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Preface.

Symbols.

Part One Advanced Analysis of Steel Frames.

Chapter 1 Introduction.

1.1 Type of Steel Frames.

1.2 Type of Components for Steel Frames.

1.3 Type of Beam–Column Connections.

1.4 Deformation of Joint Panel.

1.5 Analysis Tasks and Method for Steel Frame Design.

1.6 Definition of Elements in Steel Frames.

Chapter 2 Elastic Stiffness Equation of Prismatic Beam Element.

2.1 General Form of Equation.

2.1.1 Beam Element in Tension.

2.1.2 Beam Element in Compression.

2.1.3 Series Expansion of Stiffness Equations.

2.1.4 Beam Element with Initial Geometric Imperfection.

2.2 Special Forms of Elemental Equations.

2.2.1 Neglecting Effect of Shear Deformation.

2.2.2 Neglecting Effect of Axial Force.

2.2.3 Neglecting Effects of Shear Deformation and Axial Force.

2.3 Examples.

2.3.1 Bent Frame.

2.3.2 Simply Supported Beam.

Chapter 3 Elastic Stiffness Equation of Tapered Beam Element.

3.1 Tapered Beam Element.

3.1.1 Differential Equilibrium Equation.

3.1.2 Stiffness Equation.

3.2 Numerical Verification.

3.2.1 Symmetry of Stiffness Matrix.

3.2.2 Static Deflection.

3.2.3 Elastic Critical Load.

3.2.4 Frequency of Free Vibration.

3.2.5 Effect of Term Number Truncated in Polynomial Series.

3.2.6 Steel Portal Frame.

3.3 Appendix.

3.3.1 Chebyshev Polynomial Approach (Rice, 1992).

3.3.2 Expression of Elements in Equation (3.23).

Chapter 4 Elastic Stiffness Equation of Composite Beam Element.

4.1 Characteristics and Classification of Composite Beam.

4.2 Effects of Composite Action on Elastic Stiffness of Composite Beam.

4.2.1 Beam without Composite Action.

4.2.2 Beam with Full Composite Action.

4.2.3 Beam with Partial Composite Action.

4.3 Elastic Stiffness Equation of Steel–Concrete Composite Beam Element.

4.3.1 Basic Assumptions.

4.3.2 Differential Equilibrium Equation of Partially Composite Beam.

4.3.3 Stiffness Equation of Composite Beam Element.

4.3.4 Equivalent Nodal Load Vector.

4.4 Example.

4.5 Problems in Present Work.

Chapter 5 Sectional Yielding and Hysteretic Model of Steel Beam Columns.

5.1 Yielding of Beam Section Subjected to Uniaxial Bending.

5.2 Yielding of Column Section Subjected to Uniaxial Bending.

5.3 Yielding of Column Section Subjected to Biaxial Bending.

5.3.1 Equation of Initial Yielding Surface.

5.3.2 Equation of Ultimate Yielding Surface.

5.3.3 Approximate Expression of Ultimate Yielding Surface.

5.3.4 Effects of Torsion Moment.

5.4 Hysteretic Model.

5.4.1 Cyclic Loading and Hysteretic Behaviour.

5.4.2 Hysteretic Model of Beam Section.

5.4.3 Hysteretic Model of Column Section Subjected to Uniaxial Bending.

5.4.4 Hysteretic Model of Column Section Subjected to Biaxial Bending.

5.5 Determination of Loading and Deformation States of Beam–Column Sections.

Chapter 6 Hysteretic Behaviour of Composite Beams.

6.1 Hysteretic Model of Steel and Concrete Material Under Cyclic Loading.

6.1.1 Hysteretic Model of Steel Stress–Strain Relationship.

6.1.2 Hysteretic Model of Concrete Stress–Strain Relationship.

6.2 Numerical Method for Moment–Curvature Hysteretic Curves.

6.2.1 Assumptions.

6.2.2 Sectional Division.

6.2.3 Calculation Procedure of Moment–Curvature Relationship.

6.3 Hysteretic Characteristics of Moment–Curvature Relationships.

6.3.1 Characteristics of Hysteretic Curves.

6.3.2 Typical Phases.

6.4 Parametric Studies.

6.4.1 Height of Concrete Flange hc.

6.4.2 Width of Concrete Flange Bc.

6.4.3 Height of Steel Beam hs.

6.4.4 Strength Ratio g.

6.4.5 Yielding Strength of Steel fy.

6.4.6 Compressive Strength of Concrete fck.

6.4.7 Summary of Parametric Studies.

6.5 Simplified Hysteretic Model.

6.5.1 Skeletal Curve.

6.5.2 Hysteresis Model.

Chapter 7 Elasto-Plastic Stiffness Equation of Beam Element.

7.1 Plastic Hinge Theory.

7.1.1 Hinge Formed at One End of Element.

7.1.2 Hinge Formed at Both Ends of Element.

7.2 Clough Model.

7.3 Generalized Clough Model.

7.4 Elasto-Plastic Hinge Model.

7.4.1 Both Ends Yielding.

7.4.2 Only End 1 Yielding.

7.4.3 Only End 2 Yielding.

7.4.4 Summary.

7.5 Comparison Between Elasto-Plastic Hinge Model and Generalized Clough Model.

7.5.1 Only End 1 Yielding.

7.5.2 Both Ends Yielding.

7.5.3 Numerical Example.

7.6 Effects of Residual Stresses and Treatment of Tapered Element.

7.6.1 Effects of Residual Stresses on Plasticity Spread Along Element Section.

7.6.2 Effects of Residual Stresses on Plasticity Spread Along Element Length.

7.6.3 Treatment of Tapered Element.

7.7 Beam Element with Plastic Hinge Between Two Ends.

7.8 Subdivided Model with Variable Stiffness for Composite Beam Element.

7.8.1 Subdivided Model.

7.8.2 Stiffness Equation of Composite Beam Element.

7.9 Examples.

7.9.1 A Steel Portal Frame with Prismatic Members.

7.9.2 A Steel Portal Frame with Tapered Members.

7.9.3 Vogel Portal Frame.

7.9.4 Vogel Six-Storey Frame.

7.9.5 A Single-Storey Frame with Mid-Span Concentrated Load.

7.9.6 A Single-Storey Frame with Distributed Load.

7.9.7 A Four-Storey Frame with Mid-Span Concentrated Load.

7.9.8 A Two-Span Three-Storey Composite Frame.

Chapter 8 Elastic and Elasto-Plastic Stiffness Equations of Column Element.

8.1 Force and Deformation of Column Element.

8.2 Elastic Stiffness Equation of Column Element Subjected to Biaxial Bending.

8.3 Elasto-Plastic Stiffness Equations of Column Element Subjected to Biaxial Bending.

8.3.1 Both Ends Yielding.

8.3.2 Only End 1 Yielding.

8.3.3 Only End 2 Yielding.

8.3.4 Summary.

8.4 Elastic and Elasto-Plastic Stiffness Equations of Column Element Subjected to Uniaxial Bending.

8.5 Axial Stiffness of Tapered Column Element.

8.5.1 Elastic Stiffness.

8.5.2 Elasto-Plastic Stiffness.

8.6 Experiment Verification.

8.6.1 Experiment Specimen.

8.6.2 Set-Up and Instrumentation.

8.6.3 Horizontal Loading Scheme.

8.6.4 Theoretical Predictions of Experiments.

8.6.5 Comparison of Analytical and Tested Results.

Chapter 9 Effects of Joint Panel and Beam–Column Connection.

9.1 Behaviour of Joint Panel.

9.1.1 Elastic Stiffness of Joint Panel.

9.1.2 Elasto-Plastic Stiffness of Joint Panel.

9.2 Effect of Shear Deformation of Joint Panel on Beam/Column Stiffness.

9.2.1 Stiffness Equation of Beam Element with Joint Panel.

9.2.2 Stiffness Equation of Column Element with Joint Panel Subjected to Uniaxial Bending.

9.2.3 Stiffness Equation of Column Element with Joint Panel Subjected to Biaxial Bending.

9.3 Behaviour of Beam–Column Connections.

9.3.1 Moment–Rotation Relationship.

9.3.2 Hysteretic Behaviour.

9.4 Effect of Deformation of Beam–Column Connection on Beam Stiffness.

9.4.1 Stiffness Equation of Beam Element with Beam–Column Connections.

9.4.2 Stiffness Equation of Beam Element with Connections and Joint Panels.

9.5 Examples.

9.5.1 Effect of Joint Panel.

9.5.2 Effect of Beam–Column Connection.

Chapter 10 Brace Element and its Elastic and Elasto-Plastic Stiffness Equations.

10.1 Hysteretic Behaviour of Braces.

10.2 Theoretical Analysis of Elastic and Elasto-Plastic Stiffnesses of Brace Element.

10.3 Hysteretic Model of Ordinary Braces.

10.4 Hysteretic Characteristics and Model of Buckling-Restrained Brace.

10.5 Stiffness Equation of Brace Element.

Chapter 11 Shear Beam and its Elastic and Elasto-Plastic Stiffness Equations.

11.1 Eccentrically Braced Frame and Shear Beam.

11.1.1 Eccentrically Braced Frame.

11.1.2 Condition of Shear Beam.

11.2 Hysteretic Model of Shear Beam.

11.3 Stiffness Equation of Shear Beam.

Chapter 12 Elastic Stability Analysis of Planar Steel Frames.

12.1 General Analytical Method.

12.2 Effective Length of Prismatic Frame Column.

12.2.1 Concept of Effective Length.

12.2.2 Assumption and Analytical Model.

12.2.3 Formulations of Effective Length.

12.2.4 Simplified Formula of Effective Length.

12.2.5 Modification of Effective Length.

12.2.6 Effect of Shear Deformation on Effective Length of Column.

12.2.7 Examples.

12.3 Effective Length of Tapered Steel Columns.

12.3.1 Tapered Columns Under Different Boundary Conditions.

12.3.2 Tapered Column in Steel Portal Frame.

Chapter 13 Nonlinear Analysis of Planar Steel Frames.

13.1 General Analysis Method.

13.1.1 Loading Types.

13.1.2 Criteria for the Limit State of Ultimate Load-Carrying Capacity.

13.1.3 Analysis Procedure.

13.1.4 Basic Elements and Unknown Variables.

13.1.5 Structural Analysis of the First Loading Type.

13.1.6 Structural Analysis of the Second Loading Type.

13.1.7 Numerical Examples.

13.2 Approximate Analysis Considering PD Effect.

13.2.1 Formulation.

13.2.2 Example.

13.3 Simplified Analysis Model Considering PD Effect.

13.3.1 Development of Simplified Model.

13.3.2 Example.

Chapter 14 Seismic Response Analysis of Planar Steel Frames.

14.1 General Analysis Method.

14.1.1 Kinetic Differential Equation.

14.1.2 Solution of Kinetic Differential Equation.

14.1.3 Determination of Mass, Stiffness and Damping Matrices.

14.1.4 Numerical Example.

14.2 Half-Frame Model.

14.2.1 Assumption and Principle of Half-Frame.

14.2.2 Stiffness Equation of Beam Element in Half-Frame.

14.2.3 Numerical Examples.

14.3 Shear-Bending Storey Model.

14.3.1 Equivalent Stiffness.

14.3.2 Inter-Storey Shear Yielding Parameters.

14.3.3 Examples.

14.4 Simplified Model for Braced Frame.

14.4.1 Decomposition and Simplification of Braced Frame.

14.4.2 Stiffness Matrix of Pure Frame.

14.4.3 Stiffness Matrix of Pure Bracing System.

14.4.4 Example.

Chapter 15 Analysis Model for Space Steel Frames.

15.1 Space Bar Model.

15.1.1 Transformation from Local to Global Coordinates.

15.1.2 Requirement of Rigid Floor.

15.1.3 Global Stiffness Equation of Frame and Static Condensation.

15.2 Planar Substructure Model.

15.2.1 Stiffness Equation of Planar Substructure in Global Coordinates.

15.2.2 Global Stiffness Equation of Spatial Frame.

15.2.3 Numerical Example.

15.3 Component Mode Synthesis Method.

15.3.1 Principle of Component Mode Synthesis Method.

15.3.2 Analysis of Generalized Elements.

15.3.3 Stiffness Equation of Generalized Structure.

15.3.4 Structural Analysis Procedure.

15.3.5 Numerical Example.

Part Two Advanced Design of Steel Frames.

Chapter 16 Development of Structural Design Approach.

16.1 Deterministic Design Approach.

16.1.1 Allowable Stress Design (ASD) (AISC, 1989).

16.1.2 Plastic Design (PD) (AISC, 1978).

16.2 Reliability Design Approach Based on Limit States of Structural Members.

16.3 Structural System Reliability Design Approach.

Chapter 17 Structural System Reliability Calculation.

17.1 Fundamentals of Structural Reliability Theory.

17.1.1 Performance Requirements of Structures.

17.1.2 Performance Function of Structures.

17.1.3 Limit State of Structures.

17.1.4 Structural Reliability.

17.1.5 Reliability Index.

17.2 The First-Order Second-Moment (FOSM) Methods for Structural Reliability Assessment.

17.2.1 Central Point Method.

17.2.2 Design Point Method.

17.3 Effects of Correlation Among Random Variables.

17.4 Structural System Reliability and Boundary Theory.

17.4.1 Basic Concepts.

17.4.2 Upper–Lower Boundary Method.

17.5 Semi-Analytical Simulation Method for System Reliability.

17.5.1 General Principle.

17.5.2 Random Sampling.

17.5.3 Exponential Polynomial Method (EPM).

17.6 Example.

17.6.1 A Steel Beam Section.

17.6.2 A Steel Portal Frame.

Chapter 18 System Reliability Assessment of Steel Frames.

18.1 Randomness of Steel Frame Resistance.

18.2 Randomness of Loads.

18.3 System Reliability Evaluation of Typical Steel Frames.

18.3.1 Effect of Correlation Among Random Variables.

18.3.2 Evaluation of Structural System Reliability Under Vertical Loads.

18.3.3 Evaluation of Structural System Reliability Under Horizontal and Vertical Loads.

18.4 Comparison of System Reliability Evaluation.

Chapter 19 Reliability-Based Advanced Design of Steel Frames.

19.1 Structural Design Based on System Reliability.

19.1.1 Target Reliability of Design.

19.1.2 Load and Load Combination.

19.1.3 Practical Design Formula.

19.2 Effect of Correlation on Load and Resistance Factors.

19.3 Comparison of Different Design Methods.

19.3.1 For Steel Portal Frames.

19.3.2 For Multi-Storey Steel Frames.

References/Bibliography.

Author Index.

Subject Index.

Library of Congress subject headings for this publication:

Steel, Structural.

Structural frames.

Structural analysis (Engineering)