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 = 25 mmT = 500 N·m

A solid shaft of diameter 25 mm carries a torque of 500 N·m. Find the shear stress τρ at a radius of 10 mm from the centre.

T = 500 N·md = 25 mmρ = 10 mm
τρ = MPa
2.Easy
do​ = 80, di​ = 56 mmT = 400 N·m

A hollow circular shaft with outer diameter 80 mm and inner diameter 56 mm carries a torque of 400 N·m. Find the maximum shear stress τmax.

T = 400 N·mdo = 80 mmdi = 56 mm
τmax = MPa
3.Medium
d = 12 mmT = 30 N·m400 mmφ = 8.66°

In a torsion test, a solid specimen of diameter 12 mm is twisted by a torque of 30 N·m. The two ends of a gauge length of 400 mm rotate 8.66° relative to each other (the material is still elastic). Find the shear modulus G of the material.

T = 30 N·md = 12 mmL = 400 mmφ = 8.66°
G = GPa
4.Medium
do​ = ?T = 750 N·m

A hollow shaft must carry a torque of 750 N·m. Its inner diameter is to be 0.7 times its outer diameter, and the shear stress must not exceed 60 MPa. Find the smallest outer diameter do.

T = 750 N·mdi/do = 0.7τallow = 60 MPa
do = mm
5.Hard
Td = ?

A solid shaft must transmit 20 kW at 1500 rpm without the shear stress exceeding 75 MPa. Find the smallest diameter d that works.

P = 20 kWN = 1500 rpmτallow = 75 MPa
d = mm
6.Hard
Td = ?

A solid shaft must transmit 10 kW at 1500 rpm without the shear stress exceeding 50 MPa. Find the smallest diameter d that works.

P = 10 kWN = 1500 rpmτallow = 50 MPa
d = mm

Answer key

  1. 1. τρ = 130.4 MPa
  2. 2. τmax = 5.236 MPa
  3. 3. G = 39 GPa
  4. 4. do = 43.76 mm
  5. 5. d = 20.52 mm
  6. 6. d = 18.65 mm

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