Almodóvar-Medina, Joel M.

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    Evaluación computacional de la efectividad del método lineal equivalente para la estimación de la respuesta inelástica de pórticos de hormigón resistentes a momento
    (2018-12-11) Almodóvar-Medina, Joel M.; Suárez, Luis E.; College of Engineering; López Rodríguez, Ricardo R.; Guevara, José O.; Department of Civil Engineering; Vanacore, Elizabeth
    This thesis examined an approximate method to calculate the nonlinear seismic response of structures known as the Equivalent Linear Model (ELM) which seeks to approximate the true nonlinear response through a series of linear analyses. The method was originally developed in Geotechnical Earthquake Engineering and even though it is known to have some limitations, it yields reasonably accurate results which make it very popular. In a previous study conducted at the University of Rico at Mayaguez in which the ELM was applied to a 3D reinforced concrete frame it provided satisfactory results. Because a proof-of-concept was already carried out in the previous investigation, this thesis focused on studying the ductility limits in which the ELM is effective. To achieve this goal five reinforced concrete moment resistant frames were selected and modeled in the commercial program SAP2000. This program was used to carry out nonlinear time history analyses which were regarded as the exact results. Modal analysis in the time domain was used to implement the ELM, which requires to iteratively run linear models. From the analysis carried out it was found that the performance of the ELM strongly depends on the modification factor used to correct the system’s maximum strain in order to define its equivalent linear properties. Therefore, it was found necessary to study how to define this factor in the most precise way. Three equations were proposed to calculate this factor and a series of conditions were proposed to choose the most appropriate expression. Several records from historic earthquakes with different frequency content were used in the investigation. The records were scaled up to achieve a desired level of nonlinear response. Nonlinear analyses with the selected accelerograms were carried out to obtain the frames’ global ductility μ in terms of displacements. The ductility range found encompasses from 1 to 4.0 and afterwards the ELM analyses were run for this range. A critical column and beam element were selected for each frame to examine the accuracy of the ELM. The bending moment and shear force in the column and the moment in the beam were computed and their values were used to determine the average error in the internal forces. When the allowable error was limited to 20% it was found that the ELM is effective in the ductility range 1 < μ < 1.5. If this limit is increased by 10%, then the ductility range extends from 1 to 2.75. It is therefore concluded that in its current form the ELM can be applied to calculate the nonlinear response of the frames up to a moderate level.