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 = 25 mm

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

T = 500 N·md = 25 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 70 MPa. Find the largest torque Tmax the shaft can carry.

d = 50 mmτallow = 70 MPa
Tmax = N·m
3.Medium
T = 100 N·md = 25 mmL = 1 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 = 100 N·md = 25 mmL = 1 mG = 80 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 0.75 times its outer diameter, and the shear stress must not exceed 50 MPa. Find the smallest outer diameter do.

T = 750 N·mdi/do = 0.75τallow = 50 MPa
do = mm
5.Hard
Td = ?

A solid shaft must transmit 20 kW at 500 rpm without the shear stress exceeding 50 MPa. Find the smallest diameter d that works.

P = 20 kWN = 500 rpmτallow = 50 MPa
d = mm
6.Hard
Td = ?

A solid shaft must transmit 10 kW at 500 rpm without the shear stress exceeding 50 MPa. Find the smallest diameter d that works.

P = 10 kWN = 500 rpmτallow = 50 MPa
d = mm

Answer key

  1. 1. τmax = 163 MPa
  2. 2. Tmax = 1718 N·m
  3. 3. φ = 1.868 °
  4. 4. do = 48.17 mm
  5. 5. d = 33.89 mm
  6. 6. d = 26.89 mm

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