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 = 100 N·md = 40 mm

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

T = 100 N·md = 40 mm
τmax = MPa
2.Easy
N = 1800 rpmT = 200 N·m

A shaft turning at 1800 rpm carries a steady torque of 200 N·m. Find the power P it transmits.

T = 200 N·mN = 1800 rpm
P = kW
3.Medium
do​ = ?T = 400 N·m

A hollow shaft must carry a torque of 400 N·m. Its inner diameter is to be 0.6 times its outer diameter, and the shear stress must not exceed 75 MPa. Find the smallest outer diameter do.

T = 400 N·mdi/do = 0.6τallow = 75 MPa
do = mm
4.Medium
T = 400 N·md = 40 mmL = 2 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 = 400 N·md = 40 mmL = 2 mG = 26 GPa
φ = °
5.Hard
d = 40 mmT0​ = 200 N·mACBa = 1 mb = 1.5 m

A solid aluminium shaft of diameter 40 mm is fixed to rigid walls at both ends A and B. A torque of 200 N·m is applied at C, 1 m from A and 1.5 m from B. Find the maximum shear stress τmax in the shaft.

d = 40 mmT0 = 200 N·ma = 1 mb = 1.5 m
τmax = MPa
6.Hard
Tdo​ = 50 mm, di​ = 38 mm

A hollow shaft transmits 50 kW at 1500 rpm. Find the maximum shear stress τmax in the shaft.

P = 50 kWN = 1500 rpmdo = 50 mmdi = 38 mm
τmax = MPa

Answer key

  1. 1. τmax = 7.958 MPa
  2. 2. P = 37.7 kW
  3. 3. do = 31.48 mm
  4. 4. φ = 7.015 °
  5. 5. τmax = 9.549 MPa
  6. 6. τmax = 19.46 MPa

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