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 = 25 mmT = ?

A solid circular shaft of diameter 25 mm is made of a material with an allowable shear stress of 80 MPa. Find the largest torque Tmax the shaft can carry.

d = 25 mmτallow = 80 MPa
Tmax = N·m
2.Easy
d = 30 mmT = 400 N·m

A solid shaft of diameter 30 mm carries a torque of 400 N·m. Find the shear stress τρ at a radius of 11.3 mm from the centre.

T = 400 N·md = 30 mmρ = 11.3 mm
τρ = MPa
3.Medium
T = 200 N·md = 20 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 = 200 N·md = 20 mmL = 1.2 mG = 80 GPa
φ = °
4.Medium
T = 1000 N·md = 50 mmL = 1 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 = 1000 N·md = 50 mmL = 1 mG = 39 GPa
φ = °
5.Hard
Td = ?

A solid shaft must transmit 75 kW at 750 rpm without the shear stress exceeding 50 MPa. Find the smallest diameter d that works.

P = 75 kWN = 750 rpmτallow = 50 MPa
d = mm
6.Hard
Td = ?

A solid shaft must transmit 20 kW at 3000 rpm without the shear stress exceeding 50 MPa. Find the smallest diameter d that works.

P = 20 kWN = 3000 rpmτallow = 50 MPa
d = mm

Answer key

  1. 1. Tmax = 245.4 N·m
  2. 2. τρ = 56.84 MPa
  3. 3. φ = 10.94 °
  4. 4. φ = 2.394 °
  5. 5. d = 45.99 mm
  6. 6. d = 18.65 mm

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