Shape Optimization of Cold-Formed Steel Columns with Manufacturing Constraints and Limited Number of Rollers

The objective of this paper is to incorporate cold-formed steel manufacturing constraints, i.e., limiting the number of rollers employed for folding the section, in the constrained shape optimization of cold-formed steel columns. The aim of the constrained optimization is the creation of practical and economical cross-sections that provide significant increase in capacity from conventional cross-sections without sacrificing functionality in the field or increasing production costs dramatically. Previously, unconstrained shape optimization of cold-formed steel columns found cross-sections with enormous (as much as 140%) capacity increase above conventional sections, but with overly unconventional shapes. Implementing practical construction constraints in a simulated annealing (SA) algorithm was successful, and resulted in only marginally decreased capacity from the unconstrained optimal solution. The introduction of the manufacturing constraint whereby the number of rollers is limited, is implemented here. The procedure changes the framework of the SA code by making both strip widths and relative turn-angles as design variables for the cross-section stability models implemented in CUFSM. Members with three lengths: 0.61 m [2 ft], 1.22 m [4 ft], and 4.88 m [16 ft], are considered to reflect the impact of different buckling modes (local, distortional, and global) on the optimization results. The number of rollers is varied from 4 to 12 with an increment of 2. Optimized sections from multiple runs show uniformity. Given the larger shape variability provided by having more rollers, optimal designs have a close resemblance to the less constrained results already achieved, such as the point-symmetric ‘S’-shaped section for long columns and the singly-symmetric ‘Σ’-shaped section for shorter columns. Even with the minimal number of rollers allowed, the average strength increase over an available section is more than fifty percent, which makes the optimized cross-sections promising for developing into new commercial product families.

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