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.     

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.     

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.     

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.     

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.     

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.).     

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.     

Field Testing and Analysis of CRC Deck Girder Bridges

This paper presents findings of field tests and analysis of two conventionally reinforced concrete (CRC) deck girder bridges designed in the 1950s. The bridges are in-service and exhibit diagonal cracks. Stirrup strains in the bridge girders at high shear regions were used to estimate distribution factors for shear. Impact factors based on the field tests are reported. Comparison of field measured responses with AASHTO factors was performed. Three-dimensional elastic finite-element analysis was employed to model the tested bridges and determine distribution factors specifically for shear. Eight-node shell elements were used to model the decks, diaphragms, bent caps, and girders. Beam elements were used to model columns under the bent caps. The analytically predicted distribution factors were compared with the field test data. Finally, the bridge finite-element models were employed to compare load distribution factors for shear computed using procedures in the AASHTO LRFD and Standard Specifications.     

Full-Scale Testing of Composite Plate Girders Constructed Using 485-MPa High-Performance Steel

The 2000 interim version of the AASHTO LRFD 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. The change made in the 2000 interim code is based on analytical work. This paper provides a summary of experimental work conducted with the purpose of verifying the safety of the proposed recommendation. The results of the two tests conducted indicate that, although slightly overconservative, the code's current strength predictive equation with the proposed recommendation is adequate. It was also observed that the tension flange of composite flexural members constructed using HPS-485W steel could achieve large levels of tensile strains without fracture.     

Development of Live-Load Distribution Factors for Glued-Laminated Timber Girder Bridges

This paper presents simple relationships for calculating live-load distribution factors for glued-laminated timber girder bridges with glued-laminated timber deck panels. Analytical models were developed using the Ansys 113 finite-element program, and the results were validated using recorded data from four in-service timber bridges. The effects of the bridge span length, the spacing between girders, and the bridge width on the distribution of the live load were investigated by using the validated models. The live-load distribution factors obtained from the field test and the analytical models were compared with those obtained using the AASHTO LRFD Bridge Design Specifications2 live-load distribution relations. The comparison showed that the live-load distribution factors obtained by using the AASHTO LRFD Bridge Design Specifications2 were conservative. For this reason, statistical methods were used to develop accurate relationships that can be used to calculate the live-load distribution factors in the design of glued-laminated girder bridges.     

Effect of Multilanes on Wheel Load Distribution in Steel Girder Bridges

This paper presents the results of a parametric study that investigated the effect of multilanes and continuity on wheel load distribution in steel girder bridges. Typical one- and two-span, two-, three-, and four-lane, straight, composite steel girder bridges were selected for this study. The major bridge parameters chosen for this study were the span length, girder spacing, one- versus two-spans, and the number of lanes. These parameters were varied within practical ranges to study their influence on the wheel load distribution factors. A total of 144 bridges were analyzed using the finite-element method. The computer program, SAP90, was used to model the concrete slab as quadrilateral shell elements and the steel girders as space frame members. Simple supports were used to model the boundary conditions. AASHTO HS20 design trucks were positioned in all lanes of the one- and two-span bridges to produce the maximum bending moments. The calculated finite-element wheel load distribution factors were compared with the AASHTO and the National Cooperative Highway Research Program (NCHRP) 12-26 formulas. The results of this parametric study agree with the newly developed NCHRP 12-26 formula and both were, in general, less than the empirical AASHTO formula (S∕5.5) for longer span lengths [>15.25 m (50 ft)] and girder spacing >1.8 m (6 ft). This paper demonstrates that the multiple lane reduction factors are built into the newly developed distribution factors for steel girder bridges that were presented in the NCHRP 12-26 final report. It should be noted that AASHTO LRFD contains a similar expression that results in a value that is 50% of the value in the equations developed as a part of NCHRP 12-26. This is due to the fact that AASHTO LRFD consider the entire design truck instead of half-truck (wheel loads) as the case in the NCHRP 12-26 report and the AASHTO Standard Specifications for Highway Bridges. Therefore, this paper supports the use of the new distribution factors for steel girder bridges developed as a part of NCHRP 12-26 and consequently the distribution factors presented in the AASHTO LRFD Bridge Design Specifications.     

Evaluation of Live-Load Lateral Flange Bending Distribution for a Horizontally Curved I-Girder Bridge

This paper focuses on levels of live-load lateral bending moment (bimoment) distribution in a horizontally curved steel I-girder bridge. Work centered primarily on the examination of (1) data from field testing of an in-service horizontally curved steel I-girder bridge and (2) results from a three-dimensional numerical model. Experimental data sets were used for calibration of the numerical model and the calibrated model was then used to examine the accuracy of lateral bending distribution factor equations presented in the 1993 Edition of the (AASHTO) Guide Specifications for Horizontally Curved Bridges. It is of interest to examine these equations for potential use in preliminary design even though they have been eliminated during recent AASHTO specification modifications that addressed curved bridge analysis, the 2005 Interims to the AASHTO LRFD Bridge Design Specifications. In addition, they were developed using idealized computer models and small-scale laboratory testing with very few field tests of in-service full-scale curved steel bridges conducted to support or refute their use. Results from such experimental and numerical studies are presented and discussed herein.     

Consistent Approach to Calculating Stresses for Fatigue Design of Welded Rib-to-Web Connections in Steel Orthotropic Bridge Decks

The current (2004) fatigue design provisions in the 3rd Ed. of the AASHTO LRFD Bridge Design Specifications identify and classify the rib-to-web (rib-to-diaphragm) connections commonly utilized in steel orthotropic bridge decks where cutouts are used. The fatigue resistance of these details has been established through full-scale laboratory testing. This paper examines how the fatigue stress range was defined and determined during the testing which established the fatigue resistance of the details. A procedure to calculate or measure stresses at the rib-to-diaphragm connection, which is consistent with the fatigue resistance published in the AASHTO LRFD Bridge Design Specifications, is presented.     

Shear Live-Load Distribution Factors for I-Girder Bridges

A full scale, single lane test bridge was used to evaluate a typical slab-on-girder bridge’s response to shear. The results of the shear load test provided the means to evaluate the level of detail for a finite element model that is required to accurately replicate the behavior of bridges subject to shear loads. This finite element modeling scheme was then used to evaluate more than 200 finite element bridge models. The bridge models investigated the effects of girder spacing, span length, overhang distance and skew angle on the shear live-load distribution factor. The finite element shear distribution factors were compared with those calculated according to the American Association of State Highway and Transportation Officials load and resistance factor design (AASHTO LRFD) specifications. It was found that the AASHTO LRFD procedure accurately predicted the shear distribution factor for changes in girder spacing and span length. However, the LRFD shear distribution factor for the exterior girder was found to be unconservative for certain overhang distances and overly conservative for the interior girder for higher skew angles. Alternative equations are provided for the single and multilane exterior girder correction factor.     

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.     

Experimental Validation of a Shear Stud Connection between Steel Girders and a Fiber-Reinforced Polymer Deck in the Transverse Direction

A fiber-reinforced polymer (FRP) deck-to-girder connection was evaluated for fatigue resistance and residual capacity in the transverse direction. The connection consisted of three shear studs cast into a trapezoidal cell of a FRP sandwich deck. Steel spirals were positioned around each shear stud to aid in grout confinement. Test fixturing consisted of multiple girders and tie downs to induce realistic loading of the connection due to wheel loads. The connection was fatigued according to AASHTO LRFD Specifications for 10.5?million?cycles (75?year design life) and tested for residual capacity. The connection survived fatigue testing without failure. The haunch exhibited minimal debonding and cracking. Connection capacity after one lifetime of fatigue cycles exceeded strength limit state requirements.     

Single-Span Prestressed Girder Bridge: LRFD Design and Comparison

This report summarizes the comparative design of a single-span AASHTO Type III girder bridge under the AASHTO Standard Specification for Highway Bridges, 16th Edition, and the AASHTO LRFD Bridge Design Specification. The writers address the differences in design philosophy, calculation procedures, and the resulting design. Foundation design and related geotechnical considerations are not considered. The LRFD design was similar in most respects to the Standard Specification design. The significant differences were: (1) increased shear reinforcement; (2) increased reinforcement in the deck overhang; and (3) increased reinforcement in the wing wall. The comparisons would likely change if the bridge were designed purely according to LRFD Specifications rather than as a comparative design. Design procedures under the LRFD Specification tend to be more calculation-intensive. However, the added complexity of the LRFD Specification is counterbalanced by the consistency of the design philosophy and its ability to consider a variety of bridges.     

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.