Moment of Area
The moment of Area is a the name given to an equation in the form:
The word moment generally refers to a force multiplied by a distance. In this equation there is a distance multiplied by an area and hence it has been named the moment of area.
The power n in the above equation determines what moment of area is being calculated. If n = 1 then it is the first moment of area, if n = 2 then it is the second moment of area. The first and second moment of area are the most commonly used in structural analysis.
First Moment of Area
The first moment of area is used to calculate the centroid of a shape. The centroid (also known as the geometric centre of the shape) is the point you would need to place your finger on the shape so that it stays perfectly balanced.
The first moment of area is calculated for each axis as:
The centroid of a shape is calculated as:
Second Moment of Area
Second Moment of Area (also known as the Area Moment of Inertia) is a measure of the stiffness of a object due to its geometric shape. It is found by solving the equations:
