Advanced Steel Construction

Vol. 3, No. 3, pp. 689-705(2007)



Uroš Klanšek 1, Tomaž Žula 2, Zdravko Kravanja 3 and Stojan Kravanja 4,*

1DSc, University of Maribor, Faculty of Civil Engineering, Maribor, Slovenia

2BSc, University of Maribor, Faculty of Civil Engineering, Maribor, Slovenia

3Professor, University of Maribor, Faculty of Chemistry and Chemical Engineering, Maribor, Slovenia

4Professor, University of Maribor, Faculty of Civil Engineering, Maribor, Slovenia

* (Corresponding author: E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.)

Received: 22 September 2006; Revised: 26 April 2007; Accepted: 13 June 2007




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The paper presents the discrete dimension optimization of unbraced rigid steel plane frames. The optimization of steel frames was carried out by the Mixed-Integer Non-linear Programming (MINLP) approach. The MINLP is a combined discrete-continuous optimization technique. It performs the discrete optimization of discrete decisions simultaneously with the continuous optimization of continuous parameters. The task of the optimization is to minimize the mass of the frame structure and to find the optimal discrete sizes of standard steel sections for frame members. The finite element equations are defined as the equality constraints for the second-order elastic structural analysis. The design constraints for the steel members were formulated according to Eurocode 3. The Modified Outer-Approximation/ Equality-Relaxation algorithm and a two-phase MINLP optimization approach were applied for the optimization. The latter starts with the continuous optimization of the frame, while the standard dimensions are temporarily relaxed into continuous parameters. When the optimal continuous solution is found, standard sizes of cross-sections are re-established and the simultaneous continuous and discrete dimension optimization by MINLP is then continued until the optimal solution is found. A numerical example of the optimization of a steel frame is presented at the end of the paper to show the suitability of the proposed approach.



Optimization; mixed-integer non-linear programming; MINLP; steel structures; frames; Eurocode 3


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