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 = 200 N·md = 30 mm

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

T = 200 N·md = 30 mm
τmax = MPa
2.Easy
d = 40 mmT = 1500 N·m

A solid shaft of diameter 40 mm carries a torque of 1500 N·m. Find the shear stress τρ at a radius of 16 mm from the centre.

T = 1500 N·md = 40 mmρ = 16 mm
τρ = MPa
3.Medium
T = 200 N·md = 30 mmL = 0.5 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 = 200 N·md = 30 mmL = 0.5 mG = 80 GPa
φ = °
4.Medium
do​ = 80, di​ = 48 mmT = 1000 N·mL = 1.5 m

A hollow brass shaft (outer diameter 80 mm, inner diameter 48 mm, length 1.5 m) is fixed at one end and twisted by a torque of 1000 N·m at the other. Find the angle of twist φ in degrees.

T = 1000 N·mdo = 80 mmdi = 48 mmL = 1.5 mG = 39 GPa
φ = °
5.Hard
d = 25 mmT0​ = 500 N·mACBa = 2.5 mb = 2 m

A solid brass shaft of diameter 25 mm is fixed to rigid walls at both ends A and B. A torque of 500 N·m is applied at C, 2.5 m from A and 2 m from B. Find the reaction torque TA at wall A.

d = 25 mmT0 = 500 N·ma = 2.5 mb = 2 m
TA = N·m
6.Hard
Tdo​ = 60 mm, di​ = 42 mm

A hollow shaft transmits 30 kW at 1000 rpm. Find the maximum shear stress τmax in the shaft.

P = 30 kWN = 1000 rpmdo = 60 mmdi = 42 mm
τmax = MPa

Answer key

  1. 1. τmax = 37.73 MPa
  2. 2. τρ = 95.49 MPa
  3. 3. φ = 0.9006 °
  4. 4. φ = 0.6296 °
  5. 5. TA = 222.2 N·m
  6. 6. τmax = 8.889 MPa

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