88 STRESSES IN A TRANSVERSE BENT 



To obtain B and C a second equation is necessary. 



From the theory of flexure we have for the bending moment in 

 the column at any point y, where the origin is taken at the base of the 

 column, when y = d 



M=EI d L- = B(d-y)- C(h -y) (32) 



Integrating (32) between the limits y = o and y = d, we have 



Now (33) equals H I times the angular change in the direction of the 

 neutral axis of the column from y = o to y = d. 

 When y T d, we have 



M=E /=- M*-JO (34) 



Integrating (34) we have 



+ ft (35) 



(35) equals H I times the change in direction of the neutral 

 axis of the column at any point from y = d to y = h. 



To determine the constant F 2 in (35) we have the condition that 

 the angle at y = d must be the same whether determined from equation 

 (33) or equation (35). Equating (33) and (35) and making y = d, 

 we have 



F^^f- (36) 

 Substituting this value of F z in (35) we have 



SI d J^ = - Chy +^ + *f (37) 



Integrating (37) between the limits y = d and y = h, we have 



(38) 



