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Buckling of Open Thin-Walled Beams
Buckling of open thin-walled beams, under various load conditions, is analyzed. A short discussion on the phenomenological aspects and on the mathematical models able to describe them is preliminary carried out. The elastic stiffness differential operator is built up for a beam undergoing bending and non-uniform torsion, according to the Vlasov theory. Successively, the geometric stiffness differential operator is evaluated for a beam solicited by a constant axial force and bi-axial bending moment, either constant or variable. The equations are derived via a variational procedure and successively interpreted by direct equilibrium arguments, relevant to the adjacent deformed configuration. Passing to analyze specific problems, uniformly compressed beams are first considered, for which, under particular constraint conditions, an analytical solution is viable. Non-symmetric, mono-symmetric, and bi-symmetric cross-sections are examined, for each of which the role of flexural-torsional coupling is discussed. Thin-walled beams, bent in a generic plane, or prestressed by eccentric compression/traction, are investigated. The more complex case of beams subject to transverse loads, which induce precritical non-uniform bending, is then addressed. A model is formulated, which takes into account the stabilizing/instabilizing effect of the point of application of loads on the cross-section. A sample case of lateral instability is solved analytically, by making use of the Frobenius method. The Ritz method for determining the critical load of thin-walled beams, non-uniformly bent in the prestressed configuration, is described. Finally, a polynomial finite element is formulated, for thin-walled beams subject to traction/compression and non-uniform bending. Some numerical applications are illustrated.
Buckling of Open Thin-Walled Beams
Buckling of open thin-walled beams, under various load conditions, is analyzed. A short discussion on the phenomenological aspects and on the mathematical models able to describe them is preliminary carried out. The elastic stiffness differential operator is built up for a beam undergoing bending and non-uniform torsion, according to the Vlasov theory. Successively, the geometric stiffness differential operator is evaluated for a beam solicited by a constant axial force and bi-axial bending moment, either constant or variable. The equations are derived via a variational procedure and successively interpreted by direct equilibrium arguments, relevant to the adjacent deformed configuration. Passing to analyze specific problems, uniformly compressed beams are first considered, for which, under particular constraint conditions, an analytical solution is viable. Non-symmetric, mono-symmetric, and bi-symmetric cross-sections are examined, for each of which the role of flexural-torsional coupling is discussed. Thin-walled beams, bent in a generic plane, or prestressed by eccentric compression/traction, are investigated. The more complex case of beams subject to transverse loads, which induce precritical non-uniform bending, is then addressed. A model is formulated, which takes into account the stabilizing/instabilizing effect of the point of application of loads on the cross-section. A sample case of lateral instability is solved analytically, by making use of the Frobenius method. The Ritz method for determining the critical load of thin-walled beams, non-uniformly bent in the prestressed configuration, is described. Finally, a polynomial finite element is formulated, for thin-walled beams subject to traction/compression and non-uniform bending. Some numerical applications are illustrated.
Buckling of Open Thin-Walled Beams
Luongo, Angelo (author) / Ferretti, Manuel (author) / Di Nino, Simona (author)
Stability and Bifurcation of Structures ; Chapter: 9 ; 265-330
2023-02-17
66 pages
Article/Chapter (Book)
Electronic Resource
English
Thin-walled beams , Compressed beams , Eccentrically compressed or tensed beams , Bent beams , Geometric bearing capacity , Flexural-torsional buckling , Lateral buckling , Ritz method for lateral instability , Frobenius method for lateral instability , Polynomial finite element , Influence of warping constraints Engineering , Mechanical Statics and Structures , Solid Mechanics , Mechanical Engineering , Structural Materials , Solid Construction , Building Construction and Design
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