An approach for estimating the response of steel moment resisting frames to pulse-like ground motions
Introduction
Pulse-like ground motions are often distinguished from non-pulse-like records because of their specific effects on the structural response. The most important feature of pulse-like ground motions is the high period pulse with impulsive characteristics in the velocity time history. Such a pulse mainly delivers significant energy to the structure, generating large internal forces and drifts compared to other records, which in turn causes seismic demand along with a great deal of damage. The non-pulse section of the record, which is also known as the background or residual record, is another important aspect of these records because of traveling a short distance from the earthquake source and there are no damping waves [[1], [2], [3], [4], [5], [6], [7]]. Given the destructive effects of such earthquakes, considerable attention has been paid to the simulation of pulse-like ground motions, the structural response to pulse-like records, the methods for response estimation, and ability of the equivalent pulses to estimate the response [4,[8], [9], [10], [11], [12], [13], [14], [15], [16]]. As pulse-like motions impose severe drift demands on structures and given that inter-story drift is a comprehensive and simple parameter in evaluating structural performance, the linear and nonlinear inter-story drift has been investigated in many of these studies [[17], [18], [19], [20]]. Eventually, the use of equivalent pulse in estimating the response of SDOF systems and low-rise MDOF systems has been accepted [21].
Alavi and Krawinkler in 2001 investigated the response of structures under near-fault ground motions and stated that the behavior of buildings with the ratio of structural to pulse periods (Ts/Tp) at a range of 0.375–3 were controlled by pulse [21]. In 2010, Ghahari et al. came to relatively similar results in their studies [3].
Kalkan et al. in 2006 examined the seismic response of steel moment resisting frames (SMRFs) subjected to sinusoidal pulses to investigate the pulse period effect on the seismic demand. The results showed that the structural response is dependent on Tp/Ts. Accordingly, for Tp/Ts close to one or more, the highest seismic demand was observed in the lower levels due to the dominance of the fundamental mode. For much smaller values of Tp/Ts and Tp close to the second and the third modal periods, the maximum inter-story drift shifted to the upper stories and indicated the contribution of higher modes to the response [22].
Kalkan and Kunnath in 2007 provided a measure to determine the severity of ground motions using the concept of energy balance with the effective cyclic energy (ECE). The ECE parameter showed a good correlation with the peak system deformation. The relationship between seismic energy and displacement demands was presented as a dimensionless parameter of severity index which evaluated the performance of structures under near-fault ground motions and quantified the potential damage [9].
Rupakhety and Sigbjörnsson in 2011 assessed the effect of higher modes on the elastic response of tall buildings under equivalent pulses. This study indicated that equivalent pulses were not capable of vibration higher modes and resulted in an elastic drift ratio at the roof level with an average coefficient of 1.4 times lower than the actual value [10]. Sehhati et al. in 2011 investigated the non-elastic response of three multi-story steel structures to the Gabor wavelet pulse and showed that when Tp/Ts was at a range of 0.5–2.5, the equivalent pulse provided a similar response to the actual record. Out of this range, the response was affected by the high frequency content of ground motions and subsequently higher structural modes [4,23].
Calugaru and Panagiotou in 2012 used nonlinear time history analysis to evaluate tall cantilever wall buildings under near-fault records as well as sinusoidal and cosine equivalent pulses. The results showed the importance of Tp/Ts in vibrating higher modes of the building [24]. The study of Khoshnoudian and Ahmadi in 2013 on soil–MDOF structure systems subject to sinusoidal equivalent pulses indicated similar results [25].
Akehashi and Takewaki in 2019 proposed a method to determine the optimal location of the viscous damper for MDOF elastic-plastic structures under the critical pulse. This method can be used for broad-type building structures with various stiffness distributions [26].
The previous studies show that many simulation models captured the characteristics of the low frequency content of the earthquake record, neglecting the high frequency content. Therefore, the use of equivalent pulses to determine the response under pulse-like motions is possible with some limitations.
In this study, an approach is proposed to involve the effects of high frequency content and higher modes in structural response through the generation of significant artificial pulse-like records. Accordingly, unlike previous research that has often used simple sinusoidal and cosine pulses and irrespective of the background effects, a comprehensive study of the response of SMRFs to pulse-like motions is presented in the selected seismic regions. Part of the research is devoted to the development of earthquake records in the selected regions with record-decomposition incorporation procedure. Thus, high frequency content and subsequently site characteristics and seismic source are involved in the response and parametric development of pulse-like records has become possible [27].
One of the most important features of the present study is to consider the actual pulse event provided by the generation of artificial pulse-like ground motions based on the records in the desired seismic region. The application of high frequency content while generating artificial records covers the natural variability of earthquake motions. However, many researchers have applied sinusoidal and cosine pulses on the structures and interpreted the results without consideration of the non-stationary characteristics of the earthquake record or the history of earthquake events in the seismic region.
The generated records were applied to three SMRFs of 3, 9, and 20-story buildings from the SAC project, representing low-to high-rise buildings. The results were then presented as response contours that provided a quick estimation of the seismic demand of SMRFs, including the largest maximum inter-story drift (LMD), largest normalized base shear (LNS), and critical story. The sensitivity of SMRFs response to pulse parameters changes, damage estimation, and identification of stories susceptible to damage were also investigated.
In the following, the SMRFs have been introduced and the records in the selected seismic regions were developed. Then the results of applying artificial records to SMRFs have been presented based on the proposed approach. Eventually, the capability of the proposed approach in estimating the response has been evaluated by comparing the structural response under actual records and the results of contours.
Section snippets
Numerical modeling of moment resisting frames
The building frames examined in this study were part of the models presented in the SAC project. The behavior of 3, 9, and 20-story buildings in Los Angeles, Seattle, and Boston were evaluated based on design practices prior to and post the Northridge earthquake through improvements to the connection details according to FEMA 267 guidelines [[28], [29], [30]].
Buildings designed in Seattle prior to the Northridge earthquake were investigated in the present study. Fig. 1, Table 1, Table 2, Table 3
Generation of artificial pulse-like ground motions
The artificial ground motions must be consistent with the target record characteristics in the selected seismic regions. Accordingly, the method of Li et al. in 2017, called record-decomposition incorporation has been taken into account. This method is based on the assumption that pulse-like ground motions [V(t)] consist of two parts of velocity pulse [Vp(t)] and residual record [Vr(t)], which are separated into low and high frequency content in the frequency domain [V(t) = Vp(t)+Vr(t)]. The
The proposed approach
Fig. 4 indicates the pseudo spectral velocity (PSV) of record components, scaled PSV and, critical ratio of the artificial record with A = 95(cm/s), Tp = 1.6(s) and, γ = 5 generated from 1994 Northridge-01 earthquake, Sylmar - Converter Sta. The critical ratio is Ts/Tp, which shows the change in the contribution of pulse and residual components to the spectral response. This criterion specifies that the pulse-like ground motions have pulse-like or non-pulse-like behavior corresponding to a
Results analysis
Since inter-story drift is considered as a criterion for estimation of the damages to the structures and investigation of the seismic performance, it has been regarded as a seismic demand parameter in this study as well. In this section, a sample result is shown to indicate the effects of pulse parameters on the LMD and LNS. According to Fig. 6, damage patterns for short-to long-period buildings can be specifically presented for each region due to the effects of high frequency content. Under
Discussion
As shown in previous studies, given the destructive effects of pulse-like motions on structures, researchers have focused on investigating the effects of these motions and estimating the response of structures. A comprehensive study was conducted by Kojima and Takewaki in 2015 in which the elastic-plastic response of the SDOF system against critical excitation was presented in a closed form using the energy approach. In this regard, the effects of fling step and forward directivity in
Conclusion
A study on providing an approach to capture the maximum response characteristics of steel moment resisting frames (SMRFs) to pulse-like ground motions and equivalent pulse was carried out considering the effect of high frequency content and pulse parameters on the response. The research was implemented through the selection of 3, 9, and 20-story frames from the SAC project in Seattle prior to the Northridge earthquake. Based on the record-decomposition incorporation method and the pulses
CRediT authorship contribution statement
Zahra Minaei: Study conception and design, Data curation, Formal analysis, Writing – original draft, Critical revision. Seyed Rohollah Hoseini Vaez: Study conception and design, Data curation, Formal analysis, Writing – original draft, Critical revision. Ehsan Dehghani: Study conception and design, Data curation, Formal analysis, Writing – original draft, Critical revision.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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