Torsion of shafts worksheet with answers

Free printable Torsion of shafts worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

A solid circular shaft of diameter 40 mm is made of a material with an allowable shear stress of 40 MPa. Find the largest torque T_max the shaft can carry.

d = 40 mmτ_allow = 40 MPa

T_max = N·m

2.Easy

A solid shaft of diameter 40 mm carries a torque of 1000 N·m. Find the shear stress τ_ρ at a radius of 5 mm from the centre.

T = 1000 N·md = 40 mmρ = 5 mm

τ_ρ = MPa

3.Medium

A hollow shaft must carry a torque of 400 N·m. Its inner diameter is to be 0.7 times its outer diameter, and the shear stress must not exceed 50 MPa. Find the smallest outer diameter d_o.

T = 400 N·md_i/d_o = 0.7τ_allow = 50 MPa

d_o = mm

4.Medium

A hollow shaft must carry a torque of 200 N·m. Its inner diameter is to be 0.8 times its outer diameter, and the shear stress must not exceed 80 MPa. Find the smallest outer diameter d_o.

T = 200 N·md_i/d_o = 0.8τ_allow = 80 MPa

d_o = mm

5.Hard

A hollow shaft transmits 15 kW at 3000 rpm. Find the maximum shear stress τ_max in the shaft.

P = 15 kWN = 3000 rpmd_o = 40 mmd_i = 24 mm

τ_max = MPa

6.Hard

A solid aluminium shaft transmits 30 kW at 750 rpm. The shear stress must not exceed 40 MPa and the twist must not exceed 0.25° per m of length. Find the smallest diameter d that satisfies both limits.

P = 30 kWN = 750 rpmτ_allow = 40 MPaθ_allow = 0.25°/mG = 26 GPa

d = mm

Answer key

1. T_max = 502.7 N·m
2. τ_ρ = 19.89 MPa
3. d_o = 37.71 mm
4. d_o = 27.83 mm
5. τ_max = 4.365 MPa
6. d = 76.53 mm

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