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
d = 25 mmT = 250 N·m

A solid shaft of diameter 25 mm carries a torque of 250 N·m. Find the shear stress τρ at a radius of 9.4 mm from the centre.

T = 250 N·md = 25 mmρ = 9.4 mm
τρ = MPa
3.Medium
d = ?T = 100 N·mL = 3 m

A solid aluminium shaft 3 m long carries a torque of 100 N·m. The angle of twist between its ends must not exceed 0.5°. Find the smallest diameter d that meets this limit.

T = 100 N·mL = 3 mG = 26 GPaφallow = 0.5°
d = mm
4.Medium
do​ = 80, di​ = 56 mmT = 1500 N·mL = 3 m

A hollow brass shaft (outer diameter 80 mm, inner diameter 56 mm, length 3 m) is fixed at one end and twisted by a torque of 1500 N·m at the other. Find the angle of twist φ in degrees.

T = 1500 N·mdo = 80 mmdi = 56 mmL = 3 mG = 39 GPa
φ = °
5.Hard
do​ = ?50 kW, 1000 rpm

A hollow shaft must transmit 50 kW at 1000 rpm. Its inner diameter is to be 0.75 times its outer diameter, and the shear stress must not exceed 80 MPa. Find the smallest outer diameter do.

P = 50 kWN = 1000 rpmdi/do = 0.75τallow = 80 MPa
do = mm
6.Hard
Tdo​ = 80 mm, di​ = 60 mm

A hollow shaft transmits 75 kW at 500 rpm. Find the maximum shear stress τmax in the shaft.

P = 75 kWN = 500 rpmdo = 80 mmdi = 60 mm
τmax = MPa

Answer key

  1. 1. τmax = 40.74 MPa
  2. 2. τρ = 61.28 MPa
  3. 3. d = 60.58 mm
  4. 4. φ = 2.163 °
  5. 5. do = 35.43 mm
  6. 6. τmax = 20.84 MPa

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