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Numerical study of pin-supported cross-laminated timber (CLT) shear wall system equipped with low-yield… Ma, Siyao 2016

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NUMERICAL STUDY OF PIN-SUPPORTED CROSS-LAMINATED TIMBER (CLT) SHEAR WALL SYSTEM EQUIPPED WITH LOW-YIELD STEEL DAMPERS by  Siyao Ma  B.Eng., Tongji University, 2013  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Forestry)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  May 2016  © Siyao Ma, 2016 ii  Abstract This thesis presents a numerical study of a novel rocking cross-laminated timber (CLT) shear wall system for low- to mid-rise constructions. The system takes advantage of the high in-plane stiffness of CLT coupled with low-yield steel dampers to control the rocking motion of the CLT shear walls during earthquakes. The low-yield steel dampers connected between two rigid CLT wall panels provide the mechanism needed to dissipate the earthquake energy. This concentrates the damage in the dampers, allowing the system to be repaired efficiently after major earthquakes.  Numerical models of the CLT shear wall system have been developed using both OpenSees Navigator and ABAQUS software. Models of low-yield steel damper systems were calibrated using available experimental results. With the rigid floor/roof assumption, a simplified OpenSees model of the CLT shear wall system was demonstrated to be effective and reasonably accurate in predicting the response of the system under large excitations. Therefore, it is efficient and reliable to apply the OpenSees model to study the seismic response of CLT shear wall buildings.  A case study of a six-storey CLT shear wall building located in Vancouver, Canada was studied; and, detailed parameteric studies were conducted to investigate the influences of the damper type (damper shear strength), number of dampers, damper location, different earthquake records versus target earthquake design response spectrum, and earthquake peak ground acceleration (PGA) on the building response. It was determined that an optimized damper design with comprehensive consideration of these five factors can provide a building with a small roof drift iii  ratio, as well as minor damages on the dampers. Concepts and examples for connection design are also provided.  iv  Preface The objective of this thesis was the investigation of the characteristics of the pin-based cross-laminated timber (CLT) shear wall system when equipped with low-yield steel dampers. The research focussed on the application of this system to low- to mid-rise buildings. The research work was accomplished under the guidance of Dr. Frank Lam. This dissertation is original and has not been published by the author, Siyao Ma.  v  Table of Contents  Abstract .......................................................................................................................................... ii	Preface ........................................................................................................................................... iv	Table of Contents ...........................................................................................................................v	List of Figures ............................................................................................................................... xi	Acknowledgements .................................................................................................................... xvi	Chapter 1: Introduction ................................................................................................................1	1.1	 General ............................................................................................................................ 1	1.2	 Objectives and Scope ...................................................................................................... 3	1.3	 Description of Methodology ........................................................................................... 5	1.4	 Thesis Organization ........................................................................................................ 6	Chapter 2: Literature Review .......................................................................................................9	2.1	 Rocking Characteristics of CLT Walls ........................................................................... 9	2.2	 Passive Energy Dissipation Device .............................................................................. 12	2.3	 Low-yield Steel Damper ............................................................................................... 15	2.3.1	 Characteristics ....................................................................................................... 15	2.3.2	 Numerical Models ................................................................................................. 17	2.4	 Application Example of Pin-supported Wall System with Steel Dampers ................... 19	Chapter 3: Design and Numerical Model of Low-yield Steel Damper ...................................22	3.1	 Damper Design ............................................................................................................. 22	3.1.1	 Damper Material ................................................................................................... 22	3.1.2	 Design Method ...................................................................................................... 24	vi  3.2	 Damper Numerical Model in OpenSees Navigator ...................................................... 28	3.2.1	 Numerical Model Definition ................................................................................. 28	3.2.2	 Numerical Model Calibration ............................................................................... 34	3.3	 Damper Numerical Model in ABAQUS ....................................................................... 37	3.3.1	 Numerical Model Definition ................................................................................. 37	3.3.2	 Numerical Model Calibration ............................................................................... 41	Chapter 4: Static Analysis of a Pin-supported CLT Shear Wall System Equipped with Low-yield Steel Dampers .............................................................................................................44	4.1	 Numerical Simulation Using OpenSees Navigator ....................................................... 46	4.1.1	 Numerical Model .................................................................................................. 46	4.1.2	 Pushover Analysis ................................................................................................. 51	4.1.3	 Reversed-cyclic Analysis ...................................................................................... 53	4.2	 Numerical Simulation by Using ABAQUS .................................................................. 54	4.2.1	 Numerical Model .................................................................................................. 54	4.2.2	 Pushover Analysis ................................................................................................. 61	4.2.3	 Reversed-cyclic Analysis ...................................................................................... 61	4.3	 Results and Conclusions ............................................................................................... 64	4.3.1	 Comparison between OpenSees Results and ABAQUS Results .......................... 64	4.3.1.1	 Pushover analysis results .................................................................................. 64	4.3.1.2	 Reversed-cyclic analysis result ......................................................................... 70	4.3.2	 Influence by Damper Location ............................................................................. 74	Chapter 5: Seismic Analysis of Mid-rise CLT Building ...........................................................78	5.1	 Studied Building ........................................................................................................... 79	vii  5.2	 Numerical Simulation Model ........................................................................................ 82	5.3	 Ground Motion Selection and Scaling Methodology ................................................... 87	5.3.1	 Selection of Ground Motion ................................................................................. 87	5.3.2	 Ground Motion Scaling ......................................................................................... 91	5.4	 Results and Conclusions ............................................................................................... 93	5.4.1	 Influence of the Damper Type .............................................................................. 94	5.4.1.1	 Earthquake level of 2% probability in 50 years (2/50) ..................................... 95	5.4.1.2	 Earthquake level – PGA value of 1.0 g ............................................................. 97	5.4.1.3	 Results and Conclusion ..................................................................................... 98	5.4.2	 Influence of the Number of Dampers ................................................................... 99	5.4.2.1	 Earthquake level of 2% probability in 50 years (2/50) ................................... 100	5.4.2.2	 Earthquake level – PGA value of 1.0 g ........................................................... 102	5.4.2.3	 Results and Conclusion ................................................................................... 103	5.4.3	 Influence of the Damper Location ...................................................................... 104	5.4.3.1	 Earthquake level of 2% probability in 50 years (2/50) ................................... 105	5.4.3.2	 Earthquake level – PGA value of 1.0 g ........................................................... 107	5.4.3.3	 Results and Conclusion ................................................................................... 108	5.4.4	 Influence by Different Earthquake Records Versus Target Earthquake Design Response Spectrum ............................................................................................................. 110	5.4.4.1	 Under original earthquake excitations ............................................................ 110	5.4.4.2	 Under matched earthquake excitations (seismic hazard 2% in 50 years) ....... 111	5.4.4.3	 Under earthquake excitations with the PGA scaled to 1.0 g ........................... 112	5.4.4.4	 Results and Conclusion ................................................................................... 113	viii  5.4.5	 Influence by Earthquake Peak Ground Acceleration (PGA) .............................. 114	Chapter 6: Connection Design ..................................................................................................120	6.1	 Pin Connection ............................................................................................................ 120	6.1.1	 Design Concept ................................................................................................... 120	6.1.1.1	 Steel rod .......................................................................................................... 122	6.1.1.2	 CLT wall panel ............................................................................................... 123	6.1.1.3	 Bottom steel plate or radian of CLT panel ...................................................... 125	6.1.2	 Future Work ........................................................................................................ 125	6.2	 Connection Between Damper and CLT Wall ............................................................. 126	6.2.1	 Design Concept ................................................................................................... 126	6.2.2	 Further work ........................................................................................................ 133	Chapter 7: Conclusions and Future Work ..............................................................................135	7.1	 Conclusions ................................................................................................................. 135	7.1.1	 Conclusions from Static Analyses’ Results ........................................................ 137	7.1.2	 Conclusions from Seismic Analysis’ Results ..................................................... 138	7.2	 Future Work ................................................................................................................ 141	Bibliography ...............................................................................................................................143	  ix  List of Tables  Table 4-1 Engineering constants of the boards in CLT panels (Ashtari 2012) ............................ 56	Table 4-2 Engineering constants calculated from the experiment results (Gsell et al. 2007) ...... 56	Table 4-3 Energy dissipation qualification ................................................................................... 73	Table 5-1 Selected earthquake records ......................................................................................... 90	Table 5-2 Seismic analysis results summary ................................................................................ 94	Table 5-3 Damper distribution in the damper type study ............................................................. 95	Table 5-4 Seismic response comparison among different types of dampers for the 2/50 earthquake level ............................................................................................................................ 96	Table 5-5 Seismic response comparison among different types of dampers for an earthquake with a PGA value of 1.0 g ..................................................................................................................... 98	Table 5-6 Damper distribution along the building ...................................................................... 100	Table 5-7 Seismic response comparison among different damper numbers for the 2/50 earthquake level .......................................................................................................................... 101	Table 5-8 Seismic response comparison among different damper numbers for an earthquake with a PGA value of 1.0 g ................................................................................................................... 103	Table 5-9 Damper distributions with the building ...................................................................... 105	Table 5-10 Seismic response comparison among different damper locations for the 2/50 earthquake level .......................................................................................................................... 106	Table 5-11 Seismic response comparison among different damper locations for an earthquake with a PGA value of 1.0 g ........................................................................................................... 108	Table 5-12 Seismic response comparison among the original earthquake excitations ............... 111	x  Table 5-13 Seismic response comparison among matched earthquake excitations for the 2/50 earthquake level .......................................................................................................................... 112	Table 5-14 Seismic response comparison among earthquake excitations for a PGA of 1.0 g ... 113	Table 5-15 Total shear force of the pin connection when PGA is equal to 0.4 g and 0.5 g ....... 119	Table 5-16 Total shear force of the pin connection when PGA is equal to 0.46 g ..................... 119	 xi  List of Figures  Figure 1-1 Description of pin-supported CLT shear wall with low-yield-strength steel dampers . 4	Figure 2-1 Moment-resisting frame with strong rocking walls (Wada et al. 2009) ..................... 20	Figure 3-1 Damper hysteresis response (Choi and Abebe 2014) ................................................. 23	Figure 3-2 Tensile coupon experiment results of two specimens (Zhang et al. 2013) ................. 24	Figure 3-3 ZeroLength Element definition ................................................................................... 29	Figure 3-4 Elastic material definition ........................................................................................... 30	Figure 3-5 Steel02 material parameters of monotonic envelope (Opensees.berkeley.edu 2012) . 33	Figure 3-6 Steel02 material definition of the D30 damper ........................................................... 33	Figure 3-7 Experiment specimen detail and boundary condition (Choi and Abebe 2014) .......... 34	Figure 3-8 Damper reversed-cyclic analysis loading protocol ..................................................... 36	Figure 3-9 Comparison of hysteresis loops .................................................................................. 36	Figure 3-10 Elastic material definition for damper ....................................................................... 39	Figure 3-11 Plastic material definition for damper ....................................................................... 40	Figure 3-12 Tensile test model in ABAQUS ................................................................................ 42	Figure 3-13 Tensile numerical analysis results ............................................................................. 42	Figure 4-1 CLT shear wall system description ............................................................................. 45	Figure 4-2 CLT wall panel model in OpenSees Navigator ........................................................... 47	Figure 4-3 Rigid beam definition .................................................................................................. 49	Figure 4-4 Elastic column definition ............................................................................................ 49	Figure 4-5 Proposed shear wall system model in OpenSees Navigator ....................................... 50	Figure 4-6 Pushover analysis model in OpenSees Navigator ....................................................... 52	xii  Figure 4-7 Pushover analysis definition ....................................................................................... 52	Figure 4-8 Reversed-cyclic wall test protocol .............................................................................. 53	Figure 4-9 CLT material definition box ........................................................................................ 56	Figure 4-10 Stress-strain relationship for orthotropic material ..................................................... 57	Figure 4-11 Pin connection definition box ................................................................................... 59	Figure 4-12 Proposed shear wall system model in ABAQUS ...................................................... 60	Figure 4-13 Pushover analysis model in ABAQUS ..................................................................... 62	Figure 4-14 Pushover loading definition in ABAQUS ................................................................. 63	Figure 4-15 Pushover analysis in OpenSees-wall response .......................................................... 65	Figure 4-16 Global force analysis ................................................................................................. 65	Figure 4-17 Partial force analysis ................................................................................................. 66	Figure 4-18 Pushover analysis in OpenSees damper response ..................................................... 67	Figure 4-19 Comparison between OpenSees result and ABAQUS result for the D20 dampers .. 68	Figure 4-20 Comparison between OpenSees result and ABAQUS result- dampers D50 ............ 69	Figure 4-21 Comparison between OpenSees result and ABAQUS result- dampers D70 ............ 69	Figure 4-22 Wall response in OpenSees reversed-cyclic analysis ................................................ 71	Figure 4-23 Damper response in OpenSees reversed-cyclic analysis .......................................... 71	Figure 4-24 Comparison between OpenSees and ABAQUS results for D20 dampers ................ 72	Figure 4-25 Comparison between OpenSees and ABAQUS results for D50 dampers ................ 72	Figure 4-26 Comparison between OpenSees and ABAQUS results for D70 dampers ................ 72	Figure 4-27 Illustration of the damper location ............................................................................ 76	Figure 4-28 Damper location analysis in OpenSees Navigator .................................................... 77	Figure 4-29 Damper location analysis in ABAQUS ..................................................................... 77	xiii  Figure 5-1 Plan view of the studied building ................................................................................ 80	Figure 5-2 Building model in OpenSees Navigator ...................................................................... 83	Figure 5-3 Definition of beams ..................................................................................................... 85	Figure 5-4 Definition of columns ................................................................................................. 85	Figure 5-5 Floor element definition .............................................................................................. 86	Figure 5-6 Floor material definition ............................................................................................. 87	Figure 5-7 Vancouver design response spectrum ......................................................................... 88	Figure 5-8 Original response spectrum ......................................................................................... 92	Figure 5-9 Matched response spectrum ........................................................................................ 92	Figure 5-10 Comparison of drift-ratio time-history responses of the top floor with different damper types for the 2/50 earthquake level .................................................................................. 95	Figure 5-11 Comparison of damper responses with different damper types for the 2/50 earthquake level ............................................................................................................................ 96	Figure 5-12 Comparison of drift-ratio time-history responses of the top floor with different damper types for an earthquake with a PGA value of 1.0 g ......................................................... 97	Figure 5-13 Comparison of damper responses with different damper types for an earthquake with a PGA value of 1.0 g ..................................................................................................................... 97	Figure 5-14 Comparison of drift-ratio time-history responses of the top floor with different damper numbers for the 2/50 earthquake level ........................................................................... 100	Figure 5-15 Comparison of damper responses with different damper numbers for the 2/50 earthquake level .......................................................................................................................... 101	Figure 5-16 Comparison of drift-ratio time-history responses of the top floor with different damper numbers for an earthquake with a PGA value of 1.0 g .................................................. 102	xiv  Figure 5-17 Comparison of damper responses with different damper numbers for an earthquake with a PGA value of 1.0 g ........................................................................................................... 102	Figure 5-18 Comparison of drift-ratio time-history responses of the top floor with different damper locations for the 2/50 earthquake level .......................................................................... 105	Figure 5-19 Comparison of damper responses with different damper locations for the 2/50 earthquake level .......................................................................................................................... 106	Figure 5-20 Comparison of drift-ratio time-history responses of the top floor with different damper locations for an earthquake with a PGA value of 1.0 g ................................................. 107	Figure 5-21 Comparison of damper responses with different damper locations for an earthquake with a PGA value of 1.0 g ........................................................................................................... 107	Figure 5-22 Drift-ratio time-history response of the top floor under the original earthquake excitations ................................................................................................................................... 110	Figure 5-23 Drift-ratio time-history response of the top floor under the matched earthquake excitations for the 2/50 earthquake level .................................................................................... 111	Figure 5-24 Drift-ratio time-history response of the top floor under the earthquake excitations for a PGA of 1.0 g ............................................................................................................................ 112	Figure 5-25 IDA of the maximum drift ratio of the top floor for the seven different earthquakes..................................................................................................................................................... 115	Figure 5-26 IDA of the maximum shear displacement of damper for the seven different earthquakes ................................................................................................................................. 116	Figure 5-27 IDA of the maximum horizontal force of the pin connection ................................. 117	Figure 5-28 IDA of the maximum vertical force of the pin connection ..................................... 118	Figure 6-1 Front and side views of the pin connection ............................................................... 121	xv  Figure 6-2 Front and side views of pin connection ..................................................................... 121	Figure 6-3 Pin connection strengthened by insertion of steel plate ............................................ 124	Figure 6-4 Steel “boot” with steel side plates ............................................................................. 124	Figure 6-5 Front view of damper connection ............................................................................. 127	Figure 6-6 Plan view of damper connection ............................................................................... 128	Figure 6-7 Three-dimensional illustration for the double angle of a screw ................................ 129	Figure 6-8 Front view for the double angle of a screw ............................................................... 130	Figure 6-9 Bottom view for the double angle of a screw ........................................................... 130	Figure 6-10 Lateral view for the double angle of a screw .......................................................... 131	 xvi  Acknowledgements I would like to offer my enduring gratitude to my research supervisor, Dr. Frank Lam, for his academic guidance and support throughout my studies. Great appreciation is also given to supervisory committee member Dr. Tony Yang, who inspired the idea of this work and has provided invaluable support. I also offer my special thanks to supervisory committee member Dr. Ricardo O. Foschi, for his advice and encouragement in this work. Special thanks go to the Timber Engineering and Applied Mechanics group at the university of British Columbia for their support. I am particularly grateful to Mr. Jingjing Liu for his help and time. I am thankful to the NSERC (Natural Sciences and Engineering Research Council of Canada) strategic research Network for Engineered Wood-based Building Systems for supporting this research.  Finally, I would like to take this opportunity to express my deepest gratitude to my family for their unconditional love throughout my life. I also offer my thanks to all my friends for their understanding and support.  1   Chapter 1: Introduction  1.1 General Cross-laminated timber (CLT) is an engineered wood product. CLT panels consist of several layers of boards stacked crosswise and glued together on their wide faces. Edge gluing of the boards is possible from some manufacturers, but these products are not commonly available.  In recent years, CLT has been increasingly used in the construction of residential multi-storey buildings (Popovski and Karacabeyli 2012). A number of experimental studies (Gavric et al. 2014; Popovski and Karacabeyli 2012) on the lateral response of CLT structures have indicated that CLT wall panels behave almost as rigid bodies, with ductility and energy dissipation of the structures coming from the connections. Therefore, connection design is critical to the lateral resistance of CLT structures subjected to seismic excitations.  In recent decades, the design community has increasingly considered timber as a building material for the construction of mid-rise buildings. Given the high planar rigidity of CLT panels, CLT walls are considered suitable as lateral resistance elements in mid-rise buildings. These walls are also expected to rock under lateral loadings. Together with the large base shear force requirement, connection design is critical.  Rocking walls have inherent self-centring capacities, if its lateral movement is under control. Consider two CLT walls arranged side by side, each with a pinned connection support at the centre of its base, if they were connected to each other with appropriate energy dissipation 2   devices, their lateral response in an earthquake can be controlled, leading to good self-centring performance and reduced damage from earthquakes.  In general, there are four ways of structural control, namely active, passive, hybrid and semi-active. Among these control systems, passive control is the only system that does not require an external power source and can impart forces developed in response to motion of the structures. These distinctions make it possible to design a well-conceived, simple and economical passive control system for buildings. In a passive control system, energy dissipation can be achieved either by conversion of kinetic energy to heat or by transferring of energy among various vibrating modes. There are generally four types of damping devices, including viscous fluid, viscoelastic, metallic, and friction dampers. In order to prevent structural failure, the effective forces of dampers should be lower than the yield forces of the structures.  Previous studies (Loo et al. 2012a, 2012b, 2014) designed a type of slip-friction connection for CLT shear walls. Working with shear keys, the friction damper showed the potential to limit activated forces on the wall, to keep maximum drifts within acceptable limits, and to allow for re-centring after earthquakes. Few investigations, however, have been conducted on CLT shear walls with metallic dampers. Low-yield steel is an ideal damping material, due to its stable hysteresis curve, good low-cycle fatigue characteristic, and insensitivity to ambient temperature. Many theoretical and experimental research studies on the low-yield steel show its effective energy absorption capabilities (Ge et al. 2008; Zhang et al. 2012a).  3   Current provisions of the National Building Code of Canada (NBCC 2010) do not contain any guidelines regarding earthquake resistant structures equipped with metallic damping devices. There is also no information on the addition of dampers to a structural system.   1.2 Objectives and Scope The scope of this research was the development of a novel pin-supported CLT shear wall system equipped with low-yield steel dampers for application in low- to mid-rise wall buildings. This study used dampers as connectors between two CLT wall panels to construct an energy dissipating shear wall pair, as shown in Figure 1-1. Since rocking deformation governs the CLT wall behaviour in cases of coupled wall panels and tall wall panels (Gavric et al. 2014), the shear and bending contributions of the wall panels were negligible in the study. In addition, pin connections at the base and connections between dampers and wall panels were all designed to be elastically linear. Therefore, the dampers in the system were considered as the only way to dissipate energy. Given the relatively simple mechanism, the study was based on numerical analysis.   4    Figure 1-1 Description of pin-supported CLT shear wall with low-yield-strength steel dampers  The objectives of this study were: 1. To design a low-yield steel damper for the pin-supported CLT shear wall system. 2. To provide a numerical model for the proposed CLT shear wall system.  3. To characterize the hysteretic behaviour of the proposed CLT shear wall system by reversed-cyclic analysis. 4. To show seismic responses of mid-rise CLT buildings constructed with the proposed CLT shear wall systems. 5. To facilitate the development of CLT material in low- to mid-rise buildings. 6. To provide a database for CLT design code provisions on damping device design.  5   1.3 Description of Methodology This study simulated the hysteresis behaviour of a pin-supported CLT shear wall system equipped with the low-yield steel dampers in an OpenSees software framework through the use of OpenSees Navigator. In the numerical model, each CLT wall panel was assumed to be rigid; between the two panels, low-yield steel dampers, modeled as zero length elements, were defined as a steel02 hysteresis material type in the vertical direction and a relative rigid material in the horizontal direction. A reversed-cyclic test on the damper was used to calibrate the definition of the damper material. Static analyses were conducted on the OpenSees model.  In a parallel study, ABAQUS, a commercial finite element analysis software, was used for a comparison analysis, which considered the deformation of CLT panels by modeling them as deformable elements. Dampers were also defined as deformable elements as an isotropic material. The damper model was analyzed under tensile force and compared with subject-to-tension test results from the literature, in order to calibrate the definition of the damper material. Static analyses were also conducted on the ABAQUS model.  By comparing the results from both models, the study verified that the wall deformation could be negligible under large lateral deformations and thus proved the rigid wall assumption made in the OpenSees was appropriate. Since the OpenSees analysis was less computationally intensive compared with the ABAQUS analysis, OpenSees Navigator was used in the seismic analysis of the study.  6   A six-storey CLT mid-rise building located in Vancouver, with six proposed shear wall systems along the excitation direction, was considered for the seismic analysis. The floors and roof were assumed to be rigid; thus, the six shear wall systems were supposed to work in the same way. Therefore, the study simulated the behaviour of one of the shear wall pairs by using OpenSees Navigator. The definitions of the wall model were similar to those in the static analysis, except for the consideration of the floors, roof and mass.  As inputs to the seismic analysis, the selected ground motions were obtained from Selection and Scaling of Ground Motions S2GM Version 1.1 (2015). The seismic hazard considered was based on a 2% probability of exceedance in 50 years. The ground motions were scaled to match the Vancouver design response spectrum in the range of 0.2 to 1.5 times the fundamental period of the structural system.  Nonlinear time-history analyses were conducted to analyze five important factors that may influence seismic responses, including the damper type, number of dampers, damper location, different earthquake records versus target earthquake design response spectrum, and earthquake peak ground acceleration. Based the results, conclusions about damper optimization design were drawn.  1.4 Thesis Organization Chapter 1 summarizes the scope and objectives as well as the applied methodology of the research.  7   In Chapter 2, a detailed literature review about rocking CLT walls and passive energy dissipation devices, especially about low-yield steel dampers, is provided. The seismic retrofit study on concrete buildings improved by combining a pin-supported wall system with dampers is used as a reference.  Chapter 3 gives a detail introduction of the damper design method and numerical models of the dampers using both OpenSees Navigator and ABAQUS. Calibrations of the two models are also provided.  Chapter 4 introduces a static analysis of the pin-supported CLT shear wall system equipped with low-yield steel dampers using both OpenSees Navigator and ABAQUS. For each part, this chapter introduces its numerical model, pushover analysis and reversed-cyclic analysis. The influence of the damper location in the static analysis is also described.  Chapter 5 concentrates on the seismic analysis of a proposed building. A description of the studied building, especially its configuration, is provided. This is followed by an explanation of the OpenSees analysis model of the building. Next, based on the site condition, explanations of the ground motion selection and scaling method are provided. Results concerning the influences of each of the five factors are discussed; and, some applicable conclusions about damper optimization design are drawn.  Chapter 6 illustrates the design concepts for both pin connections and connections between the dampers and the CLT wall panels. The pin connections consisted mainly of steel rods and steel side plates. The connections between the dampers and the CLT wall panels, including both 8   welded connections and self-tapping screws, could provide adequate resistance. Design examples are provided. Future studies on the connection design are also recommended.  Chapter 7 provides conclusions and presents recommendations for future work.   9   Chapter 2: Literature Review  2.1 Rocking Characteristics of CLT Walls Cross-laminated timber (CLT) was first introduced in Europe in the 1990s. Many studies on CLT have since been conducted in Europe, leading to commercial applications of CLT as structural building material. In North America, the application of CLT products and structures has just started, with gradual implementations into North American building codes and standards. The American National Standard for CLT product production and certification, ANSI/APA PRG 320, was created in 2012. CLT handbooks have been published by FPInnovations to illustrate design recommendations as well as approaches for both U.S. and Canadian applications.  In the U.S., the 2015 edition of the National Design Specification (NDS) for Wood Construction incorporated design provisions for CLT (American Wood Council 2014).  Based on the results of research studies and standardization/codification efforts, CLT has been introduced as an alternative material for steel and concrete for use in mid-rise and tall wood buildings. In order to gain wide acceptance, many studies have been done to establish the structural properties of CLT building material. An important property is the quantification of the seismic behaviour of CLT structures.  In 2010, a series of monotonic and cyclic CLT wall tests were implemented at FPInnovations (Popovski and Karacabeyli 2012). It showed that CLT wall panels behaved almost as rigid bodies, that CLT walls could have adequate seismic resistance if nails or screws were used with 10   steel brackets and that seismic performance could be improved by using hold-downs with nails on each end of walls or by using step joints in longer walls. The use of diagonally placed long screws to connect the CLT walls with the floor underneath, however, was shown to perform relatively poorly in terms of seismic performance, due to reduced ductile wall behaviour. An important finding was that the connections in typical CLT walls were mainly responsible for energy dissipation and that their design had a significant influence on the seismic performance of the walls.  Gavric et al.’s study (2014) on the cyclic behaviour of CLT panels illustrated three predominant types of wall deformation, namely rocking behaviour, sliding behaviour and combined rocking-sliding behaviour. For coupled wall panels and tall wall panels, rocking behaviour was shown to be predominant. Shear and bending contributions were generally negligible. Therefore, under lateral excitations, CLT walls in taller buildings are likely to behave in a rocking mode.  As such, if the rocking motion is under control, self-centring behaviour can follow.  The concept of self-centring in a rocking system can be explained as follows: under lateral excitation, without considering bottom connections, rocking walls can display a nonlinear elastic response with no energy dissipation ability. Gravity loading and vertical forces transferred from the building components above the rocking wall can provide a restoring force. These walls can be post-tensioned with unbounded tendons, if the restoring force is small. If energy dissipation devices are incorporated into the system to control the motion under lateral excitation, the self-centring response rocking walls can be improved.  11   In a post-tensioned self-centring structural system, one of the characteristics is a flag-shaped hysteresis performance (Henry et al. 2011). In that study, the post-tensioned walls were assumed to process a bi-linear elastic hysteresis response and the energy dissipation devices were idealized with elasto-plastic response. The combination of the two components resulted in the idealized flag-shape response; and, the residual drift of the self-centring structures under dynamic loadings would be much less. Therefore, this type of seismic resilient building system can dissipate earthquake energy safely with minimal structural damage.  The post-tensioned damped wall system has been used with different building materials. By incorporating energy dissipation elements, post-tensioned concrete walls performed a typical flag-shaped hysteresis response with little damage and no residual deformation to the precast walls (Restrepo and Rahman 2007). Un-bonded post-tensioning techniques and energy dissipation devices were applied to timber framed buildings (Smith et al. 2008). For the wall-to-foundation experiment, the post-tensioned tendons provided a desirable re-centring characteristic and the dissipation devices enabled adequate energy absorption by the system. Cyclic tests showed that the timber framed system had a stable flag-shaped hysteretic loop with negligible residual displacement. The equivalent yielding point of the system was close to the yielding of the dissipation devices. The structure system did not have any stiffness degradation or structural damage. Therefore, rocking walls with energy dissipation devices may process very desirable seismic resistance characteristics. To achieve the self-centring ability of CLT walls, the following requirements for the life safety performance objective should be satisfied: (1) no sliding shear damage at the wall base; (2) no 12   loss of integrity of the wall; (3) no fracture of energy dissipation devices; (4) minimal significant loss of stiffness; and, (5) no yielding of tendons. Therefore, it is important to keep both walls and energy dissipation devices from damage.  In terms of CLT buildings, large vertical forces on the walls transferred from the building components above the walls and gravity forces of the walls themselves could provide restoring forces. Therefore, in this study, post-tensioned tendons were not used. Instead, control of rocking motions and self-centring behaviour of CLT walls could be achieved by applying energy dissipation devices.   2.2 Passive Energy Dissipation Device When it comes to energy dissipation, there are several ways to control seismic responses of structures, including active, passive, hybrid control and semi-active control (Housner et al. 1997). Among the four methods, only passive control does not require an external power source and can impart forces that develop in response to the motions of the structure. These distinctions make passive control a simple and economic method.  For passive control devices, energy dissipation can be achieved by the transition of kinetic energy to heat, such as frictional sliding, yielding of metals, phase transformation in metals, deformation of viscoelastic solids or fluids, and fluid orifices. Moreover, energy can also be dissipated by conversion of energy among the various vibrating modes, i.e. supplemental oscillators.  13   There have been many studies about passive control devices, and various types of devices have been developed to meet different design requirements (Wada et al. 2009; Loo et al. 2012b). For example, metallic yield dampers can provide an effective energy dissipation mechanism through the inelastic deformation of metals (Housner et al. 1997). Metallic dampers were shown to have several desirable features, including stable hysteretic behaviour, low-cycle fatigue property, long-term reliability and relative insensitivity to environmental temperature (Zhang et al. 2012a).  Another popular type of damper is the friction damper, which can also provide an excellent mechanism for energy dissipation by slipping at a predetermined optimal load. The input earthquake energy can be dissipated efficiently by slipping of friction devices, rather than by deformation of structures. Therefore, friction dampers can help reduce deformation of structures, and a wide diversity of devices have been suggested and studied in the structural engineering.  Research studies have also shown that the material selection for friction dampers is important (Housner et al. 1997). On one hand, in order to achieve minimal stick-slip phenomena, the static and kinetic friction coefficients of frictional materials should not be too different. On the other hand, compatible materials should be applied to keep a consistent friction coefficient during the design period of the device. Therefore, many factors should be considered in the design of friction dampers.  Unlike metallic and friction dampers, which were mainly designed for seismic application, viscoelastic dampers can be used to dissipate energy at all deformation levels and can be applied for both wind and earthquake protection. One distinction of viscoelastic dampers is the simple analysis. However, studies have shown that temperature has a significant influence on 14   viscoelastic materials (Housner et al. 1997). Furthermore, since the modulus of the viscoelastic materials changes with frequency, it may present some challenges in the nonlinear response analysis of a viscoelastic-damped structural system by using a frequency domain approach (Housner et al. 1997).  A type of slip-friction connector for timber shear walls was recently proposed in New Zealand (Loo et al. 2012b, 2014). The slip-friction connector consisted of brass plates or shims, which were connected between a cover plate and a wall-embedded plate. Under seismic excitations, the connector had an asymmetric sliding. The wall-embedded plate slid relative to the centre plate, and the cover plate was “dragged” along by the bolt. Since the design enabled walls to rock with one end descending while the other was uplifting, timber shear walls could exhibit good self-centring behaviour.  Moreover, the quasi-static experiment on the timber shear wall with the slip-friction connectors proved that the design was robust and durable, with few signs of wear or tear. As long as the strengths of the connectors were less than the gravity loads on the wall, the wall exhibited good elasto-plastic behaviour and rocking capability. Therefore, the results indicated that the slip-friction connector for CLT walls could reduce the range of drift, thereby having the potential to improve seismic performance. However, the configuration of the connectors was a little complex and the cost could be high.  Finally, attention should be paid to avoid premature failure of the very stiff rivet connection and to control maximum uplift under earthquake conditions at the design level.  15    2.3 Low-yield Steel Damper 2.3.1 Characteristics Metallic dampers have been widely applied in the seismic resistant design of structures (Zhang et al. 2012b). In general, seismic behaviour of metallic dampers has the following features: a) adequate elastic stiffness to sustain small earthquakes and winds; b) lower yield strength than that of the structures; c) stable hysteretic behaviour; d) good capability of energy absorption; and, e) good low-cycle fatigue behaviour.  Low-yield steel, which can be characterized by a stable hysteresis curve, good low-cycle fatigue features and insensitivity to the ambient temperature, etc., has been shown to be a desirable material for design of metallic dampers (Zhang et al. 2012a). The low-yield-strength steel damper works like a “fuse” or a fixing apparatus under small earthquakes and serves as an energy dissipation element under large earthquakes. Effective damping force should be designed to be less than the structural yield force, in order to prevent failure of the structure.  Low-yield steel dampers are already widely applied, by adjusting the damper cross section and the number of dampers. Since 1972, low-yield-strength steel dampers have been studied theoretically and experimentally by many scholars across the world (Housner et al. 1997) and have been applied to different kinds of structures, including both buildings and bridges, in China, the U.S., Japan, Canada, New Zealand and many other countries (Zhang et al. 2013).  16   Many factors, including steel material, width-to-thickness ratio and loading method, may influence the behaviour of the low-yield steel dampers and, as such, should be taken into consideration. Two types of low-yield steel materials have been widely used, LYP100 and LYP235 (Yamaguchi et al. 1998). With similar chemical compositions, both have lower and narrower range yield points, better elongation, low-cycle fatigue characteristics and good weldability. However, compared with LYP235, LYP100 has a larger work-hardening and strain rate effect and satisfies the design necessity of both lower and upper limits of the yield point.  In terms of width-to-thickness ratio, for some large-deformation structures, damper panels have always been designed with a large width-to-thickness ratio, which can lead to out-of-plane buckling failure (Zhang et al. 2012a). For dampers with small width-to-thickness ratio, instead of out-of-plane buckling, panels may be prone to crack development at the corners under hysteretic forces. According to some studies, the energy dissipation capacities of low-yield-strength steel dampers were different under static and dynamic tests. One study (Katayama et al. 2000) showed that the capacity was larger under dynamic loading; another (Zhang et al. 2012a) indicated that the seismic performance could be overestimated by static tests and that the failure mechanisms under the two tests were also different. Out-of-plane deformation was dominated by the static tests, and the response of the dynamic specimens was dominated by in-plane shear deformation. However, both of the studies agreed that the difference was rooted in the larger influence of strain rate under dynamic loading. Therefore, in order to guarantee the reliability of the steel dampers, dynamic analysis is an important consideration.  17   In order to improve the energy absorption ability of low-yield steel dampers, many studies have investigated shape optimization. Tanaka and Sasaki reported that a damper with a width-to-thickness ratio of less than 40 could exhibit excellent hysteretic performance (Tanaka and Sasaki 2000). Another study presented an in-depth optimization of the damper shape (Zhang et al. 2012a), where a small width-to-thickness ratio was applied to prevent out-of-plane buckling. In order to avoid corner stress concentration, arc transition was proposed as an effective way in the elastic range, but was not helpful in the large plastic range. The corner stress concentration could also be alleviated with the application of ribs. It was also suggested that a smooth surface should be adopted in the panel design, rather than a sharp variable cross section.  2.3.2 Numerical Models For structures with the low-yield steel dampers, it is always important to evaluate the energy absorption ability of the dampers. Therefore, the damper model is a key part for numerical analysis. Since low-yield steel materials do not have apparent yield strengths, the hysteretic behaviour can be defined in three parts, namely the elastic period, the perfect-plastic period and the smooth transition period from elastic to plastic. Several models have been developed for the steel dampers, and their characteristics have been studied. For example, among the models, the Ramberg-Osgood and Bouc-Wen models have been widely adopted to describe the smooth transition, due to their comprehensive consideration of the Baushinger effect and of strain hardening/ softening (Zhang et al. 2013).  18   The Ramberg-Osgood model was introduced in 1943 (Ramberg and Osgood 1943). With a single nonlinear equation, the model defines the normalized strain as a function of the normalized stress. It indicates that plastic strain is present, even for a very low stress level. With the material constants used commonly, the elastic strain is still dominant, and the plastic strain is negligible. However, for a high level of stress, the plastic strain became progressively larger than elastic strain.  The Skeleton Shift Model (SS-model), which originated from the Ramberg-Osgood model, was introduced in 1992 to express strain hardening or stress degrading phenomena (Tanaka and Sasaki 2000). The study also proposed a set of values for the parameters of panel dampers made of the low-yield steel materials. Regardless of the width-to-thickness ratio, the SS-model could predict the hysteresis behaviour of the panel dampers well.  The Bouc-Wen model was proposed in 1976 and it has been widely used as a macroscopic model to simulate the behaviour of energy dissipation devices (Hossain and Ashraf 2012).  A single nonlinear differential equation that connects restoring force to corresponding deformation is used to simulate hysteresis response of the target device. There have been some modifications of the Bouc-Wen model. For example, the well-known Bouc-Wen-Baber-Noori (BWBN) model considers the strength degradation and stiffness degradation characteristics of a nonlinear system. The pinching characteristic of low-yield steel dampers, which has been observed both in laboratory testing and in finite element (FE) simulation, was also incorporated in the BWBN model. Since the Bouc-Wen model only accounts for kinematic hardening, a modified model was proposed (Karavasilis et al. 2012)to simulate combined kinematic and isotropic hardening 19   by updating the yield force with consideration of the imposed cyclic deformation history. The study showed that the modified model could not only simulate the hysteresis of low-yield steel dampers, but also could predict the behaviour of the slit devices and buckling-restrained braces.  The Giuffre-Menegotto-Pinto steel model only incorporates isotropic hardening. Like the Ramberg-Osgood model, it is also defined by a nonlinear equation. The reference curve, also known as a stress-strain curve, is assumed to be tri-linear. Isotropic strain hardening is included through shifting of the reference curve as a function of the plastic strain increment. The model can describe unloading and reloading responses well.  The Giuffre-Menegotto-Pinto Steel model was used in this study.   2.4 Application Example of Pin-supported Wall System with Steel Dampers A structural system of pre-stressed concrete rocking walls with steel dampers was recently proposed for the retrofit of a steel reinforced concrete frame (Wada et al. 2009; Sakata et al. 2012; Qu et al. 2012). Since weak storey failure has long been a problem in moment-resisting frames, the walls in the retrofit system could create uniform storey drift distribution along the height of the building, in order to replace the partial failure modes with a more preferable global failure mode, as shown in Figure 2-2. The steel dampers could dissipate energy so that the global response of the building would be better and damage to the concrete frame would be greatly reduced.   20    Figure 2-1 Moment-resisting frame with strong rocking walls (Wada et al. 2009)  The innovative retrofit system was applied to an eleven-storey ductile moment-resisting frame on the campus of Tokyo Institute of Technology in Japan. Both linear-elastic and nonlinear dynamic analyses were carried out to compare seismic behaviours of the building with and without the retrofit system. The results showed that the building with the retrofit system could avoid undesirable weak storey failure. With the protection of the proposed wall systems, damage to the frame was significantly reduced. However, the results also indicated that the floors sustained relatively small deformation and the shear demand of the frame was increased, resulting in significant but effective plastic deformation. Moreover, some local parts of the frames, such as the columns connected with the steel dampers, could suffer more damage in more severe loading conditions. In conclusion, the pin-supported wall system with dampers provided a good solution for strengthening moment-resistant frames.  As with the reinforced concrete walls in Wada et al. (2009), CLT shear walls also perform a rocking motion under lateral loadings. In this study, a novel pin connection concept in CLT shear walls is introduced to replace the traditional angle bracket and hold-down connections. Along 21   with the pin-supported CLT shear walls, the use of low-yield steel dampers as energy dissipation devices is also introduced. In this way, the connection design in the CLT shear wall system can be greatly simplified, and seismic energy can also be dissipated effectively.  In summary, in order to achieve self-centring behaviour of CLT walls without using post-tensioned tendons, effective energy dissipation devices are required to control rocking motions. By comparing different types of passive energy dissipation devices, it can be concluded that low-yield steel dampers would be a desirable choice for this study. The Giuffre-Menegotto-Pinto steel model is used for the dampers during numerical analysis. Moreover, this study considered pin-connected CLT shear walls, which were inspired by the retrofit system studies of Wada et al. (2009). The pin-supported, damped CLT shear wall system has a simplified connection design and an effective self-centring capability. A detail introduction of the proposed CLT shear wall system is provided in the following chapters.      22   Chapter 3: Design and Numerical Model of Low-yield Steel Damper  This chapter introduces low-yield steel dampers. The dampers were made of low-yield steel 100 (LYS100, with a yield strength of 100 N/mm2) and were installed between two cross-laminated timber (CLT) shear wall panels. They were expected to yield when the shear force between the two wall panels exceeded the dampers’ yield capacity.  In the study, three important factors were considered for damper design: the damper’s shear strength, shear strain capacity and out-of-plane buckling. This chapter illustrates how these factors can be considered in the design; and, the design procedure is further explained by an example.   Two-dimensional (2D) numerical models of the damper were constructed using OpenSees Navigator and ABAQUS software. These models were then used for static and seismic analyses, as discussed in Chapters 4 and 5.  This chapter provides an introduction about definitions and calibration of the damper models.   3.1 Damper Design 3.1.1 Damper Material Low-yield steel material is characterized by a low and narrow-range yield point, good elongation ability, as well as good low-cycle fatigue characteristics. Moreover, this material does not exhibit 23   a specific yielding point, but produces a smooth stress-strain curve. The standard strength equivalent to the yield point 𝜎".$, called 0.2% offset yield strength or yield stress, is defined by the stress that can produce a plastic strain offset amount of 0.2%. In this study, low-yield strength steel 100 (LYS100, yield strength 100 N/mm2) was used for the damper material. The features of the material are as follows:  1. Equivalent yield strength is as low as 100 MPa; 2. Deformation capacity can be very large, but the degradation effect is negligible until the shear strain reaches 0.15 rad, as shown in Figure 3-1; 3. Elongation can reach 60%;  4. Large work-hardening and strain rate effect.  LYS100 is, therefore, a compact, low-cost material option for the damper design.    Figure 3-1 Damper hysteresis response (Choi and Abebe 2014)  24   Zhang et al. performed tensile coupon tests for LYS 100 and obtained stress-strain curves that are shown in Figure 3-2 (Zhang et al. 2013). There are four transition periods shown in the curve, including the elastic, yield, perfect plastic and degradation periods. The curve also indicates some mechanics features of the material: the yield strength 𝜎% was 100 MPa, and the maximum stress was about 265 MPa. Since the ratio of the yield shear stress to the yield tensile stress for the low-yield steel was 13, the yield shear stress was about 58 MPa; and, the corresponding maximum shear stress was around 155 MPa (Zhang et al. 2013).    Figure 3-2 Tensile coupon experiment results of two specimens (Zhang et al. 2013)  3.1.2 Design Method Dampers in the pin-supported CLT shear wall system worked as energy dissipation elements and also as connectors. The dampers, which were located between two wall panels, were assumed to mainly transfer vertical forces, while the horizontal floor/roof elements were assumed as rigid elements to mainly transfer horizontal forces (in tension or compression). Under lateral loads, the 25   two wall panels rocking together could work as one shear wall unit. The dampers bore little tension or compression forces in the horizontal direction and had minimal axial deformation. In the vertical direction, the dampers carried shear forces and were designed to dissipate energy by yielding. Therefore, the dampers’ shear strength in the vertical direction was crucial to its energy dissipation ability and was an important part in the design. However, this shear strength should not be too large, otherwise the damper cannot yield at an early stage to protect the structure. However, if the dampers’ shear strength is too small, it will not be able to dissipate enough energy. The dampers have been named according to their vertical shear strength; e.g. damper 20 (D20) means the vertical shear strength of the damper was 20 kN.  In the damper design process, the vertical design shear strength can be referenced to the design shear force between the two CLT wall panels. The geometry of the dampers can be determined by Eq. 3-1: 𝑭 = 𝝉𝒎𝒂𝒙×𝒕×𝒉  (3-1) where F is the dampers’ design shear strength; 𝜏012 is the maximum shear stress of the LYS100,  155MPa; and t and h are the thickness and height of the damper, respectively.  The performance factor, φ, associated with the safety factor for design, is not considered here. When the damper yields and exhibits stable hysteretic behaviour, it needs to reach the maximum shear stress; therefore, an unfactored maximum shear stress has been used in the design process.  Designing the damper with a factored shear stress will achieve an oversized damper, which may not yield to create the needed damping effect. 26   In this study, different types of dampers were assumed to have the same thickness and width (6 and 150 mm, respectively); thus, the heights of the different damper types could be determined by Eq. 3.1.  It is also very important to prevent out-of-plane buckling of the steel plate. Thus, the damper’s width-to-thickness ratio should be within a certain requirement and should be checked after the initial design process. Shiyekar (2007) considered the out-of-plane buckling prevention requirement, R, which is shown in Eq. 3.2, to be less than 46. Based a value of R of 46, the width (W) to thickness (t) ratio can be calculated by: 𝑅 = 45 6$ 6789 :;<=9>  (Zhang et al. 2012a)                                                                        (3-2) where the shear yield stress, 𝜏% 		= 𝜎".$ 3 = 57.7	Mpa; 𝜎".$ is the 0.2% offset yield strength of 100 MPa; 𝐸 = 206,000  MPa, 𝜗=0.3 ; and, k is the buckling coefficient. The buckling coefficient k is calculated from Eq. 3.3: 𝑘 = 5.35×(𝑊 ℎ)$ + 4.0  (3-3) where h is the height.  If R is too small, it is necessary to prevent stress concentration at panel corners rather than out-of-plane buckling.  As shown in Figure 3-1, when the shear deformation was over 0.15 rad, the shear force of the damper decreased significantly; thus, its energy dissipation ability decreased considerably. 27   Therefore, to avoid the degradation period of the damper, its shear strain (shear displacement/width) should be less than 0.15 rad. Based on this, a limitation of the shear displacement can be calculated by Eq. 3.4:  Shear displacement limit = width × 0.15                                              (3-4) In the study, the widths of the dampers were all pre-established as 150 mm. Thus, the dampers’ shear displacement was expected to be less than 22.5mm.  The following steps use D30 as a design example. Step 1. Calculate the geometry of the damper:   As mentioned above, the dampers are assumed to have the same width and thickness, which are 150 and 6 mm, respectively. The design shear force is 30 kN, and the height of the damper is calculated with Eq. 3.5: ℎ = P:QRS×5                                                             (3-5) where F is the shear strength, which is 30 kN for D30; 𝜏012 is the maximum shear stress of 155 MPa; and, t is the thickness of the damper (6 mm).  The geometry of the D30 is, therefore, a width of 150 mm, a height of 33 mm height and a thickness of 6 mm.    28   Step 2. Check out-of-plane buckling of the damper:  Based on Eq. 3.2, the R value for the damper D30 is 0.04, which is much smaller than 46. Therefore, the out-of-plane buckling prevention requirement is met.  Step 3. Check shear deformation of the damper:  In order to avoid the degradation effect, the shear displacement of the damper should be less than 22.5 mm. This value is not used here, but is a criterion to be used in the evaluation of the numerical analysis results.   In summary, the damper design process mainly considers three factors, namely vertical shear strength, shear strain capacity and out-of-plane buckling prevention. With these comprehensive considerations, different types of dampers were designed for application in numerical analyses.  3.2 Damper Numerical Model in OpenSees Navigator  3.2.1 Numerical Model Definition OpenSees software is an object-oriented open system for earthquake engineering simulation, and OpenSees Navigator is a graphical user interface pre- and post-processor for the OpenSees software framework. Static and seismic analyses were conducted based on a 2D model developed using OpenSees Navigator. 29   In this study, the damper was modelled by using a zero length element (ZeroLength Element) with three degrees of freedom. The element was formed by two nodes, which were at the same location. The force-deformation relationship of the element was defined by three uniaxial material objects assigned to its horizontal direction, vertical direction and rotation. The definition box is shown in Figure 3-3.    Figure 3-3 ZeroLength Element definition  The three uniaxial material objects were defined separately: elastic material was used for the horizontal direction and Steel02 material for the vertical direction. It was assumed that the damper plate did not rotate; therefore, no definition for rotation was required.  To be specific, in the horizontal direction, the damper was supposed to have little deformation, due to the assumption that the rigid floors/roof could prevent the two wall elements from moving 30   apart or towards each other horizontally. Therefore, in the horizontal direction, the modulus of elasticity of the damper was assumed to be very large, as shown in Figure 3-4.     Figure 3-4 Elastic material definition  In the vertical direction, the Steel02 material used was a uniaxial Giuffre-Menegotto-Pinto steel material object with isotropic strain hardening. In Figures 3-5 3-6, the definitions of yield stress for 𝐹% and modulus of elasticity for E are not correct. 𝐹% here refers to the shear capacity of the damper. For example, D30 has the design shear capacity of 30,690 N; thus, 𝐹% should be defined as 30,690 N. E refers to the initial elastic shear stiffness of the damper, which can be calculated as shown in the following paragraphs and equations.   A vertical spring with zero length was used to represent the damper acting in shear. The spring’s load deformation relationship is characterized by the following equation: 𝑭 = 𝒌𝒙                                                                                                                                                                 (3-6) 31   where F is the shear force of the damper in units of N; k is established from the initial elastic shear stiffness E, in units of N/mm; and, x is the shear deformation of the damper in units of mm. The shear force of the damper, F, should satisfy: 𝐹 = 𝜏×𝐴	 (3-7) where 𝜏 is the shear stress; and, A is the shear area, 𝐴 = ℎ×𝑡, where h is the damper height and t is damper thickness. For the shear deformation x, it should satisfy: x=𝛾×𝑤 (3-8) where 𝛾 is the shear strain, and w is the damper width. Therefore, 𝑘 = P2 = :×Z[×\ (3-9) The relationship between the shear stress and the shear strain is:  𝜏 = 𝑟×𝐺 (3-10) where the relationship of G and E for the isotropic material is: 𝐺 = >$×(6_`) (3-11) 32   Therefore, according to Eqs. 3-9 to 3-11: 𝑘 = >×5×a$×(6_`)×\ (3-12) where E is elasticity of modulus of the damper material (206,000 MPa); 𝜐 is Poisson’s ratio of the damper material (0.3); h can be calculated according to Eq. 3-5, thus ℎ = P;5×:QRS = P;cd"; t is 6 mm; and, w is 150 mm. Therefore, the initial elastic shear stiffness is: 𝑘 = 3.408𝐹% (3-13) where 𝐹% as defined earlier represents the design shear capacity of the damper. Therefore, the initial elastic shear stiffness E should be defined differently for different types of the dampers. For example, for damper D30, E calculated according to Eq. 3-13 should be 104,585 N/mm, as shown in the Figure 3-6.  Other strain-hardening parameters were calibrated through damper reversed-cyclic analysis by comparing numerical analysis results with experiment results, which is introduced in detail in Section 3.2.2. The Steel02 material definition for the D30 damper is shown in Figure 3-6.  33    Figure 3-5 Steel02 material parameters of monotonic envelope (Opensees.berkeley.edu 2012)   Figure 3-6 Steel02 material definition of the D30 damper  34   3.2.2 Numerical Model Calibration To obtain the strain-hardening parameters for the damper model, a reversed-cyclic analysis was performed on the damper using OpenSees Navigator and calibrated the parameters by comparing the numerical analysis results with experiment results (Choi and Abebe 2014). Although the experiment was conducted on a low-yield steel LYS120 panel, hysteretic behaviours of LYS100 and LYS120 are similar; thus, the difference was assumed to be negligible.  For the experiment analysis, the specimen details and experiment boundary conditions are shown in Figure 3-7. The panel was designed to undertake shear forces. The lower end plate was fixed in all directions. The upper end plate was modelled to allow movement in the X-direction and to constrain translations in the Y- and Z-axes and was, thus, unable to rotate in all directions. Therefore, the load could be applied on the upper end plate in the X-direction.    Figure 3-7 Experiment specimen detail and boundary condition (Choi and Abebe 2014) 35   For the numerical analysis in OpenSees Navigator, the D30 damper model was constructed using a ZeroLength Element, as previously mentioned. Since the damper here should yield in the horizontal direction, the Steel02 material was used for the horizontal definition and the elastic material was used for the vertical definition. There was no definition for the rotation, due to the constrained rotation in the experiment. The boundary conditions had node1 as fixed in all directions and node2 as fixed in the Y- and Z-directions and free in the X-direction.  There are two ways to apply loads: displacement-control and force-control methods. The experiment used the displacement-control loading method. The displacements (horizontal displacement/height) were ±0.025, ±0.05, ±0.1, ±0.15 and ±0.3 rad, and each had 3 cycles. The experiment test results are shown in Figure 3-1. It could be observed that the degradation period began when the shear strain reached around 15%.  In this study, the degradation of the low-yield steel material was not considered. Therefore, the reversed-cyclic analysis on the OpenSees damper model was only carried within ±0.15	rad. The test protocol changed to 0.025, 0.05, 0.1 and 0.15 rad (3 times for each value), as shown in Figure 3-8. The load was applied to node2 along the X-direction.   36    Figure 3-8 Damper reversed-cyclic analysis loading protocol  By matching the numerical analysis results with those of the experiment, the strain-hardening parameters for the damper definition were obtained. The calibration result is shown in Figure 3-9.    Figure 3-9 Comparison of hysteresis loops 37    The agreement between the OpenSees analysis and experimental results indicated that the damper model was acceptable. The damper model was used further for structural static and seismic analyses, as discussed in Chapters 4 and 5.    3.3 Damper Numerical Model in ABAQUS 3.3.1 Numerical Model Definition ABAQUS software is generally used for finite element (FE) analysis and computer-aided engineering. There are five core software products of the ABAQUS product suite: Complete ABAQUS Environment, Viewer Product, Standard, Explicit, Computational Fluid Dynamics and Electromagnetic. ABAQUS/Standard, an FE analyzer that uses an implicit integration scheme, was employed to conduct reversed-cyclic analysis on the pin-supported CLT shear wall system equipped with dampers.  ABAQUS was utilized in the static analysis because the model could represent the system better than the OpenSees model. In ABAQUS analysis, the dampers and wall panels were all modelled as deformable elements. The analysis results should be much closer to the real performance of the wall system. However, ABAQUS analysis is much more time consuming compared with the OpenSees analysis. Therefore, by conducting static analysis with both ABAQUS and OpenSees model, the differences between the two analysis results could be quantified and then used to verify whether OpenSees model could be used for further analysis.  38   It was important to build the ABAQUS model of the low-yield steel damper. Since the thickness of the damper was much smaller than its width and depth, the damper was modelled as a 2D deformable shell part. The LYS100 steel material was defined by its characteristic elastic and plastic periods. The elastic period was defined as an isotropic hyperelastic material, which is usually used for nearly incompressible materials that exhibit an instantaneous elastic response up to large strains. Young’s modulus was defined as 206,000 MPa, and Poisson’s ratio was 0.3. The definition is shown in Figure 3-10. The plastic period was defined as an isotropic plastic material, which could simulate the hardening period when the yield surface changed size uniformly in all directions so as to cause increasing (or decreasing) in all stress directions as plastic straining occurred.  The definition needed the yield stress and plastic strain at each point from the beginning of the yielding; and, the stress-strain curves obtained from tensile coupon tests on the LYS100 steel were used (Zhang et al. 2013), shown in Figure 3-2. The definition was also calibrated through tensile analysis by matching the numerical analysis results with the experiment results. The definition is shown in Figure 3-11. The calibration is introduced in Section 3.3.2.  39    Figure 3-10 Elastic material definition for damper  40    Figure 3-11 Plastic material definition for damper  41   3.3.2 Numerical Model Calibration To calibrate the damper model, especially for the plastic material definition, a tensile test was conducted on the numerical model; and, the numerical analysis results were matched with the experiment results.  For the tensile analysis in ABAQUS, the two horizontal edges of the damper were free. One of the vertical edges was fixed, and the other was under a pulling force. The test model is shown in Figure 3-12. This was a displacement-control monotonic test and was defined as a static stress procedure that neglected inertia effects and time-dependent material effects. Since the loading in the experiment test reached a strain of 60%, the maximum displacement could be calculated by: D = 60% of the width  (3-14) Therefore, the loading was 90 mm.  42    Figure 3-12 Tensile test model in ABAQUS  The numerical analysis result is shown in Figure 3-13.   Figure 3-13 Tensile numerical analysis results 43    The agreement between the numerical analysis results (Figure 3-13) and the experiment results (Figure 3-2) simply verified the damper material definition. The ABAQUS damper model was further used for static analysis on the pin-supported CLT shear wall system, which is described in Chapter 4.    44   Chapter 4: Static Analysis of a Pin-supported CLT Shear Wall System Equipped with Low-yield Steel Dampers  As introduced in Chapter 1, the proposed cross-laminated timber (CLT) shear wall system consisted of two CLT wall panels. Between the two panels, low-yield steel dampers were installed as connectors and energy dissipation elements. The base of each panel was supported by a pin connection, instead of using hold-downs and angle brackets. Connections, including pin connections and connections between dampers and CLT panels, were designed to behave linearly elastically. The dampers were considered as the only way to dissipate energy; thus, the system has a relatively simple dissipation mechanism.  In low- to mid-rise CLT buildings, the proposed shear wall system can be constructed as tall as the building, as shown in Figure 4-1(a). Floors and roofs are also important connectors between two wall panels and are incorporated into the seismic analysis in Chapter 5. However, this chapter describes the characteristics of a one-storey shear wall system and does not consider the floors/roof. The one-storey shear wall system is shown in Figure 4-1(b).  Since this is an innovative shear wall system, there is not much information about the sizing of the wall. The wall here was sized based on a previous study (Loo 2012a). The CLT shear wall system had a height of 2.44 m and a total width of 2.44 m. The CLT material was three-layer spruce-pine-fir with a thickness of 99 mm (Structurlam 2014). The density was 440 g/m3, and the modulus of elasticity was 9,094 MPa  (Horvat 2013).   45                                                                               (a) CLT shear wall in buildings (Chapter 5)             (b) one storey CLT shear wall (Chapter 4)  Figure 4-1 CLT shear wall system description 46   This chapter presents static analyses on the one-storey shear wall system using both OpenSees Navigator and ABAQUS models. The aims were to construct relatively simple numerical models of the system and to study the pushover and reversed-cyclic behaviours of the system. By comparing the OpenSees analysis results with those of the ABAQUS analysis, the differences between the two analysis results could be quantified and thus determine whether the OpenSees model could be used for further analysis.   4.1 Numerical Simulation Using OpenSees Navigator 4.1.1 Numerical Model The OpenSees damper model is introduced in Section 3.2. This section mainly explains other parts of the model. CLT wall panels are prone to rock under lateral loading; therefore, it was assumed that the two wall panels in the system to be rigid. Supported by pin connections at the base, the panels would only rock and not deform. Therefore, the two-dimensional (2D) wall model could be simplified by using five rigid beams for the horizontal direction and one elastic column for the vertical direction. The beams were evenly distributed along the height of the wall, and length was set as long as the width of the one wall panel at 1220 mm. The column supported by the pin connections went across the middle of the beams and as high as the height of the wall panels (2440 mm). The wall panel model is shown in Figure 4-2.   47    Figure 4-2 CLT wall panel model in OpenSees Navigator  48   In the OpenSees model, both the beams and column were modelled as an ElasticBeamColumn Element, with the definition of the 2D element mainly including the modulus of elasticity, cross-sectional area, moment of inertia, and geometry transformation. For the rigid beams, which are shown in Figure 4-3, the modulus of elasticity was assumed to be very large and the geometry transformation was defined as P-delta coordinate transformation. The cross-sectional area is calculated by: 𝑨 = 𝒕×𝒉 = 𝟒𝟖𝟑𝟏𝟐	𝒎𝒎𝟐  (4-1) The moment of inertia is calculated by: 𝒍𝒛 = 𝒉𝟑𝒕𝟏𝟐 = 𝟖𝟐𝟑𝟏𝟖𝟒𝟒𝟐𝟔. 𝟕	𝒎𝒎𝟒  (4-2) For the elastic column, as shown in Figure 4-4, the modulus of elasticity was defined to be the same as that of the CLT material; and, as previously mentioned, the geometry transformation was defined as P-delta coordinate transformation. The cross-sectional area is calculated by: 𝑨 = 𝒕×𝒘 = 𝟏𝟐𝟎𝟕𝟖	𝒎𝒎𝟐   (4-3) The moment of inertia is calculated by: 𝒍𝒛 = 𝒘𝟑𝒕𝟏𝟐 = 𝟏𝟐𝟖𝟔𝟎𝟎𝟎𝟎𝟎𝟎𝟎	𝒎𝒎𝟒  (4-4)  where 𝑡 = 99𝑚𝑚, ℎ = $vv"w = 488𝑚𝑚, 𝑤 = 1220𝑚𝑚.  49    Figure 4-3 Rigid beam definition   Figure 4-4 Elastic column definition  50   To model the pin connection located at the bottom of the elastic column, translations of the X- and Y-directions were both constrained, and the connections were modelled to rotate only. In this way, two such wall models were constructed for the coupled wall panels, which were connected by using dampers. Since there were five beams along the height of the panel, five locations were available to place the dampers. In the static analysis, the study applied only two dampers. Since damper location, to be discussed in Section 4.3.2, was shown to have little influence on the static analysis, the two dampers were located at the top two positions, as shown in Figure 4-5.  Figure 4-5 Proposed shear wall system model in OpenSees Navigator  51   4.1.2 Pushover Analysis Pushover analysis is a static nonlinear analysis method. In the study, the pin-supported CLT shear wall system equipped with low-yield steel dampers was subjected to a monotonic displacement-controlled lateral load pattern, which increased continuously through elastic and plastic behaviours. The pushover analysis was aimed at assessing the performance of the shear wall system through the evaluation of its strength and deformation.  The lateral load was applied to the top of the shear wall system, which in the model was the top of the rigid beam along the X-direction, as shown in Figure 4-6. The definitions for the static analysis, such as the analysis type, constraint handler type and solution algorithm type, are shown in Figure 4-7.   Since the drift limit state design for timber building is 2.5% (National Research Council of Canada 2010), the maximum displacement applied was calculated as:  𝑫 = 𝟐. 𝟓%×𝑯 = 𝟔𝟏𝒎𝒎   (4-5) where 𝐻 = 2440𝑚𝑚. The two dampers were defined as the same type of dampers for each analysis; and, three types of dampers were used: D20, D50 and D70.   52    Figure 4-6 Pushover analysis model in OpenSees Navigator   Figure 4-7 Pushover analysis definition  53   4.1.3 Reversed-cyclic Analysis The reversed-cyclic analysis, which was based on the pushover analysis, was designed to evaluate the hysteresis behaviour of the shear wall system, as well as the dampers. In the reversed-cyclic analysis, the loading point, definition for the analysis and damper type were all considered as in the pushover analysis. By following the standard procedure from EN 12512 (British Standards 2002), the loading protocol is ±2.5, ±5, ±5, ±5, ±10, ±10, ±10, ±20, ±20, ±20, ±40, ±40, ±40, ±60, ±60, ±60	mm, as shown in Figure 4-8.   Figure 4-8 Reversed-cyclic wall test protocol  54   4.2 Numerical Simulation by Using ABAQUS 4.2.1 Numerical Model The study also constructed a 2D model of the pin-supported CLT shear wall system equipped with low-yield steel dampers using the ABAQUS/Standard program. The detail of the damper model is explained in Section 3.3. In this section, the modelling methods of the other parts are discussed. The wall panels were modelled as 2D deformable shell elements, given the negligible thickness of the panels compared with their width and height. The two wall panels had the same geometric characteristics: thickness of 99 mm, width of 1220 mm, height of 2440 mm.  Another important part of the model is the definition of the CLT material. Since material properties of CLT panels may vary for different manufacturers, the focus of this study was in the properties for Canadian made CLT panels. The behaviour of the CLT material changes for each the three mutually perpendicular directions, which is defined as orthotropic material behaviour. Within one layer, the boards are put in the same direction, so that each layer can exhibit an orthotropic material behaviour. The orthotropic material usually has nine material constants, including three moduli of elasticity E, three shear moduli G, and the corresponding Poisson’s ratios 𝜗 . Table 4-1 (Ashtari 2012) provides a summary of the elastic orthotropic material constants of spruce-pine-fir (SPF) stud grade and No. 2 or better dimension lumber, which was referenced for the vibration experiments done at the Timber Engineering Applied Mechanics 55   (TEAM) Laboratory at the University of British Columbia (Yawalata and Lam 2011) and in the Wood Handbook (U.S. Department of Agriculture 2010) .  The mechanical properties of the whole panels were, however, different from the properties of individual boards. One reason was the crosswise orientation of the layers: the other factor was the influence of the glue. The in-plane behaviour of CLT wall panels was the main interest of this study. It was assumed that the three-layer CLT panels in the study were made from the same type of SPF laminate. Nevertheless, the available test data on the overall mechanical properties were limited. Thus, it was necessary to estimate the mechanical properties, in order to generate a realistic model of CLT wall panel. There were two ways for the estimation:  1) Calculation of the properties from the properties of the individual layers; 2) Experiments on the CLT panel specimen.  An experiment study (Gsell et al. 2007) provided an example for the second approach. They developed a fully automated procedure to get the elastic properties of full-scale CLT panels. They concluded that it was relatively accurate to assume the overall mechanical behaviour of CLT panels to be orthotropic, homogeneous and linear elastic. Therefore, these experiment results were used as a reference to define the mechanical properties of the CLT wall panels in the ABAQUS analysis. Table 4-2 shows the common engineering values obtained from the study. Using these properties, the required material constants could be calculated when defining an elastic orthotropic material in ABAQUS. The definition is shown in Figure 4-9.    56   Table 4-1 Engineering constants of the boards in CLT panels (Ashtari 2012)   Table 4-2 Engineering constants calculated from the experiment results (Gsell et al. 2007)    Figure 4-9 CLT material definition box 57    To calculate these constants, some rules should be followed (Dassault Systèmes Simulia Corp 2013). The stress-strain relations for an orthotropic material are shown in Figure 4-10.   Figure 4-10 Stress-strain relationship for orthotropic material  By using the engineering constants, the D matrix was defined as: 𝑫𝟏𝟏𝟏𝟏 = 𝑬𝟏(𝟏 − 𝝑𝟐𝟑𝝑𝟑𝟐)𝜸   (4-6) 𝑫𝟐𝟐𝟐𝟐 = 𝑬𝟐 𝟏 − 𝝑𝟏𝟑𝝑𝟑𝟏 𝜸                                   (4-7) 𝑫𝟑𝟑𝟑𝟑 = 𝑬𝟑(𝟏 − 𝝑𝟏𝟐𝝑𝟐𝟏)𝜸  (4-8) 𝑫𝟏𝟏𝟐𝟐 = 𝑬𝟏 𝝑𝟐𝟏 + 𝝑𝟑𝟏𝝑𝟐𝟑 𝜸 = 𝑬𝟐 𝝑𝟏𝟐 + 𝝑𝟑𝟐𝝑𝟏𝟑 𝜸  (4-9)  𝑫𝟏𝟏𝟑𝟑 = 𝑬𝟏 𝝑𝟑𝟏 + 𝝑𝟐𝟏𝝑𝟑𝟐 𝜸 = 𝑬𝟑 𝝑𝟏𝟑 + 𝝑𝟏𝟐𝝑𝟐𝟑 𝜸  (4-10) 𝑫𝟐𝟐𝟑𝟑 = 𝑬𝟐 𝝑𝟑𝟐 + 𝝑𝟏𝟐𝝑𝟑𝟏 𝜸 = 𝑬𝟑 𝝑𝟐𝟑 + 𝝑𝟐𝟏𝝑𝟏𝟑 𝜸  (4-11) 𝑫𝟏𝟐𝟏𝟐 = 𝑮𝟏𝟐  (4-12)   58   𝑫𝟏𝟑𝟏𝟑 = 𝑮𝟏𝟑 (4-13) 𝑫𝟐𝟑𝟐𝟑 = 𝑮𝟐𝟑  (4-14) where 𝜸 = 𝟏𝟏7𝝑𝟏𝟐𝝑𝟐𝟏7𝝑𝟐𝟑𝝑𝟑𝟐7𝝑𝟑𝟏𝝑𝟏𝟑7𝟐𝝑𝟐𝟏𝝑𝟑𝟐𝝑𝟏𝟑  (4-15)  Therefore, the definition constants were derived as follows (in units of MPa):  𝐷6666 = 4731.57   𝐷$$$$ = 8329.28 𝐷dddd = 512.73 𝐷66$$ = 559.81 𝐷66dd = 194.3674 𝐷$$dd = 203.3 𝐷6$6$ = 747 𝐷6d6d = 94.9 𝐷$d$d = 540 The pin connections at the base of the two wall panels were modelled as a pinned boundary condition. The translations of the X-, Y- and Z-directions were all constrained. The definition box is shown in Figure 4-11. The connections between the dampers and the CLT wall panels, which were assumed to be very strong and to perform linearly elastically, were modelled as tie constraints connecting the wall panels together. 59   The locations of the dampers were considered as in the OpenSees model.  Figure 4-12 shows the ABAQUS shear wall model.   Figure 4-11 Pin connection definition box  60    Figure 4-12 Proposed shear wall system model in ABAQUS   61   4.2.2 Pushover Analysis The displacement-controlled pushover analysis in ABAQUS was similar to the OpenSees analysis. The pushover analysis, defined as a static general procedure, neglected inertia effects and time-dependent material effects. The lateral load was also applied at the top of the wall panel along the X-direction, as shown in Figure 4.13.  The maximum displacement calculated by Eq. 4.5 was 61	mm. The static load was applied through the creation of a displacement boundary condition to prescribe the displacement along the X-direction. The Y- and Z-directions were unconstrained. Figure 4-14 shows the loading definition.  4.2.3 Reversed-cyclic Analysis The reversed-cyclic analysis was conducted under the same test protocol as used in the OpenSees analysis (Figure 4-8). The loading point was the same location with the ABAQUS pushover analysis (Figure 4-13).  Two analysis procedures in ABAQUS/Standard can be used for cyclic analysis: the static general procedure, which was already used for the pushover analysis; and, the direct cyclic procedure, which is a quasi-static analysis combining Fourier series and time integration. The static procedure was adopted for this analysis.   62    Figure 4-13 Pushover analysis model in ABAQUS   63    Figure 4-14 Pushover loading definition in ABAQUS   64   4.3 Results and Conclusions 4.3.1 Comparison between OpenSees Results and ABAQUS Results 4.3.1.1 Pushover analysis results The pushover analysis was aimed at studying the strength and deformation characteristics of the proposed CLT shear wall system. The data analysis considered the total resistant force of the pin connections, the displacement at the top of wall panels, and the shear stress and shear strain of the dampers.  The OpenSees analysis results, as shown in Figure 4-15, illustrate the relationship between the total resistant force and the displacement.  The results indicate that the damper shear strength had an important influence on the wall resistance. To be specific, the total resistant force of the two pin connections was equal to the shear capacity of the dampers, which was resulted from the lateral force transition mechanism of the system.  Under the lateral force, the global force analysis, as shown in Figure 4-16, indicated the following equations: Horizontal force balance: 𝑭𝟏 = 𝑭𝟐 + 𝑭𝟑  (4-16) Vertical force balance: 𝑭𝟒 = 𝑭𝟓  (4-17) Moment balance:	𝑭𝟏×𝒉 = 𝑭𝟒× 𝑳𝟐, where 𝑳 = 𝒉  (4-18) Therefore,	𝐹4 = 2𝐹1.  65    Figure 4-15 Pushover analysis in OpenSees-wall response   Figure 4-16 Global force analysis  66   The partial force analysis, as shown in Figure 4-17, indicated the following relationships: Vertical force balance: 𝑭𝟒 = 𝑭𝟔 + 𝑭𝟕, where 𝑭𝟔 = 𝑭𝟕  (4-19) Therefore,	𝐹6 = 𝐹7 = 𝐹1 = 𝐹2 = 𝐹3, which was in agreement with the above conclusion that, the total resistant force was equal to the shear capacity of one of the dampers.  However, the conclusion was only applicable to the specific situation where two dampers were applied and height-width ratio of each wall panels was 2.    Figure 4-17 Partial force analysis   67   The damper response in the pushover analysis, as shown in Figure 4-18, indicated that the dampers behaved as an ideal elasto-plastic material, which agreed with the characteristics of the Steel02 material (Figure 3-4).   Figure 4-18 Pushover analysis in OpenSees damper response  Comparisons between the results of the OpenSees and ABAQUS analyses, as shown in Figures 4-19, 4-20, 4-21, illustrate the following points: 1) The shear strain was less than 0.2% before the dampers yielded. The results from both analyses matched well in terms of both the wall responses and damper responses.  2) After the dampers yielded, the shear strain values were between 0.2% and 15%. The dampers modelled in the OpenSees analysis already reached the maximum shear stress at shear strains of 0.2%; however, the ABAQUS analysis had the shear stress continue to 68   increase, reaching the same maximum value when the shear strain was around 15%. The difference resulted from the differences in the damper models.  3) The results of the two model were well matched, in terms of the damper responses after the dampers reached the maximum shear stress and shear strain was larger than 15%. However, there were some differences in the wall responses, which may be explained by the different considerations of the CLT wall panels. The ABAQUS analysis considered deformation of the CLT wall panels, but the OpenSees analysis viewed the panels as rigid bodies.   Figure 4-19 Comparison between OpenSees result and ABAQUS result for the D20 dampers   69    Figure 4-20 Comparison between OpenSees result and ABAQUS result- dampers D50   Figure 4-21 Comparison between OpenSees result and ABAQUS result- dampers D70  In conclusion, the differences between the results of the OpenSees and ABAQUS pushover analyses, which were rooted in the different assumptions of the two models, were large when the dampers’ shear strain was less than 15%, but become very small when the dampers’ shear strain reached 15%.   70   4.3.1.2 Reversed-cyclic analysis result The reversed-cyclic analyses yielded the hysteresis behaviour of the dampers and the shear wall system. The shear stress / shear strain relationship of the damper was obtained, and the relationship between the total resistant force of two pin connections and the displacement at the top of wall panels was also determined.  The wall response in the OpenSees reversed-cyclic analysis, as shown in Figure 4-22, illustrated the conclusion drawn from the OpenSees pushover analysis results – that the total resistant force of the two pin connections was equal to the shear force of the dampers. The damper response, as shown in Figure 4-23, indicated that the dampers with smaller shear strengths experienced larger shear strain. Moreover, it was shown that the dampers, which exhibited stable and large hysteresis loops, could provide the shear wall system with an efficient energy dissipation capability; thus, the pin-supported shear wall system with the dampers could have good hysteretic behaviour.  The comparison between the results of the OpenSees and ABAQUS reversed-cyclic analyses, as shown in Figures 4-24, 4-25 and 4-26, indicated some differences between the two sets of results, which were rooted in the different definitions and assumptions of the two models.  71    Figure 4-22 Wall response in OpenSees reversed-cyclic analysis    Figure 4-23 Damper response in OpenSees reversed-cyclic analysis  72    Figure 4-24 Comparison between OpenSees and ABAQUS results for D20 dampers    Figure 4-25 Comparison between OpenSees and ABAQUS results for D50 dampers    Figure 4-26 Comparison between OpenSees and ABAQUS results for D70 dampers   73   Given the observed differences between the results of the two analyses, an energy dissipation qualification was conducted by comparing reversed-cyclic analysis results of the wall system equipped with two D70 dampers. Based on the wall responses, as shown in Figure 4-26, the qualification was conducted by calculating the cumulative area of the hysteresis loop under different loading amplitudes. The results are shown in Table 4-3. For example, “7.5×3" means that the largest loading amplitude of the reversed-cyclic test was 7.5 mm and that the loading was applied 3 times. During the 3 loading cycles, the areas of the hysteresis loops obtained from the ABAQUS and OpenSees analyses were 916.6 J and 3105 J, respectively. Therefore, the difference was: 𝑫 = 𝑶𝒑𝒆𝒏𝑺𝒆𝒆𝒔7𝑨𝑩𝑨𝑸𝑼𝑺𝑨𝑩𝑨𝑸𝑼𝑺 ×𝟏𝟎𝟎% = 𝟐𝟑𝟗%  (4-20)  Table 4-3 Energy dissipation qualification Amplitude (mm) 2.5 5 7.5×3 10×3 20×3 40×3 60×3 ABAQUS (J) 13.6 147.5 916.6 2409 10653 30221 47180 OpenSees (J) 21.1 418.6 3108 5116 13334 28131 45459 Difference (%) 54 184 239 112 25.17 7.43 3.78  The results showed that, before the dampers yielded, the amplitudes were less than 10 mm, and the differences between the two results were large. The OpenSees model overestimated the energy dissipation ability of the system, which resulted from the ideal elastic-plastic model of the 74   dampers. After the dampers yielded, the difference was very small. The results also showed that when the amplitudes were 40 and 60 mm,	 the areas of the hysteresis loops of the ABAQUS analysis results became larger than those of the OpenSees analysis, which could be explained by the following two points:  1) When the amplitude was large enough, the behaviours of the two damper models became similar; thus, the difference that resulted from the damper models became smaller;  2) The ABAQUS analysis considered deformation of the wall panels; thus, the energy in the ABAQUS model could be dissipated by both the wall panels and dampers’ deformation. However, in the OpenSees analysis, the wall panels were assumed to be rigid; therefore, the energy was dissipated only by the dampers. With increased loading, the deformation of the wall panels kept increasing in the ABAQUS analysis, resulting in greater energy dissipation.    In conclusion, when the loading is large, the assumptions in the OpenSees model will not cause too much difference to the analysis results, and the OpenSee model will be as accurate as the ABAQUS model. Given that the ABAQUS analysis is much more time consuming, it would be effective and efficient to apply the OpenSees model for further seismic analysis.   4.3.2 Influence by Damper Location In the static analysis, it was assumed that damper location had little influence on the analysis results. The assumption was based on two factors:  1) The two CLT wall panels were assumed to be rigid.  75   2) The dampers connecting the two panels were assumed to be rigid in the horizontal direction, thus relative vertical displacements between two wall panels should be similar along height of the wall. The damper location was, therefore, not an influential factor in the global response.  The assumption was studied using both OpenSees and ABAQUS analyses. The five damper locations, labelled as 1, 2, 3, 4, 5 from top to bottom, are shown in Figure 4-27. The OpenSees and ABAQUS reversed-cyclic analyses’ results of the two D20 dampers located at 1&2 and 1&5 were compared.  The analysis results are shown in Figures 4-28 and 4-29.  With the dampers located at 1&2 and 1&5, the wall responses of the two situations in each analysis were similar; and, the dampers in the different positions had almost the same behaviour. Therefore, damper location was proven to have little influence on the wall and damper responses during static analysis.  76    Figure 4-27 Illustration of the damper location 77           Figure 4-28 Damper location analysis in OpenSees Navigator   Figure 4-29 Damper location analysis in ABAQUS    78   Chapter 5: Seismic Analysis of Mid-rise CLT Building  This chapter focusses on the seismic analysis of a mid-rise CLT building constructed by the pin-supported cross-laminated timer (CLT) shear wall system equipped with low-yield steel dampers. An example of the building is provided and its seismic analysis using OpenSees Navigator software is presented.  This chapter describes a simplified building model of the shear wall system using OpenSees Navigator. The main difference between the wall model and the building model was that the building model considered the influence of floors and roof and assumed the rigid floor and roof to transfer mainly horizontal forces.  The studied building was designed to be located in Vancouver, Canada. Based on its ground characteristics, a suite of earthquake records from Selection and Scaling of Ground Motions S2GM Version 1.1 (Selection and Scaling of Ground Motions S2GM Version 1.1 2015) were selected. The seismic hazard level was considered as a 2% probability of being exceeded in 50 years, and the original earthquake response spectra were scaled to match with the Vancouver design response spectrum.  During the seismic analysis, five important factors – damper type, damper number, damper location, different earthquake records versus target earthquake design response spectrum, and earthquake peak ground acceleration (PGA) – were considered. The influence of each factor was analyzed, and conclusions were drawn to help with the building design.  79   5.1 Studied Building A seismic analysis was conducted on a six-storey CLT building constructed with the pin-connected damped CLT shear wall system. As mentioned in Chapter 4, this is an innovative shear wall system, and there is not too much information about the sizing of the wall. The wall here was sized based on a previous study (Loo 2012a). As in Chapter 4, the CLT wall pair for each storey had a height of 2.44 m, a length of 2.44 m and a thickness of 0.099 m. Each wall panel was supported pin connections at the base and was connected to the paired panel with low-yield dampers. The overall height of the six-storey building was 14.64 m.  The main criterion for the building design was to ensure that the pin connections could sustain base shear forces, which vary with the weight of the building. Therefore, the sizing strategy of building was as follows: 1) Estimate the number of the paired shear wall systems needed, the building geometry and the weight of the building; 2) Calculate the base shear forces of the building based on the weight and the site conditions; 3) Check the base shear force for each wall system and for each pin connection; 4) Design the pin connections using a capacity design procedure. If the size of the connections was reasonable, this plan would be feasible. However, if the required pin connections were very large, this plan would not be feasible; and, it would be necessary to add more walls or adjust the geometry of the building and to go through the process again.   80   For example, given the assumption that the earthquake excitations would be exerted along the X-direction, six CLT shear wall systems were designed along the X-direction; and, four shear walls were placed along the Y-direction. The rectangular building had a length of 15 m and a width of  10 m. The plan view of the building is shown in Figure 5-1.    Figure 5-1 Plan view of the studied building  The weight of the building needed to be estimated. The shear wall panels, which were made of the three-layer spruce-pine-fir (SPF) CLT panels, had a density of 440 kg/m3 and a modulus of elasticity of 9094 MPa.  Thus, the weight of the shear walls was:  𝑊6 = 10× 440×0.099×2.44×14.64 ×10 = 155603	𝑁                 (5-1)       81   The weight of floors was considered to have a dead load of 1500 N/m2  and a live load of 2000 N/m2 (National Building Code of Canada 2010). With the load combination, the total loading of dead and live loads was:  𝑊$ = (0.9𝐷 + 1.5𝐿)×6 = (0.9×10×15×1500 + 1.5×10×15×2000)×6 = 3915000𝑁  (5-2) The flooring cover was oak hardwood with a thickness of 19 mm and a density of 640 kg/m3; therefore, the weight of floors was: 𝑊d = 6× 640×0.01905×15×10 ×10 = 109728	𝑁 (5-3) The total weight of the building was 𝑊 = 𝑊6 +𝑊$ +𝑊d = 	4180331𝑁          (5-4) Therefore, the total seismic mass of the building was: 𝑀 = v6‘"dd66" = 418033𝑘𝑔 ≈ 418𝑡                             (5-5)      So, the equivalent seismic mass for per shear wall was: 𝑚 = v6‘” = 69.7𝑡                                                                (5-6)      With a building weight of 4180.331 kN, the base shear forces could be calculated using Eq. 5-7 (National Building Code of Canada 2010): 𝑉 ≥ — ˜R ™š›œ4žŸ   (5-7) 82    where S(𝑇1) is the design spectral acceleration values; 𝑀¡ is the higher mode factor; 𝐼> is important factor; W is the mass of the building; and, Rd and RO are also relevant factors. Based on the Vancouver site conditions, S(𝑇1) could be calculated; and, the details are discussed in Section 5.3.1.  The base shear force for the building was calculated as 1180 kN, and the base shear force for each shear wall system was 197 kN, which is not too large to sustain. Therefore, the proposed building sizing was feasible and was considered for the seismic analysis.   5.2 Numerical Simulation Model The seismic analysis of the building was conducted using OpenSees Navigator. With the assumption of rigid floors, the lateral force could be evenly distributed to the shear walls, and all shear walls were supposed to work in the same way. Therefore, in order to obtain the seismic response of the building, it was only necessary to analyze one of the shear walls; and, the numerical model could be simplified as shown in Figure 5-2. The model was similar to that of the one-storey shear wall discussed in Chapter 4. Since the six-storey shear wall was assumed as two rigid wall panels connected by dampers and floors, the wall panels were modelled as beams and columns, which were also considered as ElasticBeamColumn element objects in OpenSees.   83    Figure 5-2 Building model in OpenSees Navigator  84   The geometric parameters of the beams and columns were calculated according to the equivalent cross-section areas and the equivalent moment of inertia of the wall panel. The geometry transformation of both beams and columns were defined as P-delta coordinate transformation. For each storey, five rigid beams were applied, and the tributary area of the wall panels was distributed evenly to those beams. Therefore, the beams were of the same type and each represented 1/5 of a one-storey wall panel. Two columns were applied to model the vertical behaviour of the wall panels, with each column represents one wall panel. Therefore, the columns were also of the same type, and the width of each was equal to the width of one wall panel. Finally, the modulus of elasticity of the beams was considered to be very large, in order to model rigid behaviour. The modulus of elasticity of the columns was defined as 9094 MPa	, same as in Chapter 4. The details are shown in the following equations and figures. Beams: Cross-sectional area: 𝐴 = 𝑡× aw = 48312                                   (5-8) Moment of inertia: 𝑙𝑧 = 5 ¥¦ §6$ = 9.58767744×10‘	𝑚𝑚v                  (5-9) where 𝑡 = 99 mm and ℎ = 2440 mm. Columns: Cross-sectional area: 𝐴 = 𝑡×\$ = 120780𝑚𝑚$               (5-10) 85   Moment of inertia: 𝑙𝑧 = 5 9¨ §6$ = 1.4980746000×106"	𝑚𝑚v  (5-11) where 𝑡 = 99 mm and ℎ = 2440 mm. Definitions are shown in Figures 5-3 and 5-4.    Figure 5-3 Definition of beams   Figure 5-4 Definition of columns   86   The pin connections, as described in Chapter 4, were applied to the base of the columns, in order to model the two rocking CLT shear wall panels. The connections between the two wall panels were dampers or floors/roof. The dampers were defined as described in Chapter 3 and could also perform as connections between the two wall panels. In our case, there were four positions available for the dampers in each storey, and the number of dampers could be changed based on requirements.  The floors/roof were modelled as TwoNodeLink elements in OpenSees, as shown in Figure 5-5, which could only transfer forces along the X-direction. Since the floors/roof were assumed to be rigid, the material along the X-direction was defined as an elastic material with a large modulus of elasticity, as shown in Figure 5-6. Therefore, a simple model of the shear wall system was constructed to represent the whole building.   Figure 5-5 Floor element definition  87    Figure 5-6 Floor material definition  The seismic mass was needed for the seismic analysis and was added to the nodes of the floors/roof. As previously described (from equation 5-1 to equation 5-6), the equivalent seismic mass per shear wall was 69.7 t. Each floor/roof was modelled by six nodes; thus, the seismic mass for each node was: 𝑚©ª«¬ = ”c.­”×” = 1.936	𝑡  (5-12) The model with the seismic mass was used for the seismic analysis.   5.3 Ground Motion Selection and Scaling Methodology 5.3.1 Selection of Ground Motion The studied building was assumed to be located in Vancouver, B.C. and situated in Site Category C.  According to the National Building Code of Canada (NBCC) 2010, the seismic hazard considered was based on a 2% probability of being exceeded in 50 years (2/50). The design 88   response spectrum was determined by using linear interpolation for intermediate values of the fundamental period of vibration. Therefore, the Vancouver design spectral acceleration values of 𝑆1(𝑇) are as follows: 𝑇 ≤ 0.2	𝑠, 𝑆1 𝑇 = 0.96	𝑔                   (5-13) 𝑇 = 0.5𝑠, 𝑆1 0.5 = 0.64𝑔            (5-14) 𝑇 ≤ 1.0𝑠, 𝑆1 1.0 = 0.33𝑔                            (5-15) 𝑇 ≤ 2.0𝑠, 𝑆1 2.0 = 0.17𝑔  (5-16) 𝑇 ≥ 4.0𝑠, 𝑆1 𝑇 = 0.085𝑔     (5-17) The design response spectrum of Vancouver is shown in Figure 5-7.   Figure 5-7 Vancouver design response spectrum 89    Since no records of strong earthquakes from the Vancouver region were available, some earthquakes that occurred in other places were referenced. The earthquake information was provided by Selection and Scaling of Ground Motions S2GM Version 1.1 (Selection and Scaling of Ground Motions S2GM Version 1.1 2015). The selection of earthquake records was based on the following two standards. 1) Earthquake magnitude: There are two magnitude (M) / distance (R) scenarios that are considered to dominate the seismic hazard for Vancouver: M = 6.5 and R = 30 km, and M = 7.2 and R = 70 km (Naumoski et al. 2004). Therefore, in the selected seven earthquakes, three had magnitudes of around 6.5, and another three had magnitudes of around 7.2. In order to consider a very severe situation, an earthquake with a magnitude of 8.8 was also used. 2) Tectonic features: There are three different types of earthquakes that can occur in the Vancouver area: crustal, subcrustal and subduction seismic events. Crustal earthquakes originate in the North American plate with the depths of around 30 km. Subcrustal earthquakes extend to depths of around 100 km and occur within the Juan de Fuca Plate that slides beneath the North American Plate. Subduction earthquakes are the most damaging types of earthquakes with magnitudes of 8 or larger. These threats come from the interaction between the Juan de Fuca and North American Plates.  Onur and Seemann (2004) showed that, within the next 50 years, the probabilities of structurally damaging earthquakes due to crustal or subcrustal earthquakes in the 90   Vancouver area are 12% and 21%, respectively. The corresponding probabilities of non-structurally damaging earthquakes are 35% and 56%, respectively. The probability of the subduction interface earthquake is around 11%. Therefore, three crustal earthquakes, three subcrustal earthquakes and one subduction earthquake were selected.  The earthquake information is shown in Table 5-1.   Table 5-1 Selected earthquake records No. Source Area PGA(g) Magnitude Distance (km) File Name 1 Subcrustal Miyagi, Japan 0.243845 7.2 118.55 Miyagi_Oki_MYG0130508161146 2 Subduction Maule, Chile 0.474499 8.8 85 Maule_curico1002271 3 Crustal Chichi, Taiwan 0.283 6.2 10.1 CHICHI04_CHY074 4 Crustal Landers, USA 0.630 7.3 44.02 LANDERS_LCN345 5 Subcrustal Honshu, Japan 0.325146 6.4 33.77 SHonshu_EHM008010324152 6 Crustal Nahanni, Canada 0.935 6.8 6.8 NAHANNI_S1010 7 Subcrustal Geiyo, Japan 0.228896 6.4 40 Geiyo_YMG0180103241528  91   5.3.2 Ground Motion Scaling The ground motions were amplitude scaled, so that the mean spectrum over the period range of 0.2 to 1.5 T (where T is the fundamental period) did not fall below the target spectrum by 10% (Yang and Murphy 2014).  Minimum period: 0.2×𝑇 = 0.19188𝑠  (5-18) Maximum period: 1.5×𝑇 = 1.4391𝑠  (5-19) Fundamental period T was considered as 0.9956 s, because it was the OpenSees Eigen analysis result for the optimized design, i.e. each paired shear wall system equipped with 15 D44 dampers. The damper optimization is explained in detail in Section 5.4. However, since the stiffness of the structure could change with different applications of the dampers, T could also change. Changes in T during the scaling were not considered; however, the range of 0.2 to 1.5 T should have incorporated all the situations.  The original and matched response spectra are shown in Figures 5-8 and 5-9, respectively. “Target” in the figures refers to the Vancouver design response spectrum. The earthquake peak ground acceleration (PGA) values were scaled to 1.0 g, in order to obtain the response of the building under a larger earthquake hazard.    92    Figure 5-8 Original response spectrum   Figure 5-9 Matched response spectrum   93   5.4 Results and Conclusions In the numerical analysis, five important factors were considered: damper type, number of dampers, damper location, different earthquake records versus target earthquake design response spectrum, and earthquake peak ground acceleration (PGA). The seismic responses were evaluated with respect to the following two criteria:  1) The drift-ratio time-history response of the top floor, which illustrates the changing of displacement at the top of the wall over time during seismic excitations. For tall timber buildings, the maximum drift ratio must be less than 2%, and a residual drift ratio less than 0.2% is preferred.  2) The damper response as the relationship between the damper shear force and damper the shear displacement, which indicates the energy dissipation capability of dampers during seismic excitations. To avoid stress degradation, shear displacement of dampers should be less than 22.5 mm (shear strain of 0.15 rad).  The analysis results are summarized in Table 5-2.  The two earthquake hazard levels considered were:  1) The earthquake was based on a 2% probability of being exceeded in 50 years (2/50). 2) The earthquake PGA was considered as 1.0 g.  The influences of each factor are illustrated in detail in the following subsections.      94   Table 5-2 Seismic analysis results summary Variable Damper Type Damper Number Damper Location Earthquake Type Earthquake PGA Results Damper Type D50, D100, D200, D500 15 Shown in Table 5-3 No. 2, Maule earthquake 2/50, 1.0 g Figs. 5-10 to 5-13, Tables 5-4 and 5-5 Damper Number D44 12, 15, 18 Shown in Table 5-6 No. 2, Maule earthquake 2/50, 1.0 g Figs. 5-14 to 5-17, Tables 5-7and 5-8 Damper Location D44 15 Shown in Table 5-9 No. 2, Maule earthquake 2/50, 1.0 g Figs. 5-18 to 5-21, Tables 5-10, 5-11 Earthquake Type D44 15 No. 1 case in Table 5-9 Shown in Table 5-1 2/50, 1.0 g Figs. 5-22 to 5-24, Tables 5-12 to 5-14 Earthquake PGA D44 15 No. 1 case in Table 5-9 Shown in Table 5-1 0.1g to 1.0 g Figs. 5-25 to 5-28, Tables 5-15, 5-16  5.4.1 Influence of the Damper Type The damper type is determined by the designed shear strength. Since the width and thickness of different types of dampers are the same, i.e. 150 and 6 mm, respectively, the difference lies in the height of the dampers. For example, D30 means the designed shear strength was 30 kN; thus, the height of D30 was 33 mm. In order to illustrate the influence of damper type on the seismic response, it was necessary to control other factors. Fifteen dampers were applied to each shear wall system of the studied building; the distribution of which is as shown in Table 5-3. The No. 2 earthquake (Maule 95   earthquake, as shown in Table 5-1) was used. The two stated earthquake hazard levels were considered. Table 5-3 Damper distribution in the damper type study Number of Dampers 1st storey 2nd storey 3rd storey 4th storey 5th storey 6th storey 15 3 3 2 2 2 3  In both situations, three types of dampers were considered: D44, D100, D200. The analysis results are shown in the following subsections (5.4.1.1 and 5.4.1.2). The damper response of the No. 1 damper was recorded (the location number is shown in Figure 5-2) and was analyzed to make conclusions.    5.4.1.1 Earthquake level of 2% probability in 50 years (2/50)  Figure 5-10 Comparison of drift-ratio time-history responses of the top floor with different damper types for the 2/50 earthquake level  96     Figure 5-11 Comparison of damper responses with different damper types for the 2/50 earthquake level  Table 5-4 Seismic response comparison among different types of dampers for the 2/50 earthquake level  Damper Type D44 D100 D200 Maximum Drift Ratio (%) 0.69 0.89 1.02 Residual Drift Ratio (%) 0.07 0.08 0.020 Maximum Damper Displacement (mm) 8.83 7.29 5.6  97   5.4.1.2 Earthquake level – PGA value of 1.0 g  Figure 5-12 Comparison of drift-ratio time-history responses of the top floor with different damper types for an earthquake with a PGA value of 1.0 g   Figure 5-13 Comparison of damper responses with different damper types for an earthquake with a PGA value of 1.0 g  98   Table 5-5 Seismic response comparison among different types of dampers for an earthquake with a PGA value of 1.0 g  Damper Type D44 D100 D200 Maximum Drift Ratio (%) 1.57 1.26 Not applicable Residual Drift Ratio (%) 0.015 0.04 Not applicable Maximum Damper Displacement (mm) 20.59 16.52 Not applicable  5.4.1.3 Results and Conclusion The results show that, under the required seismic hazard level (2% in 50 years), the maximum and residual drifts of the top floor and the maximum damper displacements in all cases satisfied the requirements. However, the shear wall system with D200 dampers was too stiff to rock at that level of seismic hazard. Therefore, the displacements of the dampers were smaller, and the energy dissipation capability of the dampers was not fully utilized, resulting in a relatively larger maximum drift of the top floor than those of D44 and D100 dampers.   When the PGA of the seismic record reached 1.0 g, the damper displacements, maximum drift ratios and residual drift ratios with the D44 and D100 dampers were all less than the requirements. However, when the shear strength of the dampers was as large as 200 kN, the analysis only ran for a short period and failed to converge, because the dampers were too strong to yield and the earthquake energy could not be dissipated effectively.   99   In conclusion, dampers, on the one hand, dampers must be large enough to provide effective energy dissipation, so that drifts of the building can meet the requirements. On the other hand, if the dampers are too strong, they will hardly yield, and the energy dissipation will be work effectively. Therefore, an optimal design is required to decide the damper type. In this case, 15 D44 dampers provided a good design.   5.4.2 Influence of the Number of Dampers The damper number refers to the total number of dampers used for one shear wall system. Since the model had 24 locations available for dampers, the maximum number was 24.  To evaluate the influence of the damper number, the seismic hazard levels considered were the same as those in 5.4.1. D44 was the type of damper used. In order to minimize the influence of damper location, the dampers were as evenly distributed to each storey as possible. For example, when applying 12 dampers, each storey was equipped with 2 dampers (the locations are shown in Figure 5-2). In this study, 12, 15 and 18 dampers were investigated. the distribution of dampers for each storey with the different number of dampers is presented in Table 5-6. The study also recorded the response of the damper in the No.1 location for all situations.  The analysis results are shown in Section 5.4.2.1, 5.4.2.2 and 5.4.2.3.     100   Table 5-6 Damper distribution along the building Number of Dampers 1st storey 2nd storey 3rd storey 4th storey 5th storey 6th storey 12 2 2 2 2 2 2 15 3 3 2 2 2 3 18 3 3 3 3 3 3  5.4.2.1 Earthquake level of 2% probability in 50 years (2/50)  Figure 5-14 Comparison of drift-ratio time-history responses of the top floor with different damper numbers for the 2/50 earthquake level   101    Figure 5-15 Comparison of damper responses with different damper numbers for the 2/50 earthquake level   Table 5-7 Seismic response comparison among different damper numbers for the 2/50 earthquake level  Number of Dampers 12 15 18 Maximum Drift Ratio (%) 0.59 0.69 0.71 Residual Drift Ratio (%) 0 0.07 0.06 Maximum Damper Displacement (mm) 7.8 8.83 9.36    102   5.4.2.2 Earthquake level – PGA value of 1.0 g  Figure 5-16 Comparison of drift-ratio time-history responses of the top floor with different damper numbers for an earthquake with a PGA value of 1.0 g   Figure 5-17 Comparison of damper responses with different damper numbers for an earthquake with a PGA value of 1.0 g  103   Table 5-8 Seismic response comparison among different damper numbers for an earthquake with a PGA value of 1.0 g Number of Dampers 12 15 18 Maximum Drift Ratio (%) 2.15 1.57 1.66 Residual Drift Ratio (%) 0.40 0.015 0.43 Maximum Damper Displacement (mm) 27.18 20.59 23.00  5.4.2.3 Results and Conclusion The results show that, under the required level of seismic hazard (2% in 50 years), the maximum and residual drifts of the top floor and the maximum damper displacements satisfied the requirements in three cases. There was little difference between the results of different cases.  However, under a more severe seismic excitation (PGA = 1.0g), the results of the three cases considered were quite different. The building with 12 dampers exceeded the maximum drift limit, the residual drift limit and the maximum damper displacement. This resulted from the fact that the number of the dampers provided was inadequate. Therefore, it may be necessary to provide more dampers, so that earthquake energy can be dissipated more efficiently.  When the building was equipped with 15 dampers, the maximum drift ratio was less than 2%, the residual drift ratio was less than 0.2%, and the maximum damper displacement was less than 22.5 mm. However, if the number of employed dampers was increasing to 18, the drifts became 104   larger again, with the residual drift and maximum damper displacement exceeding the requirements. The reason may be rooted in the fact that increasing the number of dampers also increased the stiffness of the building. With too many dampers, the building was so stiff that the self-weight could not provide enough restoring force to make the building rock back.  In conclusion, the number of dampers also needs to be optimized. The dampers should provide enough energy dissipation capability and should not increase the stiffness of the building too much. In our study, the optimal number was 15 D44 dampers.   5.4.3 Influence of the Damper Location Based on previous analyses, when the model was equipped with 15 D44 dampers and the dampers were distributed in a certain pattern, its responses satisfied all the requirements. In order to study the influence of damper location, 15 D44 dampers were distributed in three different patterns, including the one used in Sections 5.4.1 and 5.4.2. The excitations of the No. 2 earthquake (Maule earthquake) considered here were also the same as in the previously mentioned sections. The distribution of dampers is illustrated by counting the number of dampers for each storey (shown in Figure 5-2) and as listed in Table 5-9. The analysis results are shown in the following subsections, with the responses of the damper at the No. 1 location recorded for the analysis.    105   Table 5-9 Damper distributions with the building Three cases 1st storey 2nd storey 3rd storey 4th storey 5th storey 6th storey No. 1 3 3 2 2 2 3 No. 2 4 4 4 3 0 0 No. 3 3 3 3 2 2 2  5.4.3.1 Earthquake level of 2% probability in 50 years (2/50)  Figure 5-18 Comparison of drift-ratio time-history responses of the top floor with different damper locations for the 2/50 earthquake level  106    Figure 5-19 Comparison of damper responses with different damper locations for the 2/50 earthquake level  Table 5-10 Seismic response comparison among different damper locations for the 2/50 earthquake level Case of Damper Distribution No. 1 No. 2 No. 3 Maximum Drift Ratio (%) 0.69 0.87 0.73 Residual Drift Ratio (%) 0.07 0.19 0.11 Maximum Damper Displacement (mm) 8.83 8.24 9.10  107   5.4.3.2 Earthquake level – PGA value of 1.0 g  Figure 5-20 Comparison of drift-ratio time-history responses of the top floor with different damper locations for an earthquake with a PGA value of 1.0 g   Figure 5-21 Comparison of damper responses with different damper locations for an earthquake with a PGA value of 1.0 g 108    Table 5-11 Seismic response comparison among different damper locations for an earthquake with a PGA value of 1.0 g Case of Damper Distribution No. 1 No. 2 No. 3 Maximum Drift Ratio (%) 1.57 2.40 1.67 Residual Drift Ratio (%) 0.015 1.07 0.38 Maximum Damper Displacement (mm) 20.59 29.13 22.44  5.4.3.3 Results and Conclusion The results show that, when the seismic hazard level was 2% in 50 years, the drifts of the top floor and the displacements of the dampers all met the requirements in all studied cases. However, both the maximum and residual drifts in the No. 2 case were larger than the other two cases. When the PGA of the earthquake reached 1.0 g, in the No. 1 case, all the requirements were still satisfied. However, the maximum and residual drifts and the maximum damper displacement in case No. 2 all exceeded the requirements; and, the residual drift and maximum damper displacement exceeded the requirements in the third case (No. 3). Therefore, the No. 1 case had the best damper distribution pattern.  These results indicate that damper location is an influential factor in a seismic analysis, which was quite different from the reversed-cyclic analysis results. The difference is rooted in the fact 109   that the forces were exerted differently in the two situations. In the reversed-cyclic analysis, the force was only applied to the top point of the shear walls. The shear forces along the height of the walls were the same. Since the dampers also had the same yield forces, the location of the dampers was not very important.  In the seismic analysis, seismic forces were, however, distributed along the height of the walls; thus, the shear forces were different at different locations. Although the dampers were assumed to be rigid along the horizontal direction, they actually could deform, especially under large lateral forces. Ideally, the two wall panels would rock together, and the shear force would redistribute equally through those dampers. However, dampers were only distributed at some locations. For example, if dampers were all distributed at the bottom, as in the No. 2 case, the two wall panels may not connect tightly at the top, and the wall system may not perform as well as assumed. This was proven by the analysis. Therefore, the damper locations do matter in a seismic analysis.  In conclusion, it was shown that damper location may influence seismic behaviour, especially on drifts of the building. This analysis also indicated that the dampers would better be distributed evenly in the building. In our case, the dampers should be located according to the pattern in the No. 1 case.  110   5.4.4 Influence by Different Earthquake Records Versus Target Earthquake Design Response Spectrum The results from previous study showed that, according to the No. 2 earthquake, the optimized design was 15 D44 dampers distributed as evenly as possible to each storey. Responses to more earthquakes needed to be investigated, in order to check the design. There were seven types of earthquakes considered, with each occurring in a different location. For each earthquake, three earthquake records were applied the original earthquake record, the earthquake record scaled to match the seismic hazard level of 2% in 50 years, and the earthquake record with the PGA scaled to 1.0 g. The results are shown in following subsections. 5.4.4.1 Under original earthquake excitations  Figure 5-22 Drift-ratio time-history response of the top floor under the original earthquake excitations 111    Table 5-12 Seismic response comparison among the original earthquake excitations Earthquake Types Maximum Drift Ratio (%) Residual Drift Ratio (%) No. 1 Original Earthquake 0.37 0.010 No. 2 Original Earthquake 0.81 0.015 No. 3 Original Earthquake 0.77 0.075 No. 4 Original Earthquake 0.53 0.14 No. 5 Original Earthquake 0.60 0.060 No. 6 Original Earthquake 0.91 0.17 No. 7 Original Earthquake 0.90 0.041  5.4.4.2 Under matched earthquake excitations (seismic hazard 2% in 50 years)  Figure 5-23 Drift-ratio time-history response of the top floor under the matched earthquake excitations for the 2/50 earthquake level 112    Table 5-13 Seismic response comparison among matched earthquake excitations for the 2/50 earthquake level Earthquake Types Maximum Drift Ratio (%) Residual Drift Ratio (%) No. 1 Earthquake 0.45 0.02 No. 2 Earthquake 0.68 0.08 No. 3 Earthquake 0.54 0.13 No. 4 Earthquake 0.85 0.21 No. 5 Earthquake 0.72 0.14 No. 6 Earthquake 0.28 0.05 No. 7 Earthquake 1.67 0.40  5.4.4.3 Under earthquake excitations with the PGA scaled to 1.0 g   Figure 5-24 Drift-ratio time-history response of the top floor under the earthquake excitations for a PGA of 1.0 g 113   Table 5-14 Seismic response comparison among earthquake excitations for a PGA of 1.0 g Earthquake Types Maximum Drift Ratio (%) Residual Drift Ratio (%) No. 1 Earthquake 1.22 0.012 No. 2 Earthquake 1.57 0.015 No. 3 Earthquake 3.00 0.91 No. 4 Earthquake 2.05 0.53 No. 5 Earthquake 1.96 0.51 No. 6 Earthquake 0.75 0.021 No. 7 Earthquake 2.67 0.52  5.4.4.4 Results and Conclusion The results showed that, under the original earthquake excitations, both the maximum and residual drifts in all seven cases satisfied the requirements. When the seismic hazard level was 2% in 50 years, all the maximum drifts were less than 2%, and most of the residual drifts (except that of the No. 7 earthquake) were less than 0.2%. When the PGA of the earthquakes reached 1.0 g, the maximum drifts of the Nos. 3, 4 and 7 earthquakes exceeded the requirement, and the residual drifts of the Nos. 3, 4, 5 and 7 earthquakes exceeded the requirement. Therefore, the design may be just an optimized option for the earthquake considered.  The reason for the large residual drifts in some cases was that the restoring force after strong excitations may not have been enough to make the wall system rock back. Therefore, it may be necessary to provide some methods to improve the restoring force, such as using post-tensioned tendons. 114   In conclusion, in order to make sure the seismic design satisfy all the requirements, the seismic excitation selected for analysis should be the best fit for the site condition of the building. Some methods for increasing restoring force are recommended, so that the design can be more effective in more cases.   5.4.5 Influence by Earthquake Peak Ground Acceleration (PGA) In order to provide a comprehensive assessment of the behaviour of the building under seismic excitations, an incremental dynamic analysis was conducted by scaling the PGA values of the seven earthquake records from 0.1 to 1.0 g.  Based on the optimized design under the No. 2 earthquake, 15 D44 dampers were distributed as evenly as possible to each storey, and the results of the seven earthquakes were compared. The analysis results are shown in Figures 5-25 and 5-26.  The analysis showed that, the PGA increased, the drift of the wall and the shear displacement of the damper both almost kept growing. Under the Nos. 3, 4 and 7 earthquakes, the maximum drift ratios of the top floor were 3.00%, 2.05% and 2.67%, respectively, which were larger than the required 2%. However, when the PGA of No. 4 earthquake was less than 1.0 g, the maximum drifts were all less than 2%. When the PGA of the No. 7 earthquake was less than 0.5 g, the maximum drifts satisfied the requirement; and, when the PGA of the No. 3 earthquake was equal to or less than 0.8 g, the maximum drifts met the requirement. In the other four cases (Nos. 1, 2 5 and 6 earthquakes), even when the PGA reached 1.0 g, the maximum drift ratio was less than 2%.   115    Figure 5-25 IDA of the maximum drift ratio of the top floor for the seven different earthquakes 00.511.522.533.50 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Drift	Rato	(%)PGA	(g)Maximum	Drift-ratio	of	the	Top	FloorNo.1No.2No.3No.4No.5No.6No.7116     Figure 5-26 IDA of the maximum shear displacement of damper for the seven different earthquakes  In terms of the dampers’ responses, under the Nos. 3 and 7 earthquakes, the shear displacements were around 35 mm (shear strain of 0.23 rad) and 27 mm (shear strain of 0.18 rad) for the Nos. 3 and 7 earthquakes, which were both larger than the required 22.5 mm. For the other five cases (Nos. 1, 2, 4, 5 and 6 earthquakes), the shear deformations were within the requirement. However, for the Vancouver area, under the design seismic hazard of a 2% probability of being exceeded in 50 years, the PGA was considered to 0.46 g. In this case, all the damper deformations were less than 22.5 mm. Therefore, the seismic responses of the building satisfied the requirements.  05101520253035400 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Displacement	(mm)PGA(g)Maximum	Shear	Displacement	of	DamperNo.1No.2No.3No.4No.5No.6No.7117   In conclusion, since seismic responses of the building increase with increasing PGA value, once responses that exceed the requirement are obtained under a certain level of seismic hazard, it is reasonable to indicate that such a level of seismic hazard is the maximum that the building can handle. The maximum resistant forces of the pin connection in both the horizontal and vertical directions were obtained in the IDA, as shown in Figures 5-27 and 5-28. These forces can be used to provide the design force of the pin connection.    Figure 5-27 IDA of the maximum horizontal force of the pin connection  0501001502002500 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Force	(KN)PGA	(g)Maximum	Horizontal	Force	of	Pin	ConnectionNo.1No.2No.3No.4No.5No.6No.7118    Figure 5-28 IDA of the maximum vertical force of the pin connection  The horizontal force kept increasing with increasing PGA value; and, the vertical force remained almost the same, regardless of earthquake type or PGA value. The total shear force for the pin can calculated according: 𝑭 = 𝒗𝒆𝒓𝒕𝒊𝒄𝒂𝒍	𝒇𝒐𝒓𝒄𝒆𝟐 + 𝒉𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍	𝒇𝒐𝒓𝒄𝒆𝟐                                                                                            (5-20) With the PGA value considered as 0.46 g for building site, there are three steps to obtain the design force: 119   1) With the IDA results, the total shear forces for the seven types of earthquakes are calculated when the PGA value is equal to 0.4 g and 0.5 g (shown in Table 5-15). 2) The shear forces for the seven types of earthquakes when the PGA value is equal to 0.46 g is calculated by using the linear interpolation method (shown in Table 5-16). 3) The average value of the seven results obtained in step 2 is used as the design shear force of the pin connection.   Table 5-15 Total shear force of the pin connection when PGA is equal to 0.4 g and 0.5 g Force (KN) No. 1 No. 2 No. 3 No. 4 No. 5 No. 6 No. 7 0.4 78.23 83.68 98.45 85.94 80.38 64.57 133.84 0.5 84.99 90.24 108.70 86.65 87.70 72.55 142.57  Table 5-16 Total shear force of the pin connection when PGA is equal to 0.46 g Force (KN) No. 1 No. 2 No. 3 No. 4 No. 5 No. 6 No. 7 0.4 82.29 87.62 104.60 86.36 84.77 69.36 139.08  The average value is calculated as: 𝑭 = 𝟖𝟐.𝟐𝟗_𝟖𝟕.𝟔𝟐_𝟏𝟎𝟒.𝟔𝟎_𝟖𝟔.𝟑𝟔_𝟖𝟒.𝟕𝟕_𝟔𝟗.𝟑𝟔_𝟏𝟑𝟗.𝟗𝟖𝟕 = 𝟗𝟑. 𝟒𝟓𝒌𝑵                                                                               (5-21) Therefore, the design force of the pin connection is 93.45 kN.    120   Chapter 6: Connection Design  This chapter introduces the conceptual design of the connections, focussing on configurations and work mechanisms. It was assumed that the connections, including pin connections and connections between dampers and CLT wall panels, behaved linearly elastically; therefore, connections should not yield at the design level.  This chapter also provides design examples to highlight the key points of the design. Of course, there are still many issues concerning the connections that need to be studied in the future. This chapter provides lists of further work recommendations.   6.1 Pin Connection 6.1.1 Design Concept Pin connections are characterized by zero moments or free rotations. The basic idea of the design included two steel side plates and one cylindrical steel rod. At the base, the two steel side plates, fixed at the ground, were placed on each side of the cross-laminated timber (CLT) wall panel. The steel rod passed through the CLT wall panel as well as the two side plates. In this way, the CLT panel could rotate around the steel rod, and the two side plates along with the CLT wall panel could share the pressure transferred from the steel rod.  In order to rotate, the CLT wall panel could be either isolated from the ground by a steel plate (as shown in Figure 6-1) or designed with a certain radian (as shown in Figure 6-2).   121                            Figure 6-1 Front and side views of the pin connection                                         Figure 6-2 Front and side views of pin connection  122   In the design, the resistances of the steel rod, CLT wall panel, side steel plate and bottom steel plate or radian of CLT panel all should be considered.   6.1.1.1 Steel rod In earthquakes, the steel rod will undergo base shear forces from both the vertical and horizontal directions. Therefore, the design force needed to be considered as the total shear forces of the two directions at the design level. The steel rod needed be designed to be elastic under the design force. The diameter of the steel rod is determined by the following equation: 𝑑 = P¹º×»¼×".”  (6-1) where F is the design force, and	𝜎½ is the steel yield stress. For example, based on the analysis results from Section 5.4.5, the incremental dynamic analysis (IDA) indicated that design force for the pin connection was 93.45 kN. The material of the steel rod was considered to be ASTM A36 (Onealsteel.com 2012), the most commonly used mild and low carbon steel, which can exhibit good strength and excellent welding properties. The ASTM A36 material has different forms available for application, including rectangular and square bars, circular rods and steel shapes, such as channels. A circular rod was used in this study. Its tensile strength was 400 – 500 MPa (58 – 80 ksi), and its yield strength was 250 MPa (36 ksi).  When the diameter was 30 mm, the shear strength could be calculated as: 𝐹 = =v ×𝑑$×𝜎½×0.6 = 106.03𝐾𝑁 > 93.45𝑘𝑁  (6-2)                                        123   Therefore, the diameter of the steel rod was designed to be 30 mm. However, reduction factors were not considered, and it was just a conceptual design.   6.1.1.2 CLT wall panel The steel rods placed on the CLT wall panels and steel panels transferred loads to the wood and the steel panels. Since the wood strength was lower than the steel yield strength, the CLT wall panel around the pin connections needed be strengthened. One way would be increased panel thickness and high-strength wood material to ensure the CLT wall panel did not have brittle failures and exhibited elastic-plastic behaviour. To work within the elastic period, a more effective way would be the insertion of steel panels into the bottom of the CLT wall panel, as shown in Figure 6-3. The steel “boot” (Figure 6-3), constructed with the steel panels, could reduce the stresses experienced by the wood element by introducing more shear planes for the steel rod.  The pin connection using the steel boot would be much more likely to behave as the numerical model. It should be noted that, in the numerical simulation, it was assumed that the pin connections were located at the bottom of the CLT wall panels. However, in the design, there was some distance from the bottom of the CLT wall panel to the pin connection. Since the steel boot could protect the CLT wall panel around the pin connection, that distance could be decreased.   124     Figure 6-3 Pin connection strengthened by insertion of steel plate   Figure 6-4 Steel “boot” with steel side plates 125    As mentioned, the side plates in the connection worked together with the CLT wall panel to sustain the pressure from the steel rod. Three parameters of the side plates were considered: width, length and height. The side plates were to remain elastic. Therefore, the yield strength of the steel material was also considered in the design.  6.1.1.3 Bottom steel plate or radian of CLT panel If using a steel plate at the bottom to support CLT panel, the weight of the wall panel and the base shear force needed be considered. The design followed capacity design. If the CLT panel was designed with a radian, the height (h), as shown in Figure 6-2, should be designed to satisfy two scenarios: 1) when shear strain of damper reached 0.15 rad; and, 2) when the drift ratio of the top floor reached 2%.  Incorporation of all these considerations in the pin-connection design, the CLT wall panels should rotate as expected.   6.1.2 Future Work Based on the design concept of the pin connection, four more things are required to be studied in the future: 1) Location of the pin connection. The pin connection should be placed in mid-width of the CLT wall panel. However, the height from the bottom of the panel to the pin connection 126   should be designed. If the height is too small, the wall panel below the pin connection may not be able to resist the pressure given by the structure. However, the large height requires large steel plates, which may increase the cost and also influence the ground floor as well.  2) Steel side plate design. The steel plates work together with the CLT wall panel to resist the force given by the steel rod. The combination work mechanism is complex, and it is difficult to determine the design force. Therefore, finite element (FE) analysis around the connection should be studied. 3) Fixation between steel rods and steel side plates. It is necessary to make sure reliable fastening of the steel rods and side plates; otherwise, early failure of the connection may occur. 4) Experimental tests. A pushover experimental test is required to obtain the yield strength and maximum strength of the connection. A reversed-cyclic experimental test is also needed to the determine the low cycle fatigue strength and hysteretic characteristics.   6.2 Connection Between Damper and CLT Wall 6.2.1 Design Concept Connections between dampers and CLT wall panels should provide strong translational and rotational constraints in a linear elastic manner. In this study, a new configuration proposed for the connection is characterized by combining welded joints and self-tapping wood screws. 127   Figures 6-5 and 6-6 show the front and plan views, respectively, of the CLT shear wall system equipped with the proposed connections. The connection consisted of two parts – a pair of steel channel plates and self-tapping wood screws. The steel channel plates and damper were welded together. During seismic excitations, it was assumed that the damper would only be under shear force along the vertical direction. Therefore, the welding connection was designed to transfer the shear force from the damper to the steel channel plates. Between the CLT wall panels and the steel channel plates, self-tapping wood screws were applied to take the forces transferred from the steel channel plates, in order to protect the CLT wall panels. These forces include the shear force and the bending moment caused by the offset of the shear force from the centre of the steel panel. In this way, the screws should resist both horizontal and vertical forces.   Figure 6-5 Front view of damper connection  128     Figure 6-6 Plan view of damper connection  The screws were to be installed in a double angle, so that both the horizontal and vertical forces would be transferred along the length of the screws via tension or compression. The three-dimensional (3D) illustration of the double angle is shown in Figure 6-7, with three view drawings shown in Figures 6-8, 6-9 and 6-10.  Horizontal and vertical forces denoted as P and V, respectively. Figure 6-9 shows the bottom view, where angle 𝛼 is determined by P and the bearing capacity of the screws (F). If P is sustained by both the screws and the CLT wall panel, P is the resultant force; and, the design force for the screws can be calculated as follows: 𝐹 = 𝑃×cos 𝛼 (6-3) However, in order to minimize the impact on the wood, P should be transferred to the screws as much as possible. Therefore, F should be the resultant force and can be calculated as follows: 𝐹 = ÅÆÇÈÉ (6-4) 129   Figure 6-10 shows the lateral view, where angle 𝛽 is determined by V and F. As explained above, F should also be the resultant force and can be calculated as follows: 𝐹 = ¡ÆÇÈË  (6-5)   Figure 6-7 Three-dimensional illustration for the double angle of a screw 130    Figure 6-8 Front view for the double angle of a screw   Figure 6-9 Bottom view for the double angle of a screw 131    Figure 6-10 Lateral view for the double angle of a screw  With the design forces for the horizontal and vertical directions, the bearing capacity of the screws and the double angle can be determined. The screw design should follow the instructions in the Wood Design Manual 2010 (Canadian Wood Council 2010), CSA O86 (Canadian Standard Association 2009), and Evaluation Report CCMC 13677-R (National Research Council of Canada 2013). There were three more key points in the design: 1) Pairs of screws were installed on both sides of the CLT wall panels, as shown in Figure 6-6. The screws needed to go through the CLT wall panels, in order to protect the wood through tension or compression. However, for most self-tapping wood screws, their 132   lengths were equal to or less than the thickness of CLT wall panels, making it difficult to use one screw to protect both sides of the wood panel.  2) Pairs of screws were installed on the top and bottom of the steel side plates. During earthquake excitations, reversed loadings on the screw connection make it difficult to decide the force direction during design; therefore, it was assumed the screws on the top and bottom sustained upward and downward shear forces separately.  For example, when designing the damper connection for the D44 damper used in Chapter 5, the vertical design force was 44 kN. “SWG ASSY® VG plus Cyl” screws with a diameter of 10 mm and a length of 140 mm were selected (National Research Council of Canada 2013). This was a type of fully threaded screw with a minimum diameter of 6.2 mm. The unfactored screw tension strength was 24 kN. If both 𝛼 and 𝛽 were 45°, the design force (F) should be adjusted as: 𝐹 = vvÆÇÈË = 63	𝑘𝑁 (6-6)  The number of screws on the top row (n) was calculated as: 𝑛 = ”d$v = 2.6	 (6-7) Therefore, the number of screws for one side was 6, and the total number of screws was 12. However, reduction factors were not considered, and it was just conceptual design.  3) The length of screws (L) inserted into the CLT wall panels satisfied the following requirements. For a given screw diameter d, L was larger than 15 to 20 d to obtain a 133   screw fracture failure mode instead of a screw withdrawal failure mode. Furthermore, the pairs of screws on both sides of the CLT wall panels were long enough to cross with their corresponding pairs to prevent the screws under tension from pulling the panels apart.   6.2.2 Further work The study has provided the concept for the damper design, but some work is needed before applying the concept into practice. 1) Capacity design procedure. The pin connection design should follow the capacity design procedure and should provide a margin of safety. It is recommended that the pin shear force needed for the top connection be calculated.   2) Design for welding connection. Since welding is the preference for the connection between splice plates, it is suggested that the connection between the damper and the steel side plate be welded. Of the two most common types of welding connections the fillet weld is recommended over the groove weld. It is necessary to consider both the dimensional requirements as well as the strength requirements during the fillet weld design.  3) Distribution of the screws. The screws in the example were distributed in a rectangular shape. However, given the same number of screws, as long as the screws on the top and the bottom are placed symmetrically, other distributions, such as in a circular shape, should be considered. Therefore, an optimized screw design can be obtained by comparing seismic responses among the different distributions.  134   4) Experimental tests. Since both screw and welding connections are included, the design is complex; and, it is hard to estimate the performance without experiments. Therefore, a pushover experiment is required to obtain the connection strength, and a reversed-cyclic experiment is needed to get the hysteretic response characteristics and fatigue strength.    135   Chapter 7: Conclusions and Future Work  7.1 Conclusions To facilitate the application of low- to mid-rise timber buildings, one of the major challenges is to improve their self-centring capabilities. In many previous studies, post-tensioned tendons were applied to improve restoring forces. Also, traditional timber connections, including hold-downs and angle brackets, were bottom connections as well as energy dissipation devices. However, the advanced wood material, cross-laminated timber (CLT), with its high strength and dimensional stability, makes it possible to achieve re-centring performance of CLT shear walls without post-tensioned tendons, as long as their rocking motions are under control.  This study proposed an innovative timber building system – a pin-supported CLT shear wall system equipped with low-yield steel dampers – to achieve good seismic performance. The system consists of pairs of CLT wall panels. Between the panels, dampers are used as connections as well as energy dissipation elements. At the base, pin connections, which are designed to behave linearly elastically, replace traditional hold-downs and angle brackets.  In this way, the dampers in the system are considered as the sole energy dissipater.  The design and analyses of the CLT shear wall buildings are relatively simple. During small earthquakes, the dampers can dissipate energy to control the motion of the building. Under large earthquakes, the dampers are designed to be the first protector and can also improve ductility of 136   the system. After major earthquakes, only some damaged dampers may need to be replaced; therefore, it will be much easier to retrofit the building.  The damper, using low-yield steel 100 (LYS100) in a rectangular shape, is one of the key parts of the system. The study suggested a design procedure for the damper and also proposed two numerical models of the damper using OpenSees Navigator and ABAQUS/Standard software. The designed rectangle-shaped dampers could have different shear capacities by changing the height. Different types of dampers were suggested keeping the same width and thickness. More importantly, the width-to-thickness ratio in the design should be checked to avoid out-of-plane buckling.  The reversed-cyclic analysis results of the OpenSees damper model were in good agreement with previous experimental results. The tensile analysis results of the ABAQUS damper model matched the tensile coupon experimental results well. Therefore, the two numerical models were been validated and can be used for future work.  Both static and seismic analyses were conducted. The static analyses, including pushover and reversed-cyclic analyses, were performed for a one-storey shear wall system equipped with two dampers using both OpenSees Navigator and ABAQUS/Standard. The seismic analysis was done on a six-storey CLT building with six proposed shear wall systems located in Vancouver, Canada. The findings are listed in the following subsections.  137   7.1.1 Conclusions from Static Analyses’ Results 1) The pushover analysis results from both methods showed that the total horizontal forces of the two pin connections were equal to the shear strength of one damper. Although this conclusion may only be applicable to this specific case, the work mechanism of the system was clearly illustrated and may help to predict behaviour of the system in further studies. 2) In both the pushover and the reversed-cyclic analyses, comparisons between the OpenSees Navigator and ABAQUS/Standard results showed that before the yielding of the dampers, the differences between the two methods were a little large. However, after the dampers’ yielding, the differences became small. The lack of agreement can be attributed to different assumptions adopted in the two numerical models. The OpenSees model assumed the damper to be ideally elastic-plastic and also assumed the wall panel to be rigid. However, in ABAQUS, both the dampers and the wall panels were modelled as deformable elements, which is much closer to their real behaviours. Therefore, the ABAQUS analysis results were more accurate. However, the OpenSees analysis results could also be accurate after yielding of the dampers. Compared with ABAQUS analyses, running OpenSees analyses may save a lot of computational time. Since dampers are supposed to yield during seismic excitations, the Oversees model would be effective and efficient to use for seismic analysis. 3) Both OpenSees and ABAQUS analyses’ results showed that the wall responses were similar when the dampers were located at different locations. Moreover, in one analysis, 138   the hysteresis loops of different dampers were shown to be almost the same. Therefore, it was concluded that damper location is not an influential factor in the static analysis.   7.1.2 Conclusions from Seismic Analysis’ Results There were five factors considered in the design of the damped shear wall system: damper type, number of dampers, damper location, different earthquake records versus target design earthquake response spectrum, and earthquake peak ground acceleration (PGA). The conclusions from the seismic analysis’ results are as follows. 1) The damper type depends on the design shear capacity of the dampers. In order to avoid exceeding the drift of the buildings, the dampers’ shear strength should be large enough to provide effective energy dissipation. Moreover, dampers should not be so large that they may not be able to yield under seismic excitations and that their energy dissipation ability may not be fully used. Therefore, the optimized damper type should exhibit its energy dissipation capability to the fullest and also control the drift of buildings. For the studied building, damper D44 was one of the optimized options. 2) The number of dampers should also be optimized. Few dampers may not provide enough energy dissipation; however, if equipped with too many dampers, the wall system will be connected so tightly to be stiff, and its self-weight may not provide enough restoring force to make it rock back and forth, resulting in a large drift. Therefore, there should be an optimized design for the number of dampers. In our case, the optimized number was 15.  139   3) In terms of damper location, the seismic analysis results indicated that dampers would better be distributed evenly along the wall. The conclusion drawn from the static analysis may not be applicable to the seismic analysis, because both models and forces were different. Under seismic excitations, seismic forces are distributed along the height of walls, and shear forces are different at different locations. Also, the dampers may not be as rigid as assumed.  Ideally, the two wall panels will rock together, and shear forces will redistribute equally through the link of dampers. However, dampers are only distributed at some locations. The distribution of dampers may influence the real performance of the wall system. For example, if dampers were all distributed at the bottom, the two wall panels may not connect very tightly at the top, and the wall system may not perform in the assumed way . It would be better to locate dampers evenly along the building, which was also suggested by the numerical analysis.  4) It is suggested that the design be tested by applying different historic earthquake excitations. Also, it is important that the selected earthquake records are the best fit for the site condition of the building. For each earthquake, three levels of records are recommended, including the original earthquake record, matched earthquake record with target design spectra, and scaled earthquake record with 1.0 g PGA.  Based on the site condition of the studied building, the study selected seven types of earthquake records, and each was scaled to these three levels. The analysis results showed that the maximum drifts of the building were almost all within the safety 140   consideration requirements. However, the residual drifts in some cases were larger than the desirable value, because the restoring forces were not large enough to make the building rock back after the strong excitations. Therefore, it would be desirable to improve the restoring capability of the system.  5) In the incremental dynamic analysis, seven different types of earthquakes scaled from 0.1 g to 1.0 g were applied to the optimized design. The results showed that the maximum drift of the top floor and the shear displacement of the dampers kept increasing with increased PGA values. In most cases, even when the PGA was equal to 1.0 g, the maximum drifts and the shear displacements all satisfied the safety requirements. Had the seismic responses under a certain level of seismic hazard exceeded the requirements, one may have concluded that such a level of seismic hazard is the maximum that can be the sustained by the building system. However, a reliability based design approach should be considered in future work to estimate the probability of failure of the building, which is beyond the scope of the current study. In summary, the seismic analysis with the case study not only elucidated the building performance using a simple numerical analysis method, but also provided some guidance and advice for the optimization of the system design.  The study provided preliminary consideration for the design concepts of both the pin connections and the connections between CLT wall panels and dampers. The design example for the pin connection showed the basic design concept. By adding a steel boot, the CLT panel around the pin connection should be well protected from a brittle failure. Moreover, since the distance from 141   the pin connection to the CLT panel bottom could be decreased with the steel boot, the pin connection would be more like it was simulated in the numerical model.  In order to rotate, the CLT wall panel can be either isolated from the ground by a steel plate or designed with a certain radian.  In terms of the damper connections, screws should be inserted at a double angle and should be placed on both sides of the CLT wall panels, in order to transfer the forces along the length of the screws in tension or compression.  With multiple rows of screws, it was assumed that the upper and lower screws took upward and downward forces, respectively. The design example based on damper D44 provided an illustration of the basic design concept.   In conclusion, the pin-supported CLT shear wall system equipped with low-yield steel dampers showed a simple and effective mechanism and good potential for self-centering capability. Based on the proposed numerical models, the analysis procedure can be greatly simplified. The suggestions for the optimization of the design of the proposed system may provide guidance for further analysis. Therefore, the proposed CLT shear wall system may be a potential way to facilitate the development of low- to mid-rise timber buildings.  7.2 Future Work There is still some work needed to allow the new shear wall system to be applied in practice.  1) The study only considered the low-yield-strength steel damper as a rectangular shape. However, there is always stress concentration around corners in small panels, which may 142   cause failure of the damper before the shear strain is fully utilized. Therefore, it may be necessary to optimize the shape of the damper. 2) As mentioned in Chapter 6, future work is needed to allow the design concepts of the connections to be used in practice. Three parts of the pin connections require further investigation: the location of the connection, the steel plates and the fixation between the steel rod and the steel plate. Future studies on damper connections should focus on welded connection design and distribution of screws. Furthermore, experimental tests of both types of connections are required: the strength of the connections can be obtained through pushover experiments; and, hysteretic responses can be determined through reversed-cyclic experiments. 3) Since the damper is the only source of protection in the system, it may be necessary to provide a second type of protection to ensure that the system will not collapse if/when the damper fails.  4) Experimental tests on the proposed shear wall system are necessary, since this research was only based on numerical analyses, with many assumptions. For example, further experiment study will be required to determine the capacity reduction factor in the low-yield steel design. 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