Assessment of probability of collapse and design for collapse safety

Abstract

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.

Error estimation of closed‐form solution for annual rate of structural collapse

“…For the aforementioned key performance measures, numerous references are available for 'closed-form' analytical solutions. The first closed-form solutions were published for the demand hazard in References [6,7], and using similar assumptions, annual frequencies of limit state exceedance and structural collapse can also be computed [8][9][10].…”

“…Mackie and Stojadinovic [11] used closed-form solutions for damage and loss limit states to propose a PBSD approach for bridges. Zareian and Krawinkler [10] used the closed form solution for the annual rate of collapse, to propose a PBSD methodology considering structural collapse. The above three implementations also separate epistemic and aleatory uncertainties in the structural response and use the mean ground motion hazard curve.…”

Research plan for the study of seismic behavior and design of deep, slender wide flange structural steel beam-column members

“…A number of investigators have conducted nonlinear response history analyses of steel moment resisting frames (MacRae et al, 1990;Krawinkler, 1999, 2000;Medina and Krawinkler, 2003;Zareian and Krawinkler, 2007, Luco and Cornell, 2000, Lee and Foutch, 2000, 2002aLignos and Krawinkler, 2009). As part of the SAC project, Luco and Cornell (2000) and Lee and Foutch (2002b) assessed the effects of brittle connection fractures on the behavior of archetype steel moment resisting frame structures ranging in height from 2-to 20-stories, with pre-Northridge connections, at various levels of ground motion intensity.…”

“…However, in this model the postcapping strength deterioration was not modeled. It has been shown both analytically Zareian and Krawinkler, 2007;Lignos and Krawinkler, 2009) and experimentally (Lignos et al, 2010(Lignos et al, , 2011dSuita et al, 2008) that the capping point is critical for assessing the collapse potential of moment resisting frames Lignos and Krawinkler, 2009;Lignos et al, 2011a). Lee and Foutch (2002a) concluded that all of the buildings with postNorthridge connections showed a high capacity-to-demand ratio ranging from 2.0 to 4.0, depending on frame configuration and height.…”

“…The collapse potential of moment resisting frames is assessed through the use of collapse fragility functions Krawinkler, 2002, 2005;Medina and Krawinkler, 2003;Zareian and Krawinkler, 2007). FEMA P-695, Quantification of Building Seismic Performance Factors (FEMA 2009b), provides a methodology for quantifying building system performance in the context of collapse safety.…”