284 Dr. B. C. Laws on Strength of the 



an expression for the bending moment of any point 

 between c and d. 



When x—a 



m(a—n) . —m{a-n)^ 



M «- m ] g m(.-»)_^-.»(«-») J m2 ' 



When %—n, 



1 1 2ica - (t<m + m'E .U) ( g y Ca - n) + ^ W(a - H) ) I _ io 



of which M >M n . 



The deflexion at any point between c and d is given by 



m 2 E . I . y = 



1 {^.a(^- w) + . " W(r " B) )-^-<C (a " n) + ^ W(a " W) ) 1 



1 (ten + m 2 E . 1 4>) (ef a ~^ + <, -'"<"-*> -2) ^ _ ^ ; ^ 



--.- ^(a-«)_^-m(«- W ) 2 



and when x—n, 



m 2 E .r.y» = 



^ _ n2) 2- j (^ (g ~ n) + ^ ffl(a " ,l) - 2)Q« + »n 4m 2 E.I<ft) | 



2 m\ ^(«-»)_ g -m(a-») f> 



. . . (b) 



in which ?/„ denotes the deflexion at c. 



Next consider the portion oc of the beam. We have : 



B.I I g=M.+ »'Jfl.I*-*^, 



rf2„ rffl M a to (a 2 -a 8 ) 



'• e " £»= mV+ irr 1 and ^ = A, -'» +Bl -'° -JWA? 



dy 



and E . hj^z= m. E . I, (A, . 4" x — B, . e„ )-— 2 . 



