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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Natural Frequency of Railway Girder Bridges under Vehicle Loads

To investigate the natural frequency of a railway girder bridge under vehicle loads, two methods are presented. First, the natural frequency of a railway girder bridge under vehicle loads is obtained by solution of the eigenvalue of the vehicle-bridge interaction equation at each step of the numerical integration. Second, based on the vehicle-bridge interaction equation, an approximate formula is developed. The results show that the natural frequency of a railway girder bridge under vehicle loads varies periodically as the vehicles pass over the bridge. The results obtained with the two methods are then compared, showing that a good agreement is achieved. From parametric studies, the effects of the unsprung mass, the sprung mass, and the stiffness of the vehicle suspension are discussed.     

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.     

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.     

Optimum Design of Welded Steel Plate Girder Bridges Using a Genetic Algorithm with Elitism

The genetic algorithm (GA) is a general optimization technique that has some unique features that are especially suitable for structural engineering problems. This work uses a simple GA with elitism to find the optimum design of welded steel plate girder bridges. The objectives are to minimize the weight and the cost of the girders. Two types of plate-girder bridges are studied: a single-span bridge and a two-equal-span continuous bridge. Bridges with various span lengths, in increments of 20?ft, are investigated; results are tabulated, parametric studies are made, and meaningful conclusions are drawn.     

Literature Review in Analysis of Box-Girder Bridges

The curvilinear nature of box girder bridges along with their complex deformation patterns and stress fields have led designers to adopt approximate and conservative methods for their analyses and design. Recent literature on straight and curved box girder bridges has dealt with analytical formulations to better understand the behavior of these complex structural systems. Few authors have undertaken experimental studies to investigate the accuracy of existing methods. This paper presents highlights of references pertaining to straight and curved box girder bridges in the form of single-cell, multiple-spine, and multicell cross sections. The literature survey presented herein deals with: (1) elastic analysis, and (2) experimental studies on the elastic response of box girder bridges.     

Construction of a Horizontally Curved Steel I-Girder Bridge. Part I: Erection Sequence

In the case of horizontally curved steel I-girder bridges, girder and cross-frame members are frequently detailed for erection in the no-load condition as a matter of convention. As a result, it is imperative that the erection sequence used to construct such bridges be comprehensively studied to ensure that the no-load condition can be achieved in the field and that significant superstructure component fit-up problems do not occur. The current research investigates the erection of a recently constructed horizontally curved steel I-girder bridge, in which significant difficulties were encountered during erection. The bridge erection is recreated through an analytical simulation using a detailed nonlinear finite element model. The analytical results demonstrate that a condition that closely resembles the no-load condition can be achieved in the field during construction with the proper implementation of temporary support structures; and that the difficulties encountered during the erection of the subject bridge superstructure could not be attributed to the erection scheme followed.     

Seismic Response of Multiple Span Steel Bridges in Central and Southeastern United States. II: Retrofitted

Part I of this two-part paper evaluated the seismic response of typical multispan simply supported (MSSS) and multispan continuous steel girder bridges in the central and southeastern United States. The results showed that the bridges were vulnerable to damage resulting from impact between decks, and large ductility demands on nonductile columns. Furthermore, fixed and expansion bearings were likely to fail during strong ground motion. In this paper, several retrofit measures to improve the seismic performance of typical multispan simply supported and multispan continuous steel girder bridges are evaluated, including the use of elastomeric bearings, lead-rubber bearings, and restrainer cables. It is determined that lead-rubber bearings are the most effective retrofit measure for reducing the seismic vulnerability of typical bridges. While isolation provided by elastomeric bearings limits the forces into the columns, the added flexibility results in pounding between decks in the MSSS steel girder bridges. Restrainer cables, which are becoming a common retrofit measure, are effective in reducing the hinge opening in MSSS bridges with steel bearings. However, when used with elastomeric bearings, the restrainer cables negate the isolation effect of the bearings.     

Implementation of a Long-Term Bridge Weigh-In-Motion System for a Steel Girder Bridge in the Interstate Highway System

This technical paper discusses the implementation of a long-term bridge weigh-in-motion system for use in determining gross vehicle weights of trucks crossing steel girder bridges. The system uses strain data to determine truck weights using an existing structural health monitoring system installed on a interstate highway bridge. The applied system has the advantage of not using any axle detectors in the roadway; and instead all analyses are performed using strain gauges attached directly to the steel girders, providing for a long-term monitoring system with minimal maintenance. Long-term data has been used to demonstrate that this method can be readily applied to gain important information on the quantity and weights of the trucks crossing the highway bridge.     

Dynamic and Impact Behavior of Half-Through Arch Bridges

The objective of this paper is to present the results of an investigation of the dynamic and impact characteristics of half-through arch bridges with rough decks caused by vehicles moving across them. Seven arch bridges modeled as three-dimensional structures with overall span lengths ranging from 20?to?200?m (65.5?to?656.2?ft) are analyzed. The American Association of State Highway and Transportation Officials Specifications HS20-44 truck is the applied vehicle loading used in the analysis and is simulated as a three-dimensional, nonlinear vehicle model with 11 degrees of freedom. Truck components include the body, suspension, and tires. The bridge deck surface is assumed to have a “good” surface roughness and is simulated using a stochastic process (power spectral density function). The effect on impact factors of span length, rise-to-span ratio, and vehicle speed is discussed. The results of the analyses show that the impact factors of bending moment and axial force will not exceed 0.4 and 0.25, respectively. The proposed impact equations are simple and conservative and can be used in the design of half-through arch bridges.