Analytical Solutions to General Orthotropic Plates under Patch Loading

Orthotropic plates are widely used in bridge deck systems. However, these are not commonly treated as such within design specifications, and semianalytical solutions are not presently available for all deck types. This paper develops deflection equations for infinitely wide and simply supported thin plates considering each of the three cases of orthotropy: (1)?relatively torsionally stiff, flexurally soft; (2)?uniformly thick plate; and (3)?torsionally soft, flexurally stiff; subjected to arbitrary patch loading. These are common boundary and loading conditions encountered for bridge deck applications. The reported analytical solutions enable rapid evaluation of multiple moving patch loads to determine maximum design load effects and permit validation of numerical and finite-element methods. Application of the solutions will produce guidelines that can prescribe design demands and establish practical design simplifications for treatment of different bridge deck and slab systems in a uniform and consistent manner.     

Replacement of Pontesei Bridge, Italy

Pontesei Dam is a major concrete dam built after World War II across the canyon of Maè Creek (Valle di Zoldo) in the Italian Eastern Alps. Just upstream from the dam, a gully discharges water from steep mountains. The only road serving the dam and the entire valley upstream of the dam runs along the mountainside and crosses the gully. In 1959, an exceptionally rainy season caused a flood, which destroyed the bridge. A temporary Bailey bridge was subsequently built by the army, but in 1990 it was decided to design a new bridge. The main challenges posed to the designer included building the new deck and the abutments underneath the Bailey bridge without disrupting traffic, hoisting the deck just to the bottom of the Bailey bridge, and finally substituting the new deck for the Bailey bridge in one day. Other problems included the instability of the rock mass at the abutments and the gravitative convergence of the two sides of the gully. This paper describes the design, construction, and testing of the bridge replacement and the bridge abutments.     

Application of Suspension Bridges Stiffened by Prestressed Concrete Slabs in China

Four suspension bridges stiffened by prestressed concrete slabs were designed and constructed on highways in southwestern mountainous areas of China. These bridges are the first applications of its kind in China. This paper discusses the site condition, adaptability, and design and construction features of these bridges. These bridges have single suspension spans between 278 and 388?m and deck width between 14.4 and 15.0?m. The longitudinal distance between hangers is only 5?m, which is relatively small for this bridge type, and there are only two lanes. The dual direction prestressed concrete slabs are 0.6?m deep, and its wind blocking area is relatively small. Dynamic analysis and wind tunnel tests verify that the wind resistance requirements are easily satisfied.     

Field Testing and Analysis of CRC Deck Girder Bridges

This paper presents findings of field tests and analysis of two conventionally reinforced concrete (CRC) deck girder bridges designed in the 1950s. The bridges are in-service and exhibit diagonal cracks. Stirrup strains in the bridge girders at high shear regions were used to estimate distribution factors for shear. Impact factors based on the field tests are reported. Comparison of field measured responses with AASHTO factors was performed. Three-dimensional elastic finite-element analysis was employed to model the tested bridges and determine distribution factors specifically for shear. Eight-node shell elements were used to model the decks, diaphragms, bent caps, and girders. Beam elements were used to model columns under the bent caps. The analytically predicted distribution factors were compared with the field test data. Finally, the bridge finite-element models were employed to compare load distribution factors for shear computed using procedures in the AASHTO LRFD and Standard Specifications.     

Field Load Tests and Numerical Analysis of Qingzhou Cable-Stayed Bridge

A field load test is an essential way to understand the behavior and fundamental characteristics of newly constructed bridges before they are allowed to go into service. The results of field static load tests and numerical analyses on the Qingzhou cable-stayed bridge (605?m central span length) over the Ming River, in Fuzhou, China are presented in the paper. The general test plan, tasks, and the responses measured are described. The level of test loading is about 80–95% of the code-specified serviceability load. The measured results include the deck profile, deck and tower displacements, and stresses of steel-concrete composite deck. A full three-dimensional finite-element model is developed and calibrated to match the measured elevations of the bridge deck. A good agreement is achieved between the experimental and analytical results. It is demonstrated that the initial equilibrium configuration of the bridge plays an important role in the finite-element calculations. Both experimental and analytical results have shown that the bridge is in the elastic state under the planned test loads, which indicates that the bridge has an adequate load-carrying capacity. The calibrated finite-element model that reflects the as-built conditions can be used as a baseline for health monitoring and future maintenance of the bridge.     

Flexural Lateral Load Distribution Characteristics of Sandwich Plate System Bridges: Parametric Investigation

The sandwich plate system (SPS) is a relatively new bridge deck system that consists of steel face plates bonded to a rigid polyurethane core. The decks are thin, lightweight, and modular in design and can be tailored to numerous applications. This system provides an excellent alternative for the rapid construction and rehabilitation of bridge decks. With any new system, there exists some uncertainty in the design procedures as a result of the limited population for comparison. This paper presents the results of a finite-element parametric investigation of the lateral load distribution characteristics of SPS bridges. The parametric study primarily focuses on the influence of deck thickness on distribution behavior as compared to conventional reinforced concrete decks. Results from the study demonstrate that the inherent flexibility of a thin SPS deck yields larger distribution factors (up to 20%) than a typical reinforced concrete deck, but these distribution factors can still be conservatively estimated with current AASHTO LRFD methods. Additional comparisons indicate that the distribution behavior of SPS bridges can also be estimated with the equations proposed by the NCHRP 12-62 project.     

Evaluation of Effective Width and Distribution Factors for GFRP Bridge Decks Supported on Steel Girders

Glass fiber-reinforced polymer (GFRP) bridge deck systems offer an attractive alternative to concrete decks, particularly for bridge rehabilitation projects. Current design practice treats GFRP deck systems in a manner similar to concrete decks, but the results of this study indicate that this approach may lead to nonconservative bridge girder designs. Results from a number of in situ load tests of three steel girder bridges having the same GFRP deck system are used to determine the degree of composite action that may be developed and the transverse distribution of wheel loads that may be assumed for such structures. Results from this work indicate that appropriately conservative design values may be found by assuming no composite action between a GFRP deck and steel girder and using the lever rule to determine transverse load distribution. Additionally, when used to replace an existing concrete deck, the lighter GFRP deck will likely result in lower total stresses in the supporting girders, although, due to the decreased effective width and increased distribution factors, the live-load-induced stress range is likely to be increased. Thus, existing fatigue-prone details may become a concern and require additional attention in design.     

Effects of Pier and Deck Flexibility on the Seismic Response of Isolated Bridges

The seismic response of bridges isolated by elastomeric bearings and the sliding system is investigated under two horizontal components of real earthquake ground motions. The selected bridges consist of multispan continuous deck supported on the piers and abutments. Three different mathematical models of the isolated bridge are considered for the analytical seismic response by considering and ignoring the flexibility of the deck and piers. The mathematical formulation for seismic response analysis of various mathematical models of the bridges isolated by different isolation systems is presented. The accuracy and computational efficiency of various mathematical models of isolated bridges is investigated by comparing their responses under different system parameters and earthquake ground motions. The important parameters selected are the flexibility of deck, piers, and isolation systems. There was significant difference in the computational time required for different models, but it was observed that the seismic response of the bridges obtained from different equivalent mathematical models is quite comparable even for an unsymmetrical bridge. Thus, the earthquake response of a seismically isolated bridge can be effectively obtained by modeling it as a single-degree-of-freedom system (i.e., considering the piers and deck as rigid) supported on an isolation system in two horizontal directions.     

Transverse Cracking of Concrete Bridge Decks: Effects of Design Factors

Early transverse cracking is one of the dominant forms of bridge deck defects experienced by a large number of transportation agencies. These cracks often initiate soon after the bridge deck is constructed, and they are caused by restrained shrinkage of concrete. Transverse cracks increase the maintenance cost of a bridge structure and reduce its life span. Most of the past efforts addressing transverse bridge deck cracking have focused on changes over the years in concrete material properties and construction practices. However, recent studies have shown the importance of design factors on transverse bridge deck cracking. This paper presents results of a comprehensive finite-element (FE) study of deck and girder bridge systems to understand and evaluate crack patterns, stress histories, as well as the relative effect of different design factors such as structural stiffness on transverse deck cracking. The results of this study demonstrate the development of transverse deck cracking and emphasize the importance of these design factors. They also recommend preventive measures that can be adopted during the design stage in order to minimize the probability of transverse deck cracking.     

Full-Scale Test of Continuity Diaphragms in Skewed Concrete Bridge Girders

Continuity diaphragms used in prestressed girder bridges on skewed bents have caused difficulties in detailing and construction. The results of the field verification for the effectiveness of continuity diaphragms for skewed, continuous, and prestressed concrete girder bridges are presented. The current design concept and bridge parameters that were considered include skew angle and the ratio of beam spacing to span (aspect ratio). A prestressed concrete bridge with continuity diaphragms and a skewed angle of 48° was selected for full-scale test by a team of engineers from Louisiana Department of Transportation and Development and the Federal Highway Administration. The live load tests performed with a comprehensive instrumentation plan provided a fundamental understanding of the load transfer mechanism through these diaphragms. The findings indicated that the effects of the continuity diaphragms were negligible and they can be eliminated. The superstructure of the bridge could be designed with link slab. Thus, the bridge deck would provide the continuity over the support, improve the riding quality, enhance the structural redundancy, and reduce the expansion joint installation and maintenance costs.     

Close Look at Construction Issues and Performance of Four Fiber-Reinforced Polymer Composite Bridge Decks

Four different fiber-reinforced polymer (FRP) panel systems were installed in a 207 m, five-span, three-lane bridge in an effort to assess the constructability, performance, and applicability of bridges with fiber-reinforced polymer composite decks. This paper examines whether four common deck systems are able to realize many of the anticipated benefits of using FRP composites in lieu of conventional reinforced concrete bridge decks. Particular installation issues, connection details, and specific construction techniques for each deck system are described, along with a discussion of the shortcomings in terms of handling, performance, and serviceability. Other factors such as key design parameters (e.g., impact factor and thermal characteristics) and unexpected responses are used to further quantify the performance of four FRP representative deck systems under identical traffic and environmental constraints.     

Performance Prediction of Bridge Deck Systems Using Markov Chains

Bridge management systems have adopted Markov-chain models for predicting the future condition of bridge components, systems, and networks. These models are developed based on two assumptions. First, bridge inspections are performed at predetermined and fixed time intervals (i.e., constant inspection period). Second, the future bridge condition depends only on the present condition and not on the past condition (i.e., state independence). This paper evaluates the impact of these assumptions on the performance prediction of bridge deck systems using field data obtained from the Ministère des Transports du Québec. Transition probability matrices are developed for the different elements of the deck system and adjusted for the variation in the inspection period using Bayes’ rule. This investigation indicated that the variation in the inspection period may result in a 22% error in predicting the service life of a bridge deck system. Also, the statistical tests used to assess the validity of the state independence assumption of Markov chains showed that this assumption is acceptable with a 95% level of confidence, which is reasonable for network level analysis.     

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.     

Balancing Connectivity of Deteriorating Bridge Networks and Long-Term Maintenance Cost through Optimization

Due to aggressive environmental stressors and increasing traffic loads, highway bridges are undergoing significant deterioration in both condition and safety. Timely and adequate maintenance interventions are therefore crucial to ensure the functionality of existing bridges in a network. Under budget constraints, it is important to prioritize maintenance needs to bridges that are most significant to the functionality of the entire network. In this paper, the network-level bridge maintenance planning problem is posed as a combinatorial optimization and is automated by a genetic algorithm (GA) to select and allocate maintenance interventions of different types among networked bridges as well as over a specified time horizon. Two conflicting objective functions are considered simultaneously: (1) The overall performance of a bridge network expressed by the time-dependent reliability of connectivity between the origin and the destination locations and (2) the present value of total maintenance cost over the specified time horizon. A variety of maintenance types, which differ in unit costs as well as in effects on bridge performance in terms of improvement in structural reliability levels, are used in the optimization. An event tree analysis is carried out to obtain a closed-form expression for the network connectivity reliability. As an illustration example, the GA-based procedure is applied to deteriorating deck slabs of an existing 13-bridge network located in Colorado. It is shown that the proposed maintenance planning procedure has the capability of both prioritizing scarce maintenance needs to deteriorating bridges that are most crucial to the network performance and cost-effectively distributing maintenance interventions over the time horizon.     

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.     

Characterization of a Low-Profile Fiber-Reinforced Polymer Deck System for Moveable Bridges

Moveable bridges in Florida typically use open steel grid decks due to weight limitations. However, these decks present rideability, environmental, and maintenance problems, as they are typically less skid resistant than a solid riding surface, create loud noises, and allow debris to fall through the grids. Replacing open steel grid decks with a lightweight fiber-reinforced polymer (FRP) deck can improve rideability and reduce maintenance costs, simultaneously satisfying the strict weight requirement for such bridges. In this investigation, a new low-profile, pultruded FRP deck system successfully passed the preliminary strength and fatigue tests per AASHTO requirements. Two two-span deck specimens were tested, one with the strong direction of the deck placed perpendicular to the supporting girders, whereas the other had a deck placed with 30° skew. This paper also describes a simplified finite-element approach that simulates the load–deformation behavior of the deck system. The results from the finite-element model showed a good correlation with the deflection and strain values measured from the tests.     

Realistic Assessment for Safety and Service Life of Reinforced Concrete Decks in Girder Bridges

The lack of safety of deck slabs in bridges generally causes frequent repair and strengthening. The repair induces great loss of economy, not only due to direct cost by repair, but also due to stopping the public use of such structures during repair. The major reason for this frequent repair is mainly due to the lack of a realistic and accurate assessment system for bridge decks. The purpose of the present paper is therefore to develop a realistic assessment system which can estimate reasonably the safety, as well as the service life of concrete bridge decks, based on the deterioration models that are derived from both the traffic loads and environmental effect. A deterioration model due to chloride ingress is first established. The damage models due to repetitive traffic loads considering the dry and wet conditions of deck slabs are proposed. These models are used to calculate the remaining life of a bridge deck slab. A prediction method for service life of deck slab due to loading and environmental effects is developed based on material, as well as structural evaluation. The proposed method includes the assessment of corrosion in material level, and the analyses of flexure, shear, and fatigue in structural level. Finally, an assessment system for prediction of safety and remaining service life is developed based on the theories established in this study. The developed assessment system will allow the correct diagnosis of damage state and the realistic prediction of service life of concrete decks in girder bridges.     

Lateral-Torsional Buckling of Stepped Beams with Continuous Bracing

Continuous span multibeam steel bridges are common along the state and interstate highways. The top flange of the beams is typically braced against lateral movement by the deck slab, and in many bridges the cross section is stepped at discrete points along the span. Design equations for lateral–torsional buckling (LTB) resistance in the American Association of State Highway and Transportation Officials “Load and resistance factor design bridge design specifications” are for prismatic beams and ignore the lateral restraint provided by the bridge deck. A new design equation is proposed that can be applied to I-shaped stepped beams with continuous top flange lateral bracing. By including the effects of the change in cross section size and the continuous top flange bracing, the calculated LTB resistance is significantly increased. Critical bending moment values from the proposed equation are compared to values from finite element method buckling analyses. The new equation is sufficiently accurate for use in design and in the evaluation of existing bridges.     

Finite-Element Modeling and Development of Equivalent Properties for FRP Bridge Panels

Fiber-reinforced polymer (FRP) composite materials are increasingly making their way into civil engineering applications. To reduce the self-weight and also achieve the necessary stiffness, sandwich panels are commonly used for FRP bridge decks. However, due to the geometric complexity of the FRP sandwich deck, convenient analysis and design methods for FRP bridge deck have not been developed. The present study aims at developing equivalent properties for a complicated sandwich panel configuration using finite-element modeling techniques. With equivalent properties, the hollowed sandwich panel can be transformed into an equivalent solid orthotropic plate, based on which deflection limits can be evaluated and designed. A procedure for the in-plane axial properties of the sandwich core has first been developed, followed by developing the out-of-plane panel properties for bending behavior of the panel. An application is made in the investigation of the stiffness contribution of wearing surface to the total stiffness of bridges with FRP panels. The wearing surface contribution is not usually accounted for in a typical design of bridges with traditional deck systems.     

Evaluation of Load Distribution Factor by Series Solution for Orthotropic Bridge Decks

In bridge engineering, the three-dimensional behavior of a bridge system is usually reduced to the analysis of a T-beam section, loaded by an equivalent fraction of the applied live load, which is called the live load distribution factor (LDF). The LDF is defined in the both the AASHTO Standard Specifications and the LRFD Specifications primarily for concrete slabs and has inherent applicable limitations. This paper provides explicit formulas using series solutions for LDF of orthotropic bridge decks, applicable to various materials but intended for fiber-reinforced polymer (FRP) decks. The present formulation considers important parameters that represent the response characteristics of the structure that are often omitted or limited in the AASHTO Specifications. A one-term series solution is proposed based on the macroflexibility approach, in which the bridge system is simplified into two major components, deck and stringers. The governing equations for the two components are obtained separately, and the deflections and interaction forces are solved by ensuring displacement compatibility at stringer lines. The LDF is calculated as the ratio of the single stringer interaction force to the summation of total stringer interaction forces. To verify this solution, a finite-element (FE) parametric study is conducted on 66 simply supported concrete slab-on-steel girder bridges. The results from the series solution correlates well with the FE results. It is also illustrated that the series solution can be applied to predict LDF for FRP deck-on-steel girder bridges, by favorable comparisons among the analytical, FE, and testing results for a one-third-scale bridge model. The scale test specimen consists of an FRP sandwich deck attached to steel stringers by a mechanical connector. The series solution is further used to obtain multiple regression functions for the LDF in terms of nondimensional variables, which can be used for simplified design purposes.