• Structural Engineering and Mechanics
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• v.32 no.3
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• pp.383-398
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• 2009

Applying nonlinear statistical analysis methods in estimating the performance of structures in earthquakes is strongly considered these days. This is due to the methods' simplicity, timely lower cost and reliable estimation in seismic responses in comparison with time-history nonlinear dynamic analysis. Among nonlinear methods, simplified to be incorporated in the future guidelines, Modal Pushover Analysis, known by the abbreviated name of MPA, simply models nonlinear behavior of structures; and presents a very proper estimation of nonlinear dynamic analysis using lateral load pattern appropriate to the mass. Mostly, two kinds of connecting joints, 'hinge' and 'rigid', are carried out in different type of steel structures. However, it should be highly considered that nominal hinge joints usually experience some percentages of fixity and nominal rigid connections do not employ totally rigid. Therefore, concerning the importance of these structures and the significant flexibility effect of connections on force distribution and elements deformation, these connections can be considered as semi-rigid with various percentages of fixity. Since it seems, the application and implementation of MPA method has not been studied on moment-resistant steel frames with semi rigid connections, this research focuses on this topic and issue. In this regard several rigid and semi-rigid steel bending frames with different percentages of fixity are selected. The structural design is performed based on weak beam and strong column. Followed by that, the MPA method is used as an approximated method and Nonlinear Response History Analysis (NL-RHA) as the exact one. Studying the performance of semi-rigid frames in height shows that MPA technique offers reasonably reliable results in these frames. The methods accuracy seems to decrease, when the number of stories increases and does decrease in correlation with the semi-rigidity percentages. This generally implies that the method can be used as a proper device in seismic estimation of different types of low and mid-rise buildings with semi-rigid connections.

• Earthquakes and Structures
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• v.9 no.2
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• pp.353-373
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• 2015

In this paper, the effects of different types of irregularity along the height on the seismic responses of moment resisting frames are investigated using nonlinear dynamic analysis. Furthermore, the applicability of consecutive modal pushover (CMP) procedure for computing the seismic demands of vertically irregular frames is studied and the advantages and limitations of the procedure are elaborated. For this purpose, a special moment resisting steel frame of 10-storey height was selected as reference regular frame for which the effect of higher modes is important. Forty vertically irregular frames with stiffness, strength, combined-stiffness-and-strength and mass irregularities are created by applying two modification factors (MF=2 and 4) in four different locations along the height of the reference frame. Seismic demands of irregular frames are computed by using the nonlinear response history analysis (NL-RHA) and CMP procedure. Modal pushover analysis (MPA) method is also carried out for the sake of comparison. The effect of different types of irregularity along the height on the seismic demands of vertically irregular frames is investigated by studying the results obtained from the NL-RHA. To demonstrate the accuracy of the enhanced pushover analysis methods, the results derived from the CMP and MPA are compared with those obtained by benchmark solution, i.e., NL-RHA. The results show that the CMP and MPA methods can accurately compute the seismic demands of vertically irregular buildings. The methods may be, however, less accurate especially in estimating plastic hinge rotations for weak or weak-and-soft top and middle storeys of vertically irregular frames.

• Journal of the Earthquake Engineering Society of Korea
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• v.6 no.4
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• pp.65-73
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• 2002

It has been recognized that the damage control must become a more explicit design consideration. In an effort to develop design methods based on performance it is clear that the evaluation of the nonlinear response is required. The methods available to the design engineer today are nonlinear time history analyses, monotonic static nonlinear analyses, or equivalent static analyses with simulated nonlinear influences. Some building codes propose the capacity spectrum method based on the nonlinear static analysis(pushover analysis) to determine the earthquake-induced demand given by the structure pushover curve. These procedures are conceptually simple but iterative and time consuming with some errors. This paper presents a nonlinear direct spectrum method(NDSM) to evaluate seismic performance of structures, without iterative computations, given by the structural initial elastic period and yield strength from the pushover analysis, especially for MDF(multi degree of freedom) systems. The purpose of this paper is to investigate the accuracy and confidence of this method from a point of view of various earthquakes and unloading stiffness degradation parameters. The conclusions of this study are as follows; 1) NDSM is considered as practical method because the peak deformations of nonlinear system of MDF by NDSM are almost equal to the results of nonlinear time history analysis(NTHA) for various ground motions. 2) When the results of NDSM are compared with those of NTHA. mean of errors is the smallest in case of post-yielding stiffness factor 0.1, static force by MAD(modal adaptive distribution) and unloading stiffness degradation factor 0.2~0.3.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2005.03a
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• pp.153-160
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• 2005

A new nonlinear static analysis method, Effective Modal Pushover Analysis (EMPA) which can evaluate earthquake responses such as story drift and plastic rotation of plastic hinges addressing higher mode effects was developed. Unlike existing nonlinear static procedure based on properties of fundamental vibration mode, the EMPA performs nonlinear static analysis using multiple effective modes constructed by direct combination of natural vibration modes. Therefore higher mode effects can be efficiently considered. In the present study, procedures of the EPMA evaluating inelastic earthquake responese were established and the results were verified by nonlinear time history analysis. The EMPA can be applied to seismic evaluation of high-rise buildings and irregular buildings where higher mode effects become conspicuous.

• Journal of the Earthquake Engineering Society of Korea
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• v.12 no.1
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• pp.79-87
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• 2008

Seismic performance evaluation of structure requires an estimation of the structural performance in terms of displacement demand imposed by earthquakes on the structure. Incremental Dynamic Analysis(IDA) is a analysis method that has recently emerged to estimate structural performance under earthquakes. This method can obtained the entire range of structural performance from the linear elastic stage to yielding and finally collapse by subjecting the structure to increasing levels of ground acceleration. Most structures are expected to deform beyond the limit of linearly elastic behavior when subjected to strong ground motion. The nonlinear response history analysis(NRHA) among various nonlinear analysis methods is the most accurate to compute seismic performance of structures, but it is time-consuming and necessitate more efforts. The nonlinear approximate methods, which is more practical and reliable tools for predicting seismic behavior of structures, are extensively studied. The uncoupled modal response history analysis(UMRHA) is a method which can find the nonlinear reponse of the structures for ESDF from the pushover curve using NRHA or response spectrum. The direct spectrum analysis(DSA) is approximate nonlinear method to evaluate nonlinear response of structures, without iterative computations, given by the structural linear vibration period and yield strength from the pushover analysis. In this study, the practicality and the reliability of seismic performance of approximate nonlinear methods for incremental dynamic analysis of mixed building structures are to be compared.

• Structural Engineering and Mechanics
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• v.59 no.3
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• pp.455-473
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• 2016

Methods for the seismic demands evaluation of structures require iterative procedures. Many studies dealt with the development of different inelastic spectra with the aim to simplify the evaluation of inelastic deformations and performance of structures. Recently, the concept of inelastic spectra has been adopted in the global scheme of the Performance-Based Seismic Design (PBSD) through Capacity-Spectrum Method (CSM). For instance, the Modal Pushover Analysis (MPA) has been proved to provide accurate results for inelastic buildings to a similar degree of accuracy than the Response Spectrum Analysis (RSA) in estimating peak response for elastic buildings. In this paper, a simplified nonlinear procedure for evaluation of the seismic demand of structures is proposed with its applicability to multi-degree-of-freedom (MDOF) systems. The basic concept is to write the equation of motion of (MDOF) system into series of normal modes based on an inelastic modal decomposition in terms of ductility factor. The accuracy of the proposed procedure is verified against the Nonlinear Time History Analysis (NL-THA) results and Uncoupled Modal Response History Analysis (UMRHA) of a 9-story steel building subjected to El-Centro 1940 (N/S) as a first application. The comparison shows that the new theoretical approach is capable to provide accurate peak response with those obtained when using the NL-THA analysis. After that, a simplified nonlinear spectral analysis is proposed and illustrated by examples in order to describe inelastic response spectra and to relate it to the capacity curve (Pushover curve) by a new parameter of control, called normalized yield strength coefficient (${\eta}$). In the second application, the proposed procedure is verified against the NL-THA analysis results of two buildings for 80 selected real ground motions.

• Journal of the Earthquake Engineering Society of Korea
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• v.14 no.5
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• pp.33-39
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• 2010

This study develops an approximate procedure for incremental dynamic analysis (IDA) using modal pushover analysis (MPA) with empirical equations of the inelastic displacement ratio ($C_R$) and the collapse strength ratio ($R_C$). By using this procedure, it is not required to conduct linear or nonlinear response history analyses of multi- or single- degree of freedom (MDF) systems. Thus, IDA curves can be effortlessly obtained. For verification of the proposed procedure, the 6-, 9- and 20-story steel moment frames are tested under an ensemble of 44 ground motions. The results show that the MPA-based IDA with empirical equations of $C_R$ and $R_C$ produced accurate IDA curves of the MDF systems. The computing time is almost negligible compared to the exact IDA using repeated nonlinear response history analysis (RHA) of a structure and the original MPA-based IDA using repeated nonlinear RHA of modal SDF systems.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.3A
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• pp.497-512
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• 2006

In this paper, a simple but effective analysis procedure to estimate seismic capacities of multi-span continuous bridge structures is proposed on the basis of modal pushover analysis considering all the dynamic modes of structure. Unlike previous studies, the proposed method eliminates the coupling effects induced from the direct application of modal decomposition by introducing an identical stiffness ratio and an approximate elastic deformed shape. Moreover, in addition to these two introductions, the use of an appropriate distributed load {P} makes it possible to predict the dynamic responses for all kinds of bridge structures through a simpler analysis procedure. Finally, in order to establish the validity and applicability of the proposed method, correlation studies between rigorous nonlinear time history analysis and the proposed method are conducted for multi-span continuous bridges.

• Earthquakes and Structures
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• v.13 no.5
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• pp.497-507
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• 2017

Flooding induced scour has been long recognized as a major hazard to river-crossing bridges. Many studies in recent years have attempted to evaluate the effects of scour on the seismic performance of bridges, and probabilistic frameworks are usually adopted. However, direct and straightforward insight about how foundation scour affects bridges as a type of soil-foundation-structure system is usually understated. In this paper, we provide a comprehensive review of applied methods centering around seismic assessment of scoured bridges considering soil-foundation-structure interaction. When introducing these applied analysis and modeling methods, a simple bridge model is provided to demonstrate the use of these methods as a case study. Particularly, we propose the use of nonlinear modal pushover analysis as a rapid technique to model scoured bridge systems, and numerical validation and application of this procedure are given using the simple bridge model. All methods reviewed in this paper can serve as baseline components for performing probabilistic vulnerability or risk assessment for any river-crossing bridge system subject to flood-induced scour and earthquakes.

• Structural Engineering and Mechanics
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• v.78 no.1
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• pp.41-52
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• 2021

Inelastic static pushover analysis has been used in the academic-research widely for seismic analysis of structures. Nowadays, the variety pushover analysis methods have been developed, including Modal pushover, Adaptive pushover, and Cyclic pushover, in which some weaknesses of the conventional pushover method have been rectified. In the conventional pushover analysis method, the effects of cumulative growth of cracks are not considered on the reduction of strength and stiffness of RC members that occur during earthquake or cyclic loading. Therefore, the Cyclic Pushover Analysis Method (CPA) has been proposed. This method is a powerful technique for seismic evaluation of regular reinforced concrete buildings in which the first mode of them is dominant. Since the bridges have different structures than buildings, their results cannot necessarily be attributed to bridges, and more research is needed. In this study, a cyclic pushover analysis with four loading protocols (suggested by valid references) by the Opensees software was conducted for seismic evaluation of two regular reinforce concrete bridges. The modeling method was validated with the comparison of the analytical and experimental results under both cyclic and dynamic loading. The failure mode of the piers was considered in two-mode of flexural failure and also a flexural-shear failure. Along with the cyclic analysis, conventional analysis has been studied. Also, the nonlinear incremental dynamic analysis (IDA) method has been used to examine and compare the results of pushover analyses. The time history of 20 far-field earthquake records was used to conduct IDA. After analysis, the base shear vs. displacement in the middle of the deck was drawn. The obtained results show that the cyclic pushover analysis method is able to evaluate an accurate seismic behavior of the reinforced concrete piers of the bridges. Based on the results, the cyclic pushover has proper convergence with IDA. Its accuracy was much higher than the conventional pushover, in which the bridge piers failed in flexural-shear mode. But, in the flexural failure mode, the results of each two pushover methods were close approximately. Besides, the cyclic pushover method with ACI loading protocol, and ATC-24 loading protocol, can provided more accurate results for evaluating the seismic investigation of the bridges, specially if the bridge piers are failed in flexural-shear failure mode.