294 



Then 



PRACTICAL MATHEMATICS 



M = E = 

 I ~R~y 



and also 



154. The Deflection of Beams. (1) A cantilever of length I ft. 

 carrying a load W tons at one end. 



W 



1 



r^""~~ - jf, - -j 



FIG. 99, 



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

 end. 



Bending moment at A = W(Z x) ft. tons. 



IT d*y 

 xi 6 ii c 6 .TJ! = W ( / cc i 



EI ^ = W/te - L 2 ^ + Const 

 ax \ 2 / 



But at O, where x = 0, -j$- = 0, since at that point the direction 

 of the beam is horizontal. Therefore Const = 0. 



and EIw = W( -lx 2 - L 8 ] + Const 



\2 6 / 



But at O, where x = 0, ?/ = 0. Hence Const = 

 Then ^ = 



W 



This gives the deflection at any point distant x ft. from the 

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



W/ 3 



Then 



Umax 



3EI 



