In structural engineering, the second moment of area, also called second moment of inertia or moment of area inertia, is a geometric property of the cross section of structural elements. Physically, the second moment of inertia is related to the maximum stresses and deformations that appear due to bending in a structural element and, therefore, together with the properties of the material, it determines the maximum resistance of a structural element under bending.

The second moment of area is a quantity whose dimensions are length to the fourth power (not to be confused with the related physical concept of rotational inertia whose units are mass times length squared). To avoid confusion, some engineers call the moment with units of mass described in this article the "mass moment of inertia."

Given a transverse plane section Σ of a structural element, the second moment of inertia is defined for each coordinate axis contained in the plane of the section Σ by the following formula:.

Where:.

If we consider again a plane cross section Σ and parameterize it using rectangular coordinates (x,y), then we can define two moments of inertia associated with bending according to X or according to Y in addition to the product of inertia by:.

These moments define the components of a second order tensor:

The axes are said to be principal axes of inertia if I = 0, and in that case we can write the perpendicular tension associated with the simple deviated bending of the structural element about each point of the section Σ studied as:.

Being M and M the components of the total bending moment on the section Σ. The units in the International System of Units for the second moment of inertia are length to the fourth power; in practice, most sections used in engineering are given in (cm). If the reference axes used are not necessarily principal axes, the complete expression of the stress at any generic point is given by:.

Steiner's theorem or parallel axes allows us to find the second moment of area (or moment of inertia) with respect to an axis (CM), knowing the second moment of area (or moment of inertia) with respect to a parallel axis that passes through the center of gravity. In engineering, a common use is to use this theorem to find the moment of inertia of a repeating pattern about a central axis. This "transfer" of the second moment of inertia is done using the formula:

Where:.

The previous result can be generalized to all the components of the inertia tensor:

Where:

are the coordinates of a point P with respect to the center of mass (CM), with respect to which the moments of inertia are to be recalculated.