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 = 30 mmT = 100 N·m

A solid shaft of diameter 30 mm carries a torque of 100 N·m. Find the shear stress τρ at a radius of 6 mm from the centre.

T = 100 N·md = 30 mmρ = 6 mm
τρ = MPa
2.Easy
N = 1800 rpmT = ?

A motor delivers 2.2 kW to a shaft turning at 1800 rpm. Find the torque T in the shaft.

P = 2.2 kWN = 1800 rpm
T = N·m
3.Medium
T = 250 N·md = 40 mmL = 0.5 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 = 250 N·md = 40 mmL = 0.5 mG = 26 GPa
φ = °
4.Medium
T = 200 N·md = 30 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 = 200 N·md = 30 mmL = 1 mG = 39 GPa
φ = °
5.Hard
Td = ?

A solid shaft must transmit 100 kW at 1800 rpm without the shear stress exceeding 75 MPa. Find the smallest diameter d that works.

P = 100 kWN = 1800 rpmτallow = 75 MPa
d = mm
6.Hard
do​ = ?20 kW, 1000 rpm

A hollow shaft must transmit 20 kW at 1000 rpm. Its inner diameter is to be 0.6 times its outer diameter, and the shear stress must not exceed 60 MPa. Find the smallest outer diameter do.

P = 20 kWN = 1000 rpmdi/do = 0.6τallow = 60 MPa
do = mm

Answer key

  1. 1. τρ = 7.545 MPa
  2. 2. T = 11.67 N·m
  3. 3. φ = 1.096 °
  4. 4. φ = 3.695 °
  5. 5. d = 33.03 mm
  6. 6. do = 26.51 mm

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