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°.     

Live Load Distribution for Steel Girder Bridges

This paper deals with distribution of truck load on girder bridges. Previous analytical studies based on finite-element method indicated that AASHTO code-specified girder distribution factors (GDFs) are inaccurate. In particular, GDFs appear to be conservative for longer spans and larger girder spacing, but too permissive for short spans and girder spacings. Therefore, a field testing program was carried out including about 20 steel girder bridges with spans up to 45 m. For each tested structure, GDFs were determined by measuring strains in the girders under heavy trucks. Test trucks were 11-axle vehicles, loaded to the legal limit in Michigan (over 650 kN). The strains were recorded for a single truck and for two trucks side-by-side. The tests were repeated for crawling speed and normal traffic speed for the location. In all tested bridges, the GDFs determined from the field measurements are lower than code-specified values. In addition, the considered bridges were analyzed using a commercial finite-element software package, ABAQUS. The analytical results were compared with those from field tests. It was observed that the maximum values of the strain and corresponding stress are lower than analytical values obtained using ABAQUS. The reason for this discrepancy is unintended composite action and partial fixity of supports (rather than simple supports).     

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%.     

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.     

Load Distribution Factors in Simply Supported Skew Bridges

Simply supported bridges consisting of five I-section concrete girders are analyzed using the finite-element method. The main parameters of this study are: girder spacing (1.8–2.7 m), span length (25–35 m), skew angle (0–60°), and different arrangements of internal transverse diaphragms. Results of reliable analysis based on the finite-element method show that, in right bridges, American Association of State Highway and Transportation Officials distribution factors are conservative and in skew bridges, these factors are very conservative.     

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.     

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.     

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.     

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.     

Short-Term Strain Monitoring of Bridge Structures

This report demonstrates how short-term field monitoring can be used to evaluate bridges when problems occur. A portable strain monitoring system with software has been used to study four different bridges. Studies to determine load-carrying capacities, causes of cracking, and load distributions are included. The work demonstrates that analytical predictions of stress∕strain levels, load distributions, and fatigue estimations are conservative. Analytical models based on conservative assumptions are suitable for the design of new bridges, but when problems occur in existing bridges, field testing combined with careful analysis can provide much more accurate answers to assist engineers on proper courses of action for repair. The field monitoring reported in this study has resulted in substantial savings in the cost and time needed in renovation and∕or repairs.     

Assessment of Bridge Remaining Fatigue Life through Field Strain Measurement

With the aging of existing steel bridges and the accumulated stress cycles under traffic loads, assessment of remaining fatigue life for continuing service has become more important than ever, especially for decisions on structure replacement, deck replacement, or other major retrofits. Experience from engineering practice indicates that fatigue analysis based on specification loads and distribution factors usually underestimates the remaining fatigue life of existing bridges by overestimating the live load stress ranges. Fatigue evaluation based on field-measured stress range histograms under actual traffic load proves to be a more accurate and efficient method for existing bridges. This paper describes the application of such a method in assessing the remaining fatigue life of bridge structures. Current AASHTO specifications for fatigue evaluation of existing bridges are reviewed and compared. Case studies of three major highway bridges are discussed. Finally, a procedure is proposed for evaluating fatigue life of existing bridges through field strain measurement.     

Distribution of Wheel Loads on Continuous Steel Spread-Box Girder Bridges

Composite concrete-steel spread (multispine) box girder bridges remain one of the most common types constructed. Current design practices in North America recommend few analytical methods for the design of such bridges in simply supported construction. However, the effects of continuous construction have not been dealt with fully. In designing a continuous bridge, it is important to determine the maximum negative and positive stresses, maximum reactions, and shears in the bridge subjected to various loadings. This paper presents an extensive parametric study using a finite-element model in which 60 continuous bridge prototypes of various geometries, each subjected to various loading conditions, are analyzed for the distribution of flexural stresses, deflection, shears, and reactions. The parameters considered in the study are span length, number of spread boxes, and number of lanes. Distribution factors for maximum flexural stresses, deflection, shears, and reactions, suitable for design, are deduced for AASHTO truck loading. Results from tests on five box girder bridge models verify the finite-element model. A design example is presented to illustrate the use of the deduced formulas for the distribution factors.     

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.     

Shear Live-Load Distribution Factors for I-Girder Bridges

A full scale, single lane test bridge was used to evaluate a typical slab-on-girder bridge’s response to shear. The results of the shear load test provided the means to evaluate the level of detail for a finite element model that is required to accurately replicate the behavior of bridges subject to shear loads. This finite element modeling scheme was then used to evaluate more than 200 finite element bridge models. The bridge models investigated the effects of girder spacing, span length, overhang distance and skew angle on the shear live-load distribution factor. The finite element shear distribution factors were compared with those calculated according to the American Association of State Highway and Transportation Officials load and resistance factor design (AASHTO LRFD) specifications. It was found that the AASHTO LRFD procedure accurately predicted the shear distribution factor for changes in girder spacing and span length. However, the LRFD shear distribution factor for the exterior girder was found to be unconservative for certain overhang distances and overly conservative for the interior girder for higher skew angles. Alternative equations are provided for the single and multilane exterior girder correction factor.     

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.     

Simplified Method of Lateral Distribution of Live Load Moment

This paper introduces a simplified method, known as Henry’s method, for the calculation of distribution factors of the live load moment. Using the simplified method, the live load effects are equally distributed in all beams, including interior and exterior beams. This method has been used in Tennessee for nearly four decades. It offers advantages in simplicity of calculation and flexibility in application. To carefully examine the simplified method, 24 actual bridges of six different types of superstructures were selected for the study. The distribution factors of actual bridges using Henry’s method were compared with the ones from the AASHTO LRFD, the AASHTO standard, and finite-element analysis. In the comparison study, the effects of bridge superstructure types and key parameters that significantly affected the calculation of distribution factors are discussed. Based on the results of the comparison and evaluation, a modified Henry’s method was proposed by introducing modification factors to Henry’s method. With proper modification, the simplified method can be used to determine reasonable and reliable distribution factors of the live load moment.     

Impact of Posted Load Limits on Highway Bridge Reliability

The effectiveness of posted load limits in reducing annual maximum live load effects, thus enhancing bridge reliability, is investigated for 12 and 40 m simple span highway bridges. Novel analytical expressions are derived for event gross vehicle weight (GVW) distributions that account for violation of posted load restrictions, and the corresponding annual maximum GVW distributions are presented. Annual reliability indices associated with load restrictions computed using typical bridge posting criteria and different compliance levels are compared to the target reliability index. For the case of perfect compliance, a posted load restriction can significantly reduce maximum annual live load effects and so enhance the reliability. Under imperfect compliance, however, a violation rate as low as 2.5% (i.e., one illegal truck in 40 ignores the posting) causes the mean value and variability of the annual maximum live load effect distribution to increase significantly, resulting in a significant loss in reliability. Thus, unless posted loads are strictly enforced, the effectiveness of enhancing existing bridge reliability with a posted load restriction is questionable.     

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.     

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.     

Quantifying Field-Test Behavior for Rating Steel Girder Bridges

Field testing is valuable for evaluating existing bridges. It allows the owner to reduce the conservatism of analytical rating methods and safely rate the bridge for higher loads. Many factors not considered in design contribute to the response of a tested bridge. Several of these, like actual load distribution and additional stiffness from curbs and railings, are welcome benefits that can be used to increase load ratings. However, there are also contributions from bearing restraint forces and unintended composite action that may not be reliable during the bridge's service life. These factors tending to increase the load capacity need to be separated and quantified so that the bridge owner can: (1) confirm the origin of the useable benefit; and (2) remove the unwanted contributions. Presented are procedures for load rating steel girder bridges through field testing. A systematic approach is presented to separate and quantify the contributions from various effects. Therefore, the responsible engineer can remove the unwanted contributions and justify an experimental load rating. The procedures are demonstrated for a three-span steel girder bridge.