Moment of Inertia

The moment of inertia of an area is the capacity of a cross section to resist bending or buckling. It represents a mathematical concept that is dependent on the size and shape of the section of the member. The bending axis of a member is also the centroidal axis; therefore, the ability to locate the centroid of a shape is closely associated with moment of inertia. Engineers use the moment of inertia to determine the state of stress in a section, and determine the amount of deflection in a beam.

The definition of the moment of inertia of an area can be thought of as the sum of the products of all the small areas and the squares of their distances from the axis being considered. This gives

If we represent the moment of inertia by the letter I, then the moments of inertia with respect to the x and y axis axis are

Units

Moment of inertia is expressed in units of length to the fourth power. Although dimensionally speaking it seems unusual, it is just a mathematical abstract and is an important property in the design of beams and columns. We will see in the following examples the methods of calculating the moment of inertia for a given beam section subjected to bending. If we choose the unit of length as mm., then the unit of the moment of inertia is

mm² x mm² = mm⁴