How to Calculate the Torsional Warping Constant


Beams find many uses in construction and machinery. Beams must be strong and flexible enough to support huge amounts of weight in sometimes adverse conditions. One way to measure this flexibility is the torsional warping constant, which is the amount the geometry of a beam is deviated from it's standard geometry when acted on by a torsional force (that is, the twisting of an object). You can calculate this constant for a standard geometry in a few short steps.

Things You'll Need

  • Paper
  • Pen or pencil
  • Calculator
  • Multiply the torque applied to the beam by the beam length. For example, if a torque of 500 Newton meters (Nm) is applied to a beam 1 meter (m) in length, the product will be 500 Newton meters squared (Nm^2). Call this product result A.

  • Multiply the angle of the beam's twist (in radians) by the shear modulus of the material. As an example, assume a steel beam, with a shear modulus of 79.3 gigapascals (GPa) is twisted by 0.2 radians. The product of these two numbers is 15.86 GPa. Call this result B.

  • Divide result A by result B. In our example, dividing 500 Nm^2 by 15.86 GPa (15 times 10 to the 9 Pa, or 15 x 10^9 Pa) gives 3.15 times 10 to the negative 8 (3.15 x 10^(-8) ). This dimensionless number is the torsional warping constant.

Tips & Warnings

  • This method applies to a beam of uniform cross-section across it's length. For other geometries, this equation may not apply.


  • "Roark's Formulas for Stress & Strain, 6th Edition"; Warren C. Young, 1989
  • Photo Credit pile of l-beams image by Mikhail Tischenko from
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