Moment of Inertia of Area:

Definition

Let an area of a surface contain large number of small elements of area dA each. The area integral of all of such elements may be written mathematically as under :

Referring to Figure, the Area Moment of Inertia of elemental area dA around x axis, in its plane is described as,

I _{x (Element)} = dA ×  y ²

I _{y (Element)} = dA × x ²

Since the axis x lies in the plane of element, these are also called as axis moment of inertia of the element dA.

Figure 4.30

Polar moment of inertia of dA, that means around z axis perpendicular to the plane of A,

I _{z (Element)} = dA ( x ²  +  y ² )

Product of Inertia of element dA w.r.t. axes x and y,

I _{xy (Element)} = dA ( x ×  y)