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05.08: Lateral‐torsional buckling of beams of monosymmetrical cross‐sections loaded perpendicularly to the axis of symmetry: Theoretical analysis
Author(s) -
Balázs Ivan,
Melcher Jindřich
Publication year - 2017
Publication title -
ce/papers
Language(s) - English
Resource type - Journals
ISSN - 2509-7075
DOI - 10.1002/cepa.149
Subject(s) - moment (physics) , beam (structure) , bending moment , perpendicular , symmetry (geometry) , mathematics , shear and moment diagram , buckling , mathematical analysis , physics , structural engineering , classical mechanics , geometry , bending stiffness , optics , engineering
Determination of the critical moment is a crucial step of the process of assessment of the buckling resistance of a metal beam with no intermediate restraints between supports. The critical moment of an ideal beam depends, among others, on support conditions and variation of the bending moment along the span of the beam. It can be found as a solution of the eigenvalue problem of differential equations of bending. This complex procedure can generally provide a formula for the calculation of the critical moment with certain coefficients varying depending on the variation of the bending moment along the span and support conditions of the beam. The formula for the critical moment and numerical values of the coefficients taking into account the type of supports and variation of the bending moment for some common cases can be found in literature. The paper focuses on process of derivation of the formula for calculation of the elastic critical moment of beams of double symmetrical and monosymmetrical cross‐sections (channels) loaded perpendicularly to the plane of symmetry. Based on classical Vlasov's theory and variational method, a formula for the elastic critical moment of beams of double symmetrical cross‐sections and channels loaded perpendicularly to the plane of symmetry and coefficients for not only simple cases of loads but also selected special cases are derived using mathematical methods and presented in the paper. Numerical values of the above mentioned coefficients are summarized in tables and charts.