An Impulse and Earthquake Energy Balance Approach in Nonlinear Structural Dynamics

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface
Authors
Chapter 1: Introduction
	1.1 Motivation of the proposed approach
		1.1.1 Simplification of near-fault pulse-type ground motion
		1.1.2 Resonant response in nonlinear structural dynamics and earthquake-resistant design
	1.2 Double impulse and corresponding one-cycle sine wave with the same frequency and same maximum Fourier amplitude
	1.3 Energy balance under earthquake ground motion and impulse
		1.3.1 Undamped model
		1.3.2 Damped model
	1.4 Critical input timing of second impulse in double impulse
	1.5 Comparison of conventional methods and the proposed method for nonlinear resonant analysis
	1.6 Outline of this book
	1.7 Summaries
	References
Chapter 2: Critical earthquake response of an elastic–perfectly plastic SDOF model under double impulse as a representative of near-fault ground motions
	2.1 Introduction
	2.2 Double impulse input
	2.3 SDOF system
	2.4 Maximum elastic-plastic deformation of SDOF system to double impulse
	2.5 Accuracy investigation by time-history response analysis to corresponding one-cycle sinusoidal input
	2.6 Design of stiffness and strength for specified velocity and period of double impulse and specified response ductility
	2.7 Application to recorded ground motions
	2.8 Summaries
	References
	A. Appendix 1: proof of critical timing of second impulse
	B. Appendix 2: derivation of critical timing
Chapter 3: Critical earthquake response of an elastic–perfectly plastic SDOF model under triple impulse as a representative of near-fault ground motions
	3.1 Introduction
	3.2 Triple impulse input
	3.3 SDOF system
	3.4 Maximum elastic-plastic deformation of SDOF system to triple impulse
		3.4.1 CASE 1
		3.4.2 CASE 2
		3.4.3 CASE 3
		3.4.4 CASE 3-1
		3.4.5 CASE 3-2
		3.4.6 CASE 4
	3.5 Accuracy investigation by time-history response analysis to corresponding three wavelets of sinusoidal waves
	3.6 Design of stiffness and strength for specified velocity and period of triple impulse and specified response ductility
	3.7 Approximate prediction of response ductility for specified design of stiffness and strength and specified velocity and period of triple impulse
	3.8 Comparison between maximum response to double impulse and that to triple impulse
	3.9 Application to recorded ground motions
	3.10 Summaries
	References
	A. Appendix 1: Proof of critical timing
	B. Appendix 2: Upper bound of maximum response via relaxation of timing of third impulse
	C. Appendix 3: Triple impulse and corresponding 1.5-cycle sine wave with the same frequency and same maximum fourier amplitude
Chapter 4: Critical input and response of an elastic–perfectly plastic SDOF model under multi-impulse as a representative of long-duration earthquake ground motions
	4.1 Introduction
	4.2 Multiple impulse input
	4.3 SDOF system
	4.4 Maximum elastic-plastic deformation of SDOF system to multiple impulse
		4.4.1 Non-iterative determination of critical timing and critical plastic deformation by using modified input sequence
		4.4.2 Determination of critical timing of impulses
		4.4.3 Correspondence of responses between input sequence 1 (original one) and input sequence 2 (modified one)
	4.5 Accuracy investigation by time-history response analysis to corresponding multi-cycle sinusoidal input
	4.6 Proof of critical timing
	4.7 Summaries
	References
	A. Appendix 1: Multi-impulse and correspondingmulti-cycle sine wave with thesame frequency and samemaximum fourier amplitude
Chapter 5: Critical earthquake response of an elastic–perfectly plastic SDOF model with viscous damping under double impulse
	5.1 Introduction
	5.2 Modeling of near-fault ground motion with double impulse
	5.3 Elastic–perfectly plastic SDOF model with viscous damping
	5.4 Elastic-plastic response of undamped system to critical double impulse
	5.5 Linear elastic response of damped system to critical double impulse
	5.6 Elastic-plastic response of damped system to critical double impulse
		5.6.1 Approximate critical response of the elastic-plastic system with viscous damping based on the energy balance law
		5.6.2 CASE 1: Elastic response even after second impulse
		5.6.3 CASE 2: Plastic deformation only after the second impulse
		5.6.4 CASE 3: Plastic deformation, even after the first impulse
		5.6.5 Maximum deformation under the critical double impulse with respect to the input velocity level
	5.7 Accuracy check by time-history response analysis to one-cycle sinusoidal wave
	5.8 Applicability of proposed theory to actual recorded ground motion
	5.9 Summaries
	References
	Appendix 1: Critical impulse timing for linearelastic system with viscousdamping
	Appendix 2: Velocity at zero restoring force after attaining umax1 in case 3
Chapter 6: Critical steady-state response of a bilinear hysteretic SDOF model under multi-impulse
	6.1 Introduction
	6.2 Bilinear hysteretic SDOF system
	6.3 Closed-form expression for elastic-plastic steady-state response to critical multi-impulse
		6.3.1 CASE 1: Impulse in unloading process
		6.3.2 CASE 2: Impulse in loading process (second stiffness range)
		6.3.3 Results in numerical example
		6.3.4 Derivation of critical impulse timing
	6.4 Convergence of critical impulse timing
	6.5 Accuracy check by time-history response analysis to corresponding multi-cycle sinusoidal wave
	6.6 Proof of critical timing
	6.7 Applicability of critical multi-impulse timing to corresponding sinusoidal wave
	6.8 Accuracy check by exact solution to corresponding multi-cycle sinusoidal wave
	6.9 Summaries
	References
	Appendix 1: Time-history response to criticalmulti-impulse and derivation ofcritical time interval
	Appendix 2: Adjustment of input level ofmulti-impulse and correspondingsinusoidal wave
Chapter 7: Critical earthquake response of an elastic–perfectly plastic SDOF model on compliant ground under double impulse
	7.1 Introduction
	7.2 Double impulse input
		7.2.1 Double impulse input
		7.2.2 Closed-form critical elastic-plastic response of SDOF system subjected to double impulse (summary of results in Chapter 2)
	7.3 Maximum elastic-plastic deformation of simplified swaying-rocking model to critical double impulse
		7.3.1 Simplified swaying-rocking model
		7.3.2 Equivalent SDOF model of simplified swaying-rocking model
		7.3.3 Critical elastic-plastic response of simplified swaying-rocking model subjected to double impulse
		7.3.4 Numerical example
	7.4 Applicability of critical double impulse timing to corresponding sinusoidal wave
	7.5 Toward better correspondence between double impulse and sinusoidal input
	7.6 Applicability to recorded ground motions
	7.7 Summaries
	References
Chapter 8: Closed-form dynamic collapse criterion for a bilinear hysteretic SDOF model under near-fault ground motions
	8.1 Introduction
	8.2 Double impulse input
		8.2.1 Double impulse input
		8.2.2 Previous work on closed-form critical elastic–perfectly plastic response of SDOF system subjected to double impulse
	8.3 Maximum elastic-plastic deformation and stability limit of SDOF system with negative post-yield stiffness to critical double impulse
		8.3.1 Pattern 1: Stability limit after the second impulse without plastic deformation after the first impulse
		8.3.2 Pattern 2: Stability limit after the second impulse with plastic deformation after the first impulse
		8.3.3 Pattern 3: Stability limit after the second impulse with closed-loop in restoring-force characteristic
		8.3.4 Additional Pattern 1: Limit after the first impulse
		8.3.5 Additional Pattern 2: Limit without plastic deformation after the second impulse
	8.4 Results for numerical example
	8.5 Discussion
		8.5.1 Applicability of critical double impulse timing to corresponding sinusoidal wave
		8.5.2 Applicability to recorded ground motions
	8.6 Summaries
	References
	Appendix 1: Maximum elastic-plastic deformationof sdof model with negativepost-yield stiffness to double impulse
	Appendix 2: Maximum elastic-plasticdeformation of sdof model withpositive post-yield stiffness todouble impulse
Chapter 9: Closed-form overturning limit of a rigid block as a SDOF model under near-fault ground motions
	9.1 Introduction
	9.2 Double impulse input
	9.3 Maximum rotation of rigid block subjected to critical double impulse
	9.4 Limit input level of critical double impulse characterizing overturning of rigid block
	9.5 Numerical examples and discussion
	9.6 Summaries
	References
	Appendix 1: Verification of critical timing ofdouble impulse for various inputlevels
Chapter 10: Critical earthquake response of a 2DOF elastic–perfectly plastic model under double impulse
	10.1 Introduction
	10.2 Double impulse input
	10.3 Two-DOF system and normalization of double impulse
	10.4 Description of elastic-plastic response process in terms of energy quantities
	10.5 Upper bound of plastic deformation in first story after second impulse
		10.5.1 Maximization of
		10.5.2 Maximization of Δ E (minimization of Δ E in addition)
		10.5.3 Minimization of (maximization of in addition)
		10.5.4 Upper bound of plastic deformation in the first story after the second impulse
	10.6 Numerical Examples of Critical Responses
		10.6.1 Upper bound of critical response
		10.6.2 Input level for tight upper bound
		10.6.3 Input level for loose upper bound
		10.6.4 Verification of criticality
	10.7 Application to recorded ground motions
	10.8 Summaries
	References
	Appendix 1: Adjustment of amplitudes ofdouble impulse and correspondingone-cycle sinusoidal wave
	Appendix 2: Upper and lower bounds of plasticdeformation in first story aftersecond impulse (case of elasticresponse in first story after firstimpulse)
	Appendix 3: Comparison of time histories to double impulse and corresponding sinusoidal wave
	Appendix 4: Input level of double impulse for characterizing critical response close to upper or lower bound
	Appendix 5: Effect of viscous damping
Chapter 11: Optimal viscous damper placement for an elastic–perfectly plastic MDOF building model under critical double impulse
	11.1 Introduction
	11.2 Input ground motion
	11.3 Problem of optimal damper placement and solution algorithm
	11.4 Three models for numerical examples
	11.5 Dynamic pushover analysis for increasing critical double impulse (DIP: Double Impulse Pushover)
	11.6 Numerical examples
		11.6.1 Examples for Problem 1 using Algorithm 1
		11.6.2 Examples for Problem 2 using Algorithm 2
		11.6.3 Examples for Mixed Problem (Problem 3) of Problem 1 and 2 using Algorithm 3
	11.7 Comparison of IDA (Incremental Dynamic Analysis) and DIP
	11.8 Summaries
	References
Chapter 12: Future directions
	12.1 Introduction
	12.2 Treatment of noncritical case
	12.3 Extension to nonlinear viscous damper and hysteretic damper
	12.4 Treatment of uncertain fault-rupture model and uncertain deep ground property
	12.5 Application to passive control systems for practical tall buildings
	12.6 Stopper system for pulse-type ground motion of extremely large amplitude
	12.7 Repeated single impulse in the same direction for repetitive ground motion input
	12.8 Robustness evaluation
	12.9 Principles in seismic resistant design
	References
Index