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Performance of strand-based wood composite post-and-beam shear wall system Lim, Hyungsuk 2016

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PERFORMANCE OF STRAND-BASED WOOD COMPOSITE POST-AND-BEAM SHEAR WALL SYSTEM by  Hyungsuk Lim  B.ScW., The University of British Columbia, 2008 M.Eng., University of Toronto, 2009   A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Forestry)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  January 2016  © Hyungsuk Lim, 2016 ii  Abstract This dissertation proposes a strand-based wood composite product to be utilized as the vertical members of post-and-beam (P&B) shear walls. Since the shear wall performance is largely governed by connection systems holding the wall components together, the research focuses on the structural behaviour of two key connection types: nail and hold-down connections. The experimental studies were designed to evaluate the effects of orthogonal properties, such as vertical density profile of the strand-based product, on the connection performance. Static load tests were conducted following ASTM standards and Japanese HOWTEC connection performance guidelines. The test results showed that the connections with fasteners mounted on the face-side of the composite product outperform the ones with fasteners mounted on the product’s edge-side. Subsequently, full-scale shear wall tests were conducted on three P&B wall types to study the effect of the fastener driving direction on the wall performance. The test results confirmed that the shear walls with face-driven nails outperforms the ones with edge-driven nails in terms of load carrying capacity.  A detailed mechanics-based finite-element connection model RHYST was also developed to predict the load-displacement relationship of a nail connection. It was developed based on an existing connection model HYST which idealizes a dowel-type connector driven into a wood medium as an elasto-plastic beam embedded in a nonlinear foundation that only acts in compression. RHYST assumes that the lateral response of the wood medium does not decrease at any compressive displacement. The presented model takes into account the contribution of the fastener’s vertical displacements on the response of the foundation. The simulation results of RHYST agreed well with the reversed-cyclic nail connection test results in terms of load iii  carrying capacity and energy dissipation. The model is also able to simulate strength and stiffness degradation between the repeated loading cycles. Moreover, the applicability of RHYST was confirmed by incorporating it as a subroutine in a finite-element shear wall model WALL2D. The simulation results of WALL2D with RHYST showed a good agreement with the wall test results.   iv  Preface This research was originally proposed by Frank Lam, and completely conducted by [Hyung Suk Lim]. Two scientific articles are planned to be published from this dissertation, which [Hyung Suk Lim] is the lead author.  The experimental studies presented in Chapter 3 and Chapter 4 are planned to be published. All the contents including methods, results and data analysis of the studies will be presented in the publication. [Hyung Suk Lim] will be the lead author and Frank Lam will be the supervisory author.    The computer modelling work presented in Chapter 5 and Chapter 6 is planned to be published as well. [Hyung Suk Lim] will be the lead author who worked on model development, verification, validation, and application. Frank Lam will be the supervisory author who provided general guidelines and suggestions. Since the presented model was developed based on the computer model written by Ricardo O. Foschi, he will be the co-author. Minghao Li will be another co-author since the applicability of the presented model was confirmed using his computer model. The co-authors also provided suggestions and feedback on the modelling work.   v  Table of Contents Abstract ................................................................................................................................................ ii Preface ................................................................................................................................................. iv Table of Contents ................................................................................................................................ v List of Tables ...................................................................................................................................... ix List of Figures .................................................................................................................................... xii List of Abbreviations ......................................................................................................................xvii Acknowledgements ........................................................................................................................... xx Chapter 1 Introduction .................................................................................................................. 1 1.1 Research work and objectives .............................................................................................. 3 1.2 Thesis organization................................................................................................................ 5  Literature Review ........................................................................................................ 7 Chapter 22.1 Strand-based wood composites ............................................................................................ 7 2.1.1 Strand-based wood composite modeling ...................................................................... 8 2.1.2 Strand orientation ........................................................................................................... 9 2.1.3 Density variation .......................................................................................................... 13 2.2 Nail connection .................................................................................................................... 16 2.2.1 European yield theory .................................................................................................. 16 2.2.2 Experimental studies .................................................................................................... 18 2.2.3 Nail connection models ............................................................................................... 20 2.3 Shear wall............................................................................................................................. 23 2.3.1 Experimental studies .................................................................................................... 23 2.3.1.1 University of British Columbia ........................................................................... 23 2.3.2 Shear wall models ........................................................................................................ 27 2.4 Summary .............................................................................................................................. 33  Experimental Study I – Connections ...................................................................... 35 Chapter 33.1 Materials............................................................................................................................... 35 3.1.1 Strand-based wood composite .................................................................................... 35 3.1.1.1 Physical properties ............................................................................................... 36 3.1.2 Sheathing panel ............................................................................................................ 39 3.1.3 Connection hardware ................................................................................................... 39 vi  3.2 Specimen configurations ..................................................................................................... 40 3.2.1 Nail connection configurations ................................................................................... 40 3.2.2 Hold-down connection configurations ....................................................................... 40 3.3 Experimental setup and procedure ..................................................................................... 41 3.3.1 Nail connection – monotonic test ............................................................................... 41 3.3.2 Nail connection – reversed-cyclic test ........................................................................ 42 3.3.3 Hold-down connection – monotonic test.................................................................... 44 3.4 Data analysis ........................................................................................................................ 46 3.5 Results and discussion......................................................................................................... 48 3.5.1 Nail connection ............................................................................................................ 48 3.5.1.1 Nail driving direction effect ................................................................................ 51 3.5.1.2 Embedment density effect ................................................................................... 53 3.5.1.3 Loading direction effect ....................................................................................... 55 3.5.1.4 Loading type effect .............................................................................................. 57 3.5.1.5 Failure modes ....................................................................................................... 58 3.5.2 Hold-down connection ................................................................................................ 61 3.5.2.1 Failure modes ....................................................................................................... 62 3.5.2.2 Further connection performance comparison ..................................................... 63 3.6 Summary .............................................................................................................................. 64  Experiment Study II - Shear Wall .......................................................................... 66 Chapter 44.1 Materials............................................................................................................................... 66 4.1.1 Strand-based wood composite posts ........................................................................... 66 4.1.2 Frame members ............................................................................................................ 67 4.1.3 Metal fasteners ............................................................................................................. 68 4.1.4 Sheathing panel ............................................................................................................ 69 4.2 Wall assembly ...................................................................................................................... 69 4.2.1 Double-braced walls .................................................................................................... 69 4.2.2 9mm-OSB-sheathed walls ........................................................................................... 71 4.2.3 11mm OSB-sheathed walls ......................................................................................... 72 4.3 Experimental setup and procedure ..................................................................................... 72 4.4 Results and discussion......................................................................................................... 75 vii  4.4.1 Double-braced walls .................................................................................................... 77 4.4.2 9mm OSB-sheathed walls ........................................................................................... 84 4.4.3 11mm OSB-sheathed walls ......................................................................................... 89 4.5 Summary .............................................................................................................................. 96  Nail Connection Model ............................................................................................. 99 Chapter 55.1 HYST ................................................................................................................................... 99 5.1.1 Model components ....................................................................................................... 99 5.1.1.1 Dowel-type fastener ............................................................................................. 99 5.1.1.2 Wood foundation ................................................................................................ 102 5.1.2 Problem formulation and solution ............................................................................ 105 5.1.3 Model inputs and logic .............................................................................................. 107 5.1.4 Limitations ................................................................................................................. 109 5.2 RHYST ............................................................................................................................... 111 5.2.1 RHYST1 ..................................................................................................................... 111 5.2.2 RHYST2 ..................................................................................................................... 116 5.3 Model validation ................................................................................................................ 131 5.3.1 Calibration .................................................................................................................. 132 5.3.2 Validation on reverse-cyclic test results ................................................................... 133 5.3.2.1 C1 configuration ................................................................................................. 133 5.3.2.2 C2 configuration ................................................................................................. 137 5.3.2.3 C3 configuration ................................................................................................. 140 5.3.2.4 C4 configuration ................................................................................................. 143 5.3.2.5 C5 configuration ................................................................................................. 146 5.4 Summary ............................................................................................................................ 149  Application of the Nail Connection Model........................................................... 151 Chapter 66.1 WALL2D ........................................................................................................................... 151 6.1.1 Frame members .......................................................................................................... 152 6.1.2 Sheathing panels ........................................................................................................ 153 6.1.3 Frame-to-frame connections ..................................................................................... 155 6.1.4 Panel-to-frame connections ....................................................................................... 156 6.1.5 Problem formulation and solution ............................................................................ 158 viii  6.2 WALL2D simulations ....................................................................................................... 160 6.2.1 Model inputs............................................................................................................... 160 6.2.1.1 Frame members .................................................................................................. 160 6.2.1.2 Sheathing panels ................................................................................................. 161 6.2.1.3 Frame-to-frame connection ............................................................................... 161 6.2.1.4 Panel-to-frame connection ................................................................................. 162 6.2.1.5 Boundary conditions and convergence criteria ................................................ 164 6.2.2 Simulation results ...................................................................................................... 164 6.2.2.1 11mm_SWALL_FACE configuration .............................................................. 165 6.2.2.2 11mm_SWALL_EDGE configuration ............................................................. 169 6.2.2.3 11mm_SWALL_HEM configuration ............................................................... 174 6.3 Summary ............................................................................................................................ 177  Conclusions and Future Work ............................................................................... 179 Chapter 77.1 Scientific contribution ....................................................................................................... 183 7.2 Future research................................................................................................................... 184 Bibliography .................................................................................................................................... 187 Appendices ....................................................................................................................................... 195 Appendix A Schematics of nail connection configurations .................................................. 195 Appendix B Connection performance parameters ................................................................ 199 Appendix C Monotonic and reversed-cyclic nail connection test curves ............................ 207 Appendix D Reversed-cyclic load test curves ....................................................................... 211  ix  List of Tables Table 2.1 Groups of panels manufactured in various combinations of random and aligned strands (McNatt, Bach, & Wellwood, 1992) ................................................................................ 10 Table 2.2 Test variables of the nail connection components (Fonseca, Rose, & Campbell, 2002) ............................................................................................................................................ 19 Table 3.1 Summary statistics of moisture content and specific gravity ......................................... 37 Table 3.2 Summary statistics of densities throughout composite laminae and selected regions .. 38 Table 3.3 T-test results on mid-lamina densities and near-the-lamina-surface densities .............. 38 Table 3.4 Seven nail connection configurations .............................................................................. 40 Table 3.5 Summary statistics of performance parameters (monotonic) ......................................... 49 Table 3.6 Summary statistics of performance parameters (reversed-cyclic) ................................. 50 Table 3.7 Null hypothesis and rejection criterion for t-tests ........................................................... 50 Table 3.8 T-test results on nail driving direction effect (monotonic) ............................................. 51 Table 3.9 T-test results on nail driving direction effect (reversed-cyclic) ..................................... 52 Table 3.10 T-test results on embedment density effect (monotonic) ............................................. 54 Table 3.11 T-test results on embedment density effect (reversed-cyclic) ...................................... 54 Table 3.12 T-test results on loading direction effect (monotonic).................................................. 56 Table 3.13 T-test results on loading direction effect (reversed-cyclic) .......................................... 56 Table 3.14 T-test results on loading type effect ............................................................................... 58 Table 3.15 Number of failure mode occurrences ............................................................................. 59 Table 3.16 Summary statistics of performance parameters of hold-down connection specimens ............................................................................................................................................ 61 Table 3.17 T-test results on performance parameters of face-driven and edge-driven specimens ............................................................................................................................................ 61 Table 3.18 Summary statistics of performance parameters of hold-down connections composed of Douglas-Fir and Japanese-Cedar columns .................................................................. 63 Table 4.1 Summary statistics of dynamic MOE of strand-based wood composite posts.............. 67 x  Table 4.2 Frame member information .............................................................................................. 68 Table 4.3 Metal member information ............................................................................................... 68 Table 4.4 Reversed-cyclic test loading history (shear wall) ........................................................... 75 Table 4.5 Summary statistics of performance parameters (double-braced walls) ......................... 77 Table 4.6 Summary statistics of performance parameters (9mm OSB-sheathed Walls) .............. 84 Table 4.7 Summary statistics of performance parameters (11mm OSB-sheathed Walls) ............ 90 Table 4.8 Number of sheathing-to-frame (nail) connections per wall specimen ........................... 90 Table 5.1 Descriptions of embedment property parameters.......................................................... 102 Table 5.2 HYST input parameters (Foschi 2000) .......................................................................... 114 Table 5.3 RHYST1 embedment response curve parameters ......................................................... 114 Table 5.4 Nail properties (sheathing-to-frame example)............................................................... 129 Table 5.5 Embedment properties (sheathing-to-frame example).................................................. 129 Table 5.6 Differences between HYST and RHYST models ......................................................... 131 Table 5.7 Embedment parameters of five nail connection configurations ................................... 133 Table 5.8 Energy dissipation during primary and trailing cycles: C1 configuration ................... 135 Table 5.9 Energy dissipation during primary and trailing cycles: C2 configuration ................... 138 Table 5.10 Energy dissipation during primary and trailing cycles: C3 configuration ................. 141 Table 5.11 Energy dissipation during primary and trailing cycles: C4 configuration ................. 144 Table 5.12 Energy dissipation during primary and trailing cycles: C5 configuration ................. 147 Table 6.1 Embedment parameters of panel-to-frame connections used in WALL2D_HYST ... 163 Table 6.2 Embedment parameters of panel-to-frame connections used in WALL2D_RHYST1 and WALL2D_RHYST2 ................................................................................................ 163 Table 6.3 Energy dissipation during primary and trailing cycles: 11mm_SWALL_FACE ....... 166 Table 6.4 Performance parameters of 11mm_SWALL_FACE configuration ............................. 169 Table 6.5 Energy dissipation during primary and trailing cycles: 11mm_SWALL_EDGE ....... 171 Table 6.6 Performance parameters of 11mm_SWALL_EDGE configuration ............................ 173 xi  Table 6.7 WALL2D_RHYST2 simulation results: energy dissipation of 11mm_SWALL_HEM, 11mm_SWALL_FACE, and 11mm_SWALL_EDGE ................................................. 175 Table 6.8 WALL2D_RHYST2 simulation results: performance parameters of 11mm_SWALL_HEM, 11mm_SWALL_FACE, and 11mm_SWALL_EDGE ......... 176  xii  List of Figures Figure 3.1 Average vertical density profile of strand-based composite laminae........................... 37 Figure 3.2 Hold-down connection configurations: a) face-driven, b) edge-driven ....................... 41 Figure 3.3 Nail connection test setup (monotonic) .......................................................................... 42 Figure 3.4 Nail connection test setup (reverse-cyclic) .................................................................... 43 Figure 3.5 CUREE basic loading protocol (ASTM Standard E2126, 2011) ................................. 44 Figure 3.6 Monotonic load test setup for face-driven hold-down specimens ................................ 45 Figure 3.7 Monotonic load test setup for edge-driven hold-down specimens ............................... 46 Figure 3.8 Load-displacement curve analysis (HOWTEC, 2009) .................................................. 47 Figure 3.9 Average reversed-cyclic test data and envelope curves of C5 nail connection configuration ...................................................................................................................... 48 Figure 3.10 Nail connection failure modes: a) pull-through, b) pull-out, and c) low cycle fatigue ............................................................................................................................................ 60 Figure 3.11 hold-down connection failure modes: a) moment failure and b) splitting failure of the post ............................................................................................................................... 62 Figure 4.1 Post orientations............................................................................................................... 66 Figure 4.2 Double-braced wall configurations: a) DWALL_FACE, b) DWALL_EDGE ........... 70 Figure 4.3 9mm-OSB-sheathed wall configurations: a) 9mm_SWALL_EDGE, b) 9mm_SWALL_FACE....................................................................................................... 71 Figure 4.4 11mm-OSB-sheathed wall configurations: a) 11mm_SWALL_EDGE, b) 11mm_SWALL_FACE..................................................................................................... 72 Figure 4.5 Shear wall test setup ........................................................................................................ 73 Figure 4.6 Load-displacement curves (double-brace walls) ........................................................... 77 Figure 4.7 Stud tension failures due to out-of-plane buckling under monotonic loads: a) DWALL_FACE, b) DWALL_EDGE .............................................................................. 79 Figure 4.8 Tension perpendicular-to-grain failure with withdrawn nails – DWALL_FACE ...... 80 Figure 4.9 Tension perpendicular-to-grain failure with withdrawn nails – DWALL_EDGE ...... 80 xiii  Figure 4.10 Progress of tension and compression perpendicular to grain failures on the sill plate of the second DWALL_FACE specimen: a) earlier-stage compression perpendicular-to-grain failure, b) earlier-stage tension perpendicular-to-grain failure, c) later-stage compression perpendicular-to-grain failure, d) later-stage tension perpendicular-to-grain failure ........................................................................................................................ 82 Figure 4.11 Progress of tension and compression perpendicular to grain failures on the sill plate of the second DWALL_EDGE specimen: a) earlier-stage compression perpendicular-to-grain failure, b) earlier-stage tension perpendicular-to-grain failure, c) later-stage compression perpendicular-to-grain failure, d) later-stage tension perpendicular-to-grain failure ........................................................................................................................ 83 Figure 4.12 Load-displacement curves (9mm OSB-sheathed Walls) ............................................ 84 Figure 4.13 Nail connection failures at the composite posts: a) pull-out (9mm_SWALL_ EDGE, monotonic), b) pull-through (9mm_SWALL_FACE, monotonic) ................................ 85 Figure 4.14 Nail pull-through failures at the frame members: a) bottom plate (9mm_ SWALL_ EDGE, reversed-cyclic test #1), b) bottom plate (9mm_SWALL_FACE, reversed-cyclic test #2),       c) middle stud (9mm_SWALL_ACE, reversed-cyclic test trial #1) ............................................................................................................................................ 86 Figure 4.15 Corner chip-out failures: a) bottom plate (9mm_SWALL_EDGE, reversed-cyclic test #1), b) top plate (9mm_SWALL_ EDGE, reversed-cyclic test #2), c) top plate (9mm_ SWALL_FACE, reversed-cyclic test #2) ........................................................... 87 Figure 4.16 Edge tear-out failures: a) top plate (9mm_SWALL_EDGE, reversed-cyclic test #1),      b) bottom plate (9mm_SWALL_FACE, reversed-cyclic test #1), c) top plate (9mm_SWALL_FACE, reversed-cyclic test #2) ............................................................ 87 Figure 4.17 Major nail connection failures at the composite posts: a) pull-out (9mm_ SWALL_EDGE, reversed-cyclic test #1), b) pull-through (9mm_SWALL_FACE, reversed-cyclic test #2) ..................................................................................................... 88 Figure 4.18 Load-displacement curves (11mm OSB-sheathed Walls) .......................................... 89 Figure 4.19 A schematic of crushing of panel corners due to different rotations of panels ......... 91 Figure 4.20 Crushing of panel corners: a) 11mm_SWALL_ EDGE, monotonic, b) and c) 11mm_ SWALL_FACE, monotonic................................................................................ 92 Figure 4.21 Rotations of panels of 11mm_SWALL_EDGE specimens: a) before the test, b) later-stage, c) final-stage ................................................................................................... 93 Figure 4.22 Final stage of an 11mm_SWALL_EDGE specimen (reversed-cyclic test #1):     a) front-view, b) side-view .................................................................................................... 94 xiv  Figure 4.23 Rotations of panels of 11mm_SWALL_FACE specimens: a) before the test, b) later-stage, c) final-stage ................................................................................................... 94 Figure 4.24 Final stage of an 11mm_SWALL_FACE specimen (reversed-cyclic test #1):     a) front-view, b) side-view .................................................................................................... 95 Figure 5.1 Deformations of two beam elements with three nodes ............................................... 100 Figure 5.2 Beam element hysteresis ............................................................................................... 101 Figure 5.3 Embedment response–displacement relationship ........................................................ 103 Figure 5.4 An example of cyclic displacement history ................................................................. 103 Figure 5.5 Positive and negative residual gaps associated with a point on a nail ....................... 104 Figure 5.6 Nail head displacement: a) specified, b) relative ......................................................... 108 Figure 5.7 HYST model flow chart ................................................................................................ 109 Figure 5.8 A simplified example of deformation of a fastener element....................................... 110 Figure 5.9 Three-parameter embedment response–displacement relationship ............................ 113 Figure 5.10 Deformed nail shapes under monotonic loads at displacements of 0mm, 4mm, 8mm, and 12mm obtained from a) HYST and b) RHYST1.................................................... 115 Figure 5.11 Simulation results of HYST and RHYST1 for a cyclic loading case ...................... 115 Figure 5.12 Processing of residual gap information for an unloading example in a) RHYST2 and b) HYST ........................................................................................................................... 117 Figure 5.13 A nail element with two nodes and seven integration points subjected to unloading .......................................................................................................................................... 118 Figure 5.14 Transverse displacements and residual gaps associated with the second integration points ξ2 and ξ2' in a) HYST and b) RHYST2; embedment response at wξ2 in c) HYST and d) RHYST2; embedment response at wξ2' in e) HYST and f) RHYST2 .............. 120 Figure 5.15 Transverse displacements and residual gaps associated with the third integration points ξ3 and ξ3' in a) HYST and b) RHYST2; embedment response at wξ3 in c) HYST and d) RHYST2; embedment response at wξ3' in e) HYST and f) RHYST2 .............. 121 Figure 5.16 Transverse displacements and residual gaps associated with the fourth integration points ξ4 and ξ4' in a) HYST and b) RHYST2; embedment response at wξ4 in c) HYST and d) RHYST2; embedment response at wξ4' in e) HYST and f) RHYST2 .............. 123 xv  Figure 5.17 a) Transverse displacements and residual gaps associated with the fifth integration points ξ5 and ξ5' in HYST and RHYST2; b) embedment response at wξ5 in HYST and RHYST2; c) embedment response at wξ5' in HYST and RHYST2 .............................. 125 Figure 5.18 Transverse displacements and residual gaps associated with the sixth integration points ξ6 and ξ6' in a) HYST and b) RHYST2; embedment response at wξ6 in c) HYST and d) RHYST2; embedment response at wξ6' in e) HYST and f) RHYST2 .............. 126 Figure 5.19 RHYST2 model flow chart ......................................................................................... 128 Figure 5.20 Simulation results of RHYST1 and RHYST2 for a cyclic loading case.................. 130 Figure 5.21 Reversed-cyclic test results of C1 configuration with:  a) average envelope curves, b) HYST results, c) RHYST1 results, and d) RHYST2 results .................................... 134 Figure 5.22 Energy dissipation of C1 configuration: experimental and simulation results ........ 136 Figure 5.23 Reversed-cyclic test results of C2 configuration with:  a) average envelope curves, b) HYST results, c) RHYST1 results, and d) RHYST2 results .................................... 137 Figure 5.24 Energy dissipation of C2 configuration: experimental and simulation results ........ 139 Figure 5.25 Reversed-cyclic test results of C3 configuration with:  a) average envelope curves, b) HYST results, c) RHYST1 results, and d) RHYST2 results .................................... 140 Figure 5.26 Energy dissipation of C3 configuration: experimental and simulation results ........ 142 Figure 5.27 Reversed-cyclic test results of C4 configuration with:  a) average envelope curves, b) HYST results, c) RHYST1 results, and d) RHYST2 results .................................... 143 Figure 5.28 Energy dissipation of C4 configuration: experimental and simulation results ........ 145 Figure 5.29 Reversed-cyclic test results of C5 configuration with:  a) average envelope curves, b) HYST results, c) RHYST1 results, and d) RHYST2 results .................................... 146 Figure 5.30 Energy dissipation of C5 configuration: experimental and simulation results ........ 148 Figure 6.1 Twisted deformation of a horizontal beam element .................................................... 152 Figure 6.2 Representation of a plate element ................................................................................. 153 Figure 6.3 A shear wall with nail connections along the edges of the sheathing panels: a) representation of the nail connections, b) idealization of the nail connections in WALL2D ......................................................................................................................... 156 Figure 6.4 a) Reversed-cyclic test results of 11mm_SWALL_FACE configuration with: b) WALL2D_HYST results, c) WALL2D_RHYST1 results, and d) WALL2D_RHYST2 results ............................................................................................................................... 165 xvi  Figure 6.5 Energy dissipation of 11mm_SWALL_FACE configuration: experimental and simulation results ............................................................................................................. 167 Figure 6.6 Average envelope curves of 11mm_SWALL_FACE configuration.......................... 168 Figure 6.7 a) Reversed-cyclic test results of 11mm_SWALL_EDGE configuration with: b) WALL2D_HYST results, c) WALL2D_RHYST1 results, and d) WALL2D_RHYST2 results ............................................................................................................................... 170 Figure 6.8 Energy dissipation of 11mm_SWALL_EDGE configuration: experimental and simulation results ............................................................................................................. 172 Figure 6.9 Average envelope curves of 11mm_SWALL_EDGE configuration ......................... 173 Figure 6.10 WALL2D_RHYST2 simulation results for 11mm_SWALL_HEM configuration 174  xvii  List of Abbreviations 9mm_SWALL_EDGE: 9mm OSB-sheathed wall configuration with the nails driven into the edge-sides of strand-based composite posts  9mm_SWALL_FACE: 9mm OSB-sheathed wall configuration with the nails driven into the face-sides of strand-based composite posts 11mm_SWALL_EDGE: 11mm OSB-sheathed wall configuration with the nails driven into the edge-sides of strand-based composite posts 11mm_SWALL_EDGE:  11mm OSB-sheathed wall configuration with the nails driven into the face-sides of strand-based composite posts ANOVA: analysis of variance ASTM: American Society for Testing and Materials BWBN: Bouc-Wen-Baher-Noori CASHEW: Cyclic Analysis of Shear Walls CEN: Comité Europeen de Normalisation CNC: computer numerical control CSA: Canadian Standard Association CUREE: Consortium of Universities for Research in Earthquake Engineering CV: coefficient of variation DWALL_EDGE: double-braced wall specimen with plate connectors amounted on the edge-sides of strand-based composite posts DWALL_FACE:  double-braced wall configuration with plate connectors amounted on the face-sides of strand-based composite posts DOF: degree of freedom xviii  EEEP: equivalent energy elastic-plastic FCC: Forintek Canada Corp. FORM: first-order reliability method GA: genetic algorithm GWB: gypsum wallboards HDD: horizontal density distribution  HOWTEC: Japan Housing and Wood Technology Center IB:  internal bond JAS: Japanese Agriculture Standard  JIS: Japanese Industrial Standard LSL:  laminated strand lumber  LVDT: linear variable displacement transducers MC: moisture content  MOE:  modulus of elasticity  MOR: modulus of rupture MTS: Material Test System NDS: National Design Specification OSB:  oriented strand board P&B: post-and-beam PF: Phenol Formaldehyde pMDI: Polymeric Diphenylmethane Diisocyanate  PSL:  parallel strand lumber RH: relative humidity xix  SADT: Structural Analysis of Diaphragms and Trusses SAWS: Seismic Analysis of Wood frame Structures SDOF: single degree of freedom SG: specific gravity SPF: spruce-pine-fir SWAP: Shear Wall Analysis Program UBC: The University of British Columbia VDP: vertical density profile    xx  Acknowledgements It would have not been possible to end the longest academic journey of my life without consistent support from my supervisor, Dr. Frank Lam, who has been a mentor and role model since my second undergraduate year. With his professional guidance, sharp advice and financial support, I was able to construct a path to and reach the highest level of academic achievement. I cannot express my gratitude enough to Dr. Ricardo O. Foschi for spending his valuable time patiently listening and sharing ideas regarding the research.  I sincerely enjoyed having discussions with him. Also, I would like to extend a warm thank you to Dr. Moon Jae Park and Dr. Terje Haukaas for their kind guidance and encouragements.    It would have been much harder to complete the PhD program without support from the people around me. Dr. Minghao Li, who has been the closest colleague and older brother-like friend, guided and taught me as if he was a supervisory committee member throughout these years. Thank you very much for reviewing my work. Dr. Danny Bae edited my dissertation with his sharp English skills after long working hours at his dental clinic. I really appreciated it. Juwon Nam, an undergraduate volunteer, assisted me in conducting an experimental study without complaining about working hours or financial compensation. I would also like to thank George Lee and Chao (Tom) Zhang for their help conducting experiments.  Without unconditional support and care from my family, I would not be able to endure the long study. My parents, Choong Nam Lim and Myung Koo Kang, always had my back, encouraged me endlessly, and patiently waited for my academic journey to be finished with endless trust. Jun Suk Matthew Lim and Ji Eun Lim were always there when I needed them. Love you all. xxi           To  Choong Nam Lim, Myung Koo Kang, and Kyungwoon Jang, the best parents and most beautiful wife  1  Chapter 1 Introduction Light-frame and post-and-beam (P&B) are the most common construction methods for wood frame structures in North America and Japan, respectively. The shear walls in both types of building provide the resistance against lateral loads such as wind or seismic forces. In the light-frame system, the shear wall is constructed with 38 x 89 mm dimension lumber and sheathing panels. In contrast, the Japanese P&B shear walls are commonly composed of 35 x 105 mm studs, 135 x 105 mm top plates, and 105 x 105 mm posts and bottom sill pla tes; 105 x 105mm posts are also known as “baby squares”. The frame members are connected using mortise-and-tenon joinery and metal hardware. Since the late 1800s, diagonal bracing techniques have been used in the P&B shear walls to carry the lateral forces (Lam et al. 2002). After the Great Hanshin-Awaji or Kobe earthquake in Japan in 1995, the use of nailed sheathing in P&B shear wall construction has been increased (Okabe et al. 2004).  Canadian timber products used to dominate Japanese P&B market. Especially, British Columbia (BC) coastal hemlock posts occupied the large portion of the baby squares market from early 1980s to early 1990s due to their aesthetic qualities. However, the coastal hemlock posts were sold in green (i.e. moisture content of 30% or more) and untreated conditions, while the products imported from Europe were kiln-dried and some were even engineered to reduce dimensional changes due to environmental factors such as relative humidity. With the increased use of high speed computer control processing technology, dimensional stability became an important issue for processing the wood to accommodate the wood-to-wood connections. Coupled with the catastrophic losses of many P&B buildings during the 1995 Kobe earthquake, even though the losses were mainly due to the absence of 2  building code prior to 1945, Japanese builders turned away from the use of the green hemlock posts. The demand for the coastal hemlock products was decreased further after the new Japanese building standards were introduced in 2000, which specified the structural performance requirements for buildings (Edgington, 2005). Moreover, increases in various costs such as regulatory, stumpage, and logging costs discouraged the BC coastal forest industry to manufacture the hemlock products (Munroe 2004). This led the hemlock posts to lose their competitiveness in the baby squares market. On the other hand, the European laminated whitewood posts took over the market, which had more predictable quality and performance compared to solid timber posts (Perez-Garcia and Barr, 2005).   The laminated lumber products occupied roughly 60% of the Japanese P&B market share by 2000, while Canadian hemlock products only accounted for about 5% of the market. These laminated products were mostly made out of domestic Japanese or European softwood species such as spruce (Russell and Gerry, 2000). Instead of coming up with strategies to compete against the European products on costs, the Coastal Forest and Lumber Association (CFLA) developed a product line called Canada Tsuga E120 to compete on quality. With further supports from the BC government on marketing and research, Canada Tsuga E120 steadily gained the Japanese P&B market share (Coastal Clarion 2010). However, in order for Canada to recapture their lost market share more aggressively, development of low-cost and high-quality products is necessary.  Instead of using solid wood to manufacture 105 x 105 mm laminated posts like Europeans, low-cost strand-based wood composite products such as Oriented Strand Board (OSB) can be utilized as a lamstock for the laminated posts. In western Canada, OSB products are usually 3  manufactured with underutilized species such as aspen and beetle-killed lodgepole pine. Therefore, using such products to manufacture the posts would also be attractive to the BC government from the forest management perspective. From the product commercialization aspect, such product will have to be evaluated by an authorized organization which confirms the performance of the product based on the regulatory standards from government bodies. In Japan, structural wood products must satisfy the requirements stated in Article 37 of Building Standard Law to be used in the buildings. This process is expensive because a variety of tests are required to be conducted. It is important that product developer should understand the factors that determine the product performance and refine the product qualities prior to the evaluation process. This refining process is typically done through empirical research which is again expensive and time consuming. As a practical alternative, computational models can be used to investigate the effects of performance-determining factors and optimize the product qualities. The behaviour of the product during the end use applications can also be simulated by computer models. For instance, a finite-element based computer model can be used to study the responses of connections and shear walls under different loading conditions.   1.1 Research work and objectives In this thesis, a commercial strand-based wood composite product, 28.6 mm thick OSB rim board has been proposed as a lamstock for 105 x 105 mm posts. Since essential technical data such as bending MOE and MOR of the rim board product are already available, the research focusses on the performance of the strand-based posts as vertical frame members in P&B shear wall system. The research presented in this thesis largely divides into two parts: experimental study and computer modelling.  4  Due to the limited size of the available press machine, 2400 mm long posts have been used in this research, which are shorter than the Japanese standard length (i.e. 2730 mm). The responses of two types of connections under static loads have been experimentally studied: the hold-down connections between the posts and sill plates, and the nail connections between the posts and sheathing panel. Only the post orientation has been taken into account in designing the hold-down connection tests while the material properties such as embedment density and strand orientation have been considered for the nail connection tests. Also, another experimental study has been conducted to evaluate the effect of post orientation on the wall performance.   A computer model which can predict the behaviour of a nail connection in terms of load-displacement relationships has been developed based on the nail connection model HYST. The modelling fundamentals such as the idealization of the connection components and problem formulation have been kept the same as the base model, while the interactions between the nail fastener and surrounding wood medium have been modified. With the changes, the proposed connection model is capable of simulating strength degradation under a repeated loading condition and also able to predict the deformed nail shapes more realistically. The model has been validated against the test results from the experimental study mentioned earlier. Moreover, the model has been incorporated into a wall model, WALL2D, to confirm its applicability and validity.  The objectives of this research work are summarized as follows: 1) To empirically investigate the effects of material properties such as density variation along the thickness and strand orientation of the proposed strand-based composite 5  posts on the performance of the nail connections under monotonic and reversed-cyclic loads. 2) To experimentally study the effect of post orientation on the performance of the hold-down connections under monotonic loads.  3) To conduct full-scale tests on three types of P&B shear walls to examine the effect of post orientation on their structural performances under monotonic and reversed cyclic loads: double-braced, 9 mm OSB sheathed, and 11 mm OSB sheathed. 4) To develop a computer model which can predict the behaviour of single-shear nail connections under lateral loads, and be incorporated into another computer model such as a shear wall model.  1.2 Thesis organization This thesis consists of seven chapters. Chapter 2 discusses the key observations and major scientific contributions from the previous research on strand-based wood composites, nail connection, and wooden shear walls.   Chapter 3 presents experimental studies conducted on nail and hold-down connections constructed with the strand-based composite posts. It provides the descriptions on the test specimen assemblies, setup, and procedures. Based on the test results, it also provides statistical analysis on the effects of embedment density, loading direction, and nail driving direction on the performance of the nail connections. Subsequently, it discusses the effect of post orientation on the performance of the hold-down connections.   6  Chapter 4 presents an experimental study conducted on three types of P&B shear walls constructed with the strand-based posts. Like Chapter 3, it provides the descriptions on the wall assemblies, test setup and procedures. Then, it discusses the test results and how they are analyzed to evaluate the effect of post orientation.  Chapter 5 describes the development of a nail connection model based on an existing computer model HYST. It thoroughly discusses the concepts, components, problem formulation and solution of the base model. Then, it explains the modelling concepts of the revised model RHYST in detail, and highlights their major improvements. Lastly, the validation process of RHYST is presented in the chapter.   Chapter 6 discusses the applicability of RHYST as a subroutine in the shear wall model WALL2D. It explains the components and construction of the wall model comprehensively. Then, it provides the simulation results of the wall model with RHYST, which were compared to the test results reported in Chapter 4. Finally, Chapter 7 draws conclusions on the presented research and provides suggestions on future research.   7   Literature Review Chapter 2This chapter provides a citied review on the available literature from previous studies on the strength properties of strand-based wood composites, nail connection, and wood shear walls. Large volume of experiment-based research was conducted on the physical and mechanical characteristics of the wood composites. Considering their distinguishable features such as strand orientations and dimensions, computer models were also developed to simulate their structural behaviour. The nails connecting timber members were studied experimentally for many decades as well. Methods for analyzing and quantifying the performance of the nail connection loaded perpendicular to its nail shank were also extensively investigated. Based on this information, computer models that are capable of simulating the load-displacement relationships of the nail connections were developed. Despite high costs of shear wall tests, the shear walls were also investigated empirically. Subsequently, analytical and numerical computer shear wall models were developed and validated against experimental results.    2.1 Strand-based wood composites In the past, strand-based wood composites such as Oriented Strand Board (OSB), Oriented Strand Lumber (OSL), Laminated Strand Lumber (LSL), and Parallel Strand Lumber (PSL) have been developed predominantly following empirical-based approaches to study their mechanical and physical properties. Relatively little research has been performed on modeling the strength properties of the wood composites (Clouston and Lam 2001). On the contrary, numerous researchers have attempted to analytically model the wood composites’ physical properties, such as density variations along thickness and length, which critically influence their mechanical properties. 8  2.1.1 Strand-based wood composite modeling Clouston and Lam (2001) summarized modeling work done on wood composites since 1970s. They reported that most models were constructed based on the linear elasticity constitutive theory although nonlinear plasticity should be considered for the composites loaded beyond their linear elastic domains (Hunt and Suddarth 1974, Triche and Hunt 1993, Cha and Pearson 1994). In contrast, the three-dimensional nonlinear finite-element model developed by Wang, Y. T. and Lam (1998) took both linear elastic and nonlinear plastic regimes into account; the model took size effect into account in predicting the failure probability and probabilistic distribution of the tensile strength of parallel-aligned wood strand composites. The tensile modulus of elasticity (MOE) and strength of an individual veneer strand were considered statistically independent.  Clouston and Lam (2001) proposed a nonlinear stochastic two-dimensional finite-element model to simulate the stress-strain behaviour of strand-based wood composites in tension and compression. The authors took the four basic stress-strain behaviour characteristics of material into account: elastic, elastoplastic, brittle postfailure, and ductile postfailure. The focus of the model was on the composites’ behaviour at the post-elastic domain which is characterized according to the orthotropic plasticity theory. Experiments were conducted with small laminated specimens to obtain the input parameters for the model: strength and stiffness properties measured in tension, compression, and shear. Then, another set of experiments were conducted to confirm the model validity. The simulation results agreed well with the experimental results.  Clouston and Lam (2002) extended the model by replacing simple planar elements with three dimensional brick elements. The modified model could predict the behaviour of symmetric and non-symmetric composite beams under both 9  in-plane and out-of-plane loading conditions. Cloutston (2007) further modified the latest model to simulate the structural behaviour of PSL by considering void content and grain angle as random variables. The model applicability was limited to the composites with the strand orientations of fifteen and thirty degrees and specific loading conditions: three point bending, compression and tension parallel to length.   Gereke et al. (2012) developed a finite-element multiscale stochastic model to predict the stiffness properties of strand-based wood composites. The model took the randomness of strand orientation into account. It was constructed with the unit cells which represent strands covered in resin. The unit cell was modeled assuming “constant resin thickness and strand geometry, elastic properties of constituents, and perfect bonding between wood and resin”. Also, the grain angles of the strands were limited to + 20°. The simulation results of a PSL beam under three-point bending showed a good agreement with the experimental results of Arwade et al. (2009). The authors also investigated the effect of the resin content on the stiffness properties of the unit cell and beam. They concluded that the resin content had an inverse relationship with the Young’s modulus and direct relationship with transverse and shear moduli.  2.1.2 Strand orientation The strength and stiffness properties of strand-based wood composites can be controlled in various ways. For instance, different species and target densities can be used to achieve desirable mechanical properties. Instead of changing the type or amount of raw material, the strand alignment can be also adjusted during manufacturing processes to control such properties. It is a well-known fact that cross-aligned strands reduce the stiffness and strength 10  of the composites in their primary axes. However, it is difficult to quantify the effect (Moses et al. 2003).   McNatt et al. (1992) conducted an experimental study to investigate the effect of strand orientation on the mechanical properties of strand-based panels: bending stiffness and strength, internal bond strength, thickness swelling, and linear expansion. Sixty four panels with four different configurations were tested under uniform loading, pure moment, and concentrated loading conditions (Table 2.1). The test results showed that a face strand orientation had a significant influence on the lengthwise bending stiffness and strength of the specimens under all three loading cases, while a core strand orientation did not have much contribution on such properties. Group B achieved the highest stiffness and strength values; however, the differences between the test results of group B and C were minimal. The bending stiffness of group A and D were lower than group B by roughly two and three times respectively. Also a significant decrease in bending strength was observed when the face strand orientation was random or perpendicular to the panel length.  The other mechanical properties such as internal bond (IB) strength and thickness swelling were not affected by the strand orientation.  Table 2.1 Groups of panels manufactured in various combinations of random and aligned strands (McNatt, Bach, & Wellwood, 1992) Group Description A Strands are randomly oriented throughout the panel layers B Strands of the surface-layers are aligned parallel to the panel length while strands of the core-layers are random C Strands of the surface-layers are aligned parallel to the panel length while strands of the core-layers are aligned parallel to the panel width D Strands of the surface-layers are aligned parallel to the panel width while strands of the core-layers are aligned parallel to the panel length 11  Wang, K. and Lam (1998) studied the effect of face-to-core ratios (30:70 and 50:50) and core orientations (random and cross aligned) on the mechanical properties of three-layer strand-based panels. The panels were constructed into four configurations using the robot system which lays strands following the instructions from a mat formation simulation program: 70% random orientation core, 50% random orientation core, 70% cross-aligned core, and 50% cross-aligned core. Subsequently, IB, thickness swelling, and non-destructive bending tests were conducted. Based on the results of analysis of variance (ANOVA), both the core ratio and orientation significantly influenced the stiffness of the panels, while neither significantly affected the IB and thickness swelling properties. The specimens with thin and randomly-oriented core layers were stiffer than the ones with thick and cross-aligned core layers. The authors also reported that the 50% random core configuration specimens had the highest average bending MOE, while the 70% cross-aligned core configuration specimens had the lowest MOE.   Moses et al. (2003) investigated the effect of strand layup and orientation on the in-plane or axial properties of the LSL panels with five different configurations. The authors confirmed the findings reported by McNatt et al. (1992). The strands oriented parallel to the panel length improved both longitudinal in-plane stiffness and strength. From a layer sequence perspective, the strand orientation of the surface layer had more critical influence on the lengthwise in-plane properties than that of the core layer. On the other hand, the crosswise in-plane properties were not affected significantly by the layer sequence. The authors developed analytical models to predict the strength and stiffness properties of the panels based on the theory of mechanics of composites. Then, the first-order reliability method (FORM) was implemented to determine the mechanical properties by considering their statistical 12  distributions. The model predictions on the in-plane mechanical properties and their statistical variabilities agreed well with the experimental data.  Fan and Enjily (2009) experimentally examined the influence of strand orientation on the flexural and shear properties of OSB panels. The panels with five different surface strand orientations were tested under flatwise bending, edgewise bending, panel (thickness-wise) shear, and planar (widthwise) shear modes. As observed from the previous experimental studies discussed earlier, the strands aligned perpendicular to the panel length decreased the flexural strength of the panels but they did not affect the shear strength significantly. The experimental results also showed that the panel specimens achieved larger strength and stiffness when they were bent flatwise than edgewise. Interestingly, from a bending stiffness perspective, loading angles had noticeable contribution only when the specimens were bent flatwise. This observation indicated that the contact and bonding between the wood strands and resin were more consistent and solid throughout thickness than width. The authors also developed a theoretical model to predict the flexural and shear properties based on Hooke’s law of elasticity in conjunction with the rule of mixtures. In general, the model predictions agreed well with the experimental results.   As a part of the research conducted by Sturzenbecher et al. (2010), the effects of strand orientation and face-to-core ratio on the mechanical properties of the composite boards constructed with large-area strands were experimentally investigated.  The veneer strands had slender dimensions of 1 x 25 x 210 mm. Tension and four-point bending tests were conducted to obtain the elastic moduli and strengths of the boards with random, cross-aligned, and aligned strand orientations. As reported in the previous studies, the specimens 13  with the strands aligned along the board length showed the best performance in terms of both mechanical properties. The authors also conducted the same set of tests on the three-layer strand boards with two different face-to-core ratios. The cross-aligned core layers of the two board configurations were constructed with the strands account for 1/3 and 2/3 of the total strand mass respectively. The test results showed that the specimens with thicker cross-aligned core layers had lower mechanical properties, which agreed with the findings by Wang and Lam (1998).   Recently, Alldritt et al. (2014) studied the effect of strand layup and orientation on the performance of 13mm-OSB panels under out-of-plane and in-plane loading conditions. The strand layups considered in this study were three-layer (0⁰/90⁰/0⁰) and six-layer (0⁰/+45⁰/-45⁰/-45⁰/+45⁰/0⁰); 0⁰ indicates the strong axis. The layers of each panel configuration had the same thicknesses. Under the in-plane loads, the six-layer specimens outperformed the three-layer specimens in terms of both shear modulus and strength. On the contrary, the three-layer specimens achieved larger modulus of elasticity (MOE) and modulus of rupture (MOR) under the strong axis bending but lower values under the weak axis bending compared with those of the six-layer specimens. However, due to the high variation of the test data, the differences between the bending MOR and shear strength values were statistically inconclusive.   2.1.3 Density variation Unlike solid timber products, the densities of wood composites are determined from complex interactions such as differential heat and mass transfer between wood elements and adhesives 14  during pressing. These interactions are greatly affected by temperature, moisture, and gas pressure. Horizontal (face) density distribution (HDD) and vertical (edge) density profile (VDP) have strong relationships with the structural performance of the wood composites. For instance, HDD and VDP influence the mechanical properties such as shear and bending strengths as well as load-bearing capacities. With growing industry interests, density measuring devices and techniques have been developed and improved through continuous research; nondestructive nuclear and X-ray instruments have become the standard density measurement means. A radiation-based density measuring system called “in-situ” has been developed to monitor the density change during consolidation and after the press (Winistorfer, Moschler, Wang, DePaula, & Bledsoe, 2000). From a modelling perspective, several researchers have attempted to simulate the horizontal and vertical density variations using statistical and empirical approaches.  Dai and Steiner (1994a, 1994b) developed a mathematical model to predict the horizontal mass density variation of strand-based composites considering the distribution of strand geometrical properties such as location of center, area coverage, and void size. The model idealized the strand-based composite as a spatial structure, which contains the voids created randomly due to the strand geometry and randomness in the packing process (Steiner & Dai, 1993). Initially, the authors developed the mathematical model that simulates the void and overlapping areas for a single layer of the randomly distributed strands; the void area was assumed to be proportional to the distance between adjacent intersecting flakes. The model was formulated based on the Poisson and exponential distributions. After validating the single layer model with Monte Carlo simulation results and experimental data, the authors extended the model applicability to multiple layers of the strands by applying the two-15  dimensional random field theory. The extended model was able to predict the horizontal mass density variation of a strand-based 250 x 250 mm mat.   Xu (1999) theoretically linked VDP to the MOE of wood composites. The author developed (Xu and Winistorfer 1996) a numerical fitting technique to characterize the VDP which was assumed to be symmetric. The technique required the VDP data collected using X-ray instruments, which were transformed through the Fourier analysis. A smooth high-density-face-low-density-core sinusoidal profile was obtained. Subsequently, a mathematical model (Xu and Suchsland 1998) was formulated based on the laminate theory (Bodig & Jayne, 1982) to compute the MOE of the composite and evaluate the contribution of each layer to the MOE. The model simulation results showed that the peak density was found near the surface of the composite, which had a linear relationship with the MOE. Also, the results led to another conclusion that the surface density had greater contribution to the MOE than the core density.  Stiedl et al. (2003) experimentally investigated the variation of the mechanical properties through the thicknesses of OSB panels. Tension and compression tests were conducted on the fifteen layers along the thickness in both parallel and perpendicular directions to the panel length; the layers close to the panel surfaces had higher densities than the core layers. The test results showed that the panel specimens were stronger under the compression, while they were stiffer under the tension. The results also showed that the panel density had a direct relationship with the tested mechanical properties in both directions. The layers with high densities outperformed the low-density layers in terms of both strength and stiffness. The r2 values, which were obtained using a linear regression method, ranged from 0.797 to 0.929. 16  Beck and Lam (2009) conducted a similar experimental study on the effect of VDP on the tensile strength and MOE of OSL. As observed in the study by Stiedl et al. (2003), the test results also showed the direct relationship between the panel density and tensile properties. Log-transform model and linear regression methods were implemented to confirm the relationship.   2.2 Nail connection Since 1940’s, numerous researchers studied nail connections to quantify their lateral resistance capacities with few performance parameters for design purposes. Other researchers worked on the analysis of the load-displacement characteristics of the connections to extract more complete sets of performance indicators such as initial stiffness and maximum load displacement. Later, computer models that can reasonably simulate the load-displacement responses of nail connections were constructed.  2.2.1 European yield theory Johansen (1949) introduced a yield theory which states that “resistance of the wood to crushing under a dowel” and “friction between abutting surfaces” determine the performance of a dowel-type connection under a shear loading condition. He constructed formulas to estimate the yield and ultimate loads of the connections assuming plasticity for both timber and fastener, and considering different failure modes. For the bolt connections, the contribution of the friction between timber members was considered. He verified the theory and formulas with single- and double-shear connection test data. The test specimens were constructed with steel bolts, dowels, and Swedish Fir lumber. Subsequently, Johansen 17  conducted further experimental research with nail connections to confirm the validity of his theory (Larsen, 1977).   Aune and Patton-Mallory (1986) summarized the experimental studies on nail connections, which were conducted to confirm the validity of Johansen’s yield theory. They also revisited the empirically validated formulas for estimating the ultimate loads of several nail connection types: all-wood members with similar embedding strengths, wood member(s) with either steel plate(s) or wood-based sheathing(s), and all-wood members with different embedding strengths.   Bejtka and Blaß (2002) extended Johansen’s yield theory by considering the effect of withdrawal resistance on lateral resistance. The connection test specimens were constructed with the timber members and long self-tapping screws instead of nails. They assumed that “withdrawal failure only occurs in one timber member and the elongation of the screw is neglected”. The calculated load carrying capacities of the screw connections agreed well with the single-shear test results. The authors insisted that the withdrawal of fasteners should be considered for dowel type connections if they fail with the yielded fasteners. In the European design standard (CEN, 2004), this withdrawal phenomenon is referred as the rope effect.    The yield theory proposed by Johansen (1949) was adopted into the Canadian (CSA O86-09), American (NDS for Wood Construction 2015 Edition), and European (Eurocode 5: Design of timber structures) design standards for estimating the lateral resistance of nail connections. In both Eurocode 5 (CEN, 2004) and CSA-O86 (CSA, 2009), the rope effect proposed by Bejtka and Blaß (2002) was considered.  18  2.2.2 Experimental studies Dolan and Madsen (1992) analyzed the effect of timber materials and loading protocols on the performance of nail connections under static loads. The nail connection specimens were constructed with 8d (63.5 mm) common nails, spruce-pine-fir (SPF) frame members, and either plywood or waferboard sheathing panels. The specimen configurations were determined considering both grain directions of the frame and sheathing materials; they were tested under monotonic, slow-cyclic, and rapid-cyclic loads. The test results were analyzed in terms of performance parameters such as initial stiffness and peak load displacement; the parameters were obtained directly from load-displacement curves. The authors found that the grain directions of both the framing and sheathing members did not have statistically distinguishable effects on the nail connection performance. Also, neither the loading rate nor type had a significant influence on the performance. Consequently, they concluded that the nail properties had the primary effect on the load-displacement characteristics of the connections.  As a part of CUREE-Caltech Woodframe Project, Fonseca et al. (2002) conducted an extensive experimental study on the lateral performance of nail connections under reversed-cyclic loads. 72 nail connection types were determined considering the variables of the connection components which are summarized in Table 2.2. Monotonic tests were conducted to obtain the reference deformation for each connection type, which was used to determine the reversed-cyclic loading protocol amplitudes. Subsequently, ten reversed-cyclic tests were conducted for each type. The test results of several connection types showed asymmetric hysteresis loops characterized by edge tear-out failures. The ten performance parameters, 19  which describe both envelope and hysteretic responses of the connections, were obtained from the test results.   Table 2.2 Test variables of the nail connection components (Fonseca, Rose, & Campbell, 2002) Component Test Variables  sheathing panel thickness, material, density frame member species, moisture content at assembly, grain orientation  nail types, sizes, penetrations, overdriven depth, edge distance   Sartori and Tomasi (2013) conducted single-shear tests on the dowel-type connections constructed with ring nails, smooth nails, screws and staples. The experiments were designed to analyze the effect of sheathing material, sheathing thickness, and fastener spacing on the lateral resisting capacities of the four fastener types under monotonic and cyclic loads. The test procedures including loading protocol and rate were determined based on the European standards EN 26891 and EN 12512. The monotonic test results showed that the lateral resistance capacity of the nail connection increased about 10% when its OSB sheathing panel thickness was increased by 25%. However, the effect of the sheathing thickness was not noticeable in the reversed-cyclic test results. Also, based on the test results, the authors concluded that the ring nails outperformed both the smooth nails and screws. This conclusion should have been stated more carefully since the fasteners had different sizes; the ring nails (2.8 x 60 mm) had a bigger diameter and longer length than the smooth nails (2.5 x 50 mm). In addition, the authors estimated the strength and stiffness values of the connections following three design standards: Eurocode 5 (European), DIN 1052 (German), and CNR-DT 206 (Italian). The estimated strength values agreed well with the experimental results but the estimated stiffness values were significantly different.  20  2.2.3 Nail connection models Foschi (1974) introduced an analytical model that simulates the behaviour of a nail connection under lateral monotonic loading. The nail connection was idealized as an elasto-plastic beam embedded in nonlinear wood foundation. The principle of virtual work was applied to equate the equilibrium conditions of the laterally loaded connection. The problem was solved using a finite-element approach and the nonlinear function minimization technique published by Fletcher and Powell (1963). The model inputs were the load-displacement curve parameters obtained from bearing tests and the mechanical properties of the nail. This analytical model was validated against the single-shear nail connection test results for 5mm of displacements. Foschi concluded that assuming a wood medium as an elastic material in nail connection models will lead to inaccurate predictions of ultimate loads.  Foliente (1995) modified Bouc-Wen-Baher-Noori (BWBN) model to simulate the hysteric responses of wood joints and structures. The original BWBN model was developed for the single-degree-of-freedom (SDOF) system that experiences strength and stiffness degradation, and hysteresis pinching under cyclic loading (Baber and Wen 1981; Baber and Noori 1986). The author modified the pinching function of the original model while keeping the strength and stiffness degradation functions, and hysteric constitutive relations the same. The model was validated by simulating the hysteretic responses of the timber structures tested by Dowrick (1986). The model parameters were either obtained from the experimental data or through trial-and-error calibration until the satisfactory hysteresis shape was reproduced.    21  Chui et al. (1998) introduced a nonlinear finite-element nail connection model that takes the friction between a nail and wood medium into account. The nail element was modeled as a Timoshenko beam element with three nodes; three degrees-of-freedom was assigned to each node. The stress-strain relationship published by Filippau et al. (1983) was adopted to represent the nail behaviour under reversed-cyclic loads. The wood medium response at each nail node was modelled using a two-node spring element. The stiffness of the spring was obtained from the load-embedment relationship defined by the hysteresis model discussed in Chui and Ni (1997). Both the nail’s stress-strain and wood medium’s load-embedment properties were empirically obtained.  The friction between the nail shank and wood was modeled based on Coulomb’s friction law. The model results were compared to the reversed-cyclic nail connection test results which had the maximum amplitude of 8 mm.   Foschi (2000) developed the mechanics-based hysteresis connection model, HYST, which idealized a dowel-type wood joint as an elasto-plastic beam embedded in a nonlinear foundation. The foundation or embedment medium was modeled to only act in compression. The response of the embedment medium was described with six parameters: K, Q0, Q1, Q2, Q3, and Dmax. An algorithm was constructed to determine the nonlinear embedment responses under loading, unloading, and reloading conditions. The permanent gap formation at the wood foundation, which causes the pinching of the hysteresis loops under a reversed-cyclic loading condition, was also determined by the algorithm. The principle of virtual work was applied to formulate the nonlinear problem in terms of finite elements. Then, the Newton-Raphson iterative procedure was implemented to solve the problem. Allotey and Foschi (2004) introduced an extended version of HYST which took an initial confining pressure and nail shaft friction into account. The authors stated that as a nail gets driven into wood, it 22  experiences the confining pressure from the surrounding medium. An elastic Coulomb-type friction model was implemented to simulate the shaft friction. A parametric study was conducted on the extended model to investigate the effect of the confining pressure and friction. Base on the study results, the authors concluded that both factors affected the withdrawal amounts but not the hysteretic response of the nail connection under the reversed-cyclic loading. Li et al. (2012) introduced another extended version of HYST which considers the stiffness and strength degradation of the wood foundation under the repeated loading. The authors introduced a new parameter α which determines the stiffness degradation amount when the nail comes into contact with the foundation after traveling through the gap formed during the previous loading cycles.  Xu and Dolan (2009) introduced another version of BWBN model. They proposed that the parameter, which controls “the ratio of the final asymptote tangent stiffness to the initial stiffness” of a wood joint, should be considered as the dependent variable that changes according to the maximum displacement of a loading cycle. The parameter was considered as a constant in the original BWBN model. Also, the authors modified the energy-based pinching function to be displacement-based. An algorithm for calculating the pinching parameters for small and unsymmetrical cyclic loading conditions was built into the improved model as well. The genetic algorithm (GA) model developed by Heine (2001) was used to estimate the model parameters from experimental data. Subsequently, the model was validated against the reversed-cyclic test results of Dolan and Carradine (2003).   23  2.3 Shear wall The structural performance of shear walls under different loading conditions has been studied by numerous researchers. In general, a series of modeling work and experimental studies have been conducted on the static behaviour of the shear wall. Some of the studies include dynamic or seismic performance analysis as well (van de Lindt, 2004).   2.3.1 Experimental studies Numerous experimental studies on shear wall static/dynamic behaviour were conducted considering different loading protocols, wall configurations, sheathing materials, and connections. van de Lindt (2004), Li (2009), and Kirkman et al. (2014) summarized the major shear wall tests performed in North America and Japan. The shear walls tested in the laboratories of North America were mostly light-frame, while the ones tested in Japan were post-and-beam (P&B). The experimental results were used to demonstrate the shear wall behaviour under different loading conditions and validate the predictions or determine the input parameters of computer models. The experiments conducted at the University of British Columbia are summarized in the following section.  2.3.1.1 University of British Columbia Dolan (1989) conducted monotonic, cyclic, sine-wave, free vibration, and dynamic tests on the 2.4 x 2.4 m shear walls that were composed of 38 x 89 mm spruce-pine-fir (SPF) frame members and sheathed with either 9.5 mm plywood or waferboard panel; the stud members were spaced at 610mm and 8d (63.5mm) nails were used. Thirty eight specimens were tested under static or dynamic loads. Three plywood-sheathed and four waferboard-sheathed specimens were tested under the monotonic loads. And two specimens of each wall type were 24  tested under the cyclic loads, while the rest of the specimens were tested under the dynamic loads. The differences between the lateral performance of the two wall types under both static and dynamic loads were insignificant. Also, the author observed that the orientation of the sheathing panels did not affect the wall performance under the dynamic loads. These test results were used to verify the author’s mathematical models and validate Filiatrault (1990)’s SWAP model described in Section 2.3.2.   Lam et al. (1997) investigated the effect of sheathing panel size on the lateral resistance of 2.4 x 7.3 m shear walls under monotonic and reversed-cyclic loading conditions; regular size (1.2 x 2.4 m) and oversize (2.4 x 7.3 m) OSB sheathing panels were used. The wall frames, with a stud spacing of 400mm, were constructed with 38 x 89 mm SPF dimension lumber using 76 mm common nails. Throughout the tests, a constant vertical load of 9.12 kN/m was applied. According to the monotonic and reversed-cyclic test results, the oversize OSB sheathed walls had higher stiffness and lateral load carrying capacity than the regular size OSB sheathed walls.   He et al. (1998) evaluated the performance of the shear walls under three different reversed-cyclic loading protocols: Forintek Canada Corp. (FCC) cyclic test protocol, Comité Europeen de Normalisation (CEN) short protocol, and the test protocol proposed by the authors. The walls were assembled in the same manner as the oversize OSB sheathed walls tested by Lam et al. (1997). When the walls were loaded using the FCC protocol which has a large number of loading cycles, the fatigue failures of the nails were observed. This unrealistic failure phenomenon was not found when the walls were tested using the CEN protocol which has the short sequence of large amplitude cycles. Instead, increases in the racking resistance of 25  the shear walls were observed. However, the determination of the cyclic amplitude of the CEN protocol was problematic and arbitrary. Consequently, the authors suggested that the proposed protocol, which was developed to overcome the shortcomings of the FCC and CEN protocols, should be used to demonstrate seismic loading conditions.   As a continuation of the experimental studies of Lam et al. (1997) and He et al. (1998), He et al. (1999) investigated the influence of openings on the strength and stiffness of shear walls under monotonic and reversed-cyclic loads. For the reversed-cyclic tests, the loading protocol proposed by He et al. (1998) was used. Two 2.4 x 7.3 m specimens were constructed for each of four wall types: regular-size-OSB-sheathed, oversize-OSB-sheathed, perforated-regular-size-OSB-sheathed, and perforated-oversize-OSB-sheathed. According to the test results, the openings significantly decreased the lateral resistance of the walls, while the oversize OSB sheathing improved the strength and stiffness of the walls. The perforated-oversize-OSB-sheathed walls obtained even higher racking resistance than the non-perforated walls with regular size OSBs. From a failure mode perspective, a combination of nail and panel failures were observed on the perforated walls, while the nail failure governed the racking of the non-perforated walls. The panel failures were found near the corners of the openings.   Durham (1998) conducted static and dynamic tests on the 2.4 x 2.4 m shear walls which were constructed in the same manner as did in the study by Lam et al. (1997), except that hold downs were installed at the bottom corners of the walls. Total of fifteen shear walls were tested; six monotonic, four reversed-cyclic, and six dynamic tests were performed. However, three static tests were exempted from analysis; one cyclic test was performed for the demonstration purpose and two monotonic test specimens were installed and assembled 26  inappropriately. Three different wall configurations were considered: regular size OSB sheathed walls with 150 mm nail spacing, oversize OSB sheathed walls with 150 mm nail spacing, and oversize OSB sheathed walls with 75 mm nail spacing. The static test results confirmed that the oversize OSB sheathed walls had significantly higher stiffness and larger lateral load carrying capacity compared to the regular size OSB sheathed walls; the results also showed that the closer nail spacing increased the wall stiffness and strength. Contrary to the long walls (2.4 x 7.3 m) tested by Lam et al. (1997), He et al. (1998), and He et al. (1999), hold-downs and vertical dead load had critical contributions to wall uplift prevention. From the dynamic tests, less damage was observed on the oversize OSB sheathed walls compared to the regular size OSB sheathed walls. Moreover, the oversize OSB sheathed walls experienced higher accelerations and lower drifts than the regular size OSB sheathed walls. Gu (2006) used these test results to validate the pseudonail model (Gu and Lam 2004) described in Section 2.3.2.   Stefanescu (2000) conducted twelve static tests on the 1.82 x 2.58 m Japanese post-and-beam (P&B) walls composed of 105 x 105 mm posts. Three wall configurations were investigated: 2-braced, 4-braced, and OSB sheathed. The wall specimens were constructed with JAS grade Hem-fir framing members, JAS grade 9 mm OSB panels, and Japanese standard metal fasteners. Five monotonic tests with a loading rate of 0.13 mm/sec and seven reversed-cyclic tests with three different loading protocols were conducted: Ministry of Construction (Japanese standard), UBC, and modified UBC protocols. The static test results showed that both 4-braced and 2-braced walls had higher stiffness and lateral loading capacity than the OSB sheathed walls. However, the failures of the braced shear walls were more brittle which led to lower ductility and energy dissipation compared to the sheathed walls. The monotonic 27  test results were similar to the reversed-cyclic test results in terms of ultimate loads but the corresponding displacements were larger.   Li (2009) analyzed the behaviour of single-braced Japanese P&B walls under static loads. JAS grade Canadian Hem-fir frame members were assembled into eight 0.91 x 2.73 m walls using JAS grade metal fasteners. Four walls were sheathed with 15.9 mm gypsum wallboards (GWB) and the rest was bare-framed. Two specimens of each wall configuration were tested under each of monotonic and reversed-cyclic loading conditions. Both bare-framed and sheathed wall configurations showed asymmetric pinched-hysteresis loops under the reversed-cyclic loads, which caused by diagonal single bracing. The author observed increases in peak load, strength, stiffness, and energy dissipation when the GWBs were added to the bare-framed walls.   2.3.2 Shear wall models Shear wall models are formulated with different objectives and end applications.  In general, simplified models only predict the load-displacement relationships of shear walls under static and/or dynamic lateral loading conditions, while sophisticated models even simulate the detailed interaction and load sharing between the wall components. From a modeling complexity perspective, the simplified models only consider the wall components that have critical contribution to the wall behaviour while the sophisticated models consider contribution of all the structural members. Inevitably, the sophisticated models are more computational intensive (Folz and Filiatrault, 2001).   28  Foschi (1977) constructed a finite-element model to approximate the ultimate loads of wooden diaphragms based on the yielding of connections. This model was incorporated into Structural Analysis of Diaphragms and Trusses (SADT) program. Sheathing, frame, and connection members were idealized as an elastic orthotropic plate, six DOF beam, and nonlinear spring element respectively. The load-deformation parameters of the nonlinear spring element were obtained from test data. The relative displacements between the sheathing and frame were taken into account as shown. SADT was improved by Dolan (1989) considering the bearing effect between the adjacent sheathing panels, the ultimate load capacity of the sheathing-to-frame connector, and the out-of-plane behaviour of the sheathing panel. This improved model was incorporated into the computer program, Shear Wall (SHWALL).  Tuomi and McCutcheon (1978) proposed the energy approach analytical model that predicts the racking strengths of light-frame shear walls by determining the lateral resistance of individual fasteners. A closed-form strength equation was obtained assuming that a shear wall frame distorts into a parallelogram, while a sheathing panel remains rectangular and nails deform linearly upon loading. Subsequently, McCutcheon (1985) further modified the model considering the nonlinear behaviour of the nails.   Gupta and Kuo (1985) developed another strain energy approach model which can also be considered as the simplified version of Easley et al. (1982) finite-element model. Gupta and Kuo took the angular deformation of vertical and horizontal shear wall edges, and the nonlinear load-displacement relationship of a nail into account. In addition, the sinusoidal deformation of wall studs under lateral loading was considered initially. After confirming 29  that the sinusoidal deformations of the studs had insignificant contribution to the model results, the studs were assumed to be infinitely rigid in bending. Consequently, this assumption on the studs reduced the model’s degrees-of-freedom (DOF) from six to three, which increased the model computational efficiency. Gupta and Kuo (1987) modified this numerical model with two additional variables that represent the uplift displacements of the frame and sheathing. The modified model was also able to simulate the behaviour of multi-storey walls subjected to lateral and uplift loads; the relative rotations of the sheathing panels of the second and higher stories were taken into account.   Filiatrault (1990) introduced the simple finite-element structural model that analyzes the nonlinear response of shear walls under both static and dynamic loading conditions. This model was embedded in Shear Wall Analysis Program (SWAP). The shear wall behaviour was described with the lateral displacement of the top frame member and the distortion of the sheathing panels; the distortion was determined by the panel’s shear deformation, and rigid-body translations and rotations. Based on these assumptions, static and dynamic equilibrium equations were established using a variational formulation. For the static analysis, the response of a sheathing-to-frame connection under lateral loads was formulated using the modified version of the functional load-displacement relationship proposed by Foschi (1977). The modified load-displacement relationship with two additional parameters was used to formulate the hysteretic response of the connection in the dynamic analysis. The simulation results of SWAP agreed well with both static and dynamic test results of Dolan (1989).   Kasal and Leichti (1992) developed two shear wall models using commercial finite-element software, ANSYS: a three-dimensional detailed model and two-dimensional equivalent 30  model. In the three-dimensional detailed model, sheathing and frame members were idealized as two-dimensional linear orthotropic shell elements while each nail connection was modeled as a node with one-dimensional springs considering its nonlinear load-displacement characteristics. Moreover, the gaps between the sheathing elements were considered. The detailed model was verified with the test results of Easley et al. (1982). The two-dimensional equivalent model was developed with decreased numbers of elements, nodes, and total degree-of-freedoms. In this model, the shear wall was idealized as the structure consists of bar, beam, and orthotropic plate elements, which laterally resisted by a nonlinear and non-conservative diagonal spring. The simulation results of the simplified equivalent model agreed well with the results of the detailed model.   Based on essentially the same kinematic assumptions used in SWAP, Folz and Filiatrault (2001) developed the simplified finite-element shear wall model that analyzes the performance of shear walls under arbitrary quasi-static cyclic loads in terms of load-displacement response and energy dissipation. The model was integrated into Cyclic Analysis of Shear Walls (CASHEW) program. On the basis of the load-displacement relationship introduced by Foschi (1977), the sheathing-to-frame connection response was modeled with six physically identifiable parameters (i.e. Fo, Ko, r1, r2, δu, and δF), two unloading stiffness parameters (i.e. r3 and r4), and two hysteretic model parameters (i.e. α and β). The principle of virtual displacements was applied to formulate the equilibrium equations of the shear wall under the static loads; the equations were solved using a displacement control solution strategy. CASHEW was validated against the full-scale static test results (Durham 1998; Durham et al. 1999). In general, the simulation results were greater than the test results in terms of the wall stiffness and load-carrying capacity. The authors remarked 31  that this overestimation of CASHEW was due to the use of an uncoupled nonlinear spring pair to represent the sheathing-to-frame connection.  As a part of a simple numerical building model, Folz and Filiatrault (2004) applied the same set of parameters used in the connection model described above to demonstrate the load-displacement response of a shear wall. Simply, the authors idealized the shear wall as a single-degree-of-freedom (SDOF) spring. This SDOF model was developed based on the concept that both sheathing-to-frame connection and shear wall deform nonlinearly under monotonic loads, while they exhibit pinched-hysteretic behaviour characterized by strength and stiffness degradation under repeated loads. This empirical model was embedded into the computer program, Seismic Analysis of Wood frame Structures (SAWS).  Gu and Lam (2004) introduced the simplified shear wall model, pseudonail, that predicts the nonlinear dynamic response of shear walls. The simplicity of this model resulted in high computational efficiency, which provided a solution to seismic reliability analysis. The modelling concept was that the shear wall can be idealized as a pseudo nail since the shapes of the general load-deformation curves of sheathing-to-frame connections and shear walls are similar. Accordingly, the wall was modelled as a nonlinear SDOF system with several shear springs. This model was formulated based on Foschi’s (2000) mechanics-based hysteresis connection model, HYST, which idealized the sheathing-to-frame connection as an elasto-plastic beam embedded in a nonlinear foundation; the details of the model are explained in Section 2.2.3. In the pseudonail, two additional parameters were considered: the length and diameter of the nail. Five non-gradient search methods were implemented to find the eight parameters of the model: hill climbing, random-search, simplex, genetic algorithm, and 32  artificial neural network. Li and Lam (2009) used the pseudonail model to simulate the asymmetric behaviour of single-braced P&B shear walls under static loads. They also developed the SDOF building model that idealizes a one-story P&B building as a rigid horizontal diaphragm amounted on eight pseudonail walls. The simulation results of the building model agreed well with the shake table test results.   Judd and Fonseca (2005) remarked that the use of a single nonlinear spring to represent the sheathing-to-frame connection in a racking shear wall will lead to the incorrect prediction of the connection displacement under reversed-cyclic loads. Whereas, the use of an non-oriented nonlinear spring pair for such connection will lead to the overestimation of the stiffness and load capacity of both connection and shear wall. In order to compensate the shortcomings described above, the authors modeled the connection as a nonlinear spring pair oriented along its initial displacement trajectory. The orientation resulted in the coupled stiffness matrix and nodal forces about the global axes. To confirm the validity of the proposed idea, the oriented spring pair connection model was implemented into a shear wall model developed using ABAQUS, commercial finite-element software, and CASHEW developed by Folz and Filiatrault (2001). The simulation results from both wall models showed that the overestimation of the wall strength and stiffness was minimized.   Li et al. (2012) introduced the finite-element shear wall model WALL2D, which was written in FORTRAN language. Frame members and sheathing panels were modeled as elastic isotropic beams and orthotropic plates respectively. Connections linking frame members together were represented using three translational and three rotational springs. The authors modified the sheathing-to-frame connection model HYST (Foschi, 2000) as described in 33  Section 2.2.3, and implemented it into WALL2D. The principle of virtual work was applied to formulate the system equilibrium of the shear wall under static loads. Then, the Newton-Raphson method was used to solve the problem. Adopting the modeling idea by Judd and Fonseca (2005) explained earlier, WALL2D was developed to consider sheathing-to-frame connections as either non-oriented spring pairs or oriented spring pairs. The model was validated against the cyclic test results on two types of Japanese P&B walls sheathed with OSB panels.   2.4 Summary The extensive experimental studies and corresponding modelling work on strand-based wood composites, nail connection, and shear wall by numerous researchers were summarized in this chapter. The critical findings from the experimental research were highlighted, while various concepts, types, and techniques of the models were discussed. Also, the experimental setups, such as methods, specimen dimensions, and loading rates, were reviewed carefully, whereas the major assumptions of the models were underlined.  The studies on strand-based wood composites mainly focus on the mechanical properties of the composites related to their end uses. For instance, the research interest for the header components of a wall system would be bending MOE in edge-wise rather than flat-wise. Interestingly, the amount of research conducted on thick strand-based composites, such as LSL and PSL, has been increased recently. As described in Section 2.1.1, computer models can be developed considering the complicated physical and mechanical features of the composites. However, a model developer has to keep it mind that there is the trade-off between the complexity and efficiency. In this research, reasonable assumptions have been 34  made to simulate the behaviour of the strand-based wood composite posts as described in Chapter 6.  Through previous experimental studies, the researchers have confirmed that the connections holding a shear wall together, especially sheathing-to-frame nail connections, determine the in-plane lateral performance of the wall. They have also found that the pinched hysteretic behaviour of the nail connection and shear wall under reversed-cyclic loads are similar in terms of their load-displacement curve shapes. To compensate the high cost of experimental studies, researchers have developed computer models for both nail connection and shear wall at different complexity levels with various assumptions. In general, the connection models have been developed to be incorporated into the static shear wall models. Looking at the big picture, there are two modelling approaches. One is establishing path rules to fit experimental data and another is solving mechanics-based equilibrium equations. The former approach is obviously more computationally efficient but its parameters do not carry physical meanings such as the bending MOE of a frame member. On the other hand, the later approach uses the physical and mechanical properties of the connection and wall components as the model inputs. However, it is computationally intensive and requires reasonable assumptions and simplifications. As one of the main objectives, the nail model with more physical meanings and a reasonable complexity level is delivered in this research work.    35   Experimental Study I – Connections Chapter 3In order to evaluate the structural performance of shear walls composed of strand-based wood composite posts, the connections between the posts and other wall components, such as the sheathing and sill plates, have to be investigated; these connections contribute significantly to the lateral load resistance of the shear wall.  In this chapter, the test results on two types of connections are presented: the hold-down connections between the posts and sill plates, and the nail connections between the posts and sheathing.   3.1 Materials 3.1.1 Strand-based wood composite 28.6 mm (1 1/8”) thick commercial OSB rim boards (Rim Board Plus) were supplied by Ainsworth Engineered mill in 100 Mile House, British Columbia (BC); the width and length of the products were 406 mm (16”) and 3658 mm (12’) respectively.  Ainsworth’s OSB boards can be made out of various species strands combinations: lodgepole pine, aspen, tamarack, spruce, birch, black poplar, ash, balm, basswood, maple, other pines and assorted hardwoods. And two types of resins are used: Polymeric Diphenylmethane Diisocyanate (pMDI) and phenol formaldehyde (PF). The products are produced to meet certain mechanical properties, such as bending and shear strength, which are related to their end uses (Ainsworth 2011). The product recipe, which includes species and resin ratio, is not provided by the manufacturer since it is proprietary information.   Each board was cut to length of 2440 mm and ripped into widths of 230 mm and 160 mm for ease of handling and further processing. The ripped strips were planed to 26 – 27 mm and laminated into 105 mm thick four-layered boards using Phenol Resorcinol Formaldehyde 36  (PRF) resin. The boards were pressed at 758 kPa (110psi) for 9 hours using the hydraulic press at UBC Sim Lab. The boards were cut to 2.4 m long posts with 105 x 105 mm cross sections. In total, 52 posts were constructed; 36 posts were kept at the full length for shear wall tests, and 17 posts were cut to 20 hold-down specimens (1100 mm in length) and 147 nail connection specimens (105 mm in length). Then, holes with diameters of 11 mm (3/7”) were predrilled for lag screw connections for the hold-down test specimens. Finally, the connection specimens were stored in the conditioning chamber that has 65% relative humidity (RH) and 20 ⁰C for a minimum of two weeks before the tests.  3.1.1.1 Physical properties The moisture content (MC) and specific gravity (SG) of the strand-based wood composite were measured in accordance with ASTM D4442-07 and ASTM D2395-14, respectively. The MC was obtained based on oven-dry mass and the difference between conditioned mass and oven-dry mass, whereas the SG was calculated as the ratio of the oven-dry mass to the conditioned volume. The properties were measured using the composite frame members of the tested nail connection specimens; one measurement was made on each specimen. The undamaged parts of the frame members were cut into 29 mm width blocks. Then, the blocks were stored in the conditioning chamber for a minimum of a week before the measurements. The average MC and SG of the strand-based composite were 9.33% and 0.59, respectively. The summary statistics of the MC and SG measurements are provided in Table 3.1.     37  Table 3.1 Summary statistics of moisture content and specific gravity  MC (%) SG at MC of 9.33% Number of measurements 140 140 Average 9.33 0.65 Standard deviation 0.23 0.016 Coefficient of Variation 0.025 0.024 Minimum 8.65 0.61 Maximum 10.13 0.69   Figure 3.1 Average vertical density profile of strand-based composite laminae  The vertical density profile (VDP) of the composite material was measured at FPInnovations using QDP X-Ray profiler. The strand-based composite posts of the tested hold-down connection specimens were used to measure such property; each lamina of the posts was cut into a 50x50 mm block. Since the thicknesses of the laminae were slightly different from each other, they were converted into a percentage scale (i.e. 0% and 100% for the each surface of the lamina). Then, the average density at each adjusted position, in terms of the percentage scale, was calculated and plotted as shown in Figure 3.1. The calculated average 50060070080090010000% 20% 40% 60% 80% 100%Density (kg/m3) Depth/Thickness  near-the-lamina-surface regions near-the-lamina-surface regions mid-lamina region 38  density at each position had coefficient of variation (CV) ranged from 0.05 to 0.10. Mid-lamina and near-the-lamina-surface regions were chosen to examine the effect of density on nail connection performance; the mid-lamina region stands for 45-55% of the depth, while the near-the-lamina-surface regions represent 5-15% and 85-95% of the depth as shown in Figure 3.1. The summary statistics of the densities throughout the laminae and the selected regions are shown in Table 3.2.    Table 3.2 Summary statistics of densities throughout composite laminae and selected regions  throughout lamina near-the- lamina-surface (5 – 15% depth) mid- lamina  (45–55% depth) near-the- lamina-surface (85–95%  depth) Number of measurements 96 96 96 96 Average (kg/m3) 641.94 764.58 526.48 746.84 Standard deviation (kg/m3) 37.25 76.16 26.15 71.25 Coefficient of Variation 0.06 0.10 0.05 0.10 Lower 95% CI (kg/m3)  634.37 749.12 521.17 732.37 Upper 95% CI (kg/m3) 649.50 780.05 531.79 761.31 5th Percentile1 (kg/m3) 576.35 630.47 480.44 621.36 1 95% probability of coverage, 75% confidence interval   Table 3.3 T-test results on mid-lamina densities and near-the-lamina-surface densities  near-the-lamina-surface (15% of depth) mid- lamina (45% of depth) mid- lamina (55% of depth) near-the- lamina-surface (85% of depth) Count 96 96 96 96 Average (kg/m3) 691.27 529.69 525.19 680.56 Standard deviation (kg/m3) 70.78 37.65 32.47 66.73 Null Hypothesis, H0 μ 15% of depth = μ 45% of depth μ 55% of depth = μ 85% of depth t o  19.75 -20.51 t critical two tail (0.025,190) 1.97 1.97 Conclusion Reject H0 Reject H0   39  In order to confirm whether the densities of the mid-lamina regions are significantly different from the near-the-lamina-surface regions, t-tests were performed; the t-test is a statistical hypothesis test, which is comprehensively described in Section 3.5.1. Instead of comparing the average densities through the selected regions, the average densities at 15%-depth and 85%-depth locations were compared to the average densities at 45%-depth and 55%-depth locations respectively (Table 3.3). The t-test statistics on the difference between the average densities of the particular locations were calculated to be larger than the t-critical two-tail value with a 95% confidence level. In other words, the t-test results concluded that the densities of the mid-lamina were significantly different from the ones of the near-the-lamina-surface.   3.1.2 Sheathing panel 11 mm thick 910x1820 mm OSB sheathing panels were supplied by Ainsworth Engineered. They were cut into 90 mm width panel strips with lengths of 340 mm and 380 mm for the nail connection monotonic and reverse-cyclic load tests respectively.  The OSB specimens were stored in the conditioning chamber for a minimum of a week before the tests.  3.1.3 Connection hardware CN 50 nails, which have length of 50.8 mm, shank diameter of 2.87 mm, and head diameter of 6.76 mm, were used for the nail connection tests. These nails are typically used in Japanese wood light-frame construction following Japanese Industrial Standard (JIS) A5508. And S-HD 20 (Z-mark) hold-down devices with 110 mm LS 12 lag screws were used for the hold-down connection tests.   40  3.2 Specimen configurations 3.2.1 Nail connection configurations Considering possible driving locations and loading directions, seven sheathing-to-frame connection configurations were constructed as described in Table 3.4 and illustrated in Appendix A.   Table 3.4 Seven nail connection configurations  Descriptions  C1 Nails were face-driven and loaded perpendicular to the strand orientation. C2 Nails were face-driven and loaded parallel to the strand orientation. C3 Nails were edge-driven at the mid-lamina regions and loaded perpendicular to the strand orientation. C4 Nails were edge-driven at the mid-lamina regions and loaded parallel to the strand orientation. C5 Nails were edge-driven at the near-the-lamina-surface regions and loaded parallel to the strand orientation. C6 Nails were edge-driven at the near-the-lamina-surface regions and loaded perpendicular to the strand orientation towards mid-lamina regions. C7 Nails were edge-driven at the near-the-lamina-surface regions and loaded perpendicular to the strand orientation towards surface layers.   3.2.2 Hold-down connection configurations Two hold-down connection configurations were considered since the hold-down devices can be attached on either side of post specimens. For the face-driven configuration, LS 12 lag screws were penetrated into different layers of laminae, while the lag screws were penetrated through two middle laminae along glue lines for the edge-driven configuration (Figure 3.2).  41   a)  b) Figure 3.2 Hold-down connection configurations: a) face-driven, b) edge-driven  3.3 Experimental setup and procedure The nail connection specimens were tested under both monotonic and reverse cyclic loads, while the hold-down connection specimens were only tested monotonically.  3.3.1 Nail connection – monotonic test The nail connection monotonic tests were conducted using Sintech 30/D testing machine with a maximum loading capacity of 220 kN (50,000 lb). The tests were prepared following ASTM D1761-12. The 11 mm OSB board with three 17.4 mm diameter holes was attached to one side of the strand-based wood composite by CN50 nail. The nail was driven at minimum distances of 50.8 mm (2”) from the top of the strand-based composite and the bottom of the OSB boards. The board was mounted on the test machine actuator with bolts, while the 42  composite frame member was fixed to the testing platform. The test setup is illustrated in Figure 3.3; the dimensions are all in millimetres.   The OSB board of each connection specimen was pulled monotonically at a rate of 5mm/min beyond its peak load until the applied load drops to at least 80% of the peak; the loading rate was chosen to cause failure in 5 to 10 minutes, which is larger than the recommended loading rate of 2.54 mm/min by ASTM D1761-12 but smaller than the rate of 10 mm/min used in the study of Dolan and Madsen (1992). For each configuration, ten replicates were tested within 24 hours of their assembly.    Figure 3.3 Nail connection test setup (monotonic)  3.3.2 Nail connection – reversed-cyclic test The nail connection reversed-cyclic tests were conducted using the Material Test System (MTS) universal material testing machine with a maximum loading capacity of 250kN 340.0 11.0 52.5 52.5 105.0 43  (55,000lbs). The tests were prepared following ASTM D1761-12 and ASTM E2126-11 as guidelines. The connection specimens were prepared in the same manner as the monotonic test specimens, except that the reversed-cyclic load test specimens were fixed on the 76.2mm (3”) thick steel block. The steel block allowed the downward movements of the OSB board without touching the machine base. The schematic of the test setup is provided in Figure 3.4; the dimensions are all in millimetres.   Figure 3.4 Nail connection test setup (reverse-cyclic)   The displacement controlled loading procedure, CUREE Basic Loading Protocol, was implemented as recommended in ASTM E2126-11. The reference deformation (Δ) was set as the ultimate displacement (Δ u), which was the post-peak displacement at 80% of the peak load, obtained from the monotonic test results of each configuration (Table 3.5). For the first 52.5 52.5 11.0 380.0   105.0 76.2 105.0 44  three steps of the protocol, which had twenty cycles, loading rates were chosen to maintain a constant frequency, while a rate of 3mm/s was assigned to the following steps; the constant frequency of each configuration was determined by its reference deformation (Figure 3.5). These loading rates were chosen to neglect inertial effects and cause failure in 5 to 10 minutes. Ten replicates of each configuration were tested within 24 hours of their assembly.   Figure 3.5 CUREE basic loading protocol (ASTM Standard E2126, 2011)  3.3.3 Hold-down connection – monotonic test Hold-down connection specimens were tested monotonically using the MTS testing machine described in Section 3.3.2. The tests were setup and carried according to ASTM D1761-12 and Japan Housing and Wood Technology Center (HOWTEC) connection performance analysis guideline.   cycles with a constant frequency cycles with a loading rate of 3mm/sec Group 1 0.22 Hz Group 2 0.21 Hz Group 3 0.24 Hz Group 4 0.16 Hz Group 5 0.20 Hz Group 6 0.23 Hz Group 7 0.24 Hz  45   Figure 3.6 Monotonic load test setup for face-driven hold-down specimens  For each configuration, eight replicates were tested within 24 hours of their assembly. A custom steel bracket was made for each configuration considering the maximum lateral resistance and eccentricity effect. The specimens were mounted to the brackets using LS12 screws which were also used to attach the S-HD 20 hold-down devices to the strand-based composite posts. The hold-down devices were bolted down to the testing platform while the brackets were tightly fixed to the actuator. Then, the brackets were pulled up at a loading rate of 2.9 mm/min beyond the peak loads until the applied loads drop to at least 80% of the peak loads. Two transducers were mounted on the hold-down specimens to measure deformation S-HD 20 534.0  110.0  110.0 110.0 110.0 110.0 110.0 55.0   91.0  46  and strain. The schematics of the test setups are presented in Figure 3.6 and Figure 3.7; the dimensions are all in millimetres.   Figure 3.7 Monotonic load test setup for edge-driven hold-down specimens  3.4 Data analysis The connection test results were analyzed according to HOWTEC connection performance analysis guideline and ASTM E2126-11. Load-displacement curves were constructed with the test results and their performance parameters were obtained: peak load (Ppeak), ultimate load (Pu), peak displacement (∆peak), ultimate displacement (∆u), and initial stiffness (K0). The S-HD 20 110.0 110.0 110.0 110.0 110.0 110.0 534.0  91.0  55.0  47  parameter K0 was calculated by connecting 40% and 10% of the peak load, and Pu was calculated as 80% of the peak load or the load when the nail fails. Then, a multi-linear curve was constructed for each test data set by connecting its true origin, 0.1P, 0.4P, 2P/3, Pmax, and Pu. Subsequently, a bilinear curve which is also known as an equivalent energy elastic-plastic (EEEP) curve was constructed to obtain corresponding yield load (Pyield) and displacement (∆yield); the bilinear curve encloses the same area as the multi-linear curve. Lastly, according to both ASTM standard and HOWTEC guideline, a ductility ratio was calculated by dividing the ultimate displacement by the yield displacement. Since there are various methods to estimate the yield point, different ductility ratios can be obtained from the same load-displacement curve (Muñoz et al. 2008). Therefore, in this dissertation, the calculated yield parameters and ductility ratios are used for the comparison purpose rather than as the representative mechanical properties of structural systems.    Figure 3.8 Load-displacement curve analysis (HOWTEC, 2009) 48  For the reversed-cyclic load test results, envelope curves were constructed for both positive and negative excursions according to ASTM E2126-11. Average envelope curves were obtained by averaging the absolute values of the positive and negative envelope curves as illustrated in Figure 3.9. The average envelope curves were analyzed as described above. The complete sets of the performance parameters obtained from the nail connection tests and the hold-down connection tests are provided in Appendix B.   Figure 3.9 Average reversed-cyclic test data and envelope curves of C5 nail connection configuration   3.5 Results and discussion 3.5.1 Nail connection In general, the average monotonic load-displacement curves embraced the average reserved-cyclic load-displacement curves as shown in Appendix C. As expected, when the edge-driven 49  specimens with nails embedded in the high-density regions were loaded perpendicular to the strand orientation (C6 and C7), severe asymmetric hysteretic responses were observed. This phenomenon was due to changes of wood densities as the nails traveled through the strand-based composites. For instance, the nails of C6 traveled toward the high-density lamina surface in their positive cycles, while they traveled toward the low-density mid-lamina in their negative cycles. Therefore, the C6 specimens had higher load carrying capacities during the positive cycles than the negative cycles. Moreover, the connection specimens experienced stiffness and strength degradation under the cyclic loads, which will be discussed further in Section 5.3.2. The summary statistics of the performance parameters obtained from the monotonic and reversed-cyclic tests are provided in Table 3.5 and Table 3.6 respectively.   Table 3.5 Summary statistics of performance parameters (monotonic) Group  Ppeak Pu Δpeak Δ u K0 Pyield Δ yield Ductility Ratio (N) (N) (mm) (mm) (N/mm) (N) (mm) C1 (n =10) Avg. 1412.97 1130.37 11.44 17.15 1222.38 1166.96 1.05 17.93 SD 253.86 203.09 1.91 2.70 492.09 225.56 0.31 6.66 CV 0.18 0.18 0.17 0.16 0.40 0.19 0.30 0.37 C2 (n =10) Avg. 1595.23 1276.19 11.29 18.69 1521.08 1339.34 1.03 21.68 SD 154.04 123.23 2.47 2.19 637.48 140.47 0.43 10.05 CV 0.10 0.10 0.22 0.12 0.42 0.10 0.41 0.46 C3 (n =10) Avg. 1246.09 996.87 8.98 14.74 2098.96 1036.30 0.56 28.34 SD 185.27 148.21 2.05 4.86 845.46 160.93 0.23 9.30 CV 0.15 0.15 0.23 0.33 0.40 0.16 0.41 0.33 C4 (n =10) Avg. 843.49 674.80 13.50 22.99 1283.97 716.38 0.70 42.36 SD 125.31 100.24 4.91 5.54 563.29 114.32 0.43 23.91 CV 0.15 0.15 0.36 0.24 0.44 0.16 0.62 0.56 C5 (n =10) Avg. 1043.43 834.75 11.45 20.20 1712.39 883.97 0.59 38.46 SD 87.90 70.32 1.91 4.34 655.81 77.22 0.25 14.44 CV 0.08 0.08 0.17 0.21 0.38 0.09 0.42 0.38 C6 (n =10) Avg. 1461.84 1169.47 9.29 15.74 1802.10 1231.98 0.94 22.32 SD 219.43 175.54 3.16 3.54 1046.43 178.11 0.53 14.21 CV 0.15 0.15 0.34 0.23 0.58 0.14 0.56 0.64 C7 (n =10) Avg. 1351.63 1081.30 10.31 17.20 1255.97 1123.98 1.00 18.98 SD 133.14 106.51 1.74 2.80 426.16 111.02 0.38 6.55 CV 0.10 0.10 0.17 0.16 0.34 0.10 0.38 0.34  50  Table 3.6 Summary statistics of performance parameters (reversed-cyclic) Group  Ppeak Pu Δpeak Δ u K0 Pyield Δ yield Ductility Ratio (N) (N) (mm) (mm) (N/mm) (N) (mm) C1 (n =10) Avg. 1188.25 995.12 6.84 12.93 1448.71 1031.19 0.81 18.26 SD 63.04 48.19 1.86 1.74 482.69 47.15 0.34 6.81 CV 0.05 0.05 0.27 0.13 0.33 0.05 0.43 0.37 C2 (n =10) Avg. 1238.95 962.14 7.38 13.63 1342.14 1046.04 0.81 17.22 SD 235.45 182.90 1.73 2.17 396.88 196.81 0.16 3.74 CV 0.19 0.19 0.23 0.16 0.30 0.19 0.20 0.22 C3 (n =10) Avg. 1071.90 857.52 8.96 13.57 2283.98 892.00 0.42 36.52 SD 185.72 148.58 1.89 2.20 766.02 148.36 0.11 21.36 CV 0.17 0.17 0.21 0.16 0.34 0.17 0.27 0.58 C4 (n =10) Avg. 815.50 612.33 12.15 18.37 2021.80 681.90 0.58 57.75 SD 156.88 179.42 3.84 4.26 1443.07 139.77 0.50 45.68 CV 0.19 0.29 0.32 0.23 0.71 0.20 0.86 0.79 C5 (n =10) Avg. 990.75 792.60 8.44 14.75 2285.03 845.42 0.40 39.72 SD 160.97 128.78 2.43 1.74 769.81 134.13 0.12 12.30 CV 0.16 0.16 0.29 0.12 0.34 0.16 0.30 0.31 C6 (n =10) Avg. 1171.50 937.20 7.16 13.00 1746.65 997.77 0.60 22.71 SD 192.11 153.69 2.58 2.11 501.15 153.49 0.12 6.44 CV 0.16 0.16 0.36 0.16 0.29 0.15 0.20 0.28 C7 (n =10) Avg. 1121.55 914.29 7.85 12.50 2565.13 954.20 0.43 34.21 SD 104.10 119.76 2.17 1.58 1088.28 97.20 0.17 16.25 CV 0.09 0.13 0.28 0.13 0.42 0.10 0.39 0.48  The performance parameters of the configurations were compared statistically against each other in order to evaluate the effects of nail driving direction, embedment density, loading direction, and loading type. Assuming that the test data sets have normal distributions and unknown population variances, t-tests at 95% confidence level were implemented on the differences in means. In each statistical hypothesis test, the null hypothesis (H0) was stated as the mean values of the parameters of two different configurations are the same. And the rejection criterion was stablished as shown in Table 3.7, which had the sample size (n) of 10 and significance level (α) of 0.05.   Table 3.7 Null hypothesis and rejection criterion for t-tests Null hypothesis Rejection criterion 21:0 H  221,2/0 nntt    or    221,2/0 nntt 51  For example, since the test statistic (t0) of 1.68 for the average peak loads of C1 and C3 is larger than – t0.025, 18 but smaller than t0.025, 18, the null hypothesis H0: μ c1 = μ c3 cannot be rejected. This means that there is no strong evidence to conclude that there is a significant difference between the mean values of the compared parameters at the 0.05 level of significance.  3.5.1.1 Nail driving direction effect CN50 nails were driven either through or along the laminae; the former is called face-driven and the latter is called edge-driven. Considering the loading directions, the performance parameters of C1 were compared to the ones of C3, C6, and C7. Then, the parameters of C2 were compared to C4 and C5. The t-test results on the nail driving direction effect are provided in Table 3.8 and Table 3.9. Only the test statistics which meet either reject criterion are highlighted in bold fonts and their conclusions are stated.     Table 3.8 T-test results on nail driving direction effect (monotonic) H0 (Null Hypothesis)   Ppeak  Pu Δpeak Δ u K0 Pyield Δ yield Ductility Ratio μ c1 = μ c3 t0 1.68 1.68 2.78 1.37 -2.83 1.49 3.97 -2.88 concl. - - reject - reject - reject reject μ c1 = μ c6 t0 -0.46 -0.46 1.84 1.00 -1.58 -0.72 0.57 -0.89 concl. - - - - - - - - μ c1 = μ c7 t0 0.68 0.68 1.39 -0.04 -0.16 0.54 0.32 -0.36 concl. - - - - - - - - μ c2 = μ c4 t0 11.97 11.97 -1.27 -2.28 0.88 10.88 1.73 -2.52 concl. reject reject - reject - reject - reject μ c2 = μ c5 t0 9.84 9.84 -0.16 -0.99 -0.66 8.98 2.85 -3.02 concl. reject reject - - - reject reject reject     52  Table 3.9 T-test results on nail driving direction effect (reversed-cyclic) H0  (Null Hypothesis)   Ppeak Pu Δpeak Δ u K0 Pyield Δ yield Ductility Ratio μ c1 = μ c3 t0 1.88 2.79 -2.54 -0.72 -2.92 2.83 3.36 -2.58 concl. - reject reject - reject reject reject reject μ c1 = μ c6 t0 0.26 1.14 -0.32 -0.08 -1.35 0.66 1.84 -1.50 concl. - - - - - - - - μ c1 = μ c7 t0 1.73 1.98 -1.12 0.57 -2.97 2.25 3.15 -2.86 concl. - - - - reject reject reject reject μ c2 = μ c4 t0 4.73 4.32 -3.58 -3.14 -1.44 4.77 1.43 -2.80 concl. reject reject reject reject - reject - reject μ c2 = μ c5 t0 2.75 2.40 -1.12 -1.27 -3.44 2.66 6.62 -5.53 concl. reject reject - - reject reject reject reject  Loading direction: perpendicular to the strand orientation In general, both monotonic and reversed-cyclic test results showed that the performance parameters of the face-driven connections (C1) were not significantly different from the ones of the edge-driven connections with high embedment densities (C6 and C7). However, under the reversed-cyclic loading, C7, which was initially loaded towards the low-density regions, achieved significantly lower yield load and displacement, but higher initial stiffness and ductility ratio than C1.   In contrast, the effect of nail driving direction became more evident when the nails were edge-driven at the low-density regions (C3). C3 was significantly stiffer at initial loading stages and more ductile than C1 under both loading cases. Moreover, C1 had larger load parameters than C3, but according to the t-test results, only the ultimate load of C1 was significantly greater than that of C3 under the reversed-cyclic loads. Interestingly, the peak and ultimate displacement parameters of C1 were larger than C3 under the monotonic loads while they were smaller under the reversed-cyclic loads.  53  Loading direction: parallel to the strand orientation Regardless of the embedment densities, the edge-driven connections (C4 and C5) showed significantly different connection performance compared with the face-driven specimens (C2). The C2 specimens achieved significantly larger load parameters and lower ductility than the C5 specimens; the differences between the compared parameters were more dramatic when the specimens were experiencing the monotonic loads. The test results also showed that the peak and ultimate displacement parameters of the connections were increased when the nails were edge-driven; however, the increased amounts were significant depend on the embedment densities of the edge-driven connections.  In general, the edge-driven specimens were more ductile and stiffer than the face-driven specimens, whereas they had lower load carrying capacities. The effect of nail driving direction became more evident when the specimens were loaded parallel to the strand orientation. Also, we could observe that such effect became more prominent as the embedment densities of the edge-driven connections decreased.   3.5.1.2 Embedment density effect The effect of the embedment density on the nail connection performance was evaluated by comparing the performance parameters of the edge-driven specimens. Considering loading directions, the performance parameters of C3 were compared to those of C6 and C7. Then, the parameters of C4 were compared to C5. The nails were driven into the mid-lamina’s low-density regions for C3 and C4, while the nails were driven into the high-density regions near the lamina surface for C5, C6 and C7. The t-test results on the embedment density effect are presented in the following tables. 54  Table 3.10 T-test results on embedment density effect (monotonic) H0 (Null Hypothesis)   Ppeak Pu Δpeak Δ u K0 Pyield Δ yield Ductility Ratio μ c3 = μ c6 t0 -2.38 -2.38 -0.26 -0.53 0.70 -2.58 -2.08 1.12 concl. reject reject - - - reject - - μ c3 = μ c7 t0 -1.46 -1.46 -1.56 -1.39 2.82 -1.42 -3.09 2.60 concl. - - - - reject - reject reject μ c4 = μ c5 t0 -4.13 -4.13 1.23 1.25 -1.57 -3.84 0.70 0.44 concl. reject reject - - - reject - -  Table 3.11 T-test results on embedment density effect (reversed-cyclic) H0 (Null Hypothesis)   Ppeak Pu Δpeak Δ u K0 Pyield Δ yield Ductility Ratio μ c3 = μ c6 t0 -1.18 -1.18 1.79 0.59 1.86 -1.57 -3.35 1.96 concl. - - - - - - reject - μ c3 = μ c7 t0 -0.74 -0.94 1.22 1.25 -0.67 -1.11 -0.07 0.27 concl. - - - - - - - - μ c4 = μ c5 t0 -2.47 -2.58 2.58 2.49 -0.51 -2.67 1.11 1.20 concl. reject reject reject reject - reject - -    Loading direction: perpendicular to the strand orientation Under both loading conditions, the connections with the nails embedded in the high-density regions (C6 and C7) achieved larger load parameters, but smaller ductility ratio and initial stiffness parameters compared to the specimens with the nails embedded in the low-density regions (C3). However, the differences in the load parameters were only significant when the connections with the high embedment densities were monotonically loaded towards the lamina surface (C6). Interestingly, the peak and ultimate displacement parameters of C3 were smaller than C6 and C7 under the monotonic loads, while they were larger under the reversed-cyclic loads. Also the effect of embedment density was abated when the specimens experienced the reversed-cyclic loads.  55  Loading direction: parallel to the strand orientation The connections with the nails embedded in the high-density regions (C5) achieved significantly larger load parameters than the connections with the nails embedded in the low-density regions (C4) under both loading cases. On the other hand, the C5 specimens achieved smaller displacement parameters than the C4 specimens; however, the differences were only significant under the reversed-cyclic loads.   We could conclude that the embedment density significantly influenced the nail connection performance in both loading directions; the lower embedment density led to the smaller load carrying capacities but higher ductility. And such effect became more evident and significant as the specimens were loaded parallel to the strand orientation.   3.5.1.3 Loading direction effect The connection test specimens had the nails driven into three locations: face-side, edge-side with the high embedment density, and edge-side with the low embedment density. These specimens were loaded perpendicular and parallel to the strand orientation to examine the effect of loading direction on the nail connection performance. The performance parameters of C1 and C3 were compared to those of C2 and C4 respectively. Then, the connection performance of C5 was compared to C6 and C7.  The t-test results on the loading direction effect are provided in Table 3.12 and Table 3.13.   56  Table 3.12 T-test results on loading direction effect (monotonic) H0 (Null Hypothesis)   Ppeak  Pu Δpeak Δ u K0 Pyield Δ yield Ductility Ratio μ c1 = μ c2 t0 -1.94 -1.94 0.15 -1.40 -1.17 -2.05 0.08 -0.98 concl. - - - - - - - - μ c3 = μ c4 t0 5.69 5.69 -2.68 -3.54 2.54 5.12 -0.90 -1.73 concl. reject reject reject reject reject reject - - μ c5 = μ c6 t0 -5.60 -5.60 1.85 2.52 -0.23 -5.67 -1.89 2.52 concl. reject reject - reject - reject - reject μ c5 = μ c7 t0 -6.11 -6.11 1.40 1.84 1.85 -5.61 -2.83 3.88 concl. reject reject - - - reject reject reject  Table 3.13 T-test results on loading direction effect (reversed-cyclic) H0 (Null Hypothesis)   Ppeak  Pu Δpeak Δ u K0 Pyield Δ yield Ductility Ratio μ c1 = μ c2 t0 -0.66 0.55 -0.68 -0.79 0.54 -0.23 -0.06 0.42 concl. - - - - - - - - μ c3 = μ c4 t0 3.34 3.33 -2.36 -3.17 0.51 3.26 -0.97 -1.33 concl. reject reject reject reject - reject - - μ c5 = μ c6 t0 -2.28 -2.28 1.15 2.02 1.85 -2.36 -3.75 3.87 concl. reject reject - - - reject reject reject μ c5 = μ c7 t0 -2.16 -2.19 0.57 3.02 -0.66 -2.08 -0.44 0.86 concl. reject reject - reject - - - -  Nail driving direction: face-driven Under both loading cases, the face-driven connections loaded parallel to the strand orientation (C2) had higher load parameters than those loaded perpendicular to the strand orientation (C1); however, the differences were not significant.   Nail driving direction: edge-driven at low embedment density regions The connections with the nails driven into the low-density regions of the edge-sides (C3 and C4) achieved significantly higher load parameters but lower displacement parameters when they were loaded perpendicular to the strand orientation under both loading cases; the lower displacement parameters led to the decrease in ductility, but not to the significant level.  57  Nail driving direction: edge-driven at high embedment density regions The connections with nails driven into the high-density regions of the edge-sides (C5, C6, and C7) significantly lost their load capacities when they were loaded parallel to the strand orientation under both loading types. Also, the parallel-loaded specimens (C5) achieved significantly higher ductility than the perpendicularly loaded specimens (C6 and C7) under the monotonic loads.  In addition, larger peak and ultimate displacement parameters were achieved when the connections were loaded parallel to the strand orientation; however, the differences were not consistently significant.   We could conclude that, the loading direction significantly influenced the connection performance of the edge-driven connections but face-driven connections. Unlike nail connections with solid timber, the edge-driven connections achieved better lateral resisting performance when they were loaded perpendicular to the strand orientation.     3.5.1.4 Loading type effect The effect of the loading type on the nail connection performance was evaluated by comparing the parameters obtained from the monotonic and reversed-cyclic test as shown in Table 3.14. The load and displacement parameters of the monotonic load test results were larger than those of the reversed-cyclic load test results.  The face-driven connection, C2, and the edge-driven connection with the high embedment density, C7, achieved significantly larger load and displacement parameters when they were monotonically loaded.  Also, the effect of the loading type was significant to C1, C5, and C6 in terms of load carrying capacities and/or corresponding displacements. These observations were different from the ones reported by Dolan and Madsen (1992); the explanation for these differences is provided 58  in the following section. Meanwhile, the connection specimens achieved higher initial stiffness under the cyclic loads. This tendency was due to the faster loading rate of the reverse-cyclic tests; the same observation was reported by Chui and Ni (1997).   Table 3.14 T-test results on loading type effect H0 (Null Hypothesis)   Ppeak Pu Δpeak Δ u K0 Pyield Δ yield Ductility Ratio μ c1 mono  = μ c1 r.cyclic t0 2.72 2.05 5.46 4.16 -1.04 1.86 1.64 -0.11 concl. reject - reject reject - - - - μ c2 mono  = μ c2 r.cyclic t0 4.00 4.50 4.10 5.19 0.75 3.84 1.56 1.31 concl. reject reject reject reject - reject - - μ c3 mono  = μ c3 r.cyclic t0 2.10 2.10 0.02 0.69 -0.51 2.08 1.76 -1.11 concl. - - - - - - - - μ c4 mono  = μ c4 r.cyclic t0 0.44 0.96 0.68 2.09 -1.51 0.6 0.6 -0.94 concl. - - - - - - - - μ c5 mono  = μ c5 r.cyclic t0 0.91 0.91 3.09 3.69 -1.79 0.79 2.24 -0.21 concl. - - reject reject - - reject - μ c6 mono  = μ c6 r.cyclic t0 3.15 3.15 1.65 2.1 0.15 3.15 1.99 -0.08 concl. reject reject - - - reject - - μ c7 mono  = μ c7 r.cyclic t0 4.3 3.3 2.8 4.62 -3.54 3.64 4.29 -2.75 concl. reject reject reject reject reject reject reject reject  3.5.1.5 Failure modes Under the monotonic loads, the sheathing-to-frame connection specimens failed when the nail fasteners either pulled through the sheathing panel or pulled out from the frame member. These two failure modes are called pull-through (Figure 3.10a) and pull-out (Figure 3.10b); the former is governed by the sheathing material properties while the latter is governed by the frame material properties. Pull-though was the dominating failure mode for the face-driven connections (C1 and C2) and C6 edge-driven connections, while the failures of C3, C4, and C5 edge-driven connections were governed by nail pull-out or withdrawal (Table 3.15).   59  Table 3.15 Number of failure mode occurrences  Monotonic Load Tests Reversed-cyclic Load Tests  Pull-out Pull-through Pull-out Pull-through Low-cycle-fatigue C1 1 9 3 0 7 C2 0 10 1 2 7 C3 8 2 4 1 5 C4 9 1 10 0 0 C5 9 1 2 6 2 C6 0 10 4 0 6 C7 5 5 6 0 4  During the reversed-cyclic tests, an additional failure mode, low-cycle-fatigue, was observed as shown in Figure 3.10c. ASTM E1823-13 defines fatigue as “the process of progressive localized permanent structural change occurring in a material subjected to conditions that produce fluctuating stresses and strains at some point or points and that may culminate in cracks or complete fracture after a sufficient number of fluctuations.” Accordingly, low cycle fatigue is defined here as the localized fracture of the nail after a relatively low number of cycles (N<60). Under the reversed-cyclic loads, most of the configurations experienced combinations of three failure modes, except the C4 specimens which all failed in pull-out (Table 3.15).  Other than C4, the governing failure mode of each configuration was changed when different load types were applied; the configurations failed in pull-through under the monotonic loads were failed in low-cycle-fatigue under the reversed-cycle loads. However, when the connections failed in low-cycle-fatigue, they lost significant amounts of load carrying capacities due to the cumulated damage on the nails.    60   a)  b)  c) Figure 3.10 Nail connection failure modes: a) pull-through, b) pull-out, and c) low cycle fatigue   61  3.5.2 Hold-down connection The summary statistics of the performance parameters obtained from the monotonic tests are provided in Table 3.16. The parameters of the face-driven and edge-driven hold-down connection configurations were compared statistically by implementing the hypothesis testing method described in Section 3.5.1 and presented in Table 3.17.   Table 3.16 Summary statistics of performance parameters of hold-down connection specimens Group  Ppeak Pu Δpeak Δ u K0 Pyield Δ yield Ductility Ratio (kN) (kN) (mm) (mm) (N/mm) (N) (mm) Face-driven (n =8) Avg. 45.49 44.28 8.96 8.98 7.78 37.84 5.15 1.88 SD 3.46 3.97 0.88 0.90 1.73 4.32 1.62 0.55 CV 0.08 0.09 0.10 0.10 0.22 0.11 0.31 0.29 Edge-driven (n =8) Avg. 34.23 27.38 6.79 8.34 10.07 28.66 3.26 2.87 SD 3.28 2.62 1.25 1.43 3.40 2.69 1.43 0.93 CV 0.10 0.10 0.18 0.17 0.34 0.09 0.44 0.32  Table 3.17 T-test results on performance parameters of face-driven and edge-driven specimens H0 (Null Hypothesis)   Ppeak  Pu Δpeak Δ u K0 Pyield Δ yield Ductility Ratio μ face-driven = μ edge-driven t0 6.68 10.04 4.00 1.07 -1.70 5.10 2.48 -2.60 concl. reject reject reject - - reject reject reject  Except the ultimate displacement and initial stiffness parameters, the two connection configurations achieved performance parameters that were different from each other. The load and corresponding displacement parameters, except ultimate displacement, of the face-driven configuration were significantly higher than those of the edge-driven configuration. Meanwhile, the face-driven connections were significantly less ductile due to their relatively large yield displacements compared with their ultimate displacements. 62  3.5.2.1 Failure modes The hold-down connections failed in two modes: moment failure and splitting failure of the vertical frame member (i.e. post). The posts of the face-driven specimens all failed in moment as shown in Figure 3.11a. This brittle failure mode led the ultimate displacements of the specimens to be almost the same as their peak displacements; therefore, they achieved low ductility ratios. In contrast, the splitting in the post was the governing failure mode for the edge-driven connections as shown in Figure 3.11b.     a)  b) Figure 3.11 hold-down connection failure modes: a) moment failure and b) splitting failure of the post  63  3.5.2.2 Further connection performance comparison Japan Housing and Wood Technology Center (HOWTEC) also conducted monotonic load tests on S-HD20 hold-down connections constructed with Japanese-Cedar (Sugi) and Douglas-Fir columns. Instead of LS12 lag crews, M12 bolts were used to connect the hold-down devices to the post specimens. The summary statistics of the test results are provided in Table 3.18.   Table 3.18 Summary statistics of performance parameters of hold-down connections composed of Douglas-Fir and Japanese-Cedar columns Post Material  Ppeak Pu Δpeak Δ u K0 Pyield Δ yield Ductility Ratio (kN) (kN) (mm) (mm) (N/mm) (N) (mm) Douglas-Fir (n =6) Avg. 48.59 42.00 36.20 45.63 2.95 40.13 13.66 3.32 SD 3.25 6.76 7.10 12.29 0.14 2.31 1.26 0.83 CV 0.07 0.16 0.20 0.27 0.05 0.06 0.09 0.25 Japanese-Cedar (Suki) (n =6) Avg. 52.87 48.34 25.67 28.48 3.60 44.01 12.22 2.32 SD 5.98 9.13 5.89 7.06 0.28 4.41 0.87 0.51 CV 0.11 0.19 0.23 0.25 0.08 0.10 0.07 0.22   The hold-down connections built with the Douglas-Fir and Japanese-Cedar posts achieved larger load and displacement parameters but lower initial stiffness than those constructed with the strand-based wood composite posts regardless of their configurations. The differences in load parameters ranged from 2 kN to 21 kN. Interestingly, the differences in the displacement and initial stiffness parameters were more dramatic; the higher values were about three times the lower values. The higher density of the strand-based composite led to the larger initial stiffness, while the ductile failure, which was hardware failure, of the hold-down connections composed of Douglas-Fir and Japanese-Cedar resulted in the larger displacement parameters.   64  3.6 Summary  An experimental study was conducted on the nail connection and hold-down connection constructed with the strand-based wood composite posts and Japanese standard metal fasteners. The nail connections were tested under the monotonic and reversed-cyclic loads, while the hold-down connections were tested under the monotonic loads only. The experiments were conducted according to ASTM standards and the HOWTEC connection performance analysis guideline.  The nail connection specimens were assembled into seven connection configurations using CN50 nails and 11mm OSB sheathing panels. The specimens were tested to investigate the effects of the nail driving directions, embedment density, loading directions, and loading types. Most of the configurations achieved significantly larger load and displacement parameters under the monotonic loads than reversed-cyclic loads. However, the same trends of the effects were observed under both loading conditions. The face-driven specimens outperformed the edge-driven specimens when they were loaded parallel to the strand orientation. The embedment density also significantly influenced the nail connection performance. A higher embedment density led to larger load carrying capacities but lower ductility. Again, such effect became more evident when the specimens were loaded parallel to the strand orientation. From the loading direction effect perspective, regardless of the embedment densities, the edge-driven specimens achieved significantly higher load parameters when they were loaded perpendicular to the strand direction.  The hold-down connection specimens were assembled into two connection configurations with S-HD20 hold-down devices and LS12 lag screws. The face-driven configuration 65  achieved significantly higher average peak, ultimate, and yield loads than the edge-driven configuration. For both configurations, the strand-based composite posts failed before either the hold-down hardware or lag screws failed. The posts failed in moment when the hold-downs were mounted on the face-sides, while they failed in splitting when the hold-downs were mounted on the edge-sides. Since the moment failure was more brittle than splitting failure, the face-driven configuration had lower ductility than the edge-driven configuration.   66   Experiment Study II - Shear Wall Chapter 4The experimental observations reported in Chapter 3 show that the orientation of strand-based wood composite posts had a significant effect on the structural responses of the nail and hold-down connections. In order to study the influence of such factors on the lateral resistance of the shear walls composed of the composite posts, another experimental study was conducted. The structural performance of three wall types subjected to monotonic and reversed-cyclic loads was investigated.    4.1 Materials 4.1.1 Strand-based wood composite posts As described in Section 3.1.1, the strand-based wood composite posts were constructed at the UBC sim lab using 28.6 mm (1 1/8”) thick commercial OSB rim boards supplied by Ainsworth Engineered. Although the standard height of a Japanese post-and-beam shear wall is 2730 mm, due to the limited hydraulic press size at the lab, the strand-based wood composite posts were constructed to heights of 2400 mm.   Figure 4.1 Post orientations Face-wise orientation Edge-wise orientation 67  Dynamic modulus of elasticity (MOE) of the composite posts was measured non-destructively according to ASTM D6874-12 using a Metriguard 340 E-Computer. The testing equipment captures the transverse vibration frequency and weight to compute MOE using measured cross-section dimensions and span.  As shown in Figure 4.1, MOE of both post orientations were measured: face-wise and edge-wise. In total, 34 posts were tested. The average MOE values of the edge-wise and face-wise posts were 5.93 GPa and 5.87 GPa. Since the difference was only 1%, the MOE property of the strand-based posts was considered to be 5.9 GPa regardless of its orientation. This value was used as one of the inputs in the shear wall model described in Chapter 6. The summary statistics of the dynamic MOE measurements are provided in Table 4.1.  Table 4.1 Summary statistics of dynamic MOE of strand-based wood composite posts  Face-wise Edge-wise Number of measurements 34 34 Average (GPa) 5.87 5.93 Standard deviation (GPa) 0.31 0.21 Coefficient of variation 0.05 0.04 Minimum (GPa) 5.31 5.55 Maximum (GPa) 6.46 6.40  4.1.2 Frame members Studs, braces, top and bottom plates were kiln dried Canadian Coastal Hem-Fir lumber with Japanese standard dimensions and quality (i.e. Canada Tsuga – E120 S-DRY CFLA1 JPS2 1 Hemfir). The product information of the members is provided in Table 4.2. The conditions of the frame members were surface-dried (i.e. less than 19% moisture content) during assembly and tests.                                                    1 CFLA: The Coast Forest & Lumber Association 2 JPS: Japanese Product Standard 68  Table 4.2 Frame member information Member Dimensions (mm) Mill Number Manufacturer Stud 1 30 x 105 COFI 03 Interfor Stud 2 45 x 105 CMSA 20 Western Forest Products Inc.  Blocking 45 x 105 CMSA 20 Western Forest Products Inc.  Brace  45 x 90 CMSA 077 Interfor Top Plate 105 x105 CMSA 20 Western Forest Products Inc.  Bottom Plate 105 x 105 CMSA 20 Western Forest Products Inc.   4.1.3 Metal fasteners Japanese Industrial Standard (JIS) metal fasteners were used to connect the wall components. The product information of the fasteners is provided in Table 4.3. The metal plates (BP, VP, and CP-T), hold-downs (S-HD20), lag screws (LS12) and bolts (M12) were Z-mark fasteners which are typically used for the framing construction method for wooden residential buildings in Japan.   Table 4.3 Metal member information Fastener Type Dimension (mm) Qty Connected components CN50 Nail Body (B) Ø: 2.87 • Head (H) Ø: 6.76 • Length (L): 50.8 1296 frame members, sheathing panels ZN65 Nail BØ: 3.33 • HØ: 7.14 • L: 63.5 300 CP-T, BP, frame members ZN75 Nail BØ: 3.76 • HØ: 7.92 • L: 76.2 84 frame members ZN90 Nail BØ: 4.11 • HØ: 8.74 • L: 88.9 144 VP, frame members M12 Bolt BØ: 12 • HØ: 22 • L: 65 24 BP, frame members M12 Hex Nut Width Across Flats (WF): 18 24 BP, frame members LS12  Lag Screw WF: 19 • BØ: 12 • L: 110 192 S-HD 20, frame members W2.3x30 Square Washer 30 x 30 x 2.3 (thickness) 24 BP, frame members S-HD20 Hold-down 40 x 446 48 frame members BP  Plate 130 x 160 24 frame members VP  Plate 70 x 115 18 frame members CP-T  Plate 150 x 200 6 frame members 69  4.1.4 Sheathing panel Japanese Agriculture Standard (JAS) grade 9 mm and 11 mm thick OSB sheathing panels supplied by Ainsworth Engineered were used. The dimensions of panels were 910 x 2580 mm and 910 x 1920 mm respectively.   4.2 Wall assembly The shear wall components described in the previous sections were assembled into six wall configurations considering three common reinforcement methods and two post orientations; three specimens were constructed for each configuration. The wall components were machined by FraserWood, an in-kind contributing industry partner, located in Squamish, BC. The company cut mortise-and-tenon joints and holes using a computer numerical control (CNC) machine Hundegger K2. The final dimensions of the assembled shear walls, which composed of two bays, were 2400 mm in height and 1820 mm in length. They were tested within one hour after the assembly.  4.2.1 Double-braced walls Double-braced walls with different post orientations were constructed as shown in Figure 4.2. Two diagonal braces were installed to reinforce the lateral resistance of each wall specimen. ZN65 nails, BP and VP connectors were used to hold the bracing and adjacent frame members together. The studs were toe-nailed to the plate members, while S-HD20 connectors were installed to anchor the posts to the plates. The middle posts and the bottom plates were connected by CP-T connectors. The wall configuration with BP, VP, and CP-T connectors on the face-sides of the posts was denoted as DWALL_FACE, while the configuration with the other post orientation was denoted as DWALL_EDGE. 70     a)               b) Figure 4.2 Double-braced wall configurations: a) DWALL_FACE, b) DWALL_EDGE Back Back CP-T CP-T 71  4.2.2 9mm-OSB-sheathed walls 9mm-OSB-sheathed walls with different post orientations were constructed as shown in Figure 4.3. The 9 mm thick OSB sheathing panels were cut to lengths of 2400 mm. Then, two 910x2400 mm OSB panels were attached to the frame members using CN50 nails with 150mm spacing and 15 mm edge distance. Meanwhile, S-HD20 hold-downs were installed to connect the posts to the plate members. The sheathed wall configuration with the nails driven into the edge-sides of the posts was denoted as 9mm_SWALL_EDGE while the configuration with the panels attached to the face-sides of the posts was denoted as 9mm_SWALL_FACE. Unlike the double-braced configurations, 105 x 45 mm Hem-Fir studs were used as the middle vertical frame members.     a)  b) Figure 4.3 9mm-OSB-sheathed wall configurations: a) 9mm_SWALL_EDGE, b) 9mm_SWALL_FACE 9mm 72  4.2.3 11mm OSB-sheathed walls 11mm-OSB-sheathed walls with two different post orientations were constructed as shown in Figure 4.4. The configurations were denoted based on the post orientations as did in Section 4.2.1 and Section 4.2.2. The sheathing-to-frame and frame-to-frame connections were assembled in the same manner as those of 9mm-OSB-sheathed walls. Due to the smaller dimensions of the 11 mm thick OSB panels, the horizontal blocking members were installed continuously at a height of 1820 mm; they were toe-nailed to the vertical frame members with ZN75 nails. Consequently, four panels were mounted to each wall specimen.    Figure 4.4 11mm-OSB-sheathed wall configurations: a) 11mm_SWALL_EDGE, b) 11mm_SWALL_FACE  4.3 Experimental setup and procedure The assembled shear wall specimens were tested under monotonic and reversed-cyclic loads following ASTM E564-06 and E2126-11. As illustrated in Figure 4.5, the bottom and top plates of each wall specimen were anchored to the test base and loading beam respectively. 73  Racking load was horizontally transferred to the wall specimens by a loading beam connected to the hydraulic actuator. The out-of-plane movements of the wall specimens were restricted by the rollers along the loading beam.  Unlike the light-frame shear walls constructed with 38 x 89 mm top plates which can be subjected to substantial flexural deformations during lateral load tests (Wilcoski 2002; Payeur 2011), as described in Section 4.2, the post-and-beam wall specimens were constructed with 105 x 105 mm top plates which are not likely to experience noticeable bending during the tests. Therefore, the high stiffness of the steel loading beam is anticipated to have an insignificant effect on the test results. Moreover, since the hold-downs are anchored to the rigid test base, the effect of the weight of the loading beam on the overturning and lateral resistance of the wall specimens is expected to be insignificant as well (Ni and Karacabeyli 2001; White et al. 2010).    Figure 4.5 Shear wall test setup Loading beam Actuator Load cell Back view Back view Test base Rigid frame String pot 1 String pot 2 LVDT 3 LVDT 4 LVDT 5 74  Three linear variable displacement transducers (LVDTs) and one string pot transducer were used to directly measure the shear displacements of the wall specimens. The vertical movements of both ends of the bottom plates, and the horizontal movements of the top and bottom plates were monitored and recorded. The diagonal elongations of the specimens were also measured using the string pot transducer to estimate the specimens’ shear displacements; the estimated displacements were used to confirm the accuracy of the direct measurements.   One monotonic and two reversed-cyclic load tests were conducted on each shear wall configuration. For the monotonic load tests, the wall specimens were pushed horizontally at a constant rate of 0.1 mm/sec beyond their peak loads until at least their ultimate loads (i.e. 80% of peak loads) were reached. For the reversed-cyclic load tests, the displacement controlled loading procedure, CUREE Basic Loading Protocol, was implemented at a loading rate of 1.0mm/sec. For each wall configuration, the incremental amplitudes of the reversed-cyclic loading protocol were determined based on the smaller of the two reference displacements (Δ): the maximum reference displacement (i.e. 2.5% of wall height) and the ultimate displacement from the monotonic load test. As presented in the following section, under the monotonic loads, all the wall configurations achieved ultimate displacements larger than the maximum reference displacement of 60 mm. Therefore, the same incremental amplitudes were applied to all the reversed-cyclic wall specimens as shown in Table 4.4.    75  Table 4.4 Reversed-cyclic test loading history (shear wall) Step Cycle Type Num. of Cycle(s)  Amplitude (mm) %  Δ 1 Primary 6 3.0 5 2 Primary 1 4.5 7.5 Trailing 6 3.4 5.6 3 Primary 1 6.0 10 Trailing 6 4.5 7.5 4 Primary 1 12.0 20 Trailing 3 9.0 15 5 Primary 1 18.0 30 Trailing 2 13.5 22.5 6 Primary 1 24.0 40 Trailing 2 18.0 30 7 Primary 1 42.0 70 Trailing 2 31.5 52.5 8 Primary 1 60.0 100 Trailing 2 45.0 75 9 Primary 1 78.0 Additional increments of 30 (until specimen failure) Trailing 2 58.5 Primary amplitude x 0.75   4.4 Results and discussion For both monotonic and reversed-cyclic load tests, the shear displacements (Δshear) of the wall specimens were calculated according to ASTM E564-06 using the measurements described in Figure 4.5. Thus, Δshear was determined taking the relative horizontal and vertical movements of the specimens into account as:    LH4351 LVDTLVDTLVDTStringPortshear   (4.1) where H and L are the height and length of the wall. 76  According to ASTM E2126-11, the load-displacement curves obtained from the monotonic load tests were directly analyzed, while the hysteresis loops obtained from the reversed-cyclic load tests were converted into average envelope curves which were then analyzed. The reversed-cyclic test curves are provided in Appendix D.  Peak load (Ppeak), ultimate load (Pu), peak displacement (∆peak), ultimate displacement (∆u), and ductility ratio parameters were obtained as described in Section 3.4. Initial stiffness (K0) was calculated by connecting 40% of the peak load and origin. Yield load (Pyield), and yield displacement (∆yield) parameters were obtained from an equivalent energy elastic-plastic (EEEP) curve which enclosed the same area as the area under a load-displacement curve until the ultimate displacement. As discussed in Section 3.4, there are various ways to estimate a yield point, which would lead to different ductility ratios. Therefore, the yield-point related parameters were used to compare the wall performances. Instead, the parameters found directly on the curves, such as peak load and displacement parameters, were primarily discussed to describe the performances.   77  4.4.1 Double-braced walls  Figure 4.6 Load-displacement curves (double-brace walls)  Table 4.5 Summary statistics of performance parameters (double-braced walls) Config. Curves Ppeak Pu Δpeak Δ u K0 Pyield Δ yield Ductility Ratio (kN) (kN) (mm) (mm) (kN/mm) (kN) (mm) DWALL_FACE Monotonic 18.93 15.15 59.43 88.75 0.80 16.62 20.68 4.29 Average Envelope 1 13.66 10.93 53.36 119.27 0.68 12.50 18.28 6.52 Average Envelope 2 16.88 13.50 53.87 90.09 0.78 14.95 19.06 4.73 DWALL_EDGE Monotonic 14.55 11.64 88.05 140.57 0.67 13.08 19.60 7.17 Average Envelope 1 15.62 12.50 56.78 100.19 0.84 13.75 16.32 6.14 Average Envelope 2 13.64 10.91 74.30 115.25 0.61 12.11 19.85 5.81  Under the monotonic loads, as presented in Table 4.5, the DWALL_FACE specimen achieved roughly 30% larger load parameters but 35% smaller displacement parameters than the DWALL_EDGE specimen. Throughout the monotonic tests, the right diagonal bracing 78  members remained under compression while the left braces were under tension. The right braces, of both wall configurations, experienced out-of-plane buckling which led to bending failures of the stud members (Figure 4.7); these brittle failures governed the post-peak performance of the diagonally braced wall specimens and also caused the sudden drops in the load-displacement curves (Figure 4.6). Although the ends of the right braces were compressed against the bottom and top plates, no severe compressive damage was found at the contact areas. Meanwhile, the behavior of the ZN65 nails in the BP joints connecting the left tensile bracing member also critically influenced the structural performance of these two wall configurations. In both configurations, these nails experienced withdrawal which initiated tension perpendicular-to-grain failure at either top or bottom plate. However, the nails of the DWALL_EDGE specimen experienced more severe withdrawal than those of the DWALL_FACE specimen as shown in Figure 4.8 and Figure 4.9. Since the failed regions of the plate members lost nail withdrawal resistance, the nails driven into the composite posts determined the pulled out amounts. In agreement with the observations discussed in Chapter 3, the nails driven into the edge-sides of the posts were subjected to more withdrawal than the face-driven nails. Consequently, these lower capacity but ductile responses of the edge-driven nail connections led the DWALL_EDGE specimen to achieve a lower load carrying capacity than the DWALL_FACE specimen under the monotonic loads.              79      a)  b) Figure 4.7 Stud tension failures due to out-of-plane buckling under monotonic loads: a) DWALL_FACE, b) DWALL_EDGE  80      Figure 4.8 Tension perpendicular-to-grain failure with withdrawn nails – DWALL_FACE       Figure 4.9 Tension perpendicular-to-grain failure with withdrawn nails – DWALL_EDGE  Under the reversed-cyclic loads, the differences between the structural performances of the double-brace wall configurations were less evident. The peak loads of the DWALL_FACE specimens were 13.66 kN and 16.88 kN with corresponding displacements of 53.36 mm and 53.87 mm while the DWALL_EDGE specimens achieved peak loads of 15.6 2kN and 13.64 kN with corresponding displacements of 56.78 mm and 74.30 mm. During the reversed-81  cyclic load tests, both left and right bracing members experienced tensile and compressive loads repeatedly. When the bracing members were under tension, BP connections holding the braces failed in nail pull-out which provoked tension perpendicular-to-grain failures in the plate members. As observed during the monotonic load tests, the nails driven into the posts of the DWALL_EDGE specimens experienced larger amounts of nail pull-out compared to those driven into the posts of the DWALL_FACE specimens. Then, when the braces went under compression, these damaged connections applied out-of-plane reaction forces which displaced the ends of the braces out-of-plane. Due to these out-of-plane displacements, the contact areas between the ends of the braces and the frame members were reduced; these reduced contact areas resulted in the load concentrations which stimulated compression perpendicular-to-grain failures on the damaged regions of the horizontal members. As the damage accumulated, the ends of braces eventually lost most of their contact areas with the frame members while the nails of BP connectors completely failed in pull-out or low-cycle fatigue. Both wall configurations experienced the same progress of the tension and compression perpendicular-to-grain failures as shown in Figure 4.10 and Figure 4.11. Consequently, under the reversed-cyclic loads, the post orientation did not have a critical influence on the structural responses of the double-brace wall specimens, which were all governed by the failures of the horizontal frame members.      82   a)  b)  c)  d) Figure 4.10 Progress of tension and compression perpendicular to grain failures on the sill plate of the second DWALL_FACE specimen: a) earlier-stage compression perpendicular-to-grain failure, b) earlier-stage tension perpendicular-to-grain failure, c) later-stage compression perpendicular-to-grain failure, d) later-stage tension perpendicular-to-grain failure 83   a)  b)  c)  d) Figure 4.11 Progress of tension and compression perpendicular to grain failures on the sill plate of the second DWALL_EDGE specimen: a) earlier-stage compression perpendicular-to-grain failure, b) earlier-stage tension perpendicular-to-grain failure, c) later-stage compression perpendicular-to-grain failure, d) later-stage tension perpendicular-to-grain failure   84  4.4.2 9mm OSB-sheathed walls  Figure 4.12 Load-displacement curves (9mm OSB-sheathed Walls)  Table 4.6 Summary statistics of performance parameters (9mm OSB-sheathed Walls) Config. Curves Ppeak Pu Δpeak Δ u K0 Pyield Δ yield Ductility Ratio (kN) (kN) (mm) (mm) (kN/mm) (kN) (mm) 9mm_ Monotonic 19.87 15.90 62.53 86.53 2.11 17.56 8.31 10.41 SWALL_ Average Envelope 1 18.83 15.07 35.88 52.51 3.33 16.59 4.97 10.55 FACE Average Envelope 2 17.75 14.20 40.54 57.51 11.10 15.28 1.38 41.81 9mm_ SWALL_ EDGE Monotonic 16.71 13.37 53.04 91.49 2.70 14.84 5.49 16.66 Average Envelope 1 15.64 12.52 37.33 65.42 3.69 13.98 3.79 17.26 Average Envelope 2 16.96 13.57 38.59 63.09 4.68 15.28 3.27 19.31  Under the monotonic loads, as presented in Table 4.6, the 9mm_SWALL_FACE specimen achieved roughly 18% higher load and peak displacement parameters but 5% smaller ultimate displacement parameter than the 9mm_SWALL_EDGE specimen. Throughout the 85  monotonic tests, the nail connections, of both configurations, holding the sheathing panels and solid-wood frame members together were either partially or completely pulled through the panels. Also, some of the panels’ corners were chipped off by the nail tear-out. In contrast, the nail connections on the post members failed in different modes. The nails driven into the posts of the 9mm_SWALL_EDGE specimen, which were embedded to the low-density regions of the posts, failed in pull-out whereas the nails driven into the posts of the 9mm_SWALL_FACE failed in partial or complete pull-through (Figure 4.13).              a) b) Figure 4.13 Nail connection failures at the composite posts: a) pull-out (9mm_SWALL_ EDGE, monotonic), b) pull-through (9mm_SWALL_FACE, monotonic)  Under the reversed-cyclic loads, the 9mm_SWALL_FACE specimens still achieved larger load carrying capacities than the 9mm_SWALL_EDGE specimens; the differences ranged from 5% to 20%. The wall specimens reached their peak loads at the displacements close to 86  each other, which ranged from 36 mm to 41 mm. Consequently, the performance differences between the wall configurations were not evident. Compared with the monotonic test results, both configurations had smaller load parameters. However, they had larger initial stiffness due to the increase in loading rate from 0.1 mm/sec to 1 mm/sec. Similar to the monotonic test results, the nails attaching the panels to the solid timber frame members were failed in pull-through (Figure 4.14). Also, as shown in Figure 4.15 and Figure 4.16, most corners of the panels were chipped off and some edges were torn by the nails. The dominating failure mode of the nail connections on the posts of the 9mm_SWALL_EDGE specimens was pull-out; few failed in pull-through (Figure 4.17a). Meanwhile, the nail connections on the posts of the 9mm_SWALL_FACE specimens nearly all failed in pull-though; few low-cycle-fatigue failures were observed (Figure 4.17b).      a)  c)   b) Figure 4.14 Nail pull-through failures at the frame members: a) bottom plate (9mm_ SWALL_ EDGE, reversed-cyclic test #1), b) bottom plate (9mm_SWALL_FACE, reversed-cyclic test #2),       c) middle stud (9mm_SWALL_ACE, reversed-cyclic test trial #1)  87    a)  b)  c) Figure 4.15 Corner chip-out failures: a) bottom plate (9mm_SWALL_EDGE, reversed-cyclic test #1), b) top plate (9mm_SWALL_ EDGE, reversed-cyclic test #2), c) top plate (9mm_ SWALL_FACE, reversed-cyclic test #2)        a)  b)   c) Figure 4.16 Edge tear-out failures: a) top plate (9mm_SWALL_EDGE, reversed-cyclic test #1),      b) bottom plate (9mm_SWALL_FACE, reversed-cyclic test #1), c) top plate (9mm_SWALL_FACE, reversed-cyclic test #2)  88    a)  b) Figure 4.17 Major nail connection failures at the composite posts: a) pull-out (9mm_ SWALL_EDGE, reversed-cyclic test #1), b) pull-through (9mm_SWALL_FACE, reversed-cyclic test #2)  The responses of the sheathing-to-post connections of the 9mm-OSB-sheathed walls agreed well with the observations reported in Chapter 3, although the panel thickness of the connections was 9 mm instead of 11 mm. Since the nail connections on the composite posts Low-cycle-fatigue Pull-through 89  of the 9mm_SWALL_FACE and 9mm_SWALL_EDGE specimens were loaded closer to parallel than perpendicular to the strand orientation, they could be considered as the C2 (face-driven) and C4 (edge-driven) configurations described in Section 3.2.1. As shown in Table 3.8 and Table 3.9, the differences between the performance parameters of the face-driven and edge-driven connections were significant under both loading types; however, the differences observed from the reversed-cyclic test results were much smaller. Accordingly, the effect of the post orientation on the performance of the 9mm-OSB-sheathed walls was more evident under the monotonic loads than the reversed-cyclic loads.  4.4.3 11mm OSB-sheathed walls  Figure 4.18 Load-displacement curves (11mm OSB-sheathed Walls) 90  Table 4.7 Summary statistics of performance parameters (11mm OSB-sheathed Walls) Config. Curves Ppeak Pu Δpeak Δ u K0 Pyield Δ yield Ductility Ratio (kN) (kN) (mm) (mm) (kN/mm) (kN) (mm) 11mm_ Monotonic 20.02 16.01 75.80 102.83 1.55 17.79 11.45 8.98 SWALL_ Average Envelope 1 19.44 15.55 55.11 78.87 2.24 16.91 7.54 10.45 FACE Average Envelope 2 19.63 15.70 54.82 77.21 2.88 17.18 5.96 12.96 11mm_ SWALL_ EDGE Monotonic 18.00 14.40 82.35 109.53 1.75 16.12 9.20 11.90 Average Envelope 1 16.35 13.08 56.16 76.61 2.57 14.18 5.51 13.91 Average Envelope 2 16.37 13.09 55.91 78.49 2.65 14.29 5.39 14.56  In agreement with the double-braced and 9mm-OSB-sheathed walls, under the monotonic loads, the 11mm_SWALL_FACE specimen reached a larger load carrying capacity but lower ductility than the 11mm_SWALL_EDGE specimen. Aside the yield displacement and ductility ratio, the performance parameters of the two wall configurations were different by less than 11% (Table 4.7). These differences were much smaller than those observed from the monotonic tests of the 9mm-OSB-sheathed specimens. These reduced differences could be explained by the increased number of the nails driven into the Hem-Fir frame members since the Hem-fir blocking members were installed. Compared with the 9mm-OSB-sheathed specimens, each 11mm-OSB-sheathed specimen had 22 more nails driven into Hem-Fir frame members as shown in Table 4.8. Therefore, the nails embedded to the composite posts of the 11mm-OSB-sheathed specimens had less contribution to the wall performance than those of the 9mm-OSB-sheathed specimens.   Table 4.8 Number of sheathing-to-frame (nail) connections per wall specimen Frame members 9mm-OSB-sheathed  11mm-OSB-sheathed  Post (Strand-based composite) 30 32 Middle stud (Hem-Fir) 30 32 Top and bottom plates (Hem-Fir) 28 28 Blockings (Hem-Fir) - 20  91  As observed in the monotonic tests of the 9mm-OSB-sheathed walls, the nails driven into the solid wood frame members failed in pull-through, edge-tear out, and corner chip-out, while the nails embedded to the posts of the 11mm_SWALL_FACE and 11mm_SWALL_EDGE specimens failed mostly in pull-through and pull-out respectively. Some of the pull-out failures were accompanied by tearing of the panel edges. Another notable observation was that the corners of the panels at the intersecting points crushed into each other due to the different rotations of the upper and lower panels which were determined by the panel geometries and nail connection properties (Figure 4.19); the crushing was more severe for the 11mm_SWALL_FACE specimen (Figure 4.20). These rotations of the panels will be further discussed later in this section.  Figure 4.19 A schematic of crushing of panel corners due to different rotations of panels   92      a) b)  c)  Figure 4.20 Crushing of panel corners: a) 11mm_SWALL_ EDGE, monotonic, b) and c) 11mm_ SWALL_FACE, monotonic  Under the reversed-cyclic loads, the 11mm_SWALL_FACE specimens achieved roughly 20% larger load parameters than the 11mm_SWALL_EDGE specimens, while their displacement parameters, except for yield displacement, differed by less than 3% (Table 4.7). Compared to the monotonic test results, these parameters were smaller, but the initial stiffness was higher due to the faster loading rate. Also, the nail connections of the wall specimens failed similarly as observed in the monotonic tests, except that some nails driven into the posts of 11mm_SWALL_FACE specimens failed in low-cycle-fatigue.  For these walls, the effect of the post orientation on the wall performance was more evident under the reversed-cyclic loading condition; the 11mm_SWALL_FACE specimens 93  noticeably outperformed the 11mm_SWALL_EDGE specimens. These performance differences were the results of the different rotational centres of the panels. As illustrated in Figure 4.21, the panels of each 11mm_SWALL_EDGE specimen rotated at the points closer to the middle stud instead of their geometric centres due to the relatively weak nail connections on the composite posts; the rotational centers of the panels in the figure were estimated based on the observations during the tests. Accordingly, the nails connecting the lower panels to the composite posts deformed much more than those driven into the middle stud; the former nails failed completely in pull-out while the latter nails were still holding the wall components together (Figure 4.22b). Once the sheathing-to-post connections of the lower panels failed, the loads applied to the wall specimens were mostly resisted by the nail connections of the upper panels. Whereas, the rotational points of the panels were almost the same as their geometric centres for the 11mm_SWALL_FACE specimens as described in Figure 4.23. The corresponding nail connections of middle stud and composite posts deformed similar amounts and failed in pull-through (Figure 4.24b).     a)  b)  c) Figure 4.21 Rotations of panels of 11mm_SWALL_EDGE specimens: a) before the test, b) later-stage, c) final-stage centre of rotation 94         a)  b) Figure 4.22 Final stage of an 11mm_SWALL_EDGE specimen (reversed-cyclic test #1):     a) front-view, b) side-view    a)  b)  c) Figure 4.23 Rotations of panels of 11mm_SWALL_FACE specimens: a) before the test, b) later-stage, c) final-stage  center of rotation 95       a)  b) Figure 4.24 Final stage of an 11mm_SWALL_FACE specimen (reversed-cyclic test #1):     a) front-view, b) side-view  Regardless of the composite post orientations, in general, the 11mm-OSB-sheathed specimens achieved larger load and displacement parameters but lower initial stiffness than the 9mm-OSB-sheathed specimens under both loading conditions. The differences between the load parameters were about 5% although each 11mm-OSB-sheathed specimens had 24 nail connections more and 22% thicker panels. The higher initial stiffness but smaller displacement parameters of the 9mm-OSB-sheathed specimens were due to the use of two panels rather than four panels with blockings. These observations agreed with the findings by Lam et al. (1997) which reported that the shear walls covered with one oversize sheathing panel had higher loading capacities and initial stiffness but smaller displacement performance parameters than those each covered with several regular size sheathing panels under 96  monotonic and reversed-cyclic loads. Consequently, the thicker panels of the 11mm-OSB-sheathed specimens compensated the loss of load carrying capacity due to the increased number of the panels with smaller sizes; however, the increased panel thickness did not improve the initial stiffness.   4.5 Summary An experimental study was conducted on the structural responses of the double-braced and OSB-sheathed post-and-beam shear walls under the monotonic and reversed cyclic loads. The height and length of the shear wall specimens were 2400 mm and 1820 mm. The frame members of the wall specimens were E120 grade Canadian Hem-fir timber products, except the wall posts which were the four-layered strand-based wood composites.   Prior to the shear wall tests, face-wise and edge-wise dynamic MOEs of the composite posts were measured non-destructively. It was found that the post orientation did not have significant effect on the MOE since the average MOE values of two orientations were only different by 1% with coefficient of variation less than 0.05.    For the double-braced wall specimens, under the monotonic loads, the behaviour of the BP connections on the left bracing members subjected to tension had a significant influence on the load-deformation responses of the walls. The critical failure mode that caused the 20% drops from the peak loads was the brittle bending failure of the stud members due to the buckling of the bracing members under compression. The BP connections of the DWALL_FACE specimen were more rigid than those of the DWALL_EDGE specimen which had significant nail withdrawals. Therefore, the DWALL_FACE specimen had a 97  higher peak load but a lower ductility ratio compared with the DWALL_EDGE specimen. Under the reversed-cyclic loads, the structural responses of the double-braced walls were determined by tension and compression perpendicular-to-grain failures of the horizontal frame members. Due to these failures, the BP connections of both configurations lost rigidity and load carrying capacities. Consequently, the influence of the post orientation on the structural performance of the walls was less evident under the reversed cyclic loads.  For the 9mm-OSB-sheathed wall specimens, under both loading conditions, the 9mm_SWALL_FACE specimens had higher peak loads but smaller ultimate deformations compared to the 9mm_SWALL_EDGE specimens. These differences were determined by the behaviour of the nails connecting the OSB sheathing panels to the composite posts. The nails driven into the posts of the 9mm_SWALL_EDGE specimens were mostly pulled out, while those driven into the posts of the 9mm_SWALL_FACE specimens were mostly pulled through. The effect of the post orientation on the performance of the 9mm-OSB-sheathed walls was more evident under the monotonic loads than the reversed-cyclic loads.  Similar to the test results of the 9mm-OSB-sheathed walls, the 11mm_SWALL_FACE specimens also outperformed the 11mm_SWALL_EDGE specimens under both loading conditions. The former specimens achieved higher load parameters than the latter specimens, but the corresponding displacement parameters were similar. Due to the increased ratio of the nails driven into the solid wood frame members to those driven into the composite posts, the effect of the composite post orientation on the wall performance was not prominent under the monotonic loads. In contrast, under the reversed-cyclic loads, the nails connecting the lower panels to the composite posts of the 11mm_SWALL_EDGE specimens governed the wall 98  performance, which failed completely in pull-out while the nail connections on the middle studs had minor deformations. These nail connection failures caused the 11mm_SWALL_EDGE specimens to have 20% smaller lateral resistances than the 11mm_SWALL_FACE specimens. 99   Nail Connection Model Chapter 5HYST model developed by Foschi (2000) in FORTRAN 77 language has been revised specifically to simulate the behaviour of single-shear nail connections under lateral loads. The original model has been rewritten in FORTRAN 90 language to understand the modelling approach and the components. Then, two modifications have been made on HYST considering the vertical displacements of the nail in determining the embedment responses of the wood medium. The revised models are called RHYST1 and RHYST2. These models have been verified against the original model and validated against the nail connection test results presented in Chapter 3.  5.1 HYST The finite element program HYST is originally based on an approach for modelling the responses of pile foundations in geotechnical engineering. When applied to wood, a dowel-type timber connection is idealized as an elasto-plastic beam surrounded by a nonlinear wood medium which only acts in compression. Considering the material properties and kinematics of these two elements, the nonlinear structural response of the connection under an applied load is formulated by applying the principle of virtual work. Then, the Newton-Raphson iterative procedure is implemented to solve the nonlinear problem.   5.1.1 Model components 5.1.1.1 Dowel-type fastener The dowel-type fastener is modelled as an elasto-plastic beam which can be divided into up to 50 beam elements. The cross-section of the beam can be rectangular, circular or annular. Each beam element has two nodes which can displace and rotate in the x-y plane (Figure 100  5.1). To idealize the large deflection of the fastener, the beam element is modelled based on Euler-Bernoulli theory incorporating von Karman strains which account for the contribution of the slope of the deflected beam to the axial strains. The strains are still assumed to be not affected by shear deformation while the cross-section of the beam remains perpendicular to its primary axis. Thus, the strain at a distance y from the beam axis is expressed as Eq. 5.1 which is composed of three terms: axial strain, bending strain, and strain due to the large slope of the deflected beam.  22221xwxwyxu   (5.1)   Figure 5.1 Deformations of two beam elements with three nodes  As described in Figure 5.1, five degrees of freedom (DOF) are assigned to each node to describe its deformation: transverse displacement (w), rotation (∂w/∂x), curvature (∂2w/∂x2), axial displacement (u), and axial strain (∂u/∂x). Also, Gauss integration points are assigned 101  along the element length in the x-direction and over the cross-section in the y-direction to approximate the integrals which will be introduced in Section 5.1.2.  The stress-strain hysteresis of the beam element is assumed to follow an elasto-plastic constitutive relationship which is applicable to metal fasteners such as nails, dowels or screws. As shown in Figure 5.2, normal stress (σ(ε)) changes linearly with normal strain (ε) at modulus of elasticity (E) until it reaches either positive or negative limits determined by yield strength (σy), E, and coefficient α. Then, the stress changes at a slope of αE until the direction of the strain changes. Since α is nearly zero, the positive and negative y-intercepts are considered to be +σy and -σy. Accordingly, the stress corresponding to a strain ε is calculated following the algorithm Eq.5.2.   Figure 5.2 Beam element hysteresis       0)(max0)(min0)(  00000000ifEEifEEifyy (5.2) where σ0 and ε0 are, respectively, stress and strain from the previous step. 102  5.1.1.2 Wood foundation The wood confining the dowel-type fastener is modelled as a nonlinear medium which only responds to the compressive forces applied by the deformed fastener. This nonlinear response (p) is expressed in force per unit length, which is assumed to be a function of a transverse displacement (w) at an integration point along the fastener length. The relationship between the embedment response and the displacement is defined by six parameters described in Table 5.1, which are formulated into a set of equations, Eq. 5.3, and illustrated in Figure 5.3.  Table 5.1 Descriptions of embedment property parameters Parameter Description K Initial stiffness Q0 Intercept of the asymptote at the maximum compressive response Q1 Slope of the asymptote a the maximum compressive response Q2, Q3  Post-peak decay factors  Dmax Displacement at the maximum compressive response          max2max4maxmax010   exp  /exp1  DwifDwQpDwifQKwwQQwp  (5.3) where the maximum compressive response and the decaying factor Q4 are calculated as:     0maxmax10max /exp1 QKDDQQp   (5.4)     23max24 0.1 / ln  QDQQ  (5.5)  103    Figure 5.3 Embedment response–displacement relationship         Figure 5.4 An example of cyclic displacement history  Let us assume that a dowel-type fastener is embedded in the wood medium which has the embedment response-displacement relationship of Figure 5.3. Also, a specific point along the fastener is subjected to the cyclic displacement history given in Figure 5.4. When the point transversely displaces by an amount of x1, the wood medium also gets compressed by the same amount. The corresponding response at x1, which is denoted as p(x1) in Figure 5.3, is obtained following the loading path of the embedment curve. Then, as the point reversely moves to a transverse displacement of x2, the compressed wood medium gets unloaded following the dashed line of the embedment response curve, which has a slope of initial 104  stiffness K. Once the wood medium gets fully recovered, its embedment response becomes zero and establishes a permanent deformation or residual gap D. Accordingly, the embedment response at x2, p(x2), becomes zero. When the loading direction changes again and the point transversely displaces to x3, the wood medium gets reloaded starting D until it reaches x3. The embedment response at x3, p(x3), is obtained following the dashed line and a part of the embedment curve. Consequently, the response of the wood medium under unloading and reloading is calculated based on the permanent deformation D.   Under reversed-cyclic loads, the residual gaps D at different points along the fastener length against the wood medium can be either positive or negative depending on the loading direction. Therefore, two residual gap amounts are assigned to each integration point in the x- or lengthwise direction of the fastener element. Figure 5.5 illustrates the positive and negative residual gaps associated with the point j on the nail.   Figure 5.5 Positive and negative residual gaps associated with a point on a nail 105  The algorithms for determining the embedment response in terms of p(w), dp/dw, and D are expressed in Eq. 5.6. In the algorithms, D represents the residual gap at the current loading step while D0 represents the residual gap at the previous step.                       KwpwDDwifPwpifKPwpifDwQPdwdpDwKPDwQpPwpKwpwDDwDifPwpifKPwpifQwQQKQdwdpDwKPwQQPwpDDDwifKdwdpwpDDDwifdwdpwpQKwQKwQKw/)(            2 /)(  exp min/)(    e)(e1 /)( e1   min      /0       0/0max21max41022max4max1max0210/10/102/1010000000 (5.6)  5.1.2 Problem formulation and solution The interaction between the dowel-type fastener and the wood medium under applied loads is formulated applying the principle of virtual work. As expressed in Eq. 5.7, the total external work due to the applied axial and lateral forces, P and F, and virtual displacements at the location of the applied forces is equal to the total work done by the fastener and the wood 106  medium over the fastener’s length (L).  The internal work of the fastener is determined by the virtual strain (δε) over its cross-section while the external work of the wood is determined by the virtual displacement (δw).       LxLxVLwuPdxwwwwpdv     F       0 (5.7)  The DOFs of the nodes i and i+1 of the fastener element illustrated in Figure 5.1 are expressed as Eq. 5.8.    ',,'',',,',,'',', 11111  iiiiiiiiiiT uuwwwuuwwwa  (5.8)  The displacements and their derivatives of the Gauss integration points along the elements are approximated using high-order shape functions; C1 continuity interpolation functions are used for u(x) and uʹ(x), while C2 interpolation functions are used for w(x), wʹ(x), and wʹʹ(x). They are written as: aNxuaNxuaMxwaMxwaMxw TTTTT 10210 )(',)(,)('',)(',)(   (5.9)  Then, the equation 5.7 can be rewritten as:       FM NM MM M MMMN )(0)(00T0T00T0T1121 LxLxVLPdxaaapdvay     (5.10) To solve for the global displacement vector, a, Newton-Raphson iteration procedures are implemented as:      - *-1**  aa  (5.11)  107  where ψ is the out-of-balance vector expressed as:       FMNM MM M MMMN )(0)(00T0T00T0T1121 LxLxVLPdxaaapdvay      (5.12)  and [∇ψ] is the corresponding tangential stiffness matrix obtained as:    a  (5.13)        MM MMMMMNMMMN0T00T11T1121T1121   LVVTdwdpayaydd  As stated in Eq. 5.11, the vector a is updated based on the information from the previous iteration: a*, ψ*, and [∇ψ*]. The iteration procedures are performed until the solution satisfies the displacement and force convergence criteria, Eq. 5.14, which are expressed in Euclidean norms at the ith iteration.    forcentdisplacemeiiiTolTolaaa  1  (5.14)  5.1.3 Model inputs and logic As discussed in Section 5.1.1, the mechanical and geometrical properties of a fastener and the embedment properties are the main inputs of the HYST model. In contrast to the fastener information which can be obtained either from its manufacturer or available literature, the embedment parameters of the wood are calibrated against either a monotonic test curve or the average envelope curve of a reversed-cyclic test. The calibration is simply a nonlinear minimization of the error between the test curve and the load-displacement curve generated by the model, based on the principle of least square fitting. The embedment parameters can 108  be also obtained from direct experimentation such as the full-hole dowel-bearing strength test described in ASTM D5764-97a. However, such approach is not recommended since it is difficult to avoid bending of the fastener. Another important model input is the number of wood layers which are allowed up to 10. If the fastener is driven into more than one wood member, at least one wood member is subjected to relative displacements as illustrated in Figure 5.6. Other model inputs are boundary conditions and total number of finite elements for the fastener. Once the inputs described above are obtained or determined, HYST can simulate the response of the connection to any imposed displacement history. A flow chart is provided in Figure 5.7 which explains the calculation process in the HYST model.       a)  b) Figure 5.6 Nail head displacement: a) specified, b) relative w w Δlayer2 Δrelative= w – Δlayer2 Layer 2 Layer 1 109   Figure 5.7 HYST model flow chart   5.1.4 Limitations Foschi (2000) stated that HYST “is intended to apply to sufficiently long members in problems where lateral deformations dominate” since the model only considers the responses of the wood medium in perpendicular to the fastener’s original primary axis. The model needs to be extended when the vertical responses of the wood medium are large enough to cause withdrawal of the fastener, which is also known as a rope effect. Another limitation is that it does not account for the friction between the fastener and wood. Allotey (1999) extended HYST model by incorporating the friction forces along the fastener based on the confining pressure of the wood medium, which is obtained from the wood embedment response curve. The model assumes that the pressure is applied normal to the initial axial axis 110  of the fastener at any lateral deformation. However, this assumption becomes invalid when the fastener is subjected to extremely large displacements and some parts of the fastener deform close to parallel to the loading direction.   In HYST, the wood embedment responses are determined by the corresponding transverse or lateral displacements of the nodes of the fastener elements. For instance, as shown in Figure 5.8, when node i of a fastener element displaces from the point A' (5, 29) to A" (10, 27), the embedment’s lateral response at A' gets updated according to the y coordinate of A". However, this assumption ignores not only the vertical reaction of the wood medium but the changes in its vertical coordinates. In Eq.5.8, the compressive forces of the wood medium are calculated based on the fastener length not the vertical length of the wood that is in contact with the fastener. Consequently, in Figure 5.8, integration of the compressive forces on the deformed fastener element at positions A" and B" is performed over the initial length of the element, 10, not 8.5 which is the vertical length of the wood medium.    Figure 5.8 A simplified example of deformation of a fastener element  111  5.2 RHYST HYST has been modified in two steps to simulate the behaviour of a nail connection more realistically. First, changes in wood medium’s vertical length corresponding to a deformed fastener have been considered. Then, the coordinate systems of the wood medium and fastener have been separated to allow the response of the wood medium, including residual gap information, to be updated based on both lateral and vertical displacements at the integration points along the fastener. HYST with the first revision is denoted as RHYST1 and the model with both revisions is denoted as RHYST2. Simply, the revised versions have taken the effect of changes in vertical coordinates of the nail on the compressive response of the wood medium.    5.2.1 RHYST1 The compressive forces of the wood medium on the nail are calculated based on the vertical coordinates of the nail which continuously change under loading. For instance, given Figure 5.8, the total compressive force on the fastener element A" and B" is calculated by the integration over the projected vertical length of the fastener to the wood medium, which is 8.5. Since HYST is constructed to capture the deformed nail shapes, the vertical length of the wood embedment, WL, can be easily calculated as a summation of the vertical distances between two nodes of each deformed element:     1111Nnnnnnnnnnn uxuxWL  (5.15)  where, N, nn, and x are the number of nodes, node number, and node’s x-coordinate respectively. Accordingly, Eq.5.7 has changed to: 112      LxLxVWLwuPdxwwwwpdv     F       (5.16) In the revised model, the shape functions (WM0) corresponding to the changed integration length of the compressive forces have been added, which changed Eq.5.10, Eq.5.12, and Eq.5.13 to:       FM N WMMM M MMMN )(0)(00T0T0T0T1121 LxLxVWLPdxaaapdvay     (5.17)       FMN WMMM M MMMN )(0)(00T0T0T0T1121 LxLxVWLPdxaaapdvay      (5.18)    a  (5.19)        WMWM MMMMMNMMMN T00T11T1121T1121   WLVVTdwdpayaydd With this simple revision, the six-parameter embedment-response curve described in Section 5.1.1.2 can be replaced with a three-parameter curve as shown in Figure 5.9. The three parameters are K, Q0, and Q1, which have the same meanings as those of the six-parameter curve described in Table 5.1. Also, the algorithms for the loading, unloading, and reloading paths, which are illustrated in Figure 5.9 and expressed in Eq.5.20, are the same except that the three-parameter curve does not have a loading function for the descending branch of the six-parameter curve. The assumption behind this modification is that the response of the wood medium should not decrease at any compressive displacement but either remains the same or even increase since the crushed wood medium will cause densification rather than splitting accompanied with microscopic buckling and shearing between wood cells (Oudjene & Khelifa, 2009).  113   Figure 5.9 Three-parameter embedment response–displacement relationship              KwpwDDwifPwpifKPwpifQwQQKQdwdpDwKPwQQPwpDDDwifKdwdpwpDDDwifdwdpwpQKwQKwQKw/)(      e)(e1 /)( e1   min      /0       0/00210/10/102/1010000000 (5.20)  In RHYST1, regardless of the embedment response curve which can either be six-parameter or three-parameter, the decrease in lateral resistance of a nail connection after it reaches the peak load results from the changes in the vertical projected length of the fastener to the wood medium. Meanwhile, the revised model does not allow the fastener nodes to override each other at large deformations. When the nodes override each other, the executed model terminates since the wood medium’s vertical length becomes negative.  114  RHYST1 has been verified against the results of the single-nail example presented in Foschi (2000). First, HYST has been executed for a monotonic lateral displacement of 12mm with the input parameters listed in Table 5.2. Then, the revised model has been calibrated to the monotonic simulation results with the same nail input information; the obtained embedment response parameters are provided in Table 5.3. In both models, a nail with 20 equal elements has been subjected to lateral displacements at the nail head which is node 21. The displacement and force convergence criteria have been set to 10-3, and the axial displacement of the nail tip, which is node 1, has been set to zero. 5 Gauss integration points have been assigned along the length of a fastener element, which each has 16 integration points over its cross-section in the y-direction. The deformed nail shapes at displacements of 0mm, 4mm, 8mm, and 12mm obtained from HYST and RHYST1 are illustrated in Figure 5.10a and Figure 5.10b respectively. The nail shape deforms unrealistically as the lateral displacement gets larger in HYST. Again, this phenomenon is due to calculating the compressive forces of the wood medium based on the nail length not the vertical length of the wood. Then, RHYST1 has been verified against the HYST simulation results for a reversed-cyclic loading case which has four cycles with amplitudes of +6mm, +4mm, ±4mm, and ±4mm.  The simulation results are shown in Figure 5.11.   Table 5.2 HYST input parameters (Foschi 2000) Nail properties  Embedment response curve parameters E (MPa) σ yield (MPa) L (mm) dia. (mm) a  K (kN/mm2) Q0 (kN/mm) Q1 (kN/mm2) Q2 Q3 Dmax (mm) 200,000 250 63.5 3.5 0.001  0.15 0.25 0.001  0.5 1.2 5  Table 5.3 RHYST1 embedment response curve parameters K (kN/mm2) Q0 (kN/mm) Q1 (kN/mm2) 0.137 0.201 0.002   115             a)  b) Figure 5.10 Deformed nail shapes under monotonic loads at displacements of 0mm, 4mm, 8mm, and 12mm obtained from a) HYST and b) RHYST1   Figure 5.11 Simulation results of HYST and RHYST1 for a cyclic loading case 116  5.2.2 RHYST2 On the basis of RHYST1, further revision has been made to separate the coordinate systems of the wood medium and nail from each other. This change allows RHYST2 to assign the residual gaps, D, at different points along the nail length to the wood medium. However, in HYST, the residual gaps are retained by the nail.   An example of a nail element subjected to reversal loading is presented in Figure 5.12a and Figure 5.12b. These figures illustrate the difference between HYST and RHYST2 in terms of processing the residual gap information. As the nail element, with two nodes and three integration points, gets loaded to position AB, it compresses the wood medium to its right and establishes a gap to its left. Then, the element displaces in the negative y and positive x directions to position A'B'. As expressed in the algorithms Eq.5.6 and Eq.5.20, HYST and RHYST2 assume that the compressed wood medium recovers elastically at a slope of the initial stiffness of its embedment response curve and leaves a residual gap to its left. As shown in Figure 5.12a, in RHYST2, the residual gap information recorded in the wood medium coordinate system does not change its vertical coordinates upon the reversal loading; the two dashed horizontal lines are provided in the figure to indicate the vertical coordinates of the element’s nodes at AB. However, in HYST, the residual gap information, which is stored with respect to the nail element coordinate system, translate according to the vertical coordinates of the nail at A'B' as shown in Figure 5.12b. Therefore, the model does not account for the vertical displacements of the nail element in processing the residual gap information. Consequently, RHYST2 processes the residual gap information more realistically than HYST.   117   a)   b)  Figure 5.12 Processing of residual gap information for an unloading example in a) RHYST2 and b) HYST    Another example of a nail subjected to reversal loading is provided in Figure 5.13. This example is provided to examine the effect of different procedures in processing the residual gap information, of RHSYT2 and HYST, in relation to the embedment responses of the wood medium against the nail in details. The nail element has two nodes (i.e. i and j) and seven integration points along its length. As the nail element gets loaded in the direction of the positive loading cycle (i.e. the positive y direction) and displaced to position AB, it leaves the gap behind its moving path while it compresses the wood medium in the loading direction. In the figure, the shape of the nail element at position AB is indicated with a dashed line. At this position, the transverse displacements of the integration points are denoted as wξ1, wξ2, wξ3, wξ4, wξ5, wξ6, and wξ7. Once the nail element displaces and deforms to position A'B', the X Y X Y X Y X Y 118  compressed wood medium recovers at the initial stiffness of its embedment curve and creates an elastic recovery region. The element shape at position A'B' is indicated with a solid line and the recovered region is shaded in light grey in the figure. Upon the reversal movement of the element, the first three integration points (i.e. ξ1', ξ2', and ξ3') settle within the residual gap region, while the other four integration points (i.e. ξ4', ξ5', ξ6', and ξ7') move to the elastic recovery region. The points in this region are still in contact with the wood medium; their transverse displacements are denoted as wξ1', wξ2', wξ3', wξ4', wξ5', wξ6', and wξ7'. Realistically, when the nail at AB deforms to A'B', the nodes i' and j' would both displace to higher x coordinates than the nodes i and j respectively. However, the nail at A'B' is assumed to deform as shown in the figure to explore more possible reversal loading cases.   Figure 5.13 A nail element with two nodes and seven integration points subjected to unloading X Y 119  The changes in the embedment responses on the integrations points ξ2, ξ3, ξ4, ξ5, and ξ6 are analyzed separately. In the analysis, the transverse displacements (w) of the integration points are limited to Dmax of the six-parameter embedment curve used in HYST. Also, the three-parameter embedment curve used in RHYST2 is assumed to have the same ascending branch as that of HYST. Thus, the embedment curves used in the two models are assumed to be the same in this example.   Integration point ξ2 As illustrated in Figure 5.14a and Figure 5.14b, as the nail element deforms to position AB, the second integration point ξ2 of the element transversely displaces to wξ2. In both HYST and RHYST2, the embedment response on ξ2 is obtained following the loading path of the embedment response curve as shown in Figure 5.14c and Figure 5.14d, which is denoted as p(wξ2). Upon the reversal loading, the point moves negatively and positively in y and x directions to ξ2', and its compressed wood medium gets laterally recovered until it reaches the residual gap Dξ2. In HYST, Dξ2 is considered as the residual gap associated with the previous point ξ2', which is denoted as D0ξ2' in Figure 5.14a. Thus, the embedment response on ξ2' is obtained following the unloading path which starts from p(wξ2) and passes through D0ξ2' as shown in Figure 5.14e, which is denoted as p(wξ2'). Meanwhile, RHYST2 linearly interpolates D0ξ2' based on the vertical coordinate of ξ2', which sits between the residual gaps established at the points ξ1 and ξ2 (Dξ1 and Dξ2) as: D0ξ2' =  2221212  - ' -  -     xxxxDDD   (5.21) The transverse displacement corresponds to D0ξ2' is denoted as wξ2* in Figure 5.14b, which has the vertical coordinate of the point ξ2'. Accordingly, as shown in Figure 5.14f, p(wξ2') is 120  obtained following the unloading path that starts from p(wξ2*) and passes through D0ξ2'. Although RHSYT2 calculates p(wξ2') based on a greater D0ξ2' than HYST, both models will predict p(wξ2') to be zero, since wξ2' is smaller than their D0ξ2' values.    a)  b)  c)     d)     e)      f) Figure 5.14 Transverse displacements and residual gaps associated with the second integration points ξ2 and ξ2' in a) HYST and b) RHYST2; embedment response at wξ2 in c) HYST and d) RHYST2; embedment response at wξ2' in e) HYST and f) RHYST2  X Y X Y 121  Integration point ξ3 As shown in Figure 5.15a and Figure 5.15b, during the initial loading, the third integration point ξ3 travels through the wood medium for a transverse displacement of wξ3. Similar to ξ2, upon the reversal loading, ξ3 becomes ξ3' and displaces into the residual gap region where the point is no longer in contact with the wood medium; the transverse displacement of ξ3' is denoted as wξ3' in the figures.   a)   b)  c)     d)          e)          f) Figure 5.15 Transverse displacements and residual gaps associated with the third integration points ξ3 and ξ3' in a) HYST and b) RHYST2; embedment response at wξ3 in c) HYST and d) RHYST2; embedment response at wξ3' in e) HYST and f) RHYST2 X Y X Y 122  At wξ3, the same wood embedment response is obtained by the two models following the loading path of the embedment curve as shown in Figure 5.15c and Figure 5.15d. The response is denoted as p(wξ3). Upon the reversal movement of the point, as shown in Figure 5.15a, HYST assumes that the previous residual gap associated with ξ3' is equivalent to the residual gap of ξ3: D0ξ3' = Dξ3. Since wξ3' is slightly larger than D0ξ3', its corresponding embedment response is calculated to be bigger than zero, which is denoted as p(wξ3') on the unloading path illustrated in Figure 5.15e. In contrast, RHYST2 assumes that the previous residual gap D0ξ3' has the same vertical coordinate as ξ3' as shown in Figure 5.15b, which is obtained as:  D0ξ3' =  3332323  - ' -  -     xxxxDDD   (5.22) Accordingly, the wood medium associated with ξ3' starts unloading from the transverse displacement corresponds to the interpolated D0ξ3', which is denoted as wξ3* in Figure 5.15b and Figure 5.15f. Since wξ3' is smaller than D0ξ3', the model predicts p(wξ3') to be zero which is smaller than that of HYST. This is because HYST interprets that the point ξ3' is still in the elastic recovery region, while RHYST2 correctly recognizes that the point is located in the residual gap region.   Integration point ξ4 As shown in Figure 5.16a and Figure 5.16b, the fourth integration point ξ4 initially compresses the corresponding wood medium by a transverse displacement of wξ4. Upon the reversal loading, it moves to the point ξ4' where the transverse displacement changes to wξ4'. The compressed wood medium engaged with ξ4 does not recover to form a residual gap of 123  Dξ4. Instead, it unloads horizontally following the dashed line to the right side of the deformed nail at A'B'. This means that ξ4' is displaced to the elastic recovery region where the point is still in contact with the wood medium. Therefore, the residual gaps of the points displaced to the elastic recovery region are projected to the left of the deformed nail. The boundary of these gaps is expressed with a long-dashed line.  a)   b)  c)     d)        e)         f) Figure 5.16 Transverse displacements and residual gaps associated with the fourth integration points ξ4 and ξ4' in a) HYST and b) RHYST2; embedment response at wξ4 in c) HYST and d) RHYST2; embedment response at wξ4' in e) HYST and f) RHYST2 X Y X Y elastic recovery region 124  HYST and RHYST2 predict the same embedment response on ξ4, which is denoted as p(wξ4) in Figure 5.16c and Figure 5.16d. Upon the reversal loading, HYST considers the previous residual gap associated with ξ4' to be the same as the residual gap engaged with ξ4: D0ξ4' = Dξ4. In contrast, RHYST2 linearly interpolates D0ξ4' based on the vertical coordinate of ξ4' as: D0ξ4' =  4443434  - ' -  -     xxxxDDD   (5.23) Based on the obtained D0ξ4' value, each model establishes an unloading path for the wood medium corresponds to ξ4'. As shown Figure 5.16e and Figure 5.16f, the unloading path starts from wξ4 in HYST, while the path starts from wξ4* in RHYST2. wξ4* is the transverse displacement of the point on the nail at AB, which corresponds to the vertical coordinate of ξ4'. Since wξ4* is larger than wξ4, the wood medium engaged with ξ4' considered to be unloaded for a larger amount in RHYST2 than HSYT. Accordingly, RHYST2 yields a lower p(wξ4'), the embedment response on ξ4', than HYST.   Integration point ξ5 Unlike the three previous integration points discussed earlier, the fifth integration point only displaces in y direction during the positive excursion. This means that the point maintains its vertical coordinate throughout the transverse displacements of wξ5 and wξ5' as shown in Figure 5.17a. Also, the residual gap associated with the point ξ5, which is denoted as Dξ5, aligns horizontally with the transverse displacements. Again, HYST stores Dξ5 in the nail coordinate system while RHYST2 stores it in the wood medium coordinate system. Thus, HYST considers Dξ5 as the previous residual gap associated with ξ5', which is denoted as D0ξ5', in calculating the embedment response on ξ5'. RHYST2 interpolates D0ξ5' with respect to the 125  vertical coordinate of ξ5' using the residual gaps of the neighbor integration points on the nail element at position AB. However, since the vertical coordinates of ξ5 and ξ5' are the same, RHSYT2 also considers D0ξ5' to be the same as Dξ5.   a)         b)     c) Figure 5.17 a) Transverse displacements and residual gaps associated with the fifth integration points ξ5 and ξ5' in HYST and RHYST2; b) embedment response at wξ5 in HYST and RHYST2; c) embedment response at wξ5' in HYST and RHYST2  Accordingly, HYST and RHYST2 yield the same embedment responses at wξ5 and wξ5' as shown in Figure 5.17b and Figure 5.17c, which are denoted as p(wξ5) and p(wξ5') respectively. The models assume that the compressed wood medium associated with ξ5' gets unloaded starting from wξ5. Consequently, if an integration point on a nail element displaces only in the transverse direction (i.e. x direction) upon reversal loading, the two models will yield the same embedment response.  X Y elastic recovery region 126  Integration point ξ6 As shown in Figure 5.18a and Figure 5.18b, when the nail element displaces to position AB, the integration point ξ6 compresses the corresponding point on the wood medium by a transverse displacement of wξ6. Then, upon the reversal movement of the nail to position A'B', ξ6 translates in the negative x and y directions to ξ6' which sits in the elastic recovery region. The transverse displacement at ξ6' is denoted as wξ6'.  a)  b)  c)     d)        e)         f) Figure 5.18 Transverse displacements and residual gaps associated with the sixth integration points ξ6 and ξ6' in a) HYST and b) RHYST2; embedment response at wξ6 in c) HYST and d) RHYST2; embedment response at wξ6' in e) HYST and f) RHYST2 X Y X Y elastic recovery region 127  Both HYST and RHSYT2 yield the same embedment response on ξ6, which is denoted as p(wξ6) in Figure 5.18c and Figure 5.18d. However, the models predict the embedment response on ξ6' to be different from each other, which is denoted as p(wξ6') in Figure 5.18e and Figure 5.18f. The response p(wξ6') is determined by D0ξ6', the previous residual gap associated with the point ξ6'. HYST and RHYST2, respectively, obtain the D0ξ6' values according to Eq.5.24 and Eq.5.25. D0ξ6' = Dξ6 (5.24) D0ξ6' =  7676767  - ' -  -     xxxxDDD   (5.25) For this specific reversal loading case, D0ξ6' of RHYST2 is smaller than that of HYST. Accordingly, in RHYST2, the wood medium engaged to ξ6' is assumed to be unloaded for a smaller amount which leads to a larger p(wξ6') as shown in Figure 5.18f .  Consequently, if an integration point along a nail is subjected to both vertical and transverse displacement, RHSYT2 processes the residual gap information engaged with the point differently from HYST. In addition, if either model considers the point to be displaced to the elastic recovery region, the models will yield different corresponding embedment responses. This also means that if both models recognize that the point has been moved to the residual gap region, they will predict the embedment response on the point to be zero; the second integration point of the previous example represents this unloading case. Depends on the direction of the point’s vertical displacement, RHYST2 yield either larger or smaller embedment response compared with HYST. However, for a single-shear nail connection under reversed-cyclic loads, the points along the nail will most likely behave similar to either 128  the third or fourth integration point of the previous example. In both cases, RHYST2 achieves smaller embedment responses than HYST. Moreover, with the revised procedures in processing the residual gap information, RHYST2 can simulate the strength degradation observed from the reversed-cyclic test results presented in Chapter 3. The model’s capability in simulating the strength degradation will be discussed later in this chapter   Figure 5.19 RHYST2 model flow chart   129  A flow chart is provided in Figure 5.19 which explains how the revised procedures in processing the residual gap information have been incorporated into RHYST2. At each iteration, the residual gap information associated with the integration points of the nail gets updated based on the vertical coordinates of the converged residual gap information at the previous loading step.  RHYST2 has been verified against the simulation results of RHYST1 for a sheathing-to-frame nail connection example. The connection is subjected to a reversed-cyclic loading case which has three repetitive cycles with amplitudes of ±8mm. The nail and embedment properties are provided in Table 5.4 and Table 5.5. As a boundary condition, the axial displacement of the node located between the two wood layers has been set to zero since it travels into neither layer under lateral loads. And the lateral displacements have been assigned to the nail head while the displacement and force convergence criteria have been set to 10-3. The simulation results are shown in Figure 5.20.   Table 5.4 Nail properties (sheathing-to-frame example) E σ yield L dia. a Number of  Gauss points (per element)  (MPa) (MPa) (mm) (mm)  elements lengthwise cross-section wise 200,000 250 52 3.0 0.01 26 5 16  Table 5.5 Embedment properties (sheathing-to-frame example) Layers K (kN/mm2) Q0 (kN/mm) Q1 (kN/mm2) thickness (mm) Number of nail elements Frame 1.240 0.195 0.008  41 21 Sheathing 0.835 0.345 0.012  11 5  130   Figure 5.20 Simulation results of RHYST1 and RHYST2 for a cyclic loading case  Both models have achieved strength degradation at the repeated cycles, which cannot be simulated by HYST. The revised gap updating feature of RHYST2 has incorporated more strength degradation than RHYST1.  As discussed throughout this section, one of the major differences between HYST and RHYST models is the assumption about the compressive response of the wood medium. Also, the base and modified models process the gap information associated with each nail element node differently. The RHYST models could predict the structural behaviour of the single-shear nail connection more realistically in term of nail deformation and load-displacement response which reflects stiffness and strength degradation. The key differences between the models are summarized in Table 5.6.  131  Table 5.6 Differences between HYST and RHYST models  HYST RHYST1 RHYST2 wood embedment curve six-parameter curve with a descending branch which determines the loss of a connection’s lateral load resistance  three-parameter curve with no descending branch  three-parameter curve with no descending branch calculation of wood medium’s compressive forces on each nail element based on the initial nail element length  based on horizontally projected vertical length of a deformed nail element based on horizontally projected vertical length of a deformed nail element storage location of the gap information nail element nodes nail element nodes wood medium coordinates corresponding to the nail element nodes linkage between nail and wood medium coupled; share one coordinate system coupled; share one coordinate system uncoupled; each has its own coordinate system   5.3 Model validation RHYST1 and RHYST2 were validated against the nail connection test data presented in Chapter 3. As a concise summary, the strand-based wood composite posts and 11mm-OSB sheathing panels described in Section 3.1 were assembled into seven single-shear connection configurations using CN50 nails which have lengths of 50.8mm and shank diameters of 2.87mm (Appendix A). Then, they were tested under the monotonic and reversed-cyclic loads. The reversed-cyclic test results were used to confirm the validity of the revised models. Since C6 and C7 configurations showed severe asymmetric hysteretic behaviour under the reversed-cyclic loads, their test results were excluded in the model validation. Consequently, the test results of C1, C2, C3, C4, and C5 configurations were used. First, the embedment parameters of each nail configuration were calibrated to the average envelope curves of the reversed-cyclic test results. Then, the models were executed for the loading histories 132  illustrated in Figure 3.5. Since the embedment parameters were calibrated to the average envelope curves which were constructed based on the primary cycles, the model predictions for the trailing cycles could be used for the model validation purpose. For the comparison purpose, HYST was also calibrated and executed.    5.3.1 Calibration HYST, RHYST1, and RHYST2 were calibrated to the average envelope curves of the five configurations, which were obtained from the averaged reserved-cyclic test results as discussed in Section 3.4 and illustrated in Appendix C. Based on JIS G3532, the modulus of elasticity and yield strength of CN50 were assumed to be 200GPa and 500MPa respectively (Li et al. 2012). In all the models, the nail was divided into 20 beam elements and its head was subjected to lateral displacements; 15 and 5 elements were assigned to the layers of the strand-based composite member and the 11mm-OSB sheathing panel respectively. The node between the two layers was constrained to zero displacement in the axial direction assuming that it travels into neither layer. The displacement and force convergence criteria were both set to 10-3 while 5 and 16 Gauss points were assigned, respectively, along the nail length in the x-direction and over the shank diameter in the y-direction.  The embedment parameters of each connection configuration were obtained by minimizing the errors between the model predictions and test results based on the principle of least square fitting (Table 5.7).   133  Table 5.7 Embedment parameters of five nail connection configurations  Config. Model(s)  K (kN/mm2) Q0 (kN/mm) Q1 (kN/mm2) Q2 Q3 Dmax (mm) C1 HYST sheathing 0.697 0.204 0.015 0.523 1.417 4.247 frame 1.709 0.298 0.006 0.426 1.505 2.842 RHYST1 & RHYST2 sheathing 0.531 0.273 0.013 - - - frame 1.936 0.281 0.006 - - - C2 HYST sheathing 0.726 0.216 0.015 0.440 1.355 4.943 frame 1.704 0.266 0.005 0.496 1.614 2.654 RHYST1 & RHYST2 sheathing 0.405 0.271 0.024 - - - frame 1.477 0.279 0.011 - - - C3 HYST sheathing 0.696 0.200 0.011 0.569 1.859 3.267 frame 2.346 0.166 0.004 0.533 1.347 3.417 RHYST1 & RHYST2 sheathing 0.723 0.200 0.031 - - - frame 2.712 0.143 0.013 - - - C4 HYST sheathing 0.431 0.163 0.012 0.269 2.739 3.006 frame 1.493 0.086 0.002 0.206 2.615 3.173 RHYST1 & RHYST2 sheathing 0.309 0.188 0.023 - - - frame 1.478 0.084 0.002 - - - C5 HYST sheathing 1.087 0.181 0.012 0.671 1.788 3.625 frame 3.184 0.151 0.002 0.636 1.404 3.283 RHYST1 & RHYST2 sheathing 0.622 0.187 0.034 - - - frame 2.334 0.134 0.014 - - -   5.3.2 Validation on reverse-cyclic test results For each nail connection configuration, the predictions of HYST, RHYST1, and RHYST2 were plotted with the test results. Then, the energy dissipation at each cycle was calculated from the predicted and test data to evaluate the accuracies of the models.   5.3.2.1 C1 configuration The predictions of all three models agreed well with the test results of C1 configuration as shown in Figure 5.21. Stiffness degradation became severe as the lateral displacement became larger, which led to the strength degradation between the primary cycles as well as the trailing cycles.  For instance, the tested configuration reached 1164N at a displacement of 134  12mm during the second last primary cycle but it only reached 402N when it was reloaded to the same displacement during the last primary cycle. Meanwhile, the strength degradation was also observed between the repeated trailing cycles but the decreased amounts were not significant. Although both revised models simulated the stiffness degradation, only RHYST2 could simulate the strength degradation to certain degree (Figure 5.21d).     a)   b)  c)  d) Figure 5.21 Reversed-cyclic test results of C1 configuration with:  a) average envelope curves, b) HYST results, c) RHYST1 results, and d) RHYST2 results   The predicted energy dissipation of the models for the primary and trailing cycles was provided in Table 5.8. Also, the predicted dissipation at each cycle was plotted in Figure 5.22 in terms of amount per cycle and cumulative amount. In general, all three models under- Strength degradation Strength degradation 135  predicted the energy dissipation until the sixth loading step and over-predicted the dissipated amounts for the following cycles. The over-prediction was the greatest at the last primary cycle which had the largest stiffness and strength degradation due to the connection failures during the second last step. As presented in Table 5.8, HYST had more accurate predictions for the earlier cycles with smaller amplitudes, while the revised models had better predictions for the cycles with larger amplitudes.  Also, from the total overall dissipated energy perspective, the revised models had smaller errors than HYST.   Table 5.8 Energy dissipation during primary and trailing cycles: C1 configuration Step Cycle(s) Experiment HSYT RHSYT1 RHYST2 D. Energy (kN·mm) D. Energy (kN·mm) Error (%) D. Energy (kN·mm) Error (%) D. Energy (kN·mm) Error (%) 1 Primary 0.81 0.76 -7.1 0.52 -57.3 0.51 -59.1 Trailing 2.94 3.44 14.5 1.72 -70.8 1.61 -82.7 2 Primary 1.29 1.08 -19.7 0.91 -42.6 0.89 -44.8 Trailing 3.49 2.19 -59.3 2.54 -37.0 2.88 -20.9 3 Primary 1.70 1.44 -17.8 1.58 -7.1 1.29 -31.7 Trailing 2.51 1.77 -41.5 1.96 -27.9 1.91 -31.7 4 Primary 5.10 4.68 -9.1 4.65 -9.7 4.69 -8.7 Trailing 4.72 4.21 -12.0 4.09 -15.2 4.22 -11.7 5 Primary 7.13 6.29 -13.4 6.53 -9.3 6.52 -9.4 Trailing 5.79 5.47 -5.9 5.32 -8.8 5.47 -5.8 6 Primary 8.16 7.47 -9.2 7.91 -3.2 7.78 -4.9 Trailing 5.79 6.17 6.3 5.91 2.2 5.93 2.4 7 Primary 17.52 17.50 -0.1 17.09 -2.5 16.50 -6.2 Trailing 7.89 10.97 28.1 10.07 21.7 10.04 21.4 8 Primary 10.04 16.93 40.7 16.63 39.7 15.88 36.8 Total Primary 51.75 56.14 7.8 55.82 7.3 54.07 4.3 Trailing 33.11 34.22 3.2 31.62 -4.7 32.06 -3.3 Overall 84.87 90.37 6.1 87.45 2.9 86.12 1.5 136   Figure 5.22 Energy dissipation of C1 configuration: experimental and simulation results 137  5.3.2.2 C2 configuration The simulation results of the three models for C2 configuration were plotted in Figure 5.23. They agreed well with the test results. The configuration showed similar levels of stiffness and strength degradation as observed in C1 configuration. The C2 connections also failed during the seventh loading step which had the primary and trailing cycles with amplitudes of ±13.13mm and ±9.85mm respectively. These connection failures caused the dramatic loss in loading capacity at the last cycle. The stiffness degradation was simulated by all three models while RHYST2 could also simulate the strength degradation to certain degree as shown in Figure 5.23d.     a)  b)  c)  d) Figure 5.23 Reversed-cyclic test results of C2 configuration with:  a) average envelope curves, b) HYST results, c) RHYST1 results, and d) RHYST2 results  138  The dissipated energy calculated from the experimental and simulation results were presented in Table 5.9 and plotted in Figure 5.24. All three models under-predicted the energy dissipation for the primary cycles of the first six loading steps, and over-predicted the energy capacities for the trailing cycles of the last three loading steps. In terms of total overall energy dissipation RHYST2 had the closest prediction compared to the experimental results with an error of 2.7%. However, HYST and RHYST1 predicted the dissipation amounts more accurately for the cycles of the earlier and later loading steps respectively.    Table 5.9 Energy dissipation during primary and trailing cycles: C2 configuration Step Cycle(s) Experiment HSYT RHSYT1 RHYST2 D. Energy (kN·mm) D. Energy (kN·mm) Error (%) D. Energy (kN·mm) Error (%) D. Energy (kN·mm) Error (%) 1 Primary 0.93 1.06 12.8 0.55 -69.4 0.54 -71.6 Trailing 3.01 2.23 -34.8 1.77 -69.7 1.62 -85.3 2 Primary 1.34 1.13 -18.1 0.90 -49.6 1.04 -28.5 Trailing 3.54 2.36 -49.8 4.84 26.8 4.76 25.6 3 Primary 1.75 1.49 -17.6 1.47 -18.9 1.33 -31.8 Trailing 2.54 1.76 -44.2 2.03 -24.8 1.99 -27.3 4 Primary 5.43 4.98 -9.1 4.68 -16.2 4.68 -16.2 Trailing 4.77 4.31 -10.9 4.64 -3.0 4.65 -2.6 5 Primary 7.56 6.80 -11.1 6.86 -10.2 6.81 -11.1 Trailing 4.60 4.57 -0.5 4.51 -1.9 4.66 1.4 6 Primary 9.70 8.44 -15.0 8.67 -11.9 8.59 -13.0 Trailing 5.73 6.16 7.0 6.10 6.0 6.28 8.8 7 Primary 18.71 19.65 4.8 18.62 -0.5 18.00 -4.0 Trailing 9.50 10.98 13.4 10.59 10.3 11.15 14.8 8 Primary 11.29 19.52 42.1 17.94 37.1 16.80 32.8 Total Primary 56.71 63.07 10.1 59.69 5.0 57.77 1.8 Trailing 33.69 32.38 -4.1 34.48 2.3 35.12 4.1 Overall 90.40 95.45 5.3 94.17 4.0 92.90 2.7    139   Figure 5.24 Energy dissipation of C2 configuration: experimental and simulation results  140  5.3.2.3 C3 configuration In general, all three models simulated the hysteretic behaviour of C3 configuration well as illustrated in Figure 5.25. Unlike the face-driven configurations C1 and C2, the C3 connections failed gradually at larger displacements. Although half of the C3 connection specimens failed in low-cycle-fatigue as discussed in Section 3.5.1.5, their nails were substantially pulled out from the strand-based composite frame members. This withdrawing behaviour of the nails led to greater stiffness degradation between the primary cycles of the pre-peak loading steps compared with those of C1 and C2 configurations, which were best simulated by RHYST1. Meanwhile, as shown in Figure 5.25d, RHYST2 predicted the peak loads of the trailing cycles most accurately.    a)  b)  c)  d) Figure 5.25 Reversed-cyclic test results of C3 configuration with:  a) average envelope curves, b) HYST results, c) RHYST1 results, and d) RHYST2 results  141  From the dissipated energy prediction perspective, all three models under-predicted the dissipated amounts of the first six loading steps, while they over-predicted those of the last four loading steps as shown in Table 5.10 and Figure 5.26. Again the dissipated energy calculated from the HYST simulation results was more accurate for the earlier loading stage. Also, in terms of total energy dissipation, the accuracy of HYST outperformed those of the revised models, which was largely due to 0.3% error on the total prediction for the trailing cycles. Meanwhile, the revised models showed substantially more accurate predictions for the later loading stage, especially the last two loading steps.   Table 5.10 Energy dissipation during primary and trailing cycles: C3 configuration Step Cycle(s) Experiment HSYT RHSYT1 RHYST2 D. Energy (kN·mm) D. Energy (kN·mm) Error (%) D. Energy (kN·mm) Error (%) D. Energy (kN·mm) Error (%) 1 Primary 0.86 0.57 -49.7 0.58 -48.0 0.62 -39.0 Trailing 2.76 1.38 -99.7 1.52 -81.6 1.39 -99.3 2 Primary 1.03 0.78 -31.7 0.76 -35.7 0.76 -34.4 Trailing 3.10 2.43 -27.4 2.16 -43.2 1.83 -69.6 3 Primary 1.26 1.09 -16.0 1.03 -22.2 1.02 -24.0 Trailing 2.06 1.28 -60.3 1.22 -68.0 1.23 -67.6 4 Primary 3.68 3.71 0.9 3.71 0.9 3.73 1.6 Trailing 3.94 3.26 -20.7 3.10 -27.1 3.12 -26.2 5 Primary 5.28 4.99 -5.8 5.07 -4.0 5.10 -3.6 Trailing 5.67 5.18 -9.6 4.91 -15.6 4.94 -14.9 6 Primary 6.58 6.18 -6.4 6.45 -2.1 6.42 -2.4 Trailing 4.51 4.77 5.4 4.50 -0.3 4.47 -0.9 7 Primary 14.31 14.31 0.0 14.36 0.3 14.21 -0.7 Trailing 7.72 8.70 11.3 7.86 1.9 8.00 3.5 8 Primary 14.56 15.32 5.0 15.77 7.7 15.15 3.9 Trailing 9.55 12.40 23.0 11.37 16.0 10.63 10.2 9 Primary 12.02 13.54 11.2 13.37 10.1 13.32 9.7 Total Primary 59.57 60.50 1.5 61.10 2.5 60.34 1.3 Trailing 39.30 39.40 0.3 36.64 -7.3 35.59 -10.4 Overall 98.87 99.90 1.0 97.74 -1.2 95.94 -3.1 142   Figure 5.26 Energy dissipation of C3 configuration: experimental and simulation results 143  5.3.2.4 C4 configuration The simulation results of the three models for C4 configuration were plotted in Figure 5.27 which agreed well with the experimental results. The C4 connections all failed in nail pull-out as discussed in Section 3.5.1.5 which led to progressive pinching of the hysteresis loops as shown in Figure 5.27a. Although 40% of the C3 specimens failed in pull-out as well, the progressively pinched hysteresis loops were not observed in Figure 5.25a since the figure represents the averaged load-displacement response. However, none of the models simulated the progressive pinching phenomenon. Among the models, as shown in Figure 5.27d, the stiffness and strength degradation between the loading cycles were most accurately simulated by RHYST2 as well as the peak loads of the trailing cycles.   a)  b)  c)  d) Figure 5.27 Reversed-cyclic test results of C4 configuration with:  a) average envelope curves, b) HYST results, c) RHYST1 results, and d) RHYST2 results  144  The dissipated energy of the C4 configuration obtained from the experimental simulated results were tabulated and presented in Table 5.11 and Figure 5.28. In general, all three models under-predicted the energy dissipation for the first three loading steps and over-predicted the dissipation thereafter. Since none of the models simulated the progressively pinched hysteresis loops, the over-prediction occurred relatively early with larger amounts compared with other configurations discussed in the previous sections. Among the models, RHYST1 most accurately predicted the dissipated energy during the trailing cycles while HYST and RHYST2 had most accurate predictions for the primary cycles of the first five and last three loading steps respectively.   Table 5.11 Energy dissipation during primary and trailing cycles: C4 configuration  Step Cycle(s) Experiment HSYT RHSYT1 RHYST2 D. Energy (kN·mm) D. Energy (kN·mm) Error (%) D. Energy (kN·mm) Error (%) D. Energy (kN·mm) Error (%) 1 Primary 1.00 0.72 -37.8 0.66 -50.6 0.67 -48.7 Trailing 2.74 1.83 -49.9 1.92 -42.4 1.79 -53.0 2 Primary 1.21 1.14 -6.5 0.94 -28.0 0.98 -23.6 Trailing 3.00 2.25 -33.6 2.52 -19.1 2.47 -21.3 3 Primary 1.40 1.24 -12.6 1.18 -18.5 1.17 -19.5 Trailing 2.03 1.85 -9.6 1.95 -3.9 1.93 -5.0 4 Primary 4.26 4.34 1.8 4.11 -3.6 4.11 -3.6 Trailing 3.44 3.94 12.8 4.02 14.5 4.07 15.5 5 Primary 5.84 5.85 0.2 5.77 -1.3 5.80 -0.7 Trailing 5.08 6.50 21.8 6.20 18.1 6.28 19.2 6 Primary 7.00 7.25 3.5 7.31 4.2 7.14 2.0 Trailing 4.25 5.71 25.4 5.41 21.3 5.49 22.5 7 Primary 14.95 15.81 5.4 15.48 3.4 15.20 1.6 Trailing 6.22 10.01 37.9 9.57 35.1 9.93 37.4 8 Primary 11.46 16.67 31.2 16.04 28.5 14.53 21.1 Total Primary 47.13 53.02 11.1 51.51 8.5 49.60 5.0 Trailing 26.76 32.07 16.6 31.60 15.3 31.96 16.3 Overall 73.88 85.10 13.2 83.11 11.1 81.56 9.4    145   Figure 5.28 Energy dissipation of C4 configuration: experimental and simulation results   146  5.3.2.5 C5 configuration The simulation results of the three models for C5 configuration were presented in Figure 5.29. They agreed well with the experimental results shown in Figure 5.29a. As discussed in Section 3.5, the nails of the C5 connections were significantly pulled out from the strand-based composite foundation during the tests, which led the connections to fail gradually at relatively large displacements. As observed in other configurations, stiffness and strength degradation were also found between the loading cycles. Again, among the models, RHYST2 simulated the stiffness and strength degradation most accurately, especially for the last primary cycle.   a)  b)  c)  d) Figure 5.29 Reversed-cyclic test results of C5 configuration with:  a) average envelope curves, b) HYST results, c) RHYST1 results, and d) RHYST2 results  147  The dissipated energy during the loading cycles was calculated from the experimental and simulated results as presented in Table 5.12 and Figure 5.30. The dissipated amounts at the first four cycles were under-predicted by all three models. Also, the revised models continued to under-predict the dissipation for another loading step. Although HYST had the smallest error at -4.0%, in terms of total overall dissipated energy, RHYST1 and RHYST2 had the most accurate predictions for the trailing cycles of the first four and last four loading steps respectively. Moreover, both revised models had better predictions on the primary cycles of the last five loading steps.   Table 5.12 Energy dissipation during primary and trailing cycles: C5 configuration  Step Cycle(s) Experiment HSYT RHSYT1 RHYST2 D. Energy (kN·mm) D. Energy (kN·mm) Error (%) D. Energy (kN·mm) Error (%) D. Energy (kN·mm) Error (%) 1 Primary 1.08 0.85 -27.8 0.77 -39.9 0.81 -33.4 Trailing 3.32 1.76 -88.6 1.86 -79.0 1.84 -80.1 2 Primary 1.35 1.07 -26.2 1.05 -29.0 1.05 -29.0 Trailing 3.70 2.08 -77.5 2.11 -75.1 2.07 -78.6 3 Primary 1.70 1.50 -13.4 1.40 -21.2 1.38 -23.1 Trailing 2.52 1.59 -58.6 1.59 -58.5 1.58 -60.1 4 Primary 4.84 4.54 -6.5 4.55 -6.4 4.61 -4.9 Trailing 4.35 3.79 -14.9 3.84 -13.5 3.83 -13.7 5 Primary 6.49 5.86 -10.7 6.13 -5.8 6.20 -4.8 Trailing 6.08 6.21 2.2 6.02 -0.9 6.03 -0.8 6 Primary 7.77 7.15 -8.6 7.56 -2.9 7.45 -4.3 Trailing 5.06 5.60 9.7 5.45 7.1 5.38 5.9 7 Primary 16.19 15.90 -1.9 16.27 0.5 15.81 -2.4 Trailing 9.14 9.98 8.5 9.76 6.3 9.37 2.5 8 Primary 15.22 17.46 12.8 16.52 7.9 15.69 3.0 Total Primary 54.64 54.34 -0.6 54.25 -0.7 52.99 -3.1 Trailing 34.18 31.03 -10.2 30.63 -11.6 30.10 -13.6 Overall 88.83 85.37 -4.0 84.88 -4.7 83.09 -6.9 148   Figure 5.30 Energy dissipation of C5 configuration: experimental and simulation results 149  5.4 Summary The concepts, components, and formulations of a mechanics-based dowel-type connection model HYST were revisited in detail and the model was rewritten in a newer language, FORTAN90. HYST idealized a dowel-type connection as an elasto-plastic beam embedded in a nonlinear foundation that only acts in compression. In the model, the interaction between the dowel-type fastener and wood medium was formulated applying the principle of virtual work. Then, the nonlinear problem was solved by implementing the Newton-Raphson iterative procedure. The properties of the fastener and the six-parameter embedment response curve of the wood medium were the main inputs of the model. The parameters of the response curve could be either calibrated to connection test results or obtained directly from bearing strength tests.   HYST was revised specifically to simulate the behaviour of a single-shear nail connection which is commonly subjected to large lateral displacements before it fails. The effect of the nail’s vertical displacements on the wood embedment response was considered in two steps. First, HYST was revised to calculate the compressive forces of the wood medium based on the vertical coordinates of the deformed nail rather than the initial length of the nail. With this revision, the six-parameter embedment curve was replaced with a three-parameter curve which does not have a descending branch assuming that the strength of the wood medium should not decrease at any compressive load due to wood densification. This revised model was denoted as RHYST1. Consequently, in RHYST1, the decrease in the lateral load resistance was controlled by the loss of the vertical length of the contact surface between the nail and wood.  Based on RHYST1, another revision was made to consider both transverse and vertical displacements of the nail in processing the residual gap between the wood 150  embedment and the fastener. This revised model was denoted as RHYST2. Even though the loading, unloading and reloading path rules were kept the same as RHYST1, this model could simulate strength degradation between cycles under reversed-cyclic loads.  RHYST1 was compared against the HYST simulation results of a reversed-cyclic loading case example. Also, RHYST1 was executed for a monotonic loading case and the coordinates of the deformed nail shapes at large displacements were extracted from the simulation results and confirmed whether the deformed shapes of the fastener were realistic at relatively large displacements. Meanwhile, the predictions of RHYST2 were compared against the RHYST1 simulation results for a simple reversed-cyclic loading case. Then, both revised models were validated against the reversed-cyclic test results of five nail connection configurations presented in Chapter 3. In general, their simulation results agreed well with the experimental results. The revised models under-predicted the energy dissipation during the pre-peak loading cycles while they over-predicted those for the post-peak loading cycles. They were able to capture stiffness degradation between the loading cycles while only RHYST2 was able to simulate strength degradation between both primary cycles and trailing cycles to certain degrees. However, neither of the models could simulate the progressive pinching phenomenon observed in the hysteresis loops of C4 configuration which failed in nail pull-out. In comparison with the simulation results of HYST, the revised models predicted the energy dissipation more accurately for the cycles with larger amplitudes while HYST predicted better for the first few loading steps when the displacement was small.   151   Application of the Nail Connection Model Chapter 6The dowel-type fastener connection model HYST is originally developed as a stand-alone FOTRAN program. It can also be incorporated into other compatible computer models as a subroutine (He et al. 2001, Lam and Foschi 2003, Gu and Lam 2004). More recently Li et al. (2012) have modified and integrated HYST into a shear wall model WALL2D. In this study, the validity and applicability of the revised HYST models, RHYST1 and RHSYT2, in WALL2D have been confirmed. This chapter explains the components of WALL2D and discusses the simulation results of WALL2D with three different connection models for the shear wall configurations presented in Chapter 4. The wall models are denoted as WALL2D_HYST, WALL2D_RHYST1, and WALL2D_RHYST2.  6.1 WALL2D The finite element program WALL2D was developed by Li et al. (2012) based on the PBWALL program developed by Foschi (2005). The model analyzes the structural responses of panel-sheathed wood shear walls under in-plane static loading. The model uses the principle of virtual work to formulate the equilibrium equation between internal work done by four wall components and external work done by the applied loads. The four components are frame members, sheathing panels, frame-to-frame connections, and sheathing-to-frame connections. The problem is solved by implementing the Newton-Raphson iterative procedure. The program was validated against reversed-cyclic test results of Japanese post-and-beam shear walls.   152  6.1.1 Frame members The model assumes that all frame members are isotropic materials. It idealizes each member as an isoparametric beam element with two nodes in accordance with the assumptions of the Euler-Bernoulli beam theory. Thus, the model assumes that the element deforms within its linear elastic limit while its cross-section remains perpendicular to its longitudinal axis. Each node can move in six rigid body modes: three translations (u, v, and w) along x, y, and z axes and three rotations (θx, θy, and θz) about u, v, and w directions. In Figure 6.1, the displacements of the node j of the horizontal beam element subjected to twisted deformation are illustrated.   Figure 6.1 Twisted deformation of a horizontal beam element 153  The normal strain (ε) and shear strain (γ) at the node j' are: 22'22'xwzxvyxujj   (6.1) yxwxx2   (6.2) where ρ is the distance from the centroid as shown in the figure above. Then, the normal stress (σ) and shear stress (τ) are obtained following the linear elastic constitutive relations as: GE  (6.3) where E and G are the modulus of elasticity and shear modulus respectively.  6.1.2 Sheathing panels Since the sheathing panel’s thickness is small compared to its other dimensions and the panel is assumed to be uniform and symmetric about the mid-plane, it can be modelled as a thin three-dimensional plate element based on the Kirchhoff plate theory. The theory assumes that shear stresses through the panel thickness are negligible and its cross-sections remain normal to the mid-plane during deformations. Similar to the beam element, each corner of the panel (i.e. node) is subjected to six DOF displacements as shown in Figure 6.2.   Figure 6.2 Representation of a plate element 154  In accordance with the plate theory, the normal strains (εx and εy) of a point along the thickness on each node in Figure 6.2 are calculated considering axial deformations and rotations about u- and v-directions but ignoring the rotation about its w-direction (θz) as expressed in Eq.6.4 and Eq.6.5.  22xwzxux   (6.4) 22ywzyvy   (6.5) Also, for each node, the shear strain at a point along the thickness of the plate (γ xy) is calculated considering axial and bending deformations along x and y axes. Furthermore, the deflection in w-direction is also considered in the calculation as expressed in Eq.6.6. Additional explanations on calculating the shear strain component due to the w-displacement are found in He’s PhD dissertation (2002). ywxwyxwzxvyuxy22  (6.6) Unlike the beam element, the plate element is assumed to be orthotropic. Therefore, the constitutive relations for normal stresses (σx and σy) and shear stress (τxy) are defined as: xyyxxyyxxyxyxxyxyyxxyxxyyxxyxxyyxGvvEvvEyvvvEvvvE  00011011 (6.7)   155  6.1.3 Frame-to-frame connections The frame-to-frame connection is represented with three rotational and three translational linear springs. These six linear springs coincide with the number of DOF assigned to each frame member node. The springs are assumed to be independent, which lead to the stiffness matrix [K] in Eq.6.8. Such connections are assumed to be semi-rigid if any hold-down device is being used to link the frame members. Otherwise, it is considered to be a pinned connection. For instance, if the frames are toe-nailed to each other with one or two smooth-shank nails, the connection is assumed to be pin-connected. Relatively large constants are assigned to its translational springs compared with the rotational springs. Meanwhile, for the semi-rigid connection, the six spring stiffness values are assigned based on available test data. zyxzyxzyxzyxzyxzyxθθθKKKKKKMMMFFFΔΔΔ  000000000000000000000000000000 (6.8) In the equation above, Δx, Δy, and Δz are the translational slips between the connected frame nodes, which result in the forces Fx, Fy, and Fz. Δθx, Δθy, and Δθz represent the relative rotations which determine the moments Mx, My, and Mz. In light timber framed shear walls, rotational stiffness of the framing connections is typically very low.   156  6.1.4 Panel-to-frame connections The model predicts the behaviour of the panel-to-frame or nail connection using three translational springs. The response due to the relative slip between the connected panel and frame members in their primary (i.e. xy) plane is calculated using orthogonal nonlinear springs which translate along x and y axes. The reaction force corresponds to the withdrawal of the nail fastener (relative displacement between the panel and frame elements in z axis) is predicted using a linear spring with a constant stiffness value. However, the rotational displacements of such connections are ignored. The force-displacement relationship of the nonlinear spring is simulated using the modified HYST which considers the stiffness and strength degradation of the wood foundation. The details about HYST including model components and concepts are discussed thoroughly in Section 5.1.   Figure 6.3 A shear wall with nail connections along the edges of the sheathing panels: a) representation of the nail connections, b) idealization of the nail connections in WALL2D  Instead of calculating the translational slips associated with the physical location of each nail connection, the model assumes that such connections are smeared along the connection lines. 157  Each line has the same number of Gauss integration points. For instance, the model can idealize a panel-sheathed shear wall with 88 nail connections as a wall with eight connection lines which each has five approximation points as shown in Figure 6.3. Accordingly, for the given example, the model will calculate the connection behaviour at 40 gauss points instead of 88 locations. The reduced number of connection calculations obviously increases the model’s computation efficiency but may affect the accuracy of the model in some cases when the wall has complicated configurations, for example, with openings. Therefore, either the number of approximation points or the connection lines have to be chosen carefully. The translational slips at each approximation point are calculated considering the nodal displacements of the associated panel and frame elements, which add up to 36 displacement DOFs. Correspondingly, the shape functions of each connection line are constructed based on the shape functions of the associated frame and panel elements.    WALL2D can consider the orthogonal nonlinear springs of the connection to be either uncoupled or coupled. When the springs are assumed to be uncoupled, their orientations coincide with the global in-plane axes (x and y axes) and their forces are directly calculated based on the corresponding translational slips. However, Folz and Filiatrault (2001) reported that such an approach will lead to overestimation of the shear wall strength. To compensate for this problem, the model can treat the springs to be coupled using the connection’s initial trajectory. The initial trajectory is obtained by executing the model for a wall drift of 0.1% wall height. Then, based on an assumption that the angle between the trajectory and the lateral axis (x axis) remains approximately the same throughout the wall deformations, the springs are coupled in x and y axes. This approach was first introduced by Judd and Fonseca (2005).  158  6.1.5 Problem formulation and solution Based on the principal of virtual work, the internal work of the wall components are formulated as follows.  For a frame member,      VF dvW  )(   (6.9) For a sheathing panel,        V xyxyxyyyyxxxP dvW  )(    (6.10) Based on Eq.6.8, the internal virtual work of a frame-to-frame connection is written as: 61iiiiFC KW   (6.11) where, i represents the ith DOF. Considering the relative slips in three directions, the internal virtual work of a panel-to-frame connection is written as: zzyyxxC FFFW   )()()(  (6.12)  As explained in the previous section, the structural responses of the panel-to-frame connections are approximated using the Gaussian integration method over the connection lines instead of calculating the reaction forces at individual connections. Therefore, the internal virtual work associated with horizontal (x direction) and vertical (y direction) panel-to-frame connection lines are respectively expressed as: LCCL dxWW0  (6.13) and, LCCL dyWW0   (6.14) where L is the length of the connection line. 159  Accordingly, the system equilibrium equation between the internal and external virtual work in WALL2D is formulated as:         0  RaWWWW TCLFCPF    (6.15) in which R and a are the external load and global nodal displacement vectors respectively. Then Eq. 6.15 can be rewritten in terms of system out-of-balance force vector as: 0 Ta   (6.16) Since the arbitrary displacement δa cannot be zero, the out-of-balance force vector has to be zero in order to achieve the system equilibrium. The system out-of-balance vector is a summation of the out-of-balance vectors of the wall components and the external load as expressed in Eq.6.17. RCLFCPF      (6.17)  WALL2D solves for the global nodal displacement vector, a, by implementing Newton-Raphson iteration procedures in the same manner as HYST described in Section 5.1.2. The vector a is updated as:    *1**   aa   (6.18) where, a* and ψ* are the displacement vector and out-of-balance force vector at the previous iteration. [∇ψ*] is the tangent stiffness matrix corresponding to a* and ψ*, which is obtained as:    ***a   (6.19) The iteration procedures continue until the displacement and force convergence criteria are satisfied.   160  6.2 WALL2D simulations The original HYST, RHYST1, and RHYST2 were each incorporated with the wall model, WALL2D, to confirm their compatibility and validity as panel-to-frame connection models of WALL2D. The three versions of WALL2D are called WALL2D_HYST, WALL2D_RHYST1, and WALL2D_RHYST2. The WALL2D versions were executed to simulate the structural response of the 11mm-OSB-sheathed walls described in Section 4.2.3 (i.e. 11mm_SWALL_EDGE and 11mm_SWALL_FACE), which were subjected to CUREE Basic Loading Protocol. Then, the simulation results were compared with the experimental results of the shear walls in terms of energy dissipation as well as the performance parameters discussed in Section 4.4.3. Also, in order to confirm the suitability of the strand-based composite posts as vertical members in a post-and-beam shear wall system, the structural response of an 11mm-OSB-sheathed wall constructed only with hem-fir frame members (11mm_SWALL_HEM) was simulated using WALL2D_RHYST2 and compared to those of the wall configurations constructed with the composite posts.  6.2.1 Model inputs Other than the panel-to-frame connection model parameters, all three wall model versions were executed with the same inputs.   6.2.1.1 Frame members The modulus of elasticity, MOE, of the Hem-fir frame members were assumed to be 12.1 GPa based on the vibration tests conducted by Li et al. (2012). This MOE value also meets the CFLA JPS 1 Standard for E-120 Hem-Fir (Coast Forest & Lumber Association, 2001). For the MOE of the strand-based wood composite posts, as presented in Table 4.1, the 161  average experimental value of 5.9 GPa was used for both orientations of the posts (i.e. edge-wise and face-wise). The shear modulus, G, of the Hem-fir and strand-based frame members were respectively estimated to be 0.79 GPa and 0.38 GPa following the Canadian standard (CSA-O86-09), which were 0.065 times their MOE values.   6.2.1.2 Sheathing panels According to CSA-O86, Young’s modulus values along and perpendicular to the OSB panel, Ex and Ey, were estimated to be 4.4 GPa and 3.3 GPa respectively, while the shear-through-thickness rigidity, Gxy, was estimated to be 1.0 GPa. The Poisson’s ratios of the OSB sheathing, vxy and vyx, were assumed to be 0.23 and 0.16 based on the experimental results of Thomas (2003).   6.2.1.3 Frame-to-frame connection The translational stiffness values of the mortise-and-tenon joinery between the strand-based composite posts and plate members, which were reinforced by S-HD20 hold-down devices, were obtained experimentally. The initial stiffness values presented in Table 3.16 were considered to be the translational stiffness values, which were 7.8 kN/mm and 10.1 kN/mm for the connections with the hold-down devices mounted on the face and edge sides of the strand-based posts respectively. The rotational stiffness of such joinery with the hold-down device was assumed to be 61.8 x103 kN•mm/rad as reported by Li et al. (2012). Other frame-to-frame connections were assumed to be pin connected with the translational and rotational stiffness of 1.0 kN/mm and 0.1 kN•mm/rad.  162  6.2.1.4 Panel-to-frame connection The panel-to-frame connections of the 11mm-OSB-sheathed wall were assumed to be smeared along 24 connection lines. 5 Gauss integration points were assigned to each connection line. The orthogonal nonlinear springs of each connection, which respond in the primary (i.e. xy) plane, were assumed to be coupled at its initial trajectory.  The panel-to-frame embedment parameters for the connections holding the OSB sheathing to the strand-based composite or Hem-fir frame members were obtained from experimental results. Two sets of parameters were assigned to each connection since WALL2D considers the relative slips parallel and perpendicular to the major axis of the frame member. These are called parallel-to-frame and perpendicular-to-frame parameters.   The parameters of the connections composed with the strand-based posts were obtained from the reversed-cyclic test data as discussed in Section 5.3. Since the nails of the 11mm_SWALL_EDGE specimens were edge-driven to the mid-lamina region of the stand-based posts, the parameters of the C4 and C3 nail connection configurations presented in Table 5.7 were used for the parallel-to-frame and perpendicular-to-frame parameters. For the nail connections holding the sheathing to strand-based posts of the 11mm_SWALL_FACE configuration, the parallel-to-frame and perpendicular-to-frame responses were characterized by the C2 and C1 configuration parameters presented in Table 5.7.  The panel-to-frame model parameters for the connections composed of the sheathing and Hem-fir frame members were obtained from the monotonic test data available at the UBC Timber Engineering Applied Mechanics research group (Yan, 2008). The grades of the 163  sheathing and frame material were the same as the ones used in this research. Since the test data showed that the performances of the nail connections loaded parallel and perpendicular to the frame members were not distinguishable, the parallel-to-frame and perpendicular-to-frame parameters were assumed to be the same. As discussed in Section 2.2.2, Dolan and Madsen (1992) observed that the loading type did not have a significant influence on the nail connection performance. Thus, the parameters were calibrated to the monotonic test results.  The panel-to-frame model parameters used in WALL2D_HYST, WALL2D_RHYST1, and WALL2D_RHYST2 are summarized in Table 6.1 and Table 6.2. Table 6.1 Embedment parameters of panel-to-frame connections used in WALL2D_HYST Connection Type Wall Configuration Loading Direction  K (kN/mm2) Q0 (kN/mm) Q1 (kN/mm2) Q2 Q3 Dmax (mm) Hem-Fir & OSB  11mm_SWALL_FACE & 11mm_SWALL_EDGE paral.-to-frame &  perp.-to-frame panel 0.693 0.266 0.014 0.522 1.207 6.397 frame 1.814 0.426 0.004 0.482 1.541 2.815 Strand-based composite & OSB  11mm_SWALL_FACE paral.-to-frame panel 0.726 0.216 0.015 0.440 1.355 4.943 frame 1.704 0.266 0.005 0.496 1.614 2.654 perp.-to-frame panel 0.697 0.204 0.015 0.523 1.417 4.247 frame 1.709 0.298 0.006 0.426 1.505 2.842 11mm_SWALL_EDGE paral.-to-frame panel 0.431 0.163 0.012 0.269 2.739 3.006 frame 1.493 0.086 0.002 0.206 2.615 3.173 perp.-to-frame panel 0.696 0.200 0.011 0.569 1.859 3.267 frame 2.346 0.166 0.004 0.533 1.347 3.417  Table 6.2 Embedment parameters of panel-to-frame connections used in WALL2D_RHYST1 and WALL2D_RHYST2 Connection Type Wall Configuration Loading Direction  K (kN/mm2) Q0 (kN/mm) Q1 (kN/mm2) Hem-Fir & OSB  11mm_SWALL_FACE & 11mm_SWALL_EDGE paral.-to-frame &  perp.-to-frame panel 0.989 0.2 0.086 frame 1.734 0.457 0.025 Strand-based composite & OSB  11mm_SWALL_FACE paral.-to-frame panel 0.405 0.271 0.024 frame 1.477 0.279 0.011 perp.-to-frame panel 0.531 0.273 0.013 frame 1.936 0.281 0.006 11mm_SWALL_EDGE paral.-to-frame panel 0.309 0.188 0.023 frame 1.478 0.084 0.002 perp.-to-frame panel 0.723 0.200 0.031 frame 2.712 0.143 0.013  164  The nail withdrawal stiffness values for all the panel-to-frame connections were assumed to be 2.2 kN/mm based on the test results of the single-nail connections constructed with CN50 nails, 11mm-OSB sheathing panels, and Hem-fir frame members (Yan, 2008). Again, the grades of the sheathing and frame materials were the same as the ones used in this study.  6.2.1.5 Boundary conditions and convergence criteria Since the bottom plate member of each shear wall specimen was anchored to the test base as illustrated in Figure 4.5, the six DOF displacements of nodes that belong to the bottom plate were restrained to be zero in the WALL2D simulations: three translations (u, v, and w) along x, y, and z axes and three rotations (θx, θy, and θz) about u, v, and w directions. Also, the out-of-plane translational displacements (w) of the nodes that belong to the top plate member were restrained to be zero since the out-of-plane movements of the plate member were restricted by the rollers along the loading beam. The displacement and force convergence criteria used in the simulations were set to 0.1.   6.2.2 Simulation results The energy dissipation of the simulated hysteretic loops of the 11mm-OSB-sheathed wall specimens were compared with those of the reversed-cyclic test results. Also, the simulation results were analyzed according to ASTM E2126-11 as discussed in Section 4.4. Initial stiffness (K0), peak load (Ppeak), ultimate load (Pu), peak displacement (Δpeak), ultimate displacement (Δu), and ductility ratio parameters were obtained from the simulation results and compared with those of the reversed-cyclic test data.   165  6.2.2.1 11mm_SWALL_FACE configuration The experimental and simulation results of the three WALL2D versions for 11mm_SWALL_FACE configuration were presented in Figure 6.4. Although the models simulated more pinched hysteresis loops compared with the experimental loops, the simulated shapes of the loops still agreed well with the experimental results. Also, the wall models reasonably simulated the loss of lateral resistance or shear wall failure (i.e. 20% drop from the peak load) during the post-peak cycles. WALL2D_RHYST2 even successfully simulated some of the strength degradations between primary cycles as shown in Figure 6.4d.   a)  b)  c)  d) Figure 6.4 a) Reversed-cyclic test results of 11mm_SWALL_FACE configuration with: b) WALL2D_HYST results, c) WALL2D_RHYST1 results, and d) WALL2D_RHYST2 results  The predicted energy dissipation of the models for the primary and trailing cycles was provided in Table 6.3. All three models underestimated the energy dissipation throughout the Strength degradation 166  reversed-cyclic loading procedures. The under-predictions were severe for the first six loading steps. The model predictions were not even half the experimental results for the first four loading steps. Therefore, the models were not capable of simulating the energy dissipation when the cycle amplitudes were relatively small. The model predictions became more accurate for the later loading steps. For instance, the predicted energy dissipation for the eighth primary cycle, where the peak loads were achieved, were only different by less than 10% compared with the experimental results. Also, it was observed that WALL2D_RHYST1 and WALL2D_RHYST2 estimated the energy dissipation more accurately during the seventh and eighth loading steps. However, their prediction accuracy rapidly dropped after the ninth primary cycle where they assume that the shear wall lost its lateral resistance due to nail connection failures.  Table 6.3 Energy dissipation during primary and trailing cycles: 11mm_SWALL_FACE Step Cycle(s) Amplitude (mm) Experiment trial 1 Experiment trial 2 WALL2D_HSYT WALL2D_RHSYT1 WALL2D_RHSYT2 1 Primary 3.0 7.82 10.27 1.83 1.95 1.99 Trailing 3.0 39.63 49.52 6.15 6.30 6.25 2 Primary 4.5 18.60 22.20 3.62 3.84 3.88 Trailing 3.4 60.91 77.49 6.42 6.72 6.67 3 Primary 6.0 32.25 40.12 5.87 6.14 6.11 Trailing 4.5 111.17 133.45 7.73 8.27 8.00 4 Primary 12.0 135.24 154.91 60.45 60.92 61.14 Trailing 9.0 186.75 220.45 55.82 55.11 55.41 5 Primary 18.0 240.49 269.32 140.44 137.83 137.84 Trailing 13.5 221.85 255.07 103.88 102.02 102.75 6 Primary 24.0 336.28 371.25 219.90 218.49 218.10 Trailing 18.0 312.36 349.48 180.65 175.53 176.89 7 Primary 42.0 833.79 892.04 679.87 700.32 695.89 Trailing 31.5 561.33 611.04 420.56 417.09 426.33 8 Primary 60.0 1140.63 1193.84 973.56 1031.15 1012.55 Trailing 45.0 751.47 773.49 665.48 671.98 689.16 9 Primary 78.0 1269.54 1325.11 1285.43 1270.96 1210.97 Trailing 58.5 734.80 768.71 923.10 668.88 508.25 10 Primary 96.0 808.23 941.75 801.90 541.78 468.28  167  The predicted dissipation at each cycle was plotted in Figure 6.5 in terms of amount per cycle and cumulative amount.   Figure 6.5 Energy dissipation of 11mm_SWALL_FACE configuration: experimental and simulation results   168  According to ASTM E2126-11, for each set of simulation results, positive and negative envelope curves were constructed and combined into an average envelope curve. The average envelope curves of the experimental and simulation results are shown in Figure 6.6. Then, the performance parameters were obtained from the average envelope curves following the procedures described in Section 4.4: initial stiffness (K0), peak load (Ppeak), ultimate load (Pu), peak displacement (Δpeak), ultimate displacement (Δu), and ductility ratio parameters. The obtained parameters are presented in Table 6.4.    Figure 6.6 Average envelope curves of 11mm_SWALL_FACE configuration   169  Table 6.4 Performance parameters of 11mm_SWALL_FACE configuration Average Envelope Curves Ppeak Pu Δpeak Δ u K0 Pyield Δ yield Ductility Ratio (kN) (kN) (mm) (mm) (kN/mm) (kN) (mm) Experiment-trial 1 19.44 15.55 55.11 78.87 2.24 16.91 7.54 10.45 Experiment-trial 2 19.63 15.7 54.82 77.21 2.88 17.18 5.96 12.96 WALL2D_HYST 20.47 16.38 67.50 82.94 0.99 18.05 18.18 4.56 WALL2D_RHYST1 20.16 16.13 58.50 71.68 1.02 18.02 17.64 4.06 WALL2D_RHYST2 20.16 16.12 58.50 77.58 1.02 17.96 17.55 4.42  In general, the parameters obtained from the simulation results agreed well with those of experimental results except K0, Δ yield, and ductility ratio. The lower K0 values of the simulation results led to the larger Δ yield which resulted in the smaller ductility ratios. Other parameters, including the load parameters, obtained from the simulation results of WALL2D_RHYST2 were more accurate than those of other two WALL2D versions.   6.2.2.2 11mm_SWALL_EDGE configuration The experimental and simulation results of the three wall models for 11mm_SWALL_EDGE configuration were presented in Figure 6.7. In general, the simulated hysteresis loops agreed well with those of the experimental results. WALL2D_RHYST2 simulated the gradual loss of lateral resistance after the primary cycle with amplitude of 60mm best among the wall models. Also, it simulated some of the strength degradations between primary cycles successfully as shown in Figure 6.7d.    170   a)  b)  c)  d) Figure 6.7 a) Reversed-cyclic test results of 11mm_SWALL_EDGE configuration with: b) WALL2D_HYST results, c) WALL2D_RHYST1 results, and d) WALL2D_RHYST2 results   In terms of energy dissipation, all three models underestimated the energy dissipation throughout the reversed-cyclic loading procedures as presented in Table 6.5. Again, the estimations showed that the models were not capable of simulating the energy dissipation for the first six loading steps where the cycle amplitudes were relatively small. The model predictions were reasonable for the cycles of the seventh, eighth, and ninth loading steps. For instance, energy dissipation predicted by WALL2D_HYST for the eighth and ninth loading steps was different by less than 12% from the experimental results. As observed in the simulation results of the 11mm_SWALL_FACE configuration, the models assumed that the 171  nail connections failed during the ninth loading step which led to the dramatic loss in lateral resistance of the shear wall in the tenth primary cycle.   Table 6.5 Energy dissipation during primary and trailing cycles: 11mm_SWALL_EDGE Step Cycle(s) Amplitude (mm) Experiment trial 1 Experiment trial 2 WALL2D_HSYT WALL2D_RHSYT1 WALL2D_RHSYT2 1 Primary 3.0 9.24 10.97 1.75 1.91 1.95 Trailing 3.0 44.02 49.77 5.70 5.94 5.85 2 Primary 4.5 21.27 23.09 3.51 3.81 3.84 Trailing 3.4 73.59 76.54 6.18 6.61 6.42 3 Primary 6.0 36.73 39.35 5.64 6.04 6.03 Trailing 4.5 125.29 129.19 10.53 11.18 10.89 4 Primary 12.0 134.53 142.02 55.90 57.34 57.56 Trailing 9.0 179.88 192.09 48.47 48.39 48.56 5 Primary 18.0 216.81 227.75 123.32 124.44 124.45 Trailing 13.5 196.39 205.26 91.80 91.13 91.74 6 Primary 24.0 291.62 300.56 191.46 193.92 193.48 Trailing 18.0 263.35 267.04 158.17 156.39 157.50 7 Primary 42.0 688.20 715.58 580.28 597.24 593.11 Trailing 31.5 468.98 464.11 373.33 363.85 373.67 8 Primary 60.0 937.26 956.33 834.43 858.74 842.66 Trailing 45.0 607.62 613.95 590.92 576.78 591.33 9 Primary 78.0 1068.03 1097.48 998.97 854.11 965.82 Trailing 58.5 637.57 650.80 638.05 481.28 544.14 10 Primary 96.0 886.23 921.43 483.07 389.97 437.75  The predicted dissipation at each cycle was plotted in Figure 6.8 in terms of amount per cycle and cumulative amount. 172   Figure 6.8 Energy dissipation of 11mm_SWALL_EDGE configuration: experimental and simulation results    173  The average envelope curves of the experimental and simulation results were also obtained according to ASTM E2126-11 as shown in Figure 6.9. The figure illustrates that the initial stiffness of the experimental curves were much higher than those of the simulated curves. However, the peak loads and descending branches of the curves were close to each other.     Figure 6.9 Average envelope curves of 11mm_SWALL_EDGE configuration  Table 6.6 Performance parameters of 11mm_SWALL_EDGE configuration Average Envelope Curves Ppeak Pu Δpeak Δ u K0 Pyield Δ yield Ductility Ratio (kN) (kN) (mm) (mm) (kN/mm) (kN) (mm) Experiment-trial 1 16.35 13.08 56.16 76.61 2.57 14.18 5.51 13.91 Experiment-trial 2 16.37 13.09 55.91 78.49 2.65 14.29 5.39 14.56 WALL2D_HYST 16.74 13.39 59.50 79.14 0.91 14.97 16.47 4.81 WALL2D_RHYST1 16.84 13.47 55.00 70.24 0.95 14.96 15.76 4.46 WALL2D_RHYST2 16.92 13.54 57.00 78.16 0.95 15.08 15.89 4.92  174  As discussed in the previous section, the performance parameters were obtained from the average envelope curves and presented in Table 6.6. Similar to the 11mm_SWALL_FACE configuration, the load parameters of the simulated results agreed well with those of experimental results. Also, the displacement parameters other than yield displacement (Δyield) of the simulation results had good agreement with the experimental results. Again, due to the underestimated initial stiffness and overestimated yield displacements, the ductility ratio values of the simulation results were significantly lower than those of the experimental results.   6.2.2.3 11mm_SWALL_HEM configuration  Figure 6.10 WALL2D_RHYST2 simulation results for 11mm_SWALL_HEM configuration  To draw a conclusion on the suitability of the strand-based composite post, WALL2D_RHYST2 was executed to simulate the structural behaviour of an 11mm OSB 175  sheathed wall constructed only with JAS grade hem-fir products (Canada Tsuga E120) and the results were compared to the ones discussed in the previous two sections. This wall configuration is denoted as 11mm_SWALL_HEM. As the model inputs for the nail connections, the parameters provided in Table 6.2 were used. The translational and rotational stiffness values of the hold-down connection were set at 10.0 kN/mm and 61.8 x103 kN•mm/rad respectively as reported by Li et al. (2012). The simulation results shown in Figure 6.10 were analyzed in terms of energy dissipation (Table 6.7) and performance parameters (Table 6.8).   Table 6.7 WALL2D_RHYST2 simulation results: energy dissipation of 11mm_SWALL_HEM, 11mm_SWALL_FACE, and 11mm_SWALL_EDGE Step Cycle(s) Amplitude (mm) 11mm_SWALL_HEM 11mm_SWALL_FACE 11mm_SWALL_EDGE 1 Primary 3.0 2.09 1.99 1.95 Trailing 3.0 6.51 6.25 5.85 2 Primary 4.5 4.05 3.88 3.84 Trailing 3.4 6.64 6.67 6.42 3 Primary 6.0 6.28 6.11 6.03 Trailing 4.5 7.82 8.00 10.89 4 Primary 12.0 63.44 61.14 57.56 Trailing 9.0 54.53 55.41 48.56 5 Primary 18.0 146.51 137.84 124.45 Trailing 13.5 103.65 102.75 91.74 6 Primary 24.0 229.78 218.10 193.48 Trailing 18.0 180.83 176.89 157.50 7 Primary 42.0 742.98 695.89 593.11 Trailing 31.5 452.61 426.33 373.67 8 Primary 60.0 1085.35 1012.55 842.66 Trailing 45.0 735.99 689.16 591.33 9 Primary 78.0 1343.77 1210.97 965.82 Trailing 58.5 945.9 508.25 544.14 10 Primary 96.0 1286.14 468.28 437.75   176  Table 6.8 WALL2D_RHYST2 simulation results: performance parameters of 11mm_SWALL_HEM, 11mm_SWALL_FACE, and 11mm_SWALL_EDGE Average Envelope Curves Ppeak Pu Δpeak Δ u K0 Pyield Δ yield Ductility Ratio (kN) (kN) (mm) (mm) (kN/mm) (kN) (mm) 11mm_SWALL_HEM 23.40 18.72 77.50 81.65 1.13 20.37 18.10 4.51 11mm_SWALL_FACE 20.16 16.12 58.50 77.58 1.02 17.96 17.55 4.42 11mm_SWALL_EDGE 16.92 13.54 57.00 78.16 0.95 15.08 15.89 4.92  The simulation results showed that 11mm_SWALL_HEM outperformed the other two wall configurations majorly due to having stronger nail connections. Among the two wall configurations constructed with the composite posts, the simulation results of 11mm_SWALL_FACE were closer to the ones of 11mm_SWALL_HEM. The differences between the estimated energy dissipation of 11mm_SWALL_FACE and 11mm_SWALL_HEM were less than 7% for the first eight loading steps. However, the differences were significant for the last two loading steps where the peak and ultimate loads were predicted. The estimated peak load and corresponding shear displacement of 11mm_SWALL_HEM were 23.4 kN and 77.50 mm, while those of 11mm_SWALL_FACE were 20.16 kN and 58.50 mm.   Considering that Canada Tsuga E120 is a proven superior product while the proposed strand-based composite post is the first trial product constructed with the rim board products which are not designed to be utilized as vertical members, the performance levels of the walls constructed with the strand-base composite posts were acceptable. Based on the experimental study conducted at Centre for Better Living by Okabe (2001), under a reversed-cyclic loading condition, 2730 x 1820 mm post-and-beam shear walls constructed with the Tsuga frame members showed 16 to 19% larger peak and ultimate loads than the walls constructed with Suki frame members which have similar structural performance as the JAS grade 177  whitewood products, E85-F300; the walls were sheathed with 9mm OSB panels using N50 nails at 150mm spacing. The initial stiffness and displacement parameters were different by less than 4%. Thus, the walls constructed with the proposed composite posts would show competitive structural performance against the walls constructed with the Suki or whitewood products. Moreover, the merit of the proposed product is that its physical and mechanical properties can be modified in more various ways than the solid lumber products. For instance, the product composition such as strand species, dimensions, orientation and vertical density profile can be changed to improve it embedment property which has a direct influence on the nail connection performance. Thus, the proposed composite post has a great potential to be developed into a high-performing commercial product.  6.3 Summary The components and formulations of a finite-element based program WALL2D were revisited in details. The main components of the model are frame members, sheathing panels, frame-to-frame connections, and panel-to-frame connections. Each node of the frame and sheathing members are allowed to translate and rotate in the x, y and z directions. WALL2D assumes that the response of the frame-to-frame connection is determined by the linear springs which correspond to six DOF displacements. Meanwhile, the response of the panel-to-frame connection is simulated using a nail connection model HYST. Based on the principal of virtual work, the model formulates the equilibrium problem between the internal work by the wall components and external work by applied loads. Then, the Newton-Raphson iterative procedure was implemented to solve the problem.   178  In order to confirm the applicability of the revised HYST models (i.e. RHYST1 and RHYST2 introduced in Chapter 5), they were incorporated into WALL2D. These WALL2D versions are called WALL2D_RHYST1 and WALL2D_RHYST2. The lateral responses of 11mm-OSB sheathed walls described in Chapter 4 under reversed-cyclic loads were simulated by the two models. The simulation results were compared with the simulation results of WALL2D with the original HYST model and the experimental results. The input parameters for the wall models were obtained either from the test data or information available in literature. For instance, the MOE of the strand-based wood composite was determined to be 5.9 GPa which was obtained from the non-destructive tests described in Section 4.1.1.  The simulation results of WALL2D_RHYST1 and WALL2D_RHYST2 agreed well with the simulation results of WALL2D_HYST in terms of energy dissipation as well as the performance parameters such as peak and ultimate loads. Therefore, the results led to a conclusion that RHYST1 and RHYST2 are compatible with WALL2D and also can be applied to other programs such as LightFrame3D (He et al. 2001) where the original HYST has been used. Compared with the reversed-cyclic test data, the simulation results of all three wall models were in good agreement for the loading cycles with relatively large amplitudes. The initial stiffness and energy dissipation during the first six loading steps were significantly different from the experimental results. Meanwhile, the models were capable of predicting load performance parameters accurately and energy dissipation for the seventh to ninth loading steps reasonably well.     179   Conclusions and Future Work Chapter 7A commercial strand-based wood composite product, 28.6 mm thick OSB rim board was proposed as a lamstock for 105 x 105mm laminated posts. In order to confirm the proposed product’s suitability as vertical frame members in the P&B shear wall system, its mechanical properties such as bending MOE needed to be investigated as well as its interactions with connected wall components. As discussed in Section 2.1, previous studies on strand-based wood composites mainly focused on the mechanical properties related to their end uses. For instance, in depth research on the effects of strand orientation, VDP, and loading directions on bending MOE of OSB products were already conducted. However, research on performance of the strand-based composite frame member as a component of connection systems was absent, which was one of the main components of the presented work.   Also as discussed in Section 2.2, there were many previous studies focused on the performance of nail connections in wood-frame shear walls based on the well-known fact that the lateral performance of a wood-frame shear wall is largely influenced by these connections. Numerous researchers conducted experimental studies on the nail connections composed of various types of solid wood frame members and sheathing materials to examine performance-determining factors such as grain direction, loading type, fastener type, and loading direction. Correspondingly, several computer models which are able to predict the behaviour of such connections were introduced. They were usually developed as components of diaphragm models such as the shear wall model SWAP discussed in Section 2.3.2. The common motivation for modelling work is to avoid high experimental costs. The computer models were developed at different complexity levels with various assumptions considering 180  the trade-off between the model complexity and computational efficiency. As one of the main objectives of the presented work, a nail connection model was proposed to be developed based on an existing computer model (i.e. HYST).  In this research, an experimental study was conducted to evaluate the effects of embedment density, loading direction, and nail driving direction on the performance of the nail connections constructed with strand-based composite members, 11mm OSB sheathing panels, and CN50 nails. Considering several possible nail driving locations, seven configurations were determined. The connection specimens were tested under monotonic and reversed-cyclic loads following ASTM standards and Japanese HOWTEC connection performance analysis guidelines. The test results were compared statistically using t-tests at 95% confidence level. The face-driven nail connections outperformed the edge-driven nail connections when they were loaded parallel to the strands. The connections with nails embedded in high density regions had higher strength, but smaller ductility ratios compared to the specimens with nails embedded in low density regions. From the loading direction effect perspective, regardless of the embedment densities, the edge connection specimens achieved significantly higher strength when they were loaded perpendicular to the strands. This observation differed from the well-known observation that a nail holding a solid wood frame member and sheathing panel together resists more lateral loads when it gets loaded parallel to the fibres of the solid wood member.   The effect of post orientation on the performance of hold-down connections constructed of the composite posts, LS12 lag screws, and S-HD 20 hold-down devices was investigated empirically as well. The connection specimens were tested under monotonic loads following 181  ASTM standards and HOWTEC connection performance analysis guidelines. T-tests at 95% confidence level were implemented to evaluate the performance differences between the two configurations: the hold-down devices installed on the face-sides and edge-sides of the posts. The face-driven specimens, which failed in moment, outperformed the edge-driven specimens, which failed in splitting, in terms of load capacities. The face-driven specimens achieved similar load capacities compared with the hold-down connections constructed with solid wood (i.e. Douglas-Fir and Japanese Cedar) posts. However, the solid wood connections had noticeably lower initial stiffness but larger ductility than the composite connections. Since the initial stiffness of such connections largely determines the uplifting resistance of shear walls, both composite hold-down connection configurations were expected to perform better than the solid wood connections as the shear wall components.   Based on the connection test results, when the proposed strand-based wood composite is used as posts in a sheathed shear wall system, the nail connections will have more critical effects on the wall performance than the hold-down connections. Accordingly, the walls with face-driven nail connections and edge-driven hold-down connections are anticipated to achieve higher lateral load resistance than the ones with edge-driven nail connections and face-driven hold-down connections. Moreover, since the face-driven nail connections are not affected by embedment densities, the performance of the walls will be more consistent.  Another experimental study was conducted to investigate the effect of post orientation on the shear wall performance. The structural behaviour of three post-and-beam wall types under static loads was examined:  double-braced, 9mm-OSB-sheathed, and 11mm-OSB-sheathed. The dimensions of the walls were 2400 mm in height and 1820 mm in length. The frame 182  members were Japanese standard grade Hem-fir lumber products except for the 105 x 105 mm posts, which were the strand-based wood composites. The sheathing panels and metal connectors used to assemble the frame members were also Japanese standard products. The static load tests were conducted and the test data was analyzed following ASTM standards. The double-braced walls lost their lateral resistances due to the failures of the frame members and connectors holding them together. In contrast, the OSB-sheathed walls failed only due to the nail connection failures. The test results confirmed that the sheathed walls with face-driven nails outperformed those with edge-driven nails. The reversed-cyclic test results showed that the effect of post orientation on the shear wall performance became more evident as the sheathing panel thickness increased. This observation leads to a minor conclusion that the post orientation has to be chosen more carefully when relatively thick OSB sheathing is being used.   As another main contribution of this research, a mechanics-based finite-element model RHYST was developed to simulate the load-displacement relationship of a single-shear nail connection under static loads. The connection model was constructed based on the existing computer model HYST which was developed by Foschi (2000). The presented modelling work focused on compensating the contribution of the nail’s vertical displacements on the lateral response of the surrounding wood medium. The major modelling concept of RHYST was that the decrease in lateral resistance of the nail connection is largely due to the loss of the wood medium’s vertical length which is horizontally projected from the deformed nail. Thus, in RHYST, three-parameter curves, which do not have descending branches, were used to represent the response of the wood medium as a function of compressive displacements. Moreover, the coordinate systems of the nail and wood medium were separated in order to 183  consider the nail’s vertical displacements in determining the lateral response of the wood medium. Using this approach, RHYST was able to simulate strength degradation under reversed-cyclic loads. The predictions of RHYST were compared with the simulation results of the base model HYST. Then, it was validated against the reversed-cyclic test data presented in Chapter 3. In comparison with HYST, RHYST was able to simulate the behaviour of a nail connection more accurately for the cycles with larger amplitudes, where the strength degradation between the cycles became more evident.   In order to confirm the applicability of RHYST, it was incorporated into a finite-element based shear wall model WALL2D which originally used HYST as a nail connection model. WALL2D with RHYST and the original WALL2D were executed to simulate the structural behaviour of 11mm-OSB sheathed walls described in Chapter 4 under reversed-cyclic loads. The simulation results of the models agreed well with each other. It proved that RHYST can be used in other computer-based structural programs where single-shear nail connection models are incorporated. In comparison with the experimental results, the peak loads of the loading cycles were predicted well by the models. Also, the models estimated energy dissipation reasonably well for the loading cycles with relatively large amplitudes. However, in general, the models underestimated wall initial stiffness and energy dissipation for the loading cycles with relatively small amplitudes.  7.1 Scientific contribution The research topic on a strand-based wood composite product used as a lamstock for vertical members of P&B shear wall is original. No previous research has been conducted to establish an extensive test database on such composite product as well as its application in a P&B 184  shear wall system. This study also investigated two types of common and critical connections which link the composite members to other wall components: nail and hold-down connections. For each connection type, specimen configurations were determined considering the highly orthogonal properties of the composite product which will affect the connection behavior. These effects were analyzed statistically by implementing t-tests at 95% confidence level. Subsequently, full-scale wall tests were conducted to evaluate the effect of the post orientation on the entire shear wall behavior.   A nail connection model was developed based on an existing computer model. The developed model considers the contribution of the nail’s vertical displacements on the lateral response of the wood medium. In the model, a three-parameter curve was used to represent the response of the wood medium at different compressive displacements based on the assumption that the compressive response of the wood medium remains nearly the same after it displaces for a specific amount. Also, the coordinate systems of the nail and wood medium were separated. With this approach, structural responses of such connection could be simulated more realistically. The model was successfully verified using the simulation results of the based model and validated against the connection test results. Also, the developed nail connection model has been successfully implemented to a finite-element based shear wall model and validated against the shear wall test results.  7.2 Future research One of the major findings in this research was that the orientation of the proposed composite post is the performance-determining factor for the shear wall system. In order for the shear walls constructed with the composite posts to achieve their optimum performances, the nails 185  have to be driven into the face-sides of the posts. Therefore, if the proposed product is to be used in construction, its orientation has to be regulated strictly. However, this orthogonal attribute leads to relatively poor workability compared to solid lumber products, which makes it less attractive to builders. To overcome such weakness, the embedment property of the edge-sides of the composite posts has to be refined by modifying the product composition. This refining process will require extensive research on the modification of the product composition such as vertical density profile and strand orientation.   From the product commercialization aspect, the proposed composite product must satisfy the standard requirements regulated by the government bodies of the regions where its target markets are located. Since the composite product is developed to be used as a vertical member of a Japanese post-and-beam shear wall, it has to meet the requirements stated in Article 37 of Building Standard Law of Japan. According to article 37, the proposed strand-based composite product falls into the “designated building material” category as “Item 11 – wood-based composite axial material”. For the composite product, the qualities listed in Ministry of Construction Notification 1446 have to be evaluated at accredited laboratories, which include not only mechanical properties but responses to other factors such as moisture content and duration of load (Tsuchimoto, 2002). Once the structural performances of the product are confirmed by the Ministry of Land, Infrastructure and Transport of Japan, a certification will be issued which allows the product to be used in Japanese buildings (Japan Testing Center for Construction Materials, 2012). Therefore, if the composite product manufacturer decides to launch the proposed product in Japan, the required tests and analysis will lead to another extensive research.   186  Also, extended experimental studies on both connection and wall tests can be conducted to establish a more comprehensive database and obtain more in-depth knowledge about strand-based wood composite posts. A relationship between the embedment density and the performance parameters of nail connections can be established through regression analysis. The experiment should be designed to measure the responses of the connections with nails embedded at different densities along the thickness of the strand-based composite laminae. Moreover, the design properties of the composite products need to be further studied before they can be extensively used in building applications. Due to the limitation of the hydraulic press used in this research, the shear walls were constructed at a height of 2400 mm instead of the standard height 2730 mm for Japanese P&B walls. Therefore, in order to compare the performance of the shear wall constructed with strand-based composite posts with other available P&B wall test data, they will need to be constructed to the standard height and tested. Also, the experimental studies in this research only covered static loading. It will be more insightful to conduct shake table tests on such a wall system with combined use of the composite posts and other solid timber members.  From the computer modelling perspective, the developed model can be further improved to simulate the fastener withdrawal by considering the frictional effect between the fastener and the wood medium. The starting point would be adopting the work done by Allotey and Foschi (2004). However, the challenges will be calculating the vertical response of the wood medium and defining the proper friction coefficient between two materials. Once the friction and vertical responses are successfully taken into account, the model will be able to capture the roping effect.   187  Bibliography Ainsworth Engineered. (2011). Ainsworth Universal OSB Material Safety Data Sheet. Ainsworth Engineered. Alldritt, K., Sinha, A., & Miller, T. H. (2014). Designing a strand orientation pattern for improved shear properties of oriented strand board. 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Vancouver: University of British Columbia.    195  Appendices Appendix A Schematics of nail connection configurations  Figure A. 1 Sides of strand-based wood composite frame member   Figure A. 2 C1 configuration Major direction of strands FACE EDGE END 196   Figure A. 3 C2 configuration  Figure A. 4 C3 configuration Major direction of strands 197   Figure A. 5 C4 configuration  Figure A. 6 C5 configuration Major direction of strands Major direction of strands 198   Figure A. 7 C6 configuration  Figure A. 8 C7 configuration 199  Appendix B Connection performance parameters Table B. 1 Nail Configuration 1 – performance parameters under monotonic loads   PT: Pull-through PO: Pull-out  Table B. 2 Nail Configuration 2 – performance parameters under monotonic loads   Ppeak Pu Δpeak Δu K0 Pyield Δyield(N) (N) (mm) (mm) (N/mm) (N) (mm)C1-1 1545.12 1236.10 8.78 17.72 1414.25 1312.67 0.93 19.09 PTC1-2 1194.86 955.89 9.59 11.95 798.11 955.31 1.20 9.98 POC1-3 1227.81 982.25 10.06 13.86 704.95 971.66 1.38 10.06 PTC1-4 1534.14 1227.31 13.80 19.14 1415.57 1231.95 0.87 22.00 PTC1-5 1516.47 1213.18 13.25 18.32 1257.54 1238.70 0.99 18.60 PTC1-6 1323.33 1058.66 11.09 16.42 643.74 1108.42 1.72 9.53 PTC1-7 993.47 794.78 14.01 17.50 769.79 823.04 1.07 16.37 PTC1-8 1616.73 1293.38 10.27 18.51 1510.12 1360.98 0.90 20.54 PTC1-9 1878.58 1502.86 10.50 16.57 2196.69 1587.97 0.72 22.92 PTC1-10 1299.15 1039.32 13.04 21.54 1513.05 1078.88 0.71 30.20 PTAverage 1412.97 1130.37 11.44 17.15 1222.38 1166.96 1.05 17.93Stdev 253.86 203.09 1.91 2.70 492.09 225.56 0.31 6.66CV 0.18 0.18 0.17 0.16 0.40 0.19 0.30 0.37Config 1Ductility Ratio Failure ModePpeak Pu Δpeak Δu K0 Pyield Δyield(N) (N) (mm) (mm) (N/mm) (N) (mm)C2-1 1501.23 1200.98 13.75 21.99 1455.27 1251.06 0.86 25.58 PTC2-2 1849.09 1479.27 8.70 16.58 2422.14 1567.33 0.65 25.63 PTC2-3 1513.86 1211.09 8.38 15.92 974.00 1289.22 1.32 12.03 PTC2-4 1695.92 1356.74 10.86 18.69 932.06 1437.93 1.54 12.11 PTC2-5 1333.26 1066.61 11.67 17.58 2325.10 1127.37 0.48 36.27 PTC2-6 1590.62 1272.50 11.37 21.23 2139.44 1346.66 0.63 33.73 PTC2-7 1599.71 1279.77 13.59 16.30 832.55 1319.22 1.58 10.29 PTC2-8 1506.54 1205.23 10.53 20.38 1969.81 1270.48 0.64 31.60 PTC2-9 1554.06 1243.25 15.68 17.76 854.38 1234.15 1.44 12.29 PTC2-10 1808.04 1446.43 8.40 20.45 1306.08 1550.03 1.19 17.23 PTAverage 1595.23 1276.19 11.29 18.69 1521.08 1339.34 1.03 21.68Stdev 154.04 123.23 2.47 2.19 637.48 140.47 0.43 10.05CV 0.10 0.10 0.22 0.12 0.42 0.10 0.41 0.46Config 2Ductility Ratio Failure Mode200  Table B. 3 Nail Configuration 3 – performance parameters under monotonic loads   Table B. 4 Nail Configuration 4 – performance parameters under monotonic loads  Ppeak Pu Δpeak Δu K0 Pyield Δyield(N) (N) (mm) (mm) (N/mm) (N) (mm)C3-1 1085.36 868.29 7.50 8.53 4190.08 881.99 0.21 40.53 POC3-2 1218.81 975.05 11.88 23.34 1901.76 1032.13 0.54 43.00 POC3-3 1285.29 1028.23 7.89 11.27 2727.57 1069.03 0.39 28.75 POC3-4 1528.04 1222.43 7.04 16.29 1434.96 1290.45 0.90 18.12 POC3-5 1394.56 1115.65 10.96 16.70 1745.83 1149.42 0.66 25.36 POC3-6 1031.94 825.55 6.55 9.77 1642.61 859.00 0.52 18.68 POC3-7 1373.44 1098.75 10.61 17.92 1745.93 1128.56 0.65 27.72 PTC3-8 1424.81 1139.85 11.33 18.32 1275.07 1194.99 0.94 19.55 PTC3-9 1147.29 917.83 9.15 16.18 2306.03 968.17 0.42 38.53 POC3-10 971.35 777.08 6.89 9.04 2019.74 789.24 0.39 23.14 POAverage 1246.09 996.87 8.98 14.74 2098.96 1036.30 0.56 28.34Stdev 185.27 148.21 2.05 4.86 845.46 160.93 0.23 9.30CV 0.15 0.15 0.23 0.33 0.40 0.16 0.41 0.33Config 3Ductility Ratio Failure ModePpeak Pu Δpeak Δu K0 Pyield Δyield(N) (N) (mm) (mm) (N/mm) (N) (mm)C4-1 752.18 601.74 14.26 23.58 1999.67 641.82 0.32 73.45 POC4-2 997.82 798.26 10.34 29.39 1573.18 867.02 0.55 53.33 PTC4-3 762.16 609.73 24.66 30.91 1731.75 640.56 0.37 83.57 POC4-4 853.25 682.60 11.27 17.48 1216.40 716.77 0.59 29.67 POC4-5 650.05 520.04 13.47 14.70 634.52 526.77 0.83 17.71 POC4-6 696.85 557.48 6.90 15.33 1110.51 600.91 0.54 28.33 POC4-7 890.91 712.73 11.95 23.62 767.47 759.79 0.99 23.86 POC4-8 862.22 689.78 18.47 25.26 404.98 725.44 1.79 14.10 POC4-9 962.20 769.76 11.38 23.68 2029.45 824.88 0.41 58.26 POC4-10 1007.30 805.84 12.26 25.91 1371.80 859.89 0.63 41.33 POAverage 843.49 674.80 13.50 22.99 1283.97 716.38 0.70 42.36Stdev 125.31 100.24 4.91 5.54 563.29 114.32 0.43 23.91CV 0.15 0.15 0.36 0.24 0.44 0.16 0.62 0.56Config 4Ductility Ratio Failure Mode201  Table B. 5 Nail Configuration 5 – performance parameters under monotonic loads   Table B. 6 Nail Configuration 6 – performance parameters under monotonic loads  Ppeak Pu Δpeak Δu K0 Pyield Δyield(N) (N) (mm) (mm) (N/mm) (N) (mm)C5-1 937.42 749.94 10.54 21.06 1543.15 804.65 0.52 40.40 POC5-2 1057.53 846.02 13.98 27.31 1618.68 906.05 0.56 48.79 PTC5-3 1010.43 808.34 9.58 17.80 2405.16 856.23 0.36 50.00 POC5-4 982.88 786.30 10.85 14.66 1588.51 818.69 0.52 28.45 POC5-5 1019.77 815.82 10.49 13.99 2058.43 852.35 0.41 33.80 POC5-6 1069.95 855.96 9.21 18.32 1048.22 915.81 0.87 20.97 POC5-7 1201.88 961.50 12.98 26.02 2050.22 1018.35 0.50 52.38 POC5-8 1185.09 948.07 10.20 21.23 2904.78 1009.37 0.35 61.11 POC5-9 986.49 789.19 14.86 22.23 1164.31 824.64 0.71 31.38 POC5-10 982.90 786.32 11.82 19.41 742.42 833.56 1.12 17.29 POAverage 1043.43 834.75 11.45 20.20 1712.39 883.97 0.59 38.46Stdev 87.90 70.32 1.91 4.34 655.81 77.22 0.25 14.44CV 0.08 0.08 0.17 0.21 0.38 0.09 0.42 0.38Config 5Ductility Ratio Failure ModePpeak Pu Δpeak Δu K0 Pyield Δyield(N) (N) (mm) (mm) (N/mm) (N) (mm)C6-1 1646.00 1316.80 7.29 18.10 1248.82 1400.73 1.12 16.13 PTC6-2 1182.00 945.60 17.03 20.54 566.12 974.83 1.72 11.93 PTC6-3 1539.37 1231.50 8.76 15.46 2445.03 1279.19 0.52 29.55 PTC6-4 1355.71 1084.57 8.58 17.84 3775.51 1168.10 0.31 57.66 PTC6-5 1725.68 1380.54 8.67 13.66 947.97 1448.31 1.53 8.94 PTC6-6 1571.65 1257.32 9.96 18.66 887.87 1341.29 1.51 12.35 PTC6-7 1137.75 910.20 5.58 7.99 3063.31 971.13 0.32 25.22 PTC6-8 1435.36 1148.29 8.85 15.96 1349.87 1215.80 0.90 17.72 PTC6-9 1748.37 1398.70 11.38 16.05 1453.26 1427.47 0.98 16.34 PTC6-10 1276.53 1021.22 6.78 13.10 2283.27 1092.99 0.48 27.37 PTAverage 1461.84 1169.47 9.29 15.74 1802.10 1231.98 0.94 22.32Stdev 219.43 175.54 3.16 3.54 1046.43 178.11 0.53 14.21CV 0.15 0.15 0.34 0.23 0.58 0.14 0.56 0.64Config 6Ductility Ratio Failure Mode202  Table B. 7 Nail Configuration 7 – performance parameters under monotonic loads   Table B. 8 Nail Configuration 1 – performance parameters under reversed-cyclic loads   LCF: low cycle fatigue Ppeak Pu Δpeak Δu K0 Pyield Δyield(N) (N) (mm) (mm) (N/mm) (N) (mm)C7-1 1374.65 1099.72 9.31 13.03 1434.54 1100.26 0.77 16.99 POC7-2 1429.06 1143.25 8.10 15.40 2014.16 1195.10 0.59 25.95 POC7-3 1307.28 1045.82 11.20 19.67 909.95 1104.34 1.21 16.21 PTC7-4 1279.94 1023.95 11.99 19.43 1349.18 1058.18 0.78 24.78 PTC7-5 1346.29 1077.03 11.50 20.93 1730.16 1138.63 0.66 31.81 PTC7-6 1626.45 1301.16 12.08 18.88 1037.53 1336.59 1.29 14.65 PTC7-7 1105.96 884.77 12.20 17.07 930.84 901.91 0.97 17.62 PTC7-8 1307.21 1045.77 7.57 13.63 1476.73 1113.06 0.75 18.08 POC7-9 1309.00 1047.20 10.24 19.10 589.86 1096.90 1.86 10.27 POC7-10 1430.45 1144.36 8.89 14.82 1086.71 1194.77 1.10 13.48 POAverage 1351.63 1081.30 10.31 17.20 1255.97 1123.98 1.00 18.98Stdev 133.14 106.51 1.74 2.80 426.16 111.02 0.38 6.55CV 0.10 0.10 0.17 0.16 0.34 0.10 0.38 0.34Config 7Ductility Ratio Failure ModePpeak Pu Δpeak Δu K0 Pyield Δyield(N) (N) (mm) (mm) (N/mm) (N) (mm)C1-1 1144.00 982.00 6.99 12.16 2191.95 989.38 0.45 26.93 LCFC1-2 1254.00 1003.20 5.26 12.42 1626.71 1083.50 0.67 18.65 POC1-3 1201.50 961.20 9.34 11.40 1167.92 1006.80 0.86 13.23 POC1-4 1242.00 1036.50 10.54 17.39 1784.21 1071.42 0.60 28.96 LCFC1-5 1187.00 1003.50 5.08 12.28 1938.90 1042.50 0.54 22.85 LCFC1-6 1167.50 934.00 6.85 14.22 1213.26 1009.50 0.83 17.09 POC1-7 1070.00 959.00 5.25 12.00 1017.48 956.05 0.94 12.77 LCFC1-8 1129.50 1001.00 5.15 12.20 1762.56 993.48 0.56 21.64 LCFC1-9 1208.50 966.80 7.00 13.16 645.55 1057.96 1.64 8.03 LCFC1-10 1278.50 1104.00 6.90 12.06 1138.61 1101.35 0.97 12.47 LCFAverage 1188.25 995.12 6.84 12.93 1448.71 1031.19 0.81 18.26Stdev 63.04 48.19 1.86 1.74 482.69 47.15 0.34 6.81CV 0.05 0.05 0.27 0.13 0.33 0.05 0.43 0.37Config 1Ductility Ratio Failure Mode203  Table B. 9 Nail Configuration 2 – performance parameters under reversed-cyclic loads    Table B. 10 Nail Configuration 3 – performance parameters under reversed-cyclic loads   Ppeak Pu Δpeak Δu K0 Pyield Δyield(N) (N) (mm) (mm) (N/mm) (N) (mm)C2-1 896.00 716.80 7.34 11.77 830.96 761.48 0.92 12.84 POC2-2 1459.00 1167.20 7.29 15.43 1931.98 1253.23 0.65 23.79 LCFC2-3 1441.50 863.00 11.63 17.79 1423.04 1161.85 0.82 21.79 LCFC2-4 1500.00 1200.00 7.28 14.54 1679.00 1290.08 0.77 18.93 LCFC2-5 1273.00 1018.40 5.23 10.72 1767.50 1073.68 0.61 17.64 LCFC2-6 1271.50 1017.20 7.34 11.81 1413.47 1067.37 0.76 15.63 LCFC2-7 799.50 639.60 7.46 15.20 741.13 679.69 0.92 16.58 PTC2-8 1291.50 1033.20 7.40 14.00 1334.11 1093.21 0.82 17.08 LCFC2-9 1116.00 892.80 5.32 12.03 1333.58 956.27 0.72 16.78 PTC2-10 1341.50 1073.20 7.50 12.97 966.65 1123.56 1.16 11.16 LCFAverage 1238.95 962.14 7.38 13.63 1342.14 1046.04 0.81 17.22Stdev 235.45 182.90 1.73 2.17 396.88 196.81 0.16 3.74CV 0.19 0.19 0.23 0.16 0.30 0.19 0.20 0.22Config 2Ductility Ratio Failure ModePpeak Pu Δpeak Δu K0 Pyield Δyield(N) (N) (mm) (mm) (N/mm) (N) (mm)C3-1 1142.00 913.60 9.62 10.78 2265.28 919.84 0.41 26.55 POC3-2 1150.50 920.40 10.41 17.32 1706.70 953.52 0.56 31.01 LCFC3-3 1055.00 844.00 10.14 13.00 2238.35 861.17 0.38 33.79 POC3-4 945.50 756.40 6.34 14.04 1559.12 805.36 0.52 27.19 PTC3-5 1179.50 943.60 10.75 14.12 1808.65 976.37 0.54 26.16 LCFC3-6 755.50 604.40 9.45 15.14 4090.73 643.98 0.16 96.15 POC3-7 1271.50 1017.20 6.35 13.65 2532.79 1086.82 0.43 31.80 LCFC3-8 1340.00 1072.00 9.50 14.00 2962.27 1096.46 0.37 37.81 LCFC3-9 1051.00 840.80 10.77 14.30 1908.18 875.27 0.46 31.17 LCFC3-10 828.50 662.80 6.25 9.36 1767.70 701.16 0.40 23.59 POAverage 1071.90 857.52 8.96 13.57 2283.98 892.00 0.42 36.52Stdev 185.72 148.58 1.89 2.20 766.02 148.36 0.11 21.36CV 0.17 0.17 0.21 0.16 0.34 0.17 0.27 0.58Config 3Ductility Ratio Failure Mode204  Table B. 11 Nail Configuration 4 – performance parameters under reversed-cyclic loads    Table B. 12 Nail Configuration 5 – performance parameters under reversed-cyclic loads   Ppeak Pu Δpeak Δu K0 Pyield Δyield(N) (N) (mm) (mm) (N/mm) (N) (mm)C4-1 848.00 678.40 16.79 21.11 1262.23 715.05 0.57 37.27 POC4-2 575.50 460.40 9.51 12.46 518.17 484.61 0.94 13.32 POC4-3 684.00 547.20 9.20 12.00 312.11 567.48 1.82 6.60 POC4-4 579.00 463.20 9.49 13.30 5184.92 488.17 0.09 141.24 POC4-5 812.00 247.50 13.72 23.93 3314.29 607.24 0.18 130.61 POC4-6 969.50 775.60 14.73 19.17 1527.26 819.66 0.54 35.72 POC4-7 1022.50 818.00 6.42 18.58 1972.63 886.41 0.45 41.35 POC4-8 852.50 682.00 16.34 20.59 1979.22 715.25 0.36 56.98 POC4-9 854.50 685.00 8.89 20.56 1348.64 728.62 0.54 38.05 POC4-10 957.50 766.00 16.45 21.99 2798.51 806.46 0.29 76.31 POAverage 815.50 612.33 12.15 18.37 2021.80 681.90 0.58 57.75Stdev 156.88 179.42 3.84 4.26 1443.07 139.77 0.50 45.68CV 0.19 0.29 0.32 0.23 0.71 0.20 0.86 0.79Config 4Ductility Ratio Failure ModePpeak Pu Δpeak Δu K0 Pyield Δyield(N) (N) (mm) (mm) (N/mm) (N) (mm)C5-1 1070.00 856.00 11.75 15.51 2981.75 900.98 0.30 51.31 POC5-2 1283.50 1026.80 7.36 15.21 2117.82 1093.81 0.52 29.45 LCFC5-3 1136.00 908.80 7.64 16.49 4049.74 979.68 0.24 68.16 POC5-4 861.50 689.20 7.52 12.57 2240.44 738.21 0.33 38.14 POC5-5 740.00 592.00 5.75 13.53 1667.63 643.48 0.39 35.05 POC5-6 917.00 733.60 5.72 11.77 2457.74 783.99 0.32 36.91 PTC5-7 1010.00 808.00 7.45 16.36 1658.45 868.73 0.52 31.22 PTC5-8 998.00 798.40 11.35 16.27 1438.76 835.73 0.58 28.01 POC5-9 1069.50 855.60 12.28 16.20 1865.06 902.60 0.48 33.48 LCFC5-10 822.00 657.60 7.58 13.56 2372.94 707.00 0.30 45.50 POAverage 990.75 792.60 8.44 14.75 2285.03 845.42 0.40 39.72Stdev 160.97 128.78 2.43 1.74 769.81 134.13 0.12 12.30CV 0.16 0.16 0.29 0.12 0.34 0.16 0.30 0.31Config 5Ductility Ratio Failure Mode205  Table B. 13 Nail Configuration 6 – performance parameters under reversed-cyclic loads    Table B. 14 Nail Configuration 7 – performance parameters under reversed-cyclic loads   Ppeak Pu Δpeak Δu K0 Pyield Δyield(N) (N) (mm) (mm) (N/mm) (N) (mm)C6-1 1328.00 1062.40 10.13 14.55 2743.85 1121.30 0.41 35.62 LCFC6-2 1333.00 1066.40 11.25 15.40 1435.37 1108.22 0.77 19.95 LCFC6-3 845.00 676.00 4.44 9.15 1123.99 730.29 0.65 14.08 POC6-4 1336.50 1069.20 9.05 14.46 1813.39 1121.99 0.62 23.37 LCFC6-5 1071.00 856.80 6.46 11.57 1431.42 916.28 0.64 18.07 LCFC6-6 1317.00 1053.60 9.46 15.52 1530.48 1112.82 0.73 21.34 POC6-7 997.50 798.00 4.80 11.16 1406.77 861.56 0.61 18.23 POC6-8 1102.50 882.00 4.79 12.78 1609.96 955.43 0.59 21.53 LCFC6-9 1393.00 1114.40 6.39 11.50 2421.38 1192.08 0.49 23.36 POC6-10 991.50 793.20 4.78 13.89 1949.84 857.75 0.44 31.58 LCFAverage 1171.50 937.20 7.16 13.00 1746.65 997.77 0.60 22.71Stdev 192.11 153.69 2.58 2.11 501.15 153.49 0.12 6.44CV 0.16 0.16 0.36 0.16 0.29 0.15 0.20 0.28Config 6Ductility Ratio Failure ModePpeak Pu Δpeak Δu K0 Pyield Δyield(N) (N) (mm) (mm) (N/mm) (N) (mm)C7-1 963.50 770.80 5.77 11.19 2453.81 828.84 0.34 33.14 POC7-2 987.00 789.60 11.18 15.70 2712.70 832.88 0.31 51.14 LCFC7-3 1056.50 845.20 6.46 10.98 1172.67 898.98 0.77 14.32 POC7-4 1101.00 880.80 9.20 12.09 2093.00 900.26 0.43 28.11 POC7-5 1270.00 1186.50 6.42 11.22 2499.32 1122.74 0.45 24.97 LCFC7-6 1065.00 852.00 8.94 12.14 5282.60 899.45 0.17 71.32 POC7-7 1222.00 977.60 10.15 14.95 1719.71 1040.24 0.60 24.71 POC7-8 1140.00 912.00 6.25 12.43 3047.93 978.81 0.32 38.71 LCFC7-9 1213.00 970.40 9.40 12.07 2234.32 1002.49 0.45 26.90 POC7-10 1197.50 958.00 4.73 12.24 2435.26 1037.27 0.43 28.74 LCFAverage 1121.55 914.29 7.85 12.50 2565.13 954.20 0.43 34.21Stdev 104.10 119.76 2.17 1.58 1088.28 97.20 0.17 16.25CV 0.09 0.13 0.28 0.13 0.42 0.10 0.39 0.48Config 7Ductility Ratio Failure Mode206  Table B. 15 Performance parameters of edge-driven hold-down specimens   CS: column split   Table B. 16 Performance parameters of face-driven hold-down specimens  CDF: column moment failure   Ppeak Pu Δpeak Δu K0 Pyield Δyield(kN) (kN) (mm) (mm) (kN/mm) (kN) (mm)EDGE1 33.00 26.40 7.57 9.23 5.89 29.31 4.97 1.86 CSEDGE2 37.54 30.03 9.20 10.72 6.08 31.12 5.12 2.09 CSEDGE3 34.32 27.45 7.08 8.72 6.27 30.41 4.85 1.80 CSEDGE4 28.21 22.56 6.32 8.78 11.40 23.70 2.08 4.23 CSEDGE5 31.43 25.15 5.86 7.26 11.41 25.66 2.25 3.23 CSEDGE6 34.93 27.95 5.51 6.32 12.32 28.26 2.29 2.75 CSEDGE7 36.78 29.42 7.24 8.79 13.43 29.70 2.21 3.97 CSEDGE8 37.64 30.11 5.54 6.89 13.73 31.13 2.27 3.04 CSAverage 34.23 27.38 6.79 8.34 10.07 28.66 3.26 2.87Stdev 3.28 2.62 1.25 1.43 3.40 2.69 1.43 0.93CV 0.10 0.10 0.18 0.17 0.34 0.09 0.44 0.32Ductility Ratio SpecimenFailure ModePpeak Pu Δpeak Δu K0 Pyield Δyield(kN) (kN) (mm) (mm) (kN/mm) (kN) (mm)FACE1 39.87 39.87 8.04 8.04 6.82 32.37 4.74 1.69 CDFFACE2 49.15 49.15 9.61 9.61 7.35 41.09 5.59 1.72 CDFFACE3 41.59 41.59 8.28 8.28 5.42 40.09 7.40 1.12 CDFFACE4 48.36 38.69 9.41 9.60 5.93 45.71 7.71 1.24 CDFFACE5 44.67 44.67 7.48 7.48 9.28 35.27 3.80 1.97 CDFFACE6 45.04 45.03 9.59 9.59 7.83 35.49 4.53 2.12 CDFFACE7 45.94 45.94 9.45 9.45 9.35 34.50 3.69 2.56 CDFFACE8 49.29 49.29 9.79 9.79 10.23 38.21 3.73 2.62 CDFAverage 45.49 44.28 8.96 8.98 7.78 37.84 5.15 1.88Stdev 3.46 3.97 0.88 0.90 1.73 4.32 1.62 0.55CV 0.08 0.09 0.10 0.10 0.22 0.11 0.31 0.29Ductility Ratio SpecimenFailure Mode207  Appendix C Monotonic and reversed-cyclic nail connection test curves  Figure C. 1 The monotonic and reversed-cyclic test curves of C1  Figure C. 2 The monotonic and reversed-cyclic test curves of C2 208   Figure C. 3 The monotonic and reversed-cyclic test curves of C3   Figure C. 4 The monotonic and reversed-cyclic test curves of C4 209   Figure C. 5 The monotonic and reversed-cyclic test curves of C5   Figure C. 6 The monotonic and reversed-cyclic test curves of C6 210   Figure C. 7 The monotonic and reversed-cyclic test curves of C7   211  Appendix D Reversed-cyclic load test curves  Figure D. 1 Reversed-cyclic test curves of DWALL_EDGE, trial #1  Figure D. 2 Reversed-cyclic test curves of DWALL_EDGE, trial #2 212   Figure D. 3 Reversed-cyclic test curves of DWALL_FACE, trial #1   Figure D. 4 Reversed-cyclic test curves of DWALL_FACE, trial #2  213   Figure D. 5 Reversed-cyclic test curves of 9mm_SWALL_EDGE, trial #1   Figure D. 6 Reversed-cyclic test curves of 9mm_SWALL_EDGE, trial #2 214  Figure D. 7 Reversed-cyclic test curves of 9mm_SWALL_FACE, trial #1   Figure D. 8 Reversed-cyclic test curves of 9mm_SWALL_FACE, trial #2 215   Figure D. 9 Reversed-cyclic test curves of 11mm_SWALL_EDGE, trial #1   Figure D. 10 Reversed-cyclic test curves of 11mm_SWALL_EDGE, trial #2 216   Figure D. 11 Reversed-cyclic test curves of 11mm_SWALL_FACE, trial #1   Figure D. 12 Reversed-cyclic test curves of 11mm_SWALL_FACE, trial #2 

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