Optimization-based minimum-cost seismic retrofitting of hysteretic frames with nonlinear fluid viscous dampers

In this paper, we discuss an optimization-based approach for minimum-costseismic retrofitting of hysteretic frames with nonlinear fluid viscous dampers.The proposed approach accounts also for moment-axial interaction in the struc-tural elements, to consider a more realistic coupling between added dampersand retrofitted structure. The design variables of the problem are the dampingcoefficients of the dampers. Indirectly, the design involves also the stiffness coef-ficients of the supporting braces. In the optimization analysis, we minimize arealistic retrofitting cost function with constraints on inter-story drifts undera suite of ground motion records. The cost function includes costs related tothe topological and mechanical properties of the dampers' designs. The struc-ture is modeled with a mixed finite element approach, where the hystereticbehavior is defined at the beams' and columns' cross sections level. We con-sider damper-brace elements with a visco-elastic behavior characterized by theMaxwell model. The dampers' viscous behavior is defined by a fractional powerlaw. Promising results obtained for a two-story, a nine-story, and a 20-story 2-Dframes are presented and discussed.