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 = 500 N·md = 60 mm

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

T = 500 N·md = 60 mm
τmax = MPa
2.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
3.Medium
T = 250 N·md = 20 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 = 250 N·md = 20 mmL = 1.2 mG = 80 GPa
φ = °
4.Medium
T = 750 N·md = 40 mmL = 1.2 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 = 750 N·md = 40 mmL = 1.2 mG = 26 GPa
φ = °
5.Hard
Tdo​ = 80 mm, di​ = 40 mm

A hollow shaft transmits 50 kW at 500 rpm. Find the maximum shear stress τmax in the shaft.

P = 50 kWN = 500 rpmdo = 80 mmdi = 40 mm
τmax = MPa
6.Hard
do​ = ?100 kW, 500 rpm

A hollow shaft must transmit 100 kW at 500 rpm. Its inner diameter is to be 0.6 times its outer diameter, and the shear stress must not exceed 80 MPa. Find the smallest outer diameter do.

P = 100 kWN = 500 rpmdi/do = 0.6τallow = 80 MPa
do = mm

Answer key

  1. 1. τmax = 11.79 MPa
  2. 2. Tmax = 628.3 N·m
  3. 3. φ = 13.68 °
  4. 4. φ = 7.891 °
  5. 5. τmax = 10.13 MPa
  6. 6. do = 51.89 mm

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