Thursday, May 21, 2020

So Many Planned Parenthood Clinics Have Closed In The United

So many Planned Parenthood clinics have closed in the United States due to the government taking away federal funding for Planned Parenthood. The reason that the government has taken away federal funding to Planned Parenthood clinics is because some planned parenthood clinics let women have abortions. Texas has been able to take away all their state funding for Planned Parenthood clinics but not federal funding. Texas government does not approve of abortions even though it is legal. There are so many people in this world who are anti-abortion and disapprove of Planned Parenthood, their strong disapproval of Planned Parenthood has caused them to target Planned Parenthood by performing violent attacks on them. For example, in Colorado†¦show more content†¦This change in the women’s health care program caused low-income women to not have access to health care services like mammograms and pap smears. Since the closures of Planned Parenthood clinics many women have resulte d to going out of the state of Texas just to get abortions and other health care services. Once the House Bill 2 was passed in Texas there were only thirty-nine Planned Parenthood clinics operating in Texas, but only five of the thirty-nine clinics perform abortions. The five clinics in Texas that do perform abortions are in the major cities in Texas. Their needs to be some significant changes made to the House Bill 2. Not all the women who walk into a Planned Parenthood clinic wants to get an abortion. Many women go to Planned Parenthood because they cannot afford to get health care services from private practices or hospitals because it is more expensive than Planned Parenthood. Instead of Texas changing their women’s health care program laws to get Planned Parenthood clinics to be removed from their state, Texas should open other health care clinics to fit their women’s health care program laws if they want to close Planned Parenthood clinics so that low income wome n can still have affordable health care services. After majority of the Planned Parenthood clinics in Texas closed there was an increase in births among low income women. The women who were in an area where a Planned Parenthood clinic had closed at some point in time had received someShow MoreRelatedShould The Government Defund Planned Parenthood?1693 Words   |  7 PagesShould the Government Defund Planned Parenthood? About a century ago, a small birth-control clinic was opened by Margaret Sanger in Brooklyn, New York. Women and families travelled to this clinic to learn about contraceptives and the perils of self-administered abortions. This was unheard of at the time, to teach a woman how to stop pregnancy in a world where the highest aspiration of a woman was supposed to become a mother. However, very soon after this clinic opened, Sanger was put incarceratedRead MoreContraception And Safe Sex Education Essay1152 Words   |  5 PagesWithin the United States, 38 states of the 48 states examined have some form of abstinence only education. Of those 38, 21 have laws in place that require schools to solely teach abstinence only sex education (Stranger-Hall, Kathrin F. and David W. Hall 4). The logic behind such practices is to prevent teenagers from engaging in intercourse and to decrease the rate of teen pregnancies. The curriculum of abstinence only programs stresses that teenagers should no t engage in intercourse since that isRead MoreAbortion As A Crime And A Sin1654 Words   |  7 Pages Every year 1,511,300 infant lives are taken; 1,500,000 are victims of abortion, not including countries other than our own. If a mother were to kill her child after it were born it would be considered murder, so why is it that when a mother is growing her child inside of her there are no legal consequences for aborting her child? Over a span of several lifetimes, and in a variety of cultures, there is history of women helping each other to abort. Over time the harmful and dangerous affects wereRead MoreMargaret Sanger : An Influential Women Of The 20th Century1375 Words   |  6 Pagesan activist, not only for feminism, but for fair working conditions in the textile industry. Margaret was a polarizing figure. She was seen as antagonistic, even by the groups she fought for. Nevertheless she continued to fight for her causes. The United States owes much to a poor woman from Corning, New York. II. Tragedies Abound Margaret Sanger was born Margaret Higgins in Corning, New York in 1879. She was one of eleven children born to Michael and Anne Higgins. As a result of such a large familyRead MoreCivil Court Case Of Roe V. Wade1332 Words   |  6 Pagessides cannot get what they each want. One wants freedom of choice and the other wants the baby’s life to matter more than the choice of termination. By 1965, it looked like Pro-Life was winning because all fifty states of America made it illegal to have an abortion except with certain cases, like rape. In 1973, however, one woman got a chance to take her argument to make abortion legal to the Supreme Court. When the Supreme Court was dismissed and the case was over that women and the side of Pro-ChoiceRead MoreLegal Abortion Is A Necessity1774 Words   |  8 PagesAbortion is a Necessity Even though many people have negative opinions on abortions, legal abortion is a necessity. Women should have access to this because those who do not can experience more stress than if she was able to have one. Women need to have legal abortions mainly for the concerns for the mother’s and/or baby s health as well as unwanted pregnancies. In 1972, the Roe v. Wade supreme court case legalized abortion nationwide but since then numerous states have passed laws to restrict the availabilityRead MoreAbortion Should Not Be An Option For Pregnant Women Essay1173 Words   |  5 Pagesmeans killing a fetus who is living being, which is murder. Abortion has been an option for centuries now even though it is murder. Abortion should not be an option for pregnant women around the United States. Killing babies is an injustice because murder is wrong. People argue that a fetus isn’t living so it doesn’t matter, but it does. When women go to the doctor to hear and ultrasound the fetus’ heart is beating. A fetus grows into a human being like you go from a kid to an adult. If killing peopleRead MoreShould Abortion Be Legal?1652 Words   |  7 Pagesbe allowed to have abortions Imagine your life in the hands of a teenager. This is the case of many unborn children. In today s society teens are allowed to have abortions with or without parental consent, even under the age of 18. Allowing abortions is overriding the basic human rights. Teens under the age of 18 shouldn t be allowed to have an abortion because of the basic human rights of a fetus. Teens themselves don t have certain rights so how are they allowed to have rights overRead MoreRoe versus Wade2014 Words   |  9 Pagesever made by the Supreme Court of the United States. This case has impacted so many peoples lives and I believe that no other topic linked to the feminist movement has produced as much debate, rage, and passion. Abortion has forever been a controversy among the old and the young, and the rich and the poor. It doesn’t matter who you are, you have an opinion on this topic and it’s most likely a strong one. The controversy stems from the fact that there are so ma ny different stances you can take on theRead MoreAbortion : A Controversial Topic2411 Words   |  10 PagesDoe. There have been many other cases that has to do that with abortion like Harris v. McRae in 1980, Webster v. Reproductive Health Services in 1989, and Planned Parenthood of Southeastern Pennsylvania v. Casey in 1992. These decisions was follow by lots of protest who was against abortion, but many people was happy for the decision. Which lead to pro-choice activists and pro-life activists. Pro-choice activists believe that abortion is woman rights and the government should not have the right

Wednesday, May 6, 2020

Fahrenheit 451 By Ray Bradbury - 1661 Words

1.) In the novel, Fahrenheit 451 by Ray Bradbury, Montag’s view on life reverses. Two characters the influence the main character Guy Montag are the old lady whose house and books were burnt down and Mildred. The old lady was caught preserving books in her home. Firemen including Montag were ordered to burn the books. The old lady refused to leave her books, so she too was burned. She bravely gave an allusion as her last words, â€Å"Play the man,’ she said, ‘Master Ridley.’ Something, something, something† (F451 37). Beatty the fire chief who ordered to burn the books replied, †We shall this day light such a candle, by God`s grace, in England, as I trust shall never be put out† (F451 37). Montag gave this incident a lot of thought. The more thought he gave it; the more he questioned why the old lady loved those books so much she would die for them. Montag, like most of his society has never read an illegal book, so he is unable t o relate to the old woman. But, he feels the urge to find out why these books are so sacred. After reading he begins to realize society is a twisted lie do to the controlling government. Montag’s wife influenced him to stop and question their way of living. Mildred’s common life style shows unhappiness to Montag. In her corrupted mind her family is the television, not Montag. Montag sees this depression and emptiness in Mildred and begins to question the way society has made her. After Mildred attempts suicide Montag tries to prevent him fromShow MoreRelatedFahrenheit 451 by Ray Bradbury719 Words   |  3 PagesThe flash point of paper, or the temperature at which paper will burst in flames, is 451 degrees Fahrenheit. In Fahrenheit 451, written by Ray Bradbury, the main character, Guy Montag, is a â€Å"fireman† in a futuristic society where he and his coworkers start fires, rather than put them out. Books are banned and burned, along with the owner of the book ’s house and sometimes even the owner of the book, upon discovery. Technology has taken over in a sense that social interaction between the average personRead MoreFahrenheit 451 By Ray Bradbury1952 Words   |  8 Pagesis clearly displayed in the plight of Ray Bradbury’s novel about a dystopian American society, Fahrenheit 451, which contains many ideas and bits of content that some people believed should be censored. In fact, one of the reasons that this novel was censored for displaying the dangers of censorship, which is both extremely ironic, and telling as to where this society is going. Thanks to several distributors and oversensitive parents and teachers, Fahrenheit 451 has been banned in many schools overRead MoreFahrenheit 451 By Ray Bradbury954 Words   |  4 Pages In Fahrenheit 451 by Ray Bradbury, the author uses allegory (often misinterpreted by readers) to show the dangers of mass media consumption and the decline of reading traditional media. Many rea ders draw incorrect conclusions (lessons learned) from the book due to how generally the book applies its theme. Government censorship, though an important topic, is not the intended focus of the novel Fahrenheit 451. Finally, Bradbury’s original message of the book shows the beauty of traditional media andRead MoreFahrenheit 451 By Ray Bradbury1592 Words   |  7 PagesWhen writing the introduction to Fahrenheit 451, author Neil Gaiman stated that â€Å"ideas--written ideas--are special. They are the way we transmit our stories and our thoughts from one generation to the next. If we lose them, we lose our shared history†. Gaiman is absolutely correct; especially because what he is saying heavily applies to books. Books are a critical aspect in shaping humanity as a whole, they create and share a network of creative ideas, history, and overall entertainment; to loseRead MoreFahrenheit 451 By Ray Bradbury918 Words   |  4 Pagesâ€Å"Fahrenheit 451,† written b y Ray Bradbury, is a futuristic, dystopian novel based upon a society secluded by technology and ignorance. In this future society, books are outlawed and firemen are presented with the task of burning books that are found in people’s homes. Montag, a fireman, finds himself intrigued with the books, and begins to take them home and read them. As the story progresses, Montag learns the truth behind why books are outlawed and flees his city to join the last remnants of age-oldRead MoreFahrenheit 451 By Ray Bradbury847 Words   |  4 PagesSet Knowledge On Fire The book Fahrenheit 451 is a postmodern work by Ray Bradbury first published in 1951. In Bradbury’s story, all books are illegal and are subject to be burned by firemen. Furthermore, the two predominant themes of Fahrenheit 451 are censorship and ignorance. The censorship implemented over the years removes all information from society that is necessary to learn, which accomplishes to prevent people from questioning anything. The ignorance of society has been fostered and theRead MoreFahrenheit 451 by Ray Bradbury818 Words   |  4 PagesFAHRENHEIT 451 BY RAY BRADBURY Important People in Montag’s Life In Partical Fulfillment Of English 2 Ms Irina Abramov By Helen Hernandez November 9, 2012 â€Å"There are worse crimes than burning books. One of them is not reading them† -Ray Bradbury. In the past there were events that affected book writers. People will get together to burn books because they thought it was inappropriate or they were against their literature. Montag is a fireman in a futuristic society who would startRead MoreFahrenheit 451 By Ray Bradbury863 Words   |  4 PagesThe novel, Fahrenheit 451 was written by Ray Bradbury and it took place in the dystopian future. Throughout each novel, we are able to see a major theme, which is censorship. In this essay, I will explain how this theme are explored in the story by using the literary devices. To begin with, in this novel, censorship is not given a straight description, but we can see how the author shows it through many literary elements, such as using the setting, tone and symbolisms even foreshadowing. This novelRead MoreFahrenheit 451 By Ray Bradbury1544 Words   |  7 PagesRay Bradbury, the author of Fahrenheit 451, expresses his perspective on life in an interview. His interview contains a common theme: Do what you love, and love what you do (Bradbury). Bradbury sends a message in his interview that people should love life, and live to the fullest because he believes life is a beautiful thing. Although Bradbury no longer can demonstrate his love for life his message still lives in the pages of Fahrenheit 451. The Government of the society in the novel has told theirRead MoreFahrenheit 451 by Ray Bradbury904 Words   |  4 PagesLiving in a world with no free thought would be bland as cardboard. But, if that cardboard illuminated with fire, would it have more mea ning than it did before? The answer is yes. In the novel Fahrenheit 451 by Ray Bradbury, the main character, Montag, finds much meaning behind the simple element of fire. The symbol of fire is used to represent how Montag changes himself and his ideas and thoughts about fire throughout the novel. At first, Montag views fire as destructive, but enjoys burning because

Steel Design Free Essays

string(213) " method for determining the elastic critical moment for lateraltorsional buckling Mcr !!!!!!!! May use ‘LTBeam’ software \(can be downloaded from CTICM \?\?\?\?\?\? website\) Or may use method presented by L\." STEEL BEAM DESIGN Laterally Unrestrained Beam Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 1 Non-dimensional slenderness Beam behaviour analogous to yielding/buckling of columns. M Wyfy Material yielding (in-plane bending) MEd MEd Elastic member buckling Mcr Lcr 1. We will write a custom essay sample on Steel Design or any similar topic only for you Order Now 0 Dr. A Aziz Saim 2010 EC3 Non-dimensional slenderness Unrestrained Beam ? LT 2 Lateral torsional buckling Lateral torsional buckling Lateral torsional buckling is the member buckling mode associated with slender beams loaded about their major axis, without continuous lateral restraint. If continuous lateral restraint is provided to the beam, then lateral torsional buckling will be prevented and failure will occur in another mode, generally in-plane bending (and/or shear). Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 3 Eurocode 3 Eurocode 3 states, as with BS 5950, that both crosssectional and member bending resistance must be verified: MEd ? Mc ,Rd Cross-section check (In-plane bending) MEd ? Mb,Rd Dr. A Aziz Saim 2010 EC3 Unrestrained Beam Member buckling check 4 Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 5 Laterally Unrestrained Beam The design of beam in this Lecture 3 is considering beams in which either no lateral restraint or only intermittent lateral restraint is provided to the compression flange Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 6 Lateral Torsional Buckling Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 7 Lateral Torsional Buckling Figure 3-1 shows an unrestrained beam subjected to load increment. The compression flange unrestrained and beam is not stiff enough. There is a tendency for the beam to deform sideways and twist about the longitudinal axis. The failure mode which may occur to the beam is called lateral torsional buckling. Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 8 ?Involves both deflection and twisting rotation ?Out-of plane buckling. Bending Resistance M c, Rd ? M pl ? W pl f y ?M0 Due to the effect of LTB, the bending resistance of cross section become less. Failure may occurs earlier then expected Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 9 Examples of Laterally Unrestrained Beam Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 10 Restrained Beam Comparsion Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 11 Intermittent Lateral Restrained Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 12 Torsional restraint Usually both flanges are held in their relative positions by external members during bending. May be provided by load bearing stiffeners or provision of adequate end connection details. See Figure 3-4. Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 13 Beam without torsional restraint Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 14 Can be discounted when: †¢ Minor axis bending †¢ CHS, SHS, circular or square bar †¢ Fully laterally restrained beams †¢ ? LT 0. 2 (or 0. 4 in some cases) – Unrestrained length Cross-sectional shape End restrained condition The moment along the beam Loading – tension or compression Unrestrained Beam 16 Dr. A Aziz Saim 2010 EC3 Lateral torsional buckling resistance Checks should be carried out on all unrestrained segments of beams (between the points where lateral restraint exists). Lateral restraint Lateral restraint Lcr = 1. 0 L Lateral restraint Beam on plan Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 17 Three methods to check LTB in EC3: †¢ The primary method adopts the lateral torsional buckling curves given by equations 6. 56 and 6. 57, and is set out in clause 6. 3. 2. 2 (general case) and clause 6. 3. 2. 3 (for rolled sections and equivalent welded sections). The second is a simplified assessment method for beams with restraints in buildings, and is set out in clause 6. 3. 2. 4. †¢ The third is a general method for lateral and lateral torsional buckling of structural components, given in clause 6. 3. 4. Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 18 Eurocode 3 states, as with BS 5950, that both cross-sectional and member bending resistance must be verified: MEd ? Mc ,Rd Cross-section check (In-plane bending) MEd ? Mb,Rd Dr. A Aziz Saim 2010 EC3 Unrestrained Beam Member buckling check 19 Lateral-torsional buckling Eurocode 3 design approach for lateral torsional buckling is analogous to the olumn buckling treatment. The design buckling resistance Mb,Rd of a laterally unrestrained beam (or segment of beam) should be taken as: Mb,Rd ? ?LT Wy fy ? M1 Reduction factor for LTB Lateral torsional buckling resistance: Mb,Rd = ?LT Wy fy ? M1 Equation (6. 55) Wy will be Wpl,y or Wel,y ?LT Dr. A Aziz Saim 2010 EC3 is the reduction factor for lateral torsional buckling Unrestrained Beam 21 Buckling curves – general case (Cl 6. 3. 2. 2) Lateral torsional buckling curves for the general case are given below : (as in Eq (6. 56)) ?LT ? 1 2 ? LT ? ?LT ? ?2 LT but ? LT ? 1. 0 ?LT ? 0. 5 [ 1 ? ?LT (? LT ? 0. ) ? ?2 ] LT Plateau length Imperfection factor from Table 6. 3 Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 22 Imperfection factor ? LT Imperfection fact ors ? LT for 4 buckling curves: (refer Table 6. 3) Buckling curve Imperfection factor ? LT a 0. 21 b 0. 34 c 0. 49 d 0. 76 Buckling curve selection For the general case, refer to Table 6. 4: Cross-section Rolled I-sections Welded Isections Limits h/b ? 2 h/b 2 h/b ? 2 h/b 2 – Buckling curve a b c d d Other crosssections Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 24 LTB curves 4 buckling curves for LTB (a, b, c and d) 1. 2 Reduction factor ? LT . 0 0. 8 0. 6 0. 4 0. 2 0. 0 0 0. 5 1 1. 5 Curve a Curve b Curve c Curve d 2 2. 5 0. 2 Dr. A Aziz Saim 2010 EC3 Non-dimensional slenderness Unrestrained Beam ?LT 25 Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 26 lateral torsional buckling slenderness ? LT Mcr ? Wy f y Mcr Elastic critical buckling moment Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 27 Non-dimensional slenderness †¢ Calculate lateral torsional buckling slenderness: ? LT ? Wy f y Mcr †¢ Buckling curves as for compression (except curve a0) †¢ Wy depends on se ction classification †¢ Mcr is the elastic critical LTB moment Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 28 BS EN 1993-1-1 does not give a method for determining the elastic critical moment for lateraltorsional buckling Mcr !!!!!!!! May use ‘LTBeam’ software (can be downloaded from CTICM website) Or may use method presented by L. You read "Steel Design" in category "Essay examples" Gardner †¦Ã¢â‚¬ ¦. Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 29 Mcr under uniform moment For typical end conditions, and under uniform moment the elastic critical lateral torsional buckling moment Mcr is: Mcr ,0 G IT Iw Iz Lcr ? EIz ? 2 Lcr 2 ? Iw Lcr GIT ? ? ? 2 ? ? EIz ? ? Iz 2 0. 5 is the shear modulus is the torsion constant is the warping constant is the inor axis second moment of area is the buckling length of the beam Unrestrained Beam 30 Dr. A Aziz Saim 2010 EC3 Mcr under non-uniform moment Numerical solutions have been calculated for a number of other loading conditions. For uniform doubly-symmetric cross-sections, loaded through the shear centre at the level of the centroidal axis, and with the standard conditions of restraint described, Mcr may be calculated by: ? EIz Mcr ? C1 2 Lcr 2 Dr. A Aziz Saim 2010 EC3 Unrestrained Beam ? Iw Lcr GIT ? ? ? 2 ? ? EIz ? ? Iz 2 0. 5 31 C1 factor – end moments For end moment loading C1 may be approximated by the equation below, though other approximations also exist. C1= 1. 88 – 1. 40y + 0. 52y2 but C1 ? 2. 70 where y is the ratio of the end moments (defined in the following table). Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 32 C1 factor – transverse loading Loading and support conditions Bending moment diagram Value of C1 1. 132 1. 285 1. 365 1. 565 1. 046 Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 33 Design procedure for LTB Design procedure for LTB: 1. Determine BMD and SFD from design loads 2. Select section and determine geometry 3. Classify cross-section (Class 1, 2, 3 or 4) 4. Determine effective (buckling) length Lcr – depends on boundary conditions and load level 5. Calculate Mcr and Wyfy Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 34 Design procedure for LTB 6. Non-dimensional slenderness ? LT ? Wy fy Mcr 7. Determine imperfection factor ? LT 8. Calculate buckling reduction factor ? LT 9. Design buckling resistance 10. Check Mb,Rd ? ?LT Wy fy ? M1 MEd ? 1. 0 Mb,Rd for each unrestrained portion Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 35 LTB Example General arrangement Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 36 LTB Example Design loading is as follows: 425. 1 kN A B C 319. 6 kN D 2. 5 m 3. 2 m 5. 1 m Loading Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 37 LTB Example 267. 1 kN A B D 52. 5 kN SF C 477. 6 kN Shear force diagram B A C D BM 1194 kNm 1362 kNm Bending moment diagram Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 38 LTB Example For the purposes of this example, lateral torsional buckling curves for the general case will be utilised. Lateral torsional buckling checks to be carried out on segments BC and CD. By inspection, segment AB is not critical. Try 762? 267? 173 UB in grade S 275 steel. Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 39 LTB Example b z tw h d y y r z tf h = 762. 2 mm b = 266. 7 mm tw = 14. 3 mm tf = 21. 6 mm r = 16. mm A = 22000 mm2 Wy,pl = 6198? 103 mm3 Iz = 68. 50? 106 mm4 It = 2670? 103 mm4 Iw = 9390? 109 mm6 Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 40 LTB Example For a nominal material thickness (tf = 21. 6 mm and tw = 14. 3 mm) of between 16 mm and 40 mm the nominal values of yield strength fy for grade S 275 steel (to EN 10025-2) is 265 N/mm2. From cla use 3. 2. 6: N/mm2. E = 210000 N/mm2 and G ? 81000 Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 41 LTB Example Cross-section classification (clause 5. 5. 2): e ? 235 / fy ? 235 / 265 ? 0. 94 Outstand flanges (Table 5. 2, sheet 2) cf = (b – tw – 2r) / 2 = 109. 7 mm cf / tf = 109. 7 / 21. 6 = 5. 8 Limit for Class 1 flange = 9e = 8. 48 5. 08 ? Flange is Class 1 Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 42 LTB Example Web – internal part in bending (Table 5. 2, sheet 1) cw = h – 2tf – 2r = 686. 0 mm cw / tw= 686. 0 / 14. 3 = 48. 0 Limit for Class 1 web = 72 e = 67. 8 48. 0 ? Web is Class 1 Overall cross-section classification is therefore Class 1. Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 43 LTB Example Bending resistance of cross-section (clause 6. 2. 5): Mc ,y,Rd ? Wpl,y fy ? M0 for Class 1 and 2 sec tions 6198 ? 103 ? 265 ? ? 1642 ? 106 Nmm 1. 0 ? 1642 kNm ? 1362 kNm ? Cross-section resistance in bending is OK. Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 44 LTB Example Lateral torsional buckling check (clause 6. 3. 2. 2) – Segment BC: MEd ? 1362 kNm Mb ,Rd ? ? LT Wy fy ? M1 where Wy = Wpl,y for Class 1 and 2 sections Determine Mcr for segment BC (Lcr = 3200 mm) Dr. A Aziz Saim 2010 EC3 ? EIz Mcr ? C1 2 Lcr 2 ? Iw Lcr GIT ? ? ? 2 ? ? EIz ? ? Iz Unrestrained Beam 2 0. 5 45 LTB Example For end moment loading C1 may be approximated from: C1 = 1. 88 – 1. 40y + 0. 52y2 but C1 ? 2. 70 1194 y is the ratio of the end moments ? ? 0. 88 1362 ? C1 ? 1. 05 ? 2 ? 210000 ? 68. 5 ? 106 Mcr ? 1. 05 ? 32002 ? 9390 ? 109 32002 ? 81000 ? 2670 ? 103 ? ? ? 68. 5 ? 106 ? 2 ? 210000 ? 68. 5 ? 106 ? ? 0. 5 = 5699Ãâ€"106 Nmm = 5699 kNm Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 46 LTB Example Non-dimensional lateral torsional slenderness for segment BC: ? LT ? Wy fy Mcr 6198 ? 103 ? 265 ? ? 0. 54 6 5699 ? 10 Select buckling curve and imperfection factor ? LT: From Table 6. 4: h/b = 762. 2/266. 7 = 2. 8 5 For a rolled I-section with h/b 2, use buckling curve b Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 47 LTB Example From Table 6. 3 of EN 1993-1-1: For buckling curve b, ? LT = 0. 34 Calculate reduction factor for lateral torsional buckling, ? LT – Segment BC: ?LT ? 1 ? LT ? ? 2 LT LT but ? LT ? 1. 0 where ? LT ? 0. 5 [ 1 ? ?LT (? LT ? 0. 2) ? ?2 ] LT Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 48 LTB Example ?LT = 0. 5[1+0. 34(0. 54-0. 2) + 0. 542] = 0. 70 ? ? LT ? 1 0. 70 ? 0. 70 ? 0. 54 2 2 ? 0. 87 Lateral torsional buckling resistance Mb,Rd – Segment BC : Mb,Rd ? ? LT Wy fy ? M1 265 ? 0. 87 ? 6198 ? 10 ? 1 . 0 3 ? 1425 ? 106 Nmm ? 1425 kNm Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 49 LTB Example MEd 1362 ? ? 0. 96 ? 1. 0 ? Segment BC is OK Mb,Rd 1425 Lateral torsional buckling check (clause 6. 3. 2. 2) – Segment CD: MEd ? 1362 kNm Mb ,Rd ? ? LT Wy fy ? M1 where Wy = Wpl,y for Class 1 and 2 sections Determine Mcr for segment CD (Lcr = 5100 mm) Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 50 LTB Example ? EIz Mcr ? C1 2 Lcr 2 ? Iw Lcr GIT ? ? ? 2 ? Iz ? EIz ? ? 2 0. 5 Determine y from Table: 0 y is the ratio of the end moments ? ?0 1362 ? C1 ? 1. 88 ? 2 ? 210000 ? 68. 5 ? 106 Mcr ? 1. 88 51002 ? 9390 ? 109 51002 ? 81000 ? 2670 ? 103 ? ? ? ? 68. 5 ? 106 ? 2 ? 210000 ? 68. 5 ? 106 ? ? 0. 5 = 4311? 106 Nmm = 4311 kNm Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 51 LTB Example Non-dimensional lateral torsional slenderness for segment CD: ? LT ? Wy fy Mcr 6198 ? 103 ? 265 ? ? 0. 62 6 4311? 10 The buckling curve and imperfection factor ? LT are as for segment BC. Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 52 LTB Example Calculate reduction factor for lateral torsional buckling, ? LT – Segment CD: ?LT ? 1 ? LT ? ? 2 LT 2 LT but ? LT ? 1. 0 where ? LT ? 0. 5 [ 1 ? ?LT (? LT ? 0. 2) ? ?2 ] LT = 0. 5[1+0. 34(0. 62-0. 2) + 0. 622] = 0. 76 ? ? LT Dr. A Aziz Saim 2010 EC3 ? 1 0. 76 ? 0. 76 ? 0. 62 2 Unrestrained Beam 2 ? 0. 83 53 LTB Example Lateral torsional buckling resistance Mb,Rd – Segment CD : Mb,Rd ? ?LT Wy fy ? M1 265 ? 0. 83 ? 6198 ? 10 ? 1. 0 3 ? 1360 ? 106 Nmm ? 1360 kNm MEd 1362 ? ? 1. 00 Mb,Rd 1360 Segment CD is critical and marginally fails LTB check. Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 54 Blank Page Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 55 Simplified assessment of ? LT For hot-rolled doubly symmetric I and H sections without destabilising loads,? may be conservatively simplified to: LT ? LT ? 1 0. 9 ? z ? C1 ?z 1 0. 9 ? 1 C1 E ? z ? L / iz ; ? 1 ? ? fy As a further simplification, C1 may also be conservatively taken = 1. 0. Simplified assessment of ? LT Substituting in numerical values for simplified expressions result. ? 1 , the following S235 ? LT ? 1 L / iz C1 104 S275 ? LT ? 1 L / iz C1 96 S355 ? LT ? 1 L / iz C1 85 C1 may be conservatively taken = 1. , though the level of conservatism increases the more the actual bending moment diagram differs from uniform moment. Simplified method (Cl. 6. 3. 2. 4) Simplified method for beams with restraints in buildings (Clause 6. 3. 2. 4) This method treats the compression flange of the beam and part of the web as a strut: b b Compression h Tension Compression flange + 1/3 of the compressed area of web Strut Dr. A Aziz Saim 2010 EC3 Beam Unrestrained Beam 58 General method (Cl. 6. 3. 4) General method for lateral and lateral torsional buckling of structural components †¢ May be applied to single members, plane frames etc. Requires determination of plastic and elastic (buckling) resistance of structure, which subsequently defines global slenderness †¢ Generally requires FE Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 59 Blank Page Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 60 Important Notes: (End Connections) When full torsional restraint exist: -both the compression and tension flanges are fully restrained against rotation on plan -both flanges are partially restrained against rotation on plan – both flanges are free to rotate on plan Unrestrained Beam 61 Dr. A Aziz Saim 2010 EC3 Connection Detail Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 62 Important Notes: (End Connections) Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 63 Important Notes: (End Connections) When both flanges are free to rotate on plan and the compression flange is unrestrained: i. torsional restraint is provided solely by connection of the tension flange to the supports, ii. torsional restraint is provided solely by dead bearing of the tension flange on support. Unrestrained Beam 64 Dr. A Aziz Saim 2010 EC3 Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 65 Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 66 How to cite Steel Design, Essay examples