Design-level estimation of seismic displacements for self-centering SDOF systems on stiff soil

Self-centering systems, which are intended to survive a major earthquake with essentially no residual displacements, are drawing increasing attention from designers. Both force-based and displacement-based design methodologies require an estimate of the peak seismic displacements. Therefore, this study focuses on estimating the peak displacements of self-centering systems based on constant-strength ( C R ) displacement demand spectra, which are calculated from more than five million nonlinear time history analyses of single-degree-of-freedom (SDOF) systems using ground motions representing a site with stiff soil conditions. Because of the ability of self-centering systems to achieve large displacement capacities while also being relatively stiff in the linear range, this study includes much lower linear limits than are used to design traditional yielding systems. Self-centering systems are shown to have displacements that are generally larger than for corresponding elastic systems, and although supplemental energy dissipation decreases the peak displacements, the influence of increasing the energy dissipation ratio, β , decreases as β approaches 100%. The secondary stiffness has relatively little influence if it is positive and small, but a negative secondary stiffness can lead to unbounded response. Using a tangent stiffness proportional damping model instead of an initial stiffness proportional damping model increases the peak displacements and makes the results more sensitive to the energy dissipation and secondary stiffness. Regression analysis is used to develop a simple equation that can be used during design to estimate the displacement demands on self-centering systems. This equation is shown to achieve a reasonable balance between simplicity and accuracy for the design of four controlled rocking steel braced frames with heights between three and nine storeys.