Period elongation of steel moment-resisting frames with strength and stiffness deterioration in incremental dynamic analysis

Change in the fundamental period of a structure during strong earthquakes (the change from the linear to nonlinear period) can be a good indicator of the damage level of the structure. Given that the incremental dynamic analysis (IDA) has played an effective role in investigating the nonlinear behavior of engineering structures, in this article, we try to use the nonlinear (fundamental) period of the structure as a damage criterion in IDA curves for multi-degree-of-freedom (MDOF) systems, which was previously introduced for single-degree-of-freedom (SDOF) systems. In this regard, the nonlinear period at different seismic intensity levels and the collapse threshold period of steel moment-resisting frame (SMRF) structures are studied by considering the spectral shape indicators of earthquake records, and the strength and stiffness deterioration parameter. For this purpose, three regular SMRF buildings with 3, 10, and 20 stories as representatives of low-, medium-, and high-rise buildings are investigated. Fast Fourier transform (FFT) is used to calculate the nonlinear period of the structures, and the eigenvalue analysis method by using the instantaneous characteristics (stiffness) of the structure is implemented to confirm it. To perform the time history analysis, the bilinear modified Ibarra-Medina-Krawinkler (IMK) model is used in modeling the structural hysteretic behavior. One of the important applications of the nonlinear period of structures is in the process of scaling records for time history analysis. This study intends to evaluate the scaling period range by computing the nonlinear period based on the records scaled to the design spectrum. The results demonstrate that the spectral shape parameters and the structural deterioration affect the nonlinear period of the case study structures in a regular manner, while the effect of the mentioned spectral parameters on the collapse threshold period does not follow a clear trend. Also, it is shown that the upper bound period (1.5 \(\:{\text{T}}_{\text{1}}\) or 2 \(\:{\text{T}}_{\text{1}}\) ) mode period for scaling ground motions is too conservative for structures with a special SMRF load-resisting system having a low deterioration.