Parametric optimization of the shape of trapezoidal sheets due to the moment of inertia or covering width

The study presented in this article focuses on the parametric optimization of trapezoidal steel sheets used in construction, aiming to enhance their structural efficiency and reduce material usage. The optimization addresses two primary criteria: maximizing the moment of inertia and maximizing the cover width of the sheets. The research employs the Sequential Quadratic Programming (SQP) method for optimization, considering the constraints and standards proposed in Eurocode 3. The study explores the design variables, including the dimensions of the web and flange sections, to achieve optimal geometries for both criteria. The results indicate that optimizing for the moment of inertia leads to designs with larger stiffeners and more vertical web sections, enhancing the sheet's resistance to bending. Conversely, optimizing for cover width results in designs with more delicate stiffeners and less steep web sections, increasing the sheet's surface area coverage. Both optimization approaches demonstrate significant improvements over traditional designs, showcasing potential material savings and reduced environmental impact. The findings highlight the importance of optimization in structural engineering, suggesting that tailored designs can meet specific performance requirements while adhering to practical manufacturing constraints. This research contributes to the development of more efficient and sustainable construction materials, promoting advancements in the construction industry.