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Mechanics of Materials

Topic: Area Moment of Inertia

Here, you can learn what an area moment of inertia (also known as second moment of area, or second-order area moment) is, where it finds application in engineering mechanics, and how to calculate it.

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The second moment of area describes the stiffness of a cross-sectional area, for example, in terms of bending, torsion, or buckling. Its unit is mm4.

The second moment of area or area moment of inertia is divided into four different area moments:

1.2.1 Definition of the Axial Area Moment of Inertia

$$ \begin{alignat}{3} I_y&= \int\limits_{(A)} z^2 \ \mathrm{d}A \qquad &&\text{Area moment of inertia with respect to the y-axis}\\[7pt] I_z&= \int\limits_{(A)} y^2 \ \mathrm{d}A \qquad &&\text{Area moment of inertia with respect to the z-axis} \end{alignat} $$

(6.2)

The two axial area moments of inertia, \(I_y\) and \(I_z\), are used in engineering mechanics, for instance, to calculate normal stresses and deformations in straight bending.

Since the distances \(y\) and \(z\) of the infinitesimal area element \(\mathrm{d}A\) to the origin of the \(y\),\(z\)-coordinate system are squared in equations (6.2), the axial area moments of inertia \(I_y\) and \(I_z\) are always greater than or equal to zero!