25. Live Loads for Railway Bridges. The loads for any par ticular railroad bridge are not always the same, on account of the great variation in the weights and wheel spacings of engines and cars. It is customary to design the bridge for the heaviest in use at the time of construction, or for the heaviest that could reasonably be expected to be built thereafter.
As the computations with engines were formerly somewhat laborious on account of the different weights and spacing of wheels, it has been proposed by some engineers to use a uniform load, called the equivalent load, which would give stresses the same, or very nearly the same, as those obtained by the use of engine loads. However, as these loads are different for each weight of engine, and also different for the chord members, the web members, and the floor-beam reaction of each different length of span, and as the labor of the computations, using engine-wheel loads, has been greatly reduced by means of diagrams, it does not seem as if this method would ever come into very general favor except for long-span bridges, where the live load is much smaller than the dead load.
The equivalent loads for Cooper's E 40 (see Fig. 85) are given in Table IV.
Most railways specify that their bridges shall be computed by using two engines and tenders followed by a train. The spacing of the wheels, and the load which comes on each wheel of the engines and tenders, are fixed by the railway company. The train is repre sented by a uniform load. Formerly there was a great diversity of practice among the different roads in regard to the engine train loads specified; but practice has of late years become quite uniform, with an apparent tendency to standardize in accordance with the classes of loading specified by Cooper. Cooper's Class E 50, which represents the heaviest engines now in common use, was invented by Theodore Cooper, a consulting engineer of New York City. It is given in Fig. 17.
Lighter loadings for light traffic on the same general plan are advocated by Mr. Cooper, and are given at length in his "General Specifications for Iron and Steel Railway Bridges and Viaducts" (1906 edition).
26. Wind Loads. Some designers require that the stresses due to wind shall be computed by using 30 pounds per square foot of actual truss surface. This requires that you know the size of the mem bers of the bridge before it is designed—which is evidently an impossibility; or that an as sumption as to their size be made—which allows a chance for a mistake in judgment, especially in an inexperienced person. A more logical method, and one used to a great extent, is to assume a force of so many pounds per linear foot to act on the top and bottom chords and on the traffic as it moves across the bridge.
In highway through bridges, it is the usual practice to take the wind load as 150 pounds per linear foot of top and bottom chords, and 150 pounds per linear foot of the amount of live load which is on the bridge.
For railroad bridges, it is customary to use considerably higher values than those used in highway practice not that the wind blows harder on than on highway bridges, but so that the bracing designed by the use of these values may be sufficiently strong to stiffen• the bridge not only against the wind, but also against the vibrations caused by the rapidly moving traffic. Good practice for through bridges is to use 150 pounds per linear foot of the top chord, 150 pounds per linear foot of the bottom chord, and 450 pounds per linear foot of live load on the bridge. This latter force is supposed to act at a line 8.5 feet above the base of the rail.
For deck bridges, for both highway and railway use, the unit-loads on the moving or live load remain the same, but the unit-loads on the top and bottom chords are reversed.
In computations involving the live load, it is always assumed that the live load moves over the bridge from right to left.
27. Principles of Analysis. The stresses in bridge trusses may be determined by both algebraic and graphic methods. In some cases, one is more expeditious than the other. Algebraic methods alone will be considered in this text.
The analysis of stresses is based upon the fact that the interior stresses in a member or group of members hold in equilibrium the exterior forces. That this is a fact, can easily be understood. Con sider a man pulling on a rope which is fastened at one end to an im movable object. There will be a stress in the rope equal to, and opposite in direction to, the pull exerted by the man. In order to prove this, cut the rope and ap ply a force equal and opposite to the pull exerted by the man, where the cut is made; and the rope and man will be in equilibrium. Also, suppose that a truss under loads, as indicated by the arrows, Fig. 18, were cut along the section a-a, and that forces equal to the stresses S, and were placed at the ends of the members as indicated in Fig. 19, then that portion of the truss to the left of the section would be in equilibrium. The interior stresses, represented by and hold in equilibrium the exterior forces p and F.