Applied Science, Faculty of
Civil Engineering, Department of
DSpace
UBCV
Vaze, Soham
Master of Applied Science - MASc
University of British Columbia
Cold-formed steel corrugated wall panels (CFSCWs) have recently gained traction as structural elements in buildings. A novel application of CFSCWs, named as Frameless system, has been developed by BEHLEN Industries LP. The Frameless systems have been used as load bearing elements. However, no investigation has been conducted to assess the seismic performance of Frameless panels under axial and shear loads. Within this context, a series of experimental and numerical studies are being conducted at the University of British Columbia to assess the seismic performance of Frameless panels. First, a robust experimental test setup is designed to simulate the effect of gravity and seismic loads on the Frameless panels simultaneously. A total of 10 specimens with different corrugation patterns and varying axial loads were tested. Subsequently, a finite element model is developed to simulate the monotonic behavior of the Frameless panels and is validated by the experiments. A comprehensive evaluation of the influence of different corrugations and axial loads on the initial stiffness, the buckling-failure mode, the peak force capacity, the post-buckling stiffness, and the residual force capacity are presented. The results of the experimental and numerical investigations show the lateral force-deformation response of Frameless panel is highly influenced by the corrugation patterns and the axial loads. A linearized backbone curve was proposed for the Frameless panels with axial loads as the design parameter. Key design parameters such as overstrength and ductility ratios of the Frameless panels have been identified. The findings from this research allow the users to design one-span Frameless panels as seismic force resisting system under different axial loads. This research is the first of a series of investigations performed to quantify the seismic safety of Frameless systems
Experimental and Numerical Investigations of Frameless Cold Form Steel Corrugated Wall Panels Subjected to In-Plane Monotonic and Cyclic Loads by Soham Vaze B.Tech, National Institute of Technology, Karnataka, 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) December 2021 © Soham Vaze, 2021ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, a thesis entitled: Experimental and Numerical Investigations of Frameless Cold Form Steel Corrugated Wall Panels Subjected to In-Plane Monotonic and Cyclic Loads submitted by Soham Vaze in partial fulfillment of the requirements the degree of Master of Applied Science in Civil Engineering Examining Committee: Tony T.Y. Yang, Professor, Department of Civil Engineering Research Supervisor Dr. Dimitrios G. Lignos, Director of Civil Engineering Institute (IIC), EPFL Supervisory Committee member iii Abstract Cold-formed steel corrugated wall panels (CFSCWs) have recently gained traction as structural elements in buildings. A novel application of CFSCWs, named as Frameless system, has been developed by BEHLEN Industries LP. The Frameless systems have been used as load bearing elements. However, no investigation has been conducted to assess the seismic performance of Frameless panels under axial and shear loads. Within this context, a series of experimental and numerical studies are being conducted at the University of British Columbia to assess the seismic performance of Frameless panels. First, a robust experimental test setup is designed to simulate the effect of gravity and seismic loads on the Frameless panels simultaneously. A total of 10 specimens with different corrugation patterns and varying axial loads were tested. Subsequently, a finite element model is developed to simulate the monotonic behavior of the Frameless panels and is validated by the experiments. A comprehensive evaluation of the influence of different corrugations and axial loads on the initial stiffness, the buckling-failure mode, the peak force capacity, the post-buckling stiffness, and the residual force capacity are presented. The results of the experimental and numerical investigations show the lateral force-deformation response of Frameless panel is highly influenced by the corrugation patterns and the axial loads. A linearized backbone curve was proposed for the Frameless panels with axial loads as the design parameter. Key design parameters such as overstrength and ductility ratios of the Frameless panels have been identified. The findings from this research allow the users to design one-span Frameless panels as seismic force resisting system under different axial loads. This research is the first of a series of investigations performed to quantify the seismic safety of Frameless systems. iv Lay Summary This study aims to understand the seismic response of a novel cold form steel corrugated wall panel, named Frameless panels, developed by BEHLEN Industries LP, under axial and shear loads. Comprehensive numerical and experimental studies were conducted to examine the effect of various parameters, including the corrugations and axial loads, on the seismic response of the Frameless panels. The findings can be used by engineers to design one-span Frameless panels under axial and shear loads. v Preface The thesis is submitted as a requirement of Master of Applied Science degree completion at the University of British Columbia. The study presented was executed under the supervision of Prof. T.Y. Yang, Department of Civil Engineering Department at the University of British Columbia. The author of this thesis was responsible for designing and calibrating the experimental setup, performing the experiments and validating the numerical models associated with these tests. The experimental set-up used for this research was designed at UBC and manufactured by BEHLEN Industries LP. The specimens are patented designs of BEHLEN Industries LP and have been tested according to their recommendations. Dywidag’ DSI Canada Civil Ltd kindly donated post-tensioned ThreadBars used in the set-up. The test rig was designed to accommodate this project's future testing phases and can be used for other similar experimental tests. 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 ......................................................................................................................................... xvii List of Abbreviations ................................................................................................................................. xix Acknowledgments ....................................................................................................................................... xx Chapter 1 : Introduction ................................................................................................................................ 1 1.1 Background ......................................................................................................................................... 1 1.2 Objectives and research scope ............................................................................................................ 4 1.3 Thesis outline ...................................................................................................................................... 5 Chapter 2 : Literature Review ....................................................................................................................... 7 2.1 Introduction ......................................................................................................................................... 7 2.1.1 Easley & McFarland (1969) ......................................................................................................... 7 2.1.2 Emami et al. (2013) .................................................................................................................... 13 2.1.3 Emami & Mofid (2014) ............................................................................................................. 18 vii 2.1.4 Zhao et al. (2017) ....................................................................................................................... 21 2.1.5 Tong et al. (2018) ....................................................................................................................... 25 2.1.6 Dou et al. (2018) ........................................................................................................................ 27 2.1.7 Farzampour et al. (2018) ............................................................................................................ 30 2.2 Summary and conclusion .................................................................................................................. 33 Chapter 3 : Experimental Program .............................................................................................................. 35 3.1 Introduction ....................................................................................................................................... 35 3.2 Experimental program overview ....................................................................................................... 35 3.3 Material testing ................................................................................................................................. 36 3.4 Wall panel testing ............................................................................................................................. 37 3.4.1 Reaction frame ........................................................................................................................... 40 3.4.2 Actuator and load cell ................................................................................................................ 40 3.4.3 Loading beam ............................................................................................................................. 41 3.4.4 Post-tensioned cables ................................................................................................................. 42 3.4.5 Foundation plates ....................................................................................................................... 44 3.4.6 Out of plane supports ................................................................................................................. 45 3.4.7 Data acquisition system ............................................................................................................. 46 3.5 Specimen assembly ........................................................................................................................... 48 3.6 Test matrix ........................................................................................................................................ 50 3.7 Loading mechanism .......................................................................................................................... 51 3.8 Loading protocol ............................................................................................................................... 52 viii 3.8.1 Monotonic loading ..................................................................................................................... 52 3.8.2 Cyclic loading ............................................................................................................................ 52 3.9 Test procedure ................................................................................................................................... 53 3.10 Summary ......................................................................................................................................... 54 Chapter 4 : Experimental Results ................................................................................................................ 55 4.1 Introduction ....................................................................................................................................... 55 4.2 Material Test ..................................................................................................................................... 55 4.3 CS75 corrugation type ...................................................................................................................... 56 4.3.1 Monotonic loading behavior ...................................................................................................... 56 4.3.2 Cyclic loading behavior ............................................................................................................. 61 4.4 CS45 corrugation type ...................................................................................................................... 69 4.4.1 Monotonic loading results .......................................................................................................... 69 4.4.2 Cyclic loading behavior ............................................................................................................. 72 4.5 Discussion ......................................................................................................................................... 77 4.5.1 Comparison between monotonic behavior ................................................................................. 77 4.5.2 Comparison between cyclic behavior ........................................................................................ 78 4.5.3 Comparison between corrugation profiles ................................................................................. 80 4.6 Backbone curve ................................................................................................................................. 82 4.6.1 Elastic stiffness .......................................................................................................................... 82 4.6.2 Plastic stiffness ........................................................................................................................... 83 4.6.3 Peak force capacity .................................................................................................................... 84 ix 4.6.4 Yielding drift .............................................................................................................................. 85 4.6.5 Buckling drift ............................................................................................................................. 86 4.6.6 Post-buckling stiffness ............................................................................................................... 87 4.6.7 Overstrength and ductility ratio ................................................................................................. 88 4.7 Summary ........................................................................................................................................... 91 Chapter 5 : Finite Element Model ............................................................................................................... 93 5.1 Introduction ....................................................................................................................................... 93 5.2 Model description ............................................................................................................................. 93 5.2.1 Material modeling ...................................................................................................................... 94 5.2.2 Mesh study and geometric imperfections .................................................................................. 95 5.2.3 Type of element ......................................................................................................................... 96 5.2.4 Boundary conditions and interactions ........................................................................................ 97 5.2.5 Residual Stress ........................................................................................................................... 99 5.3 Model validation ............................................................................................................................. 101 5.3.1 Force-drift validation ............................................................................................................... 101 5.3.2 Deformed Shape ....................................................................................................................... 104 5.4 Summary ......................................................................................................................................... 106 Chapter 6 : Conclusion and Future Work ................................................................................................. 107 6.1 Summary & conclusion ................................................................................................................... 107 6.1.1 Experimental study .................................................................................................................. 107 6.1.2 Finite element model ................................................................................................................ 109 x 6.2 Future recommendations ................................................................................................................. 109 Bibliography ............................................................................................................................................. 111 Appendices ................................................................................................................................................ 114 Appendix A ........................................................................................................................................... 114 Appendix B ........................................................................................................................................... 124 xi List of Tables Table 2.1 Test Matrix (Easley & McFarland 1970) ................................................................................ 11 Table 2.2 Test matrix for the corrugated steel plate tests (Emami et al., 2013) ...................................... 14 Table 2.3 Comparison between analytical and experimental results (Emami et al., 2013) .................... 17 Table 2.4 Test Matrix for the FEA study (Zhao et al., 2017) ................................................................. 23 Table 3.1 Test Matrix for the experimental test ...................................................................................... 50 xii List of Figures Figure 1.1 General design of Frameless systems (BHELEN Industries LP) ............................................ 2 Figure 1.2 (a) CS75 panel; (b) CS45 panel; (c) Corrugation classification (BEHLEN Industries LP); ... 4 Figure 2.1 Element in consideration and coordinate system (Easley & McFarland, 1970) ...................... 9 Figure 2.2 Repeating patterns of corrugations tested (Easley & McFarland, 1970) ............................... 11 Figure 2.3 Boundary frame details of the test rig (Easley & McFarland, 1970) ..................................... 12 Figure 2.4 Force-displacement relationship for 1:1 length-to-height ratio: (a) Trapezoidal corrugation type; (b) Sinusoidal corrugation type (2 tests) (Easley & McFarland, 1970) ......................................... 13 Figure 2.5 Trapezoidal corrugation profile (Emami et al., 2013) ........................................................... 14 Figure 2.6 Steel plate wall testing set-up (Emami et al., 2013) .............................................................. 15 Figure 2.7 Force-deformations relationship comparing numerical analysis and experimental results (Emami et al., 2013) ................................................................................................................................ 17 Figure 2.8 Analysis results for the monotonic test of vertical corrugation type: (a) Final deformed shape; (b) max in-plane principal stress (Emami & Mofid, 2014) ..................................................................... 19 Figure 2.9 Force-displacement validation of vertical corrugation type: (a) Monotonic test (b) cyclic test (Emami & Mofid, 2014) ......................................................................................................................... 20 Figure 2.10 Types of corrugation studied (Zhao et al., 2017) ................................................................. 22 Figure 2.11 Comparison between different FEA results: (a) Different types of corrugation with variation in boundary frame; (b) Backbone curves for with and without gravity load cases (Zhao et al., 2017) .. 24 Figure 2.12 Profile of specimen tested and test set-up (Tong et al., 2018) ............................................. 26 Figure 2.13 Corrugation profile and finite element model (Dou et al., 2018) ........................................ 28 xiii Figure 2.14 Three-point Design Curve (Dou et al., 2018) ..................................................................... 30 Figure 2.15 Finite element models with openings: (a) Steel plate shear wall; (b) Corrugated shear wall (Farzampour et al., 2018) ........................................................................................................................ 31 Figure 2.16 Corrugation profile considered for the study (Farzampour et al., 2018) ............................. 32 Figure 2.17 Validation of numerical models: (a) Steel plate shear wall; (b) Corrugated shear wall (Farzampour et al., 2018) ........................................................................................................................ 33 Figure 3.1 (a) Instron universal testing machine, (b) Specimen assembly, (c) Steel coupons ................ 37 Figure 3.2 Test set-up arrival and installation: (a) Receiving shipment; (b) Moving components to the lab; (c) Aligning the foundation plates; (b) Commencement of testing .................................................. 38 Figure 3.3 Overview of the test rig for the wall panel test: (a) Details of each component; (b) Global dimension ................................................................................................................................................ 39 Figure 3.4 Reaction frame housing the actuator ..................................................................................... 40 Figure 3.5 Actuator and load cell assembly ............................................................................................ 41 Figure 3.6 Loading beam assembly: (a)Details of each component; (b) Construction image ................ 42 Figure 3.7 Post-Tensioned Rods Assembly: (a) Specimen Assembly; (b) Stressing Jack ...................... 44 Figure 3.8 Foundation plate assembly .................................................................................................... 45 Figure 3.9 Out-of-plane supports ............................................................................................................ 46 Figure 3.10 (a) Load cell linear calibration plot; (b) LVDT cell linear calibration plot; (c) ACTS ....... 47 Figure 3.11 Corrugate wall assembly ..................................................................................................... 48 Figure 3.12 Specimen’s component details, (a) CS75 panel; (b) CS45 panel; (c) Roof panel; (d) Boundary column .................................................................................................................................................... 49 Figure 3.13 Loading mechanism ............................................................................................................. 51 xiv Figure 3.14 Cyclic loading protocol ....................................................................................................... 53 Figure 4.1 Tensile couple test (a) CS75, 18ga. (b) CS45 18ga. .............................................................. 56 Figure 4.2 (a) Initial state; (b) necking state; (c) fracture state ............................................................... 56 Figure 4.3 Non-axially loaded CS75 panel subjected to monotonic shear loads at relevant drift ratios ................................................................................................................ Error! Bookmark not defined. Figure 4.4 Force-Drift relationship of CS75 panel subjected to monotonic shear and 15 kips of axial loads ................................................................................................................................................................ 59 Figure 4.5 Force-Drift relationship of CS75 panel subjected to monotonic shear and 30 kips of axial loads ................................................................................................................................................................ 60 Figure 4.6 Relevant deformed shapes in individual cycles of C75 cyclic test ........................................ 63 Figure 4.7 Comparison between monotonic and cyclic performance of non-axially loaded CS75 wall panel ........................................................................................................................................................ 64 Figure 4.8 Relevant deformed shapes in individual cycles of C75 cyclic test with 15 kips axial loads . 65 Figure 4.9 Comparison between monotonic and cyclic performance of CS75 wall panel with 15 kips axial loads ............................................................................................................................................... 66 Figure 4.10 Relevant deformed shapes in individual cycles of C75 cyclic test with 30 kips axial loads67 Figure 4.11 Comparison between monotonic and cyclic performance of CS75 wall panel with 30 kips axial loads ............................................................................................................................................... 68 Figure 4.12 Force-Drift relationship of non-axially loaded CS45 panel subjected to monotonic shear loads ........................................................................................................................................................ 70 Figure 4.13 Force-Drift relationship of CS45 panel subjected to monotonic shear and 30 kips of axial loads ........................................................................................................................................................ 71 Figure 4.14 Relevant deformed shapes in individual cycles of C45 cyclic test ...................................... 73 xv Figure 4.15 Comparison between monotonic and cyclic performance of non-axially loaded CS45 wall panel ........................................................................................................................................................ 74 Figure 4.16 Relevant deformed shapes in individual cycles of C45 cyclic test with 30 kips axial loads75 Figure 4.17 Comparison between monotonic and cyclic performance of CS45 wall panel with 30 kips axial loads ............................................................................................................................................... 76 Figure 4.18 Comparison between monotonic behavior of CS75 specimens with varying axial loads ... 77 Figure 4.19 Comparison between monotonic behavior of CS45 specimens with varying axial loads ... 78 Figure 4.20 Comparison between cyclic behavior of CS45 specimens with varying axial loads ........... 79 Figure 4.21 Comparison between cyclic behavior of CS45 specimens with varying axial loads ........... 80 Figure 4.22 Comparison of monotonic behavior with varying axial loads: (a) No axial loads; (b) 30 kips axial loads ............................................................................................................................................... 81 Figure 4.23 Representative shear behavior under monotonic loads ........................................................ 82 Figure 4.24 Fitted curve for elastic stiffness against varying axial loads ............................................... 83 Figure 4.25 Fitted curve for plastic stiffness against varying axial loads ............................................... 84 Figure 4.26 Fitted curve for peak force capacity against varying axial loads ......................................... 85 Figure 4.27 Fitted curve for yielding drift against varying axial loads ................................................... 86 Figure 4.28 Fitted curve for buckling drift against varying axial loads .................................................. 87 Figure 4.29 Fitted curve for post-buckling stiffness against varying axial loads.................................... 88 Figure 4.30 Fitted design curve against axial loads: (a) overstrength ratio; (b) ductility ratio ............... 90 Figure 4.31 (a) Overstrength ratio; (b) Ductility ratio ............................................................................ 91 Figure 5.1 Mesh-sensitivity study ........................................................................................................... 95 Figure 5.2 Initial imperfections implemented in the numerical model (a) Mode 1 (b) Mode 2 ............. 96 xvi Figure 5.3 S4R element properties (Smith, 2009)................................................................................... 97 Figure 5.4 Model description (CS75 type wall panel) ............................................................................ 98 Figure 5.5 Material behavior with and without residual stress consideration ......................................... 99 Figure 5.6 Average residual stress along cold form steel channel section (Ingvarsson, 1975) ............. 100 Figure 5.7 Residual stress in the FEM at t=0 ........................................................................................ 101 Figure 5.8 Comparison between monotonic tests and FEM for CS75 type: (a) No axial loads (b) 15 kips axial loads (c) 30 kips axial loads ......................................................................................................... 103 Figure 5.9 Comparison between monotonic tests and FEM for CS45 type: (a) No axial loads (b) 30 kips axial loads ............................................................................................................................................. 104 Figure 5.10 Comparison of deformed shape in out plane direction between experimental testing and FEM (CS75): (a) No axial loads (b) 15 kips axial loads (c) 30 kips axial loads ............................................ 105 Figure 5.11 Comparison of deformed shape in out plane direction between experimental testing and FEM (CS45): (a) No axial loads (b) 30 kips axial loads ................................................................................ 106 xvii List of Symbols 𝛼𝛼 Angle of inclination with horizontal 𝜃𝜃 Angle of inclination with vertical 𝜎𝜎𝑇𝑇 True stress 𝜎𝜎 Stress 𝜖𝜖𝑇𝑇 True strain 𝛾𝛾 Drift ratio 𝜎𝜎𝑦𝑦 Yield stress 𝜇𝜇𝑦𝑦 Yielding drift 𝜇𝜇𝐵𝐵 Global buckling drift 𝜇𝜇𝑇𝑇 Period -based ductility 𝜏𝜏𝑐𝑐𝑐𝑐 Critical shear stress 𝑡𝑡𝑤𝑤 Web thickness 𝜆𝜆𝑠𝑠 Shear buckling parameter 𝑘𝑘𝑠𝑠 Buckling parameter 𝛿𝛿𝑦𝑦 Yielding displacement xviii 𝛿𝛿𝑢𝑢 Drift at 20% reduction in force Ω Overstrength factor E Young’s modulus 𝐾𝐾𝑒𝑒𝑒𝑒 Elastic stiffness 𝐾𝐾𝑝𝑝𝑒𝑒 Plastic stiffness 𝐹𝐹𝑒𝑒𝑒𝑒𝑝𝑝 Corrected force response 𝐹𝐹𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 Noted actuator force response 𝐹𝐹𝑚𝑚𝑚𝑚𝑒𝑒 Peak force carrying capacity 𝐹𝐹𝑃𝑃𝑇𝑇 Post-tensioned rod applied force 𝐾𝐾𝑃𝑃𝐵𝐵 Post-buckling stiffness I Moment of inertia K Initial stiffness M Moment V Shear force xix List of Abbreviations CFS Cold form steel CFSCP Cold form steel corrugated panel CFSCW Cold form steel corrugated wall CoSPW Corrugated steel plate shear wall DOF Degrees of freedom FEM Finite element model HSS Hollow steel section SPW Steel plate shear wall LVDT Linear variable differential transformer SPW Steel plate shear wall xx Acknowledgments I would like to express my gratitude to numerous people for their support and contribution towards the completion of this thesis. Firstly, I want to thank my supervisor, Prof. T.Y. Yang of the University of British Columbia for providing me with this opportunity, invaluable support and guidance throughout the progress of this research. His probing questions shaped me to become a better researcher and oriented me as a critical thinker. I would very much like to thank the industry collaborators from BEHLEN Industries LP, Pat Versavel and Trevor Veitch for their continuous guidance and support in every stage of this thesis. Furthermore, I would like to extend my gratitude to Don Singer from DSI International for his generous donation of post-tensioned rods and assistance in the precise application of the same for this project. I would also like to extend my great appreciation to the many technicians from the University of British Columbia Structure Laboratory who helped me advance in this project. Special thanks to Doug Hudniuk, Arthur Mak and Sylvain Picard for their invaluable assistance and suggestion during the design and construction of the experimental setup. I was also fortunate to receive assistance from Scott Jackson, Simon Lee and John Wong in the laboratory. Their expertise immensely helped in accelerating this project. Thank you for your constant support throughout my endeavors to all my colleagues from the structures department, particulary Fabrício Bagatini Cachuço, Xiao Pan and Preetish Kakoty. I wish to offer my thanks to the peers from my research group, Yu-cheng Hsu, Miaoyuan Dou and Elmira Faraji for their support in the experimental testing. I would also like to express my gratitude to Winda Banjuradja, Hengchao Xu and Xi Zuo for steady motivation throughout my program. I would not be able to accomplish this without your assistance. xxi Finally, I want to thank my parents, my mother and my father. My mom always inspires and urges me throughout my ventures, and my dad who provides firm support, I am thankful for their immeasurable love. xxii To my friends and family. 1 Chapter 1 : Introduction 1.1 Background Low-rise long span constructions are often built with portal frames composed of tapered or trussed elements. These systems localize the structural components at the frame location, which may not be an efficient approach. Cold form steel corrugated wall panels (CFSCW) have been trending lately and present an alternative over conventional portal frames. Frameless systems are specific types of CFSCWs developed by BEHLEN Industries, LP, to provide highly efficient solutions in terms of strength, function, cost and aesthetics. However, there is a perception gap regarding the applicability of Frameless panels as seismic force resisting systems. This thesis aims to investigate the seismic performance of these panels by conducting a series of experimental tests and proposing robust numerical models. Frameless structures, buildings without conventional frame elements, were introduced recently as an innovative design for single story long-spanned steel structures. Figure 1.1 presents a typical layout for a Frameless structure. CFSCWs have been explored as economical solutions for shear wall systems. Adding corrugations to cold form sheets increases the axial stiffness, making them a viable alternative for load-bearing elements in long-span applications. Supporting boundary columns provide basic out-of-plane stability to resist wind loads. Frameless panels’ light weight and ease of manufacture make them a strong economical solution over conventional steel sections. These systems have been successfully implemented in various northeastern and central parts of Canada, particularly in Nunavut and Manitoba, exhibiting their performance and ability in regions without significant seismic activity. Insufficient knowledge regarding the seismic design of Frameless systems puts forth the necessity to understand the behavior of CFSCWs under combined axial and cyclic shear loads. 2 Figure 1.1 General design of Frameless systems (BHELEN Industries LP) Work on thin corrugated steel sheets has gained interest in recent years, with researchers aiming to study the complex behavior of buckling under shear loads. One of the earliest studies conducted by Easley & McFarland (1970) discussed the possible analytical solutions for capturing the shear capacity of these systems. Thin steel sheets are not a competitive alternative to reinforced concrete shear walls since they are susceptible to buckling failure under shear loads due to out-of-plane instability. To address this problem, either additional stiffeners are provided, or corrugations are added to the thin steel sheets, effectively increasing their surface area when packed into same length of non-corrugated sheets, making it a viable option. The investigations conducted so far have fundamentally focused on exploring corrugated steel sheets as alternatives to shear wall systems, typically comparing their performances to conventional reinforced concrete shear walls or stiffened steel plate shear walls. These corrugated shear walls systems are surrounded by distinctive boundary frames, but little effort has been put forth to study frame’s influence. Effects of axial loads have been analytically presented to have negligible influence on the overall performance of these systems (Zhao et al., 2017). 3 This thesis is the first phase of a five-year, multi-phase collaborative project between the University of British Columbia and BEHLEN Industries, LP. The greater goal of this collaborative project is to conduct a comprehensive assessment of the seismic performance of Frameless systems through a battery of experimental tests followed by the proposal of robust components and systems level finite element models and, finally, the provision of building code recommendations for applications in regions of high seismic activity. The CFSCWs developed by BEHLEN Industries, LP’s Frameless panels, are used as load-bearing walls in low-rise long spanned steel structures known as Frameless systems. The load-bearing wall system has two boundary columns attached on either side of a wall panel, where the shear and axial loads are solely transferred through a bolted connection. The corrugated panels investigated are geometrically complex when compared to the previously studied ones. These panels have more than one set of corrugations, the first one being on a global scale with a sinusoidal shape, and the second being localized, as shown in Figure 1.2. They are either trapezoidal or curved (sinusoidal) at the local level, depending on their corrugation type. CS75 panels have deeper global corrugations with trapezoidal shapes at the local level, whereas CS45s are shallower and have a sinusoidal shape at the local level. This study aims to investigate the behavior of these panels under in-plane combined axial and shear loads by conducting extensive experimental tests, quantifying key design parameters and proposing a robust finite element model capable of capturing the complex behavior of Frameless panels. 4 Figure 1.2 (a) CS75 panel; (b) CS45 panel; (c) Corrugation classification (BEHLEN Industries LP); 1.2 Objectives and research scope The overall objective of this research is to investigate the seismic performance of Frameless panels under the influence of axial loads by establishing a rationale to assess the behavior of these panels under cyclic shear loads and quantifying key design parameters. The specific objectives are as follows: • Experimentally identify the seismic behavior of Frameless panels under varying axial loads. • Propose a linearized backbone curve for CS75 corrugation type panels with axial loads as the design parameter. • Quantify and evaluate the key seismic design parameters of Frameless panels, including overstrength and ductility ratios, based on FEMA P695 (2009) recommendations. 5 • Develop a robust numerical model capable of simulating the complex lateral force-deformation response of Frameless panels under varying axial loads. This study is performed in two parts: experimental and analytical (a numerical model), where the finite element models of the panels are proposed and validated by the experimental results. A unique experimental setup is designed to apply in-plane axial and shear loads to Frameless panels. BEHLEN Industries, LP manufactured the testing rig. The study's experimental testing program was conducted at the University of British Columbia and was comprised of ten test specimens with two different quasi-static lateral loads (monotonic and cyclic). This experimental research program will facilitate having a better understanding of the seismic behavior of Frameless panels under the influence of axial loads. The investigation will also explore the effect of the geometric profile, boundary columns and base connections on the seismic performance of the components. The test matrix is formulated to accommodate various configurations of Frameless panels. Particular attention is paid to evaluate the effects of axial loads on global buckling, local buckling, ultimate shear force capacity, residual shear force capacity, buckling displacement and ductility. As per FEMA P695 recommendations, trends for key seismic design parameters of seismic force resisting systems such as overstrength and ductility ratios are presented against varying axial loads. 1.3 Thesis outline Chapter 2 presents the literature review associated with the current study; it discusses in detail the nature of the research conducted on CFSCW. The experimental testing and numerical models for the research conducted in the past are briefly revisited, and the shortcomings in those investigations and motivation for conducting the applied project are assessed. Chapter 3 provides the details regarding the experimental tests conducted at the UBC structural engineering laboratory. The test setup design and its calibration are discussed, followed by the details of experimental program’s test matrix. The two displacement-controlled loading protocols used for the test, the monotonic 6 and cyclic, are presented, along with the instrumentation employed in the testing. The monotonic testing was conducted to acquire a fundamental understanding of the panel’s behavior and formulate the cyclic loading protocol. Chapter 4 presents the results of the experimental test being conducted. The details for the yielding drift, global buckling load, elastic stiffness and residual shear force capacity under different axial and shear loading conditions are provided. The formulation of linearized backbone curve for the CS75 panels is presented. The key seismic designed parameters such as overstrength and ductility ratio are quantified, and the corresponding effect of axial loads is reported. A comprehensive study of specimens with various configurations adhering to the test matrix and a brief comparison between the corrugation types is presented in this chapter. Chapter 5 contains the calibration process of robust component-level numerical models in ABAQUS/CAE. Details regarding modeling techniques such as material calibration, mesh convergence, residual stress integration, lateral and axial loading and boundary conditions are presented. The models are validated using the experimental data presented in Chapter 4. Chapter 6 summarizes the thesis and is followed by the conclusions from previous chapters. Recommendations for the project’s future phases are briefly discussed in this chapter. 7 Chapter 2 : Literature Review 2.1 Introduction Cold form steel corrugated panels (CFSCP) have been investigated since the 1970s in Japan and North America. These studies comprised of experimental tests, the proposal of analytical solutions and formulation of finite element models, where specimens were subjected to monotonic and cyclic in-plane shear loads. Research progressed from corrugated webs of plate girders to corrugated steel plate shear walls of varied scopes so as to investigate their shear capacities, buckling loads and energy dissipation capabilities. The primary purpose of these studies was to explore the corrugated steel sheets as potential elements to replace flat steel sheets. Albeit very few studies have focused on investigating their behavior under combined axial and lateral loads, they provided a good understanding of the behavior of these plates under lateral loads, creating a firm foundation for the current investigation. The idea of using corrugated patterns has emerged to tackle the high fabrication cost and low strength-to-weight ratios of stiffened steel plate shear walls, which tend to buckle under service loads. Adding corrugation has aided the shear stability and eliminated the need for transverse stiffeners, as Sause & Braxtan (2011) reported. Various shapes like trapezoids, zig-zag, rectangles, curves and diverse degrees of corrugation continuity along the panel’s length have been studied. This section summarizes, in chronological order of progression, the experimental and numerical studies that have been performed towards the development of corrugated steel plate shear walls as competitive structural elements 2.1.1 Easley & McFarland (1969) One of the earliest studies conducted on light gauge corrugated steel panels was done by Easley & McFarland (1970), which formed the foundation to explore different applications of these components seen today. This study consisted of two parts, theoretical and experimental. In the former section, equations for 8 elastic buckling of corrugated diaphragms were developed using approximate analysis methods such as the Ritz method, (Krieger, 1959). The proposed formulae were validated against the experiments conducted by the authors. The corrugated panels were assumed to be analogous to thin orthotropic plates and analyzed using both small and large plate deflection theories. Finally, the theoretical results were compared with experimental outputs obtained. The assumptions that applied due to orthotropic models’ analogy were as follows: 1) The number of repeating corrugations sections in a diaphragm is usually large, and their dimensions are small compared to the overall dimensions of the diaphragm. 2) The focus of this study is to investigate the overall buckling behavior while ignoring localized effects. 3) The buckling patterns observed are irrespective of the corrugation patterns. The equations for the orthotropic constants whose equations have been derived are presented below. 𝑀𝑀𝑒𝑒 = 𝑞𝑞𝑠𝑠 𝐸𝐸𝑡𝑡312 𝜃𝜃𝑒𝑒 (2.1) 𝑀𝑀𝑦𝑦 = 𝐸𝐸𝐼𝐼𝑦𝑦𝑞𝑞 𝜃𝜃𝑦𝑦 (2.2) 𝑀𝑀𝑒𝑒𝑦𝑦 + 𝑀𝑀𝑦𝑦𝑒𝑒 = 𝑠𝑠𝑞𝑞 𝐸𝐸𝑡𝑡36(1+𝜐𝜐)𝜃𝜃𝑒𝑒𝑦𝑦 (2.3) where 𝐸𝐸 = elastic modulus, 𝑡𝑡 = thickness, 𝑠𝑠 = arc length of one repeating corrugation, 𝑀𝑀𝑒𝑒, 𝑀𝑀𝑦𝑦are the moments about in-plane 𝑥𝑥, 𝑦𝑦 axis and 𝑀𝑀𝑒𝑒𝑦𝑦 is the torsional moment. 𝜃𝜃𝑒𝑒, 𝜃𝜃𝑦𝑦 and 𝜃𝜃𝑒𝑒𝑦𝑦 are the corresponding rotations. Figure 2.1 provides a pictorial representation of the panel and the symbols used. 9 Figure 2.1 Element in consideration and coordinate system (Easley & McFarland, 1970) The authors proposed equation (2.4) to determine the lateral displacements satisfying simply supported boundary conditions only, which was assumed based on the small deflection theory for this study. The specimens were analyzed using the Ritz method following the derivation of the small deflection theory 10 equation. The large deflection theory was considered of prime importance to provide a post-buckling and load-deflection relationship for a diaphragm. Equation (2.5) provides the equation derived from the large deflection theory. 𝑤𝑤 = ∑ ∑ 𝐴𝐴𝑖𝑖𝑖𝑖 sin 𝑖𝑖𝑖𝑖𝑒𝑒𝑚𝑚 sin 𝑖𝑖𝑖𝑖𝑦𝑦𝑏𝑏∞𝑖𝑖=1∞𝑖𝑖=1 (2.4) where Aij are coefficients that define the buckled shape. 𝑤𝑤 = 𝐴𝐴 sin𝜋𝜋𝑦𝑦𝑏𝑏sin𝑛𝑛𝜋𝜋𝑎𝑎(𝑥𝑥 − 𝛼𝛼𝑦𝑦) (2.5) where 𝑛𝑛 = the no. of half buckled waves; ∝ = the tangent of the angle between the y-axis and the direction of the buckled waves; and A is the magnitude of the max. lateral deflection. The authors conducted an experimental study on 14 specimens whose test matrix is presented in Table 2.1 and Figure 2.2 shows the types of corrugations used for testing. Parameters considered for the experimental study included length to height ratios, the thickness of the panels and two different corrugation types. Throughout this study, the boundary elements were identical and constructed to be rigid enough to ensure the damage only occurred in the corrugated panels. 11 Table 2.1 Test Matrix (Easley & McFarland 1970) Figure 2.2 Repeating patterns of corrugations tested (Easley & McFarland, 1970) Figure 2.3 presents the boundary frame details. The specimens were sheared using a hydraulic machine, and the force feedback was recorded from the Baldwin load cell. Wire gauges were used to record the displacement. The force capacities were theoretically calculated and compared to the experimental results. The comparison plots are presented in Figure 2.4. θ= tan (^-1)α , degrees nθ= tan (^-1)α, degrees n0.0191 3.1 100.0217 3.4 100.0191 3.1 60.0217 3.4 60.0191 3.1 90.0217 3.4 80.0191 3.1 150.0217 3.4 140.0363 7.6 30.0411 8.2 40.0243 6.1 40.0277 6.4 4Type 1a = 8b = 9.582 23 - 28 4Panel dimensions, ftNumber of test specimens t, inchesType 1a = 15b = 9.581 6.5 - 13 14+Type 1a = 8b = 9.582 28 - 32 4Type 1a = 9b = 13.583 6.5 - 13 6Type 1a = 9b = 9.583 6.5 - 13 8+Predicted Values Measure ValuesType 1a = 15b = 13.583 6.5 - 13 1012 Figure 2.3 Boundary frame details of the test rig (Easley & McFarland, 1970) This study concluded that the theoretical values obtained were conservative. The anomalies were attributed to the geometric imperfection present due to the intrinsic property of cold form steel and the conservative assumption of pinned boundary conditions. The authors suggested controlled and improved experiments for better understanding and predictions of the behavior of corrugated steel shear diaphragms. 13 Figure 2.4 Force-displacement relationship for 1:1 length-to-height ratio: (a) Trapezoidal corrugation type; (b) Sinusoidal corrugation type (2 tests) (Easley & McFarland, 1970) The study discussed buckling patterns across the shear panels and compared the behavior of two different corrugation types. A fundamental understanding of corrugated steel panels’ behavior under in-plane monotonic loads was gained from this study with the limitations of qualitative perceptions regarding the contribution of boundary elements on the shear wall system. 2.1.2 Emami et al. (2013) A comparative study between the seismic performances of an unstiffened steel plate shear wall and trapezoidal corrugated steel plate shear walls was performed by Emami et al. (2013). The main target of this investigation was to explore corrugated steel walls as an alternative to stiffened steel plate shear walls due to their larger out-of-plane buckling strength and cost-effective nature. This study conducted 14 experimental testing on three types of steel shear walls: an unstiffened steel plate shear wall, a steel plate shear wall with vertical corrugation, and horizontal corrugation. All the specimens were constructed to half scale, one bay and one-story size, and loaded with lateral quasi-static cyclic loads. The wall thickness and boundary conditions were kept similar in all the specimens to maintain consistency; the construction was completed without making any modifications to the test set-up. Unstiffened steel plate shear wall was designed according to the Plate Frame Interaction (PFI) method, Sabouri-Ghomi et al. (2005). The geometric properties of the corrugations adopted in this paper are presented in Figure 2.5. The beam and columns sections were adopted from European Standard, where HE-B is a typical wide flange I-shape section. Moment resting beam-column connections were implemented either through bolted connection with high strength bolts or welds. The lateral loads were applied to the top beam, HEB140. The specimens were tested under both cyclic and monotonic lateral load cases. Loading protocol recommended by AC154 for testing of metal sheeted shear walls was used for these tests. The Table 2.2 shows the dimensions of the specimens and Figure 2.6 presents the test assembly which is similar for all the tests. Figure 2.5 Trapezoidal corrugation profile (Emami et al., 2013) Table 2.2 Test matrix for the corrugated steel plate tests (Emami et al., 2013) 15 Figure 2.6 Steel plate wall testing set-up (Emami et al., 2013) 16 The experimental results attested to the claim that corrugated steel plate shear walls, irrespective of corrugation orientation, performed better than the unstiffened steel plate shear walls. Elastic stiffness of the corrugated walls was around 15% larger than its plain counterpart for the cyclic tests and 30% larger for the monotonic loading case. The ultimate strength of the unstiffened shear wall was higher than the corrugated ones, which is explained due to the ‘Accordion effect’. Corrugated specimens performed better from the seismic performance point of view since the ductility ratio and energy dissipation were 35% and 52% higher than the unstiffened specimen, respectively. An analytical study was done by analyzing the specimens with two previously recommended methods: plastic analysis of the strip model and Plate-Frame Interaction. The effects of the boundary frame were also considered in these calculations as from the unstiffened plate experimental results, and it was observed that beams had experienced yielding. Table 2.3 shows the comparison between the experimental and analytical results of this study. The authors reported that the PFI method predicts the behavior of the corrugated specimens with fair accuracy in the elastic range and for the ultimate strength, but further investigations were suggested for buckling and post-buckling behavior. Figure 2.7 presents the comparison for vertical corrugation type. The study concluded that the steel plate shear walls with corrugations yielded at a predetermined force if appropriately designed. The energy dissipation was approximately 1.52 times higher than the unstiffened steel plate, with higher initial stiffness and ductility. The steel plates were the weakest point in assembly and yielded first, wherein the yield zone is observed throughout the corrugated panel as opposed to the unstiffened steel plate shear wall. 17 Table 2.3 Comparison between analytical and experimental results (Emami et al., 2013) Figure 2.7 Force-deformations relationship comparing numerical analysis and experimental results (Emami et al., 2013) The experimental study conducted by Emami et al. (2013) provided a comprehensive understanding of the behavior of corrugated shear wall system under in-plane shear load. Their performance as a seismic force resisting system was compared to conventional unstiffened steel plate shear walls. The steel plate corrugated walls were surrounded by a boundary frame with rigid connections between the elements. It was hypothesized that this frame provides additional stiffness and lateral resistance to the shear wall system. Stable hysteresis was observed in the experiments involving corrugated shear walls with ample ductility and energy dissipation which was attributed to the accordion effect. Further investigations over the effects of boundary frame on the overall performance of the corrugated wall system under in-plane loads and the Strip modelPFI methodStrip modelPFI methodNo. 1 580 460 518 1.26 1.12 550No. 2 500 385 487 1.3 1.03 450No. 3 490 423 540 1.16 0.91 450Specimens Experimental ultimate strength (KN)Analytical ultimate strength (KN)Exp. /Ana. strength Cumulated energy at 4% drift (KN m)18 effect of axial loads applied in parallel to the corrugations were carried out in the study presented in the thesis. 2.1.3 Emami & Mofid (2014) Another study conducted by Emami & Mofid (2014) primarily focused on presenting finite element models created in ABAQUS, which were verified from the experimental results presented in section 2.1.3. Geometric and material non-linearities were incorporated considering the complex nature of the corrugated wall panels. Corrugated steel plate shear walls, steel shear walls, flat infill panels, and corrugated plate infill panels were studied. The models were created to capture the complex behavior of corrugated shear wall specimens observed in the experiment. Horizontal loads were applied at the top beam with no vertical loads. The authors performed a mesh study on the finite element models, narrowing the mesh size to the degree where it provided acceptable results coupled with reasonable analysis time, indicating that corrugated steel plate models are mesh sensitive. The models also included geometric non-linearities. The bottom edge of the finite element model was fixed at all nodes and the out-of-plane displacement at the center of the beam-column connections. The loading was applied to the control nodes at the top in the lateral direction. Material properties were adopted from the tensile coupon test, and same behavior in compression and tension was assumed. Figure 2.8 shows the deformed shape and the maximum in-plane principal stress of the finite element analysis. 19 Figure 2.8 Analysis results for the monotonic test of vertical corrugation type: (a) Final deformed shape; (b) max in-plane principal stress (Emami & Mofid, 2014) The authors tried three different algorithms from the ABAQUS library which were: (i) Static; (ii) Riks solution, Tsai & Palazotto, (1990) and (iii) explicit dynamic analysis. Static stress analysis and Riks analysis, with initial geometric imperfections added based on the first mode of buckling analysis, provided acceptable predictions for the steel plate shear walls. Accurate out-of-plane deflection and force-displacement diagram results were achieved with slightly lower ultimate strength in cyclic analysis. In the case of corrugated steel plate shear walls with vertical corrugations, neither Riks algorithm nor the static stress algorithm converged and was concluded to be impractical in analyzing corrugated finite element shell models by the authors. The authors recommended dynamic explicit analysis for corrugated models for both orientations of corrugations which was corroborated by reasonably accurate agreement of elastic stiffness, deformed shape, Von Mises stress distribution, and shear force-displacement behavior. In contrast, the strength in the plastic region differed a bit from test results, with the analytical model predicting lower values with error ranging from zero to 21%. It was also found out that initial imperfections had little effect on the results. Figure 2.9 presents the comparison for experimental and numerical results. 20 Figure 2.9 Force-displacement validation of vertical corrugation type: (a) Monotonic test (b) cyclic test (Emami & Mofid, 2014) The study concluded that the finite element models generated for each type of specimen accurately predicted the behavior in the elastic region and energy dissipation. The differences in post-buckling region of corrugated models were attributed to the unrealistic perfection aimed in the numerical models that 21 identified interactive non-linear buckling complex, meaning it is hard to predict buckling behavior in finite element models. Lastly, adding damage mechanics, fatigue and damping did not positively affect model response as seen from lower strength results. This investigation provides good insights regarding the finite element modeling techniques for corrugated steel plate shear wall systems. The suggestions were used while formulating the FEM in ABAQUS for the current study on CFSCW, such as modeling the infill walls as shell elements, considering boundary elements in the model, and analyzing the model using the dynamic explicit solver to bypass convergence difficulties. The model presented by Emami & Mofid (2014) did not include replication of bolted connections as they were assumed to be rigid. This criterion was further explored in the current research, as the effect of bolt’s stiffness along with their quantity was inspected. 2.1.4 Zhao et al. (2017) A recent analytical study on corrugated wall panels was conducted by Zhao et al. (2017), presenting the seismic performance of a different type of corrugated steel plate shear walls (CoSPW) with unstiffened special plate shear walls (SPW). Full scale numerical models for each specimen were created in ABAQUS and subjected to cyclic lateral loads. The primary motivation of this study came from the inability to use unstiffened steel plate shear walls in tall buildings due to early elastic buckling under service loads. The study aimed to investigate the hysteretic behavior, energy dissipation capacity, and lateral load distribution with varying parameters in the corrugated specimens and finally propose some preliminary design recommendations. The specimens were mainly divided into two groups based on the relative capacity of the boundary elements, strong frame and weak frame. For the “strong frame” case, the boundary frame was designed based on AISC Design Guide 20 and AISC 341-10 whereas, the “weak frame” case had 40% lower bending stiffness. The boundary frame around the specimens is kept the same for each individual case along with 22 the plate thickness. Parameters considered in this study were: two different types of corrugations patterns – sinusoidal and trapezoidal; deep and shallow corrugation depths; two different capacity designed boundary frames – strong and weak frame and application of gravity loads. All the wall specimens were modeled to have dimensions of 3m by 3m by 5mm. The corrugation profiles are presented in Figure 2.10. The test matrix for the FEA is presented in Table 2.4. S4R shell elements with reduced integration were used for modeling the members except for the wall panels, where 7 points throughout wall thickness were considered to account for the geometric and material nonlinearities. The initial geometric imperfections for SPW were set to 1/1000 of the plate length and 1/750 for the corrugated wall considering their higher out-of-plane stiffness. Boundary conditions for the base were fixed in all six degrees of freedom and out-of-plane displacements were constrained at all nodes on the top beam. The finite element model was verified with the experiments conducted by Park et al. (2007) on framed steel plate walls. Figure 2.10 Types of corrugation studied (Zhao et al., 2017) 23 Table 2.4 Test Matrix for the FEA study (Zhao et al., 2017) Note: CoSPSWs = corrugated steel plate shear wall; HSW = horizontal CoSPW; HTW = trapezoidally corrugated panel; PW = plane wall; SC = strong frame case; SPSW = special plate shear walls; VSW = vertical CoSPW; WC = weak frame case. Load carrying mechanisms for SPW were considered to be mainly due to the “tension field action” based on the recommendations from the ASIC design guide. Moreover, the study suggested shear yielding as the lateral load-carrying mechanism for corrugated wall panels based on the Design manual for PC bridges with corrugated steel webs. Lateral strength equations for each of these cases are given by equation (2.6) and (2.7) 𝑉𝑉𝑃𝑃𝑃𝑃 = 0.5𝑓𝑓𝑦𝑦𝑡𝑡𝑤𝑤𝐿𝐿𝑐𝑐𝑐𝑐 sin 2𝛼𝛼 (2.6) 𝑉𝑉𝐶𝐶𝑃𝑃 = 𝜏𝜏𝑐𝑐𝑐𝑐𝑡𝑡𝑤𝑤𝐿𝐿𝑐𝑐𝑐𝑐 (2.7) where 𝑓𝑓𝑦𝑦 is the material yield strength, 𝑡𝑡𝑤𝑤 is the thickness of the wall panel, 𝐿𝐿𝑐𝑐𝑐𝑐 is the clear distance between column flanges, 𝛼𝛼 is the angle of inclination of tension field action from the vertical direction and 𝜏𝜏𝑐𝑐𝑐𝑐 is the critical shear stress. The specimens were subjected to quasi-static pushover and cyclic loads. Loading cases with and without additional gravity loads were considered separately. The loading protocol implemented for the cyclic analysis had increasing amplitudes with a maximum story drift ratio of 4%. The study concluded that types of corrugations like sinusoidal or trapezoidal and orientation of the corrugation had little effect on the Direction Length (mm)Amplitude (mm)SC-PW Plane —— —— ——SC-HSW-I Sinusoidal Horizontal 300 60SC-HSW-II Sinusoidal Horizontal 300 30SC-VSW Sinusoidal Vertical 300 60SC-HTW Trapezoidal Horizontal 300 50WC-PW Plane —— —— ——WC-HSW Sinusoidal Horizontal 300 60WC-VSW Sinusoidal Horizontal 300 60 Top beam HM400*300*10*16Boundary sectionGroup # Notation Wall typeCorrugation wave Wall dimension (mm)1—Strong frame3,000*3,000*5Column HW400*400*13*21Top beam HM500*300*11*152—Weak frameColumn HW350*350*12*193,000*3,000*524 panels' performance in contrast to the depth of the corrugations. Figure 2.11 shows the comparison between the backbone curves of horizontal and vertical orientation; also, between different types of corrugation patterns. Shallow depth of corrugations turned out to have lower performance than conventional counterparts and hence was not recommended as an alternative. Wall panels with shallower depth of corrugation were not considered for weak frame study along with trapezoidal corrugations. Figure 2.11 Comparison between different FEA results: (a) Different types of corrugation with variation in boundary frame; (b) Backbone curves for with and without gravity load cases (Zhao et al., 2017) CoSPW were found to be indifferent to change in capacity boundary frame as compared to the SPW case. The tension field action development in SPW was incomplete when bounded by a weak frame and hence concluded to have poor performance. The influence of gravity loads was observed as hypothesized by the researchers, where the SPW buckled due to the absence of out-of-plane stiffness. CoSPWs had varying results based on the orientation of the corrugations. The vertically orientated CoSPW did not buckle, while in the case of the horizontal orientation, the panels avoided buckling altogether due to the “Accordion Effects” under the influence of gravity. Gravity loads considerably affected the SPW model as expected, but a comparatively lower influence was observed in the CoSPW, having 38% reduction is the ultimate strength. Not much difference was observed in initial stiffness while considering gravity loads. In conclusion, CoSPW performed better than SPW and was proposed as an effective alternative in tall building designs. 25 Two commonly implemented corrugation profiles, trapezoidal and sinusoidal, were numerically analyzed in this above study. A comparison between deeper and shallower corrugations was made as well. The authors concluded that the boundary columns had little effect on the initial stiffness of shear wall system. Simulating post-buckling was found out to be complex and further investigations were recommended. Depth of corrugations proportionally affected the seismic performance. Axial load cases had a negligible effect on initial stiffness, but the specimens had lower ultimate lateral resistance. The contribution of boundary elements on resisting axial loads was not explored further which is one of the aspects of the current study. The proposed design equations could be further investigated to predict the performance of Frameless panels in future phases of the current study. 2.1.5 Tong et al. (2018) A study conducted on corrugated plate shear walls done by Tong et al. (2018) proposed a new lateral loading system with two corrugated walls attached to each other, having better performance against seismic and wind loads. The study aimed to investigate the shear resistance and post-ultimate behavior of these walls. A numerical model was created in ANSYS and validated by the test results. It was subsequently used to do a parametric study to achieve the objectives of the study. The authors proposed this new system considering the limitation to use corrugated wall panels in high-rise structures which were attributed to the upper limit on the thickness which these walls can be manufactured. Two corrugated walls were attached facing each other and connected with high-strength bolts placed at predefined locations creating a matrix at the valleys of individual corrugations. Pre-tightening the high-strength bolts was implemented to achieve a stable hysteresis and prevent slippage. Figure 2.12 presents the profile of the specimens and test set-up. The double corrugated shear walls have few advantages over the single corrugated ones, like higher yield strength due to the availability of double thickness to resist shear force. The specimens' boundary conditions were found to behave like fixed connections at all four corners, unlike single corrugation type, two-side fixed and two sides simply supported. The authors further 26 discussed the behavior of the specimens by considering them as equivalent to orthotropic plates and subsequently deriving the rigidity constants and the formulae were compared with the finite element analysis. Equations (2.8) - (2.10) present the formulae derived. Figure 2.12 Profile of specimen tested and test set-up (Tong et al., 2018) 𝑚𝑚𝑒𝑒 = 𝐷𝐷𝑒𝑒 .𝜃𝜃𝑒𝑒 (2.8) 𝑚𝑚𝑦𝑦 = 𝐷𝐷𝑦𝑦 .𝜃𝜃𝑦𝑦 (2.9) 𝑚𝑚𝑒𝑒𝑦𝑦 = 𝐻𝐻.𝜃𝜃𝑒𝑒𝑦𝑦 (2.10) 27 where, 𝜃𝜃𝑒𝑒 = 𝜕𝜕2𝑤𝑤𝜕𝜕𝑒𝑒2 , 𝜃𝜃𝑦𝑦 = 𝜕𝜕2𝑤𝑤𝜕𝜕𝑦𝑦2 , 𝜃𝜃𝑒𝑒 = 𝜕𝜕2𝑤𝑤𝜕𝜕𝑒𝑒𝜕𝜕𝑦𝑦. The research concluded that the double corrugated steel plate shear walls analogy with orthotropic plates i.e. the theoretically derived formulae for the rigidity constants 𝐷𝐷𝑒𝑒, 𝐷𝐷𝑦𝑦 and torsional rigidity 𝐻𝐻 were validated in this study. The rigidity constants for double corrugated walls were higher than the single corrugated walls, which corroborates this study's initial claim and motivation. Two types of global buckling modes and a local buckling mode were observed in finite element analysis. The shear buckling load predictions presented in this study were conservative with reasonable accuracy. Lastly, the authors proposed that the normalized aspect ratio could be used as a design parameter which was reported to vary inversely with the ultimate strength and directly proportional to the maximum out-of-plane deflection. A potential modification to improve the seismic performance of a corrugated shear wall system was explored in this study. Normalized aspect ratios, similar to a single corrugated panel system, are suggested as essential design parameters. Sensitivity of bolt number and bolt distance on the DSCPW’s performance is a critical finding which can be further investigated in the Frameless panel’s case. 2.1.6 Dou et al. (2018) Dou et al. (2018) conducted a numerical investigation on steel corrugated shear walls (SCSW) to study their shear resistance and post-buckling behavior. The authors primarily focused on the effects of geometric non-linearities and material properties on post-buckling behavior while formulating the finite element models. Extensive finite element analysis was conducted where, length to height ratio was varied as a parameter. Finally, the authors presented equations in conjunction with the FEA for the shear resistance and the post-buckling behavior. The primary motivation for this research was to understand the interaction between the boundary frame and the corrugated infill walls. The finite element models were formulated by taking recommendations from past published studies conducted by Emami & Mofid (2014) and Bahrebar et al. (2016). The boundary 28 elements, beams and columns, were assumed to be rigid with pin-type connections between them. This assumption was made to ensure the infill panel solely resisted the shear loads. The corrugations were sinusoidal and were oriented parallelly to the direction of loading. The geometric dimensions of corrugation were decided based on five parameters: the panel thickness 𝑡𝑡, the panel height H, the panel width L, the corrugation length 𝐶𝐶𝑒𝑒 and corrugation depth 𝐶𝐶𝑚𝑚. The analysis was conducted in ANSYS 16.1 following previous studies’ successful implementations of corrugated steel shear wall models. The infill corrugated wall was rigidly connected to the frame members, rigid elements, to simulate welded connections. Figure 2.13 presents the FEM along with the sinusoidal corrugation profile considered for the study. The bottom connection of the system was modeled to be pinned to the ground. The shear force was applied to the top beam to a maximum of 2% drift ratio. For the material properties of the corrugated panels, the authors compared the implementation of Bilinear and Trilinear material types against tests conducted by Wang et al. (2018). After observing the effects of varying mesh size on the FEM, 14 shell elements per one line corrugation were adopted for this study taking accuracy and efficiency into consideration. The authors also noted that the mesh size had a higher effect on the residual shear resistance than the ultimate one. Figure 2.13 Corrugation profile and finite element model (Dou et al., 2018) 29 While understanding the shear resistant behavior of these infill walls, the researchers considered two main parameters: geometric imperfections and geometric dimensions. In the case of geometric imperfections, global as well as local imperfections were implemented. Considering past adaptations of different amplitudes for the imperfections, 𝐻𝐻/1000, 𝐻𝐻/500 for global and 𝑆𝑆𝑐𝑐/400 and 𝑆𝑆𝑐𝑐/200 for local imperfections were studied. Where, 𝑆𝑆𝑐𝑐 was the developed length of the axis of one repeating sinusoidal corrugation. It was concluded that the combined effect of both corrugations produced closers results to the experiments with a magnitude of H/750. The existence of geometric imperfections had a significant effect on the shear resistance, but the magnitude of the same did not vary the behavior considerably. The next parameter which was considered for this study was geometric dimensions. The authors considered three different types under this category which were 𝐿𝐿/𝐻𝐻, 𝐻𝐻/𝑡𝑡 height to thickness ratio, corrugation ratio 𝐶𝐶𝑚𝑚/𝐶𝐶𝑒𝑒 and corrugation number 𝐻𝐻/𝐶𝐶𝑒𝑒 . The effect of H/t on lateral resistance was found to be inversely proportional due to substantial reduction in out-of-plane deflection. Higher corrugation ratio resulted in lower initial lateral stiffness, but higher lateral resistance as a larger area of the plastic zone was observed. Whereas, as the corrugation number increased, a reduction in the shear resistance and the residual force capacity was observed, which was attributed to lower boundary restraining effect, which reduced the out-of-plane rigidity. On the other hand, lowering the L/H ratio increased the maximum lateral force carrying capacity and the residual force resistance due to the increase in the restraining effect provided by the boundary columns. Following these findings, the study presented design equations by conducting extensive parametric analysis of 160 models, where all the above-mentioned geometric dimensions varied. The equations thus formulated were relations between shear reduction factor 𝜑𝜑 and normalized height to thickness ratio, 𝜆𝜆𝑛𝑛. The proposed equations for maximum shear resistance produced predictions within ±5% error for 95 % of cases. Whereas in the case of post-buckling shear resistance, equations yielded acceptable results with an error of 8% in 90% of the cases. The authors noted that for large aspect ratios (𝐿𝐿/𝐻𝐻 ≥ 1.5), the maximum lateral resistance was less than shear yield force and suggested for either thicker panels or vertical corrugations. Finally, a 30 three-point curve for approximate estimation of the lateral load-displacement behavior. The points which were considered are maximum reduction factor 𝜑𝜑𝑠𝑠, reduction factor at half-story drift 𝜑𝜑0.5 and residual reduction factor 𝜑𝜑𝑐𝑐. Figure 2.14 Three-point Design Curve (Dou et al., 2018) This study discussed the sensitivity of the initial geometric imperfections with further conclusions stating the negligible effect of imperfection magnitude. The max shear resistance of corrugated panels was found out to be consistent with selected parameters whereas predicting post-buckling behavior was difficult to predict. The authors recommended to select design parameters carefully to avoid significant strength degradation in post buckling in region. Further investigations should be conducted in understanding structural behavior of the corrugated wall systems under axial loads, interaction between the frame and infill walls as well as the design of the boundary elements. 2.1.7 Farzampour et al. (2018) Following the trend of contemporary studies, Farzampour et al. (2018) conducted a parametric study on numerical models of corrugated shear walls to evaluate the damping ratios and energy dissipation. The numerical models were subjected to monotonic as well as cyclic loads. Corrugation profile angle, 31 corrugation subpanel length and the existence of an opening were the parameters accounted in this study. The performance was compared to standard steel plate shear wall with corresponding parameters. One story high panel was modeled surrounded by the boundary frame; rigid connections were implemented between the columns and beams. The authors asserted that the necessity of a boundary frame with large flexural stiffness was detrimental to the development of uniform tension field action. PFI method was implemented to formulate both steel plate shear wall and the corrugated shear wall models. Lastly, vertical load effects were ignored while analyzing the models. FEA was conducted in ABAQUS finite element modeling software. All the components were modeled as shell elements. Trilinear steel material model for the boundary frame and bilinear material model for the walls constituted the material modeling inputs for FEM. The finite element models were analyzed using the dynamic explicit solver through a displacement-controlled algorithm in both types of loading conditions. All the models were pushed to 2.5% ultimate drift ratio. The steel plate shear models were validated against the experiments conducted by G. et al. 1998 with 98% accuracy and corrugated ones against experiments conducted by Emami et al. 2013 with 85% agreement. Figure2.15 presents the models considered for this study along with the member sizes and dimensions of the individual components. Figure 2.15 Finite element models with openings: (a) Steel plate shear wall; (b) Corrugated shear wall (Farzampour et al., 2018) 32 In total, 40 models were created to conduct the parametric study. The opening sizes were 70 cm X 100 cm, 100 cm X 150 cm and 150 cm X 225 cm were investigated in both cases. For the case with no openings, similar damping coefficients were observed in either type of shear wall. Whereas in models with openings, the corrugated wall panels performed better than their steel plate counterparts due to the ability of limiting the plastic strain at the edges and corners of the opening, as observed by the authors. The following parameter studied by the authors was corrugation angle, which comprised of three values: 30°, 45° and 60° These values were chosen based on previous studies’ recommendations since, angles below 30° and above 60° did display stable hysteresis. The FEA results were normalized with corresponding corrugated shear walls with corrugation profile angle of 30°. Figure2.16 shows the definition of corrugation profile angle considered for this study. It was noted that the profile angle of corrugation was proportionally related to the general shear buckling stress. The last parameter investigated was subpanel length. Four different subpanel length values were considered 100, 150, 200, and 250 mm, and all the results were normalized to the 100 mm case. It was observed that the subpanel length had a considerable effect on corrugated shear walls’ performance, especially for the no-opening type. This parameter influenced the global buckling behavior of the system where lower values meant higher contribution of the global buckling in interactive buckling and more stable condition. Figure 2.16 Corrugation profile considered for the study (Farzampour et al., 2018) 33 Figure 2.17 Validation of numerical models: (a) Steel plate shear wall; (b) Corrugated shear wall (Farzampour et al., 2018) An extensive parametric investigation was carried out by the authors on finite element models of corrugated steel plate shear wall systems. The models were formulated and analyzed in ABAQUS using dynamic explicit solver. Bilinear material models were found to be sufficient for simulating initial stiffness and maximum shear resistance. The in-plane shear load was applied through a displacement-controlled loading protocol. These modeling techniques simulated the models with good accuracy as seen in the validation plots against previous experiments. A noteworthy conclusion from this study was increase in corrugation angle proportionally increased the performance in terms damping ratio and energy dissipation. 2.2 Summary and conclusion The literature review presented in this chapter provides a background for the current experimental and numerical investigations with a few suggestions for future phases of the project. Previous studies primarily focused on corrugated steel panels as energy dissipating components in a structure. The investigators’ approach was to improvise these elements as an effective alternative to conventional shear walls. The limitations of the previous studies can be summarized as follows: 34 • The seismic performance of these shear walls was compared to conventional stiffened steel plate or reinforced concrete shear walls. A generic design of such systems was comprised of corrugated infill walls surrounded by boundary frame to provide a higher degree of initial stiffness, improved ductility and higher energy dissipation. • The contribution of boundary frame elements to the overall lateral resistance and their interaction with the infill panels was qualitatively discussed. • The effect of axial loads was considered negligible in the design of conventional shear walls; hence, this was assumed to be absent or negligible. • The corrugations in the steel plates were symmetrically placed about a single central axis. Recommendations from past studies provided essential insight applicable to the current investigation. The sensitivity of the wall panel system’s performance due to the depth of the corrugations, the boundary columns, global and local buckling patterns and the categorizations of different types of buckling reported are a few examples of these recommendations. A general expectation of the hysteretic behavior was obtained from previous experimental investigations. Suggestions such as for the choice of shell elements, the use of a dynamic explicit solver, the magnitude of the initial geometric imperfections and the mesh size were vital in formulating the finite element model. The current study was executed taking these discernments into consideration and conducting the required modifications to accommodate the scope of this study. 35 Chapter 3 : Experimental Program 3.1 Introduction The experimental program was executed in the Structural Engineering Laboratory at the University of British Columbia (UBC). In total, 10 specimens were tested. A test rig was designed for the specific purpose of conducting the experiments on Frameless panels of different parameters. The rig was fabricated by BEHLEN Industries LP and shipped to the laboratory with the specimens. Dywidag Systems International donated the post-tensioned cables for the test. On arrival at the UBC laboratory, the testing rig was assembled, installed and the instrumentation was calibrated as per general practice. Each specimen of the Frameless panel assembly was constructed as per guidelines provided by BEHLEN Industries LP. The experimental program’s objective was to establish rationale for assessing the Frameless panels’ behavior under combined axial and cyclic shear loads followed by quantification of the key design parameters. This chapter provides the details of the experimental tests conducted on the corrugated walls for the current study. A quick overview of the program is presented by explaining different phases of the testing, including material tests and corrugated wall tests. Information regarding the test-rig and its design, and functionality are presented here. The experimental test's main focus was to study the behavior of the Frameless panels where the assembly procedure, boundary conditions, and size of the specimens were as close as possible to those of real-world situations. These details, along with their modifications made due to laboratory constraints, are presented in the subsequent sections. 3.2 Experimental program overview The corrugated wall panel test's experimental program had two components, a material test and a specimen test. The tensile coupon test (material test) was conducted on an Instron-8802 testing machine manufactured by the INSTRON Corporation at in the Materials Laboratory at UBC. The second testing phase was 36 conducted on a setup designed explicitly for this test process at UBC and manufacture by BEHLEN Industries LP. 3.3 Material testing Tensile coupon tests were conducted on Instron Machine situated in the Materials engineering lab at UBC. ASTM A370 recommendations were followed in conducting the test. The testing machine had a force capacity of 50,000 Lbs. and was capable of applying axial forces in tension and compression. A sheet of material was provided along with the specimens from which the coupons were cut for the tensile test. Dog bone shaped coupons were cut using the shear machine and sand-blasted to roughen up the surface. This ensured minimal slippage at the clamping location. Four tests were conducted for each corrugation type. The coupon was attached to the testing machine using clamps specifically designed to hold the sheet metal in place as shown in Figure 3.1. Two LVDTs were used to measure the displacement, subsequently determining the strain. 37 Figure 3.1 (a) Instron universal testing machine, (b) Specimen assembly, (c) Steel coupons 3.4 Wall panel testing Individual components of the test set-up and the specimens were shipped to the structure’s lab at the University of British Columbia from Manitoba, Canada, on a single semi with a 40 ft. bed. The components 38 were off-loaded from semi and assembled in the lab. They were affixed to the strong floor of the lab using 4 ft. long high strength steel rods and torqued to ensure no slippage occurs while testing. The individual test set-up elements were aligned with the assistance of a laser guide, which was followed by initial calibrations of the set-up as presented in Figure 3.2. Figure 3.2 Test set-up arrival and installation: (a) Receiving shipment; (b) Moving components to the lab; (c) Aligning the foundation plates; (b) Commencement of testing The set-up was carefully designed to load the specimens with in-plane forces (axial and shear). It had six main components: the reaction frame (3.4.1), actuator-load cell assembly (3.4.2), loading beam (3.4.3), post-tension cables (3.4.4), foundations plates (3.4.5), out-of-plane constraints (3.4.6) and data acquisition system (3.4.7). Figure 3.5 presents an overview of the testing rig for a single-panel specimen. The concepts for the design were adapted from previously implemented test rigs for application of in-plane loads. The test setup was designed to be compact and modular for efficient testing and easier adaptation so that further experiments might be performed in the future phases of this project. A few restrictions, including the inner 39 dimensions of the structure’s UBC laboratory and limitations on the heights of the shipping containers facilitated selecting the appropriate specimen sizes and, subsequently, the components of the setup. The shop drawings of the individual components manufactured for this set-up are presented in Appendix A. Figure 3.3 Overview of the test rig for the wall panel test: (a) Details of each component; (b) Global dimension 40 3.4.1 Reaction frame The reaction frame was designed to apply in-plane loads to the Frameless Specimens. A conventional A-frame was capacity designed to house the hydraulic jack along with the load cell. A 200 kips capacity actuator was used for the experiment. The A-frame has a W33X201 vertical element and two W12X152 diagonal elements. The frame's deflection at the maximum force capacity of the actuator was inspected and kept under 5% of the specimen's total deflection to minimize the error in the displacement data collected. Figure 3.4 presents a general 3-D diagram of the reaction frame. Figure 3.4 Reaction frame housing the actuator 3.4.2 Actuator and load cell The capacity of the actuator was chosen based on the maximum shear resistance of the specimens, which was obtained from the logged test data provided by BEHLEN Industries LP. Based on that data, 200 kips actuator manufacture by Minnesota System Testing (MTS) with a total stroke of 6 in. (± 3 in.) was chosen along with a compatible load cell, manufacture by Forsentek Co. Limited., which can record forces in tension and compression. Figure 3.5 presents the actuator and load cell assembly. The connector plates on either end of the assembly were capacity designed to effectively transmit the forces from the loading beam 41 to the reaction frame. A ratchet lever was added to align the actuator horizontally and act as a safety mechanism in the event of specimen’s failure. In-built LVDT in the actuator was used to record the lateral displacement of the specimens. The connection between the load cell and loading beam was a fixed connection, while the one between the actuator and the A-frame was a pinned connection. Figure 3.5 Actuator and load cell assembly 3.4.3 Loading beam The loading beam was designed for the effective and efficient load (shear and axial) transfer from the actuator and post-tensioned cables to the specimens. It comprises two W10X54 beams that run parallel along the length of the specimens with two channel sections placed on top at pre-determined locations to house the PTs and act as bracing between the W10X54 sections, as displayed in Figure 3.6. The post-tensioned cables' location was selected by simple calculations, ensuring equal load distribution throughout the specimens. Clean bolt type connections were capacity designed and detailed for easy repair in case of element failure. This loading beam was connected to the ceiling panel of the specimens through 9/16-inch bolts. 42 Figure 3.6 Loading beam assembly: (a)Details of each component; (b) Construction image 3.4.4 Post-tensioned cables Post-tensioned (PT) cables are usually used in concrete structures to increase tensile strength. The axial loads were simulated using the post-tensioned cables placed at strategic locations for equal distribution of loads on the wall panels. Dywidag-Systems donated their patented ThreadBars (PT rebars) for this application which had a 5/8 in. diameter and were 140 in. in length. Figure 3.7 shows the ThreadBars 43 assembly, and the hydraulic jack used to stress them to the required value. These rods were anchored at the top in the channel sections, which are part of the loading beam. The base anchorage point is an additional part of the foundation plates, a HSS 3X3X0.375, positioned on either side. 44 Figure 3.7 Post-Tensioned Rods Assembly: (a) Specimen Assembly; (b) Stressing Jack 3.4.5 Foundation plates The specimens were seated on foundation plates that supported the whole specimen assembly and transferred the loads to the strong floor underneath. The plates run along the length of the specimens. The hole pattern on the base plate was designed to consider the out-of-plane dimension of the specimen, keeping the center of the specimen in line with the direction of loading. The foundation plate assembly comprised of two components, i) baseplate and ii) shim plate. The base plate was 2 inches thick and had hole patterns detailed to house the specimens' footing channels. Shim plates, 1 inch thick, were added to provide additional support to the base plates and have an identical hole pattern. They were sized to accommodate the lip on the outer footing channel, a 90° bend, which is an implicit part of the specimen design. Two HSS beams were positioned on each side to act as anchor points at the base for the PT rods. This whole assembly was connected to the strong floor through four 2 inches in diameter high strength bolts. Figure 3.8 shows the foundation plates used in experiments. 45 Figure 3.8 Foundation plate assembly 3.4.6 Out of plane supports Two vertical columns of sections W12X87, one at the start and the other at the end, were installed, acting as out-of-plane supports for the loading beam. These columns had the angles plates attached at the bottom as guides keeping the loading beam horizontal while loading. The bottom angle plates also functioned as fail-safe supporting the loading beam after the wall panels buckled, as presented in Figure 3.9 46 Figure 3.9 Out-of-plane supports 3.4.7 Data acquisition system Data acquisition system is one of the essential components of experimental testing. It mainly comprises of three components: an analog to digital convertor, a real-time data acquisition program and a Digital Equipment Station as mentioned by Robazza, (2013). A multipurpose DAQ system, ACTS (Advanced Control Testing Systems), was used to conduct the cyclic loading tests on Frameless panels. This system worked as a data acquisition system housing a signal conditioning unit and a controller for the MTS actuator. Both of these functions were facilitated by the graphical user interface (GUI) of ALC (Advance low-level control) software. The analog data was collected from the actuator’s LVDT, load cell and servo-valve by the ACTS DAQ system. Digital data converted by the ACTS was read and processed in ALC software. The load cell and LVDT were calibrated as per standard practice before conducting the experiments. Displacement gauges were used to calibrate the LVDT in the MTS actuator whereas, the Forsentek load 47 cell was calibrated on the Baldwin-Tate-Emery Universal Testing Machine located in Structures Laboratory at the University of British Columbia. Linear calibration plots were fed into ALC for real-time display of force and displacement data while conducting the experiments. This enabled precise monitoring of the specimen’s behavior during testing. The movement of the actuator’s piston was controlled using the Proportional, Integral, Derivative (PID) control algorithm, which was efficient in quasi-static testing scenarios. The output signal was passed on to the servo-valve, which controlled the hydraulic flow to the MTS actuator. Taking in account the long time-periods of a quasi-static test, the lowest available data-logging rate of 10 Hz was chosen while saving the force-displacement data. Figure 3.10 presents an idealized linear calibration plot for load cell and displacement sensor along with the ACTS. Figure 3.10 (a) Load cell linear calibration plot; (b) LVDT cell linear calibration plot; (c) ACTS 48 3.5 Specimen assembly The complete specimen assembly was designed and manufactured by BEHLEN Industries. The assembly comprises of 4 main components: i) wall panels (CS75 & CS45)); ii) roof panel (CS45); iii) boundary columns; and iv) footing channel. The wall panels are of the same length, 41 inches, and are 114 inches in height; there are two different corrugation patterns, CS45, and CS75 where the digits represent the depth wall panel in the out-of-plane direction, which translates to 4 ½ in. depth for CS45 panels and 7 ½ in. for CS75 panels. Figure 3.11 shows the specimen assembly for the CS75 corrugation profile. Figure 3.11 Corrugate wall assembly 49 Figure 3.12 Specimen’s component details, (a) CS75 panel; (b) CS45 panel; (c) Roof panel; (d) Boundary column 50 As presented in Figure 3.12, the boundary columns are 112 in. high and are not in direct contact with the roof panel. Footing channels have identical corrugations as the respective wall panels and secure the specimens to the foundation through bolted connections. The roof panel transfers the loads, axial and lateral, to the wall panel. The roof panel and the footing channel connection to the foundation plates were over-designed, which translated to the wall panels being the weakest element in the specimen. 3.6 Test matrix The test matrix is one of the essential aspects of experimental testing to achieve the objectives effectively. The test matrix for Frameless panel testing program was created based on different factors such as corrugation types, types of loading, and axial force carrying capacity. Two profiles of corrugations were considered, CS45 with shallower corrugation depth and CS75 which had deeper corrugation depth. Axial loads were decided based on the capacity design details provided by BEHLEN Industries LP. The specimens' length is an intrinsic part of the corrugated wall design, whereas the height was restricted to 114 inches due to shipping restrictions. Table 3.1 presents the test matrix of the experimental program. Table 3.1 Test Matrix for the experimental test TEST Profile GAUGE SHEAR AXIAL (kips)1 02 153 304 05 156 309 010 3011 012 30CS45 18MonoCyclic18CyclicMonoCS7551 3.7 Loading mechanism The set-up was designed to apply in-plane lateral loads to the test specimens by transferring force from the MTS actuator to the cantilever loading beam through a fixed connection connected to the roof panel. The post-tensioned ThreadBar, connected to the loading beam, simulated the axial loads by squeezing the specimens between their anchor points. The inclination of the loading beam was taken in account and corresponding force-displacement data was corrected. Figure 3.13 Loading mechanism 52 3.8 Loading protocol 3.8.1 Monotonic loading Each type specimen was tested twice, first with monotonic loading and later with cyclic loading, where the displacement-controlled load was applied. The monotonic push over protocol sheared the specimen until failure or till the instrumentation limit was reached. Yielding displacement obtained from this test served as a reference input for the cyclic loading protocol. 3.8.2 Cyclic loading The cyclic loading protocol was formulated with the recommendation from previous studies and ATC-24 manual (Applied Technological Council-24, 1992). It had 16 cycles in total. The loading protocol starts with three cycles of 0.001 drift ratio followed by three cycles of 0.002 drift; then two cycles of 0.005, 0.0075, 0.01 each, the protocol ends with two cycles of 0.015 and 0.02. Table 3.2 provides details regarding each cycle in the protocol, and Figure 3.14 shows the pictorial representation of the same. Table 3.2 Quasi-static loading protocol matrix No Number of Cycle Amplitude (𝛾𝛾𝑡𝑡𝑜𝑜𝑡𝑡𝑎𝑎𝑜𝑜 ) 1 3 0.001 2 3 0.002 3 2 0.005 4 2 0.0075 5 2 0.01 6 2 0.015 7 2 0.02 53 Figure 3.14 Cyclic loading protocol 3.9 Test procedure Each specimen was assembled at UBC for testing; a similar procedure was implemented for all specimens with minor modifications depending on the type of corrugation. The procedure is as follows: • First, the boundary columns were attached to the foundation plates following which, the footing channels were aligned in position. • Then the inner footing channel and the boundary columns were secured using 7/8 in. (grade A490) bolts to the foundation plates. • The wall panels were brought in place and aligned with the inner footing channel, and the wall panel was bolted down to the columns and both footing channels. • The roof panel (attached to the loading beam) is lowered and secured to the wall panel. The internal bolted connection was accomplished using 9/16 in. bolts. • For the axial loading case, the post-tensioned rods were installed and secured at both ends, then stressed to pre-determined values to impart required loads. • Lastly, the initial readings from the load cell and the LVDT were noted before commencing the application of shear loads. 54 3.10 Summary The experimental testing phase of this study was carried out at the University of British Columbia. A unique testing rig was conceptualized, capacity designed and constructed this battery of tests. Ten Frameless specimens were constructed and tested to achieve the goals of this study, bearing the dimensions of 114 X 41 in. The construction and installation of the specimens were identical to the on-site assembly, which translated to an accurate representation of boundary conditions and attained the correct load transfer path in the specimen. The test matrix was comprised of varying parameters, including the corrugation profile, types of in-plane shear loads and different axial loads which assisted in quantifying the key design parameters. The yielding lateral displacement observed in the monotonic push-over tests was used as a reference for the formulation of the cyclic loading protocol. A detailed understanding of the seismic performance of Frameless panels with diverse corrugation profiles and varying axial loads was achieved. The effects of different boundary conditions, an implicit part of the design of Frameless panels, on the behavior on the wall panel system were noted down. The next chapter discusses the experimental results in detail. This data was further used to calibrate the finite element models in ABAQUS/CAE and simulate the complex behavior of these CFSCW specimens under combined axial and shear loads. 55 Chapter 4 : Experimental Results 4.1 Introduction In this chapter, the observations from the experiments conducted on the ten corrugated wall panels and material tests are discussed in detail. The experiments were conducted to understand the behavior of these loading bearing wall panels under seismic loads. The failure mechanisms, hysteresis, and buckling behavior for all the different sets of tests described in the previous chapter are presented here. Followed by a discussion about the Frameless panel’s behavior under different types of loading protocol, the effects of axial loads and a comparison between responses of the two corrugation. Subsequently, the formulation of a linearized backbone curve for CS75 panels with axial loads as design parameter is proposed. Finally, key seismic design parameters are quantified coupled with a discussion about the influence of varying axial loads on different corrugation geometries. A correction was applied to the force response data for the axially loaded tests whose response was due to the observed inclination in the top-loading beam, and this correction is presented in Appendix B 4.2 Material Test The tensile coupon tests were carried based on the recommendations provided by ASTM A370-17 (2017) on the sheets sent along with specimens. Three tests were conducted for each corrugation and thickness. The coupons were subjected to monotonic loading, and Figure 4.1 presents a stress-strain relationship for the tests, and Figure 4.2 displays the specimens at different states. Individual coupons were obtained from the sheet metal specifically used to manufacture the wall panels from corresponding profiles. The stress-strain curve presented below is the average of three tests conducted on each sheet metal. ASTM A653 Grade 40 and Grade 50 steel was used for manufacturing the wall panels. 56 Figure 4.1 Tensile couple test (a) CS75-18ga. (b) CS45-18ga. Figure 4.2 (a) Initial state; (b) necking state; (c) fracture state 4.3 CS75 corrugation type 4.3.1 Monotonic loading behavior Three tests were conducted on the CS75 corrugation type walls, with varying axial loads, which were 0 kips, 15 kips and 30 kips. Figure 4.3 presents a force-drift behavior under monotonic loading without any axial loads, along with pictorial illustrations. Yielding occurs at a 0.25% drift ratio and global buckling was observed at a 1.1% drift ratio with a yielding force of 5.2 kips and peak force capacity of 13.8 kips. An 57 increase in shear strength was noted in the post buckling region due to tension-field action until a local buckle was observed at a 2.1% drift ratio. Beyond 2.1% drift, residual strength of 6.67 kips was attained with no further increase in force carrying capacity. The second test conducted has 15 kips of axial force applied to the specimen. Similar behavior as in the non-axial loading case was observed. The force-drift relationship is illustrated by Figure 4.4. A small amount of local buckling was seen along the connection between the ceiling panel and the wall after the axial loads were applied. The panel yielded at 0.25% drift with force of 4.45 kips. Global buckling occurred at 0.6% drift ratio, where a maximum force capacity of 10.67 kips was achieved. The post-buckling stiffness, as reported in the non-axially loaded case, was considerable due to tension-field action. The local buckle in the bottom left region was observed at 1.82% drift. A total reduction of 40% in force carrying capacity was observed at the end of the test as the residual strength state was reached. Figure 4.4 shows the specimen at relevant drift ratios with corresponding force-drift ratios. The last monotonic test conducted on CS75 configuration was with a design axial loads of 30 kips. Figure 4.5 shows a force-drift relationship and deformed specimen at different drifts. Local buckles were observed along the top edge of the wall panel after the application of axial loads, which were more prominent than ones reported in the previous case. Global buckling was noted at a drift of 0.27% with a maximum force capacity of 6.63 kips. Compared to the previous two cases, the post buckling behavior was softer, possibly due to a higher magnitude of initial imperfections and the initial local buckling of the specimen. A subtle local buckle is also observed at around 1.73% drift ratio near the bottom left corner and mid-height of the panel. The residual strength of 1.87 kips was noted. 58 Figure 4.3 Non-axially loaded CS75 panel subjected to monotonic shear loads at relevant drift ratios 59 Figure 4.4 Force-Drift relationship of CS75 panel subjected to monotonic shear and 15 kips of axial loads 60 Figure 4.5 Force-Drift relationship of CS75 panel subjected to monotonic shear and 30 kips of axial load61 4.3.2 Cyclic loading behavior Each specimen was subject to cyclic loads with total of 16 cycles. The specimen with no axial loads remained mostly elastic in the first two loading cycles. In the third loading cycle, a yielding force of 4.45 kips was observed at 0.25% drift with no visual damage in the specimen. Further increase in shear strength was observed in the next loading cycle. In the fifth loading, a peak force capacity of 12.6 kips at 0.91% drift ratio, in positive loading direction, and 11.6 kips at 0.982% drift, in negative loading direction, was reported. An increase in strength due to tension-field action was observed in the sixth loading cycle. In the last loading cycle, local buckling was observed around a 1.92% drift ratio in the positive loading direction. While in the negative loading direction, it occurred at a 1.86% drift ratio. The buckling observed at 0.91% drift ratio was elastic as the panel straightened out and regained initial stiffness in the unloading cycle. Residual strength state was attained beyond the local buckling phenomenon in the last cycle. Figure 4.6 presents the relevant deformed shapes in individual cycles while Figure 4.7 presents the force-drift response. When subjected to cyclic shear loads, the specimen with a 15 kips axial force had a similar initial stiffness than its monotonically loaded counterpart. The specimen remained almost elastic in the first two loading cycles. In the loading cycle with an amplitude of 0.5% drift ratio, the specimen yielded at about 0.25% drift with a force response of 6.34 kips followed by global buckling at 0.475% drift ratio with a peak force capacity of 9.97 kips. The specimen globally buckled at 0.53% drift in the fourth loading cycle with a force response of 11.43 kips in the negative loading direction. An increase in strength due to tension-field action was observed in the fifth and sixth loading cycles. In the final cycle, local buckling was observed at 1.67% and 1.88% in positive and negative loading directions, respectively. Figure 4.8 presents the relevant deformed shapes of the specimen in individual cycles. The final deformed shape had symmetrical buckles about the specimen’s central axis depicting consistent behavior in both directions. Figure 4.9 presents a comparison between the monotonic and cyclic behavior of the specimen. 62 Figure 4.10 presents the relevant physical state of the specimen with 30 kips axial loads in individual cycles. Initial yielding of steel in the panel and local buckles were observed after applying loads to the panel. Similar to previous cases, the specimen remained almost elastic in the first two loading cycles. In the third loading cycle, the panel buckled globally in both loading directions at drifts ratios 0.3% and -0.37%. The peak force carrying capacity of 7.6 kips in the positive loading direction and 8.8 kips in the negative loading direction was reported. In the subsequent three cycles, the effect of tension-field action was observed. The local buckles were observed at -1.94% and 1.72% drifts ratios in the last loading cycle. The footing channels experienced visible uplift around the central portion during the experiment. However, the channels straightened out with negligible deformation on uninstalling the specimen, concluding that these local buckles were elastic in nature. Figure 4.11 presents the force-drift response of this specimen 63 Figure 4.6 Relevant deformed shapes in individual cycles of C75 cyclic test 64 Figure 4.7 Comparison between monotonic and cyclic performance of non-axially loaded CS75 wall panel 65 Figure 4.8 Relevant deformed shapes in individual cycles of C75 cyclic test with 15 kips axial loads 66 Figure 4.9 Comparison between monotonic and cyclic performance of CS75 wall panel with 15 kips axial loads 67 Figure 4.10 Relevant deformed shapes in individual cycles of C75 cyclic test with 30 kips axial loads 68 Figure 4.11 Comparison between monotonic and cyclic performance of CS75 wall panel with 30 kips axial loads69 4.4 CS45 corrugation type 4.4.1 Monotonic loading results The CS45 corrugation specimen was subjected to monotonic shear loads for which the force-drift behavior is presented Figure 4.12. Material yielding was observed at around 0.25% drift ratio with force capacity. The maximum force capacity was 20.84 kips and exhibited global buckling at around 1.98% drift ratio, as shown in Figure 4.12. The limitation of the testing apparatus ended the test. Residual force capacity could not be ascertained since the final state achieved was simply a global elastic buckle. The global buckling pattern seen around mid-height of the panel, spanning across its length. The second monotonic shear test conducted on the CS45 corrugation type was for the axial loading case of 30 kips. In contrast to the CS75 corrugation type, no local buckles were observed when applying axial loads for this wall panel. The peak force capacity attained was 13.8 kips at 0.88% drift ratio. Figure 4.13 presents load-drift data for the test and different deformation states at the relevant drift ratio. The post-buckling stiffness was almost zero, with little reduction in force carrying capacity. The local buckle occurred at 1.82% drift ratio, reduced the force carrying capacity by 30%, which was the residual capacity.70 Figure 4.12 Force-Drift relationship of non-axially loaded CS45 panel subjected to monotonic shear loads 71 Figure 4.13 Force-Drift relationship of CS45 panel subjected to monotonic shear and 30 kips of axial loads72 4.4.2 Cyclic loading behavior The CS45 specimen with no axial loads remained elastic in the first loading cycle. Yielding was observed at roughly 0.1% drift ratio in the second loading cycle. An increase in shear strength capacity was observed throughout cycles starting from third to sixth with now visible buckles. In the final cycle, panel underwent global elastic buckling at 1.97% and 1.67% drift ratios in positive and negative loading directions. The peak force capacity of 19.7 kips and 14.5 kips was reported at these two points of interest. Buckles in the specimen were primarily confined in the right half of the specimen. Minor uplift of the footing channel was observed at either ends of the specimen. Figure 4.14 presents the relevant deformed shapes in individual cycles while, Figure 4.15 presents the force-drift response. The last test conducted on CS45 configurations was with cyclic shear loads combined with design axial loads of 30 kips. Similar to the monotonic loading case, no initial buckling was observed after the application of axial loads. The specimen remained almost elastic in the first two loading cycles. Yielding was observed at 0.25% drift which occurred in the third loading cycle. Increase shear strength capacity was observed in the subsequent two loading cycles. In the sixth loading cycle, global elastic buckling was noted at 1.17% and 1.2% drift ratios in positive and negative loading directions. The strength degradation was softer in the positive loading direction as compared to the negative one. A single local buckle was observed in the final cycle while loading the specimen in the positive direction. The global buckles were mainly observed in the mid-section of the specimen. Minor uplift of the footing channel was observed too. Figure 4.16 presents the relevant deformed shapes in individual cycles while Figure 4.17 illustrates the force-drift relationship for this test.73 Figure 4.14 Relevant deformed shapes in individual cycles of C45 cyclic test 74 Figure 4.15 Comparison between monotonic and cyclic performance of non-axially loaded CS45 wall panel 75 Figure 4.16 Relevant deformed shapes in individual cycles of C45 cyclic test with 30 kips axial loads 76 Figure 4.17 Comparison between monotonic and cyclic performance of CS45 wall panel with 30 kips axial loads77 4.5 Discussion 4.5.1 Comparison between monotonic behavior CS75 corrugation type specimens had three axial loading cases, 0 kips, 15 kips and 30 kips. The initial stiffness was noted to be the same throughout the three axial load cases. Local buckles were consistently observed along the top edge of the wall panels subjected to axial loads. An out-of-plane deformation of the same type was noted to increase with increases in axial loads proportionally. The buckling patterns were similar in all the tests. A regain in stiffness in the post-buckling region was invariably observed in all the CS75 type tests, which can be attributed to the formation of profound tension-field activity. Figure 4.18 presents the comparison between the monotonic behavior of the CS75 specimens Figure 4.18 Comparison between monotonic behavior of CS75 specimens with varying axial loads In the case of the CS45 corrugation type, the specimens were subjected to 0 kips and 30 kips of axial loads. The initial stiffness of about 22 𝑘𝑘𝑘𝑘𝑘𝑘𝑠𝑠/𝑘𝑘𝑛𝑛 was reported for both the case as seen in Figure 4.19. Different global buckling patterns were observed. For the non -axial loading case, the global buckle spanned across 78 the panel’s length and was restricted to the mid-section. Whereas for axial case the, it extended from the center bolt of the footing channel to the mid-height of the right boundary column. Very little could be established in terms of post-buckling behavior for the non-axial load case due to instrumentation limitations, but a slight on-set of stiffness regain could be seen in the cyclic test. However, the specimen with applied design axial loads displayed minimal post-buckling stiffness, which was mainly due to the immature formation of the tension-field activity. Figure 4.19 Comparison between monotonic behavior of CS45 specimens with varying axial loads 4.5.2 Comparison between cyclic behavior Specimens subjected to cyclic shear loads with increasing amplitudes to a maximum drift ratio of 2%. For CS75 corrugation type case, a consistent buckling behavior was noted with varying axial loads. Although the increase in the degree of axial loads led to a decrease in peak force capacity and buckling drift, the residual force capacities were noted to be in a similar range. In the in-elastic region, regain of post-buckling stiffness was observed in the unloading cycle. Rocking behavior was observed due to uplift of the footing channel. Similar to the CS75 corrugations type, CS45 panels underwent global elastic buckling and local 79 buckling. The global buckling pattern observed in the non-axial case was asymmetric across the length of the panel and primarily confined to the right half specimen while in the axial loading case, symmetric global buckles about the center bolt in the footing channel were observed. Minor rocking behavior was noted in both the cases due to uplift of the footing channel. Figure 4.20 and Figure 4.21 show the cyclic force-drift responses for different axial loading cases for CS75 and CS45 respectively. Figure 4.20 Comparison between cyclic behavior of CS45 specimens with varying axial loads 80 Figure 4.21 Comparison between cyclic behavior of CS45 specimens with varying axial loads 4.5.3 Comparison between corrugation profiles The CS75 corrugation type has a deeper corrugation on the global scale, meaning a longer out-of-plane dimension, and is shaped similarly to the trapezoid ones at the local level. Specimens belonging to this corrugation type had a lower performance than their CS45 counterparts as seen in Figure 4.17(a). An asymmetrical profile of the former about the in-plane axis and deeper corrugation is suggested as one of the reasons governing their weaker performance. The CS45 corrugation type wall panels performed significantly better in terms of their peak force capacity and buckling drift ratios. Negligible rocking behavior was noted, mainly due to the design of the footing channel, where an additional bolt was present in the center. These corrugations were shallower on a global scale and sinusoidal in shape at the local level. Local buckling was not observed with the application of design loads, mainly due to improved force distribution, as a greater number of corrugations were packed into the samples as could be found in CS75 wall panels of the same length. Minimal difference was observed in the initial stiffness between the two 81 different types of corrugated wall panel specimens, as seen in Figure 4.17(b), in both the axial loading conditions. Figure 4.22 Comparison of monotonic behavior with varying axial loads: (a) No axial loads; (b) 30 kips axial loads 82 4.6 Backbone curve A procedure was proposed to define a linearized backbone of the CS75 corrugation type Frameless panels with axial loads as the key design parameter. Figure 4.23 illustrates the linearized backbone curve formulated for the Frameless panels and key parameters. The elastic stiffness, plastic stiffness, post-buckling stiffness, peak force capacity, yielding and buckling drift were used to formulate the backbone curve. The trends for these key factors and quantification of overstrength and ductility ratios are presented in the subsequent sections. Figure 4.23 Representative shear behavior under monotonic loads 4.6.1 Elastic stiffness Varying axial loads did not have a major influence on the elastic stiffness of the CS75 specimens. An average value of the 21 𝑘𝑘𝑘𝑘𝑘𝑘𝑠𝑠/𝑘𝑘𝑛𝑛. was noted. Figure 4.24 and Equation 4.1 present the fitted curve and the corresponding equation, respectively. 83 𝐾𝐾𝑒𝑒𝑒𝑒 = 0.08 × 𝑃𝑃 + 20.35 (4.1) where 𝐾𝐾𝑒𝑒𝑒𝑒 is elastic stiffness and 𝑃𝑃 is applied axial loads. Figure 4.24 Fitted curve for elastic stiffness against varying axial loads 4.6.2 Plastic stiffness The plastic stiffness was found to increase with increases in axial loads. This was observed because beyond yielding, with increasing axial loads, there was lesser headroom for stiffness degradation as panels buckled at lower drift. The equation for the linear curve fitted against experimental data is presented by Equation 4.2. Figure 4.25 shows the fitted curve along with experimental data. 𝐾𝐾𝑝𝑝𝑒𝑒 = 0.492 × 𝑃𝑃 + 9.97 (4.2) where 𝐾𝐾𝑝𝑝𝑒𝑒 is elastic stiffness and 𝑃𝑃 is applied axial loads. 84 Figure 4.25 Fitted curve for plastic stiffness against varying axial loads 4.6.3 Peak force capacity Peak force capacity varied inversely with an increase in axial loads. For the non-axial load case, the maximum shear force was 13.8 kips. Its value was reduced by 12% and 30% for 15 kips and 30 kips load cases. Equation 4.3 represents the fitted equation and Figure 4.26 compares it with experimental data. 𝐹𝐹𝑚𝑚𝑚𝑚𝑒𝑒 = −0.163 × 𝑃𝑃 + 12.92 (4.3) where 𝐹𝐹𝑚𝑚𝑚𝑚𝑒𝑒 is elastic stiffness and 𝑃𝑃 is applied axial loads. 85 Figure 4.26 Fitted curve for peak force capacity against varying axial loads 4.6.4 Yielding drift Similar to the trend observed for elastic stiffness, there was not much difference in the yielding drift with an increase in the axial loads. All the specimens yielded at around 0.26% drift ratio. The linearized equation of the fitted curve is provided by equation 4.5 and its comparison with the experimental data is shown in Figure 4.27. 𝜇𝜇𝑦𝑦 = 0.002 × 𝑃𝑃 + 0.242 (4.4) where 𝜇𝜇𝑦𝑦 is elastic stiffness and 𝑃𝑃 is applied axial loads. 86 Figure 4.27 Fitted curve for yielding drift against varying axial loads 4.6.5 Buckling drift The buckling drift ratio decreased with an increase in axial loads. The non-axial case noted the buckling drift ratio to be 1.1%, which was almost twice the one reported for the 15 kips axial load case and three times the value observed in the 30 kips case. Figure 4.28 and Equation 4.5 present the fitted curved and the corresponding equation respectively. 𝜇𝜇𝐵𝐵 = −0.02 × 𝑃𝑃 + 0.875 (4.5) where 𝜇𝜇𝐵𝐵 is elastic stiffness and 𝑃𝑃 is applied axial loads. 87 Figure 4.28 Fitted curve for buckling drift against varying axial loads 4.6.6 Post-buckling stiffness Similar to the buckling drift ratio trend, the post-buckling stiffness varied inversely with axial loads. The post-buckling stiffness was found out to be 5.625 𝑘𝑘𝑘𝑘𝑘𝑘𝑠𝑠/𝑘𝑘𝑛𝑛2, 4.73 𝑘𝑘𝑘𝑘𝑘𝑘𝑠𝑠/𝑘𝑘𝑛𝑛2 and 2.91 𝑘𝑘𝑘𝑘𝑘𝑘𝑠𝑠/𝑘𝑘𝑛𝑛2 for the non-axial, 15 kips axial load and 30 kips axial load cases, respectively. The equation for the linear curve fitted against experimental data is presented by Equation 4.6. Figure 4.29 shows the fitted curve along with experimental data. 𝐾𝐾𝑃𝑃𝐵𝐵 = −0.09 × 𝑃𝑃 + 0.967 (4.6) where 𝐾𝐾𝑃𝑃𝐵𝐵 is post-buckling stiffness and 𝑃𝑃 is applied axial loads. 88 Figure 4.29 Fitted curve for post-buckling stiffness against varying axial loads 4.6.7 Overstrength and ductility ratio FEMA P695 (2009) was referred to perform an initial seismic performance assessment of this force-resisting system. The behavior reported from nonlinear monotonic tests was used to assess the seismic performance, adhering to the recommendations. Archetype over strength ratio Ω and period-based ductility 𝜇𝜇𝑇𝑇 were calculated. The over strength ratio is the ratio between the ultimate force (maximum base shear resistance) and the force at yielding drift. In contrast, the ductility ratio is defined as the ratio between the roof displacement at 20% loss of lateral force resisting capacity and effective yield roof drift displacement. Equations 4.7 and 4.8 provide the formulae for both the parameters, Ω = 𝐹𝐹𝑚𝑚𝑚𝑚𝑒𝑒𝐹𝐹𝑦𝑦 (4.7) 𝜇𝜇𝑇𝑇 = 𝜇𝜇𝐵𝐵𝜇𝜇𝑦𝑦,𝑒𝑒𝑐𝑐𝑐𝑐 (4.8) 89 Design curves were fitted to the experimental data with axial load as the varying parameter. The fitted curves and corresponding equations are presented in Figure 4.21, and Equation 4.9 & 4.10, respectively. A slight discrepancy was observed in the axial 15 kips load case which is consistent with previous trends noted for peak force capacity and buckling drift. The accuracy of these design curves can be further refined through extensive parametric analysis with varying axial load parameters. The variation between values noted down for CS45 and CS75 configurations were more consistent between 0 kips and 30 kips axial cases as seen in Figure 4.22. The higher performance of CS45 specimens was attributed to superior geometric profile properties and the presence of an extra bolt in the base connection. Ω = −0.035 × 𝑃𝑃 + 2.51 (4.9) 𝜇𝜇𝑇𝑇 = −0.02 × 𝑃𝑃 + 1.44 (4.10) where Ω, 𝜇𝜇𝑇𝑇 and 𝑃𝑃 are overstrength ratio, ductility ratio and amount of axial load respectively. 90 (a) (b) Figure 4.30 Fitted design curve against axial loads: (a) overstrength ratio; (b) ductility ratio 91 Figure 4.31 (a) Overstrength ratio; (b) Ductility ratio 4.7 Summary A total of ten tests were conducted, which comprised two different types of corrugated wall panels. The observations noted from the tests provided a variety of information regarding the performance and behavior of these wall panels under combined axial and shear loads. Similarity between failure mechanism among both types of corrugations were observed. The buckling patterns typically observed, were along the diagonal of the specimen starting near bolted connection at the base and extending to the opposite end. In the CS45 cases, the bolted end is shifted to the central portion of the specimen based on the design, and subsequently global buckling is seen extending from center portion. Negligible difference in initial stiffness was reported between to different corrugation type specimens in all axial loading conditions. Hence, it was concluded that denser corrugation and addition of extra bolt had little effect over the system's stiffness. A linearized backbone curve for CS75 corrugation type specimens was defined with axial loads as design parameters. It was formulated based on key aspects of the shear behavior of Frameless panels such as the 92 elastic stiffness, plastic stiffness, post-buckling stiffness, peak force capacity, yielding and buckling drift. CS45 corrugation type, consistently had a better seismic performance with higher overstrength ratio and ductility as compared to CS75, which was concluded to be influenced by following aspects: stable geometric profile, presence of extra bolt in the base connection, higher grade of steel used to manufacture the panels and denser corrugation pattern. 93 Chapter 5 : Finite Element Model 5.1 Introduction Finite element model calibration is one of the more important aspects of the study. A well-calibrated model aids researcher in understanding in more detail the behavior of the elements and empowers him/her to explore a greater number of alternatives for the components. A reliable systems-level model can be developed from a well-calibrated component model. In this chapter, the modeling techniques employed, material characteristics, element types and imperfections, boundary conditions and interaction elements are discussed in detail. For this investigation, a powerful finite element modeling software, ABAQUS/CAE, was utilized to create the Frameless panels’ component level models. The graphical interface module of this software, along with Python programming, was used to produce, run and post-process the finite element models. 5.2 Model description The wall panel and two supporting boundary columns were modeled in ABAQUS, since the roofing panel and footing channel were over-designed for the test. Taking in consideration the small thickness of the elements modeled, shell elements were used. The model assembly is comprised of the aforementioned three elements. Boundary conditions were assigned to the top and bottom of the assembly thus created. The explicit dynamic solver was used since other static solvers resulted in the non-converging analysis as suggested by Emami & Mofid, (2014) The modeling was done by creating a geometric sketch of the cross-section of individual elements in the Sketch module of ABAQUS and extruded to the required height. A homogenous continuum shell element was assigned to the model. A tri-linear material stress-strain relationship was used to model the material properties. Individual components were assembled in the Assembly module in ABAQUS, where the relative 94 wall panel and the two boundary columns were arranged to replicate the experiment tests. The true stress is characterized as the stress observed instantaneously on the action of the load and similarly, the instantaneous change in gauge length of the specimen is the true strain. The material modeling is as presented in section 5.2.1. Finally, residual stresses were considered for this study considering the dense corrugated geometry of the wall panels. 5.2.1 Material modeling Steel material has different mechanical properties under cyclic and monotonic loading as presented by J. et al. (2004). However, considering the specimens’ behavior under cyclic loading, exclusive material properties had little effect on FEM behavior. Hence, a simple tri-linear material model was adopted for this study. ABAQUS/CAE employs a different method while modeling the material stress-strain relationship, which it defines as true stress and strain. The material properties extracted from the coupon tests are termed as the engineering stress and engineering strains. The conversion equation provided in the ABAQUS manual is present by the following equations. The association between engineering stress and true stress is given by: 𝜎𝜎𝑇𝑇 = 𝜎𝜎(1 + 𝜖𝜖) (5.1) Furthermore, for the true strain and engineering strain relationship, we have: 𝜖𝜖𝑇𝑇 = ln (1 + 𝜖𝜖) (5.2) The values were used from the tensile coupon tests conducted on individual gauges. The Young’s modulus was found out to be 29500 ksi. with yield stress to be 45 ksi. and ultimate strength around 55 ksi and poisson’s ratio of 0.3. 95 5.2.2 Mesh study and geometric imperfections Mesh study is one of the most critical aspects of finite element modeling. A fine mesh renders the analysis computationally inefficient whereas, a coarse one provides inaccurate results; hence different mesh sizes have a significant impact on the Finite element study. For this study, the complex geometric cross section of the specimen and adjoint boundary column required mesh convergence study for proper analysis. In this case, the mesh size was gradually reduced to find an optimum mesh size ratio to obtain reasonably accurate results within viable computational time. An element to clear height of the wall ratio of about 2.5% which translates to “mesh size-3” was found to be optimal, agreed with the boundary columns, and provided convergent analysis. Figure 5.1 Mesh-sensitivity study In components portraying significant buckling behavior, the addition of geometric imperfection becomes crucial. These imperfections account for the anomalies created in the components due to the inherent nature of cold-form steel manufacturing procedures. Sinusoidal imperfections were employed for the current spanning across the width of the specimen with an amplitude of 114/750 (height/750) as proposed by Zhao 96 et al.,(2017). The amplitude amounted to out-of-plane dimension change in the geometry of the specimen as presented in Figure 5.1, where x and y are in plane dimension of the wall. Different phase angles (modes) were iterated to calibrate the models against the experimental testing. Figure 5.2 Initial imperfections implemented in the numerical model (a) Mode 1 (b) Mode 2 5.2.3 Type of element The choice of element used in the FEM is based on several factors such as accuracy of the results, behavior of the component modelled, material properties and computational effort. In this study, shell elements were used for accurate representation at an elemental level since the thickness was considerably smaller than the geometric properties of specimen. 97 Figure 5.3 S4R element properties (Smith, 2009) ABAQUS/CAE has a large library of element types of which S4R was used for this case, a four-node shell element with reduced integration. It is a conventional type of shell element with three rotational and three translational DOFs at each node. S4R type accommodates large-strain analysis as it is a general-purpose shell element and has an adaptive nature. It uses discrete Kirchhoff thin shell theory for small thickness and thick shell theory as the thickness increases. A single integration makes it computationally efficient as well. A homogenous shell section was defined in ABAQUS where thickness properties as per the gauge of the specimen were assigned. Transverse shear was assumed to be constant over the thickness and fits well with the S4R element, allowing transverse shear deformations. Non-linear geometric transformations were accounted for using the NL Geom option in the solver. 5.2.4 Boundary conditions and interactions The boundary conditions were assigned to the top and bottom portion of the wall panel and the boundary columns representing the load transfer from the loading beam to the wall panel at the top and base connections of the boundary columns to the foundation plates. The displacement loading protocol was applied as the boundary conditions at the top simulating the actuator movement in the form of displacement-controlled loading in the U1 direction. 98 Multi-point constraints (MPC) – beam feature present in ABAQUS was used to constraint the top portion of the wall panel. The MPC comprises of master or a set of master nodes controlling the DOFs of the slave nodes about its location. Top diaphragm movement was simulated using the MPC, the master node was positioned at the central portion of the beam and the closest wall panel nodes were assigned as the slaves. Figure 5.3 presents the boundary conditions and interactions assigned in the FEM. The displacement loading protocol was assigned to the master node of the top MPC. For bottom portion, two MPC were formulated, each one for the boundary columns. Axial loads were added as concentrated loads in negative U3 direction to the master node controlling the top edge of the wall panel. Figure 5.4 Model description (CS75 type wall panel) Other interactions were used to connect the wall panels to boundary columns and simulating the footing channel connections to the wall panel at the base. The bolted connection between wall panel and the boundary columns was simulated by referring to the connector builder section in interaction module of ABAQUS. The bolt dimensions were used to assign the area of effect around the connection and number of bolts, their spacing and location were decided based on the actual specimen design. The bolts were modeled as springs with three translation DOFs whose spring constants were calibrated based on the experimental data and verified with previous studies. Springs attached at one end to the ground and the 99 other end to the wall panel's base were added to simulate the footing channel effect. These springs as well, had three DOFs and the spring constants were calibrated as mentioned before. Certain assumptions were employed for simplicity like the top edge of the wall panel was considered to be straight where in experiment, it took the shape of the roof panel and the height of the boundary column was modelled same as the wall panel. 5.2.5 Residual Stress Stressed induced the cold form steel elements as a result of manufacturing and fabricating process are residual stresses. These stresses are observed in cold form steel sheets after bending the material to required shapes. Figure 5.5 presents the difference in yield stress, with and without the inclusion of the residual stresses in a coupon test. Figure 5.5 Material behavior with and without residual stress consideration Intuitively, the steel members have lower yield stress values and reduced stiffness are observed in the steel elements as noted by Galambos, (1968). The effects of residual stresses were considered while formulating the finite element model for Frameless panels considering repeating dense corrugated patterns of the walls. An investigation conducted by Ingvarsson, (1975) on cold form steel channels sections presented the 100 residual stresses distribution along the outer and inner side of the cross section. The average of these values was referred, while assigning the residual stresses to the numerical models in this study. Figure 5.6 shows the average values along the cross-section and Figure 5.7 pictorially shows the distribution noted at t= 0 of FEA for the CS75 corrugations. Figure 5.6 Average residual stress along cold form steel channel section (Ingvarsson, 1975) 101 Figure 5.7 Residual stress in the FEM at t=0 5.3 Model validation The finite element models created in ABAQUS/CAE, as described in the previous section, were needed to be validated by the experimental tests to verify their accuracy and efficiency. The FEM were validated based on force-drift relationship and buckled shape of the wall panels. 5.3.1 Force-drift validation Calibrated of the finite element models presented for a different type of corrugation was presented in section 5.2, these models were created to simulate the monotonic behavior of specimens. During calibration, the key points considered were the initial stiffness, peak force capacity, buckling drift, and buckled shape. The 102 comparison between the simulated force-drift relationship response and experimental results is presented in Figure 5.8 and Figure 5.9 (a) (b) 103 (c) Figure 5.8 Comparison between monotonic tests and FEM for CS75 type: (a) No axial loads (b) 15 kips axial loads (c) 30 kips axial loads (a) 104 (b) Figure 5.9 Comparison between monotonic tests and FEM for CS45 type: (a) No axial loads (b) 30 kips axial loads 5.3.2 Deformed Shape The deformed shape of the numerical model was compared with the actual test results for additional validation. The out of plane buckling of numerical models and corresponding tests are presented in Figure 5.10 and Figure 5.11 at the end of the test. Local buckling was observed in the numerical models. The results presented attest the capabilities of the numerical models in simulating the Frameless panels’ responses. 105 Figure 5.10 Comparison of deformed shape in out plane direction between experimental testing and FEM (CS75): (a) No axial loads (b) 15 kips axial loads (c) 30 kips axial loads 106 Figure 5.11 Comparison of deformed shape in out plane direction between experimental testing and FEM (CS45): (a) No axial loads (b) 30 kips axial loads 5.4 Summary A consistent modeling approach is proposed using ABAQUS/CAE to simulate the nonlinear lateral force-deformation response of the Frameless panel under different axial loads. The detailed sensitivity study including the effects of the bolt connection stiffness, geometric imperfections, residual stresses and boundary conditions was conducted. The finite element model was validated using the experimental test data. The results show the proposed model was able to capture the initial stiffness, peak force capacity and buckling drift as reported in the experimental test data with reasonable accuracy. In addition, the finite element model was able to predict the deformed shape of the Frameless panel. 107 Chapter 6 : Conclusion and Future Work 6.1 Summary & conclusion A novel cold form steel corrugated wall, named the Frameless panel, was developed by BEHLEN Industries, LP, for low-rise building applications. Frameless systems have been widely used in Canada. However, no previous investigations have been done to comprehend the nonlinear response of the Frameless system under seismic loads. The seismic performance of the Frameless panels was investigated in this thesis through extensive experimental and numerical simulation. A linearized backbone curve for the CS75 corrugations type panels was defined. Key seismic design parameters, such as overstrength and ductility ratios, under varying axial loads for Frameless panels, were quantified in this thesis. 6.1.1 Experimental study In total, ten full-scale specimens were experimentally tested to study their behavior under combined axial and shear loads with two different loading protocols (monotonic and cyclic). Varying axial loads were applied using post-tensioned rods, while shear loads were applied as lateral loads using a displacement-controlled loading protocol. The cyclic loading protocol pushes the specimen using cyclic loadings at increasing amplitudes until the specimen reaches a maximum drift ratio of 2%, while the monotonic loading protocol pushes the specimen monotonically at the same target drift ratio. Material tests were also conducted on the specimens. Two different types of corrugation were studied (CS45 and CS75). CS75 has a deeper out-of-plane profile but looser corrugation compared to CS45. The effects of the varying axial loads (0 to 30 kips) were studied as parameters. Irrespective of the corrugation type, degree of axial load and type of loading protocol, the specimens exhibited similar behavior under shear loads. The specimens yielded at about 0.25% drift with a typical force response of 6 kips. The strengths of the panels increased further, reaching an ultimate shear force 108 strength which was immediately followed by global elastic buckling. Beyond this phenomenon, the CS75 formed tension-field action, while the CS45 did not. This resulted in a substantially higher post-buckling stiffness in the CS75 as compared to the CS45. Finally, a distinctive local buckle was noted after which the residual strength state was attained. Rocking behavior due to the uplift of the footing channel was consistently observed in the cyclic shear tests. This rocking behavior phenomenon was less prominent in the CS45 compared to the CS75, due to the presence of additional bolts in the footing channel. A robust procedure to define a linearized backbone curve, with axial loads as design parameters, was proposed for the CS75 panels. This backbone curve was defined by identifying the key aspects of the shear behavior, such as elastic, plastic and post-buckling stiffness; peak force capacity and yielding and buckling drift. While assessing the individual corrugations, CS75 and CS45, it was concluded that the geometrical profile profoundly influenced the seismic performance of the Frameless panel system. The CS45 with its shallower and denser corrugation pattern and higher number of bolts at its boundary connections, performed better when the specimen had a higher peak force carrying capacity, higher buckling drift and more stable hysteresis. On the other hand, a negligible effect was observed on the initial stiffness. The panel's boundary conditions influenced the buckling modes and post-buckling behavior. The CS75 corrugation type experienced local out-of-plane buckling along its top edge following applications of axial loads, while the CS45 did not display any deformations after axial load applications. The experimental program provided essential benchmark test data to propose a robust finite element model capable of capturing the complex response of Frameless panels under combined axial and shear loads. The influence of axial loads and corrugations on Frameless panels’ key seismic design parameters, such as the overstrength and ductility ratios defined by FEMA P695, were presented. These parameters were found to vary inversely with the applied axial loads. A similar trend was observed while investigating the influence of axial loads on post-buckling stiffness, peak force capacity and buckling drift. Whereas, the plastic stiffness increased with increase in axial loads. CS45 had higher overstrength and ductility ratios as 109 compared to CS75 when under the same axial loading conditions. Hence, the CS45 corrugation type was recommended as the preferred corrugation type for Frameless systems in regions with high seismic activity. 6.1.2 Finite element model A robust finite element model was developed in ABAQUS/CAE to simulate the complex behavior of the Frameless panels under combined monotonic shear and axial loads. The Frameless panel and the two boundary columns were modeled. Tri-linear material behavior, adopted from the material test data, was assigned to the finite element model. M mesh sensitivity study was performed and an element size of 2.5% of the clear wall height was considered. Displacement based shear loading and concentrated axial loads were applied to the master node controlling the top edge of the panel. Bolted connections throughout the model were simulated using wire elements. The effects of nonlinear geometry, geometric imperfections and residual stresses were considered. The boundary columns were fixed at the base, while out-of-plane constraints were employed along the top edge of the wall panel. The model was analyzed using a dynamic explicit solver. The sensitivity study demonstrated that the Frameless panel’s initial stiffness was highly influenced by the stiffness provided by boundary bolt connections. Hence, a rigid connection was not recommended for modeling the connection stiffness for the Frameless panels. Similarly, the modes of initial geometric imperfection were crucial in simulating the buckling patterns, while the imperfection magnitude had minimal effect on the lateral force-deformation response of the Frameless panel. Lastly, the initial stiffness and peak force capacity of the Frameless panel were highly dependent on the residual stress. 6.2 Future recommendations The current study focused on analyzing the seismic performance of single panel configurations of Frameless systems. The panel thickness was kept constant for this investigation and three different degrees 110 of axial load were considered while conducting the experimental tests. Taking into account the limitations of the current investigation and test setup constraints, the recommendations for future studies are as follows: • Higher L/H ratios can be investigated by stitching the individual panels in the form of a series of panel elements with boundary columns placed at both ends of the specimens. CS75 configuration’s out-of-plane instability can be explored in these tests. • The current and future phases of experimental testing are limited to gauge numbers manufactured by the industry collaborators, and other thicknesses can be explored as parameters, along with higher panels that represent real case applications. • A more efficient approach to systems-level modeling can be explored using other FEA tools such as OpenSees, which are geared more towards system-level analysis. The computational effort required by ABAQUS would be immense based on the findings from the current study. • Efforts can be made toward investigating the influence of the number of bolts on the Frameless panel’s seismic performance and variations in bolt patterns at connections between the panels and boundary columns. • Frameless panels with different openings and their out-of-plane responses will be thoroughly investigated. • Possible retrofit options on the system, such as shear- and self-centering dampers, and base isolation can be inspected depending upon the candid performance of the system. 111 Bibliography 1. Bahrebar, M., Kabir, M. Z., Hajsadeghi, M., Zirakian, T., & Lim, J. B. P. (2016). Structural performance of steel plate shear walls with trapezoidal corrugations and centrally placed square perforations. International Journal of Steel Structures, 16(3), 845–855. https://doi.org/10.1007/s13296-015-0116-y 2. Dou, C., Pi, Y. L., & Gao, W. (2018). 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International Journal of Steel Structures, 18(4), 1297–1305. https://doi.org/10.1007/s13296-018-0121-z 7. FEMA P695 (2009). Quantification of Building Seismic Performance Factors. FEMA P695. 8. G., D. R., L., K. G., Laurie, K. D. J., & E., E. A. (1998). Cyclic Test of Four-Story Steel Plate Shear Wall. Journal of Structural Engineering, 124(2), 112–120. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:2(112) 112 9. Galambos, T. V. (1968). Structural Members and Frames. Prentice-Hall. 10. Ingvarsson, L. (1975). Cold-forming residual stresses effect on buckling. 11. J., B. C., Nicos, M., & D., A. I. (2004). Component Testing, Seismic Evaluation and Characterization of Buckling-Restrained Braces. Journal of Structural Engineering, 130(6), 880–894. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:6(880) 12. Krieger, T. and W. (1959). Theory of Plates and shells. McGraw-Hill. 13. Park, H.-G., Kwack, J.-H., Jeon, S.-W., Kim, W.-K., & Choi, I.-R. (2007). 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Structural Design of Tall and Special Buildings, 26(16), 1–17. https://doi.org/10.1002/tal.1351 114 Appendices Appendix A Testing apparatus shop drawings for the corrugated wall test are presented in this section. 115 116 117 118 119 120 121 122 123 124 Appendix B Experimental data for the axial load cases were corrected due to inclination of the top loading beam which presented below. Since the load cell registered the force response directly from the top loading beam, on stressing the post-tension rods, additional force was observed. The initial angle (∠𝛼𝛼) was measured after application of axial forces for each test. It was found out that the angle of inclination remained consistent with the amount of axial loads applied. The noted values 𝛼𝛼 ∈ (0° , 1.5°) 125 Now, 𝐹𝐹𝑃𝑃𝑇𝑇𝑖𝑖′ = 𝐹𝐹𝑃𝑃𝑇𝑇 × cos𝛼𝛼 (1) 𝐹𝐹𝑃𝑃𝑇𝑇𝑖𝑖 = 𝐹𝐹𝑃𝑃𝑇𝑇 × sin𝛼𝛼 (2) Here, 𝐹𝐹𝑃𝑃𝑇𝑇 ∈ (0, 30) 𝑘𝑘𝑘𝑘𝑘𝑘𝑠𝑠. For 𝛼𝛼 ∈ (0° , 1.5°), we have 𝐹𝐹𝑃𝑃𝑇𝑇𝑖𝑖 ∈ (0, 0.63) 𝑘𝑘𝑘𝑘𝑘𝑘𝑠𝑠. and 𝐹𝐹𝑃𝑃𝑇𝑇𝑖𝑖′ ∈ (0, 29.99) 𝑘𝑘𝑘𝑘𝑘𝑘𝑠𝑠. It was assumed that the effect of change in strain due inclination of the PT was negligible. Consider 𝑥𝑥 as the displacement of the top loading beam along the inclined direction. To correct the additional force due to inclination of the post-tension rods, another correction factor was applied which is as follow: Let 𝐹𝐹𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 be the corrected experimental force response. Now for some displacement 𝑥𝑥, sin𝜃𝜃 = 𝑒𝑒120 (3) 126 𝐹𝐹𝑃𝑃𝑇𝑇𝑃𝑃 = 𝐹𝐹𝑃𝑃𝑇𝑇𝑖𝑖′ × sin𝜃𝜃 (4) ∴ 𝐹𝐹𝑃𝑃𝑇𝑇𝑃𝑃 = 𝐹𝐹𝑃𝑃𝑇𝑇𝑖𝑖′ × 𝑒𝑒120 (5) where 𝑥𝑥 ∈ (−2.5 , 2.5) 𝑘𝑘𝑛𝑛𝑖𝑖ℎ𝑒𝑒𝑠𝑠 considering full stroke in cyclic displacement loading protocol. Using equations (2) and (5), we get: 𝐹𝐹𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 𝐹𝐹𝑒𝑒𝑒𝑒𝑝𝑝 − (𝐹𝐹𝑃𝑃𝑇𝑇𝑖𝑖 + 𝐹𝐹𝑃𝑃𝑇𝑇𝑃𝑃) (6)
Thesis/Dissertation
eng
Civil Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Yang, Tony T. Y.
Experimental and numerical investigations of Frameless cold form steel corrugated wall panels subjected to in-plane monotonic and cyclic loads
Text