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These results are for the centre deflections of main girders, but Stone infers that the augmentation of stress for any member, due to causes included in impact allowance, will be the same percentage for the same ratios of live to dead load stresses. Valuable measurements of the deformations of girders and tension members due to moving trains have been made by S.W. Robinson (Trans. Am. Soc. C.E. xvi.) and by F.E. Turneaure (Trans. Am. Soc. C.E. xli.). The latter used a recording deflectometer and two recording extensometers. The observations are difficult, and the inertia of the instrument is liable to cause error, but much care was taken. The most striking conclusions from the results are that the locomotive balance weights have a large effect in causing vibration, and next, that in certain cases the vibrations are cumulative, reaching a value greater than that due to any single impact action. Generally: (1) At speeds less than 25 m. an hour there is not much vibration. (2) The increase of deflection due to impact at 40 or 50 m. an hour is likely to reach 40 to 50% for girder spans of less than 50 ft. (3) This percentage decreases rapidly for longer spans, becoming about 25% for 75-ft. spans. (4) The increase per cent of boom stresses due to impact is about the same as that of deflection; that in web bracing bars is rather greater. (5) Speed of train produces no effect on the mean deflection, but only on the magnitude of the vibrations.
A purely empirical allowance for impact stresses has been proposed, amounting to 20% of the live load stresses for floor stringers; 15% for floor cross girders; and for main girders, 10% for 40-ft. spans, and 5% for 100-ft. spans. These percentages are added to the live load stresses.
iii. Dead Load.?The dead load consists of the weight of main girders, flooring and wind-bracing. It is generally reckoned to be uniformly distributed, but in large spans the distribution of weight in the main girders should be calculated and taken into account. The weight of the bridge flooring depends on the type adopted. Road bridges vary so much in the character of the flooring that no general rule can be given. In railway bridges the weight of sleepers, rails, &c., is 0.2 to 0.25 tons per ft. run for each line of way, while the rail girders, cross girders, &c., weigh 0.15 to 0.2 tons. If a footway is added about 0.4 ton per ft. run may be allowed for this. The weight of main girders increases with the span, and there is for any type of bridge a limiting span beyond which the dead load stresses exceed the assigned limit of working stress.
Let Wl be the total live load, Wf the total flooring load on a bridge of span l, both being considered for the present purpose to be uniform per ft. run. Let k(Wl+Wf) be the weight of main girders designed to carry Wl+Wf, but not their own weight in addition. Then
Wg = (Wl+Wf)(k+k2+k3 ...)
will be the weight of main girders to carry Wl+Wf and their own weight (Buck, Proc. Inst. C.E. lxvii. p. 331). Hence,
Wg = (Wl+Wf)k/(1-k).
Since in designing a bridge Wl+Wf is known, k(Wl+Wf) can be found from a provisional design in which the weight Wg is neglected. The actual bridge must have the section of all members greater than those in the provisional design in the ratio k/(1-k).
Waddell (De Pontibus) gives the following convenient empirical relations. Let w1, w2 be the weights of main girders per ft. run for a live load p per ft. run and spans l1, l2. Then
w2/w1 = ½ [l2/l1+(l2/l1)2].
Now let w1?, w2? be the girder weights per ft. run for spans l1, l2, and live loads p? per ft. run. Then
w2?/w2 = 1/5(1+4p?/p)
w2?/w1 = 1/10[l2/l1+(l2/l1)2](1+4p?/p)
