# Theorem of Parallel Axis

It states that if the moment of intertia of a plane area about an axis in the plane of area through the C.G. of the plane area be represented by IG, then the moment of the intertia of the given plane area about a parallel axis AB in the plane of area at a distance h from the C.G. of the area is given by

But dA.y represents the moment of area of strip about X-X axis And dAy represents the moments of the total area about X-X axis. But the moments of the total area about X-X axis is equal to the product of total area (A) and the distance of the C.G. of the total area from X-X axis. As the distance of the C.G. of the total area from X-X axis is zero, hence dAy will be equal to zero.

Substituting this value in equation (ii), we get

Thus if the moment of intertia of an area with respect to an axis in the plane of area (and passing through the C.G. of the area) is known, the moment of intertia with respect to any parallel axis in the plane may be determined by using the above equation.