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研究生： 紀祖豪
Chi, Tzu-Hao
論文名稱： 三維非線性樑元素用於結構分析之研究
A Study of 3D Nonlinear Beam Element in Structural Analysis
指導教授： 朱聖浩
Ju, Shen-Haw
學位類別： 碩士
Master
系所名稱： 工學院 - 土木工程學系
Department of Civil Engineering
論文出版年： 2002
畢業學年度： 90
語文別： 英文
論文頁數： 86
中文關鍵詞： 剛性樓板 、鋼筋混凝土 、剪力牆 、非彈性 、平面應力元素 、樑柱 、柔性樓板
外文關鍵詞： Beam-column, Rigid-floor, Inelastic, Membrane element, Reinforced concrete, Shear wall, Flexible-floor
相關次數： 點閱：143  下載：6 
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    • 本論文主要是在修改NSP程式中三維樑元素的架構，並利用由平面應力元素所模擬的剪力牆和樓板來分析鋼筋混凝土結構物的非線性行為。此NSP程式是一套作結構靜力與動力分析的非線性有限元素軟體。在這個報告中，所有修改的部分均包含於nbeam.for這個副程式裡面。它簡化了三維樑元素的輸入，以及增加了剪力的降伏曲面和彈性加載與卸載的行為。
    對於三維房屋結構分析，樓板常被假設為剛性的。雖然此種假設情形適用於無剪力牆的房屋，然而在分析含有剪力牆的房屋結構行為時卻造成了誤差。以上大部分所提到的結論是由線彈性分析所得出的。因此使用非線性結構分析來探討結構物的行為模式是必須的。所以在本研究中的最後將比較在非線性行為上，房屋在剛性和柔性樓板的假設下，結構分析結果之差別。

    The main purpose of this study is to improve the 3D beam element formulations for the NSP program and design the membrane element to simulate shear walls and floor slabs for modeling the inelastic behavior of reinforced concrete (RC) structures. The NSP program is a general purpose nonlinear finite element software for static and dynamic analyses of structures. In this report, all improvements were included in a subroutine, nbeam.for. It simplifies the input data of the 3D beam and adds the shear force yielding surface and elastic loading-unloading behavior.
    For three-dimensional (3D) building analyses, floor slabs are often assumed to be rigid in their planes. This assumption was demonstrated to be adequate for buildings without shear walls. However, it can cause errors for buildings with shear walls. Most of the above conclusion was obtained from the linear-elastic analysis. Thus, analyzing the behavior of buildings using inelastic structural analyses is necessary. Therefore, comparing the difference between inelastic rigid-floor and flexible-floor structural analysis was investigated in this study.

    ABSTRACT I 誌謝 III CONTENTS IV LIST OF FIGURES VII LIST OF TABLES IX CHAPTER 1 INTRODUCTION 1 1.1 Background and purpose 1 1.2 Brief account of the research 2 1.3 Literature review 3 1.4 Illustration of the finite element program 5 CHAPTER 2 BASIC THEORY OF 3D BEAM ELEMENT 11 2.1 Introduction 11 2.2 The Stiffness Matrix of Axial Force and Torsion 12 2.3 The stiffness in the plane of axes 2-3 13 2.4 The stiffness in the plane of axes 1-3 16 2.5 The 12-degree-of-freedom global stiffness matrix 18 CHAPTER 3 ELASTIC-PLASTIC 3D MEMBRANE ELEMENTS 20 3.1 Introduction 20 3.2 Elastic-plastic constitutive equation 21 3.2.1 Flow theory 21 3.2.2 Yield criteria 22 3.2.3 Elastic-plastic stress-strain relationship 24 3.3 Membrane elements 29 3.3.1 Isoparametric formulation 29 3.3.2 Incompatible mode 32 3.3.3 Coordinate transformation 33 3.3.4 Master-slave node system 35 CHAPTER 4 THE 3D NONLINEAR BEAM ELEMENT FOR STATIC AND DYNAMIC ANALYSES 39 4.1 Introduction 39 4.2 Building code requirement for structural concrete 39 4.2.1 Introduction 39 4.2.2 Design assumptions 39 4.2.3 General principles and requirements 41 4.2.4 Minimum reinforcement of flexural members 42 4.3 The input data format of the member 42 4.4 Input data of yielding surface 45 4.4.1 RC beam type at one node 45 4.4.2 RC beam type at two nodes 47 4.4.3 The beam-column type 48 4.5 Input data of properties and size 51 4.5.1 RC beam type at one node 51 4.5.2 RC beam type at two nodes 56 4.5.3 The beam-column type 57 4.5.4 The shear force yielding surface 61 4.6 Cyclic loading behavior 62 4.6.1 Elastic loading and unloading behavior 62 4.7 The illustration of the program 65 4.7.1 Subroutine MPS (pure beam type) 65 4.7.2 Subroutine RCC (the beam-column element type) 66 CHAPTER 5 EXAMPLES OF INELASTIC BUILDING ANALYSES 70 5.1 Illustration of numerical models 70 5.2 Evaluation of collapse seismic loading for buildings 73 5.3 Investigating the difference between rigid floor and flexible floor 74 5.3.1 Examples 1 74 5.3.2 Example 2 75 CHAPTER 6 CONCLUSIONS AND FUTURE WORKS 83 6.1 Conclusions 83 6.2 Future works 84 REFERENCES 85

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    7. Kuw C. T. “Architecture of 3D beam element in nonlinear finite element analysis,” Master thesis, National Cheng-Kung University, 2001.
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    10. Rafiq, M. Y.,and C. Southcombe, “Genetic algorithms in optimal design and detailing of reinforced concrete biaxial columns supported by a declarative approach for capacity checking,” University of Plymouth, School of Civil &Structural Engineering, U. K. Received 20 January 1997; accepted 25 April 1998.
    11. Wilson, E.L., Taylor, R.L., Doherty, W.P. and Ghaboussi, J., "Incompatible Displacement Models", in Numerical and Computer Method in Structural Mechanics (Fenves, S.J., Perrone, N., Robinson, A.R. and Schnobrich, W.C. eds), Academic Press, New York, pp. 43-57, 1973.
    12. 中國土木水利工程學會, “混凝土工程設計規範與解說” 科技圖書股份有限公司, 2000.
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