First Moment of Area - Definition

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:

S_x = A \bar y = \sum_{i=1}^n {y_i \,dA_i} = \int_A y dA

and

S_y = A \bar x = \sum_{i=1}^n {x_i \,dA_i} = \int_A x dA .

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.

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