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 = 250 N·md = 30 mm

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

T = 250 N·md = 30 mm
τmax = MPa
2.Easy
d = 25 mmT = ?

A solid circular shaft of diameter 25 mm is made of a material with an allowable shear stress of 80 MPa. Find the largest torque Tmax the shaft can carry.

d = 25 mmτallow = 80 MPa
Tmax = N·m
3.Medium
d = ?T = 100 N·mL = 2.5 m

A solid aluminium shaft 2.5 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 = 2.5 mG = 26 GPaφallow = 2°
d = mm
4.Medium
T = 400 N·md = 25 mmL = 0.8 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 = 400 N·md = 25 mmL = 0.8 mG = 39 GPa
φ = °
5.Hard
do​ = ?10 kW, 3000 rpm

A hollow shaft must transmit 10 kW at 3000 rpm. Its inner diameter is to be 0.8 times its outer diameter, and the shear stress must not exceed 60 MPa. Find the smallest outer diameter do.

P = 10 kWN = 3000 rpmdi/do = 0.8τallow = 60 MPa
do = mm
6.Hard
Td = ?

A solid shaft must transmit 30 kW at 3000 rpm without the shear stress exceeding 50 MPa. Find the smallest diameter d that works.

P = 30 kWN = 3000 rpmτallow = 50 MPa
d = mm

Answer key

  1. 1. τmax = 47.16 MPa
  2. 2. Tmax = 245.4 N·m
  3. 3. d = 40.93 mm
  4. 4. φ = 12.26 °
  5. 5. do = 16.6 mm
  6. 6. d = 21.35 mm

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