Out-of-Flatness Plate Tolerance for Steel I-Shaped and Tub Highway Bridge Plate Girders
Open Access DepositedReasonable tolerances for steel plate out-of-flatness are required during fabrication and construction of built-up structural members. For American highway bridges out-of-flatness tolerances are currently set for some elements, but the engineering basis for these is not clear. For bottom flanges of tub or box girders there is no current explicit tolerance. The structural effect of out-of-flatness is most evident for slender plate components subject to local buckling. This compressive limit state is particularly consequential in webs, midspan top flanges, and continuous-over-support bottom flanges during construction. This study determines the girder strength reduction associated with the current out-of-flatness tolerances for I shaped girder webs and flanges and for tub shaped girder webs. A tolerance having a comparable reduction is then determined for tub bottom flanges. Finite element analysis (FEA) is used to construct flexural strength reduction curves for girders with various out-of-flatness magnitudes, covering a range of girder cross-sections and spans. Tub bottom flange slenderness ratios between 25 and 120 are taken as covering the practical range. Models are built with co-existing out-of-flatness imperfection in both webs and flanges. The imperfection pattern is set compatible with the first buckling mode of the built-up cross-section to match the case having the theoretical maximum effect on local buckling. The appropriate residual stress pattern is created using heat analysis. Models are laterally supported to ensure the local buckling limit state controls. Both 50 ksi and 100 ksi yield steel plate are considered with elastic-perfectly plastic material behavior. Large deflection theory is used to capture the secondary moments due to out-of-flatness. Results show current American Association of State Highway and Transportation Officials (AASHTO) compressive flexural design formulas for I and tub girders conservatively reduce the strength to account for local buckling. The current D/150 web tolerance, where D represents the depth, implicitly accepts a 20% strength reduction due to out-of-flatness. A tolerance of bf/200 for tub bottom flanges has a comparable reduction. A small range of tub bottom flange slenderness ratios has the highest strength reduction effect. This critical flange slenderness ratio decreases from the 50 to 60 range for 50 ksi steel to the 40 to 50 range for 100 ksi. Code adoption of bf/200 is recommended for the bottom flange out-of-flatness tolerance, where bf represents the bottom flange width.
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