7 s STRESSES IN BRIDGE TRUSSES 



2-4, and drawing lines 1-2 and 2-3. The equation of the line 1-2 is 



and the equation of the line 2-3 is 



a(L- X ) 



Now when x=a the two lines have a common ordinate which is equal to 



a(L a) 



- - . Also when x = L the ordinate to 1-2 = L a ; while 

 L 



when x = o, the ordinate to 2-3 is a, as is seen in Fig. 5oa. This rela- 

 tion gives an easy method of constructing an influence diagram for 

 moments for any point in a beam or truss. 



Now in Fig. 5oa the bending moment at 2' due to the loads P and 

 P 2 is 



M = P iyi + P 2 y 2 (a) 



Now move the loads P i and P 2 a short distance to the left, the dis- 

 tance being assumed so small that the distribution of the loads will 

 not be changed, and 



P 1 (y 1 -dy l )+P 2 (y 2 + dy 2 ) (b) 



Subtracting (a) from (b) and placing d M = o, we have 

 dM = P l dy 1 -\-P 2 dy 2 = o 



L a d 



But d 3/ = d x tan a = d x - , and d y 2 = d x tan a 2 = d x-, and 



L, Lt 



L a a 



from which P a P L + P 2 a = o, and (P + P 2 ) a = P 1 L 



