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 hollow circular shaft with outer diameter 50 mm and inner diameter 40 mm carries a torque of 400 N·m. Find the maximum shear stress τ_max.

T = 400 N·md_o = 50 mmd_i = 40 mm

τ_max = MPa

2.Easy

A solid shaft of diameter 40 mm carries a torque of 1500 N·m. Find the shear stress τ_ρ at a radius of 15 mm from the centre.

T = 1500 N·md = 40 mmρ = 15 mm

τ_ρ = MPa

3.Medium

A hollow shaft must carry a torque of 500 N·m. Its inner diameter is to be 0.7 times its outer diameter, and the shear stress must not exceed 60 MPa. Find the smallest outer diameter d_o.

T = 500 N·md_i/d_o = 0.7τ_allow = 60 MPa

d_o = mm

4.Medium

A hollow shaft must carry a torque of 200 N·m. Its inner diameter is to be 0.75 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 = 0.75τ_allow = 80 MPa

d_o = mm

5.Hard

A solid brass shaft transmits 5 kW at 1500 rpm. The shear stress must not exceed 60 MPa and the twist must not exceed 0.5° per m of length. Find the smallest diameter d that satisfies both limits.

P = 5 kWN = 1500 rpmτ_allow = 60 MPaθ_allow = 0.5°/mG = 39 GPa

d = mm

6.Hard

A solid shaft must transmit 20 kW at 1800 rpm without the shear stress exceeding 40 MPa. Find the smallest diameter d that works.

P = 20 kWN = 1800 rpmτ_allow = 40 MPa

d = mm

Answer key

1. τ_max = 27.6 MPa
2. τ_ρ = 89.52 MPa
3. d_o = 38.22 mm
4. d_o = 26.51 mm
5. d = 31.24 mm
6. d = 23.82 mm

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