What are Moments of Area and How Do They Measure a Body's Resistance to Stress?

[Greg Bernhardt]

Definition/Summary

Moments of area are properties of rigid bodies, they depend only on shape and not on density, and they are scalars (numbers), and are measured relative to a particular axis.

First moment of area measures a body's resistance to shear stress along an axis.

Second moment of area measures a body's resistance to bending stress perpendicular to an axis.

Polar moment of area measures a body's resistance to torsion about an axis.

First moment of area has dimensions of length to the third power, while
second moment of area and polar moment of area have dimensions of length to the fourth power.

Each, being a scalar, is additive, so that for example the second moment of area of a composite body is the sum of the second moments of area of its parts (relative to the same axis).

Equations



Extended explanation

Confusion with moment of inertia:

Structural engineers sometimes call the second moment of area the moment of inertia, and (so as to avoid confusion ) call the (usual) moment of inertia the mass moment of inertia, and denote both by the same letter, ($I$).

Of course, there is no connection: second moment of area has units of length to the fourth power ($L^4$) while (usual) moment of inertia has units of mass times length squared ($ML^2$), and relates angular acceleration to torque ($\tau\ =\ I\alpha$).

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[APhysicist]

Moments of area are properties of rigid bodies that help to measure the body's resistance to shear stress, bending stress, and torsion about an axis. They are scalars (numbers) and are measured relative to a particular axis. The first moment of area has dimensions of length to the third power, while second moment of area and polar moment of area have dimensions of length to the fourth power. All three moments of area are additive, meaning that the total moment of area of a composite body is the sum of its parts. Structural engineers often refer to the second moment of area as a moment of inertia, however, it should not be confused with the usual moment of inertia which relates angular acceleration to torque and has units of mass times length squared (ML^2).