ALGEBRAIC MOMENTS 73 



The maximum live load stress occurs when all loads are on except 

 LI, and 



C/ L 2 x 70.7 + R! x 60 = o 



U L 2 x 70. 7 = p x 60 = 576 foot-tons 



O 



U 1 L 2 = 8.14 tons 



The maximum live load stress in counter U 2 L^ occurs with a load 

 at L lf and is given by the equation 



U 2 L-L x 62.43 + R! x 60 P x 80 = o 

 U 2 LI x 62.43 = A P x 60 8 x 80 

 U 2 Lj_ = 4.10 tons 



The dead load stress in counter U 2 L when main member U^ L 2 

 is not acting will be 



U 2 LI x 62.43 = + 120 foot-tons 

 U 2 LI = + 1.92 tons 



The maximum stress in U^ L 2 is therefore 1 .70 8. 14 = 

 9.84 tons, and the minimum stress is zero. The maximum stress in 

 counter U 2 L is + 1.92 4.10 = 2.18 tons, and the minimum 

 stress is zero. 



The stresses in the remaining members may be found in the same 

 manner. To obtain stresses in upper chords U^ U 2 and U 2 U 2) take mo- 

 ments about L 2 as a center ; to obtain stress in lower chord Z, 6 L take 

 moments about C7 X as a center. The dead load and maximum live load 

 stress in post U 2 L 2 is equal to the vertical component of the dead and 

 live loads, respectively, in upper chord f/ U 2 . The stresses in L U lf 

 L L-L, L 2 IS 2 , U 2 U^ 2 and U 2 L 1 2 are most easily found by algebraic 

 resolution. 



Graphic Moments. The dead load stresses in the chords of a 

 Warren truss are calculated by graphic moments in Fig. 49. 



Bending Moment Polygon. The upper chord stresses are given 

 by the ordinates to the bending moment parabola direct, while the 

 lower chord stresses are arithmetical means of the upper chord stresses 



