CONCENTRATED MOVING LOADS 61 



Concentrated Moving Loads. Let a beam be loaded with con- 

 centrated moving loads at fixed distances apart as shown in Fig. 40. 



- ->(- - b *j - c - -| 



__ L_ . 



FIG. 40. 



To find the position of the loads for maximum moment and the 

 amount of the maximum moment, proceed as follows: The load P 2 

 will be considered first. Let x be the distance of the load P 2 

 from the left support when the loads produce a maximum moment un- 

 der load P 2 . 



Taking moment3 about R 2 we have 



and the bending moment under load P 2 will be 



(19) 



_ p 



Differentiating (20) we have 



dM__(L2x] (P, + P, + P 3 + P. l - 3 j = n . 



d x L ^ 



and solving (21) for x we have 



L_ P,g-P,b-P<(b+c) (22) 



= 2 ~ 2(P l + P 2 +P 3 + P.) 



Now P a P z b P 4 (& + c), is the static moment of the loads 

 about .P 2 and 



