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
d = 50 mmT = 2000 N·m

A solid shaft of diameter 50 mm carries a torque of 2000 N·m. Find the shear stress τρ at a radius of 15 mm from the centre.

T = 2000 N·md = 50 mmρ = 15 mm
τρ = MPa
2.Easy
N = 500 rpmT = 750 N·m

A shaft turning at 500 rpm carries a steady torque of 750 N·m. Find the power P it transmits.

T = 750 N·mN = 500 rpm
P = kW
3.Medium
T = 1000 N·md = 40 mmL = 1.2 mφ = ?

A solid brass 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 = 1000 N·md = 40 mmL = 1.2 mG = 39 GPa
φ = °
4.Medium
do​ = ?T = 250 N·m

A hollow shaft must carry a torque of 250 N·m. Its inner diameter is to be 0.6 times its outer diameter, and the shear stress must not exceed 60 MPa. Find the smallest outer diameter do.

T = 250 N·mdi/do = 0.6τallow = 60 MPa
do = mm
5.Hard
d = 50 mmTB​ = 100 N·mTC​ = 2000 N·mABC0.8 m2 m

A solid steel shaft of diameter 50 mm is fixed at A. A torque of 100 N·m acts at B, 0.8 m from A, and a torque of 2000 N·m in the opposite direction acts at the free end C, a further 2 m along. Find the magnitude of the angle of twist φC of end C, in degrees.

d = 50 mmTB = 100 N·mTC = 2000 N·mAB = 0.8 mBC = 2 mG = 80 GPa
φC = °
6.Hard
do​ = ?15 kW, 300 rpm

A hollow shaft must transmit 15 kW at 300 rpm. Its inner diameter is to be 0.5 times its outer diameter, and the shear stress must not exceed 40 MPa. Find the smallest outer diameter do.

P = 15 kWN = 300 rpmdi/do = 0.5τallow = 40 MPa
do = mm

Answer key

  1. 1. τρ = 48.89 MPa
  2. 2. P = 39.27 kW
  3. 3. φ = 7.015 °
  4. 4. do = 29 mm
  5. 5. φC = 6.443 °
  6. 6. do = 40.18 mm

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