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 = 400 N·md = 20 mm

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

T = 400 N·md = 20 mm
τmax = MPa
2.Easy
d = 20 mmT = 100 N·m

A solid shaft of diameter 20 mm carries a torque of 100 N·m. Find the shear stress τρ at a radius of 6 mm from the centre.

T = 100 N·md = 20 mmρ = 6 mm
τρ = MPa
3.Medium
do​ = 50, di​ = 35 mmT = 2000 N·mL = 1.2 m

A hollow aluminium shaft (outer diameter 50 mm, inner diameter 35 mm, length 1.2 m) is fixed at one end and twisted by a torque of 2000 N·m at the other. Find the angle of twist φ in degrees.

T = 2000 N·mdo = 50 mmdi = 35 mmL = 1.2 mG = 26 GPa
φ = °
4.Medium
d = ?T = 2000 N·mL = 3 m

A solid steel shaft 3 m long carries a torque of 2000 N·m. The angle of twist between its ends must not exceed 1°. Find the smallest diameter d that meets this limit.

T = 2000 N·mL = 3 mG = 80 GPaφallow = 1°
d = mm
5.Hard
d = 30 mmTB​ = 250 N·mTC​ = 250 N·mABC1.2 m0.8 m

A solid aluminium shaft of diameter 30 mm is fixed at A. A torque of 250 N·m acts at B, 1.2 m from A, and a torque of 250 N·m in the same direction acts at the free end C, a further 0.8 m along. Find the maximum shear stress τmax in the shaft.

d = 30 mmTB = 250 N·mTC = 250 N·mAB = 1.2 mBC = 0.8 m
τmax = MPa
6.Hard
d = 20 mmTB​ = 250 N·mTC​ = 400 N·mABC1.5 m0.5 m

A solid brass shaft of diameter 20 mm is fixed at A. A torque of 250 N·m acts at B, 1.5 m from A, and a torque of 400 N·m in the opposite direction acts at the free end C, a further 0.5 m along. Find the maximum shear stress τmax in the shaft.

d = 20 mmTB = 250 N·mTC = 400 N·mAB = 1.5 mBC = 0.5 m
τmax = MPa

Answer key

  1. 1. τmax = 254.6 MPa
  2. 2. τρ = 38.2 MPa
  3. 3. φ = 11.34 °
  4. 4. d = 81.34 mm
  5. 5. τmax = 94.31 MPa
  6. 6. τmax = 254.6 MPa

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