Bond Behavior of Post-Installed GFRP Bars in Structural Connections A Thesis SUBMITTED TO THE FACULTY OF UNIVERSITY OF MINNESOTA BY Muhammad Shahraiz Bajwa IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE Dr. Benjamin Z. Dymond and Dr. Rania Al-Hammoud June 2018 © Muhammad Shahraiz Bajwa 2018 i Acknowledgements I am grateful to my advisor Dr. Ben Dymond and the Department of Civil Engineering at University of Minnesota Duluth for giving me the opportunity to conduct this research. I would also like express my sincere gratitude to Dr. Dymond for his continuous guidance and unadulterated feedback throughout this project. In addition, I would also like to thank my co-advisor Dr. Rania Al-Hammoud for her invaluable input. Without her insight, this project would not have gone as smoothly as it did. I am also thankful to all of my fellow students for providing assistance during the construction and testing of the specimens. Assistance provided by undergraduate research assistants Jonas Bauer and Matthew McDermott during this research project is also appreciated. Furthermore, I would like to acknowledge the material support provided by Harris Rebar, Hilti Corporation, Hughes Brothers Inc., Marshall Composite Technologies and V-Rod Canada. Finally, I like to thank my parents for instilling in me the value of hard work and honesty. I would be nothing without their support and encouragement. My father passed away when I was 13 years old. His absence was always felt at each milestone that I achieved, but the realization that how proud he would be on my achievements always keeps me going. The relations that my father developed in his short life are still paving the way for me and my brothers. After the death of my father, my mother played the role of both parents and made me and my brothers her sole priority. She provided focus and clarity at each turning point in my life. I am also thankful to my brother, Zaib, for always setting the bar high in each aspect of life and giving me the motivation to make myself a better person with each passing day. His perseverance, dedication, and the ability to always follow his dreams has changed my outlook towards life. To my youngest bother Usama, I am blessed to have you in my life and consider you my best friend. I am grateful beyond belief to have you all in my life. ii Dedication I dedicate this thesis to my parents, Tanzeela and Javed, and my brothers Zaib and Usama. iii Abstract This research presents an experimental study with GFRP bars from three manufacturers, each having different bar textures (silica coated with helical wraps, silica coated and ribbed) used as post-installed (epoxy and cementitious adhesive) and cast-in- place reinforcement. Twenty test specimens were constructed and tested under static load. A test specimen was composed of two identical vertical elements, which were anchored into the base of the specimen using post-installed GFRP bars. The variables tested among different specimens included: concrete compressive strength (3 and 6 ksi), embedment length of GFRP bars (6 and 11.5 in.), and size of the post-installed GFRP bars (#4, #6, and #8). Concrete breakout was the only failure mode in all of the specimens with post-installed GFRP. Bond strengths and peak applied loads improved by increasing concrete strengths and embedment depths. The larger diameter bars (#6 and #8) showed a loss of bond strength compared to #4 bars. iv Table of Contents List of Tables .................................................................................................................... vii List of Figures .................................................................................................................. viii Chapter 1. Introduction ....................................................................................................... 1 1.1. Background .............................................................................................................. 1 1.1.1. Anchorage Systems ........................................................................................... 1 1.1.2. Post-Installed Adhesive Anchors ...................................................................... 1 1.1.3. Post-Installed Reinforcing Bars ........................................................................ 2 1.1.4. Fiber Reinforced Polymers ............................................................................... 3 1.2. Objectives ................................................................................................................ 5 1.3. Thesis Organization ................................................................................................. 5 Chapter 2. Literature Review .............................................................................................. 8 2.1. Post-Installed Anchors ............................................................................................. 8 2.1.1. Adhesives for Post-Installed Anchors ............................................................... 8 2.1.2. Load-Transfer Mechanism ................................................................................ 8 2.1.2.1. Failure Modes ............................................................................................ 9 2.1.2.2. Factors Influencing the Anchor Failure Modes ....................................... 10 2.1.3. Design Models for Adhesive Anchors ............................................................ 12 2.1.3.1. Anchor Failure Model .............................................................................. 12 2.1.3.2. Bond Model ............................................................................................. 12 2.1.3.3. Concrete Cone Model .............................................................................. 13 2.1.3.4. Combined Concrete Cone and Bond Models ........................................... 14 2.2. Post-Installed Steel Reinforcing Bars .................................................................... 15 2.2.1. Spliced and Non-Spliced Post-Installed Steel Rebar ...................................... 15 2.2.2. Splitting Design for Post-Installed Rebar ....................................................... 17 2.2.3. Post-Installed Rebar in Beam-Column Connections ...................................... 18 2.2.4. Design Methodology for Post-Installed Rebar ............................................... 19 2.2.4.1. Case I from Charney et al. (2013) ............................................................ 19 2.2.4.2. Case II from Charney et al. (2013) .......................................................... 21 2.2.4.3. Case III from Charney et al. (2013) ......................................................... 24 2.3. GFRP ..................................................................................................................... 25 2.3.1. Physical and Mechanical Properties ............................................................... 25 2.3.1.1. Density ..................................................................................................... 25 2.3.1.2. Coefficient of Thermal Expansion ........................................................... 25 2.3.1.3. Moisture ................................................................................................... 26 2.3.1.4. Tensile Properties..................................................................................... 26 2.3.1.5. Flexural Properties ................................................................................... 27 2.3.2. Bond Behavior of GFRP ................................................................................. 29 2.3.2.1. Concrete Cover ........................................................................................ 31 2.3.2.2. Bar Diameter ............................................................................................ 31 2.3.2.3. Casting Position of Bar ............................................................................ 32 2.3.2.4. Presence of Transverse Reinforcement .................................................... 32 2.3.2.5. Surface Texture ........................................................................................ 33 2.3.2.6. Concrete Strength ..................................................................................... 34 v 2.3.2.7. Embedment Depth ................................................................................... 35 2.3.2.8. Temperature ............................................................................................. 35 2.3.2.9. Environmental Degradation ..................................................................... 36 2.3.3. Flexural Design Methodology ........................................................................ 36 2.4. Post-Installed GFRP Bars ...................................................................................... 39 2.4.1. Pullout Strength of Post-Installed GFRP Bars in Unreinforced Concrete ...... 39 2.4.2. Design Models for Failure Modes .................................................................. 40 2.4.3. Pullout Strength of Post-Installed GFRP Bars in Reinforced Concrete ......... 41 2.5. Summary of Literature Review .............................................................................. 42 Chapter 3. Laboratory Specimens, Materials and Methods .............................................. 44 3.1. Specimen Geometry ............................................................................................... 44 3.2. Experimental Variables .......................................................................................... 44 3.3. Materials ................................................................................................................ 45 3.3.1. Concrete Specifications .................................................................................. 46 3.3.2. GFRP Specifications ....................................................................................... 46 3.3.3. Adhesive Specifications .................................................................................. 46 3.4. Specimen Design ................................................................................................... 46 3.5. Methods ................................................................................................................. 47 3.5.1. Specimen Construction ................................................................................... 47 3.5.1.1. Base Element ........................................................................................... 47 3.5.1.2. Post-Installed GFRP Bars ........................................................................ 48 3.5.1.3. Vertical Elements ..................................................................................... 49 3.5.2. Testing Method ............................................................................................... 49 3.5.2.1. Applied Pressure and Load ...................................................................... 50 3.5.2.2. Specimen Displacement ........................................................................... 50 3.5.2.3. Test Procedure ......................................................................................... 51 Chapter 4. Results ............................................................................................................. 61 4.1. Failure Modes ........................................................................................................ 61 4.1.1. Post-Installed Specimens ................................................................................ 61 4.1.2. Cast-in-Place Specimens ................................................................................. 62 4.2. Bond Strength and Bond Ratios ............................................................................. 63 4.2.1. Embedment Depth .......................................................................................... 64 4.2.2. Concrete Strength ............................................................................................ 65 4.2.3. Method of Bar Installation .............................................................................. 66 4.2.4. Adhesive Type ................................................................................................ 66 4.2.5. GFRP Surface Condition ................................................................................ 66 4.2.6. Bar Size ........................................................................................................... 67 4.2.7. Bar Spacing ..................................................................................................... 68 4.3. Load-Displacement Behavior ................................................................................ 68 4.3.1. Embedment Depth .......................................................................................... 68 4.3.2. Concrete Strength ............................................................................................ 69 4.3.3. Bar Size ........................................................................................................... 69 4.4. Comparison of Results with ACI 318 (2018) ........................................................ 70 4.4.1. Embedment Depth .......................................................................................... 70 vi 4.4.2. Concrete Strength ............................................................................................ 71 4.4.3. Bar Size ........................................................................................................... 71 4.5. Parametric Study .................................................................................................... 72 4.5.1. Effect of Embedment Depth ........................................................................... 72 4.5.2. Effect of Concrete Compressive Strength ....................................................... 72 4.5.3. Effect of Projected Failure Area ..................................................................... 73 Chapter 5. Summary and Conclusions .............................................................................. 89 5.1. Summary ................................................................................................................ 89 5.2. Conclusions from Testing ...................................................................................... 89 5.2.1. Failure Modes ................................................................................................. 89 5.2.2. Bond Strength and Bond Ratio ....................................................................... 90 5.2.3. Load-Displacement Behavior ......................................................................... 92 5.2.4. Comparison with 318 (2014) .......................................................................... 93 5.2.5. Parametric Study ............................................................................................. 93 5.3. Recommendations for Future Work ...................................................................... 94 References ......................................................................................................................... 96 Appendix A. Vertical Element Nominal Moment and Shear Capacity Calculations ..... 104 Appendix B. Example Reference Sheet .......................................................................... 116 Appendix C. Pictures of Failure Modes from all Specimens .......................................... 117 Appendix D. Development Length Calculations of CIP GFRP Bars ............................. 127 Appendix E. GFRP Bar Stress Calculations ................................................................... 130 Appendix F. Load-Displacement Data from each Specimen .......................................... 140 Appendix G. Concrete Breakout Strength Calculations for Specimens with Post-Installed GFRP............................................................................................................................... 149 Appendix H. Concrete Breakout Strength Calculations for Hypothetical Specimens .... 152 Appendix I. Linear Finite Element Analysis: Methods and Results ............................... 154 vii List of Tables Table 2-1. Density of steel, FRP and concrete from ACI 440.1R (2015) ......................... 43 Table 2-2. Coefficient of thermal expansion (CTE) of FRP, steel and concrete from ACI 440 (2015) ......................................................................................................................... 43 Table 2-3. Tensile properties of GFRP and steel reinforcing bars from ACI 440.1R (2015) ................................................................................................................................ 43 Table 2-4. Environmental reduction factor, CE, for GFRP bars from ACI 440.1R (2015) ........................................................................................................................................... 43 Table 3-1. Testing matrix of variables tested in laboratory specimens ............................ 52 Table 3-2. Ingredients for one cubic yard of ready mix concrete ..................................... 52 Table 3-3. Properties of GFRP bars provided by the manufacturers ................................ 53 Table 3-4. Properties of adhesives provided by the manufacturer .................................... 53 Table 3-5. Moment and shear capacity of vertical element cross sections ....................... 54 Table 4-1. Failure modes of all the experimental specimens ............................................ 75 Table 4-2. Calculated development length of GFRP bars using ACI 440.1R (2015) and Equation 2.36 .................................................................................................................... 75 Table 4-3. Test data, bond strengths, and bond ratios for GFRP and steel bars ............... 76 Table 4-4. Load-displacement behavior of specimens with GFRP bars compared to a cast-in-place steel reference specimen with f’c = 3 ksi ...................................................... 77 Table 4-5. Load-displacement behavior of specimens with post-installed #4 GFRP bars compared to a cast-in-place GFRP (SCW) specimen at le = 11.5 in. ............................... 77 Table 4-6. Effect of bar size on load-displacement behavior of specimens with post- installed GFRP bars at le = 11.5 in. and f’c = 6 ksi ............................................................ 78 viii List of Figures Figure 1-1. Anchorage types ............................................................................................... 7 Figure 3-1. Test specimen elevation and vertical element cross sections ......................... 55 Figure 3-2. GFRP bar types labeled with the manufacturer and surface texture abbreviations ..................................................................................................................... 55 Figure 3-3. (a) Base element for post-installed GFRP before concrete pour (b) Base element for cast-in-place GFRP before concrete pour (c) Post-installed GFRP in hardened concrete (d) Cast-in-place GFRP in hardened concrete .................................................... 56 Figure 3-4. (a) Wire brush attached to drill (b) Compressed air nozzle with an extension (c) Uncleaned hole (d) Cleaned hole ................................................................................ 56 Figure 3-5. (a) Two component adhesives and adhesive gun (b) GFRP bars post-installed with epoxy adhesive HIT-RE 500-SD (c) GFRP bars post-installed with cementitious adhesive HIT-HY 200-R ................................................................................................... 57 Figure 3-6. Sets of three stirrups installed at 3.5 in. on center for shear resistance .......... 57 Figure 3-7. (a) Vertical element formwork (b) Complete specimen being lifted ............. 58 Figure 3-8. Built-up HSS steel beams used for mounting hydraulic rams: (a) Beam in contact with ram base (b) Beam in contact with moveable pistons .................................. 58 Figure 3-9. (a) Hydraulic rams mounted and leveled on a test specimen (b) In-line pressure transducer and dial gauge to measure applied pressure ...................................... 59 Figure 3-10. (a) LVDT support stand and holder (b) LVDT recording vertical (upward) displacement of base element (c) LVDT recording horizontal (outward) displacement of vertical element ................................................................................................................. 59 Figure 3-11. Testing configuration with all instrumentation installed on specimen 3C4- E6PI (not pictured: LVDTs on base element) ................................................................... 60 Figure 4-1. Concrete breakout failure of post-installed specimens at (a) le = 6 in. and (b) le = 11.5 in. ....................................................................................................................... 79 Figure 4-2. Failure modes of cast-in-place specimens (a) Bond failure at le = 6 in. and (b) Combined bond and concrete breakout failure at le = 11.5 in. .......................................... 79 Figure 4-3. Bond failure of cast-in-place specimen at le = 11.5 in. and f’c = 6 ksi ........... 79 Figure 4-4. Effect of embedment depth on the bond ratio for steel and GFRP bars at f’c = 3 ksi ................................................................................................................................... 80 Figure 4-5. Effect of concrete strength on the bond ratio for specimens with cast-in-place and post-installed GFRP bars at le = 11.5 in. .................................................................... 80 Figure 4-6. Effect of bar installation method on the bond ratio of #4 steel and GFRP bars at le = 11.5 in. and f’c = 3 ksi ............................................................................................. 81 Figure 4-7. Effect of adhesive type on the bond ratio of specimens with post-installed #4 GFRP bars at le = 6 in. and f’c = 3 ksi ............................................................................... 81 Figure 4-8. Effect of GFRP surface condition on the bond ratio of specimens with post- installed #4 GFRP bars at le = 6 in. and f’c = 3 ksi ............................................................ 82 Figure 4-9. Effect of GFRP bar size on the bond ratio of specimens with post-installed bars using an epoxy adhesive at le = 11.5 in. and f’c = 6 ksi ............................................. 82 Figure 4-10. Effect of spacing on the bond ratio of specimens with post-installed #8 GFRP bars (SC) using epoxy adhesive at le = 11.5 in. and f’c = 6 ksi .............................. 83 ix Figure 4-11. Load-displacement curves for specimens with #4 bars at le = 11.5 in. and f’c = 3 ksi ................................................................................................................................ 83 Figure 4-12. Load-displacement curves for specimens with #4 bars at le = 11.5 in. and f’c = 3 ksi ................................................................................................................................ 84 Figure 4-13. Effect of concrete strength on load-displacement behavior of #4 GFRP bars at le = 11.5 in. .................................................................................................................... 84 Figure 4-14. Effect of bar size on load-displacement behavior for specimens with post- installed (epoxy adhesive) GFRP at le = 11.5 in. and f’c = 6 ksi ....................................... 85 Figure 4-15. Comparison of experimental data and theoretical results of specimens with #4 post-installed (epoxy adhesive) GFRP bars at le = 6 in. and f’c = 3 ksi ....................... 85 Figure 4-16. Comparison of experimental data and theoretical results of specimens with #4 post-installed (epoxy adhesive) GFRP bars at le = 11.5 in. and f’c = 3 ksi .................. 86 Figure 4-17. Comparison of experimental data and theoretical results of specimens with #4 post-installed (epoxy adhesive) GFRP bars at le = 11.5 in. and f’c = 6 ksi .................. 86 Figure 4-18. Comparison of experimental data and theoretical data of specimens with varying bar sizes of post-installed (epoxy adhesive) GFRP bars at le = 11.5 in. and f’c = 6 ksi ...................................................................................................................................... 87 Figure 4-19. Effect of embedment depth (le) on concrete breakout strength of post- installed #4 GFRP bars when f’c = 6 ksi ............................................................................ 87 Figure 4-20. Effect of concrete strength (f’c) on concrete breakout strength of post- installed #4 GFRP bars at le = 11.5 in. .............................................................................. 88 Figure 4-21. Effect of projected failure area (ANC) on the concrete breakout strength of post-installed GFRP bars at le = 11.5 in. and f’c = 6 ksi .................................................... 88 1 Chapter 1. Introduction 1.1. Background 1.1.1. Anchorage Systems Concrete structural members can be connected to each other through anchorage systems, which are designed to transfer loads efficiently across the connections. Cast-in- place anchorage is the oldest mechanism used in structural concrete for connecting members. In a cast-in-place anchorage system, rebar or anchors are laid out at a predesigned location and then concrete is poured to complete the connection. Lap splices and hooked or straight rebar are common methods of cast-in-place anchorage systems. Unfortunately, this type of anchorage system can only be used in new structures. Over time, a need for repairing, strengthening or modifying concrete structures has arose due to deterioration or changes in occupancy of existing structures. Post-installed adhesive anchorage systems provide the solution for this problem. Mechanical anchors, adhesive anchors, and reinforcement are common types of post-installed anchorage systems. Mechanical anchors are a type of post-installed anchorage system in which adhesives are not used. In a post-installed adhesive anchorage system, a hole is drilled in the existing concrete element and an adhesive mortar is injected in the hole. An anchor or reinforcing bar is inserted into the hole and the connection is allowed to cure. A cast-in-place reinforcing bar, a post-installed anchor, and a post-installed reinforcing bar are shown in Figure 1-1. 1.1.2. Post-Installed Adhesive Anchors Post-installed adhesive anchors are different from post-installed reinforcing bars. A post-installed adhesive anchor is defined as “an adhesive anchor employing an anchor element designed to generate expansion forces in response to tension loading” (AC-308, 2016). The earliest research on post-installed adhesive anchors did not begin until the late 20th century, according to the report on post-installed anchors published by the National Institute of Standards and Technology (NIST) (1998). It was also reported by NIST (1998) that the most extensive work on post-installed adhesive anchors was conducted at 2 the University of Stuttgart by Eligehausen et al. (1984) and Fuchs et al. (1995), at the University of Texas by Collins et al., (1989) and Doerr and Klinger (1989), and at the University of Florida by Cook et al. (1991; 1993). This early research led to an initial understanding of the behavior of post-installed anchors in different loading conditions and, eventually, of their practical application. Similar to other engineering solutions in early development, there were also some issues encountered with the adhesives used in post-installed anchorage systems. In 2006, a concrete ceiling panel inside the Interstate 90 connector tunnel in Boston collapsed and resulted in one fatality. The panel that fell was mounted on the tunnel ceiling with post- installed adhesive anchors. The subsequent investigation by the National Transportation Safety Board (NTSB) revealed that the anchors were improperly designed and were installed by untrained personnel (NTSB, 2007). The accident report also implicated the manufacturer for providing adhesives incapable of carrying the sustained load. In its report, the NTSB recommended that the designers should have a better understanding of the behavior of adhesive anchors, the installation of anchors should be done by trained personnel, and the adhesives should be evaluated for all of the intended applications (NTSB, 2007). In light of these recommendations, the design and installation methods for post-installing anchors were researched, improved, and standardized. 1.1.3. Post-Installed Reinforcing Bars A post-installed reinforcing bar is defined as “a reinforcing bar embedded in a drilled hole with an adhesive and designed in accordance with (American Concrete Institute) ACI-318 rules for cast-in-place reinforcing bar development and splices” (AC- 308, 2016). Development of the installation methods and design guides for post-installed adhesive anchors led to research into the use of steel rebar as post-installed reinforcement. Adhesives developed for the anchors were later qualified to be used for post-installed reinforcement and found to be adequate for the purpose of strengthening and modifying existing structures (ICC, 2016). The use of post-installed reinforcing bars exhibited several benefits, which included design flexibility, formwork simplification and the ability to have horizontal, vertical, and overhead applications (Hilti, 2016). Examples of applications for post-installed reinforcing bars include: diaphragm walls, slab 3 connections, misplaced bars, vertical and horizontal connections, wall strengthening, new slab constructions, joint strengthening, cantilevers, balconies, slab widening, structural upgrade, slab strengthening and sidewalk upgrade (Hilti, 2011). Steel rebar is commonly used as reinforcement in post-installed applications. This type of reinforcement material is widely known to corrode in concrete. Corroded steel rebar expands, which causes excessive cracking and spalling of concrete, resulting in the deterioration of the structural member (Perenchio, 1994). Post-installed steel reinforcement at the connection between existing and new elements can also corrode. Corrosion of steel reinforcement can diminish the bond strength, which in turn can reduce the load bearing capacity of the reinforced concrete structure (Auyeung et al., 2000). Composite (non-metallic) materials used as post-installed reinforcement present a solution for this corrosion problem. 1.1.4. Fiber Reinforced Polymers Composite materials are defined as the amalgam of two or more different materials, which together produce the desirable properties and curb the undesirable properties of each individual material (Astrom, 1997). Fiber reinforced polymer (FRP) composites have been developed for structural applications. FRP composites are made by mixing several polymers together, such as epoxy, vinylester, or polyester and reinforced with different grades of carbon, glass, or aramid fibers (Lee et al., 2012). FRP composites are gaining popularity in the field of structural engineering due to their wide-ranging applications, such as the strengthening and repairing of existing structures, as well as their use in construction of new structures. FRP composites can be used as reinforcement in concrete, as bridge decks, modular structures, formwork, and external reinforcement for strengthening and seismic upgrade (Lee et al., 2012). The use of FRP as post-installed reinforcement in concrete structures was the focus of this research project. The earliest research in the development and practical application of FRP reinforcement was done in Europe, Canada and Japan (Lee et al., 2012). In the United States, FRP reinforcing bars were developed to replace steel reinforcing bars in bridge decks because a significant amount of money was being spent on the maintenance of bridges, where deicing agents were used for melting ice (ACI 440.1R, 2006). The use of 4 deicing agents on bridge decks can contribute to corrosion of steel rebar. The United States Department of Transportation funded an initial research project to investigate the possible use of FRP reinforcement in bridge decks (Plecnik and Ahmad, 1988). Further research and the availability of design guides internationally paved the way for acceptance of FRP reinforcement as an alternative to steel rebar in reinforced concrete. A life-cycle cost analysis of bridge decks reinforced with FRP bars versus a steel reinforced deck showed that the FRP outperformed steel in all aspects of the analysis (Kawahara et al., 2012). According to the American Concrete Institute (ACI), the benefits of FRP reinforcement over steel rebar include high longitudinal tensile strength, corrosion resistance, non-magnetic in nature, high fatigue endurance, lightweight and low thermal and electric conductivity (ACI 440.1R, 2015). FRP reinforcing bars are divided into three types based on the reinforcing material used in the manufacturing process. These types of reinforcing bars are glass FRP (GFRP), carbon FRP (CFRP) and aramid FRP (AFRP). FRP reinforcing bars are commercially available in the same sizes as steel rebar. The physical and mechanical properties of FRP bars vary by manufacturer due to differences in the manufacturing process, but all FRP bars must meet the requirements set forth by ACI 440.1R (2015) for use in structural concrete. GFRP bars are the most economical and widely available among the various types of FRP bars. CFRP and AFRP bars have better strength properties than GFRP, but their cost and the environmental impact during manufacturing make GFRP bars more suitable for use in reinforced concrete (Anderson et al., 2012). According to Lee et al. (2012), “GFRP bars are a popular choice for fiber reinforcement due to advantageous properties such as high strength, tolerance to high temperatures and corrosive environments, and low cost.” Therefore, it could be concluded that GFRP bars present an economical and sustainable alternative to steel rebar in reinforced concrete. Glass based FRP bars are composed mainly of glass and silica sand. Commercially available grades of GFRP are electric (E-glass), high-strength (S-glass) and alkali-resistant glass (AR-glass). Each of these GFRP grades have their own unique properties. E-glass GFRP bars exhibit higher mechanical properties and are not 5 susceptible to moisture (Nanni et al., 2014). S-glass GFRP bars are the most expensive among the three types of GFRP and are only suitable for high stress and temperature sensitive applications (Nanni et al., 2014). AR-glass GFRP bars, as evident from their name, are useful in applications where alkali-silica reactions in concrete are likely to occur (Nanni et al. 2014). Post-installed steel reinforcement is an effective retrofitting and structural modification method. However, steel rebar is known to have corrosion problems resulting in repair and maintenance costs. GFRP bars are non-corrosive, lighter in weight and have high tensile strength properties compared to steel rebar. 1.2. Objectives The primary objective of this research project was to investigate the use of GFRP as post-installed reinforcement in structural connections (beam-column and beam-wall). Post-installed GFRP reinforcement is an effective method for the strengthening and repairing of existing structures, but it is still in the early stages of development. Research in the field of post-installed reinforcement has primarily investigated steel as the post- installed reinforcement. The benefits of GFRP have been studied and well documented, but there is a significant gap in research for the use of GFRP as the post-installed reinforcement. This project aimed to bridge this knowledge gap. The secondary objective of this research project was to compare the behavior of post-installed GFRP to post-installed steel rebar. In this study, specimens having similar design specifications such as concrete strength, bar size, and embedment depth were chosen for comparison to the literature. The results obtained from testing specimens with GFRP as post-installed reinforcement were compared with the results from testing specimens with steel rebar as post-installed reinforcement (Hamad et al., 2006). Comparison of the results made it possible to examine the behavior of steel and GFRP as post-installed reinforcement. 1.3. Thesis Organization This thesis document has five chapters. The first chapter of the thesis introduced the background and the objectives of the research project. The second chapter 6 summarizes past studies in the literature that have investigated post-installed reinforcement, the use of GFRP and its properties, and finally the use of GFRP as post- installed reinforcement. The third chapter includes a description of the experimental program, the properties of the materials used and the methods used for the construction and testing of the specimens. The fourth chapter includes the results and observations made during the testing phase of the project, a comparison of results with ACI 318 (2014) and a parametric study, which evaluated the parameters influencing the resulting failure mode. The final chapter presents the conclusions and recommendations drawn from this project. 7 Figure 1-1. Anchorage types 8 Chapter 2. Literature Review This chapter includes past studies on post-installed anchors, specifications for post-installed bars, use of GFRP bars in reinforced concrete and GFRP as post-installed reinforcement. The discussion of post-installed anchors is important because the failure modes and design recommendations are the same for post-installed bars. Some research that has been conducted on the use of steel rebar as post-installed reinforcement is discussed in section 2.2. On the basis of that research, adhesive manufacturers have developed methods for design of post-installed steel reinforcing bars using ACI 318 (2014) provisions. 2.1. Post-Installed Anchors Post-installed anchorage is an effective tool for retrofitting and structural modification. A significant amount of research has been conducted on the use of post- installed adhesive anchors and their design specifications are provided in ACI 318 (2014). 2.1.1. Adhesives for Post-Installed Anchors The design of post-installed anchorage mainly depends on the type of adhesives used for placing the anchor or rebar in concrete. Adhesives have varying properties depending on the type of application. Adhesives were classified by Collins et al. (1989) as epoxies, polyesters and vinylesters. 2.1.2. Load-Transfer Mechanism The load-transfer mechanism of post-installed anchors is different from that of cast-in-place reinforcement. Daws (1978) identified four different mechanisms that are involved in the load-transfer between post-installed anchors and concrete, which are: mechanical interlock at adhesive-concrete interface, mechanical interlock at the adhesive- rebar interface, chemical bond along the adhesive-concrete interface, and chemical bond along the adhesive-rebar interface. If the adhesives are not properly cured, chemical bond failure will occur due to weaker bond between the adhesives and both concrete and rebar interfaces (Daws, 1978). Mechanical interlock failure is attributed to improper cleaning of drilled holes or improper drilling methods, which could lead to micro-cracks (Collins 9 et al., 1989). The relevant failure modes and factors influencing those failure modes are discussed section 2.1.2.1 and 2.1.2.2. 2.1.2.1. Failure Modes Cook et al. (1993) identified that anchors installed with adhesives exhibits only four types of failure, namely: failure of anchor steel, cone failure of concrete, adhesive core pullout, and the combination of bond and cone failure. ACI Committee 355 (1990) and NIST (1998) provided a description of these failure modes. Additionally, the common failure modes observed in post-installed anchors are shown in ACI 318 (2014) Figure 17.3.1. The failure modes, which are related to the adhesive anchors, are summarized below. Steel failure occurs due to rupture of the steel bar or if the bar is significantly damaged such that the load can no longer be applied. Steel failure is common in cases when appropriate embedment depth is provided to allow the bond between both of the interfaces (adhesive-concrete and adhesive-rebar) to be sufficiently developed. As a result, the bond strength of the adhesive anchor is greater than the ultimate strength of the steel, resulting in steel anchor failure. The capacity of anchors is dependent on the ultimate strength of the anchor material and anchor size. Higher ultimate strength of an anchor material may require an increase in the embedment depth for steel failure to happen. Similarly, larger size anchors require larger embedment depths (for sufficient bond development) for steel failure to occur. Concrete cone failure frequently happens when the bond between the anchor and the surrounding concrete is sufficiently strong but not as strong as the ultimate strength of the anchor. Cone failure is observed when the concrete strength is low and embedment the depth is short. Cone failure of concrete typically occurs at or beyond the embedment depth and resembles a triangle in two dimensions and a cone in three dimensions. Adhesive core pullout failure results from a bond failure at the adhesive-concrete interface. This failure can occur in three conditions: improper cleaning of the drilled holes, insufficient embedment depth, or improper distribution of the curing agent while inserting the adhesive. Adhesive core pullout failure can be avoided by providing 10 sufficient embedment depth and proper cleaning of the drilled holes coupled with adequate adhesive coverage. In addition to the above mentioned failure modes, a splitting failure mode can also be observed in post-installed anchors. Asmus (1999) described splitting failure as a failure, which results due to the splitting forces generated by anchors subjected to tensile loadings. The splitting forces cause the formation of cracks originating from the anchors, propagating towards concrete edges and ultimately leading to spalling (Huer and Eligehausen, 2007). During the transfer of loads, compressive stresses are generated in the load bearing area of the anchor and tensile hoop stresses are generated due to compressive stresses (Huer and Eligehausen, 2007). These stresses acts like splitting forces, resulting in the splitting failure mode. 2.1.2.2. Factors Influencing the Anchor Failure Modes Factors that often influence failure modes include concrete strength, embedment depth, anchor strength, anchor size, anchor spacing, edge distance, and cleaning method of the drilled holes. Luke et al. (1985) identified embedment depth, size of the anchors and cleaning methods during anchor installation as factors that influence failure modes associated with structural members connected by means of an adhesive. The study involved the pullout testing of approximately 100 adhesive anchors installed into 5 by 8 ft concrete slabs. The anchor embedment depths were 3 and 6 in. and the anchor sizes were 0.5 and 0.75 in. The variable cleaning methods were as drilled, via syringe, compressed air to bottom of the hole with wire brush, and vacuuming from the top of the hole without inserting the compressed air nozzle inside the hole. Luke et al. (1985) reported that the anchors, which were installed with vacuuming from the top as the cleaning method, exhibited similar characteristics to the anchors installed without cleaning of the holes. The failure mode in this case was adhesive core pullout failure. The failure mode in anchors installed after cleaning withe compressed air to the bottom of the hole and with a wire brush was cone failure in anchors with an embedment depth of 6 in. Adhesive anchors with a shallow embedment depth exhibited pullout failures without the adhesive core. Results from variable anchor sizes did not provide direct correlation between failure modes and size of 11 the anchor. Bond stress at the concrete-adhesive interface was recommended to be approximately 1.8 ksi. In other words, there should be sufficient embedment for a particular anchor size to avoid bond failure. Doerr and Klinger (1989) studied the effects of spacing and embedment depth on behavior of adhesive anchors. The study involved pullout testing of 25 adhesive anchors having 0.625 in. diameter. Both the spacing and embedment depths were 4, 6, and 8 in. The results indicated that the cone failure was predominant in anchors with embedment depths of 4 and 6 in. Anchors with an embedment depth of 8 in. mainly exhibited steel yielding as the failure mode. Anchors spaced and embedded at 4 in. indicated a 5% decrease in ultimate strength when compared with the ultimate strength of a single adhesive anchor. Anchors spaced at 6 or 8 in. exhibited similar ultimate strength as the single anchors. Cook et al. (1992) studied the effects of anchor yield strength (60 and 120 ksi) and embedment depth (4.75 to 8 in.) on failure mechanisms of adhesive anchors. This experimental study involved static load pullout testing of the adhesive anchors embedded into 18 x 30 x 72 in. concrete blocks. Each concrete block had a maximum of four adhesive anchors installed to minimize the effect of edge distance and spacing on anchor pullout strength. The failure modes included steel failure without anchor slip, steel failure with anchor slip, pullout failure of cast-in-place anchors, adhesive-concrete bond failure, and adhesive-anchor bond failure. Cook et al. (1992) reported that the low strength anchors ruptured at 5 or 6 in. embedment depth, whereas high strength anchors ruptured only at an embedment depth of 8 in. Anchors with an adhesive-concrete bond failure exhibited higher bond strength and lower ductility at all embedment depths. Anchors with a bond failure at the adhesive-anchor interface demonstrated a brittle failure. Cook and Kunz (2001) studied the factors that influence bond strength of adhesive anchors. The testing program consisted of 20 different products from 12 manufacturers and 765 pullout tests. The parameters involved in this study were type of adhesive, installation factors (damped, submerged and unclean holes), and compressive strength of concrete. The study concluded that the epoxy-based adhesives developed an average uniform bond stress superior to other adhesives. Epoxy-based products also had 12 consistent bond strengths compared with theoretical bond strength values, whereas other adhesives showed variation in bond strengths. All the adhesives had reduced bond strengths when holes were damp, submerged or unclean. The compressive strength of concrete did not have a significant effect on the bond strength and did not have a consistent trend among adhesives. Coarse aggregate in the base material did influence the bond strength, which was found to be inversely related to the porosity of coarse aggregate. 2.1.3. Design Models for Adhesive Anchors Design models for adhesive anchors are based on the four failure modes (anchor, bond, concrete cone, and combined concrete cone and bond). In the literature, mathematical relationships have been developed based on experimental data and theoretical results to analyze the four different failure modes. These mathematical models are summarized for each of the four failure modes. 2.1.3.1. Anchor Failure Model The design method for the anchors with a steel failure is provided in Section 17.4.1.12 of ACI 318 (2014), which is given by the following equation. ,sa se N utaN A f  (2.1) Where: Nsa = nominal strength of an anchor in tension governed by steel, lb Ase,N = effective cross-sectional area of an anchor in tension, in.2 futa = specified steel strength of anchor steel, psi 2.1.3.2. Bond Model Cook et al. (1998) proposed the mathematical model to determine interface strength between adhesives and steel anchors. The bond model recommended using the anchor diameter because anchor diameter provided realistic bond strength values for design purposes compared to the diameter of the anchor hole. The bond model is given by the following equation. cb ef cN d h    (2.2) 13 Where: Ncb = nominal strength of the anchor as controlled by bond strength, lb τ = bond stress, psi d = diameter of anchors, in. hef = embedment depth, in. ψc = concrete modification factor The minimum and maximum limits for the embedment depth-to-bar diameter ratio were also proposed to be 4.5 and 18.7, respectively. The concrete modification factor (ψc) can be taken as 1.0, if the adhesive has little or no influence on concrete strength. In cases where the concrete strength is influenced by the adhesives, the concrete modification factor can be calculated with Equation 2.3. ' ' , c c c low f n f   (2.3) Where: n = adhesive dependent constant provided by the adhesive manufacturer f’c = specified compressive strength of concrete, psi f’c, low = concrete strength used to establish bond stress (τ), psi 2.1.3.3. Concrete Cone Model Pullout tests performed on anchors with shallow embedment depths typically exhibit concrete cone failure. This type of failure can be modeled based on concrete cone models or the concrete capacity design (CCD) approach. CCD models are based on theoretical and experimental models of cast-in-place headed anchors and assume a projected failure area around anchors to be square in plan view (Eligehausen and Sawade, 1989). Fuchs et al. (1995) recommended a cone angle of 35 degrees for CCD models and a cone side length of three times the anchor embedment depth. Cook (1999) recommended a cone angle of 45 degrees. The general form of cone models is given by the following equation. 'n c ef cN k h f   (2.4) Where: 14 Nc = pullout resistance of concrete cone, lb k = empirical coefficient based on type of anchor hef = embedded length of anchor excluding the head of headed anchors, in. n = 2 for CCD models or 1.5 for concrete cone models For post-installed adhesive anchors, Eligehausen (1984) proposed that k = 0.92 based on the assumption that the cone fails at a circular angle, resembling a semi-circle in a CCD model. 2 '0.92c ef cN h f   (2.5) ACI 349 (1985) provided the following equation for the concrete cone model. 2 ' 1 oc ef c ef d N k h f h            (2.6) Where: do = diameter of anchor hole, in. 2.1.3.4. Combined Concrete Cone and Bond Models Cook (1993) proposed models for the design of steel anchors when concrete cone failure and bond failure can occur simultaneously. These models are based on the relationship between the embedment length (hef) and depth of the concrete cone (hc). The following equations represent the combined concrete cone and bond model assuming a linear distribution of stresses along the embedded anchor depth. 2 '; 0.92 ; and 0c ef cc ef c cbh h N h f N     (2.7) 2 '; 0.92 ; and ( )c ef cc c c cb o o ef ch h N h f N d h h         (2.8) Where: '1.84 o o c c d h f     (2.9) o = uniform bond stress, psi The following equations represent the combined concrete cone and bond model assuming a non-linear distribution of stresses along the embedded anchor depth. 2 '; 0.92 ; and 0c ef cc ef c cbh h N h f N     (2.10) 15 2 ' ' max ' ; 0.92 ; and ( ) tanh c ef cc c c ef co cb o o h h N h f h hd N d d                      (2.11) Where: ' 2max ' ( ) sech 1.84 ef co c oc h hd h df                  (2.12) max = non-uniform bond stress, psi ' = an experimentally determined elastic property of the adhesive anchor system, independent of anchor area The design models for the anchor failure modes discussed here provided the basis for the design models in ACI 318 (2014). 2.2. Post-Installed Steel Reinforcing Bars The installation procedure for post-installed steel reinforcing bars is similar to that of post-installed adhesive anchors. The design and behavior of post-installed steel reinforcing bars is dependent on the same factors as post-installed adhesive anchors, such as embedment depth, concrete strength, diameter of reinforcing bar, bar spacing, and edge distance (Hilti, 2011). Research performed on post-installed steel reinforcing bars is discussed in subsequent sections. 2.2.1. Spliced and Non-Spliced Post-Installed Steel Rebar Spieth et al. (2001) performed a numerical and experimental analysis of post- installed rebar spliced with cast-in-place rebar. The study involved two types of post- installed rebar connections: without splicing with existing rebar (type 1) and spliced with existing rebar (type 2). Three different types of adhesives (epoxy, polyester and hybrid) were used for post-installing rebar. Cast-in-place rebar installed without adhesives was used as reference. For type 1 connections, confined pullout test were performed and load displacement curves were recorded. The results indicated that the rebar installed with an epoxy-based adhesive exhibited the greatest stiffness and peak load compared to polyester-based and hybrid adhesives. The stiffness and peak load was similar for both 16 cast-in-place rebar and rebar installed with a hybrid adhesive. Rebar installed with polyester-based adhesive had the greatest ductility and half of the peak load as observed in cast-in-place reinforcing bar specimens. For type 2 connections, the load carrying capacity and stiffness behavior was similar to type 1 connections for all adhesives and cast-in-place specimens, with failure mode being the only difference. The specimens with type 1 connections had concrete cone breakout failure and all the specimens with type 2 connections had splitting failure. Splitting failure was due to inadequate concrete cover and the absence of transverse reinforcement. Specimens with rebar post-installed using an epoxy adhesive had higher bond strength and bond stiffness compared to specimens with cast-in-place rebar for both connections. The authors concluded that post-installed rebar could be designed as cast-in-place reinforcement as long as minimum concrete cover and embedment depth are provided. Eligehausen and Spieth (2002) conducted an experimental research to study the factors affecting bond strength of post-installed rebar. This study also involved a comparison of manufacturer recommended bond lengths and splice lengths with those required by existing concrete codes [ACI 318M (1989), Eurocode (1992), and British Standard BS-8110 (1985)]. Two types of specimens were prepared: single post-installed bars and rebar spliced with cast-in-place bars. Pullout tests with confinement were performed for single post-installed bars. Confinement was provided to avoid concrete cone failure. The testing parameters included: concrete strength, bar diameter, embedment depth, concrete cover, hole cleaning, moisture content of concrete, and drilling system. Reinforcing bars post-installed in a concrete slab with a small concrete cover exhibited a splitting failure, whereas the bars with the same diameter and embedment exhibited a pullout failure for larger concrete cover. The manufacturer recommended hole cleaning method was the most efficient cleaning method compared to other methods tested in this study. Hammer drilling was found to be a better drilling system compared to diamond drilling for post-installing bars in dry concrete. Bond strength decreased with an increase in temperature for both adhesive manufacturers. Increase in concrete strength caused an increase in bond strength of post-installed 17 reinforcing bar, but this gain in bond strength was not as significant as observed in cast- in-place reinforcing bars. Eligehausen and Spieth (2002) used beam specimens with spliced, post-installed rebar to study the effect of splicing. Beams were prepared with cast-in-place reinforcing bars extending slightly beyond the midpoint of beams. Post-installed reinforcing bars were installed with manufacturer recommended splice lengths and code (ACI 318M, 1989) required splice lengths. The beams with post-installed rebar failed due to splitting of the concrete cover. The results showed that beams with Code required splice lengths failed at a higher load compared to reference beams with cast-in-place rebar. On the other hand, beams with manufacturer recommended splice lengths failed at a lower load than the beams with cast-in-place rebar. The authors concluded that the manufacturer recommended splice lengths were shorter than the code required splice lengths because those recommendations were typically based on specimens with large concrete cover and bar spacing. 2.2.2. Splitting Design for Post-Installed Rebar Kunz (2005) proposed a splitting design method for anchorages and splices with post-installed rebar. Splitting failure was identified as the most common failure mode for post-installed rebar applications, where spacing and edge distance were limited. The existing design for anchorage and bar splicing for cast-in-place reinforcement took into account concrete cover and the presence of transverse reinforcement. In addition to these factors, design with post-installed reinforcement required a factor to account for the adhesive between the rebar and concrete. Cast-in-place reinforcement requires a minimum length to develop a force equivalent to a splitting or pullout force. The following equation was proposed by Kunz (2005) to calculate splitting bond stress, ,sp d , which took reduced confinement and presence of an adhesive into account. ' , 2.5 2.5 4 tr c b sp d c K f d                (2.13) Where: 18 δ = splitting reduction factor, which varies between 0.7 and 0.8 based on adhesive manufacturer recommendations c = minimum concrete cover or side cover, in. Ktr = cross-sectional area of transverse reinforcement available to restrain splitting cracks along the bar being developed db = bar diameter, in.  = reinforcement size factor (0.8 for #6 and smaller bars and 1.0 for #7 and larger bars) 2.2.3. Post-Installed Rebar in Beam-Column Connections Hamad et al. (2006) conducted a research experiment to study anchorage characteristics of post-installed straight reinforcing bars. The variables investigated included bar size (0.47 and 0.55 in.), concrete strength (2.2 and 2.9 ksi), embedment depth (5.91, 9.84, and 11.42 in.), rebar placement method (cast-in-place and post- installed), anchorage method (straight and hooked bars), and adhesive type (epoxy and cementitious). A test specimen was designed to simulate a stiff connection between a column and a beam. The post-installed reinforcing bars were subjected to tensile load by means of hydraulic rams. Specimens were divided into sets of three or four with each set having variable anchorage methods but the same embedment depth, bar size, and similar concrete strength. For an embedment depth of 5.91 in., specimens with post-installed bars using a cementitious-based adhesive exhibited similar load carrying capacity and stiffness as specimens with straight, cast-in-place reinforcing bars. However, the specimens with post-installed bars using an epoxy-based adhesive achieved higher loads and greater stiffness. For embedment depths of 9.84 and 11.42 in., the stiffness was similar among all specimens, but the load carrying capacity varied. Specimens with cast-in hooked bars had the highest load due to additional bonding area between rebar and concrete. The highest to lowest loading capacities among specimens with straight bars was in this order: post- installed using an epoxy-based adhesive, cast-in-place without adhesives and post- installed using a cementitious-based adhesive. Specimens with cast-in-place hooked bars failed with excessive spalling normal to the plane of the hook. Specimens with straight bars failed with intensive cracking along the depth of the post-installed bars. Cracking patterns and failure modes among specimens with straight bars were independent of bar 19 size and concrete strength for 9.84 and 11.42 in. embedment depths. For the shorter embedment depth of 5.91 in., a concrete cone breakout failure occurred with the cone depth being equal to the embedment depth. The study concluded that post-installed reinforcing bars developed equivalent or greater bond strength than the reference specimen with cast-in-place reinforcing bars. 2.2.4. Design Methodology for Post-Installed Rebar Building Code Requirements for Structural Concrete (ACI 318-14) is the most widely accepted Code used for designing the concrete structures in the United States, but ACI 318 does not have any direct provisions for designing post-installed rebar. ACI 318 (2014) does provide provisions for designing post-installed anchors in Chapter 17 and it provides development length provisions for the design of cast-in-place reinforcing bars in Chapter 25. The aforementioned design provisions are often used in conjunction to design post-installed reinforcing bars. Charney et al. (2013) recommended that the provisions provided for post-installed anchors and cast-in-place reinforcing bars in the existing concrete Code at that time, ACI 318 (2011), be used to design post-installed reinforcing bars. These design recommendations also considered the design methodology provided by ACI 355.4 (2011). These design recommendations were divided into three broad categories: Case I – bars installed near edge conditions, Case II – bars installed away from edges, and Case III – applications that lie somewhere in between. The design procedures for these conditions are further discussed in detail below. 2.2.4.1. Case I from Charney et al. (2013) This case is encountered commonly when the post-installed reinforcing bars have to be spliced to the existing cast-in-place reinforcing bars. The failure mode is assumed to be splitting failure. Initially, the designer should select an adhesive system based on manufacturer provided bond stress values that exceed the required bond stress. Equivalent bond stresses, eq , are computed using the following equations (Equation 4a and 4b in Charney et al., 2013). For rebar size # 6 and smaller 20 4.16 ' 10.3 ' c Kb tr eq c cdb f f             (2.14) For rebar size # 7 and greater 3.33 ' 8.33 ' c Kb tr eq c cd b f f             (2.15) Where: = 0.8 for lightweight concrete and 1.0 for normal weight concrete cb = lesser of: (a) the distance from the center of a bar or wire to the nearest concrete surface, and (b) one-half the center-to-center spacing of bars or wires being developed, in. The next step is to determine the available edge distance for the installation of post-installed reinforcing bars. The drilling method, such as hammer or diamond core drilling, used for post-installing rebar is the controlling factor in these situations due to limited space between the existing rebar and concrete edge. It is important not to damage existing concrete and rebar. The final step is to calculate the required development length, ld, given by Equation 25.4.2.3a of ACI 318 (2014). ' 3 40 y e s t d b b trc b f l d c Kf d                (2.16) Where: fy = specified yield strength of reinforcing bar, psi ψe = factor used to modify the development length based on reinforcement coating ψs = factor used to modify the development length based on reinforcement size ψt = factor used to modify the development length for casting location in tension b tr b c K d  = confinement term The confinement term should be less than or equal to 2.5. In situations, where there is no transverse reinforcement or the edge distance is greater than 2.5db, the confinement term should be taken as equal to 2.5. 21 2.2.4.2. Case II from Charney et al. (2013) In applications where the post-installed reinforcing bars are away from edges, the provisions for post-installed anchors described in Appendix D of ACI 318 (2011) should be used [these provisions were moved to Chapter 17 of ACI 318 (2014)]. The predominant failure modes in this case are concrete breakout and bond failure. The design methodology is described below. The first step is to select the adhesive anchoring system based on the design bond stress value and the effectiveness factor, kc. The next step is to determine the required bar length to develop loading capacity greater than the load required for bar yielding. An equation for the force at which the bar yields is given in Charney et al. (2013) and shown below. 1.25c b yN A f (2.17) Where: Nc = resultant tensile force acting on the portion of the concrete cross section that is subjected to tensile stresses due to the combined effects of service loads and effective pressure, lb Ab = area of the reinforcing bar, in.2 fy = specified yield strength of reinforcing bar, psi The resultant tensile force (Nc) should be the greater of the concrete breakout strength in tension or the bond strength in tension. max ( , )c cbg agN N N (2.18) Where: Ncbg = nominal concrete breakout strength in tension of a group of adhesive anchors or post-installed bars, lb Nag = nominal bond strength in tension of a group of adhesive anchors or post-installed bars, lb The nominal concrete breakout strength is given by equation 17.4.2.1b in ACI 318 (2014). , , , , Nc cbg ed N c N cp N ec N b Nco A N N A       (2.19) 22 Where: ANc = projected concrete failure area of a single bar or group of bars, for calculation of strength in tension, in.2 ANco = projected concrete failure area of a single bar or group of bars, for calculation of strength in tension if not limited by edge distance or spacing, in.2 ψed,N = factor used to modify tensile strength of bars based on proximity to edges of concrete members ψc,N = factor used to modify tensile strength of bars based on absence or presence of cracks in concrete ψcp,N = factor used to modify tensile strength of post-installed bars intended for use in uncracked concrete without supplementary reinforcement to account for splitting tensile stresses due to installation ψec,N = factor used to modify tensile strength of bars based on eccentricity of the applied loads Nb = basic concrete breakout strength in tension of a single bar in cracked concrete, lb The factor ψed,N can be taken as 1.0 in this case because the bars are post-installed away from the edges. The factor ψc,N can be taken as 1.4 for post-installed bars. The factor ψcp,N can be taken as 1.0, when the minimum distance from center of a bar to the edge exceeds the critical edge distance required to prevent splitting. The factor ψec,N can be taken as 1.0 under eccentrically applied loads. The ratio between ANc and ANco becomes unity if the post-installed rebar is located beyond the 1.5 times the effective depth of the bar from the edge of the concrete member. The basic concrete breakout strength for a single bar in cracked concrete is given by Equation 17.4.2.2a of ACI 318 (2014). 1.5 'N k f h b c c ef     (2.20) Where: kc = coefficient for basic concrete breakout strength in tension (17 for cracked concrete and 24 for uncracked concrete) hef = effective embedment depth of bar, in. 23 The difference between the concrete breakout and bond strength equations is that the concrete is assumed uncracked in the latter. The bond strength in tension is determined using Equation 17.4.5.1b of ACI 318 (2014). , , , A NaN N ag ec Na ed Na cp Na baA Nao      (2.21) Where: ANa = projected concrete failure area of a single post-installed bar or group of post- installed bars, for calculation of strength in tension, in.2 ANao = projected concrete failure area of a single post-installed bar or group of post- installed bars, for calculation of strength in tension if not limited by edge distance or spacing, in.2 ψec,Na = factor used to modify tensile strength of post-installed bars based on eccentricity of the applied loads ψed,Na = factor used to modify tensile strength of post-installed bars based on proximity to edges of concrete members ψcp,Na = factor used to modify tensile strength of post-installed bars intended for use in uncracked concrete without supplementary reinforcement to account for splitting tensile stresses due to installation Nba = basic bond strength in tension of a single post-installed bar, lb. The factor ψed,Na become 1.0 in this case because bars are installed away from the edges. The factor ψcp,Na can be taken as 1.0, when the minimum distance from center of a bar to the edge exceeds the critical edge distance required to prevent splitting. The factor ψec,Na can be taken as 1.0 under eccentrically applied loads. The other terms in Equation 2.21 are illustrated below. 2(2 )Nao NaA c (2.22) Where: cNa = projected distance from center of a post-installed bar on one side of the bar required to develop the full bond strength of a single post-installed bar, in. 10 1100 uncr Na ac d     (2.23) 24 Where: da = outside diameter of bar or shaft diameter of headed stud, headed bolt, or hooked bolt, in. τuncr = characteristic bond stress of post-installed bar in uncracked concrete with a minimum value of 650 psi for outdoor applications and 1000 psi for indoor applications The basic bond strength in tension of a single post-installed bar is determined by Equation 17.4.5.2 of ACI 318 (2014). ba cr a a efN d h     (2.24) Where: τcr = characteristic bond stress of post-installed bar in cracked concrete with a minimum value of 200 psi for outdoor applications and 300 psi for indoor applications a = modification factor to reflect the reduced mechanical properties of lightweight concrete The larger of concrete breakout strength (Ncbg) or bond strength (Nag) is taken as the tensile force acting on concrete cross section (Nc), which must be greater than the yield stress of the steel bars. 2.2.4.3. Case III from Charney et al. (2013) This case is used when the other two cases do not apply because of rebar proximity to the edge of the existing concrete. This case is applicable to situations where all three predominant failures including splitting, concrete breakout and bond are likely to happen. The difference between Case II and Case III is that the factors ψed,N and ψed,Na become applicable. The rest of the design method is similar to Case II. These factors can be computed by using Equations 17.4.2.5b and 17.4.5.4b of ACI 318 (2014). ,min , 0.7 0.3 1.01.5 a ed N ef c h       (2.25) Where: ca,min = minimum distance from the center of an post-installed anchor to the edge of concrete, in. 25 ,min , 0.7 0.3 1.0 a ed Na Na c c      (2.26) 2.3. GFRP The subsequent sections cover previous research done on the use of cast-in-place GFRP in reinforced concrete. 2.3.1. Physical and Mechanical Properties The properties of FRP are divided into two categories, physical and mechanical. The physical properties deal with the molecular structure of the material, whereas the mechanical properties are associated with the response of the material during its application (i.e., under mechanical loads). The physical properties are related to geometry, mass, chemistry and temperature. The mechanical properties of GFRP bars include tensile, shear, compressive and bond strength. The flexural properties of GFRP bars in reinforced concrete are also of importance. The bond strength and bond mechanism of GFRP bars are major topics and discussed separately in Section 2.3.2. The properties of GFRP bars are discussed in detail below. 2.3.1.1. Density The properties of FRP bars vary due to variations in the manufacturing process and the type of composite materials used. GFRP is about five times lighter than steel, which means that the transportation and handling costs of GFRP bars will be lower than that of steel (ACI 440.1R, 2015). The density values of different FRP bars are listed in Table 2-1. 2.3.1.2. Coefficient of Thermal Expansion The coefficient of thermal expansion is similar in both directions in concrete and steel, but varies for FRP bars in the longitudinal and transverse directions. A negative value of the FRP coefficient of thermal expansion indicates contraction of a bar. The coefficient thermal expansion is dependent on the properties of fibers and resins respectively (Bank, 1993). The coefficient of thermal expansion of concrete and GFRP bars in the longitudinal direction is similar, which indicates that a minimal amount of internal stresses will be generated during a change in temperature. The coefficient of thermal expansion in the transverse direction for GFRP bars is twice as much as concrete, 26 as shown in Table 2-2, which can lead to concrete cracking at higher temperatures (Bank, 1993). 2.3.1.3. Moisture Moisture is considered a hygroscopic property, which has a physical impact on FRP bars. As opposed to steel rebar, the presence of moisture affects the behavior of GFRP bars. The presence of moisture can cause FRP bars to expand. The amount of moisture is quantified by the coefficient of moisture expansion. The coefficient of moisture expansion, like the coefficient of thermal expansion is anisotropic in nature for FRP bars (Bank, 1993). The expansion resulting from moisture in FRP bars can cause internal stresses in reinforced concrete. Due to this reason, ACI 440.1R (2015) limits the average size of FRP bars to be within 1% of the original size (or the diameter). FRP bars do not have uniform moisture distribution across the whole bar due to the use of multiple composite materials, with each composite material having its own hygroscopic property (Bank, 1993). Abdel-Magid et al. (2005) studied the effects of moisture on GFRP bars by submerging them for 3,000 hours in water and concluded that the absorption of water in GFRP bars led to a reduction in the stiffness of the GFRP bars. Agarwal and Broutman (1990) reported that the expansion in the longitudinal direction due to moisture is minimal and can be assumed equal to zero. The transverse coefficient of moisture expansion depends mainly on expansion of the matrix material in the FRP bar (Agarwal & Broutman, 1990). 2.3.1.4. Tensile Properties When subjected to tensile loading, GFRP bars do not exhibit plastic behavior and do not have a yield stress similar steel (ACI 440.1R, 2015). The load-displacement behavior of GFRP bars stays linear until failure. GFRP bars have a range of tensile strength much larger than that of steel. This is due to variation in the manufacturing process, quality control, and curing rates of composite materials used in GFRP bars (Wu, 1990). GFRP bars can only be bent during the manufacturing process, but they undergo a significant reduction in tensile strength (40 to 50%) when they are bent. ACI 440.1R-15 provides guidelines on bending FRP bars. The tensile properties of GFRP bars are onerous to measure and the guaranteed tensile strength can be obtained from the 27 manufacturer (ACI 440.1R, 2015). A low modulus of elasticity and a low strain at failure in GFRP bars compared to steel rebar indicates the brittle nature of GFRP bars. The tensile properties of GFRP bars are listed in Table 2-3. 2.3.1.5. Flexural Properties The flexural properties of cast-in-place GFRP bars become relevant when a reinforced concrete element is subjected to bending. The flexural properties of GFRP bars in reinforced concrete are affected by the bar diameter, reinforcement ratio (ratio of rebar area to member cross section), concrete strength, and the surface condition of the GFRP bars. The flexural properties of GFRP bars under static load have been studied in the past. Faza and GangaRao (1990) studied the crack patterns and flexural behavior of rectangular beams reinforced with GFRP bars by applying a pure bending moment. The parameters tested included bar size, concrete strength (5 and 6 ksi), rebar surface (sand coated or smooth), and different types of stirrups (steel and GFRP). The authors reported that cracks developed earlier and crack widths were wider in beams reinforced with smooth surface GFRP compared to the steel reinforced beams, whereas the beams with sand coated GFRP bars exhibited higher moment capacity and narrow crack widths than both the beams reinforced with steel and smooth surface GFRP. Ascione et al. (2010) subjected ten GFRP reinforced beams to four point bending load. The four points typically consist of two supports (bottom face of the beam) and the two point loads applied on the beam (top face of the beam). The variables studied were concrete strength (3 and 4 ksi) and reinforcement ratio (0.5 and 1.3%). The beams exhibited linear behavior in both the pre-cracking and post-cracking zone. The peak load in the reference specimens (reinforced with steel) was observed to be higher than all the specimens with GFRP reinforcement. The higher loading capacity of beams reinforced with steel under bending indicated that GFRP reinforcement is suitable in conjunction with higher strength concrete because the difference in bending capacity of GFRP reinforced beams with respect to reference beam became smaller as the concrete strength was increased. The ultimate failure in compression-controlled beams was concrete crushing. The ultimate failure in beam with balanced reinforcement (producing balanced 28 strain on both the compression and tension face of the beam) was found to be a combination of both crushing and sudden failure on the tension side indicating a brittle failure. A similar study conducted by Kalpana and Subramanian (2011) also showed that GFRP reinforced beams with higher strength concrete and a higher reinforcement ratio showed an improvement in the ultimate load and loss in ductility, respectively compared to the beams with lower strength concrete and lower reinforcement ratio. Goldston et al. (2016) studied the response of GFRP reinforced concrete beams with variable bar diameter (#2, #3 and #4), concrete strength (6 and 12 ksi) and reinforcement ratio (0.2 to 7.6%) under four point bending. The failure modes in compression controlled beams (ϕ = 0.65) was crushing of the concrete under the loading points, whereas the failure in tension controlled beams (ϕ = 0.55) was rupture of the GFRP bars. The higher strength concrete beams with a higher reinforcement ratio had an increased stiffness before initial cracking and an increased ductility after cracking occurred. The beams with a reinforcement ratio of 1% improved the stiffness by 25% compared to a bema with a reinforcement ratio of 0.2%. A further increase in reinforcement ratio to 2% did not improve stiffness compared to the beam with 1% reinforcement ratio. The increase in concrete strength had negligible impact on the moment capacity. The load-deflection behavior was bilinear in both the normal and higher strength concrete beams. The bar diameter did not significantly affect the load capacity and stiffness. Kumari et al. (2013) studied the elastic behavior of rectangular beams reinforced with GFRP bars having different surface conditions. Higher deflections were observed in beams reinforced with both sand coated and smooth GFRP bars, which resulted in higher ductility. The beam reinforced with sand coated GFRP bars failed at a higher load than the beam with smooth surface GFRP. It was also reported that the failure of beams reinforced with GFRP bars was abrupt, which was due to the splintering of the GFRP fibers under tension. It was concluded that sand coated GFRP bars improved ductility because of their higher rupture strength compared to smooth surfaced GFRP bars. El-Gamal et al. (2010) studied the deflection behavior of concrete beams reinforced with GFRP bars from three different manufacturers and three bar sizes (#5, #6 29 and #7). This study included testing beams under four point bending until failure. With a constant reinforcement ratio, the beams with smaller diameter GFRP bars were more ductile compared to beams with larger bar diameter. Additional stiffness was obtained by increasing the reinforcement ratio and increasing bar diameter. Shin et al. (2009) also studied the effect of concrete strength (4.5 and 7 ksi) and reinforcement ratio (under and over reinforced compared to balanced reinforcement) in beams reinforced with GFRP bars. This study also verified the aforementioned studies about the bilinear nature of the load deflection curves, increased ductility after initial cracking and the reduction of cracks and crack widths at higher concrete strengths for beams reinforced with GFRP bars compared to steel reinforced beams. 2.3.2. Bond Behavior of GFRP Bond between the reinforcement and the concrete is a key factor in transferring loads in a reinforced concrete member (ACI 408, 2003). Compressive loads are resisted by the concrete and tensile loads are resisted by the reinforcement. ACI 408 (2003) defines three different types of mechanisms, which are responsible for the transfer of forces between reinforcement and concrete. 1. Chemical adhesion between the bar and the concrete 2. Frictional resistance against slip due to the roughness at the interface between the reinforcing bars and the surrounding concrete 3. Mechanical anchorage of the ribs against the concrete surface Chemical adhesion between the bar and the concrete is the primary load transfer mechanism. As the concrete member ages and the adhesion between the concrete and the reinforcement becomes weaker during its service life, the frictional force and the mechanical anchorage between the concrete and rebar become the primary load transfer mechanisms. The load transfer mechanism and its relationship to bond strength are discussed in detail in ACI 408 (2003) and are summarized below. The tensile forces in the reinforcing bars are balanced by the compressive forces in the concrete. During the transfer of these opposing forces, concrete in the immediate vicinity of the reinforcing bars develop micro cracks along the length of the reinforcing bars. The transfer of forces creates radial cracks perpendicular to the reinforcement as 30 well as cracks parallel to the reinforcement. The radial micro cracks grow outward and converge towards the path of least resistance, which potentially causes a splitting failure, whereas the parallel cracks along the reinforcement may result in a pullout failure. Splitting failure occurs due to insufficient concrete cover, spacing between bars, and confining reinforcement. The bond strength can be enhanced by proper consolidation of concrete around the reinforcement, the presence of transverse reinforcement, providing sufficient bar spacing and concrete cover. The bond behavior of GFRP bars is different from the bond behavior of steel bars. The difference is mainly attributed to the mechanical properties and the varying surface texture of GFRP bars. The bond behavior of the GFRP bars also depends on the manufacturing process, loading conditions, and the environmental conditions (Bank et al., 1995). The effects of the manufacturing process are typically related to the type of resin used to bind the glass particles during the manufacturing of GFRP bars. The loading conditions include cyclic, static, and dynamic. The environmental conditions include temperature and moisture. Yan et al. (2016) identified five types of failure modes associated with GFRP bars used as reinforcement in concrete. These failure modes are pullout, splitting of concrete, peeling off the resin, GFRP bar fracture and anchorage failure. Peeling off the resin occurs when the stress applied to a GFRP bar exceeds the bond strength of the resin, which binds the glass fibers. The bond behavior and bond strength can be indicated by the failure mode and quantified by the bond strength equations recommended by ACI 440 (2015). The average bond stress of the GFRP bars is given by ACI 440 (2015) Equation 10.1b and is shown below. ' 4.0 3.0 100 b b ec du C d lf      (2.27) Where: u = average bond stress acting on the surface of the GFRP bar, psi f’c = specified concrete strength, psi C = spacing or cover dimension, in. db = diameter of the GFRP reinforcing bar, in. le = embedded length of the reinforcing bar, in. 31 The factors that affect the bond strength of cast-in-place GFRP bars in concrete are discussed in detail below. 2.3.2.1. Concrete Cover Sufficient concrete cover is essential for the bond development of GFRP bars and improves the bond strength by confining the GFRP bars (Yan et al., 2016). Aly (2007) studied the effects of concrete cover on the bond strength of GFRP bars. The study involved the testing of six beams reinforced with #5 and #6 GFRP bars under four point bending load. The results indicated that the bond strength increased by 27% when the concrete cover was increased from db to 4db. The amount of concrete cover also affects the type of failure mode in reinforced concrete members (Untrauer and Henry, 1965). Yan et al. (2016) compiled the previous studies performed on the effect of concrete cover on the type of failure in GFRP reinforced specimens. The concrete cover was equal to the bar diameter in 40 specimens. Out of these 40 specimens, 20 specimens had pullout failure and the other 20 specimens exhibited splitting failures. The increase in concrete cover to four times the bar diameter caused pullout failure in about 80% of the specimens. The authors concluded that the increase in concrete cover provided beneficial confining effects. 2.3.2.2. Bar Diameter The effect of bar diameter on bond strength of GFRP bars has been studied in detail by Faza and Gangarao (1993), Okelo and Yuan (2005), Baena et al. (2009), Ha et al. (2009) and Alves et al. (2011). An increase in the diameter of GFRP bars was found to reduce bond strength in all of the referenced studies. Larrad et al. (1993), Qayyum (2010) and Alves et al. (2011) concluded that the reduction in bond strength with larger bar diameters was attributed to an increased contact area between the concrete and GFRP bars. The increased contact area can lead to voids or other defects during the pouring of the concrete, which may result in a weakened bond between the concrete and reinforcing bar. Baena et al. (2009) attributed the reduction in bond strength to Poisson’s ratio, which is defined as the ability of a material to contract in a direction normal to the applied tensile loading. The bars with a larger diameter have a higher tendency to contract compared to the bars with a smaller diameter, which explains the reduced bond strength 32 of the larger diameter bars. Achiledes and Pilakoutas (2004) concluded that the reduction in bond strength could be due to the accumulation of bleed from the creation of voids around the larger diameter bars, which would result in a weaker bond between the concrete and GFRP bars. Yan et al. (2016) compiled the studies, which related failure types and bar diameters. The authors indicated that no direct correlation existed between the bar diameter and failure type. Pullout was the predominant failure across all GFRP bar sizes. Splitting failure became more common when the bar diameter was increeased. The rest of the failure types did not relate to bar diameter. 2.3.2.3. Casting Position of Bar The position of GFRP bars in reinforced concrete members has a significant impact on bond strength. Horizontal reinforcing bars placed in a concrete member with more than 12 in. of concrete to be poured below the bar are referred to as top reinforcing bars ( ACI 318, 2014; ACI 440, 2015). In this scenario, coarse aggregate settles below the bar and the rest of the constituent materials in the concrete mix move upwards during concrete placement. This may cause a drop in bond strength under the horizontal reinforcement (ACI 440, 2015). Ehsani et al. (1996) studied the effect of bar position on the bond strength of GFRP bars. The study involved pullout tests on 21 pairs of bottom and top bars with varying depths of concrete below the GFRP bars. The ratio of bond strength of bottom bars and top bars was computed. The ratios were observed to be greater than one for all the specimens, which verified that the top reinforcing bars exhibited lower bond strength compared to the bottom reinforcing bars. Wambeke and Shield (2006) proposed a location modification factor to account for a reduction in bond strength of top horizontal reinforcement. Wambeke and Shield (2006) noted that the computed bond stress should be divided by the location modification factor of 1.5 for top GFRP bars, whereas ACI 318 (2014) recommends the location modification factor to be taken as 1.3 for steel rebar. 2.3.2.4. Presence of Transverse Reinforcement The use of transverse reinforcement in concrete members provides confinement, delays splitting failure and increases the ductility, thus improving the bond strength between steel reinforcing bars and concrete (ACI 408, 2003). The presence of transverse 33 reinforcement does not affect the bond development of GFRP bars because the bar surfaces contain small or no ribs (Wambeke and Shield, 2006). Therefore, the development length equation for GFRP bars does not include the confinement factor (ACI 440, 2015), which is denoted as b tr b c K d  in ACI 318 (2014). 2.3.2.5. Surface Texture The surface texture of GFRP bars can vary and may include a sand coating, helical wraps with sand coating, ribs, and helical wraps. The surface texture of GFRP bars can affect the bond development and bond strength between the concrete and the bar. Mosley et al. (2008) studied the difference in bond strength of sand coated and ribbed GFRP bars. The experimental program consisted of testing 12 ft long beam specimens. The loading was applied at the end of the beams and supports were provided 3 ft from the ends. GFRP reinforcing bars were provided at the top of the beams. The results indicated that the bond strength of sand coated GFRP bars was higher compared to ribbed bars at a concrete strength of 5.6 ksi, whereas the bond strength of ribbed GFRP bars was slightly higher than that of sand coated GFRP bars at concrete strength of 4.1 ksi. This led to the conclusion that ribbed GFRP bars have higher bond strength at 4.1 ksi and sand coated GFRP bars had a higher bond strength at concrete strength at 5.6 ksi when compared with each other. Baena et al. (2009) compared the behavior of helically wrapped and ribbed GFRP bars by performing pullout tests. The bond strength of helically wrapped GFRP bars was observed to be significantly higher than ribbed GFRP bars at all of the studied concrete strengths (ranging from 60 to 230%). Ha et al. (2009) investigated the effect of rib height and rib spacing on GFRP bar bond strength. The authors reported that the bond strength of bars with rib spacing equal to the bar diameter and rib height of 6% of the bar diameter was superior to bars with greater rib spacing and heights. Yan et al. (2016) assembled the studies that correlated failure modes and the surface textures of the GFRP bars. Pullout was the predominant failure mode found in over 84% of the cases among all the surface treatments. 34 2.3.2.6. Concrete Strength In the literature, the square root of the concrete strength (f’c1/2) was found to directly relate to the bond strength between GFRP bars and concrete (Okelo and Yuan, 2005). Ehsani et al. (1996) studied the effects of concrete strength (4 and 8 ksi) on the bond strength of GFRP bars by performing pullout tests. The results showed that an increase in concrete strength lead to an increase in bond strength and initial stiffness. The bond slip at ultimate failure also occurs at lower load in higher strength concrete specimens. Davalos et al. (2012) also studied the relationship between bond strength and f’c1/2. Experimental results of their study were compared with predicted bond strengths using ACI 440 (2006) and other international codes. The results demonstrated that the bond strength predicted by ACI 440 (2006) was not conservative enough at lower concrete strengths, whereas ACI 440 (2006) was found to be more conservative at higher concrete strengths compared to the other codes. Cosenza et al. (2002) studied the bond development of GFRP bars and performed pullout tests on specimens with variable concrete strengths. For specimens with a concrete strength less than 4.35 ksi, pullout failure occurred due to a breakdown of surrounding concrete, without any damage to the GFRP bars. For specimens with a concrete strength between 4.35 and 8 ksi, the concrete broke down and the outer surface of GFRP bars was damaged, resulting in a pullout failure. For specimens with a concrete strength greater than 8 ksi, the GFRP bars were ruptured and negligible damage occurred in surrounding concrete. Therefore, an increase in the concrete compressive strength may improve the bond strength between GFRP bars and concrete. Yan et al. (2016) summarized the results of all the studies relating concrete strength and failure modes. The authors found that 90% of the specimens with concrete strengths less than 4 ksi exhibited a pullout failure and the rest of the specimens had a splitting failure. The specimens with concrete strengths greater than 8 ksi had an equal number of specimens with pullout failure and peeling off of the resin from the GFRP bars, reiterating the fact that increasing the concrete strength may improve the bond strength. 35 2.3.2.7. Embedment Depth Ehsani et al. (1995) found that an increase in the embedment depth resulted in an increased GFRP bar bond strength and more initial stiffness. The authors found that the bond slip at ultimate failure increased in specimens with a larger embedment depth. Achiledes and Pilakoutas (2004) reported that bond strength of GFRP bars increased with an increase in embedment depth. This was most noticeable at shallower embedment depths compared to longer embedment depths. An increase of bond strength at longer embedment depths was observed to be lower than the increase observed at shallower embedment depths and ultimately reached a point of diminishing returns. Makitani et al. (1993) conducted pullout tests and found that rupture failure of GFRP bars (#4 and #8) occurred at embedment depths greater than 40db. This leads to the conclusion that the embedment depth of 40db is the point of diminishing returns in terms of embedment depth for GFRP bars and any further increases of embedment depth beyond 40db may be superfluous. Yan et al. (2016) plotted a bar chart of all the past studies that related the failure modes and the ratio of embedment depth to bar diameter (ld/db). Pullout failure was the only type of failure observed in all the specimens with an ld/db ratio less than 5. An ld/db ratio of 5 to 6 was found to be optimal for increasing bond strength because test specimens with this ratio were equally likely to fail in pullout and by peeling off the resin from the GFRP bars. There were few failures via bar fracture and splitting. 2.3.2.8. Temperature Masmoudi et al. (2011) studied the effects of elevated temperatures on the bond strength of GFRP bars. The bond strength was determined by performing pullout tests on GFRP bars cast-in-place in concrete slabs at an embedment depth of 5db. The specimens were subjected to temperatures of 104, 140 and 176oF for the duration of 4 and 8 months. The pullout strength results were compared with results of a reference specimen (with GFRP bars), which was kept at 68oF over the same amount of time. The bond strength of the GFRP bars was found to be unaffected by temperature up to 140oF, regardless of the duration of the exposure. A bond strength reduction of about 10% was noticed at a temperature of 176oF without any damage to the GFRP bars. 36 2.3.2.9. Environmental Degradation Bank et al. (1998) studied the effects of environmental degradation of GFRP bars on bond behavior and developed a method called an “embedded rod-test” to study the degradation effects. This research involved two types of smooth surface and two types of sand coated #4 GFRP bars. The two types of GFRP bars that had the same surface texture had different resins (polyester and vinylester). Test specimens were prepared by inserting 20 in. long GFRP bars in concrete cylinders having a strength of 6.5 ksi. The embedment depth of GFRP bar was 10 in. and the rest of the GFRP bar was exposed. Following a 28- day curing period, the specimens were placed in a water tank at an elevated temperature (176oF) to speed up the degradation process. The specimens were divided into three categories based on the levels of degradation: mild, severe, and reference specimens having no degradation. Microscopic and mechanical tests were conducted on these specimens to study the bond behavior. The mechanical tests clearly indicated a decrease in bond strength and loss of stiffness due to environmental degradation. The microscopic test revealed degradation in both types of FRP bars regardless of surface coatings and resin type. Polyester based GFRP bars exhibited the greatest amount of degradation and were not recommended for use in reinforced concrete applications in severe environments. 2.3.3. Flexural Design Methodology The design methodology for use of GFRP bars as tensile reinforcement in concrete beams is provided in ACI 440.1R (2015). The design steps are similar to those used for steel reinforcement in a concrete member. The flexural capacity can be determined using an equivalent rectangular concrete stress distribution. The design steps are explained below. The first step is to determine the strength reduction factor using an assumed reinforcement ratio. The strength reduction factor, ϕ, is given by ACI 440 (2015) Equation 7.2.3 and is stated below. 37 0.55 for (Tension controlled) 0.3 0.5 for 1.4 (Transition) 0.65 for 1.4 (Compression controlled) f fb f fb f fb fb f fb                    (2.28) Where: ρf = FRP reinforcement ratio = fA bd ρfb = FRP reinforcement ratio producing balanced strain conditions Af = area of FRP reinforcement, in.2 b = width of rectangular cross section, in. d = distance from extreme compression fiber to centroid of tension reinforcement, in. The FRP reinforcement ratio producing balanced strain conditions is given by ACI 440.1R (2015) Equation 7.2.1b and is stated below. ' 10.85 f cuc fb fu f cu fu Ef f E f         (2.29) Where: β1 = factor taken as 0.85 for concrete strength up to 4,000 psi. For strength above 4,000 psi, this factor is reduced continuously at a rate of 0.05 for each 1,000 psi of strength, but is not taken less than 0.65 ffu = design tensile strength of GFRP bar as defined by the guaranteed tensile strength (ffu*) multiplied by the environmental reduction factor (CE) given in Table 2.4, psi Ef = design or guaranteed modulus of elasticity of FRP defined as the mean modulus from a sample of test specimens, psi εcu = ultimate strain in concrete, taken as 0.003 The second design step is to determine the stress in the tensile reinforcement at ultimate conditions. If the strength reduction factor is tension controlled, then ff = ffu. If the strength reduction factor is compression controlled or in the transition, then the stress in the tensile reinforcement at ultimate conditions, ff, is calculated by ACI 440.1R (2015) Equation 7.2.2d as stated below. 38 2 ' 1 ( ) 0.85 0.5 4f fu f cu c f cu f cu f E f f E E f             (2.30) The next step is to determine the required flexural demand, Mu, and use that as the design flexural capacity, ϕMn, to calculate the required size of the member. The required size (bd2) is calculated using ACI 440.1R (2015) Equation 7.2.2e, which is stated below. 2 ' 1 0.59 f f u n f f c f M M f b d f                 (2.31) The member should be sized in such a way that the provided bd2 should be greater than or equal to the required bd2. After sizing the member, the required area of GFRP reinforcement is calculated by the following equation. ,f required fA b d    (2.32) The size and number of bars to be provided should be selected based on the required reinforcement area. The nominal flexural strength, Mn, is computed using ACI 440.1R (2015) Equation 7.2.2a as stated below. ( ) 2 n f f a M f d     (2.33) Where: a = depth of equivalent rectangular stress block, in. The depth of the equivalent rectangular stress block is determined by ACI 440.1R (2015) Equation 7.2.2d, which is stated below. '0.85 f f c A f a f b     (2.34) When the strength reduction factor is tension controlled, the minimum reinforcement provisions have to be checked to ensure that the provided reinforcement is greater than the minimum required reinforcement. The minimum area of GFRP reinforcement required, ,minfA , is given by ACI 440.1R (2015) Equation 7.2.4 and is stated below. ' ,min 4.9 330c f w w fu fu f A b d b d f f        (2.35) 39 Where: bw = width of beam web, in. The final step is to determine the length needed to develop the required bar stress, which is given by ACI 440.1R (2015) Equation 10.3a and is stated below. ' 340 13.6 fr c d b b f f l d C d      (2.36) Where: α = top bar modification factor equal to 1.5 when top reinforcing bar is used ffr = required bar stress, which is equal to the minimum of the design tensile strength (ffu) and the stress in FRP reinforcement bar (ff), psi As per the literature, the bond strength of GFRP varies with the surface condition, but Equation 2.36 does not take into account different types of GFRP bar surface conditions. 2.4. Post-Installed GFRP Bars As mentioned in the previous chapter, there is a dearth of experimental and theoretical data on post-installed GFRP bars. Three studies were found during the literature review process. These studies included pullout strength of post-installed GFRP bars in unreinforced concrete, design models for failure modes, and pullout strength of post-installed GFRP bars in reinforced concrete. These three studies are discussed below. 2.4.1. Pullout Strength of Post-Installed GFRP Bars in Unreinforced Concrete Ahmed et al. (2008) investigated behavior of post-installed GFRP reinforcing bars under monotonous tensile loading. The experimental program included sand coated GFRP bars with three different diameters (0.25, 0.625, and 1 in.), two types of adhesives (epoxy and cement based), and three embedment depths (5db, 10db, and 15db). The GFRP bars were installed in 136 in. long by 69 in. wide by15.75 in. deep plain concrete slabs and spaced at 1.5 times the embedment depth. After installation of the GFRP bars, the slab was stored outside to undergo environmental degradation for seven months. Visual inspection before testing indicated no cracking in the slab. The concrete compressive strength was around 6.5 ksi for all the slabs. The results were reported in terms of failure 40 modes, maximum applied loads, and bond stresses. The following equation was used to compute the bond stress values, τ. u b e F d l     (2.37) Where: Fu = Maximum applied load, lb le = Embedment depth of post-installed GFRP bars, in. For bars with diameters of 0.25 and 0.625 in., concrete cracking without cone failure was the main failure for shallow embedment depth of 5db. Pullout failures of both the adhesive-concrete and adhesive-bar interfaces were observed for the embedment depths of 10db. At an embedment depth of 15db, pullout at the adhesive-concrete interface was the only failure mode, which indicated that failure loads were dependent on bond strength. For bars with a diameter of 1 in., a brittle failure due to concrete cracking followed by pullout occurred at the embedment depth of 5db. Rupture of GFRP bars was observed at embedment depth of 10db and 15db, which highlighted the relation of failure load and bar strength. Bond strength of post-installed #5 GFRP bars using epoxy adhesives were compared with post-installed #5 steel bars. Bond stresses were 34% higher at the lower embedment depth of 5db for GFRP bars than steel bars. Similarly, bond stresses were 10% higher at the embedment depth of 10db for GFRP bars than steel. 2.4.2. Design Models for Failure Modes Kim and Smith (2010) provided a mathematical relationship for the nominal strength of GFRP adhesive anchors rupturing when subjected to tensile loading. The nominal strength of FRP anchors was recommended to be 59% of the flat GFRP coupon tensile rupture strength and was calculated by the equation below. 0.59 GFRP GFRP GFRPN w t far     (2.38) Where: Nar = nominal strength of anchor in tension governed by GFRP, lb wGFRP = width of the fiber sheet used in construction of GFRP anchor, in. tGFRP = thickness of the fiber sheet used in construction of GFRP anchor, in. fGFRP = flat coupon tensile rupture GFRP strength, psi 41 Kim and Smith (2010) also proposed the following equation for computing the concrete breakout strength of GFRP bars installed in uncracked concrete based on a CCD model approach. 1.5 '9.68cc ef cN h f   (2.39) Finally, Kim and Smith (2010) proposed the following equations for combined concrete breakout and bond failure of GFRP bars post-installed in concrete. '4.62 when 3000 psicb o ef cN d h f    (2.40) '9.07 when 3000 psicb o ef cN d h f    (2.41) 2.4.3. Pullout Strength of Post-Installed GFRP Bars in Reinforced Concrete Abolghasem (2013) conducted experimental research on the pullout strength of post-installed GFRP bars for bridge barrier construction. The testing variables included embedment depth (4, 6, and 8 in.), bar sizes (#4, #5 and #6), GFRP bar surface texture (ribbed and sand coated), bar spacing (5.91, 8.85, and 11.81 in.), and grouping effect. GFRP bars were post-installed in 98.5 ft long by 4.5 ft wide by 1 ft deep reinforced concrete slabs having a concrete strength of 4.35 ksi. Two sets of slabs were prepared, one for cast-in-place GFRP bars and the other for post-installed GFRP bars. Reinforcement was provided at the top and bottom of the slabs in both directions to provide confinement. Results were reported separately based on GFRP bar installation method. For cast-in-place specimens, bar pullout (at 4 in. embedment depth) and concrete cone formations with varying cone depths (at 6 and 8 in. embedment) were common modes of failure. Failure loads were found to be independent of bar surface texture regardless of embedment depth and bar size. Bar spacing did not reduce the bond strength for #4 bars but significantly reduced the bond strength for #5 bars due to the overlapping conic stress distribution. GFRP bar rupture was the common failure mode among #4 bars, whereas interface bond failures were observed for #5 and #6 bars. A direct relation between embedment depth and failure loads was found. An increase in embedment depth led to an increase in failure load, but this increase in load was higher for an increase in embedment depth from 5.51 to 8.85 in. than for an increase in embedment depth from 8.85 to 11.81 in. The results indicated that an increase in embedment depth beyond 8.85 42 in. led to a decrease in bond stress. Finally, these results were compared with results from Ahmed et al. (2008). It was concluded that the pullout strength of post-installed GFRP bars in unreinforced slabs was lower than in reinforced slabs due to the confinement provided by the additional steel reinforcement. 2.5. Summary of Literature Review In this chapter, previous experimental and analytical studies performed on post- installed anchors, post-installed reinforcement, cast-in-place GFRP and post-installed GFRP bars were summarized. The purpose of this literature review was to develop background knowledge on the behavior of post-installed GFRP bars. An extensive amount of research has been conducted on post-installed adhesive anchors, but these studies have not led to any additional Code provisions for the design of post-installed reinforcement. Post-installed reinforcement connections are designed using manufacturer provided guidelines, which are based on the current version of ACI 318 (2014). There was a lack of experimental studies investigating member connections using post-installed reinforcement. There was a plethora of studies available on the use of GFRP as cast-in-place reinforcement in concrete. These studies have led to the development of ACI 440.1R (2015), which provides guidelines on the design of reinforced concrete members with GFRP bars. The provisions for design of concrete members reinforced with cast-in-place GFRP bars have not yet been included in ACI 318. The use of GFRP bars as post- installed reinforcement is a new application of GFRP, and no field applications were found during the literature review process. The experimental studies in this area were limited to pullout testing and a proposed area of application was reconstruction of bridge barriers. These results point to the fact that GFRP used as post-installed reinforcement is still developing, which requires further experimentation and development of design guidelines for acceptance as a reliable structural modification tool. 43 Table 2-1. Density of steel, FRP and concrete from ACI 440.1R (2015) Material Type Density (lb/ft3) Steel 493 GFRP 77.8 to 131 CFRP 93.3 to 100 AFRP 77.8 to 88.1 Concrete 115 to 170 Table 2-2. Coefficient of thermal expansion (CTE) of FRP, steel and concrete from ACI 440 (2015) Material Type Longitudinal CTE x 10-6/oF Transverse CTE x 10-6/oF Steel 6.5 6.5 GFRP 3.3 to 5.6 11.7 to 12.8 CFRP -4 to 0 41 to 58 AFRP -3.3 to -1.1 33.3 to 44.4 Concrete 4 to 6 4 to 6 Table 2-3. Tensile properties of GFRP and steel reinforcing bars from ACI 440.1R (2015) Tensile Properties GFRP Steel Nominal yield stress, ksi N/A 40 to 75 Tensile strength, ksi 70 to 230 70 to 100 Elastic Modulus, x103 ksi 5.1 to 7.4 29 Yield strain, % N/A 0.14 to 0.25 Rupture strain, % 1.2 to 3.1 6 to 12 Table 2-4. Environmental reduction factor, CE, for GFRP bars from ACI 440.1R (2015) Exposure Condition Environmental Reduction Factor, CE Concrete not exposed to earth and weather 0.8 Concrete exposed to earth and weather 0.7 44 Chapter 3. Laboratory Specimens, Materials and Methods This chapter covers the materials and experimental variables that were used during construction of the laboratory test specimens in this research project. Additionally, this chapter describes the test setup, equipment and procedure used to test the specimens. 3.1. Specimen Geometry The specimen geometry was adapted from Hamad et al. (2006). A test specimen consisted of two identical vertical elements, which were anchored into the base of the specimen with GFRP bars as post-installed reinforcement. The base element was 68 in. long, 28 in. wide and 14 in. high, with two layers of seven #6 steel bars each as longitudinal reinforcement. Two layers of ten #4 steel bars were used as transverse reinforcement in the base element. The vertical elements were 28 in. wide, 12 in. long and 30 in. high. Each vertical element had seven reinforcing bars at each outer face. The rebar at the external face of the vertical elements was cast-in-place steel for all the specimens. The rebar at the inner face of the vertical elements was either post-installed or cast-in-place GFRP for all the specimens. The number of bars at the inner face of the vertical elements depended on the bar diameter and minimum spacing between bars recommended by the adhesive manufacturer. Three #3 steel stirrups (installed in the same plane) were used as transverse reinforcement at a spacing of 3.5 in. in the vertical elements. An elevation view of a test specimen and cross sections of vertical elements for specimens with varying bar size are shown in Figure 3-1. A clear cover of 1.5 in. was used throughout. The weight of a typical specimen was approximately 4.1 kips. 3.2. Experimental Variables The experimental variables selected for this study were found to have the most influence on bond strength of both GFRP bars and post-installed reinforcing bars during the literature review. The experimental variables that were investigated included: nominal 28-day concrete compressive strength, f’c (3 and 6 ksi); embedment depth, le (6 and 11.5 in.); bar size (#4, #6 and #8); GFRP bar surface texture [helically wrapped with sand coatings (SCW), sand coated (SC) and ribbed (R)]; method of bar installation; and chemical adhesive used during post-installation. The installation methods for GFRP bars 45 were cast-in-place (CIP) and post-installed (PI). Two types of Hilti adhesives were selected: HIT-RE 500-SD, which is epoxy (E) based, and HIT-HY 200-R, which is cementitious (C) based. GFRP bars were provided by three different manufacturers. A matrix of the specimens and variables that were investigated in this research project is shown in Table 3-1. The nomenclature used to name specimens was based on the variables used during design and construction. Each specimen name consists of six symbols, with the first three and last three separated by a hyphen. The order of these symbols was: concrete strength (3 and 6 ksi), GFRP bar type (SCW, SC and R), GFRP bar size (#4, #6 and #8), type of adhesive (C and E), embedment depth (6 in. and 11.5 in.), and method of installation (CIP and PI). The symbol ϕ was used to represent absence of adhesive in specimens with cast-in-place GFRP bars. For example, a specimen with #4 post-installed SCW GFRP bars with epoxy adhesive, concrete strength of 3 ksi, and 6 in. embedment depth was identified with the name 3SCW4-E6PI. The specimens with a concrete compressive strength of 3 ksi included GFRP bars at both embedment depths, whereas the specimens with a concrete compressive strength of 6 ksi had GFRP bars only installed at an embedment depth of 11.5 in. All three types of #4 GFRP bars and both types of adhesives were used in specimens with an embedment depth of 6 in. and a concrete compressive strength of 3 ksi. The specimens with an embedment depth of 11.5 in. only included GFRP bars post-installed with the epoxy based adhesive. In terms of bar sizes, #4 and #6 post-installed GFRP bars were used in specimens with both concrete strengths, whereas #8 post-installed GFRP bars were only used in specimens with 6 ksi concrete strength. 3.3. Materials The materials used during fabrication of the test specimens included concrete, steel rebar, GFRP bars, and adhesives for post-installing GFRP bars. The properties and specifications for all of these materials are discussed below. 46 3.3.1. Concrete Specifications Concrete was ordered from Arrowhead Concrete for each concrete placement event during the construction of specimens. The specified nominal concrete compressive strength for all of the specimens was 3 or 6 ksi. The specified nominal concrete compressive strength was the same for the base and vertical elements of a specimen. The desired slump for all of the concrete mixes was 5 to 7 in. A test specimen was made up of about one cubic yard of concrete, which included 0.57 cubic yards for the base element and 0.22 cubic yards for a vertical element. The water-to-cementitious material ratio was 0.35 and 0.28 for the 3 and 6 ksi mixes, respectively. Table 3-2 summarizes the ingredients and their quantities for one cubic yard of concrete in each respective concrete mix. 3.3.2. GFRP Specifications GFRP bars were provided by three different suppliers: Hughes Brothers (HB), Pultrall Canada (PC), and Marshall Composite Technologies (MC). Each manufacturer had unique GFRP bar surface textures as shown in Figure 3-2. All of the GFRP bars met the specifications provided in ACI 440.1R (2015), except the GFRP bars with ribbed geometry. GFRP bars were used as post-installed reinforcement in 16 specimens and as cast-in-place reinforcement in four specimens. Properties of the GFRP bars used in the specimens are provided in Table 3-3. 3.3.3. Adhesive Specifications The specifications of the adhesives used in this project were provided by Hilti. The adhesives consisted of two components with the main component being epoxy or cementitious mortar and the second component being the curing agent. HIT-HY 200-R is suitable for applications requiring fast curing, whereas HIT-RE 500-SD is suitable for moderate curing times (Hilti, 2016). The properties of both adhesives are listed in Table 3- 4. 3.4. Specimen Design The test specimens were designed to represent a beam-to-column or a beam-to-wall connection and resist both flexural and shear ultimate loads. To prevent flexural failure, 47 GFRP bars were installed for this purpose at the minimum spacing recommended by the adhesive manufacturer for each bar size. The stirrups were spaced at 3.5 in. on center to prevent shear failure in vertical elements during testing. The test matrix for this experimental study consisted of specimens with variation in the number size of GFRP bars. The nominal moment and shear capacities were calculated for sections with variable concrete strength, GFRP bar type, bar sizes, and bar numbers. These calculations were performed for 12 different sections (covering all 20 specimens) having variable concrete strength, GFRP bar type, size and number of bars. The resistance factor for nominal moment was calculated using Equation 2.28, where the resistance factor for nominal shear was 0.75. The factored nominal moment and shear capacity (ϕMn and ϕVn) of various vertical element sections are listed in Table 3-5. The nominal moment and shear capacity calculations are provided in Appendix A. 3.5. Methods This section describes the test specimen construction and the procedure used for testing the specimens. 3.5.1. Specimen Construction Four specimens were built simultaneously. Fabrication of specimens was completed in the following sequence: 1) casting of the base elements, 2) installation of post-installed GFRP bars, and 3) casting of the vertical elements. There were 10 concrete pours, five each for base and vertical elements. Concrete cylinders (4 x 8 in.) were prepared at the time of casting base and vertical elements and demolded after one day. The base and vertical element formwork was removed one day after placing vertical element concrete. 3.5.1.1. Base Element The rebar cage for each base element consisted of longitudinal and horizontal steel reinforcement. The longitudinal reinforcement was composed of two layers of seven #6 bars spaced at 4.125 in., and two layers of ten #4 bars spaced at 7.125 in. were used as horizontal (or transverse) reinforcement as shown in Figure 3-3a. Hooks were installed on rebar cages in order to move specimens around the lab. Prior to concrete placement, 48 steel reinforcement at the outer face of the vertical elements was supported by a temporary 2x4 wooden frame as shown in Figure 3-3b. The embedment depth of the outer face vertical element reinforcement was 12 in. for all specimens. Figure 3-3b also shows cast-in-place GFRP bars (and their stirrup support mechanism) that were installed in four specimens. Two and a half cubic yards of concrete was ordered from Arrowhead Concrete for each of the five base element pours. Concrete slump was measured upon arrival of the concrete truck to ensure sufficient workability. A one and a half cubic yard bucket was used for placing concrete. A mechanical pencil vibrator was used to consolidate concrete. During each concrete pour, 15 concrete cylinders (4 x 8 in.) were prepared to measure compressive strength at 28-days and at the time of testing. The top surface of the base element was finished smoothly, but the base elements were roughened at the vertical element interface to ensure cohesion and transfer of shear forces. Moistened burlap and plastic sheets were placed on the finished surface during curing (one day). Typical specimens with post-installed GFRP bars and cast-in-place GFRP bars are shown in Figure 3-3c and Figure 3-3d, respectively. Lifting hooks installed to facilitate specimen movement can also be seen in Figure 3-3c. 3.5.1.2. Post-Installed GFRP Bars Post-installed GFRP bars were installed seven days after the base elements were cast. The method for post-installing bars was provided by the adhesive manufacturer. Duct tape placed on the formwork before concrete placement was used to identify the location of cast-in-place rebar to avoid hitting bars during drilling. A hammer drill with carbide drill bits was used for drilling holes. The adhesive manufacturer recommended that the diameter of holes be 1/8 in. larger than the diameter of the post-installed bars. After drilling to the required embedment depth, the holes were cleaned per the manufacturer-specified cleaning method. A wire brush was attached to the drill and moved along the hole depth (Figure 3-4a) and compressed air with an extended nozzle was blown into the hole to remove loose particles from the holes (Figure 3-4b). The process of cleaning was performed twice for each hole. Improper cleaning of holes could lead to poor bond at the adhesive-concrete interface due to the presence of loose particles 49 (Hilti, 2016). The difference between an uncleaned hole and a cleaned hole is shown in Figure 3-4c and Figure 3-4d, respectively. After cleaning the holes, adhesive was injected into the holes and GFRP bars were placed. Adhesives were inserted into the holes using an adhesive gun as shown in Figure 3-5a. Adhesive injection (mixing mortar and curing agent) began from the bottom of the hole until one-third of the hole was filled. GFRP bars were then pushed into the hole with continuous twisting to ensure a uniform coating of adhesive on the GFRP bar. The GFRP bars were centered in the hole before the initial adhesive set. The post- installed bars were not disturbed for 24 hours to allow complete curing of the adhesive. Figure 3-5b and Figure 3-5c show GFRP bars post-installed with HIT-RE-500-SD (epoxy based) and HIT-HY 200-R (cementitious based) adhesives, respectively. 3.5.1.3. Vertical Elements Vertical element construction began at least 24 hours after post-installing the GFRP to avoid misalignment of bars due to insufficient curing of adhesive. The first step was to install set of three stirrups at 3.5 in. on center around both the post-installed GFRP bars and the pre-installed steel bars. The stirrups for a typical vertical element are shown in Figure 3-6. The vertical element formwork was treated with the form releasing agent, placed around the vertical element rebar cage, and mounted on top of the base element formwork as shown in Figure 3-7a. During a concrete pour, six concrete cylinders (4 x 8 in.) were prepared to measure 28-day and test day compressive strength. A mechanical pencil vibrator was used to consolidate concrete and prevent void formation. The top surface of the vertical elements was finished smooth and cured with moistened burlap and plastic sheets for one day. The forms were stripped off after one day. A typical complete specimen can be seen in Figure 3-7b. 3.5.2. Testing Method The equipment and the procedure used for testing the specimens is discussed in detail below. 50 3.5.2.1. Applied Pressure and Load Hydraulic rams were used to apply tensile force on the post-installed GFRP bars. Built-up HSS beams 6 in. deep and 28 in. wide were attached to the specimens and used to mount two hydraulic rams. The two hydraulic rams applied static load to the testing specimens. Figure 3-8 shows how the two hydraulic rams were mounted to the built-up steel beams. The hydraulic rams were manufactured by Simplex (model #R152). These hydraulic rams had a piston diameter of 2 in., effective area of 3.14 in.2 and an extension length of 5.83 in. During installation, the rams were leveled to ensure equal application of load on both vertical elements as shown in Figure 3-9a. The hydraulic rams were connected to a manual hydraulic pump manufactured by Simplex (model #P82A). The hydraulic pump had a capacity of 10 ksi. A pressure transducer was installed in-line with the factory supplied dial gauge to continuously record applied pressure data during testing. The pressure transducer was manufactured by Omega Engineering (model #PX603). The dial gauge was used to verify the pressure transducer calibration. The pressure transducer and in-line gauge are shown in Figure 3-9b. Reference sheets were created to convert recorded pressure in psi to load in kips and identify when to label cracks for each loading increment. The recorded applied pressure values were divided by the ram piston area to obtain load values. An example reference sheet is provided in Appendix B. 3.5.2.2. Specimen Displacement Four linear variable displacement transducers (LVDTs) were used to record displacement during testing of the specimens. All four LVDTs were calibrated before conducting the tests. The LVDTs were held in place by a clamp attached to a steel support as shown in Figure 3-10a. Two TransTek LVDTs with a range of +/- 1.5 in. (model #0244-00000) were used to record vertical (upward) displacement of the base element. These LVDTs were located 14 in. from both vertical elements and 3 in. inward from the edge of the base element as shown in Figure 3-10b. Two TransTek LVDTs with a range of +/- 3 in. (model #0246-00000) were used to measure outward displacement near the top of each vertical element. These LVDTs were located 3 in. inward from the 51 side and 1 in. below the top of the vertical elements as shown in Figure 3-10c. The LVDTs were connected to the data acquisition system and data was collected at a rate of one data point per second. A specimen with installed instrumentation is shown in Figure 3-11. 3.5.2.3. Test Procedure The load was applied in increments of 2.25 kips (or 0.75 ksi pressure) during testing of all the specimens. A GoPro Hero 4 camera and LED lights were used to record videos during each loading increment. Crack patterns were marked and the peak applied load reached during each increment was labeled on the specimen using black permanent markers. Photos were captured after marking the cracks at each loading stage. The load was increased until the maximum ram stroke was reached. The pump pressure was then released at a slower rate to record displacement during unloading. The data logger was stopped when the pressure dropped below 0.1 ksi. The results obtained from testing of each specimen are discussed in Chapter 4. 52 Table 3-1. Matrix of variables tested in laboratory specimens Specimen Name* f’c (ksi) GFRP Texture Bar No. and Size Type of Adhesive le (in.) Casting Method 3SCW4-ϕ6CIP 3 SCW (7) #4 None (ϕ) 6 CIP 3SCW4-E6PI 3 SCW (7) #4 RE 500-SD (E) 6 PI 3SCW4-C6PI 3 SCW (7) #4 HY 200-R (C) 6 PI 3SC4-C6PI 3 SC (7) #4 HY 200-R (C) 6 PI 3SC4-E6PI 3 SC (7) #4 RE 500-SD (E) 6 PI 3R4-E6PI 3 R (7) #4 RE 500-SD (E) 6 PI 3SCW4-ϕ11.5CIP 3 SCW (7) #4 None (ϕ) 11.5 CIP 3SC4-ϕ11.5CIP 3 SC (7) #4 None (ϕ) 11.5 CIP 3SCW4-E11.5PI 3 SCW (7) #4 RE 500-SD (E) 11.5 PI 3SC4-E11.5PI 3 SC (7) #4 RE 500-SD (E) 11.5 PI 3SCW6-E11.5PI 3 SCW (4) #6 RE 500-SD (E) 11.5 PI 3SC6-E11.5PI 3 SC (4) #6 RE 500-SD (E) 11.5 PI 6SCW4-ϕ11.5CIP 6 SCW (7) #4 None (ϕ) 11.5 CIP 6SCW4-E11.5PI 6 SCW (7) #4 RE 500-SD (E) 11.5 PI 6SC4-E11.5PI 6 SC (7) #4 RE 500-SD (E) 11.5 PI 6SCW6-E11.5PI 6 SCW (4) #6 RE 500-SD (E) 11.5 PI 6SC6-E11.5PI 6 SC (4) #6 RE 500-SD (E) 11.5 PI 6SC(3#8)-E11.5PI 6 SC (3) #8 RE 500-SD (E) 11.5 PI 6SCW8-E11.5PI 6 SCW (4) #8 RE 500-SD (E) 11.5 PI 6SC(4#8)-E11.5PI 6 SC (4) #8 RE 500-SD (E) 11.5 PI *Nomenclature: (concrete strength in ksi) (GFRP texture) (bar size)-(chemical type) (embedment depth in in.) (casting method) For example: 3SC4-E6PI = (3 ksi concrete strength) (Silica coated texture GFRP bars) (#4 bar) - (Epoxy adhesive) (6 in. embedment depth) (Post-installed) Table 3-2. Ingredients for one cubic yard of ready mix concrete Ingredients 3 ksi Mix 6 ksi Mix Sand (lb) 1,660 1,456 ¾ in. rock (lb) 1,860 1,792 Class C fly ash (lb) 128 66.4 Cement (lb) 388.67 631.2 Water (lb) 178.33 194 Water Reducer (oz) N/A 20.4 w/cm ratio 0.35 0.28 53 Table 3-3. Properties of GFRP bars provided by the manufacturers Properties Hughes Brothers Inc. Pultrall Canada Marshall Composite Technologies Surface Texture Helically wrapped with sand coatings (SCW) Silica coated (SC) Ribbed (R) Size #4 #6 #8 #4 #6 #8 #4 Diameter (in.) 0.50 0.75 1.00 0.50 0.75 1.00 0.50 Area (in.2) 0.20 0.44 0.79 0.20 0.44 0.79 0.20 Tensile Strength (ksi) 134 107 104 199 191 155 116 Elastic Modulus (ksi) 7,037 7,051 7,052 9,090 8,943 8,851 6,000 Table 3-4. Properties of adhesives provided by the manufacturer Properties HIT-HY 200-R HIT-RE 500-SD Reinforcing bar diameter range #3 to #8 #3 to #11 Embedment range (in.) ≤ 25 ≤ 84 Installation temperature range for base material (oF) 14 to 104 41 to 104 Service temperature (oF) 40 to 176 -40 to 176 Working time (minutes) 6 to 180 12 to 240 Curing time (hours) 1 to 20 4 to 72 Diameter of drilled holes (in.) bar diameter + 1/8 bar diameter + 1/8 54 Table 3-5. Nominal moment and shear capacity of vertical element cross sections Vertical Element Cross Section Moment Capacity, ϕMn (kip-ft) Shear Capacity, ϕVn (kips) 3 ksi - SCW - 7 (#4) 65.58 129.01 3 ksi - SC - 7 (#4) 64.40 129.01 3 ksi - R - 7 (#4) 48.05 129.01 6 ksi - SCW - 7 (#4) 66.16 138.77 6 ksi - SC - 7 (#4) 83.68 138.77 3 ksi - SCW - 4 (#6) 53.60 127.43 3 ksi - SC - 4 (#6) 68.35 127.43 6 ksi - SCW - 4 (#6) 64.72 137.08 6 ksi - SC - 4 (#6) 96.81 137.08 6 ksi - SCW - 4 (#8) 92.60 135.39 6 ksi - SC - 4 (#8) 119.46 135.39 6 ksi - SC - 3 (#8) 102.29 135.39 *Nomenclature: concrete strength in ksi - GFRP texture - Number of bars (bar size) For example: 3 ksi - SC - 7 (#4) = 3 ksi concrete strength - Silica coated GFRP bar texture - 7 (#4 bars) 55 Figure 3-1. Test specimen elevation and vertical element cross sections Figure 3-2. GFRP bar types labeled with the manufacturer and surface texture abbreviations 56 Figure 3-3. (a) Base element for post-installed GFRP before concrete pour (b) Base element for cast-in-place GFRP before concrete pour (c) Post-installed GFRP in hardened concrete (d) Cast-in-place GFRP in hardened concrete Figure 3-4. (a) Wire brush attached to drill (b) Compressed air nozzle with an extension (c) Uncleaned hole (d) Cleaned hole 57 Figure 3-5. (a) Two component adhesives and adhesive gun (b) GFRP bars post- installed with epoxy adhesive HIT-RE 500-SD (c) GFRP bars post-installed with cementitious adhesive HIT-HY 200-R Figure 3-6. Sets of three stirrups installed at 3.5 in. on center for shear resistance 58 Figure 3-7. (a) Vertical element formwork (b) Complete specimen being lifted Figure 3-8. Built-up HSS steel beams used for mounting hydraulic rams: (a) Beam in contact with ram base (b) Beam in contact with moveable pistons 59 Figure 3-9. (a) Hydraulic rams mounted and leveled on a test specimen (b) In-line pressure transducer and dial gauge to measure applied pressure Figure 3-10. (a) LVDT support stand and holder (b) LVDT recording vertical (upward) displacement of base element (c) LVDT recording horizontal (outward) displacement of vertical element 60 Figure 3-11. Testing configuration with all instrumentation installed on specimen 3C4-E6PI (not pictured: LVDTs on base element) 61 Chapter 4. Results The results obtained from testing the specimens are covered in this chapter. The results are reported in terms of failure modes, bond strength, bond ratios, and load- displacement curves. In addition, a comparison of the results between specimens with GFRP bars and steel bars (Hamad et al., 2006) are also discussed in each category of results. Finally, a comparison of the results with ACI 318 (2014) was completed and a parametric study was performed to evaluate the factors influencing the failure mode of post-installed GFRP. 4.1. Failure Modes The failure modes that were observed in the specimens were limited to concrete breakout, bond failure or combined bond and concrete breakout failure. Concrete breakout failure mode was an indicator of strong bond strength between the GFRP and the surrounding concrete, but this bond strength was not as strong as the rupture strength of the GFRP bars. Bond failure or combined bond and concrete breakout failure indicated that the embedment depth provided for GFRP bars was likely not long enough to fully develop the bars to rupture under applied loads. Failure modes of all the specimens are listed in Table 4-1. Cracking patterns and failure modes of all the specimens are shown in Appendix C. The failure modes observed in specimens with post-installed GFRP and cast-in-place GFRP are discussed in detail below. 4.1.1. Post-Installed Specimens In specimens with post-installed GFRP bars embedded at 6 in., cracking began at the interface of the vertical and base elements and propagated downward, parallel to the post-installed reinforcement. The cracks began to form a cone as the applied load was increased. The depth of the concrete breakout was approximately equal to the embedment depth of the post-installed GFRP bars (6 in.). Cone-shaped cracks developed below both vertical elements and were connected by a longitudinal crack that formed along the top length of the base element as shown in Figure 4-1a. At an embedment depth of 11.5 in., the concrete cone breakout was not localized beneath each vertical element in specimens with post-installed GFRP due to the increase in embedment depth. In these specimens, the 62 concrete breakout crack ran along the bottom length of the base element between the exterior edges of vertical elements with a maximum depth of about 11.5 in. at the middle of the base element as shown in Figure 4-1b. Concrete breakout failure in the specimens with post-installed GFRP bars indicated a strong connection between the GFRP bars and the surrounding concrete, which was due to the presence of a chemical adhesive not used in the cast-in-place specimens. The failure mode in all of the specimens with post-installed GFRP bars was concrete breakout, regardless of the surface texture of GFRP bars. Hamad et al. (2006) also reported that the failure mode of specimens with post-installed steel reinforcement was concrete cone breakout. In theory, the concrete breakout failure in the specimens with post-installed GFRP installed at an embedment of 11.5 in. should have been similar to the specimen with 6 in. embedment depth, where the concrete breakout cracks formed beneath under each vertical element in a cone-shaped pattern. The only difference would have been the overlapping of the concrete breakout cracks with an 11.5 in embedment depth. The vertical specimens needed to be more than 35 in. (1.5hef = 1.5*11.5*2 = 34.5 in.) away from each other to develop individual concrete breakout cracks under each vertical element. 4.1.2. Cast-in-Place Specimens Initial cracking in specimens with cast-in-place GFRP bars began in the base element parallel to the cast-in-place GFRP bars. The depth of the initial vertical crack was similar to the embedment depth of the GFRP bars installed in the base elements (6 and 11.5 in.). A bond failure was observed in the specimen with a 6 in. embedment depth and 3 ksi concrete strength at the interface of the vertical and base element as shown in Figure 4-2a. The bond failure mode indicated a weak bond between the reinforcement and the surrounding concrete. When the embedment depth in the 3 ksi specimen was increased to 11.5 in., the failure mode was a combination of bond failure and concrete cone breakout as shown in Figure 4-2b. A combined bond and concrete breakout failure indicated an improvement in bond between the cast-in-place GFRP bars and the surrounding concrete. A disparity in failure modes between specimens with 11.5 in. embedment depth was noted when the concrete strength was increased from 3 to 6 ksi. The failure mode of the specimen 63 with 6 ksi concrete strength and 11.5 in. embedment depth was bond failure as shown in Figure 4-3, as opposed to combined bond and concrete breakout failure. Increasing the concrete strength from 3 to 6 ksi and keeping the embedment depth constant at 11.5 in. prevented the concrete breakout happening at the same time as bond failure occurred. Bond failures were expected because the provided embedment depths were less than the required GFRP development length calculated using Equation 2.36. The calculated development lengths of the cast-in-place GFRP specimens are listed in Table 4-2. The development length calculations for cast-in-place GFRP bars are provided in Appendix D. 4.2. Bond Strength and Bond Ratios Test data were normalized to the specified concrete compressive strengths of 3 and 6 ksi to account for variation in test day compressive strength and allow for comparison of results between specimens. The adjustment was made by multiplying the peak loads with a factor, which consisted of the square root of the normalized concrete strength (3 or 6 ksi) divided by the concrete strength at the day of testing (i.e., 3 or 6 ksi / f’c)1/2. Hamad et al. (2006) also performed this normalization, which allowed for comparison of results between specimens with post-installed GFRP and steel bars. Bond strength of GFRP bars anchored into the base element, at the inner face of the vertical elements, was calculated using a cracked section analysis. A cracked section analysis was performed for each section using the cracking moment, cracked moment of inertia and the normalized peak applied loads. The calculated bond strength of GFRP bars in all of the specimens were lower than the ultimate strength of the respective GFRP bars, which suggested that the GFRP bars did not rupture under the applied load. Bond ratios were computed by dividing the maximum load applied to each specimen by the maximum load applied to a reference specimen. Data collected by Hamad et al. (2006) for specimens with cast-in-place #4 steel rebar at both embedment depths (6 and 11.5 in.) were used as the reference data for all the specimens considered in this study. Results of all the specimens from this study are listed in Table 4-3. Calculation of the bond strengths for each specimen are provided in Appendix E. The effect of each variable on the bond strength of the specimens is discussed using bond ratios in the subsequent sections. 64 4.2.1. Embedment Depth The effect of embedment depth on bond strength and the bond ratios was studied using the specimens with 3 ksi concrete strength and seven #4 GFRP bars. The results from Table 4-3 indicated an increase in the bond strength of approximately 100% due to an increase in the embedment depth from 6 to 11.5 in. For example, the specimen with post- installed GFRP (3SC4-E6PI) bars had a bond strength of 21.23 ksi at the embedment depth of 6 in., whereas the bond strength of a similar specimen (3SC4-E11.5PI) increased to 51.28 ksi at the embedment depth of 11.5 in. (142% increase). Post-installed GFRP bars with a SCW surface (3SCW4-E6PI) attained the highest bond strength at an embedment depth of 6 in. compared to post-installed GFRP bars with the SC or R surface. Post-installed GFRP bars with a SC surface exhibited a higher bond strength compared to post-installed GFRP bars with a SCW surface at an embedment depth of 11.5 in. (e.g., specimen 3SCW- E11.5PI and 3SCW4-E11.5PI). The lower bond strength in the 3SCW4-E11.5PI specimen was due to use of an improper drilling technique in the base specimen while post-installing the GFRP bars. Bond ratios indicated that the bond strength of post-installed steel bars at both embedment depths was greater than the bond strength of all GFRP bars investigated in this study. For example, results in Table 4-3 show that the bond ratio of the specimen with post- installed steel embedded 6 in. (3S4-E6PI) was 39% greater than the reference specimen, whereas all of the specimens with post-installed GFRP had bond ratios similar to the reference specimen at both embedment depths (bond ratios ranging from 0.85 to 1.00). The bond ratio of the post-installed steel specimen embedded 11.5 in. (3S4-E11.5PI) was 24% greater than the reference specimen, whereas all of the specimens with post-installed GFRP had bond ratios similar to the reference specimen at both embedment depths (bond ratios ranging from 0.90 to 1.09). At an embedment depth of 6 in., the bond ratio of specimens with both post- installed and cast-in-place GFRP bars was lower (0.94 and 0.86) compared to the bond ratio of specimens with both post-installed and cast-in-place GFRP bars installed at an embedment depth of 11.5 in. (1.09 and 1.06). Bond ratios of specimens with post-installed steel bars showed the opposite trend. The bond ratio in post-installed steel specimens 65 decreased from 1.39 to 1.24 when embedment depth was increased from 6 to 11.5 in. as shown in Figure 4-4. The increase in embedment depth had a greater influence on bond strengths of GFRP bars (increases) compared to steel bars (decreases). The increase in embedment depth clearly showed an improvement in GFRP bond strength, as previously reported by Ahmed et al. (2008) and Abolghasem (2013). 4.2.2. Concrete Strength The effect of concrete strength on bond behavior of post-installed GFRP bars was studied using specimens with an 11.5 in. embedment depth, seven #4 and four #6 bars. When the concrete strength was increased from 3 to 6 ksi, the specimen with post- installed #4 GFRP (SCW) showed the highest gain in bond strength, which rose from 43.41 ksi to 79.58 ksi (83% increase). On the other hand, the specimen with post-installed #6 GFRP bars (SC) had the lowest gain in bond strength from 37.73 to 43.93 ksi (16% increase). The variation in bond strengths indicated that the increase in concrete strength was more effective for smaller diameter post-installed GFRP bars compared to the larger diameter bars. The results from specimens with cast-in-place #4 GFRP (SCW) indicated an improvement in bond ratios from 1.09 to 1.27 (18% increase) with the increase in concrete strength from 3 to 6 ksi, whereas the same specimens with post-installed GFRP bars showed an improvement of bond ratio from 0.90 to 1.64 (74% increase). This indicated that the increase in concrete strength improved the bond strength of post- installed GFRP bars more compared to cast-in place GFRP bars. This observation was also true for GFRP bars with a SC surface condition. For post-installed #6 GFRP bars, a similar improvement in bond ratio was observed, but the increase in bond ratio was less (53% for SCW GFRP bars and 56 % for SC GFRP bars) compared to the #4 GFRP bars. The bond ratios of all the relevant specimens are shown in Figure 4-5. The increase in concrete strength improved bond strength of post-installed GFRP bars. Hamad et al. (2006) also noted an increase in post-installed steel bars bond strength due to the use of higher strength concrete. 66 4.2.3. Method of Bar Installation Results from six specimens (CIP and PI specimens with SCW GFRP, SC GFRP, and steel bars) with a concrete strength of 3 ksi and seven #4 bars installed at an embedment depth of 11.5 in. were used to study the effect of bar installation method on the bond ratio of GFRP bars. A comparison of the test data indicated that the specimens with cast-in-place GFRP had a higher bond ratio (1.09 for SCW surface and 1.08 for SC surface) compared to the post-installed specimens (0.90 for SCW surface and 1.06 for SC surface). On the other hand, Hamad et al. (2006) reported that the bond strength of post- installed steel specimens was greater than the reference cast-in-place steel specimens (1.24 versus 1.00). A comparison of the bond ratios from cast-in-place steel and GFRP specimens to those from post-installed steel and GFRP specimens is illustrated in Figure 4-6. 4.2.4. Adhesive Type Specimens with a concrete strength of 3 ksi and an embedment depth of 6 in. were used to study the effect of adhesive type on bond strength of post-installed GFRP bars. For example, specimen 3SCW4-E6PI had a bond strength of 24.81 ksi compared to a bond strength of 24.28 kips for specimen 3SCW4-C6PI as shown in Table 4-3. Bond ratios of specimens having the same surface texture GFRP bars were also very similar. Two specimens with SCW GFRP bars had bond ratios of 1.00 and 0.98 for epoxy and cementitious adhesive, respectively. Similarly, bond ratios of two specimens with SC GFRP bars were 0.86 (epoxy adhesive) and 0.85 (cementitious adhesive) as shown in Figure 4-7. Test results showed that the adhesive type had a little to no influence on the bond ratios and bond strengths. This result was consistent with the study conducted by Hamad et al. (2006), which concluded that the epoxy based adhesive had a slightly higher bond ratio compared to the cementitious based adhesive (approximately 13%). 4.2.5. GFRP Surface Condition Specimens with a concrete strength of 3 ksi, an embedment depth of 6 in. and either adhesive were used to study the effect of GFRP surface condition on bond behavior of post-installed #4 GFRP bars. Among specimens with GFRP post-installed using an epoxy-based adhesive, GFRP bars with a silica coating and helical wraps (SCW) had the 67 highest bond ratio (1.00), followed by the GFRP bars with ribbed (R) geometry (0.96). GFRP bars with only a silica coating (SC) had the lowest bond ratio (0.86). A similar trend was observed in the two specimens with post-installed GFRP using a cementitious adhesive as shown in Figure 4-8. When varying the bar size (#4, #6 and #8) and concrete strength (3 and 6 ksi) at the embedment depth of 11.5, the results of specimens with SCW GFRP bars generally had higher bond ratios and bond strengths (approximately 11%) compared to SC GFRP bars with two exceptions. For example, result from specimen 3SCW4-E11.5PI showed that SCW GFRP bars had a lower bond ratio (0.90) and bond strength (43.41 ksi) compared to a similar specimen with SC GFRP bars (3SC4-E11.5PI had a bond ratio of 1.06 and bond strength of 51.28 ksi). Similarly, specimen 6SC8-E11.5PI had a higher bond ratio (0.55) and bond strength (26.66 ksi) compared to specimen 6SCW8-E11.5PI, which had a bond ratio of 0.50 and bond strength of 24.34 ksi as seen in Table 4-3. The data indicated that the GFRP bars with silica coating and helical wraps (SCW), generally exhibited superior bond strength compared to silica coated (SC) GFRP bars. The past studies performed on post-installed GFRP bars did not include SCW surface conditions. Baena et al. (2009) found the bond strength of cast-in-place GFRP bars with SCW surface condition to be superior to the bond strength ribbed GFRP bars, which was also true for post-installed GFRP bars with similar surface conditions in this study. 4.2.6. Bar Size The effect of bar size on the bond behavior of post-installed GFRP was studied using specimens with a concrete strength of 6 ksi and an embedment depth of 11.5 in. Results showed that the specimens with #4 bars had the highest bond ratio (1.64 and 1.47 for SCW and SC GFRP bars), followed by #6 in the middle (1.11 and 0.91 for SCW and SC GFRP bars) and #8 bars showing the lowest bond ratio (0.50 and 0.55 for SCW and SC GFRP bars) for both SCW and SC surface conditions, as displayed in Figure 4-9. This result was in agreement with Ahmed et al. (2008) and Abolghasem (2013), who indicated that an increase in bar size corresponded with a loss of bond strength at a constant embedment depth. 68 4.2.7. Bar Spacing Two specimens with #8 GFRP bars (SC surface) were used to study the effect of bar spacing on the bond behavior of post-installed GFRP bars. The specimen 6SC(3#8)- E11.5PI had three #8 bars spaced at 6.5 in. center-to-center and the specimen 6SC(4#8)- E11.5PI had four #8 bars spaced at 5 in. center-to-center. The adhesive manufacturer recommended a minimum of 5 in. clear spacing between #8 steel bars. The results showed that the specimen with the three #8 bars at a larger spacing had a higher bond ratio (0.72) compared to the specimen with four #8 bars at a smaller spacing (0.55), as shown in Figure 4-10. The experimental data indicated that bars spaced at or beyond the manufacturer specified minimum spacing may increase the bond strength for #8 GFRP bars. Abolghasem (2013) also found that the bond strength of post-installed GFRP bars installed at or beyond the manufacturer specified minimum spacing were unaffected by the conic stress distributions generated by the load applied to adjacent bars. 4.3. Load-Displacement Behavior Data obtained from testing was used to plot load-displacement curves for all of the specimens in this study. These load-displacement curves were used to study the effect of variable embedment depths, concrete strengths and bar sizes on the ductility and peak applied load of beam-column or beam-wall connections. Maximum horizontal displacement at the top of the vertical elements under peak applied load was used as an indicator of ductility. Ductility of a connection was taken to be directly proportional to the displacement at a certain load (e.g., lower displacement indicated lower ductility). Load-displacement curves for individual specimens were combined into single plots, based on relevant testing parameters, to discuss the results in the subsequent sections. The test data from each specimen is provided in Appendix F. 4.3.1. Embedment Depth Analysis of load-displacement curves allowed for a comparison of ductility and peak applied load for all GFRP specimens with data from cast-in-place steel specimens (Hamad et al., 2006) at both embedment depths. The displacement at the peak applied loads in specimens with cast-in-place and post-installed GFRP bars at both embedment 69 depth was more than the reference cast-in-place steel specimen. The peak applied load in all specimens with post-installed GFRP was lower than the reference cast-in-place steel specimens except the specimens with SC GFRP bars installed at an embedment depth of 11.5 in. Additionally, the specimens with post-installed steel exhibited greater peak applied loads compared to post-installed GFRP at both embedment depths. The increase in embedment depth improved both peak applied loads and the displacements at the peak applied loads. A summary of the load-displacement results is presented in Table 4-4. The results summarized in Table 4-4 are based on the load-displacement curves shown in Figure 4-11 and Figure 4-12. 4.3.2. Concrete Strength Displacement at the peak applied load and the peak applied load for each specimen relative to the specimen with cast-in-place GFRP (SCW) were used to study the effect of concrete strength on GFRP bars post-installed at an embedment depth of 11.5 in. Data from specimens with post-installed GFRP (SCW) showed that the displacement was 1.37 in. when the concrete strength was 3 ksi and the displacement was 2.11 in. when the concrete strength was 6 ksi, which indicated an improvement in ductility. Similarly, data from specimens with post-installed GFRP (SC) showed improvement in ductility by virtue of peak applied load displacement increasing from 1.02 to 1.96 in. In specimens with a concrete strength of 3 ksi, peak applied load was reduced by 18 % for post- installed GFRP (SCW) and by 1% for post-installed GFRP (SC) compared to the specimen with cast-in-place GFRP (SCW). On the contrary, specimens with a concrete strength of 6 ksi showed an improvement in peak applied by 28% in post-installed GFRP (SCW) and by 14%post-installed GFRP (SC) had an increase of 1% compared to the specimen with cast-in-place GFRP (SCW). These results are summarized in Table 4-5, which indicated that an increase in concrete strength improved both the peak applied load displacement and peak applied loads for all the specimens. The load-displacement plots of specimens with both concrete strengths are shown in Figure 4-13. 4.3.3. Bar Size Specimens with a concrete strength of 6 ksi and an embedment depth of 11.5 in. were used to study the effect of bar size on load-displacement behavior of post-installed 70 GFRP bars. Displacement at the peak applied load for specimens with GFRP (SCW) bars was 2.11 in. for #4 bars, 1.42 in. for #6 bars and 1.08 in. for #8 bars. Comparably, displacement at the peak applied load for specimens with GFRP (SC) bars was 1.96 in. for #4 bars, 1.48 in. for #6 bars and 1.20 in. for #8 bars. These trends indicated a decrease in ductility with an increase in bar size. Peak applied loads also decreased as the size of the GFRP bars was increased. A summary of the results provided in Table 4-6 indicated that an increase in GFRP bar size led to a reduction in ductility and peak applied loads when the embedment depth was kept constant at 11.5 in. The load-displacement plot for specimens with post-installed GFRP used to investigate differences in bar size is shown in Figure 4-14. 4.4. Comparison of Results with ACI 318 (2014) Concrete breakout was the sole mode of failure observed in all of the specimens with post-installed GFRP bars. The structural concrete Code, ACI 318 (2014), provides a method to compute the concrete breakout strength of post-installed bars, which was shown in Equation 2.19. The variables used in this equation are independent of the type of post-installed reinforcement used. Therefore, ACI 318 (2014) was used to determine the concrete breakout strength of the specimens considered in this study. A comparison of the calculated concrete breakout strengths and the peak load applied to each specimen was carried out and is discussed below on the basis of embedment depth, concrete strength, and GFRP bar size. Calculations for concrete breakout strength of all the specimens are provided in Appendix G. 4.4.1. Embedment Depth Among specimens with a concrete strength of 3 ksi, the concrete breakout strength of post-installed #4 GFRP bars predicted by ACI 318 (2014) exceeded the experimental data at an embedment depth of 6 in., regardless of the GFRP bar surface conditions (SCW, SC and R). For example, the experimental concrete breakout strength of post-installed GFRP bars (SC) was 11.19 kips compared to the theoretical concrete breakout strength of 17.51 kips. A comparison of the experimental data and theoretical results for specimens with an embedment depth 6 in. is shown in Figure 4-15, which 71 indicated that ACI 318 (2014) was not suitable for estimating the capacity of post- installed GFRP installed at an embedment depth of 6 in. On the other hand, the concrete breakout strength of post-installed #4 GFRP bars, predicted by ACI 318 (2014), was lower than the experimental data for GFRP bars with both SCW and SC surface condition at an embedment depth of 11.5 in. For example, the experimental concrete breakout strength of post-installed GFRP bars (SC) was 27.03 kips compared to the theoretical concrete breakout strength of 23.01 kips. A comparison of the experimental data and theoretical results for specimens with an embedment depth of 11.5 in. is shown in Figure 4-16. In this study, when the concrete strength of the base material was 3 ksi, ACI 318 (2014) was found to be sufficient for estimating the capacity of post-installed #4 GFRP bars with a minimum embedment depth of 11.5 in (23.5db). 4.4.2. Concrete Strength Among specimens with GFRP bars post-installed at an embedment depth of 11.5 in., concrete breakout strength of post-installed #4 GFRP bars predicted by ACI 318 (2014) was lower than the experimental data for both 3 and 6 ksi concrete strength regardless of the GFRP bar surface condition (SCW and SC). In the case of specimens with 6 ksi concrete strength, the experimental concrete breakout strength of post-installed GFRP bars (SC) was 37.35 kips compared to the theoretical concrete breakout strength of 32.54 kips. A comparison of the experimental data and theoretical results for specimens with a concrete strength of 3 and 6 ksi are shown in Figure 4-16 and Figure 4-17, respectively. Based on this study, ACI 318 (2014) was found to be sufficient for estimating the capacity of post-installed GFRP bars in an existing concrete member having a minimum concrete strength of 3 ksi (with GFRP bars installed at or beyond the minimum recommended embedment depth of 11.5 in. in Section 4.4.1.). 4.4.3. Bar Size Among specimens with a concrete strength of 6 ksi and GFRP bars post-installed at an embedment depth of 11.5 in., the concrete breakout strength of post-installed GFRP bars predicted by ACI 318 (2014) was lower than the experimental data for both #4 and #6 GFRP bars. For example, the experimental concrete breakout strength of post-installed #4 GFRP bars was 42.02 kips compared to the theoretical concrete breakout strength of 72 32.54 kips. On the other hand, the concrete breakout strength for post-installed #8 GFRP bars predicted by ACI 318 (2014) was 35.58 kips, which exceeded the experimental concrete breakout strength of 30.09 kips. When the bar size was increased, a trend of increased theoretical concrete breakout strength and decreased experimental concrete breakout strength was noticed, as shown in Figure 4-18. The results indicated that ACI 318 (2014) is suitable for designing post-installed reinforcement using #4 and #6 GFRP bars at the embedment depth of 11.5 in. 4.5. Parametric Study A parametric study was carried out to determine the parameters that most influenced the concrete breakout strength of post-installed GFRP bars. The factors that were studied included: embedment depth (le), concrete compressive strength (f’c), and the projected failure area (ANC). 4.5.1. Effect of Embedment Depth A specimen with geometry similar to a lab specimen was used to evaluate the effect of embedment depth (from 22db to 40db) on concrete breakout strength of post- installed GFRP. The range of embedment depth was selected on the basis of the embedment depth recommendation in Section 4.4.1. When the concrete strength was kept constant (6 ksi), the concrete breakout strength increased with an increase in the embedment depth of post-installed #4 GFRP bars. For example, the concrete breakout strength at 22db (11 in.) was 31.91 kips, which increased to 33.16 kips at 24db (12 in.). A review of concrete breakout strengths indicated that an increase in embedment depth by 2db (1 in.) resulted in increased concrete breakout strength at a decreasing rate as shown in Figure 4-19. For example, the concrete breakout strength increased by 3% from 30db to 32db, whereas the concrete breakout strength increased by 2.4% from 38db to 40db. It was concluded that an increase in embedment depth resulted in an increase in concrete breakout strength. 4.5.2. Effect of Concrete Compressive Strength A specimen with geometry similar to a lab specimen was used to evaluate the effect of concrete strength (from 3 to 8 ksi) on concrete breakout strength of post- 73 installed GFRP bars. The lower range of 3 ksi was selected based on Section 4.4.2., which was the minimum concrete strength suitable for estimating the concrete breakout strength of post-installed GFRP bars used in the laboratory specimens, and the upper range of 8 ksi was selected based the limits discussed in ACI 318 (2014) Section 17.2.7. When the embedment depth of post-installed #4 GFRP bars was kept constant (11.5 in.), the concrete breakout strength increased with an increase in concrete strength. For example, the concrete breakout strength for 3 ksi concrete strength was 23.01 kips, which increased to 24.85 kips for a concrete strength of 3.5 ksi as shown in Figure 4-20. The data indicated that every increase in concrete strength by 0.5 ksi resulted in increasing concrete breakout strength at a decreasing rate. For example, the concrete breakout strength increased by 8% from 3 to 3.5 ksi, whereas the concrete breakout strength increased by 2.9% from 7.5 to 8 ksi. It was concluded that an increase in concrete strength resulted in an increase in concrete breakout strength. 4.5.3. Effect of Projected Failure Area To demonstrate the effect of the projected failure area (ANC), a set of calculations were performed assuming a scenario in which the base material had a width much greater than the width of the beam (28 in.) and the edge distance greater than 1.5hef, which allowed for the maximization of the projected failure area by increasing the edge distance without variation in the spacing of GFRP bars. These sets of calculations were referred to as the calculations for hypothetical specimens. The calculated concrete breakout strength of specimens with (7) #4, (4) #6 and (3) #8 GFRP bars post-installed at an embedment depth of 11.5 in. and into a base material with a concrete strength of 6 ksi were chosen to compare with the concrete breakout strength of the hypothetical specimens. A comparison of the data indicated an increase in concrete breakout strength for all bar sizes when the projected failure area was increased. For example, the hypothetical specimen with (4) #6 GFRP bars had a calculated concrete breakout strength of 114.62 kips compared to a calculated concrete breakout strength of 34.44 kips for the lab specimen. The effect of projected failure area on the calculated concrete breakout strength is shown in Figure 4-21. The calculations for the hypothetical specimens are provided in Appendix H. 74 75 Table 4-1. Failure modes of all the experimental specimens Specimen Name* Failure Mode 3SCW4-ϕ6CIP Bond 3SCW4-E6PI Concrete breakout 3SCW4-C6PI Concrete breakout 3SC4-C6PI Concrete breakout 3SC4-E6PI Concrete breakout 3R4-E6PI Concrete breakout 3SCW4-ϕ11.5CIP Combined bond and concrete breakout 3SC4-ϕ11.5CIP Combined bond and concrete breakout 3SCW4-E11.5PI Concrete breakout 3SC4-E11.5PI Concrete breakout 3SCW6-E11.5PI Concrete breakout 3SC6-E11.5PI Concrete breakout 6SCW4-ϕ11.5CIP Bond 6SCW4-E11.5PI Concrete breakout 6SC4-E11.5PI Concrete breakout 6SCW6-E11.5PI Concrete breakout 6SC6-E11.5PI Concrete breakout 6SC(3#8)-E11.5PI Concrete breakout 6SCW(4#8)-E11.5PI Concrete breakout 6SC(4#8)-E11.5PI Concrete breakout *Nomenclature: (concrete strength in ksi) (GFRP texture) (bar size) - (chemical type) (embedment depth in in.) (casting method) For example: 3SC4-E6PI = (3 ksi concrete strength) (Silica coated texture GFRP bars) (#4 bar) - (Epoxy adhesive) (6 in. embedment depth) (Post-Installed) Table 4-2. Calculated development length of GFRP bars using ACI 440.1R (2015) and Equation 2.36 Specimen Name Calculated Development Length (in.) 3SCW4-ϕ6CIP 36.88 3SCW4-ϕ11.5CIP 35.55 3SC4-ϕ11.5CIP 47.60 6SCW4-ϕ11.5CIP 28.05 76 Table 4-3. Test data, bond strengths, and bond ratios for GFRP and steel bars Specimen Name (See Table 4-1) Concrete Strength at Day of Testing, f’c ksi Maximum Applied Load, kips Data Normalized to (f’c)1/2 Maximum Applied Load, kips Bond Strength, ksi Bond Ratio 3S4-ϕ6CIP (Hamad et al., 2006) 3.76 15.21 13.59 24.77 – 3S4-E6PI (Hamad et al., 2006) 4.71 23.64 18.54 34.36 1.39 3SCW4-ϕ6CIP 3.97 14.26 12.39 23.36 0.94 3SCW4-E6PI 3.97 15.14 13.16 24.81 1.00 3SCW4-C6PI 3.97 14.82 12.88 24.28 0.98 3SC4-C6PI 4.84 14.10 11.10 21.06 0.85 3SC4-E6PI 4.84 14.21 11.19 21.23 0.86 3R4-E6PI 3.97 14.62 12.71 22.04 0.96 3S4-ϕ11.5CIP (Hamad et al., 2006) 4.19 31.42 26.59 48.44 – 3S4-E11.5PI (Hamad et al., 2006) 3.80 36.92 32.85 59.89 1.24 3SCW4-ϕ11.5CIP 4.21 33.16 28.00 52.79 1.09 3SC4-ϕ11.5CIP 4.05 32.10 27.64 52.44 1.08 3SCW4-E11.5PI 4.37 27.8 23.03 43.41 0.90 3SC4-E11.5PI 4.37 32.63 27.03 51.28 1.06 3SCW6-E11.5PI 4.03 33.48 28.89 44.18 0.91 3SC6-E11.5PI 4.14 28.79 24.51 37.73 0.78 6SCW4-ϕ11.5CIP 6.03 32.78 32.69 61.33 1.27 6SCW4-E11.5PI 6.15 42.53 42.02 79.58 1.64 6SC4-E11.5PI 6.15 37.80 37.35 71.11 1.47 6SCW6-E11.5PI 6.45 36.72 35.42 53.72 1.11 6SC6-E11.5PI 6.28 31.14 30.45 43.93 0.91 6SC(3#8)-E11.5PI 6.03 30.17 30.09 34.83 0.72 6SCW(4#8)-E11.5PI 6.28 28.62 27.98 24.34 0.50 6SC(4#8)-E11.5PI 6.45 29.86 28.81 26.66 0.55 77 Table 4-4. Load-displacement behavior of specimens with GFRP bars compared to a cast-in-place steel reference specimen with f’c = 3 ksi Specimen Name (See Table 4-1) f’c = 3 ksi and le = 6 in. f ’ c = 3 ksi and le = 11.5 in. Peak Applied Load Displacement (in.) Peak Load** (%) Peak Applied Load Displacement (in.) Peak Load** (%) 3S4-ϕCIP* (Hamad et al., 2006) 0.23 – 0.67 – 3S4-EPI (Hamad et al., 2006) 0.72 +38 1.31 +24 3SCW4-ϕCIP 0.65 -6 1.17 +9 3SC4-ϕCIP N/A N/A 1.19 +8 3SCW4-EPI 0.50 0 1.37 -10 3SC4-EPI 0.50 -14 1.02 +6 3R4-EPI 0.73 -4 N/A N/A *Reference Specimen **Peak Load (%) = [(Specimen peak applied) * 100 / (Reference specimen Peak applied)] - 100 Table 4-5. Load-displacement behavior of specimens with post-installed #4 GFRP bars compared to a cast-in-place GFRP (SCW) specimen at le = 11.5 in. Specimen Name (See Table 4-1) f’c = 3 ksi and le = 11.5 in. f ’ c = 6 ksi and le = 11.5 in. Peak Applied Load Displacement (in.) Peak Load** (%) Peak Applied Load Displacement (in.) Peak Load** (%) SCW4- ϕ11.5CIP* 1.17 - 1.26 - SCW4-E11.5PI 1.37 -18 2.11 +28 SC4-E11.5PI 1.02 -1 1.96 +14 *Reference Specimen **Peak Load (%) = [(Specimen peak applied) * 100 / (Reference specimen Peak applied)] - 100 78 Table 4-6. Effect of bar size on load-displacement behavior of specimens with post- installed GFRP bars at le = 11.5 in. and f ’ c = 6 ksi Specimen Name (See Table 4-1) GFRP (SCW) GFRP (SC) Peak Applied Load Displacement (in.) Peak Load** (%) Peak Applied Load Displacement (in.) Peak Load** (%) 6(#4)-E11.5PI* 2.11 - 1.96 - 6(#6)-E11.5PI 1.42 -16 1.48 -5 6(#8)-E11.5PI 1.08 -33 1.20 -23 *Reference Specimen **Peak Load (%) = [(Specimen peak applied load) * 100 / (Reference specimen peak applied load)] – 100 79 Figure 4-1. Concrete breakout failure of post-installed specimens at (a) le = 6 in. and (b) le = 11.5 in. Figure 4-2. Failure modes of cast-in-place specimens (a) Bond failure at le = 6 in. and (b) Combined bond and concrete breakout failure at le = 11.5 in. Figure 4-3. Bond failure of cast-in-place specimen at le = 11.5 in. and f ’ c = 6 ksi 80 Figure 4-4. Effect of embedment depth on the bond ratio for steel and GFRP bars at f’c = 3 ksi Figure 4-5. Effect of concrete strength on the bond ratio for specimens with cast-in- place and post-installed GFRP bars at le = 11.5 in. 81 Figure 4-6. Effect of bar installation method on the bond ratio of #4 steel and GFRP bars at le = 11.5 in. and f ’ c = 3 ksi Figure 4-7. Effect of adhesive type on the bond ratio of specimens with post-installed #4 GFRP bars at le = 6 in. and f ’ c = 3 ksi 82 Figure 4-8. Effect of GFRP surface condition on the bond ratio of specimens with post-installed #4 GFRP bars at le = 6 in. and f ’ c = 3 ksi Figure 4-9. Effect of GFRP bar size on the bond ratio of specimens with post- installed bars using an epoxy adhesive at le = 11.5 in. and f ’ c = 6 ksi 83 Figure 4-10. Effect of spacing on the bond ratio of specimens with post-installed #8 GFRP bars (SC) using an epoxy adhesive at le = 11.5 in. and f ’ c = 6 ksi Figure 4-11. Load-displacement curves for specimens with #4 bars at le = 11.5 in. and f’c = 3 ksi 84 Figure 4-12. Load-displacement curves for specimens with #4 bars at le = 11.5 in. and f’c = 3 ksi Figure 4-13. Effect of concrete strength on load-displacement behavior of post- installed #4 GFRP bars at le = 11.5 in. 85 Figure 4-14. Effect of bar size on load-displacement behavior for specimens with post-installed GFRP bars (epoxy adhesive) at le = 11.5 in. and f ’ c = 6 ksi Figure 4-15. Comparison of experimental data and theoretical results of specimens with #4 post-installed (epoxy adhesive) GFRP bars at le = 6 in. and f ’ c = 3 ksi 86 Figure 4-16. Comparison of experimental data and theoretical results of specimens with #4 post-installed GFRP bars (epoxy adhesive) at le = 11.5 in. and f ’ c = 3 ksi Figure 4-17. Comparison of experimental data and theoretical results of specimens with #4 post-installed GFRP bars (epoxy adhesive) at le = 11.5 in. and f ’ c = 6 ksi 87 Figure 4-18. Comparison of experimental data and theoretical results of specimens with varying bar sizes of post-installed GFRP bars (epoxy adhesive) at le = 11.5 in. and f’c = 6 ksi Figure 4-19. Effect of embedment depth (le) on concrete breakout strength of post- installed #4 GFRP bars when f’c = 6 ksi 88 Figure 4-20. Effect of concrete strength (f’c) on concrete breakout strength of post- installed #4 GFRP bars at le = 11.5 in. Figure 4-21. Effect of projected failure area (ANC) on the concrete breakout strength of post-installed GFRP bars at le = 11.5 in. and f ’ c = 6 ksi 89 Chapter 5. Summary and Conclusions This chapter presents a summary and the conclusions that were drawn from this experimental study on the use of post-installed GFRP bars. In addition, recommendations are also made for future research into the potential use of post-installed GFRP bars. 5.1. Summary This research presented an experimental study with GFRP bars from three different manufacturers, each having different bar textures (silica coated with helical wraps, silica coated and ribbed), used as post-installed and cast-in-place reinforcement. Epoxy and cementitious-based adhesives were used for post-installing the GFRP bars. Twenty test specimens were constructed and tested under static load. A test specimen was composed of two identical vertical elements, which were anchored into the base element of the specimen using post-installed GFRP bars. The specimens were designed to simulate a rigid connection of two beams to a column or a wall. The variables tested among different specimens included: concrete compressive strength (3 and 6 ksi), embedment length of the GFRP bars (6 and 11.5 in.), size of the post-installed GFRP bars (#4, #6, and #8) and spacing of the #8 bars (5 and 6.5 in.). The purpose of this research was to evaluate the bond behavior of post-installed GFRP bars in structural connections and compare these results to results from cast-in-place and post-installed steel reinforcement that are available in literature (Hamad et al., 2006). The results from this study provided insight on the use of GFRP as post-installed reinforcement in existing structures. The conclusions that were made from this study are discussed in detail in Section 5.2. 5.2. Conclusions from Testing The conclusions drawn from this study are based on the specimens prepared in the laboratory and are limited to the testing parameters considered in this study. 5.2.1. Failure Modes The specimens with post-installed GFRP bars (#4, #6, and #8) exhibited concrete breakout failure for both embedment depths (6 and 11.5 in.) and concrete strengths (3 and 6 ksi), which was consistent with results from Hamad et al. (2006), who tested specimens 90 with post-installed #4 steel bars. Concrete breakout failure occurred because the bond between the GFRP bars and the surrounding concrete was greater than the tensile strength of the concrete. Concrete breakout failure developed in the form of cone shaped cracks in the member with post-installed bars. A bond failure occurred in the specimens with a concrete strength of 3 ksi and cast- in-place GFRP bars (#4) installed at an embedment depth of 6 in., whereas a combination of concrete breakout and bond failure was noted with an increase in embedment depth to 11.5 in. A bond failure was also observed in the specimens with a concrete strength of 6 ksi and cast-in-place GFRP bars at an embedment depth of 11.5 in. Bond failures occurred because the embedment depths (6 and 11.5 in.) were less than the required development lengths of the GFRP bars (#4 GFRP bars had a required development length of 35.5 in. for a SCW surface and 47.6 in. for a SC surface according to ACI 440-15). 5.2.2. Bond Strength and Bond Ratio The bond strength of the GFRP bars at the inner face of the vertical elements anchored into the base element was calculated using a cracked section analysis and bond ratios were computed by dividing the bond strength of each specimen by the bond strength of a reference specimen. Specimens with post-installed steel bars from Hamad et al. (2006) were used as reference specimens at both embedment depths (6 and 11.5 in.). For specimens with a concrete strength of 3 ksi, an increase in embedment depth (6 to 11.5 in.) had a greater influence on the bond strength of post-installed #4 GFRP bars compared to post-installed steel bars (Hamad et al., 2006). Bond strengths of post- installed #4 GFRP bars improved by a range of 127 to 142% due to an increase in embedment depth from 6 to 11.5 in. On the other hand, the bond strength of post-installed #4 steel bars increased by 74% with a similar increase of embedment depth. The effect of embedment depth on #6 and #8 post-installed GFRP bars was not studied. An increase of concrete strength (3 to 6 ksi) led to a 30 to 64% range of improvement from in bond strength of post-installed #4 GFRP bars compared to cast-in- place #4 GFRP bars, which only experienced a 17% improvement in bond strength. This indicated greater influence of concrete strength on bond strength of post-installed GFRP bars compared to cast-in-place GFRP bars. Additionally, the gain in bond strength of 91 post-installed GFRP bars, due to the increase in concrete strength from 3 to 6 ksi, was greater in #4 bars (ranging from 30 to 64%) compared to #6 bars (ranging from 22 to 43%). The bond strength improved when the concrete strength was increased because it is directly proportional to f’c1/2. The increase in concrete strength from 3 to 6 ksi resulted in an increase of 42% in terms of f’c1/2. Specimens with a concrete strength of 3 ksi and post-installed #4 GFRP bars installed at an embedment depth of 6 in., were used to study the effect of adhesive and GFRP surface condition on the bond strength. The experimentally obtained bond strength of post-installed GFRP bars installed with epoxy adhesives (24.81 ksi) was similar to GFRP bars installed with cementitious adhesives (24.28 ksi), which was in agreement with Hamad et al. (2006) regarding bond strength of post-installed steel bars installed with different adhesives. Post-installed GFRP bars with a silica coating and helical wraps (SCW) developed greater bond strength (24.81 ksi) compared to GFRP bars with silica coating (SC) and ribbed (R) surface (21.23 and 22.04 ksi, respectively). In specimens with a concrete strength of 6 ksi and post-installed GFRP bars installed at an embedment depth of 11.5 in., an increase in the bar size led to a loss of bond strength. The specimens with #4 post-installed GFRP bars exhibited greater bond strengths compared to the specimens with #6 post-installed GFRP bars (ranging from 48 to 88%), which in turn had greater bond strengths compared to the specimens with #8 post-installed GFRP bars (ranging from 42 to 121%). The loss in bond strength due to increasing bar sizes was due to decreases in the embedment depth-to-bar diameter ratio (ld/db). The ld/db ratios were 23.0, 15.3 and 11.5 for #4, #6 and #8 GFRP bars, respectively. The effect of GFRP bar spacing on bond strength was studied using two specimens with a concrete strength of 6 ksi and #8 GFRP bars installed at an embedment depth of 11.5 in. Three post-installed #8 GFRP bars transversely spaced at or beyond the manufacturer specified spacing (6.5 in.) exhibited a bond strength 30% greater than the four post-installed #8 GFRP bars spaced below the manufacturer specified spacing (5 in.). The placement of GFRP bars at 5 in. caused an overlap of the conic stress 92 distribution of each individual bar, which resulted in the loss of bond strength. The failure mode in both of these specimens was concrete breakout. 5.2.3. Load-Displacement Behavior Horizontal displacement recorded at the top of the vertical elements due to the peak applied load was referred to as ductility. Specimens with a concrete strength of 3 ksi and #4 GFRP bars (SCW) were used to study the effect of embedment depth on load- displacement behavior of post-installed GFRP bars. An increase in embedment depth from 6 to 11.5 in. improved the ductility of post-installed GFRP bars more (from 0.5 to 1.37 in.) than the ductility of cast-in-place GFRP bars (from 0.65 to 1.02 in.). The increase in embedment depth in both cases led to an increase in the bond strength of the GFRP bars, which led to an increase in ductility before reaching the peak applied load. The effect of concrete strength on the load-displacement behavior of post- installed GFRP bars was studied using specimens with #4 GFRP bars post-installed at an embedment depth of 11.5 in. An increase in concrete strength from 3 to 6 ksi led to an increase in horizontal displacement at the peak applied loads (ductility). The displacement increased from 1.37 to 2.11 in. for GFRP bars with the SCW surface condition and 1.02 to 1.96 in. for GFRP bars with the SC surface condition. This increase could be attributed to the improvement in bond strength due to increased concrete strength, which increased the ductility at the peak applied load. Specimens with a concrete strength of 6 ksi and GFRP bars post-installed at an embedment depth of 11.5 in. were used to study the effect of bar size on load- displacement behavior. An increase in the GFRP bar sizes from #4 to #6 and #6 to #8 resulted in a reduction of ductility. The decrease in ductility from #4 to #6 bars was 2.11 to 1.42 in. for SCW GFRP bars and 1.96 to 1.48 in. for SC GFRP bars. Similarly, the ductility decreased in specimens with #6 and #8 bars from 1.42 to 1.08 in. for SCW GFRP bars and 1.48 to 1.06 in. for SC GFRP bars. The increase in the area of the bars caused the reduction in ductility because of the inverse relation between modulus of elasticity and area of the bar (E = PL/Aδ). In other words, an increase in bar diameter would require additional embedment depth to gain similar ductility as the smaller sized bars. 93 5.2.4. Comparison with 318 (2014) Concrete breakout was the only failure mode observed in the specimens with post-installed GFRP bars. The results from this experimental study were compared with concrete breakout strengths calculated using ACI 318 (2014) without using any of the load resistance and strength reduction factors. Comparison of the experimental data and theoretical results led to the conclusion that ACI 318 (2014) can be used for estimating capacity of post-installed #4 GFRP bars when the concrete strength of the existing member (base material) is 3 ksi or higher and GFRP bars are installed at an embedment depth of at least 11.5 in. (23.5db). ACI 318 (2014) can be also used for determining the capacity of post-installed #6 GFRP in a base material with a minimum concrete strength of 6 ksi and an embedment depth of at least 11.5 in. (15.25db). ACI 318-14 should not be used for estimating capacity of post-installed #8 GFRP bars when the concrete strength of the base material is 6 ksi and the maximum available embedment depth is 11.5 in. because the theoretically computed concrete breakout strength (35.58 kips) exceeded the experimentally obtained concrete breakout strength (30.09 kips). 5.2.5. Parametric Study A parametric study was conducted on the factors that influenced the concrete breakout strength of post-installed GFRP bars, which included concrete strength, embedment depth and the projected failure area. The geometry of the lab specimens was used for this parametric study. An increase in concrete strength from 3 to 8 ksi (an increase of 63% in terms of f’c1/2) indicated a 63% gain in concrete breakout strength for #4 GFRP bars installed at an embedment depth of 11.5 in. Concrete breakout strength improved by 33% when the embedment depth of #4 GFRP bars, installed in a base material with a concrete strength of 6 ksi, was increased from 11.5 to 20 in. (an increase of 74%). Specimens with a concrete strength of 6 ksi and GFRP bars installed at an embedment depth of 11.5 in. were used to evaluate the effect of projected concrete failure area. The projected concrete failure area depends on the embedment depth of the GFRP bars, edge distance, and spacing of GFRP bars. The projected concrete failure area was increased to a maximum of 1.5hef (17.25 in.) in both directions by maximizing the edge distance and concrete breakout strengths were determined theoretically for #4, #6 and #8 94 GFRP bars without variation in the spacing of the bars. These concrete breakout strengths were compared with the theoretically computed results, in which the projected concrete failure area was similar to the lab specimens. In this comparison, concrete breakout strength increased by 268% for a specimen with seven #4 GFRP bars, 232% for a specimens with four #6 bars and 189% for a specimen with three #8 GFRP bars. Therefore, projected failure area was found to be the greatest influencing factor compared to concrete strength of the base material and the embedment depth of post-installed GFRP bars. 5.3. Recommendations for Future Work The application of post-installed GFRP bars in structural connections requires further evaluation of the bond behavior of post-installed GFRP bars. Investigation of a larger sample size of test parameters not considered in this study is required. Based on the reviewed literature and this study, the following recommendations are provided for future research into the applicability of post-installed GFRP bars. The spacing and size of the transverse reinforcement in the base element of the specimens was constant. Further research should be done to identify the effect of transverse reinforcement spacing and size on the failure modes of post-installed GFRP connections. A change in spacing and size of the base element transverse reinforcement may change the angle of the concrete breakout cracks, which are typically assumed to be 35o from the horizontal axis (Fuchs et al., 1995). Concrete breakout failure was the only failure mode observed in the specimens with both post-installed GFRP and post-installed steel bars (Hamad et al., 2006), but the peak applied loads were greater in steel specimens compared to GFRP specimens. This could be attributed to the deformed surface condition or ductile nature of steel rebar. Research should be performed to investigate the mechanical properties of beam-column connections using post-installed GFRP bars and provide design recommendations. The width of the base element was equal to the width of the vertical element in this study, which limited the size of the projected concrete failure area. The parametric study indicated that the projected failure area had the greatest influence on the concrete breakout strength. Experimental research with additional specimen geometries is needed 95 to verify the effect of the projected concrete failure area on the concrete breakout strength of GFRP bars. This study involved the use of adhesives from a single manufacturer. Further research should be performed on post-installed GFRP bars with adhesives from various manufacturers. Research with adhesives from additional manufacturers would allow for the development threshold design recommendations for flexural strength in post-installed applications. This study included investigation of the effect of bar spacing on the bond strength of post-installed #8 GFRP bars. More research should be performed on other GFRP bar sizes to verify the effect of spacing on the bond strength of post-installed GFRP bars. Further research could lead to minimum spacing recommendations for GFRP bars of all sizes. The depth of the base element of the specimens was constant at 14 in. The concrete breakout failure was localized beneath each vertical element when post-installed GFRP bars were installed at an embedment depth of 6 in. When the embedment depth was increased to 11.5 in., the concrete breakout failure was not localized and a single crack ran along the base element between the exterior edges of the vertical elements. Further research should be performed to investigate the concrete breakout crack patterns. Variation of the base element depth would also allow for an investigation of how additional embedment depths affect the strength of post-installed GFRP bars. 96 References Abdel-Magid, B., Saeed, Z., Katrina, G., & Marcus, S. (2005). “The combined effects of load, moisture and temperature on the properties of E-glass/epoxy composites.” Composite Structures, 71(4), 320-326. Abolghasem, A. (2013). "Experimental investigation on pull-out strength of pre- and post-installed GFRP bars for bridge barrier construction." MS Thesis, Ryerson University, Toronto, Ontario. Achillides, Z., & Pilakoutas, K. (2004). “Bond behavior of fiber reinforced polymer bars under direct pullout conditions.” Journal of Composites for Construction, 8(2), 173-181. Agarwal, B. H., & Broutman, L, J. (1990). “Chapter 8: Advanced topics in fiber composites.” Analysis and Performance of Fiber Composites, 2nd Edition, John Wiley & Sons, New York, 3(2), 324-367. Ahmed, E. A., El-Salakawy, E. F., & Benmokrane, B. (2008). “Tensile capacity of GFRP post-installed adhesive anchors in concrete.” Journal of Composites for Construction, 12(6), 596-607. Alves, J., El-Ragaby, A., & El-Salakawy, E. (2011)“Durability of GFRP bars’ bond to concrete under different loading and environmental conditions.” Journal of Composites for Construction, 15(3), 249-262. Aly, R. (2007). “Stress along tensile lap-spliced fibre reinforced polymer reinforcing bars in concrete.” Canadian Journal of Civil Engineering, 34(9), 1149-1158. American Concrete Institute Committee 349 (1985). “Code requirements for nuclear safety related concrete structures.” ACI 349R-85, American Concrete Institute, Detroit, Michigan. American Concrete Institute Committee 409 (2003). “Bond and development of straight reinforcing bars in tension.” ACI 408R-03, American Concrete Institute, Farmington Hills, Michigan. 97 American Concrete Institute Committee 440 (2006). “Guide for the Design and Construction of Structural Concrete Reinforced with FRP Bars.” ACI 440.1R-06, American Concrete Institute, Farmington Hills, Michigan. American Concrete Institute Committee 318 (2011). “Building Code Requirements for Structural Concrete.” ACI 318R-11, American Concrete Institute, Farmington Hills, Michigan. American Concrete Institute Committee 318 (2014). “Building Code Requirements for Structural Concrete.” ACI 318R-14, American Concrete Institute, Farmington Hills, Michigan. American Concrete Institute Committee 440 (2015). “Guide for the Design and Construction of Structural Concrete Reinforced with FRP Bars.” ACI 440.1R-15, American Concrete Institute, Farmington Hills, Michigan. Amus, J. (2013). "Design of tensile loaded anchorages at concrete splitting." Doctoral Dissertation, University of Stuttgart, Germany. Anderson, J., Jansz, A., Steele, K., Thistlewaite, P., Bishop, G., & Black, A. (2004). “Green guide to composites: an environmental profiling system for composite materials products.” BRE Bookshop, Watford, UK. Ascione, L., Mancusi, G., & Spadea, S. (2010). “Flexural behavior of concrete beams reinforced with GFRP bars.” An international Journal for Experimental Mechanics, 46(5), 460-469. Astrom, B. T. (1997). Manufacturing of polymer composites. Chapman & Hall, New York. Auyeung, Y., Balaguru, P., & Chung, L. (2000). “Bond Behavior of Corroded Reinforcement Bars.” ACI Materials Journal, 97(2), 214–220. Baena, M., Torres, L., Turon, A., & Barris, C. (2009). “Experimental study of bond behavior between concrete and FRP bars using a pull-out test.” Composites: Part B, 40(8), 784-797. Bank, L. C. (1993) “Properties of FRP reinforcement for concrete.” Fiber-Reinforced- Plastic (FRP) Reinforcement for Concrete Structures: Properties and 98 Applications, Developments in Civil Engineering, Elsevier, Amsterdam, 42(1), 59-86. Bank, L. C., Puterman, M., & Katz, A. (1998) “The effect of material degradation on bond properties of FRP reinforcing bars in concrete.” ACI Materials Journal, 95(3), 232-243. Cannon, R., Godfrey, D., & Moreadith, F. (1981). “Guide to the design of anchor bolts and other steel embedment.” Concrete International, 3(07), 28-41. Charney, F. A., Pal, K., & Silva, J. (2013). “Recommended Procedures for Development and Splicing of Post-Installed Bonded Reinforcing Bars in Concrete Structures.” ACI Structural Journal, 110(3), 437–446. Collins, D., Cook, R., Klingner, R., & Polyzois, D. (1989). “Load-deflection behavior of cast-in-place and retrofit concrete anchors subjected to static, fatigue, and impact tensile loads.” Center for Transportation Research Report 1126-1, University of Texas, Austin, Texas. Cook R. A., Collins, D. M., Klingner, R. E., & Polyzois, D. (1992). “Load-deflection behavior of cast-in-place and retrofit concrete anchors.” ACI Structural Journal, 89(6), 639–649. Cook, R. A., Doerr, G. T., & Klingner, R. E. (1993). “Bond stress model for design of adhesive anchors.” ACI Structural Journal, 90(5), 514–524. Cook, R. A., Kunz, J., Fuchs, W., & Konz, R. (1998). “Behavior and design of single adhesive anchors under tensile load in uncracked concrete.” ACI Structural Journal, 95(1), 9-26. Cook, R. A. (1999). Strength Design of Anchorage to Concrete. Portland Cement Association, Skokie, Illinois. Cook, R. A., & Konz, R. C. (2001). “Factors influencing bond strength of adhesive anchors.” ACI Structural Journal, 98(1), 76-86. Cosenza, E., Manfredi, G., & Realfonzo, R. (2002). “Development length of FRP straight rebar.” Composites Part B: Engineering, 33 (7), 493-504. 99 Davalos, J. F., Chen, Y., & Ray, I. (2011). “Long-term durability prediction models for GFRP bars in concrete environment.” Journal of Composite Materials, 46(16), 1899-1914. Daws, G. (1978). “Resin anchors: Part I and II.” International Journal of Rock Mechanics, Mining Sciences and Geomechanics, 17(1), A18. Doerr, G. T., & Klingner, R. E. (1989). “Adhesive anchors: Behavior and spacing requirements.” Center for Transportation Research Report 1126-2, University of Texas, Austin, Texas. Ehsani, M. R., Saadatmanesh, H., & Tao, S. (1996). “Bond behavior and design recommendations for fiber-glass reinforcing bars.” Proceedings of the First International Conference on Composites in Infrastructure, Tucson, Arizona, 466- 476. El-Gamal, S., AbdulRahman, B., & Benmokrane, B. (2010). “Deflection behavior of concrete beams reinforced with different types of GFRP bars.” Proceedings of the 5th International Conference on FRP Composites in Civil Engineering, Beijing, China, 279-282. Eligehausen, R., Cook, R., & Appl, J. (2006). “Behavior and design of adhesive bonded anchors.” ACI Structural Journal, 103(6), 822–831. Eligehausen, R., Mallee, R., & Rehm, G. (1984). “Befestigungen mit verbundankern.” Fastening with bonded anchors, (12), 825–829. Eligehausen, R., & Sawade, G. (1989). “A fracture mechanics based description of the pull-out behavior of headed studs embedded in concrete.” Fracture mechanics of concrete structures, Chapman and Hall, London, UK. Faza, S. S., & GangaRao, H. V. S. (1990). “Bending and bond behavior of concrete beams reinforced with plastic rebar.” Transportation Research Record 1290, 185- 193. Faza, S. S., & GangaRao, H. V. S. (1993). “Glass FRP reinforcing bars for concrete.” Fiber-Reinforced-Plastic (FRP) Reinforcement for Concrete Structures: Properties and Applications, Developments in Civil Engineering, Elsevier, Amsterdam, 42(1), 167-188. 100 Fuchs, W., Eligehausen, R., & Breen, J. (1995). “Concrete capacity design (CCD) approach for fastening to concrete.” ACI Structural Journal, 92(1), 73-94. Goldston, M., Remennikov, A., & Sheikh, M. N. (2016). “Experimental investigation of the behavior of concrete beams reinforced with GFRP bars under static and impact loading.” Engineering Structures, 113(15), 220-232. Hamad, B. S., Al-Hammoud, R., & Kunz, J. (2006). “Evaluation of bond strength of bonded-in or post-installed reinforcement.” ACI Structural Journal, 103(2), 207– 218. Hao, Q., Wang, Y., He, Z., & Ou, J. (2009). “Bond strength of glass fiber reinforced polymer ribbed rebar in normal strength concrete.” Construction and Building Materials, 23(2), 865-871. Hilti Inc. (2011). “Technical manual for post-installed rebar connections”, 10th edition, Zollikofen, Switzerland. Hilti Inc. (2016). “Post-installed reinforcing bar guide”, 2016, Tulsa, OK. Huer, T., & Eligehausen, R. (2007). “Splitting failure mode of bonded anchors.” Proceedings of the 6th International Conference on Fracture Mechanics of Concrete and Concrete Structures, Catania, Italy, 753-760. ICC Evaluation Service, LLC (2016). “Acceptance criteria for post-installed adhesive anchor systems in concrete elements.” AC-308, Plano, TX. Kawahara, B., Estrada, H., & Lee, L. (2012). “Life-cycle cost comparison for steel reinforced concrete and fiber reinforced polymer bridge decks.” Fiber Reinforced Polymer (FRP) Composites for Infrastructure Applications: Focusing on Innovation, Technology Implementation and Sustainability, Springer Dordrecht Heidelberg, London, 237-274. Kalpana, V. G., & Subramanian, K. (2011). “Behavior of concrete beams reinforced with GFRP Bars.” Journal of Reinforced Plastics & Composites, 30(23), 1915-1922. Kim, S. J., & Smith, S. T. (2010). “Pullout Strength Models for FRP Anchors in Uncracked Concrete.” Journal of Composites for Construction, 14(4), 406-414. 101 Kumari, G. J., Rao, P. J., & Rao, M. V. S. (2013). “Behavior of concrete beams reinforced with glass fiber reinforced polymer flats.” International Journal of Research in Engineering and Technology, 2(9), 202-208. Kunz, J. (2005). "Splitting design for anchorages and splices with post-installed reinforcement." Proceedings of 11th International Conference on Fracture, Turin, Italy. Lee, L., Jain, R., Stephenson, L., & Ramirez, C. (2012). “Introduction to fiber reinforced polymer (FRP) composites.” Fiber Reinforced Polymer (FRP) Composites for Infrastructure Applications: Focusing on Innovation, Technology Implementation and Sustainability, Springer Dordrecht Heidelberg, London, 1-21. Luke, C., Chon, C., & Jirsa, J. (1985). “Use of epoxies for grouting reinforcing bar dowels in concrete.” PMFSEL Report 85-2, University of Texas at Austin, Austin, Texas. Mahrenholtz, C., Eligehausen, R., & Reinhardt, H. (2015). “Design of post-installed reinforcing bars as end anchorage or as bonded anchor.” Engineering Structures, 100 (1), 645-655. Makitani, E., Irisawa, I., & Nishiura, N. (1993). “Investigation of bond in concrete member with fiber reinforced plastic bars." Fiber-Reinforced Plastic Reinforcement for Concrete Structures International Symposium, ACI SP138-20, 315-331. Mallick, P. K. (2007). “Chapter 6: Design with FRP reinforcing bars.” Fiber Reinforced Composites, Materials, Manufacturing, and Design, CRC Press, New York, 469- 540. Masmoudi, R., Masmoudi, A., Ouezdou, M. B., & Daoud, A. (2011). “Long-term bond performance of GFRP bars in concrete under temperature ranging from 20 °C to 80 °C.” Construction and Building Materials, 25(2), 486-493. Mosley, C. P., Tureyen, A. K., & Frosch, R. J. (2008). “Bond strength of nonmetallic reinforcing bars.” ACI Structural Journal, 105(5), 634-642. 102 Nanni, A., Luca, A. D., & Zadeh, H. J. (2014). “Chapter 2: Material properties.” Reinforced Concrete with FRP Bars: Mechanics and Design, CRC Press, New York, 23-34. National Institute of Standards and Technology (1998). “Post-installed anchors- A literature review.” Building and Fire Research Laboratory, Report NISTIR 6096, Gaithersburg, Maryland. National Transportation Safety Report (2007), “Ceiling collapse in the Interstate-90 connector tunnel.” Highway Accident Report PB2007-916203, Washington, D.C. Okelo, R., & Yuan, R. L. (2005). “Bond strength of fiber reinforced polymer rebar in normal strength concrete.” Journal of Composites for Construction, 9(3), 203- 213. Perenchio, W. F. (1994). “Corrosion of reinforcing steel.” ASTM STP 169C, 164-172. Plecnik, J., & Ahmad, S. H. (1988). “Transfer of composite technology to design and construction of bridges.” Final Report No. DTRS 5683-C000043, Washington, D.C. Quayyum, S. (2010). “Bond behavior of fiber reinforced polymer rebar in Concrete.” MS Thesis, University of British Columbia, Okanagan, British Columbia. Shin, S., Seo, D., & Han, B. (2009). “Performance of concrete beams reinforced with GFRP bars.” Journal of Asian Architecture and Building Engineering, 8(1), 197- 204. Spieth, H. A., Ozbolt, J., Eligehausen, R., & Appl, J. (2001). “Numerical and experimental analysis of post-installed rebar spliced with cast-in-place rebar.” Cachan: The Publishing Company of RILEM, 21(2), 889-898. Spieth, H., & Eligehausen, R. (2002). “Design of post-installed rebar connections.” Proceedings of the 3rd International Symposium on Bond in Concrete- from Research to Standard, Budapest, Hungary, 439-446. Untrauer, R. E. & Henry, R. L. (1965). “Influence of normal pressure on bond strength.” ACI Journal Proceedings, 62(5), 577-586. Wambeke, B. W. & Shield, C. K. (2006). “Development length of glass fiber-reinforced polymer bars in concrete.” ACI Structural Journal, 103 (1), 11-17. 103 Wu, W. P. (1990). “Thermomechanical properties of fiber reinforced plastic (FRP) Bars.” PhD dissertation, West Virginia University, Morgantown, West Virginia. Yan, F., Lin, Z., & Yang M. (2016). “Bond mechanism and bond strength of GFRP bars to concrete: A review.” Composite Part B: Engineering, 98(1), 56-69. 104 Appendix A. Vertical Element Nominal Moment and Shear Capacity Calculations Vertical elements with f’c = 3 ksi, SCW GFRP bars and (7) #4 bars b 28 in. h 12 in. d 10.25 in Af 1.4 in.2 Av 0.8 in.2 εcu 0.003 f'c 3 ksi β1 0.85 db 0.5 in. Moment Capacity: CE 0.8 Ef 7038 ksi ffu* 134 ksi ffu=CE • ffu* 107.2 ksi ρf 0.0042 ρfb (Equation 2.29) 0.0033 ρf/ρfb 1.25 Since ρfb < ρf < 1.4ρfb, section is in transition. ff (Equation 2.30) 94.47 ksi ɸf (Equation 2.28) 0.59 a (Equation 2.34) 1.87 in. Mn (Equation 2.33) 104 kip-ft ɸf • Mn 61 kip-ft Shear Capacity: ɸv 0.75 Vc = 2 • f’c0.5 • bw • d 31 kips Vs = Av • fy • d / s 141 kips ɸv • Vn 129 kips 105 Vertical elements with f’c = 3 ksi, SC GFRP bars and (7) #4 bars b 28 in. h 12 in. d 10.25 in Af 1.4 in.2 Av 0.8 in.2 εcu 0.003 f'c 3 ksi β1 0.85 db 0.5 in. Moment Capacity: CE 0.8 Ef 9090.84 ksi ffu* 199.5 ksi ffu=CE • ffu* 159.6 ksi ρf 0.0042 ρfb (Equation 2.29) 0.0020 ρf/ρfb 2.10 Since ρf > 1.4ρfb, section is compression controlled. ff (Equation 2.30) 106.25 ksi ɸf (Equation 2.28) 0.65 a (Equation 2.34) 2.08 in. Mn (Equation 2.33) 99 kip-ft ɸf • Mn 64 kip-ft Shear Capacity: ɸv 0.75 Vc = 2 • f’c0.5 • bw • d 31 kips Vs = Av • fy • d / s 141 kips ɸv • Vn 129 kips 106 Vertical elements with f’c = 3 ksi, R GFRP bars and (7) #4 bars b 28 in. h 12 in. d 10.25 in Af 1.4 in.2 Av 0.8 in.2 εcu 0.003 f'c 3 ksi β1 0.85 db 0.5 in. Moment Capacity: CE 0.8 Ef 6000 ksi ffu* 116 ksi ffu=CE • ffu* 92.8 ksi ρf 0.0042 ρfb (Equation 2.29) 0.0038 ρf/ρfb 1.10 Since ρfb < ρf < 1.4ρfb, section is in transition. ff (Equation 2.30) 88.18 ksi ɸf (Equation 2.28) 0.575 a (Equation 2.34) 1.73 in. Mn (Equation 2.33) 83.57 kip-ft ɸf • Mn 48.05 kip-ft Shear Capacity: ɸv 0.75 Vc = 2 • f’c0.5 • bw • d 31.44 kips Vs = Av • fy • d / s 140.57 kips ɸv • Vn 129.01 kips 107 Vertical elements with f’c = 6 ksi, SCW GFRP bars and (7) #4 bars b 28 in. h 12 in. d 10.25 in Af 1.4 in.2 Av 0.8 in.2 εcu 0.003 f'c 6 ksi β1 0.75 db 0.5 in. Moment Capacity: CE 0.8 Ef 7038 ksi ffu* 134 ksi ffu=CE • ffu* 107.2 ksi ρf 0.0042 ρfb (Equation 2.29) 0.0059 ρf/ρfb 0.71 Since ρf < ρfb, therefore, section is tension controlled. => ff = ffu ɸf (Equation 2.28) 0.55 a (Equation 2.34) 1.69 in. Mn (Equation 2.33) 120.28 kip-ft ɸf • Mn 66.16 kip-ft Shear Capacity: ɸv 0.75 Vc = 2 • f’c0.5 • bw • d 44.46 kips Vs = Av • fy • d / s 140.57 kips ɸv • Vn 138.77 kips 108 Vertical elements with f’c = 6 ksi, SC GFRP bars and (7) #4 bars b 28 in. h 12 in. d 10.25 in Af 1.4 in.2 Av 0.8 in.2 εcu 0.003 f'c 6 ksi β1 0.75 db 0.5 in. Moment Capacity: CE 0.8 Ef 9090.84 ksi ffu* 199.5 ksi ffu=CE • ffu* 159.6 ksi ρf 0.0042 ρfb (Equation 2.29) 0.0035 ρf/ρfb 1.19 Since ρfb < ρf < 1.4ρfb, section is in transition. ff (Equation 2.30) 145.18 ksi ɸf (Equation 2.28) 0.60 a (Equation 2.34) 1.61 in. Mn (Equation 2.33) 139.47 kip-ft ɸf • Mn 83.68 kip-ft Shear Capacity: ɸv 0.75 Vc = 2 • f’c0.5 • bw • d 44.46 kips Vs = Av • fy • d / s 140.57 kips ɸv • Vn 138.77 kips 109 Vertical elements with f’c = 3 ksi, SCW GFRP bars and (4) #6 bars b 28 in. h 12 in. d 10.125 in Af 1.76 in.2 Av 0.8 in.2 εcu 0.003 f'c 3 ksi β1 0.85 db 0.75 in. Moment Capacity: CE 0.8 Ef 7052 ksi ffu* 107 ksi ffu=CE • ffu* 85.6 ksi ρf 0.0052 ρfb (Equation 2.29) 0.0050 ρf/ρfb 1.04 Since ρfb< ρf < 1.4ρfb, section is in transition. ff (Equation 2.30) 83.58 ksi ɸf (Equation 2.28) 0.56 a (Equation 2.34) 2.06 in. Mn (Equation 2.33) 95.71 kip-ft ɸf • Mn 53.60 kip-ft Shear Capacity: ɸv 0.75 Vc = 2 • f’c0.5 • bw • d 31.06 kips Vs = Av • fy • d / s 138.86 kips ɸv • Vn 127.43 kips 110 Vertical elements with f’c = 3 ksi, SC GFRP bars and (4) #6 bars b 28 in. h 12 in. d 10.125 in Af 1.76 in.2 Av 0.8 in.2 εcu 0.003 f'c 3 ksi β1 0.85 db 0.75 in. Moment Capacity: CE 0.8 Ef 8943 ksi ffu* 190.8 ksi ffu=CE • ffu* 152.64 ksi ρf 0.0052 ρfb (Equation 2.29) 0.0021 ρf/ρfb 2.47 Since ρf > 1.4ρfb, section is compression controlled. ff (Equation 2.30) 92.80 ksi ɸf (Equation 2.28) 0.65 a (Equation 2.34) 2.29 in. Mn (Equation 2.33) 105.16 kip-ft ɸf • Mn 68.35 kip-ft Shear Capacity: ɸv 0.75 Vc = 2 • f’c0.5 • bw • d 31.06 kips Vs = Av • fy • d / s 138.86 kips ɸv • Vn 127.43 kips 111 Vertical elements with f’c = 6 ksi, SCW GFRP bars and (4) #6 bars b 28 in. h 12 in. d 10.125 in Af 1.76 in.2 Av 0.8 in.2 εcu 0.003 f'c 6 ksi β1 0.75 db 0.75 in. Moment Capacity: CE 0.8 Ef 7052 ksi ffu* 107 ksi ffu=CE • ffu* 85.6 ksi ρf 0.0052 ρfb (Equation 2.29) 0.0088 ρf/ρfb 0.59 Since ρf < ρfb, therefore, section is tension controlled. => ff = ffu ɸf (Equation 2.28) 0.55 a (Equation 2.34) 2.01 in. Mn (Equation 2.33) 117.67 kip-ft ɸf • Mn 64.72 kip-ft Shear Capacity: ɸv 0.75 Vc = 2 • f’c0.5 • bw • d 43.92 kips Vs = Av • fy • d / s 138.86 kips ɸv • Vn 137.08 kips 112 Vertical elements with f’c = 6 ksi, SC GFRP bars and (4) #6 bars b 28 in. h 12 in. d 10.125 in Af 1.76 in.2 Av 0.8 in.2 εcu 0.003 f'c 6 ksi β1 0.75 db 0.75 in. Moment Capacity: CE 0.8 Ef 8943 ksi ffu* 190.8 ksi ffu=CE • ffu* 152.64 ksi ρf 0.0052 ρfb (Equation 2.29) 0.0037 ρf/ρfb 1.4 Since ρf > 1.4ρfb, section is compression controlled. ff (Equation 2.30) 127.20 ksi ɸf (Equation 2.28) 0.65 a (Equation 2.34) 1.78 in. Mn (Equation 2.33) 148.93 kip-ft ɸf • Mn 96.81 kip-ft Shear Capacity: ɸv 0.75 Vc = 2 • f’c0.5 • bw • d 43.92 kips Vs = Av • fy • d / s 138.86 kips ɸv • Vn 137.08 kips 113 Vertical elements with f’c = 6 ksi, SCW GFRP bars and (4) #8 bars b 28 in. h 12 in. d 10 in Af 3.16 in.2 Av 0.8 in.2 εcu 0.003 f'c 6 ksi β1 0.75 db 1 in. Moment Capacity: CE 0.8 Ef 7052 ksi ffu* 104 ksi ffu=CE • ffu* 83.2 ksi ρf 0.0094 ρfb (Equation 2.29) 0.0093 ρf/ρfb 1.01 Since ρfb< ρf < 1.4ρfb, section is in transition. ff (Equation 2.30) 82.72 ksi ɸf (Equation 2.28) 0.552 a (Equation 2.34) 2.08 in. Mn (Equation 2.33) 167.75 kip-ft ɸf • Mn 92.60 kip-ft Shear Capacity: ɸv 0.75 Vc = 2 • f’c0.5 • bw • d 43.38 kips Vs = Av • fy • d / s 137.14 kips ɸv • Vn 135.39 kips 114 Vertical elements with f’c = 6 ksi, SC GFRP bars and (4) #8 bars b 28 in. h 12 in. d 10 in Af 3.16 in.2 Av 0.8 in.2 εcu 0.003 f'c 6 ksi β1 0.75 db 1 in. Moment Capacity: CE 0.8 Ef 8851 ksi ffu* 154.5 ksi ffu=CE • ffu* 123.6 ksi ρf 0.0094 ρfb (Equation 2.29) 0.0055 ρf/ρfb 1.72 Since ρf > 1.4ρfb, section is compression controlled. ff (Equation 2.30) 91.49 ksi ɸf (Equation 2.28) 0.65 a (Equation 2.34) 2.29 in. Mn (Equation 2.33) 183.78 kip-ft ɸf • Mn 119.46 kip-ft Shear Capacity: ɸv 0.75 Vc = 2 • f’c0.5 • bw • d 43.38 kips Vs = Av • fy • d / s 137.14 kips ɸv • Vn 135.39 kips 115 Vertical elements with f’c = 6 ksi, SC GFRP bars and (3) #8 bars b 28 in. h 12 in. d 10 in Af 2.37 in.2 Av 0.8 in.2 εcu 0.003 f'c 6 ksi β1 0.75 db 1 in. Moment Capacity: CE 0.8 Ef 8851 ksi ffu* 154.5 ksi ffu=CE • ffu* 123.6 ksi ρf 0.0071 ρfb (Equation 2.29) 0.0055 ρf/ρfb 1.29 Since ρfb< ρf < 1.4ρfb, section is in transition. ff (Equation 2.30) 107.45 ksi ɸf (Equation 2.28) 0.62 a (Equation 2.34) 2.02 in. Mn (Equation 2.33) 163.67 kip-ft ɸf • Mn 102.29 kip-ft Shear Capacity: ɸv 0.75 Vc = 2 • f’c0.5 • bw • d 43.38 kips Vs = Av • fy • d / s 137.14 kips ɸv • Vn 135.39 kips 116 Appendix B. Example Reference Sheet Pressure (psi) Load (kips) Pressure (psi) Load (kips) Pressure (psi) Load (kips) Pressure (psi) Load (kips) 50 0.31 1750 10.99 3450 21.67 5150 32.34 100 0.63 1800 11.30 3500 21.98 5200 32.66 150 0.94 1850 11.62 3550 22.29 5250 32.97 200 1.26 1900 11.93 3600 22.61 5300 33.28 250 1.57 1950 12.25 3650 22.92 5350 33.60 300 1.88 2000 12.56 3700 23.24 5400 33.91 350 2.20 2050 12.87 3750 23.55 5450 34.23 400 2.51 2100 13.19 3800 23.86 5500 34.54 450 2.83 2150 13.50 3850 24.18 5550 34.85 500 3.14 2200 13.82 3900 24.49 5600 35.17 550 3.45 2250 14.13 3950 24.81 5650 35.48 600 3.77 2300 14.44 4000 25.12 5700 35.80 650 4.08 2350 14.76 4050 25.43 5750 36.11 700 4.40 2400 15.07 4100 25.75 5800 36.42 750 4.71 2450 15.39 4150 26.06 5850 36.74 800 5.02 2500 15.70 4200 26.38 5900 37.05 850 5.34 2550 16.01 4250 26.69 5950 37.37 900 5.65 2600 16.33 4300 27.00 6000 37.68 950 5.97 2650 16.64 4350 27.32 6050 37.99 1000 6.28 2700 16.96 4400 27.63 6100 38.31 1050 6.59 2750 17.27 4450 27.95 6150 38.62 1100 6.91 2800 17.58 4500 28.26 6200 38.94 1150 7.22 2850 17.90 4550 28.57 6250 39.25 1200 7.54 2900 18.21 4600 28.89 6300 39.56 1250 7.85 2950 18.53 4650 29.20 6350 39.88 1300 8.16 3000 18.84 4700 29.52 6400 40.19 1350 8.48 3050 19.15 4750 29.83 6450 40.51 1400 8.79 3100 19.47 4800 30.14 6500 40.82 1450 9.11 3150 19.78 4850 30.46 6550 41.13 1500 9.42 3200 20.10 4900 30.77 6600 41.45 1550 9.73 3250 20.41 4950 31.09 6650 41.76 1600 10.05 3300 20.72 5000 31.40 6700 42.08 1650 10.36 3350 21.04 5050 31.71 6750 42.39 1700 10.68 3400 21.35 5100 32.03 6800 42.70 117 Appendix C. Pictures of Failure Modes from all Specimens Figure C-1. Crack Pattern of Specimen 3SCW4-ϕ6CIP Figure C-2. Crack Pattern of Specimen 3SCW4-E6PI 118 Figure C-3. Crack Pattern of Specimen 3SCW4-C6PI Figure C-4. Crack Pattern of Specimen 3SC4-C6PI 119 Figure C-5. Crack Pattern of Specimen 3SC4-E6PI Figure C-6. Crack Pattern of Specimen 3R4-E6PI 120 Figure C-7. Crack Pattern of Specimen 3SCW4-ϕ11.5CIP Figure C-8. Crack Pattern of Specimen 3SC4- ϕ11.5CIP 121 Figure C-9. Crack Pattern of Specimen 3SCW4-E11.5PI Figure C-10. Crack Pattern of Specimen 3SC4-E11.5PI 122 Figure C-11. Crack Pattern of Specimen 3SCW6-E11.5PI Figure C-12. Crack Pattern of Specimen 3SC6-E11.5PI 123 Figure C-13. Crack Pattern of Specimen 6SCW4-ϕ11.5CIP Figure C-14. Crack Pattern of Specimen 6SCW4-E11.5PI 124 Figure C-15. Crack Pattern of Specimen 6SC4-E11.5PI Figure C-16. Crack Pattern of Specimen 6SCW6-E11.5PI 125 Figure C-17. Crack Pattern of Specimen 6SC6-E11.5PI Figure C-18. Crack Pattern of Specimen 6SC8-E11.5PI (3 #8 bars) 126 Figure C-19. Crack Pattern of Specimen 6SCW8-E11.5PI (4 #8 bars) Figure C-20. Crack Pattern of Specimen 6SC8-E11.5PI (4 #8 bars) 127 Appendix D. Development Length Calculations of CIP GFRP Bars Cast-in-place specimen with f’c= 3 ksi and #4 SCW GFRP bars (3SCW4-ϕ6CIP) b 28 in. h 12 in. εcu 0.003 f'c 3.972 ksi β1 0.8514 db 0.5 in. CE 0.8 Ef 7038 ksi ffu* 126.14 ksi ffu = CE • ffu* 100.912 ksi Af (7 #4 bars) 1.4 in.2 ρf = Af /(b•h) 0.004167 ρfb (Equation 2.29) 0.004929 Since ρf < ρfb, section is tension controlled => ffr = ffu ffr 100.912 ksi α 1 C= 3.5•db 1.75 in. ld (Equation 2.36) 36.8764 in. Cast-in-place specimen with f’c= 3 ksi and #4 SCW GFRP bars (3SCW4-ϕ11.5CIP) b 28 in. h 12 in. εcu 0.003 f'c 4.207 ksi β1 0.83965 db 0.5 in. CE 0.8 Ef 7038 ksi ffu* 126.14 ksi ffu = CE • ffu* 100.912 ksi Af (7 #4 bars) 1.4 in.2 ρf = Af /(b•h) 0.004167 ρfb (Equation 2.29) 0.005148 Since ρf < ρfb, section is tension controlled 128 => ffr = ffu ffr 100.912 ksi α 1 C= 3.5•db 1.75 in. ld (Equation 2.36) 35.55 in. Cast-in-place specimen with f’c= 3 ksi and #4 SC GFRP bars (3SC4-ϕ11.5CIP) b 28 in. h 12 in. εcu 0.003 f'c 4.047 ksi β1 0.84765 db 0.5 in. CE 0.8 Ef 9090.84 ksi ffu* 199.5 ksi ffu = CE • ffu* 159.6 ksi Af (7 #4 bars) 1.4 in.2 ρf = Af /(b•h) 0.004167 ρfb (Equation 2.29) 0.002666 Since ρf > ρfb, section is compression controlled => ffr = ff ff (Equation 2.30) 125.1856 ksi ffr 125.1856 ksi α 1 C= 3.5•db 1.75 in. ld (Equation 2.36) 47.59741 in. Cast-in-place specimen with f’c= 6 ksi and #4 SC GFRP bars (6SCW4-ϕ11.5CIP) b 28 in. h 12 in. εcu 0.003 f'c 6.033 ksi β1 0.74835 db 0.5 in. CE 0.8 Ef 7038 ksi ffu* 126.14 ksi ffu = CE • ffu* 100.912 ksi 129 Af (7 #4 bars) 1.4 in.2 ρf = Af /(b•h) 0.004167 ρfb (Equation 2.29) 0.00658 Since ρf < ρfb, section is tension controlled => ffr = ffu ffr 100.912 ksi α 1 C= 3.5•db 1.75 in. ld (Equation 2.36) 28.0468 in. 130 Appendix E. GFRP Bar Stress Calculations 3SCW4-ϕ6CIP Height of vertical element, h 29.53 in. Width of vertical element, b 27.56 in. Distance between bars and compression fiber, d 9.25 in. Intended compressive strength of concrete, f’ci 3000 psi Compressive strength of concrete at day of testing, f’ct 3972 psi Modulus of elasticity of GFRP, EG 7037.92 ksi Modulus of elasticity of Concrete, Ec 3122.02 ksi Modular ratio, n = EG / Ec 2.25 Area of GFRP, Af = 7 • 0.2 in.2 1.4 in.2 Aeq.= n • Af 3.16 in.2 Depth of neutral axis, a 1.34 in. Icr = (b • a3/ 12) + (b • a • (a/2)2 + (Aeq. • (d – a)2) 219.57 in.4 Ultimate load, P 14.26 kip Normalized load, Pn = P • (f’ci / f’ct)0.5 12.39 kip Location of load from top of the vertical element, L 6.3 in. Cracking moment, Mcr = Pn • (h – L) 287.89 kip-in Stress on GFRP = n • (Mcr • (d – a)) / Icr 23.36 ksi 3SCW4-E6PI Height of vertical element 29.53 in. Width of vertical element 27.56 in. Distance between bars and compression fiber 9.25 in. Intended compressive strength of concrete 3000 psi Compressive strength of concrete at day of testing 3972 psi Modulus of elasticity of GFRP 7037.92 ksi Modulus of elasticity of Concrete 3122.02 ksi Modular ratio 2.25 Area of GFRP 1.4 in.2 A eq. 3.16 in.2 Depth of neutral axis 1.34 in. Cracking moment of inertia 219.57 in.4 Ultimate load 15.14 kip Load normalized to (f'c^0.5) 13.16 kip Location of load from top of the vertical element 6.3 in. Cracking moment 305.66 kip-in Stress on GFRP 24.80 ksi 131 3SCW4-C6PI Height of vertical element 29.53 in. Width of vertical element 27.56 in. Distance between bars and compression fiber 9.25 in. Intended compressive strength of concrete 3000 psi Compressive strength of concrete at day of testing 3972 psi Modulus of elasticity of GFRP 7037.92 ksi Modulus of elasticity of Concrete 3122.02 ksi Modular ratio 2.25 Area of GFRP 1.4 in.2 A eq. 3.16 in.2 Depth of neutral axis 1.34 in. Cracking moment of inertia 219.57 in.4 Ultimate load 14.82 kip Load normalized to (f'c^0.5) 12.88 kip Location of load from top of the vertical element 6.3 in. Cracking moment 299.19 kip-in Stress on GFRP 24.28 ksi 3SC4-C6PI Height of vertical element 29.53 in. Width of vertical element 27.56 in. Distance between bars and compression fiber 9.25 in. Intended compressive strength of concrete 3000 psi Compressive strength of concrete at day of testing 4840 psi Modulus of elasticity of GFRP 9090 ksi Modulus of elasticity of Concrete 3122.02 ksi Modular ratio 2.91 Area of GFRP 1.4 in.2 A eq. 4.08 in.2 Depth of neutral axis 1.51 in. Cracking moment of inertia 275.82 in.4 Ultimate load 14.1 kip Load normalized to (f'c^0.5) 11.10 kip Location of load from top of the vertical element 6.3 in. Cracking moment 257.87 kip-in Stress on GFRP 21.06 ksi 132 3SC4-E6PI Height of vertical element 29.53 in. Width of vertical element 27.56 in. Distance between bars and compression fiber 9.25 in. Intended compressive strength of concrete 3000 psi Compressive strength of concrete at day of testing 4840 psi Modulus of elasticity of GFRP 9090 ksi Modulus of elasticity of Concrete 3122.02 ksi Modular ratio 2.91 Area of GFRP 1.4 in.2 A eq. 4.08 in.2 Depth of neutral axis 1.51 in. Cracking moment of inertia 275.82 in.4 Ultimate load 14.21 kip Load normalized to (f'c^0.5) 11.19 kip Location of load from top of the vertical element 6.3 in. Cracking moment 259.89 kip-in Stress on GFRP 21.22 ksi 3R4-E6PI Height of vertical element 29.53 in. Width of vertical element 27.56 in. Distance between bars and compression fiber 9.25 in. Intended compressive strength of concrete 3000 psi Compressive strength of concrete at day of testing 3972 psi Modulus of elasticity of GFRP 6000 ksi Modulus of elasticity of Concrete 3122.02 ksi Modular ratio 1.92 Area of GFRP 1.4 in.2 A eq. 2.69 in.2 Depth of neutral axis 1.25 in. Cracking moment of inertia 190.14 in.4 Ultimate load 14.62 kip Load normalized to (f'c^0.5) 12.71 kip Location of load from top of the vertical element 6.3 in. Cracking moment 295.16 kip-in Stress on GFRP 23.87 ksi 133 3SCW4- ϕ11.5CIP Height of vertical element 29.53 in. Width of vertical element 27.56 in. Distance between bars and compression fiber 9.25 in. Intended compressive strength of concrete 3000 psi Compressive strength of concrete at day of testing 4207 psi Modulus of elasticity of GFRP 7037.92 ksi Modulus of elasticity of Concrete 3122.02 ksi Modular ratio 2.25 Area of GFRP 1.4 in.2 A eq. 3.16 in.2 Depth of neutral axis 1.34 in. Cracking moment of inertia 219.57 in.4 Ultimate load 33.16 kip Load normalized to (f'c^0.5) 28.00 kip Location of load from top of the vertical element 6.3 in. Cracking moment 650.49 kip-in Stress on GFRP 52.79 ksi 3SC4- ϕ11.5CIP Height of vertical element 29.53 in. Width of vertical element 27.56 in. Distance between bars and compression fiber 9.25 in. Intended compressive strength of concrete 3000 psi Compressive strength of concrete at day of testing 4047 psi Modulus of elasticity of GFRP 9090.82 ksi Modulus of elasticity of Concrete 3122.02 ksi Modular ratio 2.91 Area of GFRP 1.4 in.2 A eq. 4.08 in.2 Depth of neutral axis 1.51 in. Cracking moment of inertia 275.85 in.4 Ultimate load 32.1 kip Load normalized to (f'c^0.5) 27.64 kip Location of load from top of the vertical element 6.3 in. Cracking moment 642.02 kip-in Stress on GFRP 52.43 ksi 134 3SCW4-E11.5PI Height of vertical element 29.53 in. Width of vertical element 27.56 in. Distance between bars and compression fiber 9.25 in. Intended compressive strength of concrete 3000 psi Compressive strength of concrete at day of testing 4373 psi Modulus of elasticity of GFRP 7037.92 ksi Modulus of elasticity of Concrete 3122.02 ksi Modular ratio 2.25 Area of GFRP 1.4 in.2 A eq. 3.16 in.2 Depth of neutral axis 1.34 in. Cracking moment of inertia 219.57 in.4 Ultimate load 27.8 kip Load normalized to (f'c^0.5) 23.03 kip Location of load from top of the vertical element 6.3 in. Cracking moment 534.89 kip-in Stress on GFRP 43.41 ksi 3SC4-E11.5PI Height of vertical element 29.53 in. Width of vertical element 27.56 in. Distance between bars and compression fiber 9.25 in. Intended compressive strength of concrete 3000 psi Compressive strength of concrete at day of testing 4373 psi Modulus of elasticity of GFRP 9090 ksi Modulus of elasticity of Concrete 3122.02 ksi Modular ratio 2.91 Area of GFRP 1.4 in.2 A eq. 4.08 in.2. Depth of neutral axis 1.51 in. Cracking moment of inertia 275.82 in.4 Ultimate load 32.63 kip Load normalized to (f'c^0.5) 27.03 kip Location of load from top of the vertical element 6.3 in. Cracking moment 627.82 kip-in Stress on GFRP 51.26 ksi 135 3SCW6-E11.5PI Height of vertical element 29.53 in. Width of vertical element 27.56 in. Distance between bars and compression fiber 9.125 in. Intended compressive strength of concrete 3000 psi Compressive strength of concrete at day of testing 4030 psi Modulus of elasticity of GFRP 7051.66 ksi Modulus of elasticity of Concrete 3122.02 ksi Modular ratio 2.26 Area of GFRP 1.76 in.2 A eq. 3.98 in.2. Depth of neutral axis 1.48 in. Cracking moment of inertia 262.12 in.4 Ultimate load 33.48 kip Load normalized to (f'c^0.5) 28.89 kip Location of load from top of the vertical element 6.3 in. Cracking moment 671.03 kip-in Stress on GFRP 44.18 ksi 3SC6-E11.5PI Height of vertical element 29.53 in. Width of vertical element 27.56 in. Distance between bars and compression fiber 9.125 in. Intended compressive strength of concrete 3000 psi Compressive strength of concrete at day of testing 4140 psi Modulus of elasticity of GFRP 8942.88 ksi Modulus of elasticity of Concrete 3122.02 ksi Modular ratio 2.86 Area of GFRP 1.76 in.2 A eq. 5.04 in.2. Depth of neutral axis 1.65 in. Cracking moment of inertia 322.96 in.4 Ultimate load 28.79 kip Load normalized to (f'c^0.5) 24.51 kip Location of load from top of the vertical element 6.3 in. Cracking moment 569.31 kip-in Stress on GFRP 37.73 ksi 136 6SCW4-ϕ11.5CIP Height of vertical element 29.53 in. Width of vertical element 27.56 in. Distance between bars and compression fiber 9.25 in. Intended compressive strength of concrete 6000 psi Compressive strength of concrete at day of testing 6033 psi Modulus of elasticity of GFRP 7037.92 ksi Modulus of elasticity of Concrete 4415.2 ksi Modular ratio 1.59 Area of GFRP 1.4 in.2 A eq. 2.23 in.2 Depth of neutral axis 1.15 in. Cracking moment of inertia 160.39 in.4 Ultimate load 32.87 kip Load normalized to (f'c^0.5) 32.78 kip Location of load from top of the vertical element 6.3 in. Cracking moment 761.48 kip-in Stress on GFRP 61.33 ksi 6SCW4-E11.5PI Height of vertical element 29.53 in. Width of vertical element 27.56 in. Distance between bars and compression fiber 9.25 in. Intended compressive strength of concrete 6000 psi Compressive strength of concrete at day of testing 6147 psi Modulus of elasticity of GFRP 7037.92 ksi Modulus of elasticity of Concrete 4415.2 ksi Modular ratio 1.59 Area of GFRP 1.4 in.2 A eq. 2.23 in.2 Depth of neutral axis 1.15 in. Cracking moment of inertia 160.39 in.4 Ultimate load 43.05 kip Load normalized to (f'c^0.5) 42.53 kip Location of load from top of the vertical element 6.3 in. Cracking moment 988.02 kip-in Stress on GFRP 79.58 ksi 137 6SC4-E11.5PI Height of vertical element 29.53 in. Width of vertical element 27.56 in. Distance between bars and compression fiber 9.25 in. Intended compressive strength of concrete 6000 psi Compressive strength of concrete at day of testing 6147 psi Modulus of elasticity of GFRP 9090.82 ksi Modulus of elasticity of Concrete 4415.2 ksi Modular ratio 2.06 Area of GFRP 1.4 in.2 A eq. 2.88 in.2 Depth of neutral axis 1.29 in. Cracking moment of inertia 202.37 in.4 Ultimate load 38.26 kip Load normalized to (f'c^0.5) 37.80 kip Location of load from top of the vertical element 6.3 in. Cracking moment 878.01 kip-in Stress on GFRP 71.11 ksi 6SCW6-E11.5PI Height of vertical element 29.53 in. Width of vertical element 27.56 in. Distance between bars and compression fiber 9.125 in. Intended compressive strength of concrete 6000 psi Compressive strength of concrete at day of testing 6447 psi Modulus of elasticity of GFRP 7051.66 ksi Modulus of elasticity of Concrete 4415.2 ksi Modular ratio 1.60 Area of GFRP 1.76 in.2 A eq. 2.81 in.2 Depth of neutral axis 1.26 in. Cracking moment of inertia 192.26 in.4 Ultimate load 36.72 kip Load normalized to (f'c^0.5) 35.42 kip Location of load from top of the vertical element 6.3 in. Cracking moment 822.90 kip-in Stress on GFRP 53.72 ksi 138 6SC6-E11.5PI Height of vertical element 29.53 in. Width of vertical element 27.56 in. Distance between bars and compression fiber 9.125 in. Intended compressive strength of concrete 6000 psi Compressive strength of concrete at day of testing 6447 psi Modulus of elasticity of GFRP 8942.88 ksi Modulus of elasticity of Concrete 4415.2 ksi Modular ratio 2.03 Area of GFRP 1.76 in.2 A eq. 3.56 in.2 Depth of neutral axis 1.41 in. Cracking moment of inertia 237.94 in.4 Ultimate load 29.86 kip Load normalized to (f'c^0.5) 28.81 kip Location of load from top of the vertical element 6.3 in. Cracking moment 669.17 kip-in Stress on GFRP 43.93 ksi 6SC(3#8)-E11.5PI Height of vertical element 29.53 in. Width of vertical element 27.56 in. Distance between bars and compression fiber 9 in. Intended compressive strength of concrete 6000 psi Compressive strength of concrete at day of testing 6033 psi Modulus of elasticity of GFRP 8851.22 ksi Modulus of elasticity of Concrete 4415.2 ksi Modular ratio 2.00 Area of GFRP 2.37 in.2 A eq. 4.75 in.2. Depth of neutral axis 1.60 in. Cracking moment of inertia 297.80 in.4 Ultimate load 30.17 kip Load normalized to (f'c^0.5) 30.09 kip Location of load from top of the vertical element 6.3 in. Cracking moment 698.93 kip-in Stress on GFRP 34.83 ksi 139 6SC(4#8)-E11.5PI Height of vertical element 29.53 in. Width of vertical element 27.56 in. Distance between bars and compression fiber 9 in. Intended compressive strength of concrete 6000 psi Compressive strength of concrete at day of testing 6277 psi Modulus of elasticity of GFRP 7052.29 ksi Modulus of elasticity of Concrete 4415.2 ksi Modular ratio 1.60 Area of GFRP 3.16 in.2 A eq. 5.05 in.2 Depth of neutral axis 1.64 in. Cracking moment of inertia 313.94 in.4 Ultimate load 28.62 kip Load normalized to (f'c^0.5) 27.98 kip Location of load from top of the vertical element 6.3 in. Cracking moment 650.01 kip-in Stress on GFRP 24.34 ksi 6SC(4#8)-E11.5PI Height of vertical element 29.53 in. Width of vertical element 27.56 in. Distance between bars and compression fiber 9 in. Intended compressive strength of concrete 6000 psi Compressive strength of concrete at day of testing 6277 psi Modulus of elasticity of GFRP 8851.22 ksi Modulus of elasticity of Concrete 4415.2 ksi Modular ratio 2.00 Area of GFRP 3.16 in.2 A eq. 6.33 in.2 Depth of neutral axis 1.82 in. Cracking moment of inertia 381.96 in.4 Ultimate load 31.14 kip Load normalized to (f'c^0.5) 30.45 kip Location of load from top of the vertical element 6.3 in. Cracking moment 707.24 kip-in Stress on GFRP 26.66 ksi 140 Appendix F. Load-Displacement Data from each Specimen 3S4-ϕ6CIP* 3S4-C6PI* 3S4-E6PI* Load (kip) Displacement (in.) Load (kip) Displacement (in.) Load (kip) Displacement (in.) 0.00 0.00 0.00 0.00 0.00 0.00 2.26 0.00 0.00 0.00 1.81 0.00 4.02 0.00 2.03 0.00 3.72 0.01 5.97 0.01 3.98 0.01 5.36 0.01 8.17 0.03 6.01 0.02 7.07 0.02 9.97 0.06 7.93 0.02 8.83 0.03 11.89 0.12 10.06 0.04 10.69 0.05 12.25 0.12 11.89 0.07 12.35 0.07 13.37 0.23 12.12 0.08 13.02 0.09 13.17 0.30 13.36 0.10 13.76 0.10 11.61 0.51 14.31 0.12 14.43 0.16 11.45 0.51 15.23 0.37 15.93 0.31 11.03 0.57 13.71 0.82 18.55 0.50 10.53 0.62 13.67 1.23 15.86 0.74 9.84 0.71 12.96 1.36 15.50 0.76 9.33 0.80 12.89 2.03 14.66 0.79 9.13 0.82 12.80 2.03 14.44 0.81 9.08 0.91 12.79 2.35 14.22 0.83 9.08 1.21 14.20 1.24 9.27 1.61 14.12 1.24 9.20 2.79 14.03 1.25 8.62 3.06 13.95 1.25 8.43 3.06 13.66 1.25 8.39 3.06 13.26 1.25 8.31 3.06 11.39 1.24 8.28 3.06 7.70 1.18 8.08 3.05 7.27 1.18 7.61 3.04 7.08 1.17 7.10 3.04 6.24 1.16 6.10 1.16 *Hamad et al. (2006) 141 3SCW4-ϕ6CIP 3SCW4-C6PI 3SCW4-E6PI Load (kip) Displacement (in.) Load (kip) Displacement (in.) Load (kip) Displacement (in.) 0.30 0.01 0.19 0.00 0.06 0.01 3.15 0.01 3.22 0.00 2.84 0.01 4.82 0.02 4.71 0.01 4.85 0.01 6.94 0.03 6.73 0.04 7.61 0.03 8.45 0.06 8.86 0.06 9.06 0.05 10.90 0.10 10.70 0.11 10.70 0.11 12.12 0.14 13.04 0.22 12.63 0.20 11.99 0.14 14.09 0.28 14.47 0.32 12.97 0.16 14.05 0.30 12.58 0.43 14.02 0.20 12.72 0.82 10.51 0.68 13.04 0.37 13.15 3.09 11.09 1.63 12.93 0.89 9.30 3.05 6.07 2.52 10.91 1.27 4.72 3.04 4.78 2.40 9.07 1.98 2.74 2.97 2.86 2.17 6.80 2.83 0.75 2.59 0.39 1.65 5.84 3.60 2.89 3.83 0.16 3.58 142 3SC4-E6PI 3SC4-C6PI 3R4-E6PI Load (kip) Displacement (in.) Load (kip) Displacement (in.) Load (kip) Displacement (in.) 0.00 0.00 0.00 0.00 0.26 0.02 1.44 0.03 1.08 0.01 3.00 0.02 3.28 0.05 5.64 0.01 5.30 0.06 4.56 0.06 6.91 0.06 7.07 0.06 5.64 0.07 8.11 0.07 9.03 0.14 6.87 0.09 9.60 0.13 10.92 0.21 8.08 0.12 11.71 0.25 12.82 0.31 9.43 0.16 12.58 0.37 14.33 0.39 10.30 0.19 13.60 0.44 12.27 0.54 11.62 0.26 14.06 0.53 11.42 1.00 12.66 0.32 12.18 0.56 11.05 1.07 12.90 0.42 11.92 0.89 9.95 2.51 14.15 0.56 11.43 1.97 4.57 2.48 15.22 0.70 10.51 2.45 2.83 2.49 14.69 0.77 10.04 3.17 0.24 1.93 13.92 1.26 8.47 3.48 12.24 2.02 7.50 3.53 11.12 2.04 6.47 3.50 10.56 2.05 5.45 3.50 9.42 2.06 4.56 3.48 8.27 2.01 3.48 3.48 7.39 2.01 2.52 3.48 6.31 2.01 1.56 3.48 5.73 2.00 0.36 3.39 4.45 1.99 3.53 1.94 2.47 1.97 1.59 1.94 0.30 1.86 143 3S4-ϕ11.5CIP* 3S4-ϕ11.5CIP* (Cont.) 3S4-E11.5PI* Load (kip) Displacement (in.) Load (kip) Displacement (in.) Load (kip) Displacement (in.) 0.00 0.00 17.36 1.35 0.00 0.00 2.39 0.00 17.21 1.40 2.38 0.00 5.38 0.01 16.93 1.47 4.74 0.01 7.22 0.01 16.61 1.64 7.56 0.02 9.19 0.01 16.37 1.71 9.29 0.03 11.60 0.03 16.13 1.80 11.32 0.05 14.10 0.04 15.95 1.90 13.64 0.07 15.80 0.04 15.87 2.01 16.09 0.09 18.56 0.07 15.67 2.04 18.63 0.11 20.99 0.09 15.44 2.10 20.84 0.15 23.59 0.13 14.91 2.24 23.68 0.18 24.83 0.16 14.54 2.45 22.85 0.18 26.07 0.24 14.34 2.45 24.42 0.22 26.64 0.27 14.26 2.52 26.15 0.33 27.98 0.35 14.64 2.64 27.01 0.37 29.98 0.52 14.28 2.74 26.67 0.37 29.77 0.53 *Hamad et al. (2006) 28.32 0.45 30.11 0.59 32.36 0.82 29.79 0.68 32.66 0.85 29.66 0.73 33.95 1.06 28.16 0.80 34.15 1.07 28.22 0.82 33.72 1.08 27.35 0.89 34.17 1.10 26.83 0.91 34.10 1.11 25.84 0.94 34.27 1.17 24.18 1.00 33.16 1.52 22.41 1.05 32.47 1.85 21.06 1.09 32.06 1.90 20.29 1.12 31.67 1.99 19.50 1.15 31.43 2.12 18.68 1.18 31.24 2.23 17.54 1.25 30.82 2.27 17.41 1.28 30.50 2.36 17.40 1.30 30.36 2.42 30.03 2.53 144 3SCW4-ϕ11.5CIP 3SC4-ϕ11.5CIP 3SCW4-E11.5PI Load (kip) Displacement (in.) Load (kip) Displacement (in.) Load (kip) Displacement (in.) 0.00 0.00 0.00 0.00 0.00 0.00 1.58 0.00 0.88 0.01 0.51 0.02 4.62 0.03 5.63 0.05 5.66 0.03 8.96 0.04 7.33 0.06 7.15 0.07 12.09 0.13 9.13 0.10 9.53 0.10 15.88 0.23 10.97 0.15 11.91 0.14 19.81 0.37 14.53 0.30 14.47 0.28 22.38 0.46 17.18 0.37 16.04 0.30 24.87 0.56 20.02 0.43 17.21 0.42 27.64 0.71 22.57 0.54 19.20 0.59 29.01 0.84 26.55 0.70 20.65 0.64 32.74 1.05 29.93 0.91 21.90 0.77 33.01 1.16 31.28 1.07 24.12 0.89 30.45 1.58 32.08 1.16 24.87 1.03 29.04 2.09 31.10 1.24 27.30 1.37 26.84 2.62 28.86 1.33 26.42 1.67 25.25 2.95 27.21 1.56 23.52 2.39 10.14 3.13 25.90 2.24 21.46 2.64 8.36 3.09 21.97 3.06 17.76 3.07 4.90 2.86 16.80 2.99 2.74 2.68 14.00 2.87 1.39 2.55 10.88 2.72 0.23 2.38 6.41 2.61 1.47 2.49 145 3SC4-E11.5PI 3SCW6-E11.5PI 3SC6-E11.5PI Load (kip) Displacement (in.) Load (kip) Displacement (in.) Load (kip) Displacement (in.) 0.00 0.00 0.00 0.00 0.00 0.00 2.34 0.03 2.15 0.01 1.68 0.01 5.74 0.03 5.74 0.04 4.35 0.02 7.14 0.05 7.72 0.10 5.97 0.05 9.76 0.08 9.78 0.18 7.58 0.10 12.03 0.13 11.70 0.27 9.69 0.18 14.67 0.20 13.71 0.37 11.61 0.25 17.78 0.31 15.84 0.46 13.50 0.33 19.74 0.40 17.86 0.57 15.69 0.43 22.26 0.52 18.72 0.73 17.40 0.54 24.75 0.61 21.61 1.00 19.31 0.71 27.14 0.72 22.68 1.18 21.10 0.84 29.36 0.86 24.72 1.32 22.61 1.08 30.57 0.93 25.42 1.47 20.83 1.54 31.56 0.98 25.80 1.53 19.53 1.78 32.41 1.03 26.21 1.66 17.76 2.58 31.12 1.18 21.65 2.36 11.20 2.75 28.54 1.68 11.46 2.52 7.21 2.59 26.38 2.13 7.60 2.49 4.18 2.37 23.70 2.37 5.31 2.43 2.25 2.20 15.23 2.48 3.79 2.38 0.89 2.04 12.11 2.50 2.60 2.36 8.32 2.40 0.63 2.32 5.87 2.26 4.38 2.19 2.50 2.10 0.79 1.92 146 6SCW4-ϕ11.5CIP 6SCW4-E11.5PI 6SC4-E11.5PI Load (kip) Displacement (in.) Load (kip) Displacement (in.) Load (kip) Displacement (in.) 0.00 0.00 0.00 0.00 0.00 0.00 1.11 0.00 0.53 0.00 1.62 0.01 4.24 0.00 3.46 0.01 5.09 0.02 6.99 0.01 7.33 0.01 7.10 0.02 9.70 0.10 9.58 0.07 9.52 0.05 12.15 0.15 12.12 0.14 12.17 0.13 14.51 0.23 16.07 0.28 14.55 0.19 17.20 0.36 19.71 0.39 17.16 0.26 19.75 0.46 22.33 0.50 19.79 0.33 22.35 0.55 24.74 0.57 22.30 0.39 26.18 0.73 27.40 0.67 24.54 0.46 29.63 0.95 29.94 0.78 27.36 0.54 31.51 1.10 32.50 0.87 30.01 0.67 32.44 1.32 35.09 1.01 31.92 0.75 29.85 1.53 35.91 1.30 33.99 0.94 25.23 2.51 38.29 1.76 35.14 1.09 19.46 3.08 41.59 1.94 36.19 1.50 11.27 3.52 39.41 2.13 37.46 1.93 8.63 3.53 23.67 2.25 22.66 2.52 4.69 3.48 20.42 2.25 18.38 2.54 0.50 3.38 13.83 2.23 15.44 2.52 9.48 2.15 11.46 2.34 5.18 1.73 8.96 2.23 1.61 1.57 3.07 1.93 0.88 1.76 147 6SCW6-E11.5PI 6SC6-E11.5PI 6SCW(4#8)-E11.5PI Load (kip) Displacement (in.) Load (kip) Displacement (in.) Load (kip) Displacement (in.) 0.00 0.00 0.00 0.00 0.00 0.00 1.19 0.00 1.59 0.01 0.45 0.00 5.59 0.00 4.84 0.02 4.33 0.00 7.49 0.00 7.48 0.04 7.48 0.02 9.64 0.04 9.90 0.05 9.63 0.06 12.26 0.09 11.99 0.12 11.94 0.17 14.39 0.14 14.49 0.21 14.50 0.33 16.85 0.22 17.04 0.30 16.76 0.42 19.31 0.30 19.37 0.37 19.43 0.55 22.60 0.37 21.96 0.44 25.17 0.77 25.08 0.47 24.39 0.51 27.17 0.86 27.64 0.56 26.44 0.59 28.29 1.03 30.82 0.67 28.25 1.10 25.41 1.41 32.73 0.84 29.37 1.48 24.31 2.17 34.11 1.31 26.66 2.26 16.21 2.95 35.41 1.56 14.11 2.56 15.24 2.95 27.31 2.52 8.54 2.44 13.87 2.96 18.49 2.44 5.83 2.44 11.33 2.97 14.25 2.38 3.16 2.37 8.90 2.91 12.10 2.34 0.77 2.35 6.97 2.87 6.25 2.33 3.08 2.86 1.74 2.31 0.77 2.85 148 6SC(3#8)-E11.5PI 6SC(4#8)-E11.5PI Load (kip) Displacement (in.) Load (kip) Displacement (in.) 0.00 0.00 0.00 0.00 0.83 0.01 1.75 0.00 4.66 0.06 5.58 0.02 7.23 0.12 7.44 0.03 9.55 0.23 9.81 0.06 12.08 0.30 11.76 0.10 14.63 0.38 14.52 0.16 17.08 0.44 17.66 0.27 19.63 0.50 22.46 0.48 21.34 0.60 24.22 0.58 24.63 0.72 26.53 0.75 26.75 0.88 29.37 1.09 29.34 1.09 29.93 1.51 30.04 1.32 30.68 1.93 28.68 1.50 27.36 2.52 26.60 2.22 23.03 2.94 24.80 3.05 19.62 2.80 22.47 3.22 14.35 2.79 17.49 3.20 10.31 2.79 13.72 3.18 8.66 2.78 9.10 3.03 3.11 2.31 5.26 2.85 1.09 2.13 1.03 2.51 149 Appendix G. Concrete Breakout Strength Calculations for Specimens with Post-Installed GFRP (7) #4 GFRP bars(SCW, SC and R), le = 6 in. and f ’ c = 3 ksi b 28 in. hef 6 in. f’c 3000 psi Edge Spacing 2.5 in. kc 17 ANCO = 9 • hef2 324 in.2 ANC = 2 • 1.5 • hef • b 504 in.2 ψed,N (Equation 2.26) 0.783 ψc,N 1.4 ψcp,N 0.75 ψec,N 1 Ncbg (Equation 2.19) 17.51 kip (7) #4 GFRP bars(SCW and SC), le = 11.5 in. and f ’ c = 3 ksi b 28 in. hef 11.5 in. f’c 3000 psi Edge Spacing 2.5 in. kc 17 ANCO = 9 • hef2 1190.25 in.2 ANC = 2 • 1.5 • hef • b 966 in.2 ψed,N (Equation 2.26) 0.743 ψc,N 1.4 ψcp,N 0.75 ψec,N 1 Ncbg (Equation 2.19) 23.01 kip 150 (7) #4 GFRP bars (SCW and SC), le = 11.5 in. and f ’ c = 6 ksi b 28 in. hef 11.5 in. f’c 6000 psi Edge Spacing 2.5 in. kc 17 ANCO = 9 • hef2 1190.25 in.2 ANC = 2 • 1.5 • hef • b 966 in.2 ψed,N (Equation 2.26) 0.743 ψc,N 1.4 ψcp,N 0.75 ψec,N 1 Ncbg (Equation 2.19) 32.54 kip (4) #6 & #8GFRP bars (SCW and SC), le = 11.5 in. and f ’ c = 6 ksi b 28 in. hef 11.5 in. f’c 6000 psi Edge Spacing 5 in. kc 17 ANCO = 9 • hef2 1190.25 in.2 ANC = 2 • 1.5 • hef • b 966 in.2 ψed,N (Equation 2.26) 0.787 ψc,N 1.4 ψcp,N 0.75 ψec,N 1 Ncbg (Equation 2.19) 34.44 kip 151 (3) #8 GFRP bars (SC), le = 11.5 in. and f ’ c = 6 ksi B 28 in. hef 11.5 in. f’c 6000 psi Edge Spacing 6.5 in. kc 17 ANCO = 9 • hef2 1190.25 in.2 ANC = 2 • 1.5 • hef • b 966 in.2 ψed,N (Equation 2.26) 0.813 ψc,N 1.4 ψcp,N 0.75 ψec,N 1 Ncbg (Equation 2.19) 35.58 kip 152 Appendix H. Concrete Breakout Strength Calculations for Hypothetical Specimens (7) #4 GFRP bars, le = 11.5 in. and f ’ c = 6 ksi B 28 in. hef 11.5 in. f’c 6000 psi Edge Spacing (ES) 2.5 in. kc 17 ANCO = 9 • hef2 1190.25 in.2 ANC = 2 • 1.5 • hef •( b+ 2 • 1.5 • hef - 2 • ES) 1983.75 in.2 ψed,N (Equation 2.26) 1.000 ψc,N 1.4 ψcp,N 1 ψec,N 1 Ncbg (Equation 2.19) 119.83 kip (4) #6 GFRP bars, le = 11.5 in. and f ’ c = 6 ksi B 28 in. hef 11.5 in. f’c 6000 psi Edge Spacing (ES) 5 in. kc 17 ANCO = 9 • hef2 1190.25 in.2 ANC = 2 • 1.5 • hef •( b+ 2 • 1.5 • hef - 2 • ES) 1811.25 in.2 ψed,N (Equation 2.26) 1.000 ψc,N 1.4 ψcp,N 1 ψec,N 1 Ncbg (Equation 2.19) 109.41 kip 153 (3) #8 GFRP bars, le = 11.5 in. and f ’ c = 6 ksi B 28 in. hef 11.5 in. f’c 6000 psi Edge Spacing (ES) 6.5 in. kc 17 ANCO = 9 • hef2 1190.25 in.2 ANC = 2 • 1.5 • hef •( b+ 2 • 1.5 • hef - 2 • ES) 1707.75 in.2 ψed,N (Equation 2.26) 1.000 ψc,N 1.4 ψcp,N 1 ψec,N 1 Ncbg (Equation 2.19) 103.15 kip 154 Appendix I. Linear Finite Element Analysis: Methods and Results A linear finite element analysis was performed to compare the theoretical results and experimental data. For this purpose, the experimental data of specimen 6SCW4- E11.5PI was used. Preparation of Models SOLIDWORKS was used to model the test specimen. The model was very complex as it contained steel rebar in the base element as well as the vertical element. In addition to steel rebar, GFRP bars were post-installed in the base element. The portion of GFRP bars embedded in the base element was coated with a ⅛ in. thick epoxy layer. The various FEM elements of the model varied significantly in size and the entire model contained about 2 million nodes. Since the geometry of the specimen was symmetric, one quarter of the modeled specimen was used to create a less complex model and reduce the result processing time while running the analysis in ANSYS. The two models that were created are shown in Figure H-1. The uncracked model is shown in Figure H-1a and the model with cracks is shown in Figure H-1b. The cracks in the cracked model were replicated from the actual crack pattern that was observed at that particular load while testing the specimen in the laboratory. Theoretical ANSYS Analysis The first step in the analysis was assigning properties to different materials that were used in the construction of the specimen. The materials and their relevant properties, obtained from the manufacturer, are listed in Table H-1. The appropriate faces of the quarter specimen were fixed in relevant directions to mimic the boundary conditions of the whole specimen. A single, static load was applied 6 in. below the top of vertical element and a static structural analysis was performed to compute the displacement. For the uncracked model, a total load of 3.67 kips (applied in the z- direction) yielded a theoretical value of displacement equal to 0.0082 in., while the measured experimental value was 0.0114 in. In the cracked model, a total load of 6.06 kips was applied and a theoretical displacement of 0.016 in. was obtained, whereas the 155 measured experimental displacement was 0.142 in. These results are tabulated in Table H-2. The results from the linear elastic analysis, completed by ANSYS, are shown in Figures H-2 and H-3. Experimental Data vs. Theoretical Results For the initial uncracked portion of the analysis, the experimental data corresponded well with the theoretical results obtained in ANSYS and the slope of the elastic load vs. displacement lines were similar. The small difference between the experimental and theoretical values could be attributed to the difference in actual material properties (measured f’c) and the empirical properties that were assigned to the concrete. However, as the concrete specimen developed cracks, a significant difference between experimental and theoretical behavior was observed. The ANSYS model created in this study was unable to replicate the behavior observed in the experimental data. The cracked load vs. displacement curve from the ANSYS results did not accurately predicted the experimental data as demonstrated in Figure H-4. This could be ascribed to inaccurate representation of the actual loss of stiffness in the cracked specimen by the SOLIDWORKS model. Additionally, the cracks created in the SOLIDWORKS model were the cracks that were observed during testing. The invisible micro-cracks or other internal cracks unobservable during testing that were not modeled in the specimen may have caused the disparity between experimental data and theoretical results. Summary and Conclusions A concrete specimen replicating a beam-column or beam-wall connection with post-installed GFRP, tested with a single static load, was modeled in SOLIDWORKS and an analysis was performed in ANSYS to compute the displacement for two different magnitude loads. The theoretical results obtained from the analysis were compared with experimental data. A comparison of the results led to the following conclusions:  For the initial uncracked portion of the analysis, the experimental data corresponded well with the theoretical results obtained in ANSYS.  For the cracked portion of the analysis, the experimental data did not correspond well with the theoretical results obtained in ANSYS. 156 Table I-1. Properties of materials from manufacturers used in ANSYS Properties Concrete Epoxy GFRP Steel Density (lb/ft3) 150 6.01E+01 136.08 490 Elastic Modulus (psi) 4.70E+06 6.50E+05 7.04E+06 2.90E+07 Poisson's Ratio 0.2 0.4 0.19 0.3 Table I-2. Load-displacement experimental data and theoretical results for specimen 6SCW4-E11.5PI Load Applied to Half of Specimen (kip) Experimental Displacement (in.) Theoretical Displacement (in.) Before Cracking 3.67 0.0114 0.008 After Cracking 6.06 0.142 0.016 157 Figure I-1. Half of the test specimen modeled in SOLIDWORKS for the 6SCW4- E11.5PI specimen (a) Uncracked specimen (b) Cracked specimen Figure I-2. Linear finite element analysis of uncracked model in ANSYS for the 6SCW4-E11.5PI specimen 158 Figure I-3. Linear finite element analysis of cracked model (cracks highlighted in the red box) in ANSYS for the 6SCW4-E11.5PI specimen Figure I-4. Experimental data versus theoretical results for the 6SCW4-E11.5PI specimen