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
d = 30 mmT = 1500 N·m

A solid shaft of diameter 30 mm carries a torque of 1500 N·m. Find the shear stress τρ at a radius of 11.3 mm from the centre.

T = 1500 N·md = 30 mmρ = 11.3 mm
τρ = MPa
2.Easy
T = 250 N·md = 40 mm

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

T = 250 N·md = 40 mm
τmax = MPa
3.Medium
d = ?T = 1000 N·mL = 0.8 m

A solid aluminium shaft 0.8 m long carries a torque of 1000 N·m. The angle of twist between its ends must not exceed 2°. Find the smallest diameter d that meets this limit.

T = 1000 N·mL = 0.8 mG = 26 GPaφallow = 2°
d = mm
4.Medium
d = 15 mmT = 75 N·m250 mmφ = 5.54°

In a torsion test, a solid specimen of diameter 15 mm is twisted by a torque of 75 N·m. The two ends of a gauge length of 250 mm rotate 5.54° relative to each other (the material is still elastic). Find the shear modulus G of the material.

T = 75 N·md = 15 mmL = 250 mmφ = 5.54°
G = GPa
5.Hard
do​ = ?5 kW, 300 rpm

A hollow shaft must transmit 5 kW at 300 rpm. Its inner diameter is to be 0.6 times its outer diameter, and the shear stress must not exceed 75 MPa. Find the smallest outer diameter do.

P = 5 kWN = 300 rpmdi/do = 0.6τallow = 75 MPa
do = mm
6.Hard
d = 40 mmT0​ = 500 N·mACBa = 1.2 mb = 0.5 m

A solid steel shaft of diameter 40 mm is fixed to rigid walls at both ends A and B. A torque of 500 N·m is applied at C, 1.2 m from A and 0.5 m from B. Find the reaction torque TA at wall A.

d = 40 mmT0 = 500 N·ma = 1.2 mb = 0.5 m
TA = N·m

Answer key

  1. 1. τρ = 213.1 MPa
  2. 2. τmax = 19.89 MPa
  3. 3. d = 54.74 mm
  4. 4. G = 39.02 GPa
  5. 5. do = 23.16 mm
  6. 6. TA = 147.1 N·m

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