Numerical Study on Optimization of Wooden-Steel Hybrid Beams Based on Shape Factor of Steel Componen...

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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谷 贅: M10213801

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Numerical Study on Optimization of Wooden-Steel

Hybrid Beams Based on Shape Factor of

Steel Component

◊✲⏕: Le Truong Di Ha



ᣦᑟᩍᤵ ୖ Meng– Ting Tsai Ph.D

Shen – Guan Shih Ph.D

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Nowadays, the composite of steel and concrete is quite popular but it is also important to improve and develop the structural systems especially the construction and design of wooden structure Furthermore, wood components would reduce the risk 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 Flitch-beams 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 2 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, Hollow-section and I-Hollow-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

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

Content

1.1 Background and motivation 1

1.2 Objective and Research Outcomes 5

1.3 Research Approach 6

1.3.1 Comparison of shape factors 6

1.3.2 Appling shape factor to optimize the Flitch beams 6

1.4 Chapter Overview 6

2.1 Case study of hybridization 9

2.1.1 System level hybridization 9

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 3 Numerical methodology of shape factor 17 3.1 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 mid span ( l D ) 18

3.2 Shape factors 19

3.2.1 Cross-Section shapes 19

3.2.2 Identifying Cross-Section method 20

3.3 Material efficiency 22

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 4 Flitch Beam - Data Acquisition 38 4.1 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

4.2 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 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

4.4 The relevant formula and definitions review 54

4.4.1 Bending stress conditions 54

4.4.2 Deflection conditions 56

4.5 Data acquisition 58

4.5.1 Identify the maximum load for the Study beam 58

4.6 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 5 The ratio of load comparison and analysis on the equation 63 5.1 Comparison of the ratio of Load 63

5.1.1 Design Load Comparison bases on the steel thickness and span 63

5.2 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 6 Conclusion 75 6.1 Summary of finding 75

6.2 Future work 78

List of Figures

Figure 1.1 The comparison between 1 km 2 of Forest and Urban area in wood storage 2

Figure 1.2 Original beam (a) and study beam after applying study method (b) 4

Figure 1.3 Research Organization 7

Figure 1.4 Thesis structure 8

Figure 2.1 Shimouma Apartment, Tokyo, Japan 9

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 2 glue-laminated beams and 2 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

Figure 3.5 I-Section and dimensions after being modified by 2 steps 24

Figure 3.6 I-Section and dimensions after being modified by 4 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

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

List of Tables

Table 1 Cross-Section dimension profiles to be examined - Material efficiency 26

Table 2 The ratio between modified Cross-Section Moment of inertia values and basic Moment of inertia a = I i / I 27

Table 3 The ratio between modified Cross-Section Section modulus value and basic Section modulus value b = Si / S 27

Table 4 The ratio between modified Cross-Section l value and basic l value base on (E*3) & (E*4) 28

Table 5 Cross-Section profiles to be examined - Material efficiency 30

Table 6 The comparisona and b value showed by number 34

Table 7 The comparison li value and basic l value by number 35

Table 8 The ratio between modified I’’-Section Moment of inertia values and I’, / i I I a = 37

Table 9 The ratio between modified I’-section’s Section modulus value and I’’, / i S S b = 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

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 x( n)

obtained 66

Graph 1 The ratio between modified Cross-Section Moment of inertia a =I i /I 32

Graph 2 The ratio between modified Cross-Section Section modulus value b =S i/S 33

Graph 3 The ratio between modified Cross-Section li value and basic l value base on

(E6) 35

List of Abbreviations

NAHB National Association of Home Builders of the United States