Strength-Based Out-of-Flatness Tolerance for Bottom Flanges of Steel Box Girders

This study determined an explicit tolerance for bottom flanges of tub girders giving computed first yield moment including the strength reduction due to initial out-of-flatness of tub girders higher than the flexural design capacity for the limit state of bottom flange local buckling in current standards. Finite-element analysis (FEA) was used to construct flexural strength–reduction curves for tub 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 were modeled as covering the practical range. Models were built with coexisting out-of-flatness in both webs and flanges. The appropriate residual stress pattern was created using heat analysis. Models were laterally supported to ensure the local buckling limit state controls. Both 344.7-MPa (Grade 50 Steel) and 689.4-MPa (Grade 100 Steel) yield steel plates were considered with elastic-perfectly plastic material behavior. Large deflection theory was used to iteratively capture the secondary moments due to out-of-flatness. The current tolerance of $D/150$ out-of-flatness for the fascia web of an I-shaped plate girder was shown to implicitly accept a 20% strength reduction. Results showed that compressive flexural design formulas for tub girders in current standards conservatively reduce the strength to account for local buckling. Code adoption of $b_f/200$ is recommended for the tub girder bottom flange out-of-flatness tolerance, where $b_f$ represents the bottom flange width.