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 = 1500 N·md = 30 mm

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

T = 1500 N·md = 30 mm
τmax = MPa
2.Easy
do​ = 75, di​ = 56 mmT = 500 N·m

A hollow circular shaft with outer diameter 75 mm and inner diameter 56 mm carries a torque of 500 N·m. Find the maximum shear stress τmax.

T = 500 N·mdo = 75 mmdi = 56 mm
τmax = MPa
3.Medium
T = 400 N·md = 50 mmL = 0.5 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 = 400 N·md = 50 mmL = 0.5 mG = 39 GPa
φ = °
4.Medium
T = 500 N·md = 30 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 = 500 N·md = 30 mmL = 0.8 mG = 26 GPa
φ = °
5.Hard
Tdo​ = 40 mm, di​ = 24 mm

A hollow shaft transmits 75 kW at 1500 rpm. Find the maximum shear stress τmax in the shaft.

P = 75 kWN = 1500 rpmdo = 40 mmdi = 24 mm
τmax = MPa
6.Hard
Tdo​ = 40 mm, di​ = 20 mm

A hollow shaft transmits 50 kW at 750 rpm. Find the maximum shear stress τmax in the shaft.

P = 50 kWN = 750 rpmdo = 40 mmdi = 20 mm
τmax = MPa

Answer key

  1. 1. τmax = 282.9 MPa
  2. 2. τmax = 8.758 MPa
  3. 3. φ = 0.4789 °
  4. 4. φ = 11.08 °
  5. 5. τmax = 43.65 MPa
  6. 6. τmax = 54.04 MPa

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