Tuesday, December 31, 2019

Private Schools Vs Public Schools - 1723 Words

When people think of private schools they often think of a quality of education that cannot be found in a public school. Private school education is thought of to be so thorough and innovative that public vouchers are given to individuals just to attend. Many parents could rest easier at night if their kids could attend private school because for generations it has been drilled into the psyche of many that going to private school is a sure way to have a good future. In actuality however, private schools are not all they are cracked up to be. If more people knew the raw facts about private schools the adage that private school is more beneficial than public school would be considered null and void. Private schools underperform public schools academically, have a tendency to be less diverse, and are autonomous. One thing parents do before they enroll their child into a private school is look through all the school’s information to see if their child will fit into the demographic which eventually will cause a lack of diversity. The lack of diversity in private schools is not good. Attending a school without a diverse body of students does not prepare a child for life and adulthood in a diverse society. In the real world no one can choose the composition of the people that live in their society, so putting a child in a school where the demographics are carefully chosen is pointless because school is suppose to prepare children for adulthood. When discussing diversity ofShow MoreRelatedPrivate Schools Vs. Public Schools1406 Words   |  6 Pagesthat private school is more expensive than public school, but has it ever occurred to you why it is like this? Private schools are not just trying to take your money, they are just trying to provide a quality education, without the government funding that public schools get. The tuition money goes to very important things; high quality teachers, better resources and the overall quality and stability of the institutio n. It is true that private school tuition is expensive, but private schools haveRead MorePrivate Schools Vs Public Schools1428 Words   |  6 Pagesstudy in private schools, which almost represents the fifth of students in Saudi Arabia. Although a lot of families prefer to make their children study in private school, that does not mean they are completely satisfied about the schools’ quality and their children’ achievement (Al-Hagbani, 2013). Nevertheless, they still enroll their children in private schools, believing they will benefit more from studying in private schools than public schools. In addition, some parents believe that private schoolsRead MorePrivate Schools Vs Public Schools1207 Words   |  5 PagesAn Introduction of the Topic Private schools differ from public schools for many different reasons. The major difference is that the government, unlike private schools that are privately funded, funds public schools. Another difference would be that the private schools have more flexibility on what they can teach because the government does not fund them. One other difference that is very prevalent is the social goals of schooling. This topic is a very important issue that many parents struggle withRead MorePrivate Schools Vs. Public Schools998 Words   |  4 Pagesnation. People today might say that private schools are superior to public schools, saying that they are safer and a better environment to learn in. Some might say that a private school is a way of sheltering your child and not letting them experience opportunities and face many problems to learn from. There are many positives and negatives to both sides; it mainly depends on whom you are talking to. Some parents might want their child to go to a pri vate school because the class size is smaller andRead MorePublic Schools vs. Private Schools1027 Words   |  4 Pagesare things to consider before choosing to send your child to a public school or private school. Perhaps doing so would be much easier if you would take the time to research the differences between the two. Public schools are better than private schools because of the diversity, funding and extracurricular activities available. Eileen Gale Kugler, a national advocate for diverse schools, wrote an article about how the diversity in schools makes academic and social improvements. She recalls a memoryRead More Private Schools vs. Public Schools870 Words   |  4 PagesChoosing between a public or a private school for one’s education is as important as deciding where to invest one’s hard-earned money—the consequences influence one’s life forever. In the United States, it is the law for every child to be educated. However, the decision as to where to go for one’s education is up to each individual. There is a great deal of debate as to which is the better option: for-profit private schools or one’s local public school. Ultimately, the decision is made regardingRead MorePrivate Schools vs. Public Schools 1081 Words   |  5 PagesHave you ever attended a private institution? What was your experience like? Think back and compare it to your ideal public school, which on e happens to pale in comparison? Public schools, which are controlled by the government, and heavily influenced, by politicians and privateers, hurt your children, not allowing them to reap the full benefits of their growing mind. â€Å"Our schools have been scientifically designed to prevent over-education from happening. The average American [should be] contentRead MorePrivate School Vs. Public School1254 Words   |  6 PagesThesis: Private school students are more likely to have a better viewpoint in learning, a firm stance in education, and will be more successful in colleges than of public school students. I. Introduction A. Attention Getter: According to NCES data, 88 percent of private high school students apply to college, compared to 57 percent of public high school students. Every day parents contemplate whether to send their children to private or public school. There are many dangers that come with public schoolRead MorePrivate Schools Vs Public Schools921 Words   |  4 Pageschild’s education, parents want the best the school has to offer their children. Parents want a prosperous future for their child which is not only health, but a well-educated one. Education is of the utmost importance especially because it will impact the child the most in the long run. Private schools offer ample education opportunities. There are some factors to consider when choose a private school education over a public one. Many times, the private schools are religious are having certain beliefsRead MorePublic Schools Vs. Private Schools1638 Words   |  7 Pageshaving children many parents question which school system is better suited for their kids and which aspect is more important, convenience or quality education? Some people believe the public schools provide the same education but at a lower cost. Tooley, Dixon, and Gomathi state â€Å"many assume that private education is concerned only with serving the privileged, so is irrelevant to concerns about extending access to the poor.† Although there are some private schools that are expensive, most are affordable

Monday, December 23, 2019

Learning From Mistakes The Pact and The Gridiron Gang Essay

It is human nature for everybody to make mistakes. Some mistakes are as little as a typo that can simply be whited out and corrected. Some as big as infidelity in a relationship. Some mistakes are easily forgiven and others not so much. But there is one thing for sure, if mistakes are never made, a person will never know their true purpose in life. Now of course most mistakes you will have to pay for but, every great person has made some sort of mistake to get them where they are now. Every mistake in life is a lesson that contributes to making people successful. The Pact is about three young men (Sampson Davis, George Jenkins and Rameck Hunt) growing up on the streets of Newark, New Jersey around the 1980’s and follows them up until†¦show more content†¦After being straight defiant, he picked the slab up and it immediately dropped on his foot, breaking every bone is his foot. As he sat in the hospital room, looking at the x-rays of his bones, he began to ask the doc tor all kinds of questions about the formation of the bones and the ways they could be broken and so on. It was there with his broken foot that he realized that he wanted to be a doctor, and from that moment on he lived his life chasing the dream of being a doctor. Had he never dropped the slab and not listened to his brother, he would not have realized his life dream The Movie The Gridiron Gang is about a group of Compton teenage boys, who have all been convicted of felonious crimes. The crimes range from murder, to drug dealing, to armed robbery and everything in between. All of the boys have been sent to Kilpatrick Detention Center, Where Sean Porter and Malcolm Moore are the overseers. Sean is a former football star, so he believes that bringing a football team to the detention center will teach the boys some unity and discipline. Mr. Porter’s supervisors are very reluctant to let the program be started because after all, they are a group of convicts. After a while of begging, Sean is allowed to start the football team. At first many of the boys are reluctant to play. Most of them are from rival gangs and rival neighborhoods and refuse to be on the

Sunday, December 15, 2019

The Twilight Saga 4 Breaking Dawn 31. Talented Free Essays

string(77) " product of good preparation – focus and attitude,he’d declared\." â€Å"What is the werewolves’ part in this?† Tanya asked then, eyeing Jacob. Jacob spoke before Edward could answer. â€Å"If the Volturi won’t stop to listen about Nessie, I mean Renesmee,† he corrected himself, remembering that Tanya would not understand his stupid nickname, â€Å"we will stop them. We will write a custom essay sample on The Twilight Saga 4: Breaking Dawn 31. Talented or any similar topic only for you Order Now † â€Å"Very brave, child, but that would be impossible for more experienced fighters than you are.† â€Å"You don’t know what we can do.† Tanya shrugged. â€Å"It is your own life, certainly, to spend as you choose.† Jacob’s eyes flickered to Renesmee – still in Carmen’s arms with Kate hovering over them – and it was easy to read the longing in them. â€Å"She is special, that little one,† Tanya mused. â€Å"Hard to resist.† â€Å"A very talented family,† Eleazar murmured as he paced. His tempo was increasing; he flashed from the door to Carmen and back again every second. â€Å"A mind reader for a father, a shield for a mother, and then whatever magic this extraordinary child has bewitched us with. I wonder if there is a name for what she does, or if it is the norm for a vampire hybrid. As if such a thing could ever be considered normal! A vampire hybrid, indeed!† â€Å"Excuse me,† Edward said in a stunned voice. He reached out and caught Eleazar’s shoulder as he was about to turn again for the door. â€Å"What did you just call my wife?† Eleazar looked at Edward curiously, his manic pacing forgotten for the moment. â€Å"A shield, I think. She’s blocking me now, so I can’t be sure.† I stared at Eleazar, my brows furrowing in confusion. Shield? What did he mean about my blocking him? I was standing right here beside him, not defensive in any way. â€Å"A shield?† Edward repeated, bewildered. â€Å"Come now, Edward! If I can’t get a read on her, I doubt you can, either. Can you hear her thoughts right now?† Eleazar asked. â€Å"No,† Edward murmured. â€Å"But I’ve never been able to do that. Even when she was human.† â€Å"Never?† Eleazar blinked. â€Å"Interesting. That would indicate a rather powerful latent talent, if it was manifesting so clearly even before the transformation. I can’t feel a way through her shield to get a sense of it at all. Yet she must be raw still – she’s only a few months old.† The look he gave Edward now was almost exasperated. â€Å"And apparently completely unaware of what she’s doing. Totally unconscious. Ironic. Aro sent me all over the world searching for such anomalies, and you simply stumble across it by accident and don’t even realize what you have.† Eleazar shook his head in disbelief. I frowned. â€Å"What are you talking about? How can I be a shield? What does that even mean?† All I could picture in my head was a ridiculous medieval suit of armor. Eleazar leaned his head to one side as he examined me. â€Å"I suppose we were overly formal about it in the guard. In truth, categorizing talents is a subjective, haphazard business; every talent is unique, never exactly the same thing twice. But you, Bella, are fairly easy to classify. Talents that are purely defensive, that protect some aspect of the bearer, are always called shields. Have you ever tested your abilities? Blocked anyone besides me and your mate?† It took me few seconds, despite how quickly my new brain worked, to organize my answer. â€Å"It only works with certain things,† I told him. â€Å"My head is sort of†¦ private. But it doesn’t stop Jasper from being able to mess with my mood or Alice from seeing my future.† â€Å"Purely a mental defense.† Eleazar nodded to himself. â€Å"Limited, but strong.† â€Å"Aro couldn’t hear her,† Edward interjected. â€Å"Though she was human when they met.† Eleazar’s eyes widened. â€Å"Jane tried to hurt me, but she couldn’t,† I said. â€Å"Edward thinks Demetri can’t find me, and that Alec can’t bother me, either. Is that good?† Eleazar, still gaping, nodded. â€Å"Quite.† â€Å"A shield!† Edward said, deep satisfaction saturating his tone. â€Å"I never thought of it that way. The only one I’ve ever met before was Renata, and what she did was so different.† Eleazar had recovered slightly. â€Å"Yes, no talent ever manifests in precisely the same way, because no one ever thinks in exactly the same way.† â€Å"Who’s Renata? What does she do?† I asked. Renesmee was interested, too, leaning away from Carmen so that she could see around Kate. â€Å"Renata is Aro’s personal bodyguard,† Eleazar told me. â€Å"A very practical kind of shield, and a very strong one.† I vaguely remembered a small crowd of vampires hovering close to Aro in his macabre tower, some male, some female. I couldn’t remember the women’s faces in the uncomfortable, terrifying memory. One must have been Renata. â€Å"I wonder†¦,† Eleazar mused. â€Å"You see, Renata is a powerful shield against a physical attack. If someone approaches her – or Aro, as she is always close beside him in a hostile situation – they find themselves†¦ diverted. There’s a force around her that repels, though it’s almost unnoticeable. You simply find yourself going a different direction than you planned, with a confused memory as to why you wanted to go that other way in the first place. She can project her shield several meters out from herself. She also protects Caius and Marcus, too, when they have a need, but Aro is her priority. â€Å"What she does isn’t actually physical, though. Like the vast majority of our gifts, it takes place inside the mind. If she tried to keep you back, I wonder who would win?† He shook his head. â€Å"I’ve never heard of Aro’s or Jane’s gifts being thwarted.† â€Å"Momma, you’re special,† Renesmee told me without any surprise, like she was commenting on the color of my clothes. I felt disoriented. Didn’t I already know my gift? I had my super-self-control that had allowed me to skip right over the horrifying newborn year. Vampires only had one extra ability at most, right? Or had Edward been correct in the beginning? Before Carlisle had suggested that my self-control could be something beyond the natural, Edward had thought my restraint was just a product of good preparation – focus and attitude,he’d declared. You read "The Twilight Saga 4: Breaking Dawn 31. Talented" in category "Essay examples" Which one had been right? Was there more I could do? A name and a category for what I was? â€Å"Can you project?† Kate asked interestedly. â€Å"Project?† I asked. â€Å"Push it out from yourself,† Kate explained. â€Å"Shield someone besides yourself.† â€Å"I don’t know. I’ve never tried. I didn’t know I should do that.† â€Å"Oh, you might not be able to,† Kate said quickly. â€Å"Heavens knows I’ve been working on it for centuries and the best I can do is run a current over my skin.† I stared at her, mystified. â€Å"Kate’s got an offensive skill,† Edward said. â€Å"Sort of like Jane.† I flinched away from Kate automatically, and she laughed. â€Å"I’m not sadistic about it,† she assured me. â€Å"It’s just something that comes in handy during a fight.† Kate’s words were sinking in, beginning to make connections in my mind. Shield someone besides yourself she’d said. As if there were some way for me to include another person in my strange, quirky silent head. I remembered Edward cringing on the ancient stones of the Volturi castle turret. Though this was a human memory, it was sharper, more painful than most of the others – like it had been branded into the tissues of my brain. What if I could stop that from happening ever again? What if I could protect him? Protect Renesmee? What if there was even the faintest glimmer of a possibility that I could shield them, too? â€Å"You have to teach me what to do!† I insisted, unthinkingly grabbing Kate’s arm. â€Å"You have to show me how!† Kate winced at my grip. â€Å"Maybe – if you stop trying to crush my radius.† â€Å"Oops! Sorry!† â€Å"You’re shielding, all right,† Kate said. â€Å"That move should have about shocked your arm off. You didn’t feel anything just now?† â€Å"That wasn’t really necessary, Kate. She didn’t mean any harm,† Edward muttered under his breath. Neither of us paid attention to him. â€Å"No, I didn’t feel anything. Were you doing your electric current thing?† â€Å"I was. Hmm. I’ve never met anyone who couldn’t feel it, immortal or otherwise.† â€Å"You said you project it? On your skin?† Kate nodded. â€Å"It used to be just in my palms. Kind of like Aro.† â€Å"Or Renesmee,† Edward interjected. â€Å"But after a lot of practice, I can radiate the current all over my body. It’s a good defense. Anyone who tries to touch me drops like a human that’s been Tasered. It only downs him for a second, but that’s long enough.† I was only half-listening to Kate, my thoughts racing around the idea that I might be able to protect my little family if I could just learn fast enough. I wished fervently that I might be good at this projecting thing, too, like I was somehow mysteriously good at all the other aspects of being a vampire. My human life had not prepared me for things that came naturally, and I couldn’t make myself trust this aptitude to last. It felt like I had never wanted anything so badly before this; to be able to protect what I loved. Because I was so preoccupied, I didn’t notice the silent exchange going on between Edward and Eleazar until it became a spoken conversation. â€Å"Can you think of even one exception, though?† Edward asked. I looked over to make sense of his comment and realized that everyone else was already staring at the two men. They were leaning toward each other intently, Edward’s expression tight with suspicion, Eleazar’s unhappy and reluctant. â€Å"I don’t want to think of them that way,† Eleazar said through his teeth. I was surprised at the sudden change in the atmosphere. â€Å"If you’re right – ,† Eleazar began again. Edward cut him off. â€Å"The thought was yours, not mine.† â€Å"If I’m right†¦ I can’t even grasp what that would mean. It would change everything about the world we’ve created. It would change the meaning of my life. What I have been a part of.† â€Å"Your intentions were always the best, Eleazar.† â€Å"Would that even matter? What have I done? How many lives †¦Ã¢â‚¬  Tanya put her hand on Eleazar’s shoulder in a comforting gesture. â€Å"What did we miss, my friend? I want to know so that I can argue with these thoughts. You’ve never done anything worth castigating yourself this way.† â€Å"Oh, haven’t I?† Eleazar muttered. Then he shrugged out from under her hand and began his pacing again, faster even than before. Tanya watched him for half a second and then focused on Edward. â€Å"Explain.† Edward nodded, his tense eyes following Eleazar as he spoke. â€Å"He was trying to understand why so many of the Volturi would come to punish us. It’s not the way they do things. Certainly, we are the biggest mature coven they’ve dealt with, but in the past other covens have joined to protect themselves, and they never presented much of a challenge despite their numbers. We are more closely bonded, and that’s a factor, but not a huge one. â€Å"He was remembering other times that covens have been punished, for one thing or the other, and a pattern occurred to him. It was a pattern that the rest of the guard would never have noticed, since Eleazar was the one passing the pertinent intelligence privately to Aro. A pattern that only repeated every other century or so.† â€Å"What was this pattern?† Carmen asked, watching Eleazar as Edward was. â€Å"Aro does not often personally attend a punishing expedition,† Edward said. â€Å"But in the past, when Aro wanted something in particular, it was never long before evidence turned up proving that this coven or that coven had committed some unpardonable crime. The ancients would decide to go along to watch the guard administer justice. And then, once the coven was all but destroyed, Aro would grant a pardon to one member whose thoughts, he would claim, were particularly repentant. Always, it would turn out that this vampire had the gift Aro had admired. Always, this person was given a place with the guard. The gifted vampire was won over quickly, always so grateful for the honor. There were no exceptions.† â€Å"It must be a heady thing to be chosen,† Kate suggested. â€Å"Ha!† Eleazar snarled, still in motion. â€Å"There is one among the guard,† Edward said, explaining Eleazar’s angry reaction. â€Å"Her name is Chelsea. She has influence over the emotional ties between people. She can both loosen and secure these ties. She could make someone feel bonded to the Volturi, to want to belong, to want to please them___† Eleazar came to an abrupt halt. â€Å"We all understood why Chelsea was important. In a fight, if we could separate allegiances between allied covens, we could defeat them that much more easily. If we could distance the innocent members of a coven emotionally from the guilty, justice could be done without unnecessary brutality – the guilty could be punished without interference, and the innocent could be spared. Otherwise, it was impossible to keep the coven from fighting as a whole. So Chelsea would break the ties that bound them together. It seemed a great kindness to me, evidence of Aro’s mercy. I did suspect that Chelsea kept our own band more tightly knit, but that, too, was a good thing. It made us more effective. It helped us coexist more easily.† This clarified old memories for me. It had not made sense to me before how the guard obeyed their masters so gladly, with almost lover-like devotion. â€Å"How strong is her gift?† Tanya asked with an edge to her voice. Her gaze quickly touched on each member of her family. Eleazar shrugged. â€Å"I was able to leave with Carmen.† And then he shook his head. â€Å"But anything weaker than the bond between partners is in danger. In a normal coven, at least. Those are weaker bonds than those in our family, though. Abstaining from human blood makes us more civilized – lets us form true bonds of love. I doubt she could turn our allegiances, Tanya.† Tanya nodded, seeming reassured, while Eleazar continued with his analysis. â€Å"I could only think that the reason Aro had decided to come himself, to bring so many with him, is because his goal is not punishment but acquisition,† Eleazar said. â€Å"He needs to be there to control the situation. But he needs the entire guard for protection from such a large, gifted coven. On the other hand, that leaves the other ancients unprotected in Volterra. Too risky – someone might try to take advantage. So they all come together. How else could he be sure to preserve the gifts that he wants? He must want them very badly,† Eleazar mused. Edward’s voice was low as a breath. â€Å"From what I saw of his thoughts last spring, Aro’s never wanted anything more than he wants Alice.† I felt my mouth fall open, remembering the nightmarish pictures I had imagined long ago: Edward and Alice in black cloaks with bloodred eyes, their faces cold and remote as they stood close as shadows, Aro’s hands on theirs†¦. Had Alice seen this more recently? Had she seen Chelsea trying to strip away her love for us, to bind her to Aro and Caius and Marcus? â€Å"Is that why Alice left?† I asked, my voice breaking on her name. Edward put his hand against my cheek. â€Å"I think it must be. To keep Aro from gaining the thing he wants most of all. To keep her power out of his hands.† I heard Tanya and Kate murmuring in disturbed voices and remembered that they hadn’t known about Alice. â€Å"He wants you, too,† I whispered. Edward shrugged, his face suddenly a little too composed. â€Å"Not nearly as much. I can’t really give him anything more than he already has. And of course that’s dependent on his finding a way to force me to do his will. He knows me, and he knows how unlikely that is.† He raised one eyebrow sardonically. Eleazar frowned at Edward’s nonchalance. â€Å"He also knows your weaknesses,† Eleazar pointed out, and then he looked at me. â€Å"It’s nothing we need to discuss now,† Edward said quickly. Eleazar ignored the hint and continued. â€Å"He probably wants your mate, too, regardless. He must have been intrigued by a talent that could defy him in its human incarnation.† Edward was uncomfortable with this topic. I didn’t like it, either. If Aro wanted me to do something – anything – all he had to do was threaten Edward and I would comply. And vice versa. Was death the lesser concern? Was it really capture we should fear? Edward changed the subject. â€Å"I think the Volturi were waiting for this – for some pretext. They couldn’t know what form their excuse would come in, but the plan was already in place for when it did come. That’s why Alice saw their decision before Irina triggered it. The decision was already made, just waiting for the pretense of a justification.† â€Å"If the Volturi are abusing the trust all immortals have placed in them†¦,† Carmen murmured. â€Å"Does it matter?† Eleazar asked. â€Å"Who would believe it? And even if others could be convinced that the Volturi are exploiting their power, how would it make any difference? No one can stand against them.† â€Å"Though some of us are apparently insane enough to try,† Kate muttered. Edward shook his head. â€Å"You’re only here to witness, Kate. Whatever Aro’s goal, I don’t think he’s ready to tarnish the Volturi’s reputation for it. If we can take away his argument against us, he’ll be forced to leave us in peace.† â€Å"Of course,† Tanya murmured. No one looked convinced. For a few long minutes, nobody said anything. Then Iheard the sound of tires turning off the highway pavement onto the Cullens’ dirt drive. â€Å"Oh crap, Charlie,† I muttered. â€Å"Maybe the Denalis could hang out upstairs until – â€Å" â€Å"No,† Edward said in a distant voice. His eyes were far away, staring blankly at the door. â€Å"It’s not your father.† His gaze focused on me. â€Å"Alice sent Peter and Charlotte, afterall. Time to get ready for the next round.† How to cite The Twilight Saga 4: Breaking Dawn 31. Talented, Essay examples

Saturday, December 7, 2019

Beam Deflection free essay sample

The purpose of this lab is to determine the flexural elastic modulus of a Parallam woodcomposite beam by examining its behavior when simply supported and under flexural stress, and to analyze deflection data using different least-squares methods to fit theoretical deflection curves. Theory: In theory, a beam’s deflection can be mapped by the governing equation of beam flexure: EI d2y/dx2 = M(x), where E is the elastic modulus, I is the second moment of inertia about the neutral axis of the beam (the value of which changes significantly according to orientation), y is deflection, and M(x) is bending moment in the beam. This equation requires that several assumptions be made about the beam: 1) Geometric Assumption: the beam must be a straight, prismatic member with at least one axis of symmetry. 2) Material assumption: the beam must be linear, elastic, isotropic, and homogeneous, and the modulus of elasticity in tension must equal the modulus of elasticity in compression. 3) Loading Assumption: the beam must be loaded in pure moment in a plane of symmetry. 2 4) Deformation Assumption: plane sections before bending must remain in plane after bending. Making these assumptions, we can apply the general equation for beam flexure to our experiment. Assuming we are using point loads or can model our setup with point loads, we can then use singularity functions to determine that the bending moment of the beam is: 2/3 P*x – P 1 Where P is the load applied with the UTM, L is the length of the beam, and x is the distance from the origin (defined as the end closest to the applied load). From this we get: M(x) = EI d2y/dx2 = 2/3 P*x – P 1 Taking an integral of both sides with respect to x yields: where c1 is a constant. Taking another derivative yields: where c2 is a constant. Rearranging we get: . EI dy/dx = P/3 * x2 – P/2 * 2 +c1 y * EI = P/9 * x3 – P/6 * 3 +c1x + c2 y = Px3/9EI – P/6EI * 3 +c1x/EI + c2/EI To solve for the constants we need to make two more assumptions: that when x=0 and when x=L there will be no deflection (i. e. y=0). Using these assumptions, we can plug into our previous equation and use algebra to determine that c1 = -5PL2/81 and that c2 = 0. This gives us: 3 y = P/EI (x3/9 3 /6 – 5L2x/81) This is the theoretical beam deflection equation for the lab. Then, to ease calculations, we make the previous equation non-dimensional by multiplying both sides by EI/PL3, which yields: yEI/PL3 = (x/L)3/9 3/6 – 5/81 (x/L) We define this dimensionless quantity as: (x/L)3/9 3/6 – 5/81 (x/L) = ! theoretical where: ! theoretical = f(x/L) Similarly, we define: ymeasured * EI/PL3 = ! measured. If the beam were to behave as a theoretical beam, then ! theoretical would equal ! measured. E is defined as the slope of the stress-strain curve in the elastic region. However, there is no perfect way to measure stress and strain in the loaded beam. As a result, to determine E one must make some assumptions. For methods one and two the assumption made is that ! theoretical = ! measured. This is done because ! measured can only be calculated if the value of E is known (if E is unknown, then the equation ymeasured * EI/PL3 = ! measured has two unknowns and is thus unsolvable). For method one this assumption is used to write this equation: f(x/L) = E (I ymeasured/PL3). Manipulating this equation gives an equation in the form: P = E (I ymeasured/f(x/L)L3) 4 This equation is in the form of y=mx, the form of a line. Thus, if it is plotted P versus (I ymeasured/f(x/L)L3) then the slope of the line will be E. In method two, the same assumption is made, resulting in the formula: E = f(x/L)PL3/ ymeasuredI From this formula E can be calculated on a point by point basis and then the values can be averaged. Method three approaches the problem in a different way. Instead of assuming that ! theoretical = ! measured, a new quantity V was defined as: V = ! theoretical ! measured Then we make a guess for the E value and solve for the rms error, defined as: rms = sqr(1/n * sum(V2)) here V represents the difference between theoretical and measured deflection for every data point at a certain E value, and n is the total number of V values (5 loads * 4 locations = n = 20). The rms error is then plotted against the many guessed E values, and the point on the graph where the rms error is minimized is determined to best the best value of E for method three. 5 Procedure: In the lab, we tested a simply supported Pa rallam beam (nominal dimensions: 4 by 10) in two orientations while loaded in flexural stress from the UTM (setup shown in figure 1). The beam’s dimensions were 100 inches span by 3. 50 inches thick by 9. 46 inches deep. Our two orientations were with the 9. 46 inch side vertical (the ‘upright’ orientation) and then with the 9. 46 inch side horizontal (the ‘flat’ orientation). For each orientation, we applied an approximate point load by placing a roller between the UTM and the beam at the point L/3 on the span. (In fact, as the roller comes into contact with a small area of the beam and not a single point, 6 describing it as a ‘point load’ is not quite accurate. We applied the load in five increments: 240, 480, 720, 960, and 1200 psi. At each of the load increments, we measured deflection at three points: L/4, L/2, and 3L/4 (the UTM recorded deflection at L/3). We also observed the deflection and the location of maximum deflection, and calculated values of I (the second moment of inertia) for each orientation. Outside of lab, we used three methods to determine E. As di scussed in the theory, method one consisted of plotting the load P (lb) versus the quantity Iymeasured/f(x/L)L3 (in2). The slope of this graph was the first value for E. Both Matlab and KaleidaGraph were used in this process. Utilizing the same theory as method one, method two used the equation E = f(x/L)PL3/ Iymeasured to solve for E for each individual point with each load. The resulting values of E were then averaged to determine the best value of E for method two. The average was found using Matlab and the error using KaleidaGraph. Method three (also as discussed in the theory section) plots rms error against many guessed E values. The best value of E (for method three) was found by determining where the rms error was minimized. This process was done entirely in Matlab. 7 Results: E: Upright Orientation Units Method One Method Two Method Three E: Flat Orientation 10 ksi 103 ksi 3 0. 981 Â ± 0. 100 1. 253 Â ± 0. 198 1. 065 Â ± 0. 247 1. 880 Â ± 0. 046 2. 080 Â ± 0. 083 1. 881 Â ± 0. 106 Discussion: The values of E that we determined for each orientation were very close in value. The values for the upright beam all fall within error of each other, while for the flat orientation one value (while still very close) was just outside of the error of the other two, which are nearly identical. Error in our values comes partially from universal measurement error, and from flaws and inconsistencies in the beam (i. e. , a non-isotropic and non-homogeneous beam); these types of error have a global influence on our results. Other major sources of error are method-specific. In method one, there is error from fitting a line to a set of data that is not precisely linear. As a result, we took our method one values from Kaleidagraph, which is more specifically graphing software and which provides a curve fitting error. We also used Matlab values as a check of accuracy. In method two, error came from the variance in the E value of each data point. For this method, we used Kaleidagraph simply to determine error (having calculated the values in 8 Matlab), taking the standard deviation as representative of the variance. In method three, error comes from the lack of a perfect fit of a deflection graph to our data; our E value minimized the error between predicted and actual deflection, which was then represented as rms error. In all of the methods, we weighted each data point equally (this will be discussed more thoroughly later in this section). Interesting to note is the difference in the value of E for each orientation. This is partially a result of the composition of the beam, as, upon inspection, the grain of the wood is pronouncedly evident (see Appendix F). We expect the material that the beam is composed of to behave more rigidly when loaded to parallel the grain (in the upright position), and to bend more easily when loaded perpendicular to the grain (in the flat position). The grain of the wood is largely the result of the beam’s construction, as it is fabricated from strips of wood bound with glue and pressed until formed: this method of construction results in a major difference in stiffness, according to orientation. However, although the material does perform more rigidly according to grain orientation, the difference in the value of I made a more significant impact on our final values of E and, thus, the beam behaved more rigidly in the flat orientation, where the I value was significantly smaller. Another point of interest was the location-specific variation in E: upon examination of the graph for method one (in appendix B), this variation becomes apparent. The data points 9 collected at L/4 and 3L/4 are the two points closest to the left at each load; the slope of the line formed by connecting these points is steeper than the rest, which means that the resulting E value is higher. The data points from L/3 appear at the far right at each level of load, and when connected have a lower slope and therefore smaller E value. The data points from L/2 are in the middle, and have a slightly less steep slope than at L/4 and 3L/4, and thus a slightly smaller E value. It should be noted that the E value that differed most from the other values is the E value at L/3, which was the value determined in part by the deflection measured by the UTM. The difference in measuring methods may be the cause of this. It is possible, for instance, that the UTM measurements include deflection from the compression of the beam itself where the load was applied, or alternately that the measurements from the UTM were more accurate than those we found by manually reading gauges.