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 = 750 N·md = 50 mm

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

T = 750 N·md = 50 mm
τmax = MPa
2.Easy
N = 1450 rpmT = ?

A motor delivers 55 kW to a shaft turning at 1450 rpm. Find the torque T in the shaft.

P = 55 kWN = 1450 rpm
T = N·m
3.Medium
T = 200 N·md = 20 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 = 200 N·md = 20 mmL = 2 mG = 80 GPa
φ = °
4.Medium
d1​ = 50 mmd2​ = 40 mmT = 750 N·mABC2.5 m1.2 m

A stepped solid aluminium shaft is fixed at A. Segment AB has diameter 50 mm and length 2.5 m; segment BC has diameter 40 mm and length 1.2 m. A torque of 750 N·m acts at the free end C. Find the angle of twist φC of end C, in degrees.

T = 750 N·md1 = 50 mm, L1 = 2.5 md2 = 40 mm, L2 = 1.2 mG = 26 GPa
φC = °
5.Hard
Td = ?

A solid shaft must transmit 30 kW at 500 rpm without the shear stress exceeding 40 MPa. Find the smallest diameter d that works.

P = 30 kWN = 500 rpmτallow = 40 MPa
d = mm
6.Hard
Td = ?

A solid shaft must transmit 50 kW at 750 rpm without the shear stress exceeding 60 MPa. Find the smallest diameter d that works.

P = 50 kWN = 750 rpmτallow = 60 MPa
d = mm

Answer key

  1. 1. τmax = 30.56 MPa
  2. 2. T = 362.2 N·m
  3. 3. φ = 18.24 °
  4. 4. φC = 14.63 °
  5. 5. d = 41.78 mm
  6. 6. d = 37.81 mm

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