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Force based design guideline for timber-steel hybrid structures : steel moment resisting frames with… Tesfamariam, Solomon; Stiemer, Siegfried F.; Bezabeh, Matiyas; Goertz, Caleb; Popovski, Marjan; Goda, Katsuichiro 2015

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FORCE BASED DESIGN GUIDELINE FOR  TIMBER-STEEL HYBRID STRUCTURES:  STEEL MOMENT RESISTING FRAMES WITH CLT INFILL WALLS    PRINCIPAL INVESTIGATORS Dr. Solomon Tesfamariam, P.Eng. (Associate Professor, UBC Okanagan Campus)  Dr. Siegfried F. Stiemer, P.Eng. (Professor, UBC Vancouver Campus)  STUDENTS Matiyas Bezabeh  (PhD Student, UBC Okanagan Campus)  Caleb Goertz  (MASc Student, UBC Okanagan Campus)  INDUSTRIAL COLLABORATOR Dr. Marjan Popovski, P.Eng.  (Principal Scientist, FPInnovations)  ACADEMIC COLLABORATOR Dr. Katsuichiro Goda  (Senior Lecturer, Bristol University)   December 2015  ii Prepared for:  Forestry Innovation Investment Ltd. #1200 - 1130 West Pender Street, Vancouver, BC Canada V6E 4A4     By:  The University of British Columbia 3333 University Way, Kelowna, BC Canada V1V 1W7             iii Disclaimers This report includes a seismic design guideline for a timber-steel hybrid structure consisting of steel moment resisting frames with CLT infill walls. Other ways of conducting the seismic analysis and design are possible, and they may result in different seismic demands on the building. The connection detailing in this report was chosen to represent the use of off-the shelf solutions, and other ways of connection detailing are available. The report has no intention of promoting or endorsing any particular proprietary connection or building system.  The authors have taken reasonable actions and due diligence to ensure the accuracy of the information provided in this report; however, THE AUTHORS, UNIVERSITY OF BRITISH COLUMBIA, FPINNOVATIONS, OR OTHER CONTRIBUTORS ASSUME NO LIABILITY FOR ANY DIRECT OR INDIRECT DAMAGE, INJURY, LOSS OR EXPENSE THAT MAY BE INCURRED OR SUFFERED AS A RESULT OF THE USE OF THIS REPORT INCLUDING WITHOUT LIMITATION PRODUCTS, BUILDING TECHNIQUES OR PRACTICES. Neither the authors nor FPInnovations guarantee the completeness of the information published in this report. Users of this report agree to use the information in this report (analysis suggestions, design procedures, detailing, etc.) at their own risk. We will not be liable for any errors, inaccuracies, omissions or damages arising from the use of the information presented in this report, nor any action taken in reliance to the presented information.  Building science, products and construction practices change and improve over time and rather than relying on this report, it is advisable to: (a) regularly consult up-to-date technical publications on products and practices, (b) seek specific information and professional advice on the use of products mentioned in this report from manufacturers or suppliers of the products and consultants with appropriate qualifications and experience, and (c) review and comply with the specific requirements of the applicable building codes for each construction project.    iv Executive Summary Provincial code changes have been made to allow construction of light wood-frame buildings up to 6 storeys in order to satisfy the urban housing demand in western Canadian cities. It started in 2009 when the BC Building Code was amended to increase the height limit for wood-frame structures from four to six. Recently, provinces of Quebec, Ontario and Alberta followed suit. While wood-frame construction is limited to six storeys, some innovative wood-hybrid systems can go to greater heights. In this report, a feasibility study of timber-based hybrid buildings is described as carried out by The University of British Columbia (UBC) in collaboration with FPInnovations. This project, funded through BC Forestry Innovation Investment's (FII) Wood First Program, had an objective to develop design guidelines for a new steel–timber hybrid structural system that can be used as a part of the next generation "steel-timber hybrid structures" that is limited in scope to 20 storey office or residential buildings. The steel-timber hybrid structure incorporates Cross Laminated Timber (CLT) infill walls in the steel moment resisting frames. This structure is aimed to couple strong, ductile steel moment resisting frames with lighter and stiff CLT infill walls. L-shaped steel bracket connectors were proposed to connect the steel frames to the CLT panels. Thorough experimental studies have been carried out on the seismic behaviour of the bracket connections at UBC and FPInnovations for the past four years. These connections are bolted to the steel frame and nailed to the CLT infill walls. Moreover, the provided brackets ensure full confinement between the structural elements and energy dissipation under intense seismic action.   The National Building Code of Canada (NBCC) allows an Equivalent Static Force Procedure (ESFP) design method to be used with appropriate overstrength and ductility factors for the seismic design of structures. However, NBCC (NRC 2010) does not have the appropriate overstrength and ductility factors to design the proposed hybrid structure. Thus,    v in this report, overstrength and ductility factors were quantified analytically. A robust finite element model of the hybrid structure that accounts for the CLT panel and frame interactions was developed in OpenSees (Open System for Earthquake Engineering Simulation) (Mazzoni et al. 2006) and used for the analytical investigation.  Initially for buildings designed with an Rd = 2 and Ro = 1.5, 18 different hybrid buildings were modeled and subjected to monotonic static pushover loading by varying the following modeling variables: building height (1, 3, 6, 9, 12, 15 and 20 storey), CLT infill configuration (one-bay infilled and two-bay infilled), connection bracket spacing (800 mm), and ductility class (ductile D and limited ductile LD). In order to have a non-conservative and economical design, 3-, 6-, and 9-storey hybrid buildings were designed using Rd = 4 and Ro = 1.5. A nonlinear static pushover analysis has been performed to validate the overstrength factors of the hybrid buildings under consideration. In order to check the FEMA P695 (FEMA 2009) acceptable failure probabilities and collapse margin ratios, Nonlinear Time History Analysis (NLTHA) and Incremental Dynamic Analysis (IDA) were carried out using 60 ground motion records. Ground motions were selected and scaled for the city of Vancouver by considering site class C of NBCC 2010 (NRC 2010). Due to the complexity and the contributions of sub-crustal and subduction type earthquakes to the total seismic hazard, the traditional FEMA P695 (FEMA 2009) was not utilized in the ground motion selection and scaling. Therefore, a new ground motion selection criteria that specifically incorporates the seismicity of Vancouver, Canada, were utilized for this project. In the IDA, conservative collapse criteria have been followed to define the dynamic instability of the building. In this approach, structural hardening was only considered for interstorey drift values less than 10% and the lowest spectral acceleration value was considered as a limit state point. Analysis was done by a high performance computational method using 200 clusters of computers at The University of British Columbia research computing service center.     vi The results show that the presence of CLT infill walls significantly affects the systems overstrength value, by sacrificing ductility. From this research, it can be concluded that an overstrength factor of Ro = 1.5 and a ductility factor of Rd = 4 showed acceptable and economical design of the proposed hybrid structure.       vii Acknowledgements Development of the design guideline in this project was supported through the BC Forestry Innovation Investment's (FII) Wood First Program. The Timber-Steel Hybrid Structures: Steel Moment Resisting Frames with CLT Infill Walls, in collaboration with FPInnovations, was developed with support from the NSERC Strategic Network (NEWBuilds). Under the supervision of Drs. Tesfamariam and Stiemer, various students have contributed to the knowledge presented in this report:   Matiyas Bezabeh (our former M.A.Sc. and currently Dr. Tesfamariam’s Ph.D. student) has developed a displacement based design guideline for the hybrid structures. In his Ph.D. research, he is now developing a multi-hazard (wind and earthquake) framework for novel mass timber based tall buildings. Matiyas was instrumental in successfully accomplishing the 2014/2015 FII project.  Caleb Goertz (Dr. Tesfamariam’s M.A.Sc. student) was actively involved in successfully accomplishing the 2014/2015 FII project. Caleb’s research is in developing an energy based design guideline for timber-steel hybrid buildings.  Johannes Schneider (at the time of the study Ph.D. student) carried out the testing for all connections presented in this report, and developed novel connections.  Yin-Lan Shen (our former visiting Ph.D. student from China) developed analytical models for the connections.  Carla Dickof (our former M.A.Sc. student) developed analytical models of the steel-timber hybrid structures and also carried out seismic vulnerability assessment. Carla is now working as a structural engineer with Fast + Epp in Vancouver, BC.   Tobias Fast (our former M.A.Sc. student) developed a design guideline for the hybrid structures with consideration of hybrid floors/diaphragms. Tobias is now working as a structural engineer with Skidmore, Owings & Merrill (SOM) in New York.  Wu Di and Xion Yan (visiting Post Docs from Guangzhou University and University of South China, China) provided guidance in analytical modeling.  Drs. Yang Chen and Ying Zhang (visiting Professors from the University of Guangzhou) aided in various technical and FE modeling tasks.    viii Table of Contents Disclaimers .............................................................................................................................. iii Executive Summary ................................................................................................................. iv Acknowledgements ................................................................................................................. vii Table of Contents ................................................................................................................... viii List of Figures ......................................................................................................................... xii Chapter 1 Background ............................................................................................................ 20 1.1 Motivation ................................................................................................................ 20 1.2 Timber-steel hybrid systems ..................................................................................... 21 1.3 Research approach .................................................................................................... 22 1.4 Developing the force modification factors and the fundamental period .................. 23 Chapter 2 Steel-Timber Hybrid System: Component Experimental Tests ............................. 25 2.1 Conceptual design of steel moment resisting frames with CLT infill walls ............ 25 2.1.1 Steel moment resisting frames (SMRFs) ........................................................... 26 2.1.2 CLT infill walls .................................................................................................. 26 2.1.3 Infill walls to frame connection ......................................................................... 27 2.2 Experimental tests .................................................................................................... 27 Chapter 3 Steel-Timber Hybrid System: Numerical Models .................................................. 34 3.1 Component level modeling ....................................................................................... 35 3.1.1 Modeling of steel frame members ..................................................................... 36 3.1.2 Modeling of cross laminated timber (CLT) ....................................................... 37 3.1.3 Connections ....................................................................................................... 39    ix 3.2 System level modeling ............................................................................................. 41 3.3 Calibration of OpenSees models .............................................................................. 45 3.3.1 Hysteretic model calibration of connection A ................................................... 48 3.3.2 Hysteretic model calibration of connection B ................................................... 49 3.3.3 Hysteretic model calibration of connection C ................................................... 51 Chapter 4 Parametric Study on the Lateral Behaviour of Single-Storey CLT-SMRFs .......... 54 4.1 Response sensitivity to bracket spacing ................................................................... 54 4.2 Response sensitivity to gap ...................................................................................... 56 Chapter 5 Overview of Seismic Force Modification Factors ................................................. 58 5.1 Site seismic hazard ................................................................................................... 60 5.2 Evolution of ductility (Rd) and overstrength (Ro) in the Canadian building design code ........................................................................................................................ 61 5.2.1 Overstrength factor (Ro) ..................................................................................... 68 5.3 Seismic modification factors in the European code ................................................. 70 5.4 Seismic modification factors in the United States code ........................................... 72 Chapter 6 Multi-Storey Steel-Timber Archetype Buildings ................................................... 75 Chapter 7 Overstrength and Ductility Factors using Static Pushover Analysis...................... 78 7.1 Seismic performance factors of FEMA P695 and NBCC 2005 ............................... 78 7.2 Hybrid buildings considered for analysis ................................................................. 81 7.3 Pushover analysis results .......................................................................................... 86 7.4 Equivalent energy elastic-plastic approximation ...................................................... 89 7.5 Quantification of Rd and Ro factors .......................................................................... 91    x Chapter 8 Fundamental Period ................................................................................................ 96 8.1 NBCC fundamental period empirical formulas ........................................................ 97 8.2 FEMA P695 .............................................................................................................. 98 8.2.1 Proposed empirical factor considering building height only ........................... 100 8.2.2 Proposed empirical factor considering infill length and building height ......... 100 Chapter 9 Seismic Hazard for Vancouver and Ground Motion Selection ............................ 102 9.1 Seismic hazard in Vancouver ................................................................................. 102 9.2 Ground motion selection for Vancouver ................................................................ 107 9.3 FEMA P695 ground motions .................................................................................. 112 Chapter 10 Validation of Proposed Rd and Ro Factors .......................................................... 115 10.1 Performance evaluation methodology .................................................................. 115 10.2 Check for collapse prevention limit state according to NBCC 2010 ................... 123 10.3 Performance assessment of the proposed Rd factors using incremental dynamic analysis (IDA) ...................................................................................................... 125 10.3.1 Incremental dynamic analysis results ............................................................ 126 10.3.2 Total system uncertainty ................................................................................ 128 10.3.3 Collapse fragility curves ................................................................................ 129 10.3.4 Evaluation of the proposed Rd factor ............................................................. 131 10.3.5 Evaluation of the proposed Ro factor ............................................................. 133 Chapter 11 Conclusions and Future Recommendations ....................................................... 134 11.1 Component experimental tests ............................................................................. 134 11.2 Finite element numerical models .......................................................................... 134    xi 11.3 Lateral behaviour of CLT infilled SMRFs ........................................................... 135 11.4 Design approaches and static monotonic pushover analysis ................................ 136 11.5 Incremental dynamic analysis .............................................................................. 136 11.6 Suggested design approaches ............................................................................... 137 11.6.1 Suggested structural parameters .................................................................... 137 11.6.2 Design approach details ................................................................................. 138 11.7 Future research perspectives ................................................................................. 139     xii List of Figures Figure 1: CLT-steel hybrid building ....................................................................................... 21 Figure 2: Conceptual representation of proposed hybrid system............................................ 26 Figure 3: Wall configuration and L-shaped steel bracket details (Shen et al. 2013); a) wall configuration, b) Simpson strong tie bracket, and c) nails and screws used .......................... 28 Figure 4: Test set-up for bracket connections loaded parallel to the grain direction of the surface CLT layer (fully adopted from Schneider et al. 2014) ............................................... 29 Figure 5: Test set-up for bracket connections loaded perpendicular to the grain direction of the surface CLT layer (fully adopted from Schneider et al. 2014) ......................................... 30 Figure 6: Bracket connection testing; a) Parallel to the grain, and b) Perpendicular to the grain (© 2014 Johannes Schneider, by permission) ............................................................... 31 Figure 7: Typical failure mode in Connection A; a) Parallel to the grain test, and b) Perpendicular to the grain (© 2014 Johannes Schneider, by permission) .............................. 31 Figure 8: Typical failure mode in Connection C; a) Parallel to the grain test, and b) Perpendicular to the grain (© 2014 Johannes Schneider, by permission) .............................. 32 Figure 9: CLT wall testing; a) test set up, and b) rocking of wall and failure of connectors  (© 2014 Marjan Popovski, by permission) .................................................................................. 32 Figure 10: Failure of connectors during the test; a) low amplitude load, and b) high amplitude loads connectors (© 2014 Marjan Popovski, by permission) ................................................. 33 Figure 11: Failure of connectors during the test; a) full pullout failure, and b) crushing of wood connectors (© 2014 Marjan Popovski, by permission) ................................................. 33 Figure 12: Component level modeling, calibration, and assembling process flowchart ........ 35    xiii Figure 13: Modified Ibarra-Krawinkler deterioration model; a) monotonic loading curve, and b) basic modes of cyclic deterioration and associated definitions  (adopted from Lignos and Krawinkler 2011) .................................................................................................................... 36 Figure 14: Moment-curvature (rotation) relationship; a) generalized force deformation for steel elements, and b) definition of chord rotation  (fully adopted and reproduced from ASCE 41 2006) .................................................................................................................................. 37 Figure 15: CLT wall model..................................................................................................... 38 Figure 16: Connection model and details, a) modeling using two node link element, and b) typical frame to CLT panel connection failure ................................................................... 40 Figure 17: Elastic perfectly plastic gap (EPPG); a) tension-only gap, and b) compression-only gap (Mazzoni et al. 2007) ............................................................................................... 42 Figure 18: Parallel formulation of EPPG gap element and two node link element ................ 43 Figure 19: System level modeling of CLT infilled SMRFs (Bezabeh et al. 2015) ................ 44 Figure 20: Hysteretic envelope for the Pinching4 model  (fully adopted from Shen et al., 2013) ....................................................................................................................................... 45 Figure 21: Cyclic displacement schedule CUREE Test protocol for parallel to the grain test (© 2014 Johannes Schneider, by permission) ......................................................................... 47 Figure 22: Cyclic displacement schedule CUREE test protocol for perpendicular to the grain test (© 2014 Johannes Schneider, by permission) .................................................................. 47 Figure 23: Comparison of experimental and OpenSees pinching4 material model for Connection A in parallel to the grain direction ....................................................................... 48 Figure 24: Comparison of experimental and OpenSees pinching4 material model for Connection A in perpendicular to the grain direction ............................................................. 49    xiv Figure 25: Comparison of experimental and OpenSees pinching4 material model for Connection B in parallel to the grain direction ....................................................................... 50 Figure 26: Comparison of experimental and OpenSees pinching4 material model for Connection B in perpendicular to the grain direction ............................................................. 50 Figure 27: Comparison of experimental and OpenSees pinching4 material model for Connection C (parallel to the grain direction) ........................................................................ 51 Figure 28: Comparison of experimental and OpenSees pinching4 material model for Connection C (perpendicular to the grain direction) .............................................................. 52 Figure 29: Variation of capacity curves with bracket spacing ................................................ 55 Figure 30: Cyclic response sensitivity to bracket spacing ...................................................... 55 Figure 31: Variation of capacity curves with provided gap .................................................... 57 Figure 32: Cyclic response sensitivity to gap ......................................................................... 57 Figure 33: Evolution of base shear coefficients for the National Building Code of Canada, example for Vancouver, BC ................................................................................................... 60 Figure 34: Stages in the response of a frame structure (Mitchell et al. 2003) ........................ 68 Figure 35: Seven building heights: 1, 3, 6, 9, 12, 15 and 20 storeys ...................................... 76 Figure 36: Hybrid structure floor plan .................................................................................... 77 Figure 37: Two infill configurations: one interior bay, two exterior bays and all bays ......... 77 Figure 38: Illustration of seismic performance factors (R, ΩO, and Cd)  (from FEMA P695) 79 Figure 39: Idealized nonlinear static pushover curve (FEMA 2009) ..................................... 80 Figure 40: Ductility and force reduction factors of NBCC 2005 (Mitchell et al. 2003) ........ 81 Figure 41: Results of nonlinear monotonic pushover analysis for low- and mid-rise models with bracket spacing of 0.8m .................................................................................................. 87    xv Figure 42: Results of nonlinear monotonic pushover analysis for high-rise models with bracket spacing of 0.8m .......................................................................................................... 88 Figure 43: Results of nonlinear monotonic pushover analysis for high-rise models with bracket spacing of 0.8m .......................................................................................................... 89 Figure 44: EEEP curve (ASTM 2126-09 2009) ..................................................................... 90 Figure 45: Ductility factors Rd ................................................................................................ 94 Figure 46: Overstrength factor Ro ........................................................................................... 95 Figure 47: Proposed empirical formula considering only building height ........................... 100 Figure 48: Regional seismicity in south-western BC, Canada ............................................. 102 Figure 49: (a) Uniform hazard spectrum and conditional mean spectra for crustal interface, and inslab events in Vancouver, and (b) seismic deaggregation for spectral acceleration at 0.3 s in Vancouver. ..................................................................................................................... 106 Figure 50: (a) Uniform hazard spectrum and conditional mean spectra for crustal interface, and inslab events in Vancouver, and (b) seismic deaggregation for spectral acceleration at 1.5 s in Vancouver. ..................................................................................................................... 106 Figure 51: (a) Uniform hazard spectrum and conditional mean spectra for crustal interface, and inslab events in Vancouver, and (b) seismic deaggregation for spectral acceleration at 3.0 s in Vancouver. ..................................................................................................................... 107 Figure 52: Magnitude-distance plot of the selected records for T1 = 0.3 s, 1.0 s, and 3.0 s. 109 Figure 53: Comparison of response spectra of the selected ground motion records (50th/16th/84th curve) and conditional mean spectra (mean and mean plus/minus one standard deviation) for the a) crustal, b) inslab, and c) interface earthquakes for T1 = 0.3 s. ............. 110    xvi Figure 54: Comparison of response spectra of the selected ground motion records (50th/16th/84th curve) and conditional mean spectra (mean and mean plus/minus one standard deviation) for the a) crustal, b) inslab, and c) interface earthquakes for T1 = 1.5 s. ............. 111 Figure 55: Comparison of response spectra of the selected ground motion records (50th/16th/84th curve) and conditional mean spectra (mean and mean plus/minus one standard deviation) for the a) crustal, b) inslab, and c) interface earthquakes for T1 = 3.0 s. ............. 112 Figure 56: Comparison of the statistics of the response spectra (50th/16th/84th curve) for the records selected based on conditional mean spectra and for the ‘far-field’ records adopted in the FEMA P695 guideline by considering the anchor vibration periods of 0.3s, 1.5s and 3.0s................................................................................................................................................ 114 Figure 57: Performance evaluation methodology ................................................................. 116 Figure 58: Maximum interstorey drift under design based earthquake ground motions for low-rise buildings.................................................................................................................. 123 Figure 59:  Maximum interstorey drift under design based earthquake ground motions for mid-rise buildings ................................................................................................................. 124 Figure 60:  Maximum interstorey drift under design based earthquake ground motions for high-rise buildings ................................................................................................................ 125 Figure 61: IDA results for three-storey middle bay infilled archetype models. ................... 127 Figure 62: IDA results for six-storey middle bay infilled archetype models ....................... 127 Figure 63: IDA results for middle bay infilled hybrid buildings designed with Rd = 4 ........ 128 Figure 64: Collapse fragility curves for three-storey middle bay infilled archetype models 130 Figure 65: Collapse fragility curves for six-storey middle bay infilled archetype models ... 130 Figure 66: Collapse fragility curves for middle bay infilled archetype models designed with Rd = 4 .................................................................................................................................... 131    xvii List of Tables Table 1: CLT material properties ............................................................................................ 38 Table 2: Calibrated Pinching4 model parameters ................................................................... 53 Table 3: Modeling variables (Bezabeh et al. 2015) ................................................................ 54 Table 4: Evolution of Canadian design code .......................................................................... 59 Table 5: Summary of K factors representing type of construction, damping, ductility and energy absorption (Mitchell et al. 2010) ................................................................................. 62 Table 6: Structural ductility factor µ for dynamic analysis (Commentary K, 1975 NRC) ..... 62 Table 7: R factors for different reinforced concrete structural systems (NRC 1995) ............. 64 Table 8: Force modification factors Rd and Ro for seismic force-resisting systems (NRC 2005) ....................................................................................................................................... 66 Table 9: Seismic force modification factors for steel seismic force-resisting systems  (NRC 2010) ....................................................................................................................................... 67 Table 10: Sources of structure overstrength (Park 1996) ....................................................... 69 Table 11: Derivation of overstrength modification factor for steel seismic force resisting systems (Mitchell et al. 2003) ................................................................................................. 69 Table 12: Derivation of overstrength modification factor for concrete seismic force resisting systems (Mitchell et al. 2003) ................................................................................................. 70 Table 13: Derivation of overstrength modification factor for timber seismic force resisting systems (Mitchell et al. 2003) ................................................................................................. 70 Table 14: Behaviour factors for steel systems regular in elevation (CEN 2002) ................... 71 Table 15: Seismic design factors and coefficients from the ASCE 7-10 (ASCE 2010) ......... 73 Table 16: CLT-steel buildings (low-rise) ............................................................................... 82    xviii Table 17: CLT-steel buildings (mid-rise) ............................................................................... 82 Table 18: CLT-steel buildings (high-rise) .............................................................................. 82 Table 19: Designed beam dimensions for ductile type ........................................................... 84 Table 20: Designed beam dimensions for limited ductility type ............................................ 84 Table 21: Designed column dimensions for ductile type........................................................ 85 Table 22: Designed column dimensions for limited ductility type ......................................... 85 Table 23: Designed beam dimensions for Rd =4 ..................................................................... 86 Table 24: Designed column dimensions for Rd =4 ................................................................. 86 Table 25: Overstrength and ductility factors for models with ductile (D) steel moment frames................................................................................................................................................. 91 Table 26: Overstrength and ductility factors for models with limited-ductile (LD) steel moment frames........................................................................................................................ 92 Table 27: Overstrength and ductility factors for hybrid buildings designed with Rd =4 and Ro = 1.5 ........................................................................................................................................ 92 Table 28: Approximate fundamental period formulas (Kwon 2011) ..................................... 96 Table 29: NBCC empirical formulas for fundamental period (NRC 2010) ........................... 97 Table 30: Coefficient for upper limit on calculated period (ASCE 2010) .............................. 98 Table 31: Values of approximate period parameters Ct and x (ASCE-SEI 2010) .................. 98 Table 32: Fundamental period results ..................................................................................... 99 Table 33: First three fundamental periods of all building storeys and infill patterns ........... 104 Table 34: Quality rating of design requirements (FEMA 2009)........................................... 118 Table 35: Quality rating of test data from an experimental investigation program (FEMA 2009) ..................................................................................................................................... 119    xix Table 36: Quality rating of index archetype models ............................................................. 119 Table 37: Acceptable values of adjusted collapse margin ratio (ACMR10% and ACMR20%) (FEMA 2009) ........................................................................................................................ 122 Table 38: Performance evaluation table for Rd = 2 ............................................................... 132 Table 39: Performance evaluation table for Rd = 4 ............................................................... 132     20 Chapter 1 Background 1.1 Motivation The use of wood in structural applications in Canada has been promoted for the last few years by the wood industry and the provincial governments. Several Provinces, including British Columbia have adopted a "Wood First Initiative" in order to create a "Culture of Wood Use.” This initiative requires provincially-funded projects to use wood as the primary construction material and helps innovative design solutions to bring timber buildings to new heights. This also provides a unique opportunity for designers to take advantage of innovative designs (e.g. hybrid structures) and alternative solutions to overcome the height restriction required by the building code. Over the last five years, through the NSERC network funded project (Network for Engineered Wood-based Building Systems, NewBuildS) researchers from The University of British Columbia (UBC) and FPInnovations (FPI) have developed a timber-steel hybrid structural system that can potentially meet the current performance requirements and exceed the current height limit. This report contains results from the research work related to developing design guidelines for this novel timber-steel hybrid structural system that can reach up to 20 storeys. With the timber-steel hybrid structural systems, the volume of wood used in the mid- and high-rise applications can be increased.  The direction of this research is in line with the Forestry Innovation Investment's (FII’s) Wood First Program, and the following objectives are met:  Maximize the appropriate use of wood in public and private projects: increase the volume of wood used through hybrid taller structures.  Strengthen BC's capacity to produce competitive wood-based products and building systems that create and respond to market demand: the proposed hybrid structures (that utilizes steel moment resisting frames and cross-laminated timber (CLT) as infill and floor material).   21  Accelerate adoption of existing and emerging wood-based products and building systems: the proposed method will extend the work done by the applicant and develop the required design parameters (e.g. overstrength and ductility factors) needed in the building code. This will indeed motivate the engineers to adopt the proposed method and utilize it widely.  Position BC as a world leader in sustainable and innovative wood-based products, and building systems in design, production, and application: this proposed hybrid structure is novel and the knowledge and experience can be exported globally.  Figure 1: CLT-steel hybrid building  1.2 Timber-steel hybrid systems Infill walls in hybrid structures have often been considered in the design as non-structural components. However, the work undertaken so far has highlighted that CLT does indeed significantly contribute to the lateral load resistance capacity of a building (Dickof et al. 2012; Dickof 2013; Tesfamariam et al. 2014). Where different seismic force–resisting systems are combined, a conservative approach is suggested in NBCC. Without explicit consideration of the CLT, the structure will be over-designed.    22 The proposed system allows the CLT and connections to dissipate energy and sustain the damage rather than the steel frame. Adding the infill to the steel moment frame indeed reduces the ductility of the system; however, it allows the building users to occupy the space faster after an extreme event with the damage being sustained mostly by the infill panels. After the extreme event the infill panels will be crushed and need replacing, which will be a minor cost in comparison to repairing steel components of the structure. The new infill CLT panels can be replaced with new connections in a timely manner. The use of CLT panels can also reduce the cost of the entire structure by reducing the amount of steel used, allowing designers to specify the system more often.  The objective of the research presented in this report is to develop a seismic design guideline for the next generation of "wood-steel hybrid structures" that are limited to 20-storey office or residential buildings. For different building height and infill configuration, archetypical buildings were developed. Archetype is a prototypical representation of a seismic-force-resisting system. Given the limited information for the proposed wood-steel hybrid buildings in this proposal, the main objectives of the research were to develop:  Overstrength related modification factor Ro and ductility related modification factor Rd for future implementation in the NBCC.  Empirical equation to quantify fundamental period of the hybrid structures for code implementation.  Force-based design guideline following the capacity based design principles. Thus in this report, the complex interaction of steel frame, CLT infill, connection, and its impact on the overall seismic performance of the structure were considered. The overstrength and ductility factors were quantified analytically following the FEMA P695 procedure (FEMA 2009). Furthermore, an empirical equation for determining the fundamental period was developed for the proposed steel-timber hybrid structure. 1.3 Research approach The performance of the CLT-steel hybrid system is affected by CLT thickness, steel section used, connection type, distribution of connections, etc. Thus, the design consideration and   23 building type was taken into consideration. The selected structures were assumed not to have any plan irregularities (i.e. not torsionally sensitive) so that the design guidelines can make use of the results of the two dimensional frame analyses. A 3-bays SMRF with two CLT infill patterns (one interior bay and two exterior bays) is considered. For different building height and infill configurations, archetypical buildings were developed. The variables among the archetypical buildings considered were:   Building height;  CLT-steel connections and infill pattern; and  Steel moment resisting frame design level. The archetype buildings were selected based on the building type considered and FEMA’s P695 guidelines (FEMA 2009). As such, these archetype buildings were not intended to simulate a specific complex building; rather this study was to develop the required engineering design parameters needed for design of more simple regular buildings. Once the overstrength and ductility factors, and fundamental period of the hybrid building are developed, designers can use these factors to select the appropriate seismic load and proportion the loads on each floor following the standard design guideline.  1.4 Developing the force modification factors and the fundamental period The overstrength and ductility factors will be developed following the guidelines of FEMA P695. This process accounts for potential uncertainties in ground motions, component design parameters, structural configuration, and behavioral characteristics of structural elements based on available laboratory test data.  FEMA’s Quantification of Building Seismic Performance Factors document (FEMA P695) and FEMA’s Quantification of Building Seismic Performance Factors: Component Equivalency Methodology document (FEMA P-795) were followed for evaluating the seismic performance of structural components such as structural elements, connections, or subassemblies experiencing inelastic response that controls the collapse performance of the seismic-force-resisting system. The recommended Component Equivalency Methodology described in the FEMA P795 report   24 balances the competing objectives of: (1) maintaining consistency with the probabilistic, analytical, system-based collapse assessment concepts of the FEMA P695 methodology; and (2) providing simple procedures for comparing the tested performance of different components. The overall steps followed in this report and based on FEMA P695 are:  Develop the system concept. The process of quantifying overstrength and ductility starts with the development of a well-defined concept for the seismic-force-resisting system, including type of construction materials, system configuration, inelastic dissipation mechanisms, and intended range of application.  Obtain required information. Required information includes detailed design requirements and results from material, component, and system testing. This step was already achieved through the NSERC Network research grant.  Characterize the system behaviour through the use of structural system archetypes.  Develop suitable structural models for collapse assessment.  Analyze the selected models. Collapse assessment was performed using both nonlinear static (pushover) and nonlinear dynamic (response history) analysis procedures. For the latter, the collapse was studied using incremental dynamic analysis.  Evaluate the seismic performance. This step entails utilizing results from nonlinear static analyses to determine an appropriate value of the system overstrength factor, and results from nonlinear dynamic analyses to evaluate the acceptability of a trial ductility factor. Using modal analysis, the fundamental period was computed, and the code equations were calibrated to develop empirical equations.  Document the results. The results of the system were thoroughly documented for review and approval by an independent peer review panel, review and approval by an authority having jurisdiction, and eventual use in design and construction.      25 Chapter 2 Steel-Timber Hybrid System: Component Experimental Tests The steel-timber hybrid structure incorporates Cross Laminated Timber (CLT) infill walls within the steel moment resisting frames. This structure was aimed to couple the ductile and strong steel moment frames with lighter and stiff CLT infill walls. 2.1 Conceptual design of steel moment resisting frames with CLT infill walls The composite action, for the proposed hybrid system, was achieved through discrete connectors along the interface of the steel frames and infill walls (Figure 2). The connections were required to ensure the CLT is fixed to the steel frame and for energy dissipation under seismic shaking. A small gap was provided at the interface between the CLT wall and the steel frame to allow the brackets to deform and dissipate energy under lateral loading. In this research, the CLT wall to steel frame connection was achieved by angular L-shaped steel brackets. These connection brackets are bolted to the steel frames and nailed to the CLT infill walls. Recently extensive experimental tests were carried out on the seismic behaviour of bracket connectors for various nailing types and configurations at FPInnovations and UBC (Popovski and Karacabeyli 2010; Schneider et al. 2014).    26  Figure 2: Conceptual representation of proposed hybrid system 2.1.1 Steel moment resisting frames (SMRFs) Steel moment resisting frames (SMRFs) are structural systems comprised of steel beams and columns. These beams and columns are rigidly connected to allow for frame-action response under lateral loading. The frame elements and beam-column connections should be appropriately designed and detailed to resist the shear, flexural and axial load demand from earthquake and wind loads. Special detailing requirements of SMRFs are needed to ensure they have satisfactory performance under intense seismic shaking (Hamburger et al. 2009). SMRFs resist the lateral load demand without requiring steel bracing or shear walls. This necessitates the selection of bigger section sizes and labor intensive connections, requiring a higher construction cost. In order to minimize this problem, the proposed CLT infill wall was aimed to share the lateral load demand with the SMRF which leads to economical steel sections. 2.1.2 CLT infill walls Cross Laminated Timber (CLT) is a glued and laminated wood product consisting of flat dimensioned lumber layered in alternating directions and glued together. In Canada, CLT is typically made from Spruce-Pine-Fir (SPF) material that is commonly used in wood-frame   27 construction. Alternating the direction of the grain in each layer creates a more isotropic panel that has less splitting and shrinkage. Typical CLT construction uses the panels as both the floor and wall system elements, connected primarily with long screws and/or nailed L-shaped brackets that use nails or screws. CLT walls are typically fastened to concrete foundations with L-shaped steel sheet brackets and floor panels sit on the walls connected using either long screws or nailed L-shaped brackets with nails or screws. Subsequent storeys are constructed in a similar manner with the walls on top of the floor panels and typically connected with similar L-shaped brackets. 2.1.3 Infill walls to frame connection For the past four years, extensive experimental tests have been carried out on the seismic behaviour of angular L-shaped steel brackets (Schneider et al. 2014). The experimental tests considered a large number (98) of steel bracket connectors under parallel and perpendicular to the grain loading directions. Damage indices have been quantified from semi-static cyclic loading tests. From the perpendicular to the grain direction tests, the observed dominant type of failure was pull-out of nails. However, wood crushing failure mode was also observed on a few samples for tests parallel to the grain direction. In this research project, the CLT wall was connected to the steel frame using the studied angular L-shaped steel brackets. 2.2 Experimental tests This section presents a summary of the experimental tests carried out on the L-shaped steel brackets and CLT walls. The considered wall was a 3-ply CLT with an overall thickness of 94 mm. The layout of steel brackets and a sample test setup for the CLT wall is depicted in Figure 3a. During the tests, rigid body motion with negligible shear deformation was observed in the CLT walls. Moreover, for static and cyclic tests large deformations were observed in the brackets and fasteners. For details of the tested wall configurations and results; see Popovski and Karacabeyli (2010). Schneider et al. (2014) performed experimental tests by considering one commercially available type of L-shaped steel bracket: the SIMPSON Strong Tie bracket 90483.016 (Figure 3b). This bracket was implemented with different nail types including:   28 16d (3 ½ inch long) spiral nails, 590 mm and 470 mm screws, defined as Connection A, Connection B, and Connection C, respectively.     a) b) c) Figure 3: Wall configuration and L-shaped steel bracket details (Shen et al. 2013); a) wall configuration, b) Simpson strong tie bracket, and c) nails and screws used The experimental test set-ups for testing connections parallel and perpendicular to the grain of the surface CLT layer are shown in Figure 4 and Figure 5, respectively.   29  Figure 4: Test set-up for bracket connections loaded parallel to the grain direction of the surface CLT layer (fully adopted from Schneider et al. 2014)   30  Figure 5: Test set-up for bracket connections loaded perpendicular to the grain direction of the surface CLT layer (fully adopted from Schneider et al. 2014) Photos from the test setup and the typical failure modes are shown in Figures 6 to 8.    31   a) b) Figure 6: Bracket connection testing; a) Parallel to the grain, and b) Perpendicular to the grain (© 2014 Johannes Schneider, by permission)    a)   b) Figure 7: Typical failure mode in Connection A; a) Parallel to the grain test, and b) Perpendicular to the grain (© 2014 Johannes Schneider, by permission)   32  a)  b) Figure 8: Typical failure mode in Connection C; a) Parallel to the grain test, and b) Perpendicular to the grain (© 2014 Johannes Schneider, by permission)  The test set up and common failure modes for the CLT walls tested are depicted in Figures 9-11.  a)  b) Figure 9: CLT wall testing; a) test set up, and b) rocking of wall and failure of connectors  (© 2014 Marjan Popovski, by permission)   33  a)  b) Figure 10: Failure of connectors during the test; a) low amplitude load, and b) high amplitude loads connectors (© 2014 Marjan Popovski, by permission)  a)  b) Figure 11: Failure of connectors during the test; a) full pullout failure, and b) crushing of wood connectors (© 2014 Marjan Popovski, by permission)     34 Chapter 3 Steel-Timber Hybrid System: Numerical Models Numerical modeling was carried out using the Open System for Earthquake Engineering Simulation (OpenSees) finite element program (Mazzoni et al. 2006). For this research, a multi-scale modeling approach was adopted (Figure 12). The procedure outlined in Figure 12 entails:  Carrying out experimental tests for the different components and system (as provided in Chapter 2);  Calibrating the spring element of the connection for the pinching4 material model in OpenSees;  Determining the numerical model for the CLT system; and  Assembling the components to form the hybrid system. In this approach, component level modeling and calibrations were performed first for each element, i.e., steel brackets and CLT walls. Subsequently, these components were assembled in combinatorial form to achieve the desired system level property (CLT infilled SMRFs). The following subsections illustrate both the component and system level modeling and calibration approaches.    35   Figure 12: Component level modeling, calibration, and assembling process flowchart 3.1 Component level modeling The following subsections provide the details of the component model for the steel-timber hybrid structure. Assembling   36 3.1.1 Modeling of steel frame members The steel frame members were modelled with nonlinear displacement-based beam-column elements at the end of the member (to represent the spreading plastic hinge zone) as displayed in Figure 12, and linear elastic beam-column elements for the middle portion of each member following Bezabeh (2014); Dickof (2013); Dickof et al. (2014). The nonlinear steel elements use the modified Ibarra-Krawinkler Deterioration model (Lignos and Krawinkler 2011) with parameters based on the moment-curvature relationship given in ASCE 41 (2006) to account for both stiffness and strength degradation during loading. Figure 13a and 13b show the modified Ibarra-Krawinkler Deterioration model for monotonic loading and cyclic loading, respectively.   a) b) Figure 13: Modified Ibarra-Krawinkler deterioration model; a) monotonic loading curve, and b) basic modes of cyclic deterioration and associated definitions  (adopted from Lignos and Krawinkler 2011) The ASCE 41 (2006) recommendation to calculate the parameters (moment and rotation) of the model are illustrated in Figure 14a and 14b. In Figure 14, Q and Qy are the generalized component load and strength values, respectively. For frame members the rotation (θ) is calculated from the slope of the deflection curve of a beam member of length (L) as shown in Figure 13b. The plastic rotations of Figure 13a were calculated based on the class of section. The   37 detailed calculations of the parameters to define the specific deterioration model can be found elsewhere (ASCE 41 2006; Dickof 2013).   a) b) Figure 14: Moment-curvature (rotation) relationship; a) generalized force deformation for steel elements, and b) definition of chord rotation  (fully adopted and reproduced from ASCE 41 2006) 3.1.2 Modeling of cross laminated timber (CLT) Dickof et al. (2014) and Bezabeh (2014) have shown that varying the thickness of the panels has little effect on the global system behaviour during earthquake excitation. Therefore, the considered infill walls were 3-ply panels with outer lams of 32 mm and an inner lam of 35 mm, providing the overall thickness of 99 mm. The panels were modelled using quadrilateral shell elements (named Quad) in OpenSees following work by Shen et al. (2013) and Dickof et al. (2014) as shown in Figure 15.   38  Figure 15: CLT wall model In the finite element model, CLT panels were simplified to a single 99 mm panel element with homogeneous, isotropic, fully elastic properties using the OpenSees ndMaterial. ElasticIsotropic material with properties shown in Table 1 was assigned to model the ndMaterial. This simplification of the CLT panel behaviour is similar to simplifications made in other CLT panel behaviour studies (Ceccotti 2008; Fragiacomo et al. 2011; Shen et al. 2013). Table 1: CLT material properties Material Properties Design Values Elastic Modulus Ec 9500 MPa Shear Strength (Fv,c) 1.5 MPa Compression Strength (Fc,c) 30.0 MPa Compression Strength Perp-to-Grain (Fcb,c) 5.0 MPa Poisson’s Ratio 0.46  The OpenSees command to model the Quad elements according to Mazzoni et al. (2007) takes the following form:element quad $eleTag $iNode $jNode $kNode $lNode $thick $type $matTag <$pressure $rho $b1 $b2>,     39 where $eleTag = unique element object tag $iNode $jNode $kNode $lNode =  four nodes defining element boundaries input in counter-clockwise order around the element. $thick = element thickness $type = string representing material behaviour. The type parameter can be either "PlaneStrain" or "PlaneStress." $matTag = tag of nDMaterial $pressure = surface pressure (optional, default = 0.0) $rho = element mass density (per unit volume) from which a lumped element mass matrix is computed (optional, default=0.0) $b1 $b2 = constant body forces defined in the isoparametric domain (optional, default=0.0)  3.1.3 Connections The L-shaped steel brackets were modelled in OpenSees as two node link elements between the steel frame and CLT panel. The axial, shear, and rotational behaviour of these elements were defined by specific material models. Since the confinement between the frame and wall is provided with a small gap to allow for bracket deformation, the two node link elements were modelled as non-zero length elements. The rotational and transverse degrees of freedom were coupled as recommended by Mazzoni et al. (2007). However, to simplify the computational demand, P-Δ effects along the local axis were neglected. It was assumed that these elements do not contribute to the Rayleigh damping during the nonlinear stage of loading. The two node link elements were modelled using the calibrated Pinching4 material model of OpenSees consistent with the approach of Dickof et al. (2014) and Bezabeh (2014). Moreover, in this approach the rotational component of the link was considered to be rigid and the axial component represents the vertical property of the bracket as shown in Figure 16.   40  a) b) Figure 16: Connection model and details, a) modeling using two node link element, and b) typical frame to CLT panel connection failure The details of the Pinching4 material model calibration, based on experimental data produced by Schneider et al. (2014) will be discussed in subsequent sections. For this specific research project, the nonlinear behaviour of the connections was modelled in both shear and axial directions. The OpenSees command to model the two node link element model according to Mazzoni et al. (2007) takes the following form: element twoNodeLink $eleTag $iNode $jNode -mat $matTags -dir $dirs <-orient <$x1 $x2 $x3> $y1 $y2 $y3> <-pDelta (4 $Mratio)> <-shearDist (2 $sDratios)> <-doRayleigh> <-mass $m>    41 where $eleTag = unique element object tag $iNode and $jNode = end nodes $matTags = tags associated with previously-defined UniaxialMaterial objects $dirs = material directions: 2D-case: 1,2 - translations along local x, y axes; 3 - rotation about local z axis $x1 $x2 $x3 = vector components in global coordinates defining local x-axis (optional) $y1 $y2 $y3 = vector components in global coordinates defining local y-axis (optional) $Mratios = P-Delta moment contribution ratios, size of ratio vector is 2 for 2D-case and 4 for 3D-case $sDratios = shear distances from iNode as a fraction of the element length, size of ratio vector is 1 for 2D-case and 2 for 3D-case -doRayleigh = to include Rayleigh damping from the element (optional, default = no Rayleigh damping contribution) $m = element mass (optional, default = 0.0)  3.2 System level modeling Following the component level experimental tests and numerical modeling, a typical CLT infilled SMRF system as developed (Figure 19). This hybrid system combines ductile steel frames with CLT walls through angular L-shaped steel bracket connections. At the interface of the wall and frame a gap was provided in order to allow the brackets to deform and dissipate energy during the seismic shaking. The behaviour of the bracket and the confinement due to axial contact between the frame and panel were combined to form the axial component of the two node link element. The confinement behaviour to account for the space between the frame and panel was modelled using the elastic perfectly plastic gap uniaxial material (EPPG). EPPG is a trilinear hysteretic uniaxial material model which consists of a physical gap with zero stiffness and strength, linear elastic region, and post-yielding plastic region. Figure 17a and 17b show the compression-only and tension-only gap hysteretic properties, respectively.   42  a)  b) Figure 17: Elastic perfectly plastic gap (EPPG); a) tension-only gap, and b) compression-only gap (Mazzoni et al. 2007) The OpenSees command to model the EPPG uniaxial material model according to Mazzoni et al. (2007) takes the following form: uniaxialMaterial ElasticPPGap $matTag $E $Fy $gap <$eta> <damage>  where $matTag = integer tag identifying material $E =  tangent stiffness $Fy = stress or force at which material reaches plastic state $gap = initial gap $eta = hardening ratio damage = switch to accumulate damage in the material. If damage is omitted, default value, the gap material "re-centres" on load reversal.  In this study the behaviour of the CLT under compression load was modeled using the compression only gap model (Figure 17b). Since wood crushing is a local phenomenon around the steel brackets, the stress at which the material reaches a plastic state was calculated by considering the wood strength in parallel and perpendicular direction over a 200mm contact length. Reid and Peng (1997) showed the dependence of the post crushing stiffness of wood with respect to its density, and more specifically, they showed the increase in post crushing stiffness   43 due to the densification of wood. Therefore, the post-yield stiffness of the panel was assigned to be 1% of the elastic panel stiffness for this research. Following the approach of Dickof et al. (2014), this stiffness was quantified over the 200mm length and full thickness of the CLT panel. The EPPG gap material and the two node link elements of bracket connections were combined using the parallel material combination approach as shown in Figure 18. In this approach, strains are kept equal while the stresses are added up to form a single material model (Dickof et al. 2014).  Figure 18: Parallel formulation of EPPG gap element and two node link element The OpenSees command to model the parallel material combination according to Mazzoni et al. (2007) takes the following form: UniaxialMaterial Parallel $matTag $tag1 $tag2...  where $matTag = unique material object integer tag $tag1 $tag2 = identification of materials making up the material model (two node link element of brackets and EPPG)    44 Following the parallel material model formulation, all components were assembled to give the final CLT infilled SMRF as shown in Figure 19. The next sections will focus on the calibration of the component models and behaviour of the proposed hybrid system.  Figure 19: System level modeling of CLT infilled SMRFs (Bezabeh et al. 2015)   45 3.3 Calibration of OpenSees models This section presents the hysteretic model calibration of a Pinching4 material model of OpenSees. Following the experimental tests of and Schneider et al. (2014), Shen et al. (2013) calibrated the connections with Saw and Pinching4 hysteretic models of OpenSees and suggested the latter is a better representative of the seismic behaviour of connectors. In this section, calibration of the Pinching4 material model is carried out in detail considering three bracket connection types. This model comprises of piecewise linear curves to model the pinched force-deformation responses that accounts for stiffness and strength degradation when the bracket is subjected to cyclic loading (Mazzoni et al. 2007; Shen et al. 2013). This material model consists of 16 parameters, i.e., ePd1, ePf1, ePd2, ePf2, ePd3, ePf3, ePd4, ePf4, eNd1, eNf1, eNd2, eNf2, eNd3, eNf3, eNd4, and eNf4 as shown in Figure 20.   Figure 20: Hysteretic envelope for the Pinching4 model  (fully adopted from Shen et al., 2013) The main goal of this section was to calculate these parameters by tuning the values manually until the experimental and finite element results were similar. The definitions and procedures of calculations for the Pinching4 hysteretic model can be found elsewhere (Mazzoni et al. 2007;   46 Shen et al. 2013). In the Pinching4 material model the deterioration in stiffness was calculated using Equation 1 where; ki is the unloading stiffness at time ti, k0 is the initial unloading stiffness, and δki is the value of the stiffness damage index at time ti. )1(k i io kk   [1] According to Mazzoni et al. (2007), the stiffness damage index at time ti (δki) is calculated as follows:   gKLimEEgKdgKkgKmonotonicigKi 33max 21  [2] where dmax = the deformation demand (computed using Equation 3), gK1, gK2, and gK3 are floating point values to control the strength degradation, E is the hysteretic energy of the current displacement increment, Emonotonic is the energy required to define failure under monotonic load, and defmax and defmin are, respectively, positive and negative deformations to define failure (Mazzoni et al. 2007). minminmaxmaxmax ,maxdefddefdd ii  [3] Moreover, according to Lowes et al. (2003), the deformation that defines the reloading cycle (dmax i) is formulated as a function of maximum historic demand (dmax o) as: )1(maxmax ioi kdd   [4] For the purpose of calibration, the finite element model that was created in an earlier section was used as shown in Figure 19. The cyclic loading analyses were conducted by using CUREE loading protocols that consist of primary and trailing cycles which are functions of the ultimate displacement of monotonic loading analysis (Schneider et al. 2014). It is important to note that the loading protocol of the experimental tests of Schneider et al. (2014) and finite element analyses are almost identical. Figure 21 and Figure 22 show the loading schedules for parallel to the grain and perpendicular to the grain loading directions, respectively.   47  Figure 21: Cyclic displacement schedule CUREE Test protocol for parallel to the grain test (© 2014 Johannes Schneider, by permission)  Figure 22: Cyclic displacement schedule CUREE test protocol for perpendicular to the grain test (© 2014 Johannes Schneider, by permission) Cyclic loading analyses were carried out using OpenSees along both parallel and perpendicular to the outer layer grain direction for all three Connections: A, B, and C.   48 3.3.1 Hysteretic model calibration of connection A As defined in an earlier section, Connection-A consisted of a SIMPSON Strong-Tie connector (90483.016) with 18 spiral nails (16d3 ½). Shen et al. (2013) reported the loss of contact between the brackets and CLT element as deformation accumulates. The results obtained by OpenSees and experimental data are compared in Figure 23 and Figure 24 for tests along parallel and perpendicular loading directions, respectively.  Figure 23: Comparison of experimental and OpenSees pinching4 material model for Connection A in parallel to the grain direction Figure 23 shows a good agreement between the experimental and OpenSees analysis result. In general, the hysteretic envelope from OpenSees analysis is slightly larger than the experimental results. Moreover, better agreement is observed in the reloading stiffness at the initial loading stages. Figure 24 shows the comparison of responses for tests along perpendicular to the grain direction. As can be seen in Figure 24 there is better agreement in the negative backbone region than the positive loading region. For both test directions, Figure 23 and Figure 24 revealed that the OpenSees Pinching4 material model predicts the pinching part very well.  -20-1001020304050600 10 20 30 40 50 60Load (kN)Deflection (mm)OpenSees (Pinching4)Experimental  49  Figure 24: Comparison of experimental and OpenSees pinching4 material model for Connection A in perpendicular to the grain direction 3.3.2 Hysteretic model calibration of connection B Connection B consists of a SIMPSON Strong-Tie connector (90483.016) with 18 screws (590mm). The OpenSees results and experimental data are compared in Figure 25 and Figure 26 for tests along parallel and perpendicular loading directions, respectively. Figure 25 shows better agreement in the initial loading stiffness. However, the failure displacement of the experiment was shown to be larger than the Pinching4 model prediction. -80-60-40-200204060-80 -60 -40 -20 0 20 40 60 80Load (kN)Deflection (mm)ExperimentalOpenSees(Pinching4)  50  Figure 25: Comparison of experimental and OpenSees pinching4 material model for Connection B in parallel to the grain direction  Figure 26: Comparison of experimental and OpenSees pinching4 material model for Connection B in perpendicular to the grain direction -30-20-1001020304050600 5 10 15 20 25 30 35 40 45Load (kN)Deflection (mm)ExperimentalOpenSees (Pinching4)-80-60-40-200204060-80 -60 -40 -20 0 20 40 60 80Load (kN)Deflection (mm)OpenSees (Pinching4)Experiment  51 3.3.3 Hysteretic model calibration of connection C Connection C consisted of a SIMPSON Strong-Tie connector (90483.016) with 9 screws (470mm). The obtained OpenSees results and experimental data are compared in Figures 27 and 28 for tests along parallel and perpendicular loading directions, respectively. As can be seen in Figure 27, better agreement in the initial loading stiffness is obtained. However, the failure displacement obtained from the analysis is slightly larger than the one obtained from the experiment.  Figure 27: Comparison of experimental and OpenSees pinching4 material model for Connection C (parallel to the grain direction) Figure 27 shows better agreement in the negative backbone region than the positive loading region. Furthermore, for both test directions, Figure 27 and Figure 28 revealed that the OpenSees Pinching4 material model predicts the pinching part very well.  -20-1001020304050600 5 10 15 20 25 30 35 40 45Load (kN)Deflection (mm)ExperimentOpenSees (Pinching4)  52  Figure 28: Comparison of experimental and OpenSees pinching4 material model for Connection C (perpendicular to the grain direction) The final calibrated hysteretic curve parameters for all connection types are summarized in Table 2. At this point it is important to note that these parameters of the Pinching4 material model were used to model the nonlinearity and cyclic behaviour of the connection brackets that were used to perform seismic and collapse simulations of the CLT infilled SMRFs.   -60-40-200204060-80 -60 -40 -20 0 20 40 60 80Load (kN)Deflection (mm)OpenSees (Pinching4)Experiment  53 Table 2: Calibrated Pinching4 model parameters Connection type Connection-A Connection-B Connection-C Direction Parameters Parallel to grain Perpendicular to grain Parallel to grain Perpendicular to grain Parallel to grain Perpendicular to grain Positive backbone ePf1 [kN] 20 18.68 21 20.5 24 13 ePf2 [kN] 46 35.6 42 40.2 40 48.1 ePf3 [kN] 50 48 51 50.4 49 39.8 ePf4 [kN] 7 17.1 18.7 30.6 24 12.91 ePd1 [mm] 2.15 4 3.23 4.9 4 3.1 ePd2 [mm] 9 9.8 11 15 11 23.2 ePd3 [mm] 20 24 17 26 19.1 34.3 ePd4 [mm] 60 70 54 49 35 45.1 Negative backbone eNf1 [kN] -20 -18.68 -21 -20.5 -24 -13 eNf2 [kN] -46 -35.6 -42 -40.2 -40 -48.1 eNf3 [kN] -50 -48 -51 -50.4 -49 -39.8 eNf4 [kN] -7 -17.1 -18.7 -30.6 -24 -12.91 eNd1 [mm] -2.15 -4 -3.23 -4.9 4 -3.1 eNd2 [mm] -9 -9.8 -11 -15 -11 -23.2 eNd3 [mm] -20 -24 -17 -26 -19.1 -34.3 eNd4 [mm] -60 -70 -54 -49 -35 -45.1 pinching rDispP 0.55 0.5 0.65 0.5 0.72 0.6 fForceP 0.15 0.3 0.15 0.25 0.18 0.25 uForceP 0.03 0.05 0.02 0.05 0.02 0.05 rDispN 0.55 0.5 0.65 0.5 0.72 0.6 fForceN 0.15 0.3 0.15 0.25 0.18 0.25 uForceN 0.03 0.05 0.02 0.05 0.02 0.05 Unloading stiffness degradation gK1 0 0 0 0 0 0 gK2 0 0 0 0 0 0 gK3 0 0 0 0 0 0 gK4 0 0 0 0 0 0 gKLim 0 0 0 0 0 0 Reloading stiffness degradation gD1 0.97 0.95 0.97 0.97 0.97 0.95 gD2 0 0 0 0 0 0 gD3 0 0 0 0 0 0 gD4 0 0 0 0 0 0 gDLim 0.05 0.1 0.08 0.1 0.03 0.1 Strength degradation gF1 0 0 0 0 0 0 gF2 0 0 0 0 0 0 gF3 0 0 0 0 0 0 gF4 0 0 0 0 0 0 gFLim 0 0 0 0 0 0 Energy degradation gE 1 1 1 1 1 1     54 Chapter 4 Parametric Study on the Lateral Behaviour of Single-Storey CLT-SMRFs Bezabeh et al. (2015) studied the energy dissipative capacity of a single-bay single-storey CLT infilled SMRF. The authors performed a parametric study, by varying the modeling variables of the hybrid structure summarized in Table 3. A total of 243 combination of modeling variables were considered for the parametric study. Both static pushover and quasi-static cyclic loading analyses were performed. Results of the static pushover analyses were used to calculate the yield and ultimate displacement of the hybrid system. The results are discussed in the following subsections. Table 3: Modeling variables (Bezabeh et al. 2015) A: Bracket Spacing (m) B: Gap (mm) Ct: Panel Thickness (mm) D: Panel Strength (MPa) E: Post Yield Stiffness (%)  0.4 20 99 17.5 1 0.8 50 169 25 3 1.6 80 239 37.5 5  4.1 Response sensitivity to bracket spacing Figure 29 shows the variation of capacity curves with bracket spacing. The analyses were performed by keeping a constant gap of 20 mm, CLT panel thickness of 90 mm, and CLT crushing strength of 17.5 MPa. It is evident from Figure 29 that the initial stiffness was the same for all models. At approximately 50 mm of deflection, an increase in stiffness was observed for models with a bracket spacing of 0.4m. Moreover, the ultimate strength decreased as the bracket spacing was increased.    55  Figure 29: Variation of capacity curves with bracket spacing  Figure 30: Cyclic response sensitivity to bracket spacing 050010001500200025000 0.1 0.2 0.3Load (kN)Deflection (m)Bracket spacing = 0.4Bracket spacing = 0.8Bracket spacing = 1.6-2500-2000-1500-1000-50005001000150020002500-0.3 -0.2 -0.1 0 0.1 0.2 0.3Load (kN)Deflection (m)Bracket_spacing = 0.4Bracket_spacing = 0.8Bracket_spacing = 1.6  56 The cyclic response sensitivity to bracket spacing is depicted in Figure 30. The comparison of cyclic response revealed that stable hysteresis loops were obtained for models with lower bracket spacing. However, a slight increase in pinching was observed for models with a bracket spacing of 0.4 m. Comparatively, models with a bracket spacing of 0.8 m yielded a relatively stable hysteresis loops with acceptable pinching behaviour. 4.2 Response sensitivity to gap The effect of confinement gap was studied parametrically by keeping a constant panel thickness of 99 mm, CLT crushing strength of 17.5 MPa, and connection bracket spacing of 0.8 m. The results of the monotonic pushover analyses are depicted in Figure 31. Significant variation in stiffness was observed at a deflection of 75 mm (the point where the CLT starts to share the load). The post-yielding behaviour of these models is quite different as can be seen in Figure 31. Models with a gap magnitude of 80mm showed unstable response after yielding occurred. The ultimate strength of the system was higher for models with a smaller gap. Comparatively, a model with 20mm of gap has the desired stable capacity curve. Figure 32 shows the cyclic response sensitivity to the magnitude of provided gap. Models with a 20mm and 50mm gap were characterized by a high degree of pinching. Fat hysteresis loops occurred for models with a gap of 80mm. This showed that the energy dissipation increases with the gap size. However, due to its higher loading capacity and stable hysteresis loops, a 20mm gap was suggested to model the multi-storey hybrid structure.    57  Figure 31: Variation of capacity curves with provided gap  Figure 32: Cyclic response sensitivity to gap -2000-1500-1000-5000500100015002000-0.3 -0.2 -0.1 0 0.1 0.2 0.3Load (kN)Deflection (m)Gap =20mmGap = 50 mmGap = 80 mm  58 Chapter 5 Overview of Seismic Force Modification Factors The Canadian national building design code (NBCC) has evolved through time learning from the devastating earthquakes from around the world (Rainer and Northwood 1979; Heidebrecht 2003). The evolution of design base shear (V) in the NBCC is summarized in Table 4. Discussion and rationality of each design change provision shown in Table 4 are discussed by various researchers: Uzumeri et al. (1978) have described the developments of the 1941 to 1970 NBCC seismic loading provisions; Heidebrecht and Tso (1985) discussed changes in the 1985 NBCC; Tso (1992) discussed changes in the 1990 NBCC; Heidebrecht (2003) discussed changes in the 2005 NBCC and Mitchell et al. (2010) discussed the changes in 2010 NBCC. For each design code, the calculated base shear coefficient (V/W) for Vancouver is shown in Figure 33. Figure 33 shows that with the introduction of each design code, the V/W ratio has changed.  The Canadian, U.S., and European design codes utilize linear methods of analysis. However, the seismic-force-resisting systems, if detailed properly, respond in the nonlinear range. The maximum elastic base shear VE, without consideration of nonlinearity, is obtained from the response spectra (e.g. Figure 33). Subsequently, the required design loads V are obtained by modifying the VE with seismic modification factors (denoted differently various codes: R factors in the US code; q factors in in European code; a product of ductility (Rd) and overstrength (Ro) factors in the Canadian code). This chapter provides an overview of these factors. In Chapter 7, the Rd and Ro factors for the hybrid building are derived.   59 Table 4: Evolution of Canadian design code Year Base shear formula Comments NBC 1941  NBC = National Building Code; Incorporated in an appendix and were based on concepts presented in the 1937 U.S. Uniform Building Code (UBC); C varied from 0.02 to 0.05. NBC 1953 F = CW Incorporated into the main text of 1953 NBC; Inclusion of Canadian seismic zoning map; and Recognition of the influence of building flexibility; F = seismic design force; W = total weight (dead load + 25% of the design snow load); C = horizontal force factor for minimum earthquake load; Zone 1: C = 0.15/(N+4.5); Zone 2: C = 0.30/(N+4.5); Zone 2: C = 0.60/(N+4.5) NBC 1965 V = RCIFSW R = seismic regionalizing factor (values are 0, 1, 2, and 4 for earthquake intensity zones 0, 1, 2, and 3, respectively); C = type of construction factor (=0.75 for moment resisting space frame; = 1.25 for non-ductile structures); I = importance factor (1 or 1.3); F = foundation factor;; S = structural flexibility factor = 0.25/(N+9); W = total weight (dead load + 25% of the design snow load + design live load for storage area) NBC 1970 F = ¼R(KCIFW) Seismic zoning map is revised; R, I, F, and W same as NBC 1965; K = type of construction factor (values range from 0.67 to 1.33 for buildings); C = structural flexibility factor = 0.05/T1/3 < 0.10; T = fundamental period of the structure (0.05hn/D1/2 or 0.10N); hn = height of the structure in feet; D = dimension of the building in direction parallel to seismic force in feet; N = number of stories NBC 1975 V = ASKIFW I, F, and W same as NBC 1965; A = assigned horizontal design ground acceleration; S = seismic response factor (0.5/T1/3 < 1); K = numerical coefficient reflecting the influence of the type of construction on the damping, ductility, and (or) energy-absorption capacity of the structures (values range from 0.7 to 2 for buildings) NBCC 1980 V = ASKIFW  NBCC 1985 V = vSKIFW New methodology in the calculation of seismic risk; A change in the probability level at which risk is computed; Use of both the PGA and PGV as ground motion parameter to represent the intensity of shaking; An increase in the number of seismic zones in Canada; K, I, F, and W same as NBC 1980; v = zonal velocity ratio; S = new seismic response factor depending on the periods of the structure NBCC 1990 UReV90V   U = 0.6, calibration factor; R = force modification factor (Range from  1 to 4) NBCC 1995 UReVV   vSIFWeV   U = 0.6, calibration factor; R = force modification factor (Range from  1 to 4);  VE= Elastic lateral seismic force; v = zonal velocity ratio, ; S = seismic response factor, I = importance factor (1, 1.3, 1.5); F = foundation on site factor; W = dead load NBCC 2005 oRdRWEIvM)aT(SV   EI  = importance factor (1, 1.3, 1.5); oRdR : 1< dR <5 and 1< oR <1.7 NBCC 2010 oRdRWEIvM)aT(SV   EI  = importance factor (1, 1.3, 1.5); oRdR : 1< dR <5 and 1< oR <1.7    60  Figure 33: Evolution of base shear coefficients for the National Building Code of Canada, example for Vancouver, BC 5.1 Site seismic hazard Evolution of the seismic design code also entails the changes in the seismic hazard considered. The first attempt at the seismic hazard quantification in Japan and North America followed the 1923 Kanto (Tokyo) earthquake and 1933 Long Beach California earthquake (Atkinson 2004; Otani 2004). Initially, the earthquake hazard quantification was introduced through the introduction of seismic coefficients. The evolution of seismic hazard provisions in the national building code (NBC) and national building code of Canada (NBCC) is summarized in Table 4. In 1945, seismic coefficients were varied between 0.02 and 0.05 and were included as an appendix. Subsequently, in the 1953 NBC, the seismic hazard zone was introduced. However, these zones were introduced on a qualitative basis (Atkinson 2004). In the late 1960s, the probabilistic quantification of hazard gained in popularity, and for the first time, seismic hazard 0.000.020.040.060.080.100.120.140.160 1 2 3Base shear coefficient (V/W)Period, T (sec)NBC 1953NBC 1965NBC 1970NBC 1975/77NBCC 1985NBCC 1990NBCC 2005NBCC 2010  61 was evaluated probabilistically. To date, the state of knowledge has improved and more advanced probabilistic methods are used for modern design codes and engineering design purposes. These new hazard factors calibrate the newer code to a previous version (Atkinson 2004). In the 1985, 1990, and 1995 NBCC, zonal velocity ratios were introduced, whereas in the 2005 NBCC, uniform hazard spectrum (UHS) was introduced. In this paper, the UHS is used as a basis for quantifying site seismic hazard, as used in the NBCC 2005. The derivation of the UHS for Canadian cities is beyond the scope of this report, and a thorough treatise is provided in Adams and Atkinson (2003) and Atkinson (2004).  5.2 Evolution of ductility (Rd) and overstrength (Ro) in the Canadian building design code The first edition of the NBCC was published in 1941 and included provisions for seismic design based on the Uniform Building Code (UBC 1935). The 1965 code introduced the first seismic modification factor C (shown in Equation 5), as the construction factor in the calculation of the minimum seismic base shear (NRC 1965). RCIFSWV   [5] where R = the seismic regionalization factor; C = construction factor; I = importance factor; F = foundation factor; S = flexibility factor; and W = the summation of dead load, live load and 25% of the snow load. The construction factor varied based on the predicted ductile behaviour of the system. Moment resisting frames and reinforced concrete shear walls had a construction factor of 0.75 while other buildings had a factor of 1.25. In 1970 the seismic code was changed to include a construction factor (K) and structural flexibility factor (C) as shown in Equation 6 (NRC 1970). )(41KCIFWRV   [6] The structural flexibility factor was dependent on the fundamental period (T), height of the structure (hn), dimension of the building parallel to the seismic force (D) and the number of   62 storeys (N). The construction factors can be seen in Table 5 for various structural systems and their respective ductility. In 1975 the NBCC introduced limit states design allowing designers to work with load factors and material resistance factors rather than the factors of safety associated with the working stress design. Designers were also allowed to use dynamic analysis in determining the seismic design forces (Mitchell et al. 2010). Table 6 shows the structural ductility factor µ for dynamic analysis of seismic design forces. Table 5: Summary of K factors representing type of construction, damping, ductility and energy absorption (Mitchell et al. 2010) Resisting Elements K (1970) K (1975 to 1985) Ductile moment-resisting space frame resisting 100% of required force 0.67 0.7 Dual system of ductile moment-resisting space frame and ductile flexural walls (frame must be designed to resist at least 25% of total base shear) 0.8 0.7 Dual system of ductile moment-resisting space frame and shear walls or steel bracing (frame must be designed to resist at least 25% of total base shear and walls or bracing must be designed to resist 100% of base shear)  0.8 Other framing systems not defined above 1.0  Ductile flexural walls and ductile framing systems not defined above  1.0 Systems without space frames (box systems) 1.33  Dual system with ductile space frame with masonry infill (infilled wall system must be designed to resist 100% of base shear and frame; without infill, must be designed to resist at least 25% of total base shear)  1.3 Systems not defined above with continuous reinforced concrete, structural steel, or reinforced masonry shear walls  1.3 Other structural systems not defined above 2.0 2.0 Unreinforced masonry  2.0  Table 6: Structural ductility factor µ for dynamic analysis (Commentary K, 1975 NRC) Building type μ Ductile moment resisting space frame 4 Combined system of 25% ductile moment resisting space frame and ductile flexural walls 3 Ductile reinforced concrete flexural walls 3 Regular reinforced concrete structures, cross-braced frame structures and reinforced masonry 2 Structures having no ductility, plain masonry 1    63 In 1990 the NBCC replaced the construction factors with the force modification factor R. Along with this change came the introduction of the calibration factor U. Equation 7 displays these factors in the 1990 NBCC (NRC, 1990) calculation of the minimum seismic base shear. RvSIFWUV)(  [7] The calibration factor of U = 0.6 aimed at providing base shears similar to those calculated in previous codes to be consistent with the force modification factors previously used. The new force modification factor “reflects the capability of a structure to dissipate energy through inelastic behaviour” (NRC, 1990). Representing the ductile behaviour of structural systems the factor ranged from 1.0 to 4.0. Unreinforced masonry buildings had an R factor of 1.0; nominally ductile walls, concrete frames and braced steel frames had an R factor of 2.0; and ductile moment-resisting space frames had an R factor of 4.0.  In 1995 force modification factors were updated for several structural systems. Table 7 lists these factors for the relating lateral load resisting reinforced concrete systems. The table shows the design requirements for reinforced concrete structures complying with CSA standards.   64 Table 7: R factors for different reinforced concrete structural systems (NRC 1995) Cases in NBC R Type of Lateral Load Resisting System Summary of Design and Detailing Requirements in CSA Standard A23.3 with Applicable Clauses in Brackets 10 4.0 ductile moment-resisting frame (a) beams capable of significant flexural hinging (21.3 and 21.7); (b) columns properly confined and stronger than the beams (21.4 and 21.7) (c) joints properly confined and capable of transmitting shears from beam hinging (21.6) 11 4.0 ductile coupled wall (a) at least 66% of base overturning moment resisted by wall must be carried by axial tension and compression in coupled wall resulting from shears in coupling beams; (b) wall strength to permit nominal strength of coupling beams to be achieved (21.5.8); (c) ductile coupling beams capable of developing flexural hinging or provide specially detailed diagonal reinforcement (21.5.8) 12 3.5 ductile flexural wall (a) wall capable of significant flexural hinging without local instability and without shear failure (21.5 and 21.7) 12 3.5 ductile partially coupled wall (a) wall strength to permit nominal strength of coupling beams to be achieved (21.5.8); (b) ductile coupling beams capable of developing flexural hinging or provide specially detailed diagonal reinforcement (21.5.8) 13 2.0 moment-resisting frame with nominal ductility (a) beams and columns must satisfy nominal detailing requirements (21.9.2.1-2); (b) beams and columns must have minimum shear strength (21.9.2.3); (c) joints must satisfy nominal detailing requirements and must be capable of transmitting shears from beam hinging (21.9.2.4) 14 2.0 wall with nominal ductility (a) walls must satisfy dimensional limitations and minimum detailing requirements (21.9.3.1-3); (b) walls must have minimum shear strength (21.9.3.4) 15 1.5 other lateral-force-resisting systems not defined above (a) beams and columns (10); (b) joints (7.7.3 and 11.8); (c) walls (10 or 14)  The most significant change to seismic force modification factors came in the 2005 edition of the NBCC (NRC 2005). The code completely revised the base shear equation as: odEvaRRWIMTSV)(  [8] where S(Ta) = design spectral response acceleration taken at the fundamental period Ta; Mv=accounts for higher mode effects on the base shear; IE = importance factor; W=weight of the structure; Rd = ductility factor; and Ro = overstrength factor. The ductility factor Rd is similar to the force modification factor R (provided in the 1995 NBCC) accounting for the ability of a structure to dissipate energy through inelastic behaviour. However, the overstrength factor is new to the seismic design procedure, accounting for the reserve strength in a structure due to several factors including: the actual strength of material, confinement effects, contribution of   65 nonstructural elements and actual participation of some elements (Elnashai and Mwafy 2002). A minimum base shear was also introduced in the 2005 edition of the NBCC as: odEvRRWIMSV)0.2(  [9] where a V less than this limiting values indicates the case where the structure required insignificant lateral restraint. Seismic force resisting structures with a ductility factor greater than 1.5 (Rd > 1.5) were not required to exceed the base shear provided in Equation 10 (NRC 2005). odERRWISV)2.0(32  [10] The maximum base shear ensured that ductile structures were not over designed based on the proposed location of said structure. Ductility and overstrength factors were quantified for steel, concrete and timber structures as seen in Table 8. Included in the ductility and overstrength table is the height restriction on each structural system.   66 Table 8: Force modification factors Rd and Ro for seismic force-resisting systems (NRC 2005)    Restrictions          IEFaSa(0.2)      Type of SFRS Rd Ro <0.20 ≥0.20 to <0.35 ≥0.35 to ≤0.75 >0.75 IEFVSa(1.0) > 0.30 Steel structures designed and detailed according to CSA standard CSA-S16-01   Ductile moment-resisting frames 5.0 1.5 NL NL NL NL NL Moderately ductile moment-resisting frames 3.5 1.5 NL NL NL NL NL Limited-ductility moment-resisting frames 2.0 1.3 NL NL 60 NP NP Moderately ductile concentrically braced           frames           Tension-compression bracing 3.0 1.3 NL NL 40 40 40    Tension-only bracing 3.0 1.3 NL NL 20 20 20 Limited-ductility concentrically braced frames           Tension-compression bracing 2.0 1.3 NL NL 60 60 60    Tension-only bracing 2.0 1.3 NL NL 60 60 60    Chevron bracing 2.0 1.3 NL NL 40 40 40 Ductile eccentrically braced frames 4.0 1.5 NL NL NL NL NL Ductile plate walls 5.0 1.6 NL NL NL NL NL Moderately ductile plate walls 2.0 1.5 NL NL 60 60 60 Conventional construction 1.5 1.3 NL NL 15 15 15 Other steel SFRS(s) not defined previously 1.0 1.0 15 15 NP NP NP Concrete structures designed and detailed according to CSA standard CSA-A23.3-94 (2004 edition under preparation) Ductile moment-resisting frames 4.0 1.7 NL NL NL NL NL Moderately ductile moment-resisting frames 2.5 1.4 NL NL 60 40 40 Ductile coupled walls 4.0 1.7 NL NL NL NL NL Ductile partially coupled walls 3.5 1.7 NL NL NL NL NL Ductile shear walls 3.5 1.6 NL NL NL NL NL Moderately ductile shear walls 2.0 1.4 NL NL NL 60 60 Conventional construction           Moment-resisting frames 1.5 1.3 NL NL 15 NP NP    Shear walls 1.5 1.3 NL NL 40 30 30 Other concrete SFRS(s) not listed previously 1.0 1.0 15 15 NP NP NP Timber structures designed and detailed according to CSA standard CSA-O86-01   Shear walls           Nailed shear walls with wood-based panels 3.0 1.7 NL NL 30 20 20    Shear walls with wood-based and gypsum            2.0 1.7 NL NL 20 20 20       panels in combination        Braced or moment-resisting frames with           Ductile connections           Moderately ductile frames 2.0 1.5 NL NL 20 20 20    Limited-ductility frames 1.5 1.5 NL NL 15 15 15 Other wood- or gypsum-based SFRS(s) not  1.0 1.0 15 15 NP NP NP    listed previously                 67 The 2010 National Building Code of Canada saw few changes to the force modification factors as the base shear equation remained unchanged. However, there were a few seismic force-resisting steel systems added with respect to their force modification factors. Table 9 shows the updated steel seismic modification factors. Table 9: Seismic force modification factors for steel seismic force-resisting systems  (NRC 2010) Type of SFRS Rd Ro Restrictions Cases Where IEFaSa(0.2) Cases Where IEFVSa(1.0) <0.20 ≥0.20 to <0.35 ≥0.35 to ≤0.75 >0.75 >0.3 Steel Structures Designed and Detailed According to CSA S16 Ductile moment-resisting frames 5.0 1.5 NL NL NL NL NL Moderately ductile moment-resisting frames 3.5 1.5 NL NL NL NL NL Limited ductility moment-resisting frames 2.0 1.3 NL NL 60 30 30 Moderately ductile concentrically braced frames                 Tension-compression braces 3.0 1.3 NL NL 40 40 40    Tension only braces 3.0 1.3 NL NL 20 20 20 Limited ductility concentrically braced frames                 Tension-compression braces 2.0 1.3 NL NL 60 60 60    Tension only braces 2.0 1.3 NL NL 40 40 40 Ductile buckling-restrained braced frames 4.0 1.2 NL NL 40 40 40 Ductile eccentrically braced frames 4.0 1.5 NL NL NL NL NL Ductile plate walls 5.0 1.6 NL NL NL NL NL Limited ductility plate walls 2.0 1.5 NL NL 60 60 60 Conventional construction of moment-resisting frames, braced frames or plate walls                 Assembly occupancies 1.5 1.3 NL NL 15 15 15    Other occupancies 1.5 1.3 NL NL 60 40 40 Other steel SFRS(s) not defined above 1.0 1.0 15 15 NP NP NP  The current 2010 NBCC enables the designer to design the lateral force-resisting system efficiently based on the location, soil type, importance factor and type of structure. The problem arises when a designer is tasked with designing a structure using two material types (hybrid structure). In the case of hybrid structures the designer must then conduct dynamic analyses to   68 determine the resulting overstrength and ductility values or take the more conservative value and potentially overdesign the structure. 5.2.1 Overstrength factor (Ro) The overstrength factor (Ro) can be calculated by taking a ratio of the ultimate shear capacity to the yield shear capacity. The ultimate shear capacity and yield shear capacity are obtained through pushover analysis or dynamic analyses (to collapse). The results of the analysis show that the structure requires greater load to reach the actual yield point of the system as shown in Figure 34.  Figure 34: Stages in the response of a frame structure (Mitchell et al. 2003) The greater yield load is due to the overstrength in the structure as the members are typically greater than required for the design yield stress (Mitchell et al. 2003). Factors that contribute to the overstrength of the structure are summarized in Table 10.   69 Table 10: Sources of structure overstrength (Park 1996) Factors that contribute to structural overstrength factor Steel and concrete strengths greater than specified. Use of strength reduction factors or material factors in design. Section sizes larger than assumed. Effects of member deformations at large displacements. Additional reinforcement placed for construction purposes or to satisfy minimum reinforcement requirements or to satisfy available bar sizes, and unaccounted for in the design calculations. More critical loading cases for the design of some sections for gravity or wind loads. Moment redistribution after yielding greater than assumed in design. Participation of non-structural elements. Overestimation of structural stiffness leading to high design seismic forces.  Mitchell et al. (2003) formulated an equation for overstrength based on five factors as: mechshyieldsizeo RRRRRR   [11] where the Rsize = size factor, accounting for the overstrength due to rounding and limited member sizes; Rϕ = the material resistance factor, accounting for the difference between nominal and factored resistances; Ryield = the yield factor, accounting for the actual yield strength of the structure in comparison to the specified minimum yield strength; Rsh = the strain hardening factor, accounting for the overstrength due to strain hardening in a structure; and Rmech = the mechanical factor, accounting for the full capacity of the structure mobilizing to form a collapse mechanism (Mitchell et al. 2003). Table 11, Table 12, and Table 13 summarize the derivation of the overstrength factor for steel, concrete and timber structures, respectively. Table 11: Derivation of overstrength modification factor for steel seismic force resisting systems (Mitchell et al. 2003)   Calculation of Ro Type of SFRS Rsize Rɸ Ryield Rsh Rmech Ro NBCC Ro Ductile moment-resisting frames 1.05 1.11 1.10 1.15 1.00 1.47 1.5 Moderately ductile moment-resisting frames 1.05 1.11 1.10 1.15 1.00 1.47 1.5 Limited-ductility moment-resisting frames 1.05 1.11 1.10 1.05 1.00 1.35 1.3 Moderately ductile concentrically braced frames 1.05 1.11 1.10 0.05 1.00 1.35 1.3 Limited-ductility concentrically braced frames 1.05 1.11 1.10 1.05 1.00 1.35 1.3 Ductile eccentrically braced frames 1.05 1.11 1.10 1.15 1.00 1.47 1.5 Ductile plate walls 1.10 1.11 1.10 1.10 1.10 1.63 1.6 Limited-ductility plate walls 1.10 1.11 1.10 1.05 1.05 1.48 1.5 Conventional construction 1.05 1.11 1.10 1.00 1.00 1.28 1.3    70 Table 12: Derivation of overstrength modification factor for concrete seismic force resisting systems (Mitchell et al. 2003)   Calculation of Ro Type of SFRS Rsize Rɸ Ryield Rsh Rmech Ro NBCC Ro Ductile moment-resisting frames 1.05 1.18 1.05 1.25 1.05 1.71 1.7 Moderately ductile moment-resisting frames 1.05 1.18 1.05 1.10 1.00 1.43 1.4 Moment-resisting frames with conventional 1.05 1.18 1.05 1.00 1.00 1.30 1.3    construction        Ductile coupled walls 1.05 1.18 1.05 1.25 1.05 1.71 1.7 Ductile partially coupled walls 1.05 1.18 1.05 1.25 1.05 1.71 1.7 Ductile shear walls 1.05 1.18 1.05 1.25 1.00 1.63 1.6 Moderately ductile shear walls 1.05 1.18 1.05 1.10 1.00 1.43 1.4 Shear walls with conventional construction 1.05 1.18 1.05 1.00 1.00 1.30 1.3  Table 13: Derivation of overstrength modification factor for timber seismic force resisting systems (Mitchell et al. 2003)   Calculation of Ro Type of SFRS Rsize Rɸ Ryield Rsh Rmech Ro NBCC Ro Nailed shear walls with wood-based panel 1.15 1.43 1.00 1.05 1.00 1.73 1.7 Shear walls with wood-based and gypsum panels in combination 1.15 1.43 1.00 1.05 1.00 1.73 1.7 Moderately ductile braced or moment-resisting frames 1.05 1.43 1.00 1.00 1.00 1.50 1.5 Limited-ductility braced or moment-resisting frames 1.05 1.43 1.00 1.00 1.00 1.50 1.5  5.3 Seismic modification factors in the European code The European seismic design code (Eurocode 8) has a different approach to seismic force modification factors. Eurocode 8 outlines behaviour factors for concrete, steel, concrete-steel composite and timber structures. Detailing of each structure is to be completed through the procedures outlined in the code with the pertaining behaviour factor. The design base shear is formulated based on many factors and varies with period:  mTqTSaFcgb5.2 [12]   71 where Fb = the base shear; ag = design ground acceleration; S = soil factor; Tc = upper limit of period; q = behaviour factor; T = vibration period of linear single degree of freedom system; m = mass of the structure; and λ = factor based on the period and height of a structure. For steel moment resisting frames the Eurocode 8 defines the behaviour factor as: 51yuq [13] The first term in the formulation of q represents the ratio in a pushover analysis of the multiplier of the seismic forces at ultimate capacity to the multiplier at first yield (Sanchez-Ricart 2010). This ratio is known as the plastic redistribution parameter and is given a value of 1.25 if no plastic analysis is performed by the designer. If a plastic analysis is performed the maximum value is limited to 1.6. The second term in the equation represents the behaviour factor for the lateral force resisting system. In this equation that value is 5 for moment resisting steel frames. The other lateral force resisting systems behaviour factors for steel structures is summarized in Table 14. Table 14: Behaviour factors for steel systems regular in elevation (CEN 2002) Structural Type Ductility Class DCM DCH a) Moment resisting frames 4 5αu/α1 b) Frame with concentric bracings 4 4       Diagonal bracings       V-bracings 2 2,5 c) Frame with eccentric bracings 4 5αu/α1 d) Inverted pendulum 2 2αu/α1 e) Structures with concrete cores or concrete walls See section 5 f) Moment resisting frame with concentric bracing 4 4αu/α1 g) Moment resisting frames with infills 2 2      Unconnected concrete or masonry infills, in contact with the frame      Connected reinforced concrete infills See section 7      Infills isolated from moment frame (see moment frames)  4 5αu/α1    72 Unlike the NBCC, there is only one behaviour factor in the Eurocode 8. There is no specific overstrength or ductility factor contributing to the minimum base shear. However, the behaviour factor includes provisions for both ductility as well as overstrength. Sanchez-Ricart and Plumier (2008) show that the reduction factor of 6 for highly ductile MRSF cannot be justified without the consideration of structural overstrength. Therefore, it can be observed that the behaviour factors from the Eurocode 8 are quite similar to the values obtained in the NBCC from the product of the overstrength (Ro) and ductility (Rd) factors. 5.4 Seismic modification factors in the United States code The main building code in the US is the International Building Code (IBC). In addition there are other provisions that help seismic design engineers such as NEHRP and the Applied Technology Council (ATC). The seismic force modification factors are examined in ATC 19 and ATC 34 where it was observed that there have been no changes to the factors since the 1950s’ (ATC 19, 1995). Therefore, the modification factors, like in other parts in the world, have no mathematical basis in current American seismic codes and therefore cannot be justified (Sanchez-Ricart 2010). The development of the modification factor R is currently based on the engineering judgments made on observations from past earthquakes. Using the IBC code the base shear can be computed through the ASCE 7-10 as: WIRSVEDS/  [14] where V is the design base shear; SDS is the seismic design parameter; IE is the importance factor; Ris themodification factor accounting for inherent overstrength and global ductility capacity (Table 15); and W is the total seismic dead load acting on the structure. Similar to Eurocode 8, the ASCE 7-10 uses just one seismic modification factor that accounts for both overstrength and ductility in the base shear calculation. Values in Table 15 for R may seem high however; when considering other factors in the base shear equation the results are similar to the NBCC and Eurocode values.    73 Table 15: Seismic design factors and coefficients from the ASCE 7-10 (ASCE 2010) Seismic force-resisting system Response modification coefficient R Overstrength factor Ωo Deflection amplifica-tion factor Cd Structural system limitations including structural height, hn (m), limits (1)  Seismic Design Category B C D E F A. BEARING WALL SYSTEMS                 1. Special reinforced concrete shear walls 5 2 1/2 5 NL NL 48.8 48.8 30.5 2. Ordinary reinforced concrete shear walls 4 2 1/2 4 NL NL NP NP NP …             7. Special reinforced masonry shear walls 5 2 1/2 3 1/2 NL NL 48.8 48.8 30.5 …             B. BUILDING FRAME SYSTEMS                 1. Steel eccentrically braced frames 8 2 4 NL NL 48.8 48.8 30.5 2. Steel special concentrically braced frames 6 2 5 NL NL 48.8 48.8 30.5 3. Steel ordinary concentrically braced frames 3 1/4 2 3 1/4 NL NL 10.7 10.7 NP 4. Special reinforced concrete shear walls 6 2 1/2 5 NL NL 48.8 48.8 30.5 5. Ordinary reinforced concrete shear walls 5 2 1/2 4 1/2 NL NL NP NP NL …             16. Special reinforced masonry shear walls 5 1/2 2 1/2 4 NL NL 48.8 48.8 30.5 …             20. Ordinary reinforced masonry shear walls 2 2 1/2 2 NL 48.8 NP NP NP …             22. Light-frame (wood) walls sheathed with wood structural panels rated for shear resistance 7 2 1/2 4 1/2 NL NL 19.8 19.8 19.8 …             C. MOMENT-RESISTING FRAME SYSTEMS                 1. Steel special moment frames 8 3 5 1/2 NL NL NL NL NL 2. Steel special truss moment frames 7 3 5 1/2 NL NL 48.8 30.5 NP 3. Steel intermediate moment frames 4 1/2 3 4 NL NL NP NP NP 4. Steel ordinary moment frames 3 1/2 3 3 NL NL NP NP NP 5. Special reinforced concrete moment frames 8 3 5 1/2 NL NL NL NL NL 6. Intermediate reinforced concrete moment frames 5 3 4 1/2 NL NL NP NP NP 7. Ordinary reinforced concrete moment frames 3 3 3 1/2 NL NL NP NP NP …               74 D. DUAL SYSTEMS WITH SPECIAL MOMENT FRAMES CAPABLE OF RESISTING AT LEAST 25% OF PRESCRIBED SEISMIC FORCES                 1. Steel eccentrically braced frames 8 2 1/2 4 NL NL NL NL NL …                 (1) NP = system is not permitted               NL = system is permitted and not limited in height as an SFRS        The FEMA P695 is one of the most rational and comprehensive means of generating the design parameters. The R factor given in Equation 14 is equivalent in principle to the product of the Rd and Ro factor in NBCC. A recent evaluation of the FEMA P695 by NIST (2012), named Tentative Framework for Development of Advanced Seismic Design Criteria for New Buildings (NIST GCR 12-917-20), have indeed started moving forward from the single R values to the Rd and Ro factors similarly seen in the NBCC. Furthermore, NIST (2012) has shown that these factors are sensitivities to the period of the structure, and period dependent factors are suggested.    75 Chapter 6 Multi-Storey Steel-Timber Archetype Buildings The archetype buildings were selected based on the building type and FEMA’s P695 guidelines (Quantification of Building Seismic Performance Factors FEMA P695 / June 2009). As such, these archetype buildings were not intended to simulate a specific complex building to be used; rather this study was to develop the required engineering design parameters needed for design. Once the overstrength factor, ductility factor and fundamental period of the hybrid building is developed in congruence with the national building code, designers will use these factors to select the appropriate seismic load (for example) and proportion the loads on each floor following the standard design procedures. Details of the archetypical steel moment resisting frame buildings with CLT infill are outlined below. The different variation, e.g., building height, fundamental period of the structure, and seismic design consideration of the steel moment resisting frame will be used to develop different bins for the archetypical buildings (this forms performance group of each building).  Building Height: In this study, a total of seven building heights 3, 6, 9, 12, 15, and 20-storey, steel moment resisting frame buildings were considered (Figure 35) without irregularity in plan (Figure 36).  CLT Infill Configuration: For the different building heights and 3-bay frame, two infill configurations (one interior day and two exterior bays) were considered. Initial preliminary analysis was carried out, and showed the infill in all three bays had no appreciable difference than the two exterior bays infill. The bay widths considered are: 9 m for the exterior bay, and 6 m for the interior bay (Figure 35).  CLT-Steel Connections: Important component of the hybrid CLT-Steel structures are at the CLT-Steel connection details. In this report, appropriate connection models (strength, ductility, hysteretic models, etc.) that are required in analytical models were developed (Chapter 3). The connection model developed for example, can be used with SAP2000 finite element commercial software. With this connection model, designers can use and integrate this model in their routine analysis and design. A bracket spacing of 0.8 m, was considered.   76  Steel Moment Resisting Frame Design and Connections: Seismic Design Category dictates special design and detailing requirements, and subsequently influences component inelastic deformation capacity. As a result, two different design categories (ductile and limited ductility), and where appropriate, different moment connection details (e.g., welded, bolted, or reduced-beam section) were considered. Preliminary analysis showed that, the limited ductility, beyond 9 storey, showed brittle failure. As a result, the design considerations were: ductile structure (for 3, 6, 9, 12, 15, and 20-storey) and limited ductility (for 3, 6, and 9-storey).  Design and Modelling: The 3, 6, 9, 12, 15, and 20-storey archetypical buildings steel moment resisting frame buildings with CLT infill were designed for seismicity and loading conditions of Vancouver, BC. The static pushover analysis was used to derive the overstrength and ductility factors, and validated through non-linear incremental dynamic analysis.   Figure 35: Seven building heights: 1, 3, 6, 9, 12, 15 and 20 storeys The first storey height is 4.5 m and the height of all other storeys above is 3.65 m. The three bay frames considered have bay widths of 9 m for the exterior bay and 6 m for the interior bay. A simplified floor plan is shown in Figure 36. The infill walls consist of cross laminated timber (CLT) members as seen in Figure 37. Important components of the hybrid CLT-Steel structures are at the CLT-Steel connection details. The connection was varied based on the connection type and corresponding spacing.   77  Figure 36: Hybrid structure floor plan  Figure 37: Two infill configurations: one interior bay, two exterior bays and all bays   78 Chapter 7 Overstrength and Ductility Factors using Static Pushover Analysis In this chapter, the overstrength and ductility factors of the index archetype buildings of Chapter 6 are developed following the guidelines of FEMA P695. FEMA P695 prescribes an iterative approach for the derivation of seismic force modification factors of new buildings. This process accounts for the potential uncertainties in ground motions, component design parameters, structural configurations, and behaviour characteristics of structural elements based on available laboratory test data. The remainder of this chapter consisted of the following main tasks:  Discussion of calculations related to ductility Rd and overstrength Ro factors, following FEMA P695 and NBCC approaches.  Design hybrid buildings using assumed response modification factors.  Develop nonlinear hybrid building models in OpenSees.  Quantify and assess the developed nonlinear structural models using static pushover analyses. 7.1 Seismic performance factors of FEMA P695 and NBCC 2005 The National Earthquake Hazards Reduction Program (NEHRP) (FEMA 2004) and NBCC 2005 define seismic performance factors that reduce the elastic design loads of structures to ensure the ability of structures to go under inelastic deformation during a seismic event. Consistent with ASCE/SEI 7-05 and NEHRP recommended provisions, FEMA P695 developed a methodology to quantify response modification factors for new buildings. For a new structure the FEMA P695 (2009) report provides a guideline in the Quantification of Building Seismic Performance Factors, i.e. overstrength factors (denoted as Ω) and ductility factors (denoted as R). These factors are depicted in Figure 38.    79  Figure 38: Illustration of seismic performance factors (R, ΩO, and Cd)  (from FEMA P695) Figure 38 shows a plot of the lateral seismic force vs. lateral displacement curve obtained through static pushover analysis. In Figure 38, VE is the force level that would be developed in the seismic-force-resisting system, if the system remained entirely linearly elastic for design earthquake ground motions; Vmax represents the actual, maximum strength of the fully-yielded system; and V represents seismic base shear required for design. Using Figure 38, the corresponding equations used to derive Ω and R, are:  VVmax  [15] VVR E  [16] The deflection amplification factor (Cd) is given as:   80 RCEd  [17] where E /R is the drift at the design shear force and  is drift value when the system is exposed to the design based earthquake ground motion. Moreover, FEMA P695 defines the period based ductility T, from the Elastic Perfectly Plastic (EPP) approximation of idealized pushover curve as shown in Figure 39, as the ratio of collapse roof displacement u and yielding displacement (y,eff): effyuT,   [18]  Figure 39: Idealized nonlinear static pushover curve (FEMA 2009) Newmark and Hall (1982) developed relationship between the period based ductility (μT) and ductility related force reduction factor (Rμ): 𝑅𝜇 = 1 when T < 0.03 s 𝑅𝜇 =  √2𝜇 − 1 when 0.12 < T < 0.5 s [19]   81 𝑅𝜇 = 𝜇 when T > 1 s The NBCC 2005 splits the R factors of the NEHRP recommendation provisions (NEHRP 1997) into Rd (ductility related force reduction factor) and Ro (Overstrength related force reduction factor). Figure 40 defines these force reduction factors using an idealized pushover curve.   Figure 40: Ductility and force reduction factors of NBCC 2005 (Mitchell et al. 2003) 7.2 Hybrid buildings considered for analysis Following the defined index archetype buildings of Chapter 6, for the current study, different performance groups are developed by varying modeling parameters of the hybrid buildings. For these assessments two levels of Rd factors were used to design the frames. The considered ductility related factors were Rd = 2 and Rd = 4. The adequacy and collapse safety of buildings designed with these factors will be checked in Chapter 10. For Rd =2, the varied parameters for the current study were: building height (3, 6, 9, 12, 15 and 20 storeys), CLT infill configuration (one-bay infilled and two-bays infilled), and ductility class of steel members: Ductile (D) and   82 Limited Ductile (LD) (up to 9 storeys)).  The total combination of the varied parameters constitutes the 18 different buildings of the current study. The Seismic Design Category dictates special design and detailing requirements, and subsequently influences component inelastic deformation capacity. As a result, two different design categories (ductile (D) and limited ductility (LD)) were considered with the appropriate detailing requirements of CSA S16-09. Details of the hybrid buildings designed with Rd = 2 are summarized in Tables 16 to 18. In addition, for Rd = 4, middle bay infilled 3-, 6-, and 9-storey hybrid perimeter frames have been designed. The design checks have been carried out to fulfill the limited ductile requirement.  Table 16: CLT-steel buildings (low-rise) Building No. Storey height Bracket spacing (m) Ductility class Infilled bays 1 3 0.8 D 1 2 2 3 LD 1 4 2  Table 17: CLT-steel buildings (mid-rise) Building No. Storey height Bracket spacing (m) Ductility class Infilled bays 5 6 0.8 D 1 6 2 7 LD 1 8 2 9 9 0.8 D 1 10 2 11 LD 1 12 2  Table 18: CLT-steel buildings (high-rise) Building No. Storey height Bracket spacing (m) Ductility class Infilled bays 13 12 0.8 D 1 14 2 15 15 0.8 D 1 16 2 17 20 0.8 D 1 18 2    83 Each building was designed using the Equivalent Static Procedure of NBCC 2010 by considering a live load of 4.8 kPa for typical office floors and a load of 2.4 kPa elsewhere. Dead loads were considered for floors and roofs as 4.05 kPa and 3.4 kPa, respectively (NRC, 2010). The buildings studied were assumed to be located in Vancouver, BC, Canada assuming a site class C soil condition (dense soil and soft rock). The steel members designed were assumed to have properties of common hot rolled steel, such as yield strength Fy of 350 MPa and modulus of elasticity Es of 200 GPa. Initially, following Dickof et al. (2014), the design base shear was calculated for ductility and overstrength factors of Rd=2 and Ro = 1.5, respectively. An equivalent static load calculation method from NBCC 2010 was adopted to distribute the design base shear along the height of the building. For buildings with Rd = 2 and Ro = 1.5, the steel frames were then sized to meet the additional criteria for a ductile (type D) moment frame and a limited ductility (type LD), as specified in the CSA S16 code (CISC, 2010). However, design checks for Rd = 4 and Ro = 1.5 designs have been carried out to fulfill the limited ductility criteria of CSA S16 code (CISC, 2010). Tables 19 to 22 summarize the details of the designed beam and column sections for each structure including both ductile and limited ductile designs with a ductility related reduction factor (Rd) = 2. At this point it should noted that the design section details for 3-, 6-, and 9- storey hybrid buildings were adopted from Dickof (2013). Tables 23 and 24, respectively, summarize the design details of the beam and column sections for building designs with an Rd =4.          84 Table 19: Designed beam dimensions for ductile type              Table 20: Designed beam dimensions for limited ductility type       Building storey Storey no External Internal 3 1,2 W310129 W310129 3 W31067 W31067 6 1,2 W310x129 W310143 3,4,5 W310129 W310129 6 W310129 W310129 9 1,2,3 W310158 W310158 4,5,6 W310129 W310129 9 W31074 W31074 12 1,2,3 W310202 W310202 4,5 W310202 W310202 6-12 W310179 W310179 15 1-5 W310253 W310253 6-9 W310253 W310253 10-15 W310179 W310179 20 1-5 W310375 W310375 6-10 W310375 W310375 10-20 W310375 W310375     Building storey Storey no External Internal 3 1,2 W310107 W310107 3 W31067 W31067 6 1,2 W310118 W310143 3,4,5 W310118 W310129 6 W31067 W31067 9 1,2,3 W310158 W310158 4,5,6 W310129 W310129 9 W31067 W31067   85 Table 21: Designed column dimensions for ductile type Building storey Storey no Left External Right External Internal 3 1,2 W310143 W310143 W310143 3 W31086 W31086 W310143 6 1 W310202 W310202 W310202 2 W310202 W310202 W310202 3 W310179 W310179 W310179 4,5,6 W310129 W310129 W310129 9 1,2,3 W310179 W310179 W310226 4,5,6 W310143 W3101143 W310179 7,8 W310107 W310107 W310107 9 W310107 W310107 W310107 12 1,2,3 W360287 W360287 W360382 4,5 W360287 W360287 W360382 6-9 W360196 W360196 W360237 10,12 W360196 W360196 W360237 15 1-5 W360347 W360347 W360421 5-10 W360347 W360347 W360421 11-15 W360314 W360314 W360347 20 1-5 W360509 W360509 W360509 5-10 W360509 W360509 W360509 11-15 W360509 W360509 W360509 15-20 W360509 W360509 W360509  Table 22: Designed column dimensions for limited ductility type Building storey Storey no Right External Left External Internal 3 1,2 W310143 W31086 W310143 3 W31086 W31086 W310143 6 1 W310143 W310143 W310202 2 W31086 W31086 W310143 3 W31086 W31086 W310129 4,5,6 W31086 W31086 W310129 9 1,2,3 W310158 W310158 W310226 4,5,6 W310129 W310129 W310129 7,8 W31086 W31086 W31086 9 W31086 W31067 W31067      86 Table 23: Designed beam dimensions for Rd =4 Building storey Storey no External Internal 3 1,2,3 W310 W310 6 1,2,3,4 W310 W310 5,6 W310 W310 9 1,2,3,4 W310107 W310107 5,6,7 W310 W310 8,9 W310 W310  Table 24: Designed column dimensions for Rd =4 Building storey Storey no Left External Right External Internal 3 1 W310 W310 W310 2, 3 W310 W310 W310 6 1,2,3,4 W310 W310 W310 5,6 W310 W310 W310 9 1,2,3 W310143 W310143 W310143 4,5 W310143 W310143 W310143 7,8 W310129 W310129 W310129 9 W310129 W310129 W310129 7.3 Pushover analysis results Model instability and 10% drift were used as convergence criterion for the analysis. Static lateral loads with inverted triangular shape were used to push the structure until either model instability or formation of enough plastic hinges to create a sway mode of collapse. The applied static loads with the assumed distribution were increased monotonically until the point where the structure is considered to be collapsed. The results of the monotonic pushover analysis are depicted for Rd = 2 are shown in Figures 41 and 42, respectively, for low- and mid-rise, and high-rise structures. Furthermore, Figures 43 shows results of the monotonic pushover analysis for Rd = 4. The pushover analysis results indicate that bracket yielding does not influence the initial stiffness of the hybrid system. For models with one infilled bay, significant change in stiffness is observed when the steel beams are yielding. However, when the number of infilled bays increases the change in the initial stiffness comes from either column yielding or panel crushing. The panel crushing in multi-degree-of-freedom systems of the hybrid structures occurs   87 arbitrary. These reasons prompted the use of a bilinear approximation of the pushover curves to obtain the force and displacement of the hybrid structure at the yielding point.   Figure 41: Results of nonlinear monotonic pushover analysis for low- and mid-rise models with bracket spacing of 0.8m 0 2 4 6 8 1001000200030004000% Drift (mm/mm)Base Shear (KN) 1 Storey Type  D Frame  0 2 4 6 8 1001000200030004000% Drift (mm/mm) 1 Storey Type LD Frame0 2 4 6 8 1001000200030004000Base Shear (KN) 3 Storey Type  D Frame0 2 4 6 8 1001000200030004000 3 Storey Type LD Frame0 2 4 6 8 1001000200030004000Base Shear (KN) 6 Storey Type  D Frame  0 2 4 6 8 1001000200030004000 6 Storey Type LD Frame  0 2 4 6 8 1001000200030004000Base Shear (KN) 9 Storey Type  D Frame0 2 4 6 8 1001000200030004000 9 Storey Type LD FrameCLT1CLT2CLT1CLT2  88     Figure 42: Results of nonlinear monotonic pushover analysis for high-rise models with bracket spacing of 0.8m         0 2 4 6 8 10010002000300040005000% Drift (mm/mm)Base Shear (kN)15 Storey Type D Frame  CLT1CLT20 2 4 6 8 1001000200030004000500060007000% Drift (mm/mm)Base Shear (kN)20 Storey Type D Frame  CLT1CLT2  89  Figure 43: Results of nonlinear monotonic pushover analysis for high-rise models with bracket spacing of 0.8m 7.4 Equivalent energy elastic-plastic approximation An equivalent energy elastic-plastic (EEEP) curve was used to calculate the system yielding point under monotonic static pushover analysis. EEEP idealizes the elastic-plastic curve under consideration by equating areas enclosed by the envelope and approximate curve. Figure 44 shows an EEEP curve, which equates the area below the average data curve from zero with the area above this same curve until the ultimate displacement. 0 2 4 6 8 100200400600800100012001400Base Shear (kN)3 Storey Frame (Rd = 4)  CLT10 2 4 60500100015002000% Drift (mm/mm)6 Storey Frame (Rd = 4)  CLT10 2 4 6 80500100015002000% Drift (mm/mm)Base Shear (kN)9 Storey Frame (Rd = 4)  CLT1  90  Figure 44: EEEP curve (ASTM 2126-09 2009) The ultimate displacement of the system is defined as 0.8Ppeak. Once the area, force, and displacement values are known the yield force for the system can be defined: eeuuyield KKAP22 [20] where A is the area under the envelope curve from zero to the final displacement of the structure (Δu) and Ke is determined: epeakePK4.0 [21] where Ppeak is the maximum absolute load that the specimen can resist in the envelope, and finally Δe is the displacement of the specimen at 0.4PPeak.   91 In this project, as depicted in Figure 42 (e.g. the result for six storey frame), the pushover curve in the post peak region doesn’t show strength degradation up to 80% of the maximum carrying capacity. Therefore, to apply the above ASTM-EEEP approximation method, the last point of the simulation was considered as the ultimate displacement of the model.  7.5 Quantification of Rd and Ro factors The overstrength (Ro) and ductility (Rd) factors based on NBCC (NRC 2005) and Newmark and Hall (1988) are summarized in Table 25 and Table 26 for type ductile and limited ductile frames designed with an Rd =2 and Ro = 1.5. Dickof et al. (2014) compares the overstrength values that were obtained based on design base shear of frames (Vd) and base shear corresponding to the first yield of the system (Vy,sys). In this research project, consistent with FEMA P695, the overstrength factors were calculated based on the design base shear. Table 27 summarizes the calculated Rd and Ro factors of the hybrid buildings designed with Rd = 4 and Ro = 1.5.    Table 25: Overstrength and ductility factors for models with ductile (D) steel moment frames  Building No. Storey height Infilled bays Ductility factor (Rd) Overstrength factor (Ro) 1 3 1 2.77 2.41 2 3 2 3.35 3.25 3 6 1 4.60 2.64 4 6 2 7.29 3.46 5 9 1 5.04 2.25 6 9 2 5.12 2.91 7 12 1 5.33 2.43 8 12 2 5.99 3.09 9 15 1 4.51 2.4 10 15 2 5.12 3.11 11 20 1 3.56 2.23 12 20 2 3.88 2.8    92 Table 26: Overstrength and ductility factors for models with limited-ductile (LD) steel moment frames  Building No. Storey height Infilled bays Ductility factor (Rd) Overstrength factor (Ro) based on Vd 1 3 1 2.40 1.93 2 3 2 3.41 2.76 3 6 1 3.87 2.16 4 6 2 6.82 2.84 5 9 1 4.03 2.07 6 9 2 3.00 2.60  Table 27: Overstrength and ductility factors for hybrid buildings designed with Rd =4 and Ro = 1.5 Building No.  Storey height Infilled bays Ductility factor (Rd) Overstrength factor (Ro) based on Vd 1 3 1 6.03 3.54 2 6 1 4.40 2.82 3 9 1 2.42 2.46  The calculated Rd and Ro factors from the hybrid buildings that were designed with an Rd = 2 and Ro = 1.5, respectively, are compared with the provisions of NBCC 2005 values for bare steel moment frames in Figure 44 and Figure 45. NBCC 2005 recommends Rd factors of 5 and 2 for ductile and limited ductile SMRFs, respectively. In Figure 45, valid for buildings up to 9 storey, limited ductile frames show less ductility than ductile frames. For 3 and 6 storey frames increasing the infilled bays from one to two increases the ductility factor. However, for the nine storey building, the addition of infilled bays doesn’t affect the system ductility factor for ductile frames.  Moreover, limited ductile nine storey frames lose ductility with the addition of infilled bays. For all considered limited ductile frames, the obtained ductility factors are greater than the NBCC 2010 requirements. However, single storey and 20 storey buildings have shown less ductility factors than the NBCC 2010 requirement. In general the results show a minimum ductility factor of 2.77.    93 Figure 46 summarizes the Ro factors of the hybrid buildings. In general, as expected, the inclusion of CLT infill panels in SMRFs increases the Ro of the systems significantly. Irrespective of the height of the buildings, hybrid structures with two infilled bays have a larger Ro. Moreover, for all considered combinations, limited ductile frames have less overstrength than the ductile frames. Ductile and limited ductile frames in general have a greater Ro than the NBCC 2005 recommended values.     94  Figure 45: Ductility factors Rd   024681 23 storey frameDuctility factor (Rd)  Ductile frame Limited ductile frame024681 26 storey frameDuctility factor (Rd)024681 29 storey frameDuctility factor (Rd)024681 212 storey frameDuctility factor (Rd)024681 215 storey frameDuctility factor (Rd)Infilled bays024681 220 storey frameDuctility factor (Rd)Infilled bays  95  Figure 46: Overstrength factor Ro  012341 23 storey frameOverstrength factor (R0)  Ductile frame Limited ductile frame Ductile frame (NBCC) Limited Ductile frame (NBCC)012341 26 storey frameOverstrength factor (R0)012341 29 storey frameOverstrength factor (R0)012341 212 storey frameOverstrength factor (R0)012341 215 storey frameOverstrength factor (R0)Infilled bays012341 220 storey frameOverstrength factor (R0)Infilled bays  96 Chapter 8 Fundamental Period The fundamental period, Ta, is defined by the National Building Code of Canada (NBCC) as the fundamental lateral period of vibration of the structure (NRC 2010). The NBCC gives lower bound estimates of the fundamental period based on regression analysis on past earthquakes measured periods (Goel and Chopra 1997; Saatcioglu and Humar 2003). Kwon (2011) summarized the approximate fundamental period formula for different codes developed over the last forty years (Table 28). The table shows the development from just two empirical formulas for moment resisting frames (MRF) and other structural systems to five empirical formulas for reinforced concrete MRF, steel MRF, eccentrically braced frames, reinforced concrete/masonry shear walls, and other structural systems. Table 28: Approximate fundamental period formulas (Kwon 2011)   RC MRF Steel MRF EBF RC/Masonry Shear Wall Other UBC-70, 82 BOCA-75 Ta = 0.10N Ta = 0.05hn / D1/2 ATC 3-06 (1978)  Ta = Cthn3/4 Ta = 0.05hn / D1/2 Ct = 0.025 Ct = 0.035 BOCA 87  Ta = Cthn3/4 Ta = 0.05hn / D1/2 - Ct = 0.030 Ct = 0.035 UBC-88, 94, 97 Eurocode 8 (2004) Ta = Cthn3/4 Ct = 0.030 Ct = 0.035 Ct = 0.030 Ct = 0.02 or, Ct = 0.1 / Ac1/2 Ct = 0.020 ASCE 7-97 BOCA A-96 NEHRP 94, 97 Ta = Cthn3/4 Ct = 0.030 Ct = 0.035 Ct = 0.030 Ct = 0.020 Ct = 0.020 or, Ta = 0.10N - - - NEHRP 00, 03 ASCE 7-02,05 Ta = Crhnx Cr = 0.016 x = 0.9 Cr = 0.028 x = 0.8 Cr = 0.030 x = 0.75 Cr = 0.020 x = 0.75 Cr = 0.020 x = 0.75 or, Ta = 0.10N - or, Ta = 0.0019hn / Cw1/2 -  These empirical formulas depend on the type of structural system, structural materials and the dimensions of the structure. The Eurocode (CEN 2002) and ASCE (ASCE 2010) standards have   97 empirical formulas similar to that of the NBCC. The fundamental period can be different for each orthogonal direction. 8.1 NBCC fundamental period empirical formulas The 2010 NBCC determines the fundamental period by the structural system as a function of the height of the structure. Table 29 shows the fundamental period empirical formulas for steel moment frames, concrete moment frames, other moment frames, braced frames, and shear wall and other structural systems. Table 29: NBCC empirical formulas for fundamental period (NRC 2010) Fundamental period Structural system 4/3)(085.0 na hT   Steel moment frames 4/3)(075.0 na hT   Concrete moment frames NTa 1.0  Other moment frames na hT 025.0  Braced frames 4/3)(05.0 na hT   Shear wall and other structures  In Table 29, hn is the height of the building in meters and N is the total number of storeys above exterior grade. Often, the static and dynamic analyses give larger values of fundamental period than the empirical formula; therefore, the NBCC specifies that the period cannot exceed 1.5 times the empirical based period value for moment frames and 2 times for braced frames and shear walls. The limit was imposed because of the overestimation that structural models often have on the flexibility of a structural system. These structural models often neglect the non-structural stiffening elements which results in larger estimated natural periods. Moreover, the NBCC specifies a 2.0 s fundamental period maximum for moment resisting frames, braced frames, and other systems. Furthermore, for walls, coupled walls and wall-frame systems the fundamental period may not exceed 4.0 s.    98 8.2 FEMA P695 The Applied Technology Council (ATC) prepared a report for FEMA in 2009 called the “Quantification of Building Seismic Performance Factors” better known as the FEMA P695 report (FEMA 2009). In this report, the fundamental period was computed as: auTCT   [22] where T is the fundamental period of the building, Cu is the factors provided by the ASCE/SEI 7-05 shown in Table 30, and Ta is the approximate fundamental period. The approximate fundamental period equation is (NRC 2010): xnta hCT   [23] where Ct and x values are summarized in Table 31 and hn is the height of the building. Table 30: Coefficient for upper limit on calculated period (ASCE 2010) Design Spectral Response Acceleration Parameter at 1 s, SD1 Coefficient Cu ≥ 0.4 1.4  0.3 1.4  0.2 1.5  0.15 1.6 ≤ 0.1 1.7  Table 31: Values of approximate period parameters Ct and x (ASCE-SEI 2010) Structure Type Ct x Moment-resisting frame systems in which the frames resist 100% of the required seismic force and are not enclosed or adjoined by components that are more rigid and will prevent the frames from deflecting where subjected to seismic forces:      Steel moment-resisting frames 0.028 (0.0724)a 0.8    Concrete moment-resisting frames 0.016 (0.0466)a 0.9 Steel eccentrically braced frames in accordance with Table 12.2-1 lines B1 or D1 0.03 (0.0731)a 0.75 Steel buckling-restrained braced frames 0.03 (0.0731)a 0.75 All other structural systems 0.02 (0.0488)a 0.75 aMetric equivalents are shown in parentheses    The periods of the hybrid buildings were determined through eigenvalue analysis. Each structures first and second natural period were computed through the modal analysis of   99 OpenSees finite element software. Table 32 shows the fundamental natural periods of the steel-timber hybrid structures designed with an Rd = 2 and Ro = 1.5. Table 32: Fundamental period results Building No. Storey height Ductility class Infilled bays Period (s) 1 1 D 1 0.30 2 1 D 2 0.24 3 1 LD 1 0.33 4 1 LD 2 0.26 5 3 D 1 0.91 6 3 D 2 0.62 7 3 LD 1 0.96 8 3 LD 2 0.68 9 6 D 1 1.66 10 6 D 2 1.15 11 6 LD 1 1.75 12 6 LD 2 1.2 13 9 D 1 2.48 14 9 D 2 1.71 15 9 LD 1 2.52 16 9 LD 2 1.74 17 12 D 1 2.80 18 12 D 2 2.08 19 15 D 1 3.18 20 15 D 2 2.44 21 20 D 1 3.50 22 20 D 2 2.96  Results show an increase in period with an increase building height as the structure gets taller due to the ductile response. Furthermore, as the number of infilled bays increase the period decreases quite significantly since the structure becomes stiffer with additional infilled CLT walls. Finally, ductility class and bracket spacing changes had the least significant effect on the period with ductile structures having slightly lower periods than limited ductile structures and a bigger bracket spacing resulted in slightly larger period values.    100 The periods of the bare moment resisting frames resemble pure moment resisting frames which can then be compared to the empirical code values in the NBCC. 8.2.1 Proposed empirical factor considering building height only The proposed empirical formula considering only building height can be seen in Equation 24. The numerical results and analytical equation are plotted in Figure 47, and the analytical results are on the lower bound of the numerical result, indicating a conservative result and in agreement with the code formulation. 4/3)(137.0 na hT        R2 = 0.91 [24]  Figure 47: Proposed empirical formula considering only building height 8.2.2 Proposed empirical factor considering infill length and building height When considering both infill length and height of structure the proposed equation was formulated through MATLAB using least square regression and is shown in Equation 25. The infill length has a large impact on the period of a structure and therefore, should be in the empirical formula: 0.00.51.01.52.02.53.03.54.00 20 40 60 80First mode period (sec)Building height (m)Numerical dataProposed equation  101 DhT na155.0      R2 = 0.85 [25] where D is the infill length in meters, and hn is the height of the structure above grade in meters.        102 Chapter 9 Seismic Hazard for Vancouver and Ground Motion Selection 9.1 Seismic hazard in Vancouver Greater Vancouver is vital to the healthy economic growth and normal functionality of socioeconomic activities in south-western BC. It is situated in one of the most active seismic zones in Canada. Since 1900, several destructive earthquakes have occurred (Figure 48), e.g. the 1918 and 1946 earthquakes in Vancouver Island and the 1949, 1965, and 2001 (Nisqually) deep earthquakes in Washington, USA.   Figure 48: Regional seismicity in south-western BC, Canada    103 There are mainly three potential sources of damaging earthquakes: shallow crustal earthquakes, off-shore mega-thrust interface earthquakes from the Cascadia subduction zone, and deep inslab earthquakes (Hyndman and Rogers 2010). The Cascadia subduction earthquakes occur at the interface between the Juan de Fuca plate and the North American plate, where plate motions are locked and a large amount of strain is accumulated over many years (rate of convergence is about 40 mm/year). The expected moment magnitude of such events is in the range of 8 to 9, and the last event occurred in 1700 (Satake et al. 2003). The mean recurrence period of the Cascadia subduction event ranges from 500 to 600 years (typically around 530 years) with large variability (Mazzotti and Adams 2004; Goldfinger et al. 2008, 2012). In comparison with crustal and inslab earthquakes, large interface ground motions originated from the Cascadia subduction zone and have rich spectral content in the long vibration period range (because the earthquake magnitude of the Cascadia subduction events is about Mw8-9, while those of the crustal and inslab events are in the range of Mw6 to Mw7.5). Moreover, duration of the interface events will be much longer than that of the crustal and inslab events. The long duration ground motions due to a mega-thrust subduction earthquake and their influence on tall buildings at remote locations (several hundreds of kilometers from the epicenter) have been highlighted for the 2011 Tohoku, Japan, earthquake (Takewaki et al. 2011). A recent regional seismic hazard model by Atkinson and Goda (2011) has incorporated key features of seismic hazard in south-western BC, and has updated seismic hazard estimates for southwestern BC with respect to those in the NBCC 2005-2010 (Adams and Atkinson 2003). The updated assessment takes into account:  Use of a longer earthquake catalogue based on a uniform moment magnitude scale in developing revised magnitude-recurrence relationships for seismic source zones in south-western BC.   Use of newer ground motion prediction equations (GMPEs) with proper distance measure conversion by accounting for finite fault plane size.   Logic-tree representation of alternative GMPEs to account for epistemic uncertainty in ground motion prediction.   Probabilistic scenarios for the potential mega-thrust Cascadia earthquakes.    104  Seismic hazard is estimated as ‘mean’, rather than ‘median’, which is consistent with modern interpretation of probability and related assessments of seismic risk (McGuire et al. 2005). In this study, the updated seismic hazard model is adopted to characterize seismic hazard in Vancouver. The site condition for PSHA is set to site class C, which is the reference site condition for national seismic hazard mapping and NBCC and can be represented by a site parameter VS30 (average shear-wave velocity in the uppermost 30 m) of 360 to 760 m/s; this site condition is prevalent in downtown Vancouver (Cassidy and Rogers 2004).  Table 33: First three fundamental periods of all building storeys and infill patterns     Period (s)   Building storey Infill pattern Mode-1 Mode-2 Mode-3 T1 [Tmin, Tmax] 1 0-1-0 0.30 0.05 0.03 0.30 [0.05, 1.0] 1-0-1 0.24 0.05 0.03   3 0-1-0 0.92 0.29 0.14 0.80 [0.10, 2.0] 1-0-1 0.62 0.21 0.12   6 0-1-0 1.67 0.54 0.30 1.50 [0.2, 2.5] 1-0-1 1.15 0.38 0.22   9 0-1-0 2.49 0.85 0.48 2.00 [0.3, 3.0] 1-0-1 1.72 0.58 0.34   12 0-1-0 2.80 0.92 0.51 2.50 [0.4, 3.0] 1-0-1 2.08 0.69 0.40   15 0-1-0 3.18 1.07 0.60 3.00 [0.4, 3.0] 1-0-1 2.44 0.81 0.47   20 0-1-0 3.50 1.14 0.64 3.00 [0.4, 3.0] 1-0-1 2.96 0.97 0.55    The first three fundamental periods for all building heights and infill patterns are summarized in Table 33. T1 is the representative (anchor) fundamental vibration period for a given building storey class (with different infill patterns). This period is used for the record selection and scaling for seismic performance assessment. In addition, the limiting vibration period Tmin and Tmax are defined for each storey class such that the first three vibration periods fall within the specified   105 range. This range is used when response spectrum matching of candidate records with the target response spectrum is carried out (see Section 9.2). Figure 49a shows UHS at the return period (TR) of 2500 years for Vancouver (VS30 = 550 m/s). The UHS is expressed as mean estimate, which includes the effects of epistemic uncertainty in the seismic hazard model. It is important to recognize that the UHS ordinates are computed based on numerous earthquake scenarios that may occur in south-western BC, and dominant scenarios at different spectral periods are not identical, as source, path, and site characteristics affect frequency content of ground motions differently. For instance, a large magnitude event has richer long-period content in source spectrum, while short-period content of ground motion attenuates more rapidly over distance than low-frequency content. To investigate dominant earthquake scenarios contributing to overall seismic hazard in Vancouver, seismic deaggregation analysis is conducted, and the results are shown in Figure 49b, Figure 50b, and Figure 51b by considering the spectral periods of 0.3 s, 1.5 s, and 3.0 s, respectively (note: these three periods are selected for illustration). The selected vibration periods of 0.3 s, 1.5 s, and 3.0 s corresponds to the representative fundamental vibration periods (T1) of the 3-storey, 6-storey, and 15/20-storey steel-timber hybrid structures (Table 33). The dominant scenarios are represented in terms of magnitude, distance, and earthquake type (crustal/interface/inslab). Different earthquake types are associated with distinct event features in terms of magnitude and distance. For instance, the magnitude and distance of the Cascadia subduction events range between 8 and 9 and between 100 and 150 km, respectively; these are constrained by physical characteristics of the Cascadia scenarios. At the return period of 2500 years, 13% of the dominant scenarios are originated from the Cascadia subduction zone for T1 = 0.3 s (Figure 49b), whereas this percentages gradually increase as T1 becomes longer; for T1 = 3.0 s, the relative contribution of the Cascadia subduction events reaches 47% (Figure 51b). This is an important consideration in conducting record selection for seismic performance evaluation of (relatively flexible) structures in south-western BC.   106   (a) (b) Figure 49: (a) Uniform hazard spectrum and conditional mean spectra for crustal interface, and inslab events in Vancouver, and (b) seismic deaggregation for spectral acceleration at 0.3 s in Vancouver.    (a) (b) Figure 50: (a) Uniform hazard spectrum and conditional mean spectra for crustal interface, and inslab events in Vancouver, and (b) seismic deaggregation for spectral acceleration at 1.5 s in Vancouver.   107   (a) (b) Figure 51: (a) Uniform hazard spectrum and conditional mean spectra for crustal interface, and inslab events in Vancouver, and (b) seismic deaggregation for spectral acceleration at 3.0 s in Vancouver. 9.2 Ground motion selection for Vancouver The record selection is conducted based on a multiple-conditional-mean-spectra (CMS) method (Baker 2011; Goda and Atkinson 2011). This method takes into account multiple target spectra (with inter-period correlation of spectral ordinates), representing distinct response spectral features of different earthquake types (i.e. crustal versus interface versus inslab) and their relative contributions to overall seismic hazard. It utilizes seismic hazard information in terms of spectral acceleration that is available from PSHA, and has been successfully implemented for both conventional wood-frame houses (Goda and Atkinson 2011) and RC buildings with/without masonry infills (Tesfamariam et al. 2015; Tesfamariam and Goda 2015). The target CMS that are developed for crustal, interface, and inslab earthquakes are shown in Figure 49a, Figure 50a, and Figure 51a by considering different anchor periods of 0.3 s, 1.5 s, and 3.0 s, respectively (i.e. T1 for 3-storey, 6-storey, and 15/20-storey hybrid structures; see Table 33). The similarity of the target CMS for three earthquake types depends on the anchor period.   108 The record database is an extended dataset of real mainshock-aftershock sequences (see Tesfamariam and Goda 2015); it has been developed by combing the PEER-NGA (Pacific Earthquake Engineering Research–Next Generation Attenuation) database (Goda and Taylor 2012) with the updated version of the KKiKSK (K-NET, KiK-net, and SK-net in Japan) database (Goda et al. 2015). The number of available mainshock-aftershock sequences is 606; among them, there are 197 crustal earthquakes, 340 interface earthquakes, and 69 inslab earthquakes. The interface events are from the 2003 Tokachi-oki earthquake or the 2011 Tohoku earthquake (which have similar event characteristics as the expected Cascadia subduction earthquake). In this study, mainshock records of the developed database were considered. Using the target CMS, a set of ground motion records is selected by comparing response spectra of candidate mainshock records with the target spectra. The total number of selected records is set to 30 (note: each record has two horizontal components). For the 3-storey hybrid structure, 13, 4, and 13 records were selected for the crustal, interface, and inslab earthquakes, respectively (Figure 49b); for the 6-storey hybrid structure, 10, 11, and 9 records were selected for the crustal, interface, and inslab earthquakes, respectively (Figure 50b); and for the 15/20-storey hybrid structure, 10, 14, and 6 records were selected for the crustal, interface, and inslab earthquakes, respectively (Figure 51b). Figure 52 compares the magnitude-distance distributions of the selected records for the anchor vibration periods of 0.3, s, 1.5 s, and 3.0 s. Because the relative contributions of the Cascadia subduction events increase with T1 (Figures 49 to 51), larger-magnitude records are selected more frequently for the longer-period structures. More specifically, when T1 = 0.3 s, no records from the 2011 Tohoku earthquake were chosen (i.e. all records have moment magnitudes less than 8.5), whereas when T1 = 1.5 s and 3.0 s, the majority of the selected interface records are from the 2011 Tohoku earthquake (i.e. records with moment magnitude of 9.0).   109  Figure 52: Magnitude-distance plot of the selected records for T1 = 0.3 s, 1.0 s, and 3.0 s.  The detailed results for the multiple-CMS-based record selection are presented in Figure 53, Figure 54, and Figure 55 for the anchor vibration periods of 0.3 s, 1.5 s, and 3.0 s, respectively. In the CMS-based method, response spectral matching is conducted in a least squares sense by considering the geometric mean of the response spectra of two horizontal components. The vibration period ranges for spectral matching (i.e. Tmin and Tmax in Table 33) are set to: from 0.1 s to 1.0 s, from 0.2 s to 2.5 s, and from 0.4 s to 3.0 s for T1 = 0.3 s, 1.5 s, and 3.0 s, respectively (shaded segments in Figures 47 to 49). In these figures, the statistics of the response spectra of the selected ground motion records (i.e. median as well as 16th/84th percentile curves) for three earthquake types are compared with the target CMS as well as the CMS plus/minus one conditional standard deviation (Jayaram et al. 2011). Generally, the percentile curves of the selected records are consistent with the CMS and CMS plus/minus one conditional standard   110 deviation. The matching performance is poor in the vibration period range outside of [Tmin, Tmax]; this can be improved when the number of records is increased.    (a) (b)   (c)  Figure 53: Comparison of response spectra of the selected ground motion records (50th/16th/84th curve) and conditional mean spectra (mean and mean plus/minus one standard deviation) for the a) crustal, b) inslab, and c) interface earthquakes for T1 = 0.3 s.    111   (a) (b)   (c)  Figure 54: Comparison of response spectra of the selected ground motion records (50th/16th/84th curve) and conditional mean spectra (mean and mean plus/minus one standard deviation) for the a) crustal, b) inslab, and c) interface earthquakes for T1 = 1.5 s.    112   (a) (b)   (c)  Figure 55: Comparison of response spectra of the selected ground motion records (50th/16th/84th curve) and conditional mean spectra (mean and mean plus/minus one standard deviation) for the a) crustal, b) inslab, and c) interface earthquakes for T1 = 3.0 s. 9.3 FEMA P695 ground motions The FEMA P695 guideline for selecting the ground motions is briefly outlined below. Several sets of specific ground motions are already selected for seismic performance assessment in the U.S.:   Code (ASCE/SEI 7-05) Consistent: The records should be consistent (to the extent possible) with the ground motion requirements of Section 16.1.3.2 of ASCE/SEI 7-05 Minimum Design Loads for Buildings and Other Structures (ASCE 2006a) for three-dimensional analysis of structures. In particular, “ground motions shall consist of pairs   113 of appropriate horizontal ground motion acceleration components that shall be selected and scaled from individual recorded events.”  Very Strong Ground Motions: The records should represent very strong ground motions corresponding to the MCE motion. In high seismic regions where buildings are at greatest risk, few recorded ground motions are intense enough, and significant upward scaling of the records is often required.  Large Number of Records: The number of records in the set should be “statistically” sufficient such that the results of collapse evaluations adequately describe both the median value and record-to-record (RTR) variability of collapse capacity.  Structure Type Independent: Records should be broadly applicable to collapse evaluation of a variety of structural systems, such as systems that have different dynamic response properties or performance characteristics. Accordingly, records should not depend on period, or other building-specific properties of the structure.  Site Hazard Independent: The records should be broadly applicable to collapse evaluation of structures located at different sites, such as sites with different ground motion hazard functions, site and source conditions. Accordingly, records should not depend on hazard deaggregation, or other site- or hazard-dependent properties. The ground motion records selected for the FEMA P695 guideline may not be applicable to south-western BC directly for several reasons. The regional seismicity in south-western BC is contributed by not only shallow crustal earthquakes, but also mega-thrust Cascadia events and deep inslab events. The dominant frequency content and duration for these earthquakes are significantly different from those for moderate crustal earthquakes (which are adopted by the FEMA P695 guideline). To examine the differences of the response spectral characteristics of the FEMA-P695-based records and the multiple-CMS-based records (Section 9.2), the statistics of the response spectra for these record sets are compared in Figure 56 for the anchor vibration periods of 0.3, s, 1.5 s, and 3.0 s. Note that the records for the FEMA P695 guideline are the so-called far-field record set containing 22 records (i.e. 44 horizontal components) from worldwide shallow crustal earthquakes; typical magnitude ranges for these records are between Mw6.5 and Mw7.5. Note that the effects of ‘epsilon’ are not taken into account in Figure 56 for the FEMA-P695-based records. The comparisons shown in Figure 56 are carried out by considering the record scaling (target spectral ordinates are the UHS for Vancouver). Figure 56 indicates that the similarity and dissimilarity depend significantly on the anchor vibration period. When T1 = 0.3 s,   114 noticeable differences are observed in the moderate-to-long vibration period range, whereas when T1 = 1.5 s and 3.0 s, significant differences are present in the short vibration period range. Therefore, careful record selection for Vancouver is warranted.            Figure 56: Comparison of the statistics of the response spectra (50th/16th/84th curve) for the records selected based on conditional mean spectra and for the ‘far-field’ records adopted in the FEMA P695 guideline by considering the anchor vibration periods of 0.3s, 1.5s and 3.0s.   115 Chapter 10 Validation of Proposed Rd and Ro Factors This chapter presents the performance evaluation procedure and results of the initial assumed ductility (Rd) and overstrength (Ro) factors. This evaluation process includes nonlinear time history analysis using 60 ground motion records (i.e., 30 records, 2 components, each with 2 % probability of exceedance in 50 years) and Incremental Dynamic Analysis (IDA) (Vamvastikos and Cornell 2002). The chapter is organized as follows: first, the general adopted performance evaluation methodology is discussed in detail. Subsequently, results of the performance check for collapse prevention limit state according to the NBCC 2010 are presented. Finally, the obtained results and discussions are presented for performance evaluation through IDA. 10.1 Performance evaluation methodology The assumed Rd and Ro of factors of Chapter 8 were evaluated through dynamic time history analyses. For this purpose, NLTHA and IDA have been conducted using 60 ground motion records (i.e., 30 records, 2 components each) with 2 % probability of exceedance in 50 years. The former analysis was carried out to check against collapse prevention limit state of the NBCC 2010, while the latter analysis was to check the collapse margin ratio according to the FEMA P695 methodology. At this point it is to be noted that the NBCC NLTHA check was carried out for only buildings designed with an Rd = 2 and Ro = 1.5. The assessment of overall seismic performance of the hybrid buildings (designed in Chapter 7) using NLTHA was evaluated through the maximum interstorey drift (MISD) demand of the buildings. NBCC 2010 poses a 2.5% MISD limit to represent extensive damage on the buildings. In this approach, the overall objective was to make sure that the average MISD in the building (irrespective of the storey height) is less than 2.5%.    116  Figure 57: Performance evaluation methodology To verify the acceptability of the assumed Rd and Ro factors, FEMA P695 suggests the use of IDA to calculate the probability of collapse.  FEMA P695 limits the probability of collapse for each performance group to be 10% under earthquakes with 2% in 50 years hazard. According to   117 this approach, the acceptability of assumed force reduction factors is judged based on their collapse margin ratio from IDA. The considered collapse margin ratio is adjusted for total system uncertainty and spectral shapes. The general framework for the adopted methodology is depicted in Figure 57. As the first step in the performance evaluation process, according to FEMA P695, it is required to obtain the collapse data from IDA. In IDA, the considered ground motion records are scaled up until collapse is achieved. The collapse data is used to calculate the collapse margin ratio (CMR) and to draw the interim collapse fragility curves. These fragility curves show the probability of collapse with respect to ground motion intensity under consideration. In this research, each fragility curve of a given hybrid building is assumed to be a lognormal curve, as defined by the median collapse intensity ( CTSˆ ) and standard deviation of natural logarithm (βRTR). The median collapse capacity can be calculated from IDA or other simple approximation methods. Moreover, FEMA P695 defined βRTR to be a dispersion of IDA results due to the variability within ground motion records. Due its insignificance on the final CMR, FEMA P695 suggests a constant value of βRTR = 0.4 for structures with period based ductility (µ>3).  Once the median collapse intensity is evaluated from IDA, the next step is to calculate the collapse margin ratio CMR: MTCTSSCMRˆ  [26] where SMT is the spectral acceleration value at the fundamental period of the archetype structure under consideration.  Once the CMR of each archetype is calculated, FEMA P695 adjusts this value to Adjusted Collapse Margin Ratio (ACMR) to account for the Spectral Shape Factor (SSF): iii CMRSSFACMR *  [27]   118 However, in this research, ground motions were selected and scaled for each archetype model based on their spectral acceleration values at the fundamental period of the considered archetype building. Therefore, SSF was 1, and for each archetype building ACMRi = CMRi.  In order to accurately calculate the safety against collapse, FEMA P695 considers more sources of uncertainties other than βRTR during the performance evaluation process. The following set of bullets describes the considered system uncertainties.   Design requirement uncertainty (DR): according to FEMA P695, this type of uncertainty is related to the robustness and completeness of design requirements of the archetype buildings. Table 34 summarizes quantitative the factors to consider to quantify the uncertainty as the lognormal standard deviation parameter (βDR). This is assessment done qualitatively, based on completeness of the information and confidence in the basis of design requirement.  Table 34: Quality rating of design requirements (FEMA 2009)  Confidence in Basis of Design Requirements Completeness and Robustness High Medium Low High. High. Extensive safeguards against unanticipated failure modes. All important design and quality assurance issues are addressed. (A) Superior βDR = 0.1 (B) Good βDR = 0.2 (C) Fair βDR = 0.35 Medium. Reasonable safeguards against unanticipated failure modes. Most of the important design and quality assurance issues are addressed. (B) Good βDR = 0.2 (C) Fair βDR = 0.35 (D) Poor βDR = 0.5 Low. Questionable safeguards against unanticipated failure modes. Many important design and quality assurance issues are not addressed. (C) Fair βDR = 0.35 (B) Poor βDR = 0.5 _    119  Test data uncertainty (TD): uncertainty related to the quality of test data to calibrate and model the archetype buildings. Table 35 summarizes quantitative values of this uncertainty, as the lognormal standard deviation parameter (TD), based on the rating of quality of the test data.  Table 35: Quality rating of test data from an experimental investigation program (FEMA 2009)  Confidence in Test Results Completeness and Robustness High Medium Low High. Material, component, connection, assembly, and system behaviour well understood and accounted for all, or nearly all, important testing issues addressed (A) Superior βTD = 0.1 (B) Good βTD = 0.2 (C) Fair βTD = 0.35 Medium. Material, component, connection, assembly, and system behaviour generally understood and accounted for most important testing issues addressed. (B) Good βTD = 0.2 (C) Fair βTD = 0.35 (D) Poor βTD = 0.5 Low. Material, component, connection, assembly, and system behaviour fairly understood and accounted for Several important testing issues not addressed. (C) Fair βTD = 0.35 (D) Poor βTD = 0.5 _   Modeling uncertainty (MDL): uncertainty related to the accuracy, robustness and quality of the numerical models to capture seismic response and simulate the collapse mechanism of archetype buildings. Table 36 summarizes quantitative values of this uncertainty based on the rating of quality of the proposed numerical models as the lognormal standard deviation parameter (βMDL). More information can be obtained from FEMA P695.  Table 36: Quality rating of index archetype models  Confidence in Basis of Design Requirements Completeness and Robustness High Medium Low High. Index models capture the full range of the archetype design space and structural behavioral effects that contribute to collapse. (A) Superior βMDL = 0.1 (B) Good βMDL = 0.2 (C) Fair βMDL = 0.35 Medium. Index models are generally comprehensive and representative of the design space and behavioral effects that contribute to collapse. (B) Good βMDL =  0.2 (C) Fair  βMDL = 0.35 (D) Poor βMDL = 0.5 Low. Significant aspects of the design space and/or collapse behaviour are not captured in the index models. (C) Fair βMDL = 0.35 (D) Poor  βMDL = 0.5 _    120 Based on the above sources of uncertainty, the total uncertainty for the performance evaluation process is obtained by combining RTR, DR, TD, and MDL. This total uncertainty is used to modify the interim fragility curves of each archetype building. The new collapse fragility curve is defined by a random variable (SCT) as: TOTCTCT SS ˆ  [28] where ?̂?𝐶𝑇 is the median collapse intensity from IDA and 𝜆𝑇𝑂𝑇 is the lognormally distributed random variable with a unit median and standard deviation of 𝛽𝑇𝑂𝑇. The formal definition of 𝜆𝑇𝑂𝑇 according to FEMA P695 is given as: MDLTDDRRTRTOT    [29] where 𝜆𝑅𝑇𝑅 , 𝜆𝐷𝑅 , 𝜆𝑇𝐷, 𝜆𝑀𝐷𝐿 are independent lognormally distributed random variables with medians of unity and standard deviation of 𝛽𝑅𝑇𝑅 , 𝛽𝐷𝑅 , 𝛽𝑇𝐷, 𝛽𝑀𝐷𝐿, respectively. At this point it is to be noted that the above four random variables are statically independent (their joint probability distribution is the product of their marginal distribution), and the total collapse uncertainty parameter (𝛽𝑇𝑂𝑇) can be calculated as: 2222MDLTDDRRTRTOT    [30] For record-to-record uncertainty (𝛽𝑅𝑇𝑅) of 0.4, FEMA (2009) summarizes the values of 𝛽𝑇𝑂𝑇. Acceptable values of adjusted collapse margin ratio of each archetype buildings can be calculated based on the assumption that the collapse value of spectral intensity is a lognormally distributed random variable. This distribution has a median of 𝑆𝐶𝑇 and lognormal standard deviation of 𝛽𝑇𝑂𝑇. By considering 𝛽𝑇𝑂𝑇  and acceptable collapse probability as 10% and 20%, Table 37 summarizes the ACMR10% and ACMR 20%.  FEMA P695 proposed acceptability criteria to verify the adequacy of initially assumed force reduction factors is based on ACMR10% and ACMR 20%. The assumed Rd factors will be accepted if the calculated ACMR ratios within the performance group and individually fulfill the following criterion:   121  The calculated Average Adjusted Collapsed Margin Ratio (ACMR) within the defined performance group is greater than ACMR10%. 10ACMRACMR i   [31]  The calculated individual Adjusted Collapsed Margin Ratio (ACMR) of each archetype building is greater than ACMR20%. 20ACMRACMRi   [32] Evaluation of the overstrength factor was carried out based on the following recommendations from FEMA P695:  The chosen system overstrength factor should be greater than the calculated largest average value of overstrength among the considered performance groups.    Following ASCE/SEI 7-05, limiting the overstrength factor to 3 is recommended due to practical design considerations.   For this research project, following NBCC 2010, the limiting overstrength factor is 1.7.    122 Table 37: Acceptable values of adjusted collapse margin ratio (ACMR10% and ACMR20%) (FEMA 2009) Total System Collapse Uncertainty Collapse Probability 5% 10% (ACMR10%) 15% 20% (ACMR20%) 25% 0.275 1.57 1.42 1.33 1.26 1.20 0.300 1.64 1.47 1.36 1.29 1.22 0.325 1.71 1.52 1.40 1.31 1.25 0.350 1.78 1.57 1.44 1.34 1.27 0.375 1.85 1.62 1.48 1.37 1.29 0.400 1.93 1.67 1.51 1.40 1.31 0.425 2.01 1.72 1.55 1.43 1.33 0.450 2.10 1.78 1.59 1.46 1.35 0.475 2.18 1.84 1.64 1.49 1.38 0.500 2.28 1.90 1.68 1.52 1.40 0.525 2.37 1.96 1.72 1.56 1.42 0.550 2.47 2.02 1.77 1.59 1.45 0.575 2.57 2.09 1.81 1.62 1.47 0.600 2.68 2.16 1.86 1.66 1.50 0.625 2.80 2.23 1.91 1.69 1.52 0.650 2.91 2.30 1.96 1.73 1.55 0.675 3.04 2.38 2.01 1.76 1.58 0.700 3.16 2.45 2.07 1.80 1.60 0.725 3.30 2.53 2.12 1.84 1.63 0.750 3.43 2.61 2.18 1.88 1.66 0.775 3.58 2.70 2.23 1.92 1.69 0.800 3.73 2.79 2.29 1.96 1.72 0.825 3.88 2.88 2.35 2.00 1.74 0.850 4.05 2.97 2.41 2.04 1.77 0.875 4.22 3.07 2.48 2.09 1.80 0.900 4.39 3.17 2.54 2.13 1.83 0.925 4.58 3.27 2.61 2.18 1.87 0.950 4.77 3.38 2.68 2.22 1.90    123 10.2 Check for collapse prevention limit state according to NBCC 2010 In this section NLTHA is employed to assess the seismic performance of hybrid buildings. NBCC 2010 poses a 2.5% MISD to represent extensive damage on the buildings. In this approach, the overall objective is to make sure that the average MISD in the building (irrespective of the storey height that it is calculated) is less than 2.5% under the design based earthquake ground motions. For this purpose, NLTHA has been conducted using 60 ground motion records (i.e., 30 records, 2 components each) with 2% probability of exceedance in 50 years. The interstorey drift demand along the height of the buildings are presented in Figure 58, Figure 59 and Figure 60 for low-rise, mid-rise and high-rise buildings (designed with Rd = 2 and Ro  =1.5), respectively. In order to check the upper bound requirement, in the given figures, mean plus one standard deviation (SD) plots are included. The gray lines in the figures represent the response of buildings under individual earthquake ground motion records.    (a) 3-storey ductile frame (b) 3-storey limited ductile frame Figure 58: Maximum interstorey drift under design based earthquake ground motions for low-rise buildings It is evident from Figures 58 and 59 that the mean and mean + 1SD maximum interstorey drift demands are less than 2.5%. In general, the results suggest that the mean MISD responses are almost 40 % less than the limit. Therefore, the assumed Rd and Ro factors are suitable and efficient from the collapse prevention limit state requirement of NBCC 2010.   0 1 2 3 4 5 604.58.1511.8MISD (%)Storey height (m)  EQ-iMeanMean+1SD0 1 2 3 4 5 6 704.58.1511.8MISD (%)Storey height (m)  EQ-iMeanMean+1SD  124   (a) 6-storey ductile frame (b) 6-storey limited ductile frame   (c) 9-storey ductile frame (d) 9-storey limited ductile frame Figure 59:  Maximum interstorey drift under design based earthquake ground motions for mid-rise buildings  0 1 2 3 4 5 6 704.58.1511.815.4519.122.75MISD (%)Storey height (m)  EQ-iMeanMean+1SD0 1 2 3 4 5 6 704.58.1511.815.4519.122.75MISD (%)Storey height (m)  EQ-iMeanMean+1SD0 0.5 1 1.5 2 2.5 3 3.5 405101520253033.7MISD (%)Storey height (m)  EQ-iMeanMean+1SD0 0.5 1 1.5 2 2.5 3 3.5 405101520253033.7MISD (%)Storey height (m)  EQ-iMeanMean+1SD  125   (a) 12-storey ductile frame (b) 15-storey limited ductile frame   (c) 20-storey ductile frame  Figure 60:  Maximum interstorey drift under design based earthquake ground motions for high-rise buildings 10.3 Performance assessment of the proposed Rd factors using incremental dynamic analysis (IDA) Incremental dynamic analysis has been carried out to validate the proposed Rd factors for low and mid-rise buildings. Due to the huge computational effort, only single bay infilled 3- and 6-storey hybrid buildings of Chapter 7 (designed with Rd = 2 and 4) were considered for the analyses. In order to simplify the numerical computation effort, FEMA P695 suggests first to scale (match) the ground motions to a 2% in 50 years uniform hazard spectrum for the site. 0 0.5 1 1.5 2 2.5051015202530354044.65MISD (%)Storey height (m)  EQ-iMeanMean+1SD0 0.5 1 1.5 20102030405055.6MISD (%)Storey height (m)  EQ-iMeanMean+1SD0 0.5 1 1.5 2010203040506070MISD (%)Storey height (m)  EQ-iMeanMean+1SD  126 Following the FEMA P695, in this research, the selected ground motions of Chapter 9 were scaled at the fundamental period of the structure. Subsequently dynamic analyses have been carried out by scaling the ground motion records up to the collapse spectral acceleration. Initial approximation of the collapse spectral acceleration and interstorey drift were performed by using the SPO2IDA software (Vamvatsikos and Cornell 2005). Preliminary investigation using SPO2IDA results showed that the 10% interstorey drift value as a collapse point was irrespective of the building height and infill configuration. Based on a preliminary assessment, the ground motions were scaled up until a spectral acceleration value triggered the collapse of the building (exceedance of 10% MISD). In the following subsections, the obtained IDA results, collapse fragility curves, and performance evaluations of the proposed Rd factors of Chapter 7 are presented. 10.3.1 Incremental dynamic analysis results In order to compute the adjusted collapse margin ratio and to plot the collapse fragility curves, IDA has been performed using OpenSees software (Mazzoni et al. 2006). The analyses employed site specific ground motion records of Chapter 9 and archetype nonlinear building models of Chapter 7. A conservative collapse criterion was followed to define the dynamic instability of the building models. In this approach, structural hardening was only considered for interstorey drift values less than 10% and the lowest spectral acceleration value was considered as a limit state point.  Details about this approach can be found in Vamvastikos and Cornell (2002). Figure 61a and b show IDA results for 3-storey middle bay infilled hybrid buildings designed with an Rd = 2 and Ro = 1.5. In Figure 62a and b results for 6-storey middle bay infilled hybrid buildings designed with an Rd = 2 and Ro = 1.5 are presented. Figure 63 presents the IDA analysis results for 3-, 6-, and 9-storey buildings designed with an Rd = 4 and Ro = 1.5. At this point it is to be noted that, since the fundamental period of the structures designed with an Rd = 2 and Ro = 4 do not vary significantly, the same ground motion database has been used for the dynamic analysis of hybrid buildings. In the plots SCT is the median collapse acceleration value and SMT is the maximum considered spectral acceleration at the fundamental period of the hybrid buildings.    127    (a) ductile moment resisting frame (b) limited ductile moment resting frame Figure 61: IDA results for three-storey middle bay infilled archetype models.    (a) ductile moment resisting frame (b) limited ductile moment resting frame Figure 62: IDA results for six-storey middle bay infilled archetype models  0 5 10 150246810MISD (%)ST(T=0.91s) [g]SCT = 3.7gSMT0 5 10 150246810MISD (%)ST (T = 0.96s) [g]SCT = 3.38gSMT0 5 10 1502468101214MISD (%)ST (T= 1.66 s) [g]SCT = 3.64SMT0 5 10 150246810MISD (%)ST (T= 1.75 s) [g]SCT = 3.44gSMT   128   (a) 3-storey hybrid building (b) 6-storey hybrid building   (c) 9-storey hybrid building  Figure 63: IDA results for middle bay infilled hybrid buildings designed with Rd = 4 10.3.2 Total system uncertainty As pointed out earlier in this chapter, in order to accurately evaluate the safety against collapse and to calculate the ACMR, the total uncertainty (βTOT) should be determined first. Four uncertainty types were considered for this research: record-to-record (βRTR), design requirement (βDR), modeling (βMDL), and test data (βTD). Given its insignificant effect on the final ACMR value, FEMA P695 fixes the record-to-record (βRTR) uncertainty to 0.4. Design requirement uncertainty (βDR) is selected as fair (βDR = 0.35) from Table 34. For this selection the confidence in the bases of design requirement is considered as medium. Moreover, considering CLT as a 0 2 4 6 8 10 12024681012MISD (%)ST (T = 1.16 s) [g]SCT = 3.05gSMT 0 5 10 1502468101214MISD (%)ST (T=1.97 s) [g]SMT SCT = 3.490 5 10 1502468101214MISD (%)ST (T=2.83 s) [g]SCT = 2.96SMT  129 new construction material and the complexity in characterizing the structural behaviour of wood, the completeness and robustness in the design method for this hybrid building was tagged as medium. Since the experimental tests on this hybrid structure are limited to its component level, the uncertainty related to test data was selected as fair (βTD = 0.35) from Table 35. In the future, the authors intend to perform full scale experimental tests on the hybrid system. Uncertainty related to modeling was selected as fair (βMDL = 0.35) from Table 36. Finally, based on these selected values, the total uncertainty was calculated using Equation 30 to be 0.75 (βTOT ~ 0.75). 10.3.3 Collapse fragility curves In order to relate the scaled spectral acceleration values with the probability of collapse, fragility curves were developed from the IDA analysis results. Fragility curves reflect the probability of collapse of the hybrid buildings under considered ground motion records. These curves are cumulative distribution functions (CDF) that were developed by fitting a lognormal distribution through collapse data points. The probability of these collapse points was determined by dividing the number of ground motion records that initiated the collapse of building to the total number of ground motion records (60). Median collapse spectral acceleration values (SCT) and standard deviation of the collapse data were used as an input to define the CDF. Figures 64a and b show the collapse fragility curves for the 3-storey, middle bay infilled hybrid structure designed with an Rd = 2. Figures 65a and b depicts the collapse fragility curves for the 6 storey, middle bay infilled hybrid buildings designed with Rd = 4. In Figures 64a and b two fragility curves are shown to illustrate the influence of uncertainty on the shape of the curves. The fragility curve with the red line was developed by the actual obtained lognormal standard deviation of collapse data points, and the curve in blue is the “adjusted curve” developed with the same median but a standard deviation of βTOT = 0.75. Even though the median collapse acceleration value is unchanged, as depicted in the Figures, the additional uncertainty increases the probability of collapse. In Figures 65a and b, since the standard deviation is greater than βTOT = 0.75, only the actual fragility curve is presented. Figure 66a, b, and c displays the collapse fragility curves for 3, 6, and 9 storey buildings designed with a Rd = 4, respectively.     130   (a) ductile moment resisting frame (b) limited ductility moment resting frame Figure 64: Collapse fragility curves for three-storey middle bay infilled archetype models     (a) ductile moment resisting frame (b) limited ductility moment resting frame Figure 65: Collapse fragility curves for six-storey middle bay infilled archetype models  0 5 10 15 20 2500.20.40.60.81Spectral acceleration (g)Collapse probablitySCT = 3.70.5  Lognormal fitAdjusted curveFraction causing collapse0 5 10 15 2000.20.40.60.81Spectral acceleration (g)Collapse probablitySCT = 3.640.5  Lognormal fitFraction causing collapse0 5 10 15 2000.20.40.60.81Spectral acceleration (g)Collapse probablitySCT = 3.440.5  Lognormal fitFraction causing collapse  131   (a) 3-storey hybrid building (b) 6-storey hybrid building   (c) 9-storey hybrid building  Figure 66: Collapse fragility curves for middle bay infilled archetype models designed with Rd = 4 10.3.4 Evaluation of the proposed Rd factor FEMA P695 proposed acceptability criteria to verify the adequacy of initially assumed force reduction factors based on ACMR10% and ACMR 20%. The assumed Rd factors were accepted if the calculated ACMR ratios were within the performance group and individually exceeded the values in Tables 38 and 39, which are proposed by FEMA P695. Accordingly, the proposed Rd factor were accepted if the calculated average ACMR values within the performance group exceeded 0 5 10 15 2000.20.40.60.81Spectral acceleration (g)Collapse probablitySCT = 3.050.5  Lognormal fitAdjusted curveFraction causing collapse0 5 10 15 2000.20.40.60.81Spectral acceleration (g)Collapse probablitySCT = 3.490.5  Lognormal fitFraction causing collapse0 5 10 15 2000.20.40.60.81Spectral acceleration (g)Collapse probablitySCT = 2.960.5  Lognormal fitFraction causing collapse  132 ACMR10% (2.61). Moreover, for individual criteria, the proposed factors were acceptable if the calculated ACMR value exceeded ACMR20% (1.88). As discussed in the previous section, since ground motions are selected for a specific site (Vancouver) and for each building type, the calculated CMR and ACMR are the same. The performance evaluation process for Rd = 2 and Rd = 4 is summarized in Table 38 and 39, respectively.  Table 38: Performance evaluation table for Rd = 2 Performance group Hybrid Building Configuration Calculated Ro and ACMR Evaluation Low-rise No. of storey Ductility type Infilled bays Ro SCT SMT ACMR FEMA P695 requirement Pass/fail 3 D 1 2.41 3.7 0.49 7.6 1.88 Pass 3 LD 1 1.93 3.38 0.47 7.2 1.88 Pass Average       2.17     7.4 2.61 Pass Mid-rise 6 D 1 2.64 3.64 0.27 13.5 1.88 Pass 6 LD 1 2.16 3.44 0.26 13.2 1.88 Pass Average       2.4     13.4 2.61 Pass  Table 39: Performance evaluation table for Rd = 4 performance group Hybrid Building Configuration Calculated Ro and ACMR Evaluation Low-rise No. of storey Infilled bays Ro SCT SMT ACMR FEMA P695 requirement Pass/fail 3 1 3.54 3.05 0.39 7.8 1.88 Pass Average     3.54     7.8 2.61 Pass Mid-rise 6 1 2.82 3.49 0.21 17.1 1.88 Pass Average     2.82     17.1 2.61 Pass High-rise 9 1 2.46 2.96 0.14 21.14 1.88 Pass Average   2.46   21.14 2.61 Pass  As can be seen in Table 38 the considered performance group ductility related factor (Rd = 2) is acceptable. Evaluation on average basis indicates that the short period structures govern the performance. Even though the median collapse spectral acceleration decreases with respect to height, due to their height and longer period significant increase in ACMR is observed by increasing the height. Table 39 summarizes the performance evaluation for an Rd = 4. Moreover,   133 a significant decrease in the median collapse acceleration value is overserved. As indicated in Chapter 7, the cross-sectional elements for buildings designed with an Rd = 4 are smaller and economical. The increased fundamental period and lower spectral acceleration value yields a higher collapse margin ratio (particularly for the 9-storey hybrid building). The proposed Rd = 4 is deemed to be appropriate to design CLT infilled SMRFs.  10.3.5 Evaluation of the proposed Ro factor The individual and average Ro for the considered performance group (low-rise hybrid buildings) are summarized in Tables 38 and 39. FEMA P695 suggests adopting the largest average Ro from all considered performance groups. For low-rise buildings under consideration a Ro of 3.54 is obtained. At this point it is important to note that short period structures govern the average overstrength values. Considering practical design approaches, FEMA P695 and NBCC 2010 set an upper bound value on the Ro of 3 and 1.5, respectively. Considering these codified upper bound restrictions, for the proposed hybrid structure, a Ro factor of 1.5 is suggested.   134 Chapter 11 Conclusions and Future Recommendations In this research project, the force modification factors, according to the National Building Code of Canada, are developed for a steel-timber hybrid structure. The hybrid structure incorporates CLT as an infill in Steel Moment Resisting Frames (SMRFs). The FEMA P695 (FEMA 2009) was followed to develop the archetype models and to quantify the factors. Two levels of ductility factors (i.e. Rd = 2 and Rd = 4) were examined using the iterative procedure of FEMA P695 (FEMA 2009).   11.1 Component experimental tests The composite action, for the proposed hybrid system, is achieved through discrete connectors along the interface of the steel frames and infill walls. The connections are required to ensure the CLT remains fixed to the steel frame and for energy dissipation under seismic shaking. A small gap is provided at the interface between the CLT wall and the steel frame to allow the brackets to deform and dissipate energy under lateral loading. Experimental data from the component level testing program at FPInnovations and UBC were used for numerical model calibration.  Schneider et al. (2014) performed experimental tests by considering one type of L-shaped steel bracket: the SIMPSON Strong-Tie Connector 90483.016. This bracket was implemented with different nail types including: 16d spiral nails (3 ½ inch long), 5x90mm screws, and 470 mm screws, defined as Connection A, Connection B, and Connection C, respectively. 11.2 Finite element numerical models Numerical modeling was carried out using the Open System for Earthquake Engineering Simulation (OpeenSees) (Mazzoni et al. 2006) finite element program. For this research, a multi-scale modeling approach was adopted. This procedure entailed:    135  the spring element of the connection is calibrated for the pinching4 material model in OpenSees  the numerical model for the CLT system is determined, and  the components are assembled to form the hybrid system. The steel frame members are modelled with nonlinear displacement-based beam-column elements at the end of the member (to represent the spreading plastic hinge zone) and linear elastic beam-column elements for the middle portion of each member. In the finite element model, CLT panels are simplified to a single 99 mm panel element with homogeneous, isotropic, fully elastic properties using the OpenSees ndMaterial. The L-shaped steel brackets are represented in OpenSees as two node link elements between the steel frame and CLT panel. The axial, shear, and rotational behaviour of these elements are defined by specific material models. Following the component level experimental tests and numerical modeling, a typical CLT infilled SMRF system is developed. This hybrid system combines ductile steel frames with CLT walls through angular L-shaped steel bracket connections. At the interface of the wall and frame a gap is provided in order to allow the brackets to deform and dissipate energy during the seismic shaking. The confinement behaviour to account for the space between the frame and panel is modelled using the elastic perfectly plastic gap uniaxial material (EPPG). Once the numerical models are developed, based on the experimental data of Schneider et al. (2014), component level calibrations are carried out for 3 different types of L-shaped connectors. In general, better agreement is observed between the experimental and OpenSees responses in the reloading stiffness at the initial loading stages. 11.3 Lateral behaviour of CLT infilled SMRFs Using static pushover and quasi-static cyclic analysis, response sensitivity studies with variation of bracket spacing (400mm, 800mm, and 1600mm), panel thickness (99mm, 169mm, and 239mm), gap (20mm, 50mm, and 80mm), panel strength (17.5 MPa, 25 MPa, and 37.5 MPa), and post yielding stiffness of steel members (1%, 3%, and 5%) are reported (Bezabeh 2014; Bezabeh et al. 2015). From an optimal and stable response point of view a bracket spacing   136 of 800 mm, panel thickness of 99 mm (3 layers), gap of 20 mm, panel strength of 17.5 MPa, and post yielding stiffening ratio of 1% were found to be appropriate modeling parameters of the hybrid structure.  11.4 Design approaches and static monotonic pushover analysis Initially for buildings designed with a Rd = 2 and Ro = 1.5, 36 different hybrid buildings were modeled and subjected to monotonic static pushover loading by varying the following modeling variables: building height (1, 3, 6, 9, 12, 15 and 20 storey), CLT infill configuration (one-bay infilled and two-bay infilled), connection bracket spacing (800 mm), and ductility class (D and LD). For the considered Rd factor, stiffer and ductile frames were considered as ductile (D) and the less stiff and flexile system considered as limited ductile (LD). In order to have a non-conservative and economical design, 3-, 6-, and 9-storey hybrid buildings were designed using a Rd = 4 and Ro = 1.5. A nonlinear static pushover analysis was performed to quantify the overstrength factors of the hybrid buildings under consideration.  11.5 Incremental dynamic analysis In order to check the FEMA P695 (FEMA 2009) acceptable failure probabilities and collapse margin ratios, Incremental Dynamic Analysis (IDA) is carried out using 60 ground motion records. Ground motions are selected and scaled for the city of Vancouver by considering site class C of NBCC 2010 (NRC 2010). Due to the complexity and the contributions of sub-crustal and subduction type earthquakes to the total seismic hazard, the traditional FEMA P695 (FEMA 2009) is not followed in the ground motion selection and scaling. Therefore, a new ground motion database selection criteria that considers all sources of earthquake for the given hazard, together with a conditional hazard spectrum that includes the effects of ‘epsilon’ are developed for this project. In the IDA, conservative collapse criteria are followed to define the dynamic instability of building models. In this approach, structural hardening is only considered for interstorey drift values less than 10% and the lowest spectral acceleration value is considered as a limit state point. Analysis is done using a high performance computational method with 200   137 clusters of computers at The University of British Columbia research computing service center (UBCIT). The following conclusions can be made based on the IDA:  The ACMRs exceeded the FEMA P695 requirements for both Rd = 2 and Rd = 4. Due to the increased period and maximum considered spectral acceleration value, the ACMR of mid-rise buildings are larger than low-rise buildings.   One bay CLT infilled SMRFs provide more ductility and stability than multi-bay infilled hybrid structures.   Significant strain hardening is observed in the IDA responses.  In general, as the height of the hybrid buildings increased, the median collapse acceleration and maximum spectral acceleration decreased, except for 6-storey buildings.   From this research, it can be concluded that Ro = 1.5 and Rd = 4 will yield a safe and economical design of the proposed hybrid structure.  11.6 Suggested design approaches Seismic design force reduction factors are developed for SMRFs with CLT infill walls. Besides the factors, in this section, a summary of suggested structural parameters, design approaches, and design cautions are presented. At this point it is to be noted that the current study assumed the hybrid buildings are situated in Vancouver, Canada on soil class C with a maximum spectral acceleration 0.94g.  11.6.1 Suggested structural parameters The following points are suggested structural parameters primarily based on the response sensitivity study of Chapter 4. The designer should at minimum use the following parameters to establish the hybrid structure at the conceptual design stage.  Connection bracket spacing = 800mm (these should be placed uniformly at the interface of steel frame CLT infill wall).   138  CLT panel thickness = 3 layers (99mm).  CLT panel crushing strength = 17.5 MPa.  Gap between steel frame and CLT infill wall = 20mm.  Post yielding stiffness ratio of steel frames = 1%.  Infill pattern = 3 bays steel frames with central bay infilled with CLT. 11.6.2 Design approach details A force based design approaches can be used to perform the seismic design of CLT infilled SMRFs with the suggested Rd and Ro factors. Moreover, designers are recommended to perform static pushover analysis to check for sudden strength deterioration in the post peak response stage. The following bullets summarize the details of the suggested design approaches.   During the design process the selected steel sections should fulfill at least the limited ductility requirement of CSA S16-09.  For the design base shear calculation the empirical period equation of Chapter 8 should be used.   Appropriate higher mode factors of NBCC 2010 should be applied at the design base shear calculation stage.  Whenever appropriate, designers should introduce structural devices to avoid out of plane failure of CLT infill walls.  Beams and columns should be braced at the middle to avoid lateral torsional buckling and local buckling.  Qualified rigid beam-column connection is suggested to avoid fractures at weld locations and bolt holes.  Design should follow strong column-weak beam approach to avoid a soft storey mechanism during a seismic event.   139  Column splices should be detailed properly to avoid failure of gravity load carrying elements. 11.7 Future research perspectives The following list includes the future research areas that should be explored to increase the applicability of the hybrid structure under study.  Either quasi-static or dynamic (shaking table) full scale experimental tests are required to calibrate the numerical models.  Increasing the number of archetype models by varying the number of bays, infill patterns, and heights will enhance the confidence of designers and stakeholders to use the hybrid structure.  Coupling the proposed force based approach with performance based criteria to control displacements and drifts of the hybrid structure under seismic excitation.    140 Bibliography Adams, J. and Halchuk, S. 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