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 = 250 N·md = 25 mm

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

T = 250 N·md = 25 mm
τmax = MPa
2.Easy
d = 20 mmT = 400 N·m

A solid shaft of diameter 20 mm carries a torque of 400 N·m. Find the shear stress τρ at a radius of 7.5 mm from the centre.

T = 400 N·md = 20 mmρ = 7.5 mm
τρ = MPa
3.Medium
do​ = 50, di​ = 38 mmT = 2000 N·mL = 1 m

A hollow aluminium shaft (outer diameter 50 mm, inner diameter 38 mm, length 1 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 = 38 mmL = 1 mG = 26 GPa
φ = °
4.Medium
T = 500 N·md = 40 mmL = 0.5 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 = 500 N·md = 40 mmL = 0.5 mG = 26 GPa
φ = °
5.Hard
d = 40 mmT0​ = 2000 N·mACBa = 1.5 mb = 2 m

A solid steel shaft of diameter 40 mm is fixed to rigid walls at both ends A and B. A torque of 2000 N·m is applied at C, 1.5 m from A and 2 m from B. Find the maximum shear stress τmax in the shaft.

d = 40 mmT0 = 2000 N·ma = 1.5 mb = 2 m
τmax = MPa
6.Hard
Tdo​ = 50 mm, di​ = 38 mm

A hollow shaft transmits 10 kW at 1000 rpm. Find the maximum shear stress τmax in the shaft.

P = 10 kWN = 1000 rpmdo = 50 mmdi = 38 mm
τmax = MPa

Answer key

  1. 1. τmax = 81.49 MPa
  2. 2. τρ = 191 MPa
  3. 3. φ = 10.78 °
  4. 4. φ = 2.192 °
  5. 5. τmax = 90.95 MPa
  6. 6. τmax = 5.839 MPa

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