Thin-Walled Members Under Axial Force, Bending and Torsion

Nishino, Fumio; Kurakata, Yoshio; Hasegawa, Akio; Okumura, Takuji

doi:10.2208/jscej1969.1974.225_1

Cited by 11 publications

(10 citation statements)

References 2 publications

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“…The beginning of the contour coordinate s is the origin S that is the centre of the cross-section, and it is assumed that it is connected with an actual plane through a virtual plane of the thickness tZ0 (Nishino et al 1974). Given that b T is a value of the s-coordinate, which is from the shear centre M to the foot of a perpendicular pulled down to the plate to which the focus point is related, the function b T ðsÞ is a linear function of contour coordinate s that indicates the focus point.…”

Section: Derivation Of Governing Equation (A ) Equations For the Basimentioning

confidence: 99%

“…In accordance with the technique of the virtual plate (Nishino et al 1974), which connects the centre of the cross-section and the cross-section composing plates, the axial displacement is defined to be consistent here as well. If equation ð3:26Þ Therefore, this term does not appear in any traditional books or research papers.…”

Section: Derivation Of Governing Equation (A ) Equations For the Basimentioning

confidence: 99%

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A theory for the finite displacement of a thin-walled Bernoulli–Euler beam and lateral post-buckling analysis

Usuki

2008

Proc. R. Soc. A.

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The state vector equation for lateral buckling in finite displacement theory is formulated using only the hypothesis of the Bernoulli-Euler beam. By using an appropriate orthogonalization of the warping functions, the normally complicated calculation has been processed systematically using only matrix notation. As a numerical analysis, the lateral buckling load on the cantilever receiving a concentrated end load on the upper flange was calculated using the coefficient matrix of the first-order increment; the postbuckling behaviour was investigated with increasing load. Since the state vector equation is a higher order nonlinear equation, the original coefficient matrix was fixed with an arbitrary initial value and the solution was provided by the Runge-Kutta transfer matrix method. Subsequent calculations were pursued in the same way with the solution obtained via Runge-Kutta methods as a new initial value and then shifted to the next load condition. This theory and analysis method does not employ an assumed displacement function, such as the Ritz's method; it is therefore useful for the finite displacement analysis of a beam with arbitrary boundary conditions and intermediate support conditions.

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Section: Derivation Of Governing Equation (A ) Equations For the Basimentioning

confidence: 99%

Section: Derivation Of Governing Equation (A ) Equations For the Basimentioning

confidence: 99%

A theory for the finite displacement of a thin-walled Bernoulli–Euler beam and lateral post-buckling analysis

Usuki

2008

Proc. R. Soc. A.

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“…(11) can be simplified to f(oi'ei+ai'e j)dv-T, uidS=0 (13) s Substituting Eqs. (4. b), (6) and (7) into Eq. (13) and making use of linear constitutive equations both for the normal and shear stresses lead to NO …”

Section: General Stiffness Of Thin-walled Membersmentioning

confidence: 99%

A Concise and Explicit Formulation of Out-of-Plane Instability of Thin-Walled Members

Hasegawa

Liyanage

Ikeda

et al. 1985

Doboku Gakkai Ronbunshu

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The purpose of this study is to present a solution scheme for the problem of out-of-plane instability of thin-walled members. Based on the second order kinematic field, the stiffness equation of linearized finite displacements is formulated for thin-walled members, and given in a concise and explicit form. As a particular case, an important and practical application is made for the lateral-torsional buckling of in-plane beams and frames. Numerical examples are given for straight and curved members, and are compared with existing results. The analysis scheme presented is proved accurate, efficient and versatile.

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“…(1) Symmetrical buckling In this case, the term II z for the symmetrical deformation appears in Eq (5). in which the summation appeared in the coefficients of q must be carried out only for the combinations that (i± j ± k) equals to odd number.…”

Section: Calculation Of Buckling Loadsmentioning

confidence: 99%

Overall Lateral Buckling of Through Plate Girder Bridges

Itoh

Nogami

1984

Doboku Gakkai Ronbunshu

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This paper developesthe strict theory on the lateral buckling of a through plate girder bridge, and simple approximate formulae for critical loads have been proposed.The validity of this theory has been examined by comparing with some experimental results, and the elastic lateral buckling loads and the load carrying capacities for the illustrative practical bridge models have been calculated.The results have shown that the approximate formulae for critical values of symmetric and asymmetric elastic buckling under uniformly distributed load have to be useful, and that the load carrying capacity for long spans would depend on asymmetric overall lateral buckling. The symmetric buckling will be not so significant.I.

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Thin-Walled Members Under Axial Force, Bending and Torsion

Cited by 11 publications

References 2 publications

A theory for the finite displacement of a thin-walled Bernoulli–Euler beam and lateral post-buckling analysis

A theory for the finite displacement of a thin-walled Bernoulli–Euler beam and lateral post-buckling analysis

A Concise and Explicit Formulation of Out-of-Plane Instability of Thin-Walled Members

Overall Lateral Buckling of Through Plate Girder Bridges

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