On Problem of Efficient Determination of Elastic Critical Moment of Beams with Selected Types of Cross-Sections

• Published in: IOP conference series. Materials Science and Engineering 2019-02, Vol.471 (5), p.52041
• Main Authors: Balazs, Ivan, Melcher, Jindrich, Horacek, Martin, Pesek, Ondrej
• Format: Article
• Language: English
• Subjects: Buckling; Cross-sections; Derivation; Differential equations; Eigenvalues; Exact solutions; Finite element method; Formulas (mathematics); Mathematical analysis; Metal beams; Numerical analysis; Numerical methods; Variational methods
• ISSN: 1757-8981; 1757-899X; 1757-899X
• DOI: 10.1088/1757-899X/471/5/052041

Assessment of the lateral-torsional buckling resistance of slender metal beams with no intermediate restraints requires the determination of the critical moment. Nowadays, its magnitude can be found using numerical analysis e.g. by means of widely used finite element method but also available derived formulae for the calculation of the critical moment based on the mathematical solution of the eigenvalue problem of differential equations of bending are still of considerable importance. For some common cases of support and load conditions and some specific types of cross-sections of metal beams, they allow to calculate the desired magnitude of the critical moment required for the buckling resistance check practically and reliably. The paper focuses on problem of derivation of the elastic critical moment of beams of double symmetrical cross-sections and channels loaded perpendicularly to the axis of symmetry. Starting with the Vlasov's theory of stability of thin-walled members and variational methods, the process of derivation of the critical moment is briefly described. Whereas in case of beams of prismatic cross-sections the application of this method can subsequently result in general formula for calculation of the critical moment for various support and load conditions, the solution for members with variable cross-sections is much more complex and requires application of specific methods. The paper deals with application of selected methods of numerical mathematics on problem of determination of the elastic critical moment of metal beams and, when possible, compares the obtained values with analytical solution. Special attention is paid to members with variable cross-sections where primarily numerical methods can be used. Based on comparison of results, suitability of the utilized methods applied on problem of lateral-torsional buckling of metal beams is evaluated with significant emphasis on members with variable cross-sections.