Impact Factors for Curved Continuous Composite Multiple-Box Girder Bridges

The results from a parametric study on the impact factors for 180 curved continuous composite multiple-box girder bridges are presented. Expressions for the impact factors for tangential flexural stresses, deflection, shear forces and reactions are deduced for AASHTO truck loading. The finite-element method was utilized to model the bridges as three-dimensional structures. The vehicle axle used in the analysis was simulated as a pair of concentrated forces moving along the concrete deck in a circumferential path with a constant speed. The effects of bridge configurations, loading positions, and vehicle speed on the impact factors were examined. Bridge configurations included span length, span-to-radius of curvature ratio, number of lanes, and number of boxes. The effect of the mass of the vehicle on the dynamic response of the bridges is also investigated. The data generated from the parametric study and the deduced expressions for the impact factors would enable bridge engineers to design curved continuous composite multiple-box girder bridges more reliably and economically.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Erection Procedure Effects on Deformations and Stresses in a Large-Radius, Horizontally Curved, I-Girder Bridge

Special attention is required in the construction of horizontally curved steel I-girder bridges due to coupled effects of primary bending and torsional forces. Misguided steel erection procedures can lead to undesired stresses, deflections, and rotations in these types of bridges, resulting in a structure with misaligned geometry and in an unknown state of stress. Further complicating the issue, little guidance related to curved bridge behavior during construction is provided by current design codes, leaving contractors and designers uncertain as to the most appropriate steps to take to achieve an efficient, safe structure. A horizontally curved, six-span steel I-girder bridge located in central Pennsylvania that experienced severe geometric misalignments and fit-up complications during steel erection was studied to investigate curved girder behavior during construction. The structure was monitored during corrective procedures intended to realign it with the design geometry, and field data used to calibrate a three-dimensional computer model generated via SAP2000. The techniques and assumptions proven in the calibration process were used to create a numerical model of a three-span continuous portion of the bridge, which was the subject of several analyses exploring the effects erection sequencing, implementation of upper lateral bracing, and use of temporary supports had on the final deformed shape of the curved superstructure. Findings indicated that using paired girder erection produced smaller radial and vertical deformations than single girder techniques for this structure, and that the use of lateral bracing between the fascia and adjacent interior girders and the placement of temporary shoring towers at span quarter points are both effective means of further reducing levels of deflection.     

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

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

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.     

Construction of a Horizontally Curved Steel I-Girder Bridge. Part II: Inconsistent Detailing

The erection of horizontally curved steel I-girder bridges tends to be more complex than the erection of straight steel I-girder bridges. The erection of a curved steel I-girder bridge can be further complicated when the cross-frame members and girders are detailed inconsistently in an effort to force bridge components into some desirable geometric condition. Inconsistent detailing involves the intentional specification of cross-frame members that are either too long or too short to align with girder connector plates properly so as to force the girders into a given position, resulting in connection misalignments that must be resolved by applying external forces to the bridge components. The current research investigates the erection of a recently constructed horizontally curved steel I-girder bridge and highlights the fact that practice of inconsistent detailing can lead to very formidable and costly fit-up problems in the field; especially when girder sizes are large.     

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.     

Monitoring Steel Girder Stability for Safer Bridge Erection

The collapse of the State Route 69 Bridge over the Tennessee River near Clifton, Tennessee, is an example of how instability and lateral torsional buckling failure of a single steel bridge girder during erection might cause collapse of the whole steel superstructure. Close attention should be given to the stability of steel plate girders during erection when the lateral support provided to the compression flange might temporarily not be present. Rules of thumb in use today have been adopted by contractors/subcontractors to check the stability of cantilever or simply supported girders under erection using the L/b ratio, where L is the unbraced length and b is the compression flange width. For each girder section, a maximum L/b ratio exists beyond which lateral torsional buckling failure would occur under girder self-weight. Parametric studies were conducted following the latest AASHTO LRFD code in order to indentify the maximum L/b ratio for various girder sections and check the rules of thumb, as well as determine the dominating section parameters on girder stability under erection. Advanced nonlinear finite-element analyses were also conducted on a girder section for both the cantilever and the simply supported case in order to further understand the behavior of girder instability due to lateral torsional buckling under the self-weight, as well as to develop a trial-and-error methodology for identifying the maximum L/b ratio using computer analysis. At the same time, the effect of lateral bracing location on the cantilever free end has been investigated, and it turned out that bracing the top tension flange would be more effective to prevent lateral torsional buckling than bracing the bottom compression flange.     

Feasibility of a 1,400 m Span Steel Cable-Stayed Bridge

This paper describes the feasibility of 1,400 m steel cable-stayed bridges from both structural and economic viewpoints. Because the weight of a steel girder strongly affects the total cost of the bridge, the writers present a procedure to obtain a minimum weight for a girder that ensures safety against static and dynamic instabilities. For static instability, elastoplastic, finite-displacement analysis under in-plane load and elastic, finite-displacement analysis under displacement-dependent wind load are conducted; for dynamic instability, multimodal flutter analysis is carried out. It is shown that static critical wind velocity of lateral torsional buckling governs the dimension of the girder. Finally, the writers briefly compare a cable-stayed bridge with suspension bridge alternatives.     

Routing and Permitting Techniques of Overweight Vehicles

Overweight vehicles require permits to cross the highway bridges, which are designed for “design load vehicles” (prescribed in the national standards). A new, fast, and robust method is presented for the verification of bridges, which requires minimal input only: the axle loads, axle spacing, the bridge span(s), and the superstructure type. The bridge can be a single or a multispan girder, an arch bridge, a frame structure, or a box girder. The overweight vehicle may operate within regular traffic or it may cross the bridge at a given lane position while other traffic is prohibited on the bridge. The method is illustrated by numerical examples for deck-girder bridges and for a box girder.     

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.     

Investigation of Turbulence Effects on Torsional Divergence of Long-Span Bridges by Using Dynamic Finite-Element Method

Aerostatic stability of super long-span bridges is a much concerned issue during the design stage. Typical aerostatic instability is the so-called torsional divergence which may lead to abrupt structural failure. The iterative static-based FEM, which generally entails the assumption of smooth oncoming flow, has been widely used to evaluate the aerostatic stability of the bridge concerned. However, the wind in atmospheric boundary layer is naturally turbulent and the effect of turbulence on bridge torsional divergence should be therefore considered, and that is the main concern of the present study. To take into account the effects of turbulence on torsional divergence, a dynamic-based time domain finite-element (FE) procedure for predicting bridge aerostatic stability is introduced first. Then the quasi-steady wind loads expressions are presented and discussed, into which the aerodynamic torsional stiffness, which is indispensable for the evaluation of aerostatic stability, has been demonstrated to be incorporated indirectly by a frequency-domain-based approach. Finally, the aerostatic performances of the longest suspension bridge in China are investigated, of which the torsional divergence is the primary concern. Numerical results show that the torsional divergence pattern in turbulent flow differs considerably from that in smooth flow. The primary difference is, while the torsional instability in smooth flow manifests as an abrupt mounting up of the twist deformation of the main girder with the increasing of the wind velocity, that in turbulent flow manifests as an unstable stochastic vibration with large peak values. Another difference is that the wind velocity for divergence in turbulent flow is obviously lower than that in smooth wind and there does not present an obvious wind velocity threshold for divergence, which is distinguished from the torsional divergence in smooth flow characterized by a clear threshold. Based on the presented time domain FE analysis procedure, the influence of turbulence intensity and gusts spatial correlation upon torsional divergence is also investigated and shown to play an important role on the aerostatic stability.