Performance-based seismic design of buckling− restrained knee− braced frames: Cumulative damage optimization and design lateral force distribution

Buckling− restrained knee− braced frames (BRKBFs), which utilize relatively short buckling− restrained knee braces as energy dissipation devices, can provide an efficient seismic resistant structural system suitable for both seismic design of new buildings and retrofitting of existing structures. However, the optimum design of such systems under seismic excitations can be challenging due to their complex nonlinear behavior affected by cumulative damage. This study aims to develop a practical method for optimum seismic design of BRKBFs based on the concept of uniform damage distribution (UDD). For the first time, the UDD optimization framework is adopted to optimize the height-wise distribution of cumulative damage, as defined by the Park-Ang damage model, allowing direct control over damage levels during the optimization process. This approach enhances computational efficiency by gradually redistributing the underutilized capacity of energy dissipation devices, leading to an enhanced overall seismic performance by fully exploiting the energy dissipation capacity of the system. To demonstrate the efficiency of the proposed method, 3 − , 6 − , and 9 − story BRKBFs were first designed by using an energy− based design method. The cumulative damage and height− wise distribution of the damage were assessed by nonlinear analyses under a set of ground motions. The UDD optimization method was then applied to achieve the uniform damage state. Finally, the optimization results were used to develop an optimum lateral force distribution for more efficient seismic design of BRKBFs. The outcomes indicate that using the energy− based design and optimization method proposed in this study can provide an efficient methodology to achieve the optimum cumulative damage distribution and considerably improve the seismic performance of BRKBFs, leading to up to 28 % lower damage index. The proposed methodology is general and can be applied to the optimization and development of a suitable lateral force distribution for different structural systems.