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Finite element model calibration effects on the earthquake response of masonry arch bridges
Abstract
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, Osmanlı and Şenyuva, 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.
... Milani et al. [9] utilized finite element analysis to investigate the static nonlinear behavior of masonry arch bridges in 3D. Sevim et al. [10] conducted a study on the linear seismic analysis of two historical masonry arch bridges using modal analysis. Pelà et al. [11] explored the seismic evaluation of a triple curvature masonry bridge, assessing its seismic capacity through time history and pushover analysis. ...
... Milani et al. [9] wykorzystali MES do statycznej analizy nieliniowej mostów łukowych murowanych uwzględniając model 3D. Sevim et al. [10] przeprowadzili liniową analizę sejsmiczną dwóch zabytkowych mostów łukowych murowanych z zastosowaniem analizy modalnej. Pelà et al. [11] ocenili podatność sejsmiczną mostu murowanego z łukiem o trzech promieniach krzywizny, korzystając z analizy odpowiedzi w dziedzinie czasu i analizy pushover. ...
Historical structures, including historical bridges, are part of cultural heritage, conveying the traces and characteristic features of past civilizations. To protect historical structures, it is necessary to prepare their 3D photogrammetric documentation, determine detailed geometric and material properties and perform computer-aided structural analysis using appropriate modeling techniques. The aim of this study is to present an effective, reliable and fast multidisciplinary approach for the analysis of historical masonry bridges. The aforementioned approach was illustrated with an example of the historical Halilviran masonry arch bridge and its behavior under possible loadings. Terrestrial laser scanning (TLS) was used to determine the bridge geometry with high accuracy. Point cloud data obtained from TLS was simplified and a three-dimensional CAD-based solid model of the structure was created. The Halilviran Bridge case study summarized in this report was conducted to examine the technical feasibility of using la¬ser scanning technologies for obtaining as-built records for similar historic bridges. A secondary objective was to identify other applications of this technology, notably for other transportation structures, and use numerical methods to assess the seismic behavior and failure model of the bridge. The seismic behavior of the bridge was examined using a finite-element- based macromodeling technique. Nonlinear dynamic analyses were carried out subsequently to identify the most susceptible regions of the bridge. Interpretation of the results, presented in the form of contour plots illustrating tensile damage and maximum displacements, offered a comprehensive depiction of the seismic response across the entire bridge. The methodology employed in this investigation can be viewed as a robust framework for evaluating the seismic response and potential failure of historical structures.
... The K constant was selected as 0.40 according to Eurocode 6 (Standard 2008). Tensile strengths (f t ) were taken as one tenth of the compressive strengths (f c ) (Cavicchi and Gambarotta 2005;Sevim et al. 2011;Karaton et al. 2017;Yanık et al. 2022). ...
... Young modulus of masonry elements was obtained using the equation E ms = 750.f ms (Sevim et al. 2011), and Poisson's ratio was taken from the study of Sevim et al. on historical masonry bridges (Çoban 2009). These parameters obtained for the masonry elements of the bridge, when used together, create the Willam-Warnke failure criterion (Fig. 7). ...
They appear to be structures that have a very important place in defining the civilizations that lived on historical buildings. In order to preserve historical buildings and pass them on to future generations, restoration and related strengthening practices are carried out as a result of structural performance analyzes and structural health monitoring studies. In this study, the Historical Karaz Bridge, which is in the form of an arch with a masonry stone wall bearing system and located within the borders of Erzurum Province, Turkey, was evaluated from a seismic perspective. As a result of the evaluations, it was aimed to investigate whether there was a need for reinforcement to protect the cultural structure and structural safety of the Historical Karaz Bridge. In line with the purposes of the research, the time history analysis method was preferred for the seismic evaluation of the Karaz Bridge. For analyzes in the time domain, data from 11 different earthquakes experienced around the world were used by scaling them specific to the structure. Time history analyzes performed according to today's accepted standards have shown that the bridge has limited displacement. In addition, it has been determined that there is limited stress distribution in the supporting support of the Bridge and at the same time, a sufficient damping mechanism has been formed against possible earthquakes. As a result of the study, it was concluded that there was no need for any strengthening process since the Historical Bridge exhibited performance at the usable limit level.
... In a study carried out in Turkey, the behavior of stone arch bridges under the influence of nearfield and far-field earthquakes was investigated. First, the analytical models of stone arch bridges were created with the assumption that the stone mortar components are in linear elastic homogeneous continuity, and the analytical model was calibrated in the light of the information obtained from the ambient vibration data [31,32]. The response of the bridges under near-field and far-field ground motions was investigated using linear finite element analysis. ...
... The response of the bridges under near-field and far-field ground motions was investigated using linear finite element analysis. Near-field ground movements caused higher displacements and stresses on the belt than calculated under the effect of far-field ground movements [31][32][33]. The results obtained in this study were found to contrast with the experimental and analytical data widely reported on nuclear structure types, ISBN: 978-625-7341-82-0 www.anadolukongre.org ...
In the past few years, a great deal of work has been done trying to identify the natural phenomenon that characterizes earthquakes and to offer solutions to reduce the resulting damage and costs. These studies have led to important and positive results, but they do not mark the end of people's discussion and scientific demands regarding the complex earthquake phenomenon. Because water reservoirs are near faults, especially residential areas and cities have been built near faults as the primary source of seismic waves. Therefore, the examination of the studies to date will be useful in the evaluation of the civil engineering structures that have been made and are being made. Within the scope of this study, a detailed review of studies on earthquakes of near and far origin is presented. YAKIN VE UZAK KAYNAKLI DEPREMLERİN İNŞAAT MÜHENDİSLİĞİ YAPILARI ÜZERİNDEKİ ETKİSİNE AİT BİR LİTERATÜR İNCELEMESİ ÖZET Son birkaç yılda, depremleri karakterize eden doğal fenomeni tanımlamak ve ortaya çıkan hasar ve maliyetleri azaltmak için çözümler sunmak için çok sayıda çalışma yapılmıştır. Bu çalışmalar önemli ve olumlu sonuçlara yol açmıştır, ancak insanların karmaşık deprem fenomeni hakkındaki tartışmalarını ve bilimsel tartışmalarını sona erdirmemektedir. Su rezervuarları fayların yakınında olduğundan, özellikle yerleşim alanları ve şehirler, sismik dalgaların birincil kaynağı olarak fayların yakınında inşa edilmiştir. Bu nedenle bugüne kadar yapılan çalışmaların incelenmesi, inşa edilen ve yapılmakta olan inşaat mühendisliği yapılarının değerlendirilmesinde faydalı olacaktır. Bu çalışma kapsamında yakın ve uzak kaynaklı depremler üzerine yapılan çalışmaların detaylı bir incelemesi sunulmaktadır. Anahtar Kelimeler: Yakın alan, Uzak alan, Deprem etkisi. 1. Overview of far-and near-fault earthquakes In general, earthquakes that occur in fault zones and in areas close to rupture are called near-field earthquakes or near-fault earthquakes. There is some disagreement among researchers regarding the determination of a specific range in terms of proximity to the breakpoint. For example, some researchers suggest different distances around the fault, ranging from 10 km to 60 km as the near field range. On the other hand, the UBC-97 standard accepts less than 15
... There are numerous damage criteria available for the nonlinear FE analysis of masonry-type structures to determine the yield surface or the yield function of materials. Rock, concrete, and masonry are examples of frictional materials that frequently apply the Drucker-Prager (DP) criterion [51]. Additionally, Drucker and Prager were able to determine the ...
... The bridge's bond system and architectural style date to the thirteenth and fourteenth centuries [32]. The before and after the restoration process of Kurt Bridge and a scheme of the bridge cross-section are illustrated in Fig. 2. Due to the challenges in determining the material characteristics of such structures, it has been investigated in the literature successful research on comparable historic bridges, and the material properties for the parts taken into consideration have been determined as indicated in Table 1 [5,26,51]. ...
Historical masonry bridges constitute an essential part of the existing road and railway bridges. These bridges have been used for many years and have been preserved as a cultural resource. However, natural disasters have damaged or destroyed many of these historic bridges. In addition, it is crucial to ensure that historic bridges, which are still in use on some critical routes, provide safe service under increasing vehicle loads. Linear analysis approaches have been used to determine the behavior of existing historical bridges under vertical loads. However, these approaches do not give sufficient information and results to evaluate the actual capacities of bridges and result in an underestimation of the capacity of the bridges which is not appropriate from an economic point of view. Thus, further research focuses on the more advanced analysis to identify the real capacity of masonry arch bridges. The main purpose of this study is to evaluate load-carrying capacity and perform reliability analysis of an existing historical arch bridge using the response surface-based finite element model calibration process to present crucial references for the capacity evaluations of other similar masonry arch bridges. The experimental study was conducted to identify modal parameters of the masonry bridge by employing the operational modal analysis method under environmental effects. Using the modal parameters obtained from the experimental study, the approach that allows the initial finite element model of the bridge to be calibrated autonomously has been applied to create a more realistic finite element model of the bridge. Moreover, the vertical load-carrying capacity of masonry bridges with the help of nonlinear approaches was determined, and the nonlinear load-carrying capacity was used in the rating analysis of the bridge. Finally, rate ratios representing the actual performance of the bridge were obtained.
... On this basis, the results of FE-based eigenvalue analysis were compiled from the literature. All the results were obtained from different studies and modeled with different commercial software applications such as ABAQUS [4,5], ANSYS [3,[28][29][30], and SAP 2000 [31]. While compiling the data from the literature, the first FE vibration frequency values of five historical bridges (Marcello Pistoiese, Cutligliano, Fillaboa, Osmanlı, and Şenyuva) were gathered before modal updating due to the direct address of the mechanical property references. ...
... Basic components of a typical historical masonry arch bridge through cross-section[6,30]. ...
The fundamental frequency of a historical monument like a masonry bridge or any other structure provides a better and detailed seismic assessment of its demand to provide protection against unexpected seismic ground motion. On this basis, this paper aims to develop an empirical formulation to fit the ambient vibration frequency of historical masonry bridges using a nonlinear regression model. For this purpose, data series were collected from the literature especially focused on both ambient vibration measurement and finite element models of historical masonry bridges modeled on a full scale to get the first global natural frequency. The first approach is to forecast the natural vibration frequency by using only physical characteristics of the historical masonry bridges obtained from the literature-based experimental ambient vibration frequency data. The second approach consists of forecasting the first natural vibration frequency considering the unit weight and elasticity modulus of the dominant construction material based on the homogenization approach. In addition to mechanical characteristics, physical properties of historical masonry bridges were used, such as the length, height, width, and Main Arch Span (MAS) length of the masonry bridge, to predict the first natural vibration frequency. Among the proposed equations, a maximum accuracy of 58% was reached with the literature-based experimental approach. Moreover, an empirical formulation with 81% accuracy was proposed by using both physical characteristics and mechanical properties of the bridges on the basis of finite element model results. Also, this study highlights that this accuracy decreases to 35% if the modulus of elasticity and unit weight are ignored. In addition, the developed formulations are compared with other empirical formulations using the Mean Square Error (MSE), as a measure of the average of the squares of the errors. Consequently, the smallest MSE value of 1.95 was obtained with the proposed equation, whose accuracy was 81% in this study.
... These consider bricks/blocks as rigid elements and introduce nonlinear interfaces [17] for modeling the mortar joint behavior. However, Finite Element (FE) methods result more powerful than DEs, as these can rely on various discretization techniques for modeling the structure and advanced solving algorithms [18,19]. FE approaches are mainly divided into three classes [20]: micromechanical, macromechanical and multiscale models. ...
... (1) macroscopic + E k 1 given for the UC: Eq. (6) at nonlinear mortar mid-layer: Eqs. (18) and (19) Addessi, et al. Engineering Structures 211 (2020) 110428 summarizes the main steps. ...
A R T I C L E I N F O Keywords: Masonry wall Stability analysis Multiscale model Micromechanical approach Damage Corotational approach A B S T R A C T This paper presents two micromechanical and a multiscale finite element models for the analysis of masonry walls under out-of-plane instability effects. A two-dimensional modeling of the wall is considered in all approaches , assuming a cylindrical bending. The micromechanical analyses are performed considering elastic beams to model the bricks and either nonlinear beams or interfaces to model the mortar layers. The beam finite elements rely on the force-based formulation and account for large displacements by making use of the cor-otational approach. This latter is properly formulated and extended to interface elements to include nonlinear geometry effects. The multiscale model is defined by applying a two-scale beam-to-beam homogenization procedure , developed for masonry elements with periodic brick arrangements. Hence, a Unit Cell made of a single linear elastic brick and a single nonlinear mortar layer is introduced at the microscopic level, which is linked to the macroscale level through a semi-analytic homogenization technique. In all models, a damage formulation with friction plasticity governs the mortar constitutive relationship. Computational details on model implementation and solution procedures are given for all approaches. Correlation studies are performed to assess the proposed numerical micromechanical and multiscale procedures. In particular, the behavior of an un-reinforced wall tested under a compressive eccentric load is reproduced and advantages and disadvantages of the proposed approaches are discussed.
... These methods are used in the field of Structural Health Monitoring to detect anomalies in various types of structures such as reinforced concrete (RC) structures [16][17][18], masonry structures [19][20][21] or wind turbines [22]. They are also often used to assess the effectiveness of reinforcement or retrofitting of a structure [23][24][25][26], or as a tool for calibrating numerical models [18,[27][28][29][30], also referred to as 'model updating' [31]. All these contemporary applications highlight the importance of having reliable numerical models for conducting accurate modal analysis. ...
The dynamic characterization of structures using discrete models, as well as the application of modal superposition to compute their dynamic response, has been rarely explored in the literature. This is at odds with the international relevance of discrete models in structural assessment, and the multiple fields of application of modal analysis and superposition, from structural health monitoring to seismic engineering. This paper introduces a 2D discrete formulation, developed within a finite element framework, to address this gap. Initially conceived for nonlinear static analyses as HybriDFEM (Hybrid Discrete-Finite Element Method), it is now augmented with a procedure to compute the mass matrix, natural frequencies, mode shapes, and response-related quantities such as modal and dynamic contribution factors or effective modal mass. Moreover, using the structural tangent stiffness matrix in the eigenvalue problem allows tracking the evolution of natural frequencies and modes in structures loaded into their nonlinear material and geometric range. The formulation is validated through several examples, where it compares well with results from engineering beam theories, refined finite element models, and numerical time-integration methods. In an application example studying the evolution of modal properties of a progressively damaged frame, HybriDFEM is coupled with finite elements, highlighting its novel approach to integrating discrete and finite elements for enhanced structural modal analysis and superposition.
... Since measurements are generally taken under environmental and anthropic (traffic) unknown excitations, output-based procedures are commonly preferred. 23 Among the most widely adopted methodologies are Frequency Domain Decomposition (FDD) [24][25][26] (see Fig. 4), Enhanced Frequency Domain Decomposition (EFDD), [27][28][29][30] and Stochastic Subspace Identification (SSI). 31,32 In this regard, it should be noted that for stiff structures characterized by high vibrational frequencies, such as stocky masonry arch bridges, dynamic identification can be far from trivial. ...
Masonry arch bridges represent a significant part of civil infrastructure, characterized by their longevity and historical value. However, many of these structures are facing critical challenges due to aging, environmental factors, and increased loading conditions. This paper provides a comprehensive overview of structural assessment, repair, and strengthening methods applicable to masonry arch bridges, emphasizing the necessity for effective risk mitigation strategies. The study first focuses on current assessment methodologies used to evaluate the structural integrity of masonry arch bridges under various load scenarios, including traffic, seismic, and hydraulic influences. It highlights the importance of acquiring a thorough understanding of the structure under investigation by utilizing advanced surveys and diagnostic techniques. Several analytical and numerical methodologies aimed at achieving accurate assessments are explored, outlining their advantages and disadvantages. Then, the paper discusses various repair and strengthening solutions that aimed at restoring and enhancing the performance and safety of these bridges, respectively. These include traditional approaches such as repointing and arch ring reinforcement, as well as modern techniques like fiber-reinforced cementitious matrix (FRCM) applications. Additionally, the traditional technique of post-tensioning is analyzed in a modern context for the strengthening of masonry bridges. The effectiveness of these methods is assessed based on the advantages and disadvantages of each technique, providing comparisons among the commonly used methods. Overall, the paper identifies open issues within the field, such as the need for standardized assessment protocols, the integration of sustainability considerations into repair strategies, and the development of innovative strengthening techniques.
... To model these types of structures it is very common to use the Finite Element (FE) models (Sevim et al. 2011), where the material and geometrical properties are specified, and the boundary conditions are carefully defined. Therefore, it is necessary to carry out extensive experimental campaigns to characterize the bridge. ...
... Stochastic subspace identification (SSI) and enhanced frequency domain decomposition (EFDD) methods are the most frequently used techniques for output only modal identification studies in the time and frequency domains, respectively. Few studies have employed both to identify the dynamics of complicated structures and concluded that they yield similar results [42][43][44]. The well-known enhanced frequency domain decomposition method was used in this work, employing Artemis modal analysis software [36]. ...
In this study, an existing six-storey reinforced concrete building with an asymmetric structural plan and soft storey irregularity was used as a test specimen and subjected to three-step progressive structural damages to detect the variations in its dynamic properties. Mode shapes and dominant frequencies of the undamaged building were determined by the ambient vibration survey (AVS) and it was seen that its first three modes were torsion coupled. Besides, soft storey irregularity was evident due to the lack of masonry infill walls on its ground floor. Later on, three-step progressive damages were applied to the building. The first step targeted three columns and one beam of the building, located on a corner region of its ground floor to peel off their clear covers. The second step razed two adjacent corner columns which were already moderately damaged in the first step, while the third step knocked the third moderately damaged column down. After each damage step, AVS was repeated with the same details as applied for the undamaged building. The obtained dynamic properties for the four phases of the building were evaluated with the sustained damage. Numerical analyses with the finite element model of the building representing its four different phases were also performed and the unique responses due to damage effects on the structure were investigated numerically. As a result of induced damage, the quantified amount of frequency change in modes and the new mode observed after particularly column loss scenarios can be utilized for efficient structural health-monitoring strategies of plan-asymmetric buildings and post-earthquake assessment of partially damaged buildings where timely objective assessment is important.
... FVT are performed using a known excitation force applied by a shaker or hammer, and structural reaction is monitored. Because AVT is a completely non-destructive testing approach, the authors feel it is more ideal for determining the dynamic properties of historical structures than FVT [34,35] and this method was successfully practiced on many historical structures such as bridges, towers, mosques, churches, etc. [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53]. ...
This paper offers a structural assessment of the historical Santa Maria Church and its Guesthouse building in Trabzon, Turkey. This process involves non-destructive experimental investigation using ambient vibration test and numerical evaluation using finite element method. Finite element model updating procedure was employed for the buildings using experimental data such as dynamic features provided by the ambient vibration test. Time-history analyses were carried out by using initial and final finite element models to draw attention to the effectiveness of the finite element model updating procedure and evaluate the seismic performance. The 1992 Erzincan earthquake ground motion data was used for seismic analysis. The ground motion was exposed to buildings in bidirectional. The maximum displacements and principal stresses are detailed at the end of the analysis using contour diagrams. Result of the analyses, the buildings demonstrated a Limited Damage Performance Level throughout the imposed seismic record according to the Earthquake Risk Management Guide for Historical Structures which is a formal guide.
... The before and after the restoration process of Kurt bridge and a scheme of the bridge cross section are illustrated in Fig. 2. Due to the difficulties in the determination of material properties of such structures, the used material properties of the bridge (Table 1) for the initial FE model were considered in line with the studies obtained from the restoration procedures carried out on similar bridges in terms of manufacturing year and construction technique in the same region (Alpaslan and Karaca 2020). The material properties used are similar to the material properties used in successful studies on similar historical bridges in the literature (Frunzio et al. 2001;Sevim et al. 2011; Aydın and Özkaya 2018). ...
The transportation system should be sustained and given serves to improve the well-being of society and continue the improvement of civilization. Historical masonry bridges constitute a critical and sensitive part of the transportation system. As a result of being built a hundred years ago, the bridges have been exposed to many severe deterioration processes and destructive environmental and manmade damage. Therefore, the existing performance of these bridges should be determined realistically in a proper way. This study expresses a novel approach to creating a realistic finite element model of the existing masonry arc bridge. The initial finite element model of the bridge was created according to the architectural drawing of the bridge. Then, the density and elastic modulus of the bridge structural components were investigated statistically and the upper and lower limits were determined. The central composite design approach was used to generate an analytical model cloud, and experimental studies are conducted to determine the real mode shape and frequency of the bridge. Finally, a novel deep neural network approach including deep neural network and principal component analysis-based approaches is proposed to determine the realistic finite element model of the bridge using the results of the analytical models and experimental study. With the proposed methods, the difference between the natural frequency values obtained after the finite element model calibration process and those obtained from experimental measurements was obtained as 1.52% and 0.69% on average in the 6 evaluated mode shapes.
... These techniques are ranging from frequency domain algorithms based on the Fourier transform, such as peak picking and frequency domain decomposition, to time domain algorithms, such as the Eigensystem realization algorithms and the stochastic system identification [13,14]. A few studies used both methods to obtain the dynamic properties of structures and stated that they give similar findings [15][16]. The frequency domain methods are the most practical methods to apply existing civil structures [17]. ...
The dynamic properties of structures are known as inherent properties dependent on the mass and stiffness parameters. However, recent studies showed that the temperature and the magnitude of the vibration affect them. This study aims to reveal how the ambient temperature and human-induced vibrations alter the modal characteristics of pre-stressed precast isolated pedestrian bridges. For this aim, operational modal analyses have been applied to the Istanbul Medeniyet University pedestrian bridge. Three-bay pre-stressed precast and isolated bridge has been connecting the two campuses of the university for six years and its dynamic properties were investigated during its construction. In this study, the dominant frequencies of the bridge have been determined to see if they changed or not for its service life. Secondly, the dynamic response of the longest bay of the bridge has been evaluated under different temperatures and human-induced vibrations. Through a year, twelve acceleration measurements have been gathered in a temperature range of 5 – 33 °C and representing the different levels of human-induced vibrations, some jumping actions were applied and its response was recorded. While the performed analyses proved that, the dominant frequencies are dependent on the ambient temperature, no significant correlation was obtained between the amplitude of the vibration and the dominant frequencies of the bridge. High-amplitude vibrations have been used for the vibration serviceability check of the bridge, and it is seen that it satisfies the requirements set by different codes.
... The identification of these properties for such historical structures through non-destructive testing is a difficult and expensive process. Also, many tests must be performed to obtain any meaningful statistical significance [27]. Therefore, similar material properties which were obtained from the relevant papers in the literature were used in the analysed bridges. ...
Historical masonry arch bridges are a major portion of the transportation network in the world. They are mostly constructed with brick and stone materials. These structures are reasonably important, for transferring the history and life style of ancient societies. They have to protect against the unexpected effects (i.e., floods, fire, and earthquake). Due to these factors, seismic behavior of these structures must be well known. In this paper, three different single span masonry arch bridges (Veli Palas, Musa Palas and Mavilik) were chosen as a case study. ANSYS software was used to generate three-dimensional finite element model of the bridges. 1992 Erzincan, 1999 Düzce and 2003 Bingöl earthquake records were used for dynamic time history analyses. Displacements, principal stresses, potential damage regions and seismic response of masonry bridges were evaluated after the dynamic analyses.
... Another experimental procedure is the ambition vibration test for masonry arch bridges. Experimental modal shapes and frequencies are obtained with this procedure (Sevim et al. 2011;Roselli et al. 2018;Gönen and Soyöz 2021). ...
Historical masonry bridges are cultural heritage of countries and must be protected from destructive effects of nature such as earthquakes, floods, and fires. The interaction of soil and structure has a significant impact on the seismic behavior of masonry bridges. In this study, the effect of Soil-Structure Interaction (SSI) was investigated on a single-span masonry bridge using non-linear time-history analysis. A SSI model of the Velipalas masonry bridge and soil layer was created using 3D solid elements in DIANA software. The nonlinear behavior of the masonry units and soil layer was modeled using the total strain-based crack model and Mohr–Coulomb failure criteria. The earthquakes of 1992 Erzincan, 2003 Bingöl, and 2020 Sivrice were used for earthquake excitation. Results showed that considering SSI increased the periods, displacements, velocities, and principal stresses, but reduced the frequency and acceleration values. Hence, the results indicate that SSI effects are significant for the seismic response of single-span masonry bridges.
... This issue becomes even more important when tunnels were constructed adjacent of historic monuments. Afifipour et al. [1], Azadi [2], Sevim et al. [3], Russo [4] and Didem Aktas & Turer [5] researched on effect of seismic waves of historic monument. In their studies, the effect of scattering around the tunnels was not considered. ...
During the recent earthquake, a lot of damage was reported from the historical monuments in the adjacent twin tunnels. While scientific research shows, the vulnerability of other monuments is much less than the monuments adjacent twin tunnels. The first type of Hankel function was used to study scattering waves in time domain analysis. The time domain results were transferred to the frequency domain using Fourier transform criteria. Extra stress concentrations were calculated based on the results of frequency domain analysis and developed a new approach to scattering. Arg-Karim Khani citadel and twin subway tunnels in Shiraz were selected as a case study. Three near-field earthquakes to perform the time history analysis were considered. The statistical difference based on Mann–Whitney test illustrates the seismic behavior of monument with and without considering twin tunnels, which shows that there is significant difference between them. The mean of P value amount of this comparison in horizontal and vertical direction is 0.005 and 0.016, respectively (P value < 0.05). The integrated analysis shows the importance of frequencies in creating different scattering around twin tunnels, which depends on the distance tunnels, the diameter of the tunnels, the soil characteristics, the seismic wave types, etc.
... As a result of the study, the maximum and minimum principal stresses were occurred at right and left arch base of the bridge and the maximum displacement was obtained at the top of the bridge. Sevim et al. [9] investigated linear dynamic analyses of two historical masonry arch bridges with operational modal analysis. Hökelekli and Yılmaz [10] examined the in-plane and out-of-plane non-linear structural responses of the spandrel walls of a historical masonry bridge in Bartın-Turkey. ...
Historical structures which are cultural heritage have been frequently damaged or ruined because of unexpected events such as earthquakes. Masonry arch bridges constitute a significant part of historical structures. In this study, the single-span Murat Bey Bridge in the province of Kütahya, built in 1460, was selected as a numerical application. Three dimensional finite element model of the bridge was generated with SAP2000 finite element program. The dynamic characteristics of the bridge were obtained by modal analysis method. Firstly, static analysis of the bridge under its own weight was carried out. Then, time-history analysis method was used for seismic evaluation of the bridge. For this purpose, the acceleration records of the 1998 Adana, 2003 Bingöl, 2011 Van and 2020 Elazığ earthquakes were taken into consideration. As a result of the dynamic analyses carried out, the displacement and stress graphs occurring on the bridge were examined. The highest displacement and stress values on the historical bridge were obtained from the acceleration records of the 2011 Van earthquake.
... In addition, Tiberti and Milani [44]conducted a 3D voxel homogenized limit analysis of single-leaf non-periodic masonry. In this study, while preparing the finite element model of the building, the macro modeling technique, which is frequently used in the modeling of masonry structures [8,11,21,26,36,40], was preferred (Fig. 27). • In the macro modeling studies, the elasticity modules of the masonry walls were determined with the help of the formula given below. ...
Masonry buildings have been vulnerable structures to earthquakes due to the brittle nature of the materials used in their construction. Due to strong ground motions, the majority of masonry buildings built in seismic zones are damaged or collapsed. The performance-based evaluation of these structures must be conducted to improve their seismic performance. In this approach, the main goal is to determine structural damage, evaluate the condition of the building based on the results and decide on restoration techniques and materials. In this study, a performance-based evaluation was conducted on a three-story masonry building that was constructed in 1912, and the building was restored in response to the results. In this study, Performance Evaluation Studies are examined under four main steps: (1) Preliminary Evaluation, (2) Damage Survey Studies, (3) Detailed Evaluation Studies and (4) Restoration Implementations.
... The calibrated FE model has a good correlation with the static and dynamic measurements and is used for continuous structural health monitoring of the bridge (Wang et al., 2010). The sole purpose of model calibration is to improve the uncertain model parameters or imprecise modeling assumptions such that the FE model predictions are closer representations of reality (Sevim et al., 2011). The efficiencies of the cases below were studied in the Ghale Morghi Bridge finite element model for calibration: 1. Transversal element connection to girder. ...
In this paper, full scale load test of a horizontally curved steel box-girder bridge is carried out in order to detect structural defects, which reportedly result in unwanted vibrations in nearby buildings. The bridge is tested under the passage of six heavy vehicles at different speeds, so as to determine its static and dynamic responses. A total number of one hundred and two (102) sensors are used to measure the displacements, strains, and accelerations of different points of the bridge. It is observed that the bridge vibrates at a fundamental frequency of 2.6 Hz intensively and the first mode of vibration is torsional instead of flexural. The dominant frequency of vibration of the nearby buildings is computed to be approximately 2.5Hz using rational formulas. Thus, nearness of the fundamental frequency of the bridge to those of the adjacent buildings may be causing resonance phenomenon. However, in static load tests, low ranges of strain and displacement illustrated adequate structural capacity and appropriate safety under static loads. Numerical models are created using ANSYS and SAP2000 software products, so as to design the loading test and calibrate the finite element models. The connections of the transversal elements to the girders, transversal element spacing, and changes of the stiffness values of the slabs were found to be the most influential issues in the finite elements calibration process. Finally, considering the total damage of all members, the final health score of the bridge was evaluated as 89% indicating that the bridge is in a very good situation.
... Sevim ve ark. [3] tarafından Karadeniz bölgesinde bulunan Osmanlı ve Şenyuva kemer köprüleri üç boyutlu olarak ANSYS programında modellenerek bulunan frekans değerleri ile deneysel titreşim analizinden bulunan değerlerin uyumluluğu gösterilmiştir. Aksoy ve Aydoğmuş [4] tarafından yapılan çalışmada, Kargı Han'ın yapısal analizinden bulunan basınç ve kayma gerilmesi değerlerinin yönetmelikte verilen sınır değerleri aştığı görülmüştür. ...
Bu çalışmada Diyarbakır'ın en önemli kültür mirası olan Diyarbakır Surlarının en büyük burçlarından biri olan Yedikardeş burcunun (41 nolu burç) yapısal performansının değerlendirilmesi amaçlanmıştır. Yapısal özellikleri incelenen burç, makro modelleme tekniği kullanılarak üç farklı şekilde modellenmiştir. Burcun dinamik analizi ANSYS programı kullanılarak yapılmış ve sonuçlar üç model için karşılaştırılmıştır. Düşey yük ve azaltılmamış deprem etkisi altında Yedikardeş burcunun hesap dayanımlarının aşılmadığı, deplasman oranının indirgenmemiş deprem etkisi altında %0.3 sınırını aşmadığı görülmüştür. Bu nedenle Yedikardeş burcunun sınırlı hasar performans düzeyini sağladığı değerlendirilmiştir. Çalışma sonucunda büyük hacimli tarihi yapılarda gerçek davranışı yansıtan modelin yapının özel durumuna göre değişebileceği görülmüştür.
... In order to some important researches are given without regarding scattering waves. [16][17][18][19][20] An analytical solution for the dynamic stress concentration of circular twin tunnels presented against vertical and shear waves in a filled space using derivatives of complex variables. The results illustrated the main effect on the dynamic response of the walls of the tunnel. ...
Stress concentration around twin tunnels and its impact on monuments have been receiving much attention by researchers. To investigate the effect of scattering in twin tunnels, Hankel function of the first kind has been used by various researchers. The mathematical relation of Fourier expansion was modified and the time-domain analysis was transformed to frequency-domain analysis to provide a novel method for analyzing stress concentration factor. The combined finite element scattering model (FESCAM) was designed and developed in MATLAB. Analysis was performed in the presence of twin tunnels with scattering of P wave and in the absence of twin tunnels under the effect of near-field earthquake. According to the results, dynamic stress concentration factor (DSCF) for Kobe earthquake P-wave with different wave angles and maximum frequency showed maximum scattering at α=0° and θ=0° in the tunnel. In addition to increased stress concentration factor, the results of Mann-Whitney statistical test in SPSS revealed a significant difference between the seismic performance of Arg-e Karim Khani and Zand underpass in the presence and absence of the tunnel (P Value<0.05). A scattering effect of less than 10% was calculated taking into account the combined effect of the calculated seismic waves using incremental extended finite element software. Scattering depends on frequency, and higher scattering was reported for higher frequencies.
... This section includes results from a series of simplified numerical simulations of the Saint Vissariona stone masonry bridge when it is subjected to a combination of actions that include the dead weight (D) combined with extreme actions generated from seismic ground motions (Sevim Barıs, et al., 2011, Kiyono J., et al. 2012). The seismic forces were defined by making use of the current definition of the seismic forces by EURO- Code 8 (2004). ...
... According to the literature, macro-modeling approach is more useful for large scale structure models because of low computational effort [20][21][22]. This approach was used in many studies [23][24][25][26][27]. ...
Historical masonry arch bridges which might be vulnerable to natural disasters are important part of the cultural heritage. Natural disasters, especially earthquakes can inflict damage to these structural systems. This paper aims to investigate a comparison of the effects of near and far-fault ground motions on the seismic response of masonry arch bridges under different earthquakes. Kalender masonry arch bridge which is located in Ergani, Turkey is selected as a numerical model. For this purpose, three-dimensional finite element model of the bridge is generated with ANSYS finite element software with macro modelling approach. Seismic response of the bridge is assessed by means of time-history analyses. The near-fault and far-fault ground motions, which have approximately equal peak ground accelerations, of 1979 Imperial Valley, 1999 Chi-Chi, 1999 Kocaeli and 2010 Darfield earthquakes are considered for the analyses. Comparisons between maximum displacements, maximum and minimum stress, which were acquired from the dynamic analyses of the masonry bridge subjected to each fault effect, are obtained. The study demonstrates that far-fault ground motions are as important as near-fault ground motions and it can be used together with near-fault ground motion for further evaluation of such historical masonry bridges.
... Although in some studies clustering methods are used for damage identification without the need to address a numerical representation of the structure [10], usually the identification algorithms are complemented with a finite element model. In this way, the model can be calibrated so that its dynamic properties match those identified experimentally, leading to a high-fidelity digital representation of the structure [11]. ...
This article presents the structural health analysis of a full-scale vehicular bridge, using a twin model calibrated with experimental information. This structure consists of concrete arches, built more than 80 years ago, and reinforced in the 1990s with a steel structure. Different load combinations were evaluated in this model to determine the strength of the structure according to current design standards. Finally, it was found that several of its components do not meet the current design requirements, putting the structure in a vulnerable condition to seismic hazards and restricting its service to traffic loads.
... To this end, various destructive/non-destructive filed tests are employed for identifying the properties of the structure and verifying the dynamic response [3][4][5]. Moreover, results from the in situ vibration testings can be used for model calibration of the finite element model of the bridge [6]. It has to be pointed out that most such test results are limited to the linear response of the bridge. ...
This study aims to investigate the effect of soil-structure interaction (SSI) on the seismic response of a medium-span old concrete arch bridge in Iran's railway network, through incremental dynamic analysis (IDA). To this end, the finite element model of the bridge was developed and its dynamic properties were calibrated based on experimental results. The effect of soil-foundation flexibility was taken into consideration in the computational model. Results from analyses were summarized in IDA curves and the effect of SSI was assessed through the probabilistic framework. To this end, the failure state of bridges was evaluated and a comparison was made between the rigid and flexible base models. The mean annual frequency of exceeding the failure state of the rigid-base bridge was also compared with flexible-base models to investigate the effect of SSI on the return period of failure state of the bridge. Furthermore, the SSI effects were assessed on the confidence level of bridge safety. Results show that ignoring the SSI effect leads to an overestimation of bridge capacity as well as the confidence level of satisfying the safety state. Similarly, the return period of bridge failure increases when a rigid-base model is employed.
... A comprehensive review of experimental investigations and assessment methods of masonry arch bridges until year of 2016 is summarized by Sarhosis et al. (2016). Bayraktar and his colleagues have investigated the response of various masonry arch bridges in Turkey (Bayraktar et al. 2009, 2015, Altunışık et al. 2011, 2015, Sevim et al. 2011a, 2011b, 2016. Furthermore, Lancioni et al. (2016) determined seismic vulnerability of ancient stone arches by using a numerical model based on the Non-Smooth Contact Dynamics method. ...
The main structural elements of historical masonry arch bridges are arches, spandrel walls, piers and foundations. The most vulnerable structural elements of masonry arch bridges under transverse seismic loads, particularly in the case of out
of plane actions, are spandrel wall. The vulnerability of spandrel walls under transverse loads increases with the increasing of their length and height. This paper computationally investigates the out of plane nonlinear seismic response of spandrel walls of long span and high masonry stone arch bridges. The Malabadi Bridge with a main arch span of 40.86m and rise of 23.45m built in 1147 in Diyarbakır, Turkey, is selected as an example. The Concrete Damage Plasticity (CDP) material model adjusted to masonry structures, and cohesive interface interaction between the infill and the spandrel walls and the arch are considered in the 3D finite element model of the selected bridge. Firstly, mode shapes with and without cohesive interfaces are evaluated, and then out of plane seismic failure responses of the spandrel walls with and without the cohesive interfaces are determined and compared with respect to the displacements, strains and stresses.
Keywords: long span masonry arch bridge; out of plane response; seismic failure; masonry spandrel wall; transverse behavior
... Also, the soil-foundation interactions and the behavior of the filler materials may not be ignored when analyzing masonry arch bridges. Since considering all the mentioned parameters is not practical, some of the features may be taken into account indirectly in the calibration process [3,[44][45][46]. In this study, a full numerical simulation has been executed to show the real performance of these types of structures based on the past performed researches. ...
In the railway network of Iran, a large number of masonry arch bridges exist which most of them was constructed 80 years ago. Despite these types of bridges have shown an appropriate behavior under the influence of gravity (vertical) loads, they have not been designed seismically. Concerning to the seismic hazard zoning map of Iran, most of these railway infrastructures are placed in the very high seismicity zones and constructed near the major faults. So the seismic assessment of these types of bridges has become a significant subject for the engineers to explain the failure and seismic performance levels of these structures. Thus, they can be rehabilitated or removed if it is found required. Among various methods for seismic estimation of the capacity of the structures under seismic loading, the non-linear dynamic method or the incremental dynamic analysis (IDA) may be mentioned as the most precise and complete method for near-field excitations. For this purpose, by selecting 28 near-field earthquake records, this study has seismically surveyed two railway masonry arch bridges, which are respectively placed in the kilometers 23 (2L20 bridge) and 24 (5L06 bridge) of the old railway of Tehran-Qom. The macro-modeling approach was used in the finite element method. In total, 316 non-linear dynamic analyses have been carried out for the seismic assessment of the masonry arch bridges under near-field ground motion. The results found from the IDA analysis specified that the near-field seismic performance of the masonry arch bridge with lower span length (i.e., 5L06 bridge) is safer than the bridge with longer span length (i.e., 2L20 bridge). Mostly, it has to decide to retrofit the masonry bridge with longer span length to improve their performance since the seismic behavior of those has been found inappropriate under near-field earthquakes.
... Para o desenvolvimento do modelo e da análise computacional foi selecionado o software de Elementos Finitos (EF) Ansys Workbench (versão 18.2). Esse software foi escolhido devido à sua capacidade de processar análises dinâmicas e também pela diversidade de elementos disponíveis para a modelagem estrutural [10]. A estrutura modelada possui dimensões de 10 cm x 10 cm x 140 cm, armada com 4 barras de aço longitudinais de 6,3 mm de diâmetro nominal e 14 estribos de 4,2 mm de diâmetro nominal espaçados a cada 10 cm. ...
Structural Health Monitoring is a system used to periodically assess the integrity of civil structures, where modal dynamic analysis may be applied to detect stiffness differences through oscillatory modal parameters. Interest literature suggests that the correlation analysis of the mode shapes – using coefficients such as MAC and COMAC – is not always capable of satisfactorily detecting and locating damage. The present study, however, inferring about the used quality data to define these coefficients and about further analysis steps, intends to suggest the efficiency of locating damage, mainly considering the COMAC coefficient. By means of finite element analysis, using the computational software Ansys, modal analyses were developed to a small size reinforced concrete beam. Losses of concrete on the cross
sections due to physical deterioration were considered in 4 different cases. It is shown that this approach has significant accuracy in locating damage, depending on the discretization of the evaluated data and on the usage of post processing mathematical steps.
... As earthquakes are cyclical in reality, they are often calculated using historical response spectra [63,64,70]. While this approach can provide more detailed results, push-over analysis is a widely accepted approximation [3,35,42,56]. ...
Building pathology and diagnostics enable a practitioner to quantify the severity of damage to an existing structure as well as prioritize interventive and preventive measures. Two key aspects of building pathology and diagnostics are documentation and analysis to understand how damage could have occurred on a structure and how it affects overall stability. Within these two methods there are various levels which a practitioner can utilize. The aim of the present work is to quantify the differences in documentation and modeling levels to understand how they affect the overall process of building pathology and delineate the advantages and disadvantages of each approach. Using combinations of photogrammetry, laser scanning, thermal imaging, distinct element modeling, and finite-distinct element modeling, this work seeks to understand how differences in the level of numerical modeling affect damage diagnoses as well as how differences in documentation levels affect damage diagnoses. In particular, the advantages and disadvantages of simulations using simplified micro-modeling versus detailed micro-modeling, the effects of small perturbations to modeling geometry, and the influences of initial conditions are explored. These questions are examined through the use of two case studies including the foundation walls of the Baptistery di San Giovanni in Florence, Italy and a wall in Palazzo Vecchio in Florence, Italy.
... Different timber bridge structures are numerically modelled using finite element programs to determine the structural response [39,19,32,12,14,25]. Also, experimental measurements are conducted to assess structural condition and/or to validate numerical results [17,37,1,38,28,6,2,21,26,45]. Laboratory tests were carried out to determine the orthotropic material characteristics [11]. ...
Historical structures are important cultural relics which illustrate the progress of engineering development. They are a valuable source of information on construction techniques and materials selection over the centuries. However, many factors, including environmental conditions and natural disasters, contribute to damage and destruction of historical structures. Today, the aim of restoration is to carry out necessary works with care and sensitivity while ensuring historical buildings are restored as near as possible to their original structural strength. However, the extent of the contribution of the restoration to the structure and the determination of the restoration success is carried out by various non-destructive experimental studies. This aim of this paper was to obtain structural modal parameters for the historical timber Buzlupınar Bridge using non-destructive ambient vibration tests after restoration. From calculations of natural frequencies and mode shapes, it can be seen that the six natural frequencies obtained are between 2.0 and 20.0 Hz. To minimize the 34.55% differences in experimental and numerical natural frequencies, a FE model of the timber bridge was updated using manual model updating procedures. The maximum differences were reduced to below 1% except for the fourth mode.
Finite element model modification based on response surface method is an effective engineering method that can significantly improve the accuracy of finite element model and structural evaluation. In order to solve the shortcomings of the response surface method based finite element model correction, which exists that the polynomial order selection rule is unknown and the correction result is easily affected by the quality of the optimization target, based on the relationship between the polynomial order and the response surface accuracy and computation amount, a robust estimation algorithm was introduced to optimize the response surface solution process, which improves the reliability of the response surface based model correction. Taking an actual project of a cable‐stayed bridge as an example, the response surface‐based finite element model modification method was adopted to compare the response surface accuracy and computation amount of three kinds of response surface models, namely, second‐mode polynomials, third‐mode polynomials and fourth‐mode polynomials. The optimization results of the robust estimation method were compared with the traditional solution method under the conditions of large fluctuation and small fluctuation of optimization target between finite element index. The results show that with the increase of the polynomial order of the response surface model, the unknown covariates to be solved in the response surface model increase sharply, which increases the computational cost, but the effect of improving the accuracy of the response surface model is limited. When the target frequency fluctuates greatly, compared with the least‐squares method, robust estimation will not transfer the error of the correction result of the order with the large fluctuation of the index difference to the other orders, which ensures the stability of the correction results.
Historical buildings have a very important place for societies in terms of culture. For this reason, it is necessary to protect these buildings and transfer them to future generations. The most
important risk for historical buildings is the earthquake natural disaster. In order to prevent the
vulnerability of historical buildings under the earthquake effect, it is very important to know/predict the behavior of these historical buildings to possible earthquakes in advance. The most preferred way to learn this behavior is to perform numerical analyses. With these numerical analyses, finite element (FE) models of historical buildings are created and their behaviors under various loads are determined. The most important problem here is to create the most appropriate FE models that will reflect the existing condition of the historical buildings. This problem is significantly eliminated by the experimental tests, which emerged as a result of developing technology and knowledge. In this study, the historical Elazığ Government Office, which has the status of one of the first Government Offices in Türkiye and built with the use of different building materials together (adobe + cut stone + rubble stone), will be analyzed. Ambient vibration tests
of the historical office will be performed. Then, the FE model of the historical office will be updated in the light of the results obtained from the ambient vibration tests. Nonlinear analyses will be performed for the updated FE model. Acceleration record of February 6, 2023 Kahramanmaras¸ earthquake will be used in the analyses. As a result of the analyses, the seismic performance of the historical Government Office will be determined by evaluating the
displacement, base shear force and stresses.
The main aim of this study is to explore the collaborative performance of masonry structures incorporating steel slabs in their structural design. The focal point of the investigation is the historically significant Mahmut Nedim Kurkcuoglu Mansion located in Urfa, Turkey, renowned for its cultural heritage. The research methodology encompasses a comprehensive analysis of the mansion’s structural design, utilizing both numerical modeling and experimental testing. The findings of the study reveal that integrating steel beams into slabs within the structural design of masonry buildings can exert a significant influence on overall structural performance. This integration contributes to the heightened safety and durability of the structure. The results underscore the importance of accounting for the historical and cultural value of heritage buildings when implementing structural modifications. In terms of methodology, the research adds value to the field of structural engineering by offering insights into the incorporation of steel beams in the design of masonry structures. Moreover, it emphasizes the significance of preserving cultural heritage sites through sustainable and innovative engineering solutions. The study not only enriches the understanding of structural engineering but also holds practical implications for professionals such as architects, engineers, and preservationists engaged in the design and maintenance of heritage buildings. In conclusion, this research significantly contributes to the realms of both structural engineering and heritage preservation. Its implications extend to practical applications and can serve as a foundational platform for further exploration and investigation in this interdisciplinary domain.
In this research, computational models of masonry arch bridges were constructed, taking into account distinctive features such as span dimensions, height, and arch thickness, while the arch width was maintained as a constant parameter throughout the modeling process. The finite element analysis software, ANSYS version 16, was utilized to create these computational representations. To evaluate the structural integrity and load-carrying capabilities of these bridges, loading scenarios were applied to both the center section of the bridge and a quarter of the arch span. The analytical methodology adopted for this purpose was static thrust analysis. Subsequently, the study delved into the influence of the geometrical characteristics of the arches on their load-carrying capacity. The findings of this research hold potential utility in guiding and informing the reconstruction of historic bridges that have been completely or partially demolished.
Damage of the historical monuments was reported during the earthquakes in the nearby underground tunnels such as twin tunnels. The dynamic stress concentration has been used as a major parameter that evaluates the damage of underground structures. In this study, the dynamic interaction between arge-Karim Khani citadel and twin tunnels was investigated subjected to seismic P waves. The scattered wave fields by twin tunnels were determined with wave function expansion and Fourier transform criteria. In this regard, a new approach was employed to determine scattering based on dynamic stress concentration criteria around two circular tunnels. The seismic responses of twin tunnels were calculated with a verified finite element method using different ranges of the incident seismic wave. The dimensionless analysis was used to evaluate DSCF as known criteria to evaluate scattering. In this way, the different ranges of variables including incident wave angles, frequencies, tunnel sizes, and distance between monitoring point and tunnel center were considered in dimensionless analysis. The results illustrate that DSCF was decreased with increasing the position off the monitoring point and reducing the size of tunnels.
The most significant artifacts that transfer the cultural heritage of past civilizations to the present are historical structures. Historical bridges are of great importance in terms of transportation, trade and architecture from past to present. Some of these structures have been destroyed by natural disasters or have suffered significant structural damage. Especially earthquakes cause damage to these structures. In this study, the earthquake behavior of the Historical Karaz Bridge was investigated. The structural elements of the bridge and the materials connecting the bearing elements were evaluated together with the macro modeling approach. For this purpose, a 3D finite element model of the bridge was generated and its seismic behavior under different ground motion records was investigated by nonlinear analysis. Analyzes were carried out using the ground motion records of Bingöl, Elazığ, Erzincan, Van and Gölcük, and the results were evaluated mutually. In the analysis results, the dynamic behavior of the bridge was evaluated over the distribution of displacements and stresses and the earthquake behavior was investigated.
Vibration is the natural & inherent property of resistance against disturbance in a Elasto-Plastic materials. The structure are often designed in the manner that they can sustain and maintain their superstructure under the influence of dead and live loads with the minimum disturbance of their inertia. The super-structures and tunnels are generally placed on the surface of load carrying columns in the form of simply supported beams. The integration method of which generates a continuous system which is the bridge super structure. So that Natural Frequency (time function Fn) and Response Function (space function) can be generated and programmed in MATLAB.
Child quadriceps muscle injuries are common in contact sports such as football and
basketball. The rectus femoris muscle component of the quadriceps muscle ıs frequently
ınjured, while vastus lateralis component of quadriceps muscle is rarely injured. In this case report, we aimed to draw attention to children's sports and the rare vastus lateralis muscle rupture. In this case, we detected the 13 years old football player with isolated vastus lateralis tendon rupture. After, We successfully treated this child with activity modification, physical therapy rehabilitation and exercises.
In our country, activities are carried out under the title of zoning studies in order to make an area suitable for
holistic living standards. There is a hierarchy in the formation of zoning plans from the upper scale of the country
development plans to the lower scale, which are the implementation zoning plans. With this hierarchy, in the
1/1000 zoning plans, social cultural areas are determined within the zoning boundaries determined to meet the
social activity needs of the people living in a region. Socio-cultural zoning islands can have different building
regulations, precedent or building heights. There are possible building regulations within the zoning boundaries,
where there may be different types of sitting areas, such as split, block and adjacent basis. The process of granting
construction permits to the existing zoning parcels in the zoning islands, whose identities are determined by these
building regulations, is the zoning scale. Zoning diameters, planned areas are given within the framework of type
zoning regulations and plan notes. The zoning diameter is given according to the precedent, height and building
order of the island. Distance method, on the other hand, is the process of creating the right residential area with
the drawing rules of convex shapes, such as square or rectangular, according to the geometric condition of the
parcel, in order to be able to give construction permits to the clean zoning parcels in the relevant zoning islands.
In our study, it has been tried to show how the settlement areas on the floor can be given, which building order,
which precedent and how to apply the process to the convex parcels with the distance approach.
The present study presents a series of in-situ measurements conducted at selected old stone masonry bridges, using up-to-date system identification techniques, in an effort to identify their dynamic characteristics in terms of eigen-frequencies, eigen-modes and damping properties. All these information is part of a data base that can be used in the future as a reference for identifying noticeable changes in these dynamic characteristics as part of a structural health monitoring effort for these bridges. Moreover, this information provides a basis for build-ing realistic numerical simulations towards studying the structural behaviour of such stone masonry bridges and assessing their expected structural behaviour in extreme future seismic events. Selected in-situ measurements are presented together with their use in building numerical models of various levels of complexity. These numerical models are finally utilized in assessing the expected performance of specific case studies of stone masonry bridge structures in Greecetowards meeting the demands of extreme events that include design earth-quake loads. The described system identification technique can also be linked to specific actions, such as earthquake activity, and thus serve as warning for specific maintenance counter-measure.
Historical structures are cultural heritage constituents that convey the traces and characteristic features of civilizations to the present days. One of these structures, which are among the monumental artefacts, are historical bridges. To protect historical buildings, 3D photogrammetric documentation of these structures, detailed determination of geometric and material properties and performing computer-aided structural analysis using appropriate modelling techniques are very important. The aim of this study is to present an effective, reliable, and fast multidisciplinary approach for the analysis of historical masonry bridges. The aforementioned approach is presented as an example for the behavior of the recently restored historical Ayvalıkemer (Sillyon) masonry arch bridge under possible loadings. Terrestrial laser scanning (TLS) was used to determine the bridge geometry with high accuracy. The point cloud data obtained from TLS was simplified and a three-dimensional CAD based solid model of the structure was created. This solid body has been formed the basis of the macro model for structural analysis. CDP material model was used to describe the inelastic behavior of homogenized structure. Thus, an analysis was carried out which presents the structural behavior of a historical bridge with high accuracy and reliability.
The paper presents some SHM results belonging to a wide experimental campaign conducted on a multi-arch masonry bridge located near Mumbai (India), exhibiting a large longitudinal crack on one of the arches and the corresponding advanced numerical evaluations carried out with a NURBS kinematic limit analysis approach, used to assess the stability of the arch subjected to the passage of heavy traffic loads. The masonry bridge is a three-arch structure built during the mid-19th century by British engineers to connect Bombay with the inland of the Indian subcontinent. At present, it is characterized by a heavy state of degradation especially in one of the arches that requires an immediate evaluation of the safety under the passage of traffic loads and possible ideas of interventions to strengthen the structure, in order to avoid the propagation of deep cracks along the longitudinal direction. The adopted SHM includes the crack growth monitoring and tilting of the spandrels under the application of two different heavy loads (a water tank truck and a hydra crane) located in different positions of the arch. Numerical modelling is carried out with a full 3D approach with NURBS finite elements in limit analysis that takes into account the pre-existing crack opening and predicts with great accuracy the ultimate loads in different scenarios and the corresponding active failure mechanisms. From experimental monitoring and numerical simulations results, it is concluded that the bridge is still safe under the passage of traffic loads, but approaches the ultimate limit state for some specific configurations of the loads applied. A refurbishment is therefore needed to avoid any further propagation of the cracks up to collapse.
Masonry arch bridges, which were generally built using brick and stone materials, still form a significant part of the highway and railway networks in the World. The subsoil deformability may considerably affect seismic damage mechanics of masonry arch bridges. The paper investigates the effects of nonlinear foundation soil behavior on the seismic damage mechanisms of brick and stone semicircular masonry arch bridges. Direct soil-structure interaction (SSI) approach is taken into account in the 3 D finite element models of the masonry arch bridge-foundation-soil interaction systems including contact, finite and infinite elements. Nonlinear behaviors of masonry units and homogenous soil domain are modeled using the Concrete Damage Plasticity (CDP) and Mohr-Coulomb failure criteria. The selected ground motion is matched and deconvoluted for hard and medium soil domains. Seismic damage mechanisms of brick and stone masonry arch bridges subjected to combined longitudinal and vertical decon-volved ground motion components are obtained for hard, medium, and partially hard and medium soil domains and are compared with each other.
There are numerous old arch bridges in Iran that have been used as railway bridges for more than seventy years. Since most of these bridges are not designed for earthquake excitation, seismic vulnerability of these structures is uncertain. This fact necessitates the investigation of the earthquake resistance of these kinds of bridges. To evaluate complex behavior of these bridges, results of field tests are required. Since it is not possible to perform field tests for all arch bridges, these structures should be simulated correctly by computers for structural assessment. Several parameters are employed to describe the bridges, such as number of spans, length, geometrical and material properties. In this study, results of field tests are used and adapted for 32 three dimensional finite element models with various physical parameters. Modal deformations of bridges at longitudinal and transverse directions is perceived from nonlinear computer simulations. Furthermore, Seismic performance of these bridges is assessed by pushover analysis in two directions and the capacity curves of the structures and linear demand spectrum are obtained using nonlinear static analysis method suggested by the Iranian standard. The crown is selected as a control node in the pushover analysis and its influence on seismic performance of plain concrete arch bridges is considered. Finally, the demand levels of the bridges based on 475 return period earthquakes are determined and compared with capacity curves. The results show that the performance of longitudinal direction is better than transverse direction, but the earthquake resistance of these kinds of bridges totally depends on the material properties and geometry of the structures.
Commonly, material and vibration characteristics of masonry structures remain uncertain in the evaluation of existing structures under external loads such as earthquake, heat, wind, etc. In addition, determination of compressive and tensile strength of a masonry walls is not straightforward. However, it is very important to know the characteristic parameters such as eigen values, periods and mode shapes of a structure beforehand in order to create accurate and reliable physical models. Since each historical structure has its own unique wall and bearing characteristics, it is not possible to accept random initial values for the bearing capacity and other parameters of the structure. Besides, conducting vertical and lateral loading experiments is costly and time consuming. An alternative way to determine these parameters that govern the structural behavior is to carry out experimental vibration tests using accelerometers. This method, which is also called as Operational Modal Analysis (OMA), is used to obtain the free and forced vibration response of structures by experimental means and to determine the modal parameters of the structure. OMA is very important for the appropriate use of an analysis method and the model parameters used in the analysis. In this study, two masonry buildings, one of which is historical, are discussed and the modal parameters of buildings are determined experimentally with OMA. Characteristic values obtained from OMA were compared with the three dimensional finite element method by adjusting characteristic model parameters.
A specific strategy is required when performing vibration tests on civil engineering structures. The use of artificial excitation sources such as shakers or drop weights is often unpractical and expensive. Ambient excitation on the contrary is freely available (traffic, wind), but it causes other challenges. The ambient input remains unknown and the system identification algorithms have to deal with output-only measurements. Also typical for vibration testing of large structures is that not all degrees of freedom can be measured at once but that they are divided in several setups with overlapping reference sensors. These reference sensors are needed to obtain global mode shapes. In this paper a novel approach of stochastic subspace identification is presented that incorporates the idea of the reference sensors already in the identification step. The algorithm is validated with an extensive Monte-Carlo simulation study and two real-life examples.
The paper presents the experimental and analytical modal analysis of a steel-girder arch bridge. The field test is carried out by ambient vibration testing under traffic and wind-induced excitations. Both the peak picking method in the frequency domain and the stochastic subspace identification method in the time domain are used for the output-only modal identification. A good agreement in identified frequencies has been found between the two methods. It is further demonstrated that the stochastic subspace identification method provides better mode shapes. The three-dimensional finite element models are constructed and an analytical modal analysis is then performed to generate natural frequencies and mode shapes in the three-orthogonal directions. The finite element models are validated to match the field natural frequencies and mode shapes. It is observed that the finite element Model-2 with the concrete slab provides the greater stiffness in the transverse direction of the bridge. The finite element Model-1 with the lumped masses agrees well with the field tests and can serve as a baseline model of the bridge.
In this paper, the seismic performance of existing masonry arch bridges is evaluated by using nonlinear static analysis, as suggested by several modern standards such as UNI ENV 1998-1 2003, OPCM 3274 2004, and FEMA 440 2005. The use of inelastic pushover analysis and response spectrum approaches becomes more difficult when structures other than the framed ones are investigated. This paper delves into the application of this methodology to masonry arch bridges by presenting two particular case studies. The need for experimental tests in order to calibrate the materials and the dynamic properties of the bridge is highlighted, in order to correctly model the most critical regions of the structure. The choice of the control node in the pushover analysis of masonry arch bridges and its influence on seismic safety evaluation is investigated. The ensuing discussion emphasizes important results, such as the unsuitability of the typical top node of the structure for describing the bridge seismic capacity. Finally, the seismic safety of the two bridges under consideration is verified by presenting an in-depth vulnerability analysis.
The application of ground-penetrating radar (GPR) as a non-destructive technique for the monitoring of ring separation in masonry arch bridges was studied. Numerical modelling techniques were used to simulate tests using GPR—these numerical experiments were backed up and calibrated using laboratory experiments. Due to the heterogeneity of these structures, the signals coming from the interaction between the GPR system and the bridge are often complex, and hence hard to interpret. This defined the need to create a GPR numerical model that will allow the study of the attributes of reflected signals from various targets within the structure of the bridge. The GPR numerical analysis was undertaken using the finite-difference time-domain (FDTD) method. Since “micro regions” in the structure need to be modelled, subgrids were introduced into the standard FDTD method, in order to economize on the required memory and the calculation time. Good correlations were obtained between the numerical experiments and actual GPR experiments. It was shown both numerically and experimentally that significant mortar loss between the masonry arch rings can be detected. However, hairline delaminations between the mortar and the brick masonry cannot be detected using GPR.
Masonry bridges are composed of a finite number of distinct interacting blocks that have a length scale relatively comparable to the structure of interest. Therefore, they are ideal candidates for modeling as discrete systems instead of modeling as continuum systems. The discrete finite element method (DFEM) developed by the author to model discontinuum media consisting of blocks of arbitrary shapes is adopted in the static and dynamic analyses of masonry bridges. The developed DFEM is based on the principles of the FEM that incorporate contact elements. DFEM considers blocks as subdomains and represents them by solid elements. Contact elements, which are far superior to joint or interface elements, are used to model the block interactions, such as sliding or separation. In this study, the DFEM is briefly reviewed. Through some typical illustrative examples, the applicability of the DFEM to analysis of masonry arch bridges is examined and discussed. It is shown that the DFEM has the potential to become a useful tool for researchers and practicing engineers in designing, analyzing, and studying behavior of masonry bridges under static and dynamic loading.
The rehabilitation and conservation has shown in recent years the need of reliable methods for assessing masonry arch bridges: it is important not only to maintain ancient structures in good conditions, but also, when necessary, to be able to estimate their safety factor as accurately as possible.
Starting from a real case, this paper presents the results of a 3D FEM analysis of a stone masonry arch bridge, performed involving non-linear material behaviour, in which the structural role of the spandrel walls and filling is involved.
This paper presents the results of an experimental and Finite Element (FE) analysis studying the effect of backfill materials on a brickwork arch bridge's dynamic behaviour. Three different backfill materials were investigated: coarse gravel, sand, and Type 1 fill. The experimental dynamic characteristics of the arch bridge were determined using an impact hammer testing technique. A 3-D FE model was used to study the dynamic behaviour of the arch using natural frequency and mode superposition analyses. The addition of backfill material decreased the resonant frequencies and increased the damping ratios. The FE model was also used to study the effect of changes in backfill stiffness. The aim was to provide a better understanding of the dynamic behaviour of masonry arch bridges for NDT purposes.
A survey of the technology of modal testing, a new method for describing the vibration properties of a structure by constructing mathematical models based on test data rather than using conventional theoretical analysis. Shows how to build a detailed mathematical model of a test structure and analyze and modify the structure to improve its dynamics. Covers techniques for measuring the mode, shapes, and frequencies of practical structures from turbine blades to suspension bridges.
The rehabilitation and conservation has shown in recent years the need of reliable methods for assessing masonry arch bridges: it is important not only to maintain ancient structures in good conditions, but also, when necessary, to be able to estimate their safety factor as accurately as possible. Starting from a real case, this paper presents the results of a 3D FEM analysis of a stone masonry arch bridge, performed involving non-linear material behaviour, in which the structural role of the spandrel walls and filling is involved.
Existing test results of full-scale in-service masonry arch bridges are analysed to determine appropriate material properties for the modelling of this structural type. Three-dimensional nonlinear finite element models of three masonry arch bridges are generated using a commercially available finite element package. The behaviour of the masonry is replicated by use of a solid element that can have its stiffness modified by the development of cracks and crushing. The fill is modelled as a Drucker–Prager material, and the interface between the masonry and the fill is characterised as a frictional contact surface. The bridges are modelled under service loads, and the model results are compared to the results of a program of field testing of the structures. It is found that the assumption of a reasonable set of material properties, based on visual observations of the material and construction of the structure, implemented through a program of three-dimensional nonlinear finite element analysis enable good predictions of the actual behaviour of a masonry arch bridge.
In this paper a new frequency domain technique is introduced for the modal identification from ambient responses, i.e. in the case where the modal parameters must be estimated without knowing the input exciting the system. By its user friendliness the technique is closely related to the classical approach where the modal parameters are estimated by simple peak picking. However, by introducing a decomposition of the spectral density function matrix, the response can be separated into a set of single degree of freedom systems, each corresponding to an individual mode. By using this decomposition technique close modes can be identified with high accuracy even in the case of strong noise contamination of the signals.
The Tanaro Bridge, an 18 span masonry bridge built in 1866, has been investigated both in service conditions and at different stages of its demolition. A comparative characterization of the brickwork was performed by means of compressive tests on cylinders, flat jacks, sonic and sclerometer tests, while the natural frequencies and mode shapes of the bridge and the brickwork damping have been identified by dynamic tests on the bridge. Data from material testing were used to set up FEM models, so that the reliability of the material characterization procedures is demonstrated by comparison between the dynamic tests and FEM results. A rational comparative analysis of the results showed that: (i) a large part of the bridge needs to be monitored if the mode shapes are to be identified through dynamic tests; (ii) elastic FEM models can provide some information on the bridge response under service loads provided the mechanical parameters are adequately identified. Besides, some information has been deduced on the effectiveness, in service conditions, of some retrofitting technique: (i) transversal tie bars through the arch thickness have been proved almost ineffective; (ii) internal spandrels were found to be quite efficient in connecting adjacent spans.
The arch bridge forms an important part of our infrastructure, and maintenance of the bridge stock is becoming increasingly expensive. This paper presents the results of a nondestructive investigation of large scale model brickwork arches. Experiments were undertaken on brickwork arches using modal testing. The key features detected were: the effect of load on the backfill's surface, and the effect of spandrel wall separation from the arch itself. Mode shapes, fundamental frequencies, and damping ratios are presented for both qualitative and quantitative analysis of arch behaviour. Changes in these parameters were used to detect defects in the structures; as such the method may prove useful as a tool to assist civil engineers currently undertaking major bridge inspections.
This paper presents results from an ongoing investigation into non-destructive test methods which could be successfully used in conjunction with current inspection and assessment techniques. It aims to assist local authority engineers facing reassessment of their bridge stocks for up to 44 t gross vehicle, and 11.5 t axle weight limits. The use of impact hammer testing to study the dynamic response of a semicircular brickwork arch ring of 2 m span is described. The arch's response was analysed in both the time and frequency domains. Dynamic finite-element analyses were used to model its behaviour under impulse loading. The results, both in the time and frequency domains, compared well with those obtained experimentally. The resonant frequencies, and their corresponding vibration mode shapes, were successfully separated. The effects of spandrel walls and a granular backfill over the extrados were analysed. A simple defect was introduced in the form of a void in the fill over the crown; its detection was possible from observed changes in the frequency response function (FRF). The principal conclusions were that the method could be further explored within the context of structural integrity assessment of arch bridges.
Masonry bridges are composed of a finite number of distinct interacting blocks that have a length scale relatively comparable to the structure of interest. Therefore, they are ideal candidates for modeling as discrete systems instead of modeling as continuum systems. The discrete finite element method (DFEM) developed by the author to model discontinuum media consisting of blocks of arbitrary shapes is adopted in the static and dynamic analyses of masonry bridges. The developed DFEM is based on the principles of the FEM that incorporate contact elements. DFEM considers blocks as subdomains and represents them by solid elements. Contact elements, which are far superior to joint or interface elements, are used to model the block interactions, such as sliding or separation. In this study, the DFEM is briefly reviewed. Through some typical illustrative examples, the applicability of the DFEM to analysis of masonry arch bridges is examined and discussed. It is shown that the DFEM has the potential to become a useful tool for researchers and practicing engineers in designing, analyzing, and studying behavior of masonry bridges under static and dynamic loading.
Preface. 1. Introduction. 2. Finite Element Modelling. 3. Vibration Testing. 4. Comparing Numerical Data with Test Results. 5. Estimation Techniques. 6. Parameters for Model Updating. 7. Direct Methods Using Modal Data. 8. Iterative Methods Using Modal Data. 9. Methods Using Frequency Domain Data. 10. Case Study: an Automobile Body M. Brughmans, J. Leuridan, K. Blauwkamp. 11. Discussion and Recommendations. Index.
Historical structures, which constitute a very important part of our cultural heritage, should be well protected. Full comprehension of the structural behavior of historical structures is of prior importance for their protection. Due to the typical arch behavior, which is easily figured out, masonry arch bridges are the most suitable structures to be studied in the analysis methods that would be developed for masonry structures. The most appropriate analysis method for the masonry structures of brick and/or stone is the finite element analysis. For an accurate structural analysis, the model should be exactly defined. In this study, mathematical modeling techniques on a prototype model of a common arch bridge under different loading conditions are studied.
The Hilbert transform of a real-valued time-domain signal x(t) is another real-valued time-domain signal, denoted by x(t), such that z(t) = x(t) + jx(t) is an analytic signal. Like Fourier transforms, Hilbert transforms are linear operators. This chapter presents three equivalent mathematical definitions for the Hilbert transform, followed by examples and basic properties. The intrinsic nature of the Hilbert transform to causal functions and physically realizable systems is also shown. The chapter derives special formulas for the Hilbert transform of correlation functions and their envelopes. It outlines applications for both nondispersive and dispersive propagation. The computation of two envelope signals is discussed, and this is followed by correlation of the envelope signals. The Hilbert transform for general records can be defined in three ways namely, definition as convolution integrals, definition as phase shift system, and definition as imaginary part of analytic signal.
The presence of harmonic components in the measured responses is unavoidable in many applications of Operational Modal Analysis. This is especially true when measuring on mechanical structures containing rotating or reciprocating parts. This paper describes a new method based on the popular Enhanced Frequency Domain Decomposition technique for eliminating the influence of these harmonic components in the modal parameter extraction process. For various experiments, the quality of the method is assessed and compared to the results obtained using broadband stochastic excitation forces. Good agreement is found and the method is proven to be an easy-to-use and robust tool for handling responses with deterministic and stochastic content.
This paper deals with an experimental investigation on the strength of stone and stone masonry. Granitoidgneiss is commonly
used for masonry construction in India. The compressive strength of stone has been determined through 80 mm size cubes. It
has been found that the compressive strength of granitoid-gneiss is greater when the load is parallel to the mineral bands.
The compressive strength of stone masonry was studied through masonry prisms using 1∶4 and 1∶8 cement mortars. These tests
have revealed that masonry strength is higher when the load applied is parallel to the mineral bands. The flexural bond strength
of stone masonry walls was studied through full-scale tests. Flexural bond strength appears to play a major role in the failure
of stone masonry walls.
On présente une étude expérimentale de la résistance de la pierre et des maçonneries de pierre. En Inde, les pierres les plus
souvent utilisées en maçonnerie sont des gneiss granitoïdes. La résistance à la compression de la pierre a été déterminée
sur des cubes de 80 mm. Les résultats montrent que la résistance à la compression du gneiss granitoïde s'augmente lorsque
la charge est parallèle aux bandes minérales. La résistance à la compression de ces maçonneries a été étudiée à partir d'éléments
prismatiques utilisant des mortiers de ciment de 1∶4 et de 1∶8. Ces essais ont montré que la résistance de la maçonnerie est
supérieure lorsque la charge est parallèle aux bandes minérales. Des essais complets ont été effectués sur la résistance de
l'adhérence en flexion des murs en maçonnerie de pierre. La résistance de l'adhérence en flexion semble jouer un rôle important
dans la détérioration des murs en maçonnerie de pierre.
An analytical and experimental modal analysis has been carried out on the Qingzhou cable-stayed bridge in Fuzhou, China. Its main span of 605 m is currently the longest span among the completed composite-deck cable-stayed bridges in the world. An analytical modal analysis is performed on the developed three-dimensional finite element model starting from the deformed configuration to provide the analytical frequencies and mode shapes. The field ambient vibration tests on the bridge deck and all stay cables were conducted just prior to the opening of the bridge. The output-only modal parameter identification is then carried out by using the peak picking of the average normalized power spectral densities in the frequency-domain and stochastic subspace identification in the time-domain. A good correlation is achieved between the finite element and ambient vibration test results. It is demonstrated that the analytical and experimental modal analysis provide a comprehensive study on the dynamic properties of the bridge. The ambient vibration tests are sufficient to identify the most significant modes below 1.0 Hz of this kind of large span cable-stayed bridge. The validated finite element model with respect to ambient vibration test results can serve as the baseline for a more precise dynamic response prediction and long-term health monitoring of the bridge.
Random Data provides first-rate, practical tools for dynamic data and statistical methods for engineering problems. This revised bestseller presents the latest developed procedures and a complete rewrite of the Fast Fourier Transforms of applied fields. Plus, this resource includes a new chapter on frequency domain techniques. The updated book explores novel techniques on modern digital data storage, oversampling, and temporal moments. With new problem sets and examples, this guide is the ideal text and reference for students studying random data analysis theory and applications.
New tendencies on repair and strengthening on masonry arch bridges
- R O Catalan
- L E Aldea
R.O. Catalan, L.E. Aldea, New tendencies on repair and strengthening on masonry arch bridges, in: 5th International Conference on Arch Bridges, 12–14 September, Madeira, Portugal, 2007, pp. 719–724.
Masonry Arch Bridges-A State of the Art Review
- J Page
J. Page, Masonry Arch Bridges-A State of the Art Review, HMSO, London, 1993.
The model updating of historical masonry bridges using operational modal analysis method
- A Bayraktar
- A C Altunıs -Ik
- T Türker
- B Sevim
A. Bayraktar, A.C. Altunıs -ık, T. Türker, B. Sevim, The model updating of
historical masonry bridges using operational modal analysis method, in:
Proceedings of the 1st National Conference Reinforcement and Transfer into
the Future of Historical Structures, Ankara, Turkey, 2007, pp. 429-440.
Analyzers and Solutions, Release 11.2, Bruel and Kjaer, Sound and Vibration Measurement A/S, Denmark
PULSE, Analyzers and Solutions, Release 11.2, Bruel and Kjaer, Sound and
Vibration Measurement A/S, Denmark, 2006.
Modal identification from ambient responses using frequency domain decomposition
- R Brincker
- L Zhang
- P Andersen
R. Brincker, L. Zhang, P. Andersen, Modal identification from ambient responses
using frequency domain decomposition, 18th International Modal Analysis
Conference, San Antonio, USA, vol. 4062(2), 2000, pp. 625-630.
- Swanson Ansys
ANSYS, Swanson Analysis System, USA, 2008.