# What is Torsional Rigidity?

By Ritesh|Updated : November 16th, 2022
1. The torque required to produce a twist of one degree per unit length of the shaft
2. The torque required to produce a twist of one radian per unit length of the shaft
3. The torque required to produce a twist of one radian per unit area of the shaft
4. The torque required to produce a twist of one degree per unit area of the shaft

Torsional rigidity is the torque required to generate a one-radian twist per unit length of the shaft.

T/J = τ/r = Gθ/L

Torsional stiffness (k) is the torque per radian twist.

k = T/θ = GJ/L

The torsional stiffness of the shaft is the name given to the GJ parameter.

The torque necessary to generate a one-radian twist per unit length of the shaft is another definition for torsional stiffness.

GJ = T/ θ/L

Shear modulus (G) and polar moment of inertia are the components that make up torsional stiffness (J). The torsional rigidity of a material demonstrates its resistance to angular deformation. The following formula can be used to calculate a component's torsional rigidity::-

Torsional rigidity = G x J

The torsional stiffness for the component under the torque of T can be calculated using the:

GJ = TL/θ

Summary:

## What is Torsional Rigidity?

The torque necessary to create a one-radian twist per unit length of the shaft is called torsional stiffness.