# Critical Excitation Methods in Earthquake Engineering

## 2nd Edition

**Authors:**Izuru Takewaki

**eBook ISBN:**9780080994291

**Hardcover ISBN:**9780080994369

**Imprint:**Butterworth-Heinemann

**Published Date:**21st June 2013

**Page Count:**400

## Description

After the March 11, 2011, earthquake in Japan, there is overwhelming interest in worst-case analysis, including the critical excitation method. Nowadays, seismic design of structures performed by any seismic code is based on resisting previous natural earthquakes. *Critical Excitation Methods in Earthquake Engineering, 2e, *develops a new framework for modeling design earthquake loads for inelastic structures. The 2e, includes three new chapters covering the critical excitation problem for multi-component input ground motions, and that for elastic-plastic structures in a more direct way are incorporated and discussed in more depth. Finally, the problem of earthquake resilience of super high-rise buildings is discussed from broader viewpoints.

## Key Features

- Solves problems of earthquake resilience of super high-rise buildings
- Three new chapters on critical excitation problem for multi-component input ground motions
- Includes numerical examples of one and two-story models

## Readership

Structural Engineers, Structural Designers, Earthquake Engineers and Researchers

## Table of Contents

Table of Contents

Preface to the first edition

Preface to the second edition

Chapter 1: Overview of seismic critical excitation method

1-1: What is critical excitation?

1-2: Origin of critical excitation method (Drenick's approach)

1-3: Shinozuka's approach

1-4: Historical sketch in early stage

1-5: Various measures of criticality

1-6: Subcritical excitation

1-7: Stochastic excitation

1-8: Convex models

1-9: Nonlinear or elastic-plastic SDOF system

1-10: Elastic-plastic MDOF system

1-11: Critical envelope function

1-12: Robust structural design

1-13: Critical excitation method in earthquake-resistant design

**Chapter 2: Critical excitation for stationary and non-stationary random inputs **25

2-1: Introduction

2-2: Stationary input to SDOF model

2-3: Stationary input to MDOF model

2-4: Conservativeness of bounds

2-5: Non-stationary input to SDOF model

2-6: Non-stationary input to MDOF model

2-7: Numerical examples for SDOF model

2-8: Numerical examples for MDOF model

2-9: Conclusions

Chapter 3: Critical excitation for non-proportionally damped structural systems

3-1: Introduction

3-2: Modeling of input motions

3-3: Response of non-proportionally damped model to non-stationary random excitation

3-4: Critical excitation problem

3-5: Solution procedure

3-6: Critical excitation for acceleration (proportional damping)

3-7: Numerical examples (proportional damping)

3-8: Numerical examples (non-proportional damping)

3-9: Numerical examples (various types of damping concentration)

3-10: Conclusions

Chapter 4: Critical excitation for acceleration response

4-1: Introduction

4-2: Modeling of input motions

4-3: Acceleration response of non-proportionally damped model to non-stationary random input

4-4: Critical excitation problem

4-5: Solution procedure

4-6: Numerical examples

4-7: Model with non-proportional damping-1

4-8: Model with non-proportional damping-2

4-9: Model with proportional damping

4-10: Conclusions

Chapter 5: Critical excitation for elastic-plastic response

5-1: Introduction

5-2: Statistical equivalent linearization for SDOF model

5-3: Critical excitation problem for SDOF model

5-4: Solution procedure

5-5: Relation of critical response with inelastic response to recorded ground motions

5-6: Accuracy of the proposed method

5-7: Criticality of the rectangular PSD function and applicability in wider parameter range

5-8: Critical excitation for MDOF elastic-plastic structures

5-9: Statistical equivalent linearization for MDOF model

5-10: Critical excitation problem for MDOF model

5-11: Solution procedure

5-12: Relation of critical response with inelastic response to recorded ground motions

5-13: Accuracy of the proposed method

5-14: Conclusions

Chapter 6: Critical envelope function for non-stationary random earthquake input

6-1: Introduction

6-2: Non-stationary random earthquake ground motion model

6-3: Mean-square drift

6-4: Problem for finding critical envelope function

6-5: Double maximization procedure

6-6: Discretization of envelope function

6-7: Upper bound of mean-square drift

6-8: Numerical examples

6-9: Critical excitation for variable envelope functions and variable frequency contents

6-10: Conclusions

Chapter 7: Robust stiffness design for structure-dependent critical excitation

7-1: Introduction

7-2: Problem for fixed design

7-3: Problem for structure-dependent critical excitation

7-4: Solution procedure

7-5: Numerical design examples

7-6: Response to a broader class of excitations

7-7: Response to code-specified design earthquakes

7-8: Conclusions

Chapter 8: Critical excitation for earthquake energy input in SDOF system

8-1: Introduction

8-2: Earthquake input energy to SDOF system in frequency domain

8-3: Property of energy transfer function and constancy of earthquake input energy

8-4: Critical excitation problem for earthquake input energy with acceleration constraint

8-5: Critical excitation problem for earthquake input energy with velocity constraint

8-6: Actual earthquake input energy and its bound for recorded ground motions

8-7: Conclusions

Chapter 9: Critical excitation for earthquake energy input in MDOF system

9-1: Introduction

9-2: Earthquake input energy to proportionally damped MDOF system (frequency-domain modal analysis)

9-3: Earthquake input energy to non-proportionally damped MDOF system (frequency-domain modal analysis)

9-4: Earthquake input energy without modal decomposition

9-5: Examples

9-6: Critical excitation for earthquake energy input in MDOF system

9-7: Conclusions

Chapter 10: Critical excitation for earthquake energy input in soil-structure interaction system

10-1: Introduction

10-2: Earthquake input energy to fixed-base SDOF system

10-3: Earthquake input energy to SSI systems

10-4: Actual earthquake input energy to fixed-base model and SSI system

10-5: Critical excitation for earthquake energy input in SSI system

10-6: Critical excitation problem

10-7: Upper bound of Fourier amplitude spectrum of input

10-8: Solution procedure and upper bound of input energy

10-9: Critical excitation problem for velocity constraints

10-10: Solution procedure for velocity constraint problems

10-11: Numerical examples-1 (one-story model)

10-12: Numerical examples-2 (three-story model)

10-13: Conclusions

Chapter 11: Critical excitation for earthquake energy input in structure-pile-soil system

11-1: Introduction

11-2: Transfer function to bedrock acceleration input

11-3: Earthquake input energy to structure-pile system

11-4: Earthquake input energy to structure

11-5: Input energies by damage-limit level earthquake and safety-limit level earthquake

11-6: Critical excitation for earthquake energy input in structure-pile-soil system

11-7: Conclusions

Chapter 12: Critical excitation for earthquake energy input rate

12-1: Introduction

12-2: Non-stationary ground motion model

12-3: Probabilistic earthquake energy input rate: a frequency-domain Approach

12-4: Critical excitation problem for earthquake energy input rate

12-5: Solution procedure for double maximization problem

12-6: Mean energy input rate for special envelope function

12-7: Critical excitation problem for non-uniformly modulated ground motion model

12-8: General problem for variable envelope function and variable frequency content

12-9: Numerical examples

12-10: Conclusions

Chapter 13: Critical excitation for multi-component inputs

13-1: Introduction

13-2: Horizontal and vertical simultaneous inputs

13-3: Bi-directional horizontal inputs

13-4: Interpretation using inner product

13-5: Conclusions

Chapter 14: Critical excitation for elastic-plastic response using deterministic approach

14-1: Introduction

14-2: Abbas and Manohar’s approach

14-3: Moustafa and Takewaki’s approach

14-4: Conclusions

Chapter 15: Earthquake resilience evaluation of building structures with critical excitation methods

15-1: Introduction

15-2: Robustness, redundancy and resilience

15-3: Representation of uncertainty in selecting design ground motions

15-4: Uncertainty expression in terms of info-gap model

15-5: Worst combination of structural parameters and input parameters

15-6: Reality of resonance and its investigation

15-7: Conclusions

## Details

- No. of pages:
- 400

- Language:
- English

- Copyright:
- © Butterworth-Heinemann 2013

- Published:
- 21st June 2013

- Imprint:
- Butterworth-Heinemann

- eBook ISBN:
- 9780080994291

- Hardcover ISBN:
- 9780080994369

## About the Author

### Izuru Takewaki

### Affiliations and Expertise

Kyoto University, Department of Urban and Environmental Engineering, Kyoto, Japan