1. Force System
Prof. Vinod B Shikhare Page 1
Engineering Mechanics:
It is branch of science which deals with the study and effect of forces acting on the body
in motion or at rest.
Classification of Engineering Mechanics:
Statics:
Statics is that branch of Engineering Mechanics which deals with the study and effect of
forces acting on the body at rest.
Dynamics:
Dynamics is that branch of Engineering Mechanics which deals with the study and effect
of forces acting on the body in motion.
Kinetics:
Kinetics is that branch of dynamics which deals with the bodies in motion when forces
causing the motion are considered.
Kinematics:
Kinematics is that branch of dynamics which deals with the bodies in motion when forces
causing the motion are NOT considered.
Engineering
Mechanics
Statics Dynamics
Kinetics Kinematics
2. Force System
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Space:
The geometric region in which study of body is involved is called space.
Particle:
Particle is a point mass which has no dimensions. It has a mass occupying definite space.
Total mass of the body acts at a certain point within the body in downward direction and this point is
called as center of the mass.
Body:
It is a portion of matter which has dimensions. It has a mass occupying definite space.
Classification of Body:
Rigid Body:
A body which does not changes its shape and size after the application of external force
on it, is called as rigid body.
Deformable Body:
A body which changes its shape and size after the application of external force on it is
called as deformable body.
Elastic Body:
A body which regains its original shape and size when external forces acting on it are
removed is called as elastic body.
Plastic Body:
A body which does not regains its original shape and size when external forces acting on
it are removed is called as plastic body.
Body
Rigid Body
Deformable
Body
Elastic
Body
Plastic
Body
3. Force System
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Force:
An external agency which tends to change the state of rest or of uniform motion is called
as force.
Force is a vector quantity since it has both magnitude and direction.
Characteristics of Force:
1. Magnitude
2. Direction
3. Point of Application
4. Nature
1. Magnitude
The quantum of a force is known as its magnitude. For example a force of 100 N means
magnitude of force is 100 N.
2. Direction
The line of action along which force acts is known as its direction. The angle made by to
force with respect to any reference axis is known as its direction.
3. Point of application
The point at which a force acts is known as its point of application.
4. Sense or Nature
Sense or nature of a force is indicated by and arrowhead. Arrowhead indicates whether it
is a push or full force.
Effects of force
Force acting on the body may
i. Bring the body in a state of rest
ii. Start the body in motion
iii. Accelerate the body
iv. Retard body
v. Change shape and size of body
vi. Keep the body in equilibrium.
4. Force System
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Force System
Two or more forces acting on a body is called as force system.
Classification of Force System
Coplanar Forces
If line of actions of various forces acting on the body lie in the same plane, these forces
are known as coplanar forces.
Non-Coplanar Forces
If the lines of action of forces forming the system do not lie in the same plane then the
system is said to be non-coplanar.
Note: Our study is restricted to coplanar forces.
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Concurrent Force System
If the line of action of forces forming the system passes through a common point (point
of concurrence) then the system is said to be concurrent.
Non-Concurrent Force System
If the lines of action of forces forming the system do not pass through a common point,
then the system is said to be non-concurrent.
Collinear Force System
If the forces forming the system have common line of action then the system is said to be
collinear.
.
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Parallel force system
It is a particular case of non-concurrent force system in which the line of action of forces
forming the system are parallel.
Resultant (R):
If number of forces acting on a body can be replaces by a single force which can produce
the same effect on the body as it is produced by the number of forces acting on the body, then the
single force is known as resultant of the given force system.
Equilibrant (E):
It is a force which keeps the body in equilibrium. It is denoted by E. Magnitude of
equilibrant is same as that of resultant but lines of actions of resultant and equilibrant exactly
opposite to each other.
Principle of Superposition:
It states that the net outcome of a given force system does not change if we add or
subtract from it another force system which is in equilibrium.
7. Force System
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Here force system (A) consists of two forces P1 and P2 and force system (B) consists of
two forces P3 and P4. (P3=P4). Since P3=P4 force system (B) is in equilibrium. If we add force
system B to force system A we get force system (C).
According to principle of Superposition, the net outcome of force system (A) does not
change. In other word the resultant of force system (A) and (C) is same.
Principle of Transmissibility:
It states that, “The point of application of a force can be transmitted anywhere along its
line of action but within the body”.
Composition of Forces:
Composition is a process of replacing number of forces acting on a rigid body by a single
force which can produce the same effect on the body as it is produced by the number of forces
acting on the body.
In other word composition is the process of finding resultant (R).
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Methods of Composition of Forces
1. Analytical Methods
2. Graphical Methods
Low of Parallelogram
It states “if two concurrent forces acting on a rigid body are represented in magnitude,
direction and sense by two adjacent sides of parallelogram then diagonal will represent the
resultant in magnitude and direction but passing through the point of intersection of two forces”.
Magnitude of Resultant Force:
R= (𝑷² + 𝑸² + 𝟐𝑷𝑸𝒄𝒐𝒔𝜽
Or
R2
=P2
+Q2
+PQcosθ
Where θ is angle between P and Q
Direction of Resultant Force:
Let α is the angle made by R with P then,
𝛂= tan-1 𝐐𝐬𝐢𝐧 𝜽
𝑷+𝑸 𝐜𝐨𝐬 𝜽
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Limitations of Law of Parallelogram:
1. This law can be applied when only two forces are acting on the body. It becomes very
lengthy to apply it when more than two forces acting on the body.
2. Two forces acting on the body must be concurrent and coplanar.
Resolution of forces:
The method of splitting up a force into its components without changing its effect on the
body is known as resolution of forces.
This method can be used to find out resultant in magnitude and direction of two or more
forces acting on the body.
Triangle Law of forces:
It states “if two forces acting on a body can be represented in magnitude and direction by
the two sides of a triangle taken in order then resultant force may be represented in magnitude
and direction by the third side of a triangle but taken in opposite sense”.
Polygon Law of forces:
It states “if number of forces acting on a body can be represented in magnitude and
direction by the sides of polygon taken in order then resultant force may be represented in
magnitude and direction by the closing side of polygon but taken in opposite sense”.
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Moment of Force:
Moment of a force is the rotation or turning effect produced by a force.
Moment= (Force) x (Perpendicular from Point)
Mathematically,
Mo= P x d
Unit of Moment =Nm or kN-m
Types of Moment
1. Clockwise moment (taken as positive)
2. Anticlockwise moment ( taken as Negative)
Varignon’s Theorem:
“The algebraic summation of moments of all forces acting on a rigid body about any
point is equal to the moment of their resultant force about same point”.
Let, ΣMA = Algebraic summation of moments of all forces about a point A
R= Resultant Force for a given force system
d= perpendicular distance of line of action of R from point A
Mathematically, ΣMA= R x d
d=
ΣMA
𝑅
