文献综述-桥梁热效应分析解析

LiteratureReviewaboutSolarRadiation-induced

ThermalEffectonConcreteBridge

Abstract:Changingenvironmentalconditions,especiallytemperature,havebeenobservedtobeacomplicatedfactoraffectingvibrationproperties,suchasfrequencies,modeshapes,anddampingofcivilstructures.Thispaperreviewstechnicalliteratureconcerningsolarradiation-inducedtemperatureeffectonconcretebridge.Mostofthesestudiesfocusonvariationsinfrequenciesofbridgestructures,withsomestudiesonvariationsinmodeshapesanddampingandothertypesofstructures.Itisseenthatthenumericalmodelscansuccessfullypredictthestructuraltemperaturefieldandthermalstressesatdifferenttime.Themethodologyemployedinthepapercanbeappliedtootherconcretebridgesaswell.Keyword:temperature;literature;bridgestructures;methodology

1Introduction

Manyconcretebridgesaresubjectedtodaily,seasonalandyearlyenvironmentalthermaleffectsinducedbysolarradiationandambientairtemperature.Experimentsandfieldmeasurementshaveindicatedthatchangingthermalconditionsmayhaveamoresignificanteffectonconcretebridgebehaviorthanoperationalloads.Theheattransferfromsurroundingenvironmentmayinducetemperaturevariationatconcretecomponentsandtherebyproducestructuraldeformationandthermalstressesduetoredundancy.Thethermaleffectsonconcretebridgesevenlongspanbridgeshavebeeninvestigatedbymanyresearchersacrosstheworldsince50yearsagoandsomeapproacheshavebeendevelopedtoexaminetheperformanceofbridgessubjectedtotemperatureloading.Withtherapiddevelopmentofcomputationalmethodsandcomputertechnology,anumberofone-dimensionaltothree-dimensionalfiniteelementmodelshavebeendevelopedsincethe1970s.Mostofthecurrentinvestigationsmainlyfocusonthermaleffectsonconcretebridges.Theconfigurationandperformanceoflongspanbridgessuchassuspensionbridgesarequitedifferentfromthoseofcommonconcretebridges.Itisdifficultandinsufficienttoinvestigatethebridgeperformancethoroughlybyusingthetemperaturedataatafewcomponentsonly.Therefore,calculationofthetemperaturedistributionofthebridgecomponentsisimperativetostudythetemperatureeffects.Alittleworkhasyetbeencarriedouttoexaminethetime-varyingtemperaturefieldofbridgetower.Thispaperaimstoinvestigatethetemperaturedistributionofatowerofalongspansuspensionbridge.

Zukinvestigatedthethermalbehaviorofseveralconcretebridgesandfoundthatthetemperaturedistributionwasaffectedbyairtemperature,wind,humidity,intensityofsolarradiationandmaterialtype.Adamsetal.investigatedtherelationbetweentemperatureandtheaxialresonantfrequencyofabar.Cornwelletal.investigatedthethermalvariationofdynamicpropertiesoftheAlamosaCanyonBridge.Cappslatermeasuredtemperatureandtemperature-inducedlongitudinalmovementsonasteelboxbridgeintheUK.EarlystudiesinthefieldincludethoseofPriesleyandChurchwardandSokai.AskegaardandMossingstudiedathree-spanRCfootbridgeandobserveda10%seasonalhangeinfrequencyovera3-yearperiod.Cornwelletal.investigatedthethermalvariationsinthedynamicpropertiesoftheAlamosaCanyonBridgeandfoundabout5%dailychangesinthefirstthreenaturalfrequencies.PeetersandDeRoeck

1

monitoredtheZ24Bridgecontinuouslyfornearlyayearandtheyreportedabilinearrelationbetweenthefirsttwofrequenciesandthestructuraltemperature.Theyfoundthatthetwofrequenciesincreasedbyabout10%whentemperaturedecreasedfrom0to-7℃.Fortemperaturesabove0℃,thefirstfrequencydecreasedslightlywhenthewearingsurfacetemperaturewentup,whereasthesecondfrequencyincreasedslightlywhenthedecksoffittemperaturewentup.FuandDeWolfstudiedatwo-span,slightlyskewedcompositebridgeandfoundthattheexpansionbearingswereapproximatelypartiallyconstrainedbelow

F.Thefirstthreefrequenciesdecreasedby12.3,16.8,and9.0%respectively,asthetemperatureincreasedfromF(°-17.8℃)toapproximately60F(15.°6℃),whereastheychangedlittleasthetemperaturewasabove60F°.Theauthorsthensimulatedathermalaxialloadandappliedittothegirdereccentricallyforcalculatingthefrequenciesunderdifferenttemperatures.Thechangeinfrequenciesagreedwellwiththemeasurement.Nietal.extracted1-yearmodalpropertiesoftheTingKaucable-stayedbridgeinHongKong.Therelativevariationsinthemeasuredmodalfrequencies(i.e.,theratiooffrequencychangetoaveragefrequencyforeachmode)underweakwindconditionsrangedbetween1.7(the8thmode)and6.7%

(the1stmode)whenbridgetemperaturesrangedbetween3and53 ℃.Theyconcludedthattheeffective

temperature(i.e.,temperatureaveragedoverthecrosssectionweightedbyareas)wasinsufficientinformulatingagoodcorrelationbetweenthemodalfrequenciesandtemperaturesbecauseoftheexistenceoftemperaturegradientoverthecrosssection.MacdonaldandDaniellinvestigatedvariationsinnatural

frequenciesoftheSecondSevernCrossingcablestayedbridgebecauseofwind,temperature,andtrafficloading.Theyreportedthattherewasnoapparenttrendbetweenthenaturalfrequenciesandthemean

bridgedecktemperaturebecausethetemperaturechangewassmall.Desjardinesetal.studiedthevariationsinfrequenciesoftheConfederationBridge(madeofpre-stressedconcrete)overa6-monthperiod.Theyreportedacleartrendofreductioninthemodalfrequenciesbyabout4%,whentheaveragetemperatureof

theconcreteofthebridgevariedfrom-20to+25℃.LiuandDeWolfreportedthat,duringa1-yearmeasurement,thefirstthreefrequenciesofacurvedconcreteboxbridgedecreasedwhenconcrete

temperatureincreased.Alinearregressionanalysisshowedthatfrequenciesdecreasedby0.007,0.008,and0.007HzastemperatureincreasedbyoneFahrenheitdegree,whichisequivalentto0.8,0.7,and0.3%perdegreeCelsius.TheYunyangSuspensionBridgewitha1,490-mmainspanexperiencedabout2%variationinthefirstsixmodalfrequenciesduringaperiodof10months,astheambienttemperatureofthesteel

bridgevariedfrom-5to+50℃.During16daysofcontinuousmonitoringofacable-stayedbridge,Lietal.foundthatthefirstsixfrequenciesvariedbyabout1.5–3.2%asambienttemperaturechangedfrom-11.5to+3.7℃.

Alternatively,fieldmeasurmentisaneffectiveyetpracticalapproachtoobtaintheinformationofbridgetemperatureenvironment,whichprovidesthepossibilitytocarryouttemperatureeffectevaluationfromthepracticalviewpoint.Mostofthecurrentinvestigationsmainlyfocusonthethermalassessmentofbridgedeck.Thefieldmeasurementcanonlyobtainthetemperaturevaluesoflimitedtestingpointsinsteadofthedetailedthermalgradientsoftheconcretestructures.Thetime-varyingeffectsoftemperatureofconcretebridgepiershavenotbeensystematicallyinvestigated.

2

2ThermalEffectonConcreteBridge

2.1Temperaturevariationandthermalstressesonconcretebridgepiers

Manyconcretebridgesaresubjectedtodaily,seasonalandyearlyenvironmentalthermaleffectsinducedbysolarradiationandambientairtemperature.Experimentsandfieldmeasurementshaveindicatedthatchangingthermalconditionsmayhaveamoresignificanteffectonconcretebridgebehaviorthanoperationalloads.Theheattransferfromsurroundingenvironmentmayinducetemperaturevariationatconcretecomponentsandtherebyproducestructuraldeformationandthermalstressesduetoredundancy.Thetemperatureeffectsonconcretebridgeshavebeeninvestigatedbymanyresearchersacrosstheworldsince50yearsagoandsomeapproacheshavebeendevelopedtoexaminetheperformanceofbridgessubjectedtotemperatureloading.

Arealhighwaybridge(Fig1) constructedbyconcreteinnorthernChinaistakenastheexampleto

examinethefeasibilityoftheproposedanalyticalapproach.Thebirdeyeviewofthebridge’sisdisplayedinFigure1.Thebridgehasnightspansandthelengthforasinglespanis30m.Thetotalbridgelengthis278.2m.Thebridgepiershavetherectangulartubesizes.Thegeometricsizeofthepiercrosssectionis

2.5minwidthand6.5minlength.Thethicknessofthecrosssectionis0.5m.Thetime-varyingtemperaturefieldsofthepiersurfacearemeasuredbyusingthethermalinfraredimager.

Fig1.Birds’eyeviewofthebridge

Inthispart,dynamictemperaturefieldsandthermalstressesofaconcretepierareactivelystudiedwiththeaidingofthecommercialpackageANSYS.Thedifferentboundaryconditionsareappliedtoobtainthetemperaturedistributionandcomputethethermaldeformationwithintheconcretepier.Thesurfacetemperatureofthepierismeasuredbyusingthethermalinfraredimager.Theambienttemperatureandwindvelocityarealsocollectedatthesametime.Themadeobservationsdemonstratethatthesimulatedtemperaturevariationoftheconcretepieragreeswellwithmeasurementresults.Thethermalgradientof

theconcreteinthethicknessdirectionisalittlelarge.Thehorizontaldeformationismuchlargerthanthatinverticaldeformationduetotheinfluenceoftheconstraintsonthetopandbottomsidesofthepier.Thethermalstressesoftheexamplebridgepierarenotverylargeexceptforthelocalareasontopofthepiers.

3

Itisseenthatthenumericalmodelscansuccessfullypredictthestructuraltemperaturefieldatdifferenttimeinstantthestructuraltime-varyingtemperatureeffects.Themethodologyemployedinthepapercanbeappliedtootherconcretebridgesaswell.

Fig2.Temperaturefieldsofthebridgepier

Fig3.Finiteelementmodel

2.2Time-varyingtemperaturefieldofbridgetower

Longspansuspensionbridgesaresubjectedtodaily,seasonalandyearlyenvironmentalthermaleffects

inducedbysolarradiationandambientairtemperature.Theheattransferfromsurroundingenvironment

mayinducetemperaturevariationatbridgecomponentsandtherebyproducestructuraldeformationand

thermalstressesduetoredundancy.Thermaleffectsonlongspanbridgeshavebeeninvestigatedacrossthe

worldtosimulatethetemperaturedistribution ofbridgesandpredictthestructuralresponses.Thermal

effectsonbridgeshavebeeninvestigatedsincethe1960s.Withtherapiddevelopmentofcomputational

methodsandcomputertechnology,anumberofone-dimensional tothree-dimensional finite element

modelshavebeendevelopedsincethe1970s.Mostofthecurrentinvestigationsmainlyfocusonthermal

effectsonconcretebridges.Theconfigurationandperformanceoflongspanbridgessuchassuspension

bridgesarequitedifferent fromthoseofcommonconcretebridges.Itisdifficult andinsufficient to

4

investigatethebridgeperformancethoroughlybyusingthetemperaturedataatafewcomponentsonly.Therefore,calculationofthetemperaturedistributionofthebridgecomponentsisimperativetostudythetemperatureeffects.Alittleworkhasyetbeencarriedouttoexaminethetime-varyingtemperaturefieldofbridgetower.Thispaperaimstoinvestigatethetemperaturedistributionofatowerofalongspansuspensionbridge.

Toexaminethefeasibilityandvalidityoftheproposedapproach,thetowersegmentofalongspansuspensionbridgeconstructedinChinaistakenastheexample.TsingMaBridge(Fig4)inHongKongisalongspansuspensionbridgecarryingadualthree-lanehighwayontheupperlevelofthebridgedeckandtworailwaytracksandtwoprotectedcarriagewaysonthelowerlevelwithinthebridgedeck.ItspansthemainshippingchannelbetweentheTsingYiIslandandtheMaWanIslandwithamainspanof1377mandatotallengthof2132m.Theheightofthetwobridgetowers,theTsingYiTowerandtheMaWanTower,isabout206m,measuredfromthebaseleveltothetowersaddle.Thetwotowersarereinforcedconcretestructureshavingtworeinforcedconcretelegslinkedbyfourreinforcedconcretecross-beamsandsupportedbymassivereinforcedconcreteslabsfoundoncompetentrock(seeFig.1).Thetwotowerssharealmostidenticalstructuralandgeometricfeatures,exceptthatthetopmostportalbeamoftheMaWantoweris0.15mhigherthanthecounterpartoftheTsingYitowerandthustheheightofthetowerlegs.

Fig4Configurationofbridgetower

5

Fig.5Finiteelementofatowersegment

Inthispart,byassumingthetemperaturealongthebridgeheightisconstant,atypicalbridgetowersectionisanalyzedtoobtainthetemperaturedistributionofthesegment.Finefiniteelementmodelofthetowersectionisconstructedanddifferentboundaryconditionsareappliedtoobtainthetemperaturedistributionwithinthecomponentswiththeaidofthecommercialsoftwarepackage.Themethodologyemployedinthepapercanbeappliedtootherlong-spanbridgesaswell.

2.3Temperaturevariationandthermalstressesonconcreteslab

Concreteslabaresubjectedtodaily,seasonal,andyearlythermalactionduetovariationsinsolarradiation

andambientairtemperature.Variationintemperatureofbuildingroofsmaycausenon-uniformdistribution

oftemperatureandinducethermalstress.Excessivethermalstressesmaydamagetheconcreteslab.In

addition,aseriesofexperimentsandfieldinvestigationshavedemonstratedthatthechangingtemperature

conditionsmayhaveamoresignificanteffectonstructuralbehaviourthancommonoperationalloads.Itis

reportedthatmanybuilding structuresaredamagedundertheintensive temperatureloading. The

temperaureeffectsonconcretestructureshavebeeninvestigatedbymanyresearchersacrosstheworld

since100yearsagoandmanyapproacheshavebeendevelopedtoexaminetheperformanceofconcrete

structuresundertemperatureloading.

Mostofthecurrentinvestigationsmainlyfocusonthermaleffectsofconcretestructuresundercommonsolarradiation.Thesheltereffectsofthesolarradiationonthetime-varyingtemperaturedistributionoftheconcretestructureshavenotbeensystematicallyinvestigated.

Toexaminethefeasibilityandvalidityofproposedapproach,theconcreteslabofamulti-storeybuildingconstructedinsouthernChinaistakenastheexample.Thelengthandwidthoftheconcreteslabisabout5.0mand5.0m,respectively.TheconcretematerialoftheslabistheC40.ThefiniteelementmodeloftheconcreteslabisestablishedwiththeaidingofcommercialpackageANSYSasshowninFigure1.

Thefiniteelementmodeloftheconcreteslabisconstructedbyusingthesolid95element.

6

Fig6.ConfigurationofTsingMaBridge:(a)elevationand(b)crosssectionofbridegedeck.

Fig7.Finiteelementmodel

Inthispart,theevaluationoftime-varyingtemperaturedistributionandthermalstressesthermalstressesofaconcreteroofslabiscarriedout.Thesurfacetemperatureoftheconcreteslabismeasuredbyusingthethermalsensors.Theambienttemperatureiscollectedasthethermalboundaryconditionsforthethermalcomputation.FinefiniteelementmodeloftheconcreteslabisconstructedanddifferentboundaryconditionsareappliedtoobtainthetemperaturedistributionwithintheslabwiththeaidofthecommercialsoftwarepackageANSYS.Thesolarradiationmodelisutilizedtoestimatethesolarradiationreceivedby

7

theslabandthesheltereffectsarealsotakenintoconsideration.Thenumerical modelscansuccessfully

predictthestructuraltemperatureatdifferenttime.Themadeobservationsdemonstratethatthesimulatedtemperaturevariationoftheconcreteslabbasedonthesolarradiationmodelagreeswellwithmeasurementresults.Thethermalgradientoftheconcreteslabinthethicknessdirectionisobvious.Themethodologyemployedinthepapercanbeappliedtootherconcretestructuresaswell.

3Conclusions

Thispaperreviewstemperatureeffectonvariationsinmodalpropertiesofcivilstructures.Moststudiesshowthatanincreaseintemperatureleadstoadecreaseinstructuralfrequencies,whereastemperaturehaslittleeffectonmodeshapes,anditseffectondampinghasnotbeenwellunderstoodbecauseoflargeuncertaintyofdamping.Threelaboratory-testedmodelsandtwofield-monitoredlargescalestructureshavebeeninvestigated.Besidessimilarconclusionsasotherresearchershavefound,thefollowingconclusionscanbedrawnfromthepresentstudy:

Variationsinfrequenciesarecausedmainlybythechangeinthemodulusofamaterialunderdifferenttemperatures.Thatis,modalfrequenciesofthesteelstructures,thealuminumbeam,andtheRCstructuresdecreasebyabout0.02,0.03,and0.15%,respectively,whentemperatureincreasesbyonedegreeCelsius,regardlessofmodesandstructuraltypes.Frequenciesofconcretestructuresaremoresensitivetotemperaturechangethanmetallicstructures.

Modeshapesofhigh-risestructuresmayvaryatdifferenttimeinstantsastemperaturesofdifferentcomponentsvaryaswell.Thisisdifferentfromthesituationofsomebridges,inwhichtemperaturesalongthelongitudinaldirectionareregardedasidentical.

Thetemperaturedistributionoflarge-scalestructuresisusuallynon-uniform.Differentcomponentshavedifferentcontributionstotheglobalfrequencies.Usingairtemperatureoraveragedtemperatureofafewmeasurementpointsmayleadtoincorrectquantitativerelationsbetweentemperatureandfrequencies.Heat-transferanalysiscanprovidemorecomprehensivetemperaturedistribution.Thenaglobaleigenvalueanalysiscombiningtherelationofmodulustotemperaturecanpredictamoreaccuraterelationbetweentemperatureandfrequencies.

Young’smodulusofconcreteisusuallymeasuredfromultrasonicmethodsorstress–straindiagram,whichexhibitssignificantuncertainties.Inthenaturalcondition,temperaturevariationisnotsignificant

andthusthemodulusthermalcoefficientisverydifficulttobemeasuredaccurately.Ontheotherhand,vibrationfrequencyofsimplestructurescanbemeasuredwithhighaccuracy,thankstotherapiddevelopmentofhardwareandanalyticaltechniquesinmodaltesting.Inaddition,modaltestingisa

nondestructivetechniqueandcanbecarriedoutrepeatedlyunderdifferenttemperatureconditions.Thisis

anotheradvantageofthevibration-basedmethodasthetraditionaluni-axialcompressiontest maycause

damagetothespecimenandthuscannotbecarriedoutrepeatedlyunderdifferenttemperatureconditions.Consequently,thevibration-basedmethodcanbeapromisingalternativeapproachtomeasurethematerialthermalcoefficientofmodulus:largertemperaturevariation,largerfrequencychanges,andthusresultsinamoreaccuratethermalcoefficientofmodulus.

8

Forpracticalstructures,factorssuchasvaryingboundaryconditions,loadconditions,anddamagesmayalsoaffectthestructuralvibrationproperties.Measurementnoisemayalsomaskthisvariation.Inaddition,itisverydifficulttoseparatetheeffectsfromdifferentsources.Therefore,controlledlaboratory

experimentsarenecessaryandimperativetoprovideaccurateandreliableresultsregardingthetemperature

effectonthestructural vibrationproperties.Inlaboratoryexperimentsinthispaper,varyingtemperature

canbethemainreasonofthefrequencychangesandfrequenciescanbemeasuredveryaccurately.For

example,thefirstauthorhasconductedamodaltestingonaRCslabrepeatedlyunderastabletemperature

condition.Itshownthatthecoefficientofvariation(ratioofstandarddeviationtomeanvalue)ofthefirst

fourmodalfrequencieswere0.04,0.09,0.31,and0.35%,respectively,whichisequivalenttoabout0.3–2.3degreestemperaturevariationofconcrete.Doeblingetal.alsoestimat