RESTRAINED, OR BUILT-IN, BEAMS 83 



Similarly, for the portion DE, the deflection of D below E is 



P/I V 



2l2 *) 



(91) d DE = \ EI '. 



Equating these two values of the deflection and solving for x, the 



result is 



I 

 "I- 



and consquently the length of the central portion BD is 



,.4 



Therefore the moment at the center C and also at each end is of 



numerically the same amount, namely, j-^- or 

 (92) M = ?L. 



The maximum deflection for the central portion BD is the same 



I 

 2 



as for a simple beam of span - , namely, 





d ~ 



_ __ 



* D ~ 48 El ~ 384 El ' 

 and for either end AB or DE is the same as for a cantilever of 



7 p 



length - carrying a load at the end, namely, 



AB ~ 



Pl s 



Therefore the total deflection of the center C below the level of the 

 supports at A and D is the sum of these two, that is, 



PI 3 



(95) 



