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
do​ = 40, di​ = 30 mmT = 750 N·m

A hollow circular shaft with outer diameter 40 mm and inner diameter 30 mm carries a torque of 750 N·m. Find the maximum shear stress τmax.

T = 750 N·mdo = 40 mmdi = 30 mm
τmax = MPa
2.Easy
N = 1000 rpmT = 150 N·m

A shaft turning at 1000 rpm carries a steady torque of 150 N·m. Find the power P it transmits.

T = 150 N·mN = 1000 rpm
P = kW
3.Medium
T = 400 N·md = 40 mmL = 3 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 = 400 N·md = 40 mmL = 3 mG = 26 GPa
φ = °
4.Medium
T = 100 N·md = 20 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 = 100 N·md = 20 mmL = 2.5 mG = 39 GPa
φ = °
5.Hard
Tdo​ = 60 mm, di​ = 48 mm

A hollow shaft transmits 5 kW at 300 rpm. Find the maximum shear stress τmax in the shaft.

P = 5 kWN = 300 rpmdo = 60 mmdi = 48 mm
τmax = MPa
6.Hard
Td = ?

A solid shaft must transmit 10 kW at 500 rpm without the shear stress exceeding 50 MPa. Find the smallest diameter d that works.

P = 10 kWN = 500 rpmτallow = 50 MPa
d = mm

Answer key

  1. 1. τmax = 87.31 MPa
  2. 2. P = 15.71 kW
  3. 3. φ = 10.52 °
  4. 4. φ = 23.38 °
  5. 5. τmax = 6.356 MPa
  6. 6. d = 26.89 mm

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