Seismic Design Optimization of Controlled Rocking Steel Braced Frames based on Neural Dynamic Model

Controlled Rocking Steel Braced Frames (CRSBFs) are one of the modern structural systems intended to mitigate the earthquake-induced lateral vibrations and improve the dynamic performance of civil engineering structures. A CRSBF is comprised of specific shear fuses together with a group of Post-Tensioned (PT) strands. The shear fuses are installed between the column base and the foundation. When the frame rocks, and the column base moves in a vertical direction, the shear fuses are deflected and the kinetic energy is dissipated through the hysteretic behavior of butterfly-shaped elements. In addition, The PT strands directly connect the roof to the ground and provide the required self-centering force and prevent plastic deformations and residual deflections caused by severe earthquake events. The design procedure of a CRSBF must offer an economical solution to satisfy a desired structural performance level. Researchers have evaluated the benefits of CRSBF compared with traditional lateral force resisting systems using large-scale testing, developing computational models, providing performance-based methodologies, and assessment tools. Engineering optimization, in general, is essential in producing the best design to maximize factors such as productivity, strength, reliability, longevity, efficiency, and utilization. Developing a robust design optimization of CRSBF is necessary for a designer to take advantage of the benefits. This paper presents an optimal methodology for seismic design of CRSBFs using the patented Neural Dynamic (ND) model of Adeli and Park. The ND has been used to solve nonlinear design optimization problems, including the design of high-rise steel structures, structural vibration control, concrete mix design, and concrete floor design. The ND model, which is inspired by the brain neurons, integrates a penalty function, the Lyapunov stability theorem, and the Karush-Kuhn-Tucker conditions to guarantee the global convergence of the solution. The objective function is defined to minimize the cost subject to constraints based on design code requirements. The objective function is comprised of two normalized terms including the main frame weight as well as the overall cross-sectional area of the PT strands relative to the corresponding maximum values. The performance of the proposed design methodology is evaluated and compared with available experimental results for a CRSBF subjected to seismic loading. The proposed optimization methodology is studied using numerical simulations considering nonlinearities of the structural model. Artificial accelerograms generated by the Kanai-Tajimi spectrum and scaled to the Maximum Considered Earthquake (MCE) level are used to perform the nonlinear time history analyses and evaluate the dynamic behavior of the structure. The results show that the optimal design methodology leads to 9.9% reduction in overall weight of the main frame elements which subsequently reduces the overall cost of the structure. The dynamic responses of the optimal CRSBF also show that the energy dissipation mechanism effectively reduces the earthquake-induced vibrations and improves the structural performance in a way that the design code requirements for extreme event condition (MCE level) are met.