What is "second moment of area"

n. (context engineering English) A measure of a body's resistance to bending; second moment of inertia.

This article is about the geometrical property of an area, termed the second moment of area. For the moment of inertia dealing with the rotation of an object with mass, see mass moment of inertia. For a list, see list of second moments of area.

The second 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 I for an axis that lies in the plane or with a 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 is length to fourth power, L.

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.

''Note: Different disciplines use "Moment of Inertia" (MOI) to refer to either or both of the planar second moment of area, $I = \textstyle\iint_{R} x^2\, \mathrm dA$, where x is the distance to some reference plane, or the polar second moment of area, $I = \textstyle\iint_{R} r^2\, \mathrm dA$, where r is the distance to some reference axis. In each case the integral is over all the infinitesimal elements of area, dA, in some two-dimensional cross-section. In math and physics, "Moment of Inertia" is strictly the second moment of mass with respect to distance from an axis: $I = \textstyle\int_{Q} r^2 \mathrm dm$, where r is the distance to some potential rotation axis, and the integral is over all the infinitesimal elements of mass, dm, in a three-dimensional space occupied by an object . The MOI, in this sense, is the analog of mass for rotational problems. In engineering (especially mechanical and civil), "Moment of Inertia" commonly refers to the second moment of the area.''