There is provided a method of selecting a radius of curvature for a conveying structure of a continuous glass finishing apparatus for processing a flexible glass ribbon having a thickness of about 0.3 mm or less. The method includes identifying a thickness of the flexible glass ribbon. The predetermined bending stress level is selected to be suitable for the flexible glass ribbon during processing of the flexible glass ribbon. The radius of curvature is selected for the transport structure suitable for transporting the flexible glass ribbon during processing of the flexible glass ribbon through the glass processing device based on at least one of the predetermined bending stress and the web deflection angle and line tension . The glass processing apparatus is provided including a carrying structure.;
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