Probabilistic Evaluation of Residual Drift Demands in Steel Moment Resisting Frames Equipped with Linear and Nonlinear Fluid Viscous Dampers

Maximum interstory drift ratio is a useful engineering demand parameter for predicting damage and structural collapse. In recent decades, some research studies have focused on Maximum Residual Interstory Drift Ratio (MRIDR) of structures as another engineering demand parameter. MRIDR plays a key role in assessing the seismic performance of structure after seismic events, because it indicates that if structure is safe or not, and if the repair of structure is economical or not. Nowadays, passive control systems are employed for designing new structures and improving the seismic performance of existing structures. Among them, the use of Fluid Viscous Dampers (FVDs) has become very common because of their remarkable energy dissipation capacity, negligible maintenance cost and the possibility of being used in multiple earthquakes. Linear FVDs have a velocity exponent of α=1.0 and nonlinear FVDs have velocity exponents of α≠1.0. This study evaluates the effects of employing linear and nonlinear FVDs and different vertical distributions of damping coefficients on the MRIDR response of steel Special Moment Resisting Frames (SMRFs) with FVDs. For this purpose, low- and mid-rise steel SMRFs including the 3- and 9-story SMRFs designed for Los Angeles as part of SAC steel project are considered. Moreover, the height of the first story in the 3-story SMRF is increased by a factor of 1.4 to generate a 3-story SMRF with a soft story. Each of these three structures is equipped with FVDs to limit maximum interstory drift ratio under the design earthquake to 0.015. Two types of vertical distributions of damping coefficients that include uniform distribution and Interstorey Drift Proportional Distribution determined on the basis of the first mode deformations (IDPD) are assumed for each of the structures. Moreover, four values of α=0.25, 0.5, 0.75 and 1.0 are considered for FVDs. OpenSees software is applied to model the structures. Concentrated plasticity approach is used for modeling beams. In this approach, each beam is modeled by an elastic beam-column element and two zero-length elements simulating inelastic response. However, columns are modeled using nonlinear beam-column elements, which are based on the concept of distributed plasticity. The P-Delta effects of gravity columns are accounted for by a leaning column. Four MRIDR values of 0.002, 0.005, 0.01 and 0.02 are assumed as limit states, and Incremental Dynamic analyses (IDAs) are performed on the structures using a set of far-field ground motion records considering each of these limit states. For performing the IDAs, 5% damped pseudo spectral acceleration at the fundamental period of structure, Sa(T1), is selected as ground motion intensity measure. Using the results of the IDAs median MRIDR capacity, i.e., median SaRD, and its corresponding logarithmic standard deviation are calculated for each of the structures. Then, assuming lognormal distribution for SaRD, residual drift fragility curves are obtained for the structures given each of the MRIDR limit states. The results indicate that given each of these limit states, the structure equipped with linear FVDs has higher median SaRD compared with its corresponding structure equipped with nonlinear FVDs. Furthermore, reducing α causes reduction in median SaRD. Residual drift fragility curves corresponding to all the limit states for each of the structures are combined with the seismic hazard curve for the site assumed to calculate the mean annual frequencies of exceeding these MRIDR limit states (λRD). According to the results, the values of λRD for the structures with linear FVDs are between 6.87% to 80.24% lower than those for the structures with nonlinear FVDs. Comparing the results obtained using the two height-wise distributions of damping coefficients shows that when first story height is greater than typical story height, using IDPD leads to higher median SaRD and lower λRD.