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THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



QFebruaby, 



larlv upon it. It was found tliat beams of cast-iron, loaded to a 

 certiiin detrree with weifihls spread over tlieir whole leiifrth, and so 

 attached to them as not to prevent the flexure of the bar, resisted 

 greater impacts from tlie same body falling on them than when 

 the beams were unloaded, in the ratio of two to one. The bars in 

 this case were struck in llie middle bv the same ball falling verti- 

 cally, through different lieights, and the deflections were nearly as 

 the velocity of impact. 



We have also carried on a series of experiments to compare the 

 mechanical eifect j)roduced by « eights passing with more or less 

 velocity over bridges, with their effect when placed at rest upon 

 them. " For this purpose, amongst other methods, an apparatus 

 was constructed, by means of wliich a car loaded at pleasure with 

 various weights was allowed to run down an inclined plane; the 

 iron bars which were the subject of the experiment were fixed 

 horizontally at the l)ottom of the plane, in such a manner that the 

 loaded car would pass over them with the \elocity acquired in its 

 descent. Thus the effects of giving different velocities to the 

 loaded car, in depressing or fracturing the bars, could be observed 

 and compared with the effects of the same loads placed at rest 

 upon the bar. 



This apparatus was on a sufficiently large scale to give a practi- 

 cal value to the results: the upper end of the inclined plane was 

 nearly 10 feet abo\e the horizontal portion, and a pair of rails, 

 3 feet asunder, were laid along its whole length for the guidance of 

 the car, which was capable of being loaded to about 2 tons; the 

 trial bars, 9 feet in length, were laid in continuation of this railway 

 at the horizontal part,^aud the inclined and horizontal portions of 

 the railway were connected by a gentle curve. Contrivances were 

 adapted to the trial bars, by means of which the deflections pro- 

 duced by the passage of the loaded car were registered; the velo- 

 city gi\en to the car was also measured, but that velocity was, of 

 course, limited by the height of the plane, and the greatest that 

 could be obtained was 43 feet per second, or about 30 miles per 

 hour. 



A great number of experiments were tried with tliis apparatus, 

 for tlie purpose of comparing the effects of different loads and 

 velocities upon bars of \arious dimensions, and the general result 

 obtained was that the deflection produced by a load passing along 

 tlie bar was greater tlian that whicli was ])roduced by placing the 

 same load at rest upon the middle of the bar, and that this deflec- 

 tion was increased when the velocity was increased. Thus, for 

 example, when the carriage loaded to 1,120 lb. was placed at rest 

 upon a jiair of cast-iron bars, 9 feet long, i inches broad, and li in. 

 deep, it produced a deflection of -f^thi of an inch; but when the 

 carriage was caused to pass over the bars at the rate of 10 miles an 

 hour, the deflection was increased to ^ths, and went on increasing 

 as the velocity was increased, so that at 30 miles per hour the 

 deflection became l^inch; that is, more than double the statical 

 deflection. 



Since the velocity so greatly increases the effect of a given load 

 in deflecting the bars, it follows that a much less load will break 

 the bar when it passes over it than when it is placed at rest upon 

 it, and, accordingly, in the example above selected, a weight of 

 4,150 lb. is required to break the bars if applied at rest upon their 

 centres: but a weight of 5,7TS lb. is sufficient to produce fracture 

 if passed over tiiein at the rate of 30 miles an hour. 



It also ajipeared that when motion was given to the load, the 

 points of greatest deflection, and, still more, of the greatest strains, 

 did not remain in the centre of the bars, but were removed nearer 

 to tlie remote extremity of tlie bar. The bars, when broken by a 

 travelling load, were always fractured at points beyond their cen- 

 tres, and often broken into four or five pieces, thus indicating the 

 great and unusual strains they had been subjected to. 



We ha\e cndea\oured to discover the laws which connect these 

 results with eacli other and with practice, and for this purpose a 

 smaller and more delicate ajiparatus was constructed to examine 

 the phenomena in their simplest form — uanicly, in the case of a 

 single weight traversing a light elastic bar. For the weight in its 

 passage along the bar deflects it, and thus the jiath or trajectory 

 of the centre of the weight, instead of being a horizontal straight 

 line as it would be if the bar were perfectly rigid, becomes a curve, 

 the form of which dejiends u])on the relation between the length, 

 elasticity, and inertia of tlie bar, the magnitude of the weight and 

 the velocity imparted to it. If the form of this curve could be 

 perfectly determined in all cases, the effects of travelling loads 

 upon bars would be known; but unfortunately the problem in 

 question is so intricate that its complete mathematical solution 

 appears to be beyond the ]>resent powers of analysis except in the 

 simplest and most elementary case — namely, in ivhicli the load is 



so arrano-ed as to press upon the bar with one point of contact 

 only or in other words, the load is considered as a heavy moving 

 poiiit. 'in practice, on the contrary, a single four-wheeled car- 

 riage touches each rail or girder in two points, and a six-wheeled 

 engine witli its tender has five or six points in contact on each 

 sid'e. This greatly complicates the problem. , . , 



Tlie above smaller apparatus is so arranged as to comply with 

 the simple condition that the load shall press upon one point only 

 of the bar, and is also furnished with a contrivance by which the 

 efl-ects of various proportions of the mass of the bar to that of the 

 load can be examined. From the nature of the problem, it is con- 

 venient to consider, in the first place, tlie forms of the trajectories 

 that are described, and the corresponding deflections of the bar 

 w-hen the mass of the bar is exceedingly small compared with that 



" Having obtained these under different relations of the length of 

 the bridge, its statical deflection, and the velocity of the passmg 

 load, we proceed to investigate, in addition, the effect which a 

 greater proportional mass of the bar or bridge has upon the 

 deflections. We have been greatly assisted m this research by a 

 most elaborate and complete analytical investigation by George 

 Stokes Esq., Fellow of Pembroke CoUege, Cambridge, undertaken 

 at the'request of one of the members of the Commission. Ln- 

 fortunately, the extreme difiiculty of the problem has rendered its 

 solution unattainable excepting in the cases in which the mass of 

 the bridge is supposed to he exceedingly f^f 1 fon^P^^^^^ "''^'^ f'^^ 

 of the load, and in the opposite case in which the mass ot the load 

 is supposed to be small compared witli that of the bridge Che 

 exanfples that occur in practice lie between these two extreme ; 

 for iA the experiments of the Commission, performed "t I orts- 

 mouth, with the inclined plane, already described, tlie weight of 

 the load was from three to ten times tliat ot the bar; but this s a 

 much greater proportion thaji that which occurs in bridges paitiy 

 on account of the necessity for employing in experiments very 

 flexible bars, to render the changes of deflection sufhcierily appa- 

 rent, and partly on account of the great difference of legh,toi 

 if bars be,' ring the same ratio of weiglit to hat of the lo<«l "eie 

 employed in experiment, the deflection would become ^o^"^" ^^ 

 to be scarcely appreciable. This wiU readily be perceived « hen it 

 is stated that in a bridge of 33 feet long a deflection "ot^ greater 

 than one-fourth of an inch is usually allowed, which deflection is 

 only ^^th part of its length; whereas m experiment it i, neces- 

 sary to employ deflections of two or more inches. In actual 

 bridges of ibout 40 feet span, the weight of the engine and tender 

 is vei-y nearly the same as the weight of that J^aU of the bi dge 

 over whicli it passes; and in large bridges the weight of the load 

 is much less than that of the bridge. , -j „ • 



Mr. Stokes has shown, that vvhen the inertia of the bridge is 

 supposed small, the trajectories of the load and the ««"-esponding 

 defection of the bridge depend upon a certain '1"=^^ 'tJ' w '„ch he 

 terms B; this quantity varies directly as the square of tbelen^b 

 of tlie bar, and inversely as the product of the central sta ical 

 deflection (namely, that which would be produced by the load et 

 at rest on the centre of the bridge), and of the '^'l""^ ^^ o t e ^ elo- 

 city with which the load passes over the bridge. W hen U s small, 

 U^ increase of deflection due to the velocity of the load becomes 

 very great, so much so that if « be equal to 1-3, the statical deflec- 

 tions'^are doubled, and are tripled when fi = ''■'' '^''l^^'^i^.f, 

 greater as lesser v'alues of & are taken. On the .eo'f^'-J ',f sbol^ 

 Values of 6 correspond to small deflections; and it 'f?^''^'^^' '''^owa 

 by our researches that in the cases of real bridges i^/- ^'^ ^^J^^ 

 than 14 and is commonly very much greater; and that, conse- 

 quently,' the greatest increase of deflection from velocity would be 

 upon th'is thiory never gi-eater tlian one-tent i varying fom that 

 to one-hundredth, or less. As H varies directly "J. the squaie ot 

 the length of the bridge, it is plain that the n'"e-*/,^\!'.f'^ "U''^ 

 Portsmouth experiments will correspond to much e=s ^- "e ot ^ 

 than tJie 20 and 30-feet lengths of actual ^"^ges; hile t'.e ^alues 

 of B in the former cases are still furtlier diminislied b) the greater 

 deflections necessarily employed in experiments, fjf'^l^^- 

 i.lained. It is thus shown that the enormous increa,e of deflection 

 m-oduced by velocity in tlie Portsmouth experiments cannot occur 

 with real bHdges, since it appears that the phenomena in question 

 are developed to a great extent when the magnitude ot the stiuc- 

 ure is din inished. But these calculations are made upon the sup- 

 ^t on that the iirertia of the bridge is very --'l';, -^^ e^Tn 

 iients made with the small apparatus ahove-mentioned hue shown 

 that while H is less than about unity, the inertia ot tl e budge 

 ends to diminish the deflection; while, on tin. other hand, when « 

 is greater than unity (including, of course, aU practical cases), the 



