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Suggested Citation:"Chapter 1 - Background." National Academies of Sciences, Engineering, and Medicine. 2021. Proposed Modification to AASHTO Cross-Frame Analysis and Design. Washington, DC: The National Academies Press. doi: 10.17226/26074.
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Suggested Citation:"Chapter 1 - Background." National Academies of Sciences, Engineering, and Medicine. 2021. Proposed Modification to AASHTO Cross-Frame Analysis and Design. Washington, DC: The National Academies Press. doi: 10.17226/26074.
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Suggested Citation:"Chapter 1 - Background." National Academies of Sciences, Engineering, and Medicine. 2021. Proposed Modification to AASHTO Cross-Frame Analysis and Design. Washington, DC: The National Academies Press. doi: 10.17226/26074.
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Suggested Citation:"Chapter 1 - Background." National Academies of Sciences, Engineering, and Medicine. 2021. Proposed Modification to AASHTO Cross-Frame Analysis and Design. Washington, DC: The National Academies Press. doi: 10.17226/26074.
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Suggested Citation:"Chapter 1 - Background." National Academies of Sciences, Engineering, and Medicine. 2021. Proposed Modification to AASHTO Cross-Frame Analysis and Design. Washington, DC: The National Academies Press. doi: 10.17226/26074.
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Suggested Citation:"Chapter 1 - Background." National Academies of Sciences, Engineering, and Medicine. 2021. Proposed Modification to AASHTO Cross-Frame Analysis and Design. Washington, DC: The National Academies Press. doi: 10.17226/26074.
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Suggested Citation:"Chapter 1 - Background." National Academies of Sciences, Engineering, and Medicine. 2021. Proposed Modification to AASHTO Cross-Frame Analysis and Design. Washington, DC: The National Academies Press. doi: 10.17226/26074.
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Suggested Citation:"Chapter 1 - Background." National Academies of Sciences, Engineering, and Medicine. 2021. Proposed Modification to AASHTO Cross-Frame Analysis and Design. Washington, DC: The National Academies Press. doi: 10.17226/26074.
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4 Background 1.1 Problem Statement and Current Knowledge Cross-frames serve many roles throughout the construction and service life of steel I-girder bridges. A major function of cross-frames is to serve as stability braces to enhance the lateral- torsional buckling (LTB) resistance of the bridge girders. Provided that they are properly designed and detailed, cross-frames restrain the twist of a girder cross-section at discrete locations along the length; hence, they are aptly referred to as torsional braces. From a stability perspective, the critical stage for bracing often occurs during construction of the concrete bridge deck when the steel girders resist the entire construction load. Once the concrete cures and the system is composite, stability is not generally critical since the deck provides continuous lateral and torsional restraint to the top flange. In multi-span bridges, LTB is often perceived to be critical around interior supports since the bottom flange is in compression; however, this perceived problem neglects the substantial lateral and torsional restraint provided by the concrete deck. Aside from their primary role as stability braces, cross-frames also resist a variety of lateral and gravity loads throughout the life of a bridge. Cross-frames resist the applied torque on fascia girders due to typical deck overhang construction and distribute lateral loads across the structure (e.g., wind). They also restrain differential movement in girders (i.e., vertical deflection and rotation) caused by dead and construction loads on the noncomposite system (e.g., externally applied loads and locked-in fit-up forces) and live loads on the composite system. In horizontally curved bridges, cross-frames are primary members and engage the girders across the bridge width to behave as a unified structural system and to resist the torsion developed from the curved geometry. In the completed structure, the passage of heavy truck traffic often imposes cyclic loading conditions to cross-frames. Under repeated loading, cross-frames are susceptible to load- induced fatigue cracking. However, bridge owners have not typically observed extensive load-induced fatigue cracking over the past few decades. Historically, cross-frame design has largely been based on experience and general rules-of- thumb. In 1949, a 25-foot maximum spacing limit was introduced in the AASHO Standard Specifications for Highway Bridges. Similar to modern practices, most states utilized standard details and member sizes such that cross-frames were seldom engineered or designed elements. While the 25-foot requirement generally resulted in satisfactory performance of steel bridge superstructures, it was essentially an arbitrary limit that sometimes produced overly conser- vative and uneconomical cross-frame layouts. By the 1980s, spacing limits that resulted in a large number of cross-frames were recognized as undesirable since (i) cross-frames represent an expensive component of bridge fabrication and erection, and (ii) regions around cross-frame panels were found to be susceptible to distortion-induced fatigue cracking. C H A P T E R 1

Background 5 As structural analysis tools and bridge design practices advanced in the following years, updates to the cross-frame analysis and design procedures became increasingly necessary. This process was initiated in the 1st Edition of the American Association of State Highway and Transportation Officials LRFD Bridge Design Specifications (1994). This document, along with its subsequent updates, is referred to as AASHTO LRFD hereafter. In the 1994 AASHTO LRFD, the 25-foot spacing limit was removed in favor of a rational design approach. Thus, rather than using a prescriptive or standard design, the need for cross-frames was to be evaluated for all stages of construction and in the final condition of the bridge. In the past two to three decades since the rational design approach was implemented, considerable research has been conducted to improve the body of knowledge related to cross- frame behavior in steel bridge systems. Many of these past research findings are documented in the current 9th Edition of the AASHTO LRFD Specifications (2020). Note that any specific reference to AASHTO LRFD articles in this report implies the 9th Edition specifications, unless noted otherwise. Despite those advancements, several gaps in knowledge have been identified, particularly in the areas of fatigue loading and analysis of cross-frames. Before identifying the major objectives of NCHRP Project 12-113 in Section 1.2, these past research advancements and the corresponding updates to AASHTO LRFD are first reviewed. 1.1.1 Best Practices for Cross-Frame Layout and Detailing With rational analysis in the forefront of modern cross-frame analysis and design, the general framework for satisfying that requirement is provided in AASHTO LRFD Article 6.7.4.1. The major functions of cross-frames are outlined, and a distinction in the minimum design require- ments is made for straight and horizontally curved bridges. For straight bridges with normal supports, cross-frames have traditionally been designed to only transfer wind loads and meet all applicable slenderness limits. As such, refined analyses are rarely utilized by designers to obtain cross-frame force effects in these relatively simple systems. In skewed bridges, however, load-induced force effects in intermediate cross-frames are more substantial. The same is true for curved bridges, in which cross-frames are considered primary members. Therefore, refined analysis models, in which cross-frames are explicitly represented either by two-dimensional (2D) or three-dimensional (3D) methods, are commonly used for these more complex superstructures. As specified in Article 6.7.4.1, cross-frames must then be designed for all applicable limit states at all stages of construction and service, if included in the structural analysis model used to determine force effects. Thus, the design requirements for cross-frames in skewed and/or curved systems are more generally comprehensive and rigorous than those in non-skewed and straight systems. In terms of general cross-frame layout and details in skewed and curved systems, White et al. (2015) and Chavel et al. (2016) examined best detailing practices for the fit-up of cross-frames. Particularly in skewed and curved framing systems, cross-frames can be difficult to fit-up during erection due to out-of-plumbness and differential girder displacements. Through extensive analytical studies, detailing guidelines were proposed to ensure reliable fit-up in complex systems, which have since been incorporated in AASHTO Articles 6.7.2 and 6.7.4.2 and their corresponding commentary. For instance, the benefits of staggered cross-frame layouts in heavily skewed bridges to relieve load-induced force effects are outlined. Aside from this research, additional work has been conducted investigating the stiffness and fatigue performance of cross-frames in skewed bridges. Quadrato et al. (2014) proposed and experimentally tested a split-pipe connection detail to replace the bent plate detail commonly used in skewed cross-frames. Battistini et al. (2013) also investigated alternative cross-frame designs including the use of tube sections with slotted connection plates to mitigate eccentric

6 Proposed Modification to AASHTO Cross-Frame Analysis and Design connection effects. While these concepts show promise, neither has been widely adopted in the steel bridge design and construction industry. 1.1.2 Cross-Frame Fatigue Behavior Design of cross-frames for fatigue involves consideration of both fatigue loading as well as fatigue resistance. Recent studies addressing each component are discussed in this subsection. McDonald and Frank (2009) experimentally tested a variety of cross-frame members and welded gusset plate connections under cyclic loads. Significant bending deformations were observed, even under tension, due to the eccentric load path generated by the end connections. These eccentric loading effects ultimately compromised the load-induced fatigue performance of the test specimens. In fact, many of the test results indicated that eccentrically loaded single- angle details ranged from Category E to E′ performance. Battistini et al. (2013) expanded on McDonald and Frank (2009) by evaluating the fatigue performance of full cross-frame panels. A variety of typical and proposed connection details in X- and K-type cross-frame panels were fabricated and tested to failure under cyclic loading that simulated the relative girder deformations resulting from live load traffic on composite girder systems. Similar to the previous study, many common details that are prevalent in practice were shown to have poor load-induced fatigue characteristics due to the presence of localized stress concentrations near welds and/or unintended bending stresses. From these experimental studies, typical welded cross-frame connections were designated as a Category E’ detail, the lowest established level. This work has since been summarized and included in AASHTO LRFD in Table 6.6.1.2.3-1 (Condition 7.2), beginning with the 2016 Interim Specifications. Additionally, a substantial amount of research has been conducted on the distortion- induced fatigue behavior for steel bridge applications spanning several decades (Fisher et al. 1990; Keating et al. 1990; Connor and Fisher 2006; Hartman et al. 2010; Hassel et al. 2013). Distortion-induced fatigue effects, which were prevalent in cross-frame connections from the 1950s through the 1980s, are a product of out-of-plane secondary stresses due to small relative deformations of connected components, typically in localized regions. These stresses are generally not quantified in analysis nor design. Instead, designers typically address and mitigate these effects with proper detailing based on the research listed above and the guidance provided in AASHTO LRFD Article 6.6.1.3. The focus of the present study, however, is on load-induced fatigue effects. Although a substantial amount of work has been conducted in recent years to examine the load-induced fatigue resistance of cross-frames and their connections, the fatigue loading model has seen much less research. The Strategic Highway Research Program 2 (SHRP 2) Project R19B study (Modjeski and Masters 2015) recently assessed service limit state design in bridges. This study resulted in a recalibration of the fatigue load factors in the 8th Edition AASHTO LRFD (2017) Table 3.4.1.1 to better represent the force effects in girders (i.e., shears and moments) generated by modern truck traffic as indicated by weigh-in-motion (WIM) records across the country. The 2015 AASHTO LRFD Interim Specifications also recom- mended in Article C6.6.1.2.1 that a single truck in a single lane is more appropriate for fatigue loading of cross-frames than multiple presence effects. The basis for this recommendation, however, was initially an engineering judgement and visual observation of truck traffic with unknown weights. Although comprehensive in terms of girder response, the SHRP 2 R19B study (Modjeski and Masters 2015) did not explicitly evaluate fatigue loading criteria in the context of cross-frames. As such, a major objective of NCHRP Project 12-113 was to examine the appropriateness of

Background 7 the current fatigue loading model (i.e., AASHTO LRFD Articles 3.4.1, 3.6.1.4, and 6.6.1.2.1) for cross-frame analysis and design, as further outlined in Section 1.2. 1.1.3 Cross-Frame Analysis Rational analysis of cross-frames or any structural element depends on accurately analyzing the structure and determining the appropriate force effects. Improvements in the analytical tools over the last few decades allow engineers to carry out sophisticated analyses on bridge systems that can produce efficient designs satisfying both construction and in-service design requirements. However, improved analytical refinement generally comes at the cost of increased computational efforts, which is a general theme of the report herein. As with any analysis, the accuracy is limited by the modeling assumptions and level of understanding of the funda- mental behavior. Although 3D models provide the most accurate solutions, they generally require significant training and experience to use. Two-dimensional and one-dimensional (1D) models, which are much easier and time-efficient to develop, can at times offer reliable data for simple structures, particularly for girder forces. AASHTO/NSBA (National Steel Bridge Alliance) G13.1 Guidelines for Steel Girder Bridge Analysis (2019) comprehensively summarize the limits of simplified analysis techniques for complex systems with skews and/or horizontal curvature. While many of these advancements have focused on girder analysis and design, studies regarding cross-frames have been much more recent. Among other topics, White et al. (2012) investigated a variety of simplified analysis techniques with respect to cross-frame behavior in noncomposite bridge systems. In general, it was observed that cross-frame force effects are more difficult to predict in simplified 2D analyses and that careful consideration by the designer is required when developing the model. Even in the most detailed 3D design software packages, cross-frame members are generally simplified as pin-ended truss elements that do not reflect the impact of eccentric connections. As such, Wang (2013) and Battistini et al. (2016) explored the use of a simple modification factor (i.e., a stiffness reduction factor referred to as an R-factor hereafter) in 3D analysis to more accurately represent the true stiffness of the cross-frame. AASHTO LRFD Articles 4.6.3.1 and 4.6.3.3 document the key outcomes of these past investigations, including the appropriate equivalent beam approach used in 2D analysis and the modification factor used in 3D models to account for the effective connection stiffness. Despite these recent studies, little guidance has been provided on how different analysis techniques affect the predicted response of cross-frames in composite systems (i.e., cross- frame response to live loads). Thus, another major objective of NCHRP Project 12-113 was to examine the limitations of common 3D and 2D analysis methods in the context of cross-frame forces and AASHTO LRFD Articles 4.6.3.1 and 4.6.3.3. This is further outlined in Section 1.2. 1.1.4 Cross-Frame Stability Bracing Requirements As noted previously, cross-frames primarily serve as torsional braces to develop the load- carrying capacity of the bridge girders, especially during steel erection and deck construction. Like any stability brace, cross-frames must satisfy both stiffness and strength requirements to adequately brace a girder. Despite this, AASHTO LRFD (2020) currently provides no explicit guidance on stability bracing requirements. It does, however, address several stability-related issues in steel I-girder systems, which are tangentially related to cross-frames. For instance, research conducted by Yura et al. (2008) and Han and Helwig (2017) investi- gated the system buckling phenomenon in narrow I-girder systems following the collapse of

8 Proposed Modification to AASHTO Cross-Frame Analysis and Design the Marcy Pedestrian Bridge. Although the Marcy Pedestrian Bridge was a steel tub girder, the LTB failure is similar to the system buckling mode for which many narrow I-girder systems are susceptible. AASHTO Article 6.10.3.4.2 summarizes the major findings of these studies and provides design guidance to estimate the resistance of this system-level failure mode. Substantial work has also been performed in the area of lean-on bracing (Helwig and Wang 2003, Romage 2008). Lean-on bracing concepts, which have been utilized in building frame design for decades, were adapted for steel straight I-girder bridge applications. These braces include only a top and bottom strut and “lean on” adjacent cross-frames to stabilize the longitudinal girders. Several newly constructed straight skewed I-girder bridges in Texas have successfully implemented lean-on braces, which subsequently alleviate load-induced force effects in cross-frames as well as improve fabrication economy by eliminating several full cross-frame panels. Despite these recent advancements related to the topic of steel bridge stability, stability bracing requirements for cross-frames are absent from the AASHTO LRFD Specifications as of this writing. In contrast, the American Institute of Steel Construction (AISC) Specification commonly used for building design was the first major specification in the world to include guidance on stability bracing design. In the current AISC Specification (2016), the stability bracing provisions are located in Appendix 6, and Article 6.3.2a provides specific strength and stiffness requirements for torsional point braces such as cross-frames. These require- ments are largely based on the work conducted by Yura (2001), Helwig and Yura (2015), and Prado and White (2015). Note that the fundamental work that led to the stability bracing requirements in the AISC Specification was actually developed from studies on bridge girders (Yura et al. 1992). Considering that many of these stability bracing design provisions are applicable for both building and bridge applications, another major objective of NCHRP Project 12-113 was to assess the stability bracing guidance in the AISC Specification for implementation into AASHTO LRFD. 1.2 Research Objectives As outlined in the preceding section, there has been a concerted effort over the last two to three decades to improve the rational analysis and design guidelines for cross-frames in AASHTO LRFD. While these studies have advanced the understanding of the behavior, there are still significant gaps in knowledge on the analysis, design, and detailing of cross-frames. These knowledge gaps primarily fall into one of three categories: (i) fatigue loading criteria, (ii) analysis techniques, and (iii) stability bracing requirements. With that in mind, the National Cooperative Highway Research Program (NCHRP) Project 12-113, “Proposed Modification to AASHTO Cross-Frame Analysis and Design,” was conceived to address many of these knowledge gaps in an attempt to improve the reliability and economy of cross-frames in steel I-girder bridges. The fundamental objectives of NCHRP Project 12-113, as identified in the project Request for Proposal (RFP), were to produce quan- titatively based methodologies and design guidelines for the following items: a. Improved definition of fatigue loading for cross-frames in skewed steel I-girder bridges (straight or curved) analyzed using refined analysis methods; b. Investigation of the influence of girder spacing, cross-frame stiffness and spacing (including staggered layouts), and deck thickness on the force effects in cross-frame systems;

Background 9 c. Additional guidance on how to evaluate the influence of end connections on cross-frame member stiffness in refined analysis models; d. Evaluation of commercial software programs and their ability to accurately predict cross- frame forces for various bridge geometries and cross-frame configurations; and e. Development of stability bracing strength and stiffness requirements in the context for implementation in AASHTO LRFD. Objectives (a) and (b) primarily investigate the fatigue loading characteristics of cross-frames in composite, finished bridges. Objectives (c) and (d) examine the analysis procedures com- monly used by designers and commercial bridge software programs, and Objective (e) examines the stability bracing functions of cross-frames, which are currently absent from AASHTO LRFD. These five objectives also defined the five major tasks undertaken in this study. The tasks were addressed herein through a series of field experiments and analytical studies. This report summarizes the key findings of these studies for practicing engineers. Based on the findings of these five tasks, the research team developed draft specification and commentary language for proposed changes to AASHTO LRFD, which are summarized in Chapter 4 and provided in full in Appendix A. To assist the reader, references to Objectives (a) through (e) are periodi- cally made in the report hereafter. For reference, a list of the specific AASHTO LRFD articles recommended for modification in Appendix A and referenced throughout this report is provided below. For each article or set of articles, specific questions related to the five primary objectives above are also posed. These questions are systematically addressed throughout the report with recommended resolutions provided in Chapter 4. • [Fatigue loading – Articles 3.6.1.4, 6.6.1.2.1] Is the current fatigue load model in terms of truck position (i.e., single design truck passages positioned in various transverse lane positions) appropriate for cross-frame analysis and design or should multiple presence effects be considered? • [Fatigue loading – Article 3.4.1] Are the current AASHTO LRFD Fatigue I and II load factors, which were calibrated for girder force effects and recent WIM data, appropriate for cross- frame analysis and design? • [Fatigue loading – Table 6.6.1.2.5-2] Is the “n” value (i.e., number of cycles per truck passage) currently assumed for the generic “transverse member” designation applicable for cross-frames? • [Fatigue loading – Article 6.7.4.2] What is the influence of composite bridge geometry (e.g., support skew, horizontal curvature) and cross-frame layout (e.g., cross-frame spacing, staggered layout) on the load-induced fatigue behavior of cross-frame systems (including governing force effects, critical lane loading, and critical members under AASHTO fatigue loading criteria)? • [Fatigue loading – Articles 6.7.4.1, 6.7.4.2] Based on the findings of the item above, is it neces- sary to perform a refined analysis, using either simplified 2D or more advanced 3D methods for straight and non-skewed bridges? More succinctly, are the minimum design requirements outlined in Article 6.7.4.1 appropriate? • [Analysis – Article 4.6.3.3.4] Is the current established R-factor (0.65AE), which was based on analytical and experimental studies of a noncomposite system, appropriate for cross-frames in the composite condition or should alternative 3D modeling approaches be developed for cross-frames? • [Analysis – Article 4.6.3.3.2] Expanding on White et al. (2012), what are the limitations of simplified 2D analysis techniques commonly used by popular commercial bridge software programs in terms of predicting cross-frame force effects in composite systems? Are there methods available to improve these simplified techniques?

10 Proposed Modification to AASHTO Cross-Frame Analysis and Design • [Stability bracing – Article N/A] Can the AISC design guidelines for stability bracing be incorporated into AASHTO LRFD? Are special requirements needed for negative moment regions of continuous systems? • [Stability bracing – Article N/A] How are these stability bracing requirements combined with other load conditions such as wind? 1.3 Scope of Study Objectives (a) through (e) and the specific questions identified in the preceding subsection cover a wide range of behaviors and functions of cross-frames. Not only are the research objectives comprehensive in nature, but the term “cross-frame” encompasses a variety of systems and conditions as well. As noted previously, cross-frame systems are used in many steel bridge applications (e.g., I-girder bridges versus tub-girder bridges, intermediate cross-frames versus cross-frames at supports) throughout the entire construction and service life. As such, their behavior must be evaluated in both noncomposite and composite systems. In the context of tub-girder bridges, cross-frames internal to the tub girder primarily control distortion of the shape and will generally have no fatigue issues, nor do these braces significantly enhance the stability of the tub girder. Although studies related to fatigue will have application to the behavior of external cross-frames in tub-girder systems, these girder systems were not con- sidered in this study. Additionally, cross-frame configurations and details come in many shapes and sizes. Specific design and connection details are typically recommended on a state-by-state basis in the United States. Each state Department of Transportation (DOT) (or the equivalent governing agency) regulates and unifies bridge design in that state through standard details, specifications, and design guidelines. For instance, cross-frame members are commonly comprised of single-angle sections, but WT and double-angle sections are also occasionally used. Similarly, cross-frames are generally configured as X- or K-type, but different variations are utilized throughout the country. State standards also differ in how cross-frame members are connected to gusset and connection plates (i.e., welded versus bolted). An industry survey was conducted as a part of the investigation and is outlined in Section 2.1 to summarize and compile all of these unique details. To maintain a manageable scope, the research team focused its efforts on the most common and practical conditions found in steel I-girder bridges. As such, the research conducted and documented herein is dedicated only to X- and K-type intermediate cross-frames comprised of single-angle sections in steel I-girder highway bridges. As is discussed throughout the report, the effects of different angle sizes and connection details on cross-frame performance are examined, as are parameters related to the bridge geometry (e.g., girder spacing, deck thickness, etc.). 1.4 Organization of Report Including this background section, this report is organized into four chapters, followed by six appendices. Chapter 2 outlines the research approaches adopted to address the major objectives of NCHRP Project 12-113. More specifically, the flow of work that includes field experiments, model validation, and analytical studies is detailed. Four different analytical studies are described, including the major modeling assumptions and the specific parameters evaluated. Chapter 3 subsequently presents summarized results of the experimental and analytical studies. For each major study, key observations and findings are outlined. Chapter 4 then synthesizes the key findings from Chapter 3 in the context of the AASHTO LRFD provisions identified previously in Section 1.2. Specific suggestions for implementation of the findings are provided, as are areas where further research would be valuable.

Background 11 Chapters 2 and 3 of the main report are not intended to be comprehensive in nature. Rather than overwhelm the reader with the full set of experimental and analytical data, sample results are selectively presented to provide the proper context to the major conclusions summarized in Chapter 4. For a more detailed overview of the experimental and analytical studies and results, several appendices have been prepared. Based on the key findings summarized in Chapter 4, Appendix A includes the draft speci- fication revisions prepared for consideration by the AASHTO T-14 Technical Committee for Structural Steel Design and the AASHTO Committee on Bridges and Structures. Appendices B and C present cross-frame design examples for a straight bridge with normal supports and a horizontally curved bridge with radial supports, respectively. These examples articulate how the various load cases and conditions independently investigated in Chapters 2 and 3 can be combined for the various stages of construction and service. Rather than develop representative examples from scratch, the research team elected to adopt and modify previously published design examples that are commonly referenced by design engineers. As such, the design examples generally follow Steel Bridge Design Handbook (SBDH) Examples 2A (Barth 2015) and 3 (Rivera and Chavel 2015). Appendices D through F cover much of the same material as in the main body of the report. However, these appendices provide a more thorough and exhaustive overview of the research methodology, results, and critical findings. Appendix D specifically addresses Phase I of NCHRP Project 12-113, whereas Appendices E and F address Phases II and III, respectively. The various phases of the projects are detailed in Chapter 2.

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Cross-frames are important structural components that serve many functions throughout the service life of steel I-girder bridges. Under repetitive load cycles caused by heavy truck passages, cross-frames and their connections can be susceptible to load-induced fatigue cracking if not properly designed.

The TRB National Cooperative Highway Research Program'sNCHRP Research Report 962: Proposed Modification to AASHTO Cross-Frame Analysis and Design addresses knowledge gaps in an attempt to improve the reliability and economy of cross-frames in steel I-girder bridges and produces quantitatively based methodologies and design guidelines.

Appendices B through F provide examples of cross-frame design for a straight bridge and a curved bridge as well as a comprehensive overview of the work completed in Phases I, II, and III of the project. Appendix A, Proposed Modifications to AASHTO LRFD, will be published by AASHTO.

Appendix B

Appendix C

Appendix D

Appendix E

Appendix F

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