Modeling Out-of-Flatness and Residual Stresses in Steel Plate Girders

As the girder buckling strength depends on residual stresses and initial out-of-flatness, these need to be modeled when quantifying their effects. Zhang in 2007 used single plate imperfection patterns for web out-of-flatness for I-shaped plate girders. Actual girder out-of-flatness patterns include imperfections in all plate elements. This study uses a whole body out-of-flatness pattern compatible with the total body first buckling mode shape (Sadovsky 1978). An imperfection free girder Finite Element Model (FEM) is analyzed in ANSYS Software for Elastic Buckling, using the same loading and boundary conditions as the desired final imperfect steel plate girder, to generate the first buckling mode shape. The nodes of the imperfection free steel plate girder are displaced into the buckled shape and this distorted geometry is then used for non-linear analysis. Yield stress at the welded intersection of flange and web is the basis for residual stress distributions, generated using Heat Analysis in ANSYS to obtain temperature distributions. Lateral bracing is used to prevent global lateral torsional buckling so local buckling controls the flexural moment at onset of yielding. This approach allows a study of the effect of different magnitudes of geometrical imperfection for a set of girder cross-sections for I-shaped plate girders. The flexural moment at onset of yielding for various scales of the buckled shape are normalized by the imperfection free steel plate girder moment, giving a measure of the effect of the size of out-of-flatness on the performance of the girder. The results of FEA show dependency of first yield moment to web slenderness ratios and out-of-flatness in I-shaped plate girders. There is the critical web slenderness ratio of 124 for unstiffened I-shaped girders which causes the most strength reduction for positive moments and drastic strength reduction for larger slenderness for negative moment. No reverse behavior or critical web slenderness was observed in stiffened I-shaped girders for 1D, 2D, and 3D transverse stiffener spacings. The out-of-flatness tolerance was relaxed when it was strength wise possible. The proposed strength-based web out-of-flatness criteria are provided for I-shaped plate girders. Adopting total body first buckling mode shape as out-of-flatness pattern resulted in more conservative web tolerance than Zhang's proposed web tolerance for unstiffened I-shaped girders at positive moments.

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