Multicell Box Girder Bridges Research Articles

Development of Live Load Distribution Factor Equation for Concrete Multicell Box-Girder Bridges under Vehicle Loading

The evaluation and design of concrete bridges in large part depend on the transverse distribution characteristics of the live load carried and the service level. The live load distribution for continuous concrete multicell box-girder bridges varies according to bridge configuration, so when designing such bridges, it is important to determine the maximum negative stress at the piers, the midspan positive (tensile) stress and the deflection of the bridge when subjected to live loads. This paper reports an extensive parametric study to determine the maximum stress, deflection, and moment distribution factors for two span multicell box-girder bridges based on a finite element analysis of 120 representative numerical model bridges. Bridge parameters were selected to extend the parameters and ranges of current live load distribution factors defined by AASHTO LRFD specifications. The results indicate that the span length, number of boxes, and the number of lanes all significantly affect the positive (tensile) and the negative (compression) stress distribution factors. A set of equations proposed to describe the behavior of such bridges under AASHTO LRFD live loads yielded results that agreed closely with the numerically derived results for the stress and deflection distribution factors.

Load Distribution Factors for Composite Multicell Box Girder Bridges

Cellular steel section composite with a concrete deck is one of the most suitable superstructures in resisting torsional and warping effects induced by highway loading. This type of structure has inherently created new design problems for engineers in estimating its load distribution when subjected to moving vehicles. Indian Codes of Practice does not provide any specific guidelines for the design of straight composite concrete deck–steel multi-cell bridges. To meet the practical requirements arising during the design process, a simple design method is needed for straight composite multi-cell bridges in the form of load distribution factors for moment and shear. This work presents load distribution characteristics of straight composite multi-cell box girder bridges under IRC trains of loads.

Live Load Distribution Factor at the Piers of Skewed Continuous Multicell Box Girder Bridges Subjected to Moving Loads

The multicell box girder bridge is a popular choice of designers because of its large torsional stiffness. The skewness at the support line of bridges has a significant influence on distribution of live loads. The current American bridge design code, AASHTO load and resistance factor design (LRFD), defines several correction factor expressions to account for the skew effect in bridges. In addition, the effect of skewness on reactions of continuous multicell box girder bridges is obtained by using the skew correction factor of shear or by the shear distribution factor of straight bridges, despite a significant disparity between the shear and reaction that is observed in skewed bridges. This study investigated the effect of skewness on the reactions and shear distribution factors for three continuous multicell box girder bridges. There was a significant difference between reactions at the piers and the shear distribution factors of skewed bridges. Thus, a statistical analysis was used to propose new equations for the skew correction factors and the external girder correction factor of shear and reaction to improve the accuracy of the AASHTO LRFD specifications.

Stress Distribution in Continuous Thin-Walled Multi-Cell Box Girder Bridges

Several researchers have studied stresses in thin-walled box girder bridges but stress distribution in continuous thin-walled multi-cell box girder bridges has not received much attention in published literature. Hence, this research investigated stress distribution in continuous thin-walled multi-cell box girder bridges. Analysis of box girder bridges is complex and the complexity is even more when the box girder is continuous with multi-cells. The modern trend in the analysis is to program the more straightforward methods for ease of computer application. Therefore, the analytical tool for this study is a MATLAB program developed by the authors for the finite strip analysis of continuous thin-walled box girder bridges. Numerical study on stress distribution was carried out on two box girder bridges. The first was a simply supported box girder bridge subjected to eight point loads which was used primarily for comparison with literature. The result obtained by the program was in good agreement with literature. The second was a continuous thin-walled multi-cell box girder bridge subjected to vehicular loads and self weight. The beam theory solution was also used for comparison of results in both cases. The study concluded that under symmetrical loading the longitudinal normal stress, shear stress at end supports, transverse bending moment, and longitudinal bending moment are substantial while the transverse normal stress and twisting moment are negligible. The program can, therefore, be used in practice to determine stress distributions of box girders and prismatic folded plates. However, classical finite strip underestimates stress values at points of high stress concentration. http://dx.doi.org/10.4314/njt.v33i4.5

A simplified method to estimate the fundamental frequency of skew continuous multicell box-girder bridges

Here Fundamental Frequency is the main factor used to calculate the vibration of a vehicle when passing across a bridge. With knowledge of the fundamental frequency, bridges can be evaluated and designed in such a manner so as to avoid the critical range of 1.5 Hz to 4.5 Hz, which is occupied by most vehicles. Therefore it is crucial to develop a reliable method to estimate the fundamental frequency of bridges. To overcome the above issue, numerical analysis combined with a theoretical method is applied to estimate the fundamental frequency of multicell box-girder bridges. The effect of span-length, number of boxes and skew angle on the estimation of this factor is discussed. Finally, reliable expressions are proposed to predict the first fundamental frequency of this type of bridge, and the accuracy of the expressions is verified. The results indicate that the fundamental frequency decreases when span length increases, due to development of crack as well as decrease stiffness of girders.

Effectiveness of Skewness on Dynamic Impact Factor of Concrete Multicell Box-Girder Bridges Subjected to Truck Loads

Evaluation of the dynamic response of bridge–vehicle interaction is an interesting topic in bridge engineering. It is an effective way to develop the accuracy of a new generation of reliability-based bridge design specifications. Traditionally, to consider the effect of moving loads on bridge design, the response of bridges using static loads is amplified by a dynamic load factor (dynamic impact factor). Although a considerable amount of studies has been conducted to determine the dynamic impact factor of bridges, it still remains as a controversial issue. The dynamic impact factor is dependent on the dynamic properties of the superstructure and vehicle such as natural frequency, vehicle speed, and many other parameters, which are difficult to take into account. Underestimating the effect of each parameter on the development of new expressions for dynamic impact factor may lead to substantial problems. Hence, the present study focused on the dynamic behavior of multicell box-girder bridges under moving loads. Firstly, the related literature on the effect of vehicle loads on bridges was reviewed to get closer insights into the dynamic behavior of bridges. The effects of various parameters of bridge on dynamic responses are considered. Dynamic impact factor expressions for skew bridges are deduced based on upper bound values of finding results. The comparisons indicate that the current bridge codes unable to estimate accurate values for dynamic responses of skew bridges.

Effect of intermediate diaphragm on lateral load distribution factor of multicell box-girder bridges

The current American bridge design codes state that intermediate diaphragms should be used to preserve section geometry against accidental overturning of girders and during construction of a bridge. There is inconsistency in practice for the design of intermediate diaphragms, such that most specifications either ignore or underestimate the contribution of these members to the lateral distribution of live load. Current studies indicate that neglecting the effect of intermediate diaphragms might lead to highly conservative values for bending moment distribution factors and result in non-economic designs for skew bridges. This paper reports on a parametric study performed on 160 prototypes of straight and skew concrete multicell box-girder bridges. The obtained results were used to develop practical expressions to account for the diaphragm effects on American Association of State Highway and Transportation Officialsformulas for live load distribution factors. It was observed that decks with internal transverse diaphragms perpendicular to the longitudinal webs are the best arrangement for load distribution in skew bridges. Thus, a sufficient number of diaphragms should be provided between span lengths and over the supports of bridge decks.

Transverse load distribution of skew cast-in-place concrete multicell box - girder bridges subjected to traffic condition

Concrete multicell box-girder bridges are a common choice among the designers for various ranges of bridges. In order to provide safer and greater speed of traffic, the roadway is built as straight as possible. The use of skewed bridges has increased considerably in the recent years for roadway. The skewed bridges have quite different mechanical behavior from the straight bridges, although for skew angles less than 20 degrees, it is reasonably safe to ignore the effect of skew angles and analyze that at the straight bridge. In this study, in developing an analytical solution, an extensive parametric study was carried out to determine the maximum positive and negative stress distribution factors and to calculate the maximum distribution factor of deflection along the mid-span of skewed multicell box-girder bridges. A total of 240 representative bridges numerical models were selected and analyzed using SAP2000 finite element software. It was found that the span length, number of boxes, number of lanes and skew angles significantly affected the distribution factors of stress and deflection. Finally, several equations were proposed for stress and deflection distribution factors of multicell box-girder bridges for the application of American Association of State Highway and Transportation officials load and resistance factor design live loads.

Development of the applicability of simplified Henry’s method for skewed multicell box-girder bridges under traffic loading conditions

Concrete precast multicell box-girder (MCB) bridges combine aesthetics with torsional stiffness perfectly. Previous analytical studies indicate that currently available specifications are unable to consider the effect of the twisting moment (torsional moment) on bridge actions. In straight bridges the effect of torsion is negligible and the transverse reinforced design is governed by other requirements. However, in the case of skewed bridges the effect of the twisting moment should be considered. Therefore, an in-depth study was performed on 90 concrete MCB bridges with skew angles ranging from 0° to 60°. For each girder the bridge actions were determined under the American Association of State Highway and Transportation Officials (AASHTO) live load conditions. The analytical results show that torsional stiffness and live load positions greatly affected the bridges’ responses. In addition, based on a statistical analysis of the obtained results, several skew correction factors are proposed to improve the precision of the simplified Henry’s method, which is widely used by bridge engineers to predict bridge actions. The relationship between the bending moment and secondary moments was also investigated and it was concluded that all secondary actions increase with an increase in skewness.

Analysis of R/C decks in multi-cell box girder bridges under rational wheel load distributions

This paper presents the results of a finite element (FE) study on the analysis of reinforced concrete decks in multi-cell box girder bridges under wheel loading. The deck bending moments were investigated for typical multi-cell box girder bridges wit

Exact distortional behavior and practical distortional analysis of multicell box girders using an expanded method

This paper presents an expanded method for exact distortional behavior of multicell box girders subjected to an eccentric loading. This method decomposes the eccentric loading into flexural, torsional and distortional forces by using the force equilibrium. From the force decomposition, the complex behavior of the multicell box girders can be decomposed and in turn the distortional behavior can be considered independently. Based on the method, a thin-walled box beam finite element, which can be applied to practical distortional analysis of straight multicell box girder bridges, is also developed in this study. The present box beam element possesses nine degrees of freedom per node to consider each separate behavior of multicell box girders. The validation of the present box beam element is demonstrated through a series of comparative studies using a conventional shell element and a box beam element proposed by other researchers. From the independent consideration of exact distortional behavior, the present box beam element unlike shell element will be useful for practicing engineers to easily determine distortional bimoments and stresses of multicell box girders.

Impact Factors for Horizontally Curved Composite Box Girder Bridges

This paper presents a method for determining the dynamic impact factors for horizontally curved composite single- or multicell box girder bridges under AASHTO truck loading. The bridges are modeled as three-dimensional structures using commercially available software. The vehicle is idealized as a pair of concentrated forces, with no mass, traveling in two circumferential paths parallel to the curved centerline of bridges. An extensive parametric study is conducted, in which over 215 curved composite box girder bridge prototypes are analyzed. The key parameters considered in this study are: Number of cells, number of lanes, degree of curvature, arc span length, slope of the outer steel webs, number and area of bracing and top chord systems, and truck(s) speed and truck(s) positioning. Based on the data generated from the parametric study, expressions for dynamic impact factors for longitudinal moment, reaction, and deflection are proposed as function of the ratio of the arc span length to the radius of curvature. The results from this study would enable bridge engineers to design horizontally curved composite box girder bridges more reliably and economically. Furthermore, the results can be used to potentially increase the live-load capacity of existing bridges to prevent posting or closing of the bridge.

Simply Supported Curved Cellular Bridges: Simplified Design Method

The use of curved composite bridges in interchanges of modern highway systems has become increasingly popular for economic and aesthetic considerations. Bridges with a concrete deck composite with a steel multicell section can adequately resist torsional and warping effects induced by high curvature. Although current design practices in North America recommend few analytical methods for the design of curved multicell box girder bridges, economical requirements in the design process point to a need for a simplified design method. This paper summarizes the results from an extensive parametric study, using the finite-element method, in which simply supported curved composite multicell bridge prototypes are analyzed to evaluate the moment and deflection distributions between girders, as well as the axial forces expected in the bracing system, due to truck loading as well as dead load. Results from tests on four, 1/12 linear-scale, simply supported curved composite concrete deck-steel multicell bridge models are used to substantiate and verify the analytical modeling. The parameters considered in the study are cross-bracing system, aspect ratio, number of lanes, number of cells, and degree of curvature. Based on the data generated from the parametric study, expressions for moment and deflection distribution factors are deduced. Expressions for the maximum axial force in bracing members are also derived. An illustrative design example is presented.

Load Distribution Factors for Composite Multicell Box Girder Bridges

Composite steel-concrete multicell box girder bridges combine excellent torsional stiffness with elegance. While the current design practices in North America recommend few analytical methods for the design of composite multicell box girder bridges, practical requirements in the design process necessitate a need for a simpler design method. This paper presents an extensive parametric study—using the finite-element method—in which 120 bridges of various geometries were analyzed. The parameters considered are: number of cells, number of lanes, span length, and cross bracings. Results from testing a simply supported three-cell bridge model is used to substantiate the analytical modeling. Based on the parametric study, moment and shear distribution factors are deduced for such bridges subjected to AASHTO truck loadings as well as dead load. Saint-Venant torsional stiffness for composite cellular cross sections used in this study is also investigated. Recommendations to enhance the torsional stiffness are formulated. An illustrative design example is presented.

Shear Distribution in Simply-Supported Curved Composite Cellular Bridges

Composite steel-concrete multicell box girder bridges are quite often used in modern bridge superstructures with curved alignments. They provide excellent torsional resistance as well as elegant appearance. While current design practices in North America recommend few analytical methods for the design of curved multicell box bridges, practical requirements in the design process require a need for a simplified design method. This paper summarizes the results from an extensive parametric study, using a finite-element model, in which 120 simply-supported curved bridge prototypes are analyzed to evaluate the shear distribution in the webs due to truck loading as well as dead load. Results from tests on four 1/12 linear-scale simply-supported curved composite concrete deck-steel three-cell bridge models are used to substantiate the analytical modeling. The parameters considered in the study are: cross-bracing system, aspect ratio, number of lanes, number of cells, and degree of curvature. Based on the data generated from the parametric study, expressions for the shear distribution factors for truck loadings as well as dead load are deduced. An illustrative design example is presented.

A finite element with exact shape functions for shear lag analysis in multi-cell box girders

Vlasov's thin-walled beam theory is combined with special shear lag warping functions to derive a box beam finite element with exact shape functions which can be used to analyze single- and multi-cell box girders. The fundamental theory of this model is rigorous and the governing differential equations are solved exactly. A computer program based on the proposed model has been developed for the analysis of single- or multi-cell box girder bridges. Examples are presented which compare the proposed method with the facet shell finite element analysis, with good agreement between the two sets of results.

Finite strip evaluation of effective flange width of bridge girders: Discussion

The authors are commended for doing a useful study on the effective widths of flanges in beam and slab and box-girder bridges. The fact that the effective flange widths increase with the level of load in the zone of nonlinear behaviour is confirmed by several research workers. Dowling et al. (1977), after testing models of steel box girders, concluded that shear lag has little weakening effect on the flange strength. Maisel et al. (1973) , made similar remarks about concrete box girders. Consideration of the shear-lag effects can be important for working loads but at ultimate loads the usefulness of such consideration tends to diminish. In Fig. 1 the authors have shown BE to be measured from the edges of the beam flange for beam-slab bridges, from the centre line of webs for multispine box-girder bridges and from the face of webs for multicell box-girder bridges. Considering that the actual flange width of AASHTO and steel wide-flange girders was not directly considered in the idealization, why do these differences in determining 2B and BE exist? It might be appropriate to measure BE and 2B from the centre line of the webs in all cases. Such a simplification would make the use of Fig. 7 a and b even simpler. For serviceability limit states the Ontario highway bridge design code requires one-lane loaded conditions to be considered for all bridges. The empirical effective-width charts appear to have been developed for all design lane loaded conditions. Will the charts be still applicable if only one of the design lanes is loaded ? The authors clearly state that the purpose of the exercise was to determine effective widths of com-