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Probabilistic models for structures with bilinear demand‐intensity relationships
Author(s) -
O'Reilly Gerard J.,
Monteiro Ricardo
Publication year - 2019
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.3135
Subject(s) - bilinear interpolation , probabilistic logic , range (aeronautics) , polynomial , intensity (physics) , hazard , mathematics , limit (mathematics) , logarithm , extension (predicate logic) , computer science , mathematical optimization , statistics , mathematical analysis , engineering , physics , chemistry , organic chemistry , quantum mechanics , programming language , aerospace engineering
Summary An extension to the existing SAC/FEMA expressions to estimate mean annual frequency of exceedance (MAFE) for a given limit state is described. In specific, this study pertains to structural systems whose demand versus seismic intensity relationship cannot be reasonably represented by a linear fit in logspace, but rather a bilinear fit over the entire range of structural response. Using a predefined limiting intensity, the median demand is separated into two distinct zones of response. These expressions are derived using a second‐order polynomial hazard model fit and can be considered a further extension of the closed‐form expressions available in the literature. The steps in the derivation are described along with an example application of the proposed expressions. Comparing different models shows that the MAFE can be significantly misrepresented when using a linear demand‐intensity model for systems whose behaviour deviates from this assumption in logspace. Similarly, a logarithmic function demand‐intensity fit is examined and seen not to be suitable in the specific situations focused on here. Furthermore, significant underestimation or overestimation is observed when using local fits in the vicinity of the behaviour transition point, which highlights the need for such a bilinear model when assessing the structural performance at the transition point's vicinity. Adopting a bilinear model is shown to better represent structural systems with complex response characteristics, also allowing the use of a single demand model for the entire range of response. This is at the same time still compatible with the existing framework for performance‐based seismic design and assessment.