Bridge engineering handbook桥梁工程手册-15平面曲线桥梁-图文

15HorizontallyCurvedBridges15.1Introduction15.2StructuralAnalysisforCurvedBridgesSimplifiedMethod:V-Load15.3CurvedSteelI-GirderBridgesGeometricParameters•DesignCriteria•DesignExample15.4CurvedSteelBox-GirderBridges15.5CurvedConcreteBox-GirderBridgesAsaresultofcomplicatedgeometrics,limitedrightsofway,andtrafficmitigation,horizontallycurvedbridgesarebecomingthenormofhighwayinterchangesandurbanexpressways.Thistypeofsuperstructurehasgainedpopularitysincetheearly1960sbecauseitaddressestheneedsoftransportationengineering.Figure15.1showsthe20thStreetHOVinDenver,Colorado.ThestructureiscomposedofcurvedI-girdersthatareinterconnectedtoeachotherbycrossframesandareboltedtothebentcap.CrossframesareboltedtothebottomflangewhiletheconcretedeckissupportedonapermanentmetalformdeckasshowninFigure15.2.Figure15.3showstheelevationofthebridgeandtheconnectionoftheplategirdersintoanintegralbentcap.Figure15.4showstheU.S.NavalAcademyBridgeinAnnapolis,Marylandwhichisatwinsteelbox-girderbridgethatishaunchedattheinteriorsupport.Figure15.5showsRampYatI-95DaviesBlvd.InterchangeinBrowardCounty,Florida.Thestructureisasinglesteelboxgirderwithanintegralbentcap.Figure15.6showsaphotoofRoute92/101InterchangeinSanMateo,California.Thestructureiscomposedofseveralcast-in-placecurvedP/Sbox-girderbridges.TheAmericanAssociationofHighwayandTransportationOfficials(AASHTOgovernsthestructuraldesignofhorizontallycurvedbridgesthroughGuideSpecificationsforHorizontallyCurvedHighwayBridges[1].ThisguidewasdevelopedbyConsortiumofUniversityResearchTeams(CURTin1976[2]andwasfirstpublishedbyAASHTOin1980.Initsfirsteditiontheguidespecificationincludedallowablestressdesign(ASDprovisionsthatwasdevelopedbyCURTandloadfactordesign(LFDprovisionsthatweredevelopedbyAmericanIronandSteelInstituteunderproject190[15].Severalchangeshavebeenmadetotheguidespecificationssince1981.In1993anewversionoftheguidespecificationswasreleasedbyAASHTO.However,thesenewspecificationsdidnotincludethelatestextensiveresearchinthisareanortheimportantchangesthataffectedthedesignofstraightI-girdersteelbridges.AhmadM.ItaniUniversityofNevadaatRenoMarkL.RenoCaliforniaDepartmentofTransportationFIGURE15.1CurvedI-girderbridgeunderconstruction—20thSt.HOV,Denver,Colorado.BottomviewofcurvedI-girderbridge.TheguidespecificationsforhorizontallycurvedbridgesunderProject12-38oftheNationalCooperativeHighwayResearchProgram(NCHRP[3]havebeenmodifiedtoreflectthecurrentstate-of-the-artknowledge.ThefindingsofthisprojectarefullydocumentedinNCHRPinterimreports:“IGirderCurvatureStudy”and“CurvedGirderDesignandConstruction,CurrentPractice”[3].Thenew“GuideSpecificationsforHorizontallyCurvedSteelGirderHighwayBridges”[18]proposedbyHallandYeowasadoptedasAASHTOGuidespecificationsinMay,1999.Inadditiontothesesignificantchanges,theFederalHighwayAdministration(FHWAsponsoredextensivetheoreticalandexperimentalresearchprogramsoncurvedgirderbridges.Itisanticipatedthattheseprogramswillfurtherimprovethecurrentcurvedgirderspecifications.Currently,theNCHRP12–50isdeveloping“LRFDSpecificationsforHorizontallyCurvedSteelGirderBridges”[19].Theguidelinesofcurvedbridgesaremainlygearedtowardstructuralsteelbridges.Limitedinformationcanbefoundintheliteratureregardingthestructuraldesignofcurvedstructuralconcrete(R/CandP/Sbridges.Curvedstructuralconcretebridgeshaveaboxshape,whichmakesthetorsionalstiffnessveryhighandthusreducestheeffectofcurvatureonthestructuraldesign.Theobjectiveofthischapteristopresentguidelinesforthedesignofcurvedhighwaybridges.StructuraldesignofsteelI-girder,steel,andP/Sbox-girderbridgesisthemainthrustofthischapter.Theaccuracyofstructuralanalysisdependsontheanalysismethodselected.Themainpurposeofstructuralanalysisistodeterminethememberactionsduetoappliedloads.Inordertoachievereliablestructuralanalysis,thefollowingitemsshouldbeproperlyconsidered:•Mathematicalmodelandboundaryconditions•ApplicationofloadsCurvedI-girderbridgewithintegralbentcap.FIGURE15.4Twinbox-girderbridge—U.S.NavalAcademyBridge,Annapolis,Maryland.Singleboxgirderbridgewithintegralbentcap—RampY,I-95DaviesBlvd.,BrowardCounty,Florida.Themathematicalmodelshouldreflectthestructuralstiffnessproperly.Thedeckofthesuper-structureshouldbemodeledinsuchawaythatisrepresentedasabeaminagridsystemorasacontinuum.Theboundaryconditionsinthemathematicalmodelmustberepresentedproperly.Lateralbearingrestraintisoneofthemostimportantconditionsincurvedbridgesbecauseitaffectsthedesignofthesuperstructure.Thedeckoverhang,whichcarriesarail,providesasignificanttorsionresistance.Moreover,thecurvedbottomflangewouldparticipateinresistingverticalload.Thisparticipationincreasestheappliedstressesbeyondthosedeterminedbyusingsimplestructuralmechanicsprocedures[3].Duetogeometriccomplexities,thegravityloadwillinducetorsionalshearstresses,warpingnormalstresses,andflexuralstressestothestructuralcomponentsofhorizontallycurvedbridges.Todeterminethesestresses,specialanalysisaccountingfortorsionisrequired.Variousmethodsweredevelopedfortheanalysisofhorizontallycurvedbridges,whichincludesimplifiedandrefinedanalysismethods.ThesimplifiedmethodssuchastheV-Loadmethod[4]forI-girdersandtheM/Rmethodforboxgirdersarenormallyusedwith“regular”curvedbridges.However,refinedanalysiswillberequiredwheneverthecurvedbridgesincludeskewsandlateralorrotationalrestraint.Mostrefinedmethodsareformsoffinite-elementanalysis.Grillageanalysisaswellasthree-dimensional(3-Dmodelshavebeenusedsuccessfullytoanalyzecurvedbridges.Thegrillagemethodassumesthatthemembercanberepresentedinaseriesofbeamelements.Loadsarenormallyappliedthroughacombinationofverticalandtorsionloads.The3-Dmodelsthatrepresenttheactualdepthofthesuperstructurewillcapturethetorsionresponsesbycombiningtheresponsesofseveralbridgeelements.15.2.1SimplifiedMethod:V-LoadCurvedconcretebox-girderbridges—Route92/101Interchange,SanMateo,California.curvedopen-framedhighwaybridges.ThismethodisknownastheV-Loadmethodbecausealargepartofthetorsionloadonthegirdersisapproximatedbysetsofverticalshearsknownas“V-Loads.”TheV-Loadmethodisatwo-stepprocess.First,thebridgeisstraightenedoutsothattheappliedverticalloadisassumedtoinduceonlyflexuralstresses.Second,additionalfictitiousforcesareappliedtoresultinfinalstressessimilartotheonesinacurvedbridge.Theadditionalfictitiousforcesaredeterminedsothattheyresultinnonetvertical,longitudinal,ortransverseforcesonthebridge.Figure15.7showstwoprismaticgirderscontinuousoveroneinteriorsupportwithtwoequalspans,L1.Girder1hasaradiusofRandthedistancebetweenthegirdersisD.Thecrossframesareuniformlyspacedatdistanceequaltod.Asshownlater,thecrossframesincurvedbridgesareprimarymemberssincetheyarerequiredtoresisttheradialforcesappliedonthegirderduetobridgecurvature.Whenthegravityloadisapplied,theflangesoftheplategirderwillbesubjectedtoaxialforcesF=M/R,asshowninFigure15.8.However,duetothecurvatureofthegirder,laterallydistributedloadqwillbeappliedtoflangesoftheplategirderinordertoachieveequilibrium.Byassumingthattheflangesresistmostofthebendingmoment,thelongitudinalforcesintheflangesatanypointwillbeequaltothemoment,M,dividedbythesectionheight,h.Duetothecurvatureofthebridge,theseforcesarenotcollinearalonganygivensegmentoftheflange.Thus,radialforcesmustbedevelopedalongthegirderinordertomaintainequilibrium.TheforcescauselateralbendingFIGURE15.7Planviewoftwo-spancurvedbridge.Planviewofcurvedbridgetopflange.ofthegirderflangesresultinginwarpingstresses.ThemagnitudeoftheradialforcesisequaltoM/hRandhasthesameshapeofthebendingmomentdiagramasshowninFigure15.9.ThisdistributedloadcreatesequalandoppositereactionforcesateverycrossframeasshowninFigure15.10.Byassumingthespacingbetweenthecrossframesisequaltod,thereactionforceatthecrossframeisequaltoH,whichisequaltoMd/hR.Tomaintainequilibriumofthecrossframeforces,verticalshearforcesmustdevelopattheendofthecrossframesasaresultofcrossframerigidityandendfixityasshowninFigure.1GeometricParametersAccordingtothecurrentAASHTOspecifications[13],theeffectofcurvaturemaybeneglectedindeterminingtheprimarybendingmomentinlongitudinalmemberswhenthecentralangleofeachspaninatwoormorespanbridgeislessthan5°forfivelongitudinalgirders.TheframingsystemFIGURE15.9Lateralforcesoncurvedgirderflange.Reactionatcrossframelocation.forcurvedI-girderbridgesmayfollowthepreliminarydesignofstraightbridgesintermsofspanarrangement,girderspacing,girderdepth,andcrossframetypes.Thechoiceoftheexteriorspanlengthisnormallysettogiverelativelyequalpositivedead-loadmomentsintheexteriorandinteriorspans.Thearrangementresultsinthelargestpossiblenegativemoment,whichreducesbothpositivemomentsandrelateddeflections.Normally,thedepthofthesuperstructureisthesameforallspans.Previoussuccessfuldesignshowedadepth-to-spanratioequalto25fortheexteriorgirdertobeadequate.Thisratiohasbeenbasedonvibrationandstiffnessneededtoconstructtheplategirders.Also,thisratiohelpstoensurethatthegirdersdonotexperienceexcessiveverticaldeflections.Theupliftoftheexteriorgirdershouldbepreventedasmuchbyextendingthespanlengthoftheexteriorgirderratherthandealingwiththeuseoftie-downdevices.Girderspacingplaysasignificantroleinthedeckdesignandthedeterminationofthenumberofgirders.Widerspacingtendstoincreasethedeadloadonthegirders,whilecloserspacingrequiresadditionalgirders,whichincreasesthefabricationanderectionscosts.ForcurvedsteelI-girderbridges,thegirderspacingvariesbetween3.05m(10ftand4.87m(16ft.Widerspacing,commoninEuropeandJapan,requiresapost-tensionedconcretedeck,whichisnotcommonpracticeintheUnitedStates.Theoverhanglengthshouldnotexceed1.22m(4ftbecauseittendstoincreasetheloadontheexteriorgirdersbyaddingmoredeadloadandpermittingtruckloadtobeappliedonthecantilever.Theflangesoftheplategirdershouldhaveaminimumwidthtoavoidout-of-planebucklingduringconstruction.Manysteelerectorslimitthelengthofgirdershippingpiecesto85timestheflangewidth[5].Basedonthat,manybridgeengineerstendtolimitthewidthoftheflangeto40.6mm(16inbasedonamaximumshippinglengthequalto36.6m(120ft.Itisalsorecommendedthattheminimumwebthicknessbelimitedto11.1mm(⁷⁄₁₆inbecauseofwelddistortionproblems.Thethicknessofthewebdependsonitsdepthandthespacingofthetransversestiffeners.Thisrepresentsatrade-offbetweenhavingextramaterialoraddingmorestiffeners.ManybridgeengineersusetheratioofD/t=150tochoosethethicknessoftheweb.Thespacingofthecrossframeplaysanimportantfactorintheamountofforcecarriedoutbyitandthevalueofflangelateralbending.Normally,cross-framespacingisheldbetween4.57m(15ftand7.62m(25ft.15.3.2DesignCriteriaThedesignguidelines,accordingtotheRecommendedSpecificationsforSteelCurvedGirderBridges[3],areestablishedbasedonthefollowingprinciples:•Statics•StabilityEquilibriumatcrossframelocationandtheformationofV-loads.•Strengthofmaterials•InelasticbehaviorExternalandinternalstaticequilibriumshouldbemaintainedundereveryexpectedloadingcondition.Stabilityofcurvedsteelgirderbridgesisaveryimportantissueespeciallyduringcon-struction.Bytheirnature,curvedgirdersexperiencelateraldeflectionwhensubjectedtogravityloading.Therefore,thesegirdersshouldbebracedatspecifiedintervalstopreventlateraltorsionalbuckling.ThecompactnessratioofthewebandtheflangesofcurvedI-girdersaresimilartothestraightgirders.Thelinearstraindistributionisnormallyassumedinthedesignofcurvedgirderbridges.Thedesignspecificationrecognizesthatcompactsteelsectionscanundergoinelasticdefor-mations;however,currentU.S.practicedoesnotutilizeacompactsteelsectioninthedesignofcurvedI-girderbridges.Thedesigncriteriaforcurvedgirderbridgescanbedividedintotwomainsections.•Strength•ServiceabilityLimitstatedesignproceduresarenormallyusedforthestrengthdesign,whichincludesflexureandshear.Serviceloaddesignproceduresareusedforfatiguedesignanddeflectioncontrol.TheprimarymembersshouldbedesignedtobesuchthattheirappliedstressrangesarebelowtheallowablefatiguestressrangesaccordingtoAASHTOfatigueprovisions[6].Thedeflectioncheckisusedtoensuretheserviceabilityofthebridge.Accordingtotherecommendedspecificationsforthedesignofcurvedsteelbridges[3],thesuperstructureshouldbefirstanalyzedtodeterminethefirstmodeofflexuralvibration.ThefrequencyofthismodeisusedtochecktheallowabledeflectionofthebridgeasindicatedintheOntarioBridgeCode[7].15.3.3DesignExampleFollowingthe1994NorthridgeEarthquakeinCalifornia,theCaliforniaDepartmentofTranspor-tation(Caltransembarkedonataskofrebuildingdamagedfreewaysassoonaspossible.AttheSR14–I-5interchangeintheSanFernandoValley,severalspansofcast-in-placeprestressedconcreteboxgirdershavecollapsed[9].Thesewerethesamerampsthatwerepreviouslydamagedduringthe1971SanFernandoEarthquake[8].Becauseoftheurgencyofcompletionandtherestrictionsongeometry,steelplategirderswereconsideredaviablereplacementalternative.Theideawasthatthegirderscouldbefabricatedwhilethesubstructurewasbeingconstructed.Oncethefootingsandcolumnswerecompleted,thefinishedgirderswouldbedeliveredtothejobsite.Therefore,inaperiodof5weeksCaltransdesignedtwodifferentalternativesfortworampsapproximately396m(1300ftand457m(1500ftinlength.TheSouthConnectorRampwillbediscussedinthissection.The“As-Built”SouthConnectorwasapproximately397m(1302ftinlengthsetonahorizontalcurvewitharadiusof198m(650ftproducingasuperelevationof11%.ThisrampwasdesignedutilizingBridgeSoftwareDevelopmentInternational(BSDIcurvedgirdersoftwarepackage[10]asoneframewithexpansionjointsattheabutments.Thiscomputerprogramisconsideredoneofthemost-advancedprogramsfortheanalysisanddesignofcurvedgirderbridges.Theprogramanalysesthecurvedgirdersbasedon3-Dfinite-elementanalysisandutilizestheinfluencesurfaceforlive-loadanalysis.Theprogramhasalsoaninteractivepostprocessorforperformingdesignsandcodechecking.Thedesignpartoftheprogramfollowsthe15theditionofAASHTO[13]andtheCurvedGirderGuideSpecifications[1].TherampwasthencheckedusingDESCUSI[14],anothersoftwarepackage,andspot-checkedwithin-houseprogramsdevelopedbyCaltrans.Across-sectionalwidthof11.43m(37.5ftwasselectedfortwolanesoftraffic(3.66m,12ft,twoshoulders(1.52m,5ft,andtwoconcretebarriers(0.533m,1.75ft.Thisramphasa212.7mm(8⅜inchconcretedeck,whichwascompositewithfourcontinuousweldedplategirderswithboltedfieldsplicesforerection.ThematerialselectedwasA709Grade50W.Thespansrangedfrom35.97m(118ftupto66.44m(218ftinlength,whichmeantthegirderdepthsalonewerearound2.2m(7.25ftdeepandthecompositesectionwas2.44m(8ftdeep.ThecrossframeswereamixtureofinvertedKframesandplatediaphragmsatthebents.TheKframeswereinvertedsoastoplacethecatwalksbetweenthegirders,andthebraceswerechangedtoplatesectionsatthebentstohelphandlethelargeseismicforcesthataretransmittedfromthesuperstructuretothe“ham-merhead”bentcapsbothlongitudinallyandtransversely.Thebracingwasdesignedforbothlive-loadandseismic-loadconditions.Figure15.12showstheelevationofintermediatecrossframes.Thebracingwasheldtoaspacingoflessthan6.1m(20ft.TheBSDIprogramworksbyplacingunitloadsonadefinedgeometrypatternofthedeck.Thenaninfluencesurfaceisdevelopedsothatapplicationofloadsformaximumandminimumstressesbecomesasimplenumericalsolution.ThisprogramwasthoroughlycheckedutilizingtheV-LoadmethodandusinganSC-BridgepackagethatutilizesGTStrudl[11]forthemovingloadgenerator.GoodcorrelationwasseenbyallmethodswiththeexceptionoftheV-Load,whichconsistentlygavemoreconservativeresults.Asisfrequentlythecasewithcurvedgirders,theoutsidegirderendsupbeingdesignedheavierthantheremainingsections.Thisdifferencecanbeaslittleas15%,butasgreatat40%,dependingonlocation.Itshouldalsobeunderstoodthatbydesigningastiffergirderfortheoutside,thereisthetendencytoattractmoreloads,therebyrequiringmorematerial.Thisisasimilarphenomenontothatseeninseismicdesign.TheBSDIsystemallowsthedesignertocheckforconstructionloadsandsequencing.Thiswasabsolutelycriticalonaprojectlikethisasthegirdersectionswereoftencontrolledbythesequenceofconstructionloadapplication.Limitsonconcretepoursweresetaroundlimitingstressesonthegirders.Girderplatesizeswereoptimizedbothforthedesignandforthefabrication.Atypicalspanwouldhavefivedifferentsectionsinit.Thereweretwosectionsateitherendoverthebents.Thetopandbottomflangeswereverysimilaratpointofmaximumnegativemoment.Thenoneithersideatransitionsectionwouldbeutilizeduntiltheinflectionpoint.Finally,amaximumpositivesectionwherethereisusuallyasignificantdifferenceinthetopandbottomflangeswasdesigned.TheelevationoftheplategirderthatshowsthedifferentflangedimensionsisshowninFigure15.13.Thefivedifferentflangedimensionswerejustifiedbyconsideringthematerialcostsvs.theweldedsplicecosts.Inaddition,the“transition”sectionswereoftensizedsuchthatthetopflangewidthwasthesameasthenegativemomentsections.Thiswaytheplatescouldbeweldedendtoendandthenallfourgirderscouldbecutononebedwithoneoperation,savinghandlingcosts.Platesectionswerealsosetbasedonerectionandshippingcapabilities.Steelwasagoodchoiceofstructuretypeforthisprojectbecauseoftheseismicrisk,whichexistsinthislocation.Severalfaultspassinthevicinityofthisinterchange,andthestructurewouldbesubjectedto“near-fault”phenomenon.Thisstructurewasdesignedwithverticalacceleration.Theplategirderwithconcretedecksuperstructureweighsonethirdasmuchasthetraditionalcast-in-placeboxstructure.Someductilesteeldetailsweredevelopedforthisproject[12].Sincethegirdersrestonahammerheadbentcap,theloadtransfermechanismisthroughthebearingsandtheshearcanbeasmuchastheplasticshearofthecolumn.Tomakethisloadtransferpossible,platediaphragmsweredesignedatthebentcaps.Withtheplatesinplace,aconcretediaphragmcouldbepouredthatwouldnotonlyaddstiffness,butstrengthtohandletheselargeseismicforces.Thediaphragmswereapproximately0.91m(3ftwidebythedepthofthegirder.Theplateswerecoveredwithshearstudsandreinforcingwasplacedpriortotheconcrete.Inaddition,pipeshearkeyswereinstalledinthetopofthebentcaponeithersideofthediaphragm.Thisstructurewasredundantinthatifthedisplacementswereexcessive,thepipeswouldbeengaged.Elevationofintermediatecrossframes.©2000byCRCPressLLCElevationofinteriorandexteriorcurvedplategirder.©2000byCRCPressLLCThemostcommontypeofcurvedsteelboxgirderbridgesaretubgirdersthatconsistofindependenttopflangesandcast-in-placereinforcedconcretedecks.Thedesignguidelinesarecoveredinthe“RecommendedSpecificationsforSteelCurvedGirderBridges”[3].Normallythetubgirderiscomposedofabottomplateflange,twowebplates,andanindependenttopflangeattachedtoeachweb.Thetopflangesshouldbebracedtobecomecapableofresistingloadsuntilthegirderactsinacompositemanner.Thetubgirdersrequireinternalbracingbecauseofthedistortionoftheboxduetothebendingstresses.Finite-elementanalysis,whichaccountsforthedistortion,isnormallyutilizedtocalculatethestressesanddisplacementofthebox.Thewebsoftheboxgirdermaybeinclinedwitharatioofone-to-four,width-to-depth.TheAASHTOprovisionsforstraightboxgirdersapplyforcurvedboxesregardingtheshearcapacityofthewebandtheultimatecapacityofthetubgirders.Themaximumbendingstressesaredeterminedaccordingtothefactoredloadswiththeconsiderationsofcompositeandnoncompositeactions.Bendingstressesshouldbecheckedatcriticalsectionsduringerectionanddeckplacement.Thebendingstressesmaybeassumeduniformacrossthewidthofthebox.Priortocuringofconcrete,thetopflangesoftubgirdersaretobeassumedlaterallysupportedattopflangelateralbracing.Thelongitudinalwarpingstressesinthebottomflangearecomputedbasedonthestiffnessandspacingofinternalbracing.Itisrecommendedthatthewarpingstressesshouldnotexceed15%ofthemaximumbendingstresses.Asmentionedearlier,theM/Rmethodisusuallyusedtoanalyzecurvedboxgirderbridges.Thebasicconceptbehindthismethodistheconjugatebeamanalogy.Themethodloadsaconjugatesimplespanbeamwithadistributedloading,whichisequaltothemomentintherealsimpleorcontinuousspaninducedbytheappliedloaddividedbytheradiusofcurvatureofthegirder.Thereactionsofthesupportsareobtainedandthusthesheardiagramcanbeconstructedrepresentingtheinternaltorquediagramofthecurvedgirder.Aftertheconcentratedtorqueattheendsofthefloorbeamisknown,theendshearsarecomputedfromstatics.Theseshearsareappliedasverticalconcentratedloadsateachcrossframelocationtodeterminethemomentofthedevelopedgirder.ThisprocedureconstitutesaconvergenceprocesswherebytheM/Rvaluesareapplieduntilconver-genceisattained.CurrentcurvedbridgespecificationsintheUnitedStatesdonothaveanyguidelinesregardingcurvedconcretebox-girderbridges.Itisgenerallybelievedthattheconcretemonolithicboxgirdershavehightorsionalrigidity,whichsignificantlyreducestheeffectofcurvature.However,duringthelast15yearsaproblemhasoccurredwithsmall-radiushorizontallycurved,post-tensionedbox-girderbridges.Theproblemhasoccurredattwoknownsitesduringtheconstruction[16].Theproblemcanbesummarizedas,duringtheprestressingoftendonsinacurvedboxgirder,theybreakawayfromthewebtearingallthereinforcementinthewebalongtheprofileofthetendon.Immediateinspectionofthefailureindicatedthatthetendonsexertedradialhorizontalpressurealongthewalloftheoutermostweb.Inrecognitionofthisproblem,Caltranshaspreparedandimplementeddesignguidelinessincetheearly1980s[17].Chartsandreinforcementdetailsweredevelopedtocheckgirderwebsforcontainmentoftendonsandadequatestirrupreinforcementtoresistflexuralbending.Caltrans’Memo-to-Designers11-31specifiesthatdesignersofcurvedpost-tensionedbridgesshouldconsiderthelateralprestressforce,F,foreachgirder.ThisforceFisequaltothejackingforce,Pj,ofeachgirderdividedbythehorizontalradiusofthegirder.IftheratioofPj/R>100kN/mpergirderorthehorizontalradiusisequalto250morless,DetailA,asshowninFigure15.14shouldbeused.ChartsforNo.16andNo.19stirrupsweredevelopedtobeusedwiththeratioofPj/RinordertogetminimumwebthicknessandspacingbetweentheNo.16stirrups,asshowninFigure15.15.ThefirststepistoenterthechartwiththevalueofFontheverticalaxisofthechartandtravelhorizontallyuntiltheheightofthewebhcisreached.ThechartthenindicatestheminimumwebthicknessandthespacingoftheNo.16stirrups.Thesechartsweredevelopedassumingthatthegirderwebisabeamwithalengthequaltothecleardistancebetweentopandbottomslabs.Thelateralforce,F,isactingatthecenterpointofthewebcreatingabendingmomentintheweb.Thismomentiscalculatedbythesimplebeamformulareducedby20%forcontinuitybetweenthewebandslabs.ThevalueofthisbendingmomentisequaltoInthecommentaryofthismemo,Caltransconsideredthestirrupstobecapableofhandlingthebendingandshearstressesforthefollowingreasons:•MuiscalculatedforthemaximumconditionsofFactingathc/2.Thisoccursatonlytwopointsinaspanduetotendondrape.•Thejackingforce,Pj,isusedinthecalculationofMuand,atthetimePjisapplied,thestructureissupportedonfalsework.Whenthefalseworkisremovedandverticalshearforcesact,theprestressingforceswillbereducedbythelosses.Inaddition,forcurveboxgirderswithaninsideradiusofunder243.8m(800ft,intermediatediaphragmsarerequiredatamaximumspacingof24.4m(80ftunlessshownotherwisebytestsorstructuralanalysis.Thecodegoesfurthertosaythatiftheinsideradiusislessthan121.9m(400ft,thediaphragmspacingmustnotexceed12.2m(40ft.Caltransductdetailincurvedconcretebridges.Theauthorswouldlik