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​ = 40, di​ = 24 mmT = 1000 N·m

A hollow circular shaft with outer diameter 40 mm and inner diameter 24 mm carries a torque of 1000 N·m. Find the maximum shear stress τmax.

T = 1000 N·mdo = 40 mmdi = 24 mm
τmax = MPa
3.Medium
T = 200 N·md = 30 mmL = 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 = 30 mmL = 2 mG = 80 GPa
φ = °
4.Medium
T = 1000 N·md = 40 mmL = 1.2 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 = 40 mmL = 1.2 mG = 39 GPa
φ = °
5.Hard
d = 50 mmT0​ = 500 N·mACBa = 1.2 mb = 0.8 m

A solid aluminium shaft of diameter 50 mm is fixed to rigid walls at both ends A and B. A torque of 500 N·m is applied at C, 1.2 m from A and 0.8 m from B. Find the reaction torque TA at wall A.

d = 50 mmT0 = 500 N·ma = 1.2 mb = 0.8 m
TA = N·m
6.Hard
Tdo​ = 40 mm, di​ = 28 mm

A hollow shaft transmits 30 kW at 750 rpm. Find the maximum shear stress τmax in the shaft.

P = 30 kWN = 750 rpmdo = 40 mmdi = 28 mm
τmax = MPa

Answer key

  1. 1. τmax = 159.2 MPa
  2. 2. τmax = 91.43 MPa
  3. 3. φ = 3.603 °
  4. 4. φ = 7.015 °
  5. 5. TA = 200 N·m
  6. 6. τmax = 40 MPa

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