Optimum design of cold-formed steel purlins using genetic algorithms

Abstract

An important advantage of cold-formed steel is the great flexibility of cross-sectional shapes and sizes available to the structural steel designer. However, the lack of standard optimized shapes makes the selection of the most economical shape very difficult. This task is further complicated by the complex and highly nonlinear nature of the rules that govern their designs. In this thesis, genetic algorithms are used to carry out the optimization of cold-formed steel purlins, which are assumed to be continuous over two spans subjected to a gravity load.

A genetic algorithm based optimum design method for cold-formed steel purlins is developed firstly. This method obtains the optimum dimensions for purlins with the highest load efficiency subjected to the geometrical and strength constraints provided in Eurocode 3, Part 1.3, and fabrication constraints. The design of cold-formed steel purlins is based on Eurocode 3, Part 1.3. The integrated design method is general for any shape of cold-formed steel purlins. However, in this thesis, the investigations are concentrated on Z-shape and Σ-shape cold-formed steel purlins. With this design method, an optimization tool and a set of optimum sections that can be easily accessed are provided for structural steel designers and steel manufacturers.

An integration of a modified Eurocode 3 method into genetic algorithm optimization is carried out. Currently, the design of cold-formed steel purlins in Eurocode 3 relies on the effective width approach. The method works by considering the strength reduction due to local plate buckling as an effective width for each element of the cross-section and to a distortional buckling as a reduced thickness for the stiffener. In the modified Eurocode 3 method, the numerical elastic buckling stresses are introduced into the calculation of the effective section properties. Via this integration, it is shown that such numerical method as the finite strip method may also be integrated into the genetic algorithm optimization process. In addition, the modified Eurocode 3 method depends on the buckling types which differs from the variations of the dimension. Thus, the typical buckling types of the Z-shape and Σ-shape cold-formed steel purlins are investigated.