62 MOVING LOADS ON BEAMS 



= distance from p to 



center of the gravity of all the loads. 



Therefore, for a maximum moment under load P 2 , it must be as 

 far from one end as the center of gravity of all the loads is from the 

 other end of the beam, Fig. 40. 



The above criterion holds for all the loads on the beam. The only 

 way to find which load produces the greatest maximum is to try each 

 one, however, it is usually possible to determine by inspection which 

 load will produce a maximum bending moment. For example the 

 maximum moment in the beam in Fig. 40 will certainly come under 

 the heavy load P 2 . The above proof may be generalized without diffi- 

 culty and the criterion above shown to be of general application. 



For two equal loads 'P = P at a fixed distance, a, apart as in the 

 case of a traveling crane, Fig. 41, the maximum moment will occur 

 under one of the loads when 



L a 



R| ! ^C-G- of Loads TR 2 



*L 1 



r,Y_~-Y_ ?_"_ ivn r r . ?-". 2 



FIG. 41. 

 Taking moments about the right reaction we have 



# i== P ( L ~~~2' (23) 



and the maximuni bending moment is 



"-*(r-i) 



(24) 



