RESTRAINED, OR BUILT-IN, BEAMS 



87 



At the point where the maximum deflection occurs the tangent 

 is horizontal. Let the distance of this point from the fixed end 

 B be denoted by x. Then, from (40), (49), and (51), articles 37, 

 38, and 39, the condition that the total angular deflection for 

 this length x shall be zero is 



wx 8 



_Mx R'x* 

 El 2EI 



= 0. 



Inserting in this expression the values of M and R' obtained above, 

 and solving for #, the result is 



(107) 



= (15 - V33) = .578 1. 

 16 V ' 



The maximum deflection is then found by finding the total deflection 

 for the length x with re'spect to the tangent at B. Hence, from 

 (38), (47), and (50), articles 37, 38, and 39, 



wx 4 

 "SEI 9 



ZEI 3^1 

 or, inserting the values of M and R', 



(108) 



48JEJJ 



(3J 2 - 



The numerical value of 

 the deflection is most easily 

 found by first calculating 

 the numerical value of x 

 and then substituting in 

 this formula. 



49. Beam fixed at one end 

 and bearing concentrated load 

 at center. The deflection of 

 the end A (Fig. 77) with 

 respect to the fixed end B in this case consists of two parts : from 

 (38), article 37, that due to the reaction R is 



Rl* 



FIG. 77 



