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.     

Load Rating of Masonry Arch Bridges: Refinements

In a paper previously published by the first writer, a procedure for load-rating masonry arch bridges was introduced. The procedure uses the Load Factor Method of the 1994 American Association of State Highway and Transportation Officials Manual for the Condition Evaluation of Bridges, applied to a frame analysis model of a masonry arch spanning from abutment to abutment. The procedure is based on the assumption of the arch barrel having no tensile strength. The objective of this technical note is to complement the initial procedure by enabling the assessing engineer to exercise discretion in deciding whether or not a small value of tensile strength should be allowable in determining a suitable rating for masonry arch bridges. In addition the initially proposed strength values, which are considered overly conservative, are increased. The introduction of these refinements will allow a more accurate assessment of the nation’s stock of stone masonry bridges.     

Finite-Element Analysis of Steel Bridge Distortion-Induced Fatigue

Welded plate girder bridges built before the mid-1980s are often susceptible to fatigue cracking driven by out-of-plane distortion. However, methods for prediction of secondary stresses are not specifically addressed by bridge design specifications. This paper presents a finite-element study of a two-girder bridge that developed web gap cracks at floortruss-girder connections. The modeling procedures performed in this research provide useful strategies that can be applied to determine the magnitude of distortion-induced stresses, to describe the behavior of crack development, and to assess the effectiveness of repair alternatives. The results indicate severe stress concentration at the crack initiation sites. The current repair method used at the positive moment region connections is found acceptable, but that used at the negative moment region connections is not satisfactory, and additional floortruss member removal is required. Stress ranges can be lowered below half of the constant amplitude fatigue threshold, and fatigue cracking is not expected to recur if the proposed retrofit approach is carried out.     

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.     

Analytical Load Rating of an Open-Spandrel Arch Bridge: Case Study

The live load structural capacity of open-spandrel arch bridge structures is difficult to quantify. In addition to live and dead loads, geometric nonlinear effects, temperature effects, and material behavior play key roles in the design and load rating of such a structure. This paper is a case study that illustrates the effect these variables have on load rating a two-span shallow concrete arch bridge. Presented are load ratings of the structure’s arch ribs using a three-dimensional finite-element model with American Association of State Highway and Transportation Officials publications. As a result of this study, a refined analysis is recommended for load rating arch bridges.     

Nonlinear Finite-Element Analysis for Highway Bridge Superstructures

The most popular type of bridge in service today is the concrete deck on steel-girder composite bridge. A finite-element model is built to analyze the superstructure of this type of bridge under working load conditions. The deflections along a test bridge are computed by using this method; the results obtained are close to the experimental data. The concrete deck of the bridge is analyzed using nonlinear finite elements, of which the analytical procedure is described in detail. A comparison is also made between this method and the traditional transformed area method.     

Ultimate Capacity Destructive Testing and Finite-Element Analysis of Steel I-Girder Bridges

Current bridge design and rating techniques are based at the component level and thus cannot predict the ultimate capacity of bridges, which is a function of system-level interactions. While advances in computer technology have made it possible to conduct accurate system-level analyses, which can be used to design more efficient bridges and produce more accurate ratings of existing structures, the knowledge base surrounding system-level bridge behavior is still too small for these methods to be widely considered reliable. Thus, to advance system-level design and rating, a 1/5-scale slab-on-steel girder bridge was tested to ultimate capacity and then analytically modeled. The test demonstrated the significant reserve capacity of the steel girders, and the response of the specimen was governed by the degradation of the reinforced-concrete deck. To accurately capture the response of the specimen in an analytical model, the degradation of the deck and other key features of the specimen were modeled by using a dynamic analysis algorithm in a commercially available finite-element analysis program ABAQUS.     

Nonlinear Finite-Element Analysis of Posttensioned Concrete Bridge Girders

Posttensioning is an effective method for the construction of different types of bridge girders such as those used in segmentally erected bridges. Available nonlinear analysis programs for bridge girders under severe loading conditions are computationally expensive though. In addition, they neglect important phenomena such as bond-slip, friction, and anchorage losses. The objective of the proposed work is to develop a new nonlinear finite-element program for analysis of posttensioned bridge girders. The new model overcomes most of the difficulties associated with existing models. The model is based on the computationally efficient mixed formulation and considers bond, friction, and anchorage loss effects. The mixed formulation is characterized by its fast convergence, usually with very few finite elements and its robustness even under severe loading conditions. The posttensioning operation is accurately simulated using a phased-analysis technique, in which each stage of the posttensioning operation is simulated through a complete nonlinear analysis procedure. Correlation studies of the proposed model with experimental results of posttensioned specimens are conducted. These studies confirmed the accuracy and efficiency of the newly developed software program, which represents an advancement over existing commercial software packages for evaluating posttensioned bridge girders, in particular those subjected to severe loading conditions.     

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.     

Load Distribution for a Highly Skewed Bridge: Testing and Analysis

The American Association of State Highway and Transportation Officials (AASHTO) specifications provide formulas for determining live load distribution factors for bridges. For load distribution factors to be accurate, the behavior of the bridge must be understood. While the behavior of right-angle bridges and bridges with limited skews is relatively well understood, that of highly skewed bridges is not. This paper presents a study aimed at developing a better understanding of the transverse load distribution for highly skewed slab-on-steel girder bridges. The study involved both a diagnostic field test of a recently constructed bridge and an extensive numerical analysis. The bridge tested and analyzed is a two-span, continuous, slab-on-steel composite highway bridge with a skew angle of 60°. The bridge behavior is defined based on the field test data. Finite-element analyses of the bridge were conducted to investigate the influence of model mesh, transverse stiffness, diaphragms, and modeling of the supports. The resulting test and analytical results are compared with AASHTO’s Load and Resistance Factor Design formulas for live load distribution to assess the accuracy of the current empirical formulas.     

Finite-Element Model Tuning of Global Modes of a Grandstand Structure Using Ambient Vibration Testing

This paper describes the experimental and analytical modal analysis of a full-scale cantilevered grandstand. A 3D finite-element model was successfully updated manually based on the global modes identified from ambient vibration measurements. The ambient vibration testing was effective in capturing the global modes of the large grandstand. A number of global vibration modes of the entire grandstand were reliably identified in the frequency range 0–3.1 Hz, in addition to modes in the same frequency range that engaged primarily the cantilever roof structure. Following a two-stage manual FE model updating process, the correlation between the experimental and analytical results showed good agreement, with physically meaningful updated parameters. It was clearly illustrated that both the roof system and the nonstructural elements contributed significantly to the stiffness and mass of the global modes. Useful and novel lessons are highlighted for efficient and reliable future finite-element modeling of global modes of similar grandstand structures.     

Performance Assessment of a Precast-Concrete, Buried, Small Arch Bridge

Experimental field load-test and finite-element analysis were carried out for the performance assessment of a precast-concrete, modular, three-sided, low-profile, buried, arch bridge system. Finite-element analysis incorporated soil modeling and soil–structure interaction at service and limit load levels. The analytical study simulates step-by-step incremental phases of construction and service loads. The finite-element model was calibrated based on the experimental field assessment, to provide a better correlation between the analytically predicted behavior and the actual response of the structure. The study validates the incorporation of various soil models and soil–structure interaction characteristics, to allow a more cost-effective bridge design.     

Investigation of Turbulence Effects on Torsional Divergence of Long-Span Bridges by Using Dynamic Finite-Element Method

Aerostatic stability of super long-span bridges is a much concerned issue during the design stage. Typical aerostatic instability is the so-called torsional divergence which may lead to abrupt structural failure. The iterative static-based FEM, which generally entails the assumption of smooth oncoming flow, has been widely used to evaluate the aerostatic stability of the bridge concerned. However, the wind in atmospheric boundary layer is naturally turbulent and the effect of turbulence on bridge torsional divergence should be therefore considered, and that is the main concern of the present study. To take into account the effects of turbulence on torsional divergence, a dynamic-based time domain finite-element (FE) procedure for predicting bridge aerostatic stability is introduced first. Then the quasi-steady wind loads expressions are presented and discussed, into which the aerodynamic torsional stiffness, which is indispensable for the evaluation of aerostatic stability, has been demonstrated to be incorporated indirectly by a frequency-domain-based approach. Finally, the aerostatic performances of the longest suspension bridge in China are investigated, of which the torsional divergence is the primary concern. Numerical results show that the torsional divergence pattern in turbulent flow differs considerably from that in smooth flow. The primary difference is, while the torsional instability in smooth flow manifests as an abrupt mounting up of the twist deformation of the main girder with the increasing of the wind velocity, that in turbulent flow manifests as an unstable stochastic vibration with large peak values. Another difference is that the wind velocity for divergence in turbulent flow is obviously lower than that in smooth wind and there does not present an obvious wind velocity threshold for divergence, which is distinguished from the torsional divergence in smooth flow characterized by a clear threshold. Based on the presented time domain FE analysis procedure, the influence of turbulence intensity and gusts spatial correlation upon torsional divergence is also investigated and shown to play an important role on the aerostatic stability.     

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.     

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.     

Seismic Testing of a Two-Span Reinforced Concrete Bridge

A quarter-scale, two-span reinforced concrete bridge was tested using the shake-table system at the University of Nevada, Reno. The shake-table tests were part of a multiuniversity, multidisciplinary project utilizing the network for earthquake engineering simulation, with the objective of investigating the effects of soil-foundation-structure interaction on bridges. This paper discusses the development and testing of the bridge model, and selected experimental results, including those that demonstrate the effects of incoherent motions and stiffness irregularities on the distribution of forces and deformations within the bridge system. Motion incoherency affected the asymmetric bridge response (planar torsion of the superstructure), but had little effect on the symmetric bridge response (center-of-mass displacement of the superstructure). These experimental findings are consistent with conclusions from numerical analyses conducted by other researchers. During a 2.0?g PGA earthquake excitation, numerous longitudinal bars buckled and fractured at a drift ratio between 5.5 and 7.9%. Despite the level of damage, detailing of the column transverse reinforcement according to NCHRP 12-49 guidelines provided sufficient column ductility to prevent collapse during a subsequent 1.4?g PGA earthquake excitation.     

Stochastic Finite-Element Analysis of Seismic Soil–Structure Interaction

A procedure is presented for the probabilistic analysis of the seismic soil-structure interaction problem. The procedure accounts for uncertainty in both the free-field input motion as well as in local site conditions, and structural parameters. Uncertain parameters are modeled using a probabilistic framework as stochastic processes. The site amplification effects are accounted for via a randomized relationship between the soil shear modulus and damping on the one hand, and the shear strain of the subgrade on the other hand, as well as by modeling the shear modulus at low strain level as randomly fluctuating with depth. The various random processes are represented by their respective Karhunen-Loève expansions, and the solution processes, consisting of the accelerations and generalized forces in the structure, are represented by their coordinates with respect to the polynomial chaos basis. These coordinates are then evaluated by a combination of weighted residuals and stratified sampling schemes. The expansion can be used to carry out very efficiently, extensive Monte Carlo simulations. The procedure is applied to the seismic analysis of a nuclear reactor facility.     

Probabilistic Settlement Analysis by Stochastic and Random Finite-Element Methods

The paper discusses finite element models for predicting the elastic settlement of a strip footing on a variable soil. The paper then goes on to compare results obtained in a probabilistic settlement analysis using a stochastic finite element method based on first order second moment approximations, with the random finite element method based on generation of random fields combined with Monte Carlo simulations. The paper highlights the deficiencies of probabilistic methods that are unable to properly account for spatial correlation.     

Analysis of Traffic-Induced Vibrations in a Cable-Stayed Bridge. Part I: Experimental Assessment

This paper characterizes the experimental approach used for the evaluation of traffic-induced dynamic effects in Salgueiro Maia cable-stayed bridge. It presents the most significant results obtained both in terms of the static load tests developed at the commissioning phase, and of the dynamic tests under controlled heavy traffic. These tests were specifically conducted for the evaluation of dynamic amplification factors considering the passage of heavy trucks isolated or in groups, along several lanes and at different speeds. Furthermore, the experimental characterization of the random characteristics of the pavement roughness, using an appropriate spatial laser scanning measurement system, is referred.     

Nonlinear Earthquake Response Modeling of a Large-Scale Two-Span Concrete Bridge

A quarter scale model of a two-span RC bridge was tested using the Network for Earthquake Engineering Simulation (NEES) multiple shake table system at the University of Nevada, Reno, Nev. The project was funded through a National Science Foundation-NEES demonstration grant. The bridge system was tested from a preyield state until column failure. In depth analytical modeling was conducted to determine the effectiveness of current structural analysis software and methodology in predicting the bridge model response. Both SAP2000 v.9 and Drain-3DX were used for this purpose. Both models produced reasonable results up to column failure, however, the Drain-3DX model was determined to be most effective to predict the nonlinear bridge model response. Parametric studies were conducted to investigate optimal element discretization and integration parameters. Existing equations for pre and postyield column shear stiffness showed good correlation when compared with the measured data.