SUMMARYThis paper presents the description, calibration and application of relatively simple hysteretic models that include strength and sti ness deterioration properties, features that are critical for demand predictions as a structural system approaches collapse. Three of the basic hysteretic models used in seismic demand evaluation are modiÿed to include deterioration properties: bilinear, peak-oriented, and pinching. The modiÿed models include most of the sources of deterioration: i.e. various modes of cyclic deterioration and softening of the post-yielding sti ness, and also account for a residual strength after deterioration. The models incorporate an energy-based deterioration parameter that controls four cyclic deterioration modes: basic strength, post-capping strength, unloading sti ness, and accelerated reloading sti ness deterioration. Calibration of the hysteretic models on steel, plywood, and reinforced-concrete components demonstrates that the proposed models are capable of simulating the main characteristics that in uence deterioration. An application of a peak-oriented deterioration model in the seismic evaluation of single-degree-of-freedom (SDOF) systems is illustrated. The advantages of using deteriorating hysteretic models for obtaining the response of highly inelastic systems are discussed.

Reliable collapse assessment of structural systems under earthquake loading requires analytical models that are able to capture component deterioration in strength and stiffness. For calibration and validation of these models a large set of experimental data is needed. This paper discusses the development of a database on experimental data of steel components and the use of this database for quantification of important parameters that affect the cyclic moment-rotation relationship at plastic hinge regions in beams. Based on information deduced from the steel component database, empirical relationships for modeling of pre-capping plastic rotation, post-capping rotation and cyclic deterioration for beams with reduced beam section (RBS) and beams other than RBS are proposed. Quantitative information is also provided for modeling of the effective yield strength, post-yield strength ratio, residual strength, and ductile tearing of steel components subjected to cyclic loading.

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SUMMARYNear-fault ground motions impose large demands on structures compared to 'ordinary' ground motions. Recordings suggest that near-fault ground motions with 'forward' directivity are characterized by a large pulse, which is mostly orientated perpendicular to the fault. This study is intended to provide quantitative knowledge on important response characteristics of elastic and inelastic frame structures subjected to near-fault ground motions. Generic frame models are used to represent MDOF structures. Near-fault ground motions are represented by equivalent pulses, which have a comparable e ect on structural response, but whose characteristics are deÿned by a small number of parameters. The results demonstrate that structures with a period longer than the pulse period respond very di erently from structures with a shorter period. For the former, early yielding occurs in higher stories but the high ductility demands migrate to the bottom stories as the ground motion becomes more severe. For the latter, the maximum demand always occurs in the bottom stories. Preliminary regression equations are proposed that relate the parameters of the equivalent pulse to magnitude and distance. The equivalent pulse concept is used to estimate the base shear strength required to limit story ductility demands to speciÿc target values.

SUMMARY Assessing the probability of collapse is a computationally demanding component of performance‐based earthquake engineering. This paper examines various aspects involved in the computation of the mean annual frequency of collapse (λc) and proposes an efficient method for estimating the sidesway collapse risk of structures in seismic regions. By deaggregating the mean annual frequency of collapse, it is shown that the mean annual frequency of collapse is typically dominated by earthquake ground motion intensities corresponding to the lower half of the collapse fragility curve. Uncertainty in the collapse fragility curve and mean annual frequency of collapse as a function of the number of ground motions used in calculations is also quantified, and it is shown that using a small number of ground motions can lead to unreliable estimates of a structure's collapse risk. The proposed method is shown to significantly reduce the computational effort and uncertainty in the estimate. Copyright © 2012 John Wiley & Sons, Ltd.

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.

SUMMARYA process is outlined and evaluated for the estimation of seismic roof and storey drift demands for frame structures from the spectral displacement demand at the "rst mode period of the structure. The spectral displacement demand is related to the roof drift demand for the multi-degree-of-freedom (MDOF) structure using three modi"cation factors, accounting for MDOF e!ects, inelasticity e!ects, and P-delta e!ects. Median values and measures of dispersion for the factors are obtained from elastic and inelastic time history analyses of nine steel moment resisting frame structures subjected to sets of ground motions representative of di!erent hazard levels. The roof drift demand is related to the storey drift demands, with the results being strongly dependent on the number of stories and the ground motion characteristics. The relationships proposed in this paper should prove useful in the conceptual design phase, in estimating deformation demands for performance assessment, and in improving basic understanding of seismic behaviour. Copyright 2000 John Wiley & Sons, Ltd.

SUMMARYA research program is summarized in which collapse of a steel frame structure is predicted numerically and the accuracy of prediction is validated experimentally through earthquake simulator tests of two 1:8 scale models of a 4-story code-compliant prototype moment-resisting frame. We demonstrate that (1) sidesway collapse can occur for realistic combinations of structural framing and earthquake ground motion; (2) P − effects and component deterioration dominate behavior of the frame near collapse; (3) prediction of collapse is feasible using relatively simple analytical models provided that component deterioration is adequately represented in the analytical model; and (4) response of the framing system near collapse is sensitive to the history that every important component of the frames experiences, implying that symmetric cyclic loading histories that are routinely used to test components provide insufficient information for modeling deterioration near collapse.