This paper illustrates a probabilistic-based methodology for quantifying the collapse potential of structural systems, which can provide us with more accurate estimates of losses induced by earthquakes. Applications of this methodology for assessment of collapse potential of existing buildings and design for collapse safety are demonstrated by equations and example. The collapse potential is represented by the probability of collapse at discrete hazard levels and on an annualized basis (mean annual frequency). The basic ingredient of the proposed methodology is a 'collapse fragility curve' which expresses the probability of collapse as a function of the selected ground motion intensity measure. The process for estimating the collapse fragility using scalar and vector-valued ground motion intensity measure is demonstrated. The proposed assessment and design processes do incorporate the effect of aleatory and epistemic uncertainties. It was shown by example that the uncertainties, both aleatory and epistemic, have a significant effect on the outcome of the conceptual design for collapse safety. ‡ This is the same median value of collapse capacity that was obtained by performing IDA using the mathematical model of the structure with properties of its members set to their median values and the set of representative ground motions. This notation was not used previously to prevent confusion.

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SUMMARYPerformance assessment implies that the structural, non-structural, and content systems are given and that decision variables, DVs, (e.g. expected annual loss, mean annual frequency of collapse) are computed and compared to speciÿed performance targets. Performance-based design (PBD) is di erent by virtue of the fact that the building and its components and systems ÿrst have to be created. Good designs are based on concepts that incorporate performance targets up front in the conceptual design process, so that subsequent performance assessment becomes more of a veriÿcation process of an e cient design rather than a design improvement process that may require radical changes of the initial design concept. In short, the design approach could consist of (a) specifying performance targets (e.g. tolerable probability of collapse, acceptable dollar losses) and associated seismic hazards, and (b) deriving engineering parameters for system selection, or perhaps better, using the relatively simple design decision support tools discussed in this paper.

The seismic risk assessment of a structure in performance-based design (PBD) may be significantly affected by the representation of ground motion uncertainty. In PBD, the uncertainty in the ground motion is often represented by a probabilistic description of a scalar parameter, or low-dimensional vector of parameters, known as the intensity measure (IM), rather than a full probabilistic description of the ground motion time history in terms of a stochastic model. In this work, a new procedure employing relative sufficiency measure is introduced on the basis of information theory concepts to quantify the suitability of one IM relative to another in the representation of ground motion uncertainty. On the basis of this relative sufficiency measure, several alternative scalar- and vector-valued IMs are compared in terms of the expected difference in information they provide about a predicted structural response parameter, namely, the seismically induced drift in an existing reinforced-concrete frame structure. It is concluded that the most informative of the eight considered IMs for predicting the nonlinear drift response are two scalar IMs and a vector IM that depend only on the spectral ordinates at the periods of the first two (small-amplitude) modes of vibratio

This paper summarizes collapse performance measures and the probabilistic basis for their development to assist in understanding of collapse behaviour of buildings and implementation of performance objectives in design and evaluation of buildings for collapse safety. Collapse in this context is defined as the loss of lateral load‐resisting capability of a building's structural system caused by ground shaking. Estimation of collapse performance requires the relation between a ground motion intensity measure (IM) and the probability of collapse, denoted as collapse fragility curve, and the relation between the same ground motion IM and the seismic hazard for the building, denoted as seismic hazard curve. Two methods for estimating the collapse fragility curve of a building are discussed: the EDP‐based approach and the IM‐based approach. In both approaches, collapse is associated with a scalar ground motion IM and is obtained by utilizing Incremental Dynamic Analysis. The collapse performance criteria presented in this paper are compared with the collapse performance criteria recommended in the SAC/Federal Emergency Management Agency guidelines. An eight‐storey moment‐resisting frame case study is used to compare the estimates of collapse performance of various approaches discussed in this paper. Copyright © 2009 John Wiley & Sons, Ltd.

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The study presented in this paper addresses the issue of engineering validation of Graves and Pitarka's (2010) hybrid broadband ground motion simulation methodology with respect to some well-recorded historical events and considering the response of multiple degrees of freedom (MDoF) systems. Herein, validation encompasses detailed assessment of how similar is, for a given event, the seismic response due to comparable hybrid broadband simulated records and real records. In the first part of this study, in order to investigate the dynamic response of a wide range of buildings, MDoF structures are modeled as elastic continuum systems consisting of a combination of a flexural cantilever beam coupled with a shear cantilever beam. A number of such continuum systems are selected including the following: (1) 16 oscillation periods between 0.1 and 6???s; (2) three shear to flexural deformation ratios to represent respectively shear-wall structures, dual systems, and moment-resisting frames; and (3) two stiffness distributions along the height of the systems, that is, uniform and linear. Demand spectra in terms of generalized maximum interstory drift ratio (IDR) and peak floor acceleration (PFA) are derived using simulations and actual recordings for four historical earthquakes, namely, the 1979 Mw 6.5 Imperial Valley earthquake, 1989 Mw 6.8 Loma Prieta earthquake, 1992 Mw 7.2 Landers earthquake, and 1994 Mw 6.7 Northridge earthquake. In the second part, for two nonlinear case study structures, the IDR and PFA distributions over the height and their statistics, are obtained and compared for both recorded and simulated time histories. These structures are steel moment frames designed for high seismic hazard, 20-story high-rise and 6-story low-rise buildings. The results from this study highlight the similarities and differences between simulated and real records in terms of median and intra-event standard deviation of logs of seismic demands for MDoF building systems. This general agreement, in a broad range of moderate and long periods, may provide confidence in the use of the simulation methodology for engineering applications, whereas the discrepancies, statistically significant only at short periods, may help in addressing improvements in generation of synthetic records

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