Loaded Shaft supported in Three Bearings. 639 



Hence 



= I 1 Y(/a-ia s )-i 1 X 1 (« 1 a-ia 2 )fI 1 M 1 a + I 1 C s , 



which gives C 2 in terms of C L . 

 Also 



-EI 1 M a = Y(iZa 3 -ia 3 )-X 1 (ic 1 a 2 -ia 3 ) + iM 1 a 2 + C 1 a + G,, 



-EI A ==Y(ik 2 -ia 3 )-X 1 (i^ 1 a 2 -la 3 )4-iM 1 a 2 -fC 2 a + G 2 . 



^I i Y(iZa > -^-IA(^^ 1 a s ■-^ 8 )+iI 2 M 1 a 8 + IAa + I s G 1 



= IjYCiZa" - -&a 3 ) - IiXxCi^a 8 - \ a 3 ) + il^a 8 + I 1 G 2 a + I 2 G 2 . 



Already we have C 2 in terms of Q lm This equation gives 

 G 2 in terms of Ci, G 1 . 



Then we go on similarly from B to P, etc. Thus we have: 

 to A 



-EI 1 J=Y(^-i. 2 )-X 1 (, 1 r-l.c 2 )+M 1 c + C l 



A to B same, but I 2 , C 2 , G 2 . 



etc., etc. 



B to P same, but I 3 . C 3 , G 3 . 



P to 



-EI 3 J=Y(/..-i: 2 ) + K 3 , 



--EI 3 u=r(Ur 2 -l: 3 ) + K 3 r + H 3 , 

 etc., etc. 



C to L same, but T 4 , K 4 , H 4 . 



The constants are determined by -r- and m being of equal 



values at each side of a load or section change point. Also 

 u = at and L. 



Similar equations hold for the span V with v for u 9 

 X/ for X ; , Y' for Y, M/ for M b z' for c, I' for I, C/ for C, 

 G' for G, K' for K, H' for H. 



We connect Y' with Y by taking moments about the 

 origin 0. Thus 



YZ + Y / Z / -X^ 1 -X 1 V+M 1 -M 1 , =0. 



at i du dv ., . . . . Ci 0] 



Also we have — = . at the origin, . . -r- = , - 

 dz d: " i{ li 



