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 = 1000 N·md = 50 mm

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

T = 1000 N·md = 50 mm
τmax = MPa
2.Easy
do​ = 60, di​ = 42 mmT = 500 N·m

A hollow circular shaft with outer diameter 60 mm and inner diameter 42 mm carries a torque of 500 N·m. Find the maximum shear stress τmax.

T = 500 N·mdo = 60 mmdi = 42 mm
τmax = MPa
3.Medium
T = 100 N·md = 40 mmL = 2.5 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 = 100 N·md = 40 mmL = 2.5 mG = 26 GPa
φ = °
4.Medium
do​ = 60, di​ = 42 mmT = 750 N·mL = 1 m

A hollow aluminium shaft (outer diameter 60 mm, inner diameter 42 mm, length 1 m) is fixed at one end and twisted by a torque of 750 N·m at the other. Find the angle of twist φ in degrees.

T = 750 N·mdo = 60 mmdi = 42 mmL = 1 mG = 26 GPa
φ = °
5.Hard
d = ?75 kW, 750 rpm

A solid brass shaft transmits 75 kW at 750 rpm. The shear stress must not exceed 75 MPa and the twist must not exceed 0.25° per m of length. Find the smallest diameter d that satisfies both limits.

P = 75 kWN = 750 rpmτallow = 75 MPaθallow = 0.25°/mG = 39 GPa
d = mm
6.Hard
d = 50 mmT0​ = 200 N·mACBa = 2.5 mb = 1.2 m

A solid brass shaft of diameter 50 mm is fixed to rigid walls at both ends A and B. A torque of 200 N·m is applied at C, 2.5 m from A and 1.2 m from B. Find the reaction torque TA at wall A.

d = 50 mmT0 = 200 N·ma = 2.5 mb = 1.2 m
TA = N·m

Answer key

  1. 1. τmax = 40.74 MPa
  2. 2. τmax = 15.51 MPa
  3. 3. φ = 2.192 °
  4. 4. φ = 1.709 °
  5. 5. d = 86.95 mm
  6. 6. TA = 64.86 N·m

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