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 = 250 N·md = 25 mm

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

T = 250 N·md = 25 mm
τmax = MPa
2.Easy
d = 25 mmT = 500 N·m

A solid shaft of diameter 25 mm carries a torque of 500 N·m. Find the shear stress τρ at a radius of 6.3 mm from the centre.

T = 500 N·md = 25 mmρ = 6.3 mm
τρ = MPa
3.Medium
do​ = 30, di​ = 15 mmT = 500 N·mL = 0.8 m

A hollow brass shaft (outer diameter 30 mm, inner diameter 15 mm, length 0.8 m) is fixed at one end and twisted by a torque of 500 N·m at the other. Find the angle of twist φ in degrees.

T = 500 N·mdo = 30 mmdi = 15 mmL = 0.8 mG = 39 GPa
φ = °
4.Medium
T = 200 N·md = 40 mmL = 0.8 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 = 40 mmL = 0.8 mG = 39 GPa
φ = °
5.Hard
Tdo​ = 80 mm, di​ = 64 mm

A hollow shaft transmits 50 kW at 750 rpm. Find the maximum shear stress τmax in the shaft.

P = 50 kWN = 750 rpmdo = 80 mmdi = 64 mm
τmax = MPa
6.Hard
Tdo​ = 75 mm, di​ = 60 mm

A hollow shaft transmits 50 kW at 1500 rpm. Find the maximum shear stress τmax in the shaft.

P = 50 kWN = 1500 rpmdo = 75 mmdi = 60 mm
τmax = MPa

Answer key

  1. 1. τmax = 81.49 MPa
  2. 2. τρ = 82.14 MPa
  3. 3. φ = 7.882 °
  4. 4. φ = 0.9353 °
  5. 5. τmax = 10.73 MPa
  6. 6. τmax = 6.509 MPa

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