ENGINEERING MECHANICS

1. DISCOVER . LEARN . EMPOWER
ENGINEERING MECHANICS
Baba Farid College of
Engineering and Technology
Bachelor of Engineering
(MECHANICAL ENGINEERING)
Engineering Mechanics
PARVINKAL SINGH MANN
Assistant Professor
1

2. • Worked in Baba Farid College of Engineering and Technology in
2014.
• Served 8 years in CHANDIGARH UNIVERSITY as Assistant
Professor in Mechanical Engineering Department.
• Completed Doctorate of Philosophy (Ph.D) from Punjabi
University Patiala.
• Published more than 20 Research Paper in reputed journals.

3. Introduction to Mechanics
In any field the importance of a thorough
knowledge of fundamentals cannot be over
emphasized. Fundamentals have always been
stressed in the learning of new skills. Similarly, the
mechanics is the branch of science which deals with
the forces and their effect on bodies on which they
act is founded on basic concepts and forms the
ground-work for further study in the design and
analysis of machines and structures. Mechanics can
be divided into two parts

4. (i)‘Statics’ which relates to the bodies at rest and
(ii) ‘dynamics’ which deals with bodies in
motion. (In mechanics the term strength of
materials refers to the ability of the individual
parts of a machine or structure to resist loads. It
also permits the determination of dimensions to
ensure sufficient strength of the various parts).

5. • Dynamics may be further into the following
two groups :

6. • ‘Kinematics’which deals with the motion of
bodies without any reference to the cause of
motion.
• ‘Kinetics’which deals with the relationship
between forces and the resulting motion of bodies
on which they act.
• The branch of science which deals with the study
of different laws of mechanics as applied to
solution of engineering problems is called
Applied Mechanics.

7. Basic Definitions
• Length. This term is applied to the linear dimensions of a
straight or curved line. For example, the diameter of circle
is the length of a straight line which divides the circle into
two equal parts ; the circumference is the length of its
curved perimeter.
• Area. The two dimensional size of a shape or a surface is its
area. The shape may be flat (lie in a plane) or curved, for
example, the size of a plot of land, the surface of a
fluorescent bulb, or the cross-sectional size of a shaft.
• Volume. The three dimensional or cubic measure of the
space occupied by a substance is known as its volume.

8. • Force. This term is applied to any action on the body
which tends to make it move, change its motion, or
change its size and shape. A force is usually thought of a
push or pull, such as a hand pushing against a wall or the
pull of a rope fastened to a body.
• Pressure. The external force per unit area, or the total
force divided by the total area on which it acts, is known
as pressure. Water pressure against the face of a dam,
steam pressure in a boiler, or earth pressure against a
retaining wall are some examples.
• Mass. The amount of matter contained in a body is called
its mass, and for most problems in mechanics, mass may
be considered constant.

9. • Weight. The force with which a body is attracted towards the
centre of earth by the gravitational pull is called its weight.
The relation between mass (m) and weight (W) of a body is given
by the equation
W = m × g
The value of g is taken as 9.81 m/sec2 (usually 9.80 m/sec2 to
make the calculation work easier) in M.K.S. system as well as in
S.I. units.
• Density. The weight of a unit volume of a body or substance is
the density. This term is sometimes called weight density, to
distinguish it from a similary definition (mass density) made in
terms of mass.
• Moment. The tendency of a force to cause rotation about some
point is known as a moment.

10. Difference between Mass and Weight
Mass Weight
1. It is the quantity of matter
contained in a body.
1. It is constant at all places.
2. It resists motion in the body.
3. It is a scalar quantity since it has
magnitude only.
1. It can be measured by an ordinary
balance.
2. It is never zero.
3. It is measured in kilogram (kg) in
M.K.S. systemof units as well as in
S.I. units.
1. It is the force with which the body
is attracted towards the centre of
earth.
2. It is different at different places.
3. It produces motion in the body.
4. It is a vector quantity since it has
magnitude as well as direction.
5. It is measured by a spring balance.
6. It is zero at the centre of earth.
7. It is measured in kilogram weight
(kg wt. or kgf) in M.K.S. system of
units and in newton (N) in S.I.units.

11. Torque. The action of a force which causes
rotation to take place is known as torque. The
action of a belt on a pulley causes the pulley to
rotate because of torque. Also if you grasp a
piece of chalk near each end and twist your
hands in opposite directions, it is the developed
torque that causes the chalk to twist and,
perhaps, snap.

12. • Work. The energy developed by a force acting
through a distance against resistance is known as
work. The distance may be along a straight line or
along a curved path. When the distance is linear,
the work can be found from work = force ×
distance. When the distance is along a circular path
the work can be found from work = toque × angle.
Common forms of work include a weight lifted
through a height, a pressure pushing a volume of
substance, and torque causing a shaft to rotate.
• Power. The rate of doing work, or work done per
unit time is called power. For example, a certain
amount of work is required to raise an elevator to
the top of its shaft. A 5 HP motor can raise the
elevator, but a 20 HP motor can do the same job
four times faster.

13. RIGID BODY
• Rigid body is one which does not change its
shape and size under the effect of forces acting
over it. It differs from an elastic body in the
sense that the latter undergoes deformation
under the effect of forces acting on it and
returns to its original shape and size on
removal of the forces acting on the body. The
rigidity of a body depends upon the fact that
how far it undergoes deformation under the
effect of forces acting on it.

14. In real sense no solid body is perfectly rigid
because everybody changes it size and shape
under the effect of forces acting on it. It actual
practice, the deformation (i.e., change in shape
and size of a body under the effect of forces
acting on it) is very small and therefore it may be
considered as a rigid body.

15. SCALAR AND VECTOR QUANTITIES
• Scalar quantity. A scalar quantity is one that
has magnitude only.
• Examples. Mass, volume, time and density.
• Vector quantity. A vector quantity is one that
has magnitude as well as direction.
• Examples. Force, velocity, acceleration and
moment etc.

16. A vector quantity is represented by a line carrying an
arrow head at one end. The length of the line (to
convenient scale) equals the magnitude of the vector. The
line, together with its arrow head, defines the direction of
the vector. Suppose a force of 60 N is applied to point A at
an angle of 45° to the horizontal. The vector AB represents
this force since its length equals 60 N (to scale) and its
direction is proper. If the vector BA is drawn to same scale
it represents a 60 N force having a direction exactly
opposite to vector AB.

17. UNIT-1

18. FORCE
• Force is some thing which changes or tends to change
the state of rest or of uniform motion of a body in a
straight line. Force is the direct or indirect action of one
body on another. The bodies may be in direct contact
with each other causing direct motion or separated by
distance but subjected to gravitational effects.
• There are different kinds of forces such as gravitational,
frictional, magnetic, inertia or those cause by mass and
acceleration.
• The force has a magnitude and direction, therefore, it is
vector.

19. When a force acts on a body, the following effects
may be produced in that body :
(i) It may bring a change in the motion of the body
i.e., the motion may be accelerated or retarded ;
(ii) it may balance the forces already acting on the
body thus bringing the body to a state of rest or
of equilibrium, and
(iii) it may change the size or shape of the body i.e.,
the body may be twisted, bent, stretched,
compressed or otherwise distorted by the action
of the force.

20. CHARACTERISTICS OF A
FORCE
• The characteristics or elements of the force are
the quantities by which a force is fully
represented. These are :
• Magnitude (i.e., 50 N, 100 N, etc.)
• Direction or line of action (angle relative to a co-
ordinate system).
• Sense or nature (push or pull).
• Point of application.

21. REPRESENTATION OF FORCES
• Forces may be represented in the following two ways :
• Vector representation
• Bow’s notation. It is a method of designating a
force by writing two capital letters one on either
side of the force a shown in Fig., where force P1
(200N) is represented by AB, and force P2 (100
N) by CD.

22. CLASSIFICATION OF FORCES
1. According to the effect produced by the force :
• External force. When a force is applied external to a
body it is called external force.
• Internal force. The resistance to deformation, or change
of shape, exerted by the material of a body is called an
internal force.
• Active force. An active force is one which causes a body
to move or change its shape.
• Passive force. A force which prevents the motion,
deformation of a body is called a passive force.

23. 2. According to nature of the force :
• Action and reaction. Whenever there are two bodies
in contact, each exerts a force on the other. Out of
these forces one is called action and other is called
reaction. Action and reaction are equal and opposite.
• Attraction and repulsion. These are actually non-
contacting forces exerted by one body or another
without any visible medium transmission such as
magnetic forces.
• Tension and thrust. When a body is dragged with a
string the force communicated to the body by the
string is called the tension while, if we push the body
with a rod, the force exerted on the body is called a
thrust.

24. 3. According to whether the force acts at a
point or is distributed over a large area.
• Concentrated force. The force whose point of
application is so small that it may be considered
as a point is called a concentrated force.
• Distributed force. A distributed force is one
whose place of application is area.

25. 4. According to whether the force acts at a
distance or by contact.
• Non-contacting forces or forces at a distance.
Magnetic, electrical and gravitational forces are
examples of non-contacting forces or forces at a
distance.
• Contacting forces or forces by contact. The
pressure of steam in a cylinder and that of the
wheels of a locomotive on the supporting rails are
examples of contacting forces.

26. FORCE SYSTEMS
A force system is a collection of forces acting on a
body in one or more planes.
According to the relative positions of the lines of
action of the forces, the forces may be classified as
follows :
Coplanar concurrent collinear force system. It is
the simplest force system and includes those forces
whose vectors lie along the same straight line

27. Coplanar concurrent non-parallel force
system. Forces whose lines of action pass
through a common point are called concurrent
forces. In this system lines of action of all the
forces meet at a point but have different
directions in the same plane

28. Coplanar non-concurrent parallel
force system. In this system, the lines
of action of all the forces lie in the
same plane and are parallel to each
other but may not have same direction
Coplanar non-concurrent non-
parallel force system. Such a
system exists where the lines of
action of all forces lie in the same
plane but do not pass through a
common point.

29. Non-coplanar concurrent force
system. This system is evident where
the lines of action of all forces do not
lie in the same plane but do pass
through a common point. An
example of this force system is the
forces in the legs of tripod support
for camera
Non-coplanar non-concurrent force system. Where
the lines of action of all forces do not lie in the same
plane and do not pass through a common point, a non-
coplanar non-concurrent system is present.

30. FREE BODY DIAGRAMS
A body may consist of more than one element and
supports. Each element or support can be isolated from
the rest of the system by incorporating the net effect of
the remaining system through a set of forces. This
diagram of the isolated element or a portion of the body
along with the net effects of the system on it is called a
‘free-body diagram’. Free-body diagrams are useful in
solving the forces and deformations of the system.

32. TRANSMISSIBILITY OF A
FORCE
The principle of transmissibility of forces states
that when a force acts upon a body, its effect is
the same whatever point in its line of action is
taken as the point of the application provided
that the point is connected with the rest of the
body in the same invariable manner.

33. A force may be considered as acting at any point on its
line of action so long as the direction and magnitude are
not changed. Suppose a body is to be moved by a
horizontal force P applied by hooking a rope to some
point on the body.
The force P will have the same effect if it is applied at
1, 2, 3 or any point on its line of action. This property
of force is called transmissibility.

34. Particle
A particle may be defined as an object which has only
mass and no size. Theoretically speaking such a body
cannot exist. However in dealing with problems
involving distances considerably larger compared to the
size of the body, the body may be treated as a particle,
without sacrificing accuracy.
A body whose dimensions are practically negligible is
called a particle. In any problem of mechanics, when
the applied forces have no tendency to rotate the body
on which they act, the body may be considered as a
particle.

35. RESULTANT FORCE
A resultant force is a single force which can replace two
or more forces and produce the same effect on the body
as the forces. It is fundamental principle of mechanics,
demonstrated by experiment, that when a force acts on a
body which is free to move, the motion of the body is in
the direction of the force, and the distance travelled in a
unit time depends on the magnitude of the force.
Then, for a system of concurrent forces acting on a
body, the body will move in the direction of the
resultant of that system, and the distance travelled in a
unit time will depend on the magnitude of the resultant.

36. COMPONENT OF A FORCE
As two forces acting simultaneously on a particle
acting along directions inclined to each other can
be replaced by a single force which produces the
same effect as the given force, similarly, a single
force can be replaced by two forces acting in
directions which will produce the same effect as
the given force. This breaking up of a force into
two parts is called the resolution of a force. The
force which is broken into two parts is called the
resolved force and the parts are called component
forces or the resolutes.

37. Generally, a force is resolved into the following two types of
components :
• Mutually perpendicular components
• Non-perpendicular components.
• Mutually perpendicular components. Let the force P to be
resolved is represented in magnitude and direction by oc in Fig.
2.11. Let Px is the component of force P in the direction oa
making an angle  with the direction oc of the force. Complete the
rectangle oacb. Then the other component Py at right angle to Px
will be represented by ob which is also equal to ac.
From the right-angled triangle oac
Px = oa = P cos 
Py = ac = P sin 

38. Non-perpendicular components. Let oc
represents the given force P in magnitude and
direction to some scale. Draw oa and ob making
angle  and  with oc. Through c draw ca parallel
to ob and cb parallel to oa to complete the
parallelogram oacb. Then the vectors oa and ob
represent in magnitude and direction (to the same
scale) the components P1 and P2 respectively.