土木工程專業(yè)畢業(yè)設(shè)計(jì)-外文翻譯-將玻璃鋼外套用于鋼筋混凝土框架結(jié)構(gòu) 抗震加固的最優(yōu)設(shè)計(jì)

河北工業(yè)大學(xué)畢業(yè)設(shè)計(jì)(論文)外文資料翻譯學(xué)院：土木工程學(xué)院系（專業(yè)）：姓名：學(xué)號(hào)：外文出處：附件：1.外文資料翻譯譯文；2.外文原文。指導(dǎo)教師評(píng)語(yǔ)：簽名：年月日注：請(qǐng)將該封面與附件裝訂成冊(cè)。

附件1：外文資料翻譯譯文將玻璃鋼外套用于鋼筋混凝土框架結(jié)構(gòu)抗震加固的最優(yōu)設(shè)計(jì)主題：外包纖維增強(qiáng)高分子復(fù)合材料(玻璃鋼)是一項(xiàng)正在完善的為強(qiáng)化/改造鋼筋混凝土(RC)結(jié)構(gòu)的技術(shù),尤其玻璃鋼與鋼筋混凝土柱隔離外套已經(jīng)被證明能非常有效地提高了柱的強(qiáng)度和韌性,成為的鋼筋混凝土結(jié)構(gòu)抗震加固的關(guān)鍵技術(shù)但是大量的研究?jī)H限于鋼筋混凝土柱的力學(xué)性能、很少有研究含有FRP約束柱的鋼筋混凝土框架的力學(xué)性能在用玻璃鋼對(duì)鋼筋混凝土框架結(jié)構(gòu)進(jìn)行抗震加固時(shí),一個(gè)問(wèn)題是框架結(jié)構(gòu)的應(yīng)力,另外一個(gè)重要問(wèn)題就是如何利用最少的材料及其用費(fèi)達(dá)到所需的抗震性能.從這兩個(gè)問(wèn)題出發(fā),本文討論基于抗震設(shè)計(jì)性能出發(fā)的用玻璃鋼外套加固鋼筋混凝土建筑物優(yōu)化技術(shù).我們采取玻璃鋼外套厚度作為隔離柱設(shè)計(jì)變量因此,體積最小、材料成本最低就是是優(yōu)化設(shè)計(jì)目標(biāo)漂流的勸服是明確表示在使用的玻璃上漿變數(shù),虛功原理泰勒級(jí)數(shù)的逼近.？？？？？最優(yōu)準(zhǔn)則(OC)的辦法是采用非線性地震側(cè)移的設(shè)計(jì)問(wèn)題.本文通過(guò)實(shí)例介紹和討論,展示了該程序.關(guān)鍵詞:約束；纖維增強(qiáng)聚合物(玻璃鋼);性能化設(shè)計(jì);pushover分析;鋼筋混凝土;抗震加固;結(jié)構(gòu)優(yōu)化1．介紹在重力荷載下按舊規(guī)范設(shè)計(jì)裝裱現(xiàn)有鋼筋混凝土(RC)結(jié)構(gòu)抗震性能或在最近的地震證明是不夠的，橫向承載能力有限,延性差[1]這種結(jié)構(gòu)具有一種內(nèi)在的抵抗橫向載荷能力低,地震期間造成很大塑性變形而且,結(jié)構(gòu)特點(diǎn)是強(qiáng)梁弱柱，導(dǎo)致在地面強(qiáng)烈震動(dòng)脆性破壞或柱側(cè)向傾倒[2]。為了減少結(jié)構(gòu)在強(qiáng)震倒塌的風(fēng)險(xiǎn),這就迫切需要提升現(xiàn)有的鋼筋混凝土建筑物的抗震性能,以符合現(xiàn)行抗震設(shè)計(jì)規(guī)范.鋼筋混凝土建筑物的抗震加固的缺陷可能涉及的地區(qū)加強(qiáng)針對(duì)性,增強(qiáng)實(shí)力剛度和/或提高結(jié)構(gòu)延性、或提供多余承載機(jī)制.一般來(lái)說(shuō),各種技巧可以結(jié)合運(yùn)用在結(jié)構(gòu)的抗震加固.具體加固改造策略選擇的目標(biāo)應(yīng)該是基于經(jīng)濟(jì)考慮[1]加固設(shè)計(jì)應(yīng)以在指定震動(dòng)下,確保沒(méi)有損壞超過(guò)確定的程度或建筑物沒(méi)有倒塌為適當(dāng)?shù)臉?biāo)準(zhǔn)[3]另外,實(shí)施的費(fèi)用是業(yè)主和工程師都十分關(guān)心的[4]整個(gè)鋼筋混凝土框架抗震加固策略必須綜合考慮的一系列關(guān)鍵問(wèn)題。這些問(wèn)題包括加強(qiáng)橫梁,柱和梁柱節(jié)點(diǎn)脆性破壞模式等,用玻璃鋼補(bǔ)強(qiáng)外部或其他適當(dāng)方式以防止象剪切破壞的脆性破壞。一旦這些脆性破壞模式確定了，進(jìn)行抗震加固的設(shè)計(jì)以滿足地震強(qiáng)度要求，這取決于該柱下軸壓和彎曲下的承載力和延性。改造柱是最廣泛使用的提高鋼筋混凝土框架結(jié)構(gòu)抗震等級(jí)的辦法改善柱子的力學(xué)性能通常涉及提高其強(qiáng)度,韌性、剛度、在大多數(shù)情況綜合這些參數(shù).改造柱子常規(guī)措施包括加裝鋪混凝土或鋼套管.最近技術(shù)是利用纖維增強(qiáng)聚合物(玻璃鋼)外套來(lái)限制柱側(cè)向變形[5][6]在這種外套,纖維唯一或主要在法向約束混凝土,其抗壓實(shí)力與最終壓應(yīng)變明顯提高[5]、[6]、[7].傳統(tǒng)工藝相比,玻璃鋼套管容易和更快地實(shí)施幾乎不增加自重,對(duì)現(xiàn)行體制沖擊微小并且抗腐蝕.結(jié)果，玻璃鋼套管已被發(fā)現(xiàn)比傳統(tǒng)技術(shù)是一個(gè)更具成本效益的方法,因而,在許多情況被廣泛接受[5]、[6]和[8].用玻璃鋼限制鋼筋混凝土柱來(lái)對(duì)鋼筋混凝土框架結(jié)構(gòu)抗震加固,除了加固結(jié)構(gòu)的應(yīng)力外、一個(gè)重要問(wèn)題就是如何利用最少的玻璃鋼材料達(dá)到所需的抗震等級(jí).這兩個(gè)問(wèn)題出發(fā),本文為優(yōu)化技術(shù)性能的抗震設(shè)計(jì)的鋼筋混凝土建筑物加裝玻璃鋼框.玻璃鋼外套的厚度在柱加固設(shè)計(jì)視為變量，而玻璃鋼的最總材料成本(即費(fèi)用等方面,不包括交通)作為一個(gè)統(tǒng)一的延性需求的彈性設(shè)計(jì)目標(biāo)優(yōu)化設(shè)計(jì)側(cè)移的過(guò)程.2．現(xiàn)有最優(yōu)的抗震設(shè)計(jì)傳統(tǒng)抗震設(shè)計(jì)方法對(duì)現(xiàn)有建筑抗震加固,類似用傳統(tǒng)方法新結(jié)構(gòu)進(jìn)行抗震設(shè)計(jì),都假設(shè)彈性結(jié)構(gòu)在甚至是嚴(yán)重地震下反應(yīng)是彈性的，[9].基于地震反應(yīng)的抗震設(shè)計(jì),看來(lái)是抗震設(shè)計(jì)規(guī)范未來(lái)的發(fā)展方向,直接指出在結(jié)構(gòu)在地震作用下彈性變形是非彈性的[3],[9],[10].在評(píng)估框架結(jié)構(gòu)抗震性能的非線性后、Pushover分析日益被接納作為性能化設(shè)計(jì)程序.Pushover分析是一個(gè)簡(jiǎn)化的、靜態(tài)的、非線性的分析，在這個(gè)過(guò)程中預(yù)定的地震載荷模式逐步加到向結(jié)構(gòu),直到塑料破壞機(jī)制形成，結(jié)構(gòu)崩潰.這種方法采用理論分析,隨菏載不斷增加，裂縫隨塑性變化在框架構(gòu)件邊緣形成塑性鉸.橫向側(cè)移性能是多層建筑一項(xiàng)重要指標(biāo),用來(lái)衡量不論在現(xiàn)有抗震設(shè)計(jì)方法還是當(dāng)前的新發(fā)展表現(xiàn)為設(shè)計(jì)做法設(shè)計(jì)的建筑物結(jié)構(gòu)性和非結(jié)構(gòu)性部件損壞程度。[1],[3],[9],[10]和[11].考慮在橫向地震荷載下多層構(gòu)件彈性、非彈性變化對(duì)構(gòu)件進(jìn)行經(jīng)濟(jì)設(shè)計(jì)是相當(dāng)有難度的、具有挑戰(zhàn)性的任務(wù)[12]橫向側(cè)移設(shè)計(jì)尤為艱巨,因?yàn)樗枰紤]在嚴(yán)重的地震中適當(dāng)分配各構(gòu)件剛度而,以及各構(gòu)件塑性內(nèi)力重分布.在缺乏自動(dòng)優(yōu)化技術(shù)情況下、鋼筋的等級(jí)的數(shù)量是基于直覺(jué)和經(jīng)驗(yàn)來(lái)設(shè)計(jì)的[12].需要一個(gè)優(yōu)化設(shè)計(jì)方法是顯而易見(jiàn)的,過(guò)去數(shù)幾十年間動(dòng)態(tài)結(jié)構(gòu)優(yōu)化一直積極研究的課題。[12]、〔13〕、〔14〕、〔15〕、〔16〕、〔17〕、〔18〕.近年來(lái),許多研究已經(jīng)致力于專門的優(yōu)化性能設(shè)計(jì)方法.尤其是成與鄒[12],鄒、鄒、陳[16][17]和[18]提出了基于彈性、非彈性側(cè)移性能的鋼筋混凝土建筑物抗震設(shè)計(jì)優(yōu)化技術(shù).他們發(fā)現(xiàn)自動(dòng)優(yōu)化技術(shù)是用最價(jià)廉的設(shè)計(jì)實(shí)現(xiàn)了最佳抗震性能..優(yōu)化現(xiàn)有結(jié)構(gòu)抗震加固設(shè)計(jì)的具體研究太有限了.馬丁-拉、羅梅羅[19]提出一個(gè)簡(jiǎn)單的解決方法,從而優(yōu)化了非線性粘性流體阻尼改造框架地震彎矩.就作者所知，改造策略是用玻璃鋼外套限制隔離柱以對(duì)鋼筋混凝土結(jié)構(gòu)抗震加固，目前還沒(méi)有做過(guò)這方面優(yōu)化設(shè)計(jì)的研究.目前,用玻璃鋼限制隔離柱性能化改造鋼筋混凝土結(jié)構(gòu)設(shè)計(jì)只能基于主觀經(jīng)驗(yàn)和大量運(yùn)算工作的試錯(cuò)法設(shè)計(jì).最后的設(shè)計(jì)可能過(guò)于保守,改造費(fèi)用昂貴造成不必要的干預(yù)和抗震性能比降低.本文講述考慮側(cè)移性能對(duì)建筑物鋼筋混凝土框架抗震加固設(shè)計(jì)優(yōu)化技術(shù)，填補(bǔ)了現(xiàn)有研究的一項(xiàng)空白.加固策略是基于用玻璃鋼限制柱的兩端,即在塑性鉸潛在形成區(qū)域加固[20],[21],[22]和[23].優(yōu)化設(shè)計(jì)過(guò)程是一個(gè)已從原先成和鄒[12],鄒、、陳[16][17][18]制定的抗震設(shè)計(jì)體系適度修正而來(lái)的.3.進(jìn)一步的設(shè)計(jì)優(yōu)化問(wèn)題圖1、所示.玻璃鋼薄板用纖維圈從法向約束柱.\o"DisplayFullSizeversionofthisimage(11K)-Opensnewwindow"DisplayFullSizeversionofthisimage(11K)圖1，柱抗震加固的玻璃鋼外套約束區(qū)域這項(xiàng)研究認(rèn)為,一個(gè)鋼筋混凝土框架結(jié)構(gòu)潛在塑膠鉸(假定每一個(gè)構(gòu)件端部都存在一個(gè)鉸)Nc柱、Nb梁,2(Nc

+

Nb)假定柱截面是長(zhǎng)方形,寬度Bi和高度Di.由玻璃鋼約束柱的潛在塑性鉸區(qū)而取得抗震加固效果，如圖.1所示.在這項(xiàng)研究中只有約束柱塑性鉸玻璃外套的厚度被作為設(shè)計(jì)變量.這種方法是現(xiàn)實(shí)的,同時(shí)也降低了設(shè)計(jì)的管理規(guī)模.外套所需的厚度首先滿足該構(gòu)件的抗剪承載力[5]、但本文的優(yōu)化設(shè)計(jì)程序中都沒(méi)有討論這些厚度.在實(shí)際執(zhí)行的抗震加固策略時(shí),對(duì)任何一個(gè)柱子潛在的塑性鉸區(qū)玻璃鋼外套總厚度的應(yīng)該是3種失效模式分別需要厚度的總和,[5].鑒于現(xiàn)階段知識(shí)技術(shù)水平，這是一個(gè)保守而務(wù)實(shí)的考慮.在優(yōu)化過(guò)程設(shè)計(jì)變量,是厚度ti、即約束每個(gè)構(gòu)件塑性鉸的玻璃外套的厚度.對(duì)于某一類玻璃鋼材料如果拓?fù)浣Y(jié)構(gòu)是預(yù)先假定的每柱子有同樣厚度的玻璃鋼外套而同樣長(zhǎng)度的兩端約束區(qū)域,用于約束柱玻璃鋼復(fù)合材料的總成本由下式給出：(1)其中wi為玻璃鋼復(fù)合材料成本系數(shù)、wi

=

4Lci(Bi

+

Di)ρ;ρ為單位體積的玻璃鋼復(fù)合材料的費(fèi)用;Lc,是原來(lái)每個(gè)柱端部約束區(qū)域的長(zhǎng)度,即最大的可能塑性鉸長(zhǎng)度、0.5D和構(gòu)件長(zhǎng)度12.5%中的較大值[5][21].在實(shí)際執(zhí)行過(guò)程中，與原先約束區(qū)域毗鄰的二級(jí)約束區(qū)也應(yīng)約束,但玻璃外套厚度減至原約束區(qū)的一半.本文沒(méi)有進(jìn)一步考慮二級(jí)約束區(qū)所需玻璃鋼材料費(fèi)用金額.附件2：外文原文Optimalperformance-baseddesignofFRPjacketsforseismicretrofitofreinforcedconcreteframesAbstractExternalbondingoffiber-reinforcedpolymer(FRP)compositesisnowawell-establishedtechniqueforthestrengthening/retrofitofreinforcedconcrete(RC)structures.Inparticular,confinementofRCcolumnswithFRPjacketshasproventobeveryeffectiveinenhancingthestrengthandductilityofcolumns,andhasbecomeakeytechniquefortheseismicretrofitofRCstructures.DespitethelargeamountofresearchonthebehaviorofRCcolumnsconfinedwithFRP,littleresearchhasbeenconductedonthebehaviorofRCframeswithFRP-confinedcolumns.FortheseismicretrofitofRCframeswithFRP,apartfromthestructuralresponseofaretrofittedframe,animportantissueishowtodeploytheleastamountoftheFRPmaterialtoachievetherequiredupgradeinseismicperformance.Withthesetwoissuesinmind,thispaperpresentsanoptimizationtechniquefortheperformance-basedseismicFRPretrofitdesignofRCbuildingframes.ThethicknessesofFRPjacketsusedfortheconfinementofcolumnsaretakenasthedesignvariables,andminimizingthevolumeandhencethematerialcostoftheFRPjacketsisthedesignobjectiveintheoptimizationprocedure.ThepushoverdriftisexpressedexplicitlyintermsoftheFRPsizingvariablesusingtheprincipleofvirtualworkandtheTaylorseriesapproximation.Theoptimalitycriteria(OC)approachisemployedforfindingthesolutionofthenonlinearseismicdriftdesignproblem.Anumericalexampleispresentedanddiscussedtodemonstratetheeffectivenessoftheproposedprocedure.Keywords:Confinement;Fiber-reinforcedpolymer(FRP);Performance-baseddesign;Pushoveranalysis;Reinforcedconcrete;Seismicretrofit;Structuraloptimization

1.IntroductionTheseismicperformanceofexistingreinforcedconcrete(RC)framedstructuresdesignedforgravityloadsoraccordingtooldcodeshasproventobepoorduringrecentearthquakes,duetoinsufficientlateralload-carryingcapacityandlimitedductility[1].Suchstructurespossessaninherentlylowresistancetohorizontalloads,resultinginlargeinelasticdeformationsduringearthquakes.Moreover,theirstructuralbehaviorisoftheweakcolumn/strongbeamtype,whichresultsinbrittlesoft-storyorcolumnsidewaycollapsemechanismsduringstronggroundmotions[2].Inordertoreducetheriskofstructuralcollapsesduringstrongearthquakes,thereisanurgentneedtoupgradeexistingRCbuildingstomeettherequirementsofcurrentseismicdesigncodes.TheseismicretrofitofanRCbuildingmayinvolvetargetedstrengtheningofdeficientregions,toincreasethestrength,stiffnessand/orductilityofthestructure,ortoprovideredundantload-carryingmechanisms.Ingeneral,acombinationofdifferenttechniquesmaybeemployedintheseismicretrofitofastructure.Theselectionofaspecificretrofitstrategyshouldbebasedontheretrofitobjectivesaswellasoneconomicconsiderations[1].Theretrofitdesignshouldbebasedonappropriateperformancecriteriatoensurethatadefinedlevelofdamageisnotexceededorthecollapseofthebuildingispreventedduringspecifiedgroundmotions[3].Inaddition,thecostofimplementationisofgreatconcerntobothbuildingownersandpracticingengineers[4].TheoverallseismicretrofitstrategyforanRCframemustconsideranumberofkeyissuesinanintegratedmanner;theseissuesincludethestrengtheningofbeams,columnsandbeam-columnjointstopreventbrittlefailuremodessuchasshearfailuretobecomecriticalusingexternalFRPreinforcementorotherappropriatemethods。Oncethesebrittlefailuremodesaresuppressed,theseismicretrofitdesigntoenabletheframetosatisfyspecificdemandsofanearthquakedependsonthestrengthandductilityofthecolumnsundercombinedaxialcompressionandbending.RetrofitofthecolumnsisoneofthemostwidelyusedseismicupgradingapproachesforRCframes，Improvingthecolumnbehaviortypicallyinvolvesincreasingitsstrength,ductility,stiffnessorinmostcasesacombinationoftheseparameters.ConventionalretrofitmeasuresforcolumnsincludeRCoverlaysorsteeljacketing.Amorerecenttechniqueistheuseoffiber-reinforcedpolymer(FRP)jacketstoconfinecolumns[5]and[6].Insuchjackets,thefibersareorientedonlyorpredominantlyinthehoopdirectiontoconfinetheconcretesothatbothitscompressivestrengthandultimatecompressivestrainaresignificantlyenhanced[5],[6]and[7].Comparedtoconventionaltechniques,FRPjacketingiseasierandquickertoimplement,addsvirtuallynoweighttotheexistingstructure,hasminimalaestheticimpactandiscorrosion-resistant.Asaresult,FRPjacketinghasbeenfoundtobeamorecost-effectivesolutionthanconventionaltechniquesinmanysituationsandhasthusbeenwidelyaccepted[5],[6]and[8].FortheseismicretrofitofRCframesemployingFRPconfinementofRCcolumns,apartfromthestructuralresponseofaretrofittedframe,animportantissueishowtodeploytheleastamountoftheFRPmaterialtoachievetherequiredupgradeinseismicperformance.Withthesetwoissuesinmind,thispaperpresentsanoptimizationtechniquefortheperformance-basedseismicFRPretrofitdesignofRCbuildingframes.ThethicknessesofFRPjacketsinthecolumnsareconsideredasthedesignvariables,whiletheleasttotalmaterialcost(i.e.costsassociatedwithotheraspectssuchastransportationarenotincluded)ofFRPandauniformductilitydemandaretakenasdesignobjectivesoftheinelasticdriftdesignoptimizationprocess.2.Existingworkonoptimalperformanced-basedseismicdesignTraditionaldesignapproachesforseismicretrofit,similartotraditionalapproachesforseismicdesignofnewstructures,assumethatstructuresrespondelasticallyeventosevereearthquakes[9].Performance-basedseismicdesign,whichappearstobethefuturedirectionofseismicdesigncodes,directlyaddressesinelasticdeformationsinducedinstructuresbyearthquakes[3],[9]and[10].Inassessingthenonlinearseismicbehaviorofframedstructures,pushoveranalysishasbeenincreasinglyacceptedaspartoftheperformance-baseddesignprocedure.Pushoveranalysisisasimplified,static,nonlinearprocedureinwhichapredefinedpatternofearthquakeloadsisappliedincrementallytothestructureuntilaplasticcollapsemechanismisreached.Thismethodofanalysisgenerallyadoptsalumped-plasticityapproachthattracksthespreadingofinelasticitythroughtheformationofplastichingesattheendsoftheframeelementsduringtheincrementalloadingprocess.Thelateraldriftperformanceofamulti-storybuildingisanimportantindicatorthatmeasuresthelevelofdamagetothestructuralandnon-structuralcomponentsofabuildingincurrentseismicdesignapproachesandalsointhenewlydevelopedperformance-baseddesignapproach[1],[3],[9],[10]and[11].Theeconomicdesignofstructuralelementsforvariouslevelsofelasticandinelasticlateraldriftperformanceundermultiplelevelsofearthquakeloadsisgenerallyaratherdifficultandchallengingtask[12].Lateraldriftdesignisparticularlychallengingasitrequirestheconsiderationofanappropriatestiffnessdistributionofallstructuralelementsand,inasevereseismicevent,alsotheoccurrenceandredistributionofplasticityintheelements.Structuralengineersarethusfacedwiththeproblemofefficientlydistributingmaterialsthroughoutthestructuretooptimizetheelasticandinelasticdriftresponsesofstructures.Inabsenceofanautomatedoptimizationtechnique,sizesofmembersandamountsofsteelreinforcementaredesignedbytrial-and-errormethodsbasedonintuitionandexperience[12].Theneedforanoptimaldesignapproachisthusclear,andstructuraloptimizationofdynamicallyexcitedstructureshasbeenanactiveresearchtopicforthepastfewdecades[12],[13],[14],[15],[16],[17]and[18]Inrecentyears,muchresearchhasbeendevotedtotheoptimizationoftheemergingperformance-baseddesignapproach.Inparticular,ChanandZou[12],Zou[16]andZouandChan[17]and[18]proposedanoptimizationtechniqueforelasticandinelasticdriftperformance-basedseismicdesignofRCbuildings.Theyshowedthatanautomatedoptimizationtechniqueiscapableofachievingthebestseismicdriftperformancecombinedwiththeleastexpensivedesign.Specificresearchontheoptimizationofseismicretrofitdesignofexistingstructureshasbeenmuchmorelimited.Martinez-RodrigoandRomero[19]proposedasimplemethodologyleadingtoanoptimalsolutionwithnonlinearviscousfluiddampersfortheseismicretrofitofmoment–resistingframes.Tothebestoftheauthors’knowledge,noresearchhasbeenconductedontheoptimizationofseismicretrofitdesignofRCstructureswhentheretrofitstrategyistheconfinementofcolumnswithFRPjackets.Atthepresent,theperformance-basedretrofitdesignofRCstructureswithFRPconfinementofcolumnscanonlybeconductedbytrial-and-errormethodsbasedonsubjectiveexperienceandmuchcomputationaleffort.Thefinaldesignmaybeoverlyconservative,resultinginanunnecessarilyexpensiveretrofitinterventionandlessthanoptimalseismicperformance.Theoptimizationtechniqueforthedriftperformance-basedseismicretrofitdesignofframedRCbuildingspresentedinthispaperthereforefillsasignificantgapinexistingresearch.TheretrofitstrategyisbasedontheFRPconfinementofcolumnsatthetwoends,heregionsofpotentialplastichingeformation[20],[21],[22]and[23].TheoptimaldesignprocedureisonethathasbeenappropriatelymodifiedfromthatpreviouslydevelopedbyChanandZou[12],Zou[16]andZouandChan[17]and[18]fortheseismicdesignofnewstructures.3.Optimalseismicretrofitdesignproblem3.1.ImplicitdesignoptimizationproblemAsshowninFig.1,FRPsheetsforconfinementofcolumnsarewrappedaroundcolumnswiththefibersorientedinthehoopdirection.Theconsequentincreasesintheaxialcompressivestrengthandtheultimateaxialstrainoftheconcretecoredependonseveralfactors,includingthethickness,tensilestrengthandelasticmodulusoftheconfiningFRPjacket,unconfinedconcretestrengthandcross-sectionalshapeofthecolumn[7].Forgivenmaterialpropertiesandcross-sectionaldimensions,thethicknessoftheFRPjacketgovernsthestrengthandductilityoftheconfinedcross-section.\o"DisplayFullSizeversionofthisimage(11K)-Opensnewwindow"DisplayFullSizeversionofthisimage(11K)Fig.1.

FRP-jacketedregionsofcolumnforseismicretrofit.ThisstudyconsidersanRCframedstructurewithNccolumns,Nbbeams,andhence2(Nc

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Nb)potentialplastichinges(assumingonehingeateachendofeachmember).Thecolumnisassumedtohavearectangularcross-section,withwidthBianddepthDi.SeismicretrofitisachievedwithFRPconfinementofthepotentialplastichingeregionsofeachcolumn,asshowninFig.1.OnlythethicknessesoftheFRPjacke