352 Mr. B. C. Laws on the Strength 



(a) For the portion oc o£ the beam : — 



-E.lg = -M a Q +Q(a- C ). 



" dx~~ E.I ' X - 

 There is no constant of integration, since when x = 0. 



dw 



At c we have 



Q 

 dy _ M a . c— Q(a — c)c 



dx ~ ETl * 



(b) For the portion cd of the beam : — 



-E.l^ = -M?+Q(a-;r). 



d 1 _^-Q LL a Q.x 2 



" dx" E.I •^ + 2E.I +A ' 



where h is a constant. 



Q 

 dy , 7 M a . a Q . a 2 

 When a?=a, -^ =0, and & = — =-+^=— =. 



Q 



^.V _ ^-« (a — .e) Q(a — «r) 2 

 •'• flta " E7I + 2E . I 



Mq(a-P) Qfa-r) 2 . 



E.I + 2E . I * ' ' c ' 



Equating the two values for ■£- at c, we have 

 ^ " ax 



r Q Q(a 2 -c 2 ) 



M « " 2a 



L a 



When ,r=a, — ii . 1 T '', = M.„ = 5- 



dx* za 



When «=.0, -E . ig = M? = -M« + Q(a-e) = ^^ 



When x = c, — Jii . I-7-5 = ^c — iU o — ~r • 



ax" &a 



