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
do​ = 75, di​ = 38 mmT = 2000 N·m

A hollow circular shaft with outer diameter 75 mm and inner diameter 38 mm carries a torque of 2000 N·m. Find the maximum shear stress τmax.

T = 2000 N·mdo = 75 mmdi = 38 mm
τmax = MPa
2.Easy
T = 250 N·md = 40 mm

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

T = 250 N·md = 40 mm
τmax = MPa
3.Medium
T = 500 N·md = 40 mmL = 2.5 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 = 500 N·md = 40 mmL = 2.5 mG = 80 GPa
φ = °
4.Medium
d = ?T = 750 N·mL = 3 m

A solid aluminium shaft 3 m long carries a torque of 750 N·m. The angle of twist between its ends must not exceed 3°. Find the smallest diameter d that meets this limit.

T = 750 N·mL = 3 mG = 26 GPaφallow = 3°
d = mm
5.Hard
d = 50 mmTB​ = 1000 N·mTC​ = 250 N·mABC3 m0.5 m

A solid steel shaft of diameter 50 mm is fixed at A. A torque of 1000 N·m acts at B, 3 m from A, and a torque of 250 N·m in the same direction acts at the free end C, a further 0.5 m along. Find the magnitude of the angle of twist φC of end C, in degrees.

d = 50 mmTB = 1000 N·mTC = 250 N·mAB = 3 mBC = 0.5 mG = 80 GPa
φC = °
6.Hard
do​ = ?50 kW, 1500 rpm

A hollow shaft must transmit 50 kW at 1500 rpm. Its inner diameter is to be 0.6 times its outer diameter, and the shear stress must not exceed 80 MPa. Find the smallest outer diameter do.

P = 50 kWN = 1500 rpmdi/do = 0.6τallow = 80 MPa
do = mm

Answer key

  1. 1. τmax = 25.85 MPa
  2. 2. τmax = 19.89 MPa
  3. 3. φ = 3.562 °
  4. 4. d = 64.05 mm
  5. 5. φC = 4.523 °
  6. 6. do = 28.55 mm

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