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​ = 56 mmT = 500 N·m

A hollow circular shaft with outer diameter 75 mm and inner diameter 56 mm carries a torque of 500 N·m. Find the maximum shear stress τmax.

T = 500 N·mdo = 75 mmdi = 56 mm
τmax = MPa
2.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
3.Medium
T = 200 N·md = 50 mmL = 3 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 = 200 N·md = 50 mmL = 3 mG = 80 GPa
φ = °
4.Medium
do​ = 40, di​ = 24 mmT = 2000 N·mL = 1.5 m

A hollow brass shaft (outer diameter 40 mm, inner diameter 24 mm, length 1.5 m) is fixed at one end and twisted by a torque of 2000 N·m at the other. Find the angle of twist φ in degrees.

T = 2000 N·mdo = 40 mmdi = 24 mmL = 1.5 mG = 39 GPa
φ = °
5.Hard
Tdo​ = 50 mm, di​ = 40 mm

A hollow shaft transmits 5 kW at 750 rpm. Find the maximum shear stress τmax in the shaft.

P = 5 kWN = 750 rpmdo = 50 mmdi = 40 mm
τmax = MPa
6.Hard
Tdo​ = 60 mm, di​ = 45 mm

A hollow shaft transmits 75 kW at 1450 rpm. Find the maximum shear stress τmax in the shaft.

P = 75 kWN = 1450 rpmdo = 60 mmdi = 45 mm
τmax = MPa

Answer key

  1. 1. τmax = 8.758 MPa
  2. 2. τmax = 30.56 MPa
  3. 3. φ = 0.7003 °
  4. 4. φ = 20.15 °
  5. 5. τmax = 4.393 MPa
  6. 6. τmax = 17.04 MPa

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