Compute the ratio of the torque:
Compute the ratio of the torque transmitted by a hollow & a solid shaft of the similar material, length & weight.
Solution
d_{i} = internal diameter of hollow shaft
d_{0} = external diameter of hollow shaft
d = diameter of solid shaft
Similar material means modulus of rigidity and density is similar. The weight being equal means the cross-sectional areas of solid & hollow shafts are similar:
i.e.
where
∴ n = d_{i} / d_{o}
d = do
τs = 16Ts / π d ^{3} = 16Ts / π d ^{3 }(1 - n^{2 }) ^{(3/2)}
For same material τ_{s} = τ_{h}
∴ Ts /(1 - n^{2} ) ^{(3/2)} =Th/(1 - n^{4 })^{2}