82 



RESISTANCE OF MATERIALS 



46. Beam fixed at both ends and bearing concentrated load at 

 center. Following the method of the preceding article, let B and D 



denote the points of in- 

 flection of the elastic 

 curve, or positions of 

 zero moment (Fig. 74). 

 Then the equilibrium 

 would not be disturbed 

 if the beam was hinged or 

 jointed at B and D, and 

 it may therefore be con- 

 sidered as a simple beam 

 of length BD suspended 

 from the ends of two can- 

 tilevers AB and DE. 



Now consider the seg- 

 ment AD and compute 



the deflection of D below A. Then, from (44), article 37, the 

 deflection at D due to the load P is 



Pa 2 la 



(87) 



where in the present case a = - and b = #, and consequently 



(88) 



d p = 



_PT 

 8-E/V3 



But from (38), article 37, the load , acting upward at D, produces 

 a deflection upward of amount 



P 



(89) 



Consequently the total deflection of D below A is 



P/ 2 

 (90) <*- = ^ 



