Loaded Shaft supported in Three Bearings. »641 

 Also r 1= -?V; &i = 0; G/ = 0. 



lit -=— =fl m . 



§ 5. Reverting to the displacement equations we now have, 

 from to P, 



6EI niW = X 1 ^(3^ JL -^)^3M 1 e 2 -Y^(3/-^-6C^-6G m ; 

 from P to L, 



6EI„u= -Ys 2 (3Z-s)--6K n 2--6H n ; 



from to P', 



6ET^=X 1 V 2 (3^ 1 , -/)-3M 1 V 2 --YV 2 (3Z , -^)--6C w ,V 

 from P'toL', -6G m ' ; 



6ET n W _YV 2 (3r-0-6K,/*'-6H n ' ; 



and 

 C m+1 =C„/*m + i(f*ni - l)a* [Y(2Z- a Ml ) -X 1 (2r 1 -a m ) + 2M 2 ], 



■vTm+l = ^mf*m + (C m )U- Hl — C m +l) dm 



+ i(^-l)a w 2 [Y(3^a m )-X 1 (3^ 1 -a m )+3M 1 ]. 



-a^ ni ~^ //i -l)a^[Y(3/-2a m )-X 1 (32' 1 ~-2a n ,)+3M 1 ] 

 K r = a-K[X 1 (2^ l -«, r )-2M 1 ]. 

 H,.= G r + (C,-K r )c7 r -J-a r 2 [X 1 (3^ 1 -a r )-3M 1 ] 



= G r + iV[X 1 (3.e l -2« r )-3M 1 ], 

 K n+ i = K n /* n + i(^ n — l)a n Y(2Z — a»). 



H„ +1 = H ; ^-}-(K,^ l -K, l+1 )a )l + i(^-l)« /i 2 Y(3/ — a„) 

 = K nf i n - JO< - 1H 2 Y(3Z- 2a B ). 



• - r - = y4 ; Gi = 0; G/ = 0. 

 -m J-i 



^Y/ 3 + KJ + H,, =0. 



Y/ + Y7'-X 1 r 1 -X 1 ^ 1 ' + M 1 + M/-0. 



§6. For u number of loads X and M the total displace 

 ment at any point is the sum of the displacements due to 



