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An Impulse and Earthquake Energy Balance Approach in Nonlinear Structural Dynamics
Motivation of the proposed approach
Simplification of near-fault pulse-type ground motion
Resonant response in nonlinear structural dynamics and earthquake-resistant design
Double impulse and corresponding one-cycle sine wave with the same frequency and same maximum Fourier amplitude
Energy balance under earthquake ground motion and impulse
Undamped model
Damped model
Critical input timing of second impulse in double impulse
Comparison of conventional methods and the proposed method for nonlinear resonant analysis
Outline of this book
Summaries
References
: Critical earthquake response of an elastic–perfectly plastic SDOF model under double impulse as a representative of near-fault ground motions
Introduction
Double impulse input
SDOF system
Maximum elastic-plastic deformation of SDOF system to double impulse
Accuracy investigation by time-history response analysis to corresponding one-cycle sinusoidal input
Design of stiffness and strength for specified velocity and period of double impulse and specified response ductility
Application to recorded ground motions
Summaries
References
A. Appendix 1: proof of critical timing of second impulse
B. Appendix 2: derivation of critical timing
: Critical earthquake response of an elastic–perfectly plastic SDOF model under triple impulse as a representative of near-fault ground motions
Introduction
Triple impulse input
SDOF system
Maximum elastic-plastic deformation of SDOF system to triple impulse
CASE 1
CASE 2
CASE 3
CASE 3-1
CASE 3-2
CASE 4
Accuracy investigation by time-history response analysis to corresponding three wavelets of sinusoidal waves
Design of stiffness and strength for specified velocity and period of triple impulse and specified response ductility
Approximate prediction of response ductility for specified design of stiffness and strength and specified velocity and period of triple impulse
Comparison between maximum response to double impulse and that to triple impulse
Application to recorded ground motions
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
: Critical input and response of an elastic–perfectly plastic SDOF model under multi-impulse as a representative of long-duration earthquake ground motions
Introduction
Multiple impulse input
SDOF system
Maximum elastic-plastic deformation of SDOF system to multiple impulse
Non-iterative determination of critical timing and critical plastic deformation by using modified input sequence
Determination of critical timing of impulses
Correspondence of responses between input sequence 1 (original one) and input sequence 2 (modified one)
Accuracy investigation by time-history response analysis to corresponding multi-cycle sinusoidal input
Proof of critical timing
Summaries
References
A. Appendix 1: Multi-impulse and correspondingmulti-cycle sine wave with thesame frequency and samemaximum fourier amplitude
: Critical earthquake response of an elastic–perfectly plastic SDOF model with viscous damping under double impulse
Introduction
Modeling of near-fault ground motion with double impulse
Elastic–perfectly plastic SDOF model with viscous damping
Elastic-plastic response of undamped system to critical double impulse
Linear elastic response of damped system to critical double impulse
Elastic-plastic response of damped system to critical double impulse
Approximate critical response of the elastic-plastic system with viscous damping based on the energy balance law
CASE 1: Elastic response even after second impulse
CASE 2: Plastic deformation only after the second impulse
CASE 3: Plastic deformation, even after the first impulse
Maximum deformation under the critical double impulse with respect to the input velocity level
Accuracy check by time-history response analysis to one-cycle sinusoidal wave
Applicability of proposed theory to actual recorded ground motion
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
: Critical steady-state response of a bilinear hysteretic SDOF model under multi-impulse
Introduction
Bilinear hysteretic SDOF system
Closed-form expression for elastic-plastic steady-state response to critical multi-impulse
CASE 1: Impulse in unloading process
CASE 2: Impulse in loading process (second stiffness range)
Results in numerical example
Derivation of critical impulse timing
Convergence of critical impulse timing
Accuracy check by time-history response analysis to corresponding multi-cycle sinusoidal wave
Proof of critical timing
Applicability of critical multi-impulse timing to corresponding sinusoidal wave
Accuracy check by exact solution to corresponding multi-cycle sinusoidal wave
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
: Critical earthquake response of an elastic–perfectly plastic SDOF model on compliant ground under double impulse
Introduction
Double impulse input
Double impulse input
Closed-form critical elastic-plastic response of SDOF system subjected to double impulse (summary of results in Chapter 2)
Maximum elastic-plastic deformation of simplified swaying-rocking model to critical double impulse
Simplified swaying-rocking model
Equivalent SDOF model of simplified swaying-rocking model
Critical elastic-plastic response of simplified swaying-rocking model subjected to double impulse
Numerical example
Applicability of critical double impulse timing to corresponding sinusoidal wave
Toward better correspondence between double impulse and sinusoidal input
Applicability to recorded ground motions
Summaries
References
: Closed-form dynamic collapse criterion for a bilinear hysteretic SDOF model under near-fault ground motions
Introduction
Double impulse input
Double impulse input
Previous work on closed-form critical elastic–perfectly plastic response of SDOF system subjected to double impulse
Maximum elastic-plastic deformation and stability limit of SDOF system with negative post-yield stiffness to critical double impulse
Pattern 1: Stability limit after the second impulse without plastic deformation after the first impulse
Pattern 2: Stability limit after the second impulse with plastic deformation after the first impulse
Pattern 3: Stability limit after the second impulse with closed-loop in restoring-force characteristic
Additional Pattern 1: Limit after the first impulse
Additional Pattern 2: Limit without plastic deformation after the second impulse
Results for numerical example
Discussion
Applicability of critical double impulse timing to corresponding sinusoidal wave
Applicability to recorded ground motions
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
: Closed-form overturning limit of a rigid block as a SDOF model under near-fault ground motions
Introduction
Double impulse input
Maximum rotation of rigid block subjected to critical double impulse
Limit input level of critical double impulse characterizing overturning of rigid block
Numerical examples and discussion
Summaries
References
Appendix 1: Verification of critical timing ofdouble impulse for various inputlevels
: Critical earthquake response of a 2DOF elastic–perfectly plastic model under double impulse
Introduction
Double impulse input
Two-DOF system and normalization of double impulse
Description of elastic-plastic response process in terms of energy quantities
Upper bound of plastic deformation in first story after second impulse
Maximization of
Maximization of Δ E (minimization of Δ E in addition)
Minimization of (maximization of in addition)
Upper bound of plastic deformation in the first story after the second impulse
Numerical Examples of Critical Responses
Upper bound of critical response
Input level for tight upper bound
Input level for loose upper bound
Verification of criticality
Application to recorded ground motions
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
: Optimal viscous damper placement for an elastic–perfectly plastic MDOF building model under critical double impulse
Introduction
Input ground motion
Problem of optimal damper placement and solution algorithm
Three models for numerical examples
Dynamic pushover analysis for increasing critical double impulse (DIP: Double Impulse Pushover)
Numerical examples
Examples for Problem 1 using Algorithm 1
Examples for Problem 2 using Algorithm 2
Examples for Mixed Problem (Problem 3) of Problem 1 and 2 using Algorithm 3
Comparison of IDA (Incremental Dynamic Analysis) and DIP
Summaries
References
: Future directions
Introduction
Treatment of noncritical case
Extension to nonlinear viscous damper and hysteretic damper
Treatment of uncertain fault-rupture model and uncertain deep ground property
Application to passive control systems for practical tall buildings
Stopper system for pulse-type ground motion of extremely large amplitude
Repeated single impulse in the same direction for repetitive ground motion input
Robustness evaluation
Principles in seismic resistant design
References
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