An Impulse and Earthquake Energy Balance Approach in Nonlinear Structural Dynamics - 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