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Performance of timber connections with single and multiple glued-in threaded steel rods González Barillas, Enrique 2015

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  PERFORMANCE OF TIMBER CONNECTIONS WITH SINGLE AND MULTIPLE GLUED-IN THREADED STEEL RODS by  Enrique González Barillas  B.S., THE UNIVERSITY OF TEXAS AT AUSTIN, 2007   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)  September 2015  © Enrique González Barillas, 2015ii ABSTRACT  The experimental research conducted within this thesis project focused on joints composed of softwood glulam members and mild steel glued-in threaded rods.  In a first phase, the influence of the embedment length and the rod diameter using three different adhesives was studied to establish performance benchmarks.  In the second phase, the investigation focused on the influence of manufacturing defects on the capacity of timber joints with glued-in steel rods.  For this purpose, timber joints were manufactured with two different types of defects likely to be encountered during their manufacturing on-site: i) rods placed at an angle to the drill hole instead of being in the joint axis, and ii) rod placed at the edge of the drill hole instead of fully centred.  Finally, in the third phase, joints with multiple rods (two, three and four rods) were manufactured and tested.  The adhesive type and rod diameter were kept constant and the embedment length and the spacing between rods were varied during this phase.  In all phases of this experimental campaign, specimens were tested under uniaxial quasi-static tension loading.   The results showed that, for single glued-in rod joints using mild steel threaded rods, a ductile-type of failure can be consistently attained if the embedment length of the rod is long enough (>10d).  Furthermore, the results for specimens with bonding defects considered in this study had no significant negative impact on the capacity of the joints if compared to the results obtained in the first experimental phase. Finally, a spacing between rods greater than four times the rod diameter demonstrated to be sufficient to facilitate a ductile steel yielding failure as long as the joints were manufactured with sufficient embedment length (>10d).  The results from this study can contribute towards better understanding of the influence that the parameters under investigation have on the performance on timber joints with glued-in rods, as well as to translate iii this information to promote the development of more studies on further applications such as moment resisting connections.  iv PREFACE This thesis is original, unpublished & independent work by the author; Enrique Gonzalez Barillas, under the supervision of Dr. Thomas Tannert. The experimental campaign was partially done in collaboration with Coralie Avez, Masters Candidate at the University of Mons in Belgium, from May to August 2014.            v TABLE OF CONTENTS  ABSTRACT .................................................................................................................................... ii PREFACE ...................................................................................................................................... iv TABLE OF CONTENTS ................................................................................................................ v LIST OF TABLES ........................................................................................................................ vii LIST OF FIGURES ..................................................................................................................... viii ACKNOWLEDGEMENTS ............................................................................................................ x DEDICATION ............................................................................................................................... xi CHAPTER 1: INTRODUCTION ............................................................................................ 1 1.1 OVERVIEW OF GLUED-IN ROD CONNECTIONS ................................................ 1 1.2 RESEARCH NEED ...................................................................................................... 2 1.3 OBJECTIVES ............................................................................................................... 3 CHAPTER 2: STATE-OF-THE-ART REVIEW ..................................................................... 4 2.1 INTRODUCTION ........................................................................................................ 4 2.2 MATERIALS ............................................................................................................... 6 2.3 MANUFACTURING ................................................................................................... 9 2.4 MECHANICS OF GLUED-IN STEEL RODS .......................................................... 10 2.5 DESIGN PROPOSALS .............................................................................................. 18 vi CHAPTER 3: EXPERIMENTAL CAMPAIGN ................................................................... 25 3.1 MATERIALS AND METHODS ............................................................................... 25 3.2 PHASES #1 & #2:  SINGLE GLUED-IN RODS ...................................................... 34 3.3 STATISTICAL ANALYSIS FOR PHASES #1 & #2 ............................................... 43 3.4 DISCUSSION OF RESULTS FOR PHASE #1 & #2 ................................................ 46 3.5 PHASE #3:  MULTIPLE GLUED-IN RODS ............................................................ 54 3.6 STATISTICAL ANALYSIS FOR PHASE #3 ........................................................... 60 3.7 DISCUSSION OF RESULTS FOR PHASE #3 ......................................................... 64 3.8 COMPARISON WITH DESIGN MODEL PREDICTIONS ..................................... 68 CHAPTER 4: CONCLUSIONS ............................................................................................. 74 REFERENCES ............................................................................................................................. 76 APPENDIX A: LOAD DISPLACEMENT CURVES  ............................................................. 80   vii LIST OF TABLES Table 1 - Selected Adhesives Technical Data ............................................................................... 29 Table 2 – Parameters and Results for Phase #1 ............................................................................ 35 Table 3 – Relative Stiffness Results for Phase #1 ........................................................................ 36 Table 4 - Results from Phase #2 ................................................................................................... 40 Table 5 - Relative Stiffness Results for Phase #2 ......................................................................... 41 Table 6 – Variables and Results for Factorial ANOVA ............................................................... 44 Table 7 – Backwards elimination Curvi-linear Multiple Regression Analysis Results ................ 44 Table 8 - ANOVA Results for Phases #1 and #2.......................................................................... 45 Table 9 – Tukey’s HSD Test Results for factors and treatments in Phase #1&#2 ....................... 45 Table 10 - Tukey’s HSD Test Results for Statistical Significance for factors in Phase #1&2 ..... 45 Table 11 - Results for tests Phase #3 ............................................................................................ 59 Table 12 - Variables and Results for Factorial ANOVA for Phase #3 ......................................... 60 Table 13 - Curvilinear Multiple Regression Analysis Results for Phase #3 ................................. 61 Table 14 - Subsequent Two-way ANOVA Results (n & le) ......................................................... 61 Table 15 - Subsequent Two-way ANOVA Results (n & s) .......................................................... 62 Table 16 – Tukey’s HSD Test Results for factors and treatments in Phase #3 ............................ 63 Table 17 – Tukey’s HSD Test Results for Statistical Significance for factors in Phase #3 ......... 63 Table 18 - Statistical Results for Comparison of Data vs Design Models.................................... 73 viii LIST OF FIGURES Figure 1:  Schematic illustration of glued-in rod ............................................................................ 5 Figure 2:  Examples of applications of glued in steel rod connections .......................................... 5 Figure 3:  Knee joint with steel glued in rods connected to steel stiffener plate ............................ 7 Figure 4:  Steel threaded rods (left), GFRP rods (centre) & CFRP rods (right) ............................. 8 Figure 5:  Options for test loading conditions .............................................................................. 16 Figure 6:  Typical failure modes associated with glued-in rods ................................................... 17 Figure 7: Glued-in rod test specimens .......................................................................................... 27 Figure 8:  CR-421® (left); T88® (centre) and Gel Magic® (right) ............................................. 28 Figure 9:  Hundegger® Robot Drive CNC Machine .................................................................... 30 Figure 10:  Centering of rods using toothpicks ............................................................................. 31 Figure 11:  Typical test setup (left); and LVDT device (center and right) ................................... 32 Figure 12:  Geometry for specimens in Phase #1 ......................................................................... 34 Figure 13: Shear failure around rod (left); rod yielding (centre) and splitting of timber specimen (right) .................................................................................................................................... 37 Figure 14 – Avg. Load Displacement curves for tests in Phase #1 .............................................. 37 Figure 15:  Geometry of specimens with “un-centered” rods....................................................... 39 Figure 16:  Geometry of specimens with centered rods, but inserted at “an angle“ ..................... 39 Figure 17 - Avg. Load Displacement curves for tests in Phase #2 ............................................... 42 Figure 18 - Debonding failure between rod and timber ................................................................ 42 Figure 19 - Distribution of observed failure modes for d=19mm ................................................. 47 Figure 20 - Typical failure modes in Phase #1 with d=19mm: rod yielding (left), brittle pull-out of rod (right) .......................................................................................................................... 48 ix Figure 21 – Summary of capacities for d=12.7mm rods .............................................................. 49 Figure 22 - Summary of capacities for d=19mm rods .................................................................. 49 Figure 23 - Effect of manufacturing defect on Axial Capacity (5d embedment) ......................... 51 Figure 24 - Effect of manufacturing defect on Axial Capacity (10d embedment) ....................... 52 Figure 25 - Distribution of observed failure modes for d=12.7mm .............................................. 53 Figure 27 – Examples of test specimens in Phase #3 ................................................................... 54 Figure 28 – Side view of specimen geometry for Phase #3 .......................................................... 55 Figure 29 – Cross section of typical specimen geometry for Phase #3 ........................................ 55 Figure 30 – Observed failure modes in Phase #3: Pull-out (top left), splitting (top right), rod yielding (bottom) .................................................................................................................. 56 Figure 31 – Load Deformation Curve for (Le=5d, S=3d) ............................................................. 57 Figure 32 - Load Deformation Curve for (Le=7.5d, S=3d) ........................................................... 57 Figure 33 - Load Deformation Curve for (Le=7.5d, S=5d) .......................................................... 58 Figure 34 - Load Deformation Curve for (Le=15d, S=5d) ............................................................ 58 Figure 35 - Distribution of Observed Failure Modes for Phase #3............................................... 66 Figure 36 - Effect of rod spacing on avg. per rod capacity at le=15d ........................................... 66 Figure 37 - Representative (per rod) load-deformation curve ...................................................... 67 Figure 38 - Comparison of specimens with single rods (d=12.7mm) to Design Models ............. 70 Figure 39 - Comparison of specimens with single rods (d=19mm) to Design Models ................ 70 Figure 40 - Comparison of specimens with 2 rods (d=12.7mm) to Design Models ..................... 71 x ACKNOWLEDGEMENTS • To my supervisor, Dr. Thomas Tannert, for his support, patience and relentless desire for the success of this research project • Vincent Leung, for his invaluable support and patience throughout the duration of this research project • George Lee, for his patience and technical savvy for the correct execution of Phases 1 & 2 of the experimental campaign • Harald Schrempp, for his support, advise and vital involvement in the execution of Phase 3 of the experimental campaign • John Wong, for his invaluable technical support during the electrical and data collection system setup for Phase 3 • Lawrence Gunther for his generous help during fabrication of the test specimens at the CAWP • John Boys, for his contribution and support given for the execution of Phases 1 &2 of this project • Chris Whelan and Christian Lehringer from Purbond®, for their generous contribution of the CR-421® adhesive utilized throughout the execution of this research project • Coralie Avez and Adam Geber, for their support and assistance during fabrication of the test specimens • Dr. Antal Kozak for his valuable guidance and help to carry out the statistical analysis of the data collected throughout this research project • To my wife, for her optimism and vital encouragement throughout this whole process xi DEDICATION   TO MY WIFE & PARENTS, FOR THEIR UNWAVERING SUPPORT   1  CHAPTER 1: INTRODUCTION 1.1 OVERVIEW OF GLUED-IN ROD CONNECTIONS Wood has a very rich tradition as a building material in North America.  Its aesthetically pleasing appearance as well as well-established building provisions have allowed wood to become a very popular choice, especially for the residential housing market.  With the flourishing of sustainable design practices and society’s general disposition towards sustainability, wood has established itself as a premiere building material aside with reinforced concrete and structural steel.  For this reason, wood’s general acceptance and popularity has been steadily growing in North America. Connections between timber members are one of the most crucial aspects when designing timber structures.  The selection of the type of connection depends on various factors such as type of load, direction of load transfer, required strength, ductility, stiffness and finally the cost.  These connections can range from more traditional bolted or nailed connections, to more modern, but less understood joints, such as glued-in rod connections.   Joints utilizing glued-in steel rods have been used for decades for connecting new and reinforcing existing members in timber structures.  Their main advantage is that the connection itself is concealed within the timber member, effectively providing the joint with a higher fire rating as well as a more aesthetically pleasing “look” in comparison with traditional dowel-type connections.  Since the 1980s, extensive research has been conducted to better understand and predict the performance of joints with glued-in steel rods.  Unfortunately, no consensus has been agreed upon by the research community.   2 1.2 RESEARCH NEED Most of the research on timber connections with glued-in rods has been conducted on perfectly centric placed single rods, and very little tests have been carried out on connections with manufacturing inaccuracies or multiple glued-in rods.  As stated previously, despite the numerous research projects conducted in North America and the European Union over the past three decades, there is still no universal standard for the design of glued-in rods in timber applications.  The main problems have risen due to the many different approaches available in the literature for defining the behaviour of the glued-in connections.  The question lies in what kind of approach (strength analysis, linear elastic fracture mechanics, non-linear fracture mechanics) is more appropriate, and which parameters (embedment length, diameter of rod, load-to-grain angle, density of timber, moisture content) should be considered in the final design provisions (Stepinac, 2013).  Even more critical is the state of the design of multiple glued-in rods, since most of the research conducted has been concerned with uniaxial tension and axial capacity tests of single glued-in rods.    For that reason, this project focused on conducting tests of joints with single and multiple glued-in steel rods under uniaxial tension loads.  First, tests were carried out utilizing a single mild steel grade threaded rod in a glulam member, followed by similar tests on glulam members with multiple glued-in rods.  In addition, test specimens with single glued-in rods were manufactured with “defects” in order to determine the effects, if any, that these manufacturing defects have on the performance of this type of connections.   3 1.3 OBJECTIVES The main objective of this experimental study is to investigate the possible effects that various parameters (i.e., adhesive type, rod diameter, embedment length of the rod, manufacturing defect, number of rods and spacing between rods) have on the failure mode of glued-in rod connections in order to safely predict the conditions upon which a ductile type failure mode will occur. The specific objectives are to: i) Determine the performance and parameters affecting the behaviour of joints using a single glued-in steel rod (Phase #1); ii) Gain insight on the influence that manufacturing defects have on the performance and behaviour of joints using a single glued-in rod (Phase #2); and iii) Determine the performance and parameters affecting the behaviour of joints using a multiple glued-in rods (Phase #3). The data provided by this research project will shed some light on the prediction of the behaviour of this type of joint and will, eventually, promote a unified design methodology and provisions for single and multiple glued-in rod connections under uniaxial loads. 4 CHAPTER 2: STATE-OF-THE-ART REVIEW 2.1 INTRODUCTION Glued-in steel rods were originally developed in Sweden in the 1960’s (Wiktor, 1990).  Yet, it was not until the 1980’s that heavy research was initiated on the topic and is still ongoing (Tlustochowicz et al., 2011).  Although extensive research has been conducted, no general consensus over design methodology has been achieved.  For that reason, neither the Canadian nor European Timber design codes include generalized provisions for the design of glued-in steel rod connections (Tlustochowicz et al., 2011).  As a result, even though the technology of glued-in steel rods has evolved significantly in the past 20 years, in practice they are used in only a few countries (Faghani, 2013). Glued-in steel rods are considered a hybrid, modern-day solution for timber structure connections.  They are called “hybrid” because they utilize 3 different materials; rod material, adhesive and a timber host.  Essentially, this connection consists of a bar glued-in, or bonded, into the timber members by means of an adhesive.  Different types of rod materials can be glued-in to timber: steel, fibre reinforced polymers (FRP’s), and wood. Because ductility is attainable by means of using steel rods, these are most commonly used (Faghani, 2013).  Additionally, threaded rods provide the versatility in that the rods can be connected to steel elements via the use of traditional nuts and washers.  Figure 1 shows a conceptual illustration of a single glued-in steel rod. 5  Figure 1:  Schematic illustration of glued-in rod  Threaded steel rods bonded into timber elements are very efficient joints that can withstand high axial forces and exhibit excellent strength and stiffness while still being relatively lightweight (Steiger et al. 2006).  Additionally, glued-in steel rod connections are appealing because of the concealment of the connector inside the wood member.  This is both an architecturally and aesthetically pleasing feature if compared against conventional dowel-type timber connectors and is of importance because it also provides the glued-in rod with excellent fire and corrosion protection (Tlustochowicz et al., 2011).  Figure 2 shows some examples of classic applications of connections with glued-in rods (Bainbridge, 2002). These typical applications range from post-foundation connections (left), to external column-beam moment frame connections (center), to internal column-beam moment frame connections (right).  Figure 2:  Examples of applications of glued in steel rod connections 6 2.2 MATERIALS A general overview of the three materials that are utilized to fabricate a glued-in steel rod connection is presented.  These materials are: the timber host, the rod material and the adhesive. 2.2.1 Timber  In order to assure a good performance by the connection, good quality of timber must be guaranteed by exclusively using strength graded timber and glulam subjected to quality control (Tlustochowicz et al., 2011).  Glued-in rods are typically utilized for large load bearing joints, and therefore glulam members made from softwoods are normally used (Madhoushi & Ansell, 2008).  The rods are embedded into the timber element normally parallel or perpendicular to the grain orientation of the wood.  When designing glued-in rod connections, orientation of the rod with respect to the grain orientation of the timber is of critical importance as the capacity of the joint is highly dependent on the grain orientation strength.   Research efforts have been targeted to comprehend the potential effects that loading angles relative to grain angle of the timber host have on the axial capacity and subsequent failure mode.  In particular, one research project focused on the behaviour of rods glued-in parallel to the grain determined that these types of joints are highly susceptible to the density of the timber host (Steiger et al. 2006) meanwhile, a subsequent research project focused on the behaviour of rods glued-in perpendicular to the grain claimed that these types of joints are less susceptible to the timber member’s density (Widmann et al. 2007).  As these tests were done on a very specific glulam fabricated out of Norwegian spruce lamella, this general characterization is yet to be validated for North American S-P-F and Douglas fir based glulam.  7 2.2.2 Rod  The rod material selected for glued-in rod connections plays a large role in the design.  Ideally, glued-in joints should be designed in a way that allows for rod failure (yielding) to occur, rather than a brittle wood or adhesive failure mode (Steiger et al. 2006).  For that reason, the most common rod material used is mild steel because it permits ductility to control the design rather than a sudden (Gattesco & Gubana, 2006).  Most commonly, rods with threads are used because these provide an increased interface surface area for adhesion as well as the potential for mechanical interlocking to occur between rod and adhesive surface (Yeboah, Gilbert, & and Gilfillan, 2011).  Furthermore, threaded steel rods are especially convenient when using glued-in rod connections for timber-steel applications because the threads allow for easy assemblage (Tlustochowicz et al., 2011), as illustrated in Figure 3 (Malczyk, 1993).   Figure 3:  Knee joint with steel glued in rods connected to steel stiffener plate Other solutions have been presented as substitutes for threaded steel rods.  In Finland, a connection was developed using reinforcement ribbed bars (rebars) glued-in at skewed angles.  These connections, known as V-connections, have shown to be an efficient alternative regarding both manufacturing process and performance (Kangas & Kevarinmäki, 2001).  Another solution 8 that has gained popularity in recent years is the application FRP as a substitute for the rod material.  Finally, glued-in connections can also be realized by using hardwood dowels.  This last option has the advantage that it yields a much smaller difference in moduli of elasticity between the rod material and the timber elements being connected.  This type of technology is not common worldwide, and is mostly studied and used in Japan (Tlustochowicz et al., 2011). Figure 4 (Faghani, 2013) illustrates some of the different types of rod materials commonly utilized for glued-in rod connections.    Figure 4:  Steel threaded rods (left), GFRP rods (centre) & CFRP rods (right) 2.2.3 Adhesive  Similar to the mechanics of reinforced concrete, the performance of a glued-in rod highly depends upon the correct bonding properties and mechanisms developed between the rod material and the timber element that it will be embedded in.  The main purpose of the adhesive in a glued-in connection is to provide the continuous bond between the timber and the rod to effectively transfer and withstand loads.  During early works, the common adhesives used were phenol-resorcinol (PRF) and epoxy-based (EPX) adhesives.  More recently, polyurethane based adhesives (PUR) are also being utilized (Fueyo et al., 2010). The European Glued-in Rods for 9 Timber Project, GIROD, conducted extensive studies on the performance of these three adhesive types and compared their performances.  When all other parameters were held constant, PRF adhesives exhibited the lowest average axial capacity, then PUR based adhesives and EPX based adhesives showed to have the highest axial capacity (Bengtsson & Johansson, 2001).   The main goal during the design phase of a glued-in connection is to make sure that the adhesive bond will not be the weakest link of the joint.  Therefore, geometric and mechanical properties such as adhesive adherence strength, thickness of glue line, bore hole diameter, rod diameter, and embedment length of the rod should all be taken into account to avoid a brittle failure mode (Steiger et al. 2006).  More recent studies have shown that one of the most important characteristics of PUR based adhesives is their gap-filling ability.  This effectively reduces the potential for entrapment of air bubbles that could lead to a weak bond, and eventual failure in the timber-adhesive interface.  Additionally, PUR based adhesives have comparable shear strengths to that of commonly used EPX based adhesives, and it has been suggested that they can also be classified as non-brittle (Lehringer, 2012). 2.3 MANUFACTURING  As is the case for all structural adhesive joints, glued-in rod connections require special attention during the manufacturing process.  For these type of joints to perform to their expected capabilities it is essential to guarantee specific adhesive curing conditions (i.e. temperature and moisture content), as well as precise geometrical properties.  These specific characteristics demand that quality control during the manufacturing process of glued-in rod connections be very stringent (Tlustochowicz et al., 2011).  As a result, quality control is viewed as one of the biggest limitations for the use of glued-in rods for on-site applications.  Furthermore, quality 10 control regulations for factory/in-house manufacturing of glued-in rod connections still do not exist (Faye et al., 2004). In the work by Johansson (1995), the possibility of horizontally gluing in of the rods was tested.  In general, this procedure resulted in a non-uniform distribution of the adhesive interface and consequentially, led to substantial decrease in the expected pull out strength of the connection.  If the joint is to be constructed with an oversized hole, one simple method is to apply a well-defined amount of adhesive into the bottom of the hole and then insert the rod (while rotating it to assure uniform spread of the adhesive).  This method usually requires special equipment to insert the rod as it is very difficult to embed the entire length of the rod manually (Tlustochowicz et al., 2011). In Sweden, the manufacturing of bonded-in rods by the use of undersized holes has gained popularity.  Typically, the diameter of the hole is equal to the nominal size of the rod minus the depth of the thread of the rod.  By applying adhesive to the hole and the rod itself, and then screwing the rod into the hole, the bonded-in connection is formed.  One advantage of this method is that the adhesive is better retained in the hole before curing (Tlustochowicz et al., 2011).  In contrast, the disadvantage is that by using this method it is very difficult to guarantee that adhesive has reached all parts of the rod within the timber element.    2.4 MECHANICS OF GLUED-IN STEEL RODS 2.4.1 General Remarks  To better comprehend the mechanical performance of connections with glued-in rods it is important to recognize the predominant mechanisms that control the behaviour of these 11 connections.  As previously stated, this hybrid-type joint is typically made up of three different materials (timber, steel and adhesive) that have different stiffness and strength properties.  The complexity for these joints is that the three materials are expected to transfer loads and deform simultaneously under loading.  This, along with the wide range of geometric and mechanical parameters that can alter the behaviour of a glued-in connection, are the main reasons for today’s general lack of full understanding of the behaviour of this joint type and therefore one reason why there hasn’t been agreement for the use of a unique design model (Tlustochowicz et al., 2011).   Research on glued-in rods has been conducted primarily to better understand the factors that influence the joint performance, as well as to find models that can accurately predict the performance of these joints under simple load cases.  For this reason, and to reduce the amount of influential parameters that can alter performance of glued-in connections, the majority of tests have been realized on single rod glued-in joints under axial loading.  Determination of the variability and influence of material, geometric and other parameters on joint strength has been the focus of most research.   Even though in practice connections that use a single glued-in rod are not very common, testing of single rods allows for a simplified analysis and isolation of parameters and their influence on the mechanical performance of the joint (Tlustochowicz et al., 2011).  The parameters that have been investigated can be classified into three main groups (Dunky et al., 2008): i) Geometrical parameters ii) Material parameters iii) Loading/Boundary conditions  12 2.4.2 Geometrical Parameters  Various experimental studies evaluated the impact of embedment length of the rod into the timber member on axial capacity.  For example, Otero Chans et al. (2011) concluded that the failure load increases with larger rod length and larger rod diameters, but this relationship is not linear and difficult to model. Yet, previous published research concluded that increasing the embedment length of the rod increases the axial capacity of the connection, but at the same time a decrease in the nominal shear strength of the connection was noted and could be attributed to the non-uniform distribution of shear stresses along the embedded length (Steiger et al., 2006) (Kangas, 2000) (Gerold, 1992).   The diameter of the rod is another commonly investigated parameter influencing the axial capacity of single glued-in rod connections.  However, the influence of this parameter has been extremely challenging to simplify due to the many different experimental approaches taken in experimental works and the complexity and large number of variables in the joint structure. Research by Otero Chans et al. (2008 & 2010) and Broughton & Hutchinson (2001) found no significant effect of diameter of the rod on axial capacity for the range of diameter studied.  Yet, earlier studies revealed a slight dependency of the axial capacity on the rod diameter, or the drill hole diameter in case of wood failures.  Steiger et al. (2006) did not characterize the diameter of the rod as an independent influence factor.  Instead, they combined it with the embedment length of the rod into the timber member.  The influence of both parameters combined, rod diameter (d) and embedment length (le) -assuming a constant and uniform adhesive line thickness- produced their concept of a slenderness parameter (λ = le/d) as an influence parameter. 13 Other important factors that have been studied are edge distance and rod spacing.  According to many studies, there is a high influence associated with the ultimate axial capacity of glued-in rod connections attributed to the distance the center of the rod is placed from the edge of the timber element, as well as the center-to-center rod spacing between rods for multiple glued-in rod scenarios (Tlustochowicz et al., 2011).  For example, Serrano et al. (2008) claimed that if the edge distance is too small, a splitting failure mode will govern and control the strength of the connection.  Previously, it was recommended that a minimum edge distance of two-and-a-half times the diameter of the rod should be used -2.5d- as well as a minimum rod spacing distance between rods of five times the rod diameter -5d- (Blass & Laskewitz, 1999).  The New Zealand Timber Design Guide of 2007 (Buchanan, 2007) suggested that a minimum of 2d should be used as minimum rod spacing, and that a maximum of 3 rods should be used per row within a connection.    Bond line thickness influence has also been studied in research performed by Gustafsson & Serrano (2001), and Bengstsson & Johansson (2001).  Yet again, no general consensus has been reached upon the direct relationship between the thickness of the adhesive line and connection strength, and one possible reason is the fact that different adhesive thicknesses affect different types of adhesives differently.  From a theoretical point of view, an increase in the bond line thickness should increase the net surface area of bond between rod and wood element and therefore should cause a more uniform distribution of stresses and higher axial capacity. Similarly, a thicker glue line will result in a generally more flexible bond between wood and rod elements (Tlustochowicz et al., 2011).  Unfortunately, research performed on these parameters has not yielded convincing and consistent evidence to back up the previous generalization.  14 Turkovsky (1989) was among the first researchers to propose that the behaviour of connections with multiple glued-in rods varied from single glued-in connections and recommended accounting for irregular force distributions in multiple glued-in rod connections.  If a multiple rod connection is compared to a single rod connection, a non-uniform distribution of forces and interference between the rods can occur.  In cases where brittle failure modes govern the strength of the joint, it can be expected that no plastic redistribution of forces takes place and therefore, the failure of one rod may initiate the irreversible failure of the whole connection (Gehri, 2010).  A uniform distribution of forces can only be achieved if the rod strength is made the weakest and controlling factor within the connection (Tlustochowicz et al., 2011).   2.4.3 Material Parameters Opinions have differed on the influence that density of the timber member has on axial capacity.  From a theoretical point of view, the influence of the density of the timber member parameter has often been viewed as a secondary effect, meaning that changing the value of the density of the timber member will change the value of the parameters in the theoretical expressions for axial capacity (Tlustochowicz et al., 2011).  The recommendations given in Annex C to EN-1995-2 (2003) for the design of glued-in rod connections indicate that the axial capacity of these types of joints does depend on the wood density.  It is not surprising that this relationship exists knowing the influence density has on the capacity of nailed and screwed connections.  Otero Chans (2008; 2010) concluded that the correlation between timber density and axial capacity is non-linear in nature.  In contrast, other opinions state that the correlation between the density and the strength of the wood is generally poor and a generalization of the influence of density on glued-in rod connections might not be accurate (Bengtsson & Johansson, 2001).   15 Moisture content (MC) and change of MC of the timber member have been the focus of many research projects.  Shrinkage and swelling of the wood due to varying MC levels has been attributed to cause considerable stresses and cracking that may lead to a loss of adhesion of the joints with glued-in rods.  Although not explicitly referred to in any design code, all design codes limit and reduce the strength and stiffness of timber members subjected to higher MC conditions (service classes) (CEN, Eurocode 5- Part 5: Design of Timber Strctures., 2003).  This same logic should apply to glued-in rod joints; reason for which several studies have been conducted to determine the extent of the possible negative effects that higher MC can have on these types of connections.  Aicher & Dill-Langer (2001) for example, have focused on the effects that MC has on the adhesiveand found that EPX was unaffected by humid conditions in both short and long term loading conditions.  Meanwhile, connections adhered with PRF and PUR adhesives, showed a considerable decrease in strength in short term loading conditions in high humidity conditions.  Broughton et al. (2001) concluded that the use of glued-in rods in green timber members (MC>19%) is possible, if an appropriate strength reduction is included in the design. 2.4.4 Loading and Boundary Conditions  1) Loading to grain angle is relationship parameter that influences the strength of a glued-in connection.  From a theoretical point of view, bond strength between wood and rod member is highly dependent on wood strength.  Therefore, if loading is performed parallel or perpendicular to the grain orientation, the predominant strength of the wood member is different, and typically strength of the timber member is highest parallel to the grain (Tlustochowicz et al., 2011).  It could be expected that strength will be the highest when the orientation of load acts along the grain direction of the wood member, and weakest when it acts perpendicular to the grain 16 orientation (Tlustochowicz et al., 2011).  This notion was confirmed within the framework of the GIROD project (Bengtsson & Johansson, 2001) but challenged by Widmann et al. (2007) who observed that axial capacity for glued-in rods bonded perpendicular to the grain was between 20%-50% higher than for rods bonded parallel to grain of the wood member.   2) Loading and boundary conditions are test specific parameters that researchers have studied as a possible reason for variability in results.  These parameters account for how tests were set-up and how the loading was applied to the glued-in rod connection.  Different possible alternatives that have been studied are illustrated in Figure 5 (Tlustochowicz et al., 2011) with the pull-pull condition being the most commonly applied test set-up.  Figure 5:  Options for test loading conditions 3) The duration of load effect on glued-in rod connections has been studied by Aicher & Dill-Langer (2001) in combination with the effects of varying MC levels.  As previously stated, their research found that EPX adhesive suffered no significant strength decrease under humid 17 conditions in both short and long term durations, while PRF and PUR adhesive types did show a significant decrease in strength during short-term loading conditions in high humidity climates.  It should be expected that when glued-in rods find their way into a design provision, for long durations of load their strength should be reduced while for very short durations of load (i.e. impact) their strength should be marginally increased.  2.4.5 Failure Modes As explained in the previous section, the mechanical performance of glued-in rods depends on many parameters.  In general, it can be said that there are five types of principal and widely recognized failure modes associated with glued-in steel rod connections (Tlustochowicz et al., 2011), illustrated in Figure 6:  a) Shear along the steel rod (brittle) b) Tensile failure of the wood member (brittle) c) Shear block failure in the wood member (brittle) d) Cracking of the wood member (brittle) e) Yielding of the steel rod (ductile)  Figure 6:  Typical failure modes associated with glued-in rods 18 Brittle connection failure modes are generally avoided by designers as they may pose a safety hazard on occupants and users of buildings.  These failure modes may occur instantaneously and without previous warning, and therefore are at times highly difficult to accurately predict.  For that reason, it can be said the “ideal” failure mode for a glued-in connection should be ductile by means of yielding of the rod.  Furthermore, for moment-resisting joints using multiple glued-in rods, brittle shear failure in the timber is a concern where shear demands are high (i.e. close to supports) and the connection shall be designed such that adequate shear capacity is provided for the flexural strength to become effective (Buchanan et al., 2001).   2.5 DESIGN PROPOSALS 2.5.1 Theoretical Background There are three general approaches to predict the capacity of connections with glued-in rods: (Tlustochowicz et al., 2011): a) Traditional elasto-plastic strength approaches  b) Linear elastic fracture mechanics (LEFM) and  c) Nonlinear fracture mechanics (NLFM)  In a traditional strength approach, a prediction of stress or strain distribution of the joint is performed for a given loading situation and then a failure criterion is applied for this distribution.  The stress and strain distributions can be determined through the use of analytical or numerical models.  When using a LEFM approach, the assumption is made that the joint has a pre-existing crack.  Instead of following the procedure of a traditional strength approach, we then calculate the energy release rate for the joint.  The energy release rate is defined as the amount of elastic energy released during crack propagation.  By assuming that failure of the joint takes place when 19 the strain energy released is equal to the critical energy release rate of the joint, the load bearing capacity of the joint can be calculated.  Finally, a NLFM approach considers both previously mentioned methods.  In a sense, NLFM can be considered to be a unifying theory for both methods (Tlustochowicz et al., 2011).  All three approaches are results of further research done on the original Volkersen’s Theory on shear distribution of bonded joints (Volkersen, 1953). Most available design approaches for glued-in rods in regards to axial load resistance (i.e. axial capacity) are derived from one of these three general approaches.  If a technique similar to that used for reinforced concrete is applied, glued-in rods can be designed to yield before the brittle failure of the adjoining wood members and be compared against the actual experimental results of behaviour in bending.  This section will highlight some of the most prominent design methods for calculating the axial capacity of glued-in rod joints, including models proposed by Riberholt (1988), Gerold (1992), the GIROD Project (Bengtsson & Johansson, 2001), Annex C to prEN 1995-2  (CEN, 2003), Steiger et al. (2006) and the provisions within the German standards, DIN 1052: 2008-2012 (Stepinac, 2013).  2.5.2 Riberholt approach  Riberholt (1988) was a pioneer in the study of glued-in connections and established the first general design and sizing criteria for connections with glued-in rods.  The axial capacity is characterized by Equations 1 and 2, dependent upon the prescribed embedment length of the rod into the timber member. Fk = fws ∙ρk ∙ d∙√lg   for lg  ≥ 200mm    (1)  Fk = fwl ∙ ρk  d∙lg   for lg  < 200mm    (2)  20 where: Fk : characteristic failure load of joint; ρk : characteristic density of timber; d : rod diameter; lg : rod embedment length. The material constants fws and fwl also called withdrawal parameters for the root square and linear case respectively, are given by fws = 650 N/mm1.5 and fwl = 46 N/mm2 for non-brittle adhesives.  For brittle adhesives,   fws = 520 N/mm1.5 and fwl = 37 N/mm2.  These equations were derived from a purely empirical procedure by curve fitting of the experimental results. 2.5.3 Gerold approach Gerold (1992) proposed that rod slenderness should be considered in the calculation of axial capacity of a glued-in rod connection, while keeping timber density as one of the design parameters as described by Equation 3: Fmean = π d le (pmean/380)0.55 fv,mean       (3) where: Fmean : mean failure load of joint; d : rod diameter; le : rod embedment length; pmean : mean characteristic timber density; fv,mean : mean bond strength referring to a characteristic density of 380 kg/m3; 21 λ : slenderness ratio le/d with maximum value of 18. 2.5.4 GIROD approach The GIROD project concluded with preliminary design equations for the mean shear strength for EPX-based (Equation 4) and PRF-based (Equation 5) adhesives (Bengtsson & Johansson, 2001). fv,mean  = min of [8.0 N/mm2; 129 ∙ d-0.5 ∙  λ-0.62 ∙ (ρ/480)0.5]    (4)  fv,mean  = min of [6.3 N/mm2; 10.3 ∙ d-0.17 ∙  λ-0.08 ∙  (ρ/480)0.45]    (5)  where: d : d=dh;  dh  : bore hole diameter; λ : la/ dh; la : rod embedment length; dnom : nominal rod outside diameter; dh – dnom ≤ 2mm. The GIROD Project then presented a unified design formula, based on the generalized Volkersen theory (Volkersen, 1953).  In order to simplify the expressions, it was agreed that the simpler formula (Equation 6) for the pull-compression load case, which is a conservative approximation, was to be used thus the axial capacity is given by:   Pu = τf ∙  π ∙  d ∙  la ∙ (tanω / ω)        (6)  where: 22 Pu : characteristic axial capacity of a single rod glued-in connection; π d la : area of the bond; τf : local bond line shear strength; ω   = √(lgeo / lm).          The parameter lgeo, is a geometrical length parameter and lm is a material length parameter (a measure of the ductility of the bond line), and they are defined by Equations 7 & 8:  lgeo = ½ (π ∙ d ∙  le)2 ∙  (1/Ar + (Er/Ew)/Aw)      (7)  lm = Er ∙ (Gf / τf2)         (8) where: Ar : cross sectional area (mm2) of rod; Er : modulus of elasticity of rod material; Aw : cross sectional area (mm2) of timber host; Ew : modulus of elasticity of timber host; Gf : calculated from lm with the assumption Er=205,000 N/mm2. 2.5.5 Annex C to prEN 1995-2  Equation 9 was introduced as an informative Annex to prEN 1995-2  (CEN, 2003) to design for withdrawal strength of joints made with glued-in rods, in any timber type: Rax,k = π ∙ deq ∙  la ∙  fax,k ∙  (tanh ω / ω)       (9) where: 23 Rax,k : characteristic failure load of joint; fax,k  :  characteristic shear strength of the wood 5.5 N/mm2; D : hole diameter; d : rod diameter; deq : min [ D or 1.25∙d ]; la : rod embedment length; ω : 0.016 ∙ le / √deq 2.5.6 Steiger et al. Proposal  The experimental work performed by Steiger et al. (2006) led to a new design proposal: Fax,mean = fv0,mean ∙ π ∙ dh ∙ l       (10) where: Fax,mean : Characteristic failure load of joint; d  : rod diameter; dh  : hole diameter; l  : rod embedment length; λ  = le / d; ρ  : characteristic Density of timber; fv0,mean  : characteristic shear strength of the wood around the hole;   = 7.8 N/mm2 (λ/10)-1/3 (ρ/480)0.6 7.5< l / d <15 & 12< d <20 [mm]. 24 2.5.7 German Timber Design Standard, DIN 1052 The 2008 version of the German timber design provisions DIN 1052 (2008), included equation (11) to determine the capacity glued-in rod connections: Rax,k =  π ∙ d ∙ la ∙  fk1,d         (11) where: Rax,k  : characteristic failure load of joint; d  : rod diameter; la  : rod embedment length; λ  = la / d; fk1,d  : 4.0 N/mm2 for la<250 mm;   : (5.25 – 0.005) ∙ le  for N/mm2 for 250< la <500 mm;   : (3.5 – 0.15) ∙ le   for N/mm2 for 500< la <1000 mm. la (MIN) = max [0.5∙d2  ; 10∙d ]  & 6< d <30 [mm]. 25 CHAPTER 3: EXPERIMENTAL CAMPAIGN 3.1 MATERIALS AND METHODS 3.1.1 Introduction The experimental campaign for this thesis research consisted of three separate test phases and was carried out at the Materials and Wood Mechanics laboratories of the University of British Columbia Vancouver (UBC) between the months of January and October of 2014. Phase #1: Single glued-in rod;  Phase #2: Single glued-in rod with a manufacturing defect; Phase #3: Multiple glued-in rods. The specimens in each test phase had a similar layout.  For specimens with a single 12.7mm (1/2 inch) diameter rod in Phases #1 and #2, the specimen cross section was 79mm x 79mm. Moreover, for specimens with a single 19mm (3/4 inch) diameter rod in Phase #1, the specimen cross section was 114mm x 114mm.  For specimens in Phase #3, where the number of rods varied, the specimen depth was kept constant at 79mm and the specimen width varied according to the number of rods and the an established minimum edge distance, e.  This edge distance, e, between rod and the edge of the timber host was kept constant for all specimens at 3d (three times the rod diameter).  Finally, the specimen length varied as a function of the rod’s embedment length, le, as well as a function of design of the specimen “hold-down” testing connection.  Each specimen within was given an alpha-numeric tag in order to easily identify them.   26 Previous research on glued-in rod connections suggested that pull-pull loading conditions using specimens with glued-in rods in both ends of the specimens is optimal (Tlustochowicz  et al., 2011).  Yet, in order to reduce fabrication time, only one threaded rod per test sample was inserted and subsequently tested.   3.1.2 Materials As mentioned several times in the previous sections, connections with glued-in rods are complex hybrid joints as they involve three different materials simultaneously resisting the external loads (timber, rod and adhesive).  Consequently, the axial capacity of glued-in rods is strongly related to the timber species, the type of rod material and the adhesive type.  For this particular experimental project, both timber species and rod material were kept constant while different adhesive types were studied.   All test specimens were fabricated using Douglas-Fir 20f-E grade glulam and mild grade steel threaded rods (F’ymean = 360MPa). The yield strength was experimentally confirmed on five randomly selected samples following the procedure outlined in ASTM F606M-14 for carbon steel threaded rods.  It is worthwhile to mention that MC measurements were performed on all specimens before testing.  The average MC was 11.0% across all three phases with maximum and minimum values of 13.8% and 9.0%, respectively.  This is important because past studies and available design guidelines suggest a negative correlation between high MC, as well as MC variation, with axial capacity (SIA, 2003; Aicher & Dill-Langer, 2001; Broughton & Hutchinson, 2001).   27 Threaded rods were chosen because they provide the benefit that load-transfer can be assumed to occur entirely through mechanical interlock of the threads with the adhesive, instead of through bonding between adhesive and rod material (Tlustochowicz et al., 2011); (Gerold, 1992).  In addition, mild grade steel was chosen in order to facilitate a ductile type of failure of the rod.  Some representative test specimens can be seen in Figure 7.    Figure 7: Glued-in rod test specimens For Phase #1 & #2 three types of adhesives were considered: 1. CR-421 by Purbond®, (two-component polyurethane-PUR) 2. T88® by System Three® (low viscosity epoxy-EPX) 3. Gel Magic® by System Three® (high viscosity epoxy-EPX) For simplicity, from this point onward adhesives will be referred to using their commercial names; CR-421®, T88® and Gel Magic®.  All three adhesives (illustrated in Figure 8) were used in phases #1 and #2; while only CR-421® was utilized in Phase #3.  28  Figure 8:  CR-421® (left); T88® (centre) and Gel Magic® (right) PUR and EPX based adhesives are commonly used for on-site applications and this research aimed to provide results that were relevant for such applications. For simplicity, the adhesives are referred to using their commercial names; CR-421®, T88® and Gel Magic®. Both T88® and Gel Magic® are two component epoxies, yet they exhibit significantly different non-cured viscosity: 9000cps and 5,000cps for T88® and Gel Magic® respectively, which is a critical factor for on-site applications. CR-421® is a two-component PUR, with similar viscosity as T88®. and possesses a superior gap filling ability that allows to assume a better bond to the wood, but it exhibits the shortest open work time with 15 minutes compared to the 30 and 45 minutes for T88® and Gel Magic®, respectively. All three adhesives are expected to attain their bond strength by seven days of curing (Gel Magic® Data Sheet, T-88® Data Sheet, Lehringer 2012). Additionally, both structural EPXs can be relatively classified as non-brittle with 7% elongation at break, the PUR is considered brittle with 2% elongation at break.  Table 1 summarizes the main adhesive properties of interest to this study (Gel Magic® Structural Epoxy Adhesive Technical Data Sheet), (T-88® Structural Epoxy Adhesive Technical Data Sheet), 29 (Lehringer, 2012), including the percent strain values of elongation at break which allows for a relative categorization of their behaviour at failure.   Table 1 - Selected Adhesives Technical Data  Adhesive Viscosity  [cps] Open Work Time  [min] Expected Shear Strength                               (Parallel to grain)  [N/mm2] Tensile Elongation at Break  [%] CR-421® 9,000 10-20 7.8 2.0 (brittle) T88® 9,000 – 11,000 30 12.4 7.5 (non-brittle) Gel Magic® 5,300 40-60 12.4 7.0 (non-brittle) 3.1.3 Manufacturing Process Fabrication of the test samples consisted of four steps:   1)  Cutting and drilling of holes in timber specimens 2)  Cutting steel threaded rods to length 3)  Gluing and centering of rods into timber specimens 4)  Curing of glued-in rod specimens  First, timber hosts were cut into their test dimensions from a larger 6m long beam.  Blind holes were drilled where each rod would be subsequently embedded.  The embedment length, le, was varied throughout the testing campaign.  This blind hole, with diameter D, was constantly 4mm larger than the rod diameter, d, in order to maintain a constant thickness of the glue line of approximately 2mm.  Additional holes were drilled into the lower parts of the specimens for subsequently attaching them with steel bolts to metal side plates that attached the specimens to the frame of the testing apparatus.  These bolted connections were “over-designed” to guarantee failure in the glued-in rod connection while avoiding any deformation in the fixture.  Efficiency for this task was high as all specimens and holes were cut using UBC’s CNC heavy timber 30 processor Hundegger® Robot Drive, as shown in Figure 9.  To simulate normal on-site conditions, no surface preparation or sanding was performed on any of the wood members prior to insertion of the rods.   Figure 9:  Hundegger® Robot Drive CNC Machine Second, all threaded rods were cut to their appropriate lengths for gluing using a simple rebar cutter.  The rods were used as delivered by the supplier; no cleaning solvents or liquids were used on the rods prior to gluing to closely re-create on-site conditions.   Third, the required amount of adhesive was pushed into the blind holes using a standard gluing (or caulking) gun to then proceed and glue the rods into their timber hosts.  Different methods for fabrication have been used in the past (Tlustochowicz et al., 2011); herein, toothpicks were utilized to center the rods, as shown in Figure 10, for its simplicity and popularity for on-site applications among local fabricators.  Furthermore, in order to minimize the amount of entrapped air inside the adhesive after insertion, a twisting motion was performed when inserting the rods.  This helps assure that a proper bond was created throughout the entirety of the embedded rod.   Fourth, the test specimens were left to air-cure overnight in the workshop. The following morning, the test samples were placed into a constant climate room (20°C and 65%RH) for final 31 curing to achieve a minimum of 95% of their expected strength (Lehringer, 2012).  During the course of this project, none of the specimens was tested sooner than 21 days after fabrication.  Figure 10:  Centering of rods using toothpicks 3.1.4 Test Methods Steel fixtures were fabricated to connect the rod threads to the fixture by means of nuts and washers.  This approach allowed for an efficient test setup and reduced the amount of set-up time in between tests.  Tests of Phases #1 & #2 were carried out utilizing an MTS® universal testing machine (125kN capacity) located in the Wood Mechanics Laboratory, while the tests for Phase #3 were carried out utilizing an Instron® universal testing machine (250kN capacity) in the Materials Laboratory of the Civil Engineering Department at UBC.  The general test set-ups for the experimental campaigns are shown in Figure 11. The tests were performed under displacement based loading with a constant loading rate of 1.0mm/min.  This rate was chosen so tests would take between 5-7 minutes each, and the loading pattern was still considered quasi-static monotonic.  Linear Variable Differential Transformers (LVDT’s) were attached to the test specimens to capture the relative displacement between the 32 rod and the timber host.  The applied load and the relative displacement were recorded during testing to obtain the connection capacity and the load-displacement curves.  This was performed on 3 specimens selected tests series with 12.7 diameter rods.  The local joint stiffness was computed for the loading range between 10% and 40% of capacity in order to capture the initial stiffness of the joint, following the requirements set out by EN-29816.  By doing so, the initial slip and the inelastic behaviour closer to failure is not considered.  For the purposes of this research project, any calculated average initial joint stiffness that was greater than 100 kN/mm were deemed rigid for all practical purposes; these results are presented as >100 kN/mm.    Figure 11:  Typical test setup (left); and LVDT device (center and right) 3.1.5 Statistical Analysis Methods The experimental data for all three phases of the project was evaluated through a combination of multi-curvilinear regression analysis and a multi-factor, multi-level Analysis of Variance (ANOVA).  For each experimental phase, a regression model was defined to account for possible effects of the defined factors as well as interaction between them.  By running this regression model, the factor R2 (expresses how good of a fit the chosen regression model) was computed.  33 This factor served as a measurement of the percentage for which the model accounts for total variability of the independent variable, herein the axial capacity.   Following the definition of this regression model, a factorial ANOVA was performed to evaluate the particular effects of the chosen factors and their possible interactions on the overall joint strength.  This was carried out by assigning “dummy” variables within the regression model to account for the interaction effects of interest.  This factorial ANOVA test was performed on a backwards step-by-step process, each run eliminating statistically not significant parameters.  P-values were calculated on each test and compared to the significance level (α), herein and in agreement with common engineering practice, chosen as 0.05.  If the p-value was found to be greater than α then the null hypothesis was not rejected for this factor.  This means that changing the levels of that factor had no effect on the response of the system.  Following this logic; the factorial step-by-step ANOVA was used to eliminate non-significant factors, one at a time, until the analysis yielded only significant factors or interactions.  The results obtained served as indication of which variables would be further analyzed using a simpler Two-Way ANOVA test with the purposes to validate the findings of significance obtained through the factorial ANOVA test and to investigate “Main Effects” of the factors without interaction effects. Finally, as ANOVA tests only yield information about significance, but do not specifically determine the significance of the individual variable levels; Tukey’s HSD (Honest Significant Difference) test was carried out for each of the variables that were found to have a statistical significance on the dependent variable.  The purpose of Tukey's HSD test is to specifically determine which groups within the meaningful independent variables in the sample differ.    34 3.2 PHASES #1 & #2:  SINGLE GLUED-IN RODS 3.2.1 Phase #1:  ‘Control’ Series Specimen Description Phase #1 focused on single and centered glued-in rods.  A schematic illustration of the test specimens for Phase #1 is shown in Figure 12.  Figure 12:  Geometry for specimens in Phase #1  Several key parameters were left constant throughout this phase:  i) Edge distance from center of rod to edge of timber specimen (>3d) ii) Wood species & Average density (20f-E D.Fir-L with ρmean=530 kg/m3) iii) Parallel to grain orientation of rod relative to wood grain direction  iv) Thickness of glue-line (~2mm) Meanwhile, the parameters under investigation for this Phase were: i) Rod diameter;  d: 2.7mm and 19mm  ii) Effective embedment length; le : 5d, 7.5d, 10d, 15d and 20d for 12.7mm rods and  5d, 10d and 20d for 19mm rods iii) Adhesive type: CR-421®, T88® and Gel Magic® 35 Five specimens were tested for each embedment length using the same type of adhesive, and replicated for all three types of adhesives.  An additional 5 specimens were tested utilizing CR-421® adhesive and an embedment length of 5d.  In total, 110 specimens were tested in this phase.  Of those 110 total tested specimens, 65 specimens had 12.7mm rod diameters, while 45 specimens had 19mm rod diameters.   3.2.2 Phase #1:  Test Results In general, the axial capacity results obtained for specimens using different adhesives, at all different tested embedment lengths, were fairly similar.  Additionally, the failure modes observed for all specimens, without considering the adhesive utilized, were also fairly similar at all tested embedment lengths.   A summary of the parameters and results for Phase #1 is provided in Table 2.  The different types of failure modes that were observed during Phase #1 are shown in Figure 13. For Phase #1, local joint stiffness data was gathered for CR-421® specimens at 3 distinct embedment lengths (5d, 10d, 20d).  For the other two adhesives, Gel Magic® and T88®, local stiffness data was only gathered for the longer embedment length, 20d.  These results of the stiffness computations are summarized in Table 3. Table 2 – Parameters and Results for Phase #1 Rod Diameter [mm] Series Label Embedment Length      [mm] Adhesive Avg. Capacity [kN] Coefficient of Variation       [%] 12.7 A1 60 (5d) CR-421® 29.1 4 B1 T88® 20.7 6 C1 Gel Magic® 29.9 1 A7 85 (7.5d) CR-421® 36.6 8 36 A2 120 (10d) CR-421® 45.3 1 B2 T88® 44.4 4 C2 Gel Magic® 43.9 4 A8 180 (15d) CR-421® 45.6 <1 A3 240 (20d) CR-421® 45.5 1 B3 T88® 45.7 <1 C3 Gel Magic® 45.4 2 19 A4 95 (5d) CR-421® 45.5 9 B4 T88® 40.2 7 C4 Gel Magic® 54.5 15 A5 190 (10d) CR-421® 87.0 13 B5 T88® 77.8 6 C5 Gel Magic® 90.9 12 A6 380 (20d) CR-421® 106.8 1 B6 T88® 105.8 2 C6 Gel Magic® 106.8 2  Table 3 – Relative Stiffness Results for Phase #1 Rod Diameter [mm] Series Label Embedment Length      [mm] Adhesive Avg. Initial  Joint Stiffness [kN/mm] 12.7 A1 60 (5d) CR-421® 90 A2 120 (10d) CR-421® >100 A3 120 (10d) CR-421® >100 B3 T88® 75 C3 Gel Magic® >100  Generally, it was observed that for specimens with 12.7mm rods, the ductility threshold is 10d embedment length.  Beyond that point, the specimens exhibit yielding in the rods prior to failure, whereas for shorter embedment lengths (le<10d) a brittle and sudden failure was observed.  37  Figure 13: Shear failure around rod (left); rod yielding (centre) and splitting of timber specimen (right) Figure 14 presents the corresponding average load-deformation curves each of the series in Phase #1 that had their stiffness data collected.  For the complete set of load deformation plots for each individual specimen, in each series, the reader is kindly referred to the Appendix.    Figure 14 – Avg. Load Displacement curves for tests in Phase #1 05101520253035400 0.1 0.2 0.3 0.4 0.5Load [kN]Avg. Relative Displacement [mm]Avg. CR-421 - 5dAvg. CR-421 - 10dAvg. CR-421 -20dAvg. T88 - 20dAvg. Gel Magic - 20d38 3.2.3 Phase #2:  Single glued-in rods with manufacturing defect Specimen Description Phase #2, focused on connections with single glued-in steel threaded rods that were fabricated with a defect.  The main purpose of this phase was to determine the effect, if any, that common fabrication errors can have on the connection capacity, stiffness and eventual failure mode.   The two defects under investigation were:  i) Rods placed completely “off-set” to one side of the bore hole (“un-centered”)   ii) Rods placed at an angle not perfectly parallel to the timber member.   For this experimental phase, the following parameters were left constant: i) Rod diameter,  d: 12.7mm ii) Edge distance from center of rod to edge of timber specimen (>3d) iii) Wood species & average density (20f-E D.Fir-L with ρmean=530 kg/m3) iv) Orientation of rod relative to wood grain direction (parallel to grain) v) Thickness of glue-line (~2mm) Meanwhile, the parameters varied for this phase were: i) Defect: Rod at an angle or “Un-centered” ii) Effective embedment length; le : 5d, 10d, and 20d iii) Adhesive type:  CR-421®, T88® and Gel Magic® To evaluate the performance of the first defect, the rods were placed completely off-set to one side of the bore-hole (“un-centered”) to maximize the possible negative effects inherent with this construction error while maintaining a parallel orientation relative to the grain of the timber host.  This positioning effectively reduces the bond surface area between the adhesive and the timber element.  The second defect was created by placing the rods centered within the bore-hole plane, 39 but the rods were inserted at an angle inside the timber host.  As a result, the rods were not parallel but at “an angle” relative to the grain orientation of the timber host.  Schematics of these specimen configurations are illustrated in Figure 15 and Figure 16. Five specimens were tested for each embedment length using the same type of adhesive and for each type of defect; this resulted in 90 specimens tested in total.   Figure 15:  Geometry of specimens with “un-centered” rods  Figure 16:  Geometry of specimens with centered rods, but inserted at “an angle“ 3.2.4 Phase #2:  Test Results An overview of the test series parameters and the test results for Phase #2 are presented in Table 4 along with a comparison against test results from the “control” series of specimens with centered rods from Phase #1.   40 Table 4 - Results from Phase #2 Adhesive] Defect Series Label Embedment Length      [mm] Avg. Capacity [kN] COV        [%] CR-421® “Un-Centered Rod” AX1-i 60 (5d) 28.5 6 AX2-i 120 (10d) 45.7 <1 AX3-i 240 (20d) 45.6 2 Control “centered” A1 60 (5d) 29.1 4 A2 120 (10d) 45.3 1 A3 240 (20d) 45.5 1 Rod at an Angle AX1-ii 60 (5d) 27.9 9 AX2-ii 120 (10d) 45.7 <1 AX3-ii 240 (20d) 45.5 2 T88® “Un-Centered Rod” BX1-i 60 (5d) 21.2 5 BX2-i 120 (10d) 44.8 2 BX3-i 240 (20d) 46.3 <1 Control “centered” B1 60 (5d) 20.7 6 B2 120 (10d) 44.4 4 B3 240 (20d) 45.7 <1 Rod at an Angle BX1-ii 60 (5d) 20.2 13 BX2-ii 120 (10d) 45.2 11 BX3-ii 240 (20d) 45.8 2 Gel Magic® “Un-Centered Rod” CX1-i 60 (5d) 25.1 19 CX2-i 120 (10d) 37.8 17 CX3-i 240 (20d) 45.2 2 Control C1 60 (5d) 29.9 1 C2 120 (10d) 43.9 4 C3 240 (20d) 45.4 2 Rod at an Angle CX1-ii 60 (5d) 28.4 13 CX2-ii 120 (10d) 42.1 11 CX3-ii 240 (20d) 45.2 2   41 Table 5 presents the local stiffness data for Phase #2 for CR-421® specimens at 2 distinct embedment lengths (10d, 20d) for both types of manufacturing defects.  For the other two adhesives, Gel Magic® and T88®, local stiffness data was only gathered for the longer embedment length, 20d, for both manufacturing defects.   Table 5 - Relative Stiffness Results for Phase #2 Adhesive] Defect Series Label Embedment Length      [mm] Avg. Initial  Stiffness [kN/mm] CR-421® “Un-Centered Rod” AX2-i 120 (10d) >100 AX3-i 240 (20d) >100 Control “centered” A2 120 (10d) >100 A3 240 (20d) >100 Rod at an Angle AX2-ii 120 (10d) >100 AX3-ii 240 (20d) 92 T88® “Un-Centered Rod” BX3-i 240 (20d) >100 Control “centered” B3 75 Rod at an Angle BX3-ii 68 Gel Magic® “Un-Centered Rod” CX3-i 240 (20d) 52 Control “centered” C3 >100 Rod at an Angle CX3-ii ---  Figure 17 presents the corresponding average load-deformation curves each of the series in Phase #2 that had their stiffness data collected.  The complete set of load deformation plots for each individual specimen in each series is shown in the Appendix. 42  Figure 17 - Avg. Load Displacement curves for tests in Phase #2 Although very similar failure modes were observed in this phase relative to Phase #1, one commonly occurring brittle failure mode (at short rod embedment lengths) that was particular for this phase, was the “partial debonding” of the rod and adhesive, see Figure 18.  This failure mode can intuitively be attributed to the manufacturing defect as in both cases, parts of the rod laid next to the timber and left no space for proper adhesive bonding to occur.    Figure 18 - Debonding failure between rod and timber  0510152025300 0.1 0.2 0.3 0.4 0.5Load [kN]Avg. Relative Displacement [mm]Avg. CR-421 UncenteredRod- 10dAvg. CR-421 Rod at anAngle - 10dAvg. CR-421 UncenteredRod -20dAvg. CR-421 Rod at anAngle - 20dAvg. T88 UncenteredRod - 20dAvg. T88 Rod at anAngle - 20dAvg. Gel MagicUncentered Rod - 20d43 3.3 STATISTICAL ANALYSIS FOR PHASES #1 & #2 A multi-factor, curvi-linear regression model was developed first in order to assess the fit of the data model to be used for the subsequent Factorial ANOVA test that was performed. A statistical analysis was carried out for all specimens with a single glued-in rod combining both Phases #1 and #2 of this project.  The regression model defined was defined as: Y=β0+ β1X1+ β2X2+ β3X3 + β4X4+ β5X5+ β6X6+ β7X7+ β8X8+ β9X9+ β10X10+ β11X11+ β12X12+ ε where:  YN : Dependent variable for regression and factorial model, Joint capacity; XN : Independent variables for each of the n variables defined; βN : Regression coefficients of the model for each of the n variables that were defined; β0 : Intercept of the regression model;  ε : Inherent error in this model.   Table 6 shows each of the defined variables and the factor they represented within the statistical model, as well as the results for this Factorial ANOVA: the R2 values obtained by performing a step-by-step ANOVA with backwards elimination of the least statistical significant variable.  During every step of the analysis; if a statistically un-meaningful variable was found (i.e. p>0.05), it was dropped from the model and the analysis was performed again without considering it.  This process was repeated until all variables left in the model had a significant impact on the variability of the model, see Table 7.    44 Table 6 – Variables and Results for Factorial ANOVA Factor Independent variable it represents P-value X1 Rod diameter, d <0.001 X2 Rod embedment length, le <0.001 X3 Adhesive utilized 0.452 X4 Rod position (defect) 0.181 X5 Polynomial factor better defining X2 (X5=1/X2) <0.001 X6 Polynomial factor better defining X4 (X5=1/X4) 0.079 X7 X1 & X2 interaction variable <0.001 X8 X1 & X3 interaction variable 0.173 X9 X1 & X4 interaction variable 0.953 X10 X2 & X3 interaction variable 0.725 X11 X2 & X4 interaction variable 0.657 X12 X3 & X4 interaction variable 0.454  Table 7 – Backwards elimination Curvi-linear Multiple Regression Analysis Results  Run # Variables Considered R2 Variable Dropped DF 1 X1 thru X12 0.937 X9 11 9 X1, X2, X5, X7 0.934 X3, X4, X6, X8 thru X12 4  Following the findings obtained by performing a factorial ANOVA, it was determined that the only statistical significant variables were: X1, X2, X5, X7.  These variables represent the rod diameter -X1-, rod embedment length -X2 & X5-, and their interaction effect -X7-.  Following these findings, a subsequent two-factor ANOVA (with replication) test was performed to gauge the statistical significance of these variables on the capacity of a single glued-in rod joint. The variables, as defined in this test, as well as their respective resultant p-values are shown in Table 8. 45 Table 8 - ANOVA Results for Phases #1 and #2 Factor Independent variable it represents p-value X1 Rod diameter, d <0.001 X2 Rod embedment length, le <0.001 X3 Interaction effect between X1 & X2  <0.001  This test served as confirmation that the “main effects: of the variables under investigation and the interaction effect between rod diameter and embedment length are statistically significant for our model.  Here also clearly identify the important finding that the other parameters, adhesive and defect had NO impact on the results. Furthermore, Tukey’s HSD test was performed to determine the significance that each of the factor’s respective levels have on the dependent variable; the axial capacity of glued-in rods.  Table 9 presents the results of this HSD test, whereas Table 10 shows the results for significance of each of the treatments in each factor. Table 9 – Tukey’s HSD Test Results for factors and treatments in Phase #1&#2 Factor Level (treatment) HSD Value Mean Rod diameter, d 12.7mm 14.6 37.9 19mm 79.3 Embedment Length, le 5d 19.8 36.4 10d 65.4 20d 76.2  Table 10 - Tukey’s HSD Test Results for Statistical Significance for factors in Phase #1&2 Factor Levels (treatments) Diff. in Means Significant Rod diameter, d 19mm – 12.7mm 40 YES Embedment length, le 20d - 10d 11 NO 20d - 5d 39 YES 10d – 5d 29 YES  46 The calculated difference in means for 12.7mm & 19mm rod diameters yields 40, which is significantly larger that the calculated HSD value of 14.  This finding confirmed that the rod diameter has a statistically significant influence on axial capacity of glued-in rods.  Finally, the calculated difference in means for the embedment lengths were 11 (between 20d & 10d), 39 (between 20d & 5d) and 29 (between 10d & 5d).  For these values, only the difference in means between embedment lengths 5d with 10d and 20d yielded statistically significant results.  This also confirmed statistically, that embedments longer than 10d are not significant on the axial capacity of single glued-in rod joints.   3.4 DISCUSSION OF RESULTS FOR PHASE #1 & #2 3.4.1 Discussion Phase #1 The experimental campaign on centered single rods proved that the parameters under study have a substantial effect on the axial capacity and performance of wood joints with glued-in steel rods.   The first parameter under study was the rod diameter, d.  This study confirmed that splitting of the timber host with 12.7mm diameter glued-in rods can be effectively avoided with a minimum rod edge distance of 3d.  Furthermore, the connection capacity is almost doubled when using 19mm rods instead of 12mm.  This increase was expected as the capacity depends on the yield strength of the rods, as well as the bond surface area between rod surface and adhesive.   The second parameter under study was the embedment length, le.  As expected, le has statistical significance on the axial capacity of glued-in rods and also primarily defines the eventual failure mode.  For 19mm rods, the point at which a ductile steel yielding failure mode is attainable is at a higher le/d ratio than for 12.7mm rods; herein this point is referred as the “ductility threshold”.  47 The ductility threshold is the minimum embedment length at which for a glued-in rod joint rod yielding will govern the response and will be the dominant failure mode.   For 12.7mm rods this occurs at le>10d as all specimens with 7.5d exhibited a brittle failure while 100% of specimens with le>10d failed by ductile rod yielding.  For specimens with 19mm rods, at le=10d (180mm) none of the rods yielded and all specimens exhibited brittle wood shear failure. Splitting was observed in only a few specimens with 19mm rods at le=20d (380mm).  Minimum edge distance requirements for 19mm rods should therefore be reconsidered.  No shear failures around the bonded rod (pull-out) were observed at this embedment length.   Figure 19 shows the distribution of observed generalized failure modes (brittle vs. ductile) for test specimens with 19mm rod diameters and Figure 20 shows some examples of these observed failure modes.   Figure 19 - Distribution of observed failure modes for d=19mm 0%10%20%30%40%50%60%70%80%90%100%95 190 380Embedment Length [mm]Ductile Failure TypeBrittle Failure Type48  Figure 20 - Typical failure modes in Phase #1 with d=19mm: rod yielding (left), brittle pull-out of rod (right) The third varied parameter for Phase #1 was the adhesive type.  In general, results utilizing both epoxies had higher variation, whereas the results for specimens using CR-421® were more consistent.  Moreover, glued-in rods with CR421® adhesive exhibited a higher initial average stiffness (~115kN/mm) than both of the tested epoxy adhesive’s initial average stiffness (~80kN/mm).  For shorter le (before rod yielding occurred) higher capacities were obtained from specimens using Gel Magic® (the higher viscosity activated a larger timber area) while T88® resulted in the lowest brittle capacities.  These results were consistent for le=5d and 7.5d for 12.7mm rods, and for le=5d and le=10d for 19mm rods.  Yet, statistically, the variation between adhesive types was concluded to be not significant.  This implies that variation can be attributed to random chance, or more accurately aleatory uncertainty in the specimens.  After reaching the “ductility threshold”, the type of adhesive utilized became irrelevant as the yield strength of the rods governed the failure.  Therefore, it is safe to conclude that for 12.7mm 49 and 19mm glued-in mild steel threaded rods, the ductile capacity of the joint is unaltered by the type of adhesive.  This was also confirmed through the statistical tests as embedment length treatments >10d were considered not significant, as well as main effects due to the choice of adhesive.  Figure 21 and Figure 22  provide a visual summary of the average axial capacities obtained for all series of Phase #1 combining the three adhesives.    Figure 21 – Summary of capacities for d=12.7mm rods   Figure 22 - Summary of capacities for d=19mm rods 051015202530354045505d 7.5d 10d 15d 20dAvg. Axial Capacity [kN]Embedment Length0204060801001205d 10d 20dAvg. Axial Capacity [kN]Embedment Length50 The results obtained in Phase #1 demonstrated that glued-in rods should be categorized as very rigid connections.  Table 3 showed that the initial stiffness of these joints (using any of the three investigated adhesives) is very close to, and in most cases, greater than 100 kN/mm.  As a comparison, consider Table 7.1 of EN1995 (CEN 2004), which provides values for serviceability stiffness, Kser, of timber connections with mechanical fasteners. Values for connections using 12.7 mm diameter bolts are around 6 kN/mm for a typical timber density of 490 kg/m3. Therefore, connections in excess of 100kN/mm of initial stiffness, such as connections with a s glued-in threaded steel rods, can safely be categorized as very rigid connections. Finally, if mild steel threaded glued-in rods are used, ductility can be consistently achieved by choosing an appropriate embedment length that is greater than 10d (for both 12.7mm and 19mm rods).  This finding is crucial for the applicability of glued-in rods in moment resisting connections as ductility is essential for the appropriate performance of these connections.  3.4.2 Phase #2: Discussion of Results From the results obtained by the multiple factor regression and ANOVA it can be concluded that only the rod diameter, embedment length and interaction of these two parameters have a statistical significant effect on the variation of the model’s mean (their p-values are less than 0.05).  Additionally, the multi-factor curvilinear regression model performed only utilizing these factors yields an R2 of more than 0.93.  This means that more than 93% of the variation in that model can be explained by those variables.  Statistically, this proves that for the parameter variations studied in this research; the effects of adhesive, manufacturing defects and all of the interaction effects of involving these factors on the axial capacity, can be deemed statistically 51 insignificant at a 95% significance level.  Tukey’s statistical test confirmed that embedment lengths greater than 10d have no significant effect on the axial capacity.  The results gathered in Phase #2 showed a slight negative effect manifested by higher COV values for specimens with brittle failures manufactured with defects, if compared against the “centered” specimens (“control series”).  Yet, these variations were found statistically not significant.  For specimens with embedment lengths greater than 10d, the ductility threshold was also effectively achieved and therefore, no significant variation of capacity values was observed.  Moreover, if compared against the capacities of specimens that had centered rods, “un-centered rods” showed a minimal reduction on their capacity and exhibited a somewhat higher variation in their failure modes, while specimens with a rod “at an angle” were basically unaffected.  Figure 23 and Figure 24 illustrate these findings.  Figure 23 - Effect of manufacturing defect on Axial Capacity (5d embedment) 05101520253035Centered Rod Un-Centered Rod Rod @ an AngleAvg. Axial Capacity [kN]CR421Gel MagicT8852  Figure 24 - Effect of manufacturing defect on Axial Capacity (10d embedment) In addition, all specimens with le=20d were unaffected by the type of adhesive used or the manufacturing defect employed during fabrication.  All specimens satisfactorily achieved a ductile failure mode that empirically proved that at an embedment length greater than the ductility threshold the capacity of the join is not sensitive to manufacturing defects or the choice of bonding adhesive. This assertion holds only if a proper steel grade for the threaded rods is selected so as to allow these rods to achieve yielding, for this experimental project mild steel was utilized (Fy =360 N/mm2).   Finally, specimens with an “un-centered” rod, fabricated with all of the three different adhesives under consideration, showed an increase in the average initial stiffness if compared to test specimens without manufacturing defects.  On the contrary, specimens with rods inserted at an angle for all embedment lengths and adhesive types, showed a lower initial stiffness than fully centered specimens.  A possible explanation for this phenomenon could be that for “un-centered” rods the withdrawal rigidity is increased slightly by account of friction and mechanical interlock 05101520253035404550Centered Rod Un-Centered Rod Rod @ an AngleAvg. Axial Capacity [kN]CR421Gel MagicT8853 between the rod and the timber host at the interior of the bore hole.  Similarly, for rods inserted at an angle, a possible explanation could be that the inherent eccentricity in the rod softens the response slightly as a result of minor bending and uneven distribution of shear stresses around the rod bonded into the timber member.  And even though these reductions were evident, joints having any of the prescribed manufacturing defects had an average initial stiffness in excess of 60kN/mm.  Consequently, they can still be confidently termed as rigid connections. Figure 25 shows the distribution of observed failure modes for all tested specimens with rod diameter of 12.7mm.  Purposefully, all specimens from Phase #1 or #2 were included as neither the adhesive utilized or the manufacturing defect caused a significant effect on the generalized failure mode of the specimens (brittle vs. ductile).  The objective of Figure 25 is to illustrate that for glued-in rod specimens with 12.7mm diameter mild steel threaded rods, if the embedment length is long enough (past the ductility threshold), a constant ductile failure mode is attainable.    Figure 25 - Distribution of observed failure modes for d=12.7mm 0%10%20%30%40%50%60%70%80%90%100%60 85 120 180 240Observed Failure Mode in %Embedment Length [mm]Ductile Failure TypeBrittle Failure Type54 3.5 PHASE #3:  MULTIPLE GLUED-IN RODS 3.5.1 Phase #3:  Multiple glued-in rods Specimen Description For this experimental phase, the following parameters were left constant: i) Rod diameter, d: = 12.7mm  ii) Two-component Polyurethane adhesive (CR421®) iii) Edge distance from center of rod to edge of timber specimen (>3d) iv) Wood species & Average density (20f-E D.Fir-L with ρmean=530 kg/m3) v) Orientation of rod relative to wood grain direction (parallel to grain) vi) Thickness of glue-line (~2mm) Meanwhile, the parameters varied for this phase were: A. Number of Rods (2, 3 and 4) B. Effective embedment length: le: 5d, 7.5d, 10d, and 15d C. Rod Spacing (varied as a function of Rod diameter) s:  3d, 4d and 5d Three specimens were tested for each test series. Figure 26 shows some examples of test specimens prior to testing, while Figures 27 and 28 show the typical schematic layouts.  Figure 26 – Examples of test specimens in Phase #3 55  Figure 27 – Side view of specimen geometry for Phase #3  Figure 28 – Cross section of typical specimen geometry for Phase #3 Executed in similar fashion as in Phases #1 and #2, relative joint displacement data was collected during tests using LVDT’s.  For Phase #3, each individual rod had its own LVDT and therefore data was collected for each rod independently.  With this data, the stiffness curves were recreated for the test specimens utilizing the average of the rods from each test specimen.  By doing so, the 56 recreated stiffness curves effectively capture the relative displacement of the joint as a whole, instead of as a set of individual responses.   3.5.2 Phase #3:  Test Results  The observed failure modes where pull out of a wood plug surrounding the rods as well as splitting for brittle type failures, while rod yielding was observed as the ductile failure mode type, see Figure 29.  The results from Phase #3 are presented in Table 11.   Figure 29 – Observed failure modes in Phase #3: Pull-out (top left), splitting (top right), rod yielding (bottom) For Phase #3, local joint stiffness data was gathered for all of the specimens at only three of the studied embedment lengths (5d, 10d, 15d) and all rod spacing (3d, 4d, 5d).  These results are also summarized in Table 11.   57 Figures 30 to 33 show the average load deformation curves for glued-in rod specimens with multiple rods.  For the complete set of load deformation plots for each individual specimen, in each series, please refer to the Appendix.  Figure 30 – Load Deformation Curve for (Le=5d, S=3d)   Figure 31 - Load Deformation Curve for (Le=7.5d, S=3d)  0204060801001200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Load [kN]Displacement [mm]1 Rod2 Rods3 Rods4 Rods0204060801001200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Loal Capacity [kN]Displacement [mm]1 Rod2 Rods3 Rods4 Rods58  Figure 32 - Load Deformation Curve for (Le=7.5d, S=5d)   Figure 33 - Load Deformation Curve for (Le=15d, S=5d)    0204060801001201401601800 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Load [kN]Displacement [mm]1 Rod2 Rods3 Rods4 Rods0501001502002500 0.5 1 1.5 2 2.5 3 3.5 4Load [kN]Displacement [mm]1 Rod2 Rods3 Rods4 Rods59 Table 11 - Results for tests Phase #3 # Rods Embedment Length [mm] Spacing rods [mm] Series Label Avg. Axial Capacity [kN] COV              [%] Avg. Stiffness [kN/mm] 1 60 (5d) - A1 29.1 4 90 85 (7.5d) - A7 36.6 8 --- 120 (10d) - A2 45.3 1 >100 180 (15d) - A3 45.6 <1 --- 2 60 (5d) 36 (3d) M1-A   29.8 18 90 48 (4d) M1-B   36.5 17 >100 60 (5d) M1-C   49.6 11 >100 85 (7.5d) 36 (3d) M10-A   62.3 14 --- 48 (4d) M10-B   67.7 9 --- 60 (5d) M10-C   58.2 17 --- 120 (10d) 36 (3d) M2-A   83.3 8 90 48 (4d) M2-B   73.6 26 >100 60 (5d) M2-C   87.1 4 >100 180 (15d) 36 (3d) M3-A   89.2 17 80 48 (4d) M3-B 101.5 <1 >100 60 (5d) M3-C 100.6 1 75 3 60 (5d) 36 (3d) M4-A   67.5 9 >100 48 (4d) M4-B   58.4 2 >100 60 (5d) M4-C   68.2 8 >100 85 (7.5d) 36 (3d) M11-A   74.2 17 --- 48 (4d) M11-B   99.5 14 --- 60 (5d) M11-C   90.8 14 --- 120 (10d) 36 (3d) M5-A 108.1 7 >100 48 (4d) M5-B 115.8 16 >100 60 (5d) M5-C 112.2 18 >100 180 (15d) 36 (3d) M6-A 110.8 5 >100 48 (4d) M6-B 123.8 30 >100 60 (5d) M6-C 149.3 2 >100 4 60 (5d) 36 (3d) M7-A   70.8 7 >100 48 (4d) M7-B   70.3 2 >100 60 (5d) M7-C   98.7 6 >100 85 (7.5d) 36 (3d) M12-A 102.2 4 --- 48 (4d) M12-B 129.0 2 --- 60 (5d) M12-C 129.7 19 --- 120 (10d) 36 (3d) M8-A 136.3 5 >100 48 (4d) M8-B 149.6 7 >100 60 (5d) M8-C 155.9 9 >100 180 (15d) 36 (3d) M9-A 201.3 <1 >100 48 (4d) M9-B 201.6 <1 >100 60 (5d) M9-C 190.5 6 >100   60 3.6 STATISTICAL ANALYSIS FOR PHASE #3 Similarly as it was performed for the results obtained in Phases #1 and #2, a multi-factor, curvi-linear regression model was developed to be used for the subsequent ANOVA tests on the experimental data. The statistical analysis performed for this section encompassed all specimens with multiple (+2) glued-in rods.  The regression model defined as: Y=β0+ β1X1+ β2X2+ β3X3 + β4X4+ β5X5+ β6X6 + ε    where:  YN : Dependent variable for regression and factorial model, Joint Capacity; XN : Independent variables for each of the n variables defined; βN :  Regression coefficients of the regression model for each of the n variables; β0 :  Intercept of the regression model;  ε :  is the inherent error in this model.   Table 12 shows each of the defined variables and the factor they represented within the statistical model, as well as the results for this Factorial ANOVA.   Table 12 - Variables and Results for Factorial ANOVA for Phase #3 Factor Independent variable it represents P-value X1 Number of Rods, n 0.1054 X2 Rod embedment length, le 0.8652 X3 Spacing of Rods, s 0.8002 X4 X1 & X2 interaction variable <.0001 X5 X1 & X3 interaction variable 0.0004 X6 X2 & X3 interaction variable 0.6077  61 Table 13 presents the R2 values obtained by performing a step-by-step ANOVA with backwards elimination of the least statistical significant variable.  During every step of the analysis; statistically non-significant variables (i.e. p>0.05), were dropped from the model.  This process was repeated until all variables left in the model had a significant impact.  Table 13 - Curvilinear Multiple Regression Analysis Results for Phase #3 Run # Variables Considered R2 Variables Dropped DF 1 X1 thru X6 0.880 X2 6 5 X4 & X5 0.877 X1 thru X3, X6 2  The factorial ANOVA determined that the only statistical significant variables were X4 & X5, representing the interactions between number of rods (n) and rod embedment length (le) -X4-, and the interaction between number of rods (n) and rod spacing (s) -X5-.  Consequently, two independent two-factor, ANOVAs (with replication) were performed to gauge the statistical significance that these factors (“main effects”) and their interactions have the per rod capacity of multiple rod joints.  These variables, as defined in this two-way ANOVA test, as well as their respective resultant p-values are shown in Table 14 and Table 15. Table 14 - Subsequent Two-way ANOVA Results (n & le) Factor Independent variable it represents P-value X1 Number of rods, n 0.23 X2 Rod embedment length, le <0.001 X4 Interaction effect between X1 & X2  <0.001   62 Table 15 - Subsequent Two-way ANOVA Results (n & s) Factor Independent variable it represents P-value X1 Number of rods, n 0.23 X3 Rod Spacing, s 0.29 X5 Interaction effect between X1 & X3  0.99  The results partially contradict the results obtained with a factorial ANOVA.  These two-way ANOVAs confirm the statistical significance of the effect of rod embedment length and the interaction with the number of rods on the capacity of the joints (measured in these tests per rod).  Yet, it rejects the previously found significance of the main effects for number of rods and rod spacing (independently) as well as the interaction effects amongst each other on a per rod capacity of joints with multiple glued-in rods.  These contradictions can be explained by the fact that the original factorial analysis was performed on the overall joint capacity as the dependent variable, whereas the subsequent two-way ANOVA tests were performed on the per rod capacity as the dependent variable.  Therefore, it becomes evident that the number of rods and rod spacing when gauged independently have no meaningful bearing on the axial capacity of a single glued in rod.  Furthermore, the per-rod capacity is very consistent with little variation, which helps backup this assertion. Tukey’s HSD test was used in order to evaluate the level of significance that each of the factor’s levels have on the axial capacity of glued-in rods and validate the contradicting results obtained.  To correctly gauge the effect of the number of rods factor (n), the values for capacity of the joint were analyzed per rod.  Table 16 presents the results of this HSD test for the factors under investigation and their treatments, whereas Table 17Table 17 shows the results for significance of each of the treatments in each factor. 63 Table 16 – Tukey’s HSD Test Results for factors and treatments in Phase #3 Factor Level (treatment) HSD Value Mean Capacity per Rod (kN) Number of Rods, n 2 3.60 35.0 3 32.8 4 34.0 Embedment Length,     le 5d 3.94 20.3 7.5d 30.3 10d 38.2 15d 46.9 Rod Spacing, s 3d 6.15 31.9 4d 35.0 5d 35.9 Table 17 – Tukey’s HSD Test Results for Statistical Significance for factors in Phase #3 Factor Levels (treatments) Diff. in Means Significant Number of Rods, n 4 – 3 rods 1.2 NO 4 – 2 rods  1.0 NO 3 – 2 rods 2.2 NO Embedment Length,   le 15d - 10d 8.7 YES 15d – 7.5d 16.6 YES 15d - 5d 26.6 YES 10d – 7.5d 7.9 YES 10d – 5d 17.9 YES 7.5d – 5d 10.0 YES Rod Spacing, s 5d – 4d 0.9 NO 5d – 3d 4.0 NO 4d – 3d 3.1 NO   64 3.7 DISCUSSION OF RESULTS FOR PHASE #3 From the multiple factor regression and factorial ANOVAs it can be concluded that only the factors X4 (interaction between n and le) and X5 (interaction between n and s) had a statistical significant effect on the variation of the model’s mean.  The multi-factor curvilinear regression model utilizing these two factors yields an R2 of 0.87.  This means that 87% of the variation in that model can be explained by the factors X4 and X5.  Yet, by performing two-way ANOVA and Tukey’s HSD tests, it was possible to rule out the statistical significance of the main effects and interaction effects of  the parameter X5 (n and s).  It is important to understand the context of this statement: the effects of number of rods, rod spacing and their interaction do not have a statistically significant effect on the average per rod capacity of multiple glued-in rod joints under the test configurations used throughout this experimental campaign.  The number of rods glued in the joint has a significant impact on the joint’s overall axial capacity.  As the number of embedded rods increases, so does the capacity of the connection.  Yet, on a per rod capacity basis, the capacity of each individual rod does not vary statistically significantly.  Second, rod spacing, does not vary the per rod capacity of multiple glued-in rod joints significantly.  Only if the rods are embedded deep enough so that the ductility threshold is surpassed, the failure mode of the joints will vary as per the observations gathered throughout the experimental campaign: rod spacing will not affect significantly the per rod capacity of joints with glued-in rods, but it will have a direct effect on the primary failure mode of these connections (brittle vs. ductile). The embedment length (le) of the rods into the timber was also varied.  The statistical analysis confirmed that le, as well as the interaction effects of le and n have a statistical significant impact 65 on the per rod capacity of multiple glued-in rod connections.  Additionally, it was observed throughout this experimental campaign that the failure mode, similar to tests with single rods, yielding of the rods occurred at le>10d, for mild steel threaded rods with 12.7mm diameters.   As explained before, the rod spacing was varied.  For ductility to be achieved, any brittle type of failure had to be prevented by sufficient rod spacing.  A minimum of s=2d (Buchanan A. , 2007) and s=5d (Blass & Laskewitz, 1999) have been recommended in the literature to avoid group effects that lead to wood related brittle type of failures.  After the analysis in this project, to safely conclude that ductility can be reached using 12.7mm mild steel rods, if a spacing of s>4d is provisioned and will be sufficient, as long as the embedment length of the rods is le>10d.   By providing enough spacing between rods, detrimental stress interactions between the bonded-in rods (“group effect”) can be controlled.  The group effect of having the rods placed close to each other manifested itself with a sudden, dramatic splitting failure of the timber member.  The failure initiated from the loaded face where the rods were inserted and was observed for all test specimens under these conditions.  Contrary to previous research (Tlustochowicz et al., 2011) “group tear out”, which occurs when all rods pull out simultaneously along with a single block of wood, was not observed for any of the test specimens. Splitting related failures were evident, especially for specimens with small rod spacing. Figure 34 shows the distribution of failure modes observed for all test specimens with multiple glued in rods, which clearly illustrates how a ductile failure mode is positively correlated with larger embedment lengths and larger spacing between rods.  Figure 35 compares the capacities of selected test series. 66  Figure 34 - Distribution of Observed Failure Modes for Phase #3  Figure 35 - Effect of rod spacing on avg. per rod capacity at le=15d Similar to single rod glued-in joints, connections with multiple glued-in rods exhibit a very rigid behaviour, see appendix.   0%10%20%30%40%50%60%70%80%90%100%la=5ds=3dla=5ds=4dla=5ds=5dla=7.5ds=3dla=7.5ds=4dla=7.5ds=5dla=10ds=3dla=10ds=4dla=10ds=5dla=15ds=3dla=15ds=4dla=15ds=5dductilesplittingshear67 Interestingly, for ductile failure modes, the joint capacity increased slightly as a function of the number of rods. While this effect was not statistically significant, it is worthwhile to investigate. As discussed in the materials section, three representative samples of steel rods were tested in tension before testing and their experimental average load at yield was equal to their capacity and of 45 kN. Results of the joints with one rod were consistent with this finding with capacities of close to 45 KN. All test specimens with multiple rods that failed in a ductile manner, however exhibited an increase in joint capacity of 5 kN (11%) per rod as compared to single glued-in rod specimens. Failure occurred at 100 kN for specimens with two rods, at 150 kN for specimens with three rods, and at 200 kN for specimens with four rods. It is postulated that this increase in capacity was caused by minor variations in the yield strength of each rod with which led to an uneven redistribution of forces after yielding occurs in one of the rods. As the rods did not yield simultaneously; the connection system was able to sustain further loads, 5 kN per rod herein. Figure 36 depicts this phenomenon with a chosen representative load deformation curve for a specimen with 4 rods, at la=15d and s=5d. All rods, even though they have the same experimentally tested yield strength, exhibit distinct yield points and overall ductility.   Figure 36 - Representative (per rod) load-deformation curve 0501001502002500 1 2 3 4Axial Capacity [kN]Relative Displacement [mm]Average ResponseRod #1Rod #2Rod #3Rod #468 3.8 COMPARISON WITH DESIGN MODEL PREDICTIONS 3.8.1 Overview The experimental results for all single glued-in rod connections tested in Phases #1 and #2 were compared to the prediction from the design approaches as discussed in Section 2.6.  The results for multiple glued in rod connections tested in Phase #3 were also compared to these design models.  In order to do so, the models were adapted by multiplication of the expected single rod capacity by the number of rods (n) in the connection.  Results for these comparisons are presented in Figures 37 to 39. 3.8.2 Comparison of single glued-in rod test results to design model predictions From Figure 37 and Figure 38, it becomes evident that there is a lot of variation between the predictive axial capacity between each of these models, and the obtained experimental results.  This is can be mostly attributed to the large quantity of parameters and high variation of these to account for the behaviour of steel glued-in rod connections.  Additionally, as mentioned before, there is no standard testing methodology in place for glued-in rod connections.  It is possible therefore, that some of the variations between the obtained results of the many individual test campaigns that have led to the development of the presented Design Models, can be attributed to the fact that these test campaigns have utilized different test setups, distinct data collection devices, calibration processes, and loading protocols.     When plotting the experimental campaign’s data, a conservative fit can be seen with the GIROD Project, Eurocode 5 Annex and DIN1052 design proposals.  This conservative fit is evident for shorter embedment lengths only (le≤10d), and can be seen for both tested diameter sizes (12.7mm 69 & 19mm).  For design, it is acceptable to have a factor of safety inherent with design calculations to account for any unusual variations in the material that can alter the performance of the structure. For that reason, design capacity values are associated with 5th percentile rather than with average values obtained during verification testing.   By observation, this holds true for the collected test data and the previously mentioned design proposals.   Conversely, both models proposed by Riberholt and Steiger et al, unsafely over-predict capacities for specimens with both rod diameter sizes over all embedment lengths as they tend to predict higher values.  The Gerold model exhibits an appropriate fit for shorter embedment lengths (le<10d) for 12.7mm diameter rods but a very conservative estimation of the capacity of these connections at longer embedment lengths.  For 19mm rods, Gerold’s propsed model tends more towards the average capacity values obtained in this test campaign and therefore can be deemed unsafe. Additionally, this design model’s approach to reduce capacity of connections past an embedment length of 15d (for 12.7mm rods) and 10d (for 19mm rods) seems contradictory to most of the literature on glued-in rods and the results presented by this research campaing which prove that capacity of glued-in rod connections is positively correlated with longer embedment lengths.  At first sight, the EC5 and GIROD Project design models seem to appropriately predict the axial capacity of steel glued-in rod connections.  Yet, as this experimental project consistently proved that beyond the ductility threshold, le>10d, these types of connections will fail by means of rod yielding and not by pull-out.  This provides evidence that these models, even though some include separate provisions to check for rod yielding (GIROD and EC5), most do not quite adequately address this very important failure mode into their design models.  Additionally, the 70 models that do address this failure mode, very conservatively over predict the required embedment length required to achieve rod yielding which in turn can yield more inefficient, cost and labor intense connections than are actually required.    Figure 37 - Comparison of results of specimens with single rods (d=12.7mm) to Design Models  Figure 38 - Comparison of results of specimens with single rods (d=19mm) to Design Models 01020304050607080901000 50 100 150 200 250 300Axial Capacity [kN]Embedment Length, (le) - [mm]Riberholt ModelGerold ModelGIROD ProjectEC5: Part 2AnnexSteiger et. Al.DIN 1052ExperimentalRod Yield ForceTest Results(d=12.7mm)0204060801001201401600 50 100 150 200 250 300Axial Capacity [kN]Embedment Length, (le) - [mm]Riberholt ModelGerold ModelGIROD ProjectEC5: Part 2AnnexSteiger et. Al.DIN 1052ExperimentalRod Yield Force71 3.8.3 Comparison of multiple glued-in rod test results to Design Models Figure 39 shows the comparison for test results against the previously discussed design models for test specimens with 2 glued-in steel rods.  Similarly as for single glued-in rod specimens, both models proposed by Riberholt and Steiger et al, seem to overestimate the capacity of multiple glued-in rod connections consistently over all tested embedment lengths.  DIN1052 also underestimates the capacity of these joints for all number of embedded rods over all embedment lengths.  The Gerold model conservatively predicts capacities for multiple glued-in rod specimens over short embedment lengths (le<10d) but fails again to do so for longer embedment lengths when compared to our test results.  Finally, both GIROD Project and EC5 design proposals seem to agree conservatively on the prediction of multiple glued in rod capacities.    Figure 39 - Comparison of specimens with 2 rods (d=12.7mm) to Design Models 0204060801001201401601802000 50 100 150 200 250 300Axial Capacity [kN]Embedment Length, (le) - [mm]Riberholt ModelGerold ModelGIROD ProjectEC5: Part 2AnnexSteiger et. Al.DIN 1052Experimental RodYield ForceTest Results - 2Rods72 3.8.4 Statistical Comparison of Test Results to Design Models Two-tailed t-tests were performed to validate the observations gathered in the previous section The characteristic p-value used was 0.05, which means if the null hypothesis was not to be rejected, then the variation of means between the ranges of embedment lengths is the same with a confidence level of 95%.  In order to confirm that the data validates a design model, this p-value needs to be larger than 0.05 and, the test generated t-statistic has to be smaller than t-critical.  Table 18 presents the findings and confirms that only the GIROD design approach consistently predicts capacities of multiple glued-in rod connections.    73 Table 18 - Statistical Results for Comparison of Data vs Design Models Design Model Specimen Type p-value Riberholt Model Single Rods (d=12.7mm) <0.001 Single Rods (d=19mm) <0.001 Multiple Rods (2 Rods, d=12.7mm) 2.00 Multiple Rods (3 Rods, d=12.7mm) <0.001 Multiple Rods (4 Rods, d=12.7mm) <0.001 Gerold Model Single Rods (d=12.7mm) <0.001 Single Rods (d=19mm) <0.001 Multiple Rods (2 Rods, d=12.7mm) 0.011 Multiple Rods (3 Rods, d=12.7mm) 0.044 Multiple Rods (4 Rods, d=12.7mm) 0.031 GIROD Project Model Single Rods (d=12.7mm) <0.001 Single Rods (d=19mm) <0.001 Multiple Rods (2 Rods, d=12.7mm) 0.245 Multiple Rods (3 Rods, d=12.7mm) 0.570 Multiple Rods (4 Rods, d=12.7mm) 0.416 EC5: Part 2 Design of Bridges Model Single Rods (d=12.7mm) <0.001 Single Rods (d=19mm) 0.055 Multiple Rods (2 Rods, d=12.7mm) 0.001 Multiple Rods (3 Rods, d=12.7mm) 0.006 Multiple Rods (4 Rods, d=12.7mm) 0.005 Steiger et al. Model Single Rods (d=12.7mm) <0.001 Single Rods (d=19mm) <0.001 Multiple Rods (2 Rods, d=12.7mm) 0.002 Multiple Rods (3 Rods, d=12.7mm) <0.001 Multiple Rods (4 Rods, d=12.7mm) 0.0001 DIN 1052: 2008-2012 Model Single Rods (d=12.7mm) <0.001 Single Rods (d=19mm) <0.001 Multiple Rods (2 Rods, d=12.7mm) <0.001 Multiple Rods (3 Rods, d=12.7mm) <0.001 Multiple Rods (4 Rods, d=12.7mm) <0.001  74 CHAPTER 4: CONCLUSIONS The extensive experimental campaign carried out on test specimens of timber connections with glued-in rods allows drawing the following conclusions: 1) For specimens with a single centered glued-in steel threaded rod of 12.7mm diameter, the ductility threshold occurred at an embedment length close to 10d. Approximately 70% of all test specimens with an embedment length 10d and all specimens with 15d and 20d (exhibited rod yielding as their principal failure mode. Most specimens with 19mm diameter rods, exhibited to have their ductility threshold closer to~20d embedment length.  Further studies should be carried out to determine the appropriate edge distances to be utilized for specimens with larger diameter rods, as some specimens did exhibit a splitting brittle type failure mode that can be attributed to small edge distances combined with a large accumulation of shear stress near the adhesive-timber interface.   2) For all specimens fabricated with 12.7mm diameter rods and a deliberate fabrication defect, with embedment lengths past their ductility threshold (le>10d), rod yielding remained the predominant failure mode.  Furthermore, it can also be said that no significant detrimental effects to a connection’s axial capacity and stiffness was observed due to these manufacturing defects.  This assertion was validated by several statistical analyses performed on the experimental data.  As a result, it can be concluded that even though quality control should always be of high importance, it is not imperative that 12.7mm diameter glued-in mild steel threaded rods be perfectly centered, nor correctly aligned parallel to the grain of the timber element in their respective bore holes if they are properly designed to be governed by the rod’s yield capacity.   75 3) If rods are embedded past their ductility threshold, the adhesive (PUR or EPX) had negligible effects on the connection’s axial capacity, stiffness and failure mode.  Additionally, as glued-in steel rods are by nature a very stiff connection, their nonlinear behaviour will be mostly governed by the bonded-in rod’s ability to deform plastically. Specimens with rods bonded with both EPX adhesives under study, exhibited slightly higher average pull out capacity than the ones using the PUR.  Yet, these variations were not statistically meaningful and therefore it can be concluded that the choice of adhesive type (CR421®, T88® or Gel Magic®) does not have an impact on the axial capacity of glued-in steel threaded rod connections.   4) Specimens with multiple glued-in steel rods exhibited similar behaviour as specimens with single rods with regards to their ductility thresholds.  For all specimens with 12.7mm threaded rods the ductility threshold occurs at about 10d embedment length and therefore, the connection’s failure mode will be dictated by the rod’s nonlinear behaviour.  Moreover, after safely attaining this ductility threshold, the connection’s overall axial capacity will, for all practical purposes, be the linear accumulation of the yield force of each rod times the number of rods embedded into the timber host.   5) Rod spacing plays a pivotal role in the performance of specimens with multiple glued-in steel rods.  Previous research recommended that a minimum spacing of >3d should be used to reduce the incidence of group effects.  The results of this experimental campaign show that for some specimens with 4d spacing between rods and with embedment lengths greater than the determined ductility threshold have exhibited brittle-wood related failures.  For specimens with 5d rod spacing (and sufficient embedment length), ductile behaviour was properly achieved.     76 REFERENCES Aicher, S., & Dill-Langer, G. (2001). Influence of moisture, temperature and load duration on performance of glued-in rods . Materials and Structures , 44:997–1020 1019. Bainbridge, R., Mettem, C., Harvey, K., & & Ansell, M. (2002). Bonded-in rod connections for timber structures-development of design methods and test observations. International Journal of Adhesion & Adhesives, 22: 47-59. Bengtsson, C., & Johansson, C. (2001). Final Report: GIROD – Glued-in Rods for Timber Structures. SMT4-CT97-2199. 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Construction and Building Materials, 25: 2312-2317.    80 APPENDIX A: LOAD DISPLACEMENT CURVES   A 1 – Relative Load Displacement for A1 Series (CR421®, 5d, Phase #1)  A 2 - Relative Load Displacement for A2 Series (CR421®, 10d, Phase #1) 05101520250 0.2 0.4 0.6 0.8 1Load [kN]Relative Displacement [mm]CR421-5d-#1CR421-5d-#2CR421-5d-#3CR421-5d-#4CR421-5d-#5CR421 - 5d - Average051015202530350 0.2 0.4 0.6 0.8 1Load[kN]Relative Displacement [mm]CR421-10d-#1CR421-10d-#2CR421-10d-#3CR421 - 10d -Average81  A 3 - Relative Load Displacement for A3 Series (CR421®, 20d, Phase #1)  A 4 - Relative Load Displacement for B3 Series (T88®, 20d, Phase #1)  0510152025303540450 0.2 0.4 0.6 0.8 1Load[kN]Relative Displacement [mm]CR421-20d-#1CR421-20d-#2CR421-20d-#3CR421 - 20d - Average0510152025303540450 0.2 0.4 0.6 0.8 1Load [kN]Relative Displacement [mm]T88-20d-#1T88-20d-#2T88-20d-#3T88 - 20d - Average82  A 5 - Relative Load Displacement for C3 Series (Gel Magic®, 20d, Phase #1)  A 6 - Relative Load Displacement for AX2-i Series (CR421®, Un-centered Rod, 10d, Phase #2) 0510152025303540450 0.2 0.4 0.6 0.8 1Load[kN]Relative Displacement [mm]GelMagic-20d-#1GelMagic-20d-#2GelMagic-20d-#3GelMagic - 20d -Average051015200 0.2 0.4 0.6 0.8 1Load [kN]Relative Displacement [mm]CR421-Uncentered-10d-#1CR421-Uncentered-10d-#2CR421-Uncentered-10d-#3Avg. CR421-Uncentered-10d83  A 7 - Relative Load Displacement for AX2-ii Series (CR421®, Rod at an angle, 10d, Phase #2)  A 8 - Relative Load Displacement for AX3-i Series (CR421®, Un-centered Rod, 20d, Phase #2) 051015200 0.2 0.4 0.6 0.8 1Load[kN]Relative Displacement [mm]CR421-Rod@Angle-10d-#1CR421-Rod@Angle-10d-#2CR421-Rod@Angle-10d-#3Avg. CR421-Rod@Angle-10d05101520250 0.2 0.4 0.6 0.8 1Load[kN]Relative Displacement [mm]CR421-Uncentered Rod-20d-#1CR421-Uncentered Rod-20d-#2CR421-Uncentered Rod-20d-#3Avg. CR421-UncenteredRod-20d84  A 9 - Relative Load Displacement for AX3-ii Series (CR421®, Rod at an angle, 20d, Phase #2)  A 10 - Relative Load Displacement for BX3-i Series (T88®, Un-centered Rod, 20d, Phase #2) 0510152025300 0.2 0.4 0.6 0.8 1Load[kN]Relative Displacement [mm]CR421-Rod@Angle-20d-#1CR421-Rod@Angle-20d-#2CR421-Rod@Angle-20d-#3Avg. CR421-Rod@Angle-20d0510152025300 0.2 0.4 0.6 0.8 1Load [kN]Relative Displacement [mm]T88-Uncentered Rod-20d-#1T88-Uncentered Rod-20d-#2T88-Uncentered Rod-20d-#3Avg. T88-UncenteredRod-20d85  A 11- Relative Load Displacement for BX3-ii Series (T88®, Rod at an angle, 20d, Phase #2)  A 12 - Relative Load Displacement for CX3-i Series (GelMagic®, Un-centered Rod, 20d, Phase #2) 0510152025300 0.2 0.4 0.6 0.8 1Load[kN]Relative Displacement [mm]T88-Rod@Angle-20d-#1T88-Rod@Angle-20d-#2T88-Rod@Angle-20d-#3Avg. T88-Rod@Angle-20d0510152025300 0.2 0.4 0.6 0.8 1Load[kN]Relative Displacement [mm]Gelmagic-Uncentered Rod-20d-#1Gelmagic-Uncentered Rod-20d-#2Gelmagic-Uncentered Rod-20d-#3Avg. Gelmagic-Uncentered Rod-20d86  A 13 - Relative Avg. Load Displacement for M1-A Series (CR421®, 2 Rods, le=5d, s=3d, Phase #3)  A 14 - Relative Avg. Load Displacement for M1-B Series (CR421®, 2 Rods, le=5d, s=4d, Phase #3) 05101520253035400 0.5 1 1.5 2Load[kN]Relative Displacement [mm]M1-A-#1M1-A-#2M1-A-#3Avg. M1-A051015202530354045500 0.5 1 1.5 2Load[kN]Relative Displacement [mm]M1-B-#1M1-B-#2M1-B-#3Avg. M1-B87  A 15 - Relative Avg. Load Displacement for M1-C Series (CR421®, 2 Rods, le=5d, s=5d, Phase #3)  A 16 - Relative Avg. Load Displacement for M2-A Series (CR421®, 2 Rods, le=10d, s=3d, Phase #3)  0510152025303540455055600 0.5 1 1.5 2Load[kN]Relative Displacement [mm]M1-C-#1M1-C-#2M1-C-#3Avg. M1-C01020304050607080901000 0.5 1 1.5 2Load[kN]Relative Displacement [mm]M2-A-#1M2-A-#2M2-A-#3Avg. M2-A88  A 17 - Relative Avg. Load Displacement for M2-B Series (CR421®, 2 Rods, le=10d, s=4d, Phase #3)  A 18 - Relative Avg. Load Displacement for M2-C Series (CR421®, 2 Rods, le=10d, s=5d, Phase #3)  01020304050607080901000 0.5 1 1.5 2Load[kN]Relative Displacement [mm]M2-B-#1M2-B-#2M2-B-#3Avg. M2-B01020304050607080901000 0.5 1 1.5 2Load[kN]Relative Displacement [mm]M2-C-#1M2-C-#2M2-C-#3Avg. M2-C89  A 19 - Relative Avg. Load Displacement for M3-A Series (CR421®, 2 Rods, le=15d, s=3d, Phase #3)  A 20 - Relative Avg. Load Displacement for M3-B Series (CR421®, 2 Rods, le=15d, s=4d, Phase #3)  01020304050607080901001100 0.5 1 1.5 2Load[kN]Relative Displacement [mm]M3-A-#1M3-A-#2M3-A-#3Avg. M3-A01020304050607080901001100 0.5 1 1.5 2Load[kN]Relative Displacement [mm]M3-B-#1M3-B-#2M3-B-#3Avg. M3-B90  A 21 - Relative Avg. Load Displacement for M3-C Series (CR421®, 2 Rods, le=15d, s=5d, Phase #3)  A 22 - Relative Avg. Load Displacement for M4-A Series (CR421®, 3 Rods, le=5d, s=3d, Phase #3)  01020304050607080901001100 0.5 1 1.5 2Load [kN]Relative Displacement [mm]M3-C-#1M3-C-#2M3-C-#3Avg. M3-C010203040506070800 0.5 1 1.5 2Load[kN]Relative Displacement [mm]M4-A-#1M4-A-#2M4-A-#3Avg. M4-A91  A 23 - Relative Avg. Load Displacement for M4-B Series (CR421®, 3 Rods, le=5d, s=4d, Phase #3)  A 24 - Relative Avg. Load Displacement for M4-C Series (CR421®, 3 Rods, le=5d, s=5d, Phase #3) 010203040506070800 0.5 1 1.5 2Load[kN]Relative Displacement [mm]M4-B-#1M4-B-#2M4-B-#3Avg. M4-B010203040506070800 0.5 1 1.5 2Load[kN]Relative Displacement [mm]M4-C-#1M4-C-#2M4-C-#3Avg. M4-C92  A 25 - Relative Avg. Load Displacement for M11-A Series (CR421®, 3 Rods, le=7.5d, s=3d, Phase #3)  A 26 - Relative Avg. Load Displacement for M11-B Series (CR421®, 3 Rods, le=7.5d, s=4d, Phase #3)  01020304050607080900 0.5 1 1.5 2Load[kN]Relative Displacement [mm]M11-A-#1M11-A-#2M11-A-#3Avg. M11-A01020304050607080901001100 0.5 1 1.5 2Load[kN]Relative Displacement [mm]M11-B-#1M11-B-#2M11-B-#3Avg. M11-B93  A 27 - Relative Avg. Load Displacement for M11-C Series (CR421®, 3 Rods, le=7.5d, s=5d, Phase #3)  A 28 - Relative Avg. Load Displacement for M5-A Series (CR421®, 3 Rods, le=10d, s=3d, Phase #3)  01020304050607080901001100 0.5 1 1.5 2Load [kN]Relative Displacement [mm]M11-C-#1M11-C-#2M11-C-#3Avg. M11-C01020304050607080901001101200 0.5 1 1.5 2Load[kN]Relative Displacement [mm]M5-A-#1M5-A-#2M5-A-#3Avg. M5-A94  A 29 - Relative Avg. Load Displacement for M5-B Series (CR421®, 3 Rods, le=10d, s=4d, Phase #3)  A 30 - Relative Avg. Load Displacement for M5-C Series (CR421®, 3 Rods, le=10d, s=5d, Phase #3)  01020304050607080901001101201301401500 0.5 1 1.5 2Load[kN]Relative Displacement [mm]M5-B-#1M5-B-#2M5-B-#3Avg. M5-B01020304050607080901001101201301401500 0.5 1 1.5 2Load[kN]Relative Displacement [mm]M5-C-#1M5-C-#2M5-C-#3Avg. M5-C95  A 31 - Relative Avg. Load Displacement for M6-A Series (CR421®, 3 Rods, le=15d, s=3d, Phase #3)  A 32 - Relative Avg. Load Displacement for M6-B Series (CR421®, 3 Rods, le=15d, s=4d, Phase #3)  01020304050607080901001101201301401500 0.5 1 1.5 2Load [kN]Relative Displacement [mm]M6-A-#1M6-A-#2M6-A-#3Avg. M6-A01020304050607080901001101201301401501600 0.5 1 1.5 2Load[kN]Relative Displacement [mm]M6-B-#1M6-B-#2M6-B-#3Avg. M6-B96  A 33 - Relative Avg. Load Displacement for M6-C Series (CR421®, 3 Rods, le=15d, s=5d, Phase #3)  A 34 - Relative Avg. Load Displacement for M7-A Series (CR421®,4 Rods, le=5d, s=3d, Phase #3)  01020304050607080901001101201301401501600 0.5 1 1.5 2Load [kN]Relative Displacement [mm]M6-C-#1M6-C-#2M6-C-#3Avg. M6-C01020304050607080901001100 0.5 1 1.5 2Load[kN]Relative Displacement [mm]M7-A-#1M7-A-#2M7-A-#3Avg. M7-A97  A 35 - Relative Avg. Load Displacement for M7-B Series (CR421®,4 Rods, le=5d, s=4d, Phase #3)  A 36 - Relative Avg. Load Displacement for M7-C Series (CR421®,4 Rods, le=5d, s=5d, Phase #3)  01020304050607080901001100 0.5 1 1.5 2Load[kN]Relative Displacement [mm]M7-B-#1M7-B-#2M7-B-#3Avg. M7-B01020304050607080901001100 0.5 1 1.5 2Load[kN]Relative Displacement [mm]M7-C-#1M7-C-#2M7-C-#3Avg. M7-C98  A 37 - Relative Avg. Load Displacement for M12-A Series (CR421®,4 Rods, le=7.5d, s=3d, Phase #3)  A 38 - Relative Avg. Load Displacement for M12-B Series (CR421®,4 Rods, le=7.5d, s=4d, Phase #3)  01020304050607080901001100 0.5 1 1.5 2Load[kN]Relative Displacement [mm]M12-A-#1M12-A-#2M12-A-#3Avg. M12-A01020304050607080901001101201301400 0.5 1 1.5 2Load[kN]Relative Displacement [mm]M12-B-#1M12-B-#2M12-B-#3Avg. M12-B99  A 39 - Relative Avg. Load Displacement for M12-C Series (CR421®,4 Rods, le=7.5d, s=5d, Phase #3)  A 40 - Relative Avg. Load Displacement for M8-A Series (CR421®,4 Rods, le=10d, s=3d, Phase #3) 01020304050607080901001101201301401501600 0.5 1 1.5 2Load [kN]Relative Displacement [mm]M12-C-#1M12-C-#2M12-C-#3Avg. M12-C01020304050607080901001101201301401501600 0.5 1 1.5 2Load[kN]Relative Displacement [mm]M8-A-#1M8-A-#2M8-A-#3Avg. M8-A100  A 41 - Relative Avg. Load Displacement for M8-B Series (CR421®,4 Rods, le=10d, s=4d, Phase #3)  A 42 - Relative Avg. Load Displacement for M8-C Series (CR421®,4 Rods, le=10d, s=5d, Phase #3)  01020304050607080901001101201301401501600 0.5 1 1.5 2Load [kN]Relative Displacement [mm]M8-B-#1M8-B-#2M8-B-#3Avg. M8-B01020304050607080901001101201301401501601700 0.5 1 1.5 2 2.5Load[kN]Relative Displacement [mm]M8-C-#1M8-C-#2M8-C-#3Avg. M8-C101  A 43 - Relative Avg. Load Displacement for M9-A Series (CR421®,4 Rods, le=15d, s=3d, Phase #3)  A 44 - Relative Avg. Load Displacement for M9-B Series (CR421®,4 Rods, le=15d, s=4d, Phase #3)  01020304050607080901001101201301401501601701801902002100 0.5 1 1.5 2 2.5 3 3.5 4Load[kN]Relative Displacement [mm]M9-A-#1M9-A-#2M9-A-#3Avg. M9-A01020304050607080901001101201301401501601701801902002100 0.5 1 1.5 2 2.5 3 3.5 4Load[kN]Relative Displacement [mm]M9-B-#1M9-B-#2M9-B-#3Avg. M9-B102  A 45 - Relative Avg. Load Displacement for M9-C Series (CR421®,4 Rods, le=15d, s=5d, Phase #3)       01020304050607080901001101201301401501601701801902002100 0.5 1 1.5 2 2.5 3 3.5 4Load[kN]Relative Displacement [mm]M9-C-#1M9-C-#2M9-C-#3Avg. M9-C

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