Find the twist of a circular hollow shaft:
Discover the twist per metre length of a circular hollow shaft having 120 mm outer diameter and 90 mm inner diameter, respectively, if the shear stress is not to exceed 60 N/mm^{2}. Take G = 0.8 × 105 N/mm2.
Solution
d_{i} = 90 mm and d_{o} = 120 mm
τ_{m }= 60 N/mm2, G = 0.8 × 105 N/mm^{2}
Here we know,
= (π / (16 × 120) )× 60 × (120^{4 } - 90^{4} ) = 13.92 × 10^{6}
T / J = G θ/ l
=13.92 × 10^{6}/13.92 × 10^{6} =0.8 × 10^{5 }× θ / l
∴ θ/ l = 1.25 × 10^{- 5} radian
For l = 103 mm, θ= 1.25 × 10^{- 2} radian
Therefore, θ= 0.0125 rad/m length = 0.7^{o} per metre length.