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.     

Approximate Series Solution for Analysis of FRP Composite Highway Bridges

The design of a deck-and-stringer bridge system is usually reduced to the analysis of a T-beam section, loaded by concentrated loads corresponding to an equivalent fraction of the applied truck load. This equivalent load is defined by wheel load–distribution factors, which approximate the overall behavior of the bridge superstructure. In this paper, a one-term approximation of a macroflexibility series solution including deformations for fiber-reinforced polymer (FRP) deck-and-stringer orthotropic bridge systems, is used to develop explicit expressions for symmetric and asymmetric load distribution factors. It is significant that the equations presented herein include important parameters that represent, as accurately as possible, the response characteristics of the super structure, such as the geometry and material properties of the FRP deck and stringers, bridge aspect ratio, and number and spacing of stringers. As an illustration in actual design applications, the formulation presented in this paper is used to develop an analytical method for FRP deck-and-stringer bridge systems, and the method is verified by predicting the response of an all FRP model bridge in the lab and an FRP deck on steel stringers in the field. The results of the present formulation compare well with experimental lab and field results. The simplified analysis presented in this paper can be used with sufficient accuracy for the design of composite FRP deck on stringers bridges.     

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.     

Structural Behavior of FRP Composite Bridge Deck Panels

Fiber-reinforced polymer (FRP) composite bridge deck panels are high-strength, corrosion resistant, weather resistant, etc., making them attractive for use in new construction or retrofit of existing bridges. This study evaluated the force-deformation responses of FRP composite bridge deck panels under AASHTO MS 22.5 (HS25) truck wheel load and up to failure. Tests were conducted on 16 FRP composite deck panels and four reinforced concrete conventional deck panels. The test results of FRP composite deck panels were compared with the flexural, shear, and deflection performance criteria per Ohio Department of Transportation specifications, and with the test results of reinforced concrete deck panels. The flexural and shear rigidities of FRP composite deck panels were calculated. The response of all panels under service load, factored load, cyclic loading, and the mode of failure were reported. The tested bridge deck panels satisfied the performance criteria. The safety factor against failure varies from 3 to 8.     

AASHTO-LRFD Live Load Distribution for Beam-and-Slab Bridges: Limitations and Applicability

This paper presents a comparison between the live load distribution factors of simple span slab-on-girders concrete bridges based on the current AASHTO-LRFD and finite-element analysis. In this comparison, the range of applicability limits specified by the current AASHTO-LRFD is fully covered and investigated in terms of span length, slab thickness, girder spacing and longitudinal stiffness. All the AASHTO-PCI concrete girders (Types I–VI) are considered to cover the complete range of longitudinal stiffness specified in the AASHTO-LRFD. Several finite-elements linear elastic models were investigated to obtain the most accurate method to represent the bridge superstructure. The bridge deck was modeled as four-node quadrilateral shell elements, whereas the girders were modeled using two-node space frame elements. The live load used in the analysis is the vehicular load plus the standard lane load as specified by AASHTO-LRFD. The live load is positioned at the longitudinal location that produced the extreme effect, and then it is moved transversely across the bridge width in order to investigate all possibilities of one-lane, two-lane and three-lane design loads. A total of 886 bridge superstructure models were built and analyzed using the computer program SAP2000 to perform this comparison. The results of this study are presented in terms of figures to be practically useful to bridge engineers. This study showed that the AASHTO-LRFD may significantly overestimate the live load distribution factors compared to the finite-element analysis.     

Development of Live-Load Distribution Factors for Glued-Laminated Timber Girder Bridges

This paper presents simple relationships for calculating live-load distribution factors for glued-laminated timber girder bridges with glued-laminated timber deck panels. Analytical models were developed using the Ansys 113 finite-element program, and the results were validated using recorded data from four in-service timber bridges. The effects of the bridge span length, the spacing between girders, and the bridge width on the distribution of the live load were investigated by using the validated models. The live-load distribution factors obtained from the field test and the analytical models were compared with those obtained using the AASHTO LRFD Bridge Design Specifications2 live-load distribution relations. The comparison showed that the live-load distribution factors obtained by using the AASHTO LRFD Bridge Design Specifications2 were conservative. For this reason, statistical methods were used to develop accurate relationships that can be used to calculate the live-load distribution factors in the design of glued-laminated girder bridges.     

Wheel Load Distribution in Simply Supported Concrete Slab Bridges

This paper presents the results of a parametric study related to the wheel load distribution in one-span, simply supported, multilane, reinforced concrete slab bridges. The finite-element method was used to investigate the effect of span length, slab width with and without shoulders, and wheel load conditions on typical bridges. A total of 112 highway bridge case studies were analyzed. It was assumed that the bridges were stand-alone structures carrying one-way traffic. The finite-element analysis (FEA) results of one-, two-, three-, and four-lane bridges are presented in combination with four typical span lengths. Bridges were loaded with highway design truck HS20 placed at critical locations in the longitudinal direction of each lane. Two possible transverse truck positions were considered: (1) Centered loading condition where design trucks are assumed to be traveling in the center of each lane; and (2) edge loading condition where the design trucks are placed close to one edge of the slab with the absolute minimum spacing between adjacent trucks. FEA results for bridges subjected to edge loading showed that the AASHTO standard specifications procedure overestimates the bending moment by 30% for one lane and a span length less than 7.5 m (25 ft) but agrees with FEA bending moments for longer spans. The AASHTO bending moment gave results similar to those of the FEA when considering two or more lanes and a span length less than 10.5 m (35 ft). However, as the span length increases, AASHTO underestimates the FEA bending moment by 15 to 30%. It was shown that the presence of shoulders on both sides of the bridge increases the load-carrying capacity of the bridge due to the increase in slab width. An extreme loading scenario was created by introducing a disabled truck near the edge in addition to design trucks in other lanes placed as close as possible to the disabled truck. For this extreme loading condition, AASHTO procedure gave similar results to the FEA longitudinal bending moments for spans up to 7.5 m (25 ft) and underestimated the FEA (20 to 40%) for spans between 9 and 16.5 m (30 and 55 ft), regardless of the number of lanes. The new AASHTO load and resistance factor design (LRFD) bridge design specifications overestimate the bending moments for normal traffic on bridges. However, LRFD procedure gives results similar to those of the FEA edge+truck loading condition. Furthermore, the FEA results showed that edge beams must be considered in multilane slab bridges with a span length ranging between 6 and 16.5 m (20 and 55 ft). This paper will assist bridge engineers in performing realistic designs of simply supported, multilane, reinforced concrete slab bridges as well as evaluating the load-carrying capacity of existing highway bridges.     

Simplified AASHTO Load and Resistance Factor Design Girder Live Load Distribution in Illinois

Illinois began full transition to the American Association of State Highway and Transportation Officials load and resistance factor design (LRFD) bridge design specifications from the traditional load factor design code or standard specifications in 2002. To facilitate implementation of the new specification, engineers from the Illinois Department of Transportation undertook a series of investigations. The studies focused on interpretation of LRFD for the design of typical bridges in Illinois and the simplification of its procedures for determination of live load lane distributions to primary superstructure girders. Some important presented results from the conducted investigations are believed not only relevant to bridge design in Illinois, but to other states and jurisdictions which employ or will employ LRFD in the near future. The initial simplifications and interpretations focused on concrete deck-on-steel girder bridges and were subsequently expanded to include concrete deck-on-prestressed concrete girder structures. These types of structures comprise a large portion of Illinois’ inventory. Illinois Department of Transportation engineers continue to build on the studies described in the paper such that policies and procedures for other types of typical bridges can be formulated.     

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.     

Field Performance of the Fiber-Reinforced Polymer Deck of a Truss Bridge

The MD 24 Bridge over Deer Creek in Harford County, Md., was one of the projects chosen by the Federal Highway Administration’s Innovative Bridge Research and Construction Program for bridge deck replacement by fiber-reinforced polymer (FRP) composites. A thorough discussion is presented on Maryland State Highway Administration’s first bridge rehabilitation project utilizing a FRP deck. The discussion includes design details, installation procedure, construction methods and in situ load testing with a wireless monitoring system. The research team installed a monitoring system to record the effects of live loads on the bridge system, including truss members, steel stringers, and plate action of the FRP deck. Finite-element models were also used in this phase. Dynamic effects of the FRP system, composite action between steel stringers and the FRP deck as well as the effective width and distribution factors of stringers were obtained and compared with the AASHTO specifications. Recommendations are also offered on improving the design details based on this experience.     

Vehicle-Induced Dynamic Performance of FRP versus Concrete Slab Bridge

In the United States alone, about 30% of the bridges are classified as structurally deficient or functionally obsolete. To alleviate this problem, a great deal of work is being conducted to develop versatile, fully composite bridge systems using fiber-reinforced polymers (FRPs). To reduce the self-weight and also achieve the necessary stiffness, FRP bridge decks often employ hollow sandwich configurations, which may make the dynamic characteristics of FRP bridges significantly different from those of conventional concrete and steel bridges. Due to the geometric complexity of the FRP sandwich panels, dynamic analyses of FRP bridges are very overwhelming and rarely reported. The present study develops an analysis procedure for the vehicle-bridge interaction based on a three-dimensional vehicle-bridge coupled model. The vehicle is idealized as a combination of rigid bodies connected by a series of springs and dampers. A slab FRP bridge, the No-Name Creek Bridge in Kansas, is first modeled using the finite-element method to predict its modal characteristics, then the bridge and vehicle systems are integrated into a vehicle-bridge system based on the deformation compatibility. The bridge response is obtained in the time domain by using an iterative procedure employed at each time step, considering the deck surface roughness as a vertical excitation to the vehicle. The bridge dynamic response and the calculated impact factors are compared between the FRP slab bridge and a corresponding concrete slab bridge. Finally, the applicability of AASHTO impact factors to FRP bridges is discussed.     

Analytical and Experimental Investigation of Bridge Girder Shear Distribution Factors

Tests on twelve bridges (six along Interstate 55 and six along Interstate 70/270 in Illinois) were performed to determine the validity of certain provisions for calculating bearing forces in the load and resistance factor design (LRFD) and the load factor design bridge specifications. The bridges were selected to be typical of Illinois interstate highway bridges and maintain a range of parameters to study. These bridges were instrumented on their beam webs with three strain gauge rosettes installed on each beam to measure shear stresses caused by loads. Static tests and slow moving 8 km/h (5?mi/h) tests with a loaded truck in specified locations were performed. Dynamic tests at highway speeds were also completed. Finite-element models were developed and compared to the test results. The study shows that the LRFD specification procedures closely approximate the shear distribution factors determined by finite-element analysis and testing.     

Effect of Skewness on the Distribution of Live Load Reaction at Piers of Skewed Continuous Bridges

This paper presents a study of the skewness effect on live load reactions at the piers of continuous bridges. Two prestressed concrete I-beam bridges and one steel I-girder bridge were selected for the study. To evaluate the skew effect, the skew angle of the bridges was varied from 0 to 60°. Live load reaction at support and shear at the beam ends of the selected bridges were determined using finite-element analysis. The comparison of the distribution factors of live load reactions and shear revealed that the distribution factor of reaction at piers was higher than that of shear at beam ends near the same support. The increase in the reaction distribution factor was more significant than that in the shear distribution factor in the interior beam line when the skew angle was greater than 30°. The LRFD shear equations and the Lever rule method could conservatively predict live load reaction distribution for piers in exterior beam lines but underestimate live load reaction distribution in interior beam lines. It is recommended that more research be performed for the distribution factor of live load reaction to quantify the responses.     

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.     

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

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

Simplified Method for Calculating Lateral Distribution Factors for Live Load Shear

The simplified equal distribution factor (EDF) method for live load shear presented in this study originates from Henry’s method, a method that has been used in Tennessee for nearly forty years. Henry’s method allows for equal distribution of live load effects in all beams. This study focused on a careful examination and modification of Henry’s method by comparing shear distribution factors obtained from Henry’s method with those from finite element analysis and other code-specified methods for actual bridges. Twenty-four Tennessee bridges with six different types of superstructures were used in the study. The effects of structural parameters on the shear distribution factors were also studied. Modification factors to Henry’s method were proposed based on the comparison study. The proposed modification factors include structure type factors that are applied to different types of superstructures and a skew correction factor that is used to account for the effects of skew angle for skewed bridges. With proper modifications, the simplified EDF method can produce very reasonable and reliable distribution factors for live load shear.     

Testing, Analysis, and Evaluation of a GFRP Deck on Steel Girders

North Carolina has recently installed a fiber-reinforced polymer (FRP) deck on steel girders at a site in Union County. The bridge was instrumented with foil strain gauges, strain transducers, and displacement transducers. The bridge was then tested with a simulated MS-22.5 design load. Experimental data confirmed full composite interaction between the girders and the FRP deck panels. The neutral axis was measured to be 383?mm above the bottom flange of the 618-mm-deep girder. It was found that composite action could be estimated within 3% using a transformed section analysis of the deck panels. For two lanes loaded, the maximum live load distribution factor was computed to be 0.75. When looking at the overall performance of the structure, the deck deflected 5?mm, with the allowable stress at least 10 times over the maximum stress measured in the material. The girder deflection of 7?mm was well within the parameters set forth by AASHTO. Simple span deflection equations were found to conservatively model the anticipated deflection of the girders when using the transformed section properties.     

Effects of State Legal Loads on Bridge Rating Results Using the LRFR Procedure

The main objective of this research was to study the effects of different specified trucks on bridge rating with the load and resistance and factor rating (LRFR) procedure. Twelve specified trucks were selected for this study, which include one AASHTO design truck, three AASHTO legal trucks, and eight state legal trucks. These rating trucks were applied on 16 selected Tennessee Dept. of Transportation bridges to obtain the LRFR ratings. The selected bridges covered four commonly used bridge types, including prestressed I-beam bridges; prestressed box beam bridges; cast-in-place T-beam bridges; and steel I-beam bridges. The research results revealed that (1) LRFR AASHTO legal load ratings factors were enveloped by the LRFR HL-93 truck ratings factors, thereby confirming the validity of the LRFR tiered approach with regard to AASHTO legal loads; (2) the lighter state legal trucks were enveloped by the HL-93 loads, whereas the heavier state trucks with closer axle spacing typically resulted in load ratings that governed over the HL-93 loads; and (3) the bridges with both high average daily truck traffic and short spans were more likely to be governed by state legal load ratings instead of HL-93 load ratings.