U,L, _ +1.28 X 88.8 = +113.6 -1.28 X 6.7 = -8.6 U,L, = + 1.28 X 50.5 = + 64.7 0 Live-Load Stresses in the Verticals. The maximum stress in occurs when one of the large drivers is at L,, and the loads in the first panel are as near as possible one-half the sum of the loads in panels 1 and 2 and the load at L,. This can be established as a fact by use of the differential calculus. In the present case, this con dition is satisfied when wheel 4 is at L,. Then the weight of the wheels in panel 1 is 50 000 pounds,and the sum total is 116 000 pounds. If wheel 13 be placed at L the result will be the same, and then the engine diagram can be used. Fig. 94 represents the engine diagram in place, ready to use. According to Article 44, the value 480 is the moment of wheels 10 to 12 about L,. Therefore 480 _ 20 (20 is the panel length) = 24.00, is that amount of wheels 10 to 12 which is transferred to In like manner, 529 : 20 = 26.45 is the amount of wheels 14 to 16 trans ferred to As thetotal weight of the loads in the two panels is 116 000 pounds, the amount transferred to must be 116.0 (24.00 + 26.45) = 65.55, and the stress in U,L, is therefore +65.55.
The maximum live-load stress in occurs when the loading is in a position to give the maxi mum shear in the third panel, as the shear at a section cutting and is the same' as that at a vertical section in the panel. The stress equation is + +50.5 = 0, from which = 50.5. In a similar manner, the stress equation for the maximum live-load stress in is + +25.1 = 0, as is working, and therefore = 25.1. As in the case of the analysis of the Pratt truss under uniform load (see Article 39), the dead-load stress of 6.7 cannot be added to this stress of 25.1 to obtain the maximum; but the dead-load stress in must be obtained when diagonals and are in action. In the manner explained in Article 39, this is found to be +3.30.
It will be found that as come on the bridge from the left, the counters come into action in the case of and in the case of U,L both and act, thus causing the live-load stress in these verticals to be zero; and when this is the case, the dead-load stress is 6.7, which is the minimum.
Dead-Load Chord Stresses. The dead-load chord stresses can be found by any of the methods previously given; but they will be found by the tangent method as indicated below, the tangent being 20=25=0.8: Live-Load Chord Stresses. On account of the wheel loading, no ratio can be established between these stresses and the dead-load chord stresses. The maximum moments at each point must be determined, and these divided by the height of the truss will give the chord stresses. For all points to the left of the center of the bridge, the main diagonal will act. For points to the right of the center, an uncertainty exists. The shear in the panels on either side of the point under consideration should be determined when the loading is in position to give the maximum moment at that point. This will indicate which diagonals act, which fact will indicate for what chord member that point is the center of moments.
When wheel 3 is at L four feet of uniform load are on the truss, and the left reaction is: R = (16 364 + 384 X 4 + 4' _ 120 = 146.0.
The moment of this reaction about L less the moment of wheels 1 and 2 about L will be the moment at L, due to this loading. The moment of wheels 1 and 2 about L, is taken from the diagram, where it occurs in the first line of values just to the right of the vertical line through wheel 3, and therefore: X, = 146.0 X 20 230 = 2 690 000 pound-feet.
When wheel 4 is at L there are nine feet of uniform load on the truss, and the left reaction is: R, (16 364 + 284 X 9 + z2 _ 120 = 158.0; As this is less than when wheel 3 is at the point, wheel 3 gives the greatest moment.
When considering the point with wheel 6, the left reaction is: _ (16 364 + 284 X 3 + 3' 9 : 120 = 143.5 31,= 143.5 X2 X 20 1 640 = 4 100 000 pound-feet.