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 [ãad].
First moment of area is commonly used to determine the centroid of an area.
Given an area A of any shape and a division of that area into n very small elemental areas (dA<sub>i</sub>), let x<sub>i</sub> and y<sub>i</sub> be the distances (coordinates) to each elemental area measured from a given xâÂÂy axis. 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 (m<sup>3</sup>). In the American Engineering and Gravitational systems the unit is a cubic foot (ft<sup>3</sup>) or more commonly inch<sup>3</sup>.
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: