Chapter 7 Centroids and Centers of Gravity
A centroid is the geometric center of a geometric object: a one-dimensional curve, a two-dimensional area or a three-dimensional volume. Centroids are useful for many situations in Statics and subsequent courses, including the analysis of distributed forces, beam bending, and shaft torsion.
Two related concepts are the center of gravity, which is the average location of an object’s weight, and the center of mass which is the average location of an object’s mass. In many engineering situations, the centroid, center of mass, and center of gravity are all coincident. Because of this, these three terms are often used interchangeably without regard to their precise meanings.
We consciously and subconsciously use centroids for many things in life and engineering, including:
Keeping your body’s balance: Try standing up with your feet together and leaning your head and hips in front of your feet. You have just moved your body’s center of gravity out of line with the support of your feet.
Computing the stability of objects in motion like cars, airplanes, and boats: By understanding how the center of gravity interacts with the accelerations caused by motion, we can compute safe speeds for sharp curves on a highway.
Designing the structural support to balance the structure’s own weight and applied loadings on buildings, bridges, and dams: We design most large infrastructure not to move. To keep it from moving, we must understand how the structure’s weight, people, vehicles, wind, earth pressure, and water pressure balance with the structural supports.
You probably have already developed a good intuition about centroids and centers of gravity based upon your life experience, and can roughly estimate their location when you look at an object or diagram. In this chapter you will learn to locate them precisely using two techniques: integration 7.7 and the method of composite parts 7.5.