Hysteretic Damping Capacity of Steel Moment-Resisting Frames in Life Safety Performance Level Required in Direct Displacement-Based Design Method

In recent years, interests in utilizing performance-based design to achieve earthquake-resistant structures have grown. One of a robust procedure in this category, which is presented in 1993 by Prof. Priestley, is Direct Displacement-Based Design (DDBD) method. Extensive and developed researches have shown that DDBD has a great potential to overcome existing shortcomings of the force-based design method. During last decade, DDBD, which was initially proposed for designing RC buildings and bridge piers, are developed for steel structures. DDBD has two main factors: hysteretic damping capacity and yield displacement of the building. Accurate estimation of these parameters is very important to determine proper value of design base shear of the building under consideration. These factors were firstly estimated experimentally for concrete structures but now, they are intensely studied analytically by many researchers for various forms of steel structures. In this regard, this paper attempts to consider more realistic estimation of equivalent viscous damper capacity of moment resisting steel frame structures and its influence on determined base shear values.
In this paper, 30 different moment-resisting frames with various numbers of stories (3, 6, 9, 12 and 15) and spans (3 and 6) are studied. For each frame, different analysis methods are carried out: (1) nonlinear static or pushover analysis, (2) nonlinear time history analysis employing synthetic accelerograms, (3) nonlinear time history analysis employing two sinusoidal protocols with different excitation frequencies: initial and effective frequencies, (5) nonlinear static cyclic analysis using an incremental sinusoidal displacement protocol, (6) simple linear analysis of an equivalent single-degree-of-freedom (SDOF) model of the structure subjected to a sinusoidal load, and finally (7) the proposed relation in the Model Code for the Displacement-Based Seismic Design of Structures, DBD12. Comparing the results shows that the equivalent damping ratio obtained using DBD12 relation for life-safety (LS) level is significantly lower than the values obtained by the analyses conducted in this study. This means that the determined base shear for designing such steel building is much more than values for a safe building. In other words, steel buildings using relations of DBD12 tend to be stiffer and stronger than needed. Hence, a new relation is derived to determine the hysteretic damping of MR steel frame structures in the LS performance level as a function of a ductility coefficient. Furthermore, using the relationship between the initial and effective period mentioned in ATC40, another practical relationship is proposed as a ratio of the effective period over the initial period of the considered building.