Non-Linear Static and Cyclic Analysis of Steel Frames with Semi-Rigid Connections
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Table of contents
- NON-LINEAR STATIC AND CYCLIC ANALYSIS OF STEEL FRAMES WITH SEMI-RIGID CONNECTIONSiii
- Copyright Pageiv
- Contentsxiii
- FOREWORDvii
- ACKNOWLEDGEMENTSxi
- CHAPTER 1. BEHAVIOUR, ANALYSIS AND DESIGN OF STEEL FRAMES1
- 1.1 Introduction1
- 1.2 Probability of failure3
- 1.3 Loads3
- 1.4 Material properties6
- 1.5 Plastic failure8
- 1.6 Instability of a structure9
- 1.7 The P-δ effect14
- 1.8 The P-Δ effect16
- 1.9 Design of steel structures17
- 1.10 Types of analysis18
- References27
- CHAPTER 2. FIRST-ORDER LINEAR ELASTIC ANALYSIS FOR RIGID AND SEMI-RIGID FRAMES29
- 2.1 Introduction29
- 2.2 Linear analysis30
- 2.3 Coordinate systems32
- 2.4 The principle of the total potential energy for element stiffness formulation36
- 2.5 Element stiffness for semi-rigid jointed members41
- 2.6 Assembling of the stiffness matrix45
- 2.7 Member force determinations47
- 2.8 Checking of equilibrium48
- 2.9 Examples48
- 2.10 Conclusions52
- References52
- CHAPTER 3. SECOND-ORDER ELASTIC ANALYSIS BY THE NEWTON–RAPHSON METHOD55
- 3.1 Introduction55
- 3.2 Bifurcation analysis versus load-deflection analysis58
- 3.3 General solution methods for non-linear analysis59
- 3.4 The tangent stiffness matrix68
- 3.5 The secant stiffness matrix70
- 3.6 Design application72
- 3.7 Examples73
- 3.8 Conclusions75
- References75
- CHAPTER 4. NON-LINEAR SOLUTION TECHNIQUES77
- 4.1 Introduction77
- 4.2 Genuinely large deflection analysis79
- 4.3 Basic formulation79
- 4.4 Numerical examples87
- 4.5 Conclusions91
- References91
- CHAPTER 5. CONNECTION BEHAVIOUR AND MODELS93
- 5.1 Introduction93
- 5.2 Static monotonic loading tests94
- 5.3 Connection behaviour95
- 5.4 Classification of connection models98
- 5.5 Formulation of connection models100
- 5.6 Connection spring element113
- 5.7 Modified element stiffness matrix accounting for semi-rigid joints115
- 5.8 Conclusions117
- References118
- CHAPTER 6. NON-LINEAR STATIC ANALYSIS ALLOWING FOR PLASTIC HINGES AND SEMI-RIGID JOINTS123
- 6.1 Abstract123
- 6.2 Introduction123
- 6.3 Literature review125
- 6.4 Existing inelastic analysis methods127
- 6.5 Proposed refined-plastic hinge method141
- 6.6 Combined effect of joint flexibility and material yielding–the springs-in-series model152
- 6.7 Numerical examples159
- 6.8 Conclusions190
- References191
- CHAPTER 7. CYCLIC BEHAVIOUR OF FLEXIBLY CONNECTED ELASTIC STEEL FRAMES195
- 7.1 Introduction195
- 7.2 Research work on semi-rigid connections197
- 7.3 Modelling of connection behaviour under cyclic loading198
- 7.4 Connection models used in this study203
- 7.5 Hybrid element with connection springs204
- 7.6 Numerical procedure for present non-linear transient analysis206
- 7.7 Procedure for present vibration analysis216
- 7.8 Numerical examples217
- 7.9 Conclusions259
- References260
- CHAPTER 8. TRANSIENT ANALYSIS OF INELASTIC STEEL STRUCTURES WITH FLEXIBLE CONNECTIONS265
- 8.1 Introduction265
- 8.2 Review on cyclic plasticity models and methods268
- 8.3 Strain-hardening rules271
- 8.4 Existing cyclic plasticity models274
- 8.5 Proposed cyclic plasticity models used in this study278
- 8.6 Beam–column connection modelling281
- 8.7 Numerical examples283
- 8.8 Conclusions299
- References300
- APPENDIX A303
- A.1. The 12 × 12 linear stiffness matrix, [KL]303
- A.2. The 12 × 12 geometric stiffness matrix, [KG]305
- A.3. The 12 × 12 consistent mass matrix, [M]307
- APPENDIX B. USER'S MANUAL OF GMNAF311
- B.1. Introduction311
- B.2. Data preparation312
- B.3. Activation of the program314
- B.4. Example314
- LIST OF SYMBOLS325
- AUTHOR INDEX327
- SUBJECT INDEX333
This book is devoted to the discussion and studies of simple and efficient numerical procedures for large deflection and elasto-plastic analysis of steel frames under static and dynamic loading.
In chapter 1, the basic fundamental behaviour and philosophy for design of structural steel is discussed, emphasising different modes of buckling and the inter-relationship between different types of analysis. In addition to this, different levels of refinement for non-linear analysis are described. An introduction is also given to the well-known P-&dgr; and P-&Dgr; effects. Chapter 2 presents the basic matrix method of analysis and gives several examples of linear analysis of semi-rigid pointed frames. It is evident from this that one must have a good understanding of first-order linear analysis before handling a second-order non-linear analysis. In chapter 3, the linearized bifurcation and second-order large deflection are compared and the detailed procedure for a second-order analysis based on the Newton-Raphson scheme is described. Chapter 4 introduces various solution schemes for tracing of post-buckling equilibrium paths and the Minimum Residual Displacement control method with arc-length load step control is employed for the post-buckling analysis of two and three dimensional structures. Chapter 5 addresses the non-linear behaviour and modelling of semi-rigid connections while several numerical functions for description of moment versus rotation curves of typical connection types are introduced. The scope of the work in chapter 6 covers semi-rigid connections and material yielding to the static analysis of steel frames. Chapter 7 studies the cyclic response of steel frames with semi-rigid joints and elastic material characteristics. In the last chapter the combined effects of semi-rigid connections and plastic hinges on steel frames under time-dependent loads are studied using a simple springs-in-series model. For computational effectiveness and efficiency, the concentrated plastic hinge concept is used throughout these studies.
In chapter 1, the basic fundamental behaviour and philosophy for design of structural steel is discussed, emphasising different modes of buckling and the inter-relationship between different types of analysis. In addition to this, different levels of refinement for non-linear analysis are described. An introduction is also given to the well-known P-&dgr; and P-&Dgr; effects. Chapter 2 presents the basic matrix method of analysis and gives several examples of linear analysis of semi-rigid pointed frames. It is evident from this that one must have a good understanding of first-order linear analysis before handling a second-order non-linear analysis. In chapter 3, the linearized bifurcation and second-order large deflection are compared and the detailed procedure for a second-order analysis based on the Newton-Raphson scheme is described. Chapter 4 introduces various solution schemes for tracing of post-buckling equilibrium paths and the Minimum Residual Displacement control method with arc-length load step control is employed for the post-buckling analysis of two and three dimensional structures. Chapter 5 addresses the non-linear behaviour and modelling of semi-rigid connections while several numerical functions for description of moment versus rotation curves of typical connection types are introduced. The scope of the work in chapter 6 covers semi-rigid connections and material yielding to the static analysis of steel frames. Chapter 7 studies the cyclic response of steel frames with semi-rigid joints and elastic material characteristics. In the last chapter the combined effects of semi-rigid connections and plastic hinges on steel frames under time-dependent loads are studied using a simple springs-in-series model. For computational effectiveness and efficiency, the concentrated plastic hinge concept is used throughout these studies.