M l UNIVERSITE DE m SHERBROOKE Faculte de genie Departement de genie civil CONCRETE CONTRIBUTION TO THE SHEAR RESISTANCE OF FRP-REINFORCED CONCRETE BEAMS A Dissertation Submitted in Partial Fulfilment o f the Requirements for the Degree o f Doctor o f Philosophy Specialty: Civil Engineering Ahmed Kamal El-Sayed Ahmed Sherbrooke (Quebec), Canada July 2006 i Reproduced with permission of the copyright owner Further reproduction prohibited without permission Library and Archives Canada Bibliotheque et Archives Canada Published Heritage Branch Direction du Patrimoine de I'edition 395 W ellington Street Ottawa ON K1A 0N4 Canada 395, rue W ellington Ottawa ON K1A 0N4 Canada Your file Votre reference ISBN: 978-0-494-25905-4 Our file Notre reference ISBN: 978-0-494-25905-4 NOTICE: The author has granted a non­ exclusive 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 non­ commercial 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 I'lnternet, preter, 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 i*i Canada Reproduced with permission of the copyright owner Further reproduction prohibited without permission A bstract ABSTRACT Corrosion o f steel reinforcement in concrete structures causes deterioration o f concrete, resulting in costly maintenance and repair Many steel-reinforced concrete structures exposed to deicing salts and marine environments require extensive and expensive maintenance Recently, the use o f fibre-reinforced polymers (FRP) as an alternative reinforcing material in reinforced concrete structures has emerged as an innovative solution to the corrosion problem However, due to the difference in mechanical properties between steel and FRP reinforcements, the shear strength o f concrete members reinforced with FRP longitudinal reinforcement may differ from that o f members reinforced with steel An experimental program including two phases is described The experimental program was conducted at the University o f Sherbrooke to investigate the effect o f using FRP bars as longitudinal reinforcement on the shear strength and behaviour o f concrete beams without web reinforcement The first phase included 15 large-scale concrete slender beams reinforced with glass FRP, carbon FRP, or conventional steel bars Nine beams were constructed using normal-strength concrete, whereas six beams were constructed using high-strength concrete The test variables were the reinforcement ratio and the modulus o f elasticity o f the reinforcing bars as well as the concrete compressive strength The second experimental phase included 12 large-scale concrete deep beams reinforced with glass FRP, carbon FRP, or conventional steel bars The test beams o f this phase were constructed using normal-strength concrete and the test parameters were the reinforcement ratio and the modulus o f elasticity o f the reinforcing bars as well as the shear span-to-depth ratio The influence o f the considered variables on the shear strength and behaviour o f the tested beams in the two phases is presented An analytical investigation to examine the validity o f the available design provisions o f concrete contribution to shear strength for members longitudinally reinforced with FRP bars is reported For this purpose, the shear strengths o f the tested beams are analyzed using the shear design provisions o f the different available codes, manuals, and design guidelines The results o f the analysis are compared with the experimental values Based on the findings o f this investigation, a proposed shear design ii Reproduced with permission of the copyright owner Further reproduction prohibited without permission A bstract equation is presented The proposed equation is verified against experimental shear strengths o f 107 specimens tested to date, including the specimens in this investigation In addition, the proposed equation is compared to the major design provisions using the available test data to further evaluate its reliability During the course o f the research work, the following related papers have been published or submitted for publication: Journal Papers El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B., (2006a), “Shear Strength of FRP-Reinforced Concrete Deep Beams without Web Reinforcement,” Submitted to ACI Structural Journal El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B., (2006d), “Shear Capacity of High-Strength Concrete Beams Reinforced with FRP Bars,” ACI Structural Journal, Vol 103, No 3, pp 383-389 El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B., (2006e), “Shear Strength of FRP-Reinforced Concrete Beams without Transverse Reinforcement,” ACI Structural Journal, Vol 103, No 2, pp 235-243 Conference Papers El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B., (2005a), “Shear Strength of Concrete Beams Reinforced with FRP Bars: Design Method,” Proceedings o f the 7th International Symposium on Fiber Reinforced Polymer Reinforcement for Concrete Structures (FRPRCS-7), ACI-SP-230, Kansas City, MO., USA, Nov 5-9, pp 955-974 El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B., (2005b), “Analytical Modeling o f FRP-Reinforced Concrete Beams Failed in Shear,” Proceeding on CD, 1st CSCE Specialty Conference on Infrastructure Technologies, Management and Policy, Toronto, Ontario, Canada, June 2-4, FR-127, lOp El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B., (2005c), “Shear Design o f Concrete Beams Reinforced with FRP Bars,” Proceeding on CD, 4th Middle East Symposium on Structural Composites for Infrastructure Applications (MESC-4), Alexandria, Egypt, May 20-23, 12p iii Reproduced with permission of the copyright owner Further reproduction prohibited without permission A bstract El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B., (2004a), “Concrete Contribution to the Shear Resistance o f High-Strength Concrete Beams Reinforced with FRP Bars,” Proceeding on CD, International Conference: Future Vision and Challenges for Urban Development, Cairo, Egypt, December 20-22, 12p El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B., (2004c), “Evaluation o f Concrete Shear Strength for Beams Reinforced with FRP Bars” Proceeding on CD, 5th Structural Specialty Conference o f the CSCE, Saskatoon, Saskatchewan, Canada, June 2-5, ST-224, lOp Also the candidate has participated in the following publications during his doctorate study at the Universite de Sherbrooke: Journal Papers El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B., (2006b), “Mechanical and Structural Characterization o f New Carbon FRP Stirrups for Concrete Members,” Accepted for publication in the Journal o f Composites for Construction, ASCE 10 El-Sayed, A.K., El-Salakawy, E.F., and Benmokrane, B., (2005d), “Shear Strength of One-way Concrete Slabs Reinforced with FRP Composite Bars,” Journal of Composites for Construction, ASCE, Vol 9, No 2, pp 147-157 Conference Papers 11 Ahmed, E A., El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B., (2006), “Shear Behaviour o f Concrete Bridge Girders Reinforced with Carbon FRP Stirrups,” Submitted to the 7th International Conference on Short and Medium Span Bridges, Montreal, Canada, Aug 23-25, 10 p 12 El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B., (2006c), “Structural Behaviour o f Carbon FRP Stirrups Used as Shear Reinforcement for Concrete Beams.,” Proceedings on CD, 1st International Structural Specialty Conference o f the Canadian Society for Civil Engineering, CSCE, Calgary, Alberta, Canada, May 2326, 10 p iv Reproduced with permission of the copyright owner Further reproduction prohibited without permission A bstract 13 El-Sayed, A.K., El-Salakawy, E.F., and Benmokrane, B (2004b), “New Carbon FRP Stirrups as Shear Reinforcement for Concrete Beams,” Advanced Composites Materials in Bridges and Structures (IV-ACMBS), Proceedings on CD, Calgary, Alberta, Canada, July 20-23, p Technical Reports 14 Benmokrane, B., El-Sayed, A K., and El-Salakawy, E F., (2005e), “Conception de Poutres de Pont en Beton on Precontraint Renforcees avec des Etriers en Materiaux Composites,” Technical Report-Phase 2, Submitted to the Ministry o f Transportation o f Quebec, Quebec, Canada, March, 18p 15 Benmokrane, B., El-Sayed, A K., El-Salakawy, E F., and Massicotte, B., (2004d), “Conception de Poutres de Pont en Beton on Precontraint Renforcees avec des Etriers en Materiaux Composites,” Technical Report-Phase 1, Submitted to the Ministry o f Transportation o f Quebec, Quebec, Canada, January, 21 p v Reproduced with permission of the copyright owner Further reproduction prohibited without permission Resume RESUME La corrosion de l’acier d’armature des structures de beton provoque la deterioration du beton, ce qui entraine des couts de reparation et d ’entretien importants De nombreuses structures de beton arme d ’acier exposees aux sels de degla age o u a u n environnement marin necessitent des travaux de refection generalises et couteux Recemment, l’emploi de polymeres renforces de fibres (PRF) comme materiau de renfort altem atif pour les structures de beton est apparu comme etant une solution innovatrice aux problemes de corrosion Cependant, du fait des differences de proprietes mecaniques entre les armatures d ’acier et de PRF, la resistance au cisaillement des membrures de beton arme d’armature de traction en PRF peut differer de celle observee avec l’acier d ’armature Un programme experimental incluant deux phases est decrit Le programme experimental a ete mene a l’Universite de Sherbrooke afin d ’evaluer l’effet de l’utilisation des barres de PRF comme armature longitudinale de traction sur la resistance au cisaillement (ou a 1’effort tranchant) et le comportement des poutres de beton sans armature d ’ame (sans armature transversale) La premiere etape a porte sur 15 poutres elancees de beton a grande echelle renforcees avec des barres d ’armature en PRF de verre, en PRF de carbone et de Lacier d ’armature conventionnel N euf poutres ont ete fabriquees en utilisant du beton normal tandis que les six autres l’ont ete avec du beton a haute resistance Les variables d’essai etaient le taux d’armature et le module d ’elasticite des barres d ’armature de meme que la resistance a la compression du beton La seconde phase experim ental portait sur 12 poutres profondes de beton a grande echelle renforcees avec des barres d ’armature en PRF de verre, en PRF de carbone et de l’acier d ’armature conventionnel Les poutres d ’essai etudiees lors de cette phase etaient fabriquees a partir de beton normal et les parametres d’essai etaient le taux d ’armature et le module d ’elasticite des barres d’armature de meme que le rapport portee de la zone de cisaillem ent sur hauteur de la poutre L ’influence des variables considerees sur la resistance au cisaillement et le comportement des poutres d ’essai des deux phases est presentee Une etude analytique portant sur la validite des equations de calcul disponibles sur la contribution du beton a la resistance au cisaillement pour les membrures en beton vi Reproduced with permission of the copyright owner Further reproduction prohibited without permission Resume renforces longitudinalement avec des barres de PRF est aussi rapportee Dans cet objectif, les resistances au cisaillement des poutres testees ont ete analysees a l’aide des equations de calcul concemant le cisaillement a partir des divers codes, manuels et guides de calcul disponibles Les resultats de cette analyse sont compares aux valeurs experimentales Une equation de calcul pour le cisaillement est proposee et verifiee a partir des valeurs experimentales de resistance au cisaillement des 107 poutres etudiees a date, incluant les poutres de la presente etude vii Reproduced with permission of the copyright owner Further reproduction prohibited without permission A c know Iedgem ents A CKN O W LED GEM EN TS I would like to express my profound gratitude to my advisors Professor Brahim Benmokrane and Professor Ehab El-Salakawy for their support, encouragement, guidance, and valuable advice throughout the research program I would like to thank the structural laboratory technical staff in the Department o f Civil Engineering at the Universite de Sherbrooke, in particular Mr Francois Ntacorigira and Mr Simon Sindayiagaya for their help in my experimental work This research program has been carried out through the NSERC Chair o f Professor Benmokrane on FRP composite reinforcement for concrete structures at the Universite de Sherbrooke Thus, the financial support received from the Natural Sciences and Engineering Research Council of Canada (NSERC), Pultrall Inc (Thetford Mines, Quebec), the Ministry o f Transportation o f Quebec, the Network o f Centres o f Excellence ISIS-Canada, and the Universite de Sherbrooke is greatly acknowledged I would like to express my deep appreciation and thanks to my parents, my brother, and my sisters for their endless love, support, and encouragement Finally, my words stand helpless and cannot express my appreciation to my wife and my twin sons for their patience and support; to them this thesis is dedicated viii Reproduced with permission of the copyright owner Further reproduction prohibited without permission Table o f Contents TABLE OF CONTENTS ABSTRACT ii ACKNOWLEDGEMENTS viii TABLE OF CONTENTS ix LIST OF FIGURES xv LIST OF TABLES xx NOTATION xxii INTRODUCTION 1.1 General 1.2 Objectives and Originality 1.3 Methodology 1.4 Structure o f the Thesis BACKGROUND AND REVIEW ON THE SHEAR BEHAVIOUR OF CONCRETE BEAMS 2.1 General 2.2 Shear in Reinforced Concrete Beams without Transverse Reinforcement 2.2.1 Mechanism o f shear transfer 2.2.1.1 Shear stresses in uncracked concrete 2.2.1.2 Interface shear transfer 2.2.1.3 Dowel action 10 2.2.1.4 Arch action 10 2.2.1.5 Residual tensile stresses across crack 10 2.2.2 Modes of inclined cracking and shear failure 11 2.2.3 Factors affecting shear capacity 15 2.2.3.1 Tensile strength o f concrete 15 2.23.2 Longitudinal reinforcement ratio 15 2.2.3.3 Shear span-to-depth ratio 16 2.2.3.4 Axial force 16 ix Reproduced with permission of the copyright owner Further reproduction prohibited without permission Chapter 7; Summary and Conclusions reinforced with steel This may be attributed to the difference in bond characteristics between FRP and steel bars used in this investigation 11 The effect o f the modulus o f elasticity o f the reinforcing bars was more pronounced between the beams reinforced with FRP bars which had the same surface preparation (sand coated) The beams reinforced with glass FRP bras showed reduced shear strength in comparison to the beams reinforced with carbon FRP bars 12 In general, the shear strength o f the reinforced concrete deep beams without web reinforcement was proportional to the amount o f longitudinal reinforcing bars As the amount o f longitudinal reinforcing bars was increased, the obtained shear strength increased This behaviour was observed for the three different types o f reinforcing bars employed in this investigation 13 The shear span-to-depth ratio has a significant influence on the ultimate shear strength o f the reinforced concrete deep beams without web reinforcement As the shear span-to-depth ratio was decreased, the obtained ultimate shear strength significantly increased The increase in the inclined shear strength, however, was less compared with the increase o f ultimate shear strength with the decrease o f shear spanto-depth ratio 14 The flexural behaviour, in terms o f load-deflection response, o f the reinforced concrete deep beams after cracking appeared to be a function o f the axial stiffness of the reinforcing bars 7.2.3 Code predictions for slender beam specimens Based on the analysis o f the slender beam specimens using different available codes, manuals, and design guidelines recently published, the following conclusions can be drawn: 15 The C A N /C S A -S806-02 shear design method, for FRP-reinforced concrete beams without web reinforcement and having an effective depth greater than 300 mm, resulted in good predictions for beams reinforced with glass FRP bars and conservative predictions for beams reinforced with carbon FRP bars 238 Reproduced with permission of the copyright owner Further reproduction prohibited without permission Chapter 7: Summary and Conclusions 16 For FRP-reinforced concrete beams without web reinforcement, the simplified method o f determining the parameter (5 according to the CAN/CSA-S6-00 code resulted in reasonable but rather conservative results On the other hand, the general method o f determining the parameter /? according to the CAN/CSA-S6-00 code resulted in very conservative predictions This result is contrary to the common expectation that the simplified methods in any code would provide lower (more conservative) values 17 The ACI 440.1R-03 shear design method provided unduly conservative predictions, particularly for beams reinforced with glass FRP bars 18 Generally, better predictions can be obtained by both the ISIS shear design method (ISIS-M03-01) and JSCE shear design recommendations 19 For steel-reinforced beams, both the simplified method o f determining the parameter /? according to the CSA-A23.3-04 code and the ACI 318-05 code resulted in good predictions for the shear strength o f the tested beams On the other hand, the general method o f determining the parameter f3 according to the CSA-A23.3-04 code provided rather conservative results contrary to the general expectation that the general method would give less conservative predictions in comparison to the simplified method 20 Generally, the CAN/CSA-S806-02 code appeared to predict well the service load deflection o f the FRP-reinforced beams On the other hand, the ACI 440.1R-03 guide appeared to underestimate the service load deflection o f the FRP-reinforced beams 21 Both the CAN/CSA-A23.3-04 and the ACI 318-05 codes resulted in unconservative predictions for the service load deflection o f the steel-reinforced beams 22 The ACI 440.1R-03 guide appeared to reasonably estimate the crack width o f the FRP-reinforced beams considering the factor kb equal to 1.2 However, to get all predictions o f the crack widths in the conservative side using this method, the factor kb should be 1.54 and 1.37, respectively, for the carbon and glass FRP bars used in this investigation In addition, all experimental crack widths at service were in the general range o f maximum crack widths suggested by the ACI 440.1R-03 guide 23 The values of the crack width control parameter, z, calculated according to the CAN/CSA-S806-02 code were higher than the allowable code limits for the beams 239 Reproduced with permission of the copyright owner Further reproduction prohibited without permission Chapter 7: Summary and Conclusions reinforced with glass FRP bars On the other hand, the calculated values o f z were well below the allowable code limits for the beams reinforced with carbon FRP bars 24 For the steel-reinforced beams, the experimental crack width values at service were less than predicted by the CAN/CSA-A23.3-04 and the ACI 318-05 codes In addition, all experimental crack widths at service were lower than the maximum crack widths recommended by the two codes 7.2.4 Code predictions for deep beam specimens The ultimate shear strengths o f the tested deep beams were analyzed using the sectional and member approaches recommended for steel-reinforced beams Based on this analysis, the following conclusions can be drawn: 25 The sectional approach according to the ACI 318-99 code (1999) provided conservative predictions for the ultimate shear strength o f the beams either reinforced with steel or FRP bars However, this method has a drawback as it does not account for the effect o f the modulus o f elasticity o f the reinforcing bars on the ultimate shear strength 26 The strut and tie model according to the ACI 318-05 code (2005) provided unconservative predictions for the ultimate shear strength o f the tested deep beams without web reinforcement This is attributed to the result that the tested beams failed prematurely by splitting o f diagonal strut before reaching the concrete crushing capacity o f the strut due to lack o f web reinforcement which can resist diagonal splitting A further reduction in the compressive strength o f the diagonal strut may lead to conservative predictions using this model for the deep beams without web reinforcement 7.2.5 P roposed sh ear d esign m ethod A proposed modification to the shear design equation in the ACI 440.1R-03 guide is presented This modification is based on experimental findings, which represent the potential o f empirical and semi-empirical formulations The modification was extended to cover both slender and deep flexural members reinforced with longitudinal FRP bars 240 Reproduced with permission of the copyright owner Further reproduction prohibited without permission Chapter 7: Summary and Conclusions The proposed equation was used to calculate the shear strength o f 107 specimens tested in 14 different investigations, including this investigation The calculated shear strengths using the proposed equation were compared to the experimental ones Based on this comparison, the following conclusions can be drawn: 27 The proposed equation gives accurate predictions and yet conservative over the range of variables known to affect the concrete shear strength 28 The proposed equation was compared to the major provisions using the available test data More accurate and consistent predictions were obtained using the proposed equation 7.3 Recommendations for Future W ork Based on the findings and conclusions o f the current study, the following recommendations are made for future research: More research is needed to study the effect o f the bond characteristics o f the reinforcing bars on the ultimate shear strength o f reinforced concrete deep beams without web reinforcement Research is needed to systematically investigate the size effect on the shear strength of FRP-reinforced concrete members Additional experiments investigating the applicability o f the strut and tie model on the concrete deep beams reinforced with FRP bars should be conducted For this purpose, the deep beams should be provided, at least, with the minimum amount o f distributed web reinforcement Research is needed to quantify the compressive strength o f diagonally cracked concrete reinforced with FRP bars The shear behaviour o f concrete beam s reinforced with FRP stirrups should be considered for future investigations 241 Reproduced with permission of the copyright owner Further reproduction prohibited without permission References REFERENCES AASHTO, (2004), “AASHTO LRFD Bridge Design Specifications,” 3rd Edition, American Association o f State Highway and Transportation Officials, Washington D.C., 464p ACI Committee 318, (1989), “Building Code Requirements for Reinforced Concrete and Commentary,” ACI 318-89/ACI 318R-89, American Concrete Institute, Farmington Hills, MI, 353p ACI Committee 318, (1999), “Building Code Requirements for Structural Concrete and Commentary,” ACI 318-99/ACI 318R-99, American Concrete Institute, Farmington Hills, MI, 391p ACI Committee 318, (2002), “Building Code Requirements for Structural Concrete and Commentary,” ACI 318-02/ACI 318R-02, American Concrete Institute, Farmington Hills, MI, 443p ACI Committee 318, (2005), “Building Code Requirements for Structural Concrete and Commentary,” ACI 318-05/ACI 318R-05, American Concrete Institute, Farmington Hills, MI, 430p ACI Committee 440, (1996), “State-of-the-Art Report on Fibre Reinforced Plastic (FRP) Reinforcement for Concrete Structures,” ACI 440R-96, American Concrete Institute, Farmington Hills, MI., 67p ACI Committee 440, (2001), “Guide for the Design and Construction o f Concrete Reinforced with FRP Bars,” ACI 440.1R-01, American Concrete Institute, Farmington Hills, MI, 41p ACI Committee 440, (2003), “Guide for the Design and Construction o f Concrete Reinforced with FRP Bars,” ACI 440.1R-03, American Concrete Institute, Farmington Hills, M I.,41p ACI Committee 440, (2004), “Guide Test Methods for Fibre Reinforced Polymers (FRPs) for Reinforcing or Strengthening Concrete Structures,” ACI 440.3R-04, American Concrete Institute, Farmington Hills, MI, 40 p Reproduced with permission of the copyright owner Further reproduction prohibited without permission References ACI Committee 440, (2006), “State-of-the-Art Report on Fibre Reinforced Polymer (FRP) Reinforcement for Concrete Structures,” ACI 440R-06, American Concrete Institute, Farmington Hills, MI., 228p Ahmad, S H., Khaloo, A R., and Poveda, A., (1986), “Shear Capacity o f Reinforced High-Strength Concrete Beams,” ACI Journal, Proceedings Vol 83, No.2, pp 297305 Ali, M A and White, R N., (2001), “Automatic Generation o f Truss Model for Optimal Design o f Reinforced Concrete Structures,” ACI Structural Journal, Vol 98, No.4, pp 431-442 Alkhrdaji, T., Wideman, M., Belarbi, A., and Nanni, A., (2001), “Shear Strength of GFRP RC Beams and Slabs,” Proceedings o f the Int Conf Composites in Construction-CCC 2001, Porto/Portugal, pp 409-414 Alsayed, S H., Al-Salloum, Y A., and Almusallam, T H., (1996), “Evaluation o f Shear Stress in Concrete Beams Reinforced by FRP Bars,” Proceedings o f the 2nd Int Conf., Advanced Composite Materials in Bridges and Structures, Montreal, pp 173-179 Alsayed, S H., Al-Salloum, Y A., and Almusallam, T H., (1997), “Shear Design for Beams Reinforced by GFRP Bars,” Proceedings o f the Third International Symposium on Non-Metallic (FRP) Reinforcement for Concrete Structures (FRPRCS-3), Japan Concrete Institute, Sapporo, Japan, Vol.2, pp 285-292 ASCE-ACI Committee 426, (1973), “The Shear Strength o f Reinforced Concrete Members,” ASCE Proceedings, Vol 99, ST6, June, pp 1091-1187 ASCE-ACI Committee 445, (1998), “Recent Approaches to Shear Design o f Structural Concrete,” Journal o f Structural Engineering, ASCE, Vol 124, No 12, December, pp 1375-1417 Bank, L C., (1993), “Properties o f FRP Reinforcement for Concrete,” in FibreReinforce-Plastic (FRP) Reinforcement for Concrete Structures: Properties and Applications, D evelopm ents in Civil Engineering, V ol 42, A Nanni, Ed., Elsevier, Amsterdam, pp 59-86 Bedard, C., (1992), “Composite Reinforcing Bars: Assessing their Use in Construction,” Concrete International, Vol 14, N o l, pp 55-59 243 Reproduced with permission of the copyright owner Further reproduction prohibited without permission References Belarbi, A., and Hsu, T T C., (1994), “Constitutive Laws o f Concrete in Tension and Reinforcing Bars Stiffened by Concrete,” ACI Structural Journal, Vol 91, No 4, pp 465-474 Belarbi, A., and Hsu, T T C., (1995), “Constitutive Laws o f Softened Concrete in Biaxial Tension-Compression,” ACI Structural Journal, Vol 92, N o.5, pp 562-573 Bergmeister, K., Breen, J E., and Jirsa, J O., (1991), “Dimensioning o f the Nodes and Development o f Reinforcement,” Report, IABSE Colloquium on Structural Concrete, IABSE, Zurich, pp 551-564 Branson, D E., (1977), “Deformation o f Concrete Structures,” McGraw-Hill, New York, 546 p CAN3-A23.3-M84, (1984), “Design o f Concrete Structures for Buildings,” Canadian Standards Association, Rexdale, Ontario, 281 p CAN/CSA-A23.3-94, (1994), “Design o f Concrete Structures,” Canadian Standards Association, Rexdale, Ontario, 220 p CAN/CSA-A23.3-04, (2004), “Design o f Concrete Structures,” Canadian Standards Association, Rexdale, Ontario, 240 p CAN/CSA-S6-00, (2000), “Canadian Highway Bridge Design Code,” Canadian Standard Association, Rexdale, Ontario, Canada, 734 p CAN/CSA-S6-00, (2005), “Canadian Highway Bridge Design Code,” Canadian Standard Association, Rexdale, Ontario, Canada, in print CAN/CSA-S806-02, (2002), “Design and Construction o f Building Components with Fiber Reinforced Polymers”, Canadian Standards Association, Rexdale, Ontario, 177p Clark, J L., (1993), “The Need for Durable Reinforcement, in Alternative Materials for Reinforcement and Prestressing o f Concrete,” Ed J L Clark, Blackie, pp 1-33 Clark, J L., (1996), “FRP Reinforced Concrete Structures,” Proceedings o f the Second International Conference on Advanced Composites Materials in Bridges and Structures (II-AC M BS), Montreal, Quebec, Canada, pp 41-48 Collins, M P., (1973), “Torque-Twist Characteristics o f Reinforced Concrete Beams,” In Inelasticiy and Non-Linearity in Structural Concrete, University o f Waterloo Press, Waterloo Ontario: 21 lp 244 Reproduced with permission of the copyright owner Further reproduction prohibited without permission References Collins, M P., (1978), “Towards a Rational Theory for RC Members in Shear,” Journal o f the Structural division, ASCE, Vol 104, pp 649-666 Collins, M P., and Mitchell, D., (1997), “Prestressed Concrete Structures,” Response Publications, Toronto, Canada, 766p Deitz, D H., Harik, I E., and Gesund, H., (1999), “One-Way Slabs Reinforced with Glass Fibre Reinforced Polymer Reinforcing Bars,” Proceedings o f the 4th International Symposium, Fibre Reinforced Polymer Reinforcement for Reinforced Concrete Structures, MI., pp 279-286 Dowden, D M., and Dolan, G W., (1997), “Comparison o f Experimental Shear Data with Code Predictions for FRP Prestressed Beams,” Proceedings o f the Third International Symposium on Non-Metallic (FRP) Reinforcement for Concrete Structures (FRPRCS-3), Japan Concrete Institute, Sapporo, Japan, Vol.2, pp 687-694 Duranovic, N., Pilakoutas, K., and Waldron, P., (1997), “Tests on Concrete Beams Reinforced with Glass Fibre Reinforced Plastic Bars,” Proceedings o f the Third International Symposium on Non-Metallic (FRP) Reinforcement for Concrete Structures (FRPRCS-3), Japan Concrete Institute, Sapporo, Japan, Vol.2, pp 479-486 Ehsani, M R., (1993), “Glass-Fibre Reinforcing Bars,’’Alternative Materilas for the Reinforcement and Prestressing o f Concrete, J L., Clark, Blackie Academic & Professional, London, England, pp 35-54 Ehsani, M R., Saadatmanesh, H., and Tao, S., (1993), “Bond o f GFRP Rebars to Ordinary-Strength Concrete,” Fibre-Reinforced plastic Reinforcement for Concrete Structures, SP-138, American Concrete Institute, Farmington Hills , MI, pp 333-345 El-Salakawy, E F., and Benmokrane, B., (2004), “Serviceability o f Concrete Bridge deck Slabs Reinforced with FRP Composite Bars,” ACI Structural Journal, Vol 101, N o.5, pp 727-736 El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B (2004), “New Carbon FRP Stirrups as Shear Reinforcem ent for Concrete B eam s,” Advanced Com posites Materials in Bridges and Structures (IV-ACMBS), Proceedings on CD, Calgary, Alberta, Canada, p El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B., (2005), “Shear Strength of One-Way Concrete Slabs Reinforced with FRP Composite Bars,” Journal of 245 Reproduced with permission of the copyright owner Further reproduction prohibited without permission References Composites for Construction, ASCE, Vol 9, No 2, pp 147-157 Eurocrete Project, (1996), “Modification o f Design Rules to Incorporate None-Ferrous Reinforcement,” prepared by Clarke, J L., Regan, D P O., and Thriugnanendran, C., 34 p Fam, A., Rizkalla, S., and Tadros, G., (1997), “Behaviour o f CFRP for Prestressing and Shear Reinforcements for Concrete Highway Bridges,” ACI Structural Journal, Vol 94, No 1, January-February, pp 77-86 Gergely, P., and Lutz, L A., (1968) “Maximum Crack Width in Reinforced Concrete Flexural Members” Causes, Mechanisms, and Control o f Cracking in Concrete, SP-20, American Concrete Institute, Farmington Hills, Mich, pp 87-117 Gross, S P., Yost, J R., Dinehart, D W., Svensen, E., and Liu, N., (2003) “Shear Strength o f Normal and High Strength Concrete Beams Reinforced with GFRP Reinforcing Bars,” Proc o f the Int Conference on High Performance Materials in Bridges, ASCE, pp 426-437 Gross, S P., Dinehart, D W., Yost, J R., and Theisz, P M., (2004), “Experimental Tests o f High-Strength Concrete Beams Reinforced with CFRP Bars.” Proceedings o f the 4th International Conference on Advanced Composite Materials in Bridges and Structures (ACMBS-4), Calgary, Alberta, Canada, July 20-23, 8p Hsu, T T C., (1988), “Softened Truss Model Theory for Shear and Torsion,” ACI Structural Journal, Vol 85, No 6, November-December, pp 624-635 Hsu, T T C., (1993), “Unified Theory o f Reinforced Concrete,” CRC Press, INC., Boca Raton, Fla Hsu, T T C., (1996), “Towards a Unified Nomenclature for Reinforced-Concrete Theory,” Journal o f Structural Engineering, ASCE, Vol 122, No 3, March, pp 275283 ISIS-M03-01, (2001), “Reinforcing Concrete Structures with Fiber Reinforced Polym ers,” The Canadian Network o f Centers o f E xcellence on Intelligent Sensing for Innovative Structures, ISIS Canada, University o f Winnipeg, Manitoba, 81 p Japan Society o f Civil Engineers, JSCE, (1997), “Recommendation for Design and Construction o f Concrete Structures Using Continuous Fibre Reinforcing Materials,” Concrete Engineering series 23, Edited by A Machida, 325 p 246 Reproduced with permission of the copyright owner Further reproduction prohibited without permission References Jirsa, J , Breen, J E., Bergmeister, K., Barton, D., Anderson, R., and Bouadi, H., (1991), “Experimental Studies o f Nodes in Strut-and-Tie Models,” Report, IABSE Colloquium on Structural Concrete, IABSE, Zurich, pp 525-532 Kani, G N J., (1966), “Basic Facts Concerning Shear Failure,” ACI Journal, Vol 63, N o.6, pp.675-692 Kani, G N J., (1967), “How Safe are our Large Reinforced Concrete Beams?,” ACI Journal, Vol 64, N o.3, pp 128-141 Kani, M W., Huggins, M W., and Wiltkopp, P F., (1979), “Kani on Shear in Reinforced Concrete,” Department o f Civil Engineering, University o f Toronto, Canada, 225 p Kasperkiewicz, J., and Reinhardt, H W., (1993), “Aramid Fabric as a Reinforcement for Concrete,” Fibre-Reinforced Plastic Reinforcement for Concrete Structures, International Symposium, ACI-SP-138, pp 149-162 Khuntia, M., and Stojadinovic, B., (2001), “Shear Strength o f Reinforced Concrete Beams without Transverse Reinforcement.” ACI Structural Journal, Vol 98, No 5, pp 648-656 Lampert, P., and Thurlimann, B., (1968), “Torsion Tests o f Reinforced Concrete Beams.” Bericht No 6506-02, Institute Fur Baustatik, ETH, Zurich, Switzerland (in German) Leu, B., Dolan, C W., and Hundley, A., (1997), “Creep-Rupture o f Fibre-Reinforced Plastics in a Concrete Environment,” Non-Metallic (FRP) Reinforcement for concrete Structures, FRPRCS-3, Vol 2, Japan Concrete Institute, Tokyo, pp 187-194 MacGregor, J G., (1997), “Reinforced Concrete: Mechanics and Design,” 3rd Edition, Prentice Hall, New Jersey, 799 p Mallic, P K., (1988), “Fibre Reinforced Composites, Materials, Manufacturing, and Design,” Marcell Dekker, Inc., New York, 469 p Marti, P., (1985), “Basic Tools o f Reinforced Concrete Beam Design,” ACI Journal, Proceedings Vol 82, No 1, pp 46-56 Maruyama, T., Honama, M , and Okamura, H., (1993), “Experimental Study on Tensile Strength o f Bent Portion o f FRP Rods,” Fibre-Reinforced plastic Reinforcement for Concrete Structures, SP-138, American Concrete Institute, Farmington Hills , MI, pp 163-176 247 Reproduced with permission of the copyright owner Further reproduction prohibited without permission References Michaluk C R., Rizkalla, S., Tadros, G., and Benmokrane, B., (1998), “Flexural Behaviour o f One Way Concrete Slabs Reinforced by Fibre Reinforced Plastic Reinforcement,” Structural Journal, Vol.95, No 3, pp 353-364 Miller, T E., (1998), Introduction to Composites, The Composite Institute, 4th Edition, Technomic Publishing Co., Inc., Lancaster, U.S.A Minosaku, K., (1992), “Using FRP Materials in Prestressed Concrete Structures,” Concrete International, pp 41-45 Mitchell D., and Collins, M B., (1974), “Diagonal Compression Field Theory: A Rational Model for Structural Concrete in Pure Torsion,” ACI Journal, Vol.71, pp 396-408 Mizukawa, Y., Sato, Y., Ueda, T., and Kakuta, Y (1997), “A Study on Shear Fatigue Behaviour o f Concrete Beams with FRP Rods,” Proceedings o f the Third International Symposium on Non-Metallic (FRP) Reinforcement for Concrete Structures (FRPRCS3), Japan Concrete Institute, Sapporo, Japan, Vol.2, pp 309-316 Morsch, E., (1909), “Concrete-Steel Construction,” MacGraw-Hill Book Company, New York, 368p Naaman, A., and Park, S., (1997), “Shear Behaviour o f Concrete Beams Prestressed with CFRP Tendons: Preliminary Tests Evaluation,” Proceedings o f the Third International Symposium on Non-Metallic (FRP) Reinforcement for Concrete Structures (FRPRCS3), Japan Concrete Institute, Sapporo, Japan, Vol.2, pp 679-686 Nagasaka, T., Fukuyama, H., and Tanigaki, M., (1993), “Shear Performance o f Concrete Beams Reinforced with FRP Stirrups,” Fibre-Reinforced plastic Reinforcement for Concrete Structures, SP-138, American Concrete Institute, Farmington Hills , MI, pp 789-811 Nanni, A., Ed., (1993), “Fibre-Reinforced Plastic (FRP) Reinforcement for Concrete Structures: Properties and Applications” Developments in Civil Engineering, Elsevier, Vol 42, 450 p Nanni, A., Nenninger, J., Ash, K., and Liu, J., (1997), “Experimental Bond Behaviour of Hybrid Rods for Concrete Reinforcement,” Structural Engineering and Mechanics, Vol 5, No 4, pp 339-354 248 Reproduced with permission of the copyright owner Further reproduction prohibited without permission References Niwa, J., Hirai, Y., and Tanabe, T., (1997), “Size Effect in the Shear Strength o f Concrete Beams Reinforced with FRP Rods,” Proceedings o f the Third International Symposium on Non-Metallic (FRP) Reinforcement for Concrete Structures (FRPRCS3), Japan Concrete Institute, Sapporo, Japan, Vol 2, pp 293-300 Pang, X B., and Hsu, T T C., (1992), “Constitutive Laws of Reinforced Concrete in Shear,” Res Rep UHCEE 92-1, Department o f Civil and Environmental Engineering, University o f Houston, Texas Pang, X B., and Hsu, T T C., (1995), “Behaviour o f Reinforced Concrete Membrane Elements in Shear,” ACI Structural Journal, Vol 92, No 6, pp 665-679 Pang, X B., and Hsu, T T C., (1996), “Fixed-Angle Softened-Truss Model for Reinforced Concrete,” ACI Structural Journal, Vol 93, No 2, pp 197-207 Park, R., and Paulay, T., (1975), “Reinforced Concrete Structures,” John Wiley and Sons, New York, 964 pp Ramirez, J A., and Breen, J E., (1991), “Evaluation o f a Modified Truss Model Approach for Beams in Shear,” ACI Structural Journal, Vol 88, No 5, pp 562-571 Razaqpur, A G., Isgor, O B., Cheung, M S., and Wiseman, A., (2001), “Background to Shear Design Provisions o f the Proposed Canadian Standard for FRP Reinforced Concrete Structures,” Proceedings o f the International Conference, Composites in Construction-CCC 2001, Porto/Portugal, pp 403-408 Razaqpur, A G., Isgor, B O., Greenaway, S., and Selley, A (2004), “Concrete Contribution to the Shear Resistance o f Fibre Reinforced Polymer Reinforced Concrete Members,” Journal o f Composites for Construction, ASCE, Vol 8, No 5, pp 452-460 Rebeiz, K S., (1999), “Shear Strength Prediction for Concrete Members,” Journal of Structural Engineering, ASCE, Vol 125, No 3, pp 301-308 Reineck, K H., (1991), “Ultimate Shear Force o f Structural Concrete Members Derived from a M echanical M odel,” ACI Structural Journal, V ol 88, N o 5, pp 592-602 Ritter, W., (1899), “Die Bauweise Hennebique (Construction Techniques of Hennebique),” Schweizerische Bauzeitung, Zurich Robinson, J R., and Demorieux, J M., (1968), “Essais de Traction-Compression sur Modeles d ’ame de Poutre en Beton Arme,” IRABA Rep., Institut de Researches 249 Reproduced with permission of the copyright owner Further reproduction prohibited without permission References Appliqees du Beton de l’ame, Paris, France Rostasy, F S., (1993), “FRP Tensile Elements for Prestressed Concrete-State o f the Art, Potentials and Limits,” Fibre-reinforced-Plastic reinforcement for Concrete Structures, International Symposium, ACI-SP-138, pp 347-366 Rostasy, F S., (1997), “On Durability o f FRP in Aggressive Environments,” NonMetallic (FRP) Reinforcement for Concrete Structures, FRPRCS-3 Vol 2, Japan Concrete Institute, Tokyo, PP 107-114 Schell, H C., and Manning, D G., (1985), “Evaluating the Performance o f Cathodic Protection Systems on Reinforced Concrete Bridge Substructures,” Materials Performance, Vol 24, No 7, pp 18-25, National Association o f Corrosion Engineers, Houston, Texas Schlaich, J., Schafer, I., and Jennewein, M., (1987), “Towards a Consistent Design of Structural Concrete,” Journal o f the Prestressed Concrete Institute, Vol 32, No 3, May-June, pp 74-150 Shehata, E., Morphy, R., and Rizkalla, S H., (1999), “Fibre Reinforced Polymer Reinforcement for Concrete Structures,” Proceedings of the 4th International Symposium, Fibre Reinforced Polymer Reinforcement for Reinforced Concrete Structures, MI., pp 157-167 Shioya, T., Iguro, M., Nojiri, Y., Akiayama, H., and Okada, T., (1989), “Shear Strength o f Large Reinforced Concrete Beams,” Fracture Mechanics: Application to Concrete, SP-118, ACI, pp 259-279 Sonobe, Y., et al., (1997), “Design Guidelines o f FRP Reinforced Concrete Building Structures,” J o f Composites for Construction, ASCE, Vol 1, No 3, August, pp 0155 Swamy, N., and Aburawi, M (1997), “Structural Implications o f Using GFRP Bars as Concrete Reinforcement,” Proceedings o f the Third International Symposium on NonM etallic (FRP) Reinforcem ent for Concrete Structures (FRPRCS-3), Japan Concrete Institute, Sapporo, Japan, Vol 2, pp 503-510 Tariq, M., and Newhook, J P., (2003), “Shear Testing o f FRP reinforced Concrete without Transverse Reinforcement,” Proceedings o f CSCE 2003-Anuual Conference, Moncton, NB, Canada, (on CD-Rom), lOp 250 Reproduced with permission of the copyright owner Further reproduction prohibited without permission References Taubi, J., and Neville, A M., (1970), “Resistance to Shear o f Reinforced Concrete Beams, Part I: Beams without Web Reinforcement,” ACI Journal, Vol 57, N o.8, pp 193-220 Tottori, S., and Wakui, H., (1993), “Shear Capacity o f RC and PC Beams Using FRP Reinforcement,” Fibre-Reinforced plastic Reinforcement for Concrete Structures, SP138, American Concrete Institute, Farmington Hills , MI, pp 615-632 Tureyen, A K., (2001), “Influence o f Longitudinal Reinforcement Type on the Shear Strength o f Reinforced Concrete Beams without Transverse Reinforcement,” Ph.D Thesis, Purdue University, West Lafayette, Ind., 232p Tureyen, A K., and Frosch, R J., (2002), “Shear Tests o f FRP-reinforced Concrete Beams without Stirrups,” ACI Structural Journal, Vol 99, No 4, pp.427-434 Tureyen, A K., and Frosch, R J., (2003), “Concrete Shear Strength: Another Perspective,” ACI Structural Journal, Vol 100, No 5, pp.609-615 Vecchio, F., and Collins, M P., (1981), “Stress-Strain Characteristics o f Reinforced Concrete in Pure Shear,” Final Report, IABSE Colloquium, Advanced Mechanics of Reinforced Concrete, delft, Netherland, pp.211-225 Vecchio, F., and Collins, M P., (1986), “The Modified Compression Field Theory for Reinforced Concrete Elements Subjected to Shear,” ACI Journal, Proceedings Vol 83, No.2, pp 219-231 Vecchio, F., and Collins, M P., (1988), “Predicting the Response o f Reinforced Concrete Beams Subjected to Shear Using the Modified Compression Field Theory,” ACI Structural Journal, Vol 85, No.4, pp 258-268 Vijay, P V., Kumar, S V., and GangaRao, H V., (1996), “Shear and Ductility Behaviour o f Concrete Beams Reinforced with GFRP Rebars,” Proceedings o f the 2nd Int Conf., Advanced Composite Materials in Bridges and Structures, Montreal, pp 217-226 Walraven, Joost C., (1981), “Fundamental Analysis o f Aggregate Interlock,” Journal of the Structural division, A SC E, V ol 107, N o S T 11, pp 2245-2270 Winter, G., and Nilson, A., (1979), “Design o f Concrete Structures,” 9th Edition, MacGraw-Hill Book Company, New York, 647p 251 Reproduced with permission of the copyright owner Further reproduction prohibited without permission References Yost, J R., Gross, S P., and Dinehart, D W., (2001), “Shear Strength o f Normal Strength Concrete Beams Reinforced with Deformed GFRP Bars,” J o f Composites for Construction, ASCE, Vol 5, No 4, pp 263-275 Zhao, W., and Mayama, K., (1995), “Shear Behaviour o f Concrete Beams Reinforced by FRP Rods as Longitudinal and Shear Reinforcement,” Proceedings o f the Second International RILEM Symposium on Non-Metallic (FRP) Reinforcement for Concrete Structures (FRPRCS-2), Ghent, Belgium, pp 352-359 Zsutty, T., (1968), “Beam Shear Strength Prediction by Analysis o f Existing Data,” ACI Journal, Vol 65, No 11, pp 943-951 Zsutty, T., (1971), “Shear Strength Prediction for Separate Categories o f Simple Beam Tests,” ACI Structural Journal, Vol 68, No.2, pp 138-143 252 Reproduced with permission of the copyright owner Further reproduction prohibited without permission ... action” On the other hand, in reinforced concrete deep beams where the ratio a/d is lower than 2.5, most o f the shear stresses in the shear span are resisted by the so-called “arch action” The beams. .. mechanism is referred as, Vs, the contribution o f the shear reinforcement to shear resistance Due to the relatively low modulus o f elasticity o f the FRP composite material, concrete members reinforced... Deeper cracks decrease the contribution to shear strength from the uncracked concrete due to the lower depth o f concrete in compression Wider cracks, in turn, decrease the contributions from aggregate