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 = 1500 N·md = 40 mm

τ_max = MPa

2.Easy

A motor delivers 30 kW to a shaft turning at 1500 rpm. Find the torque T in the shaft.

P = 30 kWN = 1500 rpm

T = N·m

3.Medium

In a torsion test, a solid specimen of diameter 10 mm is twisted by a torque of 20 N·m. The two ends of a gauge length of 300 mm rotate 4.38° relative to each other (the material is still elastic). Find the shear modulus G of the material.

T = 20 N·md = 10 mmL = 300 mmφ = 4.38°

G = GPa

4.Medium

A stepped solid aluminium shaft is fixed at A. Segment AB has diameter 60 mm and length 1.5 m; segment BC has diameter 40 mm and length 0.8 m. A torque of 750 N·m acts at the free end C. Find the maximum shear stress τ_max in the shaft.

T = 750 N·md₁ = 60 mm, L₁ = 1.5 md₂ = 40 mm, L₂ = 0.8 m

τ_max = MPa

5.Hard

A solid steel shaft of diameter 50 mm is fixed at A. A torque of 200 N·m acts at B, 1.2 m from A, and a torque of 750 N·m in the opposite direction acts at the free end C, a further 1.5 m along. Find the maximum shear stress τ_max in the shaft.

d = 50 mmT_B = 200 N·mT_C = 750 N·mAB = 1.2 mBC = 1.5 m

τ_max = MPa

6.Hard

A solid shaft must transmit 15 kW at 1450 rpm without the shear stress exceeding 80 MPa. Find the smallest diameter d that works.

P = 15 kWN = 1450 rpmτ_allow = 80 MPa

d = mm

Answer key

1. τ_max = 119.4 MPa
2. T = 191 N·m
3. G = 79.95 GPa
4. τ_max = 59.68 MPa
5. τ_max = 30.56 MPa
6. d = 18.46 mm

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