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 = 1000 N·md = 40 mm

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

T = 1000 N·md = 40 mm
τmax = MPa
2.Easy
d = 50 mmT = ?

A solid circular shaft of diameter 50 mm is made of a material with an allowable shear stress of 60 MPa. Find the largest torque Tmax the shaft can carry.

d = 50 mmτallow = 60 MPa
Tmax = N·m
3.Medium
T = 750 N·md = 50 mmL = 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 = 50 mmL = 2 mG = 26 GPa
φ = °
4.Medium
do​ = ?T = 750 N·m

A hollow shaft must carry a torque of 750 N·m. Its inner diameter is to be 0.8 times its outer diameter, and the shear stress must not exceed 40 MPa. Find the smallest outer diameter do.

T = 750 N·mdi/do = 0.8τallow = 40 MPa
do = mm
5.Hard
Tdo​ = 40 mm, di​ = 32 mm

A hollow shaft transmits 15 kW at 300 rpm. Find the maximum shear stress τmax in the shaft.

P = 15 kWN = 300 rpmdo = 40 mmdi = 32 mm
τmax = MPa
6.Hard
Tdo​ = 50 mm, di​ = 30 mm

A hollow shaft transmits 15 kW at 1800 rpm. Find the maximum shear stress τmax in the shaft.

P = 15 kWN = 1800 rpmdo = 50 mmdi = 30 mm
τmax = MPa

Answer key

  1. 1. τmax = 79.58 MPa
  2. 2. Tmax = 1473 N·m
  3. 3. φ = 5.387 °
  4. 4. do = 54.48 mm
  5. 5. τmax = 64.36 MPa
  6. 6. τmax = 3.725 MPa

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