312 

 and 



Hence q = 



3 2l(d-y) 



Hence q = when y = d and when y = - - ; and q is greatest 



Z 



when d 2 + dy 2y z is greatest. 



Differentiating this with respect to y and equating the result 

 to zero, 



d - ty = 



or y = -d 



_ F 3d Qd 



The maximum value of q = =- x x 

 * 61 4 4. 



QFcff 

 321 



and at the centre q = 



163. Twisting Moment. Let a cylinder of length I and radius r 

 be fixed at one end and a twisting moment T applied at the other 

 end. Let AB be the position of a generator of the cylinder before 



FIG. in, 



the twisting moment has been applied. If 6 is the angle of twist, 

 the point A moves to the position C, and the generator AB takes 

 up the position OB on the surface of the cylinder (Fig. 111). 



