Mathematical and numerical analysis of local buckling thin-walled beams with non-standard cross-sections

The paper presents a novel approach to the analysis of buckling in thin-walled steel beams with modified cross-sectional shapes, focusing on their behavior under four-point bending. The aim of the study was to develop and examine new methods for determining critical loads for structural members with non-standard cross-sectional shapes, which are innovative in themselves. These methods are based on theoretical solutions grounded in the principle of potential energy conservation (an original approach). Additionally, based on the derived mathematical formulas, a custom application was developed, enabling rapid determination of critical loads using these new theoretical methods. The results show that the modified cross-sections significantly improve the mechanical properties of the beams, increasing their stiffness, buckling resistance, and load-bearing capacity. The findings provide new insights that can contribute to optimizing the design of thin-walled structures, with practical applications in the construction and automotive industries. The Finite Strip Method was used to verify the obtained results.