Sürdürülebilir Kalkınma Amaçları
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- MakaleYalnız künye2016Retrofitting Effect on the Dynamic Properties of Model-Arch Dam with and without Reservoir Water Using Ambient-Vibration Test Methods
Altunisik, Ahmet Can; Günaydin, Murat; Sevim, Baris; Bayraktar, Alemdar; Adanur, Suleyman
Continuous health monitoring and regular condition assessment is of vital importance for engineering structures in general and especially for arch dams. These structures can be exposed to many different loads such as earthquake, blast, wind, ice, and water pressure, which may cause deterioration and loss of structural integrity. Such development may have severe economic consequence and, more importantly, may present a serious risk to public safety. Therefore, the structural behavior of arch dams must be monitored at regular intervals during their service life, although the overall failure rate of these dams is around 1%. Experimental measurements by ambient vibration test methods are among the most commonly preferred inspection techniques for the evaluation of structural performance and safety. The aim of this research is to examine the retrofitting effect on the dynamic properties of a damaged arch dam model, with and without reservoir water, after retrofitting with high-strength structural repair mortar and carbon fiber reinforced polymer composite material. To this end, an arch dam-reservoir-foundation model was built. In the study, ambient vibration tests were carried out for three test-cases to determine changes in dynamic properties, such as natural frequency, mode shape, and damping ratio before and after retrofitting. The three cases were (1)a severely damaged dam with full reservoir (Case-A), (2)a repaired dam with full reservoir (Case-B), and (3)a strengthened dam with full reservoir (Case-C). In addition, all the measurement tests were repeated with an empty reservoir to extract the effect of water. Data for the ambient vibration tests were gathered from the dam body during vibrations by natural excitations. These excitations were provided through small impacts, and the response signals were measured by sensitivity accelerometers placed at the crest points. To obtain the experimental dynamic properties, the enhanced frequency domain decomposition method in the frequency domain was used. Comparisons of experimentally identified dynamic properties for the damaged and the retrofitted dam showed that the retrofitting application affected the structural behavior of the arch dam considerably. It was very effective in restoring the structure's original dynamic properties.
- MakaleYalnız künye2016Dynamic Characteristics of an Arch Dam Model before and after Strengthening with Consideration of Reservoir Water
Altunisik, Ahmet Can; Günaydin, Murat; Sevim, Baris; Bayraktar, Alemdar; Adanur, Suleyman
This technical note presents an investigation about the changing of dynamic characteristics of an arch dam model before and after strengthening considering reservoir water. To this end, an arch dam-reservoir-foundation model has been constructed in the laboratory. Ambient vibration tests have been performed on the damaged and strengthened arch dam models for empty and full reservoir to determine the effect of water on the dynamics characteristics. Enhanced frequency domain decomposition method has been used to extract the dynamic characteristics. Finally, the dynamic characteristics obtained from the damaged and strengthened dam models have been compared to with each other. Also, the natural frequencies for damaged and strengthened models are compared to detect the effect of strengthening application on the frequencies. Results indicate that the natural frequencies and damping ratios are changed with the full reservoir. However, mode shapes are not changed. Results also show that the natural frequencies of damaged dam considerably increase after strengthening applications.
- MakaleYalnız künye2016Nonlinear Earthquake Performance Evaluation of a Structure Collapsed during the Van, Turkey, Earthquake on October 23, 2011
Çavdar, Ozlem; Bayraktar, Alemdar
The paper investigates the structural performance of a seven-story reinforced concrete (RC) building that collapsed during the Van (Turkey) earthquake on October 23, 2011, using nonlinear static and dynamic methods. The selected RC building has two blocks and was designed according to the Turkish Earthquake Code (TEC) in 1975. The site investigation included sections and steel detailing and soil and concrete properties taken after the earthquake. The pushover and nonlinear time history analyses of the building were completed using the existing plan and test and observation data. It is concluded that the building collapses both analysis types. (C) 2015 American Society of Civil Engineers.
- MakaleAçık Erişim2015Time dependent changing of dynamic characteristics of laboratory arch dam model
Altunişik, Ahmet Can; Sevİm, Barış; Bayraktar, Alemdar; Adanur, Süleyman; Günaydin, Murat
This paper investigates the time dependent changing of dynamic characteristics of laboratory arch dam models using ambient vibration test. For this aim, a prototype arch dam-reservoir-foundation model is constructed in laboratory conditions. The first experimental measurement tests are performed after the poured concrete aged for 10 months for some damage scenarios such as undamaged, minor-damaged and severely damaged of dam body in November 2009. To extract the experimental dynamic characteristics such as natural frequencies, mode shapes and damping ratios, a small impact effect is used as a source of ambient vibrations. Experimental measurements tests are repeated using same excitations considering severely damaged conditions with and without reservoir water in February 2014, and the dynamic characteristics are obtained, experimentally. Enhanced Frequency Domain Decomposition Method in the frequency domain is used to extract the experimental dynamic characteristics. At the end of the study, experimentally identified dynamic characteristics are compared with each other and time effects are investigated in detail. Maximum differences between the natural frequencies obtained as 15.36% and 14.38% in the third mode for empty and full reservoir conditions, respectively. It is thought that the increase of the natural frequencies is resulted from gaining of rigidity of the concrete, ageing, temperature and different environmental effects.
- MakaleYalnız künye2015Stochastic seismic analysis of Kömürhan Highway Bridge with varying material properties
Çavdar, Özlem; Bayraktar, Alemdar; Altunışık, Ahmet Can
Stochastic seismic finite element analyses of the Kömürhan Bridge, the material properties of which are described by random fields, are presented in this paper. The stochastic perturbation technique and Monte Carlo simulation (MCS) method are used in the analyses. A summary of MCS and perturbation-based stochastic finite element dynamic analysis formulation of the structural system is given. The Kömürhan Bridge, located on the 51st km of Elazığ-Malatya highway in the east of Turkey, was chosen as a numerical example. The Erzincan earthquake in 1992 was considered a ground motion, since it took place in the vicinity of the bridge. The material properties were considered to be random variables. During the stochastic analysis, displacements and internal forces of the bridge under consideration were obtained using the perturbation-based stochastic finite element method (SFEM), as well as the MCS method. The selected random variables were elastic modulus and mass density. The efficiency and accuracy of the proposed SFEM algorithm were validated through comparison with results of the MCS method.
- MakaleYalnız künye2015CFRP composite retrofitting effect on the dynamic characteristics of arch dams
Altunişik, Ahmet Can; Günaydin, Murat; Sevim, Bariş; Bayraktar, Alemdar; Adanur, Süleyman
The purpose of this study is to investigate the effect of retrofitting dynamic characteristics of a damaged laboratory arch dam model, subsequently repaired with high-strength structural mortar and strengthened with composite carbon fiber reinforced polymer. This study constructed in laboratory conditions is a prototype arch dam-reservoir-foundation model. Five test cases of ambient vibration on the arch dam model illustrate the changes in dynamic characteristics: natural frequency, mode shape, and damping ratio, before and after retrofitting. The ambient vibration tests collected data from the dam body during vibrations by natural excitations which provided small impacts and response signals from sensitivity accelerometers placed at crest points. Enhanced Frequency Domain Decomposition Method in the frequency domain extracts the experimental dynamic characteristics. At the end of the study, experimentally identified dynamic characteristics obtained from all test cases have been compared with each other. Apparently, after the retrofitting, the natural frequencies of the dam body increased considerably, demonstrating that the retrofitting, including repairing and strengthening is very effective on the flashback of initial dynamic characteristics.
- MakaleYalnız künye2014Pushover and nonlinear time history analysis evaluation of a RC building collapsed during the Van (Turkey) earthquake on October 23, 2011
Çavdar, Özlem; Bayraktar, Alemdar
The nonlinear seismic behavior of a collapsed reinforced concrete (RC) residential building in the city of Van in Turkey is investigated by the static pushover and nonlinear time history analyses. The selected RC structure was designed according to the 1975 version of Turkish Earthquake Code (TEC-1975). The building had experienced heavy damage, and it was demolished in the Van earthquake on October 23, 2011. The 2007 version of Turkish Earthquake Code (TEC-2007) is considered for the assessing seismic performance evaluation of the selected RC building. The RC structure presents collapse performance level under the earthquake loads. Besides, the analytical solutions show that different performance levels for the sections are obtained from the pushover and nonlinear time history methods.
- MakaleYalnız künye2012Estimation of Elasticity Modulus of a Prototype Arch Dam Using Experimental Methods
Sevim, Baris; Altunisik, Ahmet Can; Bayraktar, Alemdar; Akköse, Mehmet; Adanur, Suleyman
Using experimental methods, this study presents the estimation of the dynamic and static ( secant) elasticity modules of a prototype arch dam. These experimental methods are ambient vibration tests, uniaxial compression tests, and ultrasonic velocity tests. Implementation of the methods on a prototypical arch dam-reservoir-foundation model of the dam, constructed under laboratory conditions, allows estimation of the elasticity modules. Random impact loads excite the arch dam during ambient vibration testing, which creates response signals for measurement. Commercially available software transfers the signals, and processing those signals allows estimation of the experimental natural frequencies of the arch dam. Analysis of a three-dimensional (3D) finite element model (FEM) of the arch dam determines natural frequencies. The estimation of the elasticity modules of the arch dam arises from a comparison of the experimental and analytical frequencies. The uniaxial compression tests use several specimens of the fresh and hardened concrete of the prototype model, and those tests provide the compressive strengths and stress-strain relationships. The ultrasonic velocity tests apply several velocity measurements to the arch dam and foundation, resulting in estimation of the elasticity modulus from empirical equations related to concrete mix design, compressive strength, and velocity values. This study discusses the difficulties of the determination of the elasticity modulus and suggests that ambient vibration testing and the finite element method are useful for overcoming these difficulties. DOI: 10.1061/(ASCE)MT.1943-5533.0000361. (C) 2012 American Society of Civil Engineers.
- MakaleYalnız künye2011Finite element model calibration effects on the earthquake response of masonry arch bridges
Sevim, Baris; Bayraktar, Alemdar; Altunisik, Ahmet Can; Atamtürktür, Sezer; Birinci, Fatma
The focus of this paper is to illustrate the importance of model calibration and in situ vibration testing by comparing the finite element model predictions of the earthquake response of the two historical arch bridges, Osmanli and Senyuva, before and after model calibration. The three-dimensional finite element models of these two arch bridges, built in the ANSYS finite element program, are used to predict bridge dynamic characteristics, such as natural frequencies and mode shapes. Following the analytical study, ambient vibration tests were conducted to experimentally obtain dynamic characteristics of these two bridges. During ambient vibration tests, accelerometers were placed at several points on the bridge to collect the vibration response due to natural and operational excitation sources. Enhanced frequency domain decomposition and stochastic subspace identification techniques were used to extract the experimental natural frequencies, mode shapes and damping ratios. Finite element models of the two arch bridges were adjusted such that the model predictions reproduce the ambient vibration test results with increased fidelity. The behavior of the masonry arch bridges under earthquake excitation recorded during the Erzincan Earthquake in 1992 is simulated by both the initial and adjusted finite element models. The findings of this study emphasize the importance of model calibration and ambient vibration testing. (C) 2010 Elsevier B.V. All rights reserved.
- MakaleYalnız künye2011Finite element model updating effects on nonlinear seismic response of arch dam-reservoir-foundation systems
Bayraktar, Alemdar; Sevim, Baris; Altunisik, Ahmet Can
This paper investigates the effects of finite element model updating on nonlinear seismic response of arch dam-reservoir-foundation systems. The highest arch dam in Turkey named Berke is selected for the numerical and experimental applications. Firstly, 3D finite element model of Berke Dam was constituted using an ANSYS software. In the analytical modeling, arch dam-reservoir-foundation interaction is represented by Lagrangian approach. Then ambient vibration tests were conducted to dam for four days, and experimental dynamic characteristics were estimated using an Enhanced Frequency Domain Decomposition technique. Experimental characteristics are compared with those of analytical obtained by the linear finite element analysis of the coupled system. Good agreement between mode shapes is observed during this comparison, though natural frequencies disagree by 15-20%. The linear finite element model of Berke Dam was updated by adjusting the material properties of the dam and foundation. By introducing the Drucker-Prager damage criterion, the updated linear finite element model was extended into an onlinear model. Nonlinear seismic behavior of Berke Dam was determined considering the acceleration record of Adana-Ceyhan, Turkey, earthquake in 1998 that occurred near the arch dam region. It is highlighted that the finite element model updating provides a significant influence on the nonlinear seismic response of arch dams. (C) 2010 Elsevier B.V. All rights reserved.
- MakaleYalnız künye2011Vibration-based operational modal analysis of the mikron historic arch bridge after restoration
Altunişika, Ahmet Can; Bayraktar, Alemdar; Sevima, Bariş; Birincia, Fatma
This research presents finite element modelling, vibration-based operational modal analysis, and finite element model updating of a restored historic arch bridge. Mikron historic bridge, constructed on Fi{dotless}rti{dotless}na River in Rize, Turkey, is the subject of this case study. The General Directorate for Highways of Turkey repaired the bridge's main structural elements, arches, sidewalls, and filler material in 1998. To construct a 3D finite element model of the bridge, ANSYS finite element software estimated the analytical dynamic characteristics. Induced ambient vibrations such as human walking and wind excited the model bridge to allow measurement of the bridge's responses. Enhanced frequency domain decomposition in frequency domain and stochastic subspace identification in time domain methodologies extracted experimental dynamic characteristics. A comparison of the analytical and experimental results showed significant agreement between mode shapes, but some differences in natural frequencies appeared. Consequently, updating the finite element model of the bridge by changing boundary conditions minimised the differences between analytical and experimental natural frequencies. After the finite element model updating process, the differences between natural frequencies declined from 7% to 2%.
- MakaleYalnız künye2011Effects of random material and geometrical properties on structural safety of steel-concrete composite systems
Çavdar, Özlem; Bayraktar, Alemdar; Çavdar, Ahmet
A stochastic finite element-based algorithm for probabilistic analysis of structural systems made of composite sections with random material and geometrical properties under earthquake forces is proposed in this paper. Uncertainties in the structural parameters can be taken into account in this algorithm. For the perturbation-based stochastic finite element method, only the first two moments of random variables need to be known, and is numerically much more efficient and feasible than simulation techniques. The efficiency and accuracy of the proposed algorithm are validated by comparison with results of Monte Carlo simulation method. A summary of stiffness matrix formulation and perturbation-based stochastic finite element dynamic analysis formulation of structural systems made of composite sections is given. These are followed by suitable numerical examples, which indicate that employment of such a dynamic stochastic finite element method leads to significant economical, efficient and accurate solutions for the dynamic analysis of composite structures with stochastic parameters under earthquake forces.
- MakaleYalnız künye2011Assessment of nonlinear seismic performance of a restored historical arch bridge using ambient vibrations
Sevim, Bariş; Bayraktar, Alemdar; Altunişik, Ahmet Can; Atamtürktür, Sezer; Birinci, Fatma
Historic masonry arch bridges are vital components of transportation systems in many countries worldwide, ensuring the ready access of goods and services to millions of people. The structural failure of these historic structures would severely and adversely impact the economies of these nations due to the massive disruptions of transportation systems accompanying such failures. To successfully maintain these aging masonry structures, performance assessment must incorporate the unique mechanical characteristics of masonry. Therefore, the preferred analysis technique must go beyond a linear approach. This study assesses the earthquake performance of a restored historical masonry arch bridge through nonlinear finite element analysis incorporating the Drucker-Prager damage criterion. The case study structure is the Mikron Arch Bridge, a nineteenth century Ottoman Era structure built over the Firtina River near Rize, Turkey, and restored in 1998. The Mikron Arch Bridge was first subjected to ambient vibration testing, during which accelerometers were placed at several points on the bridge span to record the bridge vibratory response. The investigators then used Enhanced Frequency Domain Decomposition and Stochastic Subspace Identification techniques to extract the experimental natural frequencies, mode shapes, and damping ratios from these measurements. Experimental results were compared with those obtained by the linear finite element analysis of the bridge. Good agreement between mode shapes was observed during this comparison, though natural frequencies disagree by 8-10%. The boundary conditions of the linear finite element model of Mikron Arch Bridge are adjusted such that the analytical predictions agree with the ambient vibration test results. By introducing the Drucker-Prager damage criterion, the calibrated linear FE model was next extended into a nonlinear model. Nonlinear analysis of seismic behavior of Mikron arch bridge was performed considering the acceleration record of Erzincan earthquake in 1992 that occurred near the Mikron Bridge region. The displacement and stress results were observed to be allowable level of the stone material. Moreover, linear FE model calibrations elicited a significant influence on the nonlinear FE model simulations.
- MakaleYalnız künye2011Experimental and analytical system identification of Eynel arch type steel highway bridge
Altunişik, Ahmet Can; Bayraktar, Alemdar; Sevim, Bariş; Özdemir, Hasan
This paper describes a full scale arch type steel highway bridges, its finite element modelling and Operational Modal Analysis. Eynel Highway Bridge which has arch type structural system with a total length of 336 m and located in the AyvacIk county of Samsun, Turkey is selected as a case study. The bridge connects the villages which are separated with Suat Uǧurlu Dam Lake. The three dimensional finite element model is constructed using project drawings and an analytical modal analysis is then performed to generate natural frequencies and mode shapes in the three-orthogonal directions. The ambient vibration tests on the bridge deck under natural excitation such as traffic, human walking and wind loads are conducted using Operational Modal Analysis. Sensitive seismic accelerometers are used to collect signals obtained from the experimental tests. To obtain experimental dynamic characteristics, two output-only system identification methods are employed namely, Enhanced Frequency Domain Decomposition method in the frequency domain and Stochastic Subspace Identification method in time domain. The correlation between the finite element model and experimental results is studied. Good agreement is found between dynamic characteristics in the all measurement test setups performed on the bridge deck. It is demonstrated that the ambient vibration measurements using Enhanced Frequency Domain Decomposition and Stochastic Subspace Identification methods are enough to identify the most significant modes of steel highway bridges. It is seen that there are some differences between analytical and experimental natural frequencies and experimental natural frequencies are generally bigger than the others.
- MakaleYalnız künye2011Investigation of water length effects on the modal behavior of a prototype arch dam using operational and analytical modal analyses
Sevim, Bariş; Bayraktar, Alemdar; Can Altunişik, Ahmet
This study determines the water length effects on the modal behavior of a prototype arch dam using Operational and Analytical Modal Analyses. Achievement of this purpose involves construction of a prototype arch dam-reservoir- foundation model under laboratory conditions. In the model, reservoir length was taken to be as much as three times the dam height. To determine the experimental dynamic characteristics of the arch dam using Operational Modal Analysis, ambient vibration tests were implemented for empty reservoir and three different reservoir water lengths. In the ambient vibration tests, the dam was vibrated by natural excitations provided from small impact effects and the response signals were measured using sensitive accelerometers. Operational Modal Analysis software process signals collected from the ambient vibration tests, and Enhanced Frequency Domain Decomposition and Stochastic Subspace Identification techniques estimated modal parameters of the dams. To validate the experimental results, 3D finite element model of the prototype arch dam was modeled by ANSYS software for empty reservoir and three different reservoir water lengths, and dynamic characteristics of each model were determined analytically. At the end of the study, experimentally and analytically identified dynamic characteristics compared to each other. Also, changes on the natural frequencies along to water length are plotted as graphs. Results suggest that reservoir water complicates the modal behavior of the arch dam significantly.
- MakaleYalnız künye2011Finite element model calibration of berke arch dam using operational modal testing
Sevim, Bariş; Bayraktar, Alemdar; Altunişik, Ahmet Can
This paper presents the finite element calibration of Berke Arch Dam by using Operational Modal Testing. Achievement of this purpose involves structural vibration characteristics of Berke Arch Dam using analytical and Operational Modal Analyses. Therefore, the study has two parts-analytical and experimental. In the analytical part of the study, the authors developed a 3D finite element model of Berke Arch Dam-reservoir-foundation system using ANSYS software, and analytically determined vibration characteristics such as natural frequencies and mode shapes. In the experimental part of the study, sensitive accelerometers were placed to several points of Berke Arch Dam, and ambient vibration tests were conducted over four days to obtain dynamic characteristics. The Enhanced Frequency Domain Decomposition technique is used to estimate natural frequencies, mode shapes and damping ratios of the Berke Arch Dam experimentally. Results showed that there were some differences between analytical and experimental natural frequencies of the dam. Therefore, an analytical model of Berke Arch Dam was calibrated to minimize these differences by changing material properties. Analytical results obtained from the calibrated model mainly conform to those of the experimental model.
- MakaleYalnız künye2010Finite element model updating of an arch type steel laboratory bridge model using semi-rigid connection
Altunişik, Ahmet Can; Bayraktar, Alemdar; Sevlm, Bariş; Kartal, Murat Emre; Adanur, Süleyman
This paper presents finite element analyses, experimental measurements and finite element model updating of an arch type steel laboratory bridge model using semi-rigid connections. The laboratory bridge model is a single span and fixed base structure with a length of 6.1 m and width of 1.1m. The height of the bridge column is 0.85 m and the maximum arch height is 0.95 m. Firstly, a finite element model of the bridge is created in SAP2000 program and analytical dynamic characteristics such as natural frequencies and mode shapes are determined. Then, experimental measurements using ambient vibration tests are performed and dynamic characteristics (natural frequencies, mode shapes and damping ratios) are obtained. Ambient vibration tests are performed under natural excitations such as wind and small impact effects. The Enhanced Frequency Domain Decomposition method in the frequency domain and the Stochastic Subspace Identification method in the time domain are used to extract the dynamic characteristics. Then the finite element model of the bridge is updated using linear elastic rotational springs in the supports and structural element connections to minimize the differences between analytically and experimentally estimated dynamic characteristics. At the end of the study, maximum differences in the natural frequencies are reduced on average from 47% to 2.6%. It is seen that there is a good agreement between analytical and experimental results after finite element model updating. Also, connection percentages of the all structural elements to joints are determined depending on the rotational spring stiffness.
- MakaleYalnız künye2010Stochastic finite element analysis of long-span bridges with CFRP cables under earthquake ground motion
Çavdar, Özlem; Bayraktar, Alemdar; Adanur, Süleyman; Başaǧa, Hasan Basri
Stochastic seismic analysis of long-span bridges with Carbon fibre reinforced polymer (CFRP) cables are presented in this study through combination of the advantages of the perturbation based stochastic finite element method (SFEM) and Monte Carlo simulation (MCS) method. Jindo cable-stayed and Fatih Sultan Mehmet (Second Bosporus) suspension bridges are chosen as an example. Carbon fibre reinforced polymer cable (CFRP) and steel cables are used separately, in which the cable's cross sectional area is determined by the principle equivalent axial stiffness. Geometric nonlinear effects are considered in the analysis. Uncertainties in the material are taken into account and Kocaeli earthquake in 1999 is chosen as a ground motion. The efficiency and accuracy of the proposed algorithm are validated by comparing with results of MCS method. It can be stated that using of CFRP cables in long-span bridges subjected to earthquake forces is feasible.
- MakaleYalnız künye2010Stochastic finite element analysis of a cable-stayed bridge system with varying material properties
Çavdar, Özlem; Bayraktar, Alemdar; Adanur, Süleyman
Stochastic seismic finite element analysis of a cable-stayed bridge whose material properties are described by random fields is presented in this paper. The stochastic perturbation technique and Monte Carlo simulation (MCS) method are used in the analyses. A summary of MCS and perturbation based stochastic finite element dynamic analysis formulation of structural system is given. The Jindo Bridge, constructed in South Korea, is chosen as a numerical example. The Kocaeli earthquake in 1999 is considered as a ground motion. During the stochastic analysis, displacements and internal forces of the considered bridge are obtained from perturbation based stochastic finite element method (SFEM) and MCS method by changing elastic modulus and mass density as random variable. The efficiency and accuracy of the proposed SFEM algorithm are evaluated by comparison with results of MCS method. The results imply that perturbation based SFEM method gives close results to MCS method and it can be used instead of MCS method, especially, if computational cost is taken into consideration.
- MakaleYalnız künye2009Stochastic finite element analysis of structural systems with partially restrained connections subjected to seismic loads
Çavdar, Özlem; Bayraktar, Alemdar; Çavdar, Ahmet; Kartal, Murat Emre
The present paper investigates the stochastic seismic responses of steel structure systems with Partially Restrained (PR) connections by using Perturbation based Stochastic Finite Element (PSFEM) method. A stiffness matrix formulation of steel systems with PR connections and PSFEM and MCS formulations of structural systems are given. Based on the formulations, a computer program in FORTRAN language has been developed, and stochastic seismic analyses of steel frame and bridge systems have been performed for different types of connections. The connection parameters, material and geometrical properties are assumed to be random variables in the analyses. The Kocaeli earthquake occurred in 1999 is considered as a ground motion. The connection parameters, material and geometrical properties are considered to be random variables. The efficiency and accuracy of the proposed SFEM algorithm are validated by comparison with results of Monte Carlo simulation (MCS) method.