Area moment of inertia

The 2nd moment of area, also known as moment of inertia of plane area, area moment of inertia, or second area moment, is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. The second moment of area is typically denoted with either an ${\displaystyle I}$ for an axis that lies in the plane or with a ${\displaystyle J}$ for an axis perpendicular to the plane. In both cases, it is calculated with a multiple integral over the object in question. Its unit of dimension when working with the International System of Units is meters to the fourth power, m⁴.

In the field of structural engineering, the second moment of area of the cross-section of a beam is an important property used in the calculation of the beam's deflection and the calculation of stress caused by a moment applied to the beam.

The second moment of area for an arbitrary shape R with respect to an arbitrary axis ${\displaystyle BB'}$ is defined as

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