Shape and cost optimization of cold formed "Z " purlin using genetic algorithms

Abstract

Cold formed "Z " purlins are widely used in civil engineering structures. An important advantage is the great flexibility of producing different geometry of this profile. In cold formed structures it is difficult (practically impossible) to change the shape along the element, so it is recommended to have "economic " shape of cross section of such purlin. The optimization process was incorporated for “Z ” purlin that works as simple beam under continuous load. Purlins were optimized for different spans and different loads. Optimization process was solved with use of genetic algorithms. This method was chosen because it is the most suitable for discreet problems with many nonlinear parameters. In addition, methods supported by genetic algorithms predominate other methods (like one direction searching method). Moreover this method was successfully exploited by us in other problems like cost and shape optimization of portal frame made of welded I beams/columns. The shape optimization were taken into consideration. Design variables were geometry of cross section, and grade of steel. Constraints were based on European national standards (Eurocode – 3, for cold formed structures). Ultimate and serviceability limit states were taken into account for elements undergoing bending. Results of analysis are presented in tables (optimal dimensions of cross sections, and grade of steel) for different spans and continuous loads. The main objective of this paper is an implementation of these results in industry (especially by producers an