Distortional Buckling Mode Research Articles

Elastic distortional buckling of doubly symmetric steel I-section beams with slender webs

Doubly symmetric steel I-section members with thin webs and stocky flanges have a tendency to buckle in a so-called distortional buckling mode, involving distortion of the web of the I-section in the plane of its cross-section. As this mode is more complicated than the local or global buckling, analytical expressions take empirical forms and vary in between different proposals. This paper has two main objectives. The first objective is to propose a complex finite strip method for distortional buckling analysis of I-section beams with slender webs and check the suitability for such analysis by comparing its accuracy with other methods and the second objective is to propose a simple method for predicting the distortional buckling loads of I-beams. The latter objective is superior to current methods with respect to the weight of the sections.

Generalized constrained finite strip method for thin-walled members with arbitrary cross-section: Secondary modes, orthogonality, examples

In this paper the generalization of the constrained finite strip method (cFSM) is provided. cFSM is an extension of the semi-analytical finite strip method (FSM), where carefully defined constraints are applied to enforce the thin-walled member to deform in accordance with desired deformations, e.g., to buckle in flexural, lateral-torsional, distortional, or local buckling mode. This paper is a companion to [1], where the method is introduced and where the primary modes are defined, i.e., modes that are associated with minimal cross-section discretization, when nodal lines are located at folds and ends only. In this paper the so-called secondary modes are defined, i.e., those with no displacements at folds and edges, which thus exist only if flat plates are discretized into multiple strips. Moreover, some practical aspects are also discussed, including how the individual base vector of the deformation spaces can be defined in a practically useful and meaningful manner. The applicability of the method is demonstrated by numerical examples.

Finite Element-Based Investigation on Performance of Intermediate Length Thin-Walled Columns with Lateral Stiffeners

Distortional buckling of compression members usually comprises rotation and translation of each flange and lip about the flange-web juncture in opposite directions. The present study makes an attempt to possibly delay or prevent the distortional buckling mode by the introduction of lateral stiffeners. The stiffened channel section has been selected based on the elastic buckling analysis using CUFSM software to ensure the occurrence of distortional buckling. The test programme consisted of two pure axial compression tests under hinged–hinged end condition. A finite element model of the tested compression members was then developed and validated with the help of experimental results and also by the column test results conducted by Young and Yan (J Struct Eng 732:728–736, 2002). Geometric, material nonlinearities and initial geometric imperfection were included in the finite element model. An extensive series of parametric analyses was undertaken using the validated finite element model to investigate the effect of varying depth and many lateral stiffeners on the ultimate capacity of the columns. The details of the parametric study results are presented as charts. The lateral stiffeners effect on behaviour and strength is discussed.

Restrained distortional buckling capacity of half-through bridge girders

Steel beams with continuous and complete tension flange restraint buckle in a restrained distortional buckling (RDB) mode. Lateral buckling of half-through girders is an important example of this phenomenon because of the restraint offered by the deck, and due to the flexibility of the web in restraining the compressive flange. A numerical study was undertaken to investigate the distortional buckling behaviour of simply supported compact steel I-beams subjected to uniformly distributed load. For this purpose, a finite-element model was developed using ABAQUS. It was then used in a parametric study to simulate the distortional buckling behaviour and capacity of half-through girders, and investigate the effect of cross-section geometry and yield strengths in a RDB mode on the buckling moments of doubly-symmetric steel I-beams. Then a new formula based on the regression analyses has been proposed to predict the member moment capacities of steel I-beams subjected to RDB. The results indicate that the proposed...

Influence of spacers on ultimate strength of intermediate length thin walled columns

The influence of spacers on the behaviour and ultimate capacity of intermediate length CFS open section columns under axial compression is investigated in this paper. The focus of the research lies in the cross- section predominantly, failed by distortional buckling. This paper made an attempt to either delay or eliminate the distortional buckling mode by the introduction of transverse elements referred herein as spacers. The cross-sections investigated have been selected by performing the elastic buckling analysis using CUFSM software. The test program considered three different columns having slenderness ratios of 35, 50 & 60. The test program consisted of 14 pure axial compression tests under hinged-hinged end condition. Models have been analysed using finite element simulations and the obtained results are compared with the experimental tests. The finite element package ABAQUS has been used to carry out non-linear analyses of the columns. The finite element model incorporates material, geometric non-linearities and initial geometric imperfection of the specimens. The work involves a wide parametric study in the column with spacers of varying depth and number of spacers. The results obtained from the study shows that the depth and number of spacers have significant influence on the behaviour and strength of the columns. Based on the nonlinear regression analysis the design equation is proposed for the selected section.

Behavior and Design of Web-Slotted Cold-Formed Channels Experiencing Local-Distortional-Global Interactive Buckling

This article aims to shed light on the nonlinear local-distortional-global interactive behavior of web-slotted channel columns by use of the finite element method. The effects of three kinds of initial geometric imperfection based on different distortional buckling mode were evaluated. It indicates that different distortional buckling mode does little difference on the nonlinear interactive buckling behavior of web-slotted channels. Based on the extensive parametric study, some modifications were made to the traditional Effective Width Method for the practical design of web-slotted channel columns undergoing local-distortional-global interactive buckling.

Numerical modelling and design of LiteSteel Beams subject to lateral buckling

The LiteSteel Beam (LSB) is a new hollow flange channel section developed using a patented dual electric resistance welding and cold-forming process. It has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a slender web, and is commonly used as flexural members. However, the LSB flexural members are subjected to a relatively new lateral distortional buckling mode, which reduces their moment capacities. Unlike lateral torsional buckling, the lateral distortional buckling of LSBs is characterised by simultaneous lateral deflection, twist and cross sectional change due to web distortion. Therefore a detailed investigation into the lateral buckling behaviour of LSB flexural members was undertaken using experiments and finite element analyses. This paper presents the details of suitable finite element models developed to simulate the behaviour and capacity of LSB flexural members subject to lateral buckling. The models included all significant effects that influence the ultimate moment capacities of such members, including material inelasticity, lateral distortional buckling deformations, web distortion, residual stresses, and geometric imperfections. Comparison of elastic buckling and ultimate moment capacity results with predictions from other numerical analyses and available buckling moment equations, and experimental results showed that the developed finite element models accurately predict the behaviour and moment capacities of LSBs. The validated model was then used in a detailed parametric study that produced accurate moment capacity data for all the LSB sections and improved design rules for LSB flexural members subject to lateral distortional buckling.

A numerical and analytical study on distortional buckling of doubly-symmetric steel I-beams

This study investigates the effect of web distortions in a lateral distortional buckling mode on the buckling moments of doubly-symmetric steel I-beams. Analytical buckling moment expressions applicable to both elastic and inelastic lateral distortional buckling were developed. These expressions account for the reductions in the torsional and warping rigidities of I-beams due to web distortions. Numerical results obtained from the finite element analysis showed that the buckling moments of steel I-beams with stocky flanges and slender webs are overestimated by the lateral torsional buckling solutions while the proposed distortional buckling solutions provide estimates in closer agreement with the numerical results. Finally, the lateral torsional buckling solutions in the structural steel standards were found to generally provide conservative buckling moment estimates for doubly-symmetric steel I-beams prone to web distortions.

Determination of Critical Distortional Buckling Load for Thin-Walled C Steel Section

The differential equations about distortional buckling are established according to the distortional buckling mode of cold-formed thin-walled C steel on the lateral and vertical loads. The formula of critical moment is obtained according to the differential equations of bending. This formula can calculate the critical moment if the properties of the section of C steel are given.

Elastic lateral stability of I-shaped cellular steel beams

In this paper, the lateral stability of cellular steel beams is numerically investigated. The study is carried out using three-dimensional finite element modeling of simply supported I-shaped cellular steel beams with a broad spectrum of cross-sectional dimensions, span lengths and web perforation configurations. Stability analyses are carried out for beams subjected to equal end moments, mid-span concentrated loads and uniformly distributed loads. Finite element results reveal that, unlike the case of conventional beams with solid webs, the moment-gradient coefficient C b is significantly influenced by the beam geometry and slenderness. In addition, the C b coefficient of cellular beams depends on the web perforation configuration. Moment-gradient coefficient values that fluctuate closely to those values recommended by design codes are associated with pure elastic lateral torsional buckling (LTB) deformations. As the beam slenderness decreases, the web distortion increases, leading to the lateral distortional buckling (LDB) mode, which is associated with lower C b values than code-recommended ones. Severe reduction in the C b coefficient to values less than 1.1 is noticed for shorter-span beams where the response is dominated by non-lateral local buckling modes. A simplified approach is developed to enable accurate prediction of a moment modification factor κ L B for cellular beams. The proposed κ L B factor is provided by an empirical formula that is derived based on the best fit of the finite element results related to lateral buckling (LTB and LDB) modes only. The proposed approach allows for accurate and conservative evaluation of the critical moment associated with the lateral torsional/distortional buckling of cellular beams. Several numerical examples are worked out to illustrate the application of the proposed procedure.

Distortional Buckling of Cold-Formed Steel Shear Wall Studs under Uplift Force

A cold-formed steel framed shear wall may fail in shear buckling of the sheathing, local buckling or distortional buckling of the framing member under compression forces or connection failures. An unusual distortional buckling mode on boundary studs under uplift forces was recently observed in a shear wall test program conducted at the University of North Texas. It was found in monotonic pushover shear wall tests that the flanges of the boundary studs undertaking uplift forces were distorted at the bottom area of the studs near the hold-down. This paper presents the test program and analysis of the unique distortional buckling mode. The paper also provides procedures for predicting the distortional buckling strength of the boundary studs, as well as the construction details to mitigate the damage by this unexpected distortional buckling mode.

Distortional Buckling of Cold‐Formed Steel Shear Wall Studs under Uplift Force

A cold-formed steel framed shear wall may fail in shear buckling of the sheathing, local buckling or distortional buckling of the framing member under compression forces or connection failures. An unusual distortional buckling mode on boundary studs under uplift forces was recently observed in a shear wall test program conducted at the University of North Texas. It was found in monotonic pushover shear wall tests that the flanges of the boundary studs undertaking uplift forces were distorted at the bottom area of the studs near the hold-down. This paper presents the test program and analysis of the unique distortional buckling mode. The paper also provides procedures for predicting the distortional buckling strength of the boundary studs, as well as the construction details to mitigate the damage by this unexpected distortional buckling mode.

Design of uniformly compressed edge-stiffened flanges and sections that contain them

Recent developments in the section approach to the design of cold-formed steel structures have led to design rules that address sections with edge-stiffened flanges, where the edge stiffeners give rise to the distortional buckling mode. However, the element approach to design (effective width method) remains unable to deal with this mode of buckling, and has been shown to routinely provide unconservative design capacities for such sections. This paper provides design rules for edge-stiffened elements that may be used in conjunction with the existing element approach in specifications, in order to determine the capacity of sections with edge-stiffened flanges in compression. The design rules are developed from an extensive analysis of the fundamental behaviour of plates simply supported on three sides with the remaining (longitudinal) edge stiffened with an edge stiffener. When used in conjunction with the effective width method they are shown to provide excellent agreement with tests of sections that contain edge-stiffened flanges in compression, thus removing the unconservatism in current specifications.

Experimental Study of Complex High-Strength Cold-Formed Cross-Shaped Steel Section

This paper describes the design and experimental investigation of a series of compressive tests on a stiffened cross-shaped section fabricated from cold-formed high-strength steel of 0.42 mm thickness and nominal yield stress of 550 MPa. The complex shape has been chosen so that it has a local buckling mode, two distinct distortional buckling modes, and a flexural-torsional mode. The first distortional buckling mode has a shorter buckle half wavelength and hence is classified as a short half-wavelength distortional buckling mode, while the other distortional mode has a much longer buckle half-wavelength and is classified as a long half-wavelength distortional buckling mode. The compression tests were carried out in a 300 kN capacity SINTEC testing machine over a range of lengths with fixed-ended conditions. The varying lengths were chosen so as to observe the buckling modes and the possibility of interaction between them. The experimental results are then compared with design methods in the existing design standards. The methods include the direct strength method (DSM) recently incorporated in the North American specification and the Australian Cold-Formed Steel Structures Standard AS/NZS 4600. When compared to the existing methods, the test results indicate that at intermediate and longer specimen lengths, the interaction of local and distortional buckling modes has a significant effect on the strength of the section. This paper presents the procedures taken to design the complex shape and the experiments carried out to obtain the geometric imperfections and material properties of the specimens and the test results. New design methods are proposed for the local buckling DSM curve as well as for the distortional buckling strength curves so as to account for the effects of interaction of local and distortional buckling modes.

Behavior of Complex Hat Shapes Used as Truss Chord Members

Cold-formed steel roof truss systems that use complex hat shape members for both top and bottom chord elements are a growing trend in the North America steel framing industry. When designing cold-formed steel sections, a structural engineer typically tries to improve the local buckling behavior of the cold-formed steel elements. The complex hat shape has proven to limit the negative influence of local buckling. However, a distortional buckling mode can be the control mode of failure in the design for the chord member with an intermediate unbraced length. The chord member may be subjected to both bending and compressive load because of the continuity of the top and bottom chord members. These members are not typically braced between each panel point in a truss. Numerical analyses using finite strip and finite element procedures were developed to compare with experimental results. A parametric study on geometric imperfection was also conducted to investigate the factors that affect the ultimate strength behavior of a particular complex hat shape. Better understanding of the flexural behavior of these complex hat shapes is necessary to obtain efficient, safe designs of a truss system. The results of these analyses will be presented in the paper.

Distortional Buckling Tests on Cold-Formed Steel Beams

Failure in cold-formed steel beams is generally initiated by one of three instabilities: local, distortional, or lateral-torsional buckling. For cold-formed steel joists, purlins, or girts, when the compression flange is not restrained by attachment to sheathing or paneling, distortional buckling may be the predominant failure mode. Experimental results on cold-formed steel beams with unrestrained compression flanges are scarce. Therefore a series of distortional buckling tests on cold-formed steel C and Z sections in bending was conducted to establish the capacity in distortional buckling failures. Test details were selected to allow distortional buckling to form, but restrict lateral-torsional buckling to the extent possible. These distortional buckling tests also provide a direct comparison against the local buckling tests previously performed by the writers. As expected, large strength reductions are observed in the tested specimens when distortional buckling initiated the failure instead of local buckling. U.S., Canadian, and joint North American standards for design, which are known to primarily focus on local buckling, provided unconservative predictions of the observed strength. The Australian/New Zealand Standard and the direct strength method, which provide explicit methods for calculating the capacity in the distortional buckling mode, provided reasonably accurate and reliable predictions.

Distortional Buckling of Cold-Formed Stainless Steel Sections: Finite-Element Modeling and Design

A recent experimental and finite-element research program was conducted on the distortional buckling of axially compressed, cold-formed stainless steel simple lipped channels. Austenitic 304 (1.4301), ferritic 430 (1.4016), and ferritic-like 3Cr12 (1.4003) chromium weldable steel were considered. Finite-element analyses demonstrate that material anisotropy can be ignored. A total of 281 distortional buckling analyses of simple lipped channels with r∕t ratios of 1 and 2.5 show that enhanced corner properties may be important for sections which have a slenderness λd<1.0 and at least 10% corner area but have little effect on sections with λd>1.0. Evaluation of current stainless steel design codes show that the Australian/New Zealand Standard AS/NZS 4673 and the ASCE Specification effective width procedures are unconservative for austenitic and ferritic stainless steels. The Eurocode 3 prEN Part 1-4/preEN Part 1-3 effective width procedures are unconservative for austenitic stainless steel but provide reasonably conservative results for ferritic 430 and 3Cr12 alloys, provided enhanced corner properties are ignored. Direct strength design guidelines for the distortional buckling mode are proposed for austenitic and ferritic stainless steels.

Distortional Buckling of Cold-Formed Stainless Steel Sections: Experimental Investigation

This paper describes the experimental investigation of cold-formed, thin-walled stainless steel sections subject to distortional buckling under compression. Austenitic 304, ferritic 430 stainless steel, and ferritic-like 3Cr12 chromium weldable steel sheets were brake-pressed into simple-lipped channels and lipped channels with intermediate stiffeners. A full set of coupon tests reveal material nonlinearity with low proportionality stress and low n-parameter, anisotropy, and yield strength enhancements up to 2.33 times due to cold-forming. A total of 19 channel sections were tested and failed by distortional buckling at average ultimate stresses greater than the proportionality stress, and hence were influenced by material nonlinearity, with greater nonlinearity evident for sections with intermediate stiffeners. This paper presents comprehensive procedures to determine stainless steel mechanical properties and their influence on the distortional buckling mode of cold-formed sections. Experimental data required to calibrate finite element models and assess current design guidelines for distortional buckling of stainless steel compression members are provided herein.

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.

Local Buckling Tests on Cold-Formed Steel Beams

\iC and \iZ sections are two of the most common cold-formed steel shapes in use today. Accurate prediction of the bending performance of these sections is important for reliable and efficient cold-formed steel structures. Recent analytical work has highlighted discontinuities and inconsistencies in the American Iron and Steel Institute (AISI) and Canadian Standards Association (S136) design provisions for stiffened elements under a stress gradient (i.e., the web of \iC or \iZ sections). New methods have been proposed for design, and an interim method has been adopted in the North American Specification (NAS). However, existing tests on \iC and \iZ sections do not provide a definitive evaluation of the design expressions, due primarily to incomplete restriction of the distortional buckling mode. Described in this paper is a series of flexural tests with details selected specifically to insure that local buckling is free to form, but distortional buckling and lateral-torsional buckling are restricted. The members selected for the tests provide systematic variation in the web slenderness (\Ih/t\N) while varying other relevant nondimensional parameters (i.e., \Ih/b, b/t, d/t, d/b\N). Initial analysis of the completed testing indicates that overall test-to-predicted ratios for AISI, S136, NAS, and the direct strength method are all adequate, but systematic differences are observed.