外文翻譯鋼筋混凝土板的拉伸硬化過(guò)程分析

外文翻譯鋼筋混凝土板的拉伸硬化過(guò)程分析R.IanGilbert摘要:當(dāng)計(jì)算一個(gè)鋼筋混凝土梁或板的承載力時(shí)混凝土的抗拉能力通常被忽視,盡管具體的拉應(yīng)力繼續(xù)進(jìn)行,由于拉鋼筋到混凝土之間裂縫的轉(zhuǎn)換力量。這一種混凝土的拉力被稱(chēng)為混凝土的張力硬化。在開(kāi)裂后它會(huì)影響鋼筋混凝土的剛度,因此它的撓度和裂縫寬度必須根據(jù)屈服強(qiáng)度負(fù)載。對(duì)輕混凝土,例如樓板,全部裂縫的彎曲剛度比沒(méi)有裂縫部分的要小很多,張力加勁有助于剛度。在本文中,ACI方法必須考慮到緊張加勁,歐洲和英國(guó)的方法是嚴(yán)格評(píng)估和預(yù)測(cè)與實(shí)驗(yàn)結(jié)果進(jìn)行比較。最后,建議書(shū)包括建模系統(tǒng)緊張撓度控制的鋼筋混凝土樓板設(shè)計(jì)變硬。分類(lèi)號(hào):1061/ASCE0733-94452007133:6899關(guān)鍵詞:開(kāi)裂;蠕變撓度,混凝土,鋼筋,適用性,收縮,混凝土磚。簡(jiǎn)介拉伸能力在計(jì)算時(shí)通常忽略鋼筋混凝土梁或板的強(qiáng)度,盡管具體的拉應(yīng)力繼續(xù)進(jìn)行,由于拉鋼筋到混凝土之間裂縫的轉(zhuǎn)換力量。這一種混凝土的拉力被稱(chēng)為張力硬化,它會(huì)影響各部分的剛度,因此必須考慮其撓度和裂縫寬度。隨著高強(qiáng)度鋼筋的到來(lái),增強(qiáng)混凝土板通常包含相對(duì)少量的拉鋼筋,經(jīng)常接近相關(guān)建筑法規(guī)允許的最低含量。對(duì)于這樣的構(gòu)件,彎曲完全開(kāi)裂的一個(gè)截面剛度比未開(kāi)裂的截面小許多倍,張力加勁大大促進(jìn)了開(kāi)裂后剛度。在設(shè)計(jì)中,撓度和裂縫的控制通常是在屈服水平調(diào)整考慮的,并在開(kāi)裂后建模精確的剛度是必需的。撓度計(jì)算中最常用的方法包括確定為破解構(gòu)件平均慣性()有效時(shí)刻。幾種不同的經(jīng)驗(yàn)公式可用于,包括著名的方程開(kāi)發(fā)Branson(1965)和ACI318(ACI2005)。其他的張力硬化模式包括在Eurocode2(CEN1992和(BritishStandardBS81101985),最近,Bischoff(2005)表明,布蘭森的方程極高估含有少量的鋼筋混凝土構(gòu)件鋼筋平均剛度,他提出了一個(gè)對(duì)于,替代方程,這基本上是與Eurocode2方案兼容。在本文中,包括張力加勁的各種方法在混凝土結(jié)構(gòu)設(shè)計(jì),包括在Eurocode2,ACI318,BS8110模式,批判性進(jìn)行評(píng)估經(jīng)驗(yàn)預(yù)測(cè)與實(shí)測(cè)撓度進(jìn)行了比較。最后,在模擬張力加勁的建議結(jié)構(gòu)設(shè)計(jì)均包括在內(nèi)。開(kāi)裂后彎曲響應(yīng)考慮簡(jiǎn)支一個(gè)負(fù)載變形響應(yīng),鋼筋混凝土板圖1所示。在負(fù)載超過(guò)負(fù)荷少的開(kāi)裂,,該構(gòu)件未開(kāi)裂和行為均勻和彈性,以及撓度斜率是成正比的未開(kāi)裂的轉(zhuǎn)動(dòng)慣量的轉(zhuǎn)化節(jié),。該構(gòu)件在第一裂縫在當(dāng)極端纖維在混凝土拉應(yīng)力的最大部分到達(dá)混凝土彎拉強(qiáng)度破裂或有一個(gè)剛度突變,并立即出現(xiàn)裂紋。在包含破碎部分,抗彎剛度顯著下降,但大部分仍然未開(kāi)裂的梁。隨著負(fù)載的增加,出現(xiàn)更多的裂縫形式和平均抗彎剛度在整個(gè)構(gòu)件中減少。如果在梁的混凝土開(kāi)裂區(qū)域進(jìn)行拉沒(méi)有壓力,負(fù)載變形關(guān)系將遵循虛線ACD,圖1。如開(kāi)裂后如果平均極端纖維拉伸在具體的壓力維持在,將遵循虛線AE。事實(shí)上,實(shí)際的響應(yīng)介于這兩個(gè)極端,是如圖1所示為實(shí)線AB型。之間的差異實(shí)際反映和零張力反應(yīng)是張力加勁影響。隨著負(fù)載的增加,平均拉應(yīng)力混凝土隨著越來(lái)越多的裂縫降低對(duì)實(shí)際的響應(yīng)趨于零緊張的反應(yīng),至少要等到裂縫模式充分開(kāi)發(fā)和裂縫的數(shù)量已趨于穩(wěn)定。對(duì)于含有少量的拉鋼筋磚(通常As/bd0.003),緊張硬化可能超過(guò)50%的鋼筋混凝土的剛度破壞屈服加載而且仍然要達(dá)到和超過(guò)的鋼產(chǎn)量和負(fù)荷接近極限地步。張力加勁的效果隨著時(shí)間負(fù)荷下降,可能是由于拉伸的綜合影響蠕變,蠕變斷裂,收縮開(kāi)裂,而這必須占長(zhǎng)期繞度計(jì)算。加勁的張力模型ACI318-2005梁或板在使用載重?fù)隙瓤梢运查g從彈性論計(jì)算采用混凝土彈性模量Ec和有效的慣性矩,例如,為構(gòu)件是價(jià)值計(jì)算Eq.1計(jì)算公式為在跨中簡(jiǎn)支構(gòu)件和加權(quán)平均值計(jì)算在連續(xù)正,負(fù)彎矩區(qū)跨度(1)Icr為換算截面慣性裂的時(shí)刻;Ig為目前的毛質(zhì)心橫截面有關(guān)慣性軸,但更應(yīng)該是正確換算截面的未開(kāi)裂的慣性力矩Iuncr;Ma為在構(gòu)件的最大彎矩階段撓度計(jì)算;Mcr為開(kāi)裂時(shí)(=ftIg/yt);ft為混凝土斷裂模數(shù);yt為從質(zhì)心的距離軸的毛截面的纖維在極端的緊張。ACI的方法的修改包括在澳大利亞標(biāo)準(zhǔn)AS3600-2001AS2001交代的事實(shí),收縮引起的緊張局勢(shì)可能會(huì)降低混凝土開(kāi)裂時(shí)刻顯著。開(kāi)裂的時(shí)刻由Mcr=(ft-fcs)Ig/yt公式?jīng)Q定,fcs是最大收縮引起的拉在未開(kāi)裂截面應(yīng)力在極端的情況在該纖維發(fā)生開(kāi)裂(Gilbert2003)。Eurocode2(1994)這種方法涉及到在特定的曲率計(jì)算交叉部分,然后結(jié)合取得的撓度。開(kāi)裂后曲率K的計(jì)算為(2)為分配系數(shù)占目前水平和打擊的程度,并給出(3)為變形鋼筋1.0和光圓鋼筋0.5;為單一的,短期負(fù)荷為1.0和重復(fù)或持續(xù)荷載為0.5;在加載應(yīng)力造成的受拉鋼筋首先開(kāi)裂,計(jì)算混凝土緊張;是在考慮鋼筋應(yīng)力加載;Kcr在截面曲率而忽視具體的緊張;Kuncr曲率的未開(kāi)裂換算截面。在純彎板,如果壓混凝土和鋼筋都是線性和彈性,等于,結(jié)合公式1和2能得(4)對(duì)于受彎構(gòu)件變形鋼筋包含短期下載入中,公式3和公式4可以重新安排,以提供下列替代表達(dá)式短期撓度最近提出的計(jì)算[Bischoff2005](5)BS8110-1985這種做法,目前已在英國(guó)已經(jīng)取代了歐洲法規(guī)2的方法,還涉及到在特定的截面曲率的計(jì)算,然后結(jié)合取得的偏轉(zhuǎn)。開(kāi)裂后的曲率K計(jì)算假設(shè)1、平面為平截面;2、在壓縮和鋼筋混凝土被認(rèn)為是線彈性;3、在緊張的混凝土應(yīng)力分布是三角形的,曾在中性軸和一個(gè)值為零值在1.0MPa的瞬間強(qiáng)度鋼質(zhì)心,減少至0.55MPa。與實(shí)驗(yàn)數(shù)據(jù)的比較為了測(cè)試ACI318,歐洲規(guī)范的適用性和BS8110鋼筋混凝土構(gòu)件的輕輕的方法,測(cè)瞬間響應(yīng)與偏轉(zhuǎn)11簡(jiǎn)支,單鋼筋單向拉伸板含鋼量在范圍進(jìn)行比較和計(jì)算的答復(fù),該板塊(指定S1至S3,S8的,到SS2的SS4型,和Z1到Z4)都是柱狀,矩形截面,850mm,并在一個(gè)有效深度載有縱向拉伸單層鋼筋d(Es=200000MPa和屈服應(yīng)力fsy=500Mpa)。每個(gè)板塊的詳細(xì)情況見(jiàn)表1,包括有關(guān)的幾何和材料特性。在每個(gè)板跨中撓度的預(yù)測(cè)結(jié)果與實(shí)測(cè)時(shí),在跨中時(shí)刻等于1.1,1.2和1.3Mcr列于表2。與瞬時(shí)變形響應(yīng)的測(cè)量時(shí)刻的兩跨中的磚。(SS2andZ3)進(jìn)行比較和計(jì)算反應(yīng)獲得圖2使用三個(gè)代碼方式同時(shí)顯示的反應(yīng),如果沒(méi)有出現(xiàn)開(kāi)裂,如果緊張僵硬被忽略。討論結(jié)果很明顯,這些輕輕鋼筋磚,緊張硬化非常顯著,提供了剛度大的比例。從表2,跨中撓度的比例得到了加勁對(duì)測(cè)量張力跨中撓度忽視(在Mcr和1.3Mcr范圍)是在1.38-3.69范圍取平均指2.12。也就是說(shuō),平均而言,緊張硬化超過(guò)50%的一個(gè)剛性板鋼筋在屈服荷載的瞬間開(kāi)裂。對(duì)于每一個(gè)板,在ACI318的方法低估了瞬間變形開(kāi)裂后,尤其如此輕率加強(qiáng)板塊。此外,在這一時(shí)刻ACI318突然不模型,偏轉(zhuǎn)方向改變最初的反應(yīng)開(kāi)裂,也沒(méi)有預(yù)測(cè)的正確形狀矩?fù)隙惹€。在短期撓度低估使用的ACI318模式是經(jīng)化驗(yàn)報(bào)告在這里在表示實(shí)踐中相當(dāng)大的比。不同于Eurocode2和BS8110,ACI318模型不承認(rèn)或?yàn)樵陂_(kāi)裂的時(shí)刻,這將不可避免地減少在實(shí)踐中出現(xiàn)的由于緊張引起的混凝土干燥收縮或熱變形。對(duì)于許多磚,開(kāi)裂會(huì)發(fā)生因提前鑄造干燥或幾周內(nèi)溫度變化,以及經(jīng)常暴露之前,其板全方位服務(wù)的負(fù)荷。通過(guò)限制在拉伸的水平拉應(yīng)力混凝土強(qiáng)化只為1.0MPa,高估了BS8110的方法測(cè)試的磚都低于并立即偏轉(zhuǎn)以上開(kāi)裂的時(shí)刻。有道理和損失的剛度,在實(shí)踐中由于克制,早期收縮和熱變形發(fā)生膨脹。不過(guò),BS8110提供了一個(gè)相對(duì)較差模型剛度,并錯(cuò)誤地認(rèn)為,平均拉力混凝土裂縫進(jìn)行了實(shí)際調(diào)高M(jìn)增大和中性軸的上升。因此,斜坡的SB8110時(shí)刻,撓度情節(jié)較陡測(cè)量所有板坡。這種方法使用比歐洲法規(guī)2或ACI兩種方式也比較繁瑣。在所有情況下,歐洲法規(guī)2撓度計(jì)算[EPS.3-5]是在更接近與實(shí)測(cè)撓度在整個(gè)負(fù)載范圍內(nèi)協(xié)議?？梢钥闯鲈趫D2,載撓度曲線的形狀獲得使用歐洲規(guī)范2是一個(gè)比這更好的代表性實(shí)際曲線獲得使用EP.1?？紤]到具體的變異材料性能影響的磚,服務(wù)行為和對(duì)開(kāi)裂的隨機(jī)性,歐洲法規(guī)2之間的協(xié)議預(yù)測(cè)和對(duì)這種范圍廣泛的測(cè)試結(jié)果拉鋼筋的比例是相當(dāng)顯著。隨著圖2()0.80和1.39之間的值平均值為1.07,歐洲法規(guī)2的方法提供了ACI318或BS8110更好地估計(jì)短期行為。結(jié)論雖然緊張僵硬只對(duì)重鋼筋梁撓度的影響相對(duì)較小,這是非常輕的比例在Iuncr/ICR的是高鋼筋構(gòu)件顯著,例如作為最實(shí)用的鋼筋混凝土樓板。加勁張力的模型納入ACI2005,歐洲法規(guī)2CEN1993,和BS81101985已提交其適用性已輕輕鋼筋混凝土樓板評(píng)估。計(jì)算模型的三個(gè)代碼瞬時(shí)撓度進(jìn)行了比較與來(lái)自11個(gè)實(shí)驗(yàn)室測(cè)試測(cè)量撓度在含有不同數(shù)量的鋼筋磚。在歐洲法規(guī)2方案(EP.5已被證明是更準(zhǔn)確地模擬了瞬時(shí)負(fù)載變形的加固構(gòu)件輕輕響應(yīng)的波形和ACI318EP.1比更為可靠的方法。出自:JOURNALOFSTRUCTURALENGINEERINGASCE/JUNE2007TensionStiffeninginLightlyReinforcedConcreteSlabs1R.IanGilbert1Abstract:Thetensilecapacityofconcreteisusuallyneglectedwhencalculatingthestrengthofareinforcedconcretebeamorslab,eventhoughconcretecontinuestocarrytensilestressbetweenthecracksduetothetransferofforcesfromthetensilereinforcementtotheconcretethroughbond.Thiscontributionofthetensileconcreteisknownastensionstiffeninganditaffectsthemember’sstiffnessaftercrackingandhencethedeflectionofthememberandthewidthofthecracksunderserviceloads.Forlightlyreinforcedmembers,suchasfloorslabs,theflexuralstiffnessofafullycrackedsectionismanytimessmallerthanthatofanuncrackedsection,andtensionstiffeningcontributesgreatlytothepostcrackingstiffness.Inthispaper,theapproachestoaccountfortensionstiffeningintheACI,European,andBritishcodesareevaluatedcriticallyandpredictionsarecomparedwithexperimentalobservations.Finally,recommendationsareincludedformodelingtensionstiffeninginthedesignofreinforcedconcretefloorslabsfordeflectioncontrol.DOI:10.1061/(ASCE)0733-9445(2007)133:6(899)CEDatabasesubjectheadings:Cracking;Creep;Deflection;Concrete,reinforced;Serviceability;Shrinkage;Concreteslabs.1ProfessorofCivilEngineering,SchoolofCivilandEnvironmentalEngineering,Univ.ofNewSouthWales,UNSWSydney,2052,Australia.Note.AssociateEditor:RobY.H.Chai.DiscussionopenuntilNovember1,2007.Separatediscussionsmustbesubmittedforindividualpapers.Toextendtheclosingdatebyonemonth,awrittenrequestmustbefiledwiththeASCEManagingEditor.ThemanuscriptforthistechnicalnotewassubmittedforreviewandpossiblepublicationonMay22,2006;approvedonDecember28,2006.ThistechnicalnoteispartoftheJournalofStructuralEngineering,Vol.133,No.6,June1,2007ASCE,ISSN0733-9445/2007/6-899?903/$25.00.11ProfessorofCivilEngineering,SchoolofCivilandEnvironmentalEngineering,Univ.ofNewSouthWales,UNSWSydney,2052,AustraliaJournalofStructuralEngineering,Vol.133,No.6,June1,2007ASCE,ISSN0733-9445/2007/6-899?903/$25.00.IntroductionThetensilecapacityofconcreteisusuallyneglectedwhencalculatingthestrengthofareinforcedconcretebeamorslab,eventhoughconcretecontinuestocarrytensilestressbetweenthecracksduetothetransferofforcesfromthetensilereinforcementtotheconcretethroughbond.Thiscontributionofthetensileconcreteisknownastensionstiffening,anditaffectsthemember’sstiffnessaftercrackingandhenceitsdeflectionandthewidthofthecracks.Withtheadventofhigh-strengthsteelreinforcement,reinforcedconcreteslabsusuallycontainrelativelysmallquantitiesoftensilereinforcement,oftenclosetotheminimumamountpermittedbytherelevantbuildingcode.Forsuchmembers,theflexuralstiffnessofafullycrackedcrosssectionismanytimessmallerthanthatofanuncrackedcrosssection,andtensionstiffeningcontributesgreatlytothestiffnessaftercracking.Indesign,deflectionandcrackcontrolatservice-loadlevelsareusuallythegoverningconsiderations,andaccuratemodelingofthestiffnessaftercrackingisrequired.Themostcommonlyusedapproachindeflectioncalculationsinvolvesdetermininganaverageeffectivemomentofinertia[Ie]foracrackedmember.SeveraldifferentempiricalequationsareavailableforIe,includingthewell-knownequationdevelopedbyBranson[1965]andrecommendedinACI318[ACI2005].OthermodelsfortensionstiffeningareincludedinEurocode2[CEN1992]andthe[BritishStandardBS81101985].Recently,Bischoff[2005]demonstratedthatBranson’sequationgrosslyoverestimatesthtieaveragesffnessofreinforcedconcretememberscontainingsmallquantitiesofsteelreinforcement,andheproposedanalternativeequationforIe,whichisessentiallycompatiblewiththeEurocode2approach.Inthispaper,thevariousapproachesforincludingtensionstiffeninginthedesignofconcretestructures,includingtheACI318,Eurocode2,andBS8110models,areevaluatedcriticallyandempiricalpredictionsarecomparedwithmeasureddeflections.Finally,recommendationsformodelingtensionstiffeninginstructuraldesignareincluded.FlexuralResponseafterCrackingConsidertheload-deflectionresponseofasimplysupported,reinforcedconcreteslabshowninFig.1.Atloadslessthanthecrackingload,Pcr,thememberisuncrackedandbehaveshomogeneouslyandelastically,andtheslopeoftheloaddeflectionplotisproportionaltothemomentofinertiaoftheuncrackedtransformedsection,Iuncr.ThememberfirstcracksatPcrwhentheextremefibertensilestressintheconcreteatthesectionofimummomentreachestheflexuraltensilestrengthoftheconcreteormodulusofrupture,fr.Thereisasuddenchangeinthelocalstiffnessatandimmediatelyadjacenttothisfirstcrack.Onthesectioncontainingthecrack,theflexuralstiffnessdropssignificantly,butmuchofthebeamremainsuncracked.Asloadincreases,morecracksformandtheaverageflexuralstiffnessoftheentirememberdecreasesIfthetensileconcreteinthecrackedregionsofthebeamcarriednostress,theload-deflectionrelationshipwouldfollowthedashedlineACDinFig.1.Iftheaverageextremefibertensilestressintheconcreteremainedatfraftercracking,theloaddeflectionrelationshipwouldfollowthedashedtheactualresponseliesbetweenthesetwoextremesandisshowninFig.1asthesolidlineAB.Thedifferencebetweentheactualresponseandthezerotensionresponseisthetensionstiffeningeffect(inFig.1)Astheloadincreases,theaveragetensilestressintheconcretereducesasmorecracksdevelopandtheactualresponsetendstowardthezerotensionresponse,atleastuntilthecrackpatternisfullydevelopedandthenumberofcrackshasstabilized.Forslabscontainingsmallquantitiesoftensilereinforcement[typicallytensionstiffeningmayberesponsibleformorethan50%ofthestiffnessofthecrackedmemberatserviceloadsandremainssignificantuptoandbeyondthepointwherethesteelyieldsandtheultimateloadisapproached].Thetensionstiffeningeffectdecreaseswithtimeundersustainedloads,probablyduetothecombinedeffectsoftensilecreep,creeprupture,andshrinkagecracking,andthismustbeaccountedforinlong-termdeflectioncalculations.ModelsforTensionStiffeningACI318-2005TheinstantaneousdeflectionofbeamorslabatserviceloadsmaybecalculatedfromelastictheoryusingtheelasticmodulusofconcreteEcandaneffectivemomentofinertia,Ie.ThevalueofIeforthememberisthevaluecalculatedusingEq.[1]atmidspanforasimplysupportedmemberandaweightedaveragevaluecalculatedinthepositiveandnegativemomentregionsofacontinuousspan(1)whereIcr=momentofinertiaofthecrackedtransformedsection;Ig=momentofinertiaofthegrosscrosssectionaboutthecentroidalaxis[butmorecorrectlyshouldbethemomentofinertiaoftheuncrackedtransformedsection,Iuncr];Ma=maximummomentinthememberatthestagedeflectioniscomputed;Mcr=crackingmoment=(frIg/yt);fr=modulusofruptureofconcrete(=7.5fcinpsiand0.6fcinMpa);andyt=distancefromthecentroidalaxisofthegrosssectiontotheextremefiberintension.AmodificationoftheACIapproachisincludedintheAustralianStandardAS3600-2001(AS2001)toaccountforthefactthatshrinkage-inducedtensionintheconcretemayreducethecrackingmomentsignificantly.ThecrackingmomentisgivenbyMcr=(fr?fcs)Ig/yt,wherefcsismaximumshrinkage-inducedtensilestressintheuncrackedsectionattheextremefibreatwhichcrackingoccurs（Gilbert2003）.(2)wheredistributioncoefficientaccountingformomentlevelanddegreeofcrackingandisgivenby(3)and1=1.0fordeformedbarsand0.5forplainbars;2=1.0forasingle,short-termloadand0.5forrepeatedorsustainedloading;sr=stressinthetensilereinforcementattheloadingcausingfirstcracking(i.e.,whenthemomentequalsMcr),calculatedwhileignoringconcreteintension;sisreinforcementstressatloadingunderconsideration(i.e.,whenthein-servicemomentMsisacting),calculatedwhileignoringconcreteintension;cr=curvatureatthesectionwhileignoringconcreteintension;anduncr=curvatureontheuncrackedtransformedsection.Forslabsinpureflexure,ifthecompressiveconcreteandthereinforcementarebothlinearandelastic,theratiosr/sinEq.(3)isequaltotheratioMcr/Ms.UsingthenotationofEq.（1）,Eq.(2)canbereexpressedas(4)Foraflexuralmembercontainingdeformedbarsundershorttermloading,Eq.(3)becomes=1?（Mcr/Ms）2andEq.（4）canberearrangedtogivethefollowingalternativeexpressionforIeforshort-termdeflectioncalculations[recentlyproposedbyBischoff(2005)]:(5)BS8110-1985Thisapproach,whichhasnowbeensupersededintheU.K.bytheEurocode2approach,alsoinvolvesthecalculationofthecurvatureatparticularcrosssectionsandthenintegratingtoobtainthedeflection.Thecurvatureofasectionaftercrackingiscalculatedbyassumingthat1planesectionsremainplane;2theconcreteincompressionandthereinforcementareassumedtobelinearelastic;and(3)thestressdistributionforconcreteintensionistriangular,havingavalueofzeroattheneutralaxisandavalueatthecentroidofthetensilesteelof1.0MPainstantaneously,reducingto0.55MPainthelongterm.ComparisonwithExperimentalDataTotesttheapplicabilityoftheACI318,Eurocode2,andBS8110approachesforlightlyreinforcedconcretemembers,themeasuredmomentversusdeflectionresponsefor11simplysupported,singlyreinforcedone-wayslabscontainingtensilesteelquantitiesintherange0.0018<<0.01arecomparedwiththecalculatedresponses.Theslabs(designatedS1toS3,S8,SS2toSS4,andZ1toZ4)wereallprismatic,ofrectangularsection,850mmwide,andcontainedasinglelayeroflongitudinaltensilesteelreinforcementataneffectivedepthd(withEs=200,000MPaandthenominalyieldstressfsy=500Mpa).DetailsofeachslabaregiveninTable1,includingrelevantgeometricandmaterialproperties.Thepredictedandmeasureddeflectionsatmidspanforeachslabwhenthemomentatmidspanequals1.1,1.2,and1.3McrarepresentedinTable2.ThemeasuredmomentversusinstantaneousdeflectionresponseatmidspanoftwooftheslabsSS2andZ3arecomparedwiththecalculatedresponsesobtainedusingthethreecodeapproachesinFig.2.Alsoshownaretheresponsesifcrackingdidnotoccurandiftensionstiffeningwasignored.DiscussionofResultsItisevidentthatfortheselightlyreinforcedslabs,tensionstiffeningisverysignificant,providingalargeproportionofthepostcrackingstiffness.FromTable2,theratioofthemidspandeflectionobtainedbyignoringtensionstiffeningtothemeasuredmidspandeflectionoverthemomentrangeMcrto1.3Mcrisintherange1.38?3.69withameanvalueof2.12.Thatis,onaverage,tensionstiffeningcontributesmorethan50%oftheinstantaneousstiffnessofalightlyreinforcedslabaftercrackingatserviceloadForeveryslab,theACI318approachunderestimatestheinstantaneousdeflectionaftercracking,particularlysoforlightlyreinforcedslabs.Inaddition,ACI318doesnotmodeltheabruptchangeindirectionofthemoment-deflectionresponseatfirstcracking,nordoesitpredictthecorrectshapeofthepostcrackingmoment-deflectioncurveTheunderestimationofshort-termdeflectionusingtheACI318modelisconsiderablygreaterinpracticethanthatindicatedbythelaboratorytestsreportedhere.UnliketheEurocode2andBS8110approaches,theACI318modeldoesnotrecognizeoraccountforthereductioninthecrackingmomentthatwillinevitablyoccurinpracticeduetotensioninducedintheconcretebydryingshrinkageorthermaldeformations.Formanyslabs,crackingwilloccurwithinweeksofcastingduetoearlydryingortemperaturechanges,oftenwellbeforetheslabisexposedtoitsfullserviceloadsBylimitingtheconcretetensilestressatthelevelofthetensilereinforcementtojust1.0MPa,theBS8110approachoverestimatesthedeflectionofthetestslabsbothbelowandimmediatelyabovethecrackingmoment.Thisisnotunreasonableandaccountsforthelossofstiffnessthatoccursinpracticeduetorestrainttoearlyshrinkageandthermaldeformations.Nevertheless,theBS8110approachprovidesarelativelypoormodelofthepostcrackingstiffnessandincorrectlysuggeststhattheaveragetensileforcecarriedbythecrackedconcreteactuallyincreasesasMincreasesandtheneutralaxisrises.Asaresult,theslopeoftheBS8110postcrackingmoment-deflectionplotissteeperthanthemeasuredslopeforallslabs.TheapproachisalsomoretedioustousethaneithertheACIorEurocode2approaches.Inallcases,deflectionscalculatedusingEurocode2[Eqs.3?5]areinmuchcloseragreementwiththemeasureddeflectionovertheentirepostcrackingloadrange.AscanbeseeninFig.2,theshapeoftheload-deflectioncurveobtainedusingEurocode2isafarbetterrepresentationoftheactualcurvethanthatobtainedusingEq.1.Consideringthevariabilityoftheconcretematerialpropertiesthataffectthein-servicebehaviorofslabsandtherandomnatureofcracking,theagreementbetweentheEurocode2predictionsandthetestresultsoversuchawiderangeoftensilereinforcementratiosisquiteremarkable.WiththeratioofinTable2varyingbetween0.80and1.39withameanvalueof1.07,theEurocode2approachcertainlyprovidesabetterestimateofshort-termbehaviorthaneitherACI318orBS8110.ConclusionsAlthoughtensionstiffeninghasonlyarelatively