tied-arch bridges - steelconstruction
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steelTRANSCRIPT
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(ImagecourtesyofMabeyBridgeLtd.)
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TiedarchbridgesFromSteelconstruction.info
Masonryarchbridges,whichhaveaverylonghistory,andmorerecentlandmarkbridges,suchasSydneyHarbourBridgeinAustraliaandtheTyneBridgeinEngland,areallthrustarchesandrelyonhorizontalrestraintfromthefoundations.Inmanycases,suchexternalrestraintisnotfeasibleorpracticalbutitcanbereplacedbyatiebetweentheendsofthearch,thuscreatingatiedarch.Thisarticledescribesthefeaturesandbehaviouroftiedarchstructures.
Contents
1Howatiedarchworks1.1Overallstructuralbehaviour1.2Articulation
2Relatedstructuralforms3SpanRange4Aesthetics5Componentsandchoiceofmaterials6Globaldesign
6.1ArchShape6.2Influencelines
7Loading8Analysis9DetailDesign
9.1Arch/tieconnection9.2Hangers9.3Splices9.4Concretedeck9.5DurableDesignandMaintenance
10FabricationandErection10.1Precamber10.2Fabrication10.3Erection
11Casestudies12References13Resources14Seealso
Howatiedarchworks
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Reactionsforathrustarchbridge
Tiedarch
Thrustarchesrelyonhorizontalrestraintfromthefoundations,asshownright.Theverticalandhorizontalreactionsresolveintoaforcealongthearchmembersthehorizontalcomponentisofsignificantmagnitude.
Thiswillbethemostsatisfactorysolutionwhenthearchbearsontogoodfoundationmaterialsuchascompetentrock.Theendsofthearchesarenormallypinned.However,rockisnotalwaysavailableandsoathrustarchwillnotbethemosteconomicsolutionattheselocations,asthehorizontalreactionsleadtoheavyuneconomicfoundations.
Thetiedarchoffersasolutionwhenitcanbearrangedthatthedeckisatsuchalevelthatitcancarrythehorizontalforceasatiemember,asshownbelow.
Thetiedarchissometimesreferredtoasabowstringarch.
Bytakingthearchthrustthroughthetiemember,theprimaryrequirementforthesubstructurereducestoonlycarryingverticalloads.Itcanbeseenthatoneendwillstillrequirealongitudinalrestrainttocarrywind,
braking,accelerationandskiddingforces,andthattheotherendispermittedtomovelongitudinally.
Overallstructuralbehaviour
Lookingatthediagramabove,itcanbeseenthatatiedarchisreallyjustasimplysupportedbeam.Thearchisheldlongitudinallyatoneend,withtheotherendfreetoexpandorcontractundervaryingtemperatures.
Ifaloadisplacedonthedeck,itistransferredtothearchviathehangers,astheglobalstiffnessofthearchisgreaterthanthebendingstiffnessofthedeck.Thiscreatesthrustinthearch,whichisbalancedbytensioninthetiebeam.Thearchwilldeformdownwards,anditwilltrytospreaditsfeet,butthisislimitedbyhavingtostretchthetiebeam.Hencetherewillbeanoutwardmovementatthefreeend.
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Structuralbehaviouroftiedarch
Articulationforatiedarchbridge
Articulation
Thedeckisconventionallyarticulatedusingtheprinciplesmentionedabove.Anexampleisgiveninthefigurebelow.Inthiscasegloballongitudinalloadsonthebridgearesharedbetweenbothbearingsatthefixedend.
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Relatedstructuralforms
Mosttiedarchbridgeshaveverticalhangers,althoughinsomebridgesthehangersarearrangedtocrisscross.Inthiscase,aswiththetiedarchwithverticalhangers,thehangerscanonlyactintension,butthecrisscrossedhangerswilltransfersomeglobalshearalongthespan.Ifthehangersareincreasedinsize,andaretriangulated,thenthetiedarchbecomesabowstringtruss.Thereisfullsheartransferthroughthetriangulatedwebmembers.
Tiedarchwithcrosshangers Bowstringtruss
SpanRange
Asaroughguide,typicalspansfortiedarchescarryinghighwaysisintherange75mto250m.Forrailways,therangewouldbe50mto200m.Asalways,thereareexceptionstotheserules.
Aesthetics
Thetiedarchformisonethatisopentomanyinterpretations,andwithcarefulconceptualimaginationandattentiontodetailingcanproducestunningandbeautifulstructures.Tiedarchbridgescanbecreatedwithasinglearchmember,twoindependentarchesortwoarchesbracedtogether,Inthelattercase,amoregracefulbridgecanoftenbecreatedbyleaningthearchestowardseachotherandthishasthestructuraladvantageofreducingthespanoftheinterarchbracing.
SinglearchmemberBarquetta,Seville
IndependentarchesToomeBypass,NorthernIreland
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Bracedtiedarches
Withinclinedarchesforroadbridges,careneedstobetakentoensurethatthereissufficientheadroombetweenthecarriagewayandthearchandthismayleadtoaslightlywiderstructure.
InclinedarchesKoickBridge,Bratislava Crosssectionthroughtiedarchwithinclinedarchplanes
ThelimitsforclearancegaugearedefinedbythehighwayauthorityforhighwaybridgesthisisgiveninTD27/05[1].Additionally,wheretheclearanceislessthanagivenlimit,accidentalactionsduetovehicularcollisionmayneedtobeconsideredindesign,AccordingtotheNationalAnnextoBSEN199117[2],impactforcemustbeconsiderediftheclearanceislessthan5.7m.Above5.7m,noimpactforcesneedbeconsidered.
Notethathismeasurednormaltotheroadsurface.
However,giventhelackofredundancy,thedesignershouldalsoconsidertherobustnessofthedesignintheeventofa
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Comparisonofstiffenedandunstiffenedarchsections
vehicleimpact,butthisislikelytobeimportantforsmallerspanswherethearchribwillbeofsmallproportions.
Forlongerspans(orwherethearchesaretall)itmaybefeasiblefortheleanofthearchestobesuchthattheymergeintooneelement.
Componentsandchoiceofmaterials
Thearchisprimarilyacompressionmemberandsoaclosedboxsectionwillbethemostefficient.Thereisachoiceofwhetherthearchshouldbestiffenedlongitudinallyornot.Thebalancetobeconsideredisonebetweenthelossofefficiencywhenusingthinplates(b/t>24),andtheadditionalfabricationcostofstiffenedpanels.
Tominimisefutureinternalmaintenance,archesarefrequentlyfabricatedfromweatheringsteel,paintingtheexterior,butleavingtheinteriorunpainted.
Bracingbetweenthearchescantakeanumberofforms,andcanevenbeomittedinsmalltomediumspans.Tubesarecommonlyused,andaregenerallytoosmallformanaccess.Theycaneitherbesealed,orventedintothearchboxeswithprovisionfordrainage.Notethathotrolledhollowsectionsarenotavailableinweatheringsteel.
Formsofarchbracing
Xbraced Rigidlyconnectedcrossbeam Kbraced Unbracedarches
Thetieisprimarilyintension,andsocanbeavarietyofshapes.OftenanIsectionischosenasbeingmosteconomic,butthiscomplicatestheconnectionwiththebaseofthearch.Anormalcarbonsteelwouldusuallybeselectedforthetiebeam.
Tiebeams
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Isectiontiebeam Boxsectiontiebeam(forbridgewithinclinedhangerplanes)
Thereisawidechoiceforhangers.Thesimplestistheroundbar,suchastheMacalloysystem.Barsareavailableupto100mmdiameter.However,althoughtheyaremadefromaqualitysteel,thisisofamuchlowerstrengththanthecableoptions,andsohangersmustbeprovidedatclosercentres.Themostcompactchoiceistouseeitherrope,spiralstrandorlockedcoilstrand.Otherwisethereareanumberofproprietarysystemsthatareusedforcablestayedbridgesthatcanbereadilyadaptedforarches.
Thebridgedeckcanbeasteelorthotropicdeckorconcrete.Generallythesimplestmeansofsupportfortheseisaladderdeckwithcrossgirders.Themainissuewithconcreteistheproblemofitinteractingwiththetensiondevelopedinthetiebeams.Thisisdiscussedfurtherbelow.
Orthotropicsteeldeckforatiedarchbridge
Orthotropicsteeldeckforatiedarchbridge
Concretedeck(precastunitsonladderdeck,beforeinsituconcreting)
Globaldesign
ArchShape
Aparabolicarchisthebestshapeforstructuralefficiencybecause,underuniformloadthereshouldjustbeaxialforcesinthearchmembers.However,thepresenceofthetiebeamcontributesstiffnesstothesystemandthismeansmeansthattherearesomemoments,especiallyaroundthearchspringings.Acirculararchwillalwayshavegreaterbendingmomentsinthearchmembers.
Influencelines
Althoughthetiedarchisessentiallyjustasimplespan,theinfluencelinesofsomeoftheelementsareworthexamining.Itisobviousthatmaximumaxialforcesaregeneratedwhenthewholespanisloaded.However,maximumbendingwilloccurwithjustpartofthespanloaded.Atypicalinfluencelineforbendinginthearchisgivenbelowleft.Notethattherearebothpositiveandnegativeparts.Theinfluencelineforaverticalhangerusuallycomprisesasinglepositivepeakasshownbelowright.
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Influencelines
Influencelineforaxialforceinarchmember Influencelineforforceinahanger
Loading
Deadloadeffectswillnormallycomprisealargeproportionofthedesignstressesformainelements,anditbecomesveryimportanttoallowfullyfortheerectionmethod.Thisparticularlyappliestobendinginthearchforthetiebeam,thelockedinbendingmomentcanbecontrolledbyadjustingthehangerlengths.
Theapplicationoftrafficloadisstraightforward,buttherewillbeavarietyofloadedlengthsandpositionsoftandemaxlesandspecialvehiclesmustbechosentosuittheinfluencelines.
Windloadingonthearchisasignificanteffectandisusuallycriticalfordesignoftheinterarchbracing.Aerodynamicinstabilitiesareunlikelytobeaproblemduetotheinherentstiffnessandhighnaturalfrequencyofthearch.However,forlongerspansandwhenindoubt,windtunneltestsshouldbeconsidered.
Dependingonthetypeandnatureofbarriersbetweenthehighwayandhangers,itmaybenecessarytodesignthebridgefortheaccidentallossofahanger.Thecriterionistopreventprogressivecollapseofthewholespan.Thisisanaccidentaldesignsituationandthusisnormallyconsideredwithcharacteristicvaluesofpermanentandvariableloads.However,itwillbenecessarytoallowfortheroutinereplacementofhangers.Asthiswillbeaplannedaction,itisusuallypossibletoreducetrafficloadforthistransientdesignsituationthroughtrafficmanagement(e.g.noabnormalloads,contraflowonoppositecarriageway).
Analysis
Ingeneral,alinearelasticanalysisissufficientforallthedesign,withthepossibleexceptionoftheresistanceofthearchtolateralbuckling.Ifthearchesarefullybracedtogether,thentherulesforbucklingresistanceofmembersbetweenrestraintscanbeappliedisastraightforwardmanner.Ifalesscompletesystemisenvisaged,thenageometricnonlinearbucklingoreigenvalueanalysiswillberequiredtoestablishelasticcriticalbucklingvaluesandmodes.RulesfordeterminingslendernesstooutofplanebucklingaregiveninAnnexDofBSEN19932[3].
DetailDesign
Arch/tieconnection
Thisislikelytobethemostcomplexareaforfabrication,particularlyifthearchisinclined.Thearrangementofplatingis
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generallyintuitiveandconfirmedbysomelocalfiniteelementmodelling.Inadditiontodealingwithforceandmomenttransfer,carefulconsiderationmustbegiventohowthepiecescanbefabricated,soastoachieveanefficient,butcosteffectivesolution.
Hangers
DesignrulesfortensioncomponentsaregiveninBSEN1993111[4].Asaruleofthumb,itisconvenienttosizethecablesunderSLSloading,limitingtensilestressesto45%ofbreakingload.Proprietarysystemmanufacturerscanprovidedataonvariousformsofrope,strandandbar.
Underaccidentallossofahanger,adjacentremaininghangersarepermittedtoworkathigherstresslevels.Cableanchorages(socketsetc)andtheirfixingsareusuallysizedsuchthattheirstrengthexceedsthebreakingloadofthecable.Localsteelworkdetailsshouldbedesignedwithrobustnessinmind.
Fatigueloadingwillneedtobeconsideredusingdatafrommanufacturerstests.
Hangerscanbeeitherterminatedinsidethearchorbelowit.Thisisapreferencedecisionasthereareprosandconsforboth.Internalconnectionswillbeneatest,butrequiresinstallationandsubsequentinspectionandmaintenanceinsideaconfinedspace(assumingitislargeenoughtoenter).Externalconnectionswillrequirespecialistaccessequipmentsuchascherrypickers,useofwhichmayinvolveunacceptabledisruptiontotraffic.
Hangersmustbeadjustabletoallowforgeometricaltolerancesbetweenarchandtie,andforinitialstressingandsubsequentadjustment.Allowancemayneedtobemadeforspacetoaccommodate,andreactionsfrom,jackingequipment.
Hangerconnection(internal)
Hangerconnection(external)
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Splices
Splicesinthearchmayofcoursebemadebyeitherboltingorwelding.IntheUKboltingisfavouredforsitesplicesinnormalbridgework.However,weldingshouldalsobeconsideredonvisualgroundsforarchsplices.Forthetiebeam,weldingisefficientintermsofdesignasthereisnolossinsectionfromboltholes.
Boltedsplicesinarchmembers
Concretedeck
Intheadditiontotheusualrequirementsfordesigningaconcretedeck,itisalsonecessarytoconsiderthepotentialhightensileforces(andassociatedhightensilestrains)inthetiebeamandtheconcretedeck.Theissuesthatariseare:
HightensilestrainsleadingtocrackingofconcreteNeedforhighlevelofshearconnectionbetweensteelandconcreteUncertaintyofloadsharingoftieforcebetweentiebeamandconcrete/reinforcement
Someusefulguidanceonthissubjectisavailable[5].Theconstructionsequenceofthewholebridgeandespeciallytheconcretedeckneedscarefulconsiderationtoensurecompatibilitywithdesignassumptions.Aconcretedeckmayneedtobecastinlongitudinalstripstoavoidcriticalhalfspanloadingcases.Tominimisetheabovedifficultiesprecastconcretepanelsmaybeused,stitchingthemtogetheroncetheyhaveallbeeninstalled.Nevertheless,carefuldetailingwillberequiredtoproduceatroublefreedesign.
DurableDesignandMaintenance
Modernpaintsystemsareverydurableandcanhavealonglife.Withlargeareasofsteellocatedabovethedeck,thoughtmustbegivenastohowrainfallwillrunoffandwhereitmaycollect.Forexample,rainwillrundownhangersandmaycollectatsocketmouths.Evenifneoprenegaitersareprovidedtokeepwaterout,drainagepathsmustbeprovidedtopreventaccumulationofwater.
Theuseofweatheringsteelforboxelementsisausefulmeasure,withbenefitsforhealthandsafety,asnopaintingwillberequiredinternally.Ifboxelementsarelargeenoughtopermitaccess,thenmanholesmustbeprovided.Theseneedtobesizedtopermitevacuationofsomeoneonastretcherthoseusedforpotholingrescuearethemostcompact.
Accesswithinanarchcanbeproblematicduetotheconstantlychangingangle,internalstiffeners,andpossiblyhanger
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Typicalcornerweldsinaboxchord
terminations.Optionsavailableincludestepirons,grabrails,highfrictionwalkingsurfaceandfallarrestlines.
FabricationandErection
Precamber
Inanormalbeamandslabbridge,precamber(allowanceforpermanentdeformation)isappliedtothesteelbeamstoshapethemsuchthatwhenfulldeadloadisappliedtheirdeflectedshapeistheintendedprofile.Thisisachievedbycuttingthewebplateaccordinglytodealwiththesebendingeffects.
Thesituationislikelytobemorecomplicatedinatiedarch.Forexample,theelasticstretchofthetiebeamduringconstructionneedstobeaccountedforthiscanbeachievedbyfabricatingitshortbytheappropriateamount.Ina200mspanbridgethismayamounttosome125mm.However,asitispossiblethroughhangeradjustmenttominimisedeadloadmoments,itisnotnecessarytoapplyanyprecamberagainstdeadloadmoments.
Thearchmaypresentmanymorechallenges,whichwillbestronglyinfluencedbytheerectionprocedure.Ifsizeablelengthsareliftedandjoinedtoothersections,theirselfweightdeflectionmaybesignificant.The60mlongcentralsectionoftheUskBridgedeflectedabout250mmwhenitwasliftedandsupportedforsplicingbyitsends.Alsoitsendskickedoutbysome40mm.Otherpartsoftheerectionsequencewillcontributedeflectionstothewholearch,suchasinstallationofhangers,deckconcrete,finishesetc.Ifthearchisinclined,theninplaneandoutofplanecomponentswillneedtoberesolved.Finally,overalllengthcompatibilitymustbemaintainedtocorrespondwiththetiebeamextension.
Fabrication
Inmostcases,thedeckwillcompriseIsections,whichcanbereadilyfabricatedusingT&Imachines.Thetiebeamtoarchjointcanoftenbeacomplexfabricationwiththerequirementforlargebuttweldsifthickplatesarebeingused.Ifindoubtadviceshouldbesoughtfromafabricator.Itmaybenecessarytospecifyplatewithimprovedthroughthicknesspropertieswherelargecruciformweldsarerequired.
Anarchboxisusuallyasimplefabricationcomprisingfourplatesjoinedalongtheiredges.Asshearsaregenerallyquitelowinthearch,therequiredsizeoftheseweldsissmall.Itisnormaltohaveaninternalfilletweldplusanexternalpartpenetrationweld.
Tomaintainsquareness,thefabricatormaywishtoaddringframesattheendsofthefabricatedsections.Buttweldsmayberequiredtojoinarchandtiebeamunitstogether.Whenusedinthearchcarefuldesignandweldingsequencemayberequiredasthereisoftenhighrestraintleadingtothepossibilityofweldcracking.Again,advicemaybesoughtfromafabricator.
Erection
Erectionmethodologieswilldependonmanyfactorsincludingbridgesize,type,obstacletobecrossedandothersiteconditions.Issuestobeconsideredmayinclude:
Availabilityofsitearepossessionsrequiredforrail,roadornavigablewaterway?Availablecraneageandlocationofcranesforlifts.Thiswilldeterminetheweightandsizesofthepiecestobelifted.Doesthebridgehavetobebuiltinitsfinalposition,oradjacentandthenlifted,floated,orlaunchedintoposition?Availability/feasibilityoftemporarysupports.Asatiedarchisasinglespan,intermediatesupportswillberequiredifnotbuiltinonepiece.
Casestudies
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RiverUskCrossing
References
1. ^TD27/05Crosssectionsandheadroom,TheDesignManualforRoadsandBridges(DMRB).TheHighwaysAgency(http://www.dft.gov.uk/ha/standards/dmrb/vol6/section1/td2705.pdf)
2. ^NAtoBSEN199117:2006.UKNationalAnnextoEurocode1.Actionsonstructures.Accidentalactions.BSI3. ^BSEN19932:2006,Eurocode3.Designofsteelstructures.Steelbridges,BSI4. ^BSEN1993111:2006.Eurocode3.Designofsteelstructures.Designofstructureswithtensioncomponents.BSI5. ^Johnson,R.P.(2003)Analysesofacompositebowstringtrusswithtensionstiffening.Proceedingsofthe
InstitutionofCivilEngineers.BridgeEngineeringVol156,IssueBE2
Resources
Hendy,C.R.Iles,D.C.(2010)SteelBridgeGroup:GuidanceNotesonbestpracticeinsteelbridgeconstruction(5thIssue).(P185).SCI
GuidanceNote4.03,Allowanceforpermanentdeformations
Seealso
LadderdeckcompositebridgesMaterialselectionandproductspecificationWeatheringsteelShearconnectionincompositebridgebeamsFatiguedesignofbridgesBracingsystemsStiffenersConnectionsinbridgesBridgearticulationandbearingspecificationDesignforsteelbridgeconstructionCorrosionprotectionWelding
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