CENTROIDS OF COMPOSITE FIGURES
In engineering, bodies frequently come in
combinations of geometrical shapes. When a body
having an irregular shape can be conveniently divided
into several parts whose centers of gravity are already
known or easily determined, the principle of moments
can be used to determine the centroid of the whole
body. In this technique, each part is considered as a
finite element of the whole. This method is referred to
as the method of composite areas which utilizes
finite summation, as contrasted to integration which
is the summation of infinitesimal elements.
If a given composite area can be divided into regular
parts, and each part has its centroid known, the
moment of the total area is the sum of the moments of
its parts. Thus,
A similar process can be applied to lines. The
composite line may be divided into finite segments
whose centroids are known, and the following
equations may be used:
Centroids for Common Geometric Shapes
CENTROIDS OF COMPOSITE FIGURES
Problem #1: Locate the centroid of the composite area
shown above the base.
Problem #2: Determine the coordinates of the centroid
of the area shown with respect to the given axis.
Problem #3: From the area shown,
• Find the area of the shaded section.
• Find the centroid of shaded section from the y-axis.
• Find the centroid of shaded section from the x-axis.
