74 



STRESSES IN BRIDGE TRUSSES 



on each side, and are given by the ordinates to the chords of the parabola 

 as shown in Fig. 49. 



The parabola is constructed as follows: The mid-ordinate, 4;, is 

 made equal to the bending moment at the center of the truss divided by 

 the depth ; in this case the mid-ordinate is the stress in 6-^r; if the num- 



ber of panels in the truss were odd the mid-ordinate would not be equal 

 to any chord stress. The parabola is then constructed as shown in Fig. 

 49. The live load chord stresses may be found from Fig. 49 by chang- 

 ing the scale or by multiplying the dead load chord stresses by a con- 

 stant. 



Shear Polygon. In Chapter IX it was shown that the maximum 

 shear in a beam at any point could be represented by the ordinate to a 

 parabola at any point. The same principle holds for a bridge truss 

 loaded with equal joint loads, as will now be proved. 



In Fig. 50 assume that the simple Warren truss is fixed at the left 

 end as shown, and that right reaction R is not acting. Then with all 

 joints fully loaded with a live load P, construct a force polygon as 

 shown, with pole o and pole distance H span L, and beginning at 

 point a in the load line of the force polygon construe! the equilibrium 

 polygon a g h for the cantilever truss. 



Now the bending moment at the left support will be equal to 



