# Influence of Directionality on the Seismic Response of Typical RC Buildings
###### Abstract  
Current seismic analysis contemplates the simultaneous use of the orthogonal components of an earthquake in order to determine the structural stresses closer to reality. This has led to these components being combined considering a fraction of them, as applying them completely would lead to excessively conservative results. However, their application is carried out considering that the direction of the components coincides with the orientation of the orthogonal axes that define the resistant structure. The assumption takes on special importance when it comes to establishing performance demands on a structure based on nonlinear time-history analysis. To establish the proportional relationship between the seismic components, the angle of incidence is used, which is one of the imponderable variables of an earthquake. In this investigation, a group of reinforced concrete structural archetypes with various typologies and regularity in plan is presented, which allow the effect of the angle of incidence in determining the maximum displacement demands to be studied. To study the response, a set of strong earthquakes recorded in Chile is used, obtaining the angle of incidence that produces the maximum displacement demands through interstory drift and roof displacement. A statistical analysis is also carried out in which the influence of the angle of incidence that produces the maximum response is studied. structural irregularity; incidence angle; nonlinear time-history analysis; maximum displacement; maximum interstory drift +
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maximum errors have been reported for story displacement and interstory drift of up to 22% and 42%, respectively, or errors of up to 37% in roof displacements and rotations in plastic hinges ([PERSON] et al. [6]). Finally, [PERSON] et al. [7] reported variations in displacement demands of up to 90%. The direction in which the earthquake interacts with the structure is arbitrary, so the structural axes do not necessarily correspond to the main axes of movement, which would present the most unfavorable situation. To study this characteristic, [PERSON] and [PERSON] [3] obtained the response of asymmetric and symmetric structures by varying the degrees of inelasticity, vibration periods, and incidence angles used, observing that the response varies depending on the fundamental period, structuring, and degree of inelasticity. In the analyses, two archetypes were used, varying the angle of incidence in increments of 5\({}^{\circ}\) from 0\({}^{\circ}\) to 180\({}^{\circ}\). According to the authors, the ratio between the maximum inelastic deformation for a given angle and the maximum obtained for an angle of 0\({}^{\circ}\) and 90\({}^{\circ}\) tends to increase along with the fundamental period, averaging between 1.1 and 1.6 for torsionally balanced and unbalanced models. It was concluded that the structural axes are not necessarily the most unfavorable and that the critical incidence angle varies depending on the intensity of the record. On the other hand, [PERSON] [8] studied two different structures, using three records and incidence angles in increments of 5\({}^{\circ}\) varying from 0\({}^{\circ}\) to 360\({}^{\circ}\). These records were used as a basis to scale an acceleration spectrum considering the first period of the structures, damping of 5%, and three levels of intensity. The response of the structures varied according to the records, intensity level, and incidence angle. In order to study the effect of the directionality of earthquakes on structures, nonlinear response analysis has frequently been used. [PERSON] et al. [9], studied the influence of directionality on seismic response variation, including in the study the variation of the angle of incidence between 0\({}^{\circ}\) and 180\({}^{\circ}\) in increments of 22.5\({}^{\circ}\), reaching the conclusion that, for the analyzed structures, the main axes underestimated the demand, especially in plan irregular structures, while in structures with double symmetry, no considerable variations were obtained.