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首页 Structural Analysis In Theory and Prac

Structural Analysis In Theory and Prac.pdf

Structural Analysis In Theory a…

caogang101
2013-07-25 0人阅读 举报 0 0 0 暂无简介

简介:本文档为《Structural Analysis In Theory and Pracpdf》,可适用于工程科技领域

ButterworthHeinemannisanimprintofElsevierCorporateDrive,Suite,Burlington,MA,USALinacreHouse,JordanHill,OxfordOXDP,UKCopyright©,InternationalCodesCouncilAllrightsreservedALLRIGHTSRESERVEDThisStructuralAnalysis:InTheoryandPracticeisacopyrightedworkownedbytheInternationalCodeCouncil,IncWithoutadvancepermissionfromthecopyrightowner,nopartofthisbookmaybereproduced,distributed,ortransmittedinanyformorbyanymeans,includingwithoutlimitation,electronic,opticalormechanicalmeans(bywayofexampleandnotlimitation,photocopying,orrecordingbyorinaninformationstorageretrievalsystem)Forinformationonpermissiontocopymaterialexceedingfairuse,pleasecontactPublications,WestFlossmoorRoad,CountryClubhills,ILPhoneICCSAFE()Trademarks:“InternationalCodeCouncil,”andthe“InternationalCodeCouncil”logoaretrademarksoftheInternationalCodeCouncil,IncLibraryofCongressCataloginginPublicationDataApplicationsubmittedBritishLibraryCataloguinginPublicationDataAcataloguerecordforthisbookisavailablefromtheBritishLibraryISBN:ForinformationonallButterworth–HeinemannpublicationsvisitourWebsiteatwwwelsevierdirectcomPrintedintheUnitedStatesofAmericaForewordItiswithgreatpleasurethatIwritethisforewordtoStructuralAnalysis:InTheoryandPractice,byAlanWilliamsLikemanyotherengineers,IhaveutilizedDrWilliams’numerouspublicationsthroughtheyearsandhavefoundthemtobeextremelyusefulThispublicationisnoexception,giventheextensiveexperienceandexpertiseofDrWilliamsinthisarea,thecredibilityofElsevierwithexpertiseintechnicalpublicationsinternationally,andtheInternationalCodeCouncil(ICC)withexpertiseinstructuralengineeringandbuildingcodepublicationsEngineersatalllevelsoftheircareerswillfindthedeterminateandindeterminateanalysismethodsinthebookpresentedinaclear,concise,andpracticalmannerIamastrongadvocateofalloftheseattributes,andIamcertainthatthebookwillbesuccessfulbecauseofthemCoverageofmanyotherimportantareasofstructuralanalysis,suchasPlasticDesign,MatrixandComputerMethods,ElasticPlasticAnalysis,andthenumerousworkedoutsampleproblemsandtheanswerstothesupplementaryproblemsgreatlyenhanceandreinforcetheoveralllearningexperienceOnemayaskwhy,inthisageofhighpoweredcomputerprograms,acomprehensivebookonstructuralanalysisisneededThesoftwaredoesalloftheworkforus,soisn'titsufficienttoreadtheuser’sguidetothesoftwareortohaveacursoryunderstandingofstructuralanalysisWhilethereisnoquestionthatcomputerprogramsareinvaluabletoolsthathelpussolvecomplicatedproblemsmoreefficiently,itisalsotruethatthesoftwareisonlyasgoodastheuser’slevelofexperienceandhisherknowledgeofthesoftwareAsmallerrorintheinputoramisunderstandingofthelimitationsofthesoftwarecanresultincompletelymeaninglessoutput,whichcanleadtoanunsafedesignwithpotentiallyunacceptableconsequencesThatiswhythisbookissovaluableItteachesthefundamentalsofstructuralanalysis,whichIbelievearebecominglostinstructuralengineeringHavingasolidfoundationinthefundamentalsofanalysisenablesengineerstounderstandthebehaviorofstructuresandtorecognizewhenoutputfromacomputerprogramdoesnotmakesenseSimplyput,studentswillbecomebetterstudentsandengineerswillbecomebetterengineersasaresultofthisbookItwillnotonlygiveyouabetterunderstandingofstructuralanalysisitwillmakeyoumoreproficientandefficientinyourdaytodayworkDavidAFanella,PhD,SE,PEChicago,ILMarchPartOneAnalysisofDeterminateStructuresPrinciplesofstaticsNotationFforcefiangleinatriangleoppositesideFiHhorizontalforcellengthofmemberMbendingmomentPaxialforceinamemberRsupportreactionVverticalforceWLLconcentratedliveloadwDLdistributeddeadloadθangleofinclinationIntroductionStaticsconsistsofthestudyofstructuresthatareatrestunderequilibriumconditionsToensureequilibrium,theforcesactingonastructuremustbalance,andtheremustbenonettorqueactingonthestructureTheprinciplesofstaticsprovidethemeanstoanalyzeanddeterminetheinternalandexternalforcesactingonastructureForplanarstructures,threeequationsofequilibriumareavailableforthedeterminationofexternalandinternalforcesAstaticallydeterminatestructureisoneinwhichalltheunknownmemberforcesandexternalreactionsmaybedeterminedbyapplyingtheequationsofequilibriumAnindeterminateorredundantstructureisonethatpossessesmoreunknownmemberforcesorreactionsthantheavailableequationsofequilibriumTheseadditionalforcesorreactionsaretermedredundantsTodeterminetheredundants,additionalequationsmustbeobtainedfromconditionsofgeometricalcompatibilityTheredundantsmayberemovedfromthestructure,andastable,determinatestructureremains,whichisknownasthecutbackstructureExternalredundantsareredundantsthatexistamongtheexternalreactionsInternalredundantsareredundantsthatexistamongthememberforcesStructuralAnalysis:InTheoryandPracticeRepresentationofforcesAforceisanactionthattendstomaintainorchangethepositionofastructureTheforcesactingonastructurearetheappliedloads,consistingofbothdeadandimposedloads,andsupportreactionsAsshowninFigure,thesimplysupportedbeamisloadedwithanimposedloadWLLlocatedatpointandwithitsownweightwDL,whichisuniformlydistributedoverthelengthofthebeamThesupportreactionsconsistofthetwoverticalforceslocatedattheendsofthebeamThelinesofactionofallforcesonthebeamareparallelWLLwDLFigurekipskipskipskipskipskipskipskipskipskips(i)(ii)FigureIngeneral,aforcemayberepresentedbyavectorquantityhavingamagnitude,location,sense,anddirectioncorrespondingtotheforceAvectorrepresentsaforcetoscale,suchasalinesegmentwiththesamelineofactionastheforceandwithanarrowheadtoindicatedirectionThepointofapplicationofaforcealongitslineofactiondoesnotaffecttheequilibriumofastructureHowever,asshowninthethreehingedportalframeinFigure,changingthepointofapplicationmayaltertheinternalforcesintheindividualmembersofthestructureCollinearforcesareforcesactingalongthesamelineofactionThetwohorizontalforcesactingontheportalframeshowninFigure(i)arecollinearandmaybeaddedtogivethesingleresultantforceshownin(ii)PrinciplesofstaticsForcesactinginoneplanearecoplanarforcesSpacestructuresarethreedimensionalstructuresand,asshowninFigure,maybeactedonbynoncoplanarforceskipskipskips(i)(ii)FigureFigureFigureInaconcurrentforcesystem,thelineofactionofallforceshasacommonpointofintersectionAsshowninFigureforequilibriumofthetwohingedarch,thetworeactionsandtheappliedloadareconcurrentItisoftenconvenienttoresolveaforceintotwoconcurrentcomponentsTheoriginalforcethenrepresentstheresultantofthetwocomponentsThedirectionsadoptedfortheresolvedforcesaretypicallythexandycomponentsinarectangularcoordinatesystemAsshowninFigure,theappliedforceFonthearchisresolvedintothetworectangularcomponents:HFVF��cossinθθFVHθFigureFFlFlFlFM�FlFFF��l(i)(ii)(iii)ForcesMomentFigureThemomentactingatagivenpointinastructureisgivenbytheproductoftheappliedforceandtheperpendiculardistanceofthelineofactionoftheforcefromthegivenpointAsshowninFigure,theforceFatthefreeendofthecantileverproducesabendingmoment,whichincreaseslinearlyalongthelengthofthecantilever,reachingamaximumvalueatthefixedendof:MFl�Theforcesystemshownat(i)mayalsobereplacedbyeitheroftheforcesystemsshownat(ii)and(iii)ThesupportreactionsareomittedfromthefiguresforclarityStructuralAnalysis:InTheoryandPracticePrinciplesofstaticsConditionsofequilibriumInordertoapplytheprinciplesofstaticstoastructuralsystem,thestructuremustbeatrestThisisachievedwhenthesumoftheappliedloadsandsupportreactionsiszeroandthereisnoresultantcoupleatanypointinthestructureForthissituation,allcomponentpartsofthestructuralsystemarealsoinequilibriumAstructureisinequilibriumwithasystemofappliedloadswhentheresultantforceinanydirectionandtheresultantmomentaboutanypointarezeroForasystemofcoplanarforcesthismaybeexpressedbythethreeequationsofstaticequilibrium:∑∑∑HVM���whereHandVaretheresolvedcomponentsinthehorizontalandverticaldirectionsofaforceandMisthemomentofaforceaboutanypointSignconventionForaplanar,twodimensionalstructuresubjectedtoforcesactinginthexyplane,thesignconventionadoptedisshowninFigureUsingtherighthandsystemasindicated,horizontalforcesactingtotherightarepositiveandverticalforcesactingupwardarepositiveThezaxispointsoutoftheplaneofthepaper,andthepositivedirectionofacoupleisthatofarighthandscrewprogressinginthedirectionofthezaxisHence,counterclockwisemomentsarepositiveyxzFigureStructuralAnalysis:InTheoryandPracticeExampleDeterminethesupportreactionsofthepinjointedtrussshowninFigureEndofthetrusshasahingedsupport,andendhasarollersupport(i)Appliedloads(ii)SupportreactionsV�kipsV�kipsV�kipsH�kipsH�kipsV�kipsftftftFigureSolutionToensureequilibrium,supportprovidesahorizontalandaverticalreaction,andsupportprovidesaverticalreactionAdoptingtheconventionthathorizontalforcesactingtotherightarepositive,verticalforcesactingupwardarepositive,andcounterclockwisemomentsarepositive,applyingtheequilibriumequationsgives,resolvinghorizontally:HHHH������kipsactingtotheleft…TakingmomentsaboutsupportandassumingthatVisupward:VHVV����V�������()kipsactingupwardasassumed…Resolvingvertically:VVVVV���������kipsactingupward…Thesupportreactionsareshownat(ii)PrinciplesofstaticsTriangleofforcesWhenastructureisinequilibriumundertheactionofthreeconcurrentforces,theforcesformatriangleofforcesAsindicatedinFigure(i),thethreeforcesF,F,andFareconcurrentAsshowninFigure(ii),iftheinitialpointofforcevectorFisplacedattheterminalpointofforcevectorF,thentheforcevectorFdrawnfromtheterminalpointofforcevectorFtotheinitialpointofforcevectorFistheequilibrantofFandFSimilarly,asshowninFigure(iii),iftheforcevectorFisdrawnfromtheinitialpointofforcevectorFtotheterminalpointofforcevectorF,thisistheresultantofFandFThemagnitudeoftheresultantisgivenalgebraicallyby:()()()cosFFFFFf���FFEquilibrantfffFFFFFFFResultant(i)(ii)(iii)Figureand:FFff�sincscor:FfFfFfsinsinsin��ExampleDeterminetheangleofinclinationandmagnitudeofthesupportreactionatendofthepinjointedtrussshowninFigureEndofthetrusshasahingedsupport,andendhasarollersupportStructuralAnalysis:InTheoryandPracticeSolutionTakingmomentsaboutsupportgives:V���kipsactingverticallyupward…Thetriangleofforcesisshownat(ii),andthemagnitudeofthereactionatsupportisgivenby:RVFVFfR�����������()()coscos(r))�kipsTheangleofinclinationofRis:θ���atan()Alternatively,sincethethreeforcesareconcurrent,theirpointofconcurrencyisatpointinFigure(i),and:θ���atan()andR����sinsinkipsF�kipsF�kipsV�kipsftftftVRθθ(i)(ii)RFigurePrinciplesofstaticsThereactionRmayalsoberesolvedintoitshorizontalandverticalcomponents:HRVR����cossinθθkipskipsFreebodydiagramForasysteminequilibrium,allcomponentpartsofthesystemmustalsobeinequilibriumThisprovidesaconvenientmeansfordeterminingtheinternalforcesinastructureusingtheconceptofafreebodydiagramFigure(i)showstheappliedloadsandsupportreactionsactingonthepinjointedtrussthatwasanalyzedinExampleThestructureiscutatsectionAA,andthetwopartsofthetrussareseparatedasshownat(ii)and(iii)toformtwofreebodydiagramsThelefthandportionofthetrussisinequilibriumundertheactionsofthesupportreactionsofthecompletestructureat,theapplied(i)Appliedloadsandsupportreactions(ii)Lefthandfreebodydiagram(iii)RighthandfreebodydiagramV�kipsV�kipsV�kipskipskipskipskipskipskipsH�kipsH�kipsH�kipsV�kipsV�kipsH�kipscutlineV�kipsV�kipsV�kipsAAFigureStructuralAnalysis:InTheoryandPracticeloadsatjoint,andtheinternalforcesactingonitfromtherighthandportionofthestructureSimilarly,therighthandportionofthetrussisinequilibriumundertheactionsofthesupportreactionsofthecompletestructureat,theappliedloadatjoint,andtheinternalforcesactingonitfromthelefthandportionofthestructureTheinternalforcesinthemembersconsistofacompressiveforceinmemberandatensileforceinmembersandByusingthethreeequationsofequilibriumoneitherofthefreebodydiagrams,theinternalforcesinthemembersatthecutlinemaybeobtainedThevaluesofthememberforcesareindicatedat(ii)and(iii)ExampleThepinjointedtrussshowninFigurehasahingedsupportatsupportandarollersupportatsupportDeterminetheforcesinmembers,,andcausedbythehorizontalappliedloadofkipsatjointftftftH�kipsH�kipsV�kipsV�kipsPVPPCutlineAA(i)Loadsandsupportreactions(ii)FreebodydiagramθFigureSolutionThevaluesofthesupportreactionswereobtainedinExampleandareshownat(i)ThetrussiscutatsectionAA,andthefreebodydiagramoftherighthandportionofthetrussisshownat(ii)Resolvingforcesverticallygivestheforceinmemberas:PV����kipscompressionsinsinθ…Takingmomentsaboutnodegivestheforceinmemberas:PV����kipstension…PrinciplesofstaticsTakingmomentsaboutnodegivestheforceinmemberas:PV����kipscompression…PrincipleofsuperpositionTheprincipleofsuperpositionmaybedefinedasfollows:thetotaldisplacementsandinternalstressesinalinearstructurecorrespondingtoasystemofappliedforcesisthesumofthedisplacementsandstressescorrespondingtoeachforceappliedseparatelyTheprincipleappliestoalllinearelasticstructuresinwhichdisplacementsareproportionaltoappliedloadsandwhichareconstructedfrommaterialswithalinearstressstrainrelationshipThisenablesloadingonastructuretobebrokendownintosimplercomponentstofacilitateanalysisAsshowninFigure,apinjointedtrussissubjectedtotwoverticalloadsat(i)andahorizontalloadat(ii)ThesupportreactionsforeachloadingV�kipsV�kipsV�kipsV�kipsV�kipsV�kipsH�kipsH�kips(i)(ii)�V�kipsH�kipsH�kipsV�kipsV�kipsV�kips(iii)�FigureStructuralAnalysis:InTheoryandPracticecaseareshownAsshownat(iii),theprincipleofsuperpositionandthetwoloadingcasesmaybeappliedsimultaneouslytothetruss,producingthecombinedsupportreactionsindicatedSupplementaryproblemsSDeterminethereactionsatthesupportsoftheframeshowninFigureSftkipskipsftftftftftftVVFigureSkipsftftMHVHVftkipsFigureSSDeterminethereactionsatsupportsandofthebridgegirdershowninFigureSInaddition,determinethebendingmomentinthegirderatsupportPrinciplesofstaticsSDeterminethereactionsatthesupportsoftheframeshowninFigureSInaddition,determinethebendingmomentinmemberkipskipsHHVVftftftftftFigureSftkipsftftHHVVFigureSSDeterminethereactionsatthesupportsofthederrickcraneshowninFigureSInaddition,determinetheforcesproducedinthemembersofthecraneStructuralAnalysis:InTheoryandPracticeftHVHVftkipsFigureSftftftftkipskipsHVVFigureSSDeterminethereactionsatthesupportsofthebentshowninFigureSInaddition,determinethebendi

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