【doc】碳纤维加固钢筋混凝土梁的界限相对受压区高度研究

【doc】碳纤维加固钢筋混凝土梁的界限相对受压区高度研究 碳纤维加固钢筋混凝土梁的界限相对受压 区高度研究 第2期后勤工程学院2002正 DiscussionofBalancedRelativeCompression Height(P6)inStrengthenedBeamwith CarbonFiber----ReinforcedPolymerSheets JIANGShiyong,FEIWei,LIYingtao,PENGFeifei,DUWenlong,WANGYuewen (1.Dept.ofCivilEng.,LEU,Chongqing400041,China; 2.Dept.ofArchitecturalandEnvironmentalEng.,LEU,Chongqing400041,China) ABSTRACTBasedonthestress—strainrelationshipandprincipleofCO—d eformation, thispaperanalysesthebalancedrelativecompressionheight(P6)ofstrengthenedbeamwith CarbonFiber—ReinforcedPolymer(CFRP)sheets,andpresentstheconceptofbalanced section.Basedonthisconcept,themethodofdecidingbalancedrelativecompressionheightis proposed. Keywords:Carbonfiber—reinforcedpolymer;sheet;beam;strengthened;b alancedsteel ratio;balancedrelativecompressionheight. CLCnumber:TU375.1Documentcode:A Force——bearingPropertyofStrengthenedBeamwithCFRP Therearemanydifferencesinpropertyofbearingforcebetweenstrengthenedstructureandgeneral structurewithoutbeingstrengthened.Theoriginalelementofstrengthenedstructurehasbeardforce beforestrengthenedandthelevelofstressinsectionisfairlyhighespeciallythereasonofstrengtheningis thatthebearingcapacityofstructureisnotadequate.Sotheloadsarenotsharedimmediatelybythe newly—increasedparts.Onlywhenthepartsbearforceforthesecondtimedotheystarttoshareloads. Sothestressofnewlyincreasedpartsalwaysfallsbehindtheaccumulatedstressoforiginalstructure duringthewholestructurebearingforcesecondly.Whentheoriginalstructurereachesthelimitstate.the stressandstrainofnewlyincreasedpartsareprobablyverylowanddontbeabletoreachthelimitstate. Thematerialisnotfullyusedinmostsituations. DAN—baseCarbonFiber—ReinforcedPolymer(CFRP)isgenerallvusedi nthefieldsofcivil engineering.CFRPhasitsproperty,suchasnon—plasticbehavior , lowshearstrength,high expenseetc.Fromtheviewpointofstructuralengineering,themostseriousoneisthematerialglinear 本论文于2001年12月在香港召开的 FRPCompositesinCivilEngineering国际研讨会上宣读. 收稿日期:2002—01—22 江世永(1965一),男,湖北天门人,教授,博士后,从事建筑物鉴定与加 固方面研究. 第2期江世永等碳纤维加固钢筋混凝土的界限相对受压区高度研究 elasticbehavioruptorupturewithouttheobviousyieldingphenomenon.Forageneralbeam,abalanced stateisdefinedasastatethatthesectionwillfailunderflexurewiththetensilesteelyieldsatthesame timetheconcreteiscrushedbycompression.ForastrengthenedbeamwithCFRP,thebalancedstateis verycomplex.SoitisnecessarytoconsiderthebalancedstateofastrengthenedbeamwithCFRP systems. 2TheDiscussionofBalancedRelativeCompressionHeight()andBalanced SteelRatioP6inStrengthenedBeamwithCFRP Forageneralbeam,abalancedsectionisdefinedasthat,thefiberstrainattheedgeofcompression regionjustreachestheultimatecompressionstrainofconcreteforflexurewhenthestressoftensionsteel barreachestheyieldstrengthatthistime.Thebalancedrelativecompressionheightofsectionofbeam 6xb/h0(where6isbalancedcompressionheightofsection,h0=h一 /ot,iseffectivesectionheight). ThereisnottheconceptofthebalancedrelativecompressionheightinACIcode.P6isdefinedas balancedsteelratiooftensionstee1.BothinChinesecodeandinACIcodeP…sregardedasthemaximum steelratioofnon—ductilereinforcedbeam.ThefollowingformulaistherelationshipbetweenP b and专binthebeamwithsinglereinforcement. fm p6考6’了 .,y (1) pb--balancedtensionsteelratio;--balancedrelativecompressionheight: lmthedesignstrengthofconcrete;fy--thedesignstrengthoftensionsteel CFRPhasthepropertyofhighstrengthandthestrengthismuchhigherthantheconstructionstee1. ThemodulusofelasticityofCFRPandconstructionsteelisatthesameleve1.theformerisalittlehigher thanthelatter.SotheallowabletensionstrainofCFRP[6]ismuchhigherthantheyieldingtension strainofsteelbar,6y. Generallyspeaking,thevalueoftensionstrainofCFRPis1owerthanthea11owable tensionstrain 【]whentheoriginalsteelbarsofstrengthenedstructurewithCFRPvield.Inorderto makethebestofthepropertiesofCFRP,prestressedtensionstresswasputonCFRP. sothatithasa preliminarystrain6~,whichcaninsureCFRPtoreachitsownallowabletensionstresswhentheorigina1 steelbarsyield.ThisarticleisbasedonthisstrengtheningsituationthatCFRPison1vstickedtothe bottomofthebeam,andassumethatthedistancebetweenCFRPandtheoriginaltensionsteelisnearbv . Inthepaperthebalancedrelativecompressionheightisdefinedasfoilows: 1)whenthetensionsteelbarsyieldbutstrengtheningCFRPsheetsdonotreachtheaUowable tensionstrain 【J,theconcreteincompressiveregionalsoreachestheultimatecompressionstrainat thesametime 2)whenthestrengtheningCFRPsheetsreachtheall.wabletensi.nstrain[]butthetensi.n steelbarsdonotyield,theconcreteincompressiveregiona1soreachestheuhimatecompression strainat thesametime. 3)WhenthestrengtheningCFRPsheetsreachthe steelbarsyield,theconcreteincompressiveregionalso sametime. allowabletensionstrain[]andthetension reachestheultimatecompressionstrainatthe Threesituationsarediscussedabout~6inthefollowing: (1)WhenthetensionsteelbarsyieldbutstrengtheningCFRPsheetsdonotreac htheallowable ensionstrain[],thec.Bereteinc.mpressiVeregiona1s.reachestheuhimatec. mpressi.nstrainat 18后勤工程学院2oo2年 thesametime. Asshowninfig.1,accordingtothestress—strainrelationship deformationandtheflat—section ofmaterial,theprincipleofco— assumptionofaveragestressofreinforcedconcretebeam. followingformulaissetup: c6 s. : “ +l 0.8Xc60.8ec 一::一 ho”+l 尚 whereey--theyieldingtensionstrainof compressionstrainofconcrete; 0.8e. 8cI’8 (2) 卜一‰— i steelbar;e~--theultimate 卜一—— . —— thestrainofsteelbar;xdmtherealheightofcompressive regionwhenasectionisinbalancedstate;0g?1 h0--theeffectivesectionheight;x6mthereducedheightofcompressiveregionofrectangularstress diagram.. Asregardsthevalueadoptedforh0,itcanbecalculatedaccordingtothehooftheoriginalreinforced concretebeamsincethedistancebetweenCFRPsheetsandtheinitialtensionsteelbarsisassumed nearbv.Itcanalsobecalculatedaccordingtothevaluethattheheightofactualbeamsubtractsthehalf distanceofCFRPsheetsandinitialsteelbar. 2)WhenthestrengtheningCFRPsheetsreachtheallowabletensionstrain[钉] butthetension steelbarsdonotyield,theconcreteincompressiveregionalsoreachestheulti matecompressionstrainat thesametime. l=[] withthesamereason: 3)Whenthestrengthening steelbarsyield,theconcretein sametime. soIy withthesamereason: = CFRPsheetsreachthe compressiveregionalso (3) allowabletensionstrain[钉]andthetension reachestheultimatecompressionstrainatthe 0.8 7 assumetheindexofstresslevelbeforestrengtheningisJB. n卢== Itcanbeobtainedfromtheaboveformula: (4) (5) (6) where6so——thepreliminarystrainofinitialtensilesteelbars; 一 thedesignvalueofstrengthoftensilesteelbars;E,--themodulusofelasticityof steelbar. AssumetheindexofadvancedtensionstresslevelofCFRPsheetsisTwhenstre ngthened then(7) T......?........上 钉 = 第2期江世永等碳纤维加固钢筋混凝土的界限相对受压区高度研究 Itcanbeobtainedfromaboveformula: =y[](8) E厂themodulusofelasticityofCFRP Theultimatecompressionstrainofconcreteis8cu =0.0033. Putformula(5)and(7)intoformula(1),(2)and(3),throughconcludingandtid ying,then comeouttheconclusion: when[]一+>y, = when = 1+(1+y)[s]/0.0033+#f/o.0033E. [],+<8y, 0,8 1ff内.0033Et Inthethirdsituationofabovediscussion, compressionstrain~cH,CFRPsheetsreachesits (9) (10) whenthecompressiveConcretereachestheultimate permissivetensionstrainandatthistimetheinitial tensionsteelsjustyield.Asregardsthissituation,itisregardedasbalancedfail ure,thefollowing formulaistheinductionabout8b 3 Itcanbeconcludedfromtheconditionofbalancedfailure: []一+=y Putformula(5)and(7)intoformula(10),then ?一 (11) (12) TheAscertainingMethodsofBalancedRelativeCompressionHeight() StrengthenedBeamwithCFRPSheets Fromtheaboveanalyses,inordertodeterminethebalancedrelativecompressionheight(),itis clearthatweshouldconsidernotonlytheindex()ofstressleveloftheoriginaltensionsteelandthe index(y)ofadvancedtensionstresslevelofCFRPsheets,butalsotheindex()ofstresslevelwhen balancedfailurehappen. Showedbyformulaas~llows: : j+(+y)[]/00?0o833+/0?0o33, ,’ Q:墨 1ff内.0033E| (13) where—theindexofstressleveloftheoriginaltensionsteelbars.itcanbecalculatedbyformula (5); theindexofprestressedtensionstresslevelofCFRPsheetswhenstrenhened , itcan becalculatedbyformula(7); 一 theindexofstresslevelwhenbalancedfailurehappen. 4Conclusions Accordingtotheaboveanalysis,thebalancedrelativecompressionheightofbeamsstrengthened 后勤工程学院2002在 withCFRPsheetsisascertained,andsomeenlightenmentaregainedasfollows. 1)SincetherelativecompressionheightofbeamsstrengthenedwithCFRPsheetsisputforward, thedesignofbeamsstrengthenedwithCFRPsheetscanproceedaccordingtothedesignofgeneral beams,assuringthequantityofcarbonfibersheetsusedintheproperscope,avoidingthephenomenaof over—reinforcement,anddecreasingthewasteofmateria1. 2)Bytheconceptionoflimitedstatepresentedinthispaper,thevalueofofbeamsstrengthened withCFRPsheetscouldbecompletelyequaltothecommonreinforcedconcretebeamsby partlyunloadingandcontrollingthestressleverindexofsteelbarsfl?,SOtheprocessofdesigncould besimplifiedfurther. 3)Sincethepropertyofhighstrengthofcarbonfiber,inordertomakefulluseofcarbonfiberthe CFRPsheetsmustbepre—stressedtosomeextent. 4)Thelimitedstresslevelindexfl6canbemaintainedbycontrollingtheprestressedtension stressindexofcarbonfiber,,andinsomecases,canbeassuredtobelowerthan3notbyunloading. Inthisway,thevalueofwouldbethesameasthegeneralreinforcedconcretebeam,SOtheprocedure ofdesignissimplified,too. References 1AASHTO.StandardSpecificationforHighwayBridges.AmericanAssociationofStateHighwayandTransportationOfficials,Washington D.C.US.1994 2ACICommittee318.BuildingCodeRequirementsforReinforcedConcreteandCommentary(ACI318—95/ACI318R一95),American ConcreteInstitute,Detroit.US.1995 碳纤维加固钢筋混凝土梁的界限 相对受压区高度研究 江世永,飞渭,李迎涛,彭飞飞,杜文龙2,王跃文2 (1.后勤工程学院军事土木工程系,重庆400041; 2.后勤工程学院军事建筑与环境工程系,重庆400041) 摘要根据材料的本构关系及平截面假定,结合预应力加固的概念推导出了碳纤维 加固钢筋混凝土梁时的三种不同的界限受压区高度,并给出了界限状态下钢筋,混凝土,碳纤 维片材的相应应力. 关键词:碳纤维;片材;加固;钢筋混凝土;梁;平衡配筋率 中图分类号:TU375.1文献标识码:A