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 = 750 N·md = 60 mm

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

T = 750 N·md = 60 mm
τmax = MPa
2.Easy
N = 750 rpmT = 750 N·m

A shaft turning at 750 rpm carries a steady torque of 750 N·m. Find the power P it transmits.

T = 750 N·mN = 750 rpm
P = kW
3.Medium
T = 400 N·md = 25 mmL = 1 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 = 400 N·md = 25 mmL = 1 mG = 26 GPa
φ = °
4.Medium
T = 200 N·md = 40 mmL = 2.5 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 = 40 mmL = 2.5 mG = 80 GPa
φ = °
5.Hard
d = 30 mmTB​ = 200 N·mTC​ = 750 N·mABC0.8 m1.2 m

A solid aluminium shaft of diameter 30 mm is fixed at A. A torque of 200 N·m acts at B, 0.8 m from A, and a torque of 750 N·m in the opposite direction acts at the free end C, a further 1.2 m along. Find the maximum shear stress τmax in the shaft.

d = 30 mmTB = 200 N·mTC = 750 N·mAB = 0.8 mBC = 1.2 m
τmax = MPa
6.Hard
Tdo​ = 80 mm, di​ = 48 mm

A hollow shaft transmits 50 kW at 1450 rpm. Find the maximum shear stress τmax in the shaft.

P = 50 kWN = 1450 rpmdo = 80 mmdi = 48 mm
τmax = MPa

Answer key

  1. 1. τmax = 17.68 MPa
  2. 2. P = 58.9 kW
  3. 3. φ = 22.99 °
  4. 4. φ = 1.425 °
  5. 5. τmax = 141.5 MPa
  6. 6. τmax = 3.763 MPa

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