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 carries a torque T. Find the maximum shear stress τ_max in the shaft.

T = 200 N·md = 30 mm

τ_max = MPa

2.Easy

A solid shaft of diameter 20 mm carries a torque of 100 N·m. Find the shear stress τ_ρ at a radius of 7.5 mm from the centre.

T = 100 N·md = 20 mmρ = 7.5 mm

τ_ρ = MPa

3.Medium

A solid aluminium shaft is fixed at the wall and twisted by a torque T at its free end. Find the angle of twist φ of the free end, in degrees.

T = 200 N·md = 50 mmL = 1.5 mG = 26 GPa

φ = °

4.Medium

A solid aluminium shaft 0.8 m long carries a torque of 250 N·m. The angle of twist between its ends must not exceed 1.5°. Find the smallest diameter d that meets this limit.

T = 250 N·mL = 0.8 mG = 26 GPaφ_allow = 1.5°

d = mm

5.Hard

A solid brass shaft transmits 75 kW at 300 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 = 75 kWN = 300 rpmτ_allow = 40 MPaθ_allow = 0.25°/mG = 39 GPa

d = mm

6.Hard

A solid aluminium shaft transmits 10 kW at 750 rpm. The shear stress must not exceed 80 MPa and the twist must not exceed 0.5° per m of length. Find the smallest diameter d that satisfies both limits.

P = 10 kWN = 750 rpmτ_allow = 80 MPaθ_allow = 0.5°/mG = 26 GPa

d = mm

Answer key

1. τ_max = 37.73 MPa
2. τ_ρ = 47.75 MPa
3. φ = 1.077 °
4. d = 41.59 mm
5. d = 109.3 mm
6. d = 48.9 mm

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