土木工程专业毕业设计英文翻译教学教材.doc

Good is good, but better carries it.精益求精，善益求善。土木工程专业毕业设计英文翻译-CriticalReviewofDeflectionFormulasforFRP-RCMembersCarlosMota1;SandeeAlminar2;andDagmarSvecova31ResearchAssistant,Dept.ofCivilEngineering,Univ.ofManitoba,WinnipegMB,CanadaR3T5V6.2ResearchAssistant,Dept.ofCivilEngineering,Univ.ofManitoba,WinnipegMB,CanadaR3T5V6.3AssociateProfessor,Dept.ofCivilEngineering,Univ.ofManitoba,WinnipegMB,CanadaR3T5V6（correspondingauthor）.Abstract:Thedesignoffiber-reinforcedpolymerreinforcedconcreteFRP-RCistypicallygovernedbyserviceabilitylimitstaterequirementsratherthanultimatelimitstaterequirementsasconventionalreinforcedconcreteis.Thus,amethodisneededthatcanpredicttheexpectedserviceloaddeflectionsoffiber-reinforcedpolymerFRPreinforcedmemberswithareasonablyhighdegreeofaccuracy.Ninemethodsofdeflectioncalculation,includingmethodsusedinACI440.1R-03,andaproposednewformulainthenextissueofthisdesignguide,CSAS806-02andISISM03-01,arecomparedtotheexperimentaldeflectionof197beamsandslabstestedbyotherinvestigators.ThesemembersarereinforcedwitharamidFRP,glassFRP,orcarbonFRPbars,havedifferentreinforcementratios,geometricandmaterialproperties.Allmembersweretestedundermonotonicallyappliedloadinfourpointbendingconfiguration.TheobjectiveoftheanalysisinthispaperistodetermineamethodofdeflectioncalculationforFRPRCmembers,whichisthemostsuitableforserviceabilitycriteria.TheanalysisrevealedthatboththemodulusofelasticityofFRPandtherelativereinforcementratioplayanimportantroleintheaccuracyoftheformulas.CEDatabasesubjectheadings:Concrete,reinforced;Fiber-reinforcedpolymers;Deflection;Curvature;Codes;Serviceability;Statistics.IntroductionFiber-reinforcedpolymerFRPreinforcingbarsarecurrentlyavailableasasubstituteforsteelreinforcementinconcretestructuresthatmaybevulnerabletoattackbyaggressivecorrosiveagents.Inadditiontosuperiordurability,FRPreinforcingbarshaveamuchhigherstrengththanconventionalmildsteel.However,themodulusofelasticityofFRPistypicallymuchlowerthanthatofsteel.ThisleadstoasubstantialdecreaseinthestiffnessofFRPreinforcedbeamsaftercracking.Sincedeflectionsareinverselyproportionaltotheflexuralstiffnessofthebeam,evensomeFRPover-reinforcedbeamsaresusceptibletounacceptablelevelsofdeflectionunderserviceconditions.Hence,thedesignofFRPreinforcedconcrete（FRP-RC）istypicallygovernedbyserviceabilityrequirementsandamethodisneededthatcancalculatetheexpectedserviceloaddeflectionsofFRPreinforcedmemberswithareasonabledegreeofaccuracy.Theobjectiveofthispaperistopointouttheinconsistenciesinexistingdeflectionformulas.Onlyinstantaneousdeflectionswillbediscussedinthispaper.EffectiveMomentofInertiaApproachACI318（ACI1999）andCSAA23.3-94(CSA1998)recommendtheuseoftheeffectivemomentofinertia,Ie,tocalculatethedeflectionofcrackedsteelreinforcedconcretemembers.Theprocedureentailsthecalculationofauniformmomentofinertiathroughoutthebeamlength,anduseofdeflectionequationsderivedfromlinearelasticanalysis.Theeffectivemomentofinertia,Ie,isbasedonsemiempiricalconsiderations,anddespitesomedoubtaboutitsapplicabilitytoconventionalreinforcedconcretememberssubjectedtocomplexloadingandboundaryconditions,ithasyieldedsatisfactoryresultsinmostpracticalapplicationsovertheyears.InNorthAmericancodes,deflectioncalculationofflexuralmembersaremainlybasedonequationsderivedfromlinearelasticanalysis,usingtheeffectivemomentofinertia,Ie,givenbyBransonsformula(1965)（1）=crackingmoment;=momentofinertiaofthegrosssection;=momentofinertiaofthecrackedsectiontransformedtoconcrete;and=effectivemomentofinertia.ResearchbyBenmokraneetal.(1996)suggestedthatinordertoimprovetheperformanceoftheoriginalequation,Eq.(1)willneedtobefurthermodified.Constantstomodifytheequationweredevelopedthroughacomprehensiveexperimentalprogram.TheeffectivemomentofinertiawasdefinedaccordingtoEq.(2)ifthereinforcementwasFRP（2）FurtherresearchhasbeendoneinordertodefineaneffectivemomentofinertiaequationwhichissimilartothatofEq.(1),andconvergestothecrackedmomentofinertiaquickerthanthecubicequation.Manyresearchers(Benmokraneetal.1996;BrownandBartholomew1996;ToutanjiandSaafi2000)arguethatthebasicformoftheeffectivemomentofinertiaequationshouldremainasclosetotheoriginalBransonsequationaspossible,becauseitiseasytouseanddesignersarefamiliarwithit.Themodifiedequationispresentedinthefollowingequation:（3）AfurtherinvestigationoftheeffectivemomentofinertiawasperformedbyToutanjiandSaafi(2000).ItwasfoundthattheorderoftheequationdependsonboththemodulusofelasticityoftheFRP,aswellasthereinforcementratio.Basedontheirresearch,ToutanjiandSaafi(2000)haverecommendedthatthefollowingequationsbeusedtocalculatethedeflectionofFRPreinforcedconcretemembers:（4）WhereIfOtherwise（5）m=3where=reinforcementratio;=modulusofelasticityofFRPreinforcement;and=modulusofelasticityofsteelreinforcement.TheISISDesignManualM03-01（RizkallaandMufti2001）hassuggestedtheuseofaneffectivemomentofinertiawhichisquitedifferentinformcomparedtothepreviousequations.Itsuggestsusingthemodifiedeffectivemomentofinertiaequationdefinedbythefollowingequationtobeadoptedforfutureuse:（6）where=uncrackedmomentofinertiaofthesectiontransformedtoconcrete.Eq.（6）isderivedfromequationsgivenbytheCEB-FIPMC-90(CEB-FIP1990).Ghalietal.(2001)haveverifiedthatIecalculatedbyEq.（6）givesgoodagreementwithexperimentaldeflectionofnumerousbeamsreinforcedwithdifferenttypesofFRPmaterials.AccordingtoACI440.1R-03(ACI2003),themomentofinertiaequationforFRP-RCisdependentonthemodulusofelasticityoftheFRPandthefollowingexpressionforIeisproposedtocalculatethedeflectionofFRPreinforcedbeams:(7)where（8）where=reductioncoefficient;=bonddependentcoefficient（untilmoredatabecomeavailable,=0.5）;and=modulusofelasticityoftheFRPreinforcement.UponfindingthattheACI440.1R-03（ACI2003）equationoftenunderpredictedtheserviceloaddeflectionofFRPreinforcedconcretemembers,severalattemptshavebeenmadeinordertomodifyEq.（7）.Forinstance,Yostetal.（2003）claimedthattheaccuracyofEq.（7）primarilyreliedonthereinforcementratioofthemember.Itwasconcludedthattheformulacouldbeofthesameform,butthatthebonddependentcoefficient,hadtobemodified.Amodificationfactor,wasproposedinthefollowingform:（9）where=balancedreinforcementratio.TheACI440Committee(ACI2004)hasalsoproposedrevisionstothedesignequationinACI440.1R-03(ACI2003).ThemomentofinertiaequationhasretainedthesamefamiliarformasthatofEq.(7)intheserevisions.However,theformofthereductioncoefficient,tobeusedinplaceofEq.(8)wasmodified.Thenewreductioncoefficienthaschangedthekeyvariableintheequationfromthemodulusofelasticitytotherelativereinforcementratioasshowninthefollowingequation:（10）MomentCurvatureApproachThemomentcurvatureapproachfordeflectioncalculationisbasedonthefirstprinciplesofstructuralanalysis.Whenamomentcurvaturediagramisknown,thevirtualworkmethodcanbeusedtocalculatethedeflectionofstructuralmembersunderanyloadas（11）whereL=simplysupportedlengthofthesection;M/EI=curvatureofthesection;andm=bendingmomentduetoaunitloadappliedatthepointwherethedeflectionistobecalculated.AmomentcurvatureapproachwastakenbyFazaandGangaRao(1992),whodefinedthemidspandeflectionforfourpointbendingthroughtheintegrationofanassumedmomentcurvaturediagram.FazaandGangaRao(1992)madetheassumptionthatforfour-pointbending,thememberwouldbefullycrackedbetweentheloadpointsandpartiallycrackedeverywhereelse.Adeflectionequationcouldthusbederivedbyassumingthatthemomentofinertiabetweentheloadpointswasthecrackedmomentofinertia,andthemomentofinertiaelsewherewastheeffectivemomentofinertiadefinedbyEq.(1).ThroughtheintegrationofthemomentcurvaturediagramproposedbyFazaandGangaRao(1992),thedeflectionforfour-pointloadingisdefinedaccordingtothefollowingequation:（12）where=shearspan.Eq.(12)haslimitedusebecauseitisnotclearwhatassumptionsfortheapplicationoftheeffectivemomentofinertiashouldbeusedforotherloadcases.However,itworkedquiteaccuratelyforpredictingthedeflectionofthebeamstestedbyFazaandGangaRao(1992).TheCSAS806-02(CSA2002)suggeststhatthemomentcurvaturemethodofcalculatingdeflectioniswellsuitedforFRPreinforcedmembersbecausethemomentcurvaturediagramcanbeapproximatedbytwolinearregions:onebeforetheconcretecracks,andthesecondoneaftertheconcretecracks(Razaqpuretal.2000).Therefore,thereisnoneedforcalculatingcurvatureatdifferentsectionsalongthelengthofthebeamasforsteelreinforcedconcrete.Thereareonlythreepairsofmomentswithcorrespondingcurvaturethatdefinetheentiremomentcurvaturediagram:atcracking,immediatelyaftercracking,andatultimate.Withthisinmind,simpleformulaswerederivedfordeflectioncalculationofsimplysupportedFRPreinforcedbeamsandareusedinCSAS806-02(CSA2002).Thedeflectionduetofourpointbendingcanbefoundusingthefollowingequation:（13）VerificationofProposedMethodsTheninemethodsofdeflectioncalculationpresentedinthispaperwereusedtoanalyze197simplysupportedbeamsandslabstestedbyotherinvestigators.MaterialandgeometricpropertiesofthebeamsusedinthisinvestigationcouldnotbepublishedduetotheextentofthestatisticalsamplebutcanbefoundinMota(2005).Table1showstherangeofsomeoftheimportantpropertiesofthemembersinthedatabase.Allinformationusedintheanalysis,suchascrackingmomentandmodulusofelasticityofconcrete,wascalculatedusingCSAA23.3-94(CSA1998)basedoninputgivenbyresearchers.Tochecktheaccuracyofformulasdevelopedbyotherinvestigators,astatisticalanalysishasbeenperformedoneachoftheequationscomparingthecalculateddeflectiontotheexperimentaldeflectionatseveralgivenloadlevels.Itmustbenotedthatthedeflectionistypicallyonlycheckedattheserviceloadlevel.However,sincetheserviceloadcriteriaisonlyexplicitlystatedintheISISM03-01(RizkallaandMufti2001),itisunclearatthispointwhattheserviceloadlevelforeachcodeis.Thus,astatisticalanalysiswascarriedoutatbothlowloadsandatelevatedloadstoencompasstheentireloaddeflectioncurve,aswellasattheservicelevelgivenbyISISM03-01（RizkallaandMufti2001）.Thiswillallowthedesignerstochooseanaccurateformula,basedontheresultsoftheanalysis,attheloadlevelwhichmostcloselyresemblestheirserviceloadcriteria.Thestatisticalanalysiswasperformedbyapplyingalogtransformationtotheratiosoftheexperimentaltocalculateddeflectionratios.Alogtransformationwasemployedtogiveequalweighttothoseratioswhichwerebelowoneandthosewhichwereaboveone.Whenconsideringlong-termdeflection,perhapsonlytheaccuracyofshort-termdeflectionequationisrequiredsincethisnumberwillbefurthermodifiedbyothercoefficients.However,sinceonlyshort-termdeflectionhasbeenconsideredhere,thepredicteddeflectionshouldbealsoconsistentlyconservative.JournalofCompositesforConstruction,Vol.10,No.3,June1,2006.©ASCE,ISSN1090-0268/2006/3-183194.FRP-RC构件的挠度计算公式的评论卡洛斯.莫塔1;桑德.阿尔米纳尔2;达格玛.斯维克瓦31.加拿大曼尼托巴大学土木工程学院研究员2.加拿大曼尼托巴大学土木工程学院研究员2.加拿大曼尼托巴大学土木工程学院副教授（通讯作者）摘要：纤维复合材料包覆钢筋混凝土（FRP-RC）的设计通常是由正常使用极限状态的要求控制,而不是像由传统的钢筋混凝土极限状态要求控制。因此,需要一种可以预测FRP-RC构件正常使用的负载变形量的精确度的方法。计算挠度的九种方法,包括被测试人员用于下一期拟议的ACI440.1R-03和CSAS806-02和ISISM03-01中的新公式设计指南中的实验197个梁和板的挠度进行测试的方法。这些构件与芳纶玻璃钢钢筋、玻璃玻璃钢或碳纤维塑料筋配筋率、几何和材料属性不同。所有构件在四点弯曲加载配置下进行测试单调递增的应用荷载。本文分析的目的是确定FRP-RC构件挠度的计算方法,也是确定最适用的可靠性的准则。分析表明,FRP的弹性模量和相对配筋率在公式的准确性中发挥重要作用。关键词:钢筋混凝土,纤维增强聚合物;挠度弯曲;规范;适用性;统计数据。介绍：纤维复合材料钢筋目前可用来代替容易受到侵蚀性腐蚀破坏的钢筋混凝土结构。除了优越的耐用性,FRP钢筋强度远高于传统的低碳钢。然而,玻璃钢的弹性模量通常比钢低得多。这导致开裂后大量减少FRP加固的梁的刚度。由于变形量和梁的抗弯刚度是成反比的,甚至一些纤维复合材料超钢筋加固梁在使用情况下容易受到不可接受的水平偏转。因此,纤维复合材料包覆钢筋混凝土的设计通常是由正常使用极限状态的要求控制，需要一个方法,计算维复合材料构件的预期工作负载挠度的合理精确度。本文的目的是指出现有的挠度公式和论证所有的通用方程在计算FRP-RC构件有局限性。本文只讨论瞬时挠度。1.有效惯性矩法ACI318（ACI1999）和CSAa23.3-94（CSA1998）推荐使用有效惯性矩计算钢筋混凝土构件破坏时的挠度。这个过程需要一个适用于整个梁长的惯性矩计算,并使用由线性弹性分析所得的挠度方程。有效惯性矩是基于半经验的考虑,虽然当它受到复杂的加载和边界条件时，与传统钢筋混凝土构件有适用性问题,但是它在大多数实际应用中取得了令人满意的结果。在北美的规范中,构件的挠度计算公式主要是由线性弹性分析所得的方程,即使用由1965年的布兰森公式所得的有效惯性矩，(1)=开裂弯矩;=毛截面惯性矩,=破坏截面混凝土惯性矩;=有效截面惯性矩1996年Benmokrane的研究表明,为了提高起始方程的性能，需要进一步修改方程（1）。可以通过综合实验修改方程的常量。如果使用FRP加固构件，此时有效惯性矩可由方程（2）所得(2)研究人员做了进一步的研究,以便于确定一个类似于方程式（1）但更快捷的有效惯性矩方程。许多研究人员（Benmokrane等1996;布朗和巴塞洛缪1996;Toutanji和萨菲2000）认为有效惯性矩方程的基本形式应尽可能接近于原始的布兰森方程,为了它容易被使用而且设计师对它比较熟悉。修改后的方程如下:(3)Toutanji和萨菲（2000）对有效惯性矩进行了进一步的研究。他们发现方程的顺序取决于FRP的弹性模量和配筋率。根据Toutanji和萨菲（2000）的研究,他们建议使用下面的方程来计算FRP构件的挠度:(4)当若（5）则m=3=配筋率;=FRP的弹性模量;=钢筋的弹性模量。ISISDesignManualM03-01（里兹卡拉和穆夫提2001）建议使用完全不同于先前方程式的形式计算有效惯性矩。它建议今后使用进行修改过的有效惯性矩方程，如下所示:（6）=未破坏截面处的惯性矩方程式（6）取自CEB-FIPMC-90（CEB-FIP1990）加利等（2001）。通过用大量的梁来进行挠度试验，这些梁是由不同类型的FRP材料制作的，大量试验所得的，与方程式（6）所得的相同。根据ACI440.1R-03(ACI2003),FRP-RC的惯性矩方程取决于FRP的弹性模量和由计算的FRP加固梁的挠度方程，可由如下方程式得:(7)（8）=换算系数;=相关系数;=FRP的弹性模量。根据ACI440.1R-03（ACI2003）中的方程可得，在工作荷载作用下，FRP构件的挠度通常是可预测的,经过几次尝试对方程修改从而得到方程式（7）。例如,约斯特等（2003）认为,方程式（7）的准确性主要依赖于其构件的配筋率，并得出结论，方程式的形式不变,但应对进行修改，由此得出的方程式：（9）=平均配筋率ACI440委员会（ACI2004)对ACI440.1R-03(ACI2003)中的方程也进行了修改。惯性矩公式延用公式（7）,但对降低系数进行了修改，降低系数取决于弹性模量相对配筋率，见以下方程:（10）2.弯矩-曲率法弯矩-曲率法是进行结构分析中计算挠度的首选。在负载情况下，当弯矩-曲率图已知,虚拟的工作法可以用来计算结构构件的挠度（11）L=简支节的长度；M/EI=截面曲率；m=质量。弯矩-曲率法由法萨和GangaRao（1992）提出,并通过四点弯曲加载配置得出假定的曲率图，定义了跨中挠度。法萨和GangaRao（1992）对四点弯曲做出假想,在负荷点和部分破坏面作用下，构件将被破坏。因此通过惯性矩加载点和方程（1）中的有效惯性矩可导出挠度方程。法萨和GangaRao（1992）通过对曲率图分析，建立出下面的方程以求得四点加载的挠度:（12）=剪跨公式（12）具有局限性,因为当有效惯性矩应用于其他负载情况下时，假设条件尚不清楚。而法萨和GangaRao（1992）对梁的挠度实验的预测十分准确。CSAS806-02（CSA2002）表明，在计算挠度时弯矩-曲率法非常适合FRP构件，因为弯矩-曲率图分为两个线性近似区域:第一个是在混凝土破坏前的区域,第二个是混凝土破坏之后的区域。Razaqpur等（2000）因此,没有必要像钢筋混凝土一样计算梁不同部分的曲率。整个曲率图可由三对坐标组成:开裂时,开裂瞬间，开裂后。由此,可推导出用于计算简支FRP加固梁的挠度公式，并于2002年用于CSAS806-02（CSA2002）。使用下面方程可得出四点弯曲的挠度：（13）验证以上方法这篇文章提出计算挠度的9个方法被人们用来分析197个简支梁和板的试验。由于出版物中统计样本的范围有限，所以用于此试验的梁的材料和几何性质不能在出版物中找到,但可以在莫塔（2005）找到。表1给出了构件的一些重要性质的取值范围。例如分析开裂时混凝土的弹性模量时所用的数据是来自于CSAA23.3-94（CSA1998）中的数据,其中的数据为研究人员通过实验所得的。表1.构件性质的取值范围最小值性质最小值52026.225.51.823.380.0010.3（MPa）（GPa）（MPa）/d264017497.414.4064.420.0389.1为了检验公式的准确性,在多次给定负荷条件下，分析由挠度试验得出的挠度和由每个方程所计算的挠度作比较。必须注意的是只有在负载的情况下才能检验挠度。然而,由于负载标准只在ISISM03-01（里兹卡拉和穆夫提2001）中明确规定,故目前尚不清楚每个规范的标准。因此,运用统计分析也是有条件的，条件是：由低负荷和提高加载所形成的载荷-挠度曲线图,以及符合ISISM03-01（里兹卡拉和穆夫提2001）所给的负载范围。设计者可以根据自己的试验结果的分析，选择一个精确的公式。对记录进行分析，可由试验所得的比率得出计算挠度的比率，所得值为最大值与最小值的平均值。相比一直不变的挠度方程,也许只需要经常改变的挠度方程,因为要不断修改其他系数从而改进方程的精确性。然而,由于在这里只有考虑改变的着挠度,故应该保守的预测挠度。-