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# Torsion constant (Rectangle)

## 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. For a rectangle cross-sectional shape bar the formula that calculates torsion constant can be used with an error of not greater than 4%.

Related formulas

## Variables

 J_τ Torsion constant (m4) a The length of the long side (m) b The length of the short side (m)