This document describes an experiment to determine the stress, deflection, and strain of a supported steel I-beam under increasing load. Key steps included measuring the beam's dimensions, applying incremental loads up to 1000 lbs using an MTS tensile testing machine, and recording the corresponding strain and deflection values. Theoretical stress and deflection values were also calculated using beam formulas. Results showed close agreement between actual and theoretical values, successfully verifying beam stress and flexure formulas.
Experiment 3
The Beam
EGME 306A
Group 2
ABSTRACT
The objective of this experiment is to determine the stress, deflection, and the strain of a simply supported beam under load. Also to experimentally verify the beam stress and flexure formulas. The experiment was done was using the machine to apply a load to a simply supported beam and measure the deflection and the strain of it. The moment of inertia was .10376 thw neutral axis was .80331, the maximum deflection was .00985.
TABLE OF CONTENTS
Abstract……………………………………………………………..………..2
Table of Contents……………………………………….……………………3
Introduction and Theory…………………………………………………….4-8
Procedures………………………………………………….……………….9-10
Summary of Important Results…………………...………………………..11-12
Sample Calculations and Error Analysis……………….………………….13-14
Discussion and Conclusion………………………………………………..15-16
References……………………………………..…………………………….17
Appendix……………………………………………………….………….18-19
INTRODUCTION AND THEORY
Structural members are usually designed to carry tensile, compressive, or transverse loads. A member which carries load transversely to its length is called a beam. In this experiment, a beam will be symmetrically loaded as shown in Fig. III-1(a), where P is the applied load. Note that at any cross section of the beam there will be a shear force V (Fig. III-1(b)) and moment M (Fig. III-1c). Also, in the central part of the beam (between the loads P/2) V is zero and M has its maximum constant value. Notice the sign convention of a positive moment, M, causing a negative (downward) deflection, y.
If in this part a small slice EFGH of the beam is imagined to be cut out, as shown, then it is clear that the external applied moment, M, must be balanced by internal forces (stresses) at the sections (faces) EF and GH. For M applied as shown in Fig. III-2(a), these forces would be compressive near the top, EG, and tensile near the bottom, FH. Since the beam material is considered elastic, these forces would deform the beam such that the length EG would tend to become shorter, and FH would tend to become longer. The first fundamental assumption of the beam theory can be stated as follows:
“Sections, or cuts, which are plane (flat) before deformation, remain plane after deformation.”
Thus, under this assumption, the parallel and plane section EF and GH will deform into plane sections E’F’ and G’H’ which will intersect at point O, as shown in Fig. III-2(b). Since E’F’ and G’H’ are no longer parallel, they can be thought of as being sections of a circle at some radial distance from O. Convince yourself of this by drawing a square on an eraser and observe its shape when you bend the eraser. Since the forces near E’G’ are compresiive, and those near F’H’ are tensile, there must be some radial distance r where the forces are neither compressive nor tensile, but zero. This axis, N-N, is called the neutral axis. Notice that N-N is not assumed to lie in the center of the beam.
Consider an arc of distance +η, from the neutral axi ...
Strength of material lab, Exp 2: Tensile test Osaid Qasim
by using our “UTM” machine that
operates on the basis of applying a load in our specimen , so if
we take this force and compare it with change in the length of
specimen “Deformation” we can obtain a (Load-Deformation
diagram) , and by applying this force and divide it by the
specimen cross sectional area we get the Stress ( σ), and divide
the “Deformation” by the original length of the specimen we
will get the Strain (ϵ) , and comparing the stress with strain
results a very Important curve that is characteristic of the
properties of the material and it’s the (Stress-Strain Diagram),
Experiment 3
The Beam
EGME 306A
Group 2
ABSTRACT
The objective of this experiment is to determine the stress, deflection, and the strain of a simply supported beam under load. Also to experimentally verify the beam stress and flexure formulas. The experiment was done was using the machine to apply a load to a simply supported beam and measure the deflection and the strain of it. The moment of inertia was .10376 thw neutral axis was .80331, the maximum deflection was .00985.
TABLE OF CONTENTS
Abstract……………………………………………………………..………..2
Table of Contents……………………………………….……………………3
Introduction and Theory…………………………………………………….4-8
Procedures………………………………………………….……………….9-10
Summary of Important Results…………………...………………………..11-12
Sample Calculations and Error Analysis……………….………………….13-14
Discussion and Conclusion………………………………………………..15-16
References……………………………………..…………………………….17
Appendix……………………………………………………….………….18-19
INTRODUCTION AND THEORY
Structural members are usually designed to carry tensile, compressive, or transverse loads. A member which carries load transversely to its length is called a beam. In this experiment, a beam will be symmetrically loaded as shown in Fig. III-1(a), where P is the applied load. Note that at any cross section of the beam there will be a shear force V (Fig. III-1(b)) and moment M (Fig. III-1c). Also, in the central part of the beam (between the loads P/2) V is zero and M has its maximum constant value. Notice the sign convention of a positive moment, M, causing a negative (downward) deflection, y.
If in this part a small slice EFGH of the beam is imagined to be cut out, as shown, then it is clear that the external applied moment, M, must be balanced by internal forces (stresses) at the sections (faces) EF and GH. For M applied as shown in Fig. III-2(a), these forces would be compressive near the top, EG, and tensile near the bottom, FH. Since the beam material is considered elastic, these forces would deform the beam such that the length EG would tend to become shorter, and FH would tend to become longer. The first fundamental assumption of the beam theory can be stated as follows:
“Sections, or cuts, which are plane (flat) before deformation, remain plane after deformation.”
Thus, under this assumption, the parallel and plane section EF and GH will deform into plane sections E’F’ and G’H’ which will intersect at point O, as shown in Fig. III-2(b). Since E’F’ and G’H’ are no longer parallel, they can be thought of as being sections of a circle at some radial distance from O. Convince yourself of this by drawing a square on an eraser and observe its shape when you bend the eraser. Since the forces near E’G’ are compresiive, and those near F’H’ are tensile, there must be some radial distance r where the forces are neither compressive nor tensile, but zero. This axis, N-N, is called the neutral axis. Notice that N-N is not assumed to lie in the center of the beam.
Consider an arc of distance +η, from the neutral axi ...
Strength of material lab, Exp 2: Tensile test Osaid Qasim
by using our “UTM” machine that
operates on the basis of applying a load in our specimen , so if
we take this force and compare it with change in the length of
specimen “Deformation” we can obtain a (Load-Deformation
diagram) , and by applying this force and divide it by the
specimen cross sectional area we get the Stress ( σ), and divide
the “Deformation” by the original length of the specimen we
will get the Strain (ϵ) , and comparing the stress with strain
results a very Important curve that is characteristic of the
properties of the material and it’s the (Stress-Strain Diagram),
Stress Analysis of Chain Links in Different Operating Conditionsinventionjournals
The work covers the stress analysis in a 3D model of chain link analitically and numerically, and based on a real model, experimental examination was carried out. First, the cases when the links are vertical to each other and their tensile load were considered. The analysis was done in both work and experimental conditions and also the tensile load just before the chain broke. Second, the position in which the links are rotated for the calculated maximum angle. Experimental analysis of the high resistance chain (high hardness), insignia stress 14x50 G80 E5 was carried out on an universal testing mashine and the results are used for verification of numerical model.
Designed a torque arm, with Multi Point Constraints applied to the center of the arm. The FEA software used for this purpose was ABAQUS. The analysis was performed two major element types: Triangular Elements and Quadrilateral Elements, with relatively equal number of nodes in each case and a convergence study was conducted. The aim of the project was to obtain the optimal design parameters of the torque arm by optimization (minimize weight).
Physics 161Static Equilibrium and Rotational Balance Intro.docxrandymartin91030
Physics 161
Static Equilibrium and Rotational Balance
Introduction
In Part I of this lab, you will observe static equilibrium for a meter stick suspended horizontally. In Part II, you will observe the rotational balance of a cylinder on an incline. You will vary the mass hanging from the side of the cylinder for different angles.
Reference
Young and Freedman, University Physics, 12th Edition: Chapter 11, section 3
Theory
Part I: When forces act on an extended body, rotations about axes on the body can result as well as translational motion from unbalanced forces. Static equilibrium occurs when the net force and the net torque are both equal to zero. We will examine a special case where forces are only acting in the vertical direction and can therefore be summed simply without breaking them into components:
(1)
Torques may be calculated about the axis of your choosing:
(2)
where torque is specified by the equation:
(3)
where d is the lever arm (or moment arm) for the force. The lever arm is the perpendicular distance from the line of force to the axis about which you are calculating the torque.
Normally, up is "+" and down is "-" for forces. For torques, it is convenient to define clockwise as "-" and counterclockwise as "+". Whatever you decide to do, be consistent with your signs and make sure you understand what a "+" or "-" value for your force or torque means directionally.
Part II: Any round object when placed on an incline has tendency of rotating towards the bottom of an incline. If the downward force that causes the object to accelerate down the slope is canceled by another force, the object will remain stationary on the incline. Figure 1 shows the configuration of the setup. In order to have the rubber cylinder in static equilibrium we should satisfy the following conditions:
(4)
Figure 1: Experimental setup for Part II
The condition that the net force along the x-axis (which is conveniently taken along the incline) must be zero yields the relationship. (Prove this!)
Without static friction the cylinder would slide down the incline; the presence of friction causes a torque in clockwise (negative) direction. In order to have static equilibrium we need to balance that torque with a torque in counterclockwise direction. This is achieved by hanging the appropriate mass m.
Applying the last condition to the center of the cylinder will result in:
where r, the radius of the small cylinder (PVC fitting), is the moment arm for the mass m and R, the radius of the rubber cylinder, is the moment arm for the frictional force which accounts for M and m. Combining this equation with the equation for Ffr from above will result in:
(5)
(6)
By adjusting the mass m, we can observe how the equilibrium can be achieved.
Procedure
Part I: Static Equilibrium
Figure 2: Diagram of Torque Experiment Setup
1. Weigh the meter stick you use, including the metal hangers.
2. Attach .
AFRICAResearch Paper AssignmentInstructionsOverview.docxSALU18
AFRICA
Research Paper Assignment
Instructions
Overview
In developing your expertise in transnational
organized crime (TOC) you will be writing a series of research papers. All
together the writing contained in all these papers combined would be quite
significant project! You will find that in some modules, the research papers
mimic our readings with respect to subject matter and some modules, the
research papers do not mimic the reading. Again, the goal of these research
papers is to stretch the depth and breadth of your knowledge. You should feel
well prepared to teach a course in TOCs after completing this course. The
research papers and PowerPoints you create could serve as the basis for such
class. Additionally, you will find that this course and the course CJUS701
Comparative Criminal Justice Systems complement each other very well.
Instructions
·
Each
research paper should be a minimum of 6 to 8 pages.
·
The
vast difference in page count is because some countries and/or crime/topics are
quite easy to study and some countries and/or crime/topics have very limited
information.
·
In
some instances, there will be a plethora of information and you must use
skilled writing to maintain proper page count.
·
Please
keep in mind that this is doctoral level analysis and writing – you are to take
the hard-earned road – the road less travelled – the scholarly road in forming
your paper.
·
The
paper must use current APA style, and the page count does not include the title
page, abstract, reference section, or any extra material.
·
The
minimum elements of the paper are listed below.
·
You
must use a
minimum
of 8 recent (some
countries/crimes/topics may have more recent research articles than others),
relevant, and academic (peer review journals preferred and professional
journals allowed if used judiciously) sources, at least 2 sources being the
Holy Bible, and one recent (some countries/crime/topics have more recent than
others) news article. Books may be used
but are considered “additional: sources beyond the stated minimums. You may use
.gov sources as your recent, relevant, and academic sources if the writing is
academic in nature (authored works). You may also use United Nations and
Whitehouse.gov documents as academic documents.
·
Again,
this paper must reflect graduate level research and writing style. If you need to go over the maximum page count
you must obtain professor permission in advance! Please reference the Research
Paper Rubric when creating your research paper.
These are minimum guidelines – you may expand the
topics covered in your papers.
1)
Begin
your paper with a
brief
analysis of the following elements:
a.
Country
analysis
i.
Introduction
to the country
ii.
People
and society of the country
iii.
What
is the basic government structure?
2)
Analyze
the nature of organized crime in the assigned area (you may narrow the scope of
your analysis through your introduction or thesis stat.
Adversarial ProceedingsCritically discuss with your classmates t.docxSALU18
Adversarial Proceedings
Critically discuss with your classmates the claim that adversarial proceedings can be distinguished as relying more on the government’s ability to prove guilt (following specific rules of criminal procedure the defendant’s guilt whereas the inquisitorial process spends more time on investigations to determine if the defendant truly committed the crime).
.
More Related Content
Similar to EGME 306A The Beam Page 1 of 18 Group 2 EXPER.docx
Stress Analysis of Chain Links in Different Operating Conditionsinventionjournals
The work covers the stress analysis in a 3D model of chain link analitically and numerically, and based on a real model, experimental examination was carried out. First, the cases when the links are vertical to each other and their tensile load were considered. The analysis was done in both work and experimental conditions and also the tensile load just before the chain broke. Second, the position in which the links are rotated for the calculated maximum angle. Experimental analysis of the high resistance chain (high hardness), insignia stress 14x50 G80 E5 was carried out on an universal testing mashine and the results are used for verification of numerical model.
Designed a torque arm, with Multi Point Constraints applied to the center of the arm. The FEA software used for this purpose was ABAQUS. The analysis was performed two major element types: Triangular Elements and Quadrilateral Elements, with relatively equal number of nodes in each case and a convergence study was conducted. The aim of the project was to obtain the optimal design parameters of the torque arm by optimization (minimize weight).
Physics 161Static Equilibrium and Rotational Balance Intro.docxrandymartin91030
Physics 161
Static Equilibrium and Rotational Balance
Introduction
In Part I of this lab, you will observe static equilibrium for a meter stick suspended horizontally. In Part II, you will observe the rotational balance of a cylinder on an incline. You will vary the mass hanging from the side of the cylinder for different angles.
Reference
Young and Freedman, University Physics, 12th Edition: Chapter 11, section 3
Theory
Part I: When forces act on an extended body, rotations about axes on the body can result as well as translational motion from unbalanced forces. Static equilibrium occurs when the net force and the net torque are both equal to zero. We will examine a special case where forces are only acting in the vertical direction and can therefore be summed simply without breaking them into components:
(1)
Torques may be calculated about the axis of your choosing:
(2)
where torque is specified by the equation:
(3)
where d is the lever arm (or moment arm) for the force. The lever arm is the perpendicular distance from the line of force to the axis about which you are calculating the torque.
Normally, up is "+" and down is "-" for forces. For torques, it is convenient to define clockwise as "-" and counterclockwise as "+". Whatever you decide to do, be consistent with your signs and make sure you understand what a "+" or "-" value for your force or torque means directionally.
Part II: Any round object when placed on an incline has tendency of rotating towards the bottom of an incline. If the downward force that causes the object to accelerate down the slope is canceled by another force, the object will remain stationary on the incline. Figure 1 shows the configuration of the setup. In order to have the rubber cylinder in static equilibrium we should satisfy the following conditions:
(4)
Figure 1: Experimental setup for Part II
The condition that the net force along the x-axis (which is conveniently taken along the incline) must be zero yields the relationship. (Prove this!)
Without static friction the cylinder would slide down the incline; the presence of friction causes a torque in clockwise (negative) direction. In order to have static equilibrium we need to balance that torque with a torque in counterclockwise direction. This is achieved by hanging the appropriate mass m.
Applying the last condition to the center of the cylinder will result in:
where r, the radius of the small cylinder (PVC fitting), is the moment arm for the mass m and R, the radius of the rubber cylinder, is the moment arm for the frictional force which accounts for M and m. Combining this equation with the equation for Ffr from above will result in:
(5)
(6)
By adjusting the mass m, we can observe how the equilibrium can be achieved.
Procedure
Part I: Static Equilibrium
Figure 2: Diagram of Torque Experiment Setup
1. Weigh the meter stick you use, including the metal hangers.
2. Attach .
AFRICAResearch Paper AssignmentInstructionsOverview.docxSALU18
AFRICA
Research Paper Assignment
Instructions
Overview
In developing your expertise in transnational
organized crime (TOC) you will be writing a series of research papers. All
together the writing contained in all these papers combined would be quite
significant project! You will find that in some modules, the research papers
mimic our readings with respect to subject matter and some modules, the
research papers do not mimic the reading. Again, the goal of these research
papers is to stretch the depth and breadth of your knowledge. You should feel
well prepared to teach a course in TOCs after completing this course. The
research papers and PowerPoints you create could serve as the basis for such
class. Additionally, you will find that this course and the course CJUS701
Comparative Criminal Justice Systems complement each other very well.
Instructions
·
Each
research paper should be a minimum of 6 to 8 pages.
·
The
vast difference in page count is because some countries and/or crime/topics are
quite easy to study and some countries and/or crime/topics have very limited
information.
·
In
some instances, there will be a plethora of information and you must use
skilled writing to maintain proper page count.
·
Please
keep in mind that this is doctoral level analysis and writing – you are to take
the hard-earned road – the road less travelled – the scholarly road in forming
your paper.
·
The
paper must use current APA style, and the page count does not include the title
page, abstract, reference section, or any extra material.
·
The
minimum elements of the paper are listed below.
·
You
must use a
minimum
of 8 recent (some
countries/crimes/topics may have more recent research articles than others),
relevant, and academic (peer review journals preferred and professional
journals allowed if used judiciously) sources, at least 2 sources being the
Holy Bible, and one recent (some countries/crime/topics have more recent than
others) news article. Books may be used
but are considered “additional: sources beyond the stated minimums. You may use
.gov sources as your recent, relevant, and academic sources if the writing is
academic in nature (authored works). You may also use United Nations and
Whitehouse.gov documents as academic documents.
·
Again,
this paper must reflect graduate level research and writing style. If you need to go over the maximum page count
you must obtain professor permission in advance! Please reference the Research
Paper Rubric when creating your research paper.
These are minimum guidelines – you may expand the
topics covered in your papers.
1)
Begin
your paper with a
brief
analysis of the following elements:
a.
Country
analysis
i.
Introduction
to the country
ii.
People
and society of the country
iii.
What
is the basic government structure?
2)
Analyze
the nature of organized crime in the assigned area (you may narrow the scope of
your analysis through your introduction or thesis stat.
Adversarial ProceedingsCritically discuss with your classmates t.docxSALU18
Adversarial Proceedings
Critically discuss with your classmates the claim that adversarial proceedings can be distinguished as relying more on the government’s ability to prove guilt (following specific rules of criminal procedure the defendant’s guilt whereas the inquisitorial process spends more time on investigations to determine if the defendant truly committed the crime).
.
Advances In Management Vol. 9 (5) May (2016)
1
Generation Gaps: Changes in the Workplace due to
Differing Generational Values
Carbary Kelly, Fredericks Elizabeth, Mishra Bharat and Mishra Jitendra*
Management Department, Grand Valley State University, 50 Front Ave, SW Grand Rapids Michigan 49504-6424, USA
*[email protected]
Abstract
The purpose of this study is to discuss the
generational gaps that are found in the workplace
today. With multiple generations working together,
and the oldest generation having to work longer and
retire later, generational changes are occurring in the
workplace and for management. There is a lack of
communication and understanding between the
different generations caused through differing values
and goals. Younger generations are also entering
different fields than those that were popular for older
generations. There is a serious new problem in the
workplace, and it has nothing to do with downsizing,
global competition, pointy-haired bosses, stress or
greed. Instead, it is the problem of distinct
generations — the Veterans, the Baby Boomers, Gen
X and Gen Y — working together and often colliding
as their paths cross.
Individuals with different values, different ideas,
different ways of getting things done and different
ways of communicating in the workplace have always
existed. So, why is this becoming a problem now? At
work, generation differences can affect everything
including recruiting, building teams, dealing with
change, motivating, managing, and maintaining and
increasing productivity All of these ideas are
explored, discussed, and evaluated, through looking
at current research on the topic and case studies that
have been conducted not only in the United States but
around the world.
Keywords: Generation gap, workplace, values.
Introduction
Throughout the years, as the population has continued to
both grow and age, it has caused generational changes to
take place in the various aspects of life. With the changes in
the demographics of the world’s population, there have also
been changes in how each group thinks and what they
value. This not only affects the way people behave in their
personal lives, but it also affects the workplace. As
generational changes occur in the workplace, a lack of
communication has caused adisconnect to occur between
the values and goals present among the different age groups
along with newer generations choosing different career
paths.
* Author for Correspondence
In order to understand where these differences stem from,
you need to analyze how each generation is different when
it comes to their beliefs and values. So, it is best to identify
the different groups present in workplace which range from
those born in 1922 to those born in the early 1990’s.
Moving chronologically, the fi.
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Advocacy & Legislation in Early Childhood Education
Advocacy & Legislation in Early Childhood Education
Advocating for Early Childhood Education
Rasmussen College
COURSE#: EEC 4910
Doreen Anzalone
July 15, 2019
Advocating for Early Childhood Education
· What is advocacy?
Advocacy is how we support our children. We as teachers give advice for our children or we listen. We let the children and families know that we believe in them and we will be there for them. Teachers, admin, staff can advocate for children as long as they are in school. Advocates are also trained people and they are not lawyers. One of their responsibility is to stay up to date with the regulations of the educational laws.
· Why is advocacy important to early childhood education?
Its important to help the families because they might be vulnerable in society. We as teachers need to make sure our children and families are being heard. We as teachers need to make sure their wishes and views are being considered when it’s about their child or family. Its because we are helping the family make life decisions about their children and even their family life. Its also important to make sure we are not judging the family or having or our own personal opinions about what is going on when we are helping advocate for the family, we need to make sure we are stating the facts for the family.
· What is your role as an early childhood educator in making legislative changes?
Our role is to be able to email them or decide how to get a hold of them and let them know our questions, comments or suggestions on things that need to be changed, updated. We need to let them know so we can support our school, children, and families. It is our role as educators to stay aware of the laws. The Federal laws we need to make sure we are aware of the
· Family Education Rights & Poverty Act
· The No Child Left Behind
· Individuals with Disabilities Education Act
With these laws and many more they need to hear from schools in the United States. The federal laws mean we need to address the issues. These issues usually involve infringement of the student’s rights and they are to protect the rights. The state laws depend on the state you are in. The state laws this is where you would go if you have a problem or need to voice about
· Teacher Retirement
· Teacher evaluations
· Charter schools
· State Testing requirements
· The required learning standards
· Much more
Your school board is also a great place to help with policies and regulations and any revisions that need to be done.
· What ethical issues must early childhood education professionals consider related to advocacy and why do those issues exit?
In NAEYC the code of Ethical Conduct and in their it describes how any educator is required to act and what they do and not to do. At times as an educator as staff we tend to do what is the simplest or sometimes, we want to please others but when it comes to this, we must remember to follow our responsi.
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Advertising is one of the most common forms of visual persuasion we encounter in everyday life. The influence of advertising in our society is persuasive and subtle. Part of its power comes from our habit of internalizing the intended messages of words and images without thinking deeply about them. Once we begin decoding the ways in which advertisements are constructed, once we view them critically, we can understand how, or if, they work as arguments. We may then make better decisions about whether to buy products and what factors convinced us or failed to convince us.
What are the different forms of advertising?
Modern media comes in many different formats, including print media (books, magazines, newspapers), television, movies, video games, music, cell phones, various kinds of software, and the Internet. Each type of media involves both content and also a device or object through which that content is delivered.
TEAM TASK:
As a team you are going to Review Chapter 4: Visual Rhetoric: Thinking About Images as Arguments. You will
be assigned a Section of the Chapter (written, visual, unfit, political, caricature, photography-maps graphs charts ) and as a Team you willResearch
the content of that Chapter Area (you will see topic page overlap ) and implement the following:
You will look at and interpret a media campaign or advertisement. Focus on social or ethical aspects * Seek to find one or more of the FALLACY TYPES identified Chapter 9 pages 363- 380. Include this information in your findings. Consider and incorporate as many of the following 16 categories :
The objectives: What role does the ad play in the economy?
The audience: Is it targeted to a group that could be considered vulnerable?
Effectiveness: Does it promote something that is socially desirable?
Role in marketing mix: What role does the ad play in the economy?
Image, product differentiation and branding: Is the ad misleading?
Other promotion factors
The unique selling proposition.
The basis for the appeal(s).
How would you make improvements?
The creative philosophy
The slogan
Secondary or supporting points or claims
The tone or mood and manner: Is the ad misleading?
Type of presenter
The motivational appeal: Does it promote something that is socially desirable?
Executional style
Each TEAM will develop a
15 minute class presentation
about their researched area. You have
options to use
power points, maps, videos, and other resources that will help educate your audience about your research.
Your Presentation should include:
A Power Point, the media piece or some type of visual presentation~~
A Question and Answer {Q & A} & Interactive session, quiz,.
Adult Health 1 Study GuideSensory Unit Chapters 63 & 64.docxSALU18
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Sensory Unit
Chapters 63 & 64
Remember that assigned textbook readings should be supplemental to reviewing & studying the Powerpoint presentations. Answers to these study guide questions can be obtained from the textbook chapters, Powerpoint presentations, as well as class lectures & in-class activities.
Chapter 63: Assessment & Management of Patients with Eye & Vision Disorders
Conditions to Know
: Glaucoma, Cataracts, Retinal Detachment, Macular Degeneration, Conjunctivitis, Eye trauma
· Know the basic structures & functions of the eye – lens, pupil, iris, cornea, conjunctiva, retina, and sclera
· Questions to ask patients regarding issues with the eyes/vision – Chart 63-1
· Snellen Chart is used to assess visual acuity – 20/20 is considered perfect vision (patient can read line 20 of chart while standing 20 feet away) – this is tested in each eye
1. What are some of the most common causes of blindness?
2. What is responsible for the damage to the optic nerve in patients diagnosed with glaucoma?
3. Glaucoma can lead to what primary complication if not treated properly?
4. What are the differences between open-angle & closed-angle glaucoma?
5. What are the primary signs & symptoms of glaucoma?
6. What are the primary treatment goals for patients with glaucoma?
7. What is the first line treatment of glaucoma? What medication teaching points would you want to include in your patient education?
8. What are some common risk factors for the development of cataracts? See Chart 63-7.
9. What are the primary signs & symptoms of cataracts?
10. The most common treatment for cataracts is outpatient surgery, in which the lens affected by the cataract is replaced with a man-made one. Explain the pre and post-operative nursing management & education that is needed for patients undergoing cataract surgery. See Chart 63-8.
11. Retinal detachment is considered a medical emergency. What happens during retinal detachment?
12. What are some symptoms of retinal detachment?
13. Macular degeneration is the most common cause of vision loss in people > 60 years old. What is macular degeneration?
14. What are some risk factors for dry macular degeneration?
15. What are some signs and symptoms of macular degeneration?
16. Nursing management for patients diagnosed with macular degeneration focus on safety & supportive measures. What are some accommodations we should make or educate patients on regarding how to help improve their vision & ADLs when they have this condition?
17. Conjunctivitis is also called “pink eye”. What are the different types of conjunctivitis and what are some symptoms of this condition? Are any of these types considered contagious?
18. What are some teaching points to include when educating a patient diagnosed with viral conjunctivitis? See Chart 63-11.
19. Explain the emergency nursing treatment needed when a patient presents with eye trauma.
Chapter 64: Assessment & Manag.
Advertising Campaign Management Part 3Jennifer Sundstrom-F.docxSALU18
Advertising Campaign Management
Part 3
Jennifer Sundstrom-Fitzgerald
1
Learning Objectives
Analyze advertising campaign parameters
Identify how a creative brief facilitates effective advertising
Describe the implications of advertising management in the global arena
2
Advertising Campaign Parameters
Advertising goals
Media selection
Tagline
Consistency
Positioning
Campaign duration
Effective advertising campaigns require careful planning and attention to specific parameters including Advertising goals, media selection, tagline, consistency, positioning and campaign duration. We will review each parameter beginning with goals.
3
Advertising Goals
A primary goal of advertising is to build brand awareness among existing and new customers. The creative should inform and persuade them to make purchases and build brand loyalty.
4
Build brand awareness
Inform, persuade, support marketing efforts
Encourage purchase decisions
Building Brand Awareness
Successful brands possess two characteristics. Top-of-mind are brands a consumer mentions first when asked about brands in a particular product category – these are brands in our Evoked Set. Top choice is the brand within a product category that consumers prefer the most. So top choice requires top-of-mind. Brand equity, which is the level of brand strength perceived by consumers, leads to top-of-mind and top choice brands.
This is also applicable on the B2B side when business people are faced with modified rebuy situations. A common dilemma I had was for every Fox Graduation Ceremony, there are three per year, and the need for graduation program booklets. There was a printer who I always wanted to hire because I enjoyed working with them, they always had fair prices and delivered high-quality programs in a timely manner. However, due to non-profit regulations, I had to bid the job to at least three vendors. So my top-of-mind, first choice brand was always included but I had to add two other vendors as well. Tell story about Bill DeVece and misspelled student names and how wonderful he was in fixing these issues.
5
Brand image begins with awareness
Consumers recognize the brand
Brand equity leads to top-of-mind and top choice
B2B important in modified rebuy situations
Building Brand Awareness
Successful brands possess:
Top-of-mind
Top choice
The 10 Most Valuable Brands in the World per 2018 study
Coca Cola brand is a good example of a brand with these characteristics. Here is a recent list of a top 10 most valuable and recognized list of global brands. (click link)
6
Goal to Persuade
Dare to be Devoted Campaign
Every Kiss Begins with Kay Campaign
Another common goal of advertising is to persuade consumers that a particular brand is superior to others and should be their top choice. Both of these brands, owned by the same parent company (Signet), do extensive advertising, but only Kay Jewelers has successfully used the same slogan, “Every Kiss Begins w.
Adopt-a-Plant Project guidelinesOverviewThe purpose of this.docxSALU18
Adopt-a-Plant Project guidelines
Overview:
The purpose of this project is for you to choose a plant, conduct online research into the biology of the plant, and communicate what you have learned. You will be preparing an annotated bibliography on the plant you choose. The entire project is worth 50 points
Annotated Bibliography (50 points)
You will prepare an annotated bibliography with a list of the top 10 most interesting facts about your plant.
· Each fact should be paraphrased (i.e. written in your own words, no quotations allowed).
· Then tell me why this is interesting to you – make connections to your life or to currents issues in our world.
· Finally, give a full citation and tell me why you think this is a reliable, trustworthy source. Use this libguide to help you come up with reasons why your source is trustworthy.
· At least one of your sources should be from a peer-reviewed, science journal article.
Here is an example:
Fact 1: Taxol is a chemotherapy agent derived from the bark of the Pacific Yew Tree. The chemical itself is derived from a fungal endophtye within the bark. I thought this was very interesting, because the Pacific Yew tree is native to the state of Washington, and my aunt Jane received Taxol while undergoing chemotherapy for ovarian cancer. I also thought it was interesting because of the mutualistic relationship between the plant and the fungus.Citation: Plant natural products from cultured multipotent cells
Roberts, Susan; Kolewe, Martin. Nature Biotechnology28.11 (Nov 2010): 1175-6.
This is a reliable source because it is published in a peer-reviewed science journal article, written by two PhDs that are providing a review of the current literature on the topic
To complete the assignment, you should first choose a plant, gather articles discussing your plant, read the articles sufficiently enough to discuss the plant, and finally write the annotated bibliography. You are expected to produce original work, and any plagiarism will receive a zero. The paper should be double-spaced, and typed in 12 point font size, with normal margins. The instructions for how to properly cite your sources are at the end of this handout.
*** Reminder: The scientific name of a plant should always be typed in italics, with the first letter of the Genus capitalized. For ex.: Digitalis lanata. When you search for information on your plant online, make sure to use the scientific name, which will bring back a wider variety of results
The bibliography is worth 50 points and will be graded on:
1. Effort
• Quality of references
•Depth/breadth/quality of material covered
2. Following directions/ requirements
I will use the following rubric to grade your bibliography:
Research, Critical Reading and Documentation
Balanced, authoritative sources; correctly cited sources; effectively integrated outside sources. Most sources from science journals
10 pts
Effective sources, correctly cited, Could have a few more.
ADM2302 M, N, P and Q Assignment # 4 Winter 2020 Page 1 .docxSALU18
ADM2302 M, N, P and Q Assignment # 4
Winter 2020 Page 1
Assignment # 4
Decision Analysis and Project Scheduling
ADM2302 students are reminded that submitted assignments must be typed (i.e. can NOT be hand
written), neat, readable, and well-organized. Assignment marks will be adjusted for sloppiness, poor
grammar, spelling, for technical errors as well as if you submit a PDF file.
The assignment is to be submitted electronically as a single Word Document file via Brightspace by
Friday April 3rd prior to 23:59. Front page of the Word document has to include title of the assignment,
course code and section, student name and student number. Second page is the individual/group
statement of integrity that must be signed.
E-mail questions related to the assignment should be sent to the Teaching Assistant or posted on the
Brightspace course website “Discussion page” (viewed by all).
Section M: Parisa Keshavarz ([email protected])
Section N: : Niki Khorasanizadeh ([email protected])
Section P: Makbule Kandakoglu ([email protected])
Section Q: Afshin Kamyabniya ([email protected])
Problem 1: Payoffs/Decision Table (13 points)
A small building contractor has recently experienced two successive years in which work opportunities
exceeded the firm’s capacity. The contractor must now make a decision on capacity for next year.
Estimated profits (in $ thousands) under each of the two possible states of nature are as shown in the
table below.
NEXT YEAR’S DEMAND
Alternative Low High
Do nothing
Expand
Subcontract
$50**
20
40
$60
80
70
** Profit in $ thousands.
Which alternative should be selected if the decision criterion is:
a. The optimistic approach? (3 points)
b. The conservative approach? (3 points)
c. Minimize the regret? (7 points)
Problem 2: Payoffs/Decision Table (15 points)
Dorothy Stanyard has three major routes to take to work. She can take Tennessee Street the entire way,
she can take several back streets to work, or she can use the expressway. The traffic patterns are,
however, very complex. Under good conditions, Tennessee Street is the fastest route. When Tennessee
is congested, one of the other routes is preferable. Over the past two months, Dorothy has tried each of
route several times under different traffic conditions. This information is summarized in minutes of
travel time to work in the following table:
mailto:[email protected]
mailto:[email protected]
mailto:[email protected]
mailto:[email protected]
ADM2302 M, N, P and Q Assignment # 4
Winter 2020 Page 2
No Traffic Congestion
(Minutes)
Mild Traffic
Congestion
(Minutes)
Severe Traffic
Congestion
(Minutes)
Tennessee Street
Back roads
Expressway
15
20
30
30
25
30
45
35
30
In the past 60 days, Dorothy encountered severe traffic congestion 10 days and mild traffic congestion
20 days. Assume that the past 60 days are typical of traffi.
After completing the assessment, my Signature Theme Report produ.docxSALU18
After completing the assessment, my Signature Theme Report produced the following results: Communication, Relator, Individualization, Consistency, and Strategic. When I first saw the themes presented, I was a little skeptical at first but after reading the detailed descriptions I felt like it made a lot of sense and mirrored a lot of what I had already thought about myself.
A core value that I would like to continue to strengthen would be the value of acceptance. One of my top five themes was relator which explained that I have a comfortability with gravitating towards people I already know and building relationships from there. I don’t have issues with making new relationships, but I can see that sometimes I close myself off initially to embracing new ones. With acceptance, you have to understand that there are some situations you can control and some that you can’t but embracing the latter can lead to new experiences that could be beneficial (Riley, 2021). Another core value that I would like to improve upon would be calmness. This fits in well with my theme of consistency. While I am a firm believer of things being fair and consistent, I can get easily upset when things don’t balance out like they are expected to. I know that working on being calm in tense situations will help me adapt easier when things don’t always work out as they should.
One of the strengths that I would like to embrace fully and continue to improve upon is communication. It was no surprise to me that communication was at the top of my list for my themes. When I am in a position of leadership at work, I make it a priority to keep my staff updated on everything that is going on for that night and it is something I expect from my charge nurse when I am working the floor also. A communicator is only effective when they are aware of their style of communicating and how others perceive or respond to it (Marshall & Broome, 2021). As a communicator I know that I can always work on how I communicate non-verbally and with body language especially. The other strength that I would like to continue to work on is of being strategic. The report explained that the strategic theme fit me because I am able to sort through the clutter and find the best route when I am trying to accomplish something. I really believe this about myself because when I have a task I need to accomplish, whether I am in a leader position or not, I will break everything down and reorganize it to make sure I have come up with the best solution. I feel like the best way to do something is the way that makes it concise and without a lot of excess getting in the way.
A characteristic of mine that I would like to strengthen would be that of instinct. My theme of individualization points out that I have an instinct about others and how they work and function. I have always felt that I easily read people and can get a sense of who they truly are and for example in the workplace how they are as a staff member. S.
After careful reading of the case material, consider and fully answe.docxSALU18
After careful reading of the case material, consider and fully answer the following questions:
1. What were the primary reasons for changing the current system at Butler?
2. What role did Butler's IS department play?
3. List the objectives of the pilot. Were there any problems?
4. Do you think Butler made the right decision to utilize this new technology? What implications does this decision hold for Butler's IT department in the long run?
NOTE: Butler refers to it's IT department as IR. You may consider these two acronyms as synonymous (i.e. IT = IS = IR for purposes of this assignment)
.
Affluent
Be unique to
Conform
Debatable
Dominant
Enforce
Ethnic
Internalize
Rank
Restrict
You will write your own sentences using each of the vocabulary words. The sentence
must be an
original sentence
created by you, AND it must use the vocabulary word correctly.
Your sentence
MUST
demonstrate that you understand the meaning of the word.
.
Advanced persistent threats (APTs) have been thrust into the spotlig.docxSALU18
Advanced persistent threats (APTs) have been thrust into the spotlight due to their advanced tactics, techniques, procedures, and tools. These APTs are resourced unlike other types of cyber threat actors.
Your chief technology officer (CTO) has formed teams to each develop a detailed analysis and presentation of a specific APT, which she will assign to the team.
.
Your report should use
The Cybersecurity Threat Landscape Team Assignment Resources
to cover the following five areas:
Part 1: Threat Landscape Analysis
Provide a detailed analysis of the threat landscape today.
What has changed in the past few years?
Describe common tactics, techniques, and procedures to include threat actor types.
What are the exploit vectors and vulnerabilities threat actors are predicted to take advantage of?
Part 2: APT Analysis
Provide detailed analysis and description of the APT your group was assigned. Describe the specific tactics used to gain access to the target(s).
Describe the tools used. Describe what the objective of the APT was/is. Was it successful?
Part 3: Cybersecurity Tools, Tactics, and Procedures
Describe current hardware- and software-based cybersecurity tools, tactics, and procedures.
Consider the hardware and software solutions deployed today in the context of defense-in-depth.
Elaborate on why these devices are not successful against the APTs.
Part 4: Machine Learning and Data Analytics
Describe the concepts of machine learning and data analytics and how applying them to cybersecurity will evolve the field.
Are there companies providing innovative defensive cybersecurity measures based on these technologies? If so, what are they? Would you recommend any of these to the CTO?
Part 5: Using Machine Learning and Data Analytics to Prevent APT
Describe how machine learning and data analytics could have detected and/or prevented the APT you analyzed had the victim organization deployed these technologies at the time of the event. Be specific.
Part 6: Ethics in Cybersecurity.
Ethical issues are at the core of what we do as cybersecurity professionals. Think of the example of a cyber defender working in a hospital. They are charged with securing the network, medical devices, and protecting sensitive personal health information from unauthorized disclosure. They are not only protecting patient privacy but their health and perhaps even their lives. Confidentiality, Integrity, Availability - the C-I-A triad - and many other cybersecurity practices are increasingly at play in protecting citizens in all walks of life and in all sectors. Thus, acting in an ethical manner is one of the hallmarks of cybersecurity professionals.
Do you think the vulnerability(ies) exploited by the APT constitutes an ethical failure by the defender? Why or why not?
For the APT scenario your group studied, were there identifiable harms to privacy or property? How are these harms linked to C-I-A? If not, what ethically si.
Advanced persistent threatRecommendations for remediation .docxSALU18
Advanced persistent threat
Recommendations for remediation of the threat
Research the use of network security controls associated to your threat and industry
Do Not use topics network security,VPN,FIREWALL,ETC
10-12 pages. Double spaced APA style
At least 10 REFERENCES
5 ATLEASt PEER REVIEWED SCHOLARLY
.
Adultism refers to the oppression of young people by adults. The pop.docxSALU18
Adultism refers to the oppression of young people by adults. The popular saying "children should be seen and not heard" is used as a way to remind a child of his or her place and reaffirm the adult's power in the relationship. The saying suggests that children's voices are not as important or as valid as an adult's and they should remain quiet. Children are often relegated to subordinate positions due to socially constructed beliefs about what they can or cannot accomplish or what they should or should not do; this in turn compromises youth's self-determination. This oppression is further highlighted when considering the intersection of age with race, ethnicity, socioeconomic status, and sexual orientation. You will be asked to consider all of these when reviewing the Logan case and Parker case.
By Day 3
Post
an analysis of the influence of adultism in the Logan case. Then, explain how gender, race, class, and privilege interact with adultism to influence the family's discourse related to Eboni's pregnancy as well as other family dynamics.
.
ADVANCE v.09212015
•
APPLICANT DIVERSITY STATEMENT IN FACULTY SEARCH PROCESS
FREQUENTLY ASKED QUESTIONS
1) How does University of California define “diversity?”
A: The academic senate adopted in 2009 the following broad definition of diversity:
Diversity - defining features of California past, present and future - refers to a variety of
personal experiences, values, and worldviews that arise from differences of culture and
circumstance. Such differences include race, ethnicity, gender, age, religion, language,
abilities/disabilities, sexual orientation, socioeconomic status, geographic region and more.
2) Why does UC Irvine expect a diversity statement from applicants for faculty positions?
A: UC Irvine’s commitment to inclusive excellence is integral to our ascendancy among globally
preeminent universities. It provides applicants with an opportunity to discuss how their past or
future contributions will advance this enduring campus commitment. For more information,
please see the Provost’s memo on Inclusive Excellence.
3) Is the diversity statement consistent with University of California policy?
A: Yes. APM 210.1-d, which governs appointment, appraisal and promotion, recommends that
faculty be both encouraged and rewarded for activity that promotes inclusive excellence:
“The University of California is committed to excellence and equity in every facet of its mission.
Teaching, research, professional and public service contributions that promote diversity and
equal opportunity are to be encouraged and given recognition in the evaluation of the
candidate's qualifications. These contributions to diversity and equal opportunity can take
a variety of forms including efforts to advance equitable access to education, public
service that addresses the needs of California's diverse population, or research in a
scholar's area of expertise that highlights inequities.”
4) Is UC Irvine alone among UC campuses in adopting this statement?
A: No. UC San Diego adopted this statement in 2010.
5) How will applicants learn about the diversity statement expectation?
A: Per Provost Gillman’s memo of June 2014, all ads for faculty positions will include the following
sentence: “Applicants are encouraged to share how their past and/or potential contributions to
diversity, equity and inclusion will advance UC Irvine’s commitment to inclusive excellence.”
6) How do applicants provide their diversity statement?
A: There is a dedicated field in UC Recruit for applicants to submit their diversity statement.
7) If an applicant does not provide a diversity statement, will his or her application be considered
incomplete?
A: Yes
http://www.provost.uci.edu/news/InclusiveExcellence.html
http://www.ucop.edu/academic-personnel/_files/apm/apm-210.pdf
http://www.provost.uci.edu/news/Diversity-Statement-June-2014.html
ADVANCE v.09212015
8) What are the components of a diversity statement?
.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
Introduction to AI for Nonprofits with Tapp Network
EGME 306A The Beam Page 1 of 18 Group 2 EXPER.docx
1. EGME 306A The Beam
Page 1 of 18
Group 2
EXPERIMENT 3:The Beam
Group 2 Members:
Ahmed Shehab
Marvin Penaranda
Edwin Estrada
Chris May
Bader Alrwili
Paola Barcenas
2. Deadline Date: 10/23/2015
Submission Date: 10/23/2015
EGME 306A – UNIFIED LABORATORY
EGME 306A The Beam
Page 2 of 18
Group 2
Abstract (Bader):
The main objective for this experiment was to determine the
stress, deflection, and strain of a supported beam
under loading, and to experimentally verify the beam stress and
flexure formulas. Additionally, maximum
bending stress and maximum deflection were determined. To
accomplish this, a 1018 steel I-beam with a strain
gage bonded to the underside was utilized in conjunction with a
dial indicator to monitor beam deflection. In
order to determine the values for strain and deflection, the beam
underwent testing utilizing the MTS Tensile
Testing machine, which applied a controlled, incrementally
increasing load to the beam. This data was then
utilized along with calculations for the beams neutral axis,
moment of inertia, and section modulus to determine
3. the required objective values. Final values of 12,150 psi for the
maximum actual stress (vs. 12,784.8 psi for
theoretical stress), and 0.0138 in for the maximum actual
deflection (vs. .0130 in for theoretical deflection)
correlated closely with each other, and successfully verify
established beam stress and flexure formulas.
EGME 306A The Beam
Page 3 of 18
Group 2
4. Table of Contents:
List of Symbols and Units 4
Theory 5
Procedure and Experimental Set-up 8
Results 9
Sample Calculations and Error Analysis 12
Discussion and Conclusion 15
Bibliography 16
Appendix 17
5. EGME 306A The Beam
Page 4 of 18
Group 2
List of Symbols and Units (Chris):
List of Symbols and Units Name of variables (units) Units
� Stress psi
� Applied load lbf
� Moment of Inertia in.4
� Strain in/in
� Length of the bar in
Z Section Modulus of Beam in3
� Distance to Beam Neutral Axis in
6. � Modulus of Elasticity psi
EGME 306A The Beam
Page 5 of 18
Group 2
Theory (Edwin):
There are two main objectives for this experiment: to determine
maximum bending stress values in
the beam and to determine the deflection in the beam. To help
visualize this phenomena, imagine
cutting a section of a symmetrically loaded beam:
Now, examine diagrams of this section before (Fig. A) and after
bending (Fig. B):
(Fig. A)
7. (Fig. B)
The main points to take away from the above diagrams are as
follows: When the moment, M is applied
as shown in Fig. A, forces will be in compression near the top
(positive moment) and in tension near
the bottom (negative moment). The effects from this moment
are seen in Fig. B.
For determining max stress values, one concept to note is that
our bending moment M can help
calculate bending stress. First, we recall our basic definition of
normal strain:
� =
�′ − �
�
EGME 306A The Beam
Page 6 of 18
Group 2
Since the beam is bending, however, we will need to alter the
above formula by taking into account
8. the radius of curvature, r, and the differential angle, �. Since
there are locations where forces are
compressive and locations where forces are tensile, there must
be a location where forces are neither
compressive nor tensile. This axis is called the Neutral Axis and
is labeled in Fig. B as N-N. We can
now alter the above formula by measuring the strain at distance
+� from the neutral axis:
� =
�′ − �
�
=
(� + �)∆� − �∆�
�∆�
=
�
�
The strain equation from above can be converted to stress by
using Hooke’s Law:
� = �
�
�
Now, if we allow c to be the max distance from the neutral axis,
9. we can build upon the above
expression as follows:
� = ��
�
�
To obtain the beam stress formula, we still need to define where
the neutral axis is located. We can do
this by relating the radius of curvature and the bending moment,
which will be determined by applying
a moment equilibrium equation about the neutral axis:
�� = ∫ �
�
�� =
��
�
∫ �
�
�� = 0
Since moment due to all forces is summed up by the product of
their forces and the moment arm about
the neutral axis, we deduce:
� = ∫ ��� = ∫ ���� =
10. ��
�
∫ �2��
We will then let I be defined as the second moment of area
about the neutral axis, commonly called
the moment of inertia:
� = ∫ �2��
Finally, we deduce the moment equation as:
�� =
��
�
=
�
�
Our final objective involved determining beam deflection.
Using similar methods from bending stress,
we will examine the relationship between the radius of
curvature, r and the moment, M, at any given
point on a beam. We begin with the radius of curvature for any
point of a function from calculus:
EGME 306A The Beam
11. Page 7 of 18
Group 2
�
�
=
�2�
��2
(1 + �
2�
��2
)
3
2
We will note that for small deflections, the first derivative or
slope is small and becomes even smaller
when it is squared and can therefore be neglected. This will
greatly simplify the radius of curvature
to:
1
�
=
�2�
��2
12. By combing the above equation with the bending stress
equation, we develop the standard moment
curvature equation:
��
�2�
��2
= �(�)
The differential equation will only be useful if we apply it to
the beam with specific boundaries, or
boundaries of integration. Integrating with M(x)=Px/2 for 0≤x≤a
andM(x)=Pa/2 for a≤x≤a+b, we get:
�(�) =
�
2��
(
�3
6
−
��(� + �)
2
) , ��� 0 ≤ � ≤ �
�(�) =
�
14. 8
)
Lastly, by allowing a=b=L/3:
−�� =
23��3
48��
=
23��3
1296��
EGME 306A The Beam
Page 8 of 18
Group 2
Procedure and Experimental Set-Up (Marvin):
This experiment requires the use of MTS Insight Tensile
Testing Machine, Beam Deflection Dial indicator,
digital caliper, a 1018 steel beam and two separate data
acquisition software. The experiment begins with the
15. measurement of the length and the cross-sectional dimensions of
the 1018 steel beam with the use of the digital
caliper. The beam is then carefully placed into the MTS
machine while making sure that the beam's black marks
are aligned with the roller supports of the bending fixture. Once
the beam is squarely nested on the roller
supports, TestWorks 4 software is accessed in order to zero the
load reading. Now that the parameters have been
set up, the MTS' handset is used to position the upper bending
fixture over the beam. While the crosshead
lowers, the digital load readout from the software is observed.
When the load increases as the upper loading
component of the fixture makes contact with the beam, the
fixture is raised until a preload of 0.2 lb is applied.
The Beam Deflection Dial indicator is positioned in the center
of the beam on the bottom side. Do note, the dial
indicator needs to be set to zero. Now, the LabVIEW software is
accessed. On the software, the strain indicator
is zeroed by pressing “zero strain”. The software also requires
the inputs dialog for the thickness and width, a
value of 0.125 is used for thickness and a value of 0.500 is used
for width. The MTS machine loads the beam
up to 1000 lb in increments of 100 lb. When the digital load
readout reaches approximately 100 lb, the “Pause”
16. button is pressed since the data readings need to be taken for
every 100 lbs. Pausing for every 100 lb increments
are continued up until 1000 lbs. The procedure is repeated again
since the average of the 2 sets of readings will
be used for experimental calculations. Keep in mind, the dial
indicator and the strain indicator needs to be re-
zeroed again for the next set of experiment.
Note: for a detailed procedure, see Appendix A.1
EGME 306A The Beam
Page 9 of 18
Group 2
17. Results (Chris):
-TEST 1 / TEST 2 - - AVERAGE OF TEST 1 & 2 -
LOAD
( lbf )
STRAIN
GAGE
ELONGATIO
N ( ε )
INDICATOR
DEFLECTIO
N (in.)
LOA
D
( lbf )
STRAIN
GAGE
ELONGATIO
N ( ε )
INDICATOR
DEFLECTIO
N (in.)
100/99 47/46 .0011/.0016 99.5 46.5 .00135
19. 797/80
0
354/355 .0109/.0114 798.5 354.5 .01115
897/89
8
318/400 .0122/.0129 897.5 359 .01255
996/99
6
365/445 .0134/.0142 996 405 .0138
TABLE 1. Strain gauge, indicator, and load data
(reference Appendix for calculations)
EGME 306A The Beam
Page 10 of 18
Group 2
LOAD
( lbf )
20. ACTUAL VALUES / DEFLECTION
( in. )
THEORETICAL VALUES / DEFLECTION
( in. )
99.5 0.00135 0.0013
200 0.0026 0.0026
305.5 0.0041 0.0039
395.5 0.0055 0.0051
498.5 0.00675 0.0065
597 0.00835 0.0077
695.5 0.00965 0.0091
798.5 0.01115 0.0104
897.5 0.01255 0.0117
996 0.0138 0.013
TABLE 2. Actual and Theoretical Values for Beam Deflection
(reference Appendix for calculations)
Figure 2-1. Actual vs. Theoretical Deflection using dial
indicator and calculated values.
The Load vs. Deflection curve consists of the actual
experimental values obtained during the
21. experiment compared with theoretical calculated values to
measure deflection in relation to
applied load.
0
200
400
600
800
1000
1200
0 0.005 0.01 0.015
Lo
ad
(
lb
f )
Deflection ( in. )
Actual vs. Theoretical Deflection
Actual Deflection
22. Theoretical Deflection
Linear (Actual
Deflection)
Linear (Theoretical
Deflection)
EGME 306A The Beam
Page 11 of 18
Group 2
LOAD
( lbf )
ACTUAL STRESS
( psi )
THEORETICAL STRESS
( psi )
99.5 1,410 1,277.20
200 2,685 2,567.23
305.5 4,125 3,921.44
395.5 5,295 5,076.70
23. 498.5 6,690 6,398.82
597 8,040 7,663.18
695.5 9,330 8,927.54
798.5 10,635 10,249.66
897.5 10,770 11,520.44
996 12,150 12,784.80
TABLE 3. Actual and Theoretical Values for Beam Stress
(reference Appendix for calculations)
Figure 2-1. Actual vs. Theoretical Stress curve using
experimental and calculated values.
The Load vs. Stress curve consists of the actual experimental
values obtained during the
experiment compared with theoretical calculated values to
measure stress in relation to applied
load.
0
200
400
24. 600
800
1000
1200
0 5,000 10,000 15,000
Lo
ad
(
lb
f )
Stress ( psi )
Actual vs. Theoretical Stress
Actual Stress
Theoretical Stress
Linear (Actual Stress)
Linear (Theoretical
Stress)
EGME 306A The Beam
Page 12 of 18
34. Δ�
�
= −0.0054985
EGME 306A The Beam
Page 15 of 18
Group 2
Discussion and Conclusion (Ahmed):
In this experiment we examined stress, deflection and strain of
the load applied to a 1018 steel I-beam. The
beam was placed horizontally and a force P was applied to it by
the MTS Insight Tensile Testing Machine. A
load was applied and readings were taken incrementally every
100 lbf until the test was concluded at 1000 lbf.
This process was repeated twice and the average of the two tests
was taken. This data was then utilized along
with calculations for the beams neutral axis, moment of inertia,
and section modulus to determine the required
objective values. Final values of 12,150 psi for the maximum
35. actual stress (vs. 12,784.8 psi for theoretical
stress), and 0.0138 in for the maximum actual deflection (vs.
.0130 in for theoretical deflection) correlated
closely with each other, and successfully verified established
beam stress and flexure formulas.
EGME 306A The Beam
Page 16 of 18
Group 2
36. BIBLIOGRAPHY (Edwin):
1) Beckwith, T. G., Buck, N. L. and Marangoni, R. D.,
Mechanical Measurements, Addison-Wesley.
2) Popov, E.P. Mechanics of Materials, Prentice-Hall Inc.
3) Sharma, P. The Beam (EGME 306A lab manual). CSU-
Fullerton.
4) Thomas, G.B., and Finney R.L., Calculus and Analytical
Geometry, Addison-Wesley,
37. EGME 306A The Beam
Page 17 of 18
Group 2
Appendix (All):
A.1 Procedures
1. Measure the cross-sectional dimensions of the beam by using
the caliper and measure the location of
the loading and support pins.
2. Place the beam into the MTS machine while making sure that
beam's black marks aligns with the
roller supports of the lower bending fixture.
3. Access the TestWorks 4 software by double clicking its icon
on the desktop
4. If prompted, make sure that the name field under the User
Login says "306A_lab" then click OK to
login
5. Under the Open Method dialog, select "exp-3 4 Point Flex
Mod X'
38. 6. Select the Motor Reset button in the bottom right corner by
clicking on it
7. Zero the "load" readout by right clicking on the "Load cell"
icon and selecting "zero channel"
8. Do not close the TestWorks 4 software as it will be used
again in the later parts of the experiment.
Leave the software running.
9. Next, use the MTS' handset to position the upper bending
fixture over the beam
10. Enable the handset by pressing "unlock" button at the top
right of the handset
11. Slowly lower the crosshead using the down arrow until
fixture is nearly touching the beam. Make
sure not to pinch the strain gauge lead wires between the fixture
and the beam while lowering.
12. Once the crosshead is near the beam, use the thumb wheel of
the handset to lower/raise the fixture
onto the beam.
13. Observe the digital load readout from the screen while
lowering/raising the fixture and aim for a pre-
load value of 0.2 lb
14. Once finished, return control to the computer software by
locking the handset by pressing the
39. "unlock" button.
15. Take the magnetic base holding the dial indicator and
position it with the dial indicator in the center
of the beam on the bottom side. Make sure the dial indicator is
not touching the strain gauge.
16. Once the dial indicator is in position, lock it to the MTS
frame by activating the magnetic base.
17. Zero the dial indicator by turning the dial of the indicator.
18. Start the LabVIEW software by double clicking its icon on
the desktop. NOTE: LabVIEW and
TestWorks 4 should be open side-by-side.
19. In LabVIEW, select "Open" and double click "exp2&3-
Strain Mod 9-15 LV7.1"
20. Press the white arrow near the upper left corner of the
screen to start the strain gauge acquisition
EGME 306A The Beam
Page 18 of 18
Group 2
21. Press the "Zero Strain" button to zero-out the strain
indicator
22. Press the Green Arrow on the TestWorks 4 window
40. 23. Name a sample ID for the test
24. Under the required inputs dialog, input 0.125 for thickness
and 0.500 for width.
25. Press OK when ready to start
26. When the digital load readout reaches approximately 100 lb,
press the "Pause" button to pause the
test.
27. Record the actual load from the digital readout, also record
the strain reading from the LabVIEW
window, and record the deflection of the beam from the dial
indicator.
28. Continue taking readings in increments of 100 lb until
reaching approximately 1000 lb (steps 26-27
will be repeated 10 times)
29. Steps 18-29 will be repeated again for the next set of
experiment.
III-1
41. Experiment III
The Beam
OBJECTIVES
The objectives of this experiment are (a) to determine the stress,
deflection and strain of a simply
supported beam under load, and (b) to experimentally verify the
beam stress and flexure
formulas.
THEORY
Structural members are usually designed to carry tensile,
compressive, or transverse loads. A
member which carries load transversely to its length is called a
beam. In this experiment, a beam
will be symmetrically loaded as shown in Fig. III-1(a), where P
is the applied load. Note that at
any cross section of the beam there will be a shear force V (Fig.
III-1(b)) and moment M (Fig.
III-1c). Also, in the central part of the beam (between the loads
P/2) V is zero and M has its
maximum constant value. Notice the sign convention of a
positive moment, M, causing a
negative (downward) deflection, y.
If in this part a small slice EFGH of the beam is imagined to be
cut out, as shown, then it is clear
that the external applied moment, M, must be balanced by
internal forces (stresses) at the
sections (faces) EF and GH. For M applied as shown in Fig. III-
2(a), these forces would be
42. compressive near the top, EG, and tensile near the bottom, FH.
Since the beam material is
considered elastic, these forces would deform the beam such
that the length EG would tend to
become shorter, and FH would tend to become longer. The first
fundamental assumption of the
beam theory can be stated as follows:
“Sections, or cuts, which are plane (flat) before deformation
remain plane after
deformation.”
Thus, under this assumption, the parallel and plane sections EF
and GH will deform into plane
sections E F′ ′ and G H′ ′ which will intersect at point O, as
shown in Fig. III-2(b). Since E F′ ′
and G H′ ′ are no longer parallel, they can be thought of as
being sections of a circle at some
radial distance from O. Convince yourself of this by drawing a
square on an eraser and observe
its shape when you bend the eraser. Since the forces near E G′ ′
are compressive, and those near
F H′ ′ are tensile, there must be some radial distance r where the
forces are neither compressive
nor tensile, but zero. This axis, N-N, is called the neutral axis.
Notice that N-N is not assumed to
lie in the center of the beam.
Consider an arc of distance +η, from the neutral axis, or
distance r + η from O (Fig. III-2(b)). At
this radius, the length of arc is l′ =(r + η) Δθ. As shown in Fig.
III-2(a), the length of the arc was
l before the deformation. This length is also equal to rΔθ
(because at N-N there are no forces to
change the length). Thus, the strain at distance +η from the
neutral axis can be found by:
43. ε
η θ θ
θ
η
=
l - l
l
=
(r + ) - r
r
=
r
′ Δ Δ
Δ
(III-1)
III-2
45. ym
b
-
Figure III-1. Symmetrically Loaded Beam (a), with Shear Force
Diagram (b)
and Bending Moment Diagram (c)
L
b c a
2
P
2
P
V
x
M
x
2
Pa
46. 2
P
+
III-3
Figure III-2. Stresses and Strains of a Beam
III-4
In other words, the axial strain is proportional to the distance
from the neutral axis. It is remarked
that this strain is positive, because positive η was taken on the
tensile side of N-N in Fig. III-
2(b). Had η been taken in the opposite direction, then the strain
would have been negative, as
appropriate for the compressive side.
The second fundamental assumption is that Hooke’s Law
applies both in tension and
compression with the same modulus of Elasticity. Thus, from
Eqs. (I-3) and (III-1),
σ
η
= E
r
47. (III-2)
If c is the maximum distance from the neutral axis (largest
positive or negative value of η), then
the maximum stress (compressive or tensile) is given by σm =
Ec/r, and Eq. (III-2) can also be
written as
σ σ
η
=
cm
(III-3)
That is, the stress at a section EF or GH, due to applied moment
M, varies linearly from zero at
the neutral axis to some maximum value σm (positive or
negative) when η = c. To obtain the
beam stress formula, it remains to define where the neutral axis
is located, and to relate σm to M.
To locate the neutral axis, it is observed that the tensile and
compressive forces on a section are
equal to the stress times a differential element of area, as shown
in Fig. III-2(c). For static
equilibrium, the sum (or integral) of all these internal forces
must be zero. That is,
m
A A
dF = dA = dA = 0
c
48. σσ η∫ ∫
where, the integrals are over the whole cross-sectional area.
Thus, it is seen that the neutral axis
is located such that the first moment of area about it is zero;
that is, the neutral axis passes
through the centroid of the cross-sectional area. In Fig. III-2(c),
a rectangular area was used for
illustration; however, any shape of vertically symmetric cross-
sectional area is valid for the area
integral.
In a similar fashion, the moment due to all the forces is the sum
(or integral) of the forces times
their moment arms about the neutral axis, and this must be
equal to the external applied moment.
Thus,
M = dF = dA =
c
dAm 2∫ ∫ ∫η ησ
σ
η (III-4)
If I is defined as the second moment of area about the neutral
axis, commonly called the moment
of inertia,
I = dA2∫η (III-5)
then Eq. (III-4) can be written as:
m =
49. Mc
I
=
M
Z
σ (III-6)
III-5
where Z = I/c is the section modulus, which depends only on the
cross-sectional geometry of the
beam. Equation (III-6) is the beam stress equation which relates
the maximum (compressive or
tensile) stress to the applied moment. Notice its similarity to
Equation (I-1), the stress equation
for uniaxial tension. It is understood, of course, that σm is the
maximum bending stress at a
particular location, x, along the beam. In general, both σm and
M are functions of x, and are
related by Eq. (III-6).
The remaining question about the beam concerns its degree of
deformation, or flexure. That is,
how is the radius of curvature, r, related to the moment M (or
load P)? From calculus, it can be
shown that the curvature of a function y(x) is given by
1
r
=
50. d y
dx
(1 +
d y
dx
)
2
2
2
2
3
2
Thus, if x is the distance along the beam, y will be the
deflection as indicated in Fig. III-1(a). For
most beams of practical interest, this deflection will be small,
so that the slope dy/dx will be very
small compared to 1. Hence, a very good approximation is
1
r
=
d y
dx
2
51. 2
But, since σm = Ec/r = Mc/I, there results the differential
equation of the elastic curve:
EI
d y
dx
= M(x)
2
2 (III-7)
To obtain the elastic curve of the beam, y(x), and the maximum
deflection, ym, it is necessary to
integrate Eq. (III-7) using the moment function M(x) in Fig. III-
1(c). Thus, using M(x) = Px/2 for
0 ≤ x ≤ a and M(x) = Pa/2 for a ≤ x ≤ a + b, it is found that
for
3P ax(a + b)xy(x) = - , 0 x a
2EI 6 2
⎛ ⎞
≤ ≤⎜ ⎟
⎝ ⎠
( ) for
3 2P ax(2a + b)a ax y x = - + , a x a + b
2EI 6 2 2
⎛ ⎞
52. ≤ ≤⎜ ⎟
⎝ ⎠
and that the maximum deflection at x = a + b/2 is
)(
8
b +
2
ab
+
3
a
2EI
Pa
= y-
22
m (III-8)
In particular, for a = b = L/3,
- y =
23 Pa
48EI
=
23 PL
1296EIm
53. 3 3
(III-9)
III-6
Although the above stress and flexure formulas are quite
simple, it took some of the best minds
of the 17th and 18th centuries to derive them correctly. Part of
the difficulty in obtaining the
correct results at that time was that there were no methods of
verifying the results
experimentally. Today, with the advent of sensitive
displacement dial gauges, the verification is
more convenient.
Figure III-3. MTS Insight Tensile Testing Machine
PROCEDURE
1. The test will be conducted on a 1018 steel beam (E = 30x106
psi) using the MTS testing
machine. The position of the beam in the testing machine is
shown in Fig. III-3.
2. Observe that the cross-section of the I-beam is not a
symmetric; one flange of the beam is
thicker than the other. Measure carefully the cross-sectional
dimensions and the location of
the loading and support points.
54. 3. Carefully place the beam into the MTS machine if it is not
already installed. Align the 12-
inch black marks on the beam with the roller supports of the
lower bending fixture. Make
sure the beam is squarely resting and centered on the lower
support with the strain gauge
facing down.
Beam
Deflection
Dial indicator
Beam to
Be Tested
III-7
4. Enter the TestWorks 4 software by double clicking on the
icon on the desktop.
a. When prompted, make sure the Name field under the User
Login says “306A_lab”.
b. Click OK to login.
c. Under the Open Method dialog, select “exp-3 4 Point Flex
Mod X”.
d. Now, select the Motor Reset button in the bottom right corner
by clicking on it.
5. Zero the “load” readout by right clicking on the “Load cell”
icon and selecting “zero
channel”.
55. 6. Next we will use the handset to position the upper bending
fixture over the beam.
a. Enable the handset by pressing the “unlock” button at the top
right of the handset
b. Slowly lower the crosshead using the down arrow until the
fixture is NEARLY touching
the beam.
c. Make sure not to pinch the strain gauge lead wires between
the fixture and the beam.
d. While observing the digital load readout on the screen, use
the thumb wheel of the
handset to lower the fixture onto the beam. Watch for the load
reading to increase when
the upper loading component of the fixture makes contact with
the beam.
e. Now, slowly raise the fixture with the thumb wheel until only
a very slight pre-load of
approximately 0.2 lb is applied.
f. When finished, return control to the computer software by
locking the handset using the
same button as before.
Note that the beam has a strain gauge bonded to its surface. See
Figure III-4. This strain
gauge has a strain gauge factor of 2.14 ± 0.5% and 350 ohm
resistance. Connect the strain
gauge lead wires to the “#1 Strain” channel of the grey DAQ
box. Data acquisition is
conducted by the LabVIEW software.
56. 7. Take the magnetic base holding the dial indicator, and
position it with the dial indicator in
the center of the beam on the bottom side. Make sure the dial
indicator is not touching the
strain gauge. Also, be VERY CAREFUL not to damage the dial
indicator while doing this!
When the dial indicator is in position, lock it to the MTS frame
by activating the magnetic
base. Finally, zero the dial indicator by turning the dial of the
indicator. Note the divisions
on the dial indicator and the accuracy with which it can be read.
8. Start the LabVIEW software.
a. Double click the LabVIEW icon on the desktop, or follow the
procedure suggested for
Experiment II.
b. Select “Open” and double click “exp2&3-Strain Mod 9-15
LV7.1”.
c. Press the white arrow near the upper left corner of the screen
to start the strain gauge
acquisition.
d. Press the “Zero Strain” button to zero-out the strain
indicator.
9. You are now ready to run the experiment.
a. Press the Green Arrow on the TestWorks 4 GUI.
b. Give the sample ID for your group.
57. III-8
c. Under the Required Inputs dialog, enter 0.125 for the
thickness and 0.500 for the width.
DO NOT press OK yet!
10. You will load the beam up to 1000 lb in increments of 100
lb. To do this:
a. “OK” the Required Inputs dialog from above and the test will
begin.
b. When the digital load readout reaches approximately 100 lb,
press the “Pause” button to
temporarily stop the test.
c. Record the actual load on your data sheet from the digital
readout.
d. Toggle over to the LabVIEW screen and record the strain
reading from the software.
e. Record the deflection of the beam from the dial indicator.
f. Return to the TestWorks 4 screen and press the “Pause”
button again to resume the test.
g. Continue pausing and taking readings approximately every
100 lb from 0 to 1000 lb.
11. At 1000 lb the test will stop. Collect your last data point
before pressing “OK” at the last
dialog.
12. Before repeating the experiment, make sure your load
readout, strain indicator, and dial
indicator are all re-zeroed.
58. 13. Repeat steps 7 through 9.
Figure III-4. Beam with Bonded Strain Gauge
REPORT REQUIREMENTS
1. Determine the neutral axis, moment of inertia, and section
modulus of the beam cross-
section.
2. Draw shear force and bending moment diagrams for the
beam for the maximum load.
3. Compute the maximum bending stress and deflection of the
beam for the maximum load.
4. Plot deflection versus load, and also stress versus load. Each
graph should contain a curve
based completely on theoretical calculations, and another using
the experimental data points.
III-9
5. By error calculation, determine if the beam theory is
vindicated within the precision of the
instruments.
REFERENCES
[1] Beckwith, T. G., Buck, N. L. and Marangoni, R. D.,
59. Mechanical Measurements, Addison-
Wesley.
[2] Popov, E.P. Mechanics of Materials, Prentice-Hall Inc.
[3] Thomas, G.B., and Finney R.L., Calculus and Analytical
Geometry, Addison-Wesley,
19
Experiment 3
The Beam
Ali Almoslim
EGME-306A
Mo-8:30a.m
ABSTRACT
The main objectives of this experiment are to determine
the stress, deflection, and the strain of a supported beam under
load. Also to experimentally verify the beam stress and flexure
formulas. The experiment was accomplished by using the
machine which applies a load to a supported beam and measure
the deflection and the strain of it. The moment of inertia was
0.0845 and deflection of 0.0083%.
TABLE OF CONTENTS
Abstract
Table of Contents
Introduction and Theory
Procedures
Summary of Important Results
60. Sample Calculations and Error Analysis
Discussion and Conclusion
References
Appendix
INTRODUCTION AND THEORY
Structural members are usually designed to carry tensile,
compressive, or transverse loads. A member which carries load
transversely to its length is called a beam. In this experiment, a
beam will be symmetrically loaded as shown in Fig. III-1(a),
where P is the applied load. Note that at any cross section of the
beam there will be a shear force V (Fig. III-1(b)) and moment M
(Fig. III-1c). Also, in the central part of the beam (between the
loads P/2) V is zero and M has its maximum constant value.
Notice the sign convention of a positive moment, M, causing a
negative (downward) deflection, y.
If in this part a small slice EFGH of the beam is imagined
to be cut out, as shown, then it is clear that the external applied
moment, M, must be balanced by internal forces (stresses) at the
sections (faces) EF and GH. For M applied as shown in Fig. III-
2(a), these forces would be compressive near the top, EG, and
tensile near the bottom, FH. Since the beam material is
considered elastic, these forces would deform the beam such
that the length EG would tend to become shorter, and FH would
tend to become longer. The first fundamental assumption of the
beam theory can be stated as follows:
“Sections, or cuts, which are plane (flat) before deformation,
remain plane after deformation.”
Thus, under this assumption, the parallel and plane section EF
and GH will deform into plane sections E’F’ and G’H’ which
will intersect at point O, as shown in Fig. III-2(b). Since E’F’
and G’H’ are no longer parallel, they can be thought of as being
sections of a circle at some radial distance from O. Convince
yourself of this by drawing a square on an eraser and observe its
shape when you bend the eraser. Since the forces near E’G’ are
61. compresiive, and those near F’H’ are tensile, there must be
some radial distance r where the forces are neither compressive
nor tensile, but zero. This axis, N-N, is called the neutral axis.
Notice that N-N is not assumed to lie in the center of the beam.
Consider an arc of distance +η, from the neutral axis, or
distance r + η from O (Fig. III-2(b)). At this radius, the length
of arc is l’=(r + η) Δθ. As shown in Fig. III-2(a), the length of
the arc was l before the deformation. This length is also equal to
rΔθ (because at N-N there are no forces to change the length).
Thus, the strain at distance +η from the neutral axis can be
found by:
(III-1)
In other words, the axial strain is proportional to the distance
from the neutral axis. It is remarked that this strain is positive,
because positive η was taken on the tensile side of N-N in Fig.
III- 2(b). Had η been taken in the opposite direction, then the
strain would have been negative, as appropriate for the
compressive side.
The second fundamental assumption is that Hooke’s Law
applies both in tension and compression with the same modulus
of Elasticity. Thus, from Eqs. (I-3) and (III-1),
(III-2)
If c is the maximum distance from the neutral axis (largest
positive or negative value of η), then
the maximum stress (compressive or tensile) is given by σm =
Ec/r, and Eq. (III-2) can also be written as
(III-3)
That is, the stress at a section EF or GH, due to applied moment
M, varies linearly from zero at
the neutral axis to some maximum value σm (positive or
negative) when η = c. To obtain the
beam stress formula, it remains to define where the neutral axis
is located, and to relate σm to M.
To locate the neutral axis, it is observed that the tensile and
62. compressive forces on a section are equal to the stress times a
differential element of area, as shown in Fig. III-2(c). For static
equilibrium, the sum (or integral) of all these internal forces
must be zero. That is,
where, the integrals are over the whole cross-sectional area.
Thus, it is seen that the neutral axis is located such that the first
moment of area about it is zero; that is, the neutral axis passes
through the centroid of the cross-sectional area. In Fig. III-2(c),
a rectangular area was used for illustration; however, any shape
of vertically symmetric cross-sectional area is valid for the area
integral.
In a similar fashion, the moment due to all the forces is the sum
(or integral) of the forces times their moment arms about the
neutral axis, and this must be equal to the external applied
moment.
Thus,
(III-4)
If I is defined as the second moment of area about the neutral
axis, commonly called the moment
of inertia,
(III-5)
then Eq. (III-4) can be written as:
(III-6)
where Z = I/c is the section modulus, which depends only on the
cross-sectional geometry of the beam. Equation (III-6) is the
beam stress equation which relates the maximum (compressive
or tensile) stress to the applied moment. Notice its similarity to
Equation (I-1), the stress equation for uniaxial tension. It is
understood, of course, that σm is the maximum bending stress at
a particular location, x, along the beam. In general, both σm and
M are functions of x, and are related by Eq. (III-6).
The remaining question about the beam concerns its degree of
63. deformation, or flexure. That is, how is the radius of curvature,
r, related to the moment M (or load P)? From calculus, it can be
shown that the curvature of a function y(x) is given by
Thus, if x is the distance along the beam, y will be the
deflection as indicated in Fig. III-1(a). For most beams of
practical interest, this deflection will be small, so that the slope
dy/dx will be very
small compared to 1. Hence, a very good approximation is
But, since σm = Ec/r = Mc/I, there results the differential
equation of the elastic curve:
(III-7)
To obtain the elastic curve of the beam, y(x), and the maximum
deflection, ym, it is necessary to integrate Eq. (III-7) using the
moment function M(x) in Fig. III-1(c). Thus, using M(x) = Px/2
for
0 ≤ x ≤ a and M(x) = Pa/2 for a ≤ x ≤ a + b, it is found that
and that the maximum deflection at x = a + b/2 is
(III-8)
In particular, for a = b = L/3,
(III-9)
PROCEDURES
This experiment will be applied on a 1018 steel beam
,which has E = 30x10*6 psi, using the MTS testing machine.
Because the beam is not perfectly symmetric we had to measure
the cross-sectional dimension carefully and the location of the
loading points. After that, we placed the beam in the testing
machine and aligned the 12-inch black marks on the beam with
roller supports of the lower fixture. We had to make sure the
beam is centered on the lower support with strain gauge facing
64. down. Then we went to the computer and entered the TestWork
4 software. When prompted, we had to make sure the name field
under login says “306A_Lab” then clicked OK to login then
under the Open Method dialog, we had to select“exp-3 4 Point
Flex Mod X” after that we had to select the Motor Reset button
right corner by clicking on it. We zeroed the load by right
clicking on the load cell icon and selecting zero channel. Then,
we had position the upper bending fixture over the beam using
the handset after enabling the handset by pressing the unlock
button, then slowly lowering the crosshead using the down
arrow until the fixture is touching the beam. After that, we used
the thumb wheel of the handset to lower the fixture onto the
beam. We watched for the load reading increase when the upper
fixture makes contact. Then, we slowly lifted the fixture until a
very slight preload of approximately 0.2 lb is applied. Then we
locked the handset. Then we connected the strain gauge wire to
the #1 strain channel of the grey DAQ box, data acquisition is
conducted by the LabVIEW software. We took the magnetic
base holding the dial indicator, and positioned it with the dial
indicator in the center of the beam on the bottom side. We made
sure the dial indicator is not touching the strain gauge, after that
we locked the MTS frame by activating the magnetic base then
zeroed the dial indicator. Next, we started the LabVIEW
software by double click the icon on the desktop, selecting
“Open” and double clicking “exp2&3-Strain Mod-15 LV7.1”
then we pressed the white arrow to start the strain gauge
acquisition then we zeroed the strain. After that we pressed the
green arrow on the TestWorks 4 GUI. We loaded the beam up to
1000 lb for each in 100 lb and recorded the data. After reaching
1000 lb we repeated the experiment after making sure it zeroed
out just to assure accuracy of our work.
SUMMARY OF IMPORTANT RESULTS
I
In graph I. we can notice that it’s a deflection vs load diagram
65. as titled. we have the theoretical values and the experimental
ones. As we can see from the graph the is a noticeable
difference between the two values as the two lines get different
slops.
II
As we can see we, graph II is about the strees vs load diagram,
where the load is the x-axis and the stress is the y-axis which is
represented in a straight line as shown.
SAMPLE CALCULATION AND ERROR ANALYSIS
To find the use the following equation:
Using the position points, calculate the neutral axis, but it is
important to remember that this value isn’t the maximum
neutral axis, which is what is needed. In that case, simply
66. subtract total distance by the calculated neutral axis.
The moment of Inertia is calculated by the following formula:
Manually determined moment of Inertia
To find the section modulus we use the formula:
Where I is the calculated moment of Inertia and c is the distance
from the neutral axis
To find the maximum bending stress we start with the following
equation:
Where,
P (maximum load) = 997.3 lb
a (distance away from reference) = 4 in
Providing the applied moment of,
Now the maximum bending stress can be found using Eq. (1)
The deflection is determined by the following formula:
Or
Now, Eq. (9) is used to find the deflection of the crossbeam
given the maximum pressure, moment of inertia, and distance
between loads on the beam. Using the previous maximum load,
initial length of 12 in, initial modulus elasticity and calculated
moment of Inertia, the maximum deflection comes out to be…
The Stress and Deflection percent error were calculated using
the results obtained by the load applied by the MTS machine
and the dial indicator and a thermometer.
Stress () % Error = x 100% = x 100% = 1.20%
Deflection % Error = x 100% = x 100% = .0083 %
Ai
Yi
Ay
D
AD^2
I
68. Error Analysis
Human error is a common one that could happen in any
experiments, in this example, human error might happened in
the setup of the equipment. Another possibility is that we didn’t
get the write readings. Also, the machine could be old and not
accurate enough. Last one is that the sample we tested might not
manufactured properly. So these reasons explain why we got
1.20% error for stress and 0.0083% for deflection.
DISCUSSION AND CONCLUSION
After finishing the experiment and calculating the data and
graph them,we figured out many features of the beam.
Whenever the load increases, the deflection and the stress
increase too. We can use the strain to find the theoretical stress
and we can use moment, moment of inertia, and the neutral axis
to find the experimental stress. And about the deflection, we
used the dial indicator to find it directly from the experiment
for the experimental and we used load, length, modulus of
elasticity, and the moment of inertia to find the theoretical data.
The graph clearly shows that the load and deflection and load
and stress have a directly proportional relationship.
REFRENCES
[1] CSUF EGME 306A Lab Manual.
Appendix
69. deflection(in)
Max Stress at B
0.0009
1225.223179
0.002
2450.446358
0.0033
3663.417306
0.0046
4888.640485
0.0059
6113.863664
0.0073
7351.339075
0.0086
8539.805559
0.0099
9814.037665
0.0103
11049.06263
0.0107
12217.92554
Distance of Neutral Axis
Moment of Inertia
Applied Moment
Modulus of Elasticity
0.5179
0.0845397
200
30000000
