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The aim of the paper is to present a critical analysis for nonlinear dynamic vibrations. It is applicable to single degree of freedom –SDOF- of reinforced concrete –RC- structures, revealing its multi degree of freedom –MDOF- performance, showing contrast using the balance of energy, using six accelerograms based on type I and II spectrum, according with Eurocode-8. The degradation curve was obtained applying a new formulation, based on the system work and complementary work, into the pushover analysis. A new method incorporating the Bouc-Wen-Baben-Noori theory and global damage was used for the analysis, adding relevance to the: energy balance in its dissipative part, analysis of the structure’s fundamental parameters, relation’s effective period, equivalent damping and global ductility.  The powers, energies and works developed are analyzed, creating a precise balance since energy enters selectively. Hence, an equivalent damping containing a viscous and hysteretic part is predictable, accordingly to the variation of the building’s nonlinear properties. Evaluation of the adequateness and safety level are also obtainable. The controlled parameters contrasted with the balance predicts the structure’s MDOF situation, at any moment related with seismic events. This methodology can be used to stablish a systematic control of nonlinearities for other structural schemes.

Energy balance analysis in non linear dynamic equivalent systems.