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 = 2000 N·md = 40 mm

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

T = 2000 N·md = 40 mm
τmax = MPa
2.Easy
d = 40 mmT = 250 N·m

A solid shaft of diameter 40 mm carries a torque of 250 N·m. Find the shear stress τρ at a radius of 10 mm from the centre.

T = 250 N·md = 40 mmρ = 10 mm
τρ = MPa
3.Medium
T = 500 N·md = 25 mmL = 1 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 = 500 N·md = 25 mmL = 1 mG = 80 GPa
φ = °
4.Medium
d = 20 mmT = 30 N·m300 mmφ = 1.26°

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 300 mm rotate 1.26° relative to each other (the material is still elastic). Find the shear modulus G of the material.

T = 30 N·md = 20 mmL = 300 mmφ = 1.26°
G = GPa
5.Hard
d = 60 mmT0​ = 2000 N·mACBa = 2.5 mb = 1.5 m

A solid brass shaft of diameter 60 mm is fixed to rigid walls at both ends A and B. A torque of 2000 N·m is applied at C, 2.5 m from A and 1.5 m from B. Find the reaction torque TA at wall A.

d = 60 mmT0 = 2000 N·ma = 2.5 mb = 1.5 m
TA = N·m
6.Hard
d = 25 mmTB​ = 200 N·mTC​ = 100 N·mABC1.5 m0.5 m

A solid brass shaft of diameter 25 mm is fixed at A. A torque of 200 N·m acts at B, 1.5 m from A, and a torque of 100 N·m in the same direction acts at the free end C, a further 0.5 m along. Find the magnitude of the angle of twist φC of end C, in degrees.

d = 25 mmTB = 200 N·mTC = 100 N·mAB = 1.5 mBC = 0.5 mG = 39 GPa
φC = °

Answer key

  1. 1. τmax = 159.2 MPa
  2. 2. τρ = 9.947 MPa
  3. 3. φ = 9.338 °
  4. 4. G = 26.05 GPa
  5. 5. TA = 750 N·m
  6. 6. φC = 19.15 °

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