FLEXURE OF BEAMS 



77 



elastic curve of a built-in beam differs from that for a simple beam in 

 having two points of inflection, A and B. At these points the curvature 



is zero, that is, -4 = 0, 

 oar 



and consequently the bend- 

 ing moment is also zero, 



since EI^- = M. ' 



FIG. 61 



Problem 82. Find the equation of the elastic curve and the maximum deflec- 

 tion for a beam of length i, fixed at both ends and bearing a uniform load of w Ib. 

 per unit of length. 



Solution. Let M a and M b denote the moments at the supports (Fig. 62). The 



wl 

 vertical reactions at the supports are each equal to 



Consequently, the bending moment at a point distant x from the left support is 



ami therefore 





B 



In teg r 



At A, x = and = ; therefore C t = 0. At B, x = I and -2 = ; therefore 



wP d* ?x 



M a = -- Substituting this value of M a in the above integral, and integrating again, 



wlx* wx* , _ 



At A, x = and y - ; therefore C 2 = 0. Consequently, the equation of the elastic 

 duction, 



21 El 



