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
N = 1000 rpmT = ?

A motor delivers 22 kW to a shaft turning at 1000 rpm. Find the torque T in the shaft.

P = 22 kWN = 1000 rpm
T = N·m
2.Easy
T = 1500 N·md = 50 mm

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

T = 1500 N·md = 50 mm
τmax = MPa
3.Medium
T = 250 N·md = 30 mmL = 2.5 mφ = ?

A solid aluminium 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 = 250 N·md = 30 mmL = 2.5 mG = 26 GPa
φ = °
4.Medium
T = 1000 N·md = 40 mmL = 2 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 = 40 mmL = 2 mG = 80 GPa
φ = °
5.Hard
Tdo​ = 40 mm, di​ = 32 mm

A hollow shaft transmits 20 kW at 500 rpm. Find the maximum shear stress τmax in the shaft.

P = 20 kWN = 500 rpmdo = 40 mmdi = 32 mm
τmax = MPa
6.Hard
d = ?20 kW, 750 rpm

A solid steel shaft transmits 20 kW at 750 rpm. The shear stress must not exceed 75 MPa and the twist must not exceed 0.5° per m of length. Find the smallest diameter d that satisfies both limits.

P = 20 kWN = 750 rpmτallow = 75 MPaθallow = 0.5°/mG = 80 GPa
d = mm

Answer key

  1. 1. T = 210.1 N·m
  2. 2. τmax = 61.12 MPa
  3. 3. φ = 17.32 °
  4. 4. φ = 5.699 °
  5. 5. τmax = 51.48 MPa
  6. 6. d = 43.9 mm

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