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 = 20 mmT = ?

A solid circular shaft of diameter 20 mm is made of a material with an allowable shear stress of 40 MPa. Find the largest torque Tmax the shaft can carry.

d = 20 mmτallow = 40 MPa
Tmax = N·m
2.Easy
T = 100 N·md = 20 mm

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

T = 100 N·md = 20 mm
τmax = MPa
3.Medium
T = 400 N·md = 40 mmL = 2.5 mφ = ?

A solid aluminium 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 = 400 N·md = 40 mmL = 2.5 mG = 26 GPa
φ = °
4.Medium
d = ?T = 1000 N·mL = 1.2 m

A solid brass shaft 1.2 m long carries a torque of 1000 N·m. The angle of twist between its ends must not exceed 1.5°. Find the smallest diameter d that meets this limit.

T = 1000 N·mL = 1.2 mG = 39 GPaφallow = 1.5°
d = mm
5.Hard
d = 60 mmTB​ = 100 N·mTC​ = 500 N·mABC1.5 m1.2 m

A solid aluminium shaft of diameter 60 mm is fixed at A. A torque of 100 N·m acts at B, 1.5 m from A, and a torque of 500 N·m in the same direction acts at the free end C, a further 1.2 m along. Find the magnitude of the angle of twist φC of end C, in degrees.

d = 60 mmTB = 100 N·mTC = 500 N·mAB = 1.5 mBC = 1.2 mG = 26 GPa
φC = °
6.Hard
Td = ?

A solid shaft must transmit 75 kW at 300 rpm without the shear stress exceeding 75 MPa. Find the smallest diameter d that works.

P = 75 kWN = 300 rpmτallow = 75 MPa
d = mm

Answer key

  1. 1. Tmax = 62.83 N·m
  2. 2. τmax = 63.66 MPa
  3. 3. φ = 8.768 °
  4. 4. d = 58.82 mm
  5. 5. φC = 2.598 °
  6. 6. d = 54.53 mm

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