• Structural Engineering and Mechanics
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• 제6권2호
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• pp.161-172
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• 1998

Reinforced concrete beams possess variable flexural and torsional stiffnesses due to formation of cracks in the tension area along the beam. In order to check the stability of the beam, it is thus more appropriate to divide the beam into a finite number of segments for which mean stiffnesses and also bending moments are calculated. The stability analysis is further simplified, by using these mean values for each segment. In this paper, an algorithm for calculating the critical lateral buckling slenderness ratio for a definite load level, in a reinforced concrete beam without lateral support at the flanges, is presented. By using this ratio, the lateral buckling safety level of a slender beam may be checked or estimated.

• Structural Engineering and Mechanics
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• 제54권3호
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• pp.579-595
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• 2015

A general geometrically non-linear model for lateral-torsional buckling of thick and thin-walled FGM box beams is presented. In this model primary and secondary torsional warping and shear effects are taken into account. The coupled equilibrium equations obtained from Galerkin's method are derived and the corresponding tangent matrix is used to compute the critical moments. General expression is derived for the lateral-torsional buckling load of unshearable FGM beams. The results are validated by comparison with a 3D finite element simulation using the code ABAQUS. The influences of the geometrical characteristics and the shear effects on the buckling loads are demonstrated through several case studies.

• Steel and Composite Structures
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• 제4권4호
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• pp.281-301
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• 2004

The paper begins by presenting a unified variational approach to the lateral-torsional buckling (LTB) analysis of doubly symmetric prismatic and tapered thin-walled beams with open cross-sections, which accounts for the influence of the pre-buckling deflections. This approach (i) extends the kinematical assumptions usually adopted for prismatic beams, (ii) consistently uses shell membrane theory in general coordinates and (iii) adopts Trefftz's criterion to perform the bifurcation analysis. The proposed formulation is then applied to investigate the influence of the pre-buckling deflections on the LTB behaviour of prismatic and web-tapered I-section simply supported beams and cantilevers. After establishing an interesting analytical result, valid for prismatic members with shear centre loading, several elastic critical moments/loads are presented, discussed and, when possible, also compared with values reported in the literature. These numerical results, which are obtained by means of the Rayleigh-Ritz method, (i) highlight the qualitative differences existing between the LTB behaviours of simply supported beams and cantilevers and (ii) illustrate how the influence of the pre-buckling deflections on LTB is affected by a number of factors, namely ($ii_1$) the minor-to-major inertia ratio, ($ii_2$) the beam length, ($ii_3$) the location of the load point of application and ($ii_4$) the bending moment diagram shape.

• 국제강구조저널
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• 제18권4호
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• pp.1440-1463
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• 2018

The Wagner coefficient is a key parameter used to describe the inelastic lateral-torsional buckling (LTB) behaviour of the I-beam, since even for a doubly-symmetric I-section with residual stress, it becomes a monosymmetric I-section due to the characteristics of the non-symmetrical distribution of plastic regions. However, so far no theoretical derivation on the energy equation and Wagner's coefficient have been presented due to the limitation of Vlasov's buckling theory. In order to simplify the nonlinear analysis and calculation, this paper presents a simplified mechanical model and an analytical solution for doubly-symmetric I-beams under pure bending, in which residual stresses and yielding are taken into account. According to the plate-beam theory proposed by the lead author, the energy equation for the inelastic LTB of an I-beam is derived in detail, using only the Euler-Bernoulli beam model and the Kirchhoff-plate model. In this derivation, the concept of the instantaneous shear centre is used and its position can be determined naturally by the condition that the coefficient of the cross-term in the strain energy should be zero; formulae for both the critical moment and the corresponding critical beam length are proposed based upon the analytical buckling equation. An analytical formula of the Wagner coefficient is obtained and the validity of Wagner hypothesis is reconfirmed. Finally, the accuracy of the analytical solution is verified by a FEM solution based upon a bi-modulus model of I-beams. It is found that the critical moments given by the analytical solution almost is identical to those given by Trahair's formulae, and hence the analytical solution can be used as a benchmark to verify the results obtained by other numerical algorithms for inelastic LTB behaviour.

• 한국공간구조학회논문집
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• 제4권1호
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• pp.87-95
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• 2004

본 논문은 화재시 온도상승에 따른 H-형강 기둥의 내력에 관한 연구이다. 주요 매개변수는 온도, 세장비와 하중비이다. 온도 상승시 강재의 물리적 특성은 EC3 Part1.2에 따랐다. 온도상승에 따른 국부좌굴의 임계온도는 재료의 항복강도와 판폭두께비가 클수록 더 낮아진다. 균등한 열을 받는 철골 기둥의 내혁 평가는 LRFD에 따른 축력과 강축 및 약축 모멘트에 대하여 고려하였다.

• Structural Engineering and Mechanics
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• 제16권3호
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• pp.259-274
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• 2003

In this paper, a novel numerical solution technique, the differential cubature method is employed to study the buckling problems of thick plates with arbitrary quadrilateral planforms and non-uniform boundary constraints based on the first order shear deformation theory. By using this method, the governing differential equations at each discrete point are transformed into sets of linear homogeneous algebraic equations. Boundary conditions are implemented through discrete grid points by constraining displacements, bending moments and rotations of the plate. Detailed formulation and implementation of this method are presented. The buckling parameters are calculated through solving a standard eigenvalue problem by subspace iterative method. Convergence and comparison studies are carried out to verify the reliability and accuracy of the numerical solutions. The applicability, efficiency, and simplicity of the present method are demonstrated through solving several sample plate buckling problems with various mixed boundary constraints. It is shown that the differential cubature method yields comparable numerical solutions with 2.77-times less degrees of freedom than the differential quadrature element method and 2-times less degrees of freedom than the energy method. Due to the lack of published solutions for buckling of thick rectangular plates with mixed edge conditions, the present solutions may serve as benchmark values for further studies in the future.

• Steel and Composite Structures
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• 제28권4호
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• pp.403-414
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• 2018

In this paper, the lateral-torsional buckling of axially-transversally functionally graded tapered beam is investigated. The structure cross-section is assumed to be symmetric I-section, and it is continuously laterally supported by torsional springs through the length. In addition, the height of cross-section varies linearly throughout the length of structure. The proposed formulation is obtained for the case that the elastic and shear modulus change as a power function along the beam length and section height. This structure carries two concentrated moments at the ends. In this study, the lateral displacement and twisting angle relation of the beam are defined by sinusoidal series. After establishing the eigenvalue equation of unknown constants, the beam critical bending moment is found. To validate the accuracy and correctness of results, several numerical examples are solved.

• Steel and Composite Structures
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• 제15권2호
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• pp.175-202
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• 2013

The super convergent laminated composite beam element is newly derived for the lateral stability analysis. For this, a theoretical model of the laminated composite beams is developed based on the first-order shear deformation beam theory. The present laminated beam takes into account the transverse shear and the restrained warping induced shear deformation. The second-order coupling torque resulting from the geometric nonlinearity is rigorously derived. From the principle of minimum total potential energy, the stability equations and force-displacement relationships are derived and the explicit expressions for the displacement parameters are presented by applying the power series expansions of displacement components to simultaneous ordinary differential equations. Finally, the member stiffness matrix is determined using the force-displacement relationships. In order to show accuracy and superiority of the beam element developed by this study, the critical lateral buckling moments for bisymmetric and monosymmetric I-beams are presented and compared with other results available in the literature, the isoparametric beam elements, and shell elements from ABAQUS.

• 대한토목학회논문집
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• 제9권3호
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• pp.13-19
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• 1989

박판으로 이루어진 아치가 양단에서 휨모멘트를 받을 때 발생하는 횡좌굴에 대한 지배 미분방정식이 제시되었다. 미분방정식은 updated Lagrangian 방법에 따른 증분형태의 가상일의 원리에 의하여 유도 되었다. 본 연구에서 구한 임계모멘트 값들을 다른 결과들과 비교함으로써 본 연구의 타당성을 검토하여 보았다.