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
d = 25 mmT = ?

A solid circular shaft of diameter 25 mm is made of a material with an allowable shear stress of 80 MPa. Find the largest torque Tmax the shaft can carry.

d = 25 mmτallow = 80 MPa
Tmax = N·m
3.Medium
T = 400 N·md = 40 mmL = 0.8 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 = 400 N·md = 40 mmL = 0.8 mG = 26 GPa
φ = °
4.Medium
T = 1000 N·md = 40 mmL = 2.5 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 = 40 mmL = 2.5 mG = 80 GPa
φ = °
5.Hard
Td = ?

A solid shaft must transmit 75 kW at 1000 rpm without the shear stress exceeding 75 MPa. Find the smallest diameter d that works.

P = 75 kWN = 1000 rpmτallow = 75 MPa
d = mm
6.Hard
d = ?50 kW, 1000 rpm

A solid aluminium shaft transmits 50 kW at 1000 rpm. The shear stress must not exceed 80 MPa and the twist must not exceed 1° per m of length. Find the smallest diameter d that satisfies both limits.

P = 50 kWN = 1000 rpmτallow = 80 MPaθallow = 1°/mG = 26 GPa
d = mm

Answer key

  1. 1. T = 210.1 N·m
  2. 2. Tmax = 245.4 N·m
  3. 3. φ = 2.806 °
  4. 4. φ = 7.124 °
  5. 5. d = 36.5 mm
  6. 6. d = 57.22 mm

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