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
do​ = 75, di​ = 60 mmT = 750 N·m

A hollow circular shaft with outer diameter 75 mm and inner diameter 60 mm carries a torque of 750 N·m. Find the maximum shear stress τmax.

T = 750 N·mdo = 75 mmdi = 60 mm
τmax = MPa
2.Easy
N = 3000 rpmT = ?

A motor delivers 11 kW to a shaft turning at 3000 rpm. Find the torque T in the shaft.

P = 11 kWN = 3000 rpm
T = N·m
3.Medium
T = 250 N·md = 30 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 = 250 N·md = 30 mmL = 1.2 mG = 39 GPa
φ = °
4.Medium
do​ = ?T = 2000 N·m

A hollow shaft must carry a torque of 2000 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 = 2000 N·mdi/do = 0.6τallow = 75 MPa
do = mm
5.Hard
Td = ?

A solid shaft must transmit 75 kW at 1800 rpm without the shear stress exceeding 50 MPa. Find the smallest diameter d that works.

P = 75 kWN = 1800 rpmτallow = 50 MPa
d = mm
6.Hard
Td = ?

A solid shaft must transmit 5 kW at 1000 rpm without the shear stress exceeding 80 MPa. Find the smallest diameter d that works.

P = 5 kWN = 1000 rpmτallow = 80 MPa
d = mm

Answer key

  1. 1. τmax = 15.34 MPa
  2. 2. T = 35.01 N·m
  3. 3. φ = 5.542 °
  4. 4. do = 53.84 mm
  5. 5. d = 34.35 mm
  6. 6. d = 14.49 mm

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