9.0 CENTROIDS AND CENTER OF GRAVITY

With the gravitational force exerted by Earth to each of the particles in a body, we have identified the replacement of this single equivalent force as the body's weight which is applied at the CENTER OF GRAVITY of the body. The term CENTER OF GRAVITY is used for bodies with the same density all throughout. Thus regular shapes use this term often.

Center of gravity is also referred to as:

• Center of mass
• Center of weight
• Centroid of mass

CENTROID is analogous to center of gravity. It is the average position of all the points of an object.

HOW TO DETERMINE THE CENTROID

The centroid of a given body is determined by passing through a line at the median of each of the sides and identifying the point of intersection.

For the given triangle, the centroid can be at the intersection of all lines passing through the midpoints of the triangle's sides.

9.1. CENTROID OF REGULAR SHAPES

9.2. CENTROID OF COMPOSITE SECTIONS

A composite section consists of different regular shapes. So in order to identify the centroid of this composite section, one has to determine the centroid of each regular shape comprising the composite section. And take the moment of areas. The principle states:

The moment of an area about an axis equals the algebraic sum of the moments of its component areas about the same axis.

In formula:

                       

                     



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EXAMPLE 9.2.1. CENTROID OF SIMPLE COMPOSITE SECTIONS
EXAMPLE 9.2.2. CENTROID OF SIMPLE COMPOSITE SECTIONS
EXAMPLE 9.2.3. CENTROID OF SIMPLE COMPOSITE SECTIONS
EXAMPLE 9.2.4. CENTROID OF COMPOSITE SECTIONS -TWO CASES
EXAMPLE 9.2.5. CENTROID OF COMPOSITE SECTIONS -TWO CASES
EXAMPLE 9.2.6. CENTROID OF COMPOSITE SECTIONS -TWO CASES