Hybrid force-displacement-based design methods for self-centering wall structures

Self-centering wall structures (SCWs) are well-developed resilient structures and are being gradually implemented in practical engineering. The direct displacement-based design (DDBD) method is commonly adopted for the seismic design of SCWs due to its predictable displacement pattern. Due to the complexity of DDBD, practical engineers still commonly use the present force-based design (FBD) methods. However, the existing FBD method is inapplicable when the deformation of SCWs is large. To make the design procedure more acceptable to engineers and promote SCWs in real practice, three design methods were proposed: a force-based design method by empirical formula, a force-based method by iteration, and a hybrid force-displacement-based design method (HBD). The applicability of FBD by existing empirical formulas of structural periods in several codes for SCWs was discussed. In FBD by iteration, the initial prestress is iterated to determine secant stiffness and the structural period so that SCWs can be designed following its constitutive relationships. HBD is carried out by comparing the resistance of the structure under the target displacement with the earthquake demand according to the deformation mode of the SCWs. Compared with the existing DDBD methods, the proposed design methods can simplify the design process in engineering applications while keeping the design outcomes consistent with DDBD and proved to be reasonable with nonlinear time history analysis. In addition, the FBD method by empirical formula and the HBD method can be implemented in the four-level seismic fortifications currently proposed in China. The proposed methods solve the issues of the existing FBD and could be a reference for engineers to design SCWs in engineering practice.