Finite-Element Analysis and Vibration Testing of a Two-Span Masonry Arch Bridge

This paper presents the analytical modeling, modal testing, and finite-element model updating for a two-span masonry arch bridge. An Ottoman masonry arch bridge built in the 19th century and located at Camlihemsin, Rize, Turkey is selected as an example. Analytical modal analysis is performed on the developed 3D finite-element model of the bridge to obtain dynamic characteristics. The ambient vibration tests are conducted under natural excitation such as human walking. The operational modal analysis is carried out using peak picking method in the frequency domain and stochastic subspace identification method in the time domain, and dynamic characteristics (natural frequencies, mode shapes, and damping ratios) are determined experimentally. Finite-element model of the bridge is updated to minimize the differences between analytically and experimentally estimated dynamic characteristics by changing boundary conditions. At the end of the study, maximum differences in the natural frequencies are reduced on average from 18 to 7% and a good agreement is found between analytical and experimental dynamic characteristics after finite-element model updating.     

Combined Experimental-Operational Modal Testing of Footbridges

In combined vibration testing, an artificial, measured force is used in operational conditions. This requires the identification of a system model that takes both the measured and the operational excitation into account. Advantages with respect to the classical operational modal analysis approach are the possibility of obtaining mass-normalized mode shapes and the increase of the excitation level and its frequency content. An advantage with respect to the classical experimental modal analysis approach, where the ambient excitation is not modeled, but considered as disturbing noise, is the possibility of using excitation levels that are of the same amplitude, or even smaller, than the ambient excitation levels. In this paper, combined modal testing of footbridges is explored using two case studies: a steel arch footbridge with spans of 75.2 m and 30.3 m and a concrete stress-ribbon footbridge with spans of 30 m and 28 m. The comparison of the modal parameters (eigenfrequencies, damping ratios, mode shapes, and modal scaling factors) obtained from a combined vibration test with the ones obtained from other modal tests and from a finite-element model, demonstrates the feasibility of using small and practical excitation devices for the modal testing of footbridges.     

Dynamic Field Test, System Identification, and Modal Validation of an RC Minaret: Preprocessing and Postprocessing the Wind-Induced Ambient Vibration Data

The investigation of dynamic response for civil engineering structures largely depends on a detailed understanding of their dynamic characteristics, such as the natural frequencies, mode shapes, and modal damping ratios. Dynamic characteristics of structures may be obtained numerically and experimentally. The finite-element method is widely used to model structural systems numerically. However, there are some uncertainties in numerical models. Material properties and boundary conditions may not be modeled correctly. There may be some microcracks in the structures, and these cracks may directly affect the modeling parameters. Modal testing gives correct uncertain modeling parameters that lead to better predictions of the dynamic behavior of a target structure. Therefore, dynamic behavior of special structures, such as minarets, should be determined with ambient vibration tests. The vibration test results may be used to update numerical models and to detect microcracks distributed along the structure. The operational modal analysis procedure consists of several phases. First, vibration tests are carried out, spectral functions are produced from raw measured acceleration records, dynamic characteristics are determined by analyzing processed spectral functions, and finally analytical models are calibrated or updated depending on experimental analysis results. In this study, an ambient vibration test is conducted on the minaret under natural excitations, such as wind effects and human movement. The dynamic response of the minaret is measured through an array of four trixial force-balanced accelerometers deployed along the whole length of the minaret. The raw measured data obtained from ambient vibration testing are analyzed with the SignalCAD program, which was developed in MATLAB. The employed system identification procedures are based on output-only measurements because the forcing functions are not available during ambient vibration tests. The ModalCAD program developed in MATLAB is used for dynamic characteristic identification. A three-dimensional model of the minaret is constructed, and its modal analysis is performed to obtain analytical frequencies and mode shapes by using the ANSYS finite-element program. The obtained system identification results have very good agreement, thus providing a reliable set of identified modal properties (natural frequencies, damping ratios, and mode shapes) of the structure, which can be used to calibrate finite-element models and as a baseline in health monitoring studies.     

Vibration Characteristics of K?mürhan Highway Bridge Constructed with Balanced Cantilever Method

K?mürhan Highway Bridge is a reinforced concrete box girder bridge located on the 51st km of Elaz??–Malatya Highway over the F?rat River. Because of the fact that the K?mürhan Bridge is the only bridge in this part of F?rat, it has major logistical importance. So, this paper aims to determine dynamic characteristics such as natural frequencies, mode shapes, and damping ratios of the bridge using experimental measurements and finite-element analyses to evaluate current behavior. The experimental measurements are carried out by ambient vibration tests under traffic loads. Due to the expansion joint in the middle of the bridge, special measurement points are selected and experimental test setups are constituted. Vibration data are gathered from the both box girder and bridge deck. Measurement time, frequency span, and effective mode number are determined by considering similar studies and literature. The peak picking method in the frequency domain is used for the output-only modal identification. An analytical modal analysis is performed on the developed two- and three-dimensional finite-element model of the bridge using SAP2000 software to provide the analytical frequencies and mode shapes. At the end of the study, dynamic characteristics of the Elaz?? and Malatya parts of the bridge obtained from the experimental measurements are compared with each other and transverse effects on the bridge are determined. Also, experimental and analytical dynamic characteristics are compared. Good agreement is found between dynamic characteristics in the all measurement test setups performed on the box girder and bridge deck and analytical modal analyses.     

Performance of a Tied-Arch Reinforced Concrete Railway Bridge: Rating, Safety Assessment, and Bond Length Evaluation

This study presents investigations regarding visual inspection, dynamic testing, and finite-element modeling of an approximately 80-year old reinforced concrete tied-arch railway bridge that is still in service in Turkey. Investigations were conducted as part of a systematic periodic inspection along Ankara-Zonguldak railway line. The bridge is subject to heavy freight trains with increasing axle loads. Field tests such as material tests and dynamic tests were used to calibrate the finite-element model of the bridge. Detailed information regarding testing and model updating procedure is given. Based on test results, computer model was refined. The calibrated model of the bridge structure was then used for structural assessment and evaluation. Despite sufficient overall safety, local details were found to be problematic. Due to insufficient bond length in hanger-to-arch connection, a strengthening scheme using steel channel sections was proposed.     

Modal Contribution Coefficients in Bridge Condition Evaluation

Impact modal testing combined with finite element (FE) analyses is currently being used to evaluate the condition of steel bridges in the state of Ohio. Using modal testing techniques, it is relatively easy to measure the dynamic response of bridges, including mode shapes, frequencies, and modal scaling factors. These responses are compared to the results of the FE analyses and the model is iteratively updated until a good agreement is obtained. After a good agreement between experimental and analytical results has been achieved, the FE model is used to obtain stresses that are used to load rate the bridge. During the iterative calibration process, several quantities, including the fundamental mode shapes and frequencies, are used to evaluate the accuracy of the FE model. Since each mode shape plays a different role in the dynamic behavior of the structure, a more efficient calibration routine can be achieved if more emphasis is placed on obtaining good matches for the modes that are most influential. The aim of this paper is to develop a quantitative measure of the contribution of different modes to the overall dynamic response of a structure. The proposed measure, a series of contribution coefficients, is used to identify which modes are most critical in the process of modal testing and FE model calibration. Several applications of the contribution coefficients are identified.     

Dynamic Testing for Structural Identification of a Bridge

Structural identification via modal analysis in structural mechanics is gaining popularity in recent years, despite conceptual difficulties connected with its use. This paper is devoted to illustrating the advantages and also the indeterminacy characterizing structural identification problems for bridge structures, even in rather simple instances. In particular, an identification procedure based on modal analysis and finite-element model updating is presented for the characterization of a concrete bridge whose constructive typology is quite diffuse in the area of Friuli Venezia Giulia, Italy. Experience has suggested (so as to restrict the indeterminacy frequently affecting identification issues) resorting to all the a priori information on the system and mindfully selecting the parameters to be identified. The analysis pointed out some particularities in the modeling of bridge typology under study, otherwise not a priori detectable from an analytical point of view.     

Output-Only System Identification of Posttensioned Segmental Concrete Highway Bridges

This paper discusses the application of system identification of a highway bridge using finite-element method and ambient-vibration testing. The posttensioned Gülburnu Highway Bridge located on the Giresun-Espiye state highway was selected as a case study. A finite-element model of the bridge was developed using SAP2000 software, and dynamic characteristics were obtained analytically. During the test, sources of ambient excitations were provided by the traffic effects over the bridge. Ambient-vibration tests were applied to the bridge to identify dynamic characteristics. The selection of measurement time, frequency span, and effective mode number was considered from similar studies in the literature. Two output-only system identification methods, enhanced frequency domain decomposition and stochastic subspace identification, were used to estimate the dynamic characteristics of the bridge experimentally. The accuracy and efficiency of both methods were investigated and compared with finite-element results. Results suggest that ambient-vibration measurements are sufficient to identify structural modes with a low range of natural frequencies. In addition, the dynamic characteristics obtained from the finite-element model of the bridge have a good correlation with experimental frequencies and mode shapes.     

Ambient Vibration of Long-Span Cable-Stayed Bridge

The investigation of dynamic response for long-span cable-stayed bridges largely depends on a detailed understanding of their dynamic characteristics, such as the natural frequencies, mode shapes, and modal damping ratios. In this paper, the dynamic characteristics of a fairly long cable-stayed bridge in Hong Kong are studied using finite-element analysis and ambient vibration measurements. A three-dimensional finite-element model is first established for the bridge based on design drawings. The dynamic characteristics are then analyzed from the statically deformed configuration. Ambient vibration measurements are also conducted to obtain the dynamic characteristics of the bridge. Comparison between these two results shows that, for the most part, a total of 31 modes can be correlated with a reasonable agreement. However, the frequency differences of the higher modes can range between 15 and 30%. This implies that, if the measurement is more reliable, a finite-element model updating is necessary in order to achieve better correlation between these two results.     

Challenges in the Application of Stochastic Modal Identification Methods to a Cable-Stayed Bridge

This paper presents an analysis of the data collected in the ambient vibration test of the International Guadiana cable-stayed Bridge, which links Portugal and Spain, based on different output-only identification techniques: peak-picking, frequency domain decomposition, covariance-driven stochastic subspace identification, and data-driven stochastic subspace identification. The purpose of the analysis is to compare the performance of the four techniques and evaluate their efficiency in dealing with specific challenges involved in the modal identification of the tested cable-stayed bridge, namely the existence of closely spaced modes, the perturbation produced by the local vibration of stay-cables, and the variation of modal damping coefficients with wind velocity. The identified natural frequencies and mode shapes are compared with the corresponding modal parameters provided by a previously developed numerical model. Additionally, the variability of some modal damping coefficients is related with the variation of the wind characteristics and associated with a component of aerodynamic damping.     

Model-Based Damage Identification in a Continuous Bridge Using Vibration Data

Damage often causes changes in the dynamic characteristics of a structure such as frequencies and mode shapes. Vibration-based damage identification techniques utilize the changes in the dynamic characteristics of a structure to determine the location and extent of damage in the structure. Such techniques are applied in this study to the Crowchild Bridge, a steel-free deck continuous bridge located in western Canada. While the numerical models of the bridge are correlated with the measured dynamic characteristics, computer simulation is used to study the identification of a number of different damage patterns, and the effects of measurement errors and incomplete mode shapes on the quality of results are evaluated. The effectiveness of some selected damage identification techniques is examined; the potential difficulties in identifying the damage are outlined; and areas of further research are suggested. A three-dimensional finite-element model and a simple two-dimensional girder model of the bridge have been constructed to study the usefulness of the selected damage identification methods. Another promising damage detection method proposed here is based on the application of neural networks that combines a vibration-based method.     

Dynamic Analysis of Curved Continuous Multiple-Box Girder Bridges

The use of horizontally curved composite multiple-box girder bridges in modern highway systems is quite suitable in resisting torsional and warping effects induced by highway curvatures. Bridge users react adversely to vibrations of a bridge and especially where torsional modes dominate. In this paper, continuous curved composite multiple-box girder bridges are analyzed, using the finite-element method, to evaluate their natural frequencies and mode shapes. Experimental tests are conducted on two continuous twin-box girder bridge models of different curvatures to verify and substantiate the finite-element model. Empirical expressions are deduced from these results to evaluate the fundamental frequency for such bridges. The parameters considered herein are the span length, number of lanes, number of boxes, span-to-radius of curvature ratio, span-to-depth ratio, end-diaphragm thickness, number of cross bracings, and number of spans.     

Roebling Suspension Bridge. I: Finite-Element Model and Free Vibration Response

This first part of a two-part paper on the John A. Roebling suspension bridge (1867) across the Ohio River is an analytical investigation, whereas Part II focuses on the experimental investigation of the bridge. The primary objectives of the investigation are to assess the bridge’s load-carrying capacity and compare this capacity with current standards of safety. Dynamics-based evaluation is used, which requires combining finite-element bridge analysis and field testing. A 3D finite-element model is developed to represent the bridge and to establish its deformed equilibrium configuration due to dead loading. Starting from the deformed configuration, a modal analysis is performed to provide the frequencies and mode shapes. Transverse vibration modes dominate the low-frequency response. It is demonstrated that cable stress stiffening plays an important role in both the static and dynamic responses of the bridge. Inclusion of large deflection behavior is shown to have a limited effect on the member forces and bridge deflections. Parametric studies are performed using the developed finite-element model. The outcome of the investigation is to provide structural information that will assist in the preservation of the historic John A. Roebling suspension bridge, though the developed methodology could be applied to a wide range of cable-supported bridges.     

Assessment of Highway Bridge Upgrading by Dynamic Testing and Finite-Element Model Updating

The Land Transport Authority of Singapore has a continuing program of highway bridge upgrading for refurbishing and strengthening bridges to allow for increasing vehicle traffic and increasing axle loads. One subject of this program has been a short-span bridge taking a busy main road across a coastal inlet near a major port facility. Experiment-based structural assessments of the bridge were conducted before and after upgrading works including strengthening. Each assessment exercise comprised three separate components: (1) a strain and acceleration monitoring exercise lasting approximately one month; (2) a full-scale dynamic test carried out in a single day without closing the bridge; and (3) a finite-element model updating exercise to identify structural parameters and mechanisms. This paper presents the dynamic testing and the modal analysis used to identify the vibration properties and the quantification of the effectiveness of the upgrading through the subsequent model updating. Before and after upgrade, similar sets of vibration modes were identified, resembling those of an orthotropic plate with relatively weak transverse bending stiffness. Conversion of bearings from nominal simple supports to nominal full fixity was shown via model updating to be the principal cause of natural frequency increases of up to 50%. The utility of the combined experimental and analytical process in direct identification of structural properties has been proven, and the procedure can be applied to other structures and their capacity assessments.     

Dynamic Monitoring of Steel Girder Highway Bridge

Currently there are different monitoring techniques that have been considered for use in the structural evaluation of bridges. These include approaches based on both static and dynamic behavior. The use of dynamic properties has advantages over static properties, since components of the dynamic properties are only marginally influenced by variations in the loading. When dynamic properties are used, field studies have shown that it is not always sufficient to use only natural frequencies and modal displacements. Some research for structural evaluation of bridges indicates that techniques based on use of derivatives of the natural frequencies and the modal displacements may be more effectively used to generate effective diagnostic parameters for structural identification. This paper presents the results of applying one of these methods, the modal flexibility approach, to a field study of a bridge in which the bearings were partially restrained in colder weather. While others have used impact methods with the modal flexibility method, in this study the approach is modified so that excitation is provided by vehicular traffic. The results show that the modified modal flexibility method provides a clear indication that there have been changes in the bridge’s structural behavior.     

Dynamic Behavior of Steel Deck Tension-Tied Arch Bridges to Seismic Excitation

The dynamic responses of steel deck, tension-tied, arch bridges subjected to earthquake excitations were investigated. The 620 ft (189 m) Birmingham Bridge, located in Pittsburgh, was selected as an analytical model for the study. The bridge has a single deck tension-tied arch span and is supported by two bridge piers, which in turn are supported by the pile foundations. Due to the complex configuration of the deck system, two analytical models were considered to represent the bridge deck system. Using the normal mode method, seismic responses were calculated for two bridge models and the results were compared with each other. Three orthogonal records of the El Centro 1940 earthquake were used as input for the seismic response analysis. The modal contributions were also checked in order to obtain a reasonable representation of the response and to minimize computational cost. Displacements and stresses at the panel points of the bridge are calculated and presented in graphical form.     

Experimental and Numerical Study of Damaged Cantilever

The introduction of a crack in a steel structure will cause a local change in the stiffness and damping capacity. The change in stiffness will lead to a change of some of the natural frequencies of the structure and a discontinuity in the associated mode shapes. This paper contains a presentation of the results from experimental and numerical tests with hollow section cantilevers containing fatigue cracks. Two different finite-element (FE) models have been used to estimate the modal parameters numerically. The first FE model consists of beam elements. The second FE model consists of traditional rectangular shell elements and one rectangular shell element with a transverse, internal, open crack. The analytical results from the numerical models are compared with data obtained from experimental tests. The numerical models give good agreements with the experimental data. The beam model takes into account only the first mode of the crack evaluation. In the shell model all three modes of the crack growth are taken into account. Nevertheless, the results obtained for both models are satisfactory because the beam is subjected to bending. It can be concluded that it is sufficient to use crack models for calculating natural frequencies in bending, taking into account the first mode of the crack extension only.     

Baseline Models for Bridge Performance Monitoring

A baseline model is essential for long-term structural performance monitoring and evaluation. This study represents the first effort in applying a neural network-based system identification technique to establish and update a baseline finite element model of an instrumented highway bridge based on the measurement of its traffic-induced vibrations. The neural network approach is particularly effective in dealing with measurement of a large-scale structure by a limited number of sensors. In this study, sensor systems were installed on two highway bridges and extensive vibration data were collected, based on which modal parameters including natural frequencies and mode shapes of the bridges were extracted using the frequency domain decomposition method as well as the conventional peak picking method. Then an innovative neural network is designed with the input being the modal parameters and the output being the structural parameters of a three-dimensional finite element model of the bridge such as the mass and stiffness elements. After extensively training and testing through finite element analysis, the neural network became capable to identify, with a high level of accuracy, the structural parameter values based on the measured modal parameters, and thus the finite element model of the bridge was successfully updated to a baseline. The neural network developed in this study can be used for future baseline updates as the bridge being monitored periodically over its lifetime.     

Cross Correlations of Modal Responses of Tall Buildings in Wind-Induced Lateral-Torsional Motion

Recent trends towards developing increasingly taller and irregularly-shaped buildings imply that these complex structures are potentially more responsive to wind excitation. Making accurate predictions of wind loads and their effects on such structures is therefore a necessary step in the design synthesis process. This paper presents a framework for dynamic analysis of the wind-induced lateral-torsional response of tall buildings with three-dimensional (3D) mode shapes. The cross correlation reflecting the statistical coupling among modal responses under spatiotemporally varying dynamic wind excitations has been investigated in detail. The effects of intermodal correlations on the lateral-torsional response of tall buildings with 3D mode shapes and closely spaced natural frequencies are elucidated and a more accurate method for quantifying intermodal cross correlations is analytically developed. Utilizing the wind tunnel derived synchronous multipressure measurements, a full-scale 60-story asymmetric building of mixed steel and concrete construction is used to illustrate the proposed framework for the coupled dynamic analysis and highlight the intermodal correlation of modal responses on the accurate prediction of coupled building acceleration.     

Vibration Studies of Tsing Ma Suspension Bridge

A three-dimensional dynamic finite element model is established for the Tsing Ma long suspension Bridge in Hong Kong. The two bridge towers made up of reinforced concrete are modeled by three-dimensional Timoshenko beam elements with rigid arms at the connections between columns and beams. The cables and suspenders are modeled by cable elements accounting for geometric nonlinearity due to cable tension. The hybrid steel deck is represented by a single beam with equivalent cross-sectional properties determined by detailed finite element analyses of sectional models. The modal analysis is then performed to determine natural frequencies and mode shapes of lateral, vertical, torsional, longitudinal, and coupled vibrations of the bridge. The results show that the natural frequencies of the bridge are very closely spaced; the first 40 natural frequencies range from 0.068 to 0.616 Hz only. The computed normal modes indicate interactions between the main span and side span, and between the deck, cables, and towers. Significant coupling between torsional and lateral modes is also observed. The numerical results are in excellent agreement with the measured first 18 natural frequencies and mode shapes. The established dynamic model and computed dynamic characteristics can serve further studies on a long-term monitoring system and aerodynamic analysis of the bridge.