FEMA 440 2005

$64.35

FEMA 440 – Improvement of Nonlinear Static Seismic Analysis Procedures

Published By	Publication Date	Number of Pages
FEMA	2005	392

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Description

PDF Catalog

PDF Pages	PDF Title
3	Title Page
5	Forward
7	Preface
9	Executive Summary 1. Overview of Inelastic Seismic Analysis Procedures 2. Evaluation of Current Nonlinear Static Procedures 3. Strength Degradation
10	4. Improved Procedures for Displacement Modification 5. Improved Procedures for Equivalent Linearization 6. Evaluation and Comparison of Improved Nonlinear Static Procedures 7. Soil-Structure Interaction Effects
11	8. Multiple-Degree-of Freedom Effects 9. Important Future Developments 10. Application Example
13	1. Introduction 1-1 2. Overview of Inelastic Seismic Analysis Procedures 2-1 3. Evaluation of Current Nonlinear Static Procedures 3-1 Table of Contents
14	4. Strength Degradation 4-1 5. Improved Procedures for Displacement Modification 5-1 6. Improved Procedures for Equivalent Linearization 6-1 7. Evaluation and Comparison of Improved Nonlinear Static Procedures 7-1 8. Procedures for Including Soil-Structure Interaction Effects 8-1 9. Multiple-Degree-of-Freedom Effects 9-1
15	10. Summary and Application Example 10-1
19	List of Figures
27	List of Tables
29	1. Introduction 1.1 Background 1.2 Project Purpose and Scope
30	1.3 Report Scope, Organization and Contents
33	2. Overview of Inelastic Seismic Analysis Procedures 2.1 Structural Modeling
34	2.2 Characterization of Seismic Ground Motion
37	2.3 Options for Inelastic Analysis
40	2.4 Current Nonlinear Static Procedures
41	2.4.1 The Coefficient Method of Displacement Modification from FEMA 356
42	2.4.2 Capacity-Spectrum Method of Equivalent Linearization in ATC-40
45	3. Evaluation of Current Nonlinear Static Procedures 3.1 Introduction 3.2 Evaluation Procedures 3.2.1 Hysteretic Characteristics
47	3.2.2 Earthquake Ground Motions
48	3.2.3 Error Measures and Statistical Study
49	3.3 Evaluation of Capacity-Spectrum Method of ATC-40 3.3.1 Summary of the Approximate Method
51	3.3.2 Iteration Procedures
52	3.3.3 Evaluation Using Ground Motion Records
53	3.4 Evaluation of Coefficient Method (FEMA 356) 3.4.1 Summary of the Approximate Method
54	3.4.2 Maximum Displacement Ratio (Coefficient C1)
59	3.4.3 Degrading System Response (Coefficient C2)
61	3.4.4 P-D Effects (Coefficient C3)
63	3.5 Nonlinear Elastic Behavior
65	4. Strength Degradation 4.1 Types of Strength Degradation 4.2 Strength Degradation and SDOF Performance
66	4.3 Global Force-Deformation Behavior with Strength Degradation
67	4.4 Limitation on Strength for In-Cycle Strength Degradation Including P-D Effects
69	5. Improved Procedures for Displacement Modification 5.1 Introduction 5.2 Maximum Displacement Ratio (Coefficient C1) 5.2.1 Simplified Expression
70	5.2.2 Limits on Maximum Displacements for Short Periods
71	5.3 Adjustment for Cyclic Degradation (Coefficient C2)
72	5.4 Limitation on Strength to Avoid Dynamic Instability for Nonlinear Static Procedures
73	6. Improved Procedures for Equivalent Linearization 6.1 Introduction
74	6.2 Basic Equivalent Linearization Parameters 6.2.1 Effective Damping
76	6.2.2 Effective Period
77	6.2.3 MADRS for Use with Secant Period 6.3 Spectral Reduction for Effective Damping
78	6.4 Solution Procedures
81	6.5 Approximate Solution Procedure
82	6.6 Iterative Strategy 6.7 Limitation on Strength to Avoid Dynamic Instability for Nonlinear Static Procedures
83	7. Evaluation and Comparison of Improved Nonlinear Static Procedures 7.1 Introduction 7.2 Summary of Evaluation Procedures 7.2.1 NEHRP Design Response Spectrum 7.2.2 Ground Motions and Ground-Motion Scaling
85	7.2.3 Characteristics of Oscillators 7.2.4 Nonlinear Static Procedure Estimates Using Smoothed or Average Spectra
87	7.2.5 Response-History Analyses 7.3 Results of the Study
92	7.4 Summary of Implications of the Results of the Study
93	8. Procedures for Including Soil-Structure Interaction Effects 8.1 Introduction
95	8.2 Procedures for Kinematic Effects
96	8.3 Procedures for Foundation Damping
101	9. Multiple-Degree-of-Freedom Effects 9.1 Introduction 9.2 Review of Current Simplified Procedures 9.2.1 Single-Mode Load Vectors
102	9.2.2 Multi-Mode Pushover Procedures 9.2.3 Summary of Current Provisions
103	9.3 Summary of Illustrative Examples 9.3.1 Load Vectors
104	9.3.2 Equivalent SDOF Estimates of Global Displacement
106	9.4 Practical Implications
107	9.4.1 Single Load Vectors
110	9.4.2 Multi-Mode Pushover Analysis
111	9.4.3 Roof Displacement Estimation 9.4.4 Limitation of Simplified Procedures
112	9.5 Potential Future Improvements 9.5.1 Incremental Response-Spectrum Analysis 9.5.2 Nonlinear Dynamic Procedure Using Scaled Response Histories
115	10. Summary and Application Example 10.1 Overview of Inelastic Seismic Analysis Procedures 10.2 Evaluation of Current Nonlinear Static Procedures 10.2.1 Key Observations: ATC-40 Version of Capacity-Spectrum Method Longer-period response.
116	Shorter-period response Degrading stiffness and strength Limitations on damping and spectral reduction factors 10.2.2 Key Observations: FEMA 356 and the Coefficient Method Transition period for the equal-displacement approximation Ratio of inelastic to elastic deformation, coefficient C1 Degradation of stiffness and strength (Coefficients C2 and C3)
117	10.3 Strength Degradation 10.4 Improved Procedures for Displacement Modification 10.4.1 Summary of Findings Pertaining to Coefficient C1
118	10.4.2 Summary of Findings Pertaining to Coefficient C2 10.4.3 Summary of Findings Pertaining to Coefficient C3
119	10.5 Improved Procedures for Equivalent Linearization 10.6 Evaluation and Comparison of Improved Nonlinear Static Procedures
120	10.7 Soil-Structure Interaction Effects 10.8 Multiple-Degree-of Freedom Effects
122	10.9 Uncertainty and Reliability
124	10.10 Important Future Developments 10.10.1 Nonlinear Modeling for Cyclic and In- Cycle Degradation of Strength and Stiffness
125	10.10.2 Soil and Foundation Structure Interaction 10.10.3 Nonlinear Multi-Degree of Freedom Simplified Modeling
126	10.11 Application Example 10.11.1 Example Building Description 10.11.2 Basic Ground Motion 10.11.3 Kinematic Soil-structure Interaction
128	10.11.4 Fixed-Base Model 10.11.5 Flexible-Base Model 10.11.6 Foundation Damping
129	10.11.7 Force-Displacement Relationships (Pushover Curves) 10.11.8 Check on Minimum Strength for Strength Degrading Model 10.11.9 Target Displacement for Displacement Modification
130	10.11.10 Calculation of the Performance Point Using Equivalent Linearization 10.11.11 Check on Assumed Ductility
143	References and Bibliography
151	Project Participants
155	A. Summary of Research on Inelastic Analysis Procedures A.1 Introduction
156	A.2 Classification of Analysis Methods
157	A.3 Nonlinear Static Procedures A.3.1 Overview of Current Procedures A.3.1.1 Capacity-Spectrum Method
158	A.3.1.2 Displacement Coefficient Method
159	A.3.1.3 Drift-Based Approaches A.3.1.4 Direct Displacement-Based Design
160	A.3.2 Fundamental Bases and Relationships A.3.2.1 Equivalent Linearization
161	A.3.2.2 Displacement Modification
162	A.3.2.3 Choosing Between Equivalent Linearization and Displacement Modification A.3.3 Near-Field Effects on SDOF Systems
163	A.3.4 Equivalent SDOF Systems A.3.5 Behavior Mode Effects A.3.6 MDOF and Inelastic Mechanism Effects
165	A.3.7 Pushover Analysis
166	A.4 Nonlinear Dynamic Procedures A.4.1 Simplified Models A.4.2 Incremental Dynamic Analysis
167	A.5 Modeling Limitations
168	A.6 Demand Characterization A.7 Applicability for Performance-Based Earthquake Engineering and Design A.7.1 Role for Inelastic Procedures
169	A.7.2 Design Formats
170	A.7.3 Quantities to be Determined and Measures of Performance A.7.4 Statistical Measures and Treatment of Uncertainty A.8 References and Bibliography
175	B. Summary of Practice using Inelastic Analysis Procedures B.1 Introduction B.2 Typical Buildings and Structural Systems B.3 Inelastic Analysis Procedures
176	B.4 Software
177	B.5 Implementation Issues
178	B.6 Use of Limitations on Coefficient C1 in FEMA 356 B.7 Practical Guidance and Education
181	C. Supplemental Data on the Evaluation of Current Procedures C.1 Ground Motions
186	C.2 Response History Results C.2.1 Effect of Site Class on C1 of SDOF Systems with Elastoplastic Perfectly Plastic (EPP) Hysteretic Behavior
187	C.2.2 Effect of Site Class on C1 of SDOF Systems with Stiffness Degrading (SD) Hysteretic Behavior
188	C.2.3 Effect of Site Class on C1 of SDOF Systems with Strength and Stiffness Degrading (SSD) Hysteretic Behavior
189	C.2.4 Effect of Site Class on C1 of SDOF Systems with Nonlinear Elastic Hysteretic Behavior
190	C.2.5 Evaluation of Coefficient C2 for Site Class B
191	C.2.6 Evaluation of Coefficient C2 for Site Class C
192	C.2.7 Evaluation of Coefficient C2 for Site Class D
193	C.2.8 Evaluation of Coefficient C2 for Site Class E
194	C.2.9 Evaluation of Coefficient C2 for Near Fault Set
195	C.2.10 Effect of Site Class on Coefficient C2 (Stiffness Degrading Hysteretic Behavior)
196	C.2.11 Effect of Site Class on Coefficient C2 (Strength-Stiffness Degrading Hysteretic Behavior)
197	C.2.12 Effect of Site Class on Coefficient C2 (Nonlinear Elastic Hysteretic Behavior)
198	C.2.13 Effect of Hysteretic Behavior on C1 of SDOF Systems (Site Class B)
199	C.2.14 Effect of Hysteretic Behavior on C1 of SDOF Systems (Site Class C)
200	C.2.15 Effect of Hysteretic Behavior on C1 of SDOF Systems (Site Class D)
201	C.2.16 Effect of Hysteretic Behavior on C1 of SDOF Systems (Site Class E)
202	C.2.17 Effect of Hysteretic Behavior on C1 of SDOF Systems (Near Fault Set)
203	C.3 Evaluation of ATC-40 Version of Capacity Spectrum Method: Summary Results C.3.1 Comparisons for Site Class B:
204	C.3.2 Comparisons for Site Class C:
205	C.3.3 Comparisons for Site Class D:
206	C.3.4 Comparisons for Site Class E:
207	C.3.5 Comparisons for Near-Fault Ground Motions:
208	C.4 Evaluation of the Coefficient Method of FEMA 356: Summary Results C.4.1 FEMA 356 Nonlinear Static Procedure (NSP) C1 Values for Different Ts Values:
210	C.4.2 FEMA 356 NSP C2 Values for Different Ts Values:
211	C.4.3 Mean Error of FEMA 356 NSP (Mean of Approximate to Exact Maximum Inelastic Displacements): C.4.3.1 Comparison with Elastic Perfectly Plastic Hysteretic Behavior:
213	C.4.3.2 Comparison with Stiffness Degrading Hysteretic Behavior:
215	C.4.3.3 Comparison with Stiffness and Strength Degrading Hysteretic Behavior:
217	C.4.4 Dispersion of the Error in FEMA 356 NSP (Standard Deviation of Approximate to Exact Maximum Inelastic Displacements): C.4.4.1 Comparison with Elastic Perfectly Plastic Hysteretic Behavior:
219	C.4.4.2 Comparison with Stiffness Degrading Hysteretic Behavior:
221	C.4.4.3 Comparison with Stiffness and Strength Degrading Hysteretic Behavior:
223	D. Supplementary Information and Data on Equivalent Linearization D.1 Introduction D.2 Capacity-Spectrum Method D.2.1 Structural Capacity: Inelastic Pushover
224	D.2.2 Seismic Demand: Response Spectra D.3 Theoretical Basis for Equivalent Linearization
227	D.4 Starting Point For Optimization
228	D.5 Alternative Statistical Analysis
229	D.5.1 Error Measure
230	D.5.2 Optimization Criterion
231	D.6 Effective Linear Parameters
233	D.7 Performance Point Errors D.8 References
237	E. Supplementary Information and Data on Soil- Structure Interaction Effects E.1 Introduction E.2 Kinematic interaction E.2.1 Shallow Foundations at the Ground Surface
239	E.2.2 Embedded Shallow Foundations
240	E.2.3 Application of Transfer Functions to Calculation of Foundation Motions
242	E.2.4 Simplified Procedure for Design
244	E.3 Foundation Damping
245	E.3.1 Analysis of Impedance Functions E.3.1.1 Basic Case
246	E.3.1.2 Nonuniform Soil Profiles
248	E.3.1.3 Embedded Foundations E.3.1.4 Foundation Shape
249	E.3.1.5 Foundation Flexibility
251	E.3.2 Analysis of System Damping Ratios
256	E.3.3 Simplified Procedure for Design
257	E.4 References
261	F. Supplementary Information and Data on Multi- Degree-of-Freedom Effects F.1 Introduction F.1.1 Objectives F.1.2 Scope F.2 Example Buildings and Demand Parameters
262	F.2.1 Prototype Buildings F.2.1.1 Regular 3-Story Frame F.2.1.2 Regular 9-Story Frame
263	F.2.1.3 3-Story Weak Story Frame F.2.1.4 9-Story Weak Story Frame F.2.1.5 8-Story Shear Wall
264	F.2.2 Modeling
266	F.2.2.1 Dynamic Characteristics of Models
268	F.2.2.2 Model Verification F.2.3 Ground Motions and Demand Intensities
272	F.2.3.1 Ordinary (Site Class C) Motions F.2.3.2 Near-Field Motions F.2.3.3 Drift Levels F.2.3.4 Ground Motion Scaling F.2.4 Extensions to Address P-Delta
273	F.3 Simplified Techniques F.3.1 Single Load Vectors F.3.1.1 First Mode
274	F.3.1.2 Inverted Triangular F.3.1.3 Rectangular F.3.1.4 Code Force Distribution
276	F.3.1.5 Adaptive First Mode F.3.1.6 SRSS
277	F.3.2 Multiple Mode Pushover Analysis
279	F.4 Accuracy of Estimates Made Using Simplified Procedures F.4.1 Error Measurement
280	F.4.2 Results for Ordinary Ground Motions F.4.2.1 Floor Displacements F.4.2.2 Interstory Drift Ratios
281	F.4.2.3 Story Shears F.4.2.4 Overturning Moments
282	F.4.3 Results for Near Field Motions F.5 Equivalent SDOF Estimates of Peak Roof Displacement Response
283	F.5.1 Analysis Details
284	F.5.2 Analysis Results F.6 Scaled NDP Analysis Method F.6.1 Background F.6.2 Elaboration of Step 3 and Examples
286	F.6.2.1 Example Illustrations F.6.3 Statistical Basis
287	F.6.4 Observed Coefficients of Variation
288	F.7 Energy-based Approaches for Pushover Analysis F.7.1 Peak Displacement Response F.7.2 Multiple Mode Estimates of Response Quantities
291	F.8 Detailed Figure Sets for the MDOF Examples
292	F.8.1 Ground Motion Details
307	F.8.2 Responses to Ordinary (Site Class C) Motions
331	F.8.3 Errors Associated with Ordinary (Site Class C) Motions
341	F.8.4 Responses to Near Fault Motions
373	F.8.5 Errors Associated with Near Fault Motions
383	F.8.6 Observed Coefficients of Variation of the Response Quantities Determined for the Ordinary (Site Class C) Motions
391	F.9 References