7 6 STRESSES IN BRIDGE TRUSSES 



To draw the shear parabola direct, without the use of the force 

 and equilibrium polygons proceed as follows : At a distance of a panel 

 length to the left of the left abutment lay off to scale a load line equal 

 to one-half the total load on the truss, divide this load line into as many 

 parts as there are panels in the truss, and beginning at the top, which 

 call I, number the points of division of the load line I, 2, 3, etc., as in 

 Fig. 49. Drop vertical lines from the panel points and number them 

 I, 2, 3, etc., beginning with the load line, which will be numbered I, 

 the left reaction numbered 2, etc. Now connect the numbered points in 

 the load line with the point /, which is under the first panel to the left 

 of the right abutment ; and the intersection of like numbered lines will 

 give points on the shear parabola. It should be noted that the line h g 

 is a secant to the parabola and not a tangent as might be expected. 



The dead load shear is laid off positive downward in Fig. 50 to the 

 same scale as the live load shears, and the maximum and minimum 

 shears due to dead and live loads are added graphically. The stresses 

 in the web members are calculated graphically in Fig. 50. 



Wheel Loads. The criteria for maximum moments and shears 

 in bridge trusses loaded with wheel loads are as follows : 



(1) Maximum Moment at any joint in a bridge loaded with 

 wheel loads will occur when the average load on the left of the section 

 is the same as the average load on the whole span. 



(2) Maximum Shear in any panel in a bridge loaded with wheel 

 loads will occur when the load on the panel is equal to the load on the 

 bridge divided by the number of panels. 



These criteria will be proved by means of the influence diagram 

 in the following discussion. 



For a more complete discussion of the subject see standard books 

 on bridge design. For the calculation of stresses in simple trusses see 

 problems in Appendix II. 



