DEFLECTION OF BEAMS 



301 



Let the centre of the beam be taken as the origin, and let A 

 be a section situated at a distance x ft. from O. The portion of 

 the load on that part of the beam to the right of A is w(a x) 

 tons. 



Bending moment at A = wa(a x) - w(a x) 2 u 



Hence 

 and 



- (a 2 - x 2 ) - u ft. tons 



I 



BM diagram, 



FIG. 104. 



dx 

 dy 



-(a*x -laA-ux+ Const 

 2 \ 3 / 



But at O, where x = 0, -f- = 0. Then Const = 

 ox 



dx 2 



At the end, that is, where a; = a, -^ = 



flu 



and 



or 





