Advanced Analysis for Three-Dimensional Semi-Rigid Steel Frames subjected to Static and Dynamic Loadings

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

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.