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 = 60 mm

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

T = 750 N·md = 60 mm
τmax = MPa
2.Easy
do​ = 50, di​ = 30 mmT = 200 N·m

A hollow circular shaft with outer diameter 50 mm and inner diameter 30 mm carries a torque of 200 N·m. Find the maximum shear stress τmax.

T = 200 N·mdo = 50 mmdi = 30 mm
τmax = MPa
3.Medium
T = 750 N·md = 30 mmL = 0.8 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 = 30 mmL = 0.8 mG = 26 GPa
φ = °
4.Medium
do​ = ?T = 500 N·m

A hollow shaft must carry a torque of 500 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 = 500 N·mdi/do = 0.75τallow = 50 MPa
do = mm
5.Hard
d = 50 mmTB​ = 1500 N·mTC​ = 200 N·mABC2 m3 m

A solid aluminium shaft of diameter 50 mm is fixed at A. A torque of 1500 N·m acts at B, 2 m from A, and a torque of 200 N·m in the opposite direction acts at the free end C, a further 3 m along. Find the magnitude of the angle of twist φC of end C, in degrees.

d = 50 mmTB = 1500 N·mTC = 200 N·mAB = 2 mBC = 3 mG = 26 GPa
φC = °
6.Hard
Td = ?

A solid shaft must transmit 100 kW at 1000 rpm without the shear stress exceeding 80 MPa. Find the smallest diameter d that works.

P = 100 kWN = 1000 rpmτallow = 80 MPa
d = mm

Answer key

  1. 1. τmax = 17.68 MPa
  2. 2. τmax = 9.362 MPa
  3. 3. φ = 16.63 °
  4. 4. do = 42.08 mm
  5. 5. φC = 7.183 °
  6. 6. d = 39.32 mm

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