Simple Interaction Equations for Beam-Columns

Chen, Wai F.; Atsuta, Toshio

doi:10.1061/jsdeag.0003271

Cited by 12 publications

(10 citation statements)

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“…It is noted that this section gives the same results as that from classical analyses of these torsion-warping-axial buckling problems [ 4 , 5 , 7 , 8 ], but the matrix analysis procedure is considerably simplified and is more systematic.…”

Section: Applications Of Torsion-warping Stiffness Matrixmentioning

confidence: 91%

“…Although a number of computer programs such as Abaqus, OpenSees, Ansys, and MSC.Marc are readily available for the structural analysis of thin-walled nanostructural members, approaches to obtain the exact solutions [ 4 , 5 , 6 , 7 , 8 , 9 , 10 ] in closed form are helpful in many situations. The matrix stiffness method (MSM) has been found to be a suitable and systematic method for such purposes [ 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 ].…”

Section: Introductionmentioning

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: Applications Of Torsion-warping Stiffness Matrixmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

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

et al. 2022

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“…All buckling modes W j (X) are orthogonal to each other, similarly their differentials ( ) W X j * and W ** j (X) are, correspondingly, orthogonal to each other [27][28][29]. Normalized initial shape of the beam is denoted as…”

Section: Discussionmentioning

confidence: 99%

Analytical modeling and design of negative stiffness honeycombs

Zhakatayev

Varol

2020

Smart Mater. Struct.

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Negative stiffness honeycombs (NSHs) have multiple advantages compared to traditional honeycomb structures. These advantages include recoverable elastic buckling, shock absorption, and vibration isolation. As a result, NSHs have great potential in applications such as acoustic wave guiding, shape morphing, design of impact-protection devices and robotic grippers. In this paper, we present a design methodology for metamaterial consisting of negative stiffness beams assembled in a honeycomb structure. Based on analytical results, our methodology allows designing NSH mesostructures with predetermined buckling sequence. An NSH prototype was designed based on our algorithm and fabricated using a 3D printer with a nylon filament. The validity of our approach was experimentally verified by performing displacement controlled compression force measurements. Our methodology gives the ability to design NSH mesostructures with desired force-displacement characteristics.

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“…In this article attention is confined to linear elastic composite beam buckling (especially lateral and lateral torsional buckling phenomena). An abbreviated and lucid literature survey and comprehensive discussion about lateral and lateral torsional buckling of structural members is rendered in the books of Chen et al [2,3], the book of Timoshenko [4], the dissertation of Raven [5] and the article of Van der Put [6]. It should be highlighted that the adjective "composite" refers to multiple homogeneous and or inhomogeneous beam segment crosssections and beam materials.…”

Section: Introductionmentioning

confidence: 99%

Linear elastic buckling of composite beams – An analytical engineering approach

Derks

2023

ce papers

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This article outlines a concise and complete versatile novel analytical framework to quickly and effectively assess lateral shear and lateral torsional buckling of composite beams build of segments with different lengths. The adjective “composite” includes dissimilar beam profiles with symmetrical homogeneous and or inhomogeneous cross‐sections and distinct beam materials. The major aim is to provide engineers with an accurate, simple but elegant analytical beam buckling tool based on advanced solid theoretical propositions. The justification of the analytical theory is supplied by demonstration of executed numerical tests, which affirm the validity of the proposed analytical buckling models adapted to the considered beam buckling cases.

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Simple Interaction Equations for Beam-Columns

Cited by 12 publications

References 0 publications

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

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

Analytical modeling and design of negative stiffness honeycombs

Linear elastic buckling of composite beams – An analytical engineering approach

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