/ 



9 



242 



; / 



I {(XX -f ji) c?.r = I 5 da 







I I 



I («a; -\- ^) . X d.v = I q . a; d, 

 



on the contrarj 6V + O, is defined by 



ƒ ( C. ^ I i>,) d.v = — Cq'dw = - f~dx 







/ < I 



I (C", A' ■[ D^) . X dm ■^ — I ^' . .(-' d.v :^: — | — . x dx. 







It follovvK, that (tx -\- ^ = ~ El(C^x -r D,), so that: 



ax + ^ , C,x ^- D, 



y' = ~i^= — k' — • 



The load wliicii really charges the beam differs from the substitute 

 load by : 



9. -= «7 - '7. = 9 - (« ■" + i') = EI (q' + C,x + D,) = Ely^. {x). 

 By adding this load (which is in eqiiilibrinni) to the load q^, we 

 would regain the real conditions of loading. 



However, if we add the load q, the beam gets a deflexion y^, 

 . determinated by : 



EIy';" = Eiy.,(x) 

 Hence : 



X X 



.'/> = fy> C'^) dx' = j ~^5C. («) d> + A, x' + B,x^ + C, X + D,. 







The second and tiiird derivates of y, being zero for x = 0, it 

 follows that ^, =0, B,=0. 

 Choosing C, and ü^ so that: 







I .'/, dx = 







I 

 1 y^ .xdx = 







we identity ?/i and — Xi ^■'')- 



