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Timber moment connections using glued-in steel rods Oh, Jiyoon 2016

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TIMBER MOMENT CONNECTIONS USING GLUED-IN STEEL RODS by  Jiyoon Oh  B.Eng., McGill University, 2012  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Civil Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  April 2016  © Jiyoon Oh, 2016 ii Abstract The experimental study completed in this thesis focused on timber-steel hybrid moment connections using d=12.7mm diameter mild steel threaded rods glued into Douglas-Fir glulam with polyurethane based adhesive. Two phases of experiments were conducted: the first to determine the minimum design parameter values that result in a ductile tensile failure of the glued-in steel rod, instead of a brittle timber or pull-out failure; and the second, to determine a relationship between the different design parameters and the moment capacity of the connection.  The work established that the moment connection fails in a ductile manner due to rod yielding and plasticizing, when the shear force induced into the system was less than 25% of the maximum axial capacity of the steel rods. Then, ductile failure occurred even when the edge distances of the steel rods were below the recommendation of a minimum 2.5d to prevent splitting of the wood. Rod pull-out failure was prevented by having a glued-in embedment length of the rods equal to or greater than 15d. In addition, ductility and equivalent viscous damping ratio were found to decrease as the moment capacity of the connection increased. The theoretical yield moment was calculated based on the assumption that the compression and tension members are timber and steel, respectively, and by applying the concept that plane-sections remain plane and the traditional elastic transform theory. The experimentally determined yield moments were established to be a close match. The results of the research provide guidance to practicing engineers to design moment connections with glued-in steel rods.  iii Preface This thesis is the original, unpublished and independent work by the author, Jiyoon Oh, under the supervision of Dr. Thomas Tannert.   iv Table of Contents Abstract .......................................................................................................................................... ii Preface ........................................................................................................................................... iii Table of Contents ......................................................................................................................... iv List of Tables ............................................................................................................................... vii List of Figures ............................................................................................................................. viii Acknowledgements ...................................................................................................................... xi Dedication .................................................................................................................................... xii Chapter 1: Introduction ................................................................................................................1 1.1 Background ..................................................................................................................... 1 1.2 Research Need ................................................................................................................ 2 1.3 Objectives ....................................................................................................................... 2 Chapter 2: State of the Art ............................................................................................................3 2.1 Timber Connections with Glued-in Rods ....................................................................... 3 2.1.1 General Overview ....................................................................................................... 3 2.1.2 Recommendations for Preventing Wood Splitting and Group Tear-out .................... 5 2.1.3 Recommendations for Preventing Shearing along Glue Line and Pull-out ................ 6 2.1.4 Recommendations for Shear Concentration at the End of Glued-in Rods ................. 7 2.1.5 Additional Measures to Ensure Ductile Failure .......................................................... 9 2.2 Timber Moment Connections ......................................................................................... 9 2.2.1 Overview ..................................................................................................................... 9 2.2.2 Timber Moment Frame Connections with Glued-In Steel Rods .............................. 10 2.2.3 Moment Resistance of Connections using Glued-in Steel Rods .............................. 12 v 2.2.4 Design of Timber Glued-in Steel Rods Moment Frame ........................................... 13 Chapter 3: Experimental Investigations ....................................................................................15 3.1 Overview ....................................................................................................................... 15 3.2 Materials ....................................................................................................................... 15 3.2.1 Timber ....................................................................................................................... 16 3.2.2 Steel........................................................................................................................... 17 3.2.3 Adhesive ................................................................................................................... 17 3.3 Specimen Descriptions.................................................................................................. 18 3.3.1 Phase 1 ...................................................................................................................... 18 3.3.2 Phase 2 ...................................................................................................................... 21 3.4 Manufacturing ............................................................................................................... 24 3.5 Test Setup...................................................................................................................... 26 3.6 Loading Protocol ........................................................................................................... 29 3.7 Phase 1 Results ............................................................................................................. 31 3.8 Phase 1 Discussion ........................................................................................................ 33 3.9 Phase 2 Results ............................................................................................................. 39 3.9.1 Monotonic Testing .................................................................................................... 39 3.9.2 Results of Cyclic Testing .......................................................................................... 55 3.10 Phase 2 Discussions ...................................................................................................... 61 3.10.1 Monotonic Testing .................................................................................................... 61 3.10.2 Quasi-Static Cyclic Testing ...................................................................................... 63 Chapter 4: Conclusions ...............................................................................................................68 References .....................................................................................................................................71 vi Appendices ....................................................................................................................................76 Appendix A Calculation of Theoretical Yield Moment Capacity ............................................ 76 Appendix B Moment-Rotation Curves under Monotonic Loading .......................................... 78 Appendix C Moment-Rotation Curves under Quasi-Static Cyclic Loading ............................ 86  vii List of Tables Table 3.1: Specified Strengths and Modulus of Elasticity for D.Fir 20f-E Glulam (CSA O86-14)....................................................................................................................................................... 16 Table 3.2: Phase 1 Specimen Layout and Parameter Variation .................................................... 19 Table 3.3: Phase 2 Specimen Layout ............................................................................................ 22 Table 3.4: Equipment Specifications ............................................................................................ 28 Table 3.5: Summary of Phase 1 Monotonic Testing..................................................................... 32 Table 3.6: Summary of Phase 1 Quasi-Static Cyclic Testing ....................................................... 33 Table 3.7: Shear Force Relative to Maximum Pure Shear Capacity for 500mm Long Specimens....................................................................................................................................................... 34 Table 3.8: Shear Force Relative to Maximum Pure Shear Capacity for 1000mm Long Specimens....................................................................................................................................................... 37 Table 3.9: Phase 2 Monotonic Testing Results ............................................................................. 41 Table 3.10: Summary of (a)-type Specimen Analysis under Monotonic Loading ....................... 51 Table 3.11: Summary of (b)-type Specimen Analysis under Monotonic Loading ....................... 53 Table 3.12: Phase 2 Cyclic Testing Results .................................................................................. 57 Table 3.13: Summary of Energy Dissipation ................................................................................ 60  viii List of Figures Figure 2.1 Edge Distance and Rod Spacing from Multiple Standards (Tlustochowicz et al., 2011)......................................................................................................................................................... 5 Figure 2.2: Recommended Transitional Area, Ac (Batchelar, 2007) .............................................. 8 Figure 2.3 Three Common Glued-In Steel Moment Joints (Fragiacomo & Batchelar, 2012) ..... 10 Figure 2.4 Example of Configuration C (Andreolli et al., 2011) .................................................. 11 Figure 2.5 Additional Glued-In Steel Plate for Shear Reinforcement (Andreolli et al., 2011) .... 12 Figure 2.6 Concepts Assumed to Calculate Moment Resistance (Fragiacomo & Batchelar, 2012)....................................................................................................................................................... 13 Figure 3.1: Layout of Phase 1 (a) U1 & U2, (b) U3, R3, U5 & R5, (c) U4, R4, U6 & R6 .......... 18 Figure 3.2: Reinforced (a) SE-R3&R5 and (b) SE-R4&R6 Specimens ....................................... 20 Figure 3.3: Layout of Phase 2 (a) A1, (b) B2, (c) C3, (d) D2, and (e) D4 Specimens ................. 22 Figure 3.4: Self-tapping Screw for Stabilization .......................................................................... 23 Figure 3.5: Phase 2 Double Ended Specimens ............................................................................. 24 Figure 3.6: Gluing and Centering of Rods .................................................................................... 26 Figure 3.7: Overview of Test Setup (Plan View) ......................................................................... 27 Figure 3.8: Test Specimen Attached: (a) to Base Plate, (b) to Load Cell ..................................... 28 Figure 3.9: Experimental Set-Up .................................................................................................. 28 Figure 3.10: (a) LVDT Placement and (b) String Pod Placement ................................................ 29 Figure 3.11: CUREE Deformation Controlled Quasi-Static Cyclic Loading History .................. 30 Figure 3.12: Gap between Load Transfer Plate and Clamping Plate ............................................ 31 Figure 3.13: Shear Failure of 500mm Long Specimens (a), (b), (d) & (e) Wood - Splitting, (c) Steel – Shear ................................................................................................................................. 35 ix Figure 3.14: Uniaxial and Shear Interaction based on Von Mises Yield Criteria ........................ 36 Figure 3.15: Moment-Rotational Plot of Monotonic Loading of 1000mm Specimens ................ 37 Figure 3.16: Hysteresis of LE-U1-1m .......................................................................................... 38 Figure 3.17: Hysteresis of LE-U2-1m .......................................................................................... 38 Figure 3.18: Reinforced Specimen Failure ................................................................................... 39 Figure 3.19: Bending of Steel Plate (Clamp) while Testing D4(a)-1 (1)...................................... 40 Figure 3.20: Ductile Failure of (a) A1(a), (b) B2(a), (c) C3(a), (d) D2(a), and (e) D4(a) Specimens under Monotonic Loading .......................................................................................... 43 Figure 3.21: Brittle Splitting Failure of (a) B2(a)-1 (2) and (b) D2(a)-1(2) under Monotonic Loading ......................................................................................................................................... 44 Figure 3.22: Moment-Rotation Curve of A1(a) Specimens.......................................................... 45 Figure 3.23: Moment-Rotation Curve of B2(a) Specimens .......................................................... 45 Figure 3.24: Moment-Rotation Curve of C3(a) Specimens .......................................................... 46 Figure 3.25: Moment-Rotation Curve of D2(a) Specimens.......................................................... 46 Figure 3.26: Moment-Rotation Curve of D4(a) Specimens.......................................................... 47 Figure 3.27: Moment-Rotation Curve of A1(a)-1 (1) ................................................................... 48 Figure 3.28: Moment-Rotation Curve of B2(a)-1 (3) ................................................................... 49 Figure 3.29: Moment-Rotation Curve of C3(a)-2 (3) ................................................................... 49 Figure 3.30: Moment-Rotation Curve of D2(a)-1 (1) ................................................................... 50 Figure 3.31: Moment-Rotation Curve of D4(a)-1 (2) ................................................................... 50 Figure 3.32: Brittle Pull-out Failures of (a) A1(b), (b) C3(b), (c) D2(b) Specimens ................... 52 Figure 3.33: Moment-Rotation Curve of A1(b) Specimens ......................................................... 54 Figure 3.34: Moment-Rotation Curve of C3(b) Specimens.......................................................... 54 x Figure 3.35: Moment-Rotation Curve of D2(b) Specimens ......................................................... 55 Figure 3.36: Ductile Failure of (a) A1(a), (b) B2(a), (c) C3(a), (d) D2(a) and (e) D4(a) Specimens Under Quasi-Static Cyclic Loading .............................................................................................. 58 Figure 3.37: Equivalent Viscous Damping Ratio for One Cycle (Piazza et al., 2011) ................. 59 Figure 3.38: Comparison of Experimental and Theoretical Yield Point ...................................... 62 Figure 3.39: Moment-Rotation Curve of A1(a)-2 (2) ................................................................... 65 Figure 3.40: Moment Rotation Curve of B2(a)-2 (3) ................................................................... 66 Figure 3.41: Moment-Rotation Curve of C3(a)-1 (1) ................................................................... 66 Figure 3.42: Moment-Rotation Curve of D2(a)-2 (1) ................................................................... 67 Figure 3.43: Moment-Rotation Curve of D4(a)-2 (3) ................................................................... 67  xi Acknowledgements I owe my endless gratitude to all my teachers and professors throughout my past, who have inspired and motivated me. I owe special thanks to Dr. Thomas Tannert, my supervisor, for his support and guidance throughout this study. Without him, this research project would not have been possible. I thank Thomas Leung, the industry partner on this project, for not only his extensive expertise but also for his boundless encouragement and support; as well as, Western Archrib and Purbond® for their generous contribution of glulam timber beams and CR-421® adhesives, respectively. I would also like to acknowledge the hard work and dedication from the technicians at Structures and Wood Mechanic laboratories who made the fabrication and experimentation of the glued-in steel rod timber moment connections possible. A special thanks to David Roberts and John Wong at the Structures laboratory, George Lee at the Wood Mechanic laboratory, and Lawrence Gunther and Joern Dettmer at the Centre for Advanced Wood Processing. To my fellow classmates and friends, who have kept me sane through reports, midterms and finals, I owe you my sanity. Finally, boundless gratitude is owed to my family for their undying support and encouragement for not only my education, but for everything I do.  xii Dedication    To my parents, for their endless sacrifice and support.  1 Chapter 1: Introduction 1.1 Background Wood is a renewable resource that is able to sequester greenhouse gases. In addition, timber structures do not only cut down the carbon footprint of buildings, but are also aesthetically pleasing and have the ability to create a healthy, nurturing atmosphere (Government of Canada, 2015). However, there are several challenges when using wood as structural material, such as its combustibility. The British Columbia Building Code (2012) limits construction of combustible material to 6 storeys, which was a significant development from its previous limit of 4 storeys. Another challenge for using wood is when it is loaded in tension perpendicular to the grain or shear parallel to the grain. Under those conditions, wood is a brittle material with very low post-elastic deformation capacity. Furthermore, due to wood being a natural material, unlike concrete and steel, its defects, such as knots, and its lack of homogeneity cause the material to exhibit large variability in its properties (Andreolli et al., 2011). However, even with the challenges of wood as a structural material, due to the aforementioned advantages and its high strength-to-weight ratio of wood (Gilbert et al., 2015), the demand and desire for taller wood structures is increasing around the world, even in high seismic areas, such as British Columbia.  For a high seismic area, ductility, which is the ability for plastic deformation without sudden brittle failure, is a key design factor. In order to achieve a ductile behavior for timber structures, the joints of the structure have to be designed to be the ductile and energy dissipative component while the main wood members remain in their elastic range (Andreolli et al., 2011). One popular method to achieve the desirable ductile behavior in the joints of timber structures is to create a hybrid connection using timber and steel such as glued-in steel rods. For a glued-in steel rod 2 timber connection to provide the desired ductility and energy dissipating mechanism, it is crucial that the steel yields, plasticizes and fails without premature failure elsewhere. Also for non-seismic design, it is often more favourable to have the failing mechanism as the yielding of the steel, as steel properties are more predictable and consistent than wood properties.  1.2 Research Need As the storey limits for wood frame structures increase, more efficient lateral force resisting systems are required, such as moment frames. It is desirable to have a ductile moment frame to ensure that there is yielding of the members to dissipate energy and to give sufficient amount of warning before the system fails. Timber moment frames using connections with glued-in steel rods have a great potential for becoming a practical, reliable lateral force resisting system. Considerable research has been done in regards to axially loaded glued-in steel rods within timber to determine methods to predict the behavior of the system, such as work done by Blass and Laskewitz (1999) and del Senno et al. (2004). However, there has been little research done with the glued-in steel rods as moment connections and further research is required to better understand the performance of such components. 1.3 Objectives The main objectives of this research is: to determine the requirements that will ensure ductile yielding of the 12.7mm diameter steel rods as the governing failure instead of a sudden brittle failure of the timber; and to determine the impact of different parameters, such as number of glued-in rod, edge/rod spacing and embedment length, on the moment capacity of the connection. Two phase experimental testing is completed in order to fulfill the objectives of this research.  3 Chapter 2: State of the Art 2.1 Timber Connections with Glued-in Rods 2.1.1 General Overview Experimental research and theoretical studies of connections consisting of steel rods glued into timber members began in the 1980’s. The studies began in pursue of general criteria and design guidelines for these connections and the investigation is still ongoing today (Otero Chans et al., 2010). These connections have become a heavily researched topic due to their many advantages, such as its high strength and stiffness properties, efficient transfer load mechanism and being a light weight solution for both existing and new structures (Tlustochowicz et al., 2011). In addition, having the steel-rods encased into the timber member, the connection is not only aesthetically pleasing, but the steel rods are protected from fire (Madhoushi & Ansell, 2008) and corrosion by the surrounding timber (Gattesco et al., 2010). In fact only 20mm of timber layer is required to covering the steel rods for each 30min of fire resistance (Kangas, 2000).  Individually, the properties, such as stiffness and strength, and the behaviour of timber, steel and adhesives under loading are well known and can be predicted; however, combining these three materials to create a hybrid connection, such as a glued-in steel rod timber connection, produces a complex system for which the behaviour is difficult to predict (Tlustochowicz et al., 2011). As a consequence, even with all the research put into glued-in rods, no general consensus has been reached on a common standardization; thus these connections are commonly used in just a few places around the world, mostly European countries (Tlustochowicz et al., 2011).  4 Out of the materials that can be used for the glued-in rod, such as glass fibre reinforced polymer (GRFP), carbon fibre reinforced polymer (CFRP), hardwood and steel, the most commonly used material is steel due to its advantageous property of being a ductile material (Tlustochowicz et al., 2011). Steel rods that are threaded are more favourable due to the fact that the threads provide an increased area for adhesion and mechanical interlocking creating a stronger bond between the rods and the timber member. Additionally, the steel threads allow for easy assembly if the glued-in timber joint were to be connected to a steel member (Tlustochowicz et al., 2011).  Wood, when subjected to tensile and shear forces, is a brittle material with very low post-elastic deformation capacity (Andreolli et al., 2011). As a result, timber failures are abrupt, sudden failures that occur without any given warning, creating an undesirable failure mode. Timber connections with glued-in rods, however, can be designed in such a way that they exhibit a ductile failure mode as long as the steel rods provide sufficient yielding and plasticization prior to any premature brittle failures (Buchanan et al., 2001), such as: 1. Splitting of wood 2. Shear failure in the glue line 3. Rod pull-out 4. Group tear out (for multiple glued-in rods) 5. Tensile failure of timber at the end of the rod (Parida et al., 2013). Even though the research community has not come to a consensus on a design standardization of timber glued-in rod connections, through experimental results, recommendations have been put forth to prevent the brittle failure modes. 5 2.1.2 Recommendations for Preventing Wood Splitting and Group Tear-out Wood splitting and group tear-out for multiple glued-in rods are common brittle failures modes that are very susceptible to occur if the necessary precautions are not taken. To avoid these undesirable failure modes, minimum edge distances and rod spacing are suggested (Parida et al., 2013). There are many different suggestions between different sources; however, the most stringent recommendation are given by the German regulation (DIN 1052:2004-08) with an edge distance of two and a half times the rod diameter (2.5d) and bar spacing of 5d (Tlustochowicz et al., 2011). Figure 2.1 outlines the different recommendations from different standards on edge distance and rod spacing for rods glued-in parallel to the grain of the wood. Following these guidelines should prevent splitting or group tear-out within the wood before all other failures, i.e. prior to plasticization of the steel rods.  Figure 2.1 Edge Distance and Rod Spacing from Multiple Standards (Tlustochowicz et al., 2011) 6 An alternative measure to prevent splitting of the wood is to reinforce the member by either using screws perpendicular to the grain or by gluing plates of plywood, or other materials, onto the ends of the timber member (Jensen & Quenneville, 2009). Self-tapping screws, which are screws that do not require pre-drilling, are an effective way of strengthening timber in their two weakest strength properties: tension perpendicular to the grain and longitudinal shear strength (Lam et al., 2008).  Lam et al. (2008) conducted an experiment using self-tapping screws as reinforcement for the timber perpendicular to the grain for bolted glulam connections with slotted steel plates. It was found that while the unreinforced specimens failed in a brittle manner due to splitting of the wood under monotonic and cyclic loading, the reinforced connections saw no splitting in the timber and in fact the failure mode shifted from brittle failure to ductile failure. Additionally, the retrofitted specimens of the original damaged unreinforced specimens achieved some ductility as well, though not as much as the initial reinforced specimens. The ductility was limited due to the previous damage imposed on the specimens 2.1.3 Recommendations for Preventing Shearing along Glue Line and Pull-out To prevent rod pull-out failures and shear failure within the glue line, the glued-in rod connection should be designed in such a way that capacity of the pull-out/shear within the glue line strength should be greater than the capacity of all other failure modes. For threaded rods, the threads provide mechanical interlocking between the steel and the adhesive, thus shear failure between the steel-adhesive interface rarely occurs (Parida et al., 2013).   7 One way to ensure adequate capacity to prevent rod pull-out due to shear failure along the adhesive and timber interface is through sufficient embedment lengths (le) or ratio between embedment length and diameter of the rod (le/d) called the slender ratio. Unfortunately, experimental studies have found that the relationship between pull-out strength of rods and rod embedment length is a complex relationship and challenging to define (Tlustochowicz et al., 2011). Otero Chans et al. (2010) concluded that the pull-out capacity of the joint does increase with increased embedment length; however, at a certain embedment length, the increase in the capacity of the joint reduces significantly, indicating that the relationship between joint capacity and embedment length is not a linear one. Recent work by González (2015) showed that glued-in mild steel rods with diameter of 12.7mm yielded and had a ductile failure mode within the steel rod when the embedment length was greater than or equal to 10d. However, it was found that for 19mm diameter mild steel rods, an embedment length of 10d led to wood shear failure. Only when the embedment length was 20d, rod yielding occurred, but even then, it was observed that some specimens failed due to splitting of the wood. As it can be seen through experimental studies, estimating the pull-out strength of glued-in rod connections is not a straight forward linear calculation. 2.1.4 Recommendations for Shear Concentration at the End of Glued-in Rods  Stress concentrations occur in the presence of sudden changes in section properties and/or when the direction of the stress path is forced to change (Fragiacomo & Batchelar, 2012). As a result, the steel rods within the timber member produce a stress concentration at the transition cross-section where the steel embedment begins, which could lead to tensile rupture of the timber member creating a premature failure (Fragiacomo & Batchelar, 2012). To prevent this type of failure, Batchelar (2007) recommended locating the cross-sectional area of timber where the rod 8 forces are transferred, and limiting the tensile stress, at that transitional area, to the allowable timber tensile stress. Batchelar (2007) suggested the transitional areas (Ac) for different scenarios as illustrated in Figure 2.2:  Figure 2.2: Recommended Transitional Area, Ac (Batchelar, 2007)  1. Single glued-in rod: cross-section width of the timber (b) multiplied by two times the edge distance of the rod (e), Ac = b(2e).  2. Individual internal rods for multiple layers of glued-in rods: cross-section width of the timber (b) multiplied by the spacing between the rods (s), Ac = b(s).  3. Outer edge rods for multiple layers of glued-in rods: cross-section width of the timber member (b) multiplied by the summation of edge distance of the glued-in rod (e) and half the spacing between the glued-in rods (s/2), Ac = b(e+s/2). Furthermore, Tlustochowicz et al. (2011) suggested that the two elements being connected, the steel rod (Er and Ar) and timber member (Ew and Aw), have similar tensile stiffness (EwAw = ErAr) for a smooth load transfer. Tlustochowicz et al. (2011) further recommended using multiple smaller rods distributed equally across the timber member rather than utilizing one single large rod. For multiple tension rods, Batchelar (2007) stated that the tensile stresses within 9 the timber member can be restrained by differing the choice of rod diameters and the tensile strength of the rod. In addition, multiple tension rods can be designed with different embedment lengths, i.e. staggering the rod embedment depths, in order to prevent accumulation of stress concentration at one plane (Batchelar, 2007).  2.1.5 Additional Measures to Ensure Ductile Failure In addition to the previous recommendations, using mild steel rods with smaller diameter, as opposed to high strength steel rods with larger diameter, will favour yielding of the steel rods as the primary failure mode and necking down the steel rods will provide additional assurance of plasticization of the steel being the governing failure mode (Parida et al., 2013). Necking of the steel rod will also ensure that the yielding of the rod will occur at the reduced cross-section; thus enable the designer to control the location of the yielding/plasticization point as well. 2.2 Timber Moment Connections 2.2.1 Overview Moment frames as lateral force resisting systems are favoured over other conventional frame systems such as concentrically braced frames, crossed braced systems, or chevron brace frames because of their ability to provide an open, uninterrupted system (Metten, 2012). There are clauses in the Canadian steel (CSA S16-09 (2010)) and concrete (CSA A23.3-14 (2014)) material code, and the National Building Code of Canada (NBCC 2010) that allow for the design of moment frames in steel or concrete, but as of date, no conventional regulation or guidelines exist for moment frames constructed from timber. This is mainly due to the fact that ductility is required for moment frames, which cannot be achieved with timber members alone.   10 2.2.2 Timber Moment Frame Connections with Glued-In Steel Rods There are many ways that glued-in steel rods can be incorporated into timber joints to create a timber moment frame, but the three most simple and common configurations are: A. To have the steel rods through both the column and the beam where the rods are glued partly along the length, either only within the column or the beam;  B. To have the steel rods through and fully glued within both the column and the beam; C. To incorporate a steel hub and connecting it to the timber column and beam using glued-in steel rods (Fragiacomo & Batchelar, 2012).  The three configurations mentioned are shown in Figure 2.3.  Figure 2.3 Three Common Glued-In Steel Moment Joints (Fragiacomo & Batchelar, 2012)  In configuration A, the steel rods go through both the timber beam and the column, but glued only within the column or only within the beam. In configuration B, the steel rods go through and are glued to both the beam and column. Both these configurations create a joint where the steel rods are fully concealed; however, the joint has an overlapping zone, between the timber beam and column, where different loading directions in the timber from perpendicular to the grain to parallel to the grain occur (Fragiacomo & Batchelar, 2012). The overlapping zone creates a complex region due to the anisotropy nature of timber, which could lead to significant deformations and stress concentrations. Configuration C, on the other hand, where an isotropic 11 material is introduced at the location where timber beam to timber column overlap, eliminate the different loading direction of the timber, thus preventing complications that arise from loading timber in two different directions (Fragiacomo & Batchelar, 2012). The moment connections shown in Figure 2.3 can alternatively be arranged to have the column extended upwards to have the beam flush against the column (Fragiacomo & Batchelar, 2012).  A stub of steel sections, such as a T-section welded onto an end plate, can be used for Configuration C, as shown in Figure 2.4 (Andreolli et al., 2011). However, it should be noted that depending on the thickness and strength of the steel stub section and the glued-in steel rods, the failure mode can range from complete yielding and plasticization of only the flange of the steel stub, to combined yielding and plasticization of the steel stub flange and glued-in steel rods, to yielding and plasticization of only the glued-in steel rods (Andreolli et al., 2011).  Figure 2.4 Example of Configuration C (Andreolli et al., 2011) In addition to rods placed at the outer ends of the beam or column for moment resistance, steel plates or additional glued-in steel rods can be inserted at the center of the beam or column for shear resistance when the shear force is high (Andreolli et al., 2011; Buchanan et al., 2001). Figure 2.5 illustrates an example of how a steel plate can be incorporated into a glued-in steel rod moment connection with Configuration C. However, when the shear force is low and the lateral 12 force can be resisted by the glued-in steel rods utilized for moment resistance alone, then the additional shear resistance is not necessary (Andreolli et al., 2011).   Figure 2.5 Additional Glued-In Steel Plate for Shear Reinforcement (Andreolli et al., 2011) 2.2.3 Moment Resistance of Connections using Glued-in Steel Rods For any structural system, accurately predicting the capacity is a crucial part of the design process to ensure a safe, efficient force resisting system, whether it be for gravity or lateral design. The same goes for hybrid timber-steel moment frame systems utilizing glued-in steel rods in timber. Fragiacomo and Batchelar (2012) proposed a theoretical approach in designing timber moment connection joints using glued-in steel rods. The assumptions made were the concept that plane sections remain plane and the traditional elastic transform section theory, which predicts a linear stress distribution for the timber compression zone. The procedure outlined by Fragiacomo and Batchelar (2012), illustrated in Figure 2.6, is similar to the procedure used to calculate the moment resistance of reinforced concrete beams in CSA A23.3-14 (2014).  13  Figure 2.6 Concepts Assumed to Calculate Moment Resistance (Fragiacomo & Batchelar, 2012) It is assumed that the tensile force is transmitted purely through the steel rods and the compressive force is transmitted through the timber-timber interface. Thus similar to reinforced concrete sections, the tensile forces are resisted by the steel rods, whereas the compression forces are resisted by only the timber section under compression if the steel rods are not fully glued along the beam and the column, or by timber and steel rod under compression if the steel rods are fully glued along their length within the beam and column (Fragiacomo & Batchelar, 2012). With this in mind, the internal resistive tensile and compression couple forces can be found, along with the internal lever arm, to calculate the moment resistance of the connection. The ultimate stress of the steel should be used in calculating the moment resistance of the hybrid connection instead of yield stress in order to take strain hardening into consideration, which will result in a more accurate estimation of the capacity (Andreolli et al., 2011). 2.2.4 Design of Timber Glued-in Steel Rods Moment Frame The glued-in steel rod connection is recommended to be designed in such a way that the steel rods yield, plasticize and fail before the timber section reaches its full compressive capacity, similar to an under-reinforced concrete beam (Fragiacomo & Batchelar, 2012). This way, sudden brittle system failure will be prevented; and even if the ultimate failure of the “under-reinforced” 14 timber section was due to compression failure, the steel would develop plastic strains and give warning beforehand (Fragiacomo & Batchelar, 2012). Furthermore, the connection should be capacity designed to ensure that the timber member and interface stay within the elastic range, to prevent brittle failures and fully utilize the ductility of the steel (Gilbert et al., 2015). This means that using the ultimate strength of the steel rods, instead of the yield strength, will give a more accurate prediction of the capacity and failure mode of the joint. 15 Chapter 3: Experimental Investigations  3.1 Overview The experimental work carried out for this thesis was conducted at the Structures and Wood Mechanics laboratories of The University of British Columbia between May 2015 and November 2015. The experiments were divided into two phases: Phase 1 (preliminary testing) and Phase 2 (main testing). The objective of Phase 1 was to determine the minimum requirement of edge and rod spacing, embedment length and length of the glulam beam, which would ensure in ductile failure. The objective of Phase 2 was to design a ductile connection utilizing the results obtained from Phase 1 and to determine the relationship between the glued-in steel rod layouts and the moment capacity of the system.  3.2 Materials Glued-in steel rod timber moment connections are timber-steel hybrid connection that consists of three materials, timber, steel and adhesive, which could be varied; however, since the main goal of this research was to determine a method on designing and predicting the capacity of ductile glued-in steel rod connections by manipulating the location of the glued-in steel rods, the three component of the materials were kept constant. The timber beams utilized were Douglas-Fir 20f-E grade glue-laminated (glulam) wood. The steel rods used for this experiment were threaded mild grade 12.7mm diameter. Finally, the adhesive was CR-421®, a two component polyurethane (PUR) by Purbond®.  16 3.2.1 Timber The specimens for the experimental work of this thesis were fabricated using Douglas-Fir glulam of grade 20f-E of cross-section ranging from 80mm by 266mm to 130mm by 456mm. These are the typical cross-sections available in Canada for glulam beams and were selected in order to closely mimic what would be specified in practice. The specified strength for the glulam is summarized on Table 3.1 (CSA O86-14). The average apparent relative density of the glulam beams were determined to be 563kg/m3 with the minimum and maximum of 514kg/m3 and 609kg/m3, respectively, The average moisture content (MC) measured of these beams, directly before testing, for Phase 2, were 10.9% with the minimum and maximum MC of 9.3% and 12.7%, respectively.  Table 3.1: Specified Strengths and Modulus of Elasticity for D.Fir 20f-E Glulam (CSA O86-14) Specified Strength Capacity (MPa) fb,pos Bending Moment (pos.) 25.6 fb,neg Bending Moment (neg.) 19.2 fv Longitudinal Shear 2.0 fc Compression Parallel 30.2 fcb Compression Parallel Combined with Bending 30.2 fcp,com Compression Perpendicular (Comp. face bearing) 7.0 fcp,ten Compression Perpendicular (Ten. face bearing) 7.0 ftn Tension Net Section 20.4 ftg Tension Gross Section 15.3 ftp Tension Perpendicular to Grain 0.83 E Modulus of Elasticity 12400    17 3.2.2 Steel Threaded mild steel bars of diameter 12.7mm (1/2 inch), with an average yield capacity of 360MPa (σy,mean = 360MPa) were utilized for this thesis. In preceding work, Gonzalez (2015) experimentally confirmed the yield strength of the rods by testing five random samples following the ASTM F606M-14 procedure. The 12.7mm diameter steel rods were chosen, as opposed to the 19mm diameter rods, since it was found that the 12.7mm diameter steel rods were able to reach ductile tensile failure in the steel rods once adequate embedment length was provided, whereas the 19mm diameter rods exhibited pull-out failure even with embedment length of 20d. In addition, the threaded steel rods were selected because, as mentioned previously, the threaded aspect of the steel rods allow for mechanical interlocking between the steel and the adhesive providing additional shear resistance (Parida et al., 2013). 3.2.3 Adhesive A two component polyurethane (PUR) adhesive, CR-421®, provided by Purbon®, was used to glue the steel threaded rods into the timber. PUR based adhesives are commonly used in the field (Gonzalez, 2015), thus seemed to be an appropriate choice for this research since one of the goals was to investigate a feasible design and construction method that could be used in the engineering world. In addition, PUR has gap filling properties which epoxy glue, another common adhesive used on-site, does not possess (Gonzalez, 2015). The main properties of the adhesive utilized were: work time of 10 – 20 minutes, curing time of 7days, viscosity of 9000cps, expected shear strength (parallel to grain) of 7.8MPa, and tensile elongated at failure at 2% (brittle) (Lehringer, 2012) 18 3.3 Specimen Descriptions 3.3.1 Phase 1  The objective of phase 1 was to determine the parameters:  1. The edge (e) / rod (s) spacing,  2. Embedment length (le) and  3. Length of the wood beam (l) which are required to ensure a ductile failure within the glued-in steel rods. Two different cross sections of Douglas-Fir glulam beams were used for phase 1: 80mm by 266mm and 265mm by 266mm in lengths of 500mm and 1000mm. A total of 22 specimens were fabricated and subsequently tested under quasi-static monotonic and quasi-static revered cyclic loading. Other parameter variations were the edge distance (e) for the glued-in steel rods, embedment length (le), and the addition of perpendicular to grain reinforcements, to prevent splitting of the wood. Figure 3.1 and Table 3.2 summarizes the parameters for each specimen.  (a)  (b) (c) Figure 3.1: Layout of Phase 1 (a) U1 & U2, (b) U3, R3, U5 & R5, (c) U4, R4, U6 & R6  19 Table 3.2: Phase 1 Specimen Layout and Parameter Variation Label Base, b (mm) Height, h (mm) Length, l (mm) Edge Dist., e1(1) (mm) Edge Dist., e2(2) (mm) Rod Spac., s2(2) (mm) Embed. Length le (mm) Perp. Reinf.  Testing Mon Cyc SE-U1-1m 80 266 1000 20 40 0 191 (15d) No 1 0 LE-U1-1m 80 266 1000 45 40 0 191 (15d) No 1 1 SE-U2-1m 80 266 1000 20 40 0 254 (20d) No 1 0 LE-U2-1m 80 266 1000 45 40 0 254 (20d) No 1 1 SE-U1 80 266 500 20 40 0 191 (15d) No 1 0 LE-U1 80 266 500 45 40 0 191 (15d) No 1 0 SE-U2 80 266 500 20 40 0 254 (20d) No 1 0 LE-U2 80 266 500 45 40 0 254 (20d) No 1 0 SE-U3 265 266 500 20 132.5 0 191 (15d) No 1 0 SE-R3 265 266 500 20 132.5 0 191 (15d) Yes 1 0 LE-U3 265 266 500 45 132.5 0 191 (15d) No 1 0 SE-U4 265 266 500 20 45 175 191 (15d) No 1 0 SE-R4 265 266 500 20 45 175 191 (15d) Yes 1 0 LE-U4 265 266 500 45 45 175 191 (15d) No 1 0 SE-U5 265 266 500 20 132.5 0 254 (20d) No 1 0 SE-R5 265 266 500 20 132.5 0 254 (20d) Yes 1 0 LE-U5 265 266 500 45 132.5 0 254 (20d) No 1 0 SE-U6 265 266 500 20 45 175 254 (20d) No 1 0 SE-R6 265 266 500 20 45 175 254 (20d) Yes 1 0 LE-U6 265 266 500 45 45 175 254 (20d) No 1 0 (1) Denotes in the direction of loading (2) Denotes perpendicular to the direction of loading Edge distance, distance from the edge of the glulam beam to the center of the glued-in steel rods, were either 20mm, less than 2d, or 45mm, greater than 3d, and were given the initials SE (small edge distance) or LE (large edge distance), respectively. The SE specimens do not meet the minimum edge distance for glued-in rods recommended by most guidelines (2.5d), thus theoretically, they should fail due to splitting of the wood beam. The LE specimens with edge distance greater than 3d exceed the minimum recommended; thus splitting should not occur.  20 Since SE specimens were expected to have brittle wood splitting failure, the SE specimens with cross section of 265mm by 266mm were fabricated with and without perpendicular to the grain reinforcement to determine if the additional reinforcements could shift the failure mode from a brittle to a ductile one. The specimens with cross section of 80mm by 266mm could not be reinforced since the base dimension of 80mm did not provide adequate width for the required spacing of the reinforcements. The labels “U” and “R” were placed after “SE-” or “LE-” to indicated unreinforced and reinforced specimens, respectively. ASSY® VG cylinder head self-tapping screws, with length of 150mm and diameter of 8mm, were used as reinforcement. The screws were drilled into the glulam as close as possible to either side of the steel rods. They were placed 50mm from the edge and SE-R3 and SE-R5, with one steel rod on each side of the glulam, were fitted with an extra row of screws spaced at 50mm on center from the first row. Figure 3.2 illustrates the placement of the self-tapping screws.   (a)  (b) Figure 3.2: Reinforced (a) SE-R3&R5 and (b) SE-R4&R6 Specimens 21 It was also planned to retrofit tested and damaged unreinforced specimens to observe if the perpendicular to the grain reinforcement could enhance the capacity of the specimens. Unfortunately, none of the unreinforced specimens were retrofitted posterior to testing due to the fact that the failure mode was either shear of the rod or localized splitting of the wood around the glued-in steel rod that could not be retrofitted with self-tapping screws. Finally, two different embedment lengths were used for each layout: 15d and 20d. Based on preceding work by Gonzalez (2015), embeddment length of 15d, for 12.7mm diameter mild steel rod, should prevent brittle pull-out failure and favour ductile steel tensile failure; furthermore, increasing the embedment length past 15d should not lead to an increase of the pull-out strength. Specimens with 20d were designed to double check that this was the case.  3.3.2 Phase 2 Once the minimum edge distance of 2.5d and rod spacing of 5d were determined to ensure a ductile failure of the connections, for Phase 2, these parameter were set constant and different layouts were investigated with respect to the connection’s capacity. In addition, the embedment length of the glued-in steel rod was also varied to verify that an embedment length of less than 15d would produce brittle pull-out failure. Figure 3.3 and Table 3.3 summarizes the parameters for Phase 2. Four monotonic tests were done on all specimens except for D4(a), where only three monotonic tests were performed. Four quasi-static cyclic tests were done on specimens A1(a) and D2(a), and three quasi-static cyclic tests were performed on specimens B2(a), C3(a) and D4(a).    22 (a) (b) (c) (d) (e) Figure 3.3: Layout of Phase 2 (a) A1, (b) B2, (c) C3, (d) D2, and (e) D4 Specimens Table 3.3: Phase 2 Specimen Layout Label Base, b (mm) Height, h (mm) Length, l (mm) Edge Dist., e1(1) (mm) Rod Spac., s1(1) (mm) Edge Dist., e2(2) (mm) Rod Spac., s2(2) (mm) Embed. Length (mm) Testing Mon. Cyclic A1(a) 80 266 1400 33 0 40 0 203 (16d) 4 4 A1(b) 80 266 1400 33 0 40 0 102 (8d) 4 0 B2(a) 130 266 1400 33 0 33 64 203 (16d) 4 3 C3(a) 175 266 1400 33 0 23.5 64 203 (16d) 4 3 C3(b) 175 266 1400 33 0 23.5 64 102 (8d) 4 0 D2(a) 130 456 1400 33 0 33 64 203 (16d) 4 4 D2(b) 130 456 1400 33 0 33 64 102 (8d) 4 0 D4(a) 130 456 1400 33 64 33 64 203 (16d) 3 3 (1) Denotes in the direction of loading (2) Denotes perpendicular to the direction of loading  23 A different labeling system was used for Phase 2 since the edge distance was kept constant; specimens were labeled based on their timber cross section, number of rods and the embedment length of the glued-in steel rods. The first alphabetical letter used indicated the dimension of the specimen: “A” – 80mm by 266mm; “B” – 130mm by 266mm; “C” – 175mm by 266mm; “D” – 130mm by 456mm. The number following the alphabetical letter specified the number of rods under tension; thus was half the number of rods utilized in the system. Finally the specimen was indicated with “(a)” or “(b)” to designate embedment lengths of 16d and 8d, respectively.  Furthermore, in order to maximize the material usage, phase 2 specimens were fabricated with glued-in steel rods on both sides of the timber beam, as shown in Figure 3.5. This allowed one timber member to produce four test specimens for monotonic testing since conceptually the damage would only occur on the glued-in steel rods on the tension side, whereas the glued-in steel rods on the compression side would obtain no damage; thus the specimen could be flipped over and be tested again with the compression glued-in steel rods now on the tension side. Self-tapping screws were utilized to stabilize the specimen in place of the damaged glued-in steel rods, as show in Figure 3.4, for the second tests performed on each sides.   Figure 3.4: Self-tapping Screw for Stabilization 24 For quasi-static cyclic testing, having glued-in steel rods on both sides of the timber beam allowed two test specimens per timber member since all glued-in steel rods would at one point be in tension during the testing. As a consequence, the timber beams were cut to length of 1400mm in order to provide adequate length of the beam to ensure a ductile failure, while also accounting for a buffer zone where the other set of glued-in rods are located.  Figure 3.5: Phase 2 Double Ended Specimens 3.4 Manufacturing The manufacturing of the test species consisted of four stages. First, the glulam was cut to the desired length and the holes, according to the specified layout with the correct diameter and depth, were drilled. A CNC heavy timber processor (Hundegger® Robot Drive) was used to cut and drill all the timber specimens in order to obtain precision and increase efficiency. Precision of the location of the holes was crucial due to the limited tolerance provide by the base plate used for testing, which will be further discussed later. In order to account for glue line thickness of approximately 2mm, a 16mm drill bit was used to drill the holes for the 12.7mm diameter steel rods. The holes were drilled to the desired embedment length of 191mm (15d), 254mm (20d), 102mm (8d), and 203mm (16d). 25 Second, the threaded rods, which were available in 3ft lengths, were cut into the desired lengths using a rebar cutter. The rods were used in the condition provided by the supplier with no additional treatments, such as cleaning or coating them, to mimic a typical site condition. The rods were cut while being rotated to prevent the threads being damaged to allow the nuts to be screwed on; however, even with this precaution, some rods had to be re-threaded manually. In phase 1, the rods were cut to lengths of the embedment length with an additional 150mm for the washer and nuts to attach the rods to the end base plate. It was found that this length was excessive and much time was spend hand tightening the nuts with a wrench. Thus, for phase 2, the rods were cut with only 75mm additional length in order to use a bolt gun to screw on the nuts (and off), which saved time. Third, the rods were glued into the holes using a duel cartridge caulking gun to insert the adhesive. The two part PUR adhesive was filled to approximately three-quarters of the holes, then the rods were inserted into the hole in a twisting motion to minimize entrapped air. Overflow of PUR adhesive onto the surface of the wood specimen, as shown in Figure 3.6, indicated that sufficient adhesive was used to cover the entire length of the rod. Then, toothpicks were used to ensure the rods were centered and straight, and a level was used to double check the levelness of the rods. During phase 1, the hardened PUR adhesive due to the excess overflow of the glue onto the face of the specimen prevented the face of the glulam beam to be flush with the steel base plate. Theoretically this would shift the compression area, thus in turn the neutral axis from the initial predictions. As a result, for phase 2, it was ensured that the excess glue was chipped away to provide a flush timber to steel base plate connection to enable a correct comparison between the predicted and experimental results 26  Figure 3.6: Gluing and Centering of Rods Fourth and finally, after gluing was completed, the specimens were left to air-cure overnight then the following morning, were placed into constant temperature and humidity room of 20°C and 65%RH, respectively. In order to cure the adhesive up to minimum of 95% of their expected end bond strength, which occurred after 7 days of curing (Lehringer, 2012) none of the specimens were testing before 19 days after fabrication. 3.5 Test Setup  The general plan view of the test set up is illustrated in Figure 3.7. The base plate to provide a fixed connection was fabricated out of 25mm thick steel plate with holes drilled through to accommodate multiple rod layouts. Due to the different size of the beams used and different edge and spacing between rods, the drilled hole location of phase 1 base plate did not match the rod layouts of phase 2, in addition, a larger base plate was required; thus a new base plate had to be fabricated for phase 2. In order to account for imperfection in fabricating, 18mm diameter holes were drilled through the base plate to give a total of 5mm tolerance for the 12.7mm diameter steel rods. The 5mm tolerance provided was adequate for set-up without over compensating.  27  Figure 3.7: Overview of Test Setup (Plan View) The base plate was then bolted onto a steel reaction frame. The rods were slotted into the drilled through holes within the steel base plate then bolted on with a washer and two nuts, as shown in Figure 3.8(a), to provide a fixed connection. Two nuts were used because it was found that using just one was not adequate to withstand the tension forces and resulted in stripping the nuts off the rods. As one end of the specimen was fixed onto the base plate with nuts, the opposite end was fixed onto the loading cell by two plates, with depth of 100mm, clamping onto the specimen as depicted on Figure 3.8(b). The two plates were tightened and held in place by washers and nuts. Initially, steel plates were used as the clamps for the ease of wrenching the nuts on and off; however, the plates were found to be lacking in strength and started bending when the larger specimens were tested. As a result, C-channels, with a depth of 130mm, were used as the clamping plate instead to provide sufficient strength and stability. This was crucial especially for the quasi cyclic testing. The result of the experimental set-up was a fixed end connection of a beam, provided by the rod connection to the base plate, with a load applied perpendicular to the beam axis at the opposite end as shown in Figure 3.9. The actuator had a displacement capacity of ± 77.1mm (3inches) and a load capacity of ± 89kN. The specifications for the equipment used are summarized in Table 3.4.  28 Table 3.4: Equipment Specifications  Company Type Model Part Serial No. Actuator MTS SYSTEMS CORPORATION SERVORAM 202.01 - 273 Load Cell BALDWIN-LIMA-HAMILTON CORP. SR-4® Load Cell U-1 - 14380 LVDT novotechnik TRS-Series - - - String Pod Automation Products Group  DT-40-A 548001-4000 03-2821    (a) (b) Figure 3.8: Test Specimen Attached: (a) to Base Plate, (b) to Load Cell   Figure 3.9: Experimental Set-Up   29 Four linear variable differential transformers (LVDT), with specifications outlined in Table 3.4, were used to measure the displacement of the wood specimens from the steel base plate in the X and Y direction, on both sides of the beam, as illustrated in Figure 3.10(a). On the other end, a string pod was hooked onto the clamping plates for phase 1 and placed 1355mm away from the face of the steel base plate and screwed onto the timber beam for phase 2 to calculate the rotation of the specimens. The string pod is shown in Figure 3.10(b) and the specification of the string pod is summarized on Table 3.4. The load was measured with a calibrated load cell.  (a)  (b) Figure 3.10: (a) LVDT Placement and (b) String Pod Placement 3.6 Loading Protocol The specimens were tested under displacement controlled quasi-static monotonic and reversed cyclic loading. The actuator was powered by hydraulic pressure and controlled with MTS 458.10 MicroConsole through DASYLab 11.0 software. In addition, DASYLab software was used to collect the experimental data from the load cell, as well as from the LVDT and displacement sensor. The maximum displacement for the monotonic loading was 50mm. However, during phase 2, it was found that the larger specimens reached their capacity at displacements greater than 50mm, thus failure did not occur even when the maximum displacement was reached. As a 30 result, the peak displacement was increased to 75mm. The loading rate, for phase 1, was set for 2.5mm/min. For phase 2, the loading rate was increased to 15mm/min.  For the reversed cyclic tests, the deformation controlled quasi-static cyclic testing protocol from CUREE publication was used. The protocol is commonly applied for testing woodframe structures. It consists of initial, primary and trailing cycles, which use a reference deformation as the peak deformation resulting from the monotonic testing (Krawinkler et al., 2000). The initial cycles are small cycles that are 5% of the reference deformation. These initial cycles serve as a check for the load cell, measuring equipment, as well as an indication of the force-deformation response at low amplitudes (Krawinkler et al., 2000). Primary cycles are peak cycles that gradually increase in amplitude as the loading history proceeds. The primary cycles are followed by trailing cycles that are 75% of the amplitude of the preceding primary cycle as illustrated on Figure 3.11. The loading protocol was set to be completed in 11 minutes.   Figure 3.11: CUREE Deformation Controlled Quasi-Static Cyclic Loading History  31 3.7 Phase 1 Results Phase 1 of the experiment was set as preliminary testing of phase 2 to determine the parameters required to induce ductile failure of the glued-in steel rod moment connection. As a result, only one specimen was fabricated and tested for each configuration. The results of phase 1 are summarized in Table 3.5 and Table 3.6 for monotonic and cyclic loading, respectively. The “measured moment arm” was the distance measured from the interface of the steel base plate and wood beam to the center of the 100mm wide clamping plate; thus the true moment arm could be ±50mm. It should be noted that bending of the steel plate, which was used to transfer the load from the load cell, was observed during testing due to the opening between the load transferring steel plate and the clamping steel plate. In consequence, wooden blocks were utilized to help reinforce the transfer plate, as illustrated in Figure 3.12; however, the wooden blocks were insufficient. For phase 2 testing, the load transfer plate was replaced with a much stronger and stiffer I-section.  Figure 3.12: Gap between Load Transfer Plate and Clamping Plate   32 Table 3.5: Summary of Phase 1 Monotonic Testing Specimen Measured Moment Arm (m) Ultimate Failure Load (kN) Ultimate Moment Resistance Experimental Type of Failure Observed Experimental (kNm) Theoretical (kNm) SE-U1-1m 0.952 16.98 16.16 9.86 Steel - Tension LE-U1-1m 0.952 11.23 10.69 8.81 Steel - Tension SE-U2-1m    8.81 No Failure LE-U2-1m 0.952 13.31 12.67 7.96 Steel - Tension SE-U1 0.457 29.88 13.66 9.86 Wood - Splitting LE-U1 0.457 24.54 11.22 8.81 Wood - Splitting SE-U2 0.457 38.08 17.41 9.86 Steel - Shear LE-U2 0.457 35.86 16.39 8.81 Wood - Splitting SE-U3 0.457 32.16 14.70 10.39 Steel - Shear SE-R3 0.451 43.15 19.46 10.39 Steel - Shear LE-U3 0.470 19.54 9.18 9.30 Wood - Splitting SE-U4 0.457 34.60 15.82 20.22 Wood - Splitting SE-R4 0.451 58.29 26.28 20.22 Wood - Splitting LE-U4 0.457 16.25 7.43 18.07 Wood - Pullout SE-U5 0.457 22.85 10.45 10.39 Wood - Splitting SE-R5 0.457 42.73 19.54 10.39 Wood - Splitting LE-U5 0.457 25.75 11.77 9.30 Steel - Shear SE-U6 0.457 43.56 19.92 20.22 Wood - Splitting SE-R6 0.457 65.98 30.17 20.22 Steel - Shear LE-U6 0.470 45.05 21.17 18.07 Steel - Threading  None of the specimens with length of 500mm failed in a ductile manner, not even the “LE” specimens with adequate edge spacing, which was theorized to fail due to yielding and plasticization of the glued-in steel rods. Instead all specimens of 500mm length failed suddenly due to shear caused by splitting of the wood or shear failure of the glued-in steel rods. However, as expected, pull-out failure was avoided for all twenty specimens, except for one (LE-U4), by providing embedment length of greater than 10d.  33 The 1000mm long specimens, on the other hand, all failed in a ductile manner due to tensile failure of the steel rods, including the “SE” specimens, which were hypothesized to fail due to splitting of the wood since they were designed with inadequate edge distance. Slippage between the clamping steel plates occurred during testing of specimen “SE-U1-1m”, thus the applied load dropped significantly whenever the clamping plates slipped and no failure of the specimen occurred. The cyclic testing for the “LE” specimens with length of 1000mm also failed due to tensile stress of the glued-in steel rods. The failure occurred at a load quite close to the failure load of the monotonic testing.  Table 3.6: Summary of Phase 1 Quasi-Static Cyclic Testing Specimen Measured Moment Arm (m) Ultimate Failure Load (kN) Ultimate Moment (kN m) Experimental Type of Failure Observed LE-U1-1m 0.952 10.19 9.70 Steel - Tension -9.87 -9.40 LE-U2-1m 0.952 10.173 9.68 Steel - Tension -10.954 -10.43  3.8 Phase 1 Discussion  The shear force induced into the 500mm long beam specimens was quite large due to the short lever arm averaging approximately 458mm. In fact, the shear force introduced into the specimen was about 53% of the maximum pure shear capacity of the steel rods based on Von Mises Yield Criteria. As a result, it was not surprising to observe that the shear force had a major effect on the failure mode of all the 500mm length specimens, whether in the steel rods or in the glulam. The shear force values relative to the maximum pure shear capacity of the steel rods for each 500mm long specimens are summarized in Table 3.7 and failure modes outlined on the table are shown in Figure 3.13. 34 Table 3.7: Shear Force Relative to Maximum Pure Shear Capacity for 500mm Long Specimens Specimen Experimental Failure Load (kN) Theoretical Pure Shear Capacity of Steel Rod (kN) % of Pure Shear Capacity of Steel Rod Experimental Type of Failure Observed SE-U1 29.88 52.66 56.7 Wood - Splitting LE-U1 24.54 52.66 46.6 Wood - Splitting SE-U2 38.08 52.66 72.3 Steel - Shear LE-U2 35.86 52.66 68.1 Wood - Splitting SE-U3 32.16 52.66 61.1 Steel - Shear SE-R3 43.15 52.66 82.0 Steel - Shear LE-U3 19.54 52.66 37.1 Wood - Splitting SE-U4 34.60 105.32 32.9 Wood - Splitting SE-R4 58.29 105.32 55.3 Wood - Splitting LE-U4 16.25 105.32 15.4 Wood - Pullout SE-U5 22.85 52.66 43.4 Wood - Splitting SE-R5 42.73 52.66 81.2 Wood - Splitting LE-U5 25.75 52.66 48.9 Steel - Shear SE-U6 43.56 105.32 41.4 Wood - Splitting SE-R6 65.98 105.32 62.7 Steel - Shear LE-U6 45.05 105.32 42.8 Steel - Threading   35  (a)  (b)  (c)  (d) (e) Figure 3.13: Shear Failure of 500mm Long Specimens (a), (b), (d) & (e) Wood - Splitting, (c) Steel – Shear However, since shear resistance of the system is not the main objective of this research, failure due to shear was not investigated in-depth. Instead, the main focus for phase 1, was on prevention of shear failure. Based on uniaxial tension and shear interaction plot following Von Mises Yield Criteria, shown in Figure 3.14, in order for the steel rods to achieve 90% of their axial strength, or greater, the shear stress induced into the rods must be 25%, or less, of the axial capacity. Thus, since flexure response of the connection is the main focus, the connection should be designed in a way to ensure that the shear stress introduced into the steel rods are within 25% of the axial capacity in order to obtain as close to the full axial capacity of the rods.  36  Figure 3.14: Uniaxial and Shear Interaction based on Von Mises Yield Criteria The 1000mm long specimens had an average of 26% of the pure shear capacity (or 15% of the ultimate axial stress) applied to the system before failure occurred, as summarized in Table 3.8; thus it was not surprising to observe the specimens fail in a ductile manner due to plasticization of the steel rods caused by tensile stresses. What was unexpected and intriguing was that the SE-U1-1m specimen, which was expected to fail by splitting of the timber since it was designed with insufficient edge spacing, was also observed to have significant yielding of the steel rod and had a tensile failure within the steel rod.  The moment-rotation plot of the 1000mm specimens are shown in Figure 3.15. The SE-U1-1m specimen had approximately 1.38 times more capacity than the average of the 1m long “LE” specimens due to the greater moment arm between the tension force within the glued-in steel rod and compression induced in the timber. Looking at the 1000mm long specimen results, it seems that ensuring shear stress of 25%, or less, of the ultimate axial strength, within the system, will indeed prevent shear failure and favour flexure failure. 00.10.20.30.40.50.60.70.80.910 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1τ xy/σyσxx/σy37 Table 3.8: Shear Force Relative to Maximum Pure Shear Capacity for 1000mm Long Specimens Specimen Experimental Failure Load (kN) Theoretical Pure Shear Capacity (kN) % of Pure Shear Capacity Experimental Type of Failure Observed SE-U1-1m 16.98 52.66 32.2 Steel - Tension LE-U1-1m 11.23 52.66 21.3 Steel - Tension LE-U2-1m 13.31 52.66 25.3 Steel - Tension   Figure 3.15: Moment-Rotational Plot of Monotonic Loading of 1000mm Specimens  The quasi-static cyclic testing of 1000mm long “LE” specimens had a ductile failure. The glued-in steel rod yielded and plasticized through the first six primary cycles and their trailing cycles before it completely failed during the final primary cycle with the peak amplitude displacement. The hysteresis of LE-U1-1m and LE-U2-1m are shown in Figure 3.16 and Figure 3.17 respectively. Due to testing just one specimen per layout, no in-depth analysis was done for the results of the 1000mm specimens. The in-depth analysis of ductile timber moment connection using glued-in steel rods is performed in Phase 2. 0246810121416180 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04Moment [kNm]Rotation [rad]SE-U1 LE-U1 LE-U238  Figure 3.16: Hysteresis of LE-U1-1m  Figure 3.17: Hysteresis of LE-U2-1m As mentioned previously, and can be seen in Figure 3.13, the splitting of the timber, for “SE” unreinforced specimens, occurred in such a way that they could not be retrofitted with screws. Furthermore, the specimens that were initially fabricated with screws as reinforcement perpendicular to the grain also failed in shear, including splitting within the timber, which is -15-10-5051015-0.02 -0.01 0 0.01 0.02 0.03 0.04Moment (kNm)Rotation (Rad)-15-10-5051015-0.01 -0.005 0 0.005 0.01 0.015 0.02 0.025 0.03Moment (kNm)Rotation (Rad)39 shown in Figure 3.18. Again these splitting failures in the wood formed in such a way that the self-tapping screws could not have prevented the splitting to occur.    Figure 3.18: Reinforced Specimen Failure 3.9 Phase 2 Results 3.9.1 Monotonic Testing The results (maximum load and displacement) of the monotonic testing are shown in Table 3.9. Four monotonic tests were performed for most of the series. The “- #” after the specimen name indicates which specimen beam was used and the “(#)” at the very end indicates the test number of the specimen. Tests (1) and (3) were done on opposite ends of the timber beam with no damaged to the glued-in steel rods. Test (2) and (4) were done on the same ends of the beam as test (1) and (3) respectively, however, with the beam flipped to have the initial compression rods now in tension, and with self-tapping screws in place to help stabilized the beam instead of the damaged glued-in steel rods that were under tension from the test prior.  The labeling corresponding to the orientation of the tests was applied for all monotonic tested specimens except for D4(a). The sudden transfer of loads at failure, from the glued-in steel rods on the tension side, caused pull-out failure of the glued-in steel rods on the compression side as 40 well as splitting of the timber beam, which is shown in Figure 3.20(e). As a result, one end of the beam could not be retested flipped over since the glued-in steel rods, which were initially on the compression side prior, was damaged as well during the first set of testing. In consequence, only three monotonic tests were performed for D4(a) and each test was done on different ends of the beam. In addition, when the first test member was tested, D4(a)-1 (1), the capacity of the specimen was so large that it bent the steel plate that was being used as clamps in the process, as shown in Figure 3.19, rendering the test result invalid. In consequence, the test result of D4(a)-1 (1) was excluded from analysis. The remaining tests were completed after the steel plate clamp was replaced with a stronger and stiffer C-channel.  Figure 3.19: Bending of Steel Plate (Clamp) while Testing D4(a)-1 (1) It should also be noted that specimen C3(a)-2 (1) did not fail under the maximum displacement set at 50mm, as a result, no failure load and displacement was found. The remaining of the monotonic test which included the rest of the C3(a) series, as well as D2(a), D4(a), and D2(b) were tested with maximum displacement set at 75 mm.  41 Table 3.9: Phase 2 Monotonic Testing Results Specimen Measured Moment Arm (m) Maximum Load  (kN) Maximum Displacement (mm) Type of Failure Observed A1(a)-1 (1) 1.250 8.77 44.83 Steel - Tension A1(a)-1 (2) 1.250 9.04 41.44 Steel - Tension A1(a)-1 (3) 1.240 9.01 43.78 Steel - Tension A1(a)-1 (4) 1.240 8.67 45.33 Steel - Tension B2(a)-1 (1) 1.240 20.02 47.80 Steel - Tension B2(a)-1 (2) 1.250 17.07 44.39 Wood - Splitting B2(a)-1 (3) 1.250 18.01 50.00 Steel - Tension B2(a)-1 (4) 1.245 16.38 47.16 Steel - Tension C3(a)-2 (1) 1.210 29.19 49.76 No Failure C3(a)-2 (2) 1.250 23.27 52.46 Steel - Tension C3(a)-2 (3) 1.240 29.06 54.29 Steel - Tension C3(a)-2 (4) 1.240 24.97 54.80 Steel - Tension D2(a)-1(1) 1.240 33.04 35.46 Steel - Tension D2(a)-1(2) 1.260 29.10 22.72 Wood - Splitting D2(a)-1(3) 1.260 29.61 33.77 Steel - Tension D2(a)-1(4) 1.270 33.81 39.59 Steel - Tension D4(a)-1(1) 1.270 65.10 51.62 Steel - Tension & Pullout D4(a)-1(2) 1.255 47.48 50.64 Steel - Tension & Pullout D4(a)-2(3) 1.265 40.07 45.47 Steel - Tension & Pullout A1(b)-1(1) 1.240 9.15 22.28 Pullout A1(b)-1(2) 1.240 8.07 18.15 Pullout A1(b)-1(3) 1.240 8.04 13.76 Pullout A1(b)-1(4) 1.235 7.42 14.10 Pullout C3(b)-1 (1) 1.210 18.84 18.19 Pullout C3(b)-1 (2) 1.240 20.37 26.81 Pullout C3(b)-1 (3) 1.240 21.29 27.69 Pullout C3(b)-1 (4) 1.240 17.37 20.28 Pullout D2(b)-1(1) 1.260 15.79 12.03 Pullout D2(b)-1(2) 1.270 21.49 16.97 Pullout D2(b)-1(3) 1.260 24.50 17.92 Pullout D2(b)-1(4) 1.260 23.66 16.90 Pullout   42 All, but two, of the (a)-type specimens (with adequate glued-in steel rod embedment length of 16d to prevent pull-out failure) failed in a ductile manner due to yielding of the glued-in steel rods as hypothesized. As mentioned previously, the D4(a) specimens did have pull-out and splitting of the wood failures in addition to tensile failure of the glued-in rod, but they also showed significant yielding, thus it is presumed that pull-out and splitting failures occurred after the tensile failure of the steel rods due to sudden load transfer. As a result, the two exceptions to ductile tensile failure of the glued-in steel rods for (a)-type specimens were specimens B2(a)-1 (2) and D2(a)-1 (2), which both failed due to splitting of the timber beams. Since these unexpected failures were one out of four tests for the specific specimen type, or overall, two out of nineteen tests, they were treated as anomalies and were not taken into consideration in the analysis. In addition, B2(a)-1 (2) had an initial split in the timber beam prior to testing, which could have led to the failure due to splitting of the wood. The failures of the (a)-type specimens under monotonic loading are shown in Figure 3.20 and Figure 3.21.     43  (a)  (b)  (c)  (d)  (e) Figure 3.20: Ductile Failure of (a) A1(a), (b) B2(a), (c) C3(a), (d) D2(a), and (e) D4(a) Specimens under Monotonic Loading 44  (a)  (b) Figure 3.21: Brittle Splitting Failure of (a) B2(a)-1 (2) and (b) D2(a)-1(2) under Monotonic Loading The moment-rotation curves for all (a)-type specimens under monotonic loading are shown in Figure 3.22, Figure 3.23, Figure 3.24, Figure 3.25 and Figure 3.26. The moment was calculated by multiplying the applied load with the measured moment arm, and the rotation was calculated by taking the inverse tangent of the displacement measured from the string pot divided by the length of the beam from the face of the steel base plate to the location of the string pod, which was measured to be 1355mm. From these moment-rotation curves, the peak moment, ultimate (or failure) moment and moment at the yield point as well as the corresponding rotations at these moments were calculated, in addition to the ductility and elastic stiffness. The results of the analysis are shown in Table 3.10. 45  Figure 3.22: Moment-Rotation Curve of A1(a) Specimens  Figure 3.23: Moment-Rotation Curve of B2(a) Specimens 46  Figure 3.24: Moment-Rotation Curve of C3(a) Specimens  Figure 3.25: Moment-Rotation Curve of D2(a) Specimens 47  Figure 3.26: Moment-Rotation Curve of D4(a) Specimens The yield point of each specimen was determined following the two methods outlined in EN 12512 (CEN, 2005) and (Piazza et al., 2011). For specimens A1(a), B2(a), C3(a), and D2(a) where the moment-rotation curve did not have a well-defined linear yield line, the experimental yielding point was determined following method (b) of EN 12512 (CEN, 2005). It determines the yield point by finding the interception point of the elastic stiffness slope line and the line tangent to the curve with a 1/6th slope of the elastic stiffness (Piazza et al., 2011), as shown in Figure 3.27, Figure 3.28, Figure 3.29 and Figure 3.30.  For D4(a) specimens, which had a well-defined linear yield portion, the yield point was found following method (a) of EN 12512 (CEN, 2005). It takes the yield load, or moment, as the load at which produces the well-defined, horizontal yield line, and the yield displacement, or rotation, as the displacement where the elastic stiffness slope line and the horizontal yield line intercept 48 (Piazza et al., 2011), as illustrated in Figure 3.31. The elastic stiffness of the moment-rotation curve of each test data was calculated by following the equation outlined by Piazza et al. (2011): 𝑘𝑒 =0.4𝐹𝑚𝑎𝑥 − 0.1𝐹𝑚𝑎𝑥𝑢0.4 − 𝑢0.1 (1) where 𝑢0.1 and 𝑢0.4 are the displacements at load of 0.1𝐹𝑚𝑎𝑥 and 0.4𝐹𝑚𝑎𝑥, respectively. Failure was determined according to EN 12512 as the first point obtained where either failure occurs, or 80% of the maximum load, or moment, is reached on the descending arm (Piazza et al., 2011). The ultimate point is also shown in the graph from Figure 3.27 through Figure 3.31. In addition, these figures also indicate the peak moment and rotation at peak moment. The moment-rotation curves of the individual tests showing the yield, peak and ultimate point not within the main body of this thesis are included in Appendix B. The experimental yield, peak and ultimate (or failure) moment, found for all the (a)-type specimens, were consistent within the test series with a coefficient of variation of less than 12%.   Figure 3.27: Moment-Rotation Curve of A1(a)-1 (1) 49  Figure 3.28: Moment-Rotation Curve of B2(a)-1 (3)  Figure 3.29: Moment-Rotation Curve of C3(a)-2 (3) 50  Figure 3.30: Moment-Rotation Curve of D2(a)-1 (1)  Figure 3.31: Moment-Rotation Curve of D4(a)-1 (2) 51 Table 3.10: Summary of (a)-type Specimen Analysis under Monotonic Loading Specimen Rot. at Peak Mom.t (rad) Peak Mom. (kNm) Rot. at Ulti. (rad) Ult. Moment (kNm) Rot. at Yield (rad) Yield Moment Ductility Elastic Stiffness (kNm/rad) Exp. Theor. (kNm) (kNm) A1(a)-1 (1) 0.020 10.96 0.033 8.77 0.010 9.39 9.31 3.32 1126 A1(a)-1 (2) 0.019 11.28 0.031 9.20 0.011 10.22 9.31 2.89 1051 A1(a)-1 (3) 0.020 11.12 0.032 8.97 0.012 10.27 9.31 2.77 917 A1(a)-1 (4) 0.019 10.75 0.033 8.60 0.010 9.77 9.31 3.15 990 Average : 0.019 11.02 0.032 8.88 0.011 9.91 9.31 3.03 1021 StDev:  0.001 0.23 0.001 0.26 0.001 0.41 - 0.25 89 B2(a)-1 (1) 0.025 24.82 0.035 22.18 0.015 22.24 18.41 2.34 1702 B2(a)-1 (2) 0.028 21.32 0.033 20.45 0.020 20.27 18.41 1.64 1052 B2(a)-1 (3) 0.024 22.51 0.037 18.01 0.017 21.15 18.41 2.16 1327 B2(a)-1 (4) 0.024 20.39 0.035 17.11 0.019 19.58 18.41 1.85 1083 Average : 0.025 22.26 0.036 19.10 0.018 20.81 18.41 2.12 1291 StDev:  0.002 1.91 0.001 2.71 0.002 1.15 - 0.25 300 C3(a)-2 (1) 0.031 35.32 - - 0.025 34.31 27.43 1.47 1379 C3(a)-2 (2) 0.028 29.07 0.039 25.44 0.018 26.33 27.43 2.17 1705 C3(a)-2 (3) 0.029 36.02 0.040 30.71 0.021 33.60 27.43 1.93 1749 C3(a)-2 (4) 0.029 30.94 0.040 24.75 0.023 29.85 27.43 1.77 1326 Average : 0.029 32.84 0.040 26.97 0.022 31.02 27.43 1.96 1540 StDev:  0.001 3.37 0.001 3.26 0.003 3.69 - 0.20 218 D2(a)-1(1) 0.021 40.97 0.026 34.06 0.013 34.07 34.49 2.02 2742 D2(a)-1(2) 0.017 36.62 0.017 36.62 - - 34.49 - - D2(a)-1(3) 0.021 37.30 0.025 32.58 0.015 34.09 34.49 1.72 2734 D2(a)-1(4) 0.024 42.94 0.029 36.91 0.020 40.92 34.49 1.43 2197 Average : 0.021 39.46 0.027 34.52 0.016 36.36 34.49 1.72 2557 StDev:  0.003 3.01 0.002 2.20 0.004 3.95 - 0.30 312 D4(a)-1(1) 0.032 82.68 0.038 82.66 0.025 82.67 55.84 1.50 3258 D4(a)-1(2) 0.025 59.58 0.037 59.56 0.022 59.58 55.84 1.68 2680 D4(a)-2(3) 0.022 50.68 0.034 50.67 0.019 50.68 55.84 1.76 2658 Average : 0.024 55.13 0.035 55.11 0.021 55.13 55.84 1.72 2669 StDev:  0.003 6.29 0.003 6.29 0.002 6.29 - 0.06 15 52 The (b)-type specimens, which were designed with insufficient embedment length, of 8d, all failed in a sudden, brittle manner from pull-out failure along the glue line as anticipated. The pull-out failures of the (b) type specimens are shown in Figure 3.32. The results of the (b)-type specimens solidifies Gonzalez’s (2015) finding that for 12.7mm diameter glued-in steel rods, embedment length less than 10d induce a brittle pull-out failure. The results of the peak moment and rotation at peak moment, as well as the failure moment and rotation at failure moment are listed in Table 3.11. These capacities were found by analyzing the moment-rotation curves of each specimen, which are shown in Figure 3.33, Figure 3.34 and Figure 3.35.  (a)  (b)  (c) Figure 3.32: Brittle Pull-out Failures of (a) A1(b), (b) C3(b), (c) D2(b) Specimens   53 Table 3.11: Summary of (b)-type Specimen Analysis under Monotonic Loading Specimen Experimental Rotation at Peak Moment (rad) Experimental Peak Moment (kNm) Experimental Rotation at Ultimate (rad) Experimental Ultimate Moment (kNm) A1(b)-1(1) 0.016 11.34 0.017 11.30 A1(b)-1(2) 0.013 10.00 0.014 9.65 A1(b)-1(3) 0.010 9.96 0.010 9.83 A1(b)-1(4) 0.010 9.16 0.010 9.13 Average : 0.013 10.12 0.013 9.98 StDev: 0.003 0.90 0.003 0.93 C3(b)-1 (1) 0.013 22.78 0.013 22.78 C3(b)-1 (2) 0.020 25.25 0.020 25.25 C3(b)-1 (3) 0.020 26.40 0.020 26.40 C3(b)-1 (4) 0.015 21.52 0.015 21.52 Average : 0.017 23.99 0.017 23.99 StDev: 0.003 2.23 0.003 2.23 D2(b)-1(1) 0.009 19.87 0.009 19.68 D2(b)-1(2) 0.013 27.21 0.013 27.21 D2(b)-1(3) 0.013 30.85 0.013 30.85 D2(b)-1(4) 0.012 29.80 0.012 29.80 Average : 0.012 26.93 0.012 26.89 StDev: 0.002 4.95 0.002 5.04 54  Figure 3.33: Moment-Rotation Curve of A1(b) Specimens  Figure 3.34: Moment-Rotation Curve of C3(b) Specimens 55  Figure 3.35: Moment-Rotation Curve of D2(b) Specimens 3.9.2 Results of Cyclic Testing The summary of cyclic testing of the peak moment and the rotation at the peak moment for both positive and negative moments, as well as the maximum rotation reached by the specimen and the corresponding moment at that rotation for both the positive and negative rotation are shown on Table 3.12. Once again, similar to the monotonic testing, the moment capacity was calculated by multiplying load applied by the load cell with the measured moment arm, which extends from the flush face of the steel base plate to the center of the clamping plates, and the rotation was calculated by taking the inverse tangent of the displacement captured by the string pod divided by the location of the string pod relative to the steel based plate, placed 1355mm away. In addition, the same labeling system was used for the cyclic test, except no one edge of the beam was used twice for testing since quasi-static cyclic loading required all the glued-in steel rods to 56 be under tension at one point or another; thus, each test was done on an untested edge of the beam.  All specimens tested under the cyclic loading were (a)-type specimens, meaning they were designed with adequate embedment length of 16d for its glued-in steel rods. Similar to (a)-type series tested under monotonic loading, these specimens also failed in a ductile manner due to yielding and plasticization of the glued-in steel rods. In addition, pull-out along the glue line and splitting of wood was also observed for the D4(a) cyclic series, but analogous to the monotonic testing of D4(a) series, significant yielding was observed before failure. Thus, it is assumed that the brittle failure modes were due to the large and sudden transfer of loads from the failed glued-in steel rods. The failure modes for the quasi-static cyclic testing are shown in Figure 3.36.  57 Table 3.12: Phase 2 Cyclic Testing Results Spec. Mom Arm (m) Positive Negative Positive Negative Type of Failure Observed Peak Mom. (kNm) Rot. at PeakMom (rad) Peak Mom. (kNm) Rot. at Peak Mom. (rad) Max. Rot. (Rad) Mom. at Max. Rot. (kNm) Max. Rot. (rad) Mom. at Max. Rot. (kNm) A1(a)-2 (1) 1.265 11.83 0.013 -11.70 -0.021 0.024 9.45 -0.021 -11.37 Tension(1) A1(a)-2 (2) 1.245 10.58 0.022 -12.24 -0.031 0.032 8.66 -0.032 -11.53 No Failure A1(a)-3 (3) 1.24 11.86 0.022 -12.59 -0.028 0.033 9.52 -0.032 -12.24 No Failure A1(a)-3 (4) 1.25 11.11 0.019 -12.15 -0.019 0.030 8.33 -0.022 -11.92 Tension(1) Average: - 11.34 0.019 -12.17 -0.025 0.030 8.99 -0.027 -11.76  StDev: - 0.62 0.004 -0.37 -0.006 0.004 0.59 -0.006 0.39  B2(a)-3 (1) 1.25 23.71 0.024 -22.95 -0.025 0.035 19.03 -0.025 -22.72 Tension(1) B2(a)-3 (2) 1.245 23.75 0.022 -23.59 -0.024 0.033 20.13 -0.025 -22.79 Tension(1) B2(a)-2 (3) 1.24 23.76 0.020 -23.99 -0.024 0.030 19.63 -0.024 -23.31 Tension(1) Average: - 23.74 0.022 -23.51 -0.024 0.033 19.59 -0.025 -22.94  StDev: - 0.03 0.002 -0.53 -0.001 0.003 0.55 -0.000 0.33  C3(a)-1 (1) 1.23 33.75 0.027 -36.14 -0.028 0.038 27.12 -0.028 -35.20 Tension(1) C3(a)-3 (2) 1.255 35.37 0.028 -34.00 -0.028 0.036 30.54 -0.028 -33.98 Tension(1) C3(a)-3 (3) 1.25 36.14 0.028 -34.01 -0.027 0.037 31.41 -0.027 -33.37 Tension(1) Average: - 35.09 0.028 -34.72 -0.027 0.037 29.69 -0.028 -34.18  StDev: - 1.22 0.000 -1.23 -0.000 0.001 2.27 -0.000 0.93  D2(a)-2 (1) 1.255 41.99 0.023 -44.47 -0.018 0.026 35.72 -0.025 -36.93 Tension(1) D2(a)-2 (2) 1.27 43.40 0.022 -44.84 -0.019 0.028 37.73 -0.019 -43.21 Tension(1) D2(a)-3 (3) 1.25 42.38 0.021 -42.07 -0.018 0.026 34.43 -0.025 -33.90 Tension(1) D2(a)-3 (4) 1.245 40.80 0.018 -42.19 -0.018 0.025 33.84 -0.025 -35.30 Tension(1) Average: - 42.14 0.021 -43.39 -0.018 0.026 35.43 -0.023 -37.33  StDev: - 1.07 0.002 -1.47 -0.000 0.001 1.72 -0.003 4.11  D4(a)-3 (1) 1.235 60.75 0.020 -60.18 -0.019 0.032 60.73 -0.027 -60.18 Tension(1) & Pullout D4(a)-3 (2) 1.24 60.99 0.025 -60.42 -0.022 0.035 60.98 -0.031 -48.03 Tension(1) & Pullout D4(a)-2 (3) 1.24 60.99 0.024 -60.42 -0.021 0.036 60.98 -0.031 -43.31 Tension(1) & Pullout Average: - 60.91 0.023 -60.34 -0.021 0.034 60.90 -0.030 -50.51  StDev: - 0.14 0.002 -0.14 0.001 0.002 0.14 -0.002 8.70  (1) Denotes tension failure within the steel rods 58  (a)  (b)  (c)   (d)  (e) Figure 3.36: Ductile Failure of (a) A1(a), (b) B2(a), (c) C3(a), (d) D2(a) and (e) D4(a) Specimens Under Quasi-Static Cyclic Loading 59 The energy dissipated at the specific primary peaks of the quasi-cyclic loading protocol is listed in Table 3.13. EN 12512 was followed to calculate the dissipation of energy of the hysteretic cuve, or also known as “the equivalent viscous damping ratio by hysteresis” (Piazza et al., 2011). The equivalent viscous damping ratio is calculated as: 𝑣𝑒𝑞 =𝐸𝑑2𝜋𝐸𝑝 (2) where Ed is the energy dissipated in one half cycle of the hysteresis and Ep is the potential energy obtainable at the corresponding one half cycle (Piazza et al., 2011). Figure 3.37 illustrates the energy dissipated and potential energy available in one cycle of a hysteretic curve.  Figure 3.37: Equivalent Viscous Damping Ratio for One Cycle (Piazza et al., 2011)   60 Table 3.13: Summary of Energy Dissipation Spec. Dis.(1) Positive Rotation Negative Rotation Ed (kNm*Rad) Ep (kNm*Rad) veq (%) Ed (kNm*Rad) Ep (kNm*Rad) veq (%) Ave. StD Ave. StD Ave. StD Ave. StD Ave. StD Ave. StD A1(a) 0.2∆ 0.020 0.013 0.041 0.018 6.98 2.37 0.003 0.003 0.003 0.003 9.35 5.04 0.3∆ 0.044 0.021 0.062 0.017 10.77 2.89 0.006 0.004 0.013 0.008 7.82 2.25 0.4∆ 0.075 0.026 0.083 0.016 14.17 2.63 0.011 0.005 0.034 0.013 5.01 0.84 0.7∆ 0.185 0.034 0.137 0.010 21.37 2.79 0.080 0.021 0.111 0.016 11.43 2.59 1.0∆ 0.272 0.006 0.159 0.010 27.17 1.09 0.201 0.010 0.189 0.005 16.95 0.39 B2(a) 0.2∆ 0.014 0.004 0.073 0.024 3.07 0.78 0.004 0.003 0.006 0.004 13.18 5.15 0.3∆ 0.033 0.012 0.126 0.028 4.05 0.80 0.011 0.006 0.024 0.006 6.93 2.27 0.4∆ 0.071 0.032 0.184 0.026 5.99 1.77 0.019 0.007 0.063 0.008 4.66 1.29 0.7∆ 0.304 0.054 0.332 0.016 14.50 1.90 0.119 0.005 0.245 0.015 7.79 0.46 C3(a) 0.2∆ 0.068 0.050 0.084 0.009 12.82 9.09 0.008 0.001 0.019 0.008 7.92 3.22 0.3∆ 0.023 0.002 0.158 0.013 2.37 0.13 0.019 0.006 0.060 0.020 5.51 2.55 0.4∆ 0.051 0.006 0.251 0.016 3.23 0.36 0.030 0.010 0.128 0.031 3.97 1.66 0.7∆ 0.354 0.031 0.527 0.026 10.72 1.25 0.196 0.063 0.426 0.027 7.26 1.90 D2(a) 0.2∆ 0.010 0.002 0.022 0.010 9.61 7.86 0.015 0.004 0.057 0.016 4.19 0.55 0.3∆ 0.016 0.004 0.062 0.016 4.15 0.22 0.027 0.007 0.117 0.023 3.68 0.41 0.4∆ 0.029 0.008 0.120 0.022 3.75 0.49 0.051 0.018 0.191 0.032 4.16 0.88 0.7∆ 0.195 0.056 0.353 0.028 8.72 2.20 0.324 0.060 0.426 0.038 12.08 1.43 D4(a) 0.2∆ 0.114 0.086 0.129 0.036 13.77 8.95 0.014 0.003 0.065 0.021 3.43 0.62 0.3∆ 0.058 0.014 0.258 0.051 3.57 0.14 0.025 0.007 0.174 0.034 2.28 0.40 0.4∆ 0.106 0.023 0.424 0.063 3.96 0.35 0.046 0.012 0.321 0.042 2.28 0.47 0.7∆ 0.380 0.073 0.875 0.050 6.89 1.04 0.262 0.031 0.783 0.031 5.31 0.47 (1) Denotes proportion of the reference displacement of the loading protocol at the primary cycle   61 3.10 Phase 2 Discussions 3.10.1 Monotonic Testing Ductility, which is the measure of plastic deformation without significant decrease in strength, thus rotation (or displacement) at ultimate divided by rotation (or displacement) at yield (Piazza et al., 2011), was also calculated. The A1(a) specimen had the greatest ductility with an average ductility of 3.0, followed by B2(a) specimens with and average ductility of 2.1, then C3(a) with an average ductility of 2.0, and finally D2(a) and D4(a) specimens with an average ductility of 1.7. It appears that the ductility of the connection, decreases with the increase in the size of the timber beam, or in general as the moment capacity of the system increases. However, more tests needs to be done to verify this speculation. Figure 3.38 compares the experimental yield point determined with the theoretical yield point calculated. The theoretical yield moment was calculated by applying the assumption that plane-sections remain plane in combination with the traditional elastic transform theory, which assumes linear stress distribution of the compression stresses within the timber compression zone (Fragiacomo & Batchelar, 2012). For two rows of tension glued-in steel rods, such as for specimen D4(a), both layers of the steel were assumed to have yielded and an equivalent moment arm from the centroid of the steel layers was used to predict the yield capacity of the member. The detailed calculation can be found in Appendix A   None, except for three, of the individual specimens achieved yield moments smaller than the theoretical yield moment hypothesized. The three specimens which had yielding points below the theoretical yielding capacity were C3(a)-2 (2) with 4.0% less, D2(a)-1(3) with 1.2% less, and finally D4(a)-2 (3) with 9.2% less. On average, the theoretical yield point calculated for the 62 specimens were close to the experimental yielding point determined, and in fact underestimated the yield moment for all the different specimen layouts. As a result, the theoretical approach used, which is similar to the procedure used to calculate moment resistance of reinforced concrete beams in CSA A23.3-14 (2014) with a replacement of the concrete compression member with timber, gives a realistic estimation of the yield moment capacity of timber moment connections with glued-in steel rods.    Figure 3.38: Comparison of Experimental and Theoretical Yield Point   63 3.10.2 Quasi-Static Cyclic Testing The moment-rotational curves of each specimen, A1(a), B2(a), C3(a), D2(a) and D4(a) under quasi-static cyclic testing are plotted in Figure 3.39, Figure 3.40, Figure 3.41, Figure 3.42 and Figure 3.43, respectively. In addition, on the plots, the monotonic backbone curve from the corresponding monotonic testing is also shown, as well as the hysteretic backbone curve with markers at the location where the peak of the primary cycle of the CUREE loading protocol occurs. The detailed moment-rotation curves of specimen members not included within the main body of this thesis can be found in Appendix C. All test series, ranging from A1(a) to D4(a), exhibited pinching during unloading. This was most likely due to the gap between the steel base plate and the specimen that was introduced through yielding and plasticization of the steel rods. Upon unloading, the gap produces almost no stiffness for the connection once the specimens have reached a position where the gap disengaged the rods from resisting any load. The load would be picked up again by the specimen once it was reloaded enough to engage the steel rods again. The side of the beam where the rods are initially under tension (under positive displacement) experienced the primary peaks prior to the opposite end of the beam, where the rods are under compression initially (and in tension under negative displacement). As a result, the positive-displacement tension rods yield and plasticize before their counter parts introducing a gap located on just that side of the beam. Looking in-depth into the development of the displacement between the steel base plate and the face of the timber beam with respect to the loading protocol, in other words, the gap created with respect to the displacement of the load cell, it appears that once the loading protocol has reached a displacement that cause the steel rods to yield, it 64 produces a gap large enough that it cannot be completely closed even when the load cell is unloaded back to zero displacement. Only when the specimen is loaded in the negative direction does the gap completely close and enable the negative-displacement tension glued-in steel rods to pick up load. This phenomenon could explain the shift of the hysteresis towards the negative rotation. In addition, the fact that the negative-displacement tension rods do not get loaded until the specimen is loaded sufficiently in negative direction contributes to the difference between the positive and negative moment-rotation hysteretic curves. As a result, it appears, that the more the hysteretic curve is shifted towards the negative rotation, the less the negative-displacement tension glued-in rods plasticize, thus creating a more uneven hysteretic curve. Overall, the positive portion of the hysteretic curve of all the specimens, A1(a) through D4(a), followed the monotonic moment-rotation backbone curve relatively closely without significant deterioration post or pre capping. Furthermore, no significant, if any, reloading or unloading stiffness deterioration, or cyclic deterioration was present in any of the layouts. Finally, no degradation was present in a cycle prior to the capping, or maximum, point.  Comparing the positive equivalent viscous damping ratio, or energy dissipation, at the primary cycle with the peak of 0.7 of the maximum displacement, the most energy dissipation is carried out by specimen A1(a) with an average of 21%, followed by specimen B2(a) with an average of 15%, then specimen C3(a) with an average of 11%, and then specimen D2(a) with an average of 9%, lastly with specimen D4(a) with an average of 7%. Although specimen D4(a) has the highest moment capacity, similar to the ductility calculated from the monotonic testing, the viscous damping ratio for specimen D4(a) is the smallest. In contrast, specimen A1(a), with the smallest moment capacity, had the greatest viscous damping ratio. In addition, no failure occurred for specimen A1(a)-2 (2) and specimen A1(a)-3 (3) even when the load cell reached the maximum 65 displacement set for the protocol was reached, which was the average failure displacement from the monotonic testing of A1(a) specimens. Furthermore, the average energy dissipated from these two specimens on the maximum peak cycle was 27%, which is greater than the energy dissipated from the preceding peak cycle with 30% less displacement. Overall, it appears, that a higher moment capacity leads to lower capability to dissipate energy. However, more research is required to prove this observation.   Figure 3.39: Moment-Rotation Curve of A1(a)-2 (2) 66  Figure 3.40: Moment Rotation Curve of B2(a)-2 (3)  Figure 3.41: Moment-Rotation Curve of C3(a)-1 (1) 67  Figure 3.42: Moment-Rotation Curve of D2(a)-2 (1)  Figure 3.43: Moment-Rotation Curve of D4(a)-2 (3)  68 Chapter 4: Conclusions Experimental and analytical work was completed on timber moment connections using 12.7mm diameter mild steel threaded rods glued into Douglas-Fir glulam timber beams with polyurethane based adhesives to determine the effect of the rod layout on the connection moment capacity. Through phase 1, it was concluded that ductile failure of the rods is achieved when the shear force induced into the connection is less than 25% of the axial rod strength. This follows Von Mises Yield Criteria, which concludes that with shear stress of 25% or less of the ultimate axial stress, the axial capacity that could be reached within a system is 90% or greater of the ultimate axial strength. As a result, only the 1000mm long specimens, which experienced shear stress of less than 20% of axial strength, had a ductile failure. This is true even for the specimens that had an edge distance of rods of less than the recommended edge distance, 2.5d. The embedment length of the glued-in rods was found to be a key factor: 8d was found to create brittle pull-out failures along the glue line, verifying Gonzalez’s (2015) work, while 15d was found to prevent any brittle pull-out failures.  Phase 2 montonic testing confirmed the computed theoretical yield moment. The theoretical approach under-predicted the experimental yield moment with a difference of 13% or less; thus would result in a safe design of the moment connection with a conservative yield moment. The average ductility was found to be in the range of 1.7 to 3.0. From these values and the moment capacity, it appears that ductility of the moment connection decreases as the moment capacity of the connection increase. However, further research comparing different connection configurations, which would result in a range of different moment capacity, against its ductility 69 as well as comparing other potential factors that could influence ductility, such as the steel to timber ratio, against ductility is required to confirm this finding.  Phase 2 reversed cyclic testing exposed some shortcomings of the test set-up, where a gap between the steel base plate and the timber beam appeared. Non-symmetric hysteresis between the positive moment-rotation curves and the negative moment-rotation curves were produced since the negative-displacement tension steel rods were not loaded until the gap closed.  Overall, however, no stiffness deterioration during reloading and unloading was found in the hysteretic curves. In addition, the positive moment-rotation curve of the hysteresis follow the monotonic moment-rotation backbone curve closely for all the specimens.  The energy dissipation, or equivalent viscous damping ratio, was calculated. The energy dissipated at the cycle with peak displacement of 70% of the maximum displacement ranged from 9% to 21%. Similar to ductility, equivalent viscous damping decreased with moment capacity. More research is required to confirm this finding.  The experimental work done throughout this research enhanced the knowledge of the behaviour of timber moment connections using glued-in steel rods. The study focused on connections with 12.7mm diameter mild steel threaded rods glued into Douglas Fir glulam beams with PUR. Minimum requirements to ensure ductile failure were determined. In addition, relationship between the different configuration layouts of the glued-in rods and the yield moment of the connection was established, fulfilling the objectives of this research.    70 The experimental work was completed with one specific material and properties for wood, steel and adhesive, thus to provide general design guideline, further experiments are required with different rod types and diameters, different adhesives, as well as different wood species. The addition of shear reinforcements and their effect on the moment capacity should also be researched since shear forces can be the governing load.  The possibility to predict the yield moment of glued-in rod timber connections will, eventually, allow design of full sized timber frames as the main moment resistance member or in combination with a steel hub. 71 References Andreolli, M., Piazza, M., Tomasi, R., & Zandonini, R. (2011). Ductile moment-resistant steel-timber connections. Proceedings of the Institution of Civil Engineers - Structures and Buildings, 164(2), 65-78. Batchelar, M. L. (2007). Timber Frame Moment Joints with Glued-In Steel Rods - A Designer's Perspective. NZ Timber Design Journal, 15(2). Blass, H., & Laskewitz, B. (1999). Effect of Spacing and Edge Distance on the Axial Strength of Glued-In Rods. (pp. CIB-W18/32-7-12). Graz: International Council for Research and Innovation in Building and Construction. British Columbia, Office of Housing and Construction Standards, National Research Council Canada. (2012). British Columbia Building Code 2012. British Columbia, Canada: Office of Housing and Construction Standards. Bruhl, F., & Kuhlmann, U. (2012). Connection Ductility in Timber Structures Considering the Moment-Roation Behavior. World Conference on Timber Engineering. Auckland. Buchanan, A., Moss, P., & Wong, N. (2001). Ductile moment-resisting connections in glulam beams. NZSEE Conference. Taupo, New Zealand. Canadian Commission on Building and Fire Codes. (2010). National Building Code of Canada 2010. 2. Ontario, Canada: National Research Council Canada. Canadian Standards Association. (2010, March). CSA S16-09 Design of steel structures. Ontario, Canada. 72 Canadian Standards Association. (2014, June). CSA A23.3-14 Design of concrete structures. Ontario, Canada. Canadian Standards Assoiation. (2014, May). CSA O86-14 Engineering design in wood. Ontario, Canada. CEN European Committee for Standardiztion. (2005). EN 12512: Timber structures - Test methods - Cyclic testing of joints made with mechanical fasteners. Brussels. del Senno, M., Piazza, M., & Tomasi, R. (2004). Axial glued-in steel timber joints - experimental and numerical analysis. Holz Roh Werkst, 62(2), 137-146. Deutsches Institut fur Normung e.V. (2004). Norm DIN 1052:2004-08 Entwurf, Berechnung und Bemessung von Holzbauwerken. Berlin, Germany: DIN. Fragiacomo, M., & Batchelar, M. (2012). Timber Frame Moment Joints with Glued-In Steel Rods. I: Design. Journal of Structural Engineering, 138(6), 789-801. Fragiacomo, M., & Batchelar, M. (2012). Timber Frame Moment Joints with Glued-In Steel Rods. II: Experimental Investigation of Long-Term Performance. Journal of Structural Engineering, 802-811. Gattesco, N., Gubana, A., & Buttazzi, M. (2010). Cyclic Behaviour of Glued-In-Joints under Bending Moments. World Conference on Timber Engineering. Riva del Garda. Gilbert, C., Gohlich, R., & Erochko, J. (2015). Nonlinear Dynamic Analysis of Innovative High R-Factor Hybrid Timber-Steel Buildings. The 11th Canadian Conference on Earthquake Engineering. Victoria. 73 Gonzalez Barillas, E. (2015, September). Performance of Timber Connections with Single and Multiple Glued-In Threaded Steel Rods. Vancouver, British Columbia, Canada: The University of British Columbia. Government of Canada. (2015, January 21). The benefits of wood in building construction. Retrieved January 18, 2016, from Natural Resources Canada: http://www.nrcan.gc.ca/forests/video/16213 Ibarra, L. F., Medina, R. A., & Krawinkler, H. (2005, June 13). Hysteretic models that incorporate strength and stiffness deterioration. Earthquake Engineering & Structural Dynamcis, 34, 1489-1511. Jensen, J. L., & Gustafsson, P.-J. (2004). Shear strength of beam splice joints with glued-in rods. The Japan Wood Research Society, 50, 123-129. Jensen, J. L., & Quenneville, P. (2009). Connections with Glued-In Rods Subjected to Combined Bending and Shear Actions. CIB-W18/42-7-9. Duebendorf: International Council for Reserach and Innovation in Building and Construction. Kangas, J. (2000). Capacity, Fire Resistance and Gluing Pattern of the Rods in V-Connections. CIB-W18/33-7-10. Netherlands: International Council for Research and Innovation in Building and Construction. Krawinkler, H., Parisi, F., Ibarra, L., Ayoub, A., & Medina, R. (2000). Development of a Testing Protocol for Woodframe Structures. Richmond: CUREE Publication No. W-02. 74 Lam, F., Schulte-Wrede, M., Yao, C., & GU, J. J. (2008). Moment resistance of bolted timber connections with perpendicular to grain reinforcements. Proceedings of 10th WCTE. Miyazaki, Japan. Lehringer, C. (2012). PURBOND 2C-Adhesives. Cost action FP 1004 Report. Wrozlaw, Poland: Purbond AG. Madhoushi, M., & Ansell, M. P. (2008). Behaviour of timber connections using glued-in GFRP rods under fatigue loading. Part II: Moment-resisting connections. Composites: Part B, 39, 249-257. Metten, A. W. (2012). Structural Steel for Canadian Buildings: A Designer's Guide. Vancouver: Andy Metten. Otero Chans, D., Estevez Cimadevila, J., & Martin Gutierrez, E. (2010). Model for predicting the axial strength of joints made with glued-in rods in sawn timber. Construction and Building Materials, 1773-1778. Parida, G., Johnsson, H., & Fragiacomo, M. (2013). Provisions for Ductile Behavior of Timber-to-Steel Connections with Multiple Glued-In Rods. Journal of Structural Engineering, 139(9), 1468-1447. Piazza, M., Polastri, A., & Tomasi, R. (2011, April). Ductility of timber joints under static and cyclic loads. Structures and Buildings, 164(SB2), 79-90. Tlustochowicz, G., Serrano, E., & Steiger, R. (2011). State-of-the-art review on timber connections with glued-in steel rods. Materials and Structures, 44, 997-1020. 75 Xu, B., Bouchair, A., & Racher, P. (2012). Analytical study and finite element modelling of timber connections with glued-in rods in bending. Construction and Building Materials, 34(1), 337-345.   76 Appendices Appendix A   Calculation of Theoretical Yield Moment Capacity   Figure A.1: Theoretical Yield Moment Calculation  Table A.1: Specimen Layout Properties  Spec. b (mm) h (mm) edge, e (mm) numrod (in tension) A1(a) 80 266 33 1 B2(a) 130 266 33 2 C3(a) 175 266 33 3 D2(a) 130 456 33 2 D4(a) 130 456 33+64 4 With the specimen layout properties summarized in Table A.1, and assuming that plane sections remain plane and that the traditional elastic transform section theory applies (illustrated on Figure A.1), the theoretical yield moment was calculated for each specimen layout. The MATLAB code used for this calculation is given below.  %Material Properties %Steel Es=2*10^5; %MPa fy=360; %MPa dim=12.7; %mm   %Wood Ew=12400; %MPa fc=30.2; %MPa  77   %calculation hs=h-edge; %mm As=pi()*(dim/2)^2*numrod; %mm^2   %finding Neutral Axis NAall=roots([1/2*b*Ew As*Es -As*Es*hs]); %polynomial constants NA=NAall(NAall>0); %keeping on positive roots   %Finding Moment Capacity ey=fy/Es; Fy=fy*As; jds=hs-NA;   ew=NA*ey/(hs-NA); Fw=1/2*b*NA*ew*Ew; jdw=2/3*NA;  if ew > fc/Ew     warning('Wood has crushed') end   if ew > fc/Ew     warning('Wood has crushed with ey') end   Mtheoryield=(Fy*jds+Fw*jdw)*10^-6; %kNm   78 Appendix B  Moment-Rotation Curves under Monotonic Loading The moment-rotation curves and the analysis of each (a)-type test specimen, under monotonic loading, not included in the main body of the thesis, are shown in Figure B.1 through Figure B.14.   Figure B.1: Moment-Rotation Curve of A1(a)-1 (2) 79  Figure B.2: Moment-Rotation Curve of A1(a)-1 (3)  Figure B.3: Moment-Rotation Curve of A1(a)-1 (4) 80  Figure B.4: Moment-Rotation Curve of B2(a)-1 (1)  Figure B.5: Moment-Rotation Curve of B2(a)-1 (2) 81  Figure B.6: Moment-Rotation Curve of B2(a)-1 (4)  Figure B.7: Moment-Rotation Curve of C3(a)-2 (1) 82  Figure B.8: Moment-Rotation Curve of C3(a)-2 (2)  Figure B.9: Moment-Rotation Curve of C3(a)-2 (4) 83  Figure B.10: Moment-Rotation Curve of D2(a)-1 (2)  Figure B.11: Moment-Rotation Curve of D2(a)-1 (3) 84  Figure B.12: Moment-Rotation Curve of D2(a)-1 (4)  Figure B.13: Moment-Rotation Curve of D4(a)-1 (1) 85  Figure B.14: Moment-Rotation Curve of D4(a)-2 (3)   86 Appendix C  Moment-Rotation Curves under Quasi-Static Cyclic Loading The moment-rotation curves and analysis of each test specimen, under quasi-static cyclic loading, which were not included within the main body of the thesis, are shown in Figure C.1 through Figure C.12.   Figure C.1: Moment-Rotation Curve of A1(a)-2 (1) 87  Figure C.2: Moment-Rotation Curve of A1(a)-3 (3)  Figure C.3: Moment-Rotation Curve of A1(a)-3 (4) 88  Figure C.4: Moment-Rotation Curve of B2(a)-3 (1)  Figure C.5: Moment-Rotation Curve of B2(a)-2 (2) 89  Figure C.6: Moment-Rotation Curve of C3(a)-3 (2)  Figure C.7: Moment-Rotation Curve of C3(a)-3 (3) 90  Figure C.8: Moment-Rotation Curve of D2(a)-2 (2)  Figure C.9: Moment-Rotation Curve of D2(a)-3 (3) 91  Figure C.10: Moment-Rotation Curve of D2(a)-3 (4)  Figure C.11: Moment-Rotation Curve of D4(a)-3 (1) 92  Figure C.12: Moment-Rotation Curve of D4(a)-3 (2) 

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