# Torsion constant (Ellipse -cross-sectional shape)

## Description

In solid mechanics, torsion is the twisting of an object due to an applied torque. The torsion constant is a geometrical property of a bar’s cross-section which is involved in the relationship between angle of twist and applied torque along the axis of the bar, for a homogeneous linear-elastic bar. The torsion constant, together with material properties and length, describes a bar’s torsional stiffness. For non-circular cross-sections, there are no exact analytical equations for finding the torsion constant. However approximate solutions have been found for many shapes. Non-circular cross-section always have warping deformations that require numerical methods to allow the exact calculation of the torsion constant.

Related formulas## Variables

J_τ | Torsion constant (m^{4}) |

π | pi |

a | The major radius of the ellipse (m) |

b | The minor radius of the ellipse (m) |