ENGINEERING MECHANICS STATICS

*Is the study which deals with the condition

Engineering Mechanics of bodies in equilibrium subjected to
*A Branch of Physical Sciences that is external forces.
concerned with the state of rest or motion of *In other words, when the force system
bodies subjected to the action of forces acting on a body is balanced, the system has
*The physical Science concerned with the no external effect on the body, the body is in
behavior of bodies that are acted upon by equilibrium.
forces DYNAMICS
*Oldest of the physical science *Is also a branch of Mechanics in which the
3 TYPES OF MECHANICS forces and their effects on the bodies in
*Mechanics of Rigid Bodies motion are studied
-Statics Subdivided into two parts:
-Dynamics Kinematics - Deals with the geometry of
* Mechanics of Deformable Bodies motion of bodies without and application of
* Fluid Mechanics external forces
RIGID BODIES Kinetics- Deals with the motion of bodies
*A basic requirement for the study of the with the application of external forces
Mechanics of Deformable bodies and fluid Mass - The quantity of the matter possessed
Mechanics by a body is called mass. The mass of a
*Essential for the design and analysis of body cannot change unless the body is
many types of structural members, damaged and part of it is physically
mechanical components, electrical devices, separated.
and encountered in engineering. Length - It is a concept to measure linear
distances.
A RIGID BODY DOES NOT DEFORM Time - Time is the measure of succession of
UNDER LOAD events. The successive event selected is the
rotation of earth about its own axis and this
is called a day. concepts independent of each other.
Space - Any geometric region in which the * Force is derived concept not independent
study of a body has been done is called of other fundamental concepts. Force acting
space. on a body is related to mass of the body and
Displacement - It is defined as the distance the variation of its velocity with time.
moved by a body/particle in the specified * Force can also occur between bodies that
direction. are physically separated (Ex. Gravitational,
Velocity - The rate of change of electrical and magnetic forces.
displacement with respect to time is defined Mass - is a property of matter that does not
as velocity change from one location to another.
Acceleration - It is the rate of change of Weight - refers to the gravitational attraction
velocity with respect to time. of the earth on a body or quantity of mass.
Momentum - The product of mass and Its magnitude depends upon the elevation at
velocity is called momentum. Thus which the mass is located.
Momentum = Mass × Velocity Concentrated Force
Particle - It can be defined as an object * Effect of a loading is assumed to act at a
which has only mass and no size. point on a body.
• Such a body cannot exist theoretically. * Provided the area over which the load is
•When we deal with the problems involving applied is very small compared to the overall
distances considerably larger compared to size of the body.
the size of the body, the body may be treated FIRST LAW: (Law of Inertia)
as particle *“A particle originally at rest, or moving in a
Force - Represents the action of one body to straight line with constant velocity, tends to
another. It is characterized by its magnitude, remain in this state provided the particle is
direction of action and its point of not subjected to an unbalanced force. “
application. Force is a Vector Quantity. * It states that everybody continues in its
Newtonian Mechanics: state of rest or of uniform motion in a
* Length, Time and Mass are absolute straight line unless it is compelled by an
external agency acting on it. CGS (Centimetre – Gram – Second) system
SECOND LAW: (Law of Acceleration) MKS (Meter - Kilogram – Second) system
* “A particle of mass m acted upon by an SI (System international dꞌunits – the
French name)
unbalanced force F experiences an
The SI system of units is said to be an
acceleration a that has the same direction as
absolute system.
the force and a magnitude that is directly
The fundamental units of the system are
proportional to the force. “
metre (m) for length, kilogram (kg) for mass
* It states that the rate of change of
and second (s) for time.
momentum of a body is directly proportional
The unit for force is newton (N). One
to the impressed force and it takes place in
newton is the amount of force required to
the direction of the force acting on it.
induce an acceleration of 1 m/sec2 on one
According to this law:
kg mass. Weight of a body (in N) = Mass of
Force = rate of change of momentum. But
the body (in kg ) × Acceleration due to
momentum = mass × velocity
gravity (in m/sec2 ). Dimension
As mass do not change
Absolute system (MLT system)
Force = mass × rate of change of velocity
* A system of units defined on the basis of
Force = mass × acceleration
length, time and mass is referred to as an
F=m×a
absolute system.
THIRD LAW: (Law of Interaction)
* According to SI system of units, three
*“For every action there is an equal and
basic units metre, second and kilogram can
opposite reaction. The mutual forces of
be used. In MLT system, M refers to Mass, L
action and reaction between two particles
refers to Length and T refers to Time.
are equal, opposite and collinear.“
Gravitational system (FLT system)
* It states that for every action there is an
* A system of units defined on the basis of
equal and opposite reaction.
length, time and force is referred to as a
There are four systems of units used for the
gravitational system.
measurement of physical quantities.
* In this system, force is measured in a
FPS (Foot – Pound – Second) system
gravitational field. Thus, its magnitude
depends upon the location where the particle and its acceleration.
measurement is made. FLT system refers to * Force is the manifestation of action of one
the Force-Length-Time system. particle on the other. It is a vector quantity.
Scalar Quantity - A quantity is said to be Characteristics of a Force:
scalar if it is completely defined by its * A Force has following basic characteristics
magnitude alone. * Magnitude
Vector Quantity: A quantity is said to be * Direction
vector if it is completely defined only when * Point of application
its magnitude as well as direction are * Line of action
specified. Force is represented as a vector i.e. an arrow
Free Vectors: whose action is not confined to with its magnitude.
or associated with a unique line in space. Coplanar Force System - When the lines of
Example: Movement of a body without action of a set of forces lie in a single plane
rotation. is called coplanar force system.
Sliding Vector: has a unique line of action in Collinear Force System - When the lines of
space but not a unique point of application action of all the forces of a system act along
Example: External force on a rigid body, the same line, this force system is called
Principle of Transmissibility, Rigid Bodies collinear force system.
Fixed Vector: for which a unique point of Parallel Force System - Forces that act in the
application is specified. same or opposite directions at different
Example: Action of a force on a deformable points on an object.
bodies Non-Coplanar Force System - When the
line of action of all the forces do not lie in one
FORCE SYSTEM
plane, is called Non-coplanar force system.
* Definition of ‘force’ can be given in
Concurrent Force System - The forces whe
several ways. Most simply it can be defined
extended pass through a single point and the
as ‘the cause of change in the state of motion
point is called point of concurrency. The
of a particle or body’. It is of course, the
lines of actions of all forces meet at the point
product (multiplication) of mass of the
of concurrency. Concurrent forces may or
may not be coplanar. of the system is equal to zero, the resultant
Non-Concurrent Force System - When the can act only along the y axis.
forces of a system do not meet at a common RESULTANT OF PARALLEL FORCES
point of concurrency, this type of force * The resultant for a parallel force system is
system is called non-concurrent force determined when its magnitude, direction
system. Parallel forces are the example of and position isknown.
this type of force system. Non-concurrent * One of the outstanding differences
forces may be coplanar or non-coplanar. between a concurrent and a parallel force
Coplanar and concurrent force system - A system is that in the former position of the
force system in which all the forces lie in a resultant is known by inspection whereas the
single plane and meet at one point, For latter it is not.
example, forces acting at a joint of a roof * To determine the R, select some
truss convenient point 0 as a moment center.
Coplanar and non-concurrent force ΣMo =R x d
system -These forces do not meet at a
RESULTANT OF DISTRIBUTED LOAD
common point; however, they lie in a single
- The resultant of a distributed load is equal
plane.
to the area of the load diagram and is acting
For example, forces acting on a beam. at the centroid of that area.
Non-Coplanar and Concurrent force FREE BODY DIAGRAMS (FBD’S)
system
* A free body diagram is a sketch of a body,
- In this system, the forces lie in a different
a portion of a body, or two or more bodies
planes but pass through a single point.
completely isolated or free from all other
Example is forces acting at the top end of an
bodies, showing the forces exerted by all
electrical pole.
other bodies on the one being considered.
Non-Coplanar and non-concurrent force
* Isolation of a part of a structure and
system - The forces which do not lie in a
showing the forces acting on it.
single plane and do not pass through a single
Characteristics of free body diagram:
point are known as non-coplanar and
* It is a diagram or sketch of a body
nonconcurrent
* The body is shown completely separated
If the sum of the x components of the forces
from all other bodies * We need the friction between the tires on
* The action on the body of each body the road surface, to let the wheels roll.
removed in the isolating process is shown as Friction is caused due to the unevenness of
a force or forces on the diagram. the surface of contact of bodies tending to
FRICTION AND FRICTIONAL move past each other.
FORCES
Friction is the contact resistance exerted by
When two bodies in contact have a tendency
one body when the second body moves or
to move over each other a resistance to the
tends to move past the first body. Friction is
movement is set up. This resistance to the
a retarding force that always acts opposite to
movement is called the Force of friction or
the motion or to the tendency to move
simply friction. Friction depends upon the
TYPES OF FRICTION
nature of the surface of contact. Friction acts
1. Dry Friction - also called Coulomb
parallel to the surface of contact. The
Friction, occurs when unlubricated surfaces
direction of this frictional force on any one
of two solids are in contact and slide or tend
of the surfaces of contact will be opposite to
to slide from each other. If lubricant
the direction in which the contact surface
separates these two surfaces, the friction
tends to move. In other words, friction
created is called lubricated friction. This
opposes motion.
section will deal only with dry friction.
* Friction is an important force in many
2. Fluid Friction - Fluid friction occurs
aspects of everyday life.
when layers of two viscous fluids moves at
* If there is too much friction, loss of
different velocities. The relative velocity
energy, wear and tear of materials in contact
between layers causes frictional forces
occurs.
between fluid elements, thus, no fluid
* If there is less friction or no friction, this
friction occurs when there is no relative
would result in ‘slipping’ all around.
velocity.
* For example oil in the engine of car is
3. Skin Friction - Skin friction also called
meant to minimize friction between moving
friction drag is a component of the force
parts in contact to reduce excessive friction
resisting the motion of a solid body through a
for reducing loss of energy and material. fluid.
4. Internal Friction - Internal friction is nature of the surfaces of contact. The
associated with shear deformation of the limiting frictional resistance is independent
solid materials subjected to cyclical loading. of the area of contact.
As deformation undergo during loading, Fourth Law (Friction during motion i.e
internal friction may accompany this Kinetic Friction). When motion takes place
deformation. as one body slides over the other the
LAWS OF FRICTION magnitude of the frictional resistance will be
The following are the laws of friction: less than that offered at the condition of
1. Friction in non-limiting equilibrium limiting equilibrium. The magnitude of the
2. Friction in limiting equilibrium friction will depend only on the nature of the
3. Friction during motion sliding and independent of the shape or the
First Law (Applicable to non-limiting, extent of the contact area.
limiting and dynamic condition). Friction
always opposes motion. Frictional forces
come into play only when a body is urged to
move. Frictional force will always act in a
direction opposite to that in which the body
is urged to move.
Second Law (Applicable to non-limiting
condition of equilibrium). The magnitude of
the frictional force is just sufficient to
prevent the body from moving. That is, only
as much resistance as required to prevent
motion will be offered as friction.
Third Law (Applicable to limiting condition
of equilibrium). The limiting frictional
resistance bears a constant ratio with the
normal reaction. This ratio depends on the