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.     

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.     

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.     

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.     

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.     

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.     

Refined Stick Model for Dynamic Analysis of Skew Highway Bridges

Stick models are widely employed in the dynamic analysis of bridges when only approximate results are desired or when detailed models are difficult or time-consuming to construct. Although the use of stick models for regular bridges has been validated by various researchers, the application of such models to skew highway bridges continues to present challenges. The conventional single-beam stick model used to represent the bridge deck often fails to capture certain predominant vibration modes that are important in obtaining the true dynamic response of the bridge. In this paper, a refined stick model is proposed for the preliminary dynamic analysis of skew bridges. The model utilizes a dual-beam stick representation of the bridge deck. The validity of the model is established by comparing results obtained from the proposed model with numerical solutions obtained for skew plates and a skew bridge. It is shown that this dual-beam stick model is superior to the conventional single-beam model in estimating the natural vibration frequencies and in predicting the predominant vibration modes of the bridge. Because of its simplicity and relative accuracy, this model is recommended for the preliminary dynamic analysis of skew highway bridges.     

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.     

Shear Lag in Box Girder Bridges

A finite-segment method for analyzing shear-lag effects in box girders is presented in this paper, with an assumption that the spanwise displacements of the flange plates are described by a third-power parabolic function. The governing differential equations for two generalized displacements are established according to the principle of minimum potential energy. In order to obtain the longitudinal stresses under the shear-lag effect, the element stiffness equations are developed based on the variational principle by taking the homogeneous solutions of the differential equations as the displacement functions of the finite segment. The effect of two major parameters on shear lag is investigated for cantilever and continuous box girders with varying depth under three kinds of loads. It is shown that the height ratio, in addition to the flange width to span length ratio, has a significant influence on the shear lag. The solutions based on the present method are compared with the results of model testing and the finite strip method. The accuracy of the present method is proved to be satisfactory.     

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.     

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.     

Truck Loading and Fatigue Damage Analysis for Girder Bridges Based on Weigh-in-Motion Data

Based on data collected by weigh-in-motion (WIM) measurements, truck traffic is synthesized by type and loading condition. Three-dimensional nonlinear models for the trucks with significant counts are developed from the measured data. Six simply supported multigirder steel bridges with spans ranging from 10.67 m (35 ft) to 42.67 m (140 ft) are analyzed using the proposed method. Road surface roughness is generated as transversely correlated random processes using the autoregressive and moving average model. The dynamic impact factor is taken as the average of 20 simulations of good road roughness. Live-load spectra are obtained by combining static responses with the calculated impact factors. A case study of the normal traffic from a specific site on the interstate highway I-75 is illustrated. Static loading of the heaviest in each truck type is compared with that of the American Association of State Highway and Transportation Officials standard design truck HS20-44. Several important trucks causing fatigue damage are found.     

Examination of Level of Analysis Accuracy for Curved I-Girder Bridges through Comparisons to Field Data

To evaluate the accuracy of different levels of analysis used to predict horizontally curved steel I-girder bridge response, a field test was performed on a three-span structure. Collected strain data were reduced to determine girder vertical and bottom flange lateral bending moments. Experimental moments were compared to numerical moments obtained from three commonly employed levels of analysis. Level 1 analysis includes two manual calculation methods: a line girder analysis method described in the AASHTO Guide Specification for Horizontally Curved Highway Bridges, and the V-load method. Grillage models represent Level 2 and were created using three commercially available computer programs: SAP2000, MDX, and DESCUS. Level 3 consists of three-dimensional (3D) finite element models created using SAP2000 and the BSDI 3D system. Responses obtained from each level are compared and discussed for a single radial cross section of the structure, and the compared results involve truck loads and placement schemes that do not represent those used for bridge design. The field test and numerical data presented are used solely to determine the accuracy of each level of analysis for predicting structure response to a specific live load at a specific cross section. Results showed that Level 2 and Level 3 analyses predict girder vertical bending moment distributions more accurately than Level 1 analyses throughout the tested cross section. The comparisons indicate that Level 3 girder vertical bending moment distributions offered no appreciable increase in accuracy over Level 2 analyses. The study also indicates that both Level 1 and Level 3 analyses provide bottom flange lateral bending moment distributions that do not correlate well with field test results for the studied bridge cross section.     

Framework for Multiobjective Optimization of Launching Girder Bridges

A framework is presented for optimizing the construction of decks of bridges using launching girder systems. The framework assists contractors in performing a time-cost trade-off analysis to optimize the use of resources. The proposed framework consists of three main components which interact in a cyclic manner. These components are simulation, optimization, and reporting modules. Processes and tasks of launching girder systems are described in order to illustrate the mechanism of the simulation module which utilizes STROBOSCOPE as a general purpose simulation language. The developments made in the optimization module are extensively detailed. The optimization module uses ant colony optimization and it accounts for seven optimization variables; location of casting yard, time lag, number of casting forms, number of preparation platform, curing method, number of yard reinforcement crews, and number of stressing crews. Two optimization approaches are coded in the optimization module in two algorithms (ant colony multiobjective optimization I and II) to carry out multiobjective optimization. These are function-transformation and modified distance approaches. A numerical example is presented to illustrate the practical use of the developed framework.     

Effect of Hanger Flexibility on Dynamic Response of Suspension Bridges

Linearized continuum models of a suspended span with unloaded backstays and of a symmetric three-span suspension bridge are used to study the effects of the flexibility of the hangers on the vertical vibrations of suspension bridges. The models include elastic parabolic cables, flexible distributed hangers with variable length, and a stiffening girder represented by an elastic beam. It is shown that the free vibrations of a suspended span with unloaded backstays are controlled by five dimensionless parameters, while six dimensionless parameters control the response of a symmetric three-span suspension bridge. The results indicate that the flexibility of the hangers has a significant effect on the natural frequencies of the higher modes only when the relative stiffness of the girder is very high. The effects of hanger flexibility on the response of a suspension bridge to localized impulsive loads are also found to be small. These findings confirm the traditional, albeit previously untested, assumption of inextensible hangers. Finally, the threshold amplitudes of free vibrations that would result in the incipient slackening of the hangers are determined.     

Damage Analysis of Hanshin Expressway Viaducts during 1995 Kobe Earthquake. III: Three-Span Continuous Girder Bridges

Almost all the single reinforced concrete (RC) piers from P35 to P350 received consistently severe damage, considering the large residual inclination of piers included in earthquake-induced severe damage. However, some of the piers in the section from P35 to P350 remained lightly damaged, and this phenomenon is observed especially in many piers under fixed bearings in continuous girder bridges. In this study, using experimentally based models for metal bearings and installing them to an existing FEM code, a nonlinear dynamic response analysis of a continuous girder bridge system is conducted. It is shown that the results depend on the ground motion, but the fuse effect of the breaking of the bearings could have been a reason for the phenomenon.     

Transverse Analysis of Strutted Box Girder Bridges

The computer program STRUTBOX is presented for the transverse analysis of strutted box girder bridges, and particularly for bridges designed and constructed using the strutted box widening method. The program allows the deck prestressing and other reinforcing to be proportioned for transverse flexure, and the web stirrups and slab reinforcing to be proportioned for longitudinal shear and torsion. The program also gives an indication as to the severity of shear lag effects. The program is based on the folded plate method and is no more difficult to use than a plane frame computer program. The paper also demonstrates how the results given by a folded plate analysis can be approximated by using some simple membrane force equations in conjunction with a plane frame analysis. What is particularly interesting is that there is danger in using a plane frame analysis alone to approximate the results of a folded plate analysis for strutted box girder bridges (as well as other box girder bridges) because there are significant differences in the axial force diagrams given by the two methods.     

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.     

Dynamic Monitoring of Steel Girder Highway Bridge

Currently there are different monitoring techniques that have been considered for use in the structural evaluation of bridges. These include approaches based on both static and dynamic behavior. The use of dynamic properties has advantages over static properties, since components of the dynamic properties are only marginally influenced by variations in the loading. When dynamic properties are used, field studies have shown that it is not always sufficient to use only natural frequencies and modal displacements. Some research for structural evaluation of bridges indicates that techniques based on use of derivatives of the natural frequencies and the modal displacements may be more effectively used to generate effective diagnostic parameters for structural identification. This paper presents the results of applying one of these methods, the modal flexibility approach, to a field study of a bridge in which the bearings were partially restrained in colder weather. While others have used impact methods with the modal flexibility method, in this study the approach is modified so that excitation is provided by vehicular traffic. The results show that the modified modal flexibility method provides a clear indication that there have been changes in the bridge’s structural behavior.