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 = 40 mmT = ?

A solid circular shaft of diameter 40 mm is made of a material with an allowable shear stress of 50 MPa. Find the largest torque Tmax the shaft can carry.

d = 40 mmτallow = 50 MPa
Tmax = N·m
2.Easy
T = 400 N·md = 50 mm

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

T = 400 N·md = 50 mm
τmax = MPa
3.Medium
T = 1000 N·md = 40 mmL = 1.2 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 = 1000 N·md = 40 mmL = 1.2 mG = 80 GPa
φ = °
4.Medium
T = 250 N·md = 30 mmL = 1.5 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 = 250 N·md = 30 mmL = 1.5 mG = 26 GPa
φ = °
5.Hard
Tdo​ = 60 mm, di​ = 45 mm

A hollow shaft transmits 100 kW at 500 rpm. Find the maximum shear stress τmax in the shaft.

P = 100 kWN = 500 rpmdo = 60 mmdi = 45 mm
τmax = MPa
6.Hard
d = 50 mmTB​ = 1000 N·mTC​ = 250 N·mABC0.5 m1 m

A solid brass shaft of diameter 50 mm is fixed at A. A torque of 1000 N·m acts at B, 0.5 m from A, and a torque of 250 N·m in the same direction acts at the free end C, a further 1 m along. Find the maximum shear stress τmax in the shaft.

d = 50 mmTB = 1000 N·mTC = 250 N·mAB = 0.5 mBC = 1 m
τmax = MPa

Answer key

  1. 1. Tmax = 628.3 N·m
  2. 2. τmax = 16.3 MPa
  3. 3. φ = 3.42 °
  4. 4. φ = 10.39 °
  5. 5. τmax = 65.87 MPa
  6. 6. τmax = 50.93 MPa

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