REACTIONS OF DRAW BRIDGES 169 



Chapter XL It is assumed that the deflection at points b and c are 

 equal. 



In (b) Fig. 8, the deflection at b from the tangent at a is found 

 by taking moments of the moment areas below b to be 



M d 2 ,M,d d 

 El A = -- d _ 

 23 23 



2 



(14) 



6EI 



The deflection at c from the tangent at a is found by taking 

 moments of moment areas below c to be 



M d 



2 



, 



A 1 - - (15) 



6EI 



But A is equal to A 1 by hypothesis, and equating (14) and (15) 

 we have 



transposing, 



MO ($hd zd 2 }=Mi ( 2 h 2 hd d 2 ) (16) 



Now in (c) Fig. 8, it will be seen that M : M :: y : d y , 

 and 



M (d-y )=M iyo (17) 



Solving (16) and (17) for y , we have 



which is the same value as was found by algebraic methods. 



Reactions of Simple Draw Bridges. The preceding methods are 

 not adapted to the solution of problems involving moving loads, as 

 in draw bridges. The following method, which is an application of 

 curved influence lines, is quite simple in theory and application, al- 



