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 shaft turning at 300 rpm carries a steady torque of 750 N·m. Find the power P it transmits.

T = 750 N·mN = 300 rpm

P = kW

2.Easy

A solid circular shaft of diameter 20 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 = 20 mmτ_allow = 40 MPa

T_max = N·m

3.Medium

In a torsion test, a solid specimen of diameter 10 mm is twisted by a torque of 30 N·m. The two ends of a gauge length of 300 mm rotate 13.47° relative to each other (the material is still elastic). Find the shear modulus G of the material.

T = 30 N·md = 10 mmL = 300 mmφ = 13.47°

G = GPa

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 = 750 N·md = 30 mmL = 1 mG = 39 GPa

φ = °

5.Hard

A solid aluminium shaft of diameter 40 mm is fixed at A. A torque of 250 N·m acts at B, 2.5 m from A, and a torque of 200 N·m in the same direction acts at the free end C, a further 0.8 m along. Find the maximum shear stress τ_max in the shaft.

d = 40 mmT_B = 250 N·mT_C = 200 N·mAB = 2.5 mBC = 0.8 m

τ_max = MPa

6.Hard

A hollow shaft transmits 50 kW at 500 rpm. Find the maximum shear stress τ_max in the shaft.

P = 50 kWN = 500 rpmd_o = 40 mmd_i = 24 mm

τ_max = MPa

Answer key

1. P = 23.56 kW
2. T_max = 62.83 N·m
3. G = 38.99 GPa
4. φ = 13.86 °
5. τ_max = 35.81 MPa
6. τ_max = 87.31 MPa

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