Restrained Circular Section - Torsional Loading

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Torsional Loaded Member

Notation and Units

Metric and Imperial Units

The above formulas may be used with both imperial and metric units. As with all calculations care must be taken to keep consistent units throughout with examples of units which should be adopted listed below:


  • L = length under consideration, in or mm
  • G = shear modulus or modulus of rigidity, psi or MPa
  • J = polar moment of inertia, in4 or mm4
  • T = applied or resulting torsion, or Nmm
  • θ = angle of twist, degrees
  • τ = shear stress, psi or MPa
  • r = radial distance from centre to point of interest, in or mm

Additional Resources

  1. A.F. Hughes, D.C. Iles, A.S. Malik. Design of Steel Beams in Torsion. UK. 2011. Print.
  2. Author Unknown. (n.d.). Beams subject to bending and torsion [PDF file]. Retrieved from
  3. G.E. Maddux, Air Force Flight Dynamics Laboratory. Strees Analysis Manual. U.S. 1970. Print.