358 PRACTICAL MATHEMATICS 



Bending moment at A = Wy 

 but bending moment = El r- 



Hence El = - Wy 



&y W 



dx* ~ FA y 



W 



= n 2 y, where n 2 = -^ 



The solution of this is : 



y = A sin nx + B cos nx 

 But when x = 0, y = 0, then B = 



and y = A sin nx 



but when x = I, y = 0, then A sin nl = 



Now A cannot be zero, for if so bending would not occur. 

 Hence sin nl = 



and nl can have the values 0, TT, 2?:, STT . . . STT. Confining our 

 attention to the least value TT, for the zero value is clearly in- 

 admissible. 



I 2 



A W ^ EI 



and W = w~ 



Case II. When the ends are fixed. 



In this case there must be acting at each end a fixing couple 



of magnitude u and this keeps the direction of an end of the 

 strut in such a condition that the slope there is zero. 



