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

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

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

A critical examination of near-field accelerograms from the sea of Marmara region earthquakes

In 1999, Turkey was struck by two major earthquakes that occurred 86 days apart on the North Anatolian Fault system. Both earthquakes had right-lateral strike-slip mechanisms with moment magnitudes greater than 7. The number of strong-motion records obtained from the Kocaeli earthquake (17 August 1999, M-w 7.4) was 34. The second event, designated as the Bolu-Duzce earthquake (12 November 1999, M-w 7.2), triggered 20 instruments. Among the records that we have from these earthquakes, seven are from near-source ground-motion data. These records were obtained from the cities of Gebze (GBZ), Yarimca (YPT), Izmit (IZT) (capital city of the province of Kocaeli), Adapazari (SKR) (capital of the province of Sakarya), Duzce (DZC) (shaken strongly in both the events), and Bolu (BOL). In many of these urban centers, extensive structural damage was observed. Although these near-field data have greatly expanded the strike-slip near-source ground-motion database worldwide for M-w > 7 earthquakes, they represent a blurred image of the actual severity of the ground motions in the epicentral area because of the sparseness of the national strong-motion network and the unrepresentative geologic conditions at the recording sites. We examine the records to determine whether they provide clues about the extensive damage on the housing stock in the epicentral region. The goal is tackled with earthquake structural engineering criteria in mind, using the drift spectrum as the primary yardstick. There appears to be conflicting evidence that the fault-normal (FN) direction should represent a greater damage-causing potential when this potential is based on ground-story drift spectra. The component with larger ground velocity does correlate better with the component with larger drift demand, but this does not always coincide with the FN direction. The period of the peak velocity pulse matches the structural period where the drift demand is the largest. Further refinements of code requirements that consider this effect are in order

A simple replacment for the drift spectrum

The elastic drift spectrum displays, as a function of period, the story drift (expressed as the ratio of the story drift to story height) that a ground motion record would cause in a multistory framed building. It is a pivotal instrument for performance-based earthquake engineering. Wave theory for a uniform shear beam is utilized for calculating this spectrum, but it requires that records of the ground velocity and displacement should be available. Alternative but less rigorous expressions of the drift spectrum for the ground story level of a multistory frame are developed. This set of formulations requires only that the displacement spectrum, or equivalently the acceleration spectrum, for which the basic input is the ground acceleration, should be at hand. We compare these expressions against both the rigorous formulation and other simple techniques. The error that the proposed formulation represents appears to be acceptable even when the comparison is done for near-field accelerograms where the drift demand is substantial

Beams on generalized foundations: Supplementary element matrices

A general analytical solution for the shape functions of a linear beam segment supported on a two-parameter elastic foundation is derived. The solution is not restricted to a particular range of magnitudes of the foundation parameters, The closed form shape functions are utilized to derive analytic expressions for work equivalent nodal forces for arbitrary transverse loads and coefficients of the consistent mass and geometrical stiffness matrices, Each work equivalent nodal force and each coefficient of the element matrices is compared with its conventional counterpart for an ordinary beam segment supported by no foundation, (C) 1997 Elsevier Science Ltd