Effective linear damping and stiffness coefficients of nonlinear systems for design spectrum based analysis

A stochastic approach for obtaining reliable estimates of the peak response of nonlinear systems to excitations specified via a design seismic spectrum is proposed. This is achieved in an efficient manner without resorting to numerical integration of the governing nonlinear equations of motion. First, a numerical scheme is utilized to derive a power spectrum which is compatible in a stochastic sense with a given design spectrum. This power spectrum is then treated as the excitation spectrum to determine effective damping and stiffness coefficients corresponding to an equivalent linear system (ELS) via a statistical linearization scheme. Further, the obtained coefficients are used in conjunction with the (linear) design spectrum to estimate the peak response of the original nonlinear systems. The cases of systems with piecewise linear stiffness nonlinearity, along with bilinear hysteretic systems are considered. The seismic severity is specified by the elastic design spectrum prescribed by the European aseismic code provisions (EC8). Monte Carlo simulations pertaining to an ensemble of nonstationary EC8 design spectrum compatible accelerograms are conducted to confirm that the average peak response of the nonlinear systems compare reasonably well with that of the ELS, within the known level of accuracy furnished by the statistical linearization method. In this manner, the proposed approach yields ELS which can replace the original nonlinear systems in carrying out computationally efficient analyses in the initial stages of the aseismic design of structures under severe seismic excitations specified in terms of a design spectrum

A novel stochastic linearization framework for seismic demand estimation of hysteretic MDOF systems subject to linear response spectra

This paper proposes a novel computationally economical stochastic dynamics framework to estimate the peak inelastic response of yielding structures modelled as nonlinear multi degreeof-freedom (DOF) systems subject to a given linear response spectrum defined for different damping ratios. This is accomplished without undertaking nonlinear response history analyses (RHA) or, to this effect, constructing an ensemble of spectrally matched seismic accelerograms. The proposed approach relies on statistical linearization and enforces pertinent statistical conditions to decompose the inelastic d-DOF system into d linear single DOF oscillators with effective linear properties (ELPs): natural frequency and damping ratio. Each such oscillator is subject to a different stationary random process compatible with the excitation response spectrum with damping ratio equal to the oscillator effective critical damping ratio. This equality is achieved through a small number of iterations to a pre-specified tolerance, while peak inelastic response estimates for all DOFs of interest are obtained by utilization of the excitation response spectrum in conjunction with the ELPs. The applicability of the proposed framework is numerically illustrated using a 3-storey Bouc-Wen hysteretic frame structure exposed to the Eurocode 8 elastic response spectrum. Nonlinear RHA involving a large ensemble of non-stationary Eurocode 8 spectrum compatible accelerograms is conducted to assess the accuracy of the proposed approach in a Monte Carlo-based context. It is found that the novel feature of iterative matching between the excitation response spectrum damping ratio and the ELP damping ratio reduces drastically the error of the estimates (i.e., by an order of magnitude) obtained by non-iterative application of the framework

Seismic response analysis of multiple-frame bridges with unseating restrainers considering ground motion spatial variation and SSI

Unseating damages of bridge decks have been observed in many previous major earthquakes due to large relative displacement exceeding the available seat length. Steel cable restrainers are often used to limit such relative displacements. Present restrainer design methods are based on the relative displacements caused by the different dynamic characteristics of adjacent bridge structures. However, the relative displacements in bridge structures are not only caused by different dynamic characteristics of adjacent bridge segments. Recent studies indicated that differential ground motions at supports of bridge piers and Soil Structure Interaction (SSI) could have a significant influence on the relative displacement of adjacent bridge components. Thus the present design methods could significantly underestimate the relative displacement responses of the adjacent bridge components and the stiffness of the restrainers required to limit these displacements. None of the previous investigations considered the effects of spatially varying ground motions in evaluating the adequacy of the restrainers design methods. Moreover, the code recommendation of adjusting the fundamental frequencies of adjacent bridge structures close to each other to mitigate relative displacement induced damages is developed based on the uniform ground motion assumption. Investigations on its effectiveness to mitigate the relative displacement induced damages on the bridge structures subjected to spatially varying ground motion and SSI are made. This paper discusses the effects of spatially varying ground motions and SSI on the responses of the multiple-frame bridges with unseating restrainers through inelastic bridge response analysis

Generalized Dynamic Analysis of Structural Single Rocking Walls (SRWs)

The investigation of structural single rocking walls (SRWs) continues to gain interest as they produce self-centering lateral load responses with reduced structural damage. The Simple Rocking Model (SRM) with modifications has been shown to capture these responses accurately if the SRW and its underlying base are infinitely rigid. This paper advances previous rocking models by accounting for: 1) the inelastic actions at or near the base of the SRW; and 2) the flexural responses within the wall. Included in the proposed advancements are hysteretic and inherent viscous damping associated with these two deformation components so that the total dynamic responses of SRWs can be captured with good accuracy. A system of nonlinear equations of motion is developed, in which the rocking base is discretized into fibers using a zero-length element to locate the associated compressive deformations and damage. The flexural deformations of the rocking body are captured using an elastic term, while the impact events are modeled using impulse-momentum equations. Comparisons with experiments of structural precast concrete and masonry SRWs show that the proposed approach accurately estimates the dynamic responses of different SRWs with and without unbonded posttensioning, for various dynamic excitations and degrees of hysteretic action. Using the proposed approach, a numerical investigation employs different configurations of structural SRWs to quantify the various sources of energy loss, including hysteretic action and impact damping, during various horizontal ground motions

A Seismic Performance Classification Framework to Provide Increased Seismic Resilience

Several performance measures are being used in modern seismic engineering applications, suggesting that seismic performance could be classified a number of ways. This paper reviews a range of performance measures currently being adopted and then proposes a new seismic performance classification framework based on expected annual losses (EAL). The motivation for an EAL-based performance framework stems from the observation that, in addition to limiting lives lost during earthquakes, changes are needed to improve the resilience of our societies, and it is proposed that increased resilience in developed countries could be achieved by limiting monetary losses. In order to set suitable preliminary values of EAL for performance classification, values of EAL reported in the literature are reviewed. Uncertainties in current EAL estimates are discussed and then an EAL-based seismic performance classification framework is proposed. The proposal is made that the EAL should be computed on a storey-by-storey basis in recognition that EAL for different storeys of a building could vary significantly and also recognizing that a single building may have multiple owners

Response And Energy - Dissipation Of Reinforced Concrete Frames Subjected To Strong Base Motions

The National Science Foundation Research Grant GK-1118X and GK 25386

Revision of the Turkish development law no. 3194 governing urban development and land use planning

This paper is based on a report1 that stemmed from an investigation into improving Turkey’s legal framework for spatial planning and physical development. The principal motivation for the investigation has been the renewed awareness in the wake of the Erzincan earthquake of 13 March 1992 that there exist systemic defects in the way the built environment in Turkey is created. These deficiencies cause the building stock to have poor record against disasters, and bleed the national economy. It drains resources in an endless cycle of rebuilding after each occurrence of a disaster. In view of the great losses from the 17 August 1999 and 12 November 1999 earthquakes in northwestern Turkey, parliamentary adoption of the types of legal and structural instruments that have been developed during the course of the investigation has become more pressing