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.     

Experimental Verification of Horizontally Curved I-Girder Bridge Behavior

Past research has been conducted on the behavior of horizontally curved girders by testing scaled models and full-scale laboratory bridges and by analyzing numerical models. Current design specifications are based on this past research; however, little field data of in-service bridges exist to support the findings of the past research on which the current design criteria are based. The purpose of the present study was to gather field response data from three in-service, curved, steel I-girder bridges to determine behavior when subjected to a test truck and normal truck traffic. Transverse bending distribution factors and dynamic load allowance were calculated from the data collected. Numerical grillage models of the three bridges were developed to determine if a simple numerical model will accurately predict actual field measured transverse bending distribution, deflections, and cross-frame and diaphragm shear forces. The present study found that AASHTO specifications are conservative for both dynamic load allowance and transverse bending moment distribution. The grillage models were found to predict with reasonable accuracy the behavior of a curved I-girder bridge.     

Evaluation of Live-Load Lateral Flange Bending Distribution for a Horizontally Curved I-Girder Bridge

This paper focuses on levels of live-load lateral bending moment (bimoment) distribution in a horizontally curved steel I-girder bridge. Work centered primarily on the examination of (1) data from field testing of an in-service horizontally curved steel I-girder bridge and (2) results from a three-dimensional numerical model. Experimental data sets were used for calibration of the numerical model and the calibrated model was then used to examine the accuracy of lateral bending distribution factor equations presented in the 1993 Edition of the (AASHTO) Guide Specifications for Horizontally Curved Bridges. It is of interest to examine these equations for potential use in preliminary design even though they have been eliminated during recent AASHTO specification modifications that addressed curved bridge analysis, the 2005 Interims to the AASHTO LRFD Bridge Design Specifications. In addition, they were developed using idealized computer models and small-scale laboratory testing with very few field tests of in-service full-scale curved steel bridges conducted to support or refute their use. Results from such experimental and numerical studies are presented and discussed herein.     

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.     

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 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.     

Effect of Skewness on the Distribution of Live Load Reaction at Piers of Skewed Continuous Bridges

This paper presents a study of the skewness effect on live load reactions at the piers of continuous bridges. Two prestressed concrete I-beam bridges and one steel I-girder bridge were selected for the study. To evaluate the skew effect, the skew angle of the bridges was varied from 0 to 60°. Live load reaction at support and shear at the beam ends of the selected bridges were determined using finite-element analysis. The comparison of the distribution factors of live load reactions and shear revealed that the distribution factor of reaction at piers was higher than that of shear at beam ends near the same support. The increase in the reaction distribution factor was more significant than that in the shear distribution factor in the interior beam line when the skew angle was greater than 30°. The LRFD shear equations and the Lever rule method could conservatively predict live load reaction distribution for piers in exterior beam lines but underestimate live load reaction distribution in interior beam lines. It is recommended that more research be performed for the distribution factor of live load reaction to quantify the responses.     

Distribution Factors for Curved Continuous Composite Box-Girder Bridges

The use of horizontally curved composite box-girder bridges in modern highway systems has become increasingly popular for economic as well as for aesthetic considerations. Based on a recent literature review on the design of box-girder bridges, it was observed that a simple design method for curved bridges, based on load distribution factors for stresses and shears, is as yet unavailable. This paper presents the results of an extensive parametric study, using a finite element method, in which the structural responses of 240 two-equal-span continuous curved box-girder bridges of various geometries were investigated. The parameters considered in this study included span-to-radius of curvature ratio, span length, number of lanes, number of boxes, web slope, number of bracings, and truck loading type. Based on the data generated from this study, empirical formulas for load distribution factors for maximum longitudinal flexural stresses and maximum deflection due to dead load as well as AASHTO live loading were deduced. An illustrative design example is presented.     

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

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

3D Coordinating Relations between Steel Cables and Concrete of Prestressed Concrete Beam Bridges

Interaction between steel cables and concrete is complicated in prestressed concrete bridges, especially in curved prestressed concrete bridges. The most significant behavior of curved beam bridges under the loads is that, at the same time of vertical flexure, torsion occurs on the cross section, which complicates the mechanical analysis to curved beam bridges. Based on coordinating relations of steel cables and concrete (CRSC), the grillage structure finite-element method was adopted to analyze the spatial effect of curved beam bridges. This way, the effect of all prestressing procedures can be simulated properly, including the prestressing loss due to concrete shrinkage and creep, batch prestressing of the cables, etc. Furthermore, it is effective to analyze the integrated behavior of the combined steel cables space out and concrete. The efficiency and reliability of the CRSC method is demonstrated by our analysis system WXQ2.0 developed for curved-skew bridges.     

Sensitivity of Live Load Distribution Factors to Vehicle Spacing

Two slab-on-girder bridge superstructures are analyzed using grillage models. Different live load placement configurations are investigated to determine the sensitivity of live load shear and moment to vehicle spacing. Results from both bridges show that the distribution factors are relatively insensitive to vehicle spacing. Therefore significant computational speedups are available when applying vehicle loads on an influence surface with a fixed spacing.     

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.     

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.     

Live Load Distribution Formulas for Single-Span Prestressed Concrete Integral Abutment Bridge Girders

In this study, live load distribution formulas for the girders of single-span integral abutment bridges (IABs) are developed. For this purpose, two and three dimensional finite-element models (FEMs) of several IABs are built and analyzed. In the analyses, the effects of various superstructure properties such as span length, number of design lanes, prestressed concrete girder size, and spacing as well as slab thickness are considered. The results from the analyses of two and three dimensional FEMs are then used to calculate the live load distribution factors (LLDFs) for the girders of IABs as a function of the above mentioned parameters. The LLDFs for the girders are also calculated using the AASHTO formulas developed for simply supported bridges (SSBs). The comparison of the analyses results revealed that LLDFs for girder moments and exterior girder shear of IABs are generally smaller than those calculated for SSBs using AASHTO formulas especially for short spans. However, AASHTO LLDFs for interior girder shear are found to be in good agreement with those obtained for IABs. Consequently, direct live load distribution formulas and correction factors to the current AASHTO live load distribution equations are developed to estimate the girder live load moments and exterior girder live load shear for IABs with prestressed concrete girders. It is observed that the developed formulas yield a reasonably good estimate of live load effects in prestressed concrete IAB girders.     

Recommended Procedures for Simplified Inelastic Design of Steel I-Girder Bridges

This paper presents summary recommendations pertaining to new AASHTO procedures for simplified inelastic design of steel I-girder bridges. First, key developments are summarized that lead to the proposed inelastic design approach. The paper then outlines a set of equations that provide an improved characterization of the inelastic moment-rotation response for a wide range of I-beams and plate girders. Effective plastic moment predictions based on these equations are combined with the recently proposed design method, resulting in greater accuracy and simplicity of the proposed approach. The ease of use of the resulting procedure is illustrated by a design example.     

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.     

Response of Prestressed Concrete I-Girder Bridges to Live Load

Design and evaluation of prestressed concrete I-girder bridges is in large part dependent on the transverse load distribution characteristics and the dynamic load amplification, as well as service level, live load, and tensile stresses induced in the girders. This study presents the results of field tests conducted on three prestressed concrete I-girder bridges to obtain dynamic load allowance statistics, girder distribution factors (GDF), and service level stress statistics. The field-based data are also compared to approximate and numerical model results. Bridge response was measured at each girder for the passage of test trucks and normal truck traffic. The dynamic amplification is observed to be a strong function of peak static stress and a weak function of vehicle speed and is independent of span length, number of axles, and configuration. GDFs for one- and two-lanes are less than code specified GDFs. Results from the numerical grillage models agree closely with experimentally derived results for transverse distribution.     

Load Distribution for a Highly Skewed Bridge: Testing and Analysis

The American Association of State Highway and Transportation Officials (AASHTO) specifications provide formulas for determining live load distribution factors for bridges. For load distribution factors to be accurate, the behavior of the bridge must be understood. While the behavior of right-angle bridges and bridges with limited skews is relatively well understood, that of highly skewed bridges is not. This paper presents a study aimed at developing a better understanding of the transverse load distribution for highly skewed slab-on-steel girder bridges. The study involved both a diagnostic field test of a recently constructed bridge and an extensive numerical analysis. The bridge tested and analyzed is a two-span, continuous, slab-on-steel composite highway bridge with a skew angle of 60°. The bridge behavior is defined based on the field test data. Finite-element analyses of the bridge were conducted to investigate the influence of model mesh, transverse stiffness, diaphragms, and modeling of the supports. The resulting test and analytical results are compared with AASHTO’s Load and Resistance Factor Design formulas for live load distribution to assess the accuracy of the current empirical formulas.     

Influence of Secondary Elements and Deck Cracking on the Lateral Load Distribution of Steel Girder Bridges

The AASHTO LRFD load distribution factor equation was developed based on elastic finite element analysis considering only primary members, i.e., the effects of secondary elements such as lateral bracing and parapets were not considered. Meanwhile, many bridges have been identified as having significant cracking in the concrete deck. Even though deck cracking is a well-known phenomenon, the significance of pre-existing cracks on the live load distribution has not yet been assessed. The purpose of this research is to investigate the effect of secondary elements and deck cracking on the lateral load distribution of girder bridges. First, secondary elements such as diaphragms and parapets were modeled using the finite element method, and the calculated load distribution factors were compared with the code-specified values. Second, the effects of typical deck cracking and crack types that have a major effect on load distribution were identified through a number of nonlinear finite element analyses. It was established that the presence of secondary elements may produce load distribution factors up to 40% lower than the AASHTO LRFD values. Longitudinal cracking was found to increase the load distribution factor by up to 17% when compared to the LRFD value while the transverse cracking was found to not significantly influence the transverse distribution of moment.     

Theoretical Evaluation of Flange Local Buckling for Horizontally Curved I-Girders

Curvature greatly complicates the behavior of horizontally curved steel plate girders used in bridge superstructures. The warping stress gradient across the width of I-girder flange plates reduces the vertical bending stress at which the flange plate buckles. The 2007 AASHTO Load and Resistance Factor Design Specifications eliminate the shortcomings of the 2003 AASHTO Guide Specifications for Horizontally Curved Bridges by unifying the flexural design of tangent and curved I-girder bridges. This paper evaluates flange local buckling resistance based upon theoretical and analytical models that consider the effect of stress gradient across the flange coupled with the influence of rotational resistance provided by the web. The developed equations are verified using the finite element method, and the potential impact is demonstrated using the design example presented in the Guide Specifications.