Stiffness Assessment through Modal Analysis of an RC Slab Bridge before and after Strengthening

As part of Main Roads Western Australia’s (MRWA) bridge management and bridge upgrading program, MRWA bridge no. 3014 was assessed to evaluate its condition before and after strengthening works with carbon-fiber-reinforced-polymers (CFRP). The assessment process coupled analytical results with field observations and dynamic testing of the structure. Vibration-based structural assessment of the bridge was conducted before and after the completion of the upgrading works. This paper presents the results of the vibration tests and modal analysis performed before and after the structure upgrading. In particular, the change in the structural properties and stiffness, before and after the strengthening, based on the analyses of the updated models of the bridge, is presented and discussed. The results demonstrate the effectiveness of using the dynamic assessment method to determine the elastic flexural stiffness of bridge structures retrofitted with CFRP.     

Evaluation of the Effectiveness of Strengthening Intervention by CFRP on MRWA Bridge No. 3014

Main Roads of Western Australia has a continuing program of bridge upgrading, to refurbish and strengthen bridges to allow for increasing vehicle traffic and increasing axle loads. A 40-year-old, four-span reinforced concrete slab bridge was retrofitted with application of CFRP laminate strips on the top of the deck over the piers, as well as on the deck soffit in the midspan regions, to reduce high moments in both hogging and sagging. The dynamic assessment of the bridge before and after strengthening works provided the opportunity to evaluate the effectiveness of the strengthening intervention through dynamic measurements. A performance evaluation of the repaired structure was carried out through traffic loading application on the updated numerical models of the bridge, before and after retrofit. As a main observation, the addition of CFRP laminate strips led to a significant increase of the structural capacity in flexure. The paper discusses the results obtained from the dynamic-based assessment in terms of effectiveness of the strengthening intervention as well as of efficiency in using such a methodology to evaluate the capacity increase of the retrofitted bridge.     

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.     

Finite-Element Model Updating for the Kap Shui Mun Cable-Stayed Bridge

This paper presents the implementation of the finite-element model updating for the Kap Shui Mun Bridge, a 430 m main span double-deck cable-stayed bridge in Hong Kong. The dynamic characteristics of the bridge have been studied through both three-dimensional finite-element prediction and field vibration measurement previously. In this paper, the developed finite-element model is updated based on the field measured dynamic properties. A comprehensive sensitivity study to demonstrate the effects of various structural parameters (including the connections and boundary conditions) on the modes of concern is first performed, according to which a set of structural parameters are then selected for adjustment. The finite-element model is updated in an iterative fashion so as to minimize the differences between the predicted and the measured natural frequencies. The final updated finite-element model for the Kap Shui Mun Bridge is able to produce natural frequencies in good agreement with the measured ones, and can be helpful for a more precise dynamic response prediction.     

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.     

Modal Testing, Finite-Element Model Updating, and Dynamic Analysis of an Arch Type Steel Footbridge

This paper describes an arch type steel footbridge, its analytical modeling, modal testing, finite-element model updating, and dynamic analysis. A modern steel footbridge which has an arch type structural system and is located on the Karadeniz coast road in Trabzon, Turkey is selected as an application. An analytical modal analysis is performed on the developed three-dimensional finite-element model of footbridge to provide analytical frequencies and mode shapes. Field ambient vibration tests on the footbridge deck under natural excitation such as human walking and traffic loads are conducted. The output-only modal parameter identification is carried out by using peak picking of the average normalized power spectral densities in the frequency domain and stochastic subspace identification in the time domain, and dynamic characteristics such as natural frequencies, mode shapes, and damping ratios are determined. The finite-element model of the footbridge is updated to minimize the differences between analytically and experimentally estimated modal properties by changing some uncertain modeling parameters such as material properties. Dynamic analyses of the footbridge before and after finite-element model updating are performed using the 1992 Erzincan earthquake record. At the end of the study, maximum differences in the natural frequencies are reduced from 22 to only 5% and good agreement is found between analytical and experimental dynamic characteristics such as natural frequencies and mode shapes by model updating. Also, maximum displacements and principal stresses before and after model updating are compared with each other.     

Bridge Structural Condition Assessment Based on Vibration and Traffic Monitoring

A stochastic model of traffic excitation on bridges is developed assuming that the arrival of vehicles traversing a bridge (modeled as an elastic beam) follows a Poisson process, and that the contact force of a vehicle on the bridge deck can be converted to equivalent dynamic loads at the nodes of the beam elements. The parameters in this model, such as the Poisson arrival rate and the stochastic distribution of vehicle speeds, are obtained by image processing of traffic video data. The model reveals that traffic excitations on bridges are spatially correlated. This important characteristic is usually incorrectly ignored in most output-only methods for the identification of bridge structural properties using traffic-induced vibration measurement data. In this study, the stochastic traffic excitation model with partial traffic information is incorporated in a Bayesian framework, to evaluate the structural properties and update their uncertainty for condition assessment of the bridge superstructure. The vehicle weights are also estimated simultaneously in this procedure. The proposed structural assessment methodology is validated on an instrumented highway bridge.     

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.     

Flexural Strengthening of Steel Bridges with High Modulus CFRP Strips

Acceptance of carbon fiber-reinforced polymer (CFRP) materials for strengthening concrete structures, together with the recent availability of higher modulus CFRP strips, has resulted in the possibility to also strengthen steel structures. Steel bridge girders and building frames may require strengthening due to corrosion induced cross-section losses or changes in use. An experimental study investigating the feasibility of different strengthening approaches was conducted. Large-scale steel-concrete composite beams, typical of bridge structures, were used to consider the effect of CFRP modulus, prestressing of the CFRP strips, and splicing finite lengths of CFRP strips. All of the techniques examined were effective in utilizing the full capacity of the CFRP material, and increasing the elastic stiffness and ultimate strength of the beams. Results of the experimental program were compared to an analytical model that requires only the beam geometry and the constitutive properties of the CFRP, steel, and concrete. This model was used to investigate the importance of several key parameters. Finally, an approach for design is proposed that considers the bilinear behavior of a typical strengthened beam to the elastic-plastic behavior of the same beam before strengthening.     

Damage Localization and Finite-Element Model Updating Using Multiresponse NDT Data

New techniques for both finite-element model updating and damage localization are presented using multiresponse nondestructive test (NDT) data. A new protocol for combining multiple parameter estimation algorithms for model updating is presented along with an illustrative example. This approach allows for the simultaneous use of both static and modal NDT data to perform model updating at the element level. A new damage index based on multiresponse NDT data is presented for damage localization of structures. This index is based on static and modal strain energy changes in a structure as a result of damage. This method depicts changes in physical properties of each structural element compared to its initial state using NDT data. Deficient or potentially damaged structural elements are then selected as the unknown parameters to be updated by parameter estimation. Error function normalization, error function stacking, and multiresponse parameter estimation methods are proposed for using multiple data types for simultaneous stiffness and mass parameter estimation. Also, multiple sets of measurements with various sizes and missing data points can be utilized. This paper uses a laboratory grid model of a bridge deck built at the University of Cincinnati Infrastructure Institute and the corresponding NDT data for validation of the above damage localization and model updating methods. Multiresponse parameter estimation has been utilized to update the stiffness of bearing pads, and both the stiffness and mass of the connections, using static and dynamic NDT data. The static and modal responses of the updated grid model presented a closer match with the NDT data than the responses from the initial model.     

Ambient Vibration Data Analysis for Structural Identification and Global Condition Assessment

System identification is an area which deals with developing mathematical models to characterize the input-output behavior of an unknown system by means of experimental data. Structural health monitoring (SHM) provides the tools and technologies to collect and analyze input and output data to track the structural behavior. One of the most commonly used SHM technologies is dynamic testing. Ambient vibration testing is a practical dynamic testing method especially for large civil structures where input excitation cannot be directly measured. This paper presents a conceptual and reliable methodology for system identification and structural condition assessment using ambient vibration data where input data are not available. The system identification methodology presented in this study is based on the use of complex mode indicator functions (CMIFs) coupled with the random decrement (RD) method to identify the modal parameters from the output only data sets. CMIF is employed for parameter identification from the unscaled multiple-input multiple-output data sets generated using the RD method. For condition assessment, unscaled flexibility and the deflection profiles obtained from the dynamic tests are presented as a conceptual indicator. Laboratory tests on a steel grid and field tests on a long-span bridge were conducted and the dynamic properties identified from these tests are presented. For demonstrating condition assessment, deflected shapes obtained from unscaled flexibility are compared for undamaged and damaged laboratory grid structures. It is shown that structural changes on the steel grid structure are identified by using the unscaled deflected shapes.     

Model Updating of Semirigid Jointed Structure Using Generic Parameters

Semirigid connections are usually found in large-scale engineering structures, and the knowledge of the dynamic characteristics of these connections is important to the accurate definition of the dynamic characteristics of the engineering structure. Different models have been presented to define the connection, but most of them are not suitable for model improvement from dynamic measurements of the structure. This paper presents a hybrid finite-element model that consists of a beam element with two semirigid connections at the ends for updating the finite-element model of the jointed structure. The parameter selection strategy of the generic element is adopted, and the stiffnesses of the joint in three dimensions are selected as generic parameters to be updated simultaneously with other structural parameters of the structure. The proposed method is applied to the model updating of a 3D steel truss in the laboratory. Results show that the method could improve significantly not only those vibration modes used in the updating but also the higher modes with a maximum error of 6%.     

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.     

Identifying Loading and Response Mechanisms from Ten Years of Performance Monitoring of a Tall Building

In 1993, Shimizu Corporation provided the opportunity to record manually, readings of stress and strain gauges they had embedded at the 18th story of a 65-story office tower under construction in Singapore. Static readings continued during construction and long after, and capitalizing on access to the building and assistance of both contractor and owner, monitoring systems for tracking wind, acceleration, and deflection were installed and progressively upgraded. Further, a comprehensive ambient vibration survey and finite element model updating exercise provided a thoroughly validated analytical model of the structure. This model has been used in parallel with the analog wind and tremor “super sensor” of the building itself to provide direct evidence and characterization of the seismic and wind loadings on the building. This paper describes the evolution of the monitoring system and its capabilities, together with some of the insights the system provided into structural and loading mechanisms during its operational life until early 2005.     

Refined Stick Model for Dynamic Analysis of Skew Highway Bridges

Stick models are widely employed in the dynamic analysis of bridges when only approximate results are desired or when detailed models are difficult or time-consuming to construct. Although the use of stick models for regular bridges has been validated by various researchers, the application of such models to skew highway bridges continues to present challenges. The conventional single-beam stick model used to represent the bridge deck often fails to capture certain predominant vibration modes that are important in obtaining the true dynamic response of the bridge. In this paper, a refined stick model is proposed for the preliminary dynamic analysis of skew bridges. The model utilizes a dual-beam stick representation of the bridge deck. The validity of the model is established by comparing results obtained from the proposed model with numerical solutions obtained for skew plates and a skew bridge. It is shown that this dual-beam stick model is superior to the conventional single-beam model in estimating the natural vibration frequencies and in predicting the predominant vibration modes of the bridge. Because of its simplicity and relative accuracy, this model is recommended for the preliminary dynamic analysis of skew highway bridges.     

Dynamic Anomalies in a Modular Bridge Expansion Joint

Environmental noise complaints from homeowners near bridges with modular bridge expansion joints (MBEJs) led to an engineering investigation into the noise production mechanism. The investigation identified modal vibration frequencies in the MBEJ coupling with acoustic resonances in the chamber cast into the bridge abutment below the MBEJ. This initial acoustic investigation was soon overtaken by observations of fatigue induced cracking in structural beams transverse to the direction of traffic. These beams are, in the English-speaking world, universally referred to as center beams. However, in Europe the term lamellae is equally common. A literature search revealed little to describe the structural dynamics behavior of MBEJs but showed that there was an accepted belief dating from around 1973 that the loading was dynamic. In spite of this knowledge many bridge design codes used throughout the world specify a static or quasi-static load case with no mention of the dynamic behavior. This paper identifies the natural modes and operational response modes of vibration of the MBEJ installed into Sydney’s Anzac Bridge. In addition, the paper will introduce the dynamic range factor (DRF) and report a DRF of 4.6 obtained after extensive static and dynamic strain gage measurements. The studies indicated that the Anzac Bridge MBEJ was very lightly damped (<2% of critical) and a reduction in the measured DRF through the introduction of additional damping was an option.     

Field Performance of FRP Bridge Repairs

Many reinforced concrete bridges throughout the United States on county and state highway systems are deteriorated and∕or distressed to such a degree that structural strengthening of the bridge or reducing the allowable truck loading on the bridge by load posting is necessary to extend the service life of the bridge. The structural performance of many of these bridges can be improved through external bonding of fiber-reinforced plastic (FRP) laminates or plates. This paper describes the rehabilitation of an existing concrete bridge in Alabama through external bonding of FRP plates to the bridge girders. Field load tests were conducted before and after application of the FRP plates, and the response of the bridge to test vehicle loadings was recorded. Results of the field tests are reported, and the effects of the FRP plates on the bridge response are identified. The repaired bridge structure exhibited a decrease in steel reinforcing bar stresses and vertical midspan deflections. These decreases ranged from 4 to 12% for various static and dynamic loading cases.     

Bridge Model Updating Using Response Surface Method and Genetic Algorithm

A finite-element (FE) model of a structure is a highly idealized engineering model that may or may not truly reflect the physical structure. The purpose of model updating is to modify the FE model of a structure in order to obtain better agreement between the numerical and field-measured structure responses. In this paper, a new practical and user-friendly FE model updating method is presented. The new method utilizes the response surface method for the best experimental design of the parameters to be updated based on which numerical analysis can be performed in order to obtain explicit relationships between the structural responses and parameters from the simulation results. The parameters are then be updated using the genetic algorithm (GA) by minimizing an objective function. A numerical example of a simply supported beam has been used to demonstrate the concept. This method has also been applied to the model updating of an existing bridge. Results show that this method works well and achieves reasonable physical explanations for the updated parameters.     

Dynamic and Static Behavior of a Curved-Girder Bridge with Varying Boundary Conditions

A curved, three-span continuous, steel I-girder bridge in Salt Lake City was tested in order to determine its dynamic and static load carrying properties for three boundary condition states. For each of the three boundary condition states, two dynamic forced vibration methods were applied to the bridge as well as a static live-load test. The first forced vibration method used an eccentric mass shaker. The second method involved striking the side of the bridge with an impact hammer. The live-load test was performed by slowly driving a truck at a crawl speed across the bridge. Velocity transducers, accelerometers, and strain gauges were utilized to record the response of the bridge. The analysis and compilation of recorded dynamic response of the bridge enabled the preparation of mode shapes and natural frequencies for each boundary condition. This paper discusses the resulting changes in relevant dynamic properties and compares them with the changes in the static properties that were determined from the bridge response recorded from the live-load tests.     

Structural Reliability Estimation with Vibration-Based Identified Parameters

This paper presents a unique structural reliability estimation method incorporating structural parameter identification results based on the seismic response measurement. In the shaking table test, a three-bent concrete bridge model was shaken to different damage levels by a sequence of earthquake motions with increasing intensities. Structural parameters, stiffness and damping values of the bridge were identified under damaging seismic events based on the seismic response measurement. A methodology was developed to understand the importance of structural parameter identification in the reliability estimation. Along this line, a set of structural parameters were generated based on the Monte Carlo simulation. Each of them was assigned to the base bridge model. Then, every bridge model was analyzed using nonlinear time history analyses to obtain damage level at the specific locations. Last, reliability estimation was performed for bridges modeled with two sets of structural parameters. The first one was obtained by the nonlinear time history analysis with the Monte Carlo simulated parameters which is called nonupdated structural parameters. The second one was obtained by updating the first set in Bayesian sense based on the vibration-based identification results which is called updated structural parameters. In the scope of this paper, it was shown that residual reliability of the system estimated using the updated structural parameters is lower than the one estimated using the nonupdated structural parameters.