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°.     

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.     

Higher Level Evaluation of a Reinforced Concrete Slab Bridge

In New Mexico, many reinforced concrete slab (RCS) bridges provide service on interstates I-10, I-25, and I-40. The load rating for this type of bridge largely depends on the live-load moment in the slab. Consequently, the objective of this study was to determine a more accurate value for the equivalent strip width using higher level evaluation techniques. A continuous RCS bridge was evaluated starting with an AASHTO load and resistance factor rating analysis. A diagnostic test was then conducted to measure live-load strains which showed that the slab stiffness fit within cracked and gross section behavior. Furthermore, slab moments from finite element analysis agreed reasonably well with experimental moments derived using the average of the cracked and gross section modulus. From refined analysis, the equivalent strip widths for positive moment were 26.1 and 22.1% greater than those calculated by the AASHTO approximate method for the exterior and interior spans, respectively. The refined widths for negative moment were greater than AASHTO by 13.1 and 11.1%. This increase in the equivalent strip width reduced the live-load effects, which proportionally increased the rating factors.     

Lateral Load Distribution in Curved Steel I-Girder Bridges

The purpose of this paper is to develop new formulas for live load distribution in horizontally curved steel I-girder bridges. The formulas are developed by utilizing computer model results for a number of different horizontally curved steel I-girder bridges. The bridges used in this study are modeled as generalized grillage beam systems composed of horizontally curved beam elements for steel girders and substructure elements for lateral wind bracing and cross frames which consist of truss elements. Warping torsion is taken into consideration in the analysis. The effect of numerous parameters, including radius of curvature, girder spacing, overhang, etc., on the load distribution are studied. Key parameters affecting live load distribution are identified and simplified formulas are developed to predict positive moment, negative moment, and shear distribution for one-lane and multiple-lane loading. Comparisons of the formulas with finite element method and grillage analysis show that the proposed formulas have more accurate results than the various available American Association of State Highway and Transportation Officials specifications. The formulas developed in this study will assist bridge engineers and researchers in predicting the actual live load distribution in horizontally curved steel I-girder bridges.     

Live Load Radial Moment Distribution for Horizontally Curved Bridges

The present study is designed to determine the effect of major parameters on maximum total bending moments of curved girders, establish the relationship between key parameters and girder distribution factors (GDFs), and develop new approximate distribution factor equations. A level of analysis study using three numerical models was performed to establish an appropriate numerical modeling method on the basis of field test results. A total of 81 two-traffic lane curved bridges were analyzed under HL-93 loading. Two approximate GDF equations were developed based on the data obtained in this study: (1) a single GDF based on total girder normal stress; and (2) a combined GDF treating bending and warping normal stress separately. The two equations were developed based on both an averaged coefficient method and regression analysis. A goodness-of-fit test revealed that the combined GDF model developed by regression analysis best predicted GDFs. The present study demonstrated that radius, span length, cross frame spacing and girder spacing most significantly affect GDFs. The proposed GDF equations are expected to provide a more refined live load analysis for preliminary design.     

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.     

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.     

Seismic Performance Assessment of Simply Supported and Continuous Multispan Concrete Girder Highway Bridges

Seismic evaluations of typical concrete girder bridges are conducted for both a multispan simply supported and a multispan continuous girder bridge common to the Central and Southeastern United States. These evaluations are performed for an approximate hazard level of 2% in 50?years by performing nonlinear time history analyses on three-dimensional analytical models. The results show significant vulnerabilities in the reinforced concrete columns, the abutments, and also in unseating of the girders. In general, the longitudinal loading of the bridges results in larger demands than the transverse loading. However, the simply supported bridge sustains bearing deformations in the transverse direction which are on the same order as their longitudinal response. These results suggest that both longitudinal and transverse loading are significant and should be considered when performing seismic hazard analyses of these bridges.     

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.     

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 Configuration and Lateral Distribution of NATO Wheeled Military Trucks for Steel I-Girder Bridges

This paper presents the lateral load distribution of various North Atlantic Treaty Organization (NATO) wheeled military trucks on a simple-span steel I-girder bridge (L = 36?m). The military trucks are classified into the military load classification (MLC) system. The MLC trucks demonstrate different load configurations when compared to the standard HS20 truck in terms of wheel-line spacing, number of axles, and weight. A calibrated three-dimensional finite-element analysis is conducted to examine the MLC load effects. The applicability of the AASHTO LRFD provisions is evaluated using 72 different load models. The wheel-line spacing and weight of the MLC trucks cause different flexural behavior and load distributions of the bridge when compared to those of HS20. The current AASHTO LRFD approach to determine live load distribution factors may be reasonably applicable to the MLC trucks, including approximately 20% of conservative predictions.     

Live-Load Distribution Factors for Concrete Box-Girder Bridges

The current American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design (LRFD) Specifications impose fairly strict limits on the use of its live-load distribution factor for design of highway bridges. These limits include requirements for a prismatic cross section, a large span-length-to-width ratio, and a small plan curvature. Refined analyses using 3D models are required for bridges outside of these limits. These limits place severe restrictions on the routine design of bridges in California, as box-girder bridges outside of these limits are frequently constructed. This paper presents the results of a study investigating the live-load distribution characteristics of box-girder bridges and the limits imposed by the LRFD specifications. Distribution factors determined from a set of bridges with parameters outside of the LRFD limits are compared with the distribution factors suggested by the LRFD specifications. For the range of parameters investigated, results indicated that the current LRFD distribution factor formulas generally provide a conservative estimate of the design bending moment and shear force.     

Identification of a Distribution of Stiffness Reduction in Reinforced Concrete Slab Bridges Subjected to Moving Loads

The method for identifying arbitrary stiffness reduction in damaged reinforced concrete slab bridges under moving loads is proposed and dynamic signals measured at several points are used as response data to reflect the properties of the moving loads sensitivity. In particular, the change in stiffness in each element before and after damage, based on the system identification method, is described and discussed by using a modified bivariate Gaussian distribution function. The proposed method in this work is more feasible than the conventional element-based damage detection method from the computational efficiency because the procedure of finite-element analysis coupled with microgenetic algorithm using six unknown parameters irrespective of the number of elements are considered. The validity of the technique is numerically verified using a set of dynamic data obtained from a simulation of the actual bridge modeled with a three-dimensional solid element. The numerical calculations show that the proposed technique is a feasible and practical method that can prove the exact location of a damaged region as well as inspect the complex distribution of deteriorated stiffness, although there is a modeling error between actual bridge results and numerical model results as well as a measurement error like uncertain noise in the response data.     

Distribution Factors for Curved Continuous Composite Box-Girder Bridges

The use of horizontally curved composite box-girder bridges in modern highway systems has become increasingly popular for economic as well as for aesthetic considerations. Based on a recent literature review on the design of box-girder bridges, it was observed that a simple design method for curved bridges, based on load distribution factors for stresses and shears, is as yet unavailable. This paper presents the results of an extensive parametric study, using a finite element method, in which the structural responses of 240 two-equal-span continuous curved box-girder bridges of various geometries were investigated. The parameters considered in this study included span-to-radius of curvature ratio, span length, number of lanes, number of boxes, web slope, number of bracings, and truck loading type. Based on the data generated from this study, empirical formulas for load distribution factors for maximum longitudinal flexural stresses and maximum deflection due to dead load as well as AASHTO live loading were deduced. An illustrative design example is presented.     

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.     

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.     

Sensitivity of Live Load Distribution Factors to Vehicle Spacing

Two slab-on-girder bridge superstructures are analyzed using grillage models. Different live load placement configurations are investigated to determine the sensitivity of live load shear and moment to vehicle spacing. Results from both bridges show that the distribution factors are relatively insensitive to vehicle spacing. Therefore significant computational speedups are available when applying vehicle loads on an influence surface with a fixed spacing.     

Application of Suspension Bridges Stiffened by Prestressed Concrete Slabs in China

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

Dynamic Behavior of Deck Slabs of Concrete Road Bridges

This paper treats the dynamic effect of traffic actions on the deck slabs of concrete road bridges using the finite-element method. All the important parameters that influence bridge-vehicle interaction are studied with a systematic approach. An advanced numerical model is described and the results of a parametric study are presented. The results suggest that vehicle speed is less important than vehicle mass and that road roughness is the most important parameter affecting the dynamic behavior of deck slabs. The type of bridge cross section was not found to have a significant influence on deck slab behavior. The dynamic amplification factor varied between 1.0 and 1.55 for the bridges and vehicles studied. These results should be validated by further work.     

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.