Introduction to Civil Engineering, BESCK104A/204A - Module 3

MODULE-3
ANALYSIS OF FORCE SYSTEMS

Lecture 7:

Engineering Mechanics:

• It is a branch of applied sciences that describes and predicts the state of rest or of uniform motion
of bodies under the action of forces
• Engineering Mechanics deals with the application of principles of mechanics and different laws in
a systematic manner

Basic Idealization:

Particle: A body with mass but with dimensions that can be neglected
• A particle is a body whose dimensions are considered to be near zero so that we may analyze it as
a mass concentrated at a point
• We often choose a particle as a differential element of the body

Rigid Body: is an idealized body composed of a large number of particles all of which always
remain at fixed distances from each other
• A rigid body is assumed to undergo no deformation under the action of applied forces
• Its shape and dimensions remain fixed under all loading conditions and at all times

Continuum: A body consists of several matters.

• The body is assumed to consist of a continuous distribution of matter. In other words, the body is
treated as continuum

Force:

• According to Newton's Fist law, force is defined as an action or agent, which changes or tends to
change the state of rest or of uniform motion of a body in a straight line.
• Units of force: The gravitational (MKS) unit of force is the kilogram force and is denoted as kgf.
The absolute (SI) unit of force is the Newton and is denoted as N. Note: 1 kgf = g N (But g =
9.81m/s2) Therefore 1 kgf = 9.81 N or 10 N.

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Introduction to Civil Engineering, BESCK104A/204A - Module 3

Characteristics of a force

These are ones, which help in understanding a force completely, representing a force and also
distinguishing one force from one another. A force is a vector quantity. It has four important
characteristics, which can be listed as follows.
1. Magnitude: It can be denoted as 10 kgf or 100 N.
2. Point of application: It indicates the point on the body on which the force acts.
3. Line of action: The arrowhead placed on the line representing the direction represents it.
4. Direction: It is represented by a co-ordinate or cardinal system.

Ex.1: Consider a body being pushed by a force of 10 N as shown in figure below

The characteristics of the force acting on the body are

1. Magnitude is 10 N.
2. Point of application is A.
3. Line of action is A to B or AB.
4. Direction is horizontally to right.

Idealization or assumptions in Mechanics

In applying the principles of mechanics to practical problems, a number of ideal conditions are
assumed. They are as follows.
1. A body consists of continuous distribution of matter.
2. The body considered is perfectly rigid.
3. A particle has mass but not size.
4. A force acts through a very small point.

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Introduction to Civil Engineering, BESCK104A/204A - Module 3

Classification of force systems

1. Collinear forces: It is a force system, in which all the forces have the same line of action.

2. Coplanar parallel forces: It is a force system, in which all the forces are lying in the same
plane and have parallel lines of action.

a.

3. Coplanar Concurrent forces: It is a force system, in which all the forces are lying in the same
plane and lines of action meet a single point

4. Coplanar non-concurrent forces: It is a force system, in which all the forces are lying in the same
plane but lines of action do not meet a single point

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Module 3- Analysis of Force systems

5. Non- coplanar parallel forces: It is a force system, in which all the forces are
lying in the different planes and still have parallel lines of action

a.

6. Non- coplanar concurrent forces It is a force system, in which all the forces are
lying in the different planes and still have common point of action

a.

7. Non- coplanar non-concurrent forces: It is a force system, in which all the forces are
lying in the different planes and also do not meet a single point

Lecture 8:

Fundamental Laws in Mechanics

1. Newton’s I law: It states, “Every body continues in its state of rest or of uniform
motion in a straight line, unless it is compelled to do so by force acting on it.” This
law helps in defining a force.
2. Newton’s II law: It states, “The rate of change of momentum is directly proportional
to the applied force and takes place in the direction of the impressed force.”
3. Newton’s III law: It states, “For every action there is an equal and opposite reaction.”
4. Principle or Law of transmissibility of forces: It states, “The state of rest or of
Uniform motion of a rigid body is unaltered if the point of application of the force is

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Module 3- Analysis of Force systems

Transmitted to any other point along the line of action of the force.”

5. Parallelogram law of forces: This law is applicable to determine the resultant of two
coplanar concurrent forces only
This law states “If two forces acting at a point are represented both in magnitude
and direction by the two adjacent sides of a parallelogram, then the resultant of
the two forces is represented both in magnitude and direction by the diagonal of
the parallelogram passing through the same point.”

6. Principle Of Superposition Of Forces

This principle states that the combined effect of force system acting on a particle
or a rigid body is the sum of effects of individual forces.

7. Principle of Physical Independence of Forces

Two or more forces acting on a body, will produce its own effect on the body
irrespective of the effect produced by the other force.

Couple:
A system of 2 equal parallel forces acting in opposite directions is said form a couple. Fig
shows a couple formed by horizontal, vertical and inclined forces.

The plane in which the two forces forming a couple lie is called the plane of the couple
and the distance between their line of action is called the arm of the couple. Any couple acting
on a rigid body produces only rotation to the body. This rotation is measured by the moment
of the couple, which is product of magnitude of the force and the distance between the two

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Module 3- Analysis of Force systems

forces (arm of the couple). In contrast, the couple does not cause any translation to the rigid
body.
The magnitude of the moment of the couple is determined by using the principle of
superposition. That is, the moment of the couple is equal to the sum of the moment of the two
forces of the couple about any point. As seen in Fig, the moment of couple about O 1 is given
by

MO1 = +F(d1) – F(a+d1) = -F*a

Similarly, the moment of the couple about point O2 is

MO2 = -F(a-d2) – F(d2) = -F*a

Therefore,
MO1 = MO2

Resolution of forces:
Splitting of a force into its horizontal component (x- component) and vertical
component (y – component) is called resolution of forces.
Sign convention for forces:

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Module 3- Analysis of Force systems

Resolving when the force is inclined at angle of θ with horizontal.

Resolving a force in the 1st quadrant: Resolving a force in the 2nd quadrant:

Resolving a force in the 3rd quadrant: Resolving a force in the 4th quadrant:

Resolving when the force is inclined at angle of θ with vertical.

END

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