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 = 500 N·md = 25 mm

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

T = 500 N·md = 25 mm
τmax = MPa
2.Easy
N = 300 rpmT = 150 N·m

A shaft turning at 300 rpm carries a steady torque of 150 N·m. Find the power P it transmits.

T = 150 N·mN = 300 rpm
P = kW
3.Medium
d = ?T = 100 N·mL = 1.2 m

A solid brass shaft 1.2 m long carries a torque of 100 N·m. The angle of twist between its ends must not exceed 2°. Find the smallest diameter d that meets this limit.

T = 100 N·mL = 1.2 mG = 39 GPaφallow = 2°
d = mm
4.Medium
T = 750 N·md = 50 mmL = 0.8 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 = 750 N·md = 50 mmL = 0.8 mG = 80 GPa
φ = °
5.Hard
Td = ?

A solid shaft must transmit 75 kW at 1800 rpm without the shear stress exceeding 50 MPa. Find the smallest diameter d that works.

P = 75 kWN = 1800 rpmτallow = 50 MPa
d = mm
6.Hard
d = ?15 kW, 1500 rpm

A solid aluminium shaft transmits 15 kW at 1500 rpm. The shear stress must not exceed 60 MPa and the twist must not exceed 0.5° per m of length. Find the smallest diameter d that satisfies both limits.

P = 15 kWN = 1500 rpmτallow = 60 MPaθallow = 0.5°/mG = 26 GPa
d = mm

Answer key

  1. 1. τmax = 163 MPa
  2. 2. P = 4.712 kW
  3. 3. d = 30.78 mm
  4. 4. φ = 0.7003 °
  5. 5. d = 34.35 mm
  6. 6. d = 45.5 mm

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