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

d = 40 mmτallow = 60 MPa
Tmax = N·m
2.Easy
T = 1500 N·md = 40 mm

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

T = 1500 N·md = 40 mm
τmax = MPa
3.Medium
T = 1000 N·md = 50 mmL = 2.5 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 = 1000 N·md = 50 mmL = 2.5 mG = 26 GPa
φ = °
4.Medium
d = ?T = 1000 N·mL = 0.5 m

A solid aluminium shaft 0.5 m long carries a torque of 1000 N·m. The angle of twist between its ends must not exceed 0.5°. Find the smallest diameter d that meets this limit.

T = 1000 N·mL = 0.5 mG = 26 GPaφallow = 0.5°
d = mm
5.Hard
d = 50 mmT0​ = 100 N·mACBa = 1.2 mb = 2 m

A solid steel shaft of diameter 50 mm is fixed to rigid walls at both ends A and B. A torque of 100 N·m is applied at C, 1.2 m from A and 2 m from B. Find the reaction torque TA at wall A.

d = 50 mmT0 = 100 N·ma = 1.2 mb = 2 m
TA = N·m
6.Hard
Td = ?

A solid shaft must transmit 100 kW at 500 rpm without the shear stress exceeding 40 MPa. Find the smallest diameter d that works.

P = 100 kWN = 500 rpmτallow = 40 MPa
d = mm

Answer key

  1. 1. Tmax = 754 N·m
  2. 2. τmax = 119.4 MPa
  3. 3. φ = 8.979 °
  4. 4. d = 68.83 mm
  5. 5. TA = 62.5 N·m
  6. 6. d = 62.42 mm

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