First moment of area

The first moment of area is based on the mathematical construct moments in metric spaces. It is a measure of the spatial distribution of a shape in relation to an axis.
The first moment of area of a shape, about a certain axis, equals the sum over all the infinitesimal parts of the shape of the area of that part times its distance from the axis [Σ("a" × "d")]. 
First moment of area is commonly used to determine the centroid of an area.
Definition.
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: 
and 
The SI unit for first moment of area is a cubic metre (m3). In the American Engineering and Gravitational systems the unit is a cubic foot (ft3) or more commonly inch3.
The static or statical moment of area, usually denoted by the symbol "Q", is a property of a shape that is used to predict its resistance to shear stress. By definition:
where
Shear stress in a semi-monocoque structure.
The equation for shear flow in a particular web section of the cross-section of a semi-monocoque structure is:
Shear stress may now be calculated using the following equation: