This dissertation presents three various advanced analysis approaches which can capture accurately and efficiently the ultimate strength and behavior of steel framed structures with nonlinear beam-to-column connections subjected to static and dynamic loadings. Three major sources of nonlinearity are considered in the analyses as follows: (1) material nonlinearity; (2) geometric nonlinearity; and (3) connection nonlinearity. Three types of nonlinear beam-column element formulation considering both geometric and material nonlinearities are coded into two nonlinear structural analysis programs: (1) Nonlinear Structural Analysis Program (NSAP) – 2-D plastic-zone finite element; (2) Practical Advanced Analysis Program (PAAP) – 3-D refined plastic-hinge element and 3-D plastic-fiber element. Three types of steel frames analyzed by the proposed program are: (1) rigid frames – beam-to-column connections are fully rigid; (2) linear semi-rigid frames – beam-to-column connections have constant stiffness; and (3) nonlinear semi-rigid frames – beam-to-column connections have continuously variable stiffness. Three types of analysis can be performed are: (1) nonlinear inelastic static analysis; (2) nonlinear elastic and inelastic time-history analysis; and (3) free vibration analysis. Three main resources of damping are taken into account in the proposed programs are: (1) hysteretic damping due to inelastic material; (2) structural viscous damping employing Rayleigh damping; (3) hysteretic damping due to nonlinear beam-to-column connections.
Two computer programs are developed: (1) Nonlinear Structural Analysis Program (NSAP) – written in the C++ programming language; (2) Practical Advanced Analysis Program (PAAP) – written in the FORTRAN 77 programming language. They are verified for accuracy and computational efficiency by comparing predicted results with those generated by the commercial finite element analysis packages of ABAQUS and SAP2000, and other results available in the literature. Through several numerical examples, the proposed program (PAAP) proves to be a reliable and efficient tool for daily practice design in lieu of using costly and time-consuming commercial software.
Table of Contents
CHAPTER 1. INTRODUCTION
1. Motivation
2. Objective and Scope
3. Organization of Dissertation
THIS DISSERTATION IS SUMMARIZED FROM JOURNAL ARTICLES
CHAPTER 2. SECOND-ORDER SPREAD-OF-PLASTICITY APPROACH FOR NONLINEAR DYNAMIC ANALYSIS OF TWO-DIMENSIONAL SEMI-RIGID STEEL FRAMES
1. Introduction
2. Nonlinear Finite Element Formulation
2.1 Second-Order Spread-of-Plasticity Beam-Column Element
2.2 Nonlinear Beam-to-Column Connections
2.2.1 Modified Tangent Stiffness Matrix including Nonlinear Connections
2.2.2 Moment-Rotation Relationship of Nonlinear Connections
2.2.3 Cyclic Behavior of Nonlinear Connections
3. Nonlinear Solution Procedures
4. Numerical Examples and Discussions
4.1 Portal Steel Frame subjected to Earthquakes
4.2 Two-Story Steel Frame with Nonlinear Connections
4.3 Vogel Six-Story Steel Frame with Nonlinear Connections – A Case Study
5. Summary and Conclusions
CHAPTER 3. SECOND-ORDER PLASTIC-HINGE APPROACH FOR NONLINEAR STATIC AND DYNAMIC ANALYSIS OF THREE-DIMENSIONAL SEMI-RIGID STEEL FRAMES
1. Introduction
2. Nonlinear Finite Element Formulation
2.1 Second-Order Plastic-Hinge Beam-Column Element
2.1.1 Stability Functions accounting for Second-Order Effects
2.1.2 Refined Plastic Hinge Model accounting for inelastic effects
2.1.3 Shear Deformation Effect
2.1.4 Element Stiffness Matrix accounting for P −Δ Effect
2.2 Semi-rigid Connection Element
2.2.1 Element Modeling
2.2.2 Semi-Rigid Connection Models for Rotational Springs
2.2.3 Cyclic Behavior of Rotational Springs
3. Nonlinear Solution Procedures
3.1 Nonlinear Static Algorithm
3.1.1 Formulation
3.1.2 Application
3.2 Nonlinear Dynamic Algorithm
3.2.1 Formulation
3.2.2 Application
4. Numerical Examples and Discussions
4.1 Static Problems
4.1.1 Vogel 2-D Portal Steel Frame
4.1.2 Stelmack Experimental 2-D Two-Story Steel Frame
4.1.3 Liew Experimental 2-D Portal Steel Frame
4.2 Dynamic Problems
4.2.1 Chan 2-D Two-Story Steel Frame
4.2.2 Vogel 2-D Six-Story Steel Frame
4.2.3 Chan 3-D Two-Story Steel Frame subjected to Impulse Forces
4.2.4 3-D Two -Story Steel Frame subjected to Earthquakes
4.2.5 Orbison 3-D Six-Story Steel Frame – A Case Study
5. Summary and Conclusions
CHAPTER 4. SECOND-ORDER SPREAD-OF-PLASTICITY APPROACH FOR NONLINEAR STATIC AND DYNAMIC ANALYSIS OF THREE-DIMENSIONAL SEMI-RIGID STEEL FRAMES
1. Introduction
2. Nonlinear Finite Element Formulation
2.1 Second-Order Spread-of-Plasticity Beam-Column Element
2.1.1 The Effects of Small P-delta and Shear Deformation
2.1.2 The Effect of Spread-of-Plasticity
2.1.3 Element Stiffness Matrix accounting for the Effect of Large P-delta
2.2 Nonlinear Beam-to-Column Connection Element
2.2.1 Element Modeling
2.2.3 Cyclic Behavior of Rotational Springs
3. Nonlinear Solution Procedures
3.1 Nonlinear Static Algorithm
3.2 Nonlinear Dynamic Algorithm
4. Numerical Examples and Discussions
4.1 Static Problems
4.1.1 Vogel Portal Steel Frame
4.1.2 Stelmack Experimental Two-Story Steel Frame
4.1.3 Vogel Six-Story Steel Frame
4.1.4 Orbison Six-Story Space Steel Frame – A Case Study
4.2 Dynamic Problems
4.2.1 Portal Steel Frame subjected to Earthquakes
4.2.2 Experimental Two-Story Steel Frame subjected to Cyclic Loadings
4.2.3 Space Six-Story Steel Frame – A Case Study
5. Summary and Conclusions
CHAPTER 5. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
1. Summary and Conclusions
2. Recommendations
REFERENCES
Research Objectives and Topics
The core objective of this dissertation is to develop advanced analysis methods for accurate and efficient evaluation of the ultimate strength and behavior of three-dimensional semi-rigid steel frames under both static and dynamic loadings. The research aims to overcome limitations in existing structural analysis software by implementing advanced nonlinear finite element formulations that account for material, geometric, and connection nonlinearities.
- Development of second-order spread-of-plasticity and plastic-hinge analysis methods.
- Simulation of nonlinear semi-rigid beam-column connections using sophisticated spring models.
- Implementation of robust numerical algorithms for static and dynamic equilibrium analysis, including HHT and Newton-Raphson methods.
- Verification of proposed analysis programs against experimental data and commercial software packages like ABAQUS and SAP2000.
- Investigation of environmental factors such as geometric imperfections and damping in steel-framed industrial structures.
Excerpt from the Book
1. Motivation
It is generally recognized that steel framed structures exhibit significantly nonlinear behavior prior to achieving their ultimate load-carrying capacity or instability. Thus, a second-order inelastic analysis or an advanced analysis is the most exactly result for predicting the real performance of steel framed structures instead of using conventional analysis/design approach. Advanced analysis can efficiently capture the ultimate strength and stability of a whole structural system and its component members so that separate member capacity checks encompassed by specification equations are no longer necessary. While greater complexity is introduced in the analysis, a significant reduction in effort is achieved in the design assessment. This may be accomplished through an efficient final checking of both member and system limit states for a structure where preliminary member sizing was based on serviceability requirements. For steel framed structures, advanced analysis methods can be generally classified into two categories of plastic hinge and plastic zone approaches based on the level of refinement used to represent yielding.
The beam-column member in the plastic hinge approaches is modeled by an appropriate way to eliminate its further subdivision, and the plastic hinges representing the inelastic behavior of material are assumed to be lumped at both ends of the member. The refined plastic hinge method is one of plastic hinge approaches. In this method, the inelastic behavior in the member is modeled in terms of member forces instead of the detailed level of stress and strain as used in the plastic zone analysis, the yielding is evaluated based on a yielding surface criteria. The principal advantages of this method are that it is simple in formulation as well as implementation and more importantly, it is relatively accurate for the assessment of strength and stability of a structural system by using the one or two elements per member in the modeling.
In the plastic zone approach, the beam-column member is discretized into several finite sub-elements along the member length, and the cross section of each sub-element is divided into several small fibers, of which the uniaxial stress-strain relationships of material are monitored during the analysis process. This method performs the spread of plasticity throughout the cross section and along the member length. Although the solution of this method is considered the “exact” solution and easily included the effects of local, flexural-torsional, and lateral-torsional buckling which are significant characteristics of steel.
Summary of Chapters
CHAPTER 1. INTRODUCTION: Introduces the research motivation, outlines the project objectives and scope, and establishes the importance of advanced nonlinear analysis for steel structures.
CHAPTER 2. SECOND-ORDER SPREAD-OF-PLASTICITY APPROACH FOR NONLINEAR DYNAMIC ANALYSIS OF TWO-DIMENSIONAL SEMI-RIGID STEEL FRAMES: Details the development of a spread-of-plasticity method for 2-D frames, focusing on element formulation and connection modeling under dynamic, seismic loads.
CHAPTER 3. SECOND-ORDER PLASTIC-HINGE APPROACH FOR NONLINEAR STATIC AND DYNAMIC ANALYSIS OF THREE-DIMENSIONAL SEMI-RIGID STEEL FRAMES: Describes the plastic-hinge approach for 3-D frames, implementing stabilization and connection elements to evaluate structural responses efficiently.
CHAPTER 4. SECOND-ORDER SPREAD-OF-PLASTICITY APPROACH FOR NONLINEAR STATIC AND DYNAMIC ANALYSIS OF THREE-DIMENSIONAL SEMI-RIGID STEEL FRAMES: Presents the application of the spread-of-plasticity approach to 3-D steel frames, validating the model through extensive numerical examples and comparisons.
CHAPTER 5. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS: Provides a comprehensive overview of the developed methodologies, consolidates research findings, and suggests directions for future advancements in structural steel research.
Keywords
Steel frames, semi-rigid connections, nonlinear analysis, second-order effects, spread-of-plasticity, plastic-hinge method, dynamic loading, seismic response, finite element method, structural stability, Rayleigh damping, hysteretic behavior, geometric imperfections, computational efficiency.
Frequently Asked Questions
What is the core focus of this dissertation?
This work focuses on developing advanced numerical methods and computer algorithms for the nonlinear analysis of three-dimensional semi-rigid steel frames under both static and dynamic loading conditions.
What are the primary nonlinear factors considered in the analysis?
The research integrates material nonlinearity, geometric nonlinearity (including P-delta effects), and connection nonlinearity to realistically model the behavior of steel-framed systems.
What is the primary objective of the research?
The goal is to provide accurate and computationally efficient analysis tools that surpass traditional design approaches and overcome the limitations found in existing commercial software.
Which mathematical methods are utilized for structural analysis?
The methods include Newmark numerical integration, Newton-Raphson iteration for nonlinear systems, Generalized Displacement Control (GDC), and the HHT (Hilber-Hughes-Taylor) alpha-method for dynamic integration.
What does the main body of the work cover?
It covers theoretical formulations for different beam-column elements, discretization techniques for fiber-based and plastic-hinge models, and extensive verification through experimental case studies of steel frames.
Which terms characterize this research?
Keywords include semi-rigid connections, second-order inelastic analysis, spread-of-plasticity, hysteretic damping, and 3-D steel structure performance-based design.
How are connection nonlinearities modeled?
Connections are simulated using zero-length rotational springs whose behavior is governed by various models, such as the Kishi-Chen power model, the Richard-Abbott model, and the Chen-Lui exponential model.
What role do geometric imperfections play in the analysis?
The dissertation demonstrates that initial geometric imperfections, such as member out-of-straightness, significantly impact the final structural response and must be included in accurate performance-based design.
How is the computational efficiency of the proposed programs demonstrated?
The programs (NSAP and PAAP) are compared against established benchmarks and commercial tools like ABAQUS and SAP2000, showing significantly reduced computation times while maintaining equivalent or superior accuracy.
- Quote paper
- Dr. Phu-Cuong Nguyen (Author), 2014, Advanced Analysis for Three-Dimensional Semi-Rigid Steel Frames subjected to Static and Dynamic Loadings, Munich, GRIN Verlag, https://www.grin.com/document/1358749
