Torque carried by the hollow shaft, Mechanical Engineering

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

∴  921_Torque carried by the hollow shaft.png

 

∴ Shearing stress on surface

 1949_Torque carried by the hollow shaft1.png ---------------- (i)

For alike material and alike weight of hollow and solid shafts

1345_Torque carried by the hollow shaft2.png

i.e.  2357_Torque carried by the hollow shaft3.png  ----------- (ii)

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

τhm = 16T / π d3

Utilizing d from Eq. (ii)

   2082_Torque carried by the hollow shaft4.png-------------------- (iii)

Equating τhm from Eqs. (i) and (iii)

1208_Torque carried by the hollow shaft5.png

Th  = (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.

Posted Date: 1/21/2013 4:28:41 AM | Location : United States







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