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 = 40 mm

τ_max = MPa

2.Easy

A motor delivers 15 kW to a shaft turning at 1000 rpm. Find the torque T in the shaft.

P = 15 kWN = 1000 rpm

T = N·m

3.Medium

A solid aluminium shaft 0.5 m long carries a torque of 100 N·m. The angle of twist between its ends must not exceed 3°. Find the smallest diameter d that meets this limit.

T = 100 N·mL = 0.5 mG = 26 GPaφ_allow = 3°

d = mm

4.Medium

In a torsion test, a solid specimen of diameter 20 mm is twisted by a torque of 50 N·m. The two ends of a gauge length of 300 mm rotate 1.4° relative to each other (the material is still elastic). Find the shear modulus G of the material.

T = 50 N·md = 20 mmL = 300 mmφ = 1.4°

G = GPa

5.Hard

A solid steel shaft of diameter 25 mm is fixed at A. A torque of 100 N·m acts at B, 3 m from A, and a torque of 100 N·m in the same direction acts at the free end C, a further 0.5 m along. Find the maximum shear stress τ_max in the shaft.

d = 25 mmT_B = 100 N·mT_C = 100 N·mAB = 3 mBC = 0.5 m

τ_max = MPa

6.Hard

A hollow shaft transmits 20 kW at 1000 rpm. Find the maximum shear stress τ_max in the shaft.

P = 20 kWN = 1000 rpmd_o = 60 mmd_i = 48 mm

τ_max = MPa

Answer key

1. τ_max = 15.92 MPa
2. T = 143.2 N·m
3. d = 24.73 mm
4. G = 39.08 GPa
5. τ_max = 65.19 MPa
6. τ_max = 7.627 MPa

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