The main goals of this article are to analyze the use of simplified deterministic nonlinear static procedures for assessing the seismic response of buildings and to evaluate the influence that the uncertainties in the mechanical properties of the materials and in the features of the seismic actions have in the uncertainties of the structural response. A reinforced concrete building is used as a guiding case study. In the calculation of the expected spectral displacement, deterministic nonlinear static methods are simple and straightforward. For not severe earthquakes these approaches lead to somewhat conservative but adequate results when compared to more sophisticated procedures involving nonlinear dynamic analyses. Concerning the probabilistic assessment, the strength properties of the materials, concrete and steel, and the seismic action are considered as random variables. The Monte Carlo method is then used to analyze the structural response of the building. The obtained results show that significant uncertainties are expected; uncertainties in the structural response increase with the severity of the seismic actions. The major influence in the randomness of the structural response comes from the randomness of the seismic action. A useful example for selected earthquake scenarios is used to illustrate the applicability of the probabilistic approach for assessing expected damage and risk. An important conclusion of this work is the need of broaching the fragility of the buildings and expected damage assessment issues from a probabilistic perspective.

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Non-linear dynamic analysis and the damage index of Park-Ang have been often used to assess expected seismic damage to a structure. Depending on the size of the structure and the duration of the record, the computational effort in dynamic analyses is usually high. In this research, a new damage index is proposed based on nonlinear static analysis. The damage index is a linear combination of two energy functions: 1) the strain energy associated with the stiffness variation and the ductility of the structure, and 2) the dissipated energy associated with hysteretic cycles. These two energy functions are obtained from the capacity curve of the structure and from the energy balance with the spectral acceleration. To show the ability of the index to represent damage, low-rise steel buildings were studied under the seismic actions that are expected in Mexico City. The results obtained with the new method show good agreement with those calculated by means of dynamic analyses using the Park-Ang damage index. On average, the Park-Ang damage index is well-fitted by the combination of 62% of the strain energy and 38% of the energy dissipated by hysteresis. Moreover, the new damage index can link damage to certain characteristics of seismic actions, such as their intensity and duration. Therefore, the new approach results in a practical, powerful tool for estimating seismic damage in buildings, especially as probabilistic approaches require massive computations.

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.