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 = 1000 N·md = 30 mm

τ_max = MPa

2.Easy

A hollow circular shaft with outer diameter 30 mm and inner diameter 18 mm carries a torque of 750 N·m. Find the maximum shear stress τ_max.

T = 750 N·md_o = 30 mmd_i = 18 mm

τ_max = 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 = 250 N·md = 50 mmL = 1 mG = 26 GPa

φ = °

4.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 = 500 N·md = 40 mmL = 1 mG = 39 GPa

φ = °

5.Hard

A solid brass shaft of diameter 50 mm is fixed at A. A torque of 100 N·m acts at B, 2.5 m from A, and a torque of 1000 N·m in the same direction acts at the free end C, a further 1.2 m along. Find the magnitude of the angle of twist φ_C of end C, in degrees.

d = 50 mmT_B = 100 N·mT_C = 1000 N·mAB = 2.5 mBC = 1.2 mG = 39 GPa

φ_C = °

6.Hard

A hollow shaft transmits 100 kW at 750 rpm. Find the maximum shear stress τ_max in the shaft.

P = 100 kWN = 750 rpmd_o = 100 mmd_i = 60 mm

τ_max = MPa

Answer key

1. τ_max = 188.6 MPa
2. τ_max = 162.5 MPa
3. φ = 0.8979 °
4. φ = 2.923 °
5. φ_C = 9.457 °
6. τ_max = 7.45 MPa

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