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 = 200 N·md = 30 mm

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

T = 200 N·md = 30 mm
τmax = MPa
2.Easy
d = 30 mmT = 200 N·m

A solid shaft of diameter 30 mm carries a torque of 200 N·m. Find the shear stress τρ at a radius of 11.3 mm from the centre.

T = 200 N·md = 30 mmρ = 11.3 mm
τρ = MPa
3.Medium
T = 1000 N·md = 20 mmL = 0.5 mφ = ?

A solid steel 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 = 1000 N·md = 20 mmL = 0.5 mG = 80 GPa
φ = °
4.Medium
T = 100 N·md = 40 mmL = 1.5 mφ = ?

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 = 100 N·md = 40 mmL = 1.5 mG = 39 GPa
φ = °
5.Hard
Td = ?

A solid shaft must transmit 75 kW at 1450 rpm without the shear stress exceeding 80 MPa. Find the smallest diameter d that works.

P = 75 kWN = 1450 rpmτallow = 80 MPa
d = mm
6.Hard
d = 50 mmTB​ = 400 N·mTC​ = 200 N·mABC3 m2.5 m

A solid steel shaft of diameter 50 mm is fixed at A. A torque of 400 N·m acts at B, 3 m from A, and a torque of 200 N·m in the same direction acts at the free end C, a further 2.5 m along. Find the maximum shear stress τmax in the shaft.

d = 50 mmTB = 400 N·mTC = 200 N·mAB = 3 mBC = 2.5 m
τmax = MPa

Answer key

  1. 1. τmax = 37.73 MPa
  2. 2. τρ = 28.42 MPa
  3. 3. φ = 22.8 °
  4. 4. φ = 0.8768 °
  5. 5. d = 31.56 mm
  6. 6. τmax = 24.45 MPa

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