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This study develops empirical equations relating viscous damping ratios (ξ) and damper coefficients (c) in steel structures for seismic design applications. The objective is to establish predictive formulas that enable conversion between equivalent viscous damping ratios and physical damper characteristics through dynamic analysis. This research employs a two-phase analytical methodology on steel building frameworks. Initially, inherent viscous damping ratios are incrementally varied from 3% to 40% to establish baseline response characteristics. Subsequently, supplemental damping devices are integrated with damper coefficients (c) adjusted according to manufacturer specifications. Linear time-history analyses are conducted for both configurations to determine equivalent damping relationships, with a particular focus on Interstory Drift Ratios (IDR) and Peak Floor Accelerations (PFA) as key seismic demand parameters. By comparing response quantities between inherent and supplemental damping scenarios, empirical relationships linking physical damper coefficients with equivalent viscous damping ratios are formulated. The resulting equations provide practicing engineers with a practical tool for estimating damper specifications based on target damping levels in steel structures. The formulations are derived from linear time-history analysis of steel frame configurations and are applicable within the scope of linear elastic response and viscous damper behavior consistent with typical design conditions.
Diamantis et al. (Tue,) studied this question.