DEFLECTION OF BEAMS 295 



155. (2) A cantilever of length / carrying a uniformly distributed 

 load of w tons per foot run. 



FIG. 100, 



Let A be a section situated at a distance x ft. from the fixed 

 end. The load on the portion of the cantilever to the right of A 



is w(l x) tons, and this acis at a distance of -(/ - x) ft. from A. 



B 



Bending moment at A = (I x) z ft. tons. 



m 



Hence El ^ = -(Z 2 - 2lx + x z ) 



dx 2 2 



and El ^ = %(l 2 x - lx* + V) + Const 



dx 2\ 3 / 



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

 dx 



Then Ely = |(i Z 2 ^ 2 - | Ix* + i a*\ + Const 



But at O, where x = 0, y = 0, Then Const = 



"* 



This gives the deflection at any point distant x feet from the 

 fixed end. The deflection is evidently greatest when x = I. 



wl* 

 Then 



w 



-m 



here W = wl, the total load on the cantilever. 



