Art. 84. 



DEFLECTION OF A BEAM. 



131 



84. Deflection of a Beam Supported at Its Ends and 

 Carrying a Single Load at Any Point. Fig. 95 shows a beam 

 carrying a load P at distances Z and 1 2 from the supports. 



For the segment AC 



Equation (39) becomes 



(> 



EIy= J a? -f Cfe-f (C 1 .=="0) (6) 



When x = 0, y = Q, and therefore C = 0. In order to 

 evaluate (7, it is necessary to find y and ^ for the segment CB ; 

 this may be done by taking A as the origin, but if B is taken as 

 the origin, the equations will be exactly similar to those above. 

 Imagining the beam turned end for end, 



= iP -^ x\ + Vxi + ( G{ = 0) (d) 



C and C' may be evaluated by means of the conditions at 

 the load where, when x = l 1 and x^ = 1 2 , y = y^ and -r = 



(J3& CtOC-\ 



The deflection is positive in both cases, but since x and x^_ hav< 

 been taken positive in opposite directions, the slopes from equa- 

 tions (a) and (c) will be the same if they are given opposite 

 signs. From (a) and (c) 



From (6) and (d) 



-lP^li 3 +Ch= -tP-b-lf+CTh 

 Multiplying (e) by 1 2 and subtracting (/) from it 



(0 



, 



C=P (l -4-21 ) y' 

 This value of G. in equation ( 6 ) gives 



