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1Â Â Introduction Cross-frames are important structural elements that serve many functions throughout the con- struction and service life of steel I-girder bridges. A primary function of cross-frames is to provide girder stability and enhance the lateral-torsional buckling (LTB) resistance of the bridge girders. In addition to the primary role as stability braces, cross-frames also resist a variety of lateral and gravity loads throughout the service life of a bridge. They also restrain differential deflections in girders caused by gravity loads on the non-composite system during construction (e.g., exter- nally applied loads and locked-in fit-up forces), as well as live loads on the in-service composite system. In horizontally curved bridges, cross-frames are considered primary structural elements 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. From a stability perspective, the critical design stage for cross-frames occurs during construc- tion of the concrete 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 concrete deck provides continuous lateral and torsional restraint to the top flange. It has also been established that cross-frame members and their connections can be susceptible to load-induced fatigue cracking due to repetitive load cycles thereby reducing the service life of the bridge (Modjeski and Masters 2015). 1.1 Background While there have been several advances in recent years towards improving the understanding of cross-frame behavior, several significant gaps in knowledge have been identified related to their design and detailing. These recognized knowledge gaps served as an impetus for NCHRP Project 12-113, which was undertaken to produce quantitatively based methodologies and design guidelines for the following items: 1. Improved definition of fatigue loading for cross-frames in straight, curved, and/or skewed steel I-girder bridges analyzed using refined analysis methods; 2. Implementation of stability bracing strength and stiffness requirements in the context of the AASHTO Load and Resistance Factor Design (LRFD) Bridge Design Specifications (henceforth referred to as AASHTO LRFD); and 3. Additional guidance on how to handle the influence of end connections on cross-frame member stiffness in refined analysis models. NCHRP Project 12-113 was divided into two stages. Stage 1 addressed these items and focused on cross-frames constructed with single-angle members. Based on the outcomes of Stage 1, pro- posed modifications for implementation into the AASHTO LRFD were drafted. These proposed C H A P T E R Â 1
2 Improved Cross-Frame Analysis and Design: Wide-Flange T-Shape Sections modifications were balloted and approved in 2021 for implementation in the 10th edition of AASHTO LRFD. The key results and recommendations from Stage 1 are published in NCHRP Report 962: Proposed Modification to AASHTO Cross-Frame Analysis and Design (Reichenbach et al. 2021). Stage 1 of NCHRP Project 12-113 focused exclusively on single-angle sections as cross-frame members, especially on how to handle the influence of end connections. Wide-flange T-shape (WT) sections, however, are also commonly used in several states. The intent of Stage 2 is to revisit the end connections on cross-frame members by investigating cross-frames made of WT sec- tions. Items 1 and 2 are not affected by the use of single-angles or WT sections as cross-frame members. 1.1.1 Current Knowledge for Cross-Frame Analysis Historically, cross-frames have been idealized as trusses with members that primarily experi- ence pure axial forces. However, cross-frames are generally made of single-angle or WT members that connect to gusset plates and connection plates. By nature of the shape of the sections along with the connections, these members possess significant connection eccentricity that leads to bending of the members from the applied forces. The effects of the connection eccentricities have been demonstrated in past research through laboratory experiments as well as through parametric finite element analysis (FEA) models that reflect the effects of the eccentric connections (Battistini et al. 2013). To capture the impact of the connection eccentricities accurately, shell-element models can be used to provide a good representation of the cross-frame behavior. However, modeling cross-fame components such as gusset plates, diagonals, and struts as shell elements is generally an overly complicated task that is not practical for design applications. As a result, widely used structural analysis software programs generally idealize cross-frame systems as pin-ended truss elements in 3D models or equivalent beams in 2D models. In these modeling approaches, the eccentric effects on the overall member stiffness are considered in a more simplified manner (i.e., the eccentric effects are not explicitly modeled). Figure 1-1 depicts a typical representation of the cross-frames using either shell elements or truss elements, and their connection details. As shown in Figure 1-1, truss-element models typically neglect the con- nection eccentricities. As noted above, past research (Battistini et al. 2013, Wang 2013, Battistini et al. 2016) has shown that the eccentric connections in the members that comprise the cross-frames result in significant reductions in stiffness compared to the truss- or equivalent beam-models. The cross-frame stiffness is typically overestimated in analytical solutions, truss-element models, and beam-element models because these approaches have historically neglected the connection eccentricities. Based on the work of Battistini et al. (2013), the current recommendation in the 9th edition of AASHTO LRFD (2020) is to reduce the stiffness of the truss or equivalent beam member, as appli- cable, with a modification factor. The stiffness modification factor, also known as the stiffness reduction factor is referred to herein as an R-factor. The R-factor can be assigned either to the Figure 1-1. Connection details for shell-element and truss-element models.
Introduction 3 elastic material stiffness (i.e., Youngâs modulus, E, for steel) or the relevant cross-sectional properties such as area, A. In AASHTO LRFD (2020), R = 0.65 is recommended for cross-frames fabricated from either single-angles or flange-connected WT sections; however, the research to date has only considered cross-frames constructed using single-angles. Note that the recommended R = 0.65 was derived based on the behavior of cross-frames during construction of a bridge when the girders are in a non-composite condition. The research recommendations in NCHRP Research Report 962 (Reichenbach et al. 2021) that document Stage 1 of NCHRP Project 12-113 have provided a more comprehensive evaluation of the impact of the eccentric connections on the in-service behavior of single-angle cross- frames. For the in-service case, cross-frames must be checked for the fatigue limit state, and the stiffness of the cross-frames significantly impacts the predicted stress ranges in the cross- frame members. Thus, errors in estimating the cross-frame stiffness can lead to over- or under- conservative designs for fatigue. The work conducted in Stage 1 of NCHRP Project 12-113 showed that the required R-factor for the in-service case is different for the construction case due to effects of the composite bridge deck on the load-induced deformations in the cross-frame members. Consequently, based on the previous study, the research team recommended providing different R-factors for the construction case and the in-service case. Based upon the recommendations from studies on single-angle members, NCHRP Research Report 962 recommended R = 0.65 for the non-composite (construction) condition, and R = 0.75 for the composite (in-service) condition. Although the commentary to the 9th edition of AASHTO LRFD (2020) recommends an R-factor of 0.65 for cross-frames with either single- angles or flange-connected WT sections, only single-angle cross-frames were considered in the published work. 1.1.2 Problem Statement Cross-frame systems consist of the cross-frame members as well as the connection plates and gusset plates. The cross-frame members are often fastened about only one leg (for angles) or only the flange or stem (for WTs). The nature of this connection introduces eccentricities about one or more axes, which inherently impacts the stiffness of the cross-frame. In terms of stability bracing applications, a reduced cross-frame stiffness has a negative impact in that the brace is less effective at stabilizing the bridge girder against LTB. Conversely, a reduced cross-frame stiffness tends to have a beneficial effect for fatigue applications since the lower stiffness of the cross-frame tends to develop less force for a given amount of girder deflection under truck traffic. In general terms, WT sections tend to be stiffer in flexure than single angles of comparable dimensions and thickness, and WTs often have less significant eccentric effects when connected about their flange or stem due to the typical location of the centroid. The difference in the cen- troidal location between common flange-connected WT sections and leg-connected single- angle sections is depicted schematically in Figure 1-2. From these sketches, it is evident that the impact of out-of-plane and in-plane eccentricities in WT cross-frame members is anticipated to be less significant than that in single-angle members. Prior to the focus of Stage 2 on WT sections in cross-frames, Stage 1 had focused on cross- frames made of single angles, and all past R-factors accounting for the effects of eccentricities were also derived based on the use of single-angle cross-frames. Therefore, the research in Stage 2 of NCHRP Project 12-113 focused on the appropriate R-factors for cross-frames that utilize WT members, both for the construction condition and the in-service condition.
4 Improved Cross-Frame Analysis and Design: Wide-Flange T-Shape Sections 1.2 Research Objectives As outlined in Section 1.1, Stage 1 of NCHRP Project 12-113 focused on three main items including: member-level, panel-level, and system-level studies to determine the appropriate R-factors for cross-frames with single-angle members. In addition, Stage 1 had also demonstrated that the effects of connection eccentricity on the cross-frame stiffness can be reasonably estimated in a three-dimensional structural analysis model by utilizing beam elements with the eccentric offsets explicitly represented. Therefore, the main objective of Stage 2 of NCHRP Project 12-113 is to verify the appropriate- ness of this proposed approach for cross-frames made of WT sections, either flange-connected or stem-connected. To accomplish this goal, a series of laboratory experiments were performed to investigate the stiffness response of single WT members. This was followed by panel-level computational studies of full cross-frame systems made of WT sections as well as system-level computational studies of bridges with a composite deck and with cross-frames. In addition to considering R-factors for the construction and in-service condition, the suitability of modeling the eccentricity explicitly with beam elements that consider the eccentricity was also evaluated. 1.3 Organization of the Report This report consists of five chapters including this introductory chapter. The research approaches adopted to address the major objectives of Stage 2 of NCHRP Project 12-113 are outlined in Chapter 2. More specifically, the flow of work that includes the experimental pro- gram, model validation, and parametric FEA studies is detailed. In Chapter 3, the experimental program conducted on 14 WT specimens is presented. The chapter provides basic information on the WT specimens, key results obtained from the experimental studies, and the FEA model validation process. Preliminary FEA results are compared to the mea- sured data, and adjustments to the modeling approach are outlined. The improved FEA results with the modifications are subsequently presented to highlight the importance of the validation phase. In Chapter 4, the stiffness modification factor (R-factor) studies for WT cross-frames are pre- sented. The chapter mainly covers extensive panel-level studies as well as specific cases evaluated at the system level (i.e., girders and cross-frames). In the panel-level and system-level studies, R-factors for both construction and in-service bridge conditions are parametrically investigated using the validated finite element models. Lastly, studies utilizing eccentric beam models for WT cross-frames are outlined. In Chapter 5, the primary conclusions from the research and recommendations based on the major findings are provided. Figure 1-2. Schematic representation of eccentricities in (a) flange-connected WT members and (b) leg-connected single-angle members. (b)(a) Centroid Gusset
