Approximate Methods to Estimate Residual Drift Demands in Steel Structures with Viscous Dampers Designed by the DDBD Approach

Nowadays, using performance-based design procedures are widely applied by structural engineers. The direct displacement-based design (DDBD) approach is also one of the most efficient and popular procedures in these frameworks. This paper investigates the residual inter-story drift ratio (RIDR) demands in the mid-rise steel structures equipped with fluid viscous dampers (FVDs) designed by the modified DDBD approach. For this purpose, the capability of three approximate methods, i.e., the FEMA P-58, Erochko et al. and coefficients methods for estimating RIDR demands is studied. These methods have been proposed for moment-resisting frames (MRFs) without dampers. In order to evaluate the estimated RIDR demands in the approximate methods, three mid-rise steel MRFs with different velocity exponents for FVDs are designed according to the modified DDBD approach. Nonlinear time-history analyses are carried out by a set of spectrum-matched records at two seismic hazard levels including the designed earthquake (DE) and maximum considered earthquake (MCE). The results show that in most cases the Erochko et al. method overestimates the mean of maximum RIDRs at both the DE and MCE hazard levels. On the other hand, although the FEMA P-58 method overestimates the median of maximum RIDRs, when compared with the corresponding values obtained from analyses at the DE level, it underestimates the values at the MCE level. Also, the coefficients method is calibrated for the structures studied. Finally, a modified equation for a more precise estimation of RIDR demands is presented, by implementing the particle swarm optimization (PSO) algorithm.