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
T = 500 N·md = 30 mm

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

T = 500 N·md = 30 mm
τmax = MPa
2.Easy
do​ = 30, di​ = 18 mmT = 400 N·m

A hollow circular shaft with outer diameter 30 mm and inner diameter 18 mm carries a torque of 400 N·m. Find the maximum shear stress τmax.

T = 400 N·mdo = 30 mmdi = 18 mm
τmax = MPa
3.Medium
d = ?T = 200 N·mL = 0.8 m

A solid aluminium shaft 0.8 m long carries a torque of 200 N·m. The angle of twist between its ends must not exceed 3°. Find the smallest diameter d that meets this limit.

T = 200 N·mL = 0.8 mG = 26 GPaφallow = 3°
d = mm
4.Medium
d = 20 mmT = 50 N·m300 mmφ = 2.1°

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 2.1° 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 = 2.1°
G = GPa
5.Hard
Td = ?

A solid shaft must transmit 20 kW at 500 rpm without the shear stress exceeding 60 MPa. Find the smallest diameter d that works.

P = 20 kWN = 500 rpmτallow = 60 MPa
d = mm
6.Hard
d = ?50 kW, 1000 rpm

A solid brass shaft transmits 50 kW at 1000 rpm. The shear stress must not exceed 80 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 = 1000 rpmτallow = 80 MPaθallow = 0.5°/mG = 39 GPa
d = mm

Answer key

  1. 1. τmax = 94.31 MPa
  2. 2. τmax = 86.69 MPa
  3. 3. d = 33.08 mm
  4. 4. G = 26.05 GPa
  5. 5. d = 31.89 mm
  6. 6. d = 61.48 mm

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