Steel Girder Stability during Bridge Erection: AASHTO LRFD Check on L/b Ratios

The erection of steel plate girders during the construction process of a steel bridge is a complex operation, which is often left to the contractor and/or the subcontractor to plan and execute. Rules of thumb have been developed through experience to check the lateral torsional buckling of the steel girder during erection using the maximum L/b (unbraced length/compressive flange width) ratio, below which no lateral torsional buckling would occur. Although the L/b ratio check has proven to be useful and convenient on-site, it is necessary to provide a more rational basis for the rules of thumb, and find the maximum L/b ratios by checking the lateral torsional buckling failure of girders under erection according to the latest AASHTO LRFD code. A series of parametric studies were conducted on cantilever and simply supported girders under self-weight as well as self-weight plus wind load, in order to: (1) check the rules of thumb on L/b ratios and (2) determine the effects of girder flange width, flange thickness, web depth, web thickness, and yield strength on the maximum L/b ratio and girder stability during erection. From the results, rules of thumb were modified for girders with common shapes, and it was obvious that (1) self-weight plus wind load controls the girder stability during erection in most cases and (2) flange width and web depth have the most effects on the maximum L/b ratio and girder stability during erection.     

Lateral Stiffness of Steel Bridge I-Girders Braced by Metal Deck Forms

The lateral-torsional buckling capacity of steel bridge girders is often increased by incorporating bracing along the girder length. Permanent metal deck forms (PMDF) that are used to support the wet concrete deck during bridge construction are a likely source of stability bracing; however, their bracing performance is greatly limited by flexibility in the connections currently used with the formwork. This paper outlines results from a research study that assessed and improved the bracing potential of metal deck forms used in bridge applications. The research study included shear tests of PMDF panels, and also lateral displacement and buckling tests of twin girder systems braced with PMDF. This paper will provide key results from the shear panel tests and then focus on the lateral displacement tests. Parametric investigations of PMDF bracing behavior were conducted using finite-element analyses and the results from the lateral displacement tests served a critical role in calibrating the finite element models. This paper documents key results from lateral load tests of 17 girder–PMDF systems using a variety of bracing details and PMDF thickness values.     

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.     

Feasibility of a 1,400 m Span Steel Cable-Stayed Bridge

This paper describes the feasibility of 1,400 m steel cable-stayed bridges from both structural and economic viewpoints. Because the weight of a steel girder strongly affects the total cost of the bridge, the writers present a procedure to obtain a minimum weight for a girder that ensures safety against static and dynamic instabilities. For static instability, elastoplastic, finite-displacement analysis under in-plane load and elastic, finite-displacement analysis under displacement-dependent wind load are conducted; for dynamic instability, multimodal flutter analysis is carried out. It is shown that static critical wind velocity of lateral torsional buckling governs the dimension of the girder. Finally, the writers briefly compare a cable-stayed bridge with suspension bridge alternatives.     

Composite Action and Adhesive Bond between Fiber-Reinforced Polymer Bridge Decks and Main Girders

This paper describes the behavior of hybrid girders consisting of fiber-reinforced polymer (FRP) bridge decks adhesively connected to steel main girders. Two large-scale girders were experimentally investigated at the serviceability and ultimate limit state as well as at failure. One of the girders was additionally fatigue loaded to 10 million cycles. Compared to the behavior of a reference steel girder, deflections of the two girders at the SLS were decreased by 30% and failure loads increased by 56% due to full composite action in the adhesive layer. A ductile failure mode occurred: Deck compression failure during yielding of the steel girder. The adhesive connections were able to prevent buckling of the yielding top steel flanges. Thus, compared to the reference steel girder, the maximum deflections at failure could be increased up to 130%. No deterioration due to fatigue loading was observed. Based on the experimental results, a conceptual design method for bonded FRP/steel girders was developed. The proposed method is based on the well-established design method for hybrid girders with concrete decks and shear stud connections. The necessary modifications are proposed.     

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.     

Lateral-Torsional Buckling of Stepped Beams with Continuous Bracing

Continuous span multibeam steel bridges are common along the state and interstate highways. The top flange of the beams is typically braced against lateral movement by the deck slab, and in many bridges the cross section is stepped at discrete points along the span. Design equations for lateral–torsional buckling (LTB) resistance in the American Association of State Highway and Transportation Officials “Load and resistance factor design bridge design specifications” are for prismatic beams and ignore the lateral restraint provided by the bridge deck. A new design equation is proposed that can be applied to I-shaped stepped beams with continuous top flange lateral bracing. By including the effects of the change in cross section size and the continuous top flange bracing, the calculated LTB resistance is significantly increased. Critical bending moment values from the proposed equation are compared to values from finite element method buckling analyses. The new equation is sufficiently accurate for use in design and in the evaluation of existing bridges.     

Stability Bracing Requirements for Steel Bridge Girders with Skewed Supports

Cross frames and diaphragms are critical elements for the stability of I-shaped steel bridge girders during construction. The AASHTO specifications are relatively vague with regards to the stability design requirements of the braces. Spacing limits that have been used in past AASHTO specifications have been removed from the Load and Resistance Factor Design Specification, which instead requires the bracing to be designed by a rational analysis. Whereas the AASHTO specification does not define what constitutes a rational analysis, stability bracing systems must possess adequate stiffness and strength. The commercially available software packages that are typically used in bridge design generally do not have the capabilities to determine the adequacy of the bracing from a stability perspective. This paper outlines the stability bracing requirements for bridges with normal and skewed supports. The effects of support skew on the stiffness and strength requirements for stability bracing are addressed. Solutions that are available for systems with normal supports were modified to account for the effects of the support skew angle. Two orientations of the intermediate bracing were considered: parallel to the skew angles and perpendicular to the longitudinal girder axis. The solutions are presented and compared with finite-element results. The design solutions have good agreement with the finite-element solutions.     

Experimental Study on Moment–Plastic Rotation Capacity of Hybrid Beams

The moment–inelastic rotation behavior of hybrid steel girder bridges is experimentally investigated. Six welded girders having compact flanges and webs are statically loaded under three-point bending condition in order to simulate the interior pier section of a two-span continuous girder. Six girders, three with hybrid sections and three with homogeneous sections, are designed with three types of web slenderness ratios, resulting in three pairs of hybrid and homogeneous girders. The inelastic rotation capacities obtained from the experimental tests are then compared between hybrid and homogeneous girders. In addition, the results are compared with the prediction moment–inelastic rotation curve proposed in 1998 by White and Barth. It is concluded that, under the condition in this study, hybrid girders have more deformation capacity than homogeneous girders, and that the prediction curve is more conservative for a specimen with higher web slenderness ratio.     

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.     

Torsional Design of Hybrid Concrete Box Girders

Hybrid concrete box-girder bridges that include prestressed slabs and corrugated steel webs provide a major improvement over traditional prestressed concrete box-girder bridges. To reduce the self-weight, high strength concrete is used for the top and bottom slabs and corrugated steel webs are employed for the webs. Because the weight of the girders has been reduced, the span length can be increased for more cost-effective design. A series of systematic tests on hybrid concrete box girders subjected to torsion has been performed. According to the test results, an analytical model was developed. Using the developed analytical model, a step-by-step procedure for torsional design of such bridges is presented in this article. Based on the design procedure proposed, a girder is designed by the analytical model and checked to satisfy structural codes.     

Effective Bond Length of Carbon-Fiber-Reinforced Polymer Strips Bonded to Fatigued Steel Bridge I-Girders

After years in service, many steel girders have deteriorated to the point where fatigue cracks have initiated in the girders. In girders having cover plates that do not terminate in a compression region, a common type of crack initiates at the weld toe at the ends of the cover plate after being subjected to cyclic tensile loads due to traffic. The use of precured carbon-fiber-reinforced polymer (CFRP) laminates, adhered to the inside face of the girder tension flange, is one proposed method for repairing these cracked bridge girders. The main advantages of using CFRP laminates are their light weight and their durability, which result in ease of handling and maintenance. For the application of this rehabilitation method, it is important to determine the effective bond length for CFRP laminates adhered to the inside face of a cracked steel girder flange. Experimental tests using a new type of effective bond length test specimen were conducted in this research on several types of adhesives and precured CFRP laminates, in addition to several different bonding configurations. The minimum bond length required to achieve the maximum strength of the rehabilitation scheme for the materials investigated in this research was determined. The experimental results also indicated that an adhesive with relatively large ductility is required to redistribute the stresses successfully within the adhesive layer during increased loading. A simple analytical solution for the shear strain distribution in the adhesive layer was proposed for estimating the effective bond length, and the results were verified with computational analyses. Good agreement was found among the computational, analytical, and experimental results.     

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.     

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.     

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.     

Stability of Slender Webs of Prestressed Concrete Box-Girder Bridges

Long-span, prestressed concrete, box-girder bridges are haunched and have a span-to-depth ratio of 15 to 20 at the piers. This leads to slender webs, particularly for bridges built with high performance concrete. For girders with sloped webs and constant bottom slab width, the web plate is normally warped, which leads to web curvature in the direction of the principal compressive stresses. It is first shown that buckling is not critical as long as the web is uncracked. But, if the webs have shear cracks, the slenderness ratio of the diagonal compression struts can be very high so that the moments and stability of the curved struts need to be studied. It is shown that the tensile forces in the stirrups—determined according to the truss analogy—will counteract the lateral deformations of the slender compression struts. The procedure, which was developed for the design of the Confederation Bridge in Eastern Canada, will be illustrated by applying it to the slender webs of that bridge.     

Static Stability of Beam-Columns under Combined Conservative and Nonconservative End Forces: Effects of Semirigid Connections

Stability criteria that evaluate the effects of combined conservative and nonconservative end axial forces on the elastic divergence buckling load of prismatic beam-columns with semirigid connections is presented using the classic static equilibrium method. The proposed method and stability equations follow the same format and classification of ideal beam-columns under gravity loads presented previously by Aristizabal-Ochoa in 1996 and 1997. Criterion is also given to determine the minimum lateral bracing required by beam-columns with semirigid connections to achieve “braced” buckling (i.e., with sidesway inhibited). Analytical results obtained from three cases of cantilever columns presented in this paper indicate that: (1) the proposed method captures the limit on the range of applicability of the Euler’s method in the stability analysis of beam-columns subjected to simultaneous combinations of conservative and nonconservative loads. The static method as proposed herein can give the correct solution to the stability of beam-columns within a wide range of combinations of conservative and nonconservative axial loads without the need to investigate their small oscillation behavior about the equilibrium position; and (2) dynamic instability or flutter starts to take place when the static critical loads corresponding to the first and second mode of buckling of the column become identical to each other. “Flutter” in these examples is caused by the presence of nonconservative axial forces (tension or compression) and the softening of both the flexural restraints and the lateral bracing. In addition, the “transition” from static instability (with sidesway and critical zero frequency) to dynamic instability (with no sidesway or purely imaginary sidesway frequencies) was determined using static equilibrium. It was found also that the static critical load under braced conditions (i.e., with sidesway inhibited) is the upper bound of the dynamic buckling load of a cantilever column under nonconservative compressive forces. Analytical studies indicate the buckling load of a beam-column is not only a function of the degrees of fixity (ρa and ρb), but also of the types and relative intensities of the applied end forces (Pci and Pfj), their application parameters (ci, ηj, and ξj), and the lateral bracing provided by other members (SΔ).     

Stiffness and Strength of Metal Bridge Deck Forms

Light gauge metal sheeting is often utilized in the building and bridge industries for concrete formwork. Although the in-plane stiffness and strength of the metal forms are commonly relied upon for stability bracing in buildings, the forms are generally not considered for bracing in steel bridge construction. The primary difference between the forming systems in the two industries is the method of connection between the forms and girders. In bridge construction, an eccentric support angle is incorporated into the connection details to achieve a uniform slab thickness along the girder length. While the eccentric connection is a benefit for slab construction, the flexible connection limits the amount of bracing provided by the forms. This paper presents results from the first phase of a research study investigating the bracing behavior of metal bridge deck forms. Shear diaphragm tests were conducted to determine the shear stiffness and strength of bridge deck forms, and modified connection details were developed that substantially improve the bracing behavior of the forms. The measured stiffness and strength of diaphragms with the modified connection often met or exceeded the values of diaphragms with conventional noneccentric connections. The experimental results for the diaphragms with the modified connection details dramatically improve the potential for bracing of steel bridge girders by metal deck forms.     

Ductility Evaluation of Concrete-Encased Steel Bridge Piers Subjected to Lateral Cyclic Loading

An experimental and analytical study was conducted to investigate the ductility of concrete-encased steel piers, referred to as “steel-reinforced concrete (SRC) construction.” Based on the cyclic lateral loading tests of SRC column specimens, the restorable and ultimate limit states are defined as the point when concrete cover spalling occurs (equivalent to longitudinal bar buckling) and the point when flange buckling of the H-shaped steel occurs, respectively. To estimate the lateral displacement capacity at both the restorable and ultimate limit states, the curvature distribution of the column was calculated based on the buckling analysis of the longitudinal bar, which was restrained by a concrete cover and transverse reinforcement, and of the steel flange encased in concrete. The lateral displacement was obtained by integrating the curvature distribution. Comparison of the computed results with experimental results, including other writers’ reports, confirmed that the proposed method can appropriately estimate the lateral displacement at the restorable and ultimate limit states, and it can accurately evaluate the buckling characteristics of the longitudinal bar and steel flange components of SRC column specimens.