Advanced Analysis and Design of Steel Frames

Professor Li received his PhD in Structural Engineering at Tongji University in 1988. That same year he started working at the University as a lecturer in Structural Engineering, and over the next six years he worked his way up to Associate Professor, and then Professor in 1994. His research interests lie mainly in the behavior and design of multi-storey steel buildings, the fire-resistance of steel structures and the dynamic identification of structures. He is an active member on the Editorial board of five International journals covering areas of research in steel and composite structures, structural engineering and materials, computational structural engineering, and advanced steel construction. He is the author of four books in Chinese, and over eighty research papers.

• Preface xiSymbols xiiiPart One Advanced Analysis of Steel Frames 1Chapter 1 Introduction 31.1 Type of Steel Frames 31.2 Type of Components for Steel Frames 31.3 Type of Beam–Column Connections 71.4 Deformation of Joint Panel 71.5 Analysis Tasks and Method for Steel Frame Design 81.6 Definition of Elements in Steel Frames 9Chapter 2 Elastic Stiffness Equation of Prismatic Beam Element 112.1 General Form of Equation 112.1.1 Beam Element in Tension 112.1.2 Beam Element in Compression 162.1.3 Series Expansion of Stiffness Equations 162.1.4 Beam Element with Initial Geometric Imperfection 172.2 Special Forms of Elemental Equations 192.2.1 Neglecting Effect of Shear Deformation 192.2.2 Neglecting Effect of Axial Force 212.2.3 Neglecting Effects of Shear Deformation and Axial Force 222.3 Examples 222.3.1 Bent Frame 222.3.2 Simply Supported Beam 24Chapter 3 Elastic Stiffness Equation of Tapered Beam Element 253.1 Tapered Beam Element 253.1.1 Differential Equilibrium Equation 253.1.2 Stiffness Equation 273.2 Numerical Verification 293.2.1 Symmetry of Stiffness Matrix 293.2.2 Static Deflection 303.2.3 Elastic Critical Load 303.2.4 Frequency of Free Vibration 303.2.5 Effect of Term Number Truncated in Polynomial Series 313.2.6 Steel Portal Frame 313.3 Appendix 333.3.1 Chebyshev Polynomial Approach (Rice, 1992) 333.3.2 Expression of Elements in Equation (3.23) 34Chapter 4 Elastic Stiffness Equation of Composite Beam Element 354.1 Characteristics and Classification of Composite Beam 354.2 Effects of Composite Action on Elastic Stiffness of Composite Beam 374.2.1 Beam without Composite Action 374.2.2 Beam with Full Composite Action 384.2.3 Beam with Partial Composite Action 394.3 Elastic Stiffness Equation of Steel–Concrete Composite Beam Element 404.3.1 Basic Assumptions 404.3.2 Differential Equilibrium Equation of Partially Composite Beam 414.3.3 Stiffness Equation of Composite Beam Element 424.3.4 Equivalent Nodal Load Vector 464.4 Example 494.5 Problems in Present Work 51Chapter 5 Sectional Yielding and Hysteretic Model of Steel Beam Columns 535.1 Yielding of Beam Section Subjected to Uniaxial Bending 535.2 Yielding of Column Section Subjected to Uniaxial Bending 535.3 Yielding of Column Section Subjected to Biaxial Bending 565.3.1 Equation of Initial Yielding Surface 565.3.2 Equation of Ultimate Yielding Surface 565.3.3 Approximate Expression of Ultimate Yielding Surface 615.3.4 Effects of Torsion Moment 625.4 Hysteretic Model 645.4.1 Cyclic Loading and Hysteretic Behaviour 645.4.2 Hysteretic Model of Beam Section 655.4.3 Hysteretic Model of Column Section Subjected to Uniaxial Bending 675.4.4 Hysteretic Model of Column Section Subjected to Biaxial Bending 675.5 Determination of Loading and Deformation States of Beam–Column Sections 68Chapter 6 Hysteretic Behaviour of Composite Beams 716.1 Hysteretic Model of Steel and Concrete Material Under Cyclic Loading 716.1.1 Hysteretic Model of Steel Stress–Strain Relationship 716.1.2 Hysteretic Model of Concrete Stress–Strain Relationship 716.2 Numerical Method for Moment–Curvature Hysteretic Curves 756.2.1 Assumptions 756.2.2 Sectional Division 756.2.3 Calculation Procedure of Moment–Curvature Relationship 766.3 Hysteretic Characteristics of Moment–Curvature Relationships 776.3.1 Characteristics of Hysteretic Curves 776.3.2 Typical Phases 786.4 Parametric Studies 796.4.1 Height of Concrete Flange hc 796.4.2 Width of Concrete Flange Bc 796.4.3 Height of Steel Beam hs 806.4.4 Strength Ratio g 836.4.5 Yielding Strength of Steel fy 846.4.6 Compressive Strength of Concrete fck 846.4.7 Summary of Parametric Studies 856.5 Simplified Hysteretic Model 866.5.1 Skeletal Curve 866.5.2 Hysteresis Model 89Chapter 7 Elasto-Plastic Stiffness Equation of Beam Element 937.1 Plastic Hinge Theory 937.1.1 Hinge Formed at One End of Element 947.1.2 Hinge Formed at Both Ends of Element 977.2 Clough Model 977.3 Generalized Clough Model 987.4 Elasto-Plastic Hinge Model 997.4.1 Both Ends Yielding 1027.4.2 Only End 1 Yielding 1037.4.3 Only End 2 Yielding 1037.4.4 Summary 1047.5 Comparison Between Elasto-Plastic Hinge Model and Generalized Clough Model 1047.5.1 Only End 1 Yielding 1047.5.2 Both Ends Yielding 1057.5.3 Numerical Example 1067.6 Effects of Residual Stresses and Treatment of Tapered Element 1077.6.1 Effects of Residual Stresses on Plasticity Spread Along Element Section 1077.6.2 Effects of Residual Stresses on Plasticity Spread Along Element Length 1097.6.3 Treatment of Tapered Element 1107.7 Beam Element with Plastic Hinge Between Two Ends 1107.8 Subdivided Model with Variable Stiffness for Composite Beam Element 1137.8.1 Subdivided Model 1137.8.2 Stiffness Equation of Composite Beam Element 1147.9 Examples 1177.9.1 A Steel Portal Frame with Prismatic Members 1177.9.2 A Steel Portal Frame with Tapered Members 1187.9.3 Vogel Portal Frame 1197.9.4 Vogel Six-Storey Frame 1207.9.5 A Single-Storey Frame with Mid-Span Concentrated Load 1217.9.6 A Single-Storey Frame with Distributed Load 1237.9.7 A Four-Storey Frame with Mid-Span Concentrated Load 1247.9.8 A Two-Span Three-Storey Composite Frame 126Chapter 8 Elastic and Elasto-Plastic Stiffness Equations of Column Element 1278.1 Force and Deformation of Column Element 1278.2 Elastic Stiffness Equation of Column Element Subjected to Biaxial Bending 1278.3 Elasto-Plastic Stiffness Equations of Column Element Subjected to Biaxial Bending 1298.3.1 Both Ends Yielding 1318.3.2 Only End 1 Yielding 1328.3.3 Only End 2 Yielding 1338.3.4 Summary 1338.4 Elastic and Elasto-Plastic Stiffness Equations of Column Element Subjected to Uniaxial Bending 1348.5 Axial Stiffness of Tapered Column Element 1358.5.1 Elastic Stiffness 1358.5.2 Elasto-Plastic Stiffness 1358.6 Experiment Verification 1368.6.1 Experiment Specimen 1368.6.2 Set-Up and Instrumentation 1398.6.3 Horizontal Loading Scheme 1408.6.4 Theoretical Predictions of Experiments 1418.6.5 Comparison of Analytical and Tested Results 144Chapter 9 Effects of Joint Panel and Beam–Column Connection 1479.1 Behaviour of Joint Panel 1479.1.1 Elastic Stiffness of Joint Panel 1479.1.2 Elasto-Plastic Stiffness of Joint Panel 1499.2 Effect of Shear Deformation of Joint Panel on Beam/Column Stiffness 1509.2.1 Stiffness Equation of Beam Element with Joint Panel 1509.2.2 Stiffness Equation of Column Element with Joint Panel Subjected to Uniaxial Bending 1539.2.3 Stiffness Equation of Column Element with Joint Panel Subjected to Biaxial Bending 1549.3 Behaviour of Beam–Column Connections 1559.3.1 Moment–Rotation Relationship 1569.3.2 Hysteretic Behaviour 1619.4 Effect of Deformation of Beam–Column Connection on Beam Stiffness 1639.4.1 Stiffness Equation of Beam Element with Beam–Column Connections 1649.4.2 Stiffness Equation of Beam Element with Connections and Joint Panels 1669.5 Examples 1669.5.1 Effect of Joint Panel 1669.5.2 Effect of Beam–Column Connection 170Chapter 10 Brace Element and its Elastic and Elasto-Plastic Stiffness Equations 17510.1 Hysteretic Behaviour of Braces 17510.2 Theoretical Analysis of Elastic and Elasto-Plastic Stiffnesses of Brace Element 17510.3 Hysteretic Model of Ordinary Braces 18110.4 Hysteretic Characteristics and Model of Buckling-Restrained Brace 18310.5 Stiffness Equation of Brace Element 185Chapter 11 Shear Beam and its Elastic and Elasto-Plastic Stiffness Equations 18711.1 Eccentrically Braced Frame and Shear Beam 18711.1.1 Eccentrically Braced Frame 18711.1.2 Condition of Shear Beam 18711.2 Hysteretic Model of Shear Beam 18911.3 Stiffness Equation of Shear Beam 190Chapter 12 Elastic Stability Analysis of Planar Steel Frames 19312.1 General Analytical Method 19312.2 Effective Length of Prismatic Frame Column 19412.2.1 Concept of Effective Length 19412.2.2 Assumption and Analytical Model 19512.2.3 Formulations of Effective Length 19712.2.4 Simplified Formula of Effective Length 20212.2.5 Modification of Effective Length 20312.2.6 Effect of Shear Deformation on Effective Length of Column 20512.2.7 Examples 20512.3 Effective Length of Tapered Steel Columns 21112.3.1 Tapered Columns Under Different Boundary Conditions 21112.3.2 Tapered Column in Steel Portal Frame 213Chapter 13 Nonlinear Analysis of Planar Steel Frames 21913.1 General Analysis Method 21913.1.1 Loading Types 21913.1.2 Criteria for the Limit State of Ultimate Load-Carrying Capacity 22013.1.3 Analysis Procedure 22113.1.4 Basic Elements and Unknown Variables 22213.1.5 Structural Analysis of the First Loading Type 22213.1.6 Structural Analysis of the Second Loading Type 22313.1.7 Numerical Examples 22313.2 Approximate Analysis Considering P_D Effect 22613.2.1 Formulation 22613.2.2 Example 22713.3 Simplified Analysis Model Considering P_D Effect 22813.3.1 Development of Simplified Model 22813.3.2 Example 231Chapter 14 Seismic Response Analysis of Planar Steel Frames 23314.1 General Analysis Method 23314.1.1 Kinetic Differential Equation 23314.1.2 Solution of Kinetic Differential Equation 23514.1.3 Determination of Mass, Stiffness and Damping Matrices 23814.1.4 Numerical Example 24014.2 Half-Frame Model 24114.2.1 Assumption and Principle of Half-Frame 24114.2.2 Stiffness Equation of Beam Element in Half-Frame 24414.2.3 Numerical Examples 24414.3 Shear-Bending Storey Model 24814.3.1 Equivalent Stiffness 24814.3.2 Inter-Storey Shear Yielding Parameters 25114.3.3 Examples 25214.4 Simplified Model for Braced Frame 25514.4.1 Decomposition and Simplification of Braced Frame 25514.4.2 Stiffness Matrix of Pure Frame 25614.4.3 Stiffness Matrix of Pure Bracing System 25714.4.4 Example 258Chapter 15 Analysis Model for Space Steel Frames 25915.1 Space Bar Model 25915.1.1 Transformation from Local to Global Coordinates 25915.1.2 Requirement of Rigid Floor 26415.1.3 Global Stiffness Equation of Frame and Static Condensation 26715.2 Planar Substructure Model 26815.2.1 Stiffness Equation of Planar Substructure in Global Coordinates 26815.2.2 Global Stiffness Equation of Spatial Frame 27115.2.3 Numerical Example 27215.3 Component Mode Synthesis Method 27415.3.1 Principle of Component Mode Synthesis Method 27415.3.2 Analysis of Generalized Elements 27615.3.3 Stiffness Equation of Generalized Structure 28115.3.4 Structural Analysis Procedure 28215.3.5 Numerical Example 283Part Two Advanced Design of Steel Frames 287Chapter 16 Development of Structural Design Approach 28916.1 Deterministic Design Approach 28916.1.1 Allowable Stress Design (ASD) (AISC, 1989) 28916.1.2 Plastic Design (PD) (AISC, 1978) 29016.2 Reliability Design Approach Based on Limit States of Structural Members 29016.3 Structural System Reliability Design Approach 292Chapter 17 Structural System Reliability Calculation 29317.1 Fundamentals of Structural Reliability Theory 29317.1.1 Performance Requirements of Structures 29317.1.2 Performance Function of Structures 29317.1.3 Limit State of Structures 29417.1.4 Structural Reliability 29417.1.5 Reliability Index 29617.2 The First-Order Second-Moment (FOSM) Methods for Structural Reliability Assessment 29717.2.1 Central Point Method 29817.2.2 Design Point Method 29917.3 Effects of Correlation Among Random Variables 30217.4 Structural System Reliability and Boundary Theory 30217.4.1 Basic Concepts 30217.4.2 Upper–Lower Boundary Method 30517.5 Semi-Analytical Simulation Method for System Reliability 30617.5.1 General Principle 30617.5.2 Random Sampling 30717.5.3 Exponential Polynomial Method (EPM) 30917.6 Example 30917.6.1 A Steel Beam Section 30917.6.2 A Steel Portal Frame 313Chapter 18 System Reliability Assessment of Steel Frames 31718.1 Randomness of Steel Frame Resistance 31718.2 Randomness of Loads 31818.3 System Reliability Evaluation of Typical Steel Frames 31918.3.1 Effect of Correlation Among Random Variables 31918.3.2 Evaluation of Structural System Reliability Under Vertical Loads 32018.3.3 Evaluation of Structural System Reliability Under Horizontal and Vertical Loads 32318.4 Comparison of System Reliability Evaluation 325Chapter 19 Reliability-Based Advanced Design of Steel Frames 32719.1 Structural Design Based on System Reliability 32719.1.1 Target Reliability of Design 32719.1.2 Load and Load Combination 32919.1.3 Practical Design Formula 32919.2 Effect of Correlation on Load and Resistance Factors 33519.3 Comparison of Different Design Methods 33719.3.1 For Steel Portal Frames 33719.3.2 For Multi-Storey Steel Frames 340References/Bibliography 345Author Index 363Subject Index 365