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.     

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.     

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.     

Comparison of Measured and Computed Stresses in a Steel Curved Girder Bridge

Steel curved I-girder bridge systems may be more susceptible to instability during construction than bridges constructed of straight I-girders. The primary goal of this research is to study the behavior of the steel superstructure of a curved steel I-girder bridge system during all phases of construction and to ascertain whether the actual stresses in the bridge are represented well by linear elastic analysis software developed for this project and typical of that used for design. Sixty vibrating wire strain gauges were applied to a two-span, four-girder bridge, and elevation measurements were taken by a surveyor's level. The resulting stresses and deflections were compared to computed results for the full construction sequence of the bridge as well as for live loading from up to nine 50-kip trucks. The analyses correlated well with the field measurements, especially for the primary flexural stresses. Stresses due to lateral bending and restraint of warping induced in the girders and the stresses in the cross frames were more erratic but generally showed reasonable correlation. In addition, it is shown that, for the magnitude of live load applied to the bridge, analyses in which composite behavior is assumed in the negative moment region yield better correlation than analyses in which just the bare steel girders are used (no shear connectors were used on the bridge in the negative moment region). It is concluded that the curved girder analysis software captures the general behavior well for these types of curved girder bridge systems at or below the service load level, and that the stresses in these bridges may be relatively low if their design is controlled largely by stiffness.     

Dynamic Analysis of Curved Continuous Multiple-Box Girder Bridges

The use of horizontally curved composite multiple-box girder bridges in modern highway systems is quite suitable in resisting torsional and warping effects induced by highway curvatures. Bridge users react adversely to vibrations of a bridge and especially where torsional modes dominate. In this paper, continuous curved composite multiple-box girder bridges are analyzed, using the finite-element method, to evaluate their natural frequencies and mode shapes. Experimental tests are conducted on two continuous twin-box girder bridge models of different curvatures to verify and substantiate the finite-element model. Empirical expressions are deduced from these results to evaluate the fundamental frequency for such bridges. The parameters considered herein are the span length, number of lanes, number of boxes, span-to-radius of curvature ratio, span-to-depth ratio, end-diaphragm thickness, number of cross bracings, and number of spans.     

Field Static Load Test on Kao-Ping-Hsi Cable-Stayed Bridge

Field load testing is an effective method for understanding the behavior and fundamental characteristics of a cable-stayed bridge. This paper presents the results of field static load tests on the Kao-Ping-Hsi cable-stayed bridge, the longest cable-stayed bridge in Taiwan, before it was open to traffic. A total of 40 loading cases, including the unit and distributed bending and torsion loading effects, were conducted to investigate the bridge behavior. The atmospheric temperature effect on the variations of the main girder deflections was also monitored. The results of static load testing include the main girder deflections, the flexural strains of the prestressed concrete girder, and the variations of the cable forces. A three-dimensional finite-element model was developed. The results show that the bridge under the planned load test conditions has linear superposition characteristics and the analytical model shows a very good agreement with the bridge responses. Further discussion of deflection and cable forces of the design specifications for a cable-stayed bridge is also presented.     

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.     

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.     

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

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

Measurement and Analysis of Distortion-Induced Fatigue in Multigirder Steel Bridges

Fatigue damage to multigirder steel bridges on skew can result from distortion caused by differential deflection of adjacent girders that impose out-of-plane bending of girder web gaps. Existing design procedures give recommendations to mitigate the effects of distortional fatigue but do not directly address secondary, out-of-plane deformations, nor do they provide guidance in determining the magnitude of out-of-plane stresses in girder webs. An experimental study was conducted to (1) implement a field monitoring program for a typical multigirder steel bridge on skew supports; (2) assess the frequency and magnitude of distortional fatigue stresses at web-stiffener connections; and (3) evaluate the impact of these stresses on fatigue life. Measurements from twelve strain gauges were continuously monitored and recorded for a period exceeding three months on Minnesota Department of Transportation Bridge #27734. Web-gap stresses in negative-moment regions were found to be much larger than flange stresses. The results of a detailed finite-element study indicate that actual strains at the web gaps may be much larger than the values measured at the strain gauge locations. This study also revealed the mechanism of web-gap distortion, suggesting an approximate method for predicting web-gap stress based on known girder differential deflection.     

Long-Term Behavior of Continuous Precast Concrete Girder Bridge Model

Continuous concrete box girder bridges composed of precast reinforced and prestressed concrete beams with a U cross section and a cast-in-place top slab are frequently used for medium spans due to their competitiveness. The service behavior of such bridges is very much influenced by their segmental construction, due to time-dependent materials behavior that makes it difficult to accurately predict the stresses, strains, and deflections at long term. A 1:2 scale model of a two-span continuous bridge was tested in order to study its behavior during the construction process and under permanent loads. Time-dependent concrete properties, as well as support reactions, deflections, and strains in concrete and steel, were measured for 500 days. Important time-dependent redistributions of stresses and internal forces throughout the bridge were also measured. The test results were compared with analytical predictions obtained by means of a numerical model developed for the nonlinear and time-dependent analysis of segmentally erected, reinforced and prestressed concrete structures. Generally good agreement was obtained, showing the adequacy of the model to reproduce the structural effects of complex interactive time-dependent phenomena.     

Dynamic Analysis of Steel Curved Box Girder Bridges

The impact of seven three-span continuous single box girder bridges, with overall span lengths ranging from 76.2 to 213.36 m (250–700 ft), due to vehicles moving across rough bridge decks is analyzed. The box girder is divided into a number of thin-walled beam elements. Both warping torsion and distortion are considered in the study. The analytical vehicle is the HS20-44 truck included in the American Association of State Highway and Transportation Officials specifications and simulated as a nonlinear vehicle model with 11 degrees of freedom. Truck parameters include the body, suspensions, and tires. The bridge deck surface is assumed to be good and was simulated using a stochastic process (power spectral density function). The analytical results show that the impact factors of torque and distortional torque for the curved single box girder bridges could be very high, while those of the other responses are generally less than that of corresponding straight box girder bridges. The proposed impact equations can be used in the design of continuous curved single box girder bridges.     

Warping Stresses in Curved Box Girder Bridges: Case Study

This paper presents a detailed investigation of warping-related stresses in 18 composite steel-concrete box girder bridges. The bridge designs were adapted from blueprints of existing bridges in the state of Florida and encompass a wide range of parameters including horizontal curvature, cross-sectional properties, and number of spans. The bridges after which the analysis prototypes are modeled were designed by different firms and constructed at different times and are considered to be representative of current design practice. Forces are evaluated from analyses that account for the construction sequence and the effect of warping. Loading is considered following the 1998 AASHTO-LRFD provisions. Differences between stresses obtained taking warping into account and those calculated by ignoring warping are used to evaluate the effect of warping. Analysis results show that warping has little effect on both shear and normal stresses in all bridges. Current design provisions are discussed in light of the analysis results.     

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.     

Improved Longitudinal Joint Details in Decked Bulb Tees for Accelerated Bridge Construction: Fatigue Evaluation

This companion paper focuses on an investigation of improved continuous longitudinal joint details for decked precast prestressed concrete girder bridge systems. Precast concrete girders with an integral deck, which are cast and prestressed with the girder, provide benefits of rapid construction along with improved structural performance and durability. Despite these advantages, the use of this type of construction has been limited to isolated regions of the United States. One of the issues limiting more widespread use is the perceived problem with durability of longitudinal joints used to connect adjacent girders. Four full-scale slabs connected by No. 16 (#5) headed reinforcement detail using a 152 mm (6 in.) lap length were fabricated and tested. An analytical parametric study was conducted to provide a database of maximum forces in the longitudinal joint. These maximum forces are then used to determine the loading demand necessary in the slab testing due to the service live load. Static and fatigue tests under four-point pure-flexural loading, as well as three-point flexural-shear loading, were conducted. Test results were evaluated based on flexural capacity, curvature behavior, cracking, deflection, and steel strain. Based on these test results, the improved longitudinal joint detail is a viable connection system that transfers the forces between the adjacent decked bulb tee girders.     

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

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

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.     

Enhancement of Flexural Design of Horizontally Curved Prestressed Bridges

In this paper, flexural behavior of horizontally curved prestressed (posttensioned) box bridges is studied by using three-dimensional and refined finite-element modeling and analysis. Bridge length, section geometry, and material properties are the same in all the models, while angle of curvature varies from 0 to 90°. The results of analysis show that in curved bridges, stress distribution is significantly different in comparison to straight bridges. Also, the level of stresses at some locations of section width is considerably high. It is proposed to vary the distribution of the prestressing tendons across section width in order to optimize the bridge capacity. Results show that by proper redistribution of prestressing in section width, significant reduction in resultant stress is possible.     

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%.