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Spectral evaluation of seismic fragility of structures
An approach for assessing seismic fragility of structures is presented. In this approach, the structural response, in terms of probability, is evaluated from inelastic response spectrum and spectral capacity, and from consistent relationships that provide the Probability Distribution Function of spectral ordinates. These relationships that are function of the structural parameters allows a direct assessment of the probability of exceeding the limit states from which the fragility curves are constructed. The crossing theory of Rice (1944, 1945) and the equivalent linearization method (Caughey, 1959) are used to obtain an approximation to this function. The theoretical results are verified with a numerical study. The ground motion is modeled as a stationary zero-mean Gaussian process characterized by an amplitude Fourier spectrum typical of far-field earthquakes (low amplitude in the short-frequency rage f < 0.2 Hz). It is shown that a Gaussian distribution can be assumed for the response of hysteretic systems under this type of excitations and that the white noise representation of ground motion may lead to large inelastic displacements, which are not likely to occur in the case of earthquake type excitations. Two case studies illustrate the possible use of this approach, and its accuracy is evaluated by comparing the predicted fragility curves with results obtained from simulations on a similar structure. A parametric study is conducted to identify the influence of the various structural parameters on fragility.