Guidelines for Analysis Methods and Construction Engineering of Curved and Skewed Steel Girder Bridges (2012)

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A-1 It is essential that the reader thoroughly understand the fundamental meaning of a number of the terms used in this report pertaining to cross-frame detailing, in order to facilitate study and interpretation of the corresponding results and discussions throughout the report. These terms and their definitions are as follows, listed in alphabetical order. •• Accurate 2D-Grid Analysis. A 2D-grid analysis that incorporates the improved I-girder torsion model of Section 3.2.2, the improved equivalent beam cross-frame model of Section 3.2.3, the improved method of calculating girder flange lateral bending stresses of Section 3.2.4, and when SDLF or TDLF detailing are employed, the procedure for calculating locked-in forces of Section 3.2.5. •• Accurate 3D FE Analysis. A 3D-FEA model that is capable of matching the benchmark 3D FEA responses of the Task 7 report (Appendix D of the contractors’ final report) as well as the FHWA Test Bridge benchmarks of Sections 3.2.2.1, 3.2.2.3, 3.2.3.6, 3.2.4, and 3.3.3.2 (Figures 3-85 through 3-91) with a normalized mean error (Equation 6) less than or equal to 6 percent. This corresponds to an A grade in Table 3-1 of Section 3.1.2. When SDLF or TDLF detailing are employed, an accurate 3D FEA must account for the corresponding locked-in forces using a procedure such as the one presented in Section 3.2.5. As shown in Section 3.3, the locked-in forces from the (beneficial) initial lack of fit of the cross-frames and girders gener- ally has a substantial effect on the distribution of internal forces and stresses. •• Conservative Elastic System. A structural system in which the response to any loading is unique (i.e., path independent), and in which, if the loading were removed, the system would return to its original undeformed geometry. Steel girder bridges are commonly idealized as conservative elastic systems for their erection analysis. Based on the assumptions that (1) yielding does not occur at any location within the structure, (2) any slip associated with frictional forces developed at the supports is negligible such that the supports may be idealized as non-frictional, and (3) slip within the structural connections (cross-frame connections to the girders, girder splices, etc.) is negligible, a structural analysis model can be developed of all the connected components/members/units for any steel erection stage and the gravity loads can simply be “turned on” to determine the unique response of the structure for that stage. Structural analysis of staged concrete deck placement is not unique because the “strain-free” position of the concrete deck, when its early stiffness first becomes significant for a given stage, depends on the sequence in which the concrete deck is placed. Staged concrete deck placement analysis is commonly handled by considering the bridge as an “incrementally conservative elastic system” in which the structure is analyzed elastically for the concrete loading increment associated with each stage, using a selected constant concrete elastic stiffness for the portions of the deck that have significant early stiffness. •• Cross-Frame Drop. The change in elevation between the ends of a fabricated cross-frame. For NLF detailing, the cross-frame drops are taken equal to the drops between the girders in A P P E N D I X A Glossary of Key Terms Pertaining to Cross-Frame Detailing

A-2 Guidelines for Analysis Methods and Construction Engineering of Curved and Skewed Steel Girder Bridges the initial fabricated (plumb and cambered) geometry. For SDLF or TDLF detailing of the cross-frames, the intermediate cross-frame drops are different from the corresponding girder drops. For SDLF detailing, the steel dead load cambers are subtracted from the above total drops between the girders to obtain the cross-frame drops. For TDLF detailing, the total dead load cambers are subtracted from the above total drops between the girders to obtain the cross-frame drops. •• Fit-Up Forces. The forces required to physically bring the components together and complete a connection during the erection of the steel. These forces can be influenced by initial lack-of-fit effects from SDLF or TDLF detailing of the cross-frames, but generally, they are distinctly different from the forces associated with the initial lack of fit between the girders and the cross-frames in their initially fabricated no-load geometry. •• Initial Lack of Fit. For analysis of SDLF or TDLF effects, the displacement incompatibility between the connection work points on the cross-frames and the corresponding points on the girders, with the cross-frames and girders in their initially fabricated no-load geometry, and in the context of this report, with plumb cambered initial girder geometry. For SDLF or TDLF detailing of cross-frames in I-girder bridges, the cross-frame may be considered to be connected to the initially plumb and cambered girder on one side, and the initial lack of fit is the displacement incompatibility with the work points on the girder on the other side. It should be noted that for cross-frames that are not normal (perpendicular) to the girders, there are generally two contributions to the initial lack of fit: (1) the difference in the vertical camber between the work points on the connected girders and (2) the major-axis bending rotations of the girders at the girder work points (see Figures 3-31 through 3-33). The initial no-load geometry defines the reference state of the corresponding conservative elastic system at which the strain energy is equal to zero. Hence, the no-load configuration is the only appropriate configuration to use as a basis for determining the corresponding lack-of-fit forces in the structure. •• Lack-of-Fit Analysis. A structural analysis in which locked-in forces are determined based on the initial lack of fit between the connection points within the structure. The designer can conduct a lack-of-fit analysis without any applied dead load on the structure to calculate the specific locked-in forces in the structure, or the steel dead load or total dead load may be included in the analysis to determine the total force effects in the structure for the selected steel dead or total dead load loading condition. •• Lack-of-Fit Analysis Configuration 1. The physical initial no-load (undeformed, unstrained) geometry of the cross-frames and of the fabricated (cambered and plumb) girders under theoretical zero load (see Figure 3-30a). One should note that defining the initial no-load (undeformed, unstrained) geometry of the structure is key to any structural analysis. The stresses and forces in the system are based on the deformations from this configuration, including any lack-of-fit effects. •• Lack-of-Fit Analysis Configuration 2. An idealized (fictitious) configuration, used for the structural analysis, in which the girders are assumed to be “locked” in their initial no-load, plumb and cambered geometry, and the cross-frames are deformed to connect them to the girder connection work points (see Figure 3-30b). For a 3D FEA, the structural analysis calculates cross-frame member initial axial strains or initial axial stresses based on a position vector analysis involving the initial lack of fit of the cross-frames to the girder connection work points. For an accurate 2D-grid analysis, the structural analysis calculates corresponding initial equivalent beam element “fixed-end forces” corresponding to the deformations required to achieve compatibility with the girder connection work points. •• Lack-of-Fit Analysis Configuration 3. The idealized deformed configuration reached by the structural system under no-load (dead load not yet applied), after resolving the initial lack of fit by connecting the cross-frames to the girders in Configuration 2, then “releasing” the locked girders to deflect under the lack-of-fit effects from the cross-frames.

Appendix A A-3 •• Lack-of-Fit Analysis Configuration 4. The final geometry reached under the targeted steel dead load or total dead load condition once the steel dead load or total dead load has been added to the structure, i.e., the geometry under the combined effects of the steel (or total) dead load plus the locked-in forces due to the SDLF or TDLF detailing of the cross-frames. •• Layover. The lateral deflection of the girder top flange relative to its bottom flange associated with twisting. •• Locked-In Forces. The internal forces induced into the structural system by force-fitting the cross-frames and girders together. These internal forces would remain if the structure’s dead load were theoretically removed. In straight-skewed bridges, the locked-in forces due to SDLF or TLDF detailing are largely opposite in sign to corresponding dead load effects, but they can be additive with the dead load effects in some locations. In curved radially supported bridges, the locked-in forces due to SDLF or TDLF detailing largely are additive with the corresponding dead load effects. The locked-in forces are never “removed” by corresponding dead load forces, but when they are opposite in sign to these forces, they can be “balanced” by the corresponding dead load forces. •• No-Load Fit (NLF) Detailing. A method of detailing of the cross-frames in which the cross-frame connection work points fit-up perfectly with the corresponding work points on the girders, without any force fitting, in the initial undeformed cross-frame geometry, and with the girders in their initially undeformed fabricated (cambered and plumb) geometry. •• Steel Dead Load Fit (SDLF) Detailing. A method of detailing of the cross-frames in which the cross-frame connection work points are detailed to fit-up perfectly with the corresponding points on the girders with the steel dead load camber vertical displacements and rotations subtracted out of the initial total camber of the girders. Also referred to commonly as “erection fit.” Detailers and fabricators work solely with the girder cambers specified on the engineering drawings to set the cross-frame drops associated with the SDLF detailing. The girders are assumed to be displaced from their initially fabricated (cambered and plumb) position to the targeted plumb steel dead load condition. Any twisting of the girders associated with the three-dimensional interactions with the cross-frames and overall structural system are not directly considered in these calculations. •• Total Dead Load Fit (TDLF) Detailing. A method of detailing of the cross-frames in which the cross-frame connection work points are detailed to fit-up perfectly with the corresponding points on the girders with the total dead load camber vertical displacements and rotations subtracted out of the initial total camber of the girders. Detailers and fabricators work solely with the girder cambers specified on the engineering drawings to set the cross-frame drops associated with the TDLF detailing. The girders are assumed to be displaced from their initially fabricated (cambered and plumb) position to the targeted plumb total dead load condition. Any twisting of the girders associated with the three-dimensional interactions with the cross- frames, slab, and overall structural system are not directly considered in these calculations. Also referred to commonly as “final fit.” •• Total Forces. The forces due to the combination of the dead load effects in the targeted condition plus the locked-in force effects from SDLF or TDLF detailing of the cross-frames. •• Uniqueness. The attribute of a conservative elastic structural system in which the state of stress and strain in the structure is path independent, i.e., in the context of steel bridge erection, independent of the sequence of erection. This assumption is a common staple of structural analysis for design. The unique solution depends not only on the targeted loading state (e.g., steel dead load or total dead load). It also depends on any specific initial lack of fit between the structural components. The influence of connection slip within tolerances also can be included to obtain a unique solution for a given slip, as demonstrated in Section 3.3.3.2. However, the influence of connection “slip” within standard connection tolerances generally is considered to be negligible for structural design purposes.