土木工程外文文献翻译.docx

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土木工程外文文献翻译

附录A科技文献翻译

原文

ConstructionandBuildingMaterials

Volume21,Issue5,May2007,Pages1052-1060

Anapproachtodeterminelong-termbehaviorofconcretemembers

prestressedwithFRPtendons

Abstract

Thecombinedeffectsofcreepandshrinkageofconcreteandrelaxationof

prestressingtendonscausegradualchangesinthestressesinbothconcreteand

prestressingtendons.Asimplemethodispresentedtocalculatethelong-termprestresslossandthelong-termchangeinconcretestressesincontinuous

prestressedconcretememberswitheithercarbonfiberreinforcedpolymer（CFRP）oraramidfiberreinforcedpolymer（AFRP）tendons.Themethodsatisfiestherequirementsofequilibriumandcompatibilityandavoidstheuseofanyempiricalmultipliers.AsimplegraphisproposedtoevaluatethereducedrelaxationinAFRPtendons.ItisshownthattheprestresslossinFRPtendonsissignificantlylessthanthatwhenusingprestressingsteel,mainlybecauseofthelowermoduliofelasticityofFRPtendons.Thelong-termchangesinconcretestressesanddeflectioncanbe

eithersmallerorgreaterthanthoseofcomparablegirdersprestressedwithsteel

tendons,dependingonthetypeofFRPtendonsandtheinitialstressprofileofthecross-sectionunderconsideration.

Keywords:

Creep;FRP;Long-term;Prestressloss;Prestressedconcrete;

Relaxation;Shrinkage

Nomenclature

Aareaofcrosssection

dverticaldistancemeasuredfromtopfiberofcrosssection

Emodulusofelasticity

age-adjustedelasticitymodulusofconcretefultimatestrengthofprestressingtendonpu

htotalthicknessofconcretecrosssectionIsecondmomentofarea

Ocentroidofage-adjustedtransformedsectiontfinaltime（endofservicelifeofconcretemember）tconcreteageatprestressing0

ycoordinateofanyfibermeasureddownwardfromO

χagingcoefficient

χreducedrelaxationcoefficientr

αratioofmodulusofelasticityofFRPorsteeltothatofconcrete

Δε（t,t）changeinconcretestrainbetweentimetandtc00

Δεchangeinaxialstrainatthecentroidofage-adjustedtransformedsectionOO

Δσ（t,t）stressappliedgraduallyfromtimettoitsfullamountattimetc00

Δσintrinsicrelaxationpr

reducedrelaxation

Δσtotallong-termprestresslossp

Δψchangeincurvature

εshrinkagestrainofconcretebetweentandtcs0

ε（t）instantaneousstrainattimetc00

（t,t）creepcoefficientbetweentandt00

σ（t）stressappliedattimetandsustainedtoalatertimetc00

σinitialstressofprestressingtendonp0

ρreinforcementratio

ψcurvature

Ωtheratioofthedifferencebetweenthetotalprestresslossandintrinsicrelaxation

totheinitialstress

Subscripts

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1transformedsectionatt0

cconcrete

ccnetconcretesection

fFRPreinforcementorflange

pprestressingFRPtendon

psprestressingsteeltendon

ssteelreinforcement

ArticleOutline

Nomenclature

1.Introduction

2.RelaxationofFRPprestressingtendons

3.Proposedmethodofanalysis

3.1.Initialsteps

3.2.Time-dependentchangeinconcretestress

3.3.Long-termdeflection

4.Applicationtocontinuousgirders

5.Developmentofdesignaids

6.Illustrativeexample

7.Summary

Acknowledgements

References

1.Introduction

Theuseoffiberreinforcedpolymer（FRP）tendonsasprestressingreinforcementshavebeenproposedinthepastdecadeandafewconcretebridgeshavealreadybeenconstructedutilizingfiberreinforcedpolymer（FRP）tendons.Comparedtoconventionalsteelprestressingtendons,FRPtendonshavemanyadvantages,includingtheirnoncorrosiveandnonconductiveproperties,lightweight,andhightensilestrength.Mostoftheresearchconductedonconcretegirdersprestressedwith

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FRPtendonshasfocusedontheshort-termbehaviorofprestressedmembers;researchfindingsonthelong-termbehaviorofconcretememberswithFRPtendonsarescarceintheliterature.TherecentACICommitteereportonprestressingconcretestructureswithFRPtendons（ACI440.4R-04[1]）haspointedoutthat:

“Researchonthe

long-termlossofprestressandtheresultanttime-dependentcamber/deflectionisneeded…”MostoftheresearchandapplicationsofFRPtendonsinconcretestructureshaveadoptedeithercarbonfiberreinforcedpolymer（CFRP）oraramidfiberreinforcedpolymer（AFRP）tendons.Theuseofglassfiberreinforcedpolymers（GFRP）hasmostlybeenlimitedtoconventionalreinforcingbarsduetotheirrelativelylowtensilestrengthandpoorresistancetocreep.Therefore,thispaperfocusesonprestressedmemberswitheitherCFRPorAFRPtendons.

Creepandshrinkageofconcrete,andrelaxationofprestressingtendons,causelong-termdeformationsinconcretestructures.Whileitisgenerallyacceptedthatlong-termlossesdonotaffecttheultimatecapacityofaprestressedconcretemember,areasonablyaccuratepredictionoftheselossesisimportanttoensuresatisfactoryperformanceofconcretestructuresinservice.Ifprestresslossesareunderestimated,thetensilestrengthofconcretecanbeexceededunderfullserviceloads,causingcrackingandunexpectedexcessivedeflection.Ontheotherhand,overestimatingprestresslossescanleadtoexcessivecamberanduneconomicdesign.Theerrorinpredictingthelong-termprestresslossescanbedueto:

（1）inaccuracyinestimationofthelong-termmaterialcharacteristics（creepandshrinkageofconcreteandrelaxationofprestressingtendons）;and

（2）inaccuracyofthemethodofanalysisused.Theobjectiveofthispaperistoaddressthesecondsourceofinaccuracybypresentingasimpleanalyticalmethodtoestimatethetime-dependentstrainsandstressesinconcretemembersprestressedwithFRPtendons.Themethodsatisfiestherequirementsofequilibriumandcompatibilityandavoidstheuseofempiricalequations,whichingeneralshowlossinaccuracytoenablegenerality.The

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inaccuracyinthematerialcharacteristicsusedcanbemitigatedbyvaryingtheinputmaterialparametersandestablishingupperandlowerboundsontheanalysisresults.Forthepurposeofthispaper,andtoavoidconfusion,aconsistentsignconventionisused.AxialforceNispositivewhenitistensile.Bendingmoment,M,thatproduces

tensionatthebottomfiberofacrosssectionandtheassociatedcurvatureψare

positive.Stress,σ,andstrain,ε,arepositivefortensionandelongation,respectively.Downwarddeflectionispositive.Itfollowsthatshrinkage,ε,isnegativequantity.cs

ThelossintensioninprestressingreinforcementduetorelaxationΔσorduetothepr

combinedeffectsofcreep,shrinkage,andrelaxation,Δσ,isnegativequantity.Thep

analysisconsideredhereinfocusesonaprestressedconcretesectionwithitscentroidalprincipaly-axisinverticaldirectionwiththecoordinateyofanyconcretefiberor

steellayerbeingmeasureddownwardfromagivenreferencepoint.

2.RelaxationofFRPprestressingtendons

Similartoconcreteandsteel,AFRPprestressingtendonsexhibitsomecreepifsubjectedtosustainedstrains.CFRPtendonstypicallydisplayinsignificantamountofcreep,whichcanbeneglectedformostpracticalapplications.Whenaprestressingtendonisstretchedbetweentwopoints,itwillbesubjectedtoaconstantstrain.Becauseofcreep,thestressinthetendondecreases（orrelaxes）withtimetomaintainthestateofconstantstrain.Thisreductioninstressisknownasintrinsicrelaxation

Δσ.Whilesteeltendonssubjectedtostresseslessthan50%oftheyieldstressdonotpr

exhibitappreciableamountofrelaxation,testsonAFRPtendonshaveshownthattheydisplayrelaxationunderverylowstresses.ThelevelofrelaxationofAFRPtendonsdependsuponmanyfactors,includingambienttemperature,environment（e.g.,air,alkaline,acidic,orsaltsolutions）,ratioofinitialstress,σ,toitsultimatestrength,f,p0pu

andtimetlapsedafterinitialstressing.BasedonextensiveexperimentationonrelaxationpropertiesofAFRPtendons,SaadatmaneshandTannous[2]suggestedarelationshipoftheform:

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（1）

whereλ=σ/f.σisthestressinthetendon1hafterstressrelease.Ratiosofσ/σp1pup1p1p0

intheirtestsvariedbetween0.91and0.96,withanaverageof0.93.Tabulatedvaluesofthevariablesaandbwereprovidedforλ=0.4andλ=0.6,andfordifferent

temperaturelevelsandsolutiontypes.ForAFRPtendonsinairatatemperatureof25?

C,relationshipsforaandbwereproposed[2]as

（2）

Inaprestressedconcretemember,thetwoendsoftheprestressingtendonconstantlymovetowardeachotherbecauseofcreepandshrinkageofconcrete,therebyreducingthetensilestressinthetendon.Thisreductionintensionhasasimilareffecttothatwhenthetendonissubjectedtoalesserinitialstress.Thus,areducedrelaxationvalue,

shouldbeusedintheanalysisoflong-termeffectsinprestressedmembers,suchthat

（3）

whereχisadimensionlesscoefficientlessthanunity.Followinganapproachr

previouslysuggestedbyGhaliandTrevino[3]toevaluateχforprestressingsteelr

tendons,χforAFRPtendonscanbecalculatedas（logtinEq.

（1）istakenequalto5r

for100,000h）:

（4）

where

（5）

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andζisadimensionlesstimefunctiondefiningtheshapeofthetendonstress–time

curve.Thevalueofζincreasesfrom0to1astimechangesfrominitialprestresstimettofinaltimet.ΩistheratioofthedifferencebetweenthetotalprestresslossΔσ（t）0ps

andintrinsicrelaxationΔσ（t）totheinitialstressσ,expressedasprp0

（6）

Fig.1showsthevariationofχwithΩforσ/f=0.4,0.5,and0.6,whichrepresentsrp0pu

thecommonvaluesofinitialprestressingratios[1].Aswillbeshowninalater

section,Ωtypical