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.     

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.     

Noise Evaluation for Pavement Maintenance in Metropolitan Highway Bridges

Dynamic response of a bridge under traffic load induces acoustic energy at the bridge surface. The acoustic energy change generates an additional coupled noise component caused by vibration of a bridge deck associated with the pavement conditions and moving velocity of the vehicle. This paper presents a three-dimensional finite-element method developed for the dynamic response and noise propagation model, and analyzes the coupled effect induced by traffic loading based on different pavement conditions. Even though vibration-induced noise at the bridge is below the audible frequency range of 20–20,000?Hz, it amplifies the traffic noise source to the highly annoyed level of noise in the metropolitan area. Among several factors that contribute to the traffic noise, interaction between pavement and vehicle is considered according to the different surface roughness and vehicle velocity. The result shows that poor pavement condition contributes to the increase of traffic noise at a high traveling speed of the vehicle. In the pavement maintenance stage, the coupled effect as an additional noise source should be considered to mitigate the traffic noise for its added value in conjunction with regulation of engine emission noise and construction of a noise barrier.     

Field Investigation of a Sandwich Plate System Bridge Deck

This paper presents the results of a live-load test of the Shenley Bridge, the first bridge application of the sandwich plate system technology in North America. The investigation focused on the evaluation of in-service performance including lateral load distribution behavior and dynamic load allowance. Real-time midspan deflections and strain values were measured under both static and dynamic conditions and under various loading configurations to assess the in-service performance. Distribution factors were determined for interior and exterior girders subjected to single and paired truck loadings. In addition, dynamic load allowance was determined from a comparison of the bridge’s response under static conditions to the response under dynamic conditions. From a comparison of measured results to AASHTO LRFD, AASHTO standard, and CHBDC provisions, it was determined that the current provisions tend to produce conservative predictions for lateral load distribution, but can be unconservative for dynamic load allowance. As a result of the testing program containing a single field test, a finite-element model was also used for determination of lateral load distribution and yielded predictions similar to measured results. The results from the finite-element models were often less conservative than the code provisions.     

Dynamic Analysis of a Composite Cable-Stayed Bridge: Escaleritas Viaduct

This work describes some of the most important results of the experimental and numerical analyses of Escaleritas Viaduct, Spain. Before the inauguration of this composite cable-stayed bridge in 2006, the bridge authority required a dynamic load test identifying, for instance, the natural vibration modes, the dynamic magnification factor, and the maximum vertical acceleration. The dynamic test was accompanied by numerical simulation performed in two different three-dimensional finite-element models, one of them composed of 145,000 shell elements. The correlation of test and analysis data is good and allows several interesting general conclusions to be drawn. It is shown that Escaleritas Viaduct complies with the requirements on the dynamic structural behavior defined in the standards.     

Design and Construction of a Bridge in Very High Performance Fiber-Reinforced Concrete

The design, technology, and construction of a small road bridge made of very high performance fiber-reinforced concrete is described in this paper. The bridge consists of precast prestressed concrete beams with a cast-in-place ordinary concrete deck. A preliminary experimental investigation was conducted to define the mix design, to establish the properties of the material and its durability, and to study the flexural behavior of the prestressed concrete beams with and without the concrete deck. The effect of steel fibers at the structural level, where there is an influence of constitutive behavior and size effects, was analyzed by testing a prestressed beam using very high performance fiber-reinforced concrete without fibers. The establishment of the structural properties of the material then allowed the design of the final section of the bridge beams and the definition of a model to justify the design rules adopted. This project represents an attempt to demonstrate the industrial feasibility of very high performance concrete structural elements manufactured with conventional raw materials and usual production techniques and to evaluate the production technology when utilizing steel fibers.     

Nonlinear Analysis of Ordinary Bridges Crossing Fault-Rupture Zones

Rooted in structural dynamics theory, three approximate procedures for estimating seismic demands for bridges crossing fault-rupture zones and deforming into their inelastic range are presented: modal pushover analysis (MPA), linear dynamic analysis, and linear static analysis. These procedures estimate the total seismic demand by superposing peak values of quasi-static and dynamic parts. The peak quasi-static demand in all three procedures is computed by nonlinear static analysis of the bridge subjected to peak values of all support displacements applied simultaneously. In the MPA and the linear dynamic analysis procedures, the peak dynamic demand is estimated by nonlinear static (or pushover) analysis and linear static analysis, respectively, for forces corresponding to the most-dominant mode. In the linear static analysis procedure, the peak dynamic demand is estimated by linear static analysis of the bridge due to lateral forces appropriate for bridges crossing fault-rupture zones. The three approximate procedures are shown to provide estimates of seismic demands that are accurate enough to be useful for practical applications. The linear static analysis procedure, which is much simpler than the other two approximate procedures, is recommended for practical analysis of “ordinary” bridges because it eliminates the need for mode shapes and vibration periods of the bridge.     

Evaluation of In-Service Performance of Tom’s Creek Bridge Fiber-Reinforced Polymer Superstructure

The Tom’s Creek Bridge is a small-scale demonstration project involving the use of fiber-reinforced polymer (FRP) composite girders as the main load-carrying members. The project is intended to serve two purposes. First, by calculating bridge design parameters such as the dynamic load allowance, transverse wheel load distribution, and deflections under service loading, the Tom’s Creek Bridge aids in modifying current American Association of State Highway and Transportation Officials bridge design standards for use with FRP composite materials. Second, by evaluating the FRP girders after exposure to service conditions, the project begins to answer questions about the long-term performance of these advanced composite material beams when used in bridge design. This paper details the in-service analysis of the Tom’s Creek Bridge. Five load tests, at 6-month intervals, were conducted on the bridge. Using midspan strain and deflection data gathered from the FRP composite girders during these tests, the aforementioned bridge design parameters have been determined. The Tom’s Creek Bridge was determined to have a maximum dynamic load allowance, IM, of 0.90, a transverse wheel load distribution factor, g, of 0.101, and a maximum deflection of L/490. Two bridge girders were removed from the Tom’s Creek Bridge after 15 months of service loading. These FRP composite girders were tested at the Structures and Materials Research Laboratory at Virginia Tech for stiffness and ultimate strength and compared to preservice values for the same beams. These measurements indicate that, after 15 months of service, the FRP composite girders have not significantly changed in stiffness or ultimate moment capacity.     

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.     

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.     

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.     

Response of Timber Bridge to Traffic Loading

This paper summarizes results from an analytical and experimental study of the response to traffic loading of a glued-laminated timber bridge. A numerical model to simulate the passage of a vehicle over a bridge was developed. Calculated modal characteristics of an existing bridge were compared with results of ambient vibration and hammer impact testing. The analysis was used to simulate passages over the bridge of a three-axle vehicle, an empty logging truck, and results were compared with experimental data for such loading. The numerical model was then used to simulate the bridge response to a fully loaded logging truck. Results of these simulations were used to study dynamic amplification factors and to assess dynamic provisions of the new Canadian Highway Bridge Design Code.     

Nonlinear Finite Element Analysis of a FRP-Strengthened Reinforced Concrete Bridge

Three-dimensional nonlinear finite element (FE) models are developed to examine the structural behavior of the Horsetail Creek Bridge strengthened by fiber-reinforced polymers (FRPs). A sensitivity study is performed varying bridge geometry, precracking load, strength of concrete, and stiffness of the soil foundation to establish a FE model that best represents the actual bridge. Truck loadings are applied to the FE bridge model at different locations, as in an actual bridge test. Comparisons between FE model predictions and field data are made in terms of strains in the beams for various truck load locations. It is found that all the parameters examined can potentially influence the bridge response and are needed for selection of the optimal model which predicts the magnitudes and trends in the strains accurately. Then, using the optimal model, performance evaluation of the bridge based on scaled truck and mass-proportional loadings is conducted. Each loading type is gradually increased until failure occurs. Structural responses are compared for strengthened and unstrengthened bridge models to evaluate the FRP retrofit. The models predict a significant improvement in structural performance due to the FRP retrofit.     

Autoparametric Resonance in a Pedestrian Steel Arch Bridge: Solferino Bridge, Paris

Autoparametric resonance is treated as the reason of arising excessive lateral vibrations in the steel arch bridge (the Solferino Bridge). To explain this phenomenon, a physical model (a double pendulum) is proposed. Its behavior, as a rule, depends on dynamic characteristics of a bridge rather than on its type. The response of a two degree-of-freedom system with quadratic nonlinearities in the presence of two-to-one autoparametric resonance is investigated. The perturbation method of multiple time scales is used to construct first-order nonlinear differential equations and to determine steady state solutions and their stability. Bifurcation analysis is performed to determine a critical (threshold) value in the external load (control) parameter. The autoparametric resonance becomes possible if an excited torsional mode is near a primary resonance and an external load parameter caused by pedestrians is equal or higher than its critical value. When the increasing load parameter passes through the critical value (because a quantity of pedestrians on the bridge is increased), a jump phenomenon (or fast growth) is observed for the lateral mode, the torsional mode is saturated and has much smaller amplitudes. Field tests were held to understand a phenomenon of an excessive lateral movement, and to enforce the Solferino Bridge. Theoretical results of the present paper are compared with those experimental measurements. Swaying of pedestrian bridges can be treated as a two-step process. The first step (achievement of parametric resonance), described in this paper, is the condition for the beginning of the second step—the process of possible synchronization of applied forces and the interactions between them and the lateral and torsional modes of vibration.     

Dynamic Response and Fatigue of Steel Tied-Arch Bridge

The Toutle River Bridge is a steel tied-arch bridge, one that vibrates extensively and has sustained significant fatigue cracking. An experimental study into the cause of this behavior is described. Computer analyses of the bridge behavior are used to estimate the expected response and to establish appropriate locations for instrumentation. The instruments were installed and field tests were performed. Controlled tests were performed with trucks of known axle weight and spacing. Some controlled tests were performed with trucks traveling at known speed and in a specific driving lane with no other traffic on the bridge. Controlled tests were used to calibrate the instrumentation and establish the basic bridge behavior. The results showed that composite action had been lost in the heavily loaded stringers, and little amplification of dynamic response was noted. The measured periods of vibration generally compared well with computer predictions. Uncontrolled truck traffic was then measured for approximately one month. This data was used to establish load spectra and to estimate the fatigue life of critical components. Fatigue, which is caused by calculated stress ranges, should not be important on this bridge for another 20 to 30 years. Existing fatigue damage is driven by distortional fatigue caused by the large bridge deformations. Several options for dealing with the problem are presented.     

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.     

Free Out-of-Plane Vibrations of Masonry Walls Strengthened with Composite Materials

The natural frequencies and the out-of-plane vibration modes of one-way masonry walls strengthened with composite materials are studied. Due to the inherent nonlinear behavior of the masonry wall, the dynamic characteristics depend on the level of out-of-plane load (mechanical load or forced out-of-plane deflections) and the resulting cracking, nonlinear behavior of the mortar material, and debonding of the composite system. In order to account for the nonlinearity and the accumulation of damage, a general nonlinear dynamic model of the strengthened wall is developed. The model is mathematically decomposed into a nonlinear static analysis phase, in which the static response and the corresponding residual mechanical properties are determined, and a free vibration analysis phase, in which the dynamic characteristics are determined. The governing nonlinear differential equations of the first phase, the linear differential eigenvalue problem corresponding to the second phase, and the solution strategies are derived. Two numerical examples that examine the capabilities of the model and study the dynamic properties of the strengthened wall are presented. The model is supported and verified through comparison with a step-by-step time integration analysis, and comparison with experimental results of a full-scale strengthened wall under impulse loading. The results show that the strengthening system significantly affects the natural frequencies of the wall, modifies its modes of vibration, and restrains the deterioration of the dynamic properties with the increase of load. The quantification of these effects contributes to the understanding of the performance of damaged strengthened walls under dynamic and seismic loads.     

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.     

Behavior of Concrete Beams Strengthened with Fiber-Reinforced Polymer Laminates under Impact Loading

Most of the research on application of composite materials in civil engineering during the past decade has concentrated on the behavior of structural elements under static loads. In engineering practice, there are many situations in which structures undergo impact or dynamic loading. In particular, the impact response of concrete beams strengthened with composite materials is of interest. This paper presents the results of an experimental investigation conducted to study the impact effects on concrete beams strengthened with fiber-reinforced polymer laminates. Two types of composite laminates, carbon and Kevlar, were bonded to the top and bottom faces of concrete beams with epoxy. Five beams were tested: two strengthened with Kevlar laminates, two strengthened with carbon laminates, and one unretrofitted beam as the control specimen. The impact load was applied by dropping a steel cylinder from a specified height onto the top face of the beam. The test results revealed that composite laminates significantly increased the capacity of the concrete beams to resist impact load. In addition, the laminates reduced the deflection and crack width. Comparing the test results of the beams strengthened with Kevlar and carbon laminates indicated that the gain in strength depends on the type, thickness, weight, and material properties of the composite laminate.