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.     

Monitoring Steel Girder Stability for Safer Bridge Erection

The collapse of the State Route 69 Bridge over the Tennessee River near Clifton, Tennessee, is an example of how instability and lateral torsional buckling failure of a single steel bridge girder during erection might cause collapse of the whole steel superstructure. Close attention should be given to the stability of steel plate girders during erection when the lateral support provided to the compression flange might temporarily not be present. Rules of thumb in use today have been adopted by contractors/subcontractors to check the stability of cantilever or simply supported girders under erection using the L/b ratio, where L is the unbraced length and b is the compression flange width. For each girder section, a maximum L/b ratio exists beyond which lateral torsional buckling failure would occur under girder self-weight. Parametric studies were conducted following the latest AASHTO LRFD code in order to indentify the maximum L/b ratio for various girder sections and check the rules of thumb, as well as determine the dominating section parameters on girder stability under erection. Advanced nonlinear finite-element analyses were also conducted on a girder section for both the cantilever and the simply supported case in order to further understand the behavior of girder instability due to lateral torsional buckling under the self-weight, as well as to develop a trial-and-error methodology for identifying the maximum L/b ratio using computer analysis. At the same time, the effect of lateral bracing location on the cantilever free end has been investigated, and it turned out that bracing the top tension flange would be more effective to prevent lateral torsional buckling than bracing the bottom compression flange.     

Stability Analysis of Box-Girder Cable-Stayed Bridges

The objective of this study is to investigate the stability characteristics of box-girder cable-stayed bridges by three-dimensional finite-element methods. Cable-stayed bridges have many design parameters, because they have a lot of redundancies, especially for long-span bridges. Cable-stayed bridges exhibit several nonlinear behaviors concurrently under normal design loads because of large displacements; the interaction among the pylons, the stayed cables, and the bridge deck; the strong axial and lateral forces acting on the bridge deck and pylons; and cable nonlinearity. A typical two-lane, three-span, steel box-girder cable-stayed bridge superstructure was selected for this paper. The numerical results indicate that, if the ratio of the main span length with respect to the total span length, L1∕L, is small, the structure usually has a higher critical load. If the ratio Ip∕Ib increases, the critical load of the bridge decreases, in which Ip is the moment of inertia of the pylon and Ib is the moment of inertia of the bridge deck. When the ratio Ip∕Ib is greater than 10.0, the decrement becomes insignificant. For cable arrangements, bridges supported by a harp-type cable arrangement are the better design than bridges supported by a fan-type cable arrangement on buckling analysis. The numerical results also indicate that use of either A-type or H-type pylons does not significantly affect the critical load of this type of structure. In order to make the numerical results useful, the buckling loads have been nondimensionalized and presented in both tabular and graphical forms.     

Dynamic Modal Analysis and Stability of Cantilever Shear Buildings: Importance of Moment Equilibrium

The dynamic modal analysis (i.e., the natural frequencies, modes of vibration, generalized masses, and modal participation factors) and static stability (i.e., critical loads and buckling modes) of two-dimensional (2D) cantilever shear buildings with semirigid flexural restraint and lateral bracing at the base support as well as lumped masses at both ends and subjected to a linearly distributed axial load along its span are presented using an approach that fulfills both the lateral and moment equilibrium conditions along the member. The proposed model includes the simultaneous effects and couplings of shear deformations, translational and rotational inertias of all masses considered, a linearly applied axial load along the span, the shear force component induced by the applied axial force as the member deforms and the cross section rotates, and the rotational and lateral restraints at the base support. The proposed model shows that the stability and dynamic behavior of 2D cantilever shear buildings are highly sensitive to the coupling effects just mentioned, particularly in members with limited rotational restraint and lateral bracing at the base support. Analytical results indicate that except for members with a perfectly clamped base (i.e., zero rotation of the cross sections), the stability and dynamic behavior of shear buildings are governed by the flexural moment equation, rather than the second-order differential equation of transverse equilibrium or shear-wave equation. This equation is formulated in the technical literature by simply applying transverse equilibrium “ignoring” the flexural moment equilibrium equation. This causes erroneous results in the stability and dynamic analyses of shear buildings with base support that is not perfectly clamped. The proposed equations reproduce, as special cases: (1) the nonclassical vibration modes of shear buildings including the inversion of modes of vibration when higher modes cross lower modes in shear buildings with soft conditions at the base, and the phenomena of double frequencies at certain values of beam slenderness (L/r); and (2) the phenomena of tension buckling in shear buildings. These phenomena have been discussed recently by the writer (2005) in columns made of elastomeric materials.     

Moment-Inelastic Rotation Behavior of Longitudinally Stiffened Beams

The significance for inelastic design of moment-inelastic rotation behavior with respect to interior pier sections of steel girder bridges is experimentally investigated. Under center span loading conditions, 12 welded, built-up, simply supported beams with various slenderness ratios of the flange and web plates are tested. In this test, lengths and locations for partial longitudinal stiffeners on the web plates are varied, and the results are then compared with the inelastic deformation capacity of beams without longitudinally stiffened web plates. The results are also compared with the inelastic design code in AASHTO LRFD bridge design specifications. It is concluded that (1) the ultimate strength of stiffened beams is governed by the local buckling at the compression flange of the far end from the loading point due to the presence of a partial longitudinal stiffener; and (2) the inelastic rotation capacity and ultimate strength of a beam with a stiffened web plate are remarkably improved. The optimum length and location of stiffeners on the plates are given.     

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.     

Design and Evaluation of Experimental Bridges in Tennessee

This paper describes the design and evaluates the adequacy of the moment connection of an experimental two-span highway bridge designed by the Tennessee Department of Transportation. The Massman Drive Bridge is an experimental design that unifies the construction economy of simple span bridges and the structural economy of continuous span bridges. The experimental connection, consisting of cover plates and kicker wedge plates, is used to connect the two adjoining girders over the center pier. As a result, the bridge is designed to function as a continuous bridge during the deck pour and behave compositely with the reinforced concrete deck under the live load. After completing a moment comparison analysis, it is concluded that the Massman Drive Bridge indeed acts as continuous over the pier as it was designed.     

Influence of Changes in Cross Section on the Effectiveness of Externally Bonded FRP Strengthening

There are many situations where strengthening might be required for a nonprismatic reinforced concrete section (i.e., a beam or slab where the depth of the section varies along its length). For example, many bridges in the United Kingdom have inadequate capacity to carry accidental vehicle loads on verges. These shallow depth verges are often cantilevered from the much deeper main bridge deck. The cantilever might be strengthened by applying fiber-reinforced polymer (FRP) composites to the top surface of the cantilever, extending transversely onto the bridge deck. However, a problem may exist with such a situation due to the potential for a dramatic reduction in the degree of strengthening which is achievable. This is due to the effects of cracking, and longitudinal shear stresses. Tests presented in this paper demonstrate that in regions where little or no cracking occurs, local or global debonding of the external FRP may result. Therefore, the strength of some nonprismatic beams, as predicted by current design guidelines, is often shown to be overly conservative and, in one case significantly unconservative. However, more importantly, the predicted failure modes and FRP strains often do not correspond to those observed. Advice on the best approach for analyzing these beams is given.     

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.     

State-of-the-Art in Design of Curved Box-Girder Bridges

The objective of this paper is to provide highlights of the most important references related to the development of current guide specifications for the design of straight and curved box-girder bridges. Subjects discussed in this review include (1) different box-girder bridge configurations; (2) construction issues; (3) deck design; (4) load distribution; (5) deflection and camber; (6) cross-bracing requirements; (7) end diaphragms; (8) thermal effects; (9) vibration characteristics; (10) impact factors; (11) seismic response; (12) ultimate load-carrying capacity; (13) buckling of individual components forming the box cross section; (14) fatigue; and (15) curvature limitations provided by the codes for treating a curved bridge as a straight one. The literature survey presented herein encompasses (1) the construction phase; (2) load distribution; (3) dynamic response; and (4) ultimate load response of box-girder bridges.     

Impact Factors for Curved Continuous Composite Multiple-Box Girder Bridges

The results from a parametric study on the impact factors for 180 curved continuous composite multiple-box girder bridges are presented. Expressions for the impact factors for tangential flexural stresses, deflection, shear forces and reactions are deduced for AASHTO truck loading. The finite-element method was utilized to model the bridges as three-dimensional structures. The vehicle axle used in the analysis was simulated as a pair of concentrated forces moving along the concrete deck in a circumferential path with a constant speed. The effects of bridge configurations, loading positions, and vehicle speed on the impact factors were examined. Bridge configurations included span length, span-to-radius of curvature ratio, number of lanes, and number of boxes. The effect of the mass of the vehicle on the dynamic response of the bridges is also investigated. The data generated from the parametric study and the deduced expressions for the impact factors would enable bridge engineers to design curved continuous composite multiple-box girder bridges more reliably and economically.     

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.     

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.     

Simply Supported Curved Cellular Bridges: Simplified Design Method

The use of curved composite bridges in interchanges of modern highway systems has become increasingly popular for economic and aesthetic considerations. Bridges with a concrete deck composite with a steel multicell section can adequately resist torsional and warping effects induced by high curvature. Although current design practices in North America recommend few analytical methods for the design of curved multicell box girder bridges, economical requirements in the design process point to a need for a simplified design method. This paper summarizes the results from an extensive parametric study, using the finite-element method, in which simply supported curved composite multicell bridge prototypes are analyzed to evaluate the moment and deflection distributions between girders, as well as the axial forces expected in the bracing system, due to truck loading as well as dead load. Results from tests on four, 1∕12 linear-scale, simply supported curved composite concrete deck-steel multicell bridge models are used to substantiate and verify the analytical modeling. The parameters considered in the study are cross-bracing system, aspect ratio, number of lanes, number of cells, and degree of curvature. Based on the data generated from the parametric study, expressions for moment and deflection distribution factors are deduced. Expressions for the maximum axial force in bracing members are also derived. 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.     

Experimental Evaluation of Compressive Behavior of Orthotropic Steel Plates for the New San Francisco–Oakland Bay Bridge

Compression tests were conducted on two reduced-scale orthotropic plates to verify the design strength of steel box girders for the new San Francisco–Oakland Bay Bridge. The first specimen was composed of three longitudinal closed ribs and a top deck plate. It failed in global buckling, followed by local buckling in the deck plate and ribs. The second specimen, which was composed of four longitudinal T-shaped ribs and a bottom deck plate, experienced global buckling as well as local buckling in the ribs and the deck plate. The ultimate strength and failure mode of both specimens were evaluated by two bridge design specifications: the 1998 AASHTO load and resistance factor design specification and the 2002 Japanese JRA specification. Findings from code comparisons showed that: (1) Sufficient flexural rigidity of ribs were provided for both specimens; (2) the JRA specification slightly overestimated the ultimate strength of both specimens; and (3) neither specifications predicted the observed buckling sequence in Specimen 2. A general-purpose nonlinear finite element analysis program (ABAQUS) was used to perform correlation study. The analysis showed that the ultimate strength and postbuckling behavior of the specimens could be reliably predicted when both the effects of residual stresses and initial geometric imperfections were considered in the model.     

Performance Evaluation of FRP Composite Deck Considering for Local Deformation Effects

We examine here the replacement of a deteriorated concrete deck in the historic Hawthorne Street Bridge in Covington, Va. with a lightweight fiber-reinforced polymer (FRP) deck system (adhesively bonded pultruded tube and plate assembly) to increase the load rating of the bridge. To explore construction feasibility, serviceability, and durability of the proposed deck system, a two-bay section (9.45 by 6.7?m) of the bridge has been constructed and tested under different probable loading scenarios. Experimental results show that the response of the deck is linear elastic with no evidence of deterioration at service load level (HS-20). From global behavior of the bridge superstructure (experimental data and finite- element analysis), degree of composite action, and load distribution factors are determined. The lowest failure load (93.6?kips or 418.1?kN) is about 4.5 times the design load (21.3?kips or 94?kN), including dynamic allowance at HS-20. The failure mode is consistent in all loading conditions and observed to be localized under the loading patch at the top plate and top flange of the tube. In addition to global performance, local deformation behavior is also investigated using finite-element simulation. Local analysis suggests that local effects are significant and should be incorporated in design criteria. Based on parametric studies on geometric (thickness of deck components) and material variables (the degree of orthotropy in pultruded tube), a proposed framework for the sizing and material selection of cellular FRP decks is presented for future development of design guidelines for composite deck structures.     

Behavior of RCC T-Beam Bridges with Cross Diaphragms in Nonlinear Range

Behavior of reinforced cement concrete (RCC) T-beam bridges with cross diaphragms is studied for a realistic range of values of three parameters, such as span, type of loading (specified by Indian Roads Congress), and type of bridge deck layout. The method used for this study is based on the grillage idealization of RCC T-beam bridge superstructures. Material nonlinearity is considered through elastoplastic idealization of moment curvature and torque-twist relationships of the cross section. Geometrical nonlinearity has been neglected. The important conclusions which have emerged from this study are as follows: The behavior of RCC T-beam bridge superstructures can be broadly classified into two categories depending on the type and location of formation of the first plastic hinge. Category I is identified with the formation of first plastic hinge, which is a torsional hinge in the mid outer cross girders. Category II is identified with the formation of the first plastic hinge, which is a flexural hinge in the exterior longitudinal girder under the maximum loading. Bridge superstructures falling under Category I are associated with a greater degree of redistribution and more ductility as compared to those under Category II.     

Number of Cable Effects on Buckling Analysis of Cable-Stayed Bridges

Cables instead of interval piers support cable-stayed bridges, and the bridge deck is subjected to strong axial forces due to the horizontal components of cable reactions. The structural behavior of a bridge deck becomes nonlinear because of the axial forces, large deflection, and nonlinear behavior of the cables and the large deformation of the pylons as well as their interactions. The locations and amplitude of axial forces acting on the bridge deck may depend on the number of cables. Agrawal indicated that the maximum cable tension decreases rapidly with the increase in the number of cables. This paper investigates the stability analysis of cable-stayed bridges and considers cable-stayed bridges with geometry similar to those proposed in Agrawal's paper. A digital computer and numerical analysis are used to examine 2D finite element models of these bridges. The eigen buckling analysis has been applied to find the minimum critical loads of the cable-stayed bridges. The numerical results indicate that the total cumulative axial forces acting on the bridge girder increase as the number of cables increases, yet because the bridge deck is subjected to strong axial forces, the critical load of the bridges decreases. Increasing the number of cables may not increase the critical load on buckling analysis of this type of bridge. The fundamental critical loads increase if the ratio of Ip∕Ib increases until the ratio reaches the optimum ratio. If the ratio of Ip∕Ib is greater than the optimum ratio, depending on the geometry of an individual bridge, the fundamental critical load decreases for all the types of bridges considered in this paper. In order to make the results useful, they have been normalized and represented in graphical form.