America’s Compulsory education Essay

This page give a concise history of the underlying foundations of America’s Compulsory training beginning in Massachusetts in 1852. This participation law required all kids to go to government funded school. The survey of instruction the nation over in advancement is expressed as such on the site: that each state in the US requires school matured youngsters (offspring of the age of 6) to join in or be tried out open or non-public school or to be self-taught. Despite the fact that in many states the age of a school going youngster is questionable, just as the age at which they may stop school (by either graduating at 17 years old or 18, or by taking their GED), the site additionally offers that keeping a kid in school (secondary school) may turn into a money related weight to the locale as standards and educators may invest a greater amount of their energy passing out disciplinary responses to the troublesome understudy as opposed to instructing. The site further expresses that truancy and school participation fluctuates from state to state. Assignment Passage #1 â€Å"Today, each state and region expects youngsters to take on open or private schooling or to be self-taught. More than halfâ€32 statesâ€require understudies to start their instruction by age 6. Some states’ set their age necessities as low as age 5 and as high as age 8. All kids are required to proceed with their training into their secondary school years, with 26 states setting the cutoff age at 16. The rest of the states expect understudies to remain in school through age 17 or 18† (The National Conference for State Legislatures, 2007). Basic Commentary on Passage #1: The above explanation proposes that the general participation of school-matured youngsters is directed by the state, not by the government. Along these lines, it is the state’s obligation to guarantee that kids are increasing appropriate instruction. The age go for an understudy to quit going to class is set at 16, yet the site makes reference to at what age the GED can be taken, or referencing at what age self-taught youngsters may pick up their degree and set off for college. Section #2 â€Å"States and domains additionally set a base age for youngsters to try out kindergarten, which is normally a couple of years sooner than the obligatory instruction age. Each state or domain with an arrangement on this issue has built up age 5 as the base age† (The National Conference for State Legislatures, 2007). Basic Commentary on Passage #2 The site appears to have clashing thoughts regarding what age a kid should start school. One entry expresses that age five is the age to start while another section expresses that age 6 is the age to start. With this adjustment in age it appears that the more seasoned the kid starts school, when the kid arrives at secondary school and can stop then the less training they would be presented to. Section #3 A few specialists state that age might be a self-assertive marker or proportion of a child’s capacity to prevail in school and ought not be utilized by any stretch of the imagination. Others bring up that when a state thinks about enactment, for example, Nebraska, permitting more youthful kids to enter kindergarten, policymakers must comprehend that there is probably going to be a huge increment in the quantity of youngsters entering kindergarten during the principal year of the new approach, consequently stressing effectively close school area financial plans and expanding the requirement for teachers† (The National Conference for State Legislatures, 2007). Basic Commentary on Passage #3 This entry makes reference to something that has been seen earlier in the paper; that is the utilization of school assets to keep kids in school who might want in any case, (for example, kids who need to join the workforce, understudies who are prepared for school and don't have to go to secondary school). It appears that as indicated by this site, school areas across America not simply confined to one state are having an incredible trouble in discovering subsidizing and instructors, in view of this absence of financing are being compelled to go to class estimates that are excessively enormous for one educator to deal with. The site doesn't make reference to explicit numbers by which the educators must instruct, yet measurements show that one instructor commonly has thirty or more understudies for every class. This ought to be and should be referenced on the site all together for a precise depiction of state funded schools and Compulsory Education to be appropriately inspected. Explanation #2 Source Information Illich, Ivan. Deschooling Society. 16 September 2007. <http://reactorcore. organization/deschooling. html> Evaluation Paragraph The page offers an assessment of the social and administrative organizations present in the United States running from Social Welfare, to schools. The writer offers to the peruser this contorted perspective on reality that has been constrained into the origination of an understudy being ‘schooled’ when in truth they’re being instructed simply to pass an evaluation and not really picking up anything of utilization. Apportionment Passage #1 â€Å"In these articles, I will show that the organization of qualities drives definitely to physical contamination, social polarization, and mental ineptitude: three measurements in a procedure of worldwide debasement and modernized misery† (Illich 2007). Basic Commentary on Passage #1: The above articulation gives the peruser the perspective of the writer and doesn't at this starting piece of the article broadly expound on realities. In spite of the fact that the page is essentially conclusion, it ought to be adjusted very of need with realities to back up the author’s perspective. The site does anyway offer captivating discourse on school change. Entry #2 â€Å"I need to bring up the general issue of the common meaning of man’s nature and the idea of current organizations which describes our reality view and language. To do as such, I have picked the school as my worldview, and I in this way bargain just in a roundabout way with other bureaucratic organizations of the corporate express: the customer family, the gathering, the military, the congregation, the media† (Illich 2007). Basic Commentary on Passage #2 In this entry again the peruser sees the assessment of the creator. The writer allows the peruser to comprehend his theme in allocation with his basic hypothesis. The way that the writer expresses that schools are turning out to be not well coordinated and matches this establishment with different foundations, for example, medical clinics and police is a road of state and government gives that must likewise be centered around in the article. Section #3 â€Å"Not just instruction yet social reality itself has become educated. It costs generally the equivalent to class both rich and poor in a similar reliance. The yearly use per understudy in the ghettos and in the rich rural areas of any of twenty U. S. urban communities lies in a similar range-and here and there is positive for the poor† (Illich 2007). Basic Commentary on Passage #3 The creator clarifies upon his essential proposition proclamation of the change of the school. In this announcement anyway the peruser can observer a few realities about how the school ought to be changed. Along this road the creator keeps on expressing that there ought not be isolation in the training framework and presents the division among rich and poor in instruction. Explanation #3 Source Information Goodman, Paul. Two Simple Proposals. 16 September 2007. < http://www. factoryschool. organization/rhood/goodman/twosimple. html> Evaluation Paragraph The site offers a short examination of advanced education with respect to absence of subsidizing for aesthetic sciences in a general public where innovation is the quickly developing product. Apportionment Passage #1 â€Å"Our instructive reality can be found in activity in the current sort of planning, testing, and evaluating; and if Dean Barzun is keen on rolling out an improvement, he can begin right here† (Goodman 2007). Basic Commentary on Passage #1: The above explanation gives the peruser a feeling that the understudy body is getting overwhelmingly worried about their own instruction. This reaches from starter tutoring to advanced education. Along these lines, this site is in concurrence with Illich’s thoughts of how summed up testing doesn't require learning, just course remembrance. Section #2 â€Å"There is little thoughtfulness regarding singular pace, beat, or decision, and none whatever to the disclosure of personality or commitment to scholarly objectives. The inclination and accomplishment testing and the savage rivalry for high evaluations are a race up the stepping stool to high-salaried occupations in the organizations of the world, including the tutoring business† (Goodman 2007). Basic Commentary on Passage #2 The writer is uncovering to the perusers that the educational system, in spite of the fact that there is a no youngster deserted law, is in certainty liable of establishing a careful tone in the study hall when the decent variety of students in the study hall would require a specific timetable. It is normal information that each individual learns at their own pace and uniquely in contrast to another understudy. The state needs to discover a measure whereby homeroom grades are obsolete models for teaching understudies. Entry #3 â€Å"The reason for this proposition is twofold: to get understudies with enough beneficial experience to be educable on the school level, particularly in the sociologies and humanities; and to break the lockstep of twelve years of doing alloted exercises for grades, so the understudy may move toward his school concentrates with some characteristic inspiration, and along these lines maybe acclimatize something that may change him† (Goodman 2007). Basic Commentary on Passage #3 The accentuation on instruction being an arrangement of evaluations is additionally stressed in this entry. All things considered, the peruser holds the information that in spite of the fact that the social structure of training is by all accounts working no matter how you look at it there are regions in which understudies are not getting enough information or if nothing else not a fair consolidation of information and hands-on understanding. Work Cited Goodman, Paul. Two Simple Proposals. 16 September 2007. < http://www. factoryschool. organization/rhood/goodman/twosim

Assessment of Mangroves Species Vulnerable to Human Threats

Evaluation of Mangroves Species Vulnerable to Human Threats Exploration PROPOSAL TITLE: ASSESSMENT OF MANGROVES SPECIES VULNERABLE TO HUMAN THREATS AT MBEGANI AND MLIGOTIN VILLAGE. JOSEPH JACOB 1.0 INTRODUCTION 1.1 BACKGROUND INFORMATION Â â Mangroves are woody plants that develop at the interface among land and ocean. happen worldwide in the tropics and subtropics, fundamentally between scopes 25â ° N and 25â ° S. they are salt open minded trees, additionally called halophytes, and are adjusted to life in brutal beach front conditions. They contain a perplexing salt filtration framework and complex root framework to adapt to salt water drenching and wave activity. They are adjusted to the low oxygen states of waterlogged mud. The word mangrove is normally viewed as a compound of the Portuguese word mangue and the English word woods. The term mangrove regularly alludes to both the plants and the woodland network. To maintain a strategic distance from disarray, Macnae (1968) recommended that mangal ought to allude to the timberland network while mangroves ought to allude to the individual plant species. Mangrove timberlands are at times called flowing backwoods, waterfront forests, or maritime downpour woods. Mangrove s wamps are found in tropical and subtropical flowing regions. Regions where mangal happens incorporate estuaries and marine shorelines. Elevated tide acquires salt water, and when the tide leave, sun powered dissipation of the seawater in the dirt prompts further increments in saltiness. The arrival of tide can flush out these dirts, taking them back to saltiness levels practically identical to that of seawater. At low tide, life forms are likewise presented to increments in temperature and drying up, and are then cooled and overflowed by the tide. Accordingly, for a plant to make due in this condition, it must endure expansive scopes of saltiness, temperature, and dampness, just as various other key natural factors consequently just a chosen few animal types make up the mangrove tree network. Around 110 species are viewed as mangroves, in the feeling of being a tree that develops in such a saline bog. Mangrove biological systems are assessed to cover 150 000 km2 around the world (Diop 1992, 1993). Mangroves can be found in more than 118 nations and domains in the tropical and subtropical locales of the world the biggest level of mangroves is found between the 5â ° N and 5â ° S scopes. Roughly 75% of universes mangroves are found in only 15 nations. Asia has the biggest sum (42%) of the universes mangroves, trailed by Africa (21%), North/Central America (15%), Oceania (12%) and South America (11%). Africa has around 35 000 km2 of mangrove biological system (Diop 1992, 1993), Nigeria has biggest mangrove region about 1mln ha. East Africa comprise of mangroves swamps along the Indian Ocean bank of East Africa in southern Mozambique, Tanzania, Kenya and southern Somalia. Delta of Zambezi in Mozambique and Rufiji River in Tanzania are huge zone of mangroves which can stretch out similarly as 50 km inland, just as littler zones along the coast. The mangroves of Bagamoyo District structure a pretty much consistent band along the 100-km coastline from Saadani tonear Kitame salt works, and afterward from Ruvu Riverto Mpiji River. They spread a territory of 5635 ha (Semesi, 1991).The primary mangrove stands are found along Wami River, 862 ha, Utondwe spring, 834 ha, Ruvu River, 2123 ha, and south of Bagamoyo to Mpiji River, 809ha. By 1989, obvious zones and salt panscovered 1639 ha (Semesi, 1991) and water in the brooks secured 812ha. 1.2 STATEMENT OF THE PROBLEM Increment in populace prompts interruption of mangroves swamps which thus has extraordinary effect on marine condition since mangroves help in break maritime waves likewise give nursery territory and natural surroundings to some marine living being. Understanding which types of mangroves are defenseless against human dangers and for what reason is progressively significant and supportive in foundation of preservation plant of specific species. 1.3 GENERAL OBJECTIVES Increment mindfulness among the individuals about significant of mangroves species and how different human exercises can divert mangroves biological system. 1.4 SPECIFIC OBJECTIVES To recognize the most undermined mangroves species found in mbegani and mlingotini town To survey different human exercises that dangers mangroves species 1.5 HYPOTHESIS 1.5.1 Null speculation. There is no mangroves species helpless against human dangers at mbegani and mlingotini town. 1.5.2 Alternative speculation. There are mangroves species helpless against human dangers at mbegani and mlingotini town. 1.6 SIGNIFICANCE OF THE STUDY Discoveries in this investigation would improve mindfulness among the nearby network about mangroves species and their imperative to the neighborhood network. Likewise the discoveries of this investigation would make mindfulness among individuals about different exercises performed by neighborhood network which dangers mangroves species. This investigation will empower characteristic asset the board by neighborhood network and upgrade definition of town strategy about condition protection. 2 LITERATURE REVIEW As per Spalding 1997 mangroves woodland vanish ordinary everywhere throughout the world. It was approximated 18.1 million km2 of mangroves woods spread worldwide however as indicated by FAO ongoing examination show that mangroves timberland is decrease to 15 million km2. Creating nations comprise 90% of mangroves woodland becoming worldwide and the greater part of them fundamentally jeopardized and about elimination in 26 nations. As indicated by duke 2007 the specialists of world mangroves give their viewâ that the endurance of mangroves in long haul is at incredible hazard because of fracture of territory and that the endure offered by the mangroves may liable to be completely lost inside 100 years. Numerous mangroves regions are feeling the squeeze of human particularly those develop along muggy protected tropical coastline. A side from man-made weight the mangroves additionally debased due natural pressure. Gauge show that worldwide misfortune every year is one million ha and s ome locale in perils of complete breakdown (kathiresan and Bingham 2001). The vast majority cause pulverization of mangroves either by intentionally or not purposely the estimation of mangroves. Livehood, biodiversity misfortune and fishery asset are decreased to mangroves misfortune, additionally decrease in populace of marine warm blooded creatures like manatees and dugongs contributed much by loss of mangroves (k. kathiresan 2001). Rates at which mangroves misfortune is a lot higher contrasted with that of tropical timberland and coral reef. 7million hectares of mangroves misfortune overall which is identical to two years loss of all woodland framework all around (k. kathiresan and Bingham 2001). Study show that man-caused exercises to contribute a lot to the annihilation of mangroves species which present critical dangers instances of those exercises are; Urbanization; inhabitation of human to numerous regions cause coast mangroves to be cleared. Territories which experience this are Singapore, Jakarta, Bangkok, Mumbai, Lagos, and free town. Horticulture; mangroves pulverized in view of farming exercises model locales of biggest delta on the planet among India and Bangladesh. As per kathiresan 2001 the mangrove territories are deforested and recovered with water to deplete the salt substance of the dirt and these zones are shielded from seawater interruption by developing banks. When the salt is filtered to adequate level, the land is developed either with paddy or coconut. Aquaculture rehearses; in a few nations aquaculture contribute in enormous scope decimation of mangroves. In 1968 and 1983, 237000 ha of mangroves were misfortune for lake development in Philippines which is half of national mangroves (Fernandez1978). As per kathiresan One significant issue related with the homesteads situated in mangrove environments is fermentation of lake waters that murders sea-going living beings. Cutting for wood, fuel and charcoal; because of its higher calorific worth twing of mangroves are utilized for kindling. Wealthy in phenol empower mangroves wood to profoundly oppose weakening as is generally utilized as lumber and their appropriate for chipboard and quality paper industry. Oil contamination; Oil or gas investigation, oil creation, and mishaps by huge oil big haulers cause critical harm to mangrove biological systems. To refer to a model, Nigeriaãšâ ¹s most extravagant oil wells are arranged near inshore where rich mangroves once existed. So also oil big hauler mishaps in the Gulf of Mexico and in the Caribbean territories brought about oil spillage that seriously harms the seaside frameworks. Accordingly, the whole mangrove biological system got influenced, causing defoliation of trees, mortality of all sessile and benthic creatures and sullying of many water fowls. When the mangrove woods is influenced by oil contamination, it will take quite a while of at any rate 10 years for recuperation of the timberland. 3 RESEARCH METHODOLOGY 3.1 STUDY AREA This work will be led in pwani locale in Bagamoyo region at mbegani and mlingotini villages.Bagamoyo is one of the 6 areas of the Pwani Region. It is circumscribed toward the North by the Tanga Region, toward the West by the Morogoro Region, toward the East by the Indian Ocean and toward the South by the Kibaha District. As per the 2012 Tanzania National Census, the number of inhabitants in the Bagamoyo District was 311,740. Mbegani and mlingotini towns found in zinga ward which its topographical directions are 6â ° 31 0 South, 38â ° 59 0 East. 3.2 STUDY MATERIAL Material which will be utilized in this investigation are: Note pad and pencil which will be utilized to take record. Downpour boots which will be utilized to shield legs from jutting mangroves root. Gloves which will be utilized for hands assurance. 3.3 DATA COLLECTION TECHNIQUES During this work information will be gathered by basic arranged surveys and through perception. 3.4 DATA ANALYSIS Assembled data from this investigation will be examined by Microsoft exceed expectations.

Accumulated Change vs. Definite Integral

Martyna Wiacek MTH 116 C-Applied Calculus 11/6/2012 Chapter 5 Writing Assignment There is a relationship between's territory, gathered change, and the distinct fundamental that we have concentrated on all through Chapter 5 in Applied Calculus. When seeing one pace of-progress work, the amassed change over an interim and the unequivocal indispensable are equal, their qualities could be sure, negative or zero. Be that as it may, the zone would never be negative since zone is consistently positive by definition. The amassed change takes a gander at the entire region of the capacity that is between the diagram and the flat axis.For example, if f (x) is a pace of-progress work the territory between f (x) and the x-hub speaks to the collected change between x = an and x = b. Nonetheless, the positive fundamental places explicit cutoff points into the capacity and the territory of a specific district can be resolved. For instance, if f (x) is a pace of-progress work it implies that: is the thing that you can think about the region. The collection of progress in a specific capacity can be assessed by utilizing the region of the district between the pace of-progress bend and the even axis.We likewise observe a comparative connection between the pace of-progress chart and the aggregated diagram that we found in subordinates. A base in the collected diagram is brought about by the pace of-progress work traverse from positive to negative. A greatest in the aggregated diagram is an aftereffect of the pace of-progress work moving from negative to positive. When there is a most extreme or least in the pace of-progress diagram you get an emphasis point in the collection chart also. Additionally, we see that in the event that the pace of-progress work is negative, at that point the gathered diagram is negative thus the collection chart is decreasing.However, when the pace of-progress diagram is expanding, it doesn't influence whether the amassed chart is expanding or diminishin g. There are a few issues in our book that show this relationship. A particular model that I accept worked superbly exhibiting it was: The diagram in the figure speaks to the pace of progress of precipitation in Florida during a serious rainstorm t hours after the downpour started falling: Part A: Use a framework to check boxes and gauge the collected region from 1 to x for estimations of x divided 1 hour separated, beginning at 0 and consummation at 6.Record the appraisals in a table. 0| 1| . 4| 2| . 65| 3| 1| 4| 1. 35| 5| 2| 6| 2. 4| Part B: Sketch the chart of the aggregation work dependent on the table qualities: Part C: Write the numerical documentation for the capacity outlined to some degree b: Part D: Write a sentence of understanding for the amassing structure 0 to 6 hours: After 6 hours of precipitation in Florida, the measure of downpour ought to gather to a gauge of 2. 4 inches.

A Lower Class Success Story

A Lower Class Success Story Which social class do you have a place with and for what reason do you have a place there? The term Âsocial classâ is ordinarily used to classify individuals into explicit gatherings in which all individuals are generally comparative. There are an enormous number of social classes in our advanced society that make up one assorted network. The individuals from a particular social class are constantly related in specific manners and for the most part share explicit things in like manner, for example, assets, pay rates, family relations, and cultural assimilation chronicles. It is generally felt that one is naturally introduced to a social class and that is the place the individual in question must stay for an amazing aggregate. While this hypothesis may at times be valid, it isn't incomprehensible for one to be naturally introduced to a lower social class, and stir their way up to an upper social class. Similarly, it is feasible for one to be naturally introduced to a status of high society and to slip into a lower class, possibly by decision or by cause and effect.Cover of the 1895 Henry T. Coates and Company edit...Through the sentiments and accounts of some of Americas present day scholars, and through an evaluation of some of Americas current big names, it very well may be fortified that the class that individuals are naturally introduced to doesn't need to be the class that they stay in for the remainder of their lives.It is unquestionably feasible for a man of lower status to accomplish an increasingly attractive position in the public eye through difficult work and assurance. A story titled ÂRagged Dick,â and composed by creator Horatio Alger (1832-1899) involves the Ârags-to-richesâ storyof a youngster named Dick who joyfully works a lower class work acquiring the lowest pay permitted by law to cover his day by day costs. While on a ship for a conference, Dick is confronted with an apparently dangerous issue in...

Macbeth As A Machiavellian Man Essays - Characters In Macbeth

Macbeth As A Machiavellian Man Macbeth was a Machiavellian man. He carried out numerous naughty violations and he paid off men to do his lethal plans. He utilized the force he had against other men to get what he needed. Macbeth needed to lead Scotland and when he was in order, on the off chance that he was stressed over a person or thing, he ensured everything was dealt with to keep his psyche very still. He had laments when he killed Duncan, however none of his transgressions sidestepped his brain, and he stayed glad during the time he ruled as lord. The main thing that he completely dreaded was Macduff and his own demise. Macbeth utilized two men to achieve his wrongdoing of executing Banquo and Fleance. Macbeth needed Banquo and Fleance dead since Macbeth didn't need any of Banquo's relatives to procure his situation after he passed on. To turn the men against Banquo, Macbeth said that it was all Banquo's shortcoming that they were poor and didn't have whatever else to live for. ?That it was he in the occasions past, which held you/So under fortune.? (3.1.117-118) Macbeth continues revealing to them how mean, childish and cutthroat Banquo was. He caused the men to accept that Banquo was their adversary. ?Both of you/Know Banquo was your foe.? (3.1.131-132) Macbeth inquires as to whether they excuse Banquo for what he has done, to test their unwaveringness towards Banquo. ?To appeal to God for this great man and for his issue,/Whose substantial hand hath bowed you to the grave.? (3.1.99-100) Macbeth can redirect the brain of an individual with his exhibition. Macbeth needed to govern Scotland and on the off chance that anything impeded him, he made certain to dispose of it, regardless of what it took. At the point when Duncan was top dog, Macbeth executed him to get his rule. When Banquo associated Macbeth with murdering the lord, Macbeth was stressed that Banquo may discover who truly slaughtered Duncan. Macbeth employed two men to execute Banquo. Macbeth likewise murdered the group of Macduff in light of the fact that Macbeth was terrified of him. ?The manor Macduff I will astound/Seize upon Fife, provide for th' edge o' th' blade? (4.1.171-172) Macduff was his adversary. Macbeth knew Macduff could murder him in a moment. Macbeth had his second thoughts after he killed King Duncan. At the point when he murdered Banquo, his apparition frequented his still, small voice by making Macbeth lament slaughtering his human structure. At the time that Macbeth killed Macduff's family, Macbeth had no second thoughts what so ever. Macbeth never however twice about the killings, in light of the fact that Macduff was unfaithful to his lord. After Macbeth slaughtered Duncan, Macbeth wished he had not killed him. ?To know my deed ?twere best not know myself./Wake Duncan with thy thumping.? (2.3.93-94) Once Macbeth was acclimated with killing individuals, he didn't have any second thoughts. There were just two things that truly made Macbeth stress and made him terrified, those being his own passing and Macduff himself. Macbeth was startled of biting the dust for he wished to be King of Scotland for eternity. One other motivation behind why he feared his passing was that the witches anticipated that Banquo's relatives would become lord, and the line of rulers would be long. Macbeth accepted that he would live perpetually he confided in the witches which likewise disclosed to him that he could never be hurt until Birnam Wood climbed Dunsinane Hill and just an individual who was not conceived from a lady could murder him. The explanation that Macbeth feared Macduff was on the grounds that Macbeth realized that he was the genuine individual who murdered the lord. Additionally, Macduff was gone to England to get the British armed force to battle Macbeth. Macbeth was frightened of Macduff in light of the fact that he was capable and sufficiently able to execute him and everybody was on Macduff, since nobody concurred with Macbeth's ways any longer. At long last, Macbeth was brutal and mean. He was a detestable man who could go to any length to be in charge. He utilized men to work, achieving his plans, and was frightened of only demise and his adversary. He didn't have any second thoughts. Macbeth was very machiavelinious. He had all the attributes of a Machavellian man. He was undoubtfully the man with the

Tips For Writing A Research Paper For Journal Publication

Tips For Writing A Research Paper For Journal PublicationThe proper course of action when it comes to how to write a research paper for journal publication is not an easy one to follow. In fact, the steps that are required to make the entire process a success are quite lengthy and complex.First and foremost, you need to have something to use as your source of original research. You can utilize anything from unpublished manuscripts to your own articles. However, it is important to remember that you should go about writing a research paper for journal publication in a systematic manner.For example, if you want to make the process more effective, the first thing that you need to do is determine the type of research paper that you will be submitting. After that, it is advisable to begin writing the topic for the paper from scratch. You need to consider your subject as well as the overall theme of the paper. This will make the entire task of writing the paper easier.Then, you need to proc eed into the initial phase. This is where you are required to state the purpose of the paper, how the paper is to be written, what type of structure should be used, what title should be assigned to the paper, and so on. Of course, you should always be specific about these things.After this, it is advisable to establish whether the paper should be based on existing material or if it should be the development of something completely new. Then, you should further elaborate on the features of the new thing that you intend to write about. This will make the entire process easier.At this point, you need to conduct interviews with the subjects of the paper. By doing so, you can get the best possible information about them. This will help you come up with excellent information about their opinions, needs, and personality traits.It is also advisable to check the availability of the information that you intend to use. If you have access to the information, then there is no need to revise the paper. However, if you do not have access to the information, then you should revise the entire research paper for journal publication before submitting it.Finally, you need to choose the type of format in which the paper should be published in. You can use the usual format of the paper or you can choose one that is easier to understand. It is important to be specific about this before starting the process of how to write a research paper for journal publication.

Modes of Interaction Between Text and Illustration in Fun Home - Literature Essay Samples

It is often thought that graphic novels and comics are in some way less sophisticated or overall lesser than traditional novels, as if the use of illustrations rather than long text descriptions makes it a more simplistic medium. However, the blending of illustrations and text in graphic novels creates just as complex of an experience, I believe, and provides an interesting opportunity to analyze the modes of interaction between text and illustrations. In this paper, I will be looking closely at Alison Bechdel’s graphic memoir Fun Home to determine some of the ways that the use of illustrations enriches the experience of reading this book. I will show, through analysis of various passages from the book, that the illustrations support the text by revealing the nature of the relationship between Alison and Bruce, using precise imagery that reflects the text, and providing further insight into the way the artist and writer of the book views her world and the people in it. The rel ationship between Alison and Bruce becomes easier for the reader to understand when looking at the subtleties in their interactions, for example a conversation between them in Bruce’s library from page 84-86 which highlights how their relationship is often cold and strained by Bruce’s disconnect with reality, and the scene between them on page 220 and 221 in the car on their way to a movie which depicts the intense struggle it is for them to communicate despite their overwhelming similarities. Precise imagery that supports the text can be found when comparing the first and last scenes in the book, which both feature Alison as a young child represented as if she is flying while she and Bruce’s relationship is compared to the myth of Icarus, and page 134 which represents Alison’s emotionally distant â€Å"artists’ colony,†(134) family in their own isolated creative bubbles in the house. Further insight into Alison’s view of the world ca n be gained by looking at examples of how she visually represents masculinity and femininity, for example the way she portrays the effeminate gay men in New York on page 190 and very masculine way she draws herself throughout the book. The multiple scenes from pages 12-21 where Alison draws Bruce as an ominous shadow like figure are also notable, as they show what an intimidating force her father was to she and her family. When the illustrations are analyzed as well as the text in Fun Home, further insight into the relationship between Alison and Bruce can be gained. One instance of this is the scene between them in Bruce’s library on pages 84-86. In text, Alison muses about her father’s mysterious ways, describing his â€Å"preference of a fiction to reality,† (85) and the eerie similarities between his death and F. Scott Fitzgerald’s, as if Bruce had planned it that way. Bruce is a mystery to her he has a complex inner world that his daughter will never understand or infiltrate, so she is left speculating after his death. Simultaneously, the images play out a seemingly mundane scene between Alison and Bruce in which she asks him for money to buy books. They are noticeably cold to each other for a father and daughter. They say only the minimum amount to each other and never make eye contact throughout the scene. Bruce never looks up from his book (a biography of Fitzgerald s wife, Zelda) and appears completely indifferent to Alison’s presence and questions. He sits surrounded by his books, reading in an armchair, looking focused and serious. Bruce is not able to break his concentration on literature for his daughter and remains in his own world despite her. Alison on the other hand has a slightly agitated facial expression, as if she dreads having to speak to her father. She is experiencing the same frustration about being locked out of her father’s world as she does when questioning his death as she writes the text portion of the book. The text is not describing literally what happens in the illustrations, however, the two components of the scene work together to build one meaning: Alisons distance from the mysterious figure that is her father. Another scene which explores their relationship is the scene in Bruce’s car on pages 220 and 221, in which they guardedly attempt to discuss their sexuality for the first time. The only te xt in the scene is their dialogue and some of Alison’s thoughts in the moment. The full spread of identical small square panels creates a feeling of suspense as if they are frozen in time. â€Å"I kept still, like he was a splendid deer i didn’t want to startle.† (120). The layout of the scene creates the intensity and stillness that she is feeling perfectly in that decisive moment where she almost makes a connection with her enigmatic father. Their quickly shifting facial expressions from one box to the next makes them both appear nervous. The sameness of the boxes, except only for the text and facial expressions of the characters, reflects the sameness of Alison and Bruce that is so apparent in this scene. They both have difficulty communicating but want to open up, they have struggled with many of the same problems related to their queer identities, they are both challenged by their complicated relationship. They are even drawn with similar facial features, s uch as their noses and jawlines, which is easy for the reader to notice when they are drawn side by side in repeating square panels for two entire pages. Fun Home is clearly a meticulously crafted book, so it is not surprising that subtle imagery in the illustrations is always working to reinforce the text. The first example of this is the comparison between the scene on the few first pages of the book which shows Alison as a young child playing â€Å"airplane† with her father, and the scene on the last few pages, which shows her again as a young child jumping into a pool as Bruce prepares to catch her. In both scenes, Alison is represented with her arms outstretched, in the air above her father as if she is flying. This is a subtle way of reflecting the text as it explores the Greek myth of Icarus, the son of the inventor Daedalus who flew so close to the sun that it melted his fake wings made of wax and feathers, and it’s reflection on Alison and Bruce. â€Å"In our particular re enactment of this mythic relationship, it was not me but my father who was to plummet from the sky.†(4). In having the ending of the b ook reflect the beginning, Alison brings the reader back to the central theme of the book: her relationship with her father. By illustrating these rare childhood moments when she felt close to her father, she brings the story away from the mysteries and complex analyses of him, and back to a place of love and innocence. Despite never understand Bruce, she still considers him her father and avoids depicting him as a villain in her story. A second instance of imagery that reinforces the text of the book is on page 134, which features an illustration of what life in Alison’s childhood home was like. â€Å"Our home was like an artists’ colony. We ate together, but otherwise were absorbed in our own separate pursuits,† (134). Both of Alison’s parents were quiet and unaffectionate people who instilled the same values in their children. She describes how she felt neglected as a child due to her parents’ â€Å"creative solitude† (133), but quickly l earned to find joy the same way. On page 134, the Bechdel family members are depicted as silhouettes in isolated bubbles across different parts of the house, all engaged in some creative activity. A home is somewhere that is expected to be lively and warm, but the feeling in this illustration is one of loneliness. The literal depiction of them in bubbles and the fact that they are only silhouettes without faces or expressions makes the home seem incredibly impersonal and distant. The emotional coldness of Alison’s family is constantly apparent in Fun Home, but this is certainly the best representation of it. The visual aspect of Fun Home also allows us to better grasp how its writer and illustrator views the world. The book deals heavily with the idea of gender and defying gender roles, so it is interesting to look at how stereotypes of masculinity and femininity are represented visually. One example is on page 190, when Alison and her family are on a trip to New York and she is exposed to the gay community for the first time. She is fascinated by â€Å"cosmeticized masculinity,† (190) that she sees in gay men, and depicts one man walking down the street with perfect hair, thick eyelashes, pierced ears, and wearing tight pants. A male ballet dancer in a show she goes to see is also drawn in an elegant pose while dancing. These things are clearly striking as feminine to Alison, and seem unnatural or strange in men to her. Another example of gender role depiction is that throughout the book, Alison is drawn in a quite masculine way. She rebels against wearing anything girly as a chi ld, and even in instances where she feels forced to wear a dress or skirt, such as her father’s funeral, they are plain and modest. The rest of the time, Alison is drawn with short hair and either androgynous or typically male clothing. When I first began reading Fun Home without any prior knowledge of the book, I assumed that Alison was a boy for the first few pages until her gender was stated. Gender and gender roles are discussed at length in the text of the book, but having visual representations reinforce this gives us as readers an even better idea of how Alison is affected by the gender roles she sees around her, and helps us question our own views of what kind characteristics we see as either masculine or feminine. Another example of how Alison’s perception of the world is subtly reinforced by the illustrations is the recurring instances in which her father is depicted as an ominous silhouette from pages 12-21. On page 12, after Alison accidentally breaks a gla ss vase, she is depicted holding the broken peice, looking terrified, as Bruce’s shadow looms over her. On page 16, he lurks behind her as she cleans a lamp. On page 21, he stands in at threshold of her bedroom after reading her a bedtime story and turning out the lights. The text explains how living with Bruce is always unpredictable and a constant source of stress for his family who are trapped, ever avoiding his wrath. â€Å"The constant tension was heightened by the fact that some encounters could be quite pleasant. His bursts of kindness were as incandescent as his tantrums were dark.† (21). The metaphor of the labyrinth from Greek mythology is used as well, to equate their extravagant house with the labyrinth and Bruce’s dark side with the minotaur hiding within. The portrayal of him as nothing more than a dark shadow makes him seem strange and inhuman, even monstrous, in moments when Alison sees him as threatening. Even as a child, she knows that her fath er has an ominous dark side which may be waiting around any corner, and she reinforces this very effectively by using creepy imagery of him as silhouette. In the graphic memoir Fun Home by Alison Bechdel, the text interacts with the illustrations in numerous interesting ways. Details found in the illustrations allow us to read more into the relationship between Alison and Bruce and add to our understanding gained from the text. Precise imagery is used to reflect and reinforce what is written in the text. Finally, close analysis of Alison’s drawings helps us to better grasp how she views her world and the people in it. Fun Home and the graphic novel medium overall are fascinating, although vastly different from the traditional novel. Illustrations combined with text, when they work together well, are just as effective as text alone at creating a complex and multi layered narrative of which deep understanding can be gained.

The Impact Of A Share Repurchase Program For A Fictional...

Summary We considered the impact of a share repurchase program for a fictional company – Blaine Kitchenware, Inc. It was determined that the liquidation of $209 million in cash and marketable securities and the addition of $50 million in long-term would result in a capital structure which was reasonable and sustainable. Overall, tax expense would be lower, the value of the firm would increase and the riskiness of the company’s equity would edge just a touch higher. From the perspective of both family and non-family shareholders, a share repurchase program is the right thing to do. The only possible objector to the proposal would likely be the U.S. Secretary of the Treasury. Background information Blaine Kitchenware, Inc. (BKI) is a publicly-traded, United States-based producer of residential kitchen small appliances (e.g. waffle irons, coffee makers, etc.). Relative to its average competitor in this marketspace, BKI has a strong EBITDA Profit Margin (22%, mean 18%) and Net Profit Margin (16%, mean 10%) but a much weaker ROE (11%, mean 25.9%). See Appendix A for a full financial comparison. The company’s current and long-standing policy to remain completely unlevered in order to keep cash available for possible future acquisitions and eliminate the interest and fee expenses associated with debt financing. As of 12/31/06 BKI had a cash stockpile of $53.6 million and no net debt. While the â€Å"appropriateness† of this policy may be debated, a few red flags have started toShow MoreRelatedWhy Satisfied Customer Defect9193 Words   |  37 Pagescompany’s success? Actually not, as Xerox Corporation discovered. Its merely s atisfied customers were six times less likely to buy again from Xerox than its totally satisfied customers. 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Earthquake - Free Essay Example

Sample details Pages: 32 Words: 9529 Downloads: 1 Date added: 2017/06/26 Category Statistics Essay Did you like this example? Abstract Earthquake is an independent natural phenomenon of vibration of the ground which can become dangerous mainly when it is considered in relation with structures. Earthquakes can be very weak, without even realizing them but (they) can also be strong enough to result serious damages to buildings which can lead to injures or even loss of human lives. In order to avoid any structural damage the legislation sets conditions on the building design. Don’t waste time! Our writers will create an original "Earthquake" essay for you Create order For that purpose, Eurocode 8 is established in European countries and sets up all the appropriate criteria and measures for the design of buildings for earthquake resistance (Eurocode 8 is established in Europe and suggests 4 different methods of analysis.) In this project the response of eight buildings is examined (investigated) under seismic excitation. Firstly, is examined the case of four buildings (1 storey, 2 storey, 3 storey and 4 storey) where all the storeys are facsimile (replica). Afterwards, is examined the case of four buildings (again 1-4 storeys) where while the storeys of each building are increased, the mass, the stiffness and the height of each floor are decreased. Both the lateral method of analysis and the modal response spectrum analysis are used as recommended by EC8 to calculate the inter-storey drifts, the total shear forces and the overturning moments at the base of each building. The results are plotted and compared so that useful outcomes can be obtained. 1. Introduction One of the most frightening and destructive phenomena of nature is a severe earthquake and its terrible aftereffects especially when they are associated with structures. An earthquake is a sudden movement of the Earth, caused by the abrupt release of strain that has accumulated over a long time. Earthquake intensity and magnitude are the most common used parameters in order to understand and compare different earthquake events.( are the most common parameters used to appreciate and compare.) In recent years have been giving increasing attention to the design of buildings for earthquake resistance. Specific (particular) legislation is (have been) established to make structures able to resist at any seismic excitation. In Europe, Eurocode 8 explains how to make buildings able to resist to earthquakes, and recommends the use of linear and non-linear methods for the seismic design of the buildings Simple structures can be modelled either as equivalent single degree of freedom systems (SDOF) or as a combination of SDOF systems. In this project 8 different buildings with a variation either on the number of storeys or on their characteristics are simulated as a combination of SDOF systems for which the mode shapes and their corresponding eigenfrequencies and periods are calculated. Afterwards the fundamental frequency is obtained for each case and the elastic design is used in order to obtain the base shear forces and the overturning moments. (INELASTIC DESIGN AND LATERAL FORCE METHOD) 2. Literature review 2.1 Introduction to earthquake engineering Definition and earthquake derivation or generation or creation or production or formation or genesis The lithosphere is the solid part of Earth which includes or consists of the crust and the uppermost mantle. The sudden movement of the earths lithosphere is called earthquake (technical name seism). Fractures in Earths crust where sections of rock have slipped past each other are called Faults. Most earthquakes occur along Faults. Generally, earthquakes are caused by the sudden release of built-up stress within rocks along geologic faults or by the movement of magma in volcanic areas. The theory of plate tectonics provides geology with a comprehensive theory that explains how the Earth works. The theory states that Earths outermost layer, the lithosphere, is broken into 7 large, rigid pieces called plates: the African, North American, South American, Australian- Indian, Eurasian, Antarctic, and Pacific plates. Several subcontinental plates also exist, including the Caribbean, Arabian, Nazca, Philippines and Cocos plates. Boundaries of tectonic plates are found at the edge of the lithospheric plates and can be of various forms, depending on the nature of relative movements. By their distinct motions, three main types can be characterized. The three types are: subduction zones (or trenches), spreading ridges (or spreading rifts) and transform faults.. convergent, divergent and conservative. At subduction zone boundaries, plates move towards each other and the one plate subducts underneath the other ( : one plate is overriding another, thereby forcing the other into the mantle beneath it.) The opposite form of movement takes place at spreading ridge boundaries. At these boundaries, two plates move away from one another. As the two move apart, molten rock is allowed to rise from the mantle to the surface and cool down to form part of the plates. This, in turn, causes the growth of oceanic crust on either side of the vents. As the plates continue to move, and more crust is formed, the ocean basin expands and a ridge system is created. Divergent boundaries are responsible in part for driving the motion of the plates. At transform fault boundaries, plate material is neither created nor destroyed at these boundaries, but rather plates slide past each other. Transform faults are mainly associated with spreading ridges, as they are usually formed by surface movement due to perpendicular spreading ridges on either side. Earthquake Location When an earthquake occurs, one of the first questions is where was it?. An earthquakes location may tell us what fault it was on and where the possible damage most likely occurred. The hypocentre of an earthquake is its location in three dimensions: latitude, longitude, and depth. The hypocentre (literally meaning: below the center from the Greek ), or focus of the earthquake, refers to the point at which the rupture initiates and the first seismic wave is released. As an earthquake is triggered, the fault is associated with a large area of fault plane. The point directly above the focus, on the earths surface where the origin of an earthquake above ground. The epicentre is the place on the surface of the earth under which an earthquake rupture originates, often given in degrees of latitude (north-south) and longitude (east-west). The epicentre is vertically above the hypocentre. The distance between the two points is the focal depth. The location of any station or observation can be described relative to the origin of the earthquake in terms of the epicentral or hypocentral distances. Propagation of seismic waves Seismic waves are the energy generated by a sudden breaking of rock within the earth or an artificial explosion that travels through the earth and is recorded on seismographs. There are several different kinds of seismic waves, and they all move in different ways. The two most important types of seismic waves are body waves and surface waves. Body waves travel deep within the earth and surface waves travel near the surface of the earth. Body waves: There are two types of body waves: P-waves (also pressure waves) and S-waves (also shear waves). P-waves travel through the Earth as longitudinal waves whose compressions and rarefactions resemble those of a sound wave. The name P-wave comes from the fact that this is the fastest kind of seismic wave and, consequently, it is the first or Primary wave to be detected at a seismograph. Speed depends on the kind of rock and its depth; usually they travel at speeds between 1.5 and 8 kilometers per second in the Earths crust. P waves are also known as compressional waves, because of the pushing and pulling they do. P waves shake the ground in the direction they are propagating, while S waves shake perpendicularly or transverse to the direction of propagation. The P-wave can move through solids, liquids or gases. Sometimes animals can hear the P-waves of an earthquake S-waves travel more slowly, usually at 60% to 70% of the speed of P waves. The name S-wave comes from the fact that these slower waves arrive Secondary after the P wave at any observation point. S-waves are transverse waves or shear waves, so that particles move in a direction perpendicular to that of wave propagation. Depending in whether this direction is along a vertical or horizontal plane, S-waves are subcategorized into SV and SH-waves, respectively. Because liquids and gases have no resistance to shear and cannot sustain a shear wave, S-waves travel only through solids materials. The Earths outer core is believed to be liquid because S-waves disappear at the mantle-core boundary, while P-waves do not. (3: https://www.globalchange.umich.edu/globalchange1/current/lectures/nat_hazards/nat_hazards.html) Surface waves: The surface waves expand, as the name indicates, near the earths surface. The amplitudes of surface waves approximately decrease exponentially with depth. Motion in surface waves is usually larger than in body waves therefore surface waves tend to cause more damage. They are the slowest and by far the most destructive of seismic waves, especially at distances far from the epicenter. Surface waves are divided into Rayleigh waves and Love waves. Rayleigh waves, also known as ground roll, are the result of an incident P and SV plane waves interacting at the free surface and traveling parallel to that surface. Rayleigh waves (or R-waves) took their name from (named for) John Strutt, Lord Rayleigh who first described them in 1885 ( who mathematically predicted the existence of this kind of wave in 1885) and they are an important kind of surface wave. Most of the shaking felt from an earthquake is due to the R-wave, which can be much larger than the other waves. In Rayleigh waves the particles of soil move vertically in circular or elliptical paths, just like a wave rolls across a lake or an ocean. As Rayleigh wave particle motion is only found in the vertical plane, this means that they most commonly found on the vertical component of seismograms. The Rayleigh equation is: Love waves (also named Q waves) are surface seismic waves that cause horizontal shifting of the earth during an earthquake. They move the ground from side to side in a horizontal plane but at right angles to the direction of propagation. Love waves took their name from A.E.H. Love, a British mathematician who worked out the mathematical model for this kind of wave in 1911. Love waves are the result from the interaction with SH-waves. They travel with a slower velocity than P- or S- waves, but faster than Rayleigh waves, their speed relate to the frequency of oscillation. Earthquake size: Earthquake measurement is not a simple problem and it is hampered by many factors. The size of an earthquake can be quantified in various ways. The intensity and the magnitude of an earthquake are terms that were developed in an attempt to evaluate the earthquake phenomenon and they are the most commonly used terms to express the severity of an earthquake. Earthquake intensity: Intensity is based on the observed effects of ground shaking on people, buildings, and natural features. It varies from place to place within the disturbed region depending on the location of the observer with respect to the earthquake epicenter. Earthquake magnitude: The magnitude is the most often cited measure of an earthquakes size. The most common method of describing the size of an earthquake is the Richter magnitude scale, ML. This scale is based on the observation that, if the logarithm of the maximum displacement amplitudes which were recorded by seismographs located at various distances from the epicenter are put on the same diagram and this is repeated for several earthquakes with the same epicentre, the resulting curves are parallel to each other. This means that if one of these earthquakes is taken as the basis, the coordinate difference between that earthquake and every other earthquake, measures the magnitude of the earthquake at the epicentre. Richter defined as zero magnitude earthquake one which is recorded with 1m amplitude at a distance of 100 km. Therefore, the local magnitude ML of an earthquake is based on the maximum trace amplitude A and can be estimated from the relation: ML= log A log A (3) Where A is the amplitude of the zero magnitude earthquake (ML=0). The Richter magnitude scale can only be used when seismographs are within 600 km of the earthquake. For greater distances, other magnitude scales have been defined. The most current scale is the moment magnitude scale MW, which can be used for a wide range of magnitudes and distances. Two main categories of instruments are used for the quantitative evaluation (estimation, assessment) of the earthquake phenomenon: the seismographs which record the displacement of the ground as a function of time, and the accelerographs (or accelerometers) which record the acceleration of the ground as a function of time, producing accelerograms. X the accelerogram of the 1940 El Centro earthquake. For every earthquake accelerogram, elastic or linear acceleration response spectrum diagrams can be calculated. (obtained, estimated) The response spectrum of an earthquake is a diagram of the peak values of any of the response parameters (displacement, acceleration or velocity) as a function of the natural vibration period T of the SDOF system, subjected to the same seismic input. All these parameters can be plotted together in one diagram which is called the tripartite plot (also known as four coordinate paper). 2.2 Earthquake and Structures simulation 2.2.1 Equation of motion of SDOF system Introduction Vibration is the periodic motion or the oscillation of an elastic body or a medium, whose state of equilibrium has been disturbed. : whose position of equilibrium has been displaced. There are two types of vibrations, free vibration and forced vibration. Vibration can be classified as either free or forced. A structure is said to be in a state of free vibration when it is disturbed from its static equilibrium by given a small displacement or deformation and then released and allowed to vibrate without any external dynamic excitation. Number of Degrees of Freedom (DOF) is the number of the displacements that are needed to define the displaced position of the masses relative to their original position. Simple structures can be idealised as a system with a lumped mass m supported by a massless structure with stiffness k. It is assumed that the energy is dissipated through a viscous damper with damping coefficient c. Only one displacement variable is required in order to specify the position of the mass in this system, so it is called Singe Degree of Freedom (SDOF) system. Undamped Free Vibration of SDOF systems Furthermore, if there is no damping or resistance in the system, there will be no reduction to the amplitude of the oscillation and theoretically the system will vibrate forever. Such a system is called undamped and is represented in the below: By taking into consideration the inertia force fin and the elastic spring force fs the equation of the motion is given by: fin + fs = 0 m+ ku = 0 Considering the initial conditions u(0) and (0), where u(0) is the displacement and (0) is the velocity at the time zero, the equation (4) has the general solution: u(t) = u(0) cosnt + sinnt where n is the natural frequency of the system and is given by, n = (6) The natural period and the natural frequency can be defined by the above equations: Tn = (7) fn = (8) Viscously damped Free Vibration of SDOF systems The equation of motion of such a system can be developed from its free body diagram below: Considering the inertia force fin, the elastic spring force fs and the damping force fD, the equation of the motion is given by: m+ c+ ku = 0 (9) Dividing by m the above equation gives: + 2n+ 2u = 0 (10) where is the critical damping and is given by: = (11) and Cc is the critical damping ratio given by: Cc = 2mn * If 1 or c Cc the system is overdamped. It returns to its equilibrium position without oscillating. * If = 1 or c = Cc the system is critically damped. It returns to its equilibrium position without oscillating, but at a slower rate. * If 1 or c Cc the system is underdamped. The system oscillates about its equilibrium position with continuously decreasing amplitude. Taking into account that all the structures can be considered as underdamped systems, as typically their damping ratio is less than 0.10 the equation (9) for the initial conditions u (0) and (0) gives the solution below: U (t) = e[u(0)cosn+[.+sinDt] (13) where D is the natural frequency of damped vibration and is given by: D = n (14) Hence the natural period is: TD = (15) Undamped Forced Vibration of SDOF system The equation of motion of such a system can be developed from its free body diagram below: Considering the inertia force fin, the elastic spring force fs and the external dynamic load f(t), the equation of the motion is given by: m+ ku = f(t) (16) where f(t) = f0 sint is the maximum value of the force with frequency By imposing the initial conditions u(0) and (0) the equation (16) has a general solution: u(t) = u(0)cosnt + sinnt + sint (17) Damped Forced Vibration of SDOF system The equation of motion of such a system can be developed from its free body diagram below: Considering the inertia force fin, the elastic spring force fs, the damping force fD and the external dynamic load f(t), the equation of the motion is given by: m+ c+ ku = f(t) (18) where f(t) = f0 sint The particular solution of equation (18) is: up = Csint + Dcost (19) And the complementary solution of equation (18) is: (20) uc = e(AcosDt + Bsinnt) (20) 2.2.2 Equation of motion of MDOF system The equation of motion of a MDOF elastic system is expressed by: M+ C+ Ku = -MAI(t) (21) where M is the mass matrix, C is the damping matrix, K is the stiffness matrix, u is the acceleration vector, u is the velocity vector and u is the displacement vector. Finally, AI is a vector with all the elements equal to unity and ug(t) is the ground acceleration. 2.2 Earthquake and Structures simulation 2.2.1 Equation of motion of SDOF system Introduction Vibration is the periodic motion or the oscillation of an elastic body or a medium, whose state of equilibrium has been disturbed. : whose position of equilibrium has been displaced. There are two types of vibrations, free vibration and forced vibration. Vibration can be classified as either free or forced. A structure is said to be in a state of free vibration when it is disturbed from its static equilibrium by given a small displacement or deformation and then released and allowed to vibrate without any external dynamic excitation. Number of Degrees of Freedom (DOF) is the number of the displacements that are needed to define the displaced position of the masses relative to their original position. Simple structures can be idealised as a system with a lumped mass m supported by a massless structure with stiffness k. It is assumed that the energy is dissipated through a viscous damper with damping coefficient c. Only one displacement variable is required in order to specify the position of the mass in this system, so it is called Singe Degree of Freedom (SDOF) system. Undamped Free Vibration of SDOF systems Furthermore, if there is no damping or resistance in the system, there will be no reduction to the amplitude of the oscillation and theoretically the system will vibrate forever. Such a system is called undamped and is represented in the below: By taking into consideration the inertia force fin and the elastic spring force fs the equation of the motion is given by: fin + fs = 0 m+ ku = 0 Considering the initial conditions u(0) and (0), where u(0) is the displacement and (0) is the velocity at the time zero, the equation (4) has the general solution: u(t) = u(0) cosnt + sinnt where n is the natural frequency of the system and is given by, n = (6) The natural period and the natural frequency can be defined by the above equations: Tn = (7) fn = (8) Viscously damped Free Vibration of SDOF systems The equation of motion of such a system can be developed from its free body diagram below: Considering the inertia force fin, the elastic spring force fs and the damping force fD, the equation of the motion is given by: m+ c+ ku = 0 (9) Dividing by m the above equation gives: + 2n+ 2u = 0 (10) where is the critical damping and is given by: = (11) and Cc is the critical damping ratio given by: Cc = 2mn * If 1 or c Cc the system is overdamped. It returns to its equilibrium position without oscillating. * If = 1 or c = Cc the system is critically damped. It returns to its equilibrium position without oscillating, but at a slower rate. * If 1 or c Cc the system is underdamped. The system oscillates about its equilibrium position with continuously decreasing amplitude. Taking into account that all the structures can be considered as underdamped systems, as typically their damping ratio is less than 0.10 the equation (9) for the initial conditions u (0) and (0) gives the solution below: U (t) = e[u(0)cosn+[.+sinDt] (13) where D is the natural frequency of damped vibration and is given by: D = n (14) Hence the natural period is: TD = (15) Undamped Forced Vibration of SDOF system The equation of motion of such a system can be developed from its free body diagram below: Considering the inertia force fin, the elastic spring force fs and the external dynamic load f(t), the equation of the motion is given by: m+ ku = f(t) (16) where f(t) = f0 sint is the maximum value of the force with frequency By imposing the initial conditions u(0) and (0) the equation (16) has a general solution: u(t) = u(0)cosnt + sinnt + sint (17) Damped Forced Vibration of SDOF system The equation of motion of such a system can be developed from its free body diagram below: Considering the inertia force fin, the elastic spring force fs, the damping force fD and the external dynamic load f(t), the equation of the motion is given by: m+ c+ ku = f(t) (18) where f(t) = f0 sint The particular solution of equation (18) is: up = Csint + Dcost (19) And the complementary solution of equation (18) is: uc = (AcosDt + Bsinnt) (20) 2.2.2 Equation of motion of MDOF system The equation of motion of a MDOF elastic system is expressed by: M+ C+ Ku = -MAI(t) (21) where M is the mass matrix, C is the damping matrix, K is the stiffness matrix, u is the acceleration vector, u is the velocity vector and u is the displacement vector. Finally, AI is a vector with all the elements equal to unity and g(t) is the ground acceleration. 3. Description of the Method 3.1 Simplified Multi-Storey Shear Building Model It is almost impossible to predict precisely which seismic action a structure will undergo during its life time. Each structure must be designed to resist at any seismic excitation without failing. For this reason each structure is designed to meet the requirements of the design spectrum analysis based in EC8. Also some assumptions are necessary in order to achieve the best and the simplest idealization for each multi store building. Initially it is assumed that the mass of each floor is lumped at the centre of the floor and the columns are massless. The floor beams are completely rigid and incompressible; hence the floor displacement is being transferred equally to all the columns. The columns are flexible in horizontal displacement and rigid in vertical displacement, while they are provided with a fully fixed support from the floors and the ground. The building is assumed to be symmetric about both x and y directions with symmetric column arrangement. The consequence of this is tha t the centre of the mass of each floor to coincide with the centre of the stiffness of each floor. The position of this centre remains stable up the entire height of the building. Finally, it is assumed that there are no torsional effects for each of the floors. If all the above assumptions are used the building structure is idealised as a model where the displacement at each floor is described by one degree of freedom. Thus, for a jth storey building, j degrees of freedom required to express the total displacement of the building. The roof of the building has always to be considered as a floor. The mass matrix M is a symmetric diagonal nxn matrix for a n-storey building and is given below. Each diagonal value in the matrix represents the total mass of one beam and its two corresponding columns which are assumed to be lumped at each level. M = Stiffness method is used to formulate the stiffness matrix. K is the lateral stiffness of each column and is given by the relationship: K = (22) where EI is the flexural stiffness of a column. The lateral stiffness of each column is clamped at the ends and is imposed in a unit sway. The stiffness of each floor is the sum of the lateral force of all columns in the floor. The stiffness matrix is for a n-storey building is: K = In order to calculate the natural modes of the vibration, the system is assumed that vibrates freely. Thus, g(t)=0, which for systems without damping (c=0) the equation (21) specializes to: M+ Ku = 0 (23) The displacement is assumed to be harmonic in time, this is: = -2Ueit (24) Hence equation (23) becomes: (K 2M)U = 0 (25) The above equation has the trivial solution u=0. For non trivial solutions, u0 the determinant for the left hand size must be zero. That is: |K 2 M| = 0 (26) This condition leads to a polynomial in terms of 2 with n roots, where n is the size of matrices and vectors as cited above. These roots are called eigenvalues. By applying the equation (6) (7), the natural frequency and the natural period of vibration for each mode shape can be determined. Each eigenvalue has a relative eigenvector which represent the natural ith mode shape. After the estimation of the eigenvector in order to compare the mode shapes, scale factors are applied to natural modes to standarise their elements associated with various degrees of freedom (X). This process is called normalization. Hence, after the estimation of the eigenvectors each mode is normalised so that the biggest value is X: eigenvector notation. unity. The eigenvectors of a symmetric matrix corresponding to distinct eigenvalues are orthogonal. This aspect is expressed by the following expression: UiTKUij = UiTMUij (27) The classical eigenvalue problem has the following form: (M-1K I) u = 0 (28) where =2 and I is the identity matrix. EC8 suggests that the response in two modes i and j can be assumed independent of each other when Tj 0.9 Ti where Ti and Tj are the periods of the modes i and j respectively (always Ti Tj). The calculated fundamental period can be checked by the equation that EC8 suggests: T = Ct*H3/4 where T is the fundamental period of the building, Ct is a coefficient and H is the total height of the building; this expression is valid buildings that their total height is not more than forty metres 3.2 Elastic Analysis The response method is used to estimate the maximum displacement (uj), pseudo- velocity (j) and acceleration (j) for each calculated natural frequency. It is assumed that the MDOF system oscillates in each of its modes independently and displacements, velocities and accelerations can be obtained for each mode separately considering modal responses as SDOF responses. Each maximum, displacement velocity and acceleration read from the design spectrum is multiplying by the participation factor i to re-evaluate the maximum values expressed ujmax, jmax, jmax respectively. The participation factor i is defined by the following equation: (28) where UijT is the transpose vector of each of the mode vectors, M is the mass matrix, AI is the unit vector and Uij is the mode shape vector. The actual maximum displacements of the jth mode are given by: u = ujmaxUj Afterwards, the root-mean-square (RMS) approximation is used in order to calculate the maximum displacement for each floor. In this approach, all the maximum values for each mode, are squared and summed and their square root is derived. If we let Dmax be the maximum displacement then: Dmax = (29) A very variable parameter to characterise the seismic behaviour of a building is the Inter-Storey Drift which can be obtained by the following equation: i = Di Di-1/hi (30) where Di, Di-1, are the horizontal displacements for two contiguous floors and hi is the corresponding height of the floor. The calculated values must be lower than 4% in order to agree with the Eurocode. Afterwards the horizontal inertia forces Fjs applied at each floor are obtained by applying the following equation: Fj = MUjjmax (31) where M is the mass matrix, Uj is the eigenvector for each mode and jmax is the maximum acceleration. As it is suggested from the EC8, the root-mean-approximation is used again in order to obtain the total lateral forces. EC8 suggests that the combined lateral force at each floor is given by the square root of the sum of the squares of each lateral force at each floor of all the modes. If we let Ftotal,i the maximum base shear force then: Ftotal,j = [1] (32) where Fij is the lateral force at floor i of the mode j. Once the total lateral forces and the shear forces have been obtained, the maximum overturning moment is calculated. 3.3 Inelastic Analysis The inelastic response spectra are generally obtained by the scaling of the elastic design spectra via the use of response modification factors. No effect of the energy absorption was assumed in the structure for the calculated values by using the elastic design spectrum. By introducing the ductility factor this parameter is taking into consideration. Newmark has described the ductility parameter as the ratio of maximum displacement to the displacement at yield. Apparently when yielding does not take place the concept of ductility is not relevant and is taken equal to unity. he system is described by the damping ratio , the natural frequency n, and the ductility factor . In order to calculate the new set of values of acceleration, displacement and velocity the design response spectrum has to be constructed. Newmarks procedure leads to the construction of two modified spectra. 1. For maximum acceleration: In this case the elastic design spectrum is reduced by the appropriate coefficients. The acceleration region of the graph is multiplied by the following factor: (33) While the displacement region is multiplied by: (34) X: Construction of the inelastic maximum acceleration design spectrum. Where AB = [AB] And CD = [CD] 2. For maximum displacement: In this case the elastic design spectrum is increased by the appropriate coefficients. The inelastic maximum displacement spectrum is constructed and is presented in X. As it is observed AB is the same as the elastic spectrum, while CD and EF are each times CD and EF on the acceleration scale. Once the construction of both the above inelastic design spectra is completed, a new set of values of acceleration and displacement can be obtained. Each displacement and acceleration read from the spectrum is multiplying by the participation factor i, in order to modify the calculated values. After the re-evaluation of the displacement and the accelerations the procedure is the same as in the elastic analysis. The participation factors remain stable for the inelastic analysis as the ductility factor does not affect them. The actual maximum accelerations and displacements of the jth mode can be obtained by applying the equation (X) and then by applying the RMS approximation. Herein, the inter-storey drift and the lateral forces FJs applied to each floor can be obtained by using the equations (X) and (X) respectively. Once the total lateral forces and the shear forces have been obtained, the maximum overturning moment is calculated. 4 Results In this project two different cases are examined: 1. Four buildings with a variation in the number of storeys and differentiation in their characteristics. 2. Four buildings from one until four storeys where all the levels are identical between them. Case 1: Firstly, a one storey building is examined and the elastic and inelastic responses are analysed. Afterwards one storey is added which means that two degrees of freedom are needed to describe the total displacement of the structure. The second floor of the building has redundant mass, height and stiffness. Afterwards, one more storey is added above the existing two storey building with even less mass, height and stiffness. The elastic and inelastic responses are then analysed for the three storey building. Finally, one more storey is added which is identical as the last one and the four storey building is analysed. One storey building The dimensions of both the building and its elements are presented in the below. X: (a) dimensions of the one storey building, (b) beam cross section (c) column cross section. By applying the equation (22) stiffness K can be obtained and the calculated value is represented below: K = 9.6*107 Afterwards, by applying the equation (26) the eigenvalue 2 is obtained as. The natural frequency, which in this case is the fundamental frequency as well, is obtained by applying the equation (6) and the period by applying the equation (7). The calculated values are represented in the table below: Eigenvalue 2 (rad2/s2) Frequency (Hz) Period (s) 192 2.205 0.453 Table X: Eigenvalue, Frequency and Period for the one storey building. Elastic Analysis The maximum displacement, Pseudo-Velocity and Acceleration are obtained from the elastic design spectrum as: Pseudo- Velocity (m/s) Displacement (m) Acceleration (g) 0.750 0.092 0.636 Table X: Maximum Displacement, Pseudo- Velocity and Acceleration for the one storey building. The Inter- Storey Drift is obtained in percentages and it is =1.840 %. Afterwards, the maximum base shear force and the maximum overturning moment for the elastic analysis are represented in Table X. Maximum Base Shear Force (N) Maximum Overturning Moment (Nm) 3.120*106 2.560*107 Table X: The Maximum Base Shear Force and the Maximum Overturning Moment for the one storey building. Inelastic Analysis The maximum displacement and Acceleration are obtained from the inelastic design spectrum as: Displacement (m) Acceleration (g) 0.193 0.123 Table X: Maximum Displacement, Pseudo- Velocity and Acceleration for the one storey building. The Inter- Storey Drift is obtained in percentages and it is =3.860 %. The maximum base shear force and the maximum overturning moment for the inelastic analysis are calculated and presented below: Maximum Base Shear Force (N) Maximum Overturning Moment (Nm) 6.033*106 1.560*107 Table X: The Maximum Base Shear Force and the Maximum Overturning Moment for the one storey building (Inelastic design) Two storey building One floor is added above the existing one storey building. The height of the new floor, the mass and the X EI are reduced as it is shown in the below. The mass matrix M for the above building is a symmetric, diagonal 22 matrix and is given below: The stiffness matrix is derived applying equation (22) to the general form of stiffness matrix ( 15). For a 2 storey building, the stiffness matrix K is a symmetric 22 matrix: By applying the equation x to x the stiffness matrix is obtained. to By applying the stiffness method to a 2 storey building, the stiffness matrix K which is a symmetric 22 matrix, becomes: By using the equation (6) (7), the natural frequency and the natural period of vibration for each mode shape can be determined. The calculated eigenvalues, and the related natural frequencies and periods are given in the table below: Mode Shape Eigenvalue 2 (rad2/s2) Frequency (Hz) Period (s) 1 93.026 1.535 0.651 2 773.974 4.428 0.226 Table X: Eigenvalues, Frequencies and Periods for the 2 storey building. The modes of the shape and their corresponding periods are shown below: Using the method of normalisation the eigenvectors become: The two different mode shapes for the 2 storey building are presented below graphically. Mode Shape Frequency (Hz) Pseudo- Velocity (m/s) Displacement (m) Acceleration (g) 1 1.535 0.750 0.113 0.510 2 4.428 0.729 0.045 1.080 Table X: Maximum Displacement, Pseudo- Velocity and Acceleration for the 2 storey building. The two calculated participation factors is are represented in the table below: 1 2 1.137 0.145 Table X: Participation Factors. The maximum displacement, Pseudo-Velocity and Acceleration from Table X are multiplied by the respective participation factors from Table X. The scaled parameters of the motion are given in the table below. Mode Shape Frequency (Hz) Pseudo- Velocity (m/s) Displacement (m) Acceleration (g) 1 1.535 0.852 0.128 0.589 2 4.428 0.106 6.541*10-3 1.158 Table X: Scaled parameters of the motion for each mode due to the participation factors. By applying the root-mean-square (RMS) approximation (equation 29) the maximum displacement can be obtained for both of the floors: D1 = 0.097 m for the first floor and D2 = 0.129 m for the second floor. Afterwards the Inter- Storey Drift is obtained in percentages for both of the floors and it is 1=1.936 % for the first one and 2 = 0.795 % for the second. The above values are in agreement with the Eurocode as they are lower than 4%. The Maximum Base Shear Force and the Maximum Overturning Moment are calculated by applying the root-mean-approximation and the results are presented in the above table: Maximum Base Shear Force (N) Maximum Overturning Moment (Nm) 4.468*106 3.168*107 Table X: The Maximum Base Shear Force and the Maximum Overturning Moment for the 2 storey building. Inelastic Analysis The inelastic maximum acceleration and the inelastic maximum displacement design spectra are constructed by using a ductility factor of 5 (=5). Hence the acceleration and the displacement are re-evaluated. The results are given in the table below. Mode Shape Frequency (Hz) Displacement (m) Acceleration (g) 1 1.535 0.198 0.100 2 4.428 0.100 0.172 Table X: Calculated displacements and accelerations for each mode (Inelastic design). Afterwards, each displacement and acceleration s multiplied by the respective participation factor from Table (X) and the scaled parameters are given below: Mode Shape Frequency (Hz) Displacement (m) Acceleration (g) 1 1.535 0.225 0.114 2 4.428 0.015 0.025 Table X: Scaled parameters of the motion for each mode due to the participation factors (Inelastic design). Herein, the Inter-Storey Drift is obtained in percentages for both of the floors and it is: 1=3.397 % for the first one and 2 = 1.390 % for the second. It is observed an increment at the above values comparing them with the corresponding values of the elastic analysis but they are still in agreement with the Eurocode as they are lower than 4%. The Maximum Base Shear Force and the Maximum Overturning Moment are calculated and the results are presented in the table below: Maximum Base Shear Force (N) Maximum Overturning Moment (Nm) 8.657*105 6.114*106 Table X: The Maximum Base Shear Force and the Maximum Overturning Moment for the 2 storey building (Inelastic design). As it is observed, there is a noticeable decrease of the values in Table (X) comparing them with the corresponding values from the elastic design in Table(x). As it is shown, the ductility factor reduces the total shear force and the total overturning moment of the building. 3. Three storey building One floor is added above the existing two storey building. The height of the new floor, the mass and the stiffness are reduced. The below represents the dimensions for the three storey building and its elements. The mass matrix M for a 3 storey building is a symmetric, diagonal 33 matrix and is given below: The stiffness matrix is derived applying equation (22) to the general form of stiffness matrix ( 15). For a 3 storey building, the stiffness matrix K is a symmetric 33 matrix: By using the equation (6) (7), the natural frequency and the natural period of vibration for each mode shape can be determined. The calculated eigenvalues, and the corresponding natural frequencies and periods are given in the above table: Mode Shape Eigenvalue 2 (rad2/s2) Frequency (Hz) Period (s) 1 70.673 1.338 0.747 2 625.839 3.982 0.251 3 2.17*103 7.414 0.135 Table X: Eigenvalues, Frequencies and Periods for the 3 storey building. The modes of the shape and their corresponding periods are shown below: Using the method of normalisation the eigenvectors become: The different mode shapes for the 3 storey building are presented below graphically. Mode Shape Frequency (Hz) Pseudo- Velocity (m/s) Displacement (m) Acceleration (g) 1 1.338 0.750 0.123 0.477 2 3.982 0.750 0.062 1.000 3 7.414 0.345 0.010 1.087 Table X: maximum Displacement, Pseudo- Velocity and Acceleration for the 3 storey building. The three calculated participation factors is are represented in the table below: 1 2 3 1.165 0.213 0.014 Table X: Participation Factors. The maximum displacement, Pseudo-Velocity and Acceleration from Table X are multiplied by the respective participation factors from Table X. The scaled parameters of the motion are given in the table below. Mode Shape Frequency (Hz) Pseudo- Velocity (m/s) Displacement (m) Acceleration (g) 1 1.338 0.874 0.143 0.556 2 3.982 0.160 0.013 0.213 3 7.414 4.705*10-3 1.364*10-4 0.015 Table X: Scaled parameters of the motion for each mode due to the participation factors. Maximum displacement and the Inter Storey Drift for each floor are given below: D1 = 0.098m, D2 = 0.136m and D3 = 0.144m 1 = 1.951 %, 2 = 0.958 % and 3 = 0.263 % The above values of the Inter Storey Drift are in agreement with the Eurocode as they are lower than 4%. The Maximum Base Shear Force and the Maximum Overturning Moment are calculating by applying the root-mean-approximation and the results are presented in the table below: Maximum Base Shear Force (N) Maximum Overturning Moment (Nm) 5.005*106 4.093*107 Table X: The Maximum Base Shear Force and the Maximum Overturning Moment for the 3 storey building. Inelastic Analysis The inelastic maximum acceleration and the inelastic maximum displacement design spectra are constructed by using a ductility factor of 5 (=5). Hence the acceleration and the displacement are re-evaluated. The results are given in the table below. Mode Shape Frequency (Hz) Displacement (m) Acceleration (g) 1 1.338 0.200 0.090 2 3.982 0.131 0.172 3 7.414 0.022 0.172 Table X: Calculated displacements and accelerations for each mode (Inelastic design). Afterwards, each displacement and acceleration is multiplied by the respective participation factor from Table (X) and the scaled parameters are given below: Mode Shape Frequency (Hz) Displacement (m) Acceleration (g) 1 1.338 0.233 0.105 2 3.982 0.028 0.037 3 7.414 3*10-4 2.435*10-3 Table X: Scaled parameters of the motion for each mode due to the participation factors (Inelastic design). Maximum displacement and the Inter Storey Drift for each floor are given below: D1 = 0.160m, D2 = 0.221m and D3 = 0.234m 1 = 3.192 %, 2 = 1.536 % and 3 = 0.439 % It is observed an increment at the values of the Inter-Storey Drift comparing them with the corresponding values of the elastic analysis but they are still in agreement with the Eurocode as they are lower than 4%. The Maximum Base Shear Force and the Maximum Overturning Moment are calculated and the results are presented in the table below: Maximum Base Shear Force (N) Maximum Overturning Moment (Nm) 9.439*105 7.721*106 Table X: The Maximum Base Shear Force and the Maximum Overturning Moment for the 3 storey building (Inelastic design). Four storey building One floor is added above the existing three storey building. The new floor has identical characteristics to the third floor. The below presents the dimensions for the four storey building and its elements. The mass matrix M is given below: The stiffness matrix K is: By using the equation (6) (7), the natural frequency and the natural period of vibration for each mode shapes can be determined. The calculated eigenvalues, and the corresponding natural frequencies and periods are given in the above table: Mode Shape Eigenvalue 2 (rad2/s2) Frequency (Hz) Period (s) 1 55.426 1.185 0.844 2 497.489 3.55 0.282 3 1.241*103 5.607 0.178 4 3.739*103 9.732 0.103 Table X: Eigenvalues, Frequencies and Periods for the 4 storey building. The modes of the shape and their corresponding periods are shown below: Using the method of normalisation the eigenvectors become: The different mode shapes for the 3 storey building are presented below graphically Mode Shape Frequency (Hz) Pseudo- Velocity (m/s) Displacement (m) Acceleration (g) 1 1.185 0.750 0.123 0.477 2 3.55 0.750 0.069 0.919 3 5.607 0.519 0.026 1.087 4 9.732 0.119 0.002 0.636 Table X: maximum Displacement, Pseudo- Velocity and Acceleration for the 2 storey building. The four calculated participation factors is are represented in the table below: 1 2 3 4 1.196 0.262 0.047 2.071*10-3 Table X: Participation Factors. The maximum displacement, Pseudo-Velocity and Acceleration from Table X are multiplied by the respective participation factors from Table X. The scaled parameters of the motion are given in the table below. Mode Shape Frequency (Hz) Pseudo- Velocity (m/s) Displacement (m) Acceleration (g) 1 1.185 0.897 0.248 0.102 2 3.55 0.197 0.041 0.045 3 5.607 0.024 2.760*10-3 8.047*10-3 4 9.732 2.464*10-3 1.242*10-5 2.360*10-3 Table X: Scaled parameters of the motion for each mode due to the participation factors. Maximum displacement and the Inter Storey Drift for each floor are given below: D1 = 0.09m, D2 = 0.129m, D3 = 0.14m and D4 = 0.148m 1 = 1.809 %, 2 = 0.963 %, 3 = 0.412 % and 4 = 0.222 %. The Maximum Base Shear Force and the Maximum Overturning Moment are calculating by applying the root-mean-approximation and the results are presented in the table below: Maximum Base Shear Force (N) Maximum Overturning Moment (Nm) 1.044*106 9.964*106 Table X: The Maximum Base Shear Force and the Maximum Overturning Moment for the 4 storey building. Inelastic Analysis The inelastic design spectrum is used with a ductility factor of 5 (=5). Hence the acceleration and the displacement are re-evaluated. The results are given in the table below. Mode Shape Frequency (Hz) Displacement (m) Acceleration (g) 1 1.185 0.207 0.085 2 3.55 0.156 0.172 3 5.607 0.059 0.172 4 9.732 0.006 0.114 Table X: Calculated displacements and accelerations for each mode (Inelastic design). Afterwards, each displacement and acceleration is multiplied by the respective participation factor from Table (X) and the scaled parameters are given below: Mode Shape Frequency (Hz) Displacement (m) Acceleration (g) 1 1.185 0.248 0.102 2 3.55 0.041 0.045 3 5.607 2.760*10-3 8.047*10-3 4 9.732 1.242*10-5 2.360*10-4 Table X: Scaled parameters of the motion for each mode due to the participation factors (Inelastic design). Maximum displacement and the Inter Storey Drift for each floor are given below: D1 = 0.155m, D2 = 0.217m, D3 = 0.238m and D4= 0.250 m 1 = 3.093 %, 2 = 1.561 %, 3 = 0.710 % and 4 = 0.399 % The values of the Inter-Storey Drift are in agreement with the Eurocode as they are lower than 4%. The Maximum Base Shear Force and the Maximum Overturning Moment are calculated and the results are presented in the table below: Maximum Base Shear Force (N) Maximum Overturning Moment (Nm) 9.439*105 7.721*106 Table X: The Maximum Base Shear Force and the Maximum Overturning Moment for the 4 storey building (Inelastic design). Then one floor is added above the existing building, which is a duplicate of the first one. Case 2: Four buildings with identical characteristics for all the floors: In this case the four buildings that will be examined they will have the exact same characteristics at all of the floors. The same procedure as in case one is followed in order to design four different building models able to resist at any seismic excitation. While the procedure is the same, only the final tables and the appropriate s for each case will be presented. The one storey building is the same as the one storey building of case one. Two storey building The dimensions of both the building and its elements are presented in the below. The mass matrix M is given below: The stiffness matrix is given below: The calculated eigenvalues, and the corresponding natural frequencies and periods are given in the above table: Mode Shape Eigenvalue 2 (rad2/s2) Frequency (Hz) Period (s) 1 73.337 1.363 0.734 2 502.663 3.568 0.280 Table X: Eigenvalues, Frequencies and Periods for the 2 storey building. The modes of the shape and their corresponding periods are shown below: Using the method of normalisation the eigenvectors become: T1= 0.734s T2= 0.280s The two different mode shapes for the 2 storey building are presented below graphically. Mode Shape Frequency (Hz) Pseudo- Velocity (m/s) Displacement (m) Acceleration (g) 1 1.363 0.750 0.118 0.497 2 3.568 0.750 0.067 0.921 Table X: Maximum Displacement, Pseudo- Velocity and Acceleration for the 2 storey building. The two calculated participation factors is are represented in the table below: 1 2 1.171 0.276 Table X: Participation Factors. The scaled parameters of the motion are given in the table below. Mode Shape Frequency (Hz) Pseudo- Velocity (m/s) Displacement (m) Acceleration (g) 1 1.363 0.878 0.138 0.582 2 3.568 0.207 0.019 0.255 Table X: Scaled parameters of the motion for each mode due to the participation factors. Maximum displacement and the Inter Storey Drift for each floor are given below: D1 = 0.087 m and D2 = 0.139 m. 1=1.747 % and 2 = 1.025 %. The above values are in agreement with the Eurocode as they are lower than 4%. The Maximum Base Shear Force and the Maximum Overturning Moment are given in the table below. Maximum Base Shear Force (N) Maximum Overturning Moment (Nm) 4.643*106 3.739*107 Table X: The Maximum Base Shear Force and the Maximum Overturning Moment for the 2 storey building. Inelastic Analysis The inelastic design spectrum is used with a ductility factor of 5 (=5). Hence the acceleration and the displacement are re-evaluated. The results are given in the table below: Mode Shape Frequency (Hz) Displacement (m) Acceleration (g) 1 1.363 0.199 0.086 2 3.568 0.151 0.172 Table X: Calculated displacements and accelerations for each mode (Inelastic design). Afterwards, each displacement and acceleration is multiplied by the respective participation factor from Table (X) and the scaled parameters are given below: Mode Shape Frequency (Hz) Displacement (m) Acceleration (g) 1 1.363 0.233 0.101 2 3.568 0.042 0.048 Table X: Scaled parameters of the motion for each mode due to the participation factors (Inelastic design). Maximum displacement and the Inter Storey Drift for each floor are given below: D1 = 0.150m and D2 = 0.234m 1 = 2.998 % and 2 = 1.690 % The values of the Inter-Storey Drift are in agreement with the Eurocode as they are lower than 4%. The Maximum Base Shear Force and the Maximum Overturning Moment are calculated and the results are presented in the table below: Maximum Base Shear Force (N) Maximum Overturning Moment (Nm) 8.041*105 6.471*106 Table X: The Maximum Base Shear Force and the Maximum Overturning Moment for the 2 storey building (Inelastic design). Three storey building g The below represents the dimensions for the two storey building and its elements. The mass matrix M is given below: The stiffness matrix K is: The calculated eigenvalues, and the corresponding natural frequencies and periods are given in the above table: Mode Shape Eigenvalue 2 (rad2/s2) Frequency (Hz) Period (s) 1 38.028 0.981 1.019 2 298.552 2.750 0.364 3 623.420 3.974 0.252 Table X: Eigenvalues, Frequencies and Periods for the 3 storey building. The modes of the shape and their corresponding periods are shown below: T1= 1.019s T2= 0.364s T3= 0.252s Using the method of normalisation the eigenvectors become: T1= 1.019s T2= 0.364s T3= 0.252s The three different mode shapes for the 3 storey building are presented below graphically Mode Shape Frequency (Hz) Pseudo- Velocity (m/s) Displacement (m) Acceleration (g) 1 0.981 0.750 0.133 0.405 2 2.750 0.750 0.082 0.720 3 3.974 0.750 0.063 0.998 Table X: Maximum Displacement, Pseudo- Velocity and Acceleration for the 3 storey building. The three calculated participation factors is are represented in the table below: 1 2 3 1.220 0.349 0.134 Table X: Participation Factors. The scaled parameters of the motion are given in the table below. Mode Shape Frequency (Hz) Pseudo- Velocity (m/s) Displacement (m) Acceleration (g) 1 0.981 0.915 0.162 0.494 2 2.750 0.262 0.029 0.251 3 3.974 0.101 8.451*10-3 0.134 Table X: Scaled parameters of the motion for each mode due to the participation factors Maximum displacement and the Inter Storey Drift for each floor are given below: D1 = 0.078 m, D2 = 0.131 m and D3 = 1.164 m. 1=1.560 %, 2 = 1.061 % and 3=0.658. The above values are in agreement with the Eurocode as they are lower than 4%. The Maximum Base Shear Force and the Maximum Overturning Moment are presented in the table below: Maximum Base Shear Force (N) Maximum Overturning Moment (Nm) 5.507*106 6.129*107 It is observed an increscent at the above values in table X comparing them with( se sxesi me) the corresponding calculated values in table X for the 2-storey building. Inelastic Analysis The inelastic maximum acceleration and the inelastic maximum displacement design spectra are constructed by using a ductility factor of 5 (=5). Hence the acceleration and the displacement are re-evaluated. The results are given in the table below. Mode Shape Frequency (Hz) Displacement (m) Acceleration (g) 1 0.981 0.207 0.072 2 2.750 0.189 0.152 3 3.974 0.134 0.172 Table X: Calculated displacements and accelerations for each mode (Inelastic design). Afterwards, each displacement and acceleration is multiplied by the respective participation factor from Table (X) and the scaled parameters are given below: Mode Shape Frequency (Hz) Displacement (m) Acceleration (g) 1 1.338 0.253 0.088 2 3.982 0.066 0.053 3 7.414 0.018 0.023 Table X: Scaled parameters of the motion for each mode due to the participation factors (Inelastic design). Maximum displacement and the Inter Storey Drift for each floor are given below: D1 = 0.131m, D2 = 0.205m and D3 = 0.258m 1 = 2.623 %, 2 = 1.486 % and 3 = 1.055 % It is observed an increment at the values of the Inter-Storey Drift comparing them with the corresponding values of the elastic analysis but they are still in agreement with the Eurocode as they are lower than 4%. The Maximum Base Shear Force and the Maximum Overturning Moment are calculated and the results are presented in the table below: Maximum Base Shear Force (N) Maximum Overturning Moment (Nm) 9.832*105 1.090*107 Table X: The Maximum Base Shear Force and the Maximum Overturning Moment for the 3 storey building (Inelastic design). 4. Four storey building The below represents the dimensions for the two storey building and its elements. The mass matrix M is given below: The stiffness matrix is: By using the equation (6) (7), the natural frequency and the natural period of vibration for each mode shapes can be determined. The calculated eigenvalues, and the corresponding natural frequencies and periods are given in the above table: Mode Shape Eigenvalue 2 (rad2/s2) Frequency (Hz) Period (s) 1 23.158 0.766 1.306 2 192 2.205 0.453 3 450.681 3.379 0.296 4 678.161 4.145 0.241 Table X: Eigenvalues, Frequencies and Periods for the 4 storey building. The modes of the shape and their corresponding periods are shown below: T1= 1.306s T2= 0.453 T3= 0.296s T4= 0.241s Using the method of normalisation the eigenvectors become: T1= 1.306s T2= 0.453 T3= 0.296s T4= 0.241s Maximum Displacement, Pseudo Velocity and Acceleration for the different frequencies Mode Shape Frequency (Hz) Pseudo- Velocity (m/s) Displacement (m) Acceleration (g) 1 0.766 0.750 0.193 0.291 2 2.205 0.750 0.092 0.636 3 3.379 0.750 0.068 0.884 4 4.145 0.750 0.055 1.087 Table X: maximum Displacement, Pseudo- Velocity and Acceleration for the 4 storey building. The four calculated participation factors is are represented in the table below: 1 2 3 4 1.241 0.333 0.184 0.080 Table X: Participation Factors. The maximum displacement, Pseudo-Velocity and Acceleration from Table X are multiplied by the respective participation factors from Table X. The scaled parameters of the motion are given in the table below. Mode Shape Frequency (Hz) Pseudo- Velocity (m/s) Displacement (m) Acceleration (g) 1 0.766 0.931 0.240 0.361 2 2.205 0.250 0.031 0.212 3 3.379 0.138 0.012 0.162 4 4.145 0.060 4.381*10-3 0.087 Table X: Scaled parameters of the motion for each mode due to the participation factors. Maximum displacement and the Inter Storey Drift for each floor are given below: D1 = 0.090 m, D2 = 0.159 m, D3 = 0.211 m and D4 = 0.242 m. 1=1.792 % , 2 = 1.397 %, 3=1.030 % and 4=0.613 % for the last one. The above values are in agreement with the Eurocode as they are lower than 4%. The Maximum Base Shear Force and the Maximum Overturning Moment are presented in the above table: Maximum Base Shear Force (N) Maximum Overturning Moment (Nm) 5.218*106 7.363*107 Inelastic Analysis The inelastic design spectrum is used with a ductility factor of 5 (=5). Hence the acceleration and the displacement are re-evaluated. The results are given in the table below. Mode Shape Frequency (Hz) Displacement (m) Acceleration (g) 1 0.766 0.211 0.040 2 2.205 0.193 0.123 3 3.379 0.187 0.172 4 4.145 0.115 0.172 Table X: Calculated displacements and accelerations for each mode (Inelastic design). Afterwards, each displacement and acceleration is multiplied by the respective participation factor from Table (X) and the scaled parameters are given below: Mode Shape Frequency (Hz) Displacement (m) Acceleration (g) 1 0.766 0.262 0.050 2 2.205 0.064 0.041 3 3.379 0.034 0.032 4 4.145 9.160*10-3 0.014 Table X: Scaled parameters of the motion for each mode due to the participation factors (Inelastic design). Maximum displacement and the Inter Storey Drift for each floor are given below: D1 = 0.117m, D2 = 0.183m, D3 = 0.232m and D4= 0.271 m 1 = 2.335 %, 2 = 1.331 %, 3 = 0.983 % and 4 = 0.764 % The values of the Inter-Storey Drift are in agreement with the Eurocode as they are lower than 4%. The Maximum Base Shear Force and the Maximum Overturning Moment are calculated and the results are presented in the table below: Maximum Base Shear Force (N) Maximum Overturning Moment (Nm) 7.325*105 1.015*107 Table X: The Maximum Base Shear Force and the Maximum Overturning Moment for the 4 storey building (Inelastic design). 5 Discussion of results Graph 1 and Graph 2 below depict the variation of the fundamental frequency for multi storey buildings, against each multi storey building. In particular, it represents the fundamental frequency of 1, 2, 3, 4 storey building for each storey respectively. At the above graph it is observed that as the floors are increased the fundamental frequency is decreased. The peak value of the graph is f11= 2.205 Hz, and represents the fundamental frequency in the case of 1 storey building. Afterwards one storey is added to the existing building with different characteristics from the existing one and the two natural frequencies are calculated. The smallest frequency of these two is the fundamental frequency and is f12= 1.535 Hz. The same procedure is applied for the rest two buildings. One storey is added each time to the previous existing building and the fundamental frequency is calculated for each one. This gives the values f13= 1.338 Hz and f14= 1.185 Hz for 3 storey and 4 storey buildings respectively. By following the same procedure as in Graph 1 the fundamental frequencies are calculated for 1, 2, 3 and 4 storey buildings and plotted the results are represented in Graph 2. However, in this case as the floors are increased the mass, the height of the each floor and the stiffness remain the same as and each floor is a duplicate of the first floor. The peak value of the graph is f11=2.205 Hz, which represents the fundamental frequency. For 2, 3 and 4 storey buildings the fundamental frequencies are: f12=1.363 Hz, f13=0.982 Hz and f14=0.766 Hz respectively. At graph 1 and graph 2, is observed that as the floors are increased the fundamental frequencies are decreased. The value of fundamental frequency for one storey building has the same value in both cases, as the two buildings are two exact replicas. After that point, by comparing the two sets of results it is observed a variation of frequencies. There is a greater decrease in the fundamental frequency values for buildings with the same characteristics at each floor. The four following graphs depict the Inter Storey Drift Number of storeys relationship. In particular the Inter-storey Drift of the first floor of each building is plotted against the total number of storeys of the corresponding building. The first two graphs represent the results of the Inter-Storey Drift for the elastic analysis.