Centroid of 2D Plane Body

The centroid of an plate is determined by the first moment of a two dimensional plane body with the method of the first moment of area.

Centroids of Shapes

1. Centroid of Parabolic Spandrel Area

   Area of Parabolic Spandrel:

   

   Coordinate x of centroid by integration.

   

   Coordinate x of centroid by integration.

   

   Similarly, coordinate y of centroid by integration.

   
2. Centroid of General Spandrel Area

   General Spandrel:

   

   Area of General Spandrel:

   

   Coordinate x of centroid by integration.

   

   Coordinate x of centroid by integration.

   

   Similarly, coordinate y of centroid by integration.

   
3. Centroid of Triangular Area

   Area of Triangle:

   

   Coordinate x of centroid by integration.

   

   Similarly, coordinate y of centroid by integration.

   
4. Centroid of Circular-sector Area

   Area of Circular-sector:

   

   Coordinate x of centroid by integration.

   

   Similarly, coordinate y of centroid by integration.