Lateral-torsional Instability Research Articles

Bracing systems for three-ribbed arch bridges against out-of-plane buckling

This paper is concerned with the design of bracing systems for three-ribbed parabolic arch bridges against out-of-plane buckling. Typical bracing systems for the three-ribbed arch bridges include K-bracing system and X-bracing system as well as transverse bracing system. The buckling criterion of the braced funicular three-ribbed arch bridge is derived from an exact matrix stiffness method (MSM) with a 14 × 14 s-order element stiffness matrix of three-dimensional beam-column elements that allows for torsional and warping deformations. The lateral torsional buckling load and mode are given by the lowest eigenvalue and eigenvector associated with the assembled structural stability stiffness matrix. A comparison study between different bracing system configurations suggests that the three-ribbed arches with the integral K- or X-bracing system (a K/X-bracing across the three arch ribs) have lower lateral torsional buckling loads than their arch counterparts with the independent K- or X-bracing system (the adjacent arch ribs are connected by K/X-bracing respectively), because the latter ones could provide more restraint on the middle arch rib to avoid early lateral torsional instability. Further, a bracing utilization efficiency index (defined as the normalized buckling capacity over material usage for bracing system) is proposed to quantify the effect of bracing systems in improving the lateral torsional buckling capacity of arch bridges. Highly efficient bracing systems that maximize the lateral torsional buckling load of three-ribbed arch structures with the lowest bracing material usage are then recommended.

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.

Lateral instability of sandwich beams under uniform bending

This paper investigates the lateral-torsional instability of soft-core sandwich beams. This physical phenomenon, which has received limited attention in the framework of sandwich structures, is investigated here in the context of fully nonlinear analysis for the first time. The research addresses, quantifies, and explores the lateral-torsional instability with emphasis on the unique features of the sandwich structure and its geometrically nonlinear response. The research questions relate to the nature of the instability and to the role of the deformability of the core layer in the unique mechanism. The results of the investigation include a new, high-order, nonlinear model for the analysis of the torsional-lateral response as well as new insight into the evolution of the phenomenon in sandwich beams.

A lateral–torsional buckling demonstration model using 3D printing

It is well-established that beams of relatively narrow cross-section have a tendency to buckle laterally when loaded. This type of lateral–torsional instability, which has considerable practical importance in a variety of thin-walled structures, is a classical buckling situation in which the critical load is related, among other things, to characteristic features of the cross-section. In this short paper, 3D-printing is exploited to provide a parametric study based on a fixed cantilever geometry in which a number of standard cross-sectional forms are compared in terms of their effect on this kind of buckling behavior.

Lateral-Torsional Instability and Biaxial Bending of Imperfect FRP I-Beams

This paper presents the outcome of a theoretical and experimental study of the behavior of Fiber Reinforced Polymer (FRP) I-beams exposed to lateral-torsional instability or when subjected to biaxial bending. Laboratory experiments involved the application of vertical and horizontal static loads to a 4 x 4 x ¼ in. I-beam with various lengths and the resulting deflections were recorded. Governing biaxial flexure and torsion differential equations were modified to account for the presence of initial imperfections and subsequently solved using a central finite-difference scheme. The theoretical predictions of the beam behavior were found to be in good agreement with what was observed in the laboratory.

Investigations on the lateral-torsional buckling of an innovative U-shaped steel beam

An innovative solution of a steel-concrete composite beam was developed for buildings with beam spans between 6 and 12 m, taking into consideration the fire situation and the construction stage. The beam is composed of an U-shaped steel part, connected to a reinforced concrete part. In the construction phase, the beam is supporting the slab and constitutes a formwork for the reinforced concrete part. When casting concrete, the steel beam is filled at the same time as the slab, this allows considerable time savings on site. In the exploitation stage, the beam behaves as a steel-concrete composite beam.The developed U-shaped section is composed of three steel parts; a hot rolled steel plate (180x8x6300 mm, and two cold-formed steel plates (470x4x6300 mm) before folding. The section was assembled together with four self-drilling screws longitudinally spaced of 150 mm.In the construction stage, the U-shaped steel beam without restraints is prone to lateral torsional buckling instability. In this paper, the mechanical behaviour of the steel beam at the construction stage, in particular its lateral-torsional buckling stability, was studied. In order to characterize this instability without lateral support, a four-point bending test was carried out on a life-size specimen. The load introduction system was developed especially for the test to allow for all displacements due to LTB. The test clearly showed the lateral torsional buckling behaviour of the steel beam. The test results are compared with numerical simulations and analytical studies. A parametrical study, covering 200 geometrical configurations of the U-shaped beam, is carried out to validate the use of the curve “b” for the design of the steel beam for lateral torsional buckling according to Eurocodes 3.

On the uniform torsional rigidity of square concrete-filled steel tubular (CFST) sections

There are a number of scenarios in which structural members experience torsion, including under the direct application of torsional loading, when transverse loading is applied at an eccentricity to the shear centre and as a second order effect arising from lateral torsional instability. To date, the torsional rigidity of concrete-filled steel tubular (CFST) sections has yet to be fully explored; hence a study into the uniform torsional rigidity of square CFST sections is presented herein. First, the strain energy of square CFST sections is formulated, in which the longitudinal warping displacement is assumed to have an undetermined constant. The undetermined constant is then deduced by means of the principle of minimum strain energy, and thus an analytical expression for the uniform torsional rigidity of square CFST sections is obtained. The accuracy of the derived formula is verified against existing theoretical solutions for simplified scenarios, test data and the results of numerical simulations. Finally, the influence of the key parameters in the derived formula for the torsional rigidity of square CFST sections are analysed, and a simplified design formula is presented.

A one-dimensional model for elastic ribbons: A little stretching makes a big difference

Starting from the theory of elastic plates, we derive a non-linear one-dimensional model for elastic ribbons with thickness t, width a and length ℓ, assuming t≪a≪ℓ. It takes the form of a rod model with a specific non-linear constitutive law accounting for both the stretching and the bending of the ribbon mid-surface. The model is asymptotically correct and can handle finite rotations. Two popular theories can be recovered as limiting cases, namely Kirchhoff’s rod model for small bending and twisting strains, |κi|≪t∕a2, and Sadowsky’s inextensible ribbon model for |κi|≫t∕a2; we point out that Sadowsky’s inextensible model may be a poor approximation even for ribbons having a very thin cross-section (say, with t∕a as small as 0.02). By way of illustration, the one-dimensional model is applied (i) to the lateral-torsional instability of a ribbon, showing good agreement with both experiments and finite-element shell simulations, and (ii) to the stability of a twisted ribbon subjected to a tensile force. The non-convexity of the one-dimensional model is discussed; it is addressed by a convexification argument.

Elastic lateral-torsional instability of monosymmetric shear deformable fixed arches under a localized uniform radial load

This paper investigates the elastic lateral-torsional instability of shear deformable fixed arches having a monosymmetric cross-section when subjected to a localized uniform radial load. Hitherto, this topic has not been addressed in the open literature. The complex in-plane internal actions in a fixed arch with a monosymmetric section are produced by a localized uniform radial load and are affected by the arc length of localized load segment. When the in-plane internal actions reach certain magnitudes, the fixed arch may fail suddenly in a lateral-torsional instability mode. The lateral-torsional instability loads of such arches considering shear deformations under a localized uniform radial load are difficult to obtain and are investigated in this paper. The strain-displacement relationships for the longitudinal normal axial and shear strains in the arch with a monosymmetric section are derived. In-plane analyses for the internal forces produced by the localized uniform radial load are firstly carried out. The analytical solution for the lateral-torsional instability load accounting for shear deformations and monosymmetry is then obtained using the principle of stationary potential energy together with the Rayleigh-Ritz method and compared with ANSYS numerical results. It is found that the monosymmetry parameter, the shear deformations, the slenderness ratio and the arc length of the localized load segment have considerable effect on the lateral-torsional instability load of fixed arches with a monosymmetric section.

Cyclic performance of bolted end-plate RWS connection with vertical-slits

The reduced beam section (RBS) connections are widely used in construction buildings due to their desirable ductility and strength. The current reduced web section (RWS) connections are produced by a reduction in the beam web as circular or rectangular cuts or as horizontal slits. This article has proposed a new detail for the RWS bolted connection by creating vertical-slits in the beam web. The aim of this investigation is the evaluation of its cyclic performance in comparison with the conventional RBS connection. Two specimens, one with vertical-slits in the web (VS-RWS) and the other one with a radial-cut in the flange (RC-RBS), were experimentally tested and the results were compared. Moreover, numerical models were employed to evaluate the behavior of connections in detail. These two connections were able to move the plastic hinge region away from the column face, exhibit good hysteresis behavior, and satisfy the AISC requirements for special moment-resisting frames. The results also showed that the flexural capacity of the proposed VS-RWS connection is 10% higher than that of the conventional RC-RBS one, while their ductility and energy dissipation were almost the same. An important advantage of VS-RWS over RC-RBS is its ability to prevent the lateral-torsional instability. Besides, a numerical study was conducted to investigate the performances of various cut shapes RWS connections with certain overall dimensions and location of the cutting region in terms of hysteresis curves, rupture index and end-plate deformations.

Experimental bending tests of partially encased beams at elevated temperatures

This paper presents the result of an experimental research about the lateral torsional buckling instability during bending tests of Partially Encased Beams (PEB) at elevated temperature. A set of twenty seven four-point bending tests, grouped in ten series, were carried out to analyse the influence of relative slenderness, beam temperature and the shear bond conditions between concrete and steel in bending. In addition, this study compares the behaviour of PEB and bare steel beam under bending at room temperature.PEB specimens are based on IPE100 steel profiles, with two different lengths 2.4 m (medium series) and 3.9 m (large series), tested in bending using simple supporting conditions and exposed to different temperatures levels of 200 °C, 400 °C, and 600 °C.Two different shear bond conditions, between steel profile and lateral concrete, were analysed at 400 °C: one series with connectors formed by welded stirrups to the web and another series with natural adherence between steel and concrete, not welded stirrups.PEB attained lateral torsional buckling as deformed failure mode at the ultimate limit state, except for the case of PEB tested at 600 °C that results in a plastic hinge failure. The bending resistance was determined for the maximum load event (Fu) and for the displacement limit corresponding to L/30 (FL/30) and compared with the results of the Eurocode 3 part 1–2 simple calculation method, considering an adaptation of its formulae to PEB. The expected reduction in bending resistance at elevated temperature is in good agreement with the experimental reduction factor, when the deformation criterion is used.

Lateral-torsional dynamic instability of uniform and double-tapered rectangular beams under harmonic shear deformation

Abstract This paper analyzes lateral-torsional dynamic instability of elastic beams with rectangular cross section having constant thickness, with the depth symmetric with respect to the midpoint and either uniform or tapered linearly in each half. Free vibrations are also investigated. The ends of the beam are prevented from twisting and are pinned with respect to bending in the weak direction. In the strong direction, one end of the beam is fixed and the other is subjected to transverse harmonic motion. This problem was motivated by “butterfly-shaped links” proposed for use in seismic mitigation. Uniform torsion is assumed. Frequencies of free vibration are computed, critical excitation frequencies for lateral-torsional instability are determined, and critical combinations of excitation amplitude and frequency are obtained. The effects of geometric parameters of double-tapered beams on instability are presented. Lateral-torsional instability may occur for very small amplitudes of the moving end of the beam, as is typical for such problems involving parametric resonance.

Use of angle cleats to restrain cold-formed channels against lateral torsional instability

It is common practice in the steel construction industry to restrain members that largely in flexure and torsion using a combination of angle cleats, connected at the top flange, and fly-bracings. This system is complicated and expensive, especially when used to restrain channels in bending. This paper investigates experimentally the use of angle cleats, connected to the webs of both the purlin and the channels, as a restraining system. Pairs of channels were subjected to a two point loading system in order to simulate a distributed load. Variable in the tests include the unbraced length between the two-point loads and the size of the channels. Failure of the channels occurred by lateral torsional buckling and catastrophic distortional buckling of the intermediate unbraced length. Tests showed that the purlin-cleat restraining system is able to resist lateral torsional buckling of the channels, and that this system can be used without any fly bracing. Distortional buckling was the final failure mode, and it occurred at moments less than the predicted lateral-torsional buckling moment of resistance. Distortional buckling is more critical in frames with shorter unbraced lengths and thicker channels.

The influence of prestressing on the twisting phenomenon of beams

The prestressing technique is often employed in engineering practice to increase the bearing capacity of concrete beams in bending. Nevertheless, prestressing has been also applied successfully in numerous cases of steel members, bars or trusses. Whilst in members with concrete sections buckling instability is unlikely to occur, the phenomenon of twisting instability may appear in prestressed steel beams under bending as a special case of the lateral-torsional instability. In the present work, the influence of prestressing on the stability (twisting instability) of a simply supported beam induced by a rectilinear tendon is thoroughly studied. Useful results are gathered and presented in the form of interaction axial force—moment diagrams that can be used for a preliminary design of beams against twisting instability.

Lateral Instability and Lateral Bracing of Steel Beams Subjected to Cyclic Loading

This paper presents an analytical study of the lateral–torsional instability and lateral bracing effects of wide-flange steel beams subjected to cyclic loading. Numerical analysis using the large deformation theory was conducted to collect the necessary data. Examined were wide-flange steel beams bent in double curvature and subjected to cyclic loading with increasing amplitudes up to the maximum beam end rotation of 0.045 rad. Cross-sectional properties, slenderness ratios, material strength, loading history, and unbraced length were chosen as analysis variables. The lateral instability effect was found to differ significantly between cyclic and monotonic loading. For slenderness ratios about the weak axis not smaller than 100, the strength that can be sustained under cyclic loading was much smaller than that obtained under monotonic loading due to the accumulation of out-of-plane deformations. Equations are proposed for the beam unbraced length with which no detrimental reduction in strength is present ...

Tension flange instability of I-beams

The possible lateral–torsional instability of an I-beam with braced compression flange is studied. It is shown that taking the sagging prior to lateral–torsional buckling into account gives a finite critical moment. A solution for a uniform I-beam under uniform bending is presented. It is further shown that this solution can be approximated by a simple geometrical relation for the critical strain. This approximation is a lower bound also where the bending is causing inelastic deformations. For normal structures tension flange instability will not be a problem but it may be necessary to consider it for very high strength shallow beams or if plastic rotations occur in the sagging region.

A simplified distortional buckling model for doubly symmetrical I-sections

Lateral torsional instability of I-beams considers the relative displacement of the unstable compression flange to the stable tension flange. It is commonly assumed that little or no distortion takes place between the two flanges. In this paper, an approach is proposed whereby the section properties that control lateral torsional buckling are adjusted to allow for the influence of cross-section distortion, by the use of simple spring models representing the relative stiffness of the flanges and the web. The model is developed for elastic, inelastic, and plastic cases and compared with the results obtained from finite element models developed by other researchers. A method of quantifying the lateral distortional buckling resistance of I-beams is of particular importance in the hogging moment region of continuous composite beams; the ability of the proposed model to deal with this complex problem has been previously demonstrated by the authors. In this paper, the proposed model is used to illustrate the influence of distortional buckling on doubly symmetrical I-sections.Key words: lateral, distortional, I-beams, elastic, inelastic.

Large-Displacement Analysis of Elastoplastic Thin-Walled Frames. II: Verification and Application

The companion paper presents a new Eulerian formulation for the large-displacement analysis of thin-walled frames, accounting for the elastoplastic material response. This paper aims at verifying the proposed formulation and providing several examples of its application ot thin-walled members and frames. In this regard, it is demonstrated that such a relatively simple formulation enables the accurate modeling of initial imperfections, residual stresses, the Wagner effect, the beam-column effect, lateral-torsional instability, and large displacements using a small number of elements and a coarse cross-sectional discretization. Moreover, it is shown that the formulation can be used in the assessment of the ultimate and postultimate response of thin-walled structures for which the design codes are either inaccurate or inapplicable. Such structures include continuous beams, simply supported beams with intermediate lateral restraints, as well as frames for which the ultimate limit state involves considerable interaction between the structural members.

Load and resistance factor design (LRFD) approach for reinforced-plastic channel beam buckling

Pultruded fiber reinforced plastic (PFRP) structural sections are rapidly gaining impetus in civil engineering applications. Thin-walled open beams with channel, I-shaped, and other types of sections are of practical importance to designers. In this paper, a load and resistance factor design (LRFD) approach for lateraltorsional buckling is presented based on an experimental and theoretical study of the behavior of PFRP channel section beams under the influence of gradually increasing static loads. Some experimental results for combined bending and torsion are also presented. Single span members with unrestrained end warping are considered with concentrated vertical loads passing through (a) the shear center, (b) the geometric centroid, and (c) a location which is neither at the shear center nor at the centroid. A pair of concentrated loads are applied symmetrically about the beam midspan, through a system of loading plates and tie rods in order to allow an unrestrained deformation of the beam. The loads are increased gradually and the resulting midspan vertical, lateral, and torsional deflections are recorded. The loads are generated with hydraulic jacks and recorded by means of calibrated load cells. Strains are also recorded at key locations using electrical resistance gages. Relationships between the applied load and the resulting deflections and strains are plotted and compared for the three load cases. The magnitude and significance of the warping stresses in comparison to the flexural stresses are identified. For the case of shear center loading, the deflections are monitored for various clear spans of the beam. This information is then utilized to generate the relationship between the lateral torsional instability load versus the minor axis slenderness ratio. An approximate theoretical formula is also developed to predict the lateral-torsional buckling load as possible prelude to the evolution of a formal construction specification formula for use by design engineers. The predicted buckling loads found using the formula are in excellent agreement with the experimental results. A comparison of the results from the formula applied to the case of compression flange loading is also made to those using the current AISC-LRFD specification. Lastly, the use of a proposed LRFD approach is demonstrated by means of analysis and design examples. The effect of the applied load height on the buckling load capacity is explained using the buckling formula.

EVALUATION OF ULTIMATE STRENGTH OF ELASTICALLY RESTRAINED I-SECTION BEAMS

In this paper, for the lateral-torsional instability of beams between cross members, the following investigations are carried out;(1) The basic strength curves of rolled and welded laterally unsupported beams with initial clockedness and residual stresses are obtained by using the FEM analysis.(2) A formula on the ultimate strength of elastically restrained beams at both ends is developed with concerning the basic strength of beams.(3) The strength of the isolated beam models restrained by intermediate descrete supports are parametrically analized.(4) The restraining effects of the adjecent members and bracing systems on the lateral buckling strength are investigated more precisely by the FEM analysis. And the practical formulae obtained by modifying Nethercot-Trahair method based on the elastic buckling theory are proposed.