Behavior of Curved I-Girder Webs Subjected to Combined Bending and Shear

Two previous papers by the writers described the buckling and finite-displacement behavior of curved I-girder web panels subjected to pure bending, presented a theoretically pure analytical model, and presented equations that describe the reduction in strength due to curvature. This paper describes the buckling and finite-displacement behavior of curved web panels under combined bending and shear. Unlike straight girder web panels, the addition of shear in curved panels is shown to increase the transverse “bulging” displacement of the web prior to buckling. The accompanying decrease in moment carrying capacity is analyzed in a manner similar to that used for the combined bending and shear nominal strength interaction for straight girder design. Preliminary recommendations are made toward forming design criteria for curved webs.     

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.     

Flutter of an Arch Bridge via a Fully Nonlinear Continuum Formulation

A fully nonlinear parametric model for wind-excited arch bridges is proposed to carry out the flutter analysis of Ponte della Musica under construction in Rome. Within the context of an exact kinematic formulation, all of the deformation modes are considered (extensional, shear, torsional, in-plane, and out-of-plane bending modes) both in the deck and supporting arches. The nonlinear equations of motion are obtained via a total Lagrangian formulation while linearly elastic constitutive equations are adopted for all structural members. The parametric nonlinear model is employed to investigate the bridge limit states appearing either as a divergence bifurcation (limit point obtained by path following the response under an increasing multiplier of the vertical accidental loads) or as a Hopf bifurcation of a suitable eigenvalue problem (where the bifurcation parameter is the wind speed). The eigenvalue problem ensues from the governing equations of motion linearized about the in-service prestressed bridge configuration under the dead loads and wind-induced forces. The latter are expressed in terms of the aeroelastic derivatives evaluated through wind-tunnel tests conducted on a sectional model of the bridge. The results of the aeroelastic analysis—flutter speed and critical flutter mode shape—show a high sensitivity of the flutter condition with respect to the level of prestress and the bridge structural damping.     

Exact Solution of Out-of-Plane Problems of an Arch with Varying Curvature and Cross Section

This paper deals with the exact solution of the differential equations for the out-of-plane behavior of an arch with varying curvature and cross section. The differential equations include the shear deformation effect. The cross section of the arch is doubly symmetric. Due to the double symmetry, in-plane and out-of-plane behavior will be uncoupled. However, a coupling of the out-of-plane bending and the torsional response will exist and will be discussed in this study. The governing differential equations of planar arches loaded perpendicular to their plane are solved exactly by using the initial value method. The analytical expressions of the fundamental matrix can be obtained for some cases. It is also possible to use these analytical expressions in order to obtain the displacements and the stress resultants for an arch with any loading and boundary conditions. The examples given in the literature are solved and the results are compared. The analytical expressions of the results are given for some examples.     

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.     

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.     

Analytical Model of Curved I-Girder Web Panels Subjected to Bending

Curvature greatly complicates the behavior of curved plate girders used in bridges. The out-of-plane “bulging” displacement of the curved web results in an increase in stress, which must be considered in the design of plate girders with significant curvature. The currently used Guide Specifications for Horizontally Curved Bridges provides web slenderness reduction equations that account for curvature effects, but these equations were based on a regression of limited data from experimental and unit-strip analyses conducted in the early 1970s. This paper presents a theoretically pure analytical model that can be used to predict the transverse displacement and induced plate bending stresses of curved I-shaped plate girder web panels subjected to bending. Several boundary conditions are demonstrated and compared, and the finite-element method is used to verify the closed-form solutions. The effects of curvature on the elastic buckling behavior of curved web panels is also presented. Furthermore, a comprehensive literature review is presented, including numerous Japanese publications not readily available to American researchers.     

Behavior of Pultruded Fiber-Reinforced Polymer Beams Subjected to Concentrated Loads in the Plane of the Web

Results of the behavior of pultruded fiber-reinforced polymer (FRP) I-shaped beams subjected to concentrated loads in the plane of the web are presented. Twenty beams with nominal depths from 152.4 to 304.8?mm were tested in three-point bending with a span-to-depth ratio of four. Load was applied to the top flange directly above the web—12 without bearing plates and 8 with bearing plates of varying width and thickness. All test specimens failed with a wedgelike shear failure at the upper web-flange junction. Finite-element results support experimental findings from strain gauge and digital image correlation data. Bearing plates increased beam capacity by 35% or more as a function of bearing plate width and thickness. Bearing plates increased average shear stress in the web at failure from 17.4 to 27.2?MPa—below the accepted value of in-plane shear strength (69?MPa). A design equation is presented, and predicted capacities are compared with experimental results. The average value of experimental capacity to predicted capacity is 1.12 with a standard deviation of 0.11 and coefficient of variation (COV) of 0.10 for sections up to 304.8?mm deep.     

Effects of Longitudinal Stiffeners on Curved I-Girder Webs

Two previous papers by the writers described the buckling and finite-displacement behavior of curved I-girder web panels without longitudinal stiffeners subjected to pure bending, presented a theoretically pure analytical model, and presented equations that describe the reduction in strength due to curvature. This paper describes the optimum location and strength effects of one and two longitudinal stiffeners attached to curved I-shaped plate girders. Using lateral load and lateral pressure analogies similar to that described in the earlier papers, strength reduction equations are formulated for curved plate girders with longitudinal stiffeners. A comprehensive comparison is made between the equations developed in this investigation and design equations used in Japanese and American design guides, and the applicability and superiority of the method is demonstrated.     

Validation of Analytical Multiparameter Homogenization Models for Out-of-Plane Loaded Masonry Walls by Means of the Finite Element Method

The linear elastic analysis of in-plane and out-of-plane loaded masonry walls is still significant under service loads and is required by codes of practice, therefore the knowledge of the homogenized mechanical properties of masonry is of relevant interest. The aim of this paper is to discuss the problem of the out-of-plane loaded masonry walls in detail and to assess the accuracy and reliability of different homogenization approaches presented in the technical literature, with particular interest in recent explicit formulas obtained through an asymptotic model (as reported by Cecchi and Sab in 2002). Several meaningful comparisons are presented for different types of new and historical masonry structures currently employed in Italy. The validation of the analytical models is carried out by means of a three-dimensional (3D) finite-element (FE) out-of-plane homogenization. A final structural comparison among analytical models, FE out-of-plane homogenization, and a computationally expensive heterogeneous 3D FE model is discussed for a simply supported square panel laterally loaded.     

Performance Evaluation of FRP Bridge Deck Component under Torsion

Torsional response of fiber-reinforced polymeric (FRP) composites is more complex than conventional materials. Therefore, understanding torsional response of FRP components along with shear behavior leads to development of safe and accurate design specifications. Experimental data of multicellular FRP bridge deck components have been compared with simplified theoretical model studies focused on torsional rigidity, equivalent in-plane shear modulus, in-plane shear strain, and joint efficiency. Simplified classical lamination theory (SCLT) is used to predict torsional rigidity. Results from SCLT, experimental data, and finite-element analysis validate proposed methodology to find torsional rigidity. Data on torsional rigidity and equivalent in-plane shear modulus correlated (less than 12%) with results from SCLT and finite-element analysis. In-plane shear strain based on SCLT is also concordant with test results. In an FRP deck system with 100% joint efficiency, the two-dimensional effect (plate action) on torsional rigidity results in a 20% higher rigidity when compared to a beam model. However, if a refined model has only 80% joint efficiency, then plate action results in a 6% difference from the beam model. In addition, service load design criteria for FRP decks under shear must not excess 16% of the ultimate strain by accounting for environmental and aging effects.     

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.     

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.     

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

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

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.     

Equivalent Beam-Column Method to Estimate In-Plane Critical Loads of Parabolic Fixed Steel Arches

The objective of this paper is to investigate the characteristics of critical loads for parabolic fixed steel tubular arches. An advanced nonlinearity finite-element program, taking into account the geometric and material dual nonlinearity, is employed. The influence of nonlinearity and initial crookedness on arch critical load is discussed. It is found that the effect of rise-to-span ratio on the critical load of arch is significant. Therefore, a new equivalent beam-column method is proposed for estimating the corresponding in-plane critical loads of arch, in which a buckling factor K1 is employed to consider influence of rise-to-span ratio and a reduction factor K2 to consider the effect of initial crookedness. Pragmatic formulas and tabulated data are provided based on the present different Chinese design codes. It is proved that the presented method is sufficiently accurate to predict the in-plane critical load of parabolic fixed steel arch subjected to compression or to both bending and compression.     

Bounds on Flexural Properties and Buckling Response for Symmetrically Laminated Composite Plates

Nondimensional parameters and equations governing the buckling behavior of rectangular symmetrically laminated plates are presented that can be used to represent the buckling resistance, for plates made of all known structural materials, in a very general, insightful, and encompassing manner. In addition, these parameters can be used to assess the degree of plate orthotropy, to assess the importance of anisotropy that couples bending and twisting deformations, and to characterize quasi-isotropic laminates quantitatively. Bounds for these nondimensional parameters are also presented that are based on thermodynamics and practical laminate construction considerations. These bounds provide insight into potential gains in buckling resistance through laminate tailoring and composite-material development. As an illustration of this point, upper bounds on the buckling resistance of long rectangular orthotropic plates with simply supported or clamped edges and subjected to uniform axial compression, uniform shear, or pure in-plane bending loads are presented. The results indicate that the maximum gain in buckling resistance for tailored orthotropic laminates, with respect to the corresponding isotropic plate, is in the range of 26–36% for plates with simply supported edges, irrespective of the loading conditions. For the plates with clamped edges, the corresponding gains in buckling resistance are in the range of 9–12% for plates subjected to compression or pure in-plane bending loads and potentially up to 30% for plates subjected to shear loads.     

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.     

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.     

Novel Technique for Inhibiting Buckling of Thin-Walled Steel Structures Using Pultruded Glass FRP Sections

The use of composite materials for strengthening the ailing infrastructure has been steadily gaining acceptance and market share. It can even be stated that this strengthening technique has become main stream in some applications such as strengthening concrete structures. The same cannot be said about steel structures; for which research on composite material strengthening is relatively new. Several challenges face strengthening steel structures using composite materials such as the need for high-modulus composites to improve the effectiveness of the strengthening system. This paper explores a new approach for strengthening steel structures by introducing additional stiffness to buckling-prone regions. The proposed technique relies on improving the out-of-plane stiffness of buckling-prone members by bonding pultruded fiber-reinforced polymer (FRP) sections as opposed to the commonly used approach that relies on in-plane FRP contribution. The paper presents results from an experimental investigation where shear-controlled beam specimens were tested to explore the feasibility of the proposed technique. Bar specimens were also tested in tension to compare between in-plane and out-of-plane contributions of FRP to the behavior and strength of thin steel plates. Based on the results, it can be concluded that this strengthening technique has great potential for altering failure modes by delaying the initiation of undesirable local buckling of thin steel plates. Recommendations for future research efforts are made to expand the knowledge base about this unexplored strengthening technique.