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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
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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.
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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.
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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
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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
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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.
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Fig6.ConfigurationofTsingMaBridge:(a)elevationand(b)crosssectionofbridegedeck.
Fig7.Finiteelementmodel
Inthispart,theevaluationoftime-varyingtemperaturedistributionandthermalstressesthermalstressesofaconcreteroofslabiscarriedout.Thesurfacetemperatureoftheconcreteslabismeasuredbyusingthethermalsensors.Theambienttemperatureiscollectedasthethermalboundaryconditionsforthethermalcomputation.FinefiniteelementmodeloftheconcreteslabisconstructedanddifferentboundaryconditionsareappliedtoobtainthetemperaturedistributionwithintheslabwiththeaidofthecommercialsoftwarepackageANSYS.Thesolarradiationmodelisutilizedtoestimatethesolarradiationreceivedby
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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.
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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
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