FLEXUKE OF BEAMS 



79 



Integrating twice, 



(39) 





At 0, x = and = ; therefore Ci = 0. Also at O, x = and y = ; therefore 

 C, = 0. 



Let x be greater than - Then the differential equation of the branch AB 

 becomes 



Integrating, 

 (40) 



FIG. 63 



At A both branches, OA and AB, have the same slope. Therefore, putting x = - 

 in (38) and (40). and r.juating the values of -j- thus obtained, 



whmoe 



ituting this value of C 8 in equation (40), and integrating again, 

 ,41) ^ = _ B .(|_|) + ^ + c, 



At A both cun-es have the same ordinate. Therefore, putting x = - in equations 

 (39) and (41), and equating the values of y thus obtained, 



