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/mm². 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/mm²

Here we know,

=          (π / (16 × 120) )× 60 × (120⁴  - 90⁴ ) = 13.92 × 10⁶

T / J = G θ/ l

=13.92 × 10⁶/13.92 × 10⁶   =0.8 × 10⁵ × 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.