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.
We analyze the case of a building that collapsed in a multifamily complex of Tlalpan borough in Mexico City during the 19 September 2017 Central Mexico earthquake. Despite having similar materials and similar structural and geometric properties, this was the only building that collapsed in the complex. A structural analysis of the building and a study of the soils' predominant periods indicated that resonance effects, if any, would not be significant. However, phenomena related to the anomalous performance of buildings in dense urban areas, such as geological soil, soil-structure interaction, and soil-city interaction effects were also investigated. A detailed analysis of the directionality of seismic actions recorded at nearby accelerometric stations and of the azimuths of sound and damaged buildings pointed to directionality effects as responsible for the collapse of the building. Subsequently, a set of fifty-eight, two-component acceleration records of the earthquake in the city was used to perform a thorough directionality analysis. The results were then compared with the foreseen uniform hazard response spectra and the design spectra in the city. Seismic actions in the city due to this earthquake were stronger than those corresponding to the uniform hazard response spectra. In addition, although design spectra have been significantly improved in the new 2017 Mexican seismic regulations, they were exceeded in eleven of the fifty-eight analyzed spectra. In four of these eleven cases, the design spectra were exceeded due to directionality effects. These results confirm the necessity of considering directionality effects in damage assessments, in strong motion prediction equations, and in design regulations. * Definitions apply for peak ground acceleration (PGA) and for response spectral accelerations, Sa (T), which are functions of the period, T, of vibration.
An efficient method for considering the directionality effect of earthquakes on structures Recent researches have proven the importance of considering the directionality effect on the expected seismic damage of structures. However, it demands a high computational effort if the nonlinear dynamic analysis (NLDA) is used to estimate the seismic response. This paper presents a simplified approach to obtain peak response parameters for a building subjected to ground motions considering the directionality effect. To do so, the maximum and median response spectra, considering all the non-redundant response spectra, of several ground motion pairs are calculated. Afterwards, a spectral matching technique is applied to these spectra and new acceleration components are obtained. A series of NLDA are performed with these new components and the roof displacement and base shear values are calculated. These results are compared with the maximum and median values, calculated by performing a series of NLDA, after rotating the earthquakes records by considering increments of 1° in the interval 0°-180°. The results agree with both approaches validating the efficiency of the simplified proposed approach.
Estimations of seismic risk in urban areas should include quantifications of the expected damage to civil structures subjected to earthquakes. In buildings, this quantification depends on the maximum inter-story drift (MIDR), among other aspects. In this study, the correlation between several intensity measures (IMs) and the maximum inter-story drift of steel structures was investigated. Three steel frame buildings of 3, 7 and 13 stories were used as a testbed. These buildings were modelled as 2D framed structures. For the seismic hazard, forty strong ground motion pairs were selected (80 individual horizontal components) from the Italian database. These records were scaled to a specific peak ground acceleration (PGA) and matched to a design spectrum from Eurocode 8. Nonlinear dynamic analysis was used to estimate the seismic response of the structures. Thus, 720 nonlinear dynamic analyses (NLDA) were performed [3 structures × (80 as recorded accelerograms + 80 scaled records + 80 matched records)]. Preliminary results indicate that PGA and MIDR show the worst correlation. A higher correlation was observed for peak ground velocity, root-mean-square velocity and specific energy density intensity-based measures. Finally, a new IM, which is highly correlated with MIDR, is proposed. This IM is called ID-PGV and considers both the PGV and the significant duration.
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