Contents lists available at ScienceDirect Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn The collapse period of degrading SDOF systems considering a broad range of structural parameters Amin Norouzi, Mehdi Poursha ⁎ Department of Civil Engineering, Sahand University of Technology, Tabriz, Iran ARTICLE INFO Keywords: Degrading SDOF system Period-based pseudo IDA curve Nonlinear period Collapse period Epsilon SaRatio P-Δ effect ABSTRACT This paper attempts to extract a period-based pseudo IDA (PBP IDA) curve in the incremental dynamic analysis (IDA). The main focus of the paper is to study the nonlinear period and the collapse period of single degree of freedom (SDOF) systems and to produce the collapse period spectrum. The parameter, Ω col , defined as the ratio between the period increase due to the nonlinear deformations of the system at the collapse state and the elastic period, is introduced. The IDA is implemented for SDOF systems with a wide range of periods to identify the condition under which the collapse period of the system is determined. The IDAs are performed using various sets of seismic ground motions selected based on epsilon and SaRatio as spectral shape indicators for SDOF systems with different periods. A broad range of structural parameters – ductility capacity, post-capping stiffness ratio, P-Δ effect, and system degradation is included in this investigation. To consider the hysteretic behavior, the modified Ibarra-Krawinkler deterioration model is utilized. The results indicate that all the above-mentioned parameters have a significant effect on the nonlinear period. On the other hand, the collapse period is affected by some structural parameters such as the P-Δ effect and system degradation, while the effect of the spectral shape on the collapse period is not clearly predictable. 1. Introduction In the study of nonlinear state of structures through the incremental dynamic analysis (IDA), there are different choices for damage mea- sures; such as peak roof drift, maximum story drift angles, node rota- tions and various parameters that show the elastic and inelastic re- sponse of structures perfectly [1]. One of the dynamic parameters that changes, when a structure is subjected to a seismic ground motion with different intensity levels, is the period. It can well display the linear and nonlinear behavior of structures [2]. In addition, studying the collapse period gives suitable information about the structure before the col- lapse state. Therefore, the period can be used as a damage measure (DM) in the representation of IDA curves. An extensive research has been done to obtain the fundamental period (frequency) of structures with various methods including experimental tests and analytical models. The period of a structure is fixed while it remains in the linear range and the period increases when it deforms into the nonlinear re- gion. Naeim [3] reported almost a 50% increase in the period of in- strumented damaged buildings during the 1994 Northridge earthquake. Moving window fast Fourier transformation (FFT) technique was used to obtain the frequency. It was also reported that the undamaged buildings didn’t have a considerable change in their periods. Mucciar- elli et al. [4] calculated the frequency changes of a 4-story reinforced concrete (RC) building. This building had been damaged by two earthquakes. They used ambient vibration before and after the second earthquake and obtained the fundamental frequency by using four different techniques. The results illustrated that the period increased between 39% and 92% in the N-S direction and between 56% and 100% in the E-W direction. A study conducted by Clinton et al. on the in- strumented building (Millikan library) in California during about 40 years under the influence of several ground motions demonstrated that the period shift is about 45% for the damaged building [5]. While many researchers studied the response of real structures subjected to seismic ground motions, some others conducted dynamic experiments in laboratories. Zembaty et al. [6] used shaking table ex- periments for two full size RC frames subjected to different levels of excitations (from about 0.15–1.1 g) to investigate changes in their dy- namic parameters due to the development of cracks in concrete. Finally, they observed a 70% reduction in the frequency with respect to the initial state. Hashemi and Mosalam [7] conducted a shaking table ex- periment on one-story prototype infilled RC frame. First, the structure was excited under a sequence of ground motions with different in- tensity levels. In the next stage, the infilled frame collapsed due to https://doi.org/10.1016/j.soildyn.2018.09.004 Received 25 January 2018; Received in revised form 8 June 2018; Accepted 7 September 2018 ⁎ Corresponding author. E-mail address: Poursha@sut.ac.ir (M. Poursha). Soil Dynamics and Earthquake Engineering 115 (2018) 730–741 0267-7261/ © 2018 Elsevier Ltd. All rights reserved. T