88 RESISTANCE OF MATERIALS 



and from (44), article 37, that due to the load P is 



(7\8 //\ 2 7 



-) P -}- 



9 / I 9 / 9 



L ) W * 



a a~ " 3 El ' 2 El 



Since A and Z? are assumed to be at the same level, the total 

 deflection of the end A with respect to the tangent at B must be 

 zero. Consequently, 



RP PI 8 PI 8 



3 El 24 El 16 El 



= 0; 



whence 



(109) R = ^Lp. 

 Therefore 



(110) R' = P-R = ^P. 



The maximum moment, which in this case occurs at B, is then 



(111) M = Rl- p 



16 



The position and amount 

 of the maximum deflec- 

 tion may be found as in 

 the preceding article. 



50. Beam fixed at one 

 end and bearing a concen- 

 trated eccentric load. The 

 deflection of the end A 

 with respect to the fixed end B (Fig. 78) also consists of two parts 

 in this case. From (38), article 37, that due to the reaction R is 



FIG. 78 



and from (44), article 37, that due to the load P is 



PI 8 Pl 2 l 

 ~ 2 El' 



