Improved Cross-Frame Analysis and Design: Wide-Flange T-Shape Sections (2023) / Chapter Skim
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From page 39... ...
39 The results documented in Chapter 3 provide valuable insight into the behavior of WT sections and the specific role that eccentricities from specific components have on the behavior. However, the experiments and FEA validation thus far focused on individual WT sections with a variety of connection details.
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40 Improved Cross-Frame Analysis and Design: Wide-Flange T-Shape Sections shell-element model stiffness and the truss-element model stiffness is represented as the R-factor. The stiffness modification factor, R, is expressed mathematically as follows: R truss shell b b = Eq.
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Parametric Studies 41 Sy 6 5 i d d = -` j Eq.
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42 Improved Cross-Frame Analysis and Design: Wide-Flange T-Shape Sections Given their prevalence, the research team considered (1) flange-connected and (2)
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Parametric Studies 43 WT section sizes. Table 4-1 presents the range of values considered for each parameter, which are the representative values in practical bridge applications and consistent with the range of parameters considered in Stage 1 of NCHRP Project 12-113.
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44 Improved Cross-Frame Analysis and Design: Wide-Flange T-Shape Sections Type (a) Additive Eccentricity Type (a)
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Parametric Studies 45 In hindsight, the research team would have likely selected a plate thickness of 9⁄16-inch or 5⁄8-inch; however, the thickness was selected as a value between these two thickness values and still satisfies the required plate slenderness limit. The connection plate dimension satisfies the stiffener slenderness ratios established by the AASHTO LRFD Equation 6.10.11.1.2-2, which states that the width of a stiffener is not to exceed 16 times its thickness (i.e., b/t = 9/0.6 = 15 < 16)
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46 Improved Cross-Frame Analysis and Design: Wide-Flange T-Shape Sections Figure 4-8. R-factor results from additive cross-frame types with ½-inch gusset plate thickness Type (a)
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Parametric Studies 47 • Type (c) : Stem-connected (coped)
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48 Improved Cross-Frame Analysis and Design: Wide-Flange T-Shape Sections • Cross-frame stiffness is closely related to not only the in-plane stiffness but also the out-ofplane stiffness of cross-frame members that impact the corresponding stiffness reduction to account for the effects of the eccentricity. As shown in Table 4-2, the in-plane and out-of-plane moment of inertia of WT sections are generally larger than that of single-angle sections.
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Parametric Studies 49 From Figure 4-10 and Figure 4-11, the following observations can be made: • For Type (a)
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50 Improved Cross-Frame Analysis and Design: Wide-Flange T-Shape Sections WT sections. This approach will result in increased conservatism from a stability perspective; however cross-frames are relatively stiff systems, and the use of a smaller R-factor for WT sections should not significantly affect the overall efficiency or economy of the system when WT sections are used for the cross-frames when stability forces or deformations are considered.
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Parametric Studies 51 Model Cross-Frame Height [inch] WT Section 1 WT4x9 2 WT4x9 3 Girder Spacing [inch]
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52 Improved Cross-Frame Analysis and Design: Wide-Flange T-Shape Sections 4.3 System-Level Parametric Study The panel-level parametric studies focused on the R-factor of an isolated cross-frame panel with a deformational mode consistent with a non-composite girder. Although panel-level studies were also conducted with deformational modes that are consistent with composite girders, these results are not generally meaningful for cross-frames in the bridge application.
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Parametric Studies 53 In each bridge model, two cross-frame panels at midspan (in the edge bay and interior bay) were investigated, as these cross-frames generally represent the most critical member forces in a single-span system.
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54 Improved Cross-Frame Analysis and Design: Wide-Flange T-Shape Sections In each box-and-whiskers plot, the corresponding Ftruss/Fshell ratios for all six cross-frame members (with respect to the two governing load cases) in every bridge model are considered.
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From page 55... ...
Parametric Studies 55 represents the assigned R-factor that provides a conservative estimate of cross-frame fatigue design forces for 75% of the bridges considered. • Using the 25th-percentile line as the metric, the most appropriate R-factor for bridges with WT cross-frames in the composite condition is 0.8.
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56 Improved Cross-Frame Analysis and Design: Wide-Flange T-Shape Sections systems in the composite condition. Although this value is a little more unconservative for systems with WTs, the values are still reasonable.
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From page 57... ...
Parametric Studies 57 models were made in the investigation; however, the research team believes that the observed behavior is representative of the accuracy of general applications to any bridge. In Figure 4-17, the box-and-whiskers components are organized by the assigned R-factor in the truss-element model, as well as the eccentric beam model (simplified model)
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