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 = 40 mmT = ?

A solid circular shaft of diameter 40 mm is made of a material with an allowable shear stress of 80 MPa. Find the largest torque Tmax the shaft can carry.

d = 40 mmτallow = 80 MPa
Tmax = N·m
2.Easy
d = 40 mmT = ?

A solid circular shaft of diameter 40 mm is made of a material with an allowable shear stress of 40 MPa. Find the largest torque Tmax the shaft can carry.

d = 40 mmτallow = 40 MPa
Tmax = N·m
3.Medium
T = 250 N·md = 20 mmL = 0.5 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 = 250 N·md = 20 mmL = 0.5 mG = 26 GPa
φ = °
4.Medium
T = 750 N·md = 40 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 = 40 mmL = 0.8 mG = 80 GPa
φ = °
5.Hard
Td = ?

A solid shaft must transmit 15 kW at 500 rpm without the shear stress exceeding 60 MPa. Find the smallest diameter d that works.

P = 15 kWN = 500 rpmτallow = 60 MPa
d = mm
6.Hard
do​ = ?50 kW, 750 rpm

A hollow shaft must transmit 50 kW at 750 rpm. 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.

P = 50 kWN = 750 rpmdi/do = 0.6τallow = 60 MPa
do = mm

Answer key

  1. 1. Tmax = 1005 N·m
  2. 2. Tmax = 502.7 N·m
  3. 3. φ = 17.54 °
  4. 4. φ = 1.71 °
  5. 5. d = 28.97 mm
  6. 6. do = 39.6 mm

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