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 = 30 mmT = 100 N·m

A solid shaft of diameter 30 mm carries a torque of 100 N·m. Find the shear stress τρ at a radius of 12 mm from the centre.

T = 100 N·md = 30 mmρ = 12 mm
τρ = MPa
2.Easy
d = 30 mmT = ?

A solid circular shaft of diameter 30 mm is made of a material with an allowable shear stress of 70 MPa. Find the largest torque Tmax the shaft can carry.

d = 30 mmτallow = 70 MPa
Tmax = N·m
3.Medium
d = ?T = 250 N·mL = 2 m

A solid steel shaft 2 m long carries a torque of 250 N·m. The angle of twist between its ends must not exceed 1.5°. Find the smallest diameter d that meets this limit.

T = 250 N·mL = 2 mG = 80 GPaφallow = 1.5°
d = mm
4.Medium
do​ = ?T = 400 N·m

A hollow shaft must carry a torque of 400 N·m. Its inner diameter is to be 0.7 times its outer diameter, and the shear stress must not exceed 75 MPa. Find the smallest outer diameter do.

T = 400 N·mdi/do = 0.7τallow = 75 MPa
do = mm
5.Hard
d = 25 mmTB​ = 200 N·mTC​ = 500 N·mABC1.2 m1.5 m

A solid steel shaft of diameter 25 mm is fixed at A. A torque of 200 N·m acts at B, 1.2 m from A, and a torque of 500 N·m in the same direction acts at the free end C, a further 1.5 m along. Find the maximum shear stress τmax in the shaft.

d = 25 mmTB = 200 N·mTC = 500 N·mAB = 1.2 mBC = 1.5 m
τmax = MPa
6.Hard
do​ = ?15 kW, 1450 rpm

A hollow shaft must transmit 15 kW at 1450 rpm. Its inner diameter is to be 0.75 times its outer diameter, and the shear stress must not exceed 75 MPa. Find the smallest outer diameter do.

P = 15 kWN = 1450 rpmdi/do = 0.75τallow = 75 MPa
do = mm

Answer key

  1. 1. τρ = 15.09 MPa
  2. 2. Tmax = 371.1 N·m
  3. 3. d = 39.49 mm
  4. 4. do = 32.94 mm
  5. 5. τmax = 228.2 MPa
  6. 6. do = 21.41 mm

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