PSI - Issue 81

Artem Bilyk et al. / Procedia Structural Integrity 81 (2026) 177–183

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imposing restrictions, a reduced FRS is obtained, in which a direct search is already carried out by the target indicator (optimality criterion). The characteristic dynamics of the reduction of the discrete FRS (for one of the specific tasks), when it is reduced due to the application of real technological and production restrictions, is shown in Fig. 3.

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The number of possible

combinations

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2

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Р arameter selection options

Fig. 3. Illustrative characteristic dynamics of changes in the volume of a discrete FRS section of a welded I-beam (explanation in the text).

In Fig. 3: 1 – theoretically possible number of combinations of flanges and walls from possible types of sheet cutting, 91204 solutions; 2 – FRS of welded I-beam taking into account technological limitations of manufacturing, 10982 solutions. As we can see, when taking into account manufacturing capabilities, the FRS is reduced by more than 8 times. 3 – FRS taking into account structural limitations on loss of local stability (8640 solutions). 4 – volume of FRS taking into account strength verification for normal and tangential stresses – 6741 solutions; 5 – added limitation for the second limit state – 1622 solutions. Among this FRS, a search for a globally optimal solution is carried out. So, as we can see, the reduction of discrete FRS, already formed on the basis of technological limitations of steel sheets, due to the imposition of production limitations of manufacturing I-beams and regulatory checks, is more than 56 times. The sequential reduction of FRS is shown for clarity. Let us consider an example of applying the proposed methodology to a specific object. 3. Results and discussion One of the current applied tasks requiring the use of metal beam structures is the construction of engineering protection structures (EPS) for critical national infrastructure (CNI) facilities. In particular, the concept "Fortress Country" provides for three levels of engineering protection (Bilyk et al. (2023); Bilyk and Kotsiuruba (2022)). The second level is designed to protect critical elements (CE) of the CNI objects from direct single hits from UAVs and indirect single hits from missiles. Let's select a beam for the floor of a protective structure of level 2 of a CNI object - an electric transformer of a distribution substation. The span of the beams is 7.5 m, the distance between beams is 1.95 m. Steel grade is S355. The scheme of supporting the beams on the walls is hinged (Fig. 4). The maximum design bending moment determined by load combinations is 1378.22 kNm, the maximum transverse force is 735.05 kN, which also takes into account the explosive effects from the explosion of a Shahed-136 UAV on the pre-detonation screen from above, made of metal mesh on steel support structures, at a distance of 6.5 m. The work of steel beams with the slab is provided separately. The maximum possible beam height is assumed to be 1100 mm. Deflections in structural calculations for survivability are not normatively limited, but in practice such limitations should be considered for design reasons, since excessive deflection affects the operation of the above-located structures and the calculation scheme. In this problem, the maximum deflections are assumed to be 1/100, based on the need to ensure the integrity of the above-located reinforced concrete roof slab. Criterion at this stage of research, is being considered only one: 1 − linear mass of the steel beam.

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Fig. 4. Schematic representation of the building: (a) general cross-section of the building; (b) a fragment of the design diagram