Translational vibration modes of a building through iterative methods and verification using Mathcad and Etabs software

Abstract

This research focuses on calculating the translational vibration modes of a three-level frame building, in order to determine its periods and way of vibrating, the evaluation was carried out using interactive methods of Stodola and Holzer, the numerical method of Jacobi, and the results obtained were verified using functions of the eigenvals vector and eigenvecs matrix of the Mathcad software. In addition, a verification was carried out with modeling in the Etabs software, following the properties established by the Technical Standard E.030 for Seismic-Resistant Design of the Reglamento Nacional de Edificaciones (RNE). Throughout the investigation, accurate results were obtained through manual calculations as well as verifications with the use of Mathcaf and ETABS software. In each instance, it was determined that these methods represent the most appropriate way to obtain approximate values with respect to the verification carried out with its period and way of vibrating. These reliable results underline the effectiveness of the tools and methods used, highlighting the deep understanding of the dynamic characteristics of the analyzed building.