Engineering Mechanics : Centroid and Centre of Gravity

By Apoorbo Roy|Updated : June 6th, 2021

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INTRODUCTION

In engineering structures, the members of various cross-sections are used to withstand loads. The load carrying capacity depends on type of material used as also cross-section of the members. The important properties of a section are centroid and moment of inertia. These properties are also important in the study of subjects as strength of materials and machine design.

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INTRODUCTION

In engineering structures, the members of various cross-sections are used to withstand loads. The load carrying capacity depends on type of material used as also cross-section of the members. The important properties of a section are centroid and moment of inertia. These properties are also important in the study of subjects as strength of materials and machine design.

CENTRE OF GRAVITY AND CENTROID

Centroid is the point where the whole area is assumed to be concentrated. It is related to shape or the geometry of object. Centre of gravity of the body or the system of particles rigidly connected together is that point where the weight of body is concentrated and gravitational force acts through it. When density is uniform i.e. the body material is homogenous, centroid and C.G are same but when density is not same, two point will not be some. C.G lies where density is more, i.e. weight more.

CENTRE OF GRAVITY

Figure shows a body of mass M. This mass can be split into an infinite number of small parts each of mass dm. Consider one such elemental mass. Let this mass be at a distance x, y and z from the zy-plane, and xy-plane, respectively. The weight of the elemental mass acts through the elemental mass is
Weight of the elemental mass = dm×g

Weight of total mass = Mg

CENTROID

The centroid C is a point which defines the geometric center of an object. Its location can be determined from formulas similar to those used to determine the body’s center of gravity or center of mass. In particular if the material composing a body is uniform or homogeneous, the density or specific weight will be constant throughout the body, and therefore this term will factor out of the integrals and cancel from both the numerators and denominators.

List of centroids of some figures: