Seismic design of multiple-rocking systems: A gradient-based optimization approach

Self-centering concentrically braced frames (SC-CBFs) have shown many advantages towards structural damage-free seismic behavior. These systems could be designed either with a single rocking section at the base or with multiple rocking sections along their height. Initial design methodologies for both cases have been proposed with an emphasis on the former case. These methods focused on simplicity of the design process and mostly relied on parametric studies. Thus, the obtained designs may violate some displacement constraints when verified using nonlinear time history analysis (NLTHA) or lead to conservative designs that may be expensive. Furthermore, focusing on simplicity, these methods are tailored for regular structures. This paper takes a different approach that leads to minimum cost designs for irregular structures that satisfy the constraints exactly when verified using NLTHA. The proposed approach allows for multiple rocking sections along the height of the designed buildings, if these lead to cost reductions. Of course, this comes with more demanding computing resources. Nevertheless, these are kept reasonable for practical use on a personal computer. For that purpose, the NLTHA is performed using the computationally efficient Mixed Lagrangian Formalism. Furthermore, an efficient gradient-based optimization framework is developed. The framework is applied for the design of 8, 12, and 20-story spine SC-CBFs and an irregular 12-story building with a setback level. These have shown promising results while revealing also non-traditional designs. This demonstrates the power of using optimization for the design of these lateral load resisting systems.