Parallel axis theorem: States that the moment of inertia

Parallel axis theorem states that the moment of inertia of a rigid body about any axis parallel to its centroidal axis is equal to the sum of the body's moment of inertia about its centroidal axis and the product of its mass and the square of the distance between the two axes. This theorem is particularly useful because if we know the centroidal moment of inertia of a shape, we can calculate its moment of inertia about any parallel axis by adding an appropriate correction factor. Alternately, if we know the moment of inertia about an axis , we can find the associated centroidal moment of inertia by subtracting the same factor. The parallel axis theorem relates the moment of inertia of a shape about an arbitrary axis to its moment of inertia about a parallel centroidal axis. This article explores the theorem ’s theory, its application in structural engineering, and a worked example involving a steel truss.