How do you as a modern reader, respond to Austen’s presentation of Mr. Knightley’s guidance of Emma in the novel as a whole?

After the episode at Box Hill, Mr. Knightley says to Emma, ‘I must once more speak to you as I have been used to do: a privilege rather endured than allowed, perhaps, but I must still use it.' How do you as a modern reader, respond to Austen's presentation of Mr. Knightley's guidance of Emma in the novel as a whole? It can be said that Emma is a novel which is based on morals and manners. In the society, and the people in which Jane Austen deals with, we see the high expectations, the pride and mainly good use of manners in their community. George Knightley is considered to be a well mannered and respectable man, and we are shown good reasons to believe so, on many occasions. He is thought of as a ‘good-catch', being rich with ‘old money', and having very high status, but does not show any signs of snobbery to or against another person. In addition, Mr Knightley has many good qualities, and we can see how fond Austen is of her ‘faultless' character. We see him in many circumstances, (mostly) being calm, polite and sharp, never succumbing to rudeness. He is always pleasant and friendly towards Miss Bates, which shows the reader a very gentle side to him, even though many other characters get agitated with her rather easily. Austen also helps us understand how courteous and patient he is, whilst dealing with Mr. Woodhouse. He is a very annoying, infuriating man so by showing Mr. Knightley to be friendly and tolerant with him, helps us see what truly great qualities this man has. When speaking to Emma, we understand how much he cares for her, though sometimes he may seem quite abrupt. Nevertheless, throughout the novel we see Emma's countless faults. She seems to be inexperienced at the start of the novel, which can be said to ‘justify' her childish behaviour. Though it appears that she does not know a lot about life in general, acting spoilt and immature; we are soon shown of her sharp, intelligent and kind self, which makes the reader realise of her desperate need of help. She is lacking parental support greatly, and quite seriously; it is clear to us that she has never had a mother figure to look up to, only ever having Miss Taylor her governess, which seems more like friendship than mother-daughter. Her father does not realise of her need of love and support, and therefore continues to act like a selfish child who needs a great deal of care, consequently ending up with Emma caring and concerning for her father and not concentrating on her own needs. Although we see of her and her sister's closeness, Isabella has her own life and is away from their estate for most of the year. As a result Mr Knightley shows to be the only one capable and willing around her, to help her through and towards her development. As Mr. Knightley acts as Emma's ‘mentor' throughout the novel, we see on many occasions, him upsetting her with the truth, them in conflict, and a lot of realisation about oneself. When she boasts of her persuading Harriet to decline Robert Martin's marriage proposal, as she is certain of Mr. Elton's love for Harriet, we see Mr. Knightley fuming with rage at her, as she does not realise the consequences of her actions, and the damage she will cause for the people involved. She is stubborn with George Knightley, and only when Mr. Elton proposes to her, does she realise the reality in what she has done and the truth in what he has said. The situation is then followed by her self-searching, and reflecting on her actions, admitting she is wrong to only herself, soon forgetting of her wrong doings. Following the incident at Box Hill, it is the first time that we see Emma break down in the novel. Mr. Knightley is very angry with Emma, but does raise his voice, simply explains their situation of how people perceive them, clarifying the importance of them setting a good example. Possibly the reason for her humiliation, is the fact that she did not realise how hurtful she was to Miss Bates, and never once took into consideration of her position in the society. By explaining how their circle of friends look up to both her and Mr. Knightley, Emma for the first time in the novel realises her situation as a woman, a mentor, and a friend. Once releasing her true, sad feelings, Mr. Knightley acts kind and careing towards her, and she accepts her mistakes, and is prepared to apologise to Miss Bates as well as being friendly and patient with her from then on. This can be seen as a self-analysis, which truly shows her willingness to develop. Even as a modern reader, it seems that Austen is simply showing two peoples love for each other, in which they both work hard to persist. Mr. Knightley cares a great deal for Emma, and we can see that all his stern and honest ways in which he has dealt with her throughout the novel, have all been on the grounds of his love for her, as a friend, a companion and a man. He is sensible and truthful during the narrative, which is how Austen gains our trust for him. He has helped her comprehend many difficult situations on many occasions, but she has also helped him to maybe not be so serious and untrusting. And it seems as though Emma realises this near the ending of the novel, whilst discussing the situation of herself and Mr. Knightley, and the situation of Frank and Jane, to Frank Churchill himself. Though at times Mr. Knightley has maybe seemed harsh and cold towards Emma, it has made her improve and mature in character greatly, ending with her fine development.

Cubism as a Modern Movement

Midterm Essay Exam Analytical & Synthetic Cubism and Modern Art Analytical Cubism, invented by Pablo Picasso and Georges Baroque, is the artistic style of creating shapes and details that represent an object or person. Braque's Violin and Palette (Figure 1 below) is a great example of Analytical Cubism. Baroque took an object, the violin, and broke it down into a series of shapes that merely represent what a violin is from multiple points of view. â€Å"l no longer believe in anything. Objects don't exist for me except in so far as a rapport exists between them r between them and myself.When one attains this harmony, one reaches a sort of intellectual non-existence what I can only describe as a state of peace which makes everything possible and right. Life then becomes a perpetual revelation. That is true poetry,† Georges Baroque. Figure 1, Georges Braque's Violin and Palette Synthetic Cubism, also developed by Pablo Picasso and Georges Baroque, slowly got developed through an alytical cubism. They developed it by repeating analytic designs in their work thus generalizing the objects even more making them more metrically simple and flat.Collage was a huge part of the synthetic style, replacing painted objects with the actual object glues onto the canvas. Picasso Still Life with Chair Caning (Figure 2 below) is an excellent example of synthetic cubism. Synthetic cubism's use of art made by artists combined with art made by manufacturer and is often said to be the first Pop Art. â€Å"In Cubism, in the end what was important is what one wanted to do, the intention one had. And that one cannot paint,† Pablo Picasso. Figure 2, Picasso Still Life with Chair Caning Their are quite a few distinct differences between Analytical and Synthetic Cubism.The first and most relevant being the use of collage in synthetic but not in analytic cubism. For example instead of Picasso painting the chair caning into the painting of his Still Life with Chair Caning, he si mply attached it onto the the picture as if it belonged onto the canvas. Compare that to how Baroque made the violin in Violin and Palette, everything is painted onto the picture and is somewhat recognizable as the object from which it represents. Analytical Cubism still had an element of three dimensionality whereas Synthetic Cubism lost all sense of three dimensional space and was Just two dimensional and flat.Analytical Cubism also involved using muted colors so the focus was on composition and the change of perspective while Synthetic Cubism used bright colors as well as graphics, words, and other media. Synthetic Cubism also had much more distinct geometrical patterns and textures. Analytical Cubism paved the way modern art breaks traditional meaner of how things are represented. It abandons perspective and dispenses with realistic enduring of figures and objects and replaces that by making representational shapes in the composition. Background is blended into foreground.Synthe tic Cubism paved the way for Pop Art using other media based matter and integrating it into the composition. â€Å"Cubism paved the way for geometric abstract art by putting an entirely new emphasis on the unity between the depicted scene in a picture, and the surface of the canvas. Its innovations would be taken up by the likes of Piety Mandarin, who continued to explore its use of the grid, its abstract system of signs, and its shallow pace,† (Wolf). Cubism was the first step of modern art towards abstraction. Cubism focused on developing a way of viewing that reflected the modern age.Technological advances lead to the rise of this new style, with the invention of cars, planes, cameras, phones, sound recording and cinematography, artists needed a new way of conveying these objects and advances. Cubism directly influenced Futurism, Vortices, Supremacist, Constructivism, and Expressionism. Modern art's time period includes approximately from the sass's to the sass's, cubism t akes place in the early sass's so it falls into his time frame. Modern art is art that usually dissociates the traditional style of art and experimenting with new ways of seeing the world around them.Modern art moves away from the narrative and becomes more and more abstract. This clearly fits into the cubist movement the Picasso and Baroque created. The concept of Modern Art is based on the modern thought, character, and practice of Modernism. It developed from the rise of industries, rapid growth of city life, and first world war. Modernism reflects the rise of the changes in traditional thinking that were considered to be outdated, these include art, architecture, literature, religion, social structure, and daily life.This change in thinking resulted in the the gradual change to modern art and modernism. Both forms of cubism, analytical and synthetic, follow this practice. Seeing everyday life and life's objects and figures in a new way is what cubism is. Braque's violin in Violi n and Palette and Picasso Still Life with Chair Caning show this style of thought process. Braque's violin shows every view point and angle of a violin all at the same time, challenging the idea of traditional thinking.All of the above mentioned subjects reflect on how both analytical and synthetic cubism are a part of the modern movement and how the two are different from each other. They both challenge traditional thinking and art by changing the way the world is seen and what art can be. The differences between the two include execution, the use or disuse of collage, and the color schemes involved in both. Analytic cubism doesn't use collage techniques, has a muted color palette, and is more three dimensional. Synthetic cubism uses collage techniques, has more a more vibrant lour palette, and is very two dimensional.Both are a part of modernism and both heavily influenced many of the art movements that appeared later in the modern art era. â€Å"Cubism came about because, in the process of analyzing form, something that lay in the form, a plane, could be lifted out to float on its own†¦ † Joseph Plackets). Graphic Champs De Mars: La Tour Rouge. Robert Delaney Bibliography Baroque, Georges. Cubism Art Quotes. Picasso, Pablo. Cubism Art Quotes. Plackets, Joseph. Cubism Art Quotes. Wolf, Justine. 2012. The Art Story Foundation.

Philosophy Ethic - Nicomachean Ethics by Aristotle Essay

Philosophy Ethic - Nicomachean Ethics by Aristotle - Essay Example This goes so far as to pinpoint the own weaknesses of the number of proposals indicated within the text itself. But what it contains and what it reflects speak highly of the way we live. He purposely sought to eliminate highly imbued ideals which are rather unfeasible to one that is attainable. This reverberates through the ages which stills makes through what Aristotle said centuries ago to the way we live in this day and age. â€Å"What then is the good of each? Surely that for whose sake everything else is done. In Medicine this is health, in strategy victory, in architecture a house, in any other sphere something else, and in every action and pursuit the end; for it is for the sake of this that all men do whatever else they do. Therefore, if there is an end for all that we do, this will be the good achievable by action, and if there are more than one, this will be the goods achievable by action† (Aristotle, Nichomachean Ethics, I-1). This he expounds further upon by giving the two kinds of virtue, being intellectual and moral or simply ethics and habit including the modes by which they are acquired. This is the movement from potentiality to habit. Arguably, this discourse gives the hold of truth for which it was based upon logical value formation. It may not always be something that is easily perceived upon as a digested quality of human action but it is upon contemplation the very essence of th e fundamentals of our existence. Thus, the understanding of every action is set down as for the creation of happiness which is in contemplation with virtue formed by habit. Many conflicts arise from this as case to case scenarios would yield it true to it fullest extent. Let’s say for example that there is a boy, let’s call him John for consistency, who was raised to a family with close ties. That while growing up and to the present point he had

Department of Maritime and Logistics Management-Voyage Planning Essay

Department of Maritime and Logistics Management-Voyage Planning Assignment - Essay Example It is not specified whether or not the ship will be able to carry a cargo on its way to either Manila or Shanghai in order to take either of the two jobs available. Conventional logic dictates that whenever a ship makes an oceanic voyage, it is more efficient for the ship to contain a cargo rather than simply travel empty. If at all possible, any cargo vessel should attempt to carry cargo of some sort even if its ultimate objective is to arrive at a different port city to undertake a more valuable cargo. Without knowledge of whether or not the vessel can undertake a cargo on its way to either of the major ports, then this analysis will presume that there is no cargo known it to be available for this ship when it arrives in Hong Kong. Therefore, if a situation arises where the cargo vessel must travel empty then the links of an empty voyage should be minimized. Therefore, it is more logical in this instance to travel from Hong Kong to Manilla due to the simple fact that the distance t he ship will have to travel without a cargo will be minimized, as opposed to a trip from Hong Kong to Shanghai, a greater overall distance in nautical miles. Moreover, a shorter journey would enable the ship to undertake the paying job faster. What this analysis must determine is whether or not the expense and profit potential of option one would outweigh the benefits of option two in the long run. If there is a potential for greater profit at the end of the final voyage, it must be great enough to outweigh the potential for lost time and the expense of traveling to either destination without cargo. The amount of the respective cargoes the ship can hold must also be considered based upon the available price. For steel, each unit will be packaged as .91 m? per tonne as opposed to 1.20 for the timber. So for the same amount of weight, a greater volume of steel can be loaded onto the ship. In addition to the weight over volume difference between the two commodities, the price for steel is also higher. By calculating cubic meters, it has been found that the same weight of steel will take up just slightly more than three fourths the volume of the same weight in timber. Under these circumstances, it is necessary to make determinations concerning the most useful cargo carrying strategy for the ship in question. Additional information that would aid in this determination is whether or not the Nunki is specialized for one cargo or the other. All ships have weight and volume limitations, the ship specialized for a particular cargo but loaded up with a different commodity with an unusual stowage factor may find itself in the situation of being unable to fully utilize its entire volume by carrying the cargo in question. The same weight in steel represents just over 75% of the same volume in timber, and this must be factored into price calculations. With the net tonnage of 18,800, we must still subtract from that 400 tons of dead weight (including freshwater and constants) leaving 18,400 tonnes remaining. Under ideal conditions, and traveling an identical distance it would be more logical to carry the steel cargo, unless specialized factors in ship construction would further reduce the available volume if steel were not the originally intended cargo of the vessel. But in this case, the different destinations will represent differences in the time and route of the two possible voyages. Calculations: Net Tonnage 18,800 0.91 / 1.2 = 0.75 Steel 24.50 per

The Question is in the Instruction part Essay Example | Topics and Well Written Essays - 2250 words

The Question is in the Instruction part - Essay Example This shows that despite the complete strangeness of a new and alien activity which initially seems incompatible to the inherent nature of Mole, the willingness to try it proves to be beneficial to him. Mole takes a splash into the water due to his excitement but he does not give up the idea of boating as incompatible to him. He perseveres and overcomes the incompatibility of his first encounter with boating. Grahame explains the different behaviors of the animals as belonging to the quaint culture called the animal-etiquette and not as incompatible elements thrown together. (Grahame 2004, p.10, 12). The narrative attributes certain behaviors to the unique animal culture when it says; 'The Rat hummed a tune, and the Mole recollected that animal-etiquette forbade any sort of comment on the sudden disappearance of one's friends at any moment, for any reason or no reason whatever.' (Grahame 2004, p.12). This mirrors the human society that is comprised of people from all walks of life. They are so different as to seem incompatible but yet co-exist in an interweaved mesh that allows for divergence and privacy. Grahame has put together a diverse set of characters that seem incompatible but they are consistent with the diversity that is present in the human population. The animals are the allegories that parallel humans. Grahame uses the setting of the River Bank and Wild Wood because it allows a diverse environment in which he can have a variety of animals and Silvey says; 'Not only is it a nostalgic evocation of the English countryside and a way of life that he felt was under threat, but in the characters of Rat and Mole we can detect aspects of himself.' (Silvey 1995, p. 87). Silvey also says that Grahame depicts human characters in the guise of animals. The rat and mole experience life in much the same way as humans. They enjoy comradeship, boating and a picnic. They exhibit some human traits. The rat is kind to the mole and forgives him for making a complete fool of himself in the water. Furthermore, he promises to teach the mole to row and swim. (Grahame 2004, p. 13). By putting toget her a group of seemingly incompatible characters, Grahame shows how friendships form, bond and cement to make life better in the community. On the other hand, Grahame shows that friendships enrich life. The underlying message is that if animals can form enduring bonds, humans should do much better. Dancygier says that Grahame uses frame metonymy, or the substitution of the name of an attribute for the name of the thing itself. (Dancygier 2005, p. 1). This camouflaging of elements give the impression that incompatible elements are thrown together. 'We are like the Rat in our book-initial quotation from The Wind in the Willows: give us a grammatical "door-scraper," and we can see a whole house, the entire experimental frame within which we understand what door-scrapers are for.' (Dancygier 2005, p. 25 ). This "door-scraper" is a symbol that draws together the seemingly incompatible elements to give an overall picture of what's going on. Rat and Mole find the door-scraper in the snowing woods. Grahame does not let Rat

Relativism and Morality Essay Example | Topics and Well Written Essays - 750 words - 3

Relativism and Morality - Essay Example It was just brave to put forth that some things are just basically wrong not because they are â€Å"never questioned or breached in practice, but because they never should be† (88). Goodman’s disagreed on Matilal’s idea of pluralism that norms differ from one society to another. Goodman argued that while Matilal’s assertion in many aspect are true, the concept of what is right and wrong is not just about common consent but unanimity. For what is agreed by many may not necessarily mean right. In plain language, mob rule is not always right. Such, Goodman puts forth the four areas which human experience where right or wrong is constant regardless of time, culture, understanding, religion or circumstance. It may already be a common knowledge but Goodman, put coherence and logic why these acts are not to be done in the first place. They are; (1) genocide, politically induced famine, and germ warfare; (2) terrorism, hostage taking, and child warriors; (3) slave ry, polygamy, and incest; and (4) rape and female genital cutting. We already know that murder is wrong much more when it is done on mass scale which what happens in genocide. Goodman succinctly put the argument what we already that â€Å"all living beings make claims to life†. ... It is not even limited to a tyrant’s prejudice, but can also be glossed over with good intention such as Maoist Cultural Revolution where â€Å"he was ready, he bragged in 1958, to sacrifice 300 million lives which composed half of China’s population, â€Å"for the victory of world revolution†. Goodman also hit the head of the nail to bury the very reason why terrorism is utterly wrong. His reasoning stood above the excuse of justifying terror that â€Å"one man’s terrorist is another man’s freedom fighter†. The excuse of subjectivity, that one group may disagree while another may find it laudable was paled with Goodman’s exposure and giving terror a face why it is just wrong. It willfully targets non-combatants and intend to intimidate and attract attention at the cost of many lives. Its obscenity and flagrancy as an act was exposed when Goodman rightfully conveyed that in terrorism, â€Å"the more helpless the victims, the more lur id the light. . . The more devastating the damage, the more inhumane, the more avidly is it sought by the strategists, ideologues, and theologians of terror†. The vileness of intention which was unmasked by Goodman just stripped terrorism any of its political justification that made it acceptable to some sectors in society. The excuse of addressing terror’s â€Å"root cause† also became moot as Goodman explained that soft pedaling the act of sowing fear make them pushes the pedal complicit with those who seek to profit politically from the mayhem. Equally unacceptable as murder in any form or method, is also the exploitation of individual be it in the form of slavery, prostitution or any form of exploitation

Hackers slang Essay Example | Topics and Well Written Essays - 1000 words

Hackers slang - Essay Example The existence of slang dictionaries, of course, cancels the effectiveness of certain words. Abbreviation. Hackers denote a word by only several of its component letters. For example: "RTFM" - "read the following manual", "IMHO" - "in my humble opinion", "BTW" - "by the way" or "LOL" - "lay of laugh". Verb doubling. Hackers double verbs as a concise, sometimes sarcastic comment on what the implied subject does. Also, a doubled verb is often used to terminate a conversation, in the process remarking on the current state of affairs or what the speaker intends to do next. Typical examples involve win, lose, hack, flame, barf, and chomp, i.e. "The disk heads just crashed." "Lose, lose." Sound-alike slang. Hackers will often make rhymes or puns in order to convert an ordinary word or phrase into something more interesting, i.e. "Plug&Play" is transformed to "Plug&Pray", "Government Property - Do Not Duplicate" to "Government Duplicity - Do Not Propagate" or "Macintosh" to "Macintrash". Overgeneralization. Many hackers love to take various words and add the wrong endings to them to make nouns and verbs, often by extending a standard rule to non-uniform cases (or vice versa). For example: "win" extends to "winnitude", "winnage", "disgust" to "disgustitude", "hack" to "hackification". "Marketdroid" is a member of a company's marketing department, especially one who promises users that the next version of a product will have features that are not actually scheduled for inclusion, are extremely difficult to implement. "Careware" is a variety of shareware for which either the author suggests that some payment be made to a nominated charity or a levy directed to charity is included on top of the distribution charge. Spoken inarticulations. Words such as "mumble", "sigh", and "groan" are spoken in places where their referent might more naturally be used. It derives from the impossibility of representing such noises in a chat or by e-mail. Anthropomorphization. Hackers often anthropomorphize hardware and software, for example, it's possible to say, "the protocol handler got confused" or "the program is died". () Comparatives. Many words in hacker slang have to be understood as members of sets of comparatives. This is especially true of the adjectives and nouns used to describe the beauty and functional quality of code. Here is an approximately correct spectrum: "monstrosity brain-damage screw bug lose misfeature" or "crock kluge hack win feature elegance perfection". (Levi, 1984, pp.56-78) Numerization. Hackers often include soundalike numbers in place of words or parts of words, for example "4 you", "2 do". (Kelly-Bootle, 1995, pp.36-101) Terms of computer hackers' dialect are often particular to their subculture. Raymond (1996) writes, "The hacker culture' is actually a loosely networked collection of subcultures that is nevertheless conscious of some important shared experiences, shared roots, and shared values. It has its own myths, heroes, villains, folk epics, in-jokes, taboos, and dreams. Because hackers as a group are particularly creative people who define themselves partly by rejection of normal' values and working habits, it has unusually rich and conscious traditions for an intentional culture less than 40 years

China and GCC relations Thesis Proposal Example | Topics and Well Written Essays - 1750 words

China and GCC relations - Thesis Proposal Example On an industry level, these needs pave the way for a new and improved breed of Chinese energy companies which are no longer characterized by low-cost and substandard quality only but by upgraded technological, financial and labor capabilities. According to Grunor (150) the China-GCC trade and transactions have increased notable in the past two decades with the Chinese exports increasing by seven-fold and the GCC increasing by five-fold. On the other hand, the member states of GCC are making efforts to improve and stabilize their economies by look for global partners to sell their products. Since the terrorist attack in the US in the year 2001, there has been a shift of attention from the west to other regions of the world. According to Brauch et al. (342) the September 11 attack affected the global trading trends with the Arab countries put under scrutiny and isolation. The Arab countries opted to move to other parts of the world to advance their economic endeavors. The research paper aims to examine the different avenues that China relates with the GCC and its member states. The objective of the research is to examine the relations between China and GCC. According to Gransow (63) the relationship between China and the Arab countries has not been put into allot of research and this can be associated to limited research work in this regions. In that manner, the research will try answer the following questions; To attain the objectives of the study, the study deployed qualitative analysis research method and inclusion of other data collection method to acquire data from both primary and secondary sources. The research will also deploy the use of quantitative analysis research method to some extent. This is because the research will focus on analyzing the economic activities and relations. According to Tolmie (218) research based on measuring extensive of figures and growth needs to deployed quantitative method.

CRJS 205 Introduction to Criminal Law Essay Example | Topics and Well Written Essays - 500 words

CRJS 205 Introduction to Criminal Law - Essay Example The client in this context is a victim of a sexual assault and she can sue the offender. However, the decisions (jail term and damages) that will be made by the jury in the criminal and civil courts will depend on the state’s statutory rape laws. When a client decides not sue the offender, the sex crime kit is usually kept for a certain period within which the victim can report to the law enforcement. In West Virginia, the sex crime kit or the evidence is stored for 18 months if the victim does not initiate an investigation. However, after 18 months the evidence is destroyed or used for research purposes or used for training; this is done after the removal of identifying information (West Virginia Foundation for Rape Information and Services [WV-FRIS], 2008). It is important to note that evidence is required if the victim desires to sue the offender. If the client has evidence, she can sue the offender for sexual assault of the first degree if sexual intercourse and bodily harm were inflicted or sexual assault of the second degree is only sexual intercourse occurred. If found guilty of first-degree sexual assault, the offender can be â€Å"imprisoned in the penitentiary between 15 and 35 years or imprisoned in the penitentiary between 15 and 35 years and fined between $1,000 and $10,000† (The Lectric Law Library, 2012). If found guilty of second-degree sexual assault, the offender can be jailed in the prison between 10 and 25 years or jailed in the prison between 10 and 25 years accompanied with a fine between $1,000 and $10,000 (The Lectric Law Library, 2012). In addition to criminal prosecution, the victim can file a civil suit with the help of a private attorney in a Civil Court. If the victim wins the civil lawsuit, the court orders the attacker to pay money for the damages caused (the damages include loss of income, suffering, pain, and medical expenses). Punitive damages are also available if the victim does

Writers’ Feminist Views Essay Example for Free

Writers’ Feminist Views Essay The themes in Jane Eyre and Arcadia vary, but one theme that unites them both is feminism. It could be argued that in Jane Eyre the main theme is Marxism, but as the main character is female there is a feminist element as well. As the story progresses the Marxist theme is diluted because Jane is more empowered, and the feminist theme is more central. In Arcadia there are many themes but they all revolve around the main theme of feminism. Whereas Jane Eyre is a typical Victorian narrator who we trust, Thomasina is a character that we are drawn to. Throughout Jane Eyre it is hard to grasp how far Brontà «Ã¢â‚¬â„¢s views are feminist. She reveals a lot of her own opinions through Jane, and there are moments when Jane expresses feelings of injustice when women are treated as though they are inferior to men, but Jane is also portrayed as a woman who knows her place, and does not feel equal to men or even women of a higher class to her. In Arcadia, Tom Stoppard conveys Thomasina as a very intelligent young woman with great wealth and a certain degree of power over Septimus. Stoppard doesn’t fail to show the attitude towards women of the Victorian era, but at the same time he shows his own view towards women. By making Thomasina’s character very intelligent (especially for her age) he instantly empowers her. A typical Victorian author would not write their female characters as intelligent, or as women with op inions different to those of their male superiors (like Thomasina). One of the last lines in Jane Eyre – â€Å"Reader I married him† is a great portrayal of feminist views. This direct address coming from a female narrator was completely unheard of during the Victorian period; it gives Jane authority. This line implies that the marriage was Jane’s decision, or that she consented it (again empowering her) as opposed to Rochester. This is echoed by Rochester’s eventual physical condition (poor, injured and impaired) where he is humbled and Jane’s status is raised, as she no longer depends on him, he depends on her. Jane was given a considerable sum of money, and she could have chosen not to spend the rest of her life with Rochester but she still did. Furthermore, the way in which Rochester used to speak to Jane (whilst still pleasant) sounded as though she were a little girl, but at the end (as a result of her sudden gain of power) he changed the way he spoke to her and spoke to her more as an equal. In some ways, Jane did grow up by the end of the book, more in certain frames of mind than physically. Whereas the ending of Jane Eyre empowers women, the ending of Arcadia portrays the inevitability of a woman’s life. The fire in both stories is symbolic, in Jane Eyre it brings Rochester and Jane together (he’s physically dependent, she still chooses him) and in Arcadia the fire is a release as well as a tragedy, but it releases Thomasina from the inevitability of womanhood. The fire brings together but sets free. In both stories the fire was a pivotal point. Jane is left empowered at the end of Jane Eyre but Thomasina is left susceptible to death, life is fragile and she’s not in control. That is of course if she didn’t deliberately cause a fire in order to end her own life, because if she did then she is as empowered as Jane, taking life in her hands and ‘playing God’. However, the very fact that the audience would consider the idea that Thomasina took her own life shows that we recognize how bleak her future seemed. The ending of Jane Eyre is considered happy, and the Ending of Arcadia tragic, but these statements could be questioned. Jane Eyre represents independent, free-thinking women during the Victorian period; she is gradually empowered with money, friendship, an independent job and newly discovered family, yet in spite of these things she still chooses to settle with Rochester, care for him, and tend to him as a loving wife. Jane succumbed to the stereotypical expectations of Victorian women, belittling her efforts and strong mindedness, and possibly leaving her unhappy or unsatisfied. Similarly, Arcadia’s ending with Thomasina’s death (although initially appearing to be tragic) could be interpreted as a happy ending. A typical Brontà « convention is the idea of death being a release, and the fire (whether it were a fault of Thomasina’s or not) could be seen as her escape from her dismal future prospects that were already set in stone. Furthermore, if the fire was of Thomasina’s doing then it amplifies even more so that it was an escape and that she felt the need to run away from what her life was becoming. Both arguments are a question of whether or not what the reader contracts from each text, is what the author intended. Thomasina’s death is one of the best dramatic ironies since Romeo and Juliet. Thomasina had a great yearning to waltz with Septimus before her 17th birthday, to have one moment where she felt the love of the man she loved who did not love her in return, but loved her mother. The play ends with a blackout, and just a candle left on stage. The candle is symbolic: it could show the last glimpse of light left in her life, that moment dancing that she’d remember forever, or it could repeat the theme of inevitability (she was sharing such an important, special and unlikely moment with somebody she loved, and all that time, the cause of her death was lighting her last happy memory). Jane Eyre initially appears to be a novel based around Marxism, but it could be argued that this is not the main theme of the novel. There are feminist elements to the novel and as the author was a Victorian woman and the main character is female, it could be said that Brontà «Ã¢â‚¬â„¢s intention was to create a feminist novel. Arcadia’s themes are much more complex as there are so many more themes of science, progress, intellect, adultery, nature, the arts and literature. The idea is played on that our planet is gradually going cold and fading to nothing. Thomasina intelligently explores these ideas; she has many intuitive opinions that she has formed about life and the universe. The criticism of art and literature is a less central theme. Despite all of these themes, the central theme is the subject of Thomasina’s wealth and intelligence through feminism and all the other themes spin around feminism because of Thomasina. This said, Lady Croome is a powerful authoritative character and in some ways takes the role of the father; she somewhat has the male role of the novel which reflects the feminist view that women are equally capable of a male role. In spite of all that Thomasina is capable of, her fate is no different to that of any other upper class Victorian girl. To conclude, Jane Eyre is a novel in which the ending is significant but doesn’t wholly focus on feminism, whereas Arcadia has more of an unjust feeling at the end, which is generated from the strong feminist views throughout (and particularly towards the end).

Simply Supported And Cantilever Beams

Simply Supported And Cantilever Beams A beam is a structural member which safely carries loads i.e. without failing due to the applied loads. We will be restricted to beams of uniform cross-sectional area. Simply Supported Beam A beam that rests on two supports only along the length of the beam and is allowed to deflect freely when loads are applied. Note see section A of unit. Cantilever Beam A beam that is supported at one end only. The end could be built into a wall, bolted or welded to another structure for means of support. Point or Concentrated Load A load which acts at a particular point along the length of the beam. This load is commonly called a force (F) and is stated in Newtons (N). A mass may be converted into a force by multiplying by gravity whose value is constant at 9.81 m/s2. Uniformly Distributed Load (UDL) A load which is spread evenly over a given length of the beam. This may be the weight of the beam itself. The UDL is quoted as Newtons per metre (N/m). Beam Failure If excessive loads are used and the beam does not have the necessary material properties of strength then failure will occur. Failure may occur in two ways:- Calculating Shear Forces (we must use the shear force rule). When looking right of a section : downward forces are positive and upward forces are negative. When looking left of a section: downward forces are negative and upward forces are positive. Starting at point A and looking left: (note: the negative sign (-) means just to the left of the position and the positive sign (+) means just to the right of the position.) SFA = 0 kN SFA + = 6 kN An alternative method of drawing the shear force diagram is to follow the directions of each force on the line diagram.SFB = 6 kN SFB + = 6 kN SFC = 6 kN SFC + = 6 kN SFD = 6 kN SFD + = 6 12 = -6 kN SFE = 6 12 = -6 kN SFE + = 6 12 = -6 kN SFF = 6 12 = -6 kN SFF + = 6 12 = -6 kN SFG = 6 12 = -6 kN SFG + = 6 12 + 6 = 0 kN Note: the shear force at either end of a simply supported beam must equate to zero. Calculating Bending Moments (we must use the bending moment rule). When looking right of a section : downward forces are negative and upward forces are positive. When looking left of a section: downward forces are negative and upward forces are positive. section F F section F + F + Hogging Beam Sagging Beam Starting at point A and looking left: BMA = 0 kNm BMB = (6 x 1) = 6 kNm BMC = (6 x 2) = 12 kNm BMD = (6 x 3) = 18 kNm BME = (6 x 4) + ( -12 x 1) = 12 kNm BMF = (6 x 5) + ( -12 x 2) = 6 kNm BMG = (6 x 6) + ( -12 x 3) = 0 kNm Note: the bending moment at either end of a simply supported beam must equate to zero. The following page shows the line, shear force and bending moment diagrams for this beam. Simply Supported Beam with Point Load 6 m F E D C G B A 6 kN 6 kN F =12 kN Shear Force Diagram (kN) 0 0 -6 6 0 Line Diagram 12 12 18 6 0 6 Bending Moment Diagram (kNm) Max Tensile Stress SAGGING (+ve bending) Max Compressive Stress F F A maximum bending moment of 18 kNm occurs at position D. Note the shear force is zero at this point. Simply Supported Beam with Distributed Load UDL = 2 kN/m F E D C G B A 6 m RA The force from a UDL is considered to act at the UDL mid-point. e.g. if we take moments about D then the total force from the UDL (looking to the left) would be: (2 x 3) = 6 kN. This force must be multiplied by the distance from point D to the UDL mid point as shown below. e.g. Take moments about D, then the moment would be: (-6 x 1.5) = -9 kNm 1.5m UDL = 2 kN/m D C B A 3 m Taking moments about point D (looking left) We must first calculate the reactions RA and RG. We take moments about one of the reactions to calculate the other, therefore to find RA: Take moments about RG ÃŽ £Clockwise moments (CM) = ÃŽ £Anti-clockwise moments (ACM) RA x 6 = 2 x 6 x 3 RA = 6 kN now, ÃŽ £Upward Forces = ÃŽ £Downward Forces RA + RG = 2 x 6 6 + RG = 12 RG = 6 kN section F + F F F + Calculating Shear Forces (we must use the shear force rule). When looking right of a section : downward forces are positive and upward forces are negative. When looking left of a section: downward forces are negative and upward forces are positive. Starting at point A and looking left: (note: the negative sign (-) means just to the left of the position and the positive sign (+) means just to the right of the position.) SFA = 0 kN SFA + = 6 kN SFB = 6 (21) = 4 kN SFB + = 6 (21) = 4 kN SFC = 6 (22) = 2 kN SFC + = 6 (22) = 2 kN SFD = 6 (23) = 0 kN SFD + = 6 (23) = 0 kN SFE = 6 (24) = -2 kN SFE + = 6 (24) = -2 kN SFF = 6 (25) = -4 kN SFF + = 6 (25) = -4 kN SFG = 6 (26) = -6 kN SFG + = 6 (26) + 6 = 0 kN Note: the shear force at either end of a simply supported beam must equate to zero. Calculating Bending Moments (we must use the bending moment rule). When looking right of a section : downward forces are negative and upward forces are positive. When looking left of a section: downward forces are negative and upward forces are positive. section F F section F + F + Hogging Beam Sagging Beam Starting at point A and looking left: BMA = 0 kNm BMB = (6 x 1) + (-2 x 1 x 0.5) = 5 kNm BMC = (6 x 2) + (-2 x 2 x 1) = 8 kNm BMD = (6 x 3) + (-2 x 3 x 1.5) = 9 kNm BME = (6 x 4) + (-2 x 4 x 2) = 8 kNm BMF = (6 x 5) + + (-2 x 5 x 2.5 = 5 kNm BMG = (6 x 6) + + (-2 x 6 x 3) = 0 kNm Note: the bending moment at either end of a simply supported beam must equate to zero. The following page shows the line, shear force and bending moment diagrams for this beam. Simply Supported Beam with Distributed Load 4 2 0 -2 -4 UDL = 2 kN/m 6 m F E D C G B A Shear Force Diagram (kN) 0 0 -6 6 0 Line Diagram 8 8 9 5 0 Bending Moment Diagram (kNm) 5 6 kN 6 kN Max Tensile Stress SAGGING (+ve bending) Max Compressive Stress F F A maximum bending moment of 9 kNm occurs at position D. Note the shear force is zero at this point. Simply Supported Beam with Point Loads 6 m F E D C G B A RA RG F = 15 kN F = 30 kN We must first calculate the reactions RA and RG. We take moments about one of the reactions to calculate the other, therefore to find RA: Take moments about RG ÃŽ £Clockwise moments (CM) = ÃŽ £Anti-clockwise moments (ACM) RA x 6 = (15 x 4) + (30 x 2) RA = 20 kN now, ÃŽ £Upward Forces = ÃŽ £Downward Forces RA + RG = 15 + 30 20 + RG = 45 RG = 25 kN section F + F F F + Calculating Shear Forces (we must use the shear force rule). When looking right of a section : downward forces are positive and upward forces are negative. When looking left of a section: downward forces are negative and upward forces are positive. Starting at point A and looking left: (note: the negative sign (-) means just to the left of the position and the positive sign (+) means just to the right of the position.) SFA = 0 kN SFA + = 20 kN SFB = 20 kN SFB + = 20 kN SFC = 20 kN SFC + = 20 -15 = 5 kN SFD = 20 -15 = 5 kN SFD + = 20 -15 = 5 kN SFE = 20 -15 = 5 kN SFE + = 20 -15 30 = -25 kN SFF = 20 -15 30 = -25 kN SFF + = 20 -15 30 = -25 kN SFG = 20 -15 30 = -25 kN SFG + = 20 -15 30 + 25 = 0 kN Note: the shear force at either end of a simply supported beam must equate to zero. Calculating Bending Moments (we must use the bending moment rule). When looking right of a section : downward forces are negative and upward forces are positive. When looking left of a section: downward forces are negative and upward forces are positive. section F F section F + F + Hogging Beam Sagging Beam Starting at point A and looking left: BMA = 0 kNm BMB = (20 x 1) = 20 kNm BMC = (20 x 2) = 40 kNm BMD = (20 x 3) + (-15 x 1) = 45 kNm BME = (20 x 4) + (-15 x 2) = 50 kNm BMF = (20 x 5) + (-15 x 3) + (-30 x 1) = 25 kNm BMG = (20 x 6) + (-15 x 4) + (-30 x 2) = 0 kNm Note: the bending moment at either end of a simply supported beam must equate to zero. The following page shows the line, shear force and bending moment diagrams for this beam. 0 20 -25 0 Shear Force Diagram (kN) 5Simply Supported Beam with Point Loads 6 m F E D C G B A 20 kN 25 kN F = 15 kN F = 30 kN Bending Moment Diagram (kNm) 0 0 45 40 20 50 25 Max Tensile Stress SAGGING (+ve bending) Max Compressive Stress F F A maximum bending moment of 50 kNm occurs at position E. Note the shear force is zero at this point. Simply Supported Beam with Point and Distributed Loads (1) 6 m F E D C G B A RA RG 15 kN 30 kN UDL = 10 kN/m We must first calculate the reactions RA and RG. We take moments about one of the reactions to calculate the other, therefore to find RA: Take moments about RG ÃŽ £Clockwise moments (CM) = ÃŽ £Anti-clockwise moments (ACM) RA x 6 = (15 x 4) + (10 x 2 x 3) + (30 x 2) RA = 30 kN now, ÃŽ £Upward Forces = ÃŽ £Downward Forces RA + RG = 15 + (10 x 2) + 30 30 + RG = 65 RG = 35 kN section F + F F F + Calculating Shear Forces (we must use the shear force rule). When looking right of a section : downward forces are positive and upward forces are negative. When looking left of a section: downward forces are negative and upward forces are positive. Starting at point A and looking left: (note: the negative sign (-) means just to the left of the position and the positive sign (+) means just to the right of the position.) SFA = 0 kN SFA + = 30 kN SFB = 30 kN SFB + = 30 kN SFC = 30 kN SFC + = 30 15 = 15 kN SFD = 30 15 (10 x 1) = 5 kN SFD + = 30 15 (10 x 1) = 5 kN SFE = 30 15 (10 x 2) = -5 kN SFE + = 30 15 (10 x 2) 30 = -35 kN SFF = 30 15 (10 x 2) 30 = -35 kN SFF + = 30 15 (10 x 2) 30 = -35 kN SFG = 30 15 (10 x 2) 30 = -35 kN SFG + = 30 15 (10 x 2) 30 + 35 = 35 kN Note: the shear force at either end of a simply supported beam must equate to zero. Calculating Bending Moments (we must use the bending moment rule). When looking right of a section : downward forces are negative and upward forces are positive. When looking left of a section: downward forces are negative and upward forces are positive. section F F section F + F + Hogging Beam Sagging Beam Starting at point A and looking left: BMA = 0 kNm BMB = (30 x 1) = 30 kNm BMC = (30 x 2) = 60 kNm BMD = (30 x 3) + (-15 x 1) + (-10 x 1 x 0.5) = 70 kNm BME = (30 x 4) + (-15 x 2) + (-10 x 2 x 1) = 70 kNm BMF = (30 x 5) + (-15 x 3) + (-10 x 2 x 2) + (-30 x 1) = 35 kNm BMG = (30 x 6) + (-15 x 4) + (-10 x 2 x 3) + (-30 x 2) = 0 kNm Notes: the bending moment at either end of a simply supported beam must equate to zero. The value of the maximum bending moment occurs where the shear force is zero and is therefore still unknown (see Shear Force diagram). The distance from point A to this zero SF point must be determined as follows:- x = 2 15 20 x = 1.5 m Total distance from point A = 2 + 1.5 = 3.5 m therefore, BM max = (30 x 3.5) + (-15 x 1.5) + (-10 X 1.5 x 0.75) = 71.25 kNm The following page shows the line, shear force and bending moment diagrams for this beam. 70 71.25 35 30 60 70 0 0 Simply Supported Beam with Point and Distributed Loads (1) 2 m x 30 -5 Shear Force Diagram (kN) 0 -35 15 0 6 m F E D C G B A 30 kN 35 kN 15 kN 30 kN UDL = 10 kN/m 20 kN Bending Moment Diagram (kNm) Max Tensile Stress SAGGING (+ve bending) Max Compressive Stress F F A maximum bending moment of 71.25 kNm occurs at a distance 3.5 m from position A. Simply Supported Beam with Point and Distributed Loads (2) 1 m RB 12 m E D C F B A 8 kN RE UDL = 6 kN/m UDL = 4 kN/m 12 kN We must first calculate the reactions RB and RE. We take moments about one of the reactions to calculate the other, therefore to find RB. Take moments about RE ÃŽ £Clockwise moments (CM) = ÃŽ £Anti-clockwise moments (ACM) (RBx10)+(6x1x0.5) = (4 x 4 x 9) + (8 x 7) + (12 x 3) + (6 x 3 x 1.5) RB = 26 kN now, ÃŽ £Upward Forces = ÃŽ £Downward Forces RB + RE = (4 x 4) + 8 + 12 + (6 x 4) 26 + RE = 60 RE = 34 kN Calculating Shear Forces Starting at point A and looking left: SFA = 0 kN SFA + = 0 kN SFB = -4 x 1 = -4 kN SFB + = (-4 x 1) + 26 = 22 kN SFC = (-4 x 4) + 26= 10 kN SFC + = (-4 x 4) + 26 8 = 2 kN SFD = (-4 x 4) + 26 8 = 2 kN SFD + = (-4 x 4) + 26 8 12 = -10 kN SFE = (-4 x 4) + 26 8 12 (6 x 3) = -28 kN SFE + = (-4 x 4) + 26 8 12 (6 x 3) + 34 = 6 kN SFF = (-4 x 4) + 26 8 12 (6 x 4) + 34 = 0 kN SFF + = (-4 x 4) + 26 8 12 (6 x 4) + 34 = 0 kN Calculating Bending Moments Starting at point A and looking left: BMA = 0 kNm BMB = (-4 x 1 x 0.5) = -2 kNm BM 2m from A = (-4 x 2 x 1) + (26 x 1) = 18 kNm BM 3m from A = (-4 x 3 x 1.5) + (26 x 2) = 34 kNm BMC = (-4 x 4 x 2) + (26 x 3) = 46 kNm BMD = (-4 x 4 x 6) + (26 x 7) + (-8 x 4) = 54 kNm BM 9m from A = (-4 x 4 x 7) + (26 x 8) + (-8 x 5) + (-12 x 1) + (-6 x 1 x 0.5) = 41 kNm BM 9m from A = (-4 x 4 x 8) + (26 x 9) + (-8 x 6) + (-12 x 2) + (-6 x 2 x 1) = 22 kNm BME = (-4 x 4 x 9) + (26 x 10) + (-8 x 7) + (-12 x 3) + (-6 x 3 x 1.5) = -3 kNm BMF = (-4 x 4 x 10) + (26 x 11) + (-8 x 8) + (-12 x 4) + (-6 x 4 x 2) + (34 x 1) = 0 kNm Point of Contraflexure At any point where the graph on a bending moment diagram passes through the 0-0 datum line (i.e. where the BM changes sign) the curvature of the beam will change from hogging to sagging or vice versa. Such a point is termed a Point of Contraflexure or Inflexion. These points are identified in the following diagram. It should be noted that the point of contraflexure corresponds to zero bending moment. Turning Points The mathematical relationship between shear force and corresponding bending moment is evidenced on their respective graphs where the change of slope on a BM diagram aligns with zero shear on the complementary shear force diagram. Thus, at any point on a BM diagram where the slope changes direction from upwards to downwards or vice versa, all such Turning Points occur at positions of Zero Shear. Turning points are also identified in the following diagram. Simply Supported Beam with Point and Distributed Loads (2) 1 m 26 kN 12 m E D C F B A 8 kN 34 kN UDL = 6 kN/m UDL = 4 kN/m 12 kN 2 6 2 -4 22 -10 Shear Force Diagram (kN) 0 -28 10 0 F F SAGGING (+ve bending) -3 22 41 54 46 34 18 -2 Bending Moment Diagram (kNm) 0 0 F F HOGGING (-ve bending) Points of Contraflexure The maximum bending moment is equal to 54 kNm and occurs at point D where the shear force is zero. Turning points occur at -2 kNm and -3 kNm. Cantilever Beam with Point Load 6 m F E D C G B A RA 12 kN Free End Fixed End In this case there is only one unknown reaction at the fixed end of the cantilever, therefore: ÃŽ £Upward Forces = ÃŽ £Downward Forces RA = 12 kN Calculating Shear Forces Starting at point A and looking left: SFA = 0 kN SFA + = 12 kN SFB = 12 kN SFB + = 12 kN SFC = 12 kN SFC + = 12 kN SFD = 12 kN SFD + = 12 kN SFE = 12 kN SFE + = 12 kN SFF = 12 kN SFF + = 12 kN SFG = 12 kN SFG + = 12 12 = 0 kN Note: the shear force at either end of a cantilever beam must equate to zero. Calculating Bending Moments NB for simplicity at this stage we shall always look towards the free end of the beam. Starting at fixed end, point A, and looking right towards the free end: (the same results may be obtained by starting at point G and looking right) BMA = -12 x 6 = -72 kNm BMB = -12 x 5 = -60 kNm BMC = -12 x 4 = -48 kNm BMD = -12 x 3 = -36 kNm BME = -12 x 2 = -24 kNm BMF = -12 x 1 = -12 kNm BMG = 0 kNm Notes: the maximum bending moment in a cantilever beam occurs at the fixed end. In this case the 12kN force in the beam is trying to bend it downwards, (a clockwise moment). The support at the fixed end must therefore be applying an equal but opposite moment to the beam. This would be 72 kNm in an anti-clockwise direction. See the following diagram. The value of the bending moment at the free end of a cantilever beam will always be zero. -12 -24 -36 -48 -60 -72 Bending Moment Diagram (kNm) 0 0 12 125 Shear Force Diagram (kN) 0 0 72 kNm 72 kNm 6 m F E D C G B A 12 kN 12 kN The following shows the line, shear force and bending moment diagrams for this beam. F F HOGGING (-ve bending) Max Tensile Stress Max Compressive Stress A maximum bending moment of -72 kNm occurs at position A. Cantilever Beam with Distributed Load UDL = 2 kN/m 6 m F E D C G B A RA To calculate the unknown reaction at the fixed end of the cantilever: ÃŽ £Upward Forces = ÃŽ £Downward Forces RA = 2 x 6 RA = 12 kN Calculating Shear Forces Starting at point A and looking left: SFA = 0 kN SFA + = 12 kN SFB = 12 (2 x 1) = 10 kN SFB + = 12 (2 x 1) = 10 kN SFC = 12 (2 x 2) = 8 kN SFC + = 12 (2 x 2) = 8 kN SFD = 12 (2 x 3) = 6 kN SFD + = 12 (2 x 3) = 6 kN SFE = 12 (2 x 4) = 4 kN SFE + = 12 (2 x 4) = 4 kN SFF = 12 (2 x 5) = 2 kN SFF + = 12 (2 x 5) = 2 kN SFG = 12 (2 x 6) = 0 kN SFG + = 12 (2 x 6) = 0 kN Note: the shear force at either end of a cantilever beam must equate to zero. Calculating Bending Moments Starting at fixed end, point A, and looking right towards the free end: (the same results may be obtained by starting at point G and looking right) BMA = -2 x 6 x 3 = -36 kNm BMB = -2 x 5 x 2.5 = -25 kNm BMC = -2 x 4 x 2 = -16 kNm BMD = -2 x 3 x 1.5 = -9 kNm BME = -2 x 2 x 1 = -4 kNm BMF = -2 x 1 x 0.5 = -1 kNm BMG = 0 kNm The following page shows the line, shear force and bending moment diagrams for this beam. Cantilever Beam with Distributed Load8 6 4 2 36 kNm 36 kNm 12 105 Shear Force Diagram (kN) 0 0 -1 -4 -9 -16 -25 -36 Bending Moment Diagram (kNm) 0 0 6 m F E D C G B A 12 kN UDL = 2 kN/m F F HOGGING (-ve bending) Max Tensile Stress Max Compressive Stress A maximum bending moment of -36 kNm occurs at position A. Cantilever Beam with Point and Distributed Loads RG 2 m 10 kN B C D E A F G 4 m UDL = 10 kN/m To calculate the unknown reaction at the fixed end of the cantilever: ÃŽ £Upward Forces = ÃŽ £Downward Forces RG = (10 x 6) + 10 RG = 70 kN Calculating Shear Forces Starting at point A and looking left: SFA = 0 kN SFA + = 0 kN SFB = -10 x 1 = -10 kN SFB + = -10 x 1 = -10 kN SFC = -10 x 2 = -20 kN SFC + = (-10 x 2) + (-10) = -30 kN SFD = (-10 x 3) + (-10) = -40 kN SFD + = (-10 x 3) + (-10) = -40 kN SFE = (-10 x 4) + (-10) = -50 kN SFE + = (-10 x 4) + (-10) = -50 kN SFF = (-10 x 5) + (-10) = -60 kN SFF + = (-10 x 5) + (-10) = -60 kN SFG = (-10 x 6) + (-10) = -70 kN SFG + = (-10 x 6) + (-10) + 70 = 0 kN Note: the shear force at either end of a cantilever beam must equate to zero. Calculating Bending Moments Starting at point A, and looking left from the free end: (the same results may be obtained by starting at point G and looking left) BMA = 0 kNm BMB = -10 x 1 x 0.5 = -5 kNm BMC = -10 x 2 x 1 = -20 kNm BMD = (-10 x 3 x 1.5) + (-10 x 1) = -55 kNm BME = (-10 x 4 x 2) + (-10 x 2) = -100 kNm BMF = (-10 x 5 x 2.5) + (-10 x 3) = -155 kNm BMG = (-10 x 6 x 3) + (-10 x 4) = -220 kNm The following page shows the line, shear force and bending moment diagrams for this beam. 70 kN 2 m 10 kN B C D E A F G 4 m UDL = 10 kN/m 0 0 Shear Force Diagram (kN) -60 -70 -10 -20 -40 -50 220 kNm 220 kNm -30Cantilever Beam with Point and Distributed Loads 0 0 Bending Moment Diagram (kNm) -220 -5 -20 -55 -100 -155 F F HOGGING (-ve bending) Max Tensile Stress Max Compressive Stress A maximum bending moment of -220 kNm occurs at position G.