Seismic analysis of safety-related nuclear structures and commentary

Content: Standard --
1.1.2.1 Types of Structures Covered by This Standard 1 --
1.1.2.2 Foundation Material Stability 1 --
1.1.3 General Requirements 1 --
1.1.3.1 Use of Analysis Results 1 --
1.1.3.2 Alternative Methodologies 1 --
2.0 Seismic Input 4 --
2.1 Seismic Ground Motions 4 --
2.2 Response Spectra 5 --
2.2.2 Site-Specific Horizontal Response Spectra 5 --
2.2.3 Site-Independent Horizontal Response Spectra 5 --
2.2.4 Vertical Response Spectra 6 --
2.3 Time Histories 6 --
2.4 Power Spectral Density Functions 8 --
2.4.1 PSD Computed from Time Histories 8 --
2.5 Additional Requirements for Structures Sensitive to Long Period Motions 8 --
2.5.1 Spectral Shape 9 --
2.5.2 Time Histories 9 --
3.0 Analysis 9 --
3.1 Modeling of Structures 9 --
3.1.1.1 Models for Horizontal and Vertical Motions 9 --
3.1.1.2 Multistep and One-Step Methods of Seismic Response Analysis 9 --
3.1.1.2.1 Models for multistep analysis 10 --
3.1.1.2.2 Models for one-step analysis 10 --
3.1.1.3 Discretization Considerations 10 --
3.1.1.3.1 Selection of finite element type 10 --
3.1.1.3.2 Selection of mesh size 10 --
3.1.1.3.3 Reduction of dynamic degrees of freedom 10 --
3.1.2 Structural Material Properties 10 --
3.1.2.1 Modulus of Elasticity and Poisson's Ratio 10 --
3.1.2.1.1 Concrete 10 --
3.1.2.1.2 Steel 10 --
3.1.2.1.3 Aluminum 10 --
3.1.2.2 Damping 10 --
3.1.3 Modeling of Stiffness 11 --
3.1.3.1 Stiffness of Reinforced Concrete Elements 11 --
3.1.4 Modeling of Mass 11 --
3.1.4.1 Discretization of Mass 11 --
3.1.4.2 Determination of Modal Mass 11 --
3.1.5 Modeling of Damping 12 --
3.1.5.1 Damping Properties of Structures 12 --
3.1.5.1.1 Proportional damping (Rayleigh damping) 12 --
3.1.5.2 Composite Damping 12 --
3.1.5.2.1 Substructures with Known Damping Ratios 13 --
3.1.5.2.2 Substructures with Proportional Damping 13 --
3.1.5.3 Composite Modal Damping 13 --
3.1.5.4 Alternate Composite Modal Damping 13 --
3.1.6 Modeling of Hydrodynamic Effects 13 --
3.1.6.1 General Requirements 13 --
3.1.6.2 Dynamic Analysis Formulation for Submerged Structures 13 --
3.1.6.3 Building Model Hydrodynamic Mass Effects 14 --
3.1.7 Dynamic Coupling Criteria 15 --
3.1.7.2 Single-Point Attachment 15 --
3.1.7.3 Multipoint Attachment and Static Constraint 15 --
3.1.8 Requirements for Modeling Specific Structures 15 --
3.1.8.1.1 Structures with rigid floors 15 --
3.1.8.1.2 Structures with flexible floors 16 --
3.1.8.1.3 Requirements for lumped-mass stick models 16 --
3.1.8.2 Requirements for Frame Structures 17 --
3.1.8.3 Requirements for Shear-Wall Structures 17 --
3.1.8.4 Requirements for Plate and Shell Structures 17 --
3.1.8.5 Requirements for Adjacent Structures 18 --
3.2 Analysis of Structures 18 --
3.2.2 Time History Method 18 --
3.2.2.2 Linear Methods 18 --
3.2.2.2.1 Modal superposition 19 --
3.2.2.2.2 Direct integration 19 --
3.2.2.3 Nonlinear Methods 19 --
3.2.3 Response Spectrum Method 20 --
3.2.3.1 Linear Methods 20 --
3.2.3.2 Nonlinear Methods 20 --
3.2.4 Complex Frequency Response Method 20 --
3.2.4.2 Response Time History 20 --
3.2.4.3 Methods to Compute Transfer Functions 21 --
3.2.5 Equivalent-Static Method 21 --
3.2.5.2 Cantilever Models with Uniform Mass Distribution 21 --
3.2.5.3 Other Simple Structures 21 --
3.2.6 Multiply-Supported Systems 22 --
3.2.6.2 Time History Method 22 --
3.2.6.3 Response Spectrum Method 22 --
3.2.7 Combination of Modal and Component Responses 22 --
3.2.7.1 Response Spectrum Analysis 22 --
3.2.7.1.1 General modal combination rule 22 --
3.2.7.1.2 Combination of spatial components 23 --
3.2.7.1.3 Multiple response parameters 23 --
3.2.7.2 Combination of Spatial Components for Time History Analysis 24 --
3.3 Soil-Structure Interaction Modeling and Analysis 24 --
3.3.1.1 Fixed-Basea Analysis 24 --
3.3.1.2 Spatial Variations of Free-Field Motion 25 --
3.3.1.3 Three-Dimensional Effects 25 --
3.3.1.4 Nonlinear Behavior of Soil 25 --
3.3.1.5 Structure-to-Structure Interaction 25 --
3.3.1.6 Effect of Mat and Lateral Wall Flexibility 25 --
3.3.1.7 Uncertainties in SSI Analysis 25 --
3.3.1.8 Model of Structure 26 --
3.3.1.9 Embedment Effects 26 --
3.3.1.10 Wave Incoherence 26 --
3.3.2 Subsurface Material Properties 26 --
3.3.2.2 Shear Modulus 26 --
3.3.2.3 Material (Hysteretic) Damping Ratio 26 --
3.3.2.4 Poisson's Ratio 26 --
3.3.3 Direct Method 26 --
3.3.3.1 Seismic Input for Model Boundaries 27 --
3.3.3.2 Lower Boundary 27 --
3.3.3.3 Selection of Lateral Boundaries 27 --
3.3.3.4 Soil Element Size 28 --
3.3.3.5 Time Step and Frequency Increment 28 --
3.3.4 Impedance Method 28 --
3.3.4.1 Determination of Input Motion 28 --
3.3.4.2 Determination of Foundation Impedance Functions 29 --
3.3.4.2.1 Equivalent foundation dimensions 29 --
3.3.4.2.2 Uniform soil sites 29 --
3.3.4.2.3 Layered soil sites 29 --
3.3.4.2.4 Embedded foundations 29 --
3.3.4.3 Analysis of Coupled Soil-Structural System 30 --
3.4 Input for Subsystem Seismic Analysis 30 --
3.4.1.1 Types of Seismic Input for Subsystem Analysis 30 --
3.4.1.2 Direction and Locations for In-Structure Response Spectra or Time Histories 31 --
3.4.1.3 Subsystem Input Away from Reference Location 31 --
3.4.1.4 In-Structure Displacements and Rotations 31 --
3.4.2 In-Structure Response Spectra 31 --
3.4.2.1 Methods for Generation of In-Structure Response Spectra 31 --
3.4.2.1.1 Time history method 31 --
3.4.2.1.2 Direct spectra-to-spectra methods 32 --
3.4.2.2 Frequency Interval for Generation of In-Structure Response Spectra 32 --
3.4.2.3 Treatment of Uncertainties in Generating In-Structure Response Spectra 32 --
3.4.2.4 Interpolation of In-Structure Response Spectra for Intermediate Damping 32 --
3.4.3 In-Structure Time History Motions 33 --
3.4.3.1 Methods for Generation of In-Structure Time History Motions 33 --
3.4.3.2 Equivalent Broadening and Lowering of In-Structure Time History Motions 33 --
3.4.3.3 Time Interval and Data Precision Requirements for In-Structure Time History Motions 33 --
3.4.4 Structural Model or Characteristics for Coupled Subsystem Analysis 33 --
3.4.4.1 Supporting Soil-Structure Model 33 --
3.4.4.2 Base Excitation 33 --
3.5 Special Structures 33 --
3.5.2 Buried Pipes and Conduits 34 --
3.5.2.1 Straight Sections Remote from Anchor Points, Sharp Bends, or Intersections 34 --
3.5.2.1.1 Maximum axial strain ignoring friction 34 --
3.5.2.1.2 Maximum axial strain considering friction 34 --
3.5.2.1.3 Maximum curvature 34 --
3.5.2.1.4 Maximum joint displacement and rotation in segmented structures 35 --
3.5.2.2 Forces on Bends, Intersections, and Anchor Points 35 --
3.5.2.3 Anchor Point Movement 35 --
3.5.3 Earth-Retaining Walls 35 --
3.5.3.1 General Requirements 35 --
3.5.3.2 Elastic Solution 35 --
3.5.3.3 Active Solution 35 --
3.5.4 Above-Ground Vertical Tanks 35 --
3.5.4.2 Horizontal Impulsive Mode 36 --
3.5.4.2.1 Effective weight of fluid--Impulsive mode 36 --
3.5.4.2.2 Spectral acceleration--Impulsive mode 36 --
3.5.4.2.3 Overturning moment at base of tank--Impulsive mode 37 --
3.5.4.2.4 Hydrodynamic pressure on tank shell--Impulsive mode 37 --
3.5.4.3 Horizontal Sloshing (Convective Mode) 37 --
3.5.4.3.1 Effective weight of fluid--Sloshing mode 37 --
3.5.4.3.2 Spectral acceleration--Sloshing mode 37 --
3.5.4.3.3 Overturning moment at base of tank--Sloshing mode 37 --
3.5.4.3.4 Hydrodynamic pressure on tank shell--Sloshing mode 37 --
3.5.4.3.5 Fluid slosh height--Fundamental sloshing mode 37 --
3.5.4.4 Vertical Fluid Response Mode 38 --
3.5.4.4.1 Hydrodynamic pressure on tank shell--Vertical mode 38 --
3.5.4.5.1 Overturningn moment and longitudinal compressive force 38 --
3.5.4.5.2 Hoop tension in tank shell 38 --
3.5.4.5.3 Freeboard requirements 38 --
3.5.4.5.4 Special provision for full tanks 38 --
3.5.4.5.5 Attached piping 38 --
3.5.4.5.6 Tank foundation 38 --
3.5.5 Raceways 38 --
3.5.5.2 Damping 38 --
3.5.6 Seismic-Isolated Structures 39 --
3.5.6.1 General Requirements 39 --
3.5.6.2 Specification of Seismic Input Motion 39 --
3.5.6.3 Modeling of Structures 39 --
3.5.6.4 Response Spectrum Analysis 40 --
3.5.6.5 Time History Analysis 40 --
Nonmandatory Appendix --
A1.0 Nonmandatory Appendix A: Evaluations Beyond the Design Basis 41 --
A2.1 History of Spra and Sma 41 --
A3.1 Purpose and Overview of Seismic Probabilistic Risk Assessment 42 --
A4.1 Purpose and Overview of Seismic Margin Assessment Methodology 44 --
A5.1 Comparison of Seismic Evaluation Methodologies 47 --
A6.1 Comparison of Spra to Standard 47 --
A7.1 Comparison of Sma to Standard 51 --
C2.0 Seismic Input 55 --
C2.1 Seismic Ground Motions 55 --
C2.1.1 General Requirements 55 --
C2.2 Response Spectra 55 --
C2.2.2 Site-Specific Horizontal Response Spectra 56 --
C2.2.3 Site-Independent Horizontal Response Spectra 56 --
C2.2.4 Vertical Response Spectra 56 --
C2.3 Time Histories 57 --
C2.4 Power Spectral Density Functions 59 --
C2.5 Additional Requirements for Structures Sensitive to Long-Period Motions 59 --
C2.5.1 Spectral Shape 59 --
C2.5.2 Time Histories 60 --
C3.0 Analysis 61 --
C3.1 Modeling of Structures 61 --
C3.1.1 General Requirements 61 --
C3.1.1.1 Models for Horizontal and Vertical Motions 61 --
C3.1.1.2 Multistep and One-Step Methods of Seismic Response Analysis 61 --
C3.1.1.3 Discretization Considerations 62 --
C3.1.1.3.2 Selection of mesh size 62 --
C3.1.1.3.3 Reduction of dynamic degrees of freedom 62 --
C3.1.2 Structural Material Properties 62 --
C3.1.2.1 Concrete 62.