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
do​ = 75, di​ = 38 mmT = 500 N·m

A hollow circular shaft with outer diameter 75 mm and inner diameter 38 mm carries a torque of 500 N·m. Find the maximum shear stress τmax.

T = 500 N·mdo = 75 mmdi = 38 mm
τmax = MPa
3.Medium
T = 200 N·md = 50 mmL = 0.8 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 = 200 N·md = 50 mmL = 0.8 mG = 39 GPa
φ = °
4.Medium
d = ?T = 100 N·mL = 2 m

A solid steel shaft 2 m long carries a torque of 100 N·m. The angle of twist between its ends must not exceed 3°. Find the smallest diameter d that meets this limit.

T = 100 N·mL = 2 mG = 80 GPaφallow = 3°
d = mm
5.Hard
d = 50 mmTB​ = 500 N·mTC​ = 750 N·mABC1 m1 m

A solid aluminium shaft of diameter 50 mm is fixed at A. A torque of 500 N·m acts at B, 1 m from A, and a torque of 750 N·m in the same direction acts at the free end C, a further 1 m along. Find the magnitude of the angle of twist φC of end C, in degrees.

d = 50 mmTB = 500 N·mTC = 750 N·mAB = 1 mBC = 1 mG = 26 GPa
φC = °
6.Hard
d = 25 mmT0​ = 500 N·mACBa = 2 mb = 1.2 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 m from A and 1.2 m from B. Find the maximum shear stress τmax in the shaft.

d = 25 mmT0 = 500 N·ma = 2 mb = 1.2 m
τmax = MPa

Answer key

  1. 1. τmax = 17.68 MPa
  2. 2. τmax = 6.462 MPa
  3. 3. φ = 0.3831 °
  4. 4. d = 26.41 mm
  5. 5. φC = 7.183 °
  6. 6. τmax = 101.9 MPa

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