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 = 750 N·md = 50 mm

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

T = 750 N·md = 50 mm
τmax = MPa
2.Easy
do​ = 60, di​ = 30 mmT = 400 N·m

A hollow circular shaft with outer diameter 60 mm and inner diameter 30 mm carries a torque of 400 N·m. Find the maximum shear stress τmax.

T = 400 N·mdo = 60 mmdi = 30 mm
τmax = MPa
3.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 75 MPa. Find the smallest outer diameter do.

T = 2000 N·mdi/do = 0.6τallow = 75 MPa
do = mm
4.Medium
T = 1000 N·md = 30 mmL = 1.2 mφ = ?

A solid brass 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 = 30 mmL = 1.2 mG = 39 GPa
φ = °
5.Hard
d = 50 mmTB​ = 2000 N·mTC​ = 250 N·mABC2 m2.5 m

A solid steel shaft of diameter 50 mm is fixed at A. A torque of 2000 N·m acts at B, 2 m from A, and a torque of 250 N·m in the same direction acts at the free end C, a further 2.5 m along. Find the magnitude of the angle of twist φC of end C, in degrees.

d = 50 mmTB = 2000 N·mTC = 250 N·mAB = 2 mBC = 2.5 mG = 80 GPa
φC = °
6.Hard
d = 50 mmTB​ = 2000 N·mTC​ = 1000 N·mABC0.5 m0.5 m

A solid steel shaft of diameter 50 mm is fixed at A. A torque of 2000 N·m acts at B, 0.5 m from A, and a torque of 1000 N·m in the same direction acts at the free end C, a further 0.5 m along. Find the maximum shear stress τmax in the shaft.

d = 50 mmTB = 2000 N·mTC = 1000 N·mAB = 0.5 mBC = 0.5 m
τmax = MPa

Answer key

  1. 1. τmax = 30.56 MPa
  2. 2. τmax = 10.06 MPa
  3. 3. do = 53.84 mm
  4. 4. φ = 22.17 °
  5. 5. φC = 5.982 °
  6. 6. τmax = 122.2 MPa

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