Bidirectional Seismic Energy Input to an Isotropic Nonlinear One-Mass Two-Degree-of-Freedom System

The test results obtained for reinforced concrete columns by several studies have revealed that the peak displacement and cumulative hysteresis energy are important parameters for evaluating the damage of columns under horizontal bidirectional and unidirectional loading. Therefore, the seismic parameters related to the nonlinear peak displacement and cumulative hysteresis energy with regard to horizontal bidirectional seismic input should be investigated. In this study, the bidirectional seismic input to an isotropic nonlinear one-mass two-degree-of-freedom system was evaluated. First, a dimensionless parameter gamma, which controls the low-cycle fatigue effect, was formulated as a function of two energy input parameters (the maximum momentary input energy and total input energy) and a nonlinear system (ductility and normalized hysteresis energy absorption during a half cycle). Then, the maximum momentary input energy and total input energy were evaluated according to the ground motion characteristics (Fourier coefficient of horizontal ground motion components) and system properties. Finally, the nonlinear peak displacement and parameter gamma of the nonlinear system were evaluated on the basis of the maximum momentary input energy and total input energy. The results revealed that the nonlinear peak displacement and parameter gamma can be properly evaluated using two energy parameters.