1. 11/26/2013
1
2-Week ISTE Workshop
Instructors:
Prof. Mandar Inamdar
(minamdar@civil.iitb.ac.in)
Prof. Sauvik Banerjee
(sauvik@civil.iitb.ac.in)
26 November- 6 December, 2013
ENGINEERING MECHANICS
Mechanics
• Mechanics is the science which describes and predicts the conditions of rest or
motion of bodies under the action of forces. Mechanics is the foundation of most
engineeringsciences and is an indispensable prerequisite to their study.
Engineers Mechanics
• Branches of Mechanics:
- Statics – body is at rest under the action of forces. All quantities are
time independent
- Dynamics – body is at motion under the action of forces. All quantities
are time dependent
2. 11/26/2013
2
What is the need for an elaborate course?
– Basic rules are simple, force balance and moment
balance, in general.
– But, there are many intricacies. Multi-body
interactions can be very complex.
– A good understanding of fundamentals goes a long
way in solving such complex problems.
– Concepts of appropriate Free Body Diagrams and
equations of equilibrium (motion in dynamics) will
be indispensable in later studies
Engineering Mechanics
Books
A major chunk of lecture materials based on:
• Vector Mechanics for Engineers, Beer, Johnston et al., McGraw-Hill
(Eds 8 and 10)
• Referred to as BJ 8 &10. Indian Edition available.
• A lot of slide contents is courtesy of McGraw-Hill
Other texts:
EngineeringMechanics: Statics and Dynamics, Meriam and Kraige, Wiley
(Eds 5 and 7).
EngineeringMechanics: Dynamics, R. C. Hibbeler, Prentice Hall.
Engineering Mechanics
Useful Links
http://www.howstuffworks.com/ http://oli.web.cmu.edu
3. 11/26/2013
3
Fundamentals
• Dimensions
• Vectors and Scalars
• Parallelogram Law
• Newton’s law
• Principle of Transmissibility
• System of Units
Engineering Mechanics
Dimensions
• Space - associated with the notion of the position of a point P given in
terms of three coordinates measured from a reference point or origin.
• Time - definition of an event requires specification of the time and
position at which it occurred.
• Mass - used to characterizeand compare bodies, e.g., response to
earth’sgravitationalattraction and resistance to changes in translational
motion.
• Force - represents the action of one body on another.
In Newtonian Mechanics, space, time, and mass are absolute concepts,
independent of each other. Force, however, is not independent of the
other three. The force acting on a body is related to the mass of the body
and the variation of its velocity with time (i.e accelaration).
Engineers Mechanics- Introduction
4. 11/26/2013
4
• Vector: parameterspossessing magnitude
and direction which add according to the
parallelogramlaw.
Examples: displacements, velocities,
accelerations, Force.
• Scalar: parameters possessing magnitude but
not direction.
Examples: mass, volume, temperature
Engineers Mechanics- Basics
Vectors and Scalars
Newton’s Law
• Newton’s First Law:
Every particle continues in a state
of rest or uniform motion in a
straight line unless it is compelled
to change that state by forces
imposed on it
• Newton’s Second Law:
The change of motion is
proportional to the natural
force impressed and is
made in a direction of the
straight line in which the
force is impressed
Engineers Mechanics- Introduction
amF
5. 11/26/2013
5
• Newton’s Third Law:
The forces of action and
reaction between two
particles have the same
magnitude and line of
action with opposite sense.
• Newton’s Law of Gravitation: Two particles (mass M and m respectively)
are attracted with equal and opposite forces,
22
,
R
GM
gmgW
r
Mm
GF
G = Universal gravitational constant
= 6.673(10-11) m3/(kg.s2)
M=mass of earth=5.976(1024) kg
R= radius of earth=6371(103) m
Newton’s Law
Engineers Mechanics- Introduction
Principle of Transmissibility:
• Principle of Transmissibility -
Conditions of equilibrium or motion are
not affected by transmitting a force
along its line of action.
NOTE: F and F’ are equivalent forces.
• Moving the point of application of
the force F to the rear bumper
does not affect the motion or the
other forces acting on the truck.
Engineers Mechanics- Introduction
• Principleof transmissibility may
not always apply in determining
internalforces and deformations.
P1=P2
6. 11/26/2013
6
Systems of Units
• Kinetic Units: length [L], time [t],
mass [m], and force.
• Three of the kinetic units, referred to
as basic units, may be defined
arbitrarily. The fourth unit, referred
to as a derived unit, must have a
definition compatible with Newton’s
2nd Law,
amF
• International System of Units (SI):
The basic units are length, time, and
mass which are arbitrarilydefined as the
meter (m), second (s), and kilogram
(kg). Force is the derived unit,
2
s
m
1kg1N1
maF
Engineers Mechanics- Introduction
• US Customary Units (FPS):
The basic units are length, time, and
mass which are arbitrarilydefined as the
foot (ft), second (s) and slug (-). Force
is the derived unit,
2
s
ft
1slug1lb1
maF
The NASA Mars Climate Orbiter, the first interplanetary weather satellite
designed to orbit Mars, was lost during entry to Mars orbit because one of the
teams used FPS system and failed to convert them to SI system. As a result, the
$125 million orbiter was lost. As Dr. Stone, director of the Jet Propulsion
Laboratory, California succinctly said "Our inability to recognize and correct this
simple error has had major implications."
Unit Conversion
Engineers Mechanics- Introduction
1 ft = 0.3048 m
1 slug = 14.59 kg
1 lb = 4.4482 N
1 kip (kilopound) = 1000 lb
Giga (G) = 109
Mega (M) = 106
Kilo (k) = 103
Milli (m) = 10-3
Micro (µ) = 10-6
Nano (n) = 10-9
FPS SI
g = 9.81 m/s2 (SI)
= 32 ft/s2 (FPS)
7. 11/26/2013
7
Idealization of Mechanics
Engineers Mechanics- Introduction
‘Rigid body assumption’
- no deformation, assumes original geometry
- pure translation and rotation
A ‘particle’idealizes a body by placing its mass at its center and
neglecting its physical size.
Method of Problem Solution
• Problem Statement:
Includes given data, specification of
what is to be determined, and a figure
showing all quantities involved.
• Free-Body Diagrams:
Create separate diagramsfor each of
the bodies involved with a clear
indication of all forces acting on
each body.
• Fundamental Principles:
The fundamentalprinciples are
applied to express the conditions of
rest or motion of each body. The
rules of algebra are applied to solve
the equations for the unknown
quantities.
• Solution Check:
- Test for errors in reasoning by
verifying that the units of the
computed results are correct,
- always apply experience and physical
intuition to assess whether results seem
“reasonable”
Engineers Mechanics- Introduction
8. 11/26/2013
8
Modeling of Real Life Problems
Engineers Mechanics- Introduction
• Any physical/mechanical model is
simply a caricature of a real-world
problem.
• Such a model is our way of
understanding of real-world in as
simple and tractable way as
possible.
• The real skill is to remove
unwanted flab, and get a bare-bones
model, which gives a quick and
reasonably accurate solution.
Draw-Bridge
Engineers Mechanics- Examples
http://oli.web.cmu.edu
9. 11/26/2013
9
Robotics
• Use of statics in Robotics to build evil Terminator.
(http://www.societyofrobots.com/mechanics_statics.shtml)
Engineers Mechanics- Examples
The main spar of an aircraft is designed to conservatively carry all of the
wing aerodynamic lift forces. For the simplified wing up-bending loads
shown, find the equivalent load system and support reactions
Engineers Mechanics- Examples
Equivalent Load System in an Aircraft Wing
11. 11/26/2013
11
Car suspension system is a good example
of mass-spring-damper system
Engineers Mechanics- Examples
Mechanical Vibrations
http://www.howstuffworks.com/
