CHAPTER XIX 



151. When a beam is subjected to some system of loading, the 

 beam is slightly bent out of its horizontal position. The bending 

 action depends upon the extent, the character, and the position 

 of the loads, and also this bending action varies at different 

 sections of the beam. If A is the section of a beam (Fig. 94) 

 situated at a distance x from the point of support, and R is the 

 reaction of the support, then all the forces to the right of A help 

 to produce the bending action at A. 



R 



FIG. 94, 



Let W x and W 2 , situated at distances a and b respectively from 

 the end of the beam, be the loads on that part of the beam to the 

 right of A. 



The bending action at A is measured by the algebraic sum of 

 the moments of R, W 1? and W 2 , and this is denned as the " Bending 

 Moment " at A. 



Thus the bending moment at A = R# W^x a) W 2 (# b). 



In general, the bending moment at any section of a beam may 

 be denned as the algebraic sum of the moments of all the external 

 forces acting on that part of the beam, to the right or to the left 

 of that section. 



Example 1. A beam 30 feet long is supported at the ends. 

 It is divided into three equal spans, which carry uniformly dis- 

 tributed loads of | ton per foot run, 1 ton per foot run, and | ton 

 per foot run respectively. Find expressions for the bending 

 moment at any point in each span, and draw the bending moment 

 diagram. 



286 



