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Proposed Modification to AASHTO Cross-Frame Analysis and Design (2021)

Chapter: Chapter 4 - Conclusions and Suggested Research

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Suggested Citation:"Chapter 4 - Conclusions and Suggested Research." 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 4 - Conclusions and Suggested Research." 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 4 - Conclusions and Suggested Research." 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 4 - Conclusions and Suggested Research." 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 4 - Conclusions and Suggested Research." 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 4 - Conclusions and Suggested Research." 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 4 - Conclusions and Suggested Research." 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 4 - Conclusions and Suggested Research." 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 4 - Conclusions and Suggested Research." 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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134 Conclusions and Suggested Research Up until the 1990s, specifications included a spacing limit that effectively standardized the design of cross-frames. AASHTO LRFD Specifications have since eliminated a spacing limit for straight bridges and instead require the design to be based on a rational analysis. Although many bridge owners still utilize typical details for cross-frames, software tools have made it possible for designers to develop improved predictions of cross-frame behavior and design forces. However, to adequately make use of these software tools, there has become an increas- ingly important need to modernize design guidance for cross-frames. Although considerable research over the past several decades has improved cross-frame design in the areas of stability bracing, load-induced fatigue resistance, erection fit-up, and analysis for the noncomposite construction condition, the design industry has generally lacked quantitatively based guidance on several other topics related to fatigue loading criteria, analysis techniques, and stability bracing. In response, NCHRP Project 12-113 identified several gaps in knowledge, including those generalized concepts as follows: (i) fatigue loading, (ii) analysis, and (iii) stability bracing requirements of cross-frame systems in steel I-girder bridges. These gaps in knowledge served as the primary objectives of this project, previously identified as Objectives (a) through (e) in Chapter 1. To further clarify the intent of the research, those five objectives were sub sequently posed as a series of questions that have been systematically addressed throughout the report. This chapter summarizes the major findings from the experimental and analytical studies performed in relation to those questions. Section 4.1 outlines the key conclusions of NCHRP Project 12-113. Section 4.2 serves as the link between the major findings of the studies and the proposed specification and commentary language provided in Appendix A. In other words, the conclusions outlined in Section 4.1 are synthesized in the context of AASHTO LRFD, and Section 4.2 explains the justification and rationale for the proposed language presented in the appendix. Lastly, although this project significantly advances cross-frame analysis and design practices, there are a number of related studies that merit additional investigation. Section 4.3 identifies research topics beyond the scope of NCHRP Project 12-113 that could further improve the understanding of cross-frame behavior in steel I-girder systems. 4.1 Major Conclusions As noted previously, this section summarizes the primary conclusions reached from the experimental and analytical studies presented in Chapter 3. Given that the major research questions introduced in Section 1.2 served as the organization throughout the report, the conclusions provided herein are also organized in the same manner. Each research question, including its overarching topic of interest (i.e., fatigue loading, analysis, or stability) and the pertinent AASHTO LRFD articles, is presented in italicized font. Bulleted items, which were C H A P T E R 4

Conclusions and Suggested Research 135 synthesized from the “Major Outcomes” sections in Chapter 3, are then provided to address each question individually. Proposed changes to the corresponding AASHTO LRFD Articles are subsequently presented in Section 4.2 based on the commentary herein. [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) appro- priate for cross-frame analysis and design? Or do multiple presence effects need to be considered? • The WIM study (Section 3.2) confirmed that the “dual truck” event, which maximizes force reversal in critical cross-frames and was initially considered in the 7th Edition AASHTO Specifications, is a rare occurrence. As such, the current 9th Edition load criteria (i.e., a single design truck positioned in all longitudinal and transverse positions with the truck confined to one critical transverse position per each longitudinal position) is more appropriate. • In evaluating the AASHTO fatigue criteria, it was concluded that additional economies are possible for cross-frame design. This is largely attributed to (i) the sensitivity of cross-frame response to transverse load position and (ii) the current fatigue load factors. The fatigue load factors introduced in the 8th Edition AASHTO LRFD, which were calibrated based on girder response, do not accurately represent the response of cross-frames. As such, one or both of these items above could be addressed to maximize the efficiency of the design criteria. • In terms of item (i) above, current design criteria require all possible lane positions be considered, regardless of design lanes or actual lane striping. A more realistic scenario would be to apply fatigue loading only in anticipated drive lanes. Item (ii) and cross-frame-specific load factors are addressed with the next question. [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? • The WIM study summarized in this report indicates that the existing load factors of 1.75 for Fatigue I and 0.8 for Fatigue II are conservative for the fatigue limit state design of cross- frames by at least 35%, specifically when the AASHTO fatigue design truck is placed in every possible transverse position during analysis and design. To improve economy in the AASHTO LRFD guidance, this study demonstrated that either the fatigue design truck could be posi- tioned in striped lanes (rather than permitting design trucks in unrealistic lane positions such as adjacent to the bridge barriers), or cross-frames could be designed to adjusted load factors. Based on feedback from the NCHRP Project 12-113 panel, it was deemed more desirable to propose adjusted cross-frame-specific load factors. • As an alternative to introducing two new load factors for the Fatigue I and II limit states for cross-frames, it is possible to apply a single adjustment factor to the existing load factors, similar to the current use of an adjustment factor in the fatigue design of orthotropic decks in AASHTO LRFD Article 3.4.4. • Using a single adjustment factor of 0.65 applied to the Fatigue I load factor of 1.75 (i.e., a resultant load factor for cross-frames of 1.14) and the Fatigue II load factor of 0.8 (i.e., a resultant load factor of 0.52), this study demonstrated that the resulting reliability indices calculated via Monte Carlo simulation satisfy a minimum assumed target reliability of unity, as recommended in SHRP 2 R19B (Modjeski and Masters 2015). [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? • The reduced fatigue load factors specific to cross-frames proposed in the preceding question are calibrated assuming the number of cycles per design truck passage, n, is equal to unity, regardless of cross-frame spacing. This is consistent with the analytical and experimental analyses conducted in this study.

136 Proposed Modification to AASHTO Cross-Frame Analysis and Design [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)? • In general, cross-frame response is sensitive to transverse truck placement. The sensitivity of cross-frame response to longitudinal truck placement depends heavily on support skew and horizontal curvature. Similarly, critical lane position also depends on a variety of parameters. For instance, truck passages closer to the outer edges of the deck tend to maximize cross-frame forces in skewed and curved bridges, but not in straight bridges with normal supports. • In terms of implementation into AASHTO LRFD, the results of this study indicate that the current specification language in Article 3.6.1.4.3a, “a single design truck shall be positioned transversely and longitudinally to maximize stress range at the detail under consideration,” is the best way to ensure the critical load position is considered by the designer. This require- ment is best executed with an influence-surface analysis. Thus, performing an influence- surface analysis for the entire bridge deck, regardless of design or striped lanes, in conjunction with the proposed cross-frame-specific fatigue load factors more accurately represents the response of cross-frames to live load traffic. • The governing cross-frame member in a given bridge depends on many variables, including girder spacing, support skew, and striped lane positions. Bottom struts tend to see the most substantial load-induced force effects in composite systems, especially those near the supports of heavily skewed bridges. However, to ensure the critical force effects are considered in design, an influence-surface analysis is necessary (i.e., to examine all possible truck positions and cross-frame force effects). • In general, heavily skewed and/or heavily curved bridges, particularly those with contiguous lines of braces, generally produce the most significant force effects in cross-frame members. To avoid an iterative “chase-your-tail” design solution, whereby the designer uses increasingly large trial sizes for cross-frame members which in turn attract larger cross-frame forces, other key bridge parameters can be adjusted to mitigate force effects. For instance, using a dis- continuous, staggered cross-frame layout is a practical and economical solution for skewed systems. Increasing the deck thickness or decreasing girder spacing can also reduce cross- frame forces. However, these measures have significant impacts on the rest of the design and may therefore be less economical. [Fatigue loading – Articles 6.7.4.1, 6.7.4.2] Is it necessary to perform a refined analysis, either simplified 2D or 3D methods, for straight and non-skewed bridges? In other words, are the mini- mum design requirements outlined in Article 6.7.4.1 appropriate? • When comparing the response of cross-frames to measured WIM records, it was observed that load-induced fatigue forces are most significant in skewed and/or curved bridges, for which Ic > 1, Is > 0.15, or Ic > 0.5 and Is > 0.1. For bridges that do not fall into one of these categories, a refined 2D or 3D analysis is likely not warranted. In these instances, other design considerations such as stability bracing during construction often govern the design. Therefore, the minimum design requirements with respect to straight bridges with normal supports in Article 6.7.4.1 (in addition to stability bracing requirements) are 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? Are there alternative 3D modeling approaches for cross-frames? • 3D commercial design software programs commonly represent cross-frames as pin-ended truss elements, which inherently misrepresent the in-plane and out-of-plane stiffness of

Conclusions and Suggested Research 137 the system. The stiffness modification approach accounts for these limitations by adjusting the axial stiffness of the cross-frame members in the analysis model. The proposed eccentric- beam approach considers flexural deformations by explicitly representing the eccentric load path through the cross-frame connections. • Cross-frame deformational response in composite systems (i.e., in-service) is different than the response in noncomposite systems (i.e., during construction). As such, the established R-factor in AASHTO LRFD that was developed specifically for the noncomposite condition should be reconsidered for composite conditions and live load force effects. • Independent stiffness modification factors are proposed for the construction stages (Rcon = 0.65) and for in-service conditions (Rser = 0.75). Note that the appropriate R-factor to be assigned for the in-service condition is largely a function of bridge geometry, cross-frame details, and uncertain loading conditions. Although scatter was observed in the results, the proposed R-factor is a simple solution to a complex problem that produces reasonably accurate approximations of the true cross-frame stiffness. Considering that many designers often prefer simple alternatives over sophisticated refined analyses, it serves an important role in AASHTO LRFD guidance moving forward. • Analytical results demonstrated that the proposed eccentric-beam analysis method improves the repeatability and reliability of 3D models by eliminating several sources of uncertainty associated with the R-factor approach. Although the R-factor approach serves a vital purpose in practice due to its ease of use, the proposed eccentric-beam method offers an alternative to engineers seeking a more refined solution. [Analysis – Article 4.6.3.3.2] What are the limitations of simplified 2D analysis techniques commonly used by popular commercial bridge design software programs in terms of predicting cross-frame force effects in composite systems? Are there methods available to improve these simplified techniques? • In general terms, designers must be cognizant of the potential trade-offs between sophis- ticated and simplified analyses. A central theme explored throughout this report is related to the balance between increased computational complexity and improved reliability versus simplified modeling and improved ease of use. The results presented in this report clearly highlight this trade-off. The conclusions below are intended to provide practicing engineers the technical and quantitative background to help them make informed decisions, while not necessarily advocating one method or the other for a specific project need. • Although 3D models are more time-consuming to develop than 2D counterparts, these models offer solutions with improved accuracy, reliability, and repeatability. 2D analysis methods have traditionally been shown to produce reasonable approximations of girder force effects, but this study demonstrated the significant limitations of 2D analyses asso- ciated with cross-frame force effects due to truck loads. • The traditional approach of connecting cross-frame members into a shared node along the web-to-flange juncture in 3D models is also acceptable, as long as the true stiffness is approximated with R-factors or the eccentric-beam approach. • 2D PEB models generally produce more accurate cross-frame results than 2D grillage models because the concrete deck is explicitly considered. Although there are methods to consider the effective transverse stiffness of the deck, it is more accurate to represent the deck as a thin shell element that is rigidly connected to the girder to simulate composite action. • Common postprocessing practices for 2D methods tend to produce erroneous results for top strut members and potentially inaccurate results for diagonal members in X-frames, regardless of bridge type. If a designer elects to use a 2D modeling approach for these complex cases, it is recommended to incorporate simple modifications to the model (e.g., utilizing the Timoshenko approach for equivalent cross-frame beams) and to the

138 Proposed Modification to AASHTO Cross-Frame Analysis and Design post processing (e.g., considering various shear force distributions in the design of X-frame diagonals or considering the contributions of the concrete deck when evaluating grillage model results similar to Figure 2-17). Still, even after implementing these improvements to 2D analyses, substantial error is likely in cross-frame force predictions, especially in bridges with significant horizontal curvature and/or support skews. • Based on the conclusions above, it is recommended that cross-frame force effects— particularly those related to live loads—for any bridge satisfying the skew and connectivity index limits established above should be evaluated using 3D modeling techniques. In general terms, this implies that obtaining live load cross-frame forces for heavily skewed and/or curved systems is best suited for 3D analysis. Although the focus of this study is related to the fatigue limit state, this statement is also directly applicable to the strength limit state design (and associated analysis) of cross-frames. [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? • Given that a composite deck provides continuous restraint to the top flange and substantial restraint to the bottom flange, cross-frame bracing requirements are only necessary to be evaluated for construction conditions. • Through FEA parametric studies, it was concluded that providing three times the ideal stiffness for cross-frames better limits girder deformations and cross-frame forces at critical buckling loads. As such, a proposed modification to the current AISC expression was provided in Eq. 3.3 for implementation into AASHTO LRFD. • The general form of the torsional bracing strength equations from the 14th Edition of AISC (2010) is more appropriate than the current 15th Edition (2016) for steel bridge applications. Based on the revisions to the torsional bracing stiffness requirements above, Eq. 3.4 was proposed for implementation into AASHTO LRFD. • For cases with reverse-curvature bending, it is recommended to conservatively base the required bracing moment on the unbraced segment that maximizes Mr/CbLb in Eq. 3.4. This ensures that, for each span (with a corresponding length, L, and number of intermediate braces, n), the critical bracing moment is considered. [Stability bracing – Article N/A] How are these stability bracing requirements combined with other load conditions such as wind? • Bracing strength demands, as computed by Eq. 3.4 or from a large-displacement analysis, can be combined with other construction-related force effects via linear superposition. These bracing forces must be evaluated at all stages of steel erection and deck construction. It is also important that the designer evaluates these load cases under the same concurrent construction conditions. For example, stability bracing force effects related to an inter mediate phase of girder erection should not be combined with dead load force effects related to wet concrete, as these two activities occur at different stages of construction. Because stability bracing force effects are a function of the factored girder moment (i.e., Mr in Eq. 3.4), no additional load factors are needed when combining these effects with the other construction- related force effects. 4.2 Suggestions for Implementation Based on the major conclusions outlined above, this section highlights the articles in the AASHTO LRFD Specifications to be modified. In general, the rationale and justification for the proposed specification and commentary language presented in Appendix A is explained.

Conclusions and Suggested Research 139 In terms of organization, each specific AASHTO LRFD Article is listed in italicized font herein followed by bulleted items that expound on the proposed modifications. Articles 3.4.1 and 3.4.5 (proposed) • As noted in Section 4.1, cross-frame-specific load factors that more accurately represent the live load response of cross-frames to the U.S. truck spectra have been proposed. Rather than introduce two new Fatigue I and II load factors, an additional adjustment factor (0.65) to be applied to the existing load factors is proposed, similar to the approach taken for the fatigue design of orthotropic decks in AASHTO LRFD Section 3.4.4. As such, a new article is proposed (Article 3.4.5) to introduce this additional adjustment factor. Article 3.6.1.4 • As noted in Section 4.1, conservatism in the current AASHTO fatigue loading model has been eliminated by proposing reduced cross-frame-specific fatigue load factors as opposed to limiting design trucks to a specified lane. As such, the findings of this study concur with and validate the current commentary language in this article, which addresses the uncertainty of future lane striping changes and deck widening. Thus, no additional specification or commentary language is recommended. Article 4.6.1.2.4 • Article 4.6.1.2.4 currently specifies that cross-frames and diaphragms in straight and slightly curved I-girder bridges shall be designed, at a minimum, for wind loads and slenderness requirements. Based on the findings of the Stability Study, it is recommended to include stability bracing as an additional minimum design requirement for these I-girder bridges, especially during deck construction. As such, a reference to proposed Article 6.7.4.2.2 is added to the specification language in this article. Article 4.6.3.3.2 • Based on the findings of this study, the commentary language in Article C4.6.3.3.2 with regards to equivalent torsional stiffness to account for warping should be maintained. It was observed that neglecting warping-torsional rigidity in composite bridges is much less impactful than in noncomposite bridges as documented by White et al. (2012). However, many designers utilize commercial design software packages that perform staged construction. Thus, it is beneficial to incorporate warping rigidity through all stages of construction and service, even if it does not significantly influence the cross-frame response to live loads. • As noted in Section 4.1, 2D PEB and grillage model approaches may lead to more significant errors in the prediction of cross-frame forces regardless of bridge geometry. This was largely attributed to the postprocessing procedures commonly implemented that convert equiva- lent beam shear and moments into cross-frame member forces. Thus, commentary language has been added to help designers make informed decisions regarding analysis for their project needs. Article 4.6.3.3.4 • Article 4.6.3.3.4 has been divided into three separate sub-articles to clarify the differences between 2D and 3D modeling techniques of cross-frames. Proposed Article 4.6.3.3.4a focuses on current 9th Edition specification and commentary language as well as proposed language with respect to 2D analysis. Proposed Article 4.6.3.3.4b outlines 3D analysis methods of cross-frames, including the traditional truss-element modeling approach and the proposed eccentric-beam approach in the commentary. Lastly, proposed Article 4.6.3.3.4c discusses the use of stiffness modification factors to be considered in both 2D and 3D models of cross-frames.

140 Proposed Modification to AASHTO Cross-Frame Analysis and Design Article 4.6.3.3.4a (proposed) • For 2D modeling of cross-frames, the proposed postprocessing tools that improve the accuracy of the force predictions are introduced with figures, as are analysis strategies that consider the transverse stiffness effects of the concrete deck in grillage-type models. Article 4.6.3.3.4b (proposed) • The eccentric-beam modeling approach is introduced in the commentary as an alternative to the truss-element (with R-factors) approach. As presented in this report, the eccentric- beam approach encompasses a wide range of modeling assumptions with varying levels of accuracy and modeling simplicity. Three specific variations were outlined and accompanied by sample calculations in Appendix F, but the possible set of assumptions is certainly not limited to those documented here. As a result, the reader can be referred to the final report of NCHRP Project 12-113 for guidance, if desired, but detailed instructions on a specific method are not offered in the specifications. Article 4.6.3.3.4c (proposed) • The stiffness response of cross-frames in noncomposite systems for stability-related deforma- tion patterns should be clearly differentiated from the response of cross-frames in composite systems subjected to highly variable live loads. This is accomplished by establishing a separate stiffness modification factor for in-service conditions (Rser = 0.75) compared to the previous recommendation of Rcon = 0.65 that was developed for noncomposite steel girders during construction. These factors are applied to both 2D and 3D cross-frame analysis models. • Currently, Article 4.6.3.3.4 references end connection eccentricities as the primary moti- vation for the stiffness modification factors. However, as discussed in this report, these modifi cation factors inherently account for other effects beyond just eccentric end connec- tions, including in-plane rotational restraint provided by the connection and gusset plates. Accordingly, the proposed specification updates broaden the language by removing the references to “end connection eccentricities” such that the reader understands the full implications of using the simplified truss-element modeling approach. Articles 6.6.1.2.1 and 6.6.1.2.2 • Based on the WIM study, it was confirmed that the removal of the “double truck case” in the 2016 Interims to the 7th Edition of the specifications was warranted. Given that Article C6.6.1.2.1 addresses this properly, no substantial changes to the specification or commentary language are recommended. However, it is suggested to move this commentary language to Article C6.6.1.2.2, along with providing additional guidance on how factored cross-frame fatigue stresses are to be computed based on computer analysis results. Table 6.6.1.2.5-2 • As noted in Section 4.1, the proposed adjustments to the Fatigue I and II load factors for cross-frame design were calibrated based on the assumption of n = 1 (i.e., one stress cycle per truck passage) given the observations made from experimental and analytical studies. As such, the ambiguous designation of “transverse members” is clarified by differentiating between cross-frames and floorbeam members. The n-value to use for cross-frames is defined as 1.0 and is independent of longitudinal spacing. Article 6.7.4.1 • Given that (i) live load cross-frame forces in geometrically simple bridges are generally small, and (ii) 3D analysis models, although more accurate, can be computationally inten- sive, it is important to establish bounds for when refined analyses are required to obtain cross-frame design forces from gravity loads (e.g., live loads). As such, the skew and

Conclusions and Suggested Research 141 connectivity index limits established previously (Ic > 1, Is > 0.15, or Ic > 0.5 and Is > 0.1) are introduced in the commentary language to expound on the minimum design consid- erations in this article. These limits also complement the general approach and language in Article 4.6.3.3.2. • In general, this proposed language helps clarify the design considerations and what consti- tutes a “rational analysis.” Article 6.7.4.2 • Article 6.7.4.2 is divided into two independent subheadings based on the addition of stability bracing requirements for cross-frames. The specification and commentary language in the original Article 6.7.4.2 are now contained in proposed Article 6.7.4.2.1. Stability bracing requirements are provided in proposed Article 6.7.4.2.2. Article 6.7.4.2.1 (proposed) • Similar to the discussion for Article 4.6.1.2.4, the minimum design requirements for cross- frames in I-girder bridges should include the applicable stability bracing checks at all critical stages of construction. Specification language is added accordingly. • This article currently highlights good design and detailing practices of cross-frames, particu- larly in skewed and/or curved systems. Given that contiguous versus discontinuous cross- frame lines are already discussed in the commentary with respect to noncomposite systems, the major findings related to the Fatigue Loading Study are best suited here. • As documented in Section 4.1, cross-frame force effects are highly variable and depend on a number of parameters. Ultimately, the two most important aspects of the findings are that: (i) bottom struts and diagonal members near supports tend to govern fatigue design in skewed and/or curved bridges and (ii) there are a number of ways that designers can mitigate design forces in cross-frame elements other than increasing the cross-sectional area. The most practical and economical way to mitigate load-induced cross-frame forces in skewed systems is to arrange the braces in a discontinuous, staggered layout. With that in mind, proposed commentary language is provided to emphasize these findings. Article 6.7.4.2.2 (proposed) • On the specification side, Eqs. 3.3 and 3.4 are included, which present the required stiff- ness and strength of cross-frames or diaphragms serving as torsional braces, respectively. Additionally, it is important to include guidance on how the total stiffness of a cross-frame system is calculated (i.e., Eq. 2.2). As such, guidance from Yura (2001) and specifically the equations to estimate the stiffness of the torsional brace considering connection flexibility, in-plane girder effects, and cross-sectional distortion effects (also documented in the AISC Specifications) are provided for reference. The geometric limits, at which in-plane girder stiffness and cross-section distortion effects become negligible, are also established. • On the commentary side, much of the information included in the AISC Specifications is adapted given that it directly applies to steel bridge applications. For instance, the basis of the original strength and stiffness requirements (Taylor and Ojalvo 1966) is outlined, as is the critical shape imperfection (Wang and Helwig 2005). Furthermore, expressions that consider the effect of skewed cross-frames relative to a line normal to the longitudinal axis of the bridge girders is provided based on work conducted by Wang and Helwig (2008). • Given the bracing strength requirements specified in proposed Article 6.7.4.2.2 herein, it is important to provide designers with guidance on how to utilize these forces in the context of strength limit state design for all stages of construction. As noted in Section 4.1, stability bracing force effects are to be combined with other construction-related load cases via principles of superposition. Additional specification and commentary language have been proposed to explain this procedure as well as the pertinent load factors. Design examples in Appendices B and C demonstrate these calculations.

142 Proposed Modification to AASHTO Cross-Frame Analysis and Design 4.3 Future Research Needs Although this project significantly advances cross-frame analysis and design practices in a wide range of areas, there are a number of related studies that merit additional investigation. These additional research topics are identified below. • Investigate the benefits of lean-on braces in terms of relieving load-induced force effects in composite skewed bridge systems. Although lean-on braces were examined during the field experimental phase of NCHRP Project 12-113, a more comprehensive review of lean-on brace response to truck traffic is warranted, especially as more lean-on systems continue to be implemented in practice across the United States. • Examine the stiffness implications of eccentric end connections on cross-frame systems utilizing tee sections. This study focused primarily on single angles, as they represent the most common steel section used in cross-frames across the Unites States. However, additional research on the behavior of tee-section cross-frame members in composite systems is needed. • Investigate methods to improve the prediction of cross-frame forces in 2D analysis software. As documented in this report, current 2D bridge design software can provide potentially erroneous predictions of cross-frame forces in composite bridges. Considering the popularity of 2D bridge design software, development of methods to provide more accurate cross-frame forces would be highly beneficial to bridge designers. • Experimentally investigate the effects of staggered cross-frame layouts on lateral flange stresses in skewed and curved bridge systems. Although substantial analytical efforts have been made with regards to lateral flange stresses in girders (White et al. 2012), the research team is unaware of any field or laboratory studies to examine the long-term fatigue ramifications of these stresses. • Develop innovative details to improve the fatigue category and reduce the cost of cross-frames. While this report focused primarily on the fatigue loading characteristics of cross-frames, additional studies on the nominal fatigue resistance of welded cross-frame details could be very beneficial to bridge designers.

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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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