A parametric model for capacity curves and capacity spectra is proposed. The

The equal displacement approximation is a well-known procedure for estimating the non-linear behavior of structures subjected to earthquake ground motions. This procedure plays a significant role in current seismic design, since it constitutes the basic assumption for defining strength reduction factors. In this paper, calculation of the performance point based on this rule is used to estimate engineering demand parameters such as those obtained by advanced probabilistic non-linear dynamic analysis, NLDA. We present a modification to the classic approach, to improve the predictability of the equal displacement rule. Uncertainties in seismic action and structural properties are considered. Mid-rise reinforced concrete buildings will be used as a testbed. To obtain a representative sample of buildings for statistical analysis, we describe the development through implementation of a numerical tool for calculating probabilistic NLDA. This tool, which is expected to evolve into interoperable software for assessing the seismic risk of structures, is developed within the framework of the KaIROS project. The results presented in this paper could be used to estimate the seismic risk of structures in a very simplified manner.

Seismic regulations and building codes experienced major advances in the last decades. Nevertheless, current trends in earthquake engineering are the assessment of the computational procedures provided by such design rules, by using probabilistic techniques, in order to test the anticipated levels of reliability and performance of the structures. While some consideration is given in codes to the uncertainties associated to the seismic action, no probabilistic requirements are posed on the responses, which determine the final design. Consequently, the risk associated to the design formulas remains unknown. The objective of this chapter is to study whether steel buildings designed and constructed according to the Load and Resistance Factor Design (LRFD) specification for Structural Steel Buildings, reasonably meet the probabilistic requirements on structural member safety applying non-linear dynamic analyses and Monte-Carlo techniques. Starting from a specific low-rise braced frame steel building existing in Manizales, Colombia, we also analyze mid-rise and high-rise braced frame buildings. Similar low-mid-and high-rise Moment-resisting frame buildings are also studied. For each building we performed more than ten thousand dynamic simulations, covering a wide range of combinations of demand and strength. In this way, we determine the exceedance probability of the construction capacity and we verify the safety and reliability of the structural members of the buildings. In the analysis of demand, we consider the probabilistic variation of the vertical gravity loads as well as of the seismic horizontal ones. The analyses of the strength of the studied buildings take into account the uncertainties and probability distributions of several parameters as: the yielding strain, the elasticity modulus, the cross-sectional area and their inertia moments. The analysis shows that in the cases here analyzed, but especially in moment-resisting frame buildings, the uncertainties in the input parameters may lead to significant failure probabilities. We conclude that braced frame steel buildings fulfil the seismic safety requirements while moment-resisting frame buildings would require a safety factor of about 2.7 for the column anchorages to the foundations.

Barcelona, as well as a large number of cities in the Mediterranean basin, has a housing stock composed of a large number of unreinforced brick masonry buildings. Motivated by different factors, the enlargement of the city (Eixample in Catalan) was held from the second half of the 19th century and the beginning of the 20th, a period in which a large number of buildings of this type were built, many of which are still used as dwellings. Although the buildings were built individually, some of them are linked to adjacent buildings by the side walls. This feature leads to the analysis of the buildings as isolated structures and also as an aggregate. Barcelona is located in a seismic region of low to moderate hazard, with macroseismic intensity between the grades VI and VII of the European macroseismic scale EMS'98. Based on the deterministic and probabilistic response spectra for the different types of soils present in Barcelona obtained in the work of Irizarry (2004), the seismic risk of four individual buildings and an aggregate is evaluated. The buildings are modeled and analyzed using the TREMURI program and MATLAB routines under the guidance of RISK-UE project.

The use of sensors to obtain the dynamic properties of structures by means of ambient vibrations has become a common practice. However, conventional and more extensively used methods require the installation of sensors, which should be in contact with the structure. These methods could be even risky in case of structures weakened by a hazardous event, for which the risk of collapse is unknown. In this study, two main subjects are analyzed and discussed. The former is related to the use of the Real-Aperture Radar (RAR) as a non-invasive, remote sensing interferometric method to measure the vibration response to ambient noise of buildings. As a test bed, two high-rise regular buildings with reinforced concrete frames (8-story) and steel frames (12-story), located in Barcelona, Spain, are analyzed. Notice that the RAR device is a sensor using the principle of interferometry to measure displacements. This type of sensors has exhibited a good performance in urban environments at different atmospheric, meteorological and lighting conditions, compared to other types of remote sensors (e.g. Laser Doppler). Another advantage is that RAR devices have a very good resolution and they can operate at great distances from the object to be measured. However, so far, RAR is rarely used in buildings, being still a poorly studied technique. The latter subject is related to the optimal post-processing of the acquired data. At this respect, the Power Spectral Density (PSD) signal-processing technique is used to process the signals acquired. From this analysis, the predominant periods of the analyzed buildings were obtained and then they were compared with those periods obtained from measurements of accelerometers located inside the structures. The results indicate that the use of RAR can be a reliable alternative to estimate the structural periods in a relatively simple and non-invasive manner.