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1 Scholars' Mine Masters Theses Student Research & Creative Works Fall 2007 Perormance evaluation o existing analytical methods to compute the shear contribution provided by externally bonded FRP sheets in concrete structures Rocio Patricia Tumialan Follow this and additional works at: Part o the Civil Engineering Commons Department: Recommended Citation Tumialan, Rocio Patricia, "Perormance evaluation o existing analytical methods to compute the shear contribution provided by externally bonded FRP sheets in concrete structures" (2007). Masters Theses This Thesis - Open Access is brought to you or ree and open access by Scholars' Mine. It has been accepted or inclusion in Masters Theses by an authorized administrator o Scholars' Mine. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction or redistribution requires the permission o the copyright holder. For more inormation, please contact scholarsmine@mst.edu.

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3 i PERFORMANCE EVALUATION OF EXISTING ANALYTICAL METHODS TO COMPUTE THE SHEAR CONTRIBUTION PROVIDED BY EXTERNALLY BONDED FRP SHEETS IN CONCRETE STRUCTURES by ROCIO PATRICIA TUMIALAN A THESIS Presented to the Faculty o the Graduate School o the UNIVERSITY OF MISSOURI-ROLLA In Partial Fulillment o the Requirements or the Degree MASTER OF SCIENCE IN CIVIL ENGINEERING 2007 Approved by Abdeldjelil Belarbi, Advisor Ashra Ayoub Victor Birman Sang-Wook Bae

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5 iii ABSTRACT External application o FRP composites has been adopted or strengthening and/or repair o concrete structures in many applications during the last two decades. However, the research into shear strengthening using FRP composites has not been widely conducted as compared to lexural strengthening and axial load capacity increase, and the results obtained thus ar are scarce and sometimes controversial. This study presents a review o analytical studies and design guidelines on shear strengthening o concrete structures with externally-bonded FRP laminates, and their assessment with experimental data collected rom the literature. The strengths and weaknesses o each model and design guidelines/codes/speciications are identiied and evaluated in order to understand the behavior o the concrete structures strengthened in shear with FRP systems and to propose additional research required to develop a more accurate analytical model. In addition, the predictions obtained by the analytical models and design guidelines/codes/speciications were compared to the experimental results to evaluate the accuracy. This comparative evaluation showed that none o the analytical models and design guidelines/codes/speciications was able to provide reliable estimates, which indicates that the mechanisms o FRP strengthening or shear are still poorly understood. As a result, parameters that are not taken into account in these analytical and design methodologies, but that aect the behavior o members strengthened in shear with FRP were identiied.

6 iv ACKNOWLEDGMENTS I would like to express my sincere appreciation to the members o my committee or their support throughout this study. It has been a great privilege to work under the guidance o Dr. Abdeldjelil Belarbi, whose continuous advice and support were crucial in the completion o this thesis. Without his dedication and willingness, this opportunity would not have been possible. I would also like to thank Dr. Ayoub Ashra and Dr. Victor Birman or their constructive evaluations and suggestions. Very special thanks to Dr. Sang-Wook Bae, to whom I am much indebted or his guidance, constant encouragement and or the technical and personal advice he has provided me throughout the progress o this study. The inancial support o this research by the University o Transportation Center is also grateully acknowledged. I would also like to take this opportunity to give my appreciation to my brother, Dr. Gustavo Tumialan, whose continuous technical advice and support has helped me get through every obstacle in this study. This acknowledgment would not be complete without expressing my since gratitude to my dear parents, Ana and Jaime, or their love, support and encouragement they have given me throughout the course o my studies. Finally, very special thanks go to my husband, Miguel, or all his love, patience, understanding, and or being always there.

7 v TABLE OF CONTENTS Page ABSTRACT...iii ACKNOWLEDGMENTS... iv LIST OF ILLUSTRATIONS... ix LIST OF TABLES... xii NOMENCLATURE...xiii SECTION 1. INTRODUCTION FIBER REINFORCED POLYMER COMPOSITE MATERIALS APPLICATIONS OF FRP IN CIVIL ENGINEERING ISSUES RELATED TO SHEAR STRENGTHENING OBJECTIVES OF THIS STUDY RESEARCH PLAN AND METHODOLOGY ORGANIZATION OF THE THESIS REVIEW OF LITERATURE GENERAL SHEAR STRENGTHENING WITH FRP SYSTEMS FRP Shear Strengthening Schemes Failure Modes Eects o Anchorage Systems EXISTING EXPERIMENTAL WORK EXISTING ANALYTICAL MODELS EXISTING DESIGN GUIDELINES PARAMETRIC STUDY OF EXISTING EXPERIMENTAL DATA GENERAL EXPERIMENTAL DATABASE PARAMETERS THAT AFFECT THE SHEAR BEHAVIOR OF RC MEMBERS STRENGTHENED IN SHEAR WITH FRP Eect o Mechanical and Geometric Properties o FRP... 23

8 vi Eect o Shear Span-to-Depth Ratio Eect o Transverse Steel Reinorcement Eect o Other Parameters Eect o scale actor Eect o longitudinal steel reinorcement Eect o concrete strength SUMMARY AND CONCLUDING REMARKS EXISTING ANALYTICAL MODELS AND DESIGN GUIDELINES ON SHEAR STRENGTHENING OF RC MEMBERS USING FRP SYSTEMS INTRODUCTION ANALYTICAL MODELS Models Based on Fixed Eective FRP Strain Models Based on Eective FRP Strain as a Function o FRP Stiness or Based on Bond Mechanism Triantaillou (1998) Triantaillou and Antonopoulos (2000) Khalia et al. (1998) Khalia et al. (1999) Pellegrino and Modena (2002) Chaallal et al.(2002) Hsu et al. (2003) Zhang and Hsu (2005) Deniaud and Cheng (2004) Models Based on Non-uniorm Strain Distribution Chen and Teng (2003) FRP debonding approach FRP racture approach Monti and Liotta (2005) Cao et al. (2005) Carolin and Taljsten (2005) DESIGN GUIDELINES Design Guidelines Based on Fixed Eective FRP Strain... 70

9 vii JBDPA guidelines (1999) CAN/CSA-S (2002) Design Guidelines Based on Eective FRP Strain as a Function o FRP Stiness or Based on Bond Mechanism ib TG 9.3 bulletin 14 (2001) JSCE recommendations (2001) ISIS design manual 4 (2001) ACI 440.2R-02 (2002) Great Britain technical report No.55 (2004) AASHTO LRFD Bridge Design Speciications SUMMARY AND CONCLUDING REMARKS EVALUATION OF EXISTING ANALYTICAL MODELS INTRODUCTION COMPARATIVE EVALUATION Chajes et al. (1995) Triantaillou (1998) Khalia et al. (1999) Triantaillou and Antonopoulos (2000) Pellegrino and Modena (2002) Chaallal et al. (2002) Hsu et al. (2003) Chen and Teng (2003) Monti and Liotta (2005) Cao et al. (2005) Zhang and Hsu (2005) Carolin and Taljsten (2005) SUMMARY AND CONCLUDING REMARKS EVALUATION OF EXISTING DESIGN GUIDELINES INTRODUCTION COMPARATIVE EVALUATION OF SHEAR DESIGN GUIDELINES Great Britain Technical Report No. 55 (2004)

10 viii ib TG 9.3 Bulletin 14 (2001) JSCE Design Recommendations (2001) ISIS Design Manual 4 (2001) ACI 440.2R-02 (2002) CAN/CSA-S (2002) SUMMARY AND CONCLUDING REMARKS APPLICATION EXAMPLES OF ANALYTICAL APPROACHES ON SHEAR STRENGTHENING WITH FRP INTRODUCTION EXAMPLES TO COMPARE THE FRP SHEAR CONTRIBUTION RC T-Beam RC T-Girder PC I-Girder SUMMARY AND CONCLUDING REMARKS CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE RESEARCH SUMMARY OF RESEARCH WORK CONCLUSIONS Review and Summary o Analytical and Design Approaches Parametric Study o the Experimental Data Comparative Evaluation o Analytical and Design Approaches RECOMMENDATIONS FOR FUTURE RESEARCH APPENDICES A. EXPERIMENTAL DATA ON SHEAR STRENGTHENING WITH FRP SYSTEMS B. COMPARISON BETWEEN EXPERIMENTAL OBSERVATIONS AND ANALYTICAL PREDICTIONS BY ANALYTICAL MODELS C. COMPARISON BETWEEN EXPERIMENTAL OBSERVATIONS AND ANALYTICAL PREDICTIONS BY DESIGN GUIDELINES BIBLIOGRAPHY VITA

11 ix LIST OF ILLUSTRATIONS Figure Page 2.1. FRP Wrapping Schemes FRP Distribution FRP Fiber Orientations Bi-axial FRP Fiber Orientations Shear Failure due to FRP Debonding Shear Failure due to FRP Fracture Mechanical Anchorage System by Sato et al. (1997) U-anchor System by Khalia (1999b) Mechanical Anchorage System by Schuman (2002) / Shear Force Gain vs. E ρ / ' c Slender Beams without Transverse Steel Reinorcement Shear Force Gain vs. a / d Beams without Transverse Steel Reinorcement Shear Force Gain vs. a / d - Beams with Transverse Steel Reinorcement Shear Force Gain vs. ρ ses / ρ E - Slender Beams Shear Force Gain vs. ρ ses / ρ E - Deep Beams Correlations between Analytical Models and Design Guidelines Eective Strain in FRP vs. ρ E FRP Eective Strain and Normalized FRP Strain vs. E ρ / ' /3 c 4.4. Deinition o Geometric Parameters Ratio o ε e / ε u in Terms o ρ E Eective FRP Width ped Eective FRP Width Side-Bonded Eective Strain in Terms o ρ tot Strain Reduction Factor in Terms o ρ E Strain Reduction Factor in Terms o ρ E / ' c General Shear Strengthening Scheme Notations... 60

12 x Relationship between w and s or Continuous FRP Sheets Stress Distribution Factor or ped and Side-Bonded Strain Distribution Factor in Terms o Shear Span-to-Depth Ratio Ratio Fiber Alignment and Shear Crack Angle ,exp /, theo V V in Terms o E ρ / ' - FRP Debonding /3 c V in Terms o 5.2.,exp, theo 5.3.,exp /, theo V V in Terms o E ρ / ' - FRP Fracture /3 c E ρ / ' - Other Failure Modes /3 c 5.4.,exp /, theo V V in Terms o a / d FRP Debonding ,exp /, theo V V in Terms o a / d FRP Fracture V in Terms o a / d Other Failure Modes ,exp, theo 5.7.,exp /, theo V V in Terms o ρ E / ρ E FRP Debonding ,exp /, theo s s V V in Terms o ρ E / ρ E FRP Fracture ,exp /, theo s s V V in Terms o ρ E / ρ E Other Failure Modes s s Comparison between Analytical Predictions o FRP Shear Contribution and Experimental Results Comparison between Analytical Predictions o Total Shear Capacity and Experimental Results ,exp /, theo V V in Terms o E ρ /( ) - FRP Debonding ' 2 /3 c 6.2.,exp /, theo V V in Terms o 6.3.,exp /, theo V V in Terms o E ρ /( ) - FRP Fracture ' 2 /3 c E ρ /( ) - Other Failure Modes ' 2 /3 c 6.4.,exp /, theo V V in Terms o a / d - FRP Debonding ,exp /, theo V V in Terms o a / d - FRP Fracture ,exp /, theo V V in Terms o a / d - Other Failure Modes ,exp /, theo V V in Terms o ρ E / ρ E - FRP Debonding ,exp /, theo s s V V in Terms o ρ E / ρ E - FRP Fracture ,exp /, theo s s V V in Terms o ρ E / ρ E - Other Failure Modes s s

13 xi Comparison between Analytical Predictions o FRP Shear Contribution and Experimental Results Comparison between Analytical Predictions o Total Shear Capacity and Experimental Results T-Beam Cross-Section FRP Shear Contribution in Terms o Axial Rigidity Side-Bonded T-Beam Cross-Section FRP Shear Contribution in Terms o Axial Rigidity ped T-Beam Cross-Section T-Girder Cross-Section FRP Shear Contribution in Terms o Axial Rigidity Side-Bonded T-Girder FRP Shear Contribution in Terms o Axial Rigidity ped T-Girder I-Girder Cross-Section FRP Shear Contribution in Terms o Axial Rigidity Side-Bonded I-Girder FRP Shear Contribution in Terms o Axial Rigidity ped I-Girder

14 xii LIST OF TABLES Table Page 3.1. Sample o Database - Cross Section Properties Sample o Database - FRP Properties Sample o Database - Failure Conditions Number o Specimens in Terms o Cross-Section Properties Number o Specimens in Terms o FRP Properties Continuation o Number o Specimens in Terms o FRP Properties Classiication o Analytical Models and Design Guidelines Values o θ and β or Sections with Transverse Steel Reinorcement Values o θ and β or Sections with Less than Minimum Transverse Steel Reinorcement Comparison o Predictions and Test Results or FRP Capacities ( V,exp, ) Comparison o Predictions and Test Results or Shear Capacities ( V exp theo ) Comparison o Predictions and Test Results or Shear Capacities ( V exp theo ) by ACI Comparison o Predictions and Test Results or Shear Capacities ( V exp theo ) by Eurocode Comparison o Predictions and Test Results or Shear Capacities ( V exp theo ) by CSA A Comparison o Predictions and Test Results or Shear Capacities ( V exp theo ) by AASHTO LRFD Comparison o Predictions and Test Results or FRP Capacities ( V,exp V, ) Comparison o Predictions and Test Results or Shear Capacities ( V exp theo ) theo theo

15 xiii NOMENCLATURE Symbol a g a / d A c A A ps A sv b w d d Description Maximum aggregate size Shear span-to-depth ratio Concrete area Cross sectional area o FRP Area o prestressing steel on lexural tension side Area o steel shear reinorcement Minimum width o cross section over the eective depth Distance rom extreme compression iber to centroid o tension reinorcement Eective FRP depth d, t Distance rom beam compression ace to upper edge o FRP d s D D θ E E s Stirrup height FRP stress distribution actor Modiied FRP strain distribution actor Elastic modulus o FRP Elastic modulus o steel reinorcement ' c Concrete compressive strength e ct Eective FRP tensile stress in direction o the principal ibers Concrete tensile strength cu Cubic concrete compressive strength dd Debonding FRP strength ed Eective FRP debonding strength u Ultimate tensile stress o the FRP yv Yield strength o stirrups

16 xiv h h e h w k a k b k e K L b L e Height o RC member Eective FRP height Height o beam web Coeicient describing anchorage condition Covering/scale actor coeicient Integer describing number o debonding ends Shear reinorcing eiciency Available bond length Eective bond length L max Maximum bond length M d M o M u Design bending moment Decompression moment Factored moment n Number o plies o FRP reinorcement N u Decompression moment P max Ultimate load capacity o the FRP sheet r c r R R * R L s s s v t T T v Corner rounding radius o beam Factor depending on the FRP strengthening scheme Ratio o eective FRP strain to its ultimate strain Additional reduction actor when transverse steel reinorcement is present Ratio o the remaining bonded width over the initial width Debonding slip between FRP and concrete Spacing o FRP strips Spacing between stirrups FRP thickness Tension orce in FRP Tension orce in stirrups

17 xv V c Concrete shear contribution V exp Experimental shear capacity V V n V p V s z b z t α β β L β w FRP shear contribution Nominal shear capacity Design bending moment Transverse steel reinorcement shear contribution Coordinate o lower edge o eective FRP Coordinate o upper edge o eective FRP Angle o the inclination o steel stirrups to longitudinal axis o member Angle o the inclination o FRP ibers to longitudinal axis o member Eect o bond length Eect o FRP to concrete width ratio ε cr Critical FRP strain ε e Eective tensile strain o the FRP ε u Ultimate tensile strain o the FRP ε max Maximum FRP strain εν cu Ultimate tensile strain o concrete φ γ b γ c γ Angle between the principal tensile stress and the iber direction Member actor Concrete partial coeicient Partial saety actor or FRP Γ Fk Speciic racture energy o the FRP-concrete bond interace η ϕ R λ θ Average FRP iber utilization Fraction o ultimate FRP strength Normalized maximum bond length Shear crack angle

18 xvi ρ ρ s FRP area raction Shear steel reinorcement ratio ρ s, stiness ratio between transverse steel and FRP reinorcement ρ tot Total shear reinorcement ratio σ,max Maximum stress in FRP intersected by the shear τ bu Bond strength between the FRP and concrete τ max Ultimate direct shear strength ψ Additional reduction actor applied to the FRP shear contribution

19 1. INTRODUCTION 1.1. FIBER REINFORCED POLYMER COMPOSITE MATERIALS Fiber Reinorced Polymer (FRP) composite materials consist o advanced composites made o small, continuous, non-metallic, and large number o ibers embedded in a resin matrix. FRP ibers are the main load-carrying components and exhibit very high strength and stiness when pulled in tension. The type o FRP ibers are selected depending on the magnitude o strength, durability, and stiness required. The type o resin is selected based on the FRP environmental exposure and the FRP manuacturing method (Nanni, 1999). FRP ibers used or civil engineering applications are classiied into carbon iber reinorced polymers (CFRP), aramid iber reinorced polymers (AFRP), and glass iber reinorced polymers (GFRP). CFRP ibers exhibit high durability, resist most environmental conditions, and withstand high atigue loading conditions. However, they exhibit susceptibility to galvanic corrosion. AFRP ibers are less attractive or strengthening applications due to their high moisture absorption, high cost, and relatively poor compressive properties. However, they exhibit excellent toughness, damage tolerance, and atigue characteristics. GFRP ibers are classiied into E-glass ibers, S- glass ibers, and AR-glass ibers. GFRP ibers are susceptible to moisture, especially in the presence o high alkaline environments, creep racture and sustained loads (Bank et al., 1995). The main advantages o GFRP ibers are their capacity o being excellent thermal insulators and inexpensive cost APPLICATIONS OF FRP IN CIVIL ENGINEERING FRP composite materials have become increasingly popular in dierent sectors o industry, such as the aerospace industry and relatively most recently in concrete and masonry construction (Nanni, 1993). The application o FRP composite materials or internal reinorcement and or repair and strengthening o reinorced concrete (RC) structures is more advantageous than traditional strengthening schemes. This is because FRP systems are more resistant to corrosion, exhibit high strength, and usually provide the most cost eective solution.

20 2 FRP composites can be produced in dierent shapes and orms such as reinorcing bars, prestressing tendons, precured laminates and iber sheets. FRP bars and prestressing tendons are applied as internal reinorcement, while FRP laminates and sheets are applied as external reinorcement or repair and strengthening purposes. FRP materials used or maintenance, repair, retroit, and strengthening o reinorced concrete (RC) structures are among the popular applications o FRP composites in structural engineering. The retroitting o existing RC inrastructures may be needed in cases where the original strength or ductility o a structure is increased due to additional loading. Repair o existing structures may also be needed when the existing structure has deteriorated due to environmental actors or mechanical actions, such as blast and impact loading. In addition, the need or repair and strengthening may be required or extending the service lie o structures or or lacking proper detailing due to design errors. The application o FRP composites externally applied or strengthening structures has evolved in the late 1980s in Europe, Japan, the United States, and Canada. Research initially ocused on lexural strengthening and coninement o RC structures. Both o these FRP applications evolved rom the experience gained in retroitting RC structures using steel plates. The FRP plate bonding technology was irst investigated at the Swiss Federal Laboratories or Material Testing and Research (EMPA) (Meier et al., 1995), where tests on RC beams strengthened with CFRP plates started in In the United States, the irst investigation on FRP strengthening developed in the early 1990s by the University o San Diego (Priestley et al., 1992). This research ocused on the evaluation o GFRP systems or seismic retroitting o RC columns. In addition, numerous investigations on lexural strengthening o RC beams using hand lay-up GFRP and CFRP sheets developed in the early 1990s (Saadamanesh, 1994). All o these and other extensive investigations on lexural strengthening have shown that FRP systems improve the bending capacity o RC structures by applying FRP sheets or plates to the tension sides o members. Numerous studies have also shown that FRP systems can improve the strength and ductility o columns by wrapping the entire column member. On the other hand, investigations on shear strengthening o RC structures started to develop quite lately (early 1990s) in comparison to those o lexural strengthening. These

21 3 investigations have shown that FRP systems improve the shear capacity o RC structures by bonding FRP sheets or plates to the web o members. FRP systems have also been used to strengthen concrete masonry wall systems to resist lateral loads. However, codebased design guidelines are yet scarce or this type o application ISSUES RELATED TO SHEAR STRENGTHENING The subject o shear has always been diicult to understand. Since shear ailures occur suddenly and catastrophically, it is generally preerred to insure that lexural ailure governs. For RC structures deicient in shear, FRP systems have been proven to increase the total shear resistance o existing RC structures by ully-wrapping or partiallywrapping FRP composites around the structures. Extensive research on the application o FRP systems by bonding FRP systems to the web o members to increase the shear capacity has been developed over the last 20 years. However, the results obtained thus ar are scarce and sometimes controversial. This is in essence due to the intrinsic diiculty o shear behavior o RC structures. Adding FRP to the equation, which has its own speciic design issues and modes o ailures, brings another level o complication in the analysis and design. In addition, since FRP strengthening systems are applied to web o concrete members, FRP shear strengthening systems are only eective over short lengths on the sides o the member, thus the area provided or anchorage o FRP systems is very limited. Most researches have provided analytical models and design approaches that assume that FRP systems behave in the same way as transverse steel reinorcement in regular RC structures. However, the behavior o FRP materials is linear elastic up to inal brittle racture when subject to tension, while steel reinorcement exhibits yielding and plastic deormation. As a consequence, the brittleness exhibited by FRP materials limits the ductile behavior o RC structures strengthened with FRP systems. Thereore, the design strain in the FRP cannot be used in the same way as the yield strain or steel stirrups because o the non-uniorm distributions o the FRP strain along the shear crack. In addition, several researches have published analytical models where a 45 deg shear crack angle is assumed, which is consistent with the assumption o the shear design provisions in current RC design codes. This simpliied truss model is known to be

22 4 conservative; however a variable concrete crack angle will give a more realistic and accurate prediction o the behavior and strength o beams ailing in shear. Another issue is that several parameters aect the behavior o RC structures strengthened in shear with FRP systems. To account all o these parameters into an analytical approach to determine the FRP shear contribution has shown to be diicult. Most analytical models have included some o these parameters into their ormulations; however, additional research studies are required to account or all these parameters and thereore develop a more accurate analytical approach. Finally, most design guidelines evaluate the shear capacity o RC structures by individually adding the shear contribution o each material used in a structural member. However, the interaction between the concrete, steel reinorcement and the FRP system used in combination to carry shear loads in RC structures needs to be taken into consideration OBJECTIVES OF THIS STUDY The objectives o this study are: 1. Review previous experimental work in order to identiy and evaluate the parameters that aect the behavior o RC structures shear strengthened with FRP systems. 2. Review and discuss existing analytical models and design guidelines that compute the shear contribution provided by externally-applied FRP sheets. 3. Perorm a comparative evaluation o the accuracy in predicting the FRP shear contribution between the examined methodologies and the experimental data collected rom the literature. 4. Propose conclusions and recommendations or additional research required to provide a better understanding o the mechanics involved in the behavior o RC structures shear strengthened with FRP systems RESEARCH PLAN AND METHODOLOGY The irst step in this study was to develop an extensive and detailed database based on previous experimental studies. From reviewing previous experimental studies,

23 5 the parameters that inluence the behavior o RC structures shear-strengthened with FRP were identiied. An in-depth analysis o the collected experimental data was perormed to evaluate the inluence o the major parameters on the behavior o RC beams shearstrengthened with externally-bonded FRP sheets. From the literature, a total o ourteen analytical models and seven design methodologies were collected. These analytical models and design guidelines were discussed and classiied according to the approach adopted to predict the FRP eective strain at the time o ailure to determine the FRP shear contribution. When perorming the comparative evaluation o the dierent methods or calculating the FRP shear contribution, only a segment o the total experimental data was used in the comparative evaluation. For this purpose, a critical review o the experimental data collected and the criteria or the selection o a subset o the data was conducted. The comparative evaluation o the dierent methods or calculating the FRP shear contribution was perormed by comparing the predicted shear strength o FRP with the observed experimental results. In addition, the FRP shear contribution or each method was evaluated in terms o parameters that aect the shear behavior o RC structures strengthened with FRP sheets. For each analytical model, the predicted total shear capacity was also compared with the observed experimental results. The predictions o total shear capacities were computed by applying each analytical model in combination with our RC design codes, i.e., ACI (2005), Eurocode 2 Part I (2003), CSA A (1994), and AASHTO LRFD Bridge Design Speciications (1998). Additionally, the predictions o total shear capacities by each design methodology were compared with the collected experimental results. The predictions o the total shear capacities were computed by applying each design guideline with their corresponding RC design code. Finally, due to the complexity and variety o the dierent methods or calculating the FRP shear contribution, the comparative evaluation between these methods was also perormed through speciic examples. These examples represent dierent types o RC structures, with dierent FRP strengthening schemes. The comparison o the magnitude

24 6 o the FRP shear contribution was perormed in terms o the axial rigidity provided by the FRP sheets ORGANIZATION OF THE THESIS This thesis is organized according to the stages ollowed or the development o the investigation. Thus, Section One introduces the signiicance o the strengthening o RC structures with FRP composite materials. In addition, issues related to shear strengthening with FRP systems are also introduced, which led to setting the objectives o the research. Section Two provides a brie description o shear strengthening with FRP composite materials, shear strengthening schemes, potential ailure modes, and the eects o dierent anchorage systems. In addition, this section summarizes and examines previous experimental work, existing analytical models and design guidelines to determine the shear strength o RC structures strengthened with FRP systems. In Section Three, the identiication and evaluation o parameters that inluence the behavior o RC beams shear strengthened with FRP systems is presented. The eect o the FRP properties, the shear span-to-depth ratio, and the interaction between transverse steel reinorcement and FRP reinorcement on the behavior o RC shear strengthened with FRP systems are analyzed in terms o the gain in shear due to FRP systems. Section Four summarizes and examines analytical models and design methodologies, to determine the shear strength o RC structures strengthened with FRP systems. Aterwards, a comparative evaluation between the analytical models and design guidelines are developed in Section Five and Section Six respectively. In addition, due to the complexity and variety o these analytical approaches to evaluate the FRP shear contribution, speciic examples are provided in Section Seven or eectively comparing the FRP shear contribution among dierent analytical approaches. Finally, Section Eight provides conclusions and recommendations or uture work in the area o shear strengthening with externally-bonded FRP sheets.

25 7 2. REVIEW OF LITERATURE 2.1. GENERAL The ollowing literature review provides inormation on the dierent types o shear strengthening schemes, and the potential ailure modes o RC structures shearstrengthened with FRP composites. In addition, the eects o anchoring FRP strengthening systems are presented and discussed. Finally, existing experimental and analytical studies, conducted to investigate the shear perormance and to evaluate the shear capacity o RC structures strengthened with FRP composites, are reviewed SHEAR STRENGTHENING WITH FRP SYSTEMS FRP Shear Strengthening Schemes. One o the main advantages o strengthening RC structures with externally-bonded FRP sheets is the availability o dierent strengthening schemes. Dierent types o strengthening schemes can be selected depending on the required application. Figure 2.1 illustrates three dierent FRP wrapping schemes than can be used to increase the shear capacity o RC structures. (a) Side-bonded FRP (b) U-wrapped FRP (c) Fully-wrapped FRP Figure 2.1. FRP Wrapping Schemes Side-bonded FRP is applied by bonding the FRP sheet on both sides o the RC member as shown in Figure 2.1 (a). This wrapping scheme is not recommended because o its vulnerability to debonding ailure o the FRP system at the ends o the members,

26 8 unless this type o ailure can be avoided by providing adequate anchorage. The second FRP wrapping scheme, known as U-wrapped, is applied by partially-wrapping the FRP sheet on the sides and bottom o the RC member as shown in Figure 2.1 (b). This strengthening scheme is moderately eective in increasing the shear resistance o the RC member; however, it is also vulnerable to debonding ailure unless anchorage is provided. The third and inal wrapping scheme, known as ully-wrapped scheme, consists on ullywrapping the FRP sheet around the RC member as shown in Figure 2.1 (c). This strengthening scheme is the most eective especially in column applications, where the member can be ully-wrapped. However, in the presence o slabs, its application can rather be complicated because the RC member cannot be ully wrapped. For both U- wrapped and ully-wrapped schemes, the corners o the RC member need to be rounded to avoid FRP ailure due to stress concentration. FRP sheets can also be applied in the orm o continuous wraps as shown in Figure 2.2 (a) or as inite strips along the side o the member as shown in Figure 2.2 (b). Among the main advantages on using FRP strips are the lexibility in controlling the amount o FRP and the potential savings in material; however, its application require more labor hours. On the other hand, the application o continuous sheets protects RC members rom urther environmental damage; however, it is more diicult to achieve a uniorm adhesive layer. (a) Continuous Figure 2.2. FRP Distribution (b) Strips Since FRP sheets are more eective when placed in the direction o its ibers, FRP sheets have to be applied in such direction to prevent shear cracks rom widening.

27 9 Typically, the ibers are oriented vertical to the beam axis or perpendicular to the shear crack as shown in Figure 2.3. FRP ibers can also be oriented at 45 to attain additional control or shear crack widening. Finally, as illustrated in Figure 2.4, FRP ibers can also be oriented at two dierent directions to increase the eectiveness o the shear strengthening system by providing additional control or shear crack widening. The application o bi-axial FRP systems consists on applying two unidirectional FRP sheets in perpendicular directions. (a) FRP ibers oriented at 90 (b) FRP ibers oriented at 45 Figure 2.3. FRP Fiber Orientations (a) FRP ibers oriented at 90 /0 (b) FRP ibers oriented at 45 /135 Figure 2.4. Bi-axial FRP Fiber Orientations Failure Modes. From previous experimental studies, RC structures shearstrengthened with FRP sheets mostly ail by diagonal tension. This ailure may be initiated prematurely due to FRP debonding (Figure 2.5) or correspond to racture o the FRP system (Figure 2.6). In addition due to strain variations in the FRP along the shear

28 10 crack, local debonding at both sides o the shear crack may occur beore ultimate ailure is governed by racture o the FRP. Shear ailure due to FRP debonding mostly occurs in the concrete at a small distance rom the concrete/adhesive interace. Since debonding ailure o the FRP occurs in the concrete, the properties related to the concrete are crucial in this mode o ailure (Chen and Teng, 2003a). Previous experimental investigations indicate that most RC members strengthened by side-bonded scheme usually ail due to FRP debonding. Additionally, some members strengthened with U-wrapped schemes ail due to FRP debonding. Shear ailure due to FRP racture occurs with the development o a diagonal shear crack. As the width o the diagonal crack increases, the FRP sheet eventually reaches its ultimate strain, and ractures, which oten occurs at the lower end o the shear crack. Fracture o the FRP continues to propagate along the shear crack leading to brittle ailure o the RC member. From previous experimental studies, RC members strengthened with ully-wrapped FRP usually ail due to FRP racture. Some members strengthened with U-wrapped schemes sometimes also ail in racture. Figure 2.5. Shear Failure due to FRP Debonding (Khalia, 1999)

29 11 Figure 2.6. Shear Failure due to FRP Fracture (Cao et al., 2005) Eects o Anchorage Systems. From numerous experimental investigations, it has been proven that anchorage o FRP systems increases the shear contribution provided by FRP composite materials. Anchorage between the FRP sheet and concrete may develop in two orms. The irst orm o providing anchorage between the FRP sheet and concrete is by ensuring that the bond at the FRP/concrete interace is maintained. This type o anchorage can provide adequate bond strength on either side o the shear crack. Chajes et al. (1995) determined that extra bond strength cannot be achieved by increasing the available bond length. Thereore, there exists an eective bond length beyond which an extension o the bond length cannot increase the bond strength (Chen and Teng 2003a). For these reasons, the application o other anchorage systems is required, to insure FRP sheets do not detach rom the concrete. The other orm o providing adequate anchorage between the FRP composite and concrete is the application o mechanical or other types o anchorage systems. Experimental investigations on the eects o anchorage systems have been developed by many researches. Sato et al. (1997) applied mechanical anchorage by means o a steel plate attached by bolting to the compression zone o the web as shown in Figure 2.7.

30 12 From the experimental results, Sato et al (1997) reported that this anchorage system eectively increased the bond strength between the FRP and the concrete, and as a consequence, the FRP shear contribution to shear capacity increased. However, one o the main disadvantages o this anchorage system is that stress concentration may develop where the mechanical anchorage system is placed. In addition, discontinuity o the FRP system due to steel bolts could be another disadvantage in applying this anchorage system. Anchor bolt Plate FRP sheets Figure 2.7. Mechanical Anchorage System by Sato et al. (1997) Khalia (1999b) introduced the concept o applying a U-anchor system. This anchorage system was obtained by grooving the concrete langes at the corner along the entire length o the beam, as shown in Figure 2.8. Then, the FRP sheets are attached to the concrete surace and the walls o the groove. The groove was then hal illed with a high viscosity epoxy paste. Aterwards, a FRP rod was placed into the groove, and it was then illed with epoxy paste. From this investigation, this anchorage system not only signiicantly increased the shear capacity, but also modiied the ailure mode rom shear ailure due to FRP debonding to lexural ailure. In addition, Khalia (1999b) concluded that this anchorage system avoided high stress concentration and durability issues in

31 13 comparison to the traditional mechanical anchorage systems made o steel plates and bolts. Micelli et al. (2002) also applied the U-anchor system or the strengthening o short shear spans RC T-joists. This anchorage system increased the shear capacity o the FRP system; however, debonding ailure due to anchor pullout could not be prevented. Thereore, the eectiveness o this anchoring coniguration needs to be urther investigated or members with short shear spans because o potential anchor pullout ailure around the web-lange corner. Figure 2.8. U-anchor System by Khalia (1999b) Finally, Schuman (2002) applied a mechanical anchorage system to increase the shear contribution o CFRP systems by means o embedding anchor rods into the crosssection with the use o a GFRP bearing plate. Schuman perormed an experimental program which covered bonded anchor rods without tying the externally bonded L- shaped CFRP systems to the longitudinal reinorcement, and anchor rods embedded past the longitudinal reinorcement as shown in Figures 2.9 (a) and (b), respectively. From this investigation, Schuman (2002) concluded that the application o shallow anchors lead to an increase in load carrying and displacement capacity. In addition, the shallow

32 14 anchors caused the CFRP reinorcement to be activated beore the steel reinorcement yielded. The application o deeper anchors showed to be more beneicial in using this anchorage system because the CFRP reinorcement was activated earlier and delayed the yielding in the steel stirrups. (a) Shallow embedment depth (b) Deep embedment depth Figure 2.9. Mechanical Anchorage System by Schuman (2002) 2.3. EXISTING EXPERIMENTAL WORK The ollowing section presents experimental studies on the behavior o RC members shear-strengthened with externally-bonded FRP sheets. Experimental data are collected rom these investigations and assembled in a database that will be discussed in Section Three. Sato et al. (1996) tested RC beams with various wrapping schemes to demonstrate the eectiveness o FRP sheets. From this study, U-wrapped schemes were ound to be more eective than side-bonded scheme. In addition, the authors concluded that the FRP strain along the shear crack is high at the middle o the shear crack, and low at the ends o the crack. Funakawa et al. (1997) tested RC beams strengthened with continuous and ullywrapped FRP sheets with dierent thickness. From this study, the authors indicated that

33 15 the shear capacity increased with the increase o FRP sheet thickness. They also conirmed that FRP ibers did not reach their ultimate tensile strength at ailure. Kamiharako (1997) tested RC beams with ully-wrapped FRP strips. Two testedbeams did not use epoxy resin to examine the eect o bond strength. From the test results, the shear capacity o beams with bonded FRP strips is higher than that o unbonded FRP strips. The authors proposed a design model assuming that the strain distribution o FRP along the shear crack is not uniorm. Sato et al. (1997) applied mechanical anchorage by means o a steel plate attached by bolting to the compression zone o the web. From the experimental results, Sato et al (1997) determined that this anchorage system eectively increased the bond strength between the FRP and the concrete. Taerwe et al. (1997) tested RC beams strengthened with U-wrapped FRP strips and continuous sheets. The authors concluded that considerable shear strengthening can be obtained by applying FRP sheets. They also suggested that FRP increases the shear capacity in a similar way to that o steel reinorcement. Taljsten (1997) presented three dierent methods or the application o CFRP sheets to RC beams; hand lay-up systems, vacuum injection systems and pre-preg systems. Test results showed that the application o FRP systems increased the shear capacity; however, signiicant energy was released at ailure, which led to brittle ailures. This study also concluded that the use o hand lay-up systems were preerable than the other systems. Umezu et al. (1997) carried out an extensive investigation to determine the eects o ully-wrapped AFRP and CFRP sheets on the shear capacity o RC beams. The authors concluded that the FRP sheets enhanced the shear capacity. In addition, they concluded that the AFRP shear contribution can be evaluated by applying the truss theory, based on an average AFRP stress equal its tensile strength multiplied by a reduction coeicient, which was ound to be 0.4 rom the analysis. Khalia et al. (1999a) carried out an experimental program that consisted o twospan continuous beams with dierent FRP wrapping schemes. The test results indicated that FRP sheets could be used to enhance the FRP shear capacity in both positive and negative moment regions. In addition, the authors concluded that the FRP shear

34 16 contribution increases or beams without stirrups than those with adequate steel shear reinorcement. The authors also proposed a design model, based on truss theory and a reduced ultimate FRP strength Khalia and Nanni (2000a) carried out an investigation to determine the eects o dierent conigurations o CFRP sheets on the shear capacity o RC T-beams. The authors concluded that the FRP can increase the shear capacity o RC beams signiicantly. In addition, the test results indicated that the most eective FRP coniguration was the U-wrapped with end anchorage. The authors also proposed a design algorithm to predict the shear capacity o RC members. Results indicated that this design model is conservative and acceptable. Khalia et al. (2000b) investigated the perormance o RC T-beams shear strengthened with FRP sheets. For this purpose, externally applied FRP sheets and nearsurace mounted (NSM) FRP rods were used. Tests results conirmed that externally bonded CFRP sheets and NSM CFRP rods can be used to increase the shear capacity. The test results were also used to validate a previously proposed design approach. Deniaud and Cheng (2001) investigated the interaction between the concrete, steel stirrups, and external FRP sheets in carrying shear loads in RC beams. Three types o FRP sheets were applied: uniaxial GFRP, uniaxial CFRP, and triaxial GFRP. Test results showed that FRP systems enhance the shear capacity o RC beams. This increase is shear capacity was ound to be not only dependent on the FRP type, but also on the amount o steel stirrups. In addition, the FRP strains were ound to be uniormly distributed along the shear crack. The authors also proposed a design approach based on the ailure mechanisms o the tested specimens. Li et al. (2002) carried out an extensive investigation on the perormance o RC beams shear strengthened with CFRP sheets. Test results indicated that the shear capacity increases as the area o FRP composite increases. In addition, test results indicated that the FRP shear contribution increases as the spacing between stirrups increases. This study also concluded that the FRP shear contribution depends on the presence o longitudinal and vertical steel reinorcement. The authors proposed an analytical approach to predict the FRP shear contribution. The results obtained rom this approach were ound to be in close agreement to the observed test results.

35 17 Khalia and Nanni (2002) examined the perormance o RC beams shear strengthened with CFRP sheets. The parameters investigated in this experimental study were the presence o internal steel reinorcement, shear span-to-depth ratio, and the amount and distribution o FRP reinorcement. Test results indicated that the FRP shear contribution is aected by the shear span-to-depth ratio. In addition, it was concluded that additional FRP reinorcement does not relect in an increase o FRP shear contribution. The FRP shear contribution was also to be dependent on the presence o internal steel reinorcement. Pellegrino and Modena (2002) investigated the behavior o RC beams shear strengthened with side-bonded FRP sheets. This study is based on an experimental program carried out on beams with and without transverse steel reinorcement. The test results provided insight in the interaction between FRP sheets and internal steel reinorcement. From the experimental study, the authors reported that the eiciency o the FRP strengthening decreases not only when the rigidity o the FRP sheets increases, but also when the ratio between the amount o transverse steel reinorcement and that o FRP shear reinorcement increases. To account or this eect, Pellegrino and Modena introduced an additional reduction actor, which acts as a urther reduction when transverse steel reinorcement is present. Deniaud and Cheng (2003) conducted an experimental investigation on the behavior o RC T-beams shear strengthened with FRP sheets. Three types o FRP sheets were applied: uniaxial GFRP, uniaxial CFRP, and triaxial GFRP. Test results indicated that the FRP shear contribution is not only dependent on the FRP type, but also on the amount o transverse steel reinorcement. In addition, the authors concluded that the shear orces carried by arching action are delayed when FRP sheets are used. In addition, it was concluded that the triaxial GFRP sheet provided the beam with more ductile ailure. The authors also presented a rational analytical model that predicted the experimental results accurately. Taljsten (2003) presented examples o shear strengthening methods, among them shear strengthening with CFRP sheets. In addition, a ield application o a parking slab shear strengthened with unidirectional CFRP sheets is presented. The experimental

36 18 results demonstrated the importance o considering the principal directions o the shear crack in relation to the unidirectional iber. Adhikary et al. (2004) carried out an experimental investigation that ocused on the behavior o RC beams shear strengthened with FRP sheets. This study ocused on the eect o extending the length o the FRP sheet on the top surace o the beam to delay or prevent debonding ailure. From test results, it was conirmed that FRP sheets with bonded anchorage is more eective than U-wrapped schemes without anchorage. The author also presented two equations or determining the FRP shear contribution, one was developed based on FRP debonding and the other one based on bonded anchorage. Monti and Liotta (2005) perormed tests involving 24 RC beams with rectangular cross-sections and with transverse steel reinorcement. They used totally-wrapped, U- wrapped and side-bonded CFRP strips and sheets at 90, 45, and 60 iber orientations. The authors proposed an analytical model to predict the shear contribution o FRP based on racture mechanics. The authors irst deined the generalized constitutive law o an FRP layer bonded to concrete. Then, the compatibility imposed by the shear crack opening and the appropriate boundary conditions were included on the ormulations to predict the shear contribution o FRP. Finally, analytical expressions that depict the behavior o the stress ield in the FRP crossing a shear crack were obtained. Carolin and Taljsten (2005a) used a database consisting o 23 RC beams with rectangular cross-sections, with and without transverse steel reinorcement. The database consisted o CFRP sheets with ibers oriented at 45 and 90 degree iber orientation. The wrapping conigurations consisted on ully-wrapping and two-side bonded FRP systems. Some o the RC beams were precracked beore the strengthening was applied, while other beams were subjected to atigue loading ater strengthening. From the experimental study, Carolin and Taljsten (2005b) derived a modiied truss model that takes into account the non-uniormity o the strain distribution and the anisotropy o the composite. Bousselham and Chaallal (2006a) presented an extensive experimental investigation on RC T-beams shear strengthened with CFRP sheets. Test results indicated that the FRP shear contribution is not proportional to the FRP stiness. In addition, it was conirmed that the FRP shear contribution depends on the presence o

37 19 internal steel reinorcement. The inluence o the shear span-to-depth ratio on the FRP shear contribution was also conirmed. Finally, a comparison between the experimental results and the predictions rom our design guidelines was perormed. From this analysis, it was concluded that these guidelines ail to take into account important parameters that aect the FRP shear contribution, and overestimate the shear resistance or high FRP stiness EXISTING ANALYTICAL MODELS This section introduces analytical models developed rom 1995 to 2005 that determine the shear capacity o RC members shear strengthened with FRP sheets. A total o ourteen analytical models were ound rom the literature. The analytical models that will be discussed in detail in Section Four are: (1) Chajes et al. (1995), (2) Triantaillou (1998), (3) Khalia et al. (1998), (4) Khalia et al. (1999), (5) Triantaillou and Antonopoulos (2000), (6) Pellegrino and Modena (2002), (7) Chaallal et al. (2002), (8) Hsu et al. (2003), (9) Chen and Teng (2003a-b), (10) Deniaud and Cheng (2004), (11) Monti and Liotta (2005), (12) Cao et al. (2005), (13) Zhang and Hsu (2005), and (14) Carolin and Taljsten (2005b) EXISTING DESIGN GUIDELINES This section introduces the design methodologies in the application o FRP composite systems or strengthening o RC structures. From the literature, seven design guidelines were collected. The ollowing are the design guidelines that will be discussed in detail in Section Four: 1. Japan Building Disaster Prevention Association (JBDPA) Guidelines (1999) 2. Great Britain Technical Report No. 55 (2004) 3. Féderation Internationale Du Béton (ib) Bulletin 14 Task Group 9.3 (2001) 4. Japan Society o Civil Engineers (JSCE) Recommendations (2001) 5. The Canadian Network o Centers o Excellence on Intelligent Sensing or Innovative Structures (ISIS) Design Manual 4 (2001) 6. American Concrete Institute (ACI) 440.2R (2002), and 7. Canadian Standards Association (CSA) S (2002).

38 20 3. PARAMETRIC STUDY OF EXISTING EXPERIMENTAL DATA 3.1. GENERAL This section identiies criteria that inluence the behavior o RC structures shearstrengthened with FRP sheets. For this purpose, an extensive and detailed database has been developed or data analysis (reer to Table A.1 in Appendix A). From the database, the parameters that are inluential to the behavior o RC structures shear-strengthened with FRP sheets are identiied and discussed. The ollowing parameters and criteria are successively subjected to an in-depth analysis: mechanical and geometric properties o FRP, shear span-to-depth ratio, and transverse steel reinorcement. Prior to perorm the parametric study o the collected experimental data, a critical discussion o the database is perormed. Additionally, other parameters that have not been suiciently evaluated and documented, but that are inluential in the behavior o RC structures strengthened in shear with FRP systems, are also identiied and discussed. These parameters include the scale actor eect, longitudinal steel reinorcement and concrete strength EXPERIMENTAL DATABASE Beore perorming the parametric study o the collected experimental data, a critical discussion o the database is perormed. An extensive and detailed database is developed or data analysis (reer to Table A.1 in Appendix A). The database conveniently allows the identiication o certain parameters and criteria that greatly inluence the behavior o RC structures strengthened in shear with FRP systems. The shear database covers 283 experimental tests collected rom papers and reports dating rom 1992 to A sample o this database is shown in Tables 3.1 through 3.3. This database includes all relevant data rom the experimental results, such as the geometry o test specimens, concrete mechanical properties, transverse steel reinorcement properties, longitudinal steel reinorcement properties, FRP properties, observed total shear resistance, shear contribution due to the FRP system, and mode o ailure. The consistency o all numerical data presented in this database has been thoroughly veriied; however, some specimens have been rejected due to inaccuracy in results or incomplete inormation.

39 21 Table 3.1. Sample o Database - Cross-Section Properties (Uji et al.) Test No. Beam Shape a/d ' c (MPa) b w (mm) Section Dimensions d (mm) d (mm) Longitudinal Reinorcement A s (mm 2 ) yv (MPa) Transverse Reinorcement A v (mm 2 ) 3 Rectangular s (mm) Table 3.2. Sample o Database - FRP Properties (Uji et al.) Test No. FRP type w (mm) t (mm) n s (mm) E (GPa) u (MPa) Wrapping Scheme β ρ (x10-3 ) 3 CFRP Total Wrap Table 3.3. Sample o Database - Failure Conditions (Uji et al.) Test Specimen V exp (kn) V (kn) Failure Mode Fracture In order to critically discuss the experimental data presented in the database, all experimental data have been distributed with respect to certain parameters. As shown in Table 3.4, nearly 70% o the beam specimens are rectangular beams. However, in practice, T-sections are more widely used than rectangular beams; thereore, additional experimental results on T-beam sections should be included. Additionally, nearly twothirds o the total beam specimens are slender beams ( a / d 2.5 ), and about 70% o beam specimens correspond to beams with a total height larger than or equal to 300 mm. Most beam specimens were tested in the presence o none or less than the minimum amount o internal transverse steel reinorcement since all beam specimens needed to ail

40 22 in shear. Nearly 60% o all beam specimens were tested without the presence o transverse steel reinorcement. In addition, as shown in Table 3.5, most experimental specimens correspond to CFRP strengthening systems, which are most widely used in practice because o their excellent mechanical properties. Moreover, s are used as wrapping coniguration or nearly 42% o the beam specimens. From Table 3.6, FRP abrics, and FRP iber orientation at 90 degrees are most used as wrapping schemes or most data specimens. Finally, o the 283 tests, 118 ailed due to FRP debonding, 57 ailed due to FRP racture, and 108 ailed due to other reasons. Table 3.4. Number o Specimens in Terms o Cross-Section Properties Beam Geometry Rectangular Beams T- Beams Beam Cross-Section a/d 2.5 a/d < 2.5 h 300 mm h < 300 mm Transverse steel reinorcement With stirrups Without stirrups Table 3.5. Number o Specimens in Terms o FRP Properties FRP Material CFRP GFRP AFRP FRP Wrapping Coniguration w/ anchor Total Wrap Other Table 3.6. Continuation o Number o Specimens in Terms o FRP Properties FRP Distribution FRP iber orientation Failure Modes Strips Continuous 90 Other than 90 Fracture Debonding Other

41 PARAMETERS THAT AFFECT THE SHEAR BEHAVIOR OF RC MEMBERS STRENGTHENED IN SHEAR WITH FRP The parameters that could aect the behavior o RC members strengthened in shear with FRP are discussed and evaluated by perorming a comparative analysis o the database. The experimental data rom the database is analyzed in terms o which simultaneously includes the eects o the amount o FRP reinorcement 2/ 3 E ρ / ' c, (expressed in terms o the FRP ratio, ρ ), the iber type (expressed in terms o the modulus o elasticity o FRP, E ), and the concrete strength, deined as ' c. Moreover, the database is evaluated in terms o the shear span-to-depth ratio, deined as a / d ; and the ratio between the transverse steel and FRP reinorcement, deined as ρ ses / ρ E, where ρ s represents the transverse steel reinorcement ratio. Each parameter is urther evaluated and discussed in terms o the increase in shear due to FRP, deined as V /( Vc + Vs) ; FRP wrapping schemes; and ailure modes. The modes o ailure included in this analysis are shear ailure due to FRP debonding, and shear ailure with or without FRP racture. The latter means that the FRP can carry additional load ater the concrete ails. Finally, in this analysis, experimental data that presented lexural ailure modes are disregarded Eect o Mechanical and Geometric Properties o FRP. I the dominant ailure mode o RC members is due to FRP racture, the type o FRP material is relevant to the shear resistance o the FRP system because o the dierent racture capacities among dierent FRP materials (Triantaillou and Antonopoulos, 2000). In addition, FRP systems have been proven to increase the total shear resistance o existing RC members by ully-wrapping or partially-wrapping FRP composites around the members. These dierent wrapping conigurations have an eect on the dominant mode o ailure. The potential ailure modes observed on RC beams shear-strengthened with FRP systems include FRP racture, shear ailure without FRP racture, and FRP debonding. The distribution o FRP ibers also inluences the perormance o the shear strengthening system. The application o FRP strips allows lexibility in controlling the amount o FRP; however the use o continuous FRP sheets allows the interception o all

42 24 diagonal cracks. Additionally, FRP ibers can be oriented in dierent directions in order to eectively control shear cracks. FRP ibers oriented at 45 are more eective in controlling shear cracks; thus the shear resistance is higher than when applying ibers oriented at 90. Previous studies have shown that the FRP properties, such as its axial rigidity, play an important role in the shear resistance attributed to FRP systems. These studies have also reported that the strain distribution along a shear crack is not uniorm, and because o possible bond ailure, it appears that the FRP contribution is limited to an eective tensile strain, ε e, which is usually lower than the ultimate tensile strain in the FRP. Triantaillou (1998) showed that the FRP eective strain decreases as its axial rigidity increases. On a later study, Triantaillou and Antonopoulos (2000) reported that the FRP eective strain not only depends on its axial rigidity, but also on the concrete compressive strength. This is attributed to the act that the eective FRP strain depends on the development length, which is the length necessary to reach FRP racture beore debonding occurs. The development length is proportional to the FRP axial rigidity and inversely proportional to the tensile concrete strength, which is a unction o its compressive strength and is deined as 2/3 ' c (Triantaillou and Antonopoulos 2000). Thereore, the parameter 2/ 3 E ρ / ' c is taken into consideration or data analysis. From analyzing the shear gain versus 2/ 3 E ρ / ' c or all test specimens that ailed due to FRP debonding and other shear ailure modes, no clear trendline could be observed. Thereore, to reine the analysis urther, the inluences o the presence o transverse steel reinorcement and the type o beam (slender vs. deep) are eliminated. Figure 3.1 illustrates the increase in shear resistance due to the FRP in terms o 2/ 3 E ρ / ' c only or slender beams without transverse steel reinorcement. For specimens that ailed due to FRP debonding, no clear trendline could be observed or specimens strengthened with U-wrapped FRP systems. However, or other type o 2/ 3 strengthening schemes, an increasing trend is observed as E ρ / ' c increases. It seems though that beyond 2/ 3 E ρ / ' c equal to 0.08, additional amount o FRP does not relect an increase in the shear gain as shown in Figure 3.1(a). The same trend is observed or specimens ailing due to other shear ailure modes. It can be observed that

43 25 beyond 2/ 3 E ρ / ' c equal to 0.05, additional amount o FRP does not relect an increase in the shear gain as shown in Figure 3.1(b) w/ anchor Total Wrap Shear Gain (%) E ρ /' c 2/3 (a) FRP Debonding w/ anchor Total Wrap NSM Two L-shaped w/ anchor Shear Gain (%) E ρ /' c 2/3 (b) Other Shear Failure Modes 2/ 3 Figure 3.1. Shear Force Gain vs. E ρ / ' c Slender Beams without Transverse Steel Reinorcement

44 Eect o Shear Span-to-Depth Ratio. The shear span-to-depth ratio plays an important role in the behavior o RC members shear-strengthened with FRP systems. The behavior o slender members ( a / d 2.5 ) is dierent rom that o deep members ( a / d < 2.5 ). Most experimental and analytical studies have ocused on the perormance o slender beams strengthened in shear with FRP systems. However, the studies rom Chaallal et al. (2002) and Zhang et al. (2004) reported test results on the perormance o deep beams strengthened in shear with FRP sheets. However, these studies did not provide a comparison in the behavior between slender and deep beams. Most recently, Bousselham and Chaallal (2006b) reported the inluence and dierence in behavior in both slender and deep beams strengthened with FRP systems. They indicated that deep beams provide higher shear resistance; however, the gain in shear capacity due to additional FRP is minimal. This could be attributed to arch action, which is the characteristic behavior o deep beams. For all these reasons, the inluence o the shear span-to-depth ratio to the shear resistance has been clearly indicated in previous studies; however, most design guidelines have not yet included the inluence o this parameter when developing ormulations to compute the FRP shear contribution. Figure 3.2 illustrates the increase in the shear contribution attributed to the FRP systems in terms o the shear span-to-depth ratio or specimens without transverse steel reinorcement ailing due to FRP debonding or other shear ailure modes. In addition, Figure 3.3 illustrates the shear gain due to the FRP systems in terms o the shear span-todepth ratio or specimens with transverse steel reinorcement. From these igures, it can be observed that the increase in shear gain attributed to the FRP seems to be greater or slender beams ( a / d 2.5 ). This could be due to arch action in a way that, in comparison to slender beams, the externally applied FRP reinorcement does not signiicantly contribute to the shear resistance. In addition, it can be observed that test specimens that ailed due to FRP debonding are more requent in members with higher a / d ratios. Furthermore, by comparing the beams with and without transverse steel reinorcement, it can be conirmed the eect o transverse steel reinorcement on additional shear gain due to FRP systems. This additional gain in shear due to the FRP is smaller in beam specimens with transverse steel reinorcement than in beam specimens without transverse steel reinorcement.

45 w/ anchor Total Wrap Shear Gain (%) a/d (a) FRP Debonding w/ anchor Total Wrap NSM Two L-shaped w/ anchor Shear Gain (%) a/d (b) Other Shear Failure Modes Figure 3.2. Shear Force Gain vs. a / d - Beams without Transverse Steel Reinorcement

46 w/ anchor Total Wrap Shear Gain (%) a/d (a) FRP Debonding Total Wrap Total Wrap (prestress) Two L-shaped w/ anchor Shear Gain (%) a/d (b) Other Shear Failure Modes Figure 3.3. Shear Force Gain vs. a / d - Beams with Transverse Steel Reinorcement

47 Eect o Transverse Steel Reinorcement. The presence o transverse steel reinorcement greatly inluences the behavior o RC members strengthened with FRP systems. Numerous studies have shown that the contribution to shear resistance o externally bonded FRP is less in beams strengthened with FRP and containing internal transverse steel than in the same retroitted beams without internal transverse steel (Pellegrino et al. 2002, Chaallal et al. 2002, Bousselham and Chaallal 2004). Most recently, Bousselham and Chaallal (2006 a-b) reported that additional internal steel reinorcement results in a signiicant decrease o shear gain provided by FRP systems in slender beams. However, this inluence is minimal in the case o deep beams. This study also showed that the internal transverse steel is less stressed in the presence o FRP reinorcement. However, the mechanisms that play a role in the interaction between the transverse steel reinorcement and the externally-bonded FRP reinorcement are not completely understood; thereore, additional experimental and analytical investigations are recommended. Figure 3.4 illustrates the increase in the shear contribution attributed to the FRP systems in terms o the amount o transverse steel reinorcement or slender beams ailing due to FRP debonding or other shear ailure modes. In addition, Figure 3.5 illustrates the shear gain due to the FRP systems in terms o the amount o transverse steel reinorcement or deep beams. These igures clearly indicate that the gain in shear resistance due to FRP decreases as the ratio o ρ ses / ρ E increases. Some data points in these igures present very low values o shear gain due to the FRP because the ailure load did not reach the maximum load attained by the corresponding control specimen. Furthermore, Figures 3.4 and 3.5 show that the gains in shear due to the FRP systems or beams with transverse steel reinorcement are greater in slender beams than those corresponding to deep beams. Finally, rom the data analysis, it can be concluded that the inluence o the transverse steel reinorcement on the FRP contribution to the total shear resistance o RC members can be now conirmed by this experimental analysis. However, additional experimental and analytical investigations may be needed to provide a better understanding o the mechanisms involved in the interaction between transverse steel and FRP reinorcement.

48 w/ anchor Total Wrap 100 Shear Gain (%) ρ s E s /ρ E (a) FRP Debonding Total Wrap Total Wrap (prestress) Two L-shaped w/ anchor 100 Shear Gain (%) ρ s E s /ρ E (b) Other Shear Failure Modes Figure 3.4. Shear Force Gain vs. ρ ses / ρ E - Slender Beams

49 Total Wrap 100 Shear Gain (%) ρ s E s /ρ E (a) FRP Debonding Total Wrap Total Wrap (prestress) Two L-shaped w/ anchor 100 Shear Gain (%) ρ s E s /ρ E (b) Other Shear Failure Modes Figure 3.5. Shear Force Gain vs. ρ ses / ρ E - Deep Beams

50 Eect o Other Parameters. Other parameters relevant to the behavior o RC members strengthened in shear with FRP, which have not been thoroughly analyzed and documented in previous studies, are discussed in this section Eect o scale actor. The majority o the experimental tests in the database correspond to small specimens. However, numerous studies have determined the inluence o the size o RC beams without transverse steel reinorcement to the shear resistance. These studies reported that as the depth o beams increases, the crack widths tend to increase, which results on a reduction o the shear stress (Mac Gregor and Wight, 2005). The assessment o the scale actor perormed by Bousselham and Chaallal (2004) indicated that the gain in shear resistance due to FRP decreases as the eective depth o the RC beams increases. Most analytical models and design guidelines that compute the FRP shear contribution have been derived based on the experimental results o small test specimens. However, since it appears the scale eect plays an important role in the behavior o RC members strengthened in shear with FRP, the reliability o these analytical models and design approaches need to be conirmed. As a consequence, additional in-depth investigations are required to provide a better understanding o the eect o this parameter Eect o longitudinal steel reinorcement. Numerous studies have determined the inluence o longitudinal steel reinorcement to the shear resistance. It has been established that the lower the longitudinal reinorcement ratio, the larger the cracks, thus the contribution rom the aggregate interlocking decreases. The assessment o this parameter perormed by Bousselham and Chaallal (2004) indicated that the gain in shear resistance due to the FRP decreases as the amount o longitudinal steel reinorcement increases. Thereore, it appears that the longitudinal steel reinorcement aects the shear strength o beams strengthened with FRP systems Eect o concrete strength. The bond strength between the FRP and concrete surace depends on the compressive strength o concrete. As the concrete compressive strength becomes stronger, the bond strength between FRP systems and concrete also increases (Zhang and Hsu, 2005); thereore, ailure due to FRP debonding is avoided. Previous analytical and experimental study rom Horiguchi and Saeki (1997)

51 33 have shown that the bond strength between FRP sheets and the concrete surace is proportional to the 2/3 power o the concrete compressive strength. Despite its importance with regards to the perormance o shear strengthening with FRP, the eect o concrete strength has not been thoroughly evaluated and analyzed. However, it is important to note that most design guidelines or RC structures strengthened with externally applied FRP take into account the concrete strength when estimating the FRP shear contribution, such as ACI-440.2R (2002), ib TG 9.3 (2001), JSCE Recommendation (2001), and the Great Britain Technical Report No. 55 (2000). Thereore, the inluence o this parameter needs to be urther evaluated and analyzed SUMMARY AND CONCLUDING REMARKS In order to attain a better understanding o the parameters that inluence the behavior o RC members shear strengthened with FRP systems, an extensive and detailed database was developed or data analysis (reer to Table A.1 in Appendix A). The shear database covered 283 experimental tests collected rom papers and reports dating rom 1992 to This database included all relevant data rom the experimental results, such as the geometry o test specimens, concrete mechanical properties, transverse and longitudinal steel reinorcement properties, FRP properties, shear span-to-depth ratio, ultimate load, shear contribution due to FRP, and ailure mode. Ater a critical review o the shear database, an in-depth analysis o the experimental data was perormed to identiy the major parameters and criteria that inluence the behavior o RC beams shear-strengthened with externally applied FRP systems. For this purpose, the tests specimens rom the subset data were analyzed in terms o the FRP axial rigidity and the concrete compressive strength, deined as 2/ 3 E ρ / ' c ; the shear span-to-depth ratio ( a / d ); and the interaction between transverse steel reinorcement and FRP reinorcement, deined as ρ ses / ρ E. Each parameter was urther evaluated and discussed in terms o the increase in shear due to FRP, deined as V c + Vs ; FRP wrapping scheme; and ailure modes. The modes o ailure included in this analysis were shear ailure due to FRP debonding, FRP racture and other shear ailure modes. From the data analysis and evaluation, the ollowing observations can be drawn:

52 34 1. As extensively conirmed in previous studies, the parameters related to the FRP properties have a signiicant inluence on the shear behavior o RC members shearstrengthened with FRP systems. From the evaluation or specimens that ailed in debonding, no clear trendline could be observed or specimens strengthened with U-wrapped FRP systems. However, or other type o strengthening schemes, an increasing trend is observed as 2/ 3 E ρ / ' c increases. However, beyond 2/ 3 E ρ / ' c equal to 0.08, additional amount o FRP does not relect an increase in the shear gain. The same trend is observed or specimens ailing in other shear ailure modes. For E ρ / ' 2/ 3 c does not relect an increase in the shear gain.. values beyond 0.05, additional amount o FRP 2. The inluence o the shear span-to-depth ratio on the shear behavior o the test specimens was investigated. From this study, it was observed that test specimens that ailed due to FRP debonding are more requent in members with higher a / d ratios. In addition, the increase in shear gain attributed to the FRP seems to be greater or slender beams ( a / d 2.5 ). This could be due to arch action in a way that, in comparison to slender beams, the externally applied FRP reinorcement does not signiicantly contribute to the shear resistance. Furthermore the eect o transverse steel reinorcement on additional shear gain due to FRP systems was observed. This additional shear gain is smaller in beam specimens with transverse steel reinorcement than in beam specimens without transverse steel. 3. The inluence o transverse steel reinorcement has been conirmed in the present study. The gain in shear resistance due to FRP decreases as the ratio o ρ ses / ρ E increases. However, the resistance mechanisms associated with this phenomenon are still not ully understood; thereore, additional experimental investigations, targeted to clariy the inluence o transverse steel reinorcement are needed. 4. Additional analytical and experimental studies are required to investigate the eect o the size actor, the longitudinal steel reinorcement and concrete strength on the behavior o RC members strengthened in shear with FRP systems.

53 35 4. EXISTING ANALYTICAL MODELS AND DESIGN GUIDELINES ON SHEAR STRENGTHENING OF RC MEMBERS USING FRP SYSTEMS 4.1. INTRODUCTION This section summarizes existing analytical models and design guidelines, developed since 1995 up to 2005 to determine the shear strength o RC members strengthened with FRP systems. A total o ourteen analytical models and seven design guidelines are discussed as shown in Figure 4.1. This igure also shows how some design guidelines relate to certain analytical models in terms o their similar approach to determine the FRP shear contribution, deined as V. Analytical Models Chajes et al. (1995) Khalia et al. (1998, 1999) Triantaillou (1998, 2000) Pellegrino and Modena (2002) Chaallal et al. (2002) Hsu et al. (2003) Chen and Teng (2003) Deniaud and Cheng (2004) Monti and Liotta (2005) Cao et al. (2005) Zhang and Hsu (2005) Carolin and Taljsten (2005) Design Methodologies ACI 440.2R-02 (2002) ISIS Design Manual 4 (2001) Great Britain Report No. 55. (2004) European ib TG9.3 (2001) JSCE Recommendations (2001) JBDPA Guidelines (1999) Canadian CSA-S (2002) Figure 4.1. Correlations between Analytical Models and Design Guidelines

54 36 Previous studies have shown that the shear strength contribution o FRP is inluenced by many actors, such as the type o FRP, the FRP strengthening scheme, the concrete strength, the beam geometry, transverse steel reinorcement, loading conditions, and the shear span to depth ratio. Design guidelines and codes establish that the nominal shear capacity o an FRP-strengthened RC member, V n, is determined by adding the contribution o the FRP strengthening systems to the existing shear capacity and is given as Vn = Vc + Vs + V (1) where: V c = shear contribution o concrete, V s = shear contribution o transverse steel reinorcement, and V = shear contribution o FRP. Both the shear contribution o concrete and steel can be calculated according to dierent shear design provisions provided by RC design codes. Almost all analytical models and design guidelines discussed in this section determine the FRP shear contribution by applying the same truss analogy used to determine the shear contribution o transverse steel reinorcement. Thus, most analytical models and guidelines assume that the FRP ibers carry tensile stresses at a strain that is equal either to its ultimate tensile strain, ε u, or to a reduced raction. Because the strain distribution along a shear crack is not uniorm and because o possible bond ailure, it appears that the FRP contribution is limited to an eective tensile strain, ε e, which is usually lower than the ultimate tensile strain in the FRP. In order to estimate the eective strain in the FRP, analytical models and design guidelines have rigorously analyzed experimental data or the purpose o developing approaches to determine the eective strain. In addition, to determine the eective FRP strain the type o ailure at ultimate needs to be identiied. This ailure could either have occurred prematurely due to bond ailure o the FRP or due to FRP racture. Thereore, the main dierence between the analytical models and design guidelines lies in the approach to predict the shear contribution o FRP by predicting the FRP strain at ultimate. Furthermore, because the eective FRP strain highly depends on the FRP bonded length and its bond strength (Triantaillou and Antonopoulos, 2000), analytical models have developed several bond strength models,

55 37 which adopt dierent type o approaches. Thereore, all analytical models and design guidelines investigated have been classiied, as shown in Table 4.1, according to the approach adopted to predict the FRP eective strain at the time o ailure to determine the FRP shear contribution. Table 4.1. Classiication o Analytical Models and Design Guidelines Category Analytical Model Design Guideline Chajes et al. (1995) JBDPA (1999) Fixed eective strain CSA S (2002) Eective strain as a unction o FRP stiness or based on bond mechanism Eective strain based on non-uniorm strain distribution Triantaillou (1998) Triantaillou and Antonopoulos (2000) Khalia et al. (1998) Khalia et al. (1999) Pellegrino and Modena (2002) Chaallal et al. (2002) Hsu et al. (2003) Zhang and Hsu (2005) Deniaud and Cheng (2004) Chen and Teng (2003) Monti and Liotta (2005) Cao et al. (2005) Carolin and Taljsten (2005) ACI 440.2R-02 (2002) ib TG 9.3 (2001) JSCE Recommendations (2001) ISIS Design Manual 4 (2001) Great Britain Technical Report No. 55 (2004) 4.2. ANALYTICAL MODELS Models Based on Fixed Eective FRP Strain. These analytical models applied a ixed eective FRP strain to determine the FRP shear contribution. From all ourteen analytical models, only the model rom Chajes et al. (1995) corresponds to this category. Chajes et al. (1995) conducted an experimental investigation o eight reinorced concrete T-beams to evaluate the eectiveness o using externally applied FRP

56 38 composite abrics to increase the shear capacity o RC beams. For this purpose, dierent types o FRP materials and dierent iber orientations were used to evaluate the inluence o diverse FRP stiness and strengths. In addition, all test specimens were strengthened with U-wrapped FRP systems. In addition, the specimens were not pre-cracked and were tested without the presence o transverse steel reinorcement. Based on the experimental results rom this investigation, Chajes et al. proposed a simple analytical model based on the ollowing assumptions: (1) Linear stress-strain behavior o the FRP composite (2) Failure o the beam is initiated by ailure o the concrete (3) Perect bond between the abric and concrete prior to ailure (4) FRP contributes to the shear resistance in a similar way as the transverse steel reinorcement. From the experimental study, an average value o 5 or the vertical strain o the concrete at ailure was determined. This average strain was used to obtain theoretical predictions or the FRP shear contribution. The equations to predict the FRP shear contribution, V, proposed by Chajes et al. are expressed as V = A E εv d or iber orientation o 90º (2) cu V = A E εv d 2 or iber orientation o 45º (3) cu where: A = cross sectional area o FRP per inch o beam length, E = elastic modulus o FRP, ε vcu = ultimate tensile strain o concrete (5), and d = distance rom extreme compression iber to centroid o tension reinorcement. From the analysis developed by Chajes et al., the theoretical predictions or the FRP shear contribution were in good agreement with the experimental results. However, the ormulations to predict the FRP shear contribution were developed based on test results o continuous FRP sheets. In addition, this analytical model only predicts the FRP shear contribution or ibers oriented at 45º and 90º. Thereore, this analytical model needed to be validated through an extensive experimental data that includes dierent strengthening schemes. Finally, this analytical model ixes a value or the strain in the FRP; however, as proven later by Triantaillou (1998), the FRP contribution is limited to

57 39 an eective tensile strain, ε e, which is usually lower than the ultimate tensile strain in the FRP. Thereore, using a ixed value o 5 or the FRP strain is conservative Models Based on Eective FRP Strain as a Function o FRP Stiness or Based on Bond Mechanism. These analytical models are based directly on the calibration o experimental data and regression analysis to estimate the eective strain in the FRP. These models basically estimated experimental values or the eective FRP strain by back calculating rom the experimental values o the FRP shear contribution. Then, a relationship or the eective FRP strain in terms o the FRP stiness was obtained by regression analysis. In addition, analytical models based on empirical bond mechanism approaches are included Triantaillou (1998). Triantaillou tested nine RC beams with rectangular cross sections reinorced in shear with side-bonded CFRP reinorcement at dierent iber orientations. There was no pre-cracking or transverse steel reinorcement. To supplement these test results, additional 33 tests specimens on RC beams rom previous experimental studies were used. These tests consisted o beams FRP-strengthened in shear with dierent FRP materials, iber orientations and wrapping conigurations. From, the experimental study, Triantaillou proposed an analytical model to predict the contribution o FRP to shear capacity based on ultimate limit states. This analytical model has been developed by adopting the classical truss analogy as in the case o transverse steel reinorcement. Thereore, the contribution o the FRP to the shear resistance, V, proposed by Triantaillou is given by where: γ = partial saety actor or FRP, thickness, 0.9 V = ρ E ε ebwd (1 + cot β )sin β (4) γ ρ = FRP area raction = 2 t / b w, t = FRP E = FRP elastic modulus, ε e = eective FRP strain, b w = minimum width o cross section over the eective depth, d = eective depth o cross section, and β = angle o strong FRP material direction to longitudinal axis o member. Triantaillou realized that the FRP contribution is limited to an eective tensile strain, ε e, which is usually lower than the ultimate tensile strain in the FRP. By

58 40 realizing that the FRP strain depends on the FRP development length, which in turn is proportional to the FRP axial rigidity, Triantaillou suggested that as the amount o FRP increases, the eective FRP strain decreases. The relationship between the FRP eective strain and the amount o FRP was estimated based on all experimental results and is shown in Figure 4.2. Figure 4.2. Eective Strain in FRP vs. ρ E (Triantaillou, 1998). From Figure 4.2, it can be observed that a single curve was used or all modes o ailure because the same trend was observed or all data points. Thereore, when determining a best-it equation or the eective FRP strain, dierent equations or dierent ailure modes were not considered necessary. From Figure 4.2, the relationship between the FRP eective strain and its axial rigidity, ρ E, was obtained rom the best - it second order equation up to ρ E equal to 1 GPa, and by the equation o a straight line or values o ρ E larger than 1 GPa. These two expressions are given by the ollowing two equations,

59 41 ( E ) ( E ) 2 ε = ρ ρ, when 0 ρ E 1 GPa (5) ε e ( ρ E ) = , when ρ E > 1GPa (6) e From the analytical study, Triantaillou determined that the eective strain in the FRP is not constant. On the contrary, it varies and is dependent on the FRP stiness. However, since this analytical model was based on limited experimental data, one single expression or determining the FRP eective strain was used without considering dierent ailure modes. Thereore, this analytical model needed to be validated through a more extensive database in order to develop ormulations to determine the eective FRP strain or dierent ailure modes. In addition, because dierent FRP materials have dierent racture capacities; the types o FRP materials needed to be included as a variable in this model. Dierent wrapping conigurations are crucial in determining the ailure mode; thereore, they should also be included in the model. Moreover, this analytical model also needed to set a limit on the maximum FRP strain to preclude web crashing ailure. Finally, the concrete strength also needed to be taken into consideration since it greatly aects the bond ailure o FRP Triantaillou and Antonopoulos (2000). The authors presented a revised and improved version o the original model proposed earlier by Triantaillou in The FRP shear contribution can be determined by applying Equation (4) rom the earlier version. From, the experimental study, the eective strain in the FRP was calibrated rom 75 experimental results. In order to determine the eective FRP strain, the type o ailure at ultimate state needs to be identiied. This ailure could either have occurred prematurely due to FRP debonding or due to FRP racture. From the experimental data, Triantaillou and Antonopoulos determined that the eective FRP strain depends on the FRP development length, which in turn is proportional to the FRP axial rigidity and inversely proportional to the tensile strength o concrete. Thereore, the FRP eective strain depends on the parameter, expressed as E ρ / ' 2/3 c. This relationship was calibrated with the experimental data and is shown in Figures 4.3 (a) and (b) or shear ailure due to FRP debonding and or shear ailure combined with or ollowed by FRP racture.

60 42 (a) Shear Failure due to FRP Debonding (a) Shear Failure due to FRP Fracture Figure 4.3. FRP Eective Strain and Normalized FRP Strain vs. E (Triantaillou and Antonopoulos, 2000) ρ / ' 2/3 c From Figure 4.3, the eective FRP strain decreases as E ρ / ' increases. For 2/3 c debonding ailure, the type o FRP material is not a crucial parameter. However, or racture ailure, the type o FRP material is important because o the dierent racture strains exhibited by dierent FRP materials. Considering the dierent types o FRP materials, the strengthening schemes o FRP, and the eect o the concrete compressive strength; the eective FRP strain, ε e, can be determined rom the ollowing expressions For ully-wrapped CFRP: For side or U-wrapped CFRP ε ε For ully-wrapped AFRP: e e 2/3 ' c = 0.17 E ρ 0.30 ε u ' = min , 0.17 E ρ E ρ /3 2/3 c 3 ' c ε u (7) (8) ε e 2/3 ' c = E ρ 0.47 ε u (9) where ' c is the concrete compressive strength, and ε u is the ultimate FRP tensile strain.

61 43 The analytical model proposed by Triantaillou and Antonopoulos takes into consideration dierent FRP materials, strengthening schemes and ailure modes when calculating the eective strain in the FRP as opposed to its earlier version. However, this analytical model does not make a distinction between specimens wrapped with sidebonded and U-wrapped FRP. In addition, the FRP bonded length should be taken into consideration since it controls FRP debonding Khalia et al. (1998). Khalia et al. assumed that the FRP contributes to the shear resistance in the same way as the transverse steel reinorcement, and is expressed as V A e(sin β + cos β ) d = (10) s where: A = area o FRP = 2t w, stress in direction o the principal ibers, w = width o FRP strip, e = eective FRP tensile d = eective FRP depth, and s = spacing o FRP strips. The geometric dimensions o a typical cross-section applied in this model are shown in Figure 4.4. d β w s w s Figure 4.4. Deinition o Geometric Parameters (Khalia, 1999) Khalia et al. proposed two dierent approaches or computing the eective FRP tensile stress. These two approaches represent two possible ailure modes: FRP

62 44 debonding and FRP racture. The irst design approach based on the eective FRP stress was modiied rom its original version, which was developed by Triantaillou (1998). The modiication consisted in using the ratio o eective FRP strain to its ultimate strain, expressed as R = ε / ε. The relationship between this ratio and the axial rigidity o e u FRP, deined as ρ E, is shown in Figure 4.5. Figure 4.5. Ratio o ε e / ε u in Terms o ρ E (Khalia et al. 1998). From Figure 4.5, a polynomial regression o the experimental data, which consisted o 48 experimental test specimens, was perormed to determine the relationship between R = ε e / ε u and ρ E or the cases where ρ E is smaller than 1.1 GPa. This polynomial regression led to the ollowing expression or estimating the ratio o eective stress o the FRP, R : 2 ( ρ ) ( ρ ) R = E E , when ρ E < 1.1GPa (11)

63 45 The upper limit o the reduction coeicient, R, limits the eective FRP strain in order to maintain the aggregate interlock. Because the behavior o FRP strengthening systems is linearly elastic up to ultimate ailure, the eective tensile stress o the FRP is expressed as: where u is the ultimate tensile stress. R = / (12) By recognizing that the eective stress method can only be applicable when ailure is governed by FRP racture, Khalia et al. (1998) proposed a bond mechanism analytical approach, which is based on the bond strength model developed by Maeda et al. in This approach takes into consideration the eect o the dierent bonded surace conigurations. e When a shear crack develops, only the portion o the FRP system extending past the shear crack by the eective bond length is able to resist the total shear capacity. Maeda et al. (1997) deined the eective bond length, L e, to be the length beyond which any increase in the available bond length does not relect an increase in the bond strength. Thereore, Khalia et al. (1998) proposes the use o an eective FRP width, u w e, which depends on the shear crack angle and the bonded surace coniguration as shown in Figures 4.6 and 4.7 t s d L e L e d 45 w e = d - L e b w Figure 4.6. Eective FRP Width ped (Khalia et al. 1998)

64 46 t s d Le d L e 45 w e = d - 2L e b w Figure 4.7. Eective FRP Width Side-Bonded (Khalia et al. 1998) The eective width proposed can be calculated by the ollowing expressions: we = d Le or U-wrapped (13) w = d 2L or Side-bonded (14) e e Maeda et al. (1997) reported that the eective bond length decreases and the FRP stiness increases. Thereore, the eective bond length is given as ollows Le ln( t E ) = e (15) In addition, rom the experimental study o Maeda et al. (1997), the average bond strength at the FRP and concrete interace, τ bu is determined as τ bu = ke t (16) where k = experimental constant equal to By considering the active FRP bond area equal to the eective bond length times the width o the bonded FRP sheet, the ultimate load capacity o the FRP sheet, P max, is expressed as: P = L w τ (17) max e bu

65 47 Khalia et al. also considered the eect o the concrete compressive strength on the bond strength between the FRP and concrete. Maeda et al. used a constant compressive strength o 42 MPa when developing the bond strength model. However, the eect o concrete strength was included by introducing a term proposed by Horiguchi and Saeki (1997). Thereore, Equation (16) was modiied by introducing this term and is expressed as ( ' / 42) 2 /3 τ = k E t (18) bu c The ultimate load capacity o the FRP sheet, P max the member; thereore, the eective stress is determined rom:, is developed on both sides o 2Pmax A e = (19) From Equations (17) and (18) τ = (20) 2L e w bu A e ' c R = Lek 42 2/3 E u (21) By using Equation (15) and k 6 = , ' ( ) 0.58 ( E t ) 2/3 42 c R = (22) ε u This expression determines that only those strips in the width, w e, are eective; thereore, Equation (22) can be modiied by multiplying w / d. The inal expression or R is given as: ' ( c ) 0.58 ( E t ) 2/3 e 42 R = we 0.50 (23) ε d u

66 48 The FRP shear contribution was computed rom Equation (10) and the eective stress was limited to the lower o the two R values rom Equations (11) and (23). Although Khalia et al. analytical model includes the eect o bonded surace coniguration and concrete compressive strength, this model exhibits some shortcomings. First, rom Equations (10) and (23), this model suggests that no more than hal the ultimate tensile stress o the FRP can be used. Khalia et al. does not provide a theoretical explanation or this small value or the reduction coeicient rather than it was obtained rom the regression data. In addition, the approach based on bond mechanism adopts the ormulation or the eective bond length rom Maeda et al. However, Equation (15) can only be applied when the FRP bonded length is larger than the eective bond length Khalia et al. (1999). This analytical model is a revised version o the original developed by Khalia et al. in The experimental study consisted o six RC beams with rectangular cross sections strengthened only with CFRP. Dierent iber orientations, wrapping schemes and amounts o FRP were applied. As on the previous version, the authors proposed two approaches representing the two possible ailure modes. The irst approach, based on eective stress, did not change rom the previous version; however, the upper limit o the reduction coeicient was reduced to 0.7 GPa. Thereore, the reduction coeicient is expressed as: 2 ( ρ ) ( ρ ) R = E E , when ρ E < 0.7 GPa (24) The design approach based on the bond mechanism rom the earlier version slightly changed. Based on analytical and experimental data rom bond tests developed by Miller in 1999, a conservative value o 75 mm or the eective bond length has been adopted in this model. This analytical model also has adopted the equation rom Miller (1999) to calculate the average bond stress, which is expressed in terms o the axial rigidity o the FRP and is expressed as τ ( ) ( ) 2 6 t E t E = bu (25)

67 49 By taking into consideration the concrete compressive strength and rom Horiguchi and Saeki (1997), Equation (25) can be modiied as τ ( t E ) ( t E ) ( ) 2 2/3 6 bu = ' c/ (26) From Equation (20) and (26), and by adopting a value o 75 mm or the eective bond length, the new reduction coeicient can be expressed as: ' ( ) 2/3 c w R = ε d u e ( t E ) 10 (27) Finally, Khalia et al. also proposed an upper limit o the eective stress ratio in order to control the shear crack width and loss o aggregate interlock. This upper limit is expressed as 6 R = (28) ε u The strain reduction actor should be taken as the least o Equations (24), (27) and (28). The shear contribution o FRP can then be determined rom Equation (10). Khalia et al. analytical model slightly improved its earlier version rom 1998; however, this model is only valid or low values FRP o axial rigidity (i.e. ρ E < 0.7 GPa). In addition, this model adopts a constant value o 75 mm or the eective bond length (Miller, 1999), which may result on conservative predictions or the FRP shear capacity. Later studies have developed bond strength models that results on more accurate predictions. The suggested value or the upper limit o the reduction coeicient is based on the limited experimental data, thus giving conservative results. Finally, Khalia et al. suggested applying this model only or CFRP systems Pellegrino and Modena (2002). The authors modiied the ormulations proposed by Khalia et al. (1999) by investigating the correlation between the transverse steel reinorcement and the FRP reinorcement. Pellegrino and Modena (2002) tested

68 50 eleven RC rectangular sectioned beams with and without transverse steel reinorcement. The FRP was side-bonded, multi-layered and oriented at a 90 degree iber orientation. From the experimental study, Pellegrino and Modena reported that the eiciency o the FRP strengthening decreases not only when the rigidity o the FRP sheets increases, but also when the ratio between the amount o transverse steel reinorcement and that o FRP shear reinorcement increases. To account or this eect, Pellegrino and Modena modiied the strain reduction actor, R, originally proposed by Khalia et al. (1999), by introducing an additional reduction actor, R *, which acts as an additional reduction actor when transverse steel reinorcement is present and is expressed as: R ρ s, * = 0.53ln with 0 R* 1 (29) where ρ s, is the stiness ratio between transverse steel reinorcement and FRP shear reinorcement, and is expressed as: ρ = E A E A (30) s, s sv / where E is the elastic modulus o steel reinorcement, and s steel reinorcement. A sv is the area o transverse The contribution o FRP to the total shear capacity o an RC beam with transverse steel reinorcement can be determined rom Equation (31), where the reduction actor, R, may be taken as the lowest o: V = ρ b 0.9 dr (sin β + cot β ) (31) w u 2 ( ρ ) ( ρ ) R = E E , when ρ E < 0.7 GPa (32) 2/3 42( ' c) w e R = R * 0.58 (33) ( E t ) ε ud 6 R = (34) ε u Pellegrino and Modena slightly improved the analytical model developed by Khalia et al. (1999). This improvement consisted o taking into consideration the eect o the transverse steel reinorcement in the behavior o RC beams shear strengthened

69 51 with FRP systems. However, since the derivation o R * was validated only with the experimental data corresponding to this study, an extensive database, which includes dierent types o FRP strengthening schemes, dierent amounts o FRP and transverse steel reinorcement, is required to validate and improve this analytical model Chaallal et al. (2002). Chaallal et al. (2002) investigated the eects o FRP strengthening systems on the behavior o deep beam specimens shear-strengthened with FRP. The experimental study consisted o twelve RC hal-scale T-section girders. Chaallal et al. included transverse steel reinorcement in the specimens. In addition, multi-layer U-wrapped CFRP systems with a 90 degree iber orientation were used in the tests. From the experimental study, the optimum number o FRP layers to achieve the maximum gain in shear resistance due to the FRP was ound to be dependent on the transverse steel reinorcement. In addition, the eective strain in the FRP depends on the amount o transverse steel reinorcement. A regression o the measured experimental FRP strains rom this study was compared to the strains calculated by using Triantaillou (1998) analytical relationships to determine the eective FRP strain. This comparison resulted in a higher correlation coeicient as illustrated in Figure 4.8. The dierence is attributed to the act that the analytical model rom Triantaillou (1998) did not take into consideration the transverse steel reinorcement. Thereore, Chaallal et al. (2002) proposed Equation (35) to determine the eective strain o the FRP, ε e, which is correlated to the total shear reinorcement consisting o the transverse steel reinorcement and externally applied FRP reinorcement. = 3(10) ( ρ ) (35) ε e tot where ρ tot is the total shear reinorcement ratio and is expressed as ρ = nρ + ρ (36) tot s where: n = E / Es, ρ s = transverse steel reinorcement ratio = Asv / svbd, and s v = spacing between stirrups.

70 52 Figure 4.8. Eective Strain in Terms o ρ tot (Chaallal et al., 2002) Furthermore, the experimental study shows that the addition o CFRP layers tends to modiy the behavior o the beam rom deep to slender type. As a consequence, Chaallal et al. proposed that the deep beam coeicient, ( a / d ), deined in Equation (37) should be included in the expression to determine the shear capacity o the FRP. In addition, this analytical model suggests that the deep beam coeicient should be related to the total shear reinorcement as given in Equation (38). The shear contribution o the FRP to the total shear capacity can then be determined rom Equation (39). ( a d ) ( a / d) = 1+ 2 / /12 (37) a 1+ 2 a, d ρtot = + (1000ρ tot 0.6) 1 d 12 (38) a A V =, ρ tot E ε ed d s (39) where: a = shear span, and a d, ρ tot = new deep beam coeicient.

71 53 This analytical model was developed based on the results o an experimental investigation on the shear perormance o large scale RC T-Girders. Thereore, the ormulations or predicting the FRP contribution were derived by analyzing the inluence o a deep beam coeicient. When calibrating the ormulations to compute both the eective FRP strain and the deep beam coeicient, only data points rom this experimental study were used, thus more research work is needed to validate these ormulations Hsu et al. (2003). The analytical model rom Hsu et al. (2003) is a modiication o the model proposed by Khalia et al. in The experimental investigations rom Hsu et al (2003) consisted o ive RC beams with rectangular crosssections and without transverse steel reinorcement or pre-cracking. The RC beams were strengthened with CFRP strips systems. The FRP ibers were oriented at 0, 45, and 90 degrees. Hsu et al. proposed two dierent approaches to determine the strain reduction actor, R, which is needed to predict the eective strain and the shear contribution o FRP. The irst analytical approach, based on test data calibration, determined that the eective FRP strain is not only a unction o the FRP axial rigidity, but also a unction o the concrete compressive strength. Thereore, a relationship between the eective strain and the FRP axial rigidity was obtained by the power regression o the experimental data. However, as the concrete compressive strength increases, the bond strength between the FRP and concrete increases; thereore by curve itting, a relationship between the eective FRP ratio and ρ E / ' was developed and is expressed as c R E = ( ρ / ' c) (40) The design approach based on bonding mechanism also considers the eect o the concrete compressive strength on the direct shear behavior. This analytical model proposes an empirical design equation or calculating the ultimate direct shear strength, which is expressed as ( c ) ( c ) τ max = ' ' (MPa) (41)

72 54 whereτ max is the ultimate direct shear strength. For design purposes, Hsu et al. simpliies the concrete shear stress distribution as a triangular shape along the eective length. Thereore, the strain reduction actor is expressed as R τ L 2 t max e = 1 (42) u where L e is taken to be equal to 75 mm rom the bond strength model o Miller (1999). The strain reduction actor should be taken as the smaller rom Equations (40) and (42). The shear contribution o FRP can then be determined rom Equation (10). The analytical model proposed by Hsu et al. (2003) improved the ormulations rom Khalia et al. (1999) by introducing the concrete compressive strength in Equation (40). This equation was derived by the calibration o a more extensive experimental database and by developing a power regression or itting the data. However, Equation (40) was calibrated only with data specimens that ailed in debonding Zhang and Hsu (2005). The authors presented a revised version o the original model proposed by Hsu et al (2003). The experimental investigation rom Zhang and Hsu (2005) consisted o eleven RC beams with rectangular cross-sections and without transverse steel reinorcement or pre-cracking. The RC beams were strengthened with CFRP strips systems. The FRP ibers were oriented at 0, 45, and 90 degree iber orientations. This analytical model consists o two dierent approaches to determine the reduction actor, R, which is needed to predict the eective FRP strain and the shear contribution o FRP. The irst analytical approach was based on test data calibration. Zhang and Hsu (2005) determined that the eective FRP strain is not only a unction o the FRP axial rigidity, but also a unction o the concrete compressive strength. A relationship between the eective FRP strain ratio, R, and its axial rigidity was obtained by a power regression instead o using a polynomial as a best it o the experimental data. For a more accurate analysis, the experimental results were divided into two categories; one was based on tests ailing due to FRP racture and the other one on tests ailing due to FRP debonding as shown in Figure 4.9.

73 55 (a) FRP Fracture (b) FRP Debonding Figure 4.9. Strain Reduction Factor in Terms o ρ E (Zhang and Hsu, 2005) Zhang and Hsu determined that as the concrete compressive strength increases, the bond strength between the FRP and concrete increases; thereore by curve itting, a relationship between the eective FRP ratio and ρ E / ' was developed and is shown in Figure 4.10 and expressed as c R E = ( ρ / ' c) (43)

74 56 Figure Strain Reduction Factor in Terms o ρ E / ' (Zhang and Hsu, 2005) c A saety actor was applied to Equation (43) to account or the data points that are not distributed on the curve. The modiied strain reduction actor was applied to Equation (43), thus resulting on Equation (40). The design approach based on bonding mechanism also considers the eect o the concrete compressive strength on the direct shear behavior. This analytical model proposes an empirical design equation or calculating the ultimate direct shear strength, which is given in Equation (41). For design purposes, Hsu et al. simpliies the concrete shear stress distribution as a triangular shape along the eective length. Thereore, the strain reduction actor based on this approach is given by Equation (42). The only modiication to the previous version was the equation to predict the shear contribution o FRP, which is expressed as For FRP continuous iber sheet: 2 V wet e sin β = (44) For FRP strips: V = A (sin β + cos β ) d e s (45)

75 57 As in the previous version, the analytical model proposed by Zhang and Hsu (2005) improved the ormulations rom Khalia et al. (1999) by introducing the concrete compressive strength in Equation (40). This equation was derived by the calibration o a more extensive experimental database and by developing a power regression or itting the data. However, Equation (40) was calibrated only with data specimens that ailed in debonding. Because when a shear crack develops, only that portion o the FRP extending past the shear crack by the eective bond length is able to resist the shear capacity. Thereore, or continuous FRP sheets, the width is suggested to be changed by expressed in Equation (44). w e, as Deniaud and Cheng (2004). Deniaud and Cheng (2004) proposed model was developed based on an experimental investigation, which consisted o 35 experimental test results. The test specimens consisted o small and ull-scale specimens. The FRP wrapping schemes applied were side-bonded and U-wrapped FRP sheets. From the experimental results, Deniaud and Cheng proposed a simpliied analytical model, which is based on the strip model developed by Alexander and Cheng (1997) and the shear riction approach developed by Loov (1998). The strip method is based on evaluating each individual FRP strip crossing the shear crack in order to ind the maximum allowable FRP strain. To evaluate the bond strength between the concrete and the FRP, and the maximum allowable FRP strain o each strip, Deniaud and Cheng developed an interace mean shear stress curve. Deniaud and Cheng then developed a parametric study to determine the maximum FRP strain, ε max, which is expressed by ε ' c d = (46) ( te ) ( ka sin β ) max (%) where k a is the coeicient describing anchorage condition It is necessary to note that both the width and the spacing o the FRP bands are taken perpendicular to the direction o the principal ibers, but not along the longitudinal direction o the beam as was done in other analytical models. From calibration o the expression above, the coeicient or anchorage conditions, k a, was ound to be equal to 0.79 when the FRP sheets were

76 58 extended underneath the lange. For FRP bonded on the sides, k a was ound to be equal to 2, while or FRP bonded as a U-wrapped, k a was ound to be equal to 1. For ullywrapped FRP sheets, Equation (46) reaches ininity; thereore, the maximum strain is not governed by debonding. From the parametric study, the ratio o the remaining bonded width over the initial width, denominated as as R L, can also be determined and is expressed R L d = exp kele sin β 0.4 (47) where k e is the integer describing number o debonding ends. For FRP bonded on the sides, k e = 2; or FRP bonded as U-wrapped, k e = 1; and or FRP extended underneath lange, k e = 1. The eective length is given by Equation (15) rom Maeda et al. (1997) bond strength model. Deniaud and Cheng developed an equation to determine the eect o the FRP sheets and is expressed as For 90 degree iber orientation: s T = d te ε R with ε max ε u (48) v max L ds For inclined iber orientations and FRP strips: w sv T d t E ε max RL sin cos sin s d β β = + β s 2 (49) where: T = tension orce in FRP and d s = stirrup height Deniaud and Cheng proposed a continuous equation to determine the total shear resistance o a beam, V n, which is expressed as s Vn = k ' c Ac ( Tv + T ) Tv (50) d s

77 59 where: k = experimentally determined actor = ( ) ' c, A c = concrete area, T v = tension orce in stirrups = Asv yv, A v = area o stirrups, and yv = yield strength o stirrups. Deniaud and Cheng used a signiicantly dierent approach in predicting the capacity o RC beams shear strengthened with FRP systems. This model is based on the shear riction theory with the lowest shear strength among all potential ailure planes governing the shear strength o the beam. In addition, this model treates and describes the interaction between the concrete, steel stirrups, and FRP. According to Deniaud and Cheng (2004), this analytical model accurately evaluates the cracking pattern as well as the resisting shear orce. The main advantage o this model is that the strain compatibility is satisactory. However, one drawback o this model is that it does not address FRP racture or ully-wrapped specimens Models Based on Non-uniorm Strain Distribution. These analytical models are based on bond strength models that have been developed based on racture mechanics at the FRP/concrete interace. These analytical models determine the speciic racture energy o the FRP/concrete interace to determine the bond strength. Beore the FRP shear contribution can be determined, the maximum shear orce transerred rom the concrete to the FRP as well as the normal and shear stressed need to be determined. The maximum shear orce between concrete and FRP prior to debonding depends on the available bond length. I the eective bond length is higher than the available bond length, debonding occurs and the orce transerred between concrete and FRP ceases Chen and Teng (2003). Chen and Teng proposed two separate analytical models or predicting the FRP shear contribution: the FRP debonding approach and the FRP racture approach. Both approaches were developed separately because o the dierence between the two possible ailure modes. Both approaches proposed an equation to determine the FRP shear contribution, V, and is expressed as V he(cotθ + cot β ) = 2 t w sin β (51) s e where: h e = eective FRP height and θ = shear crack angle

78 60 The analytical model rom Chen and Teng (2003) is based on the assumption that the shear crack ends at a distance o 0.1d below the compression ace o the beam as shown in Figure d Shear crack tip b d,t Z t t 0.9d d Z b Z d h h,e θ β b w Figure General Shear Strengthening Scheme Notations (Chen and Teng, 2003) From Figure 4.11, the ollowing expressions were determined by Chen and Teng: he = zb zt (52) z t = d (53), t z = d h + 0.9d (54) b where: z t = coordinate o upper edge o eective FRP, z b = coordinate o lower edge o eective FRP, d, t = distance rom beam compression ace to upper edge o FRP, and d = distance rom beam compression ace to lower edge o FRP. Furthermore, the analytical model rom Chen and Teng takes into consideration the orientation o the FRP ibers in the case o continuous FRP sheets shown in Figure 4.12 and given Equation (55). s = w / sin β (55)

79 61 w θ β Figure Relationship between s w and s or Continuous FRP Sheets Chen and Teng also revealed that the FRP stress distribution along the shear crack is not uniorm or both FRP racture and FRP debonding; thereore, the eective or average FRP stress, e, proposed by Chen and Teng is expressed as = D σ (56) e,max where: D = FRP stress distribution actor and σ,max = maximum stress in FRP intersected by the shear FRP debonding approach. This approach can only be applied or RC beams shear strengthened with FRP bonded on the sides and U-wrapped because debonding is the governing ailure mode. However, in the case o U-wrapped, the racture approach also needs to be evaluated because RC beams shear strengthened with U-wrapped can also ail in racture. In this case, the smaller value or the prediction o the FRP shear contribution between the two approaches needs to be taken as the controlling FRP shear capacity. Chen and Teng developed a bond strength model in 2001, which predicts the bond strength and the eective bond length between the FRP and concrete. This proposed bond strength model was used by Chen and Teng to determine the maximum stress in the FRP along a shear crack, which is limited by the ultimate bond strength or the FRP ultimate tensile stress. The maximum stress in the FRP, σ rp,max, can be determined by

80 62 σ = min,0.427β β,max u w L E t ' c (57) 1 i λ 1 βl = sin ( πλ / 2) i λ <1 (58) β = w 2 w / s sinβ 1 + w / s sinβ (59) where: β w = eect o FRP to concrete width ratio, β L = eect o bond length, λ = normalized maximum bond length = L / max L e. The maximum bond length, L max, is given by: For U-wrapped: For Side-bonded: L = h / sin β (60) max max e L = h / 2sin β (61) e The eective bond length determined rom the bond strength model developed by Chen and Teng (2001) is given by: L = E t / ' (62) e c Chen and Teng proposed an expression to determine the FRP stress distribution actor or debonding ailure by assuming that the FRP intersected by the shear crack ully develops its bond strength at the ultimate state. The FRP stress distribution actor, can be obtained rom Equation (63) and is shown in Figure D rp, D ( πλ ) ( πλ ) 2 1 cos /2 i λ 1 πλ sin /2 = π 2 1 i λ>1 πλ (63)

81 63 Figure Stress Distribution Factor or ped and Side-Bonded The FRP debonding approach developed by Chen and Teng (2003) is based on the bond strength model developed by the authors in This model was developed by combining racture mechanics analysis with experimental results. Chen and Teng assumed that the shear-slip behavior o FRP bonded to concrete can be represented as a triangular shape. In addition, this model determined that the ratio o the FRP width to the width o the concrete member greatly aects the bond strength at ailure. The eective bond length o FRP was ound to be proportional to the FRP stiness and inversely proportional to the concrete tensile strength FRP racture approach. This approach can only be applied or RC beams shear strengthened with ully-wrapped and U-wrapped FRP because racture is the governing ailure mode. As mentioned in the previous section, in the case o U-wrapped, the debonding approach also needs to be evaluated because RC beams shear strengthened with U-wrapped can also ail in debonding Chen and Teng pointed out the non uniormity o the FRP stress along a shear crack; thereore, Chen and Teng proposed a parabolic stress distribution or the FRP

82 64 intersected by the critical shear crack. However, Chen and Teng recommended the use o a linear stress distribution as approximation because the stress in the FRP can be taken to be proportional to the width o the shear crack. Thus, the stress distribution actor is expressed as D 1+ξ = (64) 2 where ξ is a coeicient and is equal to z / z t When the ultimate shear strength is reached at or ater FRP racture, the maximum stress in the FRP along a shear crack reaches its ultimate strength; thereore, the maximum stress in the FRP, σ,max b, is expressed as σ = (65),max u I the ultimate shear strength is reached beore FRP racture, the maximum allowable strain should be limited. This analytical model proposes a value o 1.5% or the maximum usable FRP strain Monti and Liotta (2005). Monti and Liotta (2005) tested 24 RC concrete beams with rectangular cross-sections and with transverse steel reinorcement. They used ully-wrapped, U-wrapped and side-bonded CFRP strips and sheets at 90, 45, and 60 iber orientations. Monti and Liotta (2005) proposed an analytical model to predict the shear contribution o FRP based on racture mechanics. First, Monti and Liotta deined the generalized ailure criteria at the FRP and concrete interace. For the case o FRP strips and sheets, the eective bond length and the debonding strength are introduced and expressed as: L e = E t 2 ct (66) dd = E ΓFk γ t (67)

83 65 where ct = concrete tensile strength = 2/ cu, R c = concrete characteristic cubic strength, and expressed as Γ Fk = speciic racture energy o the FRP-concrete bond interace and is Γ = 0.03 k ' (68) Fk b c ct The covering/scale actor coeicient is given by: k b = 2 w / s w / 400 (69) When the available bond length, the debonding strength is reduced as: L b, is lower than the eective bond length, L e, L b L dd ( Lb ) = dd 2 Le L b e (70) For the cases o FRP strips and sheets wrapped around a corner, the FRP exhibits a raction o its ultimate strength, ϕ R, which is expressed as: ϕ = rc rc R 1.6, b b (71) w When the available bond length, L b, is higher than the eective bond length, L e, the debonding strength is expressed as: ( ) ( ) u c dd R u dd w r = + ϕ (72) When the available bond length, the debonding strength is expressed as: L b, is lower than the eective bond length, L e, (, ) ( ) ( ( )) L r = L + ϕ L (73) u b c dd b R u dd b

84 66 Monti and Liotta irst deined the generalized constitutive law o an FRP layer bonded to the concrete surace. Then, the compatibility imposed by the shear crack opening and the appropriate boundary conditions were included on the ormulations to predict the shear contribution provided by the FRP systems. Finally, analytical expressions that depict the behavior o the stress ield in the FRP crossing a shear crack are derived. From these analytical expressions, equations were ormulated to compute the eective debonding strength o FRP. The expressions to predict the eective debonding strength, ed, were a unction o the FRP strengthening scheme, and some basic geometric and mechanical parameters. These expressions are given by, For Side-bonded: ed z rid, eq = dd min(0.9 d, hw ) rid, eq rid eq z L eq rid, eq 2 (74) z = z + L (75) z = min(0.9 d, h ) L sin β (76) rid w e L eq = s / E (77) dd For U-wrapped: For Fully-wrapped ed 1 Le sin β = dd 1 3 min(0.9 d, hw ) (78) 1 Le sin β 1 Le sin β ed = dd 1 + ( φr d dd ) 1 6 min(0.9 d, hw ) 2 min(0.9 d, hw ) (79) where s is the debonding slip. In the case o an RC beam shear strengthened with U-wrapped or ully-wrapped, the FRP shear contribution can be determined by 1 w V = ( 0.9d ) ed 2 t (cotθ + cot β ) (80) γ s Rd

85 67 where θ is the orientation o the shear crack. For RC beams shear strengthened with FRP bonded to the sides, the FRP shear contribution can be determined by 1 sin w V = β min(0.9 d, hw ) ed 2t γ sinθ s (81) Rd The analytical model presented by Monti and Liotta (2005) also considered the non-uniormity o the FRP eective stress along the shear crack. Thereore, this model applies racture mechanics approach as opposed to regression analysis perormed by previous analytical models. In addition, Monti and Liotta apply the truss analogy mechanism or determining the FRP shear contribution o ully-wrapped and U-wrapped coniguration. In contrast, a crack-bridging mechanism was used or side-bonded FRP Cao et al. (2005). The authors perormed tests involving twelve precracked RC beams with rectangular cross-sections. This was the irst study to investigate the eects o pre-cracking or developing an analytical model. The RC beams were strengthened with ully-wrapped CFRP and GFRP strips at a 90 iber orientation. The purpose o this study was to investigate the debonding o FRP prior to ailure because debonding can be considered a serviceability limit state, which can be assumed to be the ultimate limit state or design purposes. Furthermore, this analytical model modiied the analytical model rom Chen and Teng (2003) by considering the eects o the shear span to eective depth ratio on the critical shear angle and the strain distribution actor. Since the shear span-to-depth ratio also has a signiicant eect on the strain distribution actor, D, a modiied distribution actor, D θ = D /tanθ, was developed to represent the eects o both the strain distribution actor as well as the shear crack angle. This relationship was calibrated with the experimental results rom this study as shown in Figure Cao et al. proposed a modiied strain distribution actor, D θ, which is expressed as 1 or a / d 1.4 π 2 1 D θ = 1 or 1.4 < a / d < 3 λπ 1 0.2( λ 1.4) or a / d 3 (82)

86 68 Figure Strain Distribution Factor in Terms o Shear Span-to-Depth Ratio (Cao et al., 2005) For FRP strips oriented vertically to the longitudinal axis o the beam, the shear contribution o FRP, V, can be calculated as V 0.9d = 2D t w E ε (83) s θ,max β = w 2 w / s 1 + w / s (84) where: ε = maximum FRP strain at debonding and is expressed as:,max ε,max ( ' ) 1/ 4 c = 0.427βw (85) E t The analytical model proposed by Cao et al. (2005) modiied the FRP debonding approach proposed by Chen and Teng (2003) by introducing a modiied strain distribution actor that depends on the shear-span-to depth ratio and the shear crack angle. This modiied strain distribution actor, D θ, was derived based on experimental results or shear span-to-depth ratio between 1.4 and 3; thereore, the relationship given in

87 69 Equation (82) provides a conservative approximation; thereore additional experimental investigations are needed to validate this relationship Carolin and Taljsten (2005). Carolin and Taljsten (2005) developed a database that consisted o 23 RC beams with rectangular cross-sections, with and without transverse steel reinorcement. The database consisted o CFRP strengthening systems with ibers oriented at 45 and 90 degrees. The RC beams were strengthened with ullywrapped and side-bonded FRP strengthening schemes. From the experimental study, Carolin and Taljsten (2005) derived a modiied truss model that takes into account the non-uniormity o the strain distribution and the anisotropy o the FRP composite. Carolin and Taljsten (2005) reported that the direction o the possible shear crack is diicult to predict; thereore, three geometric angles are applied in this analysis as shown in Figure s b M V F i θ β ϕ Figure Fiber Alignment and Shear Crack Angle (Carolin and Taljsten, 2005) From Figure 4.15, θ is the shear crack inclination, β is the iber direction along the longitudinal axis o the member, and φ is the angle between the principal tensile stress and the iber direction; thereore, φ = θ + β 90. The FRP shear contribution,, according to Carolin and Taljsten (2005)is given as cosφ V = ηεcre t r (0.9 d) (86) sin θ

88 70 where η is the average iber utilization, which is deined as the average FRP strain along the beam height compared to the strain in the most stressed FRP iber. Carolin and Taljsten suggest a value o average iber utilization equal to The actor r becomes r = sin β or continuous FRP sheets and r = w / s or FRP strips. The critical FRP strain, ε cr, can be determined by ε = min ε 2 ε cr εbond ϕ u cmax cos cos 2 ϕ (87) where ε u is the ultimate tensile strain o the FRP, ε bond is the maximum allowable strain without achieving anchor ailure, and ε cmax is the maximum strain to achieve the concrete contribution. The values corresponding to the later two strains were not given in the paper and the authors did not provide a way o estimating them DESIGN GUIDELINES The design guidelines have also been categorized according to the dierent approaches to determine the eective FRP strain. Seven design guidelines are classiied into the ollowing categories: (1) Design Guidelines based on ixed eective FRP strain and (2) Design Guidelines based on eective FRP strain as a unction o FRP stiness or based on bond mechanism Design Guidelines Based on Fixed Eective FRP Strain. These design guidelines applies a ixed eective FRP strain to determine the FRP shear contribution JBDPA guidelines (1999). The Japan Building Disaster Prevention Association (JBDPA) published the Seismic Retroitting Design and Construction Guidelines or Existing Reinorced Concrete (RC) Buildings with FRP Materials (JBDPA, 1999). These guidelines condense research on seismic retroitting o RC structures using FRP systems conducted in Japan. The JBDPA guideline provides guidance on the proper handling, design, and installation o the FRP systems used in Japan.

89 71 From the Structural Regulations o Building (Building Center o Japan, 1997), the ultimate shear capacity o RC members strengthened with FRP composite systems, is evaluated by adding the contribution o the FRP and is expressed as ( + ) ρ 17.6 ' s c Vn = ρts y b(0.9 d) a / d (88) pts y = ρs yv + ρ e 10 MPa (89) where ρ ts is the total ratio o existing shear reinorcement and a / d is the shear span-todepth ratio, which must not be less than one nor larger than three. The tensile strength o FRP, e is estimated as { ε } = min E, 2 / 3 (90) e e u where ε e based on previous investigations is taken to be equal to 7. In addition, to avoid FRP racture, a value o two-thirds o the ultimate tensile strength o the FRP was adopted as a margin o saety CAN/CSA S (2002). The Canadian CAN/CSA S Design and Construction o Building Components with Fibre-Reinorced Polymers (CSA 2002) represents the only ormalized design code addressing the application o externally bonded FRP reinorcement or RC members. The CSA S was last updated on May 2004; however, no changes on the design requirements or shear strengthening were ound. From CSA A (CSA, 1994), the nominal shear capacity o beams strengthened with FRP is evaluated by adding the shear contribution o the FRP, V, to the shear contribution o concrete and transverse steel reinorcement, which according to CSA A can be computed as V = 0.2 ' b d (91) V c c w A (sinα + cos α) d sv yv s = (92) sv

90 72 The Canadian Standards Association S (CSA, 2002) estimates the shear capacity provided by FRP sheets as V A E ε e(sin β + cos β ) d = (93) s For simplicity this design code provides ixed values or the eective strain in the FRP. The value o eective strain, ε e, may be conservatively assumed to be equal to 4 or U-wrapped members, and equal to 2 or FRP systems side-bonded to the web Design Guidelines Based on Eective FRP Strain as a Function o FRP Stiness or Based on Bond Mechanism. The design guidelines corresponding to this category are based directly on the calibration o experimental data and regression analysis to estimate the eective strain in the FRP. From the regression analysis, relationships to determine the eective FRP strain were derived. In addition, design guidelines based on empirical bond mechanism approaches are included ib TG 9.3 bulletin 14 (2001). The International Federation or Structural Concrete (ib) Bulletin 14 Externally Bonded FRP Reinorcement or RC Structures (ib, 2001) produced by ib Task Group 9.3, presents a combination o design guideline and state-o-the-art report. This guideline recognizes the dierence in expected perormance, not only between FRP material types, but between preormed and wet layup FRP systems. This dierence is expressed in the orm o dierent material saety actors. A new version to ib Bulletin 14 is currently being developed and will be published very soon. From Eurocode 2 Part I (2003), the nominal shear capacity o RC members strengthened with FRP systems is evaluated by adding the shear contribution o the FRP, V, to the shear contribution o concrete and transverse steel reinorcement, which can be calculated as V min 1, 2 3 c = 100 min ( 0.02, ρs ) ' c bwd γ + c d (94)

91 73 V s A 0.9 d(1 + cot α) sinα sv yv = (95) s v The analytical model rom Triantaillou and Antonopoulos developed in 2000 was the basis or developing the analytical relationships in ib TG 9.3 bulletin 14. This design guideline calculates the shear contribution provided by the FRP system, V, as V = 0.9 ε E ρ b d(cotθ + cot β )sin β (96) e w 2t w ρ = or strips o FRP (97) b s w The eective strain o the FRP is governed by the ailure mode o the FRP, the strengthening scheme and the type o FRP. The best-it power type expressions or the eective FRP strain were calibrated rom the experimental data reported by the analytical study developed by Triantaillou and Antonopoulos in For RC members ullywrapped with CFRP systems, when FRP racture controls, the eective strain can be computed as ε e 2/3 ' c = 0.17 E ρ 0.30 ε u (98) When the strengthening scheme consists o U-wrapped or side-bonded CFRP systems, the eective FRP strain is expressed as ε e ' = min , 0.17 E ρ E ρ /3 2/3 c 3 ' c ε u (99) expressed as For ully-wrapped AFRP, when FRP racture controls, the eective FRP strain is ε e 2/3 ' c = E ρ 0.47 ε u (100)

92 74 This design guideline provides shear design provisions that takes into consideration dierent FRP materials, strengthening schemes and ailure modes when calculating the eective strain in the FRP. However, it does not make a distinction between specimens wrapped with side bonded FRP and U-wraps JSCE recommendations (2001). The Japanese JSCE Recommendations or the Upgrading o Concrete Structures with use o Continuous Fiber Sheets (JSCE, 2001) adopts a perormance-based approach to the design o externally bonded FRP materials. The shear contribution o concrete according to JSCE Recommendations can be computed as V = β β β b d / γ (101) c d p n vc w b ( d ) 1/ 4 β = 1000 / 1.5 (102) d β p ( ρ ) 1/3 = (103) s β = 1 + M / M 2 or N 0 n o d u β = 1+ 2 M / M 0 or N < 0 n o d u (104) ( ) 1/3 2 = 0.2 ' 0.72 N / mm (105) vc c where M o = decompression moment, M d = design bending moment, and γ b = member actor. The transverse steel reinorcement shear contribution provided by the JSCE Recommendations is expressed as V s A 0.9 d(sinα + cos α) sv yv = (106) s v capacity, The Japanese JSCE Recommendations calculates the FRP contribution to shear V, as V A 0.9 d(sin β + cos β ) u = (107) K s where K is shear reinorcing eiciency.

93 75 The shear reinorcing eiciency, K, is expressed in terms o elastic modulus E and the amount o FRP ρ as 0.4 K = R 0.8 (108) ( ρ E ) 2/3 1/3 1/ 4 u 1 R = E ' c, 0.5 R 2 (109) The JSCE recommendations suggests that Equation (107) is applicable or members strengthened with CFRP sheets, CFRP strands, and AFRP iber sheets since the shear reinorcing eiciency was calibrated rom experimental specimens strengthened with CFRP and AFRP systems ISIS design manual 4 (2001). The ISIS Design Manual 4 or Strengthening Reinorced Concrete Structures with Externally-Bonded Fibre Reinorced Polymers (ISIS Canada, 2001) was written as a state-o-the-art report, reerring to design recommendations o other design guidelines, such as ACI 440.2R (2002) and ib- TG 9.3 Bulletin 14 (ib, 2001). A new version to this design manual will be published by ISIS in the all o From CSA Standard A , (CSA 1994), the nominal shear capacity o a member strengthened with FRP is evaluated by adding the shear contribution o the FRP, V, to the shear contribution o concrete and steel. The values o shear resistance provided by the concrete, V c, and transverse steel reinorcement, V s are expressed as V = 0.2 ' b d (110) c c w V s A (sinα + cos α) d sv yv = (111) s v The ISIS Design Manual 4 (ISIS, 2001) calculates the FRP contribution to the total shear capacity, V, as A E ε e(sin β + cos β ) d V = (112) s

94 76 The eective FRP strain, ε e must be limited to a value o 4 to assure that aggregate interlock orces can still be transmitted through the shear plane. For ullywrapped cases, the eective strain should simply be taken to be equal to 4. For other strengthening schemes, the eective strain is computed as ollows ε e = Rε (113) u where R is the ratio o eective to ultimate strain in the FRP reinorcement, and is given by 2/3 ' c R = λ1 ρ E λ 2 (114) where or CFRP racture: λ 1 = 1.35 and λ 2 = 0.30; or AFRP and GFRP racture: λ 1 = 1.23 and λ 2 = ollows, To account or possible debonding, the eective FRP strain is computed as k k L e ε e = (115) ' c k1 = k d n L 2/3 (116) e e 2 = (117) d L e = (118) ( t ) 0.58 E where n e is the number o ree ends o the FRP reinorcement on one side o the beam. I k 2 is negative, the FRP systems is ineective unless anchorage is provided. The eective FRP strain, ε e, shall be taken as the smallest o the limiting eective strain (i.e.

95 77 4), the value obtained rom Equation (113), and the value obtained rom Equation (115) ACI 440.2R-02 (2002). The ACI 440.2R-02 Guide or the Design and Construction o Externally Bonded FRP Systems or Strengthening Concrete Structures (ACI 440, 2002) provides strength reduction actors based on ductility o the expected ailure mode consistent with ACI (1999). The nominal shear capacity o an RC member strengthened with FRP is evaluated by adding the shear contribution o the FRP, V, to the shear contribution o concrete and transverse steel reinorcement as shown in Equation (119). An additional reduction actor, ψ, is applied to the shear contribution o the FRP system. For ully-wrapped members, ψ is equal to 0.95; while or U-wrapped and side-bonded FRP, ψ is equal to V = V + V + ψ V (119) n c s The shear contribution o the concrete and transverse steel reinorcement according to ACI can be calculated as 1 Vc = ' cbwd (SI) (120) 6 V A (sinα + cos α) d sv yv s = (121) sv where ' c = compressive cylinder strength o concrete, b w = minimum width o cross section over the eective depth, d = eective depth o cross section, A v = area o shear reinorcement, yv = yield strength o shear reinorcement, α = angle o the shear reinorcement to the longitudinal axis o the member, and s = spacing o shear reinorcement measured along the longitudinal axis. The model rom Khalia et al. (1999) was the basis or developing ACI 440.2R- 02. This design guideline estimates the shear contribution o FRP systems by calculating

96 78 the orce resulting rom the tensile stress in the FRP across an assumed 45 degree crack (Khalia et al, 1998). The FRP shear capacity provided is given by V Av e(sin β + cos β ) d = (122) s The area o FRP shear reinorcement can be computed by A = 2nt w (123) v where n = number o plies o FRP reinorcement. The eective tensile stress in the FRP at ultimate is proportional to the level o strain that can be developed at ultimate and is expressed as = ε E (124) e e The eective strain o the FRP, ε e, is governed by the ailure mode o the FRP strengthening system and by the dierent conigurations o FRP laminates. For ullywrapped members, the ollowing relationship must be satisied. ε e = ε (125) u For members bonded with FRP systems as U-wrapped or side-bonded, debonding ailure will likely govern; thereore the eective strain, ε e, is calculated by using a bond reduction actor, k v. ε = k ε 4 (126) e v u The bond reduction actor is a unction o the concrete strength, the strengthening scheme and the stiness o the FRP. The bond reduction actor can be obtained rom the ollowing expressions,

97 79 k v k1k 2Le = 11900, ε u (SI) (127) 23, 300 L e = (SI) (128) ( nt E ) k 1 2 / 3 ' c = 27 (SI) (129) d Le or U - wraps d k2 = (130) d 2L e or two sides bonded d A revision to ACI 440.2R will be published in The revision will provide strength reduction actors consistent with ACI (2005). In addition, the nominal shear capacity o an RC member strengthened with FRP is evaluated by applying Equation (119); however, the additional reduction actor, ψ, or U-wrapped and sidebonded FRP will be equal to This reduction actor is recommended based on analysis using data rom Bousselham and Chaallal (2006a), Deniaud and Cheng (2001, 2003), Funakawa et al. (1997), Matthys (2000), and Pellegrino and Modena (2002) Great Britain technical report No. 55 (2004). This report is similar to ISIS Design Manual 4 and ib Bulletin 14 in its approach and scope. From the British Standards Institution BS 8110 (1997), the nominal shear capacity o RC members strengthened with FRP systems is evaluated by adding the shear contribution o the FRP, V, to the shear contribution o concrete and transverse steel reinorcement, which can be calculated as V min 1, 2 3 c = 100 min ( 0.02, ρs ) ' c bwd γ + c d (131) Asv (0.95 yv ) d Vs = s (132) where γ c is the concrete partial coeicient. v

98 80 In addition, by assuming a 45 degree shear crack inclinations, Technical Report No. 55 (2004) expresses the FRP shear contribution to the shear capacity as n d lt,max 3 V = E ε e A (cos β + sin β ) (133) s lt,max = 0.7 E t / ct (134) = 0.18( ) 2/3 (135) ctm where n = 0 or ully-wrapped beam, 1.0 or U-wrapped coniguration, and 2.0 or sidebonded coniguration; and l t,max = anchorage length. This technical report determines the FRP eective strain to be the minimum o cu ε u / 2 ct ε e = min 0.64 E t 4 (136) The irs strain limit corresponds to the average FRP strain due to FRP racture. The second limit corresponds to FRP debonding and is based on Neubauer and Rostasy (1997) bonding mechanism approach. This strain limit should also be applied or ullywrapped conigurations in order to maintain the integrity o the concrete. The inal strain limit was proposed to also ensure the integrity o concrete AASHTO LRFD Bridge Design Speciications. Although AASHTO design speciications do not provide shear design guidelines or RC structures strengthened with FRP systems, in this thesis, these design speciications will be used in combination with the ormulations rom the analytical models or comparison purposes. From the Sectional Design Model, the nominal shear capacity o RC members is expressed as Vn = Vc + Vs (137) The shear contribution o concrete and transverse steel reinorcement can be computed as

99 81 V = β ' b d (138) c c v v V s A d (cotθ + cot α) sinα sv yv v = (139) s v where β = actor indicating the ability o diagonally cracked concrete to transmit tension, b v = eective web width, d v = distance between tensile and compressive orce resultants. The values o β and θ can be determined by using the simpliied procedure and the general procedure. The simpliied procedure states that or non-prestressed members not subjected to axial tension and containing at least the minimum amount o transverse steel reinorcement as speciied in Equation (140), or having an overall depth o less than 16.0 in., β shall be taken as 2.0 and θ as 45. A sv bv sv ' c (140) yv For other cases, the general procedure provides two tables to compute the values or β and θ or members that contain at least the minimum required amount o transverse steel reinorcement (Table 4.2) and or members that contain less than that amount (Table 4.3). To obtain values or β and θ rom Table 4.2, it is necessary to compute the shear design stress ratio (v/ c) and the longitudinal strain ε x at mid-depth. The longitudinal strain ε x may be taken as one-hal o the strain in the longitudinal steel reinorcement, ε t, as computed in Equation (141). ε x ε M u / d v N u (Vu V p )cot( θ ) A t ps po = = (141) 2 2( E A + E A ) s s p ps where M u =actored moment not less than Vud v, u N = actored axial orce, V p = component in the direction o applied shear o the eective prestressing orce, o prestressing steel on lexural tension side, and po levels, A ps = area, = 0.7 pu or usual prestressing To obtain values or β and θ i the section contains less than the minimum amount o transverse reinorcement, Table 4.3 is used. The value o the longitudinal strain at

100 82 mid-depth, ε x, is computed as given in Equation (142). The crack spacing parameter, s xe, is determined rom Equation (143). ε x ε M u / dv + 0.5Nu + 0.5( Vu Vp )cot( θ ) A t ps po = = 2 2 E A + E A s s p ps (142) 1.38 sxe = sx 80in a g (in.) (143) where a g is the maximum aggregate size in inches and s x is the lesser o either dv or the maximum distance between layers o longitudinal crack control reinorcement. I ε x is negative, then the member is uncracked and the axial stiness o the uncracked concrete needs to be considered with using Equation (144). ε x M = u / d v N u (V 2( E A + E A s s p u V ps p + A )cot( θ ) A ct E c ) ps po (144) where A ct is the area o the concrete beneath mid-depth c Table 4.2. Values o θ and β or Sections with Transverse Steel Reinorcement vu ε x 1,

101 83 Table 4.3 Values o θ and β or Sections with Less than Minimum Transverse Steel Reinorcement s xe (in.) ε x SUMMARY AND CONCLUDING REMARKS The purpose o this section was to identiy and discuss the analytical models and design guidelines that will be used or a comparative evaluation. From the review o the ourteen analytical models and seven design guidelines to predict the shear contribution o FRP, it can be concluded that the main dierence between models and guidelines lies in the dierent approaches to predict the FRP eective strain at the time o ailure. Thereore, the analytical models and design guidelines were classiied according to the approach to determine the eective FRP strain. The analytical models and guidelines were categorized into approaches based on a ixed FRP eective strain, approaches based on eective strain as a unction o FRP stiness or based on bond mechanism, and approaches based on non-uniorm strain distribution. Some models and guidelines ixed the FRP eective strain to determine the FRP shear contribution. For instance, Chajes et al. (1995) ixed the strain to be the ultimate strain at ailure corresponding to the concrete. CSA S (2002) provides ixed values o eective FRP strain according to wrapping conigurations. Empirical models are based directly on the calibration o experimental data and regression analysis to estimate the eective strain in the FRP.

102 84 From the regression analysis, relationships to determine the eective FRP strain were derived. Models based on non-uniorm strain distribution determine the speciic racture energy o the FRP/concrete interace to estimate the bond strength. When determining the eective FRP strain, most analytical models, and design guidelines treat separately the mechanisms o FRP debonding and FRP racture except or Chajes et al. (1995), Triantaillou (1998), JBDPA (1999), JSCE (2001), and CSA S (2002). Thereore, most models and design standards propose two dierent approaches that represent the two possible ailure modes. When estimating the eective FRP strain, most models and design guidelines, with the exception o Chen and Teng (2003), Cao et al. (2005), Monti and Liotta (2004), and Carolin and Taljsten (2005) determined the eective FRP strain by perorming regression analysis o experimental data. Thereore, important parameters that inluence the eective FRP strain were not taken into consideration because o the diiculty o accounting all relevant parameters in one single equation. In addition, when estimating the eective FRP strain when debonding controls, models and guidelines based on data regression, did not provide an accurate bond strength model. Thereore, it seems that the models based on racture mechanics describe more accurately the behavior o RC beams shear strengthened with externally FRP as opposed to the models and guidelines based on test data calibration because the bond strength models were developed by applying racture mechanics. Bond strength models based on racture mechanics captures all the crucial parameters relevant to the bond behavior at the FRP/concrete interace. In addition, the bond strength models that apply racture mechanics recognize the non-uniormity o the FRP stress distribution along a shear crack. Finally, all analytical models with the exception o Deniaud and Cheng (2004), do not take into consideration the interaction between the concrete, transverse steel reinorcement and FRP reinorcement. Most models add the contributions o concrete, stirrups and FRP to be consistent with the truss approach used in reinorced concrete design codes without taken into account the dependence and interaction between the concrete, stirrups and FRP sheets.

103 85 5. EVALUATION OF EXISTING ANALYTICAL MODELS 5.1. INTRODUCTION This section presents a comparative evaluation o the accuracy in predicting the FRP shear contribution, deined as V, between the analytical models discussed previously in Section Four. The analytical model developed by Khalia et al. (1998) has not been considered in the evaluation since a revised version was proposed by Khalia et al. in In addition, since this section ocuses on the evaluation o analytical models or estimating V, the model rom Deniaud and Cheng (2004) is not evaluated because this analytical model needs to determine the FRP shear contribution as a unction o the concrete and transverse steel reinorcement shear contributions Beore perorming the comparative evaluation, the entire database (reer to Table A.1 in the Appendix) was reduced to a subset o data. Only test results corresponding to large and slender beam specimens are included in the comparative evaluation. One reason or not using test results on small and non-slender members is that the ixed development lengths o dierent FRP strengthening systems is a much larger percentage o the total height o a small member. Thereore by only using test results or which the height is greater than or equal to 300 mm and or which the shear-span to depth ratio a / d was greater than or equal to 2.5, only 142 test results satisied both o these criteria. Furthermore, test results with other type o strengthening systems such as near-surace mounted (NSM) rebars and prestressed straps are omitted because these types o strengthening systems present a dierent type o behavior rom the externally applied FRP systems. Ater eliminating tests results in which lexural ailures were reported and cases in which insuicient data inormation was available, there were 127 test results let to be used in the comparative evaluation. For each analytical model, the predicted shear strength provided by the FRP system, V, theo, is compared with the observed experimental results, V,exp. The FRP shear capacity ratio, deined as V,exp, theo, is evaluated in terms o E ρ / ', a / d and 2/3 c ρ E / ρ E. Each analytical model has also been analyzed in terms o ailure modes s s and FRP wrapping schemes. Furthermore, or each analytical model, the predicted total

104 86 shear capacity, V theo, is compared with the observed experimental results, V exp. The predictions o total shear capacities are computed as Vn = Vc + Vs + V, theo, where V c and V s are computed by applying our RC design codes. These design codes are the ACI (2005), Eurocode 2 Part I (2003), CSA A (1994), and AASHTO LRFD Bridge Design Speciications (1998). As a result, the evaluation or each analytical model yields to ourteen plots or each analytical model. In this section, only the plots corresponding to Chajes et al. (1995) are presented. The plots corresponding to the remaining analytical models are presented in Appendix B. Instead, in this section the mean values and coeicient o variation (COV) values o V,exp, theo and V / exp V theo are presented in Tables 5.1 through 5.6. These tables also provide statistical results or each mode o ailure. Table 5.1. Comparison o Predictions and Test Results or FRP Capacities ( V,exp, theo ) Analytical Model All Debonding Fracture Other Shear Failure Modes Mean COV Mean COV Mean COV Mean COV Chajes et al. (1995) Triantaillou (1998) Khalia et al. (1999) Triantaillou and Antonopoulos (2000) Pellegrino and Modena (2002) Chaallal et al. (2002) Hsu et al. (2003) Chen and Teng (2003) Monti and Liotta (2005) Cao et al. (2005) Zhang and Hsu (2005) Carolin and Taljsten (2005)

105 87 Table 5.2. Comparison o Predictions and Test Results or Shear Capacities ( V exp theo ) Analytical Model ACI Eurocode 2 CSA A AASHTO LRFD Mean COV Mean COV Mean COV Mean COV Chajes et al. (1995) Triantaillou (1998) Khalia et al. (1999) Triantaillou and Antonopoulos (2000) Pellegrino and Modena (2002) Chaallal et al. (2002) Hsu et al. (2003) Chen and Teng (2003) Monti and Liotta (2005) Cao et al. (2005) Zhang and Hsu (2005) Carolin and Taljsten (2005) Table 5.3. Comparison o Predictions and Test Results or Shear Capacities ( V exp theo ) by ACI Analytical Model Debonding Fracture Other Shear Failure Modes Mean COV Mean COV Mean COV Chajes et al. (1995) Triantaillou (1998) Khalia et al. (1999) Triantaillou and Antonopoulos (2000) Pellegrino and Modena (2002) Chaallal et al. (2002) Hsu et al. (2003) Chen and Teng (2003) Monti and Liotta (2005) Cao et al. (2005) Zhang and Hsu (2005) Carolin and Taljsten (2005)

106 88 Table 5.4. Comparison o Predictions and Test Results or Shear Capacities ( V exp theo ) by Eurocode 2 Analytical Model Debonding Fracture Other Shear Failure Modes Mean COV Mean COV Mean COV Chajes et al. (1995) Triantaillou (1998) Khalia et al. (1999) Triantaillou and Antonopoulos (2000) Pellegrino and Modena (2002) Chaallal et al. (2002) Hsu et al. (2003) Chen and Teng (2003) Monti and Liotta (2005) Cao et al. (2005) Zhang and Hsu (2005) Carolin and Taljsten (2005) Table 5.5. Comparison o Predictions and Test Results or Shear Capacities ( V exp theo ) by CSA A Analytical Model Debonding Fracture Other Shear Failure Modes Mean COV Mean COV Mean COV Chajes et al. (1995) Triantaillou (1998) Khalia et al. (1999) Triantaillou and Antonopoulos (2000) Pellegrino and Modena (2002) Chaallal et al. (2002) Hsu et al. (2003) Chen and Teng (2003) Monti and Liotta (2005) Cao et al. (2005) Zhang and Hsu (2005) Carolin and Taljsten (2005)

107 89 Table 5.6. Comparison o Predictions and Test Results or Shear Capacities ( V exp theo ) by AASHTO LRFD Analytical Model Debonding Fracture Other Shear Failure Modes Mean COV Mean COV Mean COV Chajes et al. (1995) Triantaillou (1998) Khalia et al. (1999) Triantaillou and Antonopoulos (2000) Pellegrino and Modena (2002) Chaallal et al. (2002) Hsu et al. (2003) Chen and Teng (2003) Monti and Liotta (2005) Cao et al. (2005) Zhang and Hsu (2005) Carolin and Taljsten (2005) COMPARATIVE EVALUATION Chajes et al. (1995). Figures 5.1 through 5.3 illustrate the variation o the FRP shear capacity ratio in terms o E ρ / ' or dierent ailure modes and 2/3 c wrapping conigurations. From Figure 5.1, the decreasing trendline indicates that i the values o E ρ / ' are smaller than 0.019, this analytical model underestimates the 2/3 c prediction o the FRP shear contribution and overestimates the FRP shear contribution when the values o E ρ / ' are greater than From Figure 5.2, it can also be 2/3 c concluded that this analytical model greatly underestimates the FRP shear contribution or lower values o E ρ / ' 2/3 c. In addition, Figures 5.1 and 5.2 also indicate that this analytical model tends to greatly underestimate the predictions or the FRP shear contribution or specimens that ailed due to FRP racture in comparison to those that ailed due to FRP debonding or other shear ailure modes.

108 w/ anchor 6.00 V,exp,theo ρ E / ' c 2/3 Figure 5.1. V,exp, theo in Terms o E ρ / ' - FRP Debonding 2/3 c Total Wrap 6.00 V,exp,theo ρ E / ' c 2/3 Figure 5.2. V,exp, theo in Terms o E ρ / ' - FRP Fracture 2/3 c

109 w/ anchor Total Wrap 6.00 V,exp,theo ρ E / ' c 2/3 Figure 5.3. V,exp, theo in Terms o E ρ / ' - Other Failure Modes 2/3 c Figures 5.4 through 5.6 illustrate the predictions o FRP shear capacity in terms o a / d or dierent ailure modes. From Figure 5.4, the FRP shear capacity ratio increases up to a / d around Aterwards, the FRP shear capacity ratio decreases up to a shear span-to-depth ratio o The same trendline is observed or specimens ailing in racture as shown in Figure 5.5. Thereore, it seems that or specimens with a / d less than about 3.0, this analytical model underestimates the FRP shear contribution, and overestimates it or a / d larger than 3.0. Figures 5.7 through 5.9 illustrate the predictions o FRP shear capacity in terms o the amount o transverse steel reinorcement or dierent ailure modes. From Figure 5.7, it can be observed that when the amount o transverse steel reinorcement increases, the shear capacity ratio o FRP increases up to 2.67 and decreases aterwards. The same trend is exhibited or those specimens that ailed due to FRP racture. Thereore, this analytical model underestimates the FRP shear contribution when the amount o transverse steel reinorcement increases.

110 w/ anchor 6.00 V,exp,theo a/d Figure 5.4. V,exp, theo in Terms o a / d FRP Debonding Total Wrap 6.00 V,exp,theo a/d Figure 5.5. V,exp, theo in Terms o a / d FRP Fracture

111 w/ anchor Total Wrap 6.00 V,exp,theo a/d Figure 5.6. V,exp, theo in Terms o a / d Other Failure Modes w/ anchor 2.50 V,exp,theo ρ s E s / ρ E Figure 5.7. V,exp, theo in Terms o ρses / ρ E FRP Debonding

112 Total Wrap V,exp,theo ρ s E s / ρ E Figure 5.8. V,exp, theo in Terms o ρses / ρ E FRP Fracture V,exp,theo ρ s E s / ρ E Figure 5.9. V,exp, theo in Terms o ρses / ρ E Other Failure Modes

113 95 From the previous analysis, it can be concluded that the analytical approach proposed by Chajes et al. (1995) cannot accurately predict the shear capacity o FRP. This could be attributed to the act that Chajes et al. (1995) applies a constant ultimate tensile strain, corresponding to the concrete ultimate strain, to calculate the shear capacity o FRP. However, as veriied rom later studies (Triantaillou, 1998), the ultimate tensile strain o FRP at ailure, deined as the eective strain o FRP, decreases as the axial rigidity o FRP, ρ E increases. In addition, the ormulations rom this model can only be applied to continuous FRP sheets. The analysis shows that this model predicts more accurately the FRP shear contribution or those specimens that ailed in racture (COV o 69%) than those that ailed in debonding (COV o 82 %). However, this model tends to underestimate the FRP shear contribution by more than twice the experimental FRP shear contribution or most test specimens ailing in racture. The inaccuracy in predicting the FRP shear contribution by this analytical model, with a COV o 116%, is also shown in Figure Debonding Fracture Other V,theo (kn) V,exp Figure Comparison between Analytical Predictions o FRP Shear Contribution and Experimental Results

114 96 Finally, the comparison between the predicted total shear capacity by applying our dierent shear design methodologies and the observed experimental results are illustrated in Figure From this analysis, Eurocode 2 exhibits a lower COV o 40% with a mean value o Thereore the shear design provisions rom Eurocode 2 predict the total shear capacity more accurately than the other design methodologies. For specimens that ailed due to FRP racture and FRP debonding, Eurocode 2 also provides lower COV values than the other design codes Debonding Fracture Other Debonding Fracture Other V th e o (k N ) V th e o (k N ) V exp (kn) V exp (kn) (a) ACI (b) Eurocode Debonding Fracture Other Debonding Fracture Other V th e o (k N ) V th e o (k N ) V exp (kn) (c) CSA A V exp (kn) (d) AASHTO LRFD Figure Comparison between Analytical Predictions o Total Shear Capacity and Experimental Results

115 Triantaillou (1998). From the analysis o this analytical model (reer to graphs in Appendix B), the analytical model proposed by Triantaillou (1998) predicted the shear capacity o FRP more accurately than the one rom Chajes et al. (1995) since it was the irst model to determine that the eective strain o the FRP is a unction o its axial rigidity. By analyzing the prediction o the FRP shear strength versus E ρ /( ), ' 2/3 c it was ound that as in Chajes et al. (1995) model, this approach overestimates the FRP shear capacity as E ρ /( ) increases. Furthermore, this analytical model predicts the ' 2/3 c shear capacity o FRP slightly more accurately or specimens that ailed due to FRP racture (COV o 56%) in comparison to those that ailed due to FRP debonding (COV o 59 %). However, or debonding and other ailure modes, most o the predictions have been overestimated. In addition, by analyzing the FRP shear strength ratio versus the shear span-todepth ratio, this analytical model seems to highly underestimate the FRP shear contribution or those specimens that ailed due to FRP racture. On the other hand, or those specimens that ailed due to debonding, this analytical model overestimates the FRP shear contribution. Furthermore, rom the analysis, it can be observed that the FRP shear capacity ratio increases up to a / d = 3.0 and decreases aterwards. Finally, rom analysis o the FRP shear strength ratio versus the eect o transverse steel reinorcement on the FRP shear contribution, it was observed that when the amount o transverse steel reinorcement increases, the shear capacity ratio o FRP increases. The same trend is exhibited or those specimens that ailed in racture and other shear ailure modes. From the analysis, this model predicts the FRP shear capacity more accurately in comparison to Chajes et al. (1995) model because this approach predicts a varying FRP strain. However, this model seems to predict the FRP shear contribution slightly more accurately or specimens that ailed due to racture ailure than or those that ailed due to debonding or other shear ailures. This could be attributed to the act that this analytical model derived an expression to compute the eective strain o the FRP without considering the dierent ailure mechanisms. As a result, it seems the eective strain o the FRP plays an important role in determining the accuracy o the predictions. In addition, this analytical model provides a COV o 77%, which indicates that this model

116 98 predicts the shear capacity due to the FRP more accurate than the model rom Chajes et al. (1995). Finally, rom the comparison between the predicted total shear capacity by applying our dierent design methodologies and the observed experimental results, it can be concluded that both Eurocode 2 and CSA A exhibit a lower COV value o 34%. Thereore the predictions o total shear capacity rom Eurocode 2 and CSA A are more accurate than those rom other design methodologies when using the analytical model rom Triantaillou (1998). For specimens that ailed due to FRP racture, Eurocode 2 design provisions provides less conservative values o V / exp V theo in comparison to other design methodologies. In addition, or specimens that ailed due to FRP racture and FRP debonding, Eurocode 2 provides lower COV values Khalia et al. (1999). From the analysis o this analytical model (reer to graphs in Appendix B), the analytical model proposed by Khalia et al. (1999) underestimates the FRP shear capacity or lower values o E ρ /( ) and ' 2/3 c overestimates it or higher values o E ρ /( ) ' 2/3 c. The predictions o the FRP shear capacity by this model are more conservative or racture ailure (mean value o FRP shear contribution o 2.65) than or debonding (mean value o 1.22) and other shear ailures. In contrast to the previously discussed analytical models, this model seems to provide better predictions or specimens that ailed in debonding (COV o 49%) probably because the ormulation applied to predict the eective FRP strain dominant to racture ailures cannot be applied or higher FRP axial rigidities. In addition, by analyzing the FRP shear strength ratio versus the shear span-todepth ratio, or specimens that ailed due to racture ailure, this model highly underestimates the FRP shear contribution or test specimens with a shear span-to-depth ratio o 3.0. However, or debonding ailure, this model overestimates the FRP shear capacity or most test specimens. Furthermore, this model is more conservative in predicting the FRP shear capacity o specimens that ailed due to FRP racture. From this analysis, it can also be observed that the FRP shear capacity ratio increases up to a / d = 3.0 and decreases aterwards. Finally, rom analysis o the FRP shear strength ratio versus the eect o transverse steel reinorcement on the FRP shear contribution, it was

117 99 observed that the FRP shear capacity ratio increases as the amount o transverse steel reinorcement increases or specimens that ailed due to FRP debonding. This increasing trendline is also present or specimens that ailed due to FRP racture. From the previous analysis, it can be concluded that the analytical model rom Khalia et al. (1999) provides a COV o 78%, thus, this analytical model does not accurately predict the FRP shear capacity in contrast to Triantaillou (1998). However, this is the irst analytical model that proposes two dierent expressions to compute the eective strain o the FRP by taking into consideration the FRP ailure mechanisms. In addition, this analytical model gives better prediction or debonding (COV o 49%) because inluential parameters to the bond behavior o the FRP/concrete interace are taken into consideration. Finally, rom the comparison between the predicted total shear capacity by applying our dierent design methodologies and the observed experimental results, it can be concluded that Eurocode 2 exhibits a lower COV value o 24%. Thereore the predictions o total shear capacity rom Eurocode 2 are more accurate than those rom other design methodologies when using the analytical model rom Khalia et al. (1999). For specimens that ailed due to FRP racture, Eurocode 2 design provisions provides less conservative values o V / exp V theo in comparison to other design methodologies. In addition Eurocode 2 provides a lower value o COV or specimens that ailed due to FRP racture; however, it exhibits a higher value o COV or specimens that ailed due to FRP debonding Triantaillou and Antonopoulos (2000). This analytical model is a revision o its earlier version (Triantaillou, 1998). This later version considered the types o FRP, the strengthening scheme o FRP, and the eect o the concrete compressive strength in the ormulation o the eective FRP strain. From the analysis o this approach (reer to graphs in Appendix B), this model underestimates the FRP shear capacity or lower values o E ρ /( ) and overestimates it or higher values o ' 2/3 c E ρ /( ) ' 2/3 c. Moreover, this model provides better predictions o FRP shear contribution or specimens that ailed due to FRP racture (COV o 39%) than or those than ailed due to debonding (COV o 53%) or other shear ailures modes. This could be

118 100 attributed to the act that this model does not make a clear distinction between sidebonded FRP systems and U-shaped FRP jackets when estimating the eective FRP strain. Furthermore, by analyzing the FRP shear strength ratio versus the shear span-todepth ratio, this model tends to overestimate the FRP shear capacity or most data specimens ailing due to FRP debonding. On the other hand, or racture ailure, this model underestimates the FRP shear capacity or most test specimens. In addition, rom this analysis, it can be observed that the FRP shear capacity ratio increases up to a / d = 3.0, and decreases aterwards. Finally, rom the analysis o the FRP shear strength ratio versus the eect o transverse steel reinorcement on the FRP shear contribution, it was observed that or debonding ailure, this model underestimates the FRP shear capacity as the amount o transverse steel reinorcement increases. For racture ailure, this model overestimates the FRP shear capacity as the amount o transverse steel reinorcement increases. This analytical model also makes better predictions or specimens than ailed due to FRP racture. From the previous analysis, the analytical model rom Triantaillou and Antonopoulos (2000) provides a lower COV (50 %) than its earlier version. Thereore, this analytical model predicts the FRP shear contribution more accurately than the older version developed by Triantaillou (1998) and the previously discussed models. This could be explained by the act that this model considers separately the dierent FRP ailure mechanisms when estimating the eective FRP strain as opposed to its earlier version. Finally, rom the comparison between the predicted total shear capacity by applying our dierent design methodologies and the observed experimental results, it can be concluded that Eurocode 2 exhibits a lower COV value o 27%. Thereore the predictions o total shear capacity rom Eurocode 2 are more accurate than those rom other design methodologies when using the analytical model rom Triantaillou and Antonopoulos (2000). By applying AASHTO LRFD in combination with this analytical model, more conservative values or V / exp Vtheo are obtained. In addition, or specimens that ailed due to FRP racture and FRP debonding, Eurocode 2 design provisions

119 101 provides less conservative values o V / exp V theo in comparison to those rom other design methodologies Pellegrino and Modena (2002). The analytical model proposed by Pellegrino and Modena slightly modiied the approach proposed by Khalia et al. (1999) by introducing an additional strain reduction actor, * R, which accounts or the correlation between the internal steel reinorcement and external FRP reinorcement. From the analysis between the FRP shear capacity ratio and E ρ /( ) (reer to ' 2/3 c graphs on Appendix B), it can be observed that or all ailure modes, this model underestimates the FRP shear capacity or higher values o E ρ /( ) and ' 2/3 c overestimates the FRP shear capacity or lower values o E ρ /( ) ' 2/3 c. The predictions o the FRP shear capacity by this model are more conservative or racture ailure V V o 2.94) than or debonding ( V,exp, theo o 1.28) and other shear ailures (,exp /, theo modes. Furthermore, by analyzing the FRP shear capacity ratio in terms o the shear spanto-depth ratio, it can be concluded that or specimens that ailed due to FRP debonding, this model tends to overestimate the FRP shear capacity or most data specimens. On the other hand, or those specimens that ailed due to FRP racture, this model tends to highly underestimate the FRP shear capacity or most test specimens. From this analysis, it can also be observed that the FRP shear capacity ratio increases up to a shear span to-depth ratio o about 3.0, and decreases aterwards. Finally, rom the analysis o the FRP shear capacity ratio in terms o the amount o transverse steel reinorcement, it can be observed that the FRP shear contribution predicted by this model decreases as the amount o transverse steel reinorcement increases or specimens ailing due to FRP racture and FRP debonding. From analysis, this analytical model provides a COV o 87%, thus, in comparison to the previously discussed models, except Chajes et al. (1995) model, this approach does not accurately predict the FRP shear contribution. This model predicts very conservative values o FRP shear capacity ratios or specimens that ailed due to FRP racture. This could be attributed to the act that the strain reduction actor, * R, was developed based on test results o specimens strengthened with side bonded FRP, which ailed due to FRP

120 102 debonding. Thereore, this additional reduction actor needs to be improved by perorming additional experimental studies. Finally, rom the comparison between the predicted total shear capacity by applying our dierent design methodologies and the observed experimental results, it can be concluded that Eurocode 2 exhibits a lower COV value o 29%. Thereore the predictions o total shear capacity rom Eurocode 2 are more accurate than those rom other design methodologies when using the analytical model rom Pellegrino and Modena (2002). By applying AASHTO LRFD in combination with this analytical model, more conservative values or V / exp V theo and higher COV values are obtained. In addition, or specimens that ailed due to FRP racture and FRP debonding, Eurocode 2 design provisions provides less conservative values o V / exp V theo in comparison to those rom other design methodologies Chaallal et al. (2002). This analytical model was developed based on the experimental results o large scale specimens under a low shear span condition. As a consequence, Chaallal et al. proposed that a deep beam coeicient, ( a / d ), should be included in the expression to determine the FRP shear contribution. By analyzing the FRP shear capacity ratio in terms o E ρ /( ) (reer to graphs in Appendix B), it can ' 2/3 c be concluded that this analytical model does not accurately predict the shear contribution o FRP or most data points. As in the previously discussed models, this analytical model under predicts the FRP shear contribution or low values o E ρ /( ) ' 2/3 c, and over predicts the FRP shear capacity or higher values o E ρ /( ). ' 2/3 c Furthermore, rom the analysis o the FRP shear capacity ratio versus the shear span-to-depth ratio, it can be observed that the FRP shear contribution, predicted by Chaallal et al. (2002), increases as the shear span-to-depth ratio increases or all ailure modes. Finally, by analyzing the FRP shear capacity ratio in terms o the amount o transverse steel reinorcement, it can be observed that the FRP shear contribution predicted by this model decreases as the amount o transverse steel reinorcement increases or specimens ailing due to FRP racture and FRP debonding. From the previous analysis, this analytical model provides a COV o 88%, thus this analytical model inaccurately predicts the FRP shear contribution. This model seems

121 103 to make slightly better predictions or specimens that ailed in racture (COV o 41%) than those that ailed in debonding (COV o 116%). This inaccuracy in the FRP shear prediction could be attributed to the act that this analytical model was developed based on the results o the experimental results o large scale specimens under a low shear span condition. Thereore, the ormulations or predicting the FRP contribution were derived by analyzing the inluence o a deep beam coeicient. When calibrating the ormulations to compute both the eective FRP strain and the deep beam coeicient, only data points rom this experimental study were used, thus more research work is needed to validate these ormulations. Finally, rom the comparison between the predicted total shear capacity by applying our dierent design methodologies and the observed experimental results, it can be concluded that Eurocode 2 provides a lower COV value o 33% and a lower mean value o Thereore the predictions o total shear capacity rom Eurocode 2 are more accurate than those rom other design methodologies when using the analytical model rom Chaallal et al. (2002). By applying AASHTO LRFD in combination with this analytical model, more conservative values or V / exp V theo and higher COV values are obtained. In addition, or specimens that ailed due to FRP racture and FRP debonding, Eurocode 2 design provisions provides less conservative values o V / exp V theo in comparison to those rom other design methodologies Hsu et al. (2003). From the analysis o this approach (reer to graphs in Appendix B), this analytical model accurately predicts the FRP shear contribution in comparison to the experimental observations (COV o 55%). By analyzing the FRP shear capacity ratio in terms o E ρ /( ) ' 2/3 c, it can be observed that, in contrast to the previously discussed models, this approach does not exhibit a clear trendline between the FRP shear capacity ratio and E ρ /( ) with the exception o specimens strengthened ' 2/3 c with FRP reinorcement to the sides. The reason behind this may be attributed to the act that the ormulations to compute the FRP shear contribution, were derived rom test specimens that ailed due to FRP debonding. Moreover, the debonding o FRP seems to occur randomly (COV o 54%). The racture o FRP also occurs randomly; however, the

122 104 data points are slightly less scatter than the ones corresponding to debonding ailure (COV o 44%). By analyzing the FRP shear capacity ratio in terms o the shear span-to-depth ratio, it can be observed that the FRP shear capacity ratio decreases, as the shear span-todepth ratio increases only or those specimens side bonded with FRP and ailing in debonding. For specimens ailing due to FRP racture, no clear trendline can be observed between the FRP shear capacity ratio and the shear span-to-depth ratio. Finally, rom the analysis between the FRP shear capacity ratio and the amount o transverse steel reinorcement, it can be observed that, in contrast to the previously discussed models, the FRP shear capacity ratio decreases as the amount o steel stirrups increases. From the previous analysis, the predictions o the FRP shear contribution by this analytical model are in better agreement to the experimental observations in comparison to the previous models with the exception o the model developed by Triantaillou and Antonopoulos (2000). In act this analytical model provides a COV o 55% or all ailure modes. For debonding and racture ailure, a COV o 54% and 44% respectively are observed rom the analysis. For this reason, this model makes more accurate predictions or those specimens that ailed due to FRP racture. Finally, rom the comparison between the predicted total shear capacity by applying our dierent design methodologies and the observed experimental results, it can be concluded that Eurocode 2 provides a lower COV value o 28% and a lower mean value o Thereore the predictions o total shear capacity rom Eurocode 2 are more accurate than those rom other design methodologies when using the analytical model rom Hsu et al. (2003). By applying AASHTO LRFD in combination with this analytical model, more conservative values or V / exp V theo and higher COV values are obtained. In addition, or specimens that ailed due to FRP racture and FRP debonding, Eurocode 2 design provisions provides less conservative values o V / exp V theo in comparison to those rom other design methodologies. Finally, in contrast to the previously discussed analytical models, the application o all our design codes with this analytical model provide conservative values o V / exp V theo or specimens ailing in debonding.

123 Chen and Teng (2003). From the analysis o this approach (reer to graphs in Appendix B), this analytical model accurately predicts the FRP shear contribution in comparison to the experimental observations (COV o 47%). By analyzing the FRP shear capacity ratio in terms o E ρ /( ) ' 2/3 c, it can be observed that as in previous models, the FRP shear capacity ratio exhibits a decreasing trend as E ρ /( ) ' 2/3 c increases. In addition, this analytical model underestimates the FRP shear capacity ratio or low values o E ρ /( ) ' 2/3 c, and overestimates the FRP shear contribution or high values o E ρ /( ) ' 2/3 c. This analytical model approach provides better predictions or the FRP shear contribution or both debonding and racture ailures. Furthermore, rom the analysis o the FRP shear capacity ratio versus the shear span-to-depth ratio, it can be observed that the FRP shear contribution, predicted by Chen and Teng (2003) increases as the shear span-to-depth ratio increases or all ailure modes. In addition, rom this analysis, it can be observed that the FRP shear capacity ratio increases up to a / d = 3.0, and decreases aterwards. Finally, by analyzing the FRP shear capacity ratio in terms o the amount o transverse steel reinorcement, it can be observed that the FRP shear contribution predicted by this model decreases as the amount o transverse steel reinorcement increases or specimens ailing due to FRP racture and FRP debonding. From the previous analysis, the predictions o the FRP shear contribution by this analytical model are in better agreement to the experimental observations in comparison to the previous models. In act this analytical model provides a COV o 47% or all ailure modes. For debonding and racture ailure, a COV o 46% and 48% respectively are observed rom the analysis. For this reason, this model makes accurate predictions or specimens ailing due to FRP debonding and FRP racture. Finally, rom the comparison between the predicted total shear capacity by applying our dierent design methodologies and the observed experimental results, it can be concluded that Eurocode 2 provides a lower COV value o 25% and a lower mean value o Thereore the predictions o total shear capacity rom Eurocode 2 are more accurate than those rom other design methodologies when using the analytical model rom Chen and Teng (2003). By applying AASHTO LRFD in combination with this

124 106 analytical model, more conservative values or V / exp V theo and higher COV values are obtained. In addition, or specimens that ailed due to FRP racture and FRP debonding, Eurocode 2 design provisions provides less conservative values o V / exp V theo in comparison to those rom other design methodologies. Finally, as in Hsu et al (2003) approach, the application o all our design codes with Chen and Teng (2003) model provide conservative values o V / exp V theo or specimens ailing in debonding Monti and Liotta (2005). From the analysis between the FRP shear capacity ratio and E ρ /( ) (reer to graphs on Appendix B), it can be observed that ' 2/3 c the analytical model proposed by Monti and Liotta does not accurately predict the shear capacity o FRP. As in previous models, this analytical model underestimates the FRP shear capacity ratio or low values o E ρ /( ) ' 2/3 c, and overestimates the FRP shear contribution or high values o E ρ /( ) ' 2/3 c. In addition, the debonding o FRP seems to occur randomly or most test specimens (COV o 67%). FRP racture also seems to occur randomly (COV o 50%); however, the data points are less scattered than the ones corresponding to debonding ailure. Thereore, this model tends to underestimate the FRP shear contribution or specimens that ailed due to FRP racture. Furthermore, by analyzing the FRP shear capacity ratio in terms o the shear spanto-depth ratio, it can be concluded that or specimens that ailed due to FRP debonding and FRP racture, the FRP shear capacity ratio increases up to a / d = 3.0, and then decreases up to Finally, rom the analysis o the FRP shear capacity ratio in terms o the amount o transverse steel reinorcement, it can be observed that or specimens that ailed due to FRP debonding, the FRP shear capacity ratio increases as the amount o transverse steel reinorcement increases. The same trendline is observed or specimens that ailed due to FRP racture. From the analysis, the analytical model by Monti and Liotta (2005) cannot accurately predict the FRP shear contribution in comparison to the previously discussed approaches. This analytical approach provides a COV o 71%. In addition, this model provides conservative values o FRP shear capacity ratio or specimens that ailed due to FRP racture.

125 107 This model makes better predictions or specimens that ailed due to FRP racture (COV o 50%), than those that ailed due to FRP debonding (COV o 67%). This may be explained by the act that this model assumes a value o 0.2mm or the interace slip corresponding to ull debonding. Finally, rom the comparison between the predicted total shear capacity by applying our dierent design methodologies and the observed experimental results, it can be concluded that Eurocode 2 provides a lower COV value o 31% and a lower mean value o Thereore the predictions o total shear capacity rom Eurocode 2 are more accurate than those rom other design methodologies when using the analytical model rom Monti and Liotta (2005). By applying AASHTO LRFD in combination with this analytical model, a higher mean value o V / exp V theo and higher COV values are obtained. In addition, or specimens that ailed due to FRP racture and FRP debonding, Eurocode 2 provides more accurate predictions o total shear capacity in comparison to other design codes. Finally, the application o all our design codes with Monti and Liotta (2005) model provide conservative values o V / exp V theo or specimens ailing due to FRP racture Cao et al. (2005). From the analysis o the FRP shear capacity ratio in terms o E ρ /( ) ' 2/3 c, it can be observed that the analytical model proposed by Cao et al. does not accurately predict the shear contribution o FRP. This analytical model predicts the FRP shear contribution more accurately or specimens that ailed due to FRP racture (COV o 45%) than those that ailed due to FRP debonding (COV o 58%). As in the previously discussed approaches, the FRP shear capacity ratio exhibits a decreasing trend as E ρ /( ) increases. Thereore, this model underestimates the FRP shear capacity ' 2/3 c or low values o or high values o E ρ /( ) and overestimates the predictions o FRP shear capacity ' 2/3 c E ρ /( ). ' 2/3 c Furthermore, by analyzing the FRP shear capacity ratio in terms o the shear spanto-depth ratio, it can be observed that or specimens that ailed due to FRP debonding, the FRP shear capacity ratio decreases as the shear span-to-depth ratio increases. In addition, this model overestimates the FRP shear contribution or most test specimens. For

126 108 specimens ailing due to FRP racture, no clear trend could be observed between the FRP shear capacity ratio and the shear span-to-depth ratio. Finally, rom the analysis between the FRP shear capacity ratio and the amount o transverse steel reinorcement, it can be observed that or specimens ailing in debonding, the FRP shear capacity increases as the amount o transverse steel reinorcement increases. For specimens ailing due to FRP racture, no clear trend could be observed between the FRP shear capacity ratio and the transverse steel reinorcement. From the previous analysis, the analytical model by Cao et al. (2005) cannot accurately predict the FRP shear capacity in comparison to the experimental observations. This approach provides a COV o 66%; however this model makes better predictions or racture ailure (COV o 45%), than or debonding ailure (COV o 58%). In addition, this model provides conservative values o FRP shear capacity ratio or specimens that ailed due to FRP racture. Finally, rom the comparison between the predicted total shear capacity by applying our dierent design methodologies and the observed experimental results, it can be concluded that both Eurocode 2 and CSA A provide a lower COV value o 29%. However, CSA A provides a mean value o 0.99; thereore, the predictions o the total shear capacity by this design code are more accurate in comparison to the other design codes. By applying AASHTO LRFD in combination with this analytical model, a higher mean value o V / exp V theo and higher COV values are obtained. In addition, or specimens that ailed due to FRP debonding, ACI provides more accurate predictions o total shear capacity; however, both Eurocode 2 and CSA A provide lower COV values. For specimens ailing in racture, Eurocode 2 provides more accurate predictions o total shear capacity and a lower COV value. As in the previous analytical models, Cao et al. (2005) approach provides conservative values o V / exp V theo or specimens ailing due to FRP racture Zhang and Hsu (2005). This analytical model is an updated version o Hsu et al. (2003) model. The only modiication was in the approach to predict the shear contribution o FRP or continuous sheets. This analytical model does not accurately predict the FRP shear contribution in comparison to its previous version (COV o 65%).

127 109 From the analysis between the FRP shear capacity ratio E ρ /( ) ' 2/3 c, it can be observed that this analytical model underestimates the FRP shear contribution or most test specimens ailing due to FRP debonding or FRP racture. As in its earlier version, or specimens ailing in debonding, no clear trendline between the FRP shear capacity ratio and E ρ /( ) can be observed. However, or specimens that ailed due to FRP, the ' 2/3 c FRP shear capacity ratio increases as E ρ /( ) increases. This increasing trendline ' 2/3 c is the opposite o the behavior observed in the previous analytical models. Moreover, the debonding o FRP seems to occur randomly (COV o 65%); however this model seems to predict more accurately the FRP shear contribution or those specimens that ailed due to FRP racture (COV o 49%). In addition, by analyzing the FRP shear capacity ratio and the shear span-to-depth ratio, it can be observed that the FRP shear capacity ratio decreases as the shear span-todepth ratio increases or specimens that ailed due to FRP debonding and FRP racture. Finally, in contrast to previously discussed models, which exhibit an increasing trend between the FRP shear capacity ratio and the amount o transverse steel reinorcement, this analytical model exhibits a decreasing trendline. Furthermore, this analytical model predicts high conservative values o FRP shear capacity ratios or most test specimens that ailed in debonding and racture. From the previous analysis, it can be concluded that the analytical model by Zhang and Hsu (2005) cannot accurately predict the FRP shear capacity in comparison to the older version rom Hsu et al. (2003). In act, this analytical model underestimates the FRP shear contribution or most data specimens. This analytical approach provides a COV o 65%; however this model makes better predictions or specimens that ailed due to racture ailure (COV o 49%), than those that ailed due to FRP debonding (COV o 65%). Finally, rom the comparison between the predicted total shear capacity by applying our dierent design methodologies and the observed experimental results, it can be concluded that Eurocode 2 provides a lower COV value o 29% and a lower mean value o Thereore the predictions o total shear capacity rom Eurocode 2 are more accurate than those rom other design methodologies when using the analytical model

128 110 rom Zhang and Hsu (2005). By applying AASHTO LRFD in combination with this analytical model, a higher mean value o V / exp V theo and higher COV values are obtained. In addition, or specimens that ailed due to FRP racture and FRP debonding, Eurocode 2 provides more accurate predictions o total shear capacity in comparison to other design codes Carolin and Taljsten (2005). By comparing the predictions o the total shear capacity by this model to the observed experimental result, it can be concluded that this analytical model does not accurately predict the shear capacity o FRP (COV o 77%). As in previous models, this analytical model underestimates the FRP shear capacity ratio or low values o E ρ /( ) ' 2/3 c, and overestimates the FRP shear contribution or high values o E ρ /( ) ' 2/3 c. In addition, the debonding o FRP seems to occur randomly or most test specimens (COV o 75%). FRP racture also seems to occur randomly (COV o 47%); however, the data points are less scattered than the ones corresponding to debonding ailure. Thereore, this model tends to underestimate the FRP shear contribution or most specimens that ailed due to FRP racture. From the analysis o the FRP shear capacity ratio in terms o the shear span-todepth ratio, it can be observed that the FRP shear capacity ratio increases as the shear span-to-depth ratio increases up to 3.0, and decreases aterwards. In addition, this model tends to provide conservative values o FRP shear capacity ratio or those specimens that ailed due to FRP racture. Finally, by evaluating the FRP shear capacity ratio in terms o the amount o transverse steel reinorcement, the FRP shear capacity ratio increases as the amount o transverse steel reinorcement increases or specimens that ailed due to FRP debonding. The same trendline is observed or specimens that ailed due to FRP racture. From the analysis, the analytical model by Carolin and Taljsten (2005) cannot accurately predict the FRP shear contribution in comparison to the previously discussed approaches. This analytical approach provides a COV o 77%. This model makes better predictions or specimens that ailed due to FRP racture (COV o 47%), than those that ailed due to FRP debonding (COV o 75%). In addition, this analytical model underestimates the FRP shear contribution or most specimens that ailed due to FRP

129 111 racture, and overestimates the FRP shear contribution or most specimens ailing in debonding. Finally, rom the comparison between the predicted total shear capacity by applying our dierent design methodologies and the observed experimental results, it can be concluded that Eurocode 2 provides a lower COV value o 32% and a lower mean value o Thereore the predictions o total shear capacity rom Eurocode 2 are more accurate than those rom other design methodologies when using the analytical model rom Carolin and Taljsten (2005). By applying AASHTO LRFD in combination with this analytical model, a higher mean value o V / exp V theo and higher COV values are obtained. In addition, or specimens that ailed due to FRP racture and FRP debonding, Eurocode 2 provides more accurate predictions o total shear capacity in comparison to other design codes. Finally, the application o all our design codes with Carolin and Taljsten (2005) model provide conservative values o V / exp V theo or specimens ailing due to FRP racture SUMMARY AND CONCLUDING REMARKS The purpose o this section was to present a comparative evaluation o the accuracy in predicting the FRP shear contribution between twelve analytical models previously discussed in the literature. For each analytical model, the predicted shear strength o FRP V, theo was compared with experimental results, V,exp, rom the database. In addition, the FRP shear capacity ratio, deined as V,exp, theo, or each analytical model was evaluated in terms o some parameters that aect shear behavior, such as the FRP axial rigidity and concrete compressive strength, the shear span-to-depth ratio, and the interaction between transverse steel reinorcement and FRP. Each analytical model was urther evaluated and analyzed in terms o ailure modes and FRP wrapping schemes. Finally, or each analytical model, the predicted total shear capacity, V theo compared with the observed experimental results, V exp, rom the shear database. The, was predictions o total shear capacities were computed by applying each analytical model in combination with our building codes.

130 112 The mean values and coeicient o variation (COV) values o V,exp, theo and V / exp V theo or all analytical models are presented in Tables 5.1 through 5.6. These tables also provide statistical results or each mode o ailure. From Tables 5.1 through 5.6, and the graphs presented in this section and in Appendix B, the ollowing conclusions and observations can be drawn: 1. As observed in Table 5.1, the mean values o V,exp, theo range rom 0.81 through 2.54, with signiicant scatter as given by the COV values o 0.47 to The high scatter in the predictions indicates that the resisting mechanisms o FRP strengthening systems still need to be urther investigated. 2. Almost all analytical models underestimate the prediction o FRP shear contribution or low values o E ρ /( ) and overestimate it or high values o ' 2/3 c E ρ /( ). ' 2/3 c On the other hand, the analytical models rom Hsu et al. (2003) and Zhang and Hsu (2005) exhibit an increasing trend between the FRP shear capacity ratio and E ρ /( ). ' 2/3 c 3. The predictions o FRP shear contribution or specimens that ailed due to FRP racture are more conservative or most models except or Triantaillou and Antonopoulos (2000), Chaallal et al. (2002), Hsu et al. (2003), Chen and Teng (2003), and Zhang and Hsu (2005). For these models, the mean values o V or both debonding and racture ailure are close to each other.,exp, theo 4. The models rom Triantaillou and Antonopoulos (2000) and Chen and Teng (2003) provide better predictions or the FRP shear contribution or both debonding and racture ailures. However, the FRP debonding approach rom Chen and Teng provides lower COV values than those corresponding to Triantaillou and Antonopoulos (2000). 5. For almost all analytical models, the FRP shear capacity ratio V,exp, increases as the shear span-to-depth ratio increases up to 3.0, and decreases aterwards. However, rom the analytical models o Chaallal et al. (2002), Cao et al. (2005) and Zhang and Hsu (2005), a decreasing trend is observed. theo

131 For almost all analytical models, the FRP shear capacity ratio V,exp, increases as the amount o transverse steel reinorcement increases. However, rom the analytical models o Hsu et al. (2003) and Zhang and Hsu (2005), a decreasing trend is observed. 7. From Table 5.2, or all building codes, the combination o the analytical model rom Cao et al. (2005) and Chaallal et al. (2002) with the CSA A design code, provide the most accurate prediction o total shear capacity. However, the combination o Chen and Teng (2003) analytical model with Eurocode 2 provides less scatter in the data points. 8. Both AASHTO speciications and ACI provide higher conservative values o V / exp V theo and higher COV values than the other design codes when applied in combination with all analytical models. 9. Eurocode 2 provides lower COV values and predicts the total shear capacity more accurately when applied in combination with most analytical models. 10. The application o the analytical model rom Triantaillou and Antonopoulos (2000) in combination with Eurocode 2 provides the most accurate predictions o total shear capacity or both debonding and racture ailures. In addition, the analytical model rom Chen and Teng (2003) in combination with Eurocode 2 provides the lower COV values or both debonding and racture ailures. 11. The predictions o total shear capacities or specimens that ailed due to FRP racture are more conservative or all models and design codes, except or the models o Triantaillou and Antonopoulos (2000), Chen and Teng (2003), and Zhang and Hsu (2005). For these three models, the mean values o V / exp V theo or both debonding and racture ailure are close to each other. theo

132 EVALUATION OF EXISTING DESIGN GUIDELINES 6.1. INTRODUCTION This section presents a comparative evaluation o the accuracy in predicting the FRP shear contribution, deined as V, between design guidelines discussed previously in Section Four. The design guideline developed by JBDPA (1999) is not considered or evaluation since the ormulation to determine the FRP shear contribution is dependent o the shear contribution rom the transverse steel reinorcement. In addition, any partial saety actors and strength reduction actors have not been considered when calculating the shear contribution o FRP or comparison purposes. Beore perorming the comparative evaluation, the entire database (reer to Table A.1 in the Appendix) was reduced to a subset o data. Only test results corresponding to large and slender beam specimens are included in the comparative evaluation. Furthermore, test results with other type o strengthening systems such as near-surace mounted (NSM) rebars and prestressed straps are omitted because these types o strengthening systems present a dierent type o behavior rom the externally applied FRP systems. Ater eliminating tests results in which lexural ailures were reported and cases in which insuicient data inormation was available, there were 127 test results let to be used in the comparative evaluation. For each design guideline, the predicted shear strength o FRP V, theo was compared with experimental results, V,exp, rom the shear database. The FRP shear capacity ratio, deined as V,exp, theo, or each design guideline is evaluated in terms o non-dimensional parameters that aect the shear behavior, such as E ρ / ', a / d, 2/3 c and ρ E / ρ E. In addition, each design guideline has been evaluated in terms o s s ailure modes and FRP wrapping schemes. Finally, the predictions o total shear capacities, V theo, with the observed test results V exp are also compared. The predictions o the total shear capacities are computed as Vn = Vc + Vs + V, theo, where V c and V s are computed using the respective RC design codes rom each design guideline

133 115 As a result, the evaluation or each design guideline yields to 11 plots or each design guideline. In this section, only the plots corresponding to the Great Britain Technical Report No.55 (2004) are presented. The plots corresponding to the remaining design guidelines are presented in Appendix C. Instead, in this section, the mean values and coeicient o variation (COV) values o V,exp, theo and V / exp V theo are presented in Tables 6.1 and 6.2. These tables also provide statistical results or each mode o ailure Table 6.1. Comparison o Prediction and Test Result or FRP Capacities ( V,exp V, theo ) Design Guideline Technical Report No.55 (2004) All Debonding Fracture Shear Failure Mean COV Mean COV Mean COV Mean COV ib TG 9.3 (2001) JSCE Recommendations (2001) ISIS Design Manual 4 (2001) ACI 440.2R-02 (2002) CSA-S (2002) Table 6.2. Comparison o Prediction and Test Result or Shear Capacities ( V exp theo ) Design Guideline Technical Report No.55 (2004) All Debonding Fracture Shear Failure Mean COV Mean COV Mean COV Mean COV ib TG 9.3 (2001) JSCE Recommendations (2001) ISIS Design Manual 4 (2001) ACI 440.2R-02 (2002) CSA-S (2002)

134 COMPARATIVE EVALUATION OF SHEAR DESIGN GUIDELINES Great Britain Technical Report No. 55 (2004). As illustrated in Figures 6.1 through 6.3, the analytical predictions proposed by the Great Britain Technical Report No.55 (2004) cannot accurately predict the shear contribution provided by the FRP. From these igures, it can be observed that as E ρ /( ) increases, the shear capacity ' 2/3 c ratio o the FRP exhibits a decreasing trend. This trendline shows that or lower values o E ρ /( ) ' 2/3 c, Technical Report No 55 underestimates the prediction o the FRP shear contribution; while or higher values o E ρ /( ) ' 2/3 c, this design guideline overestimates the prediction o the FRP shear contribution Furthermore, rom analyzing Figures 6.1 and 6.2 illustrate, this design guideline provides conservative values or the FRP shear capacity ratio. Thereore, Technical Report No. 55 tends to underestimate the FRP shear contribution or most data points, especially or those that ailed due to FRP racture w/ anchor 7.00 V,exp,theo ρ E / ' c 2/3 Figure 6.1. V,exp, theo in Terms o E ρ /( ) - FRP Debonding ' 2/3 c

135 Total Wrap 7.00 V,exp,theo ρ E / ' c 2/3 Figure 6.2. V,exp, theo in Terms o E ρ /( ) - FRP Fracture ' 2/3 c w/ anchor Total Wrap 7.00 V,exp,theo ρ E / ' c 2/3 Figure 6.3. V,exp, theo in Terms o E ρ /( ) - Other Failure Modes ' 2/3 c

136 118 Figures 6.4 through 6.6 illustrate the predictions o the FRP shear contribution in terms o the shear span-to-depth ratio or dierent modes o ailures. From Figures 6.4 and 6.5, it can be observed that the FRP shear capacity ratio increases up to values o shear span-to depth ratio o 3.0, and decreases aterwards. Moreover, as shown in Figures 6.4 and 6.5, the predictions or specimens that ailed due to FRP debonding are relatively more accurate (COV o 56%) in comparison to those that ailed due to FRP racture (COV o 66 %). In addition, this design guideline provides a very conservative mean value o V,exp V, theo or specimens ailing in racture. Figures 6.7 through 6.9 illustrate the eect o the transverse steel reinorcement on the FRP shear contribution or dierent modes o ailure. From Figure 6.7, it can be observed that when the amount o transverse steel reinorcement increases, the shear capacity ratio o FRP increases. The same trend is exhibited or those specimens that ailed in racture and other shear ailure modes w/ anchor 7.00 V,exp,theo a/d Figure 6.4. V,exp, theo in Terms o a / d - FRP Debonding

137 Total Wrap 7.00 V,exp,theo ρ E / ' c 2/3 Figure 6.5. V,exp, theo in Terms o a / d - FRP Fracture w/ anchor Total Wrap 7.00 V,exp,theo ρ E / ' c 2/3 Figure 6.6. V,exp, theo in Terms o a / d - Other Failure Modes

138 w/ anchor 3.00 V,exp,theo ρ s E s / ρ E Figure 6.7. V,exp, theo in Terms o ρses / ρ E - FRP Debonding Total Wrap 3.00 V,exp,theo /3 ρ E / ' c Figure 6.8. V,exp, theo in Terms o ρses / ρ E - FRP Fracture

139 V,exp,theo /3 ρ E / ' c Figure 6.9. V,exp, theo in Terms o ρses / ρ E - Other Failure Modes In conclusion, rom the previous analysis, Technical Report No. 55 does not accurately predict the shear capacity due to the FRP (COV o 94%). In act, the substantial majority o test specimens lie on the sae side, with the experimentally measured values exceeding those determined using the proposed design method. The analysis shows that this model predicts more accurately the FRP shear contribution or those specimens that ailed in debonding (COV o 56%) to those that ailed due to FRP racture (COV o 66 %). However, this model tends to underestimate the FRP shear contribution by more than twice the experimental FRP shear contribution or most observed test specimens. The inaccuracy in predicting the FRP shear contribution by this design guideline is also shown in Figure Finally, the analytical predictions or the shear capacity provided by the Technical Report No. 55 design guideline are also evaluated and compared to the experimental results as shown in Figure The mean value o Vn,exp Vn, theo or all specimens is around 1.27 with a COV o 28%.

140 Debonding Fracture Other V,theo (kn) V,exp (kn) Figure Comparison between Analytical Predictions o FRP Shear Contribution and Experimental Results V theo (kn) Debonding Fracture Other V exp (kn) Figure Comparison between Analytical Predictions o Total Shear Capacity and Experimental Results

141 ib-tg 9.3 Bulletin 14 (2001). From the analysis o this design guideline (reer to graphs o Appendix B), the shear design guidelines proposed by ib TG 9.3 predicted the shear capacity o FRP more accurately than the Technical Report No. 55 since it proposes an equation to determine the eective strain o FRP when racture ailure controls as opposed to providing a ixed value. By analyzing the prediction o the FRP shear strength versus E ρ /( ), it was ound that as in Technical Report No. 55 ' 2/3 c design guideline, ib-tg 9.3 overestimates the FRP shear capacity as E ρ /( ) ' 2/3 c increases. In addition, ib TG 9.3 predicts the shear capacity o FRP relatively accurately or the case o FRP racture. However, or debonding and other ailure modes, most o the predictions have been overestimated. In addition, by analyzing the FRP shear strength ratio versus the shear span-todepth ratio, ib TG 9.3 seems to predict more accurately or racture ailure (COV o 39%) than or debonding (COV o 53%). For specimens that ailed due to FRP debonding, the FRP shear capacity ratio increases up to a / d = 3.0, and then decreases up to For specimens that ailed in racture, the same trend is observed. Finally, rom analysis o the FRP shear strength ratio versus the eect o transverse steel reinorcement on the FRP shear contribution, it was observed that or specimens that ailed in FRP debonding, the FRP shear capacity ratio increases as the amount o transverse steel reinorcement increases up to around 1.0. For specimens ailing due to FRP racture, the FRP shear capacity ratio increases as the amount o transverse steel reinorcement increases. In conclusion, rom the analysis, ib TG 9.3 predicts the FRP shear capacity more accurately in comparison to Technical Report No.55 because ib TG 9.3 proposes an equation to determine the eective strain o FRP when racture ailure controls as opposed to providing a ixed value or the eective strain. However, ib TG 9.3 seems to predict the FRP shear contribution more accurately when racture ailure governs than or debonding or other shear ailures. This could be attributed to the act that ib TG 9.3 does not make a clear distinction between side and U-shaped FRP jackets, which usually tend to ail in debonding, when estimating the eective FRP strain. As a result, it seems the eective strain o the FRP plays an important role in determining the accuracy o the predictions o FRP shear contribution. From analysis, ib TG 9.3 provides a COV o

142 124 50%, which indicates that this design guideline predicts the shear capacity due to the FRP more accurate than Technical Report No.55. Finally, the analytical predictions or the total shear resistance provided by ib-tg 9.3 design guideline are also evaluated and compared to the experimental results. From the analysis, the mean value o Vn,exp Vn, theo or all test specimens is around 1.02 with a COV o 28%. This means that the predicted total shear capacity is slightly conservative, but provides better predictions in comparison to Technical Report No. 55. In addition, the FRP system provides higher values o FRP shear contribution to the total shear resistance in comparison to Technical Report No JSCE Design Recommendations (2001). From the analysis o this design guideline (reer to graphs in Appendix B), the predictions o the FRP shear contribution are overestimated; thereore, JSCE exhibit very low values o V,exp /V,theo. This can be explained by the act that this design guideline recommends the eective FRP stress to be between 0.4 and 0.8 times the racture stress o FRP, which leads to high predictions o the FRP shear contribution. By analyzing the prediction o the FRP shear strength versus E ρ /( ) ' 2/3 c, it was ound that or all ailure modes, the FRP shear capacity ratio decreases as E ρ /( ) increases. In addition, JSCE design recommendations ' 2/3 c predicts the FRP shear capacity more accurately or specimens that ailed in racture (COV o 52%) than or those than ailed in debonding (COV o 72%) or other shear ailures. This could be attributed to the act that the JSCE design recommendations treats only the case o ully-wrapped FRP laminates, which usually tend to ail in racture. Furthermore, by analyzing the FRP shear strength ratio versus the shear span-todepth ratio, it can be observed that or FRP debonding ailure, the FRP shear capacity ratio increases as the shear span-to-depth ratio increases up to a / d equal to 3.0 and decreases aterwards up to This same trend is observed or those specimens ailing due to FRP racture. Finally, rom analysis o the FRP shear strength ratio versus the eect o transverse steel reinorcement on the FRP shear contribution, it was observed that or specimens ailing due to FRP debonding and racture, the FRP shear capacity ratio increases as the amount o transverse steel reinorcement increases.

143 125 From analysis, JSCE design recommendations provides a COV o 77%, thus, in comparison to ib TG 9.3, this analytical model does not accurately predict the FRP shear capacity. This model seems to make better predictions or specimens that ailed in racture than those that ailed in debonding. This could be attributed to the act that the JSCE design recommendations treats only the case o ully-wrapped FRP laminates. In addition, this code recommends the eective stress o FRP to be between 0.4 and 0.8 times the FRP ultimate strength, which leads to high predictions o FRP shear contribution. For this reason, the JSCE design recommendations overestimate the FPR shear contribution or almost all test specimens. Finally, the analytical predictions or the total shear resistance provided by JSCE design recommendations are also evaluated and compared to the experimental results. From the analysis, the mean value o V V or all test specimens is around 0.75 with a COV o 43%. This means that n,exp n, theo the predicted total shear capacity is overestimated. This could be explained by the act that JSCE recommendations provide very high values o FRP shear contribution to the total shear resistance in comparison to both Technical Report No.55 and ib TG 9.3 design guidelines ISIS Design Manual 4 (2001). This design guideline proposes similar shear ormulations to both ACI 440.2R-02 and ib TG 9.3. By analyzing the predictions o the FRP shear strength versus E ρ /( ) ' 2/3 c, it was ound that as in previous shear design protocols, the ISIS design manual underestimates the FRP shear capacity or lower values o E ρ /( ) and overestimates the FRP shear contribution or higher ' 2/3 c values o E ρ /( ) ' 2/3 c. This design model provides very conservative values or the FRP shear capacity ratio in the case o FRP racture ailure. This could be attributed to the act that this design manual ixes the eective strain o FRP to a value o around 4 or cases o ully-wrapped FRP laminates, which usually tend to ail in racture. Furthermore, by analyzing the FRP shear strength ratio versus the shear span-todepth ratio, or specimens that ailed due to FRP debonding, the FRP shear capacity ratio increases up to a / d = 3.0, and then decreases up to For specimens that ailed in racture, the same trend is observed. In addition, rom analysis o the FRP shear strength ratio versus the eect o transverse steel reinorcement on the FRP shear contribution, it

144 126 was observed that or both debonding and racture ailure, it can be observed that the FRP shear capacity ratio increases as the amount o transverse steel reinorcement increases. In conclusion, rom the analysis, ISIS does not accurately predict the FRP shear capacity. This design manual provides very conservative values or the prediction o FRP shear capacity, especially in the case o FRP racture ailure. This could be explained by the act that ISIS provides a ixed value or the eective strain or totallywrapped FRP laminates, which tend to ail in racture. From analysis, ISIS provides a COV o 101%, which indicates that this design guideline does not accurately predict the shear capacity due to the FRP. Finally, the analytical predictions or the total shear resistance provided by ISIS design manual are also evaluated and compared to the experimental results. From the analysis, the mean value o Vn,exp Vn, theo or all test specimens is around 1.23 with a COV o 32%. This means that the predicted total shear capacity is typically conservative, but provides better predictions in comparison to Technical Report No. 55 and JSCE recommendations ACI 440.2R-02 (2002). From the analysis o this design guideline (reer to graphs in Appendix B), the analytical predictions proposed by ACI 440.2R-02 (ACI, 2002) cannot accurately predict the shear capacity o FRP. It can be observed that as E ρ /( ) increases, the shear capacity ratio o the FRP exhibits a decreasing trend. ' 2/3 c This trendline shows that or low values o E ρ /( ) ' 2/3 c, ACI 440.2R-02 underestimates the prediction o the shear capacity o FRP; while or high values o E ρ /( ) ' 2/3 c, this design guideline overestimates the prediction o the shear capacity o FRP. Furthermore, the predictions or specimens that ailed in racture are more conservative than those that ailed in debonding or other shear ailure modes. This can be explained by the act that or cases when racture ailure is likely to govern, ACI 440.2R-02 provides a ixed value o FRP eective strain around 4; thereore, this suggests that a ixed value o eective strain is conservative or racture ailure. Furthermore, by analyzing the FRP shear strength ratio versus the shear span-todepth ratio, or specimens that ailed due to FRP debonding, the FRP shear capacity ratio increases up to a / d = 3.0, and then decreases up to For specimens that ailed in racture, the same trend is observed. Finally, rom analysis o the FRP shear strength

145 127 ratio versus the eect o transverse steel reinorcement on the FRP shear contribution, it was observed that or specimens ailing due to FRP debonding and racture, the FRP shear capacity ratio increases as the amount o transverse steel reinorcement increases. From the analysis, ACI 440.2R-02 provides very conservative predictions o the FRP shear contribution. ACI 440.2R-02 provides more conservative predictions or racture ailure with a mean value o 3.94 than or debonding ailure. This could be attributed to the act that ACI 440.2R-02 provides a ixed value o FRP eective strain; thereore, suggesting that a ixed value o eective strain is conservative or racture ailure. ACI 440.2R-02 provides a COV o 96%, which indicates that this design guideline does not accurately predict the shear capacity provided by the FRP. Finally, the analytical predictions or the total shear resistance provided by ACI 440.2R-02 design guideline are also evaluated and compared to the experimental results. The mean value V V or all specimens is around 1.39 with a COV o 32%. This means that the o n,exp n, theo predicted total shear capacity is typically conservative. A signiicant portion o this conservatism is likely due to the conservative characteristics o the relationships or evaluating V c and V s CAN/CSA-S (2002). From the analysis o this design code (reer to graphs in Appendix B), the predictions o the FRP shear contribution are underestimated or the majority o data points probably because this design code ixes a conservative value o FRP eective strain. By analyzing the prediction o the FRP shear strength versus E ρ /( ) ' 2/3 c, it was ound that as in previous shear design protocols, CSA-S underestimates the FRP shear capacity or lower values o overestimates the FRP shear contribution or higher values o E ρ /( ) and ' 2/3 c E ρ /( ) ' 2/3 c. However, both CSA-S and ACI 440.2R-02 provide high values or the FRP shear capacity ratio, especially or FRP racture ailure. Thereore, the predictions o the FRP shear capacity by this design guideline are more conservative or racture ailure than or debonding and other shear ailures. Furthermore, by analyzing the FRP shear strength ratio versus the shear span-todepth ratio, it can be observed that or racture ailure, this design code tends to underestimate the FRP shear capacity or most slender beams. For both debonding and

146 128 racture ailure, the FRP shear capacity ratio increases up to a / d = 3.0, and then decreases up to Finally, rom analysis o the FRP shear strength ratio versus the eect o transverse steel reinorcement on the FRP shear contribution, it was observed that or debonding ailure, it can be observed that the FRP shear capacity ratio increases as the amount o transverse steel reinorcement increases. This increasing trendline is also present or specimens that ailed in racture From analysis, CSA-S provides a COV o 102%, thus, this analytical model does not accurately predict the FRP shear capacity in contrast to the previously discussed design guidelines. This design guideline tends to predict conservative FRP shear contributions or specimens that ailed due to FRP racture than those ailing in debonding. This could be attributed to the act that CSA-S ixes values o eective strains o 4 and 2 or both FRP racture and debonding respectively. For racture ailure, CSA-S produces high values o V,exp /V,theo. This suggests that a ixed value o eective strain around 4 is conservative or racture ailure. The results or debonding ailure suggests that i a ixed value o eective strain is used or debonding ailure, then it should be less than 4. Finally, the analytical predictions or the total shear resistance provided by CSA-S are also evaluated and compared to the experimental results. The mean value o Vn,exp Vn, theo or all specimens is around 1.22 with a COV o 35%. This means that the predicted total shear capacity is typically conservative SUMMARY AND CONCLUDING REMARKS The predictions or the FRP shear contribution and total shear resistance provided by Technical Report No.55, ib TG9.3, JSCE 2001, ISIS 4, ACI 440.2R-02, and CSA- S design guidelines or beams strengthened with FRP systems were evaluated and compared. The analytical predictions or the FRP shear contribution rom each shear design provision were compared to the experimental results observed rom the shear database. Each design guideline was also independently analyzed in detail by evaluating the inluence o some o the parameters on the behavior o RC members shear strengthened with FRP systems such as the FRP axial rigidity, concrete compressive strength, shear span-to-depth ratio, and transverse steel reinorcement.

147 129 The FRP shear capacity predictions or each design guideline discussed are presented in Table 6.1. The total shear capacity predictions by each design guideline are shown in Table 6.2. Both tables provide the mean values and coeicient o variation o V,exp V, theo and n,exp n, theo V V or all shear design guidelines. The mean and coeicient o variation (COV) are divided by the dierent ailure mechanisms. From Tables 6.1 and 6.2, and the plots discussed in the previous section, the ollowing observations can be drawn: 1. As presented in Table 6.1, the mean values o V,exp V, theo range rom 0.49 through 1.92, with signiicant scatter as given by the COV values o 0.50 to The high scatter in the predictions indicates that the mechanisms o FRP strengthening are still poorly understood. 2. From Table 6.2, the mean values o Vn,exp V n, theo range rom 0.75 through 1.39, with signiicant scatter as given by the COV values o 0.28 to The data points are less scattered because the predictions indicate that the predicted values or the total shear resistance are in good agreement with the experimental results. 3. For all design guidelines, the FRP shear capacity ratio V,exp V, theo decreases as E ρ /( ) increases. For this reason, all design guidelines underestimate the ' 2/3 c prediction o FRP shear capacity or low values o E ρ /( ) and overestimate ' 2/3 c the FRP shear contribution or high values o E ρ /( ). ' 2/3 c 4. For all design guidelines, the FRP shear capacity ratio V,exp V, theo increases as the shear span-to-depth ratio increases up to a/d equal to 3.0, and decreases aterwards up to Thereore, all design guidelines tend to overestimate the FRP shear contribution or higher a/d ratios. 5. For all design guidelines, the FRP shear capacity ratio V,exp V, theo increases as the amount o transverse steel reinorcement increases or both specimens ailing due to FRP debonding and racture. 6. The predictions o FRP shear capacity or racture ailure are more conservative or all design guidelines except or ib TG9.3 (2001). For this design guideline, the

148 130 mean values o V,exp V, theo or both debonding and racture ailure are close to each other. 7. The ib TG9.3 (2001) provides better predictions or the FRP and total shear capacities or both debonding and racture ailures. This design guideline also provides smaller COV values. 8. Technical Report No.55 (2004), ISIS Design Manual 4 (2001), ACI 440.2R-02 (2002), and CSA-S (2002) provide very conservative predictions o the FRP contribution and total shear capacities or both FRP debonding and racture ailures. 9. JSCE design recommendations overestimate the FRP shear contribution or almost all test specimens because this code recommends the eective stress o FRP to be between 0.4 and 0.8 times the FRP ultimate strength, which leads to high predictions o FRP shear contribution.

149 APPLICATION EXAMPLES OF ANALYTICAL APPROACHES ON SHEAR STRENGTHENING WITH FRP 7.1. INTRODUCTION As previously discussed in Section Five and Section Six, most analytical and design approaches were not able to provide reliable predictions o FRP shear contribution or all o the 127 RC members presented in the database. The high scatter in the predictions (COV) o the FRP shear contribution indicates that the resisting mechanisms o FRP strengthening systems still need to be urther investigated. This is urther exempliied by the large dierences in the predictions by the examined analytical and design approaches. Furthermore, as mentioned in Section Four, most RC members collected in the shear database (reer to Table A.1 in the Appendix), correspond to slender, rectangular cross-sections without internal transverse reinorcement. Thereore, the members in the evaluation database do not exactly relect the types o RC members usually ound in practice. By contrast, most RC members in real practice are large, slender, have a T-cross section, and contain internal transverse reinorcement. Thereore, due to the complexity o the analytical approaches examined, and the limited database, the FRP shear contribution predicted by these approaches can be more eectively compared by providing speciic examples. Beore perorming the comparative evaluation, it is important to note that the analytical model rom Triantaillou and Antonopoulos (2000) is omitted rom the evaluation because o its similarity to the ib TG9.3 (2001) design approach. In addition, since the examples provided consist o externally applied CFRP strips, the analytical models rom Hsu et al (2003), and Zhang and Hsu (2005) are essentially the same EXAMPLES TO COMPARE THE FRP SHEAR CONTRIBUTION This section provides three dierent application examples with dierent type o cross-sections. The irst example deals with RC T-beams, which usually are used in building structures. The second one deals with RC T-girders used in small bridges or highway overpass. The last one deals with prestressed (PC) I-cross section representing a large bridge girder. The three examples provided are used to compare the FRP shear contribution, V, among all the analytical and design approaches discussed in the

150 132 literature. The comparison o the magnitude o V is perormed in terms o the axial rigidity o FRP, ρ E. In all the relationships or estimating V, the shear crack angle is assumed to be 45 degree, and all partial saety actors are assumed to be equal to RC T-Beam. Figure 7.1 illustrates the cross-section o a T-beam having a shear span-to-depth ratio o 3.5. The concrete compressive strength is 27.6 MPa. The longitudinal steel reinorcement consists o three 36 mm diameter at the bottom o the beam section. The transverse steel reinorcement consists o 9.5M bars (A sv = 142 mm 2 ) with a yield strength o 276 MPa and a modulus o elasticity o 200 GPa. The spacing between steel stirrups is o 305 mm. The FRP strengthening system consists o CFRP strips with a width o 254 mm and spacing between strips o 305 mm. The angle o iber orientation is 90 degrees. The thickness o the CFRP is mm, the modulus o elasticity o the CFRP is 228 GPa, and the ultimate tensile strength o the CFRP is 3792 MPa. This example is evaluated by applying two types o strengthening schemes: sidebonded and U-wrapped CFRP sheets b =914 mm (36 in) h =152 mm (6 in) h=635 mm (24 in) d=533 mm (21in) d =381 mm (15 in) Φ 9.5mm 3Φ 36 mm b w =305 mm (12in) Figure 7.1. T-Beam Cross-Section Figure 7.2 compares the magnitude o V computed by the analytical and design approaches in terms o ρ E. This igure illustrates the magnitude o V by applying a side-bonded CFRP strengthening coniguration.

151 Chajes Triantaillou (1998) Khalia Pellegrino Challal Hsu (2003) Chen and Teng Monti Cao Carolin British TR 55 ib TG9.3 JSCE ACI 440 CSA S806 ISIS V (kn) ρ E (GPa) Figure 7.2. FRP Shear Contribution in Terms o Axial Rigidity Side-Bonded T-Beam Cross-Section From Figure 7.2, it can be observed that the prediction o V, by Chajes et al. (1995) analytical approach, linearly increases as the amount o FRP reinorcement increases. This behavior is explained by the act that this analytical model ixes a value or the strain in the FRP. As a result, the predictions o the FRP shear contribution by this analytical model are conservative. From the analytical approach by Triantaillou (1998), it can be observed that or values o ρ E up to about 0.43 GPa, the FRP shear contribution increases with ρ E reaching a maximum, beyond which it drops slightly and then increases again slightly. This suggests that the value o 0.43 GPa can be used to determine the limiting amount o FRP reinorcement, beyond which the eectiveness o strengthening ceases to be positive. This observed particular behavior could be attributed to the act that Triantaillou (1998) derived the eective FRP strain based on limited experimental data. As a result, Triantaillou (1998) derived a single expression or determining the eective FRP strain without taking into consideration the dierent ailure modes. Khalia et al. (1999) analytical approach indicates that or values o ρ E up to about 0.40 GPa, the FRP shear contribution increases almost linearly with ρ E reaching a

152 134 maximum, beyond which it drops up to ρ E equal to 0.7. This suggests that the value o 0.40 GPa can be used to determine the limiting amount o FRP reinorcement, beyond which the eectiveness o strengthening ceases to be positive. For values o ρ E > 0.7 GPa, additional amount o FRP results on negative values o FRP shear contribution. This means, that this analytical model is only valid or low values o FRP axial rigidity. From the analytical approach by Pellegrino and Modena (2002), additional shear gain due to the FRP contribution is not observed or axial rigidities lower than 0.17 GPa. For values o ρ E up to 1.16 GPa, the FRP shear contribution linearly increases in proportion to ρ E. However, ater this limit, the FRP shear contribution increases less than in proportion to the axial rigidity. Thereore, the eectiveness o the FRP system seems to reduce as the amount o FRP reinorcement increases beyond 1.16 GPa. This behavior conirms the observations reported by Pellegrino and Modena (2002) that the eectiveness o the FRP systems decreases as the amount o additional FRP reinorcement increases. The same trend is observed in Chaallal et al. (2002) analytical approach. The FRP shear contribution increases as the axial rigidity o FRP increases; however, ater ρ E >1.0 GPa, the FRP shear contribution increases less than in proportion to ρ E. Thereore, the eectiveness o the FRP system seems to reduce as the amount o FRP reinorcement increases beyond 1.0 GPa. This behavior conirms the observations reported by Chaallal etl al. (2002) that the FRP shear contribution depends on the amount o FRP and transverse steel reinorcement. Hsu et al. (2003) analytical approach indicates that the FRP shear contribution increases linearly up to about ρ E equal to 0.17 GPa, beyond which a constant shear gain due to the FRP contribution is observed. This behavior is explained by the act that the eective FRP strain predicted by this analytical model decreases in propotion to the FRP axial rigidity. This means that as the FRP axial rigidity increases, its eective FRP strain decreases at a decreasing rate. From the analytical approach by Chen and Teng (2003a-b), or values o ρ E up to 1.0 GPa, the FRP shear contribution increases in proportion to ρ E. However, ater this limit, the FRP shear contribution increases less than in proportion to the axial

153 135 rigidity. Thereore, the eectiveness o the FRP system seems to reduce as the amount o FRP reinorcement increases beyond 1.0 GPa. Monti and Liotta (2005) analytical approach indicates that or values o ρ E up to about 1.5 GPa, the FRP shear contribution increases with ρ E reaching a maximum, beyond which it drops slightly. Thereore, the eectiveness o the FRP system seems to reduce as the amount o FRP reinorcement increases beyond 1.5 GPa. The same trend is observed in the Cao et al. (2005) approach. The FRP shear contribution increases as the axial rigidity o FRP increases; however, ater ρ E >1.16 GPa, the FRP shear contribution starts to decrease. Thereore, the eectiveness o the FRP system seems to reduce as the amount o FRP reinorcement increases beyond 1.16 GPa. From the Carolin and Taljsten (2005) analytical approach, it can be observed that the FRP shear contribution increases linearly in proportion to the FRP axial rigidity. This behavior is explained by the act that this analytical model ixes a value or the strain in the FRP, which is equal to the ultimate FRP strain. As a result, the predictions o the FRP shear contribution by this analytical model are conservative. The design approach rom the British Technical Report No. 55 (2000) indicates that or values o ρ E up to about 1.33 GPa, the FRP shear contribution increases with ρ E reaching a maximum, beyond which it starts to decrease. Thereore, the eectiveness o the FRP system seems to reduce as the amount o FRP reinorcement increases beyond 1.33 GPa. From the design approach by ib TG 9.3 (2001), or values o ρ E up to 1.0 GPa, the FRP shear contribution increases in proportion to ρ E. However, ater this limit, the FRP shear contribution increases less than in proportion to the axial rigidity. Thereore, the eectiveness o the FRP system seems to reduce as the amount o FRP reinorcement increases beyond 1.0 GPa. From the JSCE recommendations (2001) design approach, or values o ρ E up to 0.66 GPa, the FRP shear contribution increases as ρ E increases. Beyond this limit, the FRP shear contribution increases linearly in proportion to the FRP axial rigidity. This behavior can be attributed to the act that the eective FRP strain remains constant ater 0.66 GPa. The predictions o FRP shear contribution by the JSCE recommendations are

154 136 observed to be the least conservative in comparison to all analytical and design approaches examined. Both design approaches rom ACI 440.2R (2002) and ISIS 4 (2002) indicate that or values o ρ E up to 1.0 GPa, the magnitude o V increases in proportion to ρ E. However, ater this limit, the FRP shear contribution increases less than in proportion to the axial rigidity. Thereore, the eectiveness o the FRP system or both approaches seems to reduce as the amount o FRP reinorcement increases beyond 1.0 GPa. Finally, rom the CSA S806 (2002) design approach, it can be observed that the FRP shear contribution increases linearly in proportion to the FRP axial rigidity. This behavior is explained by the act that this design approach ixes a value or the eective strain in the FRP, which is equal to 2 or side-bonded strengthening schemes. As a result, the predictions o the FRP shear contribution by this design approach are conservative. Figure 7.3 compares the magnitude o V computed by the analytical and design approaches in terms o ρ E. Figure 7.3 shows the magnitude o V by applying a U- wrapped CFRP strengthening coniguration Chajes Triantaillou (1998) Khalia Pellegrino Challal Hsu (2003) Chen and Teng Monti Cao Carolin British TR 55 ib TG9.3 JSCE ACI 440 CSA S806 ISIS V (kn) ρ E (GPa) Figure 7.3. FRP Shear Contribution in Terms o Axial Rigidity ped T-Beam Cross-Section

155 137 From Figure 7.3, the approaches rom Chajes et al., Triantaillou, Chaallal et al., Hsu et al., Carolin and Taljsten, ib TG 9.3, and JSCE do not make a distinction, in the ormulations to determine V between side-bonded and U-wrapped conigurations. Thereore, the predictions o V are the same or both strengthening conigurations. The predictions o V by the remaining approaches are higher in the case o U-wrapped coniguration than those o side-bonded coniguration. The trend between V and the FRP axial rigidity, or most approaches, exhibits the same behavior as in the case o sidebonded coniguration. However, or the approaches rom Monti and Liotta, Cao et al., and the British TR 55, the magnitude o V increases in proportion to ρ E up to 1.0 GPa. Ater this limit, the magnitude o V increases less than in proportion to the axial rigidity RC T-Girder. Figure 7.4 illustrates the cross-section o a T-girder with a shear span-to-depth ratio o 2.4. The concrete compressive strength is 34.5 MPa. The longitudinal steel reinorcement consists o our 25 mm diameter at the bottom o the cross-section. Transverse steel reinorcement consists o 9.5M bars (A sv = 142 mm 2 ) with a yield strength o 276 MPa and a modulus o elasticity o 200 GPa. The spacing between steel stirrups is o 305 mm. The FRP strengthening system consists o CFRP strips with a width o 610 mm and spacing between strips o 864 mm. The angle o iber orientation is 90 degrees. The thickness o the CFRP is mm, the modulus o elasticity o the CFRP is 228 GPa, and the ultimate tensile strength o the CFRP is 3868 MPa. h =102 mm (4 in) h=657 mm (18 in) d=406 mm (16 in) d =305 mm (12 in) Φ9.5mm 4Φ25mm b w =356 mm (14 in) Figure 7.4. T-Girder Cross-Section

156 138 Figure 7.5 compares the magnitude o V computed by the analytical and design approaches in terms o ρ E. Figure 7.5 shows the magnitude o V by applying a sidebonded CFRP strengthening coniguration Chajes Triantaillou (1998) Khalia Pellegrino Challal Hsu (2003) Chen and Teng Monti Cao Carolin British TR 55 ib TG9.3 JSCE ACI 440 CSA S806 ISIS V (kn) ρ E (GPa) Figure 7.5. FRP Shear Contribution in Terms o Axial Rigidity Side-Bonded T-Girder From Figure 7.5, it can be observed that the predictions o V, by Chajes et al. (1995) analytical approach, linearly increases as the amount o FRP reinorcement increases. This behavior is explained by the act that this analytical model ixes a value or the strain in the FRP. As a result, the predictions o the FRP shear contribution by this analytical model are conservative. From the analytical approach by Triantaillou (1998), it can be observed that or values o ρ E up to about 0.45 GPa, the FRP shear contribution increases almost linearly with ρ E reaching a maximum, beyond which it drops slightly and then increases again slightly. This suggests that the value o 0.45 GPa can be used to determine the limiting amount o FRP reinorcement, beyond which the eectiveness o strengthening ceases to

157 139 be positive. This observed particular behavior could be attributed to the act that Triantaillou (1998) derived the eective FRP strain based on limited experimental data. As a result, Triantaillou (1998) derived a single expression or determining the eective FRP strain without taking into consideration the dierent ailure modes. Khalia et al. (1999) analytical approach indicates that or values o ρ E up to about 0.36 GPa, the FRP shear contribution increases almost linearly with ρ E reaching a maximum, beyond which it drops up to ρ E equal to 0.7. This suggests that the value o 0.36 GPa can be used to determine the limiting amount o FRP reinorcement, beyond which the eectiveness o strengthening ceases to be positive. For values o ρ E > 0.7 GPa, additional amount o FRP results on negative values o FRP shear contribution. This means, that this analytical model is only valid or low values o FRP axial rigidity. From the analytical approach by Pellegrino and Modena (2002), additional shear gain due to the FRP contribution is not observed or axial rigidities lower than 0.15 GPa. For values o ρ E up to 1.0 GPa, the FRP shear contribution increases in proportion to ρ E. However, ater this limit, the FRP shear contribution increases less than in proportion to the axial rigidity. Thereore, the eectiveness o the FRP system reduces as the amount o FRP reinorcement increases beyond 1.0 GPa. The same trend is observed in Chaallal et al. (2002) analytical approach. The FRP shear contribution increases as the axial rigidity o FRP increases; however, ater ρ E >1.0 GPa, the FRP shear contribution increases less than in proportion to ρ E. Thereore, the eectiveness o the FRP system seems to reduce as the amount o FRP reinorcement increases beyond 1.0 GPa. Hsu et al. analytical approach (2003) indicates that the FRP shear contribution increases linearly up to about ρ E equal to 0.15 GPa, beyond which a constant shear gain due to the FRP contribution is observed. This behavior is explained by the act that the eective FRP strain predicted by this analytical model decreases in propotion to the FRP axial rigidity. This means that as the FRP axial rigidity increases, its eective FRP strain decreases at a decreasing rate. From the analytical approach by Chen and Teng (2003a-b), or values o ρ E up to 1.0 GPa, the FRP shear contribution increases in proportion to ρ E. However, ater

158 140 this limit, the FRP shear contribution increases less than in proportion to the axial rigidity. Thereore, the eectiveness o the FRP system seems to reduce as the amount o FRP reinorcement increases beyond 1.0 GPa. Monti and Liotta (2005) analytical approach indicates that or values o ρ E up to about 1.0 GPa, the FRP shear contribution increases with ρ E reaching a maximum, beyond which it drops slightly. Thereore, the eectiveness o the FRP system seems to reduce as the amount o FRP reinorcement increases beyond 1.0 GPa. The same trend is observed in the Cao et al. (2005) approach. The FRP shear contribution increases as the axial rigidity o FRP increases reaching a maximum at ρ E equal to 0.75 GPa, aterwards the FRP shear contribution starts to decrease. Thereore, the eectiveness o the FRP system seems to reduce as the amount o FRP reinorcement increases beyond 0.75 GPa. From the Carolin and Taljsten (2005) analytical approach, it can be observed that the FRP shear contribution increases linearly in proportion to the FRP axial rigidity. This behavior is explained by the act that this analytical model ixes a value or the strain in the FRP, which is equal to the ultimate FRP strain. As a result, the predictions o the FRP shear contribution by this analytical model are conservative. The design approach rom the British Technical Report No. 55 (2000) indicates that or values o ρ E up to about 1.0 GPa, the FRP shear contribution increases with ρ E reaching a maximum, beyond which it starts to decrease. Thereore, the eectiveness o the FRP system seems to reduce as the amount o FRP reinorcement increases beyond 1.0 GPa. From the design approach by ib TG 9.3 (2001), or values o ρ E up to 1.0 GPa, the FRP shear contribution increases in proportion to ρ E. However, ater this limit, the FRP shear contribution increases less than in proportion to the axial rigidity. Thereore, the eectiveness o the FRP system seems to reduce as the amount o FRP reinorcement increases beyond 1.0 GPa. From the JSCE recommendations (2001) design approach, or values o ρ E up to 0.60 GPa, the FRP shear contribution increases as ρ E increases. Beyond this limit, the FRP shear contribution increases linearly in proportion to the FRP axial rigidity. This behavior can be attributed to the act that the eective FRP strain remains constant ater

159 GPa. The predictions o FRP shear contribution by the JSCE recommendations are observed to be the least conservative in comparison to all analytical and design approaches examined. Both design approaches rom ACI 440.2R (2002) and ISIS 4 (2002) indicate that or values o ρ E up to 1.0 GPa, the magnitude o V increases in proportion to ρ E. However, ater this limit, the FRP shear contribution increases less than in proportion to the axial rigidity. Thereore, the eectiveness o the FRP system or both approaches seems to reduce as the amount o FRP reinorcement increases beyond 1.0 GPa. Finally, rom the CSA S806 (2002) design approach, it can be observed that the FRP shear contribution increases linearly in proportion to the FRP axial rigidity. This behavior is explained by the act that this design approach ixes a value or the eective strain in the FRP. As a result, the predictions o the FRP shear contribution by this design approach are conservative. Figure 7.6 compares the magnitude o V computed by the analytical and design approaches in terms o ρ E. Figure 7.6 shows the magnitude o V by applying a U- wrapped CFRP strengthening coniguration Chajes Triantaillou (1998) Khalia Pellegrino Challal Hsu (2003) Chen and Teng Monti Cao Carolin British TR 55 ib TG9.3 JSCE ACI 440 CSA S806 ISIS V (kn) ρ E (GPa) Figure 7.6. FRP Shear Contribution in Terms o Axial Rigidity ped T-Girder

160 142 From Figure 7.6, it can be observed that the the predictions o V by the approaches rom Chajes et al., Triantaillou, Chaallal et al., Hsu et al., Carolin and Taljsten, ib TG 9.3, and JSCE are the same or both strengthening schemes. The predictions o V by the remaining approaches are higher in the case o U-wrapped coniguration. The trend between V and the FRP axial rigidity, or most approaches, exhibits the same behavior as in the case o side-bonded coniguration. However, the analytical and design approaches rom Monti and Liotta, Cao et al., and the British TR 55, the FRP shear contribution keeps increasing as the FRP axial rigidity increases PC I-Girder. Figure 7.7 illustrates the cross-section o an I-girder with a shear span-to-depth ratio o The concrete compressive strength is 48.3 MPa. The longitudinal reinorcement consists o twenty 15.2 mm diameter prestressed tendons at the bottom o the cross-section. Transverse steel reinorcement consists o 10M bars with a yield strength o 420 MPa and a modulus o elasticity o 200 GPa. The spacing between steel stirrups is o 305 mm. The FRP strengthening system consists o CFRP strips with a width o 254 mm and spacing between strips o 305 mm. The angle o iber orientation is 90 degrees. The thickness o the CFRP is mm, the modulus o elasticity o the CFRP is 228 GPa, and the ultimate tensile strength o the CFRP is 3792 MPa mm m 8 φ 2 5 m m m m m m m m m m φ 1 0 m m 2 0 φ m m low relaxation prestressing strands φ 1 0 m m m m m m φ 1 0 m m m m m Figure 7.7. I-Girder Cross-section

161 143 Figure 7.8 compares the magnitude o V computed by the analytical and design approaches in terms o ρ E. Figure 7.8 shows the magnitude o V by applying a sidebonded CFRP strengthening coniguration Chajes Triantaillou (1998) Khalia Pellegrino Challal Hsu (2003) Chen and Teng Monti Cao Carolin British TR 55 ib TG9.3 JSCE ACI 440 CSA S806 ISIS V (kn) ρ E (GPa) Figure 7.8. FRP Shear Contribution in Terms o Axial Rigidity Side-Bonded I-Girder From Figure 7.8, it can be observed that the predictions o V, by Chajes et al. (1995) analytical approach, linearly increases as the amount o FRP reinorcement increases. This behavior is explained by the act that this analytical model ixes a value or the strain in the FRP. As a result, the predictions o the FRP shear contribution by this analytical model are conservative. From the analytical approach by Triantaillou (1998), it can be observed that or values o ρ E up to about 0.45 GPa, the FRP shear contribution increases almost linearly with ρ E reaching a maximum, beyond which it drops slightly and then increases again slightly. This suggests that the value o 0.45 GPa can be used to determine the limiting amount o FRP reinorcement, beyond which the eectiveness o strengthening ceases to

162 144 be positive. This observed particular behavior could be attributed to the act that Triantaillou (1998) derived the eective FRP strain based on limited experimental data. As a result, Triantaillou (1998) derived a single expression or determining the eective FRP strain without taking into consideration the dierent ailure modes. Khalia et al. (1999) analytical approach indicates that or values o ρ E up to about 0.50 GPa, the FRP shear contribution increases almost linearly with ρ E reaching a maximum, beyond which it drops slightly and then increases again slightly. FRP shear contribution or values beyond ρ E.o about 1.65 GPa could not be estimated because negative values o V are obtained. From the analytical approach by Pellegrino and Modena (2002), or values o ρ E up to 2.5 GPa, the FRP shear contribution increases in proportion to ρ E. However, ater this limit, the FRP shear contribution increases less than in proportion to the axial rigidity. Thereore, the eectiveness o the FRP system reduces as the amount o FRP reinorcement increases beyond 2.5 GPa. The same trend is observed in Chaallal et al. (2002) analytical approach. The FRP shear contribution increases as the axial rigidity o FRP increases; however, ater ρ E >2.5 GPa, the FRP shear contribution increases less than in proportion to ρ E. Thereore, the eectiveness o the FRP system seems to reduce as the amount o FRP reinorcement increases beyond 2.5 GPa. Hsu et al. (2003) analytical approach indicates that the FRP shear contribution increases up to about ρ E equal to 1.5 GPa, beyond which a constant shear gain due to the FRP contribution is observed. This behavior is explained by the act that the eective FRP strain predicted by this analytical model decreases in propotion to the FRP axial rigidity. This means that as the FRP axial rigidity increases, its eective FRP strain decreases at a decreasing rate. From the analytical approach by Chen and Teng (2003a-b), or values o ρ E up to 2.5 GPa, the FRP shear contribution increases in proportion to ρ E. However, ater this limit, the FRP shear contribution increases less than in proportion to the axial rigidity. Thereore, the eectiveness o the FRP system seems to reduce as the amount o FRP reinorcement increases beyond 2.5 GPa. The same type o behavior is exhibited by the analytical models rom Monti and Liotta (2005) and Cao et al. (2005).

163 145 From the Carolin and Taljsten (2005) analytical approach, it can be observed that the FRP shear contribution increases linearly in proportion to the FRP axial rigidity. This behavior is explained by the act that this analytical model ixes a value or the strain in the FRP, which is equal to the ultimate FRP strain. As a result, the predictions o the FRP shear contribution by this analytical model are conservative. The design approach rom the British Technical Report No. 55(2000) indicates that or values o ρ E up to about 2.5 GPa, the magnitude o V increases; however, ater this limit, the FRP shear contribution increases less than in proportion to the axial rigidity. This same type o trend between the FRP shear contribution and the FRP axial rigidity is observed in the ib TG 9.3 (2001) design approach. From the JSCE recommendations (2001) design approach, or values o ρ E up to 1.4 GPa, the FRP shear contribution increases as ρ E increases. Beyond this limit, the FRP shear contribution increases linearly in proportion to the FRP axial rigidity. This behavior can be attributed to the act that the eective FRP strain remains constant ater 1.4 GPa. The predictions o FRP shear contribution by the JSCE recommendations are observed to be the least conservative in comparison to all analytical and design approaches examined. Both design approaches rom ACI 440.2R (2002) and ISIS 4 (2002) indicate that or values o ρ E up to 2.5 GPa, the FRP shear contribution increases in proportion to ρ E. However, ater this limit, the FRP shear contribution increases less than in proportion to the axial rigidity. Thereore, the eectiveness o the FRP system or both approaches seems to reduce as the amount o FRP reinorcement increases beyond 2.5 GPa. Finally, rom the CSA S806 (2002) design approach, it can be observed that the FRP shear contribution increases linearly in proportion to the FRP axial rigidity. This behavior is explained by the act that this design approach ixes a value or the eective strain in the FRP. As a result, the predictions o the FRP shear contribution by this design approach are conservative. Figure 7.9 compares the magnitude o V computed by the analytical and design approaches in terms o ρ E. Figure 7.9 shows the magnitude o V by applying a sidebonded CFRP strengthening coniguration.

164 Chajes Triantaillou (1998) Khalia Pellegrino Challal Hsu (2003) Chen and Teng Monti Cao Carolin British TR 55 ib TG9.3 JSCE ACI 440 CSA S806 ISIS V (kn) ρ E (GPa) Figure 7.9. FRP Shear Contribution in Terms o Axial Rigidity ped I-Girder Figure 7.9 illustrates the comparison o the FRP shear contribution by applying a U-wrapped strengthening coniguration. The analytical and design approaches rom Chajes et al., Triantaillou, Chaallal et al., Hsu et al., Carolin and Taljsten, ib TG 9.3, and JSCE do not make a distinction, in the ormulations to determine the FRP shear contribution, between side-bonded and U-wrapped conigurations. Thereore, the predictions o FRP shear contribution are the same or both strengthening conigurations. The predictions o V by the remaining analytical and design approaches are higher in the case o U-wrapped coniguration than those o side-bonded coniguration. The trend between V and the FRP axial rigidity, or most analytical and design approaches, exhibits the same behavior as in the case o side-bonded coniguration SUMMARY AND CONCLUDING REMARKS Due to the complexity o the analytical approaches examined and the limited database presented in Section Three and Section Five, the FRP shear contribution predicted by these approaches was eectively compared by providing speciic examples. The irst example consisted o a RC T-cross section representing a beam. The second

165 147 example consisted o a RC T-cross-section representing a small bridge girder. The last example consisted o a prestressed (PC) I-cross section representing a large bridge girder. The three examples provided were applied to compare the FRP shear contribution, V, among all the analytical and design approaches evaluated in Section Five and Section Six. The comparison o the magnitude o V was perormed in terms o the axial rigidity o the provided FRP reinorcement, ρ E. In all the relationships or estimating V, the shear crack angle was assumed to be 45 degree, and all partial saety actors were assumed to be equal to 1.0. From the comparative evaluation presented in the plots discussed in the previous section, the ollowing observations can be drawn: 1. All three examples showed that there are very signiicant dierences in the prediction o V by the examined analytical and design approaches or a given level o axial rigidity o FRP. 2. For all three examples, the JSCE Recommendations (2001) approach was observed to be the least conservative. The most conservative approach was dierent or any given level o ρ E among all the examples. 3. For all three examples, the analytical and design approaches rom Chajes et al, Triantaillou, Chaallal et al., Hsu et al., Carolin and Taljsten, ib TG 9.3, and JSCE do not make a distinction, in the ormulations to determine the FRP shear contribution, between side-bonded and U-wrapped conigurations. Thereore, the magnitude o V is the same or both strengthening conigurations. 4. The predictions o V, by the approaches rom Khalia et al., Pellegrino and Modena, Chen and Teng, Monti and Liotta, Cao et al., British TR 55, ACI 440.2R, CSA S806 and ISIS, are higher in the case o U-wrapped coniguration than those o side-bonded coniguration. 5. The predictions o V or the PC I-girder are higher, or both wrapping conigurations, than those corresponding to the RC T-beam and RC T-girder. 6. The predictions o V estimated by Chajes et al., Carolin and Taljsten, JSCE and CSA S806 linearly increased in proportion to the FRP axial rigidity or all three types o cross-section and both wrapping conigurations.

166 The approaches rom Triantaillou, Khalia et al., Monti and Liotta, Cao et al., and British TR 55 established a limit on the FRP shear contribution or both the RC T- beam and T-girder with side-bonded coniguration. For U-wrapped coniguration, only the approaches rom Triantaillou and Khalia et al. placed a limit on the FRP shear contribution. 8. For both the RC T-beam and T-girder with side-bonded coniguration, V predicted by Pellegrino and Modena, Chaallal et al., Chen and Teng, ib TG 9.3, ACI 440.2R, and ISIS increased less in proportion to the FRP axial rigidity, or values o ρ E >1.0 GPa. For U-wrapped coniguration, V predicted by the approaches mentioned above, in addition to the approaches rom Monti and Liotta, Cao et al., and British TR 55, increased less in proportion to the FRP axial rigidity, or values o ρ E >1.0 GPa. 9. For the PC I-girder with both strengthening conigurations, the same approaches showed a linear increase in the magnitude o V in proportion with the FRP axial rigidity. The approaches rom Triantaillou and Khalia et al., established a limit on the FRP shear contribution. The FRP shear contribution, predicted by Pellegrino and Modena, Chaallal et al., Chen and Teng, ib TG 9.3, ACI 440.2R, ISIS, Monti and Liotta, Cao et al., and British TR 55, increased less than in proportion to the FRP axial rigidity, especially ater ρ E >2.5 GPa.

167 CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE RESEARCH 8.1. SUMMARY OF RESEARCH WORK FRP composite materials have emerged as one o the most promising materials in the use o external reinorcement or repair and strengthening o RC structures. Their application in structural engineering has become increasingly popular due to their resistance to corrosion, excellent high strength, ease in manuacturing, handling and installation, and cost-eectiveness. Extensive research to investigate the behavior o RC members strengthened in shear with FRP composite materials has been developed over the last 20 years. However, the results obtained thus ar are scarce and sometimes controversial. This is in essence due to the intrinsic diiculty o shear behavior o reinorced concrete (RC) members. Thereore, the overall objective o this study was to investigate previous analytical studies and design guidelines on shear strengthening o RC members with externallybonded FRP laminates, and their assessment with experimental data collected rom the literature. This study was organized in three main parts: review and summary o analytical and design approaches, parametric study o the experimental data, and comparative evaluation o analytical and design approaches. The irst part consisted on a summary and discussion o existing analytical models and design guidelines to determine the shear strength o RC members strengthened with FRP systems. These analytical models and design guidelines investigated were classiied according to the approach adopted to predict the FRP eective strain at the time o ailure. The second part consisted o the identiication and evaluation o parameters that inluence the behavior o RC members shear strengthened with FRP systems. For this purpose, an extensive and detailed database was developed or data analysis. The last part consisted o a comparative evaluation o the accuracy in predicting the FRP shear contribution between the analytical and design approaches. Furthermore, due to the complexity and variety o the analytical and design approaches, the comparative evaluation was also perormed through speciic examples. These examples consist on dierent type o RC members, with dierent FRP strengthening schemes.

168 CONCLUSIONS Review and Summary o Analytical and Design Approaches. The ollowing conclusions can be drawn rom the review o the analytical and design approaches. 1. The main dierence between the analytical models and design guidelines examined adopted in the dierent approaches to predict the FRP eective strain at the time o ailure. Thereore, the analytical models and design guidelines were classiied into approaches based on a ixed FRP eective strain, empirical approaches, and approaches based on non-uniorm strain distribution. 2. Some models and guidelines ixed the eective FRP strain to determine the FRP shear contribution. For instance, Chajes et al. (1995) ixed the strain to be the ultimate strain at ailure corresponding to the concrete. CSA S (2002) provided ixed values o eective FRP strain according to wrapping conigurations. 3. Empirical approaches were based directly on the calibration o experimental data and regression analysis to estimate the eective strain in the FRP. These models basically estimated experimental values or the eective FRP strain by back calculating rom the experimental values o the FRP shear contribution. Then, a relationship or the eective FRP strain in terms o the FRP stiness was obtained by regression analysis. Additionally, in this category were classiied analytical models that were based on empirical bond mechanism approaches 4. Analytical models, based on non-uniorm strain distribution, were derived rom bond strength approaches, which were based on racture mechanics at the FRP/concrete interace. The speciic racture energy o the FRP/concrete interace was used to determine the bond strength. 5. Most analytical models and design guidelines treated separately the mechanisms o FRP debonding and FRP racture except or Chajes et al. (1995), Triantaillou (1998), JBDPA (1999), JSCE (2001), and CSA S (2002). Thereore, most models and design standards proposed two dierent approaches that represent the two possible ailure modes. 6. Most models and design guidelines, with the exception o Chen and Teng (2003), Cao et al. (2005), Monti and Liotta (2004), and Carolin and Taljsten (2005)

169 151 determined the eective FRP strain by perorming regression analysis o experimental data. Thereore, important parameters that inluence the eective FRP strain were not taken into consideration because o the diiculty o accounting all relevant parameters in one single equation. 7. Models and guidelines based on data regression did not provide an accurate bond strength model. Thereore, it seems that the models based on racture mechanics described more accurately the behavior o RC beams shear strengthened with externally FRP because the bond strength models were developed by applying racture mechanics. Bond strength models that apply racture mechanics recognize the non-uniormity o the FRP stress distribution along a shear crack. 8. Most analytical models, added the shear contributions o concrete, stirrups and FRP to be consistent with the truss approach used in RC design codes, without taken into account the dependence and interaction between the concrete, stirrups and FRP sheets. The exception was the analytical model rom Deniaud and Cheng (2004) Parametric Study o the Experimental Data. The ollowing conclusions were drawn rom the parametric study. 1. No clear trendline was observed between the shear gain and 2/ 3 E ρ / ' c or specimens that ailed due to FRP debonding. However, or specimens ailing due to FRP racture, additional shear gains were observed as the amount o FRP reinorcement increases. 2. Test specimens that ailed due to FRP debonding were more requent in members with higher a / d ratios. Furthermore the eect o transverse steel reinorcement on additional shear gain due to FRP systems was observed. This additional shear gain was smaller in beam specimens with transverse steel reinorcement than in beam specimens without transverse steel. 3. The inluence o the transverse steel reinorcement was conirmed in the present study. The gain in shear resistance due to FRP decreased as the ratio o ρ ses / ρ E increased. However, additional experimental and analytical investigations are needed to provide a better understanding o the mechanisms involved in the interaction between transverse steel and FRP reinorcements.

170 Comparative Evaluation o Analytical and Design Approaches. The comparative evaluation was perormed in three parts: evaluation o analytical models, evaluation o design guidelines, and comparison o the analytical and design approaches by means o speciic examples. The comparative evaluation o the analytical models was conducted by comparing the predicted shear strength o FRP V, theo with the experimental results, V,exp addition, or each analytical model, the predicted total shear capacity, V theo compared with the observed experimental results, V exp, was. In. The predictions o total shear capacities were computed by applying each analytical model in combination with our RC design codes. From this comparative evaluation, the ollowing conclusions were drawn: 1. Almost all analytical models, underestimated the prediction o FRP shear contribution or low values o E ρ /( ) ' 2/3 c E ρ /( ) ' 2/3 c, and overestimated it or high values o. On the other hand, the analytical models rom Hsu et al. (2003) and Zhang and Hsu (2005) exhibited an increasing trend between the FRP shear capacity ratio and E ρ /( ). ' 2/3 c 2. The predictions o FRP shear contribution or specimens that ailed due to FRP racture were more conservative or most models except or Triantaillou and Antonopoulos (2000), Hsu et al. (2003), and Chen and Teng (2003). For these three models, the mean values o V,exp, theo or both debonding and racture ailure were close to each other. 3. The models rom Hsu et al. (2003) and Chen and Teng (2003) provided better predictions or the FRP shear contribution or both debonding and racture ailures. However, the FRP debonding approach rom Chen and Teng provided lower COV values. 4. For almost all analytical models, the FRP shear capacity ratio V,exp, increases as the shear span-to-depth ratio increases up to 3.0, and decreases aterwards. However, rom the analytical models o Chaallal et al. (2002), Cao et al. (2005) and Zhang and Hsu (2005), a decreasing trend is observed. theo

171 For almost all analytical models, the FRP shear capacity ratio V,exp, increases as the amount o transverse steel reinorcement increases. However, rom the analytical models o Hsu et al. (2003) and Zhang and Hsu (2005), a decreasing trend is observed. 6. For all RC design codes, the combinations o the analytical model rom Cao et al. (2005) and Chaallal et al. (2002) with the CSA A design code provided the most accurate prediction o total shear capacity. However, the combination o Chen and Teng (2003) analytical model with Eurocode 2 provided less scatter in the data points. 7. Both AASHTO speciications and ACI provided higher conservative values o V / exp V theo and higher COV values than the other design codes when applied in combination with all analytical models. Eurocode 2 provided lower COV values and predicts the total shear capacity more accurately when applied in combination with all analytical models. 8. The application o the analytical model rom Triantaillou and Antonopoulos (2000) in combination with Eurocode 2 provided the most accurate predictions o total shear capacity and lower COV values or both debonding and racture ailures. 9. The predictions o total shear capacities or specimens that ailed due to FRP racture were more conservative or all models and design codes, except or the models o Triantaillou and Antonopoulos (2000), Chen and Teng (2003), and Zhang and Hsu (2005). For these three models, the mean values o V / exp V theo or both debonding and racture ailure are close to each other. The comparative evaluation o the design guidelines was perormed by comparing the predicted shear strength o FRP V, theo with the observed experimental results, V,exp. In addition, or each design guideline, the predicted total shear capacity, V theo compared with the observed experimental results, Vexp theo, was or total shear capacity. The predictions o total shear capacities were computed by applying each design guideline with its corresponding RC design code. From this comparative evaluation, the ollowing conclusions were drawn:

172 For all design guidelines, the FRP shear capacity ratio V,exp V, theo decreased as E ρ /( ) increases. For this reason, it was ound that all design guidelines ' 2/3 c underestimated the prediction o FRP shear capacity or low values o E ρ /( ) ' 2/3 c E ρ /( ). ' 2/3 c, and overestimated the FRP shear contribution or high values o 2. For all design guidelines, the FRP shear capacity ratio V,exp V, theo increased as the shear span-to-depth ratio increased up to a/d equal to 3.0, and decreased aterwards up to Thereore, all design guidelines tended to overestimate the FRP shear contribution or higher a/d ratios. 3. For all design guidelines, the FRP shear capacity ratio V,exp V, theo increased as the amount o transverse steel reinorcement increased or both specimens ailing due to FRP debonding and racture. 4. The predictions o FRP shear capacity or racture ailure were more conservative or all design guidelines except or ib TG 9.3 (2001). For this design guideline, the mean values o V,exp V, theo or both debonding and racture ailure were close to each other. 5. The ib TG 9.3 (2001) provided better predictions or the FRP and total shear capacities or both debonding and racture ailures. This design guideline also provided smaller COV values. 6. Technical Report No.55 (2004), ISIS Design Manual 4 (2001), ACI 440.2R-02 (2002), and CSA-S (2002) provided very conservative predictions o the FRP contribution and total shear capacities or both FRP debonding and racture ailures. 7. JSCE design recommendations overestimated the FRP shear contribution or almost all test specimens because this code recommended the eective stress o FRP to be between 0.4 and 0.8 times the FRP ultimate strength, which leaded to high predictions o FRP shear contribution. Finally, the comparison o the magnitude o V was perormed in terms o the axial rigidity o the provided FRP reinorcement, ρ E. This comparative evaluation was

173 155 perormed by means o three examples that represent three dierent types o crosssections: RC T-beam, RC T-girder, and PC I-girder. From the comparative evaluation, the ollowing observations can be drawn: 1. All three examples showed that there are very signiicant dierences in the prediction o V by the examined analytical and design approaches or a given level o axial rigidity o FRP. 2. For all three examples, the JSCE Recommendations (2001) approach was observed to be the least conservative. The most conservative approach was observed to be dierent or any given level o ρ E among all the examples. 3. The predictions o V, by the approaches rom Khalia et al., Pellegrino and Modena, Chen and Teng, Monti and Liotta, Cao et al., British TR 55, ACI 440.2R, CSA S806 and ISIS, were higher in the case o U-wrapped coniguration than those o side-bonded coniguration. The predictions o V or the PC I-girder were higher, or both wrapping conigurations, than those corresponding to the RC T-beam and RC T-girder. 4. The predictions o V estimated by Chajes et al., Carolin and Taljsten, JSCE and CSA S806 linearly increased in proportion to the FRP axial rigidity or all three types o cross-section and both wrapping conigurations. 5. The approaches rom Triantaillou, Khalia et al., Monti and Liotta, Cao et al., and British TR 55 established a limit on the FRP shear contribution or both the RC T- beam and T-girder with side-bonded coniguration. For U-wrapped coniguration, only the approaches rom Triantaillou and Khalia et al. placed a limit on the FRP shear contribution. 6. For both the RC T-beam and T-girder with side-bonded coniguration, V predicted by Pellegrino and Modena, Chaallal et al., Chen and Teng, ib TG 9.3, ACI 440.2R, and ISIS increased less in proportion to the FRP axial rigidity, or values o ρ E >1.0 GPa. For U-wrapped coniguration, V predicted by the approaches mentioned above, in addition to the approaches rom Monti and Liotta, Cao et al., and British TR 55, increased less in proportion to the FRP axial rigidity, or values o ρ E >1.0 GPa.

174 For the PC I-girder with both wrapping conigurations, the approaches rom Triantaillou and Khalia et al., established a limit on the FRP shear contribution. The FRP shear contribution, predicted by Pellegrino and Modena, Chaallal et al., Chen and Teng, ib TG9.3, ACI 440.2R, ISIS, Monti and Liotta, Cao et al., and British TR 55, increased less than in proportion to the FRP axial rigidity, especially ater ρ E >2.0 GPa RECOMMENDATIONS FOR FUTURE RESEARCH It is recommended that the ollowing research be pursued as an extension o the present study. 1. Additional experimental investigations are recommended to address the inluence o transverse steel reinorcement, with emphasis on the mechanisms which can explain the experimentally observed interaction between external FRP shear strengthening and internal transverse steel reinorcement. The size eect also needs to be addressed since the available experimental data are mainly based on relatively small specimens. 2. Further experimental investigations need to careully monitor and record strain data in the dierent components (concrete, FRP, longitudinal and transverse steel reinorcement). This will provide a better understanding o the mechanisms involved and thus, more rational and accurate design methods and guidelines can be developed. 3. From previous studies, the anchorage systems appeared to be very helpul to increase the shear capacity provided by FRP by changing the ailure mode rom FRP debonding to FRP racture. Thereore, the eect o anchorage systems needs to be urther experimentally investigated. 4. The bond strength between the FRP and concrete surace depends on the compressive strength o concrete. However, the eect o concrete strength has not been thoroughly evaluated and analyzed. Thereore, the inluence o this parameter needs to be urther evaluated and analyzed. 5. The inclination o shear crack inluences the shear strengthening provided by the FRP sheet. Some analytical models take into consideration the angle o inclined

175 157 cracks. However, experimental investigations do not provide inormation on the magnitude o the angle o shear crack inclination, which is necessary to critique the dierent models. This problem should be address or urther analysis and uture research. 6. From the comparative evaluation in this study, none o the analytical and design approaches that were examined were able to provide reliable estimates o shear strengthening or all o the members in the database. This indicates that the mechanisms o FRP strengthening are still poorly understood. This is urther demonstrated by the very signiicant dierences in the predictions by the examined models. Thereore, additional parameter that are not taken into account in these approaches, but that aect the behavior o members strengthened in shear with FRP need to be urther investigated.

176 158 APPENDIX A. EXPERIMENTAL DATA ON SHEAR STRENGTHENING WITH FRP SYSTEMS

177 Table A.1. Experimental Shear Data on Shear Strengthening with FRP Systems 159

178 Table A.1. Experimental Shear Data on Shear Strengthening with FRP Systems (Contd.) 160

179 Table A.1. Experimental Shear Data on Shear Strengthening with FRP Systems (Contd.) 161