WIND STRESSES 
 
 [FLEMING] 
 
Six Jyfono&ra pAr on 
 
 ~./- , v' / 
 
 Wind 
 
 WIND PRESSURE FACTORS 
 SPECIFICATION REQUIREMENTS 
 MILL-BUILDING STRESSES 
 RIGID JOINT WIND BRACING 
 FOR OFFICE BUILDINGS 
 
 BY ROBINS FLEMING 
 Engineer, American Bridge Company , New York 
 
 REVISED AND ENLARGED REPRINTS FROM 
 ENGINEERING NEWS 
 
 ENGINEERING NEWS 
 
 HILL BUILDING, NEW YORK 
 
 1915 
 
Copyright, 1915, 
 
 by 
 Hill Publishing Co. 
 
PREFACE 
 
 Wind is everywhere. It affects all structures. Every 
 engineer, or even every person who ever sees an engineer, 
 has a personal interest in the effect of wind on structures. 
 That is the subject of the present book. 
 
 Ignorance is not always bliss. If it be true as seems 
 very likely that wind is preeminently a matter concern- 
 ing which no one knows he knows not, then this book 
 deserves to have many readers. 
 
 There is a fresh touch to what the author says. His 
 main argument throughout is common sense. In this 
 respect his frame of mind is catching; the reader will 
 find himself saner and sounder for having read the book. 
 When the author refers to intricate studies of wind 
 action, claimed to show the need for radical changes 
 in building practice, he leads us to notice the practical 
 fact that these intricate studies are based on tests made 
 in mild breezes, and can hardly be safe guides as to 
 what happens in storms. 
 
 Six articles which appeared in ENGINEERING NEWS, 
 most of them in the early months of 1915, make up 
 this book. One of the six, however No. 6 is so 
 changed from the form in which it was printed March 
 13, 1913, that it is new. And this subject, the stress 
 calculation for tier-building frames without diagonals, is 
 so far without any literature. 
 
 The many slow hours of work which the author con- 
 sumed in searching out and studying the material re- 
 quired for writing this book merit the reader's apprecia- 
 tion. 
 
 EDITOE Engineering News. 
 
 382055 
 
CONTENTS 
 
 Page 
 
 I Wind Pressure Formulas and Their Experi- 
 mental Basis 
 
 II Wind Stresses in Steel Mill Buildings . . 13 
 
 III Wind Stresses in Eailroad Bridges ^7 
 
 IV Wind Stresses in Highway Bridges . . . 
 
 V Windbracing Kequirements in Municipal 
 
 Building Codes 53 
 
 VI Windbracing without Diagonals for Steel- 
 Frame Office Buildings 61 
 
Wind Pressure Formulas and 
 Their Experimental Basis 
 
 SYNOPSIS A discussion of the current formu- 
 las for relation between wind pressure and velocity, 
 relation between pressure on normal planes and 
 planes inclined to the wind, and several other 
 phases of wind pressure. The author brings out 
 strikingly how inadequate is the experimental basis 
 for the formulas and figures commonly employed. 
 
 The purpose of this article is to give the basis from 
 which some of the commonly used formulas for wind 
 pressure are derived. Even the engineer who wishes to 
 know only the wind pressure in pounds per square foot 
 for which he shall make provision in his structure will be 
 better equipped for designing if he is acquainted with the 
 foundations on which ordinary practice rests. 
 
 KELATION BETWEEN WIND PBESSUBE AND VELOCITY 
 
 In view of the extent of the literature on the subject it 
 might reasonably be supposed that the elementary prin- 
 ciples of wind pressure are determined, at least theoretic- 
 ally. How near this is to being the case may be inferred 
 from the following extracts taken from two modern 
 American textbooks, each of which is regarded as an 
 authority. Marburg, in his Framed Structures and 
 Girders, under ''Wind Pressure," writes: 
 
 Theoretically the pressure p, in Ib. per sq.ft., on a plane 
 surface normal to the direction of flow of a fluid having a 
 relative velocity v, in ft. per sec., is equal to the weight of 
 a vertical column of the fluid having a cross-section of 1 
 sq.ft. and a height h, in ft. equal to that through which a 
 freely moving body must fall to acquire the velocity v. If 
 w denotes the weight of the fluid, in Ib. per cu.ft., 
 
 wv 2 
 
 p = Wh = _ (1, 
 
 For air at a temperature of 32 F. and at a barometric 
 pressure of 760 mm., w = 0.081. Letting g = 32.2, 
 
 p = 0.00126 v (2) 
 
 [i] 
 
If V denotes the velocity of the wind in miles per hour, 
 v =. 1.47 V, whence equation (2) becomes 
 
 p 0.0027V 2 (3) 
 
 Burr and Falk, in The Design and Construction of 
 Metallic Bridges, under "Stresses due to Wind" write: 
 
 If the wind were directed as a finite stream against an 
 infinitely large surface, so that the direction of the air is 
 completely changed, an equation expressing the force against 
 that surface may be obtained from the laws of mechanics. 
 Let 
 
 W == the weight of air directed against any normal 
 
 surface in a given time; 
 
 w = the weight in pounds of one cubic foot of air; 
 v = the velocity of wind in feet per second; 
 a == the area of cross-section of the wind stream, 
 
 Then W = wav. 
 Let 
 
 M = the mass of air of the weight W; 
 g = the acceleration due to gravity = 32.2 feet per 
 
 second; 
 P = the force acting on the area a, 
 
 Wv wav a 
 
 Then F = Mv = = (1) 
 
 g g 
 
 If a be taken at 1 sq.ft., and w at 0.0807 Ib. per cu.ft. for 
 a temperature of 32 F. and a barometric pressure of 760 
 mm., and if v be replaced by V, the velocity in miles per 
 hour, then 
 
 P = 0.0054 V 2 (2) 
 
 The reader will observe that starting with the same as- 
 sumptions one author finds the resultant pressure to be 
 twice that of the other. Both authors make haste to write 
 that the theoretical conditions upon which their formula 
 is* based do not exist. A cushion of air is formed in front 
 of the plate and a partial vacuum at the back ; there is a 
 certain amount of air friction and the change of direction 
 is not complete. The student facing such conflicting 
 theories on the very fundamentals of wind pressure may 
 well raise the question of authority. 
 
 It is almost impossible to give undue credit to Sir Isaac 
 Newton for his work in the realms of science and mathe- 
 matics. His great book was the Philosophia Naturalis 
 Principia Mathematica, or "The Mathematical Principles 
 of Natural Philosophy," commonly called the Principia. 
 Originally published in 1686, revised editions were is- 
 sued in 1713 and 1726. Modern hydrodynamics had its 
 
 [2] 
 
origin in the second book, treating of Motion of Bodies in 
 Resisting Mediums. Section VIII of this book is entitled 
 ''Of Motion Propagated through Fluids." A translation 
 of Prop. XLVIII (Newton wrote in Latin) reads: 
 
 The velocities of pulses propagated in an elastic fluid are 
 in a ratio compounded of the subduplicate ratio of the elastic 
 force directly, and the subduplicate ratio of the density in- 
 versely; supposing- the elastic force of the fluid to be pro- 
 portional to its condensation. 
 
 This means that the velocity v varies as -7, or p varies 
 
 V a 
 
 as dv 2 . For wind pressure, the density of the air being 
 constant, we have the law that the pressure varies di- 
 rectly as the square of the velocity, which has remained 
 almost undisputed since Newton's day. 
 
 Furthermore, according to Newton, for an area of 
 
 v 2 
 unity, p = dh, in which h = ^ is the distance through 
 
 which a heavy body must fall to acquire the velocity v, 
 g being the coefficient of gravity or 32.2. This may be 
 called the Newtonian theory, and has been followed by 
 a host of writers, including Marburg (quoted above). 
 
 W. J. M. Rankine was one of the master mathema- 
 ticians of the nineteenth century. In his fifteenth year 
 his uncle presented him with a copy of Newton's Prin- 
 cipia, which he read carefully. He remarks, "This was 
 the foundation of my knowledge of the higher mathe- 
 matics, dynamics and physics." But the pupil did not 
 blindly follow the master. In his Applied Mechanics, 
 he has a section devoted to "Mutual Impulse of Fluids 
 and Solids." A jet of fluid A, striking a smooth sur- 
 face, is deflected so as to glide along the surface in that 
 path which makes the smallest angle with its original di- 
 rection of motion. Let v be the velocity of the particle 
 of fluid, q the volume discharged per second equal to Av, 
 d the density, and the angle by which the direction of 
 
 motion is deflected; then is the momentum of the 
 
 y 
 
 quantity of fluid whose motion is deflected per second. 
 With these notations the general equation for the force 
 
 [3] 
 
Fx perpendicular to the plane in question is found to be 
 
 For the particular case of the plane at right angles to the 
 jet or B = 90, 
 
 9 9 
 
 This may be called the impact theory, and is followed in 
 some textbooks, including that of Burr and Falk. 
 
 From the time of Newton until this day a long line of 
 investigators have sought by experiment to obtain the 
 value of Tc in the formula P = kV 2 f in which P = pres- 
 sure in Ib. per sq.ft. and V = velocity in miles per hour. 
 As before noted, according to the Newton formula Ic is 
 0.0027 and with the same assumptions according to Ran- 
 kine Tc is 0.0054. What is known as the Smeaton for- 
 mula held almost universal sway for 150 years and is still 
 in use. It is very simple, P = 1 / 200 V 2 . In the Philoso- 
 phical Transactions of the Royal Society, England, for 
 the year 1759 is a lengthy paper entitled, An Experi- 
 mental Enquiry Concerning the Natural Power of Water 
 and Wind to Turn Mills, and Other Machines, Depend- 
 ing on a Circular Motion. By Mr. J. Smeaton, F. R. 8. 
 Part III is "On the Construction and Effects of Wind- 
 mill-Sails/' For his experiments Smeaton constructed 
 an elaborate machine or whirling-table in which fixed 
 sails revolved through the air about a given axis and their 
 velocities were measured by the weights lifted. A foot- 
 note reads: 
 
 Some years ago Mr. Rouse, an ingenious gentleman of 
 Hasborough in Leicestershire, set about trying experiments 
 on the velocities of the wind, and force thereof upon plain 
 surfaces and windmill sails. 
 
 It is presumed, though not so stated, that Mr. Rouse 
 used a whirling-table similar to that described by 
 Smeaton. Further on in the paper a table "containing 
 the velocity and force of wind, according to their common 
 
 appellations," is found introduced with : 
 
 The following table which was communicated to me by 
 my friend Mr. Rouse, and which appears to have been con- 
 structed with great care, from a considerable number of 
 
 [4] 
 
facts and experiments, and which having relation to the sub- 
 ject of this article; I here insert as he sent it to me; but at 
 the same time must observe that the evidence for those num- 
 bers where the velocity of the wind exceeds 50 miles an hour, do 
 not seem of equal authority with those of 50 miles an hour 
 and under. It is also to be observed, that the numbers in 
 column 3 are calculated according to the velocity of the 
 wind, which in moderate velocities, from what has been be- 
 fore observed, will hold very nearly. 
 
 From this introduction it is impossible to tell where ex- 
 periment ended and theory began. The coefficient of V* 
 according to the figures given in the third column of the 
 table is found to be 0.00492, or V 2 oo nearly. It is hard 
 to understand how a formula resting upon such a slender 
 foundation should have had such wide vogue. 
 
 The most careful experiments of recent years for the 
 pressure on flat plates of moderate size normal to the di- 
 rection of a uniform wind give a value of Tc from 0.0032 
 tc 0.004. Hence the formula P = 0.004 V 2 may be 
 safely used. It is interesting to note that Weisbach, in 
 his monumental work, the Mechanics of Engineering, 
 followed Newton's method but multiplied the value of Tc 
 as found by this method by a coefficient 1.86, stating that 
 about two-thirds of the action is upon the front and about 
 one-third upon the rear surface. He based his coefficient 
 upon the experiments of Dubuat (about 1780) and Thi- 
 bault (1826). 
 
 The U. S. Weather Bureau uses the formula 
 
 P = 0.004 ^-F 2 
 oO 
 
 in which B = height of barometer in inches. This for the 
 
 Tt 
 
 engineer is an unnecessary refinement as ^ varies but 
 
 oU 
 
 little from unity. Wolff in his book The Windmill as a 
 Prime Mover takes into account also the effect of tem- 
 perature in determining wind pressure. At sea level for 
 a wind velocity of 40 miles per hour he finds pressures 
 of 8.6 Ib. per sq.ft. for F. to 7.08 Ib. for 100 F. For 
 a velocity of 80 miles per hour he finds pressures of 
 34.98 Ib. per sq.ft. at F. to 28.86 Ib. at 100 F. 
 WIND-PRESSURE COEFFICIENT FOR INCLINED SURFACES 
 For the intensity of wind pressure on inclined surfaces 
 we have a wide range of values from which to choose. 
 
 [ 5 ] 
 
Tiberius Cavallo, F. E. S., etc., in 1803, published a four- 
 volume treatise on The Elements of Natural or Experi- 
 mental Philosophy. The writer has never seen the treatise 
 quoted, but Chapter IV of Book II, "Of the Action of 
 ^"onelastic Fluids in Motion," and Chapter X of the same 
 book, "Of Air in Motion, or of the Wind," are written 
 in a truly scientific spirit and are readable today. A 
 proposition of Cavallo's reads, "The forces of a fluid 
 medium on a plane cutting the direction of its motion 
 with different inclinations successively, are as the square? 
 of the sines of these inclinations." This, however, ia 
 implied by the great Newton in the Principia, Book II, 
 Prop. XXXIV. Among recent writers Spofford in "The 
 Theory of Structures" deduces the same theoretical re- 
 sults. 
 
 As these results differ widely from those obtained by 
 experiment, recourse must be had to empirical formulas. 
 Among such, Button's formula has been used in England 
 and the United States perhaps more than all others com- 
 bined. It is still found in the latest editions of many 
 technical books. The experiments upon which it is based 
 were decidedly crude. Tract XXXVI of Tracts on 
 Mathematical and Philosophical Subjects by Charles 
 Hutton, LL.D., F.E.S., Professor of Mathematics in the 
 Eoyal Military Academy of Woodwich, England, entitled, 
 "Eesistance of the Air Determined by the Whirling- 
 Machine," records his experiments. Hutton secured a 
 whirling-machine and during 1786 and 1787 experi- 
 mented with hemispheres and cones. Under date of July 
 23, 1788, he records: 
 
 Prepared the machine to make experiments with figures 
 of shapes different from the foregoing ones. Procuring a 
 thin rectangular plate of brass to fix on the arm of the ma- 
 chine; its weight 11^ oz. and its dimensions 8 in. by 4 in., 
 consequently its area was 32 sq.in. ... It was adapted 
 for fitting on the end of the arm in both directions, . . . 
 It was also contrived to incline the surface in any degree 
 to the direction of motion, to try the resistance at all angles 
 of inclination. When fitted on with its length in the direction 
 of its arm, the distance of its center from the axis of mo- 
 tion was 53% in.; and the same distance also when fitted on 
 the other way. 
 
 Experiments were carried on at different inclinations 
 of plate with a velocity of 12 ft. per sec. or 8.2 miles per 
 
 [6] 
 
hour. When attempting to bring the velocity up to 20 
 ft. per sec. or 13.6 miles per hour, the thread carrying 
 the weight broke. These experiments are recorded under 
 dates of July 24, 25, 31 and Aug. 11. The results ob- 
 tained were tabulated and the well known formula 
 Pn = P (sitfx) l -**co*x-i 
 
 was deduced. This is sometimes called Unwin's formula, 
 though for what reason is not clear, as Prof. Unwin 
 simply quotes Prof. Hutton's formula approvingly. 
 The Duchemin formula 
 
 P p 2 sin A 
 1 + sin* A 
 
 for inclined surfaces may be said to represent the best 
 knowledge on the subject and is considered the most re- 
 liable formula in use. The pressures obtained are greater 
 than those from the Hutton formula. Col. Duchemin, a 
 French army officer, made his investigations in 1829 and 
 the results were published in 1842 (Bixby).* Consider- 
 able weight has been attached to the work of Col. Duche- 
 min. Weisbach quotes it, as well as most writers since 
 his time. The Duchemin formula was verified by S. P. 
 Langley in 1888. He had erected at the Allegheny 
 (Penn.) Observatory a whirling-table consisting of two 
 symmetrical wooden arms, each 30 ft. long, revolving in 
 a plane 8 ft. above the ground. The motion thus ob- 
 tained was nearly rectilinear, quite in contrast with that 
 from Button's machine of less than 5-ft. radius. He also 
 used velocities up to 100 ft. per sec., or nearly 70 miles 
 per hour. He writes: 
 
 At the inception of the experiments with this apparatus 
 it was recognized that the Newtonian law, which made the 
 pressure on an inclined surface proportional to the square 
 of the sine of the angle, was widely erroneous. Occasional 
 experiments have been made since the time of Newton to 
 ascertain the ratio of the pressure upon a plane inclined at 
 various angles to that upon a normal plane, but the published 
 
 *The writer, while obtaining his information first hand 
 from the sources quoted, acknowledges an obligation to a 
 valuable report: Appendix C of the Report of Sept. 29, 1894, 
 of the Special Army Engineer Board as to the Maximum Span 
 Practicable for Suspension Bridges. By W. H. Bixby, Captain 
 (now General) of Engineers, U. S. A. It is really a treatise 
 on wind pressure in engineering construction. It is said only 
 500 copies were issued. This valuable paper may be found 
 reprinted entire in "Engineering News," Mar. 14, 1895. 
 
experiments exhibit extremely wide discordance, and a series 
 of experiments upon this problem seemed therefore, to be 
 necessary before taking up some newer lines of inquiry. 
 
 It is remarkable that Langley obtained results varying 
 less than 3% from those derived from the Duchemin for- 
 mula. Regarding this he writes : 
 
 Only since making these experiments my attention has 
 been called to a close agreement of my curve with the 
 formula of Duchemin, whose valuable memoir published by 
 the French War Department, "Memorial de 1'Artillerie" No. 
 V, I regret not knowing earlier. 
 
 Attention is called to the monographs by Langley, 
 Experiments in Aerodynamics and The Internal Worlc 
 of the Wind, being Numbers 801 and 884 of the "Smith- 
 sonian Contributions to Knowledge." 
 
 WIND PEESSUKE ON NONPLANAR SURFACES 
 
 When the wind blows on nonplanar surfaces the pres- 
 sure on the projected area depends upon the form of the 
 surface. This is important in the case of the cylinder 
 (standpipes, chimneys and similar objects). Rankine 
 states in his Applied Mechanics, "The total pressure of 
 the wind against the side of a cylinder is about one-half 
 of the total pressure against a diametral plane of that 
 cylinder." A theoretical value of two-thirds is found in 
 some treatises, but in engineering practice one-half is 
 generally used. 
 
 Goodman in his Mechanics Applied to Engineering, 
 London, 1904, gives the following ratios of pressure: 
 
 Plat plate 1.0 
 
 Sphere 0.36 to 0.41 
 
 Elongated projectile 0.5 
 
 Cylinder 0.54 to 0.57 
 
 Wedge (base to wind) 0.8 to 0.97 
 
 Wedge (edge to wind) 0.6 to 0.7 
 
 Vertex angle 90 
 
 Cone (base to wind) 0.95 
 Cone (apex to wind) 
 
 Vertex angle 90 0.69 to 0.72 
 
 Vertex angle 60 0.54 
 
 Lattice girders about 0.8 
 
 WIND PRESSURE ON PARALLEL PLATES 
 The pressures upon parallel plates or bars with an open 
 space between them are important in application to plate- 
 girder bridges, the trusses in a truss bridge, or parallel 
 bars in the same truss when one bar is behind another. 
 
 [8] 
 
The Committee of the National Physical Laboratory, 
 England, having decided that one of the first researches 
 to be undertaken in the Engineering Laboratory should 
 be the investigation of the distribution and intensity of 
 the pressure of wind on structures, an elaborate series of 
 experiments was conducted by Thomas Edward Stanton 
 and the results embodied in two papers contributed by 
 him to the Institution of Civil Engineers: "On the Ke- 
 sistance of Plane Surfaces in a Uniform Current of Air" 
 and "Experiments on Wind Pressure." For circular 
 plates 2 in. in diameter at 1% diameters apart, he found 
 the value of the total pressure was less than 75% of the 
 resistance on a single plate; at 2.15 diameters apart the 
 total pressure was equal to that on a single plate; while 
 at a distance of 5 diameters apart the total pressure was 
 1.78 times that on a single plate. Stanton's first experi- 
 ments were criticized because they were conducted with 
 such small models. For his second series he built a tower 
 and used larger surfaces, but found little to change his 
 previous conclusions. 
 
 Baker's experiments at the Forth Bridge led him to 
 the conclusion that in no case was the area affected by the 
 wind in any girder which had two or more surfaces ex- 
 posed more than 1.8 times the area of the surface directly 
 fronting the wind. The Board of Trade regulations 
 under which the Forth Bridge was built required that a 
 wind pressure of 56 Ib. per sq.ft. should be used in cal- 
 culations, and this twice over the area of the girder sur- 
 face exposed.* 
 
 MEASURING WIND PRESSUBE AND VELOCITY 
 
 It has been assumed by experimenters that the pressure 
 of the wind on a given shape with a certain velocity is the 
 same as that of the shape moving through the air with an 
 equal velocity. This seems to follow from Newton's 
 Corollary V to his Laws of Motion, "The motions of bod- 
 ies included in a given space are the same among them- 
 selves, whether that space is at rest or moves uniformly 
 forward in a right line without any circular motion." 
 
 *Engineers regard the requirement of 56 Ib. as needless 
 and excessive. 
 
 [ 9 ] 
 
Perhaps the only dissonant voice is that of T. Claxton 
 Fidler, who in his Bridge Construction writes: "But it 
 has not yet been ascertained that the pressure of the wind 
 is the same thing as the resistance offered by the air to 
 a moving body." 
 
 The pressure of the wind has been measured direct and 
 independently of the velocity. The methods of doing this 
 are so limited in their application that the pressure is 
 almost universally determined in terms of the velocity. 
 Hence, the prime importance of measuring the velocity 
 of the wind correctly. Attempts to do this have been 
 made by all manner of means for the past two centuries. 
 The science of Anemometry has a literature of its own. 
 The velocities obtained by all methods are more or less 
 in error some of them very much so. At present the 
 Kobinson Cup Anemometer or some modification of it is 
 used pretty generally throughout the meteorological world 
 for measuring wind velocities. 
 
 In the Transactions of the Royal Irish Academy, Vol. 
 XXII, part III (1852), is a paper: "Description of an 
 Improved Anemometer for Registering the Direction of 
 the Wind, and the Space Which it Traverses in Given In- 
 tervals of Time. By the Rev. Tfhomas] R[odney] Rob- 
 inson, D.D., Member of the Royal Irish Academy, and of 
 other Scientific Societies. Read June 10, 1850." Dr. 
 Robinson, who was connected with the observatory at 
 Armagh, Ireland, writes : 
 
 After some preliminary experiments I constructed in 1843 
 the essential parts of the machine, a description of which 
 I now submit to the Academy, and I added in subsequent 
 years such improvements as were indicated by experience. 
 It was complete in 1846, when I described it to the British 
 Association at Southampton. 
 
 He found "from sixteen experiments made in four days 
 with winds from a moderate breeze to a hard gale, 
 
 -4.011 
 
 or, in round numbers, the action on the concave is four 
 times that on the convex." From this he found the 
 theoretic value m of the ratio of the velocity of the wind 
 to that of the cup center to be m = 3.00. Dr. Robinson 
 concluded that no matter what the size of the cups or the 
 
 [10] 
 
lengths of the arms, "the centers of the hemisphere move 
 with one-third of the wind's velocity, except so far as they 
 are retarded by friction." This has been disproved. As 
 a necessary result, many published velocities are in error. 
 The U. S. Weather Bureau prescribes that each pat- 
 tern of anemometer should have its particular law of ro- 
 tation determined by special experiment. Its stand- 
 ard instruments in use throughout the United States have 
 hemispherical cups 4 in. in diameter on arms 6.72 in. 
 long from the axis to the center of the cups. To the ob- 
 served velocity the correction Log. V = 0.509 + 0.912 
 Log. v is applied in which V is the actual velocity of the 
 wind and v is the linear velocity of the cup centers, both 
 expressed in miles per hour. 
 
 EFFECT OF VABIATIONS WITHIN THE WIND 
 Measurements of either wind velocity or wind pressure 
 are complicated enormously by the variations in the wind. 
 This is illustrated by two observed facts, both of which 
 are vitally important to the structural engineer : 
 
 1. Wind pressures are less per unit of area for large 
 surfaces than for small ones. On the Forth Bridge two 
 pressure boards were set up, one 20 ft. long by 15 ft. 
 high, and 8 ft. from it a circular plate of 1% sq.ft. area. 
 The maximum pressure registered on the small plate dur- 
 ing the years 1884 to 1890 was 41 Ib. per sq.ft. The large 
 board showed at the same time a pressure of 27 Ib. per 
 sq.ft. The readings for the large board never exceeded 
 80% of those recorded for the small plate at the same 
 time, and generally were 50 to 70%. A technical journal 
 of the time hastily drew the inference from these experi- 
 ments that pressure per square foot varies inversely as 
 area, the velocity remaining the same another illus- 
 tration of generalizing from insufficient data ! 
 
 2. Wind velocity increases with the distance from the 
 ground. Thomas Stephenson from his experiments writes 
 the equation 
 
 or 
 
 [11] 
 
A limiting unit of height must be established for this 
 equation to be of any use. An anemometer placed at the 
 top of the Eiffel Tower, an elevation of 994 ft., and 
 another in the meteorological office at an elevation of 69 
 ft., showed for light winds velocities nearly four times 
 as great at the top of the tower as at the office. For 
 higher winds the velocities came nearer together. 
 
 CONCLUSION 
 
 Cavallo, previously quoted, wrote, "a great many more 
 experiments must be instituted by scientific persons be- 
 fore the subject can be sufficiently elucidated." More than 
 a hundred years after Cavallo's writing, the U. S. 
 Weather Bureau in its monograph on Anemometry, 
 after giving values for pressures and velocities with all 
 the refinements at its command, says : 
 
 Great dependence cannot be placed in these values for 
 indicated velocities beyond 50 or 60 miles per hour, as thus 
 far direct experiments have not been made at the higher 
 velocities, though it is probable the corrected values are 
 throughout much more accurate than values computed from 
 older formulas and uncorrected wind velocities. 
 
 Structures have long been designed with satisfactory 
 results to withstand wind pressure. The bracing at times 
 may have been excessive, but in the absence of better 
 knowledge on the subject, engineers cannot radically de- 
 part from present practice. 
 
II 
 
 Wind Stresses in Steel Mill- 
 Buildings 
 
 SYNOPSIS Discusses the distribution of wind 
 pressure on a sloping roof, referring to the experi- 
 ments of Irminger, Kernot, Stanton, Smith and 
 others. Analyses of stresses in Fink roof trusses 
 show that a uniform vertical excess load is suffi- 
 cient to take care of wind stresses if rigid mem- 
 bers are used. In kneebraced mill-building bents, 
 wind corrections are necessary. Suction effects 
 are to be neglected except as regards anchorage. 
 Recommends wind pressures and unit stresses, and 
 discusses special bracing. 
 
 In designing ordinary mill-buildings it is common 
 practice either (1) to neglect the wind stresses or (2) to 
 calculate them in accordance with some textbook method 
 and then tone down the results. In doing the latter, the 
 general practice of designing buildings is followed, in 
 conformity to which structures have been built that have 
 rendered excellent service for many years. To bridge the 
 gap between theory and practice, recourse is being had 
 by some to what might be called a new school, which has 
 advanced new methods and new experimental results. In 
 the present article this school will be briefly reviewed, its 
 conclusions negatived, and textbook assumptions made 
 to agree as near as possible with actual conditions the 
 object being to present a safe, sane, workable method of 
 determining and making provision for the wind stresses 
 in steel mill-buildings. 
 
 AMOUNT AND DISTRIBUTION OF WIND STRESSES 
 A recent writer 1 of the new school states the case thus : 
 
 In a high wind the maximum pressure against the roof 
 is at the windward eaves. The pressure decreases upward 
 on the windward slope, and is zero, it is claimed, at a point 
 
 ^'Insurance Engineering," August, 1912. 
 
 [ 13 ] 
 
three-fourths the distance to the ridge. Beyond the zero 
 point, up to the ridge and down the leeward slope, the pres- 
 sure is negative. The wind deflected upward by the wind- 
 ward surface of the roof rarefies the air over the leeward 
 surface, which allows the air inside the building to exert an 
 upward pressure in excess of the downward pressure on the 
 roof. In other words, there is direct or inward pressure on 
 the windward slope of the roof, center of pressure below 
 middle of slope, and at ridge and on all of leeward slope, 
 there is outward pressure or suction. 
 
 SUCTION ON EOOF 
 
 In 1894, J. 0. V. Irminger, manager of the Copen- 
 hagen Gas Works, made a number of experiments on wind 
 pressure, the description and results of which he em- 
 bodied in a paper 2 to which reference is often made. A 
 rectangular opening about 6%xll in. was made in a 
 chimney 5 ft. in diameter and 100 ft. high. Into this 
 opening was inserted a conduit 4%x9 in., polished on 
 the inside to reduce friction. Currents of air were made 
 to strike plates and models placed in this conduit and the 
 resultant pressure registered. A model of a pitched roof 
 with 45 slopes showed a normal uplift on the leeward 
 side due to suction three times as great as the normal 
 pressure on the windward side. The conclusion drawn 
 was "if the author's experiments on models represent the 
 facts with regard to buildings, the methods with which 
 roof principals are commonly calculated for wind-pres- 
 sure need revision." An enthusiastic admirer of Irminger 
 writes, 3 "It will be due to him that we surely in the 
 future shall save tons of material in our roofs." 
 
 In 1891-94, Prof. W. C. Kernot, of the University of 
 Melbourne, made the experiments connected with his 
 name. 4 By means of a gas engine and propeller, he dis- 
 charged a jet of air 12 in. by 10 in., placing into this jet 
 the plates and models he wished to test. He concluded 
 that the usual method of calculating wind stresses in 
 roofs applied only to roofs supported by columns under 
 which the air could blow freely. With roofs of a low 
 
 2 "Engineering News," Feb. 14, 1895; "Engineering," Dec. 
 7, 1895; Proc. Inst. Civ. Engrs., Vol. CXVIII, p. 468. 
 
 Theodore Nielsen, "Engineering," Oct. 9, 1903. 
 
 *"Engineering Record," Feb. 10, 1894; Proc. Inst. Civ. 
 Engrs., Vol. CLXXI, p. 218; Australian Association for the 
 Advancement of Science, Vol. V (1893), p. 573, Vol. VI (1895), 
 p. 741. 
 
 [14] 
 
pitch resting on walls having parapets, he found a tend- 
 ency to an uplift. 
 
 In 1893 and later, T. E. Stanton, of the National Phys- 
 ical Laboratory, England, made the experiments which 
 have become widely known from the papers he contrib- 
 uted to the Institution of Civil Engineers. 5 From ob- 
 servations on models of roofs the sides of which were 3 
 in. by 1 in. and sloped at 30, 45 and 60, placed in a 
 current of air having velocities of 10.0, 13.6 and 16.8 
 miles per hour, he writes, "The experiments appear to 
 indicate beyond question the importance of a consider- 
 ation of a negative pressure on the leeward side of roofs/' 
 From later experiments on pressure boards 5x5 ft. to 
 10x10 ft., he found the coefficients of wind pressure to be 
 as follows : 
 
 STANTON'S COEFFICIENTS k IN FORMULA Pn = kV 2 
 
 (a) Roof mounted on columns through which air can pass 
 
 60 45 30 
 
 Windward side +0.0034 +0.0028 +0.0015 
 Leeward side negligible 
 
 (b) Roofs of buildings in which the pressure on the interior 
 
 may be affected by the wind. 
 
 60 45 30 
 
 Windward side +0.0034 +0.0028 +0.0015 
 
 Leeward side 0.0032 0.0022 
 
 This coefficient gives the normal pressure on roof sur- 
 face in Ib. per sq.ft., if V is the wind velocity in miles 
 per hour, the wind blowing horizontal. 
 
 Prof. Albert Smith in a paper read before the West- 
 ern Society of Engineers, November, 1910, entitled 
 <r VVind Loads on Mill Building Bents," 6 among his con- 
 clusions advocates "placing the wind loads equally on the 
 two walls, and inward and outward on the windward and 
 leeward roofs respectively, as giving important changes 
 of stress in members of the roof truss, as giving less stress 
 in the kneebraces and columns, and as permitting the 
 rational design of the girts." In 1912, he made a num- 
 ber of observations on a model building 6 ft. wide by 
 15 ft. long, with wall heights of 4, 5 and 6 ft. In a 
 paper "Wind Pressure on Buildings," 7 he writes: 
 
 Proc. Inst. Civ. Engrs., Vol. CL.VI, p. 78, Vol. CLXXI, p. 175. 
 'Journal Western Soc. Engrs., February, 1911. 
 Mournal Western Soc. Engrs., December, 1912. 
 
 [ 15 ] 
 
The ordinary methods of assuming wind loads on mill 
 buildings ought to be somewhat revised. For the case of roof 
 trusses on masonry walls, or on steel bents with long diag- 
 onals, a suction effect in the neighborhood of 0.4 of the unit 
 wind pressure should be placed on the leeward roof of all 
 closed buildings, and a pressure or suction derived from the 
 curves drawn from the observations placed on the windward 
 roof. The resulting stresses will not only be different in 
 amount from those computed on the present basis, but will 
 in many members differ as to sign. Wind loads on purlins 
 might in most cases be entirely omitted. * * * * In 
 buildings with kneebraced bents, in addition to the preceding 
 points, the suctions on the leeward wall should be considered. 
 
 Prof. Boardman, University of Nevada, in 1911 made 
 experiments on a model roof 10 ft. long, each slope 6 ft. 
 wide, resting on walls 4 ft. high. His conclusions are 
 similar to those of Prof. Smith. 8 
 
 An English textbook, Brightmore's Structural Engi- 
 neering, first issued in 1908, quotes the Stanton experi- 
 ments as authority and the stress diagrams for the roof 
 truss given are made with the wind forces so acting. The 
 heading of the section is significant: "Stresses Due to 
 Wind Pressure and Wind Suction." 
 
 Another English textbook, Andrews' The Theory and 
 Design of Structures, in an appendix to the last edition, 
 1913, calls attention to Stanton's conclusions and gives 
 a stress diagram for a truss with the wind loading in ac- 
 cordance with these conclusions. In mentioning the 
 stresses due to suction on the leeward side the author 
 writes, "Few designers appear to have allowed for this 
 in their calculations for roofs, but the question is of con- 
 siderable importance and the results of these experiments 
 should either be disproved, or allowance should be made 
 for them in design." 
 
 Marburg in Framed Structures and Girders alludes to 
 the experiments of Kernot, Irminger and Stanton and 
 reproduces one of the Irminger sketches. His practical 
 conclusion is: 
 
 The experiments of Kernot, Irminger and Stanton were 
 made on much too small a scale to admit of quantitative de- 
 ductions applicable to conditions in practice. They are val- 
 uably suggestive, however, in calling attention to conditions 
 which were previously not generally or adequately recognized. 
 
 With this conclusion the writer is in thorough accord. 
 
 8 Journal Western Soc. Engrs., April, 1912. 
 
 [ 16 ] 
 
SELECTING A WIND PKESSUEE FOE DESIGN 
 
 Our knowledge of wind pressures is very imperfect. It 
 is generally agreed that the fundamental equation P = 
 kV 2 is correct for horizontal wind. There is little dispute 
 that for wind with a uniform velocity and normal to 
 plates of moderate size, the value of k is from 0.0032 to 
 0.004. Of the formulas for wind pressure on inclined 
 surfaces our best knowledge indicates that of Duchemin 
 as the most accurate. It is 
 
 2 sin A 
 I + sin* A 
 
 There remains to be assigned a value to V. Average 
 wind velocities for a day or a month or a year are use- 
 less. Shall the highest wind velocity on record be taken? 
 Is this likely to occur again? 
 
 It is useless to attempt to make provision for torna- 
 does or violent hurricanes "against which neither care, 
 nor strength, nor wisdom, can avail."* Such storms are 
 limited in area and come but seldom, perhaps once in a 
 century. The endeavor to make a mill-building strong 
 enough to resist them would not only add greatly to the 
 cost but would be ineffective, f 
 
 The highest wind velocity recorded in New York City 
 since 1871 by the U. S. Weather Bureau was 96 miles 
 per hour sustained for a period of five minutes. During 
 one minute of that time the velocity was 120 miles per 
 hour. This was in Feb. 22, 1912, a Robinson anemom- 
 eter being used in the same location as at present, about 
 20 ft. above the roof of the 33-story building at 17 Bat- 
 tery Place. A recorded velocity of 80 to 90 miles is not 
 uncommon. A recorded velocity of 90 miles per hour 
 corrected by the Weather Bureau formula gives an actual 
 velocity of 69.2 miles per hour. With this value in the 
 formula P = kV 2 , k = 0.004, the normal pressure is 
 19.2 Ib. per square foot on a vertical surface. Wind pres- 
 
 *This is the way it is stated in the Foreword of a little 
 volume issued by the Home Insurance Co., of New York, advo- 
 cating windstorm and tornado insurance. More than a 
 hundred photographs in this volume of wrecks caused by 
 windstorms illustrate the truth of the Foreword. 
 
 fEditor's Note This argument in its terms applies Just as 
 much to office buildings and all other structures as it does to 
 mill buildings. The author probably means to emphasize the 
 cost limitation, for mill-buildings alone. 
 
 [17] 
 
sure increases with the distance from the ground and 
 decreases per square foot as the area becomes larger. 
 When it is remembered that the instrument above men- 
 tioned is about 400 ft. from the ground and the cups 
 are only 4 in. in diameter, the assumptions that will be 
 made of a horizontal wind force of 20 Ib. per sq.ft. in de- 
 signing the trusses of mill-buildings, and 15 Ib. in de- 
 signing columns and kneebraces, seem to be ample and 
 fully warranted. 
 
 WIND STRESSES IN KOOF TRUSSES 
 
 Eoof trusses resting on brick walls will first be con- 
 sidered. The example taken will be a roof truss as in 
 Fig. 1, with pitch of 6 in. to 1 ft., and span of 60 ft. 
 c. to c. of bearing plates. Trusses are 16 ft. apart on cen- 
 ters. For a horizontal wind from the left, with pressure 
 of 20 Ib. per sq.ft. on a vertical surface, the normal pres- 
 sure on a surface inclined 6 in. to 1 ft. will be (by Du- 
 chemin's formula) 14.9 Ib. per sq.ft. 
 
 The following cases will be considered: 
 
 (1) Wind load of 15 Ib. per sq.ft. or 2012 Ib. per 
 panel, normal to one slope of roof, both ends of truss 
 fixed. 
 
 (2) Loads as in (1), left end fixed, right end on 
 rollers. 
 
 (3) Loads as in (1), left end rollers, right end fixed. 
 
 (4) Load of 15 Ib. per sq.ft. exposed surface or 2012 
 Ib. per panel on both sides of the roof, the loads ap- 
 plied vertically. 
 
 The stresses for these four cases are tabulated below : 
 
 It is seen at a glance that Case 4 is sufficient to cover 
 
 wind stresses. The slight excess in a few members found 
 
 in the other cases is negligible, especially when they are 
 
 considered with the combined stresses due to all loads. 
 
 With the same wind velocity as before, according to 
 Stanton, the pressure on the windward slope is about 
 n/ 2 Ib. per sq.ft. and 22 / 15 times 7^ or 11 Ib. per square 
 foot negative pressure or suction on the leeward side. 
 The forces acting upon the truss are as in Fig. 2 (reac- 
 tions are for both ends fixed, wind shear equally divided), 
 while Fig. 3 is the stress diagram for both ends fixed. 
 
 [18] 
 
The tabulation of stresses given below is for 
 
 (5) Both ends of truss fixed. 
 
 (6) Left end fixed, right end on rollers. 
 
 (7) Left end rollers, right end fixed. 
 
 It might be stated here that all the above cases with 
 one end on rollers are hypothetical, as roof trusses under 
 100-ft. span are seldom built with other than fixed ends.* 
 
 EECOMMENDED DESIGN LOAD Maximum wind load- 
 ing comes seldom and lasts but a short time. The work- 
 ing stresses used for this loading may therefore be in- 
 creased 50% above those used for ordinary live- and 
 dead-loads. A wind load of 15 Ib. per sq.ft. is thus equiv- 
 alent to a load of 10 Ib. using the working stresses for 
 other loads. 
 
 The snow load varies from 20 Ib. per sq.ft. horizontal 
 projection in the latitude of New York City to 30 Ib. in 
 parts of New England. This is equivalent to 16.6 up to 
 25 Ib. vertical load per sq.ft. surface of a 6-in. pitch 
 roof. 
 
 For combined snow and wind a load of 25 Ib. per sq.ft. 
 over entire surface, acting vertically, is ample for roofs 
 in the latitude of New York City. If to this is added the 
 weight of trusses, purlins, and roof covering, reduced to 
 square foot of exposed surface, we have the total load 
 for which the ordinary roof truss should be designed. 
 However, not less than 40 Ib. should be used except in 
 tropical climates with no snow, where the minimum load- 
 ing should be 30 Ib. Where snows are severe 5 to 10 Ib. 
 should be added to the 40 Ib. 
 
 No ALLOWANCE FOR SUCTION Turning to the tabu- 
 lation of stresses found by the Stanton assumptions, and 
 taking into account the total stresses from all loads, the 
 saving due to reduced wind stresses is small. A serious 
 objection to taking advantage of even this saving is that 
 with a monitor along the ridge, or openings in the build- 
 ing and roof, the closed roof may become a partly open 
 roof, thus changing the conditions for which the assump- 
 
 *Editor's Note The wind shear may, however, come wholly 
 on one or the other wall, due to unequal bedding of the 
 anchor bolts or to temperature movement. The condition 
 then, as regards the present calculation, is identical with one 
 end on rollers. 
 
 [ 19 ] 
 
tions were made. For a truss resting on brick walls the 
 tendency to an uplift can be met by firmly anchoring it 
 at the ends. The tendency to reversals of stress can be 
 sufficiently met by using stiff shapes for all members; 
 flats and rounds have no place in an ordinary roof truss. 
 The writer believes that the assumption of a total uni- 
 form load per square foot of exposed surface applied ver- 
 tically at the panel points, with the same working stresses 
 used throughout, is specially well adapted to the design 
 of roof trusses. 
 
 WIND STRESSES IN KNEEBRACED BENTS 
 
 KNEEBRACED BENTS The case of an intermediate 
 transverse bent of a kneebraced mill-building will now 
 be considered. The example taken will be that shown in 
 Fig. 4; span 60 ft., roof pitch 6 in. to 1 ft, height 14 ft. 
 to foot of kneebrace and 20 ft. to bottom chord. Trusses 
 are 16 ft. apart c. to c. 
 
 The wind pressure will be taken at 15 Ib. per sq.ft. 
 perpendicular to the sides of the building and the cor- 
 responding normal component on the roof at 11.2 Ib. 
 (For buildings over 25 ft. to the eave line the normal 
 component of a wind load of 20 Ib., or 14.9 Ib., would 
 be used for the roof.) The columns are assumed par- 
 tially fixed at the lower end, with the point of contraflex- 
 ure at one-third the distance between the lower end and 
 the foot of the kneebrace; the upper ends are considered 
 supported. The wind shear is divided equally between 
 the two columns. Fig. 5 is the stress diagram. 
 
 Bending moments in the columns are as follows : 
 
 At the foot of windward column 12,320 ft.-lb. 
 
 At foot of leeward column 14,940 ft.-lb. 
 
 At foot of windward kneebrace 19,410 ft.-lb. 
 
 At foot of leeward kneebrace 29,870 ft.-lb. 
 
 It is seen that the maximum bending moment is at the 
 foot of the leeward kneebrace. 
 
 RECOMMENDED METHOD For mill-building bents the 
 writer first determines the stresses in the truss due to a 
 total uniform load and then proportions it for the same. 
 The ordinary working values for medium steel are gen- 
 
 [ 20 ] 
 
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 [21] 
 
erally used 16,000 Ib. per sq.in. in net tension and (re- 
 duced by formula) for gross compression. If the wind 
 stresses in any member from Figs. 4 and 5 are greater 
 than the wind stresses from the uniform wind loading of 
 10 Ib. per sq.ft. applied vertically, that member is pro- 
 portioned for the maximum wind stress plus the stresses 
 from the uniform loads other than wind, using working 
 stresses 50% more than in the first calculation; but in 
 no case is a less section used than that first obtained. The 
 
 v^ 
 
 FIGS. 4 AND 5. KNEEBRACED BENT or A MILL-BUILDING ; 
 STRESS DIAGRAM FOR WIND LOAD 
 
 (Equal shears; contraflexure one-third height to kneebrace) 
 
 members be and fr^ will generally need be increased; 
 often cd and c^; occasionally gd, gf, gf and g^. A 
 reversal of stresses is noted in certain members, particu- 
 larly in ~bc and the lower chord. The diagonals "be and 
 biC^ can be made of two angles instead of one as wher* 
 designed for tension alone. The compressive stresses in 
 the lower chord are overcome by the tensile stresses due 
 
 [ 22 ] 
 
to the dead-load. The kneebraces have wind stresses only, 
 end are proportioned for the larger working stresses. 
 
 The column is first proportioned for carrying the di- 
 rect stress due to the total uniform load from the truss, 
 noting the flange area required. From the maximum 
 bending moment due to the wind, as in Fig. 4 and 5, the 
 sectional area required for the flanges is found using the 
 larger working stresses and considering the column as 
 a beam. If this flange area is not more than one-third 
 of that first found no change is made; if more than one- 
 third, the excess is added. The compressive stress due 
 to overturning need not be considered unless it exceeds the 
 stress from the wind portion of the uniform roof load. 
 
 GIKTS The side and end girts are proportioned as 
 beams supported at each end with a uniform horizontal 
 load of 15 Ib. per sq.ft.; an extreme fiber stress of 24,000 
 Ib. per sq.in. is used. 
 
 The girts are apparently the simplest portion of the 
 building to design, but if observation and experience 
 count they are the most difficult. Side and end girts of 
 3%x2%x}4-iii. or ^-in. angles, 16 to 20 ft. long and 
 5 ft. apart, are still in use after 20 years' service, in de- 
 fiance of all figures. Notwithstanding this, such design- 
 ing practice is reprehensible. 
 
 SPECIAL CASES OF MILL-BUILDING BRACING 
 
 Traveling cranes running through a building often bar 
 the use of kneebraces. The gussets connecting the trusses 
 to the columns should then be as large as possible and 
 calculations made accordingly. An ideal way is to trans- 
 fer the transverse thrust from the wind as well as that 
 from the cranes to the ends of the building by means of 
 diagonal bracing in the plane of the lower chords of the 
 trusses, and thence by diagonals in the ends of the build- 
 ing to the ground. Openings in the ends often interfere 
 with this expedient. Neither is it feasible in buildings 
 so long as to require provision for longitudinal expan- 
 sion and contraction due to changes in temperature. 
 
 In all cases diagonal bracing should be introduced into 
 the planes of both top and bottom chords for stiffness as 
 well as to take calculated stresses. This applies also to 
 
 [ 23 ] 
 
roof trusses resting on brick walls. Adjustable rods can 
 be used for top-chord bracing, but the bracing of the 
 bottom chord should be entirely of angles or other rigid 
 shapes, with bolted or riveted connections. 
 
 The ends of a building, the gables in particular, are 
 more liable to be severely strained from wind than any 
 other portion of the building. Generally diagonals in 
 the planes of the chords of each end panel, and in each 
 end side bay to the ground will be sufficient to take care 
 of the induced stresses. If not, the shear may be divided 
 with other braced bays. 
 
 Special types of buildings should be considered in ref- 
 erence to their own requirements. Open sheds, especially 
 if the gables are closed, may have an uplift as well as a 
 vertical load. 
 
 COMMENTS ON PRIOR KECOMMENDATIONS 
 
 The leading textbook on the subject of mill building!, 
 is Ketchum's Steel Mill-Buildings. In this book a knee- 
 braced mill bent is considered for four cases: 
 
 (1) A horizontal wind load of 20 Ib. per sq.ft. on the 
 side and vertical projection of the roof, with the columns 
 Mnged at the base. 
 
 (2) Same wind load as in Case 1, with columns fixed 
 at the base. 
 
 (3) A horizontal wind load of 20 Ib. per sq.ft. on the 
 side, and the normal component of a horizontal wind load! 
 cf 30 Ib. per sq.ft. on the roof, with columns hinged at 
 the base. 
 
 (4) Same wind load as in Case 3, with columns fixed 
 at the base. 
 
 The writer believes that the loads of 20 and 30 Ib. are 
 larger than need be used. The columns are seldom if 
 ever rigidly fixed at the base, neither are they hinged. 
 That they are partially fixed and the point of contra- 
 iiexure is at one-third the distance from base to foot of 
 kneebrace is believed to be nearer correct than either as- 
 suming it one-half the distance or assuming the columns 
 supported at the base. There seems no good reason for 
 assuming a normal component of a horizontal wind load 
 of 30 Ib. on the roof while a horizontal wind load of 20 
 
 t 24] 
 
Ib. is taken on the sides. It is not clear why the Hut- 
 ton formula is used to find the normal component. Near 
 the beginning of the book we read, "Button's formula is 
 based on experiments which were very crude and probably 
 erroneous. Duchemin's formula is based on very care- 
 ful experiments and is now considered the most reliable 
 formula in use." The specifications near the close of the 
 book call for the Duchemin formula to be used in com- 
 puting the normal wind pressure; by this formula, for a 
 30-lb. load, the 18-lb. normal pressure in Cases 3 and 
 4 would be 22 A Ib. The only increase of the usual work- 
 ing stresses allowed is 25% for laterals and 50% for 
 combined direct and flexural stress due to wind. This in- 
 crease does not apply to the combination of wind with 
 other loads though with the maximum wind load a min- 
 imum snow load of 10 Ib. per sq.ft. is allowed. (For 
 the purpose of aiding those who wish to make compari- 
 sons the same roof truss and bent have been taken in 
 this article as found in Ketchum.) 
 
 The chapter on "Iron and Steel Mill-Building Con- 
 struction" by G. H. Hutchinson in Johnson, Bryan & 
 Turneaure's Modern Framed Structures, considers three 
 cases of a mill-building bent, arriving at conclusions sim- 
 ilar to those of Ketchum. The method of obtaining re- 
 actions and moments is quite abstruse and difficult to 
 follow. No mention is made in the chapter of working 
 stresses to be used. 
 
 Smith, in "Wind Loads on Mill-Building Bents," 6 as- 
 sumes a total horizontal wind force of 30 Ib. per sq.ft. 
 on the bent considered in this article. The pressure on 
 the sides is divided equally between the two columns. 
 One-third of the normal component of the total pressure 
 on the roof, found by Duchemin's formula, is taken by 
 the windward slope and two-thirds as suction or an out- 
 ward pressure on the leeward slope. The bases of the 
 columns are considered hinged. Comparing his results 
 with those obtained by Ketchum, he shows reduced 
 stresses but is unfortunate in the example selected for 
 comparison: Ketchum's stresses are taken and 50% is 
 added to them for a 30-lb. load; but Ketchum calculate? 
 his roof for the normal component of a horizontal wind 
 
 [ 25 ] 
 
of 30 Ib. and the side for 20 lb., so that Smith is actually 
 comparing his results with those obtained from a bent 
 having a pressure on the sides of 30 lb. per sq.ft. and 
 on the roof the normal component (by the Hutton for- 
 mula) of a horizontal force of 45 lb. per sq.ft. 
 
 However, with the same wind force, the Smith method 
 does give reduced stresses, especially in the columns, 
 kneebraces and girts. The important point is whether 
 these reductions are permissible. In a modern mill-build- 
 ing the sides are from one-fourth to one-half or more of 
 glass, a large proportion of which can be opened to permit 
 of ventilation. If opened on one side only, Smith's as- 
 sumption that the pressure on the inside of a mill-build- 
 ing is a mean between the windward pressure and the lee- 
 ward suction disappears. In a high wind the windows on 
 the leeward side are liable to be open and those on the 
 windward side closed; there is then little suction. In a 
 building the sides of which are covered with sheet metal 
 there is always a probability of the covering on one side or 
 end being removed for 8 ft. or more from the ground, 
 thus completely doing away with the suction theory. For 
 these reasons it is unwise to take advantage of a theory 
 based upon assumptions which are destroyed by a prob- 
 able change of conditions. 
 
 In conclusion, while the methods advocated for treat- 
 ing wind stresses may not be thoroughly scientific, they 
 are easily workable, and experience proves that they art 
 safe and sane. The load of 15 lb., the working stress of 
 24,000 lb., and the assumed point of contraflexure, may 
 all be criticized, but for the ordinary mill-building it is 
 more rational to use these assumptions and make strict 
 provision for them than to follow the present method of 
 giving an intellectual assent to the theories of the text- 
 book and ignoring them in actual practice. 
 
Ill 
 
 Wind Stresses in Railroad 
 Bridges 
 
 SYNOPSIS The Tay Bridge failure reviewed. 
 English practice in the 70's ignored wind stresses, 
 while American engineers used methods nearly 
 equal to those of today. Empirical development 
 is the basis of practice. Modern specifications 
 show a great number of variations in detail, but 
 may be brought nearer uniformity in the future. 
 Lateral-oscillation forces should be specified sepa- 
 rate from wind pressure. 
 
 The purpose of this article is to review past and pres- 
 ent practice of the treatment of the wind forces acting on 
 railroad bridges. 
 
 THE TAY BKIDGE 
 
 On the evening of Dec. 28, 1879, occurred the "Tay 
 Bridge Disaster." During a violent gale, 11 spans of 
 245 ft. and two of 227 ft., with the train passing over 
 them at the time, fell into the river. This failure of what 
 was at the time the largest bridge in the world after a 
 service of less than two years marked an epoch in bridge 
 building in Great Britain. "Wind stresses in railroad 
 bridges had previously been almost neglected; from that 
 time they have been fully considered, if not magnified. A 
 Court of Inquiry was appointed by the English Board of 
 Trade to report on the causes of the disaster. Today the 
 testimony taken regarding the provision made in the de- 
 sign of the bridge for wind stresses is interesting reading. 
 
 Sir George Airy, Astronomer Eoyal, testified that about 
 seven years previously he had been consulted on the sub- 
 ject of the provision which should be made for wind pres- 
 sure on the plans prepared by Sir Thomas Bouch of a 
 bridge of two spans of 1600 ft. over the Forth. He gave 
 as his opinion that the greatest wind pressure that might 
 be expected over the whole extent of such a surface was 
 10 Ib. per sq.ft. 
 
 [27] 
 
Sir Thomas Bouch, the designer of the Tay bridge, tes- 
 tified that he did not specially make any allowance for 
 wind pressure, but he had seen the report on the Forth 
 Bridge; he thought the greatest pressure would be about 
 10 Ib. 
 
 The majority report of the Court of Inquiry ends : 
 
 In conclusion, we have to state that there is no require- 
 ment issued by the Board of Trade respecting wind pressure, 
 and there does not appear to be any understood rule in the 
 engineering profession regarding wind pressure in railway 
 structures; and we therefore recommend that the Board of 
 Trade should take such steps as may be necessary for the 
 establishment of rules for that purpose. 
 
 A minority report was submitted by the third member 
 of the Court. f An extract is: 
 
 It is said that Sir Thomas Bouch must be judged by the 
 state of our knowledge of wind pressure when he designed 
 and built the bridge. Be it so; yet he knew or might have 
 known that at that time the engineers in France made an 
 allowance of 55 Ib. per sq.ft. for wind pressure, and in the 
 United States an allowance of 50 Ib. 
 
 In the engineering literature of 1880 and 1881, a 
 paper often referred to is "The Tay Bridge," by Edgar 
 Gilkes, a member of the firm building the bridge. It 
 was read before the Cleveland Institution of Engineers, 
 Nov. 6, 1876. The special paragraph that must have 
 plagued the author reads: 
 
 A consideration of the action of the wind on this bridge 
 will dissipate the often-advanced theory that at some period 
 it will be blown over. The exposed surface of one large pier 
 is about 800 sq.ft., and of the superstructure which depends 
 upon it, about 800 more, and so, giving 800 ft. for a train 
 
 tThe majority of the Court of Inquiry reported that in 
 their opinion the cross bracing at the pier and its fastening 
 by lugs was the first part to yield. The evidence, however, 
 was ample to justify the language of the minority report, 
 "that this bridge was badly designed, badly constructed, and 
 badly maintained, and that its downfall was due to inherent 
 defects in the structure which must sooner or later have 
 brought it down." 
 
 The piers which failed carried two adjoining trusses and 
 consisted of a hexagonal group of six cast-iron columns 
 filled with Portland cement, two 18 in. and four 15 in. in 
 diameter. Each column in case of the higher columns was 
 made of seven lengths 10 ft. 10 in. long, united by flanges. 
 These columns were braced vertically on the exterior sides 
 by struts of two 6-in. channels and diagonals of 4%x%-in. 
 flats fastened to cast-iron lugs with 1%-in. bolts. Horizontal 
 bracing connected the four interior columns. It will readily 
 be seen that such a system is weak throughout. 
 
 As a matter of interest it may be noted that during the 
 progress of construction on the night of Feb. 2, 1877, two of 
 the 245-ft. spans were blown into the river. To this accident 
 "Engineering" of Feb. 9, 1877, devoted just 14 lines. 
 
above, we have 2400 ft. Twenty-one pounds per sq.ft. is 
 the force of a very strong gale, but it would take no less 
 than 96 Ib. per sq.ft. on the surface given to overturn the pier. 
 Even the most severe hurricane on record would equal only 
 one-half this resultant power. 
 
 C. Shaler Smith, after a careful calculation in accord- 
 ance with American rules, found the exposed surface of 
 the superstructure to be 2576 sq.ft. instead of 800, while 
 the London Engineering shows the exposed train surface 
 was 1630 sq.ft. instead of 800. 
 
 EAKLY ENGLISH PRACTICE 
 
 It is surprising how little is found in the English 
 technical books and papers of those days regarding the 
 force of the wind on structures. Humber, in his volum- 
 inous "Complete Treatise on Cast- and Wrought-Iron 
 Bridge Construction," published in 1861, does not mention 
 it. TJnwin's "Wrought-Iron Bridges and Roofs," 1869, 
 was a far better textbook than any that had preceded it. 
 What he writes regarding wind pressure on roofs is still 
 quoted; yet he says nothing of wind stresses in bridges. 
 The article on Bridges, by Prof. Jenkin, in the ninth 
 edition of the "Encyclopedia Britannica" (1876), after- 
 ward issued as a separate treatise, fills 58 closely written 
 pages, but not a line is found concerning wind bracing. 
 Thomas Cargill, in his "The Strains upon Bridge Gird- 
 ers and Eoof Trusses," 1873, writes : 
 
 No allowance is made in the theoretical calculation for the 
 violent shock, concussion and consequent vibration that attend 
 the passage of a heavy train over a bridge. This must be 
 allowed for by experience, by the introduction of such addi- 
 tional bracing as the skill of the engineer suggests. These 
 are points which cannot be learned from books. 
 
 To the effect of the wind on a bridge he makes no al- 
 lusion, though in the chapter "Curved Roof Trusses," he 
 says: 
 
 Some writers lay great stress upon providing a large 
 margin of strength for wind pressure, but there is more 
 theoretical than practical knowledge displayed in such state- 
 ments. 
 
 Rankine, in his "Manual of Civil Engineering," in the 
 early 60's, gives a formula for the effect of wind on tubular 
 girders, and in a footnote states that the greatest pres- 
 sure of wind ever observed in Britain was 55 Ib. per sq.ft., 
 
 [29] 
 
but we have no record that this observation ever entered 
 into the consideration of bridge engineers. 
 
 The first German edition of Hitter's "Elementary The- 
 ory and Calculation of Iron Bridges and Roofs," was is- 
 sued in 1862. An English translation was published in 
 1879. In this book the lateral force is taken as a per- 
 centage of the combined vertical live- and dead-loads. In 
 one particular bridge under consideration, it is assumed 
 to be one-seventh. 
 
 The outcome of the agitation following the fall of the 
 Tay Bridge was a commission appointed by the Board 
 of Trade to consider the question of wind pressure on rail- 
 way structures. This committee made its report in 1881. 
 The substance of its five recommendations was: (1) 
 That for railway bridges and viaducts a maximum wind 
 pressure of 56 Ib. per sq.ft. should be assumed for the 
 purpose of calculation. (2) That the area of exposed sur- 
 face should be taken at once to twice the front surface, 
 according to the extent of the openings in the trusses or 
 lattice-girders. (3) That a factor of safety of 4 should 
 be used for strains caused by wind pressure, and for the 
 whole structure overturning as a mass a factor of safety 
 of 2 should be used. These recommendations became law 
 in Great Britain. 
 
 EARLY AMERICAN PRACTICE 
 
 Not less interesting is the historical development of 
 wind bracing in the United States. In 1851 was pub- 
 lished, "General Theory of Bridge Construction," by 
 Herman Haupt, A.M., General Superintendent of the 
 Pennsylvania R.R., formerly professor of Mathematics 
 in Pennsylvania College. The pioneer book in which 
 bridge trusses are correctly analyzed is "A Work on 
 Bridge Building," by Squire Whipple, published at Utica, 
 N. Y., in 1847. Whipple's book was little known for a 
 ong time after its publication, while Haupt's book, written 
 without any knowledge of the existence of Whipple's, soon 
 became widely circulated and for years was regarded as 
 an authority. In Part 1 of Haupt's book we read : 
 
 The use of lateral bracing is principally to guard against 
 the effects of wind, and other disturbing causes, tending to 
 produce lateral nexure in the roadway * * * The greatest 
 
 [30] 
 
lateral strain is that produced by the action of a high wind; 
 assuming the force of wind at 15 Ib. per sq.ft., as a 
 maximum, * * * 
 
 In Part II, written some time after Part I, we read, 
 "The heaviest locomotives in use weigh about 23 tons, 
 and their length is 23 ft.," and further on : 
 
 The greatest strain upon the lateral bracing of a bridge 
 would be that caused by the action of the wind in a violent 
 tornado. It is probable that this force is far greater than 
 it is usually estimated. The observations of the writer at 
 the Susquehanna Bridge, during the tornado which caused 
 the loss of six of the unfinished spans, led him to believe that 
 the direct effect of the storm was increased by reflection from 
 the surface of the water. * * * If we suppose a storm 
 could be so violent as to cause a pressure of 30 Ib. per 
 sq.ft., * * * 
 
 The tornado alluded to occurred Mar. 27, 1849. A 
 viaduct across the Susquehanna River, near Harrisburg, 
 was being built for the Pennsylvania R.R. It was sup- 
 ported on 22 piers, 160 ft. center to center. The trusses 
 were of the Howe type, with the addition of wooden 
 arches. After the fourteenth span had been raised, the 
 storm came and carried off six spans. The contractor was 
 busy at the time putting in the arches, and as the diagonal 
 braces could not be fastened until after the arches were 
 in place, they had been omitted except over the piers and 
 in the middle of the spans. The wind came at right angles 
 to the bridge and the six spans without lateral bracing 
 gave way. 
 
 As late as the early 70's American textbooks had little 
 or nothing to say on wind bracing. De Yolson Wood de- 
 votes less than one-half a page to the subject in his 
 "Theory on the Construction of Bridges," while Greene 
 in "Bridge Trusses" spares only a page. Col. Merrill, in 
 his "Iron-Truss Bridges for Railroads," makes no men- 
 tion of wind bracing. Shreve, whose "Treatise on the 
 Strength of Bridges and Roofs" was translated into 
 French, finds vertical strains, horizontal strains, chord 
 strains, brace strains, but the word wind does not occur in 
 the book, nor is any mention made of bracing in a hori- 
 zontal plane. Nearly the same might be written of Roeb- 
 ling's "Long and Short Span Railway Bridges/' 1869. 
 
 American practice, however, was ahead of the teaching 
 profession. C. Shaler Smith, on Dec. 15, 1880, presented 
 
 [31 ] 
 
a masterly paper to the American Society of Civil Engi- 
 neers, entitled, "Wind Pressure upon Bridges." He 
 gives specifications which he had used in constructing a 
 number of bridges, some of them high and in exposed lo- 
 calities. He specifies : 
 
 The portal, vertical and horizontal bracing shall be pro- 
 portioned for a wind pressure of 30 Ib. per sq.ft. on the 
 surface of a train averaging- 10 sq.ft. per lin.ft., and on 
 twice the vertical surface of one truss. The 300 Ib. pressure 
 per lin.ft. due to the train surface shall be treated as a mov- 
 ing load, and the pressure on the trusses as a fixed load. 
 Trusses of less than 200 ft. span shall also be proportioned 
 for a pressure of 50 Ib. per sq.ft. where unloaded, and the 
 greatest strain by either method of computation shall in 
 each case be used in determining the sectional area of the 
 bracing. 
 
 Several leading railway companies at that time were us- 
 ing practically these specifications. From this same paper 
 the following is significant : 
 
 Many engineers prefer to express wind force in pounds 
 per lineal foot of bridge instead of per square foot of exposed 
 surface. Using a 200-ft. span as an example, the specifications 
 in question can be condensed as follows: 
 
 Fixed load in plane of roadway, 210 Ib. per lin.ft. 
 
 Fixed load in plane of other chord, 130 Ib. per lin.ft. 
 
 Moving load in plane of roadway, 300 Ib. per lin.ft. 
 
 It is refreshing to see C. Shaler Smith quoted as the 
 exponent of American practice for wind bracing in the 
 article on Bridges, by Unwin, in the eleventh edition of 
 the "Encyclopedia Britannica." 
 
 The rules in the Erie Specifications, formulated in 
 1878 by Theodore Cooper, were: 
 
 To provide for wind strains and vibrations, the top lateral 
 bracing in deck bridges and the bottom lateral bracing in 
 through bridges shall be proportioned to resist a lateral force 
 of 450 Ib. for each foot of the span, 300 Ib. of this to be 
 treated as a moving load. 
 
 The bottom lateral bracing in deck bridges and the top 
 lateral bracing in through bridges shall be proportioned to 
 resist a lateral force of 150 Ib. for each foot of the span. 
 
 It is thus seen that in the early days of iron railway 
 bridges, the American engineers were far in advance of 
 their English brethren in the recognition of wind forces. 
 
 FACTORS IN THE PROBLEM 
 
 "A Practical Treatise on Bridge Construction/' by T. 
 Claxton Fidler, was published in London in 1887. Chap- 
 
 [ 32 ] 
 
ter XXIV is "On Wind-Pressure and Wind-Bracing." In 
 1894, Captain (now General) Bixby, U. S. A., in a mono- 
 graph reviewing the literature on wind pressure, writes: 
 "The chapter is perhaps the best single, short, concise, 
 comprehensive and practical review of the whole sub- 
 ject yet in print." This characterization in a large 
 measure still holds true. Some concluding sentences from 
 the chapter are: 
 
 We have seen, for example, how large a proportion of the 
 metal in a long-span bridge is required for the purpose of 
 resisting wind-pressure and for the purpose of carrying the 
 metal that resists wind-pressure. But we have also seen 
 that it is really impossible to estimate the wind stresses 
 within 100% of their real value. * * * In this state of un- 
 certainty, the responsible engineer will generally be disposed 
 to err on the safe side; but it must be remarked that this 
 will be a very expensive proceeding. * * * On the other 
 hand, he knows that an error in the opposite direction might 
 be attended with still more disastrous results. 
 
 The sting of these sentences is in their truth. Our 
 knowledge of the wind is uncertain, especially regarding 
 the higher velocities. Although there are many unknown 
 quantities in the problem of wind stresses in a bridge, 
 the main questions to be considered are two : 
 
 (1) What is the pressure to be assumed per unit of 
 area? 
 
 (2) What shall be taken as the area exposed to the ac- 
 tion of the wind? 
 
 Wind pressure is generally measured in terms of the ve- 
 locity. According to the best information we have, an in- 
 dicated velocity by the ( Weather-Bureau standard) ane- 
 mometer of 100 miles per hour denotes an actual velocity 
 of 76 miles, which is equivalent to a pressure of 23 Ib. 
 per sq.ft. on a surface at right angles to its direction. A 
 pressure of 30 Ib. per sq.ft., which corresponds to an 
 indicated velocity of about 120 miles per hour, will over- 
 turn empty freight cars, the ordinary passenger car, 
 and acting over an extended area of land would sweep 
 from it all trees. No engine driver could take his train 
 upon a bridge with such a pressure, though it is possible 
 that the train during a sudden gust might be caught there. 
 A man could not keep his feet with such a pressure, no 
 matter at what angle his legs were inclined to the ground. 
 
 [33] 
 
It would seem that 30 Ib. per sq.ft. is ample for assumed 
 wind pressure. 
 
 The second question to be considered is even more diffi- 
 cult to answer than the first. In a bridge composed of two 
 or more trusses several feet apart, and each truss made 
 up of members which may shelter other members, the case 
 is far different from that of wind on a plate or on a solid 
 body. Our actual knowledge of the subject is slight. 
 Baker's experiments at the Forth Bridge* and Stanton's 
 experiments at the National Physical Laboratory f are 
 generally quoted. Bridge engineers and writers on the 
 subject vary in their methods. C. Shaler Smith, as pre- 
 viously noted, uses an exposed area of "twice the vertical 
 surface of one truss." In estimating the vertical surface 
 of one truss he adds to the elevation of the upper chord 
 and posts, as seen on the drawing, 1% times the surface of 
 the ties, and twice the surface of the lower chord. J Du 
 Bois, in his "The Stresses in Framed Structures," gives 
 as a rule this method for finding the area of surface of a 
 single truss. "In preliminary estimates," he writes, 
 "we may take the exposed surface for both trusses at 10 
 sq.ft. per lin.ft." 
 
 Johnson, Bryan and Turneaure, in "The Theory and 
 Practice of Modern Framed Structures," use "the ex- 
 posed surface of all trusses and the floor as seen in ele- 
 vation." Merriman and Jacoby, in "A Text Book on 
 Eoofs and Bridges," Heller in "Stresses in Structures," 
 and a number of other writers do the same. "Structural 
 Engineering," an English textbook by Husband and 
 Harby, says "The area of the bridge exposed to the higher 
 pressure will be from once to about three times the area 
 as seen in elevation, depending on the type of construc- 
 tion." Another English textbook, Anglin, "The Design 
 of Structures," says, "In double-webbed lattice girders, the 
 area of both webs should be taken, or double the web area 
 as seen in elevation, . . . . If a bridge consists of 
 two such main girders, the wind pressure must be taken 
 as acting on an area equal to four times that as seen in 
 
 * "Engineering-," Sept. 5, 1884. 
 
 f'Proc. of Inst. of C. E.," Vol. CLVI and Vol. CLXXI. 
 t"Trans. Am. Soc. C. E.," Vol X, pp. 170. (Private letter 
 to O. Chanute.) 
 
 [ 34] 
 
elevation." This same textbook adds, "American engi- 
 neers assume a wind pressure of 30 Ib. per sq.ft. upon 
 the loaded, and 50 Ib. upon the unloaded structure." 
 
 From the foregoing it is readily seen that specifications 
 that simply give the load per square foot of exposed sur- 
 face to be used do not fully specify. Descriptions of 
 bridges which state the lateral pressure per square foot 
 used in the calculations without defining the extent of ex- 
 posed surface intended by the designer are incomplete 
 in their description. 
 
 It is to be remembered that there are stresses due to lat- 
 eral forces other than the wind. A considerable lateral 
 force is developed by a rapidly moving train, or the lurch- 
 ing of a locomotive when it first strikes a bridge. This 
 lateral vibration appears to be much more accidental in 
 its character than the vertical vibration.* Even were there 
 no wind, rigidity would have to be maintained against 
 this lateral vibration, which in short spans is probably a 
 greater factor than the wind pressure itself. We have 
 nothing to determine a relation between lateral vibration 
 and wind strain. 
 
 Further, the compression chords of bridges must be held 
 in alignment by the lateral bracing. The amount of ma- 
 terial required to do this is not, with our present knowl- 
 edge, a matter of exact calculation.! 
 
 In some specifications provision for all lateral forces, 
 except the centrifugal force when the track is on a curve, 
 is included in that for wind pressure without being so 
 stated. In others, "for lateral forces" or "for wind loads 
 and lateral vibration" are the words used and more clearly 
 express what is intended. 
 
 Giving the lateral force in terms of pounds per lineal 
 foot of bridge (rather than in pounds per square foot) 
 has a decided advantage in the preparation of designs for 
 competition, as all bidders are working upon the same 
 basis. Theoretically, for the wind itself the pressure 
 per square foot is to be preferred and the force that pro- 
 duces lateral vibration is best represented by a percentage 
 
 *Robinson, "Vibration of Bridges." Trans. Amer. Soc. 
 C. E., Vol. XVI, p. 42. 
 
 fReichman, "Journal of the Western Soc. of Eng's," Vol. 
 29, p. 93. 
 
 [ 35 ] 
 
of the moving load. As engine weights and car loads are 
 increased, provision is thus made for the increased ten- 
 dency to vibration. Again, a different lateral force for 
 spans under 200 ft. from that for spans over 200 ft. is as- 
 sumed by some engineers. 
 
 While the wind pressure on a moving train should be 
 treated as a moving load, engineers are divided in their 
 opinions as to the wind load on the structure itself ; some 
 considering it uniform and some moving. 
 
 In regard to end anchorage, the following will be quoted 
 from Waddell's "De Pontibus" : "No matter how great 
 its weight may be, every ordinary fixed span should be 
 anchored effectively to its support at each bearing on 
 same." (Principle XXVI, in chapter "First Principles of 
 Designing.") 
 
 In passing, a criticism will be launched at the Eng- 
 lish bridges of "an early Victorian type,"* having an 
 arched portal strut at every post and no top laterals. 
 Some of these are of late date. All are wasteful in mater- 
 ial, and there is great ambiguity in regard to the lateral 
 stresses. 
 
 PRESENT SPECIFICATIONS 
 
 The specifications of the American Eailway Engineer- 
 ing Association, 1910, read : 
 
 All spans shall be designed for a lateral force on the loaded 
 chord of 200 Ib. per lin.ft. plus 10% of the specified train load 
 on one track, and 200 Ib. per lin.ft. on the unloaded chord; 
 these forces being considered as moving. 
 
 The American Bridge Co. or Schneider specifications 
 assume the wind pressure : 
 
 First, at 30 Ib. per sq.ft. on the exposed surface of all 
 trusses and the floor as seen in elevation, in addition to a 
 train of 10 ft. average height, beginning 2 ft. 6 in. above 
 base of rail, moving across the bridge. Second, at 50 Ib. 
 per sq. ft. on the exposed surface of all trusses and the floor 
 system. The greatest result shall be used in proportioning 
 the parts. 
 
 The Cooper specifications call for provision to be made 
 to resist a lateral force of 600 Ib. per lin.ft. on the loaded 
 chord, of which 450 Ib. is to be treated as a moving load 
 acting on a train of cars at a line 6 ft. above base of rail. 
 
 *The Tugela Bridge, "Engineering," Jan. 26, 1900. 
 
 [36] 
 
The unloaded chord is to resist a lateral force of 200 Ib. 
 per lin.ft. for spans up to 200 ft., and 25 Ib. for each ad- 
 ditional 50 ft. 
 
 The specifications of the railroads mentioned below are 
 selected from a larger number to show the varying assump- 
 tions made of the amount of wind and lateral forces to be 
 used in the design of railroad bridges. The wind is as- 
 sumed to act horizontally at right angles to the bridge. 
 Pounds per lineal foot means lineal foot of bridge. 
 
 Baltimore & Ohio R.R. Co. A moving lateral force of 600 
 Ib. per lin.ft. against the loaded chord, and 200 Ib. per lin.ft. 
 against unloaded chord. 
 
 Buffalo, Rochester & Pittsburgh Ry. Co. (a) On the 
 
 loaded structure, 30 Ib. per sq.ft. on the exposed surface of 
 all trusses and the floor system as seen in elevation, and on 
 a moving train surface of 10 ft. average height beginning 
 2 ft. 6 in. above base of rail, (b) On the unloaded structure, 
 50 Ib. per sq.ft. (instead of 30). In no case shall a lateral 
 force of less than 200 Ib. fixed and 300 Ib. moving per lin.ft. 
 be used for the loaded chord and less than 150 Ib. per lin.ft. 
 fixed for the unloaded chord. 
 
 Canadian Pacific Ry. Co. Same as the Schneider specifica- 
 tions. 
 
 Chesapeake & Ohio Ry. Co. Against the unloaded chord 
 a fixed force of 200 Ib. per lin.ft. for all spans of 200 ft. 
 and under, and an additional force of 10 Ib. per lin.ft. for 
 every 25 ft. increase in span over 200 ft. Against the loaded 
 chord same as above with an additional force of 500 Ib. 
 per lin.ft. acting 8 ft. above base of rail and treated as a 
 moving load. 
 
 Chicago, Milwaukee & St. Paul Ry. Co. A lateral force of 
 750 Ib. per lin.ft. against the loaded chord, and 200 Ib. per 
 lin.ft. against the unloaded chord, these forces being consid- 
 ered as moving. 
 
 Delaware & Hudson Co. For the loaded chord 300 Ib. per 
 lin.ft. moving load and 200 Ib. per lin.ft. dead-load. For the 
 unloaded chord, 200 Ib. per lin.ft. dead-load. For double-track 
 bridges these loads shall be increased one-half. 
 
 Delaware, Lackawanna & "Western R.R. A moving load 
 of 300 Ib. per lin.ft. against the loaded chord, and a uniform 
 load of 300 Ib. per lin.ft. divided equally between loaded and 
 unloaded chords. 
 
 Grand Trunk Railway System has "Private" printed on the 
 title page of its specifications and hence they can not be 
 quoted. 
 
 Harrimnii Lines Same wording as Buffalo, Rochester & 
 Pittsburgh Ry. Co. above. 
 
 Lehigh Valley R.R. Co. A moving load of 700 Ib. per lin.ft. 
 against the loaded chord and a moving load of 300 Ib. per 
 lin.ft. against the unloaded chord. 
 
 Long Island R.R. Co. (1st) A load of 30 Ib. per sq.ft. 
 "on the exposed surface of entire surface as seen in elevation" 
 (but never less than 200 Ib. per lin.ft. at the unloaded chord), 
 and on a moving train 10 ft. high beginning 2 ft. 5 in. above 
 base of rail; (2d) 50 Ib. per sq.ft. on "the exposed surface of 
 the entire structure as seen in elevation." 
 
 Mexican International R.R. Co. Six hundred pounds per 
 lineal foot against the loaded chord and 200 Ib. per lin.ft. 
 against the unloaded chord, both forces considered as moving. 
 
 National Lines of Mexico On the unloaded structure 50 Ib. 
 per sq.ft. "on the geometrical elevation of the completed 
 structure and track." On the loaded structure, "30 Ib. per 
 sq.ft. of said elevation," plus the moving surface of train 10 
 
 [37] 
 
ft. high, beginning 2% ft. above the base of rail. In no case 
 shall the fixed wind pressure be less than 150 Ib. per lin.ft. 
 for each chord of any bridge. 
 
 New York Central Lines (1st) A moving load of 30 Ib. 
 per sq.ft. on 1% times the vertical projection of the structure 
 on a plane parallel with its axis (but never less than 200 Ib. 
 per lin.ft. at the unloaded chord), and a moving load of 360 
 Ib. per lin.ft. applied 8 ft. above the base of the rail. (2d) A 
 moving load of 50 ft. per sq.ft. on 1% times the vertical pro- 
 jection of the unloaded structure on a plane parallel with its 
 axis. 
 
 New York, New Haven & Hartford R.R. Co. Same as the 
 
 A. R. E. Assn. 
 
 New York, Ontario & Western Ry. Co. Same as the A. R. 
 
 B. Assn. For double-track bridges the constants are increased 
 50% but the percentage of live-load remains the same. 
 
 Norfolk & "Western Ry. Co. Same as the Schneider speci- 
 fications, but omitting "beginning 2 ft. 6 in. above base of 
 rail." 
 
 Pennsylvania R.R. Co. Same as the Schneider specifica- 
 tions. 
 
 Pennsylvania Lines West of Pittsburgh A uniform load 
 of 150 Ib. per lin.ft. against the unloaded chord and 200 Ib. 
 per lin.ft. against the loaded chord. A moving load of 300 
 Ib. per lin.ft. against the loaded chord acting at a line 6 ft. 
 above the base of rail. 
 
 Philadelphia & Reading: Ry. Co. A uniform load of 200 
 Ib. per lin.ft. against each chord and a moving load of 400 
 Ib. per lin.ft. against the loaded chord with its point of appli- 
 cation iy 2 ft. above the rail. 
 
 Piedmont & Northern Lines Same as A. R. E. Assn. 
 
 Seaboard Air Line Ry. Same as A. R. E. Assn. 
 
 Southern Ry. Co. Same as A. R. E. Assn. 
 
 Western Maryland Ry. Co. Dead-load, 150 Ib. per lin.ft. 
 against the unloaded chord, and 200 Ib. per lin.ft. against the 
 loaded chord. Moving load, 400 Ib. per lin.ft. against the 
 loaded chord, applied at a distance of 6 ft. above the base 
 of rail. 
 
 Western Pacific Ry. Co. Same as Western Maryland. 
 
 The wide range of requirements demanded in exist- 
 ing specifications shows the difficulty of uniting on a com- 
 mon standard. At present an increasing number of 
 railroad engineers is following the specifications of the 
 American Eailway Engineering Association. In Europe, 
 bridges are built in accordance with rules and regulations 
 prepared by the respective governments. This at times is 
 an advantage, at other times it is not. Unwin writes: 
 'English bridge builders are somewhat hampered in adopt- 
 ing rational limits of working stresses by the rules of the 
 Board of Trade." 
 
 WORKING STRESSES 
 
 The required material in a bridge depends upon as- 
 sumed unit stresses as well as upon assumed loadings. 
 Some ten years ago, the late Professor Heller* found that 
 for the same live- and dead-load stresses in a bottom- 
 
 *"Engineering News," Nov. 19, 1903. 
 
 [38] 
 
chord member of a 134-ft. span, there was a variation 
 from 11.4% below to 18.6% above the average section of 
 25.4 sq.in. required by the 28 specifications he examined. 
 In the specifications of the 25 railroads mentioned above, 
 with the total stresses assumed by Heller, the variation 
 is from 11.65% below to 9.33% above the average of 
 24.97 sq.in. required. There is nearly a unanimity in 
 using for the combined stress due to lateral forces, plus 
 live- and dead-loads, a unit-stress 25 or 30% greater 
 than that due to the live- and dead-loads alone. 
 
 In this connection attention is called to the bending 
 stresses in the end posts due to portal bracing; and the 
 stresses induced in different members when the bridge 
 is figured for overturning moments. These are not to 
 be neglected, nor are centrifugal stresses when track is 
 on curve. 
 
 LONG SPANS 
 
 What has been written and the specifications quoted 
 apply primarily to railroad bridges of noncontinuous truss 
 spans. When the Ohio Eiver bridge between Cincinnati 
 and Covington was finished in 1889 with a center span 
 of 545 ft. and two spans of 486 ft., it had the distinction 
 of having the longest and heaviest simple truss that had 
 been built either in the United States or in Europe. The 
 specifications called for a wind pressure of 30 Ib. per sq.ft. 
 on the exposed surface of both trusses and the vertical 
 projection of the floor system, and on a moving-train sur- 
 face averaging 10 sq.ft. per lin.ft. 
 
 The St. Louis Municipal Bridge has three spans, each 
 of 668 ft. center to center of end pins, at present the 
 longest simple truss spans in the world.* The permissible 
 lengths of the spans are explained by 58% of the metal 
 being nickel-steel. The wind loads assumed were 300 
 Ib. per lin.ft. for the upper lateral system, and 600 Ib. per 
 lin.ft., one-half moving and one-half fixed, for the lower 
 lateral system. 
 
 *Merriman and Jacoby in the last edition of their "Roofs 
 and Bridges" enumerate 31 railway bridges and 6 combined 
 railway and highway bridges which have simple truss spans 
 of 400 ft. and over in length. Of these 15 are over 500 ft. 
 and two, including the St. Louis bridge, are over 600 ft. 
 The new Ohio River Bridge at Metropolis, recently contracted 
 for, has a noncontinuous channel span of 700 ft. clear distance 
 between piers. 
 
 [ 39 ] 
 
The Hell Gate Bridge, now building, will have the long- 
 est arch in the world a span of 977^ ft. The para- 
 graph in the specifications relating to wind pressure reads : 
 
 Wind, pressure shall be assumed as a moving load of 500 
 Ib. per lin.ft. in the plane of the tracks, plus 30 Ib. per sq.ft. 
 on such vertical surface of the unloaded bridge as shall be 
 exposed at any angle between 20 above or 20 below the 
 horizontal or at an angle of 45 from the axis of the bridge, 
 but not less than 200 Ib. per lin.ft. on any chord. 
 
 For 25 years the Forth Bridge of cantilever design, 
 in Scotland, has remained the greatest bridge in the 
 world. Its spans of 1700 ft. exceed in length and magni- 
 tude any other now standing. The wind loads and unit 
 stresses used in the design were those of the English Board 
 of Trade Eegulations, which most engineers regard as ex- 
 cessive and needlessly severe. The table below, made by 
 Sir Benjamin Baker from his calculations of stresses due 
 to the separate loadings, will show the important part 
 wind forces played in the design. 
 
 Dead Live 
 
 Load Load Wind Total 
 
 Stresses Stresses Stresses Stresses 
 
 Bottom member . 2282 1022 2920 6224 
 
 Top member 2253 997 544 3794 
 
 Vertical member 1550 705 1024 3279 
 
 Diagonal struts 802 167 414 1383 
 
 Diagonal ties 754 186 194 1134 
 
 Horizontal wind bracing. . 80 5 265 350 
 
 Vertical wind bracing 42 169 108 319 
 
 Central girder top 337 303 182 822 
 
 Central girder bottom . . . 330 301 247 878 
 Stresses are given in tons of 2240 Ibs. 
 
 The Quebec Bridge, also of cantilever design, now 
 building, will, when finished, eclipse the Forth Bridge, 
 its enormous channel span being 1800 ft. long. The as- 
 sumed wind loads are: 
 
 A wind load normal to the bridge of 30 Ib. per sq.ft. of the 
 exposed surface of two trusses and 1% times the elevation 
 of the floor (fixed load), and also 30 Ib. per sq.ft. on travelers 
 and falsework, etc. during erection. 
 
 A wind load on the exposed surface of the train of 300 
 Ib. per lin.ft. applied 9 ft. above base of rail (moving load). 
 
 A wind load parallel with the bridge of 30 Ib. per sq.ft. 
 acting on one-half the area assumed for normal wind pressure. 
 
 CONCLUSION 
 
 The writer has no intention of passing judgment upon 
 the specifications of engineers who have carried American 
 bridge building to such a marked success. Standard speci- 
 fications, as far as wind stresses are concerned, may not 
 
 [40 ] 
 
be practicable, but it should be possible to come nearer to 
 points of agreement than at present. As an instance, the 
 Lehigh Valley, the Philadelphia & Heading, and the Lack- 
 awanna railroads, all in the same territory, must have 
 practically the same lateral forces ; but the assumed forces 
 vary nearly 75%. A discussion of the reasons for these 
 variations would be interesting. 
 
 In no specifications that the writer has ever read is 
 there an attempt to separate the stresses due to wind 
 from those due to other lateral forces. The 10% of the 
 weight of the train often specified for the lateral force 
 on the loaded chord includes the wind pressure on the 
 train. The wind pressure of 30 Ib. per sq.ft. on a mov- 
 ing train, sometimes called for, includes the lateral force 
 due to vibration. When the assumed loading is given in 
 Ib. per lin.ft., the total pressure due to all lateral forces 
 is intended. 
 
 Perhaps in the future some engineer may be able to 
 assign definite amounts to the different items that make 
 up the total lateral force on a bridge. This would be one 
 of the first steps to be taken to secure any degree of uni- 
 formity in proposed requirements for lateral stresses. As 
 a beginning in this direction, the writer suggests that the 
 lateral force on the loaded chord due to oscillation of 
 the train be taken at 4% of the train load. 
 
 [41] 
 
IV 
 
 Wind Stresses in Highway 
 Bridges 
 
 SYNOPSIS A review of the varying assump- 
 tions that have been made regarding the wind 
 stresses in highway bridges. Problem complicated 
 by lateral forces due to traffic. Present-day spec- 
 ifications, and variation of practice. 
 
 EARLY AMERICAN WRITERS 
 
 WHIPPLE In the early part of 1847 there appeared 
 a pamphlet of 48 pages with the title, "An Essay on 
 Bridge Building, containing analyses and comparisons 
 of the principal plans in use, with investigations as to 
 the best plans and proportions, and relative merits of 
 wood and iron, for bridges. By S. Whipple, C. E., Mathe- 
 matical and philosophical instrument maker. Utica, N. Y. 
 H. H. Curtiss, printer, Devereux Block, 1847." After dis- 
 tributing 50 or 60 copies among friends, the author bound 
 the remainder of the edition with "Essay No. II on 
 Bridge-Building Giving Practical Details and Plans for 
 Iron and Wooden Bridges/' which he had written and 
 printed later in the year. This little book of 120 pages 
 and 10 plates was the pioneer in the mathematics of 
 bridge construction. To Squire Whipple, its author, the 
 inventor of the Whipple bridge, belongs the honor of 
 being the first to publish a correct analysis of the stresses 
 in a simple truss. His work did not become widely 
 known. In 1869 he took the copies remaining of his 
 original edition and bound them "with an appendix, con- 
 taining Corrections, Additions & Explanations, Sug- 
 gested by Subsequent Experience : to which is annexed an 
 Original Article on the doctrine of Central Forces." This 
 addition of about 150 pages the author prepared and 
 printed with his own hands. 
 
 In 1872 an enlarged and rewritten edition was pub- 
 lished by the D. Van Nostrand Co. In 1873 a chapter 
 
 [ 43 ] 
 
of 35 pages on Drawbridges was added. From a copy 
 of this 1873 edition, the following quotations regarding 
 swaybracing are taken. 
 
 The primary and essential purpose of a bridge is to with- 
 stand vertical forces which are certain and, to a large extent, 
 determinate in amount But the lateral or trans- 
 verse forces to which a bridge superstructure is liable, are of 
 a casual nature, depending upon conditions of which we have 
 only a vague and general knowledge; .... But in ar- 
 ranging his system for securing lateral stability and steadi- 
 ness, science can lend him but little assistance He 
 
 knows the wind will blow against the side of his structure, 
 but whether with a maximum force of one hundred pounds, or 
 as many thousands, he has no means of knowing with any 
 considerable degree of certainty or probability .... No 
 attempt will be made here to assign specific stresses as liable 
 to occur in sway rods or braces, based upon calculations from 
 the uncertain and indeterminate elements upon which the 
 lateral action upon bridges depends. But judging from ex- 
 perience and observation, it may be recommended that iron 
 sway rods be made of iron not less than % inch in diameter, 
 for bridges of five panels or under, %-in. from six to ten 
 panels inclusive. For twelve and fourteen panels, %-in. for 
 ten middle panels and %-in. for the rest; and for sixteen the 
 same as last above, with the addition of a pair of 1-in. rods in 
 the end panels. 
 
 These are opinions from the father of modern bridge 
 building, written only 42 years ago. 
 
 BOLLER Boiler's "Iron Highway Bridges/' first pub- 
 lished in 1876, which has passed through several editions, 
 says, 
 
 The horizontal or sway bracing may consist of very light 
 rods, if the floor is well laid, forming as it does a very effec- 
 tive system of bracing against lateral movement. Rods from 
 %- to 1-in. round will cover all but extreme requirements, and 
 they are attached by any convenient means to the floor- 
 beams near their point of support. 
 
 In modern textbooks calculation has taken the place of 
 speculation. Most of what has been written about the 
 wind stresses in railroad bridges* applies to highway 
 bridges. The same questions of the intensity of wind 
 pressure per unit of area exposed, and the amount of area 
 to be considered as exposed surface, are to be met. In- 
 duced stresses, load uniform or moving, and lateral forces 
 other than wind are also to be considered. 
 
 *In the preceding article. 
 
 [44] 
 
CHANGED TRAFFIC KEQUIBEMENTS 
 The whole subject of loadings on highway bridges is 
 being revised. This is the day of heavy concentrated 
 loads. Many present bridges are seriously overloaded 
 by the traffic coming upon them, especially in the floor- 
 beams and joists. They were often built to carry uni- 
 form live-loads of, say 125 Ib. per sq.ft. for the floor-beams 
 and 80 or 100 Ib. for the trusses. Sometimes a road roller 
 was mentioned in the specifications. Manufacturers are 
 constantly increasing the weight of road rollers and trac- 
 tion engines, and with the good-roads movement many 
 bridges are called upon to carry rollers and engines for 
 which they were not designed. Then there is the automo- 
 bile, often run at a speed of 30 mi. per hr. 
 
 But the severest tests to which some of our highway 
 bridges are being put are those from the auto trucks.** 
 The traffic of towns and cities now reaches far out into the 
 country. The road roller runs slowly, while the auto 
 truck may be driven at a speed of 12 mi. per hr. and two 
 trucks may meet or pass each other on the same bridge. 
 A load of 10 tons is often carried and the weight of 
 the truck adds another 6 tons. (In New York City a load 
 of 75 tons has been carried on a truck weighing 10 tons, 
 most of the load being on the two rear wheels.)! Trucks 
 are being made heavier and with increased capacity. 
 Greater impact stresses are induced and the tendency to 
 both vertical and lateral vibration becomes greater. Some- 
 times centrifugal forces are introduced. AH this is par- 
 ticularly true of the auto truck when fully loaded and 
 with a driver ignorant or indifferent to loadings, speed,, 
 and the strength of bridges. One writer,J however, does 
 not think the vibration effects greater than those produced 
 by a horse and wagon. Anyone who has stood on a coun- 
 try bridge of 150-ft. span while a horse drawing a light 
 buggy was crossing at a trot may have felt a decided jolt- 
 ing of the whole structure, a condition largely remedied 
 by rigid connections and stiff members. 
 
 **Motor Truck Loading on Highway Bridges "Entr 
 News," Sept. 3, 1914. 
 
 tSeaman, Proceedings, Am. Soc. C. E., December, 1911. 
 JNeff (Am. Assoc. for Advancement of Science), "Enerineer- 
 ing and Contracting," Jan. 22, 1913. 
 
 [45] 
 
Electric-car lines are being extended, and cars are be- 
 ing increased in weight and run at greater speed. When 
 a highway bridge carries electric cars it becomes in real- 
 ity a miniature railroad bridge. City or county officials 
 who, without examination by a competent engineer, will 
 sanction the use of existing bridges to carry electric cars, 
 belong to the class of undesirable citizens. 
 
 LATERAL FORCES OTHER THAN WIND PRESSURE 
 
 The assumed wind load in bridge specifications includes 
 all the lateral forces whether so stated or not. The writer 
 believes that this is sufficient (in nearly all present speci- 
 fications) to take care of the increased lateral forces due 
 to changed traffic requirements. With the exception of 
 the electric car, it is improbable that the full wind load 
 will be acting at the same time that the lateral vibration 
 occurs, due to the moving load. It should be remembered 
 that, if by any means a highway bridge is blown over, 
 there is not likely to be any loss of life, neither will traf- 
 fic be seriously interrupted. The actual loss to the au- 
 thorities is little more than the cost of the structure it- 
 self. Hence, excessive bracing in all bridges to guard 
 against a remote possibility in a single one is unneces- 
 sarily expensive. With a railroad bridge it is differ- 
 ent; provision must there be made for remote possi- 
 bilities. 
 
 The weakness of lateral systems of highway bridges in 
 the past has not been so much in the assuming of loads 
 as in the abominable details used. Witness the common 
 practice of 25 years ago and still prevalent in some quar- 
 ters of fastening the lower laterals in a nondescript way 
 to the floor-beams, which, in turn, are suspended from the 
 pins by U-bolt hangers; or, the top laterals having bent 
 eyes taking the top-chord pins and pulling against struts 
 attached to the same pins by bent plates. It is better to 
 design for a safe and sane wind loading, taking care 
 of induced stresses, and with all details fully up, than to 
 proportion the body of the lateral members for larger 
 stresses and use inefficient details. 
 
 In high-truss bridges the compression chord is kept in 
 alignment by the top lateral system. In the pony truss, 
 
 [46] 
 
recourse is often had to doubtful expedients. "One has 
 only to shake the top chord of a pony truss to see how 
 loosely it is secured laterally and to demonstrate its lack 
 of fixity at intermediate points."* With the moving loads 
 now coming into use, the pony truss is doomed. In some 
 specifications it is prohibited altogether. 
 
 The wind is generally assumed to blow horizontally, but 
 it may vary greatly from the horizontal. For high bridges 
 in exposed localities, the upward pressure should be taken 
 into account; the end anchorage should provide for any 
 possible uplift and against the structure being moved off 
 its seats either by wind pressure or by a blow from a 
 passing object. A study of the wreck of the High Bridge 
 over the Mississippi River at St. Paulf is interesting. 
 
 PRESENT SPECIFICATIONS 
 
 SCHNEIDER Passing to well known specifications, the 
 American Bridge Co. or Schneider specifications for steel 
 highway bridges read : 
 
 The wind pressure shall be assumed acting in either di- 
 rection horizontally: 
 
 First. At 30 Ib. per sq.ft. on the exposed surface of all 
 trusses and the floor as seen in elevation, in addition to a 
 horizontal live-load of 150 Ib. per lin.ft. of the span moving 
 across the bridge, but not less than 300 Ib. per lin.ft. shall 
 be used for bracing of loaded chord nor less than 150 Ib. per 
 lin.ft. of unloaded chord. 
 
 Second. At 50 Ib. per sq.ft. on the exposed surface of all 
 trusses and the floor system. 
 
 The greatest result shall be assumed in proportioning the 
 parts. 
 
 COOPER Probably more highway bridges have been 
 built in accordance with the specifications of Theodore 
 Cooper than any other. The paragraphs stating amount 
 of lateral forces are: 
 
 To provide for wind and vibrations, the top lateral brac- 
 ing in deck bridges and the bottom lateral bracing in through 
 bridges shall be proportioned to resist a lateral force of 300 
 Ib. for each foot of the span; 150 Ib. of this to be treated as a 
 moving load. 
 
 The bottom lateral bracing in deck bridges and the top 
 lateral bracing in through bridges shall be proportioned to 
 resist a lateral force of 150 Ib. for each foot of the span. 
 
 For spans exceeding 300 ft., add in each of the above cases 
 10 Ib. additional for each additional 30 ft. 
 
 Johnson, Bryan & Turneaure; Merriman & Jacoby; 
 Ketchum; and others in their textbooks follow Cooper's 
 specifications regarding wind pressure. Others, as Mar- 
 
 *Smith, Proceedings, Indiana Eng. Soc., 1911, p. 209; "En- 
 gineering Record," Jan. 21, 1911. 
 
 tTurner, Trans. Am. Soc. C. E., June, 1905, Vol. LJV, p. 31. 
 
 [47] 
 
burg, and Burr & Falk, quote both the Schneider and the 
 Cooper specifications. 
 
 WADDELL Waddell in his "Ordinary Highway 
 Bridges" assumes a wind pressure of 40 Ib. per sq.ft. for 
 spans 100 ft. and under, 35 Ib. for spans 100 to 150 ft., 
 and 30 Ib. for spans greater than 150 ft. ; these pressures 
 to be increased 10 Ib. for bridges in unusually exposed lo- 
 cations. The loads are considered moving. 
 
 The total area opposed to the wind is to be determined by 
 adding together the area of the vertical projection of the floor 
 and joists, and twice the area of the vertical projection of 
 the windward truss, hub plank, guard rail, and ends of floor- 
 beams. 
 
 In his "Specifications for Steel Highway Bridges," 
 1906, the wind loads per lineal foot of span for both the 
 loaded and unloaded chords are taken from curves shown 
 on a diagram. The diagram was figured (for a clear 
 roadway of 20 ft.) with intensities varying from 40 Ib. 
 for very short spans to 25 Ib. for very long ones. For 
 spans up to 600 ft., the curves show loads from 200 to 355 
 Ib. per lin.ft. of bridge on the loaded chord and 100 to 
 265 Ib. on the unloaded chord, according to the length 
 of span and the class of the bridge. For wider struc- 
 tures, the wind loads are to be increased 2% for each 
 foot of width in excess of 20 ft. 
 
 GREINEK The "Specifications for Steel Stationary 
 Bridges," by Greiner, require that 
 
 for city, interurban and country bridges the lateral force 
 against unloaded chords shall be assumed not less than 
 150 Ib. per lin.ft. plus 10% of the uniform load on one car 
 track or on a width of 12 ft., and for the unloaded chords 150 
 Ib. per lin.ft. In cases where a lateral force of 30 Ib. per 
 sq.ft. on 1% times the vertical projection of the structure 
 produces greater stresses than the above loads, it shall be 
 considered. All lateral loads shall be treated as moving. 
 
 OSTRUP Ostrup, in his "Standard Specifications for 
 Highway Bridges/' calls for wind bracing to be designed 
 to resist one of the following lateral loadings, whichever 
 produces the greater stress: (a) Structure unloaded, 50 
 Ib. per sq.ft. on the exposed surface of all trusses and the 
 floor as seen in elevation; or (b) Structure loaded, 
 bridges (of all classes) carrying highway traffic only, 30 
 Ib. per sq.ft. on the exposed surface of all trusses and 
 the floor as seen in elevation in addition to a uniform 
 
 [48 ] 
 
load of 150 Ib. per lin.ft. of structure applied on the 
 loaded chord; or (c) Structure loaded, bridges of all 
 classes carrying electric-railway traffic, the same loading 
 as under (b) except that the additional uniform load is 
 300 Ib. per lin.ft. of structure and is applied 7 ft. above 
 the base of rail. The minimum value of the pressure is 
 to be 250 Ib. per lin.ft. for the loaded and 150 Ib. for the 
 unloaded chord of the structure. 
 
 BOWSER Bowser, in a "Treatise on Eoofs and 
 Bridges," gives 30 Ib. per sq.ft. of exposed surface of both 
 trusses as the maximum wind load upon a highway bridge. 
 To estimate the 30-lb. pressure when the surface is not 
 known, he writes, "it is customary to use the following 
 rule : Take 150 Ib. per lin.ft. per truss, or 75 Ib. per lin. 
 ft. for each chord." 
 
 MEREIMAN In the earlier editions of Merriman's 
 work, "A Textbook on Eoofs and Bridges/' are found the 
 sentences : 
 
 For a highway bridge the surface exposed to wind action 
 is usually taken as double the side elevation of one truss. If 
 the area of this be not known, an approximation to its value 
 may be found by taking it as many square feet as there are 
 linear feet in the skeleton outline of the truss. 
 
 A number of the states, through highway commission- 
 ers or otherwise, have issued specifications for steel high- 
 way bridges. Some of them are incomplete and written 
 by men without a clear knowledge of the subject. Below 
 are given quotations from these and some other sources, 
 as to horizontal wind pressure. 
 
 COLORADO 300 Ib. per lin.ft. on the loaded chord and 
 150 Ib. per lin.ft. on the unloaded chord. 
 
 ILLINOIS Cooper's Specifications for Highway Bridges, 
 ed. of 1909, "except as hereinafter specified or as may be 
 specially indicated on the drawings." 
 
 MICHIGAN No mention made of wind loads but they may 
 be covered by the paragraph, "Any questions that may arise 
 as to the quality of material and labor shall be settled in 
 accordance with the provisions of Theodore Cooper's Specifi- 
 cations for Steel Highway Bridges, under Class B-l. 
 
 NEBRASKA 300 Ib. per lin.ft. on the loaded chord and 
 150 Ib. on the unloaded chord. 
 
 OHIO Same as the Cooper Specifications, ed. of 1909. 
 
 VIRGINIA 300 Ib. per lin.ft. on the loaded chord, 150 Ib. 
 of which is to be treated as a moving load, and 150 Ib. per 
 lin.ft. on the unloaded chord. 
 
 MASSACHUSETTS The Massachusetts Railroad Commis- 
 sion, George F. Swain, Consulting Engineer, specifies that, for 
 
 [ 49 ] 
 
bridges carrying electric railways "a lateral force of bO 11). per 
 sq.ft. on the unloaded structure, or of 30 Ib. per sq.ft. on the 
 loaded structure, shall be provided for. The surface of the un- 
 loaded structure shall, in the case of a truss, be taken as 
 twice the area of the vertical elevation of one truss, plus 
 that of the floor; and in the case of a girder, as IS times the 
 vertical surface. The surface of the loaded structure shall 
 be that of the unloaded structure plus a vertical surface 10 
 ft. in height and 50 ft. long, the pressure on which is to be 
 considered a moving load upon a car." 
 
 NEW YORK The Department of the State Engineer and 
 Surveyor of New York specifies: "The intensity of the wind 
 pressure shall be assumed at: First, 30 Ib. per sq.ft. on the 
 exposed surface of all railings, trusses, trestle posts, bracing 
 and the floor in addition to a load of 150 Ib. per lin.ft. applied 
 at 4 ft. above the floor line for all bridges which do not carry 
 electric cars, and 300 Ib. per lin.ft. applied 8 ft. above the 
 floor line for all bridges which do carry electric cars. Second, 
 50 Ib. per sq.ft. on all exposed surface of the unloaded struct- 
 ure. All parts shall be proportioned for that one of these 
 loads which gives the greater results, but in no case shall 
 the wind pressure be assumed at less than 100 Ib. per lin.ft. at 
 the unloaded chord, or less than 250 Ib. per lin.ft. at the 
 loaded chord. All wind loads shall be considered as moving- 
 loads." 
 
 PHILADELPHIA The Department of Public Works of the 
 City of Philadelphia specifies for its bridges a wind pressure 
 of 30 Ib. per sq.ft. against the side area of all trusses, railings, 
 and the end area of the floor construction. In no case is less 
 than 150 Ib. per lin.ft. to be used. In addition the system at- 
 tached to the floor is to carry a moving load of 150 Ib. per 
 lin.ft. of bridge. 
 
 HARRIMAN LINES A number of railway companies have 
 specifications for highway bridges attached to or a part of 
 their specifications for railroad bridges. The Harriman Lines 
 issue separate specifications for highway bridges in which the 
 wind pressure is taken: (a) On the loaded structure at 30 
 Ib. per sq.ft. on the exposed surface of all trusses and the 
 floor system as seen in elevation, together with a moving load 
 of 150 Ib. per lin.ft. of bridge, (b) On the unloaded struct- 
 ure at 50 Ib. per sq.ft. on the exposed surface taken as in (a). 
 
 U. S. ROADS The Office of Public Roads, U. S. Depart- 
 ment of Agriculture, issues "Typical Specifications for the 
 Fabrication and Erection of Steel Highway Bridges." The Di- 
 rector of the Office states that they are prepared "with the 
 view of furnishing a suitable guide for local highway offi- 
 cials in fixing requirements to which bridge structures must 
 conform." He further writes, "In the past many steel bridges 
 have been very poorly constructed, and it is believed that lack 
 of information on the part of highway officials concerning 
 proper specifications for this class of work has been in a large 
 measure responsible for the unsatisfactory results." It may be 
 remarked that unless the highway officials are reinforced by 
 competent engineers, the use of these specifications will not 
 prevent "unsatisfactory results." The wind loads assumed are 
 a load of 300 Ib. per lin.ft. on the loaded chord, one-half of 
 
 [50] 
 
this to be treated as moving, and 150 Ib. per lin.ft. on the un- 
 loaded chord. 
 
 ONTARIO The "General Specifications for Steel Highway 
 Bridges," of the Canadian province of Ontario are quite de- 
 tailed in their provisions for wind and lateral stresses. For 
 Class A (bridges suitable for main county roads) in spans of 
 200 ft. or less, a uniform load of 150 Ib. per lin.ft. per span is 
 used on the unloaded chord, and the same with the addition 
 of 150 Ib. per lin.ft. moving load on the loaded chord; for 
 spans exceeding 200 ft. the uniform load in each system is to 
 be increased 10 Ib. for each 30 ft. of span. For Class B 
 (bridges carrying light rural traffic), same as Class A. For 
 Class C (bridges for heavy traffic in towns and cities), for 
 spans of 200 ft. and less, a uniform load of 200 Ib. per lin.ft. 
 of span on the unloaded chord and a uniform load of 250 Ib. 
 per ft. in addition to a moving load of 250 Ib. per ft. on the 
 unloaded chord; for spans over 200 ft. the uniform load in 
 each system is to be increased 10 Ib. for every 30 ft. increase 
 of span. 
 
 TYRRELL Merriman & Jacoby in their enumeration of 
 noncontinuous bridges of 400-ft. span and over include 21 
 which are exclusively highway. Of these 21 the longest span 
 is that over the Miami River at Elizabethtown, Ohio (de- 
 stroyed by flood in March, 1913). This structure was pro- 
 portioned "for a wind load of 30 Ib. per sq.ft. acting on the 
 exposed surface of both trusses, and all bracing that is like- 
 wise exposed to wind pressure."* 
 
 UNIT-STEESSES 
 
 In the specifications mentioned, the values allowed for 
 stresses due to combined dead- and live-load and wind 
 are 20 to 30% greater than that allowed for combined 
 live- and dead-loads. The proviso is attached that the sec- 
 tion used must not be less than that required for the 
 combined dead- and live-loads. One exception is that 
 of the IT. S. Department of Agriculture: these specifica- 
 tions require that the wind stresses be proportioned with 
 the same values as other stresses without allowance for 
 any combination with other loads. This may not be in- 
 tended, but there is no doubt of the literal interpretation. 
 Another exception is the Waddell specifications, where in 
 highway bridges no reduction of working stress is allowed 
 for any combination of loads. Unless the structure car- 
 ries an electric railway, it is assumed that the live-load 
 and wind-load cannot act together, "for the reason that no 
 person would venture on the bridge when even one-half 
 of the assumed wind-pressure is acting." 
 
 *Tyrrell, The Elizabethtown Bridge. 
 
 [51] 
 
CONCLUSION 
 
 It will be seen from the above that the current require- 
 ments regarding lateral bracing vary greatly. A num- 
 ber of states have already legislated upon the subject of 
 highway bridges and others will soon follow. As far as 
 lateral bracing is concerned it might be well to divide 
 highway bridges into three classes, those which carry elec- 
 tric cars, those which carry heavy loads other than cars, 
 and ordinary country bridges. A different lateral load- 
 ing should be assigned to spans over 150 ft. than to those 
 under. It is better to state the wind pressure in pounds 
 per lineal foot of bridge rather than in pounds per square 
 foot of exposed surface, because contracts for highway 
 bridges are almost invariably let by competition, and if 
 wind loadings are given in pounds per lineal foot, the de- 
 signs of different bidders are on the same basis, which may 
 not be the case when given in pounds per square foot. 
 
 After a study of many specifications, the writer sug- 
 gests the following : 
 
 RECOMMENDED SPECIFICATIONS 
 
 For bridges carrying- electric-railway traffic the lateral 
 system shall be designed to resist a lateral force of 300 Ib. 
 per lin.ft. on the loaded chord and 150 Ib. per lin.ft. on the 
 unloaded chord, for spans of 150 ft. and under. An additional 
 allowance of 10 Ib. for every 30 ft. of span shall be made to 
 the loaded chord and 5 Ib. to the unloaded chord for spans 
 of more than 150 ft. 
 
 For bridges not carrying electric cars, but subject to heavy 
 loads such as auto-trucks, road rollers, and traction engines, 
 the lateral force shall be assumed at 250 Ib. per lin. ft. on the 
 loaded chord and 150 Ib. per lin.ft. on the unloaded chord, for 
 spans of 150 ft. and under. An additional allowance of 5 Ib. 
 for every 30 ft. of span shall be made to each chord for spans 
 of more than 150 ft. 
 
 Ordinary country bridges shall be designed for a lateral 
 force of 225 Ib. per lin.ft. on the loaded chord and 150 Ib. on 
 the unloaded chord with an additional force on the loaded 
 chord of 5 Ib. for every 30 ft. of span exceeding 150 ft. 
 
 All lateral loads are to be considered as moving loads. 
 
 In members subject to stresses from lateral forces alone 
 the unit-stresses may be increased 25% over those assumed 
 for live- and dead-loads. In bridges carying electric cars the 
 unit-stresses in chords and floor-beams for the stresses due to 
 lateral forces combined with those from the vertical forces 
 may be increased 25% over those assumed for dead- and live- 
 loads. If the track is on curve the centrifugal force shall be 
 added to the lateral live-load. For bridges not carrying elec- 
 tric traffic, unit-stresses of 50% increase may be used instead 
 of 25%. In no case shall the section be less than that re- 
 quired for the live- and dead-loads. 
 
 Provision shall be made for reversal of stress in any mem- 
 ber due to any combination of wind with other loads. The 
 end seats shall in all cases be firmly anchored against lateral 
 movement and uplift. In bridges in unusually exposed situa- 
 tions or at a great height above the water the amount of 
 anchorage shall be determined by calculation. 
 
 All details shall be designed to carry the stresses in the 
 main members. 
 
 [ 52 ] 
 
Wind-Bracing Requirements in 
 Municipal Building Codes 
 
 SYNOPSIS How 120 American cities specify 
 wind pressure for the design of buildings. Great 
 range of pressures and working stresses. Recom- 
 mendation that 20 Ib. per sq.ft., and for combined 
 stress 50% increase in working stress, be adopted 
 as standard. 
 
 The assumptions that are made for wind pressure and 
 working stresses due to wind loads play an important part 
 in the design of a many-storied hotel or office building. 
 These are seldom left to the judgment of the designer, 
 but are determined by the building code of the city in 
 which the building is located. 
 
 According to the census of 1910 there were in the 
 United States 50 cities each having a population over 
 100,000. The building codes of 45 of these cities, to- 
 gether with those of about 75 cities below 100,000, have 
 been examined with respect to their requirements for 
 wind bracing. The purpose of this article is to show 
 the wide variation in requirements in these codes, and to 
 make a plea that assumptions be made more nearly uni- 
 form. 
 
 The present Building Code of the City of New York, 
 affecting more building operations than that of any other 
 city on the continent, was adopted in 1899. The Board 
 of Aldermen passed a new code in 1909, after extended 
 discussion and bitter controversy, but the Mayor vetoed 
 it. The present code is archaic in some of its provisions 
 and is inadequate for present needs. It has been used 
 as the basis for the codes of a host of other cities. Some- 
 times it has been copied with but little change, and in 
 other cases some sections have been modified or rejected. 
 
 Regarding wind pressure the New York code requires 
 that all structures exposed to the wind (except those 
 
 [53] 
 
under 100 ft. in height in which the height does not ex- 
 ceed four times the average width of the base) be designed 
 to resist a horizontal wind pressure of 30 Ib. in any di- 
 rection for every square foot of surface exposed from the 
 ground to the top, including the roof. Regarding unit- 
 stresses the code reads : 
 
 In calculations for wind bracing, the working stresses set 
 forth in this code may be increased by 50%. 
 
 This sentence is ambiguous as it does not state whether 
 the high unit-stress is applicable to the combined stresses 
 due to wind and other loads or whether it is to be used 
 for the wind stress only. There is considerable differ- 
 ence between the two interpretations as to the amount of 
 material required in bracing a high and narrow building. 
 The Chicago code removes all doubt by specifying: 
 
 For stresses produced by wind forces combined with those 
 from live- and dead-load, the unit-stress may be increased 
 50% over those given above; but the section shall not be 
 less than that required if wind forces be neglected. 
 
 It may be said that the practice in New York and else- 
 where is to interpret the 50% as applying to combined 
 stresses. 
 
 Another sentence in the New York code reads : 
 
 In all structures exposed to wind, if the resisting moments 
 of the ordinary materials of construction, such as masonry, 
 partitions, floors and connections, are not sufficient to resist 
 the moment of distortion due to wind pressure, taken in any 
 direction on any part of the structure, additional bracing 
 shall be introduced sufficient to make up the difference in 
 the moments. 
 
 Good practice does not permit and it is not common 
 to carry the wind stresses in steel buildings either in whole 
 or in part to the ground by walls or partitions. The 
 Bridgeport code has a clause which should be followed, 
 reading : 
 
 In buildings of skeleton construction the frame must be 
 designed to resist this wind pressure. 
 
 Manchester, Albany, Utica, Jersey City, Paterson, Terre 
 Haute, Kalamazoo, Milwaukee, St. Paul, Minneapolis, 
 Louisville, Tampa, Atlanta, Dallas and Tacoma all fol- 
 low the New York code regarding wind bracing except 
 for an occasional variation for buildings under 100 ft. 
 in height. 
 
 [54] 
 
In Philadelphia a pressure of not less than 30 Ib. per 
 sq.ft. is called for on all buildings erected in open spaces 
 or on wharves. On tall buildings erected in built-up 
 districts the wind pressure is not to be figured for less 
 than 25 Ib. at tenth story, 2y 2 Ib. I GSS on each succeeding 
 lower story, and 2% Ib. additional on each succeeding 
 upper story to a maximum of 35 Ib. at the fourteenth 
 story and above. In proportioning members subject to 
 stresses due to wind loads the working stresses may be 
 increased 30%. In Washington buildings are practically 
 limited to twelve stories in height. The prescribed wind 
 pressure is the same as in Philadelphia, but no mention 
 is made of any increase of working stresses. Lowell, 
 Bridgeport, Baltimore, Buffalo and Sioux City assume 
 wind pressure at 30 Ib. per sq.ft. and are also silent on 
 the subject of working stresses being increased. 
 
 Pittsburgh calls for 25 Ib., Detroit and Jacksonville 
 30 Ib. per sq.ft. wind pressure, and each allows the work- 
 ing stresses to be increased 25%. 
 
 Cincinnati requires provision to be made for a pressure 
 of 20 Ib. per sq.ft. for the surface exposed above surround- 
 ing buildings; working stresses may be increased 25%. 
 St. Louis assumes a pressure of 30 Ib. per sq.ft. and al- 
 lows an increase of 20% to working stresses. The St. 
 Louis code has this provision : 
 
 "Where there are buildings immediately adjoining, the wall 
 surface covered by such buildings will be considered as not 
 exposed to wind pressure. 
 
 The question might be asked concerning buildings in 
 Cincinnati and St. Louis as to what would take the wind 
 pressure if the surrounding buildings were removed. 
 
 Chicago, San Francisco, Covington and Akron call for 
 20 Ib. per sq.ft. wind pressure. An increase of 50% to 
 the working stresses is allowed in Chicago and San Fran- 
 cisco, 25% in Covington and none in Akron. 
 
 Poughkeepsie, Evansville and Chattanooga call for 30 
 Ib. per sq.ft. horizontal wind pressure, and state as follows : 
 
 The additional loads caused by the wind pressure upon 
 beams, girders, walls and columns must be determined by 
 calculation and added to other loads for such members. 
 Special bracing shall be employed wherever necessary to 
 resist the distorting effect of the wind pressure. 
 
 [ 55 ] 
 
No mention is made of higher unit-stresses for wind 
 loads. 
 
 Syracuse, Erie, Cleveland, Duluth, Denver, Macon, 
 Birmingham and Portland (Oregon) for all buildings 
 whose heights exceed 1% times the width of the base fol- 
 low the wind pressures given in the Philadelphia code. 
 The Syracuse code alone allows an increase of working 
 stresses 25%. Each code has this provision: 
 
 Every panel in a curtain wall shall be proportioned to re- 
 sist a wind pressure of 30 Ib. per sq.ft. 
 
 The code of Grand Rapids copies the Schneider "Spe- 
 cifications for Structural Work of Buildings." The wind 
 pressure is assumed as acting horizontally in any direc- 
 tion, as follows: 
 
 First At 20 Ib. per sq.ft. on the sides and ends of buildings 
 and on the actual exposed surface, or the vertical projection 
 of roofs. 
 
 Second At 30 Ib. per sq.ft. on the total exposed surfaces 
 of all parts composing the metal framework. The framework 
 shall be considered an independent structure, without walls, 
 partitions or floors. 
 
 For bracing and the combined stresses due to wind and 
 other loading, the permissible working stresses may be 
 increased 25%, or to 20,000 Ib. for direct compression or tension. 
 
 The code of Memphis has the same provisions though 
 differently worded. 
 
 The code of Oakland is unusually explicit in the treat- 
 ment of wind bracing. For buildings of Class A over 
 100 ft. high, or where the height exceeds three times the 
 least horizontal dimension, or for buildings of Class B 
 over 80 ft. high where the height exceeds two times the 
 least horizontal dimension, it provides : 
 
 The steel frame shall be designed to resist a wind force of 
 30 Ib. per sq.ft. acting in any direction upon the entire 
 exposed surface. All exterior wall girders shall have knee- 
 brace connections to columns. Provision shall be made for 
 diagonal, portal or kneebracing to resist wind stresses, and 
 such bracing shall be continuous from top story to and 
 including basement. 
 
 An increase of 50% above the allowed dead- and live-load 
 stress shall be used for wind stress. Columns subjected to 
 cross-bending by wind or eccentric loading shall have addi- 
 tional area to provide for the stresses, the eccentric loading 
 being calculated as dead-load and the wind provided above. 
 The area of metal thus obtained for wind, cross-bending and 
 eccentric loading shall be added to the area provided for 
 dead- and live-load to obtain the total metal in column. 
 
 [ 56 ] 
 
In the case of reinforced-concrete buildings where pro- 
 vision must be made for wind pressure, there is this pro- 
 vision : 
 
 The reinforcing rods of columns shall be connected by 
 threading the rods and by threaded sleeve nuts or threaded 
 turnbuckles, or methods equally effective and satisfactory to 
 the Bridge Inspector. 
 
 In Salt Lake City for buildings over 102 ft. high, or 
 where the height exceeds three times the least horizontal 
 dimension, "the steel frame shall be designed to resist a 
 wind force of 20 Ib. per sq.ft. in any direction upon 
 the entire exposed surface." As in Oakland, it is re- 
 quired that the exterior wall girders shall have knee- 
 brace connections to the columns and that diagonal, por- 
 tal or kneebracing to resist wind pressure shall be used 
 from the top story to and including basement. Unlike 
 Oakland no increase of working stresses for wind loads 
 is mentioned. 
 
 The code of Waltham, Mass., has the provision : 
 
 All buildings exposed to the wind shall be calculated to re- 
 sist a pressure on either side so exposed, and upon the roof, if 
 pitched, amounting to 10 Ib. per sq.ft. of vertical projection 
 of roof between the ground and a height of 40 ft. above 
 the ground, a pressure of 15 Ib. per sq.ft. on parts between 
 40 and 60 ft. above the ground, and 20 Ib. per sq.ft. on parts 
 60 ft. above the ground. 
 
 No increased working stresses for wind are mentioned. 
 
 The code of Columbus, Ohio, adopted ten years ago, 
 reads the same on wind pressure as the New York code 
 except that working stresses may be increased 25% 
 instead of 50%. There is added the sentence: 
 
 In buildings constructed of structural steel the wind pres- 
 sure shall be allowed for as follows: Ten Ib. per sq.ft. of ex- 
 posed surface for buildings 20 ft. or less to the eaves; 20 Ib. 
 per sq.ft. of exposed surface for buildings 60 ft. to the eaves; 
 30 Ib. per sq.ft. of exposed surface for buildings over 60 ft. 
 to the eaves. 
 
 The codes of Boston, Cambridge, Haverhill and New 
 Orleans have the sentence: "Provision for wind bracing 
 shall be made wherever it is necessary." This is indefin- 
 ite and tends to put a premium on ignorance. If all 
 designers were experts there would still be enough differ- 
 ence of opinion as to the amount of wind bracing neces- 
 sary. But a design with little or no wind bracing is 
 also entitled to consideration if the maker gives assur- 
 
 [ 67 ] 
 
ance that he is furnishing bracing "wherever it is neces- 
 sary." The same might be said concerning the codes of 
 New Haven, Providence, Worcester, Springfield, Wheel- 
 ing, Youngstown, Toledo, Omaha, Lincoln, Montgomery, 
 Fort Worth, Los Angeles and others, which while giving 
 loads and stresses for structural steel generally say noth- 
 ing on the subject of wind pressure. Indianapolis and 
 Seattle allow an increase of 50% to the working stresses 
 but do not state the amount of pressure. 
 
 The codes of Fall Eiver, Pawtucket, Elizabeth, Allen- 
 town, Altoona, Fort Wayne, Dubuque and Topeka are 
 very meager or altogether silent on the whole subject of 
 loads, stresses, and structural steel. 
 
 Codes often contain blanket clauses which might be 
 used to cover a wide range of omissions thus, Cleveland, 
 Duluth, Little Eock, Fort Worth and others say: 
 
 The allowable factor or units of safety or the dimensions 
 of each piece or combination of materials required in a 
 building- or structure, if not given in this ordinance, shall 
 be ascertained by computation according to the rules pre- 
 scribed by the modern standard authorities on strength of 
 material, applied mechanics and engineering practice. 
 
 Erie, Pa., has the sentence: "In general all stresses 
 shall be figured in accordance with the standard speci- 
 fications of the American Society of Civil Engineers." 
 
 The New Haven code reads : 
 
 The dimensions of each piece or combination of materials 
 required shall be ascertained by computation according to the 
 rules and data given in Haswell's Mechanics' and Engineers' 
 Pocket Book, Trautwine's Engineers' Pocket Book, or Kid- 
 der's Architects' and Builders' Pocket Book, except ad may 
 be otherwise provided in this title. Stresses for materials 
 and forms of same not herein mentioned shall be those 
 determined by the best modern practice. 
 
 The last code from which quotations will be made is 
 that of the largest city in the world. The London Coun- 
 ty Council (General Powers) Act, 1909, in Section 22, 
 "Provisions with respect to Buildings of Iron and Steel 
 Skeleton Construction," requires: 
 
 All buildings shall be so designed as to resist safely a wind 
 pressure in any horizontal direction of not less than 30 Ib. 
 per sq.ft. of the upper two-thirds of the surface of such 
 buildings exposed to wind pressure. 
 
 Working stresses exceeding those specified "by not more 
 [ 58 ] 
 
than 25% may be allowed in cases in which such excess 
 is due to stresses induced by wind pressure." 
 
 CONCLUSION 
 
 It might seem from the foregoing that our American 
 municipalities have exhausted the combinations of wind 
 pressure and wind stress that can be made. The fact 
 that one code differs from another is not in itself a cause 
 for criticism, but a code is decidedly at fault when it 
 contains absurd or needless requirements or when its 
 requirements are not clearly expressed. To assume wind 
 pressure over a large area at 30 Ib. per sq.ft. and then 
 to add the sectional area necessary to resist wind stresses 
 to that required for live- and dead-loads is needless. 
 Where this is specified in a code it is evaded in practice. 
 It would be far better to make rational assumptions and 
 insist on a rigid adherence to them, than to insert in a 
 code improbable loadings or working stresses that will 
 be ignored in actual construction. 
 
 That the need of revision in our building codes is be- 
 ing felt by the public is evidenced by the number now 
 being revised. Although our knowledge of wind action 
 is limited we should be able to come nearer to a common 
 ground of requirement for wind bracing than we have at 
 present. As a basis for uniformity the writer suggests 
 the building ordinances of Chicago. The paragraph on 
 Wind Eesistance reads : 
 
 All buildings shall be designed to resist a horizontal wind 
 pressure of 20 Ib. per sq.ft. for every square foot of exposed 
 surface. In no case shall the overturning moment due to 
 wind pressure exceed 75% of the moment of stability of the 
 building due to the dead load only. 
 
 The paragraph relating to Wind Stress, previously 
 quoted, reads: 
 
 For stress produced by wind forces combined with those 
 from live- and dead-loads, the unit-stress may be increased 
 50% over those given above; but the section shall not be 
 less than required if wind forces be neglected. 
 
 [59] 
 
VI 
 
 Windbracing Without Diag- 
 onals for Steel-Frame 
 Office-Buildings 
 
 SYNOPSIS Exact elastic analysis of rigid 
 square-panel tier-building frames being impossible 
 in practice, approximate methods based on certain 
 arbitrary assumptions are used. The first summar- 
 ized statement of these methods was given by the 
 author in ENGINEERING NEWS, Mar. 13, 1913. The 
 present article an enlarged revision of that arti- 
 cle gives four methods, and compares their re- 
 sults for a specific example. Method II-A of this 
 article has been added, and the treatment of the 
 other three revised and corrected. 
 
 If an apology is needed for adding to the literature of 
 the above subject, it may be found in the fact that many 
 of the methods given in technical papers for determining 
 stresses due to wind loadings are not workable. That 
 is, the average engineer to whom falls the lot of designing 
 the average office-building has neither the time nor 
 the ability to handle the cumbersome equations involved. 
 One paper published a few years ago and now before 
 the writer has for its purpose "to develop the exact theory 
 of framework with rectangular panels, and then to sug- 
 gest such short-cuts as may be of use in actual designing/' 
 This is an elaborate paper in which the theorem of four 
 moments is used. A bent of two unequal bays, three col- 
 umns and two girders, is considered and by the "short- 
 cuts" seven equations are found from which the values 
 of all the moments for the floor in question may be found. 
 Whatever may be the merit of this and similar papers, 
 it has not been recognized sufficiently to be followed to 
 any appreciable extent. It is to be regretted that the 
 treatment of the subject in our textbooks is not more 
 complete and adequate. 
 
 [61] 
 
Buildings like the Trinity, the Fuller, the Singer, the 
 Woolworth, or the Metropolitan Tower, in New York 
 City, are each in a class by itself, and of necessity care- 
 ful study is given to the windbracing. For another and 
 a large class of office-buildings, little or no attention is 
 given to the matter of bracing for wind, either in the 
 proportioning of main members or in details. 
 
 Without further introduction the writer gives four 
 methods in current use of calculating wind stresses and 
 moments in office-buildings where diagonals are not per- 
 missible. Bach method has its own advocates. 
 
 Considering a single bent: It will be assumed that all 
 columns in any given story have the same sectional area 
 and the same section modulus, that all girders of the same 
 floor have the same section modulus, and that the joints 
 are perfectly rigid. It is obvious that if the forces in 
 the several members of the frame are small in relation 
 to the stiffness of the members, the longitudinal distor- 
 tions may be neglected; hence the adjacent joints oc- 
 cupying the corners of a rectangle will after distortion 
 occupy the corners of an oblique parallelogram. 
 
 It is assumed that the point of contraflexure of each 
 column is at midheight of the story. The first method 
 described further involves the tacit assumption that the 
 girders have their points of contraflexure at midlength. 
 Specific assumptions as to the distribution of column 
 shears and direct stresses are made in the several methods. 
 In only one of the four methods are the assumptions 
 strictly consistent. For example, in Method I the as- 
 sumption as to location of points of contraflexure would 
 make the distorted shape of panel constant in any given 
 story, and from this would follow that the column shears 
 must be equal; but the calculation gives column shears 
 of different amount. 
 
 The resistance to overturning will cause a direct stress 
 in tension on the windward side of the neutral axis, taken 
 by all or some of the columns on that side according to 
 the method used, and a direct stress in compression on 
 the leeward side taken by the columns on that side. 
 
 Figs. 1, 7, 9, and 12, give results obtained from calcu- 
 lations according to Methods I, II, II-A and III respec- 
 
 [63] 
 
tively. Loads and stresses are given in thousands of 
 pounds and bending moments in thousands of foot- 
 pounds. Direct stresses are given in parentheses (). 
 
 METHOD I 
 
 This may be called the Cantilever Method and is 
 a restatement with some modifications of an arti- 
 
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 isr j FLOOR _ 
 
 METHOD I tn eW 
 
 FIG. 1. EECTANGULAR BUILDING-FRAME: DIRECT AND 
 
 BENDING STRESSES CALCULATED BY APPROXIMATE 
 
 METHOD I 
 
 144.0 = Moment of 144,000 ft.-lb. 
 (4.0) = Direct stress of 4000 Ib. 
 
 [63 ] 
 
cle entitled "Windbracing with Kneebraces or Gus- 
 set-plates," by A. C. Wilson, in The Engineering Record, 
 Sept. 5, 1908. A section or bent of the building is con- 
 sidered similar to a beam loaded as a cantilever. 
 
 If a beam of rectangular section be loaded as a cantilever 
 with concentrated loads, it is possible by the theory of flexure 
 to find the internal stresses at any point. If, however, rec- 
 tangles be cut out of the beam between the loads, there will 
 then be a different condition of stress. What was the hori- 
 zontal shear of the beam will now be a shear at the point of 
 the contraflexure of the floor girders, causing bending, and, 
 as in the beam, the nearer the neutral axis the greater the 
 shear. The vertical shear in the beam would be taken up by 
 the columns as a shear at the points of contraflexure and the 
 amount of this shear taken by each column would, as in the 
 beam, increase toward the neutral axis. The direct stresses 
 of tension or compression in the beam would act on the col- 
 umns as a direct load of either tension or compression, and 
 as in the beam would decrease toward the neutral axis. 
 
 Each intersection of column with floor girders would be 
 held in equilibrium by forces acting at the points of contra- 
 flexure; and to find all the forces acting around a joint at any 
 floor the bending moments of the building at the points of 
 contraflexure of the columns above and below the floor in 
 question are found as will be explained later, 
 
 It is assumed that if a beam of constant, symmetrical 
 cross-section and homogeneous material is fixed at both ends, 
 and that if forces tend to move those ends from a position 
 in the same straight line to a position to one side with the 
 ends still parallel, reversed bending will occur with the point 
 of contraflexure in the center of the unsupported span. And 
 since this condition exists in all columns and floor girders 
 it will be necessary to find the shears at the points of con- 
 traflexure as well as the direct stresses in all members. 
 
 4 ; 7 "FLOOR 
 
 6000 
 
 6V FLOOR 
 
 5VFLOOR 
 t. \ 
 
 METHOD I 
 
 FIG. 2. COLUMN SHEARS AND GIRDER MOVEMENTS 
 
 AT SIXTH FLOOR, CALCULATED BY 
 
 METHOD I 
 
 Fig. 1 gives stresses and maximum moments in all 
 members of a section of the building in accordance with 
 the above statement. 
 
 [ 64] 
 
The calculation of stresses and bending moments in 
 members about the sixth floor will be given in detail. The 
 direct stress in any column is assumed to be proportional 
 to its distance from the neutral axis of the cross-section 
 of the building. In the cross-section considered, the 
 neutral axis coincides with the center line of the build- 
 ing. The total moment of the wind loads above the 
 sixth floor about the line of inflection of the sixth-story 
 columns must equal the moment of the direct stresses in 
 these columns about the neutral axis. Let SX be the 
 direct stress in each of the sixth-story columns B and C, 
 then 24X will be the direct stress in each of the sixth- 
 story columns A and D. Hence we have 
 
 (4000 X 30) + (6000 X 18) + (6000 X 6) = 
 (24X X 24) + (SX X 8) + (8Z X 8) 
 
 + (24X X 24) 
 From which SX = 1650 and 24X = 4950. 
 
 In the same way for the fifth-story columns we have 
 the equation 
 
 (4000 X 42) + [6000 X (30 + 18 + 6)] = 
 
 [(24X X 24) + (SX X 8)] X 2 
 
 From which 8Z == 3075, the direct stress in the fifth- 
 story columns B and (7; and 24JT = 9225, the direct 
 stress in the fifth-story columns A and D. 
 
 The total horizontal shear on any line across the build- 
 ing is the sum of the wind loads above that line. The 
 shear taken by any column in any story is proportional to 
 the total horizontal shear in that story. 
 
 In Fig. 2, if X = shear of any fifth-story column at 
 
 1 * f\r\f\ Q 
 
 its point of inflection, then ' n X or ^ X = shear at 
 
 point of inflection of the sixth-story length of the same 
 
 6,000 T- 3 
 
 column, and ^-7^7: X 01 ~^ X = increment of shear 
 
 11 
 
 taken by the column at the floor girder. 
 
 We are now ready to consider the forces about the first 
 joint, or the intersection of Col. A with the sixth-floor 
 girder, sketched separately as Fig. 3. 
 
 The difference between 9225 and 4950 = 4275 is 
 taken up as a shear in the floor girder between Cols. 
 A and B. The moments of the shears must hold the 
 
 [ 65 ] 
 
joint in equilibrium. Taking moments about the lower 
 point of inflection we have 
 
 (A ^ X 12) + ( T 3 T X X 6) = 4275 X 8 
 from which X = 3300, T 8 T X = 2400 and T 8 T X = 900. 
 The bending moment M for the floor girder is 4275 X 8 
 = 34,200 ft.-lb. The bending moment for the fifth- 
 story column is 3300 X 6 = 19,800 ft.-lb., and that for 
 the sixth-story column is 2400 X 6 = 14,400 ft.-lb. The 
 direct thrust on the floor girder is 6000 900 = 5100. 
 Proceeding to the second joint, sketched in Fig. 4 : The 
 difference between 3075 and 1650 = 1425 acts as a 
 shear in the girder between Cols. B and C. This added to 
 the 4275 shear continued from the girder between A and 
 B makes a total shear of 5700 in the girder. The equa- 
 tion of moments is 
 
 (A X X 12) + (A X X 6) = (4275 X 8) + (5700 X 8) 
 From which X = 7700; T 8 T 3T = 5600, and T 8 T X = 
 
 5100*" 
 
 FIG.3 
 
 FIG.-4 
 
 3000 
 
 6V FLOOR A (*900) 
 
 3000-j* 900 
 
 FI6. 5 
 
 FIG. 6 
 
 FIGS. 3-6. SIXTH-FLOOR JOINTS OF BUILDING-FRAME, 
 WITH STRESSES CORRESPONDING TO METHOD I 
 
2100, are the shears taken by Col. B to hold the joint 
 in equilibrium. 
 
 The bending moment M 2 of the girder from A to B at 
 Col. B is the same as at Col. A with an opposite sign; 
 M s , of the girder from B to C, is 5700 X 8 = 45,600 
 ft.-lb. The bending moment of the fifth-story column is 
 7700 X 6 = 46,200 ft.-lb., and that of the sixth-story 
 column is 5600 X 6 = 33,600 ft.-lb. The direct thrust 
 on the girder between B and C is 5100 2100 = 3000. 
 
 At the third joint, Fig. 5, the shear taken by the 
 girder between C and D is 5700 (3075 1650) = 
 4275. From the equation of moments 
 (A X X 12) + ( T \ X X 6) = (5700 X 8) + (4275 X 8) 
 whence 
 
 X = 7700, ^ X = 5600, ^ X = 2100 
 As expected, the moments in Col. C are numerically equal 
 to those in Col. B, and the girder moments M 4 = M & , 
 and M 5 = M 2 . The compression in the floor girder 
 between C and D is 3000 2100 = 900. 
 
 At the fourth joint, Fig. 6, we have 
 
 ( T \ X X 12) + (A X X 6) = (4275 X 8) 
 the same equation as at the first joint, and hence the same 
 numerical values for moments and shears. 
 
 The designer in following this method for the various 
 floors will find many short-cuts. A relationship between 
 the floors can soon be established. If the distances between 
 columns are not even spaces, or the columns have differ- 
 ent sectional areas, the direct stresses vary both in pro- 
 portion to their distances from the neutral axis and their 
 sectional areas. It will be necessary to first find the 
 neutral axis of the cross-section in question and then the 
 direct stresses. With these the shears and bending me 
 ments can be obtained. 
 
 METHOD II 
 
 This may be called the Method of Equal Shears. It is 
 assumed that the horizontal shear on any plane is equally 
 distributed among the columns cut by that plane. The 
 stresses and maximum bending moments for a cross-sec- 
 tion of the building are as given in Fig. 7. 
 
 [ 67 ] 
 
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 METHOO H 
 
 FIG. 7. RECTANGULAR BUILDING-FRAME: DIRECT AND 
 
 BENDING STRESSES CALCULATED BY APPROXIMATE 
 
 METHOD II 
 
 120.0 = Bending moment of 120,000 ft.-lb. 
 (4.0) = Direct stress of 4000 Ib. 
 
 Taking any aisle we find the direct stress in the fifth- 
 
 X 42' 
 
 story columns to be 
 
 \ + (^,X 30\ 
 
 pf9 X 6) 
 
 16 . 10,^50 
 
 The direct stresses coming upon any interior column 
 [68] 
 
from the adjacent aisles are equal in amount but op- 
 posite in direction. Hence their algebraic sum is zero 
 
 i i 
 
 B C 
 
 METHOD H 
 
 FIG. 8. COLUMN-SHEARS AND GIRDER MOMENTS AT 
 SIXTH FLOOR, CALCULATED BY METHOD II 
 
 and only the outside columns have direct stresses. This 
 may be found directly for any story, say the sixth, 
 (4000 X 30) + (6000 X 18) + (6000 X 6) 
 divided by 48 = 5500 
 
 Considering in detail, as in Method I, the sixth floor, 
 we have in Fig. 8 the direct stresses and shears in the 
 columns. 
 
 The shear in each girder is 10,250 - - 5500 = 4750. 
 The equations for bending moments in the girders can 
 be written as follows : 
 
 M, = [(4000 X6)X (5500X6) 
 M 3 = [(4000 X6) +(5500 X6) 
 M 3 = [2(4000 X6) +(5500 X6) 
 M 4 = [2(4000X6) +(5500X6) 
 M 5 = [3(4000 X6) +(5500 X6) 
 M 6 = [3(4000 X6) +(5500 X6) 
 
 [(10,2505500) X16 
 [(10,2505500) X16 
 [(10,2505500) X32 
 [(10,2505500) X32 
 [(10,2505500) X48 
 
 = +57,000 ft.-lb. 
 = 19,000 ft.-lb. 
 = +38,000 ft.-lb. 
 
 38,000 ft.-lb. 
 
 = +19,000 ft.-lb. 
 = 57,000 ft.-lb. 
 
 The bending moment at the sixth-floor girder of each 
 sixth-story column is 4000 X 6 = 24,000 ft.-lb., and of 
 each fifth-story column is 5500 X 6 = 33,000 ft.-lb. 
 
 The compression in the floor girders is 6000 1500 = 
 4500 between Cols. A and 5, 4500 1500 = 3000 be- 
 tween B and C, and 3000 1500 = 1500 between C 
 and D. General equations can easily be deduced which 
 will simplify the calculation of stresses and moments for 
 other floors. If the spaces between columns are unequal, 
 the direct stresses from adjacent aisles will be unequal. 
 This difference is a direct stress in the column between 
 the two aisles considered. If the columns have differ- 
 
 [69] 
 
ent sectional areas, the horizontal shear taken by each 
 column will be in proportion to its moment of inertia. 
 
 METHOD II-A 
 This is a special case of Method II and may be called 
 
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 (3.^ 
 
 (1.0) 
 
 1 
 
 fc 
 
 1 
 
 ^ 
 
 > 
 
 ^ 
 
 26.0 
 
 26.0 
 
 26.0 
 
 (5.0) 
 58.0 
 
 (2.0) 
 
 58.0 
 
 (1.0) 
 
 58.0 
 
 (5.0) 
 
 p.o) 
 
 d.o) 
 
 I 
 
 
 
 1 
 
 S 
 
 >- 
 
 50.0 
 
 500 
 
 50.0 
 
 (5.0) 
 
 (5.0) 
 
 d.o) 
 
 s 
 
 * 
 
 1 
 
 1 
 
 > 
 
 62.0 
 
 6^ 
 
 6^.^7 
 
 (5.0) 
 
 '^ 
 
 Q.o) 
 
 >- 
 
 74.0 
 
 74.0 
 
 74.0 
 
 (5.0) 
 
 (3-0) 
 
 d.o) 
 
 1 
 
 a 
 
 1 
 
 *3 
 
 
 /^.<? 
 
 /^^.^ 
 
 120.0 
 
 ^.(57; 
 
 C4w; 
 
 0.55) 
 
 " 
 
 ^ 
 
 
 
 % 
 
 
 <- /6' -> 
 
 
 < /6' > 
 
 8 T -"FLOOR 
 
 ^ ^ FLOOR 
 
 y 
 
 __. 
 
 y 
 
 ^ FLOOR 
 
 7 -* FLOOR 
 
 v 4^ FLOOR 
 
 A~~ 
 
 Y 3^ FLOOR 
 
 v ^ FLOOR 
 ^ ^ 
 
 t . is FLOOR 
 
 METHOD Z-A 
 
 FIG. 9. EECTANGULAK BUILDING-FEAME : DIRECT AND 
 BENDING STRESSES CALCULATED BY APPROXI- 
 MATE METHOD II A 
 
 120.0 = Bending moment of 120,000 ft.-lb. 
 (4.0) = Direct stress of 4000 Ib. 
 
 [70] 
 
the Portal Method. The structure is regarded as equiva- 
 lent to a series of independent portals. The total hori- 
 zontal shear on any plane is divided by the number of 
 aisles instead of by the number of columns as in II. An 
 outer column thus takes but one-half the shear of an in- 
 terior column. The stresses and maximum bending mo- 
 ments for a cross-section of the building are as given in 
 Fig. 9. 
 
 For equal spacing the direct or vertical axial stress due 
 to the overturning moment of the wind is all taken by the 
 outside columns and is the same in amount as in 
 Method II. 
 
 Considering in detail the sixth floor, we have in Fig. 10 
 the direct stresses and shears in the columns. 
 
 1^ FLOOR 
 
 16000^ 
 6000^ 
 
 7,333 
 
 5333 
 
 333 
 
 667 
 6 r *FLOOR 
 
 $,667 
 
 r SV FLOOR 
 
 A B <_ 
 
 METHOD 3-A 
 
 FIG. 10. COLUMN-SHEARS AND GIRDER MOMENTS AT 
 SIXTH FLOOR, CALCULATED BY METHOD II-A 
 
 The shear in each girder is 10,250 -- 5500 = 4750. 
 The equations for bending moments in the girders are as 
 follows : 
 
 M t = [(2,667 X 6) 4- (3,667 X 6)] = 438,000 
 
 M, = [(2,667 X 6) 4 (3,667 X 6) (10,250 5,500) X 16] = 38,000 
 M, = [(2,667 X 6) 4 (3,667 X 6) 4 ( 5,333 X 6) + (7,333 X 6) 
 
 (10,250 5,500) x 16] = 4 38,000 
 M 4 = [(2,667 X 6) + (3,667 X 6) + ( 5,333 X 6) 4 (7,333 X 6) 
 
 (10,250 5,500) X 32] = 38,000 
 M, = [(2,667 X 6) 4 (3,667 X 6) 4 2( 5,333 X 6) 4- 2(7,333 X 6) 
 
 (10,250 5,500) X 321 = 4 38,000 
 M 6 = 1(2,667 X 6) 4 (3,667 X 6) + 2( 5,333 X 6) 4 2(7,333 X 6) 
 
 (10,250 5,500) X 481 = 38.COO 
 
 The bending moment at the sixth-floor girder of each 
 outer sixth-story column is 2667 X 6 = 16,000 ft.-lb., 
 and of each inner sixth-story column is 5333 X 6 = 
 32,000 ft.-lb. At the fifth-floor girder the bending mo- 
 ment of each fifth-story outer column is 3667 X 6 = 
 22,000 ft.-lb. and of each fifth-story inner column is 7333 
 X 6 = 44,000 ft.-lb. 
 
 [71] 
 
The compression in the floor girders is 6000 1000 = 
 5000 between Cols. A and B, 5000 2000 = 3000 be- 
 tween B and C, and 3000 2000 = 1000 between C 
 and D. 
 
 H H 
 
 FIG. 11. CROSS-SECTION OF COLUMNS IN TRANSVERSE 
 
 BENT 
 
 It is noted from the above that the bending moment in 
 an outer column is one-half that in an interior column; 
 that the point of contraflexure of each girder is at its 
 center; and the bending moments due to wind for all 
 girders of any transverse bent on the same floor are alike. 
 This is an ideal condition for the detailer and the shop. 
 The designer finds this method very simple and his work 
 easily checked. The bending moment in a girder is the 
 mean between the bending moments in the interior col- 
 umn above and below the girder. The width of the aisle 
 does not affect the value of the bending moment.* 
 
 Methods I and II-A are specially adapted to transverse 
 bents when the columns are turned as in Fig. 11; also 
 when the outer columns carry floor loads only and the 
 stresses are but one-half those of the inner columns. 
 
 METHOD III 
 
 This may be called the Continuous Portal Method. The 
 direct stresses in the columns are assumed to vary as 
 their distances from the neutral axis, and the horizontal 
 shear on any plane is equally distributed among the 
 columns cut by that plane. Stresses and maximum bend- 
 ing moments for a cross-section of the building are as 
 given in Fig. 12. 
 
 The direct stresses in the columns are found the same 
 way and are the same in amount as in Method I. 
 
 *Burt, "Steel Construction" Section, Wind Bracing. 
 
Considering in detail the sixth floor, we have in Fig. 
 13 the direct stresses and shears in the columns. The 
 shear in the girder A to B and the girder C to D is 9225 
 4950 = 4275. The shear in the girder B to C is 
 (9225 4950) + (3075 1650) = 5700. 
 
 4.0 
 
 6.0 
 
 6.0' 
 
 6.0 
 
 6.0 
 
 6.0 
 
 6.0- 
 
 8.0' 
 
 6.0 
 
 48 
 
 6.0 
 
 
 (3.0) 
 
 
 (2.0) 
 
 
 M 
 
 5f 
 
 
 ^f\ 
 
 
 q 
 
 o 
 
 | 
 
 
 
 
 
 o 
 
 ^O 
 
 
 21.0 
 
 
 16.8 
 
 
 zt.o 
 
 
 (4.5) 
 
 
 (3.0) 
 
 
 (1.5) 
 
 s 
 
 
 
 
 
 Q 
 
 uj 
 
 
 39.0 
 
 
 3I.Z 
 
 
 390 
 
 
 (4.5) 
 
 
 (3.0) 
 
 
 (l.5) 
 
 ? 
 
 
 1 
 
 
 s 
 
 
 
 
 57.0 
 
 
 45.6 
 
 
 57.O 
 
 
 75.0 
 
 (3.0) 
 
 
 (1.5) 
 
 s 
 
 
 
 
 ^ 
 
 O 
 
 K 
 
 
 600 
 
 
 75O 
 
 
 (45) 
 
 
 
 
 (f.5) 
 
 "^ 
 
 
 ^ S 
 
 6 
 
 V 
 
 
 
 <VJ 
 
 
 93.0 
 
 
 93.0 
 
 
 (4.5) 
 
 
 (30) 
 
 
 (1.5) 
 
 ^0 
 
 
 K- 
 
 
 
 
 O 
 
 s <\3 
 
 
 K 
 
 
 5 
 
 H 
 
 
 tt/.O 
 
 
 88.8 
 
 
 l/t.O 
 
 
 180.0 
 
 (3.0) 
 
 
 (>*) 
 
 ""^T 
 
 
 Ci 
 
 o 
 
 i 
 
 
 i 
 
 t 
 
 
 /44.O 
 
 
 I6O.O 
 
 
 
 (4.0) 
 
 
 (2.0) 
 
 
 
 o 
 
 
 
 ! 
 
 <-.-, & '-o'~- 
 
 s 
 
 
 
 JgV ^ 
 
 2.)LJ5WaL. 
 
 ^ 
 
 METHOD Ht 
 
 FIG. 12. EECTANGULAR BUILDING-FEAME : DIEECT AND 
 
 BENDING STRESSES CALCULATED BY APPROXIMATE 
 
 METHOD III 
 
 144.0 = Bending moment of 144,000 ft.-lb. 
 (4.0) = Direct stress of 4000 Ib. 
 
The equations for bending moments in the girders can 
 be written as follows : 
 
 Mj = [(4000 X6) +(5500 X6) = +57,000 ft.-lb. 
 
 M, = [(4000X6) +(5500X6)1 [(9225^950) X16] = 11,400 ft.-lb. 
 
 M, = 2[(4000X6) +(5500X6)] [(9225 4950) X 16] = +45,600 ft.-lb. 
 
 2[(4000X6) +(5500X6)] [(9225-^950) X32] [(3075 1650) X16] = 
 
 45,600 ft.-lb. 
 
 3[(4000X6) +(5500X6)] [(9225 4950) X32] [(3075 1650) X16] = 
 
 + 11,400 ft.-lb 
 
 & 
 
 M 8 
 
 B. 
 
 3[(4000X6) +(5500X6)] [(9225 4950) X48] [(3075 1650) X32] + 
 [(30751650) X16] = 57,000 ft.-lb. 
 
 The bending moment at the six-floor girder of each 
 sixth-story column is 4000 X 6 = 24,000 ft.-lb., and of 
 
 6000 
 
 5500 
 to 
 
 7* FLOOR 
 
 6 r - FLOOR 
 
 A 
 
 i 
 
 B 1C 
 
 METHOD 3H 
 
 & 
 
 fvnoo* 
 !D 
 
 FIG. 13. COLUMN-SHEARS AND GIRDER MOMENTS AT 
 SIXTH FLOOR, CALCULATED BY METHOD III 
 
 each fifth-story column is 5500 X 6 = 33,000 ft.-lb. The 
 compression in the floor girders is 6000 1500 = 
 4500 Ib. between Cols. A. and B, 4500 1500 = 3000 
 between B and C, and 3000 1500 = 1500 between C 
 and D. 
 
 If the columns are unequally spaced or their sectional 
 
 LOAD JUV&DZAD) 
 
 6VFLOOR 
 
 FIG. 14. GRAPHICAL COMBINATION OF MOMENTS FROM 
 
 VERTICAL LOADS AND WIND LOADS IN FLOOR 
 
 GIRDER 
 
 areas are different, the location of the neutral axis must 
 first be found. The direct stresses in the columns will 
 vary both as their distances from the neutral axis and 
 
 [ M] 
 
their sectional areas. The horizontal shears taken by the 
 columns will vary as their moments of inertia. 
 
 CONCLUSION 
 
 It can be said of each of the above methods of calculat- 
 ing wind stresses that it is easily workable; and to quote 
 Prof. W. H. Burr : "So long as the stresses found by one 
 legitimate method of analysis are provided for, the sta- 
 bility of the structure is assured." At the present time 
 Method I is probably more used than any of the others, 
 though Methods II and II-A have been used quite exten- 
 sively. In the 36-story Equitable Building of New York 
 City, the largest office building in the world, Method I 
 was followed. In its near neighbor, the 32-story Adams 
 Express Building, Method II-A was used. Method III 
 is found in some text-books; it has been used but little 
 about New York, and only to a limited extent elsewhere. 
 The writer personally prefers Method I, though during 
 the past ten years he has used I, II, and II-A. In a 20- 
 story building in Philadelphia built in 1914-1915 he used 
 I. In an 18-story building in Atlanta, designed in 1912, 
 he used II-A. To Method III he objects not only because 
 of its practical limitations but because in theory it seems 
 farther from the truth than any of the others especially 
 when it comes to distributing the shear for bents in build- 
 ings more than four aisles wide. 
 
 The practice of the writer in calculating wind stresses, 
 using Methods I or II-A (preferably I), is first to find 
 the distance of each column from the neutral axis of the 
 transverse bent to which it belongs, and then to assume 
 the moments of inertia of the inner columns in that bent 
 to be the same and of the outer columns to be one-half 
 that of the inner. The columns are proportioned for all 
 stresses coming upon them, including both direct and 
 cross-bending due to wind. It is seldom that corrections 
 are made for moments of inertia that differ from the as- 
 sumptions. 
 
 It is often convenient to assume the wind loads on the 
 basis of using the same unit-stresses as for live- and dead- 
 loads. A number of building codes call for a horizontal 
 wind pressure of 30 Ib. per sq.ft. and allow unit-stresses 
 
 [75 ] 
 
to be increased 50% for wind-bracing. A wind load of 30 
 Ib. per sq.ft. with unit-stress of 24,000 Ib. per sq.in. is 
 equivalent to a load of 20 Ib. per sq.ft. with a unit-stress 
 of 16,000 Ib. per sq.in. the working stress generally used 
 for live- and dead-loads. The diagrams of moments for 
 any floor girder can easily be combined in one figure (see 
 Fig. 14), and the total moment at any point read by scal- 
 ing. Fig. 14 is drawn for beam with ends supported. If 
 the ends were considered fixed the beam would be re- 
 strained and the diagram for both wind and floor loads 
 would show smaller bending moments. Any saving thus 
 made is doubtful economy as in actual practice it is un- 
 certain to what extent the beams are fixed (under vertical 
 load). 
 
 The building should be examined for wind in a longi- 
 tudinal direction as well as transversely and calculations 
 made if necessary. This is a simple thing to do but in 
 some marked instances it has been neglected. 
 
 Special attention should be given the column splices, 
 and the connection of floor girders to columns. It is folly 
 to add material to columns or floor girders to meet stresses 
 and moments due to wind, and then neglect their connec- 
 tions. Care should be taken that in all cases the connec- 
 tions are made strong enough for the bending moments 
 coming upon them. Many buildings have main members 
 sufficient to meet wind stresses without efficient connec- 
 tions. In such cases it matters little what particular 
 theory of wind distribution had been adopted. 
 
 [ 70 
 

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