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Effects of ground motion duration on the seismic performance and collapse capacity of timber structures Pan, Yuxin 2018

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EFFECTS OF GROUND MOTION DURATION ON THE SEISMIC PERFORMANCE AND COLLAPSE CAPACITY OF TIMBER STRUCTURES by  Yuxin Pan  B.Eng., Sichuan University, 2010 M.Phil., The Hong Kong University of Science and Technology, 2012  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Civil Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  August 2018  © Yuxin Pan, 2018 ii  The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the dissertation entitled:  Effects of Ground Motion Duration on The Seismic Performance and Collapse Capacity of Timber Structures  submitted by Yuxin Pan  in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Civil Engineering  Examining Committee: Carlos E. Ventura, Civil Engineering Co-supervisor Haibei Xiong, College of Civil Engineering, Tongji University Co-supervisor  Liam Finn, Civil Engineering Supervisory Committee Member Gary S. Schajer, Mechanical Engineering University Examiner John A. Howie, Civil Engineering University Examiner  Additional Supervisory Committee Members: Ricardo Foschi, Civil Engineering Supervisory Committee Member Frank Lam, Wood Science Supervisory Committee Member Thomas Tannert, Civil Engineering  Supervisory Committee Member iii  Abstract  This thesis describes the performance of timber structures under long duration earthquakes. The primary objective of this study is to quantify the effects of long duration ground shaking on wood structures compared to short duration shaking. The investigation is confined to conventional low-rise and modern mid-rise woodframe buildings. Full scale models of the benchmark structures used for this investigation were also constructed and tested on shake tables. Three-dimensional numerical models of the structures were developed using the Timber3D program and validated with the shake table test data. To isolate the effects of duration, two sets of short and long duration records that had approximately the same response spectra were used for nonlinear dynamic analyses of the model structures. Their collapse capacity was evaluated using fragility curves developed by incremental dynamic analysis. The results showed the collapse rate increased under long duration shaking due to a large number of inelastic cycles and higher cumulative energy demands that timber structures experienced compare with the short duration motions. The reduction in median collapse capacity for the low-rise wood structure with engineered oriented strand board (OSB) sheathing and stucco was 26%, for the same structure but without stucco was 29%, and for structure with horizontal board sheathings was 61%, respectively. The reduction in median collapse capacity for the mid-rise woodframe structure was 18%. These results suggest that current design practice based on the response spectra analysis may not adequately characterize the potential collapse of timber structures. This study highlights the need to include ground motion duration effects into current seismic design and assessment provisions.  iv  Lay Summary  Studies have shown that the duration of an earthquake shaking has a significant impact on some types of concrete and steel structures in terms of damage potential and risk of collapse. However, very limited information is available on the duration effects on timber structures - one of the most common types of construction in North America. The purpose of this research was to investigate the effects of long duration ground shaking on timber structures. Behaviors of three typical British Columbia two-story light-frame wood houses and a six-story woodframe apartment building designed for Southern California were studied using mathematical models. The research findings were validated from full-scale shake table tests conducted on the same types of structures. The findings of this study will provide information essential for improving the seismic design of timber structures.  v  Preface  A version of Chapter 3 and Chapter 4 has been published in ASCE Journal of Structural Engineering, entitled on “Effects of ground motion duration on the seismic performance and collapse rate of light-frame wood houses” (https://doi.org/10.1061/(ASCE)ST.1943-541X.0002104). The paper was co-authored by Dr. Carlos E. Ventura and Dr. Liam Finn. I conducted all the numerical analysis and wrote most of the manuscript. Dr. Ventura was responsible for designing and conducting the shake table tests. Dr. Finn offered advice during the analysis and the manuscript.   A version of Chapter 4 has been published in the proceedings of 16th World Conference on Earthquake Engineering (16WCEE), entitled on “Nonlinear Performance and Damage Potential of Degraded Structures under Long Duration Earthquake”. The paper was co-authored by Dr. Carlos E. Ventura, Dr. Feng Xiong, Dr. Lingzhi Xie and Dr. Minjuan He. I conducted all the numerical analysis and wrote most of the manuscript. Dr. Xiong, Dr. Xie and Dr. He provided the ground motion data. Dr. Ventura offered advice during the analysis and the manuscript.   A version of Chapter 3 and Chapter 5 has been published in the proceedings of the 16th European Conference on Earthquake Engineering (16ECEE), entitled on “Effects of Long Duration Ground Motions on Mid-rise Woodframe Structure”. The paper was co-authored by Dr. Carlos E. Ventura and Dr. Haibei Xiong. I conducted all the numerical analysis and wrote most of the manuscript. Dr. Ventura provided guidance throughout the study. Dr. Xiong contributed to the preparation of the manuscript. vi  Table of Contents  Abstract ......................................................................................................................................... iii Lay Summary ............................................................................................................................... iv Preface .............................................................................................................................................v Table of Contents ......................................................................................................................... vi List of Tables ..................................................................................................................................x List of Figures ............................................................................................................................... xi List of Abbreviations ................................................................................................................. xiv Acknowledgements .................................................................................................................... xvi Dedication .................................................................................................................................. xvii Chapter 1: Introduction ................................................................................................................1 1.1 Background and motivation ............................................................................................ 1 1.2 Objectives ....................................................................................................................... 3 1.3 Organizations .................................................................................................................. 4 Chapter 2: Literature Review .......................................................................................................6 2.1 Effects of ground motion duration .................................................................................. 6 2.1.1 Definitions of ground motion duration and its influencing factors............................. 8 2.1.2 Isolation of duration from other ground motion characteristics ............................... 10 2.1.3 Selection of damage measures .................................................................................. 11 2.1.4 Ground motion selection and scaling ........................................................................ 14 2.2 Research on Seismic Response of Timber Structures ................................................... 16 2.2.1 Conventional light-frame structures ......................................................................... 17 vii  2.2.2 Modern mid-rise woodframe structures .................................................................... 21 2.2.3 Numerical studies for timber structures .................................................................... 24 2.3 Summary ....................................................................................................................... 27 Chapter 3: Model Development and Validation .......................................................................29 3.1 Introduction ................................................................................................................... 29 3.2 Modeling algorithm of the Timber3D program ............................................................ 29 3.2.1 MSTEW model ......................................................................................................... 30 3.2.2 RESST model............................................................................................................ 31 3.3 Model development and validation of low-rise wood houses ...................................... 32 3.3.1 Building description .................................................................................................. 32 3.3.2 Numerical model development ................................................................................. 34 3.3.3 Model validation ....................................................................................................... 37 3.4 Model development and validation of mid-rise woodframe ......................................... 43 3.4.1 Building description .................................................................................................. 43 3.4.2 Model development .................................................................................................. 45 3.4.3 Model validation ....................................................................................................... 48 3.5 Discussions and summary ............................................................................................. 51 Chapter 4: Effects of Ground Motion Duration on Low-rise Light-frame Wood Houses ....53 4.1 Selection of seed ground motions ................................................................................. 53 4.2 Scaling and matching of ground motions ..................................................................... 57 4.3 Collapse capacity evaluation......................................................................................... 60 4.4 Estimation of damage at design level ........................................................................... 68 4.4.1 Energy demands ........................................................................................................ 68 viii  4.4.2 Damage assessment .................................................................................................. 70 4.5 Summary ....................................................................................................................... 75 Chapter 5: Effects of Ground Motion Duration on Mid-rise Woodframe Building .............77 5.1 Ground motion database ............................................................................................... 77 5.1.1 Selection of seed ground motion ............................................................................... 77 5.1.2 Ground motion scaling .............................................................................................. 81 5.2 Unidirectional nonlinear dynamic analysis ................................................................... 82 5.2.1 Collapse capacity evaluation..................................................................................... 82 5.2.2 Damage assessment at design level .......................................................................... 85 5.3 Bi-directional nonlinear dynamic analysis.................................................................... 90 5.3.1 Collapse capacity evaluation..................................................................................... 91 5.3.2 Damage assessment at design level .......................................................................... 95 5.4 Summary ....................................................................................................................... 97 Chapter 6: Conclusions ...............................................................................................................99 6.1 Summary and contributions .......................................................................................... 99 6.2 Recommendations for future work ............................................................................. 101 Bibliography ...............................................................................................................................104 Appendix A Structural Drawings of Earthquake-99 Project .................................................. 118 Appendix B Summary of Earthquake-99 Shake Table Tests ................................................. 121 B.1 Type-1 house ........................................................................................................... 122 B.2 Type-2 house ........................................................................................................... 133 B.3 Type-3 house ........................................................................................................... 144 Appendix C Structural Drawings of NEESWood Project ...................................................... 155 ix  Appendix D Spectrally Equivalent Ground Motion Pairs for Mid-rise Woodframe .............. 160  x  List of Tables  Table 3.1 Wall hysteresis parameters used for low-rise light-frame houses ................................ 36 Table 3.2 Fundamental periods of numerical models and measured structures ........................... 37 Table 3.3 Ground motion inputs for Earthquake-99 project ......................................................... 38 Table 3.4 Unit length RESST parameters of wood shearwalls ..................................................... 47 Table 3.5 Fundamental periods for the first three modes of the mid-rise woodframe .................. 48 Table 4.1 Information of selected stations .................................................................................... 54 Table 4.2 Relationship between DI and observed damage ........................................................... 73 Table 5.1 Spectrally equivalent ground motion pairs for mid-rise woodframe ............................ 79 Table 5.2 Fragility information of the woodframe ....................................................................... 94  xi  List of Figures  Figure 2.1 Hysteretic behavior of degrading models .................................................................... 13 Figure 2.2 Full-scale cyclic test and shake table test from the Earthquake-99 project ................. 20 Figure 2.3 Photos of near-collapse woodframe buildings due to first soft/weak-story ................ 21 Figure 2.4 NEESWood testing building at the construction site .................................................. 23 Figure 2.5 Schematic illustration of a 3D one-story light-frame building in Timber3D .............. 27 Figure 3.1 Hysteretic rules of the MSTEW model ....................................................................... 31 Figure 3.2 Hysteretic rules and parameters of the RESST model ................................................ 32 Figure 3.3 Plan view of the two-story wood house ...................................................................... 33 Figure 3.4 Elevation views of three houses .................................................................................. 34 Figure 3.5 Numerical model of the Type-1 house in Timber3D .................................................. 35 Figure 3.6 Calibrated MSTEW models for different sheathing materials .................................... 37 Figure 3.7 Relative roof displacement time histories of three houses .......................................... 40 Figure 3.8 Response spectra of roof accelerations of three houses .............................................. 41 Figure 3.9 Global hysteretic loops (left) and cumulative energy dissipations (right) of three houses....................................................................................................................................................... 43 Figure 3.10 Elevation view of the mid-rise woodframe ............................................................... 44 Figure 3.11 Plan view of the first floor of the mid-rise woodframe ............................................. 44 Figure 3.12 Numerical model of the mid-rise woodframe building in Timber3D ....................... 46 Figure 3.13 Unscaled response spectra of the horizontal motions recorded at Canoga Park during Northridge earthquake (5% damping) .......................................................................................... 49 Figure 3.14 Validation of roof displacement time histories of woodframe .................................. 50 xii  Figure 3.15 Validation of global hysteretic loops of woodframe ................................................. 51 Figure 4.1 Locations of the selected strong motion stations ......................................................... 55 Figure 4.2 Response spectra of the ground motions used for this study....................................... 55 Figure 4.3 Distribution of significant durations ............................................................................ 56 Figure 4.4 Time history and significant duration of 51YAM station ........................................... 57 Figure 4.5 Long duration records matched to UHS for Vancouver .............................................. 58 Figure 4.6 Spectrally equivalent ground motions ......................................................................... 59 Figure 4.7 Roof displacement time history of Type-2 house under 51QLY motion pair ............. 61 Figure 4.8 Global hysteretic loop of Type-2 house under 51QLY motion pair ........................... 61 Figure 4.9 IDA curves of three wood houses under both sets of records ..................................... 63 Figure 4.10 Photographs of three wood houses during the shake table test ................................. 64 Figure 4.11 Collapse fragility curve of three light-frame wooden structures ............................... 66 Figure 4.12 Fragility curves of three conventional wood structures with 3% conditional drift limit....................................................................................................................................................... 67 Figure 4.13 Responses of Type-1 house under 51LSF motion pair at UHS intensity level ......... 68 Figure 4.14 Correlation of total hysteretic energy and duration for three houses ........................ 70 Figure 4.15 Damage indices for three houses under both sets of motions ................................... 74 Figure 5.1 Spectrally equivalent ground motion pair #22 ............................................................ 78 Figure 5.2 Distribution of ground motion duration ...................................................................... 80 Figure 5.3 Correlations of duration with ground motion characteristics ...................................... 81 Figure 5.4 Response spectra of scaled ground motions for mid-rise woodframe ......................... 82 Figure 5.5 Unidirectional IDA curves of mid-rise woodframe ..................................................... 83 Figure 5.6 Unidirectional collapse fragility curves....................................................................... 84 xiii  Figure 5.7 Log-log plot of collapsing spectral acceleration versus D5-95 ..................................... 85 Figure 5.8 Inter-story drift ratio at MCE level (unidirectional) .................................................... 86 Figure 5.9 Correlation of total hysteretic energy and duration (unidirectional) ........................... 87 Figure 5.10 Correlation of system damage index with duration (unidirectional) ......................... 88 Figure 5.11 Damage indices for selected walls of woodframe (unidirectional) ........................... 90 Figure 5.12 Roof displacement time histories of two corner points in the long direction ............ 91 Figure 5.13 Response spectra of ground motion pair #10 ............................................................ 92 Figure 5.14 Bidirectional IDA curves of mid-rise woodframe ..................................................... 93 Figure 5.15 Comparison of collapse fragility curves of unidirectional and bidirectional analyses....................................................................................................................................................... 94 Figure 5.16 Correlation of total hysteretic energy and duration (bidirectional) ........................... 95 Figure 5.17 Correlation of system damage index with duration (bidirectional) ........................... 96 Figure 5.18 Comparison of system damage index under unidirectional and bidirectional analyses....................................................................................................................................................... 97    xiv  List of Abbreviations  BCBC: British Columbia Building Code CLT: Cross Laminated Timber  CMR: Collapse Margin Ratio CMS: Conditional Mean Spectrum CUREE: Consortium of Universities for Research in Earthquake Engineering DBE: Design Basis Earthquake  DDD: Direct Displacement Design DDL: Design Drift Limit DOF: Degree-of-freedom EDEM: Extended Distinct Element Method EPP: Elastic-Perfectly Plastic FE: Finite Element FEMA: Federal Emergency Management Agency  GWB: Gypsum Wallboard IBC: International Building Code IDA: Incremental Dynamic Analysis IDR: Inter-story Drift Ratio MCE: Maximum Considered Earthquake MDOF: Multi-degree-of-freedom MSTEW: Modified Stewart Model NBCC: National Building Code of Canada NEES: Network of Earthquake Engineering Simulation NSMONS: National Strong Motion Observation Network System  OSB: Oriented Strand Board PBSD: Performance-based Seismic Design PGA: Peak Ground Acceleration PSHA: Probabilistic Seismic Hazard Assessment xv  RESST: Residual Strength Model SDOF: Single-degree-of-freedom SF: Scaling Factor TF2000: Timber Frame 2000 UHS: Uniform Hazard Spectrum  xvi  Acknowledgements  This research was partially supported by a Collaborative Research Project under International Joint Research Laboratory of Earthquake Engineering (ILEE) and a doctoral scholarship from the China Scholarship Council (CSC).  I feel honored to express my deepest and most sincere gratitude to my supervisor Prof. Carlos E. Ventura for the ingenious commitment, encouragement and highly valuable advice he provided through my Ph. D studies. I am highly indebted to him for giving me ample freedom to work my way and simultaneously guiding me to the completion of this work. I owe particular thanks to Prof. Liam Finn for his continuous support, immense knowledge and friendship. I would also like to express appreciation to my co-supervisor Prof. Haibei Xiong from Tongji University and my supervisory committee members, Prof. Ricardo Foschi, Prof. Frank Lam and Prof. Thomas Tannert for their kind inspirations and valuable suggestions.   I thank Dr. Weichiang Pang for sharing the Timber3D program, and Mike Fairhurst and Marisa Mulder for helping me debug the program and collect the ground motion data. I heartily thank my dear colleagues and friends in UBC, Felix Yao, Terry Moser, Yuanjie Li, Sam Gao, Xiang Li, Yu Feng, Teng Li, Steve McDonald, Ryan Xie, Kelly Zhuo, Ziya Summer and other friends who are not listed here, for their help and support during the past five years. I would also thank Sue, Zhengzhe, Trista, and Joanna for their love and warm companionship.   Finally, special thanks go to my family who unconditionally supported me during all stages of my life. Without their love, this work would never be completed.  xvii  Dedication    I dedicate this work to my Mom and Dad who offered unconditional love and support and have always been there for me. Thank you so much.  1  Chapter 1: Introduction  1.1 Background and motivation Recent earthquakes with large magnitude and long duration, such as the events in Hokkaido, Japan (Mw 8.3, 2003), Sumatra, Indonesia (Mw 9.1, 2004), Wenchuan, China (Mw 7.9, 2008), Maule, Chile (Mw 8.8, 2010), and Tohoku, Japan (Mw 9.0, 2011), have shown the significance of ground motion duration and its impact on structural damage and economic losses. Typically, short duration motions last no longer than tens of seconds, while long duration motions last longer from tens of seconds to minutes. A technical definition differentiating between long and short duration motions will be given in next Chapter. The duration of ground motion, in addition to its intensity and frequency content, plays a significant role in the seismic design and collapse risk assessment of structural systems (Hou and Qu, 2015). The importance of the latter two factors have been directly taken into account by current design codes and standards across the world based on the response spectrum of a linear single-degree-of-freedom system (SDOF) and the corresponding ductility demand (ASCE, 2010; IBC, 2012; NBCC, 2015). However, no direct consideration is given to the duration of shaking, which has been proven of significant impact in geotechnical earthquake engineering (Green and Terri, 2005; Kayen and Mitchell, 1997; Zhang et al., 2013). The main reason is that studies on this topic reported inconsistent and inconclusive results (Hancock and Bommer, 2006). Major challenges in estimating the duration effects on structural response are categorized as follows: 1) the scarcity of long duration ground motion records until recently; 2) the determination of the ideal duration metric; 3) the uncertainty of proper damage measures; 4) accurate nonlinear modeling techniques; and 5) ground motion selection and scaling to isolate duration effect from other characteristics.  2   The answer to the question “does duration really matter” has gained greater attention in recent years as researchers working on this topic have proposed ways to better correlate damage with ground motion duration. The occurrence of mega earthquakes with long duration motions recorded in recent years, have provided an extensive database for advanced nonlinear analysis. Recent studies have also shown long duration shaking can increase the damage potential and the collapse risk of conventional masonry, concrete and steel structures significantly (Barbosa et al., 2017; Chandramohan et al., 2016b; Iervolino et al., 2006; Raghunandan and Liel, 2013). It is now widely accepted that a “duration blind” seismic design and assessment will result in insufficient seismic resistance and capacity against collapse of structures.    However, studies of duration effects on timber structures are limited, even though they are the most common types of residential constructions in North America. Since the 1994 Northridge earthquake, major research efforts have been devoted to improving the seismic resistance of low-rise timber structures (up to three-story) using data from experimental tests and analytical studies. However, the issue of duration has not been addressed explicitly (CUREE, 2002; Filiatrault et al., 2002; Pei et al., 2010; Sakamoto et al., 2004; Tomasi et al., 2015; White and Ventura, 2006). More recently, there is a growing interest in the mid-rise woodframe structures in North America. Woodframe buildings up to six-story in height are now permitted by building codes (Canadian Wood Council, 2015; IBC, 2012). Since then, a large number of mid-rise woodframe buildings have been either completed or are underway in areas prone to megathrust subduction earthquakes, where long duration motions are likely to be generated (Marsh and Gianotti, 1994). The performances of these mid-rise buildings were not evaluated in response to long duration ground 3  motions. The design and evaluation for those mid-rise buildings, either code-based or performance-based, rely on design recommendations based on short duration motions only. Such a short duration bias could potentially lead to unconservative designs.  Knowledge of ground motion duration effects on the seismic performance of timber structures are sorely needed. This need motivates the current study to bridge the knowledge gap by quantifying the influence of ground motion duration on both traditional light-frame constructions and modern type mid-rise woodframe buildings.    1.2 Objectives The goal of this Ph. D dissertation is to quantify the effects of ground motion duration on seismic performance and collapse risk of timber structures. To achieve this task, the following objectives need to be satisfied:  Establish comprehensive ground motion databases that contain long duration and spectrally equivalent short duration records. These spectrally compatible ground motions allow the effect of duration to be independently quantified;  Develop robust finite element models of benchmark timber structures with advanced nonlinear modeling techniques to accurately capture the large deformation behavior and degradation characteristics;   Validate the accuracy of numerical models with full-scale shake table testing data in both component and system levels; 4   Evaluate the seismic response of timber structures under selected ground motions through extensive nonlinear dynamic analysis and assess their collapse capacities by developing the fragility curves from the incremental dynamic analysis;  Review commonly used damage measures and identify the ones that are well suited for use in the assessment of timber structures under different intensity levels of ground shaking.  1.3 Organizations To achieve the objectives described above, this dissertation is organized as follows:  Chapter 2 first provides a detailed literature review on the research work that has previously been conducted on the effects of ground motion duration. These studies were on concrete and steel structures. The results of these studies provide a picture of how duration affects seismic performance of structures. The challenges that led to the ignorance of ground motion duration by current code provisions are discussed. Next, a list of projects that studied the seismic performance of both conventional low-rise and modern mid-rise woodframes are reviewed. This includes the experimental tests and the development of numerical models.  Chapter 3 focuses on the development and validation of the numerical models of the timber structures selected to study. This includes three two-story low-rise wood houses from the Earthquake-99 project (White and Ventura, 2006) and a six-story mid-rise woodframe from the NEESWood project (Pei et al., 2010). The models are developed using the Timber3D program (Pang et al., 2012). The parameters used for different models of wood shearwalls were calibrated 5  with cyclic test data. The final numerical models are validated with results from full-scale shake table tests.  Chapter 4 investigates the effects of ground motion duration on numerical models of three low-rise wood houses that were developed in Chapter 3 by using ground motion data collected from the same instruments for two earthquakes in China. The influences on collapse capacity and several damage measures at design level intensity are quantified.  Chapter 5 establishes a ground motion database that contains 22 pairs of long and spectrally equivalent short duration motions. Both unidirectional and bidirectional incremental dynamic analyses are performed on the mid-rise woodframe. Correlations of duration with collapse capacity and damage measures are also presented.   Chapter 6 summarizes the findings and contributions of the research work and make recommendations for future study.   6  Chapter 2: Literature Review  2.1 Effects of ground motion duration The complex nature of earthquake ground motion is often characterized by its intensity, frequency content, and duration. Despite the shift from force-based methods to performance-based methods, the elastic response spectrum that reflects the amplitude and the frequency content of ground motion still remains the base for most designs. However, one of its main limitations is that it is insensitive to prolonged duration. This was first clearly shown by Murphy and O'Brien (1977). They studied the effects of a number of cycles of a harmonic wave on the spectrum and found out in fact, after only a limited number of cycles, damped single-degree-of-freedom (SDOF) oscillators could approach their peak elastic response. They showed the number of cycles (N) of sinusoidal motion needed to reach a given fraction (F) of the maximum steady-state response of an SDOF oscillator with damping ζ is defined by the equation:          2)1ln(FN                                                            Equation 2.1 For instance, it will only take 10 cycles of motions to get 95% of the maximum response regardless of how many additional cycles (duration) of motion are applied to the system. The additional energy available from prolonged duration can be expected to have a significant effect on the performance of structure when it yields. So clearly, there is a situation where the elastic response spectrum-based design may be inadequate.   The study of ground motion duration was initiated in early 60’s and contradictory findings have been reported since then. Clough et al. (1965) first examined the effect of duration by performing 7  nonlinear dynamic analysis of a 20-story frame structure with records from the 1940 EI Centro earthquake. Later, Mahin (1980) indicated that duration of severe ground shaking could have a significant effect on inelastic deformation and energy dissipation demands. Rahnama and Manuel (1996) recognized that strength demands are insensitive to strong motion duration, instead, the input energy and hysteretic energy demands are more dependent on duration. However, Cornell (1997) pointed out that a prerequisite for the meaningful study of the duration effects was the development of reliable damage measures. He suggested the ductility is not a good measure of damage, the role of hysteretic energy in predicting physical damage is still not clear, especially when the P-delta and degradation effects are taken into account. Shome et al. (1998) found that there is no strong correlation between ground motion duration and maximum inelastic displacement. Tremblay (1998) developed the inelastic design spectra for subduction earthquakes by using simulated long duration motions. His study concludes that the elastic design spectra do not adequately reflect the effects of duration and spectral shape of Cascadia earthquakes. Similar results were reported by Chai et al. (1998) where they developed a duration-dependent inelastic seismic design spectrum by considering the inelastic cycles and plastic strain energy capacity. They concluded that this duration-dependent spectrum is highly sensitive to the strength degradation. Duration is of significance when estimating losses from potential earthquakes. In the HAZUS scheme (FEMA, 1999) of calculating earthquake losses, the effect of duration was explicitly addressed by using a viscous damping reduction factor for longer duration of shaking.  The major challenges in estimating duration effects can be categorized as follows: 1) determination of an effective duration metric; 2) more sources of long duration ground motions to counter the 8  predominance of Japanese records in the current database; 3) isolation of duration from other ground motion characteristics; 4) uncertainty of proper damage measures.   2.1.1 Definitions of ground motion duration and its influencing factors There are over 30 definitions of ground motion duration in the literature (Bommer and Martinez-Pereira, 2000). The most commonly used duration measures are the uniform duration, the bracketed duration, and the significant duration, which are defined below (Hancock, 2006).   The uniform duration is defined as the sum of time intervals that acceleration exceeds a certain threshold. The bracketed duration represents the time elapsed between the first and last instances that acceleration reaches the threshold of 0.05g (Bolt, 1973). Both duration measures are conceptually simple to use, but can be uncertain since the selection of threshold is subjective (Hou and Qu, 2015).  The significant duration is defined as the time interval over a specific range of the Arias Intensity IA (e.g. 5%-75% or 5%-95% of peak value), a hybrid measure of both duration and energy contents of ground motion  (Arias, 1970; Trifunac and Brady, 1975). The IA is obtained from: max02 )(2tA dttagI                                                 Equation 2.2 where a(t) is the recorded ground acceleration, tmax is the length of record and g is the gravitational acceleration. Foschaar et al. (2012) have concluded that the 5%-95% significant duration is the most appropriate indicator of the inelastic performance of structures. Chandramohan et al. (2016b) confirmed this by comparing the coefficient of determination (R2) of several duration metrics using 9  a regression analysis. They concluded that the significant duration is a preferred duration metric for structural performance assessment and ground motion selection. The long duration ground motions in this study are defined with 5%-95% significant duration greater than 30s. The selection of this threshold is based on recommendations in literature (Hou and Qu, 2015).    The long duration ground motions are more likely generated by large magnitude subduction earthquakes that are caused by the rupture of the locked interface between tectonic plates (Marsh and Gianotti, 1994). Ground motion duration at a site also depends on various factors, such as distance to the fault rupture, local site conditions, directivity, etc. (Bommer et al., 2009). As the distance between the source and site increases, the duration of ground shaking become larger because of the scattering and dispersion of seismic waves. It is also reported that soft soil condition and deep basins could potentially increase the duration of ground motion (Kempton and Stewart, 2006).  Large magnitude earthquakes normally have a quite long return period and therefore, very limited data has been collected, which restricted the investigation of ground motion duration during the last century. To address this challenge, researchers had to rely on artificially simulated accelerograms in addition to available records from 1960 Chile earthquake, 1964 Alaska earthquake, and 1985 Mexico earthquake (Mahin, 1980; Rahnama and Manuel, 1996; Tremblay, 1998; Xie and Zhang, 1988). The main problem with artificial ground motions was that they normally had an unrealistically large number of cycles, excessive energy contents and potentially unrealistic phases in the frequency domain (Hancock, 2006).   10  Since the 1980s, there is growing evidence that large magnitude earthquakes could occur again at regular time periods along the Pacific coast (Rogers, 1992). Recent earthquake events in Hokkaido, Japan (Mw 8.3, 2003), Sumatra, Indonesia (Mw 9.1, 2004), Wenchuan, China (Mw 7.9, 2008), Maule, Chile (Mw 8.8, 2010), and Tohoku, Japan (Mw 9.0, 2011), clearly highlight this trend and progressively provide large volumes of data to address the scarcity of long duration records.   2.1.2 Isolation of duration from other ground motion characteristics Since the ground motion duration is affected by many earthquake features, it is difficult to isolate the effects of duration from other ground motion characteristics. Obviously, it is futile to explore the direct relationship between duration and damage, since ground motions with higher intensity will be more damaging regardless of duration (Hancock and Bommer, 2006). Also, differences in spectral shape and amplitude can also lead to different structural responses.   To address this issue, a so-called “spectrally matched” method was proposed by Hancock and Bommer (2007) where the selected accelerograms were adjusted with wavelets so that they all have similar smooth response spectra. Ideally, it is more desirable to have ground motion data collected from the same instrument during different events with different duration. In this way, the effects of local site conditions and travel paths can be greatly minimized. The argument existing in this approach is that the matching process will affect the inherent characteristics of the motions and the duration measure should be re-evaluated (Hou and Qu, 2015; Ou et al., 2013).   Alternative method called the “spectrally equivalent” method was proposed by Chandramohan et al. (2013) where for each selected long duration record, a corresponding short duration ground 11  motion with inherently similar response spectrum is chosen from the database for nonlinear dynamic analysis. This method has been recognized as a more efficient solution to separate records with similar amplitude and spectra but different duration, and it has been implemented in many nonlinear analyses (Barbosa et al., 2017; Chandramohan et al., 2016b). Both methods are applied in this study to generate two spectrally compatible ground motion databases.    2.1.3 Selection of damage measures  In addition to the issues discussed above, challenges exist in choosing proper damage measures since it may influence the interpretation of duration effects. The damage in structures is affected by many factors, such as the load-deformation relationship of the structures, the onset of nonlinearity and the ground motion characteristics, etc., (Samanta et al., 2012). A wide range of  damage measures have been proposed in the literature, which can be categorized in four groups: 1) maximum response measures; 2) energy measures (e.g. hysteretic energy dissipation); 3) cyclic fatigue measures; and 4) combined measures (Hancock and Bommer, 2006).   It is now widely accepted that there is no correlation between the ground motion duration and the maximum response measures (e.g. drift or displacement) for non-degrading structures. Instead, the energy-based damage measure, such as the hysteretic energy dissipation has shown a relatively good correlation. Bommer et al. (2004) investigated the influence of duration on numerical models of masonry structures and explored the correlation of duration with various damage measures. They found measures related to peak drifts do not reveal a strong correlation with duration for the non-degrading masonry models. Iervolino et al. (2006) investigated the effects of duration on a number of SDOF systems by statistical analyses. They concluded that duration of ground motion 12  has insignificant impact on displacement ductility and cyclic ductility, but greatly affects the normalized hysteretic energy. The study of Shome et al. (1998), referred to early, also observed some degrees of correlation of the normalized hysteretic energy measure on duration for non-degrading models. Ruiz-Garcia (2010) reported strong motion duration has no significant influence on residual displacement demands of lower stories of non-degrading multi-degree-of-freedom (MDOF) systems, except in upper stories where displacement tends to increase with longer duration. Hou and Qu (2015) simulated the nonlinear response of several representative SDOF with elastic-perfectly plastic (EPP) non-degrading models. By performing statistical evaluations, they found longer durations lead to higher normalized hysteretic energy dissipation demands.  Recent studies on structures that incorporate cyclic and in-cycle degradations, on the other hand, have shown good correlation between duration and maximum response measures (Chandramohan et al., 2016b; Raghunandan and Liel, 2013). Cyclic degradation is characterized by loss of strength and stiffness occurring in subsequent cycles. In-cycle degradation is characterized by loss of strength and negative stiffness occurring within a single cycle, as illustrated in Figure 2.1 (FEMA, 2009a). The longer the ground shaking, the more hysteretic cycles each component is subjected to, and as a result, more strength and stiffness of the structure will be lost. A parametric study by Chandramohan et al. (2016b) revealed that structures with rapid cyclic degradation feature are more sensitive to the ground motion duration.  13           a) Cyclic degradation                                                             b) In-cycle degradation Figure 2.1 Hysteretic behavior of degrading models (FEMA, 2009a)  Moreover, studies based on incremental dynamic analysis (IDA) on those degrading structures have shown stronger correlation when structures are approaching collapse states rather than the yielding or post-yielding states (Ibarra et al., 2005; Liel and Raghunandan, 2013; Vamvatsikos and Cornell, 2002). In IDA, each selected ground motion is linearly scaled to multiple levels of intensity to approach collapse. The spectral acceleration at the fundamental period of the structure, Sa(T1), is normally used as intensity measure, and the structural response is monitored with the maximum inter-story drift ratio (IDR). The linear scaling process of IDA will not affect the spectral shape and significant duration of ground motions, and therefore, it has been widely adopted for investigating the effects of duration.  The effect of ground motion duration is very obvious when fatigue-related damage measures are used since cumulative plastic deformation plays a significant role in seismic design. Chai (2005) 14  developed a duration-dependent inelastic design spectrum incorporating a classical low-cycle fatigue model, as expressed below:    cfyumym N2                                              Equation 2.3   where Nf is the number of load cycles to cause failure, c is a fatigue parameter, Δum is the ultimate displacement under monotonic loading, Δm and Δy are peak and yield displacements, respectively. The constructed inelastic design spectrum in this study indicated the lateral strength of structures must be increased to compensate an increased number of inelastic cycles from long duration motions. For structures that have highly nonlinear behavior and strong energy dissipation ability, a combined damage measure that accounts for both displacement (ductility) and energy demands is more suitable. One such integral damage measure, the Park and Ang damage index, has been shown to be an excellent indicator for assessing the effect of ground motion duration by many recent studies (Barbosa et al., 2017; Hou and Qu, 2015; Park and Ang, 1985; Van de Lindt and Goh, 2004).   2.1.4 Ground motion selection and scaling Seismic design of new structures and assessment of existing structures that rely on a target spectrum first involve the selection and scaling of ground motions that closely represent the seismic hazard at the structure site. The uniform hazard spectrum (UHS) which the hazard curves are developed by performing the probabilistic seismic hazard analysis (PSHA), has been commonly used as target spectrum by many countries. This spectrum is called uniform hazard spectrum because each period has an equal target rate of exceedance, e.g. 2% in 50 years (Baker, 2008; NBCC, 2015). Physical meanings of an earthquake in terms of magnitude, source-to-site distance, and ground motion deviation, can be obtained through deaggregation of the PSHA 15  (Katsanos et al., 2010). These parameters, in addition to the local site conditions (i.e. shear wave velocity) and fault mechanism, are used to select ground motions that reflect dominant earthquakes for that specific site (NIST, 2011). The UHS has been considered conservative since the spectral acceleration at other non-target periods are exceeded with the same probability. To overcome the shortcoming of UHS, a conditional mean spectrum (CMS) has been proposed by Baker (2010), which is defined by the conditional mean and variance of spectral values at other periods.   The ground motion selection and scaling that are based on UHS and CMS, directly account for the effects of spectral shape and amplitude of ground motion. However, the procedures seldom suggest to include the duration as one selection criterion. The bias in estimating collapse capacity by using short duration ground motions only from the PEER NGA-West2 database or the FEMA P695 far-field sets may underestimate the potential collapse risk of structures (FEMA, 2009b; PEER, 2018). A recent study by Chandramohan et al. (2016a) demonstrated that the mean annual frequency of collapse of a ductile reinforced concrete building located in Seattle is underestimated by 29% when using short duration records selected from PEER NGA-West2 database only. Although the latest National Building Code of Canada (NBCC) has incorporated the Cascadia subduction earthquake into a probabilistic manner rather than deterministic, and requires at least 3 crustal, 3 subcrustal and 3 subduction motions to be selected for the nonlinear dynamic analysis in British Columbia, the duration effects are not explicitly stated in the selection process (NBCC, 2015; Tremblay et al., 2015; Ventura et al., 2015).  16  2.2 Research on Seismic Response of Timber Structures By reviewing the studies in the area of ground motion duration in last two decades, one can conclude that the ground motion duration has a significant influence on the seismic performance of structures constructed with conventional masonry, concrete and steel materials. However, there are no studies of its influence on timber structures, although they are one of the most prevalent construction types in North America. Light-frame wood structures consist of wood shearwalls and horizontal diaphragm components. The lateral loads induced by wind and earthquake are mainly resisted by the shear deformation of wall elements and the ductile sheathing-to-framing connections.  Historically, woodframe construction has performed quite well during earthquakes as it is flexible, light-weight, and its numerous connections and load paths could provide high ductility and absorb large amounts of earthquake input energy. As late as the 1970s, woodframe constructions were considered to be very safe in earthquakes and the existing building code was confidently believed to be sufficient (Li and Ellingwood, 2007). However, during the 1994 Northridge earthquake in the United States, at least half of the $40 billion property loss was attributed to wood building damage. Of the 25 fatalities associated with structural damage, 24 occurred in wood constructions. There were much more damages identified in non-engineered light-frame wood structures than engineered wood structures (CUREE, 1998; Hall, 2000; Hall et al., 1996). Some of the damages were attributed to poor construction practice such as missing hold-down, lack of wall-to-wall straps, inadequate tie-down devices, improper nailing, narrow walls, and poor quality control (Lam et al., 2002).  17  The damages exposed the deficient specifications of timber design and general lack of understanding of how wood structures behave in earthquakes. Since then, studies on the seismic response of conventional woodframe constructions have been actively carried out by many research institutions all over the world. Those projects and studies, either analytical or experimental, aimed to 1) provide a better understanding of the seismic resistance of existing woodframe; 2) revise the current building codes and standards for light-frame timber design; 3) develop specialized computer programs for nonlinear modeling and analysis of woodframe; and 4) propose effective and economical retrofit techniques for old non-engineered woodframe construction. This section presents a review of experimental and computational research on the seismic performance of timber structures.   2.2.1 Conventional light-frame structures The CUREE-CalTech Woodframe Project (also referred as the CUREE project), was launched in 1998 with the goal to significantly reduce earthquake losses to woodframe construction. This $6.9 million project was funded by the Federal Emergency Management Agency (FEMA), and subcontracted to the Consortium of Universities for Research in Earthquake Engineering (CUREE) and the California Institute of Technology (CalTech). A series of cyclic tests of wood shearwalls as well as several full-scale shake table tests of low-rise woodframe were carried out within the project (CUREE, 2002; Filiatrault et al., 2002). Topics such as the soft/weak story failure mechanism and the development of loading protocols for tests on wood shearwalls were well addressed by this project. Many significant findings, such as the building period determination and its use in demand estimation, influence of finishing materials on building dynamic behavior, energy dissipation through ductile yielding of the sheathing nailing, etc., were reported to 18  recommend modifications to codes and standards on woodframe design. Following these tests, a shake table test of a full-scale structure designed within the CUREE project were conducted at the University at Buffalo. The structure was excited at both design basis earthquake (DBE) and maximum considered earthquake (MCE) hazard levels with ground motions from the 1994 Northridge earthquake. In addition to the findings from CUREE project, the estimation of damping and the quantification of seismic energy were further investigated (Christovasilis et al., 2007). During the same period, a four-year special research project of wooden buildings was initiated in Japan, where a full-scale test at the world’s largest shake table at Miki city was conducted to investigate the collapse capacity of existing wood houses and to provide effective seismic retrofit solutions (Miyake et al., 2008). Several seismic retrofits for existing wood houses were studied and a seismic collapsing response analysis was developed which well predicted the actual collapse of the tested house.   In 1999, the University of British Columbia (UBC) and its industry partners undertook an experimental project, the Earthquake-99 Project, at the Earthquake Engineering Research Facility (EERF) laboratory to evaluate the seismic resistance of several typical single family houses (White and Ventura, 2006). There were a number of serious seismic deficiencies considered in this study, such as 1) non-engineered building with no effective shearwalls; 2) shearwalls with no anchorage or hold-downs; 3) low-cost construction with horizontal board sheathing; etc., were investigated and studied in this project. The contribution of non-structural sheathings on the overall stiffness and strength was also investigated.  19  Several common sheathing materials used in Canada were tested, including oriented strand board (OSB), plywood, horizontal board, and gypsum wallboard (GWB). In total, 23 standard 8ft by 8ft wood panels constructed with those sheathing materials were tested under both quasi-static and dynamic loading. Tests of 20 panels with stucco were also carried out to evaluate the performance of stucco cladding. Shake table tests were conducted on 6 single-story subsystems and 10 two-story wood houses, respectively. All the specimens were subjected to a sequence of ambient vibration testing, sinusoidal sweep testing and real earthquake ground motion inputs (Ventura et al., 2002). Examples of a wall test and a shake table test are shown in Figure 2.2a and b.  a) Shearwall test 20   b) Shake table test of the Type-2 house Figure 2.2 Full-scale cyclic test and shake table test from the Earthquake-99 project (White and Ventura, 2006)  In the 1989 Loma Prieta earthquake, six of the seven collapsed buildings in San Francisco were four-story wood apartment buildings with first-story parking. Perhaps two hundred such buildings were severely damaged and even collapsed during the 1994 Northridge earthquake, as illustrated in Figure 2.3a and b (FEMA, 2012). The first soft/weak-story was primarily caused by large openings and few partition walls at the ground level. This structural deficiency considered in this study has come to researchers’ attention in the past decade. At present, thousands of this type of woodframe buildings have been identified in California and about 4400 buildings in San Francisco are vulnerable to have a first story collapse (Jennings et al., 2015).  21    a) Building in 1989 Loma Prieta earthquake                        b) Building in 1994 Northridge earthquake Figure 2.3 Photos of near-collapse woodframe buildings due to first soft/weak-story (FEMA, 2012)   In 2012, FEMA proposed the P-807 Guidelines to assist engineers in retrofitting soft-story light-frame wood houses in an economical and efficient manner (FEMA, 2012). To further address this issue, a five-university multi-industry project, the NEES-Soft project, was launched in 2013 (Bahmani et al., 2014; Van de Lindt et al., 2012). Advanced real-time hybrid testing of a three-story light-frame building with soft-story was conducted at University at Buffalo. Retrofit schemes proposed by FEMA P-807, including the Cross Laminated Timber (CLT) rocking wall and cantilevered column, as well as the newly developed distributed knee brace, steel moment frame, and wood panels, were implemented into a benchmark building. It was concluded that both sets of retrofit techniques provide adequate collapse resistance to the first floor (Jennings et al., 2015).    2.2.2 Modern mid-rise woodframe structures The timber industry in recent years has busily promoted in North America to use wood materials for mid-rise buildings. Five- and six-story midrise woodframe buildings have proven popular among developers, architects, and contractors, who see them as a cost-effective and sustainable 22  alternative to other materials. However, owing to the fire regulations and the lack of knowledge of the seismic performance of taller wood buildings, wood constructions were limited to four stories in the late twentieth century (Pang et al., 2010). In 2000, a full-scale six-story woodframe building was constructed and tested in the laboratory in United Kindom as a major task of the Timber Frame 2000 (TF2000) project (Grantham et al., 2003). The experimental tests have addressed various issues of the performance of mid-rise woodframe in terms of fire safety, sound insulation, and structural stability.   To develop a performance-based seismic design (PBSD) approach to safely and economically increase the height of woodframe structures in the United States, the NEESWood Capstone project was initiated (Van de Lindt et al., 2006). Within the project, a simplified direct displacement design (DDD) procedure for mid-rise woodframe was developed and implemented for designing a six-story woodframe apartment building. The building was designed for Southern California seismic hazard conditions to meet three main performance objectives: damage limitation, life safety, and collapse prevention for far-field and near-fault events (Pang et al., 2010). DDD was originally introduced by Priestley (1999) to design concrete structures to avoid use of complex nonlinear time-history analysis. This design procedure estimated the target inter-story drift by using modal analysis that considered all vibration modes. A simplified version of the method was then proposed by Pang and Rosowsky (2009) for multistory woodframe structures. This simplified DDD procedure allowed consideration of various drift limits and non-exceedance probabilities, and therefore was suitable to implement into a PBSD framework where multiple objectives were targeted. In July 2009, the designed building was tested in full scale at the Miki shake table, as seen in Figure 2.4.  23   Figure 2.4 NEESWood testing building at the construction site (photo by John van de Lindt)  The building was constructed with standard North American style engineered wood shearwalls. The seismic performance of the building at different hazard levels was examined by running three components’ ground excitation obtained the Northridge earthquake. The building, as expected, met all the design requirements at different intensity levels and performed excellently under MCE level with a maximum inter-story drift ratio (IDR) below the 3.5% limit (Van de Lindt et al., 2010).   In 2009, the British Columbia Building Code (BCBC) in Canada officially permitted six-story woodframe residential buildings after a comprehensive consultation process (Canadian Wood Council, 2015). The technical challenges such as fire safety, structural and building envelop integrity, and sound transmission have been carefully investigated to prepare for the development of the code. In addition, many technical advisory groups were formed to help develop appropriate mitigation and implementation strategies. For example, the FPInnovation group investigated the seismic response of both 4-story and 6-story woodframe residential buildings that were designed 24  for Vancouver on a site with soil Class C as per the old 2006 BCBC and new 2010 NBCC, respectively (Ni and Popovski, 2009). Nonlinear dynamic analyses on numerical models of these structures were conducted by using ground motions from crustal and subcrustal earthquakes. All building performed well and met the design requirement with maximum inter-story drift less than 2.5%. Three years later, the International Building Code (IBC) also amended the height limit of woodframe to six-story (IBC, 2012). Innovative wood products and technologies were introduced to increase the opportunities for mid-rise wood buildings, such as the prefabricated systems and mass timber products. To date, more than 300 mid-rise woodframe buildings have been completed or are underway in North America, and this number is soaring year by year.  2.2.3 Numerical studies for timber structures Shake table tests provide information on just the specimen tested. Generalization of the results requires theoretical models, as repetition of the shake table tests are expensive. Alternatively, numerical analysis by computer simulation provides an effective way to study the seismic behavior of other woodframe structures, especially when thousands of nonlinear time history analyses are required to evaluate the structural reliability and fragility functions on those woodframe structures (Li et al., 2010).   Studies on concrete and steel structures have shown that the effects of ground motion duration are highly dependent on the nonlinear model using in the analysis. (Chandramohan et al., 2016b; Hou and Qu, 2015; Ibarra et al., 2005). Therefore, an accurate model that accounts for the degradation and nonlinearity is essential to capture the near collapse response under long duration shaking. However, unlike typical concrete and steel structures, it is very difficult to model the large 25  deformation dynamic response of light-frame wood structures that have many redundant members and interconnected framing elements (Pang et al., 2012).   The numerical modeling of light-frame buildings began in the 1980s, and progressive advancements were made from linearized static analysis at the component level to full-scale nonlinear dynamic analysis using finite element programs. Easley et al. (1982) developed a wood shearwall model based on the nail deformation from experimental tests. Two equations were proposed to estimate both the linear and nonlinear responses of typical 4ft by 8ft sheathing panels by pre-defining the force distribution in nail connectors. Falk and Itani (1989) developed a finite element model to simulate the wood shearwall where the wall and studs were modeled with elastic elements and the nonlinear material model was used for nail connectors.   To capture the overall performance, Foliente (1993) developed an SDOF that included the degradation and pinching effects. The stochastic excitations generated from Monte Carlo simulation were applied to the model that gave a reasonably accurate prediction of the structural response of wooden shear wall. Foschi (2000) developed a mechanical-based finite element (FE) wood diaphragm model HYST to simulate the nail connection. This protocol-independent model was improved by Li et al. (2011) and then implemented into a detailed FE computer program WALL2D to predict the cyclic tests of two types of shearwalls.   As part of the CUREE project, program SAWS was developed for seismic analysis where zero-length nonlinear spring models were used for shearwalls (Folz and Filiatrault, 2004a; Folz and Filiatrault, 2004b). The seismic analysis package of light-frame buildings, the SAPWood software, 26  was developed within the NEESWood Project (Van de Lindt et al., 2009). The models implemented into SAPWood have incorporated coupled shear-bending deformation and the out-of-plane behavior of diaphragms, which could accurately predict the seismic response of wood houses under design level of earthquakes in terms of inter-story drift ratio and uplift forces in hold-downs. The shake table test results of the mid-rise woodframe in NEESWood project were also used to calibrate a three-dimensional numerical model constructed in SAPWood software, demonstrating the feasibility and effectiveness of the developed analysis tool for modeling light-frame structures (Pei and Van de Lindt, 2011). To further simulate the collapsing process that involves large deformation and highly nonlinear behavior of material and geometry, a new simulation method based on the extended distinct element method (EDEM) was developed and calibrated with a real-size wooden house by Japanese research team. The damage propagation and fracturing behavior were simulated (Nakagawa et al., 2010).   More recently, a state-of-the-art three-dimensional modeling package specialized for simulating nonlinear behavior and collapse of light-frame structures, Timber3D, was developed as part of the NEES-Soft project (Pang et al., 2012). Timber3D is a MATLAB-based package which implements a nodal condensation technique to balance the computational overhead and model accuracy. The 3D model is based on the large deformation theory and corotational formulation, and both the in-plane and out-of-plane motions of the diaphragms under strong shaking can be properly modeled (Pang and Hassanzadeh Shirazi, 2012). This package has also been adopted into the ATC-116 project which focuses on “solutions of the issues of short-period building performance” (ATC, 2017). The applications of Timber3D in development, modeling, and analysis of wood archetype buildings with pushover and IDA schemes are well documented. Figure 2.5 illustrates a model 27  developed in Timber3D of a one-story light-frame building (ATC, 2017). Timber3D also provides an option to model the soil-structure interaction by including the soil-rigid link elements.  Figure 2.5 Schematic illustration of a 3D one-story light-frame building in Timber3D (ATC, 2017)  2.3 Summary Studies of ground motion duration on concrete, steel, and masonry structures were reviewed. They found the “significant duration” is a preferable measure for ground motion duration and the spectrally equivalent method is an effective approach to isolate the duration from other ground motion features. It was found that the effects of duration on collapse capacities of those structures are primarily dependent on the numerical modeling and the chosen damage measures. For the SDOF and MDOF systems that adopt non-degrading models, no correlation between duration and the maximum response measures have been observed. But, the cumulative damage measure, such as the hysteretic energy dissipation, have shown a relatively stronger correlation. They also found long duration motions have greatest impact when the materials of the structures are degradable.  28   It was notable that no analytical studies have been conducted on duration effects on timber structures. A number of shake table tests were carried out to identify the structural deficiencies and failure mechanisms of timber structures. Analytical models to capture the degradation and pinching effects of wood shearwalls were also developed. However, these studies are limited to the use of ordinary duration motions. Two groundbreaking studies, the Earthquake-99 Project at UBC which studied the seismic resistance of low-rise wood houses and the NEESWood Project of a six-story mid-rise woodframe structure conducted on the Miki shake table provided data for the validation of numerical models used in this study to investigate the duration effects.   29  Chapter 3: Model Development and Validation  3.1 Introduction This chapter presents the numerical modeling of woodframe structures that is used for quantifying the effects of ground motion duration, including three low-rise light-frame wooden houses that were constructed and tested as part of Earthquake-99 project, and a mid-rise woodframe that was designed by using the performance-based seismic design (PBSD) procedures and tested in full-scale as part of NEESWood Capstone project. The models were developed by using the Timber3D package. The modeling algorithm, element type and shearwall models of Timber3D will be first introduced. The calibrations of different types of wood shearwalls will also be described. Lastly, 3D models of the full structures will be developed and validated with shake table test data by performing modal analysis and nonlinear dynamic time history analysis.   3.2 Modeling algorithm of the Timber3D program In Timber3D, the wood diaphragms and roof are modeled as two-node, 12 degree-of-freedom (DOF) elastic beam elements that account for geometric nonlinearity. The wall studs are modeled as 12 DOF elastic frame elements. The wood shearwalls and sheathing materials are modeled as 6 DOF link elements that incorporate nonlinear hysteresis models of shearwalls calibrated with testing data. Link elements are also capable to model the anchored bolts and hold-down devices.   Two material hysteretic models for wood shearwalls available in Timber3D, namely the Modified Stewart (MSTEW) model and the Residual Strength (RESST) Model, will be briefly introduced here.  30   3.2.1 MSTEW model MSTEW model, which is also known as the CUREE model, was originally developed by Folz and Filiatrault (2001) as part of the CUREE project. The nonlinear behavior of the MSTEW model is controlled by 10 parameters: K0, r1, r2, r3, r4, Fo, Fi, δu, α and β, and its nonlinear backbone envelope curve is defined by the equation below:   ffuuuouooooKrFFKKrFF0)(exp1)()( 21                   Equation 3.1  uoopFKK                                                        Equation 3.2 where K0 is the initial stiffness, r1, r2, r3, r4 are dimensionless ratios of stiffness at different loading paths, Fo is the backbone tangent intersection, Fi is the loading path intersection, δu and δf are the ultimate and failure displacements (corresponding to a post-capping strength of 80% of the peak strength), and α and β are dimensionless hysteretic degradation parameters that determine the degree of stiffness degradation. They are obtained by fitting the model to connection test data, as illustrated in Figure 3.1. As a consequence of stiffness degradation, strength degradation is also introduced in the response. 31   Figure 3.1 Hysteretic rules of the MSTEW model  The loading force-deformation path of the MSTEW model follows a nonlinear exponential curve, while all other unloading and re-loading paths are assumed to be linear. This hysteretic model can capture the degradation in stiffness and strength as well as post-capping residual strength. A variety of wood shearwalls can be modeled with MSTEW model, such as OSB, GWB, stucco and so on.   3.2.2 RESST model RESST is an extension of the MSTEW model for wood shearwalls (ATC, 2017; Mulder, 2017; Pang et al., 2007). The nonlinear behavior of the RESST model is controlled by 12 parameters (K0, r1, r2, r3, r4, fx, f1, f2, f3, Du, α, and β), where a user-defined post-capping residual strength of walls is introduced, as shown in Figure 3.2. RESST improves the MSTEW model by assuming a nonlinear S-shape decaying backbone curve anchored at a displacement Dx and converging to pre-determined post-capping residual strength fx at large deformation. This improvement provides more realistic lateral displacement capacities of buildings.  32    Figure 3.2 Hysteretic rules and parameters of the RESST model  3.3 Model development and validation of low-rise wood houses 3.3.1 Building description In this study, three representative two-story houses with different sheathing configurations were selected for comprehensively investigating the effects of duration on conventional light-frame wooden structures, including 1) Type-1 has blocked shearwalls with OSB panels, exterior stucco sheathing, and interior GWB sheathing; 2) Type-2 has blocked shearwalls with OSB panels and interior GWB sheathing only; and 3) Type-3 has horizontal boards with interior GWB sheathing. The design/construction procedures for the first two houses followed the 1997 Uniform Building Code, where the third house followed the 1995 National Building Code of Canada (NBCC) with no seismic provisions (White and Ventura, 2006). All the three houses had same plan dimensions of 6.1m by 7.6m (20ft by 25ft). The plan view and elevation views of three houses are presented in Figure 3.3 and Figure 3.4. A proprietary innovative prefabricated nailed wood shearwall panel called “strong wall” was constructed in the two ends of each house (Simpson-Strong-Tie). Detailed structural and architectural drawings can be found in Appendix A.  33   All the three structures were subjected to strong motion excitations in the long direction (north-south) only, and the data from the tests and results were used to calibrate and verify the numerical models. The weights of the first floor diaphragm were 8.8 tons, 10.1 tons and 9.4 tons, and the weights of the roof diaphragm were 9.0 tons, 9.7 tons and 9.6 tons for Type-1, Type-2 and Type-3 houses, respectively.  Figure 3.3 Plan view of the two-story wood house   a) Elevation view of Type-1 house 34   b) Elevation view of Type-2 house  c) Elevation view of Type-3 house Figure 3.4 Elevation views of three houses  3.3.2 Numerical model development The 3D numerical models of all three houses were developed by using the Timber3D program. Figure 3.5 illustrates the model of the Type-1 house, where the 2 by 4 framing studs and 2 by 10 rim joist diagrams are modeled as frame elements, and the blocked shearwalls with the OSB, GWB and stucco sheathing materials are modeled with a 10 parameters MSTEW model. A proprietary 35  innovative prefabricated nailed wood shearwall panel called strong wall (Simpson Strong-Tie) was constructed in the two ends of each house.   Figure 3.5 Numerical model of the Type-1 house in Timber3D  Extensive test data on wood shearwalls from the CUREE project, Earthquake-99 project and the Seismic Retrofit Guidelines for Schools project in British Columbia were used to calibrate the parameters of each sheathing material (APEGBC, 2013; CUREE, 2002; White and Ventura, 2006). Figure 3.6 presents the experimental data compared to the MSTEW hysteretic parameters for blocked OSB, GWB, and horizontal board panels. Table 3.1 also summarizes the wall hysteresis parameters for GWB, stucco and horizontal boards. The overall dimensions of panels are all standard 8ft by 8ft. The 7/16” OSB panel was fastened with 50mm spiral nails at 150mm o/c along edges and 300mm o/c on intermediate members. The 1/2" GWB panel was fastened with 38mm roofing nails at 200mm o/c along edges and intermediate members. The horizontal boards were fastened with 50mm bronze smooths nails, 2 per stud. Sill plate anchor bolts were 5/8 diameter, 36  A407 bolts. Input cyclic protocols had 17 cycles increasing in amplitude from 5mm to 130mm. Initial stiffness and strength are proportionally scaled with the actual wall length in the construction. Direct superposition of different layers of finishing materials was used to build up the required lateral strength.  Table 3.1 Wall hysteresis parameters used for low-rise light-frame houses Wall type Ko (kip/in) r1 r2 r3 r4 Fo (kip) Fi (kip) δu (in) α β Blocked OSB 7.71 0.06 -0.11 1.01 0.04 6.34 0.92 2.84 1.00 1.47 Stucco 6.21 0.07 -0.27 1.00 0.01 7.33 0.81 2.83 0.80 1.10 Horizontal boards 0.63 0.11 -0.60 1.47 0.04 0.55 0.17 9.46 0.47 1.03 GWB 2.59 0.05 -0.02 1.01 0.01 0.62 0.10 1.56 0.88 1.65    a) Blocked OSB panel                                                               b) GWB panel 37   c) Horizontal boards Figure 3.6 Calibrated MSTEW models for different sheathing materials  3.3.3 Model validation Results from ambient vibration testing on wood houses were used to validate the modal dynamic properties of the three numerical models. The fundamental periods of Type-1, Type-2 and Type-3 structures obtained from ambient test data and from modal analysis of modeled structures are presented in Table 3.2. Overall, the periods of numerical models match the measured results well in a range less than 13%. The type-1 house has the lowest period due to large stiffness provided by the stucco while Type-3 house constructed with low stiffness horizontal boards has a longer period.  Table 3.2 Fundamental periods of numerical models and measured structures House type Measured periods [s] Model periods [s] Type-1 house 0.27 0.26 Type-2 house 0.29 0.32 Type-3 house 0.37 0.42  38  Next, the results of full-scale shake table tests are used to verify the nonlinear modeling capacity of Timber3D. All the three wooden houses were subjected to ground motions that were selected and modified to represent the seismicity in the Lower Mainland of Vancouver region (White and Ventura, 2006). Table 3.3 summarizes the ground motion inputs used for the shake table tests. More detailed shake table test results of three houses can be found in Appendix B. As suggested by many researchers, a nominal viscous damping value, 2% Rayleigh damping assigned to modes 1 and 2, was used in the nonlinear dynamic time history analysis as most of the damping is accounted directly in the hysteretic model of shearwalls (Kim, 2003; Pang et al., 2012).  Table 3.3 Ground motion inputs for Earthquake-99 project House type Earthquake Station PGA [g] Tpye-1 house 1985 Nahanni, Canada UBC modified Nahanni 0.32 Type-2 house 1994 Northridge, USA Sherman Oaks 0.45 Type-3 house 1995 Kobe, Japan KJMA 0.59  The results of the nonlinear time history analysis show that all the three structures exhibit primarily first weak/soft-story behavior since larger spaces were present in the first floor, as seen by the plan view in Figure 3.3. The large openings and few partition walls at the ground level mainly cause this behavior which has been identified in many conventional wood houses in North America in past earthquakes (Van de Lindt et al., 2012). The open space conditions with significantly reduced lateral stiffness and strength may result in a weak/soft-story for large levels of ground shaking, and consequently lead to side-sway collapse under both long and short duration records presented in next chapter.  39  Figure 3.7 compares the simulated roof displacement time histories at the centroid location of three houses with experimental results. As one can see from the figure, the numerical models in Timber3D can capture the overall shape of the time history responses for Type-1 and Type-2 houses in terms of peak displacements and residual displacements. For the Type-3 house (that was sheathed with horizontal boards), the peak response was underestimated. This can be explained by that the material model for horizontal boards was based on a cyclic test which only reached a 5% drift, while the shake table test under the Kobe motions led to a relatively higher drift over 8% (200mm). The structure did not collapse but it came into an unstable state where the numerical model could not predict the response accurately.    40   Figure 3.7 Relative roof displacement time histories of three houses  The numerical models were also validated by plotting the response spectra of roof accelerations of three houses, as shown in Figure 3.8. The numerical models of Type-1 and Type-2 houses slightly overestimated the spectral accelerations at very short period range (below 0.2s), but for a wider period range that covers the fundamental periods of the wood houses and above, good agreement between numerical simulation and test results is obtained. For Type-3 house, the numerical model slightly underestimates the spectral demand, but the difference is insignificant at the fundamental period (T=0.42s).  41   Figure 3.8 Response spectra of roof accelerations of three houses  Similar results can also be found in Figure 3.9 where the hysteretic loops, defined as the relationship between base shear and the first floor deformation, are compared for three houses. Both the degradation and energy dissipation predicted by Timber3D match the experimental tests. It can be clearly seen that the pinching effect from shake table test on Type-3 house was also captured by the numerical model.   Figure 3.9 also shows the cumulative energy dissipation comparison between the outputs of numerical models and actual test data of three houses. The numerical model of Type-3 house predicts the cumulative energy dissipation well when compared to test result. The numerical models of Type-1 and Type-2 houses also predict the energy dissipations well throughout the entire loading history, demonstrating the capacity of Timber3D in modeling the nonlinear behavior of light-frame wood structures under earthquake excitations and validating the developed numerical models for further study in next Chapter.  42        a) Type-1 house      b) Type-2 house 43       c) Type-3 house Figure 3.9 Global hysteretic loops (left) and cumulative energy dissipations (right) of three houses  3.4 Model development and validation of mid-rise woodframe  3.4.1 Building description The benchmark building studied is a six-story multi-unit woodframe structure. The building has a plan dimension of 60ft by 40ft, and a total height of 56ft with 9ft clear story height for the first floor and 8ft for the upper five floors (Pei et al., 2010). Figure 3.10 shows the elevation view of the building and a typical plan view for the second floor is shown in Figure 3.11 where the wall type, sheathing configuration, and nail spacing are illustrated. Detailed architectural and structural plans for the test building can be found in Appendix C.  44   Figure 3.10 Elevation view of the mid-rise woodframe (Pei et al., 2010)   Figure 3.11 Plan view of the first floor of the mid-rise woodframe  Single and double sides of oriented strand board (OSB) fastened to Douglas fir and spruce pine fir studs with 10d common nails are used for almost the entire building. An innovative midply shearwall system was adopted to increase the shear resistance in the longitudinal direction. For the 45  midply walls, the sheathing material is fastened to the wide sides of studs that are rotated 90 degrees with respect to those in standard walls. Compared to the nail connections in standard shearwall that work in single shear, the nails in midply shearwalls work in double shear, which increases the load-carrying capacity of midply walls by over threes times than the standard walls (Varoglu et al., 2006). All interior walls were sheathed with 1/2 in thick gypsum wall board (GWB). The total weight of the structure was 314 tons. 2 by 6 dimensional lumber was the main framing member for the entire building except for the end-studs for midply shearwall and sill plates used 2 by 8 and 3 by 6 dimensional lumber, respectively. The complete construction of the building can be seen in Figure 2.4.   3.4.2 Model development Following the same philosophy for modeling low-rise wood houses in previous section, the three-dimensional numerical model of the benchmark building was developed in Timber3D, as seen in Figure 3.12. The framing studs, floor diaphragms, and roof are modeled as frame elements, and the OSB panels and GWB sheathing materials are modeled as link elements. After balancing the accuracy in nonlinear modeling and computational efficiency, the 12-parameter Residual Strength Hysteresis (RESST) material model was used for wood shearwalls. Table 3.4 lists the RESST parameters per one-foot unit length for representative shearwalls. The wall parameters used in this study were obtained from the simplified DDD design (Pang et al., 2010). Shearwalls with different story heights are presented. Initial stiffness and strength are proportionally scaled with the actual wall length in the construction. Direct superposition of different layers of finishing materials is used to build up the required lateral strength. It should be noted since the final constructed building used Douglas-Fir-Larch North material for the lower three floors and Spruce-Pine-Fir for the upper 46  floors, 16% reductions of stiffness and strength were allocated for numerical modeling of upper three floors (Pei and Van de Lindt, 2011).  Figure 3.12 Numerical model of the mid-rise woodframe building in Timber3D 47  Table 3.4 Unit length RESST parameters of wood shearwalls Type Edge Nail*  (in) Ko (kip/in) r1 r2 r3 r4 Fx (kip) f1 f2 f3 Dx (in) α β Wall height = 9ft OSBa 2 3.95 0.03 -0.08 1.01 0.03 2.78 0.68 0.09 0.01 4.66 0.76 1.24 3 3.24 0.03 -0.07 1.01 0.02 1.93 0.66 0.08 0.01 4.49 0.76 1.29 Midplyb 3 4.37 0.01 -0.10 1.01 0.04 3.65 0.79 0.04 0.01 4.61 0.76 1.20 GWBc 16 0.84 0.00 -0.03 1.01 0.01 0.20 0.70 0.06 0.01 2.28 0.99 1.10 Wall height = 8ft OSBa 2 4.23 0.03 -0.08 1.01 0.03 2.92 0.68 0.08 0.01 4.31 0.76 1.24 3 3.79 0.03 -0.07 1.01 0.02 2.04 0.63 0.08 0.01 3.83 0.71 1.29 4 3.03 0.03 -0.07 1.01 0.02 1.61 0.62 0.09 0.01 3.73 0.76 1.29 Midplyb 3 4.58 0.02 -0.09 1.01 0.04 3.77 0.77 0.04 0.01 4.32 0.81 1.24 4 2.59 0.05 -0.13 1.01 0.05 2.87 0.75 0.04 0.01 4.44 0.72 1.15 GWBc 16 0.84 0.00 -0.03 1.01 0.01 0.20 0.70 0.06 0.01 2.28 0.99 1.10 * Field spacing is 12 in for all walls;  a11.9 mm thick OSB connected to framing members by 10d common nails (3.76 mm diameter) in single shear; b11.9 mm thick OSB connected to framing members by 10d common nails (3.76 mm diameter) in double shear; c12.7 mm thick GWB connected to framing members by No. 6 bugle head drywall screws (3.61 mm diameter) in single shear. 48  3.4.3 Model validation  The first three modes estimated from the initial design, white noise excitation test, as well as modal analysis in Timber3D, are compared in Table 3.5. The building has two pure translational modes in both directions and one pure torsional mode as the third mode. Overall, the numerical model matches the experimental data well except that a slightly longer period of the first longitudinal mode is observed from Timber3D model.   Table 3.5 Fundamental periods for the first three modes of the mid-rise woodframe Mode Period (s) Mode Shape DDD design White noise test Timber3D 1 0.50 0.42 0.47 First translational mode in long direction 2 0.47 0.41 0.42 First translational mode in short direction 3 0.41 N/A 0.39 First torsional mode  Next, a nonlinear time history analysis was performed on the numerical model to further examine the modeling capacity of Timber3D at large deformation. Shake table test data was used to validate the numerical analysis results. The full-scale shake table test of the building was carried out at the Miki shake in Japan in 2009. The test aimed to examine the seismic performance of the structure at different hazard levels and verify the proposed PBSD procedures for mid-rise woodframe building. The input ground motions were selected from the Canoga Park station during the 1994 Northridge earthquake. Figure 3.13 shows the spectral accelerations of two horizontal components of the unscaled ground motions and the design spectrum (2% probability of exceedance in 50 years).  Four intensity levels with 50%, 10%, 7%, and 2% probability of exceedance in 50 years 49  were tested by adjusting the input motions with scale factors of 0.53, 1.20, 1.40 and 1.80, respectively.   Figure 3.13 Unscaled response spectra of the horizontal motions recorded at Canoga Park during Northridge earthquake (5% damping)  The nonlinear time history analysis was conducted at the highest intensity level (MCE level) only for validation purpose with 2% probability of exceedance in 50 years (return period of 2475 years). The horizontal components of the scaled motions had peak ground accelerations (PGA) of 0.76g and 0.64g for short and long direction, respectively.   The time history responses of the roof displacements in two directions from the numerical model and test measurements are first compared in Figure 3.14. As one can see from the plots, the responses predicted by Timber3D match the test results well in terms of the peak value and overall shape. Figure 3.15 presents the comparison of global hysteresis response in both directions. Due to the limited availability of test data, the errors in cumulative energy dissipations cannot be 50  presented. The numerical model is able to capture the maximum base shear and energy dissipation accurately, but a slightly larger pinching effect is observed from the numerical model in the long direction. The less pinching from the shake table test is likely caused by the non-uniform participation of the wall components in test building. Overall, the numerical model could predict the seismic response of the mid-rise woodframe with considerable accuracy, and it is validated for assessing the effects of ground motion duration.   a) Long direction  b) Short direction  Figure 3.14 Validation of roof displacement time histories of woodframe   51             a)  Long direction                                                           b) Short direction Figure 3.15 Validation of global hysteretic loops of woodframe  3.5 Discussions and summary This chapter presents the development of finite element models for three low-rise wood houses and a mid-rise woodframe structure by using the Timber3D program. These structures were selected since they well represented typical timber constructions in North America, and the full-scale shake table test of the structures provided valuable information for calibrating the numerical models. Several analytical models for wood shearwall in Timber3D were introduced. The MSTEW model in Timber3D, and the RESST model that accounts for the residual strength of the MSTEW model were used to model the wall members of all four structures. Modal analyses and nonlinear dynamic analyses were conducted on numerical models by using same input motions from shake table tests. The results showed that numerical models predicted the seismic response of structures well in terms of displacement time histories and global hysteretic curves. The degradation characteristics and energy dissipation of woodframe were also captured accurately by numerical 52  models. The validated models will be then used for evaluating the effects of duration in next chapters.  53  Chapter 4: Effects of Ground Motion Duration on Low-rise Light-frame Wood Houses  This chapter studies the effects of ground motion duration on numerical models of the three light-frame wooden houses that were developed and calibrated in Chapter 3. Two suites of ground motions collected at the same instrument locations from the 2008 Wenchuan earthquake and the 2014 Lushan earthquakes in China were selected for this study. Incremental dynamic analysis (IDA) was performed for each type of structure and the fragility curves for collapse and drift exceedance were developed.    4.1 Selection of seed ground motions Normally, long duration ground motions are associated with large magnitude subduction earthquakes. However, the ground motion records from two crustal events in China, the 2008 Wenchuan earthquake (surface magnitude Ms8.0) and the 2013 Lushan earthquake (surface magnitude Ms7.0), were selected for this study because of their special characteristics. Both earthquakes occurred along the same Longmenshan Fault and were recorded by the same instrument locations. Therefore, the site conditions are the same for both sets of records. And because they occurred in the same region, 87km apart from each, the travel path effects are greatly minimized.   Both earthquakes hit the rural counties in western China, where the most prevalent type of construction is characterized by low-rise buildings, self-built unreinforced masonry and wood 54  structures. The data from seven strong motion stations (namely, 51YAM, 51LSF, 51YAL, 51QLY, 51PJD, 51HYY, and 51WCW) operated by the National Strong Motion Observation Network System (NSMONS) of China were used to study the effects of duration, see Table 4.1. The station locations are shown in Figure 4.1 and the elastic acceleration spectra of the recorded motions are compared in Figure 4.2. It can be seen the Wenchuan motions generate a broader frequency content in the short period range and decay slower than the Lushan motions as the period increases. For reference, the spectra from these motions are compared with the Chinese code spectra (GB50011-2010, 2010) for 2% and 10% probabilities of exceedance in 50 years, as shown in Figure 4.2.  Table 4.1 Information of selected stations No. Station Location Site condition Site-to-source Distance (km) Wenchuan Lushan 1 51YAM 30.070N, 103.109E soil 104.2 27.2 2 51LSF 30.021N, 102.895E soil 119.3 32.6 3 51QLY 30.407N, 103.266E soil 67.2 28.2 4 51YAL 29.866N, 102.848E soil 136.9 50.4 5 51PJD 30.241N, 103.419E soil 89.0 40.8 6 51HYY 29.648N, 102.448E soil 182.9 89.9 7 51WCW 31.039N, 103.198E soil 19.1 80.2  55   Figure 4.1 Locations of the selected strong motion stations   Figure 4.2 Response spectra of the ground motions used for this study  Among the many definitions of ground motion duration reviewed in Chapter 2, the 5-95% significant duration D5-95, defined as the time interval from 5% of the total Arias Intensity IA to 95% is adopted here (Arias, 1970; Trifunac and Brady, 1975). The IA is obtained as Equation 4.1: 56  max02 )(2tA dttagI                                            Equation 4.1 where a(t) is the recorded ground acceleration, tmax is the length of record and g is the gravitational acceleration. The distribution of significant durations for the selected records at each station is displayed in Figure 4.3. The average D5-95 of the Wenchuan records is around 90s while that for the Lushan records has an average of 21s. Figure 4.4 compares the acceleration time histories and the corresponding significant durations of the records from station 51YAM for the two events. It shows that the energy accumulates more slowly for the Wenchuan event as compared to the shorter Lushan event. In this study, a duration of 30s was used as the upper limit for short duration motions.  Figure 4.3 Distribution of significant durations  57   Figure 4.4 Time history and significant duration of 51YAM station  4.2 Scaling and matching of ground motions The concept of “spectrally equivalent” ground motions presented by Chandramohan et al. (2013) was adopted here to ensure that the long duration motion and its corresponding short duration motion have the same response spectrum. By using this approach, any differences in response could be attributed to the difference of their durations.   For the purpose of investigating the duration effects and performing the incremental dynamic analysis (IDA), it is desirable to have a suite of records scaled to a common target spectrum. In this study, the selected long duration Wenchuan records were first scaled and spectrally matched to the design level of uniform hazard spectrum (UHS) for Vancouver, Canada with Site Class C soil condition over a period range of 0.2T to 1.5T, where T is the fundamental period of each house 58  in this study (NBCC, 2015), as illustrated in Figure 4.5. Next, for each matched long duration motion, the corresponding short duration record collected from the same station during the Lushan earthquake was spectrally matched to the long duration ones so that each pair of motions have a similar response spectrum. Examples of the spectrally equivalent motions from 51WCW and 51PJD stations are shown in Figure 4.6.   Figure 4.5 Long duration records matched to UHS for Vancouver   a) 51WCW station                                                            59   b) 51PJD station Figure 4.6 Spectrally equivalent ground motions  The matching process has some effects on the ground motion characteristics and it is always recommended to examine the new D5-95 values after matching (Hou and Qu, 2015). In this study, a slight change was observed where the D5-95 values of the Lushan records were increased by only 11% after matching, so the influence on the duration can be neglected. Hence, two suites of motions with similar local site conditions, travel path effects, and response spectra are established.   The seismic responses of three light-frame wooden houses were evaluated by incremental dynamic analysis (IDA). The “spectrally equivalent” ground motion suites were scaled to multiple levels of intensity to approach collapse with respect to the spectral acceleration at the fundamental period of three wood houses, Sa(T=0.26s), Sa(T=0.32s) and Sa(T=0.42s), respectively. In each analysis, the maximum inter-story drift ratio (IDR) was monitored as the engineering demand parameter. A peak IDR threshold of 10% indicates structural collapse (FEMA, 2009b). In total, 1344 runs of nonlinear dynamic analysis were conducted (i.e. 2 suites × 7 records × 32 intensity levels × 3 house models) and selected results are shown below. 60   4.3 Collapse capacity evaluation Figure 4.7 first shows the roof displacement time history of the Type-2 house due to both the Wenchuan and Lushan motions recorded at 51QLY station. It is surprising to see that under ground motions with similar amplitude, spectral shape, local site conditions and minimized path effect, the structure stood well under short duration Lushan motion with a small residual displacement of 33mm, but eventually collapsed when subjected to the long duration Wenchuan motion. A side-sway collapse mechanism was identified where the first story acted as a soft-story and hence the second order effect (p-delta) propagated the collapse (Ibarra et al., 2005; Van de Lindt et al., 2012). One can see clearly that under long duration shaking, the structure experienced a great number of hysteretic cycles with large deformation, which increased the degradation in strength and stiffness and eventually led to a collapse when compared to the short duration shaking. This can be further explored by comparing the global hysteretic response (defined as the relationship between base shear and roof displacement) in Figure 4.8. Significant degradations were observed within the post-peaking range (where roof displacement was greater than 70mm) for the Wenchuan motion and therefore, a significant amount of strength loss occurred in the following cycles (where roof displacement was around 170mm), which caused the structural instability. However, for the Lushan motion, only an obvious in-cycle degradation was observed due to the maximum pulse of the motion and lesser strength was lost. The results are consistent with previous findings on concrete structures where the effects of ground motion duration can only be seen at the higher level of shaking (Chandramohan et al., 2016b). 61   Figure 4.7 Roof displacement time history of Type-2 house under 51QLY motion pair   Figure 4.8 Global hysteretic loop of Type-2 house under 51QLY motion pair  Figure 4.9 summarizes the IDA curves for all three types of wooden houses subjected to both short (left) and long (right) duration ground motions. The vertical dash lines represent the average value of seven peak IDRs before the collapse. It should be noted since all the structural models 62  experience a first-story side-sway collapse mechanism regardless of short or long duration motions, the engineering demand parameter here is the maximum IDR of the first floor. Overall, lower peak IDR are observed from all three types of houses subjected to long duration shaking before collapse compared with short duration motions. For the Type-1 structure with engineered OSB shear walls and GWB/stucco sheathing, the onsets IDR of collapse are approximately 7.6% under short duration motions and 6.7% under long duration motions. The results are comparable with many recent studies on the seismic performance of pre-1970s construction of light-frame structures (Pang et al., 2012). Specifically, for Type-3 structures with low-cost horizontal board sheathing, as low as 5.0% peak IDR is captured under the Wenchuan motions before causing collapse.   a) Type-1: blocked shearwalls with OSB panels, GWB, and stucco  63   b) Type-2: blocked shearwalls with OSB panels and GWB   c) Type-3: horizontal boards with GWB Figure 4.9 IDA curves of three wood houses under both sets of records  The simulation results are consistent with the experimental data from the Earthquake-99 Project tests, as seen in  Figure 4.10 (White and Ventura, 2006). The building with engineered shearwalls performed better than the non-engineered one in terms of the horizontal displacements. The 64  contributions of non-structural sheathing materials improved the seismic resistance of light-frames significantly.    a) Type-1 house                                                                           b) Type-2 house  c) Type-3 house Figure 4.10 Photographs of three wood houses during the shake table test  Based on the analysis results presented above, it can be concluded that the long duration ground motions have a significant impact on the collapse capacity of the analyzed light-frame wood houses, and the influences are consistent for all three constructions chosen in this study. To further 65  quantify the damaging effect of long duration shaking, fragility curves for all three houses under both suites of motions are generated based on the IDA results.   The fragility curves are constructed assuming a lognormal distribution. The cumulative probability of occurrence of the damage equal to or higher than the specified drift limit is given as Equation 4.2:  XPln1                                                          Equation 4.2 where X is the ground motion intensity index (e.g. spectral acceleration at fundamental period), µ and σ are the mean and standard derivation of lnX.  Figure 4.11 shows the collapse fragility curves of the three types of structures under the Lushan and Wenchuan earthquake excitations. It can be clearly seen that the median collapse capacity (defined as the spectral acceleration corresponding to 50% probability of collapse) estimated using long duration records is 26% lower than the equivalent short record set for Type-1 structure, 29% lower for Type-2 house, and 61% lower for Type3-house. Clearly, Type-3 house with horizontal board sheathing is a poor seismic design and should be avoided. However, at UHS design level intensity, the differences in probability of collapse for all three houses under both sets of motions are insignificant.    66             a) Type-1 house                                                                  b) Type-2 house                              c) Type-3 house                                                      d) comparison at UHS design level Figure 4.11 Collapse fragility curve of three light-frame wooden structures  Overall, long duration motions resulted in higher probability of collapse than short duration motions regardless of the construction type. However, this difference is negligible at low intensity levels of ground shaking (spectral acceleration below 2g). These findings are similar to conclusions drawn from previous studies on steel and concrete structures.   In addition to the collapse rate, fragility curves for exceeding a 3% design drift limit (DDL) were also derived to examine the effects of long duration motions at other performance levels. The 3% 67  DDL proposed by the Seismic Retrofit Guidelines for Schools in British Columbia is based on a large number of analytical and experimental studies of many existing light-frame wood constructions in British Columbia, Canada (APEGBC, 2013). The conditional probabilities (fragilities) of drift exceedance for three houses subjected to both record sets are presented in Figure 4.12. The probabilities of exceeding 3% DDL for long duration records for all three structures are around 17% higher than for short duration shaking. Better performances were achieved by Type-1 and Type-2 structures with engineered OSB sheathing. It was also observed that the probabilities of exceedance of Type-2 house are more sensitive to the duration effects. The results indicate that the construction with horizontal board sheathing is not a desirable option for low-rise wood houses for regions of significant seismic activity.   Figure 4.12 Fragility curves of three conventional wood structures with 3% conditional drift limit  68  4.4 Estimation of damage at design level  4.4.1 Energy demands The results in the previous section have clearly shown that the ground motion duration has a significant impact on the collapse capacity of all three conventional light-frame wood houses. However, the effects of duration cannot be easily detected at the design level intensity (referred to the UHS intensity level with 2% probability of exceedance in 50 years) by using the drift-based damage measure (i.e. IDR), as seen in Figure 4.11d.  IDR is a commonly used performance criterion in evaluation of a given structure for design. Whereas the results in previous section showed that the IDR is not a sensitive measure of damage to duration at design level. For example, for Type-1 house under excitations of 51LSF motion pair at design level (spectral acceleration at fundamental period is 1.06g), the maximum IDR was 0.34% for short duration motion and 0.45% for long duration motion, as seen in Figure 4.13.   Figure 4.13 Responses of Type-1 house under 51LSF motion pair at UHS intensity level  69  The use of dissipated energy damage measure, one of the cumulative damage measures, would result in a different assessment and show long duration motion does have a significant effect on performance. This has been reported by previous studies that cumulative damage measures are shown a strong correlation with ground motion duration (Barbosa et al., 2017; Hancock and Bommer, 2007; Iervolino et al., 2006; Raghunandan and Liel, 2013; Teran-Gilmore and Bahena-Arredondo, 2008).   The hysteretic energy dissipated by a structural component equals to the area enclosed by the hysteresis loop constructed by the earthquake-induced shear forces and the displacement. For the light-frame structure, the total hysteresis energy is calculated as the sum of hysteretic energy dissipated by individual walls at all floors during the ground excitation, as presented below:  NiMjhjiH EE1 1,,                                                      Equation 4.3 where  hjiE ,, is the energy dissipated by a single wall element, where M is the total number of both shearwalls and partition walls per each floor, and N indicates a total number of floors (2 for all wood houses). The difference in total hysteretic energy for Type-1 house under the 51LSF motion pair is significant, being 3.1 kN-m for the Lushan motion and 14.4 kN-m for the Wenchuan motion, as seen in Figure 4.13.  Figure 4.14 shows the calculated total hysteretic energy for three houses at the UHS level and their correlations with duration. Despite of configuration type, more energy is dissipated by structures under the long duration Wenchuan motions in comparison to the short duration Lushan motions. This is attributed to the larger number of inelastic cycles associated with long duration records. 70  From simple linear regression analysis, the effect of duration on energy demand becomes more significant for Type-3 house. It is also found the house sheathed with horizontal boards experienced more inelastic deformations than the other two houses, and therefore more energy is dissipated with the increasing duration. The observations at the design level demonstrate that damage indices that account for both drift and energy dissipation demands are needed to adequately characterize the effects of duration.       Figure 4.14 Correlation of total hysteretic energy and duration for three houses  4.4.2 Damage assessment Recent studies on timber structures have shown that displacement alone may not be a reliable and accurate indicator for seismic performance of wood structures (Liang et al., 2010). It was suggested 71  that a damage-based criterion that accounts for both displacement (or ductility) and energy demands is more suitable for wood structures. In this study, the widely used Park and Ang damage index is selected to evaluate the effects of ground motion duration on three wood houses at design level because of its simplicity and effectiveness.    The Park and Ang damage index was originally proposed by Park and Ang (1985) for reinforced concrete buildings. This index linearly combines the maximum deformation and dissipated hysteretic energy. The equation for a single wall component can be written as:  huyumwasll EFDI                                               Equation 4.4 where δm is the maximum deformation under earthquake excitation, δu and Fy are ultimate deformation and yield strength under either monotonic loading or pushover analysis, β is a non-negative degradation parameter that needs to be calibrated experimentally. Once the damage index is computed from each wood wall, the index for the entire wood house can be derived by weighting the individual assemblies based on the dissipated hysteretic energy during the dynamic analysis. The weighting of the damage indices is obtained as follows:  NMiiwallisystem DIDI1,                                         Equation 4.5 HhiEE                                                       Equation 4.6            Extensive tests have been conducted to determine the β parameter for concrete and steel structures in both component and system levels, and it was found this value would not change much from different structural members and hence, a constant value between 0.025 to 0.05 is normally applied 72  to the entire building for simplicity. However, the highly nonlinear response in woodframe varies significantly from wall to wall and system to system. Van de Lindt (2005) conducted static and dynamic tests on isolated wood shearwalls and calibrated the β factor based on a survey that was conducted by a group of engineers independently. A broad range from 0.05 to more than 1.0 was obtained for this parameter. Based on a regression analysis, a linear function of the perimeter nail spacing on shearwalls was developed to estimate β factor (Van de Lindt, 2005). Park and Van de Lindt (2009) enhanced this process and applied it to a two-story light-frame wood house. The original linear function for β was further improved by introducing the width-to-height aspect ratio of the shearwalls in a second order polynomial format (Park and van de Lindt, 2009). More recently, an IDA-based calibration process was developed by Liang et al. (2011) and validated with experimental test results. In this process, IDA is first carried out to determine the collapsing point for the selected ground motion. Next, by setting the damage index to unity and substituting the corresponding maximum displacement and hysteretic energy into Equation 4.7 by rearranging Equation 4.4, the damage parameter β can be determined:  hmuyEF 0.1                                           Equation 4.7 This approach was adopted in this study for the following reasons: 1) it is considered more suitable to quantify the duration effect since the mean β value and standard deviation derived from a large number of IDA are more stable and accurate than that obtained from limited dynamic tests at low intensity level; and 2) it can estimate the damage to structural and non-structural components separately where the walls in wood houses are modeled as a combination of multiple layers of sheathing (OSB, stucco, GWB, etc.). Liang et al. also proposed damage limit states and corresponding damage descriptions based on a verification process with experiments, as 73  summarized in Table 4.2. Similar to the damage states proposed for reinforced concrete structures, five levels of damage are categorized from “None” to “Collapse”. Specifically, the estimated indices for non-structural wall damage are all below 0.7, while for walls with structural damage, the estimated indices are greater than 0.7.  Table 4.2 Relationship between DI and observed damage (Liang et al., 2010) DI range Damage Level Description DI>1.0 Collapse Total or partial collapse 0.7<DI<1.0 Severe Partial or complete failure of any structural component; severe cracks in walls; separation of sheathing from studs 0.4<DI<0.7 Moderate Extensive cracking in walls, permanent deflection or near failure in structural component, severe damage of non-structural walls 0.25<DI<0.4 Minor Hairline cracks in non-structural walls DI<0.25 None No visible damage  Following the procedures described above, the damage indices for individual walls and the whole system of the three wood houses were calculated for both sets of motions at the design level. The results are presented in Figure 4.15. Generally, long duration motions make all three houses more fragile. The median DIsystem for Type-1, Type-2, and Type-3 houses are 0.12, 0.21, and 0.44 when subjected to short duration motions, respectively. Higher values of 0.22, 0.40 and 0.69 associated with long duration motions are estimated for three houses. Although Wenchuan motions have an insignificant impact on overall damage indices for Type-1 and Type-2 houses sheathed with OSB panels, the damage for several individual walls are identified as “Minor” to “Moderate”. For example, the computed damage indices for walls W1-4 for the Type-1 house were about 0.25 for 74  short duration excitations. The estimate was verified by the shake table test where GWB experienced no damage and only small cracks were observed in the stucco (White and Ventura, 2006). However, for long duration motions, the associated indices increased more than 60%, where severe damages would be expected on non-structural partition walls. Similar results were also found in Type-2 and Type-3 houses. For the Type-3 house with horizontal board sheathing, long duration motions resulted in damage indices as high as 0.80 for walls W3 and W4 where “partial or complete failure” of structural walls could occur.   Figure 4.15 Damage indices for three houses under both sets of motions 75   4.5 Summary This chapter studied the effects of long duration earthquakes on three conventional low-rise wood houses. Two sets of ground motions collected at the same instrument locations but from two different earthquakes in China were selected to minimize the differences in site conditions and paths effects. The records were then spectrally matched so that essentially the only difference was duration. The seismic responses of the houses were investigated by incremental dynamic analysis (IDA).  The results indicate that under long duration motions, median collapse capacities for Type-1, Type-2, and Type-3 houses were reduced by 26%, 29%, and 61%, respectively, with respect to that obtained from short duration motions. The peak IDRs approaching collapse for each house under short duration shaking were 7.6%, 6.8% and 6.4% for Type-1, Type-2, and Type-3 house, but under long duration shaking, peak IDRs of 6.7%, 5.7% and 5.0% were obtained. It was also found that under long duration ground motions, there was 17% higher probability of exceeding 3% design drift limit than under short duration motions. At the design level where the effect of duration cannot be clearly observed by using a drift-based measure, the cumulative hysteretic energy and the Park and Ang damage index were calculated. Strong correlations with duration were then observed. The damage indices associated with short duration motions were, at most, 77% of the corresponding values for long duration motions. Type-3 construction is more vulnerable to long duration shaking with a median system damage index of 0.69. From the design point of view, Type-1 construction with engineered OSB sheathing and stucco had significantly more seismic resistance than Type-2 construction without stucco or Type-3 with horizontal board sheathings. The results showed that 76  Type-3 construction with horizontal boards sheathing is not a suitable for use in seismic prone regions, especially in areas of subduction earthquakes.     77  Chapter 5: Effects of Ground Motion Duration on Mid-rise Woodframe Building This chapter studies the effects of ground motion duration on a numerical model of the six-story woodframe apartment building that was developed and calibrated in Chapter 3. A database of 22 pairs of long duration and spectrally equivalent short duration motions was generated. The collapse capacity of the building under two sets of motions was evaluated by incremental dynamic analysis (IDA). Effects of earthquake orthogonal component were also evaluated by comparing seismic responses under both unidirectional and bidirectional analyses. Influences of ground motion duration on at design intensity level were assessed with various damage measures, including peak drift, hysteretic energy dissipation, and the combined Park and Ang damage index. With the results obtained, correlations between duration and damage measures were generated.    5.1 Ground motion database 5.1.1 Selection of seed ground motion To consider a wide range of ground motion durations, a database that consists of 22 pairs of long duration and short duration motions was generated. For comparison purpose with previous studies, the 5-95% significant duration D5-95 is adopted here and the ground motions with D5-95 equal to or greater than 30s are defined as long duration motions. Table 5.1 lists the complete information of all 22 pairs of selected ground motions. The majority of the long duration records were selected from subduction events, such as the 1985 Mexico earthquake, the 2003 and 2011 Japan earthquakes, and the 2010 Chile earthquake. Several records from the 2008 Wenchuan earthquake provided by the National Strong Motion Observation Network System (NSMONS) of China are 78  also included. For each of these long duration motions, a corresponding spectrally equivalent short duration motion was retrieved from the PEER NGA-West2 database (PEER, 2018).   To illustrate the process, Figure 5.1 presents the response spectra, acceleration time histories, and the Arias Intensity accumulations of ground motions pair #22. Detailed information of other record pairs can be found in Appendix D. It can be seen clearly that both records have very similar spectra shape and amplitude at a wide period range. The ground motion from Okudo station during Tohoku earthquake has a significantly longer duration of 109s than the spectrally equivalent motion from Taiwan Smart1 earthquake which has only 20s in duration.  Figure 5.1 Spectrally equivalent ground motion pair #22  79  Table 5.1 Spectrally equivalent ground motion pairs for mid-rise woodframe 80  Figure 5.2 presents the distribution in duration among the selected ground motions. The median significant duration D5-95 for the long duration set and the spectrally equivalent short duration set are 74.3s and 10.9s, respectively. It has been reported that the long duration ground motions are more likely recorded from stations that are located far from the source during large magnitude earthquakes (Bommer et al., 2009). This can be observed clearly in Figure 5.3 where the duration increases with the earthquake magnitude and epicentral distance. All the long duration records selected in this study were recorded from earthquakes with magnitudes greater than 7.5. There is also an apparent relationship between duration and the peak ground acceleration (PGA). As the duration increases with the distance, the seismic energy attenuates significantly during the wave propagation, and therefore, lower PGA values are associated with long duration motions.  Figure 5.2 Distribution of ground motion duration  81   Figure 5.3 Correlations of duration with ground motion characteristics  5.1.2 Ground motion scaling In order to perform an incremental dynamic analysis (IDA) for quantifying the effects of duration, it is desirable to have all the candidate ground motions scaled to a common target spectrum. Therefore, both the long duration and short duration motions selected in this study were scaled to the maximum considered earthquake (MCE) design spectrum (with 2% probability of exceedance in 50 years) for a Southern California site on stiff soil (site class D) for which this woodframe was originally designed for (Pang et al., 2010). In accordance with ASCE/SEI 41, a period range of 0.2T to 1.5T was used for scaling the records, where T is the fundamental period of the woodframe building. The lower bound 0.2T accounts for the higher modes contribution and the upper bound 1.5T accounts for the system softening. Figure 5.4 shows the response spectrum of each individual long and short duration motions that are matched to the target MCE design spectrum. The scaling factors (SF) for each record are summarized in Table 5.1. 82         a) Long duration motions                                              b) Short duration motions Figure 5.4 Response spectra of scaled ground motions for mid-rise woodframe  5.2 Unidirectional nonlinear dynamic analysis 5.2.1 Collapse capacity evaluation The effects of ground motion duration on the collapse capacity of the benchmark woodframe were evaluated by an incremental dynamic analysis (IDA). Unidirectional IDA was first carried out in the long direction of the building as this was identified as the weak direction of the building. For each ground motion, 25 nonlinear time history analyses are performed to cover a wide range of intensity levels. In each analysis, the peak inter-story drift ratio (IDR) was monitored as the engineering demand parameter and a 7% threshold was used to indicate a structural collapse. In contrast with concrete and steel structures where the onset of collapse is normally defined as a peak IDR of 10%, many previous analytical studies and experimental tests have shown that 7% IDR is a more reasonable criterion for multi-story woodframe structures (Christovasilis et al., 2007; FEMA, 2009b; Isoda et al., 2007; Van de Lindt et al., 2010).  83  Figure 5.5 presents the unidirectional IDA curves of the numerical model for both long and short duration motions. At MCE design level with spectral acceleration of 1.5g, the woodframe performs quite well and meet the design objectives under both sets of ground motions. The maximum IDR are all below the 3.5% drift limit as per the code requirements. However, the influence of duration can be observed with an increase of intensity level. The median collapse spectral acceleration for the short duration motions is approximately 2.65g, while for long duration motions, a relatively lower spectral acceleration of 2.25g is obtained. Under long duration motions, the building obviously exhibits a lower safety margin against collapse.       a) Short duration motions                                                   b) Long duration motions Figure 5.5 Unidirectional IDA curves of mid-rise woodframe  To quantify the collapse rate of the building for both sets of unidirectional ground excitations, the collapse fragility curves were derived from the IDA results. The construction of fragility curve is based on Equation 4.2 where the cumulative probability of occurrence of the damage equal or greater than 7% IDR limit is calculated with a lognormal distribution. Figure 5.6 shows the collapse fragility curves for the building. It can be seen clearly that the benchmark building has 84  low probabilities of collapse under both long and short duration motions at MCE design level, demonstrating the effectiveness of the PBSD procedures. However, with the increase of intensity, the structure starts to exhibit a higher probability of collapse under long duration motions. For instance, at a spectral acceleration of 2g, the probability of collapse under long duration motions is 26%, which is 17% higher than that under short duration motions (9%). This trend is observed within a broad range of intensity level (until spectral acceleration of 3.5g). The median collapse capacity, defined as the spectral acceleration at 50% probability of collapse, is reduced by over 18% under long duration shaking compared with that under short duration motions.  Figure 5.6 Unidirectional collapse fragility curves  The influence of ground motion duration on collapse capacity is further illustrated by plotting a log-log relationship of spectral acceleration at collapse versus 5-95% significant duration D5-95, as seen in Figure 5.7. The negative trend line indicates that the collapse capacity decreases with the 85  increase of duration, although the correlation is not very strong. Under excitations with longer duration, the building tends to collapse at a lower ground intensity.  Figure 5.7 Log-log plot of collapsing spectral acceleration versus D5-95  5.2.2 Damage assessment at design level The previous section has shown that the ground motion duration affects the collapse rate of the benchmark mid-rise woodframe significantly. At the design level, however, the effects of duration on maximum IDRs were not clearly observed. This has been demonstrated in Chapter 4 for the low-rise wood houses. Figure 5.8 compares the median IDR of the building under both sets of motions at MCE level. The structure tends to have slightly larger IDR above the fourth floor under long duration motions since a 16% reduction of stiffness and strength were allocated for numerical modeling of upper three floors. Beyond that, the influence of duration on IDR is negligible. The total hysteretic energy and the Park and Ang damage index that were evaluated for the low-rise wood houses in previous chapter are also investigated for the mid-rise woodframe here.  86              a) Short duration motions                              b) long duration motions Figure 5.8 Inter-story drift ratio at MCE level (unidirectional)  The total hysteretic energy (EH), as defined in Equation 4.3, is calculated as the sum of hysteretic energy dissipated by individual walls at all floors during the ground excitation. It should be noted for the unidirectional analysis, only the walls along the long side of the building are considered. Figure 5.9 shows the calculated total hysteretic energy from all the 44 nonlinear time history analyses at the design level and their correlations with the 5-95% significant duration. One can see clearly from the linear regression that the energy dissipation of the woodframe is highly correlated with ground motion duration. More energy is dissipated by the woodframe under long duration shaking in comparison to short duration shaking. The median EH calculated from all long duration excitations is 970kN-m, which is three times as many as that from short duration excitations (289kN-m). The strong correlation here is consistent with the findings from the three low-rise light-frame structures studied in Chapter 4. The results indicated that many existing seismic design 87  codes that rely on peak responses may not be adequate to characterize the effects of duration. This highlights the need for considering damage indices that account for the effects of both drift and energy dissipation demands.   Figure 5.9 Correlation of total hysteretic energy and duration (unidirectional)  An IDA-based Park and Ang damage index for timber structures was introduced in Chapter 4. The results from the incremental dynamic analysis in the previous section were first used to calibrate the damage parameter β for each wall along the long direction. Next, the Park and Ang damage indices for the individual walls as well as for the entire woodframe building were calculated by using Equations 4.4 to 4.7.   Figure 5.10 presents the estimated system damage indices for the 22 pairs of long and short duration motions. Similarly, a strong correlation of damage index with duration was observed.  The median DIsystem under short duration motions was 0.39, which was 36% lower than the value 88  under long duration motions (0.53). Based on the performance criterion proposed by Liang et al. (2011) for woodframe in Table 4.2, the woodframe has been deemed to experience “Minor” to “Moderate” damage during short duration shaking, as the main structural components were essentially undamaged and only cracks in non-structural walls were expected. The simulation results were supported by the test report that shows during the Northridge earthquake excitation at the MCE level, no structural damage was observed and only limited propagations of cracks on GWB panels were seen (Pei et al., 2010). However, during long duration shaking, the estimated damage indices of the woodframe mainly fall into “Moderate” state. Moreover, two extreme “Severe” cases were estimated by numerical simulation where failures on structural components were expected.    Figure 5.10 Correlation of system damage index with duration (unidirectional)  89  The influences of ground motion duration on damage indices of individual walls were also investigated. Figure 5.11 compares the median DIwall of four walls (A2, D2, D3, and E5) selected from the first, second and sixth (roof) floor for both sets of ground motions. In total, 12 walls in the long direction of the building are evaluated. Overall, the indices for the walls associated with long duration motions are about 35% higher than the corresponding values for short duration motions. For example, the estimated DI for Wall A2 and E5 at the first and second floors were all below 0.4 under short duration motions, whereas under long duration motions, DI values greater than 0.4 were estimated for these walls. The walls alone the center line (D2 and D3) perform better and the influence of duration is not significant since they were constructed with OSB panels with smaller nail spacing. Negligible damages are estimated for the walls at roof level despite that long duration motions pose slightly higher damage due to the reduction in strength and stiffness for the upper floors.            a) Selected walls at 1F                                                           b) Selected walls at 2F 90   c) Selected walls at 6F (roof) Figure 5.11 Damage indices for selected walls of woodframe (unidirectional)  5.3 Bi-directional nonlinear dynamic analysis Current findings on the effects of ground motion duration on steel and concrete structures are limited to analyses of two-dimensional nonlinear models (Barbosa et al., 2017; Chandramohan et al., 2013; Raghunandan and Liel, 2013). Bidirectional analysis that accounts for torsional effects has been ignored in previous studies on duration effects. For the benchmark woodframe building, torsional behavior was clearly observed during the shake table tests although the center of mass and center of rigidity were designed to coincide (Van de Lindt et al., 2011). Figure 5.12 compares the displacement time histories of two corner points at the roof in the long direction when subjected to bidirectional motions from the Urakawa station during the 2003 Hokkaido earthquake. The differences in displacements at 33.21s and 33.61s and the corresponding building deformation plot (exaggerated with a scale factor of 15) indicate the significant torsional effects in the building. It has been reported that the orthogonal earthquake component could largely change the structural performance and bidirectional analysis is always recommended for structures that are sensitive to 91  torsional and coupling effects (De Stefano et al., 1998; FEMA, 2009b). Therefore, it is of significant interests to examine the effects of ground motion duration on the mid-rise woodframe when bidirectional ground motions are inputted.   Figure 5.12 Roof displacement time histories of two corner points in the long direction  5.3.1 Collapse capacity evaluation  Ideally, bidirectional nonlinear dynamic analysis should use both horizontal components of an earthquake as input motions. However, it is impossible to have a pair of long and short duration motions that have congenital equivalent spectra for both horizontal components simultaneously. This can be explained in Figure 5.13 where the response spectra of ground motion pair #10 and its orthogonal components are plotted and compared. The components of long and short duration 92  motions used in this study have naturally similar response spectra (see Figure 5.13a), while the response spectra of the orthogonal components are quite different (see Figure 5.13b).     a) components used in this study                                           b) orthogonal components Figure 5.13 Response spectra of ground motion pair #10  Therefore, in this study, bidirectional incremental dynamic analysis was performed by applying identical motion to both directions of the building so that both long and short duration motions at two orthogonal directions have similar response spectra. Like the unidirectional analysis, 25 intensity levels with the same scaling factors were considered. The larger value of peak IDR experienced in any directions of the woodframe was as the engineering demand parameter in bidirectional analysis.  Figure 5.14 presents the bidirectional IDA curves of the building under both long and short duration motions. It can be seen that long duration motions accelerate the collapse of the building at smaller spectral accelerations than short duration motions. The median collapse spectral acceleration for the short and long duration motions are 2.43g and 2.07g, respectively. The findings 93  here are consistent with the findings from unidirectional analysis. However, by introducing two orthogonal component motions as inputs, the building experiences larger IDR under both short and long duration motions than that under unidirectional analysis at the MCE intensity level. Especially, there are 3 long duration motions generate maximum IDR exceeding the 3.5% drift limit.   a) Short duration motions                                                   b) Long duration motions Figure 5.14 Bidirectional IDA curves of mid-rise woodframe  The bidirectional collapse fragility curves using identical motion at both directions were also derived and was shown in Figure 5.15. For comparison purpose, the unidirectional collapse fragility curves were also plotted in same figure. Long duration motions reduced the median collapse capacity of the woodframe by 17%. Fragility information extracted from both unidirectional and bidirectional IDA results is presented in Table 5.2. Listed in these tables are the median collapse spectral acceleration and the dispersion factor σ along with the probability of collapse at MCE intensity level. The bidirectional analyses reduced the median collapse capacity Sa(T, 5%) [g]94  estimated from the unidirectional analyses by approximately 9% for both short and long duration motions, as seen in Figure 5.15.    Figure 5.15 Comparison of collapse fragility curves of unidirectional and bidirectional analyses   Table 5.2 Fragility information of the woodframe Excitation direction Ground motion duration Lognormal CDF Probability of Collapse MCE level (Sa=1.5g) Median [g] β Unidirectional Short 2.65 0.46 0.5% Long 2.25 0.40 1.0% Bidirectional Short 2.43 0.48 0.6% Long 2.07 0.30 1.2%  95  5.3.2 Damage assessment at design level The influence of ground motion duration on damage measures of the building under bidirectional analysis was also investigated at design level. Figure 5.16 shows the calculated total hysteretic energies and their correlations with the 5-95% significant durations. It should be noted that the total hysteretic energy in the bidirectional analysis includes all the walls in both orthogonal directions. Since the benchmark woodframe was designed to have equal resistance in both long and short directions, the calculated EH, as expected, are almost twice the values from the unidirectional analysis. The median EH calculated from long and short duration excitations are 1898kN-m and 613kN-m, respectively. The strong correlation between energy measure and duration can be seen clearly in Figure 5.16.   Figure 5.16 Correlation of total hysteretic energy and duration (bidirectional)  96  The system damage indices and their correlations with the duration under bidirectional excitation are presented in Figure 5.17. The positive regression line demonstrates that long duration motions, again, cause a higher level of structural damage than the short duration motions. The median DIsystem under short and long duration motions are 0.43 and 0.61. Figure 5.18 compares the system damage indices estimated from both unidirectional and bidirectional analyses. It was found in general, the DIsystem calculated from bidirectional analysis were about 10% larger than the values obtained from unidirectional analysis. The difference increased with the increase of duration.   Figure 5.17 Correlation of system damage index with duration (bidirectional)  97   Figure 5.18 Comparison of system damage index under unidirectional and bidirectional analyses  5.4 Summary The influence of ground motion duration on the performance of a six-story woodframe apartment building was investigated using nonlinear dynamic analyses. The input motions were 22 long duration records and corresponding 22 short duration motions with similar spectrum. Both sets of motions were then scaled to the design level of the benchmark building. The seismic performance of the woodframe was studied by using unidirectional and bidirectional incremental dynamic analysis, where structural responses in terms of peak inter-story drift ratio, hysteretic energy, damage index and collapse rate were examined.   In the unidirectional analysis, the median collapse capacity of the mid-rise woodframe was reduced by 18% under long duration motions compared to short duration motions. The median collapse 98  spectral acceleration for short duration shaking was approximately 2.65g. For the long duration shaking, it was 2.25g. Both intensity measures exceeded the design intensity level for southern California site, the building under long duration motions showed a relatively lower safety margin against collapse. At the design intensity level, over three times more energy was dissipated by the woodframe under long duration shaking in comparison to short duration shaking. The median system damage index of the woodframe was increased by 36% under long duration motions.  Similar conclusions were drawn from bidirectional analysis. A 17% reduction in median collapse capacity was found under long duration shaking. It is worth pointing out that bidirectional analysis posed about 9% lower median collapse capacity and 10% higher damage indices when compared to the unidirectional analysis under both sets of motions. It was concluded that the unidirectional analyses underestimated the effects of ground motion duration on the mid-rise woodframe structure. It is recommended to perform bidirectional analysis to sufficiently characterize the effects of duration on structural collapse capacity and damage potential.     99  Chapter 6: Conclusions 6.1 Summary and contributions The duration of ground motion is not taken into account by many current codes. The influence of ground motion duration on timber structures has not been studied in detail. This dissertation aims to bridge this knowledge gap for timber structures.  The effects of ground motion duration on the numerical models of both low-rise and modern mid-rise woodframe buildings were evaluated in this study. Three types of code-compliant low-rise structures were analyzed. They are two-story light-frame wood houses designed for British Columbia. The mid-rise structure analyzed is a six-story woodframe building that was designed for Southern California by using a performance-based seismic design (PBSD) approach. All the prototype timber structures were tested on a shake table at full scale, and the test results were used to validate the numerical models of the structures that were developed by using the Timber3D program.   Two databases of ground motions were established to isolate the effect of duration from other ground motion characteristics. The first database had two sets of long and short duration ground motions collected at the same instrument from two different earthquakes in China to minimize the effects of site conditions and travel paths. These records were then spectrally matched to each other so that the only difference, from the design point of view between them is duration. The second database contained 22 long duration motions collected from recent mega earthquakes (M8-M9) and corresponding 22 short duration motions that were selected to be spectrally equivalent to 100  the long duration records. The seismic responses of the timber structures were investigated by incremental dynamic analysis (IDA).   The major findings and contributions of this dissertation are: 1. This dissertation is the first study that investigated in detail the effects of ground motion duration on timber structures; 2. Long duration motions reduced the median collapse capacities of both conventional low-rise and modern mid-rise woodframe structures significantly. Specifically, the reduction was 18% for the mid-rise woodframe building, and 61% for the low-rise woodframe with horizontal board sheathing.  3. The quantification of duration effects depends on the level of ground shaking and damage measure used. The peak inter-story drift ratio approaching collapse was lower under long duration shaking compared to short duration shaking. At the design intensity level, the use of drift may not be adequate to characterize the effects of duration. The use of cumulative damage measures would result in a different assessment and showed long duration motion does have a significant effect on performance. 4. This study showed that it is necessary to use a three-dimensional model of the building in order to capture the torsional effects adequately.  5. Bidirectional analysis reduced the median collapse capacity of the woodframe by 9% and increased the system damage indices by 10% for both short and long duration sets compared to the unidirectional case.    101  The findings and results of this study help current seismic design practice gain a better understanding of the effects of ground motion duration and provide information essential for improving the seismic design of timber structures. The existing seismic design approaches conducted at or below the design intensity level which are based on the spectral demands, the amplitude of ground motion, and peak values of drift and forces, are unlikely to detect the influence of ground motion duration. It is suggested that a collapse risk analysis on a structure designed according to the codes should be conducted to incorporate the duration of ground motion. If the structure is shown to be sensitive to the duration effects, it should be re-designed with higher seismic resistance so that under long duration motions, it would have the same level of collapse capacity and damage index when compared to short duration motions.    6.2 Recommendations for future work This dissertation has presented a detailed study of the effects of ground motion duration on timber structures. On the basis of the observations and discussions above, some of the future suggestions on this topic are recommended in the following: 1. This study focuses on the impact of long duration motions. Further research is needed to determine a way to modify current design provisions to account for duration effects. It is believed by many researchers that the duration effects could be addressed when nonlinear inelastic response spectra are used in the design codes. But to achieve this, it requires the development of nonlinear inelastic response spectra. For example, Chai (2005) developed duration-dependent inelastic design spectra for concrete and steel structures where the base shear coefficient is increased for longer ground motions. Alternatively, an adjustment factor that accounts for the duration, could be incorporated for the equivalent lateral force 102  procedures. For example, Chandramohan (2016) developed a site and structural system-specific adjustment factor for the design base shear in his Ph. D thesis to account for both spectral shape and duration. There was at least 43% increase in base shear estimated for the studied concrete building by considering contribution of different earthquake sources. These options and other possible ones require further examinations to implement into timber design procedures. 2. There are limited experimental tests on woodframe structures, especially for mid-rise structures under long duration shaking. The numerical models developed in this study are validated with the test results of four specified buildings. There is a strong need for more experimental data to support the nonlinear dynamic analyses by considering the randomness involved in the input earthquake excitations, the structural properties (i.e. wood species and nail spacing in shearwalls), and the construction practice. A reliability analyses proposed by Li (2009) that accounts for different combinations of the previously mentioned random valuables is recommended for future work.    3. The effects of ground motion duration are closely related to the accuracy of numerical modeling in terms of strength and stiffness degradation. It has been reported that structural components generally pose different hysteretic responses when subjected to different loading protocols (FEMA, 2009a; Krawinkler, 2009; Ou et al., 2013). This study involved load-dependent shearwall models. To expand the study will require test data on shearwall models that are loading-independent. An example of this type of model was developed by Foschi (2000) and then updated by Li et al. (2011) where the behavior of panel-frame nail connections was represented by mechanics-based hysteretic algorithms.  103  4. FEMA P-807 has recommended retrofit options for woodframe structures with soft/weak-first story. These techniques worked properly and effectively during shake table tests when short duration motions were inputted. It is desirable to further examine these retrofitting schemes under long duration shaking by using the framework proposed in this study. 5. This study focuses on the low-rise to mid-rise woodframe constructions. The high-rise timber structures, either employ advanced building materials (i.e. the cross laminated timber) or adopt the hybridization concept with wood participation to concrete or steel structures, have been developed in recent years. 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Earthquake Engineering Research Facility Rep. No. 06, 3.  Xie, L., and Zhang, X. (1988). Engineering duration of strong motion and its effects on seismic damage. Paper presented at the Proceedings of the Ninth World Conference on Earthquake Engineering. Zhang, S., Wang, G., Pang, B., and Du, C. (2013). The effects of strong motion duration on the dynamic response and accumulated damage of concrete gravity dams. Soil Dynamics and Earthquake Engineering, 45, 112-124. 118  Appendix A   Structural Drawings of Earthquake-99 Project The following materials are the structural drawings of two-story light-frame wood house in Earthquake-99 Project provided by White and Ventura (2006). 119   Figure A.1 Elevation view of two-story light-frame 120   Figure A.2 Plan view of two-story light-frame 121  Appendix B  Summary of Earthquake-99 Shake Table Tests The following materials are the Earthquake-99 shake table test reports of three two-story light-frame wood houses provided by Kharrazi (2002).   122  B.1 Type-1 house  123    124    125    126    127    128    129    130    131    132    133  B.2 Type-2 house  134    135    136    137    138    139    140    141    142    143    144  B.3 Type-3 house  145    146    147    148    149    150    151    152    153    154    155  Appendix C  Structural Drawings of NEESWood Project The following materials are the structural drawings of the six-story mid-rise woodframe apartment building of NEEWood Project provided by Pei et al. (2010).  156   Figure C.1 Elevation view of the mid-rise woodframe 157    Figure C.2 Plan view of mid-rise woodframe (1F) 158   Figure C.3 Plan view of mid-rise woodframe (2F-5F) 159   Figure C.4 Plan view of mid-rise woodframe (6F)160  Appendix D  Spectrally Equivalent Ground Motion Pairs for Mid-rise Woodframe     Spectral Acceleration [g]0 0.5 1 1.5 2 2.5 3Period [s]00.511.522.53Spectral Acceleration [g]Pair #2Short durationLong durationSpectral Acceleration [g]Spectral Acceleration [g]Spectral Acceleration [g]Spectral Acceleration [g]161      Spectral Acceleration [g]Spectral Acceleration [g]Spectral Acceleration [g]Spectral Acceleration [g]Spectral Acceleration [g]Spectral Acceleration [g]162      Spectral Acceleration [g]Spectral Acceleration [g]Spectral Acceleration [g]Spectral Acceleration [g]Spectral Acceleration [g]Spectral Acceleration [g]163    Spectral Acceleration [g]Spectral Acceleration [g]Spectral Acceleration [g]Spectral Acceleration [g]

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