FRP Shear Strengthening Of RC Beams And Walls

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2008:39L ICE N T IAT E T H E S I SGabriel SasFRP shear strengthening of RC beams and walls2008:39Universitetstryckeriet, LuleåFRP shear strengtheningof RC beams and wallsGabriel SasLuleå University of TechnologyDepartment of Civil, Mining and Environmental EngineeringDivision of Structural engineering2008:39 : -1757 : -lic -- 08 39 --

Licentiate Thesis 2008FRP shear strengthening ofRC beams and wallsGabriel SasDivision of Structural EngineeringDepartment of Civil and Environmental EngineeringLuleå University of TechnologySE-971 87 ion.project.ltu.se/

PrefacePrefaceThe present licentiate thesis is the result of the work carried out between May 2006and November 2008 at the Division of Structural Engineering, Department if Civil,Mining and Environmental Engineering at Luleå University of Technology, Sweden.The work presented in this thesis has been carried out in the research group“Innovative Materials and Structures”.First I would like to thank God for giving me strength and knowledge to carry thiswork.I would like to acknowledge the European Network for Composite Reinforcement(Hn.core) for providing the financial support for the work presented here.I would like to thank my supervisor Dr. Anders Carolin for his invaluable scientific andmoral support provided during this period. I know sometimes things did not goaccording to plan but you were always there to guide me on the right path. I reallyhope we will have the opportunity to work again in the close future. I will always begrateful to my co-supervisor Prof. Björn Täljsten for showing high interest for the shearstrengthening work, for the practical applications that he got me involved in and for hispositive way of motivating me.I would also like thank my dear PhD student colleagues and friends: Alann André,Thomas Blanksvärd, Peter Simonsson, Markus Bergtröm and Anders Bennitz for thescientific discussions, deep chats and great parties we had together.Many thanks for helping me in gathering the basic knowledge about FRPstrengthening go to the fellow researchers at the Civil Engineering Department fromthe Politehnica University of Timiúoara, România. I am looking forward to a fruitfuland long collaboration.To pass the long and cold winter days up north, close to the Arctic Circle, I havealways had support from all my good friends that I made in Luleå. Since the list ofnames would be too long to mention here and I don not want to leave anyone out, Iwould just like to express my gratitude to all of you. You are the best!Cu siguranĠă cea mai importantă parte din viaĠa mea e familia. Mamă, tată chiar dacă mii dekilometri ne despart, vreau să útiti că v-am simĠit prezenĠa tot timpul. SunteĠi singurelepersoane care mă iubesc úi sprijină necondiĠionat úi pentru asta am să vă fiu recunoscătortoata viaĠa. Vă voi iubi mereu.Luleå, November 2008I

SummarySummaryThe shear failure of Fibre Reinforced Polymers (FRP) strengthened reinforcedconcrete (RC) beams has not been studied to the same extent as bending failuremechanism over the past decade. The complex nature of the shear failure mechanismjust for reinforced concrete beams is still being debated among scientists and not fullysolved yet. If we add the FRP for shear strengthening to the already existing shearproblems the failure mechanism becomes more complicated. In other words an extrauncertainty to the already existing ones is complicating more the problem of shear inconcrete. It is of utmost importance to understand the shear failure mechanism ofreinforced concrete beams and for this all the known theories for designing reinforcedconcrete beams subjected to shear are presented: truss analogy, theory of plasticity forconcrete and modified compression field theory. The use of these theories in two ofthe most commonly used standards is also exemplified. Further on, a design model forthe shear strengthening of concrete beams by using fibre-reinforced polymers (FRP) ispresented in one of the appended papers, and the limitations of the truss model analogyare highlighted. The fracture mechanics approach is used in analyzing the bondbehaviour between the FRP composites and concrete. The fracture energy of concreteand the axial rigidity of the FRP are considered to be the most important parameters.The effective strain in the FRP when debonding occurs is determined. The limitationsof the anchorage length over the cross section are analyzed. A simple iterative designmethod for the shear debonding is finally proposed. Since the model’s predictions areconsidered satisfactory but not really precise, a deep literature review has beenperformed. All the significant theoretical models for predicting the shear capacity ofFRP strengthened RC beams developed during the years are analyzed, commented onand compared with an extensive experimental database. The database contains theresults from more than 200 tests performed in different research institutions across theworld. The results of the comparison are not very promising and the use of theadditional principle in the actual shear design equations should be questioned. Thelarge scatter between the predicted values of different models and experimental resultsis of real concern bearing in mind that some of the models are used in present designcodes.Furthermore, the influence of the FRP composites to strengthen openings in RC wallsis analyzed. In the same manner as for RC beams the current design methods existingin two of the most commonly used standards are presented. Since the strengthening ofRC walls was studied even less than FRP strengthened RC beams an up to dateliterature review of the experimental and theoretical work is presented. A concept,developed in collaboration with the Civil Engineering Department from PolitehnicaUniversity of Timiúoara, is presented for testing RC walls with openings subjected toIII

Notations and symbolslateral and gravitational loads. From a matrix of 50 different practical configurations ofopenings 12 walls are selected which make the subject of an ongoing experimentalprogram. Eight walls with different opening configurations are subjected to cycliclateral loading under constant gravitational load to simulate the seismic behaviour ofFRP strengthened walls with openings. Four walls with different openingconfigurations are to be tested to monotonic gravitational loading up to failure. Thepossibility for strengthening RC walls with opening is exemplified in a case study. Asimplified design procedure for strengthening RC walls with openings is presented.This procedure is considered to be the basis for a future theoretical model that isintended to be derived.Keywords: reinforced concrete, FRP, strengthening, shear, carbon fibre, model, comparison, walls.IV

Notations and symbolsNotations and symbolsGeneral notation listRoman lettersDescriptionUnitaMaximum aggregate size[m] gGross area of the wall panel[m2]AsShear reinforcement area[m2]AstTensile reinforcement area for beams[m2]AsvSteel vertical reinforcement area[m2]bWidth of the cross section[m]bwMinimum width of the T cross section[m]dLever arm[m]DfrpStress/strain distribution factor in the FRP[-]EfrpModulus of elasticity of FRP[N/m2]eEccentricity of the load[m]eaAdditional eccentricity due do deflections in the wall[m]f1Principal tensile stress[N/m2]f2Principal compressive stress[N/m2]fc'Compressive strength of concrete[N/m2]fcc'Compressive strength of the confined concrete[N/m2]fc0Compressive strength of the unconfined concrete[N/m2]ffrpTensile strength of the FRP[N/m2]fyYield stress of steel[N/m2]fysYielding stress of the shear reinforcement[N/m2]fxStress in the longitudinal bars[N/m2]fvStress in the stirrups[N/m2]V

Notations and symbolsGfFracture energy of concrete[N/m2xm]hheight of the considered element[m]hfrp,eEffective height of the FPR over the cross section[m]HHeight of the wall[m]H0Height of the opening in the wall[m]HweEffective height of the wall[m]k1and k2Empirically determined factors for walls with openings[m]kcCoefficient depending on the quality of the concrete[-]kM Coefficient depending on the slenderness of the column[-]LLength of the wall[m]L0Length of the opening in the wallLmaxMaximum bond length of the FRP[m]LeEffective bond length of the FRP[m]LcrCritical anchorage length[m]MBending moment in the centre of gravity of the cross section[Nm]MdDesign bending momentMpYield moment in pure bending[Nm]NNormal force in the centre of gravity of the cross section[N]NpTension yield load[N]NpsDesign axial load of a solid wall[N/m]Np0Ultimate load of a wall with opening[N/m]NhHorizontal projection of the shear force[N]PiDefines arbitrary loads on a rigid body[N]QiGeneralized stress[N/m2]qiGeneralized strain[-]q1,2, Plastic strains equivalent to the arbitrary loads Pi[-]sStirrups spacing[m]smT Average spacing of the cracks[m]smxAverage crack spacing that would result if the member would [m]be subjected to longitudinal tensionsmvAverage crack spacing that would result if the member was [m]VI

Notations and symbolssubjected to transverse tensionsfrpHorizontal spacing of the FRP strips[m]tfrpThickness of the FRP[m]twThickness of the wall[m]uiCorresponding displacements of loads Pi[m]VExternal shear force[N]VcConcrete contribution to the shear force capacity of a beam[N]VdDesign shear force[N]VsSteel stirrups contribution to the shear force capacity of a beam[N]VpAxial load contribution to the shear force capacity of a beam[N]ViOther contributions to the shear capacity of a beam[N]VfrpFRP contribution to the shear capacity[N]WWork produced by the arbitrary loads Pi[J]wfrpWidth of the FRP[m]y0Length of the compressed area used in Theory of Plasticity[m]ztCoordinate of the top end of the effective FRP[m]zbCoordinate of the bottom end of the effective FRP[m]DescriptionUnitAngle between shear reinforcement and the beam axisperpendicular to the shear forceFactor considering the bond characteristics of the reinforcementFactor considering the load typeExperimentally determined factor considering the eccentricityeffectFibre alignment angle with respect to the longitudinal axis ofthe beamExperimentally determined factor considering the aspect ratioand the slenderness of the wallLongitudinal strainTransversals strainPrincipal tensile strain[-]Greek lettersD D D Dw E Ew Hx Ht H1 [-][-][-][ ][-][-][-][-]VII

Notations and symbolsH2 Hbond Hc,max Hfrp,e Hfrp,u Jfrp Jxy MefT O Op P PS Kfrp K K UfrpVA Vfrp,maxXci Z F W max]Principal compressive strainStrain in fibre at debonding failureStrain in the fibre depending on the concrete contributionEffective strain in the FRPUltimate strain in the FRPPartial safety factor for FRPShear strainEffective creep numberCrack inclination angle with respect to the longitudinal axis ofthe beamNormalized maximum bond lengthNon dimensional factor used in defining the plasticityProportionality factor used for determining the yield conditionProportionality factor when the yield condition is fulfilledStress distribution factor in the FRP over the cross section of abeam, equals 0.6.Position of the centre of gravity of the opening with respect tothe left edge of the wallPosition of the centre of gravity of a wall with opening withrespect to the left edge of the wallFRP reinforcement ratioconfinement pressure provided by the FRPMaximum stress in fibresShear stresses along the crack defined in the Compressive FieldTheoryis the crack widthNon dimensional factor accoutring for the geometrical propertiesof a wall with openingsShear stress of the concrete in a bonded elementFactor considering the effective bonded area at the top andbottom of the beam[-][-][-][-][-][-][-][-][ N/m2][-]Eurocode (2004a, b and 2005) notation listRoman lettersDescriptionUnit slis the area of tensile reinforcement, which extends beyond the [m2]section consideredACArea of concrete cross sectionVIII[m2]

Notations and symbolsAhis the horizontal area of the wallAswAvCross-sectional area of the shear reinforcementVertical area of the wall[m2]avClear span between the support and applied load[m]bw0bwThe minimum width between tension and compression chordsThe smallest width of the cross-section in the tensile area[m][m]bwoThickness of the web of the wall[m]eEccentricity of P with respect to the centroid of stiffness[m]fcvdConcrete design strength in shear and compression[N/m2]fcdConcrete design strength in compression[N/m2]fckConcrete characteristic compressive strength[N/m2]fctdConcrete design strength in tension[N/m2]fydDesign value of the yield strength of the reinforcement[N/m2]fyd,hDesign value of the yield strength of the horizontal web [N/m2]reinforcementfyd,vDesign value of the yield strength of the vertical web [N/m2]reinforcementfywdFtdDesign yield strength of the shear reinforcementDesign value of the tensile force in the longitudinalreinforcementDesign value of the concrete compression force in the directionof the longitudinal member axis.Height of the wallGeometrical factorFcdhwk[N/m2][N/m2][N][m][-]k1Partial safety factor equals to 0.15 or defined in National [-]Annexk1wPartial factor equals 1.0 or the value given in National [-]Annexk2Partial factor equals 0.85 or the value given in National [-]Annexk3Partial factor equals 0.75 or the value given in National [-]AnnexkwFactor prevailing the prevailing failure mode[-]lwLength of the wall[m]MRdDesign flexural resistance at the base of the wall[Nm]IX

Notations and symbolsMEdDesign bending moment at the base of the wallNEdPAxial force in the cross-section due to loading or prestressing [N](NEd 0 for compression)Applied load[N]PnLateral load on wall n[N]qBehaviour factor used in design[-]q0Behaviour factor depending on the regularity in elevation of [-]the wall structurerfrpFactor accounting for the type of strengthening configuration [-]usedSe(Tc)Ordinate of the elastic response spectrum[m]s[m]shSpacing of the stirrupsSpacing of the horizontal reinforcement[m]svSpacing of the vertical reinforcement[m]slSpacing of the vertical stirrups[m]sbSpacing of the inclined stirrups[m]TTensile force in a tie[N]T1Fundamental period of vibration of the building in the [s]direction of shear forces VEdTCUpper limit period of the constant spectral acceleration region of [s]the spectrumVEdDesign shear forceVccdDesign value of the shear component of the force in the [N]compression area, in the case of an inclined compression chordV’EdDesign shear force determined form seismic analysisVRd,cDesign shear resistance of the member without shear [N]reinforcementVRd,sDesign value of the shear force which can be sustained by the [N]yielding shear reinforcementVRd,maxDesign value of the maximum shear force which can be [N]sustained by the member, limited by crushing of thecompression strutsVtdX[Nm][N][N]Design value of the shear component of the force in the tensile [N]reinforcement, in the case of an inclined tensile chord

Notations and symbolsYnis the distance of wall n from the centroid of stiffness[m]zInner lever arm, for a member with constant depth, [m]corresponding to the bending moment in the element underconsideration. In the shear analysis of reinforced concretewithout axial force, the approximate value z 0.9d maynormally be used.Greek lettersDescriptionD DsUnitAngle between shear reinforcement and the beam axis [-]perpendicular to the shear force[-]Shear reinforcement ratioJc Coefficient taking account of the state of the stress in the [-]compression chord[-]Magnifying factorPartial safety factor equals 1.2 for persistent and transient [-]loads and 1.5 for accidental loadsynDistance of wall n from the centroid of stiffnessJRdFactor to account for over strength due to steel strain- [-]hardening; in the absence of more precise data, JRd may betaken equal to 1.2T UlAngle between the concrete compression strut and the beam [-]axis perpendicular to the shear force[-]Longitudinal reinforcement areaUwUhShear reinforcement ratioReinforcement ratio of horizontal web bars[-][-]UvReinforcement ratio of vertical web bars[-]VcpMean compressive stress, measured positive, in the concrete dueto the design axial force. This should be obtained by averagingit over the concrete section taking account of the reinforcement.The value of Vcp shall not be calculated at a distance less than0.5d cotT from the edge of the support.Design strengthStrength reduction factor for concrete cracked in shear NEd/Ac 0,2 fcd[N/m2]DcwH VRd,maxQ1 cp[m][N/m2][-][N/m2]XI

Notations and symbolsACI (2005) notation ListRoman lettersDescriptionUnitAcvGross area of concrete section bounded by web thickness andlength of section in the direction of shear force consideredAcwArea of concrete section of the coupling beam resisting shearAgGross area of concrete sectionAvArea of shear reinforcementbwWeb width[m]dDistance from extreme compression fibre to centroid oflongitudinal tension reinforcement[m]lnClear span of the coupling beam[m]hHeight of the wall[m]hbClear height of the coupling beam[m]lwOverall length of the wall[m]MuFactored moment in the section[Nm]MNominal flexural moment in the coupling beam[Nm]NuFactored axial force[N]sStirrups spacing[m]twThickness of the wall[m]VcNominal shear strength provided by concrete[N]VnLateral load[N]VsNominal shear strength provided by shear reinforcement[N]VuFactored shear force[N]DescriptionUnitAngle between inclined stirrups and longitudinal axis of themember[-][m2]Greek lettersD XII

Notations and symbolsDcCoefficient defining the relative contribution of concrete strength [-]to nominal shear strengthUtSteel transverse reinforcement area[-]UwRatio of tension reinforcement to bwd[-]Betonghandboken (1997) notation listRoman lettersDescriptionUnitAcArea of the concrete[m2]As0Longitudinal tensile reinforcement[m2]bWidth of the beam[m]dEffective height of the beam[m]eis the eccentricity[m]EModulus of elasticity of concrete[N/m2]fccConcrete compression strength[N/m2]fckCharacteristic compression strength of concrete[N/m2]fctConcrete tensile strength, limited to the value 2.7 MPa[N/m2]fstSteel tensile strength[N/m2]fvConcrete formal strength determined according to:[N/m2]fwUtilized stress in shear reinforcement[N/m2]IMoment of inertia[m4]M2is the resulted bending moment due to eccentricity e and the [Nm]reaction force R2NsdThe design value of the pre-stressed force or other compression [N]forceR2is the reaction force of the assumed frame[N]sStirrups longitudinal spacing[m]V2is the shear force acting on the assumed frame[N]VcConcrete contribution to the shear capacity[N]XIII

Notations and symbols[N/m2]VRdsShear reinforcement capacityzInternal level arm of the steel reinforcement, set to be 0.9d if [m]not other provisionsGreek lettersDescriptionUnitEInclination angle of the steel stirrups[ ]U Tensile reinforcement ratio[-]T Angle of the compression struts with respect to a beam axisperpendicular to the shear force direction[ ]XIV

Table of contentTable of contentPREFACE . ISUMMARY.IIINOTATIONS AND SYMBOLS .V1INTRODUCTION.11.1Aim.21.2Method .21.3Limitations .31.4Content .32SHEAR DESIGN.52.1Shear design principles .52.1.1Truss model .52.1.2Limit Analysis and Concrete Plasticity .72.1.3Modified Compression Field Theory .102.2Shear design in Standards .142.2.1Eurocode (2004a, b) .142.2.2ACI (2005).172.3Shear in beams .182.3.1Introduction.182.3.2Shear in beams according to Eurocode (2004a, b).202.3.3Shear in beams according to ACI (2005).202.3.4Shear in beams according to Betonghandbok (1997) .202.3.5Calculation example for beams.222.4Reinforced concrete walls .242.4.1Introduction.242.4.2Reinforced concrete walls according to Eurocode (2004a, b) .262.4.3Reinforced concrete walls according to ACI (2005).322.4.4Walls with openings .352.4.5Theoretical models for walls with openings .372.4.6Calculation example for walls .41XV

3FIBRE REINFORCED POLYMERS . 453.1Composites. 453.1.1Components of the composites. 453.1.2Fibres . 453.1.3Matrices . 494SHEAR STRENGTHENING . 514.1General rehabilitation principles. 514.2FRP strengthening. 544.2.1General . 544.2.2Shear strengthening of beams. 574.2.3Calculation example for FRP strengthened beams . 644.2.4Strengthening of RC walls with openings . 704.3Calculation procedure for walls with openings FRP strengthened. 784.3.1Determining the efforts in the frame. 814.3.2FRP strengthening design. 834.3.3Concluding remarks and research questions. 855CASE STUDY FOR WALLS WITH OPENINGS FRPSTRENGTHENED . 875.1General description . 875.2Available data for analysis and simplifications . 875.3Analysis and evaluations . 905.4Design of the FRP strengthening . 925.5Concluding remarks. 946CONCLUSIONS AND FUTURE RESEARCH . 95REFERENCES. 99PUBLICATIONS . 107XVI

Introduction1 IntroductionWith the evolution of the human society, the complexity of structures has undergoneits own evolution too. Humans started using caves, then building tents, huts, igloos,castles multi-story buildings or skyscrapers, but regardless of our development all thesebuildings are still subjected to the laws of nature i.e. deterioration. In general,constructions are designed for a minimum life span and have a precise functionality.There are several causes other than natural forces which diminish the performance ofconstructions, such as change of functionality (eg. from an apartment building to anoffice building), structural intervention (eg. new openings are created or bearingelements are removed), design errors, construction faults or exceptional events(calamities or explosions). When one or more of these actions are presentsimultaneously, and no responsible action has been taken to re-establish the safeperformance of the building, catastrophic consequences may result. The bearingcapacity is of utmost importance for the safety of their users but, in some cases this isnot enough to ensure good performance. The durability, the functionality or theaesthetics are important factors to consider. For example a bridge may have thenecessary bearing capacity but can be too narrow, so it does not fulfil its main function.In general, for a structure all these three additional criteria have to be satisfied up to acertain level required for the main purpose of the building. For instance a school,beside load bearing capacity, needs to fulfil the function and durability demand at ahigher level and the aesthetics at a lower level. The class rooms have to be largeenough to host students and the corridors wide enough to allow emergencyevacuations. Therefore it is of high interest to have durable structures with long life andlow maintenance costs.In the case of newly built constructions a high degree of complexity and long termperformance is being achieved, but at the same time a large number of older structuresare not performing according to the expectations. Sometimes, to prevent deteriorationor possible collapse these structures are kept in service with partial or total restrictionsto the usage until appropriate measures can be taken. Usually, when speaking aboutappropriate measures to apply to a structure the replacement of the structure orrehabilitation of the initial capacity through different methods of strengthening orretrofitting has to be considered. Normally an economical study leads to a decision toeither replace a structure or retrofit it or vice versa.For strengthening or retrofitting structural buildings several methods have been usedwith success in the past. Among these we can mention the new structural materialadded to an already existing structural element to increase the gross section, the posttensioning technique, total replacement of some structural elements or changing the1

structural system (Carolin, 2003). Although these methods can be viable and successfulin some cases they are uneconomical or inefficient in terms of time. An alternativerehabilitation system to the ones mentioned above is the plate bonding technique. In itsbeginnings the rehabilitation was performed by attaching steel plates to a concretesurface. Nowadays the steel plates have been replaced by fibre reinforced polymers(FRP) and as bonding agent the epoxy resigns are used. Fibre reinforced polymers arethe result of the conjugated effort of continuous improvement of construction materialsand innovation in construction technology. Among others (aviation industry, carindustry, medicine, etc.), FRP composites are used in the construction industry too,and are a real and viable solution to rehabilitate a structure. The outstandingmechanical properties combined with the low weight makes the FRP composites a realchallenge for the classic strengthening techniques (Täljsten, 2006).1.1AimThe overall aim of the present thesis is to investigate and improve the understanding ofshear FRP strengthening of reinforced concrete beams and FRP strengthening ofreinforced concrete walls with openings. This main goal was divided into four differentsub-aims:x To evaluate and analyse different methods of determining the shear capacity ofRC beams and the capacity of RC walls with openings.x To analyse, evaluate and compare the existing theoretical models for FRP shearstrengthening of reinforced concrete beams.x To develop a simple to use design model for strengthening concrete beams inshear.x To assess the work performed on FRP strengthened reinforced concrete wallswith openings and develop the bases for a theoretical model.1.2MethodTo achieve the above mentioned goals a step by step procedure has been used. Tounderstand the shear failure mechanism of the FRP strengthened reinforced concreteelements the behaviour of these elements has been studied. An important issue was toasses and understand the work done until and during the work carried for this research.This has been done through a literature review study. A very important aspect isconsidered to be the accuracy of the existing theoretical model to predict the shearcapacity of strengthened structural elements. This was performed by comparing thepredictions of different models found in the literature with a large database ofexperimental results and an analytical shear model for strengthening concrete elementshas been derived based on the fracture mechanics approach. A literature survey hasbeen performed to assess the design methods for RC walls with openings and FRPstrengthened RC walls with openings. The static analysis of frames was used to developthe bases for a theoretical model for FRP strengthened RC walls with openings.2

Introduction1.3LimitationsThe theoretical model for shear strengthening of RC beams involves derivations onlyfor the debonding failure mechanism and is intended to complete the model derived byCarolin (2003) and Carol

Concrete contribution to the shear force capacity of a beam [N] V d Design shear force [N] V s Steel stirrups contribution to the shear force capacity of a beam [N] V p Axial load contribution to the shear force capacity of a beam [N] V i Other contributions to the shear capacity of a beam [N] V frp FRP contribution to the shear capacity [N]

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