Roebling Suspension Bridge. II: Ambient Testing and Live-Load Response

This is the second part of a two-part paper on the evaluation of the historic Roebling suspension bridge using dynamic-analysis techniques. Dynamic properties are determined using ambient field testing under natural excitation. The finite-element (FE) model described in the first part of this two-part paper is modified to more accurately represent current bridge properties. Modifications of the model are based on correlating the FE model frequencies with ambient test frequencies by adjusting the FE model stiffness parameters. The updated 3D FE model is subsequently subjected to an extreme live-load condition to evaluate static safety margins. In addition, cable areas are reduced by 10 to 40% to simulate further deterioration and corrosion. The safety margin of the main cables is demonstrated to be good even when assuming a very conservative 40% cable area reduction, and truss member forces remain within the maximum load-carrying capacity even when the cable areas are reduced by 40%.     

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.     

Effect of Hanger Flexibility on Dynamic Response of Suspension Bridges

Linearized continuum models of a suspended span with unloaded backstays and of a symmetric three-span suspension bridge are used to study the effects of the flexibility of the hangers on the vertical vibrations of suspension bridges. The models include elastic parabolic cables, flexible distributed hangers with variable length, and a stiffening girder represented by an elastic beam. It is shown that the free vibrations of a suspended span with unloaded backstays are controlled by five dimensionless parameters, while six dimensionless parameters control the response of a symmetric three-span suspension bridge. The results indicate that the flexibility of the hangers has a significant effect on the natural frequencies of the higher modes only when the relative stiffness of the girder is very high. The effects of hanger flexibility on the response of a suspension bridge to localized impulsive loads are also found to be small. These findings confirm the traditional, albeit previously untested, assumption of inextensible hangers. Finally, the threshold amplitudes of free vibrations that would result in the incipient slackening of the hangers are determined.     

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.     

Dynamic Response of Suspension Bridge to High Wind and Running Train

A framework is presented for predicting the dynamic response of long suspension bridges to high winds and running trains. A three-dimensional finite-element model is used to represent a suspension bridge. Wind forces acting on the bridge, including both buffeting and self-excited forces, are generated in the time domain using a fast spectral representation method and measured aerodynamic coefficients and flutter derivatives. Each 4-axle vehicle in a train is modeled by a 27-degrees-of-freedom dynamic system. The dynamic interaction between the bridge and train is realized through the contact forces between the wheels and track. By applying a mode superposition technique to the bridge only and taking the measured track irregularities as known quantities, the number of degrees of freedom of the bridge-train system is significantly reduced and the coupled equations of motion are efficiently solved. The proposed formulation is then applied to a real wind-excited long suspension bridge carrying a railway inside the bridge deck of a closed cross section. The results show that the formulation presented in this paper can predict the dynamic response of the coupled bridge-train systems under fluctuating winds. The extent of interaction between the bridge and train depends on wind speed and train speed.     

Unbonded Posttensioned Concrete Bridge Piers. I: Monotonic and Cyclic Analyses

The monotonic and cyclic behavior of a proposed unbonded, posttensioned concrete bridge pier system is studied using finite-element analyses. A procedure to evaluate seismic capacities based on results from the monotonic and cyclic analyses is described in the framework of a two-level approach considering functional- and survival-performance limits. A set of criteria to define functional-and survival-level displacement capacities for the system is developed. The proposed criteria represent improvements over existing criteria in that they are applicable to both conventional reinforced concrete structures and unbonded posttensioned structures. The monotonic and cyclic behavior of prototype single-column pier and two-column bent designs is presented. Monotonic analyses are performed to characterize the stiffness, strength, ductility, and limit-state behavior of these systems. Cyclic analyses are carried out to estimate energy dissipation capacity, residual displacements, and general hysteretic behavior. The influence of the degree of unbonded posttensioning on bridge pier behavior is examined. Using the finite-element results and the proposed criteria, seismic capacities of the prototype bridge pier systems are established.     

Bridge Structural Condition Assessment Using Systematically Validated Finite-Element Model

The structural condition assessment of highway bridges is largely based on visual observations described by subjective indices, and it is necessary to develop a methodology for an accurate and reliable condition assessment of aging and damaged structures. This paper presents a method using a systematically validated finite-element model for the quantitative condition assessment of a damaged reinforced concrete bridge deck structure, including damage location and extent, residual stiffness evaluation, and load-carrying capacity assessment. In a trial of the method in a cracked bridge beam, the residual stiffness distribution was determined by model updating, thereby locating the damage in the structure. Furthermore, the damage extent was identified through a defined damage index and the residual load-carrying capacity was estimated.     

Stochastic Free Vibration Response of Soft Core Sandwich Plates Using an Improved Higher-Order Zigzag Theory

In this paper, an improved higher-order zigzag theory for vibration of soft core sandwich plates with random material properties is proposed. The theory satisfies the condition of continuity in transverse shear stresses at all the layer interfaces and transverse shear stress free condition at the top and bottom of the plate, including the transverse flexibility effect of the core. The variation of in-plane displacements through thickness is assumed to be cubic while transverse displacement varies quadratically within the core and constant throughout the faces. The core is modeled as a 3D elastic continuum. An efficient C0 finite element in conjunction with a first-order perturbation approach is developed for the implementation of the proposed plate theory in a random environment and is employed to evaluate the second-order statistics of the eigensolutions by modeling lamina material properties as basic random variables. The mean and standard deviations of natural frequencies and their mode shapes are computed and validated with Monte Carlo simulation.     

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.     

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.     

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 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.     

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 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.     

Load Transfer and Recovery Length in Parallel Wires of Suspension Bridge Cables

A new simplified contact model aimed at capturing the load transfer and recovery length in parallel steel wires, commonly used in main cables of suspension bridges, is presented. The approach is based on placing elastic–perfectly plastic spring elements at the contact region between the objects. These springs have varying stiffness (Model?I) or yielding (Model?II) depending on their proximity to the clamping loads. Their stiffness or yielding is highest when they are closer to this force, and it decays when they are farther away from the clamp. This decayed behavior is assigned according to Boussinesq’s well-known solution to a point load (applied on a half space). Both models converge quickly compared with a full contact model and recover Coulomb friction law on a two-dimensional (2D) benchmark problem. Moreover, when the same properties are chosen for all springs (disregarding Boussinesq solutions), the models reduce to the classical shear-lag model, which for high clamping (point) loads gives inaccurate results. The spring models are validated experimentally on a seven-wire tightened strand. In this case study, the outer wires are axially pulled, whereas the middle wire, slightly shorter than the outer wires, experiences no direct applied axial load. However, because the strand is radially fastened at several locations, the axial load is transferred to the inner wire by an interfriction mechanism between the wires. The strains at the center points of the outer and inner wires are measured via neutron diffraction for different clamping loads, showing that the inner wire is capable of recovering most of the load.     

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.     

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.     

Construction of a Horizontally Curved Steel I-Girder Bridge. Part I: Erection Sequence

In the case of horizontally curved steel I-girder bridges, girder and cross-frame members are frequently detailed for erection in the no-load condition as a matter of convention. As a result, it is imperative that the erection sequence used to construct such bridges be comprehensively studied to ensure that the no-load condition can be achieved in the field and that significant superstructure component fit-up problems do not occur. The current research investigates the erection of a recently constructed horizontally curved steel I-girder bridge, in which significant difficulties were encountered during erection. The bridge erection is recreated through an analytical simulation using a detailed nonlinear finite element model. The analytical results demonstrate that a condition that closely resembles the no-load condition can be achieved in the field during construction with the proper implementation of temporary support structures; and that the difficulties encountered during the erection of the subject bridge superstructure could not be attributed to the erection scheme followed.     

Dynamic Response of a Highway Bridge Subjected to Moving Vehicles

Several full-scale load tests were performed on a selected Florida highway bridge. The bridge was dynamically excited by two fully loaded trucks, and the strain, acceleration, and displacement at selected points were recorded for the investigation of the bridge’s dynamic response. Experimental data were compared with simplified vehicle and bridge finite-element models. The vehicle was represented as a three-dimensional mass–spring–damper system with 11?degrees of freedom, and the bridge was modeled as a combination of plate and beam elements that characterize the slab and girders, respectively. The equations of motion were formulated with physical components for the vehicle and modal components for the bridge. The coupled equations were solved using a central difference method. It was found that the numerical analysis matched well with the experimental data and was used to successfully explain critical dynamic phenomena observed during the testing. Impact factors for this tested bridge were thoroughly investigated by using these models.     

Effect of Intermediate Diaphragms on Decked Bulb-Tee Bridge System for Accelerated Construction

One of the promising systems for accelerated bridge construction is the use of the decked precast prestressed concrete girders or decked bulb-tee girders for the bridge superstructure. Using the calibrated three-dimensional finite-element models through field tests, a parametric study was conducted to determine the effect of intermediate diaphragms on the deflections and flexural strains of girders at the midspan as well as the live load forces in the longitudinal joint. The following diaphragm details were considered: different diaphragm types (steel and concrete), different diaphragm numbers between two adjacent girders, and different cross-sectional areas for steel diaphragms. Five bridge models with different diaphragm details were developed, and the short span length effect on the bridge behavior was also studied. It was found that as long as one intermediate diaphragm was provided between two adjacent girders at midspan, changing the diaphragm details did not affect the girder deflection, the girder strain, and the live load forces in the longitudinal joint significantly. The effect of diaphragms on the midspan deflection was more prominent in the short span bridge; however, the reduction in the maximum bending moment by the diaphragms was more significant in the long span bridge than in the short span bridge. Specific design recommendation is provided in this paper.