SHAFTING STRESSES :

SOLID AND HOLLOW SHAFT -Solid shaft Diameter = D, Hollow shaft Outside diameter = D₂ Hollow shaft inside diameter = d₂

We have T\J =q\r

Where, T = Torque on shaft, J = Polar second moment of area of shaft, q = Working shear stress maximum, r = Shaft radius.

Strength of solid shaft \ Strength of hollow shaft  = Torque Solid (T,) \  Torque hollow (T₂) =  q,J₁r₁ \ q₂J₂r₁                 

For the same working stress,

Strength Solid \ Strength hollow  = J₁- D₁   \  J₂ - D₁   =  D₁⁴ \ 32. D₁   x 32 . D₂    \  (D₂⁴ - d₂⁴)                      

 = D₁³  - D₂    \ (D₂⁴ - d₂⁴)

So, Strength Solid \ Strength hollow  =   360³ x 380 \ (380⁴ - 250⁴) = 1.76 \ 1.66

i.e. approximate the same strength but 40% reduction in weight for the same length. Hollow shafting is however more expensive.

For solid shaft of 300 mm dia with a flaw detected at 25 mm deep, then the shaft power which is proportional to torque, T\J = q\r , T = 2 Jq \ D = 2  D⁴ .q \ D.32 =   D³ .q \16

Thus Power a Torque a (Diameter)³.

Power reduction for 25 mm flaw,

Reduction ratio = 250³  \  300²  = 1.56 \ 2.76  power reduction to about 58% of original power.

SHAFTING STRESSES

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