86 



RESISTANCE OF MATERIALS 



The maximum deflection D is then found to be 



Jif R 



~ 



and, inserting in this expression the values of 

 obtained, it reduces to 



^ 



and x, just 



48. Uniformly loaded beam fixed at one end. In this case 

 (Fig. 76) the deflection of the end A with respect to the fixed 



,. end B consists of two parts: 



J ^ that due to the reaction R is 

 B 



Moment diagram. 



FIG. 76 



and that due to the total uniform 

 load wl is 



2 ~ ' 



wl* 



Since the ends A and B are 

 assumed to be at the same 

 level, the total deflection of A 

 from the tangent at B must be zero ; that is, 



ZEI 8 El 

 whence the reaction at the unrestrained end is 



(104) 



JB = 



8 



The reaction JK r at the restrained end B is therefore 



(105) R' = wl _ R = ^L. 



The maximum moment, which in this case occurs at the fixed end 

 B, is then 



(106) M = HI 



