Application of Fuzzy Set Theory to the Serviceability Limit State of a Steel Beam under Bending

Deformations of an I-section steel beam under equal end moments are studied in this article. Initial geometric imperfection of the beam axis was introduced according to the Eurocode standard. Numerical studies have shown that the lateral deflection of slender beams under major axis bending can be relatively high. The acceptability of high values of lateral deflections within the framework of the serviceability limit state is discussed. In the next part of the paper, the limit value of maximum deflection was introduced as a fuzzy number. Fuzzy analysis of the maximum moment, which causes maximum deflection, was performed. The slenderness values of beams for which the serviceability limit state is the limiting condition for design were identified.

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