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 25 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 = 25 mmτ_allow = 40 MPa

T_max = N·m

2.Easy

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

T = 500 N·md = 50 mm

τ_max = MPa

3.Medium

A solid brass 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 = 400 N·md = 50 mmL = 1.2 mG = 39 GPa

φ = °

4.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 = 25 mmL = 1.2 mG = 26 GPa

φ = °

5.Hard

A solid brass shaft transmits 50 kW at 750 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 = 50 kWN = 750 rpmτ_allow = 60 MPaθ_allow = 0.5°/mG = 39 GPa

d = mm

6.Hard

A solid aluminium shaft of diameter 30 mm is fixed at A. A torque of 400 N·m acts at B, 2 m from A, and a torque of 250 N·m in the opposite direction acts at the free end C, a further 1 m along. Find the maximum shear stress τ_max in the shaft.

d = 30 mmT_B = 400 N·mT_C = 250 N·mAB = 2 mBC = 1 m

τ_max = MPa

Answer key

1. T_max = 122.7 N·m
2. τ_max = 20.37 MPa
3. φ = 1.149 °
4. φ = 13.79 °
5. d = 66.07 mm
6. τ_max = 47.16 MPa

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