Torque carried by the hollow shaft:

A hollow and a solid shaft of similar material have the same weight when the inner diameter of the hollow shaft is half its outer diameter. What shall be the torque carried by the hollow shaft if the solid shaft may carry a torque T for alike maximum shearing stress in both of the shafts.

Solution

For hollow shaft, di  =  do /2

∴ 

∴ Shearing stress on surface

  ---------------- (i)

For alike material and alike weight of hollow and solid shafts

i.e.    ----------- (ii)

If on solid shaft torque T induces maximum stress τ_h on surface, then

τ_hm = 16T / π d³

Utilizing d from Eq. (ii)

   -------------------- (iii)

Equating τ_hm from Eqs. (i) and (iii)

T_h  = (0.9375/0.625 )T

 = 1.442 T

Hollow shaft shall carry 44.2% more torque if two shafts weigh equal and are subjected to similar surface stress.