1. Composite Bodies From this point on you may use the tables in the appendix that provide the centroids of common shapes. Here we will find the centroid of a complex shape by breaking it into a series of simple shapes for which the centroid can easily be determined. Once the centroid of the individual pieces is known we can find the centroid of entire object by finding the center of the centroids of the pieces. For example taking the shape on the right and breaking it into a series of rectangles, will allow us to determine the centroid of the entire object. We will use the discrete form of the centroid expressions. The centroid of each piece must be known in order to find the centroid of the entire object. When there is a hole in the object the centroid of the hole can be subtracted in order to account for the empty space. These expressions can be modified for center of gravity or center of mass.

2. Irregular shapes For irregular 3D shapes you can also separate the object into segments, determine the cross- sectional area of each piece and then plot the cross-sectional area vs. position to determine the centroid of the shape. The centroid of each area segment must be determined. The expressions are modified as follows: