Engineering Mechanics Fundamentals

Fundamentals Of EngineeringFundamentals Of Engineering
MechanicsMechanics
Fundamentals Of EngineeringFundamentals Of Engineering
MechanicsMechanics

EngineeringEngineering
The profession in which knowledge of the mathematical and
natural sciences gained by study, experience, and practice is
applied with judgment to develop ways to use economically the
materials and forces of nature for the benefit of mankind
OR
The discipline dealing with the art or science of
applying scientific knowledge to practical problems.

What is MechanicsWhat is Mechanics
Mechanics is a branch of the physical sciences that is concerned
with the state of rest or motion of bodies that are subjected to the
action of forces.
• Knowledge of Engineering Mechanics is very essential for an engineer in
planning, designing and construction of various types of structures &
machines.

MechanicsMechanics
Mechanics is divided into two areas;
• Satatics &
• Dynamics
Satatics deals with the equilibrium of
bodies , those that are either at rest or
move with a constant velocity
OR
Statics is branch of mechanics, which deals
with the forces and their effects, while
acting upon the bodies at rest.

MechanicsMechanics
Dynamics
• Dynamics is concerned with the accelerated motion of bodies
OR
• Dynamics is branch of mechanics, which deals with the forces and their
effects, while acting upon the bodies in motion.

Rigid BodyRigid Body
• A body is said to be rigid if the position of its various particles remain fixed
relative to one another.
• A rigid body can be considered as a combination of a large number of
particles in which all the particles remain at a fixed distance from one another,
both before and after applying a load.

MassMass
It is matter contained in a body. Mass is scalar property of matter that does not
change from one location to another.

WeightWeight
• It is force by which the body is attracted towards the center of earth.
• The weight of an object is defined as the force of gravity on the object and
may be calculated as the mass times the acceleration of gravity,
w = mg.
• Since the weight is a force, its SI unit is the Newton.

Newton’s laws of motionsNewton’s laws of motions
• Newton's First Law of Motion:
It states that Every object in a state of rest or of uniform motion tends to remain
in that state unless an external force is applied to it.

Newton’s laws of motionsNewton’s laws of motions
• Newton's Second Law of Motion:
It states that “the rate of change of momentum is directly proportional to the
force and takes place in the same direction in which the force acts”.
The relationship between an object's mass m, its acceleration a, and the applied
force F is F = ma.
• Newton's Third Law of Motion
For every action there is an equal and opposite reaction.

Newton’s Law of Gravitational AttractionNewton’s Law of Gravitational Attraction
• After formulating his three laws of motion, Newton postulated a law governing the
gravitational attraction between any two particles, Stated mathematically,

ForceForce
• Force is considered as “push” or “pull” exerted by one body on another.
• Its unit is N.
• When force is applied to an object , the velocity of that object changes. This
change in velocity constitutes an acceleration.
• Force is a vector quantity, therefore a force is completely described by;
magnitude, direction and point of application

Types of ForcesTypes of Forces
• Concurrent Force System
The force system in which line of action of
forces intersects through a common point.
• Parallel Force System
forces are parallel to each other.

Types of ForcesTypes of Forces
• Collinear Force System
forces lie on the same path.
--------------------------------------------
--------------------------------------------
• Coplanar Force System
forces lie on the same plane.

Force systemForce system
• Concentrated Force.
A concentrated force represents the effect of a loading which is assumed to act at a
point on a body. We can represent a load by a concentrated force, provided the area
over which the load is applied is very small compared to the overall size of the body. An
example would be the contact force between a wheel and ground.

Units of MeasurementUnits of Measurement
Fundamental Units
• Every quantity is measured in terms of some arbitrary, but internationally accept
units, called fundamental units.
• Length
• Mass and
• Time
Derived Units
• Some units are expressed in terms of other units, which are derived from some
fundamentals units are known as derived units.
• E.g. units of force, area, velocity, acceleration, pressure etc.

• The basic quantities - length, time, mass, and force are not all independent from
one another; in fact, they are related by Newton’s second law of motion.
• The equality F = ma is maintained only if three of the four units, called base units
(length, time, mass) , are defined and the fourth unit (force) is then derived from
the equation.

System of unitsSystem of units
International System of units (SI Units)
•The International System of units, abbr. SI is a modern version of the metric system
which has received worldwide recognition. As shown in Table 1–1, the SI system
defines length in meters (m), time in seconds (s), and mass in kilograms (kg). The unit
of force, called a newton (N), is derived from thus, 1 N is equal to a force required to
give 1 kilogram of mass an acceleration of 1 m/s2
(N = kg x m/s2
).
F = maF = ma

• If the weight of a body located at the “standard location” is to be determined in newtons,
then Eq. W = mg must be applied. Here measurements give g = 9.806 65 m/s2,
however for
calculations, the value g = 9.81 m/s2
is be used.
• Thus, W = mg (g = 9.81 m/s2
), Therefore, a body of mass 1 kg has a weight of 9.81 N, and
2-kg body weighs 19.62 N, and so on, Fig. (a).

U.S. Customary system of units (FPS Units)
•In the U.S. Customary system of units (FPS) length is measured in feet (ft), time in
seconds (s), and force in pounds (lb),
•Table 1–1.The unit of mass, called a slug, is derived from
•Hence,1 slug is equal to the amount of matter accelerated at 1 ft/s2
when acted upon
by a force of 1 lb (slug = lb.s2
/ft)
F = maF = ma

• Therefore, if the measurements are made at the “standard location,” where g = 32.2
ft/s2
then from Eq. W = mg OR m = W/g,
(g = 32.2 ft/s2
)
• So a body weighing 32.2 lb has a mass of 1 slug, a 64.4-lb body has a mass of 2 slugs,
and so on.. .Fig-b

Conversion of UnitsConversion of Units
Table 1–2 provides a set of direct conversion factors between FPS and SI units for
the basic quantities.
We also know, in the FPS system,
1 ft = 12 in. (inches),
5280 ft = 1 mi (mile),
1000 lb=1 kip (kilo-pound),and 2000 lb=1ton

PrefixesPrefixes
• When a numerical quantity is either very large or very small, the units used to define
its size may be modified by using a prefix.

General Procedure for AnalysisGeneral Procedure for Analysis
• The most effective way of learning the principles of engineering mechanics is to
solve problems.
• It is important to always present the work in a logical and orderly manner as
suggested by the following sequence of steps:
• Read the problem carefully and try to correlate the actual physical situation
with the theory studied.

General Procedure for AnalysisGeneral Procedure for Analysis
1. Tabulate the problem data and draw any necessary diagrams.
2. Apply the relevant principles, generally in mathematical form. Be sure equations
are dimensionally homogeneous.
3. Solve the necessary equations, and report the answer with three significant
figures.
4. Study the answer with technical judgment and common sense to determine
whether or not it seems reasonable.

Important Points (Review)Important Points (Review)

Exercise:1 (solution)Exercise:1 (solution)

Exercise: 2 (solution)Exercise: 2 (solution)

Exercise:2 (solution)Exercise:2 (solution)

Finding Unknown AnglesFinding Unknown Angles
• For solving problems it is necessary to find the required unknown angle by applying basic
geometric facts.
• As you have studied in lower classes, the basic facts about angles, triangles and
quadrilaterals, some important are given here.

Angle FactsAngle Facts
• Vertical angles have equal measure.
• The sum of adjacent angles on a straight line is 1800
.

• The sum of adjacent angles around a point is 3600
• Triangle Facts
The angle sum of any triangle is 1800
(The three angles always add to 180°)

Triangle FactsTriangle Facts
• When one angle of a triangle is a right
angle, the other two angles add up to
900
• The exterior angle of a triangle is equal
to the sum of the interior
opposite angles.

Triangle FactsTriangle Facts
• Base angles of an isosceles
triangle are equal.
(A triangle containing two equal sides and
angels)
• Each interior angle of
equilateral triangle is 600
(3 equal sides, 3 equal angles, always 60°)
Scalene Triangle: No equal sides, No equal
angles

Quadrilateral FactsQuadrilateral Facts
• Opposite angles in a parallelogram are equal.
• We already know that the sum of interior angles
of a triangle is 1800,
and sum of Quadrilateral is
360

• For a right triangle:
• a2
+ b2
= c2
• sin(θ) = b/c =opposite side/hypotenuse
• cos(θ) = a/c = near side/hypotenuse
• tan(θ) = b/a =opposite side/near side

For a general triangle:
α + β + γ = 180ο
•Sine law:
•Cosine law:

Engineering Mechanics Fundamentals

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Engineering Mechanics Fundamentals