Which quantity is most directly related to a cross-section's resistance to twisting?

Which quantity is most directly related to a cross-section's resistance to twisting?

• A. Mass Moment of Inertia
• B. Moment of Area
• C. Second Moment of Area
• D. Polar Moment of Area

Answer: (D)

Torsion resistance of a cross-section is quantified by the polar moment of area. This quantity comes directly into the fundamental torsion relationships: the shear stress at a distance r from the center is proportional to T r divided by J, and the twist per unit length is proportional to T divided by GJ, where T is the applied torque and G is the shear modulus. Thus, a larger polar moment means the cross-section twists less under the same torque. The other quantities relate to different mechanical responses. The mass moment of inertia describes how difficult it is to accelerate the cross-section as a whole in rotation (dynamic inertia), not how it resists twisting under torque. The second moment of area governs bending stiffness and deflection, not torsion. The term “moment of area” is a broader or ambiguous term in some contexts and does not directly capture a cross-section’s resistance to twisting the way the polar moment does.

Torsion resistance of a cross-section is quantified by the polar moment of area. This quantity comes directly into the fundamental torsion relationships: the shear stress at a distance r from the center is proportional to T r divided by J, and the twist per unit length is proportional to T divided by GJ, where T is the applied torque and G is the shear modulus. Thus, a larger polar moment means the cross-section twists less under the same torque.

The other quantities relate to different mechanical responses. The mass moment of inertia describes how difficult it is to accelerate the cross-section as a whole in rotation (dynamic inertia), not how it resists twisting under torque. The second moment of area governs bending stiffness and deflection, not torsion. The term “moment of area” is a broader or ambiguous term in some contexts and does not directly capture a cross-section’s resistance to twisting the way the polar moment does.