Influence of Bend Radii on Local Buckling in Cold Formed Shapes

The stress that causes local buckling is related to the width/thickness ratio of the element in compression. In current codes for the strength design of shapes cold formed from sheet metal, the presence of corner bend radii is treated by considering only the “flat width” portion of the element. This can lead to serious errors in the predicted buckling stress. An analysis of the influence of the corner radii is given together with the justification that the full distance between the intersections of the median lines of the elements be used for the design of typical cold formed shapes. In the case of simple formed angle shapes, a radiused bend at the heel actually reduces the critical stress. For trapezoidal deck sections and box shapes the critical stress calculated using the distance between the intersections of the median lines is not significantly influenced by the presence of corner radii <1/20 of the plate width. The theoretical critical stress is compared with that obtained using the “flat width,” which is shown to be unconservative.