Finite element modelling of externally shear -strengthened beams using fibre reinforced polymers

UNIVERSITE DE SHERBROOKE Faculte de genie Departement de genie civil FINITE ELEMENT MODELLING OF EXTERNALLY SHEAR-STRENGTHENED BEAMS USING FIBRE REINFORCED POLYMERS MODELISATION PAR ELEMENTS FINIS DU RENFORCEMENT EXTERNE EN CISAILLEMENT DES POUTRES EN BETON ARME EN UTILISANT LES POLYMERES RENFORCES DE FIBRES These de doctorat es sciences appliquees Speciality genie civil Jury: Dominique Levebvre Fredric Legeron Kenneth W Neale Pierre Labossiere Emmanuel Ferrier Omer Chaallal Amir Fam President Rapporteur Directeur de recherche Codirecteur Examinateur Examinateur Examinateur Ahmed GODAT Sherbrooke (Quebec), CANADA \ ii-irn J -1 Juillet 2008 1*1 Library and Archives Canada Bibliotheque et Archives Canada Published Heritage Branch Direction du Patrimoine de I'edition 395 Wellington Street Ottawa ON K1A0N4 Canada 395, rue Wellington Ottawa ON K1A0N4 Canada Your file Votre reference ISBN: 978-0-494-42676-0 Our file Notre reference ISBN: 978-0-494-42676-0 NOTICE: The author has granted a nonexclusive license allowing Library and Archives Canada to reproduce, publish, archive, preserve, conserve, communicate to the public by telecommunication or on the Internet, loan, distribute and sell theses worldwide, for commercial or noncommercial purposes, in microform, paper, electronic and/or any other formats AVIS: L'auteur a accorde une licence non exclusive permettant a la Bibliotheque et Archives Canada de reproduire, publier, archiver, sauvegarder, conserver, transmettre au public par telecommunication ou par Plntemet, prefer, distribuer et vendre des theses partout dans le monde, a des fins commerciales ou autres, sur support microforme, papier, electronique et/ou autres formats The author retains copyright ownership and moral rights in this thesis Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission L'auteur conserve la propriete du droit d'auteur et des droits moraux qui protege cette these Ni la these ni des extraits substantiels de celle-ci ne doivent etre imprimes ou autrement reproduits sans son autorisation In compliance with the Canadian Privacy Act some supporting forms may have been removed from this thesis Conformement a la loi canadienne sur la protection de la vie privee, quelques formulaires secondaires ont ete enleves de cette these While these forms may be included in the document page count, their removal does not represent any loss of content from the thesis Bien que ces formulaires aient inclus dans la pagination, il n'y aura aucun contenu manquant Canada Resume Le besoin en rehabilitation des structures en beton est bien connu Un grand nombre de recherches sont dans ce domaine L'utilisation de polymeres renforces de fibres dans la rehabilitation a montre que cette solution est competitive du point de vue de sa performance structurale et de son aspect economique Le renforcement au cisaillement des poutres en beton est necessaire quand la poutre est deficiente en cisaillement, ou quand sa capacite au cisaillement devient insufBsante apres de son renforcement en flexion Une technique qui a fait ses preuves pour le renforcement des poutres en beton est de coller des lamelles de composites additionnelles Au cours des dernieres annees, une grande quantite de travaux de recherche a ete conduite sur le renforcement au cisaillement avec des composites et cela a mene a une meilleure comprehension du comportement Plusieurs equations de design ont ete proposees pour le calcul de poutres de beton arme renforcees au cisaillement avec des composites La plupart des parametres qui controlent le comportement des poutres renforcees au cisaillement ont ete identifies Les equations de design, qui decrivent le comportement des poutres renforcees au cisaillement, ne sont pas sufhsantes pour evaluer la contribution au cisaillement des composites PRF utilises Ceci peut etre attribue a l'absence d'un modele numerique precis, dont l'utilisation est plus economique que l'experimentation, pour tenir compte des complexites du comportement des poutres renforcees au cisaillement et pour atteindre une meilleure comprehension des mecanismes de rupture Des analyses limitees par element finis ont ete effectuees sur les poutres renforcees en cisaillement Comme contribution pour remplir ce manque, un modele numerique versatile est developpe dans cette etude pour predire le comportement des poutres renforcees au cisaillement par des composites, avec une emphase sur le comportement de l'interface et le probleme du delaminage Cette recherche est divisee en trois parties : (1) le developpement d'un modele numerique capable de capturer le comportement reel des poutres renforcees en cisaillement; (2) le modele numerique propose applique a differents cas de configurations de renforcement, tel que, poutres avec des lamelles verticales ou des lamelles inclinees, des poutres avec des enveloppes en forme de U, ainsi que des poutres avec des lamelles ancrees aux extremites et; (3) une etude parametrique faite pour evaluer l'innuence sur le comportement au cisaillement du taux d'armature des etriers, de la resistance a la compression du beton, du module elastique du composites, ainsi que son epaisseur, et du rapport entre la largeur du composites et celle de la poutre Le modele numerique propose ici est valide avec les resultats experimentaux provenant de la litterature Les resultats predits concordent bien avec ceux des experimentations On va montrer que l'element essentiel de 1'analyse par element finis est la modelisation de l'interface composite-beton L'utilisation des elements d'interface predit de bons resultats du comportement des poutres renforcees en cisaillement En outre, 1'analyse numerique nous permet d'avoir des informations sur le glissement et la propagation du delaminage du composite le long de l'interface Des analyses des deformations des les lamelles sont aussi presentees Des equations de regression ont ete developpees, sur la base d'une approche statistique (RSM) De nouvelles equations de design ont ete proposees pour les cas de lamelles collees et pour les enveloppes en forme de U Les equations proposees peuvent etre utilisees dans un guide de conception de la contribution du composites au cisaillement Quelques resultats de ce travail de recherche peuvent etre trouves dans Godat et al [2007a,b] Abstract The need for structural rehabilitation of concrete structures all over the world is well known A great amount of research is going on in this field The use of fibre reinforced polymer (FRP) plate bonding has been shown to be a competitive solution regarding both the structural performance and the economical aspects Shear strengthening of reinforced concrete beams is required when the beam is deficient in shear, or when its shear capacityfalls below its flexural capacity after flexural strengthening An accepted technique for the shear strengthening of reinforced concrete beams is to provide an additional FRP web reinforcement in the form of externally bonded FRP sheets Over the last few years, a considerable amount of research has been conducted on shear strengthening with FRP composites and that has led to a better understanding of the behaviour Hence, many design equations have been proposed to design shear-strengthened beams Most of the parameters that control the behaviour of shear-strengthened beams have been addressed However, the design equations describing the behaviour of shearstrengthened beams are not sufficient to properly evaluate the shear contribution of the FRP composites This might be attributed to the absence of an accurate numerical model, which is more economical than the experimental tests, to capture the complexities of shear-strengthened beams and to lead to a better understanding of the failure mechanisms Limited finite element analyses have been carried out on FRP shear-strengthened beams As a contribution to fill this need, a versatile numerical model is developed in this study to predict the response of reinforced concrete beams strengthened in shear with bonded FRP composites, with a particular emphasis on the interfacial behaviour and debonding phenomena This research consists of three phases They are: (1) the development of a reliable numerical model that can capture the real behaviour of FRP shear-strengthened beams; (2) the use of the proposed numerical model to verify various cases having different strengthening configurations: beams with vertical and inclined sidebonded FRP sheets, the U-wrap scheme, as well as anchored FRP sheets and; (3) a parametric study conducted to identify design variables that have the greatest influence on the behaviour of shear-strengthened beams such as the steel stirrup reinforcement ratio, concrete compressive strength, FRP elastic modulus, FRP thickness, and ratio between FRP width to beam width The proposed numerical model is validated against published experimental results The predicted results are shown to compare very well with test results It is shown that the formulation of the FRP/concrete interfacial behaviour is essential to analyses utilizing finite element models The implementation of interface elements produces accurate predictions of the response of shear-strengthened beams Furthermore, the numerical analysis provides useful information on the slips and propagation of debonding along the FRP/concrete interfaces Predicted strain profiles along the FRP sheet depth are also presented Regression equations based on the statistical approach of the response surface methodology (RSM) are developed New design equations to describe the FRP axial effective strain at the state of debonding are proposed for both side-bonded and U-wrap strengthening schemes The proposed design equations can be used to provide simple design guidelines to predict the FRP shear contribution Some of the results of this thesis research can be found in Godat et al [2007a,b] To my mother and father to my brothers and sisters to those gave me their hearts and their hearts are always with me Acknowledgements Praise be to Allah Almighty and Peace be upon His Prophet Mohammed After thanking God for giving me the opportunity and strength, I would like to express my gratitude to the institutions and people who contributed, one way or another, in making this work come true and helping me reach this station in my academic life For them I would like to say thank you with all my respect and appreciation First, I would like to thank my supervisors Professors Pierre Labossiere and Kenneth Neale Professor Kenneth Neale is a rich source of information He taught me that academic work has neither limit, nor boundary I would like to thank him for being patient, helpful and an ambitious supervisor He is a tough examiner, yet has a kind personality I am also deeply thankful to my supervisor, Professor Pierre Labossiere, for his valuable backup and guidance We had together very fruitful discussions that cleared my mind and lit my thoughts With special love I would like to acknowledge the encouragement from my family in Sudan They have always been there for me, with their endless love and support I would like to thank all my colleagues at the Civil Engineering Department at the University of Sherbrooke Special thanks go to my colleagues and friends Hussien Abdel Baky and Walid Elsayed, for their deep discussions, endless support and for making the difficult moments fun and easy I would like also to thank the Sudanese Society at Montreal for the continuous inspiration during my studies My special thanks go to my friends Nazar Alameen and Mohammed Askri, for being such wonderful and supporting friends This research was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC), and the Canadian Network of Centres of Excellence on Intelligent Sensing for Innovative Structures (ISIS Canada) This support is gratefully acknowledged List of Notation Contents Introduction 1.1 General 1.2 Scope 1.3 Research Objectives 1.4 Outline 1 5 Literature Review 2.1 Introduction 2.2 Techniques for the Shear Strengthening of Beams 2.2.1 Traditional Techniques 2.2.2 Fibre Reinforced Polymer Technique 2.3 Concept of Shear Strengthening using FRP composites 2.4 Shear Behaviour of Reinforced Concrete Beams 2.4.1 Shear Behaviour of RC Beams without FRP Strengthening 2.4.2 Shear Behaviour of FRP Shear-Strengthened RC Beams 2.4.2.1 Shear Failure Controlled by FRP Rupture 2.4.2.2 Shear Failure Controlled by FRP Debonding 2.5 Parameters Influencing Shear-Strengthened Beams 2.5.1 Beam Dimensions 2.5.2 Strengthening Schemes 2.5.3 FRP Dimensions and Characteristics 2.6 Anchorage of the FRP plates 2.7 FRP Shear-Strengthened Design Models 2.7.1 Truss Design Model 2.7.1.1 ACI Model 2.7.1.2 ISIS Model 2.7.1.3 FIB Model 2.7.1.4 BS Model 2.7.1.5 Taljsten Model 2.7.2 Modified Compression Field Theory (MCFT) 2.7.3 Shear Friction and Strip Model l 7 10 14 15 15 17 17 18 20 21 22 24 25 30 31 31 33 33 34 35 36 37 CONTENTS 2.8 2.9 Axial Strain Profile along the FRP Composites Numerical Modelling 2.9.1 Introduction 2.9.2 Finite Element Packages 2.9.3 Modelling of Concrete 2.9.3.1 Concrete in Compression 2.9.3.2 Crack Modelling 2.9.3.3 Tension Stiffening Model 2.9.3.4 Shear Retention Factor 2.9.3.5 Convergence of Results 2.9.4 Modelling of Bonded FRP Composites 2.9.5 Modelling of FRP/Concrete Interfacial Behaviour 2.10 Summary 38 40 40 41 42 42 43 45 45 46 47 48 53 Development of a Reliable Numerical Model 3.1 Introduction 3.2 ADINA Finite Element Model 3.2.1 Material Modelling 3.2.1.1 Concrete 3.2.1.2 Steel Reinforcement and FRP Composites 3.2.1.3 FRP/Concrete Interface 3.2.2 Structural Modelling 3.2.2.1 Modelling of FRP Composites 3.2.2.2 Modelling of FRP Concrete Interface 3.2.3 Horizontal Interface Elements 3.2.4 Finite Element Discretization 3.3 DIANA Finite Element Model 3.3.1 Concrete 3.3.2 Steel Reinforcement and FRP Composites 3.3.3 FRP/Concrete Interface 3.4 Specimens Investigated 3.4.1 Pellegrino and Modena Specimens 3.4.2 Chaallal et al specimens 3.4.3 Adhikary and Mutsuyoshi Specimens 3.4.4 Khalifa and Nanni Specimens 3.4.5 Lee and Al-Mahaidi Specimens 3.5 Summary 54 54 55 56 56 57 57 59 60 60 63 64 64 65 65 66 67 69 70 70 72 73 73 Validation of Numerical Results 4.1 Introduction 4.2 Comparison Between Shell and Truss Modelling of FRP Composites 77 77 77 n BIBLIOGRAPHY B Aedy, J San Roman, and E Bruhwiller Carbon fibre shear strengthening of rectangular concrete beams Final Report 97.02, Ecole Polytechnique de Lausanne, Switzerland, 1999 B Agarwal and L Broutman Analysis and Performance of Fibre Composites John Wiley and Sons, USA, 1st edition, 1990 R Al-Mahaidi, K Lee, and G Taplin Behavior and analysis of RC T-beams partially damaged in shear and repaired with CFRP laminates In P.C Chang, editor, 2001 Structural Congress and Exposition, Washington, D C , May 21-23 2001 ASCE G Al-Sulaimani, A Istem, A Basunbul, M Bluch, 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composites M.A.Sc Thesis, University of Toronto, Toronto, Ontario, 2001 R.S.Y Wong and F.J Vecchio Toward modeling of reinforced concrete members with externally bonded fiber-reinforced polymer composites ACI Structural Journal, 100(1): 47-55, 2003 X Yang, A Nanni, and G Chen Effect of corner radius on the performance of externally bonded frp reinforcement In C Burgoyne, editor, 5th Int Symposium, FRP Reinforcement for Concrete Structures (FRPRCS-5), pages 197-204, UK, 2001 Z Zhang and C Hsu Shear strengthening of reinforced concrete beams using carbonfiber-reinforced polymer laminates Journal of Composites for Construction, ASCE, (2):158-169, 2005 198 Appendix A ADINA Concrete Constitutive Model It is well accepted that concrete is a very complex material The concrete constitutive model provided in ADINA may not be capable to simulate all structural applications However, it works well for simple applications, such as FRP shear-strengthening of reinforced concrete beams The concrete model is a hypoelastic concrete model It is based on three features: concrete in compression; post-cracking model; and failure envelope The nonlinear stress-strain relation allows for weakening of the material under increasing compressive stresses Failure envelopes that define failure in tension and crushing of concrete in compression A fixed smeared crack model is used to describe the post-cracking behaviour of concrete The objective of this appendix is to provide a brief description of the characteristics of ADINA, version 8.4, concrete material model A.l Concrete in Compression The general multiaxial stress-strain relations are derived from a uniaxial (incremental) stress-strain relation When the concrete in tension the stress-strain relation is linear until tensile failure In this case, an incremental relation between stress (a) related to the strain (i) through a modulus of elasticity ([C]) Such relation can be expressed as: H = [cm 199 (A.I) APPENDIX A ADINA CONCRETE CONSTITUTIVE MODEL e* strain, Epi Figure A l : Equivalent uniaxial stress-strain relationship under multiaxial state of stress When the concrete is under compression and before the cracking initiated, the following relation is used to calculate the matrix of modulus of elasticity: Ec[l - B{^)2 - 2C(^) ] R pi• •ism where, A = [l + A(£-£ + B(£-£)2 + C(£f)3}2 f^+(P3-2P2|£-(2P3-3P2+l)] -^ T^-*P+m (A.2) • B = [(2|-3)-2A], C = [(2-f+A] and the values of Es = V-, P = A"- and the parameters ( e u , e m , a ' anda' ) are computed in relation to their corresponding uniaxial values (eu, em, auandcrm), as shown in Figure A.l as: eu = (Ci7i2 + C K = (Ci7i + C i ) ^ CT m = (A.3) (A.4) l\Vu (A.5) 71*11 (A.6) 200 A.2 FE MATERIAL FAILURE ENVELOPES where Cx and C2 are taken as 1.4 and -0.4, respectively The value of 71 is calculated from the biaxial failure envelope of the concrete according to the ratio {crp2/crm), as depicted in Figure A.2 In the region of concrete cracking, the stress-strain relations are evaluated differently The material is considered as orthotropic with the direction of orthotropy being defined by the principal stress directions The matrix of modulus of elasticity has the following form: (l-v)Epl C = vEl2 vE13 0 (l-v)Ep2 vE23 0 0 0.5(1 - 2v)E12 0 0 0.5(1 - 2v)E13 (l-v)Ep3 ( l + ) ( l + 27) symetric 0.5(1 - where Epi,EP2andEp3 (A.7) are the equivalent multiaxial modulus of elasticity in the principal directions, computed according to the value of principal strain, e^ Additionally, the off-diagonal components are computed using: _ WPi\Bpi + \crpj\Epj h H ~ 1 , • I I ^ pi I I &pj J (A-8) where api is the principal stress value, i 7^ j and i,j=l to When the principal stress state lies on the failure envelope, it is assumed that the material strains soften isotropically in all directions This corresponds to the case of £pi < £u- The stresses, in all principal directions, are assumed to linearly reduce to zero using the following modulus: Epi = A.2 — (A.9) F E Material Failure Envelopes After the principal stresses ( o"p3), the stresses