Optimal folding of cold formed steel cross sections under compression

• A hybrid strategy is used to find the optimal cross sections for open cold formed steel (CFS) columns under compression.
• The impact of column's boundary condition as well as its length on the final optimal cross section is investigated.
• Practical designs are sought by imposing constraints on the geometrical properties of the optimal cross sections.
• Strategies for identification of different instability modes and their associated critical loads are explored.
• Optimal designs are scrutinized through detailed finite strip analysis.

This paper aims at finding the optimal folding of open cold formed steel cross sections under compression. Starting with a fixed coil width, a design point in the design space is defined by a vector of turn angles at a set of points along the coil width. Generalized Finite Strip Method (FSM) and Direct Strength Method (DSM) are combined to calculate the nominal compressive strength for a given cross section (a given design with a given set of turn angles). The design space is searched primarily via a stochastic search algorithm, Genetic Algorithm (GA). The near-optimal folding of the cross section is then fine-tuned through a few steps of the gradient descent optimization. To arrive at practical designs the optimization problem is augmented with constraints on the geometrical properties of the cross section. The optimal cross sections are found to have compressive capacities that are higher than the original designs by a factor of more than three in many cases. The shape of the optimal folding is shown to be greatly influenced by the choice of boundary condition. Strategies for identification of instability modes, a necessary first step to using DSM, are also discussed in detail.