Course
on
FCME006: Basics of Mechanical Engineering
Mr. Sanjay Gupta
Department of Mechanical Engineering
Netaji Subhas University of Technology
Room No.: 136/VI
Email: sgupta@nsut.ac.in
Introduction of Subject
Basics of Mechanical Engineering
Mechanical Engineering: is one of the
oldest and broadest of the engineering branches.
Mechanical engineering is an engineering branch that
combines engineering physics and mathematics
principles with materials science to design, analyze,
manufacture, and maintain mechanical systems.
This subject is divided into five units which is consist of
Unit I
Introduction to
Engineering
Mechanics
Unit II
Introduction to
Strength of Materials
Unit IV
Introduction to
Thermodynamics
Unit III
Introduction to
Manufacturing
Engineering
Unit V
Introduction to
Fluid Mechanics
Unit I: Introduction to Engineering Mechanics
Lecture No.
Topic Covered
1.
Introduction, Rigid and Elastic bodies, Force and its type
2.
Types of forces
3.
Moment of forces
4.
Equilibrant and equation of equilibrium
5.
Concept of Free Body Diagram (FBD), resultant and its calculation
6.
Laws of Coulomb friction and other definition
7.
Trusses
8.
Trusses Cont…
Unit II: Introduction to Strength of Materials
Lecture No.
Topic covered
1.
Introduction, Normal, Shear stresses and volumetric stresses and strains, Stress- Strain
Diagrams for ductile and brittle material (Hooke’s law) and Tension test
2.
Derivation on Elastic Constants
3.
Numerical on One Dimensional Loading of members of varying cross-sections
4.
Basic concepts of shear force, bending moment, Types of loading, Types of beam
5.
Various types of Numerical on point load for Simple and Cantilever beams
6.
Various types of Numerical of uniform distributed load UDL for Simple and Cantilever
beams
7.
Various types of Numerical on Varying load for different type of beams.
8.
Miscellaneous numerical problems
Unit III: Introduction to Manufacturing Engineering
1.
Classification and use of engineering materials
2.
Basic principles and applications of methods of manufacturing:
Casting
3.
Forming
4.
Joining
5.
Working principles and applications of machining operations:
Turning, Thread cutting, Milling
6.
Working principles and applications of machining operations:
Shaping, Grinding
7.
Use of automation in manufacturing
Unit IV: Introduction to Thermodynamics
1.
Thermodynamic system, Cycle, Path, Thermodynamic properties,
Extensive and intensive properties
2.
Thermodynamic equilibrium
3.
Reversible and irreversible processes, isochoric,
Isobaric, Isentropic and Polytropic processes
4.
First law of thermodynamics applied to a cycle and process
5.
Kelvin-Planck and
thermodynamics
6.
Carnot cycle, Entropy, Clausius inequality
Clausius
statements
of
Isothermal,
Second
law
of
Unit IV: Introduction to Thermodynamics
7.
Carnot cycle, Entropy, Clausius inequality
8.
Internal combustion (IC) engines, IC engines terminology
9.
Spark ignition (SI) and Compression ignition (CI) engines
10.
Two and four stroke engines
11.
Air standard cycles such as Otto, Diesel
12.
Dual and Brayton cycles
13.
Numerical problems
Unit V: Introduction to Fluid Mechanics
1.
Properties of fluids: Density or mass density, Specific weight or weight
density, Specific volume, Specific gravity, numerical problems
2.
Viscosity: Units of viscosity, Kinematic viscosity, Newton’s Law of viscosity,
Variation of viscosity with temperature, types of fluids
3.
Pressure and Its measurement: Fluid pressure at a point, Pascal’s Law,
Pressure variation in a fluid at rest
4.
Kinematics of Flow: Method of describing fluid motion, Types of fluid flow –
steady and unsteady flows, uniform and non-uniform flows, laminar and
turbulent flows, compressible and incompressible flows, rotational and
irrotational flows, 1D, 2D and 3D flows
5.
Kinematics of Flow Cont.…: Rate of flow or discharge, Continuity Equation
Unit V: Introduction to Fluid Mechanics
6.
Dynamics of fluid flow: Equation of motion, Euler’s Equation of Motion,
Bernoulli’s Equations from Euler’s Equations
7.
Practical Applications of Bernoulli’s Equations: Venturimeter,
Orifice meter, Pitot-tube
8.
Numerical problems
Unit I: Introduction to Engineering Mechanics
Text/Reference Books
1. H. Shames, Engineering Mechanics: Statics and dynamics, 4th Ed, PHI,
2002.
2. F. P. Beer and E. R. Johnston, Vector Mechanics for Engineers, Vol I Statics, Vol II – Dynamics, 9th Ed, Tata McGraw Hill, 2011.
3. J. L. Meriam and L. G. Kraige, Engineering Mechanics, Vol I – Statics, Vol II –
Dynamics, 6th Ed, John Wiley, 2008.
4. R. C. Hibbler, Engineering Mechanics: Principles of Statics and Dynamics,
Pearson Press, 2006.
5. Andy Ruina and Rudra Pratap, Introduction to Statics and Dynamics, Oxford
University Press, 2011
Lecture 1
Topics Covered in Lecture 1:
Introduction: Definition of mechanics, types of mechanics, standard units used.
Rigid and Elastic bodies
Force and its type
●
●
●
●
Concept of space, time, mass and force.
Explain the force.
Discuss the difference between scalar and vector quantities.
Explain the laws of motion. There are three types of Newton’s laws of motion
which are First law of motion, Second law of motion and Third law of motion.
● Explain the Principle of transmissibility it states that the condition of
equilibrium or of motion of rigid bodies will remain unchanged if the point of
application of a force acting on the rigid body is transmitted to act at any other
point along its line of action.
Mechanics: Oldest of the Physical Sciences
Mechanics is a branch of the physical sciences that is
concerned with the state of rest or motion of bodies subjected
to the action of forces.
Depending upon the nature of body involved,
mechanics can be classified as:
Rigid-body Mechanics
Statics
Deformable-Body Mechanics
Dynamics
Fluid Mechanics
In this Unit - 1 we study the mechanics of Rigid-body
Rigid-body Mechanics is essential for the design and analysis of
many types of structural members, mechanical components,
electrical devices, etc, encountered in engineering.
A rigid body does not deform under load!
Rigid Body : It is the body that deforms negligible under the action of
external forces. It represents the definite amount of matter, the part of
which are fixed in position relative to one another. Thus, the rigid body is
assumed as no deformation body under the action of external forces.
Statics: deals with equilibrium of bodies under action of
forces (bodies may be either at rest or move with a constant
velocity).
Dynamics: deals with motion of bodies (accelerated motion)
Kinetics is the study of the relationship between
the forces and the resulting motion.
While, Kinematics is the study of motion of bodies without
any reference to the forces causing motion or forces
produced as a result of the motion.
Mechanics: Fundamental Concepts
Length (Space): needed to locate position of a point in space, & describe size
of the physical system
Distances, Geometric Properties
Time: measure of succession of events
Mass: quantity of matter in a body
resistance to change in velocity)
basic quantity in dynamics
measure of inertia of a body (its
Force: represents the action of one body on another
characterized by
its magnitude, direction of its action, and its point of application
Force is a Vector quantity.
Mechanics: Fundamental Concepts
Newtonian mechanics is based on application of Newton's Laws of motion
which assume that the concepts of distance, time, and mass, are absolute, that
is, motion is in an inertial frame.
Length, Time, and Mass are absolute concepts independent of each other
Force is a derived concept
not independent of the other fundamental concepts. Force acting on a
body is related to the mass of the body and the variation of its velocity with
time.
Force can also occur between bodies that are physically separated
(Ex: gravitational, electrical, and magnetic forces)
Mechanics: Fundamental Concepts
Remember:
● Mass is a property of matter that does not change from one location to
another.
● Weight refers to the gravitational attraction of the earth on a body or
quantity of mass. Its magnitude depends upon the elevation at which the
mass is located
Weight of a body is the gravitational force acting on it.
Mechanics: Idealizations
To simplify application of the theory
Particle: A body with mass but with dimensions that can be neglected
Size of earth is insignificant compared to
the size of its orbit. Earth can be
modeled as a particle when studying its
orbital motion
Mechanics: Idealizations
Rigid Body: A combination of large number of particles in which all
particles remain at a fixed distance (practically) from one another
before and after applying a load.
Material properties of a rigid body are not required to be considered
when analyzing the forces acting on the body.
In most cases, actual deformations occurring in structures, machines,
mechanisms, etc. are relatively small, and rigid body assumption is
suitable for analysis
Mechanics: Idealizations
Concentrated Force: Effect of a loading which is assumed to act at a
point (CG) on a body.
Provided the area over which the load is applied is very small
compared to the overall size of the body.
Mechanics: Laws of Motion
Basis of formulation of rigid body mechanics.
First Law: A particle originally at rest, or moving in a straight line with
constant velocity, tends to remain in this state provided the particle is
not subjected to an unbalanced force.
First law contains the principle of the equilibrium
of forces
main topic of concern in
Statics
Mechanics: Laws of Motion
Second Law: A particle of mass “m” acted upon by an unbalanced force “F”
experiences an acceleration “a” that has the same direction as the force and a
magnitude that is directly proportional to the force.
Mechanics: Laws of Motion
Second Law forms the basis for most of the analysis in Dynamics
Mechanics: Laws of Motion
Third Law: The mutual forces of action and reaction between two
particles are equal, opposite, and collinear.
Third law is basic to our understanding of Force
always occur in pairs of equal and opposite forces.
Forces
Mechanics: Newton’s Law of Gravitational Attraction
Mechanics: Newton’s Law of Gravitational Attraction
Scalars and Vectors
Scalars: only magnitude is associated. Ex: time, volume, density,
speed, energy, mass
Vectors: possess direction as well as magnitude, and must obey the
parallelogram law of addition (and the triangle law).
Ex: displacement, velocity, acceleration, force, moment, momentum
Speed is the magnitude of velocity.
Scalars and Vectors
Equivalent Vector: V = V1 + V2 (Vector Sum)
Scalars and Vectors
Scalars and Vectors
Principle of Transmissibility
The effect of a force acting at any point of rigid body is unchanged if
the point of application of force is changed to any other point on ts line
of action, provided that these two points are rigidly connected to each
other.
Principle of Transmissibility
For further explanation, take moment in both cases (about X). Moment
is multiplication of force and its perpendicular distance between line of
action of force and point about which moment is to be taken. As only
one perpendicular can be drawn on one line (i.e. line of action of force)
from one point (i.e. point about which moment is to be taken). So, both
moments will have same value.
Thus, force can be considered to be exerted at any point on its line of
action.
Lecture 2
In last lecture we discuss about the Introduction of
Engineering Mechanics. What is rigid and elastic bodies.
Finally, we discuss about the forces and laws of motion.
Topics Covered in Lecture 2:
System of forces
●
●
●
●
Different type of forces.
Resultant of several concurrent coplanar forces with numerical.
Triangle law of forces
Resultant (Law of parallelogram of forces) of a several concurrent
coplanar forces by summing rectangular component with numerical.
● Polygon law of forces
● Resolution of forces with numerical.
● Lami’s theorem
Force System
Force: Magnitude (P), direction
(arrow) and point of application
(point A) is important
Change in any of the three
specifications will alter the effect
on the bracket.
Force is a Fixed Vector
In case of rigid bodies, line of action of force is important (
Force System
In case of rigid bodies, line of action of force is important (not its point
of application if we are interested in only the resultant external effects
of the force), we will treat most forces as
External effect: Forces applied
(applied force); Forces exerted by
bracket, bolts, Foundation (reactive
force)
Internal effect: Deformation, strain
pattern
–
permanent
strain;
depends on material properties of
bracket, bolts, etc.
Type of Forces
Concurrent Forces: The forces, which meet at a point or passes
through a point in the space, are called concurrent forces.
F1, F2 are concurrent forces; R will be on
same plane; R = F1+F2
Forces act at same point
Type of Forces
Coplanar Forces: The forces,
which are acting on a plane, are
known as coplanar forces.
Compressive Forces: The forces,
which try to contract the body
(shorten the length), are termed as
compressive forces.
Type of Forces
Tensile Forces: The forces,
which try to elongate the body
(increasing the length), are
termed as compressive forces.
Shear Forces: The forces,
which act tangential to the body
and try to shear the body, are
known as shear force.
Type of Forces
Bending Forces: The forces, which try to bend the body (in a
curvature shape), are termed as bending forces.
Resolution of Forces
Resultant: When a system of forces acting on a body is being
replaced by a single force such that the effect of the system of
forces on the body is exactly same of the single force. Then,
such single force is known as the resultant.
Resolution of Forces
Any inclined force will have two components. Say force P is acting at any point
with angle q from vertical, then it will have two components, one in horizontal
direction or in X-axis Direction (PX) and second in vertical direction or in Y-axis
direction (PY). the direction will be such that all the arrow are point in same
direction. The component on the side of angle will be “cos” component. And,
other component will be of “sin” component.
Resolution of Forces
Laws of Resolution of Forces: There are following Laws to
resolve the forces :
●
●
●
●
Law of Parallelogram
Law of Triangle
Law of Polygon
Lami’s Theorem
Resolution of Forces
The Parallelogram Law: If two forces acting at a point are represented in
magnitude and direction by the adjacent sides of a parallelogram, then the
diagonal passing through their points of intersection represent the resultant in
both, direction and magnitude.
Resolution of Forces
Law of Triangle of Forces: If two forces acting at a point are
represented by the two sides of a triangle taken in order, the
their sum or resultant will be represented by the third side of the
triangle taken in reverse order.
Resolution of Forces
Law of Polygon of Forces: If the number of coplanar forces
are acting at a point such that they can be represented in
magnitude and direction by the sides of a polygon taken in an
order, then their resultant will be represented by the closing side
of that polygon taken in opposite order (in both, magnitude and
direction). Here, the resultant will not depend upon the order or
sequence of considered forces (take 1,2, 3 or take 2,1,3..)
Resolution of Forces
Resolution of Forces
Resolution of Forces
Three ways to represent the vector
Resolution of Forces
Resolution of Forces
Resolution of Forces
Resolution of Forces
Classroom Tutorial
Problem 1: The two forces
act on a bolt at A. Determine
their resultant.
Problem 2: Tension in cable
BC is 725-N, determine the
resultant of the three forces
exerted at point B of beam
AB.
Lecture 3
In last lecture we discuss about the system of forces
Topics Covered in Lecture 3-5:
●
●
●
●
●
Resolution of forces in space (Rectangular component)
Moment of forces
Rectangular components of a moments
Moment of a force about a given axis
Moment of a couple
Solution of classroom tutorial
question given in previous lecture
Resolution of forces in space
Resolution of forces in space
Resolution of forces in space
Resolution of forces in space
Example on Resolution of forces in space
Example on Resolution of forces in space
Example on Resolution of forces in space
Vector Products
Vector Products
Moment of a Force
Moment: Moment of a force about any point is equal to the
multiplication force and its perpendicular distance from that
point.
Moment = Force x perpendicular Distance (N-m)
Moment of a Force
Moment of a Force
Principle of Transmissibility
Any force that has the same magnitude and
direction as F, is equivalent if it also has the
same line of action and therefore, produces
the same moment.
Varignon’s
Theorem
(Principle
of
Moments)
Moment of a Force about a point is equal to
the sum of the moments of the force’s
components about the point.
Rectangular Components of a Moment
Moment of a Force
Rectangular Components of a Moment
Moment of a Force About a Given Axis
Moment of a Force About a Given Axis
Example on moment of force
Example: Calculate the magnitude of
the moment about the base point O of
the 600 N force in different ways
Solution of example on moment of force
Solution of example on moment of force
Moment of a Couple
Moment produced by two equal, opposite and
non-collinear forces is called a couple.
Magnitude of the combined moment of the two
forces about O:
Moment of a Couple
The moment vector of the couple is
independent of the choice of the origin
of the coordinate axes, i.e., it is a free
vector that can be applied at any point
with the same effect.
Moment of a Couple
Moment of a Couple
Moment of a Couple
Moment of a Couple
Question ??
Moment required to turn the shaft connected at center of the
wheel = 12 Nm.
Case I
Case I: Couple Moment produced by 40 N
forces = 12 Nm
Case II: Couple Moment produced by 30 N
forces = 12 Nm
Tell me the answer in next lecture
If only one hand is used?
Force required for case I is
??
Force required for case II is
??
What if the shaft is not connected at the center of the wheel?
Is it a Free Vector?
Case II
Classroom Tutorial
Problem 1
Classroom Tutorial
Problem 2
Classroom Tutorial
Problem 3
Classroom Tutorial
Problem 4
Solution of classroom tutorial
Problem 1
Problem 2
Solution of classroom tutorial
Problem 3
Problem 4
Lecture 4-5
In last lecture we discuss about the Moment of forces
and moment of couple
Topics Covered in Lecture 4-5:
Equilibrant and equation of equilibrium
● Explain the equation of equilibrium for a system of concurrent forces in
plane.
● Explain the equilibrium of a body subjected to two and three forces with
numerical.
● Different types of numerical on the equation of equilibrium.
Concept of Free Body Diagram (FBD), resultant and its calculation
● Explain the constraint, action, reaction.
● Explain the different type of supports like frictional less, roller and knife
edge, hinged, built in supports.
● Explain the free body diagram with external and internal forces with
numerical.
Rigid Body Equilibrium
A rigid body will remain in equilibrium provided
Sum of all the external
forces acting on the
body is equal to zero
Sum of the moments
of the external forces
about a point is equal
to zero
Equivalent Systems: Resultants
Magnitude and direction of the resultant force R is obtained by
forming the force polygon where the forces are added head to
tail in any sequence
Equivalent Systems: Resultants
Equivalent Systems: Resultants
Equivalent Systems: Resultants
Equivalent Systems: Resultants
Equilibrant: The single force, which when applied to a system
of forces acting on a body or particle, puts the body or particle in
equilibrium condition, is known as equilibrant. In magnitude, it is
same as resultant, but direction is just opposite.
Example on Equivalent Systems: Resultants
For the beam, reduce the system of forces shown to (a) an equivalent
force-couple system at A, (b) an equivalent force couple system at B,
and (c) a single force or resultant.
Note: Since the support reactions are not included, the given system will not maintain the
beam in equilibrium.
Example on Equivalent Systems: Resultants
a) Compute the resultant force for the forces shown and the resultant
couple for the moments of the forces about A.
Example on Equivalent Systems: Resultants
b) Find an equivalent force-couple system at B based on the forcecouple system at A. The force is unchanged by the movement of the
force-couple system from A to B.
The couple at B is equal to the moment about B of the force-couple
system found at A.
Example on Equivalent Systems: Resultants
Rigid Body Equilibrium: Free-Body Diagrams
Space
Diagram:
A
sketch
showing the physical conditions of
the problem.
Free-Body Diagram: A sketch
showing only the forces on the
selected particle.
Rigid Body Equilibrium: Free-Body Diagrams
Various Supports 2-D Force Systems
Type of contact force origin
Action on body to be isolated
Various Supports 2-D Force Systems
Type of contact force origin
Action on body to be isolated
Various Supports 2-D Force Systems
Type of contact force origin
Action on body to be isolated
Various Supports 2-D Force Systems
Type of contact force origin
Action on body to be isolated
Various Supports 2-D Force Systems
Type of contact force origin
Action on body to be isolated
Various Supports 2-D Force Systems
Type of contact force origin
Action on body to be isolated
Various Supports 2-D Force Systems
Type of contact force origin
Action on body to be isolated
Various Supports 2-D Force Systems
Type of contact force origin
Action on body to be isolated
Various Supports 2-D Force Systems
Type of contact force origin
Action on body to be isolated
Mechanical System: FBD
Mechanical System
FBD
Mechanical System: FBD
Mechanical System
FBD
Categories of Equilibrium 3-D Systems
Various Supports 3-D Force Systems
Type of contact force origin
Action on body to be isolated
Various Supports 3-D Force Systems
Type of contact force origin
Action on body to be isolated
Various Supports 3-D Force Systems
Type of contact force origin
Action on body to be isolated
Various Supports 3-D Force Systems
Type of contact force origin
Action on body to be isolated
Various Supports 3-D Force Systems
Type of contact force origin
Action on body to be isolated
Various Supports 3-D Force Systems
Type of contact force origin
Action on body to be isolated
Categories of Equilibrium 3-D Systems
Categories of Equilibrium 3-D Systems
Rigid Body Equilibrium: Example
Rigid Body Equilibrium: Example
Rigid Body Equilibrium: Example
Classroom Tutorial Question
Problem 1
Classroom Tutorial Question
Problem 1
Classroom Tutorial Question
Problem 2
Classroom Tutorial Question
Problem 2
Classroom Tutorial Question
Problem 3
Classroom Tutorial Question
Problem 3
Classroom Tutorial Question
Problem 4
Classroom Tutorial Question
Problem 4
Classroom Tutorial Question
Problem 5
Classroom Tutorial Question
Problem 5
Classroom Tutorial Question
Classroom Tutorial Question
Classroom Tutorial Question
Classroom Tutorial Question
Classroom Tutorial Question
Classroom Tutorial Question