Sensitivity-based study of the influence of brace over-strength distributions on the seismic response of steel frames with BRBs

Steel frames with buckling-restrained braces (BRBs) have low lateral post-elastic stiffness, especially in the case of non-moment resisting beam-to-column connections, due to the brace limited post-yield stiffness. Thus, a tendency to soft storey formation, fostered by nonhomogeneous distributions of brace over-strength, might be observed during seismic events. The objective of this paper is to study the effects of brace over-strength distributions on the expected maximum reduction of seismic performance, as measured by local and global engineering demand parameters (EDPs). This goal is pursued using response sensitivity analysis and solving a constrained extreme problem. The general framework of the proposed sensitivity-based approach is presented and its application to steel frames with BRBs is described in detail. Realistic case studies are considered, taking as reference solution the design based on the modal response spectrum method. Interstorey drifts are used as global EDPs related to the damage of nonstructural elements, while maximum plastic strains and cumulative plastic strains of the braces are considered as local EDPs to monitor the damage of braces. The brace over-strength patterns that are the most unfavourable for each EDP are identified and the relevant maximum increment of each EDP with respect to the reference design solution is determined, obtaining a relation between the maximum seismic performance reduction and the brace over-strength used in the design. In this way, the proposed approach can be used as a tool for safer and more effective seismic designs of steel frames with BRBs.