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
d = 50 mmT = 2000 N·m

A solid shaft of diameter 50 mm carries a torque of 2000 N·m. Find the shear stress τρ at a radius of 6.3 mm from the centre.

T = 2000 N·md = 50 mmρ = 6.3 mm
τρ = MPa
2.Easy
T = 250 N·md = 40 mm

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

T = 250 N·md = 40 mm
τmax = MPa
3.Medium
T = 750 N·md = 30 mmL = 1.2 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 = 750 N·md = 30 mmL = 1.2 mG = 80 GPa
φ = °
4.Medium
d = ?T = 200 N·mL = 3 m

A solid steel shaft 3 m long carries a torque of 200 N·m. The angle of twist between its ends must not exceed 1°. Find the smallest diameter d that meets this limit.

T = 200 N·mL = 3 mG = 80 GPaφallow = 1°
d = mm
5.Hard
Td = ?

A solid shaft must transmit 50 kW at 3000 rpm without the shear stress exceeding 75 MPa. Find the smallest diameter d that works.

P = 50 kWN = 3000 rpmτallow = 75 MPa
d = mm
6.Hard
Td = ?

A solid shaft must transmit 100 kW at 500 rpm without the shear stress exceeding 80 MPa. Find the smallest diameter d that works.

P = 100 kWN = 500 rpmτallow = 80 MPa
d = mm

Answer key

  1. 1. τρ = 20.53 MPa
  2. 2. τmax = 19.89 MPa
  3. 3. φ = 8.106 °
  4. 4. d = 45.74 mm
  5. 5. d = 22.11 mm
  6. 6. d = 49.54 mm

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