OPTIMIZING HOLLOW-BOX FLOOR SYSTEMS WITH STRUCTURAL COMPOSITE LUMBER THROUGH SCREW-GLUING METHOD AND PARAMETRIC MODELLING by Tianci Huangfu Bachelor of Engineering (Honours), University of Queensland, 2020 THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE IN ENGINEERING UNIVERSITY OF NORTHERN BRITISH COLUMBIA November 2024 © Tianci Huangfu, 2024 Abstract Mass timber construction gained significant attention for its sustainability and off-site construction, but conventional mass timber products like cross-laminated timber (CLT) often faces challenges in long-span applications due to material inefficiency. Structural composite lumber (SCL), including mass ply panels (MPP), laminated veneer lumber (LVL), and laminated strand lumber (LSL), can offer a more efficient solution with superior material utilization, dimensional stability, and mechanical properties. This research focused on developing an optimized, prefabricated hollow-box floor system using SCL, integrated with the screw-gluing method and optimization algorithm to improve both structural performance and material efficiency. Experimental tests demonstrated that screws could provide sufficient pressure required by the adhesive instead of a conventional hydraulic press for MPP flange-to-web connections. Key findings indicated that increasing screw spacing, rib width, and flange thickness negatively impact connection performance, with screw spacing reducing shear stress at failure by up to 28%, rib width by up to 45%, and flange thickness by up to 8%. No significant difference in results was observed between groups with 100 mm, 120 mm, and 160 mm long screws in both 50 mm and 75 mm flange groups. Smaller screw spacing improved connection performance, while increasing spacing decreased shear resistance. In the 50 mm flange group, 250 mm spacing was the limit, whereas in the 75 mm flange group, connections with spacing within 300 mm provided acceptable results. ANOVA results indicated that rib widths of 75 mm or more reduced connection performance with a single screw row arraignment but performed acceptably with staggered two row arrangement. Flange thicknesses also had a minor influence, with increased thickness from 75 mm to ii 100 mm negatively impacting load-carrying capacity by 8%. These findings provided essential insights into fabricating hollow-box floors using the screw-glued technique. In addition, a parametric optimization algorithm was developed by integrating parametric geometry modelling, material databases, design verification methods, including the stressed skin design method in CSA O86, Gamma method, and the shear analogy method. Genetic algorithm was also used to automatically iterate through input parameters, overcoming the drawbacks of conventional, manually iterative, and time-consuming structural design process. The study also compared different methods for calculating the effective width of hollow-box floor modules, with CSA O86 and Kikuchi methods yielding similar results, while Eurocode 5 provided more conservative estimates. The optimization results demonstrated that hollow-box floor systems could achieve up to 75% material savings compared to CLT and 67% compared to solid MPP panels, while also reducing floor height by approximately 30% relative to I-joist systems under deflection-controlled conditions. Furthermore, vibration-controlled criteria were considered as an additional optimization objective, achieving up to 60% and 50% material savings compared to CLT and MPP solid panels, respectively. iii Acknowledgements First and foremost, I would like to express my deepest gratitude to my supervisor, Dr. Jianhui Zhou, for his invaluable guidance and support throughout my master’s research and studies. His mentorship has been instrumental in shaping this thesis. I also extend my heartfelt thanks to my co-supervisor, Maik Gehloff and advisor, Dr. Thomas Tannert, for their insightful suggestions and guidance, which have greatly contributed to the advancement of my research. This research was made possible by the support of several funding supports: BC Forestry Innovation Investment - Wood First Program, Natural Sciences and Engineering Research Council of Canada (NSERC), and the University of Northern British Columbia (UNBC). Additionally, I am grateful for the in-kind materials donated by Freres Engineered Wood (MPP), Herrmann’s – Quality Building Products (Heco screws), and Henkel (adhesives). The experiments for this research were conducted in the Wood Innovation Research Lab at UNBC, where I received valuable assistance from two dedicated technicians, James Andal and Nathan Downie. I would also like to thank my fellow colleagues at the Wood Innovation and Design Centre (WIDC) for their support throughout my studies. Special thanks go to Maomao and my partner for their emotional and practical support, which has been essential in both my studies and daily life. Finally, I extend my deepest gratitude to my family, particularly my parents, for their unwavering support and encouragement. I love you all. iv Table of Contents Abstract ............................................................................................................................... ii Acknowledgements ............................................................................................................ iv Table of Contents ................................................................................................................ v List of Figures .................................................................................................................. viii List of Tables ..................................................................................................................... xi List of Abbreviations and Symbols................................................................................... xii Abbreviations ................................................................................................................ xii Symbols ........................................................................................................................ xiii Chapter 1 Introduction ..................................................................................................... 1 1.1 Background ............................................................................................................... 1 1.2 Research need ............................................................................................................ 4 1.3 Objective ................................................................................................................... 4 1.4 Thesis Organization................................................................................................... 5 References ....................................................................................................................... 7 Chapter 2 Literature Review............................................................................................ 9 2.1 Introduction ............................................................................................................... 9 2.2 Engineered wood products ........................................................................................ 9 2.2.1 Lumber-based MTP ............................................................................................ 9 2.2.2 Structural composite lumber ............................................................................. 11 2.3 Timber floor systems ............................................................................................... 12 2.3.1 Light wood joisted floor ................................................................................... 12 2.3.2 Mass timber floor.............................................................................................. 14 2.3.3 Ribbed floor ...................................................................................................... 16 v 2.4 Screw-gluing method .............................................................................................. 20 2.5 Composite floor design methods ............................................................................. 24 2.5.1 CSA O86........................................................................................................... 25 2.5.2 Eurocode 5 ........................................................................................................ 29 2.5.3 Shear analogy method ...................................................................................... 32 2.5.4 Effective width of hollow-box floor modules .................................................. 34 2.6 Parametric design .................................................................................................... 35 2.7 Summary ................................................................................................................. 36 References ..................................................................................................................... 38 Chapter 3 Experimental Investigation on the Connection Performance of Screw-glued Joints with Mass Ply Panels .............................................................................................. 48 3.1 Introduction ............................................................................................................. 49 3.2 Materials and Methods ............................................................................................ 51 3.2.1 Materials ........................................................................................................... 51 3.2.2 Specimen fabrication and experimental design ................................................ 52 3.2.3 Block shear tests of MPP .................................................................................. 60 3.2.4 Push-out connection tests ................................................................................. 61 3.2.5 Data analysis ..................................................................................................... 63 3.3 Results and Discussion ............................................................................................ 64 3.3.1 Block shear strength of MPP ............................................................................ 64 3.3.2 Screw-only tests ................................................................................................ 65 3.3.3 Glue-only tests .................................................................................................. 68 3.3.4 Screw-glued tests .............................................................................................. 72 3.4 Conclusions ............................................................................................................. 97 References ................................................................................................................... 100 vi Chapter 4 Parametric Modelling and Structural Optimization of Prefabricated Structural Composite Lumber Hollow-box floor Modules ............................................. 103 4.1 Introduction ........................................................................................................... 104 4.2 Methodology ......................................................................................................... 108 4.2.1 Structural analysis and design methods .......................................................... 111 4.2.2 Structural optimization algorithm ................................................................... 118 4.3 Results and discussion ........................................................................................... 125 4.3.1 Comparison of different effective width calculation methods ....................... 125 4.3.2 Comparison of different design methods........................................................ 127 4.3.3 Optimal hollow-box floor design case study .................................................. 131 4.3.4 Material usage comparison with other wood floor systems ........................... 134 4.4 Conclusion............................................................................................................. 138 References ................................................................................................................... 139 Chapter 5 Conclusions and Recommendations ........................................................... 144 5.1 Conclusions ........................................................................................................... 144 5.2 Recommendations ................................................................................................. 146 Appendix A Detailed Results of Connection Tests ..................................................... 148 Appendix B Objective Function Python Code for Genetic Algorithm ....................... 189 Appendix C ANOVA Result for Each Group ............................................................. 190 vii List of Figures Figure 1.1 Section comparison between MPP (Top) and CLT (Bottom) ............................ 3 Figure 2.1 Example of lumber-based EWPs (Forestry Innovation Investment, 2024c). .. 10 Figure 2.2 Variations of SCL (APA-The Engineered Wood Association, 2024a) .............11 Figure 2.3 I-joist and wood joist floor (BCI® Joists, 2024) ............................................. 13 Figure 2.4 Example building with mass timber floor (Forestry Innovation Investment, 2024a) .............................................................................................................................. 14` Figure 2.5 Closed (a) and open (b) type ribbed floor system and the example application(c) (Stora Enso, 2024a) ................................................................................... 16 Figure 2.6 Geometry requirement in current standards (Bratulic & Augustin, 2016) ...... 21 Figure 2.7 Schematic models of closed (right) and open (left) hollow-box floor modules ........................................................................................................................................... 25 Figure 2.8 Relationship between beam span and ߛ ........................................................... 31 Figure 3.1 Conceptual closed type (left)) of hollow-box floors and basic shape for connection testing ............................................................................................................. 53 Figure 3.2 Schematic drawing of the test specimens ........................................................ 54 Figure 3.3 Application of PLMAX ................................................................................... 57 Figure 3.4 Sample arrangement for 150 mm spacing staggered group (top view) ........... 59 Figure 3.5 Screw arrangement for 300 mm staggered group (top view) .......................... 60 Figure 3.6 Dimension and test setup of block tests (ASTM, 2021b) ................................ 61 Figure 3.7 Test schematic drawing and real setup ............................................................ 62 Figure 3.8 Load-displacement curve example .................................................................. 62 Figure 3.9 Typical load-displacement diagram of screw-only groups .............................. 65 Figure 3.10 Failure mode of screw-only groups ............................................................... 66 Figure 3.11 Load-carrying capacity and slip modulus of screw-only group .................... 67 Figure 3.12 Typical load-displacement diagram of glue-only tests .................................. 68 Figure 3.13 Typical Failure mode of glue-only groups .................................................... 69 Figure 3.14 Load-carrying capacity and slip modulus for glue-only groups .................... 70 Figure 3.15 Shear stress at failure for glue-only groups ................................................... 70 Figure 3.16 Typical load-displacement diagram of 150 mm spacing screw glued tests ... 72 viii Figure 3.17 Typical failure mode of fully (left) and partially (right) threaded groups ..... 73 Figure 3.18 Load-carrying capacity and slip modulus for different adhesive with 50mm flange group ...................................................................................................................... 74 Figure 3.19 Load-carrying capacity and slip modulus for different screw type and adhesive with 50mm flange group .................................................................................... 75 Figure 3.20 Load-carrying capacity and slip modulus of different spacing with 50 mm flange group ...................................................................................................................... 77 Figure 3.21 Shear stress of different spacing with 50 mm flange group .......................... 78 Figure 3.22 Example failure mode of 50_50_250s (left) and 50F_50R_100L_300s (right) group ................................................................................................................................. 80 Figure 3.23 Load-carrying capacity and slip modulus of different rib width with 50 mm flange group ...................................................................................................................... 81 Figure 3.24 Shear stress of different rib width with 50 mm flange group ........................ 82 Figure 3.25 Example failure mode of 100 mm(left) and 150 mm(right) rib width group 83 Figure 3.26 Load-carrying capacity and slip modulus of different rib width with 75-and 100- mm flange group ....................................................................................................... 85 Figure 3.27 Shear stress of different rib width with 75-and 100- mm flange group ........ 86 Figure 3.28 Example Failure mode of 75F_75R_150L_160s (left) and 100F_75R_160L_150s (right) .......................................................................................... 88 Figure 3.29 Load-carrying capacity and slip modulus of different spacing with 75 mm flange group ...................................................................................................................... 90 Figure 3.30 Shear stress of different spacing with 75 mm flange group .......................... 91 Figure 3.31 Example Failure mode of 75F_75F_150L _160s (left) and 75F_75F_160L_300s (right) ............................................................................................. 92 Figure 3.32 Load-carrying capacity and slip modulus of different screw arrangement with 75 mm flange group .......................................................................................................... 94 Figure 3.33 Shear stress of different screw arrangement with 75 mm flange group ........ 95 Figure 3.34 Example failure mode of 75F_150R_160L_150s (left) and 75F_150R_160L_300s (right) .......................................................................................... 96 Figure 4.1 Schematic model and configuration of the I (a) and T (b) section ................ 109 Figure 4.2 The logic of optimization algorithm ...............................................................119 ix Figure 4.3 Visual model of I (top) and T (bottom) section floor module ....................... 121 Figure 4.4 Input variables of optimization algorithm ..................................................... 121 Figure 4.5 Galapagos settings (left) and optimization process (right) ............................ 124 Figure 4.6 Different effective width based on change of panel width ............................ 126 Figure 4.7 Different effective width based on change of panel span .............................. 126 Figure 4.8 bending stress distributions with different design methods (I-section) ......... 128 Figure 4.9 shear stress distributions with different design methods (I-section) ............ 128 Figure 4.10 Diagram illustration of bending stress with different design methods (Tsection) ............................................................................................................................ 129 Figure 4.11 Diagram illustration of shear stress with different design methods (T-section) ......................................................................................................................................... 130 Figure 4.12 Material usage and floor height comparison for deflection-controlled criteria between 6m and 9m span and 1.2 m width ..................................................................... 135 Figure 4.13 Material usage and floor height comparison for vibration-controlled criteria width 1.2 m floor width .................................................................................................. 137 x List of Tables Table 2.1 Eurocode 5 Maximum effective flange width calculation method ................... 35 Table 3.1 Detailed specimen information for preliminary study tests .............................. 56 Table 3.2 Detailed group information for parameter study tests ...................................... 58 Table 3.3 P-values for glue-only tests ............................................................................... 71 Table 3.4 P-values of different screw type and adhesives with 50 mm flange group ....... 76 Table 3.5 P-values for 50 mm thick flange varying spacing group .................................. 79 Table 3.6 P-values for 50 mm thick flange varying rib width group ................................ 84 Table 3.7 P-values for 75- and 100-mm thick flange varying rib width group ................ 87 Table 3.8 P-values for 75 thick flange varying screw spacing group ............................... 92 Table 3.9 P-values for 75 mm flange staggered arrangement groups ............................... 96 Table 4.1 Eurocode 5 maximum effective flange width calculation method ...................110 Table 4.2 F16 grade MPP design values ......................................................................... 120 Table 4.3 Example scenario used to compare calculation methods ................................ 125 Table 4.4 Structural analysis results for different design methods (I-section)................ 127 Table 4.5 Structural analysis results for different design methods (T-section) ............... 129 Table 4.6 Optimization results for I section .................................................................... 131 Table 4.7 Optimization results for T section ................................................................... 132 Table 4.8 Optimization result for deflection-controlled span ......................................... 134 Table 4.9 Optimization result for vibration-controlled span ........................................... 136 xi List of Abbreviations and Symbols Abbreviations CLT Cross-Laminated Timber DLT Dowel-Laminated Timber NLT Nail-Laminated Timber Glulam Glued-laminated timber MTP Mass Timber Panels SCL Structural Composite Lumber MPP Mass Plywood Panels LVL Laminated Veneer Lumber EWP Engineered Wood Product LSL Laminated Strand Lumber OSL Oriented Strand Lumber PSL Parallel Strand Lumber TCC Timber-Concrete Composite TSC Timber-Steel Composite TTC Timber-Timber Composite GPRF Gap-Filling Phenol Resorcinol Formaldehyde STS Self-Tapping Screw ULS Ultimate Limit State SLS Serviceability Limit State xii Symbols ‫ܣ‬ The contact area ‫ܣ‬௜ The cross-section area of the ݅ ௧௛ layer ܽ௜ The distance from the centroid of the ݅ ௧௛ layer to the neutral axis ‫ܤ‬௔ The specified axial stiffness of the flange ‫ܤ‬௔௧ The specified axial stiffness of tension flange ‫ܤ‬௔௖ The specifies axial stiffness of compression flange ܾ The half of the rib spacing ܾଵ The flange width ܾଶ The width of rib ܾ௘௙ The effective width of hollow-box floor module ܾ௙ The total panel width ܾ௚ The contact width between flange and rib ܾ௜ The width of cross section of the ݅ ௧௛ layer ‫ܦ‬ The dead load ‫ܦ‬ଵ଴ The displacement at 10% of maximum load ‫ܦ‬ସ଴ The displacement at 40% of maximum load ‫଺ܦ‬଴ The displacement at 60% of maximum load ݀ The deflection of the floor panel ‫ܧ‬ The modulus of elasticity of rib ‫ܧ‬௜ The Young’s Modulus of the ݅௧௛ layer in the composite beam ‫ܫܧ‬ଵ௠ The effective bending stiffness of the floor width 1 metre width (‫)ܫܧ‬஺ The bending stiffness for the virtual beam A (‫)ܫܧ‬஻ The bending stiffness for the virtual beam B xiii (‫)ܫܧ‬௘௙ The effective stiffness (‫)ܫܧ‬௪ The stiffness of ribs ‫ܨ‬ଵ଴ The 10% of maximum load ‫ܨ‬ସ଴ The 40% of maximum load ‫଺ܨ‬଴ The 60% of maximum load ‫ܨ‬ The achieved mean load ݂ The applied force ‫ܨ‬௠௔௫ The maximum load ݂ଵ The calculated fundamental natural frequency ݂௕ The specified strength in bending of ribs ݂௩ The specified strength in shear of ribs ‫ܩ‬ The shear modulus (‫)ܣܩ‬௘௙ The effective shear rigidity ‫ܪ‬ The current total height of the cross-section ℎଵ The top flange thickness ℎଶ The height of the rib ℎଷ The bottom flange thickness ℎ௖ The greatest distance from neutral axis to outer edge of tension flange ℎ௙ The flange thickness of hollow-box floor module ℎ௜ The height of cross section of the ݅௧௛ layer ℎ௧ The greatest distance from neutral axis to outer edge of compression flange ‫ܫ‬௜ The moment of inertia of the cross section of the ݅ ௧௛ layer ‫ܭ‬஽ The load-duration factor ‫ܭ‬ு The system factor xiv ‫ܭ‬௜ The slip modulus of the mechanical fastener ‫ܭ‬௅ The lateral-stability factor for bending members ‫ܭ‬ௌ The service-condition factors ‫ܭ‬ௌ௕ The service-condition factors for bending ‫ܭ‬ௌா The service-condition factors for modulus of elasticity ‫ܭ‬௦௘௥ The slip modulus in serviceability limit state conditions ‫ܭ‬ௌ௩ The service-condition factor for shear ‫்ܭ‬ The treatment factor ‫ܭ‬௨ The slip modulus in ultimate limit state conditions ‫ܭ‬௭௕ The size factor for bending ‫ܭ‬௭௩ The size factor in shear ݇ The confidence level factor ‫ܮ‬ The live load ݈ The span of panel ‫ܯ‬஺,ௗ The amount of design bending moment in virtual beam A ‫ܯ‬஻,ௗ The amount of design bending moment in virtual beam B ‫ܯ‬ௗ The design bending moment ‫ܯ‬௥ The bending resistance ݉ The linear mass of floor width 1 metre width ܲ The minimum curing pressure of adhesive ‫݌‬௣ The specified strength capacity of flange in axial compression ∑ ܳ௪ The sum of moments of area of all ribs about neutral plane ‫ݏ‬ The standard deviation of the sample xv ܵ௙ The fastener distance ‫ݏ‬௜ The spacing of fasteners of the ݅ ௧௛ layer ‫ݏ‬௖௟௘௔௥ The clear spacing between the ribs ‫ݐ‬௣ The specified strength of capacity of flange in axial tension ‫ݑ‬ௗ The ratio of the actual deflection to the deflection limit ‫ݑ‬ெ The ratio of the actual bending moment to the bending moment capacity ‫ݑ‬௏ The ratio of the actual shear force to the shear force capacity ‫ݒ‬௣௙ The specified strength capacity in planar shear of the rib ܸ The volume of current panel ܸ஺,ௗ The amount of shear force in virtual beam A ܸ஻,ௗ The amount of shear force in virtual beam B ܸௗ The design shear force V୰ The shear resistance for the neutral plane of panel ܸ௥௣ The flange-rib shear resistance in flange ܸ௥௣௪ The flange-rib shear resistance in rib ‫ݒ‬ The total volume ‫ݓ‬ The uniform distributed load ܺത The mean value of the sample ܺீ The panel geometry reduction factor ܺ௃ The stress-joint factor ܺ௩ The shear-modification factor ‫ݖ‬ଵ The distance from half of the top flange to the neutral axis xvi ‫ݖ‬ଷ The distance from half of the bottom flange to the neutral axis ‫ݖ‬௦,ଶ The greatest distance from neutral axis to outer edge of rib ‫ݖ‬௦,௜ The distance between any point and the neutral axis ‫ݖ‬௜ The distance between the neutral axis of the ݅ ௧௛ layer and the neutral axis of the beam ߛ The greater value of distance from half of the flange to neutral axis ∆ The deflection ∆௠௔௫ The total deflection of virtual beam A and B ߶ The resistance factor for flange ߶௩ The resistance factor for shear ߶௩௙ The resistance factor for shear in flange ∅௪ The resistance factor for rib ߪ஺ The bending stress for virtual beam A ߪ஻ The bending stress for virtual beam B ߪ௜ The bending stress ߬ଶ,௠௔௫ The maximum shear stress ߬௔௩௚ The average shear stress ߬௠௔௫ The shear strength ߬௫௭ The total shear stress of virtual beam A and B ߬஺,௜ The shear stress for virtual beam A ߬஻,௜ The shear stress for virtual beam B xvii Chapter 1 Introduction 1.1 Background Wood has been utilized in building construction for centuries, primarily due to its abundance and ease of use (Seim, 2024). Historical evidence indicates that ancient civilizations employed logs or planks to construct both residential buildings and even multi-story towers (Smith & Snow, 2008). This conventional approach to construction continues to be relevant today. In contemporary timber construction, dimensional lumber is widely used for single-family homes and low-rise multifamily structures (Burrows, 2006). Beginning in the late 20th century, advancements in science, technology, and regulatory frameworks enabled the exploration of wood for mass timber construction (Kesik & Martin, 2021). Despite significant innovations in alternative construction materials, such as modern reinforced concrete, wood remains a favored choice due to its inherent properties, cost-effectiveness, sustainability, and versatility (Ministry for Primary Industries, 2019). The development of cross laminated timber (CLT) marked a pivotal advancement in mass timber construction. CLT, being significantly lighter than conventional materials such as steel and concrete, coupled with its prefabrication potential, has enabled more efficient construction processes, thus contributing to its growing popularity (FPInnovations, 2019). In addition to CLT, other engineered timber products, including dowel-laminated timber (DLT), nail-laminated timber (NLT), and glue-laminated timber (Glulam), have played a substantial role in advancing mass timber construction. These engineered products are considered to offer improved structural performance compared to single sawn lumber; however, fire performance remains an important factor to consider. In response to fire 1 safety concerns, the National Building Code of Canada (NBCC) reduced the allowable height for wooden structures from seven to four stories in 1953. However, subsequent advancements in these materials and in fire science prompted a reassessment of building standards, leading to the relaxation of this restriction in the 2020 edition of the NBCC, which now permits buildings up to 12 stories (Canadian Commission on Building and Fire Codes, 2022; Kesik & Martin, 2021). With the increasing adoption of mass timber construction since early 21st century due to its sustainability and ease of use, certain material limitations also became evident. Lumberbased mass timber panels (MTP) have inherent material inefficiencies due to the low logto-lumber conversion rate of just 40%-50% (Kerbes & McIntosh, 1969). As a result, structural composite lumber (SCL) is increasingly recognized as a viable alternative to lumber-based MTP in mass timber structures. The SCL manufacturing process removes defects found in ordinary sawn lumber, enhancing product reliability. SCL products are formed by bonding veneers, flakes, or strands into large dimension billets, which can then be sawn to the required dimensions. This process allows SCL to utilize small-diameter trees and branches that are typically discarded in conventional lumber manufacturing, achieving a yield rate of 80%-90% (Gao et al., 2021). Consequently, SCL products are renowned for their dimensional stability and fabrication flexibility (Bejo & Lang, 2004). Due to the superior material utilization and dimensional stability, SCL will be the material studied in this research. This research focuses on mass ply panels (MPP), a specific variant of SCL. MPP is manufactured by layering thin sheets of wood veneer, which are bonded together using adhesives under high pressure. MPP were chosen for this research because of their unique 2 cross-grain configuration, which involves alternating veneer layers oriented both parallel and perpendicular to the grain, like CLT, as shown in Figure 1.1. This configuration enhances the panel's two-way bending capacity, providing improved performance over conventional plywood and laminated veneer lumber (LVL) (Freres Engineered Wood, 2024). Additionally, MPP offers advantageous material properties, including a high strength-to-weight ratio, dimensional stability, and sustainability. These features make MPP particularly suitable for advanced timber floor systems, especially when combined with hollow-box floor systems, to develop innovative, high-performance structural solutions. Figure 1.1 Section comparison between MPP (Top) and CLT (Bottom) Timber hollow-box floor systems, like those made from concrete or steel, are composed of multiple I-shaped or T-shaped sections (Di Lorenzo et al., 2017). Compared to solid panel floors, hollow-box floor systems offer more efficient material usage, potentially reducing construction costs and optimizing cross-sectional design. 3 1.2 Research need In assembling MTP that use adhesives, such as CLT or Glulam, heavy hydraulic equipment was normally required to apply pressure during the adhesive curing process, ensuring a solid bond line (Forest Products Laboratory, 2021). As a result, production was often constrained by limitations in site conditions or available equipment, restricting material dimensions and production capacity. To address these challenges, this study employed the screw-gluing method for fabricating hollow-box composite panels. The screw-gluing method combined mechanical fasteners and adhesives, using screws instead of hydraulic equipment to provide the necessary pressure for bonding. The downward axial force exerted by the screws ensured adequate adhesive contact. This approach offered greater flexibility and adaptability, allowing for customized assembly processes that catered to different site and material requirements, and facilitated on-site construction. Therefore, combining a hollow-box floor system with MPP and the screw-gluing method resulted in an innovative flooring system that could be structurally efficient, cost-effective, and optimized material use. This system not only achieved the same strength compared to other mass timber floor systems but also improved material utilization. 1.3 Objective The primary objective of this study is to optimize hollow-box floor system with SCL through screw-gluing method and parametric modelling. To achieve this objective, the following sub-objectives will be completed: • Obtain the load-carrying capacity and slip modulus of screw-glued MPP hollowbox floor modules through experimental testing to provide data for subsequent research. 4 • Investigate the effect of different connection parameters such as material dimensions and fastener properties on connection performance. • Develop a structural optimization algorithm incorporating different design methods for prefabricated hollow-box floor systems with SCL through parametric modelling and genetic algorithm while considering the availability of different SCL products and design situations. 1.4 Thesis Organization This thesis follows a manuscript-based format, detailing the research on the development of a hollow-box floor system utilizing MPP material and the screw-gluing method. The thesis is structured into five chapters: Chapter 1 introduces the background, motivation, and objectives of the research. Chapter 2 reviews various engineered wood products and floor systems, summarizing different design methodologies for wood-based composite floors. It also introduces parametric design concepts and provides an overview of the screw-gluing method, summarizing recent literature and studies relevant to this method. Chapter 3 assesses the connection performance of the screw-glued method for fabricating hollow-box floor modules using MPP. Two phases of tests are included in this chapter: the first phase involves preliminary testing and performance evaluation of the screw-gluing method, while second phase focuses on a detailed parameter investigation, including material geometry and fastener properties. 5 Chapter 4 presents a parametric optimization algorithm for designing hollow-box floor modules, incorporating existing structural design approaches to derive optimal combinations of material usage and floor height. Additionally, the effective width of hollow-box floor panels is compared, and evaluations against other floor systems are provided. Chapter 5 concludes by summarizing the research outcomes and proposing recommendations for future research. 6 References Bejo, L., & Lang, E. (2004). Simulation based modeling of the elastic properties of structural composite lumber. Wood and Fiber Science, 36, 395–410. Burrows, J. (with Canada Mortgage and Housing Corporation). (2006). Canadian woodframe house construction (2nd combined imperial/metric ed.; Rev. ed). Canada Mortgage and Housing Corporation. Canadian Commission on Building and Fire Codes. (2022). National building code of Canada: 2020 (978-0-660-37913–5). National Research Council of Canada. Di Lorenzo, G., Formisano, A., & Landolfo, R. (2017). On the origin of I beams and quick analysis on the structural efficiency of hot-rolled steel members. The Open Civil Engineering Journal, 11, 332–344. Forest Products Laboratory. (2021). Wood handbook—Wood as an engineering material (General Techinical Report FPL-GTR-282; pp. 11–21). United States Department of Agriculture Forest Service. https://www.fpl.fs.usda.gov/documnts/fplgtr/fplgtr282/fpl_gtr282.pdf FPInnovations. (2019). Canadian CLT handbook. FPInnocations. https://web.fpinnovations.ca/wp-content/uploads/clt-handbook-complete-versionen-low.pdf Freres Engineered Wood. (2024). Mass plywood—Plywood paneling. Freres Engineered Wood. https://frereswood.com/products-and-services/mass-ply-products/ Gao, Z., & Gong, M. (2021). Strand-Based Engineered Wood Products in Construction. In Engineered Wood Products for Construction. New York: IntechOpen. 7 Kerbes, E. L., & McIntosh, J. A. (1969). Conversion of trees to finished lumber—The volume losses. The Forestry Chronicle, 45(5), 348–353. Kesik, T., & Martin, R. (2021). Mass timber building science primer. Mass Timber Institute. Ministry for Primary Industries. (2019, November). Benefits of wood in construction. New Zealand Government Procurement. https://www.procurement.govt.nz/assets/procurementproperty/documents/benefits-of-wood-construction-procurement.pdf Seim, W. (2024). Structural Timber Design. Ernst & Sohn. Smith, I., & Snow, M. A. (2008). Timber: An ancient construction material with a bright future. The Forestry Chronicle, 84(4), 504–510. 8 Chapter 2 Literature Review 2.1 Introduction This chapter provides an overview of recent advancements in engineered wood products and briefly discusses various wood floor systems. The design methods for composite timber components are reviewed and an introduction to the screw-gluing method is included. 2.2 Engineered wood products Plywood is considered to be the world's first engineered wood product (EWP) and its use dates back to the early 20th century (APA-The Engineered Wood Association, 2024a). It was not until the mid-20th century that the potential of plywood as a competitor to conventional lumber for structural applications in building construction was recognized. With technological advancements, various EWPs were developed and gradually integrated into mass timber structures. EWPs refer to a broad category of products bonded from lumber, veneer, strands, fibers, flakes, or particles. This includes mass timber panels (MTP) such as glue-laminated timber (Glulam), cross-laminated timber (CLT), dowel laminated timber (DLT), and nail-laminated timber (NLT); floor system components like I-joists and rim boards; as well as structural composite lumber (SCL), including laminated veneer lumber (LVL), laminated strand lumber (LSL), oriented strand lumber (OSL), parallel strand lumber (PSL), and mass ply panels (MPP). Notably, SCL products are also considered a part of mass timber panels. 2.2.1 Lumber-based MTP Lumber-based MTPs refer to a category of building materials are generally created by stacking or aligning wood planks or lumber side by side and then bonding them together 9 using adhesives or mechanical fasteners such as nails or dowels. The main products in this category typically include aforementioned Glulam (Figure 2.1a) CLT (Figure 2.1b), DLT (Figure 2.1c), and NLT (Figure 2.1d). Figure 2.1 Example of lumber-based EWPs (Forestry Innovation Investment, 2024c). MTP could serve as a cost-effective alternative to concrete and steel, offering reduced embodied carbon. Compared to DLT and NLT, CLT is produced by gluing multiple layers of lumber perpendicular to each other in grain direction and bonding them with structural adhesives, which improves dimensional stability and load-carrying capacity. This technique provided two-way bending resistance when CLT is used as floor panels. (FPInnovations, 2019). In mass timber buildings, lumber-based MTPs are often used for floor systems and roofs due to high degree of prefabrication and dry construction compared to concrete (Breneman, 2016; Hassan et al., 2019). Mass timber floor design is often governed by deflection limits, and lumber-based solid MTPs are material inefficiency, especially over long spans, due to the increased depth required for bending stiffness (Zhou et al., 2020). The need for thicker or higher-grade materials, combined with the limited yield rate of lumber-based mass timber products, reduced material utilization efficiency. 10 2.2.2 Structural composite lumber SCL is a category of EWPs that includes products like LVL, PSL, LSL, OSL, and MPP, as shown in Figure 2.2. These products are produced as the whole large panels from wood veneers, strands, or fibers, bonded together using adhesives under high temperature and pressure. Figure 2.2 Variations of SCL (APA-The Engineered Wood Association, 2024a) As a type of composite material, SCLs are known for their excellent load-carrying capacity, featuring superior strength and stiffness that significantly surpass the raw materials used for their production. The layered structure of SCLs also enhanced their durability and resistance to warping, splitting, and shrinking (Canadian Wood Council, 2024). As a result, SCL is considered a viable alternative to heavy structural applications, especially for mass timber structures. For instance, Stora Enso reported that its 8-story Wood City Office project in Helsinki, Finland, used LVL for beams, columns, and ribbed floors, in addition to a concrete core (Stora Enso, 2024c). SCLs can be derived from underutilized wood species generated by other wood production processes or from small-diameter trees that were unsuitable for lumber production. This efficient use of resources contributed to improved forest management and waste minimization (Virginia Polytechnic Institute and State University, 2024). The 11 manufacturing process also mitigates common defects inherent in lumber, thereby reducing performance issues and associated material loss. Moreover, SCL exhibits superior dimensional stability compared to lumber, which reduced deformation due to moisture fluctuations (Forest Products Laboratory, 2021). 2.3 Timber floor systems 2.3.1 Light-frame wood joisted floor Light-frame wood joisted floor systems are widely used in residential and multi-unit light frame wood buildings. These systems utilize dimensional lumber, typically 2×8 or 2×10, I-joists or trusses arranged in a structural frame to support floor decking. The construction of these floors includes key components such as joists, girders, and sheathing. Girders serve as horizontal supports for the joists, while the joists, arranged repetitively, support the sheathing and transfer loads to walls, columns, or girders. The sheathing, typically made of oriented strand board (OSB) or plywood, acts as the surface panel of the floor system, providing load support and distributing loads across the structure (Sherwood & Moody, 1989; U.S. Department of Housing and Urban Development, 2017). Stressed skin panels (SSPs) were first introduced in the 1930s as a solution to the limitations of conventional joist floor systems (Bazli et al., 2022). Structurally, SSPs resemble timber joist floors, but they incorporate a firmly glued sheathing on the top or bottom, creating a composite cross-section that can function like a T or I section. As a result, SSPs offer enhanced structural characteristics, such as increased strength, stiffness, and bending capacity, compared to conventional joisted floor systems (Gerber, 2007). Light wood joisted floor systems offer several advantages, including cost-effectiveness, ease of construction, and efficient space utilization. Their lightweight nature makes them 12 easier to prefabricate and install on-site, reducing labor costs and construction time (Forestry Innovation Investment, 2024b). Additionally, these systems provide design flexibility, allowing for insulation between joists to improve energy efficiency and reduce space usage (Davids et al., 2011). In recent years, I-joists have become the commonly used EWP in light wood frame systems and are considered a viable alternative to dimensional lumber for joists and girders, as shown in Figure 2.3. Figure 2.3 I-joist and wood joist floor (BCI® Joists, 2024) An I-joist consists of two parallel flanges, typically made from OSB or plywood, with a central rib made from sawn lumber or LVL (American Wood Council, 2021). Despite being optimized structural components, I-joists are generally unsuitable for large spans due to an increased depth. The common floor span of light wood frame with I-joist can reach from 3.6 m to 4.8 m (Forest Products Laboratory, 2021), and according to Weyerhaeuser Company (2024), the maximum span for an I-joist is 11 meters under ultimate limit state 13 design with a spacing of 300 mm and an I-joist depth of 400 mm. Moreover, their super lightweight leads to challenges in meeting vibration and sound insulation requirements, making them unsuitable for large spans (Bazli et al., 2022; Weckendorf et al., 2014). 2.3.2 Mass timber floor Solid panel floor systems typically use large prefabricated MTPs, such as CLT. These mass timber panels are pre-manufactured to meet specific structural requirements. Prefabrication allows for quick and efficient on-site assembly, significantly reducing construction time and labor costs. The panels are designed with specially engineered connectors and fasteners, enabling interlocking or seamless connections, which simplified installation (Mohammad, 2011). An example building, Wood Innovation and Design Centre is shown in Figure 2.4. Figure 2.4 Example building with mass timber floor (Forestry Innovation Investment, 2024a) 14 This floor system provides open spaces but often conflicts with mechanical and electrical systems, requiring holes to be drilled into beams, potentially compromising structural integrity (Oliver & White, 2020). A new point-supported CLT system was used in the Brock Commons student residence at the University of British Columbia. This innovative floor design relied solely on columns to support the CLT panels, which minimized the impact of beams on mechanical and electrical routing, avoiding conflicts and maximizing clear space (Fast + Epp, 2024). Mass timber slab floors provide moderate fire resistance due to their inherent charring properties, which protect the inner layers from rapid combustion (Su, 2018). Additionally, the aesthetic appeal of exposed wood surfaces enhances the visual warmth of interior spaces, often reduce the need for additional finishes (Gold & Rubik, 2009). However, mass timber slab floors also have limitations. For large mass timber buildings, transportation limitations often restrict the size of prefabricated solid wood panels, potentially affecting the maximum span of the floor system (SmartLam, 2020). Additionally, oversize panels increase transportation costs (Chen et al., 2019). Due to the relatively low modulus of elasticity of wood, the use of thicker panels is avoidable for large floor spans, which lead to material inefficiency and increased costs (Bazli et al., 2022; Zhou et al., 2020). Moisture is another concern during construction, as prolonged exposure to water can damage the timber panels, making proper sealing and protection during construction essential (Dietsch et al., 2012; Forest Products Laboratory, 2021; Schmidt et al., 2019). Mass timber slab systems often require extra acoustic insulation layers to achieve adequate noise control between floors (Vardaxis et al., 2022; Zhao, 2022). 15 2.3.3 Ribbed floor The ribbed floor system was initially developed in the early 20th century for reinforced concrete applications (Halpern et al., 2013). A timber ribbed floor system is similar to concrete ribbed floors. It consists of ribs supporting top panels, optionally including a bottom panel, connected by mechanical fasteners or adhesives, as illustrated in Figure 2.5. This configuration offers significant advantages in terms of material efficiency due to its optimized geometric structure. Under the same span conditions, a ribbed floor system can achieve greater bending resistance with only a slight increase in overall thickness compared to solid floors (Mata-Falcón et al., 2022). a) b) c) Figure 2.5 Closed (a) and open (b) type ribbed floor system and the example application(c) (Stora Enso, 2024a) Some of the timber-concrete composite (TCC) floors are designed as ribbed types to utilize the complementary properties of timber and concrete. TCC effectively leverages the 16 benefits of timber, including great tensile strength and carbon sequestration (Bouhaya et al., 2009). Compared to non-composite timber structures, TCC provide higher bending strength and lower deflection (Weaver et al., 2004).In summary, the TCC approach also capitalize on the unique advantages of each material, providing improved stiffness, strength, and fire resistance characteristics (Yeoh et al., 2011). The steel-timber composite (STC) system is another composite timber floor system that can be constructed as a ribbed floor. Similar to TCC, STC aims to harness the strengths of both steel and timber, but differs in that STC uses timber panels, while TCC typically incorporates concrete as the panel material. STC systems take advantage of the high tensile strength and ductility of steel while utilizing the sustainability and high strength-to-weight ratio of timber. Hassanieh et al. (2016) indicated that comparing to the TCC or conventional reinforced concrete floor, the STC composite floor has lower weight and reduce the cost of construction. Loss & Davision (2017) reported that prefabricated modular STC components offer benefits such as reduced construction time, improved sustainability, and lightweight structures that are easier to assemble compared to concrete-based systems. As EWP evolved, the increased strength and reliability of timber facilitated the adoption of ribbed floors made entirely of wood, known as timber-timber composite (TTC). These floors feature either open or closed ribbed structures, depending on specific design requirements. Ribbed floors using CLT as flanges and Glulam as ribs have been successfully implemented in construction projects (Stora Enso, 2024a). This type of floor system, consisting of multiple T-shaped elements, is lighter than TCC systems and effectively reduces carbon emissions. A variation, known as the hollow (or boxed) floor system, adds a lower flange to the open ribbed structure, providing additional benefits 17 compared to standard ribbed floors. This lower flange enhances fire protection for the upper flange and rib while also improving overall stiffness (Negrao & Jorge, 2016). Sustersic et al. (2016) introduced the concept of ribbed CLT panels to bridge the gap between conventional CLT floor systems (typically suitable for spans of 4-6 m) and CLTGlulam composite floors (commonly used for spans of 8-12 m). By using CLT as the panel and lumber as the rib, they created ribbed CLT panels suitable for spans ranging from 2-8 m. Numerical modelling was conducted to determine the optimal plate geometry, combined with four point bending tests to evaluate the material usage and structural performance of ribbed CLT panels compared to regular CLT panels. The results showed that ribbed CLT panels could save up to 50% of timber for roof elements and up to 40% for floor elements compared to conventional CLT, while maintaining high load-carrying properties. Lavrenčič & Brank (2018) investigated the failure mechanisms of ribbed CLT plates through experimental bending tests and numerical simulations. They found that initiation and propagation of cracks within the ribs was progressive. The numerical model, which utilized Hashin failure criteria and a material softening approach, effectively predicted the load-displacement behavior, including crack development, as well as the ultimate load and displacement capacities of the ribbed CLT plates. Shahnewaz et al. (2022) conducted small-scale shear tests, full-scale four-point bending tests, and vibration response tests to evaluate how different connection techniques influenced vibration control and flexural stiffness. The results indicated that the connection types had negligible effects on the dynamic performance of the composite floor segments. The screw-glued connection exhibited the highest flexural stiffness and lowest deflection in the full-scale test using a 1626 mm wide panel, achieving a bending stiffness of 63,899 18 kNm², and reduced interface slip by over 95% compared to connections using 45-degree inclined screws. For all connections, the experimental flexural stiffness was close to the predicted values, validating the use of the gamma method for predicting the performance of CLT-Glulam composite floors. In addition to lumber-based EWPs, Kairi et al. (1999) investigated the impact of different gluing pressures and the feasibility of the screw-gluing method in LVL ribbed floors. They applied varying pressures (ranging from 0.03 to 0.8 MPa) to test the effects of glue spread amount, moisture content, and screw spacing on the quality of glue lines. The results indicated that the glue line quality remained consistent under both lower pressure (0.03 to 0.1 MPa) and higher pressure (0.6 to 0.8 MPa). Screw spacing and glue spread are crucial for ensuring the quality of the glue line. The ribbed floor system offers several advantages, including material efficiency and enhanced structural performance. Compared to light wood joist floors, ribbed floors are better suited for accommodating large spans, making them ideal for applications with greater structural capacity requirements (Negrao & Jorge, 2016). The spaces between ribs are also suitable for installing insulation materials and utilities, such as piping and wiring, which eliminates the need for drilling holes and thus maintains the structural integrity of the system (Stora Enso, 2024b). However, ribbed floor systems also have certain drawbacks. The intricate design requires precise fabrication and assembly, which could lead to increased manufacturing costs. Ribbed floors require more optimization calculations, as multiple factors such as the width and thickness of the flanges and ribs significantly influence their structural performance (Ma et al., 2022). Ribbed floor systems have limited serviceability performance, 19 particularly in terms of acoustics, vibration, and deflection (Bazli et al., 2022). Additionally, in current applications, assembling ribbed floors still involves adhesives and heavy hydraulic equipment, and the irregular shapes pose challenges for the use of hydraulic equipment (Metsä Group, 2023). 2.4 Screw-gluing method The screw-gluing method represents an efficient and convenient approach in wood engineering, combining mechanical fasteners and adhesives to create flexible structural connections. This part provides an overview of the screw-gluing method, its applications, and its advantages over conventional press gluing techniques, offering improved convenience and flexibility in structural connections. Using screws and glue for wood connections is a common practice, mainly in nonstructural applications like furniture assembly. However, in terms of timber construction, this approach represents a novel connection method. First introduced by Kairi (2000) in 1999. The screw-gluing method applied pressure to bonded wood joints using screws during adhesive curing. Conventional adhesive bonding required high compressive pressure (over 0.6 MPa), typically necessitating heavy hydraulic equipment. In contrast, the screw-gluing method used screws to achieve the necessary pressure, making it more accessible, cost-effective, and easier to implement (Schiere et al., 2018). Since this method is relatively new for structural applications, few design standards provided guidelines for its implementation. At the time, only Germany standard DIN 105210:2012 (2012) and Austrian standard ÖNORM B 1995-1-1:2019 (2019) referenced this method, specifying various requirements for wood and screws, such as, 20 • The panel used as a flange must have a maximum thickness of 50 mm. • Partially threaded screws can be used only. • The thread length in the rib or any reinforced adherend must be at least 40 mm or equal to the board/plate thickness, whichever is greater. • The spacing of the screws in any direction must be ≤ 150 mm. The specific details can be illustrated as shown in the Figure 2.6 below. Figure 2.6 Geometry requirement in current standards (Bratulic & Augustin, 2016) However, Aicher et al. (2021) challenged the existing standards in their article, stating that due to the rapid evolution of the timber engineering, the existing design standards are no longer adequate for the materials used today. Kurt (2003) investigated the effectiveness of the screw-gluing method using gap-filling phenol resorcinol formaldehyde (GPRF) adhesive compared to the traditional press-gluing method for wood-plywood composite. They found that screw-gluing with GPRF adhesive was more effective than press-gluing for glue lines thicker than 0.508 mm, achieving block 21 shear strength values up to 6.76 MPa. Screw-gluing showed a 50.31% higher strength than press-gluing for thicker glue lines, demonstrating its cost-effective potential for bonding non-uniform surfaces. Gerber et al. (2006) investigated screw-gluing and nail-gluing techniques for wood composite structures, finding that polyurethane adhesive provided superior adhesion compared to elastomeric adhesive. Screw-glued assemblies achieved an ultimate shear strength of up to 7.81 MPa, while elastomeric assemblies showed lower strength (3.68 MPa), making polyurethane adhesives preferable for screw-gluing applications under lowpressure conditions. Bratulic & Augustin (2016) investigated the distribution of screw pressure in screw-gluing applications for ribbed CLT floor systems. The study utilized both theoretical modelling and experimental evaluation to assess glue line strength and pressure distribution. Their findings demonstrated that screw gluing can serve as a viable alternative to hydraulic pressing. However, connection parameters including screw type, screw head diameter, screw length, and the quality of the adherent surface had a significant impact on connection quality. Additionally, the study observed a reduction in screw pressure by 20-35% due to relaxation effects over time. Franke et al. (2018) investigated screw and nail press gluing techniques and developed a method to measure the compression loads generated by different fasteners. They found that the compression load varied significantly based on the fastener type and recommended optimizing the choice of fastener to achieve higher curing pressures and better bond quality. Schiere et al (2018) offered recommendations for drafting new standards for screw-gluing, 22 suggesting that when using polyurethane adhesive and a single row of screws, the maximum fastener spacing could be calculated using Equation 2.1. ܵ௙ = ݂ ܲ ܾ௙ (2.1) where ܵ௙ is the fastener distance, mm; ݂ is the achieved mean load, N; ܲ is the minimum curing pressure of adhesive, MPa. Additionally, using washers with regular screws was believed to improve load transfer within the structure (Schiere et al., 2018). Newly available full-thread screws with variable thread angles also had the potential to achieve greater loads with smaller diameters. Aicher et al. (2021) utilised numerical finite element simulations to investigate the effects of screw spacing and plate stiffness on the cramping pressure distribution in screw-glued ribbed CLT composite and found that smaller screw spacings resulted in more uniform pressure distribution. They also indicated that less stiff plates experienced greater cramping pressure variation, and the use of staggered screw configurations reduced these variations by approximately 10% compared to non-staggered placements. Hull & Lacroix (2023a) conducted experimental research on the shear performance of screw-glued connections in CLT-Glulam composite. They fabricated the structure with screw-glued connections and tested their flexural performance. The results showed that screw-glued connections provided high shear stiffness and strength, enabling the use of long-span panels beyond the limitations of conventional mass timber slabs. This study demonstrated the potential of screw-gluing to achieve nearly full composite action, making it a viable method for long-span timber floor systems. 23 Hogger et al. (2024) investigated the pressing time required for one-component polyurethane adhesives in wood joints. They evaluated various pressing times to determine the minimum required for achieving optimal adhesive strength. Their results indicated that a pressing time of at least 25 minutes was essential for effective bonding, particularly when aiming for high internal bond strength. The study also found that closed assembly time had a favorable effect on the required pressing time, with higher moisture content in the wood leading to faster strength development but lower overall strength values. 2.5 Composite floor design methods Composite floor systems combine the advantages of different materials to create efficient, multifunctional structures widely used in modern architecture. Various design methods were developed to predict the behavior of composite floor systems under different loading conditions accurately. These methods provide guidance for calculating load-carrying capacity, stiffness, and deflection while considering interactions and connection properties between materials. This section introduces various connection design methods based on the geometries shown in Figure 2.7. 24 Figure 2.7 Schematic models of closed (right) and open (left) hollow-box floor modules 2.5.1 CSA O86 In Canada, CSA O86 provides design provisions for stressed skin panels, which have the same theory of mechanics for hollow-box floors. According to this clause, the standard limited the design of stressed skin panels to materials such as lumber, Glulam, plywood, and OSB. However, the CSA O86 standard did not address the design of ribbed floors using SCL or CLT. This limitation highlighted the need for continued research and potential updates to incorporate these innovative materials. Additionally, CSA O86 stated that the method applied only to glued members and did not accurately predict the behavior of semirigid connections in the screw gluing method examined in this thesis. Clause 10 in CSA O86 provides guidelines for designing floor systems regarding bending resistance, shear resistance, and deflection. It included a method for calculating effective stiffness, accounting for the effects of different materials, dimensions, and connections within the I-beam. The effective stiffness (‫)ܫܧ‬௘௙ can be calculated as follows: 25 (‫)ܫܧ‬௘௙ = (‫)ܫܧ‬௪ ‫ܭ‬ௌா + ܾ௙ (‫ܤ‬௔௧ ‫ݖ‬ଵଶ + ‫ܤ‬௔௖ ‫ݖ‬ଷଶ )‫ܭ‬ௌ (2.2) where, (‫)ܫܧ‬௪ is the stiffness of lumber ribs, Nmm2; ‫ܤ‬௔௧ is the specified axial stiffness of tension flange, N/mm; ‫ܤ‬௔௖ is the specified axial stiffness of compression flange, N/mm; ܾ௙ is the total panel width, mm; ‫ݖ‬ଵ is the distance from half of the top flange to the neutral axis, mm; ‫ݖ‬ଷ is the distance from half of the bottom flange to the neutral axis, mm. In the standard, the tension flange, compression flange, and rib are evaluated for their bending resistance. The bending resistance ‫ܯ‬௥ of each component is determined as following Equation 2.3-2.9: The moment resistance in tension flange can be calculated by Equation 2.3, ‫ܯ‬௥ = ϕܶ௣ ܺ௃ ܺீ (ாூ)೐ ஻ೌ ௄ೄ ௛೟ (2.3) The bending resistance in compression flange can be calculated as Equation 2.4, ‫ܯ‬௥ = ϕܲ௣ ܺ௃ ܺீ (‫)ܫܧ‬௘ ‫ܤ‬௔ ‫ܭ‬ௌ ℎ௖ (2.4) And the bending resistance in the rib can be calculated as follows. ‫ܯ‬௥ = ∅௪ ‫ܨ‬௕ ‫ܭ‬௭௕ ‫ܭ‬௅ ܺீ (‫)ܫܧ‬௘ ‫ܭܧ‬ௌா ‫ݖ‬௦,ଶ (2.5) ܶ௣ = ‫ݐ‬௣ (‫ܭ‬஽ ‫ܭ‬ௌ ‫) ்ܭ‬ (2.6) ܲ௣ = ‫݌‬௣ (‫ܭ‬஽ ‫ܭ‬ௌ ‫) ்ܭ‬ (2.7) ‫ܨ‬௕ = ݂௕ (‫ܭ‬஽ ‫ܭ‬ௌ௕ ‫ܭ ்ܭ‬ு ) (2.8) ‫ݏ‬௖௟௘௔௥ ଶ ቁ ݈ (2.9) ܺீ = 1 − 4.8 ቀ 26 where ߶ is the reduction factor for flanges, 0.95; ∅௪ is the reduction factor for rib, 0.9; ‫ݐ‬௣ is the specified strength of capacity of flange in axial tension, N/mm; ‫ܭ‬஽ , ‫ܭ‬ௌ , ‫ ்ܭ‬are loadduration factor, service-condition factors and treatment factor, respectively; ‫݌‬௣ is the specified strength capacity of flange in axial compression, N/mm; ݂௕ is the specified strength in bending of ribs, MPa; ‫ܭ‬ௌ௕ and ‫ܭ‬ு are service-condition factor for bending and system factor, respectively; ܺ௃ is the stress-joint factor; ܺீ is the panel geometry reduction factor, which can be calculated by Eq. 2.9; ‫ܤ‬௔ is the specified axial stiffness of the flange, N/mm; ℎ௧ and ℎ௖ are the greatest distance from neutral axis to outer edge of tension and compression flange, mm; ‫ܭ‬௭௕ , ‫ܭ‬ௌா and ‫ܭ‬௅ are the size factor for bending for sawn lumber, the service-condition factor for modulus of elasticity and the lateral-stability factor for bending members, respectively; ‫ ܧ‬is the modulus of elasticity of rib, MPa; ‫ݖ‬௦,ଶ is the greatest distance from neutral axis to outer edge of rib, mm. Except the bending resistance check, CSA O86 also provides the shear resistance check for the neutral plane of the whole panel V୰ , and the flange-rib shear resistance which is the shear resistance of connection part between the flange and rib of the stressed skin panel, ܸ௥௣ , these can be calculated as following Equation 2.10-2.15: The shear resistance for the whole panel could be calculated as Eq. 2.10, ܸ௥ = ߶௩ ‫ܨ‬௩ ‫ܭ‬௭௩ (‫)ܫܧ‬௘ ∑ ܾ௚ ‫ܭܧ‬ௌா ∑ ܳ௪ + ‫ܤ‬௔ ‫ܭ‬ௌ ܾ௙ ߛ (2.10) Equation 2.11 can be used to calculate the shear resistance for the connection in flange, ܸ௥௣ = ߶௩௙ ܸ௚ (‫)ܫܧ‬௘ ∑൫ܾ௚ ܺ௩ ൯ ‫ܤ‬௔ ‫ܭ‬ௌ ܾ௣ γ (2.11) 27 And the shear resistance for the connection in wen can be calculated by following equations, ܸ௥௣௪ = ߶௩ ܸ௚௪ (‫)ܫܧ‬௘ ∑൫ܾ௚ ܺ௩௪ ൯ ‫ܤ‬௔ ‫ܭ‬ௌ ܾ௣ ߛ (2.12) ‫ܨ‬௩ = ݂௩ (‫ܭ‬஽ ‫ܭ‬ௌ௩ ‫ܭ ்ܭ‬ு ) (2.13) ܸ௚ = ‫ݒ‬௣௙ (‫ܭ‬஽ ‫ܭ‬ௌ ‫) ்ܭ‬ (2.14) ܸ௚௪ = ݂௩ (‫ܭ‬஽ ‫ܭ‬ௌ ‫) ்ܭ‬ (2.15) where ߶௩ and ߶௩௙ are the reduction factors, 0.95 and 0.9, respectively; ݂௩ is the specified strength in shear, MPa; ‫ܭ‬௭௩ is the size factor in shear; ܾ௚ is the contact width between flange and rib, mm; ∑ ܳ௪ is the sum of moments of area of all ribs about neutral plane, mm3; ߛ is the greater value of ‫ݖ‬ଵ or ‫ݖ‬ଷ , mm; ‫ܭ‬ௌ௩ is the service-condition factor for shear; ‫ݒ‬௣௙ is the specified strength capacity in planar shear of the rib, MPa; ܺ௩ is the shear modification factor in Clause 10.2; ܺ௩௪ = 2. CSA O86 also mentions that the deflection can be calculated by using the effective stiffness (‫)ܫܧ‬௘௙ multiply by the panel geometry reduction factor ܺீ , therefore, the deflection ∆ can be calculated as following Eq. 2.16: ∆= ܺீ 5‫݈ݓ‬ସ 384(‫)ܫܧ‬௘ (2.16) where ‫ ݓ‬is the uniform distributed load, N/mm. The terms related to component 3 and tension flange in the formula should be disregarded for open type section (Canadian Wood Council, 2021). 28 2.5.2 Eurocode 5 Eurocode 5 (EC5) serves as the directive standard for designing timber structures in Europe. It provided guidelines for the structural design of timber buildings, including composite floor systems. EC5 included the gamma method for designing composite floors, which offered a systematic approach to account for partial interaction between different components and materials in composite floor structures (European Committee for Standardization & British Standards Institution, 1994). The gamma method is based on the concept of partial interaction, which recognizes that perfect bond and full interaction between the composite materials are not always achievable. Instead, it used a factor ߛ to account for slip between the layers. This factor adjusted stiffness and strength calculations to better reflect the actual behavior of the composite system (Huber & Deix, 2021). Zhang et al. (2022) offers a more refined approach for predicting behavior under realistic boundary conditions, thus contributing to the enhancement of EC5's applicability in practical design scenarios. Appendix B of EC5 detailed the gamma method for designing I-beams of varying sizes or materials. This method provided a means to calculate normal and maximum shear stress. Similar to CSA O86, the gamma method began with a formula for calculating effective stiffness, (‫)ܫܧ‬௘௙ , as shown in the following Equations 2.17-2.23: ଷ (‫)ܫܧ‬௘௙ = ෍( ‫ܧ‬௜ ‫ܫ‬௜ + ߛ௜ ‫ܧ‬௜ ‫ܣ‬௜ ܽ௜ଶ ) (2.17) ௜ୀଵ ‫ܣ‬௜ = ൜ ܾ௘௙ ℎ௜ ݂‫ = ݅ ݎ݋‬1 ܽ݊݀ 3 ܾ௜ ℎ௜ ݂‫ = ݅ ݎ݋‬2 (2.18) 29 ܾ ℎଷ ⎧ ௘௙ ௜ ݂‫ = ݅ ݎ݋‬1 ܽ݊݀ 3 12 ‫ܫ‬௜ = ܾ௜ ℎ௜ଷ ⎨ ݂‫ = ݅ ݎ݋‬2 ⎩ 12 (2.19) γଶ = 1 (2.20) γ௜ = [1 + πଶ ‫ܧ‬௜ ‫ܣ‬௜ ܵ௜ /(‫ܭ‬௜ /݈ଶ )]ିଵ ݂‫ = ݅ ݎ݋‬1 ܽ݊݀ ݅ = 3 (2.21) ܽଶ = γଵ ‫ܧ‬ଵ ‫ܣ‬ଵ (ℎଵ + ℎଶ ) − γଷ ‫ܧ‬ଷ ‫ܣ‬ଷ (ℎଶ + ℎଷ ) 2 ∑ଷ௜ୀଵ ߛ௜ ‫ܧ‬௜ ‫ܣ‬௜ ܽଵ ୟ୬ୢ ଷ = ‫ݖ‬௜ − ܽଶ (2.22) (2.23) where ‫ܧ‬௜ is the Young’s Modulus of the ݅ ௧௛ layer in the composite beam, MPa; ‫ܫ‬௜ is the moment of inertia of the cross section of the ݅ ௧௛ layer, mm4; ‫ܣ‬௜ is the cross-section area of the ݅ ௧௛ layer, mm2; ܽ௜ is the distance from the centroid of the ݅ ௧௛ layer to the neutral axis, mm; ܾ௜ is the width of cross section of the ݅ ௧௛ layer, mm; ℎ௜ is the height of cross section of the ݅ ௧௛ layer, mm; ‫ݏ‬௜ is the spacing of fasteners of the ݅ ௧௛ layer, mm; ‫ܭ‬௜ is the slip modulus of the mechanical fastener, N/mm, which will be taken as ‫ܭ‬௦௘௥ or ‫ܭ‬௨ depending on serviceability or ultimate limit state calculations; ݈ is the span of beam, mm. In Eurocode 5, the normal stress ߪ and maximum shear stress ߬ଶ,௠௔௫ can be calculated as following Equation 2.24-2.25: ߪ௜ = ߛ௜ ‫ܧ‬௜ ܽ௜ ‫ܯ‬ௗ (‫)ܫܧ‬௘௙ ߛଷ ‫ܧ‬ଷ ‫ܣ‬ଷ ܽଷ + 0.5‫ܧ‬ଶ ܾଶ ℎଶଶ ߬ଶ,௠௔௫ = ܸௗ ܾଶ (‫)ܫܧ‬௘௙ (2.24) (2.25) 30 where ‫ܯ‬ௗ is the design bending moment, Nmm and ܸௗ is the design shear force, N (European Committee for Standardization & British Standards Institution, 1994). The gamma method in EC5 provided a practical approach for designing composite flooring by accounting for effective bending stiffness (Estévez-Cimadevila et al., 2022). It allowed a more realistic assessment of flooring performance, improving both safety and efficiency. However, this method required precise determination of the factor ߛ, which was positively correlated with the beam length, as shown in Eq. 2.21. Although the beam length did not affect its intrinsic properties, significant differences were observed between the calculations for long and short beams. An example of ߛ and beam length under identical conditions (same geometry and material) is illustrated in Figure 2.8 below. 1 0.8 γ 0.6 0.4 0.2 0 0 4000 8000 12000 Span (mm) Figure 2.8 Relationship between beam span and ߛ 31 2.5.3 Shear analogy method The shear analogy method, introduced by Kreuzinger (1999), provides an approach for analyzing composite beams. It accurately modelled interlayer shear flow in composite materials, enabling more precise calculations of structural performance (Mestek et al., 2008). In the shear analogy method, the composite beam is transformed into two virtual beams, referred to as Virtual Beam A and Virtual Beam B. • Virtual Beam A: This beam primarily undergoes bending, assuming an infinite shear modulus. It accounts for the bending moments in the composite beam. • Virtual Beam B: This beam primarily bears normal stress and shear stress. It handles the shear forces within the composite beam. These two beams are connected rigidly, ensuring that their deformations are identical at any given point. By using this approach, it is possible to simultaneously consider both bending and shear effects on the beam for comprehensive analysis (Kreuzinger, 1999). According to EOTA TR019 (2020) and Mestek et al (2008), the effective bending stiffness (‫)ܫܧ‬௘௙ , normal stress ߪ௠ , shear stress ߬௫௭ and maximum deflection ∆௠௔௫ can be calculated as following Equation 2.26-2.37: ௡ (‫)ܫܧ‬஺ = ෍ ‫ܧ‬௜ ‫ܫ‬௜ (2.26) ‫ܧ‬௜ ‫ܣ‬௜ ‫ݖ‬௜ଶ (2.27) (‫)ܫܧ‬௘௙ = (‫)ܫܧ‬஺ + (‫)ܫܧ‬஻ (2.28) ௡ (‫)ܫܧ‬஻ = ෍ ௜ୀଵ ௜ୀଵ 32 ଶ ⎧ 1 ൭෍ ‫ݏ‬௜ + ℎଵ + ℎଶ + ℎଷ ൱ ݂‫ ܫ ݎ݋‬− ‫݊݋݅ݐܿ݁ݏ‬ ⎪݀ ଶ 1 ݇௦௘௥ 2‫ܩ‬ଵ ܾଵ ‫ܩ‬ଶ ܾଶ 2‫ܩ‬ଷ ܾଷ ௜ୀଵ = (‫)ܣܩ‬௘௙ ⎨ 1 ‫ݏ‬௜ ℎଵ ℎଶ ⎪ ൬ ൰ ݂‫ ܶ ݎ݋‬− ‫݊݋݅ݐܿ݁ݏ‬ + + ଶ ⎩ ݀ ݇௦௘௥ 2‫ܩ‬ଵ ܾଵ 2‫ܩ‬ଶ ܾଶ (2.29) ‫ܯ‬஺,ௗ = ‫ܯ‬ௗ (‫)ܫܧ‬஺ (‫)ܫܧ‬஺ + (‫)ܫܧ‬஻ (2.30) ‫ܯ‬஻,ௗ = ‫ܯ‬ௗ (‫)ܫܧ‬஻ (‫)ܫܧ‬஺ + (‫)ܫܧ‬஻ (2.31) ܸ஺,ௗ = ܸௗ (‫)ܫܧ‬஺ (‫)ܫܧ‬஺ + (‫)ܫܧ‬஻ (2.32) ܸ஻,ௗ = ܸௗ (‫)ܫܧ‬஻ (‫)ܫܧ‬஺ + (‫)ܫܧ‬஻ (2.33) ‫ܯ‬஺,ௗ ‫ݖܧ‬ (‫)ܫܧ‬஺ ௜ ௜ (2.34) ߪ஺ = ± ‫ܧ‬௜ ‫ݖ‬ (‫)ܫܧ‬஻ ௦,௜ (2.35) ߬஺,௜ = ܸ஺,ௗ 3 1 ‫ܧ‬௜ ‫ܫ‬௜ (‫)ܫܧ‬஺ 2 ℎ௜ ܾ௜ (2.36) ߬஻,௜ = ܸ஻,ௗ ∑ଵ௜ୀଵ ‫ܧ‬௜ ‫ܣ‬௜ ‫ݖ‬௜ (‫)ܫܧ‬஻ ܾଶ (2.37) ߪ஻ = ±‫ܯ‬஻,ௗ where (‫)ܫܧ‬஺ is the bending stiffness for the virtual beam A, Nmm2; (‫)ܫܧ‬஻ is the bending stiffness for the virtual beam B, Nmm2 ; ‫ݖ‬௜ is the distance between the neutral axis of the ݅ ௧௛ layer and the neutral axis of the beam, mm; (‫)ܣܩ‬௘௙ is the effective shear rigidity, N; G is the shear modulus, MPa; ‫ܯ‬஺,ௗ and ‫ܯ‬஻,ௗ are amount of design bending moment distributed to virtual beam A and B, respectively, Nmm; ܸ஺,ௗ and ܸ஻,ௗ are the amount of 33 shear force distributed to virtual beam A and B, respectively, N; ‫ݖ‬௦,௜ is the distance between any point and the neutral axis of beam, mm ; ߪ஺ and ߪ஻ are the bending stress for virtual beam A and B, respectively, MPa, and ߬஺,௜ and ߬஻,௜ are the shear stress for virtual beam A and B, respectively, MPa. The total deflection, ∆௠௔௫ , bending stress, ߪ௠ , and shear stress, ߬௫௭ , are calculated as follows: 5‫ ݈ݓ‬ସ ‫ ݈ݓ‬ଶ ∆௠௔௫ = + 384(‫)ܫܧ‬௘௙ 8(‫)ܣܩ‬௘௙ (2.38) ߪ௠ = ߪ஺ + ߪ஻ (2.39) ߬௫௭ = ߬஺,௜ + ߬஻,௜ (2.40) 2.5.4 Effective width of hollow-box floor modules Due to shear lag effects and moment distribution, the effective width, ܾ௘௙ , of the flange around each rib for the hollow-box floor system also needed to be determined. The Canadian current standard CSA O86 provides calculation methods for the entire panel, while shear analogy mentioned in European Organisation for Technical Approvals (EOTA) TR 019, recommend determining effective width using method in Eurocode 5 (Canadian Wood Council, 2021; European Organisation for Technical Approvals, 2020). The Gamma method mentioned in Eurocode 5, however, does not address effective width calculations. Masoudnia et al. (2020) and Thiel & Bradner (2016) reviewed the effective width calculation method of TCC or TTC structure. Eurocode 5 mentioned that for materials include plywood, oriented strand board, and particleboard or fibreboard, the effective width is calculated as shown in Table 2.1 (European Committee for Standardization & British Standards Institution, 1994). 34 Table 2.1 Eurocode 5 Maximum effective flange width calculation method Flange Material Plywood outer plies grain parallel to the ribs Plywood outer plies grain perpendicular to the ribs Oriented strand board Particleboard or fibre board with random fibre orientation Shear lag 0.1 ݈ 0.1 ݈ 0.15 ݈ Plate buckling 20 ℎ௙ 25 ℎ௙ 25 ℎ௙ 0.2 ݈ 30 ℎ௙ Note: ݈ is the panel span, mm and ℎ௙ is the flange thickness, mm. CSA O86:24 mentioned that the effective width can be reduced by reduction factor ܺீ that can be calculated by follow Equation 2.41: ܺீ = 1 − 4.8 ቀ ‫ݏ‬௖௟௘௔௥ ଶ ቁ ݈ (2.41) where ‫ݏ‬௖௟௘௔௥ is the clear spacing between the ribs, mm; ݈ is the panel span, mm (Canadian Wood Council, 2021). Additionally, Kikuchi et al. (2007) proposed an approximate formula based on experimental tests for stressed skin panel to calculate the ܾ௘௙ as Eq. 2.42: ௟ ቆି଴.ଷ଼ଷ଼ቀ ି଴.ସ଺଼଻ቁቇ ‫ܤ‬௘௙ ௦ = ‫ܭ‬଴ = 1 − ݁ ‫ݏ‬ (2.42) 2.6 Parametric design Parametric design and optimization methods have gained significant attention in structural engineering for their ability to enhance efficiency in cross-sectional design. These methods involve using parametric modelling tools to create adaptable and flexible structural models, enabling rapid exploration of design alternatives and optimization of structural elements. By integrating optimization algorithms such as genetic algorithms or gradient-based 35 methods, these approaches help identify optimal configurations that balance strength, stiffness, and material usage. For instance, Jelušič (2018) developed an optimal design for timber beams with nonuniform cross-sections using multi-parametric mixed-integer non-linear programming and found that response surface optimization effectively improved material efficiency. Similarly, Abejide & Konitufe (2015) assessed the flexural prediction for ribbed floors using optimization techniques and reported that these methods effectively improved material efficiency and reduced costs. Stanić et al. (2016) developed an economic-design optimization method for ribbed CLT plates to minimize structural volume while adhering to EC5 requirements, including constraints on deflections, stresses, and fundamental eigenfrequency. They employed a gradient-based optimization approach, utilizing a finite element model for precise stress and displacement predictions. The results demonstrated the feasibility of achieving an optimized ribbed CLT configuration that complies with EC5, leading to a significant reduction in material usage of up to 50%. Additionally, van Stijin (2017) demonstrated the application of parametric optimization in designing ribbed floors, which led to substantial material savings and increased structural efficiency, contributing to sustainable construction practices. 2.7 Summary In this chapter, various aspects of EWPs and their applications are summarized. EWPs, such as CLT, Glulam, and LVL, have contributed significantly to the evolution of timber construction, offering enhanced material properties and design flexibility. 36 The chapter discussed different floor systems, with a focus on ribbed floor configurations. Open type hollow-box floors, which utilize T-shaped elements made of timber, are lighter compared to TCC and TSC floors and offer carbon emission reductions. Closed type hollow-box floor systems, featuring additional lower flanges, improve stiffness and fire resistance, making them a favorable option in mass timber construction. Design methods for composite timber floors are reviewed, including the CSA O86 standard, the gamma method, and the shear analogy method. Additionally, parametric design approaches have been discussed for optimizing composite floors. The hollow-box floor cross-section optimization, as demonstrated by Stanić et al., has also shown that parametric design can significantly reduce material usage while ensuring compliance with structural requirements comparing to solid wood panels. State-of-the-art research of screw-gluing method have also been explored, showing promising results for assembling hollow timber floor elements. 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TJI® 110, TJI® 210, TJI® 230, TJI® 360, TJI® 560, and TJI® 560D joists featuring trus joist® TJI® joists for floor and roof applications. https://www.weyerhaeuser.com/woodproducts/document-library/ Winter, S., Kreuzinger, H., & Mestek, P. (2008). Teilprojekt 15-Flächen aus Brettstapeln, Brettsperrholz und Verbundkonstruktionen. München: Lehrstuhl für Holzbau und Baukonstruktionen, TU München. Yeoh, D., Fragiacomo, M., De Franceschi, M., & Heng Boon, K. (2011). State of the art on timber-concrete composite structures: Literature review. Journal of Structural Engineering, 137(10), 1085–1095. Zhang, Y., Zhang, L., & Zhang, S. (2022). Exact series solutions of composite beams with rotationally restrained boundary conditions: Static analysis. Archive of Applied Mechanics, 92(12), 3999–4015. Zhao, P. (2022). Impact sound insulation performance of floating floor assemblies on mass timber slabs [Thesis, University of Northern British Columbia]. https://unbc.arcabc.ca/islandora/object/unbc:59324 Zhou, J., Chui, Y. H., Niederwestberg, J., & Gong, M. (2020). Effective bending and shear stiffness of cross-laminated timber by modal testing: Method development and application. Composites Part B: Engineering, 198, 108225. 47 Chapter 3 Experimental Investigation on the Connection Performance of Screw-glued Joints with Mass Ply Panels Abstract: Hollow-box floor systems reduce material usage and improve efficiency, making them a preferred choice in mass timber construction. Compared to conventional mass timber panels like Crossed-laminated Timber (CLT) which face material inefficiency in long-span applications, Structural Composite Lumber (SCL) offers a more efficient alternative. Meanwhile, conventional gluing methods often require heavy hydraulic equipment, limiting their practicality for modular timber products. The screw-gluing method is a promising alternative without complex equipment. This research investigated the structural performance of screw-glued joints using SCL, specifically Mass Ply Panels (MPP). In the preliminary study, the performance of screw-gluing in hollow-box floor systems was evaluated, while in the parameter study, the effects of parameters such as screw type, length, adhesive, and spacing on connection performance were examined. Oneway ANOVA was used to determine the statistical significance of differences among different groups. Fully threaded screws with variable pitch combined with structural adhesives enhanced connection stiffness by up to 18% and load-carrying capacity by 16% compared to those using partially threaded screws. Joints with thicker flange, wider rib, and increased screw spacing exhibited a negative impact on performance. Staggered screw pattern improved shear resistance by 53% and stiffnesses by up to 66.4%, compared to single-row installation. These findings provide insights into optimizing screw-glued connections in fabricating prefabricated modular floor systems, highlighting the importance of rib width, screw type and spacing on the performance of the screw-glued joints. 48 Keyword: Screw-gluing, Connection Properties, Structural Composite Lumber, Hollowbox floor 3.1 Introduction The rapid evolution of the timber construction industry has led to increased emphasis on sustainable building practices. Mass timber products (MTP), particularly cross-laminated timber (CLT) and glued-laminated timber (Glulam), have been widely used in mid-rise and large-scale buildings over the past decade. These products are prefabricated in controlled factory environments, allowing efficient on-site assembly using dry construction methods, which reduces construction time, increases productivity, and reduces cost (Ashiru & Anifowose, 2021). Prefabrication also ensures higher quality control, minimizes waste, and lowers environmental impact, aligning with broader sustainability goals. However, lumber-based MTP products like CLT have low bending stiffness, limiting their efficiency for long-span applications (Zhou et al., 2020). Moreover, the conversion rate from logs to lumber is also low, at 40-50%, contributing to material inefficiency (Kerbes & McIntosh, 1969). Therefore, structural composite lumber (SCL), including products like laminated veneer lumber (LVL), laminated strand lumber (LSL), and mass ply panels (MPP), represents a viable alternative to conventional lumber-based MTPs due to its higher material efficiency, and superior dimensional stability. SCL is manufactured using wood strands, veneers, and flakes (APA-The Engineered Wood Association, 2024a), achieving a high wood yield rate of 80% to 90% (Gao et al., 2021). The production process results in large billets that can be used similarly to CLT in mass timber construction. 49 Solid wood panels are frequently used in mass timber structures for floor construction, typically utilizing lumber-based MTP. However, this approach can lead to material underutilization, especially in long-span applications, highlighting the need for alternative solutions. Hollow-box floor systems have emerged as a preferred solution in timber construction due to their optimized geometric structure, which provides sufficient structural performance with reduced material usage compared to solid floor systems. Furthermore, hollow-box floor systems offer improved bending resistance with only a marginal increase in thickness compared to solid panels (Mata-Falcón et al., 2022). In the manufacturing of wood products requiring structural adhesives (such as CLT and Glulam), pressure is required to maintain contact between bonded surfaces and ensure adhesive penetration into the wood for improved bonding quality (Forest Products Laboratory, 2021). This pressure is usually provided by heavy hydraulic equipment. For example, Metsä Group (2024) developed an optimized boxed/ribbed floor design using LVL with press, which has since been brought to market. The screw-gluing method, by contrast, employs the fastening force of screws to provide the required adhesive pressure, reducing the need for heavy hydraulic equipment and enhancing production efficiency (Kairi, 2000; Schiere et al., 2018). Sustersic et al. (2016) introduced a CLT ribbed floor with an optimized design that simplified the production process. Hull et al. (2023a) demonstrated the feasibility of the screw-gluing method in mass timber composite structures by applying it to create CLT and Glulam ribbed floors. However, these previous examples either relied on hydraulic press or used lumber-based EWP as the material. Therefore, a detailed study is required on hollow-box floor systems produced using the screw-gluing method with SCL. 50 Currently, only the design standards DIN 1052-10:2012 (2012) and ÖNORM B 1995-11:2019 (2019) in German and Austria, along with a few research papers such as Aicher et al. (2021) and Bratulic & Augustin (2016) provide design guidelines for the screw-gluing method. These guidelines include specifications for screw spacing, screw pressure, screw length, and material requirements. For example, the maximum flange thickness must be less than 50 mm, and only partially threaded screws can be used. The thread length in the rib or reinforced adherend must be at least 40 mm or equal to the board/plate thickness, whichever is greater. However, these guidelines are primarily tailored for Glulam or CLT, and further research is needed for the use of SCL in screw-gluing applications. To address these gaps, the experimental method was applied on the connection performance of screw-glued joints in SCL, specifically focusing on MPP. The primary objective of this study is to evaluate the feasibility of screw-gluing method in MPP based joints. Then, the detailed parameter analysis is required to determine the effect of geometry of sample and fastener properties on the performance of screw-glued joints. 3.2 Materials and Methods 3.2.1 Materials This study utilised MPP, a type of SCL produced by Freres Engineered Wood in Oregon. The MPP used was F10 and F16 grade, manufactured from Douglas-fir veneers. The Young's modulus is 6205.3 MPa in the joist direction and 5860.5 MPa in the plank direction for the F10 grade, and 11032 MPa in the joist direction and 9653 MPa in the plank direction for the F16 grade (Freres Engineered Wood, 2023; Maureen & Arijit, 2020). According to DIN 1052-10:2012 (2012), only partially threaded self-tapping screws (STS) should be used in the screw-gluing method. However, Aicher et al. (2021) noted that fully 51 threaded STS with varying pitch could also be used. Thus, HECO-TOPIX®-PLUS screws by HECO-Schrauben GmbH & Co. KG were employed in this study. The screws used included two types, partially threaded (P) and fully threaded (F). For the partially threaded type, lengths of 100 mm and 120 mm were used, while for the fully threaded type, lengths of 100 mm, 120 mm, and 160 mm were used. All screws had a diameter of 6 mm. Two types of polyurethane structural adhesives were used for bonding between MPP ribs and flanges. LOCTITE HB X602 PURBOND (X602), a one-component polyurethane structural adhesive, served as the primary adhesive. It has an open time of 60 minutes and a minimum press time of 150 minutes at 20°C, with 65% relative humidity and a wood moisture content of 12%. However, the X602 adhesive is typically available in bulk quantities, which may be excessive for smaller projects. Therefore, an additional adhesive, LePage PL Premium Construction Adhesive Glue (PLMAX), was used for comparison. PLMAX has an open time of 20 minutes and a minimum press time of 24 to 48 hours at 25°C and 50% relative humidity. 3.2.2 Specimen fabrication and experimental design The experiments were conducted into two studies. Preliminary study involved preliminary testing and performance evaluation of the screw-gluing method, while parameter study focused on detailed parameter investigation. 3.2.2.1 Preliminary study In the preliminary study, experimental evaluations were conducted to assess the performance of the screw-gluing method compared to glue-only and screw-only groups, as well as to examine the effects of different adhesives and screw spacing. The specimens were assembled into I-shaped sections, representing the basic structure of a hollow-box 52 floor system, as illustrated in Figure 3.1. Each specimen consisted of two flanges and one rib, with the dimensions illustrated in Figure 3.2. Figure 3.1 Conceptual closed type (left)) of hollow-box floors and basic shape for connection testing 53 Figure 3.2 Schematic drawing of the test specimens To facilitate the push-out tests, the rib and flange were offset by 50 mm to provide additional space. This adjustment made it easier to conduct the tests and handle the specimens during assembly and measurement. There were ten groups in total, including three screw-only groups, labelled as SF100, SF120 and SP100, with 100 mm and 120 mm long fully threaded and 100mm long partially threaded STS in 150 mm spacing, respectively. Two glue-only groups labelled as GF100 and GP100, with X602 adhesive. These two groups were assembled with fully threaded and partially threaded 100 mm long STS in 150 mm spacing, respectively, and then tested without the screws. Two groups with screw gluing method, labelled as 50_50_100F and 50_50_100P, consist of 100 mm long fully and partially threaded STS spaced in 150 mm and X602 adhesive, respectively. Two 54 groups with screw gluing method, named 50_50_200s and 50_50_250s, were prepared with 100 mm long fully threaded STS and X602 adhesive, but in 200 mm and 250 mm spacing respectively. One last group called 50_50_PLMAX, with 100 mm long, fully threaded STS in 150 mm spacing, but used PLMAX as the adhesive. Four screws were used in each specimen, staggered 20 mm to each other in opposite direction, as shown in Figure 3.2. All the detailed group information is shown in Table 3.1. 55 Table 3.1 Detailed specimen information for preliminary study tests Dimensions (mm) Screw (mm) Adhesive Group Replicates Flange thickness Rib width Length Spacing Type Name SF120 3 50 50 120 150 F N/A SF100 3 50 50 100 150 F N/A SP100 3 50 50 100 150 P N/A GF100 3 50 50 100 150 F X602 GP100 3 50 50 100 150 P X602 50_50_100P 6 50 50 100 150 P X602 50_50_100F 6 50 50 100 150 F X602 50_50_200s 3 50 50 100 200 F X602 50_50_250s 3 50 50 100 250 F X602 50_50_PLMAX 3 50 50 100 150 F PLMAX All screws were inserted at an angle of 90 degrees perpendicular to the flange, penetrating both the flange and the rib until the screw heads were flush with the outermost layer of the flange. All adhesives were applied according to the manufacturers' recommendations. For X602, an application rate of 160 g/m² was used as stated in manufacturer’s product sheet. In contrast, the application rate for PLMAX was not explicitly quantified. Instead, it was described as applied using a 1/4-inch-wide nozzle. Therefore, in this experiment, PLMAX was applied in two parallel lines on the rib, as shown in Figure 3.3, to ensure the adhesive was evenly distributed across the surfaces of both the flange and the rib. The presence of 56 slight adhesive squeeze-out along the bond line after pressure was applied indicated that enough adhesive had been applied, as shown in Figure 3.3. The amount of adhesive was measured as 1500 g/m2. Figure 3.3 Application of PLMAX 3.2.2.2 Parameter study In the parameter study, detailed experiments investigated the effects of various parameters on the connection performance of the screw-glued joints. Based on the preliminary study results, the fully threaded screws were used as well as X602 adhesive with 160 g/m². The parameter study included 12 groups with various combinations of screw spacing, flange thickness, rib width, screw length, and screw installation configurations. The detailed group information is shown below in Table 3.2. 57 Table 3.2 Detailed group information for parameter study tests Dimensions (mm) Flange Rib thickness width Group Replicates 50F_75R_100L_ 150s 6 50 50F_100R_100L_ 150s 6 50F_150R_100L_ 150s Screw (mm) Length Spacing Arrangement 75 100 150 single 50 100 100 150 single 6 50 150 100 150 single 50F_50R_100L_ 300s 6 50 50 100 300 single 75F_75R_160L_ 150s 6 75 75 160 150 single 75F_75R_120L_ 150s 6 75 75 120 150 single 6 75 150 160 150 single 6 75 150 160 150 double 6 75 75 160 225 single 75F_75R_160L_ 300s 6 75 75 160 300 single 75F_150R_160L_ 300s_s 6 75 150 160 300 double 100F_150R_160L _150s 6 100 150 160 150 single 75F_150R_160L_ 150s 75F_150R_160L_ 150s_s 75F_75R_160L_ 225s In the parameter study, all samples with 150 mm screw spacing and single-row screw installation were assembled like preliminary study as shown in Figure 3.2. For the 75F_150R_160L_150s_s group, where the screws were arranged in a staggered pattern with 150 mm spacing, the sample assembly was conducted as illustrated in Figure 3.4. 58 Figure 3.4 Sample arrangement for 150 mm spacing staggered group (top view) However, due to the limitations in material dimensions, the 75F_150R_160L_300s_s group, with screws arranged in a staggered pattern at 300 mm spacing, could not achieve the ideal 1/2 spacing, which would have provided a 150 mm end distance. Instead, the end distance was reduced to 55 mm, as shown in Figure 3.5. 59 Figure 3.5 Screw arrangement for 300 mm staggered group (top view) 3.2.3 Block shear tests of MPP Two groups of block shear tests were conducted to specifically test the shear strength of the MPP material as a reference for comparison with the bonding strength of screw-glued specimens. The MPP was cut into two slightly offset sections, each approximately 50.8 mm × 44.4 mm × 19 mm, with a 6.3 mm offset, and the sections were connected by the original adhesive layer of the MPP, the dimensions and the test setup are shown in Figure 3.6. The block shear tests were conducted according to ASTM D905-08 with a load rate of 2 mm/min (ASTM, 2021b). 60 Figure 3.6 Dimension and test setup of block tests (ASTM, 2021b) Since MPP is composed of veneers oriented in both directions, the experiment was divided into two parts to test the shear strength between two parallel veneers and between two perpendicular veneers. The shear strength ߬௠௔௫ of MPP were calculated as Equation 3.1. ߬଴,ெ௉௉ = ‫ܨ‬ ‫ܣ‬ (3.1) where ‫ ܨ‬is the applied force, N and ‫ ܣ‬is the contact area, mm2. 3.2.4 Push-out connection tests In this study, all experiments in both studies, were conducted in accordance with ASTM D5652-21 (ASTM, 2021a). Two string potentiometers were installed on either side of each specimen, as shown in Figures 3.7, to measure the displacement caused by the applied load. A load cell was used to apply the load at a rate of 2 mm/min to determine the load-carrying capacity. 61 Figure 3.7 Test schematic drawing and real setup After testing, the load-displacement curves for each specimen were plotted for analysis, as shown in Figure 3.8. The surface failure percentage of the flange were estimated as well. 100 10% max load 40% max load 60% max load Kser Ku Fmax Load (kN) 80 60 40 20 0 0 1 2 Displacement (mm) 3 4 Figure 3.8 Load-displacement curve example 62 Additionally, the serviceability slip modulus (‫ܭ‬௦௘௥ ) and ultimate slip modulus (‫ܭ‬௨ ) were calculated from the measured load-displacement curves using the following equations (The International Organization for Standardization, 1983), ‫ܭ‬௦௘௥ = ‫ܭ‬௨ = ிరబ ିிభబ ஽రబ ି஽భబ ிలబ ିிభబ ஽లబ ି஽భబ (3.2) (3.3) where ‫ܨ‬ସ଴ is 40% of max load, kN; ‫ܨ‬ଵ଴ is 10% of max load, kN; ‫଺ܨ‬଴ is 60% of max load, kN; ‫ܦ‬ସ଴ is the displacement at 40% of max load, mm; ‫ܦ‬ଵ଴ is the displacement at 10% of max load, mm and ‫଺ܦ‬଴ is the displacement at 60% of max load, mm. The shear stress at failure (߬௠௔௫ ) were calculated as following equations: ߬௠௔௫ = ‫ܨ‬௠௔௫ ‫ܣ‬ (3.4) Where ‫ܨ‬௠௔௫ is the load-carrying capacity, N and ‫ ܣ‬is the contact area, mm2. 3.2.5 Data analysis All results were analyzed using one-way analysis of variance (ANOVA) in IBM® SPSS to compare the means of shear stress and stiffness across different groups and determine if there were significant differences. First, maximum shear stresses of all groups were compared to identify any significant differences. Then, each group was compared to the shear strength obtained from block shear tests to determine if failure occurred due to the material or glue line. Comparisons were also made between groups to further investigate the effects of various parameters on structural performance. The use of one-way ANOVA ensures that the effects of various parameters on the outcomes are rigorously assessed, with 63 the significance level (α) set at 0.05 for this test. In the SPSS output tables, the term "sig." denotes the significance level, commonly referred to as the p-value. Additionally, the characteristic value of shear stress for each group were calculated according to ASTM D2915-17, as shown in the following Equation 3.5 (ASTM, 2022), ܲܶ‫ܺ = ܮ‬ത − ݇‫ݏ‬ (3.5) where ܺത is the mean value of the sample; ݇ is the factor found in Table 3 of ASTM D291517, corresponding to the 5th percentile with a 75% confidence level; ‫ ݏ‬is the standard deviation of the sample. Therefore, the data analysis in this study includes the average shear stress at failure in each group compared to the mean shear strength, multiple comparisons between maximum shear stress for each group to shear strength and each parameter within each group if the ANOVA test result shows a significance level less than 0.05. It also includes the comparison between the characteristic value of maximum shear stress for each group and the characteristic value of MPP shear strength. 3.3 Results and Discussion 3.3.1 Shear strength of MPP Block shear tests were conducted to confirm the shear strength of the MPP material. Since MPP consists of multiple veneers with grain directions either parallel or perpendicular, both orientations were tested. The average shear strength parallel to the grain was 5.6 MPa (range from 3.9 MPa to 6.7 MPa), with a coefficient of variation (COV) of 0.19 and a characteristic value of 3.23 MPa. The average shear strength perpendicular to the grain was 2.2 MPa (range from 0.9 MPa to 4.4 MPa), with a COV of 0.44 and a characteristic value 64 of 0.11 MPa. Detailed results are presented in Table A1. These shear strength values serve as a reference for assessing the bonding quality of the screw-glued joints. 3.3.2 Screw-only tests Three screw-only groups were tested to compare the difference between partially threaded STS and fully threaded STS with the same screw length and diameter, as well as the effect of screw length. The typical load-displacement curves from each group are shown in Figure 3.9 and the failure modes are presented in Figure 3.10. 25 20 Load (kN) 15 10 SF100 SP100 5 SF120 0 0 5 10 15 20 Displacement (mm) 25 30 Figure 3.9 Typical load-displacement diagram of screw-only groups 65 Figure 3.10 Failure mode of screw-only groups As shown in Figure 3.9, the three screw-only test groups exhibited a similar trend. The load initially increased rapidly until reaching a maximum value, after which it remained relatively stable with a slight downward trend, even as displacement increased to a significantly value. In these three test groups, it can be observed that, compared to the other two groups, the SF120 group reached its load-carrying capacity at a lower displacement. This indicates that the curve for this group was steeper before reaching the peak, suggesting a higher initial stiffness. As observed in the failure modes shown in Figure 3.10, under load, the screws yielded within the rib, leading to an embedment failure in the surrounding MPP. This indicates that the failure of the samples was not sudden but occurred gradually as the load increased. 66 35 25 Fmax Kser 20 Ku Load(kN) 25 15 20 15 10 10 Slip modulus (kN/mm) 30 5 5 0 0 SF100 SP100 SF120 Figure 3.11 Load-carrying capacity and slip modulus of screw-only group Figure 3.11 shows the load-carrying capacity, ultimate, and serviceability stiffness for each group with standard deviation error bars. All three groups had similar load-carrying capacity, ranging from 18 kN to 20 kN. The SF120 group had the highest ‫ܭ‬௦௘௥ of 19.0 kN/mm, followed by the 100F group at 13.6 kN/mm, while the 100P group had a significantly lower serviceability slip modulus of 2.9 kN/mm. The ultimate slip modulus values were 6.8 kN/mm, 5.37 kN/mm, and 1.7 kN/mm for SF120, SF100, and SP100, respectively. Fully threaded STS provided higher connection strength and stiffness compared to partially threaded STS. The screw length of 120 mm showed only marginal improvements over 100 mm. Therefore, SF100 was chosen for subsequent screw-gluing groups. 67 3.3.3 Glue-only tests Two glue-only connection groups were tested to evaluate the effectiveness of screw-gluing method. Figures 3.12 shown the typical load-displacement curves, and the failure modes are shown in Figure 3.13. 80 GF100 GP100 Load (kN) 60 40 20 0 0 1 2 Displacement (mm) 3 4 Figure 3.12 Typical load-displacement diagram of glue-only tests 68 Figure 3.13 Typical Failure mode of glue-only groups The glue-only group's load-displacement curve showed a shorter displacement range compared to the screw-only group. The load initially increased rapidly to a first peak, dropped quickly, and then increased again to a second peak. This failure pattern resulted from the successive failure of the two glue lines. The failure mode showed that the veneer on the flange sheared off, causing the entire specimen to fail. Notably, the adhesive layer of X602 remained intact, with average surface failure percentages, calculated based on the proportion of the damaged surface area to the total contact area through visual inspection, of 94% for GF100 and 83% for GP100. This observation suggests that the STS provided sufficient pressure during the experiment to ensure an effective bond with the adhesive. The intact X602 layer confirmed effective bonding under the pressure provided by the screws, validating the screw-gluing method. 69 160 100 Fmax 120 Kser 95 Ku 90 Load(kN) 100 80 85 60 80 40 Slip modulus (kN/mm) 140 75 20 0 70 GF100 GP100 Figure 3.14 Load-carrying capacity and slip modulus for glue-only groups 7 Shear stress (MPa) 6 5 4 3 2 1 0 GF100 GP100 Figure 3.15 Shear stress at failure for glue-only groups 70 Figure 3.14 and Figure 3.15 indicate that with 100 mm fully threaded STS, the ‫ܨ‬௠௔௫ reaches to 79.8 kN, ‫ܭ‬௦௘௥ comes to 80.7 kN/mm, ‫ܭ‬௨ is 94.5 kN/mm and shear stress ߬௔௩௚ is 5.3 MPa. In contrast, for the GP100 group, ‫ܨ‬௠௔௫ reaches to 67.8kN, ‫ܭ‬௦௘௥ comes to 94.2 kN/mm, ‫ܭ‬௨ is 110.3 kN/mm and shear stress is 4.5 MPa. This demonstrates a higher load capacity in the GF100 group compared to the GP100 group, while the stiffness, or resistance to deformation, was greater in the GP100 group. The glue-only group showed high load-carrying capacity but exhibited brittle behavior, leading to a rapid drop in load capacity upon glue layer failure. Compared to screw-only connections, the ‫ܨ‬௠௔௫ , ‫ܭ‬௦௘௥ , ‫ܭ‬௨ , and shear stress of the glue-only connections were 5.9, 17.6, and 4.4 times higher, respectively. ANOVA results for the block test and glue-only groups are shown in Table 3.3 (N = 9 for block test, N = 3 for GF100 and GP100). The Sig. values for average shear stress comparisons (߬଴,ெ௉௉ vs. GF100, ߬଴,ெ௉௉ vs. GP100, and GF100 vs GP100) were 0.29, 0.65, 0.12, and 0.35, respectively. The Sig. values for ‫ܭ‬௦௘௥ and ‫ܭ‬௨ between two groups were 0.61 and 0.57, respectively. All values were greater than 0.05, indicating no significant statistical difference. This evidence suggests that structural failure was due to the material rather than the adhesive layer. Table 3.3 P-values for glue-only tests p-values 0.29 ߬଴,ெ௉௉ vs. GF100 0.65 ߬଴,ெ௉௉ vs. GP100 0.35 ‫ܭ‬௦௘௥ N/A N/A 0.61 ‫ܭ‬௨ N/A N/A 0.57 Parameter All Groups ߬௔௩௚ 71 3.3.4 Screw-glued tests 3.3.4.1 Effect of different screw types and adhesives on 50 mm thick flange groups Three screw-glued groups were tested to compare the effects of different screw types and adhesives on connection performance. Figure 3.16 shows the typical load-displacement curves, and Figure 3.17 shows the failure modes. The load initially increased linearly with displacement, indicating elastic behavior, until the load-carrying capacity was reached, followed by brittle failure in the veneer of the flanges. This failure mode was similar to that in the glue-only specimens. 120 50_50_100F 50_50_100P 100 50_50_PLMAX Load (kN) 80 60 40 20 0 0 1 2 3 4 Displacement (mm) 5 6 Figure 3.16 Typical load-displacement diagram of 150 mm spacing screw glued tests After reaching the load-carrying capacity, the load dropped sharply to 20-30% of the loadcarrying capacity as displacement increased. The residual load was higher than in the 72 screw-only groups, indicating better post-peak performance for screw-glued connections. The primary failure mode was veneer failure in the second layer of the flanges, with no failure in the glue lines at the flange or rib surface. This suggests that the screw-gluing method effectively maintained adhesive bond integrity under significant loading, with failure localized within the wood material. Figure 3.17 Typical failure mode of fully (left) and partially (right) threaded groups Based on the evaluation of the failure modes, the flange surface failure percentage was 97% for the group using fully threaded screws, 82% for the group using partially threaded screws, and 100% for the group using fully threaded screws with PLMAX adhesive. 73 Fmax 140 Kser 120 Ku 114.5 114 Slip modulus (kN/mm) Load(kN) 160 113.5 100 113 80 112.5 60 112 40 111.5 20 0 111 50_50_100F 50_50_100P 50_50_PLMAX Figure 3.18 Load-carrying capacity and slip modulus for different adhesive with 50mm flange group 74 9 8 Shear stress (Mpa) 7 6 5 4 3 2 1 0 50_50_100F 50_50_100P 50_50_PLMAX Figure 3.19 Load-carrying capacity and slip modulus for different screw type and adhesive with 50mm flange group According to Figure 3.18 and 3.19, when comparing the different screw and adhesive, the 50_50_PLMAX group shows the highest ‫ܨ‬௠௔௫ of 113.9 kN, followed by the 50_50_100F group with 90.7 kN. The group with the lowest ‫ܨ‬௠௔௫ is the 50_50_100P group with 78.4. ‫ܭ‬௦௘௥ are 88.2 kN/mm, 112.0 kN/mm and 86.5 kN/mm for 50_50_PLMAX, 50_50_100F and 50_50_100P groups, respectively. ‫ܭ‬௨ are 94.6 kN/mm, 112.2 kN/mm and 95.1 kN/mm, respectively. The shear stresses are 6.0 Pa, 5.2MPa and 7.6 MPa, respectively. The test results show that the type of screw has a significant effect on the load-carrying capacity and stiffness of the specimen in the screw-gluing method, with the ‫ܨ‬௠௔௫ of fully threaded screws being 15.7% higher than that of partially threaded screws, while the ‫ܭ‬௦௘௥ , ‫ܭ‬௨ and shear stress are 29.5% and 18.0% higher than that of partially threaded screws. 75 Table 3.4 P-values of different screw type and adhesives with 50 mm flange group 0.07 ߬଴,ெ௉௉ vs. 100F 0.37 ߬଴,ெ௉௉ vs. 100P 0.39 ‫ܭ‬௦௘௥ 0.30 N/A N/A ‫ܭ‬௨ 0.54 N/A N/A Parameter All Groups ߬௔௩௚ Sig. level ߬଴,ெ௉௉ vs. PLMAX 0.00 100F vs. 100P 100F vs. PLMAX 0.12 0.20 N/A 0.15 0.26 N/A 0.33 0.40 As shown in Table 3.4, for the parameter shear stress, the significance levels for the comparisons of all group, ߬଴,ெ௉௉ vs. 100F, ߬଴,ெ௉௉ vs. 100P, and 100F vs. 100P are all greater than 0.05, indicating no statistically significant differences. However, the comparison between ߬଴,ெ௉௉ vs. PLMAX is less than 0.05, showing a statistically significant difference. However, when comparing characteristic values, the PLMAX group exhibited higher shear stress than the shear strength, which led to this difference. For ‫ܭ‬௦௘௥ , the comparisons of all groups, 100F vs. 100P and 100F vs. PLMAX are greater than 0.05, indicating no statistically significant differences. For ‫ܭ‬௨ , the comparisons of all groups, 100F vs. 100P and 100F vs. PLMAX are both greater than 0.05, indicating no statistically significant differences. The different type of adhesive has a significant effect on ‫ܨ‬௠௔௫ and shear stress, which are 25.6% and 25.7% higher for the group using PLMAX than X602, while it is relatively lower for ‫ܭ‬௦௘௥ and ‫ܭ‬௨ , about 21.3% and 15.7%, respectively. 76 3.3.4.2 Effect of different spacing on 50 mm thick flange groups Four groups of screw-glued connections were compared to investigate the effects of different screw spacings on the connection performance. The load-displacement curves were similar to those of other screw glued specimens. 180 160 160 Fmax Kser 140 Ku 120 140 100 Load (kN) 120 100 80 80 60 60 40 40 20 20 0 Slip modulus (kN/mm) 200 50_50_100F 50_50_200s 50_50_250s 50F_50R_100L_300s 0 Figure 3.20 Load-carrying capacity and slip modulus of different spacing with 50 mm flange group 77 7 Shear stress (Mpa) 6 5 4 3 2 1 0 50_50_100F 50_50_200s 50_50_250s 50F_50R_100L_300s Figure 3.21 Shear stress of different spacing with 50 mm flange group According to Figure 3.20 and Figure 3.21, when all other conditions remained constant but screw spacing was increased, ‫ܨ‬௠௔௫ increased from spacing 150 mm to 250 mm, but dropped from spacing 250 mm to 300 mm, whereas shear stress in the range of 4.3 MPa to 6.0 MPa. For 150 mm spacing group, it has ‫ܨ‬௠௔௫ of 90.7 kN, ‫ܭ‬௦௘௥ of 112.0 kN/mm, ‫ܭ‬௨ of 112.2 kN/mm and shear stress of 6.0 MPa. For 200 mm spacing group, it has ‫ܨ‬௠௔௫ of 92.3 kN, ‫ܭ‬௦௘௥ of 97.9 kN/mm, ‫ܭ‬௨ of 99.7 kN/mm and shear stress of 4.6 MPa, for 250 mm spacing group, the ‫ܨ‬௠௔௫ and shear stress increased to 124.6 kN and 5.0 MPa, but ‫ܭ‬௦௘௥ and ‫ܭ‬௨ dropped to 83.3 kN/mm and 88.0 kN/mm, and for 300 mm spacing groups, the ‫ܨ‬௠௔௫ and shear stress reaches to 120.3 kN and 4.3 MPa, but ‫ܭ‬௦௘௥ and ‫ܭ‬௨ increase to 136.7 kN/mm and 149.6 kN/mm respectively. In this group, the ‫ܭ‬௦௘௥ and ‫ܭ‬௨ shown comparable range, while the difference of shear stress can be explained by the differences of failure veneer surface areas. 78 Table 3.5 P-values for 50 mm thick flange varying spacing group Sig. level Parameter All Groups ߬଴,ெ௉௉ ߬଴,ெ௉௉ ߬଴,ெ௉௉ ߬଴,ெ௉௉ vs. vs. vs. vs. 150 200 250 300 150 vs. 200 150 vs. 250 150 vs. 300 200 vs. 250 200 vs. 300 250 vs. 300 ߬௔௩௚ 0.01 0.33 0.07 0.23 0.00 0.02 0.07 0.00 0.57 0.58 0.23 ‫ܭ‬௦௘௥ 0.22 N/A N/A N/A N/A 0.59 0.30 0.27 0.63 0.16 0.06 ‫ܭ‬௨ 0.05 N/A N/A N/A N/A 0.58 0.29 0.06 0.65 0.040 0.02 As shown in the Table 3.5, for ߬௔௩௚ , the comparisons between ߬଴,ெ௉௉ vs. 150, ߬଴,ெ௉௉ vs. 200, ߬଴,ெ௉௉ vs. 250, 150 vs. 250, 200 vs. 250, 200 vs. 300, and 250 vs. 300 all have significance levels greater than 0.05, indicating no statistically significant differences. On the other hand, the comparisons for All Groups, ߬଴,ெ௉௉ vs. 300, 150 vs. 200, and 150 vs. 300 all have significance levels less than 0.05, suggesting statistically significant differences. For ‫ܭ‬௦௘௥ , all comparisons are greater than 0.05, except for 250 vs. 300, which is just slightly above the threshold, suggesting no statistically significant differences. For ‫ܭ‬௨ , the comparisons for 200 vs. 300, and 250 vs. 300 are less than 0.05, indicating statistically significant differences. Other comparisons, such as all groups, 150 vs. 250 and 150 vs. 300, show values greater than 0.05, indicating no significant differences. The significance levels between the 50_50_100l_300s group and other groups were generally less than 0.05. Besides, surface failure rates for the 150 mm, 200 mm, 250 mm, and 300 mm groups were 97%, 99%, 99%, and 70%, respectively, as shown in Figure 3.22. 79 This suggests that for the group with a 50 mm thick flange, the 100 mm fully threaded screw at 300 mm spacing or greater may not provide adequate connection pressure. Figure 3.22 Example failure mode of 50_50_250s (left) and 50F_50R_100L_300s (right) group Additionally, the significance level of less than 0.05 between the 50_50_100F and 50_50_200s groups does not conclusively indicate that a 200 mm spacing fails to achieve good connection quality, particularly since the 200 mm group passed the MPP shear strength comparison. This may also be due to the small sample size (only three samples), which could affect the accuracy of the one-way ANOVA analysis. 80 3.3.4.3 Effect of different rib width on 50 mm thick flange group Four experimental groups were compared to investigate the impact of different rib widths on the connection performance. In these tests, the flange thickness was kept constant at 50 mm, and the flange width was 200 mm. 300 Fmax Kser Ku 200 Load(kN) 200 150 150 100 100 50 50 0 Slip modulus (kN/mm) 250 250 50_50_100F 50F_75R_100L_150s 50F_100R_100L_150s 50F_150R_100L_150s 0 Figure 3.23 Load-carrying capacity and slip modulus of different rib width with 50 mm flange group 81 7 6 Shear stress (Mpa) 5 4 3 2 1 0 50_50_100F 50F_75R_100L_150s 50F_100R_100L_150s 50F_150R_100L_150s Figure 3.24 Shear stress of different rib width with 50 mm flange group Figure 3.23 and Figure 3.24 showed that varying rib width, while keeping other conditions constant, led to significant differences in the performance of screw-glued connections. For the group with a rib width of 50 mm, using 150 mm screw spacing and X602 adhesive, the average maximum load ‫ܨ‬௠௔௫ was 90.7 kN, with an initial stiffness ‫ܭ‬௦௘௥ of 112.0 kN/mm, ultimate stiffness ‫ܭ‬௨ of 112.2 kN/mm, and a shear stress of 6.04 MPa. When the rib width was increased to 75 mm under the same conditions, the ‫ܨ‬௠௔௫ increased significantly to 123.1 kN, and both ‫ܭ‬௦௘௥ and ‫ܭ‬௨ also showed improvements to 136.9 kN/mm and 153.7 kN/mm, respectively. The shear stress, however, showed a slight decrease to 5.47 MPa, indicating that while the load-carrying capacity and stiffness improved with thicker ribs, the shear stress decreased because of larger contact area. 82 Further increasing the rib width to 100 mm resulted in an average ‫ܨ‬௠௔௫ of 118.8 kN, with ‫ܭ‬௦௘௥ and ‫ܭ‬௨ reaching 161.6 kN/mm and 179.7 kN/mm, respectively. The shear stress decreased to 3.96 MPa Finally, for the group with the thickest ribs (150 mm), the ‫ܨ‬௠௔௫ reached an average of 148.6 kN, and both ‫ܭ‬௦௘௥ and ‫ܭ‬௨ increased to 200.4 kN/mm and 212.0 kN/mm, respectively. However, the shear stress continued to decline, averaging 3.30 MPa. The results indicated that increasing rib width generally enhanced load-carrying capacity and stiffness but reduced shear stress, likely due to changes in stress distribution and failure modes within thicker ribs. The 75Rgroup had an average wood failure of 89% on both flange surfaces, while the 100R group had 83%. The 150 mm rib spacing group had the lowest wood failure percentage at 55%. An example failure mode of highest and lowest percentage wood failure surface is shown in Figure 3.25. Figure 3.25 Example failure mode of 100 mm(left) and 150 mm(right) rib width group 83 Table 3.6 P-values for 50 mm thick flange varying rib width group Sig. level Parameter All Groups ߬଴,ெ௉௉ ߬଴,ெ௉௉ ߬଴,ெ௉௉ vs. vs. vs. 50 75 100 ߬଴,ெ௉௉ vs. 150 50 vs. 75 50 vs. 100 50 vs. 150 75 vs. 100 75 vs. 150 100 vs. 150 ߬௔௩௚ 0.00 0.35 0.73 0.00 0.00 0.24 0.00 0.00 0.00 0.00 0.18 ‫ܭ‬௦௘௥ 0.01 N/A N/A N/A N/A 0.33 0.06 0.00 0.33 0.02 0.13 ‫ܭ‬௨ 0.00 N/A N/A N/A N/A 0.10 0.01 0.00 0.29 0.03 0.19 As shown in Table 3.6, the significance levels for the comparisons of ߬௔௩௚ between the group ߬଴,ெ௉௉ vs. 50R, ߬଴,ெ௉௉ vs. 75R, 50Rvs. 75R, and 100R vs. 150R are all greater than 0.05, indicating that there are no statistically significant differences between these groups. On the other hand, the significance values for the comparisons between all groups, ߬଴,ெ௉௉ vs. 100R, ߬଴,ெ௉௉ vs. 150R, 50R vs. 100R, 50R vs. 150R, 75R vs. 100R and 75R vs. 150R are all less than 0.05, indicating statistically significant differences. For ‫ܭ‬௦௘௥ , the comparisons between 50R vs. 75R, 50R vs. 100R, 75R vs. 100R and 75R vs. 150R showed significance levels greater than 0.05, indicating no statistically significant differences. However, the rest comparisons have the significance level below 0.05, indicating a statistically significant difference. For ‫ܭ‬௨ , the comparison between 50R vs. 75R, 75R vs. 100R and 100R vs. 150R showed a significance level greater than 0.05, indicating no significant difference between these groups. Other comparisons, including all groups, 50R vs. 100R, 50R vs. 150R, and 75R vs. 100R, all have significance levels less than 0.05, indicating statistically significant differences. 84 The results indicate that when using 50 mm thick flange, increase rib width from 50 mm to 75 mm will increase the connection performance as well. However, beyond 75 mm, the connection performance, including shear stress, shows a declining trend. 3.3.4.4 Effect of different rib width on 75- and 100-mm thick flange group Six groups of experimental tests were conducted in this comparison. Four groups were tested to evaluate the effects of rib width and screw installation method on connection performance for a 75 mm flange with 160 mm screws. Additionally, a control experiment was conducted using 120 mm screws to assess the impact of screw length. To explore the influence of flange thickness, another group with a 100 mm flange and a 150 mm rib was tested to determine if a thicker flange would enhance connection performance. 500 400 Fmax Kser Ku 400 350 350 300 Load (kN) 300 250 250 200 200 150 150 100 100 50 50 0 Slip modulus (kN/mm) 450 450 0 75F_75R_120L_150s 75F_75R_160L_150s 75F_150R_160L_150s 100F_150R_160L_150s 75F_150R_160L_150s_s Figure 3.26 Load-carrying capacity and slip modulus of different rib width with 75-and 100- mm flange group 85 8 Shear stress (MPa) 7 6 5 4 3 2 1 0 75F_75R_120L_150s 75F_75R_160L_150s 75F_150R_160L_150s 100F_150R_160L_150s 75F_150R_160L_150s_s Figure 3.27 Shear stress of different rib width with 75-and 100- mm flange group As detailed in Figure 3.26 and Figure 3.27, the experimental results for connections with varying rib widths and screw configurations demonstrate notable differences in performance across the different groups. For the group with a 75 mm thick flange, 75 mm thick rib, and 120 mm long screws, the average maximum load ‫ܨ‬௠௔௫ was 129.78 kN, with an initial stiffness ‫ܭ‬௦௘௥ of 237.69 kN/mm, ultimate stiffness ‫ܭ‬௨ of 234.43 kN/mm, and shear stress of 5.77 MPa. When the screw length was increased to 160 mm while maintaining the same rib width, the ‫ܨ‬௠௔௫ improved to 141.20 kN, though the ‫ܭ‬௦௘௥ and ‫ܭ‬௨ showed more variability, with averages of 149.33 kN/mm and 155.31 kN/mm, respectively. The shear stress also increased slightly to 6.28 MPa. For the group with a 150 mm thick rib and 75 mm flange using 160 mm screws, the ‫ܨ‬௠௔௫ further increased to 152.57 kN, with corresponding ‫ܭ‬௦௘௥ and ‫ܭ‬௨ values of 231.30 kN/mm and 242.38 kN/mm, respectively, though the shear stress decreased to 3.39 MPa. This trend 86 of increasing ‫ܨ‬௠௔௫ and fluctuating stiffness values continued in the group with a 100 mm thick flange and 150 mm thick rib, where the ‫ܨ‬௠௔௫ averaged 140.54 kN, ‫ܭ‬௦௘௥ and ‫ܭ‬௨ values of 247.24 kN/mm and 246.91 kN/mm, respectively but the shear stress was notably lower at 3.12 MPa. The staggered screw configuration group with a 150 mm thick rib and 75 mm flange displayed the highest performance across the board, with an ‫ܨ‬௠௔௫ of 233.22 kN, ‫ܭ‬௦௘௥ of 355.61 kN/mm, ‫ܭ‬௨ of 391.67 kN/mm, and a shear stress of 5.18 MPa. The One-way ANOVA test results is shown in Table 3.7. Table 3.7 P-values for 75- and 100-mm thick flange varying rib width group Sig. level Parameter All Groups ߬଴,ெ௉௉ ߬଴,ெ௉௉ vs. vs. 120L 160L ߬଴,ெ௉௉ vs. 150R ߬଴,ெ௉௉ vs. 100F ߬଴,ெ௉௉ vs. 150R_s 120L vs. 160L 75R vs. 150R 75F vs. 100F 150R vs. 150R_s ߬௔௩௚ 0.00 0.75 0.15 0.00 0.00 0.32 0.31 0.00 0.59 0.23 ‫ܭ‬௦௘௥ 0.00 N/A N/A N/A N/A N/A 0.05 0.07 0.72 0.00 ‫ܭ‬௨ 0.00 N/A N/A N/A N/A N/A 0.11 0.08 0.93 0.00 As shown in Table 3.7, the significance levels for the comparisons of ߬௔௩௚ between ߬଴,ெ௉௉ vs. 120L, ߬଴,ெ௉௉ vs. 160L, ߬଴,ெ௉௉ vs. 150R_s, 120L vs. 160L, 75F vs. 100F and 75F_150Rvs. 75F_150R_s are all greater than 0.05. In contrast, the remaining comparisons have significance levels below 0.05. For ‫ܭ‬௦௘௥ , the significance levels between all groups and 75F_150R vs. 75F_150R_s was less than 0.05, indicating significant differences between these groups, as well as for ‫ܭ‬௨ . 87 From failure modes, the average surface percentage for 120L group is 70%, and for 160L group is 96%. The 150R group only has 51%, and 100F group has 48%. The 75F_150R_s group has 79%, the example failure modes of 160L and 100F are shown in Figure 3.28. Figure 3.28 Example Failure mode of 75F_75R_150L_160s (left) and 100F_75R_160L_150s (right) These results indicated that, for a 75 mm flange, 150 mm screw spacing, and 75 mm rib, both the 120 mm and 160 mm screw lengths performed comparably to the shear strength, suggesting that the failure was due to the material itself. Therefore, these findings do not align with the guidelines from the standard, which require that the thread length in the rib or any reinforced adherend must be at least 40 mm or equal to the board/plate thickness, whichever is larger (DIN 1052-10:2012, 2012; ÖNORM B 1995-1-1:2019, 2019). In this study, when 60% of the screw length that required by the standard was embedded in the adhered material, the connections still outperformed the MPP shear strength. 88 Increasing the rib width to 150 mm with the single-row screw installation method decreased connection performance, suggesting that rib widths of 150 mm or more significantly reduce connection strength. With a 150 mm rib width, the double-row staggered screw installation method improved connection performance. Increasing the flange thickness from 75 mm to 100 mm, while keeping the rib width at 150 mm, did not improve connection performance. This aligns with the findings from Bratulic & Augustin (2016), which suggest that a thicker covering may reduce pressure. 3.3.4.5 Effect of different spacing on 75 mm thick flange group Four groups with a 75 mm thick flange were compared to investigate the effect of different spacing with 75 mm flange on connection performance, with the rib width kept constant at 75 mm across all groups. 89 350 250 Load(kN) 250 200 200 150 150 100 100 Slip modulus (kN/mm) 300 300 Fmax Kser Ku 50 50 0 0 75F_75R_150s 75F_75R_225s 75F_75R_300s Figure 3.29 Load-carrying capacity and slip modulus of different spacing with 75 mm flange group 90 8 7 Shear stress (MPa) 6 5 4 3 2 1 0 75F_75R_150s 75F_75R_225s 75F_75R_300s Figure 3.30 Shear stress of different spacing with 75 mm flange group Based on the results in Figure 3.29 and Figure 3.30, for the group with a 150 mm screw spacing, the average maximum load ‫ܨ‬௠௔௫ was 141.20 kN, with an initial stiffness ‫ܭ‬௦௘௥ of 149.33 kN/mm and ultimate stiffness ‫ܭ‬௨ of 155.31 kN/mm. The shear stress averaged 6.28 MPa. In the group with a 225 mm screw spacing, the ‫ܨ‬௠௔௫ increased to 168.45 kN, while ‫ܭ‬௦௘௥ and ‫ܭ‬௨ also improved to 195.01 kN/mm and 223.87 kN/mm, respectively. However, the average shear stress decreased to 4.99 MPa. For the group with the screw spacing of 300 mm, the ‫ܨ‬௠௔௫ reached 206.43 kN, with a ‫ܭ‬௦௘௥ of 203.86 kN/mm and a ‫ܭ‬௨ of 226.71 kN/mm. The shear stress averaged 4.91 MPa. 91 The wood surface failure percentages are 96%, 70% and 40% for 150 mm, 225 mm and 300 mm groups, respectively. The example of best and worst failure mode as shown in Figure 3.31. Figure 3.31 Example Failure mode of 75F_75F_150L _160s (left) and 75F_75F_160L_300s (right) Table 3.8 P-values for 75 thick flange varying screw spacing group All Groups ߬଴,ெ௉௉ vs. 150s ߬଴,ெ௉௉ vs. 225s Sig. level ߬଴,ெ௉௉ vs. 300s ߬௔௩௚ 0.09 0.23 0.24 0.19 0.04 0.03 0.90 ‫ܭ‬௦௘௥ 0.34 N/A N/A N/A 0.26 0.18 0.82 ‫ܭ‬௨ 0.19 N/A N/A N/A 0.12 0.11 0.95 Paramete r 150s vs. 225s 150s vs. 300s 225s vs. 300s 92 The ANOVA results in Table 3.8 showed that the significance level for comparisons of ߬௔௩௚ between all groups was 0.086, indicating no statistically significant differences. Comparing the shear strength results with the groups using screw spacings of 150 mm, 225 mm, and 300 mm showed significance levels of 0.229, 0.235, and 0.186, respectively, indicating no statistically significant differences between these groups and the MPP shear strength. However, comparing the 150 mm screw spacing group with the 225 mm screw spacing group showed a significance level of 0.035, while the comparison between the 150 mm and 300 mm screw spacing groups had a significance level of 0.026. These values indicate statistically significant differences between the 150 mm group and both the 225 mm and 300 mm groups. In contrast, the comparison between the 225 mm and 300 mm groups showed no statistically significant difference, with a significance level of 0.897. This suggests that the performance differences between the 225 mm and 300 mm screw spacings were negligible, while the 150 mm group exhibited distinct performance. All significance levels for ‫ܭ‬௦௘௥ and ‫ܭ‬௨ comparisons were greater than 0.05, indicating no significant differences between these groups. These results indicate that, for the 75 mm thick flange, increasing the screw spacing up to 300 mm does not significantly affect the overall connection performance. The lack of statistically significant differences between the 225 mm and 300 mm screw spacing groups suggests that the connection's structural integrity is maintained even with longer screw spacing. However, the differences observed between the 150 mm group and the larger spacings indicate that reducing the screw spacing to 150 mm may offer some performance benefits, though the overall impact of increasing the spacing is minimal. 93 3.3.4.6 Effect of different screw configuration on 75 mm thick flange group Two groups with a 75 mm thick flange and a 150 mm rib width were compared. This comparison focused on the effect of longer screw spacing on the structural behavior of the connections. 600 470 Fmax Ku 450 440 Load(kN) 400 430 300 420 410 200 400 Slip modulus (kN/mm) 500 460 Kser 390 100 380 0 370 75F_150R_160L_150s_s 75F_150R_160L_300s_s Figure 3.32 Load-carrying capacity and slip modulus of different screw arrangement with 75 mm flange group 94 7 6 Shear stress (MPa) 5 4 3 2 1 0 75F_150R_160L_150s_s 75F_150R_160L_300s_s Figure 3.33 Shear stress of different screw arrangement with 75 mm flange group Based on the results shown in the Figure 3.32 and Figure 3.33, the group with 150 mm screw spacing reached the average maximum load ‫ܨ‬௠௔௫ of 233.22 kN, with an initial stiffness ‫ܭ‬௦௘௥ of 355.61 kN/mm and an ultimate stiffness ‫ܭ‬௨ of 391.67 kN/mm. The shear stress for this group averaged 5.18 MPa. In comparison, the group with 300 mm screw spacing exhibited a significantly higher average ‫ܨ‬௠௔௫ of 383.49 kN, with ‫ܭ‬௦௘௥ and ‫ܭ‬௨ values of 399.93 kN/mm and 456.24 kN/mm, respectively. However, the average shear stress for this group was slightly lower at 4.57 MPa. The wood failure percentages are 79% and 84% for 150 mm and 300 mm groups, respectively. The example failure mode of these two groups as shown in Figure 3.34. 95 Figure 3.34 Example failure mode of 75F_150R_160L_150s (left) and 75F_150R_160L_300s (right) Table 3.9 P-values for 75 mm flange staggered arrangement groups Sig. level N/A ‫ܭ‬௨ N/A ‫ܭ‬௦௘௥ 0.10 ߬௔௩௚ All Groups Parameter ߬଴,ெ௉௉ vs. 150s 0.35 ߬଴,ெ௉௉ vs. 300s 0.03 N/A N/A N/A N/A 150s vs. 300s 0.23 0.38 0.23 The ANOVA results presented in Table 3.9 indicate the significance levels for the comparison of staggered screw arrangement groups with a 75 mm thick flange. The comparison of ߬௔௩௚ between all groups and ߬଴,ெ௉௉ vs. 75_150_160l_300s shows a significance level less than 0.05, suggesting a statistically significant difference in 96 performance. Comparisons for all other groups, including ‫ܭ‬௦௘௥ and ‫ܭ‬௨ , showed significance levels greater than 0.05, indicating no significant differences. This implies that although the 300 mm spacing group showed a notable difference compared to the MPP shear strength, the overall impact of varying screw spacing between the 150 mm and 300 mm groups was relatively minor because the ANOVA results among all groups and between 150 mm and 300 mm are larger than 0.05. These results suggest that increasing screw spacing from 150 mm to 300 mm in a staggered arrangement led to a decline in structural performance. 3.4 Conclusions In this study the performance of screw-glued joints in MPP was evaluated under different screw spacing, rib width, and adhesive configurations. The results highlighted key findings about the mechanical behavior of screw-glued connections. 1. For the MPP flange-to-rib connections using 6 mm diameter and 100 mm long screws, the fully threaded screws demonstrated an ultimate stiffness of 5.37 kN/mm and a load-carrying capacity of 18.1 kN. In contrast, the partially threaded screws exhibited a load-carrying capacity of 20.23 kN and an ultimate stiffness of 1.69 kN/mm. The flange-to-rib connections in the screw-only configuration exhibited low load-carrying capacity and low stiffness, insufficient to achieve a high composite action. In the glue-only tests, the screws were found to provide sufficient pressure to ensure good bonding quality, leading to veneer failure in the flanges. In the screw-gluing connections, a stiffness of up to 112.18 kN/mm and a loadcarrying capacity of 90.66 kN were achieved, significantly outperforming both the screw-only and glue-only groups. 97 2. For screw-glued MPP flange-to-rib connections, increasing rib width from 50 mm to 75 mm improved load-carrying capacity by 35.8% and stiffness by up to 37%, but decreased shear stress at failure by 9.4%. From 75 mm to 100 mm, loadcarrying capacity dropped by 3.5%, shear stress decreased by 27.6%, and stiffness increased by up to 18.1%. From 100 mm to 150 mm, load-carrying capacity increased by 25% and stiffness increased by up to 24.0%, but shear stress decreased by 16.7% due to larger contact area. Increasing rib width negatively impacted shear resistance due to insufficient pressure distribution by screws. ANOVA test results showed groups with wider rib widths (>75mm) are unacceptable with a single row screw pattern. Increasing flange thickness from 75 mm to 100 mm decreased shear stress by 8.0% and stiffness by up to 6.9%. Decreasing screw length from 160 mm to 120 mm reduced shear stress by 8.1% and increased stiffness by up to 59.2%. 3. In the 50 mm flange group, increasing screw spacing from 150 mm to 200 mm reduced shear stress at failure by 23.7% and stiffness by up to 11.2%. Increasing spacing to 250 mm increased shear stress by 8.0% but reduced stiffness by up to 14.9%. From 250 mm to 300 mm, shear stress decreased by 13.7% and stiffness increased by up to 70.9%. In the 75 mm flange group, increasing spacing from 150 mm to 225 mm and 225 mm to 300 mm reduced shear stress by 20.5% and 1.6%, respectively, while stiffness increased by up to 44.1% and 4.5%. Changing the screw installation configuration from a single row to a double row staggered arrangement improved shear stress by 52.8% and stiffness by up to 61.6%. Changing screw spacing in the double row staggered group from 150 mm to 300 mm reduced shear stress by 11.7% but increased stiffness by up to 16.5%. All test 98 results still compared favorably with the MPP shear strength, showing acceptable connection performance. 4. When using 75-mm-thick or thinner MPP as flanges and ribs, fully threaded HECO screws (Magic Close) with a 6 mm diameter and a length at least of 100 mm can provide sufficient connection performance at a spacing of up to 300 mm. For wider ribs, fully threaded HECO screws with a length of at least 120 mm should be installed in a double row staggered configuration at a maximum spacing of 300 mm. Either PLMAX adhesive with a spread rate of 1500 g/m2 or X602 adhesive with a spread rate of 160 g/m2 can be utilized. 99 References Aicher, S., Zisi, N., & Simon, K. (2021). Screw-gluing of ribbed timber elements—Effects of screw spacing and plate stiffness on bond line cramping pressure Schraubenpressklebung von holzrippen- elementen -einfluss des schraubenabstandes und der plattensteifigkeit auf den klebfugen- pressdruck. 20, 9–38. APA – The Engineered Wood Association. (2024a). Structural composite lumber (SCL)— APA – the engineered wood association. APA. https://www.apawood.org/structural-composite-lumber Ashiru, A., & Anifowose, K. (2021). An investigation into application of dry construction technique in providing low-cost housing for Nigerians. Civil Engineering and Architecture, 9, 206–213. https://doi.org/10.13189/cea.2021.090117 ASTM. (2021a). Standard Test Methods for Single-Bolt Connections in Wood and WoodBased Products (ASTM D5652-21). ASTM. (2021b). Standard Test Method for Strength Properties of Adhesive Bonds in Shear by Compression Loading (ASTM D905-08(2021)). ASTM. (2022). Standard Practice for Sampling and Data-Analysis for Structural Wood and Wood-Based Products (ASTM D2915-17(2022)). Bratulic, K., & Augustin, M. (2016). Screw gluing-theoretical and experimental approach on screw pressure distribution and glue line strength. DIN 1052-10:2012. (2012). Design of timber structures – Part 10: Additional provisions. German Institute for Standardization (DIN). 100 Forest Products Laboratory. (2021). Wood handbook—Wood as an engineering material (General Techinical Report FPL-GTR-282; pp. 11–21). United States Department of Agriculture Forest Service. https://www.fpl.fs.usda.gov/documnts/fplgtr/fplgtr282/fpl_gtr282.pdf Gao, Z., Gong, M., Gao, Z., & Gong, M. (2021). Strand-based engineered wood products in construction. In Engineered Wood Products for Construction. IntechOpen. https://doi.org/10.5772/intechopen.100324 Hull, T., & Lacroix, D. (2023). Parametric analysis of the effective flange width of mass timber composite floor panels. Engineering Structures, 291, 116370. https://doi.org/10.1016/j.engstruct.2023.116370 Kairi, M. (2000). Screw gluing gives new possibilities for wood engineering. 5. Kerbes, E. L., & McIntosh, J. A. (1969). Conversion of trees to finished lumber—The volume losses. The Forestry Chronicle, 45(5), 348–353. https://doi.org/10.5558/tfc45348-5 Mata-Falcón, J., Bischof, P., Huber, T., Anton, A., Burger, J., Ranaudo, F., Jipa, A., Gebhard, L., Reiter, L., Lloret-Fritschi, E., Van Mele, T., Block, P., Gramazio, F., Kohler, M., Dillenburger, B., Wangler, T., & Kaufmann, W. (2022). Digitally fabricated ribbed concrete floor slabs: A sustainable solution for construction. RILEM Technical Letters, 7, 68–78. https://doi.org/10.21809/rilemtechlett.2022.161 Maureen, P., & Arijit, S. (2020, November). Life Cycle Assessment of Mass Ply Panels Produced in Oregon (pp. 16–17). WoodLife Environmental Consultants, LLC. 101 Metsä Group. (2023, November 20). Benefits of building with Kerto® LVL. Webinar recording. https://www.metsagroup.com/metsawood/news-andpublications/videos/benefits-of-building-with-kerto-lvl-tomorrow/ ÖNORM B 1995-1-1:2019. (2019). Eurocode 5: Design of timber structures—Part 1-1: General—Common rules and rules for buildings—Consolidated version with national specifications. Austrian Standards International. Schiere, M., Franke, S., & Franke, B. (2018). Investigation and analysis of press glued connections for timber structures [Research Report]. Bern University of Applied Sciences. https://doi.org/10.13140/RG.2.2.26301.31208 Sustersic, I. (2016). Less is more – optimized ribbed CLTs – the future. 22. Internationales Holzbau-Forum, Garmisch-Partenkirchen, Germany. the International Organization for Standardization. (1983). Timber structures—Joints made with mechanical fasteners—General principles for the determination of strength and deformation characteristics. Zhou, J., Chui, Y. H., Niederwestberg, J., & Gong, M. (2020). Effective bending and shear stiffness of cross-laminated timber by modal testing: Method development and application. Composites Part B: Engineering, 198, 108225. https://doi.org/10.1016/j.compositesb.2020.108225 102 Chapter 4 Parametric Modelling and Structural Optimization of Prefabricated Structural Composite Lumber Hollow-box floor Modules Abstract Conventional solid mass timber panels such as cross-laminated timber (CLT) face inefficiencies in long spans, and hollow-box floor system is a promising solution for long spans. The conventional floor structural design practice relies on experiences and manual iterative calculations. This study developed a parametric structural optimization model for prefabricated hollow-box floor systems made of structural composite lumber (SCL) based on the Grasshopper platform. The proposed optimization algorithm incorporates parametric geometry modelling, material databases, and design verification methods, including CSA O86, Gamma method, and Shear Analogy method. Genetic algorithms are employed to find optimal cross-section designs based on various constraints, including floor height limitations and structural volume. The study also compared different methods for calculating the effective width of hollow-box floor modules, including CSA, Eurocode 5 (EC5), and Kikuchi method. Results showed that the CSA and Kikuchi methods were similar, while the EC5 method provided more conservative result. The optimization results showed that hollow-box floor sections made from MPP can reduce material usage by 67% compared to solid MPP and up to 75% compared to CLT while also achieving significant savings in floor height, particularly in comparison to I-joist systems. Keywords: section optimization, genetic algorithm, prefabricated modular floor 103 4.1 Introduction Floor construction is a critical aspect of building design, often accounting for a significant proportion of the materials used. Conventional wood joisted floor systems consist of closely spaced joists that support floor decking, providing a lightweight and flexible solution. These systems remain popular in residential and low-rise wood construction, such as single-family houses or low-rise multi-unit buildings, due to their cost-effectiveness and ease of installation. However, these systems are less effective for longer span floor solutions or in mass timber building applications because of their material limitations. In mass timber buildings, studies indicate that floor systems can consume up to 70% of the total wood material (Truong-Regan, 2023). For such buildings, conventional solid mass timber floor systems are often used, constructed with lumber-based engineered wood products (EWP) such as cross-laminated timber (CLT) and glued laminated timber (Glulam). However, these materials face structural inefficiencies, particularly in long-span applications. The inefficiencies of lumber-based mass timber panels arise from their relatively low bending stiffness and the limited yield rate of lumber production (Kerbes & McIntosh, 1969). Although wood-based materials are known for their reduced carbon footprint and potential to act as carbon sinks, improving material utilization in floor systems offers a substantial opportunity to further lower the environmental impact of timber construction. SCL presents a viable alternative to conventional lumber-based EWPs. SCL products, such as laminated veneer lumber (LVL), mass ply panels (MPP), laminated strand lumber (LSL), and parallel strand lumber (PSL), are made from veneers and strands, achieving a wood yield rate of up to 90% (Gao et al., 2021). This enhanced material utilization makes SCL 104 an attractive option for prefabricated hollow-box floor systems, particularly for long-span applications where both material efficiency and structural performance are crucial. There has been increasing interest in composited hollow-box floor systems other than solid wood panel floor system, that improve structural efficiency while maintaining the benefits of mass timber construction. For example, timber-concrete composite (TCC) systems and steel-timber composite (STC) systems have been developed to enhance the performance of timber floors by integrating different materials to achieve better stiffness and load-carrying capacity. However, these systems often require heavier materials and increased carbon emissions compared to all-timber solutions, making them less desirable for projects prioritizing sustainability and ease of construction. Therefore, following these, recent developments have introduced ribbed CLT panels that utilize optimized dimensions to achieve superior structural performance (Sustersic, 2016). Zhang et al. (2021) studied six types of connections using different flange material (CLT, LSL, and LVL) with two glulam beam webs and self-tapping screws to develop a large span timber-based box girder composite floor system. It was reported that the 12m long full-scale floor module with 44.5-mm-thick LVL flanges and 80 mm by 418 mm glulam beams had a bending stiffness that was 2.5 times of the combined stiffness of the two glulam beams with a composite efficiency of 68%. Luengo et al. (2024) researched the bending behavior of stressed-skin panels made by CLT as flanges and finger-jointed lumber as webs and found that these floors could effectively serve as an alternative to conventional CLT panel floors. Holstein & Bohnhoff (2013) investigated the bending properties of wood I-beam fabricated with screws and polyurethane adhesive. They reported that the addition of polyurethane adhesive significantly increased bending strength and stiffness, making the screw-glued I105 sections a viable alternative for applications requiring enhanced structural performance. Additionally, European manufacturers like Metsä Group and Stora Enso have advanced the development of boxed and ribbed floor systems using LVL and CLT-Glulam composites. These systems, which incorporate design software to optimize floor designs based on project requirements, have demonstrated improved performance (Metsä Group, 2023; Stora Enso, 2024b). However, their production processes either rely on large hydraulic presses for gluing or used lumber-based EWP, which can reduce material utilization and limit manufacturing flexibility. Recent research has explored the potential of screw-gluing methods to fabricate CLTGlulam composite floors for long-span applications, Aicher et al. (2021) researched the screw spacing and clamping force provided by screws. Bratulic & Augustin (2016) investigated the pressure distribution between the flange and rib, while Shahnewaz et al. (2022) reported the vibration and deflection behaviour of screw-glued CLT-Glulam composited hollow-box floor section. The Germany standard DIN 1052-10:2012, 2012 (2012) currently limits screw-gluing to flange thicknesses of up to 50 mm, yet Aicher et al (2021) suggested that the axial clamping force provided by partially threaded self-tapping screws can offer sufficient adhesive pressure for flange thicker than standard required. In addition to acting as a secondary connector in case of glue line failure, screws can reduce the shear and compressive stress in the wood products, making them a viable option for long-span composite floors (Izzi & Polastri, 2019). Though SCL products have been produced in North America for more than three decades, they have been mainly used in light wood framing. As SCL is produced as large dimension billets with various strength grades and can be subsequently sawn into specified sizes. Their 106 superior material utilization makes SCL a viable substitute for current mass timber options, particularly in developing prefabricated hollow-box floor systems for long-span applications. Moreover, common floor structural design practice relies on experiences and manual iterative calculations, which can be time-consuming for hollow-box floors with various choices of member sizes and grades. To address these challenges, and to provide a more efficient design process for hollow-box floor modules, a structural optimization tool can assist designers and engineers in evaluating different section profiles made possible by the versatility of SCL products. Fiore et al. (2016) developed a Differential Evolution algorithm to optimize the structural design of hollow-section steel trusses. They found that this method effectively minimized the weight of the trusses while ensuring optimal performance, demonstrating its utility in practical applications involving size, shape, and topology optimization. Ismail et al. (2021) investigated the optimization of shaped beams for efficient structural design. The study employed both analytical and numerical shape optimization methods to analyze the effects of various beam geometries on material efficiency, specifically focusing on minimizing the volume while maintaining structural performance. The results demonstrated significant potential for reducing embodied energy, with volume reductions of up to 30% compared to prismatic beams, highlighting the advantages of optimized beam designs in reducing the environmental impact of construction. Nesheim (2021) researched the optimization of hollow-section timber floor elements for adaptable buildings and found that optimized designs significantly improved the competitiveness and adaptability of timber floor systems, particularly in long-span applications. 107 Therefore, the research objective of this chapter is to develop a structural optimization algorithm incorporating current design methods for prefabricated hollow-box floor systems with SCL through parametric modelling and genetic algorithm. This chapter is organized as follows: The methodology is first presented, including an introduction to various structural analysis and design methods, as well as the structural optimization algorithm. This is followed by the results and discussion, which include comparisons of different effective width calculation methods, an evaluation of the results from different structural analysis and design methods, and the final optimization results, along with a comparison of material usage across different floor systems. Finally, the chapter concludes with a summary of the key findings. 4.2 Methodology To achieve the abovementioned objective, a structural optimization design tool for SCL prefabricated hollow-box floor module was developed. Both the I section (closed type) and T section (open type) floor module were analyzed, as shown in Figure 4.1. The space between the centre of the ribs is half of the panel width. 108 (a) (b) Figure 4.1 Schematic model and configuration of the I (a) and T (b) section 109 To compare and discuss different structural analysis and design methods, the effective width ܾ௘௙ should be calculated. There are three major effective width calculation methods in different code, standard and research for timber-timber composite structure, which are the method from CSA O86(CSA), Eurocode 5(EC5) and the method developed by Kikuchi et al. (2007). The CSA provision introduced the panel geometry reduction factor ܺீ , and the effective width can be calculated as follows (Canadian Wood Council, 2021): ܺீ = 1 − 4.8 ቀ ‫ݏ‬௖௟௘௔௥ ଶ ቁ ݈ (4.1) (4.2) ܾ௘௙ = ܾܺீ where ‫ݏ‬௖௟௘௔௥ is the clear spacing between ribs, mm; ݈ is the panel span, mm; ܾ is the half of rib spacing, mm. EC5 proposed the effective width calculation method for materials such as plywood, oriented strand board and particleboard or fibre board, the effective width can be calculated based on Table 4.1 (European Committee for Standardization & British Standards Institution, 1994; European Organisation for Technical Approvals, 2020). Table 4.1 Eurocode 5 maximum effective flange width calculation method Flange Material Plywood outer plies grain parallel to the ribs Plywood outer plies grain perpendicular to the ribs Oriented strand board Particleboard or fibre board with random fibre orientation Note: ݈ is the panel span, mm and ℎ௙ is the flange thickness, mm. Shear lag 0.1 ݈ 0.1 ݈ 0.15 ݈ 0.2 ݈ Plate buckling 20 ℎ௙ 25 ℎ௙ 25 ℎ௙ 30 ℎ௙ 110 Additionally, the effective width can also be calculated using a formula derived by Kikuchi et al. (2007), which was validated through experimental test for stressed skin panels, resulting in the following formula: ௟ ቆି଴.ଷ଼ଷ଼ቀ ି଴.ସ଺଼଻ቁቇ ܾ௘௙ ௦ = ‫ܭ‬଴ = 1 − ݁ ‫ݏ‬ (4.3) where ‫ ݏ‬is the spacing between centre of the ribs, mm; ݈ is the panel span, mm. 4.2.1 Structural analysis and design methods The gamma method is a simplified structural analysis technique that incorporates a factor, ߛ , to account for partial composite action within the system (Huber & Deix, 2021). Eurocode 5 adopts gamma method for the design of mechanically jointed beams. The following equations are used to calculate the effective bending stiffness (‫)ܫܧ‬௘௙ , ߛ, bending stress ߪ௜ for the ݅ ௧௛ layer and maximum shear stress ߬ଶ,௠௔௫ for the rib (European Committee for Standardization & British Standards Institution, 1994). ଷ (‫)ܫܧ‬௘௙ = ෍(‫ܧ‬௜ ‫ܫ‬௜ + ߛ௜ ‫ܧ‬௜ ‫ܣ‬௜ ܽ௜ଶ ) (4.4) ௜ୀଵ ܾ௘௙ ℎ௜ ݂‫ = ݅ ݎ݋‬1 ܽ݊݀ 3 ܾ௜ ℎ௜ ݂‫ = ݅ ݎ݋‬2 (4.5) ܾ ℎଷ ⎧ ௘௙ ௜ ݂‫ = ݅ ݎ݋‬1 ܽ݊݀ 3 12 ‫ܫ‬௜ = ܾ௜ ℎ௜ଷ ⎨ ݂‫ = ݅ ݎ݋‬2 ⎩ 12 (4.6) ߛଶ = 1 (4.7) ‫ܣ‬௜ = ൜ ߛ௜ = ቂ1 + గ మ ா೔ ஺೔ ௦೔ ௄೔ ௟ మ ିଵ ቃ (4.8) 111 (4.9) ܽଵ ୟ୬ୢ ଷ = ‫ݖ‬௜ − ܽଶ ܽଶ = ఊభ ாభ ஺భ(௛భ ା ௛మ )ି ఊయாయ ஺య (௛మ ା ௛య ) ଶ ∑య೔సభ ఊ೔ ா೔ ஺೔ (4.10) ఊ೔ ா೔ ௔೔ ெ೏ (ாூ)೐೑ (4.11) ߪ௜ = ఊ ா ஺ ௔ ା଴.ହாమ ௕మ ௛మమ ߬ଶ,௠௔௫ = భ భ భ௕ భ(ாூ) మ ೐೑ ܸௗ (4.12) where ‫ܧ‬௜ is the Young’s Modulus of the ݅ ௧௛ layer in the composite beam, MPa; ‫ܫ‬௜ is the moment of inertia of the cross section of the ݅ ௧௛ layer, mm4; ‫ܣ‬௜ is the cross-section area of the ݅ ௧௛ layer, mm2; ܽ௜ is the distance from the centroid of the ݅ ௧௛ layer to the neutral axis, mm; ܾ௜ is the width of cross section of the ݅ ௧௛ layer, mm; ℎ௜ is the height of cross section of the ݅ ௧௛ layer, mm; ‫ݏ‬௜ is the spacing of fasteners of the ݅ ௧௛ layer, mm, in this case, ‫ݏ‬௜ = 150݉݉ has been used; ‫ܭ‬௜ is the slip modulus of the mechanical fastener, N/mm, which will be taken as ‫ܭ‬௦௘௥ or ‫ܭ‬௨ depending on serviceability or ultimate limit state calculations; ݈ is the span of beam, mm; ‫ܯ‬ௗ is the design bending moment, Nmm and ܸௗ is the design shear force, N. For T-sections, ℎଷ = 0. Based on the connection test results from Chapter 3, the obtained ‫ܭ‬௨ values range from 153.7 kN/mm to 391.7 kN/mm. Given the scenario where the panel range from 6 m to 12 m long, 1.2 m wide, and has a 150 mm screw spacing, the calculated ߛ values range from 0.92 to 0.99, which are very close to 1. This indicates that the connection can be considered as nearly fully rigid. 112 However, based on Equation 4.8, the ߛ increases with the increase of the floor span ݈, as the inherent property, the factor ߛ should remain unchanged. This changing of factor ߛ makes the gamma method less accurate compared with other analysis methods. In addition to the gamma method, the shear analogy method, proposed by Kreuzinger (1999) is recommended for the structural analysis of prefabricated wood-based load-carrying stressed skin panels, including composite floor and roof systems (European Organisation for Technical Approvals, 2020). The shear analogy method simplifies the analysis by converting a composite beam into two virtual beams: virtual beam A and virtual beam B. Virtual beam A is assumed to primarily resist bending actions, with an infinite shear modulus, while virtual beam B primarily resists normal and shear stresses. These two beams are connected by a rigid link, ensuring that both beams experience the same deformation at any given point. This approach allows for a comprehensive analysis of the combined effects of bending and shear in the composite structure (Kreuzinger, 1999). According to EOTA TR019 (2020) and Mestek et al (2008), the effective bending stiffness (‫)ܫܧ‬௘௙ , normal stress ߪ௠ , shear stress ߬௫௭ and maximum deflection ∆௠௔௫ can be calculated as follows: ௡ (‫)ܫܧ‬஺ = ෍ ‫ܧ‬௜ ‫ܫ‬௜ (4.13) ‫ܧ‬௜ ‫ܣ‬௜ ‫ݖ‬௜ଶ (4.14) (‫)ܫܧ‬௘௙ = (‫)ܫܧ‬஺ + (‫)ܫܧ‬஻ (4.15) ௜ୀଵ ௡ (‫)ܫܧ‬஻ = ෍ ଵ ௗమ ଵ = ቐ (ீ஺)೐೑ ቀ∑ଶ௜ୀଵ ௦೔ ௞ೞ೐ೝ ଵ ௦೔ ௗ ቀ మ + ௞ೞ೐ೝ ௛భ ଶீభ ௕భ ௛భ + + ଶீభ ௕భ + ௜ୀଵ ௛మ ீమ ௕మ ௛మ + ଶீమ ௕మ ௛య ଶீయ ௕య ቁ ݂‫ ܫ ݎ݋‬− ‫݊݋݅ݐܿ݁ݏ‬ (4.16) ቁ ݂‫ ܶ ݎ݋‬− ‫݊݋݅ݐܿ݁ݏ‬ 113 (ாூ) ಲ ‫ܯ‬஺,ௗ = ‫ܯ‬ௗ (ாூ) ା(ாூ) ಲ (4.17) ಳ (ாூ)ಳ ‫ܯ‬஻,ௗ = ‫ܯ‬ௗ (ாூ) ಲ ା(ாூ)ಳ (ாூ)ಲ ܸ஺,ௗ = ܸௗ (ாூ) ಲ ା(ாூ)ಳ (ாூ)ಳ ܸ஻,ௗ = ܸௗ (ாூ) ಲ ା(ாூ)ಳ ெ ಲ,೏ ߪ஺ = ± (ாூ) ‫ܧ‬௜ ‫ݖ‬௜ (4.18) (4.19) (4.20) (4.21) ಲ ா ߪ஻ = ±‫ܯ‬஻,ௗ (ாூ)೔ ‫ݖ‬௦,௜ (4.22) ಳ ௏ ಲ,೏ ߬஺,௜ = (ாூ) ‫ܧ‬௜ ‫ܫ‬௜ ಲ ௏ ಳ,೏ ߬஻,௜ = (ாூ) ಳ ଷ ଵ ଶ ௛೔ ௕೔ ∑భ೔సభ ா೔ ஺೔ ௭೔ ௕మ (4.23) (4.24) where (‫)ܫܧ‬஺ is the bending stiffness for the virtual beam A, Nmm2; (‫)ܫܧ‬஻ is the bending stiffness for the virtual beam B, Nmm2; ‫ݖ‬௜ is the distance between the neutral axis of the ݅ ௧௛ layer and the neutral axis of the beam, mm; (‫)ܣܩ‬௘௙ is the effective shear rigidity, N; G is the shear modulus, MPa; ‫ܯ‬஺,ௗ and ‫ܯ‬஻,ௗ are amount of design bending moment distributed to virtual beam A and B, respectively, Nmm; ܸ஺,ௗ and ܸ஻,ௗ are the amount of shear force distributed to virtual beam A and B, respectively, N; ‫ݖ‬௦,௜ is the distance between any point and the neutral axis of beam, mm; ߪ஺ and ߪ஻ are the bending stress for virtual beam A and B, respectively, MPa, and ߬஺,௜ and ߬஻,௜ are the shear stress for virtual beam A and B, respectively, MPa. The total deflection, ∆௠௔௫ , bending stress, ߪ௠ , and shear stress, ߬௫௭ , are calculated as follows: 114 ∆௠௔௫ = 5‫ ݈ݓ‬ସ ‫ ݈ݓ‬ଶ + 384(‫)ܫܧ‬௘௙ 8(‫)ܣܩ‬௘௙ (4.25) ߪ௠ = ߪ஺ + ߪ஻ (4.26) ߬௫௭ = ߬஺,௜ + ߬஻,௜ (4.27) In addition to the gamma method and shear analogy method, the current Canadian engineering wood design standard, CSA O86, provides design provisions for stressed skin panels. The standard introduces a calculation model based on the parallel-axis theorem, which assumes full composite action through gluing. In this model, various parameters, such as the effective stiffness (‫)ܫܧ‬௘ , bending moment resistance ‫ܯ‬௥ , factored shear resistance of the rib at the neutral axis ܸ௥ , and factored shear resistance of the glued interface between the flange and rib ܸ௥௣ , are calculated. Additionally, deflection ∆௦ is determined using the equations provided in the standard, as detailed below: (‫)ܫܧ‬௘ = (‫)ܫܧ‬௪ ‫ܭ‬ௌா + ܾ௙ (ܾ௔௧ ‫ݖ‬ଷ ଶ + ܾ௔௖ ‫ݖ‬ଵ ଶ )‫ܭ‬௦ (4.28) where (‫)ܫܧ‬௪ is the stiffness of rib, Nmm2; ܾ௙ is the total width of the panel, mm; ܾ௔௧ and ܾ௔௖ are specified axial stiffness of tension and compression flange, respectively, N/mm. To calculate bending moment resistance, the bending moment resistance in tension flange can be calculated as follows, ‫ܯ‬௥ = ∅௙ ܶ௣ ܺ௃ ܺீ (‫)ܫܧ‬௘ ‫ܤ‬௔ ‫ܭ‬ௌ ℎ௧ ܶ௣ = ‫ݐ‬௣ (‫ܭ‬஽ ‫ܭ‬ௌ ‫) ்ܭ‬ (4.29) (4.30) 115 where ∅௙ is 0.95; ‫ݐ‬௣ is specified strength capacity of flange in axial tension, N/mm; ܺ௃ is the stress-joint factor, can be found in CSA O86 Clause 10.4. The bending moment resistance in compression flange can be calculated as follows, ‫ܯ‬௥ = ∅௙ ܲ௣ ܺ௃ ܺீ (‫)ܫܧ‬௘ ‫ܤ‬௔ ‫ܭ‬௦ ℎ௖ (4.31) ܲ௣ = ‫݌‬௣ (‫ܭ‬஽ ‫ܭ‬ௌ ‫) ்ܭ‬ (4.32) where ‫݌‬௣ is the specified strength capacity of flange in axial compression, N/mm. Also, the calculation of bending moment resistance in the rib is shown below. ‫ܯ‬௥ = ∅௪ ‫ܨ‬௕ ‫ܭ‬௭௕ ܺ௅ ܺீ (‫)ܫܧ‬௘ ‫ܭܧ‬ௌா ܿ௪ (4.33) ‫ܨ‬௕ = ݂௕ (‫ܭ‬஽ ‫ܭ‬ௌ௕ ‫ܭ ்ܭ‬ு ) (4.34) ‫ݏ‬௖௟௘௔௥ ଶ ) ݈ (4.35) ܺீ = 1 − 4.8( where ∅௪ is 0.9; ݂௕ is the specified strength in bending of ribs, MPa; ‫ ܧ‬is the Youngs’s modulus of rib, MPa; ‫ݏ‬௖௟௘௔௥ is the clear spacing between longitudinal rib members, mm. The following equations are used to calculate the shear resistance at the neutral plane, ܸ௥ = ∅௪ ‫ܨ‬௩ ‫ܭ‬௓௩ (‫)ܫܧ‬௘ ∑ ܾ௚ ‫ݖ‬ଵ ‫ܭܧ‬ௌா ∑ ܳ௪ + ‫ܤ‬௔ ‫ܭ‬௦ ܾ௘௙ ݉ܽ‫ ݔ‬ቄ‫ݖ‬ (4.36) ଷ ‫ܨ‬௩ = ݂௩ (‫ܭ‬஽ ‫ܭ‬ௌ௩ ‫ܭ ்ܭ‬ு ) (4.37) where ݂௩ is the specified strength in shear of ribs, MPa; ܾ௚ is the contact width between flange and rib, mm; ∑ ܳ௪ is sum of moments of area of all ribs about neutral plane, mm3. 116 The flange-rib shear resistance for flange can be calculated as follows, ܸ௥௣ = ∅௙ ܸ௚௙ (‫)ܫܧ‬௘ ∑(ܾ௚ ܺ௩௙ ) ‫ݖ‬ଵ ‫ܤ‬௔ ‫ܭ‬௦ ܾ௘௙ ݉ܽ‫ ݔ‬ቄ‫ݖ‬ ଷ ܸ௚௙ = ‫ݒ‬௣௙ (‫ܭ‬஽ ‫ܭ‬ௌ ‫) ்ܭ‬ (4.38) (4.39) where ‫ݒ‬௣௙ is the specified strength capacity in planar shear of the rib, MPa; ܺ௩௙ is the shear-modification factor, see CSA O86 Figure 10.2. To calculate the shear resistance to the rib, the following equations can be used. ܸ௥௣ = ∅௙ ܸ௚௪ (‫)ܫܧ‬௘ ∑(ܾ௚ ܺ௩௪ ) ‫ݖ‬ଵ ‫ܤ‬௔ ‫ܭ‬௦ ܾ௘௙ ݉ܽ‫ ݔ‬ቄ‫ݖ‬ ଷ ܸ௚௙ = ݂௩ (‫ܭ‬஽ ‫ܭ‬ௌ ‫) ்ܭ‬ (4.40) (4.41) where ܺ௩௪ is 2.00. All the K factors are assumed as 1. The terms related to component 3 and tension flange in the formula should be disregarded for T section (Canadian Wood Council, 2021). The deflection ∆௦ can be calculated based on the formulas below: ∆௦ = ܺீ 5‫݈ݓ‬ସ 384(‫)ܫܧ‬௘ (4.42) Besides above design checks, the fundamental natural frequency and deflection under 1 kN point load can be calculated as well. The vibration-controlled span design equation for wood joist floors from CSA O86 was considered as an additional potential criterion for reference (Hu & Chui, 2004). However, future research is required to confirm the applicability of the design criteria for hollow-box floor systems using SCL. 117 ݂ଵ ≥ 18.7 (4.43) ݂ଵ = ߨ ‫ܫܧ‬ଵ௠ ඨ 2݈ ଶ ݉ (4.44) ݀= 1000݈ܲଷ 48(‫)ܫܧ‬௘௙ (4.45) ݀ ଴.ସସ where ݂ଵ is the calculated fundamental natural frequency of floor, Hz; ‫ܫܧ‬ଵ௠ is the effective bending stiffness of the floor with 1 metre width, Nm2; ݉ is the linear mass of floor with 1 metre width, kg/m; ݀ is the deflection of the floor panel, mm; P = 1000 N. 4.2.2 Structural optimization algorithm In this study, Rhinoceros 3D, along with its visual programming language and environment called Grasshopper, was used to develop a structural optimization algorithm for prefabricated hollow-box floor modules using SCL and screw gluing. The optimization program consists of five main components: a parametric geometry model, a material database containing strength grades and design values, a CSA O86-based stressed skin panel design module, an optimization module utilizing a genetic algorithm, a verification module based on both the gamma method and the shear analogy method. Consequently, the CSA O86 design equations are programmed as the primary design method to determine optimal cross-sections and material selections based on given spans and corresponding floor height limitations. The gamma method and shear analogy method are used as alternative approaches to analyze and design the optimized cross-section. The complete optimization algorithm is illustrated in Figure 4.2. 118 Figure 4.2 The logic of optimization algorithm The material database contains varies of material properties, such as the elastic modulus, shear modulus, bending strength, shear strength, density and compression for both parallel and perpendicular to grain direction, etc. For now, the F16 grade MPP from Freres Engineered Wood was used as the initial material for all the component of the panel in the database, while additional materials can be added to the material database in the future. The design values of F16 grade MPP are shown in Table 4.2 (Freres Engineered Wood, 2023; Ho et al., 2022; Maureen & Arijit, 2020). 119 Table 4.2 F16 grade MPP design values Properties Bending strength (݂௕ ) MPa Joist direction 24.0 Plank direction 15.9 Young’s modulus (‫ )ܧ‬MPa 11032 9653 Screw Shear modulus (‫ )ܩ‬MPa 527.8 461.9 Shear strength (݂௩ ) MPa 3.3 0.97 Compression strength (݂௖௣ ) MPa 9.4 6.2 Tension strength (݂௧ )MPa Density at 12%MC (ߩ) kg/m3 16.6 550 In accordance with the NBCC 2020, two load scenarios were considered for this study: a live load of 1.9 kPa for bedrooms in residential areas and a live load of 2.4 kPa for office spaces. The worst-case load combination, 1.25‫ ܦ‬+ 1.5‫ܮ‬, was applied for the ultimate limit state (ULS) design. The entire section was assumed as simply supported during the calculation (Canadian Commission on Building and Fire Codes, 2022). For serviceability limit state design, the deflection limit ∆௥ can be calculated according to the worst load combination, selected between 1.0D + 1.0L with a corresponding deflection limit of ‫ܮ‬/180 and 1.0‫ ܮ‬with a corresponding deflection limit of ‫ܮ‬/360 (Canadian Commission on Building and Fire Codes, 2022). The vibration-controlled span also has been calculated for reference. The material properties and grades, as well as the thicknesses of the flange and rib, are defined as discrete variables. The thickness of component ℎଵ and ܾଶ can be cut from the MPP panels in increments of 25.4 mm, while the width of the flange ܾଶ and the height of the rib ℎଶ are considered continuous variables. For I sections, the upper and lower flange are always assumed to the same (ℎଵ = ℎଷ ). 120 Figure 4.3 Visual model of I (top) and T (bottom) section floor module Figure 4.4 Input variables of optimization algorithm A visualization model was developed in Grasshopper as shown in Figure 4.3, and the genetic algorithm component, Galapagos, was employed for the optimization of the crosssection design. During the optimization process, Galapagos adjusts the thickness of the flange, as well as the height and thickness of the rib, as illustrated in Figure 4.4. Comparing to I-joist and CLT panel, the ranges for these values are presented as Equation 4.46-4.48. 121 800 ݉݉ ݂‫ > ݈ ݎ݋‬9000 ݉݉ 50 ݉݉ ≤ ℎଶ ≤ ൜ 500 ݉݉ ݂‫ ≤ ݈ ݎ݋‬9000 ݉݉ (4.46) 25.4 ݉݉ ≤ ℎଵ ≤ 254 ݉݉ (4.47) 25.4 ݉݉ ≤ ܾଶ ≤ ൜ 508 ݉݉ ݂‫ > ݈ ݎ݋‬9000 ݉݉ 254 ݉݉ ݂‫ ≤ ݈ ݎ݋‬9000 ݉݉ (4.48) The total height of the section is constrained to a maximum of 500 mm for all spans, referencing the floor span table for wood I-joisted floors (National Research Council of Canada, 2020). Additionally, the flange width ܾଵ can be manually selected within the range of 1200 mm to 2400 mm. Other parameters, such as the floor type, floor span, design live load, and all adjustment factors for wood design, need to be manually specified. The available span options for the optimization are 6 m, 9 m, or 12 m. Then the algorithm will go through the CSA design method to obtain the bending moment and shear force resistance for current configuration, as well as the deflection. The design criteria for the genetic algorithm can be described as multiple equations. Equations 4.49-4.52 are used to calculate and prerequisite constraint of the algorithm, include utilization ratio of bending moment, shear force and deflection, the design check must be satisfied before entering objective function. ெ ‫ݑ‬ெ = ெ೘ < 1 (4.49) ௏೘ (4.50) ೝ ‫ݑ‬௏ = ௏ೝ ௠௜௡൜௏ ೝ೛ ‫ݑ‬ௗ = <1 ∆௦ <1 ∆௥ (4.51) 122 where ‫ݑ‬ெ is the ratio of the actual bending moment to the bending moment capacity. ‫ݑ‬௏ is the ratio of the actual shear force to the shear force capacity. ‫ݑ‬ௗ is the ratio of the actual deflection to the deflection limit. Generally, deflection becomes the governing check for wood-based floor systems. Additionally, the total height ‫ ܪ‬can be constrained as well, by using the following, ‫ < ܪ‬500 mm (4.52) The additional vibration-controlled condition can be considered as an extra reference to enter the prerequisite, the equation is shown as below, ݂ଵ ݀ ଴.ସସ ≥ 18.7 (4.53) Then the objective functions could be defined as following to consider the balance between floor height or volume, ‫ ܪ × ܽ = ݊݋݅ݐܿ݊ݑ݂ ݁ݒ݅ݐ݆ܾܿ݁݋‬+ ܾ × ܸ (4.54) where ܸ is the total volume in m3, and ‫ ܪ‬is the floor height in mm, ܽ and ܾ are constant depending on user’s optimization goal. ܽ and ܾ were set to be 0.01 and 100 in this study, respectively. In this study, the setup for the genetic algorithm and the optimization process is illustrated in Figure 4.5. Galapagos, the default genetic algorithm plugin in Grasshopper, was used for the optimization. The initial geometry of the floor system is input into the genetic algorithm, which then iteratively modifies the design parameters to optimize structural performance. The algorithm evaluates each generation based on design criteria mentioned above. It selects the best-performing individuals to undergo mutation and crossover, ensuring that the next generation has improved design characteristics. This process continues until the optimal solution is found, balancing all the terms in the objective function. The term "Max stagnant" represents the number of generations the algorithm will run without improvement, while "population" refers to the number of individuals within each generation. "Initial boost" is a factor applied to the population size in the first generation to prevent the algorithm from prematurely converging to a local optimum. The 123 "Maintain" term indicates the percentage of the best-performing individuals from each generation that are carried over to the next generation, while "inbreeding" refers to the breeding of solutions that share a very similar genetic makeup. In this case, the gene represents the variables controlled by Galapagos. Each generation consists of 30 individuals, evaluated based on the objective function. The population was set to 30, with an initial boost applied twice to gather sufficient samples. The top 30% of individuals were retained for the next crossover, while 70% shared similar genetic traits. Crossover continued until 40 generations were completed. Figure 4.5 Galapagos settings (left) and optimization process (right) After executing the optimization process, optimized results were obtained for different spans and section widths. Due to the presence of multiple terms in the optimization equation, the multi-objective optimization process may not directly produce a single solution, but rather yields different outcomes based on various optimization objectives. As a result, for each variation, both the minimum volume and minimum height configurations were identified if no best option was found. 124 4.3 Results and discussion To compare different effective width calculation and structural analysis methods, the calculations will be based on the scenario shown in Table 4.3. Table 4.3 Example scenario used to compare calculation methods I-section Live load (kPa) ݈ (mm) ܾଵ (mm) ℎଶ (mm) ܾଶ (mm) ℎଵ (mm) 1.9 8000 1800 290 101.6 25.4 4.3.1 Comparison of different effective width calculation methods Since the three different effective width calculation methods involve multiple factors, such as the span and width of the panel, the comparison is divided into two cases for discussion. In this study, the panel was assumed as stressed skin panel to fit the CSA and Kikuchi method and assumed as made of plywood to adapt the EC5 method. First, the panel span is fixed at 8000 mm, and the panel width was gradually increased from 600 mm to 3000 mm. The resulting relationships between the different effective widths ܾ௘௙ are shown in Figure 4.6. 125 1400 CSA ܾ݂݁ (mm) 1200 EC5 1000 Kikuchi 800 600 400 200 0 600 1000 1400 1800 2200 Panel width (mm) 2600 3000 Figure 4.6 Different effective width based on change of panel width Next, the panel width was fixed at 1800 mm, and the span was gradually increased from 2000 mm to 9000 mm. The relationships between the three different effective width ܾ݂݁ (mm) calculations under this condition were shown in Figure 4.7. 1000 900 800 700 600 500 400 300 200 100 0 CSA EC5 Kikuchi 2000 3000 4000 5000 6000 7000 8000 9000 Panel span (mm) Figure 4.7 Different effective width based on change of panel span The results shown in Figure 4.6 indicated that when varying the panel width, the results obtained from the CSA and Kikuchi methods are quite similar, with no significant 126 differences. In contrast, the EC5 method, which was constrained by panel span and flange thickness, produces a constant ܾ௘௙ of 508 mm in this scenario. Moreover, in Figure 4.7, where the panel span was varied, the CSA and Kikuchi methods showed significant differences when the span is less than 3500 mm, with Kikuchi providing larger values of ܾ௘௙ . The EC5 method remains more conservative compared to the other two methods, consistently providing lower ܾ௘௙ values. In summary, the CSA method showed a similar trend to the Kikuchi method for spans above 3.5 m, while the EC5 method showed more conservative results. Considering that the Kikuchi approach is based on experimental results and is similar to the CSA approach, in this study, the Kikuchi method has been used for calculating the effective width. 4.3.2 Comparison of different design methods The comparison of different structural analysis methods for stress and deflection calculations are shown in Table 4.4-4.5 and Figure 4.8-4.11. Table 4.4 Structural analysis results for different design methods (I-section) Calculation method Bending stress (MPa) Shear stress (MPa) Deflection (mm) CSA-structural analysis 3.09 0.40 6.5 Gamma method 3.02 0.41 6.9 Shear analogy 3.01 0.41 7.6 127 Thickness (mm) Gamma Method Shear Analogy Simple Beam Method 200 150 3.19 100 50 0 -4 -2 0 2 4 -50 -100 -150 -200 Bending stress (MPa) Figure 4.8 bending stress distributions with different design methods (I-section) 200 150 Shear Analogy Thickness (mm) 100 Simple Beam Method 50 0.42 Gamma Method 0 -50 0 0.1 0.2 0.3 0.4 0.5 -100 -150 -200 Shear stress (MPa) Figure 4.9 shear stress distributions with different design methods (I-section) 128 Table 4.5 Structural analysis results for different design methods (T-section) Calculation method Bending stress (MPa) Shear stress (MPa) Deflection (mm) CSA 9.15 0.49 21.6 Gamma method 9.80 0.51 16.8 Shear analogy 9.56 0.55 17.9 Gamma Method Thickness (mm) Shear Analogy -10 Simple Beam Method 250 9.15 200 150 100 50 0 -5 0 5 10 15 -50 -100 -150 Bending stress (MPa) Figure 4.10 Diagram illustration of bending stress with different design methods (Tsection) 129 250 200 Thickness (mm) 150 Shear Analogy 100 Simple Beam Method 50 Gamma Method 0.51 0.49 0 -50 0 0.2 0.4 0.6 -100 -150 Shear stress (MPa) Figure 4.11 Diagram illustration of shear stress with different design methods (T-section) Based on the results in Table 4.4, all three methods, CSA O86, gamma method, and shear analogy, produced similar values for bending stress, shear stress, and deflection in the Isection analysis. The CSA method resulted in a slightly higher bending stress (3.09 MPa) compared to the gamma method (3.02 MPa) and shear analogy (3.01 MPa). Regarding deflection, the shear analogy method showed the highest value (7.6 mm), while the CSA method produced the lowest deflection (6.5 mm). This suggests that all three methods offer relatively accurate results for the I-section, with the shear analogy method being more conservative in deflection calculations, likely due to its consideration of shear deformation effects. In Table 4.5, which presents the T-section analysis, the three methods again yielded comparable values but with some variations. The gamma method resulted in the highest bending stress (9.80 MPa), followed by the shear analogy method (9.56 MPa), and the CSA method showed the lowest bending stress (9.15 MPa). For deflection, the CSA method 130 exhibited the highest value (21.6 mm), whereas the gamma method produced the lowest deflection (16.8 mm), with the shear analogy method in between (17.9 mm). This indicates that while all methods are consistent in their stress predictions, they differ in deflection calculations for the T-section. The higher deflection predicted by the CSA method suggests it may be more conservative in this case. 4.3.3 Optimal hollow-box floor design case study Under the residential floor scenario (1.9 kPa), the optimization results based on ULS and deflection for both 1.2 m and 2.4 m widths and for each span (6 m and 9 m) for I-section and T-section are shown in Table 4.6 and 4.7. Table 4.6 Optimization results for I section Floor span Properties 6m 9m 12m Floor module width 1.2 m 2.4 m 1.2 m 2.4 m 2.4 m ℎଶ (mm) 95 90 80 195 190 185 100 305 125 ܾଶ (mm) 50.8 228.6 50.8 50.8 101.6 50.8 101.6 50.8 101.6 ℎଵ (mm) 25.4 25.4 25.4 25.4 25.4 25.4 50.8 25.4 76.2 ‫ݑ‬ௗ (%) 96.1 98.2 94.5 95.8 90.0 97.2 99 97.1 94.3 ‫ݑ‬ெ (%) 16.5 15.6 21.1 23.7 22.7 27.3 14.7 33.2 13.5 ‫ݑ‬௏ (%) 26.4 7.7 61.0 20.3 9.4 44.9 36.5 37.2 40.2 ‫( ܪ‬mm) 145.8 140.8 130.8 245.8 240.8 235.8 201.6 355.8 277.4 ܸ (m3) 0.42 0.61 0.78 0.73 0.98 1.26 2.38 1.83 4.69 131 Table 4.7 Optimization results for T section Floor span Properties 6m 9m 12m Floor module width 1.2 m 2.4 m 1.2 m 2.4 m 2.4 m ℎଶ (mm) 235 140 240 165 360 220 440 265 445 300 ܾଶ (mm) 50.8 254 76.2 254 50.8 254 50.8 254 127 508 ℎଵ (mm) 25.4 25.4 25.4 25.4 25.4 25.4 25.4 25.4 25.4 25.4 ‫ݑ‬ௗ (%) 97.8 98.6 94.1 92.2 98.8 99.7 97.0 96.0 99.5 99.3 ‫ݑ‬ெ (%) 46.9 26.0 70.4 39.1 49.6 30.8 72.5 40.0 52.9 36.1 ‫ݑ‬௏ (%) 60.6 16.9 91.5 36.0 44.8 12.3 91.7 25.0 36.4 10.8 ‫( ܪ‬mm) 260.4 165.4 265.4 190.4 385.4 245.4 465.4 290.4 470.4 325.4 ܸ (m3) 0.33 0.61 0.59 0.87 0.60 1.28 0.95 1.76 2.08 4.39 Based on the optimization results presented in Table 4.6 for the I-section, the rib height (ℎଶ ) increased with the floor span length, indicating a direct relationship between span and required rib height for structural efficiency. For a 6 m span, h₂ ranged from 80 mm to 95 mm depending on the section width, while for a 12 m span, it increased significantly to between 125 mm and 305 mm. This trend demonstrated the necessity for taller ribs to accommodate longer spans. The rib width (ܾଶ ) varied between 50.8 mm and 228.6 mm across different spans and section widths but remained relatively stable within each span category. The flange height ( ℎଵ ) varies between 25.4 mm and 76.2 mm across all configurations, suggesting that flange height is less sensitive to changes in span length and 132 section width in the optimization process. The deflection utilization rate (‫ݑ‬ௗ ) remained consistently high, ranging from 90% to 99%, which indicated that the designs were optimized close to the allowable deflection limits. The bending utilization rate ( ‫ݑ‬ெ ) remained relatively low, ranging from 13.5% to 27.3% while the shear utilization rate (‫ݑ‬௏ ) ranged 7.7% to 61%, showing a large variation in the data. In Table 4.7, which presented the optimization results for the T-section, similar trends were observed with some notable differences. ℎଶ increased more dramatically with span length compared to the I-section. For a 6 m span, ℎଶ ranged from 140 mm to 235 mm, while for a 12 m span, it escalated to between 300 mm and 445 mm. This significant increase suggested that the T-section required a taller rib height to achieve structural efficiency over longer spans. ܾଶ in the T-section showed greater variability, ranged from 25.4 mm to 508 mm, indicating that the optimization process adjusted rib width more substantially in response to span length and section width changes. The flange height ℎଵ remained mostly constant at 25.4 mm. ‫ݑ‬ௗ ranged from 92.2% to 99.5%, similar to the I-section, showing that the T-section designs were also optimized close to deflection limits. ‫ݑ‬ெ ranged from 26% to 72.5% and ‫ݑ‬௏ ranged from 10.8% to 91.7%, both the utilization rates were higher than I-section group. The primary differences between the I-section and T-section configurations lie in the behavior of ℎଶ and ܾଶ . The T-section exhibited more substantial increased in ℎଶ with span length, indicating a greater sensitivity to span changes. Additionally, the variability in ܾଶ is more pronounced in the T-section, suggesting that adjustments in rib width were more critical for T-sections to meet structural demands. Both configurations, however, 133 maintained a relatively constant ℎଵ underscoring its lesser impact on the overall optimization. 4.3.4 Material usage comparison with other wood floor systems To compare the material usage of hollow-box floor module made from MPP with other materials, deflection and vibration should be considered in the serviceability limit state (SLS) design in condition of meeting ULS design. When considering deflection, the combination of dead load D was set to 2.0 kPa to facilitate comparison with other floor systems. The optimization results based on this condition are shown in Table 4.8. Table 4.8 Optimization result for deflection-controlled span I-section Total Volume Span (m) Height (m3) (mm) 6 1200 95 50.8 25.4 96.1 16.5 26.4 145.8 0.423 9 1200 195 50.8 25.4 95.9 24.1 20.8 245.8 0.727 Note: Live load is 1.9 kPa and dead load is set to 2 kPa for comparison. Load case is based on 1.25‫ ܦ‬+ 1.5‫ܮ‬. ܾଵ (mm) ℎଶ (mm) ܾଶ (mm) ℎଵ (mm) ‫ݑ‬ௗ (%) ‫ݑ‬ெ (%) ‫ݑ‬௏ (%) According to Wood Design Manual (2021) and Freres Engineered Wood (2024), to achieve deflection-controlled span of 6 m with 2.0 kPa dead load, and 1.9 kPa live load, at least 5 ply CLT of 175 mm or 156 mm MPP solid floor must be used. For the I joist, according to Weyerhaeuser Company (2024), at least 241 mm thick 230 TJI ® with 304 mm spacing and 18.3 mm oriented strand board (OSB) sheathing should be used. For the 9 m span, at least 9 ply CLT or 207 mm thick MPP solid floor is required. For the I joist, at least 301 mm thick, 560 TJI ® with 304 mm spacing and 18.3 mm sheathing should be used. The detailed material usage for each type of floors with the same floor width 1.2 m is shown in Figure 4.12. 134 Material usage span=9m Floor height span=6m Floor height span=9m 3.5 300 3 Volume (m^3) 350 250 2.5 200 2 150 1.5 100 1 Floor Height (mm) 4 Material usage span=6m 50 0.5 0 0 Hollow floor CLT MPP I-joist Figure 4.12 Material usage and floor height comparison for deflection-controlled criteria between 6m and 9m span and 1.2 m width The figure illustrates that material usage for solid CLT is the highest in both span conditions, being approximately three times and four times that of the hollow-box floor module for 6 m and 9 m spans, respectively. Similarly, the MPP system requires substantially more material, with nearly 2.5 times the volume of the hollow-box floor module for the 6 m span and 3 times for the 9 m span. The I-joist system, on the other hand, uses around 50% and 70% of the material compared to the hollow-box floor module for the 6 m and 9 m spans, respectively. However, its floor height is about 60% and 20% greater than that of the hollow-box floor module for each span length. In contrast, both the CLT and MPP panels have higher material usage compared to the hollow-box floor module for both spans. While the floor height of these panels is similar to the hollow-box floor module in the 6 m span, the MPP system shows a reduced floor height in the 9 m span. The I-joist follows a 135 consistent trend across both spans, using less material than the hollow-box floor module but requiring a greater floor height. When considering vibration as the extra SLS design criteria, the vibration-controlled design criteria, as shown in Equation 4.53, was incorporated into the design criteria as a potential reference, and the optimization results are presented in Table 4.9. Table 4.9 Optimization result for vibration-controlled span I-section Span (m) 6 9 ܾଵ ℎଶ ܾଶ ℎଵ ‫ݑ‬ௗ (mm) (mm) (mm) (mm) (%) 1200 170 50.8 25.4 35.0 1200 380 50.8 50.8 25.6 ‫ݑ‬ெ ‫ݑ‬௏ Total Height Volume (m3) (mm) (%) (%) 12.0 15.8 220.8 0.469 14.5 10.6 430.8 0.90 According to Wood Design Manual (2021) and Freres Engineered Wood (2024), to meet the vibration-controlled span criteria for a 6 m single-span bare floor, at least a 7-ply 35 mm CLT or a 208 mm MPP must be used as a solid wood panel floor. However, neither of these solid wood panels can achieve a 9 m span under vibration-controlled conditions. The calculated fundamental natural frequency ݂ଵ calculated for 6 m span is 16.4 Hz and for 9 m span is 14.2 Hz. The detailed material usage diagram is shown below in Figure 4.13. 136 Material usage Floor height 2.5 250 Volume (m^3) 230 1.5 220 1 210 200 0.5 Floor Height (mm) 240 2 190 0 180 Hollow floor CLT MPP Figure 4.13 Material usage and floor height comparison for vibration-controlled criteria width 1.2 m floor width Similar to deflection-controlled condition, for a 6 m vibration-controlled span, the material usage of the solid CLT floor system is still the highest among the three options, reaching approximately 2.4 m³. The MPP system also requires significant material usage, with a volume close to 2.0 m³, while the hollow-box floor module has the lowest material usage, at around 0.96 m³. In terms of floor height, the CLT floor system has the highest height at approximately 245 mm, followed by the hollow-box floor module at about 220 mm. The MPP system has the lowest floor height, reaching just below 210 mm. This indicates that the CLT floor requires the most material and has the greatest height, while the hollow-box floor module provides a least material usage. 137 4.4 Conclusion This chapter demonstrates that SCL-based prefabricated hollow-box floor systems offer a feasible and more material-efficient alternative for long-span floor applications. These systems can replace conventional solid wood products like CLT and Glulam. By using parametric modelling and genetic algorithms for structural optimization, the research achieved significant material savings and improved structural performance. The main findings of this study are as follows, • Effective width comparisons showed that the CSA O86 and Kikuchi methods provided similar results, whereas the Eurocode 5 method exhibited more conservative for hollow-box floor systems. • A structural design and optimization tool using parametric modeling and a genetic algorithm was developed, enabling automatic optimization of the cross-section geometry and material selection. This tool allows the structural analysis of hollowbox floors using three different methods, simple beam method according to CSA O86, Gamma method and Shear Analogy method. • MPP-based hollow-box floor module demonstrated significant material efficiency, reducing usage by 67% compared to solid MPP and up to 75% compared to CLT, while maintaining comparable floor height under ULS and deflection-controlled conditions. 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Impact sound insulation performance of floating floor assemblies on mass timber slabs [Thesis, University of Northern British Columbia]. https://unbc.arcabc.ca/islandora/object/unbc:59324 143 Chapter 5 Conclusions and Recommendations 5.1 Conclusions In this study, the experimental investigations were conducted on hollow-box floor systems assembled with SCL materials using the screw-gluing method. An optimization algorithm was also developed for the SCL-based prefabricated hollow-box floor system. Experimental investigations on MPP-based I-section connections for hollow-box floor systems have been conducted to study the feasibility of the screw-gluing method and the factors affecting connection performance. Various factors, including screw types, adhesives, flange and rib widths, screw lengths, screw spacings, and arrangements, were tested. Additionally, a structural optimization algorithm for hollow-box floor modules was developed using Rhino Grasshopper platform to identify the optimal design. This process included comparisons of effective width calculation methods (CSA O86, EC5, and Kikuchi) and structural analysis and design methods (CSA O86, Gamma method, and Shear analogy method). Finally, the optimization results for different spans and widths of both open-type and closed-type hollow-box floor modules were analyzed, aiming to minimize material usage or floor height while ensuring high material utilization. As a result, the following conclusions were drawn: 1. For MPP I-section connections using 6 mm diameter, 100 mm long screws, fully threaded screws demonstrated a stiffness approximately 218% higher than that of partially threaded screws, while partially threaded screws achieved a load-carrying capacity about 11.8% greater than fully threaded screws. Screw-only connections demonstrated insufficient load-carrying capacity and stiffness for effective 144 composite action. In glue-only tests, screws provided adequate pressure for strong bonding, resulting in veneer failure in the flanges. Notably, screw-gluing connections achieved a remarkable stiffness of 112.18 kN/mm and a load-carrying capacity of 90.66 kN, far surpassing both screw-only and glue-only configurations. 2. In specimens with 50 mm flanges and a single row of screws, increasing rib width from 50 mm to 75 mm, 75 mm to 100 mm, 100 mm to 150 mm decreased the shear stress at failure by 9.4%, 27.6% and 16.7%, due to the insufficient pressure distribution to wider ribs. Similarly, increasing flange thickness at the same rib width from 75 mm to 100 mm also had a negative impact, decreased shear stress at failure by 8.0%. 3. Screw length had a minimal effect on connection performance. When comparing 100 mm fully threaded self-tapping screws with 120 mm fully threaded screws in a 50 mm thick flange, and 160 mm fully threaded screws with 120 mm screws in a 75 mm thick flange, no significant difference in results was observed between these groups. However, screw spacing played a critical role, with shorter spacings leading to better performance. In the 50 mm flange group, increasing the screw spacing from 250 mm to 300 mm led to connection failure due to the glue line, while in the 75 mm flange group, screw spacing less than 300 mm provided acceptable connection performance. For wider ribs, the staggered screw arrangement, compared to the single-row arrangement, provided better bonding quality, improving the wood failure percentage from 51% to 79% and enhancing the connection performance by increasing the shear stress at failure by 52.8%. 145 4. Among the methods for calculating effective width and assessing structural performance, the CSA O86 methodology demonstrated comparable outcomes to the Kikuchi method for spans exceeding 3.5 m, whereas the EC5 approach provided more conservative estimates. Furthermore, structural performance assessments using CSA O86, the shear analogy, and the gamma method were generally consistent, with the shear analogy proving to be more conservative in deflection predictions due to its explicit accounting for shear deformation effects. 5. Optimization results demonstrated that SCL-based hollow-box floor systems could achieve up to 70% material savings compared to CLT and MPP solid panel floor systems under ultimate limit state and deflection-controlled conditions. While hollow-box floors required slightly more material than I-joist systems, they provided a 30% reduction in floor height. Furthermore, under vibration-controlled design criteria, material savings of approximately 60% and 50% were achieved compared to CLT and MPP solid panel floors, respectively. Additionally, comparisons of effective width showed that the CSA O86 and Kikuchi methods yielded similar results, while the Eurocode 5 method was more conservative for hollow-box floor systems. 5.2 Recommendations Based on the findings of this research, several areas for further investigation and development are recommended. 1. In Chapter 3, MPP was the only SCL material tested. This limitation restricts the findings to MPP, and additional tests using other SCL materials, such as LVL and LSL, are necessary to validate the broader applicability of the screw-gluing method. 146 2. Future studies should explore the performance of large-scale hollow-box floor modules with screw-gluing method to verify the parametric modelling results, as well as vibration, fire resistance and acoustic performances. 3. It is recommended that further investigations be conducted on the effective width of large-scale hollow-box floor panels. Currently, there exist multiple methodologies for calculating effective width, each yielding significantly divergent results. Further investigation is crucial to comprehensively predict the behaviour of hollow-box floor systems under shear lag effects and to understand the distribution of bending moments. 4. Currently, the optimization algorithm focuses solely on gravitational loads. Future work should consider extending the approach to address in-plane loads for prefabricated floor systems. 5. In the connection tests, the load-carrying capacity of the screw-glued group did not drop as drastically as the glue-only group after adhesive layer failure. Instead, it stabilized at around one-third of the load-carrying capacity, similar to the screwonly group, but with a higher load-carrying capacity. This behavior is likely due to the 'rope effect,' where friction between components contributes to load-carrying capacity. However, the specific details and implications of the 'rope effect' require further investigation. 147 Appendix A Detailed Results of Connection Tests Table A.1 Results of block shear tests Groups Parallel to grain Perpendicular to grain Replicates Number 1 2 3 4 5 6 7 8 9 Average Max Min COV Characteristic value 1 2 3 4 5 6 7 8 9 Average Max Min COV Characteristic value (kN) 8.62 12.63 12.09 11.36 8.14 7.56 12.76 13.03 11.84 10.78 13.03 7.56 0.19 Shear Strength (MPa) 4.45 6.53 6.25 5.87 4.21 3.91 6.59 6.73 6.11 5.57 6.73 3.91 0.19 N/A 3.23 4.03 3.56 3.45 2.61 4.00 8.51 1.78 3.51 4.82 4.20 8.51 1.78 0.44 2.08 1.84 1.78 1.35 2.06 4.40 0.92 1.81 2.49 2.17 4.40 0.92 0.44 N/A 0.11 ‫ܨ‬௠௔௫ 148 Figure A.1 Failure mode for parallel to grain group block shear test 149 Figure A.2 Failure mode for perpendicular to grain group block shear test 150 Table A.2 Detailed results for screw-only groups Groups SF100 SP100 SF120 Replicates Number 1 2 3 Average Max Min COV Characteristic value 1 2 3 Average Max Min COV Characteristic value 1 2 3 Average Max Min COV Characteristic value ‫ܨ‬௠௔௫ (kN) 16.44 21.10 16.74 18.10 21.10 16.44 0.12 ‫ܭ‬௦௘௥ (kN/mm) 16.16 8.35 16.21 13.57 16.21 8.35 0.27 ‫ܭ‬௨ (kN/mm) 7.65 3.74 4.71 5.37 7.65 3.74 0.31 N/A 23.35 16.51 20.83 20.23 23.35 16.51 0.14 3.28 2.87 2.60 2.91 3.28 2.60 0.10 0.66 2.24 1.51 1.32 1.69 2.24 1.32 0.23 N/A 17.33 19.79 20.20 19.11 20.20 17.33 0.07 11.71 30.92 14.39 19.01 30.92 11.71 0.45 N/A Shear Stress (MPa) 1.10 1.41 1.12 1.21 1.41 1.10 0.12 1.56 1.10 1.39 1.35 1.56 1.10 0.14 0.62 4.84 9.15 6.53 6.84 9.15 4.84 0.26 1.16 1.32 1.35 1.27 1.35 1.16 0.07 0.95 151 25 Load (kN) 20 15 Test 1 10 Test 2 5 Test 3 0 0 5 10 15 20 Displacement (mm) 25 30 Figure A.3 Load vs. displacement curve for SF100 group 25 Load (kN) 20 15 Test 1 10 Test 2 5 Test 3 0 0 5 10 15 20 Displacement (mm) 25 30 Figure A.4 Load vs. displacement curve for SP100 group 152 25 Load (kN) 20 15 Test 1 10 Test 2 5 Test 3 0 0 5 10 15 20 Displacement (mm) 25 30 Figure A.5 Load vs. displacement curve for SF120 group Table A.3 Detailed results for glue-only groups Groups GF100 Replicates Number ‫ܨ‬௠௔௫ (kN) ‫ܭ‬௦௘௥ (kN/mm) ‫ܭ‬௨ (kN/mm) 1 68.34 65.74 76.03 Shear Stress (MPa) 4.56 2 84.45 114.88 128.49 5.63 3 86.59 61.38 78.98 5.77 Average 79.79 80.67 94.50 5.32 Max 86.59 114.88 128.49 5.77 Min 68.34 61.38 76.03 4.56 COV 0.10 0.30 0.25 0.10 Characteristic value GP100 N/A 3.22 1 58.31 66.66 79.74 3.89 2 79.03 127.46 143.59 5.27 3 66.19 88.58 107.45 4.41 Average 67.84 94.23 110.26 4.52 Max 79.03 127.46 143.59 5.27 Min 58.31 66.66 79.74 3.89 COV 0.13 0.27 0.24 0.13 Characteristic value N/A 2.33 153 100 Test 1 Load (kN) 80 Test 2 Test 3 60 40 20 0 0 1 2 Displacement (mm) 3 4 Figure A.6 Load vs. displacement curve for GF100 group 100 Test 1 Load (kN) 80 Test 2 Test 3 60 40 20 0 0 0.5 1 1.5 Displacement (mm) 2 2.5 Figure A.7 Load vs. displacement curve for GP100 group 154 Table A.4 Detailed results for different adhesives 50 mm flange groups Groups 50_50_100F 50_50_100P 50_50_PLMAX Replicates Number 1 2 3 4 5 6 Average Max Min COV Characteristic value 1 2 3 4 5 6 Average Max Min COV Characteristic value 1 2 3 Average Max Min COV Characteristic value Fmax (kN) 91.85 79.81 87.08 88.96 105.74 90.54 90.66 105.74 79.81 0.09 Kser (kN/mm) 152.14 94.81 113.80 53.50 127.76 130.19 112.04 152.14 53.50 0.28 Ku (kN/mm) 164.69 94.71 117.27 63.51 98.13 134.76 112.18 164.69 63.51 0.29 N/A 69.40 65.08 83.39 74.75 92.00 85.75 78.39 92.00 65.08 0.12 92.76 123.19 102.30 43.60 85.59 71.72 86.52 123.19 43.60 0.29 4.72 109.13 103.72 118.40 46.29 111.71 81.43 95.11 118.40 46.29 0.26 N/A 106.53 109.35 125.77 113.88 125.77 106.53 0.07 100.21 73.51 90.73 88.15 100.21 73.51 0.13 N/A Shear Stress (MPa) 6.12 5.32 5.81 5.93 7.05 6.04 6.04 7.05 5.32 0.09 4.63 4.34 5.56 4.98 6.13 5.72 5.23 6.13 4.34 0.12 3.61 103.22 88.52 91.96 94.57 103.22 88.52 0.07 7.10 7.29 8.38 7.59 8.38 7.10 0.07 5.41 155 100 Test 1 Test 2 Load (kN) 80 Test 3 Test 4 60 Test 5 Test 6 40 20 0 0 1 2 3 4 5 6 Displacement (mm) Figure A.8 Load vs. displacement curve for 50_50_100F group 120 Test 1 100 Load (kN) Test 2 80 Test 3 Test 4 60 Test 5 Test 6 40 20 0 0 1 2 3 4 Displacement (mm) 5 6 Figure A.9 Load vs. displacement curve for 50_50_100P group 156 140 Test 1 Load (kN) 120 Test 2 100 Test 3 80 60 40 20 0 0 1 2 3 4 Displacement (mm) 5 6 Figure A.10 Load vs. displacement curve for 50_50_PLMAX group 157 Figure A.11 Failure mode of 50_50_100F group 158 Figure A.12 Failure mode of 50_50_100P group 159 Figure A.13 Failure mode of 50_50_PLMAX group 160 Table A.5 Detailed results for different spacing 50 mm flange groups Groups 50_50_100F 50_50_200s 50_50_250s 50F_50R_100L_30 0s Replicates Number 1 2 3 4 5 6 Average Max Min COV Characteristic value 1 2 3 Average Max Min COV Characteristic value 1 2 3 Average Max Min COV Characteristic value 1 2 3 4 5 6 Average Max Min COV Characteristic value Fmax (kN) Kser (kN/mm) Ku (kN/mm) 91.85 79.81 87.08 88.96 105.74 90.54 90.66 105.74 79.81 0.09 152.14 94.81 113.80 53.50 127.76 130.19 112.04 152.14 53.50 0.28 N/A 146.07 69.36 78.16 97.86 146.07 69.36 0.35 N/A 81.74 84.62 83.44 83.26 84.62 81.74 0.01 N/A 80.09 187.82 128.85 170.59 160.12 92.83 136.71 187.82 80.09 0.29 N/A 164.69 94.71 117.27 63.51 98.13 134.76 112.18 164.69 63.51 0.29 106.75 90.99 79.02 92.25 106.75 79.02 0.12 127.57 128.47 117.79 124.61 128.47 117.79 0.04 144.17 112.24 120.52 113.56 122.86 108.42 120.29 144.17 108.42 0.10 135.69 78.64 84.58 99.64 135.69 78.64 0.26 82.02 85.06 96.80 87.96 96.80 82.02 0.07 114.44 175.82 127.26 187.14 174.42 118.24 149.56 187.14 114.44 0.20 Shear Stress (MPa) 6.12 5.32 5.81 5.93 7.05 6.04 6.04 7.05 5.32 0.09 4.72 5.34 4.55 3.95 4.61 5.34 3.95 0.12 2.42 5.10 5.14 4.71 4.98 5.14 4.71 0.04 4.24 5.15 4.01 4.30 4.06 4.39 3.87 4.30 5.15 3.87 0.10 3.22 161 120 100 Test 1 Test 2 Test 3 Load (kN) 80 60 40 20 0 0 2 4 6 Displacement (mm) 8 10 Figure A.14 Load vs. displacement curve for 50_50_200s group 160 140 Test 1 Test 2 Test 3 Load (kN) 120 100 80 60 40 20 0 0 2 4 6 Displacement (mm) 8 10 Figure A.15 Load vs. displacement curve for 50_50_250s group 162 160 test 1 140 test 2 test 3 test 4 Load (kN) 120 100 test 5 test 6 80 60 40 20 0 0 1 2 3 4 Displacement (mm) 5 6 Figure A.16 Load vs. displacement curve for 50F_50R_100L_300s group 163 Figure A.17 Failure mode of 50_50_200s group 164 Figure A.18 Failure mode of 50_50_250 group 165 Figure A.19 Failure mode of 50F_50R_100L_300s group 166 Table A.6 Detailed results of different rib width on 50 mm thick flange group Groups 50_50_100F 50F_75R_100L_150 s 50F_100R_100L_15 0s 50F_150R_100L_15 0s Replicates Number 1 2 3 4 5 6 Average Max Min COV Characteristic value 1 2 3 4 5 6 Average Max Min COV Characteristic value 1 2 3 4 5 6 Average Max Min COV Characteristic value 1 2 3 4 5 6 Average Max Min COV Characteristic value Fmax (kN) Kser (kN/mm) Ku (kN/mm) 91.85 79.81 87.08 88.96 105.74 90.54 90.66 105.74 79.81 0.09 152.14 94.81 113.80 53.50 127.76 130.19 112.04 152.14 53.50 0.28 164.69 94.71 117.27 63.51 98.13 134.76 112.18 164.69 63.51 0.29 122.02 133.61 85.95 119.84 153.49 123.88 123.13 153.49 85.95 0.16 104.76 159.31 169.15 114.16 136.93 136.91 136.87 169.15 104.76 0.17 N/A 188.86 203.89 152.11 40.88 206.13 177.64 161.59 206.13 40.88 0.35 N/A 246.03 137.20 213.18 222.55 166.50 216.71 200.36 246.03 137.20 0.18 N/A 130.51 166.63 174.16 137.11 150.56 163.35 153.72 174.16 130.51 0.10 144.27 126.67 123.00 92.86 109.32 116.80 118.82 144.27 92.86 0.13 163.90 152.39 141.50 118.71 178.80 136.04 148.56 178.80 118.71 0.13 193.17 223.00 194.01 48.40 221.43 197.86 179.65 223.00 48.40 0.33 248.56 158.09 237.21 219.65 189.70 219.00 212.03 248.56 158.09 0.14 Shear Stress (MPa) 6.12 5.32 5.81 5.93 7.05 6.04 6.04 7.05 5.32 0.09 4.72 5.42 5.94 3.82 5.33 6.82 5.51 5.47 6.82 3.82 0.16 3.19 4.81 4.22 4.10 3.10 3.64 3.89 3.96 4.81 3.10 0.13 2.61 3.64 3.39 3.14 2.64 3.97 3.02 3.30 3.97 2.64 0.13 2.20 167 180 test 1 test 2 test 3 test 4 test 5 test 6 160 140 Load (kN) 120 100 80 60 40 20 0 0 2 4 Displacement (mm) 6 8 Figure A.20 Load vs. displacement curve of 50F_75R_100l_150s group 160 140 test 1 test 2 test 3 test 4 test 5 test 6 Load (kN) 120 100 80 60 40 20 0 0 2 4 Displacement (mm) 6 8 Figure A.21 Load vs. displacement curve of 50F_100R_100L_150s group 168 200 180 test 1 test 2 test 3 test 4 test 5 test 6 160 Load (kN) 140 120 100 80 60 40 20 0 0 1 2 3 4 Displacement (mm) 5 6 Figure A.22 Load vs. displacement curve of 50F_150R_100L _150s group 169 Figure A.23 Failure mode of 50F_75R_100L_150s group 170 Figure A.24 Failure mode of 50F_100R_100L_150s group 171 Figure A.25 Failure mode of 50F_150R_100L_150s group 172 Table A.7 Detailed results for 75 mm and 100 mm thick flange with different rib width groups Groups 75F_75R_120L_150 s 75F_75R_160L_150 s 75F_150R_160L_ 150s 100F_150R_160L _150s Replicates Number 1 2 3 4 5 6 Average Max Min COV Characteristic value 1 2 3 4 5 6 Average Max Min COV Characteristic value 1 2 3 4 5 6 Average Max Min COV Characteristic value 1 2 3 4 5 6 Average Max Min COV Characteristic value 1 Fmax (kN) Kser (kN/mm) Ku (kN/mm) 149.32 154.92 119.38 123.67 105.06 126.31 129.78 154.92 105.06 0.13 329.05 225.01 302.12 200.86 220.54 148.55 237.69 329.05 148.55 0.26 N/A 89.35 245.58 141.38 144.66 154.75 120.24 149.33 245.58 89.35 0.32 N/A 253.44 420.96 132.90 156.94 209.91 213.67 231.30 420.96 132.90 0.40 N/A 179.90 384.71 239.19 188.37 212.95 278.35 247.24 384.71 179.90 0.28 N/A 318.50 313.40 247.21 254.55 230.57 202.85 158.00 234.43 313.40 158.00 0.20 146.32 160.70 128.70 119.48 160.99 131.03 141.20 160.99 119.48 0.11 130.99 184.85 145.39 151.41 147.15 155.61 152.57 184.85 130.99 0.11 83.37 192.39 127.87 124.58 159.84 155.16 140.54 192.39 83.37 0.24 264.26 92.76 247.95 166.62 75.13 207.61 141.81 155.31 247.95 75.13 0.39 197.58 484.47 138.76 159.25 211.63 262.57 242.38 484.47 138.76 0.48 176.98 375.06 238.94 139.28 272.12 279.08 246.91 375.06 139.28 0.31 384.82 Shear Stress (MPa) 6.64 6.89 5.31 5.50 4.67 5.61 5.77 6.89 4.67 0.13 3.81 6.50 7.14 5.72 5.31 7.15 5.82 6.28 7.15 5.31 0.11 4.46 2.91 4.11 3.23 3.36 3.27 3.46 3.39 4.11 2.91 0.11 2.46 1.85 4.28 2.84 2.77 3.55 3.45 3.12 4.28 1.85 0.24 1.19 5.87 173 75F_150R_160L_15 0s_s 2 3 4 5 6 Average Max Min COV Characteristic value 244.79 180.29 219.90 259.56 230.52 233.22 264.26 180.29 0.12 332.42 354.16 259.12 436.43 433.05 355.61 436.43 259.12 0.18 N/A 340.12 381.66 310.20 449.39 483.81 391.67 483.81 310.20 0.15 5.44 4.01 4.89 5.77 5.12 5.18 5.87 4.01 0.12 3.58 180 160 test 1 140 test 2 test 3 Load (kN) 120 test 4 100 test 5 80 test 6 60 40 20 0 0 2 4 Displacement (mm) 6 8 Figure A.26 Load vs. displacement curve of 75F_75R_120L_150sgroup 174 180 test 1 Load (kN) 160 test 2 140 test 3 120 test 4 test 5 100 test 6 80 60 40 20 0 0 2 4 6 Displacement (mm) 8 10 Figure A.27 Load vs. displacement curve of 75F_75R_160L_150s group 250 test 1 200 test 2 Load (kN) test 3 150 test 4 test 5 test 6 100 50 0 0 2 4 Displacement (mm) 6 8 Figure A.28 Load vs. displacement curve of 75F_150R_160L_150s group 175 250 test 1 test 2 test 3 test 4 test 5 test 6 Load (kN) 200 150 100 50 0 0 2 4 Displacement (mm) 6 8 Figure A.29 Load vs. displacement curve of 100F_150R_160L_150s group 300 test 1 test 2 test 3 test 4 test 5 test 6 250 Load (kN) 200 150 100 50 0 0 1 2 3 4 Displacement (mm) 5 6 Figure A.30 Load vs. displacement curve of 75F_150R_160L_150s_s group 176 Figure A.31 Failure mode of 75F_75R_120L_150s group 177 Figure A.32 Failure mode of 75F_75R_160L_150s group 178 Figure A.33 Failure mode of 75F_150R_160L_150s group 179 Figure A.34 Failure mode of 100F_150R_160L_150s group 180 Figure A.35 Failure mode of 75F_150R_160L _150s_s group 181 Table A.8 Detailed results for 75 thick flange varying screw spacing groups Groups 75F_75R_160L _150s 75F_75R_225s 75F_75R_300s 75F_150R_300s_s Replicates Number 1 2 3 4 5 6 Average Max Min COV Characteristic value 1 2 3 4 5 6 Average Max Min COV Characteristic value 1 2 3 4 5 6 Average Max Min COV Characteristic value 1 2 3 4 5 6 Average Max Min COV Characteristic value Fmax (kN) Kser (kN/mm) Ku (kN/mm) 146.32 160.70 128.70 119.48 160.99 131.03 141.20 160.99 119.48 0.11 89.35 245.58 141.38 144.66 154.75 120.24 149.33 245.58 89.35 0.32 N/A 290.61 170.00 119.36 267.49 145.91 176.70 195.01 290.61 119.36 0.32 N/A 203.78 207.47 138.73 271.34 303.73 98.12 203.86 303.73 98.12 0.35 N/A 561.22 466.51 320.55 304.24 376.53 370.54 399.93 561.22 304.24 0.22 N/A 92.76 247.95 166.62 75.13 207.61 141.81 155.31 247.95 75.13 0.39 198.19 183.21 140.13 207.63 145.76 135.77 168.45 207.63 135.77 0.17 240.65 186.17 150.66 241.02 250.71 169.34 206.43 250.71 150.66 0.19 437.02 333.73 367.87 355.65 434.95 371.73 383.49 437.02 333.73 0.10 322.62 196.56 153.44 313.51 185.89 171.22 223.87 322.62 153.44 0.30 246.45 246.00 144.15 284.10 313.63 125.92 226.71 313.63 125.92 0.30 618.99 538.77 339.78 380.36 438.27 421.25 456.24 618.99 339.78 0.21 Shear Stress (MPa) 6.50 7.14 5.72 5.31 7.15 5.82 6.28 7.15 5.31 0.11 4.46 5.87 5.43 4.15 6.15 4.32 4.02 4.99 6.15 4.02 0.17 2.80 5.73 4.43 3.59 5.74 5.97 4.03 4.91 5.97 3.59 0.19 2.53 5.20 3.97 4.38 4.23 5.18 4.43 4.57 5.20 3.97 0.10 3.38 182 250 test 1 test 2 test 3 test 4 test 5 test 6 Load (kN) 200 150 100 50 0 0 2 4 6 Displacement (mm) 8 10 Figure A.36 Load vs. displacement curve of 75F_75R_225s group 300 test 1 test 2 test 3 test 4 test 5 test 6 250 Load (kN) 200 150 100 50 0 0 2 4 6 Displacement (mm) 8 10 Figure A.37 Load vs. displacement curve of 75F_75R_300s group 183 500 450 test 1 400 test 2 test 3 Load (kN) 350 test 4 300 test 5 250 test 6 200 150 100 50 0 0 2 4 6 8 Displacement (mm) 10 12 14 Figure A.38 Load vs. displacement curve of 75F_150R_300s_s group 184 Figure A.39 Failure mode of 75F_75R_255s group 185 Figure A.40 Failure mode of 75F_75R_300s group 186 Figure A.41 Failure mode of 75F_150R_300s_s group 187 Table A.9 Detailed results of different screw arrangement with 75 mm thick flange group Groups 75F_150R_160L_15 0s_s 75F_150R_300s_s Replicates Number 1 2 3 4 5 6 Average Max Min COV Characteristic value 1 2 3 4 5 6 Average Max Min COV Characteristic value Fmax (kN) 264.26 244.79 180.29 219.90 259.56 230.52 233.22 264.26 180.29 0.12 437.02 333.73 367.87 355.65 434.95 371.73 383.49 437.02 333.73 0.10 Kser (kN/mm) 318.50 332.42 354.16 259.12 436.43 433.05 355.61 436.43 259.12 0.18 N/A 561.22 466.51 320.55 304.24 376.53 370.54 399.93 561.22 304.24 0.22 N/A Ku (kN/mm) 384.82 340.12 381.66 310.20 449.39 483.81 391.67 483.81 310.20 0.15 618.99 538.77 339.78 380.36 438.27 421.25 456.24 618.99 339.78 0.21 Shear Stress (MPa) 5.87 5.44 4.01 4.89 5.77 5.12 5.18 5.87 4.01 0.12 3.58 5.20 3.97 4.38 4.23 5.18 4.43 4.57 5.20 3.97 0.10 3.38 188 Appendix B Objective Function Python Code for Genetic Algorithm Code B.1 Python Code for deflection-controlled condition # check if bending_ratio, shear_ratio, deflection ratio <1 if bending_ratio <= 1 and shear_ratio <= 1 and deflection_ratio <= 0.95 and total_height <= 500: objective = (1-deflection_ratio) * 100 + total_height / 100 + volume * 10 else: # if anyone > 1, return a large number objective = 9999 # output a = objective Code B.2 Python Code for vibration-controlled condition # check if bending_ratio, shear_ratio, deflection ratio <1 and deflection criteria if bending_ratio <= 1 and shear_ratio <= 1 and deflection_ratio <= 0.95 and total_height <= 500 and frequency / deflection_f ** 0.44 >= 18.7: objective = (1-deflection_ratio) * 100 + total_height / 100 + volume * 10 else: # if anyone > 1, return a large number objective = 9999 # output a = objective 189 Appendix C ANOVA Result for Each Group Table C.1 ANOVA result for serviceability stiffness of glue-only tests ANOVA Kser Sum of Squares df Mean Square F Sig. Between Groups 276.082 1 276.082 .302 .612 Within Groups 3661.593 4 915.398 Total 3937.675 5 Table C.2 ANOVA result for ultimate stiffness of glue-only tests ANOVA Ku Sum of Squares df Mean Square F Sig. Between Groups 372.566 1 372.566 .393 .565 Within Groups 3787.587 4 946.897 Total 4160.153 5 190 Table C.3ANOVA result for shear stress of glue-only tests ANOVA Shear stress Sum of Squares df Mean Square F Sig. Between Groups 2.747 2 1.373 1.393 .286 Within Groups 11.829 12 .986 Total 14.576 14 Multiple Comparisons Dependent Variable: shear stress LSD (I) Glue-Only GF100 GP100 Shear Strength (J) Glue-Only Mean Difference (I-J) Std. Error Sig. GP100 .79667 .81065 Shear Strength -.30778 GF100 95% Confidence Interval Lower Bound Upper Bound .345 -.9696 2.5629 .66189 .650 -1.7499 1.1344 -.79667 .81065 .345 -2.5629 .9696 Shear Strength -1.10444 .66189 .121 -2.5466 .3377 GF100 .30778 .66189 .650 -1.1344 1.7499 GP100 1.10444 .66189 .121 -.3377 2.5466 191 Table C.4 ANOVA result for serviceability stiffness of different screw types and adhesives on 50 mm thick flange groups ANOVA Kser Sum of Squares df Mean Square F Sig. Between Groups 2249.075 2 1124.537 1.353 .295 Within Groups 9972.548 12 831.046 Total 12221.623 14 Multiple Comparisons Dependent Variable: Kser LSD (I) Screw_150 100F 100P PLMAX (J) Screw_150 Mean Difference (I-J) Std. Error Sig. 100P 25.50667 16.64377 PLMAX 23.88333 100F 95% Confidence Interval Lower Bound Upper Bound .151 -10.7570 61.7703 20.38438 .264 -20.5304 68.2971 -25.50667 16.64377 .151 -61.7703 10.7570 PLMAX -1.62333 20.38438 .938 -46.0371 42.7904 100F -23.88333 20.38438 .264 -68.2971 20.5304 100P 1.62333 20.38438 .938 -42.7904 46.0371 192 Table C.5 ANOVA result for ultimate stiffness of different screw types and adhesives on 50 mm thick flange groups ANOVA Ku Sum of Squares df Mean Square F Sig. Between Groups 1071.478 2 535.739 .647 .541 Within Groups 9941.885 12 828.490 Total 11013.363 14 Multiple Comparisons Dependent Variable: Ku LSD (I) Screw_150 100F 100P PLMAX (J) Screw_150 Mean Difference (I-J) Std. Error Sig. 100P 17.06500 16.61817 PLMAX 17.61167 100F 95% Confidence Interval Lower Bound Upper Bound .325 -19.1429 53.2729 20.35302 .404 -26.7337 61.9571 -17.06500 16.61817 .325 -53.2729 19.1429 PLMAX .54667 20.35302 .979 -43.7987 44.8921 100F -17.61167 20.35302 .404 -61.9571 26.7337 100P -.54667 20.35302 .979 -44.8921 43.7987 193 Table C.6 ANOVA result for shear stress of different screw types and adhesives on 50 mm thick flange groups ANOVA Shear stress Sum of Squares df Mean Square Between Groups 12.069 3 4.023 Within Groups 14.919 20 .746 Total 26.988 23 F Sig. 5.393 .007 Multiple Comparisons Dependent Variable: Shear stress LSD (I) Screw_150 100F 100P PLMAX Shear Strength (J) Screw_150 Mean Difference (I-J) Std. Error Sig. 100P .81833 .49864 PLMAX -1.54500* Shear Strength 95% Confidence Interval Lower Bound Upper Bound .116 -.2218 1.8585 .61071 .020 -2.8189 -.2711 .41722 .45520 .370 -.5323 1.3667 100F -.81833 .49864 .116 -1.8585 .2218 PLMAX -2.36333* .61071 .001 -3.6373 -1.0894 Shear Strength -.40111 .45520 .389 -1.3506 .5484 100F 1.54500* .61071 .020 .2711 2.8189 100P 2.36333* .61071 .001 1.0894 3.6373 Shear Strength 1.96222* .57578 .003 .7612 3.1633 100F -.41722 .45520 .370 -1.3667 .5323 100P .40111 .45520 .389 -.5484 1.3506 PLMAX -1.96222* .57578 .003 -3.1633 -.7612 *. The mean difference is significant at the 0.05 level. 194 Table C.7 ANOVA result for serviceability stiffness of different spacing on 50 mm thick flange groups ANOVA Kser Sum of Squares df Mean Square F Sig. Between Groups 6719.859 3 2239.953 1.656 .222 Within Groups 18941.362 14 1352.954 Total 25661.221 17 Multiple Comparisons Dependent Variable: Kser LSD (I) Screw_spacings 150 200 250 300 (J) Screw_spacings Mean Difference (I-J) Std. Error Sig. 200 14.17000 26.00918 250 28.76667 300 95% Confidence Interval Lower Bound Upper Bound .594 -41.6141 69.9541 26.00918 .287 -27.0175 84.5508 -24.68333 21.23640 .265 -70.2309 20.8642 150 -14.17000 26.00918 .594 -69.9541 41.6141 250 14.59667 30.03281 .634 -49.8173 79.0106 300 -38.85333 26.00918 .157 -94.6375 16.9308 150 -28.76667 26.00918 .287 -84.5508 27.0175 200 -14.59667 30.03281 .634 -79.0106 49.8173 300 -53.45000 26.00918 .059 -109.2341 2.3341 150 24.68333 21.23640 .265 -20.8642 70.2309 200 38.85333 26.00918 .157 -16.9308 94.6375 250 53.45000 26.00918 .059 -2.3341 109.2341 195 Table C.8 ANOVA result for ultimate stiffness of different spacing on 50 mm thick flange groups ANOVA Ku Sum of Squares df Mean Square F Sig. Between Groups 9891.187 3 3297.062 3.373 .049 Within Groups 13685.192 14 977.514 Total 23576.379 17 Multiple Comparisons Dependent Variable: Ku LSD (I) Screw_spacings 150 200 250 300 (J) Screw_spacings Mean Difference (I-J) Std. Error Sig. 200 12.54167 22.10785 250 24.21833 300 95% Confidence Interval Lower Bound Upper Bound .579 -34.8749 59.9583 22.10785 .292 -23.1983 71.6349 -37.37500 18.05098 .057 -76.0905 1.3405 150 -12.54167 22.10785 .579 -59.9583 34.8749 250 11.67667 25.52794 .654 -43.0753 66.4287 300 -49.91667* 22.10785 .040 -97.3333 -2.5001 150 -24.21833 22.10785 .292 -71.6349 23.1983 200 -11.67667 25.52794 .654 -66.4287 43.0753 300 -61.59333* 22.10785 .015 -109.0099 -14.1767 150 37.37500 18.05098 .057 -1.3405 76.0905 200 49.91667* 22.10785 .040 2.5001 97.3333 250 61.59333* 22.10785 .015 14.1767 109.0099 *. The mean difference is significant at the 0.05 level. 196 Table C.9 ANOVA result for shear stress of different spacing on 50 mm thick flange groups ANOVA Shear stress Sum of Squares df Mean Square F Sig. Between Groups 11.957 4 2.989 4.789 .006 Within Groups 13.733 22 .624 Total 25.689 26 Multiple Comparisons Dependent Variable: Shear stress (I) Screw_spacings 150 200 250 300 Shear Strength (J) Screw_spacings Mean Difference (I-J) Std. Error Sig. 200 1.43167* .55867 250 1.06167 300 95% Confidence Interval Lower Bound Upper Bound .018 .2731 2.5903 .55867 .071 -.0969 2.2203 1.74833* .45615 .001 .8023 2.6943 Shear Strength .41722 .41641 .327 -.4464 1.2808 150 -1.43167* .55867 .018 -2.5903 -.2731 250 -.37000 .64510 .572 -1.7079 .9679 300 .31667 .55867 .577 -.8419 1.4753 Shear Strength -1.01444 .52672 .067 -2.1068 .0779 150 -1.06167 .55867 .071 -2.2203 .0969 200 .37000 .64510 .572 -.9679 1.7079 300 .68667 .55867 .232 -.4719 1.8453 Shear Strength -.64444 .52672 .234 -1.7368 .4479 150 -1.74833* .45615 .001 -2.6943 -.8023 200 -.31667 .55867 .577 -1.4753 .8419 250 -.68667 .55867 .232 -1.8453 .4719 Shear Strength -1.33111* .41641 .004 -2.1947 -.4675 150 -.41722 .41641 .327 -1.2808 .4464 200 1.01444 .52672 .067 -.0779 2.1068 250 .64444 .52672 .234 -.4479 1.7368 300 1.33111* .41641 .004 .4675 2.1947 197 Table C.10 ANOVA result for serviceability stiffness of different rib width on 50 mm thick flange group ANOVA Kser Sum of Squares df Mean Square F Sig. Between Groups 25529.662 3 8509.887 4.652 .013 Within Groups 36584.443 20 1829.222 Total 62114.105 23 Multiple Comparisons Dependent Variable: Kser LSD (I) Rib_width 50 75 100 150 (J) Rib_width Mean Difference (I-J) Std. Error Sig. 75 -24.83667 24.69293 100 -49.55167 150 95% Confidence Interval Lower Bound Upper Bound .327 -76.3452 26.6719 24.69293 .058 -101.0602 1.9569 -88.32833* 24.69293 .002 -139.8369 -36.8198 50 24.83667 24.69293 .327 -26.6719 76.3452 100 -24.71500 24.69293 .329 -76.2235 26.7935 150 -63.49167* 24.69293 .018 -115.0002 -11.9831 50 49.55167 24.69293 .058 -1.9569 101.0602 75 24.71500 24.69293 .329 -26.7935 76.2235 150 -38.77667 24.69293 .132 -90.2852 12.7319 50 88.32833* 24.69293 .002 36.8198 139.8369 75 63.49167* 24.69293 .018 11.9831 115.0002 100 38.77667 24.69293 .132 -12.7319 90.2852 *. The mean difference is significant at the 0.05 level. 198 Table C.11 ANOVA result for ultimate stiffness of different rib width on 50 mm thick flange group ANOVA Ku Sum of Squares df Mean Square F Sig. Between Groups 32056.008 3 10685.336 6.155 .004 Within Groups 34721.446 20 1736.072 Total 66777.454 23 Multiple Comparisons Dependent Variable: Ku LSD (I) Rib_width 50 75 100 150 (J) Rib_width Mean Difference (I-J) Std. Error Sig. 75 -41.54167 24.05599 100 -67.46667* 150 95% Confidence Interval Lower Bound Upper Bound .100 -91.7216 8.6383 24.05599 .011 -117.6466 -17.2867 -99.85667* 24.05599 .000 -150.0366 -49.6767 50 41.54167 24.05599 .100 -8.6383 91.7216 100 -25.92500 24.05599 .294 -76.1049 24.2549 150 -58.31500* 24.05599 .025 -108.4949 -8.1351 50 67.46667* 24.05599 .011 17.2867 117.6466 75 25.92500 24.05599 .294 -24.2549 76.1049 150 -32.39000 24.05599 .193 -82.5699 17.7899 50 99.85667* 24.05599 .000 49.6767 150.0366 75 58.31500* 24.05599 .025 8.1351 108.4949 100 32.39000 24.05599 .193 -17.7899 82.5699 *. The mean difference is significant at the 0.05 level. 199 Table C.12 ANOVA result for shear stress of different rib width on 50 mm thick flange group ANOVA Shear stress Sum of Squares df Mean Square F Sig. Between Groups 35.187 4 8.797 12.863 .000 Within Groups 19.149 28 .684 Total 54.337 32 Multiple Comparisons Dependent Variable: Shear stress LSD (I) Rib_width 50 75 100 150 Shear strength (J) Rib_width Mean Difference (I-J) Std. Error Sig. 75 .57167 .47746 100 2.08500* 150 95% Confidence Interval Lower Bound Upper Bound .241 -.4064 1.5497 .47746 .000 1.1070 3.0630 2.74500* .47746 .000 1.7670 3.7230 Shear strength .41722 .43586 .347 -.4756 1.3100 50 -.57167 .47746 .241 -1.5497 .4064 100 1.51333* .47746 .004 .5353 2.4914 150 2.17333* .47746 .000 1.1953 3.1514 Shear strength -.15444 .43586 .726 -1.0473 .7384 50 -2.08500* .47746 .000 -3.0630 -1.1070 75 -1.51333* .47746 .004 -2.4914 -.5353 150 .66000 .47746 .178 -.3180 1.6380 Shear strength -1.66778* .43586 .001 -2.5606 -.7750 50 -2.74500* .47746 .000 -3.7230 -1.7670 75 -2.17333* .47746 .000 -3.1514 -1.1953 100 -.66000 .47746 .178 -1.6380 .3180 Shear strength -2.32778* .43586 .000 -3.2206 -1.4350 50 -.41722 .43586 .347 -1.3100 .4756 75 .15444 .43586 .726 -.7384 1.0473 100 1.66778* .43586 .001 .7750 2.5606 150 2.32778* .43586 .000 1.4350 3.2206 200 Table C.13 ANOVA result for serviceability stiffness of different rib width on 75- and 100-mm thick flange group ANOVA df 4 Kser Between Groups Sum of Squares 129791.231 Within Groups 141381.829 25 Total 271173.060 29 Mean Square 32447.808 F 5.738 Sig. .002 5655.273 Multiple Comparisons Dependent Variable: Kser LSD (I) rib_width_75_100 75_75_120l_150s 75_75_160l_150s 75_150_160l_150s 100_150_160l_150s 75_150_160l_150s_s (J) rib_width_75_100 Mean Difference (IJ) Std. Error Sig. 95% Confidence Interval 75_75_160l_150s 88.36167 43.41764 75_150_160l_150s 6.38500 100_150_160l_150s Lower Bound Upper Bound .053 -1.0586 177.7820 43.41764 .884 -83.0353 95.8053 -9.55667 43.41764 .828 -98.9770 79.8636 75_150_160l_150s_s -117.92500* 43.41764 .012 -207.3453 -28.5047 75_75_120l_150s -88.36167 43.41764 .053 -177.7820 1.0586 75_150_160l_150s -81.97667 43.41764 .071 -171.3970 7.4436 100_150_160l_150s -97.91833* 43.41764 .033 -187.3386 -8.4980 75_150_160l_150s_s -206.28667* 43.41764 .000 -295.7070 -116.8664 75_75_120l_150s -6.38500 43.41764 .884 -95.8053 83.0353 75_75_160l_150s 81.97667 43.41764 .071 -7.4436 171.3970 100_150_160l_150s -15.94167 43.41764 .717 -105.3620 73.4786 75_150_160l_150s_s -124.31000* 43.41764 .008 -213.7303 -34.8897 75_75_120l_150s 9.55667 43.41764 .828 -79.8636 98.9770 75_75_160l_150s 97.91833* 43.41764 .033 8.4980 187.3386 75_150_160l_150s 15.94167 43.41764 .717 -73.4786 105.3620 75_150_160l_150s_s -108.36833* 43.41764 .020 -197.7886 -18.9480 75_75_120l_150s 117.92500* 43.41764 .012 28.5047 207.3453 75_75_160l_150s 206.28667* 43.41764 .000 116.8664 295.7070 75_150_160l_150s 124.31000* 43.41764 .008 34.8897 213.7303 100_150_160l_150s 108.36833* 43.41764 .020 18.9480 197.7886 201 Table C.14 ANOVA result for ultimate stiffness of different rib width on 75- and 100-mm thick flange group ANOVA df Ku Sum of Squares Mean Square F Sig. Between Groups 175556.563 4 43889.141 6.411 .001 Within Groups 171136.695 25 6845.468 Total 346693.258 29 Multiple Comparisons Dependent Variable: Ku LSD (I) rib_width_75_100 75_75_120l_150s 75_75_160l_150s 75_150_160l_150s 100_150_160l_150s 75_150_160l_150s_s (J) rib_width_75_100 Mean Difference (IJ) Std. Error Sig. 95% Confidence Interval 75_75_160l_150s 79.11667 47.76843 75_150_160l_150s -7.94667 100_150_160l_150s Lower Bound Upper Bound .110 -19.2643 177.4976 47.76843 .869 -106.3276 90.4343 -12.48000 47.76843 .796 -110.8609 85.9009 75_150_160l_150s_s -157.23667* 47.76843 .003 -255.6176 -58.8557 75_75_120l_150s -79.11667 47.76843 .110 -177.4976 19.2643 75_150_160l_150s -87.06333 47.76843 .080 -185.4442 11.3176 100_150_160l_150s -91.59667 47.76843 .067 -189.9776 6.7843 75_150_160l_150s_s -236.35333* 47.76843 .000 -334.7343 -137.9724 75_75_120l_150s 7.94667 47.76843 .869 -90.4343 106.3276 75_75_160l_150s 87.06333 47.76843 .080 -11.3176 185.4442 100_150_160l_150s -4.53333 47.76843 .925 -102.9143 93.8476 75_150_160l_150s_s -149.29000* 47.76843 .004 -247.6709 -50.9091 75_75_120l_150s 12.48000 47.76843 .796 -85.9009 110.8609 75_75_160l_150s 91.59667 47.76843 .067 -6.7843 189.9776 75_150_160l_150s 4.53333 47.76843 .925 -93.8476 102.9143 75_150_160l_150s_s -144.75667* 47.76843 .006 -243.1376 -46.3757 75_75_120l_150s 157.23667* 47.76843 .003 58.8557 255.6176 75_75_160l_150s 236.35333* 47.76843 .000 137.9724 334.7343 75_150_160l_150s 149.29000* 47.76843 .004 50.9091 247.6709 100_150_160l_150s 144.75667* 47.76843 .006 46.3757 243.1376 202 Table C.15 ANOVA result for shear stress of different rib width on 75- and 100-mm thick flange group ANOVA Shear stress Sum of Squares df Mean Square F Sig. Between Groups 53.625 5 10.725 15.308 .000 Within Groups 23.119 33 .701 Total 76.744 38 Multiple Comparisons Dependent Variable: Shear stress LSD (I) rib_width_75_100 75_75_120l_150s 75_75_160l_150s 75_150_160l_150s 100_150_160l_150s (J) rib_width_75_100 Mean Difference (IJ) Std. Error Sig. 95% Confidence Interval 75_75_160l_150s -.50333 .48325 75_150_160l_150s 2.38000* 100_150_160l_150s Lower Bound Upper Bound .305 -1.4865 .4798 .48325 .000 1.3968 3.3632 2.64667* .48325 .000 1.6635 3.6298 75_150_160l_150s_s .58667 .48325 .233 -.3965 1.5698 Shear strength .14222 .44114 .749 -.7553 1.0397 75_75_120l_150s .50333 .48325 .305 -.4798 1.4865 75_150_160l_150s 2.88333* .48325 .000 1.9002 3.8665 100_150_160l_150s 3.15000* .48325 .000 2.1668 4.1332 75_150_160l_150s_s 1.09000* .48325 .031 .1068 2.0732 Shear strength .64556 .44114 .153 -.2520 1.5431 75_75_120l_150s -2.38000* .48325 .000 -3.3632 -1.3968 75_75_160l_150s -2.88333* .48325 .000 -3.8665 -1.9002 100_150_160l_150s .26667 .48325 .585 -.7165 1.2498 75_150_160l_150s_s -1.79333* .48325 .001 -2.7765 -.8102 Shear strength -2.23778* .44114 .000 -3.1353 -1.3403 75_75_120l_150s -2.64667* .48325 .000 -3.6298 -1.6635 75_75_160l_150s -3.15000* .48325 .000 -4.1332 -2.1668 75_150_160l_150s -.26667 .48325 .585 -1.2498 .7165 203 75_150_160l_150s_s Shear strength 75_150_160l_150s_s -2.06000* .48325 .000 -3.0432 -1.0768 Shear strength -2.50444* .44114 .000 -3.4020 -1.6069 75_75_120l_150s -.58667 .48325 .233 -1.5698 .3965 75_75_160l_150s -1.09000* .48325 .031 -2.0732 -.1068 75_150_160l_150s 1.79333* .48325 .001 .8102 2.7765 100_150_160l_150s 2.06000* .48325 .000 1.0768 3.0432 Shear strength -.44444 .44114 .321 -1.3420 .4531 75_75_120l_150s -.14222 .44114 .749 -1.0397 .7553 75_75_160l_150s -.64556 .44114 .153 -1.5431 .2520 75_150_160l_150s 2.23778* .44114 .000 1.3403 3.1353 100_150_160l_150s 2.50444* .44114 .000 1.6069 3.4020 75_150_160l_150s_s .44444 .44114 .321 -.4531 1.3420 *. The mean difference is significant at the 0.05 level. 204 Table C.16 ANOVA result for serviceability stiffness of different spacing on 75 mm thick flange group ANOVA Kser Sum of Squares df Mean Square F Sig. Between Groups 10279.016 2 5139.508 1.146 .344 Within Groups 67272.948 15 4484.863 Total 77551.964 17 Multiple Comparisons Dependent Variable: Kser LSD (I) spacing_75 150 225 300 (J) spacing_75 Mean Difference (I-J) Std. Error Sig. 225 -45.68500 38.66464 300 -54.53500 150 95% Confidence Interval Lower Bound Upper Bound .256 -128.0967 36.7267 38.66464 .179 -136.9467 27.8767 45.68500 38.66464 .256 -36.7267 128.0967 300 -8.85000 38.66464 .822 -91.2617 73.5617 150 54.53500 38.66464 .179 -27.8767 136.9467 225 8.85000 38.66464 .822 -73.5617 91.2617 205 Table C.17 ANOVA result for ultimate stiffness of different spacing on 75 mm thick flange group ANOVA Ku Sum of Squares df Mean Square F Sig. Between Groups 19611.514 2 9805.757 1.879 .187 Within Groups 78261.824 15 5217.455 Total 97873.338 17 Multiple Comparisons Dependent Variable: Ku LSD (I) spacing_75 150 225 300 (J) spacing_75 Mean Difference (I-J) Std. Error Sig. 225 -68.56000 41.70314 300 -71.39500 150 95% Confidence Interval Lower Bound Upper Bound .121 -157.4481 20.3281 41.70314 .107 -160.2831 17.4931 68.56000 41.70314 .121 -20.3281 157.4481 300 -2.83500 41.70314 .947 -91.7231 86.0531 150 71.39500 41.70314 .107 -17.4931 160.2831 225 2.83500 41.70314 .947 -86.0531 91.7231 206 Table C.18 ANOVA result for shear stress of different spacing on 75 mm thick flange group ANOVA Shear stress Sum of Squares df Mean Square F Sig. Between Groups 7.327 3 2.442 2.482 .086 Within Groups 22.633 23 .984 Total 29.959 26 Multiple Comparisons Dependent Variable: Shear stress LSD (I) spacing_75 150 225 300 Shear Strength (J) spacing_75 Mean Difference (I-J) Std. Error Sig. 225 1.28333* .57272 300 1.35833* Shear Strength 95% Confidence Interval Lower Bound Upper Bound .035 .0986 2.4681 .57272 .026 .1736 2.5431 .64556 .52282 .229 -.4360 1.7271 150 -1.28333* .57272 .035 -2.4681 -.0986 300 .07500 .57272 .897 -1.1098 1.2598 Shear Strength -.63778 .52282 .235 -1.7193 .4438 150 -1.35833* .57272 .026 -2.5431 -.1736 225 -.07500 .57272 .897 -1.2598 1.1098 Shear Strength -.71278 .52282 .186 -1.7943 .3688 150 -.64556 .52282 .229 -1.7271 .4360 225 .63778 .52282 .235 -.4438 1.7193 300 .71278 .52282 .186 -.3688 1.7943 *. The mean difference is significant at the 0.05 level. 207 Table C.19 ANOVA result for serviceability stiffness of different screw arrangement on 75 mm thick flange group ANOVA Kser Sum of Squares df Mean Square F Sig. Between Groups 5892.344 1 5892.344 .829 .384 Within Groups 71072.630 10 7107.263 Total 76964.974 11 Table C.20 ANOVA result for ultimate stiffness of different screw arrangement on 75 mm thick flange group ANOVA Kser Sum of Squares df Mean Square F Sig. Between Groups 5892.344 1 5892.344 .829 .384 Within Groups 71072.630 10 7107.263 Total 76964.974 11 208 Table C.21 ANOVA result for shear stress of different screw arrangement on 75 mm thick flange group ANOVA Shear stress Sum of Squares df Mean Square F Sig. Between Groups 4.068 2 2.034 2.686 .095 Within Groups 13.630 18 .757 Total 17.697 20 Multiple Comparisons Dependent Variable: Shear stress LSD (I) staggered group 150s 300s Shear Strength (J) staggered group Mean Difference (I-J) Std. Error Sig. 300s .61833 .50239 Shear Strength -.44444 150s 95% Confidence Interval Lower Bound Upper Bound .234 -.4372 1.6738 .45862 .345 -1.4080 .5191 -.61833 .50239 .234 -1.6738 .4372 Shear Strength -1.06278* .45862 .032 -2.0263 -.0992 150s .44444 .45862 .345 -.5191 1.4080 300s 1.06278* .45862 .032 .0992 2.0263 *. The mean difference is significant at the 0.05 level. 209