What is the equation for Torsional Stiffness?

Torsional stiffness is a measure of a member's ability to resist twisting. The correct equation for torsional stiffness is represented by the formula ( \frac{GJ}{L} ), where ( G ) is the shear modulus of the material, ( J ) is the polar moment of inertia of the cross-section, and ( L ) is the length of the member subjected to torsion.

In this equation, the shear modulus ( G ) indicates how easily the material deforms under shear stress. The polar moment of inertia ( J ) reflects the geometrical distribution of the cross-section about the axis of torsion, which influences how effectively the member can resist twisting. By dividing ( GJ ) by the length ( L ), we obtain a measure that relates the material properties and geometry to the resulting angular displacement under a torque applied along the member. A higher value of torsional stiffness indicates that a member is less likely to twist under load, which is critical in structural design for ensuring rigidity and stability.

The other choices do not appropriately match the physical interpretation of torsional stiffness because they rearrange the fundamental relationship inaccurately or introduce elements that do not reflect the direct relationship between material properties, geometry, and length