Damage-based strength reduction factor spectra of structures subjected to bidirectional ground motions

The current research on the damage-based strength reduction factor has been completely based on the inelastic single-degree-of-freedom systems that are more suitable for two-dimensional analyses. Therefore, it is necessary to construct damage-based strength reduction factor spectra for systems subjected to bidirectional ground motions. In this study, an inelastic single-mass bi-degree-of-freedom (SMBDOF) system subjected to the orthogonal bidirectional ground motions with the hysteretic property of two-dimensional yield-surface plasticity function is presented, and the x-component of the system is used to construct the damage-based strength reduction factor spectra of the system (R b spectra). The Park-Ang damage model is used to determine the constant damage index of the R b spectra. In addition, 178 ground motion records for site classes C, D, and E are considered as ground excitations of the SMBDOF system to construct the mean R b spectra with the format of R b -D-T for a given ductility capacity and R b -μ u -T for a given damage level. The R b spectra of the SMBDOF system is compared with the corresponding R spectra of the SDOF system. Statistical analysis considering different values of the natural period, ductility capacity, damage index, period ratio, and site condition is conducted. Analysis results show that the coupling of two-component responses of an inelastic system could increase the strength demand of the system in certain cases; the trend of the R b spectra presented in this study is approximately consistent for different site classes, but the spectral values have the characteristic of site conditions. Therefore, the influence of the period ratio should be considered because a large period difference between two components of the SMBDOF system could aggravate seismic damage in certain situations. Based on the statistical analysis, the expression of R b spectra curves with a period ratio γ = 1 is derived using the regression analysis, and the correction expression is obtained considering the influence of the period ratio on the R b spectra. Then, the construction procedure of the R b spectra is introduced. The predicted R b spectra obtained by the proposed procedure is compared with the actual mean spectra, and comparison results indicate a good match.