360 



PRACTICAL MATHEMATICS 



take up its proper direction when bending occurs. Let the free 

 end be considered to slide in a frictionless guide, the normal 

 reaction at the guide being Q. 



w 



Considering the fixed end as the origin. 

 Bending moment at A = Q(Z #) Wy 



W 



Let 



Q 



4- _ 



W 



Q 



Q 



- (Z - ), where n 2 = . 



Then -r 2 = 



The solution of this is : 



when 

 also 



when 

 Hence 



= A sin nx + B cos 



:os 

 Q/ 



Q 



rr? (Z a?) = A sin T^c + B cos m 1 



W 



x = 0, y = 0, then B = - 



dii Q 



-r- + TTT = nA cos nx nB sm wa; 

 ax W 



//?y (j 



= 0, -^ = 0, then nA. = ^ 



da; W 



Q 



Q 



sm ^" w cos nx 



Q r i . 



Win 51 



sin nx I cos 



