Case 3 -- Deflection (Machinery's Handbook)
Shaft supported at each end and concentrated load at any point between supports
(W*a(sq)*b(sq))/(3*E*I*L) = deflection at load
(W*a*v(power 3))/(3*E*I*L) = deflection at longer segment
                 
Total Load (W) = Lbs. Max deflection at load = ( solid shaft)
Length Between Supports (L) = inches   (hollow shaft)
Shaft Diameter (D) = inches    
I.D. of Hollow Shaft (d) = inches (optional) Max deflection = ( solid shaft)
Short segment between load & support (a) = inches (at long segment) (hollow shaft)
                 
Long segment (b) = L -a = inches  
                 
Modulus of Elasticity (E) (steel) Steel Shaft Weight = Lbs. (solid)
Moment of Inertia (I) (for solid shaft) Steel Shaft Weight = Lbs. (hollow)
Moment of Inertia (I) (for hollow shaft)  
v = b*sq-rt((1/3)+(2a/3b) = (for solid shaft)  
           
  do not modify            
W * a(sq) * b(sq) =    
W * a * v(power 3) = (for solid shaft)  
           
3 * E * I * L (solid shaft)  
3 * E * I * L (hollow shaft)  

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