Constant damage inelastic permanent period shift ratios spectra

The phenomenon of elongation of the structural period after earthquake excitation has been widely observed, and elongated period obtained after earthquake excitations can be used for post-earthquake assessment. The inelastic permanent period shift ratio, an indicator representing the degree of stiffness degradation and closely relating to the damage state, is defined as the ratio of the elongated period Tin of single-degree-of-freedom (SDOF) systems after earthquake excitations to the initial period Tel. The objective of this paper is to investigate the inelastic permanent period shift ratios under constant damage performances through nonlinear timehistory analysis of SDOF systems, and the modified Park-Ang damage index is employed to characterize the structural damage. Inelastic permanent period shift ratio spectra are statistically constructed considering both the ground motion characteristics (such as site conditions, velocity pulse, magnitude, closet distance, directivity effects, significant duration and frequency contents) and structural parameters (including damage states, hysteretic models, ultimate deformation capacity, energy dissipation factor and postyield ratio). The results showed that the permanent period shift ratio is a reliable damage indicator for assessment of global damage states. The influence caused by ground motions on the estimation of the mean of the permanent period elongation ratio under constant damage performances is limited, while the effects caused by different structural damage and deformation capacity can reach up to approximately 70% and 33%, respectively. An expression for the relationship between the damage index and the permanent period shift ratio is established. Ignoring the differences of structural performances, using the period shift ratios to directly assess the global damage states will lead to erroneous results.