A New Method for Estimation of Target Displacement in Nonlinear Static Analysis of Structures Subjected to Near-Fault Ground Motions

The recent trend in structural earthquake engineering practice is to use performance-based seismic evaluation methods for the estimation of inelastic demands in structures. Nonlinear static analysis, commonly referred to as pushover analysis, is becoming a popular simplified tool for seismic performance evaluation of existing and new structures. The pushover analysis of a structure is a static nonlinear analysis under permanent vertical load vectors and gradually increasing lateral loads until reaching the predetermined target displacement at roof level. Target displacement serves as an estimate of the global displacement of the structure expected to experience in a design earthquake. The accurate estimation of target displacement associated with specific performance objective affect the accuracy of seismic demand predictions of pushover analysis. Recently, the researchers have proposed various enhanced methods that aim to capture the true seismic-induced target displacements. Most of the reported research on development of improved Nonlinear Static Procedures (NSPs) is based on the response of analytical models subjected to Far-Fault (FF) earthquake records and less have been investigated for Near-Fault (NF) ground motions. NF motions differ from FF ones in that they often contain strong coherent dynamic long period pulses and/or permanent ground displacements. Out of the two kinds of NF ground motions, ground motions with velocity pulses caused by NF directivity effects have received a great deal of attention because of their potential to cause severe damage to structures. Capacity Spectrum Method (CSM) and Displacement Coefficient Method (DCM) are the two methods presented in FEMA-440 (2005) and ASCE/SEI 41-13 (2013) as standard methods of estimating the target displacement. DCM is considered in this paper as the basis of the presented method. In DCM, the target displacement, which corresponds to the displacement at roof level of a building, shall be calculated by applying appropriate modification factors to the elastic spectral displacement of SDOF system. In this method, C0 is modification factor to relate spectral displacement of an equivalent SDOF system to the roof displacement of the building, C1 is the modification factor to relate the expected maximum displacements of an inelastic SDOF oscillator, and C2 is the modification factor to represent the effect of pinched hysteretic shape, stiffness degradation, and strength deterioration on the maximum displacement response. It should be noted that the coefficients of this equation have been derived from FF motions in FEMA-440 (2005). Therefore, applying these coefficients to estimate the target displacement for NF ground motion may not yield accurate results. Due to this, CN, need to be used to modify the C1 coefficient when a SDOF system is subjected to NF ground motion. This modification factor was previously presented by Esfahanian and Aghakouchak (2015). This paper investigates inelastic seismic demands of the normal component of near-fault pulse-like ground motions. 20 near-fault and 20 far-fault ground motions and the responses of 10-, 15-, and 20-story multi degrees of freedom (MDOF) systems constitute the dataset. These systems are all steel moment-resisting frames, designed according to allowable stress design method. The buildings’ lateral load-resisting system is steel special moment-resisting frame. All buildings are 15 m in width.
The bays are 5 m on center with three bays. Story heights of all buildings are 3.2 m. The seismic masses of all level floors for each structure are assumed to be equal and consist of dead load plus 20% of live load. Dead and live loads are equal to 650 and 200 kg/m2 on the floor area that loading width of the frames is assumed to be 5 m. Design is performed based on the weak beam-strong column. In analysis and design, P-Δ (second order) effects are included. Nonlinear static and dynamic analyses were performed by the OpenSees (2013) software to simulate the performance of structural systems subjected to earthquakes. Both geometrical nonlinearity and material inelasticity were taken into account in the models. The material inelasticity was explicitly considered by employing a fiber modeling approach. Beams and columns have been modeled as finite elements with distributed inelasticity in a specified length of the member ends, using force-beam-column elements. For all of the NL-THAs, the damping matrix was defined using Rayleigh damping with a damping ratio of 5% for the first and third modes of vibration. In this paper, wavelet analysis method, presented by Baker (2007, 2008) is used for selecting pulse-like NF ground motions. NL-THA is utilized as the benchmark for comparison with nonlinear static analysis results. A new method for estimating target displacements are presented, using response spectrum analysis method and appropriate modification factors. As the proposed method considers the MDOF effects, C0 coefficient is not used in this method and only C1, C2, and CN are applied in this method. The target displacements resulting from the proposed procedure are then compared to those from the NL-THA and displacement coefficient method of ASCE 41-13, as well as to those predicted from Modal Pushover Analysis (MPA) methods. MPA is an enhanced NSP presented by Chopra, which utilizes the concept of modal combinations through several pushover analyses using invariant load patterns based on elastic mode shapes where the total response is determined with combination of each mode at the end (Chopra and Goel, 2001, 2002). It should be noted that, various methods applied to nonlinear models developed using generally accepted methods provide either overestimation or underestimation of the target roof displacement when compared to the value derived from NL-THA of recorded motions. It is shown that these procedures may lead to significantly different estimates of the target displacement, particularly for high-rise buildings responding in the nonlinear range. The results of the proposed procedure demonstrate acceptable values for target displacement, especially for near-fault earthquake records in comparison to the approximate and exact ones.