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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
do​ = 60, di​ = 36 mmT = 2000 N·m

A hollow circular shaft with outer diameter 60 mm and inner diameter 36 mm carries a torque of 2000 N·m. Find the maximum shear stress τmax.

T = 2000 N·mdo = 60 mmdi = 36 mm
τmax = MPa
2.Easy
d = 30 mmT = 100 N·m

A solid shaft of diameter 30 mm carries a torque of 100 N·m. Find the shear stress τρ at a radius of 9 mm from the centre.

T = 100 N·md = 30 mmρ = 9 mm
τρ = MPa
3.Medium
T = 200 N·md = 25 mmL = 3 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 = 25 mmL = 3 mG = 80 GPa
φ = °
4.Medium
d = 20 mmT = 30 N·m400 mmφ = 1.68°

In a torsion test, a solid specimen of diameter 20 mm is twisted by a torque of 30 N·m. The two ends of a gauge length of 400 mm rotate 1.68° relative to each other (the material is still elastic). Find the shear modulus G of the material.

T = 30 N·md = 20 mmL = 400 mmφ = 1.68°
G = GPa
5.Hard
d = 40 mmT0​ = 200 N·mACBa = 2.5 mb = 2 m

A solid aluminium shaft of diameter 40 mm is fixed to rigid walls at both ends A and B. A torque of 200 N·m is applied at C, 2.5 m from A and 2 m from B. Find the maximum shear stress τmax in the shaft.

d = 40 mmT0 = 200 N·ma = 2.5 mb = 2 m
τmax = MPa
6.Hard
d = 50 mmTB​ = 400 N·mTC​ = 750 N·mABC3 m0.8 m

A solid aluminium shaft of diameter 50 mm is fixed at A. A torque of 400 N·m acts at B, 3 m from A, and a torque of 750 N·m in the opposite direction acts at the free end C, a further 0.8 m along. Find the maximum shear stress τmax in the shaft.

d = 50 mmTB = 400 N·mTC = 750 N·mAB = 3 mBC = 0.8 m
τmax = MPa

Answer key

  1. 1. τmax = 54.18 MPa
  2. 2. τρ = 11.32 MPa
  3. 3. φ = 11.21 °
  4. 4. G = 26.05 GPa
  5. 5. τmax = 8.842 MPa
  6. 6. τmax = 30.56 MPa

Full step-by-step solutions: practise this topic on examproblems.com.