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BRIDGES 373 Soc. C. E., xvi.) and by Mr Turneaure [Proc. Am. Soc. C. E. xli.). directly carried by the piers. IV. The horizontal pressure latter used a recording deflectometer and two recording is due to a wind blowing transversely to the span. V. The The The observations are difficult, and the inertia of longitudinal drag is due to the friction of a train when extensometers. the instrument is liable to cause error, but much care wras taken. braked (about ith of the weight of the train). VI. On The most striking conclusions from the results are that the a curved bridge the centrifugal load is due to the radial locomotive balance weights have a large effect in causing vibration, and next, that in certain cases the vibrations are cumulative, acceleration of the train. VII. In some cases changes of reaching a value greater than that due to any single impact action. temperature set up stresses equivalent to those produced Generally: (1) At speeds less than 25 miles an hour there is not by an external load. much vibration. (2) The increase of deflection due to impact at In the earlier girder railway bridges the live load was taken to 40 or 50 miles an hour is likely to reach 40 to 50 per cent, for be equivalent to a uniform load of one ton per foot run for each girder spans of less than 50 ft. (3) This percentage decreases of way. that time locomotives on railways 4 ft. rapidly for longer spans, becoming about 25 per cent, for 75-feet Live load, line gi jn> gauge At weighed at most 35 to 45 tons, andoftheir spans. (4) The increase per cent, of boom stresses due to impact is length between buffers was such that the average load did not exceed about the same as that of deflection ; that in web bracing bars is one ton per foot run. Trains of waggons did not weigh more than rather greater. (5) Speed of train produces no effect on the mean three-quarters of a ton per foot run when most heavily loaded. The deflection, but only on the magnitude of the vibrations. A purely empirical allowance for impact stresses has been weights of engines and waggons are now greater, and in addition it is recognized that the concentration of the loading under the axles proposed, amounting to 20 per cent, of the live load stresses for floor stringers ; 15 per cent, for floor cross girders ; and for main gives rise to straining actions greater than those due to the same load uniformly distributed. A modern heavy English tank loco- girders, 10 per cent, for 40-feet spans, and 5 per cent, for 100-feet motive may weigh 47 tons with a length over butlers of 30^ feet, spans. These percentages are added to the live load stresses. The dead load consists of the weight of main girders, flooring, and a wheel base of 16 feet. This corresponds to I'SS tons per foot run of engine length. American locomotives are heavier. and wind-bracing. It is almost always reckoned as uniform per . .oa . Thus, a consolidation engine and tender may weigh 126 tons, with foot run, though sometimes allowance should be made Uea n ‘ a,length over buffers of 57 feet, corresponding to an average load of for the increase of weight towards the centre of the 2 55 tons per foot run. In America long ore waggons are some- span. The weight of the bridge flooring depends on the type times used which weigh loaded two tons per foot run. It is clear, adopted. Roughly, the weight of sleepers, rails, &c., is 0 ‘25 ton with such variation in weight and in its distribution, that some per foot run for each line of -way, while the rail girders, cross typical arrangement of loads must be assumed representing in girders, or troughing weigh 0 15 to 0‘25 ton. The weight of given cases the worst to be expected. Mr Waddell (De Pontibus, main girders increases rapidly with the span, and there is for any New York, 1898) proposes to arrange railways in seven classes, type of bridge a limiting span beyond which the dead load stresses according to the live loads which may be expected from the exceed the assigned limit of working stress. Let Wz be the total live load, Wy the total flooring load on a character of their traffic, and to construct the bridges in accordance with this classification :—For the lightest class, he takes bridge of span l, both being considered for the present purpose to a locomotive and tender of 93 5 tons, 52 feet between buffers be uniform per foot run. Let &(WZ + W/) be the weight of main (average load = 1‘8 tons per foot run), and for the heaviest, a girders designed to carry Wz + Wy, but not their own weight in locomotive and tender weighing 144'5 tons, 52 feet between buffers addition. Then W*=(Wz + W/)(£+£2+P. . .) (average load = 2-77 tons per foot run). Waggons he assumes to weigh for the lightest class 1 '3 tons per foot run, and for the will be the weight of main girders to carry W +Wy and their own heaviest 1-9 tons. Then he takes the live load for a bridge to weight (Buck, Proc. Inst. C. E. Ixvii. p. 331). z Hence, consist of two such engines, followed by a train of waggons covering W<,=(Wz + W»£/(l-£). the span. If a vertical load is imposed suddenly, but without velocity, work Since in designing a bridge Wz + Wy is known, £(Wz + AVy) can be is done during deflection, and the deformation and stress are found from a provisional design in which the weight is neglected. double those due to the same load at rest The actual bridge must have the section of all members greater Impact. momentarily on tjle strUcture. No load of exactly this kind is ever than those in the provisional design in the ratio &/(l - k). applied to a bridge. But if a load is so applied that the deflection Mr Waddell [De Pontibus) gives the following convenient emincreases with speed, the s‘ress is greater than that due to a very pirical relations. Let -uq, w2, be the weights of main girders per gradually applied load, and vibrations about a mean position are foot run for a live load p per foot run and spans l.,. Then set up. The rails not being absolutely straight and smooth, centrifugal and lurching actions occur which alter the distribution of the loading. Again, rapidly-changing forces, due to the moving parts of the engine which are unbalanced vertically, act on the Now let wf vfl be the girder weights per foot run for spans lx, l,, bridge ; and, lastly, inequalities of level at the rail ends give rise and live loads f per foot run. Then to shocks. For all these reasons the stresses due to the live load are greater than those due to the same load resting quietly on the w2 l[ 1 + 4 P J bridge. This increment is larger on the flooring girders than on w2 L[h++ the main ones, and on short main girders than on long ones. The vq ioU impact stresses depend so much on local conditions that it is !)•]('+> difficult to fix what allow'ance should be made. Mr E. H. Stone A partially rational approximate formula for the weight of main [Trans. Am. Soc. of Civil Engineers, xli. p. 467) collated some girders is the following (Unwin, Wrought-Iron Bridges and Roofs, measurements of deflection taken during official trials of Indian 1869, p. 40) :—Let W be the total distributed load on a girder bridges, and found the increment of deflection due to impact to exclusive of its own weight, in tons ; W1; the weight of the girder ; depend on the ratio of dead to live load. By plotting and l, the span, in ft. ; s, average stress, in tons, per sq. in. on gross averaging he obtained the following results : — section of members ; d = depth of girder at centre, in ft. ; r—ratio Excess of Deflection and straining Action of a moving Load over that of depth of girder to span. Then due to a resting Load. W72 1 _ WZr 1 Cds - l’ Cs- Ir Dead load in per cent, of 10 20 30 40 50 70 90 total load where C is a constant for any type of bridge. It is not easy to fix the average stress s per sq. in. of gross section. Hence the formula Live load in per cent, of 90 80 70 60 50 30 10 is more useful in the form total load _ W72 _ AV/r l ^ ~kd-P~k-lr' 2-3 1‘5 1-0 0-43 0T0 Ratio of live to dead load where k = (AYq + AV)7r/AV: is to be deduced from the data of some bridge previously designed for the same live load per foot run and Excess of deflection and 5-5 4-0 1-6 I 0-3 the same working stresses. From some known examples, C varies stress due to moving load 23 13 per cent. from 1500 to 1800 for iron, and from 1200 to 1500 for steel bridges. £ = 6000 to 7200 for iron, and =4800 to 6000 for steel bridges. These results are for the centre deflections of main girders, but Much attention has been given to wind action since the disaster Mr Stone infers that the augmentation of stress for any member, to the Tay Bridge in 1879. As to the maximum wind pressure on due to causes included in impact allowance, will be the same per- small plates normal to the wind, there is not much ^ . centage for the same ratios of live to dead load stresses. Valuable doubt. Anemometer observations show that pressures ppressure measurements of the deformations of girders and tension members of 30 lb per sq. ft. occur in storms annually in many due to moving trains have been made by Mr Robinson [Proc. Am. localities, and that occasionally higher pressures are recorded im