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.     

Rotation Compatibility Approach to Moment Redistribution for Design and Rating of Steel I-Girder Bridges

Recent research has culminated in the development of moment redistribution design and rating procedures based on a “rotation compatibility” procedure. The key aspects of the rotation compatibility method are presented herein along with the resulting series of simple equations that may be used for both design and rating of straight continuous-span steel I-girders. This procedure has several advantages over the previous moment redistribution procedures. Most significantly, the rotation compatibility method provides a rational basis for removing the current restrictions on girder geometries permissible for use with moment redistribution provisions. Thus, sections that are more slender and/or have greater unbraced lengths, compared to previous inelastic procedures, may be considered. This is particularly beneficial for incorporating inelastic methods into rating specifications because many existing bridges have geometries such that they have previously been outside the scope of applicability of inelastic procedures. A second key advantage of the rotation compatibility procedure is that maximum allowable redistribution moments are specifically computed, which justifies the use of higher levels of moment redistribution and consequently greater design economy in some cases.     

Simplified Moment Redistribution of Hybrid HPS 485W Bridge Girders in Negative Bending

Simplified moment redistribution procedures based on shakedown have recently been approved by AASHTO LRFD Bridge Design Specifications (AASHTO 2004). These procedures are currently only applicable for homogeneous girders, and thus, the objective of this study is to evaluate whether these procedures can be further applied for hybrid HPS 485W girders. A parametric study is carried out using validated three-dimensional finite-element (FE) analyses to study the inelastic behavior of hybrid HPS 485W girders in negative bending for this purpose. The effective plastic moments obtained from the FE studies are compared with those from the proposed prediction equations, where good correlation is observed. A design example of a three-span slab-on-girder bridge with hybrid HPS 485W girders using both elastic design and the simplified moment redistribution procedures is also presented, where it is shown that the use of moment redistribution procedures results in a negative bending section that is 13% lighter than the corresponding elastic design.     

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.     

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.     

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.     

Steel Girder Design per AASHTO LRFD Specifications (Part 2)

This is the second of two companion papers discussing and illustrating the AASHTO LRFD Bridge Design Specifications for the design of steel girders subject to flexure and shear. In the first paper, notation was introduced that allows reformulation of the AASHTO design equations in a more convenient format and the design of steel I-girders in flexure was presented. The second paper addresses design of box girders for flexure and design of box and I-girders for shear. The design approach is illustrated by two detailed example problems.     

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.     

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.     

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.     

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.     

Live-Load Distribution Factors for Concrete Box-Girder Bridges

The current American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design (LRFD) Specifications impose fairly strict limits on the use of its live-load distribution factor for design of highway bridges. These limits include requirements for a prismatic cross section, a large span-length-to-width ratio, and a small plan curvature. Refined analyses using 3D models are required for bridges outside of these limits. These limits place severe restrictions on the routine design of bridges in California, as box-girder bridges outside of these limits are frequently constructed. This paper presents the results of a study investigating the live-load distribution characteristics of box-girder bridges and the limits imposed by the LRFD specifications. Distribution factors determined from a set of bridges with parameters outside of the LRFD limits are compared with the distribution factors suggested by the LRFD specifications. For the range of parameters investigated, results indicated that the current LRFD distribution factor formulas generally provide a conservative estimate of the design bending moment and shear force.     

Probabilistic Characterization of Live Load Using Visual Counts and In-Service Strain Monitoring

It has been argued that the AASHTO LRFD design code for maximum live loads on highway bridges is overly conservative. In an attempt to determine the level of conservativeness, if any, the writers developed a methodology incorporating real-time visual data collection from traffic cameras coupled with structural strain response of girder bridges. Average daily truck traffic along with frequency of multiple presences (same lane as well as adjacent lanes) and lane-wise truck traffic distribution were estimated for a steel-girder highway bridge on I-95 in Delaware. These data compared well with predictions from a Poisson process based model developed for this study. Statistical properties of girder moments in single and multiple presence conditions were determined as well. In this particular example, the girder design moment on the 24.6?foot approach span according to AASHTO specifications was found to be about 3.5 times higher than that estimated from the in-service data.     

Influence of Skew Angle on Reinforced Concrete Slab Bridges

The effect of a skew angle on simple-span reinforced concrete bridges is presented in this paper using the finite-element method. The parameters investigated in this analytical study were the span length, slab width, and skew angle. The finite-element analysis (FEA) results for skewed bridges were compared to the reference straight bridges as well as the American Association for State Highway and Transportation Officials (AASHTO) Standard Specifications and LRFD procedures. A total of 96 case study bridges were analyzed and subjected to AASHTO HS-20 design trucks positioned close to one edge on each bridge to produce maximum bending in the slab. The AASHTO Standard Specifications procedure gave similar results to the FEA maximum longitudinal bending moment for a skew angle less than or equal to 20°. As the skew angle increased, AASHTO Standard Specifications overestimated the maximum moment by 20% for 30°, 50% for 40°, and 100% for 50°. The AASHTO LRFD Design Specifications procedure overestimated the FEA maximum longitudinal bending moment. This overestimate increased with the increase in the skew angle, and decreased when the number of lanes increased; AASHTO LRFD overestimated the longitudinal bending moment by up to 40% for skew angles less than 30° and reaching 50% for 50°. The ratio between the three-dimensional FEA longitudinal moments for skewed and straight bridges was almost one for bridges with skew angle less than 20°. This ratio decreased to 0.75 for bridges with skew angles between 30 and 40°, and further decreased to 0.5 as the skew angle of the bridge increased to 50°. This decrease in the longitudinal moment ratio is offset by an increase of up to 75% in the maximum transverse moment ratio as the skew angle increases from 0 to 50°. The ratio between the FEA maximum live-load deflection for skewed bridges and straight bridges decreases in a pattern consistent with that of the longitudinal moment. This ratio decreased from one for skew angles less than 10° to 0.6 for skew angles between 40 and 50°.     

Analysis and Design Procedure for FRP-Strengthened Prestressed Concrete T-Girders Considering Strength and Fatigue

Controlling the prestressing strand-stress range in precracked prestressed concrete girders is critical in the FRP strengthening process to avoid long-term fatigue failures. This paper will address the details of a design procedure that was developed to satisfy target-strengthening requirements while imposing stress range serviceability limits. Two main CFRP flexural strengthening designs were established for use in the experimental program herein. In the first, the amount of CFRP was designed to limit the average strand-stress range to 125?MPa (18?ksi), as per AASHTO requirements, under service live load while maintaining the service-ultimate moment relationship constant. The second design was intended to double the strand-stress range under service live load while keeping the same service-ultimate moment relationship. This was accomplished with iterative cycles of nonlinear sectional analysis to determine the amount of external CFRP reinforcement needed to yield both the targeted stress range and ultimate capacity. The girders were overly reinforced for shear with internal steel stirrups. However, external CFRP stirrups were used to prevent the longitudinal CFRP from premature separation and to develop full flexural capacity. The ACI 318-05 model for shear friction was used for this purpose. The paper also presents analysis results to qualify the experimental behavior of the tested girders. Load-deflection, load-strain, and moment-strand stress variations are seen to have excellent correlation with corresponding experimental curves. CFRP is shown to develop higher strains across cracks relieving strand stresses at these critical locations.     

Design Recommendations for a FRP Bridge Deck Supported on Steel Superstructure

No appropriate provisions from either AASHTO Standard (2002) or AASHTO LRFD (2004) bridge design specifications are available for the design of fiber-reinforced polymer (FRP)-deck-on-steel-superstructure bridges. In this research, a parametric study using the finite-element method (FEM) is conducted to examine two design issues concerning the design of FRP-deck-on-steel-superstructure bridges, namely deck relative deflection and load distribution factor (LDF). Results show that the strip method specified in AASHTO LRFD specification as an approximate method of analysis, can also be applied to FRP decks as a practical method. However, different strip width equations have to be determined by either FEM or experimental methods for different types of FRP decks. In this study, one such equation has been derived for the Strongwell deck. In addition, both FEM results and experimental measurements show that the AASHTO LDF equations for glued laminated timber decks on steel stringers provide good estimations of LDF for FRP-deck-on-steel-superstructure bridges. Finally, it is found that the lever rule can be used as an appropriately conservative design method to predict the LDF of FRP-deck-on-steel-superstructure bridges.     

Tests on the Ductility of Reinforced Concrete Beams Retrofitted with FRP and Steel Near-Surface Mounted Plates

Reinforced concrete beams are now commonly retrofitted using externally bonded (EB) fiber reinforced polymer (FRP) plates as the technique is both inexpensive and unobtrusive. However, tests have shown that EB carbon FRP plates tend to debond at low strains, which can severely limit the ductility or moment redistribution to such an extent that guidelines often preclude moment redistribution. This paper reports the moment redistribution achieved in tests on nine near full-scale two-span continuous reinforced concrete beams that were retrofitted with near-surface mounted (NSM) plates. The plates were either carbon FRP or high yield steel strips which were adhesively bonded within saw grooves cut into the concrete cover on the tension face or sides of the beam. It was found that the debonding strains of these NSM plates were considerably larger than those associated with EB plates and that substantial amounts of moment redistribution occurred. These tests suggest that NSM plates can be used to increase the strength of reinforced concrete structures with little, if any, loss of ductility.     

Connection of Concrete Railing Post and Bridge Deck with Internal FRP Reinforcement

The use of fiber-reinforced polymer (FRP) reinforcement is a practical alternative to conventional steel bars in concrete bridge decks, safety appurtenances, and connections thereof, as it eliminates corrosion of the steel reinforcement. Due to their tailorability and light weight, FRP materials also lend themselves to the development of prefabricated systems that improve constructability and speed of installation. These advantages have been demonstrated in the construction of an off-system bridge, where prefabricated cages of glass FRP bars were used for the open-post railings. This paper presents the results of full-scale static tests on two candidate post–deck connections to assess compliance with strength criteria at the component (connection) level, as mandated by the AASHTO Standard Specifications, which were used to design the bridge. Strength and stiffness until failure are shown to be accurately predictable. Structural adequacy was then studied at the system (post-and-beam) level by numerically modeling the nonlinear response of the railing under equivalent static transverse load, pursuant to well-established structural analysis principles of FRP RC, and consistent with the AASHTO LRFD Bridge Design Specifications. As moment redistribution cannot be accounted for in the analysis and design of indeterminate FRP RC structures, a methodology that imposes equilibrium and compatibility conditions was implemented in lieu of yield line analysis. Transverse strength and failure modes are determined and discussed on the basis of specification mandated requirements.     

Wheel Load Distribution in Simply Supported Concrete Slab Bridges

This paper presents the results of a parametric study related to the wheel load distribution in one-span, simply supported, multilane, reinforced concrete slab bridges. The finite-element method was used to investigate the effect of span length, slab width with and without shoulders, and wheel load conditions on typical bridges. A total of 112 highway bridge case studies were analyzed. It was assumed that the bridges were stand-alone structures carrying one-way traffic. The finite-element analysis (FEA) results of one-, two-, three-, and four-lane bridges are presented in combination with four typical span lengths. Bridges were loaded with highway design truck HS20 placed at critical locations in the longitudinal direction of each lane. Two possible transverse truck positions were considered: (1) Centered loading condition where design trucks are assumed to be traveling in the center of each lane; and (2) edge loading condition where the design trucks are placed close to one edge of the slab with the absolute minimum spacing between adjacent trucks. FEA results for bridges subjected to edge loading showed that the AASHTO standard specifications procedure overestimates the bending moment by 30% for one lane and a span length less than 7.5 m (25 ft) but agrees with FEA bending moments for longer spans. The AASHTO bending moment gave results similar to those of the FEA when considering two or more lanes and a span length less than 10.5 m (35 ft). However, as the span length increases, AASHTO underestimates the FEA bending moment by 15 to 30%. It was shown that the presence of shoulders on both sides of the bridge increases the load-carrying capacity of the bridge due to the increase in slab width. An extreme loading scenario was created by introducing a disabled truck near the edge in addition to design trucks in other lanes placed as close as possible to the disabled truck. For this extreme loading condition, AASHTO procedure gave similar results to the FEA longitudinal bending moments for spans up to 7.5 m (25 ft) and underestimated the FEA (20 to 40%) for spans between 9 and 16.5 m (30 and 55 ft), regardless of the number of lanes. The new AASHTO load and resistance factor design (LRFD) bridge design specifications overestimate the bending moments for normal traffic on bridges. However, LRFD procedure gives results similar to those of the FEA edge+truck loading condition. Furthermore, the FEA results showed that edge beams must be considered in multilane slab bridges with a span length ranging between 6 and 16.5 m (20 and 55 ft). This paper will assist bridge engineers in performing realistic designs of simply supported, multilane, reinforced concrete slab bridges as well as evaluating the load-carrying capacity of existing highway bridges.