First moment of area

The first moment of area, sometimes named as the first moment of inertia, is based in the mathematical construct moments in metric spaces, stating that the moment of area equals the summation of area times distance to an axis . It is a measure of the distribution of the area of a shape in relation to an axis. The first moment of area, sometimes named as the first moment of inertia, is based in the mathematical construct moments in metric spaces, stating that the moment of area equals the summation of area times distance to an axis . It is a measure of the distribution of the area of a shape in relation to an axis. First moment of area is commonly used to determine the centroid of an area. Given an area, A, of any shape, and division of that area into n number of very small, elemental areas (dAi). Let xi and yi be the distances (coordinates) to each elemental area measured from a given x-y axis. Now, the first moment of area in the x and y directions are respectively given by: