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 = 60 mm

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

T = 1500 N·md = 60 mm
τmax = MPa
3.Medium
d1​ = 60 mmd2​ = 30 mmT = 100 N·mABC2 m1.5 m

A stepped solid brass shaft is fixed at A. Segment AB has diameter 60 mm and length 2 m; segment BC has diameter 30 mm and length 1.5 m. A torque of 100 N·m acts at the free end C. Find the angle of twist φC of end C, in degrees.

T = 100 N·md1 = 60 mm, L1 = 2 md2 = 30 mm, L2 = 1.5 mG = 39 GPa
φC = °
4.Medium
do​ = ?T = 2000 N·m

A hollow shaft must carry a torque of 2000 N·m. Its inner diameter is to be 0.6 times its outer diameter, and the shear stress must not exceed 40 MPa. Find the smallest outer diameter do.

T = 2000 N·mdi/do = 0.6τallow = 40 MPa
do = mm
5.Hard
d = 20 mmTB​ = 250 N·mTC​ = 100 N·mABC1.2 m3 m

A solid steel shaft of diameter 20 mm is fixed at A. A torque of 250 N·m acts at B, 1.2 m from A, and a torque of 100 N·m in the same direction acts at the free end C, a further 3 m along. Find the maximum shear stress τmax in the shaft.

d = 20 mmTB = 250 N·mTC = 100 N·mAB = 1.2 mBC = 3 m
τmax = MPa
6.Hard
d = 40 mmT0​ = 500 N·mACBa = 2.5 mb = 3 m

A solid aluminium shaft of diameter 40 mm is fixed to rigid walls at both ends A and B. A torque of 500 N·m is applied at C, 2.5 m from A and 3 m from B. Find the angle of rotation φC of section C, in degrees.

d = 40 mmT0 = 500 N·ma = 2.5 mb = 3 mG = 26 GPa
φC = °

Answer key

  1. 1. Tmax = 754 N·m
  2. 2. τmax = 35.37 MPa
  3. 3. φC = 3.002 °
  4. 4. do = 66.39 mm
  5. 5. τmax = 222.8 MPa
  6. 6. φC = 5.978 °

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