Flexural-torsional Buckling Research Articles

Bending, torsion and flexural-torsional buckling of back-to-back cold-formed steel channels

The bending moment resistance of cold-formed steel channels can be improved by combining two channel sections with a pair of screw fasteners in the webs spaced intermediately along the member. By combining the two channels in this way, the moment capacity of the beam can be increased beyond the capacity of two single channels. Another advantage of this type of section is the coincidence of the centroid and shear centre which reduces the effects of stresses due to eccentric load and torsion. Most research on back-to-back channels in bending has focused on local and distortional buckling while data on flexural-torsional buckling is scarce. The flexural-torsional buckling resistance of a beam depends on various section properties which include the minor axis second moment of area, and the torsion and warping constants of the section. Although the flexural-torsional buckling moment can be easily determined for a single channel section because these section properties are relatively straightforward to calculate, the calculation of the flexural-torsional buckling moment for back-to-back channels with intermediately spaced screw fasteners is much more complicated due to the discontinuity of the cross-section along the length of the beam. In this paper, the shear stiffness of the screw fasteners connecting the channels is obtained from test results. The shear stiffness is then used to model the screw fasteners in a finite element analysis to analyse a beam composed of back-to-back channels under bending and torsion. The results are compared with two single channel sections and with back-to-back channels assuming full composite action. The effect of different screw fastener spacings is also investigated. Simple relationships between the bending and torsion section properties for single channels and back-to-back channels are presented. Suggestions for the design of back-to-back channels in bending are also proposed.

Analysis of the Effect of Slenderness Ratio on Axial Force in T-Section

This study extensively investigates T-shaped axial compression members with varying wing-flange width-to-thickness ratios, focusing primarily on the influence of section width-to-thickness ratio and effective width on the sectional resistance. Based on the AISC 2017 specifications, assuming the overall component is a stable member, the study analyzes the impact of varying the wing-flange width-to-thickness ratio on the sectional stability and resistance of the structure. Especially for slender sections that exceed the width-to-thickness ratio limits specified in AISC 2017, it is necessary to consider the sectional resistance affected by local buckling. Therefore, the concept of reduced section is proposed - effective width constraint, which accurately reflects the actual resistance of the component. As the T-shaped section is a singly symmetric profile, a detailed analysis will be conducted on flexural buckling (FB) and flexural-torsional buckling (FTB) under various wing-flange width-to-thickness ratio conditions. Through the analysis of these two buckling behaviors, a more comprehensive understanding of the stability and resistance of T-shaped section members under different wing-flange width-to-thickness ratio conditions can be achieved. This study contributes to the understanding of the stability and cross-sectional solid of T-shaped members, providing insights for the design analysis of AISC2017-specified T-shaped section components. Particularly, it focuses on research related to section width-to-thickness ratio, slender section considerations, and sectional resistance. Further research is conducted on the issue of reduced resistance due to excessively slender cross-sections. This not only aids in better understanding the resistance of cross-sections but also provides practical design references. Therefore, this study holds research value regarding the analysis of the width-to-thickness ratio design for T-sections in the AISC 2017 specification, particularly when considering factors related to slender sections and cross-sectional resistance.

Experiment and design of cold-formed steel equal-leg lipped angle under axial compression

To study the buckling behavior and the design method of the load-carrying capacity of cold-formed thin-walled lipped angle, axial compression tests were carried out on 32 lipped angle columns with different sections and slenderness ratios which were manufactured with high strength zinc-coated grades G450 structural steel sheets. The experimental results showed that the long column with a small width-to-thickness ratio displayed global flexural-torsional buckling, local buckling was found for the short column with a large width-to-thickness ratio. Other specimens demonstrated interactive buckling with local buckling and flexural-torsional buckling. The specimens with torsional buckling all showed post-torsional buckling strength. Then ABAQUS finite element software was used to simulate the lipped angle specimens. The simulation results were in good agreement with the test results about buckling modes and ultimate strength which indicated that the established finite element analysis model was reasonable and feasible. Therefore, the influences of the slenderness ratio, width-thickness ratio, and width ratio of the leg to lip on the ultimate strength of cold-formed thin-walled lipped angle were analyzed using finite element software. The analysis showed that the ultimate capacity of the angle decreased greatly with the increase of the slenderness ratio. The ultimate capacity increased in the range of width-to-thickness ratios of 15–30 when the angles had the same lengths. The increasing of the width of the lips increased the ultimate capacity, but the increase of the ultimate capacity of the angles would lower when local buckling occurred at the lips. Finally, based on the test results, the modified effective width method and direct strength method were proposed to calculate the capacity of the cold-formed thin-walled lipped angle under axial compression. The comparison between the predicted results with the test and finite element analysis showed that the proposed methods were accurate and feasible.

Experimental investigation of long-span cold-rolled aluminium built-up section portal frames: Braced columns and ultimate strength enhancement

This paper presents an experimental program on a series of long-span cold-rolled aluminium portal frames with various configurations subjected to different load combinations. The main structural members of the portal frame systems, including columns and rafters, were constructed using cold-rolled aluminium back-to-back built-up channel sections made from aluminium alloy 5052-H36 materials. The objectives of this paper are to understand the structural behaviour of different portal frame configurations and to explore possibilities for improving the performance of the structural systems, including strength and ductility enhancements. A total of four full-scale two-bay portal frame systems, each featuring two end frames and a central frame, were tested. The columns were braced against flexural-torsional buckling by girts spanning between the columns of the central frame and the columns of the two end frames. As a result, the portal frames failed due to in-plane sway deformations with the columns reaching their full section capacities. The tests revealed that the addition of rafter tie and sleeve stiffeners significantly improved the performance of the cold-rolled aluminium portal frame systems. Described in a separate publication, the authors also conducted a study to experimentally investigate the behaviour of the same system but with unrestrained columns, resulting in failure due to flexural-torsional buckling. Collectively, these two works form the foundation for further studies on cold-rolled aluminium portal frames in particular, and aluminium structures more generally.

Lateral buckling of the compressed edge of a beam under finite bending

This paper investigates the critical condition whereby the compressed edge of a beam subjected to large bending exhibits a sudden lateral heeling. This instability phenomenon occurs through a mechanism different from that usually studied in linear theory and known as flexural–torsional buckling. An experimental test device was specifically designed and built to perform pure bending tests on soft materials. Thus, the experimental campaign provides not only the moment-curvature behavior of beams of narrow rectangular cross section, but also information regarding the post-critical lateral buckling behavior. To study the local bifurcation phenomenon, an analytical model is proposed in which a field of small transversal displacements, typical of the linear stability of thin plates, is superimposed on the large vertical displacement field of an inflexed beam in the nonlinear elasticity theory. Furthermore, numerous numerical simulations through nonlinear FE analysis have been performed. Finally, the results provided by the different methods applied were compared and discussed.

Flexural–torsional buckling with enforced axis of twist and related problems

The classical lateral–torsional instability of a cantilever beam with continuous elastic lateral restraint and a transverse point-load applied at the free end is discussed here through the lens of asymptotic simplifications. One of our main goals is to provide analytical approximations for the critical buckling load, as well as its dependence on various key non-dimensional groups. The first part of this study is concerned with a scenario in which a doubly symmetric beam is constrained to rotate about a fixed axis situated at an arbitrary height above the shear centroidal axis. The second part examines a beam that features a continuous elastic lateral restraint spanning its entire length. Assuming that the stiffness of the constraint, κ (say), is finite, the buckling equations in the second case are described by a system of two coupled fourth-order differential equations in the lateral displacement and the angle of twist. We show that as κ → ∞ , the problem discussed in the first part provides an outer solution for the aforementioned system; the relevant boundary conditions for the next-to-leading-order outer approximation are also derived using matched asymptotics. Our theoretical findings are confirmed by comparisons with direct numerical simulations of the full buckling problem.

Axial compression tests on CFRP strengthened CFS plain angle short columns

A comprehensive test program was performed to experimentally investigate the effect of CFRP strengthening on the axial strength and stability of CFS plain angle short columns subjected to monotonic axial compression. A total of 28 specimens were tested by varying the CFRP strengthening configurations for different column heights. Both uni-directional (CF_UD) and bi-directional (CF_BD) CFRP were considered. The influence of various parameters such as the type of CFRP, fiber orientation, and number of CFRP layers was investigated and discussed in detail. For single layer (ply) of CFRP, CF_UD-0° strengthening configuration resulted in maximum increase of axial capacity by 58.33% and 45.72% (in comparison to bare steel specimens), corresponding to 0.5 m and 1.0 m column lengths respectively. All the bare steel and skin-strengthened specimens failed predominantly due to torsional–flexural buckling mode. Additional layer of CFRP wrapping was found to enhance the axial capacity further and CF_UD-0°/BD was found to possess greater capacity in the case of double layer of CFRP. Adopting cardboard in-fill in addition to CF_UD-0° wrap has prevented the torsional mode of buckling and resulted in a peak increase of axial capacity by 192.55% and 240.61% corresponding to 500 mm and 100 mm long specimens, respectively.

Experimental investigation of long-span cold-rolled aluminium built-up section portal frames: Unbraced columns and flexural-torsional buckling

The paper presents an experimental program on a structural system, consisting of three long-span portal frames. The primary structural members, including columns and rafters, were constructed using cold-rolled aluminium back-to-back built-up channel sections. The system configuration featured two bays of single-span cold-rolled aluminium portal frames connected in parallel by a series of purlins spanning between the rafters to create a free-standing structure. A total of three full-scale tests (Frame Tests 1,2 & 3) were conducted with two loading scenarios. Frame Tests 1&2, which were identical to ensure accuracy, were subjected to vertical loads only, while Frame Test 3 underwent testing with combined horizontal and vertical loads. In all the tests, the columns were unbraced. The main objectives of this paper are, first, to describe the test setups and observe the structural behaviours of the portal frame systems. Consequently, the ultimate capacities were determined, and the predominant failure modes of the portal systems were identified as flexural-torsional buckling of the unbraced columns. The paper also provides information on the mechanical properties of the aluminium alloy 5052-H36 materials used to fabricate the structural members and frame components, obtained from compressive and tensile coupon tests. Further, the elastic buckling loads of the columns in the frame systems are reported in this paper, as determined from the measured load-deformation curves. While this paper primarily delves into the behaviour of the cold-rolled aluminium portal frames with a focus on flexural torsional buckling failures of unbraced columns, the authors have also conducted a separate study on the same system. In that separate study, the portal frames with the columns predominantly restrained against flexural-torsional buckling were investigated to enhance the ultimate capacities of the portal frame systems.

New beam-based models for fire-induced buckling analysis of class 4 steel columns

Steel cross-sections with thin walls are vulnerable to fire-induced buckling instability, which reduces their load-bearing capacity. Eurocode 3 design provisions have been found inadequate, leading to alternative methods such as effective design strategies and advanced structural models built mostly with shell FE, which can be complex. For Class 4 steel beam-columns subjected to fire conditions, beam-type modelling to predict the Flexural-Torsional Buckling (FTB) strength has been proposed as an alternative approach, but it has not yielded satisfactory results for large compressive load eccentricities. This paper presents two new low computational cost modelling strategies based on Timoshenko's beam FE to address this issue: the Single beam-column Model (SbcM) and the Cruciform beam-column Model (CbcM). The first consists of a single line of beam FE, while the second uses a grid of beam FE for more flexibility. Both strategies effectively simulate the FTB behaviour in Class 4 steel beam-column during a fire, offering quicker computations compared to shell models. Still, the single-line model is favoured for its simplicity, making it more efficient in analysing complex fire engineering problems.

Flexural Torsional Buckling of a Beam from the Dee Bridge of 1846 - Analytical and Finite Element Analyses

The Industrial Revolution in Victorian England was a period marked by rapid development of the machine industry, accompanied by new technologies in metallurgy and a need for transport between economic areas that was fast, cheap and convenient. This is a period when the railway transport arose and in a short time acquired an image familiar to us to this day. Passage of train sets across rivers and hard-to-reach areas requires transport facilities. In this period, an extremely large number of bridges and aqueducts were built, which have different constructive solutions, different technologies are applied and they are made of different materials, depending on the preference of their creator. This paper examines the collapse of one of the beams of the Dee Bridge on 24 May 1847. The analysis carried out shows the irrationality of the cross-sectional dimensions and types of girder supports witch generate large compressive forces in the beam, leading to flexural torsional buckling.

Experimental investigation of fixed-ended hot-rolled austenitic stainless-steel unequal-leg angles under compression

Structural stainless steel is gaining traction in the structural engineering field, however, there is currently limited published data on the performance of stainless steel unequal-leg single-angle compression members. This limitation of published data is reflected in the recently released AISC 370: Specification for Structural Stainless Steel Buildings which is limited in scope to equal-leg cross sections. Furthermore, the Specification requires the consideration of flexural–torsional buckling for single angles which is in contrast to the original design guidelines from AISC published in 2013, which mirrored the carbon steel specifications and did not required checking for flexural–torsional buckling for single angles. This paper reports a comprehensive experimental study on the behavior of hot-rolled austenitic stainless steel unequal-leg angle columns. A series of unequal-leg angles with cross-sectional dimensions of 76.2 × 50.8 × 6.35 mm (3″× 2″× 1/4″) and lengths ranging from 250 mm (10″) to 3760 mm (148″) were tested in compression. The ultimate loads were recorded in addition to displacements, twists, and failure modes through the use of strain gauges and an optical tracking system. The material properties were obtained through a series of tensile coupon tests, and the member geometric imperfections were measured through a non-contact 3D laser scanning technique. In addition, residual stress distributions were measured by the sectioning method. The results obtained from this experimental investigation indicated: (1) that torsional buckling is dominant in the shorter lengths and minor-axis flexural buckling in the longer lengths, with a transition occurring gradually in the middle lengths; (2) that the measured material properties are significantly higher than nominal values, and that this had a significant effect on the capacity predicted by the design provisions; (3) flexural buckling design provisions provide a better estimation than flexural–torsional buckling design provisions, although both are conservative.

Flexural–torsional buckling of steel circular arches with I-section under central concentrated load in elevated-temperature environment

This article reports the fire resistance experiments conducted on I-section circular steel arches, as well as the observed out-of-plane flexural–torsional buckling (FTB) behavior and in-depth finite element numerical simulation results. The test was carried out using a large fire test furnace to provide a real fire environment with a nonuniform temperature field. A specially designed loading device allowed for unconstrained out-of-plane deformation of the specimens inside the furnace, thereby achieving effective load conditions and noncoupled response of the components. Numerical analyses were performed using a combination of the general codes Fluent and Abaqus, with the former used for heat transfer analyses, and a structural FE model including the loading device and complex geometric imperfections was established based on the measured data. Thus, accurate simulation of the out-of-plane behavior of the steel arches at elevated temperature was achieved. On this basis, an in-depth parametric study was carried out to investigate the effects of temperature field variations, load ratio (LR), and geometric imperfection. The analysis results show that FTB occurs at nonuniform temperatures for the arches under concentrated load, and the difference in temperature distribution in fire has a minimal effect on the FTB behavior. LR is negatively correlated with critical temperature; the smaller the LR, the more significant the weakening of critical loads by fire. The effect of initial geometrical imperfections on FTB at elevated temperatures is similar to that at ambient temperatures, and the effect on the critical temperature of FTB can almost be ignored when the imperfection amplitude is less than S/400.

Beneficial effects of the precritical nonlinearities on the lateral buckling of extremely flexible beams

The lateral buckling of extremely flexible beams, uniformly or non-uniformly bent in a principal inertia plane, is studied. An exact polar continuum model of an internally constrained 1D straight beam, immersed in the 3D space, is formulated. The model is linearized in the out-of-plane displacement only, so that it is able to capture: (i) the exact planar non-trivial fundamental path, and (ii) the exact critical point along it, at which the beam experiences out-of-plane flexural–torsional buckling. It is proven that the precritical deflections increase the critical load with respect to that evaluated by the classic theory, in which a trivial fundamental path is assumed, thus playing a beneficial role. Moreover, when the beam is extremely flexible, bifurcation disappears, similar to what discussed in literature for axially soft compressed beams, although via a different mechanism of the eigenvalues.

Non-linear analysis of the flexural-torsional stability of slender tropical glulam beams

The main objective of this manuscript is to model the flexural-torsional buckling of slender tropical glulam beams using the finite element method. The non-linear approach to quantify both the buckling strength and the lateral geometrical features of wooden beams is proposed. A very rigorous methodology is used which is based on the kinematic Vlasov’s theory to determine the displacement field of the beam section by considering an updated Lagrangian description. For the finite element discretization, the Author develop a single wood element characterized by 14 degrees of freedom, i.e. seven degrees for each nodal point, and derive non-linear stiffness matrices by using the virtual works principle. The model is implemented in MatLab and the numerical results are compared with results based on the classical linear stability theory of slender wood beams. The selected case-studies are a cantilever beam and a beam on two supports.

Test and design of cold-formed steel closed built-up beams with double sigma sections and triple lipped channel sections

Built-up section beams fabricated from several single sections are finding increasing use in the cold-formed steel (CFS) industry due to various advantages such as higher bending capacities, innovative new shapes, and elimination of eccentricity. However, a built-up beam is connected at discrete points along the longitudinal direction, which weakens the shear and flexural rigidities of the built-up section. The structural behaviour of built-up CFS beams is therefore more complicated than that of single section beams. This paper presents an experimental investigation on the moment capacity of screw fastened built-up CFS beams. To investigate the local, distortional, and flexural-torsional buckling of built-up CFS beams, four-point bending tests of 8 braced and 24 unbraced built-up C2C (fabricated from 2 sigma sections) section beams and C3C (fabricated from 3 lipped channels) section beams are conducted. Unbraced bending test specimens are tested at three lengths covering inelastic failure at short lengths to essentially elastic failure at long lengths. The strength predictions for the tested built-up beams are calculated using the current Direct Strength Method (DSM) in the AISI-S100 Specification. The comparison between the experimental results and DSM predictions indicates that the current DSM in AISI specification is overly conservative and unreliable for the types of built-up beam sections examined in this research, due to the incorrect failure mode prediction and underestimation of the critical elastic buckling stresses which is a key input to the DSM.

Geometrically nonlinear analysis of steel structures with nonsymmetric sections under elevated temperatures

Steel members using nonsymmetric sections are envisioned as popular because of the advancement in manufacturing techniques, in which frame analysis method under extreme scenarios, such as fire hazards, has not been thoroughly established. The element formulation for those members has been commonly derived based on either the updated-Lagrangian (UL) or the total-Lagrangian (TL) methods. However, the UL method is difficult to analyze the steel member exposed to fires because the previous equilibrium conditions may be destroyed due to the material stiffness degradation at elevated temperatures. Nevertheless, the TL method can be used for studying steel members under fire, but it is inefficient, time-consuming, and requires starting-over computation at every temperature increment. To this, the co-rotational (CR) method could be a promising solution for tackling the analysis problems of steel members in fire efficiently and accurately. The CR method separately describes the element and its rigid body movements, such that the material stiffness degradation can be considered at the element level without the starting-over computation at new temperature increments, which is numerically efficient. This paper reformulates the beam-column element formulation with the warping degree of freedom for nonsymmetric section members using the CR method, which can conveniently consider the material degradation and the thermal expansion for the analysis of steel members at elevated temperatures. The lateral-torsional and flexural-torsional buckling of nonsymmetric section members can be captured robustly. Detailed derivation for element formulation is given, and several examples are provided for verifying the accuracy and examining the robustness of the proposed method.

Interaction of Local, Flexural-Torsional, and Flexural Buckling in CFS Lipped Angle Compression Members

Interaction of Local, Flexural-Torsional, and Flexural Buckling in CFS Lipped Angle Compression Members

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

Experimental investigations on innovative built-up lattice steel beams

Spatial truss beams are an extremely efficient typological solution for covering large spans, especially in the cases where members do not have lateral restraints capable of preventing flexural–torsional buckling phenomena In this study the structural behaviour of innovative steel 3D lattice beams in combination with structural glass slabs, used as roof decks, is investigated for protection of historical assets and archaeological sites. After a brief description of the novel structural system, the attention is focused on the experimental activities carried out for the mechanical characterization of both material and structure. In particular, four-point bending tests are carried out on full-scale prototypes in order to both validate the design procedure and calibrate numerical models useful to extend the achieved results through Geometrically and Materially Nonlinear Analysis with Imperfections (GMNIA analysis).

A consistent approach for global buckling of steel structures

AbstractThe ”General Method“ according to chapter 6.3.4 of EN1993‐1‐1 or 8.3.4 of prEN1993‐1‐1 deals with the verification of stability problems of frame and beam structures with loadings in‐plane. The ”General method“ according to Eurocode is intended for the general case of a combined moment and normal force. For the choice of the reduction factor χop, there are two options for applying the reduction curve, either the minimum of lateral torsional buckling (LTB) and flexural buckling (FB) or a weighted combination of both. With the use of analytical derivations, it can be shown that this approach leads to inconsistencies which can possibly lead to incorrect results. In this paper an alternative approach is presented which leads to unification and fully mechanical justification in verification. The approach allows e.g. the verification of stability of an entire frame system directly and without interaction factors (as in the equivalent member method). In addition, the issue of a consistent equivalent imperfection is addressed. With the use of this method, geometrical non‐linear analyses of structures showing out‐of‐plane instability can be omitted; only an in‐plane calculation and a determination of a linear buckling analysis is necessary. Finally, examples are presented in this paper that demonstrate the application of the approach shown.