302 PRACTICAL MATHEMATICS 



This gives the actual magnitude of the fixing couple, 



and El ^ = (a*x - V) - \ wa?x 



dx 2 \ 3/3 



= f ( 2 ^- 3 ) 



Then El?/ = | (1 a 2 * 2 - 1 **) + Const 



But at O, where x = 0, t/ = 0. Then Const = 

 and 



w 



id OC ~~ OC j 



This gives the value of ?/ for any point distant a; feet from the 

 centre, and y is greatest when x = a. 



w 



24EI 



wl* .1 



; since a = - 







WZ 3 

 " 384EI 



where W = wl, the total load on the beam. 



This also gives the maximum value of the deflection. 

 In order to obtain S, the deflection at any point, 



8 = yma* - y 



WO, 4 * W 



wa q 



2 2 



Since the bending moment , at any point is -(a 2 x 2 } u and 



2 



wa 2 



Then 



