Dimensional response analysis of bilinear SDOF systems under near-fault ground motions with intrinsic length scale

Abstract

Abstract This paper proposes an intrinsic length scale with unambiguous physical significance for dimensional response analysis of inelastic systems, and establishes a versatile regression model for the self-similar response spectra of bilinear single-degree-of\ufeff-freedom (SDOF) under near-fault ground motions. Firstly, according to the dimensional analysis of elastic SDOF systems subjected to analytical pulses, the intrinsic length scale is proposed to compare with the widely used energetic length scale. It is shown that the normalized displacement with respect to the intrinsic length scale is compatible with the analytical solution, and the overall absolute dispersion in the normalized responses is effectively reduced and is more evenly distributed in the entire frequency-ratio range. Then, the intrinsic length scale is adopted in the case of bilinear SDOF systems under analytical pulses, and similar results are observed. Finally, 30 near-fault ground motion records are selected as seismic input of the bilinear SDOF systems. Results indicate that both overall absolute and relative dispersions associated with intrinsic length scale are smaller than those with energetic length scale, when the normalized yield displacement is large. Therefore, the intrinsic length scale is recommended as an alternative length scale for dimensional analysis of elastoplastic structures. Moreover, it is illustrated that there exist two states of complete similarity in the normalized yield displacement. Accordingly, a versatile regression model is suggested for self-similar response spectrum, which can predict structural response.