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​ = 40, di​ = 32 mmT = 1000 N·m

A hollow circular shaft with outer diameter 40 mm and inner diameter 32 mm carries a torque of 1000 N·m. Find the maximum shear stress τmax.

T = 1000 N·mdo = 40 mmdi = 32 mm
τmax = MPa
2.Easy
N = 750 rpmT = ?

A motor delivers 45 kW to a shaft turning at 750 rpm. Find the torque T in the shaft.

P = 45 kWN = 750 rpm
T = N·m
3.Medium
d = ?T = 200 N·mL = 1.2 m

A solid steel shaft 1.2 m long carries a torque of 200 N·m. The angle of twist between its ends must not exceed 1°. Find the smallest diameter d that meets this limit.

T = 200 N·mL = 1.2 mG = 80 GPaφallow = 1°
d = mm
4.Medium
T = 400 N·md = 50 mmL = 1 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 = 400 N·md = 50 mmL = 1 mG = 80 GPa
φ = °
5.Hard
d = 40 mmTB​ = 1000 N·mTC​ = 750 N·mABC1 m2 m

A solid steel shaft of diameter 40 mm is fixed at A. A torque of 1000 N·m acts at B, 1 m from A, and a torque of 750 N·m in the same direction acts at the free end C, a further 2 m along. Find the maximum shear stress τmax in the shaft.

d = 40 mmTB = 1000 N·mTC = 750 N·mAB = 1 mBC = 2 m
τmax = MPa
6.Hard
Td = ?

A solid shaft must transmit 75 kW at 1450 rpm without the shear stress exceeding 50 MPa. Find the smallest diameter d that works.

P = 75 kWN = 1450 rpmτallow = 50 MPa
d = mm

Answer key

  1. 1. τmax = 134.8 MPa
  2. 2. T = 573 N·m
  3. 3. d = 36.38 mm
  4. 4. φ = 0.4669 °
  5. 5. τmax = 139.3 MPa
  6. 6. d = 36.92 mm

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