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Aerodynamic

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Aerodynamic

    Aerodynamic

    JournalofZhejiangUniversitySCIENCEA

    ISSN1673?565X(Print);ISSN1862?1775(Online)

    www.zjuedu.cn0zus;wwwspringedink.com

    E?mail:jZUS@ZjUeducn

    Zhangeta1./JZhejiangUnivSciA20078(51:693-698

    Aerodynamicstabilityofcable.supportedbridgesusingCFRPcables

    ZHANGXin-jun,YINGLei-dong

    (CollegeofCivilEngineering

    H(,rcf,Pc,"rP,ZhejiangUniversityofTechnology,Hangzhou310014,China) E-mail:xjzhang@zjut.edu.ca

    ReceivedAug.16,2006;revisionacceptedNov.21,2006

    Abstract:Togainunderstandingoftheapplicabilityofcarbonfiberreinforcedpolymer(CFRP,cableincable.suppoRed

    bridges,basedontheRunyangBridgeandJinshaBridge,asuspensionbridgeusingCFRPcablesandacablestayedbridgeusing

    CFRPstaycablesaredesigned,inwhichthecable'scross.sectionalareaisdeterminedbytheprincipleofequivalentaxialstiffness

    Numericalinvestigationsontheaerodynamicstabilityofthetwobridgesareconductedby3Dnonlinearaerodynamicstability

    analysis.TheresultsshowedthatasCFRPcablesareusedincable.supportedbridges.forsuspensionbridge.itsaerodynamic

    stabilityissuperiortothatofthecaseusingsteelcablesduetothegreatincreaseofthetorsionalfrequency;forcablestayedbridge.

    itsaerodynamicstabilityisbasicallythesameasthatofthecaseusingsteelstaycables.Thereforeasfarasthewindstabilityis

    considered.theuseofCFRPcablesincable.supportedbridgesisfeasible.andthecable'scross

sectionalareashouldbedeter

    minedbytheprincipleofequivalentaxialstiffness. Keywords:Cable

    supportedbridges,Carbonfiberreinforcedpolymer(CFRP)cable,Aerodynamicstability

    doi:10.163l~zus.2007.A0693Documentcode:ACLCnumber:U448.25

    INTRODUCTION

    Bytheendofthelastcentury.theAkashiKaikyo Bridge(1990m)inJapanandtheGreatBeltBridge (1624m)inDenmarkrepresentanoutstandingengi. neeringachievementinbuildingsuspensionbridge withaspanapproaching2000m.Meanwhile,the NormandyBridge(856m,inFranceandtheTatara Bridge(890m)inJapanmadecable-stayedbrie competewithsuspensionbridgeforspansaround l000m.Intothe21stcentury.theworld'sbridge constructionenteredintoaneweraofbuilding sea-crossingandisland.1inkingprojects.Tomeet withthenavigationrequirementandovercomethe constructiondifficultyofdeep.waterfoundation, longerandlongerspanofcable-supportedbriesis beingplanned,suchastheMessinaBridge(3300m) inItalyandtheGibraltarBridgebetweenSpainand Morocco(3550m)forsuspensionbridges.forca. ble.stayedbridgessuchastheStonecuttersBridge 'Project(No.502118,supportedbytheNaturalScienceFoundation

    ofZhejiangProvince,China

    (1018m,inHongKongandtheSutongBridge(1088 m)inChina(XiangandGe.2002).

    Withtherapidincreaseofspanlength.bridges arebecominglighter,slenderandmoresensitiveto

    windaction,andsomenewproblemsarearising.One ofthemostimportantthingsoftheseisstructural design.Generally,thedesignofsuperlong-span suspensionbridgesismainlycontrolledbystructural deadload.withthecablesplayinganimportantrolein structuraldeadload.Therefore.usingmaterialswith highertensilestrengthandlowermassdensityforthe cablescandecreasethecable'sdeadload,savecable materials,decreasethedimensionsofsubstructures, andfinallydecreasethecostandconstructiondi. cultyforsuspensionbridges.Forcable-stayedbridges, thestaycablesarealsoimportantstructuralelements. withsignificantinfluencesonstructuralperformance andappearance.Atpresent.thestaycableiscorn. monlymadeoftraditionalsteelwires.Onthestruc. turalperformance.thesteelcableisrelativelyheavy. resultinginsignificantsaggingeffectduetoits self-weight,thusreducingtheeffectivestiffnessof thestaycableandmakingitbehavesofterunderser.

    Zhangetal/dZhefiangUnivSciA20078(5):693?698 viceload.Inaddition.forthetraditionalsteelcable. corrosionandfatiguearetwomajorproblemsin bridgeswithhightrafficvolumeorbridgeslocatedin corrosionenvironment,whichcausethepremature breakageofthewiresinsidethecable.Moreover.the costofreplacementandmaintenanceofthesteel cableisgenerallyhigh.

    Continuousattemptsarebeingmadetoimprove

    traditionalcablematerials;atthesametimeengineers andresearcherstrytodevelopnewengineeringma

    terials.Amongthem.moreattentionisattractedtothe CFRPmateria1.Comparedtothetraditionalcable materialofhighstrengthstee1.CFRPhasproperties ofabout2timeshighertensilestrength.about80%of theelasticmodulus.onlyabout20%ofthemass densityofsteel,withotheroutstandingadvantages includingexcellentcorrosionresistantandfa

    tigueresistantability.1owthermalexpansioncoe筒一

    cient.etc.(Cheng1999).AlthoughCFRPmaterial hashighcostandlowshearcapacity.withthein

    creaseofproductionanddevelopmentofnewan

    choragesystem,theseproblemsarebeingsolved,and CFRPmaterialisbelievedtohavethegreatestpo

    tentialapplicationprospect.Atpresent.CFRPmate

    rialiswidelyusedintheseismicretrofitandreha

    bilitationofexistingconcretebridges.AsCFRPhas thehighestmodulusdensityratioamongavailable

    structuralmaterials.itismostsuitableforapplication asstructuralmemberwheremaximumstiffnessand lightweightarerequired.suchasinthecablesin cablestayedandsuspensionbridges.Itshighstiff- nessmassdensityratiocanreducethelongitudinal deformationofthecablesunderloadsandthesagging effectduetotheself-weight.Theoutstandingfatigue resistantpropertyofCFRPalsosatisfiesthetypical loadingconditionsofthecablestayedbridgewith

    largecyclicloadamplitudes.Theexcellentcorrosion resistanceofCFRPmakesitmoreeconomicalfor

    maintenanceascomparedtostee1.Therefore,the feasibilityofusingCFRPcablesinlongspanca

    blesupportedbridgesattractsincreasingattention fromcivilengineers(Meier.1992;MeierandMeier. 1996;Noisternig,2000).Thefirstapplicationof CFRPcablesinarealcablestayedbridgeistheStork

    BridgeinSwitzerlandin1996.butonlytwoofthe24 cablesaremadeofCFRP(Cheng.1999).Afewca

    blestayedpedestrianbridgesusingCFRPstaycables havebeensuccessfullybuiltforresearchpurpose suchastheHerningFootbridgeinDenmark,the LaroinFootbridgeinFrance,etc.Also,someca

    blestayedbridgesusingCFRPstaycableshavebeen proposedasdesignalternatives.Butforsuspension bridges.theactualapplicationofCFRPmaterialas maincableshasnotbeenreporteduntilnow. Comprehensivestudiesonthematerialand mechanicalperformance,economy,construction, anchoragesystem.etc.oftheCFRPcableandits applicationincablestayedbridgeshavebeendone

    (Cheng,1999;Kremmidas,2004;KaoandKou,2005; Koueta1.,2005;Xiea1.,2005).However,very littleresearchonthewindstabilityofcablesupported

    bridgesusingCFRPcableshasbeenconducted(Kao a1.,2006;Nonuakieta1.,1999;Cheng,1999;Fang andXiang.1999).Duetotheirgreatflexibilityca

    blesupportedbridgesareverysusceptibletowind action,withthewindstabilitygenerallybecomingan importantcontrollingfactoroftheirdesignandcon

struction.Forlongspansuspensionbridges.in

    creasingstructuraldeadloadcangreatlyimprove theirgravitystiffness.andthusthemechanicalper

    formance.Therefore.useofCFRPmaterialwith lowerelasticmodulusandmassdensityinthemain cablesseemstobenotadvisable.Whetherornotthe windstabilityofsuspensionbridgesusingCFRP cablesbecomesworseneedstobefurtherinvestigated. FangandXiangf1999)investigatedtheaerostatic stabilityofsuperlongspansuspensionbridgesusing CFRPcables,andconcludedthattheaerostaticsta

    bilityworsenswithuseofCFRPcables.Butinhis study.thecablecrosssectionalareawasdetermined bytheprincipleofequivalentcablestrength.Inaddi

    tiontothismethod.thecablecrosssectionalareacan

    alsobedeterminedbytheprincipleofequivalentaxial stiffness(Cheng,1999).Nonuakieta1.f1999)inves

    tigatedthefluttercharacteristicsofadualcableSUS

    pensionbridgeof3000mcenterspanusingadvanced compositesbythedirectflutterFEM.Chengf1999) investigatedtheflutterstabilityofacablestayed

    bridgeusingCFRPstaycables.Butintheirstudies. theimportantefFectofnonlinearwindstructurein

    teractionwasneglected.

    Inthiswork,basedontheRunyangBridgeand JinshaBridge,asuspensionbridgeusingCFRPcables andacablestayedbridgeusingCFRPstaycables weredesigned.Numericalinvestigationsonthe aerodynamicstabilityofthetwobridgeswerecon

    Zhangeta1./JZhejiangUnA,SciA20078(5):693-698 ductedby3Dnonlinearaerodynamicstabilityanaly

    sis,andthefeasibilityofusingCFRPcablesinca

    blesupportedbridgeswasalsodiscussedbasedonthe windstability.

    AER0DYNAMICSTABILITYOFSUSPENSION

    BRIDGEUSINGCFRPCABLES

    Descriptionofthesamplebridge

    Inthiswork,theRunyangBridgetakenasex

    ampleisthelongestsuspensionbridgeasof2005in China.Thebridgehasa1490mmainspanandtwo 470msidespans,asshowninFig.1(ChenandSong, 2000).Thecable'ssagtospanratiois1/10.andthe spacingofthetwocablesis34.3m.Thedeckisasteel streamlinedboxgirderof3.0mheightand35.9m width.Theconcretedoor-shapedtowersareabout 209mhigh.Forthepurposeofdiscussion,asame spanlengthofsuspensionbridgeusingCFRPcables isdesigned.Exceptforthematerialandsectional propertiesofthecablesandhangers,otherdesign parametersofthetwobridgesarekeptthesame. Structuralmaterialandsectionalpropertiesforthe twocasesarepresentedinTable1.

    ThecrosssectionalareasofCFRPcablesand

    hangersaspresentedinTable1aredeterminedbythe fa1

    695

    equivalentaxialstiffness,andcalculatedbythefol

    lowingequation(Cheng,1999):

    ECFRpACFRp=EsteeStee1,

    whereEcFRP,Estee1aretheelasticmodulusofCFRP andsteelrespectively;ACFed~,Astee1arethe crosssectionalareasofCFRPandsteelcablesre spectively.

    Aerodynamicstabilityanalysis

    Windtunneltestrevealedthatthebridgeisprone towindinstabilityunderpositivewindattackangle (ChenandSong,2000).Thereforeinthefollowing analysis.thecommonwindattackanglesof0.and +3.areselected.Aerodynamicstabilityofthebridge usingCFRPandsteelcableswasinvestigatedbv3D nonlinearaerodynamicstabilityanalysis(Zhangeta1., 2002).andthecriticalwindspeedsofaerodynamic instabilityarepresentedinTable2.Intheanalysis. thebridgeisidealizedtoa3Dfiniteelementmodelas showninFig.2.inwhichthedeckandtowersare modeledby3Dbeamelements,andthehangersand cablesaremodeledbv3Dbarelements.withrigid beamsprovidedtomodeltheconnectionsbetweenthe deckandthehangers.Thedeck'saerodynamicde

    rivativesareobtainedfromthesectional.modelwind tunneltestofthebridge(ChenandSong,2000),the first20modesareinvolved.andthemodaldamping ratioistakenas0.5%.

    Fig.1GenerallayoutoftheRunrangBridge.(a)Ele- vation;(b)Cross

    sectionofthestiffeninggirderFig.23DfiniteelementmodeloftheRunyangBridge

    Table1Structuralmaterialandsectionalproperties Note:E:elasticmodulus;:cross-sectionalarea;Jd:polarmomentofinertia;

:momentofinertiaforverticalbending;:momentof

    inertiaforlateralbending;massperunitlength;Jm:polarmassmomentofinertiaperunitlengt

    h

    Zhangeta1./dZhejiangUnivSciA20078(5):693-698 Table2Effectofcablematerialsonthecriticalwind speedunderwindattackanglesof0.and+3. WindattackangleCriticalwindspeed(m/s) SteelcablesCFRPcables

    InthecaseofCFRPcablesused.thecritical windspeedsareincreasedbvl7.2%underwindat. tackangleof+3..andl4.8%underwindattackangle Of0..ascomparedtothecaseofusingsteelcables. Thereforeviewedfromtheaerodynamicstability,the CFRPcablesareconfirmedanalyticallytobesuperior tosteelcables.Theimprovementofaerodynamic stabilitycanbeexplainedfromthesimplifiedformula ofcriticalwindspeedexpressedas

    =,Ts,7~vc0,=2.5cf,B,

    C=

    nob2,,/',/

    whereqsisthemodifiedcoefficientofcrosssection shape;,7"isthemodifiedcoefficientofwindattack angle;0isthecriticalwindspeedofthecoupled flutterofathinplate;isthefundamentaltorsional frequency;Bisthewidthofthedeck;"isthedensity ratioofthebridgetoair;misthemassofthedeckand cablesperunitlength;Pisthemassdensityofair;/m iSthemassinertiaofthedeckandcablesperunit length.

Themassofthebridgeisabout26020kg/min

    thecaseofsteelcables.whereasinthecaseofCFRP cables,itisabout20180kg/m,anddecreasedby 22.4%.Similarly.themassmomentofinertiaofthe bridgeisabout2.97xl0.k2?m/minthecaseofsteel cables.whereasinthecaseofCFRPcables.itisabout 2.12×l0.kg?m/m,anddecreasedby28.6%.The

    coefficientCisthereforedecreasedbyl3.7%.Be. causetheCFRPcableisdesignedbytheprincipleof equivalentaxialstiffness.thestructuralstiffnessun. derthetwocasesisalmostthesame.Witbthesame stiffnessandmuchlowermassandmassmomentof inertia.structuralnaturalfrequencies.whicharein. verselyproportionaltothemassandmassmomentof inertia.arethereforeincreased.asshowninTable3. AsCFRPcablesareused.thenaturalfrequencies ofbothverticalandlateralbendingmodesare Table3Efrectofcablematerialsonstructuralnatu. ralfrequencies(Hz)

    Note:S:symmetric;AS:antisymmetric

    increasedbylessthan9%ascomparedtothecaseof usingsteelcables.andparticularlythetorsionalfre. quencyisremarkablyincreasedby29.6%.Although thecoefficientCisdecreased.theincreaseinthe fundamentaltorsionalfrequencyismorethan2times ofreductionofthecoefficientC.andthereforethe criticalwindspeedisgreatlyincreased.Viewedfrom theaspectofaerodynamicstability,theuseofCFRP cablesinlong.spansuspensionbridgesisfeasible. AERODYNAMICSTABILITYOFCABLE.

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