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.     

Condition Assessment of the Eastbound 6th Avenue Viaduct Using Strain Gauges

This paper presents the procedure and results of a strain gauge study completed on the eastbound 6th Avenue Viaduct in Denver. The 6th Avenue Viaduct was modified in a 1997–1998 rehabilitation, making the entire superstructure continuous. New sliding bearing pads failed to properly accommodate expansion and contraction of the bridge superstructure due to temperature changes. Visible damage due to contraction of the superstructure in the winter of 1999–2000 prompted a study of substructure elements to determine the short-term safety and long-term viability of the bridge. Substructure elements were instrumented with a total of 62 strain gauges and two concrete crack gauges. Data were taken for a period of 3 months. Analysis of the data suggests that the bridge is safe for short-term use, but that the long-term viability of the structure has been compromised. Repair or replacement of substructure elements is recommended, along with frequent monitoring during the interim period.     

Effect of Vehicle Velocity on the Dynamic Amplification of a Vehicle Crossing a Simply Supported Bridge

Many writers, using both experimental tests and complex numerical models, have examined the effect of vehicle velocity on a highway bridge’s dynamic amplification. Although these tests and models give valuable quantitative information on dynamic amplification, they give little insight into how amplification is affected by individual vehicle/bridge parameters. This paper uses relatively simple numerical models to investigate the effect of vehicle velocity on a bridge’s dynamic amplification. A single vehicle crossing a simply supported bridge is modeled as a constant point force. A set of critical velocities are determined associated with peaks of dynamic amplification for all beams. The reasons for these large amplifications are discussed. A more complex finite element model, validated with field tests, is used to test the applicability of the conclusions obtained from the simple models to a realistic bridge/vehicle system.     

Application of Fuzzy Sets for Remaining Life Assessment of Corrosion Affected Reinforced Concrete Bridge Girders

A methodology for remaining life assessment of reinforced concrete bridge girders affected by chloride-induced corrosion of reinforcement is proposed. The uncertainties in the values of the parameters characterizing the environment and, the variables affecting the time to corrosion initiation, and the rate of corrosion propagation are taken into account by treating them as fuzzy variables. The usefulness of the proposed methodology is illustrated through a case study, by comparing the times to reach different damage levels for a severely distressed beam, of Rocky Point Viaduct, determined using the proposed methodology with the observations from the field investigations. It is noted that the predicted times are in satisfactory agreement with the reported values. Hence, the methodology will be useful for the scheduling of inspections for reinforced concrete girders subjected to chloride-induced corrosion of reinforcement.     

Analysis of Traffic-Induced Vibrations in a Cable-Stayed Bridge. Part II: Numerical Modeling and Stochastic Simulation

This paper describes the development of a numerical model to simulate the dynamic response of the bridge–vehicle system of Salgueiro Maia cable-stayed bridge, using the results from an extensive experimental investigation to calibrate this model. Further, a set of stochastic Monte Carlo simulations of the bridge–vehicle dynamic response is also presented, with the purpose of evaluating dynamic amplification factors, taking into account the randomness of different factors associated to characteristics of the pavement, of the vehicles and of the traffic flow.     

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.     

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.     

Feasibility of a 1,400 m Span Steel Cable-Stayed Bridge

This paper describes the feasibility of 1,400 m steel cable-stayed bridges from both structural and economic viewpoints. Because the weight of a steel girder strongly affects the total cost of the bridge, the writers present a procedure to obtain a minimum weight for a girder that ensures safety against static and dynamic instabilities. For static instability, elastoplastic, finite-displacement analysis under in-plane load and elastic, finite-displacement analysis under displacement-dependent wind load are conducted; for dynamic instability, multimodal flutter analysis is carried out. It is shown that static critical wind velocity of lateral torsional buckling governs the dimension of the girder. Finally, the writers briefly compare a cable-stayed bridge with suspension bridge alternatives.     

Dynamic Stress Analysis of Long Suspension Bridges under Wind, Railway, and Highway Loadings

Computation of the dynamic stress of long suspension bridges under multiloadings is essential for either the strength or fatigue assessment of the bridge. This paper presents a framework for dynamic stress analysis of long suspension bridges under wind, railway, and highway loadings. The bridge, trains, and road vehicles are respectively modeled using the finite-element method (FEM). The connections between the bridge and trains and between the bridge and road vehicles are respectively considered in terms of wheel-rail and tire-road surface contact conditions. The spatial distributions of both buffeting forces and self-excited forces over the bridge deck surface are considered. The Tsing Ma suspension bridge and the field measurement data recorded by a wind and structural health monitoring system (WASHMS) installed in the bridge are utilized as a case study to examine the proposed framework. The information on the concerned loadings measured by the WASHMS is taken as inputs for the computation simulation, and the computed stress responses are compared with the measured ones. The results show that running trains play a predominant role in bridge stress responses compared with running road vehicles and fluctuating wind loading.     

Effect of Vehicle Velocity on the Dynamic Amplification of Two Vehicles Crossing a Simply Supported Bridge

The effect of multiple vehicles on a bridge’s dynamic amplification is a complex problem. Previously writers have examined multiple vehicle presence by constructing elaborate finite element models or undertaking field tests. Although both these methods give valuable information regarding the magnitude of dynamic amplification, the results tend to be site specific and give limited insight into how large amplifications occur. This paper examines the dynamic amplification factor of a simply supported bridge being crossed by two loads traveling in both the same and opposing directions. Simple numerical point load models are used to determine the critical load velocities and load positions that result in high amplifications. An experimentally validated finite element model is used to examine the applicability of the conclusions to real bridge/vehicle systems.     

Examination of Level of Analysis Accuracy for Curved I-Girder Bridges through Comparisons to Field Data

To evaluate the accuracy of different levels of analysis used to predict horizontally curved steel I-girder bridge response, a field test was performed on a three-span structure. Collected strain data were reduced to determine girder vertical and bottom flange lateral bending moments. Experimental moments were compared to numerical moments obtained from three commonly employed levels of analysis. Level 1 analysis includes two manual calculation methods: a line girder analysis method described in the AASHTO Guide Specification for Horizontally Curved Highway Bridges, and the V-load method. Grillage models represent Level 2 and were created using three commercially available computer programs: SAP2000, MDX, and DESCUS. Level 3 consists of three-dimensional (3D) finite element models created using SAP2000 and the BSDI 3D system. Responses obtained from each level are compared and discussed for a single radial cross section of the structure, and the compared results involve truck loads and placement schemes that do not represent those used for bridge design. The field test and numerical data presented are used solely to determine the accuracy of each level of analysis for predicting structure response to a specific live load at a specific cross section. Results showed that Level 2 and Level 3 analyses predict girder vertical bending moment distributions more accurately than Level 1 analyses throughout the tested cross section. The comparisons indicate that Level 3 girder vertical bending moment distributions offered no appreciable increase in accuracy over Level 2 analyses. The study also indicates that both Level 1 and Level 3 analyses provide bottom flange lateral bending moment distributions that do not correlate well with field test results for the studied bridge cross section.     

Natural Frequency of Railway Girder Bridges under Vehicle Loads

To investigate the natural frequency of a railway girder bridge under vehicle loads, two methods are presented. First, the natural frequency of a railway girder bridge under vehicle loads is obtained by solution of the eigenvalue of the vehicle-bridge interaction equation at each step of the numerical integration. Second, based on the vehicle-bridge interaction equation, an approximate formula is developed. The results show that the natural frequency of a railway girder bridge under vehicle loads varies periodically as the vehicles pass over the bridge. The results obtained with the two methods are then compared, showing that a good agreement is achieved. From parametric studies, the effects of the unsprung mass, the sprung mass, and the stiffness of the vehicle suspension are discussed.     

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.     

Dynamic Monitoring of Steel Girder Highway Bridge

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

Vibration Control of Stay Cables of the Shandong Binzhou Yellow River Highway Bridge Using Magnetorheological Fluid Dampers

The Shandong Binzhou Yellow River Highway Bridge is a three-tower, cable-stayed bridge in Shandong Province, China. Because the stay cables are prone to vibration, 40 magnetorheological (MR) fluid dampers were attached to the 20 longest cables of this bridge to suppress possible vibration. An innovative control algorithm for active and semiactive control of mass-distributed dynamic systems, e.g., stay cables, was proposed. The frequencies and modal damping ratios of the unimpeded tested cable were identified through an ambient vibration test and free vibration tests, respectively. Subsequently, a series of field tests were carried out to investigate the control efficacy of the free cable vibrations achieved by semiactive MR dampers, “Passive-off” MR dampers and “Passive-on” MR dampers. The first three modal damping ratios of the cable incorporated with the MR dampers were also identified from the in situ experiments. The field experiment results indicated that the semiactive MR dampers can provide significantly greater supplemental damping for the cable than either the Passive-off or the Passive-on MR dampers because of the pseudonegative stiffness generated by the semiactive MR dampers.     

Dynamic Analysis of Metallic Arch Railway Bridge

This work describes some of the most interesting aspects of the experimental and numerical dynamic analyses of the Luiz I Bridge, an old arch double-deck iron bridge, when subjected to the moving loads of the new light metro of Porto. Presented are the methodology and computational tools developed, as well as some of the most significant results obtained from numerical simulations conducted on the basis of an experimentally calibrated finite-element model, both in terms of structural safety and of the comfort of pedestrians and train passengers.     

Impact Factors for Curved Continuous Composite Multiple-Box Girder Bridges

The results from a parametric study on the impact factors for 180 curved continuous composite multiple-box girder bridges are presented. Expressions for the impact factors for tangential flexural stresses, deflection, shear forces and reactions are deduced for AASHTO truck loading. The finite-element method was utilized to model the bridges as three-dimensional structures. The vehicle axle used in the analysis was simulated as a pair of concentrated forces moving along the concrete deck in a circumferential path with a constant speed. The effects of bridge configurations, loading positions, and vehicle speed on the impact factors were examined. Bridge configurations included span length, span-to-radius of curvature ratio, number of lanes, and number of boxes. The effect of the mass of the vehicle on the dynamic response of the bridges is also investigated. The data generated from the parametric study and the deduced expressions for the impact factors would enable bridge engineers to design curved continuous composite multiple-box girder bridges more reliably and economically.     

Inelastic Damage Analysis of Reinforced Concrete Bridge Columns Based on Degraded Monotonic Energy

This paper summarizes the prediction of seismic damage of two existing bridges. The objective is to apply a damage index definition for reinforced concrete bridge columns under cyclic loading to existing bridge columns that might experience real seismic loading in the future, and to evaluate the ability of the damage index in describing the damage progression of the bridge columns during real seismic loading. Two existing bridges were selected from the Greater Vancouver Area in Canada. The first bridge, the Garneau Flyover, was designed in 1985 to ATC-6-1981 and is expected to have sufficient resistance to lateral earthquake loading. The second bridge, the Clydesdale Street Underpass, was designed long before ATC-6-1981 and is expected to show little or no lateral earthquake resistance. The damage index is applied to each of these structures, with columns modeled using the CANNY nonlinear structural analysis program. Shear and bond slip deformations were considered by making a simple modification to the column flexural properties. A series of nonlinear dynamic analyses were performed using records from the 1971 San Fernando, 1978 Miyaki-Oki (Japan), 1989 Loma Prieta, and 1999 Taiwan earthquakes fitted to the Vancouver firm ground spectrum. The calculated damage index provides a simple numerical indicator of the damage during an earthquake, easily computed from the results of a nonlinear dynamic analysis.     

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.