74 RESISTANCE OF MATERIALS 



Therefore, by addition, the total deflection of the end A with respect 

 to the tangent at B is 



Now, forming a moment equation for the portion AB, taking center 

 of moments at B, we have 



whence Sf = - (J^ - M^ + ?(! - kj, 



\ 



and eliminating ^ between this equation and the expression for 

 Z>., the result is 



Similarly, to find the deflection at (7, measured from the tangent 

 to the elastic curve at B, treat the portion BC as a cantilever fixed 

 at B and subjected to the moment M^ the shear S% considered as 

 a load, and the concentrated load ^. Then, calling these partial 



deflections d^ d z , d^ we have 



(Eq. (50), Art. 39) 



<* 2 = j** (Eq. (38), Art 37) 



, Art. 37) 



or, since in the present case a = & 2 Z 2 , 5 = Z 2 (l & 2 ), the expression 



for d s becomes 



Therefore the total deflection D c from the tangent at B is 



