Lecturer Mechanical Department Covernment Polytechnic,KAMPLI

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THAURYA NAIK LECTURER MECHANICAL DEPT. Page 1

Strength Of Materials ( III Semester)

SUBJECT CODE: 15ME31T

Centre of Gravity and Moment of Inertia

THAURYA NAIK

Lecturer

Mechanical Department

Covernment Polytechnic,KAMPLI



Centre of Gravity

2.1 Introduction:

The every particle of a body is attracted by the earth towards its centre. The force of attraction

which is proportional to the mass of a particle acts vertically downward and is known as weight

of the body. As the distance between the different particle of a body and the centre of the earth is

the same, therefore these forces may be taken to act along the parallel lines.

Centre of Gravity: A point through which the whole weight of the body acts. A body is having

only one centre of gravity for all the positions.

Centre of Gravity is the term for 3-dimensional shapes.

It is represented by C.G. or G.

Centroid : The Geometrical centre of an object is defined as its Centroid.

OR

The point which the total area of a plane figure (Triangle, square, rectangle, quadrilateral,

circle etc.) is assumed to be concentrated is known as the centroid of that area.

2.2 Methods for Centre of Gravity:

The centre of gravity (or centroid) may be found out by any one of the following methods:

1. By geometrical considerations

2. By moments

3. By graphical method

2.2.1 Centre of Gravity By geometrical considerations:

Centre of gravity of the simple figures may be found out from the geometry of the figures

as shown below.



Centroid of a rectangle =(l/2, h/2)

Area of Rectangle A= l X h



Axis of reference:

➢ The CG of a body always calculated with reference to some assumed axis(XY), these

axis are known as axis of reference.

➢ The Axis of reference of plane figure is generally taken as the lowest line of the figure

for determining Y and left line of the figure for calculating X.

2.2.2 Centre of Gravity by moments:



2.3 C.G. of plane figure:



2.4 Centre of Gravity of Symmetrical Sections:

➢ The given section, whose centre of gravity is required to be found out,is symmetrical

about X-X axis or Y-Y axis.

➢ In such cases, the procedure for calculating the centre of gravity of the body is very much

simplified as we have only to calculate either x or y.

➢ This is due to the reason that the centre of gravity of the body will lie on the axis of

symmetry.

2.5 PROBLEMS.

Problems: 1



Problem 2:

Problem 3:



C.G of Unsymmetrical sections:

Problem 4:



Problem 5:





Problem 6:





Problem 7:



Problem 8:





Moment of Inertia

2.5 Introduction:

Moment of a force (P) about a point is the product of the force and perpendicular distance

(x) between the point and the line of action of the force (i.e P.x). This moment is also called first

moment of force. If this moment is again multiplied by the perpendicular distance (x) between

the point and the line of action of the force i.e P.x(x)=Px2 , then this quantity is called moment of

the moment of a force or second moment of a force or Moment of inertia (written as M.I).

Sometimes, instead of force, area or mass of a figure or body is taken in to consideration.

Then the second moment is known as second moment of area or second moment of mass. But all

such second moment is broadly termed as moment of inertia.

2.6 Moment of inertia of a plane area:

2.7 Moment of inertia of a rectangular section:



M.I of a rectangular section horizontal axis

M.I of a rectangular section vertical axis

2.8 M. I. of a Hollow rectangular section:



2.9 Theorem of Perpendicular axis:

Statement:

2.10 Theorem of Parallel axis:

Statement:



2.11 Moment of Inertia for Standard Sections



2.12 Problems on M.I

Problem 1: T SECTION





Problem 2:



Problem 3:





Problem 4:

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Lecturer Mechanical Department Covernment Polytechnic,KAMPLI