Application of CQC method to seismic response control with viscoelastic dampers

Abstract

The complete quadratic combination (CQC) modal combination rule for seismic analysis of structures is a great achievement of Professor Armen Der Kiureghian. Among the other various uses of the CQC method, this chapter introduces the application of the CQC method to seismic response control of buildings with dampers to highlight the practical value of the CQC method. The expanded CQC method can accurately estimate the maximum response of buildings installed with response control damping devices and enables performance-based placement design of dampers. In this chapter, the performance-based design pro- cedure of a viscoelastic damper (VED) is introduced for finding the storywise distribution of VEDs in a building such that each peak interstory drift coincides with the corresponding prescribed value. The mechanical properties of the employed VED’s dependence on amplitude and frequency of the excitation as well as material temperature are taken into account and a mechanical nonlinear four-element model that comprises two dashpot elements and two spring elements is proposed for the VED. The developed performance-based design procedure utilizes equivalent linearization of the VED and the expanded CQC method, which involves modal analysis with complex eigenvalue analysis. Seismic response analyses are carried out for high-rise building models with optimally placed VEDs, with the results demonstrating the effectiveness of the expanded CQC method and the validity of the proposed performance-based placement-design procedure.