# Torsion Constant

In structural elements capable of sustaining torsional moments it is necessary to define a constant to specify the ‘twisting stiffness’.

This term is referred to as the Torsion Constant. The following notes offer guidance on how to calculate the Torsion Constant. More detailed information may be found in the standard texts.

In the literature there is some confusion over the symbol used to represent the Torsion Constant. In many texts it is referred to as $J$. Elsewhere the symbol $C$ is used in an effort to distinguish the Torsion Constant from the polar moment of inertia. In GSA and in these notes the symbol $J$ is adopted.

If a circular bar of constant cross section and of length $l$ is subjected to a constant torque $T$, the angle of twist $\theta$ between the ends is

$\theta = \frac{Tl}{GI}$

where $G$ is the shear modulus and $I$ the polar moment of inertia.

When the cross section of the bar is non-circular, plane cross sections do not remain plane after deformation and warping will occur. Nevertheless the above equation can still be used with good accuracy, but I should be taken as the appropriate Torsion Constant $J$ as defined below.