Steel Girder Design per AASHTO LRFD Specifications (Part 1)

The primary objective of this paper and its companion is to give the practicing engineer tools for quick design of steel and composite girders in flexure and shear and to provide a reference to aid with the transition to the AASHTO LRFD Specifications. The AASHTO equations are presented in a modified form, using newly introduced notation that allows formulation of most of the equations without explicit dependency on the steel strength. Based on these modified equations, charts are developed that help to visualize the sometimes complex design equations and which also may be found useful as design aids for preliminary designs. For noncompact sections the AASHTO equations are expressed consistently in a dual form that emphasizes the distinction between slender and nonslender elements. This is the first of two papers and addresses the design of I-girders for flexure.     

Shear Capacity of Hybrid Plate Girders

The AASHTO LRFD Bridge Design Specifications, in versions up to and including the 2003 interim, limit the shear resistance of hybrid steel I-girders to the shear buckling or shear yield load and prevent consideration of the additional capacity due to tension field action, which homogeneous girders are allowed to include. This limitation severely affected the economy of girders utilizing high-performance steel, whose optimum configuration is often hybrid. Therefore, an experimental investigation was initiated by the National Bridge Research Organization at the University of Nebraska-Lincoln to address the limitation on the consideration of tension field action in hybrid girders. This paper presents the findings of that research. Eight simply supported steel I-girders were designed, constructed, and loaded to failure to investigate their failure mechanisms and shear capacities. All girders tested were capable of supporting loads greater than those predicted, considering full contribution from tension field action. Further, despite the coincidence of high levels of both shear and moment, relative to their respective capacities, the specimens were all capable of supporting loads greater than those predicted if shear and moment interaction were ignored. Due in part to the results of the research being presented, modifications appeared in the 2004 version of the AASHTO LRFD bridge design specifications such that the shear strength provisions apply equally to both hybrid and homogeneous girders.     

Transverse Stiffener Requirements in Straight and Horizontally Curved Steel I-Girders

Prior research has demonstrated that transverse stiffeners in straight I-girders are loaded predominantly by bending induced by their restraint of web lateral deflections at the shear strength limit state, not by in-plane tension field forces. This is at odds with present specification approaches for the design of these components. Furthermore, recent studies have confirmed that curved I-girders are capable of developing substantial shear postbuckling resistance due to tension field action and have demonstrated that the AASHTO LRFD equations for the tension field resistance in straight I-girders may be applied to curved I-girders within specific limits. However, the corresponding demands on transverse stiffeners in curved I-girders are still largely unknown. In this paper, the behavior of one- and two-sided transverse stiffeners in straight and horizontally curved steel I-girders is investigated by full nonlinear finite element analysis. New recommendations are developed for design of transverse stiffeners in straight and curved I-girders based on the results of this and prior research.     

Strength and Ductility of HPS-100W I-Girders in Negative Flexure

In current AASHTO LRFD bridge design specifications, the nominal flexural strength of I-girders made from steel with a yield stress >345 MPa (>50 ksi) is limited to the yield moment rather than the plastic moment and inelastic design procedures are not permitted. With the recent development of high performance steel (HPS) for highway bridges, the need for these restrictions should be revisited. This paper focuses on I-girders made from HPS-100W steel. Two I-girders were designed with HPS-100W steel according to the AASHTO LRFD specifications, neglecting current restrictions related to the use of high strength steels. The I-girders were tested to failure under three-point loading, which simulated the condition of negative flexure at the pier of a continuous-span bridge. The flexural strength and ductility of the HPS-100W I-girders are compared with the strength and ductility anticipated by the AASHTO LRFD specifications for conventional steel I-girders. In addition, the results of relevant previous tests of conventional steel I-girders are summarized and compared with the HPS-100W I-girder test results.     

Flexural Reliability of Reinforced Concrete Bridge Girders Strengthened with Carbon Fiber-Reinforced Polymer Laminates

This paper presents the development of a resistance model for reinforced concrete bridge girders flexurally strengthened with externally bonded carbon fiber-reinforced polymer (CFRP) laminates. The resistance model is limited to pure flexural failure and does not address shear failure, laminate debonding, or delamination. The resistance model is used to calculate the probability of failure and reliability index of CFRP-strengthened cross sections. The first-order reliability method is employed to calibrate the flexural resistance factor for a broad range of design variables. The study shows that the addition of CFRP improves reliability somewhat because the strength of CFRP laminates has a lower coefficient of variation than steel or concrete. However, the brittle nature of CFRP laminates necessitates a reliability index that is greater than that generally implied in the AASHTO LRFD for 1998. This leads to a lower resistance factor than is currently accepted for reinforced concrete sections in flexure.     

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.     

Improved Moment Strength Prediction of Composite Steel Plate Girders in Positive Bending

This paper contains an alternate method for the calculation of the predicted positive bending moment capacity of composite steel girders. The 2000 interim version of the American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design Bridge Design Specifications has extended the applicability of the provisions for the design of composite plate girders in positive bending to include 485 MPa high performance steel. Observations made during numerical studies performed in conjunction with this extension demonstrated a need for a more comprehensive study encompassing a larger and more diverse set of parameters. This paper provides a summary of the analytical and experimental work that was carried out to develop provisions for predicting the ultimate strength and assuring the ductility of composite girders constructed using 250, 345, or 485 MPa steels. The new provisions outlined in this paper are more accurate and require less calculation. The recommended equations only require calculation of the plastic moment capacity, while current AASHTO Specification provisions require the calculation of both plastic and yield moment capacities of the section.     

Assessment of AASHTO LRFD Specifications for Hybrid HPS 690W Steel I-Girders

This paper details research conducted to determine the applicability of the 2nd and 3rd editions of the AASHTO LRFD Specifications to hybrid I-girders fabricated from high-performance steel (HPS) 690W (100?ksi) flanges and HPS 480W (70?ksi) webs. Specifically, the scope of this paper is to evaluate the applicability of the negative moment capacity prediction equations for noncomposite I-girders subjected to moment gradient. This evaluation is carried out using three-dimensional nonlinear finite-element analysis to determine the ultimate bending capacity of a comprehensive suite of representative hybrid girders. In addition, a design study was conducted to assess the economical feasibility of incorporating HPS 690W (100?ksi) in traditional bridge applications. This was accomplished by designing a series of I-girders with varying ratios of span length to girder depth (L/D ratios) for a representative three-span continuous bridge. Results of this study indicate that both the 2nd and 3rd editions of the specifications may be used to conservatively predict the negative bending capacity of hybrid HPS 690W (100?ksi) girders, however increased accuracy results from use of the 3rd edition of the AASHTO LRFD Specifications. Thus, it is concluded that the restriction placed on girders fabricated from steel with a nominal yield strength greater than 480?MPa (70?ksi) can be safely removed. Additionally, results of the design study demonstrate that significant weight saving can result from the use of hybrid HPS 100W girders in negative bending regions, and that hybrid HPS 690W/HPS 480W girders may be ideally suited to sites with superstructure depth restrictions.     

Rotation Requirements for Moment Redistribution in Steel Bridge I-Girders

One of the key assumptions in inelastic design is that members have adequate ductility to allow moments to redistribute. However, while AASHTO specifications contain moment redistribution provisions for steel I-girders, the amount of ductility that is adequate for this specific design situation has not been studied in detail. As a result, the scope of these specifications is limited to beam types known to have significant ductility, which restricts the use of these procedures and causes negative economic consequences. The goal of this work is to determine ductility requirements specifically applicable to AASHTO moment redistribution procedures that are valid for all I-girders. This is accomplished through an analytical procedure, detailed herein. The results of this work are empirical equations predicting the amount of rotation required as a function of the intended level of moment redistribution as well as the material properties and span configuration of the girder. With these requirements known, there is a basis for reducing the overly conservative nature of the existing AASHTO moment redistribution specifications.     

Relaxing the Stud Spacing Limit for Full-Depth Precast Concrete Deck Panels Supported on Steel Girders (Phase I)

The AASHTO LRFD Bridge Design Specifications state that the spacing between the shear connectors for steel girders should not exceed 610 mm (24 in.). This decision was made based on research conducted more than three decades ago. The goal of this research is to investigate the possibility of extending this limit to 1,220 mm (48 in.) for stud clusters used with full-depth precast concrete deck panels installed on steel girders. This paper presents the history of the 610 mm (24 in.) limit, various formulas developed to calculate fatigue and design capacity for stud clusters and concerns about extending the current LRFD limit. This paper also presents information on the first phase of the experimental investigation, which is conducted on push-off specimens to validate extending the limit to 1,220 mm (48 in.).     

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.     

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.     

Flexural Capacity of Compact Composite I-Girders in Positive Bending

Current American Association of State Highway and Transportation Officials (AASHTO) bridge specifications for compact composite steel girders in positive bending with adjacent compact pier sections limit the allowable maximum strength to a value between the full plastic moment and the hypothetical yield moment of the cross section as a function of the depth of web in compression. The strength prediction equations derived using these methods provide conservative values when compared to the results of the parametric studies used to develop the equations. Recent experimental tests coupled with finite-element analysis and mechanistic evaluations of the cross-section flexural capacity suggest that larger capacities may be achieved than those determined from AASHTO’s prediction equations. This paper presents an assessment of the behavior of composite positive bending specimens. A summary of a comprehensive literature review is provided coupled with results of the analytical and experimental evaluation of the nominal moment capacity of composite girders. Lastly, a less conservative design moment capacity expression developed from this assessment is provided.     

Shear Behavior and Mode of Failure for ASTM C1433 Precast Box Culverts

This study evaluates the shear behavior and capacity of the precast concrete box culverts subjected to HS 20 truck wheel load. The most critical culvert behavior was considered by studying culverts subjected to zero depth of the fill and placed on a rigid bedding material. Full-scale experimental tests, with wheel load placed at the distance d from the tip of the haunch to the edge of the load plate, were conducted on 24 typical precast concrete box culverts designated as per ASTM C1433-05. The test results further indicated that flexure governed the behavior up to and beyond AASHTO 2005 factored load. Three-dimensional nonlinear finite-element models (FEMs) of the test specimens were developed and verified with the experimental results. The three-dimensional volumetric shear force distributions on the top slab of the 42 ASTM C1433-05 boxes were obtained by using the FEM from which the distribution width for each box was calculated. This was used to obtain the critical factored shear force for all the boxes which were then compared with the American Concrete Institute shear capacity equations. It was shown that the shear capacity exceeded the factored critical shear force for all the ASTM C1433-05 boxes. This study shows that the AASHTO 2005 provision with regard to the shear transfer device across the joint is unsupported.     

Stiffness and Strength Evaluations of a Shear Connection System for FRP Bridge Decks to Steel Girders

This paper reports on research investigating a nongrouted sleeve-type connection used to attach fiber-reinforced polymer (FRP) decks to steel girders. The connection system was investigated for stiffness, strength, fatigue resistance, and degree of composite action. Static and fatigue tests were conducted first at the component level on push-out specimens to obtain P-Δ (load-displacement) and S-N (stress range–fatigue life) relationships, from which design formulas were developed. Then tests were conducted at the system level on a 1∶3 scaled-bridge model by using this sleeve-type connection, and the results showed this shear connection can satisfy requirements from AASHTO specifications for fatigue, strength, and function. Further, three-point bending tests were conducted on a T-section model cut from the scaled bridge, and approximately 25% composite action was achieved for two different connection spacings. The structural efficiency of this shear connection is shown, and this connection design is applied in practice.     

Development and Implementation of a Continuous Strain Monitoring System on a Multi-Girder Composite Steel Bridge

This paper describes the implementation and evaluation of a long-term strain monitoring system on a three-span, multisteel girder composite bridge located on the interstate system. The bridge is part of a network of bridges that are currently being monitored in Connecticut. The three steel girders are simply supported, whereas the concrete slab is continuous over the interior supports. The bridge has been analyzed using the standard AASHTO Specifications and the analytical predictions have been compared with the field monitoring results. The study has included determination of the location of the neutral axes and the evaluation of the load distributions to the different girders when large trucks cross the bridge. A finite-element analysis of the bridge has been carried out to further study the distribution of live load stresses in the steel girders and to study how continuity of the slabs at the interior joints would influence the overall behavior. The results of the continuous data collection are being used to evaluate the influence of truck traffic on the bridge and to establish a baseline for long-term monitoring.     

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.     

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.     

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

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

Finite-Element Modeling of Heat-Curved I-Girders

Heat curving is extensively used for fabricating structural steel girders for bridges. Current American Association of State Highway and Transportation Officials (AASHTO) specifications limit usage to Grade 345 steel (Fy = 50?ksi), ruling out Grade 485 (Fy = 70?ksi) high performance steel (HPS). This paper presents results of a three-dimensional finite-element analysis to assess the applicability of existing AASHTO provisions for HPS 485W sections. The finite-element package NASTRAN was used to conduct the analysis and the model calibrated against experimental data obtained from full-scale tests conducted previously by U.S. Steel Corporation. Comparisons include curvatures, lateral deformations, and residual stresses. The calibrated model was used to predict the performance of an identical HPS girder subjected to the same heat/cool cycles. The three-dimensional analysis predicted smaller curvatures as compared with Grade 250 (Fy = 36?ksi) or Grade 345 (Fy = 50?ksi) steel. Comparable curvatures could be obtained by using higher temperatures.