Advanced Sampling of Populations

Contents 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 effect 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 Eq. (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 compsite 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 resent 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 Characteristic of hysteretic curves 6.3.2 Typical phases 6.4 Parametric studies 6.4.1 Height of concrete flange hc 6.4.2 Breadth 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 Equation 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 Behavior 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 Behavior 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 brace 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 type 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 P-D effect 13.2.1 Formulation 13.2.2 Example 13.3 Simplified analysis model considering P-D effect 13.3.1 Development of simplified model 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 story 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 coordinate 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 Fundamental of structural reliability theory 17.1.1 Performance requirement 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-order 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