SUMMARYThe yield level of an insulator is one of the important parameters which are related to responses and absorbing energy under seismic input energy in isolated structures. The purpose of this paper is to determine the optimal ratios of yield force of the isolator (Q ) to the total weight of the structures (=). To obtain the optimal ratio, 1044 two-degree-of-freedom isolated bridge models, which have bilinear isolators, were selected. These 2-DOF isolated bridge models with superstructure isolation can consider pier #exibility and various parameters of the isolator. Two formulas for determining the optimal yield ratio are proposed and compared with the previous researches. RAE (the ratio of absorbed energy by the isolator to the total input energy) is related directly to structural responses, and Optimal Yield Ratio (OYR), de"ned as a yield ratio at maximum RAE, can be obtained from the relationship between RAE and Q /=. Here, we found that RAE is a reliable factor to evaluate OYR, and it is proportional to earthquake amplitudes under the same kinds of earthquake loadings. Using the proposed formulas, OYR is determined and the optimal yield force of the isolator can be obtained easily and reliably at a seismic isolation design stage.

The equivalent linearization method (ELM) is often used to estimate the maximum displacement of isolated structures. Damping-dependent coefficients (CD) which are a scale multiplier required to give simplified elastic acceleration design spectra (EADS) for greater damping values are proposed. The CD is obtained from the relationship between nonlinear time history analysis (NTHA) and ELM using the standard waves from various ground types and different types of earthquakes. The proposed CD is compared to the previous one and validated for various isolated structures under a natural earthquake and standard waves.