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英文原文:RehabilitationofrectangularsimplysupportedRCbeamswithsheardeficienciesusingCFRPcompositesAhmedKhalifaa,*,AntonioNannibaDepartmentofStructuralEngineering,UniversityofAlexandria,Alexandria21544,EgyptbDepartmentofCivilEngineering,UniversityofMissouriatRolla,Rolla,MO65409,USAReceived28April1999;receivedinrevisedform30October2001;accepted10January2002AbstractThepresentstudyexaminestheshearperformanceandmodesoffailureofrectangularsimplysupportedreinforcedconcrete(RC)beamsdesignedwithsheardeficiencies.Thesememberswerestrengthenedwithexternallybondedcarbonfiberreinforcedpolymer(CFRP)sheetsandevaluatedinthelaboratory.Theexperimentalprogramconsistedoftwelvefull-scaleRCbeamstestedtofailinshear.Thevariablesinvestigatedwithinthisprogramincludedsteelstirrups,andtheshearspan-to-effectivedepthratio,aswellasamountanddistributionofCFRP.TheexperimentalresultsindicatedthatthecontributionofexternallybondedCFRPtotheshearcapacitywassignificant.Theshearcapacitywasalsoshowntobedependentuponthevariablesinvestigated.Testresultswereusedtovalidateasheardesignapproach,whichshowedconservativeandacceptablepredictions.eq\o\ac(○,C)2002ElsevierScienceLtd.Allrightsreserved.Keywords:Rehabilitation;Shear;Carbonfiberreinforcedpolymer1.IntroductionFiberreinforcedpolymer(FRP)compositesystems,composedoffibersembeddedinapolymericmatrix,canbeusedforshearstrengtheningofreinforcedcon-crete(RC)members[1–7].ManyexistingRCbeamsaredeficientandinneedofstrengthening.TheshearfailureofanRCbeamisclearlydifferentfromitsflexuralfailure.Inshear,thebeamfailssuddenlywithoutsufficientwarninganddiagonalshearcracksareconsid-erablywiderthantheflexuralcracks[8].Theobjectivesofthisprogramwereto:1.InvestigateperformanceandmodeoffailureofsimplysupportedrectangularRCbeamswithsheardeficien-ciesafterstrengtheningwithexternallybondedCFRPsheets.2.Addressthefactorsthatinfluenceshearcapacityofstrengthenedbeamssuchas:steelstirrups,shearspan-to-effectivedepthratio(a/dratio),andamountanddistributionofCFRP.3.Increasetheexperimentaldatabaseonshearstrength-eningwithexternallybondedFRPreinforcement.4.Validatethedesignapproachpreviouslyproposedbytheauthors[9].Fortheseobjectives,12full-scale,RCbeamsdesignedtofailinshearwerestrengthenedwithdifferentCFRPschemes.Thesemembersweretestedassimplebeamsusingafour-pointloadingconfigurationwithtwodifferenta/dratios.2.Experimentalprogram獨(dú)2.1.踩Tes族tsp挑ecim屋ens究and冰mate辛rial帆s丘Twel終vef徐ull-蹤scal怖ebe碌ams蛾peci怒mens跌wit永ha楊tota茄lsp扮ano槽f30如50m林m.a訪nda軋rec菊tang故ular搭cro乖ss-s君ecti駛ono赴f15惜0-mm涼-wid規(guī)ean歌d30鉆5-mm第-dee慣pwe遺ret檢este滑d.T掙hes聲peci懼mens科wer貫egr姓oupe邁din梢tot祖wom痛ain格seri纖esd勢esig沾nate心dSW攏and鑼SO介depe臂ndin椒gon蜘the蜂pre緞senc躍eof嫁ste際els忍tirr梅ups種int浪hes雙hear釀spa錄nof迎int賄eres狗t.薪Seri常esS餃Wco挽nsis葬t(yī)ed低off母our柴spec耕imen等s.T印hed某etai韻lsa翅ndd欠imen長sion坡sof賤the椒spe許cime貼nsd陜esig品nate嗚dse爛ries旅SW忠are相illu襯stra檔ted賢inF艦ig.渾1a.去Int平his繼seri石es,史four棗32-益mms活teel產(chǎn)bar板swe漸reu球sed言asl移ongi筆tudi達(dá)nal梢rein石forc勝emen雨twi圈tht梅woa兇tto命pan哥dtw害oat刑bot靜tom酒face惹of滔the怠cros斯s-se欲ctio氧nto約ind江uce廊ash鬧ear攀fail耳ure.譽(yù)The充spe盼cime楚nsw愧ere宅rein綿forc妥edw記ith盡10-m咳mst撇eel刻stir你rups驗(yàn)thr應(yīng)ough感out銹thei哪ren柜tire擱spa掛n.T巖hes智tirr錢ups度spac殘ing界int矮hes噸hear遙spa盈nof話int獸eres蹄t,r偵ight拌hal男f,w夜ass光elec南ted排toa代llow劃fai唱lure血in窮that許spa生n.鈔Seri布esS罵Oco懲nsis裳ted凈ofe斯ight濱bea浩msp墾ecim祥ens,雀whi臘chh莖adt季hes維ame慌cros若s-se巧ctio子ndi墓mens胡ion葬and盜long震itud礙inal冊ste或elr艇einf叉orce舉ment煉as失for負(fù)seri炭esS脂W.N止ost逮irru搖psw榆ere賣prov夢ided撇in身the姓test淡h(huán)al可fsp禿ana球sil凍lust拜rate竹din做Fig爭.1b拿.坡Each輛mai半nse析ries答(i.撫e.s滾erie廟sSW晃and某SO)撲was陣sub書divi贈ded靜into倒two多sub牙grou忍psa知ccor笛ding跟to貌shea泄rsp毅an-t晨o-ef我fect有ive縮dept戚hra泰tio.釀Thi釣swa翼sse蒸lect肺edt非obe豈a/d體=3腸and酷4,姜resu喊l(fā)tin拌gin灣the柄fol骨lowi萄ngf敞our約subg伏roup喪s:S標(biāo)W3;S省W4;秘SO3;宇and生SO4蕩.把The侍mech呼anic索alp足rope叔rtie根sof描the烏mat病eria距l(xiāng)su應(yīng)sed津for員manu昂fact移urin秀gth喜ete住sts他peci屋mens花are際lis腦ted躲inT反able杠1.F誦abri外cati對ono攝fth眾esp膜ecim簡ens胃incl館udin默gsu芬rfac僻epr眉epar智atio愿nan郊dCF始RPi卸nsta森llat毒ion害isd伯escr欄ibed揉els洲ewhe頭re[息10].械Tabl撓e1飽2.2.姓Str圈engt岸heni悄ngs授chem竭es嫁One版spec必imen黎fro揀mea傭chs殺erie那s(S根W3-1套,SW頓4-1,說SO3懼-1a縮ndS殊O4-1省)wa哄sle父ftw斥itho嚼uts籍tren務(wù)gthe筍ning六as雙aco輸ntro駁lsp錫ecim狠en,編wher肺eas吐eigh御tbe拳ams賢peci監(jiān)mens叫wer披est廢reng議then工edw饅ith腸exte局rnal景l(fā)yb錯onde稼dCF誠RPs未heet扯sfo歪llow燒ing斬thre芹edi侄ffer伯ent燕sche訪mes沈asi符llus季trat傘edi場nFi勤g.2痰.歪Ins品erie估sSW腰3,s蝶peci扭men汪SW3-撈2wa斬sst盤reng霉then我edw裳ith擇two皇CFRP桐pli題esh唇avin轎gpe管rpen斯dicu益lar奴fibe店rdi刑rect慚ions曬(90幫°/0°耍).T丹hef及irst式ply敬was演att貪ache怨din驢the豆for枯mof持con菠tinu暖ous草U-wr顫apw核ith帽the退fibe計(jì)rdi隙rect簡ion爽orie客nted醫(yī)per捎pend殊icul粥art翻oth起elo耳ngit憐udin容ala磨xis赴oft蛙hes做peci恨men丑(90°省).貪The斬seco臨ndp涂lyw而asb焰onde促don刮the種two討sid膛eso圍fth伙esp傭ecim寶enw嫁ith緣the猜fibe悔rdi憤rect泳ion提para獻(xiàn)llel植to愈the唇beam腸axi論s助(縮0主°眉)氏.Thi鏟spl攏y[i位.e.賞0°pl既y]w角ass糧elec泡ted大toi透nves擺tiga腎tet己hei丈mpac遮tof肌add掏itio漸nal儲hori白zont讓alr羊estr虛aint敵on位shea買rst沾reng臉th.燈Ins逢erie達(dá)sSW嚴(yán)4,s輩peci佩men回SW4-塑2wa虛sst溝reng向then養(yǎng)edw飛ith計(jì)two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upp戶ort,砍res站pect款ivel綱y.F辯ig.哭10s煌hows忍tha察tth付eCF趙RPs耀trai各nwa叉sze弟rop珠rior漂to日diag屑o(jì)nal目cra鎮(zhèn)ckf脫orma污tion順,th考en馳incr吊ease宵dsl手owly逮unt斑ilt笛hes填peci慎men擋reac解hed艱alo豎adi程nth涼ene咽ighb織orho蔥odo腔fth夜eul高tima閃tes語tren登gth搬oft兔hec貢ontr亂ols態(tài)peci靠men.嫌At洽this盡poi朝nt,悲the里CFRP爬str著ain停incr摔ease慌dsi狼gnif系ican耗tly而unti詳lfa抬ilur吹e.T僚hem孤axim酸uml衰ocal偏CFR萍Pve滾rtic嚼als狐trai仁nme惹asur胃eda驗(yàn)tfa娃ilur峽ewa交sap巾prox太i-m瑞atel跑y0.雙0045栽mm/辟mm.執(zhí)When鐘com深pari肝ngt轉(zhuǎn)her慕esul辱tso桿fbe紛ams們SO3-太4an購dSO充3-2,歪t(yī)he態(tài)CFR括Pam襲ount程use枯dto掉str賣engt狼hen熱spec賞imen顛SO3迎-4w虧as2貌50%梯oft修hat易u(yù)sed回for跳spe觀cime參nSO舊3-2.柿Onl扛ya售10%象incr顛ease低in愧shea爛rca惹paci竭tyw爬asa手chie源ved匆for發(fā)the受addi若tion摔ala舉moun險(xiǎn)tof泰CFR壽Pus昏ed.去This旁mea絕nst香hat嶼ifa俯nen鑄dan尾chor驕to俗cont園rol舉FRP答debo迅ndin逼gis致not鍵use米d,t師here露is帖ano礦ptim閱umF怎RPq字uant兼ity,膨bey暴ond冰whic綢hth膊est拆reng露then端ing暮effe餅cti栽squ吐esti元onab劇le.惹Apr詞evio銜uss掉tudy兔[11汽]sh維owed岸tha汪tby仙usi陸nga咱nen催dan巡chor垃sys繳tem,伍the西fai癥lure危mod究eof惡FRP緊deb間ondi問ngc衰ould蠻be恐avoi盈ded.厲Rep接orte污dfi被ndin友gsa巡rec據(jù)onsi招sten幅twi射tht痛hose懲of腸othe渾rre斯sear兇ch[遼7],蝶whic裝hwa貿(mào)sba是sed哥ona亂rev蘋iew黃oft輔hee避xper鞠imen勿tal罰resu亡lts邊avai框labl逢ein釋the感l(wèi)it非erat顧ure,屢and瓦ind憤icat標(biāo)edt淘hat腫the潮cont想ribu警tion泰of檔FRP直tot誰hes煩hear蜜cap延acit宅yin意crea孩ses洋almo伶stl暗inea殲rly,美wit森h(huán)FR墾Pax億ial喇rigi掉dity皂exp閃ress昂edb爬y落(賄is提t(yī)he屑FRP宴area哈fra鍋ctio碰nan櫻d換ist殼heF狹RPe港last日icm天odul嘉us)徹upt塑oap鍛prox扭imat猜ely側(cè)0.4茶GPa.喂Bey勉ond糾this嚴(yán)val尋ue,滋the篩effe載ctiv廈enes瓜sof向FRP雀cea懇ses填tob孟epo叨siti懲ve.剪Ins精peci盈men喪SO3-旨5,t遇heu采seo謎fa難hori攜zont醒a(bǔ)lp躺lyo今ver甘the秘cont概inuo掉usU犯-wra散p(i姜.e.把90°/廁0°)炮resu臭lted河in黃aco食ncre烈tes辜plit妻ting胳fai籃lure話rat侍her秤than廢aC隆FRP急debo武ndin料gfa潤ilur廢e.T河hef卵a(bǔ)ilu討reo當(dāng)ccur滿red冒att清otal議app海lied支loa拋dof刑339基kN尚with茅a1青20%摸incr鋼ease括in毛the先shea由rca機(jī)paci旦tyc禮ompa縮red穿tot明hec融ontr板ols擴(kuò)peci壤m(xù)en畜SO3-聚1.T救hes榆tren漆gthe但ning亦wit橫htw狼ope竭rpen參dicu婚lar認(rèn)plie類s(i表.e.竹90°/禍0°)餡resu編lted封in競a17尿%in紋crea頭sei成nsh斤ear炊capa北city承com憑pare僅dto由the棚spe系cime瓶nwi與tho胖nly付one今CFRP堂ply籮in叨90°述orie耍ntat池ion余(i.e鞏.sp獅ecim井enS遵O3-4湊).T已hem詢axim靜uml狂ocal憂CFR釀Pve壽rtic醉als避trai箭nme漢asur見eda劈tfa育ilur債ewa五s0.次0043午mm/槍mm.協(xié)Byc映ompa辨ring墓the莫tes踢tre斜sult己sof俊spe彈cime溫nsS妨W3-2斗and撓SO3礎(chǔ)-5,趟havi攏ngt網(wǎng)hes靠ame可a/d架rat蟲ioa謠nds迷tren求gthe率ning申sch社emes莫but榴wit炊hdi政ffer炒ent柔stee繪lsh森ear蝴rein擋forc認(rèn)emen諸t,t蝕hes蘆hear鑰str政engt揀h(i暢.e.胡177餅and杯169.妖5kN近for要spe回cime襯nsS誼W3-2菜and每SO3漫-5,張resp座ecti俯vely否),a園ndt鞭hed防ucti肉lity宰are胖alm踢ost管iden別tica框l.O秧nem尼ayc缸o(hù)ncl劫ude憤that立the耍con渾trib佩utio虛nof派CFR魯Pbe疊nefi蚊tst殊heb打eam扒capa亭city唱to撫agr木eate誼rde斯gree下for藥bea攔msw穿itho椒uts痰teel糞she折arr輸einf再orce旬ment幻tha渠nfo咳rbe商ams戒with毅ade嶼quat披esh忍ear廟rein時(shí)forc盛emen抹t.桌Fig.輩8.托Fail笨ure紹mode長sof彩ser輪ies尺SO3累spec弓imen奶s.優(yōu)Fig.地9.捏Appl艷ied怖load拳vs.鉗mid匆-spa俊nde動flec軍tion丸for揚(yáng)ser譽(yù)ies瞇SO3擋spec陶imen賣s.仍Fig.并10.枕Mea巾sure孩dve抗rtic潛alC甩FRP吹stra戶inf括ors尸peci稈men誤SO3-佩4.辛3.4.雨Ser任ies延SO4滿Seri旅esS沖O4e熱xhib碎ited喊the新lar奶gest湖inc豪reas跌ein玻she森arc副apac央ity隊(duì)comp瓦ared推to吸the死othe滑rse寸ries叨inv恭esti站gate咬dwi愚tht完his護(hù)rese崗arch賤stu艷dy.境The自expe奴rime疲ntal輩res乒ults短in故term腫sof勞app披lied芬loa里dvs淡mid賀-spa紗nde鴉flec傷tion旗for潑thi立sse酷ries鉛is及illu間stra糊ted癢inF能ig.吧11.坡The倦cont賢rol蹤spec秤imen歇SO4株-1f驚aile備das摧ar綿esul逢tof當(dāng)she屑arc肉ompr益essi造ona攪ta垂tota營lap糾plie丈dlo均ado爽f13你0kN仁.Sp棟ecim忠enS朝O4-2善,st位reng使then揪edw炮ith幻CFRP咳str丘ips,指the茫fai剪lure選was瓶con敏trol胞led暫byC百FRP英debo累ndin你gat嫁at寺otal非loa隨dof乘255壓kN魚with寧96%趙inc單reas未ein筍she卡arc府a(chǎn)pac永ity詢over娃the搭con畏trol命spe怪cime姻nSO館4-1.擴(kuò)The揚(yáng)max妙imum員loc享alC抱FRP貞vert讀ical寧str石ain奏meas沖ured滴at掉fail穩(wěn)ure濃was萬0.00挑62寒mmym哨m.漁When郵com拜pari壘ngt溜het蠟est風(fēng)resu竿lts軟ofs誘peci秘men銳SO4-倒2to份tha懶tof再spe制cime撒nSO牧3-2,闊the透揉enha務(wù)nced挑she捏arc院apac融ity吊ofs柴peci加men景SO4-丸2(羊a/d襖=4)抗due黎toa俗ddit風(fēng)ion仁ofC汗FRP悲stri犁psw評as6受2.5紛kN,肺whil刮esp速ecim軌enS宏O3-2犯(小a/d惰=3)拘resu堆lted熟in形adde糟dsh鉛ear察capa議city窗of運(yùn)54k畜N.A饅sex穩(wěn)pect那ed,穗the悼cont扣ribu錄tion砍of橡CFRP巡rei網(wǎng)nfor君ceme粒ntt雞ore紹sist決the重she電ara贏ppea鎖red彈tod猜ecre漂ase質(zhì)with測dec劈reas號ing顆a/d餃rat鞭io.狗Spec騾imen廣SO4貝-3,菌stre漁ngth蠶ened樓wit談hco芝ntin犯uous攜U-庸wrap聯(lián),fa輛iled赤as熄are憂sult摧of圾conc遮rete信spl惠itti殼nga理tan臭app展lied續(xù)loa肆dof詢310員kN疫with坦a1探38%激incr塌ease餅in絹shea監(jiān)rca歐paci阻tyc姐ompa框red斯tot友hat珍ofs些peci缺men軌SO4-膚1.T兔hem蘋axim赴uml溫ocal繼CFR偵Pve景rtic逆als鏟trai沉nme白asur鑒eda牢tfa崗ilur灘ewa亞s0.宏0037嘆mm/膚mm.戴4.D進(jìn)esig饞nap畢proa死ch束The疼desi恢gna辯ppro址ach嗓for京comp趙utin帥gth喚esh絲ear君capa輩city則of鍵RCb好eams凈str己engt粒hene湯dwi燕the姿xter渣nall餃ybo機(jī)nded腿CFR防Pre摩info覺rcem懇ent,蹄exp障ress結(jié)edi雹nAC濤Ide壁sign楊cod數(shù)e[1鑼2]f帖orma勉t,w湯asp些ropo槍sed件and欄publ嚷ishe呼din聾199念8[1輩3].孟The妥desi響gnm炭odel簡des健crib擱edt跳wop印ossi呈ble譽(yù)fail胸ure艱mech賽anis庫mso隆fCF殖RPr獄einf框orce桃ment字nam城ely:個(gè)CFR誼Pfr藥actu河re;藥and泛CFRP萬deb穗ondi撓ng.輸Furt傘herm市ore,暮two汗lim拔its悔ont華hec珠ontr儲ibut另ion頂ofC使FRP次shea競rwe隆rep輝ropo揮sed.耐The霜fir喝stl載imit姻was解set畫to故cont蛛rol光the月shea湯rcr原ack箭widt襯han稱dlo只sso猶fag宇greg癢ate腳inte志rloc期k,a紐ndt肉hes劃econ田dwa辜sto厚pre豎clud黨ewe南bcr部ushi罪ng.糊Also法,th憶eco瞞ncre擋tes憂tren煩gth誓and宣CFRP紹wra星p-p做ing囑sche合mes半were渡inc遞orpo盯rate批das春des披ign織para狗mete搞rs.差I(lǐng)nr嚼ecen問tst贏udy釣[9,1刺0],壺modi差fica群tion陡swe再rep姿ropo薦sed痕tot饒he1卷998企desi為gna浪ppro全ach企toi難nclu列der近esul喜tso普fa稅new沖stud雕yon誦bon練dme外chan籮ism很betw職een踢CFRP萄she焦ets顏and陽conc暈rete閱sur京face樂[14駝].I鄙nad襪diti研on,襯the農(nóng)mode戴lwa隆sex潔tend揀edt詠opr拒ovid霉eth歇esh銹ear茄desi恰gne交quat合ions層in益Euro耗code飼as圣well孫as裹ACI轎form先at.等Comp池arin罰gwi爛tha躲llt儀est邁resu壺lts仿avai肯labl昆ein吊the嫂lit舊erat容ure抽tod俯ate,愁76傻test汽s,t薪hed蔥esig念nap四proa多chs間howe池dac捐cept巷able善and筑con攪serv喪ativ湖ees滋tima訪tes疾[10,燃13].冊In遍this價(jià)sec敬tion奴,th蠅esu返mmar礦yof桂the溫des成igna謠ppro縮ach個(gè)isp眼rese瘦nted霞.Th燒eco所mpar擴(kuò)ison獄bet霞ween腐exp局erim暢enta系lre島sult臭san看dth組eca截lcul蜓a(bǔ)ted自fac珠tore廉dsh烈ear抗stre蝶ngth始dem款onst壇rate接sth岔eab寺ilit暗yof銹the寧des生ign廟appr羨oach身to滲pred蹲ict幅the祝shea鞭r(nóng)ca春paci斧tyo商fth宮est職reng貴then友edb攝eams題.de亡mons澇trat欠est匆hea市bili綠tyo吩fth劑ede僑sign籮app巴roac衡hto刮pre推dict叢the集she篇arc鳥apac疫ity悶oft碑hes篩tren傲gthe透ned翼beam夢s.修Fig.礙11.倦App頂lied赤l(xiāng)oa道dvs待.mi拳d-sp茂and它efle傷ctio麻nfo謝rse寺ries巷SO4呢spe蠟cime秘ns.務(wù)Fig.眨12.糊Dim掠ensi燥ons嶼used昌to畝defi泰net彼hea佛rea國ofF弟RP(那a)v默erti吸c(diǎn)al繡orie抽nted捏FRP處str套ips,佳a(bǔ)nd確(b)伶inc帥line侮dst饑rips少.價(jià)4.1.漁Sum首mary旦of捆the賓shea洋rde章sign恢app很roac響h斬每—厲ACI報(bào)for郵mat睜Int達(dá)radi啊tion岔als優(yōu)hear委des攔ign率(inc撈ludi繡ngt既heA求CIC難ode)拍,th去eno旅mina炕lsh棄ear兇stre咳ngth勝of畜anR罵Cse怨ctio勝nis匠the固sum篇of巧the臨nomi筋nal貫shea故rst片reng躁ths浩ofc陰oncr將ete處and葡stee窄lsh睡ear妄rein銹forc每emen物t.F光orb芬eams索str蠻engt住hene公dwi己the弓xter販nall輛ybo雄nded幅FRP棚rei兵nfor嶼ceme穗nt,乘the懼shea賤rst鋤reng哭thm街ayb退eco浪mput削edb袖yth其ead書diti侮ono鄙fa態(tài)thir免dte現(xiàn)rmt良o(jì)ac飾coun胞tof槽the絹FRP投con遲trib呈utio心n.T蓄his祖ise納xpre談ssed閉as姐foll窩ows:Thedesignshearstrength,,isobtainedbymultiplyingthenominalshearstrengthbyastrengthreductionfactorforshear,.Itwassuggestedthatthereductionfactor至=0.8劇5gi泉ven趁inA役CI[亂12]產(chǎn)bem監(jiān)ain-燃tain渡edf倦ort瓦h(yuǎn)ec罩oncr螺ete駝and腹stee甩lte梢rms.刺How靠ever歷,a孩more勿str乒inge雨nts疾tren吊gth憑redu車ctio虎nfa鋪ctor側(cè)of祥0.7茶for拴the鍵CFRP犧con勿trib殘utio蜻nwa并ssu漏gges奇ted纏w10x還.Th默isi繁sdu脊eto坡the溜rela列tive簽nov拋elty凱of通this桃rep姻air奶tech牌niqu湊e.T亦hus,凱津the拌desi渠gns蓬hear川str零engt艦his續(xù)exp敞ress材eda荷sfo繪llow抱s.4.2.ContributionofCFRPreinforcementtotheshearcapacityTheexpressionusedtocomputeshearcontributionofCFRPreinforcementisgiveninEq.(3).ThisequationissimilartothatforshearcontributionofsteelstirrupsandconsistentwiththeACIformat.TheareaofCFRPshearreinforcement,,isthetotalthicknessofthesheet(usuallyorsheetsonbothsidesofthebeam)timesthewidthoftheCFRPstrip.ThedimensionsusedtodefinetheareaofCFRPinadditiontothespacingandtheeffectivedepthofCFRP,,areshowninFig.12.Notethatforcontinuousverticalshearreinforcement,thespacingofthestrip,,andthewidthofthestrip,,areequal.InEq.(3),aneffectiveaverageCFRPstress,smallerthanitsultimatestrength,,wasusedtoreplacetheyieldstressofsteel.Attheultimatelimitstateforthememberinshear,itisnotpossibletoattainthefullstrengthoftheFRP[7,13].FailureisgovernedbyeitherfractureoftheFRPsheetataveragestresslevelswellbelowFRPultimatecapacityduetostressconcentrations,debondingoftheFRPsheetfromtheconcretesurface,orasignificantdecreaseinthepost-crackingconcreteshearstrengthfromalossofaggregateinterlock.Thus,theeffectiveaverageCFRPstressiscomputedbyapplyingareductioncoefficient,R,totheCFRPultimatestrengthasexpressedinEq.(4).Thereductioncoefficientdependsonthepossiblefailuremodes(eitherCFRPfractureorCFRPdebonding).Ineithercase,anupperlimitforthereductioncoefficientisestablishedinordertocontrolshearcrackwidthandlossofaggregateinterlock.4.3.ReductioncoefficientbasedonCFRPsheetfracturefailureTheproposedreductioncoefficientwascalibratedonallavailabletestresultstodate,22testswithfailurecontrolledbyCFRPfracture[10,13].Thereductioncoefficientwasestablishedasafunctionof(whereistheareafractionofCFRP)andexpressedinEq.(5)for0.7GPa.4.4.ReductioncoefficientbasedonCFRPdebondingfailureTheshearcapacitygovernedbyCFRPdebondingfromtheconcretesurfacewaspresented[9,10]asafunctionofCFRPaxialrigidity,concretestrength,effectivedepthofCFRPreinforcement,andbondedsurfaceconfigurations.Indeterminingthereductioncoefficientforbond,theeffectivebondlength,,hastobedeterminedfirst.Basedonanalyticalandexperimentaldatafrombondtests,Miller[14]showedthattheeffectivebondlengths
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