Evaluation of Displacement Amplification Factor of Regular and Irregular Steel Moment Frames Using FEMA P695 Methodology

In recent decades, several destructive earthquakes resulted in extensive structural and non-structural damage in structures, which was produced by lateral displacements. Therefore, it reveals the necessity for the accurate estimation of the lateral displacement of structures in the design procedure.Present seismic codes using structural overstrength and the ability of energy dissipation capacity of the structures allow a structure to be designed for reduced seismic design forces with force reduction factor. As a result of this, the response of the structure lies beyond the elastic region in the event of strong ground motions; thus, simple linear analyses procedures fail to predict the structure deformations accurately. On the other hand, due to complexity and time consuming nonlinear dynamic analysis, this type of analysis has not been acknowledged as an applicable method for structural engineers. Efforts in the direction of finding a procedure to estimate the maximum lateral inelastic displacement began years ago.According to present seismic design provisions, displacement amplification factor (Cd) is being applied to elastic lateral displacements in order to assess inelastic displacements due to ground motions. Although, the factor of Cd in the codes are not in accordance with the actual behavior of the structure, the empirical does, based on the structural performance observed in the past earthquakes and should be corrected according to the effect of height and number of stories. In this paper, the effect of Cd on seismic performance of steel special moment frames is evaluated. In this regard, six types of buildings are designed with different values of Cd (i.e., 4, 5, 5.5, 6, 7, and 8); and, in order to investigate low to high-rise buildings, 5 heights (i.e., 5-, 10-, 15-, 20- and 25-stories) are considered in two regular and irregular states. Irregularity is considered to be a mass irregularity in the first floor, so that the mass of the first floor is 50% higher than the mass of the adjacent floor. The numerical finite element models are developed in OpenSEES software. Incremental dynamic analysis (IDA) and nonlinear static analysis are performed to quantify structures’ seismic performance; Nonlinear static analyzes are performed to determine overstrength and ductility factors of buildings. Also, the effect of earthquakes on buildings is investigated using incremental dynamic analysis that is accomplished with 22 far-field earthquake record pairs proposed in FEMA P695. Eventually, the effect of different values of Cd on seismic performance of the buildings are quantified and investigated using FEMA P695 methodology and fragility curves in terms of the adjusted collapse margin ratio (CMR) and the probability of collapse (Pf).The results demonstrate that the probability of collapse (Pf) of short and medium-rise buildings with Cd equal to 5.5 is higher than 10%, which is the targeted value of Pf according to design codes; therefore, considering Cd equal to 5.5 in the design of these buildings does not provide real displacement and leads to underestimated design of buildings. In irregular buildings, although the Pf values increased compared to regular buildings, a similar trend was observed in general. In short, the amount of Cd that leads to an acceptable performance of collapse in the structures is equal to 8, 8, 7, 6 and 5.5 in regular 5, 10, 15, 20 and 25 story buildings, respectively; moreover, similarly in 5, 10, 15, 20 and 25 story buildings with mass irregularity are equal to 7, 7, 6, 5.5 and 5.5, respectively. Based on these values, relations are proposed to correct the displacement amplification factor in regular and mass irregular steel special moment frames.Also, comparison of Pf and weight of structures designed with ASCE 7-10 and ASCE 7-16 regulations revealed that design of structures according to ASCE 7-10 criteria with modified values of Cd that is presented in this paper will be economical in addition to achieve the intended collapse performance.