- 277 - CHAPTER 5 EXPERIMENTAL INVESTIGATION ON MOMENT REDISTRIBUTION CONTENTS 5EXPERIMENTAL INVESTIGATION ON MOMENT REDISTRIBUTION277 5.1Introduction279 5.2Literature Review280 5.2.1Definition of Ductility280 5.2.2Definition of Moment redistribution281 5.2.3Tests on Continuous Plated RC Beams283 5.3Experimental Studies on RC Beams with Externally Bonded Steel/FRP Plates286 5.3.1Geometry of Test Specimens286 5.3.2Test Setup and Instrumentation288 5.3.3Material Properties290 5.3.4Test Results293 5.3.4.1Beam SS1 (Steel 75x3)294 5.3.4.2Beam SS2 (Steel 112x2)300 5.3.4.3Beam SS3 (Steel 224x1)306 5.3.4.4Beam SF1 (CFRP 25x2.4)312 5.3.4.5Beam SF2 (CFRP 50x1.2)317 5.3.4.6Beam SF3 (CFRP 80x1.2)322 5.3.4.7Beam SF4 (CFRP 100x0.6)327 5.3.5Summary and Discussions333 5.3.5.1Journal Paper: Moment Redistribution in Continuous Plated RC Flexural Members Part 1 - Neutral Axis Depth Approach and Tests333 5.4Experimental Studies on RC Beams with Near Surface Mounted Steel/FRP Strips351 5.4.1Geometry of Test Specimens351 5.4.2Test Setup and Instrumentation355 5.4.3Material Properties359 5.4.4Test Results361 - 278 - 5.4.4.1Beam NS_F1 (5 x CFRP1.2mm)362 5.4.4.2Beam NS_F2 (2 x CFRP1.2mm)369 5.4.4.3Beam NS_F3 (1 x CFRP1.2mm)376 5.4.4.4Beam NS_F4 (1 x 2CFRP1.2mm)383 5.4.4.5Beam NS_S1 (4 x Steel 0.9mm)389 5.4.4.6Beam NS_S2 (2 x 2 Steel 0.9mm)394 5.4.4.7Beam NB_F1 (2 x CFRP1.2mm)400 5.4.4.8Beam NB_F2 (2 x CFRP1.2mm)407 5.4.4.9Beam NB_F3 (2 x 2CFRP1.2mm)414 5.4.5Summary and Discussions421 5.4.5.1Journal Paper: Tests on the Ductility of Reinforced Concrete Beams Retrofitted with FRP and Steel Near Surface Mounted Plates421 5.5Summary441 5.6References442 5.7Notations444 Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 279 - 5.1 INTRODUCTION Reinforcedconcretebeamsretrofittedwithexternallybonded(EB)ornearsurfacemounted(NSM) platescaneffectivelyincreasethestrengthofmembers(Oehlers&Seracino2004;Swamy&Gaul 1996;Spadeaetal.2001),however,duetoprematuredebondingoftheplatesaspreviously discussed in Chapter 1, the ductility of plated beams can be severely reduced to such an extent that platingguidelinesoftenexcludemomentredistribution(fib2001;ConcreteSociety2000).This exclusion may reduce the application of plating, particularly when retrofitting buildings where ductility is often a requirement.It has been shown in Chapter 1 that plate end (PE) debonding can be prevented by the position of the terminationoftheplates.Criticaldiagonalcrack(CDC)debondingcanalsobepreventedthrough properdesignusingthepassiveprestressedmodelproposedinChapter4.Theproblemis intermediatecrack(IC)debonding,whichisdifficulttopreventeventhoughananalyticalmodelhas beenproposedinChapter 2tomodelitsbehaviour. Studiesconductedbyvariousresearchers have showedthateventhoughtheuseofendanchoragecanpreventprematurePEdebonding,local debonding,thatisICdebonding,canstilloccuralongthespanofthebeamandleadtopremature failurepriortoachievingthedesiredstrengthorductility(Ashouretal.2004;Swamy& Mukhopadhyaya1999;Garden&Hollaway1998;Spadeaetal.1998;Lamannaetal.2001). Therefore,theductility,andconsequentlythemomentredistributioncapacityofplatedcontinuous members is dependent on the IC debonding resistance.Very little research has been carried out on moment redistribution of EB or NSM beams, even though many in-situ RC beams are continuous members (El-Rafaie et al. 2002, 2003; Khalifa et al. 1999). It is suggestedbybothfib(2001)andConcreteSociety(2000)thatmomentredistributionshouldnotbe allowedforplatedRCbeams,howeverMukhopadhyayaetal.(1998)showedthattheductilityofa plated beam could be higher than that of an unplated beam if designed properly, and from a few tests carriedoutbyvariousresearchers(El-Rafaieetal.2002,2003;Ashouretal.2004),moment redistributionis observed. Testsonsimplysupported RCbeamswithNSMstrips (Hassan&Rizkalla 2003;Taljsten&Carolin2003;Blaschko2003)haveshownthatNSMplatesdebondorfailatmuch higherstrainsthanEBplates,and,hence,itwouldbeexpectedthatNSMplatedbeamsshow substantiallygreaterductilitythanEBplatedbeams.Itisthereforenecessarytoperformfurther research on the moment redistribution of EB and NSM members. Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 280 - InthisChapter,aliteraturereviewiscarriedoutontheexistingtestsperformedbydifferent researchersoncontinuousplatedRCbeams.Throughtheselimitedtestresults,itisshownthat momentredistributioncanbeobtainedinplatedmembers,howeverfurtherexperimentalstudiesare neededtoinvestigatethemomentredistributionbehaviourofplatedmemberssothatdesign approaches can be developed to analyse the moment redistribution of continuous plated members. In this research, an experimental program was carried out to investigate the behaviour of continuous RC beams with EB and NSM plates. A series of seven full-scale tests on two span continuous beams with EB steel or CFRP plates was performed and analysed, and is described in detail in Section 5.3 with a summaryanddiscussionofthetestresultspresentedinthejournalpaperOehlersetal.(2004) included in Section 5.3.5.1. In Section 5.4, nine two-span continuous beams retrofitted with NSM steel orCFRPstripsweretestedtoexaminetheductilitycapacityasmeasureddirectlybythemoment redistributed. A summary and discussion of the test results are presented in the journal paper Liu et al. (2005)includedinSection5.4.5.1.ThetestresultspresentedinthisChapterwillbeusedlaterin Chapter 6 to verify the flexural rigidity approach developed in this research for analysing the moment redistribution of plated members. 5.2 LITERATURE REVIEW In this Section, the importance of ductility and how the member ductility can be affected by externally bondedplatesisfirstdiscussed.Thedefinitionandwaysofmeasuringmomentredistributionis describedinSection5.2.2.Finally,areviewoftheexistingliteratureoftestsperformedbyvarious researchers on continuous plated RC beams is presented in Section 5.2.3. 5.2.1DEFINITION OF DUCTILITY Ductility is an important property of structural members that allows large deformations and deflections tooccurunderoverload(plastic)conditions.Itprovideswarningoftheimminenceoffailurefor staticallydeterminatebeams,anditallowsmomentredistributiontooccurinstaticallyindeterminate beamatoverload(Warneretal.1998).Theductilityofamembercanbedeterminedfrommoment curvature relation, where larger deformations indicate better ductility. Factors such as material ductility andsectionalpropertiesinfluencetheductilityofthemember.Formomentredistributiontooccur, Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 281 - sufficient ductility is required in the structure, hence it is a fundamental behaviour when designing for continuous plated beams. Ductilityhasalwaysbeenaconcernwhenretrofittingabeamusingexternalplates,asitiswidely acknowledged that this retrofitting technique will reduce the ductility of the member due to the external plate(Bencardinoetal.1996,2002;Swamyetal.1996;Spadeaetal.2001;El-Refaieetal.2002, 2003). The ductility of a member is largely dependent on the material and the geometry of the plates used.ForbeamsexternallybondedwithFRPplates,becauseofthelinearelasticstress-strain behaviour of FRP and its high tensile strength and high strain at fracture, tests have shown that these beamsarepronetobrittleprematuredebondingfailure,wellbeforethedesigncapacityisreached (Spadeaetal.2001;Ritchieetal.1991;Saadatmanesh&Ehsani1991).Beamsplatedwithsteel platescanprovidegoodductility,butdependingontheplatinggeometry,itispossiblethatbrittle debonding failure occurs prior to concrete crushing as have been shown by numerous tests performed by different researchers (Mohamed Ali 2000; Ashrafuddin et al. 1999; Oehlers & Moran 1990; Nguyen & Oehlers 1997). Duetothe additional plate and thebondinthe plate/concreteinterface,thestrainatwhichfailureof the beam occursisreduced,thereforethe ductilityof platedmembers andtheir abilitytoredistribute momentislessthanthatofunplatedRCbeams.Atpresent,thereareonlyrulesofthumb(i.e.fib 2001),suchasensuringthatinternalreinforcingbarsyieldbeforeplatesdebondorfracture,to guarantee that there is adequate amount of ductility. The ductility index used in many international RC codes that places limits on the neutral axis depth dn cannot be used in plated beams. This is because thecurvatureofanRCmemberisbased on thestrainintheconcrete,whereas forplatedmembers thecurvatureisusuallydependentonthestrainintheplate.Afewresearchershavelookedinto definingtheductilityofplatedRCbeamsbasedondeflectionandenergy.Althoughductilityindices were found to give good representation of the physical aspects of the ductility of the beams (Spadea et al. 2001; El-Refaie et al. 2002, 2003), how the concept of ductility indices can be applied in practice is unclear. 5.2.2DEFINITION OF MOMENT REDISTRIBUTION Momentredistributioninastaticallyindeterminatebeamisthetransferofmomentbetweenhigh moment regions in the member, while maintaining the overall strength. At the initial stage of loading, the continuous beam will behave linear elastically such that both span moments and support moments Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 282 - willincreaseproportionaltotheincreaseinappliedload.Eventually,theultimatestrengthwillbe reached at the maximum moment sections upon further increase in the applied moment. Now as the loadisincreasedfurther,themomentswillredistributefromthemaximummomentsectionstoother parts of the beam, such that the total static moment in the beam remains unchanged.TherearevariouswaysofmeasuringthedegreeofmomentredistributionasshowninTable5.1 (Rebentrost2003),anditisfoundthatthemajorityofthesemethodsaredependentonthe comparison of the plastic and elastic moments. Rebentrost (2003), Lin & Chien (2000) and many other researchers relate the difference between the actual and elastic moments to the elastic moment as a percentage (Table 5.1). An approach similar to Rebentrosts (2003) is adopted in this research, where itisassumedthattheflexuralrigidityofanRCbeamisconstantinordertodeterminetheelastic distributionofmoments.Therefore,themomentredistributionisdefinedasthechangeinmoment fromtheelasticmomentbasedontheflexuralrigiditybeingconstantthroughoutthebeam,withthe percentage redistribution of moment from the hogging region given by Equation 5.1.Table 5.1 Definitions of moment redistribution (Rebentrost 2003) ReferenceDefinition of moment redistribution Trichy and Rakosnik (1977) plultww= , p = moment redistribution wult = ultimate load wpl = plastic failure load Cohn (1986)M Mel = M = actual moment Mel = elastic moment due to ultimate load Arenas (1985) f plf colPAR =PAR=plastic adaptation ratio; f =load factor at failure; col =collapse load factor; fpl=plastic failure load factor Bennett (1960); Moucassian (1988) el plel nlw ww w= wel,pl,nl = loads based linear elastic, plastic and non-linear analysis Scholz (1990) max1 + =ult pl elult fpM M MM M max = maximum % MR required for wpl Mult = ultimate moment Mf = factor moment Mpl = plastic moment Rebentrost et al. (1999) elelMM M = M = actual moment Mel, Mpl=elastic M corresponding to P, Ppl Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 283 - ( ) ( )( )100 %..=const EIhogtesthogconst EIhogMM MMREquation 5.1 WhereinEquation5.1foraspecificstaticmoment,(Mhog)EI.constisthetheoreticalhoggingmoment from a linear elastic analysis which assumes that the flexural rigidity EI is constant and (Mhog)test is the experimental hogging moment for the same static moment, that is for the same applied load. 5.2.3TESTS ON CONTINUOUS PLATED RC BEAMS Themajorityofexistingresearchonplatedstructuresfocusesonthedebondingmechanismsof simplysupportedbeamsandverylimitedresearchhasbeencarriedoutoncontinuousbeamswith externallybondedplates.Park(Park&Oehlers2000)performedtestsonaseriesofcontinuous beamswithexternallybondedsteelorFRPplatesoverboththesaggingandhoggingregions.The plates were applied on either the tension face or the side faces of the beam. For both steel and FRP plated beams, plate debonding was observed. This indicates that although steel is a ductile material, theEBsteelplatescanstillreducetheductilityoftheretrofittedbeamdependingontheplating dimensions and positions. Due to the geometry of the beams and the test set-up, almost zero moment redistribution was obtained in all the tests. El-Refaieetal.(2002,2003;Ashouretal.2004)performedtestsonsixteenRCcontinuousbeams with different arrangements of internal and external reinforcement. All beams were plated with CFRP sheetsorplatesoverthehoggingand/orsaggingregionsasshowninFigure5.1.Thespecimens wereclassifiedintothreegroups:H,S,andE,wherethebeamswithineachgrouphavethesame geometricaldimensions.Forthethreegroupsofbeamstested,thelength,thickness,formand positionoftheCFRPplateswerevariedtoinvestigateitseffectsonthestrengthandductilityofthe platedmembers.The dimensionsoftheplatesareshowninTable 5.2whereNp, L1,and L2 arethe numberofCFRPsheets;lengthoftheplateoverthehoggingandsaggingregionsrespectively.All specimenswereplatedwithCFRPsheets,eachlayerof0.117mmthickness,exceptforbeamsE2, E3,E4whichwerestrengthenedwithCFRPplatesof1.2mmthickness.Thepercentageofmoment redistributionforthemaximumsagging%MRsandhogging%MRhmomentsatfailureareshownin Table 5.2, where %MR was calculated based on the definition adopted by Rebentrost et al. (1999) in Table5.1.Notethatforbeamswith%MRh0 i.e. group S.Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 284 - Figure 5.1 Tests performed by El-Refaie et al. (2002, 2003) Table 5.2 Beam details and results of tests performed by El-Refaie et al. (2002, 2003) hoggingsagging%moment redistribution specimen Top reinf. Bottom reinf. NpL1 (m)NpL2 (m)%MRh%MRs H1-----6438 H222.0---3119 H362.0---1911 H4102.0---116 H561.0---3119 H6 2T8 steel bars 2T20 steel bars 23.021.0-3521 S1----87-52 S2--22.061-37 S3--62.055-33 S4--63.545-27 S5 2T20 steel bars 2T8 steel bars --103.521-12 E1-----11 E212.5---2415 E3--13.528-17 E412.513.57-4 E5 2T16 steel bars 2T16 steel bars 62.5---2314 Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 285 - Through these tests, it was found that premature plate debonding was the dominant failure mode, and significantamountsofmomentredistributionwereobtainedinallthebeams(Table5.2).This contradictstheexistingdesignguidelines(fib2001;ConcreteSociety2000)whichsuggestthat momentredistributionshouldnotbeallowedforplatedRCbeams.TheunplatedcontrolbeamsH1 and S1 showed significantly greater %MR than the plated beams, indicating reduction in ductility as a resultofplating.ForthegroupEbeamswhichhadthesameinternalreinforcementatthetopand bottom of the beams, the unplated beam E1 had almost zero %MR, while moment redistribution was observedintheplatedbeamsinthistestgroup,especiallyforthebeamsplatedovereitherthe hogging or sagging region only (Table 5.2). This is because, when the hogging or sagging regions are plated, thestiffnessofthis regionwasincreased,whichcaused avariationofflexuralstiffnessalong the beam such that more moment was attracted to the strengthened region as compared to before the region was plated. Therefore, the redistribution of the moments is largely dependent on the positions and dimensions of the plates (Table 5.2), and consequently the variation in flexural stiffness along the beam.ThetestsalsoshowedthatalthoughCFRPwasplatedalongtheentirehoggingorsagging region,thisdidnotpreventprematuredebondingoftheplates.Therefore,furtherresearchintothe moment redistribution of EB beams is essential.TestsonsimplysupportedRCbeamswithNSMstrips (Hassan&Rizkalla2003;Taljsten&Carolin 2003;Blaschko2003)haveshownthatNSMplatesdebondorfailatmuchhigherstrainsthanEB plates,thereforeingeneralNSMplatedbeamsareexpectedtobemoreductilethanEBplated beams. However, depending on the anchorage length of the NSM strips, premature debonding failure priortoconcretecrushingispossible(Hassan&Rizkalla2003;Barros&Fortes2005).Thismeans thattheexistingdesignapproachesforductilityandmomentredistributionofunplatedRCbeams cannotbeappliedtoNSMbeamsastheformerrequiresthatconcretecrushingoccurs.Mostofthe testscarriedoutanNSMplatedbeamsaresimplysupport,thereisnoexperimentalnortheoretical studies carried out on the moment redistribution of continuous NSM plated beams. As many in-situ RC beams are of continuous construction, investigation is needed to examine the behaviour of continuous beams with NSM plates. Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 286 - 5.3 EXPERIMENTAL STUDIES ON RC BEAMS WITH EXTERNALLY BONDED STEEL/FRP PLATES Inthistestprogram,sevencontinuousRCbeamswithexternallybondedsteelorCFRPplatesof variousdimensionsweretested.Thespecificaimofthesetestswastobothdemonstrateand measure moment redistribution in externally bonded plated flexural members and not to demonstrate the effectiveness of the strengthening method. In this Chapter, the specimens, the test set-up and the material properties are first described, followed by thorough descriptions of the results from each test. FinallyinSection5.3.5,asummaryofthetestresultsarepresentedintheattachedjournalpaper, alongwith acomparison betweentheresultsfor the differentbeamstoillustratetheeffectivenessof the various plating systems.

5.3.1GEOMETRY OF TEST SPECIMENS EachofthesevenspecimenstestedconsistsofthetwospansoflengthL=2400mmasillustrated in Figure5.2withthecross-sectionofthebeamsshowninFigure5.3andthegeometryoftheplates given in Table 5.3, where tp, bp and be are the plate thickness, plate width, and the distance from the edge of the plate to the side of the beam. The three steel plated test beams are denoted as SS1, SS2, and SS3; and the four CFRP plated specimens are denoted as SF1, SF2, SF3, and SF4. The hogging regions of each beam was plated over the tension face with steel or FRP plates of length Lp=2200mm, andthesaggingregionswereleftunplatedasinFigure5.2.Theinternalreinforcementisthesame throughoutthebeam,wheretwomildsteelbarsofdiameter12mmwereplacedatthetopofthe beam, and four mild steel bars of diameter 16mm were placed at the bottom of the beam. Therefore, thetensilereinforcementinthehoggingregion,2Y12bars,wasmuchlessthanthetensile reinforcement in the sagging region, 4Y16 bars, to ensure that the plated hogging region reached its moment capacity first; this then allowed the hogging region to shed moment, or redistribute moment, tothesaggingregionasthestaticmomentwasbeingincreased,thereby,increasingthesagging moment.Theinternalbarswereequallyspacedwithadistanceof20mmfromtheedgeofthe concretetothecentreofthebarsasillustratedinFigure5.3.AllbeamstestedhadW10stirrups placed at 1200mm centre to centre (c/c) to hold the longitudinal bars in position.Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 287 - All dimensions in mm East West Plate 24002400 100100 5000 1200 11001100 1200 2Y12 4Y16 W10 stirrup @1200c/cInterior supportsupport support PP Figure 5.2 Two span continuous beam specimens 2Y12 4Y16 W10 @ 1200c/c 120 375 2Y12 4Y16 W10 @ 1200c/c 120 375 be bp tp Saggi ng region Hogging region 20 20 be Figure 5.3 Cross-sectional details of EB test series Table 5.3 Geometrical properties of externally bonded plates Specimenmaterialtp (mm)bp (mm)be (mm) SS1Steel plate375150 SS2Steel plate2112131.5 SS3Steel plate122475.5 SF1CFRP plate2.425175 SF2CFRP plate1.250162.5 SF3CFRP plate1.280147.5 SF43 x CFRP sheeta 2.44b 100137.5 a 0.2mm thick carbon FRP fabric b measured thickness Themainvariableofthedifferentspecimenswastheplatepropertieswithdetailsoftheplate geometrygiveninTable5.3.SpecimensSS1toSS3usedadhesivelybondedmildsteelplateswith platethicknessestpthatvariedfrom1mmto3mm.Theplatewidths(bp)werevariedtoensure virtually the same cross-sectional area and, hence, the same axial rigidity (EA) so that the theoretical Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 288 - moment-curvaturerelationships,ignoringintermediatecrackdebonding,wouldbeidentical. Specimens SF1 to SF3 used adhesively bonded pultruded carbon FRP plates of thicknesses 1.2 mm and 2.4 mm. Whereas, Specimen SF4 used three layers of carbon FRP fabric, each with a thickness of 0.2mm, that was applied using the wet lay-up procedure; its thickness and Youngs modulus were measureddirectlyfromspecimensthatweretakenfromtheplatedbeam.Theplatewidthswere varied from 25 mm to 100 mm and specimens SF1 and SF2 had plates of the same axial rigidity.The specimens were designed such that CDC and PE debonding did not precede IC debonding. PE debondingwaspreventedbyterminatingtheplatebeyondthepointofcontraflexureandontothe compression faces of the sagging regions. CDC debonding was prevented by ensuring that a critical diagonalcrack,associatedwiththeconcretecomponentoftheverticalshearcapacityVc,didnot occurpriortoplatedebonding;becauseoftheCDCrequirementtheslabshapedcross-sectionwas used. Toexplainthereasonfortheslabshapedcross-sectionshowninFigure5.3,letusconsiderthe capacityofabeamorslabwithoutstirrupssothatthestrengthiscontrolledbyeithertheflexural capacityortheconcretecomponentoftheshearcapacityVc,asthelattercontrolsCDCdebonding. Let us consider a rectangular beam or slab which has the same cross-sectional area of concrete and thesamecross-sectionalareaoflongitudinaltensionreinforcingbars.Thebeamshapedcross-section,inwhichthewidthislessthanthedepth,ismorepronetoverticalshearfailure,andCDC debonding at Vc, than the slab shaped cross-section, in which the width is greater than the depth. This isbecausetheconcretecomponentoftheverticalshearcapacityofthesetwoshapesVcisroughly equaland,hence,theirresistancetoCDCdebonding. However,thebeamshapedcross-sectionwill have a higher flexural capacity than the slab shaped cross-section due to the increased depth (lever arm) and, consequently, can resist a greater applied load at flexural failure with its associated greater vertical shear force. Therefore, beam shapes without stirrups are more prone to shear failure at Vc and consequentlyCDCdebondingthanslabshapes.Hencearelativelylargebutrealisticspan-to-depth ratioof20wasrequiredandtheuseofaslabshapedcross-sectioninwhichthewidthwasgreater than the depth as shown in Figure 5.3. 5.3.2TEST SETUP AND INSTRUMENTATION Identical test setup and instrumentation was used in all seven specimens. The concentrated loads P wereappliedatmid-spanasinFigure5.4sothat,foranelasticdistributionofmomentwithan Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 289 - assumedconstantflexuralrigidity,themaximumhoggingmomentwouldbe20%greaterthanthe maximum sagging moment. As the system is symmetrical, the specimen can be analysed as a single span with the moment distribution illustrated in Figure 5.5, where Mstatic, Mhog, and Msag are the static, hoggingandsaggingmomentsrespectively.Fromsimilartriangles,MstaticisalsogivenbyEquation 5.2. The loads were applied on the top of the beam by hand operated hydraulic jack through load cells andknifeedgebearingsof100mminwidth.ThetestrigoveronespanisshowninFigure5.6. DeflectionsweremeasuredundertheappliedloadsPusingLVDTs,loadcellswereplacedatthe appliedloadsandatthewestsupportinFigure5.4sothatthedistributionofforcescouldbe determineddirectly.TwoLVDTswereplacedovertheexternallybondedplateat100mmfromthe interior support as illustrated in Figure 5.7 to measure the slip between the concrete and the plates. LC3 LVDT 1LVDT 1 East West LC1LC2 Plate 24002400 100100 5000 1200 11001100 1200 PP 100100 Figure 5.4 Test set-up Mhog P Msag Mstatic=PL/4 L/2 L R Figure 5.5 Moment distribution 2 4hogsag staticMMPLM + = =Equation 5.2 Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 290 - Figure 5.6 Test rig 100 LVDT 3 LVDT 4 Plate 11001100 900900100 100 100 Figure 5.7 LVDT positions for slip between concrete and EB plates Seven strain gauges (SG) were bonded along the centre of the external plate of each specimen over the interior support at 200mm centre to centre spacing, and two strain gauges were placed at 100mm from each end of the plate as illustrated in Figure 5.8. These strain gauges were used to measure the strains in the plates, as well as to detect the propagation of the debonding cracks. 200 Plate 11001100 100 200 200400200 100 200 200400 SG5 SG6 SG7 SG8 SG9 SG4 SG3 SG2 SG1 Figure 5.8 Strain gauges positions for externally bonded plated 5.3.3MATERIAL PROPERTIES Thetestbeamswerecastfromasingleconcretepour,butbecausethespecimenswheretestedat differenttimes,theconcretepropertiesforthespecimensweresubstantiallydifferent.Theconcrete Interior support Hydraulic jack Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 291 - propertiesofspecimensSS1,SF1,SF2andSF3aregiveninTable5.4,whereEcandfcarethe Youngsmodulusand thecylindercompressivestrengthrespectively.Theremainingspecimenshad concretepropertiesgiveninTable5.5,whereindirecttensiletestswerealsocarriedouttomeasure the tensile strength ft of the concrete. Table 5.4 Concrete properties for beams SS1, SF1, SF2, SF3 AgeSample No. Ec (MPa)fc (MPa)Density (x10-3 g/mm3) 136,32739.12.33 235,25138.82.32 335,70539.82.36 50a (Days) Average35,76139.22.34 133,79735.92.32 235,66138.22.32 335,62640.82.33 59b (Days) Average35,02838.32.32 Average35,39438.82.33 a Concrete age of the first test b Concrete age of last test Table 5.5 Concrete properties for beams SS2, SS3, SF4 AgeSample No. Ec (MPa)ft (MPa)fc (MPa)Density (x10-3 g/mm3) 1398144.3948.032.31 2445974.9849.292.36 3395784.9647.492.32 439023-48.272.33 330 (Days) Average407534.7848.272.33 Tensile tests were performed on the internal reinforcing bars used in the test specimens to obtain the yield fy and fracture frac strengths of the bars as given in Table 5.6. Being mild steel, the bars Youngs modulus Eb can be assumed to be 200GPa. The material properties of the externally bonded plates were obtained from tensile tests and are given inTable5.7.Forthemildsteelplates,aYoungsmodulusEpof200GPaisassumed.BeingFRP plates,theplatesdonotyieldandthelongitudinalYoungsmodulus(i.e.paralleltothedirectionsof the fibres) was measured directly. For the CFRP wet lay-up used in specimen SF4, its thickness and material properties were measured directly from specimens that were taken from the plated beam. Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 292 - Table 5.6 Material properties of reinforcing bars for EB test series BarsSample no. fy (MPa)fu (MPa) 1592711 2592720 3619714 Y12 Average601715 1532686 2549679 3537674 Y16 Average540680 Table 5.7 Properties of EB plates Material Sample no.tp (mm)fy (MPa)fu (MPa)Ep (GPa) 13331462- 23340468- 33340466- average3337466200 12245317- 22244317- 32243319- average2244 (223a)318200 11247302- 21248304- 31248303- Steelaverage1248 (211a)303200 12.4-2800144 Pultruded CFRP 11.2-2800144 12.35-39843843 22.38-33645202 32.60-31740618 CFRP wet lay-up average2.44b-35043221 a Proof stress b tp is the measured thickness of 3 layers of 0.2mm thick CFRP fibres plus the adhesive Properpreparationoftheplatesandtheconcretesurfacebeforeapplicationisnecessarytoallowa goodbondtoformbetweentheplateandtheconcrete.Beforeadhesivelybondingtheplatestothe Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 293 - concretesurface,thesurfacewaspreparedbygritblastingtoremovelaitanceandexposethe aggregates. The surface was then brushed mechanically to remove all loose particles. The remaining dust and debris was then removed by blowing air. The steel plates were sand blasted to remove rust orlooseparticles,andanygreaseoroilwasremovedbyapplyingnon-inflammablesolvents.The CFRPpultrudedplateswerecleanedwithanygreaseoroilremovedusingasolventpriorto application. AralditeK340andMBraceLaminateadhesiveweretheepoxyresinsusedforthesteelandCFRP platesrespectively.Themanufacturersspecificationsofthematerialpropertiesoftheepoxyresins aregiveninTable5.8.Thetensilestrength,longitudinal(i.e.paralleltothedirectionsofthefibres) Youngsmodulus(Ea)l,andtheperpendicular(i.e.perpendiculartothedirectionsofthefibres) Youngsmodulus(Ea)poftheadhesivestestedinthisresearcharealsoshowninTable5.8.The adhesives used were mixed according to the specifications recommended by the resin manufacturer, whichensuredthatnoairbubblesorvoidswereentrappedintheadhesivewhencured.Forsteel plates,theadhesivewasappliedtothebeamsurfaceandtheplatewaspressedontoconcreteall over,andsurplusadhesivewassqueezedoutattheedges.ForCFRPplates,acoatofMBrace Primer was applied on the bonding surface using a roller or brush and when it was tack-free the plate was adhesively bonded as follows: the laminate surface was cleaned with MBT Thinner and a 1.5mm thicklayerofMBraceLaminateAdhesivewasappliedonboththeconcreteandlaminatesurfaces; then a layer of laminate was applied to the concrete substrate by hand and pressed onto the adhesive with a rubber roller. Additional CFRP layers were applied the same way on the uncured wet adhesive, and finally, the plates were left for curing for at least seven days.Table 5.8 Properties of adhesives from manufacturers specifications Manufacturers specificationsFrom tests Epoxy resin Compressive strength (MPa) Tensile strength (MPa) Flexural strength (MPa) Tensile bond strength (MPa) Max. operating temp. Tensile strength (MPa) (Ea)l (MPa) (Ea)p (MPa) Araldite K340 100-12030-4020-3015-1785oC24.7453812109 MBrace>60N/A>30>3.5N/A16.1535217030 5.3.4TEST RESULTS Inthefollowingsection, descriptions of thebehaviour ofthebeams asloadsweregraduallyapplied, and analyses of the test results are presented for each test specimen. Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 294 - 5.3.4.1 BEAM SS1 (STEEL 75X3) The beam was plated with a 3mm thick steel plate on the tension face over the interior support. As the hoggingregionofthebeamismuchweakerthanthesaggingregion,failurewasexpectedinthe hogging region. The test specimen was designed against CDC and PE debonding failure, therefore IC debonding failure was expected to occur. The beams were initially tested under load control where a loadPwasappliedatsmallincrementsateachspanasshowninFigure5.4untilthemaximum applied load was obtained, and thereafter the beam was loaded under deflection control up to failure. Asthebeamwasgraduallyloaded,thefirstflexuralcrackwasfoundattheinteriorsupportatan applied load P of 9kN, with an average reaction force R of 2.9kN at the external supports. This caused amaximummomentatthehoggingMhogandsaggingMsagregionsof3.72kNmand3.45kNm respectively. As the beam was further loaded, more flexural cracks formed over the hogging region as showninFigure5.9,wherethecracksweremarkedbytheblacklinesandthenumbersdenotethe loadPatwhichthecrackformed.AtP=30kN(R=9.9kN,Mhog=12.2kNm,Msag=11.9kNm),theplate yielding strain was recorded at SG5 and still no sign of debonding was observed. Figure 5.9 Beam SS1: Prior to debonding (P=32kN) Initial debonding occurred at a load P of 37kN (R=12.6kN, Mhog=14.2kNm, Msag=15.1kNm), as shown bytheformationoftheICinterfacecrackspropagatingfromtherootoftheflexuralcrackoverthe interiorsupportinFigure5.10.Uponfurtherloading,moreICinterfacecracksformedattherootsof theflexuralcracksneartheinteriorsupportasshowninFigure5.11foranappliedloadof47kN (R=16.6kN,Mhog=16.7kNm,Msag=19.9kNm).Initially,theICinterfacecrackspropagatedgradually towardstheplateend,joiningotherICinterfacecracksastheymovedalong.WhenaloadP=48kN (R=17kN, Mhog=16.9kNm, Msag=20.3kNm) was applied, the IC interface cracks propagated very rapidly Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 295 - to the east plate end, causing sudden complete debonding of the plate at a displacement of 10.3mm in the east span as shown in Figure 5.12. A maximum plate strain of 0.004446 at SG5 was measured just prior to IC debonding failure. Aftertheplatecompletelydebonded,thebeamcontinuedtobeloadeduntilverticalshearfailure occurredataloadP=76.45kN,atamaximumdisplacementof45.84mm.Basedonthemeasured platestrain andfrom fullinteractionanalysis,itisestimated thatthetensilebars yieldedataloadof 44.9kN,beforecompletedebondingoftheplate.Thedistributionofflexuralcracksinthehogging region over the east span is shown in Figure 5.12, where it is evident that the cracks spacings varied, with the last flexural crack in the region, crack D, at approximately 400mm from the interior support. Figure 5.10 Beam SS1: Initial debonding (P=37kN) Figure 5.11 Beam SS1: Debonding propagation (P=47kN) IC Interface cracks Interior support Debonding propagation Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 296 - Figure 5.12 Beam SS1: Debonding failure (P=48kN) Thevariationofmoment,atthepositionofmaximumhoggingMhogandsaggingMsagmomentsas showninFigure5.5,withthemeandeflectionundertheappliedloadsatmid-spans,areplottedin Figure 5.13.Itcanbeseenthatnearthestart,inregionA,thehoggingmoment wasslightlygreater thanthesaggingmomentaswouldbeexpectedfromanelasticanalysis.Aftertheplateyieldedat point B, the hogging moment then reduced relative to the sagging moment. Initial debonding occurred atpointC,anditwasestimatedthatthetensilebarsyieldedatpointD.Themaximumhogging moment and the maximum plate strain were obtained just prior to IC debonding failure, after which a sudden reduction in Mhog occurred and the behaviour of the hogging region reverts back to that of the unplated section at E.0510152025303540450 10 20 30 40 50displacement(mm)Moment (kNm)MsagABshear failureCDIC debonding failureEMhog Figure 5.13 Beam SS1: Moment vs displacement After the plate completely debonded at point E, the sagging moment continually increased relative to thehoggingmomentwhichsignifiesmomentredistribution;itwasforthisreasonthatthesagging regionwasmademuchstrongerthanthehoggingregioninordertoachieveasmuchmoment East support P Debonding propagation AB D CIntermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 297 - redistributionaspossible.Itisworthnotingthatthecontinuousbeameventuallyfailedbyvertical shear failure in Figure 5.13. However, this occurred well after the plate had IC debonded so that the vertical shear failure had no effect on the redistribution of moment.Figure 5.14 shows the plate strains measured along the plate as the moment over the interior support increased up to IC debonding failure, where the positions of the strain gauges SG are given in Figure 5.8.ThesteelplatefirstyieldedatstraingaugeSG5overtheinteriorsupportatamoment Mhog=12.2kNm.Aftertheplateyielded,theplatestrainatSG5increasedrapidlyduetotheductile behaviourofsteel.WhenthemomentatinteriorsupportMhogwas15.6kNm,the plateyieldingstrain p.y was also reached at SG4. The strain along the plate continued to increase as Mhog increased up to IC debonding failure. This shows that the bond at the plate/concrete interface remained strong along the beam until rapid debonding occurred, which resulted in zero bond at the interface. Therefore, the maximum plate strain was achieved just prior to debonding failure. 024681012141618-1000 0 1000 2000 3000 4000 5000strain (x10-6)moment at interior support (kNm)SG1 SG2SG3 SG4SG5 SG6SG7 SG8SG9SG7 SG3 SG1EASTSG2 SG5 SG4 SG6WESTSG8 SG9 p.ySG3SG4SG5SG6SG7 Figure 5.14 Beam SS1: Moment vs plate strain ThevariationofthemaximumhoggingmomentinthebeamMhogasaproportionofthemaximum saggingmomentinthebeamMsagisshowninFigure5.15.FromanelasticanalysisinwhichEIis assumedtobeconstant,Mhog/Msag=1.2whichisshownaslineAinFigure5.15.Theabscissain Figure 5.15 is the applied static moment, Mstatic given by Equation 5.2, as a proportion of the ultimate maximum static moment, (Mstatic)u = (Msag)u + (Mhog)u/2, based on nonlinear full interaction analysis of theultimatecapacityofthehoggingandsaggingsections,(Mhog)uand(Msag)u,andignoringIC debondinginthecaseofthehoggingregion;hencetheupperlimitofMstatic/(Mstatic)u=1.0.Forthe platedbeamconsidered,(Mstatic)u=47.1kNm.ThelinemarkedBisthemaximumredistribution Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 298 - assuming the sagging region achieved its theoretical moment capacity Msag=(Msag)u, while the capacity ofthehoggingregionisthemomentexperimentallymeasuredatfailureMhog=(Mhog)fail;andtheline markedCisthemaximumredistributionafterplatedebondingthatiswhen(Mhog)uisthetheoretical ultimate capacity of the unplated section.00.20.40.60.811.21.40 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Mstatic/(Mstatic)ultMhog/Msagtest resultsABCDEplate yield1st debondingbar yieldFGHIC debonding failureelastic (EI constant)shear failureIJMstatic / (Mstatic)u Figure 5.15 Beam SS1: hogging-moment/sagging-moment WhentheloadwasfirstappliedMhog/Msagapproaches1.2inregionDinFigure5.15;onecanstill notice a slight divergence from this value because the beam was bedding or settling down under very smallloads.Soon after,Mhog/MsagreducedgraduallyandthedivergencefromMhog/Msag equalto 1.2 signifies moment redistribution. The first flexural crack was observed at point E, and at point F yielding of the plate occurred over the interior support. This was shortly followed by the appearance of the first ICinterfacecrackatGandeventuallyICdebondingfailureatpointHwhichcoincidedwiththe maximumplatestrain. Aftertheplatecompletely debondedinregionI,the behaviourofthehogging regionrevertsbacktothatoftheunplatedsection.Theunplatedbeameventuallyfailedinshearat pointJ.ItcanbeseenfromFigure5.15thatduetoprematuredebonding,themaximumallowable moment redistribution of the plated beam, line B, could not be achieved. Figure5.16showsthevariationofthemaximumhoggingMhogandsaggingMsagmomentsasthe applied loads P increased. (Mhog)el and (Msag)el are the hogging and sagging moments obtained based onelasticanalysisofconstantEI.Thegreaterthedivergencefromtheelasticmomentsmeansthat more moment is being redistributed. It can be seen from Figure 5.16 that the beam behaved elastically untilthefirstflexuralcrackoccurredatpointA,afterwhichsmallamountsofhoggingmomentwere redistributedtothesaggingregions.ItwasaftertheyieldingoftheplateatpointBwhensignificant amountsofmomentredistributionwereobserved.WhentheplatedebondedatpointE,asudden Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 299 - reduction in applied load, and hence the moments, was observed. However, as the unplated RC beam had not yet failed, the load increased again with the behaviour of the hogging region now that of the unplatedsection,suchthatMhogisnowsignificantlylessthanpriortodebonding.Mhogremained roughlyconstantuptoshearfailureatpointF,whilemuchmomentwastakenupbythesagging region, indicating that the flexural capacity of the unplated hogging section was reached. 0510152025300 20 40 60 80applied load P (kN)Mhog (kNm)0510152025303540450 20 40 60 80applied load P (kN)Msag (kNm)1st flexuralcrackplateyield1st debondingbaryield IC debondingfailureshearfailureshearfailureAB CDEFABCDEF(Mhog)el(Msag)el Figure 5.16 Beam SS1: Maximum hogging and sagging moments The variation of percentage of moment redistribution %MR, calculated using Equation 5.1, is shown in Figure5.17fordifferentMstaticapplied.Astheappliedload,andhenceMstaticincreased,the%MR increaseduptoamaximumof20%atICdebondingfailure.Aftertheplatedebonded,theflexural strengthofthehoggingregionreduced,thereforethehoggingmomenthadtoredistributetothe saggingregiontoallowforthisreductioninstrengthasshowninFigure5.16.Thisresultedina sudden increase in %MR as shown by region A in Figure 5.17. As the ductility of the unplated hogging regionismuchgreaterthanbefore,large%MRoccurredandamaximumof62%moment redistribution was obtained at shear failure of the unplated beam.0102030405060700 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Mstatic/(Mstatic)ult% Moment redistributionu 1st flexuralcrackplate yield 1st debonding baryield IC debondingfailureshearfailureA Figure 5.17 Beam SS1: percentage of moment redistribution Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 300 - 5.3.4.2 BEAM SS2 (STEEL 112X2) No sign of cracking was observed until, at an applied load P of 14.8kN, three flexural cracks appeared near the interior support. A resultant reaction force R of 4.6kN was measured at the external supports, whichcausedamaximummomentatthehoggingMhogandsaggingMsagregionsof5.5kNmand 6.7kNm respectively. As the beam was further loaded, more flexural cracks formed over the hogging region. AtP=19.8kN(R=6.38kN,Mhog=8.4kNm,Msag=7.65kNm),theplatereachedtheyieldingstrain at SG5. ICdebondingfirstoccurredataloadPof29.8kN(R=10kN,Mhog=11.8kNm,Msag=12kNm)nearthe interior, as shown by the formation of the IC interface cracks propagating from the root of the flexural cracks in Figure 5.18, where the cracks were marked by the black lines and the numbers denote the loadPatwhichthecrackformed.TheICinterfacecracksthatformedbetweencracksBandCin Figure 5.18 were propagating in opposite directions, as shown by the arrows, which indicate that there was a reverse in slip in between the two cracks. Upon further loading, more IC interface cracks formed at the roots of the flexural cracks near the interior support as shown in Figure 5.19 for an applied load of 38kN. These debonding cracks propagated mainly towards the plate end, joining other IC interface cracks as they moved along, such as between cracks A, B and C in Figure 5.20. It is worth noting that eventuallynomoreflexuralcracksformedasmoreloadwasapplied,andcracksDandEinFigure 5.20 are the last flexural cracks in the hogging region, i.e. no further flexural cracking occurred in the hogging region beyond cracks D and E. Figure 5.18 Beam SS2: Initial debonding (P=30kN) A B CD IC interface cracks Interior support East West Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 301 - Figure 5.19 Beam SS2: Debonding propagation (P=38kN) Figure 5.20 Beam SS2: Debonding propagation (P=55kN) The IC interface cracks propagated rather gradually until they reached the last flexural crack, crack D inFigure5.21,afterwhichthecrackspropagatedrapidlytowardstheplateendcausingcomplete debondingoftheplateatP=64.5kN(R=24.2kN,Mhog=19.3kNm,Msag=29kNm)asshowninFigure 5.22. A maximum displacement of 17.3mm was recorded in the east span beneath the applied load at failure.JustpriortoICdebondingfailure,theplatereachedamaximumstrainof0.005926atSG5. Basedonthemeasuredplatestrainandfromfullinteractionanalysis,itisestimatedthatthetensile barsyieldedataloadof46.8kN,beforecompletedebondingoftheplate.Irregularflexuralcrack spacings were observed in the test.The distribution of flexural cracks was similar to Specimen SS1, AB C D Interior support East Debonding propagation E ABCD Interior support East West Debonding propagation Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 302 - where four cracks formed in the hogging region of the east span as shown in Figure 5.22, with the last crack, crack D, at approximately 300mm from the interior support. Figure 5.21 Beam SS2: Debonding failure (P=65kN) Figure 5.22 Beam SS2: Debonding failure (P=65kN) Figure5.23showsthevariationofmoment,atthepositionofmaximumhoggingMhogandsagging Msagmoments,withthemeandeflectionundertheappliedloadsatmid-spans.Itcanbeseenthat nearthestart,inregionA,thehoggingmomentwasgreaterthanthesaggingmomentaswouldbe expectedfromanelasticanalysis.Afterflexuralcracking(pointB)occurredandtheplateyielded (pointC),thehoggingmomentthenreducedrelativetothesaggingmoment.OnceICdebonding beganatpointD,thedivergencebetweenMhogandMsagbecomesgreater,indicatingthatmore moment is being redistributed from the hogging to the sagging region. The maximum hogging moment and the maximum plate strain were obtained just prior to IC debonding failure.ABC D Interior support East Debonding propagation E A BC D Interior support East Debonding propagation Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 303 - 051015202530350 5 10 15 20displacement(mm)Moment (kNm)MsagABC1st ICdebondingIC debonding failurebarsyieldMhogplateyieldD Figure 5.23 Beam SS2: Moment vs displacement Figure 5.24 shows the plate strains measured along the plate as the moment over the interior support increased up to IC debonding failure, with the positions of the strain gauges SG given by Figure 5.8. The steel plate first yielded at strain gauge SG5 over the interior support at a moment Mhog=8.4kNm. Soon after, the plate yielding strain p.y was reached at SG6 and SG4 at moments Mhog of 10kNm and 10.3kNm respectively. After the plate yielded, the plate strains at SG4, SG5 and SG6 increased more rapidly due to the ductile behaviour of steel. The strain along the plate continued to increase as Mhog increased up to IC debonding failure, and a maximum plate strain of 0.0059 was achieved just prior to debonding failure at Mhog=19.3kNm. 0510152025-1500 0 1500 3000 4500 6000plate strain (x10-6)Mhog (kNm)SG1 (east)SG2SG3SG4SG5 (centre)SG6SG7SG8SG9 (west) p.ySG3SG4SG5SG6SG7SG9SG1 Figure 5.24 Beam SS2: Moment vs plate strain Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 304 - ThevariationofthemaximumhoggingmomentinthebeamMhogasaproportionofthemaximum saggingmomentinthebeamMsagisshowninFigure5.25,wheretheultimatemaximumstatic moment(Mstatic)u=47.8kNmfortheplatedbeamconsidered.LineAinFigure5.25istheelastic distribution assuming EI is constant i.e. Mhog/Msag = 1.2, line marked B is the maximum redistribution fortheplatedsectionandthelinemarkedCisthemaximumredistributionfortheunplatedsection. WhentheloadisfirstappliedMhog/Msagapproaches1.2inregionDinFigure5.25.Theslight divergence from this value is because the beam was bedding or settling down under very small loads. Soonafter,Mhog/MsagreducesgraduallyandthedivergencefromMhog/Msagequalto1.2signifies momentredistribution.ThefirstflexuralcrackisobservedatpointE,thisisshortlyfollowedbythe appearanceofthefirstICinterfacecrackatFandeventuallyICdebondingfailureatpointGwhich coincidedwiththemaximumplatestrain.FromFigure5.25,itcanbeseenthatthebeamwas relatively close to reaching the maximum allowable moment redistribution, Line B. 00.20.40.60.811.21.40 0.2 0.4 0.6 0.8 1Mstatic/(Mstatic)uMhog/MsagIC debonding max plate strain reachedABCtest resultsDF1st IC interface crack1st flexutral crack occurredEGmaximum moment redistribution for unplated structuresmax. moment redistribution for plated structureselastic (EI constant) Figure 5.25 Beam SS2: hogging-moment/sagging-moment Figure5.26showsthevariationofthemaximumhoggingMhogandsaggingMsagmomentsasthe applied loads P increased. (Mhog)el and (Msag)el are the hogging and sagging moments obtained based on elastic analysis of constant EI. It can be seen from Figure 5.26 that the beam behaved elastically untiltheplateyieldedatpointB,afterwhichthemomentsobtaineddivergedfromtheelastic moments,indicatingthatmomentisbeingredistributed.Aftertheyieldingofthetensilereinforcing bars in the hogging region at point D, much of the load was taken by the sagging region, as indicated by the rapid increase in Msag. This shows that more moment is being redistributed from the hogging to the sagging region. Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 305 - 0510152025300 20 40 60applied load (kN)Mhog (kNm)051015202530350 20 40 60 80applied load (kN)Msag (kNm)1st flexuralcrackplateyield1st debondingbaryieldIC debondingfailureABCDE(Mhog)el(Msag)el1st flexuralcrackplateyield1st debondingbaryieldIC debondingfailureABCDE Figure 5.26 Beam SS2: Maximum hogging and sagging moments The variation of percentage of moment redistribution %MR calculateed using Equation 5.1 is shown inFigure5.27fordifferentMstaticapplied.Initially,beforeflexuralcracking,thebeambehaved elasticallysuchthatthereiszeromomentredistribution.Thediscrepancyofresultsbeforeflexural crackingisbecausethebeamwasbeddingorsettlingdownunderverysmallloads.Astheapplied load,andhenceMstaticincreased,the%MRincreaseduptoamaximumof33%atICdebonding failure.Thisshowsthatalthoughprematuredebondingoccurredinthebeam,largemoment redistribution still occurred, and the beam achieved 80% of the ultimate static moment. -10010203040500 0.2 0.4 0.6 0.8 1Mstatic/(Mstatic)ult% Moment redistribution1st flexuralcrackplate yield1st debondingbaryieldIC debondingfailureu Figure 5.27 Beam SS2: percentage of moment redistribution Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 306 - 5.3.4.3 BEAM SS3 (STEEL 224X1) Theexternallybondedsteelplateusedinthisspecimenhadalowyieldingstrainp.yof0.00124. Therefore,theyieldingstrainwasrecordedatthecentreoftheinteriorsupportevenbeforeany flexuralcrackswerevisible.TheplatefirstyieldedatSG5atanappliedloadPof13.6kN,witha reaction force R of 4.25kN measured at the external supports, resulting in maximum moments at the hogging Mhog and sagging Msag regions of 6.12kNm and 5.1kNm respectively. Flexural cracks formed soonaftertheyieldingoftheplateatanappliedloadPof17.7kN(R=5.65kN,Mhog=7.68kNm, Msag=6.78kNm), where two cracks, cracks A and B in Figure 5.28 appeared near the interior support. Figure 5.28 Beam SS3: Initial debonding (P=25kN) The formation of herringbone cracks close to the plate/concrete interface in Figure 5.28 indicates that ICdebondingoccurredataloadPof24.5kN(R=8.28kN,Mhog=9.48kNm,Msag=9.93kNm)nearthe interior.Asecondarycrack,crackCinFigure5.29,formedinbetweencracksAandB,whichcausedIC debondingtooccurpropagatingfromtherootsofthecrack.TheICinterfacecracksthatformed betweencracksBandCinFigure5.29werepropagatinginoppositedirections,asshownbythe arrows,whichindicatethattherewasareverseinslipinbetweenthetwocracks.However,the dominant direction of propagation was towards the plate end as evident from the extent of propagation of the IC interface cracks east of crack B in Figure 5.29. Figure 5.30 shows a close up of IC debonding AB IC interface cracks Interior support EastWest AB Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 307 - oftheplate.Itisinterestingtonotehowripplesappearedintheplatewheretheflexuralcracks intercepted, which indicates that the plate had been stretched. Figure 5.29 Beam SS3: Debonding propagation (P=53kN) Figure 5.30 Beam SS3: IC debonding Upon further loading, the IC interface cracks continued to propagate towards the plate end, however atP=78.4kN(R=31.1kN,Mhog=19.4kNm,Msag=37.7kNm)acriticaldiagonalcrackformednearthe appliedloadintheeastspanresultinginshearfailureofthebeamasshowninFigure5.31.A maximum displacement of 28.2mm was recorded in the east span beneath the applied load at failure. IC debondingIntermediate crack AB Interior support Debonding propagation EastWest C Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 308 - A maximum plate strain of 0.015 was reached at SG5 upon failure. Figure 5.32 shows the extent of IC debondingoverthehoggingregionatfailure.Itcanbeseenfromthetestthat,althoughthelow stiffnessandhighductilenatureofthesteelplatepreventedprematureICdebondingfailurefrom occurring, severe debonding was still evident in the beam. The extent of the permanent elongation of thesteelplateduetoyieldingcanbeseenfromFigure5.33whenthebeamwasunloadedafter failure.Basedonthemeasuredplatestrainandfromfullinteractionanalysis,itisestimatedthatthetensile barsyieldedataloadof34.5kN.Fromthetest,itcanbeseenthatassecondarycracksformin between cracks, it affects the debonding behaviour of the beam. The flexural cracks of this Specimen weremorecloselyspacedthanSpecimenSS1andSS2,wherethreecracksformedinthehogging region of the east span as shown in Figure 5.22, with the last crack, crack B, at less than 200mm from the interior support as shown in Figure 5.32. Figure 5.31 Beam SS3: shear failure in sagging region (P=81kN) Figure 5.32 Beam SS3: hogging region at failure (P=81kN) A B IC interface cracks Interior support EastWest C Critical diagonal crack East P EB plate Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 309 - Figure 5.33 Beam SS3: deformation of EB plate (P=81kN) Figure5.34showsthevariationofmoment,atthepositionofmaximumhoggingMhogandsagging Msagmoments,withthemeandeflectionundertheappliedloadsatmid-spans.Atinitialstagesof loading,thebeambehavedelastically,i.e.regionAinFigure5.34,sothehoggingmomentwas greaterthanthesaggingmoment.Yieldingoftheplatewasfoundtooccurwhilethebeamwasstill linear elastic as shown by point B in Figure 5.34. Soon after, flexural cracking (point C) occurred and the hogging moment then reduced relative to the sagging moment. After IC debonding began at point D,themomentinthehoggingregionbecamelessthanthatinthesaggingregion,indicatingthat moment is being redistributed from the hogging to the sagging region. Upon further loading, the tensile barsyieldedatpointE,andsoonafter,Mhogbegantoleveloff,whichsuggeststhattheflexural capacityhasbeenreachedinthehoggingregionandadditionalmomentswereredistributedtothe sagging region until shear failure occurred.05101520253035400 10 20 30 40displacement(mm)moment (kNm)MsagABC1st ICdebondingshear failure at midspan (east)barsyieldMhog1st flexuralcrackDE Figure 5.34 Beam SS3: Moment vs displacement Interior support EB steel plate eastwest Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 310 - Figure 5.35 shows the plate strains measured along the plate as the moment over the interior support increased up to shear failure, with the positions of the strain gauges SG given by Figure 5.8. The steel platefirstyieldedatstraingaugeSG5overtheinteriorsupportatamomentMhog=6.12kNm.At Mhog=8kNm the plate yielding strain p.y was reached at SG6, and SG4 at moments Mhog=11kNm. After theplateyielded,theplatestrainsatSG4,SG5andSG6increasedveryrapidlyduetotheductile behaviourofsteel.ThestrainalongtheplatecontinuedtoincreaseasMhogincreaseduptoshear failure. The strains at SG4, SG5 and SG6 intercepted at point A in Figure 5.35 , after which the strains at SG4 and SG5 began to converge. This suggests that major debonding occurred between SG4 and SG5 at A, which caused a loss of bond, and hence, resulted in rapid increases in plate strains and the convergence of strains at SG4 and SG5. It is worth noting that although the plate strains obtained at SG4, SG5, and SG6 were much higher than those achieved in specimens SS1 (Figure 5.14) and SS2 (Figure5.24),the platestrainsat 400mmfromtheinteriorsupport(SG3 andSG7)weresignificantly less than SS1 and SS2. 0510152025-2000 0 2000 4000 6000 8000 10000 12000 14000 16000strain (x10-6)Mhog (kNm)SG1 (east)SG2SG3SG4SG5SG6SG7SG8SG9 (west) p.ySG1 & SG9SG4SG5SG6SG3 & SG7A Figure 5.35 Beam SS3: Moment vs plate strain ThevariationofthemaximumhoggingmomentinthebeamMhogasaproportionofthemaximum saggingmomentinthebeamMsagisshowninFigure5.36,wherefortheplatedbeamconsidered (Mstatic)u=47.6kNm.LineAinFigure5.36istheelasticdistributionassumingEIisconstanti.e. Mhog/Msag=1.2,thelinemarkedBisthemaximumredistributionfortheplatedsectionandtheline markedCisthemaximumredistributionfortheunplatedsection.Whentheloadisfirstapplied Mhog/Msag approaches 1.2 in region D in Figure 5.36. The slight divergence from this value is because Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 311 - the beam was bedding or settling down under very small loads. After the plate yields at point E, and theflexuralcracksformsatpointF,Mhog/MsagreducesgraduallyandthedivergencefromMhog/Msag equal to 1.2 signifies moment redistribution. From Figure 5.36, it can be seen that the beam achieved the maximum allowable moment redistribution, Line B, at failure at Mstatic/(Mstatic)u=1.0, i.e. the ultimate static moment was achieved. 00.20.40.60.811.21.40 0.2 0.4 0.6 0.8 1Mstatic/(Mstatic)uMhog/Msagtest resultsABCDEplate yield1st debondingbar yieldFGHelastic (EI constant)shear failureI Figure 5.36 Beam SS3: hogging-moment/sagging-moment Figure5.37showsthevariationofthemaximumhoggingMhogandsaggingMsagmomentsasthe applied loads P increased. (Mhog)el and (Msag)el are the hogging and sagging moments obtained based on elastic analysis of constant EI. It can be seen from Figure 5.37 that the beam behaved elastically untiltheflexuralcracksoccurredatpointB,afterwhichthemomentsobtaineddivergedfromthe elastic moments, indicating that moment is being redistributed.05101520253035400 20 40 60 80applied load (kN)Mhog (kNm)05101520253035400 20 40 60 80applied load (kN)Msag (kNm)1st flexuralcrackplateyield1st debondingbaryieldAB CD(Mhog)elEABC D(Msag)elE Figure 5.37 Beam SS2: Maximum hogging and sagging moments Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 312 - The variation of percentage of moment redistribution %MR calculated using Equation 5.1 is shown in Figure 5.38 for different Mstatic applied. Initially, before flexural cracking, the beam behaved elastically such that there is zero moment redistribution. The discrepancy of results at initial loading is because the beam was bedding or settling down under very small loads. As the applied load, and hence Mstatic increased, the %MR increased up to a maximum of 45% at shear failure. It is interesting to note how the%MRobtainedinSS3 wasmuchgreaterthan SS1andSS2,howeverthelength ofthecracked region,whichisalsodefinedasthepartialinteractionorhingeregionaspreviouslydiscussedin Chapter2,issignificantlylessthaninSS1andSS2,whichsuggeststhatthehingelength,i.e.the region where large rotation occurs, reduces as more moment is redistributed. -1001020304050607080901000 0.2 0.4 0.6 0.8 1Mstatic/(Mstatic)u% Moment redistribution1st flexuralcrackplate yield1st debondingbaryieldshearfailure Figure 5.38 Beam SS3: percentage of moment redistribution 5.3.4.4 BEAM SF1 (CFRP 25X2.4) Thisbeamwasexternallybondedwitha2.4mmthickCFRPpultrudedplate.Asthebeamwas graduallyloaded,thefirstflexuralcrack,crackAinFigure5.39,formedatanappliedloadPof8kN (R=2.53kN, Mhog=3.12kNm, Msag=3.0kNm) at the interior support. At P=14.6kN (R=4.8kN, Mhog=6kNm, Msag=5.76kNm),ICdebondingwasinitiatedattheplate/concreteinterfaceasindicatedbythe formationofICinterfacecrack,DinFigure 5.39,whichpropagatedfromtherootofcrack Atowards the west plate end as indicated by the arrows. This IC interface crack propagated gradually along the beam upon further loading, until at P=23kN (R=8.2kN, Mhog=8.6kNm, Msag=9.9kNm) when the second flexuralcrack,crackB,formedeastofcrackA,followedalmostimmediatelybytheformationof anotherflexuralcrack,crackC,westofcrackAasshowninFigure5.39.FormationofICinterface cracks E and F were then observed, propagating from the roots of crack B and C respectively as more load was applied, while IC interface crack D did not propagate any further. A maximum plate strain of Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 313 - 0.00203wasrecordedatstraingaugeSG6,200mmfrominteriorsupport,atP=32.5kN(R=11.9kN, Mhog=10.4kNm, Msag=14.3kNm). Figure 5.39 Beam SF1: Debonding propagation (P=31kN) Thedebondingpropagationwasgradualatfirst,withthedebondingattheeastspanbeingmore severe.However,astheICinterfacecrackEpropagatedtoapproximately400mmfromtheinterior support(nearSG3)atP=32.5kN,thedebondingpropagationbecameveryrapidasshowninFigure 5.40, where crack E travelled a long distance along the beam as the load was increased from 33kN to 34kN.EventuallycompletedebondingoftheeastplateendoccurredatP=39.5kN(R=14.8kN, Mhog=12kNm, Msag=17.7kNm) in Figure 5.41. Figure 5.40 Beam SF1: Debonding propagation (P=34kN) A B Debonding propagation Interior support EastWest C D E F Debonding propagation A B Debonding propagation Interior support East West E Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 314 - Figure 5.41 Beam SF1: IC debonding failure (P=40kN) Aftertheplatecompletelydebonded,thebeamcontinuedtobeloadeduntilverticalshearfailure occurred at a load P=76.5kN, at a maximum displacement of 45.8mm. Only two flexural cracks formed inthehoggingregionoftheeastspanasshowninFigure5.40,withthelastcrack,crackB,at approximately 200mm from the interior support.Figure5.42showsthevariationofmoment,atthepositionofmaximumhoggingMhogandsagging Msagmoments,withthemeandeflectionundertheappliedloadsatmid-spans.Atinitialstagesof loadingthebeambehavedelastically,i.e.regionAinFigure5.42,andsothehoggingmomentwas greater than the sagging moment. After crack B and IC interface crack E in Figure 5.40 formed (point FinFigure5.42),themomentinthehoggingregionbecamelessthanthatinthesaggingregion, indicating that moment is being redistributed from the hogging to the sagging region. Maximum plate strainwasachievedatpointGinFigure5.42,andsoonafter,ICdebondingfailureoccurredwhich caused a reduction in Mhog as shown by point H in Figure 5.42.0510152025303540450 10 20 30 40 50displacement(mm)Moment (kNm)Msagmajordebondingshear failuremax pIC debonding failureFMhogGHI Figure 5.42 Beam SF1: Moment vs displacement East E Debonding propagation Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 315 - Figure 5.43 shows the plate strains measured along the plate as the moment over the interior support increased up to IC debonding failure, with the positions of the strain gauges SG given by Figure 5.8. When the IC interface crack D in Figure 5.39 propagated towards the west plate end, it caused a rapid increaseintheplatestrain atSG6 asindicatedbypointAinFigure5.43a.AsICinterfacecracksE and F in Figure 5.39 formed and propagated to distances 200mm and 400mm from the east and west of the interior support respectively,this caused a rapid increase in SG4 (point B in Figure 5.43b) and SG7 (point C in Figure 5.43a). As IC interface crack E propagated further towards the east plate end, thiscausedarapidincreaseinstrainatSG3(pointDinFigure5.43b).AtMhog=10.4kNm,the maximum plate strain of 0.002027 was obtained at SG6 (point D in Figure 5.43a). Soon after, due to severe debonding occurring in the region between SG3 and SG7 (Figure 5.39), this caused a sudden reductionin platestrain at SG3toSG7while asuddenincreaseinSG1 andSG2wasobserved,as denotedbyEandFinFigure5.43respectively.Eventually,ICdebondingfailureoccurredwitha maximum plate strain of 0.00116 recorded at SG6. Note that at approximately Mhog=8kNm, the strains at SG4, SG5 and SG6 began to converge. This indicates that there is almost zero resultant bond force between SG4 to SG6 due to debonding. However, as the bond at the plate/concrete interface was still strongfurtheralongthebeam,thisallowedtheplatestrainstocontinuetoincreaseuntilatpointD, where debonding propagated further along the beam, causing the plate strains to reduce.02468101214-1000 -500 0 500 1000 1500 2000 2500strain (x10-6)Mhog (kNm)SG5 (centre)SG6SG7SG8SG9 (west)A02468101214-500 0 500 1000 1500 2000strain (x10-6)Mhog (kNm)SG1 (east)SG2SG3SG4SG5 (centre)BCDEEEFSG9 SG8SG7 SG6SG5SG5SG4SG3SG2SG1(a)(b) Figure 5.43 Beam SF1: Moment vs plate strain Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 316 - ThevariationofthemaximumhoggingmomentinthebeamMhogasaproportionofthemaximum saggingmomentinthebeamMsagisshowninFigure5.44.Fortheplatedbeamconsidered, (Mstatic)u=49.2kNm.LineAinFigure5.44istheelasticdistributionassumingEIisconstanti.e. Mhog/Msag = 1.2, line marked B is the maximum redistribution for the plated section and the line marked Cisthemaximumredistributionfortheunplatedsection.FromFigure5.44,itcanbeseenthatthe plated beam only reached approximately 50% of the ultimate static moment when IC debonding failure occurred. 00.20.40.60.811.21.40 0.2 0.4 0.6 0.8 1Mstatic/(Mstatic)uMhog/Msagtest resultsABC1st flexural crack1st debondingIC debonding failureelastic (EI constant)shear failuremajor debondingmax p reached Figure 5.44 Beam SF1: hogging-moment/sagging-moment Figure5.45showsthevariationofthemaximumhoggingMhogandsaggingMsagmomentsasthe applied loads P increased. (Mhog)el and (Msag)el are the hogging and sagging moments obtained based on elastic analysis of constant EI.024681012141618200 20 40 60 80load (kN)Mhog (kNm)05101520253035400 20 40 60 80load (kN)Msag (kNm)1st debondingIC debondingfailureshear failuremajor debondingmax p reached(Mhog)el(Msag)el Figure 5.45 Beam SF1: Maximum hogging and sagging moments Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 317 - The variation of percentage of moment redistribution %MR calculated using Equation 5.1 is shown in Figure5.46fordifferentMstaticapplied.Astheappliedload,andhenceMstaticincreased,the%MR increaseduptoamaximumof32.5%atICdebondingfailure.Aftertheplatedebondedtheflexural strength of the hogging region is reduced, therefore the hogging moment had to be redistributed to the saggingregiontoallowforthisreductioninstrengthasshowninFigure5.45.Thisresultedina sudden increase in %MR as shown by region A in Figure 5.46. As the ductility of the unplated hogging regionismuchgreaterthanbefore,large%MRwasallowedandamaximumof62%moment redistribution was obtained at shear failure of the unplated beam. 0102030405060700 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Mstatic/(Mstatic)u% Moment redistributionA1st flexural crack1st debondingIC debonding failureshear failuremajor debondingmax p reached Figure 5.46 Beam SF1: percentage of moment redistribution 5.3.4.5 BEAM SF2 (CFRP 50X1.2) The flexural crack marked A in Figure 5.47 first occurred immediately over the hogging support at an appliedloadP=9kN(R=2.9kN,Mhog=3.6kNm,Msag=3.48kNm).Thisinduced,atahigherload,theIC interfacecracksthatareparalleltotheplateandpropagateinbothdirectionsthatisB-CandB-D. FirstsignofdebondingwasobservedatP=16.8kN(R=5.57kN,Mhog=6.72kNm,Msag=6.69kNm).On further loading in Figure 5.48, the IC interface cracks gradually propagated away from the position of maximummomentsuchasfromCtoEandfromFtoGuntiltherewasrapidcrackpropagationat which IC debonding occurred in Figure 5.49 from H to I which caused the plate strains to reduce which signifiedICdebonding.Themaximumplatestrainof0.00292wasobtainedatstraingaugeSG6at P=42kN (R=15.4kN, Mhog=13.4kNm, Msag=18.5kNm), and soon after, IC debonding failure occurred at theeastplateendatP=49kN(R=18.6kN,Mhog=14kNm,Msag=22.3kNm)witharecordedmaximum platestrainof0.00262atSG6andamaximumdisplacementof12.3mmintheeastspan.After complete debonding of the plate, loading of the beam was continued until shear failure occurred in the Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 318 - saggingregionatP=76.5kN(R=32.7kN,Mhog=13.2kNm,Msag=39.3kNm).LikespecimenSF1,inthe hoggingregionoftheeastspan,wherefailureoccurred,onlytwoflexuralcracksformed(Figure 5.49)at approximately 150mm spacing. Figure 5.47 Beam SF2: Flexural crack and IC interface cracking (P=24kN) Figure 5.48 Beam SF2: IC interface cracks propagation (P=35kN) Figure 5.49 Beam SF2: IC debonding failure (P=45kN) J Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 319 - Figure5.50showsthevariationofmoment,atthepositionofmaximumhoggingMhogandsagging Msag moments, with the mean deflection under the applied loads at mid-spans. Mhog reduced relative to Msag after the first appearance of the IC interface cracks at point A in Figure 5.50, which indicates that moment is being redistributed from the hogging to the sagging region. Maximum plate strain was achieved at point B, and soon after, IC debonding failure occurred at point C which caused a reduction inMhog.Asloadingwascontinuedaftertheplatecompletelydebonded,Msagcontinuedtoincrease while Mhog remained constant until shear failure in the sagging region at point D. 0510152025303540450 10 20 30 40 50displacement (mm)Moment (kNm)Msag1stdebondingshear failuremax pIC debonding failureAMhogBCD Figure 5.50 Beam SF2: Moment vs displacement Figure 5.51 shows the plate strains measured along the plate as the moment over the interior support increaseduptoshearfailure,withthepositionsofthestraingaugesSGgivenbyFigure5.8.The behaviourwassimilartothatobservedinspecimenSF1(Section5.3.4.4).Whenaflexuralcrack formed in between SG5 and SG6 at P=17kN (Figure 5.47), large increases in the plate strain occurred at SG6 as marked by A in Figure 5.51a. As IC interface cracks formed and propagated towards SG4 at P=19.7kN, i.e. from B-C-E in Figure 5.48, this caused a rapid increase in SG4 (B in Figure 5.51b), eventually causing strains at SG4 and SG5 to converge. As the IC interface crack propagated further towards the SG3 (i.e. from F to G in Figure 5.48), sudden increases in strain at SG3 was observed (C inFigure5.51b).AtMhog=13.4kNm,themaximumplatestrainof 0.00292wasobtainedatSG6(Din Figure 5.51a). Soon after, due to severe debonding in the region between SG3 and SG5 (from interior support to H in Figure 5.49), this causeda sudden drop in plate strains at SG3, SG4 and SG5, while a rapid increase in SG1 and SG2 was observed, as denoted by E and F in Figure 5.51 respectively. Eventually, IC debonding failure occurred with a maximum plate strain of 0.00262 recorded at SG6. It is worth noting that sudden reductions in plate strains due to debonding propagation did not occur in Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 320 - theEBsteelplatedspecimenstested,evenwhenseveredebondingwasobservedi.e.specimens SS1(Section5.3.4.1)andSS2(Section5.3.4.2).ItisinterestingtonotethatthestrainsatSG5and SG6 intercepted at point G in Figure 5.51a, after which the strains at SG6 became greater than that at SG5.ThismaybebecauseoftheflexuralcrackthatformednearSG6,i.e.crackJinFigure5.48, which caused large plate strains to develop as the crack widened.0481216-1000 -500 0 500 1000 1500 2000 2500 3000strain (x10-6)Mhog (kNm)SG1 (east)SG2SG3SG4SG5 (centre)0481216-1000 -500 0 500 1000 1500 2000 2500 3000strain (x10-6)Mhog (kNm)SG5 (centre)SG6SG7SG8SG9 (west)(a)(b)ABCDEEFSG9SG8SG7SG6SG5SG5SG4SG3SG2SG1FG Figure 5.51 Beam SF2: Moment vs plate strain ThevariationofthemaximumhoggingmomentinthebeamMhogasaproportionofthemaximum sagging moment in the beam Msag is shown in Figure 5.52. In this case, (Mhog)u is the experimentally measured moment at plate debonding and (Msag)u is the rigid plastic strength and from which (Mstatic)u and line B were calculated. The first IC interface crack at F occurred at a very early stage of loading. The maximum plate strain of 0.00292 occurred at H prior to IC debonding at I.After IC debonding of the plate, the beam behaves as an unplated beam and the test was continued until the beam failed in shearatpointJjustshortofitstheoreticalunplatedflexuralcapacityallowingforfullmoment redistribution. Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 321 - 00.20.40.60.811.21.40 0.2 0.4 0.6 0.8 1Mstatic/(Mstatic)uMhog/MsagIC debonding ABCtest resultsF1st IC interface crackmax plate strain reachedHImaximum moment redistribution for unplatedstructuremax. redistribution for plated structureelastic (constant EI)shear failureJ Figure 5.52 Beam SF2: hogging- moment / sagging-moment Figure5.53showsthevariationofthemaximumhoggingMhogandsaggingMsagmomentsasthe applied loads P increased. (Mhog)el and (Msag)el are the hogging and sagging moments obtained based on elastic analysis of constant EI.05101520250 20 40 60 80load (kN)Mhog (kNm)0102030400 20 40 60 80load (kN)Msag (kNm)1st debondingIC debondingfailureshear failuremax p reached(Mhog)el(Msag)el Figure 5.53 Beam SF2: Maximum hogging and sagging moments The variation of percentage of moment redistribution %MR calculated using Equation 5.1 is shown in Figure 5.54 for different Mstatic applied. The initial divergence from zero moment redistribution is due to bedding of the beam. At the first sign of debonding, there was already 11% of moment redistribution, and as more load was applied such that the maximum plate strain was obtained in the plate, 29% of moment redistribution was recorded. Upon further loading, the strain in the plate began to reduce due toseveredebonding,butthe%MRcontinuedtoincreaseasthestiffnessinthehoggingregionwas less than before.At IC debonding failure, 36% moment redistribution was recorded, which is greater Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 322 - than that obtained in Specimen SF1 as premature debonding occurred at a higher load. After the plate debonded the flexural strength of the hogging region is reduced, therefore the hogging moment had to be redistributed to the sagging region to allow for this reduction in strength as shown in Figure 5.53. This resulted in a sudden increase in %MR as denoted by region A in Figure 5.54. A maximum of 62% moment redistribution was obtained at shear failure of the unplated beam. 0102030405060700 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Mstatic/(Mstatic)u% Moment redistributionA1st flexural crack1st debondingIC debonding failureshear failuremax p reached Figure 5.54 Beam SF2: percentage of moment redistribution 5.3.4.6 BEAM SF3 (CFRP 80X1.2) As the beam was gradually loaded, the first flexural crack, crack A in Figure 5.55, formed at an applied loadPof9.8kN(R=3.35kN,Mhog=3.72kNm,Msag=4.0kNm)attheinteriorsupport.Uponfurther loading,twoflexuralcracks,crackBandCinFigure5.55,formedatapproximately200mmonthe east and west of the interior support. When two secondary cracks formed between crack A and C and crackAandB,thecrackingspacingwasreducedtoapproximately100mm.AtP=28kN(R=10.1kN, Mhog=9.36kNm,Msag=12.1kNm),thefirstICinterfacecrack,DinFigure5.55,wasfoundpropagating from the root of crack A towards the west plate end. At P=34kN, IC interface cracks F and G formed from the roots of crack A and crack B respectively.As more load was applied, IC interface crack G in Figure 5.56 started to gradually propagate towards the west plate end to point H at P=38kN, while no furtherpropagationwasobservedatotherICinterfacecracks.EventuallyICdebondingfailure occurredfromthelastflexuralcrack,crackBinFigure5.56,tothewestplateendatP=40.9kN (R=14.9kN,Mhog=13.3kNm,Msag=17.9kNm)inFigure5.57withadeflectionof9.7mmbeneaththe applied load. A maximum plate strain of 0.00249 was recorded at strain gauge SG5 immediately prior to IC debonding failure.After the plate completely debonded, the beam continued to be loaded until Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 323 - verticalshearfailureoccurredataloadP=77.4kN,atamaximumdisplacementof35.65mm.Three flexural cracks formed in the hogging region of the west span, where failure occurred, (Figure 5.55) at approximately 100mm spacing. Figure 5.55 Beam SF3: Flexural crack and IC interface cracking (P=34kN) Figure 5.56 Beam SF3: Debonding propagation (P=38kN) Figure 5.57 Beam SF3: IC debonding failure (P=41kN) ABCDF Gwesteast BG Hwest Hwest Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 324 - Figure5.58showsthevariationofmoment,atthepositionofmaximumhoggingMhogandsagging Msagmoments,withthemeandeflectionundertheappliedloadsatmid-spans.Atinitialstagesof loading the beam behaved elastically. After the first flexural crack formed, the moment in the hogging region became less than that in the sagging region, indicating that moment is being redistributed from thehoggingtothesaggingregion.MaximumplatestrainwasachievedjustpriortoICdebonding failure, after which a reduction in Mhog occurred as shown by point A in Figure 5.58.0510152025303540450 5 10 15 20 25 30 35 40displacement (mm)Moment (kNm)Msag1stflexural crackshear failure & max p reachedIC debonding failureAMhog1stdebonding Figure 5.58 Beam SF3: Moment vs displacement Figure 5.59 shows the plate strains measured along the plate as the moment over the interior support increased up to IC debonding failure, with the positions of the strain gauges SG given by Figure 5.8. It can be seen that after the first flexural crack formed, the plate strain at SG4 and SG6 increased much more rapidly, as shown by A in Figure 5.59. When the IC interface crack G in Figure 5.55 formed near SG6 at Mhog=11.4kNm and propagated towards the west plate end, this caused the plate strain at SG6 toreduce(BinFigure5.59),whilearapidincreaseintheplatestrainatSG7wasobserved(Cin Figure5.59).ICdebondingfailurethenfollowed(atMhog=13.3kNm)withamaximumplatestrainof 0.00249recordedatSG5asdenotedbypointDinFigure5.59.ItisworthnotingthatbecauseIC debonding propagated from SG6 to the west plate end and not from the interior support, therefore the plate strain at SG4 and SG5 did not reduce prior to debonding failure. Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 325 - 024681012141618-1000 -500 0 500 1000 1500 2000 2500 3000strain (x10-6)Mhog(kNm)SG1 (east)SG2SG3SG4SG5 (centre)SG6SG7SG8SG9 (west)SG1&SG9SG2&SG8SG3SG7SG6SG4SG5ACBD Figure 5.59 Beam SF3: Moment vs plate strain ThevariationofthemaximumhoggingmomentinthebeamMhogasaproportionofthemaximum saggingmomentinthebeamMsagisshowninFigure5.60.Fortheplatedbeamconsidered, (Mstatic)u=51.8kNm.LineArepresentstheelasticdistributionassumingEIisconstanti.e.Mhog/Msag= 1.2,linemarkedBisthemaximumredistributionfortheplatedsectionandthelinemarkedCisthe maximumredistributionfortheunplatedsection.FromFigure5.60,itcanbeseenthattheplated beamonlyreachedapproximately50%oftheultimatestaticmomentwhenICdebondingfailure occurred. 00.20.40.60.811.21.40 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Mstatic/(Mstatic)uMhog/Msagtest resultsAB&C1st flexural crack1st debondingIC debonding failureelastic (EI constant)shear failure& max p reached Figure 5.60 Beam SF3: hogging-moment/sagging-moment Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 326 - Figure5.61showsthevariationofthemaximumhoggingMhogandsaggingMsagmomentsasthe applied loads P increased. (Mhog)el and (Msag)el are the hogging and sagging moments obtained based on elastic analysis of constant EI.05101520253035400 20 40 60 80load (kN)Mhog (kNm)05101520253035400 20 40 60 80load (kN)Msag (kNm)1st debondingIC debondingfailureshear failure(Mhog)el(Msag)el1st flexuralcrack Figure 5.61 Beam SF3: Maximum hogging and sagging moments The variation of percentage of moment redistribution %MR calculated using Equation 5.1 is shown in Figure5.62fordifferentMstaticapplied.Astheappliedload,andhenceMstaticincreased,the%MR increaseduptoamaximumof27.6%atICdebondingfailure.Aftertheplatedebonded,muchof hoggingmomentwasredistributedtothesaggingregiontoallowforthisreductioninstrengthas showninFigure5.61.Thisresultedinasuddenincreasein%MRasshownbyregionAinFigure 5.62, and 56% moment redistribution was obtained at shear failure of the unplated beam. 0102030405060700 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Mstatic/(Mstatic)u% Moment redistributionA1st flexural crack1st debondingIC debonding failureshear failure& max p reached Figure 5.62 Beam SF3: percentage of moment redistribution Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 327 - 5.3.4.7 BEAM SF4 (CFRP 100X0.6) ThisbeamwasexternallybondedwiththreeCFRPfibresheetsof0.2mmthicknesseachusingthe wetlay-uptechnique.ThebehaviourofthebeamwassimilartotheotherspecimenswithCFRP pultruded plates, but was more ductile due to the low stiffness of the plate. As the beam was gradually loaded,thefirstflexuralcrack,crackBinFigure5.63,formednearstraingaugeSG6atanapplied load P of 15kN (R=5.03kN, Mhog=5.76kNm, Msag=6.03kNm). Note that crack A in Figure 5.63 is a pre-existing crack which formed over the interior support during preparation. Upon further loading, several primary cracks, cracks C and D, and secondary cracks, cracks E, F and G, were found. The adhesive overthesurfaceoftheplatemadeitdifficulttoseetheformationofICinterfacecracks.Thefirst visiblesignofdebondingoccurrednearSG6,markedHinFigure5.63,whensmallherringbone crackswerefoundpropagatingfromtherootofcrackBatP=30kN(R=10.7kN,Mhog=10.3kNm, Msag=12.8kNm).DebondingwasalsoobservedattherootsofflexuralcracksFandC,denotedbyI and J in Figure 5.63. The arrows in the Figure 5.63 represent the directions of debonding propagation. Basedonthemeasuredplatestrainandfromfullinteractionanalysis,itisestimatedthatthetensile bars yielded at P=56.9kN (R=21.2kN), before complete debonding of the plate. Figure 5.63 Beam SF4: Flexural crack and IC interface cracking (P=50kN) Uponfurtherloading,ICinterfacecrackHinFigure5.64startedtograduallypropagatetowardsthe westplateendtopointKatP=62kN,andfromJtoLintheeastspan.Whentheloadwasfurther increased to P=63.4kN, a rapid debonding propagation in the west span occurred, as denoted by I-H-K-MinFigure5.65.EventuallytheICinterfacecrackpropagatedtotheplateend,fromMtoNin A B CDF Geastwest Interior support HI J E Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 328 - Figure5.66,tocauseICdebondingfailuretooccuratP=64.8kN(R=25.6kN,Mhog=16.3kNm, Msag=30.7kNm)withadeflectionof15.9mmbeneaththeappliedload.Amaximumplatestrainof 0.0042wasrecordedatstraingaugeSG6priortoICdebondingfailureatP=62.7kN(R=23.7kN, Mhog=18.2kNm, Msag=28.5kNm).After the plate completely debonded, loading continued until vertical shearfailureoccurredataloadP=82kNintheeastspanneartheappliedload,atamaximum displacement of 45.2mm. Figure 5.67 shows the hogging region over the interior support upon shear failureoccurring,whereitcanbeseenthattheplatehascompletelydetachedfromthebeaminthe west span. Figure 5.64 Beam SF4: Debonding propagation (P=62kN) Figure 5.65 Beam SF4: Debonding propagation before failure (P=63.4kN) H I KL ABC DJ Interior support eastwest I MInterior support A B DK HIntermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 329 - Figure 5.66 Beam SF4: IC debonding failure (P=65kN) Figure 5.67 Beam SF4: Hogging region at shear failure (P=82kN) The variation of the moment, at the position of the maximum hogging and sagging moments, with the mean deflection under the applied loads at mid-spans, are plotted in Figure 5.68. It can be seen that nearthestart,inregionA,thehoggingmomentwasslightlygreaterthanthesaggingmomentas would be expected from an elastic analysis. The hogging moment then reduced relative to the sagging momentandtheyhaveanequalmagnitudeatpointB.Themaximumhoggingmomentandthe maximum plate strain occurred at the same applied load at C, although the plate did not debond until after both the plate strain and hogging moment had reduced slightly at D. It is felt that this reduction in moment and plate strain from C to D, just prior to IC debonding, may have been partly due to the slip between the plate and the beam, that is partial interaction, which would reduce the flexural rigidity as well as the plate strain in the hogging region. After IC plate debonding, the behaviour of the hogging region reverts back to that of the unplated section at E.H MNK eastwest Interior support A B DCIntermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 330 - 0 10 20 30 40 0 1020304050Displacement (mm) Moment (kNm) Mhog Msag max plate strainplat e IC debondingshear failureFFA B C D E Figure 5.68 Beam SF4: Moment vs displacement ItisworthnotingthatthecontinuousbeameventuallyfailedbyverticalshearfailureatpointFin Figure5.68.However,thisoccurredwellaftertheplatehadICdebondedsothattheverticalshear failure had no effect on the redistribution of moment. It is also worth noting that the sagging moment is continually increasing relative to the hogging moment which signifies moment redistribution; it was for thisreasonthatthesaggingregionwasmademuchstrongerthanthehoggingregioninorderto achieve as much moment redistribution as possible. Figure 5.69 shows the plate strains measured along the plate as the moment over the interior support increased up to IC debonding failure, with the positions of the strain gauges SG given by Figure 5.8. After flexural cracks B and C in Figure 5.63 formed near SG6 and SG4 respectively, large increases in plate strains at SG4 and SG6 were observed, as marked by A and B in Figure 5.69, and upon further loading, the flexural cracks widened, inducing slip at the interface and causing convergence in strains atSG5andSG6.ThatistheresultantbondforcebetweenSG5andSG6iszero.WhentheIC interfacecracknearSG4propagatedfromJtoLinFigure5.64atMhog=17.6kNm,thiscausedthe plate strain at SG3 to increase (C in Figure 5.69). After the maximum plate strain was reached, small reductionsinSG3andSG4wasobserved.Thesamehappenedinthewestspan,whereafterthe maximumplatestrainwasreachedatSG6(DinFigure5.69),theICinterfacecracknearSG6 propagated from H to K in Figure 5.64 which caused the plate strain at SG7 to increase rapidly (E in Figure5.69)andtheplatestrainatSG5andSG6reduced(FinFigure5.69).Asthedebonding propagated further from I to M in Figure 5.65, this caused sudden reductions in plate strains between SG5 and SG8. IC debonding failure soon followed (at Mhog=16.3kNm) with a maximum plate strain of 0.00218 recorded at SG6.Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 331 - 048121620-1000 0 1000 2000 3000 4000 5000strain (x10-6)Mhog (kNm)SG1 (east)SG2SG3SG4SG5 (centre)SG6SG7SG8SG9 (west)SG1SG2SG3SG7SG6SG4SG5ACBDSG8SG9EF Figure 5.69 Beam SF4: Moment vs plate strain ThevariationofthemaximumhoggingmomentinthebeamMhogasaproportionofthemaximum saggingmomentinthebeamMsagisshowninFigure5.70.Fortheplatedbeamconsidered, (Mstatic)u=51.8kNm.LineArepresentstheelasticdistributionassumingEIisconstanti.e.Mhog/Msag= 1.2,linemarkedBisthemaximumredistributionfortheplatedsectionandthelinemarkedCisthe maximumredistributionfortheunplatedsection.Theinitialdiscrepancyisbecausethebeamwas beddingorsettlingdownunderverysmallloads.Aftertheflexuralcracksforms,Mhog/Msagreduces graduallyandthedivergencefromMhog/Msagequalto1.2signifiesmomentredistribution.Itcanbe seenthatICdebondingfailureoccurredclosetoB,and80%oftheultimatestaticmomentwas achieved. 00.20.40.60.811.21.41.60 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1Mstatic/(Mstatic)uMhog/Msagtest resultsABC1st flexural crack1st debondingIC debonding failureelastic (EI constant)shear failurebar yieldmax p reached Figure 5.70 Beam SF4: hogging-moment/sagging-moment Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 332 - Figure5.71showsthevariationofthemaximumhoggingMhogandsaggingMsagmomentsasthe applied loads P increased. (Mhog)el and (Msag)el are the hogging and sagging moments obtained based on elastic analysis of constant EI.0510152025300 20 40 60 80 100load (kN)Mhog (kNm)0510152025303540450 20 40 60 80 100load (kN)Msag (kNm)1st debondingIC debondingfailureshear failure(Mhog)el(Msag)el1st flexural crackbar yieldmax p reached Figure 5.71 Beam SF4: Maximum hogging and sagging moments The variation of percentage of moment redistribution %MR calculated using Equation 5.1 is shown in Figure 5.72 for different Mstatic applied. The initial discrepancy from zero moment redistribution is due to the beam still settling. When flexural and debonding cracks formed the %MR increased up to 35.3% asthemaximumplatestrainof0.0042wasreached,andamaximumof44%momentredistribution wasobtainedatICdebondingfailure.Aftertheplatedebonded,muchofhoggingmomentwas redistributed to the sagging region to allow for this reduction in strength as shown in Figure 5.71. This resultedinasuddenincreasein%MRasshownbyregionAinFigure5.72,and60.3%moment redistribution was obtained at shear failure of the unplated beam. -20-100102030405060700 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1Mstatic/(Mstatic)u% Moment redistributionA1st flexural crack1st debondingIC debonding failureshear failuremax p reachedbar yield Figure 5.72 Beam SF4: percentage of moment redistribution Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 333 - 5.3.5SUMMARY AND DISCUSSIONS Asummaryofthetestresultsispresentedinthefollowingjournalpaper alongwithacomparisonof results for the different specimens. 5.3.5.1 JOURNALPAPER:MOMENTREDISTRIBUTIONINCONTINUOUSPLATEDRCFLEXURAL MEMBERS PART 1 - NEUTRAL AXIS DEPTH APPROACH AND TESTS Thispaperfocusesonthemomentredistributionbehaviourofbeamswithexternallybondedplates, where the series of tests on EB beams carried out in this research are presented. The applicability of the commonly used neutral axis depth approach for moment redistribution in RC flexural members on platedstructureswasalsoassessedinthispaper.Furtherdiscussionontheneutralaxisdepth approach can be found in the literature review in Chapter 6 of this thesis.Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution - 334 - Intermediate Crack Debonding of Plated RC BeamsExperimental Investigation on Mo