Applied Science, Faculty of
Civil Engineering, Department of
DSpace
UBCV
Fairhurst, Michael
Master of Applied Science - MASc
University of British Columbia
The advantages of using timber as the primary construction material in mid- and high-rise buildings are undisputed. Timber is sustainable, renewable, and has a very good strength-to-weight ratio, which makes it an efficient building material. However, perceived shortcomings with respect to its ductility and system level behavior; along with lack of appropriate design guidance currently limits the use of timber in taller structures. Overcoming these obstacles will allow timber, and its wood product derivatives, to further expand into the multi-storey construction sector - most likely in hybrid-type structures. The “Finding the Forest Through the Trees” (FFTT) system is an innovative timber-steel hybrid system that may allow high-rise timber construction, even in highly seismic regions. The FFTT system utilizes engineered timber products to resist gravity and lateral loads with interconnecting steel members to provide the necessary ductility and predictability for seismic demands. For a novel hybrid system, such as the FFTT, to gain recognition, experimental data must be gathered and supported by computational modeling and analysis in order to prove its component- and system-level performance. This thesis presents research utilizing nonlinear dynamic analysis of finite element (FE) models of the FFTT system, with properties calibrated to physical component tests, to capture the response under significant wind and seismic loads. From the results presented herein, it appears that the FFTT system can meet the design performance requirements required for seismic loading; however, due to its relatively low weight, may be susceptible to wind induced vibrations. All results are based on Vancouver, BC loading as specified by 2010 the National Building Code of Canada.
DYANMIC ANALYSIS OF THE FFTT SYSTEM by Michael Fairhurst B.ASc., The University of British Columbia, 2012 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Civil Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) August 2014 © Michael Fairhurst, 2014 ii Abstract The advantages of using timber as the primary construction material in mid- and high-rise buildings are undisputed. Timber is sustainable, renewable, and has a very good strength-to-weight ratio, which makes it an efficient building material. However, perceived shortcomings with respect to its ductility and system level behavior; along with lack of appropriate design guidance currently limits the use of timber in taller structures. Overcoming these obstacles will allow timber, and its wood product derivatives, to further expand into the multi-storey construction sector - most likely in hybrid-type structures. The ―Finding the Forest Through the Trees‖ (FFTT) system is an innovative timber-steel hybrid system that may allow high-rise timber construction, even in highly seismic regions. The FFTT system utilizes engineered timber products to resist gravity and lateral loads with interconnecting steel members to provide the necessary ductility and predictability for seismic demands. For a novel hybrid system, such as the FFTT, to gain recognition, experimental data must be gathered and supported by computational modeling and analysis in order to prove its component- and system-level performance. This thesis presents research utilizing nonlinear dynamic analysis of finite element (FE) models of the FFTT system, with properties calibrated to physical component tests, to capture the response under significant wind and seismic loads. From the results presented herein, it appears that the FFTT system can meet the design performance requirements required for seismic loading; however, due to its relatively low weight, may be susceptible to wind induced vibrations. All results are based on Vancouver, BC loading as specified by 2010 the National Building Code of Canada. iii Preface The methodology and results presented in Chapters 2 and 3 of this thesis were published and presented at the World Conference on Timber Engineering (Quebec City, Quebec, 2014). The paper included in the conference proceedings was: ―Fairhurst M., Zhang X., Tannert T., 2014. Nonlinear Dynamic Analyses of a novel Timber-Steel Hybrid System. Proceedings of the 2014 World Conference on Timber Engineering, Quebec City, Quebec, Canada.‖ I prepared the majority of the manuscript and developed the numerical models and results presented in the paper. Tannert, T. and Zhang, X. helped to prepare and edit the manuscript and provided invaluable guidance and discussion throughout the study. The study described in Chapter 5 is part of a manuscript which is currently under review: ―Zhang X., Fairhurst M., Tannert T., 2014. Ductility Estimation for a Novel Timber-Steel-Hybrid System. Submitted and Under Review.‖ I helped to prepare and edit the manuscript and provided the three dimensional structural numerical modeling and results for a study to support the results developed by Zhang, X. and myself using simplified two dimensional models. Zhang, X. and Tannert, T. prepared the majority of the manuscript. Tannert, T. provided guidance and feedback about the study and results. iv Table of Contents Abstract .................................................................................................................................... ii Preface ..................................................................................................................................... iii Table of Contents ................................................................................................................... iv List of Tables ........................................................................................................................ viii List of Figures ......................................................................................................................... ix Acknowledgements ............................................................................................................... xv Dedication ............................................................................................................................ xvii Chapter 1: Introduction ........................................................................................................ 1 1.1 Tall Wood-Based Building ....................................................................................... 1 1.2 Research Needed ....................................................................................................... 2 1.3 Objectives ................................................................................................................. 2 1.4 Scope ......................................................................................................................... 3 Chapter 2: Literature Review ............................................................................................... 4 2.1 History of Tall Wood Buildings ............................................................................... 4 2.2 Future of Tall Wood Buildings ................................................................................. 8 2.2.1 Timber Hybridization.......................................................................................... 10 2.2.2 Glued Laminated Timber (Glulam) .................................................................... 14 2.2.3 Mass Timber ....................................................................................................... 15 2.2.3.1 Cross Laminated Timber (CLT) ................................................................. 16 v 2.2.3.2 Laminated Strand Lumber (LSL)................................................................ 18 2.2.3.3 Laminated Veneer Lumber (LVL) .............................................................. 18 2.3 Previous Research Related to Modeling and Design of Tall Timber Structures .... 19 2.3.1 The FFTT System ............................................................................................... 20 2.3.2 Experimental Research on the FFTT System ..................................................... 27 2.3.3 Glulam Frame Connections ................................................................................ 30 2.3.4 Lateral Resistance of CLT Walls ........................................................................ 32 2.3.5 Seismic Force Modification Factors for CLT Buildings .................................... 35 Chapter 3: Three-dimensional Models for the FFTT System ......................................... 37 3.1 Structural Member Specifications ........................................................................... 38 3.2 Glulam Columns and Beams .................................................................................. 39 3.3 Glulam Frame Connections .................................................................................... 40 3.4 CLT Shearwalls ...................................................................................................... 43 3.4.1 Orthotropic CLT Properties ................................................................................ 44 3.4.2 Composite Theory – k Method ........................................................................... 45 3.4.3 Anisotropic CLT Numerical Modeling ............................................................... 47 3.5 CLT Wall Connections ........................................................................................... 49 3.5.1 Axial springs for CLT Panel Connections .......................................................... 50 3.5.2 Rotational springs for CLT Panel Connections .................................................. 53 3.6 CLT Slabs ............................................................................................................... 54 3.7 Steel Beams ............................................................................................................. 55 3.7.1 Spring Properties for Steel Beam Models ........................................................... 57 3.7.2 Beam-Column Element Modeling ...................................................................... 60 vi 3.8 Other Modeling Considerations .............................................................................. 63 3.8.1 Supports .............................................................................................................. 63 3.8.2 Gravity Loads...................................................................................................... 66 3.8.3 Mass .................................................................................................................... 68 3.8.4 Damping .............................................................................................................. 68 3.9 Summary of developed models ............................................................................... 72 Chapter 4: Non-linear Dynamic Seismic Analysis ............................................................ 75 4.1 Seismic Analysis ..................................................................................................... 75 4.1.1 Ground Motion Selection .................................................................................... 75 4.1.2 Ground Motion Scaling....................................................................................... 78 4.2 Performance Criteria ............................................................................................... 80 4.2.1 Interstorey Drifts ................................................................................................. 82 4.2.2 Plastic Rotations.................................................................................................. 84 4.3 Results of Non-linear Seismic Analyses ................................................................. 86 4.3.1 Interstorey Drift Results ...................................................................................... 87 4.3.2 Beam Plastic Rotation Results ............................................................................ 91 4.3.3 Base Shear ........................................................................................................... 94 4.4 Discussion of Seismic Analyses ............................................................................. 96 Chapter 5: Dynamic Wind Analysis ................................................................................... 97 5.1 Introduction ............................................................................................................. 97 5.2 NBCC Dynamic Procedure ..................................................................................... 98 5.2.1 External Pressure Coefficients ............................................................................ 99 5.2.2 Exposure Factor .................................................................................................. 99 vii 5.2.3 Gust Effect Factor ............................................................................................. 100 5.3 Wind Analyses ...................................................................................................... 103 5.4 Results of Wind Analyses ..................................................................................... 103 5.5 Discussion of Wind Analyses ............................................................................... 104 Chapter 6: Force Reduction Factor Study ...................................................................... 106 6.1 Seismic Force Modification Factors in the NBCC ............................................... 106 6.2 Force Reduction Factor Study for the FFTT System ............................................ 108 6.2.1 Two Dimensional Model .................................................................................. 109 6.2.2 Three Dimensional Model ................................................................................ 111 6.2.3 Ground Motion Record Selection and Scaling ................................................. 111 6.2.4 Results from the Three Dimensional Model ..................................................... 115 Chapter 7: Conclusions ..................................................................................................... 120 7.1 Summary ............................................................................................................... 120 7.2 Recommendations for Design ............................................................................... 121 7.3 Recommendations for Future Studies ................................................................... 122 Bibliography ........................................................................................................................ 123 Appendix A – FFTT Numerical Model Mode Shapes and Periods ................................ 127 viii List of Tables Table 1: Mass Timber Strength Properties ............................................................................. 19 Table 2: FFTT Option Summary ............................................................................................ 22 Table 3: Structural Member Specifications ............................................................................ 39 Table 4: Glulam Beam and Column Material Properties........................................................ 40 Table 5: Orthotropic Stiffness Used for Modeling ................................................................. 45 Table 6: Composition Factors for Wood Panels with Cross Layers (FPInnovations, 2012) .. 46 Table 7: CLT Shear Wall Anisotropic Material Properties .................................................... 47 Table 8: CLT Shear Wall Strength Properties ........................................................................ 47 Table 9: Composite Factors for CLT Walls ............................................................................ 48 Table 10: Orthotropic Modeling Parameters for 6 Layer CLT Wall ...................................... 48 Table 11: Orthotropic Modeling Parameters for 8 Layer CLT Wall ...................................... 48 Table 12: Design Gravity Loads ............................................................................................. 66 Table 13: Heights (Number of Stories) Modelled for each FFTT Option .............................. 73 Table 14: Ground Motion General Information ...................................................................... 76 Table 15: Ground Motion Database Information .................................................................... 76 Table 16: 12 Storey Option 1 Model Beam Sections Design with RdRo = 7.5 ..................... 111 Table 17: Ground Motion Summary ..................................................................................... 114 ix List of Figures Figure 1: The Landing, Gastown, Vancouver (Koo, 2013) ...................................................... 5 Figure 2: Leckie Building, Yaletown, Vancouver (Koo, 2013) ............................................... 5 Figure 3: Wood Frame Structure Height by Regulation in British Columbia (Green and Karsh, 2012) .............................................................................................................................. 6 Figure 4: Stadthaus, London (Image: Waugh Thistleton Architects) ....................................... 7 Figure 5: Wood Innovation Design Center, Prince George (jtst.gov.bc.ca) ............................. 8 Figure 6: Forte, Sydney, Australia (victoriaharbor.com.au) ..................................................... 8 Figure 7: Vasterbroplan, Stockholm (skyscrapercentral.com) ............................................... 10 Figure 8: Kanazawa M Building, Japan (Koshihara et al. 2005) ............................................ 12 Figure 9: Rendering of (a) Concrete Jointed Timber Frame System and (b) SOM’s Prototype 42 storey building (SOM 2013) .............................................................................................. 13 Figure 10: Glulam Frame System from the Center of Interactive Research on Sustainability (CIRS), UBC (naturallywood.com) ........................................................................................ 14 Figure 11: CLT Panels (structurlam.com) .............................................................................. 17 Figure 12: Rolling Shear (Stalnaker and Harris, 1997) .......................................................... 17 Figure 13: LSL Panel (Green and Karsh, 2012) ..................................................................... 18 Figure 14: LVL Board (awc.org) ............................................................................................ 19 Figure 15: FFTT Option 2 Rendering (Green and Karsh, 2012) ............................................ 20 Figure 16: Beam-diaphragm-wall Connection (Green and Karsh, 2012) ............................... 21 Figure 17: FFTT Option 1 Structural System (Green and Karsh, 2012) ................................ 22 Figure 18: FFTT Option 1 (Green and Karsh, 2012) .............................................................. 23 Figure 19: FFTT Option 2 (Green and Karsh, 2013) .............................................................. 24 x Figure 20: FFTT Option 3 (Green and Karsh, 2013) .............................................................. 25 Figure 21: FFTT Option 4 (Green and Karsh, 2013) .............................................................. 26 Figure 22: Typical Beam Embedment Procedure (Bhat, 2013) .............................................. 27 Figure 23: Typical Setup and Instrumentation (Bhat, 2013) .................................................. 28 Figure 24: HSS Section Test Results (a) Beam Yielding at the Interface and (b) Wood Crushing at Beam End (Bhat, 2013) ....................................................................................... 29 Figure 25: Sample HSS Section Hysteretic Response (Bhat, 2013) ....................................... 29 Figure 26: Beam-column Test Layout (Buchanan and Fairweather, 1993) ............................ 30 Figure 27: Hysteretic Response for a Beam-Column Subassembly with Steel Beam Brackets (Buchanan and Fairweather, 1993) ......................................................................................... 31 Figure 28: Local Bending of Steel Bracket (Buchanan and Fairweather, 1993) .................... 32 Figure 29: Brackets Types Tested (Popovski et al., 2010) ..................................................... 33 Figure 30: FPInnovation CLT Wall Test Setup (Popovski et al., 2010) ................................. 33 Figure 31: Sample Hysteresis Loop From CLT Panel with ―Type A‖ Brackets (Popovski et al., 2010) ................................................................................................................................. 34 Figure 32: Bracket Failure Mechanism (Popovski et al., 2010) ............................................. 35 Figure 33: Vancouver, BC 2% in 5 year 5% Damped Design Spectrum for Site Class C Soil................................................................................................................................................. 38 Figure 34: Beam-column Connection Modeling Details ........................................................ 40 Figure 35: Pinching4 Material Backbone and Cyclic Behavior (Lowes et al. 2004) ............. 42 Figure 36: Pinching4 Material Calibration for Column-beam Connections ........................... 42 Figure 37: Cross Section for (a) Six Layer Wall and (b) Eight Layer Wall ........................... 44 Figure 38: CLT Shear Wall Orthogonal Axes ........................................................................ 44 xi Figure 39: Wall Spring Illustration ......................................................................................... 49 Figure 40: (a) In-plane Rocking and (b) Out-of-plane Rocking ............................................. 50 Figure 41: OpenSees Model for CLT Panel Connections ...................................................... 51 Figure 42: SAWS Material Backbone and Cyclic Behavior (Folz and Filiatrault, 2001) ...... 51 Figure 43: SAWS Material Calibration for Wall Axial Springs ............................................. 52 Figure 44: Example Wall Spring Time History Response to an Earthquake Record ............. 53 Figure 45: SAP2000 Model First Mode Shape ....................................................................... 54 Figure 46: FFTT Ductile Failure Mechanism ......................................................................... 55 Figure 47: Laterally Loaded Beam Deformed Shape and Corresponding Bending Moment Diagram................................................................................................................................... 57 Figure 48: SAWS Material Calibration for Beam-Wall Connections .................................... 58 Figure 49: Assumed Moment-rotation Backbone Response of a Steel Beam ........................ 60 Figure 50: FFTT Failure Mechanism ...................................................................................... 63 Figure 51: Wall Boundary Conditions Including Rocking Springs ........................................ 64 Figure 52: Rocking Spring Backbone Curve .......................................................................... 66 Figure 53: Rayleigh Damping Plot ......................................................................................... 72 Figure 54: FE Model for Typical Storey of (a) Option 1, (b) Option 2, (c) Option 3, and (d) Option 4 .................................................................................................................................. 74 Figure 55: Ground Motion Component 1 Spectra .................................................................. 77 Figure 56: Ground Motion Component 2 Spectra .................................................................. 77 Figure 57: Ground Motions Scaling Example ........................................................................ 80 Figure 58: Typical Discrete Performance Levels (ATC, 2009) .............................................. 81 xii Figure 59: Hysteresis Loops for Beam-Column Assembly with Steel Beam Brackets (Buchanan and Fairweather, 1993) ......................................................................................... 83 Figure 60: Moment-Rotation Results from Steel Beam-CLT Wall Test ................................ 85 Figure 61: Example 30 Storey Model Displacement subjected to the Chi-Chi, Taiwan Ground Motion at two Orientations ..................................................................................................... 86 Figure 62: Interstorey Drift Combined Results: a) Mean Results and b) Mean Plus One Standard Deviation results ...................................................................................................... 87 Figure 63: Interstorey Drift Results for (a) Option 1, (b) Option 2, (c) Option 3, and (d) Option 4 Models ..................................................................................................................... 88 Figure 64: Roof Drift Combined Results: a) Mean Results and b) Mean Plus One Standard Deviation results ..................................................................................................................... 89 Figure 65: Roof Drift Results for (a) Option 1, (b) Option 2, (c) Option 3, and (d) Option 4 Models..................................................................................................................................... 90 Figure 66: Beam Plastic Rotations Combined Results: a) Mean Results and b) Mean Plus One Standard Deviation results .............................................................................................. 92 Figure 67: Plastic Rotation Results for (a) Option 1, (b) Option 2, (c) Option 3, and (d) Option 4 Models ..................................................................................................................... 93 Figure 68: Base shear results from model compared to those predicted by the NBCC (NRC, 2010) for different R (RdRo) values ......................................................................................... 94 Figure 69: Base Shear Results for (a) Option 1, (b) Option 2, (c) Option 3, and (d) Option 4 Models..................................................................................................................................... 95 Figure 70: Frequency Ranges for Excitations of Structures (Holmes, 2001.) ........................ 98 xiii Figure 71: Wind Loading External Pressure Coefficients from Figure I-15 of the NBCC (NRC, 2010) ............................................................................................................................ 99 Figure 72: Gust Energy Ratio as a Function of Wave Number ............................................ 102 Figure 73: (a) Wind Loading Interstorey Drift Results and (b) with h/500 limits ................ 104 Figure 74: Ductility Factor Based on Equal Displacement Approximation ......................... 108 Figure 75: Simplified Model Illustration (Zhang et al., 2014) ............................................. 110 Figure 76: Example CDF for a 12 Storey Model Design with Different Rd Factors (Zhang et al.) ......................................................................................................................................... 110 Figure 77: Vancouver, BC Site Hazard De-aggregation at 2 Seconds for (a) Distance and (b) Magnitude ............................................................................................................................. 112 Figure 78: Spectral Accelerations for (a) Linearly Scaled Motions and (b) Spectrally Matched Motions ................................................................................................................................. 114 Figure 79: Interstorey Drift Results for Matched Motions Applied in (a) Direction 1 and (b) Direction 2 ............................................................................................................................ 116 Figure 80: Interstorey Drift Results for Matched Motions Applied in (a) Direction 1 and (b) Direction 2 ............................................................................................................................ 116 Figure 81: Steel Beam Rotations Results for Scaled Motions Applied in (a) Direction 1 and (b) Direction 2 ....................................................................................................................... 117 Figure 82: Steel Beam Rotations Results for Matched Motions Applied in (a) Direction 1 and (b) Direction 2 ....................................................................................................................... 117 Figure 83: Storey Acceleration Results for Scaled Motions Applied in (a) Direction 1 and (b) Direction 2 ............................................................................................................................ 118 xiv Figure 84: Storey Acceleration Results for Matched Motions Applied in (a) Direction 1 and (b) Direction 2 ....................................................................................................................... 119 xv Acknowledgements First, I would like to thank my supervisor: Dr. Thomas Tannert, for giving me the opportunity to work on this research project. His guidance and support was invaluable throughout my research. It was a pleasure working with him. I would also like to thank my co-supervisor: Dr. Terje Haukaas. His enthusiasm for the topic was extremely motivating, and I appreciate his dedication to provide advice and discussion, no matter the time or place. His commentary and questions were always valuable and thought-provoking. I also sincerely thank Drs. Armin Bebamzadeh and Carlos Ventura for their support and for giving me the opportunity to work on many other extremely interesting projects outside of my thesis work. My time at UBC would not have been nearly as rewarding without them and the rest of the team at the Earthquake Engineering Research Facility (EERF). I thank Dr. Kenneth Elwood for his advice and support throughout my undergrad and graduate studies at UBC. He was always available for discussion and questions, and greatly helped me all the way from my application to completion of my M.ASc degree. I offer my enduring gratitude to the faculty, staff, and my fellow students and teammates at UBC, who have inspired and motivated me and made my time at, and away from, UBC much more enjoyable. Special thanks to my parents: Donna, Bob, and Nancy; who always offered support and advice throughout my years of education. And of course my siblings: Chris, Matt, and Sarah; xvi who always believed in me. I also thank my grandparents: Ron, Doreen, Gordon, and Dorothy; along with the rest of my family, for their unlimited encouragement and support. I also must thank all my friends, who have continued to support me throughout all my years of study and made my time in Vancouver much more enjoyable. I could not have made it this far without you all. The research funding was provided by Natural Sciences and Engineering Research Council of Canada (NSERC) through a grant to Dr. Tannert, as part of a project within the NEWBuildS strategic research network. xvii Dedication Dedicated to AL and JA… 1 Chapter 1: Introduction 1.1 Tall Wood-Based Building Throughout the early 20th century, numerous mid-rise timber structures were constructed across Canada and North America. However, since then, area and height restriction have been put on buildings that use combustible construction materials due to fire incidents. These restrictions remain to this day in the National Bulking Code of Canada (NBCC) (NRC, 2010). Recent regulatory changes, such as the introduction of light frame wood construction up to 6 stories in British Columbia (BCBC, 2012) now allow for mid-rise timber construction once again. Additionally, engineered wood products such as glued laminated timber (glulam), cross laminated timber (CLT), laminated veneer lumber (LVL), and others provide a more sustainable building material compared to concrete or steel, with reliable structural properties. These products may push the feasible height of timber structures into the high rise-building range (8+ stories). As a consequence, mass timber is increasingly gaining popularity in mid- and high-rise residential and commercial construction both in British Columbia and worldwide. Studies such as Gagnon et al., 2011; Ceccotti et al., 2010; Popovski et al., 2010; and others have shown good structural performance of CLT structures, including good seismic performance when combined with ductile connectors. Timber as a building material is lightweight, sustainable, and can provide efficient and elegant structural solutions. Currently, the most promising method for utilizing timber in mid- and high-rise construction, however, is as part of steel- or concrete-hybrid systems. This allows the design to reap the benefits of timber as a building material while exploiting the 2 properties of steel and concrete such as their weight and ductility. Several innovative timber hybrid systems have been already been developed including those proposed by SOM, 2013; Professner and Mathis, 2012; and the ―Finding the Forest Through the Trees‖ (FFTT) system proposed by Green and Karsh (2012). 1.2 Research Needed For a novel hybrid system to gain recognition, experimental data must be gathered and supported by computational modeling and analysis to predict its structural performance. For hybrid high-rise timber buildings, both component and system level testing are required, along with detailed finite element analyses (FEA) to optimize the structural details. Once this work is done, sophisticated, nonlinear system level models must be developed and used to predict the structural and dynamic behavior of the systems under gravity and lateral loads, including wind and seismic induced forces. Only after completing these steps can the performance of a proposed system be determined and proper design guidance be given. 1.3 Objectives The first main objective of the research is to determine whether the ―Finding the Forest Through the Trees‖ (FFTT) system (Green and Karsh, 2012) is structurally feasible, as proposed, in a moderately seismic environment accounting for both significant seismic and wind events. The second objective of this research is to gain a preliminary understanding of the dynamic behavior of tall hybrid timber structures including the determination of the governing lateral load to help provide design guidance and direction for further studies of this type of structure. 3 Other objectives involve using the results and methodology presented herein to further develop and refine the FFTT concept and to developed further design guidance for high-rise timber construction in general. Furthermore, the models and framework developed in for this study will be refined and modified as more physical and numerical test results are developed to further study the dynamic response of the FFTT structural system. 1.4 Scope Although there are several proposals for hybrid high-rise timber structural systems, this research is focused on the FFTT system proposed by Green and Karsh (2012) for Vancouver, BC. This research focused on the non-linear dynamic behavior of this system designed over its range of proposed heights (6-30 stories) under seismic and wind loading. 4 Chapter 2: Literature Review 2.1 History of Tall Wood Buildings The concept of tall timber buildings is not a new one – there are 19 storey pagodas built in Japan as far back as 1400 years ago which are still standing despite being located in a highly seismically active region (Green and Karsh, 2012). Additionally, mid-rise buildings have been commonly built in across Canada from the 1850s up until 1940. Typical timber buildings during that time consisted of unreinforced masonry on the exterior and heavy timber beam and post construction in the interior. These structures were commonly built as factories, warehouses, manufacturing plants, and other industrial buildings during the industrial era. The buildings were built up to nine stories and up to 30m tall. Some of the building had a total floor space of up to 312,000 ft2 (29,000 m2) (Koo, 2013). These buildings are commonly referred to as ―brick and beam‖ buildings. Locations such as Gastown and Yaletown in Vancouver, BC, are areas with a high concentration of early-20th century brick and beam buildings. One example is ―The Landing‖ (Figure 1), which was constructed in 1905 in Vancouver’s Gastown as a large warehouse. It is one of the largest brick and beam buildings with a floor space of 175,000 ft2 (16,000 m2) (Koo, 2013). It is nine stories high and was retrofitted in 1987 to meet modern building code requirements. 5 Figure 1: The Landing, Gastown, Vancouver (Koo, 2013) Another example is the Leckie building, a six-storey warehouse/factory building built in Yaletown in 1993 and renovated in 1991 (Figure 2). Figure 2: Leckie Building, Yaletown, Vancouver (Koo, 2013) As concrete and steel technology and design methods developed, timber construction for taller buildings diminished in Canada and the prime use of timber for construction became low-rise residential buildings and smaller low-rise commercial buildings. One of the main 6 reasons that tall timber construction diminished was building code regulations that limited the height of ―combustible‖ building material structures. Timber construction was considered unsafe for taller buildings because the wood could combust and provide additional fuel for a fire and evacuation of the upper stories was not easily possible. Figure 3 presents a timeline of timber structure construction and height limits in British Columbia from pre-1900 to the present. Currently timber construction is allowed by the British Columbia Building Code (BCBC, 2009) up to six stories provided proper fire suppression features are included. Figure 3: Wood Frame Structure Height by Regulation in British Columbia (Green and Karsh, 2012) Currently, tall timber buildings are making a comeback in mid- and even high-rise construction. With modern mass timber building products (see Section 2.2.3) and fire suppression technology, it is possible to build timber buildings well beyond the current six storey limit in British Columbia. The Stadthaus project in London (Figure 4) is an excellent example. The Stadthaus is a nine storey building with a structural system constructed entirely from timber. It utilizes large CLT walls as its structural system to resist both gravity and lateral loads. At its time of completion in 2008, it was claimed to be the world’s tallest pure timber structure. 7 Figure 4: Stadthaus, London (Image: Waugh Thistleton Architects) In British Columbia the tallest timber building is the recently completed Wood Innovation Design Center (WIDC) located in downtown Prince George (Figure 5). The WIDC is 7 stories and 30 m tall with a structural system comprising CLT and LVL panels with glulam beams and columns. The WIDC is projected to be an iconic and inspirational building that contributes to BCs expertise and reputation as a global leader in wood construction and design. A 10 storey timber apartment building, called Forte, has recently been completed in Australia as the world’s tallest timber building (Figure 6). Forte was constructed from CLT panels which reduced carbon emissions by over 1,400 tonnes compared to conventional construction methods (theurbandeveloper.com). 8 Figure 5: Wood Innovation Design Center, Prince George (jtst.gov.bc.ca) Figure 6: Forte, Sydney, Australia (victoriaharbor.com.au) 2.2 Future of Tall Wood Buildings Over the last century high-rise development has been dominated by the steel and concrete industries. These materials are well understood and have excellent structural properties 9 including strength, stiffness, and ductility which allowed engineers and architects to construct taller buildings then could have been imagined at the beginning of the 20th century, even in windy and earthquake prone regions. However, these building materials are accompanied with severe environmental consequences. Studies by the Canadian Wood Council (CWC) estimate that using steel and concrete for buildings requires 26% and 57% more energy, emits 34% and 81% more greenhouse gasses, releases 24% and 47% more pollutants, and discharges 400% and 300% more water compared to using timber for similar buildings, respectively (CWC, 2004). According to UN Habitat, currently 50% of the world’s population lives in urban environments – and by 2050 this number is estimated to surpass 70% (UN-Habitat, 2008). This change will require huge developments in infrastructure and affordable high-density housing. Building the approximately 3 million homes (UN Habitat, 2008) from steel or concrete will have huge impacts on the environment especially in terms of greenhouse gas emissions. One solution is to build these homes from timber. Timber is renewable and timber actually stores – rather than emits – carbon, since trees grow using carbon from the environment. Yet, to build the necessary homes, large high-rise structures will be required to provide the population density essential in large cities, which is typically the domain of steel and concrete. However, with the recent development of mass timber products such as CLT and LVL, it may be possible to begin constructing 30+ storey mass timber structures to provide a more environmentally friendly solution to this global housing problem. The previously mentioned examples demonstrate that taller wood construction is not only possible but rapidly increasing in both in BC and around the world. The Vasterbroplan 10 (Figure 7) is another example. The Vasterbroplan is a 34 storey timber (approximately 110m) building proposed for construction in Stockholm, Sweden. Other extreme tall wood buildings have been proposed around the world. Examples in include the FFTT system (Green and Karsh, 2012) and the Skidmore, Owings & Merrill (SOM) Tall Timber Research Project (SOM, 2013). Figure 7: Vasterbroplan, Stockholm (skyscrapercentral.com) 2.2.1 Timber Hybridization Timber members have high strength to weight ratio compared to steel and concrete which can result in lighter structures and subsequently lower forces during ground excitation. Timber does have several disadvantages however; the most prominent from a structural, or more specifically seismic, perspective is its brittle nature when loaded in tension or shear. Under these loadings, timber will break in a very non-ductile manner, which is not ideal 11 during an intense ground motion as it does not dissipate energy and could lead to a brittle, catastrophic failure of the structure. Due to this characteristic, the most promising approach for using timber in mid- and high-rise construction is as part of hybrid structural systems. Hybridization refers to combining two different materials to form a system that makes use of the unique advantages of each material. Hybridization can occur on both a component level, such as reinforced concrete, or on a system level. System hybridization combines two materials at the structural level to distribute and share the loads acting on them. Through designing hybrid structures, engineers are able to capitalize on the light weight and environmental benefits of timber while exploiting the unique benefits of the other building materials, such as the ductility that can be provided by steel, or the weight that can be provided by reinforced concrete. The Kanazawa M Building (Figure 8), constructed in 2005 in Kanazawa, Japan, provides an example of both system and component hybridization. It is a 5 storey building with four timber-steel composite levels supported by a reinforced concrete first floor. The building system comprises steel-timber composite frames, concrete floors slabs and roof, plywood walls, and stairs constructed with a steel frame. The composite frames consist of laminated timber with built-in square steel bars. The steel bars resist load while the timber provides restraint from buckling and increases the fire resistance of the members, providing an efficient hybrid-type component (Koshihara et al., 2005). System level hybridization, as used in the Kanazawa Building, may be necessary to build taller timber buildings up to and beyond 30 stories. Two studies that exemplify this are ―The 12 Case for Tall Wood Buildings‖ (Green and Karsh, 2012), which introduced the FFTT design concept, and the SOM Tall Timber Research Project (SOM, 2013). Figure 8: Kanazawa M Building, Japan (Koshihara et al. 2005) The goal of the SOM Tall Timber Research Project was to develop a mass timber structural system for high-rise buildings – up to 42 stories in Chicago, Il. SOM proposed an innovative system called the ―Concrete Jointed Timber Frame‖ to effectively resist the overturning and lateral forces induced by significant wind loading. The SOM system relies on stiff mass timber panels for the main structural elements and lateral force resisting system, supplemented with reinforced concrete at the connecting joints. The reinforced concrete joints provide any necessary ductility, while effectively distributing the majority of the mass at each floor to its perimeter, where it is most useful in resisting overturning forces. The result is an efficient system that benefits from the unique advantages of the three materials (steel, concrete, and timber) while reducing the carbon footprint of the structure by 60 to 13 75% compared to an equivalent concrete building (SOM, 2013). Figure 9a illustrates the Concrete Jointed Timber Frame system, and shows how the mass timber panels could be connected through reinforced concrete joints. Figure 9b presents a rendering of the 42 storey prototype structure considered in the report (SOM, 2013). Although this idea is still in its proposal phase, SOM considers it to be feasible from the standpoint of structural engineering, architecture, interior layouts, and building services. Additional studies, however, are required to verify the performance of the structural system, possibly requiring physical testing. The structure was designed with particular attention to its constructability, cost, and fire protection; however, expert review and physical testing related to its fire safety may also be required (SOM, 2013). (a) (b) Figure 9: Rendering of (a) Concrete Jointed Timber Frame System and (b) SOM’s Prototype 42 storey building (SOM 2013) 14 2.2.2 Glued Laminated Timber (Glulam) Glulam is a structural engineered timber product manufactured by bonding a number of layers of dimensioned timber with a durable, moisture-resistance, structural adhesive. These members are extensively used as columns and beams in timber construction and can be manufactured in curved or arch shapes for a wide variety of architectural designs (see Figure 10). Glulam members optimize wood as a building material because they allow for construction of large members from small trees, which gives them the advantage over large sawn timber members which must be manufactured from old-growth trees. Because glulam members can be manufactured in large sizes they can be utilized for long spans and large loads. Size is only constrained by transportation and handling limits. Glulam can even offer greater pound-for-pound strength than steel (APA, 2010) and may be slightly more cost-effective (Sathre and O’Connor, 2008). Glulam also performs well in fires, as it burns slowly and maintains strength and stiffness. Figure 10: Glulam Frame System from the Center of Interactive Research on Sustainability (CIRS), UBC (naturallywood.com) 15 2.2.3 Mass Timber In order to efficiently construct mid- and high-rise timber structures, traditional sawn timber and glulam will need to be supplemented with mass timber products. Mass timber utilizes large, solid wood panels which can range in size up to 2.4 x 20m and can be constructed up to or greater than 400mm in thickness. The three primary mass timber products are:  Cross Laminated Timber (CLT)  Laminated Strand Lumber (LSL)  Laminated Veneer Lumber (LVL) Mass timber construction is very different from typical light-frame construction used in residential building, and offers significant advantages in fire, acoustic, and structural performance as well as building scale, construction efficiency, and material stability and reliability. Mass timber, and engineered timber products in general have a wide variety of unique benefits. Compared to traditional sawn lumber, mass timber:  Can be designed for specific performance objectives  Is very versatile. A wide variety of thicknesses, sizes, and grades are available and can be custom manufactured.  Is engineered to maximize the strength and stiffness properties of natural wood while limiting potential material disadvantages.  Is dimensionally stable.  Is reliable. Strength and stiffness characteristics can be more accurately determined than in sawn lumber.  Performs well in fire.  Makes efficient use of wood since it can be made from small or defective pieces. 16 And compared to steel and concrete, mass timber:  Has very good strength and stiffness properties, especially per unit mass.  Is easy to work with and to assemble.  Is prefabricated, allowing for rapid on-site construction.  Provides very good natural acoustic and heat insulation.  Is sustainable.  Stores carbon rather than produces it.  Comes from a renewable resource. 2.2.3.1 Cross Laminated Timber (CLT) CLT panels consist of layers of sawn lumber which are stacked in perpendicular orientations. The wide faces of the boards are glued together with an adhesive providing a strong and stiff bond between layers. Although timber is highly anisotropic and much stronger when loaded parallel to its grain orientation compared with loading perpendicular to its grain, when glued together in alternating orientations, this property is reduced and a more dimensionally stable product is achieved. CLT panels can be produced up to 12m in length (structurlam.com) and are extensively used in walls and floor systems where long spans are required. In the FFTT systems, CLT panels may be utilized in the walls and slabs of the structures due to their ability to span long distances and their in-plane stiffness and strength properties. CLT panels are able to be manufactured thicker than LSL or LVL panels, which is a benefit for the taller designs. 17 Figure 11: CLT Panels (structurlam.com) One of the major drawbacks with CLT, however, is its material efficiency under axial loading. Under axial loading, up to half of the area of a panel under load will be loaded perpendicular to its grain (the weaker direction), which limits the overall strength of a panel. Another drawback is related to the rolling shear strength and stiffness in the panel cross layers. Rolling shear is the rolling of the wood fibers when loading in shear perpendicular to the grain of the wood, as illustrated in Figure 12. Timber is much weaker and softer in rolling shear compared to regular shear, and consequently, the shear deformation of a panel will be greatly amplified due to the rolling shear in the cross layers of the panel. Rolling shear stiffness is approximately one tenth of parallel-to-grain shear (Mestek et al., 2008). Figure 12: Rolling Shear (Stalnaker and Harris, 1997) 18 2.2.3.2 Laminated Strand Lumber (LSL) LSL is produced from strands of timber glued together orientated parallel to the length of the member. LSL is highly consistent and has a uniform structure and predictable strength and stiffness properties. Because it can be made from small trees and defective wood, LSL is a sustainable building material. In the FFTT system, LSL may be specified for use as floors, slabs or walls. Figure 13: LSL Panel (Green and Karsh, 2012) 2.2.3.3 Laminated Veneer Lumber (LVL) LVL is manufactured by laminating layers of wood veneers using a waterproof adhesive. The grain of each layer is orientated in the same direction to achieve predictable behavior and uniformity. Due to the controlled manufacturing process, LVL products are straight and defect free. LVL may also be specified for the slabs or walls or the FFTT system. 19 Figure 14: LVL Board (awc.org) LVL and LSL panels can be manufactured up to 20m long and have higher shear strength than CLT. Additionally, since bearing depends on grain orientation in CLT panels, LVL and LSL may perform better at steel beam connections than CLT panels. Table 1 summarizes some of the key strength properties of the three mass timber products based on typical manufacturer’s data (redbuilt.com; lpcorp.com) for LVL and LSL, and local manufacturer’s data for CLT (structurlam.com). Table 1: Mass Timber Strength Properties Bending Compression Tension Shear CLT 11.8 MPa 11.5 MPa 5.5 MPa 1.5 MPa LVL 15-21 MPa 15-21 MPa 9-12 MPa 1.5-2 MPa LSL 12-19 MPa 11-17 MPa 9-15 MPa 1-3 MPa 2.3 Previous Research Related to Modeling and Design of Tall Timber Structures The FFTT system is an innovative structural system recently proposed in The Case for Tall Wood report (Green and Karsh, 2012), and little additional literature is available on the 20 system. However, the individual components of the system; such as CLT shear walls, glulam frames, and steel beam-CLT wall connections; have been researched. 2.3.1 The FFTT System The FFTT system, an acronym for ―Finding the Forest Through the Trees‖ is an innovative building system designed for high-rise timber-steel composite structures using mass timber panels connected with steel beams (Green and Karsh, 2012). This system uses engineered timber products to resist lateral and gravity induced forces, and utilizes the ―strong-column weak-beam‖ design methodology in that interconnecting steel beams are designed to yield before the vertical timber elements exhibit damage or break and therewith provide energy dissipation and ductility for seismic induced demands. The timber members provide a stiff system that, if properly designed, stays rigid and will deflect little under wind induced loads. A rendering of a 20 storey FFTT building is presented in Figure 15 and a beam-wall-diaphragm connection is presented in Figure 16. Figure 15: FFTT Option 2 Rendering (Green and Karsh, 2012) 21 Figure 16: Beam-diaphragm-wall Connection (Green and Karsh, 2012) The advantage of the FFTT system is that it optimizes the unique benefits of the two materials for an efficient and sustainable design. Timber provides a lightweight, stiff, and sustainable building material, that not only is renewable, but stores carbon emissions rather than producing them. This is combined with steel which can provide a reliable and ductile failure mechanism as well as significant energy dissipation which allows the system to perform adequately during seismic events. Four different Options were proposed for the FFTT system (Green and Karsh, 2012), all of which are based off of this design methodology and contain interior mass timber shearwalls (either CLT or LVL) interconnected with steel elements. The structural system of Option 1 is shown in Figure 17. 22 Figure 17: FFTT Option 1 Structural System (Green and Karsh, 2012) The main lateral load resisting systems of the four FFTT options are summarized in Table 2. Table 2: FFTT Option Summary Option 1 Option 2 Option 3 Option 4 LRFS Core shearwalls Core and interior shearwalls Core and exterior shearwalls Core, interior and exterior shearwalls GFRS Shearwalls and exterior columns Shearwalls and exterior columns Shearwalls Shearwalls Height limit (stories) 12 20 20 30 The first option (Figure 18), for structures up to 12 stories, utilizes perimeter glulam columns and beams as part of the gravity force resisting system (GFRS). Interior core shearwalls provide the lateral force resisting system (LFRS). 23 Figure 18: FFTT Option 1 (Green and Karsh, 2012) Option 2, illustrated in Figure 19, which may be viable up to 20 stories is based on the same layout, and includes additional interior shearwalls to increase the lateral load capacity of the system. Because these shearwalls effectively separate and compartmentalize the area within each storey, this layout may be well suited for residential construction. 24 Figure 19: FFTT Option 2 (Green and Karsh, 2013) Option 3 (Figure 20) uses the Option 1 plan and incorporates exterior shearwall connected with steel beams. Similar to Option 2, it was designed for structures up to 20 stories. Because this design provides a more open floor layout it would be well suited to a commercial or office type building. 25 Figure 20: FFTT Option 3 (Green and Karsh, 2013) The final design, Option 4 (Figure 21), combines the previous two designs to create an extremely stiff, strong system that may be feasible in structures up to 30 stories. 26 Figure 21: FFTT Option 4 (Green and Karsh, 2013) 27 2.3.2 Experimental Research on the FFTT System As part of a Master’s thesis at the University of British Columbia (UBC), Bhat (2013) tested a variety of steel beams embedded into CLT panels as a first step towards understanding the behavior of the FFTT system. Her tests involved static and cyclic in-plane loading of a setup comprising a steel beam embedded into a 7 layer CLT panel. Tests were conducted, both monotonic and cyclic, on a variety embedment lengths and embedment depths. Both a wide flange section, with and without notches cut into the flanges at the plastic hinge zone, and a rectangle hollow structural steel (HSS) section were tested. To build the connections, a steel beam was embedded into slots cut into a CLT panel as shown in Figure 22, and then held in place with lag screws. A typical test setup is shown in Figure 23. Beams were pin-connected at two points along the CLT panel and loaded by an actuator at one end of the cantilevered beam. Displacements along the beam were measured by six linear variable differential transformers (LVDTs). Figure 22: Typical Beam Embedment Procedure (Bhat, 2013) 28 Figure 23: Typical Setup and Instrumentation (Bhat, 2013) Two sections were tested: a W150x100 wide flange section and a HSS 100x50x3.125 hollow section. Embedment lengths and depths and bolted connections were varied between tests. None of the sections were laterally supported and the stronger wide flange sections consistently buckled out of plane and produced lopsided hysteresis curves under cyclic loading. The HSS tests yielded and plastified and demonstrated much more symmetric and predictable hysteresis curves. Yielding of the beam, followed by local crushing in the CLT panel was observed, as shown in Figure 24. The connection was highly ductile with a pinched hysteretic response (Figure 25). 29 (a) (b) Figure 24: HSS Section Test Results (a) Beam Yielding at the Interface and (b) Wood Crushing at Beam End (Bhat, 2013) A typical hysteretic curve for the HSS section embedded at a depth of 50.8mm for a length of 304.8mm is presented in Figure 25. The beam was loaded cyclically with the CUREE loading protocol (Krawinkler et al., 2001) and displacements were measured at the end of the 1.8m beam where the actuator force was applied. Figure 25: Sample HSS Section Hysteretic Response (Bhat, 2013) 30 2.3.3 Glulam Frame Connections Buchanan and Fairweather (1993) present an overview of the seismic performance of glulam timber frame structures. They describe a wide range of connections available for glulam frames with particular reference to seismic loading and present test results for several new connection types. The arrangement used for the beam-column connection testing is presented in Figure 26. This arrangement was designed to give a representative force and moment distribution while under a simulated lateral load, which was applied to the top of the frame. The mid-height of the column and mid-lengths of the beams were points of contraflexure, similar to lateral loading in a multistorey building. Figure 26: Beam-column Test Layout (Buchanan and Fairweather, 1993) Test load-deflection hysteretic results for a beam-column subassembly with steel beam brackets are shown in Figure 27. 31 Figure 27: Hysteretic Response for a Beam-Column Subassembly with Steel Beam Brackets (Buchanan and Fairweather, 1993) The particular test setup that produced Figure 27 was comprised of 495 x 135mm glulam beams connected to 495 x 180mm glulam columns with steel brackets connecting the members. The beams had steel bars epoxied into the end grain, while the columns had bars epoxied through the joint region. All the connections were bolted together. A high degree of ductility was observed and most of the energy absorption was accomplished through local bending of the steel beam bracket. Local splitting of the bracket near the weld on the web was observed, in the final load cycle, however no catastrophic failure occurred. Figure 28 shows the local bending of the steel bracket at the end of a test. 32 Figure 28: Local Bending of Steel Bracket (Buchanan and Fairweather, 1993) 2.3.4 Lateral Resistance of CLT Walls Popovski et al. (2010) conducted a series of quasi-static tests on CLT wall panels to investigate the behavior of the panels and their connections under lateral loads. A wide range of configurations and connection details were considered. Single panel walls with three different aspect ratios, multi-panel walls connected with step joints, as well as two storey walls were all tested. Connections tested included steel brackets with annular ring nails, spiral nails, and screws; combinations of steel brackets and hold-downs; diagonal long screws; and custom made brackets with timber rivets. The brackets tested are shown in Figure 29. An example test setup is presented in Figure 30. 33 Figure 29: Brackets Types Tested (Popovski et al., 2010) (a) (b) Figure 30: FPInnovation CLT Wall Test Setup (Popovski et al., 2010) 34 Results showed that both nails and screws can perform adequately under seismic loading while the use of hold-downs with nails at wall ends can further improve the performance. Diagonally placed screws to connect the walls to the floor displayed less ductile behavior and were not recommended. Timber rivets with custom brackets were also demonstrated to be effective. The hysteretic response of a single storey wall with ―Type A‖ brackets is presented in Figure 31. The brackets were connected to the CLT panels with 16 – 89mm long, 3.9mm spiral nails and bolted to the ground. The majority of the deformation was in the connections and the panels moved almost like rigid bodies. A very ductile failure mechanism was observed, as shown in Figure 32, which included nail withdrawal, nail yielding, and timber yielding. Figure 31: Sample Hysteresis Loop From CLT Panel with “Type A” Brackets (Popovski et al., 2010) 35 Figure 32: Bracket Failure Mechanism (Popovski et al., 2010) 2.3.5 Seismic Force Modification Factors for CLT Buildings Pei et al. (2013) modelled CLT wall buildings and estimated their potential seismic force reduction factors (Rd and Ro). These are factors that allow for a reduction in design base shear of a structure due to its inelastic response and predicted overstrength when using an elastic static force method, which is one of the acceptable solutions for seismic design in the NBCC (NRC, 2010). Currently, no modification factors are listed in the NBCC for CLT wall buildings, which means designers must either design CLT buildings to remain elastic under seismic loading (which can be very difficult and costly in high seismic zones) or try to generate and justify their own modification factors. In this study, material models were developed based on the tests conducted by Popovski et al. (2010) and then input into numerical models of multistorey low- and mid-rise CLT wall buildings, designed using the NBCC 2010 (NRC, 2010) provisions with multiple trial ductility factors (Rd). The models were subjected to a suite of 22 earthquake acceleration 36 time-history records, and the interstorey drift was recorded. Acceptable Rd factors were developed through limiting interstorey drift to 2.5% (as is commonly used for life safety performance in the NBCC 2010 (NRC, 2010) and other building codes) with an acceptable level of confidence (80% probability of non-exceedance). Vancouver, BC was considered as the location of these fictional buildings to provide the hazard level. The Vancouver 2% in 50 year 5% damped spectrum was used as a design spectrum. Results indicated that an Rd equal to 2.0, with a Ro (overstrength reduction factor) equal to 1.5 would produce desirable performance during a design level earthquake in Vancouver. These values were considered in the design of the FFTT system options (Green and Karsh, 2012) as well. 37 Chapter 3: Three-dimensional Models for the FFTT System A number of non-linear three-dimensional finite element models were developed in order to analyze the four FFTT options over their range of proposed heights. These models are able to capture both the linear and post-yielding behavior of the structures and were assessed with a suite of bi-directional time-history earthquake records and a series of dynamic wind analyses. All models were developed using OpenSees, the Open System for Earthquake Engineering Simulation (McKenna et al. 2000). OpenSees is an open-source, object-orientated framework developed for finite element applications to simulate structural and soil response of structures to earthquakes. OpenSees offers a wide variety of one, two, and three dimensional materials and element types, making it suitable for a wide variety of structural and geotechnical simulations. OpenSees used input files written in Tool Command Language (Tcl) (tcl.tk), a free scripting language commonly used for rapid prototyping, scripted applications, graphical user interfaces and testing. Due to this open nature, OpenSees is highly programmable and allows any user with basic Tcl programming knowledge to develop simple or sophisticated codes and analyze models. In order to model the proposed system, six main elements had to be considered:  Glulam columns  Glulam beams  CLT shear walls  CLT slabs  Connections between timber elements  Steel beams including connections to the other components 38 3.1 Structural Member Specifications The models were initially designed using an equivalent static force procedure based on the NBCC (NRC, 2010) methodology. Timber gravity resisting elements (beams and columns) were sized based on their specified dead load, while the lateral force resisting members (walls and steel beams) were sized to resist the forces determined from the static analyses. The Vancouver, BC, 5% damped 2% in 50 year design spectrum for Site Class C (NRC, 2010) was used to determine the elastic base shear for the analyses (Figure 33). A Ro of 1.5 and Rd of 2.0 were considered as the force reduction factors according the preliminary results by Pei et al. (2013) and recommendations from Green and Karsh (2012). The members were selected based on the suite of options so that similar sections could be used in all the models. Table 3 summarizes the members specified for the models. Figure 33: Vancouver, BC 2% in 5 year 5% Damped Design Spectrum for Site Class C Soil 39 The main model difference between the four different options is that 6 layer CLT panels were chosen for Options 1, 2, and 3; while 8 layer CLT panels were chosen for the shear walls in the Option 4 models. Table 3: Structural Member Specifications Member Material Section Glulam Beam D. Fir 16c-E 264x484mm Glulam Column D. Fir 20f-EX 418x418mm Steel Beam Grade 350W W250x33 CLT Wall D. Fir 204mm (6 layers) or 274mm (8 layers) 3.2 Glulam Columns and Beams All FFTT systems were designed with glulam columns as part of the gravity load resisting system. Some of the systems, such as Option 1, included exterior columns to provide significant resistance to gravity induced loads. Whereas, other systems, such as Option 4, utilized exterior and interior shearwalls to provide the majority of the gravity load resistance. To avoid a brittle failure mechanism, the glulam columns must be designed to remain elastic. Due to this requirement, it was deemed acceptable to model these timber members with elastic elements. To ensure the validity of this assumption, the stresses from both shear forces and combined axial and bending forces were recorded during the analyses. These stresses were compared to the strength values of the timber material to ensure that they were below the typical strength values of the material. The elastic beam-column elements used to model these elements included the elastic shear and axial modulus values for a typical glulam 40 member as presented in Table 4. These values were obtained from the 2010 Canadian Wood Design Handbook (CSA, 2009). Similar to the glulam columns, the glulam beams were modelled with the same type of elastic beam-column element with the same elastic material properties. Table 4: Glulam Beam and Column Material Properties Material Modeling Parameters Strength Parameters Elastic Modulus Shear Modulus Compression (Parallel to Grain) Tension (Parallel to Grain) Shear (Perpendicular to Grain) D. Fir 16c-E 12400 MPa 530 MPa 30.2 MPa 20.4 MPa 2.0 MPa 3.3 Glulam Frame Connections The columns were modelled with two degree of freedom rotational springs at the top and bottom of each storey. These hinges were included to model the flexibility and nonlinear behavior of the glulam column to beam connections. The springs were included at half of the beam depth above or below the beam-column connection node to simulate the depth of the beam. Between the beam and each spring a rigid elastic element was included. This detail is illustrated in Figure 34. Figure 34: Beam-column Connection Modeling Details 41 The springs were modelled with a zero-length element which included the connection rotational stiffness in the two rotational degrees of freedom. The springs were modelled to be rigid axially and in torsion and shear. The nonlinear properties of these springs were not known explicitly since this part of the FFTT system has not been sufficiently investigated. It is known, however, that there will be some flexibility associated with these connections and that they should not be modelled as completely rigid. To get a reasonable estimate of the possible behavior of these connections, results presented by Buchanan and Fairweather (1993) on tests of glulam beam-column connections with steel brackets were considered. The test setup was presented in Figure 26 was numerically modelled in OpenSees with the beam and columns modelled as elastic elements. The hinges were modelled as zero-length rotational springs with material behavior defined by the Pinching4 material model (Lowes et al., 2003), as shown in Figure 35. This model provides a uniaxial ―pinched‖ force-deformation response with degradation under cyclic loading. Strength and stiffness degradation occur through cyclic stiffness degradation, reloading stiffness degradation, and strength degradation. The model was developed to simulate reinforced concrete beam-column joints – but can also be applicable to timber-steel connections, as seen in studies of bracket connections of CLT shear walls (Shen et al., 2013). In this model (ePdx, ePfx) and (eNdx, eNfx) provide the positive and negative backbone curves for the material. The d and f parts of the names refer to displacement and force, and x is 1:4. The factors uForceP and uForceN describe the unloading properties, while rDispP, rForceP, rDispN, and rForceN determine the reloading properties. 42 Figure 35: Pinching4 Material Backbone and Cyclic Behavior (Lowes et al. 2004) The material model was calibrated in an iterative process, with the resulting hysteretic response as illustrated in Figure 36. Figure 36: Pinching4 Material Calibration for Column-beam Connections 43 3.4 CLT Shearwalls Any of the three mass-timber products, as introduced in Section 2.2.3, are suitable for use in the FFTT system. For this study, however, only CLT panels were considered due to their ability to be manufactured thicker than LVL or LSL panels. However, since LSL or LVL exhibit similar stiffness, the conclusions of this study are still applicable to these materials. The lateral force resisting system (LFRS) for all of the proposed FFTT layouts comprises CLT shearwalls. All of the options include CLT shearwalls in the core, and several also include additional interior or exterior walls to add lateral stiffness to the system. Options 3 and 4 also utilize interior and exterior shearwalls as the main gravity force resisting system. CLT shearwalls, six layer and 204mm thick, were used in all layouts, except in the taller Option 4 designs, where eight layer 274mm thick panels were required. Figure 37 presents the cross section for the type CLT wall thicknesses. The shearwalls were modelled with a grid of shell elements at each storey level. The elements are four-noded quad elements that utilize a bilinear isoparametric formulation as well a modified shear interpolation. The elements are formulated with thin-plate expressions and can resist both in-plane and out-of-plane deflections (Dvorkin and Bathe, 1984). 44 (a) (b) Figure 37: Cross Section for (a) Six Layer Wall and (b) Eight Layer Wall 3.4.1 Orthotropic CLT Properties Due to the orientation of timber layers in CLT panels, as well as the anisotropic nature of timber, the wall elements had to be modelled with different properties in each orthogonal direction shown in Figure 38. Figure 38: CLT Shear Wall Orthogonal Axes 45 3.4.2 Composite Theory – k Method In order to determine the orthotropic stiffness properties of the CLT walls the CLT handbook (FPInnovations, 2012) presents a method called the ―k method‖ (Blass, 2004) which proposes a method to calculate the effective bending stiffness of a CLT panel given its layer geometry and material properties based on the loading configuration. Several assumptions are made in this method, including: 1) Plane sections are assumed to remain plane, resulting in a linear stress-strain distribution. 2) The stiffness of layers loaded perpendicular and parallel to the grain are considered. 3) Shear deformation is not taken into account. 4) Stiffness factors are based on the loading configuration. Given these assumptions, the composition (k) factors can be calculated as illustrated in Table 6. Note that not all loading configurations are presented in this table – only the cases particularly important for an in-plane bending shear wall. E0 and E90 refer to the elastic moduli when considering loading parallel and perpendicular to the grain, respectively. Table 5 shows how these factors can be implemented into the orthotropic shell elements. Table 5: Orthotropic Stiffness Used for Modeling Loading Effective Stiffness Perpendicular to Plane Loading Bending Parallel Eo·k1 In-Plane Loading Bending Parallel Bending Perpendicular Eo·k3 Eo·k4 46 Table 6: Composition Factors for Wood Panels with Cross Layers (FPInnovations, 2012) Loading Configuration k 47 3.4.3 Anisotropic CLT Numerical Modeling To model the anisotropic CLT walls, an elastic orthotropic material that has been implemented in OpenSees was utilized. This material required three elastic moduli, three shear moduli, and three Poisson ratios, to create a material with unique properties in each orthogonal direction. Purely elastic behavior of the CLT was assumed based on the fact that they would be capacity designed to remain elastic while the steel beams that connected the panels yielded. Material properties for the CLT wall panels were based on local manufacturer’s data (structurlam.com), values proposed by Blass and Görlacher (2004), and relationships as observed by Stürzenbecher et al. (2010) as summarized in Table 7. E0 and G0 refer to the elastic and shear moduli parallel to the grain of the timber laminations, respectively. E90 and G90 refer to the elastic properties perpendicular to the grain of the timber and are assumed to be identical for the radial or tangential direction of the grain of the laminations. Table 7: CLT Shear Wall Anisotropic Material Properties E0 9500 MPa G0 950 MPa E90 700 MPa G90 50 MPa The strength properties are also summarized in Table 8. All values were based on local manufacturer’s data (structurlam.com). Table 8: CLT Shear Wall Strength Properties Bending Compression (Parallel to Grain) Tension (Parallel to Grain) Shear (Perpendicular to Grain) 11.8 MPa 11.5 MPa 5.5 MPa 1.5 MPa 48 For these two walls considered in the FFTT system, the equations and properties from Table 6 and Table 7 were utilized to calculate the composite factors as summarized in Table 9. Table 9: Composite Factors for CLT Walls k1 k3 k4 Six Layer Wall 0.93 0.675 0.377 Eight Layer Wall 0.95 0.758 0.295 Using these composite factors the modeling parameters for the 6 and 8 layer CLT wall were calculated as summarized in Table 10 and Table 11, respectively. Table 10: Orthotropic Modeling Parameters for 6 Layer CLT Wall Direction E (MPa) G (MPa) υ 1 3,590 360 0.04 2 6,400 640 0.04 3 700 70 0.40 Table 11: Orthotropic Modeling Parameters for 8 Layer CLT Wall Direction E (MPa) G (MPa) υ 1 2,800 280 0.04 2 7,200 720 0.04 3 450 45 0.40 49 3.5 CLT Wall Connections Since CLT panels can only be constructed with a limited height, modeling one continuous panel over the height of a high-rise building would be inappropriate. This is because, in reality, several panels would have to be connected together over the height of the building, and these connections add flexibility to the system that would not be accounted for using one continuous panel in the model. Additionally, it could be possible for these connections to yield and add nonlinearity to the system. A maximum feasible length of a panel would be about four – 3m high stories (12m total height) (Green and Karsh, 2012). Based on this panel length, axial and one degree of freedom rotational springs were added between adjacent wall nodes at every fourth storey of every wall to model the connections, as shown in Figure 39. Figure 39: Wall Spring Illustration These springs allowed for in-plane and out-of-plane rocking of the panels at the connections (Figure 40a and b). The springs were modelled with zero length elements containing the material properties desired to represent the flexibility of the connections as described in the following sections. 50 (a) (b) Figure 40: (a) In-plane Rocking and (b) Out-of-plane Rocking 3.5.1 Axial springs for CLT Panel Connections In order to model the axial springs which account for in-plane wall rocking, the tests conducted by Popovski et al. (2011) at FPInnovations were considered. The test comprised a single storey CLT panel with steel brackets nailed into the panel and bolted to the ground. The test setup was modelled in OpenSees, as illustrated in Figure 41, with axial springs to represent the bracket connections. The SAWS material was used to model the behavior of the springs (Folz and Filiatrault, 2001). This material provides a one-dimensional hysteretic model developed as part of the CUREE Caltech project for the seismic analysis of wood frame structures. This material model is defined by an initial tangent slope, S0; a second, softer slope, R1*S0; and a strength degradation slope, R2*S0. A pinching slope is defined by R4*S0 and stiffness degradation is included through two factors: ALPHA and BETA. The general backbone curve and hysteretic properties of the SAWS material model are illustrated in Figure 42. 51 Figure 41: OpenSees Model for CLT Panel Connections Figure 42: SAWS Material Backbone and Cyclic Behavior (Folz and Filiatrault, 2001) The results of the numerical model with a calibrated material compared to the test by Popovski et al. (2011) are presented in Figure 43. 52 Figure 43: SAWS Material Calibration for Wall Axial Springs Similar spring properties were given to the axial springs at the panel connections at every fourth storey. However, these connections only work in tension, when the panels are pulled apart. In compression, the panels would contact each other and form a rigid connection. To account for different behavior in each direction, two zero-length springs were modelled in each connection. One element contained the SAWS material properties shown in Figure 43, and the other had bilinear axial properties, in which compression was rigid, and tension was almost completely flexible. This means that in tension, the combined springs behave with the SAWS material properties; while in compression; they form a rigid connection between the adjacent panels to simulate the physical contact between the two panels. An example response to an earthquake time history record of one of these compound spring components is illustrated in Figure 44. This example shows the displacement time history of a spring in the first storey of a 12 storey Option 1 model subject to the Chi-Chi, Taiwan 53 earthquake. The downwards gravity forces hold the wall down for the first 8 seconds, but then large pulses in the ground motion cause forces which overcome the gravitational forces and cause the wall to rock slightly – as seen by the positive displacements in the spring. This configuration produces a slightly more flexible system than if the walls were modelled as continuous over the height of the building. Figure 44: Example Wall Spring Time History Response to an Earthquake Record 3.5.2 Rotational springs for CLT Panel Connections The rotational springs were included to model out-of-plane rocking of the CLT panel elements. This type of behavior has not been studied in depth and no test results could be found for this type of connection. Since the panels do not resist much lateral force out-of-plane, decreasing the stiffness of this property was found to have a negligible effect on the structure as a whole. Due to this finding, the springs were modelled as elastic and very stiff; as a consequence, out-of-plane rocking did not occur in the model. 54 3.6 CLT Slabs The floor slabs specified for the FFTT systems were nine layer, 309mm thick, CLT panels with a thin concrete topping. These stiff floors were assumed to be rigid in the OpenSees models based on modal analysis of elastic models with explicitly modelled slabs. SAP2000 (CSI, 2002) was used to create preliminary elastic models of several heights from each FFTT system option. The models included all beam, column, wall, and slab elements. The slabs were modelled with a grid of shell elements at each storey. A typical example of a first mode shape for a 30 storey Option 4 model is presented in Figure 45. Figure 45: SAP2000 Model First Mode Shape Based on these preliminary SAP results, the effect of the slabs in the OpenSees models were captured using rigid diaphragm constraints at each storey in lieu of a grid of two dimensional finite elements. This approach constrained the in-plane translation of the nodes at each storey and provided the same effect as a rigid diaphragm. Modal analyses of the OpenSees and the SAP200 models, which included the slabs explicitly, showed equivalent dynamic behavior, 55 validating this simplification. Not only did this simplification decrease the modeling complexity, but by limiting the number of elements in the model, also significantly decreased the analysis time. 3.7 Steel Beams In the FFTT system, the steel beams, which connect the shearwalls and columns, are designed to yield before the timber elements and to deform inelastically in order to provide energy dissipation and a ductile failure mechanism (Figure 46). Due to this requirement, the nonlinear modeling of these beam elements was quintessential to the accuracy of the models. Figure 46: FFTT Ductile Failure Mechanism To accomplish the nonlinear modeling of these steel beam elements, nonlinear rotational springs were included at each interface between a steel beam and timber element. This type of model is widely used in nonlinear analysis and referred to as a concentrated plasticity model, since all plasticity in a member is concentrated into one spring element at each end. 56 This type of element modeling can be compared to the modeling of a distributed plasticity element in which plasticity is integrated over the element section and then over the length. This approach allows for yielding to occur at any length along the element, which is more representative of the physical behavior of a structural element. Nevertheless, concentrated plasticity was chosen for the models for three main reasons. First, a beam element fixed at both ends and then rotated so that it deforms in double curvature, such as under lateral load, will have its highest moment at each end of the element, as illustrated in Figure 47. Because of this, for a uniform section, yielding will occur at the end points of the beam, which is where the spring elements are modelled in a concentrated plasticity model. Due to the locations of the hinges, this type of model will be able to capture yielding in the proper location, similar to a distributed plasticity model. Second, because all nonlinearity is concentrated at one point in each element, the rest of the element can be modelled as elastic. An elastic element with all of it plasticity concentrated into springs is much faster to solve since there is no section and length integration required at each analysis step. Finally, and most importantly for this study, is that a member modelled with distributed plasticity is only able to capture the plastic behavior of the member itself (based on its sectional and material properties) - the connection behavior is not captured unless separately modelled. In capacity designed steel-timber connections, however, the steel member will (ideally) yield first, but once this happens, the force in the connection can still increase as the steel begins to harden due to strain-hardening. This strength increase can lead to additional timber crushing after the initial steel yielding. With concentrated plasticity models the total 57 behavior of the connection (steel yielding and timber crushing) can be captured with one spring. Figure 47: Laterally Loaded Beam Deformed Shape and Corresponding Bending Moment Diagram 3.7.1 Spring Properties for Steel Beam Models Springs were modelled at each end of each steel beam element as previously described. There were three main steel-timber connections that had to be considered: 1) Beam to wall (in-plane) 2) Beam to wall (out-of-plane) 3) Beam to column The spring properties were modelled from the tests performed by Bhat (2013) as described in Section 2.3.2. As previously noted, the HSS sections produced much more consistent results, as the wide flanged sections had lateral stability problems and tended to buckle out-of-plane, which affected the test results. Due to this better experimental performance, a test done on a HSS section was used for calibration and considered in the OpenSees models, even though wide flange sections would most likely be used in the design of a FFTT system due to their 58 superior strength. However, if the wide flange sections were restrained from out-of-plane buckling, it is postulated that their test results would likely be similar. The test considered for calibration comprised a HSS 100 x 50 x 3.125mm hollow rectangular beam embedded into a 239mm seven layer CLT panel at a depth of 50.8mm for a length of 304.8mm. The 1.8m beam was loaded at its far end from the panel and the displacements were recorded at six locations along the length of the beam and into the panel. The beam was first loaded quasi-statically and then reversed-cyclically using the CUREE loading protocol (Krawinkler et al., 2001). The test setup and loading protocol was modelled with OpenSees. The HSS beam was modelled as elastic with one rotational spring located at the interface of the connection with the SAWS material. The resulting force-deflection plot is shown in Figure 48 along with the test results. Figure 48: SAWS Material Calibration for Beam-Wall Connections 59 The simulation matched very well with the test results; therefore, the same cyclic properties were utilized for the model springs. The elastic properties (stiffness and yielding moment) were calculated based on the properties of the chosen beams. Additionally, several assumptions were made to extend the test results to predict the response from other steel sections with a similar connection detail. First, the rotation at each change in stiffness of the backbone curve was assumed to be constant for each steel section. Secondly, the ratio of the each subsequent moment along the moment-rotation curve to the initial yield moment was assumed to be constant. Finally, the hysteretic behavior and strength degradation properties of each model were similar. These assumptions are summarized and illustrated in Figure 49, where My*, M1*, M2*, and M3* represent the backbone shape from the test results; while My, M1, M2, and M3 represent the assumed backbone shape from other steel sections. Also the hysteretic behavior and strength degradation properties were modelled identically. These assumptions allowed the material model calibrated to the HSS section tests conducted by Bhat (2013) to be easily modified for the steel sections considered in the numerical models. 60 Figure 49: Assumed Moment-rotation Backbone Response of a Steel Beam The other two connections, the steel beam to wall (out-of-plane) and to column, were not previously experimentally tested. Therefore, they were modelled with elastic properties based on the selected member properties, with the same backbone behavior observed in the glulam column-beam connections (Section 3.3). This seemed rationale because both systems have a similar failure mechanism of steel yielding followed by local timber crushing, with a pinched hysteresis. 3.7.2 Beam-Column Element Modeling The steel beams were modelled as elastic beam-column elements, with rotational zero length elements at each end. Tests conducted by Bhat (2013) showed that, if properly capacity designed, the steel beams would consistently yield first, and therefore the elastic spring properties depended solely on the steel section. The yielding moment of the hinges were calculated as the yielding moment of the steel beams, and the initial stiffness was based on 61 the element and section properties of these beams. Because the beams are laterally loaded, they will deform in double curvature (Figure 47) and thus will have a resulting stiffness of: ( ) ( 1 ) Where kmember is the stiffness of the total member, including the elastic beam and rotational springs. Because both the springs and elastic beam members have an inherit elastic flexibility, the stiffness of the complete member is equal to the stiffness of the resulting components acting as a pair of springs in series: ( ) ( ) ( 2 ) Where ks is the stiffness of the spring, and kbc is the stiffness of the elastic beam-column element. In order to reduce the number of variables in the previous equation, the spring stiffness is defined as a multiple of the beam-column stiffness: ( 3 ) Which leads to two expressions for the spring and beam stiffness: ( 4 ) and, ( ) ( 5 ) Where n is a factor from zero to infinity that defines the spring stiffness in terms of the beam-column stiffness. Any value for n will work in Equations 3-5, although, some values clearly are not ideal. For example, n = infinity would mean that the springs are completely rigid, and 62 thus, the stiffness of the element is equal to the stiffness of the beam-column member. This is not ideal because then the springs would have no effect on the system and the nonlinear properties assigned to the springs would never be realized. Basically, the element would be modelled as an elastic beam-column element, fixed at each end. The other extreme, n = 0, would result in an ill-defined kmember and would produce a laterally unstable system. Based on the recommendations by Ibarra and Krawinkler (2005), n = 10 was chosen. To implement these results into the model the second moment of area of the beam element, Ibc, is modified to: ( ) ( 6 ) Where Ibeam is the second moment of area for the beam section. And the initial elastic stiffness of the spring is defined as: ( ) ( 7 ) By implementing these stiffness values, the stiffness of the complete member model is equal to the appropriate stiffness of a simple elastic model, without added flexibility from the inclusion of the spring elements. 63 3.8 Other Modeling Considerations 3.8.1 Supports In order to avoid creating a rigid moment connection at the base, each wall could only be modelled with a single pin support in order to achieve the desired failure mechanism as illustrated in Figure 50. Figure 50: FFTT Failure Mechanism Large shear walls sitting on single pins are, however, not a realistic modeling assumption. Thus, in order to capture to behavior of the foundation and hold-downs, a pair of springs were modelled at each end of the wall as shown in Figure 51. 64 Figure 51: Wall Boundary Conditions Including Rocking Springs These springs allowed the wall to resist a small moment, but would then yield to allow the desired failure mechanism to form. The springs were capacity designed so that yielding of the springs would occur before the wall could reach its yielding stress – effectively guaranteeing that the assumption of the wall remaining elastic would hold true. These springs were modelled with separate tension and compression properties. In tension, to model the behavior of the hold-downs, the same material properties as in the wall connection springs were utilized, since these springs were calibrated to tests performed on CLT walls with hold downs. In compression, the effect of the foundation was simplified to an elastic-perfectly-plastic (EPP) response. The yielding moment was calculated so that the yielding stress in the wall could not develop: ( ) ( 8 ) 65 Where σmax is the maximum stress in the extreme fibers of the section, M is the moment applied to the section, h is the length of the wall section, and I is the second moment of area of the walls section. Substituting the CLT yield stress for σmax and inputting the appropriate geometric section properties gives a simple expression for the maximum moment that the wall should be able to resist. Since the two springs produce a force couple at a distance equal to the section length of the wall, the moment resisted by the rocking wall is: ( 9 ) Where fy,spring is the yielding force of the spring. Since the spring was modelled as EPP, no further force can develop after yielding so Mmax will be the maximum moment possible. Combining Equations 8 and 9 yields a simple result for the maximum possible yielding force of the spring: ( 10 ) The yield stress, σmax, was taken as 11.5 MPa based on local manufacturers data (structurlam.com) (see Table 8). The general backbone curve of this spring is shown in Figure 52. 66 Figure 52: Rocking Spring Backbone Curve The springs were modelled with the Pinching4 material with tension properties which were based on the tension properties of the wall connection springs. The compression properties were determined as explained before, with a yielding displacement, Δy, based on an assumed 1% rotation at yielding. 3.8.2 Gravity Loads The gravity induced loading on the building prototypes was specified in the Tall Wood report (Green and Karsh, 2012) and is summarized in Table 12. Table 12: Design Gravity Loads Floors Roof Dead Load (DL) 4.00 kPa + perimeter wall weight 3.00 kPa Live Load (LL) 1.90 kPa 1.82 kPa Snow Load (Ss) - 1.80 kPa Rain Load (Sr) - 0.2 kPa 67 The loading combinations applied to the structures for the two types of lateral load analysis, based on the relevant load combinations as specified in the NBCC (NRC, 2010), were: 1) 1.0DL + EQ + 0.5LL + 0.25SL 2) 1.4DL + 1.4WL + 0.5LL 3) 0.9DL + 1.4WL + 0.5SL Where the bold terms; EQ and WL, represent the forces induced from the earthquake and wind dynamic analyses, and the snow load SL is as defined in the NBCC (NRC, 2010) based on Ss and Sr from Table 12. The two wind load cases (2) and (3) were chosen to estimate the worst case for wind induced forces and wind induced uplift, respectively. The higher mass in case (2) will cause greater forces in the structure, while the lower weight in (3) will provide less resistance against uplift. The loads from Table 12 were multiplied by the total floor area of the structures to determine the weight per storey which was then distributed as point loads on the nodes at each floor. The forces were applied based on the assumption of a rigid slab, so that the force resisted by a gravity force resisting element (column or shear wall) was proportional to its axial stiffness. This way the nodes at each floor would all displace equally, as if they were rigidly connected by a thick slab. All analyses were conducted with P-Delta effects considered. The P-Delta effect is the nonlinear geometric effect caused by weights moving through displacements which cause additional moment demand at the base of a structure. 68 3.8.3 Mass In OpenSees, mass is applied to a model separately from the weight of the structure. Weight is applied as point or distributed loads which induce forces in the elements. Mass can be applied at points or distributed over elements and causes inertial forces when subjected to accelerations. In this modeling approach, the mass was applied as point loads on each node at each floor level, similar to the weight. The mass was applied in the two horizontal directions, but not in the vertical direction, since the ground excitations were only applied in the horizontal directions, as is common practice in earthquake and structural engineering. When accelerations in the structure are induced by the lateral loads, the masses at each load will induce forces in the structure according to Newton’s Second Law of Motion. Since the nodes at each floor are rigidly constrained in the horizontal directions, each node at each floor level will accelerate at the same rate, causing a lateral force at the floor level that is distributed into the lateral force resisting elements based on their respective stiffness’s. 3.8.4 Damping Damping can be defined as the effect that reduces motions in oscillating systems and is related to the energy absorption of the system due to the combined effect of elastic deformations and hysteretic energy absorption during inelastic response. Although it is a highly complex phenomenon, damping is typically applied as a factor that induces a force that opposed the oscillation of the system that is linearly proportional to the velocity of the system. This allows for the development of a convenient mathematic expression for the motion of a vibrating system, and allows the derivation following second order linear differential equation for the motion of a single degree of freedom (SDOF) system: 69 ( ) ( ) ( ) ( ) ( 11 ) Where M, C, and K are the mass, damping, and stiffness values of the SDOF system, F(t) is a time-dependent force induced on the system, and u is the displacement of the system at any time. The first and second derivatives of u with respect to time define the velocity and acceleration of the system, respectively. Since, under a ground motion excitation, the forces applied on the system are equal to the mass time the ground acceleration, according to Newton’s Second Law of Motion, the equation may be rewritten as follows: ( ) ( ) ( ) ( ) ( 12 ) Where ug is the ground displacement. By dividing each term in the equation by the mass of the system, M, Equation ( 12 ) becomes: ( ) ( )( ) ( ) ( ) ( 13 ) Where, ω, the circular frequency of the system, is defined as: √ ( 14 ) Then, the following relationship can be derived: ( ) ( 15 ) 70 Where ζ is the damping of the system, as a percent of the critical damping. Critical damping is defined as the damping level in the system at which no oscillatory motion would occur. This relationship holds true in the more general multi degree of freedom case, except that ω and ζ are specific to each individual mode of vibration and the mass, stiffness, and damping values become matrices. The mass and stiffness of a structure are measurable, physical quantities that are typically well defined. However, the damping in the structure is much more difficult to accurately define. One common method to define the damping properties of a system is Rayleigh’s Method (Chopra, 1995). Rayleigh’s method simplifies the derivation of defining a damping matrix by noting that damping of a system is typically related to both the mass and stiffness of the system. This can be defined mathematically as: [ ] [ ] [ ] ( 16 ) Substituting this relationship into Equation ( 15 ) yields: ( 17 ) Where n can be any mode of the structure. To solve the two variables, α and β, two equations are required which can be defined by choosing any two significant modes and their respective circular frequencies and damping ratios. Damping ratios in the range of 1% to 5% are typically recommended with up to 10% being possible under significant seismic demands (Deierlein et al. 2010). Since the FFTT system has a large number of ductile steel connections which can provide significant energy dissipation under seismic loads, and steel 71 and timber buildings are typically considered to have relatively high damping ratios, a value of 5% was chosen as the damping ratio. A convenient method for solving for the Rayleigh damping coefficient is described by Hall (2006). In this method, a damping range (Δ) is defined over a range of frequencies (ω’ to Rω’) based on the assumed behavior of the structure. The parameter ω’ is set to two thirds of the first fundamental frequency of the structure to account for frequency change due to nonlinear softening of the structure. Rω’ is set to the second mode of the structure, which in a typical shear-beam type structure is about three times the first mode frequency. This results in an R value of 4.5. Then, the range of damping can be defined as: √ √ ( 18 ) And the Rayleigh coefficients can be determined from: √ ( 19 ) √ ( 20 ) The resulting damping ratio as a function of the circular frequency of the system is illustrated in Figure 53. 72 Figure 53: Rayleigh Damping Plot Using these relationships, the Rayleigh damping coefficients are calculated and applied to the models based on the first circular frequency as determined through modal analysis. In a nonlinear numerical model, the stiffness can change throughout the analysis, so the stiffness that the β coefficient will be applied to must be specified. This is typically either the initial (elastic) stiffness, the tangent stiffness (which changes as the stiffness of the structure changes), or a committed stiffness matrix, which is a less common approach. The initial stiffness matrix was chosen for this study for three reasons. First, the tangent stiffness matrix can rapidly change, which may potentially cause convergence problems. Secondly, there is not physical basis to a tangential stiffness proportional damping matrix. And finally, a well-defined committed stiffness matrix would be difficult to determine (Hall, 2006). 3.9 Summary of developed models In order to assess the seismic and wind performance of the FFTT system, a total of 39 models ranging from 6 to 30 stories were developed and analyzed. All models were developed in 73 OpenSees using a MATLAB preprocessor to write the Tcl files. Table 13 summarizes the range of models considered. Figure 54 illustrates typical stories of the OpenSees models for each of the four options. Initially a modal analysis was performed on each model. The results of these analyses, including the fundamental period of each model and typical mode shapes for each option, are presented in Appendix A. Table 13: Heights (Number of Stories) Modelled for each FFTT Option FFTT Option 1 Option 2 Option 3 Option 4 No of stories 6-12 11-20 11-20 19-30 74 (a) (b) (c) (d) Figure 54: FE Model for Typical Storey of (a) Option 1, (b) Option 2, (c) Option 3, and (d) Option 4 75 Chapter 4: Non-linear Dynamic Seismic Analysis 4.1 Seismic Analysis The NBCC (NRC, 2010) requires that a dynamic procedure be used to analyze regular structures taller than 60m or with a period greater than 2 seconds in either of the two primary orthogonal directions. For seismic analyses, the majority of models were too tall to be analyzed with an equivalent static force method, and therefore, dynamic analyses had to be completed instead. The methods used to perform these analyses are described in the following sections. 4.1.1 Ground Motion Selection In order to evaluate the seismic performance of the FFTT system, nonlinear dynamic analyses were conducted with a suite of ten ground motions as summarized in Table 14. In their recommendations for nonlinear dynamic analysis, Deierlein et al. (2010) state that a minimum of seven ground motions is required to determine the mean values for design, however it may be possible with even fewer records. Seven motions is also the recommendation in both the NBCC (NRC, 2010) and ASCE 07 (ASCE, 2013). Ten motions were considered to give a slightly broader range of results and to help account for the difference between the spectra of the ground motions and the design spectrum. All ground motions were obtained from the PEER strong motion database (Chiou et al., 2008). The ground motion database information is listed in Table 15. 76 Table 14: Ground Motion General Information Earthquake Source GM Number M Year Name Recording Station Type Distance (km) 1 6.7 1994 Northridge Beverly – Mulholland Thrust 13.3 2 6.7 1994 Northridge Canyon Country - WLC Thrust 26.5 3 7.1 1999 Duzce, Turkey Bolu Strike-slip 41.3 4 7.1 1999 Hector Mine Hector Strike-slip 26.5 5 6.5 1979 Imperial Valley Delta Strike-slip 33.7 6 7.5 1999 Kocaeli, Turkey Duzce Strike-slip 98.2 7 7.3 1992 Landers Yermo Fire Station Strike-slip 86 8 6.9 1989 Loma Prieta Gilroy Array #3 Strike-slip 31.4 9 6.5 1987 Superstition Hills Poe Road Strike-slip 11.2 10 7.6 1999 Chi-Chi, Taiwan CHY101 Thrust 32 Table 15: Ground Motion Database Information PEER-NGA Record Information Recorded Motions GM Number Record No. Component 1 Component 2 PGA (g) PGV (cm/sec) 1 953 NORTHR/MUL009 NORTHR/MUL279 0.52 63 2 960 NORTHR/LOS000 NORTHR/LOS270 0.48 45 3 1602 DUZCE/BOL000 DUZCE/BOL090 0.82 62 4 1787 HECTOR/HEC000 HECTOR/HEC090 0.34 42 5 169 IMPVALL/H-DLT262 IMPVALL/H-DLT352 0.35 33 6 1158 KOCAELI/DZC180 KOCAELI/DZC270 0.36 59 7 900 LANDERS/YER270 LANDERS/YER360 0.24 52 8 767 LOMAP/G03000 LOMAP/G03090 0.56 45 9 725 SUPERST/B-POE270 SUPERST/B-POE360 0.45 36 10 1244 CHICHI/CHY101-E CHICHI/CHY101-N 0.44 115 77 The ground motions were all far-field events as defined by FEMA P695 (FEMA, 2009) and selected based on their agreement with the Vancouver 2% in 50 year 5% damped design spectrum. The response spectra of the two components of the recorded motions, compared with the Vancouver design spectrum, are illustrated in Figure 55 and Figure 56. Figure 55: Ground Motion Component 1 Spectra Figure 56: Ground Motion Component 2 Spectra 78 4.1.2 Ground Motion Scaling Once a target (design) spectrum has been chosen and a set of motions selected, the records of the motions still must be modified in order to appropriately reflect the hazard defined by the target spectrum. There are many commonly used methods to modify ground motions. The simplest would be selecting ground motion records that match the target spectrum in the desired period range (typically, near the fundamental period of the structure). Since the records do not need to be modified, they retain all their natural characteristics, which make this method preferred in most cases. However, it is very difficult, if not impossible in some cases to select appropriate unmodified records for most structures and sites due to the limited number of records available. Since selecting real, unscaled records is not typically feasible (especially when several records are required), often recorded motions will be linearly scaled to reflect the hazard defined by the target spectrum. This method retains the characteristics of the recorded motion including spectral ratios at different periods, and is usually considered appropriate if required scaling factors are reasonable (extreme scaling factors may distort motions outside of the scaling range and produce unrealistic records). Records can be scaled at a single period or scaled to an average over a range of periods, typically to an acceleration spectrum, however scaling to other parameters is often possible including velocity spectra, peak ground acceleration, peak ground velocity, etc. The reader is referred to ―Selecting and Scaling Ground Earthquake Ground Motions for Performing Response History Analysis” (NIST, 2011), specifically Chapter 3, for more information about the state of practice for ground motion selection and scaling. 79 Other, more sophisticated methods for selecting appropriate ground motions also exist. An example is spectral matching, which involves modifying the frequency content of a recorded motion in either the time or frequency domain so that is matches a target spectrum at a specific period or range of periods. However, it has been argued that this procedure may produce unrealistic ground motion signatures and may even induce lower demands from nonlinear analysis due to the resulting unnaturally smooth ground motion spectrum in period range matched motions (Atkinson and Macias, 2009). In this study, the ground motion suite was collectively scaled by a linear factor so that the median of the geometric mean (geomean) or the motions matched the design spectral acceleration at the fundamental period, T1, of the structure. The geomean is simply defined as the square root of the product of the spectral accelerations of each direction: √ ( ) ( ) ( 21 ) This method was selected to maintain the natural characteristics and variability of the motions; additionally, the geomean of most of the motions already matched reasonable well with the Vancouver 2% in 50 year spectrum. Also, the method was simple and computationally efficient to implement for the large number of models that each required individual scaling factors for the motions. An example of this scaling procedure is illustrated in Figure 57. The thick line is the Vancouver 2% in 50 year Site Class C spectrum, while the thinner solid and dashed lines are the median geomean of the ground motion suite, unscaled, and scaled at a period of 1 second, respectively. 80 Figure 57: Ground Motions Scaling Example 4.2 Performance Criteria Before the dynamic analyses were conducted, performance criteria had be developed in order to assess the results of the analyses. Performance criteria comprise a set of standards that a structural model must conform to in order to be classified under a certain performance level. Typically four discrete performance levels are considered, as illustrated in Figure 58: operational, immediate occupancy, life safety, and collapse prevention (ATC, 2009). Operation performance, as it relates to earthquake engineering, requires that a structure be completely operational after a significant seismic event and is typically defined by very strict criteria, such as very small interstorey drift levels and little to no plastic deformations. Immediate occupancy performance does not require everything in the structure to be operable after a seismic event, but does require the structural system to be completely intact so the structure can provide a safe area of refuge in a post-disaster situation. Life safety 81 performance allows for structural damage, yet ensures the safety of any occupants inside must be conserved. For most regular buildings (i.e., not essential or emergency buildings and not post-disaster areas of refuge) this is the type of performance criterion typically specified. Finally, collapse prevention performance is considered for buildings with no permanent occupancy and little importance, and allows for major structural damage. As long as the gravity resisting system remains intact and the building does not collapse, collapse prevention performance is met. Figure 58: Typical Discrete Performance Levels (ATC, 2009) Performance criteria, however, are much easier to describe than to explicitly or numerically define. Often times performance levels can be difficult to distinguish and may be completely different for different structural systems. Performance measures such as interstorey drift, plastic deformations, strain in reinforcement, etc. may be used to define the performance of different structural systems. In this study, interstorey drift and steel beam plastic rotations were considered as the main performance criteria. Roof drift and base shear were also presented. Additionally, the stress 82 state in all timber members was monitored throughout the analyses to ensure they remained elastic; this is also a performance requirement by definition. 4.2.1 Interstorey Drifts For most applications, differential movement between stories, or interstorey drift, is considered as the main indicator of damage (Mayes, 1995; ATC, 2009). For this reason, the NBCC (NRC, 2010) limits interstorey drift in regular structures to 2.5%, and considers this appropriate to maintain the life safety of building occupants during severe seismic events. This limit is also the value proposed in the Tall Wood report (Green and Karsh, 2012). However, since the FFTT is not a typical building system, the usual interstorey drift limit is not necessarily appropriate. For any type of structural system, a life safety interstorey drift limit should be chosen to maintain the integrity of the gravity resisting system at each storey. This is because loss of the gravity resisting system will almost definitely result in the catastrophic collapse of a structure or storey of a structure. The lateral deformation resisting system (LDRS) is of secondary importance in that it is only required to maintain enough integrity to limit storey drifts to a level that protects the gravity resisting system. In the FFTT system, the gravity resisting system comprises glulam columns and frames interconnected with steel connections. For this study, physical tests conducted by Buchanan and Fairweather (1993) were consider to be representative of typical glulam frame connections, so these tests were also consulted to help determine the appropriate performance criterion. The hysteresis loops from the test of a beam-column assembly with steel brackets by Buchanan and Fairweather (1993) is shown in Figure 59. 83 Figure 59: Hysteresis Loops for Beam-Column Assembly with Steel Beam Brackets (Buchanan and Fairweather, 1993) From these test results it is noted that the assembly was able to undergo very large interstorey drifts, however yielding occurred at about 1% interstorey drift. Since the FFTT system is designed to rely on its steel beams for all required ductility, ideally, the glulam gravity resisting frame should not undergo any yielding. Unexpected yielding of the glulam perimeter frames would change the source of ductility in the system and the proposed ductility factor would not be appropriate. The total interstorey drift at the yielding of this type of joint in this structure is calculated by adding the elastic displacement of the glulam column to the 1% drift from the connection. This can be done by considering the relative stiffness of these two components. The elastic stiffness of the joint connection, kc, obtained from Figure 59 is approximately 264,000N/rad. The elastic stiffness of the 418x415mm glulam column, kbc, is calculated as: ( 22 ) 84 ( ) Then, the total deflection, Δt is calculated as: ( 23 ) Where Δc and Δbc are the elastic deformations in the connection and column element, respectively. Equations 21-23 can be rearranged based on the relative stiffness of the two components: ( ) ( 24 ) ( ) Which yields an interstorey drift of 1.12*1%, or about 1.1%. This value is the interstorey drift where the steel connections in the glulam frame are expected to yield. Thus, the interstorey drift should be limited to 1.1%, rather than 2.5% to ensure ductility is provided solely by the yielding of the steel beams. 4.2.2 Plastic Rotations Another indicator of damage in a structure which is subjected to significant ground shaking is the maximum plastic rotation observed in its header beams (ASCE, 2013). Too much plastic rotation in these members can affect their ability to transfer shear between the walls they connect, which in turn, affects the degree of coupling between the walls. Since coupled walls are much stiffer than uncoupled walls, if shear transfer between coupled walls is lost, 85 coupling between the walls will be lost, and the total storey stiffness provided by the walls will significantly decrease. Thus, beam plastic rotation is included as a criterion for structural performance in documents such as ASCE/SEI 41-06 (ASCE, 2007). In ASCE/SEI 41-06 (ASCE, 2007), life safety performance criteria for Class I steel sections is defined as the plastic rotation at which strength degradation in the section begins. This methodology was adopted for this study. To determine the degradation limit, the tests conducted by Bhat (2013) were consulted. The moment-rotation hysteretic result from the same test that was considered for the calibration of the OpenSees material models is reproduced in Figure 60, modified to shown moment-rotation rather than force-displacement. From this figure, a rotation of about 0.15 rad is observed as the capping point, at which strength degradation commences. By subtracting an elastic rotation of about 0.1 rad, a life safety plastic rotation for the steel beams of approximately 0.05 rad is obtained. Figure 60: Moment-Rotation Results from Steel Beam-CLT Wall Test 86 4.3 Results of Non-linear Seismic Analyses For each considered model and bi-directional ground motion, two analyses were run, one for each of the two main ground motion orientations (orientation of the primary component of the motion). The ground motions were always applied parallel to the primary axes of the structure. Then, for each scenario (a particular height of a particular building plan option subjected to a particular ground motion), the results were taken as the maximum of the two ground motion orientations. Figure 61 exemplarily presents the displacement results of a 30 storey model (FFTT Option 4) subjected to the Chi-Chi, Taiwan ground motion orientated in both directions. The orientation which produces the higher response is taken as the result for that scenario (the solid line). Figure 61: Example 30 Storey Model Displacement subjected to the Chi-Chi, Taiwan Ground Motion at two Orientations 87 4.3.1 Interstorey Drift Results For the performance-based design of structures, building codes typically specify that mean response values may be used for design if seven or more ground motions are used in the analysis (NRC, 2010; ASCE, 2013; Deierlein et al., 2010). Since this study considered 10 unique motions, it is reasonable to base the performance on the mean structural response from the 10 motions. The results for the mean and mean plus one standard deviation are combined for the suite of models in Figure 62. Additionally, the interstorey drift results for each model for all the four FFTT system options are illustrated in Figure 63. (a) (b) Figure 62: Interstorey Drift Combined Results: a) Mean Results and b) Mean Plus One Standard Deviation results 88 (a) (b) (c) (d) Figure 63: Interstorey Drift Results for (a) Option 1, (b) Option 2, (c) Option 3, and (d) Option 4 Models 89 From the results presented in Figure 63 it can be seen that the mean results are consistantly below the 2.5% interstorey drift limit typically considered for life safety performance as well as the 1.1% limit chosen to prevent yielding of the glulam perimeter frame. The mean plus one standard deviation and maximum results are all below 2.5% as well. Because the mean results conform to the life safety drift limit, interstorey drift life safety performance is achieved. Figure 65 and Figure 64 illustrate the roof drift results for four combined and individual options, respectively. (a) (b) Figure 64: Roof Drift Combined Results: a) Mean Results and b) Mean Plus One Standard Deviation results 90 (a) (b) (c) (d) Figure 65: Roof Drift Results for (a) Option 1, (b) Option 2, (c) Option 3, and (d) Option 4 Models 91 Roof drift does not necessarily predict damage in a structure; however it is correlated to the performance of the structure and is included here as it may be useful to compare the modelled seismic behavior of the structures. Similar to the interstorey drift results, mean roof drift tends to decrease as the height of the structures increases, indicating that the taller models are less affected by the effects induced by ground motions. 4.3.2 Beam Plastic Rotation Results Figure 67 and Figure 66 present the maximum steel beam plastic rotation results for all structural options. All results are normalized by the life safety plastic rotation, θLS, defined as 0.05 in Section 4.2.2. Since the results are normalized, any result below 1.0 meets life safety performance, which is the case for all mean results and even all mean plus standard deviation results. As well, very few of the maximum recorded rotations exceed this limit. These results indicate well above adequate performance for all of the modelled structures. 92 (a) (b) Figure 66: Beam Plastic Rotations Combined Results: a) Mean Results and b) Mean Plus One Standard Deviation results 93 (a) (b) (c) (d) Figure 67: Plastic Rotation Results for (a) Option 1, (b) Option 2, (c) Option 3, and (d) Option 4 Models 94 4.3.3 Base Shear Also relevant for this study was the maximum base shear experienced by the structures under seismic excitation. Because the models were fixed at their base, they were essentially rigid in shear. Thus, for the design of this type of structure, it would be necessary to know the base shear demands so the foundation and base connections can be properly designed. Individual option base shear results are presented in Figure 69. The mean results for each model were compiled and compared to the NBCC (NRC, 2010) base shear predicted values for several different R factors (R = RdRo) in Figure 68. Figure 68: Base shear results from model compared to those predicted by the NBCC (NRC, 2010) for different R (RdRo) values 95 (a) (b) (c) (d) Figure 69: Base Shear Results for (a) Option 1, (b) Option 2, (c) Option 3, and (d) Option 4 Models 96 As previously mentioned, the structures were designed with an RdRo of 3.0 (Rd = 2.0; Ro = 1.5). All of the results are normalized by the weight of the structure, W. The computed base shears correlate well with predictions based on the NBCC for an R factor of 3.0. Moderately higher than predicted base shears were observed in the taller Option 4 models, that match more closely to the R = 2.0 calculations. This difference could be for several reasons including higher mode effects increasing the base shear force in the structure more than anticipated. Also the taller models had stiffer LFRSs comprising many thick shear walls which would induce large base reactions. 4.4 Discussion of Seismic Analyses From the results presented in Chapter 4.3, it appears that the FFTT systems, as they were designed for this study, meet the performance required under seismic loading. Interstorey drifts were lower than required and local plastic deformations were within a reasonable range for life safety performance. Base shears correlated well with those predicted by the NBCC (NRC, 2010). Maximum drifts and plastic deformations tended to decrease with taller structures, as these more flexible structures were less impacted by the seismic excitations. This is because the taller, softer structures had lower seismic forces and consequently less yielding in the interconnecting steel beams. However, these characteristics, which made the taller structures less susceptible to damage induced by ground shaking, may cause serviceability issues under high wind loads. Previous studies, such as Reynolds et al. (2012) have indicated unacceptable dynamic response of tall timber buildings under significant wind loading, based on human perception of vibrations, primarily due to their light weight. The potential problematic performance of the FFTT system under wind loads will be investigated in Chapter 5. 97 Chapter 5: Dynamic Wind Analysis 5.1 Introduction In order to fully assess the structural feasibility of the FFTT building system, wind loading also had to be checked to ensure serviceability requirements could be met under wind load. To accomplish this, the NBCC (NRC, 2010) Dynamic Wind Procedure was adopted (NRC, 2010). According to the NBCC Sentence 4.1.7.2(1): the use of the Dynamic or Experimental Procedure is required for buildings whose height is greater than 4 times their minimum effective width, or greater than 120m, and other buildings whose properties make them susceptible to vibration. Since the taller FFTT models are relatively flexible, especially compared to typical reinforced concrete shearwall structures (see table A1 in Appendix A), they were deemed as potentially susceptible to vibration under wind loading. Typically, longer period structures, such as bridges or high-rise buildings, are more susceptible to dynamic wind effects, while shorter buildings with shorter periods are excited more through seismic loading, as illustrated by Figure 70. As seen previously, the period range of the FFTT models ranges from about 1 to 3 seconds (frequencies of 1 to 0.33Hz) which puts them in the range between maximum earthquake and wind spectral density. Since the structures were designed and analyzed for seismic loading from Vancouver, BC, the wind pressures were also based on Vancouver data from the NBCC (NRC, 2010). The 1 in 50 year hourly wind pressure for Vancouver is 0.48 kPa, which was considered for all the wind analyses. 98 Figure 70: Frequency Ranges for Excitations of Structures (Holmes, 2001.) 5.2 NBCC Dynamic Procedure The NBCC Dynamic Procedure for wind analysis (NRC, 2010) comprises a static analysis with forces determined accounting for the dynamic effects of the loading and structure: ( 25 ) Where Pe is the pressure applied the structure, Iw is the importance factor (taken as 1.0), q is the wind pressure (0.48kPa), and Ce, Cg, and Cp are the exposure, gust, and external pressure coefficients. The wind load is applied with a load factor of 1.4 to the structure with a dead load factor of 1.25 or 0.9. The governing case is used for the design or assessment of the structure. Additionally, the wind load must be applied in both primary directions of the structure to determining the governing wind direction. 99 5.2.1 External Pressure Coefficients The external pressure coefficient, Cp, is based on Figure I-15 of the NBCC (NRC, 2010), which is reproduced in Figure 71. This factor accounts for uplift on the roof of the structure as well as suction on the side of the building opposite to the wind direction. Figure 71: Wind Loading External Pressure Coefficients from Figure I-15 of the NBCC (NRC, 2010) 5.2.2 Exposure Factor Because the exposure of a structure will significantly affect how wind pressure can be applied to it, the NBCC (NRC, 2010) wind loading procedure accounts for three different levels of exposure: A, B, and C. Exposure B, which is defined as rough terrain, such as urban, suburban, or wooded terrain, was chosen as the factor for these buildings. Based on this assumption, the exposure factor is calculated as: 100 ( ) ( 26 ) Where h is the height of the building in meters. 5.2.3 Gust Effect Factor The gust effect factor is used to account for the effect of short periods of very high wind velocities, or gusts, on the response of a structure. It is based on a general probabilistic expression for peak wind loading, Wp: ( 27 ) Where μ is the mean wind loading, gp is the statistic peak factor of the wind loading, and σ is the ―root mean square‖ of the wind loading effect. This is a statistical measure of the magnitude of a varying quantity - in this case wind pressure. By defining the gust effect factor, Cg, as: ( 28 ) The previous equation for peak wind loading can be substituted in resulting in the statistical expression for the wind gust effect factor: ( ⁄ ) ( 29 ) The term (σ/μ), referred to as the coefficient of variation of the loading, is calculated as: ( ⁄ ) √ (𝐵 𝑠 ) ( 30 ) Where K is set as 0.10 for Exposure B, CeH is a similar factor that accounts for the exposure at the top of the building, B is the background turbulence factor, s is the size reduction factor 101 of the structure, F is the gust energy ratio at the natural frequency of the building, and is the damping ratio in the structure. Because the structure is not expected to undergo plastic deformation during wind loading, the previous 5% damping ratio is no longer appropriate as a significant proportion of that ratio comes from energy dissipation due to inelastic deformation in the members of the structure. Instead a ratio of 2% is adopted based on recommendations from the NBCC (NRC, 2010). The background turbulence factor, B, is calculated through the following integral: 𝐵 ∫ [ 𝑥𝐻 ] [ 𝑥𝑤 ] [𝑥( 𝑥 ) ] 𝑥 ( 31 ) Where H is the building height, and w is the effective (average) building width: 𝑤 ∑ 𝑤 ∑ ( 32 ) The size reduction factor, s, of a structure is calculated as: 𝑠 𝜋 [ 8 𝐻 𝑉 ] [ 𝑤𝑉 ] ( 33 ) Where fn is the natural frequency of the building, and VH is the mean wind speed at the top of the building, defined from: 𝑉 𝑉√ ( 34 ) 𝑉 √ The reference velocity pressure q, was defined earlier for Vancouver as 0.48 kPa. 102 The gust energy factor, F, is defined as the following function based on the wave number as follows: 𝑥 ( 𝑥 ) ( 35 ) Where xo is defined as: 𝑥 𝑉 ⁄ ( 36 ) The gust energy factor as a function of wave number is illustrated in Figure 72. Figure 72: Gust Energy Ratio as a Function of Wave Number Finally, the peak factor, gp, is calculated as: √ 𝑙 𝜐 √ 𝑙 𝜐 ( 37 ) Where the time, T is taken as 3600 sec and the average fluctuation rate, υ, is defined as: 103 𝜐 √𝑠 𝑠 𝐵 ( 38 ) For which all the variables have previously been defined. 5.3 Wind Analyses The equations in the previous section were solved in order to determine the wind pressure including dynamic effects, Pe, for each model. This pressure was applied both laterally to the exterior nodes of the building models and upwards on the roof nodes of the models according to Figure 71. The pressure was applied as forces on nodes according to their tributary area. Gravity loads and snow were also applied according to the relevant load combinations as specified in the NBCC (NRC, 2010): 1) 1.4DL + 1.4WL + 0.5LL 2) 0.9DL + 1.4WL + 0.5SL Static analyses were run in OpenSees with the wind acting in both major directions of the models for both load cases. Second order P-Delta effects were included in the analyses. 5.4 Results of Wind Analyses The result of each structure was taken as the maximum result from the two directions and two wind analysis cases. The results for the suite of models are illustrated in Figure 73a. Acceptable performance under wind loading is defined in the NBCC as a maximum interstorey drift of h/500, or 0.2%, (NRC, 2010). This interstorey drift limit is chosen to preserve occupant comfort in a significant wind event. Adding this limit to the figure and then excluding the models that did not meet this performance objective yields the results shown in Figure 73b. Option 1 models are limited to 8 stories; Option 2 and 3 models are 104 limited to 16 stories; and Option 4 models and FFTT system, as design for this study, may be limited to about 22 stories. (a) (b) Figure 73: (a) Wind Loading Interstorey Drift Results and (b) with h/500 limits 5.5 Discussion of Wind Analyses The results presented in the previous section show that even in a moderately high seismic zone, such as Vancouver, BC, wind loading may govern the design of tall wood buildings, such as the FFTT system. These results agree with the conclusions of Reynolds et al. (2012), that tall timber structures may be susceptible to significant wind induced vibrations. Since timber buildings are relatively light and flexible compared to steel and concrete structures, these significant wind effects, which are normally only problematic in much taller buildings, 105 begin to affect shorter timber high-rise structures. In order to remedy the wind effects either the stiffness or mass of the structures may have to be increased (Reynolds et al., 2012). Reynolds et al., (2012) also note that stiffness in timber joints tends to decrease over their lifetime through repeated loading, and that this would change the dynamic characteristics of these structures over their lifetime and more susceptible to wind later in their lifespan. This would both increase the dynamic effects of wind, and make the lateral force resisting system more flexible, so it would displace more under lateral loading. Combined, these two effects could considerably increase the deflections under wind, as well as seismic loading. Whether or not this may be a problem in the timber-steel beam connections required by the FFTT system has not been thoroughly investigated at this point in time but should not be neglected by potential designers. 106 Chapter 6: Force Reduction Factor Study 6.1 Seismic Force Modification Factors in the NBCC One of the benefits of the research presented herein is that a framework for modeling the FFTT system and its four options was developed. This framework may be useful for other studies about the behavior of the FFTT system. As an example, the framework for the models developed in this thesis was also used to study proposed seismic force reduction factors for the FFTT structural system. One of the seismic design approaches specified in the NBCC (NRC, 2010) is the Equivalent Static Force Procedure (ESFP). This procedure is meant as a simple process that can be used for seismic design of regular structures. It begins by taking a design spectrum (usually the 2% in 50 year 5% damped spectrum for the building site) and an estimate of a structures weight and fundamental period (determined either through code equations of finite element models), and an importance factor (1.0 for normal buildings). Then, a design elastic base shear is determined by multiplying the weight of the structure by the spectral acceleration from the design spectrum at the fundamental period of the structure (force equals mass times acceleration) and then by the importance factor. A higher mode factor is also applicable to more flexible buildings that may have a significant contribution from higher modes. This method gives a reasonable estimate of the elastic base shear expected by a structure under design seismic loading. The base shear can then be distributed along the height of the structure in a reverse triangular shape to get the design forces at each level and for each component in the structure. 107 The NBCC (NRC, 2010) does not require structures to behave purely inelastically during rare earthquake events. Due to this, two reduction factors may be used to reduce the design base shear of a structure based on its expected inelastic behavior. The first is an overstrength factor, Ro, which accounts for reserve structural capacity from sources such as member oversizing in design and strain hardening of materials. The second is a ductility factor, Rd, which accounts for the lower forces induced in a structure behaving inelastically compared to an equivalent elastic structure and is related to the ductility able to be provided by a structural system. In this case, ductility refers to the ability to deform inelastically past yielding. More ductile systems can deform further before degrading in strength, which allows them to be designed with lower forces. Figure 74 illustrates the application of the ductility reduction factor based on the equal displacement approximation proposed by Newmark and Hall (1982). In this figure μ is the displacement ductility and Rμ is the ductility reduction factor (Rd in the NBCC). Ve is the elastic base shear, Vi, is the inelastic base shear, Δy, is the yielding displacement, and Δmax is the maximum displacement obtained by either system. Based on the work by Newmark and Hall (1982), it can be shown that for structures with periods greater than 0.5 sec, that the displacement of an equivalent structure behaving elastically or inelastically will be approximately equal. It can also be shown that for structures that follow (or nearly follow) this equal displacement approximation, that Rμ will equal μ. This is what the NBCC ESFP is based on, since most typical structures will follow the equal displacement approximation. The implication of this is that the force reduction allowed in the ESFP is directly equal to the amount of expected ductility of the system. The NBCC (NRC, 2010) provides these factors for most typical systems. 108 Figure 74: Ductility Factor Based on Equal Displacement Approximation Note that Figure 74 only illustrates an idealized, elastically-perfectly-plastic, response. A more realistic response would be more curved and include some strain hardening. The use of the ESFP allows for efficient structural solutions since the design base shear can be lowered significantly depending on the type of structural system being used. For example, a ductile steel moment frame has a Rd equal to 5.0 and Ro equal to 1.5 (NRC, 2010), which allows a 7.5 times reduction in the elastic base shear for design of this type of system. 6.2 Force Reduction Factor Study for the FFTT System Currently, no provisions regarding the seismic force reduction factor are given in the NBCC for hybrid timber-steel systems such as the FFTT system. The study by Pei et al. (2013) (see Section 2.3.5) proposed a ductility factor of 2.0 for CLT shear wall systems. However, this value was based on ductility provided by the wall hold-downs and may not be appropriate for a CLT shear wall system such as the FFTT system, in which ductility is provided through 109 yielding of steel beams which interconnect the CLT panels. Due to this mechanism, the FFTT system may behave more like the ductile steel moment frame, which is allowed to be designed with a ductility factor of 5.0 according to the NBCC (NRC, 2010). A study was carried out by Zhang et al.1 to address this issue using simplified two dimensional and more complex three-dimensional structural models of the FFTT Option 1 system to assess the expected ductility of this system. 6.2.1 Two Dimensional Model The two dimensional models were developed similar to the models in Chapter 3 of this thesis, with material properties based on the same tests by Bhat (2013). The models were designed using an ESFP using several ductility factors from 1.5 to 6.0 and an assumed Ro of 1.5 based on the Vancouver design spectrum. Models were developed in OpenSees for three, six, nine, and 12 storey buildings. All ductility was assumed to be provided by the yielding of the steel beams and thus the wall hold downs/base connection and gravity system were not modelled. This simplified model is illustrated in Figure 75, which shows the CLT walls, modelled with shell elements; the steel beams, modelled using elastic beam elements with concentrated plasticity idealized with the Pinching4 material (Lowes et al., 2004); and a P-Delta (leaning) column to include second order nonlinear geometric effects (P-Delta effects) applied to the shear walls by the weight of the structure not directly applied to the walls. 1Zhang, X., Fairhurst M., Tannert, T. (2014). Ductility Estimation for a Novel Timber-Steel Hybrid System. Submitted and Under Review. 110 Figure 75: Simplified Model Illustration (Zhang et al., 2014) The 22 FEMA P695 (FEMA, 2009) far-field ground motion set was modified to match the Vancouver spectrum and applied to each model to get a reliable estimation of the interstorey drift expected. Figure 76 presents an exemplarily cumulative distribution function (CDF) for a three storey model designed with different ductility factors. Figure 76: Example CDF for a 12 Storey Model Design with Different Rd Factors (Zhang et al.) 111 An acceptable ductility factor was considered one that limited interstorey drift to 2.5% with an 80% probability of non-exceedance. Based on the all the models considered and two different ground motion scaling techniques, an Rd of 5.0 was proposed. 6.2.2 Three Dimensional Model In order to support the FFTT ductility factor study, the OpenSees framework for the FFTT system as presented in Chapter 3 of this thesis was considered. Based on the proposed ductility factor of 5.0 and overstrength factor of 1.5, a 12 storey Option 1 model was redesigned using an ESFP. The resulting beam sections chosen are summarized in Table 16. No other aspects of the model were varied from the previous study except that the base of the structure and the glulam frame system were pinned in order to be consistent with the assumptions made for the simplified models. Table 16: 12 Storey Option 1 Model Beam Sections Design with RdRo = 7.5 Stories Section Yielding Moment (kN·m) 1-3 W360x33 163.5 4-6 W250x22 78.3 7-9 W250x22 78.3 10-12 W150x18 41.4 6.2.3 Ground Motion Record Selection and Scaling An essential step in any nonlinear time history analysis is the selection and scaling of ground motion time history records to use for the analyses. Typically 7 records are chosen and the mean response from the record set is used for design or assessment of a structure (Deierlein et al., 2010; NRC, 2010) and scaled to a design acceleration spectrum (2% in 50 year 5% 112 damped spectrum in the NBCC (NRC, 2010)). The records should be chosen to match the characteristics (distance, magnitude, fault-type, duration, etc.) of a ground motion expected at the site of the structure being assessed and should be similar to the design spectrum so that adequate scaling can be achieved with low or moderate scaling factors. This helps to ensure the motions will be reasonable realistic and representative of a similar possible earthquake event at the building location. In order to choose suitable records, first a site de-aggregation was carried out for the proposed location of the fictional structure: Vancouver, BC, using EZFrisk software (McGuire, 1995). The purpose of this is to de-aggregate all the sources that contribute to the design acceleration spectrum at the period of the structure (T = 2.0 seconds) so that ground motions can be selected to best represent the hazard at the site of the proposed structure. The resulting distance and magnitude de-aggregations for Vancouver, BC at 2 seconds, which is the fundamental period of the model, are presented in Figure 77a and b, respectively. (a) (b) Figure 77: Vancouver, BC Site Hazard De-aggregation at 2 Seconds for (a) Distance and (b) Magnitude 113 The ground motions listed in Table 17 were chosen to match as closely as possible to these two types of event while maintaining similar spectral values between 0.2T-1.5T to the Vancouver design spectrum. All of these records were from shallow crustal source type earthquakes, which are similar to the type of earthquake commonly used for assessment of structures in Vancouver (relatively short, high frequency motions). All ground motions were downloaded from the PEER strong-motion ground motion database (Chiou et al., 2008). The linear scaling factors used to scale the ground motions for the first scaling approach are also summarized in Table 17. In this approach, the average geometric means (geomeans) of the ground motions were scaled to match the average of the Vancouver spectrum between periods of 0.2T-1.5T seconds on average. As a second modification method, the motions were also spectrally matched in both directions to the Vancouver spectrum for this same period range. To accomplish this matching, the motions were modified in the time domain through the wavelet algorithm proposed by Abrahamson (1992) and Hancock et al. (2006) using the commercially available SeismoMatch program (Seismosoft, 2013). Figure 78 shows the spectral values of the ground motion suite obtained using these two common record scaling methods. These two hazard matching methods were chosen to gain insight into the effect of how ground motion modification could impact the results. The linearly scaled records are much more variable, even in period range of the structure since it is only the average of the spectra that matches the target spectrum. Therefore, these records are predicted to produce more scattered results. The spectrally matched motions agree very well with the specified design spectrum at and around the period range of the structures, making them a potentially viable choice for the analysis of the structure. However, it has been theorized that the smooth 114 spectrum over the matched period range may lower the demand in the structures (Atkinson and Macais, 2009) and limit some of the natural variability of the results of the motions. Table 17: Ground Motion Summary Record Magnitude Name Station Epicentral Distance (km) Scaling Factor 1 6.7 Northridge Beverly Hills - Mulhol 13.3 0.50 2 7.1 Hector Mine Hector 26.5 0.90 3 6.9 Kobe, Japan Nishi-Akashi 8.7 0.70 4 7.5 Kocaeli, Turkey Arcelik 53.7 1.60 5 6.9 Loma Prieta Capitola 9.8 0.75 6 6.5 Superstition Hills Poe Road (temp) 11.2 1.00 7 7.6 Chi-Chi, Taiwan CHY101 32 0.65 (a) (b) Figure 78: Spectral Accelerations for (a) Linearly Scaled Motions and (b) Spectrally Matched Motions 115 6.2.4 Results from the Three Dimensional Model The two suites of scaled motions were applied in the two directions of the model. Figure 79 and Figure 80 present the interstorey drift results for the two direction components of the two scaling methods, respectively. The mean and 80th percentile results from the maximum response observed from the seven motions are presented, along with the minimum and maximum values to give insight into the range of results. From these figures it can be seen that the maximum response was observed when the primary component of the motions was applied in direction 2 (N-S direction of the building) of the models, and that the mean interstorey drift response of the suite of results was approximately 2% drift. The 80th percentile drift was approximately 2.5%, which is reasonable and expected given that the reduction factors were chosen to give 80% probability of non-exceedance at 2.5% drift (Zhang et al.12). Additionally it can be observed that the interstorey drift was relatively constant over the height of the structures, meaning that the core walls were almost rigid and rocked at their base, distributing damage over the height of the building, rather than concentrating it at certain stories. 1Zhang, X., Fairhurst M., Tannert, T. (2014). Ductility Estimation for a Novel Timber-Steel Hybrid System. Submitted and Under Review. 116 (a) (b) cdc Figure 79: Interstorey Drift Results for Matched Motions Applied in (a) Direction 1 and (b) Direction 2 (a) (b) Figure 80: Interstorey Drift Results for Matched Motions Applied in (a) Direction 1 and (b) Direction 2 Next, the beam plastic rotations at each storey are presented in Figure 81 and 83. As mentioned earlier, beam plastic rotations are another commonly used performance measurement. The results show a wide range of responses from the different motions. 117 However the mean response in the critical direction from both scaling methods is less than 0.05, which was the life safety criteria considered previously in Section 4.3.2. (a) (b) Figure 81: Steel Beam Rotations Results for Scaled Motions Applied in (a) Direction 1 and (b) Direction 2 (a) (b) Figure 82: Steel Beam Rotations Results for Matched Motions Applied in (a) Direction 1 and (b) Direction 2 118 Figure 83 and Figure 84 illustrate the maximum accelerations observed at each storey over the suites of analyses. Accelerations peaked at the base and near the top of the structures, but were within reasonable limits to maintain non-structural integrity. All results support the results generated from the simplified two dimensional models and show that the proposed reduction factors can lead to a design that satisfies all applicable life safety performance criteria. (a) (b) Figure 83: Storey Acceleration Results for Scaled Motions Applied in (a) Direction 1 and (b) Direction 2 119 (a) (b) Figure 84: Storey Acceleration Results for Matched Motions Applied in (a) Direction 1 and (b) Direction 2 120 Chapter 7: Conclusions 7.1 Summary This thesis presented the work done on the modeling and dynamic analyses of the FFTT structural system. The FFTT system comprises four proposed structural layout options for the design of high-rise (up to 30 stories) timber-steel composite structures. The modeling included the nonlinear behavior of steel elements and connections with material models calibrated to physical test results. The dynamic analyses comprised both dynamic earthquake analyses with a suite of 10 bidirectional ground motions and wind analyses in accordance to the NBCC guidelines (NRC, 2010). The entire suite of building layouts options and proposed heights were analyzed. This included four different building options modelled with a range of heights from 6 to 30 stories. In total over 800 nonlinear dynamic analyses were performed on 40 different models. The results showed good seismic behavior in response to ground motions scaled to the Vancouver 2% in 50 year design spectrum. The entire suite of models performed to an acceptable level of performance considering mean interstorey drift, roof drift, steel beam plastic rotation, timber stresses, and base shear. The taller structures were less affected by the ground motions. The subsequent wind analyses, however, showed that wind load governed the height limits of many models. As designed for this study, the models with heights above 22 stories did not meet the wind load serviceability limits. A study about acceptable ductility reduction factors was also presented to highlight how the models and framework developed for this thesis could be utilized outside the scope of this 121 study. The preliminary results presented herein indicate that higher Rd factors, up to 5.0, may be appropriate for the FFTT timber-steel hybrid system. 7.2 Recommendations for Design Based on the results presented in this thesis, the FFTT system may be viable for high rise construction in earthquake prone regions. However, the tall and flexible structures will likely be governed by wind loading rather than seismic loads. This means that the FFTT system will need to be re-designed to provide either more stiffness or more mass to limit wind induced vibrations. Such a change, however, will simultaneously increase the seismic demand, so caution must be exercised and additional seismic analyses are required. Designers must also consider the long term performance of the connections they design for this type of structure to ensure stiffness does not degrade over long-term due to repeated cyclic wind loading. Also in structures governed by wind load, designers must ensure that adequate ductility can be developed by the system, since if a structure is limited by its ductility the elastic seismic force may become large enough to govern the design once again. Ductility factors of 2.0 have previously been considered for CLT construction (Pei et al., 2013), the FFTT system, however, may be able to reach ductility factors of up to 5.0. Potential designers would be encouraged to explore using higher ductility factors, up to and including 5.0, if acceptable performance can be demonstrated. The resulting reduction in base shear demand will allow for much more economic and competitive structural designs. 122 7.3 Recommendations for Future Studies This thesis only scratched the surface of analyses that need to be performed in order to assess the viability of the novel FFTT hybrid system. Further component-level physical tests accompanied by sophisticated component finite element models will be required to optimize the design of these components and to more accurately model and subsequently optimize the design of these components. It is recommended that additional steel beam-CLT panel tests be conducted to assess the performance of stronger wide flange steel sections when they are embedded into CLT panels. Tests should also be performed to assess the stiffness of the glulam and CLT-steel beam connections after repeated loading to determine if the long term performance of the connections is acceptable. After the component-level behavior is better understood, system level, large-scale static and possibly dynamic tests may be required to gain better insight into the system level behavior. Additionally, more design and testing needs to be implemented to the wall base connections of the FFTT system. In order to develop the ductile, rocking failure mechanism in the system, the CLT walls will have to be essentially pinned at their base and allowed to rock. Such a boundary condition will require very stiff shear connections along with ductile hold-downs that allow for yielding and plastic deformation without buckling or deteriorating over a number of earthquake induced load cycles. Others may want to investigate other components of this type of system including damping, fire resistance, and its performance in regions with higher seismic demands. Additionally, research into the reliability of the FFTT system when subjected to different material and loading uncertainties will be required to ensure the ultimate feasibility of the system. 123 Bibliography American Society of Civil Engineers. (2013). Minimum Design Loads for Buildings and Other Structures. Reston, VA: American Society of Civil Engineers. American Society of Civil Engineers. (2007). 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Vancouver: Wood Enterprise Coalition- (Used under a Creative Commons (CC) License-Attribution Non-Commercial ShareAlike). <http://wecbc.smallboxcms.com/database/rte/files/Tall%20Wood.pdf> Hall, J. F. (2006). Problems encountered from the use (or misuse) of Rayleigh damping. Earthquake engineering & structural dynamics, 35(5), 525-545. Holmes, J. D. (2001). Wind Loading of Structures. CRC Press. Ibarra, L. F., & Krawinkler, H. (2005). Global collapse of frame structures under seismic excitations. Pacific Earthquake Engineering Research Center. Krawinkler, H., Parisi, F., Ibarra, L., Ayoub, A., & Medina, R. (2001). Development of a Testing Protocol for Woodframe Structures. Richmond, CA: CUREE Publication No. W-02. 125 Koo, K. (2013). A Study on Historical Tall Wood Buildings In Toronto and Vancouver. Canadian Forest Service Final Report. Koshihara, M., Isode, H., & Yusa, S. (2005). The Design and Installation of a Five-Story New Timber Building in Japan. 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UN-HABITAT. 127 Appendix A – FFTT Numerical Model Mode Shapes and Periods This appendix summarizes the mode shapes and periods of the numerical FFTT models. Table A1 presents the weight and fundamental periods of the FFTT numerical models and compares them to a typical equivalent concrete structure. Figures A1-A4 illustrate the first three mode shapes and periods of four typical FFTT numerical models: a 12 storey Option 1 model, a 20 storey Option 2 model, and 20 storey Option 3 model, and a 30 storey Option 4 model. For each of the four options these models represent the typical mode shapes. 128 Table A1. FFTT Weight and Fundamental Periods Compared with a Typical† Concrete Structure FFTT* Typical† Concrete Height (stories) Weight‡ (kN) Period (sec) Weight‡ (kN) Period§ (sec) 6 11200 0.90 28600 0.44 7 13100 1.04 33400 0.49 8 15000 1.21 38200 0.54 9 16900 1.38 42900 0.59 10 18800 1.57 47700 0.64 11 20700 1.75 52500 0.69 12 22600 1.95 57200 0.73 13 26500 1.68 62000 0.78 14 28600 1.83 66800 0.82 15 30600 1.98 71500 0.87 16 32700 2.14 76300 0.91 17 34700 2.30 81100 0.95 18 36800 2.46 85800 1.00 19 38900 2.63 90600 1.04 20 40900 2.79 95400 1.08 21 44100 1.89 100100 1.12 22 46200 1.99 104900 1.16 23 48300 2.10 109700 1.20 24 50500 2.22 114500 1.24 25 52600 2.33 119200 1.27 26 54700 2.45 124000 1.31 27 56800 2.56 128800 1.35 28 58900 2.68 133500 1.39 29 61100 2.80 138300 1.42 30 63200 2.93 143100 1.46 * Option 1 for 6-12 stories; average of Options 2 and 3 for 13-20 stories; Option 4 for 21+ stories †Assuming the same basic floor plan as the FFTT options with a 10kPa dead load ‡ Dead load only §Period calculated as: T = 0.05h3./4 (NRC, 2010) 129 (a) (b) (c) Figure A1: 12 Storey Option 1 (a) Mode 1; T1 = 1.95 sec (b) Mode 2; T2 = 1.74 sec (c) Mode 3; T3 = 1.47 sec 130 (a) (b) (c) Figure A2: 20 Storey Option 2 (a) Mode 1; T1 = 2.65 sec (b) Mode 2; T2 = 2.35 sec (c) Mode 3; T3 = 1.85 sec 131 (a) (b) (c) Figure A3: 20 Storey Option 3 (a) Mode 1; T1 = 2.94 sec (b) Mode 2; T2 = 2.58 sec (c) Mode 3; T3 = 2.07 sec 132 (a) (b) (c) Figure A4: 30 Storey Option 4 (a) Mode 1; T1 = 2.93 sec (b) Mode 2; T2 = 2.78 sec (c) Mode 3; T3 = 2.13 sec
Thesis/Dissertation
eng
Civil Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivs 2.5 Canada
Graduate
Dynamic analysis of the FFTT system
Text