Controlling All Interstory Displacements in Highly Nonlinear Steel Buildings Using Optimal Viscous Damping

Abstract

A gradient-based optimization algorithm is used to simultaneously control all interstory displacements in nonlinearly degrading steel buildings using optimal viscous dampers. Optimal damping ratios are computed in each mode of vibration such that the sum of the errors between the interstory displacements and the “just-yielded” performance objectives is minimized. A representative damping formulation is used to determine the sizes and locations of the damper devices. The members of the buildings are assumed to degrade smoothly according to a constitutive rule that was developed to model the behavior of kinematically strain-hardened materials. Numerical examples are used to demonstrate the ability of the algorithm to control potential damages in a 10-story building and also in an 8-story building responding at significant higher modes of vibration. It is found that the interstory displacements in the 10-story building are very adequately controlled. Although demands in the 8-story building are significantly reduced, some modes remain overdamped and not all performance levels are exactly met as some stories remain marginally damaged. Finally, the algorithm is applied in a 20-story benchmark building, and it is shown that the interstory displacements, postyield curvatures, and plastic damages are very adequately controlled.