Second-order stiffness matrix and load vector of an imperfect beam-column with generalized end conditions on a two-parameter elastic foundation

Colorado-Urrea, G.J.; Aristizábal-Ochoa, J. Darío

doi:10.1016/j.engstruct.2014.03.035

Cited by 7 publications

(3 citation statements)

References 18 publications

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“…In the simplified expression (Equation (5)), the element stability functions are modified from the element stability functions T EB , Q EB , S EB , and C EB of axial-loaded Euler-Bernoulli beam-columns, which are functions of the axial force factor λ EB for Euler-Bernoulli beams. In addition, the relationship between the axial force factor λ and λ EB (for Timoshenko and Euler-Bernoulli beams, respectively) can be derived based on Equations (9) and (12).…”

Section: Comparison With the Simplified Expression By Ekhande Et Almentioning

confidence: 99%

“…Among the various structural analysis methods [1][2][3][4][5][6], the matrix structural analysis [7][8][9][10][11][12][13][14][15] is found to be an efficient method ideally suitable for obtaining the exact solutions and for convenient computer implementations. The matrix structural analysis approach is essentially a matrix form of the displacement (stiffness) method [16,17] in basic structural mechanics and has been widely 2 of 12 used in the traditional analysis associated with the flexural deformations of beam-column elements.…”

Section: Introductionmentioning

confidence: 99%

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Exact Solutions for Buckling and Second-Order Effect of Shear Deformable Timoshenko Beam–Columns Based on Matrix Structural Analysis

Pan

Tong

2019

Applied Sciences

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Shear deformable beams have been widely used in engineering applications. Based on the matrix structural analysis (MSA), this paper presents a method for the buckling and second-order solutions of shear deformable beams, which allows the use of one element per member for the exact solution. To develop the second-order MSA method, this paper develops the element stability stiffness matrix of axial-loaded Timoshenko beam–columns, which relates the element-end deformations (translation and rotation angle) and corresponding forces (shear force and bending moment). First, an equilibrium analysis of an axial-loaded Timoshenko beam–column is conducted, and the element flexural deformations and forces are solved exactly from the governing differential equation. The element stability stiffness matrix is derived with a focus on the element-end deformations and the corresponding forces. Then, a matrix structural analysis approach for the elastic buckling analysis of Timoshenko beam–columns is established and demonstrated using classical application examples. Discussions on the errors of a previous simplified expression of the stability stiffness matrix is presented by comparing with the derived exact expression. In addition, the asymptotic behavior of the stability stiffness matrix to the first-order stiffness matrix is noted.

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Section: Comparison With the Simplified Expression By Ekhande Et Almentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact Solutions for Buckling and Second-Order Effect of Shear Deformable Timoshenko Beam–Columns Based on Matrix Structural Analysis

Pan

Tong

2019

Applied Sciences

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“…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 ]. The basic idea of the matrix stiffness method is to establish the equilibrium relationship between the element-end displacements

and the element-end forces

of a beam-column element (where u i , d i , and q i are element-end axial displacement, translational displacement, and rotation angle, respectively; F i , V i , and M i are element-end axial load, shear force, and bending moment, respectively, as shown in Figure 1 ) as

where [ K e ] is the element stiffness matrix for flexural-axial problems.…”

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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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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Second-order analysis of an imperfect corroded tubular member on a two-parameter elastic foundation

Monsalve-Giraldo

Giraldo-Londoño

Colorado-Urrea

et al. 2017

Engineering Structures

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Second-order stiffness matrix and load vector of an imperfect beam-column with generalized end conditions on a two-parameter elastic foundation

Cited by 7 publications

References 18 publications

Exact Solutions for Buckling and Second-Order Effect of Shear Deformable Timoshenko Beam–Columns Based on Matrix Structural Analysis

Exact Solutions for Buckling and Second-Order Effect of Shear Deformable Timoshenko Beam–Columns Based on Matrix Structural Analysis

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

Second-order analysis of an imperfect corroded tubular member on a two-parameter elastic foundation

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