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 = 2000 N·md = 40 mm

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

T = 2000 N·md = 40 mm
τmax = MPa
2.Easy
do​ = 80, di​ = 56 mmT = 500 N·m

A hollow circular shaft with outer diameter 80 mm and inner diameter 56 mm carries a torque of 500 N·m. Find the maximum shear stress τmax.

T = 500 N·mdo = 80 mmdi = 56 mm
τmax = MPa
3.Medium
T = 200 N·md = 50 mmL = 2.5 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 = 200 N·md = 50 mmL = 2.5 mG = 39 GPa
φ = °
4.Medium
T = 750 N·md = 30 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 = 750 N·md = 30 mmL = 2.5 mG = 80 GPa
φ = °
5.Hard
d = ?5 kW, 300 rpm

A solid steel shaft transmits 5 kW at 300 rpm. The shear stress must not exceed 80 MPa and the twist must not exceed 0.25° per m of length. Find the smallest diameter d that satisfies both limits.

P = 5 kWN = 300 rpmτallow = 80 MPaθallow = 0.25°/mG = 80 GPa
d = mm
6.Hard
Td = ?

A solid shaft must transmit 50 kW at 1800 rpm without the shear stress exceeding 80 MPa. Find the smallest diameter d that works.

P = 50 kWN = 1800 rpmτallow = 80 MPa
d = mm

Answer key

  1. 1. τmax = 159.2 MPa
  2. 2. τmax = 6.545 MPa
  3. 3. φ = 1.197 °
  4. 4. φ = 16.89 °
  5. 5. d = 46.42 mm
  6. 6. d = 25.66 mm

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