Performance-based multi-objective collaborative optimization of steel frames with fuse-oriented buckling-restrained braces

A multi-objective collaborative optimal design procedure for steel frames equipped with buckling-restrained braces (BRBs) is proposed under the framework of performance-based seismic design (PBSD) in order to minimize the damage of the primary structure as well as the material cost. For this purpose, a so-called BRB energy dissipation ratio is defined and introduced in the optimization to characterize the involvement of fuse-type BRBs in hysteretic energy dissipation in building stories. Three groups of constraints obtained from the rules on geometrical and conceptual design, the requirements regarding strength and stability, and the PBSD-based story drift limits are considered. To address the discrete-continuous hybrid design variables, a hybrid coding scheme is proposed to modify the non-dominated sorting genetic algorithm II (NSGA-II). The rationality of the proposed procedure is demonstrated by a case study on a seven-story planar steel frame with BRBs. The demonstration indicates that the proposed optimization procedure can make BRBs play the role of a structural fuse successfully in steel frames. The BRB energy dissipation ratios of case C are distributed nearly uniformly along the structural height. The weak-beam-strong-column design principle can be satisfactorily achieved through the maximization of the story BRB energy dissipation ratios. Additionally, the modified hybrid coding NSGA-II algorithm is computationally efficient and stable.