Design formulations for supplemental viscous dampers to building structures

The existing design formulas such as those provided by FEMA 273 (or FEMA 356) and other research reports have provided significantly convenient tools to practical engineers in determining the damping coefficients of the supplemental viscous dampers corresponding to an expected added damping ratio to the structure. However, the relative vertical deformation between the ends of the damper was not considered when the formulas were derived. This has resulted into the lack of accuracy for predicting the added damping ratio of medium-rise to high-rise buildings compared with low-rise buildings. This is primarily due to the fact that, for the medium-rise and high-rise buildings, the flexural deformation is as significant as the shear deformation of the building when subjected to earthquake loading, and thus the vertical relative deformation may be comparable with the horizontal relative displacement between the ends of the damper. In this study, new design formulas are derived for commonly used installation schemes of viscous dampers. Numerical verifications have indicated that the new design formulas predict a more accurate viscous damping ratio contributed by linear viscous dampers and ensure a more conservative design for the structure with nonlinear viscous dampers.