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.     

Live Load Distribution Formulas for Single-Span Prestressed Concrete Integral Abutment Bridge Girders

In this study, live load distribution formulas for the girders of single-span integral abutment bridges (IABs) are developed. For this purpose, two and three dimensional finite-element models (FEMs) of several IABs are built and analyzed. In the analyses, the effects of various superstructure properties such as span length, number of design lanes, prestressed concrete girder size, and spacing as well as slab thickness are considered. The results from the analyses of two and three dimensional FEMs are then used to calculate the live load distribution factors (LLDFs) for the girders of IABs as a function of the above mentioned parameters. The LLDFs for the girders are also calculated using the AASHTO formulas developed for simply supported bridges (SSBs). The comparison of the analyses results revealed that LLDFs for girder moments and exterior girder shear of IABs are generally smaller than those calculated for SSBs using AASHTO formulas especially for short spans. However, AASHTO LLDFs for interior girder shear are found to be in good agreement with those obtained for IABs. Consequently, direct live load distribution formulas and correction factors to the current AASHTO live load distribution equations are developed to estimate the girder live load moments and exterior girder live load shear for IABs with prestressed concrete girders. It is observed that the developed formulas yield a reasonably good estimate of live load effects in prestressed concrete IAB girders.     

Live-Load Distribution Factors for Prestressed Concrete, Spread Box-Girder Bridge

This study presents an evaluation of shear and moment live-load distribution factors for a new, prestressed concrete, spread box-girder bridge. The shear and moment distribution factors were measured under a live-load test using embedded fiber-optic sensors and used to verify a finite element model. The model was then loaded with the American Association of State Highway and Transportation (AASHTO) design truck. The resulting maximum girder distribution factors were compared to those calculated from both the AASHTO standard specifications and the AASHTO LRFD bridge design specifications. The LRFD specifications predictions of girder distribution factors were accurate to conservative when compared to the finite element model for all distribution factors. The standard specifications predictions of girder distribution factors ranged from highly unconservative to highly conservative when compared to the finite element model. For the study bridge, the LRFD specifications would result in a safe design, though exterior girders would be overdesigned. The standard Specifications, however, would result in an unsafe design for interior girders and overdesigned exterior girders.     

The beta-adrenomimetic effect of human and animal blood serum

The conventional analysis and design of highway bridges ignore the contribution of sidewalks and∕or railings in a bridge deck when calculating the flexural strength of superstructures. The presence of sidewalks and railings or parapets acting integrally with the bridge deck have the effect of stiffening the outside girders and attracting more load while reducing the load effects in the interior girders. This paper presents the results of a parametric study showing the influence of typical sidewalks and railings on wheel load distribution as well as on the load-carrying capacity of highway bridges. A typical one-span, two-lane, simply supported, composite steel girder bridge was selected in order to investigate the influence of various parameters such as: span length, girder spacing, sidewalks, and railings. A total of 120 bridges were analyzed using three-dimensional finite-element analysis. American Association of State Highway and Transportation Officials (AASHTO) HS20 design trucks were positioned in both lanes to produce the maximum moments. The finite-element analysis results were also compared with AASHTO wheel load distribution factors. The AASHTO load and resistance factor design (LRFD) wheel load distribution formula correlated conservatively with the finite-element results and all were less than the typical empirical formula (S∕5.5). The presence of sidewalks and railings were shown to increase the load-carrying capacity by as much as 30% if they were included in the strength evaluation of highway bridges.     

Full-Scale Test and Analysis of a Curved Steel-Box Girder Bridge

Since the first edition of the AASHTO Guide Specifications for Horizontally Curved Steel Girder Highway Bridges was published in 1980, there have been two more editions including many revisions to the specifications. Some changes were based on valid research results and others were based on limited or uncertain research results and information. The current edition of the specifications contains provisions that may result in unreasonably conservative load capacity ratings. In this paper, the results of field tests and analyses conducted on the Veterans’ Memorial curved steel-box girder bridge are discussed. Test and analytical results show: (1) current AASHTO guide specifications regarding the first transverse stiffener spacing at the simple end support of a curved girder may be too conservative for bridge load capacity ratings; (2) current AASHTO guide specifications may greatly overestimate the dynamic loadings of curved box girder bridges with long span lengths; and (3) a plane grid finite-element model of about 20 elements per span in the longitudinal direction can be used to analyze curved multigirder bridges with external bracings located only over supports. The research results are instructive and applicable to bridge design and bridge load-rating activities.     

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.     

Effect of Multilanes on Wheel Load Distribution in Steel Girder Bridges

This paper presents the results of a parametric study that investigated the effect of multilanes and continuity on wheel load distribution in steel girder bridges. Typical one- and two-span, two-, three-, and four-lane, straight, composite steel girder bridges were selected for this study. The major bridge parameters chosen for this study were the span length, girder spacing, one- versus two-spans, and the number of lanes. These parameters were varied within practical ranges to study their influence on the wheel load distribution factors. A total of 144 bridges were analyzed using the finite-element method. The computer program, SAP90, was used to model the concrete slab as quadrilateral shell elements and the steel girders as space frame members. Simple supports were used to model the boundary conditions. AASHTO HS20 design trucks were positioned in all lanes of the one- and two-span bridges to produce the maximum bending moments. The calculated finite-element wheel load distribution factors were compared with the AASHTO and the National Cooperative Highway Research Program (NCHRP) 12-26 formulas. The results of this parametric study agree with the newly developed NCHRP 12-26 formula and both were, in general, less than the empirical AASHTO formula (S∕5.5) for longer span lengths [>15.25 m (50 ft)] and girder spacing >1.8 m (6 ft). This paper demonstrates that the multiple lane reduction factors are built into the newly developed distribution factors for steel girder bridges that were presented in the NCHRP 12-26 final report. It should be noted that AASHTO LRFD contains a similar expression that results in a value that is 50% of the value in the equations developed as a part of NCHRP 12-26. This is due to the fact that AASHTO LRFD consider the entire design truck instead of half-truck (wheel loads) as the case in the NCHRP 12-26 report and the AASHTO Standard Specifications for Highway Bridges. Therefore, this paper supports the use of the new distribution factors for steel girder bridges developed as a part of NCHRP 12-26 and consequently the distribution factors presented in the AASHTO LRFD Bridge Design Specifications.     

Predicted and Measured Performance of Prestressed Concrete Bridges

Testing results of six existing prestressed concrete bridges are used to evaluate analytical methodologies. These bridges cover different span lengths, number of lanes, and skew angles. Strains, load distribution factors, and ratings predicted by finite-element analyses and AASHTO code specifications are compared with those from measurements. The comparison reveals a significant difference between the analytical and test results due to the effects of many field factors. Factors that exist in reality but whose effects on bridge performance cannot easily be quantified are defined as field factors. Due to these field factors, existing bridges are different from idealized calculation models and are thus defined as field bridges. To examine this difference and to quantify their effects, some field factors are modeled in a more refined finite-element analysis. It is found that the field factors have a larger effect on the maximum strain than on the load distribution factor. Parametric studies of the effects of diaphragms, bearing stiffness, and skew angles on the load distribution and maximum strain are conducted.     

Field Investigation of a Sandwich Plate System Bridge Deck

This paper presents the results of a live-load test of the Shenley Bridge, the first bridge application of the sandwich plate system technology in North America. The investigation focused on the evaluation of in-service performance including lateral load distribution behavior and dynamic load allowance. Real-time midspan deflections and strain values were measured under both static and dynamic conditions and under various loading configurations to assess the in-service performance. Distribution factors were determined for interior and exterior girders subjected to single and paired truck loadings. In addition, dynamic load allowance was determined from a comparison of the bridge’s response under static conditions to the response under dynamic conditions. From a comparison of measured results to AASHTO LRFD, AASHTO standard, and CHBDC provisions, it was determined that the current provisions tend to produce conservative predictions for lateral load distribution, but can be unconservative for dynamic load allowance. As a result of the testing program containing a single field test, a finite-element model was also used for determination of lateral load distribution and yielded predictions similar to measured results. The results from the finite-element models were often less conservative than the code provisions.     

Live Load Distribution in Girder Bridges Subject to Oversized Trucks

A significant challenge facing motor carriers and engineers in this nation is the limitation of vehicle size and weight based on pavement and bridge capacity. However, the current demands of society and industry occasionally require a truck to carry a load that exceeds the size and weight of the legal limit. In these cases, engineering analysis is required before a permit is issued to ensure the safety of the structures and roadways on the vehicle's route. A truck with a wheel gauge larger than the standard 1.83 m (6 ft) gauge requires additional engineering effort because the wheel load girder distribution factors (GDFs) established by AASHTO cannot be used to accurately estimate the live load in the girders. In this study, the finite-element method is used to develop modification factors for the AASHTO flexure and shear GDFs to account for oversized trucks. The results of the analysis showed that the use of the proposed modification factors with the specification-based GDFs can help increase the allowable loads on slab-on-girder bridges.     

Live-Load Analysis of a Curved I-Girder Bridge

Horizontally curved, steel girder bridges are often used in our modern infrastructural system. The curve in the bridge allows for a smother transition for traffic, which creates better road travel. However, some of the disadvantages of horizontally curved bridges are that they are more difficult to analyze, design, and sometimes construct in comparison to conventional straight bridges. This study focuses on a three-span, curved steel I-girder bridge which was tested under three boundary condition states to determine it’s response to live load. The measured live-load strains were used to calibrate a finite-element model. The finite-element design moments and distribution factors for the three condition states were then compared with the results based on the V-load method. These different boundary conditions provided the researchers a unique opportunity to evaluate the impact that these changes had on the bridges behavior. It was found that while the V-load method produced positive bending moments that were close to the finite-element moments for some of the girders, this was a result of the V-load moment being unconservative and the distribution factor being conservative.     

Development and Implementation of a Continuous Strain Monitoring System on a Multi-Girder Composite Steel Bridge

This paper describes the implementation and evaluation of a long-term strain monitoring system on a three-span, multisteel girder composite bridge located on the interstate system. The bridge is part of a network of bridges that are currently being monitored in Connecticut. The three steel girders are simply supported, whereas the concrete slab is continuous over the interior supports. The bridge has been analyzed using the standard AASHTO Specifications and the analytical predictions have been compared with the field monitoring results. The study has included determination of the location of the neutral axes and the evaluation of the load distributions to the different girders when large trucks cross the bridge. A finite-element analysis of the bridge has been carried out to further study the distribution of live load stresses in the steel girders and to study how continuity of the slabs at the interior joints would influence the overall behavior. The results of the continuous data collection are being used to evaluate the influence of truck traffic on the bridge and to establish a baseline for long-term monitoring.     

Design Recommendations for a FRP Bridge Deck Supported on Steel Superstructure

No appropriate provisions from either AASHTO Standard (2002) or AASHTO LRFD (2004) bridge design specifications are available for the design of fiber-reinforced polymer (FRP)-deck-on-steel-superstructure bridges. In this research, a parametric study using the finite-element method (FEM) is conducted to examine two design issues concerning the design of FRP-deck-on-steel-superstructure bridges, namely deck relative deflection and load distribution factor (LDF). Results show that the strip method specified in AASHTO LRFD specification as an approximate method of analysis, can also be applied to FRP decks as a practical method. However, different strip width equations have to be determined by either FEM or experimental methods for different types of FRP decks. In this study, one such equation has been derived for the Strongwell deck. In addition, both FEM results and experimental measurements show that the AASHTO LDF equations for glued laminated timber decks on steel stringers provide good estimations of LDF for FRP-deck-on-steel-superstructure bridges. Finally, it is found that the lever rule can be used as an appropriately conservative design method to predict the LDF of FRP-deck-on-steel-superstructure bridges.     

Stability Bracing Requirements for Steel Bridge Girders with Skewed Supports

Cross frames and diaphragms are critical elements for the stability of I-shaped steel bridge girders during construction. The AASHTO specifications are relatively vague with regards to the stability design requirements of the braces. Spacing limits that have been used in past AASHTO specifications have been removed from the Load and Resistance Factor Design Specification, which instead requires the bracing to be designed by a rational analysis. Whereas the AASHTO specification does not define what constitutes a rational analysis, stability bracing systems must possess adequate stiffness and strength. The commercially available software packages that are typically used in bridge design generally do not have the capabilities to determine the adequacy of the bracing from a stability perspective. This paper outlines the stability bracing requirements for bridges with normal and skewed supports. The effects of support skew on the stiffness and strength requirements for stability bracing are addressed. Solutions that are available for systems with normal supports were modified to account for the effects of the support skew angle. Two orientations of the intermediate bracing were considered: parallel to the skew angles and perpendicular to the longitudinal girder axis. The solutions are presented and compared with finite-element results. The design solutions have good agreement with the finite-element solutions.     

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.     

Shear Capacity of Hybrid Plate Girders

The AASHTO LRFD Bridge Design Specifications, in versions up to and including the 2003 interim, limit the shear resistance of hybrid steel I-girders to the shear buckling or shear yield load and prevent consideration of the additional capacity due to tension field action, which homogeneous girders are allowed to include. This limitation severely affected the economy of girders utilizing high-performance steel, whose optimum configuration is often hybrid. Therefore, an experimental investigation was initiated by the National Bridge Research Organization at the University of Nebraska-Lincoln to address the limitation on the consideration of tension field action in hybrid girders. This paper presents the findings of that research. Eight simply supported steel I-girders were designed, constructed, and loaded to failure to investigate their failure mechanisms and shear capacities. All girders tested were capable of supporting loads greater than those predicted, considering full contribution from tension field action. Further, despite the coincidence of high levels of both shear and moment, relative to their respective capacities, the specimens were all capable of supporting loads greater than those predicted if shear and moment interaction were ignored. Due in part to the results of the research being presented, modifications appeared in the 2004 version of the AASHTO LRFD bridge design specifications such that the shear strength provisions apply equally to both hybrid and homogeneous girders.     

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.     

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.     

Ultimate Capacity Destructive Testing and Finite-Element Analysis of Steel I-Girder Bridges

Current bridge design and rating techniques are based at the component level and thus cannot predict the ultimate capacity of bridges, which is a function of system-level interactions. While advances in computer technology have made it possible to conduct accurate system-level analyses, which can be used to design more efficient bridges and produce more accurate ratings of existing structures, the knowledge base surrounding system-level bridge behavior is still too small for these methods to be widely considered reliable. Thus, to advance system-level design and rating, a 1/5-scale slab-on-steel girder bridge was tested to ultimate capacity and then analytically modeled. The test demonstrated the significant reserve capacity of the steel girders, and the response of the specimen was governed by the degradation of the reinforced-concrete deck. To accurately capture the response of the specimen in an analytical model, the degradation of the deck and other key features of the specimen were modeled by using a dynamic analysis algorithm in a commercially available finite-element analysis program ABAQUS.     

Influence of Parapets and Aspect Ratio on Live-Load Distribution

Significant discrepancies in girder distribution factors have been observed between actual bridge field-testing results and AASHTO code predictions. One of the reasons for the discrepancies is that code methods fail to account for the existence of secondary members such as parapets in bridges. This research investigates the effects of parapets and bridge aspect ratio on live-load moment distribution for bridge girders. The influence on distribution factors of parapets with varying overhang lengths and of aspect ratio with varying roadway width is investigated. To study the effects of parapets and aspect ratios, 34 two-span continuous bridges with a 0° or a 45° skew angle and with varied structure parameters are analyzed using the finite element method. The distribution factors obtained from these analyses are compared with those from the AASHTO methods. The presence of parapets is shown to reduce distribution factors by as much as 36 and 13% for exterior and interior girders, respectively. The effect of parapets is slightly less for skewed bridges. Aspect ratio is shown to have very little effect on distribution factors until the ratio exceeds 1.8.