Torsional rigidity, also known as torsional stiffness or torsional resistance, refers to a measure of a structure’s resistance to torsional deformation when subjected to an applied torque. It represents the degree to which a structural member can resist twisting. The torsional rigidity of a structure can be defined mathematically as,

Where:

• $K$ is the torsional rigidity, 
• $G$ is the shear modulus of elasticity of the material,
• $J$ is the polar moment of inertia of the cross-sectional area of the structure,
• $L$ is the length of the structural member.