S.S.F.Mehanny , A.S. Ayoub
Abstract: Quantifying the relative contribution of (1) widely recognized Record-to-Record variability, versus (2) inherent randomness in system parameters to the total variance in the inelastic displacement ratios for first mode-dominant structures with equal nominal relative lateral strength,is the major goal of this paper. Random System Parameters addressed herein are: the system normalized lateral yield strength and the system viscous damping ratio, independently considered. Monte Carlo Simulation technique is used to generate a large number of displacement ratios for a wide range of SDOF systems subjected to a selected set of 20 scaled earthquake records. Various central tendency measures, as well as coefficients of variation to quantify dispersions, are evaluated for the resulting displacement ratios. It has been noted that the dispersion in the values of the displacement ratios that is explained by randomness in system parameters is much smaller than the dispersion due to Record-to-Record variability. Estimates for such dispersions have been reported for potential implementation in emerging probabilistic performance-based seismic design and evaluation methods. It has been also demonstrated that the resulting dispersion in displacement ratios due to uncertainty in system parameters is less than the intrinsic dispersion in the system parameters themselves except at a very few situations and for short periods only.
1.Introduction
Recently introduced performance-based seismic design criteria use displacements rather than forces as basic demand parameters for the design, evaluation and rehabilitation of civil structures. Moreover, current recommendations for the assessment of existing structures have establishedsimplified analysis methods in which SDOF systems are adopted to estimate global inelastic displacement demands on structures. Examples of those recommendations are the ATC-40 guidelines [1], FEMA-273 [2], and FEMA- 356 [3]. In these resource documents, global inelastic displacement demands of structures are computed taking into account the relationship between the maximum inelastic displacement demands of nonlinear SDOF systems and the maximum elastic displacement demands of linear elastic SDOF systems. Therefore, there is a recent renewed interest on approximate methods to compute reasonable estimates for maximum displacements demands of inelastic SDOF systems. Furthermore, probabilistic-based seismic design/evaluation methods are gaining growing attention in the seismic engineering community at the level of both researchers and designers. Hence, comprehensive information on estimates of expected mean values (i.e. central tendency measures) of maximum inelastic displacement for a wide range of first mode-dominant structures and the associated variability (i.e. dispersion) in this response parameter is of high importance for the effective implementation of such probabilistic-based methods.
The first study that investigated the relationship between the maximum deformations of inelastic and elastic systems, referred to in the sequel as inelastic displacement ratios, DRin, was conducted by Veletsos et al. [4]. They studied SDOF systems with an elasto-plastic hysteretic behaviour subjected to simple pulses and to three recorded earthquake ground motions. They observed that in the low frequency region the maximum deformation of the inelastic and elastic systems was approximately the same. This observation gave rise to the well-known “Equal Displacement Rule”. More recent studies have provided a wealth of valuable information regarding central tendency measures for inelastic displacement ratios, DRin, of elasto-plastic and bilinear SDOF systems [5–10]. These recent studies showed that drawing definite conclusions regarding inelastic displacement ratios for different SDOF systemsthatwouldbevalidforvariousfrequencyregionsisnot a straightforward task. In addition, Gupta and Krawinkler [11] extended such ongoing research to cover various types of degrading systems. They accordingly proved that nonlinear SDOF oscillators having pinched stiffness-degrading hysteretic behaviour led to larger maximum inelastic displacements than pure stiffness-degrading systems. Furthermore, in one of the most complete studies on the effect of structural deterioration on inelastic displacement demands, Pekoz and Pincheira [12]
reported that maximum inelastic displacements for degrading systems are larger than those of nondegrading systems when the period of vibration is shorter than the predominant period of the ground motion (defined as the peak in the input energy spectra of an elastic SDOF system). While all these studies provided significantinformationregardingcentraltendencymeasuresfor inelastic displacement ratios of SDOF systems, only very few provided reliable information on the dispersion of these ratios mainlydueto therelativelysmallsampleofconsideredground motions. Toremedy this shortage inprevious statistical studies,Ruiz-Garcia and Miranda [13] used a particularly large number of ground motions (240 records) in order to carefully assess the dispersion of the so-called “constant relative lateral strength”inelastic displacement ratios, DRin. However, such resulting dispersion has been evaluated considering deterministic system parameters, and Record-to-Record (RTR) variability has been the only source of uncertainty included in the dispersion estimation of DRin values.
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