Buckling Of Thin-walled Beams Research Articles

Effect of local stiffeners and warping constraints on the buckling of symmetric open thin-walled beams with high warping stiffness

Local stiffeners affect the behaviour of thin-walled beams (TWBs). An in-house code based on a one-dimensional model proved effective in several instances of compressive buckling of TWBs but gave counterintuitive results for locally stiffened TWBs. To clarify the matter, we investigated TWBs with multi-symmetric double I cross-section, widely used in practical applications where high bending stiffness is required. Several samples were manufactured and stiffened on purpose, closing them over a small portion of the axis at different places. The samples were tested with end constraints accounting for various warping conditions. The experimental and numerical outputs from a commercial FEM code gave a key to overcome the unexpected results by the in-house code, paving the way for further studies.

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

AbstractIn this paper the influence of bimoment, induced by external axial loads, on the global buckling of thin-walled Z-section beams, subjected to different boundary conditions, is studied. Sinc...

Influence of bimoment on the torsional and flexural–torsional elastic stability of thin-walled beams

This article studies the influence of the bimoment on the buckling of thin-walled beams with open cross section subjected to axial loading. In the case of torsional and torsional-flexural buckling of thin-walled Z-section beam, it is shown that influence of the bimoment could be of importance in the assessment of buckling loads. In order to verify the accuracy and validity of this analysis, the obtained results are compared with those calculated by ANSYS software.

Investigation of Lateral-Torsional Buckling Strength Trends in Monosymmetric Stepped I-Beams Subjected to Several Loading Conditions

일축대칭 I형 단면보의 횡-비틀림 좌굴강도를 고려하는 데 있어서 강도기준 하중조건이 순수휨 작용시가 아님을 보여주는 연구가 제시된 바 있다. 이러한 연구결과는 오랫동안 적용해온 순수휨 작용시 가장 작은 횡-비틀림 좌굴강도를 보인다는 접근과는 다른 방법이다. 이에 본 연구에서는 제안된 새로운 경향을 확인하고 일축대칭 스텝보를 적용한 경우에도 같은 경향을 보이는 지 확인하고자 한다. 본 논문에는 다양한 하중조건을 고려하고 있으며 단면은 조밀단면을 적용하였다. 연구에 사용된 유한요소해석 프로그램은 ABAQUS이며, 스텝보에 적용한 일축대칭도는 0.5~0.9이다. 또한 본 연구에 고려한 해석모델의 <TEX>$L_b/h$</TEX>(지간/보 높이)비율은 20이다. 본 해석연구를 통하여 얻어진 새로운 경향과 결론을 자세하게 본 논문에 기술하였다. It has been proven in recent studies that for monosymmetric I-section beams, in considering bending moment diagrams caused by any combination of applied end moments and transverse loads acting at the shear centre, the lowest critical lateral torsional buckling moment does not necessarily correspond to uniform bending. This finding is different from the intuitive expectation that researchers have that for lateral torsional buckling of thin walled beams, the lowest critical lateral torsional buckling moment always corresponds to a uniform bending moment diagram. To determine the applicability of the findings stated, considering stepped beams, this study will be focusing on the comparison of the lateral torsional buckling strength trends in monosymmetric I-beams having doubly stepped and compact cross section. Several loading conditions will be applied to see the effect of different moment diagrams having different inflection points on the lateral torsional buckling strength of stepped beams. The study will be made using the finite element program, ABAQUS. The study will investigate stepped beams having monosymmetric ratios ranging from 0.5 to 0.9. These ratios correspond to varying bottom flange width while keeping the top flange width unchanged. Unbraced length to height ratio of the beam to be analyzed is 20. Finally, the findings for this study will be shown using illustrative figures and conclusions will be made.

Lateral Flexural-Torsion Buckling of Thin-Walled Cold-Formed Steel Beams with Holes - Design Resistance Evaluation Based on Test Results

The paper is focused on problems of the design resistance of thin-walled cold-formed steel beams with holes, respecting the lateral flexural-torsion buckling effects. The attention is mainly paid to the design resistance determination using the results of experimental verification of the objective resistance and their statistic elaboration and probabilistic evaluation. The lateral buckling of thin-walled beams with holes is a specific problem, because of the holes influence on the torsion stiffness, and usual calculating procedures according to the rules given by the European Standards are not always generally usable. The methods based on the approaches of the design assisted by testing are used for the design resistance evaluation, here. The determination of the design resistance using test results respects the statistic characteristics and probabilistic distribution of all input variables, on which the resistance is depended. This method also takes into account the form of the probabilistic model of the resistance, from the viewpoint of the form of mathematical function and its influence on the resistance variability. The design resistance derivation applying the design assisted by testing can be used as an alternative procedure instead of the design resistance determination according to the normative documents, especially in the cases, when the usual procedures are not sufficiently usable.

Coupled static and dynamic buckling of thin walled beam by spline finite element

For the coupled static and dynamic buckling of thin walled beam subjected to various forces, such as axial force, uniform bending moment, and bending moment due to concentrated and distributed lateral forces, the spline finite element method is employed to obtain the dynamic stiffness matrix. Second order effects of the axial force and moment are considered. A doubly symmetric cantilever beam with uniform cross-section is investigated. Extensive static and dynamic interaction diagrams are plotted. The effects of warping rigidity, torsional rigidity, axial tension and compression on moment buckling, moment on axial buckling compression, higher buckling modes are discussed in detail. The spline finite element method is proved to be very efficient for the present problem and many interaction diagrams can be plotted easily. Some new results are presented. The methodology is based on finite element formulation and therefore it can be easily extended to analyze structural frames.

Symbolic computation and differential quadrature method - A boon to engineering analysis

Nowadays computers can perform symbolic computations in addition to mere number crunching operations for which they were originally designed. Symbolic computation opens up exciting possibilities in Structural Mechanics and engineering. Classical areas have been increasingly neglected due to the advent of computers as well as general purpose finite element software. But now, classical analysis has reemerged as an attractive computer option due to the capabilities of symbolic computation. The repetitive cycles of simultaneous - equation sets required by the finite element technique can be eliminated by solving a single set in symbolic form, thus generating a truly closed-form solution. This consequently saves in data preparation, storage and execution time. The power of Symbolic computation is demonstrated by six examples by applying symbolic computation 1) to solve coupled shear wall 2) to generate beam element matrices 3) to find the natural frequency of a shear frame using transfer matrix method 4) to find the stresses of a plate subjected to in-plane loading using Levy`s approach 5) to draw the influence surface for deflection of an isotropic plate simply supported on all sides 6) to get dynamic equilibrium equations from Lagrange equation. This paper also presents yet another computationally efficient and accurate numerical method which is based on the concept of derivative of a function expressed as a weighted linear sum of the function values at all the mesh points. Again this method is applied to solve the problems of 1) coupled shear wall 2) lateral buckling of thin-walled beams due to moment gradient 3) buckling of a column and 4) static and buckling analysis of circular plates of uniform or non-uniform thickness. The numerical results obtained are compared with those available in existing literature in order to verify their accuracy.

Effects of load height application and pre-buckling deflections on lateral buckling of thin-walled beams

Based on a non-linear model taking into account flexural-torsional couplings, analytical solutions are derived for lateral buckling of simply supported I beams under some representative load cases. A closed form is established for lateral buckling moments. It accounts for bending distribution, load height application and pre-buckling deflections. Coefficients C1 and C2 affected to these parameters are then derived. Regard to well known linear stability solutions, these coefficients are not constant but depend on another coefficient k1 that represents the pre-buckling deflection effects. In numerical simulations, shell elements are used in mesh process. The buckling loads are achieved from solutions of eigenvalue problem and by bifurcations observed on non linear equilibrium paths. It is proved that both the buckling loads derived from linear stability and eigenvalue problem lead to poor results, especially for I sections with large flanges for which the behaviour is predominated by pre-buckling deflection and the coefficient k1 is large. The proposed solutions are in good agreement with numerical bifurcations observed on non linear equilibrium paths.

Torsional vibrations and buckling of thin-walled beams on elastic foundation

The problem of free torsional vibration and buckling of doubly symmetric thin-walled beams of open section, subjected to an axial compressive static load and resting on continuous elastic foundation, is discussed in this paper. An analytical method based on the dynamic stiffness matrix approach is developed, including the effects of warping. The resulting transcendental equation is solved for thin-walled beams clamped at one end and simply supported at the other. A computer program is developed, based on the dynamic stiffness matrix approach. The software consists of a master program to set up the dynamics stiffness matrix and to call specific subroutines to perform various system calculations. Numerical results for natural frequencies and buckling load for various values of warping and elastic foundation parameter are obtained and presented.

Closure to “Large-Deflection Spatial Buckling of Thin-Walled Beams and Frames”

Closure to “Large-Deflection Spatial Buckling of Thin-Walled Beams and Frames”

Discussion of “Large-Deflection Spatial Buckling of Thin-Walled Beams and Frames”

Discussion of “Large-Deflection Spatial Buckling of Thin-Walled Beams and Frames”