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 70 MPa. Find the largest torque Tmax the shaft can carry.

d = 20 mmτallow = 70 MPa
Tmax = N·m
2.Easy
T = 400 N·md = 40 mm

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

T = 400 N·md = 40 mm
τmax = MPa
3.Medium
d = ?T = 500 N·mL = 1 m

A solid aluminium shaft 1 m long carries a torque of 500 N·m. The angle of twist between its ends must not exceed 0.5°. Find the smallest diameter d that meets this limit.

T = 500 N·mL = 1 mG = 26 GPaφallow = 0.5°
d = mm
4.Medium
T = 250 N·md = 30 mmL = 3 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 = 30 mmL = 3 mG = 80 GPa
φ = °
5.Hard
Tdo​ = 80 mm, di​ = 60 mm

A hollow shaft transmits 75 kW at 500 rpm. Find the maximum shear stress τmax in the shaft.

P = 75 kWN = 500 rpmdo = 80 mmdi = 60 mm
τmax = MPa
6.Hard
do​ = ?5 kW, 500 rpm

A hollow shaft must transmit 5 kW at 500 rpm. Its inner diameter is to be 0.5 times its outer diameter, and the shear stress must not exceed 80 MPa. Find the smallest outer diameter do.

P = 5 kWN = 500 rpmdi/do = 0.5τallow = 80 MPa
do = mm

Answer key

  1. 1. Tmax = 110 N·m
  2. 2. τmax = 31.83 MPa
  3. 3. d = 68.83 mm
  4. 4. φ = 6.755 °
  5. 5. τmax = 20.84 MPa
  6. 6. do = 18.65 mm

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