introduction
TRANSCRIPT
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2-Week ISTE Workshop
Instructors:
Prof. Mandar Inamdar([email protected])
Prof. Sauvik Banerjee([email protected])
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 engineering sciences 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
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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
BooksA 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:Engineering Mechanics: Statics and Dynamics, Meriam and Kraige, Wiley (Eds 5 and 7).Engineering Mechanics: Dynamics, R. C. Hibbeler, Prentice Hall.
Engineering Mechanics
Useful Links
http://www.howstuffworks.com/ http://oli.web.cmu.edu
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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 characterize and compare bodies, e.g., response to earth’s gravitational attraction 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
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• Vector: parameters possessing magnitude and direction which add according to the parallelogram law.
Examples: displacements, velocities, accelerations, Force.
• Scalar: parameters possessing magnitude but not direction.
Examples: mass, volume, temperature
Engineers Mechanics- BasicsVectors 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
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• 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
GMgmgWrMmGF
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 LawEngineers 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
• Principle of transmissibility may not always apply in determining internal forces and deformations.
P1=P2
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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 arbitrarily defined as the meter (m), second (s), and kilogram (kg). Force is the derived unit,
2sm1kg1N1
maF
Engineers Mechanics- Introduction
• US Customary Units (FPS):The basic units are length, time, and mass which are arbitrarily defined as the foot (ft), second (s) and slug (-). Force is the derived unit,
2sft1slug1lb1
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 ConversionEngineers Mechanics- Introduction
1 ft = 0.3048 m1 slug = 14.59 kg1 lb = 4.4482 N1 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)
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Idealization of MechanicsEngineers 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 diagrams for each of the bodies involved with a clear indication of all forces acting on each body.
• Fundamental Principles:The fundamental principles 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
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Modeling of Real Life ProblemsEngineers 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-BridgeEngineers Mechanics- Examples
http://oli.web.cmu.edu
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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- ExamplesEquivalent Load System in an Aircraft Wing
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Engineers Mechanics- ExamplesBridge
Loading, supports and connections of a bridge
http://oli.web.cmu.edu
Rigid Body Dynamics
Fthrust
Flift
Fdrag
Engineers Mechanics- Examples
Kinematics
Kinetics
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Car suspension system is a good example of mass-spring-damper system
Engineers Mechanics- ExamplesMechanical Vibrations
http://www.howstuffworks.com/