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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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