Simple Iterative Use of Lyapunov's Solution for the Linear Optimal Seismic Design of Passive Devices in Framed Buildings

This article presents a Lyapunov-based analysis/redesign approach for the optimal seismic design of added viscous dampers in 3D framed structures. The optimal solution minimizes the total added damping while the mean squared drifts at the peripheral frames are constrained to allowable values under a white noise excitation. The proposed approach uses Lyapunov equation for analysis and an optimality criterion that dictates “fully stressedness” for redesign. Hence, the design process is actually comprised of an iterative solution of a set of algebraic equations. Three examples are solved so as to highlight the advantages of the proposed approach — a 3-story shear frame, an 8-story, 3-bay by 3-bay setback frame, and a 10-story industrial frame.