61 



The maximum bending moment occurs at the point 

 where the vertical shear equals zero and will be at one 

 of the loads P, P lt or P 2 depending upon their amounts 

 and spacing if W 2 is neglected. 



Let /?=Reaction at left support. 



Bending moment at P= 



Bending moment at P l = 



[W^a , 2 

 ^ + P <i 



Bending moment at /% =M f2 = Ra 2 



Shear or reaction at left support = 



1 2 



Shear or reaction at right support = 



W 

 2 



Diagram for superimposed load: Draw as in case (5) 

 the ordinates FC, GD and HE representing the bend- 

 ing moments due to loads /*, /*, and P \ respectirely. 

 Produce FC to P, making PC=fC+IC+jC{ GD to Q. 

 making QD=GD+KD+LD\ and //^ to /?, making 

 RE=HE+ME+NE. Join the points ^, /, ^2, R and 

 ^, then the ordinates between A B and polygon A P 

 Q R B will represent the bending moments for corre- 

 sponding points on beam. 



