Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Tadele, Sisay
Master of Applied Science - MASc
University of British Columbia
Bridge structures are essential components of infrastructure that play a pivotal role in connecting areas with difficult geography, such as across a river. Apart from ensuring ultimate life safety and serviceability limit state performance, their performance during seismic events determines the safety of the user and economic growth of the region. With advancements in technology, new construction materials are being produced. One of the commonly promoted types of new materials in construction is high-strength steel (HSS). The use of HSS for instance has a wide range of applications in construction, from reducing bar congestion and reducing labor as well as construction costs. Nonetheless, the use of HSS has been restricted, or no guidelines are available in many cases for the design of seismic-resistant members. In this study, the performance of CSA G30.18 500W is evaluated to study its suitability for the seismic design of reinforced concrete bridges. This study involves extensive experimental research work involving material tests of the HSS reinforcing steel and large-scale reinforced concrete bridge pier tests to assess the performance of the material. The examinations of low-cycle fatigue were conducted with various bar sizes, unsupported lengths, and strain amplitudes. Notably, the CSA G30.18 500W exhibited satisfactory low-cycle fatigue performance, wherein the effect of bar unsupported length and strain amplitude were more pronounced. Additionally, two large-scale bridge piers were tested under seismic loads to study the performance of the reinforced bridge columns, which are the location of plastic hinges in bridges and undergo large inelastic deformation. The test results of the columns indicated that the bridge piers achieved comparable drift levels and energy dissipation capacities with columns reinforced with regular steel ASTM A706 Grade 420. Moreover, the strain limits for performance-based design (PBD) of bridges utilizing CSA G30.18 500W were derived from the measured material strain limits. Lastly, a comparative study of the seismic performance of bridge piers containing ASTM A1035 Grade 690, CSA G30.18 400W, and CSA G30.18 500W was conducted through fragility curve analysis.
SEISMIC RESPONSE OF CIRCULAR CONCRETE COLUMNS REINFORCED WITH CSA G30.18 500W STEEL by Sisay Tadele B.Sc., Technion Israel Institute of Technology, 2020 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE COLLEGE OF GRADUATE STUDIES (Civil Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Okanagan) August 2023 © Sisay Tadele, 2023 ii The following individuals certify that they have read, and recommend to the College of Graduate Studies for acceptance, a thesis entitled: SEISMIC RESPONSE OF CIRCULAR CONCRETE COLUMNS REINFORCED WITH CSA G30.18 500W STEEL submitted by Sisay Tadele in partial fulfillment of the requirements of the degree of Master of Applied Science . Dr. M. Shahria Alam, School of Engineering Supervisor Dr. Ahmad Rteil, School of Engineering Supervisory Committee Member Dr. Suliman Gargoum, School of Engineering Supervisory Committee Member Dr. Sina Kheirkhah, School of Engineering University Examiner iii ABSTRACT Bridge structures are essential components of infrastructure that play a pivotal role in connecting areas with difficult geography, such as across a river. Apart from ensuring ultimate life safety and serviceability limit state performance, their performance during seismic events determines the safety of the user and economic growth of the region. With advancements in technology, new construction materials are being produced. One of the commonly promoted types of new materials in construction is high-strength steel (HSS). The use of HSS for instance has a wide range of applications in construction, from reducing bar congestion and reducing labor as well as construction costs. Nonetheless, the use of HSS has been restricted, or no guidelines are available in many cases for the design of seismic-resistant members. In this study, the performance of CSA G30.18 500W is evaluated to study its suitability for the seismic design of reinforced concrete bridges. This study involves extensive experimental research work involving material tests of the HSS reinforcing steel and large-scale reinforced concrete bridge pier tests to assess the performance of the material. The examinations of low-cycle fatigue were conducted with various bar sizes, unsupported lengths, and strain amplitudes. Notably, the CSA G30.18 500W exhibited satisfactory low-cycle fatigue performance, wherein the effect of bar unsupported length and strain amplitude were more pronounced. Additionally, two large-scale bridge piers were tested under seismic loads to study the performance of the reinforced bridge columns, which are the location of plastic hinges in bridges and undergo large inelastic deformation. The test results of the columns indicated that the bridge piers achieved comparable drift levels and energy dissipation capacities with columns reinforced with regular steel ASTM A706 Grade 420. Moreover, the strain limits for performance-based design (PBD) of bridges utilizing CSA G30.18 500W were derived from the measured material strain limits. Lastly, a comparative study of the seismic performance of bridge piers containing ASTM A1035 Grade 690, CSA G30.18 400W, and CSA G30.18 500W was conducted through fragility curve analysis. iv LAY SUMMARY The utilization of high-strength steel (HSS) in the field of construction offers several benefits, such as the reduction of bar congestion and the enhancement of concrete placement. Nevertheless, its application has been limited in the seismic design of reinforced concrete members due to the reduced ductility of HSS, which may have a negative impact on the response of RC members. In this study, an extensive experimental and numerical investigation has been conducted to examine the applicability of CSA G30.18 500W HSS for the seismic design of bridges. The findings reveal that the HSS material presents a promising performance for seismic application. Therefore, the existing restrictions and non-recommendations of design codes regarding the use of HSS for seismic applications are somewhat excessively restrictive. v PREFACE The research findings that are presented in this thesis were carried out by Sisay Kahsu Tadele, under the supervision and guidance of Dr. M. Shahria Alam, at the University of British Columbia, Okanagan. It is worthy to note that several sections of this thesis will be submitted for publication, as evidenced by the following list. Journal papers ▪ Part of the material presented in Chapter 3 will be submitted to Engineering Structures [Tadele, S., and Alam, M. S. Low-cycle fatigue performance of Canadian CSA G30.18 500W high strength rebars with the effect of inelastic buckling included]. Tadele was the lead investigator, responsible for conceptualization, data collection and preparation, formal analysis, visualization, writing, and manuscript composition. Dr. M. S. Alam supervised the research and reviewed/edited the manuscript. ▪ Part of the material presented in Chapter 4 and Chapter 5 will be submitted to journal of Journal of Bridge Engineering. [Tadele, S., Aldabagh, S., and Alam, M. S. Seismic Performance of Bridge Columns Reinforced with CSA 500W High Strength Steel]. Tadele was the lead investigator, responsible for conceptualization, data collection and preparation, formal analysis, visualization, writing, and manuscript composition. Aldabagh assisted in reviewing, conceptualization as well as editing. Dr. M. S. Alam supervised the research and reviewed/edited the manuscript. Conference paper ▪ Tadele, S., Li, H., Zhang, Q., Hossain, F., Alam, M.S., Ahmadnia, A., and Jiang, J. (2023). “Seismic Design and Analysis of Bridge Columns Reinforced with Rebar Types of CSA 500W, CSA 400W, and ASTM 1035 Grade 690,” Canadian Conference-Pacific Conference on Earthquake Engineering (CCEE-PCEE), Vancouver, BC, June 26-30, 2023. vi TABLE OF CONTENTS ABSTRACT ................................................................................................................................................ iii LAY SUMMARY ....................................................................................................................................... iv PREFACE .................................................................................................................................................... v TABLE OF CONTENTS .......................................................................................................................... vi LIST OF TABLES ...................................................................................................................................... x LIST OF FIGURES ................................................................................................................................... xi ACKNOWLEDGEMENTS .................................................................................................................... xiv DEDICATION........................................................................................................................................... xv CHAPTER 1: INTRODUCTION .............................................................................................................. 1 1.1 Background ............................................................................................................................... 1 1.2 Objective and Scope of Thesis .................................................................................................. 4 1.3 Thesis Organization ................................................................................................................... 5 CHAPTER 2: PERFORMANCE OF REINFORCED CONCRETE COLUMNS WITH CHANGING MATERIAL AND GEOMETERIC DESIGN PARAMETERS -STATE- OF-THE-ART-REVIEW ........................................................................................................................................... 8 2.1 Background ............................................................................................................................... 8 2.2 Reinforced Concrete Column Response .................................................................................... 9 2.2.1 Effect of Reinforcement Grade ......................................................................................... 10 2.2.2 Effect of Longitudinal Reinforcement Steel Ratio ............................................................. 11 2.2.3 Transverse Reinforcement ................................................................................................ 12 2.2.4 Member Geometry ............................................................................................................ 13 2.3 Summary ................................................................................................................................. 14 CHAPTER 3: LOW CYCLE FATIGUE BEHAVIOR OF HIGH STRENGTH REINFORCING STEEL ........................................................................................................................................................ 15 3.1 Background ............................................................................................................................. 15 vii 3.2 Experimental Program ............................................................................................................. 18 3.3 Mechanical Properties of CSA G30.18 500W ........................................................................ 20 3.4 Uniaxial Tensile Results .......................................................................................................... 23 3.5 Low-cycle Fatigue Results ...................................................................................................... 24 3.5.1 Effect of Strain Amplitude ................................................................................................. 29 3.5.2 Effect of Bar Unsupported Length .................................................................................... 30 3.5.3 Effect of Bar Size ............................................................................................................... 31 3.6 Low-cycle Fatigue Models ...................................................................................................... 31 3.6.1 Strain-Based Fatigue Model ............................................................................................. 31 3.6.2 Energy-Based Fatigue Model ........................................................................................... 37 3.7 Summary ................................................................................................................................. 39 CHAPTER 4: SEISMIC PERFORMANCE OF BRIDGE COLUMNS REINFORCED WITH CSA G30.18 500W HIGH-STRENGTH STEEL ............................................................................................ 41 4.1 Background ............................................................................................................................. 41 4.2 Experimental Program ............................................................................................................. 44 4.2.1 Material Properties ........................................................................................................... 45 4.2.2 Instrumentation ................................................................................................................. 46 4.2.3 Test Specimen Set-Up ....................................................................................................... 46 4.2.4 Loading Protocol .............................................................................................................. 47 4.3 Results ..................................................................................................................................... 48 4.3.1 General Damage Observation .......................................................................................... 49 4.3.2 Hysteresis Response .......................................................................................................... 50 4.3.3 Comparison with Previous Studies ................................................................................... 51 4.3.4 Strain Gauge Measurements ............................................................................................. 53 4.3.5 Curvature Measurements .................................................................................................. 54 4.3.6 Energy Dissipation ........................................................................................................... 55 viii 4.4 Summary ................................................................................................................................. 57 CHAPTER 5: PERFORMANCE-BASED DESIGN AND LIMIT STATES OF BRIDGE COLUMNS REINFORCED WITH CSA G30.18 500W HIGH STRENGTH STEEL ...................... 59 5.1 Background ............................................................................................................................. 59 5.2 Performance Limit-States in CHBDC ..................................................................................... 61 5.2.1 Column Capacity and Overstrength Factors .................................................................... 62 5.2.2 Bridge Column Limit States Reinforced with CSA G30.18 500W .................................... 63 5.2.3 Buckling Limit State of Bridge Columns ........................................................................... 64 5.3 Performance Evaluation of Columns Analytically .................................................................. 67 5.3.1 Numerical Modeling ......................................................................................................... 68 5.3.2 Parametric Study .............................................................................................................. 71 5.4 Summary ................................................................................................................................. 73 CHAPTER 6: SEISMIC DESIGN AND ANALYSIS OF BRIDGE COLUMNS REINFORCED WITH REBAR TYPES OF CSA G30.18 500W, CSA G30.18 400W, AND ASTM 1035 GRADE 69075 6.1 Background ............................................................................................................................. 75 6.2 Design of Bridge Column ........................................................................................................ 77 6.3 Numerical Modeling and Validation ....................................................................................... 79 6.4 Pushover Analysis ................................................................................................................... 81 6.5 Ground Motion ........................................................................................................................ 83 6.6 Fragility Analysis and Results ................................................................................................. 84 6.7 Summary ................................................................................................................................. 86 CHAPTER 7: SUMMARY AND CONCLUSION ................................................................................. 87 7.1 Summary and Conclusion ....................................................................................................... 87 7.2 Recommendation for Future Study ......................................................................................... 91 7.3 Recommendation for Future Study ......................................................................................... 91 Bibliography .............................................................................................................................................. 93 ix Appendices ............................................................................................................................................... 118 Appendix A ...................................................................................................................................... 118 Appendix B: Pictures from Construction Procedure ........................................................................ 119 Appendix C: Additional Pictures from Test ..................................................................................... 124 C.1 Unit 1 ..................................................................................................................................... 124 C.1 Unit 2 ..................................................................................................................................... 127 Appendix D: Additional Measurements from Installed Instruments. .............................................. 131 Appendix E ....................................................................................................................................... 135 x LIST OF TABLES Table 1: Values of a and b. ......................................................................................................................... 23 Table 2: Mechanical properties of CSA G30.18 500W .............................................................................. 24 Table 3: Low-cycle fatigue results for 10M bar size .................................................................................. 26 Table 4: Low-cycle fatigue results for 15M bar size. ................................................................................. 27 Table 5: Values of parameters for low-cycle fatigue model. ...................................................................... 33 Table 6: Regression results values for parameters of energy-based fatigue model. ................................... 38 Table 7: Test matrix .................................................................................................................................... 44 Table 8: Control specimen design matrix (Barbosa et al. 2016) ................................................................. 52 Table 9: Cumulative dissipated specified energy........................................................................................ 56 Table 10: Column capacity and overstrength factors. ................................................................................. 63 Table 11: Measured material strain values for observed damage states. .................................................... 64 Table 12: Longitudinal bar buckling limit state values. .............................................................................. 66 Table 13: Column geometry and material matrix ....................................................................................... 79 Table 14: Performance limit criteria from CHBDC .................................................................................... 83 Table 15: Properties of the Concrete01 Constitutive Model Used for Numerical Model Validation of Units Tested in this Study. .................................................................................................................................. 118 Table 16: : Properties of the Steel02 Constitutive Model Used for Numerical Model Validation ............ 118 xi LIST OF FIGURES Figure 1:Sinusoidal loading waveform utilized for testing. ........................................................................ 20 Figure 2: Uniaxial tensile test results and analytical strain hardening models for bar size a) 10M, b) 15M .................................................................................................................................................................... 22 Figure 3: Cyclic stress strain response for CSA G30.18 500W strain amplitude of 0.03 for 15M bar size of (a) 6𝑑𝑏, (b) 8𝑑𝑏, (c) 10𝑑𝑏 ........................................................................................................................... 28 Figure 4: Cyclic stress strain response for CSA G30.18 500W 15M with L/D = 6db strain amplitude of (a) 0.01, (b) 0.02, (c) 0.03, and (d) 0.04. ..................................................................................................... 28 Figure 5: Plastic strain based low-cycle fatigue models for CSA G30.18 500W. ...................................... 34 Figure 6: Relationship between  and 𝜀𝑓′................................................................................................... 36 Figure 7: Relationship between  and c. ..................................................................................................... 36 Figure 8: Buckling parameter based low-cycle fatigue life models for CSA G30.18 500W 15M of bar unsupported lengths (a) 6𝑑𝑏, (b) 8𝑑𝑏, and (d) 10𝑑𝑏 .................................................................................. 37 Figure 9: Comparison between energy-based low-cycle fatigue model for CSA G30.18 500W bar unsupported length of 6db. .......................................................................................................................... 39 Figure 10: Test units’ geometry and cross-section details. ......................................................................... 45 Figure 11: (a) experimental test set-up and (b) Instrumentation. ................................................................ 47 Figure 12: Loading protocol for (a) Unit 1, and (b) Unit 2. ........................................................................ 48 Figure 13 Damage progression of Unit 1 (North side). .............................................................................. 50 Figure 14: Experimental hysteresis curves for (a) Unit 1 and (b) Unit 2 ................................................... 51 Figure 15: Normalized shear force vs drift of (a) aspect ratio of 3 (b) aspect ratio of 6 ............................. 53 Figure 16: Longitudinal strain measurements for (a) Unit 1, and (b) Unit 2. ............................................. 54 Figure 17: Curvature profiles for Units (a) Unit 1, and (b) Unit 2. ............................................................. 55 Figure 18: Cumulative specified dissipated energy. ................................................................................... 57 Figure 19: Column discretization for numerical modeling ......................................................................... 69 xii Figure 20: Experimental and predicted hysteresis response of (a) Unit 1, and (b) Unit 2. ......................... 71 Figure 21: Measured and predicted force-displacement response envelopes for (a) Unit 1 and (b) Unit 2. .................................................................................................................................................................... 71 Figure 22: Measured drift results from parametric study. ........................................................................... 73 Figure 23: Column element discretization for modeling. ........................................................................... 80 Figure 24: SeismoStruct model verification based on: (a) Moyer and Kowalsky (2003) (b) Restrepo et al. (2006). ......................................................................................................................................................... 81 Figure 25: Pushover response curves for columns of category: a) a b) b c) c, and d) d. ............................ 82 Figure 26: Ground motion records: (a) unmatched design spectrum (b) matched to design spectrum ..... 84 Figure 27: Fragility curve response for bridge columns of the category of a) a, b) b, c) c, and d) d. ......... 85 Figure 28: Column specimen rebar cage preparation. .............................................................................. 119 Figure 29: Column rebar cage Assembled. ............................................................................................... 120 Figure 30: Formwork installation of specimens. ...................................................................................... 121 Figure 31: Column specimens after concrete casting ............................................................................... 121 Figure 32: Column specimen attached for testing..................................................................................... 122 Figure 33: Cylinder preparation for concrete strength test. ...................................................................... 123 Figure 34: Concrete spalling at south face of Unit 1 at drift ratio of 1.6% (at end of displacement ductility of 1.5). ....................................................................................................................................................... 124 Figure 35: Extent of damage and crack pattern at south face of Unit 1 at drift ratio of 2.1% (at end of displacement ductility of 2). ..................................................................................................................... 124 Figure 36: Extent of damage and crack pattern at north face of Unit 1 at drift ratio of 5.89% (at end of displacement ductility of 4) ...................................................................................................................... 125 Figure 37: Damage profile of Unit 1 at the end of the test. ...................................................................... 125 Figure 38: Sample cylinder compressive test for specimen Unit 1. .......................................................... 126 Figure 39: Concrete cover spalling of on north face of Unit 2 at drift ratio of 2.7% (beginning of displacement ductility 3). .......................................................................................................................... 127 xiii Figure 40: Damage profile and crack pattern of Unit 2 on north face at drift ratio of 3.6% (end of displacement ductility of 4). ..................................................................................................................... 127 Figure 41: Damage profile and crack pattern of Unit 2 on north face at drift ratio of 5.47% (beginning cycle of displacement ductility of 6). ....................................................................................................... 128 Figure 42: Damage profile and crack pattern of Unit 2 on north face at drift ratio of 5.47% (at end of second cycle of displacement ductility of 6). ........................................................................................... 128 Figure 43: Damage profile and crack pattern of Unit 2 on north face at drift ratio of 7.2% (at end of first cycle of displacement ductility of 8). ....................................................................................................... 129 Figure 44: Damage profile of Unit 2 at the end of the test. ...................................................................... 129 Figure 45: Sample cylinder compressive test for specimen Unit 2. .......................................................... 130 Figure 46: Strain measurements in longitudinal rebar of Unit 1 at face of footing. ................................. 131 Figure 47: Strain measurements in longitudinal rebar of Unit 1 due to penetration effects at 150 mm below surface of footing. .......................................................................................................................... 131 Figure 48: Strain measurements in longitudinal rebar of Unit 2 at face of footing. ................................. 132 Figure 49: Strain measurements in longitudinal rebar of Unit 2 due to penetration effects at 150 mm below surface of footing. .......................................................................................................................... 132 Figure 50: Concrete cover strain measurements of Unit 2 at 75 mm above the footing. .......................... 133 Figure 51: Typical concrete cylinder stress-strain response for column concrete mix. ............................ 133 Figure 52: Typical concrete cylinder stress-strain response for footing concrete mix. ............................ 134 xiv ACKNOWLEDGEMENTS My master's study has enabled me to gain a wealth of knowledge and develop numerous skills. However, without the support and encouragement of many individuals, I would not have attained this level of achievement. I am deeply grateful to my supervisor, Dr. M. Shahria Alam, who has served as an excellent mentor and role model throughout my academic endeavors. It is indeed an honor and a privilege to have had the opportunity to work under his supervision. I shall be forever grateful for his immense expertise, humility, and support. I would like also to express my enduring gratitude to my supervisory committee, Dr. Ahmad Rtiel and Dr. Suliman Gargoum for being part of my supervisory committee members and reviewing my thesis work. I would like to acknowledge and thank students from my graduate team as well whose support has been very crucial to my successful completion of my studies. My special thanks go to Dr. Saif Aldabagh whose immense support has been important throughout my studies. I am also grateful for the support I got from members of our graduate team. My special thanks go to Tadesse Wakjira, Jhordy Rodriguez, Sherif M. Shaaban Osman, Ali Younesian, Deepak Saud, Ahmad Rahmzadeh, Peng Zhang, Mohammad Ramezankhani, Radin Hoque, Akifrazi Amu, and Biniam Teweldebrhan for making my masters study a pleasant and rewarding experience. I would like to sincerely acknowledge the funding organizations. Funds were received from the University of British Columbia through University Graduate Fellowship and Eminence Program. I would also like to express my gratitude to NSERC, S-Frame, and Mitacs for their financial support. Financial contributions of the BC Ministry of Transportation and Infrastructure and WSP Canada through the NSERC Alliance Grant were critical to conduct this research and are gratefully acknowledged. I would also like to acknowledge Nucor Steel - a North American producer for their generous donations of CSA G30.18 500W reinforcing steel bars. I extend my gratitude and love to my mother as well as my siblings whose support, and encouragement have been vital. xv DEDICATION To My Mother Hadas Tesfay 1 CHAPTER 1: INTRODUCTION 1.1 Background The seismic design of bridges involves critical analysis and evaluation of the potential impact of earthquakes on the structure. This requires a thorough analysis and evaluation of various factors, including the intensity and duration of the earthquake, soil conditions, and bridge design. The primary objective is to ensure that the bridge remains functional after an earthquake by withstanding seismic forces (Murtuz et al. 2022). Additionally, minimizing inelastic deformation and residual drift in ductile substructures can help reduce repair costs (Sudheer et. al. 2021). Overall, the seismic design of bridges is a complex process that requires careful consideration of multiple factors to ensure the safety and functionality of the structure in the event of an earthquake. The performance-based design (PBD) philosophy has shown acceptance and development over the past decades. The first PBD idea for the seismic design of bridges has been introduced in New Zealand in the 1970s (Priestley 2000). Performance levels for ordinary and important bridge categories were defined in terms of structural damage and serviceability limits. Performance-based seismic design of reinforced concrete (RC) bridges involves the design of bridges to achieve certain predictable performance objectives under given seismic demand. This approach takes into account the potential damage that may occur during an earthquake and aims to ensure that the bridge remains functional and safe for use after a seismic event (Burrell 2012). The PBD also allows for more cost-effective and efficient designs, as engineers can optimize the use of materials and construction techniques to achieve the desired performance objectives. The design philosophy of PBD is based upon the notion that a given structure should be able to attain a specified level of performance under the influence of seismic hazards. Such performance levels are predetermined via a variety of engineering limit states, including drifts, material strain limits, and curvatures. The Canadian Highway Bridge Design Code (CHBDC) (CSA 2014) incorporated PBD as the seismic design approach for both major-route and lifeline bridges, as well as for irregular bridges constructed in high seismic areas. The CHBDC (CSA 2019b) 2 establishes performance levels based on the strain limits of both concrete and reinforcing steel for the design of bridges according to PBD method. These service levels are classified as immediate, service-limited, service disruption, and life safety performance levels, and correspond to minimal, repairable, extensive, and probable replacement damage states, respectively (CSA 2019b). The PBD philosophy is different from the traditional force-based design (FBD) philosophy in a way that the FBD is based on balancing resistance and loads to prevent structural collapse, while PBD approach matches a structure's capacity to achieve a specific level of performance when subject to specified seismic hazard levels (Lopez et al. 2020). This approach allows for a more comprehensive and realistic assessment of the seismic performance of RC bridges, leading to safer and more resilient structures. Advancements in technological procedures for rebar production have allowed for the manufacturing of steel rebars with higher grades. Steel rebars with a minimum yield strength of 550 MPa are commonly classified as high-strength steel (HSS) bars (Ghannoum et al. 2016). The benefits of using HSS in construction are numerous, including the reduction of bar congestion, and reduced labor costs. Consequently, the demand for HSS in construction is on the rise. However, the application of HSS in RC structures designed for seismic loads may result in their poor performance. This is due to the lower tensile to yield strength ratio and reduced plastic strain capacity of HSS, ultimately leading to reduced ductility of RC members. Therefore, the use of HSS in structures designed to resist seismic loads is restricted by most design codes as their performance in RC members has not been extensively studied. To determine if HSS could serve as a substitute for regular steel, a comparison of their performance in RC members designed for seismic loads is necessary. In addition, the established limit states in PBD are based on regular steel rebars of lower grade and are not applicable for RC members containing HSS as reinforcement. Therefore, evaluating the performance of reinforced concrete members containing HSS through engineering limit states that are consistent with appropriate PBD philosophy is essential. As such, several studies have been carried out over the years to investigate the seismic performance of RC members reinforced with HSS. Canadian reinforcing steel rebars are manufactured in a variety of classifications based on 3 historical categorizations, namely "Weldable" ("Type W") and "Regular" ("Type R"). The bars designated as "Type W" are produced with more stringent composition, strength, and performance requirements and are highly ductile compared to the "Type R" reinforcing steel. The Canadian market for reinforcing steel has shifted towards the “Type W” rebars over the years owing to their superior performance compared to “Type R”. Rebars of “Type W” are produced in accordance with CSA G30.18 (CSA 2021) standards and are available in various grades, including 400 MPa, 500 MPa, and 600 MPa. The Canadian steel market is experiencing an increase in demand for reinforcing steel of superior grade. However, the design codes for RC members in place are designed for regular reinforcing steel, which hinders the use of high-strength steel rebars in such members. One of the primary challenges associated with the use of higher grade is the mechanical property variation between HSS and regular steel rebars. This variation can lead to undesirable performance of RC members, particularly those designed for seismic loads, which require more stringent design procedures and material requirements (Aldabagh et. al 2021b). In addition, the performance limit states in CHBDC (CSA 2019b) are based on reinforcing steel rebars of regular grade, and the PBD philosophy does not apply to members reinforced with HSS. Therefore, it is essential to understand the performance of RC members reinforced with HSS to determine the applicability of HSS in RC members. Currently, there is no existing research work involving the HSS of Canadian manufactured steel. This study delves into the seismic behavior of bridge columns reinforced with CSA G30.18 500W HSS. Additionally, it examines the low-cycle fatigue performance of CSA G30.18 500W through material testing, with the aim of promoting the utilization of HSS in the PBD of bridges. A critical aspect of this study is the understanding of the materials' tendency to accommodate large inelastic deformations prior to failure, which is known as low-cycle fatigue performance. Such large inelastic deformations are expected in longitudinal reinforcing steel rebars of RC compression members that are subject to high seismic loads, such as ductile substructure bridge components of columns and columns. In particular, the longitudinal rebars in the regions of the plastic hinge length of bridge columns experience large strain reversals when the compression members experience high 4 seismic loads. These strain reversals of the longitudinal rebars lead to damage accumulation, which ultimately causes buckling and fracture of the rebars. Therefore, it is crucial to have a thorough understanding of the low cycle fatigue performance of the rebars before their application in the seismic design of bridges. The experimental investigation of low-cycle fatigue behavior of CSA G30.18 500W HSS was carried out by examining several specimens and considering various variables such as inelastic buckling, strain amplitude, and bar size. The analysis of low-cycle fatigue provided critical insights into the performance of CSA G30.18 500W HSS, including the fatigue life, that is, the number of cycles to failure, and energy dissipation. The relationship between strain amplitude, fatigue life, and energy dissipation was established using established energy and strain models. To further investigate the applicability of the CSA G30.18 500W HSS for the seismic design of bridges, an experimental study was conducted to study the seismic performance of large-scale bridge columns containing CSA G30.18 500W as their longitudinal reinforcement. The study involved testing two bridge column units having aspect ratios 3 and 6, which were subjected to constant axial load and displacement-controlled quasi-static lateral loads. The observed damages during the tests were utilized to establish different performance limits for the bridge columns, expressed as column drift and material strains. Additionally, the engineering limit states for the bridge columns were compared with the existing engineering limit states CHBDC (CSA 2019b) for PBD of bridges that are based on regular steel. 1.2 Objective and Scope of Thesis The overall objective of this thesis is to investigate seismic performance of circular concrete columns reinforced with CSA G30.18 500W HSS and to quantify the various limit states suitable for performance-based design of bridge columns. The study will be conducted using a combination of experimental testing and numerical works. The scope of the thesis is limited to the following specific objectives. 5 ▪ To experimentally investigate the low cycle fatigue performance of CSA G30.18 500W steel rebar. This is achieved by conducting low-cycle fatigue tests on several specimens of CSA G30.18 500W. ▪ To study the seismic performance of circular bridge columns that are reinforced with longitudinal rebars of CSA G30.18 500W, through both experimental and numerical means. This will involve conducting quasi-cyclic loading tests on circular RC columns reinforced with CSA G30.18 500W steel rebar. ▪ To evaluate the seismic performance of the CSA G30.18 500W steel rebar in accordance with the CHBDC (CSA 2019) bridge design code. This will be done by comparing the results of the experimental and numerical tests to the requirements outlined in the CHBDC (CSA 2019b). ▪ To assess the seismic vulnerability of bridge columns reinforced with CSA G30.18 500W, CSA G30.18 400W, and ASTM A615 Grade 690 HSS through fragility response. 1.3 Thesis Organization The present thesis comprises a total of 7 chapters, which includes an introductory chapter that familiarizes the reader with the concepts of PBD and FBD philosophy, highlights the challenges associated with the implementation of HSS in the seismic design of bridges, and provides an overview of the reinforcing steel manufactured in Canada. Chapter 1 is succeeded by Chapter 2 which discusses an introduction to performance-based design, and aspects of using high-strength steel as reinforcement in construction by reviewing previously conducted research on this topic. A state-of-the-art review on low-cycle fatigue performance of HSS, and seismic performance bridge columns reinforced with HSS is briefly presented. Chapter 3 is dedicated to conducting a low-cycle fatigue performance analysis of CSA G30.18 500W HSS. This chapter endeavors to examine the low-cycle fatigue behavior of CSA G30.18 500W by subjecting the rebars to experimental testing, thereby enabling the assessment of their fatigue life. The evaluation of the number of cycles to failure, dissipated energy, and the impact of inelastic 6 buckling on fatigue life are the key aspects investigated. Additionally, existing low-cycle fatigue life models based on strain and energy are employed to determine the low-cycle fatigue parameters of CSA G30.18 500W. Chapter 4 presents the experimental findings regarding the seismic performance of circular bridge columns that are reinforced with CSA G30.18 500W HSS. The chapter commences with a discussion of the initial design of circular bridge column specimens that were prepared for testing, accompanied by a brief overview of the loading protocol employed and the construction materials utilized. Subsequently, the experimental procedures and testing program are elucidated, followed by an assessment of the experimental findings in terms of the obtained drifts, dissipated hysteretic energy, and various types of damages recorded. Furthermore, a comparison of the experimental results with those of a previous study involving bridge columns reinforced with regular ASTM A706 Grade 420 steel is presented. Chapter 4 is succeeded by Chapter 5, which introduces a performance-based design approach for the seismic design of bridges. The various damages observed during the testing of the circular bridge columns are quantified in terms of material strain limits and drifts in order to develop different limit states that are useful for the performance-based design of bridges employing CSA G30.18 500W HSS. Given the existing performance limit states in CHBDC (CSA 2019b) are based on regular steel, various performance limits are established for RC members which utilize CSA G30.18 500W as their longitudinal reinforcement. The established performance limits are expressed in terms of experimentally measured reinforcing steel, and concrete material strain limits. As part of evaluating the performance of the CSA G30.18 500W HSS, fragility analysis study is presented in Chapter 6. This chapter compares the performance of various reinforcing steels of CSA G30.18 500W, CSA G30.18 400W, and ASTM A1035 Grade 690 to evaluate their seismic performance. An analytical study is conducted to evaluate the seismic performance of bridge columns containing those rebars as their longitudinal reinforcement. The performance of the bridge columns containing those rebars is studied with changing design parameters including aspect ratio, axial load ratio, concrete strength, and spiral reinforcement ratio. Chapter 7, which is the last chapter of this 7 study, presents general conclusions and findings from this study. In this section, the experimental and numerical findings of this study are briefly presented with a focus given to the major findings. A brief overview of the experimental results from the low-cycle fatigue test is presented together with the results obtained and the effects of the various test parameters considered included. In addition, the experimental results of the column test are briefly presented, and the seismic performance of the bridge columns is compared. 8 CHAPTER 2: PERFORMANCE OF REINFORCED CONCRETE COLUMNS WITH CHANGING MATERIAL AND GEOMETERIC DESIGN PARAMETERS -STATE- OF-THE-ART-REVIEW 2.1 Background The manufacture and quality assurance of reinforcing steel bars require meticulous monitoring of chemical compositions, refining methods, and adherence to established industry standards. Various production techniques have been proposed to produce high-performance rebar with specific chemical and mechanical properties. Technological advancements have facilitated the production of superior quality rebars with desirable attributes. Typically, the desired quality of rebar is achieved by modifying its chemical composition through alloying. For instance, HSS bars can be fabricated using different methods and compositions. One approach involves adjusting the chemical composition and rolling process of conventional steel bars to fully exploit the reinforcing effects of vanadium, thereby enhancing the overall performance of the steel bars. Another technique entails utilizing a particular combination of carbon, vanadium, and manganese, as well as regulating temperature during smelting, continuous casting, rolling, and cooling procedures. The demand for HSS has grown in the construction industry, especially for members with higher rebar congestion, as higher strength rebars have been found to offer ideal construction solutions. The use of higher-strength steel rebars in construction has various benefits, such as reducing rebar congestion, construction cost, and labor. However, their use in the construction industry, particularly for members designed for seismic loading, has been limited as there are no guidelines in the Canadian design codes regarding their performance. The Canadian design codes currently lack provisions regarding the use of CSA G30.18 500W in the seismic design of reinforced concrete structures. While there are no explicit restrictions on the use of this material, the codes advise designers to consider the expected increase in strain demands when incorporating HSS into reinforced concrete members. Moreover, there is a lack of research on the performance of CSA G30.18 500W in seismic design 9 applications for RC members. 2.2 Reinforced Concrete Column Response Several investigations have been undertaken pertaining to reinforced concrete (RC) columns when subjected to seismic loading. The primary objective of these studies was to evaluate the impact of various factors on the seismic behavior of the columns. For instance, Ghannoum et al. (2012) conducted a series of shaking table tests to examine the effects of loading rates on the structural response of lightly confined RC columns. Additionally, Rajput and Sharma (2018) conducted an experimental study aimed at assessing the effects of corrosion on the seismic performance of RC columns. Sinha and Roy (2004) quantitatively analyzed the energy absorption capacity of RC columns under repeated loading. Collectively, these studies contribute significantly to the comprehension of the behavior and performance of RC columns under seismic loading conditions. Various factors that have been investigated in relation to the seismic performance of RC columns comprise loading axial load ratios, stirrup ratios, longitudinal reinforcement ratios, and aspect ratios. The investigation of these factors was aimed at comprehending their effects on failure patterns, hysteretic behavior, ultimate strength, ductility, stiffness degradation, energy dissipation capacity, and rigidity of the columns (Zixue et al. 2010). The findings indicate that the axial compression ratio, stirrup ratio, and steel ratio had substantial impacts on the seismic performance of the columns. Furthermore, the longitudinal reinforcement ratio, and core area size were discovered to influence the ductility and energy dissipation characteristics of the columns. These studies provide valuable insights for the purpose of designing and retrofitting reinforced concrete columns to enhance their seismic performance. The following section presents the response of RC column to seismic loading, along with the effect of various design parameters. In order to provide a comprehensive understanding, the effect of parameters was thoroughly considered and the response of the RC columns to seismic loading is presented accordingly. Additionally, research findings from previous studies are also presented for each parameter that was considered. 10 2.2.1 Effect of Reinforcement Grade The application of HSS as a reinforcing material in reinforced concrete elements designed to withstand seismic loads has exhibited favorable outcomes in numerous research endeavors. In-depth investigations have revealed that the utilization of high-strength reinforcement, such as ASTM A706 Grade 550, is achievable with minimal modifications to design requirements and steel specifications (Barcley and Kowalsky 2020). Various studies have demonstrated the potential of utilizing HSS as reinforcing steel in reinforced concrete members designed for seismic loads. Experimental studies have been carried out to assess the seismic behavior of concrete columns that have been reinforced with high-strength steel. investigating the impact of different grades of steel on strain demands. Studies on the use of high-strength reinforcement, such as ASTM A706 Grade 550, showed that design requirements and steel specifications remain largely unchanged (Barcley and Kowalsky 2020). It has been observed that columns with HSS reinforcement achieve comparable resistance, maximum lateral displacements, and curvature ductility values to those with conventional reinforcement (Barbosa et al 2016). In the realm of bridge seismic design, researchers are delving into the potential of HSS reinforcement. Studies of the mechanical properties and seismic performance of reinforcement in bridge structures have been carried out through experimental and analytical studies. Most of the studies have been carried out in order to establish standard design criteria and PBD methodologies for sub-structure components of bridges designed for seismic loads and to suggest appropriate design parameters to be incorporated into seismic design codes. For instance, Ding et al. (2021) conducted a study to examine the low-cycle fatigue and the performance of columns reinforced with high strength steel HTRB600 and standard steel HRB400E. Based on their discoveries, it was observed that the ductility and low-cycle fatigue performance of HTRB600 was low in comparison to the regular steel HRB400E. However, the deformational capacity of columns reinforced with HTRB600 was greater than those reinforced with regular steel. ASTM A706 rebar type being the preferred type of reinforcing 11 steel for seismic design, Barcley and Kowlaskiy (2020) carried out a study on the suitability of ASTM A706 Grade 550 HSS as reinforcing steel for seismic design RC columns. Their findings indicated that although HSS can be utilized in RC members designed for seismic loads, further research is required to fully comprehend its performance. Zhang et al. (2020a) on the other hand conducted a study to examine how high-strength concrete (HSC) columns reinforced with HSS perform during seismic events. The researchers utilized both testing and finite element analysis to investigate the effects of different factors, such as the strength grade of longitudinal reinforcement, concrete strength, and axial load ratio, on the seismic behavior of these columns. The results of the investigation revealed that HSC columns that were reinforced with HSS exhibited a displacement ductility greater than 4 which was a good level of performance. Aboukifa and Moustafa (2021) conducted a study to explore the seismic response of fully reinforced Ultra-High-Performance Concrete (UHPC) columns subjected to axial and cyclic lateral loading. The investigation involved using both conventional and HSS reinforcement. The findings indicate that a higher reinforcement grade or steel ratio is required to effectively harness the exceptional mechanical characteristics of UHPC. 2.2.2 Effect of Longitudinal Reinforcement Steel Ratio The response and failure modes of RC columns may be impacted by the longitudinal reinforcement ratio. It is anticipated that the longitudinal reinforcement ratio will decrease the ultimate curvature of members failing in compression, while an increase in the longitudinal steel ratio will raise displacement capacity for members failing in tension (Lehman and Moehle, 1998). Numerous studies have explored the effect of longitudinal reinforcement steel ratio on the performance of RC columns. Pham et al. (2021) discovered that the longitudinal reinforcement ratio significantly affected the failure modes and impact-resistant capacity of concrete columns reinforced with fiber-reinforced polymer (FRP) reinforcements. Shi et al. (2021) examined the seismic behavior of square concrete columns reinforced with Grade 600 MPa steel and concluded that the longitudinal reinforcement ratio influenced the strength capacity, flexural ductility, energy dissipation capacity, and stiffness 12 deterioration of the columns. Aghdasi and Ostertag (2020) focused on the interaction between Ultra-High-Performance Fiber-Reinforced Concrete (UHP-FRC) composites and rebars and recommended a minimum longitudinal reinforcing ratio to ensure ductile performance under tension. Zhou et al. (2020) evaluated the enhancement in seismic performance of corroded RC columns with large rupture strain (LRS) FRP strengthening and found that the longitudinal reinforcement ratio influenced the ductility and energy dissipation capacity of the columns. 2.2.3 Transverse Reinforcement Transverse reinforcement plays a significant role in both confining and restraining the core concrete as well as longitudinal reinforcement to provide sufficient flexural response of the reinforced column. Furthermore, it aids in delaying the local buckling of longitudinal bars, resisting shear forces, preventing sudden shear failure, and confining the concrete to enhance its strength and ductility (Saidi et al. 2019). The configuration and strength of transverse reinforcement have a notable impact on the behavior of columns subjected to seismic loads. Numerous studies have demonstrated that transverse reinforcement affects the compressive strain capacity of confined concrete. For instance, Paulay and Priestley (1992) proposed an expression for predicting the compressive strain capacity (𝜀𝑐𝑢) of confined concrete columns, which is a function of the transverse steel volumetric ratio (𝜌𝑠), transverse yield strength (𝑓𝑦ℎ), confined concrete strength (𝑓′𝑐𝑐), and tensile strain of longitudinal steel at ultimate stress (𝜀𝑠𝑢). The proposed for predicting the compressive strain capacity of confined concrete is given as follows: 𝜀𝑐𝑢 = 0.004 + 1.4𝜌𝑠𝑓𝑦ℎ𝜀𝑠𝑢𝑓′𝑐𝑐 (3) The effect of transverse reinforcement steel ratio on reinforced concrete columns has been the focus of many studies. Recently, Shi et al. (2021) conducted experiments on high strength reinforced concrete cantilever columns and proposed a novel configuration of transverse reinforcement that was found to ensure favorable seismic performance. In another study by Hua et al. (2022), full-scale RC 13 intermediate short columns with square cross-sections were subjected to displacement histories oriented at different angles to the column faces. The columns had varying ratios of transverse reinforcement, and their performance was evaluated based on cracking patterns, shear strengths, effective stiffnesses, and inelastic shear deformations. The study proposed a new model to predict the cyclic force-deformation response of the columns, taking into account the contribution of both concrete and transverse reinforcement to shear strength. Additionally, Xiao and Martirossyan (1998) investigated the response of high-strength concrete columns with varying axial load ratios, longitudinal steel ratios ranging from 2.46 to 3.53% of the gross sectional area, and volumetric ratios of transverse reinforcement ranging from 1.63 to 3.67%. The study concluded that columns with a higher amount of transverse reinforcement than required by seismic provisions exhibited ductile behavior. 2.2.4 Member Geometry The response of a reinforced concrete column to force-displacement is influenced by numerous variables related to its geometry, including the cross-sectional area and length of the member. The aspect ratio, represented by the ratio of member length (L) to diameter (D), is a crucial variable that impacts the response of RC columns. In the following section, the impact of aspect ratio is briefly discussed, along with the outcomes from various studies. The aspect ratio, also known as the moment-shear span ratio, is a primary factor that has been observed to have a significant impact on the performance of bridge columns. The column aspect ratio is defined as the ratio between the column height, L, and the column diameter, D. An increase in aspect ratio, for a given constant in cross-section, results in an increase in column length. This increase in column length is expected to increase the shear demand and the displacement for a given curvature demand, as noted by Lehman and Moehle (1998). Furthermore, the aspect ratio has been observed to affect the curvature ductility and strain penetration effects of longitudinal reinforcement. Several studies have been conducted on the effect of 14 aspect ratio on the seismic performance of bridge columns. For instance, Barbosa et al. (2016) compared RC columns with aspect ratios of 3 and 6 in terms of energy dissipation, curvature, and overstrength factors. The results indicated that aspect ratio has little effect on the overstrength factors, while the reduction in aspect ratio caused an increase in the curvature values at the base of the column. Another study by Iwasaki et al. (1985) conducted an experimental study on the hysteretic behavior of reinforced concrete columns. The study tested three columns with increasing aspect ratios of 2.2, 3.8, and 5.4, and revealed that the columns with aspect ratios of 3.8 and 5.4 failed in flexural mode, while the column with an aspect ratio of 2.2 failed in shear failure mode. In addition, Zhang et al. (2020b) conducted an experimental study on rectangular double-skin tubular columns and found that a larger aspect ratio had no negative effect on the confinement effect. Larger aspect ratios generally resulted in larger ultimate axial strain and higher axial stress at the ultimate axial strain. 2.3 Summary This chapter was dedicated to investigating the performance of reinforced concrete columns considering the effect of various design parameters. A brief introduction to the CSA G30.18 500W mechanical properties is also presented. An analytical model was developed for the stress-strain response of the CSA G30.18 500W HSS utilizing previously developed models. The developed model showed a good level of accuracy in predicting the stress-strain response. The evaluation of the performance of the RC columns was achieved through an extensive state-of-the-art review. The effect of steel ratio and aspect ratio were studied by analyzing results from previous studies. The findings show that the response of RC columns is indeed affected by the various design parameters where the effect of longitudinal steel ratio, and aspect ratio had generally higher impact. 15 CHAPTER 3: LOW CYCLE FATIGUE BEHAVIOR OF HIGH STRENGTH REINFORCING STEEL 3.1 Background Bridge columns are the vulnerable substructure components of a bridge due to the presence of plastic hinges, which make them susceptible to large inelastic deformations under seismic loading. For this reason, the nonlinear response of bridge columns usually governs the overall behavior of bridges when subjected to seismic loads (Brown and Kunnath 2004). Despite being designed to fail in a ductile mode of failure, longitudinal reinforcing rebars in bridge columns may experience inelastic buckling followed by fracture during high-intensity seismic events (Tripathi et al. 2018). Especially in medium to high seismic regions, longitudinal rebars in RC members experience large strain reversals which lead to their early buckling and fracture. The phenomenon of inelastic buckling of the reinforcement bars in the context of cyclic loading presents a potential concern, as it may result in a reduction of the fatigue life of the bars and ultimately lead to premature failure (Ding et al. 2021). The buckling of these reinforcing rebars is caused by a significant increase in axial compressive strain resulting from monotonic axial compression and bending induced by seismic loads (Brown and Kunnath 2004; Lehman et al. 2004). Buckled longitudinal reinforcing steel rebars can lead to a reduction in axial compression capacity, which can negatively impact the section capacity and ductility of bridge columns. Research has demonstrated that the performance of bridge columns is significantly affected by the low-cycle fatigue performance of high-strength steel (Brown and Kunnath 2004, Tripathi et al 2018. Mander et al. 1994). Specifically, an increase in the slenderness ratio (L/D) which is representative of the center-to-center spacing between transverse reinforcements can result in a considerable reduction in the low-cycle fatigue life of steel bars due to premature buckling. Several investigations have additionally examined the impact of the magnitude of strain on the low-cycle fatigue behavior of reinforcing bars, which denotes the level of seismic intensity to which the bars may 16 be subjected. The results demonstrated that a decrease in the strain magnitude resulted in a substantial increase in the fatigue life and overall energy dissipation of the reinforcing bars. HSS has gained significant attention in the construction industry due to their demonstrated ability to improve concrete placement, minimize rebar congestion, and decrease labor costs (Ghannoum et al. 2016). These qualities, in conjunction with their superior strength, augment section capacity. Comprehending the low-cycle fatigue performance of HSS will enhance their suitability for utilization in bridges designed for medium to high seismic loads. Prior research has indicated that buckling of reinforcing steel rebars in compression, followed by fracture of reinforcing rebars in the tension side of bridge columns, is a common failure mode due to large-cyclic strain amplitude loadings (Su et al. 2015, Yang et al. 2020, Tripathi et al. 2018). Therefore, it is crucial to minimize the reduction in axial compressive stress of longitudinal reinforcing steel rebars to enable bridge columns to achieve their full plastic deformation and ductile failure. This can be accomplished by gaining a better understanding of the low-cycle fatigue performance of steel rebars, which can enhance the accuracy of the seismic design of bridge columns. The utilization of high strength steel has been constrained by design guidelines, such as the AASHTO LRFD Bridge Design Specifications (AASHTO 2017), since the currently acknowledged values for the fatigue or endurance limit for reinforcing steel are established for standard steel rebars and may not be relevant and are probably less conservative with respect to high strength steel rebars. The low-cycle fatigue of CSA G30.18 500W HSS has not been investigated, therefore requiring extensive analysis of its performance under various conditions, including bar unsupported length (L/D), strain amplitude, and bar diameter. For this purpose, axial-strain-controlled reversed cyclic tests of equal amplitude and constant strains were carried out to evaluate the low-cycle fatigue performance of the rebar, with the objective of determining its appropriateness for the seismic design of RC members. The low-cycle fatigue performance of the rebar was evaluated using a range of test result parameters, such as the number of cycles to failure, total dissipated hysteretic energy, and inelastic 17 buckling. Moreover, fatigue-life models based on strain and energy were utilized to predict the low-cycle fatigue life of the rebar. The constants of these models were adjusted using the generated experimental fatigue data. The constants of the proposed models were also associated with a buckling parameter to incorporate the effect of inelastic buckling. The research on the low-cycle fatigue behavior of steel bars has primarily centered on regular rebars, with limited attention paid to the low-cycle fatigue performance of HSS. Nonetheless, some studies have explored the low-cycle fatigue performance of HSS, investigating a range of variables such as strain amplitudes, inelastic buckling, slenderness ratio, and surface roughness. Koh and Stephens (1991) examined the low-cycle performance of quenched and tempered HSSB with a yield strength of 1170 MPa at varied strain ratios (R) and strain amplitudes. Their study involved axial strain-controlled fatigue tests on smooth specimens, with a focus on mean stress-strain effects. The experimental results for mean stress were best represented by the log-log linear Smith, Watson, and Topper (SWT) model. Mander et al. (1994) conducted a study on the low-cycle fatigue behavior of A722 pre-stressing thread HSS, which has an ultimate strength of 1083 MPa. The study involved axial-strain controlled reversals of tension-compression tests with varying strain amplitudes ranging from yield to 6%. The results were compared to those of ordinary deformed steel rebar of ASTM A615 Grade 280. It was observed that the low-cycle fatigue life and modulus of toughness of the two steel rebars were similar. Meanwhile, Ghannoum and Slavin (2016) investigated the low-cycle fatigue performance of ASTM A615 Grade 690 and ASTM A706 Grade 550. The study evaluated the effect of production method, bar size, loading protocols, and bar unsupported length (i.e., potential buckling length) on the fatigue performance of the steel rebars. The study demonstrated that standard steel rebars exhibit superior fatigue performance over HSS. Among the variables considered, the unsupported length of the bar was found to have a significant impact on the rebars' performance. Specimens with shorter unsupported length demonstrated better performance and withstood a higher number of cycles before failure, as well as exhibiting smaller buckling amplitude. Kashani et al. (2015) 18 examined the effect of inelastic buckling on the low-cycle high amplitude fatigue life of reinforcing bars through fatigue experimental tests on 90 specimens at strain amplitudes ranging from 1% to 5%. Their findings indicated that inelastic buckling, bar diameter, and surface condition are the primary parameters influencing the low-cycle fatigue life of reinforcing bars. The study also developed a new set of experimental equations that account for the influence of inelastic buckling on the low-cycle fatigue performance of steel rebars. Tripathi et al. (2018) conducted a study that examined the impact of inelastic buckling on the low-cycle fatigue behavior of Grade 300E and 500E reinforcing bars. Their findings indicated that the slenderness ratio and inelastic buckling had a notable effect on the low-cycle fatigue performance of the steel rebars. Specifically, they observed that an increase in the slenderness ratio of the reinforcing bars led to an increase in buckling amplitude and a significant reduction in the low-cycle fatigue life of the rebars. 3.2 Experimental Program In order to evaluate the performance of the rebar, a series of tests were conducted on prepared specimens utilizing a 500 kN MTS servo-hydraulic universal testing machine, including both uniaxial tensile and low-cycle fatigue tests. The MTS is equipped with two V-shaped grips and can execute displacement-controlled or force-controlled test procedures. Both the monotonic uniaxial tensile test and low-cycle fatigue tests were performed using a displacement-controlled procedure. During production, the rolling process results in the hardening of the surface of the rebar with deformations, causing stress concentration and the initiation of fatigue cracks (Brown and Kunnath 2004). As a result, the surface of the rebar was left unaltered and not machined to ensure that the uniaxial and fatigue performance of the rebar would be representative of those used in RC. The rebars were secured on either end using V-shaped hydraulic grips at a maximum pressure of 28 MPa and a grip penetration length of 70 mm to ensure adequate gripping. Monotonic tensile tests were carried out on displacement-controlled loading procedure using a constant loading rate of 1.0 mm/min. An extensometer with a gauge length of 25 mm and travel range of 12.5 mm was utilized to measure the 19 stress-strain response. In order to maintain result consistency, two tests were carried out for each specimen of bar sizes 10M (No. 3) and 15M (No. 5). In the second phase of the experimental testing, bar specimens underwent a low-cycle fatigue test under axial strain-controlled conditions. A total of 48 specimens were utilized for this test in order to investigate their low-cycle fatigue performance while considering various test parameters. The experimental program included specimens with bar sizes of 10M and 15M, unsupported lengths of 6𝑑𝑏,8𝑑𝑏, and 10𝑑𝑏, and strain amplitudes ranging from 1% to 4%. The unsupported length was selected to accurately reflect the common buckling modes of longitudinal reinforcements within RC columns. The unsupported lengths of a bar, as measured by the distance between its grips, represent the true rotational stability provided by transverse reinforcement. Studies have demonstrated that the buckling length of a bar corresponds to the tie spacing of the longitudinal rebars used in reinforced concrete structures (Dhkal and Maekawa 2002). As part of this inquiry, unsupported bar lengths of 6𝑑𝑏, 8𝑑𝑏, and 10𝑑𝑏 were utilized to study the low-cycle fatigue performance of CSA G30.18 500W. During the test, specimens were subjected to sinusoidal loading waveform that entailed fully reversed constant-amplitude strain cycles. The study employed a sinusoidal loading technique for its low-cycle fatigue examination, as illustrated in Figure 1:. The crucial aspects of the method, such as period (T) and frequency (f), are presented in the graph. The loading procedure utilized frequencies (f) that varied within the range of 0.00625 to 0.025 Hz, leading to an average strain rate of 0.001/s (peak-to-peak), as suggested by (Ghannoum & Slavin, 2016). In the loading protocol, 𝜀𝑎, max ,and 𝜀𝑎, min stands for the maximum and minimum total strain amplitude the specimens were tested for. The experiments measuring low-cycle fatigue were carried out with a constant mean strain ratio (R) of -1. It is important to note that R is defined as the ratio of minimum and maximum strain amplitude, as stated by Collins (1993). However, the current study disregards the effect of mean strain ratio (R) as previous investigations, such as those by Mander et al. (1994), have demonstrated that it has a negligible impact on the low-cycle fatigue performance of steel bars. Definition of R and 𝜀𝑎 is given as follows: 20 𝑅 =𝜀𝑠,min𝜀𝑠,max if |𝜀𝑠,max| ≥ |𝜀𝑠,min| (4) 𝑅 =𝜀𝑠,max𝜀𝑠,min if |𝜀𝑠,max| < |𝜀𝑠,min| (5) 𝜀𝑎 =Δ𝜀2=𝜀𝑠,max−𝜀𝑠min2 (6) Figure 1: Sinusoidal loading waveform utilized for testing. 3.3 Mechanical Properties of CSA G30.18 500W The CSA G30.18 500W deformed bars possess a maximum chemical composition of 0.33% Carbon, 1.65% manganese, 0.043% Phosphorus, 0.053% Sulphur, and 0.55% Silicon for finished bars (CSA 2021). To accurately capture the significant mechanical properties of the CSA G30.18 500W steel rebar, a uniaxial tensile test was performed on prepared sample specimens. These specimens varied in bar nominal diameters (db) of 11.3 mm, and 16.0 mm. A monotonic tensile test was conducted to generate the stress-strain curves for the rebars. Each bar size had several specimens prepared for the tensile test, with the length of the specimens equal to the summation of unsupported length and gripping length. The specimens were varied by bar size, with two specimens considered for ensuring the repeatability of the results. In total, 4 specimens were prepared to capture the tensile properties of the bars. These specimens were subjected to a constant 21 loading rate of 1 mm/min while being placed on the MTS with an extensometer mounted at mid-height of the specimen to measure axial strain. The axial strain was measured using the extensometer over a gauge length of 25 mm. In addition to the readings from the extensometer, the axial strain was also measured by the MTS. However, axial readings from the MTS were not used to obtain the mechanical properties of the bar, as they could be affected by bar slippage, gripping pressure applied, and other factors. Stress-strain curves were generated for all the specimens tested. Figure 2provides average stress-strain curves for the specimens. The stress-strain curves have a well-defined yield point and plateau, which makes it easy to obtain the yield strength values from the curves. The accurate evaluation of steel stress-strain response is crucial for the numerical modeling of reinforced concrete structures, as it can greatly improve the efficiency of the simulation. A simple and efficient stress-strain model for steel can ensure accurate predictions of the structural response under various loading conditions. The stress-strain response of steel rebar is characterized by several distinct regions, including the linear elastic zone, yield plateau, strain hardening region, and post-ultimate region. In order to capture the different regions of the monotonic response, an efficient stress-strain model should be able to account for the nonlinear behavior of the material. The choice of model for steel is also influenced by the carbon content, which affects the strength of the steel. For example, normal strength steel can be represented by a simple model, while high strength steel may require a more complex model to capture its unique properties (Martinez et al. 1998). In this study, the monotonic stress-strain response of the CSA G30.18 500W rebar is modeled based on the assumption of perfectly elastic-plastic behavior with strain hardening region. The strain hardening component of the curve is represented by an analytical model proposed by Burns et al. (1962) given in Eq. (1). 𝑓𝑠 = 𝑓𝑦 [112 (𝜀𝑠−𝜀𝑠ℎ)+260(𝜀𝑠−𝜀𝑠ℎ)+2+(𝜀𝑠−𝜀𝑠ℎ)(𝜀𝑠−𝜀𝑠ℎ)(𝑓𝑠𝑢𝑓𝑦− 1.7)] (1) Where 𝑓𝑠 is the steel stress, 𝜀𝑠 stands for steel strain, 𝑓𝑦 is yield strength, 𝑓𝑠𝑢 represents ultimate tensile strength, and 𝜀𝑠ℎ is the strain corresponding to initial strain hardening. An equation based on 22 the Burns et al. (1962) proposed model is suggested in this study (see Eq. 2) where constant parameters of a, and b are introduced into the equation and estimated using curve fitting to the strain hardening region of uniaxial tensile test data of CSA G30.18 500W. The values of the yield strength (𝑓𝑦), ultimate tensile strength (𝑓𝑠𝑢), and strain corresponding to initial strain hardening (𝜀𝑠ℎ) were taken from the experimentally measured stress-strain values of CSA G30.18 500W. 𝑓𝑠 = 𝑓𝑦 [𝑎(𝜀𝑠−𝜀𝑠ℎ)+2𝑏(𝜀𝑠−𝜀𝑠ℎ)+2+(𝜀𝑠−𝜀𝑠ℎ)(𝜀𝑠−𝜀𝑠ℎ)(𝑓𝑠𝑢𝑓𝑦− 1.7)] (2) Where a, and b are constants estimated by curve fitting the analytical equation to the strain-hardening region of the experimentally measured tensile test data. Uniaxial tensile test stress-strain plots and fitted strain hardening curves for bar sizes of 10M and 15M are given in Figure 2and are fitted using the proposed equation and regression results for values of a, and b are provided in Table 1 An adjusted R2 statistical parameter was utilized in order to compare the level of prediction of the chosen model. The results showed an R2 values of 0.98, and 0.99 for bar sizes 10M and 15M respectively which signify good level of prediction by the model. (a) (b) Figure 2: Uniaxial tensile test results and analytical strain hardening models for bar size a) 10M, b) 15M 23 Table 1: Values of a and b. Bar type Bar size Equation parameter a b CSA G30.18 500W 10M 53.41 22.66 15M 52.58 23.65 3.4 Uniaxial Tensile Results Table 2 displays the average mechanical properties of each bar size, which were extracted from the stress-strain response. Figure 2 showcases the stress-strain response obtained from the extensometer, which was measured over a gauge length of 25 mm. The stress-strain response is characterized by a linear section until a clearly defined yield point, a yield plateau, and ultimately a non-linear strain hardening curve. An existing stress-strain model was utilized to perform an analytical prediction of the stress strain response. The steel's tensile test stress-strain response captured significant mechanical properties. The rebar's stress-strain response exhibits a linear portion until yielding, followed by a distinct yield point and plateau, and ultimately a non-linear strain hardening portion curve. The CSA G30.18 500W is an HSS having a well-defined yield point, which enables easy determination of yield strength and yield strain. The mechanical properties obtained comprise the modulus of elasticity (𝐸𝑠), yield strength (𝑓𝑦), ultimate tensile strength (𝑓𝑠𝑢), the ratio of ultimate tensile strength to yield strength (T/Y), and strain at failure (𝜀𝑠𝑓), all of which are presented in Table 2. Additionally, Figure 2: Uniaxial tensile test results and analytical strain hardening models for bar size a) 10M, b) 15M shows sample stress-strain responses for bar sizes of 10M and 15M. The average yield strength for the two specimens is 614.8 MPa for 10M bar size and 586.8 MPa for 15M bar size. The T/Y ratio ranged from 1.31 to 1.32, with an average value of 1.315, which is higher than the minimum specified T/Y ratio in ASTM A706 (ASTM 2016) for ASTM A706 reinforcing bars, commonly used in seismic applications. The mean calculated value of 𝜀𝑠𝑓 for the two specimens is 0.112 for a 10M bar size and 0.118 for the 15M 24 bar size. The measurements of stress-strain responses using the extensometer over a gauge length of 25 mm gauge can be observed in Figure 2. The impact of bar size on the stress-strain response is relatively insignificant. Yield strength, and modulus of elasticity values for the bar size 15M are smaller than the 10M bar size. This is attributed to the fact that larger bar size with the larger cross-section area makes the movement of a dislocation along a slip plane easier compared to a smaller cross-section area. Table 2: Mechanical properties of CSA G30.18 500W Bar size Specimen no. Mechanical property 𝑓𝑦 𝑓𝑠𝑢 𝐸𝑠 T/Y 𝜀𝑠𝑓 (MPa) (MPa) (GPa) 10M 1 602.7 795.5 192.8 1.32 0.110 2 626.8 820.0 192.9 1.31 0.113 15M 1 584.3 767.8 182.5 1.31 0.119 2 589.2 775.0 181.9 1.32 0.117 3.5 Low-cycle Fatigue Results Low-cycle fatigue tests were performed on prepared specimens, utilizing a range of test parameters such as bar diameter, unsupported length, and strain amplitudes. The rebars were tested until a noticeable fracture was observed. All samples exhibited the same failure mode, and none failed in the grips. Each sample was tested twice to ensure the repeatability of the results. To achieve low-cyclic loading, strain amplitudes were selected to surpass the elastic limit of the steel, leading to a degradation in its stiffness. The steel was observed to undergo non-linear degradation and deform beyond its elastic limit at strain amplitudes of 1% or greater. The total strain amplitude (𝜀𝑎) which is defined as the sum of elastic and plastic strains utilized in this study include 1%, 2%, 3%, and 4%. The cyclic stress-strain response of reinforcing steel is characterized by several mechanisms, which include the Bauschinger effect, cyclic strain-hardening, and cyclic strain-softening. The Bauschinger effect occurs when steel is subjected to stress beyond its limit of elasticity, a phenomenon commonly referred to as yielding. When the loading is then reversed, a softening of resistance is 25 experienced by the steel before the stress magnitude during loading in the opposite direction reaches the initial yielding stress value of the material (Stanton and McNiven 1979). Cyclic strain-hardening is representative of the increase in the stress of the steel beyond the value of the initial yielding of the stress of the steel. Conversely, cyclic softening represents the degradation in the stiffness of the steel, i.e., the tangent modulus of steel during inelastic reversals. The outcomes of the tests on the specimens are presented in Table 3 and Table 4 with specific labeling, indicating the bar size, strain amplitude, and specimen number. For example, the label 10M-6𝑑𝑏-±1% (1) refers to specimen 1 with a bar size of 10M, unsupported bar length of 6𝑑𝑏, and subjected to a strain amplitude load of ±0.01. Various parameters are calculated to evaluate the low-cycle fatigue efficacy of the HSS. These parameters constitute the number of half-cycles to failure (2Nf), the energy dissipation in the first cycle (W𝑃1), the total hysteretic energy dissipated to failure (W𝑓𝑇), as well as the average hysteretic energy dissipated per cycle (W𝑃,𝑎𝑣𝑔) which is equivalent to W𝑓𝑇 divided by the total number of cycles to failure (2Nf). Unlike high cycle fatigue, where a specimen is subjected to repeated stress much lower than the yield strength could reach up to millions of cycles before failure, low-cycle fatigue is characterized by a smaller number of cycles since it is subjected to repeated inelastic strain. This is why the number of cycles to failure (2Nf) is given as fractions or decimal numbers. The computation of hysteretic energy was carried out using the trapezoidal rule, which involved the numerical integration of the area beneath the hysteresis loops. 26 Table 3: Low-cycle fatigue results for 10M bar size Specimen Buckling length,  Frequency, f(Hz) 2Nf WfT (MPa) W𝑃,avg (MPa) 10M-6𝑑𝑏-±1% (1) 0.025 116.9 7.8 1836.1 15.7 10M-6𝑑𝑏-±1% (2) 125 8 1952.8 15.6 10M-6𝑑𝑏 -±2% (1) 0.0125 9.8 19.8 383.1 39.1 10M-6𝑑𝑏-±2% (2) 14.88 9.8 19.8 385.4 39.3 10M-6𝑑𝑏-±3% (1) 0.00833 4.7 32.5 281.6 59.9 10M-6𝑑𝑏-±3% (2) 3.8 32 241.3 63.5 10M-6𝑑𝑏-±4% (1) 0.00625 1.6 41.3 150.4 94 10M-6𝑑𝑏-±4% (2) 1.7 41.8 162.3 95.5 10M-8𝑑𝑏-±1% (1) 0.025 65.1 7.8 972 15.4 10M-8𝑑𝑏- ±1% (2) 63.1 8.2 1018.5 15.6 10M-8𝑑𝑏-±2% (1) 0.0125 5.8 17.7 189.8 32.7 10M-8𝑑𝑏- ±2% (2) 19.84 5.9 18 196 33.2 10M-8𝑑𝑏-±3% (1) 0.00833 3 26.4 152.4 50.8 10M-8𝑑𝑏-±3% (2) 3.2 25.9 156.5 48.9 10M-8𝑑𝑏-±4% (1) 0.00625 1.7 32.4 121.7 71.6 10M-8𝑑𝑏-±4% (2) 1.9 34.7 145 76.3 10M-10𝑑𝑏-±1% (1) 0.025 33 7.9 428.1 13 10M-10𝑑𝑏-±1% (2) 37.9 7.8 469.4 12.4 10M-10𝑑𝑏-±2% (1) 0.0125 6.7 15.7 169.5 25.3 10M-10𝑑𝑏-±2% (2) 24.80 5.9 15.7 151 25.6 10M-10𝑑𝑏-±3% (1) 0.00833 1.7 24.1 88.7 52.2 10M-10𝑑𝑏-±3% (2) 2.9 20.9 118.5 40.9 10M-10𝑑𝑏-±4% (1) 0.00625 1.9 25.4 109.6 57.7 10M-10𝑑𝑏-±4% (2) 2 24.5 113.1 56.5 W𝑃1 (MPa) 27 Table 4: Low-cycle fatigue results for 15M bar size. Specimen Buckling length,  Frequency, f(Hz) 2Nf WfT (MPa) W𝑃,avg (MPa) 15M-6𝑑𝑏-±1% (1) 0.025 75 7.7 1187.4 15.8 15M-6𝑑𝑏-±1% (2) 77.1 7.7 1406.1 18.2 15M-6𝑑𝑏 -±2% (1) 0.0125 5.9 28.2 319.2 54.1 15M-6𝑑𝑏-±2% (2) 14.53 6.7 18.7 246.1 36.7 15M-6𝑑𝑏-±3% (1) 0.00833 2.8 29.4 160.4 57.3 15M-6𝑑𝑏-±3% (2) 2.8 29 158.4 56.6 15M-6𝑑𝑏-±4% (1) 0.00625 1 38.1 96.2 99.1 15M-6𝑑𝑏-±4% (2) 0.8 37.4 90.1 112.6 15M-8𝑑𝑏-±1% (1) 0.025 45 7.7 659 14.6 15M-8𝑑𝑏-±1% (2) 52.3 7.5 753.7 14.4 15M-8𝑑𝑏-±2% (1) 0.0125 4.9 17.7 154.1 31.5 15M-8𝑑𝑏- ±2% (2) 19.38 4.9 17.2 146.9 30 15M-8𝑑𝑏-±3% (1) 0.00833 2.7 24.3 121.8 45.1 15M-8𝑑𝑏-±3% (2) 2.7 23.5 119.6 44.3 15M-8𝑑𝑏-±4% (1) 0.00625 1.7 29.2 105.5 62.1 15M-8𝑑𝑏-±4% (2) 1.7 29.1 106.2 62.5 15M-10𝑑𝑏-±1% (1) 0.025 20 7.8 257.7 12.9 15M-10𝑑𝑏-±1% (2) 24.2 7.5 325.3 13.4 15M-10𝑑𝑏-±2% (1) 0.0125 6.4 14.8 100.7 15.7 15M-10𝑑𝑏-±2% (2) 24.22 6.4 14.7 101 15.8 15M-10𝑑𝑏-±3% (1) 0.00833 3.5 19.9 83.5 23.9 15M-10𝑑𝑏-±3% (2) 3.5 19 82.3 23.5 15M-10𝑑𝑏-±4% (1) 0.00625 1.8 23.3 90.3 50.2 15M-10𝑑𝑏-±4% (2) 1.7 22.7 89.3 52.5 W𝑃1 (MPa) 28 Figure 3: Cyclic stress strain response of 15M bar made of CSA G30.18 500W at the strain amplitude of 0.03 gripped at (a) 6𝑑𝑏, (b) 8𝑑𝑏, (c) 10𝑑𝑏 Figure 4: Cyclic stress strain response of 15M bar made of CSA G30.18 500W with L/D = 6db at a strain amplitude of (a) 0.01, (b) 0.02, (c) 0.03, and (d) 0.04. 𝑏) 𝑎) 𝑐) 𝑑) 𝑏) 𝑎) 𝑐) 29 The influence of inelastic buckling is considered using the non-dimensional bar buckling parameter , which was originally proposed by Dhakal and Maekawa (2002). More specifically, the  parameter for bar buckling is defined as follows: 𝜆 =𝐿𝐷√𝑓𝑦100 (7) In this study, the ratio of unsupported length to bar diameter is denoted as L/D. Additionally, the yield strength in MPa is represented by 𝑓𝑦. For this investigation, 𝑓𝑦 is taken to be the average yield strength for two specimens. Specifically, the yield strength for the 10M bar size is 614.8 MPa, while the yield strength for the 15M bar size is 586.8 MPa. 3.5.1 Effect of Strain Amplitude The hysteresis loops provided in Figure 4 pertain to strain amplitudes of 1%, 2%, 3%, and 4% for bar unsupported lengths of 6db. The findings demonstrate that an increase in strain amplitude results in a decrease in the low cycle fatigue life, and dissipated energy of the reinforcing steel as only a small number of cycles are accomplished for higher strain amplitude. This was because they achieved the plastic range and exhausted available energy at a faster rate. For instance, specimens 10M-6𝑑𝑏-±1% and 10M-6𝑑𝑏-±4% have shown a difference in number of cycles up to 100 which is significant. Subjecting the specimens to higher levels of strain amplitudes caused a significant molecular dislocation, defects and microcracks in the rebars. Therefore, a higher level of strain amplitudes promotes the growth of the microcracks, and defects which could lead to the initiation of cracks in the rebar. This trend of a reduction in cycles with an increase in strain amplitude has been observed in numerous studies (Aldabagh et al.2021b; Brown and Kunnath 2004; Egger et al. 2021; Mander et al. 1994; Hawileh et al. 2010; Hawileh et al. 2016). Aldabagh et al. (2021b) found that a reduction in strain amplitude had a generally positive effect on both the fatigue life and total energy dissipation of ASTM A1035 Grade 690 reinforcing bars. Similarly, Egger et al. (2021) observed that an increase in 30 strain amplitude led to decreased fatigue performance in high-strength steel rebars. The hysteresis response displays a Bauschinger effect for the different strain amplitudes, wherein a prompt deviation from the linear elastic response of the hysteresis response is observed during strain reversal from tension to compression. When comparing the fatigue life with regular steel, CSA G30.18 500W HSS exhibits a reduced quantity of cycles to failure in comparison to the ASTM A706 Grade 420 when subjected to an equivalent level of strain amplitude loading. For instance, for L/D of 6 and εa of 0.03, the mean number of cycles to failure for CSA G30.18 500W is 3.52. In contrast, Hawileh et al. (2010) reported an average value of 2Nf as 39.1 for the ASTM A706 Grade 420, thereby highlighting the variation in performance between the two grades of steel. 3.5.2 Effect of Bar Unsupported Length The evaluation of low-cycle fatigue performance in high-strength steel reinforcing bars requires careful consideration of the unsupported length of the bar, commonly referred to as the slenderness ratio. The cyclic stress-strain response for 15M bar size and strain amplitude of 0.03 is provided in Figure 3. It has been observed that the fatigue life, and dissipated energy of the rebars is considerably impacted by their slenderness ratio. In order to scrutinize the effect of the slenderness ratio on the low-cycle fatigue performance of the CSA G30.18 500W, this study incorporated bar unsupported lengths of 6db, 8db, and 10db. The results indicate that with an increase in the slenderness ratio, the buckling of high strength reinforcing bars leads to significant degradation of their fatigue life performance, and reduction in the total dissipated energy. An increase in slenderness ratio results in a slender bar specimen which makes it more prone to buckling. Buckling has a direct negative impact on the low-cycle fatigue response of the rebars as the specimen undergoes significant lateral deformation experiencing reduced load carrying capacity. This is because buckling induces a localized stress concentration in the specimens which could initiate fatigue cracks. Several studies have examined the impact of bar unsupported length on the low-cycle fatigue performance of high-strength steel rebars. As per the observations, a reduction in the bar unsupported length leads to a general increase in the 31 fatigue life and total energy dissipation of the rebars (Aldabagh et al. 2021b). In addition to this, it has been found that the slenderness ratio of the rebars plays a crucial role in determining their fatigue life. An increase in the slenderness ratio results in a degradation of the rebars' fatigue performance (Egger et al. 2021). In a study conducted by Tripathi et al. (2018), the impact of the slenderness ratio on the low-cycle fatigue life of 300E and 500E reinforcing bars was analyzed. The results of the study demonstrated that the buckling of reinforcing bars, which was directly linked to a decrease in the low-cycle fatigue life of the reinforcing bars, was more prominent in specimens with a larger slenderness ratio. 3.5.3 Effect of Bar Size This study entailed the utilization of 10M and 15M bar types to assess the low-cycle fatigue of the CSA G30.18 500W. As revealed in Table 3 and Table 4, the results demonstrate that the number of cycles (2Nf) and total hysteretic energy dissipated to failure (W𝑓𝑇), for the 10M bar size is somewhat higher compared to the 15M bar size. For instance, the ratio of the number of cycles (2Nf) for 0.01 and 0.02 strain amplitudes for both bar sizes are 1.56, and 1.66, respectively. Similarly, the total hysteretic energy dissipated to failure (W𝑓𝑇), ratio for strain amplitudes of 0.01 and 0.02 are 1.55 and 1.2, respectively. Nevertheless, the overall impact of bar size on the low-cycle fatigue performance may be deemed negligible. Comparable observations were made by Aldabagh et al. (2021b) where they examined 12.7 mm and 15.88 mm bar sizes and obtained low-cycle fatigue performance of 12.7 mm to be slightly higher than the 15.88 mm bar size. 3.6 Low-cycle Fatigue Models 3.6.1 Strain-Based Fatigue Model Several studies have been conducted focusing on estimating the fatigue life of rebars through strain amplitude. Coffin-Manson equation (Coffin 1954; Manson 1953) was proposed as an empirical equation for estimating the overall fatigue life of a material. This equation is comprised of both elastic 32 and plastic components. The former predicts high-cycle fatigue, while the latter represents low-cycle fatigue. The fatigue life model is expressed as follows: 𝜀𝑎 =Δ𝜀2=𝜎𝑓′𝐸(2𝑁𝑓)𝑏+ 𝜀𝑓′ (2𝑁𝑓)𝑐 (8) whereas 𝜀𝑎 denotes the total strain range, 𝜀𝑠,𝑚𝑎𝑥- 𝜀𝑠,𝑚𝑖𝑛, 𝜎𝑓′ represents the fatigue strength coefficient. Additionally, E stands for the modulus of elasticity, b is the fatigue strength exponent, 𝜀𝑓′ denotes the fatigue ductility coefficient, and c represents the fatigue ductility exponent. Koh and Stephens (1991) discovered that in the analysis of low-cycle fatigue, solely the second component of the Coffin Manson (1954) is satisfactory, with the elastic portion being negligible. The simplified equation for low-cycle fatigue as recommended by Koh and Stephens (1991) is presented as follows: 𝜀𝑎 =Δ𝜀2= 𝜀𝑓′ (2𝑁𝑓)𝑐 (9) Koh and Stephens (1991) presented an empirical equation in accordance with the plastic fatigue life model that applies to all rebar classifications (see Eq. 9). Eq. 9 was derived through a series of low-cycle fatigue tests with constant amplitude, employing completely reversed cycles where the value of R was -1. The constants outlined in Eq. 8 were estimated utilizing the method of linear least-squares regression analysis, which was performed within the logarithmic space of the experimental data. The proposed empirical equation is expressed as follows: 𝜀𝑎 =Δ𝜀2= 0.08(2𝑁𝑓)−0.3333 (10) Mander and Panthaki (1994) conducted a comprehensive low-cycle fatigue evaluation on mild steel and high alloy prestressed steel bars. They evaluated their experimental findings with the use of existing low-cycle fatigue models, and they proposed a low-cycle fatigue model that could be applied universally to all reinforcing steels. The proposed model was based on Koh-Stephens (1991) model. The model formulated by Mander and Panthaki (1994) is presented below. 33 𝜀𝑎 = 0.08(2𝑁𝑓)−0.500 (12) In this investigation, the fatigue model proposed by Koh and Stephens (1991) was utilized to fit the low-cycle fatigue data that was experimentally obtained. The constant parameters of Eq. (8) were determined via the utilization of the least-square regression analysis technique. Figure 5 provides the low-cycle fatigue data of CSA G30.18 500W in plotted log-log space, with the Koh and Stephens (1991) model. The results demonstrate that the Koh and Stephens (1991) based model was able to accurately predict the low-cycle fatigue life of CSA G30.18 500W, as measured experimentally. The parameters for the Koh Stephen’s model fitted to the experimental low-cycle fatigue data are provided in Table 5. Table 5: Values of parameters for low-cycle fatigue model. Slenderness ratio (L/D) Buckling parameter () Fatigue ductility coefficient (𝜀𝑓′ ) Fatigue ductility exponent (𝑐) Square of the Correlation Coefficient (𝑟2) 6 14.70 0.0401 -0.333 0.949 8 19.61 0.0501 -0.490 0.960 10 24.51 0.0507 -0.481 0.929 34 Figure 5: Plastic strain based low-cycle fatigue models for CSA G30.18 500W. The inclusion of inelastic buckling in fatigue life models was accomplished by the introduction of the non-dimensional buckling parameter lambda as defined in Equation 33. The buckling parameter was first employed by Kashani et al. (2015) in the Koh-Stephens model. Kashani et al. (2015) endeavored to establish a correlation between the buckling parameter and the exponents and coefficient of the Koh-Stephens model through regression analysis. The model proposed by Kashani et al. (2015) is given as follows. 𝜀𝑓′ = 0.007𝑒(0.045𝜆) + 0.03 (13) c = −0.018𝜆 − 0.159 (14) 𝜀𝑓′ denotes the fatigue ductility coefficient, and c represents the fatigue ductility exponent, which are the same as those listed in the fatigue life prediction Koh-Stephens (1991) model. The model was subsequently utilized by Tripathi et al. (2018) to forecast the low-cycle fatigue behavior of New Zealand's manufactured Grade 300E and 500E reinforcing steel while accounting for the influence of inelastic buckling. The model proposed by Tripathi et. al (2018) is given as follows: 35 𝜀𝑓′ =−𝜆350+ 0.2 (15) 𝑐 = − (𝜆1200+ 0.441) (16) In this study regression analysis was performed to obtain a model with correlates the buckling parameter with the fatigue life parameters for CSA G30.18 500W. The results of the regression are presented as follows: 𝜀𝑓′ = 0.01833𝑒(0.03929𝜆) + 0.008325 (17) c = 173.4𝑒(−0.4611𝜆) − 0.5294 (18) The values of 𝑟2 corresponding to the aforementioned regression fits were 0.91 and 0.999, respectively. A comparative analysis was conducted to evaluate the efficacy of the fatigue life prediction models proposed in this study, in conjunction with those presented by Kashani et al. (2015) and, Tripathi et al. (2018) with respect to their ability to fit the experimental low-cycle fatigue measurements, as illustrated in Figure 8. The models were fitted to the low-cycle fatigue measurements of bar unsupported lengths of 6𝑑𝑏, 8𝑑𝑏, and 10𝑑𝑏. The findings indicate that the model developed by Tripathi is comparatively less accurate in predicting the low-cycle fatigue of the rebars for all unsupported lengths, as opposed to the other models. Moreover, the proposed model demonstrates a higher degree of prediction accuracy in comparison to the other models, specifically in predicting the low-cycle fatigue life of the CSA G30.18 500W reinforcing steel, particularly for bar unsupported lengths of 6𝑑𝑏 and 8𝑑𝑏. 36 Figure 6: Relationship between  and 𝜀𝑓′ Figure 7: Relationship between  and c. 37 Figure 8: Buckling parameter based low-cycle fatigue life models for CSA G30.18 500W 15M of bar unsupported lengths (a) 6𝑑𝑏, (b) 8𝑑𝑏, and (d) 10𝑑𝑏 3.6.2 Energy-Based Fatigue Model The calculation of the hysteretic dissipated energy (energy per unit volume) during the cyclic deformation of rebars involves numerical integration of the area under the cyclic stress-strain response of the rebars. Energy-based low-cycle fatigue models have been proposed and implemented to predict the fatigue-life of rebars. These models aim to correlate the dissipated hysteretic energy with fatigue life (Hawileh et al., 2010; Tong et al., 1989) or strain amplitude and maximum stress (Brown and Kunnath, 2004; Mander et al., 1994). One such model, proposed by Tong et al. (1989), correlates the number of cycles to failure (2Nf) with total dissipated hysteretic energy (WfT). The model by Tong et al. (1989) is presented as follows: 𝑊𝑓𝑡 = 𝐶1(2𝑁𝑓)𝛾1 (19) a) b) c) 38 The material constants 𝐶1 and 𝛾1, necessary for low-cycle fatigue experimental data analysis, are to be derived. A linear regression analysis is conducted to ascertain the values of 𝐶1 and 𝛾1,. The fatigue model is fit to the experimental data of both rebar types. Table 6 presents the values of the parameters obtained through regression and their r2 values. The r2 values range between 0.92 to 0.98 indicating high accuracy of the energy-based fatigue model. Table 6: Regression results values for parameters of energy-based fatigue model. Slenderness Ratio (L/D) Buckling Parameter (λ) Material Constant (𝐶1) Material Constant (𝛾1) Square of the Correlation Coefficient (𝑟2) 6 14.70 108.3 0.62 0.94 8 19.61 63.93 0.64 0.98 10 24.51 48.13 0.61 0.92 Mander et al. (1994) proposed an energy-based fatigue model by calibrating Tong et al.'s (1989) model. The models were developed for high-alloy prestressing thread bars and ordinary mild-steel deformed reinforcing bars. In this study, both models suggested by Mander et al. (1994) are fit to the experimental data. The proposed models by Mander et al. (1994) are presented below for both high-alloy prestressing and regular mild steel: 𝑊𝑓𝑡 = 126.2(2𝑁𝑓)0.486 (20) 𝑊𝑓𝑡 = 74.4(2𝑁𝑓)0.439 (21) A comparison is made in Figure 9 between the recommended model and previous models for an unsupported bar length of 6db. The findings indicate that the model proposed by Tong et. al (1989), which was calibrated to the experimental results, is highly effective in predicting the overall dissipated hysteretic energy. Furthermore, the model developed by Mander et al. (1994) for deformed mild steel rebars exhibits superior accuracy in predicting the total dissipated hysteretic energy when compared to the model developed for prestressing high-alloy steel. 39 Figure 9: Comparison between energy-based low-cycle fatigue model for CSA G30.18 500W bar unsupported length of 6db. 3.7 Summary The present section of the investigation has presented experimental findings derived from the low-cycle fatigue examinations of the CSA G30.18 500W. A comprehensive study was conducted on the impact of various parameters, including unsupported length, bar size, and strain amplitude. The results revealed that the bar size has an insignificant impact on the response of the rebar, whereas both the bar unsupported length and strain amplitude have an inverse correlation with the fatigue life of the rebar, i.e., an increment in either bar unsupported length or strain amplitude has led to a reduction in the low-cycle fatigue life of the rebar. Furthermore, the existing low-cycle fatigue models were utilized to predict the fatigue life of the reinforcing steel. Previously developed strain-based and energy-based fatigue life were presented together with the proposed fatigue life models. The outcomes have demonstrated that the proposed models have greater precision in predicting the low-cycle fatigue response of the rebar. Along with the low-cycle fatigue test, monotonic tension tests were executed to acquire the essential mechanical properties of the rebar and generate the stress-strain response. The findings have shown that the CSA G30.18 500W has a typical stress-strain response with a yield 40 plateau. Additionally, the achieved mechanical properties have unveiled that the rebar possesses sufficient ductility and strain hardening capability in addition to superior strength. 41 CHAPTER 4: SEISMIC PERFORMANCE OF BRIDGE COLUMNS REINFORCED WITH CSA G30.18 500W HIGH-STRENGTH STEEL 4.1 Background Reinforced concrete (RC) structures that are expected to experience significant inelastic deformation require reinforcing steel bars that can endure substantial plastic displacements. Bridge columns’ longitudinal reinforcing rebars have shown buckling, followed by fatigue fracture, especially on the tension side of the RC members (Yang et al. 2020). The current research presents the results of an experimental investigation conducted on the seismic performance assessment of two circular RC bridge columns with varying aspect ratios, both reinforced with CSA G30.18 500W. A parametric numerical study is also conducted with the effect of several variables including reinforcement grade, axial load ratio, and aspect ratio being investigated. The seismic performance of the bridge columns is evaluated by comparing obtained hysteresis response, dissipated energy, drift, and ductility measurements against those of columns reinforced with normal-strength steel. The results show that CSA G30.18 500W exhibits acceptable performance where ultimate drifts of 6.35% and 7.3% were achieved for aspect ratios of 3 and 6, respectively. The utilization of reinforcing steel bars that can endure considerable plastic displacements is essential for RC members anticipated to encounter significant inelastic deformation beyond yielding, particularly those with plastic hinge regions. The damage caused by earthquakes in the past to bridges has highlighted the necessity for seismic design and detailing in bridge construction. Current seismic designs allow for the utilization of the capacity design technique to design and detail RC components for use in seismic zones (Priestley et al. 1996). It is expected that RC members with plastic hinge sections will undergo significant inelastic deformations while other portions of the member remain relatively undamaged (Barcley and Kowalsky 2020). While plastic hinges are capable of dissipating seismic energy, they must also be constructed with strength and ductility in mind (Ghee 1985). Therefore, to gain approval for use in seismic design, it is imperative to have a thorough understanding 42 of the ductility of reinforcing bars utilized in plastic hinges. HSS bars are known to offer a range of benefits when compared to conventional mild carbon steel bars. These advantages include reduced labor, ease of construction in high rebars congestion areas, such as RC frame joints, and a reduced number of reinforcing bars. It is evident that seismic performance is a critical consideration in the design of bridge columns. The existing studies on the seismic behavior of bridge columns and columns reinforced with HSS provide valuable insights into the possible replacement of regular steel with HSS. However, it is essential to note that the use of HSS comes with some drawbacks, such as a lower strain at the ultimate strength and a reduced tensile-to-yield strength ratio. These factors could potentially decrease the ductility of RC members, which poses a significant concern for structures built in seismic zones where the structure must withstand considerable horizontal stresses and deformations. The Canadian Highway Bridge Design Code (CHBDC) (CSA 2019b) recommends that designers and engineers consider the increased strain demands for seismic force-resistant structures designed and detailed using reinforcing grade of over 400 MPa. It is important to note that the increased strain demands required for higher-strength steel may ultimately reduce a structure’s ductility (CSA 2019b). CSA G30.18 500W is Canadian-produced reinforcing steel that comes with a minimum specified yield strength of 500 MPa produced following the production guidelines of CSA G30.18 (CSA 2021). The grade label 500W signifies a minimum yield strength of 500 MPa and the “W” stands for the bar weldability. Its application as longitudinal bars in concrete members has been restricted to members of RC structures that are not designed to bear seismic loads due to a lack of experimental data on their seismic performance. Incorporating CSA G30.18 500W HSS in the construction of reinforced concrete bridges carries paramount significance owing to its high demand. The key objective of this study is to narrow down the existing knowledge gap in relation to the seismic performance of RC bridge columns reinforced with CSA G30.18 500W. The objective will be achieved through the implementation of experimental investigations into the seismic behavior of two circular bridge columns that have been reinforced with CSA G30.18 500W HSS. A parametric study has also been conducted numerically to 43 study the effect of reinforcement grade, axial load ratio, and aspect ratio on the seismic performance of bridge columns reinforced with CSA G30.18 500W and ASTM A706 Grade 420. Furthermore, the findings of this study are expected to play key roles in shaping future seismic codes and guidelines for the use of CSA G30.18 500W HSS in RC structures. The seismic performance of bridges is primarily dictated by the seismic performance of bridge columns, given the location of plastic hinges in said columns. Prior studies have explored the performance of circular bridge columns reinforced with ASTM A706 Grade 550 HSS, including research conducted by (Barcley and Kowalsky 2020), (Barbosa et al. 2016), (Sokoli et al. 2017). Most of the studies suggest that ASTM A706 Grade 550 can be used as a replacement for ASTM A706 Grade 420. The research conducted by Barbosa et al. in 2016 presented the outcomes of a testing program that was designed to evaluate the performance of circular RC bridge columns that were reinforced with ASTM A706 Grade 550 HSS reinforcement. The Grade 550 HSS reinforcement was found to exhibit comparable levels of resistance and displacement in comparison to the Grade 420 reinforcement. Ding et al. (2021) conducted a study on the seismic performance of bridge columns reinforced with high-strength steel reinforcement. The study found that HTRB600 HSS has lower ductility and inferior low-cycle fatigue performance compared to HRB400E regular steel. Furthermore, RC columns with HTRB600 steel have higher or comparable deformation capacity than those with HRB400E steel. Su et al. (2019) conducted a study on the effect of the yield strength of longitudinal steel bars and concrete compressive strength on the seismic performance of reinforced concrete bridge columns. The study examined different grades of longitudinal steel bars of HRB335, HRB500E and HRB600. The use of high-strength steel reinforcement resulted in increased lateral bearing capacity, yield displacement, and total deformation, but decreased displacement ductility and residual displacement. Li et al. (2018) conducted a study on the seismic behavior of concrete columns reinforced with high-strength steel bars. Six concrete columns were tested with variable steel grades of conventional steel HRB400 and HRB600 HSS under cycle loading. The test results showed that high-strength steel bars exhibited larger flexural strength and energy dissipation, similar drift capacity, and 44 smaller ductility compared to control columns reinforced with regular steel. A study by (Restrepo et al. 2006) investigated the seismic response of circular columns constructed with high-performance materials, wherein circular columns reinforced with HSS were tested under quasi-cyclic tests. There is currently no available experimental study on the seismic behavior of CSA G30.18 500W in RC members. 4.2 Experimental Program Units were originally designed according to the force-based design guidelines outlined in CHBDC (CSA 2019b). These units were purposefully designed to represent single and double-bending responses of bridge columns, with Unit 1 exhibiting a single-bending response and Unit 2 displaying a double-bending response. The two large-scale bridge column Units have been constructed to undergo testing at the Structural Laboratory of the University of British Columbia, Okanagan. Both specimens are composed of a circular section with a diameter of 406 mm and clear heights of 1218 mm and 2436 mm for Units 1 and 2, respectively. The geometry and cross-section details of test units is given in Figure 10. The two test units were reinforced with HSS longitudinal reinforcement of CSA G30.18 500W, which meets CSA G30.18 (CSA 2021) specifications. Furthermore, both Units were reinforced with 10M ASTM A706 Grade 420 spiral reinforcement. Table 7 provides test matrix details of the tested columns. Columns denoted as Unit 1 and Unit 2 are characterized by aspect ratios of 3 and 6, respectively. Table 7: Test matrix Column D (mm) L/D 𝜌𝑙 (%) 𝜌t (%) 𝐴𝐿𝑅 (%) f'c (MPa) Unit 1 406 3 1.85 1.1 14.5 36.7 Unit 2 406 6 1.85 1.1 14.5 38 45 Figure 10: Test units’ geometry and cross-section details. 4.2.1 Material Properties Column and footing elements were constructed using concrete mixes having target strengths of 35 and 40 MPa at 28 days, respectively. To determine the compressive concrete strength of the column specimen at the age of testing, compressive tests were conducted on concrete cylinders that were made from fresh concrete mixes of both the column and footing. These cylinders, which had a length of 200 mm and a diameter of 100 mm, were subjected to the standard compressive cylinder tests as per ASTM C39 (ASTM 2018). The measured compressive strengths of concrete for the columns were determined to be 36.7 and 38 MPa for Units 1 and 2, respectively. Conversely, the compressive strength of footing concrete was found to be 40.5 MPa for Unit 1 and 43.2 MPa for Unit 2. The longitudinal and spiral reinforcements of bar diameters 15M (No.5) and 10M (No.3), respectively, utilized in the columns were obtained from the same heat. The longitudinal reinforcement exhibited a yield strength of 583.4 MPa, while the transverse steel had a yield strength of 434 MPa. 46 4.2.2 Instrumentation Several instruments were installed to observe both local and global response quantities. The monitored response quantities include lateral loads, axial loads, column curvature, longitudinal bar deformations, and concrete strains. The acquisition of data system (DAQ) was utilized to interpret the measured displacement, strain, curvature, and force responses. During the test, load cells closely monitored applied axial and lateral loads. The axial load was measured using a load cell that was placed on top of the column between the post-tensioning rod and hydraulic jack, as seen in Figure 11a. Meanwhile, lateral load was observed through the load cell connected to the hydraulic actuator. Vertical strain pots were installed on opposing faces of the column to monitor rotation and vertical extension. Strain pots with gauge lengths of 250 mm were placed at intervals of 168, 268, 368, and 468 mm on both the north and south faces of the lower portion of the column, and extension wires were included in some cases to prevent the strain pots from exceeding their gauge length limit. Strain gauges were utilized to monitor internal steel strains of longitudinal reinforcement and cover concrete strains at various locations. Tokyo Measuring Instruments lab (TML) manufactured the strain gauges. The longitudinal bars’ strain gauges were placed at intervals of 85 mm, 170 mm, 255 mm, and 340 mm above the top face of the footing and at 85 mm and 170 mm. below the footing’s face, as depicted in Figure 11b. The strain gauges were situated at identical heights on the north and south faces of the columns. The North and south faces of the column had two concrete strain gauges placed 75 mm above the top face of the footing to measure concrete cover strain. 4.2.3 Test Specimen Set-Up The experimental program was meticulously designed to ensure a similar setup for both columns. Once the specimen was prepared for testing, it was transported using a crane and positioned on the strong floor. The specimen’s footing consisted of six 101 mm diameter holes, which were utilized to anchor the specimen to the strong floor using 50.8 mm threaded rods. These threaded rods were prestressed to 28 MPa to attain the desired anchorage. After anchoring the specimen to the floor, the axial load was applied using a load cell attached at the top of the column. The axial load was applied in 47 approximately 100 kN increments until the target load was reached. Finally, the instruments i.e., strain gauges, and strain pots were connected to the DAQ and calibrated. Lastly, the hydraulic actuator was attached to the column at the top cap beam using four holes. The experimental configuration employed for testing is presented in Figure 11a. (a) (b) Figure 11: (a) experimental test set-up and (b) Instrumentation. 4.2.4 Loading Protocol Units were subject to both axial and lateral loads during the test. Applied axial load for both tests Units 1 and 2 were 690 and 720 kN respectively, which corresponds to a 14.5% axial load ratio (𝐴𝐿𝑅). Both Units 1 and 2 were subjected to a quasi-static reversed and displacement-controlled loading procedure. The test employed a loading protocol that adhered to the typical symmetric three-set loading procedure used to evaluate the seismic performance of bridge columns (see Figure 12). The analytical yield displacement was estimated in CUMBIA (Montejo and Kowalsky 2007) for both Units. Predicted yield displacements for Units 1 and 2 were 13.2 and 22.2 mm, respectively. The pre-48 yield and post-yield displacement levels applied to test units consist of different sets. The loading history of both units consisted of reversed single cycles with increments of 0.25, 0.5, 0.75, of the analytically measured first yield displacement for the pre-yield, followed by subsequent three-cycle displacements with predefined increments for post-yield. Pre-yield and post-yield displacements of the analytical first yield (1) were applied under a loading rate of 0.25 mm/s. Successive post-yield displacements were then applied at varying loading rates, ranging between 0.5-1 mm/s. a) b) Figure 12: Loading protocol for (a) Unit 1, and (b) Unit 2. 4.3 Results Measured experimental results of the two Units are provided in this study including hysteresis response, observed damages, and their corresponding drift values. In addition, measurements from installed strain gauges, and strain pots which express the measured strains of the longitudinal rebar, and measured curvature of the bridge columns at various heights respectively are also provided. The experimental findings were utilized in two ways. Firstly, the seismic performance of the two bridge columns was compared by studying the effect of aspect ratio on the seismic performance using the obtained experimental results. Secondly, a methodology was adopted to investigate the impact of various parameters including reinforcement grade, axial load ratio, and aspect ratio on the seismic 49 performance of the bridge columns, utilizing previous studies and numerical investigations. 4.3.1 General Damage Observation The Units were subjected to both lateral and axial loads, resulting in a variety of damages. Figure 13 shows the general damage progression of Unit 1. Additional plots showing the damage on specimen units during the test are provided in Appendix C of this thesis. The sequence of damage observed in both Units was found to be similar, as both units experienced minor cracking initially, followed by yielding of the longitudinal reinforcement, minor spalling, crushing of the cover concrete, buckling of the longitudinal reinforcement, and ultimately, fracture of the longitudinal reinforcement. Transverse steel rupture was not detected in either specimen. The failure pattern of both Units is similar in that both Units followed flexure failure mechanism i.e., buckling of rebar followed by its fracture. First flexural cracks were observed in the lower portion of both Units at a drift ratio of about 0.2%. The minor cracks displayed a tendency to widen and extend horizontally as the displacement levels increased. Moreover, in Unit 1, some cracks were observed to expand diagonally owing to the influence of shear damages. Unit 2 experienced flexural cracks with a width of up to 2 mm at the beginning of displacement ductility of 4 on its south side. The concrete cracking was subsequently accompanied by the yielding of longitudinal reinforcement in both Units. The longitudinal reinforcement reached yield at a drift ratio of 1.61% for Unit 1, while for Unit 2, it occurred at a relatively lower drift ratio of 1.24%. Cover Spalling was another type of damage observed during the test. Initiation of minor to moderate spalling was detected at a drift ratio of 3.18% for Unit 1, and 2.74% for Unit 2. As the loading progressed, the observed spalling aggravated to full concrete cover loss at a drift of 4.23% for Unit 1 and 3.65% for Unit 2. After the full concrete cover spalling, the concrete core remained intact, and the bridge columns were able to perform well during the proceeding load cycles. The longitudinal reinforcing bars of Unit 1 began to buckle when the drift ratio reached 5.32% on the north side and 5.46% on the south side. In contrast, Unit 2 revealed buckling of the longitudinal reinforcement at increased drift values of 6.37% and 6.28% for the north and south sides 50 of the column respectively, indicating a higher degree of deformation before buckling occurred. A significant reduction in ultimate lateral load capacity is observed after buckling of longitudinal reinforcing steel which resulted in a stiffness reduction for both Units. The core concrete also started to disintegrate a few cycles after buckling was initiated. The final type of damage recorded in the Units was the fracture of the longitudinal rebars, indicating failure of Units. Initial fracture of the longitudinal rebars for Unit 1 occurred at the last cycle of the three-set displacement ductility 6 corresponding to a drift ratio of 6.35%. Conversely, the fracture of the bar for Unit 2 occurred at a displacement ductility of 8, which corresponds to a drift ratio of 7.3%. a) Cover spalling b) 80% Core crushing c) Core crushing Figure 13 Damage progression of Unit 1 (North side). 4.3.2 Hysteresis Response Measured force-displacement with drift values on the second axis can be found in Figure 14. The plots within the figure also reveal damage that has been observed at various levels of displacement. It is important to note that the shear force values that are represented in the hysteresis curves have not been reduced to consider the geometry effects of the applied axial (P-delta) effect. Nevertheless, the P-delta effect is indicated by the inclined dashed line and demonstrates a reduction (shift) in the maximum lateral load capacity of the hysteresis responses when the P-delta effect is accounted for. To 51 obtain the p-delta shift, both hysteresis responses with and without p-delta were plotted. The shift in the lateral load carrying capacity was then represented by the dashed line. The fracture of longitudinal bars is indicated by the sudden change with sharp curving in the hysteresis response. Post-fracture performance of the bridge columns was evaluated by testing the Units till fracture of the second longitudinal reinforcing rebar was detected. However, the post-fracture response in the hysteresis plots is only presented for Unit 1 only. When the longitudinal reinforcement buckles or full concrete cover loss occurs, there is a decrease in the lateral load-carrying capacity. A reduction is shown by the decrease in the maximum lateral load that the hysteresis curve achieves in comparison to the previous cycle. (a) (b) Figure 14: Experimental hysteresis curves for (a) Unit 1 and (b) Unit 2 4.3.3 Comparison with Previous Studies To understand the effect of reinforcement grade on the seismic performance of bridge columns, experimental results are compared with the control specimens tested by Barbosa et al. (2016). The experimental work of Barbosa et al. (2016) involved studying the effect of aspect ratio and reinforcement grade on the seismic performance of bridge columns. The objective was achieved by conducting experimental tests on four bridge columns where two of them were reinforced with HSS 52 ASTM 𝐴706 Grade 550, and the remaining two were reinforced with regular steel ASTM 𝐴706 Grade 420. Table 8 provides the design matrix for the control column specimens tested by Barbosa et. al (2016). The experimental results of the reinforced columns having aspect ratios of 3, and 6 reinforced with ASTM 𝐴706 Grade 420 regular steel is used in this study to observe the effect of reinforcement grade on the seismic performance of the tested bridge column Units. Table 8: Control specimen design matrix (Barbosa et al. 2016) Specimen L/D 𝜌𝑙 (%) 𝐴𝐿𝑅 (%) f'c (MPa) fyl (MPa) G60-s 3 2.19 5.5 24.65 420 G60 6 2.19 5.5 24.7 420 Data normalization techniques are utilized to account for the existing variation in the flexural and shear capacity of the columns tested in this study and by Barbosa et al. (2016). Hysteresis response is normalized by reducing the nominal shear capacity (𝑉𝑛) from the shear force (𝑉) and dividing it by the maximum shear capacity (𝑉𝑚𝑎𝑥). The obtained hysteresis response of the Units in this study together with the experimental findings of Barbosa et al. (2016) are provided in Figure 15. Unit 1 displays a hysteresis response characterized by significantly higher drift levels. However, this outcome is attributed to the post-fracture response of Unit 1. Notably, the hysteresis response of Barbosa et al. (2016) tests only presented up to the fracture of the first longitudinal rebar, whereas this study presents the hysteresis response of Unit 1 up to the fracture of the second reinforcing rebar. Unit 2 is observed to have a similar hysteresis response and attains comparable drift values with G60. The broad hysteresis response observed in bridge columns reinforced with ASTM 𝐴706 Grade 420 suggests that these columns have a higher capacity for energy dissipation. This phenomenon is elaborated further in the energy dissipation section. 53 (a) (b) Figure 15: Normalized shear force vs drift of (a) aspect ratio of 3 (b) aspect ratio of 6 4.3.4 Strain Gauge Measurements Strain gauges were installed for longitudinal bars located at the extreme tension and compression fibers of the cross-section to capture the strain response of the steel. Tension compression longitudinal rebar strains measured at various column heights are provided in Figure 16. The strains are captured from the maximum tension and compression longitudinal steel strains recorded at the end of the first cycle, the three-cycle lateral displacements. In addition, the yield strain (0.0031) of the longitudinal reinforcing steel measured from the experimental uniaxial tensile test is shown in the plots with dashed vertical lines. The longitudinal reinforcement for Unit 1 initially yielded at a drift ratio of 1.61% which corresponds to a tip displacement of 20.07 mm. The initial yielding of longitudinal rebars on the tension face of Unit 1 was observed at footing level (i.e., 0 mm). while the longitudinal rebars on the compression face of Unit 1 initially yielded 85 mm above the footing. The yielding of longitudinal rebar for Unit 2 occurred at a relatively higher tip displacement of 30.2 mm which corresponds to a drift ratio of 1.24%. The plots show that the first yielding of longitudinal reinforcement for Unit 2 was observed at column height above the face of the footing of 170 mm for tension strain, and 85 mm for compression strain. Longitudinal reinforcements of Unit 2 showed higher tension strains compared to Unit 1. However, this is attributed to the fact that most of the strain gauges for Unit 1 failed at a 54 displacement ductility level of 4 which limits the measured strains. (a) (b) Figure 16: Longitudinal strain measurements for (a) Unit 1, and (b) Unit 2. 4.3.5 Curvature Measurements The curvature of the column cross-section at different heights was monitored using the installed strain pots. Strain pot devices measure the vertical displacement of the section which was then converted into curvature. Curvature profiles were obtained by subtracting the measurements of the north-side strain pot from those of the south strain pot and dividing the resultant value by the horizontal distance between the strain pots and the gauge length of the strain pots. Measured curvature profiles at various heights of the column are provided in Figure 18. The curvature profiles are observed to be higher at the lower end of the member (i.e., close to column footing interface) where the localized plastic hinge is expected to occur with higher deformation. Curvature measurements for Unit 2 are higher at column heights of 268 compared to Unit 2. 55 (a) (b) Figure 17: Curvature profiles for Units (a) Unit 1, and (b) Unit 2. 4.3.6 Energy Dissipation The computation of energy dissipation during each full hysteretic cycle was achieved by determining the area beneath the force-displacement curves using the Simpson integration rule. To obtain the specific dissipated energy, the total hysteretic energy dissipated at every cycle is divided by the overall mass of the bridge columns subjected to testing. This dissipated energy is anticipated to consider the impacts of variances in geometry, flexural capacity, and shear capacity of the bridge columns tested in this study and by (Barbosa et al. 2016). The cumulative dissipated specific energy for the first yield, reference yield, and fracture of the first longitudinal rebar are presented in Table 9 for both units tested in this study as well as bridge columns tested by (Barbosa et al. 2016). The outcomes reveal that Unit 1 has dissipated a greater amount of specific energy at the first yield of longitudinal rebar compared to all the other Units. Furthermore, the total dissipated specified energy at the fracture of the first longitudinal rebar is higher for columns with an aspect ratio of 3 for both higher strength reinforced and regular steel reinforced columns. The issue could potentially be connected to the feasible damages that are caused by shearing, which are more prone to occur in short columns, ultimately resulting in a reduction of overall stiffness and energy dissipation. Additionally, Unit 2 has exhibited considerable deformation up to a drift ratio of 7.3%, whereas Unit 1 has displayed bar fracture at a lesser drift ratio of 6.35%, thereby contributing 56 to the higher energy dissipation of Unit 2. Table 9: Cumulative dissipated specified energy Specified dissipated energy G60-s G60 Unit 1 Unit 2 At first yield (kN-m/ton) 0.7 0.8 3.8 1.24 At reference yield (kN-m/ton) 1.6 1.2 1.5 0.64 At column failure (kN-m/ton) 78.2 88.8 70.3 76.7 The diagram in Figure 18 displays the cumulative specified dissipated energy related to the columns. It is worth noting that the dissipated energy at each cycle, which corresponds to three cycles with the same displacement ductility (𝜇), is added together to determine the total dissipated energy at every cycle. In comparison to columns G-60 and Unit 2, both columns G60-s and Unit 1 exhibited a lower amount of energy dissipation. The total dissipated hysteretic energy is observed to increase with increasing aspect ratio. An increase in aspect ratio is associated with a reduction in stiffness of the bridge columns thereby allowing the specimen to undergo large flexural deformations and causing higher energy dissipation through plastic hinging mechanism during a seismic action. A bridge column with lower aspect ratio on the other hand is stiffer and thus will experience smaller deformation during an earthquake causing a reduction in the energy dissipation. 57 Figure 18: Cumulative specified dissipated energy. 4.4 Summary This study focuses on the seismic performance of bridge columns with CSA G30.18 500W reinforcement through a series of large-scale column tests and numerical evaluations. Experimental findings, which included observed damages at various stages and corresponding drifts, were presented. The results indicate that the application of CSA G30.18 500W in the seismic design of bridge columns is highly promising, as the tested columns' performance was comparable to that of regular steel-reinforced steel. The findings of this study present a positive indication for the utilization of CSA G30.18 500W in the seismic design of bridge columns and RC members. Given the constraints of the examined variables, it is recommended that supplementary experimental investigation be carried out to scrutinize the influence of diverse design parameters, such as steel ratios The main conclusions that can be drawn from this study are the following. ▪ Tested columns displayed a mode of failure in flexure, which was identified by the buckling of the longitudinal bar accompanied by its fracture. The specimens were intended to undergo failure in flexure and were sufficiently confined to prevent shear failure. Nevertheless, certain diagonal cracks were observed in column Unit 1, which may be attributed to shear damages. 58 ▪ Similar drift capacities were attained by column units that were reinforced with CSA G30.18 500W in comparison to those columns that were reinforced with ASTM A706 Grade 420. In Unit 1, a higher drift was achieved in comparison to G60-s and this was attributed to the post fracture response ▪ Columns that were reinforced with HSS demonstrated greater capacity for energy dissipation at the first yield. Nonetheless, the overall cumulative dissipated energy value specified is comparatively greater in columns reinforced with conventional steel in contrast to those reinforced with HSS. 59 CHAPTER 5: PERFORMANCE-BASED DESIGN AND LIMIT STATES OF BRIDGE COLUMNS REINFORCED WITH CSA G30.18 500W HIGH STRENGTH STEEL 5.1 Background The performance-based design (PBD) philosophy has been incorporated into the Canadian Highway Bridge Design Code (CHBDC) (CSA 2014) as a necessary design approach for major-route and lifeline bridges. The latest version of the CHDBC (CSA 2019b) also employs the PBD design philosophy. The prior iterations of the code (CSA 2006) employed force-design philosophy (FBD), which determines seismic design forces via elastic analysis, with a reduction factor R accounting for possible overstrength. Other factors considered in FBD include important factors and the type of soil profile. However, using FBD for seismic design has been associated with certain limitations, as described in Priestley, M. J. N. and Calvi 2007; Calvi et al. 2013. Some of the issues with FBD include the assumption of the equal displacement rule, which does not always apply for many instances, as well as the invalid assumption that yield curvature is proportional to flexure strength, as it has been observed that yield curvature is independent of strength. The concept of designing structures based on their performance has gained widespread acceptance, largely due to the significant damage experienced by structures as a result of earthquakes, which necessitated the development of more effective design alternatives. The first-generation performance-based design, as proposed in various publications such as ATC-40 (1996b), FEMA 273(1997), and FEMA 350 (2000b), has represented a major advancement in seismic design. As such, any design philosophy, whether displacement-based or first-generation performance-based earthquake engineering, is considered to be a performance-based design (PBD) philosophy, as it guarantees that the structure achieves a certain level of performance objective. Over the years, one of the most significant improvements in the performance-design philosophy has been the careful investigation and quantification of structural damages, including deformational capacity, drifts, and material strains of 60 structural components. For example, the substructure of bridges, such as columns and columns, are extensively studied to understand and quantify the damage associated with the bridge when subjected to a particular level of seismic loads. This is accomplished by designing the column and conducting tests through loads that simulate the seismic loads, ultimately quantifying the damages that occur at various stages. These damages are then utilized to establish performance limit state values that are useful for performance-based design philosophy. The establishment of performance-limit states and the comprehension of the extent of damage that a structure can endure are of paramount importance when incorporating new materials for the seismic design of members. With the development in technology and demand for superior quality construction materials, there is an increase in the utilization of high-performance materials such as high-strength steel, high-strength concrete, and ultra-high-performance concrete in structures that undergo significant inelastic deformation. Therefore, it is critical to initially study and quantify the level of damages structural components involving high-performance materials can endure before utilizing. With the Canadian construction market growing demand for high-strength steel, owing to its beneficial constructional advantages, such as reduced bar congestion, and reduced labor; it is essential to establish performance limit states for bridges that incorporate CSA G30.18 500W HSS as their longitudinal reinforcement. This chapter provides a brief overview of the performance of the tested bridge columns as presented in Chapter 4. The various damage states are measured and quantified to establish the performance limit state for bridge columns that incorporate CSA G30.18 500W reinforcing steel as their longitudinal reinforcement. The experimental findings are further utilized to develop and validate an OpenSees numerical model for additional evaluation of the performance of the bridge columns containing CSA G30.18 500W. To evaluate the performance of the bridge columns using the validated numerical model, a parametric methodology is developed. The analytical study is further implemented with various design parameters, including axial-load ratio, aspect ratio, longitudinal reinforcement ratio, and reinforcing grade, to investigate the seismic performance of 61 bridge columns. The performance of the bridge columns is evaluated with respect to the existing performance limit states outlined in CHBDC (CSA 2019b). 5.2 Performance Limit-States in CHBDC Existing performance limit states for the seismic design of bridges in CHBDC (CSA 2019b) are based on regular reinforcing steel of 400 MPa. The code doesn’t explicitly restrict the use of reinforcing steel of grade above 400 MPa for seismic design. However, the code outlines the need for considering the increased strain demands expected in members that utilize steel grades above 400 MPa as reinforcement. Generally, an increased strain demand is expected to reduce the ductility and deformational capacity of members (CSA 2019b). The various limit states and service levels defined in CHBDC (CSA 2019b) are presented in Table 11 including the concrete and steel material strain limits. The limit states are defined in terms of the service level of the structure and the extent of damage it may experience. The first definition of service level is immediate where the bridge is expected to be fully serviceable with no traffic disruption. In this service level bridge is expected to be in its elastic state sustaining minor damages that don’t affect its performance. Following the immediate service level comes the limited-service state in which a bridge is expected to provide service with the minor repair without the need for its closure and giving service for emergency traffic. The level of damage for this service level is defined as repairable damage which shows moderate bridge damage with some degree of inelasticity. The third level of bridge service is service disruption where a bridge is expected to be open to emergency traffic after inspection. However, this service level might cause the closure of traffic for repair. The associated damage level for this service is termed as extensive damage where the bridge is expected to undergo inelastic behavior with visible damages including spalling of concrete, and steel bracing buckling. The last stage of service level is life-safety where the bridge is expected to sustain major damage but no collapse. For the life-safety service level, the bridge sustains extensive damage, mainly, its superstructure members such as the bridge spans are expected either to be replaced or extensively repaired. 62 5.2.1 Column Capacity and Overstrength Factors The capacity of the columns tested in this study is analyzed by evaluating the flexural and shear capacities achieved during testing. Maximum shear capacity, also known as plastic shear capacity, is obtained from the measured base shear values. Overstrength factors are a requirement in reinforced concrete design, as they ensure the overall ductile behavior of structures and account for uncertainties in material properties and construction quality. The evaluation of overstrength factors for reinforced concrete design can be accomplished by considering the nominal to plastic flexural moment capacity. Tested moment capacities, shear capacities, and estimated ratio factors are presented in Table 10. The reported column forces represent the highest column shear force and tested moment capacity. It is essential to emphasize that the maximum column shear forces were reduced to account for the P-delta effects of the applied axial. The horizontal component of the axial load was reduced from the base shear to account for P-delta effects. The estimation of the nominal moment capacity is based on either a cover concrete compression strain of 0.04 or a steel tension strain of 0.015, whichever occurs first. In addition, the table includes the ratio of the tested moment capacity to the plastic moment capacity. Results from Barbosa et al. (2016) for ASTM A706 Grade 420 regular steel bars are also provided for comparison purposes. The findings indicate a nominal overstrength factor of 1:36/1:14 and 1:36/1:18 for Columns Unit 1/G60-s and Unit 2/G60, respectively. It is noteworthy that columns reinforced with steel of higher strength exhibit reduced overstrength factors. It is plausible that this phenomenon is attributed to the comparatively lower steel reinforcement ratio of the columns reinforced with high strength steel. The impact of aspect ratio on overstrength factors is found to be insignificant, even though Unit 2 exhibits slightly higher overstrength factors in comparison to Unit 1. This outcome may probably be associated with uncertainties in the experimentally measured quantities. 63 Table 10: Column capacity and overstrength factors. Column 𝑉𝑚𝑎𝑥 (kN) 𝑀𝑛 (kN-m) 𝑀𝑇 (kN-m) 𝑀𝑇/𝑀𝑛 G60-s 446.6 628 853 1.36 G60 213 628 856 1.36 Unit 1 216 259 295 1.14 Unit 2 104 259 307 1.18 5.2.2 Bridge Column Limit States Reinforced with CSA G30.18 500W The latest edition of the Canadian Highway Bridge Design Code, CSA S6-19 (CSA 2019), has considered the seismic design of important bridges in areas of significant seismic activity by adopting a performance-based design strategy. The Code outlines the strain limits for reinforcement steel and concrete that define the onset of damage in ductile concrete members. The limit denotes the onset of a damage state in ductile concrete members. Additionally, the BC Ministry of Transportation and Infrastructure (BC MoTI) outlines several limit states for different levels of damage, in addition to the CHBDC (CSA 2019b) code. The corresponding damage states and strain limits from both CHBDC (CSA 2019b) are presented in Table 11. The confined concrete strains were not measured as there were no instruments installed in the core concrete to measure. Some of the reinforcing steel strain values were also not measured due to the failure of installed strain gauges at some stage during the cyclic loading. The results obtained from the measurements exhibit a commendable level of conformity with the strain limits stipulated by the code. Most of the limits stipulated are in close proximity of the values set in the code. For instance, immediate service level measured strain limits for concrete and steel are lower than the limit in the design code indicating that this service level is achieved early in the columns containing CSA G30.18 500W compared to bridges with regular steel. For the limited-service level on the other hand both columns exhibited higher strain limits indicating a higher performance of the columns compared to those reinforced with regular steel. Both service disruption and life-safety service levels are achieved 64 early by column Unit 2 as the measured strain values are lower than those defined in the code. The overall performance of the columns is commendable as the measured strain limits showed closeness to those specified in CHBDC (CSA 2019b). Therefore, this is a promising result for the possible utilization of CSA G30.18 500W for the seismic design of bridges. However, given the scope of the design parameters considered in this study is low, further experimental works are recommended in order to fully comprehend the seismic performance of the columns reinforced with CSA G30.18 500W. Table 11: Measured material strain values for observed damage states. Service Damage state Strain limits Measured Strains Unit 1 Unit 2 Immediate Minimal damage c ≤ 0.006 c ≤ -0.0012 c ≤ -0.0045 s ≤ 0.01 s ≤ 0.00972 s ≤ 0.00259 Limited Repairable damage s ≤ 0.025  s ≤ 0.0248 service disruption Extensive damage s ≤ 0.05  s ≤ 0.0471 cc ≤ 0.8 cu   life safety Probable replacement s ≤ 0.075  s ≤ 0.0634 cc ≤ cu   Notes: c = concrete compressive strain; s = flexural reinforcing steel strain; cc = confined concrete strain; and cu = ultimate confined concrete strain. N/M = Not Measured. 5.2.3 Buckling Limit State of Bridge Columns The utilization of high-strength steel rebars in the seismic design of bridges has been limited by design codes due to their diminished low-cycle fatigue performance. In areas with high seismic activity, compression members such as bridge columns undergo significant inelastic deformations beyond yielding. The longitudinal reinforcing rebars in these compression members are subjected to high tension-compression strain reversals, also known as low-cycle high amplitude lateral loading. Therefore, reinforced concrete designed to withstand such loads is expected to exhibit sufficient performance by undergoing significant inelastic deformations to satisfy the seismic load demands. The primary reason for restricting HSS in such reinforced concrete members is associated with their 65 reduced ductility, which arises from the reduced yield-to-tensile strength ratio, low elongation fracture, and reduced yield plateau of HSS. This may lead to poor low-cycle fatigue performance of the HSS rebars, which ultimately diminishes the ductility of the reinforced concrete section. During high seismic loads, the longitudinal reinforcements undergo significant inelastic deformations beyond yielding, resulting in the buckling of rebars, which is usually followed by their fracture. The buckling of longitudinal reinforcement often leads to a loss of ultimate load-carrying capacity and reduced stiffness in compression members (Leham et al. 2004). Therefore, when developing damage models for RC members, it is crucial to consider the effect of inelastic buckling to accurately estimate overall structural damage. Estimating the buckling of longitudinal reinforcing rebars is crucial to predict the capacity of structural sections. Buckling models have been incorporated into sectional analysis routines to predict the full-member behavior of reinforced concrete structures. Various models have been developed to predict the inelastic buckling of longitudinal reinforcing steel bars in RC members. One practical bar buckling model, proposed by Berry and Eberhard (2005), was designed to predict the likelihood of longitudinal bar buckling in reinforced concrete members for earthquake engineering applications. This model takes into account multiple factors, such as effective confinement ratio, axial-load ratio, aspect ratio, and longitudinal bar diameter, and is based on plastic rotation, drift ratio, and displacement ductility. The model was calibrated using observations from cyclic tests of rectangular-reinforced and spiral-reinforced concrete columns, and there was excellent agreement between measured and calculated displacements at bar buckling. Feng et al. (2015) developed a finite-element method to predict reinforcement buckling in RC structures under seismic loading, combining a fiber-based model to simulate the RC member with a finite-element model of the plastic hinge region. They concluded that the seismic load history and its resultant strain history on a single reinforcing bar have the potential to impact the required maximum strain for bar buckling. The columns’ ultimate limit state was determined by the buckling and fracture of the longitudinal reinforcing bars. Hence, comprehending the buckling behavior of the longitudinal rebars is imperative 66 in establishing the buckling limit state of the bridge columns under investigation. The deformational capacity of the columns, at which buckling is probable, is assessed and compared with existing models. The buckling of longitudinal reinforcing bars located at the extreme fiber of the section is expressed through the drift of the columns. Measured drift ratios are compared with the existing model used for predicting the drift at buckling by (Berry and Eberhard 2005) (see Eq. 2). Moyer and Kowalsky (2003) have demonstrated that the buckling of longitudinal rebars is correlated with the peak tensile strain of the longitudinal rebar in the preceding cycle prior to the onset of bar buckling. Buckling phenomena is observed when the longitudinal rebar experiences increased tensile strain while it was expected to experience compressive strain (Barcley and Kowalsky 2020). Table 12 presents the maximum measured tensile strain as well as predicted tensile strains according to Goodnight et al.(2013) (see Eq. 3). Peak tensile strain for Unit 1 was not measured as most of the strain gauges failed at lower displacement ductility prior to buckling initiation. Slightly higher peak tensile strains are recorded compared to the predicted peak tensile strains for Unit 2. The predicted column drifts exhibit a minor reduction when compared to the measured drift values as well. 𝜀𝑏𝑏 = 0.03 + 700𝜌𝑡𝑓𝑦𝑡𝐸𝑠−𝑃𝑓𝑐𝑒′ 𝐴𝑔 (22) Δ𝐿= 3.25 (1 + 150𝜌𝑑𝑏𝑙𝐷) (1 −𝑃𝑓𝑐𝑒′ 𝐴𝑔) (1 +𝐿10𝐷)𝑦 (23) Table 12: Longitudinal bar buckling limit state values. Column Column side Peak tensile strain Equation 2 Column drift ratio (%) Equation 3 Unit 1 North N/M 0.0322 5.32 3.90 South N/M 0.0322 5.46 3.90 Unit 2 North 0.0347 0.0322 6.37 4.77 South 0.0368 0.0322 6.28 4.77 67 5.3 Performance Evaluation of Columns Analytically The performance of bridge columns is influenced by several factors, such as the axial load ratio, aspect ratio, reinforcement and concrete grade, spiral reinforcement ratio, and quantity of longitudinal reinforcement. The spiral reinforcement ratio has a significant impact on the performance and deformational capacity of reinforced columns. Augmenting the spiral reinforcement ratio enhances the strength, ductility, and energy dissipation capacity of the columns, resulting in improved behavior. The utilization of spiral reinforcement assists in confining the core concrete and restraining the longitudinal reinforcement, leading to enhanced ductile behavior. Furthermore, an increase in the spiral reinforcement ratio improves the lateral expansion resistance of the concrete, thereby enhancing its deformation capacity and strength. The longitudinal reinforcement ratio is a significant design parameter that influences the performance of bridge columns. Although it does not have a proportional effect, it has been observed to increase the ultimate bearing capacity of the column. Other design parameters, such as the column aspect ratio, and longitudinal reinforcement ratio have also been noted to significantly impact the performance of bridge columns when compared to other design parameters. Therefore, it is crucial to evaluate the performance of bridge columns under various design conditions and investigate the effect of specific design parameters to fully comprehend their performance. The present study aims to evaluate the performance of bridge columns by modifying design parameters, including longitudinal reinforcing steel grade, aspect ratio, longitudinal reinforcement ratio, and axial load ratio. The CHBDC performance limit guidelines were used to assess the performance of the bridge columns at various damage states. The CHBDC (CSA 2019b) outlines that the assessment of performance levels specified in the code shall be carried out either through non-linear time history analysis or pushover analysis. To achieve this evaluation, an analytical approach was adopted, using a verified OpenSees model for analysis. The analytical study was carefully designed to replicate the experimental program described in Chapter 4 of this thesis. 68 5.3.1 Numerical Modeling Both cyclic and pushover responses of both specimens are predicted in OpenSees (McKenna et al. 2000) using a displacement-based beam-column element which considers the distribution of plasticity along the element. The column was partitioned into six displacement-based beam-column elements, each spanning a length equivalent to the plastic hinge length (Lp) estimated according to Priestley and Park's (1996) (see Eq. 4). The beam-column element, with a length equivalent to the plastic hinge length, was comprised of ten integration points, whereas the remaining lengths of the column (i.e., L-Lp) was comprised of five equally sized elements, each with five integration points (see Figure 19) The displacement-based elements were defined between nodes that had a length equivalent to the plastic hinge length between them. The initial element was a zero-length element utilized to account for the effect of strain penetration between the column and footing. All the remaining elements with lengths equal to the plastic length were designated to make up the total length of the column. The base of the node was restrained as fixed in translation in all directions, and rotation. A circular fiber section was allocated to the elements. Lp = 0.08L + 0.022𝑓𝑦𝑒𝑑𝑏𝑙 ≥ 0.044𝑓𝑦𝑒𝑑𝑏𝑙 (24) whereas L is the span length from the critical section of the plastic hinge to the point of contraflexure in mm, 𝑓𝑦𝑒 stands for the yield strength of transverse reinforcement in MPa, and 𝑑𝑏𝑙 signifies the diameter of the longitudinal reinforcement. This fiber section comprises three material types, namely confined concrete, reinforcing steel and unconfined concrete sequentially allocated from the internal radius to the outer perimeter. Each discretized material definition was defined with respective geometric definitions, i.e., distance from the center of the section, and appropriate constitutive models to define the material properties. The constitutive material models were chosen to accurately represent the actual stress-strain response of the concrete and reinforcing steel. OpenSees Concrete01 is utilized to model the confined and unconfined concrete response of the bridge columns. Concrete01 uses the nonlinear uniaxial Kent- Scott concrete model. Concrete01 incorporates 69 concrete’s complex behavior, including strain-hardening and strain-softening of concrete, as well as compressive and tensile strength, and considers the zero tensile strength of concrete and linear unloading/loading stiffness degradation. The properties of the confined concrete for circular sections were predicted using Mander (Mander et al. 1988) confinement model. The reinforcing steel is modeled using the Steel02 uniaxial material in OpenSees (McKenna et al. 2000). This model is based material model originally developed by Giuffrè Menegotto Pinto (Giuffrè 1970), and later improved including by (Filippou et al. 1983). To capture the strain penetration effects between column-to-footing, a bond-slip model is introduced in the OpenSees model. The BondSP01 material model in OpenSees takes several input parameters which represent the different portions of the monotonic bar stress vs. slip response (Zhao and Sritharan 2007). Figure 19: Column discretization for numerical modeling 70 The present study employed the experimental results of the examined bridge columns to assess the accuracy of the OpenSees model in predicting the experimental response. The experimental outcomes, which are presented in Chapter 4, pertain to columns with aspect ratios of 3 and 6, reinforced with CSA G30.18 500W longitudinal reinforcement. The geometric and material characteristics of the columns are further elaborated on in Chapter 4 of this thesis. The parameters utilized to establish the constitutive material properties of the model are based on the experimental outcomes presented in Chapter 4. Furthermore, the parameters utilized for defining the constitutive models are provided in Appendix B. The model's accuracy at the global level was evaluated by comparing the force-displacement responses obtained from OpenSees and the experimental outcomes. The hysteresis response, i.e., the force-displacement relationship, is useful in measuring the accuracy of the model in predicting the maximum base shear, maximum drift, and associated stiffness degradation resulting from the buckling of longitudinal reinforcement. The hysteresis response of Units 1 and 2 was numerically predicted in OpenSees (McKenna et al. 2000). The hysteresis responses, as displayed in Figure 20, indicate that the developed numerical model possesses a high level of predictive accuracy. It is noteworthy that the accuracy of the prediction for Unit 2 surpasses that of Unit 1 in simulating the behavior of the column response. Unit 1 has shown a higher level of degradation during the last cycles, which is related to the post-fracture response. In general, the predicted force-displacement response accurately predicts both the lateral load capacity and the maximum displacement achieved by the experimentally measured response. 71 (a) Unit 1 (b) Unit 2 Figure 20: Experimental and predicted hysteresis response of (a) Unit 1, and (b) Unit 2. A comparison between experimentally measured and predicted force-displacement envelopes is provided in Figure 21. Pushover response curves developed in OpenSees have good correlation with slight deviation in the regions beyond yielding where the tested columns have shown higher level degradation due to stiffness degradation associated with buckling of longitudinal reinforcement. (a) (b) Figure 21: Measured and predicted force-displacement response envelopes for (a) Unit 1 and (b) Unit 2. 5.3.2 Parametric Study A parametric analysis was undertaken to examine the impact of reinforcement grade, steel ratio, aspect ratio, and axial load ratio. The examination involved conducting quasi-static cyclic analysis of several circular bridge columns modeled in OpenSees (McKenna et al. 2000), with varying design 72 parameters. The numerical program was configured to simulate the experimental test program, hence the validated models developed above were utilized for the parametric study, with specific parameters under investigation varying. Moreover, the analysis employed an identical loading protocol as the experimental study, while multiplying the protocol with specific reference yield for each bridge model. The determination of the reference yield for the bridge models was accomplished using a bi-linear approximation developed in CUMBIA (Montejo and Kowalsky 2007). Various damage states were identified using performance limit state criteria from the CHBDC provided in Table 11 at the end of the analysis. The CHBDC identifies four damage states based on the maximum limits of concrete and longitudinal steel strain. The drift ratio of the bridge column models was determined for each damage state by utilizing the material strain limits. The drift response outcomes are presented in Figure 22 for various models of bridge columns. Different symbols are used to indicate the drift of the four damage states for each bridge column. A vertical line is used to differentiate bridge columns of comparable nature identified by class number, with only one specific parameter being varied in each column (varying parameters are highlighted in bold). The initial investigation i.e., Class 1, concerns the examination of the effect of reinforcement grade on the performance of the bridge columns designed to possess comparable flexural capacity. The investigation of the impact of reinforcement grade was conducted under two conditions by changing the steel ratio i.e., i.e., with varying l and under the same l. In the first case where the l was changed, the bridge models containing ASTM A706 Grade 420 exhibited superior performance, reaching the four damage states at higher drift. For the second condition of constant l, both types of rebars displayed comparable performance, with CSA G30.18 500W reaching damage states 3 and 4 at slightly higher drift. The subsequent investigations i.e., Class 2 and 3, focused on the impact of axial load ratio, revealing that bridge column models with lower axial load ratios exhibited better performance for both CSA G30.18 500W and ASTM A706 420 reinforced columns. The fourth and fifth classes were also included in the investigation to assess the impact of aspect ratio with L/D of 3 73 and 6. The results indicate that bridge models with higher aspect ratios exhibited better performance for both rebar types. Figure 22: Measured drift results from parametric study. 5.4 Summary A numerical model that was calibrated using the experimental results was subsequently utilized to conduct a parametric study that examined the effects of various parameters, such as reinforcement grade, steel ratio, aspect ratio, and axial load ratio. The columns' performance was then assessed using code-based performance criteria, existing buckling limit state models, and column capacity as well as the overstrength factors. The effects of various parameters, such as reinforcement grade, steel ratio, aspect ratio, and axial load ratio were studied. The columns' performance was then assessed using code-based performance criteria, existing buckling limit state models, and energy dissipation capacities. The results show that the overstrength factors, which were computed through the ratio of the tested moment capacity to the nominal moment capacity, indicate that columns that are reinforced with steel of lower grades exhibit larger overstrength factors in comparison to those that are reinforced with HSS. This is attributable to the reduced steel ratios of columns reinforced with HSS. The existing buckling models of longitudinal reinforcement were effective in predicting the maximum compressive 74 strain of the longitudinal rebar before buckling. The findings of the study suggest that, in terms of reinforcing grade, bridge models comprising ASTM A706 Grade 420 demonstrated superior performance, achieving the four damage states at higher drift. Additionally, bridge column models with lower axial load ratios demonstrated better performance for both CSA G30.18 500W and ASTM A706 420 reinforced columns, while bridge column models with higher aspect ratios also exhibited better performance for both types of rebars. 75 CHAPTER 6: SEISMIC DESIGN AND ANALYSIS OF BRIDGE COLUMNS REINFORCED WITH REBAR TYPES OF CSA G30.18 500W, CSA G30.18 400W, AND ASTM 1035 GRADE 690 6.1 Background The use of high-strength steel (HSS) reinforcement in concrete structures has been gaining popularity. However, concerns have been raised about the ductility of structures reinforced with HSS, particularly when subjected to strong earthquakes. To this end, this research compares the seismic performance of bridge columns constructed with three different types of rebars, namely regular rebar CSA G30.18 400W, and HSS rebars of CSA G30.18 500W, and ASTM 1035 Grade 690. The reinforced concrete (RC) column design matrix comprising several models with varying design parameters was generated. Nonlinear static pushover analyses were then conducted on each column model to compare their drift ratios at various damage states. To further compare the seismic performance of these bridge columns, dynamic nonlinear time history analyses were conducted, and their seismic performances were presented through fragility curves for the various damage states. This study aims to provide engineers with useful information regarding the comparative seismic response of columns reinforced with regular and HSS reinforcement, as well as the seismic design of RC bridge columns using HSS rebars. Bridges are essential components of transportation infrastructure, connecting cities and regions. Damage to bridge structures can cause severe disruptions to traffic, resulting in economic losses and even fatalities. To improve the seismic performance of bridges, engineers have implemented several measures, such as using stronger materials including high-strength concrete and steel. However, before using high-strength steel (HSS) reinforcement in reinforced concrete (RC) bridge columns located in seismic zones, it is important to address some critical issues. Firstly, it is crucial to ensure that the increased strength does not compromise the ductility of the structures. Secondly, it is essential to be able to model the post-yielding behaviour of RC members with HSS reinforcement. Bridge columns are ductile members, and members connected to columns, 76 such as column caps and foundations, are capacity-protected members. Before the implementation of HSS reinforcement, engineers have to be able to predict the overstrength/probable resistance of bridge columns so that other capacity-protected members can be properly designed. This study performs a preliminary evaluation and comparison of RC columns with different types of reinforcing steel. This study compares the seismic performance of bridge columns reinforced with various types of longitudinal reinforcing steel rebars, including regular rebar CSA G30.18 400W, and HSS rebars of CSA G30.18 500W and ASTM 1035 Grade 690. Static pushover and analytical fragility curves are presented. Several bridge column designs were conducted considering different parameters including specified concrete strength (f'c), aspect ratio (L/D), transverse reinforcement ratio (s), and axial load ratio (P/Ag•fc). However, the focus of this paper is on the effects of different types of reinforcing steel. This study aims to develop an understanding of the seismic performance of bridge columns reinforced with longitudinal rebar types of CSA G30.18 400W, CSA G30.18 500W and ASTM A1035 Grade 690 under different design scenarios. The comparison of seismic performance is achieved through fragility analysis, which has been widely employed to evaluate the probability of reaching a given damage state for given levels of seismic intensities, such as Peak Ground Acceleration (PGA) (Kibboua et al. (2011) and Mosleh et al. (2016)). For instance, Karim et. al (2003) designed bridge columns following Japanese seismic design guidelines and developed their corresponding fragility curves. Nonlinear dynamic response evaluations were carried out using strong motion records from Japan and the US, and the damage indices for the bridge columns were determined. Based on a collection of ground motions observed in Korea, Nguyen et al. (2018) also developed seismic fragility curves for bridge columns. A number of damage states were identified by nonlinear time history studies using a damage index expressed in terms of the column displacement ductility ratio. Avşar et al. (2011) developed analytical fragility curves for bridges built in Turkey before 1990. The seismic response of the bridges was analyzed by conducting a component-based approach where several engineering demand parameters were employed to study the 77 seismic response of bridge components. The study shows bridges having larger skew angles or single-column bents were the most seismically vulnerable structures. Nielson et al. (2007) developed analytical fragility curves for different bridge classes common to the central and southeastern United States. The study concluded that multispan steel girder bridges are the most seismically vulnerable while single-span bridges are the least vulnerable. Billah and Alam (2013) performed a seismic fragility assessment of a typical multi-span highway bridge in BC considering soil-structure interaction. They concluded that although the soil–structure interaction has some effect on the component fragility, this effect is not very significant at the bridge system level. A number of studies using fragility curves can be referred to in literature (Sarraf et al. (2018), Zourgui (2018), and Shinozuka et al. (2000)) 6.2 Design of Bridge Column This study focuses on the seismic performance of the bridge column models reinforced with different rebar types including CSA G30.18 400W, CSA G30.18 500W, and ASTM A1035 Grade 690. A prototype column is first designed with CSA-400W reinforcing steel. Based on the prototype column, a number of other equivalent designs are determined. In developing different design options, the flexural capacity of the different options remains the same as the prototype column. To consider the potential interactions with other design parameters, other varying parameters include concrete strength, aspect ratio of the column and transverse reinforcement ratios. Fragility curves are derived to compare the seismic performances. Numerical analyses are performed using the finite element software SeismoStruct (SeismoSoft. 2022). The parameters analyzed in this paper are presented in 13 including aspect ratios, reinforcing steel strengths, concrete strengths, and reinforcement ratios. When re-designing the bridge columns and to achieve the same flexural capacity as the prototype bridge column, a number of moment curvature analysis was performed in CUMBIA software (Montejo and Kowalsky 2007) until the moment curvature of the prototype bridge column and other equivalent designs are closely matched. The 78 column design options are developed with specified concrete strengths of 30 MPa and 45 MPa. Longitudinal reinforcement has yield strength, fy of 440 MPa, 587.7 MPa, and 774 MPa. Two cross sections with diameters of 406 mm, and 450 mm are considered. The column sections are relatively small as some of the design options will be tested in the lab in future studies. The effect of the transverse reinforcement ratio is also studied by using two types of 10M, and 20M spiral reinforcements of the same grade. In Table 13, bridge columns are grouped into 4 categories represented by letters a, b, c and d. Within each category, the only difference among the columns is the rebar type. For instance, 406-30-CSA-400W-a stands for bridge column with 406 mm diameter, 30 MPa concrete strength, having longitudinal reinforcement of rebar type CSA-400W, and belongs to column category a. The seismic performance evaluation will be focused on comparing bridge columns with different rebar types that belong to the same category, which means that the focus is on the effect of different rebar types. In Table 13, model 406-30-CSA-400W-a is the prototype column. All other columns are designed to have equivalent flexural strength compared with the prototype column. 79 Table 13: Column geometry and material matrix Specimen no. D fy f'c P/Ag.fc l s (mm) (MPa) (MPa) (%) (%) (%) 406-30-CSA-400W-a 406 440 30 7.72 2.16 1.18 406-30-CSA-500W-a 406 587.7 30 7.72 1.7 1.18 406-30-ASTM-A1035-a 406 774 30 7.72 1.24 1.18 406-45-CSA-400W-b 406 440 45 5.15 2.01 1.18 406-45-CSA-500W-b 406 587.7 45 5.15 1.7 1.18 406-45-ASTM-A1035-b 406 774 45 5.15 1.08 1.18 406-30-CSA-400W 406 440 30 7.72 2.32 0.71 406-30-CSA-500W 406 587.7 30 7.72 1.85 0.71 406-30-ASTM-A1035-c 406 774 30 7.72 1.24 0.71 406-30-CSA-400W-d 450 440 30 6.29 1.38 1.05 406-30-CSA-500W-d 450 587.7 30 6.29 1.13 1.05 406-30-ASTM-A1035-d 450 774 30 6.29 0.75 1.05 Note: D is the column diameter, fy is the steel strength, f'c is the concrete compressive strength, P/Ag.fc is the axial load ratio, l is the longitudinal reinforcement ratio, s is the transverse reinforcement ratio. 6.3 Numerical Modeling and Validation To study the seismic performance of the bridge columns listed in Table 13, finite element models were created in SeismoStruct (SeismoSoft. 2022). The models employed the Menegotto-Pinto steel model (Menegotto-Pinto 1973) and the Mander concrete model (Mander et al. 1998) to simulate the nonlinear material properties of the reinforcing steel rebar and concrete, respectively. The bridge columns were modeled using inelastic displacement-based elements (DBE) and were discretized into five equal-length elements along the height. 80 Figure 23: Column element discretization for modeling. The model validation is conducted by comparing experimental results of bridge column responses and simulated column responses via SeismoStruct (SeismoSoft. 2022) The model validations are performed for both regular steel reinforced columns and high-strength steel reinforced columns based on experimental works conducted by Moyer and Kowalsky (2003) and Restrepo et al. (2006) respectively as shown in Figure 24. It can be seen that the models can capture the responses of the tested columns with acceptable accuracy. 81 (a) (b) Figure 24: SeismoStruct model verification based on: (a) Moyer and Kowalsky (2003) (b) Restrepo et al. (2006). 6.4 Pushover Analysis To perform a preliminary comparison of the effects of different reinforcing steel on the lateral response of bridge columns, static pushover analysis is performed to predict the failure mechanisms and other important parameters such as base shear, yield displacement, and ductility capacity of the columns. Pushover analyses are conducted under a constant gravity load of 300 kN and monotonically increasing lateral loads. During the analysis, materials strains are recorded to identify damage states as per CHBDC (CSA 2019b) as shown in Table 14. The drift limit state values corresponding to the four damage states are also derived and presented in Table 14, which includes minimal damage, moderate damage, extensive damage, and probable replacement. These drift values are established using the concrete and longitudinal reinforcement strain limits provided in Table 14 The ratio of the drifts at Replacement to Minimal Damage ranges from 2.6 to 3.7, indicating the columns are generally ductile. The ratio of the drifts at Replacement to Minimal Damage can be defined as ductility. When comparing the ductility of RC columns reinforced with different reinforcing steel types, the columns with CSA G30.18 400W have an average ductility of 3.2, and the columns with CSA G30.18 500W have an average ductility of 3.0. The average ductility of columns reinforced with A1035 Garde 690 is 3.4. When comparing bridge columns of the same category, i.e., within 82 categories a, b, c, or d, columns with higher-strength steel reach the damage states at a higher drift ratio, meaning that high-strength steel delays the damage. For instance, for bridge category a, the drift ratios corresponding to Minimal Damage are 1.94%, 1.70%, and 1.55% for columns reinforced with ASTM A1035 Garde 690 (with yield strength fy of 774 MPa), CSA G30.18 500W (with yield strength fy of 587.7 MPa) and CSA G30.18 400W (with yield strength fy of 440 MPa), respectively. Pushover curves of all columns are presented in Figure 25 The pushover curves for columns in the same category are plotted in the same figure for comparison. Although efforts have been made to design all columns with the same strength, columns with longitudinal reinforcement of ASTM A1035 Grade 690 have lower yielding base shear compared with other columns. Columns with longitudinal reinforcement of CSA G30.18 500W tend to show higher strength compared to CSA G30.18 400W. a) b) c) d) Figure 25: Pushover response curves for columns of category: a) a b) b c) c, and d) d. 83 Table 14: Performance limit criteria from CHBDC Service Damage state Material strain limits Immediate Minimal damage c ≤ 0.006 s ≤ 0.01 Limited Repairable damage s ≤ 0.025 service disruption Extensive damage s ≤ 0.05 cc ≤ 0.8 cu life safety Probable replacement s ≤ 0.075 cc ≤ cu c = concrete compressive strain; s = flexural reinforcing steel strain; cc = confined concrete strain; and cu = ultimate confined concrete strain. 6.5 Ground Motion When using fragility analysis to compare the seismic performance, nonlinear time history analyses have to be performed first. For the nonlinear time history analysis, representative near-fault ground motions are selected from Pacific Earthquake Engineering Research Center (PEER 2011). The selected ground motions have a PGA ranging from 0.67g to 0.75g. Ground motions parallel to the fault are used to conduct the nonlinear time history analysis. A total of 12 ground motions are used to meet the requirements in CHBDC (CSA 2019b). Ground motions are scaled to match a uniform hazard design response spectrum of Vancouver for a 2% probability of exceedance in 50 years. A wavelets algorithm by Hancock et al. (2006) available in SeismoMatch (SeismoSoft 2023) is used to scale the ground motions. Figure 26 shows the individual records before and after matching to the design spectrum. The Mean spectrum from the matched records is slightly greater than the target spectrum. The scaled ground motions are then utilized as the inputs of nonlinear dynamic time history analysis of the column models. 84 (a) (b) Figure 26: Ground motion records: (a) unmatched design spectrum (b) matched to design spectrum The seismic fragility of bridge columns was studied to compare the performance of RC columns with different types of reinforcing steel. To develop the seismic fragility curves, Incremental Dynamic Analysis (IDA) is performed, which involves conducting a series of nonlinear dynamic analyses of the structures subject to scaled ground motions. 6.6 Fragility Analysis and Results Figure 27 presents the fragility curves for the bridge columns. The fragility curves are developed based on the results of pushover analysis and nonlinear time history analysis. Fragility curves for the bridge columns that belong to the same category are plotted in one figure for comparison. The legend of the figures is provided in the footnotes. The damage states are denoted and represented by different line colors. And line style represents different rebar types of the bridge columns, where solid line, fine dashed, and wide-spaced lines denote CSA G30.18 400W, CSA G30.18 500W, and ASTM A1035 Grade 690 rebar types, respectively. The development of fragility curves is based on the procedures suggested by Cornell et al. (2002). The fragility curves show that for the same level of seismic intensity, i.e., PGA, bridge columns reinforced with ASTM A1035 Grade 690 tend to have a lower probability of failure across most PGA ranges. For instance, in the fragility curves for bridge category b (see Figure 27 below), the fragility curve for minimal damage state (colored in red) shows that columns reinforced with ASTM 1035 (i.e., 85 wide spaced line) have a lower probability of damage compared to columns with CSA G30.18 500W, and CSA G30.18 400W. Moreover, bridge columns reinforced with CSA G30.18 500W have a lower probability of suffering a minimal damage state compared to columns reinforced with CSA G30.18 400W. a) b) c) d) Legend Figure 27: Fragility curve response for bridge columns of the category of a) a, b) b, c) c, and d) d. 86 6.7 Summary This study compared the seismic response of bridge columns reinforced with various rebar types of CSA G30.18 400W, CSA G30.18 500W, and ASTM A1035 Grade 690. Pushover analyses were performed to predict drifts corresponding to different damage states. It was found that bridge columns with high strength rebars have higher drift capacity corresponding to the same level of damage states, meaning that high strength rebar delays the damage. In addition, the ductility of different columns is calculated using the drifts at the Replacement Damage state and Minimal Damage State. This ratio ranges from 2.6 to 3.7, indicating the columns are generally ductile. The columns with CSA G30.18 400W, CSA G30.18 500W, and A1035 Garde 690 have average ductility of 3.2, 3.0, and 3.4. Thus, the columns with A1035 Garde 690 are the most ductile and the columns with CSA G30.18 500W are the least ductile. However, the parameters and number of analyses in this preliminary are limited and this conclusion may not be generalized. Further studies are needed to generalize this conclusion while considering higher axial load ratios, larger column diameter, validated low cycle fatigue models for different steel reinforcements, etc. After the pushover analysis, nonlinear time history analyses were performed to compare the performance of bridge columns subject to earthquake ground motions. The fragility curves show that the probability of damage was generally lower for bridge columns reinforced with high strength rebars. 87 CHAPTER 7: SUMMARY AND CONCLUSION 7.1 Summary and Conclusion The presented study has provided experimental and numerical findings in relation to the seismic performance of bridge columns reinforced with HSS. The focus of this study was to evaluate the applicability of HSS in Canadian construction and to propose design recommendations that can be applicable to bridge columns reinforced with HSS. To achieve this, several experimental investigations and numerical studies were conducted. The specific objectives achieved in this study include: 1) the evaluation of the low-cycle fatigue performance of CSA G30.18 500W HSS through experimental tests, 2) the experimental evaluation of the seismic performance of bridge columns reinforced with CSA G30.18 500W as their longitudinal reinforcement, 3) the proposal of design limit state values that are applicable to bridges containing CSA G30.18 500W HSS as their longitudinal reinforcement in their sub-structure members, and 4) the development of the fragility curve response of bridge columns containing both regular steel of ASTM A706 Grade 420, and HSS of CSA G30.18 500W, and ASTM A1035 Grade 690. The study commenced with a discussion on the response of reinforced concrete columns and the various design parameters that influence it. This was accomplished by conducting a comprehensive literature review of prior works that involved reinforced concrete columns, with a focus on the seismic response of the columns. Subsequently, the study evaluated the low-cycle fatigue performance of the CSA G30.18 500W by comparing it to previous experimental works on the low-cycle fatigue response of conventional steel rebars. Additionally, monotonic tension tests were conducted to obtain significant mechanical properties and the stress-strain response of the material. A stress-strain response for bar sizes of 12.7 mm and 15.8 mm was generated, characterized by an initial linear portion, followed by yielding and yield plateau, and finally the strain hardening portion. The tensile test results indicated that the reinforcing steel has sufficient ductility and strength. The tensile to yield strength ratio was greater than 1.25, which is the minimum requirement by codes for applicability in the seismic design of 88 members. The low-cycle fatigue study was conducted considering various test variables, including the bar size, unsupported length, and strain amplitude. The effect of bar size was observed to be negligible, while the strain amplitude and unsupported length had a significant impact on the response of the rebar. An increase in the strain amplitude was observed to reduce the low-cycle fatigue response of the rebar. Similarly, higher bar unsupported lengths gave reduced fatigue life of the rebar. Existing plastic strain-based and energy-based low-cycle fatigue models were utilized to predict the low-cycle fatigue response of the reinforcing steel. The effect of inelastic buckling was incorporated into the low-cycle fatigue models. The results demonstrate that the proposed models had better accuracy in predicting the low-cycle fatigue response of the rebar. The subsequent chapter presents experimental findings on the seismic performance of bridge columns that have been reinforced with CSA G30.18 500W HSS. Initially, a brief overview of the design and construction of the reinforced concrete columns is provided, followed by the presentation of experimental results. The design of the column specimens was achieved by following the force-based design guidelines stipulated in the CHBDC. Two column specimens, with aspect ratios of 3 and 6, were prepared for testing at the Structural Laboratory of the University of British Columbia, Okanagan. The experimental results, which include the force-displacement hysteretic response, measurements from installed instruments, and the various damages that were measured, are presented. Additionally, the experimental works were compared with columns reinforced with ASTM A706 Grade conventional reinforcing steel. The hysteresis response indicates that the columns showed a comparable level of drift levels when compared to columns reinforced with conventional reinforcing steel. Maximum drift values of 4.35% and 7.3% were recorded for both specimen Units 1 and 2. The energy dissipation of the columns was also analyzed by computing the hysteretic dissipated energy under the force-displacement response using Simpson's integral rule. The dissipated energy was comparable to that of the columns containing regular steel, with energy dissipation by columns with HSS at the initial stage being higher than those of the columns reinforced with regular steel and ultimately with slightly lower values than those reinforced with conventional steel. Instrument measurements of strain gauges and 89 strain pots are also presented, which reveal the strain in the longitudinal reinforcing steel rebars and the curvature of the column at various heights, respectively. Column capacity of shear and moment capacity were also presented together with the overstrength factors. The results revealed that the overstrength factors for columns reinforced with HSS were lower than those for the columns reinforced with conventional steel. This was associated with the fact that the columns having HSS contain a less longitudinal reinforcement ratio, which resulted in lower overstrength factor values. The following portion of this examination was based on experimental results of the seismic response of the column Units presented in Chapter 4. Within this chapter, the various types of damages recorded during the column test were employed to establish the limit-states for performance-based design of bridges containing CSA G30.18 500W as their longitudinal reinforcement in their sub-structure components i.e., columns. The present limit-states in the CHBDC are based on regular steel of CSA G30.18 400W. The limit state values for performance-based design in CHBDC were established in accordance with material strains of concrete and reinforcing steel strains. Then, the experimental results were employed to establish the limit state values for columns encompassing the HSS. The acquired limit-states presented comparable limit-state values to those established for regular steel. Therefore, only minor changes were required in the limit-state values which portray adequate performance of the bridge columns. Since the considered experimental column tests were inadequate for two test Units, further investigation was carried out to investigate the performance of the bridge columns reinforced with CSA G30.18 500W as their longitudinal reinforcement. The numerical investigation encompassed evaluating the performance of the bridge columns with the effect of various design parameters considered, including the impact of reinforcing grade, longitudinal reinforcement steel ratio, aspect ratio, and axial-load ratio. The numerical investigation was meticulously designed to simulate the experimental program of the column tests where a similar loading protocol of quasi-cyclic displacement-controlled loading test with constant axial load was applied. The results show that for the effect of reinforcing grade, the bridge models comprising ASTM A706 Grade 420 displayed superior performance, achieving the four damage states at higher drift. Moreover, bridge column models with 90 lower axial load ratios demonstrated better performance for both CSA G30.18 500W and ASTM A706 420 reinforced columns. Bridge column models with higher aspect ratios also exhibited better performance for both types of rebars. The final portion of the research was directed at comparing the seismic reaction of various bridge columns, which were reinforced with CSA G30.18 400W, CSA G30.18 500W, and ASTM A1035 Grade 690 rebar types. To evaluate the performance of the bridge columns, a numerical program was utilized in the study including pushover analysis, which aimed to determine the drifts corresponding to the various damage states that had been established in CHBDC. Additionally, non-linear time-history analysis was performed through incremental dynamic analysis, whereby 11 ground motions were incrementally applied to the column models in order to determine their fragility curve response. The fragility curves showed that the probability of damage was generally reduced for bridge columns that had been reinforced with high strength rebars. The research showed that bridge columns reinforced with high strength rebars possessed greater drift capacity for the same degree of damage states, indicating that high strength rebar can postpone damage. This thesis comprises a comprehensive investigation on the low-cycle fatigue response of CSA G30.18 500W steel rebar, as well as the seismic performance of bridge columns through both experimental and numerical works. The failure mode of compression members, such as columns, can be governed by the low-cycle fatigue failure of longitudinal rebar during a seismic event. Therefore, it was deemed crucial to examine the performance of CSA G30.18 500W prior to its application in seismic design. Furthermore, comprehending the low-cycle fatigue response and performance of the RC columns is vital to correlating failure limit state in design codes with seismic damage levels of RC members. As there is a lack of experimental work and guidelines on the application of CSA G30.18 500W steel for seismic design, this study provides a considerable amount of information regarding the performance of such reinforcing steel. Moreover, the provided performance limit-states of RC bridge columns obtained from this study could be utilized for the development of a performance-based design procedure of bridges involving CSA G30.18 500W as their longitudinal reinforcement. 91 7.2 Recommendation for Future Study The limitations in this study include the following: • In the present investigation, solely the low-cycle fatigue tests for CSA G30.18 500W HSS were presented. Hence, it is recommended to conduct low-cycle fatigue tests for CSA G30.18 400W regular steel to comprehensively comprehend and evaluate the low-cycle fatigue performance of the HSS. • The experimental works related to the column tests in this study were confined to aspect ratio as the only test variable. Therefore, further experimental works are anticipated, wherein the effect of various design parameters, such as longitudinal reinforcement ratio, reinforcing grade, and axial load ratio, are taken into consideration. • The numerical modeling employed in this study does not account for the foundation flexibility and soil interaction. • Due to the limitation of the MTS testing machine capacity, the rebar size considered in this study was confined to 15.8 mm. Thus, tests with larger bar sizes, which are more common for seismic design applications, are expected. • The numerical study in this investigation was conducted on a prototype bridge based on the geometric details of the tested large-scaled column specimens. However, these large-scale prototype bridge columns are unlikely to be representative of real-world bridge columns. 7.3 Recommendation for Future Study The research work in this study could further be extended through an in-depth study of the following recommendations: • Low-cycle fatigue performance assessment of large bar diameter rebars could be conducted given the larger size bar diameter is widely used for seismic applications. 92 • The column test experimental program could be extended with further testing of bridge columns considering various additional design parameter variations including but not limited to the effect of longitudinal reinforcement ratio, axial load ratio, and spiral reinforcement ratio. • The developed performance limit-states could be further verified by testing more column specimens so that they could be included in the CHBDC design code. • The fragility curve study could be further expanded by considering a larger database of ground motions, and a more realistic bridge geometry prototype for analysis with dimensions representative of real-world size. 93 Bibliography AASHTO. 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Test study on seismic performance of high-strength concrete columns with central reinforcement. Journal of Building Structures, 31(12), 83. 118 Appendices Appendix A Table 15: Properties of the Concrete01 Constitutive Model Used for Numerical Model Validation of Units Tested in this Study. Specimen Concrete Type Fpc (MPa) epsc0 Fpcu (MPa) epsU Unit 1 Unconfined -36.7 -0.0020 0.0 -0.0040 Confined -51.8 -0.0064 -37.3 -0.0145 Unit 2 Unconfined -38.0 -0.0020 0.0 -0.0040 Confined -52.5 -0.0072 -48.7 -0.0148 Table 16: : Properties of the Steel02 Constitutive Model Used for Numerical Model Validation Specimen fy (MPa) Es (MPa) b R0 cR1 cR2 Unit 1 584.3 190300 0.01 15 0.925 0.15 Unit 2 584.3 190300 0.028 15 0.925 0.15 119 Appendix B: Pictures from Construction Procedure Figure 28: Column specimen rebar cage preparation. 120 Figure 29: Column rebar cage Assembled. 121 Figure 30: Formwork installation of specimens. Figure 31: Column specimens after concrete casting 122 Figure 32: Column specimen attached for testing. 123 Figure 33: Cylinder preparation for concrete strength test. 124 Appendix C: Additional Pictures from Test C.1 Unit 1 Figure 34: Concrete spalling at south face of Unit 1 at drift ratio of 1.6% (at end of displacement ductility of 1.5). Figure 35: Extent of damage and crack pattern at south face of Unit 1 at drift ratio of 2.1% (at end of displacement ductility of 2). 125 Figure 36: Extent of damage and crack pattern at north face of Unit 1 at drift ratio of 5.89% (at end of displacement ductility of 4) Figure 37: Damage profile of Unit 1 at the end of the test. 126 Figure 38: Sample cylinder compressive test for specimen Unit 1. 127 C.1 Unit 2 Figure 39: Concrete cover spalling of on north face of Unit 2 at drift ratio of 2.7% (beginning of displacement ductility 3). Figure 40: Damage profile and crack pattern of Unit 2 on north face at drift ratio of 3.6% (end of displacement ductility of 4). 128 Figure 41: Damage profile and crack pattern of Unit 2 on north face at drift ratio of 5.47% (beginning cycle of displacement ductility of 6). Figure 42: Damage profile and crack pattern of Unit 2 on north face at drift ratio of 5.47% (at end of second cycle of displacement ductility of 6). 129 Figure 43: Damage profile and crack pattern of Unit 2 on north face at drift ratio of 7.2% (at end of first cycle of displacement ductility of 8). Figure 44: Damage profile of Unit 2 at the end of the test. 130 Figure 45: Sample cylinder compressive test for specimen Unit 2. 131 Appendix D: Additional Measurements from Installed Instruments. Figure 46: Strain measurements in longitudinal rebar of Unit 1 at face of footing. Figure 47: Strain measurements in longitudinal rebar of Unit 1 due to penetration effects at 150 mm below surface of footing. 132 Figure 48: Strain measurements in longitudinal rebar of Unit 2 at face of footing. Figure 49: Strain measurements in longitudinal rebar of Unit 2 due to penetration effects at 150 mm below surface of footing. 133 Figure 50: Concrete cover strain measurements of Unit 2 at 75 mm above the footing. Figure 51: Typical concrete cylinder stress-strain response for column concrete mix. 134 Figure 52: Typical concrete cylinder stress-strain response for footing concrete mix. 135 Appendix E TCL OpenSees code used for modeling of bridge columns: wipe model basic -ndm 2 -ndf 3 node 1 0.000 0.000 node 3 0.000 0.000 node 44 0.000 0.000 node 4 16.000000 0.000 node 5 32.000000 0.000 node 6 46.000000 0.000 node 7 64.000000 0.000 node 8 80.000000 0.000 node 2 96.000000 0.000 fix 1 1 1 1; fix 3 0 1 0; equalDOF 3 44 1 3 # Define uniaxial materials required for section file mkdir Push_Moy_DL6; # create data directory uniaxialMaterial Concrete01 1 -5.2 -0.002600 -0.000000 -0.004000 uniaxialMaterial Concrete01 2 -7.508 -0.006446 -5.49700000 -0.01161554 #uniaxialMaterial ReinforcingSteel 3 84.651 111.18600 29000.0000 824.928 0.00800 0.080 #uniaxialMaterial Steel01 3 84.651 27550.00 0.019285163 0 55 0 55 #uniaxialMaterial Bond_SP01 4 68.400000 0.016797 100.9780000 0.604704 0.500000 0.500000 uniaxialMaterial Steel02 3 84.651 27550.0 0.028 18 0.925 0.15 #uniaxialMaterial Bond_SP01 4 60.030000 0.013000828 74.0 0.455028992 0.400000 0.50000 uniaxialMaterial Bond_SP01 4 84.651 0.013001136 111.1860 0.455039767 0.5000 1.00000 section Fiber 1 { patch circ 2 20 10 0.0 0.0 0.0 7.00 0.0 360.0 patch circ 1 20 3 0.0 0.0 7.000 8.000000 0.0 360.0; layer circ 3 12 0.31 0.0 0.0 6.6875 0.0 330; } section Fiber 2 { patch circ 2 20 10 0.0 0.0 0.0 7.00 0.0 360.0 patch circ 1 20 3 0.0 0.0 7.000 8.000000 0.0 360.0; layer circ 3 12 0.31 0.0 0.0 6.6875 0.0 330; } geomTransf Linear 1 element zeroLengthSection 7 1 3 2 136 element dispBeamColumn 1 44 4 10 1 1; element dispBeamColumn 2 4 5 5 1 1; element dispBeamColumn 3 5 6 5 1 1; element dispBeamColumn 4 6 7 5 1 1; element dispBeamColumn 5 7 8 5 1 1; element dispBeamColumn 6 6 2 5 1 1; set eleForRecord 1; set sectionRecord 2; uniaxialMaterial Elastic 300 515359.36; uniaxialMaterial Elastic 400 9.000E+009; element zeroLength 10 3 44 -mat 400 300 400 -dir 1 2 6; recorder Element -file Push_Moy_DL6/unc-left-430.out -time -ele $eleForRecord section $sectionRecord fiber -6.6875 0.0 1 stressStrain recorder Node -file Push_Moy_DL6/FD-430.out -time -node 2 -dof 2 disp; recorder Element -file Push_Moy_DL6/unc-right-430.out -time -ele $eleForRecord section $sectionRecord fiber 8.0000 0.0 1 stressStrain recorder Element -file Push_Moy_DL6/con-right-430.out -time -ele $eleForRecord section $sectionRecord fiber 7.4000 0.0 2 stressStrain pattern Plain 1 "Constant" { load 2 -166.5 0.0 0.0; } integrator LoadControl 0; system SparseGeneral -piv; test NormDispIncr 1.0e-4 10; numberer Plain; constraints Plain; algorithm KrylovNewton; analysis Static; analyze 1; pattern Plain 2 "Linear" { load 2 0.0 1.0 0.0; } puts " .... Start Cycle : 0.25 (Peak Disp +/-)" integrator DisplacementControl 2 2 0.010000 ; analyze 17 integrator DisplacementControl 2 2 -0.010000 ; analyze 35 integrator DisplacementControl 2 2 0.010000 ; analyze 17 puts ". ..... 0.25 Done " puts " .... Start Cycle : 0.5 (Peak Disp +/-)" integrator DisplacementControl 2 2 0.010000 ; analyze 39 integrator DisplacementControl 2 2 -0.010000 ; analyze 79 integrator DisplacementControl 2 2 0.010000 ; analyze 39 puts ". ..... 0.5 Done " puts ". ..... 0.75 Done " 137 puts " .... Start Cycle : 0.25 (Peak Disp +/-)" integrator DisplacementControl 2 2 0.010000 ; analyze 63 integrator DisplacementControl 2 2 -0.010000 ; analyze 126 integrator DisplacementControl 2 2 0.010000 ; analyze 63 puts ". ..... 0.75 Done " puts " .... Start Cycle : 1 (Peak Disp +/-)" integrator DisplacementControl 2 2 0.010000 ; analyze 87 integrator DisplacementControl 2 2 -0.010000 ; analyze 173 integrator DisplacementControl 2 2 0.010000 ; analyze 87 integrator DisplacementControl 2 2 0.010000 ; analyze 87 integrator DisplacementControl 2 2 -0.010000 ; analyze 173 integrator DisplacementControl 2 2 0.010000 ; analyze 87 integrator DisplacementControl 2 2 0.010000 ; analyze 87 integrator DisplacementControl 2 2 -0.010000 ; analyze 173 integrator DisplacementControl 2 2 0.010000 ; analyze 87 puts ". .....1 Done " puts " .... Start Cycle : 1.5 (Peak Disp +/-)" integrator DisplacementControl 2 2 0.010000 ; analyze 130 integrator DisplacementControl 2 2 -0.010000 ; analyze 260 integrator DisplacementControl 2 2 0.010000 ; analyze 130 integrator DisplacementControl 2 2 0.010000 ; analyze 130 integrator DisplacementControl 2 2 -0.010000 ; analyze 260 integrator DisplacementControl 2 2 0.010000 ; analyze 130 integrator DisplacementControl 2 2 0.010000 ; analyze 130 integrator DisplacementControl 2 2 -0.010000 ; analyze 260 integrator DisplacementControl 2 2 0.010000 ; analyze 130 puts ". .....1.5 Done " puts " .... Start Cycle : 2 (Peak Disp +/-)" integrator DisplacementControl 2 2 0.010000 ; analyze 173 integrator DisplacementControl 2 2 -0.010000 ; analyze 347 integrator DisplacementControl 2 2 0.010000 ; analyze 173 integrator DisplacementControl 2 2 0.010000 ; analyze 173 integrator DisplacementControl 2 2 -0.010000 ; analyze 347 integrator DisplacementControl 2 2 0.010000 ; analyze 173 integrator DisplacementControl 2 2 0.010000 ; analyze 173 integrator DisplacementControl 2 2 -0.010000 ; analyze 347 integrator DisplacementControl 2 2 0.010000 ; analyze 173 puts ". .....2 Done " puts " .... Start Cycle : 3 (Peak Disp +/-)" integrator DisplacementControl 2 2 0.010000 ; analyze 260 integrator DisplacementControl 2 2 -0.010000 ; analyze 519 integrator DisplacementControl 2 2 0.010000 ; analyze 260 integrator DisplacementControl 2 2 0.010000 ; analyze 260 integrator DisplacementControl 2 2 -0.010000 ; analyze 519 integrator DisplacementControl 2 2 0.010000 ; analyze 260 integrator DisplacementControl 2 2 0.010000 ; analyze 260 138 integrator DisplacementControl 2 2 -0.010000 ; analyze 519 integrator DisplacementControl 2 2 0.010000 ; analyze 260 puts ". .....3 Done " puts " .... Start Cycle : 4 (Peak Disp +/-)" integrator DisplacementControl 2 2 0.010000 ; analyze 346 integrator DisplacementControl 2 2 -0.010000 ; analyze 691 integrator DisplacementControl 2 2 0.010000 ; analyze 346 integrator DisplacementControl 2 2 0.010000 ; analyze 346 integrator DisplacementControl 2 2 -0.010000 ; analyze 691 integrator DisplacementControl 2 2 0.010000 ; analyze 346 integrator DisplacementControl 2 2 0.010000 ; analyze 346 integrator DisplacementControl 2 2 -0.010000 ; analyze 691 integrator DisplacementControl 2 2 0.010000 ; analyze 346 puts ". .....4 Done " puts " .... Start Cycle : 6 (Peak Disp +/-)" integrator DisplacementControl 2 2 0.010000 ; analyze 519 integrator DisplacementControl 2 2 -0.010000 ; analyze 1039 integrator DisplacementControl 2 2 0.010000 ; analyze 519 integrator DisplacementControl 2 2 0.010000 ; analyze 519 integrator DisplacementControl 2 2 -0.010000 ; analyze 1039 integrator DisplacementControl 2 2 0.010000 ; analyze 519 integrator DisplacementControl 2 2 0.010000 ; analyze 519 integrator DisplacementControl 2 2 -0.010000 ; analyze 1039 integrator DisplacementControl 2 2 0.010000 ; analyze 519 puts ". .....6 Done " puts " .... Start Cycle : 8 (Peak Disp +/-)" integrator DisplacementControl 2 2 0.010000 ; analyze 693 integrator DisplacementControl 2 2 -0.010000 ; analyze 1385 integrator DisplacementControl 2 2 0.010000 ; analyze 693 integrator DisplacementControl 2 2 0.010000 ; analyze 693 integrator DisplacementControl 2 2 -0.010000 ; analyze 1385 integrator DisplacementControl 2 2 0.010000 ; analyze 693 integrator DisplacementControl 2 2 0.010000 ; analyze 693 integrator DisplacementControl 2 2 -0.010000 ; analyze 1385 integrator DisplacementControl 2 2 0.010000 ; analyze 693 puts ". .....8 Done "
Thesis/Dissertation
eng
Civil Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Alam, M. Shahria
Seismic response of circular concrete columns reinforced with CSA G30.18 500W steel
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