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 = 20 mm

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

T = 250 N·md = 20 mm
τmax = MPa
2.Easy
do​ = 40, di​ = 30 mmT = 1500 N·m

A hollow circular shaft with outer diameter 40 mm and inner diameter 30 mm carries a torque of 1500 N·m. Find the maximum shear stress τmax.

T = 1500 N·mdo = 40 mmdi = 30 mm
τmax = MPa
3.Medium
T = 250 N·md = 50 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 = 250 N·md = 50 mmL = 2.5 mG = 80 GPa
φ = °
4.Medium
d = ?T = 2000 N·mL = 1 m

A solid aluminium shaft 1 m long carries a torque of 2000 N·m. The angle of twist between its ends must not exceed 1.5°. Find the smallest diameter d that meets this limit.

T = 2000 N·mL = 1 mG = 26 GPaφallow = 1.5°
d = mm
5.Hard
Td = ?

A solid shaft must transmit 30 kW at 1450 rpm without the shear stress exceeding 40 MPa. Find the smallest diameter d that works.

P = 30 kWN = 1450 rpmτallow = 40 MPa
d = mm
6.Hard
Tdo​ = 80 mm, di​ = 64 mm

A hollow shaft transmits 15 kW at 750 rpm. Find the maximum shear stress τmax in the shaft.

P = 15 kWN = 750 rpmdo = 80 mmdi = 64 mm
τmax = MPa

Answer key

  1. 1. τmax = 159.2 MPa
  2. 2. τmax = 174.6 MPa
  3. 3. φ = 0.7295 °
  4. 4. d = 73.96 mm
  5. 5. d = 29.3 mm
  6. 6. τmax = 3.218 MPa

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