This document provides an introduction to an Engineering Mechanics course. It outlines the course goals, objectives, content, assessment, and textbook. The course aims to introduce concepts of forces, moments, and analytical skills for two and three dimensional systems. Upon completion, students should be able to determine force systems, centroids, and apply equilibrium concepts. The course covers topics like forces, moments, trusses, and beams. Student assessment includes assignments, quizzes, and exams. Rules for the course require high attendance, on-time assignments, and prohibit cell phone use during class.
Concept of Particles and Free Body Diagram
Why FBD diagrams are used during the analysis?
It enables us to check the body for equilibrium.
By considering the FBD, we can clearly define the exact system of forces which we must use in the investigation of any constrained body.
It helps to identify the forces and ensures the correct use of equation of equilibrium.
Note:
Reactions on two contacting bodies are equal and opposite on account of Newton's III Law.
The type of reactions produced depends on the nature of contact between the bodies as well as that of the surfaces.
Sometimes it is necessary to consider internal free bodies such that the contacting surfaces lie within the given body. Such a free body needs to be analyzed when the body is deformable.
Physical Meaning of Equilibrium and its essence in Structural Application
The state of rest (in appropriate inertial frame) of a system particles and/or rigid bodies is called equilibrium.
A particle is said to be in equilibrium if it is in rest. A rigid body is said to be in equilibrium if the constituent particles contained on it are in equilibrium.
The rigid body in equilibrium means the body is stable.
Equilibrium means net force and net moment acting on the body is zero.
Essence in Structural Engineering
To find the unknown parameters such as reaction forces and moments induced by the body.
In Structural Engineering, the major problem is to identify the external reactions, internal forces and stresses on the body which are produced during the loading. For the identification of such parameters, we should assume a body in equilibrium. This assumption provides the necessary equations to determine the unknown parameters.
For the equilibrium body, the number of unknown parameters must be equal to number of available parameters provided by static equilibrium condition.
Concept of Particles and Free Body Diagram
Why FBD diagrams are used during the analysis?
It enables us to check the body for equilibrium.
By considering the FBD, we can clearly define the exact system of forces which we must use in the investigation of any constrained body.
It helps to identify the forces and ensures the correct use of equation of equilibrium.
Note:
Reactions on two contacting bodies are equal and opposite on account of Newton's III Law.
The type of reactions produced depends on the nature of contact between the bodies as well as that of the surfaces.
Sometimes it is necessary to consider internal free bodies such that the contacting surfaces lie within the given body. Such a free body needs to be analyzed when the body is deformable.
Physical Meaning of Equilibrium and its essence in Structural Application
The state of rest (in appropriate inertial frame) of a system particles and/or rigid bodies is called equilibrium.
A particle is said to be in equilibrium if it is in rest. A rigid body is said to be in equilibrium if the constituent particles contained on it are in equilibrium.
The rigid body in equilibrium means the body is stable.
Equilibrium means net force and net moment acting on the body is zero.
Essence in Structural Engineering
To find the unknown parameters such as reaction forces and moments induced by the body.
In Structural Engineering, the major problem is to identify the external reactions, internal forces and stresses on the body which are produced during the loading. For the identification of such parameters, we should assume a body in equilibrium. This assumption provides the necessary equations to determine the unknown parameters.
For the equilibrium body, the number of unknown parameters must be equal to number of available parameters provided by static equilibrium condition.
Dimensional analysis offers a method for reducing complex physical problems to the simplest (that is, most economical) form prior to obtaining a quantitative answer.
Introduction;
Resultant of Two Forces;
Vectors;
Addition of Vectors;
Resultant of Several Concurrent Forces;
Sample Problem ;
Rectangular Components of a Force; Unit Vectors;
Addition of Forces by Summing Components ;
Equilibrium of a Particle;
Free-Body Diagrams;
Rectangular Components in Space;
Sample Problem;
Dimensional analysis offers a method for reducing complex physical problems to the simplest (that is, most economical) form prior to obtaining a quantitative answer.
Introduction;
Resultant of Two Forces;
Vectors;
Addition of Vectors;
Resultant of Several Concurrent Forces;
Sample Problem ;
Rectangular Components of a Force; Unit Vectors;
Addition of Forces by Summing Components ;
Equilibrium of a Particle;
Free-Body Diagrams;
Rectangular Components in Space;
Sample Problem;
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
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Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
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Understanding Inductive Bias in Machine LearningSUTEJAS
This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
The presentation also covers the positive and negative aspects of inductive bias, along with strategies for mitigating potential drawbacks. We'll explore examples of how bias manifests in algorithms like neural networks and decision trees.
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Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
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The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
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Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
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In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
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3. COURSE GOALS
• This course has two specific goals:
• To introduce students to basic concepts of force,
couples and moments in two and three
dimensions.
• To develop analytical skills relevant to the areas
mentioned in above.
4. COURSE OBJECTIVES
Upon successful completion of this course, students
should be able to:
• Determine the resultant of coplanar and space force
systems.
• Determine the centroid and center of mass of plane
areas and volumes.
• Distinguish between concurrent, coplanar and space
force systems.
• Draw free body diagrams.
5. COURSE OBJECTIVES CONTD.
• Analyze the reactions and forces induces in
coplanar and space systems using equilibrium
equations and free body diagrams.
• Determine friction forces and their influence
upon the equilibrium of a system.
• Apply sound analytical techniques and logical
procedures in the solution of engineering
problems.
6. Course Content
• Introduction
• Forces and Moments
• Equilibrium of Rigid bodies
• Geometrical Properties of Plane Areas
• Friction
• Virtual Work (Significance and Applications)
• Analysis of structures (Trusses, Frames and
Machines)
• Forces in Beams
7. Course Textbook
• Text Book
Engineering Mechanics by J.L. Miriam, 5th ed.
• Reference Books
1. Engineering Mechanics – Statics and Dynamics by
R.C. Hibbeler.
2. Engineering Mechanics – Statics and Dynamics by
J.L. Meriam & L.G. Kraige.
3. Vector Mechanics for Engineers – Statics by
Ferdinand P. Beer and E. Russell Johnston Jr.
8. RULES TO BE FOLLOWED
• 80% attendance is must. Otherwise no exam.
• Come in class on time. Otherwise absent.
– 10 minutes relaxation in case of emergency.
• Submit assignments on time.
– Negative 2 (-2) marks/day delay
– After 2 days , it will not be counted.
• Quiz will not be repeated. Absent student will get zero marks.
• Cell phone should be on silent. Preferably switched off.
– Should NOT attend at all.
• Contact me only in office hours.(xx to xx). Alternately email
me. No phone calls.
11. 1.1 MECHANICS
• It deals with the study and prediction of the state
of rest or motion of particles and bodies under
the action of forces
• Why we study mechanics?
This science form the groundwork for further study
in the design and analysis of structures
12. PARTS OF MECHANICS
Mechanics
Mechanics of
rigid bodies
Statics
Dynamics
Mechanics of
deformable
bodies
Mechanics of
fluids
Incompressible
Fluids
(Hydraulics)
Compressible
fluids (Gases)
13. 1.2 STATICS
• Statics is the study of forces on rigid bodies
which are at rest or moving at a constant
velocity, and the forces are in balance, or in
static equilibrium.
▫ Rigid Body: the relative movement between its
parts are negligible
• Dynamics is the study of forces on bodies with
accelerated motion.
14. 1.3 Fundamental Concepts
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.
15. 1.3 Fundamental Concepts Contd
• 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. A force is characterized by its point of
application, magnitude, and direction, i.e., a
force is a vector quantity.
16. 1.3 Fundamental Concepts Contd
Idealizations
• Particles
– Consider mass but neglect size
• Rigid Body
– Neglect material properties
17. 1.4 Fundamental Principles
• Newton’s First Law: If the resultant force on a
particle is zero, the particle will remain at rest or
continue to move in a straight line.
• Newton’s Second Law: A particle will have an
acceleration proportional to a nonzero resultant
applied force.
• 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 are
attracted with equal and opposite forces,
a
m
F
2
2
,
R
GM
g
mg
W
r
Mm
G
F
18. 1.5 Systems of Units
• Kinetic Units: length, time,
mass, and force.
• Three of the kinetic units are
basic units: length, time, and
mass
• The fourth unit, force is derived
unit, must have a definition
compatible with Newton’s 2nd
Law,
a
m
F
•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,
2
s
m
1
kg
1
N
1
ma
F
19. Multiples or submultiples of SI used
Multiples Submultiples
1 kilogram is 1 kg or 103 g 1 millimeter is 1 mm or 10-3 m
1 megagram is 1 Mg or 106 g. 1 micrometer is 1μm or 10-6m
1 gigagram is 1 Gg or 109g 1 nanometer is 1nm or 10-9m
20. 1.6 Mathematics Required
The followings are the mathematics skills that are
important for this module:
• Quadratic equations
• Simultaneous equations
• Trigonometry functions of a right-angle triangle
• Sine and cosine rules
21. 1.6.1 Quadratic equations
• The equation has the standard form as follows
𝑎𝑥2 + 𝑏𝑥 + 𝐶 = 0
• The standard solution to this equation is
𝑥 =
−𝑏± 𝑏2−4𝑎𝑐
2𝑎
22. Example
• Solve for x in the equation 5x2+12x-2=0
▫ Comparing with equation 𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0
a= 5, b= 12 & c= -2
▫ The standard solution to this equation is
𝑥 =
−𝑏± 𝑏2−4𝑎𝑐
2𝑎
x=+0.156 or – 2.56
23. 1.6.2 Simultaneous Equation
The equation has two unknowns x and y in the form of
ax + by + c = 0
px + qy + r = 0
Example
Find the values of x and y satisfying the given
equations:
4x + 3y + 10 = 0 ….. (1)
20x + 30y + 5 = 0 ….. (2)
There are two methods to solve these equations
24. Method of Substitution
We can start by expressing x in terms of y, or y in terms of x.
Let us choose to express x in terms of y, thus from (1)
𝑥 =
−3𝑦−10
4
…… (3)
Substituting (3) into (2) , yielding
20 × (
−3𝑦−10
4
)+30y +5=0
-15y -50 + 30y + 5 = 0
15y – 45 = 0
y = 3
To find x, substitute the value of y into (3)
𝑥 =
−3×3−10
4
= −4.75
25. Method of Elimination
This method looks for a way to eliminate one of
the unknowns.
This can be done by making the constant factor of
that unknown or variable the same in both
equations by multiplying or dividing one equation
by a selected constant:
26. 4x + 3y + 10 = 0 …… (1)
20x + 30y + 5 = 0 ….. (2)
Divide (2) by 5
4x + 6y + 1 = 0 …. (3)
Subtract (3) by (1)
3y - 9 = 0
y = 3
Substitute the value of y into (1) or (2)
4x + 3(3) + 10 = 0
4x = - 9 - 10
x = - (19/4)= -4.75
Method of Elimination Contd
27. 1.6.3 Trigonometry Functions Of a
Right-Angle Triangle
Some people have curly black hairs through their proper brushes
Sine θ = Perpendicular / Hypotenuse
Base
Perpendicular
Cosine θ = Base / Hypotenuse
Tangent θ = Perpendicular / Base
28. 1.6.4 Sine And Cosine Rules
• For triangles that are not right-angle, the
following two laws are important
Sine Rule a = b = c
sin sin sin
Cosine Rule a2 = b2 + c2 – 2bc cos
b2 = a2 + c2 – 2ac cos
c2 = a2 + b2 – 2ab cos
29. • If the cosine rule is applied to a right-angle
triangle where = 900
b
c
a2 = b2 + c2 – 2bc cos 90 0
Since cos 900 = 0
a2 = b2 + c2 (Pythagoras Theorem)
30. Example
Find the length of the unknown side a and the angle
Cosine rule : a2 = b2+c2-2xbxcxcos 20o
a2 = 62+42-2x6x4xcos200
a2 = 36 +16-48xcos200
a2= 6.895 ⇒ a= 2.626
Sine rule : 2.626 = 4
sin 200 sin
sine = 4 x sin 200
2.63
= 31.40
20o
6m 4m
a