The paper presents the Finite element method (FEM) that calculates the internal force and the displacement of beams on elastic foundation in the case of the uncertainty input parameters described in terms of the number intervals. Using the interval function optimization algorithm combined with the FEM to determine the internal force values of the span reinforced concrete beam structure. This study applies the hybrid differential evolutionary optimization algorithm combined with FEM interval functions to determine the required internal force results of reinforced concrete beams placed on an elastic foundation. The calculation process is programmed using Maple.17 software to determine the displacement output and the resulting internal force in the beam. To check the correctness of the program calculated on Maple.17, the input declared dataset corresponds to the central values of the interval numbers and is recalculated by SAP2000v21 software, then evaluates the results error of internal force on the beam under consideration.

This article presents an approach to assess safety levels of structures. A new formula for determining the fuzzy reliability of structures is proposed for the case where the set of loading effect and set of structural durability are general fuzzy sets. Illustration example concerning the bending strength evaluation of a simple-beam structure, is presented with the choice of triangular fuzzy sets for loading effect and structural durability.