Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Amiri Gheshlaghi, Amirhossein
Master of Applied Science - MASc
University of British Columbia
Reinforced concrete core wall buildings are the prevalent construction method for high-rise buildings in North America. The seismic performance of these buildings largely depends on the hysteretic response of coupling beams. This thesis studies the impact of design details on the hysteretic response of coupling beams in two phases. Phase one focuses on the diagonally-reinforced coupling beams, while phase two investigates the steel and composite coupling beams. A new database, including 51 tested diagonally-reinforced coupling beams, was developed in phase one. This database investigated the effect of design considerations, such as aspect ratio, beam and diagonal ties, axial restraint, and embedded longitudinal reinforcing, on the structural performance parameters, such as maximum shear capacity, initial stiffness, and rotational capacity of the diagonally-reinforced coupling beams. The analysis of this database led to new insights into the performance of diagonally-reinforced coupling beams. One key finding shows that the rotational capacity of low aspect ratio beams depends on the diagonal reinforcing ratio. Consequently, new design recommendations have been developed. The second phase focused on developing improved wall-to-beam connection detailing for steel and composite coupling beams. The current method, requiring the steel beam to be embedded into the wall with a long embedment length, is challenging to construct. Alternatively, welded bars called auxiliary transfer bars could be utilized to reduce embedment length, which is also challenging to construct. This thesis proposes a new connection method that utilizes compression steel bars, supporting the embedded beam in the bearing and making it easier to construct. The mechanics of the innovative detailing have been explained, and design plots have been provided. To investigate the seismic performance of this new detailing, a finite element model was developed using DIANA FEA 10.6 and verified through experimental studies from the literature. Overall, it was found that the structural performance of steel and composite coupling beams, such as shear force capacity, initial stiffness, and rotational capacity, can be improved by implementing this new connection detailing. Both phases of this thesis offer new insights into improving the seismic performance of diagonally-reinforced, steel, and composite coupling beams, resulting in higher-performing high-rise buildings in Canada.
DATABASE ANALYSIS OF DIAGONALLY- REINFORCED COUPLING BEAMS AND DEVELOPMENT OF NEW CONNECTION DETAILING FOR STEEL AND COMPOSITE COUPLING BEAMS by Amirhossein Amiri Gheshlaghi 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) April 2024 © Amirhossein Amiri Gheshlaghi, 2024 ii The following individuals certify that they have read, and recommend to the College of Graduate Studies for acceptance, a thesis entitled: DATABASE ANALYSIS OF DIAGONALLY- REINFORCED COUPLING BEAMS AND DEVELOPMENT OF NEW CONNECTION DETAILING FOR STEEL AND COMPOSITE COUPLING BEAMS submitted by Amirhossein Amiri Gheshlaghi in partial fulfillment of the requirements of the degree of Master of Applied Science. Dr. Lisa Tobber, School of Engineering Supervisor Dr. Perry Adebar, University of British Columbia – Vancouver Supervisory Committee Member Dr. Mohammad Tiznobaik, School of Engineering Supervisory Committee Member Dr. Mohammad Zarifi, School of Engineering University Examiner iii Abstract Reinforced concrete core wall buildings are the prevalent construction method for high-rise buildings in North America. The seismic performance of these buildings largely depends on the hysteretic response of coupling beams. This thesis studies the impact of design details on the hysteretic response of coupling beams in two phases. Phase one focuses on the diagonally-reinforced coupling beams, while phase two investigates the steel and composite coupling beams. A new database, including 51 tested diagonally-reinforced coupling beams, was developed in phase one. This database investigated the effect of design considerations, such as aspect ratio, beam and diagonal ties, axial restraint, and embedded longitudinal reinforcing, on the structural performance parameters, such as maximum shear capacity, initial stiffness, and rotational capacity of the diagonally-reinforced coupling beams. The analysis of this database led to new insights into the performance of diagonally-reinforced coupling beams. One key finding shows that the rotational capacity of low aspect ratio beams depends on the diagonal reinforcing ratio. Consequently, new design recommendations have been developed. The second phase focused on developing improved wall-to-beam connection detailing for steel and composite coupling beams. The current method, requiring the steel beam to be embedded into the wall with a long embedment length, is challenging to construct. Alternatively, welded bars called auxiliary transfer bars could be utilized to reduce embedment length, which is also challenging to construct. This thesis proposes a new connection method that utilizes compression steel bars, supporting the embedded beam in the bearing and making it easier to construct. The mechanics of the innovative detailing have been explained, and design plots have been provided. To investigate the seismic performance of this new detailing, a finite element model was developed iv using DIANA FEA 10.6 and verified through experimental studies from the literature. Overall, it was found that the structural performance of steel and composite coupling beams, such as shear force capacity, initial stiffness, and rotational capacity, can be improved by implementing this new connection detailing. Both phases of this thesis offer new insights into improving the seismic performance of diagonally-reinforced, steel, and composite coupling beams, resulting in higher-performing high-rise buildings in Canada. v Lay Summary With cities expanding upwards to keep up with the fast-paced urbanization, tall skyscraper construction can be considered a solution. Since many of these skyscrapers are located in seismically active locations, safe structural design under earthquake loads is essential for public safety. Core wall systems featuring coupled shear walls connected by coupling beams are common in North America. These beams come in different types, including diagonally-reinforced, steel, and steel-reinforced (composite) varieties, each incorporating diverse design considerations to enhance building resilience. In the first phase of this study, a detailed review was conducted of previously tested diagonally-reinforced coupling beams to determine the effect of each design parameter on the structural response of these beams. The outcomes of the first phase of the study provided new design recommendations. In the second phase of this study, a new connection detailing was proposed to facilitate the construction process of steel and composite coupling beams. Practical design plots were developed for practitioners to use the proposed connection detailing. Additionally, two parametric studies using advanced numerical models were undertaken to investigate the impact of the new connection, detailing the structural behaviour of these beams. The outcomes of the second phase study provided a new connection detailing which facilitates the construction process while ensuring high structural performance in terms of shear capacity, initial stiffness, and rotational capacity. vi Preface Various parts of this thesis work have been published or are under preparation for submission. The following summarises each publication and its specific contributions. Conference publications Parts of Chapter 2 and 3 were developed into a conference paper that I presented at the Canadian Society of Civil Engineering (CSCE) Conference in Whistler in May 2022. [3] Amiri, A., Tobber, L., and Atkinson, J. (2022). Canadian design recommendations for diagonally-reinforced coupling beams using a new comprehensive database. Proceedings of the Annual Conference of Canadian Society of Civil Engineering (CSCE) May 2022, Whistler, Canada. Parts of Chapter 4 were developed into a conference paper that I presented at CCEE-PCEE in Vancouver in June 2023. [4] Amiri, A., and Tobber, L. (2023). Review and Analysis of Codes and Experimental Tests for Steel and Steel-Reinforced Coupling Beams: Advancing Canadian Design. Submitted and presented at the Canadian Conference - Pacific Conference on Earthquake Engineering CCEE-PCEE June 2023, Vancouver, Canada. Journal publications Part of Chapters 2 and 3 were developed into a journal paper currently under preparation. [1] Amiri, A., Atkinson, J.C., and Tobber, L. (2023). Diagonally-reinforced Coupling Beams: Seismic Response Database. (Under-preparation). vii Additional contributions I also contributed to two other published conference papers, primarily assisting with data analysis, manuscript drafting, critical editing, and the review process. [5] Dehghani, S., Amiri, A., and Tobber, L. (2022). Mitigation of higher mode effects in controlled rocking walls. Proceedings of the Annual Conference of Canadian Society of Civil Engineering (CSCE) May 2022, Whistler, Canada. [6] Tobber, L, Dehghani, S., and Amiri, A. (2022). Canadian seismic design recommendations of outriggers in high-rise buildings. Proceedings of the Annual Conference of Canadian Society of Civil Engineering (CSCE) May 2022, Whistler, Canada. viii Table of Contents Abstract ...................................................................................................................................... iii Lay Summary .............................................................................................................................. v Preface........................................................................................................................................ vi Table of Contents ..................................................................................................................... viii List of Tables ............................................................................................................................. xi List of Figures ........................................................................................................................... xii List of Abbreviations ................................................................................................................ xx List of Symbols ....................................................................................................................... xxii Acknowledgments.................................................................................................................. xxxi Dedication ............................................................................................................................. xxxii Chapter 1: Introduction ............................................................................................................... 1 1.1 Background ................................................................................................................... 1 1.2 Goals and Objectives .................................................................................................... 7 1.3 Organization ................................................................................................................. 7 Chapter 2: Review of diagonally- reinforced coupling beams and database development ...... 10 2.1 Introductions ............................................................................................................... 10 2.2 Mechanical behaviour of diagonally-reinforced coupling beams .............................. 10 2.3 Building code provisions for designing diagonally-reinforced coupling beams ........ 17 2.4 Database development of diagonally-reinforced coupling beams .............................. 22 2.5 Summary ..................................................................................................................... 29 Chapter 3: Analysis of diagonally-reinforced coupling beam database ................................... 30 ix 3.1 Introduction ................................................................................................................ 30 3.2 Impact of design parameters on overstrength ............................................................. 30 3.3 Impact of design parameters on θ80% .......................................................................... 35 3.4 Impact of the quantity of diagonal reinforcement on θ80% ......................................... 36 3.5 Specimens without diagonal ties: impact of ties on θ80% ............................................ 39 3.6 Specimens with diagonal ties: impact of ties in on θ80% ............................................. 42 3.7 Initial stiffness (Ki) ..................................................................................................... 44 3.8 Conclusions ................................................................................................................ 45 Chapter 4: New connection detailing for steel and composite coupling beams ....................... 47 4.1 Introduction ................................................................................................................ 47 4.2 Review of mechanical behaviour and design codes ................................................... 47 4.3 Proposed connection ................................................................................................... 72 4.4 Mechanics of the proposed innovative connection detailing ...................................... 74 4.5 Performance of new connection using a mathematical model ................................... 80 4.6 Summary ..................................................................................................................... 82 Chapter 5: Finite element modelling of new connection detailing for steel and composite coupling beams ......................................................................................................................... 83 5.1 Introduction ................................................................................................................ 83 5.2 Modelling approach .................................................................................................... 83 5.3 Specimen used for calibration .................................................................................... 93 5.4 Preliminary studies ................................................................................................... 103 5.5 Conclusion ................................................................................................................ 110 Chapter 6: Conclusions and future work ................................................................................ 111 x 6.1 Phase 1: Diagonally-reinforced coupling beams ...................................................... 111 6.2 Phase 2: Steel and composite coupling beams ......................................................... 113 6.3 Future work............................................................................................................... 116 Bibliography ........................................................................................................................... 117 Appendices .............................................................................................................................. 121 : Summary of experimental studies on diagonally-reinforced coupling beams......................................................................................................................................... 121 : Tables of information of diagonally-reinforced coupling beams specimens......................................................................................................................................... 155 : Summary of experimental data of steel and composite coupling beams . 158 xi List of Tables Table 2.1: General information about studied specimens. ............................................................ 25 Table 2.2: Seismic parameter values of studied specimens. ......................................................... 28 Table 5.1: Model material parameters for confined and unconfined concrete of specimen SCBC1. ....................................................................................................................................................... 95Table 5.2: Details of the specimens studied in the conducted preliminary studies. ................... 104Table B-1: Tests results of the studied diagonally-reinforced coupling beams......................... 155Table B-2: Reinforcing detailings of studied diagonally-reinforced coupling beams. .............. 156Table C-1: General information about steel and composite coupling beams specimens. ......... 159Table C-2: Test results of studied steel and composite coupling beams specimens.................. 161xii List of Figures Figure 1.1: General sketch of a building with slab/column and core walls carrying gravity and lateral loads, respectively. ............................................................................................................... 2 Figure 1.2: Details of a typical (a) conventionally-reinforced (b) diagonally-reinforced with beam confinement [13](c) diagonally-reinforced with diagonal confinement[13] (d) steel and (e) steel-reinforced (composite) coupling beam. .......................................................................................... 5 Figure 2.1: Performance of shear walls as (a) coupled and (b) partially coupled. ....................... 11 Figure 2.2: Internal forces of a typical diagonally-reinforced coupling beam. ............................ 12 Figure 2.3: Correlation between aspect ratio and angle between diagonal bars and horizontal direction in diagonally-reinforced coupling beams. ..................................................................... 13 Figure 2.4: The deformation of coupling beams before (Detail a) and after (Detail b) of applying the lateral loads. ............................................................................................................................ 14 Figure 2.5: ACI 318-19 requirements for a typical DRCB with diagonal confinement. .............. 19 Figure 2.6: CSA A23.3-19 requirements for a typical DRCB with anti-buckling ties around diagonal bars. ................................................................................................................................ 20 Figure 2.7: ACI 318-19 requirements for a typical DRCB with full beam confinement. ............ 21 Figure 2.8: Distribution of specimens of different (a) aspect ratios and (b) axial restraint. ........ 24 Figure 2.9: Backbone curve for coupling beam models. .............................................................. 27 Figure 3.1: Range of 𝑉𝑚𝑎𝑥𝑉𝑛𝑒 for specimens with different characteristics: i) All specimens, ii) Axial restraint only (AR Only), iii) Embedded Longitudinal Bars only (ELB Only), iv) Both AR and ELB (AR+ELB), and v) Neither AR nor ELB. ....................................................................... 31 Figure 3.2: Distribution of specimens with ELB based on 𝑉𝑚𝑒𝑉𝑡. ............................................. 33 Figure 3.3: Range of 𝑉𝑚𝑎𝑥𝑉𝑡 for specimens with different characteristics: i) All specimens, ii) Axial restraint Only (AR Only), iii) Embedded Longitudinal Bars Only (ELB Only), iv) Both AR and ELB (AR+ELB), and v) Neither AR nor ELB. ....................................................................... 34 xiii Figure 3.4: Range of 𝑉𝑚𝑎𝑥𝑉𝑚𝑡 for specimens with different characteristics: i) All specimens, ii) Axial restraint only (AR Only), iii) Embedded Longitudinal Bars only (ELB Only), iv) Both AR and ELB (AR+ELB), and v) Neither AR nor ELB. ....................................................................... 35 Figure 3.5: Range of 𝜃80% for specimens with different characteristics: i) All specimens, ii) Axial restraint only (AR Only), iii) Embedded Longitudinal Bars only (ELB Only), iv) Both AR and ELB (AR+ELB), and v) Neither AR nor ELB. ...................................................................................... 36 Figure 3.6: Damage patterns of DRCBs at the joints of the shear walls for specimens (a) D-6db [25] (b) Beam 395 [3]. .................................................................................................................. 37 Figure 3.7: θ80% versus 𝑉𝑛𝑒𝐴𝑐𝑤𝑓𝑐′ for specimens with L/h≤ 1.5. ............................................... 38 Figure 3.8: θ80% versus 𝑉𝑚𝑎𝑥𝐴𝑐𝑤𝑓𝑐′ for specimens with (a) L /h≤ 1.5 and (b) L/h>1.5. .......... 39 Figure 3.9: θ80% versus 𝑉𝑚𝑎𝑥𝐴𝑐𝑤𝑓𝑐′ for specimens with (a) L /h≤ 1.5 and (b) L/h>1.5. .......... 41 Figure 3.10: 𝜃80% versus a) 𝐴𝑠ℎ per ACI 318-19 for specimens with diagonal confinement. .. 43 Figure 3.11: 𝜃80% versus a) the beam tie spacing per the diagonal bars and b) the diagonal tie spacing for specimens with diagonal confinement. ...................................................................... 43 Figure 3.12: Various values for 𝐶𝑘 based on experimental results and various amounts of αf and αs. .................................................................................................................................................. 44 Figure 4.1: PCI Design Method 1971 embedment model [32]. .................................................... 49 Figure 4.2: Kriz and Raths, 1974 [33] embedment model accounting for additional welded reinforcement. ............................................................................................................................... 51 Figure 4.3: Marcakis and Mitchell, 1980 embedment model. ...................................................... 53 Figure 4.4: Marcakis and Mitchell, 1980 [35] simplified embedment model. ............................. 55 Figure 4.5: Marcakis and Mitchell, 1980 [35] embedment model including additional welded reinforcements............................................................................................................................... 56 Figure 4.6: Ratio of 𝑓𝑏𝑓𝑐′ versus the ratio of bf/tw developed based on the test results of Mattock and Gaafar, 1982 [36]. .................................................................................................................. 63 xiv Figure 4.7: Park et al., 2005 embedment model [41].................................................................... 65 Figure 4.8: (a) 2D and (b) 3D sketches of the proposed embedment model with bearing system........................................................................................................................................................ 73 Figure 4.9: Proposed embedment model. ..................................................................................... 75 Figure 4.10: Design plot associated with the mathematical model of proposed connection detailing........................................................................................................................................................ 81 Figure 5.1: Element types utilized by DIANA 10.6. .................................................................... 86 Figure 5.2: Hysteresis curve for Maekawa and Fukuura concrete model [44]. ............................ 88 Figure 5.3: Predefined tension softening for Maekawa-Fukuura concrete model [44]. ............... 89 Figure 5.4: Yielding condition of the Von Mises and Tresca plasticity theory ............................ 92 Figure 5.5: Variables of three-dimensional surface interfaces. .................................................... 93 Figure 5.6: Lateral loading protocol of specimen SCBC1 [47]. ................................................... 95 Figure 5.7: Stress-strain relationship of steel plates with thickness of (a) 6 mm and (b) 10 mm [47]........................................................................................................................................................ 96 Figure 5.8: Stress-strain relationship of steel rods with diameter of (a) 8 mm and (b) 12 mm [47]........................................................................................................................................................ 96 Figure 5.9: Mesh discretization of (a) shear wall and (b) embedded steel of SCBC1. ................. 98 Figure 5.10: Hysteretic curves of FEM and experimental results of SCBC1. .............................. 98 Figure 5.11: Slippage of the embedded steel beam of specimen SCBC1. .................................... 99 Figure 5.12: Initial cracking of specimen SCBC1. ..................................................................... 101 Figure 5.13: Crack pattern of SCBC1 based on (a) FEM and (b) experimental results. ............ 102 Figure 5.14: Stiffness degradation plots developed based on FEM and experimental results of SCBC1. ....................................................................................................................................... 103 xv Figure 5.15: 3D finite element model of specimens (a) with proposed connection detailing and (b) without proposed connection detailing. ...................................................................................... 105 Figure 5.16: Backbone diagrams of specimens with additional compression steel bars (15M-Inf with ω=0.03 and 20M-Inf with ω=0.05) and without additional reinforcement. ....................... 107 Figure 5.17: Backbone diagrams of specimens with auxiliary transfer bars (20M-ATB-Inf with ω=0.1), with additional compression steel bar (20M-Inf with ω=0.05), and without any additional reinforcement. ............................................................................................................................. 109 Figure 5.18: Vertical displacement of (a) specimen with auxiliary transfer bars (20M-ATB-Inf) and (b) specimen with compression steel reinforcing (20M-Inf) ............................................... 109 Figure A-1: Cracking pattern at final loading stage of specimens (a) Beam 316, (b) Beam 317, and (c) Beam 395 tested by Paulay and Binney, 1974 [3]. ................................................................ 122 by Sonobe et al., 1995 [50]. ........................................................................................................ 124 ..................................................................................................................................................... 125 2000 [31]. .................................................................................................................................... 126 ..................................................................................................................................................... 127 ..................................................................................................................................................... 129 ..................................................................................................................................................... 130 Figure A-2: Cracking pattern at final loading stage of specimens (a) NX7L and (B) LX7L testedFigure A-3: Details of specimens a) P07 and b) P12 tested by Galano and Vignoli, 2000 [31].Figure A-4: Hysteresis diagrams of specimens a) P07 and b) P12 tested by Galano and Vignoli,Figure A-5: (a) Details and (b) hysteresis diagram of specimen K1 tested by Gonzalez, 2001 [24].Figure A-6: Test setup used by Dugas, 2002 [27]. .................................................................... 128Figure A-7: Details of specimens (a) D30 and (b) D30H tested by Dugas, 2002 [27].............. 128Figure A-8: Hysteresis diagrams of specimens (a) D30 and (b) D30H tested by Dugas, 2002 [27].Figure A-9: Details of specimens (a) CCB11 and (b) CCB12 tested by Kwan and Zhao, 2002 [51].xvi ..................................................................................................................................................... 133 [52]. ............................................................................................................................................. 134 [26]. ............................................................................................................................................. 135 [30]. ............................................................................................................................................. 136 [30]. ............................................................................................................................................. 137 ..................................................................................................................................................... 139 al., 2008 [54]. .............................................................................................................................. 139 Figure CB24F-PT, (e) CB24F-1/2-PT, (f) CB33F, and (g) CB33D tested by Naish et al., 2013 [2], [55]...................................................................................................................................................... 143 ..................................................................................................................................................... 143 Figure A-10: Hysteresis diagrams of specimens (a) CCB11 and (b) CCB12 tested by Kwan andZhao, 2002 [51]........................................................................................................................... 131Figure A-11: Details of specimens (a) CB-1 and (b) CB-2 tested by Zhou, 2003 [28]............. 133Figure A-12: Hysteresis diagrams of specimens (a) CB-1 and (b) CB-2 tested by Zhou, 2003 [28].Figure A-13: Hysteresis diagrams of specimens (a) N-1 and (b) N-2 tested by Shimazaki, 2004Figure A-14: Hysteresis diagrams of specimens (a) S1 and (b) S3 tested by Canbolat et al., 2005Figure A-15: (a) Used test setup and (b) details of specimens CB1/2 tested by Yun et al., 2008Figure A-16: Hysteresis diagrams of specimens (a) CB1 and (b) CB2 tested by Yun et al., 2008Figure A-17: Details of specimen (a) DCB-1 and (b) DCB-2 tested by Fortney et al., 2008 [54].Figure A-18: Hysteresis diagrams of specimens (a) DCB-1 and (b) DCB-2 tested by Fortney etFigure A-19: Used test setup by Naish et al., 2013 [2], [55]. .................................................... 140A-20: Hysteresis diagrams of specimens (a) CB24F, (b) CB24D, (c) CB24F-RC, (d)Figure A-21: Details of specimens (a) CB10-1 and (b) CB20-1 tested by Lim et al., 2015 [14].Figure A-22: Hysteresis diagrams of specimens (a) CB10-1 and (b) CB20-1 tested by Lim et al.,2015 [14]. .................................................................................................................................... 145Figure A-23: Details of specimen CC-16db tested by Howard, 2017 [25]. ............................. 146xvii ..................................................................................................................................................... 149 [16]. ............................................................................................................................................. 150 2018 [17]. .................................................................................................................................... 151 Han et al., 2019 [13]. .................................................................................................................. 154 Figure [10]. ............................................................................................................................................. 163 Shahrooz et al.,1993 [10]. ........................................................................................................... 165 [8]. ............................................................................................................................................... 169 Shahrooz et al., 2001 (a) [9]........................................................................................................ 170 Figure A-24: Hysteresis diagrams of specimens tested by Howard, 2017 [25]......................... 148Figure A-25: Damage of specimens (a) CC-16db, (b) MD-10db, (c) MD-8db, and (d) D-6db [25].Figure A-26: Hysteresis diagrams of specimens (a) CB1 and (b) CB2 tested by Ameen et al., 2017Figure A-27: Test setup associated with the experimental program conducted by Poudel et al.,Figure A-28: Hysteresis diagram of specimen CB1A tested by Poudel et al., 2018 [17]. ........ 151Figure A-29: Test setup used by Han et al., 2019 [13]. ............................................................. 152Figure A-30: Hysteresis diagrams of specimens with L/h equals to (a) 2.0 and (b) 3.5 tested byFigure C-1: Sketch of (a) steel and (b) composite couplings without wall’s reinforcements.... 159C-2: General geometrical dimensions of the tested specimens by Shahrooz et al., 1993Figure C-3: Shahrooz et al., 1993 test setup [10]. ..................................................................... 164Figure C-4: Hysteresis diagrams of specimens (a) Wall 1, (b) Wall 2, and (c) Wall 3 tested byFigure C-5: Specimen’s details tested by Harries et al.,1993 [39]. ........................................... 166Figure C-6: Harries et al., 1993 test setup [39].......................................................................... 167Figure C-7: Specimen’s details tested by Harries et al.,1997 [8]. ............................................. 168Figure C-8: Hysteresis diagrams of the specimens tested by Harries et al., 1993 and 1997 [39],Figure C-9: (a) General geometry details of the tested specimens, and (b) the test setup used byxviii Figure al.,2001 (b) [57]. ......................................................................................................................... 175 et al., 2005 [41]. .......................................................................................................................... 180 et al., 2006 [11]. .......................................................................................................................... 184 [58]. ............................................................................................................................................. 185 2014 [7]. ...................................................................................................................................... 188 Figure C-10: Hysteresis diagram of specimens (a) CB1, (b) CB2, (c) CB3, and (d) CB4 tested byShahrooz et al., 2001 (a) [9]........................................................................................................ 171Figure C-11: General specimens’ details tested by Shahrooz et al., 2001 (b) [57]. .................. 173C-12: Hysteresis diagrams of specimens WB1, WB2, and WB3 tested by Shahrooz etFigure C-13: Specimens’ details tested by Park et al., 2005 [41].............................................. 177Figure C-14: Test setup used by Park et al., 2005 [41].............................................................. 178Figure C-15: Hysteresis diagrams of specimens (a) SBVRT, (b) SCF, and (c) FCF tested by ParkFigure C-16: Specimens’ details tested by Park et al., 2006 [11].............................................. 182Figure C-17: Hysteresis diagrams of specimens (a) PSF, (b) PSFF, and (c) PSFFT tested by ParkFigure C-18: Specimen SCB (a) details and (b) hysteresis diagram tested by Fortney et al., 2007Figure C-19: Geometrical layouts of the specimens tested Motter et al., 2014 [7]. .................. 185Figure C-20: Test setup used by Motter et al., 2014 [7]. ........................................................... 186Figure C-21: Hysteresis diagram of specimen SRC1 tested by Motter et al., 2014 [7]. ........... 187Figure C-22: Hysteresis diagram of specimen SRC2 tested by Motter et al., 2014 [7]. ........... 187Figure C-23: Hysteresis diagrams of specimens (a) SRC3 and (b) SRC4 tested by Motter et al.,Figure C-24: General geometry layout of the specimens and (b) used test setup by Li et al., 2019[59]. ............................................................................................................................................. 191Figure C-25: Hysteresis diagrams of the specimens tested by Li et al., 2019 [59]. .................. 192Figure C-26: Used test setup by Nahvinia et al., 2019 [12]....................................................... 194xix Figure C-27: Hysteresis diagrams of specimens (a) SCBC1 and (b) SCBC2 tested by Nahvinia etal., 2021....................................................................................................................................... 195xx List of Abbreviations ACI = American Concrete Institute AISC = American Institute of Steel Construction AR = Axial restraint ASCE = American Society of Civil Engineers ATR = Auxiliary transfer bar BP = Bearing plate CE = Concrete encasement C-OSW = Composite ordinary shear wall CSA = Canadian Standards Association C-SSW = Composite special shear wall DIANA = Displacement analyzer (Commercial finite element analysis software) DOC = Degree of coupling DRCB = Diagonally-reinforced coupling beam ELB = Embedded longitudinal bar FEA = Finite element analysis HPFRC = High-performance fibre-reinforced cement JSCE = Japan society of civil engineers LATBSDC = Los Angeles Tall Buildings Structural Design Council NBC = National building code PCI = Precast concrete institution PT = Pot-tensioned xxi RC = Reinforced concrete SCB = Steel coupling beam SFRS = Seismic force resisting systems SRCB = Steel-reinforced coupling beam SSB = Shear stud bolt WHT = Web horizontal tie WS = Web stiffener xxii List of Symbols 𝑎 = Eccentricity of the applied shear load measured from the beam-wall interface in steel and composite coupling beams 𝐴𝑐ℎ = Confined area provided around each group of diagonal bars, measured to the outside edges of transverse reinforcement 𝐴𝑐𝑤 = Shear area of concrete in coupling beam section 𝐴𝑔 = Gross area of concrete in coupling beam section 𝐴𝑠 = Area of additional reinforcements on the embedded steel flanges located near the beam-wall interface in steel and composite coupling beams 𝐴𝑠′ = Area of additional reinforcements located at the back of the embedded steel flanges in steel and composite coupling beams 𝐴𝑠𝑑 = Area of diagonal bars in each diagonal bar group in diagonally-reinforced coupling beam 𝐴𝑠ℎ = Total cross-section area of transverse reinforcement in the coupling beam 𝐴𝑠𝑙 = Area of shear wall vertical reinforcement in steel and composite coupling beams 𝐴𝑠𝑙 = Area of longitudinal bars in diagonally-reinforced coupling beam 𝐴𝑠,𝐿𝑜𝑛𝑔 = Total area of coupling beam transverse bars 𝐴𝑠𝑟 = Area of transverse reinforcement in composite coupling beams 𝐴𝑡𝑤 = Area of steel beam web 𝐴𝑣𝑒 = Effective shear area of reinforced concrete xxiii 𝑏 = Width of the bearing width steel beam in steel and composite coupling beams 𝑏𝑐 = Confined beam width or depth measure to the outside edges of the transverse reinforcement around the confined area 𝑏𝑒𝑓𝑓 = Effective depth of bearing width in steel and composite coupling beams 𝑏𝑓 = Steel beam flange width 𝑏𝑤 = Diagonally-reinforced coupling beam width (Equation 2.10) 𝑏𝑤𝑐 = Width of concrete encasement 𝑐 = Shear wall concrete cover 𝐶 = Resultant compression force from applied lateral force (Figure 2.1) 𝐶𝑏 = Resultant concrete compressive force at the back of the embedded steel beam in steel and composite coupling beams 𝐶𝑓 = Resultant concrete compressive force at the front (beam-wall interface) of the embedded steel beam in steel and composite coupling beams 𝐶𝑘 = Unitless parameter representing the flexural and shear deformations in diagonally-reinforced coupling beam 𝐶𝑢 = Developed compression force in diagonal bars corresponding to applied shear force (Figure 2.2) 𝑑 = Effective depth of concrete in diagonally-reinforced coupling beam 𝑑 = Distance from the neutral axis to the back of the embedded steel beam in steel and composite coupling beams xxiv 𝑑′ = Effective depths of longitudinal bars compression zone for diagonally-reinforced coupling beam 𝑑𝑏 = Diameter of the diagonal bar 𝑑𝑐 = Effective depth of concrete encasement in steel and composite coupling beams 𝑑𝑡𝑖𝑒 = Diameter of the anti-buckling ties in diagonally-reinforced coupling beam 𝐸𝑐 = Modulus of elasticity of concrete 𝐸𝑠 = Elastic modulus of steel (𝐸𝐴)𝑒𝑓𝑓 = Effective axial rigidity (𝐸𝐴)𝑡𝑟𝑎𝑛𝑠 = Axial rigidity of the cracked transformed section of concrete 𝐸𝐼𝑒𝑓𝑓 = Effective flexural rigidity (𝐸𝐼)𝑡𝑟𝑎𝑛𝑠 = Flexural rigidity of the cracked transformed section of concrete 𝑓𝑐 = Concrete compressive stress corresponding to ∈𝑐 𝑓𝑐′ = Concrete compressive strength 𝑓𝑐𝑐′ = Confined peak stress of concrete 𝑓𝑐𝑢 = Ultimate compressive stress of concrete 𝑓𝑠 = steel stress in welded reinforcement near front face (beam-wall interface) of embedded steel beam 𝑓𝑠′ = steel stress in welded reinforcement at the back of embedded steel beam 𝑓𝑠𝑏 = Stress of additional compression bars located at the back of the embedded steel beam 𝑓𝑠𝑓 = Stress of additional compression bars near front face (beam-wall interface) of embedded steel beam xxv 𝑓𝑡 = Maximum tensile stress of concrete 𝑓𝑦𝑎 = Specified yield strength of the auxiliary transfer bars 𝑓𝑦𝑑 = Yield strength of diagonal bar in diagonally-reinforced coupling beam 𝑓𝑦𝑙𝑒 = Yielding strength of longitudinal bars in diagonally-reinforced coupling beam 𝑓𝑦𝑟 = Yielding strength of welded additional reinforcements to the embedded steel flanges in steel and composite coupling beams 𝑓𝑦𝑠𝑙 = Nominal yielding strength of the shear wall vertical bars in steel and composite coupling beams 𝐹𝑦𝑠𝑟 = Nominal yielding strength of transverse reinforcement in composite coupling beams 𝑓𝑦𝑡= Yield strength of the transverse bars 𝑔 = clear length of coupling beam plus the cover of shear wall at each side 𝐺𝐴𝑒𝑓𝑓 = Effective shear rigidity 𝐺𝑐 = Shear modulus of concrete ℎ = Height of diagonally-reinforced coupling beam ℎ𝑐 = Overall depth of concrete encasement in composite coupling beam ℎ𝑠 = Overall depth of steel beam ℎ𝑥 = Maximum distance measured from centerline to centerline of laterally supported diagonal bars in each group of diagonal bars 𝐼𝑒𝑓𝑓 = Effective moment of inertia of reinforced concrete xxvi 𝐼𝑔 = Gross moment of inertia of coupling beam 𝐼𝑠 = Moment of inertia of the steel coupling beam 𝐾𝑖 = Initial stiffness 𝐿 = Clear length of coupling beam 𝐿𝑒 = Steel embedment length into the adjacent shear wall 𝑚 = Distance from neutral axis to the beam-wall interface 𝑀1 and 𝑀2 = Base overturning moment in coupling beam (Figure 2.1) 𝑀𝑐1 = Positive moment capacity with the top of diagonally-reinforced coupling beam in compression (Equation 3.5) 𝑀𝑐2 = negative moment capacity with the bottom of diagonally-reinforced coupling beam in compression (Equation 3.5) 𝑀𝑛𝑒 = Moment capacity of coupling beam with embedded longitudinal bar 𝑀𝑝 = Plastic flexural moment of embedded steel beam 𝑀𝑢 = Flexural moment corresponding to the applied shear force (Figure 2.2) 𝑝 = Applied axial load on the shear wall 𝑅𝑐 = Factor to account for the expected strength of concrete 𝑅𝑦 = Ratio of the expected yield stress of the steel profile material to the specified minimum yield stress 𝑅𝑦𝑟 = Ratio of the expected yield stress of the transverse reinforcement material to the specified minimum yield stress xxvii 𝑠 = Spacing measured from the center of the additional reinforcements located at the front and 𝑠 = Spacing of transverse reinforcement in composite coupling beams (Equations 4.41 and 4.42) 𝑆𝑏 = Compression force of compression steel reinforcement located at the back of the embedded steel beam in steel and composite coupling beams 𝑠𝑑 = Spacing of ties around diagonal bars in diagonally-reinforced coupling beam 𝑆𝑓 = Compression force of compression steel reinforcement located at the front face of the embedded steel beam in steel and composite coupling beams 𝑠𝑡 = Spacing between ties in beam confinement option in diagonally-reinforced coupling beam 𝑇 = Resultant tension force from applied lateral force (Figure 2.1) 𝑡𝑓 = Steel beam flange thickness 𝑇𝑢 = Developed tension force in diagonal bars corresponding to applied shear force (Figure 2.2) 𝑡𝑤 = Shear wall thickness 𝑡𝑤𝑠 = Steel beam web thickness 𝑢 = Distance measured from the centroid of the front additional rods to the beam-wall interface in steel and composite coupling beams 𝑉𝑚𝑎𝑥 = Maximum shear force 𝑉𝑚𝑒 = Shear force corresponding to the flexural capacity of the coupling beam with embedded longitudinal bar 𝑉𝑚𝑡 = Shear capacity corresponding to the flexural capacity of a diagonally-reinforced coupling beam in double curvature xxviii 𝑉𝑛,𝑐𝑜𝑚𝑝 = Shear strength of the composite coupling beam by considering the concrete encasement, longitudinal and transverse reinforcement in the reinforced concrete beam 𝑉𝑛,𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑜𝑛 = Minimum required shear strength at the wall-beam interface for steel and composite coupling beams 𝑉𝑛𝑒 = Expected shear capacity of diagonally-reinforced coupling beam 𝑉𝑝 = Nominal shear strength of embedded steel beam 𝑉𝑟 = Shear capacity of the steel and composite coupling beams due to the welded additional reinforcements to the embedded steel flanges 𝑉𝑡 = Total shear strength of coupling (Equation 3.1) 𝑉𝑢 = Applied shear force (Figure 2.2) 𝑤 = Distance measured from the centroid of the additional rods located at the back of the embedded steel beam flange to the beam-wall interface in steel and composite coupling beams 𝑥𝑏 = Depth of the concrete strain distribution from the back of the connection to the neutral axis location in steel and composite coupling beam (Figure 4.3) 𝑥𝑐𝑏 Distance measured from the centroid of the resultant concrete compression force at the back of the embedded steel beam to the beam-wall interface in steel and composite coupling beams 𝑥𝑐𝑓 = Distance measured from the centroid of the resultant concrete compression force at the front of the embedded steel beam to the beam-wall interface in steel and composite coupling beams 𝑥𝑐−𝐶𝑏 = Centroid of the compression force at the back of the embedment region from the beam-wall interface 𝑥𝑐−𝐶𝑓 = Centroid of the concrete compression force at the front face of the embedded steel beam from the beam-wall interface xxix 𝑥𝑐−𝑆𝑏 = Centroid of the compression force, developed by the rods at the back of the embedment region, from the beam-wall interface 𝑥𝑐−𝑆𝑓 = Centroid of the compression force, developed by the rods at the front of the embedment region, from the beam-wall interface 𝑍 = Plastic section modulus 𝛼 = Angle between diagonal bars and horizontal direction in diagonally-reinforced coupling beam 𝛼 = Stress block factors (Equations 4.8 and 4.9) 𝛼𝑓 = Modification factor reducing the flexural moment of inertia of concrete 𝛼𝑠 = Modification factor reducing the shear area of concrete 𝛽1 = ACI stress block factor for concrete 𝛽 = Stress block factors (Equations 4.8 and 4.9) 𝛾𝑐 = Concrete density ∆𝐹 = Flexural deflection in diagonally-reinforced coupling beam ∆𝑆 = Shear deflection in diagonally-reinforced coupling beam ∆𝑡 = Total deflection in diagonally-reinforced coupling beam ∈0 = Strain of concrete corresponding to 𝑓𝑐′ ∈𝑏 = Maximum strain of concrete in compression at the back of the embedded steel beam in steel and composite coupling beams ∈𝑐 = Strain of concrete in compression xxx 𝜀𝑐𝑐 = Confined peak strain of concrete 𝜀𝑡𝑢 = Maximum tensile strain of concrete 𝜃80% = Degradation rotation defined as the rotation of coupling beam corresponding to 80% of the peak shar capacity of these beams 𝜃𝑉𝑚𝑎𝑥 = Rotation corresponding to maximum shear capacity of steel and composite coupling beams 𝜈= Poisson ratio of reinforced concrete 𝜔 = Additional reinforcement index in steel and composite coupling beams back of the embedded steel beam in steel and composite coupling beams 𝜔′ = Additional reinforcement index in steel and composite coupling beams by considering strip-loading effect xxxi Acknowledgments First and foremost, I extend my deepest gratitude to my supervisor and mentor, Dr. Lisa Tobber, for her invaluable support and insights during my M.A.Sc. Studies. Words can not adequately convey the profound impact of her efforts in enriching my academic foundation in structural and earthquake engineering. Her constant guidance has undoubtedly shaped my perspective and skills as a structural engineer, for which I am truly appreciative. I am grateful to have been Dr. Lisa Tobber's student. I am also proudly thankful to my committee members, Prof. Perry Adebar and Dr. Mohammad Tiznobaik, for their valuable constructive comments. Your effort in elevating my research to outstanding and productive levels is immensely appreciated. I want to give special recognition to our esteemed industrial partners, Kor Structural Engineers and BC Housing, for their exceptional contributions towards advancing the resiliency in structural engineering and the the construction of high-rise buildings. In particular, I am deeply honoured to have had the opportunity to collaborate with Mr. Jeremy Atkinson, principal at Kor Structural Engineers Consulting Firm. The knowledge I gained from him during our meetings has provided me with a profound understanding of the design of high-rise buildings. Last but not least, I wish to express my heartfelt appreciation towards my beloved family. My deepest gratitude goes to my father, Kazem Amiri, and my mother, Mozhgan Khalili, for their unwavering support and for shaping me into who I am today. Words fall short of expressing the depth of my gratitude for their faith in my abilities and their encouragement towards achieving my goals. I am also incredibly fortunate to have my sister, from whom I have learned invaluable life lessons. Maryam, your presence in my life has been an unparalleled blessing. xxxii Dedication I dedicate this thesis to my family, who has supported me in many ways.1 Chapter 1: Introduction 1.1 Background More high-rise buildings are being constructed in response to the pressing need for additional residential and commercial units in densely populated cities with limited available land. With many of these buildings being built in high seismic regions, implementing robust seismic force-resisting systems (SFRS) in these buildings is critical for public safety and community resilience. In North America, the reinforced concrete (RC) core wall system is one of the most common types of SFRSs used in high-rise buildings [1]. An RC core wall system consists of walls, called shear walls, that are interconnected with stiff beams, called coupling beams. A common construction method is for a central RC core wall to resist all the lateral loads and some gravity loads while the slabs and columns resist the remaining gravity loads. Figure 1.1(a) shows a 3D view of a building in which slabs and columns transfer the gravity loads, and the core wall system transfers the lateral loads. Figure 1.1(b) shows the cross-section of a typical building floor, including the core wall system, coupling beams, columns, and slabs. When the RC core wall system experiences a large earthquake shaking, the coupling beams experience large inelastic rotations to absorb energy. Consequently, the seismic response of coupling beams plays a crucial role in the overturning resistance, stiffness, and energy dissipation of the RC core wall system. Therefore, improving the performance of coupling beams is essential for enhancing the overall system performance. 2 Figure 1.1: General sketch of a building with slab/column and core walls carrying gravity and lateral loads, respectively. Various types of coupling beams are used in the North American construction industry. Figure 1.2 shows a summary of the different coupling beam types. Conventionally-reinforced coupling beams (Figure 1.2(a)) dissipate energy through the flexural yielding of longitudinal bars at the top and bottom of the section. The longitudinal bars cannot directly resist the shear forces. As a result, significant flexural cracks form at the coupling beam-shear wall interface. When undergoing large deformations, these cracks widen significantly, which can result in a sliding shear failure at the connection [2]. With the multiple cycles of cracks opening and the longitudinal bars unable to close the cracks, these beams experience significant pinching within the hysteresis, resulting in low energy dissipation and limited rotational capacity. Diagonally-reinforced coupling beams, shown in Figure 1.2 (b) and (c), introduced by Paulay and Binney in 1974 [3], are an alternative to conventionally-reinforced coupling beams. These beams resist forces through a group of diagonal bars that make an "X" shaped configuration. This 3 configuration allows for a direct transfer of shear forces, reducing sliding shear failures and increasing the inelastic rotation capacity and energy dissipation compared to conventionally-reinforced coupling beams [3]. Diagonally-reinforced coupling beams can exhibit high ductility so long as there are sufficient beam ties around the beam (referred to as beam confinement in ACI 318-19 [4] shown in Figure 1.2(b)) or around the bundle of diagonal bars (referred to as buckling prevention ties in CSA A23.3-19 [5] and diagonal confinement in ACI 318-19 [4] shown in Figure 1.2(c)). This superior performance makes diagonally-reinforced coupling beams the preferred coupling beam construction method in RC high-rise buildings in the US and Canada. The performance of the diagonally-reinforced coupling beam depends on the coupling beams’ aspect ratio, L/h, where 𝐿 refers to the clear span between walls and ℎ refers to the depth. For instance, while diagonally-reinforced coupling beams may demonstrate excellent ductility, they may not be efficient for high aspect ratios (where the length-to-depth ratio is greater than 4.0) due to the small angle between the horizontal axis and the diagonal bars. This necessitates a significant amount of reinforcing area to achieve adequate strength [6]. Steel coupling beams can be an alternative to diagonally-reinforced coupling beams in cases requiring a high aspect ratio and strength. Steel coupling beams, shown in Figure 1.2(d), consist of embedded steel sections (typically wide-flange shapes) within adjacent walls. Steel sections have high stiffness and strength for high aspect ratios and high ductility if embedment detailing is sufficient [7]. The design of the embedment region is critical to the performance of steel coupling beams, where low embedment can result in excessive damage at the beam-wall interface since the loads can not be transferred through bearing forces along the embedment length [8]. Steel-reinforced coupling beams, also known as composite coupling beams, were developed to address the vulnerability of exposed steel to fire and improve design flexibility and strength. As 4 shown in Figure 1.2(e), composite coupling beams have concrete encasement around the structural steel beam, improving fire protection and confinement around the section and reducing local buckling [9]. Compared to steel coupling beams, composite coupling beams utilize the composite action of reinforced concrete to improve the strength and stiffness of the response. However, like steel coupling beams, composite coupling beams require the same detailing in the wall to ensure a stable hysteretic response. Based on Figure 1.2(d), various detailings might be required in steel and composite coupling beams in addition to providing sufficient embedment length. For instance, auxiliary transfer bars, defined as additional bars welded to the embedded steel beam flanges, are required when insufficient vertical reinforcing is provided in the adjacent shear walls. In this regard, auxiliary transfer bars facilitate the load-transferring mechanism in the embedment region [10]. Furthermore, the web stiffener plates are used between the flanges of the steel beam in the clear span to prevent the web buckling of the steel section under shear loads [8]. Additionally, bearing plates are placed at the beam-wall interface and the back of the embedded steel beam to assist with the load-transferring mechanism between the embedded steel section and the structural wall. The bearing plates allow the formation of a diagonal strut between the two plates [11]. In some steel and composite coupling beams, shear stud bolts may be incorporated in the embedment region to enable more composite action between the steel section and surrounding concrete [12]. 5 (a) (b) (c) (d) (e) Figure 1.2: Details of a typical (a) conventionally-reinforced (b) diagonally-reinforced with beam confinement [13](c) diagonally-reinforced with diagonal confinement[13] (d) steel and (e) steel-reinforced (composite) coupling beam. Experimental studies have shown that diagonally-reinforced, steel, and composite coupling beams can provide better seismic performance than conventional coupling beams. However, there are practical challenges and gaps in design provisions for these beams in the Canadian standard, CSA A23.3-19 [5], and the US standard, ACI 318-19 [4], which may limit their use. For instance, CSA A23.3-19 [5] does not have design provisions for steel and composite coupling beams, which 6 restricts their usage in Canada. Moreover, the diagonally-reinforced coupling beam provisions in CSA A23.3-19 [5] and ACI 318-19 [4] were developed based on a small sample of tests. It is unclear whether the current requirements are suitable for the range of diagonally-reinforced coupling beams used in practice. Therefore, a comprehensive analysis of the performance of these beams using a large sample of experimental testing programs is necessary to create comprehensive design provisions. Canadian industry professionals have also identified practical issues related to the design of diagonally-reinforced coupling beams in Canada. For example, based on the ACI 318-19 [4] for confining reinforcing, US building codes allow diagonally-reinforced coupling beams to be designed without ties along the diagonal bundles so long as there is sufficient beam confinement. However, Canadian provisions only allow for diagonally-reinforced coupling beams to be designed using buckling prevention ties placed around diagonal bars, which poses constructability challenges. Additionally, the limit of inelastic rotational capacity of diagonally-reinforced coupling beams in the current Canadian code, CSA A23.3-19 [5], has been limited to 4%, which is lower than observed in many experimental studies [2] [13] [14] [15] [16] [17], resulting in inefficient designs. Steel and composite coupling beams also have several practical challenges. For example, no specific design provisions exist for designing steel and composite coupling beams according to Canadian building codes, i.e., CSA A23.3-19 [5]. AISC 341-16 [18] mandated using auxiliary transfer bars and face-bearing plates (Figure 1.2(d)) for specific types of SFRS systems to ensure that the loads in the embedment region are properly transferred from the wall to the beam. Implementing these additional structural components (auxiliary transfer bars and bearing plates) complicates the construction process, which can result in increased project delays and costs. 7 In AISC 341-22[19], the requirement of using auxiliary transfer bars is relaxed upon designing the wall vertical bars based on the determined forces proportioned to the back bearing force of concrete. Long embedment lengths are necessary in place of using other special detailing, such as ATB, but they can lead to constructability and cost issues. On the other hand, available detailing (i.e., ATB, studs, etc.) is often labour-intensive and can result in congestion and constructability issues on-site. Therefore, there is a need for new, more practical detailing solutions. 1.2 Goals and Objectives This dissertation seeks to contribute to developing practical solutions to improve the seismic response of coupling beams through two phases. Below are the goals and objectives for each phase of the thesis: The goal of phase 1 is to improve our understanding of the seismic response of diagonally-reinforced coupling beams. The objectives of this phase are to 1) develop a comprehensive database of previously tested diagonally-reinforced coupling beams and 2) analyze the database to evaluate current design provisions and to develop new empirical relations for design that will enhance the seismic performance of these beams. The goal of phase 2 is to develop new detailing to improve the seismic response and construction process of steel and composite coupling beams. The objectives of this phase are to 1) develop mathematical and finite element analysis (FEA) models to simulate the response of the new connection and 2) conduct a preliminary analysis of the response of the new connection to understand the impact of design parameters on its performance. 1.3 Organization This thesis is organized into seven chapters with the following content. 8 Chapter 1: Introduction describes the background, motivation, thesis goals and objectives, and thesis organization. Chapter 2: Review of diagonally-reinforced coupling beams and database development explains the mechanical behaviour of diagonally-reinforced coupling beams, current Canadian and the USA building code provisions for designing these beams, and database development of previously experimental programs conducted on diagonally-reinforced coupling beams. Chapter 3: Analysis of diagonally-reinforced coupling beam database summarises a systematic review conducted on the developed database to determine the influence of specific parameters on the seismic performance of these beams. Chapter 4: New connection detailing for steel and composite coupling beams reviews the mechanical behaviour of these beams, current USA building code provisions for designing these beams, and introduces a new connection detailing in steel and composite coupling beams. This chapter also includes the load-transferring mechanism of the steel and composite coupling beams equipped with this new connection detailing and governing equations. Chapter 5: Finite element modelling of new connection detailing for steel and composite coupling beams describes the finite element model developed based on previously tested steel coupling beams, the details of the modelling approach, such as material properties to get the verification, and the comparison between the verified FEM and corresponding experimental data. This chapter includes preliminary studies in which the seismic response of a steel coupling beam equipped with the new connection detailing is investigated. Chapter 6: Conclusions and future work discusses the results of the research conducted on diagonally-reinforced, steel, and composite coupling beams in this thesis. This chapter also 9 explains the potential research works related to the seismic response of coupling beams for the future. 10 Chapter 2: Review of diagonally- reinforced coupling beams and database development 2.1 Introductions Diagonally- reinforced coupling beams (DRCBs) were introduced by Paulay and Binney in 1974 [3] to improve ductility and energy dissipation compared to conventionally-reinforced coupling beams. Since their introduction, numerous experimental studies have been conducted on these beams. Appendix A provides a summary of these experiments. Researchers have explored how various details have impacted the response, and many of these tests have informed the current building code. This chapter reviews the mechanical response of diagonally-reinforced coupling beams, including the basic equations used to calculate shear strength and initial stiffness. After discussing the mechanical behaviour of diagonally-reinforced coupling beams, the current design guidelines for designing these beams in the USA and Canada are described in detail. Finally, a comprehensive database of previously tested diagonally-reinforced coupling beams with different testing variables is developed and presented. 2.2 Mechanical behaviour of diagonally-reinforced coupling beams Coupled shear walls can be defined by the degree of coupling (DOC). DOC is defined as the portion of base overturning moment resistance (𝑀1 and 𝑀2 in Figure 2.1) provided by axial forces in wall piers resulting from shear in coupling beams (Equation 2.1). Based on CSA A23.3-19 [5], if the DOC ratio is higher or equal to 66% is classified as a ductile coupled wall, where a significant portion of the overturning moment is a result of the tension (T) or compression (C) forces (Figure 11 2.1(a)) in the wall piers. Figure 2.1(a) and Figure 2.1(b) show a highly coupled wall and a wall with no coupling, respectively. 𝐷𝑂𝐶 =𝑇𝐿𝑇𝐿 +𝑀1 +𝑀2 2.1 Figure 2.1: Performance of shear walls as (a) coupled and (b) partially coupled. When shear forces are applied to a typical diagonally-reinforced coupling beam, they are transferred to the adjacent shear walls through diagonal bars. Within these bars, one group functions as a compression strut, while the other serves as a tension tie. Figure 2.2 shows the simplified load-transferring mechanism in DRCBs, where 𝐴𝑠𝑑 is the area of diagonal bars in each 12 direction, 𝑓𝑦𝑑 is the yield strength of diagonal bars, 𝐿 is the clear span length, 𝛼 is the angle between diagonal bars and horizontal direction, 𝑣𝑢 is the applied shear force, 𝑀𝑢 is the resultant moment due to the applied shear force, and 𝐶𝑢 and 𝑇𝑢 are the compression and tension forces developed in the diagonal bars, respectively. Figure 2.2: Internal forces of a typical diagonally-reinforced coupling beam. The equation for the equilibrium of vertical forces is shown below. ∑𝐹𝑦 = 0 → 𝐶𝑢𝑠𝑖𝑛𝛼 + 𝑇𝑢𝑠𝑖𝑛𝛼 − 𝑉𝑢 = 0 → 𝐴𝑠𝑑𝑓𝑦𝑑𝑠𝑖𝑛𝛼 + 𝐴𝑠𝑑𝑓𝑦𝑑𝑠𝑖𝑛𝛼 − 𝑉𝑢 = 0 Since the capacity of concrete is lower than diagonal steel bars, generally, the contribution of concrete is neglected, and it can be assumed that 𝑇𝑢 = 𝐶𝑢. Consequently, the shear capacity of a DRCB is calculated by Equation 2.2. 𝑉𝑢 = 2𝐴𝑠𝑑𝑓𝑦𝑑𝑠𝑖𝑛𝛼 2.2 Similarly, the moment corresponding to the shear capacity of a DRCB is obtained by Equation 2.3. 𝑀𝑢 =𝑉𝑢𝐿2 2.3 13 According to Equation 2.2, the shear capacity of DRCBs highly depends on the angle between diagonal bars and horizontal direction (𝛼) Based on Figure 2.3, by increasing L/h and consequently decreasing 𝛼, sin⁡(𝛼) will be decreased, where 𝛼 = tan−1ℎ𝐿. According to Equation2.2, by assuming a constant value for diagonal bars area (𝐴𝑠) and decreasing sin⁡(𝛼), the shear capacity of DRCBs will decrease. Hence, more 𝐴𝑠 is required to achieve high shear strength for high aspect ratio coupling beams. Figure 2.3: Correlation between aspect ratio and angle between diagonal bars and horizontal direction in diagonally-reinforced coupling beams. To understand the lateral displacements of coupling beams during the earthquakes, Figure 2.4 shows the typical deformations. Since it is assumed that coupling beams are fixed at the beam-wall interface, these beams exhibit double curvatures in terms of deformation. Generally, coupling beams experience both shear and flexural displacements. It has been observed that stocky coupling beams with low aspect ratios have significant shear deformation [14]. However, in slender 14 coupling beams with a high aspect ratio, the predominant mode of deformation is flexural displacements [2] [13]. Figure 2.4: The deformation of coupling beams before (Detail a) and after (Detail b) of applying the lateral loads. 15 Under large deformations, the coupling beams crack; as a result, modification factors 𝛼𝑓 and 𝛼𝑠 can be used to reduce the flexural moment of inertia and shear area, respectively. Using these modification factors, the effective moment of inertia (Ieff) and shear area (A𝑣𝑒) can be calculated by Equations 2.4 and 2.5, respectively. 𝐼𝑒𝑓𝑓 = 𝛼𝑓𝐼𝑔 2.4 𝐴𝑣𝑒 = 𝛼𝑠𝐴𝑔 2.5 Where I𝑔 is the gross moment of inertia of the coupling beam section, 𝐴𝑔 is the gross area of concrete beam section as a product of beam’s width (𝑏𝑤) and depth (ℎ). CSA A23.3-19 [5] recommends 𝛼𝑠 = 0.45 and 𝛼𝑓 = 0.25 for the modification factors for shear and flexural stiffness, respectively. ACI 318-19 [4] recommends modifying the flexural stiffness by 𝛼𝑓 = 0.35 and assuming elastic properties for shear stiffness (𝛼𝑠 = 1.00). When using nonlinear analysis, both ACI 318-19 [4] and Los Angeles Tall Buildings Structural Design Council (LATBSDC) 2023 [20] recommend 𝛼𝑓 = min (0.3,0.07𝐿ℎ) for the initial flexural stiffness and 𝛼𝑠 = 1.00 for shear stiffness. The total deflection of DRCBs (𝛥𝑡) that includes flexural (𝛥𝐹) and shear (𝛥𝑠) deformations can be calculated using Equation 2.6. Δt =𝑉Ki= ΔF + ΔS 2.6 where 𝑉 is the applied shear force, 𝐾𝑖 is the stiffness, 𝛥𝐹 is the flexural deformation shown in Equation 2.7, and 𝛥𝑠 is the shear deformation shown in Equation 2.8. ΔF =𝑉 × L312𝛼f × Ec × Ig 2.7 16 ΔS =𝑉 × L𝛼𝑠 × Gc × Av 2.8 where 𝐺𝑐 is the shear modulus of reinforced concrete (𝐺𝑐 =𝐸𝑐2(1+ν)), ν is Poisson ratio (0.25 used for reinforced concrete), and 𝐸𝑐 is the elastic modulus of reinforced concrete obtained by 3300√𝑓𝑐′ + 6900 + (𝛾𝑐2300)1.5 (MPa units) based on CSA A23.3-19 [5] and 0.043√𝑓𝑐′𝛾𝑐1.5⁡(MPa units) based on ACI 318-19 [4], where 𝛾𝑐 is the concrete density (assumed 2300 kg/m3) and 𝑓𝑐′ is the concrete compressive strength. By substituting Equations 2.7 and 2.8 in Equation 2.6, Equation 2.9 is obtained. Δt =𝑉Ki=𝑉 × L312𝛼f × Ec × Ig+𝑉 × L𝛼𝑠 × Gc × Av=𝑉L312𝛼fEc112 𝑏ℎ3+𝑉L𝛼𝑠𝐸𝑐2(1 + ν)bh 2.9 By substituting Equation 2.9 into Equation 2.6, the initial stiffness of the coupling beam is determined by Equation 2.10. Ki = bwEcCK 2.10 where 𝐶𝑘 is a unitless parameter representing the effect of flexural and shear deformations shown by Equation 2.11. CK =αf×αs2(1+ν)×αf×Lh+αs×(Lh)3 2.11 Note that 𝐶𝑘 is a unitless parameter introduced in this thesis and will be further discussed in Section 3.7. 17 2.3 Building code provisions for designing diagonally-reinforced coupling beams This section highlights the essential design parameters for coupling beams designed according to Canadian design (CSA A23.3-19 [5]) and US design (ACI 318-19 [4]). These procedures outline the detailing requirements to produce ductile DRCBs, suitable for use in special coupled walls (ACI 318-19 [4]) or ductile coupled wall systems (CSA A23.3-19 [5]). While both CSA A23.3-19 [5] and ACI 318-19 [4] aim to ensure a stable ductile response, their detailing requirements differ. For instance, ACI 318-19 [4] allows for beam confinement, in which beam ties encase the concrete surrounding the beam while no ties are provided on the diagonal reinforcement, as well as the so-called diagonal confinement, where ties are applied around the diagonals, with minimal beam ties. In contrast, CSA A23.3-19 [5] only includes provisions for buckling prevention ties on the diagonals without specific requirements for beam ties. There are also specific geometric conditions that must be met to use DRCBs. For instance, ACI 318-19 [4] specifies that the aspect ratio must be L/h≤4. CSA A23.3-19 [5] dimensional limits include L/h ≥0.5, and the beam width (b) must be less than or equal to the wall thickness (tw). Both CSA A23.3-19 [5] and ACI 318-19 [4] assume that the shear force in a DRCB is entirely resisted by the diagonal bars, with the concrete's contribution being neglected when calculating the shear strength. Following this design philosophy, the nominal shear strength of a DRCB, where the top diagonal bundle has an equal area to the bottom bundle, can be determined using Equation2.2. 18 ACI 318-19 [4] limits the maximum nominal shear capacity (Equation 2.2) to Equation 2.12. This limit was informed by Barney et al., 1980 [6], which showed that specimens under this limit behaved in a reasonably ductile manner. CSA A23.3-19 [5] has no such limit. 𝑉𝑛 ≤ 0.83√𝑓𝑐′𝐴𝑐𝑤 2.12 In terms of diagonal ties, Both ACI 318-19 [4] and CSA A23.3-19 [5] include an option for providing ties around the diagonal bundles, which involves tying the diagonal bars with hoops or stirrups at specified spacing. Minimum longitudinal bars and beam ties are provided to control the width of inclined cracks and are not intended to contribute to confinement. ACI 318-19 [4] requires a minimum total cross-section area of transverse reinforcement in the beam (𝐴𝑠ℎ) to prevent buckling of the diagonal bars and provide confinement for the whole beam. According to Clause 18.10.7.4c, 𝐴𝑠ℎ is calculated per Equation 2.13. 𝐴𝑠ℎ⁡ ≥ 𝑚𝑎𝑥 {0.09𝑠𝑑𝑏𝑐𝑓𝑐′𝑓𝑦𝑡, 0.3𝑠𝑑𝑏𝑐(𝐴𝑔𝐴𝑐ℎ− 1)𝑓𝑐′𝑓𝑦𝑡} 2.13 𝑏𝑐 is the confined beam width or depth measure to the outside edges of the transverse reinforcement around the confined area; 𝑓𝑦𝑡 is the yield strength of the transverse bars; 𝐴𝑔 is the confined area calculated using the concrete cover on all four sides of each group of diagonal bars and including the transverse bars; 𝐴𝑐ℎ is the confined area provided around each group of diagonal bars, measured to the outside edges of transverse reinforcement; and sd is the spacing of ties around diagonal bars (Equation 2.14). 𝑠𝑑 ≤ 𝑚𝑖𝑛{6𝑑𝑏 , 𝑠0} 2.14 𝑑𝑏 is the diameter of diagonal bars, and 𝑆0 is determined using Equation 2.15. 19 100⁡𝑚𝑚 ≤ 𝑠0 = 100⁡mm +350mm − ℎ𝑥3≤ 150⁡𝑚𝑚 2.15 ℎ𝑥 is the maximum distance measured from centerline to centerline of laterally supported diagonal bars in each bundle. ACI 318-19 [4] Clause 18.10.7.4c requires crack control transverse bars in the beams. The minimum total area of beam transverse bars is shown in Equation 2.16. 𝐴𝑠,𝐿𝑜𝑛𝑔 ≥ 0.002𝑏𝑤𝑠𝑡 2.16 𝑠𝑡 is the spacing between ties, which should be less than 300 mm, and 𝑏𝑤 is the coupling beam’s width. Figure 2.5 illustrates the design requirements recommended by ACI 318-19 [4] of an DRCB with diagonal confinement. Figure 2.5: ACI 318-19 requirements for a typical DRCB with diagonal confinement. CSA A23.3-19 [5] design only requires buckling prevention ties around the diagonal bars, without any specific requirements for beam ties. The buckling prevention ties are required to have a minimum spacing of sd, determined in 21.5.8.2.4 and shown in Equation 2.17. 𝑠𝑑 ≤ 𝑚𝑖𝑛{6𝑑𝑏 , 24𝑑𝑡𝑖𝑒 , 100𝑚𝑚} 2.17 𝑑𝑡𝑖𝑒 is the diameter of the buckling prevention ties. 20 Figure 2.6 illustrates the design requirements recommended by CSA A23.3-19 [5] of an DRCB with anti-buckling ties around diagonal bars. Figure 2.6: CSA A23.3-19 requirements for a typical DRCB with anti-buckling ties around diagonal bars. Installing ties around each group of diagonals presents constructability challenges, particularly at the intersection point. To overcome the constructability issues, full beam confinement was introduced in ACI 318-08 [21]. Full beam confinement entails confining the entire beam section with an outer hoop and crossties. In this scenario, hoops or stirrups do not confine the diagonal bar bundles. This method is often preferred in the US due to the simplified installation of diagonal reinforcement [2]. However, CSA A23.3-19 [5] does not provide guidance for full beam ties. ACI 318-19 [4] Clause 18.10.7.4d recommends that for beam confinement, the minimum amount of total cross-section area of transverse reinforcement in the beam (𝐴𝑠ℎ) is calculated using Equation 2.18. 𝐴𝑠ℎ ≥ 𝑚𝑎𝑥 {0.09𝑠𝑡𝑏𝑐𝑓𝑐′𝑓𝑦𝑡, 0.3𝑠𝑡𝑏𝑐(𝐴𝑔𝐴𝑐ℎ− 1)𝑓𝑐′𝑓𝑦𝑡} 2.18 21 𝑏𝑐 is the beam’s width or depth excluding the concrete cover from each side; 𝐴𝑔 is the gross area of the beam’s section; 𝐴𝑐ℎ area of the beam’s section excluding the concrete cover from each side, and 𝑠𝑡 is the maximum spacing between the tie legs, which is determined in Equation 2.19. 𝑠𝑡 ≤ 𝑚𝑖𝑛{6𝑑𝑏 , 150𝑚𝑚} 2.19 Figure 2.7 depicts the design requirements recommended by ACI 318-19 [4] of a typical DRCB with full beam confinement. Figure 2.7: ACI 318-19 requirements for a typical DRCB with full beam confinement. Design forces and deformation demand in coupled wall systems are typically determined using the linear dynamic method in the ASCE 7-16 [22] or NBC 2020 [23]. During earthquakes, the DRCBs stiffness degrades due to the cracking of concrete. Therefore, an effective cracked section stiffness is required by design codes in the linear dynamic analysis (Section 2.2). In addition to initial stiffness as a critical parameter in the behaviour of coupling beams, ductility defined as a structure's ability to deform significantly without a substantial loss of strength, becomes pivotal in seismic design. In seismic-prone areas, coupling beams must exhibit ductile 22 behaviour to absorb and dissipate energy during earthquakes. Therefore, coupling beams are expected to undergo inelastic rotation beyond the elastic limit. CSA A23.3-19 [5] requires the inelastic rotational demand to be less than 4%. ACI 318-19 [4] does not have such a check on the rotational capacity of beams. However, LATBSDC 2023 [20], recommends a total chord rotation capacity of 6%. 2.4 Database development of diagonally-reinforced coupling beams An extensive database was compiled using experimental data from 51 diagonally-reinforced coupling beam specimens tested between 1974 and 2019 (Table 2.1). Specimens used in this database underwent cyclic loading until failure, except for Paulay and Binney, 1974 [3] and Gonzalez, 2001 [24]. These beams were subjected to peak cyclic loading of 1.2% and 6.5%, respectively, followed by monotonic loading until failure. A detailed summary of all of the testing programs can be found in Appendix A. In addition to studying many of the parameters used in the design, described in Section 2.3, researchers also explored different aspect ratios (L/h), the presence of axial restraint (AR), embedded longitudinal bars (ELB), and the presence of diagonal ties on the cyclic response of DRCBs. Specimens were classified as low or high aspect ratios based on L/h=1.5 as the limit. This deviates from ACI-318-19's [4] classification based on L/h≤2.0. However, the test data indicated that specimens with L/h≤1.5 exhibited significant shear deformation and failure modes commonly associated with shear failures. Therefore, L/h≤1.5 was used in this study [25][26][27][28][29]. Figure 2.8(a) shows the aspect ratio distribution within the database, with 14 (27%) specimens considered low aspect ratio (L/h≤1.5) and 37 (73%) as high aspect ratio (L/h>1.5). 23 Under cyclic loading, DRCBs experience elongation due to concrete cracking and reinforcement yielding. However, adjacent walls and floor diaphragms can restrain this elongation, generating axial forces that may influence the strength and rotational capacity of these beams. Consequently, axial restraint (AR) was identified as a critical test characteristic. AR is divided into three categories: 1) the presence of slab, 2) the presence of post-tensioned (PT) rods, and 3) rigid constraint in the testing setup. If the slab is present, it means that the researchers have tested a T-beam. The flanges on top of the beam represent a slab in this case. In some experiments, researchers included post-tensioned (PT) rods to provide limited restraint. When a displacement occurred in the beam, the PT rods elongated, adding an additional axial force to the beam. Finally, the rigid constraint indicates that the experimental setup prevented any axial elongation [13]. Appendix A includes an example of such a setup. Additionally, in the developed database, there were two specimens (CB24F-PT and CB24F-1/2-PT) tested by Naish et al., 2013 [2], which had both PT rods and slab simultaneously providing axial restraint. Figure 2.8(b) shows the distribution of AR in the database. As shown in Figure 2.8(b), 34 (67%) specimens did not have axial restraints, with slightly over half (58%) of the 17 specimens with axial restraints having rigid constraints. 24 Figure 2.8: Distribution of specimens of different (a) aspect ratios and (b) axial restraint. The literature review in Appendix A highlights that many experiments have longitudinal bars with long embedment lengths into walls, ensuring that the bars develop tension strength into the adjacent shear walls (Greater than 1.25⁡𝑓𝑦 development length). While such specimens are not allowed in CSA A23.3-19 [5] or ACI 318-19 [4], they can significantly contribute to strength. Therefore, it is worth including them in the database as their performance could provide insight into the performance of DRCBs. In the provided database, 22 (43%) specimens had embedded longitudinal bars referred to as ELB. It is difficult to categorize the beams based on confinement without assuming confinement assumptions. This is particularly challenging since some of the specimens were designed without considering either CSA A23.3-19 [5] or ACI 318-19 [4]. As a result, the beams were categorized based on whether they included ties in the diagonals. In the analyzed specimens, 35 (69%) did not include diagonal ties, while 16 (31%) included diagonal ties. 25 Table 2.1 summarizes the authors, specimen names, geometry, material strengths, and reinforcement details of the studied diagonally-reinforced coupling beams through the literature review. In Table 2.1, 𝑠𝑑, 𝑠𝑡, and ℎ are defined as spacing between ties around diagonal bars, spacing between beam ties, and coupling beams’ overall depth, respectively. Table 2.1: General information about studied specimens. Author Name L/h Category AR type sd, st, α bw, h, f'c, Diagonals mm mm ° mm mm MPa # Name fy, MPa ≤ Paulay & Binney, 1974 Beam 316* 1.29 ELB Only None None 150 36 152 787 33 4 #7 288 3 #8 287 Beam 317 1.29 Neither ELB nor AR None 100 150 36 152 787 51 4 #7 306 3 #8 270 Beam 395 1.03 Neither ELB nor AR None 100 150 20 152 991 36 4 #7 259 3 #8 289 Galano et al., 2000 P07 1.5 AR+ELB Rigid None 120 28.5 150 400 54 8 #3 566 P12 1.5 AR+ELB Rigid 150 120 28.5 150 400 42 8 #3 566 Dugas 2002 D30 1.136 Neither ELB nor AR None 60 275 30 300 880 33 8 20M 456 Kwan et al., 2002 CCB11 1.17 ELB only None 60 140 35.8 120 600 37.8** 12 T8 517 Canbolat et al., 2005 S1 1 ELB only None 75 75 36 200 600 41 8 D13 450 Yun et al. 2008 CB-1 1 AR+ELB Rigid None 150 30 200 600 44 4 D16 474 Lim et al., 2015 CB10-1 1 ELB only None None 100 26 250 500 35 8 D25 486 Howard, 2017 CC-16db 1.136 Neither ELB nor AR None 320 300 30 300 880 38 8 20M 457 MD-10db 1.136 Neither ELB nor AR None 200 300 30 300 880 42 8 20M 457 MD-8db 1.136 Neither ELB nor AR None 160 300 30 300 880 43 8 20M 457 D-6db 1.136 AR only PT 120 300 30 300 880 45 8 20M 457 L/h>1.5 Barney et al., 1980 C6 2.5 Neither ELB nor AR None None 33.8 19 102 169 18.1 1 #4 408 C8 5 Neither ELB nor AR None None 33.8 9.5 102 169 23.9 1 #4 433 Ishikawa et al., 1991 1 1.78 ELB only None None 90 17.5 300 450 42 4 D22 523 2 1.78 ELB only None None 90 17.5 300 450 46 6 D22 523 3 1.78 ELB only None None 90 17.5 300 450 45 6 D22 523 4 1.78 AR+ELB Slab None 90 17.5 300 450 48 6 D22 523 5 1.78 ELB only None None 45 17.5 300 450 27 6 D22 523 6 1.78 ELB only None None 25 17.5 300 450 51 6 D22 523 7 1.78 ELB only None None 90 17.5 300 450 52 6 D22 523 8 1.78 ELB only None None 90 17.6 300 450 45 8 D19 387 Sonobe et al. 1995 LX7L 2.8 ELB only None None 80 12.9 240 350 37.7 8 D16 528 NX7L 2.8 ELB only None None 80 12.9 240 350 38.1 8 D16 528 Gonzalez, 2001 K1* 2.74 AR only PT 100 244 12.3 305 445 35.6 8 30M 464 Zhou, 2003 CB-2 3 ELB only None None 110 14.6 300 500 35.6 4 25M 461 Shimazaki, 2004 N-1 2.5 ELB only None None 150 19.3 200 400 54 8 D16 476 N-2 2.5 ELB only None None 100 19.3 200 400 51 8 D16 459 Fortney et al, 2008 DCB1 2.57 ELB only None 76 76 13 254 356 37.6 4 #8 431 DCB2 3 Neither ELB nor AR None 51 51 13 254 305 55.3 4 #7 477 26 Author Name L/h Category AR type sd, st, α bw, h, f'c, Diagonals mm mm ° mm mm MPa # Name fy, MPa L/h>1.5 Naish et al., 2013 CB24F 2.4 Neither ELB nor AR None None 76 15.7 305 381 47.2 12 #7 482 CB24D 2.4 Neither ELB nor AR None 63.5 63.5 15.7 305 381 47.2 12 #7 482 CB24F-RC 2.4 AR only Slab None 76 15.7 305 381 50.4 12 #7 482 CB24F-PT 2.4 AR only PT+Slab None 76 15.7 305 381 49.9 12 #7 482 CB24F-1/2-PT 2.4 AR only PT+Slab None 152.4 15.7 305 381 48.2 12 #7 482 CB33F 3.33 Neither ELB nor AR None None 76 12.3 305 457 47.2 12 #7 482 CB33D 3.33 Neither ELB nor AR None 63.5 63.5 12.3 305 457 47.2 12 #7 482 Lim et al., 2015 CB20-1 2 ELB only None None 100 16 300 500 52.1 8 D29 466 Lim et al., 2016 CB30DA 3 ELB only None 150 200 8.8 300 500 39.7 8 #10 464 CB30DB 3 ELB only None None 100 8.8 300 500 38.4 8 #10 464 Ameen et al., 2017 CB1 1.89 Neither ELB nor AR None None 76.2 18 254 457 41 12 #7 434 Poudel, 2018 CB1A 1.89 AR only PT None 76.2 18 250 460 44 12 #7 434 Han et al., 2019 T1002.0 2 AR only Rigid None 120 20.4 250 525 44 8 D22 477 T772.0 2 AR only Rigid None 170 20.4 250 525 43 8 D22 477 T502.0 2 AR only Rigid None 250 20.4 250 525 43 8 D22 477 T302.0 2 AR only Rigid None 300 20.4 250 525 43 8 D25 481 T1003.5 3.5 AR only Rigid None 110 8.9 250 300 43 8 D25 481 T50-3.5 3.5 AR only Rigid None 250 8.9 250 300 44 8 D25 481 T30-3.5 3.5 AR only Rigid None 500 8.9 250 300 44 8 D25 481 * These specimens were loaded cyclically until a specific total chord rotation, then continued monotonically until failure. ** Value is calculated cylinder strength based on cube test. In the developed database, key backbone parameters from the tested DRCBs are documented, specifically maximum shear (𝑉𝑚𝑎𝑥), degradation rotation (𝜃80%), and initial stiffness (𝐾𝑖). 𝑉𝑚𝑎𝑥 is an important parameter since it indicates the maximum shear capacity of a coupling beam before strength degradation happens. 𝜃80% is also a crucial parameter in the seismic design of coupling beams as it reparents the ability of a coupling beam to undergo inelastic rotations prior to losing a significant portion of its load-resisting capability. Finally, 𝐾𝑖 is an important parameter by which the total and inter-story displacements of buildings can be calculated. Figure 2.9 illustrates the studied parameters. For each studied specimen, the backbones are digitized based on the provided hysteresis diagrams in the literature, and a MATLAB code was written for data processing. 27 Figure 2.9: Backbone curve for coupling beam models. 𝑉𝑚𝑎𝑥 represents the largest shear force magnitude sustained by the specimen, taken as the maximum absolute value of shear in both positive (loading) and negative (unloading) directions (i.e., 𝑉𝑚𝑎𝑥 =max (+𝑉𝑚𝑎𝑥, |- 𝑉𝑚𝑎𝑥 |)). Initial stiffness (𝐾𝑖) corresponds to the stiffness of the beam at the hysteresis diagram's first breaking point in both positive and negative directions. Degradation rotation (𝜃80%) is the total chord rotation determined when strength degrades to 80% of the peak resisted shear force. In the conducted analysis, degradation rotation in positive (loading) and negative (unloading) directions (i.e., 𝜃80%=min (+ 𝜃80%, |- 𝜃80%|)) was examined. Additionally, specimens were considered ductile if they had a minimum θ80% of 6%, corresponding to the performance limit recommended by LATBSDC 2023 [20]. Table 2.2 presents the maximum shear capacity and degradation rotation of the specimens in the database. Additionally, in this thesis, initial stiffness (𝐾𝑖) corresponds to the stiffness of the beam at the hysteresis diagram's first breaking point in both positive and negative directions. Having said this, 𝐶𝑘,𝑒𝑥𝑝 can be calculated for each studied specimen upon Equation 2.20. 𝐶𝐾,𝑒𝑥𝑝 =𝐾𝑖,𝑒𝑥𝑝𝑏𝑤𝐸𝑐⁡⁡ 2.20 The calculated values for 𝐶𝑘,𝑒𝑥𝑝 can be found in Table 2.2. 28 Table 2.2: Seismic parameter values of studied specimens. Author Name L/h Category AR type Vmax, θ80% Ck,exp kN rad ≤ Paulay & Binney, 1974 Beam 316* 1.29 ELB Only None 633.5 0.063 0.037 Beam 317 1.29 Neither ELB nor AR None 611.0 0.061 0.031 Beam 395 1.03 Neither ELB nor AR None 644.9 0.062 0.044 Galano et al., 2000 P07 1.5 AR+ELB Rigid 236.1 0.049 0.014 P12 1.5 AR+ELB Rigid 237.7 0.037 0.010 Dugas 2002 D30 1.136 Neither ELB nor AR None 619.3 0.028 0.068 Kwan et al., 2002 CCB11 1.17 ELB only None 342.5 0.053 0.027 Canbolat et al., 2005 S1 1 ELB only None 474.5 0.037 0.031 Yun et al. 2008 CB-1 1 AR+ELB Rigid 725.2 0.015 0.035 Lim et al., 2015 CB10-1 1 ELB only None 1457.1 0.061 0.024 Howard, 2017 CC-16db 1.136 Neither ELB nor AR None 688.5 0.025 0.049 MD-10db 1.136 Neither ELB nor AR None 773.8 0.031 0.041 MD-8db 1.136 Neither ELB nor AR None 736.6 0.028 0.036 D-6db 1.136 AR only PT 998.8 0.019 0.046 L/h>1.5 Barney et al., 1980 C6 2.5 Neither ELB nor AR None 63.9 0.061 0.009 C8 5 Neither ELB nor AR None 37.2 0.067 0.002 Ishikawa et al., 1991 1 1.78 ELB only None 471.9 0.096 0.012 2 1.78 ELB only None 670.7 0.069 0.012 3 1.78 ELB only None 713.0 0.050 0.013 4 1.78 AR+ELB Slab 749.0 0.069 0.013 5 1.78 ELB only None 615.0 0.076 0.013 6 1.78 ELB only None 771.5 0.102 0.012 7 1.78 ELB only None 708.6 0.053 0.012 8 1.78 ELB only None 620.1 0.073 0.014 Sonobe et al. 1995 LX7L 2.8 ELB only None 389.7 0.066 0.006 NX7L 2.8 ELB only None 370.2 0.067 0.006 Gonzalez, 2001 K1* 2.74 AR only PT 983 0.128 0.008 Zhou, 2003 CB-2 3 ELB only None 482 0.037 0.005 Shimazaki, 2004 N-1 2.5 ELB only None 370.6 0.025 0.009 N-2 2.5 ELB only None 405.5 0.037 0.011 Fortney et al., 2008 DCB1 2.57 ELB only None 613.05 0.047 0.008 DCB2 3 Neither ELB nor AR None 413.5 0.120 0.008 Naish et al., 2013 CB24F 2.4 Neither ELB nor AR None 760.82 0.098 0.009 CB24D 2.4 Neither ELB nor AR None 708.20 0.087 0.016 CB24F-RC 2.4 AR only Slab 848.5 0.104 0.010 CB24F-PT 2.4 AR only PT+Slab 942.3 0.090 0.011 CB24F-1/2-PT 2.4 AR only PT+Slab 864.5 0.083 0.010 CB33F 3.33 Neither ELB nor AR None 551.4 0.080 0.004 CB33D 3.33 Neither ELB nor AR None 536.6 0.060 0.007 Lim et al., 2015 CB20-1 2 ELB only None 1078.4 0.078 0.009 Lim et al., 2016 CB30DA 3 ELB only None 688.7 0.076 0.005 CB30DB 3 ELB only None 737.5 0.082 0.006 Ameen et al., 2017 CB1 1.89 Neither ELB nor AR None 824.0 0.076 0.017 Poudel, 2018 CB1A 1.89 AR only PT 1070.4 0.071 0.017 Han et al., 2019 T1002.0 2 AR only Rigid 1079.0 0.061 0.010 T772.0 2 AR only Rigid 914.1 0.059 0.009 T502.0 2 AR only Rigid 826.2 0.045 0.009 T302.0 2 AR only Rigid 866.0 0.033 0.008 T1003.5 3.5 AR only Rigid 499.0 0.098 0.004 T50-3.5 3.5 AR only Rigid 380.8 0.056 0.004 T30-3.5 3.5 AR only Rigid 280.9 0.029 0.004 29 2.5 Summary This chapter studied the mechanical behaviour of diagonally-reinforced coupling beams (DRCBs). Through this study, a unitless parameter called 𝐶𝐾 was developed by which the initial stiffness of diagonally-reinforced coupling beams can be calculated (will be discussed in Section 3.7). Moreover, the current design guidelines for designing diagonally-reinforced coupling beams in Canada and the USA were reviewed in detail. Based on the code review section, it was found that the beam tie option is missing in CSA A23.3-19 [5]. A new database was developed based on a comprehensive literature review of 51 tested diagonally-reinforced coupling beams (presented in Appendix A). This database included several features of previously tested diagonally-reinforced coupling beams, such as embedded longitudinal bars (ELB), axial restraint (AR), and diagonal or beam ties provided for diagonal bars. Furthermore, structural parameters such as shear strength and degradation rotation of each studied diagonally-reinforced coupling beam in the database were derived and presented. Since each experimental program conducted in these beams had a limited scope of the study (i.e., specific range of L/h, presence of ELB or AR, and different transverse reinforcing orientation), the effect of each of these parameters on the seismic behaviour of diagonally-reinforced coupling beams could not be determined. Therefore, a systematic review of diagonally-reinforced coupling beams is needed to investigate the trends between specific design requirements and seismic/design parameters. 30 Chapter 3: Analysis of diagonally-reinforced coupling beam database 3.1 Introduction This chapter analyses the diagonally-reinforced coupling beams (DRCBs) database developed in Chapter 2. It aims to evaluate the current design procedures and suggest new design recommendations. Specifically, it examines the impact of design parameters on overstrength and develops recommendations for estimating overstrength for beams with embedded longitudinal bars (ELBs) and axial restraints (AR). The chapter also investigates the impact of various detailing, such as beam ties, diagonal ties, and the quantity of diagonal reinforcing, on the rotational capacity of the beams (i.e., 𝜃80%) in detail. Finally, the chapter concludes with an in-depth investigation into the stiffness of the diagonally-reinforced coupling beams, using the newly developed 𝐶𝑘 factor previously introduced in Section 2.2. 3.2 Impact of design parameters on overstrength Overstrength is defined as a ratio of maximum recorded shear strength (𝑉𝑚𝑎𝑥) over the expected shear capacity (𝑉𝑛𝑒) calculated per Equation 2.2 with measured material strength (from Table 2.1). Figure 3.1 depicts the range of overstrength (𝑉𝑚𝑎𝑥𝑉𝑛𝑒) for all specimens and specimens with only axial restraints (AR Only), only embedded longitudinal bars (ELB Only), both AR and ELB (AR+ELB), and with neither AR nor ELB. Values of 𝑉𝑚𝑎𝑥𝑉𝑛𝑒 Specimens with Neither AR nor ELB had a median overstrength of about 1.25, which aligns with the overstrength used in the capacity design procedure by CSA A23.3-19 [5]. The presence of an axial restraint increased the overstrength. Specimens with AR Only had a median overstrength of can be found in Table B-1 in Appendix B.31 1.64, about 30% higher than the overstrength used in the CSA A23.3-19 [5] design. Specimens with ELB Only and specimens with ELB+AR had the highest overstrength, with a median overstrength of 1.86 and 1.8, respectively, about a 40% higher overstrength than used in the CSA A23.3-19 [5] design. Specimens with Neither ELB nor AR had a low range of overstrength compared to other specimens. Specimens with AR+ELB had a significant dispersion, with overstrength ranging from 1.54 to 3.8. The specimen with an overstrength equal to 3.8 is CB-1 tested by Yun et al. in 2008 [30]. This significant overstrength is attributed to substantial ELBs and an experimental setup which ensured a rigid boundary condition. In specimens with AR Only, overstrength ranged from 0.9 to 2.1, while the overstrength of specimens with ELB Only ranged from 1.5 to 2.3. The higher dispersion for overstrength in specimens with axial restraints and embedded longitudinal bars indicates that Equation 2.2 underestimates the shear strength of DRCBs. Figure 3.1: Range of 𝑉𝑚𝑎𝑥𝑉𝑛𝑒 for specimens with different characteristics: i) All specimens, ii) Axial restraint only (AR Only), iii) Embedded Longitudinal Bars only (ELB Only), iv) Both AR and ELB (AR+ELB), and v) Neither AR nor ELB. MaxMin75%Median25% utlier 32 In the case of ELB, the determination of strength could be improved by considering the total shear strength (𝑉𝑡), shown in Equation 3.1, which includes the contribution from the ELB bars. 𝑉𝑡 = 𝑉𝑚𝑒 + 𝑉𝑛𝑒 3.1 Where 𝑉𝑚𝑒 is the shear force corresponding to the flexural capacity of the ELB, shown in Equation 3.2. 𝑉𝑚𝑒 =2𝑀𝑛𝑒𝐿 3.2 ⁡ Figure 3.2 shows the distribution of 𝑉𝑚𝑒𝑉𝑡 for ELB specimens. Most of these specimens had over 30% of the shear strength being contributed from the longitudinal reinforcing, accounting for the high overstrength observed in Figure 3.1. Where 𝑀𝑛𝑒 is the moment capacity of the ELB.For a symmetric section, 𝑀𝑛𝑒 can be approximated using Equation 3.3, assuming a simple,symmetric section, neglecting skin reinforcing, and axial forces.𝑀𝑛𝑒 = 𝐴𝑠𝑙𝑓𝑦𝑙𝑒(𝑑 − 𝑑′) 3.3where 𝐴𝑠𝑙 is the area of longitudinal bars, 𝑓𝑦𝑙𝑒 is the expected yield strength of longitudinal bars,and d and d′ are the effective depths of longitudinal bars in tension and compression zones,respectively (Table B-2).33 Figure 3.2: Distribution of specimens with ELB based on 𝑉𝑚𝑒𝑉𝑡. Figure 3.3 shows the total overstrength (i.e., 𝑉𝑚𝑎𝑥𝑉𝑡) for all specimens and specimens with AR Only, ELB Only, AR+ELB, and Neither AR nor ELB. In the calculation of 𝑉𝑡 axial forces were not included. As a result, the overstrength for specimens with AR Only and specimens with Neither AR nor ELB are unchanged from Figure 3.1. In other words, for specimens with AR Only and neither AR nor ELB, the 𝑉𝑚𝑒 term in Equation 3.1 is zero. Using 𝑉𝑡 to calculate shear strength results in a more uniform overstrength between specimen categories. Specimens with ELB Only and AR+ELB now have similar median values, equal to 1.18 and 1.21, respectively. These results indicate that Equation 3.1 is a reasonable approximation to account for the added strength provided by ELB. Values of 𝑉𝑚𝑎𝑥𝑉𝑡 and 𝑉𝑚𝑒 can be found in Table B-1in Appendix B.34 Figure 3.3: Range of 𝑉𝑚𝑎𝑥𝑉𝑡 for specimens with different characteristics: i) All specimens, ii) Axial restraint Only (AR Only), iii) Embedded Longitudinal Bars Only (ELB Only), iv) Both AR and ELB (AR+ELB), and v) Neither AR nor ELB. Equation 3.1 does not consider the concrete contribution or axial loads. However, concrete can significantly contribute to the ultimate strength of the beam, particularly when the slab is considered. To address this issue, flexural capacity at the beam-wall interface using an equivalent stress block for concrete, as prescribed in CSA23.3-19 [5] for typical beams, is calculated. When applicable, the capacity was computed with the inclusion of slabs and applied axial stress. The moment capacity only considers resistance longitudinal to the beam; thus, the area of the steel diagonals was reduced in accordance with Equation 3.4. The shear force corresponding to the flexural capacity for a beam in double curvature is shown in Equation 3.5. 𝐴𝑚 = Asd𝑐𝑜𝑠(𝛼)⁡⁡ 3.4 𝑉𝑚𝑡 = (𝑀𝑐1 +𝑀𝑐2𝐿) 3.5 35 Where 𝑀𝑐1 is the positive moment capacity with the top of the beam in compression, and 𝑀𝑐2 is the negative moment capacity with the bottom of the beam in compression. Figure 3.4 presents a comparison of 𝑉𝑚𝑎𝑥𝑉𝑚𝑡 values. As depicted, the median for the majority of cases is approximately one, suggesting that this method is reasonable. However, a few specimens exhibited 𝑉𝑚𝑎𝑥𝑉𝑚𝑡 values of less than one, indicating that the failure mechanism was more likely associated with a shear response rather than a flexural response. Values of 𝑉𝑚𝑎𝑥𝑉𝑚𝑡 can be found in Figure 3.4: Range of 𝑉𝑚𝑎𝑥𝑉𝑚𝑡 for specimens with different characteristics: i) All specimens, ii) Axial restraint only (AR Only), iii) Embedded Longitudinal Bars only (ELB Only), iv) Both AR and ELB (AR+ELB), and v) Neither AR nor ELB. 3.3 Impact of si param t rs o θ80% Rotational capacity, specifically 𝜃80%⁡is crucial for ensuring a ductile response. For performance-based design in the US (e.g., ACI 318-19 [4], LATBSDC 2023 [20]), a total chord rotation demand Table B-1in Appendix B.36 of less than 6% is deemed appropriate. In CSA A23.3-19 [5], an inelastic rotation demand is limited to 4%. Figure 3.5 illustrates θ80% for all specimens and those with AR Only, ELB only, AR+ELB, and neither AR nor ELB. The dispersion for all categories shown in Figure 3.5 is significant. Particularly, for AR+ELB and AR category. The dispersion attributed to these categories can be partially because of the presence of rigid walls acting as axial restraints. This type of axial restrain prevents the coupling beam from undergoing high inelastic rotation which was discussed in Section 2.4. In the following sections, factors contributing to the range of 𝜃80% values are introduced, and possible explanations for the lower 𝜃80% values are provided. Figure 3.5: Range of 𝜃80% for specimens with different characteristics: i) All specimens, ii) Axial restraint only (AR Only), iii) Embedded Longitudinal Bars only (ELB Only), iv) Both AR and ELB (AR+ELB), and v) Neither AR nor ELB. 3.4 Impact of th qua tity of ia o al r i forc m t o θ80% Upon reviewing the specimen responses exhibiting low 𝜃80% values, it was observed that many of these specimens had low aspect ratios. Further investigation of these specimens revealed that the failure mechanism occurred through a single plane at the wall connection (Figure 3.6(a)). This 37 sliding shear failure is inconsistent with the failure modes observed in similar aspect ratio specimens tested by Pauly et al., 1974 [3]. For these tests, diagonal cracking was followed by extensive yielding of the diagonals, followed by either buckling or tension failure in the bars, as shown in Figure 3.6(b). Examining the low aspect ratio tests indicates that numerous sliding shear failures occurred at these connections, reducing the rotational capacity. (a) D-6db (b) Beam 395 Figure 3.6: Damage patterns of DRCBs at the joints of the shear walls for specimens (a) D-6db [25] (b) Beam 395 [3]. It was hypothesized that the sliding shear failure mode occurs due to an inadequate quantity of diagonal reinforcing. To evaluate the minimum amount of provided diagonal bars, 𝜃80% was compared versus 𝑉𝑛𝑒𝐴𝑐𝑤√𝑓𝑐′ (𝐴𝑐𝑤 is the shear area of concrete in coupling beam section), shown in Figure 3.7. Figure 3.7 shows only specimens with L/h≤1.5, as in specimens with L/h>1.5, the sliding shear failure mode was not observed. 38 Figure 3.7: θ80% versus 𝑉𝑛𝑒𝐴𝑐𝑤√𝑓𝑐′ for specimens with L/h≤ 1.5. As illustrated in Figure 3.7, specimens with 𝑉𝑛𝑒 greater than about 0.5𝐴𝑐𝑤√𝑓𝑐′ (MPa units) exhibit 𝜃80% values greater than 6%. In contrast, specimens with 𝑉𝑛𝑒 less than 0.5𝐴𝑐𝑤√𝑓𝑐′ (MPa units) demonstrate 𝜃80% values below 6%. This trend suggests that reduced diagonal reinforcing leads to a sliding shear failure mode, resulting in lower rotational capacity. Therefore, this limit can be considered crucial in the design of diagonally-reinforced coupling beams with L/h≤ 1.5 since underestimating the diagonal bar’s ratio can lead to low rotational capacity based on current currently design guidelines in Canada and the US. According to ACI 318-19 [4] commentary, DRCBs should have adequate ductility if the applied shear forces are less than 0.83𝐴𝑐𝑤√𝑓𝑐′ (MPa units) (Equation 2.12). Figure 3.8(a) and (b) depict the value of θ80% versus 𝑉𝑚𝑎𝑥𝐴𝑐𝑤√𝑓𝑐′ for specimens with L/h≤1.5 and L/h>1.5, respectively. There are a significant number of specimens which have reasonable rotational capacity that exceed this limit. Therefore, providing an upper-bound limit for applied shear force in the design of diagonally-reinforced coupling beams does not seem to improve the rotational capacity of these beams. 39 Figure 3.8: θ80% versus 𝑉𝑚𝑎𝑥𝐴𝑐𝑤√𝑓𝑐′ for specimens with (a) L /h≤ 1.5 and (b) L/h>1.5. 3.5 Specimens without diagonal ties: impact of ti s o θ80% To evaluate the impact of beam confinement, 𝜃80% was compared to the ratio of 𝐴𝑠ℎ to 𝑏𝑐𝑠𝑡𝑓𝑐′𝑓𝑦𝑡, which are the variables used in the confinement equations recommended by ACI 318-19 [4] (Equation 2.18). In this comparison, 0.3𝑏𝑐𝑠𝑡𝑓𝑐′𝑓𝑦𝑡(𝐴𝑔𝐴𝑐ℎ) (Equation 2.18) were not considered to be compared with 𝐴𝑠ℎ since 𝐴𝑐ℎ is a function of cover, but for most of the specimens, the cover was not scaled appropriately. Figure 3.9(a) shows 𝜃80% versus the ratio of 𝐴𝑠ℎ to 𝑏𝑐𝑠𝑡𝑓𝑐′𝑓𝑦𝑡. The ACI 318-19 [4] requirement of 𝐴𝑠ℎ ≥ 0.09𝑏𝑐𝑠𝑡𝑓𝑐′𝑓𝑦𝑡 (Equation 2.18) is also depicted in Figure 3.9(a). All specimens which met this requirement had 𝜃80% greater than 6%. Figure 3.9(a) also indicates that some specimens with 𝐴𝑠ℎ𝑏𝑐𝑠𝑡𝑓𝑐′𝑓𝑦𝑡 less than 0.09 still maintained θ80% more than 6%, indicating that high rotational capacity may still be achieved, even if some of the confinement equations are not satisfied. 40 Beam tie spacing is a possible reason for the high rotational capacity for some specimens with 𝐴𝑠ℎ𝑏𝑐𝑠𝑡𝑓𝑐′𝑓𝑦𝑡 less than 0.09. Figure 3.9(b) shows the θ80% versus beam tie spacing (𝑠𝑡) normalized by diagonal bar diameter (db). In Figure 3.9(a) and (b), specimens are classified based on L/h and diagonal reinforcing quantity. This classification was implemented to find trends between the low rotational capacity of studied specimens (i.e., 𝜃80%) and their aspect ratio and provided diagonal bars area. 41 Figure 3.9: θ80% versus 𝑉𝑚𝑎𝑥𝐴𝑐𝑤√𝑓𝑐′ for specimens with (a) L /h≤ 1.5 and (b) L/h>1.5. According to ACI 318-19 [4] clause 18.10.7.4(d) (Equation 2.19), the beam tie spacing for the beam confinement option must be limited by either 150mm or 6𝑑𝑏. In this study, most specimens had a limiting factor for beam tie spacing of 6𝑑𝑏, except for two specimens (CB30-DB [15] and CB20-1 [14]) in which the beam tie spacing was limited by 150 mm. Thus, 𝑠𝑡 was normalized by 𝑑𝑏 rather than 150mm. Based on Figure 3.9(b), most specimens with 𝑠𝑡⁡less than 𝑑𝑏 had degradation rotation exceeding 6%, but limited exceptional specimens were seen which had degradation rotation less than 6% and had a low quantity of diagonally reinforcing (i.e., 𝑉𝑛𝑒𝐴𝑐𝑤√𝑓𝑐′<0.5 (MPa units)). Overall, the results indicate that specimens which utilize beam confinement limits by ACI 318-19 [4] can provide suitable rotational capacity as long as appropriate confinement and beam tie spacing are applied. 42 3.6 Specimens with diagonal ties: impact of ti s i o θ80% Figure 3.10 illustrates 𝜃80% versus the 𝐴𝑠ℎ𝑏𝑐𝑠𝑑𝑓𝑐′𝑓𝑦𝑡 ratio for specimens with diagonal ties. Generally, specimens which had 𝐴𝑠ℎ𝑏𝑐𝑠𝑑𝑓𝑐′𝑓𝑦𝑡≥ 0.09 had reasonable rotational capacity (𝜃80%), except specimens S1, D30, and P12 tested by Canbolat et al., 2005 [26], Dugas, 2002 [27], and Galano et al., 2000 [31], respectively. The low rotational capacity of these specimens can be attributed to the low quantity of diagonal reinforcing described in Section 3.4. Based on Figure 3.10, no significant trend can be determined between 𝜃80% and transverse reinforcing area (𝐴𝑠ℎ) for specimens with diagonal ties. Therefore, it might be concluded that the rotational capacity of DRCBs with ties around diagonal bars depends on the diagonal tie spacing. 43 Figure 3.10: 𝜃80% versus a) 𝐴𝑠ℎ per ACI 318-19 for specimens with diagonal confinement. Figure 3.11(a) and Figure 3.11(b) compares the 𝜃80% to diagonal tie spacing (𝑠𝑑) normalized by diagonal bar diameter (𝑑𝑏) and the 𝑠𝑑, respectively. In the database, no specimen was limited by 24𝑑𝑡𝑖𝑒 spacing recommended by CSA A23.3-19[5]. Specimens with tie spacing less than 150mm and less than 6𝑑𝑏 showed good performance, except for those with a low quantity of diagonal reinforcing. Based on Figure 3.11(a) and (b), it can be concluded that DRCBs detailed as per Equation 2.17 can exhibit high rotational capacity. Figure 3.11: 𝜃80% versus a) the beam tie spacing per the diagonal bars and b) the diagonal tie spacing for specimens with diagonal confinement. 44 3.7 Initial stiffness (Ki) Calculating appropriate values for initial stiffness (𝐾𝑖) is important for determining the dynamic response of coupled wall buildings. Given the relatively low aspect ratio of DRCBs, consideration of both shear and flexural stiffness is needed to determine 𝐾𝑖. To study initial stiffness, which considers both shear and flexural deformation, a new parameter 𝐶𝑘 (Equation 2.11) is developed. Figure 3.12 shows different values of 𝐶𝑘 corresponding to experimental results (Equation 2.11) and values of αf and αs related to ACI 318-19 [4], LATBSDC 2023[20], and CSA A23.3-19[5]. Figure 3.12: Various values for 𝐶𝑘 based on experimental results and various amounts of αf and αs. According to Figure 3.12, the code values for effective stiffness calculation generally provide an upper-bound value meaning that the effective stiffness is overestimated. This overestimation might not be suitable for calculating the inter-story displacement (drift), as overestimating the effective stiffness can lead to underestimating the displacements of the building. 45 3.8 Conclusions In this study, a comprehensive database of previously tested diagonally-reinforced coupling beams (DRCBs) was developed. This developed database included 51 tested diagonally-reinforced coupling beams with different features such as embedded longitudinal bars, axial restraint, and diagonal or beam ties. A deep systematic review was conducted on the developed database to evaluate current design requirements, and to introduce new limits as necessary. This study reveals a pronounced overstrength in specimens equipped with AR or ELB. By incorporating the flexural capacity of longitudinal bars into the shear strength calculations, this overstrength phenomenon can be mitigated. The current overstrength factor of 1.25, as specified in CSA A23.3-19[5], is deemed appropriate for diagonally-reinforced coupling beams lacking AR or ELB; however, the introduction of AR or ELB can lead to an overstrength increase of average 30-40%. Additionally, a total chord rotation of 6% is achievable under specific conditions, some of which align with existing standards in ACI 318-19 [4] and CSA A23.3-19 [5], while others emerge from the novel insights of this research. Notably, a deficiency in diagonal reinforcing in diagonally-reinforced coupling beams with a low aspect ratio (L/h≤1.5) significantly diminishes 𝜃80%, suggesting a new design threshold for diagonally-reinforced coupling beams where 𝑉𝑛 ≥ 0.5𝐴𝑐𝑤√𝑓𝑐′ (MPa units). Moreover, the established upper-bound limit of 0.83𝐴𝑐𝑤√𝑓𝑐′ (MPa units) in ACI 318-19 [4] may not accurately reflect rotational capacity and could be considered excessive. Furthermore, the impacts of beam tie spacing within beam confinement and diagonal bar tie spacing within diagonal confinement on the degradation rotation of diagonally-reinforced coupling beams were explored. For diagonally-reinforced coupling beams with beam confinement, it is essential to comply with both 𝐴𝑠ℎ ≥ 0.09𝑏𝑐𝑠𝑡𝑓𝑐′𝑓𝑦𝑡 and a beam tie spacing of 𝑠𝑡 ≥ 6𝑑𝑏 to achieve 46 satisfactory rotational capacity. In contrast, diagonally-reinforced coupling beams utilizing diagonal ties display no clear correlation between 𝐴𝑠ℎ𝑏𝑐𝑠𝑑𝑓𝑐′𝑓𝑦𝑡 and rotational capacity; rather, it is the diagonal tie spacing that significantly influences the rotational outcome. Based on the findings presented in this chapter, the rotational capacity of diagonally-reinforced coupling beams in the best condition can not be considered more than 6%. Also, the difficulties associated with the construction of the diagonally-reinforced coupling beams with diagonal ties can not be neglected. In addition to this, for design layouts in which the clear span of the beam is quite high (i.e., L/h>2.0) and also based on the high-rise building’s location, high rotational capacity is required, diagonally-reinforced coupling beams can not be the best options as in high aspect ratios, the angle between the horizontal direction and the diagonal bars is reduced significantly (less than 10 degrees), and the sin(α) in Equation 2.2 will decrease the shear strength of coupling beams. In this case, diagonally-reinforced coupling beams will behave as conventional beams, which inherently can not provide high rotational capacity due to the shear failure of the beam-wall interfaces. Due to these limitations associated with diagonally-reinforced coupling beams, practitioners may choose steel or composite coupling beams, in which high strength and rotational capacity can be provided by steel sections serving as connecting beams between two adjacent shear walls. In the next chapter, steel and composite coupling beams will be discussed in detail. 47 Chapter 4: New connection detailing for steel and composite coupling beams 4.1 Introduction The demand for coupling beams with higher aspect ratios, in addition to having high strength and ductility, has led to the development of steel and composite coupling beams (SCB/SRCBs) as a viable solution. However, to ensure good seismic performance, the connection between the wall and beam must be designed to minimize extensive damage at the connection, which could lead to early failure. It is also important for the connection to be practical for construction purposes to facilitate adoption in the construction industry. This chapter aims to introduce new connection detailing which is both practical and can improve the seismic performance of steel and composite coupling beams. To achieve this, Section 4.2. reviews of the mechanical response of various beam-to-wall connections, and Section 4.3 shows the code limitations related to these beams. As there are no specific Canadian design guidelines for designing steel and composite coupling beams, only the current design guidelines in the USA will be discussed and reviewed later in this chapter. Sections 4.2 and 4.3 inform the conceptual development of the new connection detailing for steel and composite coupling beams, which is described in Section 4.4, followed by a detailed explanation of the mechanics of the proposed connection, including a new embedment model. 4.2 Review of mechanical behaviour and design codes This section describes the mechanism of transferring loads in the embedment region by the embedded steel beam and current design considerations. Several experimental programs have been 48 carried out to develop the mechanical models of SCBs and SRCBs. A detailed summary of these tests can be found in Appendix C. 4.2.1 Mechanical behaviour To determine the load-transferring mechanism in systems with steel and composite coupling beams, different mechanical models have been introduced by researchers since 1980. Basically, loads are transferred through the bearing forces developed by concrete surrounding embedded steel sections at the front and back regions in the steel and composite coupling beams. Therefore, the strength of the beam-wall connection is highly dependent on the embedment length of the steel. In 1971, an embedment model including the bearing forces of concrete at the front and back embedment regions was developed by Precast Concrete Institution (PCI) [32] for steel sections embedded into the adjacent columns. Figure 4.1 shows the embedment mode proposed by the PCI in 1971. According to the PCI Design Handbook in 1971 [32], a parabolic stress-strain distribution was assumed for the concrete compressive force at the back of the embedded member (𝐶𝑏). It was assumed that the resultant compressive force of 𝐶𝑏 is located at 11/12 of the embedment length (𝐿𝑒), is the nominal capacity of the connection compressive stress-strain distribution for concrete at the front face of the embedded member with a width of 𝑏 equal to the width of the embedded steel section and a depth of 𝐿𝑒3. The block stress has a uniform stress of 0.85𝑓𝑐′, and the compressive strain at the front face is assumed to be 0.003. By these assumptions, they calculated the resultant compressive force of concrete located 𝐿𝑒3 at the front face of the column (𝐶𝑓) to be calculated per Equation 4.1. 𝐶𝑓 = 0.85 ×𝑓𝑐′𝑏𝐿𝑒3 4.1 49 By taking the moment of forces about 𝐶𝑏, we will have: 𝑉𝑛 ∗ (𝑎 +1112𝐿𝑒) = 𝐶𝑓 ∗ (34𝐿𝑒) Where 𝑉𝑛 is the nominal capacity of the connection and 𝑎 is the eccentricity of the load measured from the face of the column. Therefore, 𝑉𝑛 is calculated upon Equation 4.2. 𝑉𝑛 =0.85 × 𝑓𝑐′𝑏𝐿𝑒3.67 + 4 ×𝑎𝐿𝑒 4.2 Figure 4.1: PCI Design Method 1971 embedment model [32]. Later in 1974, Kriz and Raths [33] extended the PCI Design Method developed in 1971 to include the effects of additional reinforcements welded to the top and bottom flanges of the embedded steel section on the strength of embedded connections. Kriz and Raths [33] assumed a linear strain distribution with a maximum strain equal to 0.003 at the front face of the column and zero strain 50 measured at 𝐿𝑒3 from the face of the column (Figure 4.2). It was assumed that the additional reinforcements were located at 𝐶𝑓 and 𝐶𝑏. By assuming that the reinforcements will yield, taking the moments about 𝐶𝑏 will give: 𝑉𝑟 × (𝑎 +1112𝐿𝑒) = 𝐴𝑠𝑓𝑦 × (34𝐿𝑒) Where 𝑉𝑟 is the additional capacity of the connection due to the welded reinforcements, 𝐴𝑠 is the total area of welded reinforcement at the front face of the embedded steel member, and 𝑓𝑦𝑟 is the yield stress of the reinforcements. Therefore, 𝑉𝑟 will be calculated upon Equation 4.3. 𝑉𝑟 =3𝐴𝑠𝑓𝑦𝑟3.67 + 4 ×𝑎𝐿𝑒 4.3 Assuming that the welded reinforcements at the back of the embedded steel section will yield and write the equilibrium in the vertical direction, the required area of reinforcing steel at the back of the embedded steel section (𝐴𝑠′ ) is calculated per Equation 4.4. 𝐴𝑠′ = (12𝑎 + 2𝐿𝑒12 + 11𝐿𝑒)𝐴𝑠 4.4 51 Figure 4.2: Kriz and Raths, 1974 [33] embedment model accounting for additional welded reinforcement. Based on the studies carried out by Kriz and Raths in 1974 [33], in the 1978 edition of the PCI Design Handbook [34], the total nominal capacity of the connection of the embedded steel members in the columns, including additional welded reinforcements, is calculated per Equation 4.5. 𝑉𝑛 =0.85 × 𝑓𝑐′𝑏𝐿𝑒3.67 + 4 ×𝑎𝐿𝑒+3𝐴𝑠𝑓𝑦3.67 + 4 ×𝑎𝐿𝑒 4.5 Regarding the PCI Design Method, there are number of assumptions which seemed to be inconsistent as follow: 1. The neutral axis depth of the assumed strain distribution coincides with the depth of the equivalent rectangular stress block, which is inconsistent with the flexural theory for reinforced concrete structures. 2. A constant depth of 𝐿𝑒3 was assumed for both the strain distribution and the equivalent rectangular stress distribution. However, this depth should vary with the eccentricity of the applied load and the additional reinforcement area. 52 Marcakis and Mitchell., 1980 [35] proposed a new embedment model in 1980 based on the above inconsistent assumptions. The main objective of the experimental program conducted by Marcakis and Mitchell., 1980 [35] was to develop a rational analytical model of the behaviour of precast connections incorporating embedded steel members. Figure 4.3 demonstrates the embedment model proposed by Marcakis and Mitchell, 1980 [35] with the simplified stress-strain distribution of concrete at the front and back of the embedment region, where ∈𝑐⁡is defined as the strain of concrete in compression, which is considered as 0.003 at the beam-wall interface where the concrete reaches its maximum strain corresponding to crushing. 𝐶𝑓 is the compression force of concrete near the beam-wall interface. For simplification of the stress distribution related to 𝐶𝑓, it is assumed that the stress is governed by the Whitney stress block, where 𝑥 is the distance from the neutral axis to the beam-wall interface, and 𝛽1 is the ACI stress block factor. Marcakis and Mitchell, 1980 [35] assumed a parabolic stress-strain relationship to determine the stress distribution in the back section of the embedment region. Based on this stress-strain relationship, the concrete compressive stress corresponding to ∈𝑐 is calculated per Equation 4.6. 53 Figure 4.3: Marcakis and Mitchell, 1980 embedment model. 𝑓𝑐 = 𝑓𝑐′ [2∈𝑐∈0− (∈𝑐∈0)2] 4.6 Where ∈0 is the strain corresponding to 𝑓𝑐′. Since the material testing data is not always available, ∈0 can be assumed as 0.002. By considering ∈0= 0.002, the stress-strain relationship of concrete at the back of the embedment region can be calculated per Equation 4.7. 𝑓𝑐 = 1000𝑓𝑐′ ∈𝑐 (1 − 250 ∈𝑐) 4.7 For simplification, Marcakis and Mitchell, 1980 [35] used an equivalent stress distribution instead of the parabolic one at the back of the embedded steel member. This equivalent distribution had a uniform stress of 𝛼𝑓𝑐′ over the depth of 𝛽𝑥𝑏 where 𝑥𝑏 is the depth of the strain distribution measured from the back of the connection to the neutral axis location, and the stress block factors, 𝛼 and 𝛽, were determined through Equations 4.8 and 4.9, respectively. 54 𝛼𝛽 =∈𝑏∈0−13(∈𝑏∈0)2 4.8 𝛽 =4 −∈𝑏∈06 − 2∈𝑏∈0 4.9 Where ∈𝑏 is defined as the maximum strain of concrete in compression at the back of the embedment region. By having the stress block factors and the simplified stress-strain distribution at the back of the embedment length, Marcakis and Mitchell, 1980 [35] calculated 𝐶𝑏 per Equation 4.10. 𝐶𝑏 = ⁡𝛼𝑓𝑐′𝑏𝛽𝑥𝑏 4.10 Where 𝑏 is defined as the bearing width, considered as the width of the embedded member; however, Marcakis and Mitchell, 1980[35] modified it based on the test results, which will be discussed later in this chapter. Based on Figure 4.4., Marcakis and Mitchell, 1980 [35] considered the simplified stress-strain distribution at the front face of the connection with the width of 0.85𝑓𝑐′ over the depth of 𝛽𝑥𝑓, where 𝑥𝑓 is defined as the depth of the strain distribution from the face of the connection to the neutral axis location. Therefore, 𝐶𝑓 will be calculated per Equation 4.11. 𝐶𝑓 = ⁡0.85𝑓𝑐′𝑏𝛽1𝑥𝑓 4.11 By writing the equilibrium equation of forces in the vertical direction we will have: ∑𝐹𝑦 = 0 → 𝑉𝑛 + 𝐶𝑏 = 𝐶𝑓 → 𝑉𝑛 = 𝐶𝑓 − 𝐶𝑏 55 → 𝑉𝑛 = 0.85 ∗ 𝑓𝑐′𝛽𝑥𝑓 − 𝛼𝑓𝑐′𝑏𝛽𝑥𝑏 By summing the moment at the connection, we will have: ∑𝑀 = 0 → 𝑉𝑛 ∗ 𝑎 + 𝐶𝑓 ∗𝛽1𝑥𝑓2= 𝐶𝑏 ∗ 𝑥𝑏 → 𝑉𝑛 ∗ 𝑎 + 0.85 ∗ 𝑓𝑐′𝛽1𝑥𝑓 ∗𝛽1𝑥𝑓2= 𝛼𝑓𝑐′𝑏𝛽𝑥𝑏 (𝐿𝑒 −𝛽𝑥𝑏2) Figure 4.4: Marcakis and Mitchell, 1980 [35] simplified embedment model. Marcakis and Mitchell, 1980 [35] also developed a model including additional welded reinforcements located at the front and back of the embedded steel member (Figure 4.5). In their model, it was assumed that the steel reinforcement can act in tension or compression and that the strain in the steel is equal in magnitude to the compressive strain in the concrete at the same location as the steel. Proper development length must be provided to enable the reinforcement to 56 reach yield. By adding the additional reinforcements, the equilibrium conditions will become as follows: 𝑉𝑛 = 0.85 × 𝑓𝑐′𝛽1𝑥𝑓 + 𝐴𝑠𝑓𝑠 − 𝛼𝑓𝑐′𝑏𝛽𝑥𝑏 − 𝐴𝑠′ 𝑓𝑠′ 𝑉𝑛 × 𝑎 = 𝛼𝑓𝑐′𝑏𝛽𝑥𝑏 (𝐿𝑒 −𝛽𝑥𝑏2) + 𝐴𝑠′ 𝑓𝑠′𝑑𝑏 − 0.85 × 𝑓𝑐′𝛽1𝑥𝑓 ×𝛽1𝑥𝑓2− 𝐴𝑠𝑓𝑠𝑑𝑓 Where 𝑓𝑠 and 𝑓𝑠′ are the steel stress in welded reinforcement near front and back, respectively, 𝑢 is the distance from front face to center of reinforcement near front, and 𝑤 is the distance from front face to center of reinforcement near back. The steel stresses 𝑓𝑠 and 𝑓𝑠′ can be calculated per Equations 4.12 and 4.13, respectively (Es is the elastic modulus of steel). . 𝑓𝑠 = 0.003𝐸𝑠 [1 −𝑢𝑥𝑓] ≤ 𝑓𝑦 4.12 𝑓𝑠′ = 0.003𝐸𝑠 [𝑤𝑥𝑓− 1] ≤ 𝑓𝑦 4.13 Figure 4.5: Marcakis and Mitchell, 1980 [35] embedment model including additional welded reinforcements. 57 Marcakis and Mitchell, 1980 [35] tested 25 specimens with various geometrical layouts, additional welded reinforcements, and loading conditions (pure shear, pure moment, and pure axial loads). All specimens were tested under monotonic loads to reach the failure point. Marcakis and Mitchell, 1980 [35] used the results of the tested specimens to calibrate the proposed embedment models. Their results suggested taking the bearing width equal to the minimum of the column’s width and 2.5 times the embedded steel member width. This recommendation came from their observation from the test results, in which the concrete cover was spalled to the outside of the column confining ties, indicating that the load spreading is not limited to the width of the embedded steel member. Accordingly, they observed that for the specimens in which the distance from the outside of the column ties is significantly larger than the width of the embedded steel member, they put the limits of load spreading to be 3.2 times the width of the embedded member. Marcakis and Mitchell, 1980 [35] proposed Equations 4.14 and 4.15 for practitioners, one without, and one with the additional welded reinforcements, respectively to calculate the nominal shear capacity of connections with embedded steel members. 𝑉𝑐 =0.85𝑓𝑐′𝑏𝑒𝑓𝑓𝐿𝑒1 +3.6𝑒𝐿𝑒 4.14 𝑉𝑟 =2𝜔𝑓𝑐′𝑏𝑒𝑓𝑓𝐿𝑒1 +6𝑒𝐿𝑒4.8𝑠𝐿𝑒− 1 4.15 Where 𝑏𝑒𝑓𝑓 is the minimum of the column’s width and 2.5 times the width of the embedded steel member, 𝑒 is the eccentricity of resultant of vertical loads from the center of embedment (𝑒 = 𝑎 +𝐿𝑒2), 𝑠 is the spacing measured from the center of the additional reinforcements located at the front 58 and back of the embedment region, and 𝜔 is defined as the reinforcement index, is calculated per Equation 4.16. 𝜔 =𝐴𝑠𝑏𝑒𝑓𝑓𝐿𝑒∗𝑓𝑦𝑓𝑐′ 4.16 Finally, the total shear capacity of the connection based on the Marcakis and Mitchell, 1980 [35] can be calculated upon Equation 4.17. 𝑉𝑛 =0.85𝑓𝑐′𝑏𝑒𝑓𝑓𝐿𝑒1 +3.6𝑒𝐿𝑒+2𝜔𝑓𝑐′𝑏𝑒𝑓𝑓𝐿𝑒1 +6𝑒𝐿𝑒4.8𝑠𝐿𝑒− 1 4.17 At the same time in the 1980s, when Marcakis and Mitchell proposed an embedment model for embedded steel members, Mattock and Gaafar, 1982 [36] developed an embedment model (Figure 4.3) with the same load-transferring mechanism as Marcakis and Mitchell, 1980 [35], but with a different simplification for calculating Cb. Mattock and Gaafar, 1982 [36] conducted an experimental program in which they tested five steel sections embedded in a reinforced concrete column as brackets under monotonic loading up to the failure point. The main object of their study was to determine the strength of the connection in the brackets and the width of the bearing stress. Mattock and Gaafar, 1982 [36] considered the same stress-strain distributions for compressive forces at the front and back of the embedded steel section (Equations 4.6and 4.7). According to Figure 4.3, ∈𝑏 is obtained through Equation 4.18. ∈𝑏=0.003(𝐿𝑒 − 𝑥)𝑥 4.18 59 According to Figure 4.3, ∈𝑐 as a function of d, where d is the distance from neutral axis to the back of the beam, is obtained through Equation 4.19. ∈𝑐=∈𝑏 (d𝐿𝑒 − 𝑥) 4.19 By substituting Equation 4.19 into Equation 4.7, 𝑓𝑐 can be obtained by Equation 4.20. 𝑓𝑐 = 1000𝑓𝑐′ ∈𝑏 (d𝐿𝑒 − 𝑥) × (1 − 250 ×∈𝑏 (d𝐿𝑒 − 𝑥)) 4.20 By substituting Equation 4.18 into Equation 4.19, Equation 4.21 is developed, by which 𝑓𝑐 is shown as a function of 𝑥. 𝑓𝑐 = 1000𝑓𝑐′ ×0.003(𝐿𝑒 − 𝑥)𝑥× (d𝐿𝑒 − 𝑥) × (1 − 250 ×0.003(𝐿𝑒 − 𝑥)𝑥× (d𝐿𝑒 − 𝑥)) 4.21 By taking the integral of Equation 4.21 times the width of the embedded steel beam (𝑏), the concrete compressive force at the back region is calculated by Equation 4.22. 𝐶𝑏 =5003𝑓𝑐′ (0.003(𝐿𝑒 − 𝑥)𝑥) × (3 − 500 ∗ (0.003(𝐿𝑒 − 𝑥)𝑥))𝑏(𝐿𝑒 − 𝑥) 4.22 Also, Mattock and Gaafar, 1982 [36] developed a coefficient (kb) which is used to determine the centroid of the compression force at the back of the embedment region. This coefficient is multiplied to the 𝑥𝑏 to produce the centroid corresponding to 𝐶𝑏. 𝑘𝑏 is obtained by Equation 4.23. 𝐾𝑏 =1 − 0.375 × (𝐿𝑒𝑥 − 1)3 − 1.5 × (𝐿𝑒𝑥 − 1) 4.23 60 Consequently, 𝑋𝑐𝑏 defined as the centroid of the compression force at the back of the embedment region from the column face is obtained by Equation 4.24. 𝑋𝑐𝑏 = 𝐿𝑒 − 𝐾𝑏 × (𝐿𝑒 − 𝑥) 4.24 According to Figure 4.3, the compression force of concrete at the front region (𝐶𝑓) and the distance of the corresponding centroid to the column face (𝑋𝑐𝑓) can be calculated by Equation 4.25, and 4.26, respectively. 𝐶𝑓1 = 0.85𝑓𝑐′𝛽1𝑥𝑏 4.25 𝑋𝑐𝑓 =𝛽1𝑥2 4.26 By writing the equilibrium equation of forces in the vertical direction we will have: ∑𝐹𝑦 = 0 → 𝑉𝑛 + 𝐶𝑏 = 𝐶𝑓 → 𝑉𝑛 = 𝐶𝑓 − 𝐶𝑏 → 𝑉𝑛 = 0.85𝑓𝑐′𝛽1𝑥𝑏 +5003𝑓𝑐′ (0.003(𝐿𝑒 − 𝑥)𝑥)(3 − 500 (0.003(𝐿𝑒 − 𝑥)𝑥)) 𝑏(𝐿𝑒 − 𝑥) 4.27 By summing the moment at the beam-wall interface we have: ∑𝑀 = 0 → 𝑉𝑛 × 𝑎 + 𝐶𝑓 ×𝛽1𝑥2= 𝐶𝑏 × 𝑋𝑐𝑏 → 𝑉𝑛 × 𝑎 + 0.85𝑓𝑐′𝛽1𝑥𝑏 ×𝛽1𝑥2=5003𝑓𝑐′ (0.003(𝐿𝑒 − 𝑥)𝑥)(3 − 500(0.003(𝐿𝑒 − 𝑥)𝑥)) 𝑏(𝐿𝑒 − 𝑥) × (𝐿𝑒− (1 − 0.375 ∗ (𝐿𝑒𝑥 − 1)3 − 1.5 ∗ (𝐿𝑒𝑥 − 1)) (𝐿𝑒 − 𝑥)) 4.28 61 By substituting Equation 4.27 in Equation 4.28, the value of x (neutral axis) can be determined by solving Equation 4.29. (0.85 ∗ 𝑓𝑐′𝛽1𝑥𝑏 +5003𝑓𝑐′ ∗ (0.003(𝐿𝑒 − 𝑥)𝑥) ∗ (3 − 500 ∗ (0.003(𝐿𝑒 − 𝑥)𝑥)) ∗ 𝑏 ∗ (𝐿𝑒 − 𝑥)) ∗ 𝑎 + 0.85∗ 𝑓𝑐′𝛽1𝑥𝑏 ∗𝛽1𝑥2−5003𝑓𝑐′ ∗ (0.003(𝐿𝑒 − 𝑥)𝑥) ∗ (3 − 500 ∗ (0.003(𝐿𝑒 − 𝑥)𝑥)) ∗ 𝑏 ∗ (𝐿𝑒 − 𝑥)∗ (𝐿𝑒 −(1 − 0.375 ∗ (𝐿𝑒𝑥 − 1)3 − 1.5 ∗ (𝐿𝑒𝑥 − 1)) ∗ (𝐿𝑒 − 𝑥)) = 0 4.29 By knowing the neutral axis location, Mattock and Gaafar, 1982 [36] concluded that Vn can be determined by Equation 4.30 by summing moments about Cb. 𝑉𝑛 = 0.85𝑓𝑐′𝛽1𝑏𝐿𝑒 (𝑥𝐿𝑒) [1 − 𝐾𝑏 (1 −𝑥𝐿𝑒) −𝛽12 (𝑥𝐿𝑒)1 − 𝐾𝑏 (1 −𝑥𝐿𝑒) +𝑎𝐿𝑒] 4.30 Since Equation 4.30 might not seem practical for practitioners, Mattock and Gaafar, 1982 [36] conducted a sensitivity study to find a proper value of the neutral axis depth (𝑥) ratio to the embedment length (𝐿𝑒). Mattock and Gaafar, 1982 [36] assumed the ratio of 𝑎𝐿𝑒 between 0.1 and 0.5 for a range of 𝑓𝑐′ values from 28 to 40 MPa. Mattock and Gaafar, 1982 [36] reported that the average value of the 𝑥𝐿𝑒 was found to be 0.66 with a variation coefficient of 3.5%. Since the coefficient variation is considered negligible in practice, the 𝑥𝐿𝑒 was considered 0.66. Consequently, Mattock and Gaafar, 1982 [36] suggested Equation 4.31 to calculate 𝑉𝑛. 𝑉𝑛 = 0.85𝑓𝑐′𝛽1𝑏𝐿𝑒 [0.58 − 0.22𝛽10.88 +𝑎𝐿𝑒] 4.31 62 Mattock and Gaafar, 1982 [36] later tested five steel sections embedded into concrete columns in which the required embedment length of each specimen was calculated per Equation 4.31. Based on the test results, Mattock and Gaafar, 1982 [36] reported that to consider the effects of the confinement on the embedment length and capacity of steel coupling beams, they considered an increase in the bearing stress at the column face, which is attributed to the effect of lateral confining. Since the bearing stress (𝑓𝑏) is assumed to happen at the column face, Mattock and Gaafar, 1982 [36] calculated the bearing strength based on the measured embedment length (𝑉𝑛,𝑡𝑒𝑠𝑡). 𝑓𝑏0.85𝑓𝑐′=𝑉𝑛,𝑡𝑒𝑠𝑡⁡𝑉𝑛 4.32 Mattock and Gaafar, 1982 [36] plotted the ratio of 𝑓𝑏 over 𝑓𝑐′ versus the ratio embedded steel member width (𝑏𝑓) over the column’s width (𝑡𝑤) depicted by Figure 4.6, concluded that the curve-fitting to the test results based on Equation 4.32, led to the development of Equation 4.33, by which the bearing stresses at the column face can be expressed as the ratio of the shear wall’s thickness(𝑡𝑤) to the flanges’ width (𝑏𝑓). 𝑓𝑏0.85𝑓𝑐′= (𝑡𝑤𝑏𝑓)0.66 4.33 63 Figure 4.6: Ratio of 𝑓𝑏𝑓𝑐′ versus the ratio of bf/tw developed based on the test results of Mattock and Gaafar, 1982 [36]. Consequently, the modified design equation including the effect of lateral confinement on the capacity of embedded steel section in shear wall/columns is shown by Equation 4.34. 𝑉𝑛 = 0.85𝑓𝑐′ (𝑡𝑤𝑏𝑓)0.66𝛽1𝑏𝑓𝐿𝑒 [0.58 − 0.22𝛽10.88 +𝑎𝐿𝑒] 4.34 In light of the studies conducted by Kriz and Raths, 1974 [33], Hawkins, 1970 [37], and Williams, 1979 [38] concluding that the concrete bearing strength under strip loading should be proportioned to concrete tensile strength rather than compressive strength, Mattock and Gaafar, 1982 [36] modified Equation 4.33 by changing the term 0.85𝑓𝑐′ with 4.5√𝑓𝑐′, where 𝑓𝑐′ is assumed to be 28 MPa. The modified design equation is shown by Equation 4.35. 𝑉𝑛 = 4.5√𝑓𝑐′ (𝑡𝑤𝑏𝑓)0.66𝛽1𝑏𝑓𝐿𝑒 [0.58 − 0.22𝛽10.88 +𝑎𝐿𝑒] 4.35 64 Harries et al., 1993 and 2000 [39] [40] recommended modifying the design equations of the embedded steel section by considering the effect of concrete spalling at the beam-wall interface since the concrete spalling will increase the cantilever distance and decrease the embedment length. Therefore, by considering the effect of concrete spalling, Equation 4.35will be modified as follows: 𝑉𝑛 = 4.5√𝑓𝑐′ (𝑡𝑤𝑏𝑓)0.66𝛽1𝑏𝑓(𝐿𝑒 − 𝑐) [0.58 − 0.22𝛽10.88 +𝑎 + 𝑐𝐿𝑒 − 𝑐] 4.36 Where 𝑐 is defined as the concrete cover in the shear wall. Based on the recommendation of Harries et al., 1993 and 2000 [39] [40] regarding the consideration of concrete spalling in determining the minimum required embedment length of steel beams, the modified equation accounting for concrete spalling based on the Marcakis and Mitchell, 1980 [36] proposed model without the effect of additional welded reinforcement is shown by Equation 4.37. 𝑉𝑛 =0.85𝑓𝑐′𝑏𝑒𝑓𝑓(𝐿𝑒 − 𝑐)1 + 3.6 [𝑎 + 𝑐 +(𝐿𝑒 − 𝑐)2𝐿𝑒 − 𝑐] 4.37 Later, in 2005, Park et al. [41] proposed a new model of steel beam embedded into the shear walls, including the effect of auxiliary transfer bars _ the same concept of adding welded reinforcement introduced by Marcakis and Mitchell, 1980 [36] on the beam’s strength (Figure 4.7). Park et al., 2005 [41] modified Equation 4.36 by adding the tension and compression forces endured by auxiliary transfer bars, as shown by Equation 4.394.38. 65 𝑉𝑛 = 4.5√𝑓𝑐′ (𝑡𝑤𝑏𝑓)0.66𝛽1𝑏𝑓𝐿𝑒 [0.58 − 0.22𝛽10.88 +𝑎𝐿𝑒] +2(0.88 −𝑎𝐿𝑒)∑ 𝐴𝑠𝑖𝑓𝑠𝑖𝑛𝑖=10.88 +𝑎𝐿𝑒 4.394.38 Figure 4.7: Park et al., 2005 embedment model [41]. In conclusion, researchers have developed and proposed different embedment models since 1971. The load-transferring mechanism in all these models is based on the bearing stresses developed in the concrete around the front and back of the embedded steel members in either shear walls or columns. In the models with additional welded reinforcement, the strain of the steel rebars is assumed to be the same as the concrete surrounding them. The main difference between the models is the simplified profile of the stress-strain distribution for the bearing stresses at the back of the embedded steel member. Furthermore, determining the effective bearing width of the proposed models differed since the researchers used their test results to determine this parameter. Since the geometrical, material properties, and loading conditions were not the same for each conducted experimental program, the final terms for determining 𝑏𝑒𝑓𝑓 varied from one study to another. The most recent large-scale experimental program on the steel and steel-reinforced coupling beams has been conducted by Motter et al., 2014 [7], [42]. Based on the conclusions of Motter et al., 2014 66 [7], [42] study, they recommended the embedment model developed by Mattock and Gaafar, 1982 [36] by accounting for the effect of concrete spalling due to the cyclic loadings (Equation 4.36). Also, according to the American Institute of Steel Construction (AISC) 341-22 [19] standard, the embedment length of the steel coupling beams is calculated upon Equation 4.36. The discussion about code requirements on the design of steel and steel-reinforced coupling beams will be presented in the next section. 4.2.2 Building code provisions for designing steel and composite coupling beams At present, Canadian design codes, such as the National Building Code (NBC) 2020 [23] and CSA A23.3-19 [5], do not provide guidance for steel and composite coupling beams. In contrast, the US has provisions for these in their codes. ASCE 41-17 [43] categorizes coupled shear walls incorporating SCB or SRCB as composite walls. Composite Ordinary Shear Walls (C-OSW) and Composite Special Shear Walls (C-SSW) are two types of composite walls. C-OSW is designed for limited inelastic deformations, while C-SSW is intended to dissipate substantial energy through inelastic deformations. Both C-OSW and C-SSW share the same seismic force reduction factors as walls as the equivalate Reinforced Concrete (RC) coupling beams. According to ASCE 41-17 [43], the C-OSW and C-SSW must adhere to AISC 341-22 [19] standard. The AISC 341-22 [19] standard recommends design provisions for steel and composite coupling beams specific to whether the coupling beam will be within a C-OSW or a C-SSW. For both C-OSW and C-SSW systems, the shear strength of the SCB is selected as the minimum of 2𝑀𝑝𝐿 and 𝑉𝑝, where 𝑀𝑝 is the plastic flexural moment, and 𝑉𝑝 is the nominal shear strength of the steel section calculated per Equation 4.39 and 4.40, respectively. 67 𝑀𝑝 = 𝑓𝑦𝑍⁡⁡ 4.39 𝑉𝑝 = 0.6𝑓𝑦𝐴𝑡𝑤 4.40 Where fy is the specified yield strength of the steel section, Z is the plastic section modulus about the axis of bending, and Atw is the area of the steel beam web. For both C-OSW and C-SSW, the shear strength of the SRCB should be taken as the minimum of 2𝑀𝑝𝐿 and 𝜑𝑉𝑛,𝑐𝑜𝑚𝑝 (with 𝜑 = 0.9), which 𝑀𝑝 is using either the plastic stress distribution or the strain compatibility method, considering the effects of the concrete encasement and existing reinforcement in the beams’ cross section. 𝑉𝑛,𝑐𝑜𝑚𝑝 is the available shear strength of the composite coupling beam by considering the concrete encasement, longitudinal and transverse reinforcement in the reinforced concrete beam, and are calculated per Equation 4.41 and 4.42 for C-OSW and C-SSW systems, respectively. 𝑉𝑛,𝑐𝑜𝑚𝑝 = 𝑉𝑝 + (0.166√𝑓𝑐′𝑏𝑤𝑐𝑑𝑐 +𝐴𝑠𝑟𝐹𝑦𝑠𝑟𝑑𝑐𝑠) 4.41 𝑉𝑛,𝑐𝑜𝑚𝑝 = 1.1𝑅𝑦𝑉𝑝 + 0.21√𝑅𝑐𝑓𝑐′𝑏𝑤𝑐𝑑𝑐 +1.33𝑅𝑦𝑟𝐴𝑠𝑟𝐹𝑦𝑠𝑟𝑑𝑐𝑠 4.42 Where 𝑏𝑤𝑐 is the width of concrete encasement, 𝑑𝑐 is the effective depth of concrete encasement, 𝐴𝑠𝑟 is the area of transverse reinforcement, 𝐹𝑦𝑠𝑟 is the nominal yielding strength of transverse reinforcement, 𝑠 is the spacing of transverse reinforcement, 𝑅𝑦 is the ratio of the expected yield stress of the steel profile material to the specified minimum yield stress, 𝑅𝑐 is the factor to account for expected strength of concrete which is considered as 1.5, and 𝑅𝑦𝑟 is the ratio of the expected yield stress of the transverse reinforcement material to the specified minimum yield stress. 68 The reason for the difference between the equations proposed by AISC 341-22 [19] for calculating the shear strength of steel and composite coupling beams relies on the fact that each of the C-OSW and C-SSW systems provides different levels of nonlinearity to the whole structure. Therefore, in the C-SSW system in which higher plastic deformations are expected, the shear strength of the SRCBs is increased by 𝑅𝑦, 𝑅𝑐, and 𝑅𝑦𝑟, in addition to some coefficients to consider the strengths of the expected materials. To ensure proper anchorage and transfer of forces between the beam and the surrounding concrete, steel sections in both steel and composite coupling beams are required to be embedded into the adjacent walls. The embedment length is determined per Equation 4.43 for steel and composite coupling beams in both C-OSW and C-SSW systems. Equation 4.42 was developed based on the test results of the conducted research programs by Mattock and Gaafar, 1982 [36], Shahrooz et al., 1993 [10], Harries et al., 1993 and 1997 [8], [39]. The term 𝑏𝑤𝑏𝑓 in Equation 4.43 accounts for the spreading of the compressive stress beneath the beam flange. Equation 4.43 includes an inherent strength reduction factor of 𝜑 = 0.9. 𝑉𝑛,𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑜𝑛 = 4.04√𝑓𝑐′ (𝑡𝑤𝑏𝑓)0.66𝛽1𝑏𝑓𝐿𝑒 (0.58 − 0.22𝛽10.88 +𝐿 + 2𝑐2𝐿𝑒) 4.43 𝑉𝑛 =2(1.1𝑅𝑦)𝑀𝑝𝑔≤ (1.1𝑅𝑦)𝑉𝑝 4.44 Where 𝑉𝑛,𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑜𝑛 is the minimum required shear strength at the wall-beam interface, which in the C-OSW system it should be taken as the smallest of Equation 4.39 and 4.40 for steel coupling beam and Equation 4.41 for composite coupling beams, and in C-SSW system it should be taken 69 as Equation 4.44 for steel and Equation 4.41 for composite coupling beams. g is the clear length of coupling beam plus two times of concrete (𝐿 + 2𝑐). AISC 341-22 [19] offers information on the detailing of steel beams and refers to ACI 318-19 [4] for detailing reinforced concrete walls, except for clause H4.5b.(c), which necessitates additional vertical reinforcing. The vertical reinforcement bars in the adjacent walls assist in transferring the stresses resulting from applied lateral forces due to earthquakes from the coupling beam to the walls, spreading them more uniformly and reducing the possibility of localized damage or failure. Additionally, wall vertical bars in the embedment region control the crack propagation in the wall-beam interface, particularly at the steel section flange location, avoiding the creation of gaps in that region. According to AISC 341-22 [19], the provided force by wall vertical bars in the embedment region should be at least equal to the required shear strength at the beam-wall interface (𝑉𝑛,𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑜𝑛). Thus, the area of required wall vertical bars (𝐴𝑠𝑙) is obtained per Equation 4.45. 𝐴𝑠𝑙 ≥𝑉𝑛,𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑜𝑛𝑓𝑦𝑠𝑙×(𝐿 + 2𝑐)2(𝐿𝑒 − 𝑐)+ 0.33𝛽10.88 − 0.33𝛽1 4.45 Where 𝑓𝑦𝑠𝑙 is the nominal yielding strength of the wall vertical bars (MPa) and 𝑐 is the wall cover (mm). For the C-SSW system, AISC 341-22 [19] mandated to use of auxiliary transfer bars unless wall vertical bars were designed per Equation 4.45, in which the first layer is placed at a distance no less than ℎ𝑠2 from the embedment length end, and the second one be located to coincide with the location of wall vertical bars closest to the face of the wall, where ℎ𝑠 is the steel beam overall depth. Auxiliary transfer bars are placed in the boundary region since they facilitate the transfer of bearing stresses from the flanges to the surrounding concrete, and allow for a more symmetric 70 distribution of strength and stiffness under load reversal due to the transfer of tension at the flange concrete interface, thereby limiting the separation of flange and concrete. Also, these bars will assist the load-transfer mechanism in the embedment region by transferring the axial forces resulting from overturning moments and gravity loads applied on the wall to the steel section in the boundary region. Auxiliary transfer bars should be welded to the top and bottom of the steel profile’s flanges by mechanical couplers. The area of auxiliary transfer bars at (each layer) at each side of the steel section flanges should be at least 0.03𝑓𝑐′ 𝐿𝑒𝑏𝑓𝑓𝑦𝑎, and the total area of these bars in the boundary region should not exceed 0.08𝐿𝑒𝑏𝑤 − 𝐴𝑠𝑙, where 𝑓𝑦𝑎 is the specified yield strength of the auxiliary transfer bars (MPa), Based on AISC 341-22 [19], face bearing plates and web stiffeners should be utilized at the beam-wall interface and certain locations throughout the clear span of the steel coupling beams in the C-SSW system, respectively. Face bearing plates are important in the design procedure since they allow the formation of a diagonal strut between the two plates. Also, web stiffeners are important since they will resist the concentrated loads applied on the coupling beams and prevent the crippling of the steel section web. The spacing of the web stiffeners is a function of the coupling beams' clear span length and expected total chord rotation. For modelling purposes, AISC 341-22 [19] recommended considering cracked effective stiffness for elastic analysis according to ACI 318-19 [4] for all concerned concrete structural elements. In this regard, ACI 318-19 [4] clause 6.6.3.1.1. recommended that the cracked effective moment of inertia for walls and beam would be considered 0.35𝐼𝑔, where 𝐼𝑔 is the gross moment of inertia of the structural element. For calculating the effective stiffness of composite coupling beams, the 71 transformed concrete section using elastic material properties is suggested. According to AISC 341-22 [19] and LATBSDC 2023 [20], the effective flexural, axial, and shear rigidity of the composite coupling beam can be calculated per Equation 4.46, 4.47, and 4.48, respectively. 𝐸𝐼𝑒𝑓𝑓 = 0.07 (𝐿ℎ) (𝐸𝐼)𝑡𝑟𝑎𝑛𝑠 4.46 𝐸𝐴𝑒𝑓𝑓 = 1.0(𝐸𝐴)𝑡𝑟𝑎𝑛𝑠 4.47 𝐸𝐴𝑒𝑓𝑓 = 1.0𝐺𝐴𝑤 4.48 Where (𝐸𝐼)𝑡𝑟𝑎𝑛𝑠 is the flexural rigidity of the cracked transformed section (N-mm2), (𝐸𝐴)𝑡𝑟𝑎𝑛𝑠 is the axial rigidity of the transformed section (N), 𝐺 is the shear modulus of steel (MPa), and 𝐴𝑤 is the area of steel beam web (mm2). LATBSDC 2023 [20] recommends calculating (𝐸𝐼)𝑡𝑟𝑎𝑛𝑠 of composite coupling beams per Equation 4.49. (𝐸𝐼)𝑡𝑟𝑎𝑛𝑠 = (𝐸𝑐𝐼𝑔5) + 𝐸𝑠𝐼𝑠 4.49 Where 𝐼𝑠 is the moment of inertia of the steel coupling beam (mm2) and 𝐸𝑠 is the modulus of elasticity of steel (MPa). AISC 341- 22 [19] has relaxed the requirement of providing auxiliary transfer bars for steel and composite coupling beams in the C-SSW system provided that the wall vertical bars are designed per Equation 4.45. However, numerous ongoing research programs still aim to improve constructability while still achieving comparable performance. Based on the comprehensive literature presented in Appendix C, it was shown that many steel and composite coupling beams experienced extensive damage at the beam-wall interface due to the high rotations of the embedded steel beam in that region. This damage at the beam-wall interface can significantly decrease the 72 initial stiffness of the embedded steel beams. Solutions such as auxiliary transfer bars or significant embedment of the steel beam can result in impractical and expensive construction detailing. 4.3 Proposed connection The constructability issues of the steel and composite coupling beams have motivated the author of this thesis to work with the industry to develop new connection details. According to AISC 341-22 design provisions described in Section 4.2., excessive damage at the beam-wall connection can be minimized by providing sufficient vertical reinforcing in the wall Equation 4.45 or adding auxiliary transfer bars welded to the embedded steel flanges. Leveraging the same concept, a new type of connection detailing is proposed in this section in which additional steel reinforcing is provided in the embedment region but only works in a compression manner (transferring bearing forces). This new connection detailing was proposed with the collaboration of the affiliated industry partner (Kor Structural), in which a bearing system, including headed rebar (generally larger than 30M), is placed between the steel beams. The top and bottom of the headed bars bear on the steel beams. In other words, the plates only transfer bearing stresses once a compression interaction occurs between them and the steel beam flanges. If the tensile stresses developed through the steel beam due to the applied cyclic shear load, these headed bars no longer have any contact with the beam’s flanges to transfer the tensile stresses. Figure 4.8 (a) and (b) show 2D and 3D sketches of the proposed model, respectively. 73 (a) (b) Figure 4.8: (a) 2D and (b) 3D sketches of the proposed embedment model with bearing system. Headed bars (here shown as steel plates) 74 This new connection also provides construction benefits. The headed bars can be positioned to support the steel beams during construction. Since the beams are heavy and require support during the construction process, the compression bars offer an advantage by being able to seat them during installation. 4.4 Mechanics of the proposed innovative connection detailing Figure 4.9 depicts the free-body diagram of the proposed embedment model. By assuming that the cantilever beam is loaded down (negative direction), the bottom, and top flanges of the embedded steel beam at the beam-wall, and back of the embedment region will experience compression stresses, respectively. Therefore, the rods of the bearing system in these locations (Sf and Sb) would be in compression. According to Figure 4.9, m is the distance from the neutral axis to the beam-wall interface. As mentioned in Section 4.2, the same procedure for determining the compression and tension forces distributed in the embedment region will be described in this section by considering the effect of the bearing system on the shear capacity of the embedded steel beam. 75 Figure 4.9: Proposed embedment model. According to Section 4.2, parabolic stress-strain relationship to determine the stress distribution in the back section of the embedment region can be assumed for concrete in steel and composite coupling beams (Equations 4.6 and 4.7). Based on Figure 4.9, the maximum strain at the back of the embedded beam is obtained through Equation 4.50. ∈𝑏=0.003(𝐿𝑒 −𝑚)𝑚 4.50 As shown by Figure 4.9, the strain at the back of the embedded beam as a function of 𝑥, where 𝑥 is the distance from neutral axis to the back of the beam, is obtained through Equation 4.51. 76 ∈𝑐=∈𝑏 (𝑥𝐿𝑒 −𝑚) 4.51 By substituting Equation 4.51 into Equation 4.7, we will have Equation 4.52. 𝑓𝑐 = 1000𝑓𝑐′ ∈𝑏 (𝑥𝐿𝑒 −𝑚) ∗ (1 − 250 ∗∈𝑏 (𝑥𝐿𝑒 −𝑚)) 4.52 By substituting Equation 4.50 into Equation 4.52, we will have Equation 4.53. 𝑓𝑐 = 1000𝑓𝑐′ ∗0.003(𝐿𝑒 −𝑚)𝑚∗ (𝑥𝐿𝑒 −𝑚) ∗ (1 − 250 ∗0.003(𝐿𝑒 −𝑚)𝑚∗ (𝑥𝐿𝑒 −𝑚)) 4.53 The compression force at the back of the embedment region is obtained through the integration of Equation 4.53, times the width of the beam (𝑏). This force is shown in Equation 4.54. 𝐶𝑏 = ( ∫ 𝑓𝑐𝑑𝑥𝐿𝑒−𝑚0) ∗ 𝑏 4.54 The centroid of the compression force at the back of the embedment region from the neutral axis is obtained by Equation 4.55. 𝑥𝑛 =𝑏 ∗ ∫ 𝑥𝑓𝑐𝑑𝑥𝐿𝑒−𝑚0∫ 𝑓𝑐𝑑𝑥𝐿𝑒−𝑚0 4.55 To be consistent with the findings found by Mattock and Gaafar, 1982 [33], [36] and Kriz and Raths, 1974 [33], in the mechanics of the proposed innovative model, the modified concrete compressive strength can be calculated upon Equation 4.56. 77 𝑓𝑐𝑚′ =4.5√𝑓𝑐′0.85= 5.3√𝑓𝑐′ 4.56 By doing the integrals, 𝐶𝑏 and ?̅?𝑛−𝐶𝑏 are calculated by Equation 4.57 and Equation 4.58, respectively. 𝐶𝑏 = −(3 ∗ 𝑓𝑐𝑚′ ∗ (𝐿𝑒 −𝑚)2 ∗ (𝐿𝑒 − 3 ∗ 𝑚)4 ∗ 𝑚2) ∗ 𝑏 4.57 ?̅?𝑛−𝐶𝑏 =((𝐿𝑒 −𝑚) ∗ (9 ∗ 𝐿𝑒 − 25 ∗ 𝑚))(12 ∗ (𝐿𝑒 − 3 ∗ 𝑚)) 4.58 Consequently, 𝑥𝑐−𝐶𝑏 defined as the centroid of the compression force at the back of the embedment region from the beam-wall interface is obtained by Equation 4.59. 𝑥𝑐−𝐶𝑏 =((𝐿𝑒 −𝑚) ∗ (9 ∗ 𝐿𝑒 − 25 ∗ 𝑚))(12 ∗ (𝐿𝑒 − 3 ∗ 𝑚))+ 𝑚 4.59 The compression force of the rods located at the behind region can be calculated per Equation 4.60, where 𝑤 is the distance of the back rods’ centroid from the beam-wall interface. In Equation 4.60, it was assumed that the yielding stress of the rods are 400 MPa. 𝑆𝑏 = 𝐴𝑠 ∗ 𝑓𝑠𝑏 = 𝐴𝑠 ∗ 𝐸𝑠 ∗∈𝑏= 𝐴𝑠 ∗ 𝐸𝑠 ∗0.003(𝐿𝑒 −𝑚)𝑚∗ (𝑤 −𝑚𝐿𝑒 −𝑚) < 𝐴𝑠 ∗ 𝐸𝑠 ∗ 0.002 4.60 The centroid of the compression force, developed by the rods at the back of the embedment region, from the beam-wall interface is obtained by Equation 4.61. 𝑥𝑐−𝑆𝑏 = 𝑤 4.61 78 By assuming the Whitney compression block for concrete behaviour, the concrete compression force at beam-wall region can be calculated by Equation 4.62. 𝐶𝑓 = 0.85 ∗ 𝑓𝑐𝑚′ 𝛽1𝑚𝑏 4.62 The centroid of the concrete compression force at the front region from the neutral axis is obtained by Equation 4.63. 𝑥𝑐−𝐶𝑓 =𝛽1𝑚2 4.63 The compression force of the rod located at the front region can be calculated per Equation 4.64, where 𝑢 is the distance of the front rods’ centroid from the beam-wall interface. In Equation 4.64, it was assumed that the yielding stress of the rods are 400 MPa. 𝑆𝑓 = 𝐴𝑠 ∗ 𝑓𝑠𝑓 = 𝐴𝑠 ∗ 𝐸𝑠 ∗0.003(𝑚 − 𝑢)𝑚< 𝐴𝑠 ∗ 𝐸𝑠 ∗ 0.002 4.64 The centroid of the compression force, developed by the rods at the front of the embedment region, from the beam-wall interface is obtained by Equation 4.65. 𝑥𝑐−𝑆𝑓 = 𝑢 4.65 By writing the equilibrium equation of forces in the vertical direction we will have: ∑𝐹𝑦 = 0 → 𝑉𝑛 + 𝐶𝑏 + 𝑆𝑏 = 𝐶𝑓 + 𝑆𝑓 → 𝑉𝑛 = 𝐶𝑓 + 𝑆𝑓 − 𝐶𝑏 − 𝑆𝑏 79 → 𝑉𝑛 = 0.85 ∗ 𝑓𝑐𝑚′ ∗ 𝛽1𝑚𝑏 + 𝐴𝑠 ∗ 𝐸𝑠 ∗0.003(𝑚 − 𝑢)𝑚+ ((3 ∗ 𝑓𝑐𝑚′ ∗ (𝐿𝑒 −𝑚)2 ∗ (𝐿𝑒 − 3 ∗ 𝑚)4 ∗ 𝑚2) ∗ 𝑏) − 𝐴𝑠 ∗ 𝐸𝑠∗0.003(𝐿𝑒 −𝑚)𝑚∗ (𝑤 −𝑚𝐿𝑒 −𝑚) 4.66 By summing the moment at the beam-wall interface we have: ∑𝑀 = 0 → 𝑉𝑛 ∗ 𝑎 + 𝐶𝑓 ∗ 𝑥𝑐−𝐶𝑓 + 𝑆𝑓 ∗ 𝑥𝑐−𝑠𝑓 = 𝐶𝑏 ∗ 𝑥𝑐−𝐶𝑏 + 𝑆𝑏 ∗ 𝑥𝑐−𝑆𝑏 → 𝑉𝑛 ∗ 𝑎 + (0.85 ∗ 𝑓𝑐𝑚′ ∗ 𝛽1𝑚𝑏) ∗𝛽1𝑚2+ (𝐴𝑠 ∗ 𝐸𝑠 ∗0.003(𝑚 − 𝑢)𝑚) ∗ 𝑢= −(3 ∗ 𝑓𝑐𝑚′ ∗ (𝐿𝑒 −𝑚)2 ∗ (𝐿𝑒 − 3 ∗ 𝑚)4 ∗ 𝑚2) ∗ 𝑏∗ (((𝐿𝑒 −𝑚) ∗ (9 ∗ 𝐿𝑒 − 25 ∗ 𝑚))(12 ∗ (𝐿𝑒 − 3 ∗ 𝑚))+ 𝑚) + (𝐴𝑠 ∗ 𝐸𝑠∗0.003(𝐿𝑒 −𝑚)𝑚∗ (𝑤 −𝑚𝐿𝑒 −𝑚)) ∗ 𝑤⁡ 4.67 According to the above-mentioned equations (Equations 4.66 and 4.67), we have two unknowns, 𝑉𝑛 and m. By substituting term 𝑉𝑛 in Equation 4.66 by 𝑉𝑛 in Equation 4.67, we will have: 80 ( 0.85 ∗ 𝑓𝑐𝑚′∗ 𝛽1𝑚𝑏+𝐴𝑠 ∗ 𝐸𝑠 ∗0.003(𝑚−𝑢)𝑚+( (3 ∗ 𝑓𝑐𝑚′∗ (𝐿𝑒−𝑚)2 ∗ (𝐿𝑒−3∗𝑚)4 ∗𝑚2) ∗ 𝑏) −𝐴𝑠 ∗ 𝐸𝑠∗0.003(𝐿𝑒−𝑚)𝑚 ∗ (𝑤−𝑚𝐿𝑒−𝑚)) ∗ 𝑎 + (𝐴𝑠 ∗ 𝐸𝑠 ∗0.003(𝑚−𝑢)𝑚 )∗𝑢+ (3 ∗ 𝑓𝑐𝑚′∗ (𝐿𝑒 −𝑚)2 ∗ (𝐿𝑒 − 3 ∗ 𝑚)4 ∗ 𝑚2) ∗ 𝑏 ∗ (((𝐿𝑒 −𝑚) ∗ (9 ∗ 𝐿𝑒 − 25 ∗ 𝑚))(12 ∗ (𝐿𝑒 − 3 ∗ 𝑚))+ 𝑚)− (𝐴𝑠 ∗ 𝐸𝑠 ∗0.003(𝐿𝑒−𝑚)𝑚 ∗ (𝑤−𝑚𝐿𝑒−𝑚)) ∗𝑤 = 0 4.68 By solving Equation 4.68, two values will be provided for the neutral axis depth. One of these answers are not acceptable as based on that of value m, the strain values in the rods exceed 0.002 which was assumed to be the strain corresponding to the yielding of the rods. Once the proper value of 𝑚 is calculated, the shear capacity of the embedded steel beam by considering the effect of bearing system can be obtained upon Equation 4.66. 4.5 Performance of new connection using a mathematical model The design plot was developed by considering practical aspects of the proposed novel connection detailing. According to Figure 4.10, the required connection capacity of steel and composite coupling beams is obtained based on various area of used steel compression reinforcement, where 𝑠 is the distance between the rods at the front and back of the beam (c.c.) and 𝐴𝑠 is the total steel compression reinforcement area placed on either top or bottom side of the steel beam flange. The provided design plot can be used according to the following steps. • Determine the demand (𝑉𝑛 =𝑉𝑢𝜑=0.9) 81 • By having embedment length, determine 𝑉𝑛√𝑓𝑐′𝐿𝑒𝑏𝑒𝑓𝑓 • By having the clear span length determine 𝑎𝐿𝑒 • By having points on X and Y axis, read 𝜔′ =𝐴𝑠𝑏𝑒𝑓𝑓𝐿𝑒∗𝑓𝑦√𝑓𝑐′ • By having 𝜔′, calculated the required 𝐴𝑠. Figure 4.10: Design plot associated with the mathematical model of proposed connection detailing. According to Figure 4.10, for a given value of normalized shear force on the Y-axis (i.e., 0.6), the normalized embedment length can be decreased on the X-axis from 0.6 without using any additional compression steel reinforcing (𝜔′ = 0) to 0.4 by using 35M as additional compression steel reinforcing (𝜔′ = 0.777). This shows that using new connection detailing can decrease the minimum required steel beam embedment length. 82 4.6 Summary In this chapter, an extensive review of previous connection detailings and code requirements demonstrated a need for new connection detailing that is both practical and can improve the performance of steel and composite coupling beams (SCB/SRCBs). Based on the review of current embedment models, a new connection detailing was proposed. In the proposed connection detailing, additional compression steel reinforcing (i.e., headed reinforcing steel) is placed near the beam-wall interface and the end of the embedded steel beam. The headed bars are not welded to the flanges (not fixed) to allow the additional compression bars to transfer compression forces and be neutral when the surrounding concrete is in tension. Such a connection reduces compression stresses in the concrete, enabling smaller embedment length for a given shear strength. The mechanics of the proposed connection detailing were explained in detail and design equations were developed. Furthermore, a practical design plot was provided according to the developed mathematical model associated with the load-transferring mechanism of the additional compression steel reinforcing. However, a finite element model is required to examine the seismic response, such as shear capacity, rotational capacity, and initial stiffness of steel and composite coupling beams having compression steel reinforcing, which will be discussed in the next chapter. 83 Chapter 5: Finite element modelling of new connection detailing for steel and composite coupling beams 5.1 Introduction This chapter focuses on the development of a finite element model to further understand the performance of the proposed connection from Chapter 4. This analysis used DIANA FEA 10.6 finite element software to develop continuum finite element models. This chapter starts by presenting the available tools and features of DIANA FEA 10.6. Various element and material models were considered to simulate the failure mechanism and overall performance of previously tested steel and composite coupling beams (SCB/SRCBs). A 3D modelling approach was followed. The developed calibrated finite element model of the previously tested steel and composite coupling beams is described following the modelling approach section. To investigate the effect of quantity and size of compression steel reinforcement used in new connection detailing on the hysteretic response of steel and composite coupling beams, preliminary studies using the calibrated finite element model were conducted. Finally, the chapter concludes with a summary of the findings. 5.2 Modelling approach The finite element method is a method for the approximate solution of governing differential equations on continuous media. This is accomplished by forming and solving a system of algebraic equations related to a limited number of variables. Nodal points are located at the border of the elements or inside them. The change of places and forces in the nodes are obtained as separate variables. 84 This method involves decomposing the desired surface or volume into an array of triangular components or quadrilaterals and connecting them at specific points in the border area. The stiffness of each component is calculated according to the geometry and characteristics of its materials. By combining the stiffness matrix of the components, the stiffness matrix of the whole structure becomes available. With the external forces and the stiffness matrix of the whole structure, the changes in place and nodal forces are calculated. This method has the ability to use networks of finite elements in areas with complex geometry or concentrated stresses, and in areas without specific problems and with uniform stress, using networks of coarse elements. In addition, complex areas of a structure can be modelled using the membrane finite element method and other areas using the equivalent frame method. One of the elements used in modelling the nonlinear behaviour of a structure is the interface element. Due to the lack of connection between the embedded steel beam and the surrounding concrete, there is a possibility of nonlinear behaviour at the contact surface of these two materials, based on the fact that the tensile, compressive, and shear behaviour of concrete and steel is very different from each other. This nonlinear behaviour includes the sliding and separation of two surfaces relative to each other, and the creation of a gap at the contact surface under tensile stress. Therefore, interface elements can significantly affect on the response of composite structures in finite element analyses. 5.2.1 Elements In DIANA finite element analysis software, there is a wide range of elements with different characteristics and behaviour. Generally, in terms of dimensions, there are three categories of elements including one-dimensional or linear elements, two-dimensional elements and three-dimensional elements in finite element software. Linear or one-dimensional elements model 85 components with a long length compared to their other dimensions in the cross-section, such as beams, reinforcements. Two-dimensional elements or shell or membrane elements that are used to model planar components and members, such as walls, slabs, etc. Other members and elements of finite elements include three-dimensional elements that are used for modelling the three-dimensional behaviour of elements and elements. Since the interaction between the embedded steel beam and the concrete in the embedment region can be too complex due to the high nonlinearity of concrete and composite action between these two materials, all the steel and concrete components in this region are modelled as 3D solid elements. The wall reinforcing elements were modelled as lines transferring only axial loads. Two types of reinforcement elements can be defined in concrete. The first type is the embedded type, in which the strains of the bars are equal to the strains of the three-dimensional or two-dimensional components surrounding the reinforcement. The second type of reinforcement element is a sliding element. In the latter type, the nonlinear behaviour of the refinements will be modelled interpedently from the surrounding components. However, the embedded reinforcement will be deformed in the same way as the surrounding concrete will be. Since in this work the slippage of shear wall’s reinforcements will not affect the overall performance of the embedded steel beam, for modelling purposes the reinforcements are assumed to be embedded in the shear wall. Figure 5.1 shows different types of elements implemented by DIANA 10.6. 86 Figure 5.1: Element types utilized by DIANA 10.6. 5.2.2 Mesh discretization It is crucial to create a nonlinear finite element model with accurate mesh discretization, since incorrect parameters can alter results and behaviour. Using the proper mesh size should be determined according to the corresponding experimental test for which the finite element model is being developed. Generally, fine mesh sizes bring more accurate response of the system, very similar to the actual testing data. However, finer mesh size may alter the behaviour of the specimen, as small crack band widths can lead to a mesh-induced directional bias. On the other hand, using coarser mesh sizes, particularly in the embedment region where concrete and steel beam are fully connected, may lead to the wrong stress-strain distribution. This wrong function may cause the omission of relatively large elements such as concrete, connected to other elements such as steel beam flanges. In this case, since the concrete mesh size is determined large and it has already reached its cracking stress, the attached steel section to this concrete par may be omitted by the software since the steel and concrete are supposed to fully work with each other. a) 2 Plane elements b) 3 Solid elements c) egular truss element d) mbedded reinforcement87 5.2.3 Materials DIANA 10.6 has various models modelling the behaviour of different materials such as concrete, steel, brick, mortar, etc. in tension, compression, and shear. Based on the experimental studies which have been studied in this work, the following theories for steel and concrete have been selected: 5.2.3.1 Concrete Maekawa-Fukuura [44] concrete model was chosen for to simulate the behaviour of concrete in DIANA models. The Maekawa-Fukuura [44] concrete model in DIANA is a combination of the Total Strain crack model combined with the Maekawa [44] Cracked Concrete curves, and the Elasto-plastic Damage model. In contrary to the Total Strain crack model the Maekawa-Fukuura [44] concrete model makes use of a non-orthogonal crack definition. The Maekawa and Fukuura [44] Cracked Concrete curves are uniaxial stress-strain relations for loading, unloading and reloading conditions in respectively the tensile and compressive strain domains. Figure 5.2 shows the Maekawa-Fukuura concrete curves utilized for modelling aspect. According to Figure 5.2 the following stages can be recognized: • 0-1 Compressive loading • 1-2 Compressive unloading • 2-3 Compressive reloading • 3-4 Compressive unloading • 4-5 Tensile loading • 5-6 Tensile loading • 6-7 Tensile unloading • 7-8 Tensile reloading 88 • 8-9 Tensile unloading • 9-10 Compressive reloading • 10-11 Compressive loading Figure 5.2: Hysteresis curve for Maekawa and Fukuura concrete model [44]. To predict the behaviour of concrete in tension based on Maekawa-Fukuura concrete model, DIANA 10.6 utilizes different stress-strain distribution (Figure 5.3). 89 Figure 5.3: Predefined tension softening for Maekawa-Fukuura concrete model [44]. In this work, the Japan Society of Civil Engineers (JSCE) [45] anisotropic tension stiffening curve (Figure 5.3(h)) for stimulation the tensile behaviour of concrete was chosen. Equation 5.1 shows the stress-strain relationship of the JSCE [45] tension stiffening curve for concrete. 𝜎 = 𝑓𝑡 (𝜀𝑡𝑢⁡𝜀)𝑐 5.1 Where 𝑓𝑡 is the maximum tensile stress of concrete, 𝜀𝑡𝑢 is the maximum tensile strain of concrete (𝜀𝑡𝑢 = 0.0002) and 𝑐 is the power equal to 0.4. 90 Since DIANA 10.6 has an option by which the presence of the confinement around bars in the reinforced concrete can be defined, in this work it was decided to model the compressive behaviour of concrete by considering unconfined concrete, and increase the compressive strength of concrete by Mander et al., 1988 [46] Constitutive Model, in which 𝑓𝑐′ is calculated by considering confined concrete. According to Mander et al., 1988 [46], the compressive of strength of confined concrete is calculated by Equation 5.2. Consequently, the compressive stress-strain relationship of the confined concrete based on Mander et al., 1988 [46] can be canulated by Equation 5.3. 𝑓𝑐𝑐′ = 𝑘𝑐𝑓𝑐′ 5.2 𝑓𝑐 ={ 𝑓𝑐𝑐′ (1 − |1 − 𝑥|𝑛)⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡𝑖𝑓⁡0 ≤ 𝑥 < 1𝑓𝑐𝑐′ − (𝑘𝑐𝑓𝑐′ − 𝑓𝑐𝑢𝑥𝑢 − 1) (𝑥 − 1)⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡𝑖𝑓⁡⁡1 ≤ 𝑥 < 𝑥𝑢⁡𝑓𝑐𝑢 (𝑥 − 𝑥𝑓𝑥𝑢 − 𝑥𝑓) ⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡𝑖𝑓⁡𝑥𝑢 ≤ 𝑥 < 𝑥𝑓 5.3 Where 𝑓𝑐𝑐′ is the confined peak stress, 𝑥 is the normalized strain 𝜀𝑐𝜀𝑐𝑐, 𝜀𝑐 is the compressive concrete strain, 𝜀𝑐𝑐 is the confined peak strain, 𝑘𝑐 is the confined ratio, 𝑓𝑐𝑢 is the ultimate stress, 𝑥𝑢 is the normalized strain 𝜀𝑐𝑢𝜀𝑐𝑐, 𝜀𝑐𝑢 is the ultimate strain, 𝑥𝑢 is the normalized strain 𝜀𝑓𝜀𝑐𝑐, and 𝜀𝑓 is the failure strain. 5.2.3.2 Steel Steel shows similar behaviour in tension and compression. Therefore, a stress-strain diagram can be defined for both compressive and tensile state for steel material. The tensile and compressive behaviour of steel is usually linear up to the yield point. This region of the diagram is called the 91 elastic deformation region. Then, after some changes in strain in constant stress, the stress increases to the ultimate point, which is called the hardening region. After this point, the hardening parameters are used to calculate the increase in stresses and strains. In this case, the increase in plastic strain will be irreversible. In this work, Von Mises and Tresca plasticity theory is followed to simulate the behaviour of the steel in the finite element models. According to this theory, the yielding point is reached once the second variable of the deviatoric stress tensor reaches the critical value of 𝐾 (Equation 5.4), where 𝐾 is the yielding stress in pure shear (Equation 5.5). 𝑓(𝑗2) = √𝑗2 − 𝑘 = 0 5.4 𝐾 =𝜎𝑦√3 5.5 Where 𝜎𝑦 is the yielding stress of the material. By having the principal stresses in each direction (𝜎1, 𝜎2⁡, 𝑎𝑛𝑑⁡𝜎3), the equation of the surface of a cylinder whose cross-section in the deviating plane is a circle with the radius of 𝐾 =𝜎𝑦√3 is achieved (Equation 5.6). Figure 5.4 shows yielding condition of the Von Mises and Tresca plasticity theory. (𝜎1 − 𝜎2)2 + (𝜎2 − 𝜎3)2 + (𝜎1 − 𝜎3)2 = 6𝐾2 = 2𝜎𝑦2 5.6 92 Figure 5.4: Yielding condition of the Von Mises and Tresca plasticity theory 5.2.4 Interfaces Structured interface elements describe interface behaviour as a function of normal and shear tractions and normal and shear relative displacements. Typical applications for structural interface elements are elastic bedding, nonlinear elastic bedding (for instance no-tension bedding), discrete cracking, bond-slip reinforcement, friction between surfaces, joints in rock, masonry etc. The connectivity of interfaces does not change during analysis, and therefore these elements should not be used in models with large slip (relative slip displacements in order of element edge or larger). Different types of structural interfaces are introduced by DIANA 10.6. Based on the calibrated specimens in this work, shell interface was selected since the faces of the steel flanges and surrounding concrete were supposed to have composite actions. Figure 5.5 shows the variables of a three-dimensional surface interfaces. In Figure 5.5(c), the normal traction 𝑡𝑛𝑧 is perpendicular to the interface; the shear tractions 𝑡𝑠𝑥 and 𝑡𝑠𝑦 are tangential to the interface. 93 Figure 5.5: Variables of three-dimensional surface interfaces. According to Figure 5.5(a), (b), and (c), the actual displacements, relative displacements, and tractions of a structural 3D surface interface can be defined by Equation 5.7, 5.8, and 5.9, respectively. Finally, the linear relationship between relative displacements and tractions can be defined by Equation 5.10. 𝑢 = {𝑢𝑥𝑢𝑦𝑢𝑧} 5.7 ∆𝑢 = {∆𝑢𝑠𝑥∆𝑢𝑠𝑦∆𝑢𝑛𝑧} 5.8 𝑡 = {𝑡𝑠𝑥𝑡𝑠𝑦𝑡𝑛𝑧} 5.9 {𝑡𝑠𝑥𝑡𝑠𝑦𝑡𝑛𝑧} = [𝑘𝑠𝑥000𝑘𝑠𝑦000𝑘𝑛𝑧] {∆𝑢𝑠𝑥∆𝑢𝑠𝑦∆𝑢𝑛𝑧} 5.10 Where 𝑘𝑠𝑥, 𝑘𝑠𝑦, and 𝑘𝑛𝑧 are the tangential and normal stiffness values in x, y, and z directions, respectively. 5.3 Specimen used for calibration To verify the proposed modelling approach, specimen SCBC1 tested by Nahvinia, 2018 [47] was chosen for calibration. Specimen SCBC1 was a steel coupling beams designed to experience failure of the concrete at the beam-wall connection. Since it was proposed that the new connection detailing is capable of reducing excessive damage at the beam-wall interface, specimen SCBC1 with the same failure mode was considered ideal for this finite element study. 94 5.3.1 Geometry details Specimen SCBC1 tested by Nahvinia, 2018 [47]. Specimen SCBC1 consisted of flanges with the width of 130 mm and thickness of 10 mm, a web with the depth of 250 mm and thickness of 6 mm. Web stiffeners with the same dimensions as beam’s web were placed every 150 mm only outside the embedment region (three stiffeners in total). In terms of transverse and longitudinal reinforcements, SCBC1 was designed and constructed with dense transverse reinforcement according to clause 18.10.6.4 of ACI 318-14 [48], and longitudinal reinforcement met the requirements of AISC 341-10 [49]. Additionally, in specimen SCBC1, none of the ties were welded to the web of the steel beam in the embedment region. The embedment length of SCBC1 was determined as 420 mm calculated per Equation 4.36. The cyclic shear load was applied from a distance of 375 mm measure from the beam-wall interface to the end side of the cantilever steel beam outside the wall. Specimen SCBC1 designed and tested as a benchmark in the Nahvinia, 2021 [47] experimental program, exhibiting a damage and failure at the beam-wall connection. 5.3.2 Test setup and loading protocol The constant gravity load with the magnitude of 1.16 MPa was applied to the top surface of the shear wall. Additionally, cyclic shear load with the load steps shown in Figure 5.6 was applied to the steel coupling beam. Figure C-26 demonstrates the used test setup in Nahvinia, 2018 [47] experimental program. Since SCBC1 was tested while placed in the plane of the string floor, out of plane restrains was modelled by edge constraints in modelling. 95 Figure 5.6: Lateral loading protocol of specimen SCBC1 [47]. 5.3.3 Material properties Based on the material properties reported by Nahvinia, 2018 [47], Table 5.1 summarises the model material parameters for confined and unconfined concrete. Table 5.1: Model material parameters for confined and unconfined concrete of specimen SCBC1. Confinement Ec (MPa) Poisson’s ratio (υ) f’c (MPa) ft (MPa) Gf (N/mm) Unconfined concrete 28975 0.25 36.6 3.25 0.01 Confined concrete 55 3.25 0.01 96 To model the tensile behaviour of steel plates and rods used in the construction of SCBC1, a piecewise multiple-linear stress-strain relationship was developed based on the material testing conducted on steel plates, and steel rods (Figure 5.7 and Figure 5.8), respectively. (a) (b) Figure 5.7: Stress-strain relationship of steel plates with thickness of (a) 6 mm and (b) 10 mm [47]. (a) (b) Figure 5.8: Stress-strain relationship of steel rods with diameter of (a) 8 mm and (b) 12 mm [47]. 5.3.4 Interface elements Since the embedded steel beam in specimen SCBC1 was not fixed to the end of the shear wall indicating that slippage can happen, and on the other hand the shear wall itself was modelled to be 97 able experience nonlinear deformations/cracking, it was assumed that after some loading steps the bond between the embedded steel beam and surrounding concrete may not exist anymore. In other words, it was assumed that after number of loading steps, the composite action between concrete and embedded steel beam will disappear. Having said this, for modelling purposes, interface element between embedded steel beam and surrounding concrete was modelled. A parametric study was conducted to determined the values for normal stiffness and shear stiffness in x and y directions which matches with the experimental results. Based on the results, the normal stiffness modules of 30 N/mm3 and 0.25 N/mm3 for the shear stiffness modules in x and y directions were determined. Since after some cycles the perfect bond between the embedded steel beam and surrounding concrete disappears, it was required to determine the energy dissipated through the concrete in tension. In this regard, JSCE [45] softening theory was chosen to represent the tensile behaviour of concrete with tensile strength of 0.0 MPa and fracture energy equal to 0.001 N/mm. 5.3.5 Evaluation and analysis results 5.3.5.1 Hysteretic response Figure 5.9 shows the mesh discretization of SCBC1. By considering the computational costs and time limitations, 75 mm was the considered mesh size for mesh dissertation of specimen SCBC1. The hysteretic curves representing shear force to drift ratio for both FEM and experimental results are depicted in Figure 5.10. 98 (a) (b) Figure 5.9: Mesh discretization of (a) shear wall and (b) embedded steel of SCBC1. Figure 5.10: Hysteretic curves of FEM and experimental results of SCBC1. Figure 5.10 shows a well match between the hysteretic curves developed by the finite element model and experimental results. The FEM hysteresis loops almost captured the experimental ones precisely, with a low error. The maximum lateral strength in positive direction (loading) was 99 estimated by the model at 278.2 KN, while experimental results recorded 278 KN. In the unloading part, the maximum lateral strength was estimated by the model at -291.5 KN, while experimental results recorded -262 KN, resulting in a reasonable error of 10%. 5.3.5.2 Failure mechanism and cracking patterns Specimen SCBC1 was designed to tolerate significant inelastic rotations and deformations at the beam-wall interface. According to Nahvinia, 2018 [47] test results, the embedded steal beam was moved about 60 mm to the onside of the wall representing the slippage which was in accordance with the FEA results (Figure 5.11). Figure 5.11: Slippage of the embedded steel beam of specimen SCBC1. According to the test results, the initial cracking occurred at the rotation of almost 0.02 in the second cycle. Figure 5.12 (a) shows the crack stresses at load-step 13 of the cyclic loading. According to Figure 5.12 (a), the initial cracks started from the bottom of the beam-wall interface, propagated through the left side of the concrete shear wall. At this stage, the normal stress 100 calculated in the cracks was 3.25 MPa. By pushing the cantilever steel beam (load step 15), these cracks were increased in width led to the decrease of stress to 1.39 MPa in the bottom side of the connection and occurrence of cracks at the top side of the beam-wall interface (Figure 5.12 (b)). According to Figure 5.12 (c) showing the cracks at the rotation of 0.02 based on experimental results, slight cracking at the connection can be observed. Also, at load step 15, Figure 5.12 (d) shows the effective stresses of the web and flanges of the embedded steal beam. Based on Figure 5.12 (d), the steal beam did not reach any yielding limits (300 MPa) at the initial cycles as indicated by Nahvinia, 2018 [47]. (a) (b) 101 (c) (d) Figure 5.12: Initial cracking of specimen SCBC1. Figure 5.13 shows a comparison between the cracking pattern at the last cycle of the finite element model and experimental testing results. According to Figure 5.13 (a) it can be observed that the cracks near the beam-wall interface has occurred and propagated in the height of the wall. The same cracking pattern in shown by the experimental observation, confirming the finite element results. 102 (a) (b) Figure 5.13: Crack pattern of SCBC1 based on (a) FEM and (b) experimental results. 5.3.5.3 Stiffness degradation Figure 5.14 shows the stiffness degradation of specimen SCBC1 based on finite element model and experimental results up to 21 mm displacement. According to Figure 5.14, the finite element model can properly estimate the stiffness degradation in each cycle as the modelling results has captured the experimental ones well. 103 Figure 5.14: Stiffness degradation plots developed based on FEM and experimental results of SCBC1. 5.4 Preliminary studies To investigate the performance of the new connection detailing, two preliminary studies were undertaken using the FEM approach developed in Section 5.2. These studies utilized DIANA FEA 10.6 to model specimens with a mesh size of 25 mm, analyzed under pushover loading. In the first preliminary study, three specimens were modelled, two were reinforced according to the proposed connection detailing and one without any additional reinforcing. Comparative analysis in preliminary study 1 aims to examine the contributions of the proposed connection detailing towards the structural performance of steel coupling beams where additional compression steel reinforcements are used. In the second preliminary study, three specimens were modelled, one was detailed by using auxiliary transfer bars. The other specimen was modelled by incorporating additional steel reinforcing (proposed connection detailing). Finally, the third specimen was modelled without having any additional reinforcing. The main reason for conducting the second preliminary study 104 was to compare the effectiveness of each reinforcing configuration (auxiliary transfer bars or compression steel reinforcing) in improving the structural performance of steel coupling beams. In both preliminary studies 1 and 2, it was assumed that the embedded steel beam did not yield (assigning modulus of elasticity to a steel beam with a value of more than 100,000 Mpa). The reason behind this was to ensure that the concrete at the beam-wall interface would fail prior to steel beam yielding. In this regard, the effectivity of compression steel reinforcing could be evaluated in preventing excessive damage at the beam-wall interface. Table 5.2 summarises an overview of the preliminary studies, where the specimen properties are shown. Table 5.2: Details of the specimens studied in the conducted preliminary studies. Study Specimen ID Additional reinforcement configuration Bar diameter (mm) Fy steel beam (MPa) 1 No rods- Inf None None infinite 15M-Inf Proposed connection 15 20M- Inf Proposed connection 20 4 20M-Inf Proposed connection 20 infinite 20M-ATB-Inf Auxiliary transfer bars 20 No rods-Inf None None 5.4.1 Preliminary study 1 In preliminary study 1, the effect of the proposed connection detailing on the structural performance of SCBs experiencing extensive damage at the beam-wall interface was investigated. The analyzed specimens had the same geometrical and material properties of the verified model in Sections 5.2 and 5.3 (SCBC1 tested by Nahvinia, 2018 [47]), with the exception that compression steel bars were added, shown in Figure 5.15(a) and (b). 105 (a) (b) Figure 5.15: 3D finite element model of specimens (a) with proposed connection detailing and (b) without proposed connection detailing. 106 Figure 5.16 shows the backbones of three specimens with additional compression steel bars (15M-Inf and 20M-Inf) and without additional compression steel bars (No rods-Inf). In Figure 5.16, the reinforcement ratio (ω) was calculated per Equation 4.16. By considering the No rods-Inf specimen as the benchmark, specimen 15M-Inf with ω equal to 0.03 and specimen 20M-Inf with ω equal to 0.05 show a normalized value of 1.33 in terms of θVmax (rotational capacity of beam corresponding to the maximum shear capacity). This represents an increase in rotational capacity by 33%, when compared to the No rods-Inf specimen. This considerable increase indicates that additional compression steel reinforcement significantly enhances the deformation capability of the SCBs when the concrete at the beam-wall interface fails. The normalized maximum shear force for 15M-Inf and 20M-Inf specimens are 1.46 and 1.56, respectively. These values indicate an increase in shear force capacity by 46% and 56%, respectively, compared to the benchmark No rods-Inf specimen. The initial stiffness is slightly above the benchmark for both specimens with additional compression steel bars, with the 15M-Inf specimen at 1.02 and the 20M-Inf specimen at 1.09. This indicates an increase in stiffness of 2% for the 15M and 9% for the 20M over the No rods-Inf specimen. To summarize, the inclusion of the proposed connection detailing in SCBs with the failure mode of concrete at the beam-wall interface substantially improves their rotational capacity, shear force resistance, and initial stiffness. Additionally, analysis results showed that increasing the compression steel bar size can improve the structural performance of SCBs. 107 Figure 5.16: Backbone diagrams of specimens with additional compression steel bars (15M-Inf with ω=0.03 and 20M-Inf with ω=0.05) and without additional reinforcement. 5.4.2 Preliminary study 2 In preliminary study 2, analysis results of specimens with auxiliary transfer bars, with additional compression steel bars, and without any additional bars are discussed and compared to each other. All the specimens in preliminary study 2 were modelled and analyzed to experience significant damage at the beam-wall interface. Figure 5.17 shows the backbones of three analyzed specimens with additional compression steel bars (20M-Inf), with auxiliary transfer bars (20M-ATB-Inf), and without any additional reinforcement (No rods- Inf). By considering the No-rods Inf specimen as the benchmark, the following results can be provided: 108 𝜃𝑉𝑚𝑎𝑥: Both 20M-ATB-Inf and 20M-Inf specimens demonstrate a normalized θVmax value of 1.33, which is a substantial increase of 33% in rotational capacity compared to the No rods-Inf specimen. These increases highlight the beneficial impact of reinforcement on the rotational capacity of the beams. 𝑉𝑚𝑎𝑥: For the maximum shear force, the ATB specimen shows a significant increase with a normalized value of 1.73 (73% higher than the No rods-Inf specimen), while the 20M0-inf specimen has a normalized value of 1.57 (57% increase). This suggests that the ATB specimen offers greater shear resistance. 𝐾𝑖: The initial stiffness normalized values are notably higher for the ATB specimen at 1.74 (an increase of 74%), and for the 20M-Inf specimen, the increase is 10% with a normalized value of 1.1. This indicates that the ATB specimen has a significantly higher initial stiffness, suggesting that the amount and type of reinforcement have a marked effect on the beam stiffness. A major reason for this superior initial stiffness can be the type of connection in which additional bars are welded (fixed) to the embedded steel beam flanges, resulting in a load-transferring mechanism in both compression and tension. Figure 5.18 (a) and (b) show the vertical displacements of specimens with auxiliary transfer bars (20M-ATB-Inf) and with compression steel reinforcing (20M-Inf), respectively. According to Figure 5.18 (a), all the modelled auxiliary transfer rods experienced deformation due to applied shear force. This means that all these bars are working in both tension and compression. However, according to Figure 5.18 (b), the modelled compression steel bars only displaced vertically due to compression forces attributed to the bearing forces. Therefore, Figure 5.18 (a) and (b) show the different connections between additional bars and the embedded steel flanges, leading to transferring shear forces in tension and compression. 109 Figure 5.17: Backbone diagrams of specimens with auxiliary transfer bars (20M-ATB-Inf with ω=0.1), with additional compression steel bar (20M-Inf with ω=0.05), and without any additional reinforcement. (a) (b) Figure 5.18: Vertical displacement of (a) specimen with auxiliary transfer bars (20M-ATB-Inf) and (b) specimen with compression steel reinforcing (20M-Inf) 110 5.5 Conclusion This chapter proposes a new modelling approach for the steel and composite coupling beams (SCB/SRCBs). A detailed finite element model was developed and validated using experimental results regarding hysteretic response, stiffness degradation, and cracking pattern. Based on the matching between modelling and experimental results, it can be concluded that the proposed modelling approach is suitable. Using this new modelling approach, two preliminary studies were completed. Based on the first preliminary study results, it was found that specimen with larger compression steel bars (20M-Inf) can experience higher shear capacity and initial stiffness compared to specimen with smaller compression steel bars (15M-Inf) by 7%. Based on preliminary study 2, it was observed that the specimen with auxiliary transfer bars and the specimen with additional compression steel bars had relatively high structural performance in terms of shear capacity, initial stiffness, and rotational capacity when steel coupling beams experienced extensive damage at the beam-wall interface. According to the finite element analysis conducted in preliminary study 2, it was found that the shear capacity and initial stiffness of the specimen with auxiliary transfer bars (20M-ATB-Inf) can be increased by 11% and 60% compared to the specimen with compression steel bars (20M-Inf), respectively. By observing comparable performance between specimens with auxiliary transfer bars and compression steel bars, using the new connection detailing can be considered a viable solution in terms of constructability. 111 Chapter 6: Conclusions and future work The main focus of this thesis was to examine the effects of design detailing on the hysteretic response of coupling beams. The study was conducted in two phases. In phase 1, diagonally-reinforced coupling beams were investigated, while in phase 2, steel and composite coupling beams were studied. The objectives of each phase are outlined below, along with a description of how these objectives were achieved in this thesis. 6.1 Phase 1: Diagonally-reinforced coupling beams The goal of phase 1 was to improve our understanding of the seismic response of diagonally-reinforced coupling beams. The objectives of this phase were to 1.1) develop a comprehensive database of previously tested diagonally-reinforced coupling beams and 1.2) analyze the database to evaluate current design provisions and create new empirical relations for design that will enhance the seismic performance of these beams. Objective 1.1 was achieved by gathering a wide range of previously tested diagonally-reinforced coupling beams, consisting of 51 specimens. For each specimen, the backbone of the hysteresis diagram was determined and documented in the database. The database also documented different features of each specimen, including embedded longitudinal bars (ELBs), axial restraint (AR), tie configurations, material properties, and geometry. Furthermore, the strengths, stiffnesses, and rotational capacities were determined and documented in the database for each specimen. The database includes, a new unitless parameter called “𝐶𝑘” that was developed in which both shear and flexural deformations of coupling beams are considered for calculating the effective stiffness (𝐾𝑖 = 𝑏𝑤𝐸𝑐𝐶𝑘). 𝐶𝑘 included modification factors to consider the stiffness degradation due to the shear and flexural deformations (𝛼𝑠 and 𝛼𝑓), respectively. Important seismic response 112 parameters, such as overstrength, defined as the ratio of maximum shear force over expected shear capacity (𝑉𝑚𝑎𝑥𝑉𝑛𝑒), and rotational capacity, determined by degradation rotation (𝜃80%), were recorded. For each specimen, level of confinement from the beam ties was determined using ACI 318-19 [4]. For specimens that used diagonal ties, the tie properties and spacing were determined in the database, and calculations using ACI 318-19 [4] and CSA A23.3-19 [5] were provided in Table B-2. This database represents a significant contribution, as future researchers and designers may use it to improve design philosophy or enhance understanding of diagonally-reinforced coupling beams. To accomplish objective 1.2, the developed database was analyzed in detail. The effect of each of the various design details on the key hysteretic responses was analyzed. From this analysis, the following conclusions were drawn: • An overstrength factor of 1.25, used in CSA A23.3-19 [5], is suitable for diagonally-reinforced coupling beams without AR or ELB; however, additional AR or ELB can result in an average 30-40% higher overstrength. • All specimens which met the ACI 318-19 [4] beam confinement provisions had a total chord rotation of 6%. • After evaluating the diagonal confinement, no clear trend was observed. This suggests that considering diagonal ties as confinement may not be a reasonable assumption. However, the spacing of diagonal ties did show good trends. Therefore, the buckling prevention tie approach by CSA may be more suitable. • Many low aspect ratio specimens with L/h<1.5 that had suitable detailing according to current codes exhibited low rotational capacity (i.e., less than 4%). It was determined that 113 these specimens experienced shear sliding failure, which was attributed to the low diagonal bar ratio. Therefore, a new minimum shear capacity limit was introduced in which it was recommended that diagonally-reinforced coupling beams with L/h<1.5 shall have 𝑉𝑛 >0.5𝐴𝑐𝑤√𝑓′𝑐 (MPa units). • Ck values were calculated for each specimen based on test results and compared to those calculated by recommended values for 𝛼𝑠 and 𝛼𝑓 based on Canadian and American codes. According to the results, it was observed that current values determined by CSA A23.3-19 [5], ACI 318-19 [4], and LATBSDC 2023 [20] for 𝛼𝑠 and 𝛼𝑓 can lead to upper-bound relations for stiffness, which may result in underestimating displacements. 6.2 Phase 2: Steel and composite coupling beams The goal of phase 2 was to develop a new connection detailing to improve the seismic response and construction process of steel and composite coupling beams. The objectives of this phase were to 2.1) develop mathematical and finite element analysis (FEA) models to simulate the response of the new connection and 2.2) conduct a preliminary analysis of the response of the new connection to understand the impact of design parameters on its performance. The new connection was developed by collaborating with industry partner Kor Structural Engineers. In the proposed connection detailing, additional compression steel reinforcements were proposed, which were fixed to elastic steel plates. These elastic steel plates were placed on the flanges of the embedded steel beam in the shear wall, working in a friction manner. Since these plates are not bolted or welded to the steel beam flanges, the compression steel reinforcements transfer only compression forces. This new connection facilitates a smoother construction process and improves the structural performance of steel and composite coupling beams. 114 Objective 2.1 was to simulate the response of the novel connection. This objective was completed using two methods: a) the development of a mathematical model and b) the development of a finite element model. The mathematical model was developed by first reviewing mathematical connection detailings for steel and composite coupling beams. From this review, it was shown that existing mathematical models could not represent the actual load-transferring mechanism of the new connection. Therefore, a mathematical model presenting the load-transferring mechanism was derived and proposed. The basic assumptions in the developed mathematical model, such as the stress-strain distribution of concrete in tension and compression, aligned with the current embedment models. Based on the developed mathematical model of the proposed connection detailing, a design plot was developed for practitioners. The finite element model was developed using DIANA FEA 10.6. The 3D model of specimen SCBC1 tested by Nahvinia, 2018 [47] was validated using nonlinear material behaviour specified for concrete, steel, and reinforcing. Additionally, a cyclic shear load was used for the steel beam. At the same time, constant compression force was applied on the adjacent shear wall to consider the effect of gravity loads on the wall in the analysis. Since the composite action between concrete and embedded steel beam can be reduced due to wide cracking at high cyclic loads, the interface element was determined between the embedded steel beam and surrounding concrete with a specified reduction factor for stiffness in different directions. Objective 2.2 was completed by using the FEM developed in objective 2.1 and conducting two preliminary studies. The first preliminary study was to determine how the size of the compression steel reinforcing impacts the performance of the connection. The other preliminary study was conducted to determine how the new connection compares to auxiliary transfer bars. The following conclusions were determined. 115 • Increased Structural Performance: Specimens with the proposed connection detailing exhibited a 57% increase in shear capacity, a 10% increase in initial stiffness, and a 33% increase in rotational capacity compared to specimens without additional reinforcements. • Comparison with Auxiliary Transfer Bars (ATB): The shear and rotational capacities of specimens with the proposed connection detailing were nearly equivalent to those with ATB. However, the initial stiffness of specimens with ATB was 60% higher, attributed to the reinforcement configuration that allows for load transfer in both tension and compression. Despite the slight difference in initial stiffness, the proposed connection detailing can be considered a practical alternative that overcomes construction difficulties associated with auxiliary transfer bars and significantly enhances the structural performance of steel and composite coupling beams. 116 6.3 Future work There are several avenues for future work related to coupling beams, as follows: 1. Since some of the studied diagonally-reinforced coupling beams had rigid adjacent shear walls acting as axial restraints, an accurate value of axial forces could not be estimated. In this regard, a finite element analysis can be conducted in which specimens with rigid adjacent shear walls are modelled and analyzed under cyclic loads, and accurate axial loads can be calculated. Obtained axial loads can provide insight into the calculation of the overstrength of diagonally-reinforced coupling beams with rigid axial restraint. 2. The finite element model developed for steel and composite coupling beams in this thesis only included a constant compression axial load applied to the wall and a cyclic shear load applied to the steel coupling beam. A more robust finite element model can be developed in which other types of loads, such as tension forces in the wall, overturning moments on the wall, axial forces in the coupling beam, and shear forces on the wall, would be considered. 3. Experimental testing can be conducted on steel and composite coupling beams equipped with the new connection detailing to produce actual testing data for further analysis. 117 Bibliography [1] Tobber, Lisa, “ evelopment of an innovative earthquake-resilient reinforced concrete core wall system.” University of British Columbia, 2021. [2] Naish, ., Fry, A., Klemencic, . and Wallace, J., “Reinforced Concrete Coupling Beams—Part I: Testing,” SJ, vol. 110, no. 06, 2013, doi: 10.14359/51686160. 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Yang, “ amage eformation of Flexure-Yielding Steel-Reinforced Concrete Coupling Beams: xperimental and Numerical Investigation,” Advances in Civil Engineering, vol. 2019, pp. 1–15, Jun. 2019, doi: 10.1155/2019/7071243. 121 Appendices : Summary of experimental studies on diagonally-reinforced coupling beams This appendix summarises the previously conducted experimental tests on diagonally-reinforced coupling beams (DRCBs) used in the developed database. A.1 Pauly and Binney, 1974 In 1974, Paulay and Binney [3] introduced the diagonally-reinforced coupling beams to overcome the deficiencies associated with the low performance of conventionally beams such as relatively low inelastic rotation. The main motivation for the development of diagonally-reinforced coupling beams was to improve the rotational capacity of these beams after high magnitude reversed cyclic loadings particularly when the beams experience sliding shear failure. Paulay and Binney [3] tested three deep diagonally-reinforced coupling beams (L/h<2) named Beam 316, Beam 317, and Beam 395 to assess the rotational capacity of these beams under reserved cyclic loads. The main test variables were aspect ratio and utilizing diagonal ties. Beam 316 (L/h=1.29) which had beam-confinement was loaded cyclically up to rotation 1.2% and recorded overstrength equals to 1.22. After this point, this specimen was tested monotonically up to 4.9% rotation when the test was stopped due to the buckling of diagonal bars and severe concrete crushing at the beam-wall region. Specimen Beam 317 was designed similarly to Beam 316 but with ties placed around diagonal bars (diagonal confinement). This specimen recorded overstrength of 1.21 and was loaded up to rotation of 6.0% when the horizontal bars and diagonal bars buckled. Specimen Beam 395 was the same as Beam 317 but with L/h equal to 1.03. This specimen experienced ultimate rotation of 6.1% and overstrength of 1.22 before failure when the 122 diagonal bars buckled and surrounding concrete around these were completely spalled. Figure A-1 (a), (b), and (c) shows the cracking pattern of specimens Beam 316, Beam 317, and Beam 395, respectively. Paulay and Binney, 1974 [3] concluded that all these diagonally-reinforced coupling beams with diagonal confinement experienced relatively higher total chord rotation compared to one with beam confinement. However, since the diagonal bars will be compression in each loading cycle, the buckling of these bars can be problematic. Therefore, they suggested that adequate ties around diagonal bars should be utilized to prevent the diagonal bars from buckling in compression. (a) (b) (c) Figure A-1: Cracking pattern at final loading stage of specimens (a) Beam 316, (b) Beam 317, and (c) Beam 395 tested by Paulay and Binney, 1974 [3]. 123 A.2 Barney et al., 1980 In 1980, Barney et al. [6] tested eight coupling beams which various reinforcing orientations two of which were diagonally-reinforced (C6 and C8) with L/h 2.5 and 5.0, respectively. The main testing variables were the size of the confined concrete core and aspect ratio. Both C6 and C8 specimens had beam ties. Specimen C8 with higher aspect ratio experienced a total chord rotation of 7% and maximum shear capacity of 33.3kN resulting in overstrength equals to 1.56. Compare to specimen C8, specimen C7 which had conventional reinforcing layout but the same aspect ratio experienced total chord rotation and shear capacity of 6% and 23.1 kN, respectively. Additionally, specimen C6 experienced 6% as total chord rotation and 1.56 as overstrength. Compared to specimen C6, specimen C2 with the same characteristics but with conventional reinforcing layout experienced ultimate rotation and shear capacity of 3.6% and 45.7 kN, respectively. Based on these comparisons, Barney et al., 1980 [6] concluded that diagonally-reinforced coupling beams exhibited higher rotational capacity and shear capacity compared to the conventional ones. Conclusions of the experimental program conducted by Barney et al., 1980 [6] were the basis of the ACI 318-08 [21] clauses for designing diagonally-reinforced coupling beams. A.3 Ishikawa et al., 1991 In 1991, Ishikawa and Kimura [29] tested ten diagonally-reinforced coupling beams with test variables namely, aspect ratio, diagonal bar’s ratio, beam ties ratio, concrete compressive strength, presence of slab, presence of opening in the concrete section, and utilising high-performance steel rebars. All the tested specimens had embedded longitudinal bars and beam confinement. Ishikawa and Kimura, 1990 [29] concluded that the beam with opening experienced relatively low rotational capacity (2.5%) compared to other specimens. Additionally, they reported that the specimen with a slab recorded higher stiffness and strength compared to the ones without any axial restraint. They 124 also concluded that utilizing high-performance steel rebars can increase the nominal shear strengthof the coupling beams compared to the ones with normal steel rebars. Finally, they concluded thatthe specimens with higher transverse bar’s ratio experienced higher rotational capacity comparedto other specimens.A.4 Sonobe et al., 1995Sonobe et al., 1995 [50] tested two diagonally-reinforced coupling beams with beam confinement.The test parameter in this study was the effect of concrete type either normal or lightweight.According to the test data, the recorded overstrength of specimen with normal type of concrete(NX7L) was 1.95 which was 5% greater lower than that of specimen with lightweight concrete(LX7L). However, both these specimens sustained 6% of total chord rotation. Additionally, Figure2.8 depicts the cracking pattern of Specimens NX7L and LX7L. According to Figure A-2, shearcracking can be noticed in the direction of diagonal bars indicating that shear loads were developedby these bars. Based on the literature the rupture of diagonal bars was determined as the failuremode of specimens NX7L and LX7L.(a) (b)Figure A-2: Cracking pattern at final loading stage of specimens (a) NX7L and (B) LX7L tested by Sonobe et al., 1995 [50].125 A.5 Galano et al., 2000In 2000, Galano and Vignoli [31] tested 16 short coupling beams (L/h<2.0), two of which werediagonally-reinforced (P07 and P12), and the main test variable was the transverse reinforcementlayouts. Both P07 and P12 specimens had embedded longitudinal bars and rigid adjacent shearwalls providing axial restraint for the beams. Based on the experimental data, specimen with tiesaround diagonal bars (P12) experienced almost 4% chord rotation corresponding to the 80% ofmaximum shear force applied to the coupling beam, which was 1% lower than that of the specimenwith beam confinement (P07). Additionally, recorded overstrength for specimen P07 and P12 werealmost the same equal to 1.55 indicating that the type of transverse reinforcement layout does notaffect the overall shear capacity of diagonally-reinforced coupling beams. Figure A-3 and FigureA-4 illustrate the details and hysteresis diagrams of specimens P07 and P12, respectively.Figure A-3: Details of specimens a) P07 and b) P12 tested by Galano and Vignoli, 2000 [31].126 (a) (b)Figure A-4: Hysteresis diagrams of specimens a) P07 and b) P12 tested by Galano and Vignoli, 2000 [31].A.6 Gonzalez, 2001In 2001, Gonzalez [24] tested one diagonally-reinforced coupling beam (K1) with L/h equals 2.74.The main objectives of this experimental program were to investigate the structural behaviour ofDRCBs with relatively high aspect ratio (i.e., L/h>2) and the effect of axial restraint on the sameparameters. The diagonal bars of this specimen were tied with 10M bars. In addition to havingdiagonal ties, the specimen K1 were tested under Dywidag bars which adding some level of axialrestraint to the coupling beam. This specimen experienced total chord rotation corresponding tothe 80% of maximum shear force applied to the coupling beam up to 8%. Based on the test results,specimen K1 recorded overstrength of 1.77. According to the test results, high magnitude ofoverstrength was attributed to the presence of axial restraint. In other words, axial restraints incoupling beams such as slabs prevent the formation of cracking in coupling beams resulting127 increasing the shear capacity of these beams. Figure A-5 (a) and (b) illustrate the details and hysteresis diagram of the specimen K1, respectively. Figure A-5: (a) Details and (b) hysteresis diagram of specimen K1 tested by Gonzalez, 2001 [24].A.7 Dugas, 2002Dugas, 2002 [27] tested two short diagonally-reinforced coupling beams (L/h =1.136). The onlytest variable was the type of ties around the diagonal bars. Specimen D30 was designed andconstructed by having #4 seismic hoops. The other specimen (D30H) had the same details asspecimen D30 with the only difference of using #4 headed bars as ties around diagonal bars. FigureA-6 and Figure A-7 show the used test setup and details of the tested specimens by Dugas, 2002[27], respectively. According to the test results, specimen D30 with seismic hoops around diagonalties recorded total chord rotation of 2.8% and overstrength of 1.132, which were almost the samevalues for specimen D30H. Figure A-8 shows the hysteresis diagrams of specimens D30 andD30H, respectively. Based on the test results, Dugas, 2002 [27] concluded that using headed barsinstead of normal seismic hoops for avoiding the buckling of diagonal bars would not only128 facilitate the construction process, but also will improve the hysteretic performance of diagonally-reinforced coupling beams in terms of energy dissipation. Figure A-6: Test setup used by Dugas, 2002 [27].Figure A-7: Details of specimens (a) D30 and (b) D30H tested by Dugas, 2002 [27].129 (a) (b)Figure A-8: Hysteresis diagrams of specimens (a) D30 and (b) D30H tested by Dugas, 2002 [27].A.8 Kwan et al., 2002In 2002, Kwan and Zhao [51] tested six coupling beams (L/h<2.0) one of which was diagonally-reinforced and the rest were conventionally-reinforced. The main test variables were aspect ratio,reinforcement layout, and longitudinal bars ratio. The diagonally-reinforced specimen (CCB11)had L/h equals to 1.17 and its diagonal bars were tied with 8-mm diameter rebars. SpecimenCCB12 had the same aspect ratio as specimen CCB11 but was designed as a conventional couplingbeam (Figure A-9). For both specimen CCB11 and CCB12, longitudinal bars at the corners of the130 beam were fully extended into the adjacent shear walls, and skin reinforcements were hooked with180 degrees in the walls to provided complete bonding with the surrounding concrete. SpecimenCCB11 recorded the total chord rotation of almost 5.7% and overstrength of 1.89. Compared tospecimen CCB11, specimen CCB12 recorded the same value of total chord rotation but loweroverstrength equal to 1.7. Figure A-10 illustrates the hysteresis diagrams of specimens CCB11and CCB12. According to Figure A-10, although both specimens CCB 11 and 12 recorded samerotational and shear force capacity, the energy dissipation of specimen CCB11 was greater thanthat of specimen CCB12 due to the more stable and larger cyclic loops. Based on the test results,fully extended longitudinal bars can increase the overstrength.(a) (b)Figure A-9: Details of specimens (a) CCB11 and (b) CCB12 tested by Kwan and Zhao, 2002 [51].131 A.9 Zhou, 2003In 2003, Zhou [28] tested two conventionally and diagonally-reinforced coupling beams with L/hequal to three based on the test setup shown by Figure A-6. The only test variable was thereinforcement layout, one with vertical and horizontal reinforcement (CB-1) and one with diagonalbars (CB-2). Both these specimens were tested under the reversed cyclic loads and longitudinalbars were embedded into the adjacent shear walls. Figure A-11 shows the details of each specimen.According to the test results specimen CB-1 designed as a conventionally-reinforced couplingbeam experienced total chord rotation of 2.6% which was smaller than that of recorded byspecimen CB-2 by 54%. Regarding shear capacity, specimen CB-1 tolerated maximum shear forceof 248 kN which was lower than that of tolerated by specimen CB-2 by 94%. Zhou, 2003concluded that based on the test results, the diagonally-reinforced specimen (CB-2) had morestable hysteretic response compared to the conventional coupling beam (CB-1) in which thepinching was visible (Figure A-12).(a) (b)Figure A-10: Hysteresis diagrams of specimens (a) CCB11 and (b) CCB12 tested by Kwan and Zhao, 2002 [51].132 (a) (b) 133 Figure A-11: Details of specimens (a) CB-1 and (b) CB-2 tested by Zhou, 2003 [28].(a) (b)Figure A-12: Hysteresis diagrams of specimens (a) CB-1 and (b) CB-2 tested by Zhou, 2003 [28].A.10 Shimazaki, 2004Shimazaki, 2004 [52] tested multiple diagonally-reinforced coupling beams with different aspectratios, concrete compressive strength, diagonal bar sizes, etc. Among the tested specimens, twospecimens (N-1 and N-2) had bonded diagonal bars with different concrete compressive strengthand transverse bars ratio. Both of these specimens had beam confinement with different tie spacing(N-1 at 150mm and N-2 at 100mm) and the longitudinal bars were extended into the wall piers.According to the test results, specimen N-2 recorded maximum chord rotation equal to 4% whichwas greater than that of recorded by specimen N-1 by 30%. Additionally, the overstrengthrecorded by specimen N-2 was 1.7 kN which was 5% greater than the one recorded by specimenN-1. Figure A-13 shows the hysteresis diagrams of specimens N-1 and N-2. According to FigureA-13, it can be concluded that both these specimens exhibit a stable cyclic performance, with theonly significant difference in rotational capacity which is attributed to the spacing of the tiesaround beam’s longitudinal bars.134 (a) (b)Figure A-13: Hysteresis diagrams of specimens (a) N-1 and (b) N-2 tested by Shimazaki, 2004 [52].A.11 Canbolat et al., 2005In 2005, Canbolat et al. [26] tested four coupling beams with different reinforcement layouts toinvestigate the seismic behaviour of high-performance fiber-reinforced cement composite beams.Out of four tested specimens, two of them was diagonally-reinforced. Between the two diagonally-reinforced specimens one (S3) was constructed by using high-performance fiber-reinforcedcement (HPFRC), and the other one (S1) with normal concrete. Specimen S1 had anti bucklingdiagonal ties designed according to ACI 318-99 [53] except for the “one-quarter of the minimummember dimension” requirement for the spacing of ties around the diagonal bars. Compared tospecimen S1, specimen S3 was constructed with HPFRC concrete and without any ties arounddiagonal bars. All the specimens tested by Canbolat et al., 2005 [26] had embedded longitudinalbars. Based on the test results, specimen S1 with normal concrete experienced total chord rotationof 3.8% which was lower than that of specimen S3 (4.9%). Additionally, the maximum shearcapacity of specimen S1 was recorded as 470 kN resulting in overstrength of 1.5 which was lowerby 69% compared to specimen S3. Figure A-14 shows the hysteresis diagrams of specimens S1135 and S3. According to Figure A-14, Canbolat et al., 2005 [26] concluded that high-performancefiber-reinforced cement composite coupling beams exhibited higher shear strength and rotationalcapacity compared to the coupling beams with normal concrete.(a) (b)Figure A-14: Hysteresis diagrams of specimens (a) S1 and (b) S3 tested by Canbolat et al., 2005 [26].A.12 Yun et al., 2008Yun et al., 2008 [30] tested two diagonally and one conventionally-reinforced short couplingbeams (L/h<2). The main test variables were different reinforcement layouts and use of fiber-reinforced cement composites. Among the tested diagonally-reinforced coupling beams, one wasconstructed with normal concrete s a control specimen (CB1) and the other one had the samecharacteristics of specimen CB1 but was constructed with fiber-reinforced cement compositesconcrete (CB2). Figure A-15 (a) and (b) show the used test setup and details of specimens CB1and 2, respectively. All the tested specimens by Yun et al., 2008 [30] had embedded longitudinalbars and the adjacent shear walls were designed rigidly providing axial restraint for the beams.136 (a) (b)Figure A-15: (a) Used test setup and (b) details of specimens CB1/2 tested by Yun et al., 2008 [30].According to the test results, specimen CB1 experienced the maximum shear capacity and totalchord rotation of 704 kN (overstrength of 3.8) and 1.54%, respectively. These values wereincreased by 44.8% and 26.9% for specimen CB2, respectively. The reason for relatively smalltotal chord rotations for both specimen CB1 and CB2 was reported to be the lack of any types ofties around diagonal bars. Therefore, the diagonal bars buckled at a very small chord rotation.However, since specimen CB2 was constructed with fiber-reinforced cement composites concrete,it exhibited more shear strength compared to specimen CB1 constructed with normal concrete.Additionally, since both specimens had fully embedded longitudinal bars and rigid adjacent shearwalls, the authors reported that the specimens recorded significantly high shear capacity andoverstrength. Figure A-16 (a) and (b) show the hysteresis diagrams of specimens CB1 and CB2,respectively.137 (a) (b)Figure A-16: Hysteresis diagrams of specimens (a) CB1 and (b) CB2 tested by Yun et al., 2008 [30].A.13 Fortney et al., 2008Fortney et al., 2008 [54] tested two diagonally-reinforced coupling beams specimens to investigatethe effect of the transverse bars on the performance of these beams. Specimen DCB-1 had anti-buckling ties around diagonal bars placed at 76 mm through the clear span. For this particularspecimen, the longitudinal bars were extended to the adjacent shear walls. However, specimenDCB-2 was designed to have ties around diagonal bars at every 51 mm through the clear spanexcept at the intersection region where two groups of diagonal bars cut each other. Figure A-17(a) and (b) depict the details of specimens DCB-1 and DCB-2, respectively.138 (a) (b) 139 A.14 Naish et al., 2013 In 2013, Naish et al. [2] conducted a comprehensive experimental to assess the seismic performance of diagonally-reinforced coupling beams with diagonal or beam confinement options. Tested specimens had L/h equal to 2.4 (residential spaces) and 3.0 (office spaces). Figure A-19 shows the used test setup by Naish et al., 2013 [2], [55] . The main test variables were aspect ratio, transverse reinforcement orientation, and the presence of axial restraints such as post-tensioned (PT) rods or slab. Figure A-17: Details of specimen (a) DCB-1 and (b) DCB-2 tested by Fortney et al., 2008 [54].Figure A-18 shows the hysteresis diagrams of tested specimens by Fortney et al., 2008 [54].According to Figure A-18, specimen DCB-2 recorded significantly higher total chord rotation(11%) compared to the specimen DCB-1 (5%). Based on the test results, Fortney et al., 2008concluded that providing ties around diagonal bars through the clear span must be considered.(a) (b)Figure A-18: Hysteresis diagrams of specimens (a) DCB-1 and (b) DCB-2 tested by Fortney et al., 2008 [54].140 Figure A-19: Used test setup by Naish et al., 2013 [2], [55].Based on the test results, specimen CB24F with L/h equals to 2.4 and had beam confinementrecorded total chord rotation of 9.5% and maximum shear strength of 761 kN resulting inoverstrength of 1.25. Relatively to specimen CB24F, specimen CB24D had the samecharacteristics unless having anti-buckling ties around diagonal instead of beam confinement. Forspecimen CB24D, total chord rotation and overstrength were reported as 8.75% and 1.17 kN,respectively indicating relatively small decrease compared to that of specimen CB24F. Naish etal., 2013 tested one specimen named CB24-RC with the same details as specimen CB24F but hadslab providing axial restraint for the beam. According to the test results, total chord rotation andmaximum shear strength for CB24F-RC increased by 7.15% and 10.38%, respectively relativelyto the results of specimen CB24F. Regarding the type of axial restraint, Naish et al., 2013 testedspecimen CB24F-PT with 1.1 MPa post-tensioned slab. Compared to specimen CB24F-RC, totalchord rotation was decreased by 13% and maximum shear strength was increased by 10% forspecimen CB24F-PT, respectively. Specimen CB24F-1/2-PT was designed with the samecharacteristics of specimen CB24F-PT unless with spacing of the beam ties being closer (half)than that of determined for specimen CB24F-PT. According to the test results, specimen CB24F-141 1/2-PT experienced total chord rotation and maximum shear strength of 8.25% and 844 kN(overstrength of 1.42), respectively.Regarding specimens with L/h 3.3, Naish et al., 2013 [2], [55] tested two specimens one with beamconfinement option (CB33F) and one with ties around diagonal bars (CB33D). Based on the testresults, specimen CB33F recorded total chord rotation and overstrength of 9% and 1.16,respectively. These values were decreased by 3% for specimen CB33D relatively to specimenCB33F ones.According to the test results, all the diagonally-reinforced coupling beams tested by Naish et al.,2013 [2], [55] experienced total chord rotation more than 6%. In addition to this, the specimenswith axial restraint such as PT rods or slabs (CB24F-RC, CB24F-PT, and CB24F-1/2-PT) hadhigher rotational capacity compared to the ones without any axial restraint. Naish et al., 2013 [2],[55] also concluded that the new type of confinement for diagonal bars called full beamconfinement would result in higher rotational capacity of diagonally-reinforced coupling beams.Additionally, Naish et al., 2013 [2], [55] reported for specimens with axial restraint, overstrengthwas recorded relatively higher than that of without any axial restraints. Figure A-20 shows thehysteresis diagrams of the specimens by Naish et al., 2013 [2], [55] .142 (a) (b) (c) (d) (e) (f) 143 (g)Figure A-20: Hysteresis diagrams of specimens (a) CB24F, (b) CB24D, (c) CB24F-RC, (d) CB24F-PT, (e) CB24F-1/2-PT, (f) CB33F, and (g) CB33D tested by Naish et al., 2013 [2], [55].A.15 Lim et al., 2015In 2015, Lim et al. [14] tested four short coupling beams, two of which were diagonally-reinforcedwith L/h equals to 1.0 (CB10-1) and 2.0 (CB20-1). Both these specimens had beam confinement(Figure A-21). The main test variables for this experiment were aspect ratio and diagonalreinforcement ratio.Figure A-21: Details of specimens (a) CB10-1 and (b) CB20-1 tested by Lim et al., 2015 [14].144 (a) (b) Figure A-22 illustrates the hysteresis diagrams of the tested specimen by Lim et al., 2015 [14].According to Figure A-22, specimen CB10-1 with embedded longitudinal bars into the adjacentshear walls experienced total chord rotation of 7.2% and maximum shear strength of 1444 kN(overstrength of 1.74). At the final stage, crushing of concrete occurred near the end of the strutand buckling of the diagonal reinforcement was observed. The failure mode for this specimen(CB10-1) was flexural-shear failure. Compared to specimen CB10-1, total chord rotation wasincreased by 20% and shear strength of specimen CB20-1 was decreased by 34.5%. For specimenCB20-1, Buckling of diagonal bars was also observed at this final stage. The test was terminatedat the first cycle at a DR of 9.4% and was determined to have failed from flexural failure.According to the test results, Lim et al., 2015 [14] conclude that diagonally-reinforced couplingbeam specimens exhibited more stable hysteretic performance compared to conventionally ones.Additionally, specimen with higher diagonal reinforcement ratio (CB20-1) experienced highertotal chord rotation (9.4%) compared to the one (CB10-1) with lesser diagonal reinforcement ratio(7.3%).145 A.16 Lim et al., 2016In 2016, Lim et al. [15] conducted another experimental program on intermediate coupling beams(2<L/h<4), two of which were diagonally-reinforced. The main difference between these twodiagonally-reinforced coupling beams were the type of confinement where specimen CB30-DAhad diagonal ties and CB30-DB had beam confinement. Based on the test results, specimen CB30-DB with full beam confinement and L/h equals to three, experienced larger total chord rotation(8.2%) compared to the one (CB30-DA) with diagonal ties (7.6%). Additionally, specimen CD30-DA recorded overstrength equals to 1.48 which was increased by almost 8% for specimen CB30-DB. Lim et al., 2016 [15] concluded that the relatively high overstrength of the tested specimenswere mainly attributed to the embedded longitudinal bars.A.17 Howard, 2017In 2017, Howard [25] tested four diagonally-reinforced coupling beams with L/h equals to 1.136detailed for different levels of rotational capacity in accordance with the CSA A23.3-14 [56].Figure A-6 shows the test setup used by Howard, 2017 [25]. The main test variable was the spacingof the ties around diagonal bars. By using diagonal bar size as 20M, specimens CC-16db, MD-10db, MD-8db, and D-6db had sd/db equal to 16, 10, 8, and 6, respectively. All the specimens hadembedded longitudinal bars. Only one specimen (D-6db) was axial restrained by post-tensionedrods (30kN). Figure A-23 illustrates the details of specimen CC-16db tested by Howard, 2017[25].Figure A-22: Hysteresis diagrams of specimens (a) CB10-1 and (b) CB20-1 tested by Lim et al., 2015 [14].146 designed similarly to specimen MD-10db but with 𝑠𝑑𝑑𝑏 equals to 8, total chord rotation was 3% and Figure A-23: Details of specimen CC-16db tested by Howard, 2017 [25].According to the test results, specimen CC-16db with conventionally designed shear wall recordedtotal chord rotation of 2.2% and overstrength of 1.26. For specimen MD-10db with moderatelyductile shear wall these values increased by 42% and 11%, respectively. For specimen MD-8dbmaximum shear strength reached 736.6 kN (overstrength of 1.42). These values were increase by14% and 27%, respectively for specimen D-6db with axial strain and designed to have ductileshear walls. Figure A-24 shows the hysteresis diagram of the specimens tested by Howard, 2017[25].147 Based on the test results, Howard concluded that the ratio of spacing of the buckling prevention ties around diagonal bars over the diagonal bar’s diameter (𝑠𝑑𝑑𝑏) plays a crucial role in the post- 2017 [25] experienced sliding shear failure at the beam-wall interface. This mode of failure generally happens due to the lack of diagonal reinforcing ratio. Although all the tested specimens by Howard, 2017 [25] had the minimum shear stress of 0.83𝐴𝑐𝑤√𝑓𝑐′ (MPa units) recommended by ACI 318-19 [4], still these specimens were failed in abrupt shear manner. As an overall trend, specimens with tighter anti-buckling ties around diagonal bars experienced higher rotational capacity. Additionally, Howard concluded that providing axial restraint for coupling beams will increase both rotational capacity and shear capacity of these beams. yielding response of the coupling beams. According to Figure A-25, specimens tested by Howard,148 (a) (b) Figure A-24: Hysteresis diagrams of specimens tested by Howard, 2017 [25].149 (c) (d)Figure A-25: Damage of specimens (a) CC-16db, (b) MD-10db, (c) MD-8db, and (d) D-6db [25].A.18 Ameen et al., 2017In 2017, Ameen et al. [16] tested two diagonally-reinforced coupling beams to investigate theeffect of high-strength steel bars on the seismic performance of coupling beams. The main testvariables in this study were the diagonal bars’ ratio, nominal yielding strength of diagonal steelbars, and the development of longitudinal bars into the adjacent shear walls. Figure A-26 showsthe hysteresis diagrams of specimens tested by Ameen et al., 2017 [16]. According to Figure A-26,specimen CB1 with yield strength of diagonal bars equals to 434 MPa recorded total chord rotationof 7.9% and overstrength 1.32. For specimen CB2 with yield strength of diagonal bars equal to883MPa, total chord rotation and overstrength were 6% and 1.35. respectively. Based on the testresults, Ameen et al., 2017 [16] concluded that by using high-strength steel bars the rotationalcapacity of coupling beams will decrease slightly. However, utilizing high-strength steel bars willincrease the shear capacity of these beams.150 Figure A-26: Hysteresis diagrams of specimens (a) CB1 and (b) CB2 tested by Ameen et al., 2017 [16].A.19 Poudel et al., 2018In 2018, Poudel et al. [17] tested one diagonally-reinforced coupling beam with L/h equals to 1.89two investigate the effect of axial restrain on the performance of coupling beams. Specimen CB1Awas designed similarly to specimen CB1 tested by Ameen et al., 2017 but was strained axially byPT rods. Figure A-27 shows the test setup used in Poudel et al., 2018 experimental program. Basedon the test results, specimen CB1A reached a maximum chord rotation of 7.3% and overstrengthof 1.71. Figure A-28 shows the hysteresis diagram of specimen CB1A tested by Poudel et al.,2018 [17]. Compared to the test results of specimen CB1 tested by Ameen et al., 2017, Poudel etal., 2018 [17] concluded that using axial restraints such as slab or PT rods in coupling beams willincrease both rotational and shear capacity of these beams.151 Figure A-27: Test setup associated with the experimental program conducted by Poudel et al., 2018 [17].Figure A-28: Hysteresis diagram of specimen CB1A tested by Poudel et al., 2018 [17].152 A.20 Han et al., 2019In 2019, Han et al. [13] conducted a comprehensive experimental program of testing sevendiagonally-reinforced coupling beams with beam confinement and restrained axially by rigid walls(Figure A-29). The main test variables of this study were aspect ratio and the transverse bars’ratio.Figure A-29: Test setup used by Han et al., 2019 [13].According to the test results, by increasing the spacing of the ties around entire coupling beam(𝑠𝑡), the ultimate chord rotation and maximum shear strength of coupling beams will be decreased.Additionally, according to Figure A-30 (a) and (b) which shows the hysteresis diagrams of thetested specimens with L/h equals to 2.0 and 3.5, respectively, it can be concluded that specimenswith closer ties recorded bigger cyclic loops. This trend implies that providing closer ties for entirecoupling beams with beam confinement will increase the energy dissipation capacity.153 (a) (b) 154 stress capacity less than 0.83𝐴𝑐𝑤√𝑓𝑐′ (Mpa units) recommended by ACI 318-19 [4]. This observation indicates that although these specimens had diagonal reinforcing ratio in the range provided by ACI 318-19 [4], they still experienced sudden shear failure at the connection. Based on the conducted literature review, it was found that using high-performance concrete in the construction of coupling beams can result in higher shear and rotational capacity required by current building design codes. The presence of axial restraint such as PT-rods in slabs, reinforced concrete slabs, and relatively rigid adjacent shear walls can result in significantly high overstrength of coupling beams. In cases with axial restrains, crack propagation was postponed. However, presence of axial restraint limits the coupling beam from experiencing inelastic rotation and deformation resulting in less rotational capacity. : Figure A-30: Hysteresis diagrams of specimens with L/h equals to (a) 2.0 and (b) 3.5 tested by Han et al., 2019 [13].Based on the conducted literature review, it was revealed that diagonally-reinforced have relativelyhigher rotational capacity and shear strength to that of conventionally-reinforced coupling beams.it was found that coupling beams with beam confinement option in which ties are provide for theentire beam experienced ultimate chord rotation more than 4% and 5% required by CSA A23.3-19 [5] and ACI 318-19 [4], respectively. Also, specimens detailed according to above-mentionedcodes in terms of diagonal and beam ties showed relatively large cycles indicating theirperformance in dissipating energy by undergoing nonlinear rotations and deformations.It was also found using high-strength steel bars with fy greater than 400 MPa may result in highershear capacity but due to the brittle behaviour associated with this type of bars, they showedpinching in cyclic behaviour and consequently, lower rotational capacity. Additionally, forspecimens with relatively low aspect ratio (i.e., L/h<1.5) some specimens such as the ones testedby Howard, 2017 [25] experienced sliding shear failure although they were designed with shear155 : Tables of information of diagonally-reinforced coupling beams specimens Author Name L/h Category AR type Vmax/Vne Vmax/Vt Vmax/Vmt Vme kN ≤ Paulay & Binney, 1974 Beam 316* 1.29 ELB Only None 1.22 1.22 1.08 0.00 Beam 317 1.29 Neither ELB nor AR None 1.21 1.21 1.00 0.00 Beam 395 1.03 Neither ELB nor AR None 1.22 1.22 0.81 0.00 Galano et al., 2000 P07 1.5 AR+ELB Rigid 1.54 1.09 0.98 63.08 P12 1.5 AR+ELB Rigid 1.55 1.10 1.00 63.08 Dugas 2002 D30 1.136 Neither ELB nor AR None 1.13 1.13 0.72 0.00 Kwan et al., 2002 CCB11 1.17 ELB only None 1.88 0.99 0.94 165.05 Canbolat et al., 2005 S1 1 ELB only None 1.50 1.12 0.84 106.40 Yun et al. 2008 CB-1 1 AR+ELB Rigid 3.8 1.37 1.14 337.83 Lim et al., 2015 CB10-1 1 ELB only None 1.74 1.33 0.96 259.19 Howard, 2017 CC-16db 1.136 Neither ELB nor AR None 1.26 1.26 0.83 0.00 MD-10db 1.136 Neither ELB nor AR None 1.42 1.42 0.92 0.00 MD-8db 1.136 Neither ELB nor AR None 1.35 1.35 0.87 0.00 D-6db 1.136 AR only PT 1.83 1.83 1.12 0.00 L/h>1.5 Barney et al., 1980 C6 2.5 Neither ELB nor AR None 1.56 1.56 1.57 0.00 C8 5 Neither ELB nor AR None 1.56 1.56 1.63 0.00 Ishikawa et al., 1991 1 1.78 ELB only None 1.94 1.38 0.78 98.56 2 1.78 ELB only None 1.84 1.19 0.85 197.13 3 1.78 ELB only None 1.95 1.27 1.02 197.13 4 1.78 AR+ELB Slab 2.05 1.33 0.84 197.13 5 1.78 ELB only None 1.68 1.09 0.82 197.13 6 1.78 ELB only None 2.11 0.98 0.73 421.63 7 1.78 ELB only None 1.94 0.90 0.67 421.63 8 1.78 ELB only None 2.31 1.33 0.89 197.13 Sonobe et al. 1995 LX7L 2.8 ELB only None 2.08 1.27 1.11 119.75 NX7L 2.8 ELB only None 1.97 1.20 1.05 119.75 Gonzalez, 2001 K1* 2.74 AR only PT 1.77 1.77 1.28 0.00 Zhou, 2003 CB-2 3 ELB only None 2.11 1.06 1.11 228.10 Shimazaki, 2004 N-1 2.5 ELB only None 1.48 0.98 0.99 128.96 N-2 2.5 ELB only None 1.68 1.11 1.09 124.36 Fortney et al, 2008 DCB1 2.57 ELB only None 1.56 1.17 0.98 131.78 DCB2 3 Neither ELB nor AR None 1.25 1.25 1.12 0.00 Naish et al., 2013 CB24F 2.4 Neither ELB nor AR None 1.26 1.26 1.09 0.00 CB24D 2.4 Neither ELB nor AR None 1.17 1.17 1.03 0.00 CB24F-RC 2.4 AR only Slab 1.40 1.40 1.19 0.00 CB24F-PT 2.4 AR only PT+Slab 1.56 1.56 1.28 0.00 CB24F-1/2-PT 2.4 AR only PT+Slab 1.43 1.43 1.19 0.00 CB33F 3.33 Neither ELB nor AR None 1.16 1.16 1.04 0.00 Table B-1 summarizes the test results of diagonally-reinforced specimens studied in this thesis.Table B-2 summarizes reinforcing detailings of the studied diagonally-reinforced specimens in this thesis.Table B-1: Tests results of the studied diagonally-reinforced coupling beams.156 Author Name L/h Category AR type Vmax/Vne Vmax/Vt Vmax/Vmt Vme kN L/h>1.5 Naish et al., 2013 CB33D 3.33 Neither ELB nor AR None 1.13 1.13 1.00 0.00 Lim et al., 2015 CB20-1 2 ELB only None 1.63 1.19 1.03 242.73 Lim et al., 2016 CB30DA 3 ELB only None 1.48 1.48 0.96 0.00 CB30DB 3 ELB only None 1.59 1.34 0.99 87.83 Ameen et al., 2017 CB1 1.89 Neither ELB nor AR None 1.32 1.32 1.06 0.00 Poudel et al., 2018 CB1A 1.89 AR only PT 1.72 1.72 1.04 0.00 Han et al., 2019 T1002.0 2 AR only Rigid 2.16 2.16 1.95 0.00 T772.0 2 AR only Rigid 1.74 1.74 1.65 0.00 T502.0 2 AR only Rigid 1.57 1.57 1.49 0.00 T302.0 2 AR only Rigid 1.65 1.65 1.17 0.00 T1003.5 3.5 AR only Rigid 1.71 1.71 1.62 0.00 T50-3.5 3.5 AR only Rigid 1.30 1.30 1.23 0.00 T30-3.5 3.5 AR only Rigid 0.96 0.96 0.91 0.00 Author Name L/h Cover, Longitudinal bars Transverse bars mm # Name fyl, MPa Name fyt, MPa ≤ Paulay & Binney, 1974 Beam 316* 1.29 38 4 #5 321 #2 420 Beam 317 1.29 25 4 #5 321 #2 420 Beam 395 1.03 25 4 #5 321 #2 420 Galano et al., 2000 P07 1.5 15 6 #2 566 #2 566 P12 1.5 15 6 #2 566 #2 566 Dugas 2002 D30 1.136 40 8 10M 476 10M 476 Kwan et al., 2002 CCB11 1.17 10 8 T8 517 R8 346 Canbolat et al., 2005 S1 1 40 10 D6 450 D6 450 Yun et al. 2008 CB-1 1 20 4 D16 474 D6 291 Lim et al., 2015 CB10-1 1 40 10 D10 475 D13 468 Howard, 2017 CC-16db 1.136 20 8 10M 431 10M 431 MD-10db 1.136 20 8 10M 431 10M 431 MD-8db 1.136 20 8 10M 431 10M 431 D-6db 1.136 20 8 10M 431 10M 431 L/h>1.5 Barney et al., 1980 C6 2.5 7 4 D6 459 #2 420 C8 5 7 4 D6 459 #2 420 Ishikawa et al., 1991 1 1.78 58 4 D16 358 D6 953 2 1.78 58 8 D16 358 D6 953 3 1.78 58 8 D16 358 D6 953 4 1.78 58 8 D16 358 D6 953 5 1.78 58 8 D16 358 D6 953 6 1.78 58 6 D19 724 D6 953 7 1.78 58 6 D19 724 D6 953 8 1.78 58 8 D16 358 D6 953 Sonobe et al. 1995 LX7L 2.8 35 4 D16 528 D6 923 NX7L 2.8 35 4 D16 528 D6 923 Gonzalez, 2001 K1* 2.74 25 4 10M 464 10M 464 Zhou, 2003 CB-2 3 40 4 25M 461 10M 486 Shimazaki, 2004 N-1 2.5 15 4 D16 476 D6 331 N-2 2.5 15 4 D16 459 D6 337 Fortney et al, 2008 DCB1 2.57 35 4 #6 418 #2 414 DCB2 3 19 12 #2 461 #2 461 Naish et al., 2013 CB24F 2.4 19 10 #2 482 #3 482 CB24D 2.4 19 10 #2 482 #2 482 CB24F-RC 2.4 19 10 #3 482 #3 482 CB24F-PT 2.4 19 10 #3 482 #3 482 CB24F-1/2-PT 2.4 19 10 #3 482 #3 482 CB33F 3.33 19 12 #3 482 #3 482 CB33D 3.33 19 12 #2 482 #2 482 Lim et al., 2015 CB20-1 2 40 10 D13 502 D13 502 Lim et al., 2016 CB30DA 3 40 4 #4 441 D13 441 Table B-2: Reinforcing detailings of studied diagonally-reinforced coupling beams.157 Author Name L/h Cover, Longitudinal bars Transverse bars mm # Name fyl, MPa Name fyt, MPa L/h>1.5 Lim et al., 2016 CB30DB 3 40 10 #3 475 D10 475 Ameen et al., 2017 CB1 1.89 20 8 #3 476 #3 469 Poudel, 2018 CB1A 1.89 20 8 #3 434 #3 468 Han et al., 2019 T1002.0 2 20 14 D13 506 D13 506 T772.0 2 20 14 D13 506 D13 506 T502.0 2 20 14 D13 506 D13 506 T302.0 2 20 14 D13 506 D13 506 T1003.5 3.5 20 10 D13 506 D13 506 T50-3.5 3.5 20 10 D13 506 D13 506 T30-3.5 3.5 20 10 D13 506 D13 506 158 : Summary of experimental data of steel and composite coupling beams (a) (b) This appendix summarises all the test data for the review of steel and composite coupling beams(SCB/SRCBs). Since 1993, several experimental studies have been conducted on steel andcomposite coupling beams to investigate the structural and seismic performance of these beams.During these years, researchers have tested various ideas and innovations to improve theperformance of steel and composite coupling beams. Figure C-1 (a) and (b) demonstrate a typicalsketch of steel and composite coupling beams without wall’s reinforcements, respectively.159 Author Name CE L/hs L/hc BP ATR SSB WHT WS AR Shahrooz et al., 1993 Wall 1 - 2.33 - - - - Yes - - Wall 2 - 2.33 - - - - Yes - - Wall 3 - 2.33 - - Yes - Yes - - Harries et al., (1993) & (1997) * S1 - 3.43 - Yes - - - outside - S2 - 3.46 - Yes - - - Inside & outside - S3 - 1.29 - Yes - - - inside & outside - S4 - 3.44 - Yes - - - - - Shahrooz et al., 2001(a) CB1 - 5.34 - - Yes - - outside - CB2 Yes 5.34 4.00 - Yes - - outside - CB3 Yes 5.34 4.00 - Yes - - inside & outside - CB4 Yes 5.34 4.00 - Yes - - - - Shahrooz et al., 2001(b) WB1 Yes 5.34 4.00 - Yes - - - - WB2 Yes 5.34 4.00 Yes Yes - - - - WB3 Yes 5.34 4.00 Yes Yes - - - Slab Park et al., (2005) SBVRF - 2.29 - Yes Yes Yes Yes - - SCF - 2.46 - Yes Yes Yes Yes - - Figure C-1: Sketch of (a) steel and (b) composite couplings without wall’s reinforcements.In Table C-1, the collected specimens were categorized as whether they had concrete encasement(CE) or, in other words, if the specimen was a composite coupling beam. Out of the 33 specimens,48% had concrete encasement. Table C-1 also shows the aspect ratio, which is the clear span length over the depth of the steel beam (hs), and the composite beam's aspect ratio, defined as theclear span length over the depth of the concrete-encased beam (hc). Only 36% of the specimenshad bearing plates (BP). Some tested specimens had auxiliary transfer bars (ATR) and shear studbolts (SSB). According to Table C-1, almost half of the specimens had auxiliary transfer bars andshear stud bolts. Some specimens (30%) had web horizontal ties (WHT), meaning that horizontalties were passed through the steel section's webs in the boundary region. Out of 33 specimens, 11specimens had web stiffeners (WS) placed inside or outside the boundary region to stop the webcrippling of the steel sections. Only two specimens had axial restraint (AR). The axial restraintsused in these experimental programs were post-tensioned rods or floor slabs. The embedmentlength was determined for each specimen based on different models developed for calculating theminimum required embedment length.Table C-1: General information about steel and composite coupling beams specimens.160 Author Name CE L/hs L/hc BP ATR SSB WHT WS AR Park et al., (2005) FCF - 4.92 - Yes Yes Yes Yes - - Park et al., (2006) PSF - 3.43 - - Yes Yes - outside - PSFF - 3.43 - Yes Yes Yes - outside - PSFFT - 3.43 - Yes Yes Yes Yes outside - Fortney et al., (2007) SCB - 2.57 - Yes Yes - - - - Motter et al., (2014) SRC1 Yes 4.72 3.33 - - - Yes - - SRC2 Yes 4.72 3.33 - - - Yes - - SRC3 Yes 3.40 2.40 - - - Yes - - SRC4 Yes 4.72 3.33 - - - - - PT rods Li et al., (2019) Beam 1 Yes 3.45 2.00 - - Yes - - - Beam 2 Yes 5.17 3.00 - - Yes - - - Beam 3 Yes 8.62 5.00 - - Yes - - - Beam 4 Yes 3.42 2.00 - - Yes - - - Beam 6 Yes 5.00 3.00 - - Yes - - - Beam 7 Yes 4.84 3.00 - - Yes - - - Nahvinia et al., (2021) SCBC2 - 2.78 - - - Yes - outside - SCBC3 - 2.78 - - - Yes - outside - Author Name bf/tw a/ Le Le (mm) L (mm) f’c (MPa) Shahrooz et al., 1993 Wall 1 0.4 0.30 864 267 35 Wall 2 0.4 0.30 864 267 35 Wall 3 0.4 0.30 864 267 35 Harries et al., (1993) & (1997) * S1 0.45 - 600 1200 26 S2 0.45 - 600 1200 43 S3 0.42 - 500 450 33 S4 0.42 - 600 1200 35 Shahrooz et al., 2001(a) CB1 0.67 1.88 216 406 14 CB2 0.67 1.88 216 406 12 CB3 0.67 1.88 216 406 16 CB4 0.67 1.88 216 406 14 Shahrooz et al., 2001(b) WB1 0.67 1.18 343 406 58 WB2 0.67 1.18 343 406 58 WB3 0.67 1.18 343 406 52 Park et al., (2005) SBVRF 0.58 1.33 300 400 30 SCF 0.58 1.00 300 300 30 FCF 0.58 2.00 300 600 30 Park et al., (2006) PSF 0.58 1.00 300 300 30 PSFF 0.58 1.20 250 300 30 PSFFT 0.58 1.20 250 300 30 Fortney et al., (2007) * SCB 0.5 - 775 914 35 Motter et al., (2014) SRC1 0.46 0.94 813 762 51 SRC2 0.46 1.25 610 762 51 SRC3 0.46 0.83 660 549 35 SRC4 0.46 1.25 610 762 32 Li et al., (2019) Beam 1 0.3 0.71 700 500 58 Beam 2 0.3 1.07 700 750 58 Beam 3 0.3 1.79 700 1250 58 Beam 4 0.27 0.71 700 500 58 Beam 6 0.4 1.07 700 750 58 Beam 7 0.4 1.07 700 750 58 Nahvinia et al., (2021) SCBC2 0.48 1.3 290 375 40 SCBC3 0.48 1.3 290 375 41 CE: Concrete Encasement, BP: Bearing Plate, ATR: Auxiliary Transfer Bars, SSB: Shear Stud Bolt, WHT: Web Horizontal Ties, WS: Web Stiffener, AR: Axial restraint, bf: steel beam’s flange width, tw: wall’s thickness. 161 Author Name Wall's loading protocol Wall’s stress/f’c Shahrooz et al., 1993 Wall 1 reversed-cyclic moment, and constant axial load 0 Wall 2 reversed-cyclic moment, and constant axial load 0.044 Wall 3 reversed-cyclic moment, and constant axial load 0.044 Harries et al., (1993) & (1997) S1 Constant axial load (compression) 0.116 S2 Constant axial load (compression) 0.070 S3 Constant axial load (compression) 0.091 S4 Constant axial load (compression) 0.086 Shahrooz et al., 2001(a) CB1 Constant axial load (compression) 0.180 CB2 Constant axial load (compression) 0.210 CB3 Constant axial load (compression) 0.160 CB4 Constant axial load (compression) 0.175 Shahrooz et al., 2001(b) WB1 reversed-cyclic moment, and constant axial load 0.043 WB2 reversed-cyclic moment, and constant axial load 0.043 WB3 reversed-cyclic moment, and constant axial load 0.048 Park et al., (2005) SBVRF Constant axial load (compression) 0.185 SCF Constant axial load (compression) 0.185 FCF Constant axial load (compression) 0.185 Park et al., (2006) PSF Constant axial load (compression) 0.185 PSFF Constant axial load (compression) 0.185 PSFFT Constant axial load (compression) 0.185 Fortney et al., (2007) SCB Constant axial load (compression) 0.085 Motter et al., (2014) SRC1 reversed-cyclic lateral loading and overturning moment 0 SRC2 reversed-cyclic lateral loading and overturning moment 0 SRC3 reversed-cyclic lateral loading and overturning moment, and constant axial load 0.066 SRC4 reversed-cyclic lateral loading and overturning moment, and constant axial load 0.072 Li et al., (2019) Beam 1 None 0 Beam 2 None 0 Beam 3 None 0 Beam 4 None 0 Beam 6 None 0 Beam 7 None 0 Nahvinia et al., (2021) SCBC2 Constant axial load (compression) 0.029 SCBC3 Constant axial load (compression) 0.028 Table C-2 shows summary of the test results of the previously tested steel and composite couplingbeams specimens.Table C-2: Test results of studied steel and composite coupling beams specimens.162 Author Name θ80% Initial stiffness (Ki) KN/mm Failure mode Shahrooz et al., 1993 Wall 1 4.6% 166.0 Flexural failure at connection Wall 2 4.6% 220.8 Flexural failure at connection Wall 3 6.8% 244.0 Flexural failure at connection Harries et al., (1993) & (1997) S1 8.7% 50.7 Shear failure at connection S2 7.5%* 41.8 Shear failure through clear span S3 6.9%* 1887.7 Shear failure through clear span S4 3.3%* 38.0 Flexural failure at connection Shahrooz et al., 2001(a) CB1 5.8% 51.5 Shear failure at connection CB2 4.6% - Shear failure at connection CB3 4.9% 61.4 Shear failure at connection CB4 5.2% 66.6 Shear failure at connection Shahrooz et al., 2001(b) WB1 9.4% 52.0 Shear failure at connection WB2 13.9% 67.0 Shear failure at connection WB3 9.9% 231.0 Shear failure at connection Park et al., (2005) SBVRF 5.2% 49.8 Shear failure at connection SCF 12.9% 32.0 Shear failure through clear span FCF 4.6% 19.8 Flexural failure through clear span Park et al., (2006) PSF 11.4% 80.1 Shear failure at connection PSFF 12.7% 88.7 Shear failure at connection PSFFT 12.3% 94.4 Shear failure at connection Fortney et al., (2007) SCB 4.1% 83.0 Shear failure at connection Motter et al., (2014) SRC1 13.3% 47.7 Flexural failure at connection SRC2 9.6% 54.3 Flexural failure at connection SRC3 11.5% 42.0 Flexural failure at connection SRC4 9.5% 30.6 Flexural failure at connection Li et al., (2019) Beam 1 7.0% 425.0 Flexural failure at connection Beam 2 6.4% 163.0 Flexural failure at connection Beam 3 6.0% 291.9 Flexural failure at connection Beam 4 6.1% 428.8 Flexural failure at connection Beam 6 6.7% 367.5 Flexural failure at connection Beam 7 6.9% 357.8 Flexural failure at connection Nahvinia et al., (2021) SCBC2 5.7% 283.5 Shear failure at connection SCBC3 9.3% 288.0 Flexural failure through clear span 163 C.1 Shahrooz et al., 1993In 1993, Shahrooz et al. [10] tested three steel coupling beams with L/hs equal to 2.34. The maintest variables were the application of auxiliary transfer bars and the presence of constant axial loadon the wall. All the specimens were tested under reversed cyclic loads applied to the couplingbeams and simulated overturning moments on the walls. The required embedment length for eachspecimen was calculated according to Mattock and Gaafar, 1982 [36] embedment model. FigureC-2 and Figure C-3 show the general geometrical layout of the tested specimens and the test setupused by Shahrooz et al., 1993 [10].Figure C-2: General geometrical dimensions of the tested specimens by Shahrooz et al., 1993 [10].164 no. 1 but was tested in addition under the gravity loads with 𝑝𝐴𝑔𝑓𝑐′ equals to 0.04, where 𝑝 is the applied axial load on the wall and 𝐴𝑔 is the gross area of the wall, experienced an initial stiffness equal to 220.8 KN/mm, indicating that the initial stiffness will be increased by considering the simulated gravity load on the adjacent shear walls. Compared to Wall no. 1, specimen Wall no. 3 had 47% higher initial stiffness due to the implementation of both gravity loads on the wall and Figure C-3: Shahrooz et al., 1993 test setup [10].Figure C-4 shows the hysteresis diagrams of the tested specimens by Shahrooz et al., 1993 [10].According to the results of Shahrooz et al., 1993 [10] research program, by having the sameembedment length of the steel section, the specimen with auxiliary transfer bars would experiencealmost 2% higher 𝜃80%, indicating that the auxiliary transfer bars delay the strength degradationat some points.Based on the test results, Shahrooz et al., 1993 [10] reported that specimen Wall no. 1 had thesmallest initial stiffness equal to 166 KN/mm. Specimen Wall no. 2, which was similar to Wall165 auxiliary transfer bars attached to the embedded steel beam’s flanges. Shahrooz et al., 1993 [10] considered the effective fix point of the beams at Le/3 from the beam-wall interface for calculating the shear force corresponding to the flexural resistance. Shahrooz et al., 1993 [10] test results revealed that although the beams were not fixed at the beam-wall interface, still the majority of the energy dissipation occurred through the steel beam in the clear span, rather than damage in the connection, showing that the embedment length was adequate to prevent any damages in the connection. (a) (b) (c)Figure C-4: Hysteresis diagrams of specimens (a) Wall 1, (b) Wall 2, and (c) Wall 3 tested by Shahrooz et al.,1993 [10].C.2 Harries et al., 1993In 1993, Harries et al. [39] tested two steel coupling beams with L/hs equal to 3.43 while the wallwas post-tensioned to simulate constant axial load. Both the specimens had face bearing plates atthe beam-wall interface. Since the first specimen experienced severe shear deformation anddamage at the connection and embedment region (which is called shear failure at the connection),the researchers decided to place stiffeners at the connection and through embedment length.Therefore, the second specimen experienced web crippling throughout the clear span rather than166 Specimen S1 the embedment region. Figure C-5 and Figure C-6 show the specimens’ details and the test setupused in Harries et al., 1993 [39] research program.Specimen S2Figure C-5: Specimen’s details tested by Harries et al.,1993 [39].167 Figure C-6: Harries et al., 1993 test setup [39].Harries et al., 1993 [39] research program showed that by using web stiffeners throughout theembedded region, the failure mode of the steel coupling beam can be changed from shear failureat the connection to the shear failure throughout the clear span by dissipating energy through thecrippling of web stiffeners. This failure transfer led to the θ80% decrease from 8.7% to 7.5%.,meaning that in the shear failure at the clear span, the rotational capacity will be decreased a bit.In terms of initial stiffness, specimen S2 experienced an initial stiffness equal to 41.8 KN/mm,which was slightly 21% lower than that of specimen S1.C.3 Harries et al., 1997Harries et al., 1997 [8] tested two more unencased steel coupling beams (S3 and S4, according toFigure C-7) with different L/hs and expected failure modes. The first specimen had L/hs equal to1.29 and was designed to dissipate energy by severe shear deformation throughout its clear span.However, the second specimen had L/hs equal to 3.43 by placing additional steel plates at the topof the flanges to ensure that flexural failure would not occur in the embedment region. None of thetested specimens had auxiliary transfer bars. According to their results, specimen S4 experiencedflexural failure by creating moment hinges at the beam-wall interface.168 Specimen S3 Specimen S4Figure C-7: Specimen’s details tested by Harries et al.,1997 [8].Hysteresis diagrams of the tested specimens by Harries et al., 1993 and 1997 [39], [8] are shownby Figure C-8. By comparing the test results of Harries et al., 1993 and 1997 [39], [8], it can beconcluded that for specimens with shorter embedment length and designed for shear failure, θ80would be decreased. Also, it can be concluded that steel coupling beam specimens designed forflexural failure experience significantly lower 𝜃80% than those designed to experience shear failurethrough the clear span. The specimen with shear failure (S3) experienced 7% chord rotation tillthe tearing failure occurred. The specimen S4, however, did not experience any pinching orstrength degradation up to 3.2% total chord rotation. After this point, the loading protocol waschanged from reversed-cyclic to monotonic due to out-of-plane web local buckling. In terms ofinitial stiffness, specimen S3 experienced failure in shear and had an initial stiffness equal to 188.7KN/mm, which was significantly higher (80%) than that of specimen S4, which was designed tofail in a flexural manner.169 S1 S2 S3 S4 Figure C-8: Hysteresis diagrams of the specimens tested by Harries et al., 1993 and 1997 [39], [8].C.4 Shahrooz et al., 2001(a)Shahrooz et al., 2001(a) [9] tested one Steel coupling beam (CB1) and three composite couplingbeams (CB2-CB4). The test variables were the presence of concrete encasement, the presence ofthe web stiffeners in the embedment region and the clear span of the beam, and the spacing of web170 stiffeners. All the specimens had the same embedment length, auxiliary transfer bars, and face bearing plates. The specimens were tested under cyclic load applied on the beam, and the walls were post-tensioned (𝑝𝐴𝑔𝑓𝑐′ the tested specimens and the test setup used by Shahrooz et al., 2001 (a) [9]. = 0.17). Figure C-9 (a) and (b) show the general geometry details of(a) (b)Figure C-9: (a) General geometry details of the tested specimens, and (b) the test setup used by Shahrooz et al., 2001 (a) [9].All specimens were designed to experience shear failure at the beam-wall interface. They reportedthat one of the most probable reasons for having shear failure at the connection is inadequateembedment length.All the specimens demonstrated stable hysteretic behaviour (Figure C-10). The tests were stoppedat 6% chord rotation. Specimen CB1 without concrete encasement experienced 𝜃80% and initialstiffness equal to 5.8% and 51.5 KN/mm, respectively. In the case of Specimen CB2, which wassimilar to specimen CB1 but with concrete encasement, θ80% was decreased by 26%. For this171 specimen, no value of initial stiffness was reported due to the instrumentation issues during the test. Specimen CB3 had web stiffeners with half spacing compared to CB2, experienced θ80% and initial stiffness equal to 5.8% and 51.5 KN/mm, respectively 4.9% and 61.4 KN/mm, respectively. Specimen CB4 without any web stiffeners outside the embedment region had 11% lower and 22.5% higher 𝜃80% and initial stiffness compared to specimen CB1, respectively. Figure C-10: Hysteresis diagram of specimens (a) CB1, (b) CB2, (c) CB3, and (d) CB4 tested by Shahrooz et al., 2001 (a) [9].Shahrooz et al., 2001(a) [9] concluded that the presence of stiffeners in the composite couplingbeams is not necessary as the concrete encasement protects the steel web section from crippling172 under shear loads. Also, they suggested considering the embedded steel beam fixed at 1/3 and 1/4 of the embedment length for encased and unencased steel coupling beams, respectively. Shahrooz et al., 2001 (a) [9] also concluded that since the effect of concrete encasement was not considered in calculating the required embedment length, significant nonlinearity was observed in the embedment region for the specimens with concrete encasement. In other words, if the increase attributed to the concrete encasement is not considered, significant damage will happen at the beam-wall interface. Consequently, the full capacity of the steel section will not be mobilized. Based on this observation, Shahrooz et al., 2001(a) [9] recommended that for designing composite coupling beams, the shear capacity of concrete encasement might be considered in calculating the minimum required embedment length. Therefore, the damage will be limited to the steel section rather than the connection at the beam-wall interface. Shahrooz et al., 2001(a) [9] proposed a new equation to calculate the expected shear strength of composite coupling beams in which the effect of concrete encasement in considered (Equation C.1), where ℎ𝑠 is the depth of the steel section, 𝑡𝑓 is the flange thickness, and 𝑡𝑤𝑠 is the web thickness. 𝑉𝑛𝑒 = 1.6(0.6𝑓𝑦(ℎ𝑠 − 2𝑡𝑓)𝑡𝑤𝑠 + 2√𝑓𝑐′𝑏𝑤𝑐𝑑𝑐 +𝐴𝑠𝑟𝑓𝑦𝑟𝑑𝑐𝑠 C.1 According to the test results of Shahrooz et al., 2001(a) [9], it can be concluded that by only having concrete encasement, 𝜃80% will not increase. However, concrete encasement will postpone the yielding of the web section outside the wall. Additionally, it can be seen that by providing tighter web stiffeners in the embedment region for SRCBs, 𝜃80% will be increased, but not significantly. 173 Figure C-11: General specimens’ details tested by Shahrooz et al., 2001 (b) [57].Shahrooz et al., 2001(b) [57] tested their specimens by considering the effect of overturningmoments and axial load on the walls (Figure C-3). Therefore, they used a different test setupcompared to Shahrooz et al., 2001(a) [9]. Like the specimens tested in 2001(a), Shahrooz et al.,2001(b) [57] designed their specimens to experience shear failure at the connection.The diagonal cracking in the embedment region for the test beams showed that face bearing platesmobilized the concrete struts on the embedment region. The existence of bearing plates has led toa delay in stiffness degradation as these plates increase the energy dissipation by mobilizingdiagonal compression struts. In other words, bearing plates dissipate energy through theC.5 Shahrooz et al., 2001(b)In 2001, Shahrooz et al., (b) [57] conducted another study that tested three encased steel couplingbeams with L/hc equal to 4.0. The test variables were the presence of a floor slab and face bearingplates. The embedment length was increased by 60% compared to the Shahrooz et al., 2001(a) [9]by considering the expected shear strength of the beam calculated by Equation 4.35. Figure C-11depicts the specimens’ details.174 deformations of beam-wall connection rather than relying on only bearing stresses developedbetween the embedded steel beam flanges and surrounding wall’s concrete.Figure C-12 shows the hysteresis diagrams for the tested specimens by Shahrooz et al., 2001 (b)[57]. Specimen WB1, which had concrete encasement and no web stiffeners outside theembedment region, experienced 𝜃80% and initial stiffness equal to 9.4% and 52 KN/mm,respectively. All the tested specimens tested by Shahrooz et al., 2001 (b) [57] had longerembedment length by 37% compared to those tested by Shahrooz et al., 2001 (a) [9]. Therefore,one reason for such a higher degradation rotation and initial stiffness recorded by specimens inShahrooz et al., 2001 (b) [57] experimental program is the longer embedment length used in thattesting. Specimen WB2, similar to specimen WB1 only with additional face bearing plates,experienced θ80% and initial stiffness equal to 13.9 % and 67 KN/mm, respectively, showing theeffect of face bearing plates on these parameters. Specimen WB3 was the same as specimen WB2but was tested by considering the floor slab. θ80%, and initial stiffness for this specimen wereincreased by 5% and 77.5%, respectively compared to specimen WB1. Shear capacity of specimenWB3 was also higher the other specimens due to the presence of floor slab providing additionalconfinement for the beam-wall interface.175 WB1 WB2 WB3Figure C-12: Hysteresis diagrams of specimens WB1, WB2, and WB3 tested by Shahrooz et al.,2001 (b) [57].Based on the test results of Shahrooz et al., 2001(b) [57], the presence of floor slab would increaseboth 𝜃80% and initial stiffness, but this increase in the latter will be diminished by occurring smalldeformations in the beams. Therefore, Shahrooz et al., 2001(b) [57] suggested not considering theeffect of floor slabs in calculating embedment length and initial stiffness. Shahrooz et al., 2001(b)[57] also showed that the presence of face bearing plates can increase the 𝜃80% significantly.By comparing the test results of Shahrooz et al., 2001(a) and (b) [9] [57], it can be concluded thatthe increase of steel profile embedment length, and simulating cyclic wall overturning momentwill result in higher 𝜃80% and initial stiffness. They also reported that the concrete strut can bemobilized by using face bearing plates. Also, face bearing plates delay the strength degradation byconducting the energy dissipation at the beam-wall interface.176 wall’s gravity load, 𝑝𝐴𝑔𝑓𝑐′ equals to 0.18 (Figure C-14). Park et al., 2005 [41] calculate the embedment length of the steel beam upon Equation 4.37, in which the effect of auxiliary transfer bars and web horizontal ties are considered. C.6 Park et al., 2005Park et al., 2005 [41] tested three unencased steel coupling beams with different failure modes.Test variable was L/hs and for all specimens the embedment length was equal to 300mm. Allspecimens had auxiliary transfer bars, web horizontal ties, and shear studs. Figure C-13 shows thegeometry details of each tested specimen. The specimens were tested under cyclic loads appliedto the coupling beams and constant axial force applied on the adjacent shear wall to simulate the177 Figure C-13: Specimens’ details tested by Park et al., 2005 [41].178 𝐿𝑀𝑛𝑉𝑛 equals to 1.8 experienced connection failure. This specimen did not show stable hysteretic Figure C-14: Test setup used by Park et al., 2005 [41].Figure C-15 (a), (b), and (c) show the hysteresis diagrams of the specimens SBVRT, SCF, andFCF tested by Park et al., 2005 [41], respectively. Specimen SBVRT with L/hs equals to 2.28 andloops due to premature connection failure in which the web and flanges of the steel beam failedafter the failure of the concrete and rebars in the embedment region. This specimen recorded 5.2%and 49.82 KN/mm values for 𝜃80% and initial stiffness, respectively. According to Figure C-15(a),specimen SBVRT experienced some level of pinching during the test attributed to the bearingfailure in the beam-wall interface region, showing that the strength capacity of the steel beam wasnot facilitated before the connection failed.179 Compared to specimen SBVRT, specimen SCF with L/hs equals to 2.46 and 𝐿𝑀𝑛𝑉𝑛 equals to 1.4 Park et al., 2005 [41] tested specimen FCF with L/hs 4.9 and 𝐿𝑀𝑛𝑉𝑛 equals to 2.8 which experienced (a) (b) experienced failure of the steel beam in the clear span. Figure C-15 (b) shows that specimen SCFexhibited relatively large and stable loops with negligible strength and stiffness degradation. Thisideal performance of specimen SCF is attributed to the full mobilization of the steel beam capacityand the failure of the beam in the clear span before any significant damage occurs at the beam-wall connection region. For this specimen, 𝜃80% and initial stiffness were increased by 60% anddecreased by 56% compared to specimen SBVRT, respectively.flexural failure at the connection region. According to Figure C-15(c), specimen FCF exhibited avery unstable and pinched response compared to both SBVRT and SCF specimens. This poorperformance is attributed to the local concrete bearing failure due to the buckling of thecompression flange at the beam-wall interface. Based on the test results, this specimen experienced𝜃80% and initial stiffness equal to 4.6% and 19.81 KN/mm, respectively.180 ⁡ (c)Figure C-15: Hysteresis diagrams of specimens (a) SBVRT, (b) SCF, and (c) FCF tested by Park et al., 2005 [41].According to the test results of Park et al., 2005 [41], it can be concluded that the specimendesigned to experience flexural failure by developing plastic hinges through clear span (FCF) hadsmaller 𝜃80% compared to the ones with shear failure at the connection and throughout the clearspan (SCF and SBVRT). Specimen SBVRT, which had a bigger section and longer clear lengthdesigned to fail at the connection due to inadequate shear capacity, experienced significantly lower𝜃80% than the specimen SCF designed to dissipate energy through steel profile web throughout themidspan. Park et al., 2005 [41] concluded that steel coupling beams designed to experience shearfailure throughout the clear span exhibit a more stable hysteretic response compared to the onesthat experienced flexural or connection failures. Therefore, steel coupling beams with shear-critical failure dissipate a larger amount of energy due to the high capacity of steel beams.181 C.7 Park et al., 2006Park et al., 2006 [11] tested three other unencased steel coupling beams designed to experienceshear failure at the beam-wall interface. All the specimens had L/hs equal to 3.43, auxiliary transferbars, and shear studs (Figure C-16). Park et al., 2006 [11] used the same test setup as Park et al.,2005 [41] experimental program (Figure C-14). Specimens PSF, PSFF, and PSFFT had shearstuds, shear studs and face bearing plates, and shear studs and face bearing plates and webhorizontal ties passed through the web of the steel beam in the beam-wall connection, respectively.182 Figure C-16: Specimens’ details tested by Park et al., 2006 [11].Figure C-17 (a), (b), and (c) show the hysteresis diagrams of the specimens PSF, PSFF, and PSFFTtested by Park et al., 2006 [11], respectively. Specimen PSF experienced initial vertical crackingon the wall face at a rotation angle of about 0.017 rad, indicating the formation of diagonalcompression struts in the outer concrete panel. At the end of the test, the connection region wassignificantly damaged, revealing the loss of bond between the longitudinal bars and the concreteshear wall. Based on test results, specimen PSF experienced θ80% and initial stiffness equal to11.4% and 80.1 KN/mm, respectively.Compared to specimen PSF, specimen PSFF had face bearing plates in addition to shear studs.According to the test results, specimen PSFF showed a similar cracking pattern to specimen PSF.However, in terms of rotational capacity and initial stiffness, implementing face bearing pates ledto a significant increase in both parameters by roughly 10% and 9.6%, respectively, compared tothat of recorded by specimen PSF.183 Park et al., 2006 [11] tested another specimen (PSFFT) similar to the specimen PSFF but with web horizontal ties. Based on the test results, Park et al., 2006 [11] concluded that adding web horizontal ties increased the connection strength by up to 21%. Compared to specimen PSFF, recorded 𝜃80% for specimen PSFFT was not changed significantly; however, initial stiffness increased slightly by 6%. (a) (b) (c) 184 this experimental study was post-tensioned to simulate axial loads on the wall (𝑝𝐴𝑔𝑓𝑐′ = 0.09). (a) (b) However, no overturning moments or shear loads were applied to the wall. The tested specimenby Fortney et al., 2007 [58] had auxiliary transfer bars and face bearing plates at the beam-wallinterface, and the back of the embedded beam extended into the wall. The required embedmentlength for the tested specimen was calculated using Equation 4.35, developed by Mattock andGaafar in 1982 [36]. Reversed-cyclic loading was applied to the steel beam up to 4% rotation whenthe researchers decided to continue the test by applying monotonic loading to the specimen up to11% rotation due to concerns about the stability of the loading frame. Figure C-18(a) and (b) show the geometry details and the hysteresis diagram of specimen SCB. Based onFigure C-18 (b), specimen SCB recorded 𝜃80% equal to 4.1%.Figure C-17: Hysteresis diagrams of specimens (a) PSF, (b) PSFF, and (c) PSFFT tested by Park et al., 2006 [11].C.8 Fortney et al., 2007In 2007, Fortney et al., [58] tested one steel and a series of fuse coupling beams. The steel couplingbeam specimen was designed to fail in shear at the clear span with L/hs 2.57. The adjacent wall in185 Figure C-19: Geometrical layouts of the specimens tested Motter et al., 2014 [7].Figure C-18: Specimen SCB (a) details and (b) hysteresis diagram tested by Fortney et al., 2007 [58].C.9 Motter et al., 2014In 2014, Motter et al. [7] tested four SRCBs with different L/hc. They designed all the specimensto experience flexural failure at the connection. The main test variables were axial load on the wall,axial restraint on the coupling beam, embedment length, and vertical and transverse reinforcementratio in the boundary region. Figure C-19 and Figure C-20 show the geometrical layouts of thetested specimens and the test setup tested by Motter et al., 2014 [7], respectively.186 Figure C-20: Test setup used by Motter et al., 2014 [7].Specimen SRC1 (L/hc =3.33), which had sufficient embedment length (calculated per Equation4.36) and low demands on the wall exhibited a stable hysteretic performance under testing (FigureC-21). This specimen was tested under cyclic loading on the beam, cyclic overturning momentand shear force on the wall. Based on the test results. Specimen SRC1 recorded 𝜃80% and initialstiffness equal to 13.3% and 47.7 KN/mm.187 Figure C-21: Hysteresis diagram of specimen SRC1 tested by Motter et al., 2014 [7].Specimen SRC2 had the embedment length calculated per Equation 4.36, which was lower thanthe one calculated for SRC1. The demand on the wall for this was significantly higher than the oneon SRC1. Therefore, SRC2 was intended to test a more critical scenario.According to the test results, specimen SRC2 experienced more damage and cracking at the beam-wall interface than SRC1 since the shorter embedment length and higher wall demands wereutilized for SRC2. Based on Figure C-22, specimen SRC2 exhibited greater pinching, strengthdegradation, and lower energy dissipation than SRC1. The greater pinching in specimen SRC2 isattributed to the gap between the steel flanges and the concrete in the embedment region, resultingin the loss of the composite action between steel and concrete. Compared to specimen SRC1, 𝜃80%and initial stiffness for specimen SRC2 decreased by 40% and increased by 12%, respectively,compared to that recorded by specimen SRC1.Figure C-22: Hysteresis diagram of specimen SRC2 tested by Motter et al., 2014 [7].188 Specimens SRC3 and SRC4 had the same embedment length calculated based on the averages ofEquations 4.36 and 4.37. Both these specimens were axially restrained by utilizing post-tensionedrods. Unlike the first two specimens, constant axial load was applied on specimens SRC3 andSRC4. Additionally, the ratio of the boundary vertical reinforcement for specimens SRC 3 andSRC4 was reduced significantly to assess the effect of vertical bars in the wall in transferring wallloads. The difference between specimens SRC3 and SRC4 was utilizing web horizontal ties, whichspecimen S C3 had its steel beam’s web drilled to put the rods as the web horizontal ties.However, specimen SRC4 had U-shaped ties. Figure C-23 (a) and (b) show the hysteresisdiagrams of specimens SRC3 and SRC4, respectively. In addition, specimen SRC4 had asignificantly lower wall vertical bar ratio than specimen SRC3 (one-third).(a) (b)Figure C-23: Hysteresis diagrams of specimens (a) SRC3 and (b) SRC4 tested by Motter et al., 2014 [7].According to the test results, specimens SRC3 and SRC4 demonstrated extensive damage at thebeam-wall interface after completing cycles to 3% rotation. Also, the wall boundary longitudinalbars of these specimens were fully buckled in the embedment region by the end of the test. Basedon the test results, specimen SRC3 and SRC4 recorded 11.5% and 9.5% as 𝜃80%, respectively.189 Also, test results recorded the initial stiffness for specimens SRC3 and SRC4 as 42 KN/mm and30.6 KN/mm, respectively.According to the Motter et al., 2014 [7] research program, a specimen with a longer embedmentlength and lower load demands on the wall would experience higher 𝜃80% than the one withinadequate embedment length and higher load demands on the wall. Based on these numbers, itcan be concluded that the presence of axial force on the wall will result in higher 𝜃80%. However,the axial restraint increased the initial stiffness of the coupling beam and did not impact therotational capacity significantly.The test results of the research program conducted by Motter et al., 2014 [7] showed that bothadequate and high ratios of transverse and vertical bars in the embedment region would lead tohigh 𝜃80%. In other words, a high level of 𝜃80% strongly depends on the sufficient embedmentlength, although a significant ratio of vertical and transverse reinforcement would have beenprovided.Motter et al., 2014 [7] recommended to calculate the elastic effective bending stiffness of steel andsteel-reinforced coupling beams per Equation C.2 based on the recorded values of the stiffnessdegradation of their tested specimens. Equation C.2 is recommended for modelling purposes whererigid behaviour for shear stiffness and beam-wall interface connection is assumed.𝐸𝐼𝑒𝑓𝑓 = 0.06𝛼𝐸𝑠𝐼𝑡𝑟𝑎𝑛𝑠 C.2C.10 Li et al., 2019In 2019, Li et al. [59] tested six SRCBs designed to experience flexural failure at the beam-wallinterface. The main test variables were L/hc, steel flange area over steel web area, and the steelsection and concrete gross area ratio. All the specimens were loaded cyclically, and no loading190 (a) was simulated on the adjacent walls. The embedded steel beams were fully developed into thepedestal, acting as the fully elastic shear wall for all these specimens. Therefore, the embeddedsteel beam in all the specimens was fixed to the bottom of the pedestal. The minimum embedmentlength requirement for all the specimens was calculated using Equation 4.36. Figure C-24 (a) and(b) show the general geometry detail and the test setup used by Li et al., 2019 [59].191 Beam1 Beam2 (b)Figure C-24: General geometry layout of the specimens and (b) used test setup by Li et al., 2019 [59].According to the test results of Li et al., 2019 [59] research program, by increasing L/hc, 𝜃80%would be decreased. However, increasing the steel flange area over the steel web area, 𝜃80% willbe increased significantly. Also, it has been seen that there is a direct relationship between anincrement of the ratio of steel section and concrete gross area and an increase of 𝜃80%. Figure C-25shows the hysteresis diagrams of the tested specimens by Li et al., 2019 [59]. One reason for therelatively high initial stiffness of the specimens tested by Li et al., 2019 [59] compared to otherstudied specimens is that Li et al., 2019 [59] fixed the end of the embedded steel section to thebottom of the pedestal. This fixity prevented the slippage of the embedded steel section, meaningthat the primary sources of stiffness degradation were flexural and shear deformations.192 Beam3 Beam4 Beam5 Beam6 Beam7Figure C-25: Hysteresis diagrams of the specimens tested by Li et al., 2019 [59].193 constant axial forces were applied to the beams and walls, respectively (𝑝𝐴𝑔𝑓𝑐′ = 0.03). Both tested specimens (SCBC1 and SCBC2) had shear studs connected on each flange of the embedded steelbeam. The embedment length for both these specimens was determined by 70% of the embedmentlength required by Equation 4.36 for steel coupling beams. The difference between specimensSCBC1 and SCBC2 was that the latter had web horizontal ties welded to the web of the embeddedsteel beam in the embedment region. The specimens were tested under cyclic shear load appliedon a steel beam and constant compression load acting as the gravity loads of the higher stories onthe adjacent shear wall. Figure C-26 show the tested specimens’ geomatical details and used testsetup by Nahvinia et al., 2021 [12].C.11 Nahvinia et al., 2021In 2021, Nahvinia et al. [12] tested two steel coupling beams with L/hs equal to 2.78. The primarytest variable was the transverse and vertical bars ratio in the embedment region. Cyclic shear and194 Figure C-26: Used test setup by Nahvinia et al., 2019 [12].According to the test results, specimen SCBC2 with closely-placed ties and horizontal stirrupsexperienced the shear failure of the steel beam through the clear span, indicating that the beam-wall interface did not endure significant damage. However, specimen SCBC1 with widely-placedties in the beam-wall interface experienced severe damage in the connection region. Figure C-27(a) and (b) show the hysteresis diagrams of specimens SCBC1 and SCBC2, respectively; SCBC2with tighter ties demonstrated more stable and larger loops than SCBC1 with greater pinching andstrength degradation. Based on the test results, specimen SCBC1 experienced 5.7% and 41KN/mm in terms of 𝜃80% and initial stiffness, respectively. Compared to specimen SCBC1,specimen SCBC2 with additional ties went through the web of the embedded steel section in theembedded section experienced 39% and 18% higher 𝜃80% and initial stiffness, respectively.195 (a) (b)Figure C-27: Hysteresis diagrams of specimens (a) SCBC1 and (b) SCBC2 tested by Nahvinia et al., 2021.
Thesis/Dissertation
eng
Civil Engineering
Vancouver : University of British Columbia Library
Attribution-NoDerivatives 4.0 International
Graduate
Tobber, Lisa
Database analysis of diagonally- reinforced coupling beams and development of new connection detailing for steel and composite coupling beams
Text