Estimation of Uniform Risk Spectra Suitable for the Seismic Design of Structures

The aim of this paper is to present a performance-based method to estimate uniform risk spectra (URS) for the seismic design and assessment of structures. These spectra, computed with the proposed methodology, provide the lateral capacity (in terms of spectral acceleration) that should be given to a structure, characterized by a reference single degree of freedom system, to achieve a predetermined exceedance rate of economic loss. This procedure involves the seismic hazard assessment necessary to define a seismic design level consistent with the accepted loss value, using a large enough number of synthetic seismic records of several magnitudes, which were obtained by means of an improved empirical Green function method. The statistics of the expected losses of a reference single degree of freedom system are obtained using Monte Carlo simulation, considering the seismic demand and the lateral strength of the structure as random variables. The method is divided into two main stages: (1) definition of the seismic hazard at the site of interest and (2) the probabilistic analysis of the seismic performance in terms of an economical loss ratio of nonlinear SDOF. To illustrate the proposed methodology and, subsequently, to validate it, a URS was computed for a site located in the Mexico City lake-bed zone, and its use in the design of three reinforced concrete frames is shown. The results show that the proposed spectra provide a sufficient approximation between the seismic risk level considered in the seismic design and that of the designed structure. It is concluded that the proposed procedure is a significant improvement over others considered in the literature and a useful research tool for the further development of risk-based earthquake engineering.

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