Elastic Flexural-torsional Buckling Research Articles

Refined energy method for the elastic flexural-torsional buckling of steel H-section beam-columns. Part II: Comparison and verification for elements LTU and LTR

Refined energy method for the elastic flexural-torsional buckling of steel H-section beam-columns. Part II: Comparison and verification for elements LTU and LTR

Refined energy method for the elastic flexural-torsional buckling of steel H-section beam-columns Part I: Formulation and solution

Refined energy method for the elastic flexural-torsional buckling of steel H-section beam-columns Part I: Formulation and solution

Experimental investigation on post-flexural–torsional buckling strength of CFS compression members

Recent studies have indicated that cold-formed steel (CFS) members could have strength above the global elastic flexural–torsional buckling (FTB) load. No test result demonstrating the post-buckling strength of channel compression members undergoing only FTB before failure is reported in the literature. Test results on a total of 25 CFS specimens, which included 19 channels (hat section, lipped channel, and plain channel) and 6 angles which experience only FTB under axial compression, carried out in this study, are presented. The interaction of other modes (flexural, local, and distortional) with FTB, which may reduce the ultimate strength of the member, was eliminated in this study by choosing the geometry of test specimens having elastic FTB load much smaller than the elastic buckling loads corresponding to other modes. The global buckling strength equations in the design standards and the modified equations reported in the literature are evaluated using the results generated in this study. The modified procedures proposed by Dinis et al. (2020), and Dinis and Camotim (2019) are found to be the most accurate for channel and angle compression members failing under FTB mode, respectively.

Investigations into the Flexural-Torsional Buckling Behavior of Steel Open-Section Beam-Columns

This paper is in the field of elastic flexural-torsional buckling of steel beam-columns of bisymmetric narrow-flange and wide-flange I-section shape. Investigations are focused on the derivation of the strain components and the energy equation, based on the displacement-field formulation in the deflected configuration. At the same time, a review of analytical solutions based on the classical and refined energy-equations are summarized, presented and discussed. The relationship between the maximum in-plane bending moment and the compressive force of beam-columns is the main objective of this research investigation. Simple boundary conditions of end-sections free to deflect and to warp are considered, together with an arbitrary loading-pattern. The principle of superposition and the moment amplification rule for considering the second-order effects are widely used. The main conclusions are drawn in relation to the flexural-torsional resistance-evaluation design of steel beam-columns in modern design codes for steelwork.

Elastic Flexural-Torsional Buckling of Steel I-Section Members Unrestrained Between End Supports

Elastic Flexural-Torsional Buckling of Steel I-Section Members Unrestrained Between End Supports

Out-of-plane buckling resistance of rolled steel H-section beam-columns under unequal end moments

A novel analytical model is proposed for establishing design criteria based on the decomposition of the in-plane deformation and out-of-plane stability states. First part of this study considered the in-plane buckling resistance of beam–columns. This study uses the results from Gizejowski et al. [42] to develop an analytical model for the inelastic out-of-plane buckling resistance of beam–columns subjected to a moment gradient. The elastic flexural–torsional buckling solution is combined with the in-plane solution via the generalised Ayrton–Perry model. In order to unify the recommendations for the resistance evaluation of beams, columns, and beam–columns, the model is customised to conform to the standard Eurocode technique of modelling buckling resistance of steel elements in compression or bending about the cross-sectional axis with the greater moment of inertia. As a result, the out-of-plane resistance interaction curves, expressed in dimensionless coordinates, which describe the beam–column flexural–torsional buckling resistance and consider lateral–torsional buckling effects, are obtained. The results of finite element simulations are used for the verification of the developed analytical formulation. Two numerical techniques of imperfection modelling are used: an equivalent geometric imperfection approach with the Maquoi–Rondal generalised initial imperfection and an approach that individually considers geometric and material imperfections. The results obtained from the proposed analytical model and those obtained using the Eurocode design criteria and other recent analytical proposals are compared. Finally, concluding remarks and directions of future studies are also presented.

Study on Calculation Theory of Elastic Flexural-Torsional Buckling Bearing Capacity for Castellated Beams

The structure of castellated beams is complex, using the computation theory of elastic flexural-torsional buckling of H-shaped beams to study the elastic flexural-torsional buckling strength of castellated beams under different loads, based on simplifying the section's eigenvalues. In addition to the theoretical investigation, the finite element analysis of the accurate critical loads of the beams had been done by the ABAQUS software, a comparison has been made between the calculated loads and analyzed results, error is smaller. Analyzing the effects that divergence ratio, depth-span ratio and distance-height ratio has on the elastic flexural-torsional buckling loads of castellated beams and draw out some reduced calculation methods for the section's eigenvalues and elastic flexural-torsional buckling critical load of castellated beams.

Loss-of-stability induced progressive collapse modes in 3D steel moment frames

This paper deals with the progressive collapse analysis of a tall steel frame following the removal of a corner column according to the alternate load path approach. Several analysis techniques are considered (eigenvalue, material nonlinearities, material and geometric nonlinearities), as well as 2D and 3D modelling of the structural system. It is determined that the collapse mechanism is a loss-of-stability-induced one that can be identified by combining a 3D structural model with an analysis involving both material and geometric nonlinearities. The progressive collapse analysis reveals that after the initial removal of a corner column, its two adjacent columns fail from elastic flexural-torsional buckling at a load lower than the design load. The failure of these two columns is immediately followed by the failure of the next two adjacent columns from elastic flexural–torsional buckling. After the failure of these five columns, the entire structure collapses without the occurrence of any significant plastification. The main contribution is the identification of buckling-induced collapse mechanisms in steel frames involving sequential buckling of multiple columns. This is a type of failure mechanism that has not received appropriate attention because it practically never occurs in properly designed structures without the accidental loss of a column.

Effects of shape functions on flexural–torsional buckling of fixed circular arches

Because fixed arches have much higher flexural–torsional buckling resistance than pinended arches, they are used for engineering structures in many cases. However, studies on their flexural–torsional buckling behaviour have rarely been reported in the open literature hitherto. This paper investigates the elastic flexural–torsional buckling of fixed circular arches subjected to uniform compression and uniform bending because they play important roles in the design of steel arches against their flexural–torsional failure. One of the major difficulties in solving the flexural–torsional buckling problem of a fixed arch is to determine its accurate buckling shapes. The flexural–torsional buckling shapes are studied using a finite element (FE) method in association with eigenvalue analyses. It is found that the flexural–torsional buckling shape of a fixed arch becomes more complicated than the case of a straight beam-column or a shallow arch when the rise-to-span ratio increases, and so the theoretical analysis requires more terms of Fourier trigonometric series to describe the buckling shapes. Based on this, analytical solutions for flexural–torsional buckling loads of fixed arches are derived both by the Rayleigh–Ritz method and by solving differential equations for buckling deformations. Comparisons with the FE results show that the analytical solutions by the Rayleigh–Ritz method are reasonably accurate and that the analytical solutions by solving the equations for buckling deformations are exactly the same as the FE results. Simple approximate formulas for buckling loads of fixed arches with box-sections are proposed based on the extensive FE results for structural designers to use. The validity of the effective length method for the fixed arches is also discussed. It is found that in the case of circular arches the effective length method should not be used because the rise-to-span ratios and boundary conditions have complicated and significant influence on the buckling load.

Elastic Flexural-Torsional Buckling of Beam-Column with Equal-Leg Angle Cross-Section

The flexural-torsional buckling of equal-leg angle member under compression is analyzed and calculated. Based on General bending theory and the section properties of angle, the governing equations of the spatial buckling are presented and the formula of Wagner effect coefficient is deduced. The method can also be used for beam-columns with any type section, and the computational efficiency is much higher than numerical methods. The critical buckling loads of equal-leg angle members with different sizes are calculated and the column curves of critical load and slenderness ratio are plotted which will guide efficiently the actual engineering design.

Elastic Stability of Circular Arches with the Open Thin-walled Monosym-metric Section Considering the Prebuckling Deformation

The effect of prebuckling in-plane deformations on the elastic flexural-torsional buckling of arches is studied in this paper. Nonlinear strain-displacement relations considering initial curvature effects and higher order prebuckling de-formation terms with curvature in deriving process are substituted into the second variation of the total potential to obtain the buckling energy equation. The analytical solutions for the flexural-torsional buckling moment of arches in uniform bending, containing the effects of the prebuckling deformation, are proposed. Also, the influence of the higher order prebuckling deformation terms with the curvature effects is investigated according to the ratio of the minor axis flexural stiffness to the major axis flexural stiffness.

Flexural-torsional buckling strength of I-girders with discrete torsional braces under various loading conditions

Torsional bracing systems have been used widely in I-girder bridges to increase the flexural-torsional buckling strength and distribute the load to the adjacent girders. To evaluate the required stiffness of the bracing and the flexural-torsional buckling strength of the I-girder with a multiple torsional bracing system, the equivalent continuous torsional bracing concept is often adopted regardless of the type of torsional bracing system. However, a previous study on the I-girder with discrete torsional bracings under uniform bending reported that the equivalent continuous torsional bracing concept has certain limitations on discrete torsional bracing problems and it needs to be investigated for general loading cases. This article presents an analytical solution for the elastic flexural-torsional buckling strength and stiffness requirements of I-girders with discrete torsional bracings under various loading conditions. First, a review was performed of the previous study on the elastic critical buckling moment and torsional stiffness requirement of the I-girder with discrete torsional bracings under uniform bending. This solution was then extended for various loading conditions. From the derived analytical solutions, the equivalent moment factor was proposed for practical engineering purposes and the proposed solutions were verified by comparing them with the results of finite element analysis and those of other previous studies. Finally, non-linear finite element analyses including the effects of the initial imperfection and residual stresses were conducted to examine the inelastic buckling strengths of I-girders with discrete torsional bracings under various loading conditions. The results showed that the buckling curves from the current design specification provide reasonably conservative flexural-torsional buckling strengths of the I-girder with discrete torsional bracings when the proposed elastic solutions are applied to obtain the buckling parameters.

Closure to “Elastic flexural–torsional buckling of thin-walled cantilevers” by Lei Zhang and Geng Shu Tong [Thin-Walled Structures 46(1) (2008) 27–37

Closure to “Elastic flexural–torsional buckling of thin-walled cantilevers” by Lei Zhang and Geng Shu Tong [Thin-Walled Structures 46(1) (2008) 27–37

Flexural-Torsional Buckling of Cantilever Strip Beam-Columns with Linearly Varying Depth

In this paper, one investigates the elastic flexural-torsional buckling of linearly tapered cantilever strip beam-columns acted by axial and transversal point loads applied at the tip. For prismatic and wedge-shaped members, the governing differential equation is integrated in closed form by means of confluent hypergeometric functions. For general tapered members 0hmaxhmin / hmax1, the solution to the boundary value problem is obtained in the form of a Frobenius' series, which is shown to converge in the interior of the domain and at the boundary if and only if 0hmaxhmin/hmax1 /2. Therefore, for 1 /2hmaxhmin/hmax1 the Frobenius' series solution cannot be used to establish the characteristic equation for the cantilever beam-columns; the problem is then solved numerically by means of a collocation procedure. Some of the analytical solutions buckling loads were compared with the results of shell finite- element analyses and an excellent agreement was found in all cases, thus validating the mathematical model and confirming the correct- ness of the analytical results. The paper closes with a discussion on the convexity of the stability domain in the load parameter space and the accuracy of approximations based on Dunkerley-type theorems.

Discussion on the paper of Zhang and Tong, Elastic flexural–torsional buckling of thin-walled cantilevers, Thin-Walled Structures 46 (2008) 27–37

Discussion on the paper of Zhang and Tong, Elastic flexural–torsional buckling of thin-walled cantilevers, Thin-Walled Structures 46 (2008) 27–37

Discussion on the paper Elastic flexural–torsional buckling of thin-walled cantilevers by Lei Zhang and Geng Shu Tong [Thin-walled Structures, 46(1), 2008, 27–37

Discussion on the paper Elastic flexural–torsional buckling of thin-walled cantilevers by Lei Zhang and Geng Shu Tong [Thin-walled Structures, 46(1), 2008, 27–37

Energy equations for elastic flexural–torsional buckling analysis of plane structures

Lateral–torsional buckling is a critical mode of failure of metal structures. When the values of the loadings on a member of a structure reach a limiting state, the member will experience out-of-plane bending and twisting. This type of failure occurs suddenly in members with a much greater in-plane bending stiffness than torsional or lateral bending stiffness. Slender members of a structural system may buckle laterally and twist before their in-plane capabilities can be reached. Energy equations are derived by considering the total potential energy of a beam-column element. The second variation of the total potential energy equal to zero indicates the transition from a stable state to an unstable state, which is the critical condition for buckling. Several energy equations are derived analytically by calculating the second variation of the total potential energy of a double symmetric thin wall beam-column element. In this article, in-plane deformations of the beam-column element are disregarded. Then energy equations are derived expressing in dimensional and non-dimensional forms. These energy equations will be implemented in a future article to derive elastic and geometric stiffness matrices for the beam-column element and calculate the lateral–torsional buckling of plane structures. Examples are provided to show the accuracy of the equations and applications.

Simple solutions for the flexural-torsional buckling of laterally restrained I-beams

This paper describes a method for analysing the lateral buckling of beams continuously restrained at one flange. The deformed configuration is governed by a system of differential equations solved by the Galerkin method. The matrices of rigidities, restraints and geometry are specified as well as the problem with the eigenvalues, with a view to predicting the buckling loads and the corresponding buckling shapes. The effects of moment distribution and continuous restraints on the elastic flexural-torsional buckling of beams are also studied. The results show that the restraint of the tensioned flange can have a weak influence on the critical buckling moment.

Elastic flexural-torsional buckling of thin-walled cantilevers

Previous studies by the authors revealed that the two representative theories with slight differences between, widely used in investigating the flexural-torsional buckling of thin-walled beams, have led to two different solutions in well-known literature for assessing critical loads of simply supported beams of monosymmetric cross section. With these two solutions, significant differences in critical loads may be found for these monosymmetric beams. Based on the classical variational principle for buckling analyses, a new theory on the flexural-torsional buckling of thin-walled members was proposed by the authors. In this paper, this new theory as well as the other two typical theories is employed to investigate the flexural-torsional buckling of cantilevers. This paper first gives a brief review and a careful comparative study on the flexural-torsional buckling of thin-walled cantilevers employing three different buckling theories. Differences between these theories are demonstrated with investigations on buckling of cantilevers under pure bending and two typical transverse loads. Explicit solutions, capable of considering variations of beam length and loading position along the vertical axis of cross section, are presented for predicting the critical loads of doubly symmetric cantilevers under two typical transverse loads. Advantages of presented solutions, such as good accuracy and ease of use, are exploited through the comparisons of critical results with those from existing solutions and finite element analyses.

Elastic flexural-torsional instability of structural arches under hydrostatic pressure

This paper addresses the mechanics of the flexural-torsional buckling instability of pin-ended elastic circular arches, which are acted upon by a hydrostatic loading. This loading arrangement differs from the gravity-based loading usually considered in the literature, in that the load changes its direction with the deformation of the elastic arch during its flexural-torsional buckling, always remaining normal to the contour profile of the arch. The previous treatments of the mechanics of the problem, that assume the load direction remains invariant during flexural-torsional buckling, have been motivated by applications in structural engineering in which this loading regime is valid, but there are a number of applications in more general mechanics where this assumption cannot be made and a solution is needed. Both a mathematically based virtual work principle and a mechanical visualisation of the mechanics of the deformation are considered separately, and they are shown to arrive at the same formulation of the linear differential equations of equilibrium of the buckled arch when the buckling deformations are considered infinitesimal. The differential equations for buckling under radial loading that is distributed uniformly around the circumference of the arch are shown to be solvable in analytic form, resulting in a closed form solution for the elastic buckling load of the arch that hitherto has not been formulated. The buckling equation demonstrates that an arch is stiffer under hydrostatic loading than under gravity loading in its resistance to elastic flexural-torsional buckling.