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LeTruongDiHa TV pdf M10213801 Numerical Study on Optimization of Wooden Steel Hybrid Beams Based on Shape Factor of Steel Component Le Truong Di Ha Meng– Ting Tsai Ph D Shen – Guan Shih Ph D i ii Abst[.]
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of buckling on individual activity of steel and thus leads to more efficient hybrid steel-timber structural systems in the future As traditional way, designing a beam has been simply achieved and the geometry of the timber-steel-hybrid beam is really ideal advantageous to improve their work According to the first generation of timber-steel-hybrid beams called “Flitch-beams”, the aim of this study is to follow and develop a method in order to provide more efficient shape factor performance for Flitchbeams Basing on the main concept of data tables from National Association of Home Builders of the United States (NAHB) builders’ beam showing the capacity of flitch-beams with variety sizes, this study chooses one fixed pattern of wood pieces (2x8’’) inserts by a straight steel-plate-core to evaluate and the optimized morphology among the variety cross-sections is then applied in to the beam as replacing for straight steel-plate-core The three types Rectangular-section, Hollowsection and I-section which base on the same area condition and material should be assessed properly The first result shows that the comparison relies on numerical of Maximum bending stress ( s ) and deflection at mid span Following this, the new flitch beam is re-calculated and the results in comparison with the NAHB builders’ beam pattern Similarly, the final result indicates that the coordination of optimized steel core is more advantageous than the pattern beam Keywords: efficient hybrid steel-timber structural system, Flitch-beams, cross-sections, shape factor, optimized morphology, numerical ii Acknowledgement I would like to thank all the people who helped me to finish this thesis First, I would like to express my deep gratitude to my advisors Professor Shen – Guan Shih, Professor Meng – Ting Tsai for their valuable guidance and ideas Their valuable guidance and enthusiasm overcome many problems as well as encourage me in the process of finishing this thesis I also would like to thank my parents who support me not only material side but also spiritual side throughout my life Finally, I would like to thank the help of Architecture Department, classmates, and my friends who always give me encouragements and supports during my research iii Content Abstract i Acknowledgement iii Content iv List of Figures viii List of Tables xi List of Abbreviations xiii Chapter Introduction 1.1 Background and motivation 1.2 Objective and Research Outcomes 1.3 Research Approach 1.3.1 Comparison of shape factors 1.3.2 Appling shape factor to optimize the Flitch beams 1.4 Chapter Overview Chapter Literature review iv 2.1 Case study of hybridization 2.1.1 System level hybridization 2.1.2 Component level hybridization 10 2.1.3 The combination of System level and component level hybridization 13 2.2 Relevant research 14 2.2.1 A design optimum cross-sections using a multi-objective evolutionary algorithm 14 2.2.2 Optimal cross-section alternatives with comparison via a mathematical method based on steel shape factor 14 2.2.3 National Association of Home Builders of the United States (NAHB) builders’ beam 15 Chapter Numerical methodology of shape factor 3.1 17 Relevant formula and definitions review 17 3.1.1 Moment of inertia (I) 17 3.1.2 Section modulus (S) 17 3.1.2 Maximum bending stress at mid span ( s ) and maximum deflection at D mid span ( l ) 18 3.2 3.3 Shape factors 19 3.2.1 Cross-Section shapes 19 3.2.2 Identifying Cross-Section method 20 Material efficiency 22 v 3.3.1 Cross-Section profiles 22 3.3.2 Application methods of calculation and result tables 26 3.4 Shape factor study 28 3.5 Conclusion 36 Chapter Flitch Beam - Data Acquisition 4.1 4.2 38 Introduction of NAHB builders’ beam 38 4.1.1 Conversion Factors for cases of symmetrical concentrated load 39 4.1.2 Flitch plate beam (NAHB) description 40 4.1.3 Design table information 41 Issue definition 43 4.2.1 Buckling 43 4.2.2 The impact of loads differ on different shape factor 46 4.2.3 The maximum span efficiency of the beam applying optimal steel core 48 4.3 4.4 Study Flitch plate beam description 49 4.3.1 Study Flitch plate beam structure 49 4.3.2 Study Flitch plate beam cross section 49 4.3.3 Material properties 52 The relevant formula and definitions review 54 4.4.1 Bending stress conditions 54 4.4.2 Deflection conditions 56 vi 4.5 Data acquisition 58 4.5.1 4.6 Identify the maximum load for the Study beam 58 Comparison of acquisition 61 4.6.1 Design Load Comparison bases on the Steel thickness 62 4.6.2 Design Load Comparison bases on the span of the beam 14 Chapter The ratio of load comparison and analysis on the equation 63 5.1 Comparison of the ratio of Load 63 5.1.1 5.2 Design Load Comparison bases on the steel thickness and span 63 Equation analysis 65 5.2.1 The ratio values of Design Load description conversion into a quadratic polynomial 65 5.2.2 K value and its implications 65 5.3 Douglas Fir – Larch and California Redwood 69 5.4 Summary of research methodology 71 Chapter Conclusion 75 6.1 Summary of finding 75 6.2 Future work 78 Reference 80 vii List of Figures Figure 1.1 The comparison between km2 of Forest and Urban area in wood storage Figure 1.2 Original beam (a) and study beam after applying study method (b) Figure 1.3 Research Organization Figure 1.4 Thesis structure Figure 2.1 Shimouma Apartment, Tokyo, Japan Figure 2.2 Design proposal of plan-mixed hybrid timber structural system 10 Figure 2.3 The specimens of wood–steel plate beam 11 Figure 2.4 Cross section of hybrid beams tested 12 Figure 2.5 Assembly process of completed timber-steel hybrid beam 12 Figure 2.6 The samples consist of glue-laminated beams and cold-formed U steel profiles 12 Figure 2.7 Kanazawa M building, Japan 13 Figure 2.8 Cross sections of column, beam, and brace 13 Figure 2.9 Type of the hybird beam that have been approved by Athourities 14 Figure 2.10 Optimum cross section for cases with variety of shape factors 24 Figure 2.11 Optimization of the Cross-Section of a Beam Subjected to Bending Load 15 Figure 2.12 Yield strength and Deflection of different profiles 15 Figure 2.13 Flitch plate and steel I beam 16 Figure 3.1 Cross-Section profiles to be examined 20 Figure 3.2 Flow of numerical methodology 21 Figure 3.3 Rectangular Section 22 Figure 3.4 Hollow-Section and dimensions after being modified 23 viii Figure 3.5 I-Section and dimensions after being modified by steps 24 Figure 3.6 I-Section and dimensions after being modified by steps 25 Figure 3.7 Hollow Section after being modified by Splitting geometric method 29 Figure 3.8 I Section after being modified by Splitting geometric method 30 Figure 3.9 Additional method I Section 36 Figure 4.1 NAHB’s Uniform load 39 Figure 4.2 NAHB’s Five concentrated loads 39 Figure 4.3 Converson factors for all conditions of symmetrical concentrated loads 40 Figure 4.4 The Flitch beam basic fastener layout 41 Figure 4.5 The Flitch beam basic fastener layout in details 41 Figure 4.6 Buckling in steel plate 44 Figure 4.7 Typical flitch beams 44 Figure 4.8 Glulam member with inserted steel members 44 Figure 4.9 Glulam member with two wooden blocks at sides 45 Figure 4.10 Comparison of Size and Shape 46 Figure 4.11 Shape factor measures efficiency for major second moment of area 46 Figure 4.12 Shape factor measures efficiency for major second moment of area 47 Figure 4.13 Shape factor measures efficiency for section modulus bending 47 Figure 4.14 Shape factor measures efficiency torsion moment of area and section modulus for torsion 48 Figure 4.15 The Study Flitch plate beam layout 49 Figure 4.16 The NAHB beam cross section 50 Figure 4.17 Dividing method of steel straight core into I shape 51 ix Figure 4.18 The Study beam cross section 51 Figure 4.19 Bending of an Euler–Bernoulli beam Each cross-section of the beam is at 90 degrees to the neutral axis 54 Figure 4.20 Simply-supported beam with a uniform distributed load 56 Figure 4.21 Design Load by increasing steel thickness comparing between NAHB beam and Study beam (1) 61 Figure 4.22 Design Load by increasing the length of span comparing between NAHB beam and Study beam (2) 62 Figure 5.1 Design Load bases on the steel thickness and span comparing between NAHB beam and Study beam 63 Figure 5.2 The ratio of Design Load comparing between NAHB beam and Study beam64 Figure 5.3 The ratio of Design Load comparing between NAHB beam and Study beam in details 68 Figure 5.4 The ratio of Design Load totally comparing between NAHB beam and Study beam using K value 69 Figure 5.5 The comparison the maximum load (q) between Study beams under the characteristic of Douglas Fir – Larch (colors) and California Redwood (grey) 70 Figure 6.1 The ratio shows that the I-shape always presents a highest efficiency 75 Figure 6.2 The Study beam indicated the higher efficiency compared with the NAHB’s beam 76 Figure 6.3 The K value indicates how efficient by applying this method 77 Figure 6.4 Recommended types of joints in a hybrid beam in the next research 78 x List of Tables Table Cross-Section dimension profiles to be examined - Material efficiency 26 Table The ratio between modified Cross-Section Moment of inertia values and basic Moment of inertia a = I i / I 27 Table The ratio between modified Cross-Section Section modulus value and basic Section modulus value b = Si / S 27 Table The ratio between modified Cross-Section l value and basic l value base on (E*3) & (E*4) 28 Table Cross-Section profiles to be examined - Material efficiency 30 Table The comparison a and b value showed by number 34 Table The comparison li value and basic l value by number 35 Table The ratio between modified I’’-Section Moment of inertia values and I’, a = I i / I 37 Table The ratio between modified I’-section’s Section modulus value and I’’, b = Si / S 37 Table 10 The ratio between modified Cross-Section “l” value and basic “l” value base on (E5) 37 Table 11 The NAHB beam designs results 42 Table 12 The NAHB beam designs results in metric system 42 Table 13 Characteristic of sample Flitch beam by California Redwood and Steel 53 Table 14 The comparison the maximum load (q) between NAHB beam and Study beam under the characteristic of California Redwood 59 xi Table 15 The comparison the maximum load (q) between NAHB beam and Study beam under the characteristic of Douglas Fir – Larch 60 Table 16 K values and F ( xn ) obtained 66 Graph The ratio between modified Cross-Section Moment of inertia a = I i / I 32 Graph The ratio between modified Cross-Section Section modulus value b = Si / S 33 Graph The ratio between modified Cross-Section li value and basic l value base on (E6) 35 xii List of Abbreviations NAHB National Association of Home Builders of the United States WCTE World Conference on Timber Engineering AISI American Iron and Steel Institute “ Inch (1”=25.4mm) ft Foot (1ft=304.8mm) psi Pounds per square inch (1psi= 68x10-3 N/mm2) lbs/ft Pounds per foot (1lbs/ft=1.49Kg/m=14.9x10-3 kN/m) GPa Gigapascal (1GPa=103 N/mm2) xiii