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
do​ = 50, di​ = 25 mmT = 1000 N·m

A hollow circular shaft with outer diameter 50 mm and inner diameter 25 mm carries a torque of 1000 N·m. Find the maximum shear stress τmax.

T = 1000 N·mdo = 50 mmdi = 25 mm
τmax = MPa
2.Easy
do​ = 40, di​ = 24 mmT = 2000 N·m

A hollow circular shaft with outer diameter 40 mm and inner diameter 24 mm carries a torque of 2000 N·m. Find the maximum shear stress τmax.

T = 2000 N·mdo = 40 mmdi = 24 mm
τmax = MPa
3.Medium
T = 400 N·md = 30 mmL = 3 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 = 400 N·md = 30 mmL = 3 mG = 39 GPa
φ = °
4.Medium
do​ = 50, di​ = 38 mmT = 2000 N·mL = 1.2 m

A hollow aluminium shaft (outer diameter 50 mm, inner diameter 38 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 = 38 mmL = 1.2 mG = 26 GPa
φ = °
5.Hard
d = ?10 kW, 1500 rpm

A solid steel shaft transmits 10 kW at 1500 rpm. The shear stress must not exceed 50 MPa and the twist must not exceed 0.5° per m of length. Find the smallest diameter d that satisfies both limits.

P = 10 kWN = 1500 rpmτallow = 50 MPaθallow = 0.5°/mG = 80 GPa
d = mm
6.Hard
d = 50 mmT0​ = 250 N·mACBa = 1.5 mb = 0.5 m

A solid aluminium shaft of diameter 50 mm is fixed to rigid walls at both ends A and B. A torque of 250 N·m is applied at C, 1.5 m from A and 0.5 m from B. Find the maximum shear stress τmax in the shaft.

d = 50 mmT0 = 250 N·ma = 1.5 mb = 0.5 m
τmax = MPa

Answer key

  1. 1. τmax = 43.46 MPa
  2. 2. τmax = 182.9 MPa
  3. 3. φ = 22.17 °
  4. 4. φ = 12.93 °
  5. 5. d = 31.04 mm
  6. 6. τmax = 7.639 MPa

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