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
N = 1200 rpmT = 250 N·m

A shaft turning at 1200 rpm carries a steady torque of 250 N·m. Find the power P it transmits.

T = 250 N·mN = 1200 rpm
P = kW
2.Easy
d = 60 mmT = 2000 N·m

A solid shaft of diameter 60 mm carries a torque of 2000 N·m. Find the shear stress τρ at a radius of 24 mm from the centre.

T = 2000 N·md = 60 mmρ = 24 mm
τρ = MPa
3.Medium
T = 100 N·md = 30 mmL = 2.5 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 = 100 N·md = 30 mmL = 2.5 mG = 26 GPa
φ = °
4.Medium
d = ?T = 1500 N·mL = 2.5 m

A solid steel shaft 2.5 m long carries a torque of 1500 N·m. The angle of twist between its ends must not exceed 3°. Find the smallest diameter d that meets this limit.

T = 1500 N·mL = 2.5 mG = 80 GPaφallow = 3°
d = mm
5.Hard
Tdo​ = 40 mm, di​ = 30 mm

A hollow shaft transmits 100 kW at 1000 rpm. Find the maximum shear stress τmax in the shaft.

P = 100 kWN = 1000 rpmdo = 40 mmdi = 30 mm
τmax = MPa
6.Hard
d = 30 mmT0​ = 2000 N·mACBa = 0.8 mb = 1.2 m

A solid aluminium shaft of diameter 30 mm is fixed to rigid walls at both ends A and B. A torque of 2000 N·m is applied at C, 0.8 m from A and 1.2 m from B. Find the maximum shear stress τmax in the shaft.

d = 30 mmT0 = 2000 N·ma = 0.8 mb = 1.2 m
τmax = MPa

Answer key

  1. 1. P = 31.42 kW
  2. 2. τρ = 37.73 MPa
  3. 3. φ = 6.928 °
  4. 4. d = 54.95 mm
  5. 5. τmax = 111.2 MPa
  6. 6. τmax = 226.4 MPa

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