大多數地震下的支承分析會假設有恢復力與摩擦力，但往往只能取得支承之最終位移和力量等數據，無法取得個元件之影響比重。本研究將使用FBM模擬支承，其中由三種元件組成，分別為於橋面板與支承上方間之摩擦元件、支承中間模擬橡膠之恢復力元件與支承下方與柱頂間之摩擦元件。
本研究使用近域地震波集集大地震TCU068, TCU102和TCU052進行分析，並符合規範之台中設計地震反應譜，再與遠域地震El-Centro大地震ELX354, ELX421和ELX600進行比較。在使用FBM支承系統於本橋梁進行分析時，將證實恢復力元件和摩擦元件可以獨立運算。本研究的目的為替換數種不同的摩擦係數以觀察橋梁動力反應之變化；其次，透過比較不同摩擦係數所造成之橋梁行為，找出最適合之摩擦係數使消能行為最佳；第三，確定最佳摩擦參數便於設計兩個甲板間隙，以避免地震發生時甲板發生碰撞；第四，確定最佳摩擦參數便於設計帽梁寬度，以避免地震發生時橋面版滑落。

Functional Bearing Model (FBM) is an idea to represent 1 link analysis that used in common with divide it into 3 links based on each function. In this research, the rubber bearing divided into 3 elements as representation of rubber bearing system, they are: Friction element in the top of sliding interface between bearing and deck, Rubber in the middle link as a restoring element, and Frictional element in the bottom of sliding interface between bearing and column.
A shaking table size bridge proposed under the normalized peak ground acceleration under the design spectra of the near fault ground motions of Chi-Chi earthquakes TCU068, TCU102, and TCU052. In this research of FBM analysis, proof that the contribution of the rubber element and friction elements can be calculated independently.
The purposes of this research are: First, to study about the effect of variation of the friction coefficient that applied on the top surface and bottom surface of the rubber bearing system. Second, to study about determining several configuration of the friction coefficient to design a proper rubber bearing system. Third, to study about determining several configuration of the friction coefficient to design a gap between two decks in order to avoid the decks crashing when the earthquakes happen. Fourth, to study about determining several configuration of the friction coefficient to design enlargement of the column’s cap beam in order to avoid the decks falling when the earthquakes happen.

CHAPTER I – INTRODUCTION 1
1.1 Background 1
1.2 Research Objectives 4
1.3 Research Scope and Limitation 6
1.4 Research Outline 6
CHAPTER II – LITERATURE REVIEW 8
2.1 Introduction 8
2.2 Highway Bridge Structure 8
2.3 Earthquake Ground Motion 9
2.3.1 Near Fault Earthquake 11
2.3.2 Earthquake Response in Linear System 12
2.3.3 Earthquake Response in Non-Linear System 13
2.4 Isolation System 15
2.4.1 Rubber Bearing 16
2.4.2 Functional Bearing Model (FBM) 17
2.5 Structural Optimization 18
2.5.1 Earthquake Response and Design Spectrum Analysis 18
2.5.2 Numerical Evaluation 20
2.6 Software Simulation 21
CHAPTER III – FUNDAMENTAL THEORY AND METHODOLOGY ANALYSIS 22
3.1 Functional Bearing Model (FBM) 22
3.2 State Space Analysis Process 23
3.2.1 Sticking State 26
3.2.2 Sliding State 27
3.3 Fundamental Theory 30
3.3.1 Free Body Diagram 30
3.3.2 Conditions 31
3.3.3 Sliding Mechanism 35
3.4 Research Flowchart 38
3.5 Modelling 40
3.5.1 Bridge Model 40
3.5.2 Material and Section Properties 41
3.5.3 Comparison Proposed Model with Previous Experimental Model 42
3.5.4 Resonance Possibility 46
3.6 Earthquake Input 47
3.6.1 Near Fault Earthquake 47
3.6.2 Far Fault Earthquake 51
3.6.3 Design Spectra Analysis 51
3.7 Bearing System 56
3.7.1 Functional Bearing Model (FBM) and Link Definition 57
3.7.2 Non Linear Boundary Condition 58
3.8 Variation of the Coefficient of Friction 59
3.9 System Analysis 61
3.9.1 Loading Definition and Loading Case 61
CHAPTER IV – NUMERICAL ANALYSIS: VARIATION OF FRICTION COEFFICIENT EFFECT ON FUNCTIONAL BEARING MODEL (FBM) ANALYSIS 63
4.1 Case Details 63
4.2 Near Fault Analysis 64
4.2.1 Duration of the Peak Response 64
4.2.2 Displacement Contribution 65
4.2.3 Energy Absorptions 69
4.2.4 Friction Element Contribution 73
4.3 Far Fault Analysis 76
4.3.1 Duration of the Peak Response 76
4.3.2 Displacement Contribution 77
4.3.3 Energy Absorptions 80
4.3.4 Friction Element Contribution 83
4.4 Conclusion 85
CHAPTER V – NUMERICAL ANALYSIS: BRIDGE FALLING PREVENTION 86
5.1 Case Details 86
5.2 Design A Proper Rubber Bearing 87
5.2.1 Maximum Deformation of the Rubber 87
5.2.2 Time Reference 89
5.2.3 Behavior of the Rubber Bearing System at the Certain Time 90
5.3 Design the Gap Distance of the Deck 100
5.3.1 Maximum Deck Displacement 100
5.3.2 Maximum Sliding Deformation of the Top Friction Surface 102
5.3.3 Time Reference 104
5.3.4 Behavior of the Rubber Bearing System at the Certain Time 104
5.4 Design the Column’s Cap Beam Size 111
5.4.1 Maximum Column Displacement 111
5.4.2 Maximum Sliding Deformation of the Bottom Friction Surface 113
5.4.3 Time Reference 115
5.4.4 Behavior of the Rubber Bearing System at the Certain Time 116
5.5 Standard Design Code 122
5.6 Conclusion 122
CHAPTER VI – OVERALL CONCLUSIONS 127
6.1 Conclusions 127
6.2 Recommendations 128
REFERENCES 130
APPENDIX 132

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