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.     

Innovative Bridge Condition Assessment from Dynamic Response of a Passing Vehicle

An innovative approach for damage assessment of a bridge deck is proposed with the measured dynamic response of a vehicle moving on top of a structure. The simply supported bridge deck is modeled as a Euler–Bernoulli beam. The moving vehicle serves as a smart sensor and force transducer in the structural system. The damage is defined as the flexural stiffness reduction in the beam finite element. The identification algorithm is based on dynamic response sensitivity analysis, and it is realized with a regularization technique from the measured vehicle acceleration measurement. Measurement noise, road surface roughness, and model errors are included in the simulations, and the results indicate that the proposed algorithm is computationally stable and efficient, and the identified results are acceptable and not sensitive to the different parameters studied.     

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.     

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.     

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.     

Dynamic and Impact Behavior of Half-Through Arch Bridges

The objective of this paper is to present the results of an investigation of the dynamic and impact characteristics of half-through arch bridges with rough decks caused by vehicles moving across them. Seven arch bridges modeled as three-dimensional structures with overall span lengths ranging from 20?to?200?m (65.5?to?656.2?ft) are analyzed. The American Association of State Highway and Transportation Officials Specifications HS20-44 truck is the applied vehicle loading used in the analysis and is simulated as a three-dimensional, nonlinear vehicle model with 11 degrees of freedom. Truck components include the body, suspension, and tires. The bridge deck surface is assumed to have a “good” surface roughness and is simulated using a stochastic process (power spectral density function). The effect on impact factors of span length, rise-to-span ratio, and vehicle speed is discussed. The results of the analyses show that the impact factors of bending moment and axial force will not exceed 0.4 and 0.25, respectively. The proposed impact equations are simple and conservative and can be used in the design of half-through arch bridges.     

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.     

Experimental Evaluation of Dynamic Effects for a Selected Highway Bridge

The paper presents an experimental study of the actual dynamic effects for a preselected typical highway bridge. Knowledge of the dynamic impact factors is important for accurate determination of the ultimate load capacity and performance assessment of constructed bridges. Static and dynamic field tests were performed on a two-lane concrete highway bridge built in 1999 on U.S. 90 in northwest Florida. During the tests, one or two fully loaded trucks crossed over the bridge, which was instrumented with strain gauges, accelerometers, and displacement transducers. A wooden plank was placed across the lanes for some runs to trigger extensive dynamic vibration and to simulate poor road surface conditions. Data collected from the tests were used for comprehensive assessment of the bridge under dynamic loading. Impact factors obtained from the tests with higher speeds were found larger than corresponding values recommended by bridge codes. Analysis revealed that stiff vehicle suspension, road surface imperfection, and “bouncing” of the truck loading contributed to the high impact factors. Experimental data were also used for validation of the finite-element models developed for the vehicle–bridge system.     

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.     

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.     

Vehicle Induced Dynamic Behavior of Short-Span Slab Bridges Considering Effect of Approach Slab Condition

In this paper the vehicle induced dynamic bridge responses are calculated by modeling the bridge and vehicle as one coupled system. The dynamic behavior of short slab bridges with different span lengths induced by the AASHTO HS20 truck is investigated. A parametric study is conducted to analyze the effects of different truck speeds and different road surface conditions. Critical truck speeds that result in peaks of dynamic response are found to follow the rule that describes the resonant vibration of bridges due to train loading. The approach slab condition that consists of faulting at the ends and deformation along the span is considered in the analysis. Although the effect of the along-span deformation on the dynamic response of bridges is trivial, the faulting condition of the approach slab is found to cause significantly large dynamic responses in short-span slab bridges. Impact factors obtained from numerical analyses are compared with those values specified in the AASHTO codes.     

Development of FRP Short-Span Deployable Bridge—Experimental Results

For military and civilian applications, there exists a need for lightweight, inexpensive, short-span bridges that can be easily transported and erected with minimal equipment. Owing to its favorable properties, fiber-reinforced polymer (FRP) has been shown to be feasible for the construction of such bridges. Investigations into the behavior of a short-span bridge structural concept, adapted to the material properties of commercially available glass FRP (GFRP) pultruded products, are presented. A 4.8-m span prototype was built from GFRP sections, bonded throughout to form a tapered box beam, with a width of 1.2?m and a height at midspan of approximately 0.5?m. The box beam represents a single trackway of a double-trackway bridge, whose trackways could be connected by light structural elements. The quasi-static and dynamic behavior of the prototype box beam was investigated in ambient laboratory and field conditions to assess the design and construction techniques used, with a view to designing a full-scale 10-m GFRP bridge. Laboratory testing of the prototype box beam used single and pairs of patch loads to simulate wheel loading. These tests confirmed that the box beam had sufficient stiffness and strength to function effectively as a single trackway of a small span bridge. Field testing of the structure was undertaken using a Bison vehicle (13,000?kg), driven at varying speeds over the structure to establish its response to realistic vehicle loads and the effects of their movement across the span.     

Bridge Structural Condition Assessment Based on Vibration and Traffic Monitoring

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

Safety Analysis of Moving Road Vehicles on a Long Bridge under Crosswind

This paper presents a safety analysis of high-sided road vehicles running on a long span cable-stayed bridge when the road vehicle enters a sharp-edged crosswind gust while the bridge is oscillating under fluctuating winds. Road vehicle accidents, including overturning, excessive sideslip, and exaggerated rotation, are defined first. The mathematical model and the equation of motion of coupled road vehicle–bridge systems under crosswind are then established, which include road surface roughness, vehicle suspension, and the sideslip of the vehicle tire relative to the bridge deck in the lateral direction. A case study using a real long cable-stayed bridge and a high-sided road vehicle is finally conducted, and an extensive computational work is performed to obtain a series of accident vehicle speed against mean crosswind speed, by which the decision on the threshold of mean wind speed above which the bridge should be closed to the road vehicle can be made. The obtained accident vehicle speeds are also compared with those for the same vehicles running on the ground. It is shown that the oscillation of the cable-stayed bridge will lower the accident vehicle speed when wind speed reaches a certain level.     

Vehicle Condition Surveillance on Continuous Bridges Based on Response Sensitivity

This paper presents the parameter identification of a vehicle moving on a multispan continuous bridge deck modeled as a continuous beam based on dynamic response sensitivity analysis. This technique is for the monitoring of “road-friendliness” of vehicles using the highway pavement. The moving vehicle is modeled as a single degree-of-freedom system comprising three parameters, a two degrees-of-freedom system comprising five parameters, or a four degrees-of-freedom system comprising 12 parameters. The modified beam functions are used to calculate the response of the continuous bridge. Starting with an initial guess on the unknown parameters, the identification can be realized based on least-squares method and regularization technique from measured strain, velocity, or acceleration measurement from as few as a single sensor. Simulation studies and experimental results indicate that the identified results are acceptable, and the responses reconstructed from the identified parameters agree well with the measured responses.     

Impact Factors for Horizontally Curved Composite Box Girder Bridges

This paper presents a method for determining the dynamic impact factors for horizontally curved composite single- or multicell box girder bridges under AASHTO truck loading. The bridges are modeled as three-dimensional structures using commercially available software. The vehicle is idealized as a pair of concentrated forces, with no mass, traveling in two circumferential paths parallel to the curved centerline of bridges. An extensive parametric study is conducted, in which over 215 curved composite box girder bridge prototypes are analyzed. The key parameters considered in this study are: Number of cells, number of lanes, degree of curvature, arc span length, slope of the outer steel webs, number and area of bracing and top chord systems, and truck(s) speed and truck(s) positioning. Based on the data generated from the parametric study, expressions for dynamic impact factors for longitudinal moment, reaction, and deflection are proposed as function of the ratio of the arc span length to the radius of curvature. The results from this study would enable bridge engineers to design horizontally curved composite box girder bridges more reliably and economically. Furthermore, the results can be used to potentially increase the live-load capacity of existing bridges to prevent posting or closing of the bridge.     

Fatigue Damage of Steel Bridges Due to Dynamic Vehicle Loads

This paper focuses on the fatigue damage caused in steel bridge girders by the dynamic tire forces that occur during the crossing of heavy transport vehicles. This work quantifies the difference in fatigue life of a short-span and a medium-span bridge due to successive passages of either a steel-sprung or an air-sprung vehicle. The bridges are modeled as beams to obtain their modal properties, and air-sprung and nonlinear steel-sprung vehicle models are used. Bridge responses are predicted using a convolution method by combining bridge modal properties with vehicle wheel forces. A linear elastic fracture mechanics model is employed to predict crack growth. For the short-span bridge, the steel-sprung vehicle caused fatigue failure up to 6.5 times faster than the air-sprung vehicle. For the medium-span bridge, the steel-sprung vehicle caused fatigue failure up to 277 times faster than the air-sprung vehicle.     

Dynamic Performance Simulation of Long-Span Bridge under Combined Loads of Stochastic Traffic and Wind

Slender long-span bridges exhibit unique features which are not present in short and medium-span bridges such as higher traffic volume, simultaneous presence of multiple vehicles, and sensitivity to wind load. For typical buffeting studies of long-span bridges under wind turbulence, no traffic load was typically considered simultaneously with wind. Recent bridge/vehicle/wind interaction studies highlighted the importance of predicting the bridge dynamic behavior by considering the bridge, the actual traffic load, and wind as a whole coupled system. Existent studies of bridge/vehicle/wind interaction analysis, however, considered only one or several vehicles distributed in an assumed (usually uniform) pattern on the bridge. For long-span bridges which have a high probability of the presence of multiple vehicles including several heavy trucks at a time, such an assumption differs significantly from reality. A new “semideterministic” bridge dynamic analytical model is proposed which considers dynamic interactions between the bridge, wind, and stochastic “real” traffic by integrating the equivalent dynamic wheel load (EDWL) approach and the cellular automaton (CA) traffic flow simulation. As a result of adopting the new analytical model, the long-span bridge dynamic behavior can be statistically predicted with a more realistic and adaptive consideration of combined loads of traffic and wind. A prototype slender cable-stayed bridge is numerically studied with the proposed model. In addition to slender long-span bridges which are sensitive to wind, the proposed model also offers a general approach for other conventional long-span bridges as well as roadway pavements to achieve a more realistic understanding of the structural performance under probabilistic traffic and dynamic interactions.     

Dynamic Response of Three Fiber Reinforced Polymer Composite Bridges

Fiber reinforced polymer (FRP) composite bridge decks are gaining the attention of bridge owners because of their light self-weight, corrosion resistance, and ease of installation. Constructed Facilities Center at West Virginia University working with the Federal Highway Administration and West Virginia Department of Transportation has developed three different FRP decking systems and installed several FRP deck bridges in West Virginia. These FRP bridge decks are lighter in weight than comparable concrete systems and therefore their dynamic performance is equally as important as their static performance. In the current study dynamic tests were performed on three FRP deck bridges, namely, Katy Truss Bridge, Market Street Bridge, and Laurel Lick Bridge, in the state of West Virginia. The dynamic response parameters evaluated for the three bridges include dynamic load allowance (DLA) factors, natural frequencies, damping ratios, and deck accelerations caused by moving test trucks. It was found that the DLA factors for Katy Truss and Market Street bridges are within the AASHTO 1998 LRFD specifications, but the deck accelerations were found to be high for both these bridges. DLA factors for Laurel Lick bridge were found to be as high as 93% against the typical design value of 33%; however absolute deck stress induced by vehicle loads is less than 10% of the deck ultimate stress.     

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.