64 



RESISTANCE OF MATERIALS 



and similarly, from equation (40), the angular deflection at the load is 



JP 2 



(42) 



tan = 



2EI 



Consequently, the additional deflection d' from the load to the free 

 end of the cantilever is 



(43) <*' = 6ta^ 



The total deflection D at the free end is therefore 



EI\3 ' 2, 



It is often convenient to let b = kl, where k denotes a proper 

 fraction. Then in the present case a = I b = I (1 &), and the 

 expression for the deflection at the end becomes 



PI 3 



(45) D -- 



For instance, if the load 

 is at the middle of the 

 cantilever, then k = ^, 

 and the deflection at 

 the free end becomes 



(46) J D = -1L'. 

 48 EI 



38. Cantilever bear- 

 ing uniform load. For 

 a uniformly loaded 

 cantilever the moment 

 diagram is a parabola 

 2 and the moment at 



the support is M wl* = - (Fig. 65). Also, from article 17, 



1 /- 7 8 



the area of the moment diagram is A = -- 1 = -^- and the dis- 



3-2 f, t> 



tance of its centroid from the free end is X Q = - 1. Therefore the 

 deflection at the free end is 



FIG. 65 



(47) 



1 



d = - 

 EI 



wl* 

 - 

 8 EI 



