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 .
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. Let xi and yi be the distances 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. In the American Engineering and Gravitational systems the unit is a cubic foot 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
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: