Instability-driven family optimization of cold-formed steel lipped-channel cross-sections with strength and stiffness constraints

The objective of this study is to advance a solution scheme that can produce a family of optimized thin-walled cold-formed steel lipped-channel sections under combined compressive and flexural loading subjected to both strength and stiffness constraints. In this new study, the solution scheme is extended from previous work considering strength constraints only to include stiffness constraints to address the serviceability requirement as well for a more practical reflection of behavior whereby stiffness is reduced due to member instabilities. The stiffness constraint is driven by a novel method for estimating effective moment of inertia due to cross-section instabilities such as local and distortional buckling modes. A two-level optimization framework is utilized to produce a family of optimized sections. The first level focuses on individual member optimization of the P−M demand space as derived from current commercially available lipped-channel sections in the United States; the second level focuses on a new family of optimized sections capable of covering the same design space at a minimal family size. The results of the study show that a family of only 8 unique optimized sections can replace 186 commercially available sections and still achieve the same or improved performance in terms of both strength and stiffness compared to strength constraints only. The developed family of sections demonstrates that optimization techniques, employing complicated design constraints, have a great potential for improving cold-formed steel production on currently widely-used cross-section shapes such as lipped channels.