RESTRAINED, OR BUILT-IN, BEAMS 81 



and, computed from the segment FE, is 



(81) d= ^ EI f + ^ 



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

 result is , 



2V3 



The length of the central portion BF is therefore 2 x = = , and 

 the maximum moment, which occurs at the center (7, is 



(82) M c = ~ 



Similarly, the negative moment at the support A or E is 



(I \ 2 

 ,\."(H 



and, since # = -p. , this reduces to 



2V3 



(83) ^ 5- 



The maximum deflection for the central portion BF, considered 

 as a simple beam, is, from (57), article 41, 



ye/ 9 



( 84 ) M 384 AY 



and for one end, say J#, considered as a cantilever, is, from (38) 

 and (47), articles 37 and 38, 



(I _ I V wl II _ l V 4 ;4 

 "^2 2 V3/ 2V3V2 2 V3/ 9 

 (85) ^- 8^7 3 El "384 AY* 



Therefore, since the total deflection of the center C below the sup- 

 ports at A or E is the sum of these two, we have 



wl* 

 (86) z, mM = ___. 



