SECTION VII 



RESTRAINED, OR BUILT-IN, BEAMS 



45. Uniformly loaded beam fixed at both ends. By a restrained, 

 or built-in, beam is meant one which is fixed in direction at certain 

 points of its length, usually the ends as, for example, beams built 

 into a wall or forming a part of monolithic concrete construction. 

 The simplest form of restrained beam is a cantilever, which can be 

 treated by ordinary methods, as explained in articles 37, 38, and 39. 



Consider first a uni- 

 formly loaded beam fixed 

 at both ends, as shown in 

 Fig. 73. Let B, F denote 

 the points of inflection 

 of the elastic curve ; that 

 is, the points at which 

 the bending moment is 

 zero. Then the central 

 portion BF may be con- 

 sidered as a simple beam 

 of length 2 x bearing a 

 total uniform load of 

 FIG. 73 amount 2 wx, and each 



of the ends, AB and FE, 



as a cantilever uniformly loaded and carrying a concentrated load 

 wx at the end, equal to one of the reactions for the portion BF. 



If, then, d denotes the deflection of the point F with respect to 

 A or E, assumed to be at the same level, the value of d, computed 

 from the segment AF, is, from (38) and (47), articles 37 and 38, 



WX' 



(80) 



d = 



i Y 



wx[- + x\ 



8 JET 



