# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

34 Pages

### ME85-Lecture25

Course: ME C85, Spring 2010
School: Berkeley
Rating:

#### Document Preview

25 Lecture Singularity Function Method for Beam Deflection What is the external load distribution for this beam ? Wait a minute: What those are bracket functions ? I am totally at loss ! This is singularity function Method at its best ! Summary

Register Now

#### Unformatted Document Excerpt

Coursehero >> California >> Berkeley >> ME C85

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
25 Lecture Singularity Function Method for Beam Deflection What is the external load distribution for this beam ? Wait a minute: What those are bracket functions ? I am totally at loss ! This is singularity function Method at its best ! Summary
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

Berkeley - ME - C85
Lecture 26 Introduction to StabilityMarble Analogy Consider model with two rods and torsionalspring. After a small perturbation,K (2 ) = restoring momentLLP sin = P = destabilizing moment22 Column is stable (tends to return to alignedorientatio
Berkeley - ME - C85
Lecture 20Composite Beams and Asymmetric BendingLets recapitulate the main pointsof the last lectureStrain Due to BendingConsider a beam segment of length L.After deformation, the length of the neutral surfaceremains L. At other sections,L = ( y )
Berkeley - ME - C85
Lecture 19 Beam BendingStep 3Step 3Pure bendingExamples of Pure BendingPure BendingPure Bending: Prismatic memberssubjected to equal and opposite couplesacting in the same longitudinal planeBernoulli-Euler Kinematic AssumptionBending Deformation
Berkeley - ME - C85
Who wants to win a million dollars ?Who wants to drop the lowest score of his/her HW ?\$ 10,000 question\$ 100,000 question\$500,000 question\$1,000,000 question\$10,000 question\$100,000 question\$500,000 question\$1,000,000 questionLecture 21 Shearing
CUHK - STAT - 3008
STAT3008 Applied Regression Analysis (2011-2012 1st Semester)Revision on Mid-term ExaminationExercises:Question 1E (Y X 1 , X 2 ) = + 3.2 X 1 0.5 X 2 + 1.1X 1 X 21.5For the above fitted model, one unit increase in X 1 will lead to an increaseof 3.2
CUHK - STAT - 3008
STAT3008 Applied Regression Analysis (2011-2012 1st Semester)Revision on Mid-term ExaminationExercises:Question 1E (Y X 1 , X 2 ) = + 3.2 X 1 0.5 X 2 + 1.1X 1 X 21.5For the above fitted model, one unit increase in X 1 will lead to an increaseof 3.2
CUHK - STAT - 3008
D.MatrixCalculusD1D2Appendix D: MATRIX CALCULUSIn this Appendix we collect some useful formulas of matrix calculus that often appear in niteelement derivations.D.1 THE DERIVATIVES OF VECTOR FUNCTIONSLet x and y be vectors of orders n and m respe
CUHK - STAT - 3008
MODULE 6MULTIPLE REGRESSIONCONTENTS:MODULE 61. Introduction2. Matrix Notation3. Forecasting4. Data Problems4.1 Multicollinearity4.2 Measurement Errors4.3 Outliers and Undue Influence5. The F Test for Linear Restrictions5.1 The Redundant Variab
CUHK - STAT - 3008
MODULE 5SIMPLE LINEAR REGRESSIONWITH FINANCIAL APPLICATIONSCONTENTS:MODULE 51. Introduction2. Model Specification2.1 The Nature of Stochastic Functions2.2 The Types of Mathematical Functions2.3 The Choice of Variables2.4 The Assumptions about th
CUHK - STAT - 3008
Solutions forApplied Linear RegressionThird EditionSanford Weisberg2005, Revised February 1, 2011ContentsPrefacevii1Scatterplots and Regression12Simple Linear Regression73Multiple Regression354Drawing conclusions475Weights, Lack of Fi
Ashford University - ECE - 332
DEVELOPMENTALDevelopmental Milestones of a PreschoolerSharon StoneECE 332Jennifer AshtonJanuary 15, 2012Developmental Milestones of a PreschoolerThe preschool age is a wonderful time for children; they start to trust other individuals beyondtheir
Boise State - HIST - 100
A Brief History of LifeHow Did Everything Begin?Intelligent Design Theories(Creation Myths)More Stories from Around theWorldon how the world beganall of them uniqueIf the earth has existed for 4.5 billion years,what about life on earth? Earliest
Boise State - HIST - 100
Before we begin!Political: Who controls what? What type ofgovernment is there? Anything to do withlaws or war.Economic: What type of economy? Howdo people make a living?Geography: Where is it? Is the landmountainous? Desert? Oceanic?Social: Religi
Boise State - HIST - 100
Ancient Greece500-323 B.C.E.Geography Greeceis apeninsula aboutthe size ofLouisiana in theMediterraneanSea. Its very close toEgypt, the Persianempire (includesTurkey) and Rome.Greek geographyGreece is mountainousGreek communitiesoften tim
Boise State - HIST - 100
AncientMexicoAncientMexicoMayan,Incan,andAztecCivilizationsBy:Mrs.MeredithSandersTeotihuacanTeotihuacan4 well-knownbuildings in thisancient city:Pyramid of the SunPyramid of the MoonTemple of QuetzalcoatlTemple of the JaguarsOlmecsOlmecs T
Boise State - HIST - 100
Boise State - HIST - 100
AsiaPowerPointMr.ClutterVillegasMiddleSchoolThreeEmpiresMongols12601294OttomanEmpire1400s&amp;1500sMughalEmpire15561605GenghisKhanFactsMilestones1187?AssumedthetitleofGenghisKhan(Khankingpresident1206WasproclaimedrulerofallMongolpeoplebyanassemblyo
Boise State - HIST - 100
BhopalGasTragedyPreviewAmongsttheworstIndustrailDisastersofitstime.Occurrence:3rdDecember1984.Placeofoccurrence:Bhopal,MadhyaPradesh,India.Company:UnionCarbideCorporation.Chemical:MethylIsocyanate(27tons)Among the 500,000 people exposed to the gas,
Boise State - HIST - 100
Britis h His to ryB ritisThis powerpoint was kindly donated towww.worldofteaching.comhttp:/www.worldofteaching.com is home to over athousand powerpoints submitted by teachers. This is acompletely free site and requires no registration. Pleasevisit
Boise State - HIST - 100
The City-States of GreeceSparta and AthensThe Persian WarsThe Delian LeagueThe Decline of AthensThe City-States ofAncient GreeceSparta and AthensThe Persian WarsThe Delian LeagueThe Decline of AthensNow thats tough! There is a story about a Sp
Boise State - HIST - 100
USCivilRightsMovementBeginnings through the 60sBy J. Aaron CollinsAbolitionistsFrederick Douglas was the editor of anabolitionist newspaper.Onasidenote. Arethey related?HarrietTubmanHelped slaves escape via the UndergroundRailroad.JohnBrown H
Boise State - HIST - 100
ClassicalGreeceClassicalPeriod500339BC &quot;Classical&quot;means: Standardagainstwhichothersarejudgedorevaluated Greatest Enduring Stylisticform(music,art,etc) Stylisticperiod(e.g.afterBaroque) GoldenageofacivilizationClassicalPeriodorTheGoldenAgeofGre
Boise State - HIST - 100
ClassicalGreekPhilosophySocrates Simple man Stonemason Shrewish wife Loyal service in the war Incredible concentration Wisest man in Athens (oracle) Gad fly (Dialectics/Socratic method) Theunexaminedlifeisnotworthliving.Socrates Convicted of co
Boise State - HIST - 100
Review of our Presidents fromthe Progressive Era to Cold WarTeddy Roosevelt , William Howard Taft , WoodrowWilson (D)Warren G. Harding , Calvin Coolidge (D),Herbert Hoover , FDR (D)Kamikaze Japanese pilots crashed their bomb-filledplanes into Allie
Boise State - HIST - 100
The Cold War 1945The1991Two sides of Cold War NATO North Warsaw Pact proAtlantic TreatySoviet countries OrganizationUSSR, and allcountries controlled USA, France, Greatby the USSR.Britain, West COMMUNISMGermany CAPITALISMCold War The Cold
Boise State - HIST - 100
Villegas Middle SchoolFall 2007Mr. ClutterAfricawasthehomeoffourgreatcivilizations;Nubia,Ghana,MaliandSonghay.MaliEnterSonghayEnterEnterEnterNubiaGhanaGhanadevelopedinWestAfricabetweentheNiger(NIjhur)andtheGambiaRivers.Itwasanimportantking
Boise State - HIST - 100
AmericasGreatDisastersMr.RyanGreatDisastersGreatDisasters ManyterriblethingshavehappenedtoAmericaandhercitizens Floods,Hurricanes,Fires,Blizzards,Explosions,Diseases Causesdeath,injuries,lossofhomes,money,jobs,communities,friendships Butmanygoo
Boise State - HIST - 100
Early Christian IrelandThe Arrival of Christianity fromAD 400 onwardsPalladius introducing Christianityto Ireland before St. PatrickDied432;feastdayformerlycelebratedonOctober7.ThestoryofPalladius,recordedbySaintProsperofAquitaine,iscaughtupinthato
Boise State - HIST - 100
Boise State - HIST - 100
Boise State - HIST - 100
EUROPEAN RULERS IN THE AGE OFABSOLUTISMBy CountryA TIME OF EMPIRES1533-1603ENGLANDElizabeth IE N GL A N DJames I The 1 StuartKingstJames sonE N GL A N DCharles ISPAINPhilip II SpainThe GoldenAgeFRANCELouis XIV The Sun KingLOUIS XIVPRUS
Boise State - HIST - 100
The Fall of Rome and thebeginning of the MiddleAges.Fall of the Roman EmpireRome was the mostpowerful empire theworld had ever seen.Its architecture wasHellenistic and its roadsystem was asimpressive as that ofthe Inca in S. AmericaRoman Empir
Boise State - HIST - 100
Boise State - HIST - 100
Black History Month2008Mr. ClutterVMS LibraryIntroductionCarter G. Woodson was an African American historian, author, journalist andthe Founder of Black History Month. He is considered the first to conduct ascholarly effort to popularize the value
Boise State - HIST - 100
George WashingtonThomas JeffersonTheodoreRooseveltAbrahamLincolnMount Rushmore Facts The carving started in 1927 and finished in1941few injuries but no deaths. They stand at over 5,500 feet Each presidents head is as tall as a 6 storybuilding
Boise State - HIST - 100
The French Revolution1789Causes of French RevolutionIdeas of liberty and equality fromthe American Revolution (note:Constitution was signed 2 yrsbefore in 1787)Enlightenment ideas of JohnLockeCauses of French Revolution Vastmajority of people w
Boise State - HIST - 100
Great DepressionBrother can you spare a dime?OBJ #1 - Describe the CAUSES and SPARK of the Great Depression. How didOverproduction affect both farmers and industry? What system collapsed and causedmillions to lose their savings? Explain how buying on
Boise State - HIST - 100
EarlyGreekScienceandPhilosophyThis Powerpoint is hosted on www.worldofteaching.comPlease visit for 100s more free powerpointsEarly GreeceGreece and Greek ColoniesRome and Roman ColoniesPhoenicia, Carthage and Punic ColoniesThalesofMiletus625BC F
Boise State - HIST - 100
H alloweenOrigins and TraditionsO rigins Halloween began two thousand years ago inI reland, England, and Northern France with theancient religion of the Celts (Paganism).T heycelebratedtheirNew stYearonNovember1 . This day marked the beginning of
Boise State - HIST - 100
Facts ofHalloweenHalloweenactuallyhasitsoriginsintheCatholicChurch.ItcomesfromacontractedcorruptionofAllHallowsstEve.November1 ,AllHallowsDay(orAllSaintsDay)isaCatholicdayofobservanceinhonorofsaints.In Mexico, theycelebrate El Dia de losMuerto
Boise State - HIST - 100
Boise State - HIST - 100
How did Life in Egypt affectMedicine?Ancient MedicineAncient Medicine3000BC 500ADEgyptians 3000BC-1000BCGreeks 1000BC 500BCRomans 500BC 500 ADKey examine patterns and themesacross the period Focus: EgyptEgypt A Wealthy CountryWealthy countryP
Boise State - HIST - 100
People of the Stone AgeHunters and GatherersCh.1, Lesson 1Mr. Bennetts 6th GradeThe earliest humansprobably lived in Africa.They spread to therest of the world overthe next tens ofthousands of yearsas they hunted andgathered food tosurvive.Ge
Boise State - HIST - 100
Immigrants inAmericaMillions of immigrants moved tothe United States in the late1800s &amp; early 1900s.Immigration Stations Once immigrants arrived in the U.S., theywent through immigration stations, such asEllis Island in New York Harbor.Government
Boise State - HIST - 100
StandardStandard10.3StudentsanalyzetheeffectsoftheIndustrialRevolutioninEngland,France,Germany,Japan,andtheUnitedStates.IndustrialRevolutionIndustrialRevolution TheIndustrialRevolutionwasthemajorshiftoftechnological,socioeconomicandculturalc
Boise State - HIST - 100
Industrial RevolutionBy J. CollinsIndustrial RevolutionThe IR is whenpeople stoppedmaking stuff athome and startedmaking stuff infactories.Cottage IndustryFactory systemCotton gin His cotton ginremoved theseeds out ofraw cotton.Steam Engin
Boise State - HIST - 100
IRELAND IN CONFLICT 1909 - 1922Test your knowledge of whos who in the Ireland in Conflicttopic with the following slideshowAs the images of historical personalities from the topic appear,try to work out who they are and what view they held over Irelan
Boise State - HIST - 100
Islam:History, values and cultureShahbaz YounisPRESENTATION OUTLINEIntroductory RemarksHistorical overviewIslam as a monotheistic religionthe QuranGod or Allahpillars and valuessocial code and reformsrelation with other faithsthe Sunni and Shi
Boise State - HIST - 100
JerusalemMount Zion, JerusalemAn early historyAncient Canaan 1700 - 1386B.C.EPharaoh Amenhotep ruled overEgypt and CanaanThe Pharoah Ramses III forcedthe Philistines to settle in CanaanIn 1750 B.C.E - The12 tribes ofIsrael settled in Egypt from
Boise State - HIST - 100
Kennedy AssassinationKennedyCutting through ConspiraciesNovember 22, 1963NovemberJFK was in DallasJFKtrying to getsupport for nextyears election.years Dallas had anDallasunfriendlyreputation towardspoliticians.politicians.Lee Harvey Oswal
Boise State - HIST - 100
Renaissance Man:Leonardo Da VinciMr. ClutterVMS LibrarySpring 200811/23/111Leonardo the ScientistStudied many topics suchas anatomy, zoology,botany, geology, optics,aerodynamics andhydrodynamics amongothersHe was fascinated by thestudy of p
Boise State - HIST - 100
Lincoln and the EmancipationProclamationProclamationRace Relations in the SouthRace1863-19121863-1912Unit 4What motives lay behind Lincolnsissuing of the EmancipationProclamation?Proclamation?Underlying questions:What was the EmancipationWha
Boise State - HIST - 100
Louis Pasteur &amp; Germ TheoryBeliefs about disease in19thCentury People knew there was a link between dirtand disease, but could not explain the link. People explained disease as seeds bad seedsin the air known as miasma. 1850s &amp;1860s breakthrough in
Boise State - HIST - 100
MagellanandCoronadoBy: Mrs. MaysFerdinand MagellanMagellan Ferdinand Magellan was a Portugesemaritime (sea) explorer who sailed for thecountry of Spain (just like Columbus andCortes). He led the 1st successful attemptto sail around the entire Ea
Boise State - HIST - 100
Dr. Martin Luther King, Jr.1929-1968Michael Luther King, Jr. wasborn on January 15th toschoolteacher, Alberta Kingand Baptist minister, MichaelLuther King residing at 501Auburn Avenue. His fatherlater changed both their namesto Martin Luther King
Boise State - HIST - 100
Fully qualified 14years at university, 7of those yrs he studiedmedicine, therealways men.Knowledge: 5Experience: 5Cost of treatment: 1Success rate: 5Knowledge: 4Experience: 4Cost of treatment: 3Success rate: 3He sells andmixesmedicine.Pres
Boise State - HIST - 100