Bimoment Contribution to Buckling of Thin-Walled Beams with Different Boundary Conditions

Prokić, Aleksandar; Mandić, Rastislav; Bešević, Miroslav

doi:10.1061/(asce)em.1943-7889.0001216

Cited by 3 publications

(2 citation statements)

References 9 publications

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“…Besides the usual assumptions of the linear theory of elasticity, the following assumptions [ 5 , 6 , 10 , 26 , 27 , 28 ] of classical theory for members with a thin-walled cross-section are employed in the analysis:…”

Section: Equilibrium Analysismentioning

confidence: 99%

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Exact Solutions for Torsion and Warping of Axial-Loaded Beam-Columns Based on Matrix Stiffness Method

et al. 2022

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The typically-used element torsional stiffness GJ/L (where G is the shear modulus, J the St. Venant torsion constant, and L the element length) may severely underestimate the torsional stiffness of thin-walled nanostructural members, due to neglecting element warping deformations. In order to investigate the exact element torsional stiffness considering warping deformations, this paper presents a matrix stiffness method for the torsion and warping analysis of beam-columns. The equilibrium analysis of an axial-loaded torsion member is conducted, and the torsion-warping problem is solved based on a general solution of the established governing differential equation for the angle of twist. A dimensionless factor is defined to consider the effect of axial force and St. Venant torsion. The exact element stiffness matrix governing the relationship between the element-end torsion/warping deformations (angle and rate of twist) and the corresponding stress resultants (torque and bimoment) is derived based on a matrix formulation. Based on the matrix stiffness method, the exact element torsional stiffness considering the interaction of torsion and warping is derived for three typical element-end warping conditions. Then, the exact element second-order stiffness matrix of three-dimensional beam-columns is further assembled. Some classical torsion-warping problems are analyzed to demonstrate the established matrix stiffness method.

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Section: Equilibrium Analysismentioning

confidence: 99%

“…Based on these assumptions, a compatibility equation relating the angle of twist φ and the cross-sectional bimoment B ω is formulated as Equation (7). The St. Venant torque T s is formulated as Equation (8) [ 5 , 6 , 10 , 26 ].

where I ωω denotes the warping constant.…”

Section: Equilibrium Analysismentioning

confidence: 99%