Temporal Nature of Fatigue Damage in Highway Bridges

AndrewT.Metzger,Ph.D.,P.E.1;andArthurA.HuckelbridgeJr.,D.Eng.,P.E.2

Abstract:Todevelopavalidmethodofestimatingfatiguelifeofahighwaybridge,itisfirstnecessarytohaveareasonableunder-standingofthemannerinwhichfatiguedamageoccursovertime.Thispaperpresentsthefindingsfromanextensivehighwaybridgemonitoringprogramfocusedonmonitoringvehicle-inducedstraincycles;thecauseoffatiguedamage.Thepurposeofthestudywastoidentifythetemporalcharacter͑ifany͒offatiguedamageaccumulation.Asampleof24bridgesintheStateofOhiowasmonitored;eachbridgeinthesamplefor1year.Thedatacollectedduringthestudycapturedhourly,daily,andmonthlyvariationinfatiguedamageaccumulation.Therawdatawereresolvedtoafatiguedamagemetricrepresentation.Thedamagemetricwasanalyzedwiththeintentofdeterminingthetemporalnatureoffatiguedamageaccumulation.Theanalysesledtothedevelopmentofpostulatesregardingfatiguedamageinhighwaybridges.Thepostulatesstatedinthisstudyshouldprovideasoundbasisfordevelopmentofafatigue-lifeestimationprocedureusingsite-specificstraincyclehistogramscollectedoveranabbreviatedtimewindow.DOI:10.1061/͑ASCE͒1084-0702͑2009͒14:6͑444͒

CEDatabasesubjectheadings:Fatigues;Damage;Bridges,Highway.

Downloaded from ascelibrary.org by Southeast University on 12/03/14. Copyright ASCE. For personal use only; all rights reserved.Introduction

Itisknownthatdetailscomprisingstructuralsteelelementsofhighwaybridgesaresusceptibletofatiguefailure.Forthisreasonconsiderationoffatigueisrequiredinthedesignandevaluationofsuchelements.Presentstandardsthataddressfatigueinhigh-waybridgesrelyonbroadassumptions—oftencharacterizingtrafficvolumes,vehicleweights,etc.,fromshort-terminforma-tion,thenapplyingthesevaluesasaconstantoverthedesignlifeofthestructure.

Inreality,onemayexpectthemechanismsthataffecttheoc-currenceoffatiguedamagetovarywithtime.Collectively,theoccurrenceofstraincyclesthatcontributetofatiguedamagewillbereferredtoasthestraincycleprocess,orSCP,inthispaper.UnderstandingthenatureoftheSCPwillprovideinsightintotheaccumulationoffatiguedamageandperhapsfacilitateamoreaccurate,empiricallybased,fatigue-lifeestimationprocedure.ThepurposeofthisstudyistocollectanadequatesampleoftheSCPtoprovideinsightintothetemporalnatureoffatiguedamageaccumulation.Thiswasaccomplishedbylong-termmonitoringofin-servicehighwaybridges.Thedatawereana-lyzedtorevealtemporaltrends,ifany.Postulatesregardingtheoccurrenceoffatiguedamageinhighwaybridgesweredevelopedandarepresented.

BackgroundandPreviousWork

Twogeneralfatigueconditionsareaddressedinbridgedesign.Load-inducedfatiguemayoccurwhenliveloadsproduceanettensilestressinamember.Distortion-inducedfatiguecanoccurwhencross-girderconnectingelementscausegirderwebstode-flect͑ordistort͒outofplane͑BarkerandPuckett1997͒.Thisstudyfocusesonload-inducedfatigue;althoughdistortion-inducedfatiguecouldbeaddressedbyalteringthemethodofstrainmeasurement.

ThegeneralapproachforaddressingfatigueinbridgedesignintheUnitedStatesistoinvokeafatiguelimitstateinwhichadesigntruckisassumedtopassoverthebridgeanumberoftimes͑alsoassumed͒͑AASHTO2007͒.TheAASHTOloadandresis-tancefactorrating͑LRFR͒istheauthoritativedocumentforevaluatingexistinghighwaybridges͑AASHTO2003͒.Chapter7ofthatdocumentisdedicatedtofatigueevaluationofexistingsteelbridgesandisbasedontheAASHTOpublication:GuideSpecificationsforFatigueEvaluationofExistingSteelBridges͑AASHTO1990͒.FatigueevaluationofexistingsteelbridgesisbasedextensivelyonAppendixAofNationalCooperativeHigh-wayResearchProgram(NCHRP),Report299.͑Mosesetal.1987͒.Provisionsinthisdocumentallowforresidualfatiguelifetobeevaluatedusingweigh-in-motion͑WIM͒data,weighstationrecords,anassumedfatiguetruck,ordirectmeasurementsofstrain.Thegeneralphilosophyinallfouroptionsistodefineanequivalentconstantparameter͑constanttruckweightinthefirstthreeoptionsorconstantamplitudestressrangewhenusingdirectmeasurements͒basedonavailabledata;occurringoverthelifeofthebridge.TheLRFRdoesnotfurnishcriteria͑timeframeandduration͒regardinghowinformationiscollectedforthispurpose.Inthecontextofbridgeengineering,areasonabledefinitionforfatiguelifeisgivenbyYenetal.͑1990͒:

“…thelengthoftimebeforeaninitiallymicroscopicflawinacriticalstructuralelementdetaildevelopsintoacrackofcertainlength(typicallyaboutaninchorthethicknessofthematerial)andbecomesdetectablebynor-

AssistantProfessor,Dept.ofCivilandEnvironmentalEngineering,CollegeofEngineeringandMines,Univ.ofAlaskaFairbanks,Fairbanks,AK99775͑correspondingauthor͒.E-mail:atmetzger@alaska.edu2

Professor,Dept.ofCivilEngineering,CaseSchoolofEngineering,CaseWesternReserveUniv.,Cleveland,OH44106.

Note.ThismanuscriptwassubmittedonAugust22,2007;approvedonApril21,2009;publishedonlineonOctober15,2009.DiscussionperiodopenuntilApril1,2010;separatediscussionsmustbesubmittedforindividualpapers.ThispaperispartoftheJournalofBridgeEngi-neering,Vol.14,No.6,November1,2009.©ASCE,ISSN1084-0702/2009/6-444–451/$25.00.

1

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malnon-destructiveinspectiontechniques(mostcom-monlyvisualobservation)”

Anumberofstudiesregardingtheestimationofremainingfatiguelifehavebeenconductedreliantupondevelopingaloadspectrumbasedonshort-termWIMmeasurements.Tonameafew,͑Khazemetal.2006;SivakumarandChang2006;ChotickaiandBowman2006;Davisetal.2006͒,thesestudiesdevelopedloadspectrumsbymonitoringonetoninebridgesfordurationsof1weekto2years.Intheseworks,afatiguetruckandpassagefrequencyweredeterminedbasedontheWIMdataandprovi-sionsoftheLRFR.

Huckelbridgeetal.͑2002͒proposedamethodologyforimple-mentingfieldstrainmeasurementsforfatigue-lifetimeevaluationofbridges.Thismethodologyutilizesstrainmeasuringequipmenttocollectstraincyclehistogramsfromdetailsonabridgeusingarainflowcyclecountingalgorithm.Thevariablestrainsofthehis-togramareresolvedtoanequivalentconstantamplitudestressrange.Theconstantamplitudestressrangerepresentsaleveloffatiguedamageequivalenttothevariablestrainhistogramoverthesamenumberoftotalcycles.TheconstantamplitudestressrangealongwiththePalmgren-MinerruleandtheAASHTOS-Ncurvesarethenusedtoestimatethenumberofcyclesthatcanbetoleratedduringtheservicelifeofabridge͑Huckelbridgeetal.2002͒.Acriticaldeficiencypointedoutinthisinvestigationwastheabsenceofanappropriatedatabasewhichcouldbeutilizedtoextrapolateashort-term“snapshot”ofthefatigueenvironmentofaparticulardetailtoaresidualfatigue-lifeestimate.

Ofthemanypreviousstudiesrelatedtofatigueinbridgesandestimatingfatiguelifeinbridges,theredoesnotappeartobeasignificantamountofstudyrelatedtothetemporalmannerinwhichfatiguedamageaccumulates.Knowledgeofthetemporalnatureoffatiguedamageisnecessaryforthedevelopmentofafatigue-lifeestimationprocedurebasedonshort-termsite-specificmonitoring—likethatproposedinthepreviousreference.ContributionofThisStudy

Thepurposeofthisstudyistoprovidesubstantialinsightintotheaccumulationoffatiguedamageinhighwaybridges—downtoanhour-by-hourbasis.Theresultsofsuchaneffortwillexpandtheknowledgebaseregardingfatigueinhighwaybridgesaswellasprovideabasisforthedevelopmentofamethodoffatigue-lifeestimationbasedonshort-term͑substantiallylessthanayear͒monitoringofastructureunderscrutiny.

Table1.OhioDOTHighwayFunctionalClassesOhioFC126711121416

Description

Principalarterial—interstate͑rural͒Principalarterial—other͑rural͒

Minorarterial͑rural͒Majorcollector͑rural͒

Principalarterial—interstate͑urban͒

Principalarterial—otherfreeway/expressway͑urban͒

Principalarterial—other͑urban͒

Minorarterial͑urban͒

Downloaded from ascelibrary.org by Southeast University on 12/03/14. Copyright ASCE. For personal use only; all rights reserved.accessibility,structuraltypeandcondition,highwayfunctionalclassification͑threebridgesforeachfunctionalclassinthestudy͒,andproximitytothestudylocation͑Cuyahoga,Medina,Rich-land,andSummitcounties͒.IndividualbridgesusedinthisstudyarelistedinTable2.Carewastakentoselectbridgesoflike-functionalclassthatweredissociatedtothemostpracticaldegree;soastodecreasethelikelihoodofmonitoringthesametrafficatmorethanonelocation.Instrumentation

Commercial“clamp-on”straintransducersmanufacturedbyZ&MEnterpriseswereusedtomeasuredynamicstraincyclesforthisproject.Theparticulartransducermodelutilizedwasdevel-opedforearlygenerationWIMtechnologyandisknowntocol-lectdataappropriateforthisproject.Thiswasverifiedinapreviousstudy͑Huckelbridgeetal.2002͒.

Table2.SubjectBridgeListFunctionalclass111222666777111111121212141414161616

RoadwayservedbybridgeI71I76I80SR18SR224US30SR3SR39SR83SR303SR42SR603I271I480I77SR176SR422SR8SR14SR82SR87SR17SR21TurneyRoad

ODOTdistrict33433333343312121212124121212121212

Location

I71overGridderRoadI76overRyanRoadI80overI271SR18overCSXTRRSR224overE.ForkCr.US30overKoogleRoad

SR3overI71SR39overCSXTRRSR83overSR224SR303overI271SR42overSR224SR603overCSXTRRI271overSolonRoadI480overLeeRoadl77overHillsideRoadSR176overValleyRoadSR422overMilesRoad

SR8overI80SRl4overI49OSR82overI71SR87overI271SR17overCSXRRSR21overCSXRRTurneyRoadoverI480

CountyRichlandMedinaSummitMedinaMedinaRichlandMedinaRichlandMedinaSummitMedinaRichlandCuyahogaCuyahogaCuyahogaCuyahogaCuyahogaSummitCuyahogaCuyahogaCuyahogaCuyahogaCuyahogaCuyahoga

MonitoringProgramBridgeSample

Priortodatacollection,itwasnecessarytoidentifysubjectbridgestobemonitored.Preliminarycalculationsbasedonpub-lishedtruckcounts͑ODOT-OTS2007͒indicatedthatthetrafficvolumesformostroadwaysclassifiedaslocalorcollectorarenotaslikelytoproducefatigueconcernsasthearterialroadways.Forthisreason,subjectbridgeswereconfinedtotheOhioDOThigh-wayfunctionalclassesshowninTable1.

Samplesizeandbridgelocationwerelimitedbyavailablere-sources.Also,trafficcontrolsandliftequipmentwerenotavail-ableforthecollectionperiod.Foreachyearofthe2-yearstudy,12bridgesweremonitoredforafullweek͑168h͒ineachmonthofacalendaryear.Bridgeswereselectedforthestudybasedupon

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Downloaded from ascelibrary.org by Southeast University on 12/03/14. Copyright ASCE. For personal use only; all rights reserved.Fig.1.Deployeddataloggerandclamp-onstraintransducer͑note:leftphotoshowsinstrumentationasdatawerebeingdownloaded;whendeployed,thedataloggerboxisclosedandlocked͒

Theoverallmeasurablestrainrangearbitrarilychosenfortheprojectwas400␮␧.Noindicationofstrainsbeyondthisrangewasobservedduringthe2-yearstudy.Thefullstressrangecon-sideredisdividedintosubintervalsorbinsof10␮␧inwidth͑0–10␮␧,10–20␮␧,...,390–400␮␧͒.Thefirstbin͑0–10␮␧͒isdisregardedaselectronic“noise”inherenttothedataloggerandofnointerestwithrespecttofatiguedamage.

Strainwasmeasuredatarateof50Hzandcategorizedintobincountsbyrainflowcounting.Bincountswererecordedeachhour.Table3isanexampleofbincountdata.

Dataloggersweredeployedtoruncontinuouslyfor1weekandthenredeployedtoanothersubjectbridge.Thisprocesswascon-ductedonamonthlycycleandeachofthethreedataloggerswasrotatedbetweenfourbridgesinthisway.Theassumptionismadethataweekofdatacollectedinaparticularmonthisindicativeofalldayswithinthatmonth.Thisprocedureallowsonedataloggertocollectmonthlydatafromfourbridgespermonth—thusallow-ingforalargersample.Monthlydataarerepresentedasallthedatacollectedduringanentireweekwithinaparticularmonth—168h/setsofbincounts.Ayearsampleconsistsof168hofbincounts͑1week͒foreachmonthoftheyear—atotalof2,016hperbridgemonitored.

ThefirstyearofmonitoringcommencedinDecemberof2004andconcludedinFebruaryof2006.ThesecondyearcommencedinAprilof2006andconcludedinAprilof2007.

LostData

DatawereusuallycollectedonFridays.Onetothreehoursofdatawasnotmonitoredeachweekduetoscheduling͑pickupthroughredeployment͒.ThemethodforfillinginthedatagapwastocopythecorrespondingbincountsfromThursdaytoFriday.

Onoccasions,aweekofdatawaslostduetopowersupplyfailure.Theresultinggapswerereconciledbyaveragingthebincountsfromtheadjacentmonths.Itwasnecessarytodothisonsevenoccasionsoutof288datacollectedweeks.Thisdidnotoccurmorethantwiceonanyonebridge.

ThestraintransducersweredrivenbyCampbellScientific͑Logan,Utah͒CR5000digitaldataloggers.Dataloggerswerepoweredby12Vmarinebatteries,whichwereswitchedoutweeklyasdataloggerswerecycledbetweenbridges.Fig.1showsdeployedinstrumentation.

TransducerLocations

Inselectingtransducerlocations,thefollowingconcernshadtobeaddressed:

•Safeaccessfromtheroadwayshoulderthroughouttheyear;•Accesscouldnotrequiretrafficcontrols;

•Gagelocationshadtobeaccessiblebyladder;

•Monitoringsiteshadtobelocatedatapositiononthegirderwithasignificantresponsetovehicularloads;and

•Relativeconsistencyingagelocationthroughoutsample.Basedontheaboveconcerns,gaugesweregenerallylocatedatpiersadjacenttoanabutment.Twotransducerswereinstalledduringeachdeployment.Thegirdersselectedformonitoringwereclosesttotheoutboardslow-lanewheellineandthenextinteriorgirder.Withtwotransducersdeployedinthisway,itwaspossibletocrossreferencethereadingsfromeach.Theintegrityofthedatacollectionsystemcouldbe͑andwas͒verifiedbycomparingtheresultsofthetwogauges.

Transducerlocationsweremarkedduringtheinitialdeploy-mentandreturnedtothesamelocationthereafter.Dataloggerswerededicatedtospecificbridges.

DataCollection

TodevelopanunderstandingoftheSCP,itwasnecessarytocollectdatathatadequatelycharacterizeditstemporalcharacter-istics.Themonitoringschemeusedinthisstudyrecordedvaria-tionsintheSCPbyhourofday,dayofweek,andmonthofyear.Resourceswerenotavailableforaddressingyear-to-yearvaria-tions.

AnalysisDataProcessing

Eachweek,therainflow͑bincount͒dataweredownloadedfromthedataloggeronsite.Afterreturningtothelaboratory,thedatawerereviewedforirregularities.Whennecessary,gapswererec-onciledasdescribedabove.Toaidinthegoalsoftheproject,thebincountdatawereresolvedintofatiguedamagemetrics.Thefatiguedamagemetricrepresentsameasureoffatiguedamageforagiventimeframe.

Forthisinvestigationthefatiguedamagemetricforagivenstressmagnituderangewasdefinedas

D=nS3R

͑1͒

wheren=numberofstresscyclesatstressrangeSRandSR=stress

rangemagnitudecorrespondington͓SeeAppendixIforthemo-tivationbehindEq.͑1͔͒.SRwascalculatedbymultiplyingthemidwidthvalueofabinbythemodulusofelasticityforsteel;takentobe29,000ksi.ThenumberofcountswithinaparticularbinwasthenmultipliedbythecubeofSR.Thisresultsinadam-agemetricvalueforeachbinofeachhourofdata.Summationofthebinvaluesresultsinanhourlydamagemetricvalue.Thehourlydamagemetricrepresentstheamountoffatiguedamagethatoccurredinaparticularhourofmonitoring.Table4shows

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Table3.ExampleofBinCountData͑NotAllBinRangesAreShown͒

177MondayMarch21,2005

0–1010–2020–3030–4040–5050–6060–7070–8080–9090–100100–110110–120120–130130–140140–150150–160160–170170–180180–190190–200200–210210–220220–230230–240240–250250–260͑hourof

day͒␮in./in.␮in./in.␮in./in.␮in./in.␮in./in.␮in./in.␮in./in.␮in./in.␮in./in.␮in./in.␮in./in.␮in./in.␮in./in.␮in./in.␮in./in.␮in./in.␮in./in.␮in./in.␮in./in.␮in./in.␮in./in.␮in./in.␮in./in.␮in./in.␮in./in.␮in./in.

all rights reserved.1:002:003:004:005:0000000220153223276419363126495093517853181163511170245535403034221121020234403333112001041000000001011000000000000000000000000000000000000000000000000JOURNALOFBRIDGEENGINEERING©ASCE/NOVEMBER/DECEMBER2009/4476:000795842310136114174401000000000007:0001,85420343264022777491541000100000008:0001,88022945272720126568510000000000009:0002,2353138239573619467910520000000000010:0002,046292763347281512451711430000000000011:0001,8692298136542999621510321000000000012:0001,8472578244422813296139210010000000013:0001,760244693750191473679630000000000014:00

01,852229803062241177278411000000000015:0001,595221622432141281368401000100000016:0001,563191652534131492473301000000000017:0001,26517249262115944424210000000000018:0001,36417143222210976343210000000000019:0001,0371104171914454046200000000000020:00086111020121910441336300000000000021:000672732512109323434010000000000022:0005534811584333227000100000000023:000392471967431020430000000000000:00

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J. Bridge Eng. 2009.14:444-451.

Downloaded from ascelibrary.org by Southeast University on 12/03/14. Copyright ASCE. For personal use only; Table4.HourlyDamageMetricsCorrespondingtoTable3Data177MondayMarch21,2006͑hourofday͒1:002:003:004:005:006:007:008:00

177MondayMarch21,2006͑hourofday͒9:0010:0011:0012:0013:0014:0015:0016:00

177MondayMarch21,2006͑hourofday͒17:0018:0019:0020:0021:0022:0023:000:00

Hourlydamagemetric5863944418285341,0422,5961,675

Hourlydamagemetric2,7852,9872,6812,5492,4752,2692,0221,657

Hourlydamagemetric1,2731,3211,1101,088849858611653

Downloaded from ascelibrary.org by Southeast University on 12/03/14. Copyright ASCE. For personal use only; all rights reserved.thehourlydamagemetricsforthedatainTable3.

Fig.2isanexampleofthedamagemetricsfromayearofmonitoring.Thereisconsistencyamongall24hourlydamagemetricplots,representingdatafromallthebridgesstudied,withregardtothegeneraltemporalstructure—alloftheplotshavethesamegeneralformasFig.2.PlotsforallbridgesmonitoredmaybefoundinMetzgerandHuckelbridge͑2006͒.DirectObservation

DamageMetricPlots

Inspectionofall24hourlydamagemetricplots͑likeFig.2͒revealedsomegeneralcharacteristicsregardingtheoccurrenceoffatiguedamage.Fromtheplotsitisapparentthatthemagnitudeofthehourlydamagemetrichasaweeklycycle.Withintheweeklycyclearesevendistinctdailycycles.Eachweekbeginswithfivedistinctdays͑MondaythroughFriday͒thathavesimilarcharacteristics.Theseweekdaysarefollowedbyweekenddays͑SaturdayandSunday͒withtheirowndailyforms.Thisaspectisconsistentthroughoutthesample.Whilethepatternismostcon-spicuousinfunctionalclassesthatprovidethehighestlevelofservice͑principlearterials͒,itexistsinalloftheplots.

Fig.3.ComparisonbetweenweekdaytemporalfractionsandODOTtruck-countdata

Anumberofexamplesofdamageaccumulationonholidayswereobservedinthesample.HolidaydamagecharacteristicscanbeseeninFig.2;theMondaysinSeptemberandDecembercorrespondtonationalholidays.

ComparisonwithTruckCounts

Forthepurposeofcomparison,ODOTtruck-countdata͑ODOT-OTS2007͒hasbeenplottedwiththeaveragetemporalfractions͑atfs͒ofthehourlydamagemetrics.Theatfisthefractionofthetotaldailyvalue͑ofthedamagemetricorofthetruckcount͒thatoccurs,onaverage,ineachhouroftheday.Fig.3showstheplots.Itisapparentfromtheplotsthatthetruckcountandthedamagemetrichourlyfractionsaresimilarforruralfunctionalclasses.Forurbanfunctionalclasses,thedifferencebetweenthevaluestendstoincreaseinthemid-dayhours.However,theredoesappeartobeagreementingeneralformoftheplotsinallcases.

“Truck”referstovehiclesdesignatedas“B&CCOM’L”bytheOhioDOT.B&CCOM’LcorrespondstoFHWA“SchemeF,”Classes4through13͑ODOT-OTS2007͒.Thecountinforma-tiondoesnotdistinguishtrucktypes.Vehiclecountsareobtainedbybothmanualandautomaticmeans.

HourlyFractionComparisonbetweenFunctionalClassesHour-of-dayfractionsforeachbridgemonitoredwerecalculatedinamannersimilartothediscussionaboveandrepresentthefractionofthetotaldailydamagethatoccurs,onaverage,foraparticularweekdayhourofday.ThesecomparisonsareshowninFig.4.

Fig.2.Fatiguedamagemetricplot

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Downloaded from ascelibrary.org by Southeast University on 12/03/14. Copyright ASCE. For personal use only; all rights reserved.Fig.4.Averagehour-of-dayfractionsforweekdays;comparisonbe-tweenindividualbridgesandFCs

Fig.6.Month-of-yearfractions;comparisonbetweenindividualbridgesandFCs

Day-of-weekfractionswerecalculatedinasimilarmanner:thatis,thefractionofthetotalweeklydamagethatoccurs,onaverage,duringaparticulardayoftheweek.ThesecomparisonsareshowninFig.5.

Asimilarcalculationwasusedtocalculatethemonth-of-yearfractionrepresentingthefractionofthetotalyearlydamagethatoccurredinaparticularmonthoftheyear.ThesecomparisonsareshowninFig.6.Fig.6plotsindicatethatthereisrelativelylittlemonthly/seasonalvariationinthehigherfunctioningroadways.Fromthosefiguresitcanbeseenthatthetemporalfractionsgenerallyagreebetweenbridgesofagivenfunctionalclass͑FC͒.Furthermore,thereisagreementbetweencertainFCs.DamageMetricSpectra

Thefrequencyspectraofthehourlydamagemetricvalueswerecalculatedinanefforttogainadditionalinsightintothetemporalnatureoffatiguedamageinhighwaybridges.ThespectrawerecalculatedusingMathematica.Priortocalculation,samplesetswereexpandedtoayearbyappendingeachsampleweektoitselfmultipletimes—resultingin48weeklysets͑8,064hourlydamagemetricvalues͒:thefirstfourweekscomprisingJanuary,thesecondfourweekscomprisingFebruary,etc.

WithaNyquistfrequencyof1h,themaximumperceptiblefrequencyinthespectrumis4,032cycles/year—oratime-domainwaveformwithaperiodof2h.Themagnitudesofthe͑complex͒discreteFouriertransform͑DFT͒resultsforallsampleswerenormalized,plotted,examined,andcompared.AtypicalspectrumoftheDFTisshowninFig.7.Thetwodominantfrequenciesseeninallofthesamplesetsoccurredatvaluesof48and336ontheabscissa.Statedanotherway,thetwomostpromi-nenttime-domainwaveformsoccur48and336timesinasampleset͑i.e.,inayear͒.Consideringthatthereare8,064valuesintheset,thetwofundamentalperiodsareat168and24hrespectively—168hcorrespondingtoacalendarweekand24hcorrespondingtoacalendarday.

Asequenceofincidental“peaks”isalsopresentinthespectrum—someofwhichcanbeseeninPlotb.Thesepeaksoccuratmultiplesof48alongtheabscissa.Thisisequivalenttothepeaknumber͑countingfromtheorigin͒indicatingthenumberoftimesthewaveformoccursinaweek.

ExaminationofPlotcinFig.7indicatesthatthereisnegli-giblefrequencycontentatvalueslessthan48.Thisimpliesthattherearenoappreciablewaveformswithaperiodgreaterthan168h—48cycles/year.ThisstatementissupportedbyinspectionofFig.6.

Fig.5.Averageday-of-weekfractions;comparisonbetweenindi-vidualbridgesandFCs

Fig.7.Typicaldamagemetricfrequencyspectrum

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Monitoringforeachbridgeoccurredat4-weekintervals.Pre-sumably,anymonthlyvariationshouldhavemanifestedintheweeklysetsofdata.Verylittle,ifany,monthlyvariationwasobserved.Theresultsdescribedabovewereconsistentthroughoutthesample.Summary

Theanalysesperformedonthedamagemetricrepresentationofthebincountsindicategeneralcharacteristicswithrespecttotheoccurrenceoffatiguedamageinhighwaybridges.Comparisontopublishedtruckcountsprovidesadegreeofvalidationtothedam-agemetricconceptusedinthisstudy.Basedontheanalysesinthissection,thefollowingpostulatesareproposed:

Postulate1.Thereisageneraltemporalstructuretotheoc-currenceoffatiguedamageinhighwaybridges.

Postulate2.Temporalcharacteristicsoffatiguedamageareconsistentbetweenbridgesofagivenfunctionalclass;withcon-sistencyalsoamongcertainfunctionalclasses.

Postulate3.Aweeklyfatiguedamagemetric“signal”forahighwaybridgeiscomposedoftwoprominenttime-domainwave-forms,withperiodsof168and24h;correspondingtocalendarweeksanddays,respectively.

“snapshot”ofasite-specificSCPislikelyfeasible.Suchamethodwouldprovideameansforrapidandjudiciousassessmentofabridgeinventory;providinginsightintothefatiguehealthofabridgeinventory.Developmentofsuchamethodshouldbepur-suedand,inreality,maybeconsideredanevolutionoftheAASHTOLRFR͑AASHTO2003͒Chapter7provisionsformea-suredstrains.

Acknowledgments

ThewritersthanktheOhioDepartmentofTransportationforfundingtheprojectthroughthePartneredResearchExplorationProgram.TheCivilEngineeringDepartmentatCaseWesternRe-serveUniversityhassupportedtheeffortsoftheprojectinvariousways;inparticulartheSaadaFamilyFellowshiphassupportedamajorpartofthisresearchandweacknowledgedthisfactwithadeepsenseofgratitude.AppreciationisalsoextendedtoRichlandEngineering,Ltd.fortheiractiveparticipationinthecollectionofdatainRichlandCounty.

Downloaded from ascelibrary.org by Southeast University on 12/03/14. Copyright ASCE. For personal use only; all rights reserved.Results

Anextensive,andtotheknowledgeofthewriters,unprecedentedinscope,highwaybridgemonitoringprogramhasbeencom-pleted.TheprogrammonitoredtheSCPforasampleofin-servicebridgesfromvarioushighwayfunctionalclassesthroughoutayear.TherawdatafromthemonitoringprogramwereanalyzedtoprovideinsightintothetemporalnatureoftheSCP.

Datacollectedduringthelong-termmonitoringprogramwereresolvedtoafatiguedamagemetricrepresentationthatisconsis-tentwithcurrentstandardsofpractice.Thedamagemetricswereanalyzedbydirectobservationofplots,spectralcontent,andcomparisonwithpublishedtruck-countdata.ThetemporalnatureoftheSCPwasstudiedwithatfscalculatedfromthedamagemetricdata.Theresultoftheseanalysesisausefuldegreeofunderstandingregardingtheaccumulationoffatiguedamageinthehighwaybridgesmonitored.Postulatesbasedontheresultsoftheanalyseshavebeenproposed.Thefindingsinthisstudymaybeusedtodevelopamethodofestimatingresidualfatiguelife.

AppendixI.MotivationforDefiningtheDamageMetric,D,UsingEq.„1…

RearrangingEq.͑6.6.1.2.5-1͒ofAASHTO͑2007͒andsubstitut-ingthenotationofSRfor͑⌬F͒nresultsinthefollowing:

N=

ͩͪAS3R

͑2͒

whereA=thefatiguecategoryconstantfoundin͑AASHTO2007͒

andN=presumably,thetolerablenumberofcyclesatstressrangeSRforaparticulardetailcategory,“A.”Eq.͑2͒representstheAASHTOS-Nrelationshipwrittenintermsofthe͑presumed͒allowablenumberofstresscyclesatstressamplitude,SR.

Palmgren-MinerRule

Considerasituationwhereasequenceofloadsthatvaryinmag-nitudeisappliedtoamaterialwithadefinedstress-amplitudeversusnumberofcyclestofailure,orS-N,relation.BasedontheS-Nrelationship,aparticularmagnitudeofstresshasacorre-spondingnumberofloadcyclesthatthematerialmaytoleratepriortofracture.Thatnumberofcyclesrepresentsthefatiguelifeforaparticularstressrange.Thenumberofcyclesincurred,n,dividedbythenumberofcyclesinthefatiguelife,N,representsthefatigue-lifefraction,n/N͑Dowling2007͒.

Foragivensequenceofstresscyclesthatvaryinamplitude,afatigue-lifefractionwillbegeneratedforeveryamplitudevalue.ThePalmgren-Minerrulestatesthatfatiguelifehasendedwhenthefatigue-lifefractionssumtounity

Conclusions

Byexaminationofempiricaldata,thisprojecthasdemonstratedthattheoccurrenceoffatiguedamageinhighwaybridgescanhaveageneraltemporalstructure;andlikelydoesinthemajorityofcases.Thetemporalstructurecanbedecomposedintohour-of-dayvariationandvariationincalendardaysandmonths.InthisstudythetemporalnatureisfairlyconsistentbyfunctionalclassandcertaingroupsofFCsexhibitconsistency.ItislikelythatthetemporalcharacteristicsoftheSCPcanbeexploitedtodevelopamethodofestimatingyearlyfatiguedamagefromashort-termsample.

͚i=1

m

ni

=1Ni

͑3͒

Recommendations

Basedontheresultsofthisstudy,amethodoffatigue-lifeextrapolationfromashort-term͑ontheorderofhoursordays͒

whereni=numberofcyclesincurredatstressmagnitude;i;Ni=numberofcyclesrepresentingthefatiguelifeatstressampli-tude,i;andm=numberofdifferentstressamplitudes.SeeDowl-ing͑2007͒foradditionaldiscussionofthePalmgren-Minerrule.SubstitutingEq.͑2͒intoEq.͑3͒resultsin

450/JOURNALOFBRIDGEENGINEERING©ASCE/NOVEMBER/DECEMBER2009

J. Bridge Eng. 2009.14:444-451.

͚i=1

m

m

ͫͬni

AS3R

=1

i

͑4͒

NotingthatAisaconstantintheaboveexpressionyields

niS3͚Ri=Ai=1

͑5͒

Downloaded from ascelibrary.org by Southeast University on 12/03/14. Copyright ASCE. For personal use only; all rights reserved.Thisistosaythatfatiguelife͑presumably͒endswhenthecumu-lativedamagemetric,asdefinedinEq.͑1͒,foradetailequatestothecorrespondingAASHTOfatiguedetailconstant.

Thefatiguedamageresultingfrominumberofdifferentstressamplitudesoccurringoversometimeframe,t,mayberepresentedwiththesummationinEq.͑5͒

Dt=

niS3͚Rii

͑6͒

Foraparticular“bin”ofdatacollectedduringthisstudy,repre-sentingaparticularstrain͑andcorrespondingstress͒amplitude,thefatiguedamagemayberepresentedbyEq.͑1͒.Eq.͑5͒maybeusedforestimatingresidualfatiguelifeandisthemotivationbehindEq.͑1͒.

References

AASHTO.͑1990͒.Guidespecificationsforfatigueevaluationofexistingsteelbridges,AmericanAssociationofStateHighwayandTranspor-tationOfficials,Washington,D.C.

AASHTO.͑2003͒.Guidemanualforconditionevaluationandloadandresistancefactorrating(LRFR)ofhighwaybridges(with2005interimrevisions),AmericanAssociationofStateHighwayandTrans-portationOfficials,Washington,D.C.

AASHTO.͑2007͒.AASHTOLRFDbridgedesignspecifications(with2008interimrevisions),4thEd.,AmericanAssociationofStateHigh-wayandTransportationOfficials,Washington,D.C.

Barker,R.M.,andPuckett,J.A.͑1997͒.Designofhighwaybridges,Wiley,NewYork.

Chotickai,P.,andBowman,M.D.͑2006͒.“Applicationoftrafficcountdatainfatiguelifeprediction.”Proc.,Int.Conf.onFatigueandFractureinInfrastructure,LehighUniv.,Philadelphia.

Davis,J.C.,Nassif,H.H.,andSuksawang,N.͑2006͒.“Anapproachtoestimatingremainingfatiguelifeinsteelgirderbridgesbasedonshort-termfieldmeasurements.”Proc.,Int.Conf.onFatigueandFractureinInfrastructure,LehighUniv.,Philadelphia.

Dowling,N.E.͑2007͒.Mechanicalbehaviorofmaterials:Engineeringmethodsfordeformation,fracture,andfatigue,3rdEd.,Prentice-Hall,UpperSaddleRiver,N.J.

Huckelbridge,A.,Kafali,G.,andGilmore,D.͑2002͒.“Implementationoffieldstrainmeasurementsforfatiguelifetimeestimation.”Rep.No.FHWA/OH-2002/025,FederalHighwayAdministration,Washington,D.C.

Khazem,D.etal.͑2006͒.“Site-specificfatigueloadingutilizingWIMdata.”Proc.,Int.Conf.onFatigueandFractureinInfrastructure,LehighUniv.,Philadelphia.

Metzger,A.T.,andHuckelbridge,A.͑2006͒.“Predictingfatiguelifetimefromstrainhistogramsinanabbreviatedtimewindow.”Rep.No.FHWA/OH-2006-26,FederalHighwayAdministration,Washington,D.C.

Moses,F.,Schilling,C.G.,andRaju,K.S.͑1987͒.“Fatigueevaluationproceduresforsteelbridges.”NCHRPRep.No.299,TransportationResearchBoard,NationalResearchCouncil,Washington,D.C.

ODOT-OTS.͑2007͒.“Technicalservicesproductsandservices:Trafficmonitoringsection.”͗http://www.dot.state.oh.us/Divisions/Planning/TechServ/Prod_Services/Pages/default.aspx͑͘Apr.2007͒.

Sivakumar,B.,andChang,J.͑2006͒.“BridgefatigueevaluationonAASHTOloadandresistancefactorrating͑LRFR͒manualandweigh-in-motion͑WIM͒data.”Proc.,Int.Conf.onFatigueandFractureinInfrastructure,LehighUniv.,Philadelphia.

Yen,B.T.,Huang,T.,Lai,L.Y.,andFisher,J.W.͑1990͒.“Manualforinspectingbridgesforfatiguedamagecondition.”Rep.No.FHWA-PA-89-022ϩ85-02,FederalHighwayAdministration,Wash-ington,D.C.

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