Lateral distortional buckling of monosymmetric I-beams under distributed vertical load

An energy method is developed for analyzing the lateral buckling behaviour of beams subjected to distributed vertical load, with full allowance for distortion of the web. The paper presents a simple method which uses nonlinear elastic theory to obtain the external work due to buckling, and which obtains a new formulation of total potential energy for a monosymmetric I-beam. The method is validated by comparison with the classical energy methods when distortion of the web is suppressed (rigid web case). For both uniform distributed load and end moments the solution matches the critical lateral load obtained from the classical energy equations. For the case when the web is flexible, a 5th order polynomial shape function is used to describe the web buckling shape. The accuracy of the method is verified by results obtained from ABA QUS. The paper shows that for short beams the classical method seriously overestimates the critical load.     

Lateral buckling of web-tapered I-beams: A new theory

This paper presents a new theory for the lateral buckling of web-tapered I-beams. Linear analysis is first conducted by taking account into the tapering effects of web-tapered I-beams, where the deformation compatibilities of the two flanges and web are considered in terms of the basic assumptions of thin-walled members. Subsequently, the total potential for the lateral buckling analysis of web-tapered I-beams is developed, based on the classical variational principle for buckling analysis. The lateral buckling loads of web-tapered cantilevers and simply supported beams of I-sections from the proposed theory are compared with those from the finite element (FE) analyses using two shell element models and two widely used beam element models. The two beam element models respectively represent the equivalent method using prismatic beam elements and the typical tapered beam theory in existing literature. These comparisons show that the results based on the total potential proposed in this paper are more accurate in predicting the lateral buckling loads of web-tapered I-beams than those in existing theories, indicating that the theory proposed in this paper is superior to existing theories. It is also found that the equivalent method using prismatic beam elements may yield unreliable buckling loads of tapered beams.     

Lateral buckling resistance of inelastic I-beams under off-shear center loading

Lateral-torsional buckling (LTB) strength of steel I-beams subjected to moment gradient loading is scaled by the moment gradient factor, C_b. The C_b factor depends on the non-uniformity of moment diagram, the height of the applied transverse loads within the unbraced length and end conditions. Generally, the C_b factors given by codes have been derived from elastic LTB analysis theory. However, the same C_b factors are used for beams that buckle inelastically. This paper develops a three dimensional finite element model using ANSYS for the inelastic nonlinear flexural-torsional analysis of I-beams and uses it to investigate the effects of unbraced length and central off-shear center loading (located at center, top flange and bottom flange) on the moment gradient factor in inelastic behavioral zone. It is found that the C_b factors given by AISC-LRFD in Specification for structural steel buildings (AISC 360-05) and Structural Stability Research Council Guidelines are not accurate for the point load cases applied at center and bottom flange in which I-beam buckles inelastically. It is seen also that the AISC-LRFD flexural resistance equations overestimate the actual moment capacity of inelastic I-beams under moment gradient. Therefore, a simple equation is proposed to be used instead of the code equation in inelastic zone for the investigated load cases in this paper.     

Finite element modelling of cold-formed steel beams under local buckling or combined local/distortional buckling

The finite element (FE) method is capable of solving the complex interactive buckling of cold-formed steel beams allowing for all important governing features such as geometrical imperfections, material nonlinearity, postbuckling, etc.; this is unlikely to be achieved by analytical methods. In this paper, two series of finite element models for buckling behaviour of laterally-restrained cold-formed steel Z-section beams have been developed with special reference to material and geometrical nonlinearities: one to allow for the possibility of combined local/distortional buckling and the other to allow for local buckling only. Four-point bending tests carried out by previous researchers have been used to verify the FE models. A simplified configuration of the test setup has been modelled in ABAQUS. In the local buckling FE models, distortional buckling has been restricted in the member using translational springs applied to the lip/flange corner of the beam. Predictions of load carrying capacity and deformed shapes exhibit excellent agreement with both the results from the more extensive models and laboratory tests. Further papers will exploit the developed FE models to investigate the different forms of buckling that occur in laterally-restrained cold-formed steel beams i.e. local, distortional and combined local/distortional.     

Lateral distortional buckling tests of a new hollow flange channel beam

The LiteSteel beam (LSB) is a new hollow flange channel section developed by OneSteel Australian Tube Mills using their patented dual electric resistance welding and automated continuous roll-forming process. It has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. The LSBs are commonly used as flexural members in buildings. However, the LSB flexural members are subjected to lateral distortional buckling, which reduces their member moment capacities. Unlike the commonly observed lateral torsional buckling of steel beams, the lateral distortional buckling of LSBs is characterised by simultaneous lateral deflection, twist, and cross sectional change due to web distortion. An experimental study including more than 50 lateral buckling tests was therefore conducted to investigate the behaviour and strength of LSB flexural members. It included the available 13 LSB sections with spans ranging from 1200 to 4000 mm. Lateral buckling tests based on a quarter point loading were conducted using a special test rig designed to simulate the required simply supported and loading conditions accurately. Experimental moment capacities were compared with the predictions from the design rules in the Australian cold-formed steel structures standard. The new design rules in the standard were able to predict the moment capacities more accurately than previous design rules. This paper presents the details of lateral distortional buckling tests, in particular the features of the lateral buckling test rig, the results and the comparisons. It also includes the results of detailed studies into the mechanical properties and residual stresses of LSBs.     

Distortional buckling of monosymmetric I-beams

A finite element method which is applicable to studying the distortional buckling of fabricated monosymmetric I-beams is briefly described. The method is used to demonstrate the effects of web slenderness on a monosymmetric I-beam whose smaller flange is in compression. A study is also made of the effects of monosymmetry on the distortional buckling of an I-beam with a slender web in uniform moment and moment gradient. Based on parameter studies using the finite element method, a design equation is developed which may be used to determine the distortional buckling stress of a monosymmetric I-beam under moment gradient.     

Distortional buckling in monosymmetric I-beams

This paper deals with distortional buckling of simply supported monosymmetric I-beams under three types of load: a central point load, a uniformly distributed load and a uniform sagging moment. ABAQUS is used for the investigation. Top-flange and bottom-flange load positions are considered for the first two load cases. It is found that for comparatively short beams, buckling may be governed by distortion of the web. Moment modification factors are calculated based on the present analysis, which accounts for the distortion of web and these are compared with those based on SSRC Guidelines, which are based on lateral-torsional buckling analysis only. It is seen that for short beams, provisions in SSRC Guide-1998 seriously overestimate the critical load.     

Distortional buckling in braced-cantilever I-beams

This paper deals with distortional buckling of braced-cantilever monosymmetric I-beams under three types of load: a tip point load, a uniformly distributed load and a moment at the end. Top-flange and bottom-flange load positions are considered for the first two load cases. ABAQUS is used for the investigation. The effect of different types of bracing on buckling load is investigated. Results are compared with results from previous experimental investigations. It is also found that top lateral bracings are very effective for beam sections having larger bottom-flanges when a point load or a uniformly distributed load acts at the top-flange, and for the uniform moment case, except for the T-section or the inverted T-section cantilever beams. On the other hand, bottom lateral bracings are very effective for beam sections having larger top-flanges. When loads are placed at the bottom-flange, position of any kind of lateral bracing has practically no effect on the buckling capacity of a monosymmetric cantilever beam, except for the inverted T-section cantilever beams.     

Strength of cold-formed lipped channel beams under interaction of local,distortional and lateral torsional buckling

Cold-formed thin-walled lipped channel steel beams may undergo buckling modes such as short half-wavelength local buckling, intermediate half-wavelength distortional buckling and long half-wavelength lateral-torsional buckling or a combination of these before failure. ABAQUS software based on finite element analysis is used to analyse the interaction behaviour of these buckling modes in this study. The finite element model, after calibration with experimental results available in the literature, is used to perform parametric studies, to evaluate the behaviour and strength of such beams under different types of interactions due to variation of material and member properties. The large volume of synthetic data thus generated over a range of failure modes along with the available test results are used to evaluate different equations for calculating the strength of such cold-formed lipped channel beams. Based on the comparison, a method for the design of lipped channel beams failing under the interaction of local, distortional and overall lateral torsional buckling is recommended.     

Elastic distortional buckling of tee-section cantilevers

The paper presents the results of a finite element study of the elastic distortional buckling of tee-section cantilevers, which can be thought of as beams fully braced at one end and unbraced at the other. The finite element procedure is described briefly, and then three loading cases, viz., a tip moment, a tip load and a uniformly distributed load are considered. All of these loading cases place the unstiffened or free edge of the stem or web into compression. The effects of distortion are quantified for the three loading cases, as are the effects of fully restraining the top flange against lateral deflection and twist by a discrete brace positioned anywhere along the cantilever. It is shown that the effects of distortion during buckling cannot be ignored in a tee-section cantilever with even a moderately slender web.     

Design of thin-walled purlins for distortional buckling

Roof purlins and sheeting rails are generally loaded through the cladding members that they support and this provides both rotational and translational restraint. This restraint reduces the tendency to lateral torsional buckling and thus increases the importance of distortional buckling in the design procedure. This paper shows that the fundamental behaviour of restrained purlins under both downward and uplift load can be best understood with the aid of ‘Generalized Beam Theory’ (GBT). GBT also provides a yardstick by which approximate design methods can be assessed. The existing approximate methods are evaluated and an improvement is proposed. The proposed design approach is then validated by comparison with test results.     

Lateral-distortional buckling of I-beams and the extrapolation techniques

Various extrapolation techniques are utilized for predicting the critical buckling load of structural members undergoing lateral buckling. For the application of these methods it is only necessary to have data relating load to a deformation characteristic. In order to obtain an experimental comparison of the Southwell, Modified, and Massey Plot methods, these have been applied on lateral deflections and web transverse strains of four full-scale simply supported I-beams subjected to a central concentrated load with an effective lateral brace at the midspan of the top flange, undergoing inelastic lateral-distortional buckling. Although there is some scatter due to the application of various deformation variables and extrapolation techniques, the agreement between the extrapolated and the maximum test loads is generally good. The smallest discrepancy is found in the case of the Modified Plot. Moreover, in addition to demonstrating direct coupling between the lateral deflections and the web transverse strains representing web distortion, it is also shown that good predictions are provided by applying the Meck Plot on these deformation variables.     

Local and distortional buckling of thin-walled short columns

This paper assesses the applicability of Eurocode 3 (EC3) to the prediction of the compression capacity of short fixed-ended columns with different cross-sections. This compression capacity is determined by combining the effective width of plane elements due to local buckling and the effective stiffener thickness due to distortional buckling. Numerical calculations have been carried out in order to compare alternative methods for determining the minimum elastic distortional buckling stress in compression. The method given in EC3 does not correlate as well as Lau and Hancock's method with the results given by Generalized Beam Theory (GBT). The end boundary conditions have a significant influence on the distortional buckling strength, and thus also on the compression capacity of short columns. Selected experimental results from compression tests on C-, Hat- and rack upright-sections are compared with the predictions given by EC3. The procedure in EC3 was modified by determining the distortional buckling stress using GBT, taking into account the actual column length and the end boundary conditions. This lead to better agreement between the experimental results and the theoretical predictions.     

Design for distortional buckling of flexural members

For thin-walled flexural members composed of high-strength steel and/or slender elements in the section, a mode of buckling at half-wavelengths intermediate between local buckling and flexural—torsional or flexural buckling can occur. The mode is most common for edge-stiffened sections such as C- and Z-purlins, and involves rotation of the flange and lip about the flange—web junction. The mode is commonly called distortional buckling. This paper presents a design method for distortional buckling of flexural members recently drafted for use in the Australian/New Zealand Standard for Cold formed Steel Structures. Methods for computing the elastic buckling stress, and design curves for determining the distortional buckling strength are presented. Comparisons of different methods for computing the elastic distortional buckling stress are made with accurate solutions based on the finite strip method of structural analysis.     

Inelastic restrained distortional buckling of continuous composite T-beams

This paper develops a method of inelastic buckling analysis of thin-walled sections to study buckling characteristics of single span and two-span composite T-section beams in the inelastic range of structural response. The method is based on a bubble-augmented spline finite strip method, developed elsewhere by the authors, and confirmed as both accurate and efficient for the elastic buckling analysis of thin-walled structural members and plates. The method admits both flexural and membrane buckling deformations and it allows for consideration of structures with intermediate supports and a variety of boundary conditions that may be prescribed at the ends of plate assembly. The analysis includes the so-called Tendon Force Concept developed at Cambridge University for residual stresses caused by the process of fabrication, and the non-linear stress-strain properties of the structural steel from which the joist section is made. The inelastic restrained distortional buckling (RDB) of continuous composite T-section beams under transverse loading and moment gradient is investigated, and conclusions are drawn that address the influence of geometry, residual stresses, member length, the rigid restraint provided by the concrete and the degree of reinforcement in the concrete element.     

Elastic distortional buckling of continuously restrained I-section beam-columns

Doubly symmetric steel I-section members with thin webs and stocky flanges that have their tension flange restrained fully against translational and lateral rotational buckling deformations and elastically against twist rotation during buckling by the flexibility of a continuous restraint have been shown in previous studies to buckle in a so-called restrained distortional buckling (RDB) mode, involving distortion of the web of the I-section in the plane of its cross-section. These bifurcative buckling modes must necessarily occur in the negative moment region of composite T-beams and in half-through girder bridges. The present paper describes the elastic RDB analysis of a simply supported doubly symmetric I-section beam-column subjected to combined uniform axial force and moment gradient. The study adopts an energy method of analysis. The numerical solutions are used to develop a simple method of predicting the elastic RDB loads of beam-columns for use in design.     

Distortional buckling strength of elastically restrained monosymmetric I-beams

An inelastic method of analysis of the distortional buckling of monosymmetric I-beams is augmented to include the effects of elastic restraints against translation, minor axis rotation, torsion and warping. The method is validated for problems for which inelastic, distortional and restraint solutions are known. A study is made of a monosymmetric beam with separate translational, rotational and torsional restraints, and conclusions are made regarding the strength of the beam when the cross-section is free to distort.     

Distortional buckling in monosymmetric I-beams: Reverse-curvature bending

This paper deals with distortional buckling in monosymmetric propped cantilever I-beams under two types of load: a central point load and a uniformly distributed load. Top-flange and bottom-flange load positions are considered. ABAQUS is used for the investigation. Moment modification factors are obtained and are compared with those based on Structural Stability Research Council Guidelines, which take into account lateral–torsion buckling only. It is seen that provisions in SSRC Guidelines seriously overestimate the critical load, especially for short beams.     

Simulation of cold-formed steel beams in local and distortional buckling with applications to the direct strength method

A nonlinear finite element (FE) model is developed to simulate two series of flexural tests, previously conducted by the authors, on industry standard cold-formed steel C- and Z-section beams. The previous tests focused on laterally braced beams with compression flange details that lead predominately to local buckling failures, in the first test series, and distortional buckling failures, in the second test series. The objectives of this paper are to (i) validate the FE model developed for simulation of the testing, (ii) perform parametric studies outside the bounds of the original tests with a particular focus on variation in yield stress and influence of moment gradient on failures, and (iii) apply the study results to examine and extend the Direct Strength Method of design. The developed FE model shows good agreement with the test data in terms of ultimate bending strength. Extension of the tested sections to cover yield stresses from 228 to 506 MPa indicates that the Direct Strength Method is applicable over this full range of yield stresses. The FE model is also applied to analyze the effect of moment gradient on distortional buckling. It is found that the distortional buckling strength of beams is increased due to the presence of moment gradient. Further, it is proposed and verified that the moment gradient effect on distortional buckling failures can be conservatively accounted for in the Direct Strength Method by using an elastic buckling moment that accounts for the moment gradient. An empirical equation, appropriate for use in design, to predict the increase in the elastic distortional buckling moment due to moment gradient, is developed.     

Compression tests of longitudinally stiffened plates undergoing distortional buckling

This paper describes a series of compression tests performed on longitudinally stiffened plates fabricated from a mild steel plate of thickness of 4.0 mm with nominal yield stress of 235.0 MPa. The stiffened plates with longitudinal stiffeners of a range of rigidities were tested to failure. The ultimate strengths and performances of the longitudinally stiffened plates in compression undergoing distortional buckling or interaction between local and distortional buckling were investigated experimentally and theoretically. The compression tests indicated that the critical buckling mode was dependent mainly on the rigidity of the longitudinal stiffeners and the width-to-thickness ratio of the sub-panels. A noticeable interaction between local and distortional buckling was also observed for some stiffened plates. A significant post-buckling strength reserve was shown for those sections with distortional buckling and for those sections showing interaction between local and distortional buckling. A limiting strength curve for distortional buckling of longitudinally stiffened plates was studied. Simple design strength formulas in the direct strength method are proposed to account for the distortional buckling and the interaction between local and distortional buckling of longitudinally stiffened plates. The strength curves were compared with the test and FE results conducted. The adequacy of the strength curve was confirmed. A set of conclusions on the buckling behavior of longitudinally stiffened plates was drawn from the experimental studies.