tables, in conjunction with Figs. 92-Q, R and S, and the three sheets of details, showing slab and girder construction, give the complete design of Girder Bridges for spans of twenty, twenty-five, thirty, thirty-five and forty feet. The standard bridges have been figured for the three classes of loadings, but with only one depth of fill eighteen inches. A minimum depth of fill of twelve inches is re- quired on all girder bridges. The slab has in all cases been made five inches thick. The two girders under the car tracks have been figured to carry the full car load. Girders Gl in Class 1 and Class 2 Bridges, and Girders G2 in Class 3 Bridges have been de- signed for that proportion of the roller load which may come upon them. For the sake of uniformity Girders G2 in Class 3 Bridge-s have been made the same depth as Girders G3. The standard designs for Class 3 Bridges are based on the sections shown in Fig. 92-S, page 241. The tables, however, apply just as well to the "Alternate Section," which may be preferred by some engineers. 238 REINFORCED CONCRETE. TABLE LIX-F. CLASS 1 BRIDGES. GIRDERS Gl. See Detail Sheet, Page 243. Clear Span. h. b. f. Reinforcement. Bent Bars. Stirrups. 20'-0" 32" 12" 15" 6-%" Corr. Rounds. In Beams with 6 Bars Bend up 1 Bar at the $ Point. Bend up 2 Bars at the ^ Point. In Beams with 8 Bars Bend up 2 Bars at the \ Point. Bend up 2 Bars at the ^ Point. l /z * Corr. Rounds Bent as Shown on Detail Drawing. Spacing: 12' to the i Point, 18 "Beyond. 25 '-0" 38" 12" 15" 6- 7 A'-' Corr. Rounds. 30'-0" 44" 12" 15" 3- 7 / s " Corr. Rounds. 3-1" Corr. Rounds. 35 '-0" 50" 14* 18" 6-1" Corr. Rounds. 40'-0" 53" 15" 21" 8-1 * Corr. Rounds. GIRDERS G2. See Detail Sheet, Page 244. 20'-0" 25" 12" 15" 6-1 " Corr. Rounds. . 'a -" "3 a 25'-0" 29" 14" 15" 8-1 " Corr. Rounds. gP-i ^RP-i 1 ^ 2 a .al II a -3 30'-0' 34" 14" 15" 8-1 J/s" Corr. Rounds. . ~-o 2 2 co b fe oo b ' ^- 1 1 jap^n ^apppQ 3 1 -Sn 35 '-0" 39" 14" 18" 4-1^ "Corr. Rounds. 4-1 \i" Corr. Rounds. g rH IM -g a For vertical shear V=Vi for .*<<* V=V^W for^>a and for normal stress in ,rib at x N = (Vsin$+Hcos$) J W (l-a) Parabolic Arch without Hinges. Assuming the cross-sec- tion of the rib to so vary from the crown toward each end that at any section I=I sec A = A Q sec$ (see p. 272) where 7 and A Q denote the moment of inertia and cross- section of the rib at the crown and introducing these to- gether with the equation of parabola we get H= where Mv = l*+12lnf> \^(^+* hln *)- w { (aP-6nt>)(l-aV+6l*p{> \ 1 2 = . (radius of gyration) 248 REINFORCED CONCRETE. where n = 4h and Neglecting the effect of axial stress since the term ought then to disappear, we get: _ and for temperature stresses at springing and and neglecting axial stress and Mt = Hi h at crown /"t = . at springing at crown where t = temperature change in number of degrees F. f = Coefficient of expansion and contraction. //t = Horizontal reaction at the left support due to the temperature change. BRIDGE DESIGN AND CONSTRUCTION. 249 For a Parabolic Arch with Two Hinges, we have 15 and neglecting axial stress, we get 5a( L= 8A2 iU 15 + Ah and neglecting the axial stress, we get For Flat Parabolic Arch with Two Hinges, we have i H= - W 2 ' and neglecting axial stresses _ Sa(l-a) (P+al-a*) ... For full uniform load, we have approximately where w is uniformly distributed load per unit length of span. Well proportioned arches of 3, 5 or 7 centers are drawn according to following method. 250 REINFORCED CONCRETE. It should be borne in mind that 3-center arches are used only for 5-center arches for 7-center arches for h = 0.3 /to 0.36 / A = 0.25 to 0.33 / . 92-x. For 3-Center Arch. Strike semicircle with diameter = J and divide same in 3 equal parts at a and c. Draw chords and radii. Select rise of arch at B and draw BA =E ba and BC ^ be intersecting chords from a and c. BRIDGE DESIGN AND CONSTRUCTION. 251 For 5-Center Arch. Divide the semicircle in 5 equal parts, draw chords and radii and select the smallest radius r, thus determining points A and and proceed as for 3-center arch. Fig. 92-Y. For 7-Center Arch we select r l and r z . The following table forms a guide for selection of these radii : TABLE LXIII-A. 5 Centers. 7 Centers. h / TI ~ h / ri / *"2 ~~T 0.36 0.35 0.34 0.33 0.32 0.31 0.30 .278 .265 .252 .239 .225 .212 .198 .33 .32 .31 .30 .29 .28 .27 .26 .25 .228 .216 .203 .192 .180 .168 .156 .145 .133 .315 .302 .289 .276 .263 .249 .236 .223 .210 252 REINFORCED CONCRETE. THE ELASTIC THEORY OF ARCHES SIMPLIFIED.* Introduction. Formerly, when stresses in plain masonry arches were computed, the engineer was satisfied when the line of resistance was within the middle third of the arch ring, and this is satisfactory for symmetrical loading and heavy voussoir arches, where the ratio of the live load to the dead load is a small one and here the graphostatic method was considered sufficient, even though arbitrary. But with the advent of reinforced concrete it has become necessary to resort to the elastic theory to properly deter- mine the stresses under symmetrical and unequal loadings for comparatively light structures, where temperature stresses also become very important. The application of this theory has not come into general use among engineers, notwithstanding the fact that experi- ments undertaken by the Austrian Association of Architects and Engineers have demonstrated that arches can be consid- ered elastic curved beams and computed accordingly. While we admit that even the elastic theory does not give mathematically correct results, owing to the questionable rigidity of the abutments, a marked improvement is found as compared with the usual assumption of three points through which the pressure line is supposed to pass. The designing engineer must be qualified to judge as to the correctness of these assumptions. The method here given will in an extremely simple way permit of ascertaining the intensities of stresses in any part of the arch ring, whether it be due to live or to dead loads *From a translation by Mr. C. W. Hoffman, C. E., of Mr. Th. Landsberg's article in "Zeitschrift des Vereins fur Deutscher Ingenieure," Dec. 14, 1901. BRIDGE DESIGN AND CONSTRUCTION. 253 and will also lead to formulas whereby the arch ring ma> be dimensioned in advance of the statical examination. An arch fixed at both ends is statically threefold indeter- minate and the three unknowns which cannot be determined by the static theory can be found by the elastic theory. Preliminary Examination of Reactions Caused by a Con- centrated Load. As a concentrated load G, Fig. 93, moves over the arch, it produces in each position two reactions, 7? A and R B , which must be in equilibrium with the concentrat- ed load G. Fig. 93. The point E in which the two reactions intersect the load G describes a line, the form of which depends upon the curve of the arch ring. This line will herein be called the "line of reactions." During the progress of the moving load G the two reactions will envelop curves, which will be called "involute of reactions." The line of reactions and the involute of reactions being known, the location, direction and magnitude of the reactions can readily be found for any given position of the concentrated load G. We will, however, show that we can dispense with the in- volute of reactions. If the line of reactions is known, the reactions can be de- termined when for the reactions other points, A' and B', Fig. 93, are established, through which the reactions must pass as we know that both reactions pass through point E, which In turn is located by the positions of load G. 254 REINFORCED CONCRETE. Therefore lines passing through E and through A' and B\ respectively, represent the reactions. We will next show how to quickly determine the direc- tion, location and magnitude of the reactions for any given concentrated load G. To simplify matters, we will assume the arch to be a flat parabola, though the results can, without hesitation, be ap- plied to flat circular arches, or other curves by a slight modi- fication of the formulas. Let /~span or horizontal projection of neutral axis of arch between its intersections with the skew- back or springing line s the rise of the neutral axis. The arch is assumed to be symmetrical, with the spring- ing lines on same level. Then we have from Fig. 94: (1) The line of reactions is a straight line at a distance of gs above and parallel to AB. (2) If a second line is drawn at a distance of Is above and parallel to AB intersecting the perpendiculars through the neutral axis at the skewbacks at Ao and Bo, then the lefthand reaction, due to a concentrated load at a distance x to the right from the center intersects the perpendicular through A at a distance v below Ao Bo and the righthand reaction in- tersects the perpendicular through B at a distance if below Ao Bo', or, geometrically expressed: -J. 15 The following simple construction results (Fig. 95): Diaw line AoB at a distance of f s above and parallel to AB and a parallel II at a distance f s s below A B . BRIDGE DESIGN AND CONSTRUCTION. 255 Producing the load line G at a distance x from the center will cut off the length D' D" = fts between the parallel lines ..-o Lin? of Reactions A line connecting Ao with D" intersects the perpendicular through the crown at L and we have OL A s FT 7T + X OL = ~ ; A horizontal line through L will intersect the vertical through A and A', which passes through the lefthand reaction. Fig. 95. The construction of v' and B' is done in the same manner, as is indicated in Fig. 95. 256 REINFORCED CONCRETE. Connecting these points with E gives us the reactions in regard to location and direction. Their magnitude is easily found by means of a force polygon. If (Fig. 94) ab = concentrated load at E, then be = R t and ca = tf . A B Similarly, lines from the points of intersection A' and B', are drawn for different positions of the concentrated load and the reactions determined. It is sufficient to find these intersections on one side only and transfer them for sym- metrical loads to the opposite side. Successive Steps in the Design of an Arch. In computing an arch we proceed as follows: (1) Establish the arch ring. (2) Locate point O in the perpendicular through the crown at a distance f s above AB. (3) Draw the line A B through O parallel to AB. (4) Draw a horizontal line II at a distance T 8 gS below A B or T 2 g s above A B. (5) Subdivide the span AB in a number of equal parts. (6) Establish the points of intersection A' and B' of the reactions with the perpendiculars through A and B for all po- sitions of load G. (Fig. 95.) (7) Draw the line of reactions A" B" a distance f s above AB. (8) Lay off the reactions as to location and direction for all positions of load G by connecting the points A' and B' with the points E on the line of reactions. (9) Determine graphically the magnitude of reactions. This construction is indicated in Fig. 96, except that for the sake of simplicity the lines for finding v and if have been omitted. Line of Pressure Due to Dead Load. Determine weights for each point of loading as usual (Fig. 96) and for each of these loads find the left and righthand reaction. BRIDGE DESIGN AND CONSTRUCTION. 257 The loads G are conveniently laid off at the points marked 5, 4, 3 Ill, IV V, where they can be resolved into the two reactions which now are combined to form a force poly- gon, a, h c m, which hereafter will be called polygon of reactions. Fig. 96. Since all stresses due to dead load act simultaneously, all reactions act simultaneously and the resulting abutment reac- tion R^ has the direction a m. The location of this reaction R A is determined by an equilibrium polygon 5' 4' 3' II' III' IV V with an arbitrary pole O/. 258 REINFORCED CONCRETE. The point of intersection L' of the extreme sides of this polygon is the point through which the resulting reaction, which is parallel to am, must pass. Combining 7? A with G*> G the line of resistance and the line of pressure can be drawn, as shown in Fig. 96. It will be noted that this construction is free from ar- bitrary assumptions and we can easily check the location of point m, as the vertical component of am must be equal to one-half of the total vertical load. Line of Pressure for the Critical Condition of Loading. We will demonstrate later how to determine the critical po- sition of the live load for any section; for the present be it assumed that these positions are known. Then determine the amount of live load which under most unfavorable conditions will come upon each point of loading that is, a load Le, where L equals live load per lin. ft. and e the distance between assumed points of loading. This load is then consecutively placed on all points of loading and the resulting reactions are determined as in Fig. 96 and combined to form the left (right) hand reaction poly- gon; then draw the equilibrium polygon with the arbitrary pole O. In Fig. 97 a b c m represents the reaction poly- gon and O 2 the pole. The equilibrium polygon is marked V" , IV", III", II", I", 1", 2", 3", 4", 5". With these two polygons the corresponding line of pressure for any condition of loading can be deter- mined. Let it be assumed arbitrarily that in order to produce maximum stress in Joint 2 the points 7, II, III, IV, V would have to be loaded. The loads I, II, III, IV, V produce a re- action on the lefthand side, the magnitude and direction of which are represented by fm in the reaction polygon. The location is determined by the condition that the resultant fm = R l _ v must pass through the intersection of those sides of the equilib- rium polygon which border the forces R l and R V that is, point a. Combining R^ with the reaction caused by the dead load BRIDGE DESIGN AND CONSTRUCTION. 259 in Joint 2 gives us the total resultant due to this condition of loading and acting at Joint 2. This force was determined in regard to location, direction and magnitude under the head of line of pressure due to dead loads. Fig. 97. Assuming now that the maximum stress in Joint 2 would occur when points 5, 4 and 3 were loaded, the procedure would be similar to that just illustrated. The lefthand reaction R :> .^ is first determined as to location, direction and magnitude, and combined with the loads to the left of Joint 2, t. e., with the loads at points 5, 4, 3. The" re- sultant R intersects Joint 2 at 5, and is finally to be combined with the reaction due to the dead load. 260 REINFORCED CONCRETE. It is clear that by this method the critical position of the line of pressure and its deviation from the neutral axis, as well as the intensity of stress for any section of the arch ring can be found, provided the most unfavorable condition of loading is found. Critical Condition of Loading for a Given Section, The reactions due to a moving concentrated load at once dis- close the most unfavorable condition of loading, so that the involute of reactions may be dispensed with. Considering the points near the intrados of a section, then any force in this section passing above the middle third produces tension at the intrados; any force in the section passing below the upper limit of the middle third produces compression at the intrados. For points of loading at the right of the assumed sec- tion under a moving concentrated load, the lefthand reac- tion is determinate and for points of loading at the left of the section, we must consider the righthand reaction. We recommend that both right and left reactions be drawn. However, if the reactions for but one side are drawn, the opposite reactions may be examined in a section located symmetrically with the one under investigation letting the reactions act there. In Fig. 97 the lefthand reaction at section 3 for a con- centrated load at point 2 accidentally passes through K, the tipper limit of the middle third, but the reactions due to a load in 1, I, II, III V, intersect below the middle third, produc- ing compression near the intrados at section 3, while a load at point 3 produces tension at these points. In order to find the stress produced by a load in 4 and 5 (at the left of 3) we investigate section /// with reference to the effect of a load at IV and V. A load at 4 and 5 will have the same effect on section ///. We see that loads at IV and V produce tension at the in- trados of section /// because the reactions R ly and R v pass the section far above the middle third. BRIDGE DESIGN AND CONSTRUCTION. 261 Maximum tension in section 3 therefore is found by load- ing points 5, 4 and 3, maximum compression is found by loading points 2, 1, /, //., V, while a load at point 2 pro- duces a stress equal to zero. It is sufficient to consider the points on one side of a section as fully loaded and the points on the other side as not loaded. Proof of the Correctness of Locating Points A' and B'. If, according to Muller-Breslau (Die neueren Methoden der festigkeitslehre, 2d edition, p. 115), the two forces X and Y, acting at O and the moment Z be considered as the three un- known quantities, then X can be found from the condition that the algebraic sum of the moments of X and Y and of the mo- ment Z with the point A as a center must be equal to the re- sisting moment at the springing or skewback A, Fig. 98. The origin O must be so chosen that in each of the three equations for elastic arch all unknowns are eliminated but one. With this in view the point O must represent the center of gravity of the neutral axis, and X and Y must coincide with the two principal axes of the arch center line. If the latter is a flat parabola with a nse = ,y and a span = /, the point O will be located at a distance $s above AB. Assuming a load at a distance x to the right of the center, we may write the three following equations: (25) 262 REINFORCED CONCRETE. By means of Formulas (25) the influence lines for the three unknown quantities, X, Y and Z, can easily be drawn. For two positions of the load symmetrical with respect to the vertical axis, X and Y have equal values. Y changes its sign with x, hence symmetrical positions of Y only change the sign. Uniform load equal on both sides of the center makes 7 = 0. In order to replace X, Y and Z by their resultant, we com- bine the resultant of X and Y with the moment Z, which causes a parallel shifting of the resultant of X and Y. Since its di- rection is given by Y tan 8 = -j it will be sufficient to establish one point through which it must pass. Assuming that the resultant intersects the vertical center line at S, a distance m below O, then the algebraic sum of the static moments of X, Y and Z must equal zero; that is, the fol- lowing equation for m must be satisfied: Fig. 99. X m Z = 0, whence m = -y Substituting the values of Formulas (25) for X and Z, The resultant passing through 5 forms the angle 5 with the horizontal, and if the negative sign of Y is taken care of by laying it off downwards, we have BRIDGE DESIGN AND CONSTRUCTION. 263 Y 32sx = X = 15 (J 2 - and with the relations in Fig. 99, I u = tan 5 = IQslx m u = At point ^4i the resultant of X, Y and Z is combined with the vertical component of the left hand abutment reaction. The reaction we find (Fig. 100), therefore, must pass through Ai. When the load advances to the left of the center line we obtain similarly, Fig. 100. m = 8sP IGslx l = 15 (P 4* 2 ) Particular notice must be given to the fact that MI is posi- tive when laid off downwards while u is positive when laid off upwards. By addition we obtain 8sl The values for v\ hold good for loads at the right of the center for righthand reactions, and the values v for righthand reactions when the load is at the lefthand side from the center. Approximate Analysis of Dead Load. In the following investigation we assume the upper limit of the dead load diagram to be a straight line, as shown in Fig. 101, the in- 264 REINFORCED CONCRETE. trades to form a parabola, the rise of the arch to be s and the height of the dead load diagram at center equal to r. At any point a distance x from the center the height of the dead load diagram is r + 4s* 2 or with a weight per unit of D the load over dx is (4sx 2 \ r + -p-J dx t= Fig. 101. For this condition of loading Formulas (25) furnish the following values: .... (26) 81 BRIDGE DESIGN AND CONSTRUCTION. or when integrating, 265 K D =0 DP = 60 < 5r (27) Since V D = 0, the resultant from X D and Y D is acting hori- zontally, and is of the magnitude X D , intersecting the vertical center line at a point m D below O. We have 0, or m. Referring to Formulas (27), we get X, 8 always intersects the vertical through the springing line at a distance m D below O. The resultant of all forces acting at the left (or right) of the crown intersects the vertical center line at a distance above O, which is equal to n and subject to the following conditions (Fig. 102): Fig. 112. 266 REINFORCED CONCRETE. 10r The point of intersection between the resultant and the center line is located at a distance X below the neutral axis ai the crown, and we have The abutment reaction intersects the vertical through the springing at a distance w below the axis AB, and we have w = m The intercepts between the neutral axis and the lines of pressure are, at the crown, downward, BRIDGE DESIGN AND CONSTRUCTION. 267 at the springing, downwards, IV *= T5 TABLE LX. VALUES OP X AND w FOR VARIOUS VALUES OP . 5 f 1 1.5 2 2.5 3 4 X 0.01255 0.0185 0.02s 0.026s 0.03s 0.036s W 0.0335 0.0475 0.065 0.067s 0.07s 0.093s With these three points, the location of the line of pres- ure and the intensities of stress on any part of the arch ring are established. Thickness of Arch Ring at Crown and Springing. The course of investigation is as follows: The condition of loading which is most unfavorable at the crown is determined, and as the line of pressure due to the dead load deviates downwards, it is obvious that such position of the live load as will make the pressure line de- viate still further is especially unfavorable. For a given load this position of the live load can be easily determined by drawing a tangent to the involute of reactions passing through the upper limit of the middle third of the ring at the crown (Fig. 103). Their intersections L? and L" with the Jine of reactions indicate the points to which the live loads REINFORCED CONCRETE. must advance. All loads at the left and right of points L' and L" produce compression in the parts of the crown near the intrados. In order to obtain the maximum stresses this space must be completely covered by the live load. For approximate calculations we may assume that L'L" represents the middle third of the span and the two outer thirds are supposed to be under a live load L per lin. ft. Then we have, according to Formulas (26), , Line of ReacJ-'ions or Locus t_ Fig. 103. 2 x 15 4# 2 ) 2 dx = -- (approximately) (28) x= (approximately ) The intersection of X, Y, Z with the vertical center line is located W L below O (Fig. 104), and we have X T w Z,= L L L _LZ_ 2 645 m L ~ 24 ' 3LZ 2 ~ 5 The resultant X L intersects the vertical axis at a distance of BRIDGE DESIGN AND CONSTRUCTION. 269 The resultant of the forces acting on one side of the ver- tical axis intersects same at a point located a distance t below the crown, t being found as follows: Fig. 104. 3LI* 645 or LZ 2 645 3 6 X, = ' = *( V - !f) = 2P7 The resultant of all forces on one side of the vertical axis dead load and live load intersects the joint at the crown at a point T (Fig. 105). The location of point T is as follows: Fig. 105. X X, * 270 REINFORCED CONCRETE. S is the maximum deviation at the crown and is figured positive downwards. If we simplify matters by making 21 and we have C = n r 5 8 L C s C I - 27_X + 27 = * U = 27 + C or approximately 27 For These values are shown in Table LXI. TABLE LXI. VALUES OF C, X AND S' FOR VARIOUS VALUES OF . 5 r i 1.5 2 2.5 3 4 C 0.492 0.772 0.875 1.036 1.180 1.432 X 0.01255 0.0185 0.025 0.0265 0.035 0.0365 S'j 0.0125* + 0.0182 0.0185 + 0.0286 0.025 + 0.0324 0.026s + 0.0384 0.03? + 0.0437 0.0365 + 0.0530 The maximum intensity of stress S m at the crown occurs at a deviation 5" of the resultants from the neutral axis. Ii the thickness of crown = d, we have BRIDGE DESIGN AND CONSTRUCTION. 271 C _ where X = X + X L If K denotes the maximum permissible unit stress, we have the following equation for d, d 65 * K~ 2K hence, _Dl* _DP If we assume ~ we have and Y A (D+L) "- 85 For convenience we will here repeat the notation in above formula: d = thickness of crown in feet. D = weight per cu. ft. of masonry in Ibs. / = span of neutral axis in ft. .y^rise of neutral axis in ft. / = permissible pressure on masonry in Ibs. per sq. ft. r = height at crown of dead load diagram in ft. (Fig. 101). L= : live load in Ibs. per sq. ft. 272 REINFORCED CONCRETE. Example. Find thickness of crown in parabolic arch for the following conditions: I = 60, 5 = 6, r =3, L = 100 Ibs. D = 150 Ibs. We have then = TJ- 2, K = 144 X 400 = 57,600 Ibs. sq. ft. hence S = 0.025 + 0.0325 = 0.1525 = 4.11. From Formula (29) , 4.11 X 150 X 60 2 2 l^ I 6 I 1 + V 1 + 192 x 0.1525 X 57,600 X 16 X 57,600 X 6 \ A r \ A 4.11 x 150 x 60 2 / = 1.334 ft. for a plain concrete arch. Thickness of Arch Ring on Both Sides of Crown Down to the Skewback. A quick and practical method of finding the thickness of the arch at any point after finding the crown thickness is as follows (Fig. 106) : Fig. 106. Diagram Showing Fig. 107. Diagram Showing Lo- Method of Finding Thick- cation of Neutral Axis, ness of an Arch. (1) Draw radial lines dd intersecting the neutral axis at right angles, and perpendicular lines through the points of intersection. (2) On these perpendicular lines lay off the crown thick- ness ab and produce horizontally to the radial lines dd, cutting them at points c. Then the distances cc represent the arch thicknes-s at the various points. BRIDGE DESIGN AND CONSTRUCTION. 273 Location of Neutral Axis. According to Prof.E. Moersch in "Der Eisenbetonbau," 1906, we have the following equation for the location of the neutral axis, p being the percentage of reinforcement on each side of the neutral axis (Fig. 107) : Making e = OA2d and F e = pbd, we have M_ -x 3 + \dx* + 31.75ft N~d~ Here N = hence _M _5 Nd d The curves, Fig. 108, are plotted for values of x = O.ld; 0.2d, 0.3d, etc., as abscissas and j for different percentages of reinforcement p = 0.001, p = 0.002, p = 0.003., etc., as ordinates. Fig. 108. Diagram of Curves for Different Values of P. When x is found either by trial from Fcrmula (41) or taken from the diagram, Fig. 108, the different stresses are found as follows (Fig. 107): 274 REINFORCED CONCRETE. (32) c W or ob = bx_ f c n , 2 xd) " (32a) where f c is the reinforcement at either extrado or intrado providing they are alike. Tension: 5 e = 5 b ~ = 15S b - 92 ^~- r (33) X X Compression: 6V= 156"b ~~ ~ (34) where j*- = 15 Thermal Stresses. According to Prof. Cain, the thermal stresses in a reinforced concrete arch ring may be expressed as follows : TT E c let 7 C nl s /Q r, ti. = ~^r~, ^ ^r~7 r c. (oo) 2, {y^) m Z \y) o where H = the horizontal thrust at the crown due to change of the length of the arch line with change of temperature, t = degrees change in temperature, e = expansion per degree. a a = number of segments, s, in the arch ring, / = span, y = the ordinates of s. The normal force at any joint will be the component of H perpendicular to that joint, and the bending moment will be Buel & Hill give, p. 136 of Reinforced Concrete, = DE C (/c + /) (36) ss (xy) where D deflection at crown due to change of length of arch ring with changes of temperature and H the corresponding hori- zontal thrust. BRIDGE DESIGN AND CONSTRUCTION. 275 By tabulating the values xy for all the segments s of the ring from one springing to the other, the solution is quite simple, since E c (7 C 4- n/ B ). . - is constant. Prof. Cain* suggests that an increase of steel should be used in arches to satisfy the condition at any critical point, that all the bending moments due to load and temperature should be borne entirely by the steel at some stress under the elastic limit, say 20,000 Ibs. EXAMPLE OF AN ARCH DESIGNED ACCORDING TO THE ELASTIC THEORY. Assumptions. In a bridge of 84 ft. span, having a rise of 10 ft. 6 ins., we have a live load of 250 Ibs. per sq. ft., a 6-in. earth fill at the crown and a 12-in. pavement. Thickness of arch ring is assumed to be 14 ins. at the crown and 20 ins. at the springing. To find r we have, reduced to concrete weight : 1.167 ft. concrete at 150 Ibs. per cu. ft. = 1.167 6 in. earth fill at 120 Ibs. per cu, ft. = 0.4 12 in. pavement at 150 Ibs. per cu. ft. = 1.0 r = 2.567 ft. / = 84ft. s = 10.5 ft. r 2.567 ft. Constructing the Arch Ring. Assuming a parabolic arch, the ordinates are conveniently found by using the formula : (37) 1 14 21 & 35 Fig. 109. Parabolic Arch-Ring for 84-Ft. Arch. * Theory of Concrete Steel Arches (p. 79). 276 REINFORCED CONCRETE. One-half the span is divided into 12 equal parts, each 3.5 ft. long, as shown in Fig. 109. The values for y are shown in Table LXII. The ordinates 3; of the parabola are checked by their dif- ferences as shown, the second difference being a constant. TABLE LXII. ORDINATES OF PARABOLA WITH VARIOUS VALUES FOR x. Values of x. Values of y. First difference Second difference. Q K 4X10.5 O C / O 4 O C\ 1 A77 #= O . y o.o (o$ 6.0) 84 = 1,9 f 4 1.531 x=7. y= 7(84-7) = 3.208 0.146 168 1.385 1 *=10.5 y = 10.5(84-10.5) = 4.593 0.145 168 1.240 1 *=14. y = 14(84-14) - 5.833 0.146 168 1.094 1 *=17.5 y = 17.5(84-17.5) - 6.927 0.146 168 0.948 1 *=21. y = 21 (84-21) = 7.875 0.146 168 0.802 *=24.5 y = 24.5(84-24.5) = 8.677 0.146 168 0.656 1 *=28. y = 28 (84-28) = 9.333 0.145 168 0.511 1 *=31.5 y 31.5(84-31.5) = 9.844 0.147 168 0.364 1 x = 35. y 35(84-35) = 10.208 0.145 168 0.219 1 *=38.5 y- 38.5(84-38.5) = 10.427 0.146 168 0.073 1 *=42. : , = 42(84-42) = 10.5 168 BRIDGE DESIGN AND CONSTRUCTION. 277 Dead Load Diagram. Next the dead load ordinates are reduced to concrete weights by multiplying by Jfg and the dead load line drawn. The lengths of the center lines of the panels are as follows: C a = 10 ft. 2 ins. GV=7 ft. 8 ins. G 4 = 5 ft. 9 ins. 3 4 ft. 3 ins. 2 = 3 ft. 3 ins. d = 2 ft. 9 ins. The panel loads are found as follows : Go = 10% X 7 X 150 = 10,700 G 5 = 7% X 1050 = 8,000 C4 = 5% X 1050 = 6,000 3 = 4}i X 1050 = 4,500 ,=1314 x 1050 = 3,400 G, = 2% X 1050 = 2,900 Total dead load on half span = 35,500 Ibs. We have s = 10.5, hence $s = 7 ft. and T s s = 5.6 ft., locating lines A B , /-/ and A" B" in Fig. 110. The line A" B" incidentally coincides with the reduced load line. The force triangles are next drawn, combining each two reactions with the panel loads, and the reaction polygon is plotted and checked by finding its vertical ordinate equal to 35,500 Ibs. or the half span dead load. The pressure line is next transferred to the arch from the equilibrium polygon, and we find that for the dead load alone, the pressure line deviates considerably from the center line of the arch, which therefore in practice would be modified to coin- cide more closely with the line of pressure. With the adoption of a new center line, the same calculations would have to be repeated. In the present example, however, the original center line has been adhered to. The rays 0-6 0-5 O-l, in Fig. 110, represent the forces acting at joints 6, 5 .... measured in the scale of forces. The 278 REINFORCED CONCRETE. BRIDGE DESIGN AND CONSTRUCTION. 279 intercepts between the line of pressure and the center line of the arch are their levers measured perpendicular to the center line and in the dimension scale of inches. It must be noted that the forces acting at the joints when taken from the force polygon will not intersect the joints at right angles. To obtain the normal forces N D we must multiply the polygon forces by the cosine of the angle which they form with the perpendicular to the joints. This is done simply by project- ing them graphically. These normal forces N , their levers S and the correspond- ing moments all due to dead load, are found in table LXIII, where they will be combined with the moments due to live load in order to find the maximum. Live Load Diagram. The live load was assumed to be 250 Ihs. per sq. ft., hence the load for a panel 3.5 ft. in length and 1 ft. depth is 250 X 3.5 X 1 =875 Ibs. Three different positions of loading will be considered in this example, namely: (1) Arch completely covered with live load. (2) Arch one-half covered with live load. (3) One-third arch from each end covered with live load. (1) The right and left hand reactions for a concentrated moving load are first determined and combined to form the re- action polygon, and then the line of pressure drawn exactly as described for dead load. The values of A/" L (normal pressure at joints due to live loads) and their levers at the several joints are scaled off from the diagram. Fig. Ill, and their values recorded in Table LXIII, together with the resulting moments. The line of pressure is symmetrical about the center and has been plotted for one-half of the arch only. (2) When the arch is covered with live load over one-half the span only the forces (J<. G\ are acting. The resultant reaction R^\ due to this condition of loading passes through point C, which is the intersection of the sides 6 and in the equilibrium polygon. With the direction and location of the left 280 REINFORCED CONCRETE. BRIDGE DESIGN AND CONSTRUCTION. 281 hand reaction given, the line of pressure due to this condition of loading is easily drawn as shown in the live load diagram, Fig. 111. (3) The line of pressure for the arch when covered with live load on the two outer thirds is found when the loads Ge 6r B G Gz and G m G lv G v G yl are acting. The construction is similar to the one described and the line of pressure is symmetrical about the center of the arch, therefore only one-half is drawn in the diagram. The resulting normal forces and their levers are again scaled off and with their corresponding moments plotted in Table LXIII. Maximum Fiber Stresses. An examination of Table LXIII readily gives the maximum moments due to the four conditions of loading at any joint, and when added they will give the maximum at the joint in question. These maximum figures are underlined in the tables. It will be noticed that the moments due to dead load are by far the greatest, while the moments due to full live load over the entire arch do not produce maximum stresses in any joint. From Table LXIII we determine the fiber stresses. The percentage of reinforcement at the crown is assumed as p = 1 per cent = 0.01 for extrados and 1 per cent for the intrados. The same size of reinforcement is maintained through- out the arch, hence the percentage at the springing is p = 1 per cent X f$ = 0.007 The stresses produced in each joint we have learned are due to a normal force N and a moment M, and they are figured un- der the usual assumption that the stress, and consequently the deformation in any fiber, is directly proportional to its distance from the neutral axis, so that a section which is plane before bending remains plane after bending. The distance x of the 282 REINFORCED CONCRETE. & (0 . *s SLg | : : rtC/3 10 6 c * 1 CO CM CD o o i CO o O5 o" 1C CM '' 1 : g" "C a X rt * O O5 CO 1 CO CO 1C 1C " CM ! ic o ; o oo" - 1C CO 1C *< CM" Tt<~ r-i 1C 1C l si s g o o oo o> CO CD 89 CO CO 1 !- 1C o o * 1C ^" CM" 1 i.S * CO 1 I i 1 CO CO 1 + CO | CO 1 1 CM 1 CO * 1 1 1 1 1 ?, o CO CO CO CM CNJ CO CM CO 1C o CO g g ,Q g CO CO oe i g 5 g 1 g oo 1 g CO CD J s n '-I r ~ > 1-1 "- 1 p I i g o o g g | 1C g || || oo - - J O5 O 00 so CM' o" 3 Hi CM CO s 5 CN 1 00 Tt< I 2JSJ \ ul OJ (N + 1 1C 1 1 >c : ; + c CM 1 10 1 CM Oi 1 + 1 s* o 1 1 g g O o 1C o i i i i " 1 *"" i CO * 1C 1C CO 1C 1C s g g g 1C r>oQr\r\ \ 61900 20 + 2 x 8 - 42 ) = -5757.7 x s + 0.23* 2 + 338.6* 5757.7 = from which x = 11.9 BRIDGE DESIGN AND CONSTRUCTION. 285 (Using Fig. 108 for n = 15, we would have S = -rr = 10.08, -r = T^T = 0.5 and x = 0.565d = 11.3 ins.) Substituting as before, we have 2 X 61900 X 11.9 754 lbs. f 12 X 11. 9 2 + 2 X 0.007 X 12x20x20(2x11. 9- 20) per sq. in. S e = 20 X 754 ' n ~ = 8,234 Ibs. per sq. in. 11 9-0.08 X 20 S e ' = 20 X 754 - n Q - = 13,044 Ibs. per sq. in. Moments, Stresses, etc., at Joint 4. M = 320,200 N = 55,300 d = 18 p = x 0.01 = 0.00778 n = 20 A = -9.63 B = 194.4 C = -3671.1 x s _ 9.63* 2 + 194.4^ 3671.1 = which gives x = 14.2 (Using Fig. 108 for n = 15, we would have 5 =^-= 5.79, j = fg- = 0.322 and ^=0.757^=13.6 ins.) Therefore 2 X 55300 X 14.2 5b = 12 X 14.2 2 + 2 X 0.00778 X 12 X 18 X 20(2 X 14.2 - 18) " per sq. in. 0.92 X 18 14.2 S e = 20 X 504 - ~J4~2 "" = 1675 lbs< per sq * * n * 14.2 0.08 X IS S e ' 20 x 504 -g = 9058 Ibs. per sq. in. 286 REINFORCED CONCRETE. Construction of Arch Centering. The centering employed for a concrete arch is similar to that used for a masonry arch, except that in the former the lagging must be made smooth, so as to give the exact shape to the concrete and so constructed that the concrete will not adhere to it. The ad- hesion of the concrete to the lagging would mar the smooth- ness of the finished arch, and might cause difficulty in strik- ing the centers. This last item is of more serious consequence Fig. 112. Center for 50-Ft. Arch. Fig. 113. Center for 50-Ft. Arch, B. & O. R. R. BRIDGE DESIGN AND CONSTRUCTION. 287 than a possible roughness in the cases where the bridge is to be given a pebble-dash or other rough finish. To prevent the concrete from adhering and to obtain a smooth surface, the lagging is dressed smooth and covered with cloth or paper. Soap or oil are used to diminish the tendency to ad- hesion. Where centering is to remain in place for a long period, however, it is found that there is very little liability that the concrete will adhere to the wood. As in masonry construction, arch centers for concrete must be rigid to prevent any settlement of the concrete. Since timber is not absolutely rigid, but is apt to settle, the rise of the centering is made slightly greater than the rise designed for the arch. Mr. Edwin Thacher provides for an additional rise in the centering of one eight-hundredth of the span. Examples of Centering for Two 50-Ft. Arches. Two forms of centering for 50-ft. arches are shown in Figs. 112 and 113, the latter being erected without support between the abutments. Centering for the Pollasky Bridge. Fig. 114 shows the centering for a bridge at Pollasky, Calif. There are ten 75-ft. arch spans. Six sets of false work were used for the bridge, and were moved from span to span until the work was completed. Each center was carried on five bents of Fig. 114. Centering and Molds, Pollasky Bridge. 288 REINFORCED CONCRETE. 8xl2-in. posts having 6xl2-in. caps. Just below the caps each longitudinal line of posts was connected by a pair of 2x8-in. planks. The five frames of the center were supported on the caps by wedges. The ribs of the center on which the 2^x8- in. lagging was placed, were pairs of 2xl2-in. plank with 4x10- in. fillers between them, the whole nailed together by 7-in. spikes. The struts consisted of a pair of 2x6-in. planks with a 4x6-in. piece between them, the latter projecting up into the space between the outside planks of the rib. At the bot- tom each strut is butted on a 6x8-in. stringer. On either side of the latter was a 1^2xl2-in. plank, and ^-in. bolts passed through the plank and the feet of the struts. In laying out the centers provision was made for a 1-in. camber by using a radius of 61 ft. 11 in. instead of 62 ft. 3^4 in. This gives a rise of 10 ft. ll$4 ins. in place of 10 ft. 10^4 ins. designed for the arch. Concreting the Arch. Wherever possible, it is best to make the concreting of the arch continuous, so that there will be no possibility of a future separation on a plane bound- ing two days' work. Where it is impracticable to concrete in one continuous operation, the arch ring is divided into sections, either longitudinal or transverse, each section repre- senting a day's work. Both methods have given equally satis- factory results. In either case, great care must be taken at the joining of the new concrete, in order that it may be as nearly monolithic as possible. The joint is made rough, to assist in securing a firmer bond. When the sections are longitudinal, they are so chosen that none of the reinforcing is exposed at any joint between two days' work. When the sections are transverse, the concreting commences either at the crown or the springing, care being taken that no joint is made at the crown, and also that the concreting proceeds symmetrically on both sides of the crown. The sections are not bounded by vertical planes, as in the case of longitudinal sections, but by radial planes, so that all pressure brought upon the planes of juncture will be normal to them. Great care must be taken that the concrete entirely surrounds the reinforcement, and that the reinforcing material is not dis- placed in the slightest degree in concreting. The spacing and location of reinforcing material are designed very accu- rately to meet the stresses in the bridge, and unless great care is taken in placing the reinforcement and in concreting, the reinforcement will not fulfill the mission for which it is designed. BRIDGE DESIGN AND CONSTRUCTION. 289 Removal of Arch-Centering. As a rule, arch-centering should be left in place as long as possible. Since concrete shrinks in setting and since wood shrinks in drying, there is a tendency of the concrete to separate from the centering unless the latter be kept wet. This wetting of the forms also supplies the water needed by concrete in setting. There is no definite rule as to the length of time the centering re- mains in place. In cases where the arch is to be given a form of tooled finish, so that the forms must be removed while the concrete is still green, or in cases where the struc- ture is in several spans and the centering is needed for the others, it is removed earlier. When forms are removed early, great care must be taken that they are lowered grad- ually. While concrete begins to be self-supporting as soon as it begins to set, it does not reach its maximum strength for some time after setting, so that the removal of forms should be especially provided for. The devices usually em- ployed are wedges or sand boxes. Wedges can be driven out gradually, so that the strain comes upon the arch very slowly. Sand boxes are satisfactory if the necessary pre- cautions are taken to keep the sand from packing or cak- ing, due to the presence of dirt or cement. Care should be taken that the sand is very clean, and that the boxes are sealed up, to prevent the entrance of foreign matter. Grand River Bridge, Grand Rapids, Mich. As a typical example of bridge construction, the following description of Grand River bridge will show the general construction, cen- tering and details: There are five arch spans, one 87 ft., two 83 ft., and two 79 ft. One of the 79-ft. spans is shown in Fig. 115. The arch rings of the 79-ft. spans are 18 ins. thick at crown and 3 ft. at the springing, and are reinforced by two courses of \ l /4-\r\. Thacher bars placed 3 ins. from the extradosal and the intradosal faces. Each pair of rods is connected every 4 ft. by means of a 6-in. rod with a hook at each end. The rods have 3-in. washers and nuts to anchor them in the abutments, and are 290 REINFORCED CONCRETE. made continuous from end to end of span by means of turn buckles. The arch ring was built in transverse sections, each sec- tion being built in one continuous operation in a day, first the crown section, then the two skewback sections, and finally the intermediate sections, the entire ring being com- pleted in five days. Expansion joints in the spandrel walls were formed by laying the concrete against a vertical form and then butting the concrete of the following section against this smooth surface with a sheet of tar paper inserted between. Fig. 116 Longitudinal Section Fig. 115. Details of 79-Ft. Span, Grand River Bridge. is instructive in illustrating details of railing and forms for making them. The following loads were assumed: Lbs. per Dead Load: cu. ft. Concrete 150 Earth filling 120 Pavement, 12 ins. deep 150 Lbs. per Live Load: sq.ft. Center 20-f t. roadway ,..... 250 Remainder of roadway 150 Sidewalks 100 BRIDGE DESIGN AND CONSTRUCTION. 291 It should be noticed that these requirements are consid erably above the actual loads that will usually come on a bridge. A concentrated load was assumed on the roadway, , Plan. Mold for "A Fig. 116. Details of Railing and Forms, Grand River Bridge. consisting of a 15-ton steam roller having axles 11-ft. cen- ters with 6 tons on the forward wheel 4 ft. wide and 4^ tons on each of the two rear wheels 20 ins. wide and 5 ft. 292 REINFORCED CONCRETE. apart on centers. The ratio EC was taken as 20, maximum compression in concrete 500 Ibs. per sq. in. not including temperature stresses, and 750 Ibs. per sq. in. including tem- perature stresses. Tension and shear in con- crete were assumed not to exceed 75 Ibs. per sq. in. and reinforcement stress 18,000 Ibs. per sq. in. It was also required that the percentage of steel reinforcement in the crown should be at least equal to 2. Centering for one of the 83-ft. spans is shown in Fig. 117. The Santa Monica Via- duct. In 1902 a viaduct of two 67-ft. spans 100 ft. wide was built at Santa Monica, Cal. by Mr. Carl Leonardt, contractor, Los Angeles, Cal., according to plans and specifications prepared by the author. Owing to the 40-ton trolley cars, the arches, 22 ft. in width, were made 12^-in. crown and 16- in. springing, while the bal- ance of the viaduct has a thickness of only 6 inches at the crown and 10 inches at the abutments. The rein- forcement consists of two i_ BRIDGE DESIGN AND CONSTRUCTION. 293 nets of carrying rods spaced 6 inches on centers for the general viaduct and 3 inches on centers under the trolley tracks. The distributing rods are all 6 ins. on centers and at every second crossing are carefully wired to the carrying rods. The carrying rods in the lower net are y% in. in diameter for one-third of the arch up from the 60'0'Span- Fig. 118. Centering and Reinforcement for Santa Monica Viaduct. abutments, the balance of the rods being l / 2 in. in diame- ter. The top net consists entirely of l / 2 -\n. rods. The nets were connected by means of No. 8 wires tying them together and keeping them apart. The intrado net was clasped in hoop iron chairs, tacked on to the form every 30 to 36 ins. square, 294 REINFORCED CONCRETE. and pulled off with a pair of pinchers as the concreting pro- ceeded. Owing to the fact that the Southern Pacific R. R. Co.'s tracks run under the north span on a curve, the clearance caused the necessity of a slight distortion of the parabola, and was made from one radius 65 ft. and two radii 27 ft. 9 ins. The total rise is 13 ft. 7 ins. As an extra precaution, 3 brack- ets or counterforts were placed under the trolley line part of the arch, extending from skewbacks over one-third of the arch towards the crown. For arches of this character it is of the greatest import- ance that the centering is carefully designed, placed and adjusted by means of wedges so as to maintain the proper curvature during the placing of reinforcement and concrete, and that any shrinkage or swelling of the lumber is com- pensated for. The forms were built of 2xlO-in. planks, spiked together and braced by means of 2xlO-in. planks bolted to posts and joists. The posts were slotted at the lower end and rested on 2xl2-in. planks firmly bedded in the ground, being made adjustable by means of double maple wedges. The lagging consisted of Ix6-in. boards nailed on top of the rafters transversely across the viaduct, and on top of the lagging was nailed 1x6 dressed flooring bent exactly to the curve of the arch. After both arches were completely scaffolded and centered, the steel rods were laid from the abutment towards the center, the lower netting being kept at the proper distance from the forms by means of hoop iron snap saddles, so arranged that they could be withdrawn after the concreting had proceeded sufficiently to insure that the steel would keep its position. The two nets were kept at the proper distance by No. 8 wire stiffeners at every eighth intersection. The concreting was started at the abutments and the work made continuous until finished. The mixture was fairly wet, of 1 Portland cement to 4 parts clean, coarse, sharp sand, and the concrete was carefully tamped to a thickness regulated by straight edges with prongs penetrat- ABUTMENTS AND RETAINING WALLS. 295 ing to the centering. Three weeks after the concreting was finished the backfilling of earth and sand was put in and the roadway completed. This is probably the lightest Monier viaduct in the United States. There are, however, a number of reinforced con- crete bridges in Germany, Switzerland and France even con- siderably lighter in construction. Descriptions of these can be found in the files of Beton & Eisen and in catalogues of Wayss & Freitag, Hennebique and others. CHAPTER IV. ABUTMENTS AND RETAINING WALLS. Inasmuch as an abutment is a retaining wall with a sur- charge, we will consider the two classes of construction tmdjer one head. The author is under obligations to Prof. Milo S'.' Ketchum, of the University of Colorado, for much of the following, which by permission has been compiled from "The Design of Walls, Bins and Grain Elevators." THEORIES FOR PRESSURE OF THE FILLING. The most important theories for finding the pressure of the filling on a retaining wall are as follows: Rankine's Theory. Here the filling is assumed to con- sist of an incompressible, homogeneous, granular mass, with- out cohesion, the particles being held in position by friction on each other, the mass being of indefinite extent, having a plane top surface and resting on a homogeneous foundation, and being subjected to its own weight. These assumptions lead to the ellipse of stress and make the resultant pressure on a vertical wall parallel to the top surface. The pressure on other than vortical walls can be determined by the el- lipse of stress. Weyrauch's Theory. Here the filling is assumed to be without cohesion and to be held in equilibrium by friction of the particles on each other. It is also assumed that the forces upon any imaginary plane section through the mass of earth have the same direction. These assumptions lead to two formulas, one giving the amount of the thrust and the other giving its direction, the angle that the resultant makes with a normal to the wall. The formulas deduced by Weyrauch may be obtained more simply by means of the ellipse of stress, and are therefore subject to the same lim- itations. 296 BRIDGE DESIGN AND CONSTRUCTION. 297 Coulomb's Theory. Here a wedge is assumed, having the wall as one side and a plane of rupture as the other side, which exerts a maximum thrust on the wall. The plane of rupture lies between the angle of repose of the rilling and the back of the wall. It may coincide with the plane of repose. For a wall without surcharge (horizontal surface back of the wall) and a vertical wall, the plane of rupture bisects the angle between the plane of repose and the back of the wall. This theory does not determine the direction of the thrust, and leads to many other theories having as- sumed directions for the resultant pressure. Cain's Theory. Prof. William Cain assumes that the resultant thrust makes an angle with the normal equal to 0', the angle of friction of the filling on the back of the wall, or equal to 0, the angle of repose of the filling, if 0' is greater than 0. Other authorities assume that the resultant thrust is nor- mal to the back of the wall. For a smooth vertical wall without surcharge, all of the above formulas lead to the same result for the amount, direction and point of applica- tion of the resultant thrust. Trautwine's Theory. In Trautwine's Engineers' Pocket- book it is assumed, for a wall nearly vertical, that the plane of rupture in all cases bisects the angle between the plane of repose and the back of the wall. This theory gives cor- rect results for a vertical wall with horizontal surface back of the wall, but is in error for all other cases. Rankine's Formulas. For vertical retaining walls with- out surcharge: q = wy 298 REINFORCED CONCRETE. where P = resultant earth pressure per foot length of wall. w = weight of filling per cubic foot. y = depth of foundation below earth surface. q horizontal pressure at a depth equal to y. h = vertical height of wall in feet. = angle of repose of the filling. For angle of surcharge = 8, Rankine's formula is: cos 5 V cos 2 8 cos 2 Cain's Formulas.- If <})' angle of friction of the filling on the back of the wall = angle between back of wall and the horizontal running back into the filling for 8 = ^-^7 (44) si" ( (b -4- 0"> sin where n -\ l~ \ If 0' = 0, we have p = %wh z tan 2 U5 -TJ- j (45) For surcharge = 8 , the value of P is the same as in For- mula (45) except that I sin (0 + 0') sin (0 8) ^| cos 0' cos 8 For inclined wall with horizontal surfaces : sin ( e -J- sin # )',in^+*)-- (46 > ,'sin (0 + 0') sin0 W=AL: n ^/ _j_ e ) sin For inclined wall with surcharge = cJ , the value of P is the same as in Formula (46) except that /sin (0 + 7 ) sin (0 8) n ^^sin (0' + ) sin (05) ABUTMENTS AND RETAINING WALLS. 299 GENERAL DISCUSSSION. Thrust. In calculating the thrust on a retaining wall, great care must be used in selecting the proper value for the angle of repose and the conditions of surcharge, as the value of the thrust increases very rapidly as the angle of repose decreases and as the angle of surcharge increases. Back Filling. The filling back of the wall should be de- posited and tamped in approximately horizontal layers, or in layers sloping back from the wall, and a layer of sand, gravel or other porous material should be deposited between the fill and the wall to drain the fill downwards. Drainage. To insure drainage of the filling, drains should be provided back of the footing, and weep-holes located in the body of the wall at close intervals. The filling in front of the wall should also be carefully drained. Expansion Joints. In order to prevent the heaving of the foundation by frost, it is usual to provide from 2 l /2 to 5 ft. of filling in front of the wall. While in solid masonry walls it is necessary to locate expansion joints at intervals of from 30 to 50 ft., to prevent cracks, such joints are fre- quently omitted in retaining walls of reinforced concrete, and reinforcement is placed in the direction of the length of the wall for such purpose. Temperature Cracks. Mr. A. L. Johnson gives the fol- lowing formula for the amount of reinforcement required to prevent temperature cracks.* tensile strength of concrete Area of steel = ~ e l^tic"limif^f^te~el~ X area of concrete. For mild steel the elastic limit is 33,000 Ibs. per sq. in., the tensile strength of concrete is about 200 Ibs. per sq. in., and the area of steel is 1 -^v of the area of the wall. 165 For high steel of an elastic limit of 55,000 Ibs. per sq. in., we find the area of steel required to prevent temperature *Railroad Gazette, March 13, 1903. 300 REINFORCED CONCRETE. cracks equal to of the area of the wall. 7o Mr. W. W. Colpitts recommends 0.6 sq. in. of steel per sq. ft. of concrete* which is the area of the wall. ^T-V The author recommends a wire fabric of high carbon steel with the carrying rods running horizontally and located not more than 2 ins. from the face of the wall. /: / / i i UiC'M'idd/e Third / I'dJItQm i '' k,^il__!:iln""'"" Center of Base /'' BA*^B^ Fig. 119. Diagram of Forces for Masonry Retaining Wall. MASONRY RETAINING WALL. Design a retaining wall by means of the ellipse of stress, where height = h, angle of surcharge =22 30', and the angle of repose, 37 30*. See Fig. 119. Railway Age, January, 1904. ABUTMENTS AND RETAINING WALLS. 301 Calculation of Resultant Pressure. To calculate the re- sultant pressure, P, proceed as follows: Draw AO parallel to the surcharge A'M" and at any convenient point O in AO draw OD at right angles to AO. Draw OM vertical and locate M by strik- ing the arc DM with O as a center, and OD as a radius. Draw OC, making the angle with OD. At any point e in OD describe an arc tangent to OC and cutting OM at /. Through M draw MG parallel to ef. Bisect the angle DGM and through O draw OR parallel to GR'. Then OR is the principal axis of the el- lipse of stress and OM" the maximum stress that can occur in the filling. To calculate the maximum stress at A, draw OG' at right angles to the back of the wall AA', and make OG' = OG. With G' as center and OG' as radius, describe an arc cutting the principal axis OR at t. Draw G't, and with G' as a center and GM as a radius locate M'. Then M'O acting as shown is the in- tensity of the stress at A. The resultant pressure P is equal to the area of the stress triangle AA'N X w, where w is the weight per cu. ft. of the fill. P acts on AA' at Vz the height of the wall. The weight of the masonry, W, combined with P gives the resultant E, which must cut the foundation within the middle third. The vertical component of E is F. Stability Against Overturning. Through B draw O'S and produce cd to S. Then the factor of safety against overturning is ; . HE passes through B, the wall would be on the point of overturning and -7 would be equal to 1. Stability Against Sliding. The angle of friction of the masonry against the footing we will take as, <' = 30 Through O' draw gk, cutting the base of the wall at i at 30 to the vertical. Then the factor of safety against sliding will be 302 REINFORCED CONCRETE. Stability Against Crushing. The direct pressure per sq. ft. will be F where BA is the width of the base. l/dcf/e Third Fig. 120. Diagram of Moments for Masonry Retaining Wall. The pressure due to the bending moment will be (see Fig. 120): 6F6* The maximum pressure will be p = pi+p* t and the minimum, p pi h. If, in addition to the foregoing assumptions, we assume the wa)l to be 18 ft. high, A'B' = 2 ft Gins. AB = 7 ft. 6 ins., the batter of the back wall AA' % in. per ft., the masonry to weigh 150 Ibs. per cu. ft, and the fill, w, 100 Ibe. per cu. ft., we find the following result: * Note.* is distance from center of base to where resultant E cuts base. ABUTMENTS AND RETAINING WALLS. 303 P - ^ |-^ X 100 = 4880. 2.5 + 7.5 W = x 18 x 15 = 1350 lbs - P er lin - f t- of wall. E = 16500 6 =1.1 ft. F = 16000 16000 fr P2 P 7.5 6F6 = 2133 6 X 16000 x 1.1 1877, where d=J5A d 2 7.5 X 7.5 4010 or 256. REINFORCED CONCRETE RETAINING WALL OF BEAM TYPE. Design a reinforced concrete retaining wall of the beam type, to carry a sand filling 16 ft. high, weighing 100 lbs. per cu. ft., and having an angle of repose of 35, and sloping back at that angle. Fig. 121. Diagram of Forces for Reinforced Concrete Retaining Wall. The Vertical Beam. The bottom of the foundation will need to be about 4 ft. deep and we will assume the stem of the wall to be 18 ft. high. In Fig. 121 the pressure is P -= A SEN x w = 12,200 Ibs. 304 REINFORCED CONCRETE. and is parallel to the top surface. The horizontal compo- nent of P is H= 10,000 Ibs. The bending moment about B is M' = 10,000 X 6 = 60,000 ft. Ibs., for 1 ft. wide, or inch Ibs. for 1 in. wide. Instead of using Table XLVI, we will make w = 12, /> = 0.006 and /" = 16,000. According to Table XXXIX, we have, k 1 - TT = 0.896 and 60,000 = 26.6 ms. 1.006 X 16,000 X 0.896 and h = 30 ins. The top is 12 ins. thick. The steel reinforcement required per foot width of the wall is A* = 26.6 X 12 X 0.006=1.915 sq. ins. Three 1-in. rods = 3 X 0.7854 = 2.356 sq. ins, or 1-in. rods, 4 ins. on centers, with 4 in. by 6-in. mesh No. 7 and No. 11 fabric on both sides for temperature stresses. Foundation. We will assume that the footing is 10 ft. long, as shown in Fig. 122. Then the pressure on the plane A'F is P' = 19,900 Ibs. The weight of the earth prism AA'BF is 7,425 Ibs. and p = 25,000 Ibs. Combining P and the weight of the wall, which, including re- inforcement, we will call 7,725 Ibs., we have = 31,000 Ibs., which cuts the base 2 ft. to the left of the center, outside the middle third. ABUTMENTS AND RETAINING WALLS. 305 Now F = 24,000 Ibs., and />i = 2,400 Ibs. per sq. ft., 6F6 p 2 = p- = 2,880 Ibs., hence (d= = 5,280 or -480 Ibs. per sq. ft. Fig. 122. Diagram of Forces for Reinforced Concrete Retaining Wall. 306 REINFORCED CONCRETE. Since the foundation cannot take tension, we wil! hav* to let all the load be taken by compression as follows: 2F 2 X 24000 p' = -^ = 3 x 3 = 5,330 Ibs. per sq. ft. This pressure is safe for good gravel or clay. While the resultant cuts outside the middle third, the base is sufficiently long for the conditions named. To calculate the bending moment to the left of D, take the lower stress diagram, 4-5-6-7, Fig. 122, and multiply it by the distance of its center of gravity to the left of D. Then M' = Table XLVI gives for a moment of 49,465, h = 24. and for 40,880, 7z = 22. We will put in 0.17 X 4^ = 0.765 sq. ins., or 1-in. rods 4^ ins. on centers, the full length of the foundation. Rods will be placed 2 ins. from top of the in- ner surface, as shown, and these rods we will make 1 in. in di- ameter, and 8 ins. on centers. See Fig. 123. REINFORCED CONCRETE RETAINING WALL WITH COUNTERFORTS. Design a reinforced concrete retaining wall with counterforts to carry a sand filling 175^ ft. above ground, which ?ods, 6 "c. toe. Fig. 123. Section of Rein- forced Concrete Retain- ing Wall. weighs 100 Ibs. per cu. ft., has an angle of repose of 37 30', and carries a railroad track which is equivalent to a sur- charge of 6 ft. Counterforts to be spaced 10 ft. on cen- ters, as shown in Fig. 125. ABUTMENTS AND RETAINING WALLS. 307 Calculation of Pressure P. The pressure P' on the vertical plane 2-B is calculated graphically as shown in Fig. 124. A SeN X w = pressure- on the vertical plane B-Q, and the pressure triangle is 5-6-4. Resultant pressure P' acts through the center of gravity and is equal to the area 5-2-3-4, equals 9,200 Ibs. Resultant pressure P" acting on plane G-2 is found to be 7,720 Ibs. Fig. 124. Moment and Stress Diagram for Reinforced Concrete Retaining Wall. The weight of the prism of filling O-1-2-G is 15,000 Ibs., and combining this weight with P', we have p = 17,500 Ibs. acting as shown. The weight of the concrete wall per linear foot is approximately 6,500 Ibs., which when combined with P gives E = 23,200 Ibs. 308 REINFORCED CONCRETE. Resultant E cuts the base at a distance 1.6 ft. from the center, and the vertical component of E is F = 21,500 Ib's. Vertical Wall. In designing the center slab the span will be taken as 10 ft. (Where the wall has no cracks the r i 6 1- Ground level Fig. 125. Plan and Section of Wall, Showing Reinforcement. actual span is less than the clear span of 8 ft. 6 ins.) Tak- ing the bottom strip, 1 ft. wide, and 10 ft. long, we design a simple beam that will carry a load of 623 Ibs. per linear ft. ABUTMENTS AND RETAINING WALLS. 309 623 x 10 2 M = - -- = 7,788 ft. Ibs. (or inch Ibs. per inch). Again making n 12, p = 0.006, and / = 16,000, we get 7 788 d =\/n n^g .. -la nnn v, n ona = 9.5 ins. and h = 12 ins. ~\ 0.006 X 16,000 X 0.896 The steel area per foot is : 0.006 X 9.5 X 12 = 0.684 sq. ins., or 24-in. rods, 8 ins. on centers, grading the distance between rods according to the decreasing pressure toward the top. See Fig. 125. The temperature stresses will be taken care of by means of 4 X 6 ins. No. 7 and No. 11 fabric, to which the rods are fastened by wire usually doubled No. 18 an- nealed wire. Counterforts. The bending moment on a counterfort at OG in Fig. 124 will be, jlf' = 7,720X8X10 = 617,600 ft. Ibs, or 7,411,200 in. Ibs. If the counterfort is 18 ins. wide we have: M = ' t g = 411,733 in. Ibs., for 1 in. width. 7,411.200 18 By Formula (11) and for / = 16,000, p = 0.006, and n = 15, we find (l-|) = 0.885. 411 733 Hence d=+L nnft , R nnn^v n Q^ = 70 ins. = 5 ft. 10 ins. %|U.UUO A lOivUU /\ U.ooO Steel area for 18 ins. width is 0.006 X 70 X 18 = 7.56 sq. ins., or 8 rods, 1% ins. diameter. Rods */ 2 in. in diameter will be placed as shown in addition to fabric to take vertical and horizontal shear. 310 REINFORCED CONCRETE. Foundation. In Fig. 124 the direct pressure pi is 1,600 Ibs. per sq. ft., while the pressure due to the moment is p 2 =.- -^ = +1,120 Ibs. per sq. ft. Then /> = 2,720 or 480 Ibs. per sq. ft. which is entirely safe for ordinary conditions. The maximum moment at K in the outer toe is found in Fig. 124 by taking the moment area to the left of K, and is M< = ( 2 ' 72 + 2 2 ' ) 5 X 2.6 = 30,680 ft. Ibs. By Table XLVI this corresponds to a slab between 19 and 20 ins. However, we have assumed 24 ins. We will use steel area of 0.15 sq. in. per inch, or %-in. rods 4 ins. on centers and place %-in. rods 8 ins. on centers at top of slab as shown. At the bottom we will, in addition to 4 X 6-in. fabric of Nos. 7 and 11 gage, place fys-in. distributing rods longitudinally 8 ins. on centers. Conclusion. It will be noticed that in the foregoing ex- ample a rib is placed longitudinally underneath the heel and the toe of the base. This is largely for the purpose of con- fining the soil between the two ribs and to aid in preventing sliding. For long retaining walls the face slab should be decreased in thickness from bottom towards the top, as the saving in concrete will be greater than the additional cost of the ta- pered forms. RETAINING WALL FORMS. Setting the Forms. In setting the forms, great care is taken to set the apparatus on a firm base and thoroughly brace it. The first panels are set in a line end to end with tight joints and absolutely leveled. After the lower line is set correctly, the others will come all right, and as soon as the lower line is in place the concreting may begin. The concrete is placed in layers not to exceed 12 ins. in thick- ness and the face is thoroughly spaded so as to bring the ABUTMENTS AND RETAINING WALLS. 311 The following tables give the intensity of the horizontal pressure, p, at any depth, h, the total pressure H, above the section considered and the overturning moment, M, in inch Ibs., at the section A-B -.("Designing Methods") HORIZONTAL SURFACE SURCHARGE. 0=30 a/=1001bs. a/=100lbs. E 1 f* ^ 1 f \o'^v m : tf 33 * -XA\0'J* ''f /& a r iS ^ d ^ p TABLE LXIV-A TABLE LXIV-B , _ H=P i a Overturning Moment Pcos0 4 / H=P Overturning Moment h 1 ^ 7/J/f = 1-0 h 74. cos o 7% A/fsec V l-O Zf fl wh? a/A 3 X12 wh wh? a/A 3 X 12 Feet. Pounds. Pounds. Inch Pounds. Feet. Pounds Pounds. Inch Pounds. j 33 17 67 1 75 38 150 2 67 67 533 2 150 150 1200 3 100 150 1800 3 225 338 4050 4 133 267 4267 4 500 600 9600 5 167 417 8333 5 375 938 18750 6 200 600 14400 6 450 1350 32400 7 233 817 22867 7 525 ] 838 51450 8 267 1067 34133 8 300 2 400 76800 9 300 1350 48600 9 675 3038 109350 10 333 1667 66667 10 rso 3 750 150000 11 367 2017 88733 11 825 4538 199650 12 400 2400 115200 12 XX) 5 400 259200 13 433 2817 146467 13 975 6338 329550 14 467 3267 182933 14 1 )50 7 350 411600 15 500 3750 225000 15 1125 8438 506250 16 533 4267 273067 16 11 JOO 8 600 614400 17 567 4817 327533 17 1275 10838 736950 18 600 5400 388800 18 13 550 12 150 874800 19 633 6017 457267 19 1425 13538 1028850 20 667 6667 533333 20 u >00 15 000 1200000 21 700 7350 617400 21 1, >75 16 538 1389150 22 733 8067 709867 22 1650 18150 1597200 23 767 8817 811133 23 r r25 19 838 1825050 24 800 9600 921600 24 1800 21600 2073600 25 833 10417 1041667 25 1* 575 23 438 2343750 26 867 11267 1171733 26 1950 25350 2636400 27 900 12150 1312200 27 2( )25 27 338 2952450 28 933 13067 1463467 28 2100 29400 3292800 29 967 14017 1625933 29 2] 75 31 538 3658350 30 1000 15000 1800000 30 2250 33750 4050000 312 REINFORCED CONCRETE. fine mortar to the face, or a cement mortar of same mixture as mortar in the concrete may be slushed along the face. The next panel above may be placed as the concrete is brought up without interfering with the placing of the con- crete so that carpenters and concrete men may be working at the same time and place. Removing the Forms. After the concrete against the lower line of panels is placed the panels can be removed after 18 hours in the summer and 24 to 30 hours in the win- ter, and floating of the surface can be started, even though concreting may be going on at the top of the wall. After the proper lapse of time on the other lines of panels they may be removed and the wall floated until the top is reached. To remove the panels, the wedges are drawn, the blocks are removed, and the panels are drawn out endwise. When forms are removed the walls should be green and easily worked. The floating is done with wooden floats or cement bricks. Cement plaster should be positively forbid- den, though fresh water may be splashed over the wall to assist the rubbing off of all board marks or ridges and to bring to a uniform smooth surface. Expansion Joints. Expansion joints are formed from 25 to 35 ft. apart by placing tar paper through the entire area of wall section. The number of thicknesses depends upon the season of year, only 1 in the summer and 5 or 6 in the winter. The first cost of these forms is high, but for a considerable stretch of work they can be used over and over again if made of good material and tak- en care of properly. Wall Form Tie. Fig. 127 is a simple form for a heavy wall, such as is employed by the au- thor. The tie is formed of wire, which is tightened by twisting, as shown. Fig. 127. Wall Form Tie. ABUTMENTS AND RETAINING WALLS. 313 EXAMPLES OF CONSTRUCTION. Retaining Wall, Paris, France. Fig. 128 shows a modifi- cation of the usual type of wall with counterforts. This wall is of Hennebique construction and was built to support the sides of a depressed street near the gardens of the Troca- dero, at the Paris Exposition of 1900. The wall was built Horizontal Section A-B. 128. Retaining Wall for Sunken Street, Paris, France. in sections about 20 ft. in length, each section being made up of a facing strengthened at its back by three buttresses. Two horizontal beams connected the facing and the but- tresses. The base slab was strengthened at the toe of the wall by buttresses underneath the street level, as shown. 314 REINFORCED CONCRETE. By this arrangement of horizontal beams the retaining wall is assisted in sustaining the earth pressure by the weight of this earth upon the horizontal beams and does not, as in ordinary retaining walls, depend upon its weight alone. The employment of the two separate beams at different levels, instead of the one at the same total width, results in largely decreasing the thrust of the earth upon the vertical face and reduces the excavation required. The two rear beams are only used in nine panels, as the retaining wall is protecting a sloped street, and the height of the wall is reduced at one end so as to need but one base. The width of the front horizontal beam was fixed by assuming a top load of 2,048 Ibs. per sq. ft. upon soil of this nature. The width of the back of the wall was figured with an average factor of safety of 2, in calculating the moment of stability of the wall. The reinforcement of the vertical face consists of two series of vertical bars combined with one series of horizontal bars, the distances between which increase towards the top of the wall. These bars are bent over at right angles at the top to give support for a coping of the same construc- tion as the facing. The illustration gives the sizes of the different bars or rods. t Retaining Wall, Great Northern Ry., Wash. A good ex- ample of a high reinforced concrete retaining wall is here reprinted.* The wall, Fig. 129, is of the counterfort type and is used in the terminal yard of the Great Northern Railway at Seattle, Wash. The wall supports a street and varies in height from 2 to 37.8 ft. and is approximately 2,000 ft. in length. Mr. C. F. Graff of the engineering staff of the Great Northern Railway states that a comparison of cost between a plain concrete wall of gravity section and a wall of counterfort type gave a noticeable saving for the lat- ter, as shown in Table LXIV. The heights vary from 10 to *Reid's Concrete and Reinforced Concrete Construction. ABUTMENTS AND RETAINING WALLS. 315 40 ft, the section of wall is assumed 1 ft. long, figuring the amount of steel used at 4*/ 2 cts. per lb., evaluated in terms of concrete at $6.00 per cu. yd. in place. Part- Plan., Fig. 129. Retaining Wall, Great Northern Ry., Seattle, Wash. TABLE LX IV. COMPARATIVE QUANTITIES OP CONCRETE IN PLAIN AND REINFORCED CONCRETE RETAINING WALLS. Height Wall in feet. Cu. Ft. Concrete Plain Wall. Cu. Ft. Concrete Reinforced Wall. Saving Per cent. 10 20 30 40 44 110 226 396.4 34.9 69.9 127.8 20.4 36.4 43.4 45.0 316 REINFORCED CONCRETE. It was assumed in this estimate that the extra cost for forms and a higher grade of concrete for a reinforced wall was counterbalanced by the saving in piling necessary for the plain concrete wall. Fig. 129 shows elevation, section and plan of wall at its highest point; where it joins the portal at the highest point it is 37 ft. 7 ins. high. The gen- eral dimensions and reinforcement employed are shown on the drawing. In computing sections of face and base of wall they were considered as composed of a series of independent beams lying side by side, giving an additional factor of safety, as there is really a supported slab action. Piles were driven, as shown, to compact the earth, to support the toe of the wall and to prevent the structure from sliding for- ward. Scaffolding was put up to facilitate the erection of the skeleton steel work. Near the top of this scaffolding the two top 1-in. horizontal face bars were securely fastened in exact line and elevation and the long diagonal 1^4 -in. bars running down the back of each rib were hooked on these and swung into proper position at the bottom. Some of these bars were 42 ft. in length, and were kept from sagging by wooden crosspieces nailed to falsework. The J^-in. ver- tical face bars were then hung from the top and held in place in a similar manner. Next the vertical bars in each rib were placed, being stuck in the ground at the bottom and held at the top by wire tied to the scaffolding. In construction, 3 ins. of concrete was first placed above the top of the piles, the horizontal longitudinal rods were put in place, and then the concreting carried tip throughout the whole section. As the work was .brought up, the horizontal bars in the face and ribs were put in place, care being taken in all cases to bed them in fresh concrete. The laps, where the rods were spliced, were made at the ribs, a 2-ft. lap being used for the base and 1^-ft. lap for the face wall. Corrugated bars were used throughout. A 1-2-4 mixture of Portland cement, sand and trap rock was used for the concrete. A fairly wet mixture was employed, being deposited in 6-in. lay- ers and thoroughly tamped. ABUTMENTS AND RETAINING WALLS. 317 SPECIFICATIONS FOR REINFORCED CONCRETE RETAINING WALL. The following specifications for reinforced concrete re- taining wall have been used by the author and show the method of construction: General. The concrete used in reinforced concrete must be of the classes called for on the plan, or as directed by the engineer, and must be in accordance with the general specifications for .concrete. It must be mixed, generally, to the consistency known as "wet concrete," or such that a man walking on same will sink ankle deep. The decision of the engineer as to the proper consistency of any batch of concrete must be binding upon the contractor. Special ram- mers must be used as directed by the engineer, to properly pack the concrete between and around the steel bars. Workmanship. Particular care must be exercised in the execution of reinforced concrete work in order to procure a dense and uniform mixture, thoroughly compacted around the reinforcing material. Reinforcement. The contractor must furnish and embed in the concrete round rods or bars of dimensions shown on plans, wherever same are called for by the plans, or when directed to do so by the engineer.. The bars must be of medium open-hearth steel, in strict conformity to Manufacturers' Standard Specifications for 1903, and must be in accordance with the specifications under heading "Iron and Steel." The section of the rod or bar must be the same as that called for on the plan. The rods or bars must be cleaned of all dirt, grease and other adhering substances, and must be free from rust and mill scale. In placing them the direc- tions of the engineer must be strictly followed in regard to spacing, position in the cross-section of the concrete, length, laps, wiring, bending, etc. In placing the reinforcement the following modus op- erandi should be observed: After the piles have been driven, the ground properly lev- eled off and the forms for the base plate have been set in the ground, the 4xl2-in. mesh American wire netting No. 9 and No. 11 mesh should be unrolled longitudinally with the abutments from one side of the same to the other and con- nected properly with clips, stretched and attached to the side forms. In a similar manner the netting for the two wing walls should run parallel with the outside face, lapping the other netting 12 ins. and also fastened to same with clips r 318 REINFORCED CONCRETE. These clips are furnished free with the netting. On top of this netting should be located the rods as shown in the plan and tied to same at every fourth intersection with No. 18 annealed wire laid double, using a No. 8 pair of nippers for the purpose. While cutting the above mentioned netting in lengths, a double set is cut and laid ready, so as to be pre- pared to place same as soon as the concrete has reached near the top of the slab. Stakes should be driven back of the base form with cross arms to support the outmost rods of the counterforts which are to be embedded in the con- crete. The concrete is now placed as rapidly as possible and fairly dry and tamped, and in placing, by means of separate hooks the lower wire netting is pulled and shook away from 'the soil, leaving a cover of about \ l /t ins. to 2 ins. between the soil and the reinforcement. While this is going on, the reinforcing gang is preparing for the second layer of netting and the top rods, and must have them all laid out in the rotation in which they are to be placed. The reason that the concrete in the base plate is to be fairly dry is for the purpose of being able to place the wire netting and rods, gradually following up the complete concreting. The top concreting can commence at one end of the wing wall and one end of the abutment, while they are still concreting the lower part of the opposite end. Im- mediately after the top layer of netting and rods is laid, the oblique tension rods in the counterforts are stuck in the con- crete as far down as they can go and stayed at the top by means of stay laths fastened to stakes driven in the ground on both sides of the base plate. This is done during the top finishing. Meanwhile the lumber and braces for the front slab and wing walls have been made ready for rapid erection and the 4x6-in. No. 9 and No. 11 American wire is placed horizontally in one length around the circumference of the wing walls and abutments, suspended at the top from hooks or nails fastened to the studs of the front form, not to the forms themselves. The second layer of netting is suspended to the first one by means of the clips and so on until the bottom is reached. Then the rods are fastened to the wire netting by means of annealed wire at every fourth intersection until the bottom is reached. When this is done the rods of the counterforts which have been embedded in mortar are bent forward un- til they are in proper position and the 6x6-in. mesh No. 9 and No. 11 American wire is wired to each set of rods in the counterfort and also wired to the front netting and one side of the counterfort forming as erected, the other side ABUTMENTS AND RETAINING WALLS. 319 being made in one piece with the part of the forms for the face slab running between the counterforts, in sections about 2 ft. high. Then concreting can commence and section by section carefully spaded, and a somewhat more wet con- sistency may be used than in the bottom slab. Any other method of work accomplishing the same pur- pose namely: the proper location of all netting and all rods may be used at the contractor's discretion, with the approval of the engineer. As all rods of every description are to be hooked at least 1 in., it may be added that the corners of these hooks need not be square but may be made to a radius of 1 in. All splices of rods are done by hooking both ends and lapping them 50 diameters with three ligatures of No. 18 annealed wire, and all splices must break joints. Rods or bars must be braced so as not to be displaced by springing or by the ramming of the concrete. No reinforce- ment will be allowed within 1 in. of any exposed surfaces. No concrete except the foundation course can be placed un- til the entire reinforcement has been placed, wired and ap- proved by the engineer. Vertical and horizontal rods or bars shall be of the lengths shown on the plans. In beams, face slabs and floor slabs, the rods shall be continuous over two supports. Loading and Risks. No vertical or heavy loads shall be allowed on any reinforced concrete structure within 30 days after the completion thereof, nor until such time as the en- gineer may designate. The contractor will be held respon- sible for any failure due to faulty workmanship or material, premature loading or premature removal of forms. Measurement and Payment. The steel rods or wire net- ting or bars shall be paid for at the unit price per pound or per square foot named in the contract. Payment will be made upon the estimated weight of rods and bars computed upon the basis of 490 Ibs. per cu. ft., for the lengths and cross sections indicated on the plans or placed by order of the engineer. If bars of larger cross section than called for are used the excess shall not be paid for. No allowances will be made for waste or laps, except where laps are shown on plans, or made by direction of the engineer. The unit price per pound must include the furnishing, bending, plac- ing and wiring of the rods or bars, and all labor, tools, wire, and other material necessary to complete the work. Reinforced concrete, exclusive of the reinforcing material shall be paid for at the unit prices named in the contract, and no deduction will be made tor the volume of concrete dis- placed by the steel. CHAPTER V. CULVERTS, CONDUITS, SEWERS, PIPES, AND DAMS ARCH CULVERTS. For arch culverts the design is made the same as for arches in bridge construction, the elastic theory forming the basis. If extradosal and intradosal reinforcement is em- ployed, it is not necessary that the pressure line comes within the middle third, and therefore quite light constructions may be made with safety. The thrust from the arch is trans- ferred to the base by means of buttresses, which thus with the comparatively thin face walls and the base replace the heavy abutments in masonry construction. Culverts are built with or without inverts according to the stability of the soil and the local conditions. BOX CULVERTS. Box culverts are calculated like floor slabs. The follow- ing method of rinding the pressure on a box culvert is based upon the method outlined by Mr. W. W. Colpitts, C. E., in "Railway Age," Aug., 1907: Assumptions. The live load is taken at 10,000 Ibs. per linear foot of track uniformly distributed by the ties over 8 ft. width of roadway. The further distribution of the load downwards is based upon the unfavorable assumption that the zero load line follows a slope of 5^ to 1. Design of Covers for Box Culverts. Let DL = dead load per sq. ft. on a plane h ft. from the base of rail. 320 CULVERTS, CONDUITS, SEWERS, DAMS. 321 g = weight of fill per cu. ft. Then L>L = gh. LL = live load in Ibs. per sq. ft. Q = DL + LL. For g 100 Ibs., we have: DL 100 A, or for a factor of safety of 2 for the dead load, DL = 200 h. 20 000 LL = . ' lfi for a 10,000 Ibs. train load. Taking an impact of 50 per cent and a factor of safety of 4 for the live load, we have: 120,000 " h+ 16 and Q = DL + LL = 200 Then we have M = ^12 = 300 1* (^r^j + *) (47) where / is the span of the culvert in feet. For n = 15, and p = 0.0072, we find by interpolation in Table XXXIX, k = 0.369. Therefore A = 0.0072 X 12 X d = 0.086 d (48) Assuming fo = 2,300 Ibs. per sq. in. (ultimate), and substi- tuting in Formula (10), M = H fe (1 */3) bd* we get M ^ = 40 (49) where M represents the ultimate moment. Diagram for the Design of Covers for Box Culverts. In Fig. 130, plotted from Formulas (47), (48) and (49), Curve A gives the theoretical thickness of cover for various spans under banks between 30 and 40 ft. high. Curve a gives the area of 322 REINFORCED CONCRETE. steel reinforcement per linear foot of cover for banks between 30 and 40 ft. high. Curves B and b and Curves C and c corre- qmooo Fig. 130. Diagram for the Design of Covers for Box Culverts. spond to the above under banks respectively 22 to 30 ft. high and to 22 ft. high. CULVERTS, CONDUITS, SEWERS, DAMS. 323 Each curve is calculated for the maximum height of bank shown. To the theoretical thickness of the cover, d, should be added from 1% to 3 ins., sufficient to embed the bars. Design of Sides of Box Culverts. For the sides of box culverts the resultant horizontal pressure on the walls is ap- proximately and the horizontal pressure at base of wall in Ibs. per sq. ft. is pr I* ^ - 2 P = p> 60,000 /* + 16 + 100 h (50) in Ibs. per sq. ft. applied over the entire surface of the side wall of the culvert. Diagram for the Design of Sides of Box Culverts. Fig. 131 is plotted from Formulas (47), (48) and (50). Curve D is x"f & J"' /O' ~7s r Depth Bottom? 0f Cwer to Top 0f Base Fig. 131. Diagram for the Design of Sidewalls for Box Culverts. 324 REINFORCED CONCRETE. used when the bank is between 30 and 40 ft. high and gives the theoretical thickness for various spans. Curve d is used when the bank is between 30 and 40 ft. high and gives the area of steel reinforcement per lin. ft. of side wall, while curves E and e and curves F and / correspond to the above under banks re- spectively 20 to 30 ft. high and to 20 ft. high, each curve being calculated for the maximum height of bank. As in Fig. 130, the thickness of the side wall, d, should be increased 1% to 3 ins., sufficient to embed the bars. It is customary to put either brackets or braces in the cor- ners to take care of unequal pressures. The side rods should be bent inward at the top and extend through the thickness of both top and bottom. All rods should be hooked at each end. When the fill comes below 3 ft. above the top of culvert the impact is figured at 100 per cent, and for large spans the live loads are assumed to be concentrated. Cost of Concrete Culverts. Mr. Colpitts* gives the follow- ing cost of retaining walls, abutments and box culverts, for the permanent way of the Kansas City Outer Belt & Electric Ry. These figures are of particular interest, for the variation in prices of materials during the two-year period while work was in progress and as giving the average cost of the work on the whole line as well as for individual structures. The culverts were all box culverts with wing walls and the abutments were for girder bridges. Walls and abutments were of L section with triangular or trapezoidal counterforts at the back between base slab and coping. The form work was thus rather complex. All work was reinforced concrete, and was done by contract under the following conditions : The work of preparing founda- tions, including excavation, pile driving, diversions of streams, etc., was done by the railroad company, which also bore one-half the cost of keeping foundations dry while forms were being built and concrete placed. The railroad company also furnished the reinforcing bars at the site of each opening. The concrete work was let at $9 per cu. yd., which figure covered all the labor and materials necessary to complete the work, other than the *Railway Age, Aug. 2, 1907. CULVERTS, CONDUITS, SEWERS, DAMS. 325 exceptions mentioned. The concrete proportions were 1-3-5. The cement used was lola Portland and Atlas Portland. The sand was obtained from the bed of the Kansas River in Kansas City. The rock used was crushed limestone, passing a 2-in. ring and freed from dust by screening. Corrugated reinforcing bars, having an elastic limit of from 50,000 to 60,000 Ibs. per sq. in., manufactured by the Expanded Metal & Corrugated Bar Co. of St. Louis, Mo., were used exclusively. The concrete in the smaller structures was mixed by hand, in the larger by a No. 1 Smith mixer. In the first structures built 2-in. form lumber was used, with 2x6-in. studs placed 3 ft. on centers. This was abandoned later for 1-in. lumber with 2x6-in. studs, 12 ins. on centers, and was found to be more satisfactory in producing a better face. The structures were built in the period from April, 1905, to May, 1907. Costs and wages were as follows : Cement Per barrel at structure, April, 1905 $1.25 Per barrel at structure, April, 1907 1.92 Average cost per barrel at mill 1.42 Freight per barrel 0.21 Hauling iVz miles and storage 0.12 Average cost at structure 1.75 Average cost per cu. yd. concrete (1.1 bbls.) 1.93 Sand Per cu. yd. at structure, April, 1905 $0.625 Per cu. yd. at structure, April, 1907 0.75 Average cost per cu. yd., river bank 0.30 Freight per cu. yd 0.22 Hauling IV-2 miles 0.20 -Average cost at structure 0.72 Average cost per cu. yd. concrete (Ms cu. yd.) 0.36 Stone Per cu. yd. at structure, April, 1905 $ 1.10 Per cu. yd. at structure, April, 1907 1.75 Average cost per cu. yd. at crusher 0.65 Hauling 4 miles 0.84 Average cost at structure 1.49 Average cost per cu. yd. concrete (0.9 cu. yd.) 1.34 326 REINFORCED CONCRETE. Lumber Per M. ft. at structure, April, 1905 $15.00 Per M. ft. at structure, April, 1907 22.50 Average cost per M. at structure 19.00 Average cost per cu. yd. concrete 0.49 Labor Max. Min. Common labor, cts. per hour 20 17 Carpenters, cts. per hour 40 30 With these prices and wages the average cost of concrete work for the whole line was : Item. Per cu. yd. Form building and removing $1.98 Mixing and placing concrete 0.74 Placing reinforcement 0.10 Wire, nails, water, ttc 0.20 1.1 bbls. cement at $1.75 1.93 % cu. yd. sand at $0.72 0.36 0.9 cu. yd. stone at $1.49 1.34 Lumber for forms 0.49 Total .$7^14 The following are the costs of specific structures built at different times : Example /.Indian Creek Culvert. 14x15 ft., 250 long, com- pleted November, 1905: Percu. yd. Cement $1.37 Sand 34 Stone 1.10 Labor 2.48 Lumber 76 Miscellaneous 18 Total $6.23 Example II. Third Street Abutments and Retaining Wall. Completed November, 1906: Per cu. yd. Cement $1-78 Sand 35 Stone 1.35 Lumber 74 Labor . 2.75 Miscellaneous 16 Total . $7.13 CULVERTS, CONDUITS, SEWERS, DAMS. 327 Example III. Abutments, Overhead Crossing with Union Pacific and Rock Island. Completed May, 1007: Per cu. yd. Cement $1.92 Sand 32 Stone 1.74 Lumber 98 Labor 2.96 Miscellaneous 16 Total $8.08 EXAMPLES OF ARCH CULVERTS. Reinforced concrete culverts have been adopted as standard by several American railroads, and while practical experience may tend to reduce dimensions more in conformity with theoreti- cal research and foreign practice, a few examples will illustrate recent application of concrete steel in culvert construction. _ Top of Tie Fig. 132. Standard Arch Culverts for Inside Dimensions of 4x4 ft., 5x5 ft., and 6x6 ft., C., B. & Q. Ry. Standard Arch Culverts, C., B. & Q. R. R. Fig. 132 illus- trates standard arch culverts adopted by the C., B. & Q. R. R., in which L=-^h + x + 4:it (51) -where x = width of the roadbed at the crown, the other quanti- ties being as shown in Fig. 132. Table LXV gives various dimensions for this type of culvert. 328 REINFORCED CONCRETE. TABLE LXV. DIMENSIONS AND MATERIALS FOR STANDARD ARCH CULVERTS, C., B. & Q. R. R. Inside Length of Cu. yds. Cu. yds. Lbs. metal, Lbs. metal, dimensions wing walls, concrete lin. ft. of " wing walls. lin. ft. of in feet. ft. ins. wing walls. barrel. barrel. 4x4 5-3 6 0.5 236 54 5x5 6-11 10 0.71 401.7 76.7 6x6 8-6 12 1.00 553.5 103.4 Arch Culvert, Kalamazoo, Mich. Fig. 133 illustrates a culvert of 9 ft. 10 ins. span and 1,080 ft. long built at Kalamazoo, Mich. The reinforcement consists of woven steel wire fabric of No. 11 wire laid in two layers each, at the intrado, extrado and invert as indicated in the drawing. The total length of Fig. 133. Arch Culvert at Kalamazoo, Mich. fabric surrounding the culvert in one section is 175 ft. There is an average of 5 wires per linear foot enclosing the culvert ex- cept where the inner and outer reinforcement overlaps. The bearing portion of the concrete in the inverted arch was changed in form as shown in the drawing by dotted lines, according to the character of the soil. Where quicksand was encountered two CULVERTS, CONDUITS, SEWERS, DAMS. 329 6-in. tile drains were laid under the invert and these by remov- ing the excess of water from the quicksand made it a firm and good foundation. The use of a wire fabric as reinforcement is a safeguard against mistakes or omissions in placing the reinforce- ment during construction. Arch Culvert, Great Northern Ry. A reinforced concrete arch culvert of large span* is shown in Fig. 134. The plans were calculated for heights of bank of both 22 and 40 ft., weight of fill being taken at 100 Ibs. per cu. ft. A uniform live load of 10,000 Ibs. per lin. ft. of track was assumed, 50 per cent added for impact, a factor of safety of 4 used on such live load plus impact, and of 2 on dead load. The figures for the ultimate strength of concrete in tension, compression and shear were 200, 2,000, and 400 Ibs. respectively. Modulus of elasticity of concrete in compression was taken at 3,000,000 Ibs. per sq. in., elastic limit of the corrugated bar reinforcement, 50,000 Ibs. pet sq in., and weight of concrete, 150 Ibs. per cu. ft. It was found that the plans shown in Fig. 134 could be used for a fill of 50 or even 60 ft. without changing them appreciably. It was also found that, so far as quantities are concerned, rein- forced concrete arch culverts are more economical than those of the box pattern for any span exceeding 6 ft. The form work for an arch culvert is more expensive than for one of the box shape, but the extra expense is not believed to be large enough to justify the adoption of the latter style of structure for spans ex- ceeding 6 ft. Table LXVI contains quantities of concrete and steel for culverts similar to Fig. 134, also for pipe and box culverts. As compared with quantities contained in plain concrete culverts as commonly built and accepted as good practice in this country, a marked difference is seen to exist. Thus, the 8x8 ft. reinforced concrete arch culvert, contains 1.37 cu. yds. of concrete and 158 Ibs. of steel per linear foot of barrel, which steel, fig- ured at 3% cts. in place, is equivalent to 0.69 cu. yd. of concrete when the latter is taken at $8.00 per cu. yd. in place. The total equivalent concrete yardage is then 1.37 + 0.69 = 2.06 cu. yds. *C F. Graff, C. E.. Engineering News. Vol. LV, No. 1. 330 REINFORCED CONCRETE. per lin. ft. of barrel. As against this we have in plain concrete culverts of the same span and of usual standard designs from 3 to 4 cu. yds. Also, in this particular culvert, one pair of wing walls is observed to contain 11.22 cu. yds. of concrete and 793 Ibs. of steel, or a total equivalent concrete quantity of 11.22 4- 3.47 = 14.69 cu. yds. of concrete, as against 40 to 50 cu. yds. in ordinary plain concrete construction. Part Plan. Fig. 134. Reinforced Concrete Arch Culvert of 20-Ft. Span. TABLE LXVI. DIMENSIONS AND MATERIALS FOR REINFORCED CONCRETE CULVERTS, G. N. Ry. Size, ft. in. Barrel per lin. ft. One Pair Wing Walls. Remarks. Concrete cu. yds. Steel, pounds. Paving, cu. yds. Concrete cu. yds. Steel, pounds. Paving, cu. yds. 2x 3x 4x 4x 4 4x 6 6x 6 8x 8 12x12 17x16 16x20 16x20 0.10 0.23 0.30 0.54 0.72 0.86 1.37 2.78 3.70 5.00 5.05 5 10 12 61 73 116 158 237 287 300 307 Pipe Culvert Box Arch M 2.38 2.50 5.16 11.22 37.25 51.80 45.60 46.02 141 128 397 793 1,850 2,579 2,143 2,277 "26! 2" 0.66 CULVERTS, CONDUITS, SEWERS, DAMS. 331 EXAMPLES OF BOX CULVERTS. Standard Box Culverts, C., B. & Q. R. R. Fig. 135 and Table LXVII give dimensions and quantities of materials for culverts from 4x4 ft. to 7x8 ft., inside dimensions, and Fig. 136 and Table LXVIII give similar data for box culverts from 8x6 TABLE LXVII. DIMENSIONS AND MATERIALS FOR STANDARD Box CULVERTS, C., B. & Q. R. R. Inside dimens. Length of wing walls, Cu. yds. concrete Cu. yds. concrete 1i f+ Thickness, side walls, Thickness, roof slab, Thickness, floor slab in ft. ft. and ins. wing walls. Jin. it. barrel. in ins. in ins. in ins. 4x4 5 10 7.4 0.75 12 12 12 4x5 7 6 9.2 0.83 12 12 12 4x6 9 2 11.6 0.9 12 12 12 5x4 6 1 9.0 0.91 12 14 14 5x5 7 9 11.3 0.99 12 14 14 5x6 9 6 13.9 .06 12 14 14 6x5 8 13.5 .18 12 16 16 6x6 8 16.5 .25 12 16 16 6x8 12 9 18.3 .60 15 16 16 7x5 8 4 15.65 .39 12 18 18 7x7 11 5 24.9 .72 15 18 18 7x8 13 29.13 1.82 15 18 18 TABLE LXVIII. DIMENSIONS AND MATERIALS FOR STANDARD Box CULVERTS, C., B. & Q. R. R. Inside dimens. in ft. Length of wing walls , ft. and ins. Cu. yds. concrete wing walls. Cu. yds. concrete lin. ft. of barrel. Thickness, side walls, in ins. Thickness, roof slab, in ins. Thickness, floor slab, in ins. 8x6 8x8 8x 10 10x10 10x12 10 13 4 10 5 17 20 4 31.0 39.7 57.1 62.3 76.0 1.89 2.08 2.51 3.07 3.3 15 15 18 18 18 20 20 20 24 24 20 20 20 24 24 ft. to 10x12 ft. inside dimensions, as adopted by the C, B. & Q. R. R. In Table LXVII, the formula for L is as follows : 10 L= 3 h + 3ft. (52) 332 REINFORCED CONCRETE. Fig. 135. Standard Box Culvert for Clear Widths of 1 ft., C., B & Q. Ry. x' K-- A ' 5MX v J" -$ : ^^ | Ry.M.8,6. ^ 1 K y *t Fig. 136. Standard Box Culvert for Clear Widths of 8 Ft. and over, C., B. & Q. Ry. CONDUITS, SEWERS AND PIPES. Erosive and Transporting Powers of Water. The erosive power of water, or its power of overcoming cohesion, varies as the square of the velocity of the current The transporting power of a current varies as the sixth power of the velocity. Hence a current running 3 ft. per second or about 2 miles per hour, will carry fragments of stone the size of a hen's egg or about 3 oz. in weight. A current of 3 miles an hour will carry fragments of IVz tons, and a current of 20 miles an hour will carry fragments of 100 tons. The transporting power of water must not be confounded with i':s erosive power. The resistance to be overcome in the one case is weight, in the other cohesion ; the latter varies as the square, the former as the sixth power of the velocity. Resistance of Soil to Erosion by Water. Prof. W. A. Burr in "Engineering News," Feb. 8, 1894, gives a diagram showing the resistance of various soils to erosion by flowing water. The following figures show the comparative resistance; CULVERTS, CONDUITS. SEWERS, DAMS. 333 Pure sand resists erosion by flow of 1.1 ft. per second. Sand soil, 15 per cent clay, 1.2 ft. per second. Sandy loam, 40 per cent clay, 1.8 ft. per second. Loamy soil, 65 per cent clay, 3 ft. per second. Clay loam, 85 per cent clay, 4.8 ft. per second. Agricultural clay, 95 per cent clay, 6.2 ft. per second. Clay, 7.35 ft. per second. Kutter's Formula. Kutter's formula for velocity of water in conduits is as follows : v 1.811 0.00281 - + 41.6 + 41.6 + 0.0028U n (53) in which v = mean velocity in ft. per second a r = = hydraulic mean depth in feet a = area of cross section in sq. ft. p = wetted perimeter in linear feet s =-j- = sine of slope, or the fall of a given distance divided by said distance. n = a coefficient, depending on the nature of the lining 01 surface of the channel If we call 1.811 0.00281 "~ + 41.6 + ~ .6 + 0.00281\ n we have (54) which is Chezy's formula. Table LXIX for the flow of water in pipes is based upon Kutter's formula. Since n varies with the roughness of the surface of the chan- 334 REINFORCED CONCRETE. TABLE LXDL FLOW OF WATER IN CIRCULAR PIPES, SEWERS, ETC,, FLOWING FULL. Based on Kutter's Formula, with n= .013. Slope is head divided by length of pipes. (From Kent.) Diam. Discharge in cubic feet per second for varying slopes. Slope . . . 1 in ICO 1 in 200 1 in 300 1 in 400 1 in 500 1 in 600 1 in 700 1 in 800 15 n. ... 6.18 4.37 3.57 3.09 2.77 2.52 2.34 2.19 16 * .. 7.38 5.22 4.26 3.69 3.30 3.01 2.79 2.61 18 ' .. 10.21 7.22 5.89 5.10 4.56 4.17 3.86 3.61 20 ' .. 13.65 9.65 7.88 6.82 6.10 5.57 5.16 4.83 22 ' .. 17.71 12.52 10.22 8.85 7.92 7.23 6.69 6.26 Slope . . 1 in 200 1 in 400 1 in 600 1 in 800 1 in 1000 1 in 1250 1 in 1500 1 in 1800 2 ft. in. 15.88 11.23 9.17 7.94 7.10 6.35 5.80 5.29 2 " 2 " 19.73 13.96 11.39 9.87 8.82 7.89 7.20 6.58 2 ., 4 .. 24.15 17.07 13.94 12.07 10.80 9.66 8.82 8.05 2 " 6 " 29.08 20.56 16.79 14.54 13.00 11.63 10.62 9.69 2 " 8 " 34.71 24.54 20.04 17.35 15.52 13.88 12.67 11.57 Slope . . 1 in 500 1 in 750 1 in 1000 1 in 1250 1 in 1500 1 in 1750 1 in 2000 1 in 250Q 2ft.lOin. 25.84 21.10 18.27 16.34 14.92 13.81 12.92 11.55 3 " " 30.14 24.61 21.31 19.06 17.40 16.11 15.07 13.48 3 " 2 " 34.90 28.50 24.68 22.07 20.15 18.66 17.45 15.61 3 " 4 " 40.08 32.72 28.34 25.35 23.14 21.42 20.04 17.93 3 " 6 " 45.66 37.28 32.28 28.87 26.36 24.40 22.83 20.41 Slope . . 1 in 500 1 in 705 1 in 1000 1 in 1250 1 in 1500 1 in 1750 1 in 2000 1 in 2500 3 ft. 8 in. 51.74 42.52 36.59 32.72 29.87 27.66 25.87 23.14 3 " 10 " 58.36 47.65 41.27 36.91 33.69 31.20 29.18 26.10 4 " " 65.47 53.46 46.30 41.41 37.80 34.50 32.74 29.28 4 " 6 " 89.75 73.28 63.47 56.76 51.82 47.97 44.88 40.14 6 " " 118.9 97.09 84.08 75.21 68.65 63.56 59.46 53.18 Slope . . 1 in 750 1 in 1000 1 in 1500 1 in 2000 1 in 2500 1 in 3000 1 in 3500 1 in 4000 5 ft. 6 in, 125.2 108.4 88.54 76.67 68.58 62.60 57.96 54.21 6 " " 157.8 136.7 111.6 96.66 86.45 78.92 73.07 68.35 6 " 6 " 195.0 168.8 137.9 119.4 106.8 97.49 90.26 84.43 7 " " 327.7 205.9 168.1 145.6 130.2 118.8 110.00 102.9 7 " 6 " 285.3 247.1 201.7 174.7 156.3 142.6 132.1 123.5 Slope . . 1 in 1500 1 in 2000 1 in 2500 1 in 3000 1 in 3500 1 in 4000 1 in 4500 1 in 5000 8 ft. in. 239.4 207.3 195.4 169.3 156.7 146.6 138.2 131.1 8 " 6 " 281.1 243.5 217.8 198.8 184.0 172.2 162.3 154.0 9 " " 327.0 283.1 253.3 231.2 214.0 200.2 188.7 179.1 9 " 6 " 376.9 326.4 291.9 266.5 246.7 230.8 217.6 206.4 10" " 431.4 373.6 334.1 305.0 282.4 264.2 249.1 236.3 For U. S. gallons, multiply the figures in the table by 7.4805. For a given diameter the quantity of flow varies as the square root of the sane of the slope. By using this principle the flow for other slopes than those given in the table may be found CULVERTS, CONDUITS, SEWERS, DAMS. 335 nel, we are here interested only in that value of n relating to concrete. The value is n = 0.013, which gives the values in Table LXX for c, when s > 0.001, From this table the velocity, and hence the quantity, of water flowing in any pipe may be determined. TABLE LXX. VALUES FOR c IN CHEZY'S FORMULA. (From Kent.) n = 0.013. Diam. in ft. c Diam. in ft. c 0.5 69.5 8. 130.4 1.0 85.3 9. 132.7 1.5 94.4 10. 134.5 2. 101.1 11. 136.2 3. 110.1 12. 137.7 4. 116.5 14. 140.4 5. 121.1 16. 142.1 6. 124.8 18. 144.4 7. 127.9 20. 146. Grade of Sewers. The correct limit of grades which can be flushed, 0.1 to 0.2 per cent, may be assumed for sewers which are sometimes dry, while 0.3 per cent is allowable for the trunk sewers in large cities. Sewers should run dry as rarely as possible. Calculations. For conduits the calculations are somewhat complex owing to varying conditions and uncertain stresses, as consideration must be given to eventual future superimposed loads. The maximum live load with its impact in addition to the weight of the backfill should be taken to find the maximum stress, although the actual stress in most cases will be consid- erably less. Here the judgment of the designer must be used. Calculation for Internal Pressure. For internal pressure the calculation is as follows : 336 REINFORCED CONCRETE. Let po = internal pressure Ibs. per sq. in. d := diameter of conduit in inches. A s = area of steel reinforcement per lin. ft. in sq. in. / 8 = unit stress in steel reinforcement. If concrete is to take no part of the tension, we have _ pod or AS 2f Longitudinal reinforcement is provided for bending and tem- perature stresses. For bending moments the pipe is calculated like a beam and for temperature stresses the author allows about 1/500 of the area of the shell similarly as for retaining walls, but for conduits the range of maximum and minimum temperature is considerably less. For small pipes running over a long distance, expansion joints should be provided similar to those in use for iron pipes, particularly where the back fill is shallow and the range of temperature great. Calculation for External Pressure. For large pipes or conduits the regular arch calculation becomes necessary, where- by the pressure line is traced and abutments determined. For smaller pipe it has been found sufficient to calculate the external live and dead load per linear foot and make the com- bined thickness of the two sides of the shell sufficiently large so that the resulting compression is taken by the concrete alone. Reinforcement in the form of a fabric or a rod netting is then added to provide for bending moments and temperature stresses Myer's Formula. A= area of waterway in sq. feet. M area drained, in acres. c= 1 as a minimum for flat country. 1.6 for a hilly compact ground. c= 4. as a maximum for mountains. CULVERTS, CONDUITS, SEWERS, DAMS. 337 Talbot's Formula. notations as above, c as stated below. This formula is not intended for use for drainage area larger than 400 sq. miles. It was derived with special ref- erence to areas under 77 sq. miles. c: For rolling country subject to floods during melting snow, and with a length of valley 3 or 4 times the width let c = ft. In districts not affected by snow, or where length of valley is several times the width let c = 1-5 to 1-6. For steep slopes, increase c. Latham's Rule. /=-^ 100 d= depth of excavation. r= external radius of sewer. /= thickness of brick work in feet. Rankine's Rule. = thickness in feet. r~=. internal radius in feet. c= 0.2 for concrete. 0.3 for block stone. 0.4 for brick. 0.45 for rubble. Reinforcement for Sewers. If one set of reinforcement is used, y* per cent of the shell area usually is sufficient. If two sets of reinforcement are used, one at intrado and one at extrado, y\ per cent is usually employed. For circular pipes the thickness for constructive reasons usually is made con- stant. For longitudinal or distributing rods the author uses one-half the area of carrying rods, spacing them 50 per cent further apart. If the annular or carrying rods are separate, they are spliced by lapping or hooking. In either 338 REINFORCED CONCRETE. case all rods should have hooked ends. If the reinforcement is spiral, the ends of the helices are hooked, overlapping 40 diameters and tied together by means of No. 1.8 an- nealed wire. The carrying and distributing rods are likewise tied to- gether at crossings, so as to keep them stiff and in their proper position during concreting. In most instances a fabric will be found most economical for conduit reinforcement. In many instances one or two layers of fabric are suffi- cient; if not, l / 2 in. or ^ in. steel rods are tied to the fabric where required. A conduit located in an arch fill is stressed according to the line of a parabola and if built according to this line can be of remarkably light dimensions and still withstand a very heavy uniform load. Such conduits must of course be carefully back filled, but after filling there is little danger of damaging them. Thickness and Weight of Reinforced Concrete Pipe. Table LXXI gives a list of light weight reinforced concrete sewer pipe as manufactured in Germany and Austria. TABLE LXXI. THICKNESS AND WEIGHT OF CONCRETE PIPE. Circular pipe. Egg-shaped pipe. Diam. in inches. Thickness inches. Wt. per lin. ft. in Ibs. Diam. in inches. Thickness inches. Wt. per lin. ft. in Ibs. 4 91 7x11 1 23 6 111 10x15 { 33 8 17 12x18 46 10 24 14x21 52 12 30 16x24 67 14 37 20x30 | 87 16 j 44 22x33 I 105 18 1 50 24x36 I 110 20 22 !i 60 67 25x37i 28x42 120 127 27 \\ 100 29x43 1 140 33 n 146 31x47 ii 173 43 if 224 40x60 2 266 55 2i 335 51x80 21 366 63 2i 426 75 3 580 CULVERTS, CONDUITS, SEWERS, DAMS. 339 TABLE LXXI-A. Thickness and weight of reinforcement in culvert and sewer pipe, used by the author. ( NOTE. These culverts are furnished by Kansas City Concrete Pipe Co., Kansas City, Mo.; Diameter. Thickness. A. S. & W. Co. Triangular Mesh Wire Reinforcing. Weight per sq. ft. Draw Bars. Number 24 inches 3 inches 6 (Single) .271bs. l /i inch roun 27 3}/ " 6 .27 y% ' 30 3/^2 " 27 .41 y% ' 33 4 26 .50 y% ' 36 4 26 .50 y% ' 39 4 || 26 .50 y% ' 42 26 .50 y% * 45 4/^ " 26 .50 y% ' 48 5 " 23 .72 y% ' 54 5/^ " 23 .72 y% ' 60 6 " 23 .72 y% " 66 6^2 " 23 .72 yi 72 7 " 26 (Do able) .50ea ch 78 7/^ " 25 .55 84 8 23 .72 K2 " These pipes come in 4-foot lengths, complete with locking pins. Stresses in Pipes and Rings According to Talbot's Re- searches. Prof. A. N. Talbot gives the following data in his paper on results of tests of cast iron and concrete pipes (Bul- letin No. 22, University of Illinois Experiment Station, Urbana, 111., April 29, 1908) : Concentrated Load. For a concentrated load, Q applied at the crown of a ring, the bending moment Mb for a pipe of mean external diameter D is M B = 0.159 QD. The resisting moment is M R = \f c f> where f c = unit stress at the most remote fiber t = thickness of the ring. 340 REINFORCED CONCRETE. Distributed Vertical Load. For a distributed vertical load on thin elastic ring, the determination of the values of M and M B is given as follows (see Fig. 137) : If a system of horizontal forces equal to the vertical forces here considered be ap- plied to a ring, the bending moment pro- duced at A by the horizontal forces will be the same as that produced at B with the vertical load, and the bending moment pro- duced at B will be the same as that found at A with a vertical load, but with opposite signs in each case. Similarly, at any point between A and B it is evident that an equal numerical bend- ing moment will be produced with the new loading as at corre- sponding points with the old loading, but with opposite signs. The effect of a combination of the vertical and horizontal loads will be the same as that of a load normal to every part of the ring and making the bending moment at every section zero. It follows then that WD J Fig. 137. M 16 where W = the total distributed load on a ring of unit length, and D the mean diameter of the ring. Taking 45 the bending moment above this point of the ring is positive, below it is negative. Distributed Vertical and Horizontal Load. In thin elastic ring it is found that wr* (56) where 2r = average diameter of ring. q = the ratio of the horizontal to the vertical pressure. The bending moment becomes zero at = 45, as in the Other case. CULVERTS, CONDUITS, SEWERS, DAMS. 341 If the horizontal pressure has the same value as the vertical pressure, q = 1 and M becomes zero at all points. This corre- sponds to a uniform external pressure and produces equal com- pression in all parts of the ring. Thus for a concentrated load we have for the most remote fiber (57) At any point of the ring forming an angle with the hori- zontal, we have: For a uniformly distributed horizontal load the stress at the crown B will be WD /= I 1 * -pr ..................... : .......... (59) At/4, W WD f=%--l- t - ..................... . ..... , (60) and at any given point, wr cos 2 M f = -- Y~ " - J7 For a distributed horizontal and vertical load, we have at the crown B, qwr Ac WD f^^r*-^ ......................... (62) At A, the extremity of the horizontal diameter, wr J WD 1-~t~^~ .> .................. ...... (63) and at any given point, wr cos 2 , at any depth, h, the total pressure H, above the section considered, and the overturning moment, M, in inch Ibs., at the section A-B : ("Designing Methods") FLUID PRESSURE. a/=62.5 Ibs. Fig. 144-A. TABLE LXXI-A. h t>=wh H= Yrth Overturning Moment M=Hh * t>=wh H= Yrth Overturning Moment M=Hh Feet. Pounds. Pounds. Inch Pounds. Feet. Pounds. Pounds. Inch Pounds. 1 62.5 31 124 16 1000.0 8000 512000 2 125.0 125 1000 17 1062.5 9031 614108 3 187.5 281 3372 18 1125.0 10125 729000 4 250.0 500 8000 19 1187.5 11281 857366 5 312.5 781 15620 20 1250.0 12500 1000000 6 375.0 1125 27000 21 1312 5 13781 1157604 7 437.5 1531 42868 22 1375.0 15125 1331000 8 500.0 2000 64000 23 1437.5 16531 1520852 9 562.5 2531 91116 24 1500.0 18000 1728000 10 625.0 3125 125000 25 1562.5 19531 1953100 11 687.5 3781 166364 26 1625.0 21125 2197000 12 750.0 4500 216000 27 1687.5 22781 2460348 13 812.5 5281 274612 28 ,1750.0 24500 2744000 14 875.0 6125 343000 29 1812.5 26281 1 3048596 15 937.5 7031 421860 30 1875.0 28125 3375000 354 REINFORCED CONCRETE. done by anchoring or filling the hollow space with sand and gravel or lean concrete. Computing the dimensions of slabs, beams or counterforts is very simple after the pressures have been determined, and is done according to the methods laid down for floors and girders of buildings. Types of Construction. There are three principal types of construction the open front dam, the half apron dam and the curtain dam. cite* Fig. 145. Reinforced Concrete Dam, Theresa, N. Y. The Open Front Dam. An example of this type of dam is the one built at Theresa, N. Y., shown in Fig. 145. This dam is built of concrete reinforced with Thacher rods and expanded metal; it is 120 ft. long and 11 ft. high and is founded on solid rock. The structure consists of a series of solid concrete but- tresses 12 ins. thick and spaced 6 ft. apart center to center, and of a reinforced plate supported on the inclined tops of the but- tresses. At the crest the plate is stiffened by a reinforced beam 6x8 ins. in section. The plate was made of concrete composed of 1 part Portland cement, 2 parts sand, and 4 parts broken lime- stone; the toe and buttresses were made of a 1-3-6 mixture. The buttresses were anchor-bolted to the rock by 3-ft. 1^4-in. bolts. The drawing shows the spacing of the rods and their di- CULVERTS, CONDUITS, SEWERS, DAMS. 355 mensions. The dam is so constructed that the resultant pressure falls always within the base, and it is therefore a gravity dam un- der all heads of water. About 125 cu. yds. of concrete were re- quired to construct the dam. It was constructed by the Ambur- sen Hydraulic Construction Co., Boston. The open front type is used for moderate heights, and when located on a ledge of hard rock is able to withstand the erosion from the overflow of water and ice. The Half Apron Dam. This type is a modification of the former and consists in carrying the apron down in front to with in 6 or 8 ft. of the bottom, so curved as to discharge the water with a high velocity in a horizontal direction, as shown in Fig. 146. ^ Roll way \Rbck Line ^ Fig. 146. Half Apron Type of Dam. The Curtain Dam. This type goes still further and con- tinues the apron to the river bed, entirely enclosing the interior, as illustrated in Fig. 147. It is customary to place vents in the apron just below the crest for the purpose of admitting air behind the sheet of water to destroy the partial vacuum which would otherwise form under high velocities of overflow during floods a nd which is the cause of the so-called trembling of dams. 356 REINFORCED CONCRETE. Where foundations are on hard clay or cemented sand, sheet piling is often driven at the heel and toe to a sufficient depth to insure tightness, and the concrete is placed over and about the head of the piling. Drain holes are placed in the toe to Fig. 147. Curtain Type of Dam. carry off seepage. Weep holes may be placed in the floor to pre- vent upward pressure on the floor, which might endanger the safety of the dam. CHAPTER VI. TANKS, RESERVOIRS, BINS AND GRAIN ELEVATORS. TANKS AND RESERVOIRS. General Discussion. The construction of tanks and reser- voirs in reinforced concrete is like pipes, in that it is one of the first applications of this material in building construction. Monier constructed a 42,000-gallon tank at Maisons-Alfort in 1868 and another of 23,000 gallons' capacity at Bougival in 1872 for the local water works. The number of reinforced concrete tanks already in existence is a proof of their fast increasing popularity. Reinforced concrete is not only suitable and adapted for wa- ter storage, but likewise for wines, vinegar, petroleum, oil, and solid substances, such as grain, cement in bulk, coal, ore, ashes, etc. They are used for these purposes with great success in tan- neries, distilleries, sugar refineries, breweries, paper mills, bleach- cries, and other places where reservoirs are wanted for any pur- pose. Their cheapness, remarkable lightness and elasticity cause great reduction in the size and character of supports and foundations, and the minimum cost of maintenance and atten- tion required has recommended reinforced concrete as an ideal material of construction for these various purposes. Shape or Form of Tanks and Reservoirs. For covered tanks the roofs assume the form of cones, domes, and spheres, or are also flat and calculated accordingly. The shape or form of the reservoirs may be round, elliptical, square, or polygonal, and the tanks may be located in, on, or above the ground, like- wise supported on columns, walls, or girders, as the case may be. The cost largely depends upon the form, the cylindrical tanks being the more simple inasmuch as only the tension from 357 358 REINFORCED CONCRETE. the interior pressure and the compression due to the weight of the walls and the roof must be considered, while in the rectan- gular or hexagonal structures the bending moments come promi- nently into consideration. If reservoirs are placed on the ground and subjected to compression from underneath, the spherical bottoms are concave and are turned downwards. Calculations. The calculations for circular tanks contain- ing liquids are very simple. Let T = tensile stress exerted on wall for 1 foot in height at a depth of h from the top. A B = area of steel required in 1 -ft. of height. d = diameter of tank in feet. w = weight per cu. ft. of the liquid contained in the tank. f s = unit stress in the reinforcement. h = depth of the tank at a point where the thickness is sought. Then (68) (69) Table Giving Capacity of Tanks. Table LXXII gives the capacity in cubic feet and gallons for each 1 ft. depth of tanks of different diameters. To obtain the number of bushels ca- pacity, multiply the number of cubic feet by 0.8. For example, a tank 12 ft. in diameter contains 113.10 cu. ft.; for each foot in height it would contain 113.10 X 0.8 = 90.48 bu. Foundations. Tank bottoms may rest on rock or hard- pan and need be only of sufficient thickness to contain the re- inforcement and insure proper connection with the side walls. On soft homogeneous ground, a layer of common concrete placed under the bottom is usually sufficient. Where the soil contains water under pressure, very careful calculations must be made to enable the bottom to withstand the buoyancy of the tank, and in these cases a rib or gridiron construction is often resorted to. TANKS, BINS, GRAIN ELEVATORS. 359 TABLE LXXII. CAPACITY OP TANKS. 5 1 ill I!? Diameter. i Gallons for depth of 1 foot. Diameter. ll* 1 ft. ins. ft. ins. ft. 1 .785 5.87 5 19.63 146.88 33 855.30 6398.1 1 .922 6.89 3 21.65 161.93 34 907.92 6791.7 2 1.069 8.00 6 23.76 177.72 35 962.11 7197.1 3 1.227 9.18 9 25.97 194.25 36 1017.88 7614.3 4 1.396 10.44 6 28.27 211.51 37 1075.21 8043.1 5 1.576 11.79 3 30.68 229.50 38 1134.11 8483.8 6 1.767 13.22 6 33.18 248.23 39 1194.59 8936.2 7 1.969 14.73 9 35.78 267.69 40 1256.64 9400.5 8 2.182 16.32 7 38.48 287.88 41 1320.25 9876.2 9 2.405 17.99 3 41.28 308.81 42 1385.44 10363.9 10 2.640 19.75 6 44.18 330.48 43 1452.20 10863.2 11 2.885 21.58 9 47.17 352.88 44 1520.53 11374.4 2 3.142 23.50 8 50.27 376.01 45 1590.43 11897.3 1 3.409 25.50 3 53.46 399.88 46 1661.90 12431.9 2 3.687 27.58 6 56.75 424.48 47 1734.94 12978.3 3 3.976 29.74 9 60.13 449.82 48 1809.56 13536.5 4 4.276 31.99 9 63.62 475.89 49 1885.74 14106.4 5 4.587 34.31 3 67.20 502.70 50 1963.50 14688.0 6 4.909 36.72 6 70.88 530.24 51 2042.82 15281.4 7 5.241 39.21 9 74.66 558.51 52 2123.72 15886.5 8 5.585 41.78 10 78.54 587.52 53 2206.18 16503.4 9 5.940 44.43 6 86.59 647.74 54 2290.22 17132.1 10 6.305 47.16 11 95.03 710.90 55 2375.83 17772.5 11 6.681 49.98 6 103.87 776.99 56 2463.01 18424.6 3 7.069 52.88 12 113.10 846.0 57 2551.76 19088.5 1 7.467 55.86 6 122.72 918.0 58 2642.08 19764.2 2 7.876 58.92 13 132.73 992.9 59 2733.97 20451.6 3 8.296 62.06 6 143.14 1070.8 60 2827.43 21150.7 4 8.727 65.28 14 153.94 1151.5 61 2922.47 21861.6 5 9.168 68.58 6 165.13 1235.3 62 3019.07 22584.3 6 9.621 71.97 15 176.71 1321.9 63 3117.25 23318.7 7 10.085 75.44 16 201.06 1504.1 64 3216.99 24064.8 8 10.559 78.99 17 226.98 1697.9 65 3318.31 24822.7 9 11.045 82.62 18 254.47 1903.6 66 3421.19 25592.4 10 11.541 86.33 19 283.53 2120.9 67 3525.65 26373.8 11 12.048 90.13 20 314.16 2350.1 68 3631.68 27166.9 4 12.566 94.00 21 346.36 2591.0 69 3739.28 27971 .8 1 13.095 97.96 22 380.13 2843.6 70 3848.45 28788.5 2 13.635 102.00 23 415.48 3108.0 71 3959.19 29616.9 3 14.186 106.12 24 452.39 3384.1 72 4071.50 30457.0 4 14-748 110.32 25 490.87 3672.0 73 4185 39 31308.9 6 15.321 114.61 26 530.93 3971.6 74 4300.84 32172.6 6 15.904 118.97 27 572.53 4283.0 75 4417.86 33048.0 7 16.498 123.42 28 615. Vo 4606.2 76 4536.46 33935.2 8 17.IC5 127.95 29 660 . 52 4941.0 77 4656.63 34834.1 9 17.721 132.56 30 706.86 5287.7 78 4778.36 35744.7 10 18.343 137.25 31 754.77 5646.1 79 4901.67 36667.1 11 18.993 142.02 32 804.25 6016.2 80 5026.55 37601.3 *Also area of circle in square feet. 360 REINFORCED CONCRETED Tightness of Tanks. The question of tightness of the tanks is of the greatest importance and this is accomplished in various ways by different constructors. Often a tank is per- mitted to leak through its porous parts for several weeks, after which time the magnesia, lime, aluminum salts or impurities con- tained in the liquid will, to a great extent, close up the pores by silting. The author has found that the best method of making a tank tight is by hard troweling on the inside of the tank, such plastering being done before the final setting of the mortar or concrete of which the tank is constructed. The author Fig. 148. Reinforcement for Tanks. prefers for tanks a rather dry mixture of 1 cement to 4 coarse sand well tamped. If a wet mixture is used, the mortar or con- crete is apt to contract in setting, thereby causing initial com- pressive stresses in the steel reinforcement. When the tank is filled the concrete will crack in various places until the steel re- ceives its tension stress. This is the common cause of leaky tanks, which must be plastered or painted afterwards. Reinforcement. The reinforcement of tanks consists of carrying and distributing rods, as indicated in Fig. 148, in which TANKS, BINS, GRAIN ELEVATORS. 361 the mesh and dimensions are proportioned to withstand the pressure and tension according to the head of liquid contained. The reinforcement is usually round rods, placed annularly round the tank either in separate circles or in helices, such reinforce- ment being closer together and stronger nearer the bottom of the tank, decreasing in area towards the top. The distributing rods are usually the same from the top to the bottom and equal to about Vz per cent of the area of the tank wall. For square tanks, reinforcement of the sides by brackets or buttresses usually on the inside becomes necessary, and the walls are then calculated as retaining walls supported on these brackets. When the tanks are not covered, a strong rib is usually run around th top construction, similar to the construc- tion used in open steel tanks which are invariably strengthened and stiffened by riveting an angle iron around the top. Cost. The cost of reinforced concrete tanks built of light dimensions, but of rich material, resting on the ground and without roof, will be approximately as follows: For 1,000 gallons' capacity 6 1 A cts. per gallon For 2,000 gallons' capacity 5 cts. per gallon For 5,000 gallons' capacity 4^ cts. per gallon For 10,000 gallons' capacity 3% cts. per gallon For 20,000 gallons' capacity. 3 cts. per gallon For 100,000 gallons' capacity 2 cts. per gallon For 200,000 gallons' capacity 1% cts. per gallon Tank for Montgomery Ward & Co., Chicago Heights, 111. In 1901 the author constructed a 40-ft. tank, 8 ft. deep, for Montgomery Ward & Co., Chicago Heights. The tank is 5 ft. underground and 3 ft. above ground. A sump 1 ft. in diameter and 18 ins. deep was put at a point near the circumference and was kept empty by means of a hand pump, the water being con-^ veyed away for a distance of about 100 ft. in a wooden trough. The walls and the roof are only 2% ins. thick, as shown in Fig. 149. A wire fabric of No. 9 wire, Ix6-in. mesh, was erected near the center of the wall, and reinforcing rods placed on the inside of the netting tied at the side by means of annealed wire. 362 REINFORCED CONCRETE. The soil was stiff enough to stand for 5 ft., so that no form was necessary for this height. The bottom being 3 ins. thick, it was depressed about 1 ft. in the center and two layers of net- ting were laid across the same at right angles. Around the circumference ^-in. rods 3 ft. long were hooked at both ends, bent to a right angle and spaced as a corner angle connection Fig. 149. Roof Plan and Section of Tank for Montgomery Ward & Co. every 12 ins. The bottom was plastered with a mortar of 1 part Portland cement to 3 parts clean, coarse torpedo sand. The wire mesh around the sides of the tank was steadied by means of wooden pegs driven into the earth. The plaster on the sides commenced at the bottom, the mortar being thrown through the mesh against the earth and of such a consistency that it just could TANKS, BINS, GRAIN ELEVATORS. 363 be retained by the mesh. A few minutes later a second man threw on the next coat covering the mesh and the rods to a depth of l /z in., and about half an hour later followed a third man with a third coat Vz in. thick. After this coat was almost set the finisher followed up with a 1-2 mixture, which was trow- eled smooth with an iron tool. The last operation gave the tank a practically glossy surface on the inside similar to a side- walk finish. As the wooden pegs were reached they were pushed Fig. 150. Detail of Connection at Roof Tank for Montgomery Ward & Co. into the earth and new pegs put in near the top. A form 3 ft. high made of %-in. boards nailed to 2x6-in. ribs was then placed around the circumference and braced back on the ground and the plastering operation continued until the entire tank was plas- tered to the top, which took four plasterers and two helpers two days. An angle iron was laid around the top of the tank to take the thrust of the roof, and anchored by running the ends of the wire fabric through holes punched in the flange of the angle iron, as shown in Fig. 150. Then a conical form was erected 364 REINFORCED CONCRETE. ^Center Post Braced from Outside Scaffolding \ 1 1 T \- ^ ff^ ,** P " 6" 1 B f\ $ ^^^ : j) --x^"^^^ i*- Strap Iron v5>^ */na 'Form /a H j- 5 ' t ' f ^ 9 l~ f* '0"Ben}-Rod5 1'0"C toC %"xc_'0"F?ocfsJ'0"C1-oC ^ A 4 j I f I If ^11 1 te/^^ Bllfl ^^ It li j' T \ L I" 4'^"- ^*- u "_i- "S 1 ' ^ Fig. 151. Section of Tank, American Steel & Wire Co. TANKS, BINS. GRAIN ELEVATORS. 365 40 ft. in diameter and 4 ft. high at the apex to support the roof, the form being supported on studs set on planks laid on the bottom of the tank. The form consisted of 2x6-in. joists and %-in. sheathing bent down on the radial joists. Wire fabric was laid on top of the form and tied to radial steel rods, which were run down to the angle iron and well heeled. An expanded Fig. 152. Plan of Fabric in Roof Tank for American Steel & Wire Company. metal apron was thrown over the angle iron and fastened to the wire netting of the sides, as well as the wire netting in the roof, so as to form a clinch for the mortar around the top cor- ner. In Fig. 149 only the carrying rods, spaced 4 ins., are shown. The distributing rods of the fabric are spaced 1 in. apart. The roof was plastered 2% ins. thick in a manner simi- 366 REINFORCED CONCRETE. lar to the one used for the sides. A manhole was left in the roof through which the forms were taken out. The sump was made tight by placing a nipple 18 ins. long with a flange at the lower end- in the sump, and concrete placed around same under "f?0ds, 4 C.foC. ^ ,Wetied Fabric Fig. 153. Falsework and Girders, Tank for American Steel & Wire Company. continuous pumping, so that the space above the flange was kept dry until the concrete was set. Then a cap was placed over the upper end of the nipple in the tank. Thimbles were left in the tank for intake and discharge pipes. The cost of the TANKS, BINS, GRAIN ELEVATORS. 367 Fig. 154.-Construction of Intake Tank, LaSalle. 111. 368 REINFORCED CONCRETE. tank was about $1,300.00, or 1.6 cts. per gallon, the remarkable cheapness being due to the fact that no forms were required for the sides, and that very little trouble was experienced with pumping. Tank for American Steel & Wire Co., Cleveland, O. Fig. 151 shows a cross-section and Fig. 152 the plan of a tank built by the ^author for the American Steel and Wire Company at the Emma Furnace, Cleveland, Ohio. This tank is 18 ft. in diameter and 24 ft. high, the sides being 3 ins. thick, the bottom 4 ins", and the roof 2Vz ins. The capacity is 45,000 gallons, and it cost $2,500.00, which is 5% cts. per gallon. It was built in the winter, and the floor of the tank was on a pedestal 40 ft. above the ground. The floor consisted of girders shown in Fig. 153. The reinforcement consisted of an electrically welded fabric of Ix6-in. mesh used for distributing rods, and annular rings of from % to */4 ins. diameter steel for carrying rods, which were tied to the fabric every 9 ins. by means of No. 18 annealed wire. In the roof the sheets of fabric, 62% ins. wide, overlapped one another and were carefully tied down by means of No. 18 wire. After the tank was completed and filled with water a slight leakage was found in the side of the tank, but after one week had elapsed the tank was perfectly tight through silting. Forms for an Intake Tank. Fig. 154 shows how concrete was kept moist and also protected against freezing, in the con- struction of an intake tank, which was sunk into a river bank near La Salle. 111., by the author some years ago. The tank, which consisted of a reinforced concrete cylinder, was jetted down as fast as it was built, the concreting being done at the same level while the tank was sinking. Fig. 155 shows the manner of raising the forms. Battery Vaults. The author has manufactured a large number of battery vaults, 4 ft. diameter by 6 ft. high, for block signal purposes on railroads. These vaults were lj/2 ins. thick at bottom, sides and roof, with a manhole cover and frame. The reinforcement consisted of a wire fabric for the sides and %-in. rods with wire fabric for the top and bottom. The mor- tar consisted of 1 Portland cement to 3% coarse, sharp sand, TANKS, BINS, GRAIN ELEVATORS. 369 Fig. 155. Manner of Raising Forms, Intake Tank, LaSalle, 111. 370 REINFORCED CONCRETE. and the tanks were plastered on detachable outside molds, and made perfectly water-tight. Similar tanks are now manufac- tured by Trusswall Mfg. Co., Kansas City, Mo. BINS AND GRAIN ELEVATORS. The designing of grain elevators and storage structures is a specialty regarding which little literature is at hand, as it re- quires a practical knowledge not generally possessed by engi- neers. The author having had over 20 years' experience in the ' design and construction of grain elevators, and being the first designer of reinforced concrete grain elevators in the United States, here adds some remarks and suggestions relative to cal- culations and constructions in this special line, based upon ex- perience of his own, as well as that of his confreres in elevator construction, which has come under his observation. The researches and writings of Mr. J. A. Jamieson, the well- known elevator builder of Montreal, are particularly valuable and agree with the ideas of the author. Action of Grain Flowing From a Bin. If grain is allowed to run from a spout to a floor it will pile up until its slope reaches a certain angle called the angle of repose, when the grain will slide down the* surface of the cone. If a hole be cut in the side of a bin the grain will flow out until the open- ing is blocked up by the outflowing grain. There is no ten- dency for the grain to spout up as in the case of fluids. If grain be allowed to flow from an opening it flows at a con- stant rate, which is independent of the head and varies approxi- mately as the cube of the diameter of the orifice. The law of grain pressure has been studied by several engineers and as a result has been fairly well established. Bridging Action of Grain in a Bin. It has been found that in storing materials in bulk a certain bridging takes place to such an extent that at quiescent loads the lateral pressure becomes practically constant, and accordingly the weight of the contents of a bin partly rests on the bin walls. . Table of Grain Pressure. Table LXXIII is taken from Mr. J. A. Jamieson's tests on the Canadian Northern elevator at TANKS, BINS, GRAIN ELEVATORS. 371 Port Arthur, Ont., which had cribbed wooden bins built of lami- nated planks, 2x6 ins. to 2x10 ins. The lateral and vertical pres- sures are given for heights to 65 ft. in a bin 13 ft. 4 ins. x 13 ft. 4 ins. TABLE LXXIII. GRAIN PRESSURE IN DEEP BINS.* Height in Feet. Lateral Pressure in Lbs. Vertical Pressure in Lbs. Height in Feet. Per sq. in. Total per ft. section. Per sq. in. Wt. on bottom. 1 .347 8,900 1 2 67 17,152 2 3 0.22 1,690 95 24,320 3 4 43 3,302 1.21 30,916 4 5 0.61 4,685 1.45 37,120 5 6 0.80 6,144 1.67 42,752 6 7 0.95 7,296 1.87 47,872 7 8 .08 8,294 2.05 52,480 8 9 .19 9,139 2.22 56,832 9 10 .28 "9,830 2 37 60,672 10 11 .40 10,752 2 51 64,256 11 12 .50 11,520 2.64 67,584 12 13 1.58 12,134 2.76 70,656 13 14 1.66 12,749 2.87 73,472 14 15 1.75 13,340 2.97 76,032 15 16 1.81 13,901 3 07 78,592 16 17 1.90 14,592 3.17 81,152 17 18 1.97 15,130 3.26 83,456 18 19 2.00 15,360 3.34 85,504 19 20 2 05 15,744 3.42 87,552 20 21 2.12 16,281 3.50 89,660 21 22 2.18 16,742 3.57 91,392 22 23 2.21 16,973 3.63 92,928 23 24 2.30 17,664 3.70 94.720 24 25 2.34 17,971 3.76 96,256 25 26 2.37 18,202 3.81 97,536 26 27 2 40 18,432 3.85 98,560 27 28 2.41 18,509 3.89 99,584 28 29 2.43 18,662 3.93 100 608 29 30 2 45 18,816 3.97 101,632 30 31 2 50 19,200 4.02 102,912 31 32 2.51 19,277 4.05 103,680 32 33 2.52 19,354 4.0-8 104,448 33 Ratio of Grain to Liquid Pressure. Figure 156 is derived from experiments by Mr. J. A. Jamieson and closely con- forming to Janssen's formula: 372 REINFORCED CONCRETE. in which L = lateral pressure of grain in Ibs. per sq. ft. TABLE LXXIII, (Continued). GRAIN PRESSURE IN DEEP BINS. Height in Feet. Lateral Pressure in Lbs. Vertical Pressure in Lbs. Height in Feet. Per sq. in. Total per ft. section. Per sq. in. Wt. on bottom. 34 2.53 19,430 4.11 105,216 34 35 2.55 19,584 4.15 106,240 35 36 2.58 19,814 4.17 106,752 36 37 2.60 19,968 4.19 107,264 37 38 2.61 20,045 4.24 108,544 38 39 2.615 20,083 4.26 109,056 39 40 2.62 20,122 4.28 109,568 40 41 2.63 20,198 4.30 110,080 41 42 2.64 20,275 4.33 110,848 42 43 2 65 20,352 4 35 111,360 43 44 2.66 20,429 4.37 111,872 44 45 2.67 20,506 4.38 112,128 45 46 2.68 20,582 4.39 112,384 46 47 2.69 20,659 4.41 112,896 47 48 2.70 20,736 4.41 112,896 48 49 2.70 20,736 4.44 113,664 49 50 2.70 20,736 4.45 113,920 50 51 2.70 20,736 4.46 114,176 51 52 2.71 20,813 4.47 114,432 52 53 2.71 20,813 4.48 114,688 53 54 2.71 20,813 4.49 114,944 54 55 2.72 20,890 4.50 115,200 55 56 2.72 20,890 4.51 115,456 56 57 2.73 20,966 4.52 115,712 57 58 2.74 21,043 4.52 115,712 58 59 2.75 21,120 4.55 116,220 59 60' 2.76 21,197 4.55 116,220 60 61 2.77 21,274 4.55 116,220 61 62 2.77 21,274 4.55 116,220 62 63 2.77 21,274 4.55 116,220 63 64 2.77 21,274 4.55 116,220 64 65 2.77 21,274 4.55 116,220 65 area of bin in sq. ft. = '; c,. = hydraulic radius. circumference of bin = the base of Naperian logarithms = 2.718281. TANKS, BINS, GRAIN ELEVATORS. 373 .50 ,30 4 I JO > 34 5,6 7 d ? JO Valves 0f % Fig. 156. Graphic Diagram of Wheat Pressure in Bins. //' = coefficient of friction of grain on cement = 0.41667. The values of K are shown for different values of 374 REINFORCED CONCRETE. h_ b which is the ratio of the depth of grain to the side of a square bin, or least side of a rectangular bin. The following notation is used in constructing the diagram: Angle of repose = 28. Coefficient of friction = 0.41667. Lateral pressure 0.6 vertical pressure. h = height or depth of grain. b = least side of bin. K == ratio of actual grain pressure to liquid pressure. w = weight of wheat = 50 Ibs. per cu. ft. Side pressure per sq. it. == Kwh. Bottom pressure at any depth = 1.667 Kwh. Maximum bottom pressure occurs when - = 3.5. Maximum bottom pressure per sq. ft. = wb. Example. Let it be required to find the vertical and hori- zontal pressures at the bottom of a bin 10 ft. square and 40 ft. deep. h r = 4 From the curve, K = .149. Side pressure =Kwh = .U9 X 50 X 40 = 298 Ibs. per sq. ft. Bottom pressure = 1.667 Kwh == 4Q7 Ibs. per sq. ft. Vertical load carried by side walls = 200,000 (497 X100) = 150,300 Ibs. Vertical Pressure. The vertical pressure in a deep grain tin is calculated as follows: The grain supported by the side walls is equal to the lateral pressure multiplied by the coeffi- cient of friction of the grain on the bin wall. The grain car- ried on the bottom of the bin is equal to the total weight of grain, minus the weight carried by the side walls. The bot- tom pressure is not uniformly distributed, but is a minimum at TANKS, BINS, GRAIN ELEVATORS. 375 the side walls and a maximum at the center. The grain mass producing bottom pressure may be represented by a portion of an ellipsoid of revolution with the major axis of the el- lipse vertical. Ratio Between Lateral and Vertical Pressure. The value of the ratio between lateral and vertical pressure in a bin, is not a constant for grain in a bin at different depths, being greater for small than for large depths of grain and varying with different bins and different grains. Average values of k for wheat and rye are given in Table LXXIV. TABLE LXXIV. VALUES OP fe= IN DIFFERENT BINS. V Bins. L k= V Wheat. Rye. Cribbed bin 0.4 to 0.5 0.4 to 0.5 0.34 to 0.46 0.3 0.3 to 0.35 0.23 to 0.32 0.3 to 0.34 0.3 to 0.45 0.23 to 0.28 0.3 Ringed cribbed b Small plank bin Large plank bin . Reinforced concr etc bin .... The Coefficient of Friction. The coefficient of friction of grain on concrete is 0.4 to 0.425, according to roughness of the concrete. The coefficient of friction of wheat on wheat is 0.532, or tan 28. Table LXXV, coefficients of friction for various ma- terials, is compiled by Mr. Wilfred Airy as a result of his ex- periments, printed in the proceedings of Inst. of Civ. Eng., Vol. CXXXI, 1897. 376 REINFORCED CONCRETE. TABLE LXXV. COEFFICIENTS OF FRICTION OF VARIOUS MATERIALS. Weight loose. Coefficient of Friction. Grain on grain. Grain on rough wood. Grain on smooth wood. Grain on iron. Grain on cement. Wheat 49 ,466 .412 .361 .414 .444 Barley 39 .507 .424 .325. .376 .452 Oats ... . 28 .532 .450 .369 .412 .466 Corn . . . 44 .521 .344 .308 .374 .423 Beans. 46 .616 .435 .322 .366 .442 Peas ..... 56 .472 .287 .268 .263 .296 Tares 49 .554 .424 .359 .364 .394 Flaxseed 41 .456 .407 .308 .339 .414 rr Mr/) j Pressure of Coal in Bins. Tables LXXVI and LXXVII, giving the pres- sure of coal in bins, are taken from the paper by Mr. R. W. Dull, printed in Enginering News, July 21, 1904. See Fig. 157. In the formulas, = angle of repose 0'= angle of friction between ma- terial and bin wall angle between direction of thrust and normal to bin wall P = total thrust against bin wall per ft. N ^= horizontal component of P 8' angle of slope of surface of material. For both the tables, Col. 1 gives normal component of total pressure on vertical side, when surface is level. Fig. 157. cos 2 wh* where sin (0 4- ') sin cos ..:'(70) TAXKS. BINS, GRAIN ELEVATORS. 377 TABLE LXXVI. TOTAL PRESSURE AT DEPTH h FOR BITUMINOUS COAL. Wt. per c,u. ft. = 50 Ibs. Angle of repose = = 35. Pressures for a section of material 1 ft. wide. 1 2 3 4 5 6 Depth in feet. rr * i A h rf * $f h , n\ ?P A dr 1 IT ur tT & i 1 8 fe * 0'=18 '=0 5 3=0 8= 3=0 1 5.83 6.75 16.75 20.5 4.27 5.13 2 23.32 27.00 67.00 82.0 17.1 20.5 3 52.47 60.75 150.75 184.5 38.4 46.2 4 93.4 108.00 268.00 328 68.3 82.0 5 145.7 168.75 418.75 513 107 128.0 6 209.4 243 603 738 156 184.5 7 286 333 821 1,005 209 257 8 373 432 1,072 1,312 273 328 9 472 547 1,357 1,661 346 415 10 583 675 1.675 2,050 427 513 11 705 817. 2,027 2,481 516 615 12 840 972 2,412 2,952 615 738 13 985 1,141 2,831 3,465 722 866 14 1,143 1,323 3,283 4,018 838 1,005 15 1,312 1,519 3,769 4,613 960 1,152 16 1,492 1,728 4,288 5,248 1,093 1,311 17 1,685 1,951 4,841 5,945 1,232 1,480 18 1,889 2,187 5,427 6,642 1,382 1,660 19 2,105 2,437 6,047 7,400 1,541 1,852 20 2,332 2,700 6,700 8,200 1,708 2,052 21 2,571 2,977 7,387 9,041 1,883 2,262 22 2,821 3,267 8,102 9,922 2,065 2,483 23 3,084 3,571 8,861 10,845 2,259 2,560 24 3,358 3,888 9,648 11,808 2,460 2,810 25 3,644 4,219 10,469 12,813 2,669 3,206 26 3,941 4,563 11.323 13,858 2,887 3,468 27 4,250 4,923 12.211 14,945 3,113 3,740 28 4,570 5,292 13,142 16,072 3,348 4,022 29 4,903 5,677 14,087 17,241 3,591 4.314 30 5.247 6,075 15.075 18.450 3.843 4,617 378 REINFORCED CONCRETE. TABLE LXXVII. TOTAL PRESSURE AT DEPTH h FOR ANTHRACITE COAL. Wt. per cu. ft. = 52 Ibs. Angle of repose = = 27. Pressures for a section of material 1 ft. wide. 1 2 3 4 5 6 Depth " r" A in feet. rr 1 T ^ l^\ ih i.e- h ^ i rt LL B' 1 1 . 4- h #'- 0'=0 -* 3= 5= 5=0 1 8.39 9.75 20.05 23.17 6.38 2 33.5 39.0 82.0 93.3 25.5 3 75.5 87 184.5 208.6 57 5 4 134 2 156 328 371 102.0 5 210 244 513 579 159.5 6 302 351 738 834 230 7 411 478 1,005 1,135 313 8 536 624 1,312 1,482 402 9 680 790 1,661 1,876 517 10 839 975 2,050 2,317 638 11 1,014 1,180 2,481 2,802 773 925 12 1,209 1,405 2,952 3,340 920 1,100 13 1,418 1,648 3,465 3,918 1,080 1,290 14 1,643 1,910 4,018 4,540 1,250 1,497 15 1,887 2,193 4,613 5,220 1,436 1,720 16 2,145 2,500 5,248 5,930 1,636 1,953 17 2,421 2,808 5,945 6,696 1,845 2,207 18 2,718 3,160 6,642 7,507 2,064 2,471 19 3,030 3,521 7,400 8,363 2,310 2,758 20 3,350 3,902 8,200 9,268 2,554 3,053 21 3,700 4,303 9,041 10,218 2,820 3,372 22 4,061 4,718 9,922 11,214 3,086 3,701 23 4,438 5,156 10,845 12,257 3,372 4,040 24 2,833 5,611 11,808 10,346 3,680 4,398 25 5,244 6,097 12,813 14,481 3,985 4,770 26 5,672 6,600 13,858 15,663 4,521 5,160 27 6,116 7,112 14,945 16,891 4,650 5,560 28 6,578 7,638 16,072 18,165 5,000 5,979 29 7,056 8,202 17,241 19,486 5,370 6,421 30 7,551 8,775 18,450 20,853 5,742 6,880 TANKS, BINS, GRAIN ELEVATORS. 379 Col. 2 gives pressure against vertical plane AB when friction is not considered, i. e., is taken as O. wh* f (f>\ N = ~2~ tan 2 (^45 -y j ............ (71) Col. 3 gives normal component of total pressure on vertical side when surface is surcharged to the angle of repose, and the bin is unlimited in horizontal extent. N = cos 2 ~2~ ................ (72) Col. 4 gives the same as Col. 3, except that angle of friction is neglected. wh* N = cos ~2~ ............... (73) Col. 5 gives normal component of total pressure on vertical side when material slopes downward along angle of repose. /cos (J>\*wh- sin(0 +0') sin (0 + 5) -\-^T) T where ->|- cos ' cos - Col. 6 gives same as Col. 5, except that friction is neglected. cos (t>\ z wh* sin --* as far as to zero, but all will haye the same sign. Hence the core circumference really represents the line in which all zero points are located. The core radius r is the section modulus W divided by the area F (See Fig. 163). Fig. 163. Cross- Section Showing Neutral Core in Chimney. Now and hence w )'] for a homogeneous section. It is not within the province of this book to enter into the more intricate methods of calculations, such as described by Dr. R. Salinger in Beton u. Eisen, 1905, pages 253 and 273, as the 392 -REINFORCED CONCRETE. method herein given is safe enough both for original calcula- tions and review. Wind Pressure and Velocity. From experiments made by Prof. C. F. Marvin of U. S. Weather Bureau (see Anemometry, Circular D, second edition, 1900) it is found that wind pres- sures are not so great as generally computed and are quite ac- curately given by the following equation : P = 0.004 ^ (SF 2 ) ."'..,' (79) Where P = pressure in pounds. S = surface in sq. ft. V == corrected velocity of wind in miles per hour. B = height of barometer in inches. For stations near the sea level, where the barometric pres- r> sure does not vary much from 30 ins., the ratio -^. need not be considered. The relation between the wind velocity V in miles per hour and the linear velocity v of the cup centers of an anemometer, also in miles per hour, can be expressed by the following equation : Log V 0.509 +.0,9012 log v (80) and Table LXXX gives true velocities as compared with indi- cated velocities, and corresponding wind pressures. Approximate Mfithod of Calculation. A simple and safe approximate method for calculating chimneys is given in Beton und Eisen, 1905. Heft X, and is as follows : F = the cross section of the outer shell in sq. ins. r the mean radius of cross section in ft. As cross section of vertical bars in sq. ins. _ 100Q ^8 R = the lever arm from the center of the chimney to the resultant of the weight in tons of the chimney Q and the wind pressure W. CHIMNEYS AND MISCELLANEOUS DATA. 393 TABLE LXXX. WIND VELOCITIES AND PRESSURES AS INDICATED BY ROBINSON'S ANEMOMETER. (Corrected to true velocities.) Indi- cated veloc- ity. True Velocity. + + 1 + 2 . + 3 + 4 + 5 + 6 + 7 + 8 + 9 10 20 30 40 50 60 70 80 90 ' 'g'.e' 17.8 25.7 33.3 40.8 48.0 55.2 62.2 69.2 5. 13.8 21.8 29.6 37.1 44.4 51.6 58.7 65.7 6. 14.6 22.6 30.3 37.8 45.1 52.3 59.4 66.4 6.9 15.4 23.4 31.1 38.5 45.9 53.0 60.1 67.1 7.8 16.2 24.2 31.8 39.3 46.6 53.8 60.8 67.8 8.7 17.0 24.9 32.6 40. 47.3~ 54.5 61.5 68.5 10.4 18.6 26.5 34.1 41.5 48.7 55.9 62.9 11.3 19.4 27.3 34.8 42.2 49.4 56.6 63.6 12.1 20.2 28.0 35.6 43.0 50.2 57.3 64.3 12.9 21.0 28.8 36.3 43.7 50.9 58.0 65.0 Pressure (Lbs. per sq. ft.) 104 144 190 243 303 10 .369 .433 .511 .586 .666 .762 .853 .949 1.05 i.16 20 1.27 1.38 1.50 1.63 1.76 1.90 2.04 2.19 2.34 2.48 30 2.64 2.81 2.98 3.14 3.32 3.50 3.67 3.87 4.04 4.24 40 4.44 4.64 4.84 5.07 5.27 5.51 5.72 5.93 6.18 6.40 50 6.66 6.89 7.12 7.4 7.64 7.88 8.14 8.43 8.69 8.95 60 9.22 9.49 9.76 10.1 10.4 10.6 10.9 11.2 11.6 11.9 70 12.2 12.5 12.8 13.1 13.5 13.8 14.1 14.4 14.8 15.1 80 15.5 15.8 16.2 16.5 16.9 17.3 17.6 18.0 18.4 18.8 90 19.2 f c = maximum stress in concrete in Ibs. per sq. in. fs = maximum compression in steel in Ibs. p ; er sq. in. f s = maximum tension in steel in Ibs. per sq. in. M = moment of wind pressure in foot tons. , Then we have and fc ~ AF fs = nf c = i- 15 , (81) (82) f s =Bf c (83) where A ana -B are constants taken from the Tables LXXXI and LXXXI1. 394 REINFORCED CONCRETE. Example. The external diameter of a chimney is 14.5 ft., its height 225 ft., and the thickness of the shell assumed to be 6 ins Effective wind pressure is 20 Ibs. per sq. ft. Q = weight of shaft, approximately 360 tons F = cross section of shell, approximately 3150 square inches TABLE LXXXI. VALUES FOR A IN FORMULA (81). R A r. M = 2.5 5 10 15 20 25 30 35 40 5 500 0.519 0.538 0.575 0.613 0.650 0.688 0.6 444 461 480 515 550 584 618 0.7 8 380 306 400 342 421 365 455 402 489 437 521 470 553 500 6 530 0.9 1.0 220 291 253 319 283 360 325 394 358 425 388 455 418 485 446 1.1 1.2 223 199 254 230 297 273 328 303 357 331 385 358 413 384 0.438 407 1.3 1.4 1.5 1.6 1.8 ! !! 180 163 150 138 211 195 181 170 151 253 235 219 206 184 282 264 247 233 209 309 290 272 257 231 334 313 295 279 251 358 336 317 300 270 381 358 338 320 289 6!380 358 340 307 2 137 166 189 210 229 246 263 279 2 2 151 173 193 210 225 241 256 2 4 160 178 195 209 223 236 2 6 149 166 181 195 208 220 TABLE LXXXII. VALUES FOR B IN FORMULA (83). r. M = 2.5 5 10 15 20 25 30 35 40 0.5 6 2.5 2.4 2.4 2.3 2.2 2.1 2.0 7 7 1 6 2 5.7 5 1 4 6 4 2 4 8 17. 12. 10. 8.5 7.3 6.7 6.3 5.9 0.9 1 44. 19. 26. 14.8 19.6 11.5 14.5 9.9 12.2 8.9 10.9 8.2 10. 7.7 9.3 ...... 1.1 32. 23.8 17.1 14.3 12.7 11.6 10.7 10. 1 .2 .3 39.5 45. 27.5 30.9 19.5 21.6 16.1 17.8 14.2 15.6 13. 14.2 12. 13.1 11.2 12.3 4 50. 33.8 23.4 19.3 16.9 15.3 14.1 13.3 12 6 .5 54. 36.5 25. 20.6 18. 16.3 15. 14.2 13.4 .6 g 57. 39. 43 2 26.6 29.3 21.8 23 7 19. 20 7 17.2 18 7 15.8 17 2 14.9 16 2 14.1 15 4 2 47. 31.8 25.4 22.1 20. 18.4 17.3 16 5 2 2 34. 26 9 23 3 21 1 19 3 18 2 17 4 2 4 28 2 24 4 22 1 20 2 19 1- 18 2 2 6 29 3 25 3 23 21 1 19 8 18 9 CHIMNEYS AND MISCELLANEOUS DATA. 395 W wind pressure, assumed to average 14.5 X 200 X 20 29 tons M - 29 X 100 ft. = 2900 foot tons A B - f-in. rods 6 ins. on centers - 2?rl4 X 0.4418 39 sq. ins. 1000 A s 1000 X 39 m = ~T~ 3150 M _ 2900 Q == 360 r - J (14.05 .05) = 7 ft. Then we have, according to Tables LXXXI and LXXXII, by interpolation, A - 0.301 B = 15.6 Q 720000 hence f = -^ = .301 x 3150 " 76 bs> per sq> m /'- 15 X f e - 11400 lbs. per sq. in. / 8 - / c - 15.6 X 760 - 11,856 lbs. per sq. in. *Approximate Computation of Dimensions. For the thickness of the steel, considered as a solid shell /= r X I 77:7; | , where d = internal diameter in feet; wall a \1UU/ j TT2 thickness of concrete = 0.1 X 42 Q Q5H ^ ~rf~* If we use 1-in. round bars instead of a steel ring, the number of rods may be found in following table: TABLE LXXXIII. H 100' 125' 150' 175' 200' 225' 250' No. of Rods 43 77 110 150 192 240 300 Wall thickness for H d = 20 6" 7" 8" 10" 13" 15" 18" Summary of Points in Design of Chimneys. Mr. San- ford E. Thompson sets forth the following summary of es- sentials in design and construction of a reinforced concrete chimney.t (1) Design the foundations according to the best engi- neering practice. (2) Compute the dimensions and reinforcement in the *From Heiniche's Catalog. t Bulletin American Portland Cement Manufacturers' Association. 396 REINFORCED CONCRETE. chimney with conservative units of stress, providing a factor of safety in the concrete of not less than 4 or 5. (3) Provide enough vertical steel to take all of the pull without exceeding 14,000 or, at most, 16,000 Ibs. per sq. in. (4) Provide enough horizontal or circular steel to take the vertical shear and to resist the tendency to expansion due to interior heat. (5) Distribute the horizontal steel by numerous small rods in preference to larger rods spaced farther apart (6) Specially reinforce sections where the thickness in the wall of chimney is changed or which are liable to marked changes of temperature. (7) Select first class materials and thoroughly test them before and during the progress of the work. (8) Mix the concrete thoroughly and provide enough water to produce a quaking concrete. (9) Bond the layers of concrete together. (10) Accurately place the steel. (11) Place the concrete around the steel carefully, ram- ming it so thoroughly that it will slush against the steel and adhere at every point. (12) Keep the form rigid. The fulfillment of these requirements will increase the cost of the chimney, but if the recommendations are fol- lowed there should be no difficulty in erecting concrete chimneys, which will be very satisfactory and last forever. Construction. During the past few years reinforced con- crete chimneys have been built in great numbers, both on account of their strength and their cheapness. The construction is generally carried on continuously from the base to the top, and the materials consist of cement and coarse sand proportioned one to four. Concrete Chimneys. Fig. 164 shows a chimney built for the United Shoe Machinery Co., at Beverly, Mass., and gives the characteristic features of a Weber chimney. It is 6 ft. in diameter and 142 ft. 1 in. in height from bottom of founda- tion to top. The foundation extends about 16 ft. below ground. The shell is double to the height of 48 ft. above. CHIMNEYS AND MISCELLANEOUS DATA. 397 Plan of Foundation. Fig. 164. Chimney for United Shoe Machinery Co., Beverly, Mass 398 REINFORCED CONCRETE. ground, the inner shell being 4 ins. thick and the outer 6 ins. The upper single shell portion is 5 ins. thick. The reinforce- ment consists of 1^x1^x3/16 in. vertical and Ixlx^ in. horizontal T irons. The number of bars in the circumference and the arrangement of rods in the foundation are given in the cut. Construction of Molds. The molds in the construction of Weber chimneys consist of two rings of six sections, each about 3 ft. wide and connected by iron fastenings. They are held in place by friction on the concrete only and are dis- connected before being hauled up to the required position. A flat ring is located above the forms to hold the vertical steel bars in position and alignment by running them through holes in the plate. This ring is made of two ^4-in. layers of wood and is pushed on ahead of the forms, also carrying the beam for the hoisting pulley. All materials are hoisted in- side the chimney. No interior scaffold is needed for the double shell and usually one form a day is filled and moved up. For the single shell, two forms a day are filled. The vertical bars lap 24 ins. where spliced. Formerly a very dry mix was used and carefully tamped, but recently several mishaps have occurred, largely attributed to lack of water in the mortar, so at present a wetter mixture is being used. The rings are fastened to the vertical bars by means of wire or special clamps. The air space at the bottom is connected with the atmosphere and at the top of the inner shell with the flue proper. Care must be taken to keep the openings at the bottom clean from waste concrete in order to allow free circulation of air around the inner shell. The Wiederholt Concrete Steel Chimney. The Wieder- holt chimney is built without forms by the means of thin H-shaped tiles placed edge to edge so as to contain the con- crete and the reinforcement. Horse-Power of Chimneys. (Kent) Let ^4 = area in sq. ft. of chimney. /f=height in ft. H. P. = horse-power. then H. P. =3.33 (A-0. CHIMNEYS AND MISCELLANEOUS DATA. 399 MANUFACTURED ARTICLES. Among the manufactured articles of reinforced concrete should be named railroad ties, fence posts, telegraph poles, electric transmission poles, smoke jacks, tubs and tanks of every description, coffins, roofing and siding plates, electrier conduits, floor slabs, floor beams, pile protection, stair steps, balusters, building blocks, garden benches, manhole covers, chimney tops, door and window frames, sills, lintels and cornices. Each of these items introduces a new field in the world of manufacture, the development of which largely be- longs to the future and the ingenuity of the concrete student. INSPECTION. In no other kind of building construction is there so much need for inspection as in reinforced concrete. Inspection of the cement in its manufacture, after delivery, and on the job; inspection of the sand as to its cleanness and condition; in- spection of the stone as to its strength and size; inspection of the mixture of the three materials mentioned, and inspec- tion of the amount of water added to make the proper con- sistency constitute only a small part of what is required of an inspector on an important reinforced concrete construc- tion. There is the inspection of the steel in the reinforce- ment, the method of making and shaping and of assembling and connecting the reinforcement, and, finally, of placing and fastening it. There is the inspection of the forms, the quality of the timber, the method of putting it together to meet the intention of the designing engineer, and with a view to its easy removal so as to be used again. The filling of forms, the spading and tamping of the concrete around the reinforcement and against the forms and the joining of new work to old must be watched. An eye must be kept on the forms ahead of the concreting to see that they are cleaned free of shavings and dirt. While this is going on the inspector must watch the action of the forms and the setting of the cambers, look out for leaks, and at the same time keep an eye on the contractor's men to see that they do not run wheel barrows or carry heavy loads over the finished work. 400 REINFORCED CONCRETE. During the hardening, the concrete surface must be kept moist. This item is often overlooked in rush work. After the concrete is finally placed, with good materials and mixing and good workmanship, the inspector must see that the forms remain undisturbed until the concrete is hard- ened sufficiently to enable the removal of the struts and braces keeping them in position. Too early removal of forms has been the cause of most of the deplorable acci- dents which have tended to retard the advancement of rein- forced concrete in the United States, and which has caused investors to look askance at this construction, otherwise so desirable from an engineering and economical standpoint. It is far better to be a few days behind time than to take chances on a too early removal of the forms. It is also the inspector's duty to see that the naked concrete is protected, in summer from the sun by wet saw dust or wet blankets and in the winter from freezing. The cleaning of the molds is an important item and should be well looked after by the inspector. If the in- spector is employed by the contractor, he should also be entrusted with the keeping of costs, a matter which will be treated later. PROGRESS REPORTING AND KEEPING OF COSTS. To enable the engineer or contractor to estimate work in a rational manner it is absolutely necessary for him to note down the detail cost of the practical execution of the work. This will also enable the contractor to analyze his expendi- tures with the view to improving his foremanship, laborers, plant equipment, and the like. By comparing his cost re- ports with the different items of his estimate he may be able either to find leaks in his methods or mistakes in his estimating. The cost of keeping progress and cost reports is always justified by the results. Several of the best con- struction companies in America, through a careful system of progress and cost reporting, have materially improved their CHIMNEYS AND MISCELLANEOUS DATA. 401 working methods and their knowledge of the work itself, besides securing data of value for use in future estimates. When the manager, superintendent, foreman and men know that their work is closely watched and that not only are successive days' performances compared but that com- parison is made with similar work previously executed and the result shown to the credit or discredit of the persons in charge of the work, they are spurred to do their best. In addition padded pay rolls are practically done away with, and thefts of tools and materials are reduced to a minimum. Machines are all kept in better order, as a falling off in out- put is quickly discovered, and it is a fact that the contractor who has a reputation of having a good system of watching the cost of his work is more apt to be trusted with per- centage work or actual cost plus a fixed sum for his super- vision and the use of his plant. To the engineer in charge of the work such reporting is of incalculable value, and he will soon find in Gillette's words that "it is fatal to good en- gineering to copy a specification without weighing the dol- lars and cents effect of every word and phrase. He will see that there is more than strains and stresses in the design of a bridge and more than coefficients of friction in conduits and canals." The labor items in reinforced concrete of which costs are to be recorded generally are as follows: (1) Stone crushing. (2) Concrete mixing and spreading. (3) Making and placing reinforcement. (4) Making and placing forms, including removal of same. (5) Finishing. For each of these items the author prefers to use a card to be filled out daily in duplicate by using a carbon sheet, the original being sent to the office to be entered on the weekly report by a person kept in the office for this particular pur- pose, and the copy to remain at the job. The weekly report should be made in a form comparable with the estimate form and in such a shape that at any time the total cost of labor 402 REINFORCED CONCRETE. to date can be added up for each item. The daily report cards should be numbered and dated and show remarks re- ferring to such materials or other items as will be directly needed to prevent any stoppage or delay of the work so that the office is constantly kept informed as to proper delivery of material. A copy of all contracts with all conditions for delivery of tools or materials should be on hand at the con- struction office on the job so the superintendent may know exactly how to act without being compelled to await in- structions from the office in case he sees he will run short of material. All orders issued from the office or from the job should be in triplicate, one for the party furnishing mate- rials, one for the office or the job as the case may be, and one for file. It will be found convenient to make these re- port cards suitable for an index card file, hence of fairly stiff paper, the ones sent to the office being perforated and torn out of the book and those on the job to remain in the book. Sample cards as used by the author are shown herewith. Contract No. BLASTING. New York 19... No. of Bias No. of houi Remarks ts Foreman Engineer Firemen Derrick Lahore Coal. . . men ; .... rs . . . . .... Rockmen Drillers. . Repair; Sundrie ; ;S Total Pay rolls. Hauled to crushers Hauled to dump. Used in walls. Blasted cu. yds. Feet drilled. Average cost ru. yd. Cost hauling. Previous. . To-day Total Clerk Supt. CHIMNEYS AND MISCELLANEOUS DATA. 403 REINFORCED CONCRETE FORMS. ' Where workini j Foreman Carpenters Remarks. . . Laborers Lathers Sundries Sq. ft. slabs. Lin. ft. beams. Lin. ft. col's. Pay Feet Old New roll. B. M. stuff. material. Previous To-day Total Clerk Siint Contract No CRU SHING. New York 19. Teams to "A" Street Teams to "B" Street Remarks $ Foreman . . . $ Engineers Laborers .... . . Repairs Lumber Delivered to "A" St. Delivered to "B" St. Hauling. crushers. Pay roll Pay roll crushing. "A" St. "B" St. To-dav On hand Total Clerk . Supt. 404 Contract No. REINFORCED CONCRETE. MASONRY. New York ..19. Where working. Remarks. Foreman. Masons. . Laborers. Sundries. Pay rolls. Bbls. cement. Bbls. lime. Yards sand. Yards rock. Yards Masonry. Average cost per yard. Previous. . . To-day.. . . Total Clerk Supt. SAND. Contract No. New York, . ., .19. Remarks. Wagon loads received from Cubic yards received. Cubic yards used masonry. Cubic yards used brickwork. Cubic yards used concrete. ibic yards ed reinforced ncrete. o38 Today Total Clerk Supt. CHIMNEYS AND MISCELLANEOUS DATA. 405 CEMENT. Contract No. New York 19... Receivec I. Ba gs. 1 d . Remarks. Car numbers. No. bbls. d o S g* o -^ 5 X * 1 > c g C u a ^0 1 $ 1 rt 1 3 l^ t> To-day , Total - Clerk , Supt. NOTES ON ESTIMATING.* In estimating unit prices, too much reliance should not be placed on the published prices for similar work. Conditions vary greatly in places but a short distance apart; thus wages may be different, engineers may have entirely different in- terpretations of identical specifications, and bidding prices as published may be perfectly unbalanced, being too high on certain items with a view of getting the money out of the job at once, and too low on others. It must be remembered that a unit price that is fair for a large job is generally too low for a small job, and furthermore a contractor already equipped with a plant can often afford to bid lower than contractors who may be compelled to buy a new plant. For this reason each item should be estimated in detail and as a rule may be considered under the following heads: *Summarized from Gillette's "Handbook of Cost Data." 406 REINFORCED CONCRETE. (1) Plant expenses and supplies. (2) Materials. (3) Labor. (4) Superintendence and general expense. The plant expense includes interest and depreciation on all tools, machines, buildings, store materials, trestles, false work, and also cost of maintaining the plant during its operation, new parts, fuel, oil, etc. Materials include only such materials as actually go into the finished structure and the waste of materials due to breakage in handling or saw- ing and shaping. The cost of materials also includes the freight and the hauling to the site of the work. Labor in- cludes all skilled and common labor including foreman and time Leeper, but excluding superintendent and office expense. Superintendence and general expense include all general office expenses which are to be divided on all jobs, such as rents, taxes, telephones, traveling and entertaining expenses, stationery, etc. Plant Expense. In estimating the cost of a plant it must be based upon a time limit at least 20 per cent less than the one mentioned in the contract, in addition to liberal allow- ances for bad weather, delivery delays and break downs. Use with great caution the figures of output given in cata- logs; they are almost invariably based upon ideal conditions and frequently wholly deceptive. For example, while a derrick may be able to handle 200 cu. yds. a day, in a confined space its actual output may not exceed 30 cu. yds. Do not guess at anything; if you have no other data secure some estimates of output of a similar plant from large and old manufacturing firms and compare their statements. Having liberally estimated the size and kind of plant required, charge the full cost of the plant up to the job to be done and determine how many cents per CHIMNEYS AND MISCELLANEOUS DATA. 407 yard or other units involved, are thus chargeable to the first cost of plant. This will give a maximum charge, and it is well to know the worst; but if the full cost of a plant is charged to a small job some other contractor will probably get the work. Go therefore to a dealer in second-hand ma- chinery and ask him to name a fair price on a second-hand plant such as yours will be, when you are through with it. If you can secure a tentative bid on the machinery, you will have a fairly reliable estimate of its salvage value. A plant can also be rented at so much a day or a month, and for short jobs this is usually the best policy, inasmuch as it never pays a contractor to be encumbered with much ma- chinery, etc. Depreciation of a plant should include all the cost of housing and caring for the same, and be distributed over the average number of days that the plant is actually worked. Current repairs cannot always be separated from depre- ciation and it is well to consider the replacing of all parts that wear out rapidly as being current repairs. Of course depreciation is a variable item; thus a cable-way, for exam- ple, may last two years if it handles only 2S,000 skip-loads per year, but if 100,000 loads are handled in a year two cables will be worn out. In figuring cost of fuel for engines, it is customary to allow one-third of a ton of coal for each 10 H. P. per 10- hour shift. General expenses on contracts of $100,000 or more run about 2>}/2 per cent, and under $100,000 from 4 per cent up. The author has for many years used 3 per cent and found that it averaged just about right. Percentage to Allow for Profits. This is a question which has been much discussed. The percentage should depend upon the ratio between materials and labor employed and the duration of the contract, as well as its size. A percentage 408 REINFORCED CONCRETE. of 10 for material and 20 to 25 on labor, where the material is furnished by some one else, is fair and customary. In addition to the percentage for profit there should be added a small percentage, say 2 or 3 per cent, for contingencies. Accident Insurance. The following is taken from a lec- ture to the students of engineering of Columbia University by Mr. Gillette: "Never omit an allowance for accidents and other unfore- seen contingencies. Second, never neglect to insure the workmen. "A blanket policy covering all the men can be taken out. The premium is a given percentage of the pay roll. This in- surance does not give to each man a weekly stipend in case of accident or to his heirs a designated sum in case of death. But what the insurance company does do is to protect a con- tractor by assuming all liabilities from claims made by in- sured workmen or their heirs. The insurance company lim- its this liability, however, so that in case a number of men are killed by one accident the contractor may have to stand part of the damages. No matter how safe the work seems to be, a contractor should never neglect to take out a pay roll insurance policy. Many a contractor just starting in business has been ruined through failure to insure against accident." In making estimates of any structure the first step should be to make a list of all the items which possibly may come into consideration, and the engineer or contractor should look over this list for every estimate he makes and check off such items as they have been covered. Such list of items should also be prepared and completed from the speci- fications, every item in the specification being represented on the estimating sheet. A sample estimate is here added for the guidance of an engineer or contractor on similar work. CHIMNEYS AND MISCELLANEOUS DATA. 409 BLANK FORM FOR ESTIMATE OP BUILDING. Excavation. Wrecking. Blasting. Sheeting. Excavating. Piling. White oak piling. Mixed piling. Snubbing* piles. Concrete piles. Caissons. Lumber. Rings. Excavating. Dampproofing. Masonry. Plain concrete. Dimension stone. Rubble work. Granite. Carving. Lewising. Cartage. Setting. Cut Stone. Exterior marble. Carving. Lewising. Cartage. Setting. Blue Stone. Sills and lintels. Copings. Walks. Curbs. Cartage. Setting. Terra Cotta. Cartage. Setting. Brickwork. Common brick. Pressed brick. Glazed brick. Hollow brick. Plastering. Lathing. Suspended ceilings. Corner beads. Patching. Reinforced Concrete. Forms. Concrete. Reinforcement. Finishing. Cement floors. Marble. Mosaic and tile. Scagliola. Terrazzo. Concrete base for same, Fire Proofing. Hollow tile. Book tile. Iron fittings or rods. Patching. Structural Steel and Iron. Castings. Cartage. Setting. Inspection. Shop drawings. Painting. Chimney. Ornamental Iron. Stairways. Railings. Elevator enclosures. Bronze. Prismatic lights. Stair treads. Hardware. Nails. Screws. Bolts. Ladders and fire escapes. Straps. Gratings. Hinges. Plumbing. Gas fitting. Electric Wiring. Bells. Speaking tubes. Telephones. Watchman's clocks. Electric fixtures. Lamps. Pneumatic tubes. 410 REINFORCED CONCRETE. Mail Chute. Power Plant. Boilers. Boiler setting. Engines. Foundations. Dynamos. Switchboards, etc. Feed pump. Fire pump. Steam piping. Water intake. Water piping. Condenser. Hot well. Sprinkler System. Dust Collecting. Heating. Ventilating. Elevators. Passenger elevators. Freight elevators. Sidewalk lifts. Dumbwaiters. Signal device. Esculators. Drawn Metal Covered WorK. Metal frames. Tin doors. Shutters. Sheet Metal and Roofing. Corrugated iron covering. Flashings. Cornices. Gutters. Downpipes. Skylights. Roof covering. Carpentry. Rough carpentry. Finishing work. Closet work. Ml II work. Frames. Sash. Trim. Filling. Priming. Glass. Leaded glass. Screen prisms. Plate glass. Common glass. Glazing. Painting. Varnishing. Tinting. Paper hanging. General Expenses. Tools and tackles. Freight on same. Traveling expense. Liability insurance. Fire insurance. Storehouse and office sheds. Salvage. Depreciation. Office expenses. Inspection. Winding up. To these items are added in grain elevator construction; Sheet Iron Linings. Garners. Scales. Receiving hoppers. Shipping bins. Elevator heads. Spouting. Machinery. Power transmission complete. Scales. Steam shovels. Car pullers. Elevator legs. Cleaner legs. Belting. Erection of machinery. Elevator house castings. Elevator boot tanks. Conveyors. Framing for conveyors R. R. Track Doors. Portable Spouts. Scale Spouts. Stand Pipes. Hoods Over Loading Spouts. Painting Name. Lettering house inside. SPEC I PICA TIONS. 41 1 GENERAL SPECIFICATIONS FOR REINFORCED CONCRETE. In General. Special attention must be given to the quality of materials, labor and character of workmanship and these specifications are intended to include all that is considered best in theory and practice. Only persons or firms thoroughly experienced in this class of work will be considered as bidders. Bidders must submit drawings indicating their method of construction and calculation; the arrangement and nature of their steel reinforcement must be plainly stated and must have been approved by the building departments of such of the principal cities in the United States as have studied reinforced concrete and have embodied conditions for gov- erning its use in their building codes, such as New York, Brooklyn, Minneapolis, St. Louis, Philadelphia, Washington, Cleveland, San Francisco and Chicago. Dimensions of beams, columns, slabs and other parts of the construction indicated on the drawings shall be con- sidered a minimum. Samples of all materials must be submitted to the en- gineer for approval before being used and all rejected mate- rials must immediately be removed from the building, if re- quested by the engineer. No bids will be considered without submission to these conditions. In calculations beams and slabs continuous over their supports may be computed for a bending moment of ~-rx and slabs continuous over supports on four sides may be pr- computed for a bending moment -^ft- In all such cases sufficient reinforcement must be provided at the top of the slab to take care of all regular bending moments at the sup- ports. 412 REINFORCED CONCRETE. Particular attention must be given to the compression on under side of beams, where four beams or girders meet in a column. Cement. Standard specifications adopted by American Society for Testing Materials (see page 3) : The contractor shall notify the engineer as soon as each car of cement is placed, so samples may be taken therefrom without delay. The cement shall be stored in a suitable weatherproof building having the floor blocked up from the ground and in a manner easy of access, and proper inspection and identifi- cation of each carload. Fourteen days at least shall be allowed for inspection and tests. The name and brand of manufacturer shall be on each bag. Cement failing in the seven day requirement may be held awaiting the results of the 28 days' test before rejec- tion. Sand. Shall be coarse, sharp, clean, a combination of coarse and fine, approximately 3 parts of coarse to 1 part of fine as hereinafter described. All sand shall pass through a screen of 5 rneshes to the linear inch, approximately 75% of above shall be rejected by a screen of 12 meshes to the inch; the other quarter shall be fine sand. Salt water beach sand shall be washed, and any sand containing more than 3% loam or other impurities shall be rejected. Gravel or Stone. Gravel shall pass through a 2^-in. mesh and be rejected by a ^-in. mesh. If salt water gravel is used it shall be washed clean the day previous to incor- poration in the concrete. Stone shall be hard granite, trap rock or limestone, and crushed to pass a %-in ring, while re- jected on a J4~ m - ring. Proportion. The mixture shall be 1 volume of Portland cement as specified to 6 volumes of aggregates, whose re- spective quantities will give a maximum density. To determine the minimum volume differently propor- tioned mixtures shall be placed in a vessel (say a piece of SPECIFIC A TIONS. 413 wrought iron pipe 9 ins. diameter by 12 ins. high) and mixed and stirred with water until the proportion is found, which for the same combined weight gives the minimum volume. Mixing. Shall be done by batch mixer, the mixing being continued at least 3 minutes to each batch, resulting in a uniform, evenly tempered concrete. Enough water shall be added to result in a small quantity of free mortar appearing on top of the concrete under tamping. A competent fore- man or inspector must at all times be watching the mate- rial going into the mixer, as well as the concrete coming out. Placing Concrete. Concrete shall be placed as rapidly as possible after leaving the mixer and shall at once be thor- oughly puddled, spaded and tamped. Any concrete not placed after it is H hour old shall be thrown away. Concreting when started shall be vigorously carried on to completion. If concreting is stopped before an entire floor is completed the stop shall be made in the center of the beams and center of floor slabs. The plane where concrete work is stopped must be at right angles to the direction of the beam or slab. In no event shall work be terminated in beams or floor slabs where future shearing action becomes great, as at their ends or directly under a heavy concentrated load. Before work is resumed, the old work shall be thor- oughly sprinkled with water and pure cement strewn over the joint to be abutted. Wet all forms just before concreting. Reinforcement. Reinforcing steel shall be so arranged, designed and manufactured that it cannot be misplaced in the forms, and that it of itself maintains the proper distance from bottom and side of forms. It shall be calculated to provide for all horizontal and diagonal tension, vertical shear and compression where there is not sufficient concrete for the purpose. Concrete shall not be charged with more than 75 Ibs. per sq. in. for shearing stress. No steel shall be closer to the form than Y in. Steel rods shall have an elastic limit not to exceed 50,000 Ibs. Wire in fabric shall have an elastic limit of 80,000 Ibs. 414 REINFORCED CONCRETE. or more. No iron shall be painted. A slight film of rust is not objectionable, but no scale will be permitted. All rods shall have ends bent 1 in. up at 90. All steel shall bend cold 180 around its own diameter without cracking. All reinforcement shall be anchored to its surroundings, structural steel, brick work, or masonry, and if rods are spliced they shall overlap each other at least 40 diameters for steel rods and 50 diameters for wire. Expansion. Expansion and contraction from temperature changes or other causes shall be taken up by distributing rods in slabs and walls, preferably in the shape of a wire fabric of high tensile strength wire. Centering. All centering must be true, rigid and prop- erly braced, and able to carry the dead loads, including weight of construction considered as a liquid, without deflec- tion. Forms are to be bolted and all slab forms arranged to be given a camber, so as to leave the slab perfectly horizontal after setting. If the reinforced concrete rests on structural steel or part of the reinforcement consists of structural steel, the forms shall be suspended from said steel, so that the latter may obtain its deflection or initial stresses due to the dead loads while the concrete is setting. Removal of Forms. Centering must not be removed un- til the concrete has thoroughly set and not until permission has been obtained from the engineer. Beams shall remain supported for at least two weeks after all other false work has been removed. Columns shall not be given their full load in less than five weeks after concret- ing. Freezing Weather. Concrete shall be placed in freezing weather only when it cannot possibly be avoided. Precau- tion shall be taken to protect the finished work. Forms for such work shall be left in place at least three weeks longer than customary. Protecting Work. All floors shalf be covered with saw- dust and sprinkled for four days after concreting, and 'all SPECIFICATIONS. 415 work exposed to the weather shall be kept moist by sprink- lin'g or wet canvas for at least one week. Fireproofing Structural Steel. All structural steel shall be protected by 1:2^ mortar plastered on a wire fabric, such plastering being l l / 2 ins. thick. Cement Finish. Cement finish for floors shall not be leaner than 1:2, using in all cases a specially sharp, clean and gritty sand. It shall be troweled to a thoroughly smooth and even surface and be cut in squares not less than 8 ft. square. Cement finish when applied to a concrete base must be laid at the same time as the concrete and shall not be less than l /2 in. thick. Stresses. For hooped columns 750 Ibs. per sq. in. For latticed columns, 500 Ibs-. per sq. in. For shearing stresses in concrete, 75 Ibs. per sq. in. For shearing stresses in steel, 10,000 Ibs. per sq. in. For tension stresses in steel, l / 2 of the elastic limit. For tension stresses in wire, l /3 of the elastic limit. Extreme fiber stress in slabs, 800 Ibs. per sq. in. Extreme fiber stress in beams and girders, 750 Ibs. per sq. in. Ratio of moduli of elasticity of concrete and steel, 1 to 20. The tensile strength of concrete shall not be considered. Tests. Floors shall be tested one month after the cen- tering has been removed, to a uniformly distributed load equal to twice the safe live load. With this load there shall not be a deflection exceeding 1/400 of the span, and the floor shall return to its normal position after the removal of the load. Finally. At such time as the engineer directs and finally upon completion of the work the contractor shall remove all rubbish and surplus materials and repair such damage as may have been done to the work by other contractors in the course of ordinary building construction, and shall leave the premises in a neat, clean and perfect condition acceptable to the engineer. 416 REINFORCED CONCRETE. STANDARD SPECIFICATIONS FOR CEMENT OF THE AMERICAN SOCIETY FOR TEST- ING MATERIALS. (1) All cement shall be inspected. (2) Cement may be inspected either at the place of manu- facture or on the work. (3) In order to allow ample time for inspecting and test- ing, the cement should be stored in a suitable weather-tight building having the floor properly blocked or raised from the ground. (4) The cement shall be stored in such a manner as to permit easy access for proper inspection and identification of each shipment. (5) Every facility shall be provided by the contractor and a period of at least twelve days allowed for the inspection and necessary tests. (6) Cement shall be delivered in suitable packages with the brand and name of manufacturer plainly marked thereon. (7) A bag of cement shall contain 94 pounds of cement net. Each barrel of Portland cement shall contain 4 bags, and each barrel of natural cement shall contain 3 bags of the above net weight. (8) Cement failing to meet the seven-day requirements may be held awaiting the results of the twenty-eight day tests before rejection. (9) All tests shall be made in accordance with the methods proposed by the Committee on Uniform Tests of Cement of the American Society of Civil Engineers, pre- sented to the society January 21, 1903, and amended Janu- ary 20, 1904, with all subsequent amendments thereto. (10) The acceptance or rejection shall be based on the following requirements: (11) Natural Cement. Definition: This term shall be ap- plied to the finely pulverized product resulting from the cal- cination of an argillaceous limestone at a temperature only sufficient to drive off the carbonic acid gas. SPECIFICATIONS. 417 (12) The specific gravity of the cement thoroughly dried at 100 C. shall be not less than 2.8. (13) Fineness. It shall leave by weight a residue of not more than W% on the No. 100 and 30% on the No. 200 sieve. (14) Time of Setting. It shall develop initial set in not less than ten minutes and hard set in not less than thirty minutes, nor more than three hours. (15) Tensile Strength. The minimum requirements for tensile strength for briquettes 1 in. square in cross section shall be within the following limits, and shall show no retrogression in strength within the periods specified: (For example > the minimum requirement for the twenty- four hour neat cement test should be some value within the limits of 50 and 100 pounds, and so on for each period stated.) Age. Neat Cement. Strength. 24 hours in moist air ' 50-100 Ibs. 7 days (1 day in moist air, 6 days in water) 100-200 Ibs. 28 days (1 day in moist air, 27 days in water).. ..200-300 Ibs. One part cement, three parts standard sand 7 days (1 day in moist air, 6 days in water) 25-75 Ibs. 28 days (1 day in moist air, 27 days in water) 75-150 Ibs. (16) Constancy of Volume. Pats of neat cement about 3 ins. in diameter, ^ in. thick at center, tapering to a thin edge, shall be kept in moist air for a period of twenty-four hours. (a) A pat is then kept in air at normal temperature. (b) Another is kept in water maintained as near 70 F. as practicable. (17) These pats are observed at intervals for at least 28 days, and, to satisfactorily pass the tests, should remain firm and hard and show no signs of distortion, checking, cracking, or disintegrating. (18) Portland Cement. Definition: This term is applied to the finely pulverized product resulting from the calcina- tion to incipient fusion of an intimate mixture of properly proportioned argillaceous and calcareous materials, and to 418 REINFORCED CONCRETE. which no addition greater than 3% has been made subse- quent to calcination. (19) Specific Gravity. The specific gravity of the cement, thoroughly dried at 100 C, shall not be less than 3.10. (20) Fineness. It shall leave by weight a residue of not more than 8% on the No. 100 and not more than 25% on the No. 200 sieve. (21) Time of Setting. It shall develop initial set in not less than thirty minutes, but must develop hard set in not less than one hour, nor more than ten hours. (22) Tensile Strength. The minimum requirements for tensile strength for briquettes 1 in. square in section shall be within the following limits, and shall show no retrogression in strength within the periods specified. (For example, the minimum requirement for the twenty- four hour neat cement test should be some value within the limits of 150 and 200 pounds and so on for each period stated.) Age. Neat Cement. Strength. 24 hours in moist air 150-200 Ibs. 7 days (1 day in moist air, 6 days in water) 450-550 Ibs. 28 days (1 day in moist air, 27 days in water).. ..550-650 Ibs. One part cement, three parts sand 7 days (1 day in moist air, 6 days in water) 150-200 Ibs. 28 days (1 day in moist air, 27 days in water) 200-300 Ibs. (23) Constancy of Volume. Pats of neat cement about 3 ins. in diameter, H in. thick at center, and tapering to a thin edge shall be kept in moist air for a period of twenty- four hours. (a) A pat is then kept in air at normal temperature and observed at intervals for at least 28 days. (b) Another pat is kept in water maintained as near 70 F. as practicable, and observed at intervals for at least 28 days. (c) A third pat is exposed in any convenient way in an atmosphere of steam, above boiling water, in a loosely closed vessel for five hours. SPECIF 1C A TIONS. 419 (24) These pats, to satisfactorily pass the requirements, shall remain firm and hard and show no signs of distortion, checking, cracking or disintegrating. (25) Sulphuric Acid and Magnesia. The cement shall not contain more than 1.75 per cent of anhydrous sulphuric acid (SO 3 ), nor more than 4 per cent of magnesia (MgO). UNIFORM TESTS OF CEMENT. (Condensed from methods recommended by the committee on uniform tests of cement of the Am. Soc. of C. E.) Sampling. The sample shall be a fair average of the con- tents of the package; it is recommended that where condi- tions permit one barrel in every ten be sampled. All samples should be passed through a sieve having twenty meshes per linear inch, in order to break up lumps and remove foreign material; this is also a very effective method for mixing them together in order to obtain ,an average. For determining the characteristics of a shipment of cement the individual samples may be mixed and the average tested; where time will permit, however, it is recom- mended that they be tested separately. Cement in barrels should be sampled through a hole made in the center of the staves, midway between the heads or in the head by means of an auger or a sampling iron similar to that used by sugar inspectors. If in bags it should be taken from surface to center. Chemical Analysis. The method proposed by the com- mittee on Uniformity in the Analysis of Materials for the Portland Cement Industry, of New York Section of the Society for Chemical Industry, should be used as published in the journal of the society for January 15, 1902. Specific Gravity. The determination of specific gravity should be made with Le Chatelier's apparatus, and benzine (62 Baume naphtha) and kerosene free from water should be used in making the determination. The specific gravity is the weight of the cement divided by the displaced volume. Fineness. Fineness is determined on circular sieves about 7.87 ins. in diameter 2.36 ins. high and provided with a pan 420 REINFORCED CONCRETE. 1.97 ins. deep and a cover, and provided with a woven wire cloth from brass wire having the following diameters: No. 100, 0.0045 ins.; No. 200, 0.0024 ins. No. 100 should have 96 to 100 meshes to the linear inch. No. 200 should have 188 to 200 meshes to the linear inch. Normal Consistency. This is best determined by Vicat needle apparatus, a description of which may be found in any of the treatises of cement or reinforced concrete. Standard Sand. The Sandusky Portland Cement Com- pany of Ohio will furnish on application prepared sand from Ottawa, 111., at the price only sufficient to cover the actual cost of preparation. Form of briquette and molds to be for samples 1 in. square and 3 ins. long of the form illustrated in all text books. Mixing. Proportions by weight, the metric system, an average temperature of 21 C.,. dry sand, cement mixed on plate glass and hand kneading are required, and the molds should be filled at once, the material being pressed in firmly with the fingers and smoothed out with a trowel without ramming. Storage of the Test Pieces. Moist air for 24 hours and then immersed in water as near 21 C. as possible. Tensile Strength. Tests to be made on a standard ma- chine without cushioning the points and immediately after removing the test pieces from the water. Constancy of Volume. Pats to be 2.95 ins. in diameter, 0.49 in. thick in center and tapering to a thin edge are sub- mitted to a normal test and an accelerated test. The first, after immersion in water for 28 days, the other exposed in an atmosphere of steam. To pass these tests satisfactorily, the pats should remain firm and hard and show no signs of cracking, distortion or disintegration. Miscellaneous Information. To determine the quantity of materials required for a known mixture of concrete: Example. Materials required for 1,000 cu. yds. of 1-2-4 concrete: SPECIFIC A TIONS. 421 1 bbl. cement 3.8 cu. ft., sand 30 per cent voids, stone 45 per cent voids. 1 bbl. cement 3.8 cu. ft 3.80 cu. ft. 2 bbls. sand 7.6 cu. ft., 30 per cent voids 5.32 cu. ft. 4 bbls. stone 15.2 cu. ft, 45 per cent voids 8.36 cu. ft. Loose material 26.6 cu ft in place 17.48 cu. ft. 1 bbl. cement produces 17.48 cu. ft. concrete. GLOSSARY OF TERMS USED IN PLAIN AND REIN- FORCED CONCRETE. Accelerated Test. A test generally made to determine soundness of a cement, hastened by subjecting the test specimen to heat, sometimes dry heat, sometimes hot or boiling water. Such tests are determined by hours, while long time tests require days, months or even years. Activity. Relating to the rate of hardening of cement. Aggregate. The sand and gravel or crushed stone combined with cement in the formation of concrete. Armored Concrete. See Reinforced Concrete. Bag of Cement. Weighs 95 Ibs. or is equivalent to one- fourth of a barrel. Ball Mills. Circular drums used in cement manufacture, grinding clinkers or stone between circumference of the rotating drums and forged steel balls contained in same. Barrel cf Cement. Weighs 380 Ibs. net, contains four bags of cement. Batch. The definite quantity of concrete made at one mix- ing. Beton. The French term for concrete. Beton Arme. The French term for reinforced concrete. Blowing. Effect of air bubbles on finished surface, due to overwet mixtures not properly stirred or tamped. Bond, Mechanical. See Mechanical Bond. Bonding. The uniting of one layer or course of concrete with another. 422 REINFORCED CONCRETE. Briquet'te. A small brick of cement paste, mortar, or con- crete having a definite area at the smallest section and made for testing purposes. Bush-hammered. A method of dressing stone, applicable to concrete, produced by dressing with a hammer having large point-like teeth on the striking face. Carrying Rods. Term used to designate those rods which carry or sustain the load; they extend lengthwise in the reinforced member. Cement. A preparation of calcined clay and limestone or their equivalents possessing the property of hardening into a solid mass when moistened with water. Cement Mortar.- Mortar composed of cement, sand and water. Cement Sampler. A small tool used to take a sample of cement from a barrel, for testhig purposes. Centering. A wooden form giving shape to a concrete arch while setting. Centers. Same as Centering. Checks.- Same as hair cracks. Cinder Concrete. Concrete in which cinders are used as one of the aggregates. Concrete. A compact mass of broken stone, gravel or other suitable material mixed together with cement mortar and allowed to harden. Concrete Steel. See Reinforced Concrete. Construction Joint.' The seam between two successive days' work in concrete laying. Corrugated Bar. A form of reinforcing steel, made by press- ing the surface of a plain bar into a series of ridges or corrugations. Craze. Same as hair cracks generally the result of too rich a mixture occasionally a sign of unsound cement. Crusher Run. -Crushed stone taken directly from the crushei with none of the fine material screened out. GLOSSARY. 423 Distributing Rods. Term used to designate those rods which distribute the load over the carrying rods; they extend crosswise in the reinforced member. Dressing. The finish given to the surface of concrete. Dry Mix or Dry Mixture. A concrete mixed with so little water that very hard ramming is required to show moist- ure on the surface. Early Stage. The first part of the chemical action cement mortar undergoes after mixing, such as initial set and final set, both of which precede hardening. Efflorescence. A white discoloration appearing on the sur- face of concrete, due to the leaching out of soluble salts. Expanded Metal. A form of reinforcing material, made by cutting sheet steel in a series of short parallel rows, and drawing the sheet to form diamond-shaped meshes. Expansion Crack. Cracking in concrete work caused by ex- pansion. Expansion Joint. A vertical joint or opening between two masses of concrete to allow for variations due to changes of temperature. Fabric, Wire. See Wire Fabric. Facing. A rich mortar placed on exposed surfaces to pro- duce a smooth finish. Falsework. Wooden or other supports for holding concrete in position while setting. Ferro-cement. See Reinforced Concrete. Ferro-concrete. See Reinforced Concrete. Final Set. Is reached when a paste, mortar or concrete will support a pressure of the thumb without indenting an arbitrary period of setting of concrete just preceding hardening. Fineness of Cement. Is the degree of pulverization, and for either cement or sand is measured in terms of the num- bers of the two sieves between which it is held. Finishing. Working the concrete or mortar surface with steel trowels or similar tools, as for instance by brush, called brush finish. 424 REINFORCED CONCRETE. Fireproofing. Method of protecting structural parts that are subject to damage by fire, by covering them with a material that is not affected by high temperature, for instance reinforced concrete. Floating. Preparing the roughly spread mortar for the steel trowel by the use of a wooden or cork float. If this floating is used for a finish, it is called float-finish. Flush. To bring water to the surface of concrete by com- pacting or ramming. Forms. Wooden or other molds to give concrete the de- sired shape until hardened, Gaging. Determining the proportions of cement, sand, gravel or broken stone and water in concrete. Generally used in specifying the quantity of water that will produce a certain consistency. Granolithic. Concrete in which the stone aggregate is very finely crushed; its most general use being as a top sur- face for concrete walks. Grappiers Cement. A French cement made by grinding hard, under-burned nodules which have escaped disintegration in the manufacture of hydraulic limes. Gravel. Mixture of coarse rounded pebbles and sand, or pebbles without sand. Grout. A thin mortar composed of sand, cement and water; either poured or applied with a brush. Hair Cracks. Fine hair-like cracks on the surface of a ce- ment or concrete structure which has stood for some time. Hardening. Commences after the final set of a cement, mortar or concrete and continues for a number of years. High Carbon Steel. A steel in which the elastic limit is not less than 52,500 Ibs. per sq. inch. Hinge Joints. Joints which divide a structure into several sections, each one of which can expand independent of the others. Hooped Concrete. Concrete columns reinforced with wires wound spirally or placed in annular rings. GLOSSARY. 425 Hydrated Lime. Made by mixing quicklime and water; the chemical formula is CaO + H 2 O = CaOzH* Hydraulic Cement. Any cement which sets or hardens un- der water. Initial Set. Takes place when a mass of cement begins to solidify; is defined by the length of time required, vary- ing according to the kind of cement under test. Kahn Bar. A form of reinforcement named after the inven- tor, consisting of a special rolled section of steel with diagonal members sheared directly from the sides of the bar and bent upward. Kiln. A stationary or rotary furnace used in cement manu- facture. Laitance. Pulpy, gelatinous fluid washed from cement that is deposited in water. Lean Mixture. A concrete containing a relatively small proportion of cement. Limestone. An aggregate for concrete, consisting largely of CaO, CO 2 , and SiO 2 . Loam. Earth or vegetable mold composed largely or en- tirely of organic matter. Matrix. A term sometimes used for Mortar. Mechanical Bond. Increased adhesion due to deformations in reinforcing material. Mix. A shortened term for Mixture. Mixer. A machine for mechanically mixing concrete. Mixture or Mix. Refers either to the proportions of mate- rials composing concrete or to its consistency. Molds. Wooden or other forms used to hold concrete in the desired shape until hardened. Monolithic. Built in one solid, continuous piece. Mortar, Cement. A mixture of cement, sand and water. Very finely crushed stone may be used in place of the sand. Natural Cement. The finely pulverized product resulting from the calcination of an argillaceous limestone at a temperature only sufficient to drive off the carbonic acid gas. 426 REINFORCED CONCRETE. Neat Cement. Or cement paste, is cement mixed with water without the addition of any aggregate. Paste, Cement. A mixture of cement and water. Pat. A small quantity of neat cement spread upon glass for testing purposes. Pointing. Filling in joints or depressions on the face of concrete. Portland Cement. The finely pulverized product resulting from the calcination to incipient fusion of an intimate mixture of properly proportioned argillaceous and cal- careous materials and to which no addition greater than 3 per cent has been made subsequent to calcination. Puddling. The mechanical or hand stirring of wet concrete in the mold when too wet to be tamped or rammed. Pozzolan. Same as Puzzolan. Puzzolan. An intimate mixture made by grinding together granulated furnace slag and slaked lime without further calcination, possessing the hydraulic qualities of cement. Quaking Concrete. Concrete mixed with that proportion of water which will cause it to quake like jelly when heavily tamped. Quick Setting. Term applied to cement which takes an ini- tial set in a comparatively short time; is an arbitrary term. Ramming. Heavy compacting of concrete with a suitable tool. Regaging. Adding water to mortar which has become stiff and working same until plastic. Reinforced Concrete. Variously known as armored concrete, steel concrete, concrete steel, etc., is concrete in which is embedded steel in such form as to take up the tension and assist in resisting shear. Reinforcement. The iron or steel used in reinforced con- crete. Reinforcing. Applying the reinforcement also used in the same sense as reinforcement. GLOSSARY. 427 Rich Mixture. A concrete containing relatively a large pro- portion of cement. Roman Cement. The English term for natural cement Rosendale Cement. A natural cement from the Rosendale district in eastern New York. Rotary Kiln or Rotary. Used in cement manufacture see Kiln. Rubble Concrete. Concrete in which rubble stone are im- bedded. Sampler. See Cement Sampler. Sand. Aggregate of particles of gravel passing a No. 5 sieve (having openings .16 in. wide), the grains being 1/16 in. in diameter or under. Sand Cement. Same as Silica Cement. Scale. To flake off in thin layers. Screenings. A fine aggregate separated from crushed stone and used in the place of sand. Set. Solidification to such a degree that change of form will produce rupture. In cement, set begins when a Vicat needle 0.039 in. in diameter weighing 10.58 oz. penetrates only .20 in. into the mortar, and is complete when the needle will not penetrate at all. Approximately, when cement paste resists a light pressure of the finger nail. Shrinkage Cracks. Due to contraction of concrete on ac- count of temperature changes. Silica Cement. Clean sand and Portland cement ground together. Slag Cement. Another name for Puzzolan Cement. Sloppy Concrete. Concrete mixed with that proportion of water which prevents it from being piled up in the barrow. Slow Setting Cement. That which requires two hours or longer in setting. The term is arbitrary. Soundness. Refers to property of not expanding, contracting or checking in setting. 428 REINFORCED CONCRETE. Standard Sand. Recommended by the American Society for Testing Materials is the natural sand from Ottawa, Illi- nois, screened to pass a sieve having 20 meshes per linear inch and retained on a sieve having 30 meshes per linear inch; the wires to have diameters of 0.0165 and 0.0112 ins., respectively, i. e., half the width of the opening in each case. Sand having passed the No. 20 sieve shall be con- sidered standard when not more than 1 per cent passes a No. 30 sieve after one minute continuous sifting of a 500-gram sample. Steel-Concrete. See Reinforced Concrete. Tamp. To firmly compact concrete with a suitable tool. Test. An examination into the condition or quality of a cement, a concrete or its aggregates. Thacher Bar. A deformed bar used in reinforced concrete, named after its inventor. Top Surface. The exposed horizontal surface of cement or concrete work; usually applied to the finishing coat of sidewalks. Trap Reck. A heavy rock which when crushed forms an excellent aggregate for concrete. Trowel. A steel tool used in finishing a cement or concrete surface; also the act of using said tool. Tube Mill. A rotary mill or furnace used in the manufac- ture of cement in conjunction with ball mills. Twisted Steel. Reinforcing material made by twisting square steel bars. Underburned Cement. A cement burned at too low tempera- ture; the clinker of such cement is lacking in density. Vassy Cement. The product obtained by heating limestone containing much clay at the lowest temperature that will decarbonate the lime; it sets very rapidly but hardens very slowly. Vicat Needle. An apparatus containing a needle named after its inventor, used in testing cement pats. GLOSSARY. 429 Voids. The spaces between the particles of sand, gravel, crushed stone or other aggregate. Wearing Surface. Finished surface exposed to wear. Wet Mix or Wet Mixture. Concrete mixed with enough water so that little or no ramming is needed. Wire Fabric. A reinforcing material composed of wires crossing at right angles and secured at the intersections. 430 REINFORCED CONCRETE. USEFUL INFORMATION. WEIGHT OF STEEL BRIDGES. 1. Weight of steel in single-track, I-beam span, no ballast. ZF=3.5 Z, 2 +352+1215. 2. Single-track deck plate girder span, no ballast, W=9.5 2 +200+450 (less than 70 feet), JF=28 2 +2280Z: +83400 (more than 70 feet). 3. Single-track through plate girder span, no ballast, W=1S24L 26160 (less than 76 feet), W= 75Z, 2 2927^+433740 (more than 76 feet). 4. Single-track through pin span, no ballast, W= 7.9Z, 2 +870Z, + 1 1500. 5. Double-track through plate girder span (2 light and 1 heavy girders) (no ballast floor), fF=4Z, 2 +2980Z 44000 (30-80 feet span), JF=68 2 +352800 (80-100 feet span). 6. Double-track through pin span (2 light and 1 heavy girders) (no ballast floor), RAPID SOLUTION OF QUADRATIC AND CUBIC EQUATIONS, BY SUBSTITUTION 1. Quadratic Eq: Ex: 3jtr 2 +18 x = 48 6 x = 16 p = 6, q = 16 2. Cubic Eq: f + py-g USEFUL INFORMATION. If the equation is we make 431 -\- nx x = y - and have (3) Here and n ~ is the p of eq. (1) m ( 2m* \ r g- ^ 9~ - I is the q of eq. ( hereby we find y, and from eq. (3) we find x. (Engineering and Contracting, Jan. 11, 1911.) TABLE LXXXIV. LIFE OF PLANT m YEARS. Rate of Interest of Installments, Per Cent. Depreciation of Plant. 3% 4% 5% 6% 8% 1 46.90 41.04 36.73 33.40 28.55 2 31.00 28.01 25.68 23.79 20.91 3 23.45 21.50 20.10 18.85 16.88 4 18.93 17.62 16.62 15.73 14.28 5 15.90 14.99 14.21 13.53 12.42 6 13.72 13.02 12.42 11.90 11.01 7 12.05 11.52 11.04 10.62 9.90 8 10.77 10.34 9.95 9.60 9.01 9 9.72 9.37 9.05 8.76 8.26 10 8.88 8.58 8.31 8.07 7.64 11 8.16 7.91 7.68 7.47 7.10 12 7 06 13 6.60 14 6 30 15 5.85 16 5 55 17 5 33 18 5.04 19 4 91 20 4.56 432 REINFORCED CONCRETE. AMORTIZATION. R y=annual installment of interest N r> I p 18" ~ N= number of years Z=fo of depreciation TABLE LXXXV. log Life of Plant, Years. 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Annual Installments. Rate of Interest of Installments, Per Cent. 3% 4% 5% 6% 8% $ .1810 .1465 .1230 .1050 .0907 .0795 .07039 .06283 .06646 .05103 .04634 .04227 .03870 .03555 .03275 .03024 $''06903 .06008 .05269 .04652 .04130 .03683 .03298 .0?963 .02670 .02413 .02185 $ .08723 .07808 .07046 .06403 .05853 .05376 .04961 .04595 .04271 .03891 .03722 $ .08330 .07416 .06656 .06015 .05467 .04994 .04582 .04220 .03899 .03614 .03058 $ .07587 .06679 .05928 .05296 .04759 .04296 .02895 .03544 .03236 .02962 .02718 INDEX. Page Accident insurance 408 Adhesion, concrete to forms.. 197 concrete to steel 76 Aggregates, choice of. 5 cinders 13 crushed stone 11 graded, voids in 13 gravel 10 kinds of 4 slag 14 voids in, determination of. 5 graded 13 tables of 6 Angles, properties of 58 Arch bridge, Grand River, Grand Rapids, Mich.... 28 9 Santa Monica Viaduct, Cal- ifornia 292 Arch centers, construction of. 28 6 examples of 287 Grand River bridge 292 Pollasky bridge 287 removing, time and meth- ods of 289 Santa Monica viaduct 293 Arch construction, centers. . .286 classification of arches. . . .286 concreting arch ring 288 Arch design, assumptions. . . .275 constructing arch ring 275 dead load diagram 277 elastic theory simplified. . .252 example of, by elastic theory 275 live load diagram 279 maximum fiber stresses. . .281 Area, of circles 64 of round rods 31 of steel reinforcement. . .33-35 Beams, bending moments for. 69 calculation, numerical ex- ample 168 designing, table for 140 formulas for ultimate strength of 140 Pittsburgh Steel Products Go's 51 reinforcement for, Colgnet.126 Coularou 126 frame systems 127 Hennebique 125 Locher 126 loose rod 125 Page Beams (Continued). safe load and steel area tables 127 stirrups, location of... 74, 170 tests of tee-beams 77 Bending moments', beams... 69 slabs 120 maximum in 120 table for 71 Bins, grain flowing from.... 3 70 bridging action of grain in.370 capacity of 379 cement storage, Illinois Steel Co 382 design of 370 diagram of wheat pressure in 373 friction of grain on con- crete 375 lateral and vertical pres- sures, ratio between. .. .375 pressure of coal in .'376 pressure of grain in, Ketch- urn's conclusions 380 tables of 370 ratio of grain to liquid pressure 372 vertical pressure in 374 Bridges', arch, classification of 246 classification, by loadings. 211 general 211 design and construction of. 211 diagrams for loadings. 212, 213 flat slab, detailed designs of 216-221 flat slab and girder, gen- eral discussion 211 formulas for arches. .246-251 girder, detailed design of 221-229 designs complete for spans of 20 to 40 ft, tables for 238-240 standard designs, table loadings, class 1 233 class 2 234 class 3 235 Impact, diagram illustrat- ing 215 live loads, data for weights and dimensions of elec- tric cars 216 433 434 INDEX. Page Bridges (Continued) distribution of 214 method of finding wheel loads on roadway, dia- gram illustrating 214 on track 215 Building construction, clear- ing the site. ... . 183 concreting columns 186 in freezing weather 189 walls 187 delivering concrete. ...... .186 depositing concrete 186 eliminating forms in 201 finishing concrete surfaces.204 forms and falsework 189 kind of lumber 190 making the concrete 185 ordering materials 184 placing reinforcement 184 safe loads for spruce or pine beams, table 190 safe loads for wooden pil- lars, table 191 separately molded members for 200 sequence of operations. .. .183 small tools for 202 Building design, adhesion of concrete to steel 76 assumptions made in.. 67, 167 beams . .168 beams and girders 125 beams, bending moments.. 69 bracket connections 165 columns 144 dead loads, assumptions for 68 elasticity, modulus of 77 example of warehouse. .. .167 floors 94 foundations 78 live loads, assumptions for. 69 percentage of reinforce- ment 68 roofs 160 slabs, bending moments for. 71 stairs . 160 steel or cast iron columns. 161 stirrups, location of, in beams 74 stresses, allowable in con- crete 69 Cement, barrel of, volume... 2 weight 2 color of 4 fineness 3 magnesia in, allowable. ... 3 packages for shipment.... 1 Portland, definition of 1 ) Page Cement (Continued). setting, thumb nail test for 4 time of 3 specifications for 2, 416 specific gravity 3 storage, requirements for. . 2 strength, tensile 3 sulphuric aid in, allowable 3 testing, necessity of 3 samples, method of tak- ing 4 test requirements for 3 volume, constancy of 3 Channels, properties of 56 Chimneys, calculation of.... 390 approximate method. .. .392 core theory 391 design of, summary of points in 395 horse power of 327 forms, construction of. ...398 steel concrete 396 Wiederholt construction. . .398 wind pressure and velocity.392 Cinders, choice and use of . . 13 Circles, areas and circumfer- ences of 64 Columns, calculation of, nu- merical example 172 cast iron 161 classification of 147 concreting, method of 186 crushing strength, Kim- ball's tests, table 145 diagram showing average unit stress, Lindau 146 Talbot's tests, table 145 Euler's formula for 159 full-sized specimens, tests 146 hooped, calculation of 149 Considered formula for. 156 forms of r . . . 149 tables for designing 150 rectangular, calculation . . .147 forms of 147 spiral, Talbot's tests of... 158 structural steel 161 table for wire spirals. .. .156 Concrete, adhesion of, to forms 197 to steel 76 consistency, proper 24 definition of 17 depositing in building con- struction 186 finishes for, see Concrete finishes. hair cracks in, eliminating.205 joining new to old 188 INDEX. 435 Page Concrete (Continued). mixing, hand or machine. . 24 requirements of 21 mixtures, plain concrete. . . 22 reinforced concrete 22 wet vs. dry 21 proportioning, Fuller's rule for 20 maximum density 20 strength 18 methods of 17 Thacher's tables for 19 proportions for different classes of work 21 protection from freezing. . .189 while setting 188 sand for, best 8 small tools for 202 specifications for 411 stresses in, allowable 69 transporting in building construction 186 Concrete carts 203 Concrete finishes, dry mix- tures for 206 mortar facing 205 painting and varnishing. .207 plastering 207 scrubbed and acid work. ..206 tooling 207 types of 205 Concrete mixers, batch, clas- sification of 24 sizes and capacities 26 batch or continuous 24 continuous, classification of 27 sizes and capacities 28 gravity, Hains 28 Concrete, reinforced, defini- tion of 1 names for, various' 1 Conduits, calculations, char- acter of 335 cast pipe, stresses, concen- trated load 339 distributed vertical load 340 Talbot's tests 339 tests on, summary of... 342 thickness and weight of. 338 external pressure, calcu- lation for 336 flow of water in circular. .334 internal pressure, calcula- tion for . .335 Myer's formula 336 Rankine's rule 337 sewer, grades in 335 reinforcement for 337 Page Conduits (Continued). soil, resistance to erosion by water 332 Talbot's formula 337 velocity of water in, Che- zy's formula for 333 Kutter's formula for. . . .333 water, erosive and trans- porting power of 332 Connections, examples of. . . .165 Corrugated bars, weight and area 38 Cost keeping, methods of . . . .400 Costs, conc_ete culverts 324 tanks 361 timber and concrete grain elevators 382 timber and concrete piles. 84 Crus-hed stone, choice of. ... 11 crusher run 12 size of 11 voids in, table of 14 Culvert and sewer pipe, table thickness and weight of reinforcement for 339 Culverts, arch, design of.... 320 Great Northern Ry 329 Kalamazoo, Mich 328 standard, C., B. & Q. Ry. .327 Culverts, box, assumptions for .320 covers, design of 320 diagram for design of.. 3 21 sides, design of 323 diagram for design of.. 323 standard, C., B. & Q. Ry.. .331 Culverts 1 , cost of 324 Dams, classification of 347 construction, types of 352 curtain type 355 half apron type 355 open front type 354 pressures on immersed surface 350 stresses in, comparison of gravity and pressure dams 1 347 Decimals, feet, inches and fractions 64 Designing methods, Lindau, tables for beams and slabs 141, 142, 143 Elastic theory of arches. ... 252 critical condition of loading for given section 260 line of pressure for 256 from dead load 256 436 INDEX. Page Elastic Theory (Continued), reactions from concentrat- ed load 253 successive steps in arch de- sign 256 thermal stresses 274 thickness of arch ring 267 Elasticity, modulus of 77 Estimating, suggestions for. 405 Finishes for concrete, see Concrete finishes. Floors, arch, forms of 101 Monier 101 Roebling 101 Wuensch 101 beam and tile 100 beam, forms of 99 classification of 95 Heidenreich flat slab sys- tem 106 loads', specified 94 manufactured, Siegwart. . . 102 Visintini 102 "mushroom" system 103 safety, factor of 95 slab, calculation of 106 Columbian 96 Cottancin 97 expanded metal 96 forms of 97 Matrai 95 Monier 96 Roebling 97 umbrella flat slab system. 104 Forms, adhesion of concrete.197 alignment of 196 chimneys 398 column*, example of 199 combined steel and con- crete construction 199 design of 193 fastening, methods of 194 grain elevator 388 joints in 194 lagging, thickness of 196 lumber for, kinds of 190 railing for bridge 291 removing, time for 197 removing 312 setting 310 rotation in use of 196 studs, for spacing of 196 tank 368 Formulas, Cain's, for retain- ing walls 297 beams reinforced for com- pression 113 Chezy's, for flow of water.333 columns . . .115 Page Formulas (Continued). Considered for hooped col- umns 149 Euler's, for columns 159 for beams 70, 71 ultimate strength of 104 for deflection 194 for hooped columns 149 for parabola 275 for strength of mortar. ... 15 for wind pressure 79 Johnson's, for temperature cracks 299 Kutter's, for velocity of water 333 parabolic line 118 Rankine's, for retaining walls 297 rectangular beams 108 shear bond and arch rein- forcement 114 straight line 108 rectangular beams Ill tee beams Ill Foundations, concrete pile, see Piles, concrete, concrete pile, types of. ... 79 loads on 79 mat 92 portable 92 raft, calculation of, numer- ical example 172 for warehouse 90 slab, kinds of 83 types of, for buildings 78 Girders, see Beams. Glossary of terms used 421 Grain, action of, in flowing from bins 370 bridging action of 370 pressures, table of 370 Grain elevators, Canadian Pacific, Port Arthur, Ont.386 classification of 381 forms for Port Arthur, Ont., elevator 388 Heidenreich 389 timber and concrete, com- parative cost 382 Gravel, characteristics of. ... 10 Hair cracks, eliminating, methods of 205 Hinges, parabolic arch with two . ..248 I-beams, properties of.... 56, 57 Inertia, moment of, for vari- ous sections 66 INDEX. 437 Page Inspection, necessity of 399 Leaks, stopping leaky floors.209 Loads, dead, assumed in building design 68 floor, specified 94 live, assumed in building design 69 Oakum, for waterproofing. . .209 Manufactured articles 399 Measuring box 203 Mixers (see Concrete mixers). Modulus of elasticity 77 of sections 66 Moment of inertia of sections 66 Mortar, definition of 15 retempered 16 sand for, best 7 strength of, conditions gov- erning 15 tests, of, value of 16 volume of, with varying proportions of sand 16 weight of 16 Oakum, for waterproofing. . . 209 Painting concrete 207 Piles, concrete, Chenoweth. . 88 corrugated 87 cost of, compared with wood 84 driving, methods of 88 Pedestal 87 Raymond 80 Simplex 85 types of 79 unpatented forms 88 Plastering concrete 207 Profits, percentage to allow for 407 Protection of steel in con- crete 209 by Tockolith 209 Rammers, cast iron 203 wood 204 Reinforcement, against shear 73 American hooped column... 54 American wire fabric 46 angles, properties of 58 channels, properties of . .56, 57 Coignet for beams 126 Colling's corrugated bars, tests of 40, 41 Columbian for floors 96 column J 1 f> compression 113 corrugated bars, weights and areas of 37 Page Reinforcement (Continued), table of spacing for given area 124 Cottancin for floors 97 Coularou for beams 126 Cummings girder frame... 50 Cummings hooped column. 53 cup bars, weights and sizes of 40 diamond bars, weights and areas of 38 expanded metal 48 flats, areas of 33, 34 weights of 33, 34 frame sy stems for beams. 127 Heidenreich flat slab sys- tem, floor and column.. 106 Hennebique, for beams. . . .125 hooped column 53 I-beams, properties of.. 56, 57 Kahn rib metal 48 Kahn trussed bar. . . 51 Locher for beams 126 lock woven fabric 46 loose rods for 35 Luten truss.. 53 Matrai, for floors 97 mechanical bond 32 Monier, for floors 96 "Mushroom" system 103 percentage of 31, 68 placing, in building con- struction 184 rods, areas of square and round 31 weights of square and round 31 Roebling for floors 97 round rods for 35 spacing for given area.. 123 weight for given spacing. 123 sections, properties of vari- ous 66 Smith hooped column 54 square bars, table, areas of 124 square rods for 35 steel, adhesion of concrete to 76 high vs. low carbon 39 medium 30 strength of 29 steel woven wire, triangle mesh 43 structural steel 55 styles of 33 T-beams 115 Thacher bars, weights and areas 39 triangle mesh, tables of.44, 45 438 INDEX. Page Reinforcement (Continued), twisted bars, weights and areas 35 "umbrella" flat slab sys- tem, floor and column.. 10 4 "Unit" frame 51 units beam and girder.... 50 welded wire fabric 47 wire, standard gages 42 Xpantrus bar 51 Reservoirs 1 , see Tanks. Retaining wall design, ma- sonry, example of 300 reinforced concrete beam type, example of 303 Retaining walls, backfilling. 299 Cain's formulas 298 expansion joints 299, 312 Great Northern Ry 314 masonry, crushing of, sta- bility against 302 overturning, stability against 301 resultant pressure, calcu- lation of 301 sliding, stability against. 3 01 Paris' Exposition, 1900 313 Retaining Walls (Continued), pressures on, Cain's theory.297 Coulomb's theory 297 Rankine's theory 296 Trautwine's theory 297 Weyrauch's theory 296 Rankine's formulas for 297 reinforced concrete, beam type, foundation 304 vertical beam 303 with counterforts 309 foundations 310 pressure, calculation of.307 vertical slab 308 specifications for 317 temperature cracks. 299 thrust 299 R. I. W. for putty 180 for waterproofing 180 Rock crushers, capacity of . . 12 gyratory, sizes and capac- ity 13 Round rods, table of spacing for given area 123 table of weights for given spacing 123 Roofs, forms of 160 Sand (see also Screenings). Sand, cleanness, requirements for 8 concrete, best for 8 definition of 6 Page Sand (Continued). mortar, best for 7 selection of 6 standard, definition of 10 voids in, conditions govern- ing 9 table of 9 theory of 9 washing, method of 8 weight of 10 Santa Monica viaduct 292 for putty 180 Screenings', characteristics re- quired 10 Section modulus 66 Sections, properties of 66 Sewers, see Conduits. Shearing provisions 73 Slabs, bending moments for. 70 maximum 120 calculation, notation used. 106 parabolic line formula.. 118 straight line formula. . .108 designing, table for. . .142, 143 thickness and reinforce- ment, table showing.. 122 Slag, aeration of 14 Soils, bearing power of 79 Specifications, Portland ce- ment 417 reinforced concrete con- struction 411 retaining wall construction. 3 17 Square bars, table areas of. 124 Stairs, kinds of, construction. 160 Stirrups', location of, in beams 74, 69 Stresses, allowable In con- crete 170 Tanks, American Steel & Wire Co 368 calculation of 358 capacity, table of 359 cost of 361 foundations for 358 general discussion 357 intake, forms for 368 Montgomery Ward & Co. .361 shapes of 357 tightness of 360 Tee-beams, design of, table for 116, 117, 118 tests of 77 Tie for wall forms 312 Timber, strength of 191 Tockolith 209 Tooling concrete 207 Tools 1 , small for concrete work . . . 202 INDEX. 439 Toxement Page . .210 Useful information 430 quadratic and cubic equa- tions, rapid solution of.. 430 plant, life of in years.... 430 amortization 430 Voids, in graded mixtures. . . 13 in loose broken stone 13 in sand 9 table of 5 Walls, concreting, methods of 187 Water, erosive and trans- porting power 332 Page Waterproofing, directions for. 2 07 cracked walks or joints... 209 necessity of 208 protection of steel in con- crete 209 toxement 210 Weight of brick walls per superficial foot 95 Weights of various sub- stances stored in ware- houses 94 Wheelbarrows 203 Wind pressures, table of 393 Wire gage, area of wire for 1 ft. in width 42 Xpantrus bar 61 UNIVERSITY OF CALIFORNIA LIBRARY THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW KB 6 1919 FEB 18 1924 30m-l,'15 O <*\*^ST .YB 51929 314622 ^^OJLxvxO UNIVERSITY OF CALIFORNIA LIBRARY