Experimental and Analytical Studies of a Horizontally Curved Steel I-Girder Bridge during Erection

A series of studies on an experimental, full-scale curved steel bridge structure during erection are discussed. The work was part of the Federal Highway Administration’s curved steel bridge research project (CSBRP). The CSBRP is intended to improve the understanding of curved bridge behavior and to develop more rational design guidelines. The main purpose of the studies reported herein was to assess the capability of analytical tools for predicting response during erection. Nine erection studies, examining six different framing plans, are presented. The framing plans are not necessarily representative of curved bridge subassemblies as they would be erected in the field; however, they represent a variety of conditions that would test the robustness of analysis tools and assess the importance of erection sequence on initial stresses in a curved girder bridge. The simply supported, three I-girder system used for the tests is described and methods for reducing and examining the data are discussed. Comparisons between experimental and analytical results demonstrate that analysis tools can predict loads and deformations during construction. Comparison to the V-load method indicates that it predicts stresses in exterior girders well, but can underpredict them for interior girders.     

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.     

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.     

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.     

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.     

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.     

Live Load Radial Moment Distribution for Horizontally Curved Bridges

The present study is designed to determine the effect of major parameters on maximum total bending moments of curved girders, establish the relationship between key parameters and girder distribution factors (GDFs), and develop new approximate distribution factor equations. A level of analysis study using three numerical models was performed to establish an appropriate numerical modeling method on the basis of field test results. A total of 81 two-traffic lane curved bridges were analyzed under HL-93 loading. Two approximate GDF equations were developed based on the data obtained in this study: (1) a single GDF based on total girder normal stress; and (2) a combined GDF treating bending and warping normal stress separately. The two equations were developed based on both an averaged coefficient method and regression analysis. A goodness-of-fit test revealed that the combined GDF model developed by regression analysis best predicted GDFs. The present study demonstrated that radius, span length, cross frame spacing and girder spacing most significantly affect GDFs. The proposed GDF equations are expected to provide a more refined live load analysis for preliminary design.     

Shear Live-Load Distribution Factors for I-Girder Bridges

A full scale, single lane test bridge was used to evaluate a typical slab-on-girder bridge’s response to shear. The results of the shear load test provided the means to evaluate the level of detail for a finite element model that is required to accurately replicate the behavior of bridges subject to shear loads. This finite element modeling scheme was then used to evaluate more than 200 finite element bridge models. The bridge models investigated the effects of girder spacing, span length, overhang distance and skew angle on the shear live-load distribution factor. The finite element shear distribution factors were compared with those calculated according to the American Association of State Highway and Transportation Officials load and resistance factor design (AASHTO LRFD) specifications. It was found that the AASHTO LRFD procedure accurately predicted the shear distribution factor for changes in girder spacing and span length. However, the LRFD shear distribution factor for the exterior girder was found to be unconservative for certain overhang distances and overly conservative for the interior girder for higher skew angles. Alternative equations are provided for the single and multilane exterior girder correction factor.     

Live-Load Distribution Factors for Concrete Box-Girder Bridges

The current American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design (LRFD) Specifications impose fairly strict limits on the use of its live-load distribution factor for design of highway bridges. These limits include requirements for a prismatic cross section, a large span-length-to-width ratio, and a small plan curvature. Refined analyses using 3D models are required for bridges outside of these limits. These limits place severe restrictions on the routine design of bridges in California, as box-girder bridges outside of these limits are frequently constructed. This paper presents the results of a study investigating the live-load distribution characteristics of box-girder bridges and the limits imposed by the LRFD specifications. Distribution factors determined from a set of bridges with parameters outside of the LRFD limits are compared with the distribution factors suggested by the LRFD specifications. For the range of parameters investigated, results indicated that the current LRFD distribution factor formulas generally provide a conservative estimate of the design bending moment and shear force.     

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.     

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 of Live-Load Distribution Factors for Glued-Laminated Timber Girder Bridges

This paper presents simple relationships for calculating live-load distribution factors for glued-laminated timber girder bridges with glued-laminated timber deck panels. Analytical models were developed using the Ansys 113 finite-element program, and the results were validated using recorded data from four in-service timber bridges. The effects of the bridge span length, the spacing between girders, and the bridge width on the distribution of the live load were investigated by using the validated models. The live-load distribution factors obtained from the field test and the analytical models were compared with those obtained using the AASHTO LRFD Bridge Design Specifications2 live-load distribution relations. The comparison showed that the live-load distribution factors obtained by using the AASHTO LRFD Bridge Design Specifications2 were conservative. For this reason, statistical methods were used to develop accurate relationships that can be used to calculate the live-load distribution factors in the design of glued-laminated girder bridges.     

Field Evaluation of Decommissioned Noncomposite Steel Girder Bridge

Field tests conducted on a noncomposite steel girder bridge are described. Two separate 36.6 m (120 ft) units, each three-span continuous, were subjected to increasing static loads by means of a trailer and concrete barriers. Results show that the girders acted as partially composite sections in the positive moment region up to the onset of yield. Due to curb participation and the transverse location of the applied load, exterior girders exhibited a higher degree of partially composite action. In the negative moment region, partially composite action was evident only in the exterior girders. As a result of partially composite action and curb participation, the yield load was about 7% higher than predicted. Bearing restraint is shown not to have a significant impact on the behavior of the tested bridges. In addition, the stiffness of the interior girders, as measured under the constant weight of a dump truck, are shown to be virtually unaffected by the heavy trailer loads. More significant changes in girder stiffness were observed between different transverse load positions of the dump truck.     

Curved Steel I-Girder Bridge Response during Construction Loading: Effects of Web Plumbness

Horizontally curved steel I-girder bridge systems tend to deflect and rotate out of plane under the action of gravity. Oftentimes, this response will lead to a condition wherein the subsequent girder cross-sectional orientation is one where the web is out of plumb. Currently, there exists little guidance concerning what effect this web out of plumbness has on structural performance. As a result of this lack of guidance from design specifications, there is tendency within current practice to work to alleviate the out of plumb condition through various detailing and erection strategies, since the performance implications of its presence within the structure are poorly understood. The present research employs nonlinear finite-element modeling strategies to study the various effects that web out of plumbness has on flange tip stresses, vertical and lateral deflections, cross-sectional distortion, and cross-frame demands. The focus of the present work is the construction stage, and thus steel dead load is the governing loading condition treated. Web out of plumbness magnitudes of up to 5° are considered.     

Parapet Strength and Contribution to Live-Load Response for Superload Passages

The main objective of this study is to evaluate the effects of parapets on the live-load response of slab-on-girder steel bridges subjected to superload vehicles and the effects of these loads on the parapets. A superload is a special permit truck that exceeds the predefined weight limitation. The presence of parapets can result in reduced girder distribution factors (GDFs) for critical girders, and this reserve strength can be considered for passage of a superload truck. This reduction is investigated, as well as the effects of discontinuous parapets and the capacity of parapets. Two steel bridges with significantly different geometric proportions were analyzed to evaluate the sensitivity of the structure to the effects of parapets. It was found that the GDFs can be decreased by as much as 30%, depending on the stiffness of the girders and the transverse truck position if the parapets are included in the analysis. The axial forces and bending moments resisted by the parapets were compared with the capacity of the parapets. The parapets and their connection with the deck were found to have adequate strength to accommodate the demand imposed by the superload trucks included in the study. For the discontinuous parapets, the open joint was determined to be acting like a notch, which increases the bottom flange stresses in the positive moment region and the tensile deck stresses in the negative moment region.     

Load Configuration and Lateral Distribution of NATO Wheeled Military Trucks for Steel I-Girder Bridges

This paper presents the lateral load distribution of various North Atlantic Treaty Organization (NATO) wheeled military trucks on a simple-span steel I-girder bridge (L = 36?m). The military trucks are classified into the military load classification (MLC) system. The MLC trucks demonstrate different load configurations when compared to the standard HS20 truck in terms of wheel-line spacing, number of axles, and weight. A calibrated three-dimensional finite-element analysis is conducted to examine the MLC load effects. The applicability of the AASHTO LRFD provisions is evaluated using 72 different load models. The wheel-line spacing and weight of the MLC trucks cause different flexural behavior and load distributions of the bridge when compared to those of HS20. The current AASHTO LRFD approach to determine live load distribution factors may be reasonably applicable to the MLC trucks, including approximately 20% of conservative predictions.     

Live-Load Distribution Factors for Prestressed Concrete, Spread Box-Girder Bridge

This study presents an evaluation of shear and moment live-load distribution factors for a new, prestressed concrete, spread box-girder bridge. The shear and moment distribution factors were measured under a live-load test using embedded fiber-optic sensors and used to verify a finite element model. The model was then loaded with the American Association of State Highway and Transportation (AASHTO) design truck. The resulting maximum girder distribution factors were compared to those calculated from both the AASHTO standard specifications and the AASHTO LRFD bridge design specifications. The LRFD specifications predictions of girder distribution factors were accurate to conservative when compared to the finite element model for all distribution factors. The standard specifications predictions of girder distribution factors ranged from highly unconservative to highly conservative when compared to the finite element model. For the study bridge, the LRFD specifications would result in a safe design, though exterior girders would be overdesigned. The standard Specifications, however, would result in an unsafe design for interior girders and overdesigned exterior girders.     

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.