Applied Science, Faculty of
Civil Engineering, Department of
DSpace
UBCV
Chaudhry, Hamza Zulfiqar
Master of Applied Science - MASc
University of British Columbia
With rapid population growth worldwide and increasing urbanization, there is a growing demand for infrastructure that can be constructed quickly, while maintaining sustainability and resilience. In order to enhance the seismic resilience and constructability, this thesis introduces a novel self-centering modular rocking composite sandwich wall (SC-MRCSW) system. SC-MRCSW system consists of steel plates in-filled with concrete, where the steel plates are tied using steel bolts. The steel plates reduce the need for concrete formwork which significantly reduces the on-site constriction time, making SC-MRCSW system a highly efficient structural system for high rise application. To improve the performance of the SC-MRCSW, novel self-centering friction dampers are added to the system to ensure SC-MRCSW system can dissipate earthquake energy and self center after strong earthquake shaking. This makes SC-MRCSW system highly resilient. This thesis focuses on the seismic design of SC-MRCSW system. This is achieved using the novel Equivalent Energy Design Procedure (EEDP). Detailed numerical model of the SC-MRCSW system was developed to simulate the non-linear dynamic response of the system. The results show that SC-MRCSW system is able to achieve superior performance at different levels of earthquake shaking intensities. This thesis shows that the proposed SC-MRCSW system can be used as a reliable seismic force resisting system and can be designed efficiently using EEDP.
Seismic design and evaluation of self-centering modular rocking composite sandwich wall (SC-MRCSW) system by Hamza Zulfiqar Chaudhry B.Eng. (Hons.), Heriot-Watt University, 2018 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Civil Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) November 2025 © Hamza Zulfiqar Chaudhry, 2025ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled: Seismic design and evaluation of self-centering modular rocking composite sandwich wall (SC-MRCSW) system submitted by Hamza Zulfiqar Chaudhry in partial fulfilment of the requirements for the degree of Master of Applied Science in Civil Engineering Examining Committee: Tony Yang, Professor, Department of Civil Engineering, UBC Supervisor Musab Al-Janabi, Professor, Department of Civil Engineering, Al-Nahrain University Supervisory Committee Member iii Abstract With rapid population growth worldwide and increasing urbanization, there is a growing demand for infrastructure that can be constructed quickly, while maintaining sustainability and resilience. In order to enhance the seismic resilience and constructability, this thesis introduces a novel self-centering modular rocking composite sandwich wall (SC-MRCSW) system. SC-MRCSW system consists of steel plates in-filled with concrete, where the steel plates are tied using steel bolts. The steel plates reduce the need for concrete formwork which significantly reduces the on-site constriction time, making SC-MRCSW system a highly efficient structural system for high rise application. To improve the performance of the SC-MRCSW, novel self-centering friction dampers are added to the system to ensure SC-MRCSW system can dissipate earthquake energy and self center after strong earthquake shaking. This makes SC-MRCSW system highly resilient. This thesis focuses on the seismic design of SC-MRCSW system. This is achieved using the novel Equivalent Energy Design Procedure (EEDP). Detailed numerical model of the SC-MRCSW system was developed to simulate the non-linear dynamic response of the system. The results show that SC-MRCSW system is able to achieve superior performance at different levels of earthquake shaking intensities. This thesis shows that the proposed SC-MRCSW system can be used as a reliable seismic force resisting system and can be designed efficiently using EEDP. iv Lay Summary Growing populations and increasing urbanization impose crucial demand to build quicker, more resilient to disasters and sustainable for the environment. This research introduces a new type of structural wall system named the self-centering modular rocking composite sandwich wall (SC-MRCSW). The SC-MRCSW system is made from steel plates filled with concrete. The steel plates act as a formwork for the concrete and add strength and stiffness to the system. The SC-MRCSW system incorporates self-centering friction dampers to absorb energy during earthquake shaking. This ensures the SC-MRCSW is damage free after a major earthquake event. This thesis focuses on the seismic design and performance evaluation of the SC-MRCSW under different levels of seismic shaking intensities. The results show the SC-MRCSW system can perform well and be used as a reliable structural system for earthquake applications. v Preface The research presented in this thesis is the original work of the author, Hamza Zulfiqar Chaudhry. The author worked under the supervision of Professor Tony T.Y. Yang to define the research program and carried out the design and analysis produced in this thesis. Generative artificial intelligence (AI) is not utilized for any aspects of the work in this thesis. The contents of this thesis are expected to be published in a journal paper. vi Table of Contents Abstract ......................................................................................................................................... iii Lay Summary ............................................................................................................................... iv Preface .............................................................................................................................................v Table of Contents ......................................................................................................................... vi List of Tables ................................................................................................................................ xi List of Figures .............................................................................................................................. xii List of Symbols ........................................................................................................................... xvi List of Abbreviations ................................................................................................................ xxii Acknowledgements ....................................................................................................................xxv Dedication ................................................................................................................................. xxvi Chapter 1: Introduction ........................................................................................................... 1 1.1 Background ................................................................................................................. 1 1.2 Research scope and objectives .................................................................................... 5 1.3 Thesis organization ..................................................................................................... 5 Chapter 2: Literature review ................................................................................................... 7 2.1 Modular systems for high-rise construction ............................................................... 7 vii 2.2 Energy dissipation devices ........................................................................................ 11 2.3 Low damage LFRS ................................................................................................... 14 2.4 Seismic design methodologies .................................................................................. 18 Force Based Design (FBD) ............................................................................... 18 Direct Displacement-Based Design (DDBD) ................................................... 18 Energy Based Design (EBD) ............................................................................ 19 2.5 Summary ................................................................................................................... 20 Chapter 3: Self-centering modular rocking composite sandwich wall (SC-MRCSW) system ....................................................................................................................................... 21 3.1 System overview ....................................................................................................... 21 Modular steel-concrete composite wall ............................................................ 23 Self-centering coupling beams .......................................................................... 24 Rocking base with friction dampers ................................................................. 29 System behavior ................................................................................................ 30 3.2 Performance objectives ............................................................................................. 32 3.3 Summary ................................................................................................................... 33 Chapter 4: Design procedure for SC-MRCSWS ................................................................. 34 4.1 Step 1: Select earthquake shaking intensities ........................................................... 37 viii 4.2 Step 2: Design of SC-MRCSW system for SLE intensity ........................................ 37 4.3 Step 3: Design of SC-MRCSW system for DBE intensity ....................................... 39 4.4 Step 4: Design of SC-MRCSW system for MCE intensity ...................................... 42 4.5 Step 5: Distribute design forces to the primary and secondary fuse systems ........... 44 4.6 Step 6: Design primary fuse system and secondary fuse system dampers ............... 46 4.7 Step 7: Capacity design of steel-concrete composite wall ........................................ 50 4.8 Summary ................................................................................................................... 53 Chapter 5: Prototype building ............................................................................................... 54 5.1 Overview ................................................................................................................... 54 5.2 EEDP requirement .................................................................................................... 56 5.3 Damper design .......................................................................................................... 57 5.4 Wall design ............................................................................................................... 59 5.5 Summary ................................................................................................................... 61 Chapter 6: Numerical modeling of the SC-MRCSW for the prototype building ............. 62 6.1 Model overview ........................................................................................................ 62 6.2 Component modelling ............................................................................................... 64 Self-centering coupling beams .......................................................................... 65 Base Dampers ................................................................................................... 67 ix Rocking base-Elastic No-Tension material ...................................................... 68 6.3 Modal properties ....................................................................................................... 69 6.4 Summary ................................................................................................................... 70 Chapter 7: Seismic performance of the SC-MRCSW ......................................................... 71 7.1 Ground motion selection and scaling ........................................................................ 71 7.2 Roof displacement and interstory drift ..................................................................... 74 7.3 Residual drifts ........................................................................................................... 76 7.4 Coupling beam performance ..................................................................................... 77 7.5 Base Dampers ........................................................................................................... 79 7.6 Wall performance...................................................................................................... 80 7.7 Summary ................................................................................................................... 81 Chapter 8: Conclusion ............................................................................................................ 82 8.1 Summary ................................................................................................................... 82 8.2 Limitations and recommendations for future work .................................................. 83 References .....................................................................................................................................85 - NLTHA results .....................................................................................................89 A.1 SLE coupling beam forces ........................................................................................ 89 A.2 SLE displacement time history ............................................................................... 100 x A.3 DBE coupling beam forces ..................................................................................... 111 A.4 DBE displacement time history .............................................................................. 122 A.5 MCE coupling beam forces .................................................................................... 133 A.6 MCE displacement time history.............................................................................. 144 xi List of Tables Table 1 Design summary for the prototype building .................................................................... 57 Table 2 Summary of SCFD and base damper design forces. ....................................................... 58 Table 3 Scale factors of GM for each hazard ............................................................................... 72 xii List of Figures Figure 1 Modular fabrication types: a) Panelized 2-D; b) Volumetric 3-D (Thai et al., 2020) ...... 1 Figure 2 Murray Grove panelized construction scheme (Waugh et al., 2010). .............................. 2 Figure 3 Ten Degrees tower construction (Maleki et al., 2024) ..................................................... 3 Figure 4 Precast modular concrete system for tall buildings (Wang et al., 2020) .......................... 7 Figure 5 Prototype 40 story building using the precast concrete modules (Wang et al., 2020) .... 8 Figure 6 CC-PSW/CF system; a) panel assembly, b) assembled wall section ............................... 9 Figure 7 Force-deformation performance of CC-PSW/CF for lateral loads (Broberg et al., 2022)....................................................................................................................................................... 10 Figure 8 WWFF; a) Assembly, b) Mechanism (Yang et al., 2021). ............................................. 11 Figure 9 VCDs; a) Assembly. b) Energy dissipation (Montgomery et al., 2021). ....................... 12 Figure 10 Components of Self-Centering Nonlinear Friction Damper (SCNFD) (Yang et al., 2023)........................................................................................................................................................ 13 Figure 11 Force-deformation response for SCNFD (Yang et al., 2023). ..................................... 14 Figure 12 Rocking wall experimental setup and prototypes analyzed (Khanmohammadi & Heydari, 2015). ............................................................................................................................. 15 Figure 13 DLRF RCB assembly and rocking mechanism (Wang et al., 2021). ........................... 15 Figure 14 DSCW system assembly (Lepine-Lacroix & Yang, 2023). ......................................... 16 Figure 15 CROCW system assembly (Tobber et al., 2023). ........................................................ 17 xiii Figure 16 Design process using DDBD (M. N. Priestley et al., 2007). ........................................ 19 Figure 17 SC-MRCSW system components................................................................................. 22 Figure 18 SC-MRCSW system mechanism .................................................................................. 22 Figure 19 Typical wall section for steel-concrete composite sandwich wall ............................... 23 Figure 20 Typical failure mode for steel-concrete composite wall system (Eom et al., 2009; Epackachi et al., 2015). ................................................................................................................. 24 Figure 21 SCFD assembly (Yang et al., 2020). ............................................................................ 25 Figure 22 SCFD mechanism and hysteresis response (Yang et al., 2020). .................................. 25 Figure 23 Elevation view of self-centering coupling beam .......................................................... 26 Figure 24 a) Free body diagram for SCFD; b) SCFD hysteresis (Yang et al., 2020). .................. 27 Figure 25 (a) Section for LED; (b) Force-deformation response for LED (Rodgers et al., 2006) 30 Figure 26 Forces at the base of the wall during rocking ............................................................... 31 Figure 27 Idealized force-deformation response for the SC-MRCSW system. ............................ 32 Figure 28 EEDP concept (Yang et al., 2018)................................................................................ 36 Figure 29 Demand capacity curve based on seismic hazard intensity .......................................... 37 Figure 30 Selecting performance objectives based on design period ........................................... 38 Figure 31 Performance criteria at DBE intensity .......................................................................... 40 Figure 32 EEDP for MCE intensity .............................................................................................. 44 xiv Figure 33 Independent bilinear fuse system (a); Dependent trilinear system (b) ......................... 45 Figure 34 (a) Combined mechanism; (b) Primary fuse (SCFD); (c) Secondary fuse (Base Dampers)....................................................................................................................................................... 47 Figure 35 Plastic mechanisms for the SC-MRCSW system of a) the primary fuse system and b) the secondary fuse system ............................................................................................................. 50 Figure 36 Plan and elevation view for the prototype building...................................................... 55 Figure 37 Seismic hazard selected for the prototype building ...................................................... 56 Figure 38 EEDP response for the prototype building ................................................................... 56 Figure 39 Shear force distribution between the primary and secondary system .......................... 57 Figure 40 Design coupling beam shear force distribution for prototype building ........................ 59 Figure 41 Final wall section of the prototype building ................................................................. 60 Figure 42 Final wall elevation for the prototype building ............................................................ 60 Figure 43 Numerical model of the SC-MRCSWS for prototype building ................................... 63 Figure 44 SCFD material formulation .......................................................................................... 66 Figure 45 Numerical calibration for SCFDs. ................................................................................ 66 Figure 46 Base damper backbone curve ....................................................................................... 67 Figure 47 Experimental and numerical model for rocking base calibration ................................. 68 Figure 48 Numerical calibration results for rocking base ............................................................. 69 xv Figure 49 Mode shapes for the first three modes .......................................................................... 70 Figure 50 Ground motion scaling for SLE, DBE and MCE hazard ............................................. 73 Figure 51 Interstory drift for each hazard ..................................................................................... 74 Figure 52 Roof displacement for each hazard .............................................................................. 75 Figure 53 Average roof displacement vs. EEDP roof displacement ............................................ 76 Figure 54 Residual inter-story drift performance. ........................................................................ 77 Figure 55 Sample hysteresis of SCFD from NLTHA ................................................................... 78 Figure 56 Nominal coupling beam forces for each hazard ........................................................... 79 Figure 57 Average base damper force for each hazard ................................................................. 80 Figure 58 Maximum average shear strain in the wall for each hazard ......................................... 81 xvi List of Symbols ∆= Damper displacement ∆𝑝 = Design roof displacement at DBE ∆𝑦 = Yield/Roof displacement ∆𝐸𝐸 = Total strain energy stored in a system ∆𝐸𝑁𝐷 = Total non-linear dynamic energy stored in a system 𝐴𝑤.𝑒𝑓𝑓 = Effective cross-sectional area of a wall pier 𝐴𝑐 = Area of concrete 𝐴𝑠 = Area of steel 𝐴𝑠𝑤 = Area of steel plate in the wall 𝐴𝑤= Area of web for steel beam 𝑏 = Post yielding stiffness of the system 𝐵𝑊 = Length of the wall 𝜆𝑝 = Ratio of the DBE base shear to SLE base shear 𝑏𝑢 = Unsupported length of steel plate 𝐶𝑜 = Displacement modification factor 𝑑𝑐 = Distance from the centroid of the wall pier to the centroid of the core wall 𝑑𝑡𝑖𝑒 = Effective diameter of the tie xvii 𝐸𝑎 = Strain energy 𝐸𝑐 = Elastic modulus of concrete 𝐸𝑑 = Damping energy 𝐸ℎ = Hysteric energy 𝐸𝑘 = Kinetic energy 𝐸𝑁𝑀 = Total non-linear monotonic energy stored in a system 𝐸𝑠 = Elastic modulus of steel 𝐸𝑠𝑒 = Elastic strain energy 𝐸𝑠𝑤 = Elastic modulus of the wall 𝑓𝑏 = Yield force of the dampers at base 𝛼2 = Stiffness factor 𝑓𝑐′ = Concrete compressive stress 𝐹𝑀𝐶𝐸 = Elastic base shear at the MCE 𝐹𝑝 = Design base shear at DBE 𝐹𝑃𝑅 = Force resisted by the primary fuse system 𝐹𝑝𝑡0 = Initial force in the PT tendons 𝐹𝑆𝐸 = Force resisted by the secondary fuse system xviii 𝐹𝑦 = Yield base shear 𝐹𝑦𝑠 = Yield stress 𝐺= Shear modulus 𝐻 = Total height of the wall 𝐼𝑏= Moment of inertia for steel beam 𝐼𝑇𝑒 = Effective moment of inertia of the wall 𝐼𝑤 = Moment of inertia of a wall 𝐾𝑏= Flexural stiffness of steel beam 𝑘𝑐𝑏,𝑝 = Post-yield stiffness ratio of the coupling beam 𝑘𝑐𝑏 = Initial stiffness of the coupling beam 𝐾𝑒= Elastic stiffness of steel beam 𝑘𝑜= Elastic stiffness of the system 𝑘𝑝= Post yield stiffness of damper 𝑘𝑝𝑡= Initial axial stiffness of the PT tendon 𝐾𝑠= Shear stiffness of steel beam 𝑘𝑢= Unloading stiffness of damper 𝐿𝑐 = Length of coupling beam from wall face xix 𝑚 = Seismic mass 𝑀𝐶= Moment in the compression wall 𝑀𝑜𝑡= Overturning moment at the base of the wall pier 𝑀𝑇= Moment in the tension wall 𝑃0= Damper activation force 𝑃𝑔 = Force in pier due to gravity 𝑃𝑚= Maximum damper sliding force 𝑃𝑛 = Nominal tensile strength 𝑃𝑛𝑜 = Nominal compressive strength 𝑃𝑝 = Force generated in pier through coupling beams 𝑃𝑢 = Unloading force of damper 𝑆 = Tie spacing 𝑆𝑎 = Spectral acceleration 𝑆𝑑 = Spectral displacement 𝑇𝑛 = Building period 𝑡𝑝 = Thickness of steel plate 𝑡𝑠𝑐 = Thickness of composite wall xx 𝑉𝑝,𝑟 = Coupling beam shear at roof 𝑉𝑝,𝑥 = Coupling beam shear at any given story 𝑉𝑛 = Nominal shear 𝑊𝑒𝑥𝑡,𝑝𝑟 = External work done, primary system 𝑊𝑖𝑛𝑡,𝑝𝑟 = Internal work done, primary system 𝑥𝑐𝑔 = Distance from the rocking toe of the “tension” wall to the centerline of the wall 𝛼2𝑘𝑝 = Stiffness parameter 𝛼𝑐 = Stiffness factor 𝛼𝑐𝑝 = Relative stiffness parameter of the coupling beams to the wall 𝛽0 = Dynamic factor 𝛽𝑥 = Ratio of shear in coupling beams normalized to shear in coupling beam at roof 𝛾𝑎 = Energy modification factor 𝛾𝑏 = Energy modification factor 𝛥𝑀𝐶𝐸 = Elastic roof displacement at the MCE 𝛥𝑢 = Maximum roof displacement at MCE 𝛥𝐸𝐸1 = Elastic energy under ELSDOF 𝛥𝐸𝐸2 = Elastic energy under ELSDOF xxi 𝛥𝐸𝑁𝐷1 = Non-linear dynamic energy under ENLSDOF 𝛥𝐸𝑁𝑀1 = Nonlinear monotonic energy 𝛥𝐸𝑁𝑀2 = Nonlinear monotonic energy 𝜃 = Angle of deviation 𝜃𝑝𝑟 = Base rotation of the walls 𝜃𝑠𝑒 = Rotation of the pier at its rocking tow 𝜆𝑥 = Distribution factor 𝜇𝑝 = Ratio of the design DBE roof displacement to SLE roof displacement 𝜇= Coefficient of friction between the flat plates 𝜇′= Coefficient of friction between the cones 𝛷𝑝 = Ratio of design base shear at DBE over the design base shear at SLE 𝛷𝑠 = Ratio of the elastic DBE hazard to elastic MCE hazard xxii List of Abbreviations AI: Artificial Intelligence AISC: American Institute of Steel Construction BC: British Columbia CC-PSW/CF: Coupled Composite Plate Shear Walls/ Concrete Filled CLT: Cross Laminated Timber CORW: Controlled Outrigger Rocking Wall CP: Collapse Prevention CROCW: Controlled Rocking Outrigger Core Wall CSP: Corrugated Steel Plate DBE: Design Base Earthquake DDBD: Direct Displacement-Based Design DLRF: Ductile Linked Rocking Steel Frame DOC: Degree-Of-Coupling DSCW: Dual-Pinned Self-Centering Coupled CLT Shear Wall EEDP: Equivalent Energy Design Procedure EBD: Energy Based Design ELSDOF: Equivalent Linear Single-Degree-Of-Freedom xxiii ENLSDOF: Equivalent Nonlinear Single-Degree-Of-Freedom ENT: Elastic No-Tension FBD: Force-Based Design FEMA: Federal Emergency Management Agency GM: Ground Motion IO: Immediate Occupancy ISD: Inter-Story Drift LED: Lead Extrusion Damper LFRS: Lateral Force Resisting System LS: Life Safety MCE: Maximum Credible Earthquake MDOF: Multi-Degree-Of-Freedom NBCC 2020: National Building Code of Canada 2020 NLTHA: Non-Linear Time History Analysis OpenSees: Open System for Earthquake Engineering Simulation PT: Post-Tension RCB: Rocking Column Bases RR: Rapid Return xxiv RSA: Response Spectrum Analysis SCCW: Self-Centering Coupled Wall System SCFD: Self-Centering Conical Friction Damper SC-MRCSW: Self-Centering Modular Rocking Composite Sandwich Wall SC-MRCSWS: Self-Centering Modular Rocking Composite Sandwich Wall System SCNFD: Self-Centering Nonlinear Friction Damper SDOF: Single-Degree-Of-Freedom SFRS: Seismic Force Resisting System SLE: Service Level Earthquakes SSI: Soil-Surface Interaction TMD: Tuned Mass Dampers VCD: Viscoelastic Coupling Dampers VE: Viscoelastic WWFF: Welded Wide Flange Fuses xxv Acknowledgements I would like to express my deepest gratitude to my mentor and supervisor, Professor Tony T.Y. Yang for his constant support, invaluable guidance and encouragement throughout the course of this research. His guidance has been monumental in shaping this thesis, as well as my personal growth to be a researcher and engineer. I would also like to thank Professor Musab Al-Janabi for his support and guidance in helping me refine my thesis and dedicating hours to provide valuable feedback. I am profoundly thankful to my family, their patience, love and unyielding support have made this journey possible. To my parents, for their sacrifices and unconditional support, which became the foundation for my achievements. To my siblings, for their encouragement and laughter, their presence has been my source for strength and resilience. To my partner, Archana, thank you for your constant support, patience and encouragement. Not only as my partner, but as a colleague and friend. Lastly, I want to acknowledge all those who offered support, advice and encouragement. Their time and knowledge have helped me tremendously throughout this journey. xxvi Dedication To my family, for all their love and support. 1 Chapter 1: Introduction 1.1 Background In recent years, the global demand for housing and infrastructure has increased at an unprecedented rate (ESCAP , 2023). This has led to rapid urbanization, where the infrastructure needs to be built at a rapid scale and yet be resilient and sustainable. To address these issues, modular construction methods have emerged as a promising alternative to conventional building practices. Modular construction can offer faster build times, better quality control, reduced on-site labor requirements, reduced waste and a more sustainable construction alternative to traditional construction methodology (Jin et al., 2020). Figure 1 shows the major types of modular construction. Modular construction can usually be classified as 1) 2-D panelized systems or 2) 3-D volumetric systems (Thai et al., 2020). 2-D panelized systems consist of building components, such as, walls and floor/roof panels, that are then assembled on-site. On the other hand, volumetric system delivers fully built modules that are stacked and connected with other modules on site. The panelized system approach helps with transportation of the system and allows for more on-site flexibility during construction. The volumetric systems usually require more detail to the transportation of the units but offer faster on-site construction. a b) Figure 1 Modular fabrication types: a) Panelized 2-D; b) Volumetric 3-D (Thai et al., 2020) 2 Similar to conventional construction, modular construction also requires a lateral system to resist wind and seismic forces. In modular construction, the lateral stability is either achieved by the modules themselves acting as shear walls/brace or moment frames or by having a separate core or lateral system attached to the modules. Figure 2 shows the construction scheme for Murray Grove, London, UK, a nine-story timber building that utilizes panelized modular construction. In this case, the lateral stability is achieved through timber shear walls acting as the core for stairwells and elevators located at the center of the building (Waugh et al., 2010). Figure 3 shows the construction of Ten Degrees, Croydon, UK, a 38-story tower that utilizes steel-concrete volumetric modular construction with a concrete core for stability (Maleki et al., 2024). The modules are made of steel frames with concrete panels for floors and roof. The lateral stability for the tower is achieved through connecting the modules to a concrete core. The concrete core is constructed first and then the modules are stacked. The project took 26 months from excavation to completion, which is 42% faster compared to traditional construction methods (Vision Volumetric, 2022). Figure 2 Murray Grove panelized construction scheme (Waugh et al., 2010). 3 Regardless of the type of construction method used, buildings and infrastructure, especially in high seismic zones, need to be safe, sustainable and resilient. The current standard for structural design allows the building’s lateral force resisting system (LFRS) to be damaged during an earthquake to dissipate energy. This approach focuses on achieving Life Safety (LS) performance objective, which is typically achieved through significant inelastic deformations in the LFRS. The inelastic deformations can lead to excessive residual drifts in the structure, which can be difficult and costly to repair. To achieve superior performance objective, low damage LFRS have been developed. Low damage LFRSs are designed to limit structural damage, while providing sufficient energy dissipation and re-centering capabilities. Innovative structural systems and devices are utilized to allow structures to remain operational, and easily repairable after a seismic event. Hence, the reduced downtime and repair demands makes these low damage LFRSs more resilient with a lower life-cycle cost. Several low damage LFRSs have been proposed in the past. Structural systems such as, rocking concrete shear wall (Khanmohammadi & Heydari, 2015), ductile linked rocking steel frame (DLRF) (F. Wang et al., 2021), dual-pinned self-centering coupled CLT shear wall (DSCW) Figure 3 Ten Degrees tower construction (Maleki et al., 2024) 4 (Lepine-Lacroix & Yang, 2023) and controlled rocking outrigger core wall (CROCW) (Tobber et al., 2023), offer superior seismic performance and minimize overall damage to the structure.. However, there is a gap for a resilient and low damage seismic system that utilizes modular construction technology to not only boost structural performance but also incorporate construction and sustainability benefits from modular construction. 5 1.2 Research scope and objectives The research scope of this thesis focuses on developing a high-performance modular system which can be constructed quickly, offers resilient seismic performance with low damage. This is achieved through the following objectives: Objective #1: Developing a design procedure to design the proposed system. Objective #2: Demonstrating the seismic performance of the proposed system. 1.3 Thesis organization This thesis is organized into 8 chapters, and the content of each chapter is summarized below: Chapter 1: Describes the background, scope and objectives of this thesis. Chapter 2: Overview of research in different types of energy dissipating systems, energy dissipating dampers/fuses and design methodologies Chapter 3: Presents an overview of the novel self-centering modular rocking composite sandwich wall (SC-MRCSW). Chapter 4: Describes a design procedure that can be used to design the SC-MRCSW. Chapter 5: Describes how the design procedure described in Chapter 4 was used to design the SC-MRCSW of a 15-story prototype building located in Vancouver, Canada. Chapter 6: Presents the numerical modelling of SC-MRCSW of the prototype building. Chapter 7: Discusses the results of dynamic analysis conducted for the numerical model developed in Chapter 6 6 Chapter 8: Presents a summary of the work presented in this thesis and conclusions. This chapter also presents recommendations for future studies. 7 Chapter 2: Literature review This chapter reviews various modular systems, energy dissipation devices, low damage LFRS and design methodologies for the current state of best practices. Section 2.1 discusses the advancements in modular construction methods, specifically for high-rise structures. Section 2.2 reviews the state-of-the-art energy dissipation devices that have been developed to improve the seismic performance of structures. Section 2.3 presents an overview of high performance LFRS, with a focus on low damage rocking systems. Finally, Section 2.4 summarizes different seismic design methodologies used in building codes and industry practice. 2.1 Modular systems for high-rise construction Modular construction is gaining popularity due to faster speed of construction, better quality control, improving sustainability and reduction of on-site waste and labor resources. Wang et al., (2020) propose a volumetric modular lateral force resisting system which consists of precast concrete shear walls. Figure 4 shows the precast modules and their connection using cast-in place stripes on site. Figure 4 Precast modular concrete system for tall buildings (Wang et al., 2020) 8 The precast module consists of floor and roof slabs connected to walls. The modules are connected together onsite through cast-in-place strip joints. Energy dissipation occurs through the deformation of the wall at base, similar to typical concrete shear wall LFRS. Wang et al., (2020) also shows the design for a prototype 40 story building located in Hong Kong (Figure 5). A nonlinear dynamic analysis for wind and earthquake loading is conducted to show the performance of the proposed system. According to the dynamic analysis, the system shows adequate response for both wind and earthquake loading. Higher mode response has a significant effect on the forces induced in the wall system. The dynamic analysis also shows the possibility of a second plastic hinge forming at the mid-height of the building after plastic deformation occurs at the bottom. This would require the system to be inspected and evaluated for repairs or demolition after a significant seismic event. Figure 5 Prototype 40 story building using the precast concrete modules (Wang et al., 2020) 9 Research by Varma et al. has proposed a coupled modular lateral force resisting system combining steel and concrete called coupled composite plate shear walls/ concrete filled (CC-PSW/CF) system (Varma et al., 2011; Varma et al., 2019). This system is also recognized as SpeedCore in American Institute of Steel Construction (AISC). The system comprises of steel plate modules with tie bars and shear studs bonded with concrete in the middle. The empty steel modules are transported on-site and erected. The steel modules act as reinforcement for the concrete, as well as the formwork to pour the concrete. Figure 6 shows the typical module section as well as the assembled CC-PSW/CF system. a) b) Figure 6 CC-PSW/CF system; a) panel assembly, b) assembled wall section (Varma et al., 2019). 10 The CC-PSW/CF system greatly reduces the construction time in tall buildings. The steel modules can be prepared in advance and transported to site. Varma et al. (2019) have shown that the modules themselves have enough rigidity to withstand concrete pouring and act as formwork for construction activity. This reduces the typical 14-28 day wait period for curing the concrete core before continuing to build vertically (M.Post, 2023). The use of steel plates also alleviates the effort of assembling complex and often congested rebar cages for both zones in a typical concrete core-wall and coupling beams. Analytical and experimental results on dynamic performance of the CC-PSW/CF system show that it can adequately dissipate energy for both wind and seismic events. Figure 7 shows force-deformation mechanism for the CC-PSW/CF system (Broberg et al., 2022). Energy dissipation is typical as other coupled core-wall systems where the energy is dissipated through plastic deformation of coupling beams between the walls, followed by plastic hinge forming at the base. Therefore, after a significant seismic event, the coupling beams and the core-wall need to be investigated for damage and repair. Figure 7 Force-deformation performance of CC-PSW/CF for lateral loads (Broberg et al., 2022) 11 2.2 Energy dissipation devices Specialized energy dissipation devices have been developed and implemented to enhance the seismic performance of seismic force resisting systems. Among these energy dissipation devices, designated energy dissipating dampers for coupling beams have been proposed to be used with shear wall systems. For instance, Yang et al. (2021) proposed the welded wide flange fuses (WWFF). WWFF are assembled using commonly available welded wide flange sections, the concept is to dissipate energy through the shear deformation of the web while keeping the flanges capacity protected (Yang et al., 2021). Figure 8 shows the undeformed and deformed shape for the damper. Experimental testing on the WWFF shows a reliable hysteresis response to dissipate energy. However, once the web deforms after an earthquake, there is permanent deformation and damage to the yielding element, and the fuse must be inspected for replacement/repair. Figure 8 WWFF; a) Assembly, b) Mechanism (Yang et al., 2021). 12 Similarly, Constantin et. al. proposed a viscoelastic coupling dampers (VCDs) (Montgomery et al., 2021). The VCDs consist of layers of viscoelastic (VE) material bonded to steel plates. The sandwiched steel plates extend out and can be connected to a variety of different applications, such as walls, steel fuses, braces etc. Figure 9a. shows the assembly for the VCDs, and Figure 9b. shows the hysteresis response. The viscoelastic material reduces initial vibration response of the structure as it adds additional damping through friction between the VE material and steel plates. The VCDs can replace tuned mass dampers (TMDs) in buildings to add more distributed damping throughout a structure rather than having focused damping around certain modes. This can be potentially used for scenarios in tall buildings where high wind loads can cause unfavorable dynamic response. However, for high seismic zones, the VCDs need to be connected to a steel fuse to dissipate significant energy induced during an earthquake. The energy dissipation depends on the steel fuse used, which will usually be designed for plastic response and be damaged after a significant seismic event, causing permanent deformation in the VCD. a) b) Figure 9 VCDs; a) Assembly. b) Energy dissipation (Montgomery et al., 2021). 13 Self-centering dampers are energy dissipation devices that provide energy dissipation along with force restoring mechanism where the damper restores to its original position. The self-centering behavior is achieved by combining energy dissipation mechanisms with restoring elements such as springs, post tension tendons (PT) or shape memory alloy (SMA). Figure 10 shows the assembly for Self-Centering Nonlinear Friction Damper (SCNFD) by Yang et al. (2023). The SCNFD consists of combination of plates and springs. As shown in Figure 10, plate A consists of vertically slotted holes while the two plate B elements have circular holes. This configuration ensures that the damper displaces vertically as other degrees of freedom are restricted. The energy dissipation occurs through the friction plates sandwiched between plate A and plate B connected through clamped bolts. The self-centering property of the damper is achieved by two compressed springs connected to the pivot plate. Figure 11 shows the force-deformation plot for the SCNFD. As the damper moves vertically, plate A, connected to the pivot plate, slides between the friction plates to dissipate energy while the springs connected to the pivot plate provide the self-centering response. This makes the SCNFD highly customizable as the energy dissipation and self-centering can be fine tuned for specific scenarios. Figure 10 Components of Self-Centering Nonlinear Friction Damper (SCNFD) (Yang et al., 2023). 14 2.3 Low damage LFRS Another way to enhance resiliency of traditional seismic systems is to avoid plastic deformation in the structure. For example, plastic hinging at the base of the wall can cause significant residual deformation in shear wall systems, rendering the structure unusable after a seismic event. One way to avoid plastic deformation at the base is by letting the wall rock during a seismic event with a damper connecting the wall to the foundation or post-tensioned (PT) strands. The rocking wall mechanism can significantly enhance the resiliency of a lateral force resisting system. Research by Khanmohammadi & Heydari, (2015) shows the seismic behavior of concrete shear walls can be improved using rocking mechanisms. In this study, multiple rocking systems along with energy dissipating devices are analyzed to study the seismic performance of concrete shear walls. Figure 12 shows the physical testing of the rocking model and the parametric rocking segments considered for this study. Figure 11 Force-deformation response for SCNFD (Yang et al., 2023). 15 This research establishes that implementing robust rocking mechanisms with energy dissipating devices can result in mitigating higher mode effects along the shear wall, while maintaining similar drift ratios as traditional shear wall systems and minimizing residual drifts post seismic event. Another study by conducted by Wang et al. (2021) proposed a ductile linked rocking steel frame (DLRF) (Wang et al., 2021). The DLRF system connects two rocking steel braced frames with a corrugated steel plate (CSP) link element. The bottom of steel braced columns is connected to the foundation via rocking column bases (RCBs). The RCBs are restrained in the lateral direction but released vertically. The RCBs have fuse attached to it that exhibit flag-shaped hysteric response. Figure 13 shows the RCBs and the DLRF system mechanism. Figure 13 DLRF RCB assembly and rocking mechanism (Wang et al., 2021). Figure 12 Rocking wall experimental setup and prototypes analyzed (Khanmohammadi & Heydari, 2015). 16 The seismic analysis of DLRF shows it can achieve sufficient energy dissipation along with self-centering after a seismic event. Overall, the DLRF system exhibits sufficient safety margin against collapse. However, since the column is allowed to rock, the foundation can experience significant rotation/overturning forces and must be designed carefully to accommodate the uplifting mechanism of the steel column. Research by Lepine-Lacroix & Yang, (2023) shows the application of using SCFDs with pinned CLT shear walls called dual-pinned self-centering coupled CLT shear wall (DSCW). This novel system utilizes SCFDs as coupling beams to link the CLT shear walls. The walls are pinned at the bottom, hence avoiding any damage to the wall base after a seismic event. Figure 14 shows the DSCW system. The system dissipates energy and achieves self-centering through the SCFD flag shape hysteresis. The DSCW shows it can achieve multiple seismic performance objectives through Equivalent Energy Design Procedure (EEDP) and satisfies the performance requirements of FEMA P695. Figure 14 DSCW system assembly (Lepine-Lacroix & Yang, 2023). 17 Research by Tobber et al. (2023) proposes a novel controlled rocking outrigger core wall (CROCW) system for tall buildings. The CROCW integrates a controlled rocking mechanism at the base of the wall to reduce damage to the core-wall after a seismic event. Figure 15 shows the CROCW system (Tobber et al., 2023). This CROCW system consists of two high-performing lateral force resisting systems in each principal direction of the wall. The controlled outrigger rocking wall (CORW) utilizes dampers in the outrigger and the rocking base to dissipate energy and reduce damage to the wall base, where the plastic hinge would normally occur. The other principal direction deploys a self-centering coupled wall system (SCCW) where novel self-centering coupling beams are used along with a rocking base with dampers to dissipate energy during an earthquake and reduce residual drifts after a seismic event. Figure 15 CROCW system assembly (Tobber et al., 2023). 18 2.4 Seismic design methodologies Force Based Design (FBD) Seismic design methodologies have evolved over many years of research, experimental testing and monitoring real world performance of structures during and after a seismic event. Historically, building codes in North America and other parts of the world prescribe a Force-Based Design (FBD) approach to design LFRS for seismic application. In FBD, engineers estimate the seismic demand on the structure using equivalent lateral forces derived from either a Response Spectrum Analysis (RSA) or by simply multiplying the seismic weight of the building with its estimated spectral acceleration value. The forces derived are amplified or reduced based on factors such as the importance of the structure, the ductility and overstrength of the LFRS and the influence of higher mode effect. The yielding components of the LFRS are expected to dissipate energy through plastic deformation, while rest of the structure is capacity designed to ensure the system has sufficient strength and ductility. The FBD approach makes it relatively simple to design the structure. However, the FBD procedure requires iterations to ensure the structure has sufficient strength, stiffness and ductility. Nevertheless, the structure is likely to undergo extensive repair or even be demolished after a significant seismic event. Moreover, FBD typically limits the engineers to use predefined LFRS in the building code, designing novel systems outside the scope of building codes becomes challenging. Direct Displacement-Based Design (DDBD) Direct Displacement-Based Design (DDBD) uses target drift as the primary performance objective. Figure 16 shows the basic design philosophy for DDBD (Priestley et al., 2007). The structure is represented by an equivalent single-degree-of-freedom (SDOF) system with effective mass and height, a performance drift is selected which determines the equivalent viscous damping and the displacement ductility of the system. By knowing the target displacement and the damping 19 parameter, the effective period of the system can be determined. The effective mass and effective period are then used to calculate the secant stiffness of the equivalent system. Finally, the design base shear can be calculated using the secant stiffness and the design displacement. Energy Based Design (EBD) Energy Based Design (EBD) is a performance-based design methodology that utilizes the energy equivalence principle to analyze and design LFRS (Leelataviwat et al., 2002). By quantifying the energy entering the system through seismic shaking and equating it to the energy dissipation capacity of the LFRS, EBD allows the designer to control for strength and displacement together (Yang et al., 2018). This enables EBD to account for more complex non-linear hysteresis along with multiple levels of seismic shaking with no iterations. EEDP is a form of EBD introduced by Yang.et al. (2018) This procedure is discussed in detail in Chapter 4 of this thesis. Figure 16 Design process using DDBD (M. N. Priestley et al., 2007). 20 2.5 Summary This chapter summarizes the recent advancements in modular construction, energy dissipation devices and low damage structural systems to improve seismic resilience. High-rise modular systems have proven to enhance seismic performance, and sustainability, while also maintaining structural integrity under seismic loading. Moreover, the integration of novel energy dissipation devices in high performance structural systems can improve resiliency and reduce damage to the main structure. Despite these latest developments, there is still limited insight in developing a modular seismic system that incorporates advanced energy dissipation devices to minimize structural damage after a seismic event, while also capitalizing on the inherent advantages of modular construction. 21 Chapter 3: Self-centering modular rocking composite sandwich wall (SC-MRCSW) system This chapter presents a novel structural system named Self-Centering Modular Rocking Composite Sandwich Wall (SC-MRCSW) system. The SC-MRCSW system adopts the self-centering coupled wall system (SCCW) and combines it with a modular composite sandwich wall. This chapter highlights the mechanism and targeted performance objectives of the SC-MRCSW system. Section 3.1 discusses the overview and components of the SC-MRCSW system. Section 3.2 presents the system’s targeted performance objectives across varying seismic hazard levels. 3.1 System overview The SC-MRCSW system consists of three distinct components, the modular composite steel-concrete sandwich wall, the self-centering coupling beams and the rocking base with base dampers. Figure 17 shows the overview for the SC-MRCSW system. The modular composite steel-concrete sandwich wall allows the system to benefit from the advantages that come with modular construction, in reducing construction time and improving sustainability. The wall is designed to remain elastic during a seismic event. The earthquake energy induced in the system is dissipated through two mechanisms as shown in Figure 18. The primary energy dissipation mechanism occurs through the self-centering coupling beams, while the secondary energy dissipation occurs through the rocking base with base dampers. The coupling beams utilize the self-centering conical friction damper (SCFD) developed by Yang et al., (2020). The wall is allowed to rock at the base on its toes with dampers attached to each corner of the wall. The self-centering mechanism of the coupling beams along with the rocking behavior of the wall allows for the system to self-center after a seismic event. Dampers are attached to the base to enhance induced seismic energy 22 dissipation. Following sections explain each of the three components that make up the SC-MRCSW system. Figure 17 SC-MRCSW system components Figure 18 SC-MRCSW system mechanism 23 Modular steel-concrete composite wall The modular steel-concrete composite wall is based on coupled composite plate shear walls/ concrete filled (CC-PSW/CF) system. CC-PSW/CF system consists of a concrete core sandwiched between steel plates. The steel plates are connected with tie rods/tension restraint bolts through which the composite concrete-steel interaction occurs as shown in Figure 19. The steel plates confining concrete act as both formwork and reinforcement for the shear wall while the shear transfer between the plates and concrete happens through the tie rods and studs. The SC-MRCSW system is designed to keep the modular steel-concrete composite wall elastic through capacity design while the earthquake energy is dissipated two distinct mechanisms, self-centering coupling beams and rocking base with dampers. Figure 20 shows the potential failure modes for the wall panels. The flexural failure modes for a ductile response of a steel-concrete composite wall include tensile cracking of concrete, crushing of concrete at the wall base/toe, tensile yielding of steel plates, outward buckling of steel plates and tie rod fracture (Eom et al., 2009; Epackachi et al., 2015). Therefore, the composite wall for the SC-MRCSW must be detailed to prevent these failure modes. Figure 19 Typical wall section for steel-concrete composite sandwich wall 24 Self-centering coupling beams The self-centering coupling beams utilize the self-centering conical friction damper (SCFD) developed by Yang et al. (2020). The damper is assembled as a male-female conical cone with clamping plates using post-tension tendons (PT) (Yang et al., 2020). The conical cone is allowed to be displaced in both translation and rotational directions. Figure 21 shows the assembly for the SCFD. Utilizing conical geometry along with disc springs and PT tendons allows the damper to self-center. Numerical and experimental studies have shown that the SCFD provides a stable hysteretic response with consistent energy dissipation and excellent re-centering capability. These characteristics are particularly advantageous in performance-based seismic design, where minimizing damage and downtime post-earthquake is a priority. Figure 20 Typical failure mode for steel-concrete composite wall system (Eom et al., 2009; Epackachi et al., 2015). 25 Figure 22 shows the mechanism and force-deformation response of the SCFD. Damper activation is mostly governed by the initial clamping force of the post-tension tendons (PTs). However, once the damper is activated, i.e. the cone starts sliding, the post activation stiffness becomes a function of the PT force along with the friction between the cones and steel plates. This makes the SCFD force-deformation response adjustable, so the damper can be tuned to address specific energy dissipation requirements. Figure 21 SCFD assembly (Yang et al., 2020). Figure 22 SCFD mechanism and hysteresis response (Yang et al., 2020). 26 The SCFD in the coupled wall application is allowed to slide vertically to dissipate energy. The self-centering coupling beams utilize the SCFD embedded between two beams as shown in Figure 23. Since the initial stiffness of the SCFD is considered reasonably rigid, the stiffness of the coupling beam, 𝑘𝑐𝑏 can be approximated as 𝐾𝑒 = 𝑘𝑐𝑏. However, if the initial stiffness of the self-centering damper used is not considered rigid, the initial stiffness of the coupling beam can be calculated as a series of springs. The elastic stiffness of the steel beam, 𝐾𝑒, is taken as its shear stiffness, 𝐾𝑠, and flexural stiffness, 𝐾𝑏, in series, given by Eq. 3.1-3.3 𝐾𝑒 =𝐾𝑠𝐾𝑏𝐾𝑠 + 𝐾𝑏 (3.1) 𝐾𝑠 =𝐺𝐴𝑤𝐿𝑐 (3.2) 𝐾𝑏 =12𝐸𝐼𝑏𝐿𝑐3 (3.3) Figure 23 Elevation view of self-centering coupling beam 27 Where, 𝐺 is the shear modulus, 𝐴𝑤 is the area of web for the steel beam, 𝐿𝑐𝑏 is the length of coupling beam measured from wall face, 𝐸 is the elastic modulus, and 𝐼𝑏 is the moment of inertia for the steel beam. Figure 24 shows the free body diagram as the inner plate moves to the right. The external force, P, can be calculated using the Eq. 3.4. 𝑃 = 𝐹𝑝𝑡 ∙ 𝐵1 = (𝐹𝑝𝑡0 + 𝑘𝑝𝑡 ∙ 𝛥 ∙ 𝑡𝑎𝑛𝜃) ∙ 𝐵1 (3.4) Where 𝐹𝑝𝑡0 is the initial force in the PT tendons, 𝑘𝑝𝑡 is the initial axial stiffness of the PT tendon and 𝐵1 relates the cone angle to the coefficient of friction between the cones (𝜇′) and the flat plates (𝜇), given by 𝐵1 =𝑡𝑎𝑛𝜃+𝜇′1−𝜇′∙𝑡𝑎𝑛𝜃+ 𝜇. The activation force, 𝑃0, at ∆= 0 is calculated using Eq. 3.5. 𝑃0 = 𝐹𝑝𝑡0 . 𝐵1 (3.5) The maximum sliding force, 𝑃𝑚, at ∆= ∆𝑚 is given by Eq. 3.6. 𝑃𝑚 = (𝐹𝑝𝑡0 + 𝑘𝑝𝑡 ∙ 𝛥𝑚 ∙ 𝑡𝑎𝑛𝜃) ∙ 𝐵1 (3.6) Figure 24 a) Free body diagram for SCFD; b) SCFD hysteresis (Yang et al., 2020). 28 The post yield stiffness, 𝑘𝑝, is given by Eq. 3.7. 𝑘𝑝 =𝑃𝑚 − 𝑃0𝛥𝑚= 𝑘𝑝𝑡 ∙ 𝑡𝑎𝑛𝜃 ∙ 𝐵1 (3.7) Similarly, the unloading force 𝑃𝑢 at ∆= ∆𝑚, the residual force 𝑃𝑟 at ∆= 0 and unloading stiffness, 𝑘𝑢, is given by Eq. 3.8-3.10. 𝑃𝑢 = (𝐹𝑝𝑡0 + 𝑘𝑝𝑡 ∙ 𝛥𝑚 ∙ 𝑡𝑎𝑛𝜃) ∙ 𝐵2 (3.8) 𝑃𝑟 = 𝐹𝑝𝑡0 . 𝐵2 (3.9) 𝑘𝑢 =𝑃𝑢 − 𝑃𝑟𝛥𝑚= 𝑘𝑝𝑡 ∙ 𝑡𝑎𝑛𝜃 ∙ 𝐵2 (3.10) Where B2 is given by 𝐵2 =𝑡𝑎𝑛𝜃−𝜇′1+𝜇′∙𝑡𝑎𝑛𝜃− 𝜇. During unloading, 𝐹𝑝𝑡. 𝑘𝑝𝑡 and 𝑡𝑎𝑛𝜃 will always be positive, therefore, the polarity of B2 governs the unloading hysteresis. If B2 is positive, then the unloading force, residual force and unloading stiffness will be positive and vice versa. However, if 𝜃 = 𝜃𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙, then B2 will be zero. The critical angle, 𝜃𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙, is given by Eq. 3.11. 𝜃𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 = atan (𝜇 + 𝜇′1 − 𝜇 ∙ 𝜇′) (3.11) 29 Rocking base with friction dampers Typically, shear walls are fixed at the base to resist lateral forces and dissipate energy through plastic deformation. However, since the objective of this novel system is to keep the wall damage free with minimal residual drifts, a rocking shear wall mechanism is considered. Rocking shear walls allow for intentional uplift at the base of the wall during a seismic event. The walls are designed to rock in a controlled manner, where the energy dissipation occurs through additional energy dissipating devices and re-centering through either the gravity load acting on the wall or post-tensioning. For the SC-MRCSW system, the wall is designed to uplift and rock about its toes while axially restrained through base dampers. The addition of base dampers enhances the energy dissipation of the system, specially under extreme seismic events. The foundation for rocking walls plays an important role in ensuring adequate and predictable rocking performance. The foundation needs to reliably transfer large axial and shear forces during rocking while evenly distributing the forces between the wall and foundation. Research and experimental testing for rocking walls suggests the foundation preparation include a high strength grouting layer to ensure even contact between the wall and foundation, especially during re-seating where uneven contact can lead to unusually high stresses at the rocking toe of the wall (Liu et al., 2023). A shear key is also recommended to ensure adequate shear transfer between the foundation and wall, slippage between the wall and foundation can lead to reduced energy dissipation within the system (Kalliontzis & Nazari, 2021). Lead Extrusion Dampers (LEDs) are added to the base of the wall for additional energy dissipation. LEDs consist of a steel shaft attached to a piston, surrounded by a lead core. As the piston moves due to external force, i.e. during an earthquake, the lead crushes and flows around the steel piston 30 (Rodgers et al., 2006). This flow creates the energy dissipation mechanism. Figure 25 shows the section of a LED and the force deformation response. Due to material properties inherent to lead, such as low-melting point and high ductility, the damper is able to provide large amount of stable energy dissipation within a relatively small volume of material. System behavior The initial stiffness of the system depends on the elastic stiffness of the walls and the degree of coupling between the walls, dictated by the stiffness of the coupling beams. As soon as the system reaches the activation point for the coupling beams, the overall stiffness of the system is dictated by the post yield stiffness of the coupling beam and the elastic stiffness of the wall. The type of damper used at the base of the wall can influence the stiffness of the structure as well. If the base damper is elastic-perfectly plastic, then the stiffness of the system needs to take the elastic stiffness of the base damper in series with the stiffness of the system (coupled walls). Whereas, if the base damper is rigid-plastic, then the influence of the base damper stiffness is less apparent on the initial stiffness of the system until the damper is activated. Moreover, due to the nature of coupled wall systems, there is an inherent uplift from the coupling beams at one of the walls while an equal but opposite compressive force acts on the other wall. Figure 25 (a) Section for LED; (b) Force-deformation response for LED (Rodgers et al., 2006) 31 This affects the design force of the base dampers as one wall will experience an uplift, referred to as the “tension wall”, while the other wall will experience an additional compressive force, referred to as “compression wall” as shown in Figure 26. The moment at the base of the wall can be calculated using Eq 3.12 and 3.13. 𝑀𝐶 = (𝑃𝑔 + 𝑃𝑝). 𝑥𝑐𝑔 + 𝑓𝑏 ∗ 𝐵𝑤 (3.12) 𝑀𝑇 = (𝑃𝑔 − 𝑃𝑝). (𝐵𝑊 − 𝑥𝑐𝑔) + 𝑓𝑏 ∗ 𝐵𝑤 (3.13) where, 𝑀𝐶 is the moment in the compression wall, 𝑀𝑇 is the moment in the tension wall, 𝑃𝑔 is the gravity load acting on the wall, 𝑃𝑝 is the axial force in the wall due to coupling beams, 𝐵𝑤 is the length of the wall, 𝑥𝑐𝑔 is the distance to the edge of the wall from its center of gravity and 𝑓𝑏 is the force in the dampers at the base of the wall. Figure 26 Forces at the base of the wall during rocking 32 3.2 Performance objectives The SC-MRCSW system is designed to satisfy multiple performance objectives over varying earthquake intensities as shown in Figure 27 . At service level earthquakes (SLE), the SC-MRCSW system is designed to achieve immediate occupancy (IO), where all the structural components are designed to remain elastic. At the design base earthquake (DBE) shaking intensity, the SC-MRCSW system is designed to dissipate the earthquake energy through friction sliding of SCFDs, while the remaining structure is capacity protected to remain undamaged. This allows the SC-MRCSW system to achieve rapid return (RR) performance objective, where only SCFDs need to be inspected and replaced if needed, while the remaining structure is designed to remain elastic. At the maximum credible earthquake (MCE), the wall piers are designed to uplift, and the earthquake energy is dissipated through yielding the base dampers and the SCFDs. The collapse prevention (CP) performance objective is provided by a combination of two of these yielding mechanisms, while all other structural components of SC-MRCSW system are capacity designed to remain undamaged. Figure 27 shows the plastic mechanism and idealized trilinear force-deformation of the proposed SC-MRCSW system. Figure 27 Idealized force-deformation response for the SC-MRCSW system. 33 3.3 Summary This chapter presents the conceptual development of a novel high performance modular system named Self-Centering Modular Rocking Composite Sandwich Wall (SC-MRCSW) system. The system combines a modular composite steel-concrete wall with novel energy dissipation components and controlled rocking with base dampers to establish a promising solution for fast construction with high seismic performance while ensuring rapid post-disaster rapid post seismic recovery. 34 Chapter 4: Design procedure for SC-MRCSWS To ensure the SC-MRCSW system can achieve multiple performance objectives at different shaking intensities as presented in Figure 27, equivalent energy design procedure (EEDP) proposed by Yang et al., (2018) is utilized. EEDP uses the energy-based design approach to size the yielding structural elements which allow designers to satisfy both the stiffness and strength of the system at different levels of shaking intensities. EEDP is based on the principle of energy equivalence between the nonlinear seismic response of a structural system and equating that stored energy to a more simplified, linear structural system with well-defined properties. The underlying assumption behind EEDP is that during a seismic event, the total energy entering a structural system must be absorbed and dissipated through a combination of mechanism within the system. The energy dissipation can be classified into following categories: • Strain Energy, 𝐸𝑎- This is the energy dissipation stored in a linear elastic structural system. • Hysteric energy, 𝐸ℎ- This is how most energy entering a system is dissipated. Essentially, this is the energy absorbed by the structural system through inelastic deformation of structural components (plastic hinge formation in a lateral force resisting system) or specialized energy dissipation devices (fuses, dampers and friction devices) • Elastic strain energy, 𝐸𝑠𝑒- The is the recoverable portion of energy stored in elastic components of the structural system, e.g. rocking joints, PT tendons, shape memory alloys etc. This portion of the energy is what allows a structural system to recenter after a seismic event • Damping and Kinetic Energy, 𝐸𝑑 + 𝐸𝑘- Damping and Kinetic energy is not explicitly accounted for in EEDP but it is implicitly considered as a part of the transient response of 35 the structural system during an earthquake. Moreover, most of the Kinetic energy is converted into hysteric energy (𝐸ℎ). The EEDP methodology simplifies this conversion of energy by simplifying the dynamic response of a multi-degree-of-freedom (MDOF) structure into an equivalent single-degree-of-freedom (SDOF) system. The elastic energy, 𝐸𝑎, stored in an equivalent linear single-degree-of-freedom system (ELSDOF) can be equated to the 𝐸𝑠𝑒 and 𝐸ℎ stored in an equivalent nonlinear single-degree-of-freedom system (ENLSDOF). However, to calculate the energy stored in an ENLSDOF system, a non-linear analysis is required which is a limiting factor for designers looking to design performance based novel structural systems since the components and size of structural system will need to be designed and iterated initially. In-lieu of this iterative method, Yang et al. propose the energy stored in an ENLSDOF can be approximated by pushing the ENLSDOF monotonically to the desired energy dissipation required for design through an energy modification factor, 𝛾. Eq 4.1 below summarizes this concept as ∆𝐸𝐸 = ∆𝐸𝑁𝐷 = 𝛾𝐸𝑁𝑀 (4.1) where; ∆𝐸𝐸 is the total strain energy stored in a system ∆𝐸𝑁𝐷 is the total non-linear dynamic energy stored in a system 𝐸𝑁𝑀 is the total non-linear monotonic energy stored in a system Figure 28 illustrates the concept of EEDP. The force-deformation response of a structure is approximated by an ENLSDOF system. The vertical axis shows the base shear, which is calculated using the first mode spectra acceleration of the ENLSDOF multiplied by the seismic mass. The 36 horizontal axis represents the roof displacement calculated using the first mode spectra displacement of the ENLSDOF multiplied by the higher mode effect. The EEDP for SC-MRCSW system is a modified version of the original EEDP proposed by Yang et al., 2018. The modified EEDP is proposed by Tobber et al., 2023. The original proposed EEDP calculated the energy modification factors for a bi-linear force deformation response of the system while the modified EEDP calculated the required dynamic factors for the tri-linear dependent system. This modified procedure utilizes the same concept by equating the ENLSDOF and ELSDOF. EEDP for SC-MRCSW system is shown in the following step by step procedure. For derivations of equations please refer to work done by Tobber et al., 2023. Figure 28 EEDP concept (Yang et al., 2018). 37 4.1 Step 1: Select earthquake shaking intensities The first step of EEDP is to select the seismic hazard intensities and the corresponding objectives of the system. For the SC-MRCSWS, the SLE, DBE and MCE determine the IO, RR, CP performance objectives, respectively. Once the seismic hazard has been identified, a demand capacity spectrum can be created as shown in Figure 29. The base shear is determined by multiplying the seismic mass (m) by spectral acceleration (Sa) of the ELSDOF and dynamic factor (𝛽0). The roof displacement of the multi degree-of-freedom (MDOF) is estimated by multiplying the spectral displacement (Sd) with displacement modification factor (𝐶𝑜). The displacement modification factor is needed to account for higher mode effects. This factor converts the displacemnt of single degree-of-freedom systems (SDOF) to MDOF. 4.2 Step 2: Design of SC-MRCSW system for SLE intensity At the SLE shaking intensity, SC-MRCSW system is designed to meet the IO performance objective, where the system is designed to remain elastic. At this shaking intensity, the yield base shear (Fy) or the yield displacement (∆𝑦) can be selected from the hazard demand curve shown in Figure 29 Demand capacity curve based on seismic hazard intensity 38 Figure 30. This allows the designer to calculate the corresponding yield displacement or base shear, respectively. Once the yield base shear and displacement are selected, the period (𝑇𝑛) of SC-MRCSW system can be calculated using Eq. 4.2. 𝑇𝑛 = 2𝜋√𝑚∆𝑦𝐶0𝐹𝑦= 2𝜋√𝐶0𝑠𝑑(𝑇𝑛)𝛽𝑜𝑠𝑎(𝑇𝑛) (4.2) where 𝑚 is the building mass; ∆𝑦 is the roof displacement of the SC-MRCSWS; 𝐶0 is the displacement modification factor; and 𝐹𝑦 is the base shear of the SC-MRCSWS. At this stage of the design, the geometry and mass can be estimated through architectural consultation. In this case, the fundamental period can be estimated by using Eq. 4.3. T1,SC−MRCSWS ≈ 1.85√𝑚H3E𝑠ITe (4.3) where H is the total height of the wall; Es is the elastic modulus of steel; ITe is the effective moment of inertia of the wall, determined using parallel axis theorem considering effective area of each pier and the moment of inertia of each wall, shown in Eq. 4.4. Figure 30 Selecting performance objectives based on design period 39 𝐼𝑇𝑒 ≈ 𝛼2A𝑤,𝑒𝑓𝑓𝑑𝑐2 + 4𝐼𝑤 (4.4) where A𝑤.𝑒𝑓𝑓 is the effective cross-sectional area of a wall pier; 𝐼𝑤 is the moment of inertia of the wall; 𝑑𝑐 is the distance from the centroid of the wall pier to the centroid of the core wall; and 𝛼2, shown in Eq. 4.5, is a stiffness factor which relates the coupling beam stiffness to the stiffness of the wall. 𝛼2 = (0.06𝐻𝑑𝑐+ 0.3) 𝛼c ≤ 𝛼c2 (4.5) where 𝛼c is shown in Eq. 4.6. A 𝛼c=1 indicates infinitely rigid coupling beams and 𝛼c=0 indicates negligible coupling beam stiffness. 𝛼𝑐 =11 +Es𝐴𝑤,𝑒𝑓𝑓𝑛f𝐻𝑘𝑐𝑏 (4.6) where 𝑛f is the number of stories; Es is the elastic modulus of the wall; 𝑘𝑐𝑏 is the initial stiffness of the coupling beams. 4.3 Step 3: Design of SC-MRCSW system for DBE intensity After estimating the initial stiffness of the system in step 1, the performance of SC-MRCSW system at DBE intensity can be determined. In this step, the design base shear (𝐹𝑝), design displacement (∆𝑝) and the post yielding stiffness of the system can be determined as shown in Figure 31. 40 Using equivalent energy concept, the elastic energy (Δ𝐸𝐸1) under ELSDOF must be dissipated by the non-linear dynamic energy (Δ𝐸𝑁𝐷1) under ENLSDOF. The elastic energy can be calculated by Eq. 4.7 Δ𝐸𝐸1 =12(𝐹𝐷𝐵𝐸 + 𝐹SLE)(Δ𝐷𝐵𝐸 − Δ𝑆𝐿𝐸) (4.7) And the corresponding energy dissipated by ENLSDOF (Δ𝐸NM1) under monotonic pushover is given by Eq. 4.8: Δ𝐸NM1 =12(𝐹𝑝 + 𝐹SLE)(Δ𝑝 − Δ𝑆𝐿𝐸) (4.8) where 𝐹𝑝 is design base shear at DBE and Δ𝑝 is the design roof displacement at DBE. The nonlinear monotonic energy (Δ𝐸NM1) can be converted to nonlinear dynamic energy (∆𝐸𝑁𝐷1) using an energy modification factor (𝛾𝑎) as shown in Eq 4.9. Figure 31 Performance criteria at DBE intensity 41 ∆𝐸𝐸1 = ∆𝐸𝑁𝐷1 = 𝛾𝑎Δ𝐸NM1 (4.9) where 𝛾𝑎 is the energy factor that converts the energy dissipated by the monotonic pushover of the system to energy dissipated by dynamic loading as the intensity level goes form SLE to DBE. The energy modification factor 𝛾𝑎 for this system can be calculated by Eq 4.10. 𝛾𝑎 = (3.37𝑏 − 2.5)Φ𝑝 − 2.17𝑏 + 2.8 (4.10) where Φ𝑝 = ratio of design base shear at DBE (𝐹𝐷𝐵𝐸) over the design base shear at SLE (𝐹𝑆𝐿𝐸) and b is the post yielding stiffness of the system. The post-yielding stiffness of the system (b) is related to the post-yielding stiffness of the coupling beams. If the coupling beams have minimal post-yielding stiffness, then the lateral stiffness of the system is completely dependent on the lateral stiffness of the walls. If the post-yielding stiffness of the coupling beam remains elastic, then the post-yielding stiffness of the system (b) equals to 1. Eq 4.11 shows this relationship as 𝑏 ≈ITe,post𝐼𝑇𝑒≈(𝛼2kpA𝑤,𝑒𝑓𝑓𝑑𝑐2 + 4𝐼𝑤)(𝛼2A𝑤,𝑒𝑓𝑓𝑑𝑐2 + 4𝐼𝑤) (4.11) where (𝛼2kp) is a stiffness parameter as shown by Eq 4.12. 𝛼2kp = (0.06𝐻𝑑𝑐+ 0.3) 𝛼cp ≤ 𝛼cp2 (4.12) where (𝛼cp) is the relative stiffness parameter of the coupling beams to the wall calculated by Eq 4.13. 42 𝛼𝑐𝑝 =11 +Es𝐴𝑤,𝑒𝑓𝑓𝑛f𝐻𝑘𝑐𝑏,𝑝 (4.13) Where (𝑘𝑐𝑏,𝑝) is the post-yield stiffness ratio of the coupling beams. By substituting Eq 4.7 and 4.8 into Eq. 4.9, the design base shear (𝐹𝑝) and design displacement (∆𝑝) can be determined by Eq 4.14 and Eq 4.15, respectively. 𝐹𝑝 = 2Δ𝐸𝐸1𝛾𝑎(Δ𝑃 − 𝛥𝑆𝐿𝐸)− 𝐹𝑆𝐿𝐸 (4.14) 𝛥𝑝 =𝐹𝑝 − 𝐹𝑆𝐿𝐸𝑘𝑜b+ 𝛥𝑆𝐿𝐸 (4.15) where 𝑘𝑜 is the elastic stiffness of the system. 4.4 Step 4: Design of SC-MRCSW system for MCE intensity In this step, the maximum roof displacement (Δ𝑢) of the system is calculated for the MCE hazard as shown in Figure 32. At MCE intensity, the maximum roof displacement (Δ𝑢) can be determined by equating the elastic energy (Δ𝐸𝐸2), shown in Eq. 4.16 to the nonlinear energy (Δ𝐸𝑁𝑀2). Δ𝐸𝐸2 =12(𝐹𝑀𝐶𝐸 + 𝐹𝐷𝐵𝐸)(Δ𝑀𝐶𝐸 − Δ𝐷𝐵𝐸) (4.16) where FMCE is the elastic base shear at the MCE intensity and ΔMCE is the elastic roof displacement at the MCE intensity. The non-linear monotonic energy at this intensity can be calculated by Eq. 4.17 Δ𝐸NM2 = Fp(Δ𝑢 − Δ𝑝) (4.17) 43 where Fp is the elastic base shear at the SLE hazard and Δu and Δpis the elastic roof displacement MCE and roof displacement at SLE hazards respectively. The nonlinear dynamic energy calculated from the ENLSDOF can be converted to nonlinear monotonic pushover energy as shown in Eq. 4.18. The energy modification factor 𝛾𝑏 can be calculated using Eq. 4.19 ∆𝐸𝐸2 = ∆𝐸𝑁𝐷2 = 𝛾𝑏Δ𝐸NM2 (4.18) 𝛾𝑏 = (5𝜆𝑝/μ𝑝 − 9.5)Φ𝑠 − 5.5𝜆𝑝/μ𝑝 + 9 (4.19) where 𝜆𝑝 is the ratio of the DBE base shear to SLE base shear; μ𝑝 is the ratio of the design DBE roof displacement to SLE roof displacement (i.e., μ𝑝 = ∆𝑝/∆𝑆𝐿𝐸); and Φ𝑠 is the ratio of the elastic DBE hazard to elastic MCE hazard. Eq. 4.20 below provides the maximum roof displacement (Δ𝑢) , according to the EEDP philosophy. Δ𝑢 =Δ𝐸𝐸2𝛾𝑏𝐹𝑃+ Δ𝑃 (4.20) where Δ𝐸𝐸2 is the energy calculated from the DBE hazard to MCE hazard. 44 4.5 Step 5: Distribute design forces to the primary and secondary fuse systems Original formulation of EEDP is based on the assumption that the primary and secondary fuse system act independently, and thus results in two bi-linear curves that make up the tri-linear system level response shown in Figure 33a. However, in the self-centering rocking wall system, the coupling beam stiffness, especially after yielding, influences the stiffness of the wall and the rocking mechanism. Due to this change in stiffness, the secondary energy dissipation mechanism forms a tri-linear response as shown in Figure 33b. Figure 32 EEDP for MCE intensity 45 For coupled wall systems, the distribution of force that is resisted by the coupling beams (i.e., 𝐹𝑃𝑅) is estimated based on the degree-of-coupling (DOC). DOC is defined as the ratio of total overturning moment due to coupling action to the total overturning moment at the base of the wall as shown in Eq 4.21 DOC =𝑃𝑝𝑑𝑐∑ 𝑀𝑜𝑡 + 𝑃𝑝𝑑𝑐 (4.21) where 𝑀𝑜𝑡 represents the overturning moment at the bottom of each wall pier. DOC is hard to define before designing the primary and secondary fuses, therefore, Lisa et. al recommend a new parameter called Degree of Axial Stiffness (DAS) defined by Eq. 4.22 DAS =𝛼2𝐴𝑤𝑑𝑐2𝐼𝑇𝑒 (4.22) Figure 33 Independent bilinear fuse system (a); Dependent trilinear system (b) 46 𝐼𝑇𝑒 is the effective moment inertia of the wall, A𝑤 is the cross-sectional area of a wall pier; 𝑑𝑐 is the distance from the centroid of the wall pier to the centroid of the core wall; and 𝛼2 is an empirical reduction factor which is a function of the coupling beam stiffness, 𝑘𝑝. Using DAS, the DOC can be estimated using Eq 4.23 DOC = 0.85𝐷𝐴𝑆 (4.23) Once the degree of coupling is established, the forces can be distributed between the primary and secondary system using Eq 4.24 and 4.25, respectively. 𝐹𝑃𝑅 = DOC ∗ 𝐹𝑦 (4.24) 𝐹𝑆𝐸 = 𝐹𝑝 − 𝐹𝑃𝑅 (4.25) 4.6 Step 6: Design primary fuse system and secondary fuse system dampers Once the energy has been distributed between the primary and secondary system, the coupling beam and damper forces can be determined. To determine the respective design forces, the overall system mechanism is separated into primary and secondary energy dissipating system as shown in Figure 34 and then superimposing the equal work. The SC-MRCSW system is the primary system as shown in Figure 34b while the controlled rocking system using Lead Extrusion Damper (LED) is shown in Figure 34c. The SC-MRCSW localizes all the non-linear deformation in the coupling beams while the base is assumed to be pinned. For the controlled rocking system with LED, the wall piers are assumed to not be influenced by the coupling beams and the non-linear energy dissipation is concentrated to the base LED and rocking mechanism. 47 The design forces for the primary and secondary systems are then distributed as shown in Figure 35. The base shear for the primary system is distributed along the wall by the proposed static load distribution by Chao et al. (2007) shown in Eq. 4.26. λ𝑥 = (β𝑥 − βx+1)1β1 (4.26) where β𝑥 is the coupling beam shear (𝑉𝑝,𝑥), at a given story x normalized to the roof coupling beam shear (𝑉𝑝,𝑟), as shown in Eq 4.27. β𝑥 =𝑉𝑝,𝑥𝑉𝑝,𝑟 (4.27) The coupling beam forces can be determined by equating the external and internal work of both the SC-MRCSW system (shown in Figure 35a) and the secondary system (shown in Figure 35b). Eq 4.28 shows the external work on the primary system. a) b) c) Figure 34 (a) Combined mechanism; (b) Primary fuse (SCFD); (c) Secondary fuse (Base Dampers) 48 𝑊𝑒𝑥𝑡,𝑝𝑟 = 𝜃𝑝𝑟𝐹𝑃𝑅 ∑ 𝜆𝑥ℎ𝑥𝑛𝑥=1 (4.28) Eq 4.29 shows the internal work on the primary system. 𝑊𝑖𝑛𝑡,𝑝𝑟 = 2 ∑ 𝑉𝑃𝑅𝛽𝑥𝑑𝑐𝜃𝑝𝑟𝑛𝑥=1 (4.29) where 𝜃𝑝𝑟 is the base rotation of the walls; 𝑉𝑝,𝑟 is the shear force of the coupling beam at the roof level; 𝑑𝑐 is the distance between the centroid of the wall piers; 𝛽𝑥 is the coupling beam shear distribution factor and 𝜆𝑥 is the force distribution factor. Therefore, the coupling beam design force at roof level can be determined by Eq. 4.30. While the coupling beam shear force at any given level can be determined by Eq. 4.31. 𝑉𝑝,𝑟 =𝐹𝑃𝑅2𝑑𝑐∑ 𝜆𝑥ℎ𝑥𝑛𝑖=1∑ 𝛽𝑥𝑛𝑖=1 (4.30) 𝑉𝑃,𝑥 = 𝛽𝑥𝑉𝑃𝑅 (4.31) Figure 35b shows the distribution of forces for the secondary energy dissipation system. In this system mechanism, the plastic deformations are localized within the base dampers located at the controlled rocking base. Due to the nature of coupling between the two systems (primary and secondary), the rocking mechanism will form a tension wall and a compression wall. The tension wall will experience an uplift from the coupling beams while the compression wall will experience an equal but opposite downward force (𝑃𝑝). The wall piers will recenter by the gravity forces on the respective piers (𝑃𝑔). 49 Eq 4.32 shows the external work on the secondary energy dissipation system. 𝑊𝑒𝑥𝑡,𝑠𝑐 = 𝜃𝑠𝑒𝐹𝑆𝐶 ∑(𝜆𝑥ℎ𝑥)𝑛𝑥=1− Pg𝐵𝑊𝜃𝑠𝑒 + 𝑃𝑝(𝐵𝑊 − 𝑥𝑐𝑔)𝜃𝑠𝑒 (4.32) where 𝜃𝑠𝑒 represents the rotation of the pier at its rocking tow; 𝐵𝑊 is the length of the wall; 𝑥𝑐𝑔 the distance from the rocking toe of the “tension” wall to the centerline of the wall; Pg is the gravity load; and Pp is the result of the axial couple force from the coupling beams. This axial couple provided by the primary energy dissipation system can be calculated using Eq. 4.33. 𝑃𝑝 =𝐹𝑃𝑅𝑑𝑐∑(𝜆𝑥ℎ𝑥)𝑛𝑥=1 (4.33) Eq 4.34 shows the internal work on the secondary system 𝑊𝑖𝑛𝑡 = 2𝐵𝑊𝜃𝑠𝑒 fb (4.34) where fb is the yield force of the dampers at a wall corner. By equating Eq. 4.32 to Eq 4.34, the rocking base damper can be calculated as shown in Eq. 4.35 fb =𝐹𝑆𝐶2𝐵𝑊∑(𝜆𝑥ℎ𝑥)𝑛𝑥=1− Pg + 𝑃𝑝 (1 −𝑥𝑐𝑔𝐵𝑊) (4.35) 50 4.7 Step 7: Capacity design of steel-concrete composite wall Once the yield force of the two energy dissipating system have been designed, the individual wall piers are capacity designed to remain relatively damage free under the required gravity loads and maximum probable lateral loads coming from the two energy dissipating systems. According to the AISC 38 (Design of SpeedCore systems for Steel Structures), the steel plates should comprise of minimum 1% of concrete area and maximum of 10%. The steel plates must be connected through tie bars, the spacing of the tie bars govern the buckling in the steel plates and the stability of the modules during transportation, erection and pouring of concrete. Work done by Zhang et al., (2014) shows the relationship between critical buckling strain and plate slenderness ratio. They conclude that the slenderness ratio of steel plates must follow: Figure 35 Plastic mechanisms for the SC-MRCSW system of a) the primary fuse system and b) the secondary fuse system 51 𝑏𝑢𝑡𝑝≤ 1.2√𝐸𝑠𝐹𝑦𝑠 (4.36) where, 𝑏𝑢 = unsupported length of steel plate, in. (mm) 𝑡𝑝 = thickness of steel plate, in. (mm) The tie bar plays an important role in both the ductility and stability of the system. Work by Varma et al., 2019 shows that the tie bar spacing requirement is based on the stability and shear buckling of empty modules before concrete is poured. The tie spacing, S, is limited as follows: 𝑆𝑡𝑝≤ 1.0√𝐸𝑠2𝛼 + 1 (4.37) 𝛼 = 1.7 [𝑡𝑠𝑐𝑡𝑝− 2] [𝑡𝑝𝑑𝑡𝑖𝑒]4 (4.38) where, 𝑆 = largest clear spacing of ties 𝑡𝑠𝑐 = thickness of composite wall 𝑑𝑡𝑖𝑒 = effective diameter of the tie. The nominal compressive strength 𝑃𝑛𝑜 is calculated as: 52 𝑃𝑛𝑜 = 𝐹𝑦𝑠𝐴𝑠 + 0.85𝑓𝑐′𝐴𝑐 (4.39) The nominal tensile strength 𝑃𝑛 is calculated as: 𝑃𝑛 = 𝐹𝑦𝑠𝐴𝑠 (4.40) The nominal flexure strength of the system can be calculated using plastic stress distribution where the steel plates are assumed to reach yield stress of 𝐹𝑦𝑠 either due to axial compression or tension and concrete stress distribution is limited to 0.85𝑓𝑐′ in compression only. However, since the wall is expected to remain damage free, the flexure strength of the wall should be calculated using the elastic section analysis where the extreme fiber of steel reaches 𝐹𝑦𝑠 and the strain is capped at 0.2%. The in-plane shear behavior of the shear wall is governed by the elastic behavior of concrete cracking in tension and the plane stress in steel plates. Work done by Varma et al. (2014) shows the in-plane behavior of composite shear walls. The nominal shear, 𝑉𝑛, can be calculated as: 𝑉𝑛 =𝐾𝑠 + 𝐾𝑠𝑐√3𝐾𝑠2 + 𝐾𝑠𝑐2𝐹𝑦𝑠𝐴𝑠𝑤 (4.41) 𝐾𝑠 = 𝐺𝑠𝐴𝑠𝑤 (4.42) 𝐾𝑠𝑐 =0.7(𝐸𝑐𝐴𝑐)(𝐸𝑠𝐴𝑠𝑤)4𝐸𝑠𝐴𝑠𝑤 + 𝐸𝑐𝐴𝑐 (4.43) where, 𝐺𝑠 = Shear modulus for steel Since the wall is designed to remain damage free, the elastic shear capacity of the wall is calculated using Eq. 4.43 53 𝑉𝑒 = 0.6 𝐹𝑦𝑠 𝐴𝑠𝑤 (4.44) The shear stiffness of the wall panel can be estimated using the effective elastic shear stiffness shown in Eq. 4.44. (𝐺𝐴)𝑒𝑓𝑓 = 𝐺𝑠𝐴𝑠𝑤 + 𝐺𝑐𝐴𝑐 (4.45) 𝐺𝑐 = Shear modulus for concrete, taken as 0.4 𝐸𝑐. 4.8 Summary This chapter presents a detailed performance-based design procedure that can be utilized to design SC-MRCSW through the application of EEDP. EEDP enables engineers to account for both strength and stiffness across multiple hazard intensities. Moreover, EEDP streamlines the design process by requiring no iterations, as strength and stiffness are presented as a function of stored energy within the system, resulting in valuable time savings. 54 Chapter 5: Prototype building This chapter details the design of a 15-story prototype building using SC-MRCSW system. Section 5.1 presents the location, dimension and loading for the prototype building. Section 5.2 summarizes the EEDP design parameters selected for the prototype building. Section 5.3 and 5.4 detail the distribution of forces for the primary and secondary energy dissipation system, as well as a summary for the design of the modular steel-concrete composite wall. 5.1 Overview A 15-story prototype building was designed to validate the performance of the SC-MRCSW system. The prototype building is located in downtown Vancouver, British Columbia. The shear wave velocity, 𝑉𝑠30, is assumed to be 450m/s, which is classified as site class C as per National Building Code of Canada (NBCC 2020) (Canada, 2022). Figure 36 shows the typical elevation and plan of the building. The prototype building has a total height of 52.5m with a typical height of 3.5m per floor and plan dimensions of 27m by 27m. The SC-MRCSW system is located in the center of the building where a typical concrete corewall would be placed. The seismic weight of the building is estimated to be 6 MN per floor; this included the self-weight of the structural components as well as a super-imposed dead load (SDL) of 1kPa. The floors are designed as 0.25m thick concrete slabs with 0.5m×0.5m rectangular columns providing vertical support on the corners of the building. The floor diaphragms are considered rigid, typical for concrete slabs. The foundation for the building assumes a shear key to prevent the sliding effect from the rocking mechanism. PT is not considered for the wall in this design as the self-weight of 55 the wall along with the vertical force from the slab is considered enough to stabilize the rocking mechanism. The hazard intensity to validate the performance of the SC-MRCSW system is selected as 50% in 30 years for SLE, 10% in 50 years as DBE and 2%in 50 years for MCE, as shown in Figure 37. As discussed in chapter 4, the design criteria for prototype building are selected so that all dampers remain elastic within the SLE hazard. The coupling beams begin to yield at DBE, while the base dampers begin to dissipate energy at MCE. N Figure 36 Plan and elevation view for the prototype building. 56 5.2 EEDP requirement The hazard demand shown in Figure 37 is converted to force-deformation demand using step 1 of the EEDP in Chapter 4. Based on the building dimensions and architectural layout, the seismic mass of the building can be estimated. A 5m coupled wall is assumed at this stage of the design procedure to estimate the fundamental period using eq 4.2. Following steps 3-4 from Chapter 4 yields the EEDP demand for the prototype building shown in Figure 38. Figure 37 Seismic hazard selected for the prototype building Figure 38 EEDP response for the prototype building 57 Table 1 shows the final design summary for the protype building using EEDP mentioned in chapter 4. The fundamental period of the building (T) is calculated to be 1.4s. The SLE (∆𝑦), DBE (∆𝑝) and MCE (∆𝑢) roof displacements are designed as 29.2mm, 91mm and 375mm, respectively. Table 1 Design summary for the prototype building Story L (mm) B (mm) Lcb (mm) tp (mm) Δy (mm) T (s) Δp (mm) Δu (mm) γa γb 15 5000 600 2000 10 29.2 1.4 91 375 1.55 4.02 5.3 Damper design Given the symmetrical plan of the prototype building, the system is analyzed in North-South direction. SCFDs were used to connect modular composite steel-concrete wall panels. LEDs were selected as base dampers. Figure 39 shows the trilinear distribution of forces between the two energy dissipation systems. Figure 39 Shear force distribution between the primary and secondary system 58 The force is distributed between the primary and secondary system using step 5 of the EEDP mentioned in Chapter 4. The force resisted by the primary and secondary system is calculated to be 𝐹𝑃𝑅 = 1580 𝑘𝑁 and 𝐹𝑆𝐸 = 3130𝑘𝑁, respectively. The SCFDs were designed with a post-activation stiffness of 10 kN/mm with the maximum displacement capacity of 80mm. The LEDs were designed to have a yielding force of 7450 kN. Figure 40 shows the distribution of shear force in the coupling beams along the wall height. The wall height is displayed in terms of floors while the shear force is shown as a factor of design shear for the roof coupling beam. The LEDs were designed to have a yielding force of 7450 kN. Table 2 below summarizes the design forces for each damper on every floor. Table 2 Summary of SCFD and base damper design forces. Floor # Coupling Beam Activation Force (kN) Floor # Coupling Beam Activation Force (kN) Damper Force (kN) 1 394.25 9 413.83 7450 2 434.19 10 394.54 3 461.39 11 375.15 4 474.84 12 353.39 5 475.93 13 326.63 6 467.34 14 294.19 7 452.18 15 260.05 8 433.50 - - 59 5.4 Wall design For the design of the composite wall, all structural steel for wall panels is assumed to be ASTM A992/992M with Fy= 350MPa and elastic modulus, Es= 200,000 MPa. The 28day concrete compressive strength for wall panels is taken as f’c= 40 MPa, the elastic modulus is calculated as per CSA A23.3. Using Eq 3.12 and 3.13, the maximum probable moment at the base of the wall is 𝑀𝐶 =103,500 𝑘𝑁. 𝑚 and 𝑀𝑇 = 73,450 𝑘𝑁. 𝑚. The elastic moment capacity of the wall is calculated as 𝑀𝑒 = 125,800 𝑘𝑁. 𝑚. Figure 41 shows the final dimensions for the wall panels section. Figure 42 shows the wall panel elevation. The wall panels are 5m long and 0.6m wide with steel plate thickness of 10mm. 19×15mm dia. tie rods are required along the length of the wall. The required tie rod spacing vertically is calculated to be 250mm along the panel height. The wall panels are designed to be capacity protected as discussed in chapter 3 and 4. Figure 40 Design coupling beam shear force distribution for prototype building 60 Figure 41 Final wall section of the prototype building Figure 42 Final wall elevation for the prototype building 61 5.5 Summary This chapter outlines the design of a 15-story prototype building located in downtown Vancouver, BC using the design procedure presented in Chapter 4. This prototype building is designed for three hazards, 50% in 30 years for SLE, 10% in 50 years for the DBE, and 2% in 50 years for the MCE. All dampers are designed to remain elastic within the SLE hazard. The coupling beams are designed to yield at DBE, while the base dampers are design to fully yield at MCE. A summary of all design components for the prototype building is provided. 62 Chapter 6: Numerical modeling of the SC-MRCSW for the prototype building This chapter presents how the SC-MRCSW system is modelled to evaluate the structural and seismic performance. Section 6.1 of this chapter presents the model overview for the global numerical model, detailing the use of particular elements and material models to accurately capture the behavior of the system. Section 6.2 of this chapter explains the calibration of individual structural components within the global model. All structural components modelled are calibrated against their experimental data, the calibration is scaled to meet the design requirements detailed in chapter 5. Section 6.3 of this chapter presents a brief overview of the modal results for the global model. 6.1 Model overview To assess the performance of the prototype building a detailed numerical model was developed using Open System for Earthquake Engineering Simulation (OpenSees) (McKenna, 2011). The modelling approach focuses on accurately capturing key structural components such as behavior of dampers (LEDs) and fuses (SCFDs) as well as material and geometrical nonlinearity. Due to the symmetry of the prototype building in both directions, only one couple wall system in the N-S direction was modeled to assess the structural and seismic performance. Since the wall is designed to be capacity protected, the wall elements are modelled as a linear elastic element with stresses/strains checked at the end of the analysis. This is done mainly to reduce computational time and ease of convergence for NLTHA. The nonlinearity in this system is lumped at the coupling beams as SCFDs and base dampers as LEDs. Material nonlinearity also exists when modelling the rocking behavior of the system. 63 As shown in Figure 43, the modular steel-concrete composite wall panels are modelled as Timoshenko Beam-Column element with 𝑃 − ∆ transformation. The line element is defined using the effective area and stiffness values of the wall shown in Figure 43. The base of the wall rests on a rigid elastic beam-column element matching the length of the wall. The wall is designed to be capacity protected, therefore, the demand/capacity ratio for the wall is checked in post processing of the NLTHA results to ensure the stress in the wall elements do not exceed the elastic limit for the design of the wall. Figure 43 Numerical model of the SC-MRCSWS for prototype building 64 The rocking of the wall is simulated via corotational truss elements beneath the rigid elastic beam element. The truss elements have their base restrained in all translational degrees of freedom. An elastic no tension material is used for the truss elements to simulate rocking behavior. The LEDs are also modelled at the base of the wall using corotational truss element and Steel02 material with a rigid-plastic force-deformation relationship. The base of the wall is laterally restrained to avoid sliding. A rigid beam column element is used to connect the coupling beams to the wall. The length of the rigid beam column element extends till the face of the wall. The coupling beams are connected to the wall using a steel W360×147 section, modeled as elastic beam column. The SCFDs are modelled as zero length non-linear hinge elements connected to the steel beam section. The flexural and axial properties of the coupling beam are modelled as rigid, whereas the shear properties are modelled using gap materials in series with the numerical self-centering material model. Each floor was assigned a horizontal multi-point constraint to simulate rigid diaphragm behavior. The seismic mass of each floor was assigned horizontally to the wall nodes at the respective floors. The vertical loads on the wall piers were modelled as vertical nodal forces on each wall pier. 2.5% Rayleigh damping proportional to stiffness and mass was defined based on the first and third mode of the prototype building. 6.2 Component modelling This section discusses the numerical modelling of various non-linear components in the SC-MRCSW. As mentioned previously, the non-linearity is modelled for three key components of the system, the coupling beams modelled as SCFD, the base dampers modelled as LEDs and the rocking base of the wall. The following sections elaborate on the numerical models used to represent these elements and the validation of their nonlinear behavior against experimental 65 results. Once the material models were calibrated, their deformation response was scaled to match the design values shown in Table 3 of chapter 5, section 5.1. Self-centering coupling beams The coupling beams are modelled to exhibit the force-deformation behavior of the SCFDs. The damper used as a coupling beam is assumed to exhibit this behavior in shear deformation. The coupling beam is then modelled as a zero-length element located in the middle of the coupling beam. The coupling beam is connected to an elastic beam column element modelled as a W360×147 section. The steel section attaches to the wall as a rigid element to transfer forces from the zero-length element to the wall element. The zero-length element has its axial and moment deformation modelled as rigid elastic, while the shear deformation is modelled as a series of SelfCentering material and gap material from OpenSees. Figure 44 shows the material models used to emulate the force-deformation behavior of the SCFDs. The gap material is needed when modelling SCFDs due to the limitation of SelfCentering material model not having a parameter for the unloading stiffness. The SelfCentering material model follows the same unloading stiffness as the post activation/loading stiffness, however, in case of SCFDs the unloading stiffness can differ based on the coefficient of friction of the cone and plates as well as the angle of the cone itself. Therefore, the SelfCentering material simulates the unloading stiffness of the SCFDs as the post-activation stiffness of the material. The gap material has the same elastic stiffness as the initial stiffness of the SelfCentering material, with a hardening ratio representing the difference between the loading and unloading stiffness for the damper. Figure 45 shows the verification of the combined material model against the testing results for specimen DF6-P10W10 from Yang et al., (2020) . The overall calibration model follows the loading and unloading stiffness accurately as well as the activation point for the tested damper specimen. 66 Figure 45 Numerical calibration for SCFDs. Figure 44 SCFD material formulation 67 Base Dampers The base dampers are modelled as corotational truss elements, which are pinned at the bottom. The dampers are connected to the rigid beam element, which emulates the base of the wall. The material model used to emulate the behavior is Steel02 with elastic-perfectly plastic hysteresis. Figure 46 below shows the calibration of the dampers against experimental work by Quaglini et al., (2023). Figure 46 Base damper backbone curve 68 Rocking base-Elastic No-Tension material The rocking base for the wall was calibrated against experimental work done by Perez et al., (2007). The rocking elements were modelled as truss elements with elastic no-tension (ENT) material. Figure 47 below shows the experimental setup and the numerical model. The area of each spring is calculated based on the area at the base of the wall that it covers. The PT bars are modelled as truss elements with Steel02 material and the required prestress force according to the experiment for this wall. The wall is modelled as a beam column element with fiber section, using Concrete02 material model with the confined and unconfined sections and their respective stiffness. A rigid elastic beam column element connects the wall and the PT bars together at the top. Figure 48 below shows the results of material calibration for the ENT material. The numerical model predicts the initial and unloading stiffness of the wall accurately, however, it overestimates the capacity of the wall while underestimating the degradation shown by the experimental results. Figure 47 Experimental and numerical model for rocking base calibration 69 For the purposes of this study, this is an adequate response since the most crucial part of the design of SC-MRCSW system is the accurate depiction of the initial stiffness as that influences the modal properties and consequently the design of the dampers themselves. 6.3 Modal properties The first mode period for the numerical model is calculated to be 1.4s. This value matches closely with the design period of the prototype building. The first and third natural periods of the model were used to assign a 2.5 % Rayleigh damping to the model. Figure 49 shows the first three modes from the modal analysis. Figure 48 Numerical calibration results for rocking base 70 6.4 Summary This chapter details the numerical modelling of the prototype building. A 2-D finite element model was created in OpenSees. Since the wall is designed to remain damage free, i.e. within the elastic limit for the material, the nonlinear behavior was modelled for three components: the coupling beams as SCFD, the base dampers as LEDs and the rocking behavior at the base of the wall. All nonlinear components were calibrated against their experimental data as outlined under Section 6.2. The modal analysis shows that the EEDP presented in Chapter 4 can accurately predict the fundamental period of the prototype building. Mode 1 T- 1.44s Mode 2 T- 0.32s Mode 3 T- 0.13s Figure 49 Mode shapes for the first three modes 71 Chapter 7: Seismic performance of the SC-MRCSW The seismic performance of the prototype building with SC-MRCSW is evaluated using Non-Linear Time History Analysis (NLTHA). This chapter summarizes the GM scaling and the results of the analysis. Section 7.1 shows the ground motion (GM) selection and scaling. Section 7.2 discusses the peak roof displacement and the interstory drifts. Section 7.3 discusses the residual drifts in the structure after seismic shaking. Section 7.4 shows the results for SCFD hysteresis, as well as a discussion on the yielding of coupling beams. Section 7.5 shows the base damper results. Section 7.6 discusses the deformations in the wall panels of the prototype building. 7.1 Ground motion selection and scaling In order to evaluate the seismic performance of the prototype SC-MRCSW building, a suite of 11 ground motions was selected from the PEER NGA-West database (Ancheta et al., 2014) for each hazard shaking intensity. The ground motions were scaled to cover a period range of 0.15T1 : 2.0T1 (0.21s-2.74s). Ground motions were selected with a minimum magnitude of 5.0 and a maximum magnitude of 8.0. Table 3 summarizes the scale factors of each ground motion, Figure 50 shows the scaling for each ground motion along with the mean and hazard spectra. 72 Table 3 Scale factors of GM for each hazard SLE DBE MCE NGA Location SF NGA Location SF NGA Location SF 25 Northern Calif 0.97 6 Imperial Valley 0.37 68 San Fernado 1.69 31 Parkfield 0.37 9 Borrego 1.99 139 Tabas 1.98 65 San Fernando 0.58 28 Parkfield 2.23 143 Tabas 0.48 164 Imperial Valley 0.25 96 Managua 0.53 187 Imperial Valley 2.65 187 Imperial Valley 0.32 138 Tabas 0.95 285 Irpinia 2.22 280 Trinidad 0.62 294 Irpinia 2.62 292 Irpinia 1.26 281 Trinidad 0.39 302 Irpinia 0.91 313 Corinth 1.77 288 Irpinia 0.32 352 Coalinga 0.91 587 New Zealand 1.90 294 Irpinia 0.85 832 Landers 0.78 725 Loma Prieta 1.35 353 Coalinga 0.52 3750 Cape Mendocino 0.42 796 Loma Prieta 3.43 832 Landers 0.26 4843 Chuetsu-oki 0.63 1633 Manjil 1.15 73 Figure 50 Ground motion scaling for SLE, DBE and MCE hazard 74 7.2 Roof displacement and interstory drift Figure 51 shows the average interstory drift (ISD) of the prototype building for each of the hazards. At SLE, the maximum average ISD is 0.052%, at DBE, the drift reaches 0.26% and finally at MCE, the maximum average drift is recorded as 0.79%. At MCE, the maximum ISD reaches 1.4% for one of the GM. Overall, the SC-MRCSW shows excellent performance and stays well within the 2.5% drift limit set by NBCC2020 for all GMs. Figure 51 Interstory drift for each hazard 75 Figure 52 shows the maximum roof displacement for the suite of GMs in each hazard normalized to the design displacement calculated for the prototype building using EEDP. The average roof displacement for each hazard is calculated to be 27.3mm (SLE), 98mm (DBE) and 354mm (MCE). Overall, the NLTHA shows a good agreement with the design roof displacement using EEDP shown in Table 1. Figure 53 shows the comparison between the target displacement from EEDP and the average roof displacement from the NLTHA for each hazard. The average roof displacement from NLTHA shows a good match with the predicted displacement from EEDP. SLE DBE MCE Figure 52 Roof displacement for each hazard 76 7.3 Residual drifts Figure 54 shows the average residual ISD for the prototype building after time history analysis. The residual drifts are calculated by running all GMs to 90s and then taking the average of the free form displacement at each floor. The residual drifts for SLE and DBE are extremely low (<0.002%), representing strong self-centering behavior for the system. The maximum mean residual ISD is recorded as 0.035% for MCE hazard. For resilient buildings, the acceptable industry criterion for residual drifts is considered to be 0.5% after an MCE level earthquake event (Almufti & Willford, 2013). This result solidifies the self-centering capabilities of the SC-MRCSW system. Figure 53 Average roof displacement vs. EEDP roof displacement 77 7.4 Coupling beam performance The coupling beams were designed to remain elastic at SLE, and yield during DBE and MCE intensity seismic events. Figure 55 shows selected hysteresis results of SCFDs at different hazard intensities. At SLE, the hysteresis shows the coupling beam damper has not yet reached its activation force. At DBE, the hysteresis shows the coupling beam damper has reached the activation force and started to dissipate energy. Finally, at MCE, the coupling beam damper has Figure 54 Residual inter-story drift performance. SLE DBE MCE 78 reached its activation force and is fully dissipating energy. Appendix A shows the hysteresis results of all SCFDs for each hazard and ground motion. Figure 56 shows the nominal coupling beam forces at each level, i.e. average of highest coupling beam forces from each ground motion normalized to their design values. The average coupling beam forces during SLE were less than 1, including the response from most GMs at SLE, except for two GMs where the force exceeds the design activation force by 7%. This indicates that the coupling beams remained mostly elastic for SLE level shaking. The average nominal coupling beam forces were greater than 1, including all GMs for DBE and MCE. This indicates that the coupling beams were dissipating energy at DBE and MCE level events, as per the design criteria set during prototype design. Figure 55 Sample hysteresis of SCFD from NLTHA 79 7.5 Base Dampers Figure 57 shows the average base damper force for each hazard. The base dampers were designed to activate and dissipate energy at MCE, while remaining elastic at SLE and DBE. The results show that the total damper force was below activation for SLE and DBE while the base dampers were fully engaged at MCE. Figure 56 Nominal coupling beam forces for each hazard 80 7.6 Wall performance Figure 58 shows the maximum average shear strain of the wall at each level normalized to its elastic strain limit. The elastic strain limit is calculated using Eq. 36 and 37 from section 4.7. The maximum shear strain is always the highest at the bottom stories for each hazard. The maximum shear strain is recorded at 0.34 during MCE level shaking. The shear strain in the wall remains below 1 for all hazards, indicating that the wall remains elastic throughout each hazard, meeting the low damage performance criteria of EEDP. Figure 57 Average base damper force for each hazard 81 7.7 Summary Overall, the NLTHA analysis of the SC-MRCSW system for the prototype building shows excellent seismic performance. The coupling beams and base dampers exhibit their design forces and displacements at correct hazard intensity. The non-linearity in this system is isolated to the coupling beams and base dampers, leaving the modular walls to be relatively damage free. The NLTHA of the prototype building validates the design procedure detailed in Chapter 4. The EEDP was able to design for the target roof displacement, coupling beam energy dissipation and base damper energy dissipation reliably for the prototype building, while keeping the deformations in the wall within the elastic limit. Figure 58 Maximum average shear strain in the wall for each hazard 82 Chapter 8: Conclusion 8.1 Summary This thesis introduces a novel high-performance lateral force resisting system named self-centering modular rocking composite sandwich wall (SC-MRCSW). The SC-MRCSW combines a modular composite steel-concrete sandwich wall along with innovative self-centering conical friction dampers (SCFDs) and a rocking wall base with lead extrusion dampers (LEDs). The SC-MRCSW is designed to achieve high performance, where it will be damage free under different levels of earthquake shaking intensities. The SCFDs and LEDs are designed to dissipate energy while the composite steel-concrete sandwich wall remain elastic during all design levels of earthquake shaking intensities. The SCFD allows the SC-MRCSW to self-center resulting in minimal residual drift under all levels of earthquake shaking intensities, making the system highly resilient. To achieve the superior performance at different levels of earthquake shaking intensities, the modified Equivalent Energy Design Procedure (EEDP) proposed by Tobber et al., (2023) was adopted to design the SC-MRCSW system. EEDP uses an energy-based design approach to size the yielding structural elements which enable designers to satisfy both the strength and deformation of the system at different levels of shaking intensities without iterations. A 15-story prototype building in Vancouver, British Columbia was designed. A detailed numerical model was developed to verify the prototype design of the building. Non-linear time history analysis (NLTHA) was conducted to verify the performance of the system under a range of seismic hazards. Following observations were concluded from the NLTHA: 1. The structural period of the SC-MRCSW can be accurately calculated using Eq 4.2. In this study, the dominant period of the prototype structure was calculated by EEDP as 1.4s, which is consistent with the fundamental period of 1.44s determine from the modal analysis 83 2. EEDP can accurately predict the roof drift ratio where the average roof displacement from NLTHA is within 5% of the target roof displacements calculated through EEDP for each of the seismic hazard levels 3. The SC-MRCSW system shows superior seismic performance where the maximum mean interstory drift for the prototype building is recorded as 0.79% at MCE shaking which is well below the 2.5% target displacement through NBCC 2020 criteria 4. The SC-MRCSW system exhibits exceptional self-centering behavior, as the maximum average residual drift is recorded as 0.035% at MCE, which is well below the 0.5% limit for resilient buildings (Almufti & Willford, 2013) 5. The wall was designed to remain elastic through all levels of seismic shaking intensities. The deformations in the wall remained within its elastic limit 6. The SC-MRCSW demonstrates clear yielding mechanisms, where all dampers remained elastic for SLE level shaking, the coupling beams began yielding at DBE level shaking and the base dampers along with the coupling beams were fully engaged at MCE level shaking Overall, the results show the EEDP presented in chapter 4 can be used effectively to design the SC-MRCSW under different levels of earthquake shaking intensities. The SC-MRCSW can be used as a high-performance and reliable seismic force resisting system. 8.2 Limitations and recommendations for future work The prototype building design and numerical models created were primarily done using planar wall sections. However, for tall building design, it is often useful to use a core-wall section instead due to the architectural preferences of having elevators and emergency stairs near the middle of the buildings due to regulations and parking restrictions. Moreover, the prototype design was conducted for one archetype in a single seismic hazard environment. To display a more robust 84 performance, several archetypes in different seismic zones in Canada should be considered. This research also utilized one type of coupling beam damper. The effect of damper stiffness and hysteresis should be studied for wide variety of dampers. 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Effect of shear connectors on local buckling and composite action in steel concrete composite walls. Nuclear Engineering and Design, 269, 231–239. 89 - NLTHA results A.1 SLE coupling beam forces Figures A.1-11 show the hysteresis for coupling beams at each level for SLE level shaking. A. 1 SLE Coupling beam hysteresis – RSN25 90 A. 2 SLE Coupling beam hysteresis – RSN31 91 A. 3 SLE Coupling beam hysteresis – RSN65 92 A. 4 SLE Coupling beam hysteresis – RSN164 93 A. 5 SLE Coupling beam hysteresis – RSN187 94 A. 6 SLE Coupling beam hysteresis – RSN280 95 A. 7 SLE Coupling beam hysteresis – RSN281 96 A. 8 SLE Coupling beam hysteresis – RSN288 97 A. 9 SLE Coupling beam hysteresis – RSN294 98 A. 10 SLE Coupling beam hysteresis – RSN353 99 A. 11 SLE Coupling beam hysteresis – RSN832 100 A.2 SLE displacement time history Figures A.12-22 show the displacement time history at each level for SLE level shaking. A. 12 SLE Displacement Time History – RSN25 101 A. 13 SLE Displacement Time History – RSN31 102 A. 14 SLE Displacement Time History – RSN65 103 A. 15 SLE Displacement Time History – RSN164 104 A. 16 SLE Displacement Time History – RSN187 105 A. 17 SLE Displacement Time History – RSN280 106 A. 18 SLE Displacement Time History – RSN281 107 A. 19 SLE Displacement Time History – RSN288 108 A. 20 SLE Displacement Time History – RSN294 109 A. 21 SLE Displacement Time History – RSN353 110 A. 22 SLE Displacement Time History – RSN832 111 A.3 DBE coupling beam forces Figures A.23-33 show the hysteresis for coupling beams at each level for DBE level shaking. A. 23 DBE Coupling beam hysteresis – RSN6 112 A. 24 DBE Coupling beam hysteresis – RSN9 113 A. 25 DBE Coupling beam hysteresis – RSN28 114 A. 26 DBE Coupling beam hysteresis – RSN96 115 A. 27 DBE Coupling beam hysteresis – RSN138 116 A. 28 DBE Coupling beam hysteresis – RSN294 117 A. 29 DBE Coupling beam hysteresis – RSN302 118 A. 30 DBE Coupling beam hysteresis – RSN352 119 A. 31 DBE Coupling beam hysteresis – RSN832 120 A. 32 DBE Coupling beam hysteresis – RSN3750 121 A. 33 DBE Coupling beam hysteresis – RSN4843 122 A.4 DBE displacement time history Figures A.34-44 show the displacement time history at each level for DBE level shaking. A. 34 DBE Displacement time history - RSN6 123 A. 35 DBE Displacement time history – RSN9 124 A. 36 DBE Displacement time history – RSN28 125 A. 37 DBE Displacement time history – RSN96 126 A. 38 DBE Displacement time history – RSN138 127 A. 39 DBE Displacement time history – RSN294 128 A. 40 DBE Displacement time history – RSN302 129 A. 41 DBE Displacement time history – RSN352 130 A. 42 DBE Displacement time history – RSN832 131 A. 43 DBE Displacement time history – RSN3750 132 A. 44 DBE Displacement time history – RSN4843 133 A.5 MCE coupling beam forces Figures A.45-55 show the hysteresis for coupling beams at each level for MCE level shaking. A. 45 MCE Coupling beam hysteresis – RSN68 134 A. 46 MCE Coupling beam hysteresis – RSN139 135 A. 47 MCE Coupling beam hysteresis – RSN143 136 A. 48 MCE Coupling beam hysteresis – RSN187 137 A. 49 MCE Coupling beam hysteresis – RSN285 138 A. 50 MCE Coupling beam hysteresis – RSN292 139 A. 51 MCE Coupling beam hysteresis – RSN313 140 A. 52 MCE Coupling beam hysteresis – RSN587 141 A. 53 MCE Coupling beam hysteresis – RSN725 142 A. 54 MCE Coupling beam hysteresis – RSN796 143 A. 55 MCE Coupling beam hysteresis – RSN1633 144 A.6 MCE displacement time history Figures A.12-22 show the displacement time history at each level for MCE level shaking. A. 56 MCE Displacement time history - RSN68 145 A. 57 MCE Displacement time history – RSN139 146 A. 58 MCE Displacement time history – RSN143 147 A. 59 MCE Displacement time history – RSN187 148 A. 60 MCE Displacement time history – RSN285 149 A. 61 MCE Displacement time history – RSN292 150 A. 62 MCE Displacement time history – RSN313 151 A. 63 MCE Displacement time history – RSN587 152 A. 64 MCE Displacement time history – RSN725 153 A. 65 MCE Displacement time history – RSN796 154 A. 66 MCE Displacement time history – RSN1633
Thesis/Dissertation
eng
Civil Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Yang, Tony T. Y.
Seismic design and evaluation of self-centering modular rocking composite sandwich wall (SC-MRCSW) system
Text