Large-Deflection Spatial Buckling of Thin-Walled Beams and Frames
01 Jan 1973-Journal of Engineering Mechanics-asce (American Society of Civil Engineers (ASCE))-Vol. 99, Iss: 6, pp 1259-1281
TL;DR: In this paper, the potential energy expression and stiffness matrix of a straight thin-walled beam element of open asymmetric cross section, subjected to initial axial force, initial bending moments, and initial bimoment, are derived.
Abstract: The potential energy expression and the (14 by 14) stiffness matrix of a straight thin-walled beam element of open asymmetric cross section, subjected to initial axial force, initial bending moments, and initial bimoment, are derived. The transformation matrix relating the forces and displacements (including bimoment and warping parameter) at the adjacent end cross section of two elements meeting at an angle is deduced as the limiting case of a transfer matrix of a curved beam. To cope with asymmetric cross sections, some element displacements and forces are referred to the shear center and others to the cross-sectional centroid and the matrix for transformation from shear center to centroid is set up. The incremental larger-displacement analysis is formulated using the Eulerian coordinate approach with updating of the local coordinate systems at each load increment. The deformed beams are imagined to be composed of straight elements. Results of lateral post-buckling analysis of various beams are presented.
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TL;DR: In this article, an updated Lagrangian and a total Lagrangians formulation of a three-dimensional beam element are presented for large displacement and large rotation analysis, and it is shown that the two formulations yield identical element stiffness matrices and nodal point force vectors.
Abstract: An updated Lagrangian and a total Lagrangian formulation of a three-dimensional beam element are presented for large displacement and large rotation analysis. It is shown that the two formulations yield identical element stiffness matrices and nodal point force vectors, and that the updated Lagragian formulation is computationally more effective. This formulation has been implemented and the resulted of some sample analyses are given.
633 citations
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TL;DR: In this article, a stiffness matrix for the analysis of thin walled beams is derived, starting from the principle of virtual displacements, and an updated Lagrangian procedure for nonlinear analysis is developed.
Abstract: A new stiffness matrix for the analysis of thin walled beams is derived. Starting from the principle of virtual displacements, an updated Lagrangian procedure for nonlinear analysis is developed. Inclusion of nonuniform torsion is accomplished through adoption of the principle of sectorial areas for cross‐sectional displacements. This requires incorporation of a warping degree of freedom in addition to the conventional six degrees of freedom at each end of the element. Problems encountered in the use of this and similar matrices in three‐dimensional analysis are described.
167 citations
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TL;DR: In this article, a model is developed for beam lateral buckling stability analysis based on Eurocode 3, which is used for checking the stability of laterally unrestrained beams with open sections.
91 citations
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TL;DR: In this article, a general variational formulation to analyze the elastic lateral-torsional buckling behavior of singly symmetric thin-walled tapered beams is presented, numerically implemented, validated and illustrated.
Abstract: A general variational formulation to analyze the elastic lateral-torsional buckling (LTB) behavior of singly symmetric thin-walled tapered beams is presented, numerically implemented, validated and illustrated. It (1) begins with a precise geometrical definition of a tapered beam; (2) extends the kinematical assumptions traditionally adopted to study the LTB of prismatic beams; (3) includes a careful derivation of the beam total potential energy; and (4) employs Trefftz's criterion to ensure the beam adjacent equilibrium. In order to validate and illustrate the application and capabilities of the proposed formulation, several numerical results are presented, discussed and, when possible, also compared with values reported by other authors. These results (1) are obtained by means of the Rayleigh-Ritz method, using trigonometric functions to approximate the beam critical buckling mode, and (2) concern the critical moments of doubly and singly symmetric web-tapered I-section simply supported beams and cantilevers acted by point loads. In particular, one shows that modeling a tapered beam as an assembly of prismatic beam segments is conceptually inconsistent and may lead to rather inaccurate (safe or unsafe) results. Finally, it is worth mentioning that the paper includes a state-of-the-art review concerning one-dimensional analytical formulations for the LTB behavior of tapered beams.
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TL;DR: In this article, a theory for the nonlinear axial strain and Kirchhoff stress resultants for a thin-walled beam-column whose cross-section is tapered is presented.
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