The Viaduct Works' Handbook

100 described as follows:—Assume the weight for a pair of girders, including the floor, railway, and heaviest load that will be passed over them, to be 270 tons evenly distributed, the half of this weight, or 135 tons, will be supported by each girder, and distributed. Thus, 95 = 15 tons to be supported on each division of the top flange; the top flange being considered inflexible between the points of support, or intersection of the diagonals, may be con- sidered as nine separate beams, each 15 tons weight, supported on the points of the triangles formed by the diagonal struts and ties, as indicated by Fig. 1. Now, if we trace the effect of these loads upon the diagonals, and mark the results on each, after we have gone through the whole number of weights, we have only to add up the results on each diagonal to give the maximum strain on it. For instance, the results of the load of 15 tons at @ are indicated for one-half the girder by the O figures, the sign + indicating com- pressive strain, and the sign — indicating tension; at the same time the load b is supported, the effect of which is shown by the — figures; likewise the load c, shown by the black figures; and, lastly, the load d shown by the — figures. The result shows (in O) that the load @ produces on the strut @ 1 a strain of + 15 tons, which is supported by the tie b 1, — 15 tons; and this has to be held by the strut b 2, which is supported at the point 2 by the tie c 2, which presses upon the point 3 through the strut c8; and so on to the point of support e. The strut b 2 has to support, in addition to the load 15 tons from @, similar weight b, 15 tons, which is pressed upon the point 2, and supported by c 2, and so on; making the total + strain on b2 equal to 30 tons. In like manner, c3 has to support + 45 tons and d4 has to support + 60 tons; the other half of the girder being loaded equally, precisely similar strains take place in the similar parts. It will be noticed that only half the weight at each end division from d to e, Fig. 1, or 74 tons, has to be supported by the diagonals; the other half is directly supported by the pier, and has no effect upon the girder. The total addition of strains passing through the diagonals is concentrated in the end tie e, No. 4, and amounts to 60 tons; this, added to the 7% tons passing down the pier, makes 67% tons at each support, which is half the total load, 135 tons, being supported half by one pier and half by the other.