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Out-of-Flatness Plate Tolerance for Steel Tub Highway Bridges Open Access

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This numerical research studies the effect of considering total body out-of-flatness pattern on design strength of typical steel bridge girders constructed in the United States with the purpose of modifying the current American Welding Society (AWS) out-of-flatness allowances accepted by American Association of State and Highways Officials (ASSHTO). Analyses of numerical models having web and flange simultaneous out-of-flatness compatible with first buckling mode, modeling grade 100 steel, and higher slenderness ratios are specifically advanced state-of-the art in this research. There are currently out-of-flatness tolerances provided for some elements of steel bridges in relevant specifications which the theoretical bases for them are not clear. The impact of out-of-flatness on the structural strength of the webs and flanges in steel plate girders must be understood to specify proper tolerances for these elements. The structural strength effect of out-of-flatness in plate elements can vary with the slenderness of the plate. The interaction of the slenderness and out-of-flatness should be fully studied, and the geometrical tolerances should be based on strength studies to assure safety of the structures. This research consists of numerical analysis of Finite Element Models (FEMs) of geometrically imperfect steel plate girders. The tolerances that address global out-of-flatness are not the source of interest in this study. The onsite surveys of actual steel plate bridges indicate that web and flange out-of-flatness almost always exist together. Hence, the whole body out-of-flatness pattern compatible with first buckling shape are adopted for the out-of-flatness pattern in the FEMs in this research. In the prior researches exclusively, web plate out-of-flatness only or bottom flange out-of-flatness only was considered. Large strain, large deflection, elastic-perfectly plastic constitutive material laws and residual stresses are used in the analysis of the models. The appropriate residual stress pattern is created using heat analysis. The FEMs include I-shaped steel girders and tub girders for variety of lengths, dimensions and thicknesses. These dimensions are based on actual bridges built in the state of Texas. Grade 50 and Grade 100 steel are used in the FEMs. Eleven different sizes steel tub girders are modeled which are simply supported at the two ends and they are exposed to upward force in the middle span to create compressive stresses in the bottom flange. Six unstiffened I-shaped plate girders simply supported at the two ends and six continuous unstiffened I-shaped plate girders are also modeled. Six different sizes two-sided stiffened I-shaped plate girders each with four different intermediate transverse stiffeners spacing are modeled and analyzed to obtain strength at onset of yielding called in this study first yield moment. Full width yield of bottom flange in tub girders possessing out-of-flatness is the first yield moment definition. The I-shaped steel plate girders FEMs range from 75 feet to 125 feet in length, while the tub girder FEMs vary from 33.3 feet to 133.3 feet in length. The FEMs plate dimensions cover all arrays of plate slenderness including compact, non-compact and slender. Each steel plate girder is modeled for seven to eight different magnitudes of out-of-flatness. The out-of-flatness existed both on flanges and webs, whole body, and they are compatible with the first buckling mode shape under the same loading and boundary conditions. Critical plate slenderness ratios are identified at which the same amount of plate out-of-flatness causes the maximum strength reduction in the girder. It is observed that American Welding Society (AWS) D1.5 allowances for webs can be relaxed without decreasing the design strength of the steel girder. The modified strength based out-of-flatness as functions of slenderness are offered in this research as graphs for some web tolerances. These functions are obtained using regression analysis of the FE analysis results. In tub girders, critical ranges of bottom flange slenderness ratios are found to have the highest strength reduction effect, and the allowable bottom flange out-of-flatness based on strength analysis is shown to be \frac{b_f}{200}, where b_f\ is tub girder bottom flange width. Yielding stress of steel, steel grade, causes no major change in the strength reduction pattern of steel bridge girders.

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