Seismic retrofit of frame structures using passive systems based on optimal control

This paper proposes a new seismic modification methodology for optimal design of multistory frame structures to avoid damage and attain a robust response to extreme hazards. The methodology determines added damping devices of optimal size at strategic locations and modifies story stiffnesses, by solving a newly formulated constrained optimization problem. The objective is to minimize a cost function representing total energy while satisfying the equations of motion and allowable interstory drifts for given severe ground motions. The proposed methodology combines the classical linear quadratic regulator, which searches for an optimal gain matrix, with an analysis-redesign iterative procedure to produce a robust analysis redesign (RAR) iterative approach. A new algorithm approximates the equivalent stiffness to fit the displacement gains. At convergence, the RAR procedure will yield optimal sizing and new topology for the designed system. The RAR procedure is developed here for shear structures. However, RAR can be utilized for complex structures by modeling them first as equivalent shear-type structures having stiffness properties that yield the same maximum interstory drifts for the given records. Two numerical examples of shear-type structures are examined. These examples use structures already having an “optimal” configuration, which are further optimized using the methodology developed herein. In addition, a numerical example comprised of a 10-story moment resisting frame structure is presented to illustrate the use of the equivalent shear structure approach. The results of the exemplified retrofitted moment resisting frame structure show great improvements in its dynamic response.