Two-level optimization for a new family of cold-formed steel lipped channel sections against local and distortional buckling

The objective of this paper is to provide the development of a new algorithm that produces a family of minimal weight cold-formed steel lipped channels with the smallest number of individual cross-sections (family size) that are still capable of covering the current engineering design demands as commonly found in light steel framing. Current research in cold-formed steel optimization has largely sought optimal cross-sections for single members under a single applied action. In this paper, the optimization effort is extended to a broad set of axial (P) and bending (M) demands. A two-level optimization framework is proposed: level one focuses on member optimization of the P-M demand space as derived from current commercially available lipped channel sections in the United States; while level two focuses on the selection of a new family of optimal lipped channel sections that have the same efficiency in covering the design space, but utilize a minimal family size. As the focus of the effort is on the two-level optimization the cross-section optimization is simplified in this case to lipped channels against local and distortional buckling only; however the adopted algorithms are readily extensible. The results show that a new family of shapes with only 12 sections can achieve the same or better performance as the 108 sections commercially available in the United States. The developed family of shapes provides a direct demonstration of the potential for optimization to improve cold-formed steel manufacturing. In the future, the first-level member optimization will include new cross-section shapes, e.g., sigma sections, as well as global buckling, and will be performed along with the second family-level optimization to demonstrate additional potential benefits.