The article describes the gradient-iterative optimization method and outlines the method’s basic assumptions and illustrates its general use. The method’s implementation was illustrated based on a steel I-beam. The described calculation example concerns the optimization of the height of the web of a multi-span beam. The method enables finding an optimal solution with the use of simple and commonly available software.
To illustrate the effectiveness of the optimization method, multiple calculations were performed for beams with various spans and various load conditions.
If the inline PDF is not rendering correctly, you can download the PDF file here.
1. Jasińska D and Kropiowska D 2018. The optimal design of an arch girder of variable curvature and stiffness by means of control theory. Hindawi Mathematical Problems in Engineeringhttps://doi.org/10.1155/2018/8239464.
2. Kropiowska D and Mikulski L and Szeptyński P 2018. Optimal design of a Kirchhoff plate of variable thickness by application of the minimum principle. Structural and Multidisciplinary Optimizationhttps://doi.org/10.07/s00158-018-2148-3.
3. Laskowski H 2017. Optimal design of structural elements as a control theory problem. Technical Transactions6 119-134.
4. Mikulski L and Laskowski H 2009. Control theory in composite structure optimizing. Measurement Automation Monitoring6 346-351.
5. Mikulski L 2004. Control structure in optimization problems of bar systems. International Journal of Applied Mathematics and Computer Science14 515-529.
6. Pesch HJ 1994. A practical guide to the solution of real-life optimal control problems. Control and Cybernetics23 7-60.
7. Sobczyk Sz and Mikulski L 2016. A method of optimum selection of post-tensioned concrete beam prestressing by example of a symmetrical three-span beam. Measurement Automation Monitoring62 139-145.
8. Sobczyk Sz and Mikulski 2014. A different way of finding optimal solution for steel portal frame. Measurement Automation Monitoring60 1060-1064.
9. EN 1990 – Basis of structural design.
10. EN 1991-1-1 – Actions on structures. General actions – Densities self-weight imposed loads for buldings.
11. EN 1993-1-1 – Design of steel structures. General structural rules.
12. EN 1993-1-5 – Design of steel structures. Plated structural elements.