Performance Design of Low to Mid-Rise Steel Structures Equipped with Viscous Damper

The direct displacement-based design (DDBD) method is one of the most powerful and efficient performance-based design procedures. This method has the ability to consider the nonlinear behavior of structures under seismic excitation with acceptable accuracy. The methodology of this method is based on substituting a multi-degree of freedom (MDOF) system into a single degree of freedom (SDOF) system associated with the peak displacement response. The SDOF system is defined by implementing equivalent parameters such as effective mass and height, design displacement, yield displacement, ductility, effective damping, and effective period. Up to now, the DDBD method has been applied and developed by many researchers and the last version of the model code for DDBD was published as DBD12.
Over the past three decades, using fluid viscous dampers as a manner for more reliable and safer design of structures, particularly in seismic regions, has steadily increased. Consequently, the equivalent lateral force (ELF) procedure as an allowable method for designing structures equipped with dampers has been presented by ASCE-7. However, the DDBD method also suggests the procedure to design structures equipped with dampers. Previous studies showed that although structures equipped with viscous dampers designed by the DBD12 approach can satisfy the target performance limit states, a significant overestimation may be seen between the performance target limit and inert-story drift ratios (IDRs) obtained from nonlinear time-history analyses. In other words, the structures are not economically designed.
To solve this drawback, the present study proposes modifications for low to mid-rise steel moment-resisting frames (MRFs) with dampers in the DDBD method. In doing so, the effect of interaction between ductility demand and added extra damping related to the viscous damper is considered to calculate effective damping. Moreover, a velocity modification factor is also applied for calculating damper constants. In order to compare the proposed modifications with the conventional DBD12 approach, 3-, 6- and 9-story steel MRFs are designed by each of mentioned procedures separately. Furthermore, linear and nonlinear dampers with velocity exponent values equal to 0.35, 0.5, 0.7, and 1 are used. To investigate the seismic performance of the structures designed, nonlinear time-history analyses are performed under the ground motions that the average of their pseudo-acceleration response spectra is matched with 2800 standard design spectrum. Then, the IDRs and displacement profiles of the structures are compared at the maximum considerable earthquake (MCE) hazard level. The results obtained from the analyses of the structures designed by DBD12 confirm the overdesign of this approach. On the other hand, the obtained results of structures designed via proposed modifications validate the efficiency of these modifications. Low-rise MRFs in all of the velocity exponent values can significantly decrease the difference between the peak IDR and target limit. Also, implementing the proposed modifications for mid-rise MRFs with linear damper and damper velocity exponent values equal to 0.7 can acceptably match the peak IDR and target limit. In addition, the seismic behavior of structures designed by the proposed modifications at the MCE hazard level is also checked at the design earthquake (DE) hazard level. The results show the satisfaction of life safety performance level for these structures. It is worth to mention that the peak IDRs in the mid-rise MRFs with damper velocity exponent values equal to 0.5 and 0.35 designed by the proposed modifications exceed the target limits at both the MCE and DE levels. Therefore, more studies are suggested for mid-rise MRFs with nonlinear dampers.
Finally, comparison between two mentioned procedures reveals that using the proposed modification in the DDBD method leads to about 8% decrease for used steel and about 30% decrease for damper constants.