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​ = 80, di​ = 40 mmT = 1500 N·m

A hollow circular shaft with outer diameter 80 mm and inner diameter 40 mm carries a torque of 1500 N·m. Find the maximum shear stress τmax.

T = 1500 N·mdo = 80 mmdi = 40 mm
τmax = MPa
2.Easy
T = 100 N·md = 30 mm

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

T = 100 N·md = 30 mm
τmax = MPa
3.Medium
T = 100 N·md = 20 mmL = 1.5 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 = 100 N·md = 20 mmL = 1.5 mG = 39 GPa
φ = °
4.Medium
T = 1000 N·md = 30 mmL = 0.8 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 = 1000 N·md = 30 mmL = 0.8 mG = 80 GPa
φ = °
5.Hard
d = 40 mmT0​ = 200 N·mACBa = 2.5 mb = 0.5 m

A solid brass 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 0.5 m from B. Find the angle of rotation φC of section C, in degrees.

d = 40 mmT0 = 200 N·ma = 2.5 mb = 0.5 mG = 39 GPa
φC = °
6.Hard
d = ?10 kW, 1000 rpm

A solid brass shaft transmits 10 kW at 1000 rpm. The shear stress must not exceed 80 MPa and the twist must not exceed 0.25° per m of length. Find the smallest diameter d that satisfies both limits.

P = 10 kWN = 1000 rpmτallow = 80 MPaθallow = 0.25°/mG = 39 GPa
d = mm

Answer key

  1. 1. τmax = 15.92 MPa
  2. 2. τmax = 18.86 MPa
  3. 3. φ = 14.03 °
  4. 4. φ = 7.205 °
  5. 5. φC = 0.4871 °
  6. 6. d = 48.9 mm

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