18S0.1 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



51 



inertia of the bridge tends to increase tlie deflections, obtained 

 upon tlie above supposition. Lastly, the total increase of the 

 statical deflection, wlieu the inertia of the bridge is taken into 

 account, will be found much greater for short bridges than for 

 long bridges. Supposing, for exam])le, the mass of the travelling 

 load and of the bridge to be nearly equal, the increase of the 

 statical deflection at the highest velocities for bridges of 20 feet in 

 length and of the ordinary degree of stiffness may be more than 

 one-half; whereas for bridges of 50 feet in length, the increase 

 will not be greater than one-seventh, and will rapidly diminish as 

 greater lengths are taken. But as it has been shown that the 

 increase ceeteris paribus is diminished by increasing the stiffness of 

 the bridge, we always ha^•e it in our power to reduce its amount 

 within safe limits. Hence in estimating the strength of a railway 

 bridge, this increase of the statical deflection must be taken into 

 account, by calculating it from the greatest load which is likely to 

 pass over the bridge, and from the liighest ])0ssible \elocity. It 

 must be remembered, also, that this deflection is liable to be in- 

 creased by jerks produced by the passage of the train over the 

 joints of the raUs. 



^V^e also made some experiments by means of the large appara- 

 tus, before mentioned, on curved bars, and tliese bore much greater 

 weights at high velocities than straight bars; but the deflections 

 of these bars were very great, compared with their length. In 

 drawing attention to these experiments, we would remark that, in 

 actual structures, where the deflections are so very small, the effect 

 of cambering the girders, or of forming a curved pathway for the 

 load, would be of less comparative importance, and might tend to 

 introduce practical inconvenience. 



The general impression amongst engineers appears to be at 

 variance with the above results. They, for the most part, state 

 their belief that the deflection caused by passing a weight at a 

 high velocity over a girder is less than the deflection which would 

 be produced by the same weight at rest; even when tliey ha,ve 

 observed an increase, they have attributed it solely to the jerks of 

 the engine or train produced by passing over inequalities at the 

 junction of the rails, or other similar caiises. 



For the ])urpose of examining this question, we have submitted 

 two actual bridges to the test of experiment. These bridges, one 

 of ivhich, the Ewell Bridge, is situated upon the Croydon and 

 Epsom line, and the other, the Godstone Bridge, upon the South 

 Eastern line, are both constructed to carry tlie railway over a road. 

 A scaffold was constructed, which rested on the road, and was, 

 therefore, unaffected by the motion of the bridge, and a pencil was 

 fixed to the under side of one of the girders of the bridge, so that 

 when the latter was deflected by the weight of the engine or train 

 either placed at rest or passing over it, the pencil traced the extent 

 of deflection vipon a drawing-board attached to the scaffold. An 

 engine and tendei', which had been in each case liberally placed 

 under our orders by the directors of the companies, was made to 

 tra^verse the bridges at different velocities, or rest upon tliem at 

 pleasure. The span of tlie Ewell Bridge is -IS feet, and the stati- 

 cal deflection due to the above load rather more tlian one-fifth of 

 an inch. This was slightly but decidedly increased when the 

 engine was made to pass over the bridge, and at a velocity of about 

 SO miles per hour, an increase of one-seventh was observed. As 

 it is known that the strain upon a girder is nearly proportional to 

 the deflection, it must be inferred that in this case the velocity of 

 the load enabled it to exercise the same pressure as if it had been 

 increased by one-seventh, and placed at rest upon the centre of 

 the bridge. The weight of the engine and tender was 39 tons, 

 and the velocity enabled it to exercise a pressure upon the girder 

 equal to a weight of about ^3 tons. Similar results were obtained 

 from the Godstone Bridge. We would take this opportunity of 

 mentioning how much we are indebted to Mr. P. W. Barlow and 

 to Mr. Hood for the assistance they afforded us in making these 

 experiments. 



We have also to express our obligations to the Astronomer 

 Royal for the advantage of his presence during the above and 

 other experiments, as well as for many valuable suggestions during 

 the progi-ess of the inquiry. 



In addition to the above experiments, we have made many for 

 the purpose of supplying data for completing the mechanical 

 theory of elastic beams. If a beam be in any manner bent, its 

 concave side will be compressed, and its convex side extended. An 

 exact knowledge of the laws which govern its compression and 

 extension must precede any accurate general theory of its deflec- 

 tions, vibrations, and ruptures. 



The law which is usually assumed in mathematical investigations, 

 and by which the longitudinal compressions and extensions, within 



certain limits, are assumed to be directly proportional to the 

 forces by which they are produced, although very nearly true in 

 some bodies, is not, perhaps, accurately true for any material. 



Experiments have, therefore, been made to determine with pre- 

 cision the dii'ect longitudinal extension and compression of h ;ig 

 liars of cast and wrought iron. The extensions were determined 

 by attaching a bar, 50 feet in length and 1 inch square, to the 

 roof of a lofty building, and suspending weights to its lower ex- 

 tremity. 



The compressions were ascertained by enclosing a bar 10 feet 

 long and 1 inch square in a groove, ]ilaced in a cast-iron frame, 

 which allowed the bar to slide freely without friction, and yet per- 

 mitted no lateral flexure. Tlie bar was then compressed by means 

 of a lever, loaded with various weights. Every possible precau- 

 tion was taken to ensure accuracy. The following formulie were 

 deduced for expressing the relation between the extension and 

 com])ression of a bar of cast-iron, 10 feet long and 1 inch square, 

 and the weights producing them respectively: — 



Extension, w = 116117e — 20190oe- 

 Compression, w = 107T63d — 36318rf-. 

 AT'here «■ is the weight in pounds acting upon the bar, e the exten- 

 sion and d the compression in inches. 



And the formulje deduced from these, for a bar 1 inch square 

 and of any length, are — 



For Extension, 



13934040 ^ — 2907432000 j. 



For Compression, w = 1293I5G0 — ■ 



522979200 -. 



AV'liere I is the lengtli of the bar in inches. 



These formulfe were obtained from the mean results of four 

 kinds of cast-iron. 



The mean tensile strength of cast-iron derived from these ex- 

 periments is 15,711 lb. per square inch, and the ultimate extension 

 5^5 of the length, and this weight would compress a bar of iron 

 of the same section yf^ of its length. It must be observed, that 

 the usual law is very nearly true for wrought-iron. 



Many denominations of cast-iron have got into common use, of 

 which the properties had not yet been ascertained with due pre- 

 cision. Seventeen kinds of them i^ave been selected, and their 

 tensile and crushing forces determined. Experiments have also 

 been made upon the transverse strength and resistance of bars of 

 wrought and cast iron acted upon by horizontal as well as vertical 

 forces. These experiments will be found to exhibit very fully the 

 deflections and sets of cast-iron and the defect of its elasticity. 



The bars which were experimented upon by transverse pressure, 

 were of sections varying from 1 incli square to 3 inches square, 

 and of various other sections, and the actual breaking weights 

 show that the strength of a bar 1 inch square should not be taken as 

 the unit for calculating the strength of a larger casting of similar 

 metal, although the practice of doing so has been a preva- 

 lent one, for it appears that the crystals in the jiortion of the bar 

 which cools first, are small and close, whilst the central portion of 

 bars 2 inches square, and 8 inches square, is composed of compara- 

 tively lai-ge crystals, and bars of 3 inches square in section planed 

 down on all sides alike to f of an inch square, are found to be 

 \'ery weak to resist both transverse and crushing pressure. Hence 

 it appears desirable in seeking for a unit for the strength of iron 

 of whicli a large casting is to be made, that the bar used should 

 equal in thickness the thickest part of the proposed casting. 



The performance of these various experiments has been greatly 

 facilitated by the permission wliich was liberally granted to us by 

 the Lords Commissioners of the Admiralty, to make use of Ports- 

 mouth Dockyard in carrying on our investigations, in addition to 

 which, liowever, we found it necessary to hire for several months 

 some premises in Lambeth. This was found requisite for the per- 

 formance of those portions of the experimental inquiry which had 

 been undertaken by Eaton Hodgkiuson, Esq. Although we are 

 aware that, to point out the labours of individual members of the 

 Commission would be impossible, and that it may appear invidious 

 to single one out for praise, « e cannot resist the expression of our 

 thanks to the above-named gentleman for the zeal and intelligence 

 with which he has carried out the remarkable series of experi- 

 ments which are detailed in the Appendix to this Report, and 

 which constitute a large proportion of those which have beea 

 already described. 



In addition we have obtained, from many of the iron-masters, 

 information respecting the various processes employed by them in 

 the manufacture of their irons, and the effect of such processes 



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