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.     

Live-Load Distribution Factors in Prestressed Concrete Girder Bridges

This paper presents an evaluation of flexural live-load distribution factors for a series of three-span prestressed concrete girder bridges. The response of one bridge, measured during a static live-load test, was used to evaluate the reliability of a finite-element model scheme. Twenty-four variations of this model were then used to evaluate the procedures for computing flexural live-load distribution factors that are embodied in three bridge design codes. The finite-element models were also used to investigate the effects that lifts, intermediate diaphragms, end diaphragms, continuity, skew angle, and load type have on distribution factors. For geometries similar to those considered in the development of the American Association of State Highway and Transportation Officials Load and Resistance Factor Design Specifications, the distribution factors computed with the finite-element models were within 6% of the code values. However, for the geometry of the bridge that was tested, the discrepancy was 28%. Lifts, end diaphragms, skew angle, and load type significantly decreased the distribution factors, while continuity and intermediate diaphragms had the least effect. If the bridge had been designed using the distribution factors calculated with the finite-element model rather than the code values, the required concrete release strength could have been reduced by 6.9 MPa (1,000 psi) or the live load could have been increased by 39%.     

Effects of Edge-Stiffening Elements and Diaphragms on Bridge Resistance and Load Distribution

This research investigates the effects of barriers, sidewalks, and diaphragms (secondary elements) on bridge structure ultimate capacity and load distribution. Simple-span, two-lane highway girder bridges with composite steel and prestressed concrete girders are considered. The finite-element method is used for structural analysis. For the elastic range, typical secondary elements can reduce girder distribution factors (GDF) between 10 and 40%, depending on stiffness and bridge geometry. For the inelastic response, steel is modeled using von Mises yield criterion and isotropic (work) hardening. Concrete is modeled with a softening curve in compression with the ability to crack in tension. At ultimate capacity, typical secondary elements can reduce GDF an additional 5 to 20%, and bridge system ultimate capacity can be increased from 1.1 to 2.2 times that of the base bridge without secondary elements, depending on bridge geometry and secondary-element dimensions.     

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.     

Girder Differential Deflection and Distortion-Induced Fatigue in Skewed Steel Bridges

The prevalence of fatigue cracking in steel bridge girders due to out-of-plane web distortion motivates development of procedures to evaluate the effects of distortional fatigue. In a previous study sponsored by the Minnesota Department of Transportation (Mn/DOT) the frequency and magnitude of distortional stresses on a typical skewed, steel bridge with staggered, bent-plate diaphragms were assessed. The results revealed a diaphragm deformation mechanism that causes distortional fatigue in the girder web gap, leading to simple, accurate estimates of fatigue stress if bridge properties and differential vertical deflection between girders are known. In the present study, linear finite element models are used to represent composite steel bridges and identify bridge parameters that influence relative deflection of adjacent girders. Parameters found to have a significant effect on differential deflection include girder spacing, angle of skew, span length, and deck thickness. These results are incorporated in a simple procedure that is intended for use in management schemes for skewed, steel-girder bridges, with staggered, bent-plate diaphragms, susceptible to web gap distortional fatigue.     

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 Intermediate Diaphragms on Decked Bulb-Tee Bridge System for Accelerated Construction

One of the promising systems for accelerated bridge construction is the use of the decked precast prestressed concrete girders or decked bulb-tee girders for the bridge superstructure. Using the calibrated three-dimensional finite-element models through field tests, a parametric study was conducted to determine the effect of intermediate diaphragms on the deflections and flexural strains of girders at the midspan as well as the live load forces in the longitudinal joint. The following diaphragm details were considered: different diaphragm types (steel and concrete), different diaphragm numbers between two adjacent girders, and different cross-sectional areas for steel diaphragms. Five bridge models with different diaphragm details were developed, and the short span length effect on the bridge behavior was also studied. It was found that as long as one intermediate diaphragm was provided between two adjacent girders at midspan, changing the diaphragm details did not affect the girder deflection, the girder strain, and the live load forces in the longitudinal joint significantly. The effect of diaphragms on the midspan deflection was more prominent in the short span bridge; however, the reduction in the maximum bending moment by the diaphragms was more significant in the long span bridge than in the short span bridge. Specific design recommendation is provided in this paper.     

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.     

Influence of Skew Angle on Reinforced Concrete Slab Bridges

The effect of a skew angle on simple-span reinforced concrete bridges is presented in this paper using the finite-element method. The parameters investigated in this analytical study were the span length, slab width, and skew angle. The finite-element analysis (FEA) results for skewed bridges were compared to the reference straight bridges as well as the American Association for State Highway and Transportation Officials (AASHTO) Standard Specifications and LRFD procedures. A total of 96 case study bridges were analyzed and subjected to AASHTO HS-20 design trucks positioned close to one edge on each bridge to produce maximum bending in the slab. The AASHTO Standard Specifications procedure gave similar results to the FEA maximum longitudinal bending moment for a skew angle less than or equal to 20°. As the skew angle increased, AASHTO Standard Specifications overestimated the maximum moment by 20% for 30°, 50% for 40°, and 100% for 50°. The AASHTO LRFD Design Specifications procedure overestimated the FEA maximum longitudinal bending moment. This overestimate increased with the increase in the skew angle, and decreased when the number of lanes increased; AASHTO LRFD overestimated the longitudinal bending moment by up to 40% for skew angles less than 30° and reaching 50% for 50°. The ratio between the three-dimensional FEA longitudinal moments for skewed and straight bridges was almost one for bridges with skew angle less than 20°. This ratio decreased to 0.75 for bridges with skew angles between 30 and 40°, and further decreased to 0.5 as the skew angle of the bridge increased to 50°. This decrease in the longitudinal moment ratio is offset by an increase of up to 75% in the maximum transverse moment ratio as the skew angle increases from 0 to 50°. The ratio between the FEA maximum live-load deflection for skewed bridges and straight bridges decreases in a pattern consistent with that of the longitudinal moment. This ratio decreased from one for skew angles less than 10° to 0.6 for skew angles between 40 and 50°.     

Experimental Determination of Resistance Characteristics of Support Details Used in Prestressed Concrete Bridge Girders

Static load tests were performed on support details used at the ends of prestressed concrete pedestrian bridge girders to determine the resistance characteristics of girder supports in the direction perpendicular to the longitudinal axis of the girders. The specimens tested represent support details that have also been widely used in prestressed concrete highway bridges in Minnesota and in other states. Two specimens, one representing the free-end detail and one representing the restrained-end detail were subjected to a combination of vertical and lateral loads. The applied loading was intended to simulate the loading conditions to which the girder ends would be subjected in the event of an over-height vehicle collision with the bridge. The tests revealed two types of lateral load resisting mechanisms depending on the type of support detail. The specimen with the free-end detail resisted the lateral loading through sliding friction between the components of the support assembly. Deformation of this specimen was a combination of shear deformation of the bearing pad and sliding of various support components. The restrained-end detail exhibited larger lateral load capacity than the free-end detail due to the resistance provided by the anchor rods that were intended to prevent the lateral movement of the girder ends. Failure of the specimen with restrained-end detail was due to the concrete breakout and bending of the anchor rods.     

Rating and Reliability of Existing Bridges in a Network

Currently, the load rating is the method used by State DOTs for evaluating the safety and serviceability of existing bridges in the United States. In general, load rating of a bridge is evaluated when a maintenance, improvement work, change in strength of members, or addition of dead load alters the condition or capacity of the structure. The AASHTO LRFD specifications provide code provisions for prescribing an acceptable and uniform safety level for the design of bridge components. Once a bridge is designed and placed in service, the AASHTO Manual for Condition Evaluation of Bridges provides provisions for determination of the safety and serviceability of existing bridge components. Rating for the bridge system is taken as the minimum of the component ratings. If viewed from a broad perspective, methods used in the state-of-the-practice condition evaluation of bridges at discrete time intervals and in the state-of-the-art probability-based life prediction share common goals and principles. This paper briefly describes a study conducted on the rating and system reliability-based lifetime evaluation of a number of existing bridges within a bridge network, including prestressed concrete, reinforced concrete, steel rolled beam, and steel plate girder bridges. The approach is explained using a representative prestressed concrete girder bridge. Emphasis is placed on the interaction between rating and reliability results in order to relate the developed approach to current practice in bridge rating and evaluation. The results presented provide a sound basis for further improvement of bridge management systems based on system performance requirements.     

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.     

Verification of Incremental Launching Construction Safety for the Ilsun Bridge, the World’s Longest and Widest Prestressed Concrete Box Girder with Corrugated Steel Web Section

The Ilsun Bridge is the world’s longest (801?m in total length) and widest (30.9?m in maximum width) prestressed concrete box girder bridge incorporating a corrugated steel web. This bridge has fourteen spans, twelve of which were erected using an incremental launching method, a method that is rarely applied in this type of bridge. To verify the construction safety of the Ilsun Bridge, this investigation focuses on the span-to-depth ratio, buckling shear stress of the corrugated steel webs, optimization of the length of the steel launching nose, detailed construction stage analysis, and the stress level endured by the corrugated steel webs during the launching process. The span-to-depth ratio of the Ilsun Bridge was found to be well-designed, using a conservative corrugated steel web design. Further, our investigation revealed that the conventional nose-deck interaction equation was not suitable for corrugated steel web bridges. As a result, a detailed construction stage analysis and measurements of this bridge was performed to examine stress levels and ensure safety during the erection process. The results revealed that there are essential design issues that should be considered when designing prestressed concrete box girder bridges with corrugated steel webs and that, when constructing them, the incremental launching method should be used.     

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.     

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.     

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.     

Influence of Secondary Elements and Deck Cracking on the Lateral Load Distribution of Steel Girder Bridges

The AASHTO LRFD load distribution factor equation was developed based on elastic finite element analysis considering only primary members, i.e., the effects of secondary elements such as lateral bracing and parapets were not considered. Meanwhile, many bridges have been identified as having significant cracking in the concrete deck. Even though deck cracking is a well-known phenomenon, the significance of pre-existing cracks on the live load distribution has not yet been assessed. The purpose of this research is to investigate the effect of secondary elements and deck cracking on the lateral load distribution of girder bridges. First, secondary elements such as diaphragms and parapets were modeled using the finite element method, and the calculated load distribution factors were compared with the code-specified values. Second, the effects of typical deck cracking and crack types that have a major effect on load distribution were identified through a number of nonlinear finite element analyses. It was established that the presence of secondary elements may produce load distribution factors up to 40% lower than the AASHTO LRFD values. Longitudinal cracking was found to increase the load distribution factor by up to 17% when compared to the LRFD value while the transverse cracking was found to not significantly influence the transverse distribution of moment.     

Experimental Study on Prefabricated Concrete Bridge Girder-to-Girder Intermittent Bolted Connections System

This paper reports on a new bridge deck slab flange-to-flange connection system for precast deck bulb tee (DBT) girders. In prefabricated bridge system made of DBT girders, the concrete deck slab is cast with the prestressed girder in a controlled environment at the fabrication facility and then shipped to the bridge site. This system requires that the individual prefabricated girders be connected through their flanges to make it continuous for live load distribution. The objectives of this study are to develop an intermittent bolted connection for DBT bridge girders and to provide experimental data on the ultimate strength of the connection system. This includes identifying the crack formation and propagation, failure mode, and ultimate load carrying capacity. In this study, three different types of intermittent bolted connection were developed. Four actual-size bridge panels were fabricated and then tested to collapse. The effects of the size and the level of the fixity of the connecting steel plates, as well as the location of the wheel load were examined. The developed joint was considered successful if the experimental wheel load satisfied the requirements specified in North American bridge codes. It was concluded that location of the wheel load at the deck slab joint affected the ultimate load carrying capacity of the connections developed. Failure of the joint was observed to be due to either excessive deformation and yielding of the connecting steel plates or debonding of the embedded studs in concrete.     

Effect of Edge Stiffening and Diaphragms on the Reliability of Bridge Girders

Secondary elements such as barriers, sidewalks, and diaphragms may affect the distribution of live load to bridge girders. The objective of this study is to evaluate their effect on girder reliability if these elements are designed to be sufficiently attached to the bridge so as not to detach under traffic live loads. Simple-span, two-lane structures are considered, with composite steel girders supporting a reinforced concrete deck. Several representative structures are selected, with various configurations of barriers, sidewalks, and diaphragms. Bridge analysis is performed using a finite-element procedure. Load and resistance parameters are treated as random variables. Random variables considered are composite girder flexural strength, secondary element stiffness, load magnitude (dead load and truck traffic live load), and live load position. It was found that typical combinations of secondary elements have a varying influence on girder reliability, depending on secondary element stiffness and bridge geometry. Suggestions are presented that can account for secondary elements and that provide a uniform level of reliability to bridge girders.