Displacement response spectra based on 2DOF system for the isolated design of railway bridges

Abstract

The displacement response spectrum is a crucial step in the displacement-based seismic design method for bridge structures. However, for seismic isolation railway bridge structures, the traditional single-degree-of-freedom (SDOF) displacement response spectra cannot separately take into account the displacement requirements of the bridge piers and bearings. To address this limitation, this study develops displacement response spectra of the isolated design of railway bridges based on a simplified 2DOF system, categorized into elastic and inelastic versions according to specified design needs. These spectra comprise the peak displacement spectra of piers and bearings (i.e. PPDRS and PBDRS) and residual displacement spectra of bearings (i.e. RBDRS). The 2DOF analytical model and analysis procedure for 2DOF displacement response spectra are introduced. Subsequently, the influence of the key performance parameters of the structure on displacement response spectra is investigated, including the mass ratio (r), effective period of piers (T_p), effective isolated damping ratio (ζ_b), ductility ratio of bearings (μ_b), and post-yielding stiffness ratio of bearings (α). The results indicate that r and T_p exert a more pronounced influence on PPDRS, whereas the influence of ζ_b, μ_b, and α is more significant on PBDRS and RBDRS, with changes all exceeding 40% for key periods. Furthermore, the comparison of elastic and inelastic displacement response spectra is discussed. It shows that the displacements predicted by elastic and inelastic response spectra are with discrepancies within 25%. Accordingly, the conventional DDBD procedure is extended and refined, and an example is finally designed to validate the proposed design procedure.