A non-dimensional parametric approach for the design of PT tendons and mild steel dissipaters in precast rocking walls

In recent years, important benefits for the seismic design of precast reinforced concrete wall structures have been obtained from the use of jointed wall-to-foundation connections, where gap openings are permitted, thus resulting in a rocking motion. The lumped rotation at the wall base protects the panels from damage, while gravity loads and unbounded post-tensioned (PT) tendons, designed to remain elastic, re-center the structure after an earthquake, thus solving the problem of residual displacements. External dissipaters, herein partially unbounded mild steel bars, limit the amplitude of lateral displacements providing the required dissipating capacity. The resulting response is characterized by flag-shaped hysteretic loops. The paper investigates the parameters that may influence the design of rocking walls with supplemental energy dissipation devices in the form of mild reinforcing steel and aims to develop a parametric approach for the design of such systems. In this research, an analytical system of non-dimensional equations is developed for the design of PT tendons and dissipaters: location, area and prestressing force of the former, and location, area and unbounded length of the latter. A parametric approach suitable for the design practice is developed. This allows obtaining a simplified, quick, and accurate approach for the selection of PT tendons and energy dissipaters following a performance-based design approach. The procedure has been applied to a selected case study and validated by means of non-linear time history analyses.