Citation: Buendía, L.; Niño, M.; Reinoso, E.; González, C. Estimation of Uniform Risk Spectra Suitable for the Seismic Design of Structures. Buildings 2023, 13, 2165. https:// doi.org/10.3390/buildings13092165 Academic Editor: Annalisa Greco Received: 30 June 2023 Revised: 15 August 2023 Accepted: 19 August 2023 Published: 26 August 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). buildings Article Estimation of Uniform Risk Spectra Suitable for the Seismic Design of Structures Luis Buendía 1 , Mauro Niño 2, * , Eduardo Reinoso 1,3 and Carlos González 3 1 Evaluación de Riesgos Naturales y Antropogénicos, Mexico City 01050, Mexico; luis.buendia@ern.com.mx (L.B.); ereinosoa@iingen.unam.mx (E.R.) 2 Departamento de Estructuras, Facultad de Ingeniería, National Autonomous University of Mexico, Mexico City 04510, Mexico 3 Instituto de Ingeniería, National Autonomous University of Mexico, Mexico City 04510, Mexico; carlosecalva@gmail.com * Correspondence: mninol@ingenieria.unam.edu Abstract: 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. Keywords: seismic risk; design spectrum; damage analysis; seismic vulnerability; earthquake engineering 1. Introduction A natural risk has several definitions, and from an economic point of view, it may be defined as the potential economic consequences derived from a natural phenomenon in a region, city, or country. Currently, seismic risk assessments have acquired importance because of the large losses presented due to recent earthquakes. The World Economic Fo- rum [1] shows that even though the seismic codes are less permissive, earthquake-related losses keep increasing. This may be explained because, nowadays, there are more exposed assets (several new buildings are built) and most of the seismic building codes are oriented toward achieving only two main performance goals during the design process: (1) avoiding structural damage under frequent earthquakes and (2) avoiding building collapse under rare earthquakes, without considering the structural behavior and consequences of seismic events with intermediate intensities. This increases the uncertainty of damage occurrence and, consequently, the risk of uncontrolled losses, causing economic plans or emergency actions to lack a solid basis upon which to make decisions before and after a seismic event. Fortunately, there are very detailed methodologies [2–5] to assess structural performance, Buildings 2023, 13, 2165. https://doi.org/10.3390/buildings13092165 https://www.mdpi.com/journal/buildings