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.     

Experimental Verification of Horizontally Curved I-Girder Bridge Behavior

Past research has been conducted on the behavior of horizontally curved girders by testing scaled models and full-scale laboratory bridges and by analyzing numerical models. Current design specifications are based on this past research; however, little field data of in-service bridges exist to support the findings of the past research on which the current design criteria are based. The purpose of the present study was to gather field response data from three in-service, curved, steel I-girder bridges to determine behavior when subjected to a test truck and normal truck traffic. Transverse bending distribution factors and dynamic load allowance were calculated from the data collected. Numerical grillage models of the three bridges were developed to determine if a simple numerical model will accurately predict actual field measured transverse bending distribution, deflections, and cross-frame and diaphragm shear forces. The present study found that AASHTO specifications are conservative for both dynamic load allowance and transverse bending moment distribution. The grillage models were found to predict with reasonable accuracy the behavior of a curved I-girder bridge.     

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.     

Predicted and Measured Response of an Integral Abutment Bridge

This project examined several uncertainties of integral abutment bridge design and analysis through field-monitoring of an integral abutment bridge and three levels of numerical modeling. Field monitoring data from a Pennsylvania bridge site was used to refine the numerical models that were then used to predict the integral abutment bridge behavior of other Pennsylvania bridges of similar construction. The instrumented bridge was monitored with 64 gages; monitoring pile strains, soil pressure behind abutments, abutment displacement, abutment rotation, girder rotation, and girder strains during construction and continuously thereafter. Three levels of numerical analysis were performed in order to evaluate prediction methods of bridge behavior. The analysis levels included laterally loaded pile models using commercially available software, two-dimensional (2D) single bent models, and 3D finite element models. In addition, a weather station was constructed within the immediate vicinity of the monitored bridge to capture environmental information including ambient air temperature, solar radiation, wind speed and direction, humidity, rainfall, and barometric pressure. Laterally loaded pile models confirmed that inclusion of multilinear soil springs created from p-y curves is a valid approach for modeling soil–pile interaction within a finite element program. The 2D and 3D numerical models verified the field data indicating that primary accommodation of superstructure expansion and contraction is through rotation of the abutment about its base rather than longitudinal translation, as assumed in the original design of this bridge. Girder axial forces were suspected to be influenced by creep and shrinkage effects in the bridge superstructure. Pile strains were found to be well below strains corresponding to pile plastic moment. Overall, the 2D numerical model and the 3D numerical model predicted very similar behavior.     

Equivalent Wheel Load Approach for Slender Cable-Stayed Bridge Fatigue Assessment under Traffic and Wind: Feasibility Study

In the current AASHTO LRFD specifications, the fatigue design considers only one design truck per bridge with 15% dynamic allowance. While this empirical approach may be practical for regular short and medium span bridges, it may not be rational for long-span bridges (e.g., span length >152.4?m or 500?ft) that may carry many heavy trucks simultaneously. Some existent studies suggested that fatigue may not control the design for many small and medium bridges. However, little research on the fatigue performance of long-span bridges subjected to both wind and traffic has been reported and if fatigue could become a dominant issue for such a long-span bridge design is still not clear. Regardless if the current fatigue design specifications are sufficient or not, a real understanding of the traffic effects on bridge performance including fatigue is desirable since the one truck per bridge for fatigue design does not represent the actual traffic condition. As the first step toward the study of fatigue performance of long-span cable-stayed bridges under both busy traffic and wind, the equivalent dynamic wheel load approach is proposed in the current study to simplify the analysis procedure. Based on full interaction analyses of a single-vehicle–bridge–wind system, the dynamic wheel load of the vehicle acting on the bridge can be obtained for a given vehicle type, wind, and driving condition. As a result, the dimension of the coupled equations is independent of the number of vehicles, through which the analyses can be significantly simplified. Such simplification is the key step toward the future fatigue analysis of long-span bridges under a combined action of wind and actual traffic conditions.     

In-Service Diagnostics of a Highway Bridge from a Progressive Damage Case Study

Development of diagnostic and prognostic routines for application to in-service measurements from highway bridges necessitates analysis of experimental measurements from in-service highway bridges under natural or prescribed induced damage. This is generally limited to the unique opportunity of investigating end-of-service life bridges prior to reconstruction and consequently only a limited library of such case studies exist. This paper documents a field test of an end-of-service bridge span with prescribed progressive damage to a bearing as well as several diaphragm connections. Thirty dual-axis accelerometers were distributed across the bridge span with data acquisition and transmission facilitated by a real-time lossless wireless sensor network. A highway department service truck applied traffic excitation to the structure through routine passes on a consistent lane of traffic. Output-only system identification was applied to the baseline time history response to develop a state-space model of the bridge dynamics used for forward prediction in the form of a Kalman filter. Simple statistical evaluation of the prediction error in the model demonstrates the variance can be used to localize and generally quantify the degree of damage in the structure. The case study additionally illustrates the potential importance of monitoring lateral acceleration along the girders to permit identification of damage to elements, such as the diaphragms, that contributing primarily to the lateral and torsional response of primary structural members.     

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.     

Bridge Falsework Productivity—Measurement and Influences

One principal element of the construction cost of a cast-in-place prestressed box girder concrete bridge is the erection of falsework. This paper presents the results of the analysis of labor-hours and quantity of work in erecting the falsework for 20 such bridges. Analysis of the bridge data has shown that the best productivity for falsework erection occurs when constructing a low structure on relatively flat ground. Location and design factors such as steep slopes, traffic openings, and tall structures, as well as such construction techniques as the use of cranes or lifts and the type of bent material selected, can reduce falsework erection productivity (measured through installation data for setting of pads, constructing bents, setting stringers, and rolling out the soffit) by over 50%. A belief network diagram was constructed to show graphically the falsework erection productivity influences identified through a study of the 20 bridges. With the collection of additional data, the belief network can be used to calculate a total falsework erection productivity value based on dozens of combinations of influencing factors.     

Development of the Vertical Lift Bridge: Squire Whipple to J. A. L. Waddell, 1872–1917

The development of canals started in the mid 18th century in England and Europe and in the 1820s in the United States. They required the design and construction of many bridges to provide canal crossings for carriages, wagons, animal herds, and pedestrians. The cost of building bridges of masonry or wood to carry roadway traffic high over the towpaths and waterways of canals was very great so engineers of the day developed bridges that could be moved out of the way when a canal boat was coming through and then moved back over the canal to provide roadway access. The Dutch developed a type of bascule bridge for many canals, while the British developed swing or pull back bridges. The swing bridge for narrow canals had a turntable on shore with a short counterweight span over land and a cantilever span over the canal. This bridge could be worked by hand with a simple crank. The pull back bridges, while not as common, ran on tracks and had the same type of counterweight span and cantilever span over the canal. On wide canals, as well as on the C & O Canal in the 1830s, the swing bridges had a central pier on which the turntable was mounted and the bridge cantilevered out on both sides to the shore when closed, and frequently onto an extended pier parallel to the canal when the bridge was open for canal boat passage. In the United States the most common bridge on canals and waterways was a side mounted or center mounted swing bridge well into the 20th century. The development of the metal vertical lift bridge can be traced to the late 1840s in England where several small lift spans were built. After a review of early European spans, this paper covers the period starting in 1872 with Squire Whipple and his Erie Canal bridges, and terminates in 1917 with Waddell’s Columbia River Bridge.     

Evaluation of the Effectiveness of Strengthening Intervention by CFRP on MRWA Bridge No. 3014

Main Roads of Western Australia has a continuing program of bridge upgrading, to refurbish and strengthen bridges to allow for increasing vehicle traffic and increasing axle loads. A 40-year-old, four-span reinforced concrete slab bridge was retrofitted with application of CFRP laminate strips on the top of the deck over the piers, as well as on the deck soffit in the midspan regions, to reduce high moments in both hogging and sagging. The dynamic assessment of the bridge before and after strengthening works provided the opportunity to evaluate the effectiveness of the strengthening intervention through dynamic measurements. A performance evaluation of the repaired structure was carried out through traffic loading application on the updated numerical models of the bridge, before and after retrofit. As a main observation, the addition of CFRP laminate strips led to a significant increase of the structural capacity in flexure. The paper discusses the results obtained from the dynamic-based assessment in terms of effectiveness of the strengthening intervention as well as of efficiency in using such a methodology to evaluate the capacity increase of the retrofitted bridge.     

Extreme Thermal Loading on Steel Bridges in Tropical Region

In the design of highway bridges, it is important to consider the thermal stresses induced by the nonlinear temperature distribution in the bridge deck irrespective of their spans. To cope with this, design temperature profiles are provided by many bridge design codes, which are normally based on extensive research on the thermal behavior of bridges. This paper presents the results of a comprehensive investigation on the thermal behavior of steel bridges carried out in Hong Kong. A method for predicting bridge temperatures from given meteorological conditions is briefly discussed. The theoretical results have been validated by temperature measurements on experimental models mounted on the roof of a building as well as on an existing steel bridge. Both the theoretical and field results confirm the validity of the one-dimensional heat transfer model on which most design codes are based. Values of design thermal loading for a 50-year return period are determined from the statistics of extremes over 40 years of meteorological information in Hong Kong. The design temperature profiles for various types of steel bridge deck with different thickness of bituminous surfacing are developed.     

Overview of Potential and Existing Applications of Shape Memory Alloys in Bridges

Bridges are the backbones of transportation lines for modern cities. Damage to bridges could disrupt the flow of traffic and be disastrous for the communities they serve, especially when reconstruction and recovery activities are needed, such as after strong earthquakes and hurricanes. Recent earthquake and hurricane damage has exposed the vulnerability of existing bridges under strong ground motions and unexpected wave loads. In recent decades, several kinds of smart materials have been investigated to improve the performance of bridge structures during extreme events such as earthquakes and strong winds. Among these materials, shape memory alloys (SMAs) have exhibited great potential in enhancing the performance of bridge structures because of their unique properties, such as the shape memory effect and superelasticity effect. This paper, for the first time, systematically reviews and summarizes the applications of SMAs in bridge structures. The unique properties of SMAs are presented first, and several simplified one-dimensional constitutive material models of superelastic SMAs are introduced. Finally, applications of SMAs in five areas of bridge engineering are discussed.     

Probabilistic Characterization of Live Load Using Visual Counts and In-Service Strain Monitoring

It has been argued that the AASHTO LRFD design code for maximum live loads on highway bridges is overly conservative. In an attempt to determine the level of conservativeness, if any, the writers developed a methodology incorporating real-time visual data collection from traffic cameras coupled with structural strain response of girder bridges. Average daily truck traffic along with frequency of multiple presences (same lane as well as adjacent lanes) and lane-wise truck traffic distribution were estimated for a steel-girder highway bridge on I-95 in Delaware. These data compared well with predictions from a Poisson process based model developed for this study. Statistical properties of girder moments in single and multiple presence conditions were determined as well. In this particular example, the girder design moment on the 24.6?foot approach span according to AASHTO specifications was found to be about 3.5 times higher than that estimated from the in-service data.     

Design for Shear in Curved Composite Multiple Steel Box Girder Bridges

Modern highway bridges are often subject to tight geometric restrictions and, in many cases, must be built in curved alignment. These bridges may have a cross section in the form of a multiple steel box girder composite with a concrete deck slab. This type of cross section is one of the most suitable for resisting the torsional, distortional, and warping effects induced by the bridge’s curvature. Current design practice in North America does not specifically deal with shear distribution in horizontally curved composite multiple steel box girder bridges. In this paper an extensive parametric study, using an experimentally calibrated finite-element model, is presented, in which simply supported straight and curved prototype bridges are analyzed to determine their shear distribution characteristics under dead load and under AASHTO live loadings. The parameters considered in this study are span length, number of steel boxes, number of traffic lanes, bridge aspect ratio, degree of curvature, and number and stiffness of cross bracings and of top-chord systems. Results from tests on five box girder bridge models verify the finite-element model. Based on the results from the parametric study simple empirical formulas for maximum shears (reactions) are developed that are suitable for the design office. A comparison is made with AASHTO and CHBDC formulas for straight bridges. An illustrative example of the design is presented.     

Response of Prestressed Concrete I-Girder Bridges to Live Load

Design and evaluation of prestressed concrete I-girder bridges is in large part dependent on the transverse load distribution characteristics and the dynamic load amplification, as well as service level, live load, and tensile stresses induced in the girders. This study presents the results of field tests conducted on three prestressed concrete I-girder bridges to obtain dynamic load allowance statistics, girder distribution factors (GDF), and service level stress statistics. The field-based data are also compared to approximate and numerical model results. Bridge response was measured at each girder for the passage of test trucks and normal truck traffic. The dynamic amplification is observed to be a strong function of peak static stress and a weak function of vehicle speed and is independent of span length, number of axles, and configuration. GDFs for one- and two-lanes are less than code specified GDFs. Results from the numerical grillage models agree closely with experimentally derived results for transverse distribution.     

Routing and Permitting Techniques of Overweight Vehicles

Overweight vehicles require permits to cross the highway bridges, which are designed for “design load vehicles” (prescribed in the national standards). A new, fast, and robust method is presented for the verification of bridges, which requires minimal input only: the axle loads, axle spacing, the bridge span(s), and the superstructure type. The bridge can be a single or a multispan girder, an arch bridge, a frame structure, or a box girder. The overweight vehicle may operate within regular traffic or it may cross the bridge at a given lane position while other traffic is prohibited on the bridge. The method is illustrated by numerical examples for deck-girder bridges and for a box girder.     

Vertical Excitation of Stochastic Soil-Structure Interaction Systems

This paper considers two stochastic models for a soil-structure interaction problem with vertical propagation of P waves during strong earthquake motion. These models include the horizontal and vertical spatial variability of stiffness of the soil medium. The first model involves a two-dimensional stochastic Winkler foundation, which takes into account the horizontal variability of the soil. This model elucidates some experimental results obtained on a nuclear power station physical model built in Hualien (Taiwan). The second model is developed as a continuum system of random columns involving, this time, horizontal and vertical random characteristics of the soil medium. For both models a statistical analysis was performed with respect to determining probabilistic properties resonance frequencies and amplitudes of the corresponding transfer functions. The theoretical development and numerical results demonstrate the importance of considering soil variability for geotechnical design applications.     

Theories of Aerodynamic Forces on Decks of Long Span Bridges

Long span bridges are one of the most challenging kinds of structures in civil engineering. Wind loading and wind effects are highly important aspects when designing this typology. The interaction between wind and structure, studied by using aeroelasticity theory, allows us to understand several classes of structural instabilities that may appear. Also, wind tunnel data, obtained by conducting careful testing of reduced models of bridges, produce useful information about prototypes' characteristics. A fundamental aspect of bridge design under aeroelastic constraints is identification of aerodynamic forces; several models for this purpose are presented in this paper. First, a model based on a two-degrees-of-freedom plane plate moving in an incompressible fluid is reviewed; this approach, although useful in airfoil engineering, is not valid any longer in civil engineering, as bridge decks are bluff bodies. Second, a linearized theory, also based on a two-degrees-of-freedom model is analyzed; in this case, obtaining aerodynamic forces requires identification of a set of coefficients, called flutter derivatives, that can be found by carrying out testing of reduced models of a segment of bridge deck. Finally, an extension of that approach, leading to a linearized theory of a three-degrees-of-freedom model is presented.     

Probability-Based Bridge Network Performance Evaluation

This paper presents a comprehensive mathematical model for evaluating the overall performance of a bridge network based on probability analyses of network connectivity, user satisfaction, and structural reliability of the critical bridges in the network. A bridge network consists of all nodes of interest in a geographical region. These nodes of interest are connected to each other through multiple paths. The network performance evaluation in terms of connectivity is formulated by using an event tree technique. The network performance measure of user satisfaction deals with traffic demand and capacity of each link in the network. Moreover, the shortest paths in terms of total traffic costs are identified by network optimization algorithms for each pair of the origin and destination nodes of interest under the specified traffic demands. Using this information, the minimum-weight spanning tree (MST) that consists of the identified shortest paths is constructed. The bridges associated with MST are defined as the critical bridges in the network. The network performance in terms of structural reliability of the critical bridges can be computed from system reliabilities of the critical bridges by using a series-parallel system model. Finally, by combining the above three criteria, a single numerical measure is proposed to evaluate the overall performance of the bridge network. This novel approach is illustrated on a group of fourteen existing bridges with different reliability profiles located in Colorado. This study provides the basis of a network-level bridge management system where lifetime reliability and life-cycle costs are the key considerations for optimal bridge maintenance strategies.     

Impact of Commercial Vehicle Weight Change on Highway Bridge Infrastructure

Heavy trucks represent a major load to highway bridges in the transportation infrastructure system. These loads are directly related to the truck weight limits of the jurisdiction, and largely determine the standard loads for bridge design and evaluation. Thus, truck weight limit is one of the major factors affecting bridge deterioration and expenditure for maintenance, repair, and/or replacement. Truck weight in this paper not only refers to the truck gross weight but also to the axle weights and spacings that affect load effects. This paper presents the concepts of a new methodology for estimating cost effects of truck weight limit changes on bridges in a transportation infrastructure network. The methodology can serve as a tool for studying impacts of such changes. The resulting knowledge is needed when examining new truck weight limits, several of which have been and are still being debated at both the state and federal levels in the United States. The development of this estimation method has considered maximizing the use of available data (such as the bridge inventory) at the state infrastructure system level. In application examples completed (but not reported herein), the costs for relatively inadequate strength of existing bridges and for increased design requirement for new bridges were found dominant in the total impact cost.