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
N = 1450 rpmT = 500 N·m

A shaft turning at 1450 rpm carries a steady torque of 500 N·m. Find the power P it transmits.

T = 500 N·mN = 1450 rpm
P = kW
2.Easy
T = 500 N·md = 60 mm

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

T = 500 N·md = 60 mm
τmax = MPa
3.Medium
T = 400 N·md = 40 mmL = 2 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 = 400 N·md = 40 mmL = 2 mG = 80 GPa
φ = °
4.Medium
do​ = 80, di​ = 40 mmT = 1500 N·mL = 1.5 m

A hollow aluminium shaft (outer diameter 80 mm, inner diameter 40 mm, length 1.5 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 = 40 mmL = 1.5 mG = 26 GPa
φ = °
5.Hard
d = 50 mmT0​ = 1000 N·mACBa = 1.5 mb = 1.2 m

A solid aluminium shaft of diameter 50 mm is fixed to rigid walls at both ends A and B. A torque of 1000 N·m is applied at C, 1.5 m from A and 1.2 m from B. Find the maximum shear stress τmax in the shaft.

d = 50 mmT0 = 1000 N·ma = 1.5 mb = 1.2 m
τmax = MPa
6.Hard
do​ = ?20 kW, 1450 rpm

A hollow shaft must transmit 20 kW at 1450 rpm. Its inner diameter is to be 0.75 times its outer diameter, and the shear stress must not exceed 50 MPa. Find the smallest outer diameter do.

P = 20 kWN = 1450 rpmdi/do = 0.75τallow = 50 MPa
do = mm

Answer key

  1. 1. P = 75.92 kW
  2. 2. τmax = 11.79 MPa
  3. 3. φ = 2.28 °
  4. 4. φ = 1.315 °
  5. 5. τmax = 22.64 MPa
  6. 6. do = 26.97 mm

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