Statics

Centroid / Centre of area

The point where the area of a figure is assumed to be concentrated.

Located on the axes of symmetry.

First moment of area

Measure of spatial distribution of a shape in relation to an axis.

Here:

• - Centroid’s coordinate
• - Centroid’s coordinate
• - Total area

About an axis of symmetry, first moment of area is .

Second moment of area

Always positive.

For common shapes

Shape	Description
Rectangle or Parallelogram	Base . Height . About centroidal axis parallel to base.
Triangle	Base . Height . About base.
Triangle	Base . Height . About centroidal axis parallel to base.
Circle	Diameter . About centroidal axis.

The product of moment of area about x,y axes

The polar moment of area about z axis

Radius of gyration