Case 4 -- Deflection (Machinery's Handbook)
Shaft supported at each end and Two symmetrical loads equal distance from each end
(Wa/24EI)*(3L(sq)-4a(sq)) = Max deflection at shaft midpoint
(W*a(sq)/6EI)*(3L-4a) = Deflection at loads
*** 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)
Distance between load & support (a) = inches   (at shaft midpoint) (hollow shaft)
*** Enter total roll weight  
Modulus of Elasticity (E) (steel) Steel Shaft Weight = Lbs. (solid)
Moment of Inertia (I) (for solid shaft)   Lbs. (hollow)
Moment of Inertia (I) (for hollow shaft)  
  do not modify    
W *a/2 =    
W * a(sq)/2 =    
24 * E * I = (for solid shaft)  
24 * E * I = (for hollow shaft)  
3*L(sq) - 4*a(sq) =    
3L - 4a =    
6 * E * I = (for solid shaft)  
6 * E * I = (for hollow shaft)  

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