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.     

Application of direct strength method to axially loaded perforated cold-formed steel studs: Distortional and local buckling

A study to develop methods of analyzing perforated, axially loaded, cold-formed steel studs using the provisions of the Direct Strength Method [American Iron and Steel Institute (AISI). North American Specification for the Design of Cold-Formed Steel Structural Members 2001 Edition with Supplement 2004 (AISI/COFS/NASPEC 2004) and Commentary (AISI/COFS/NASPEC 2004), Washington, DC; 2004] was undertaken using the Finite Strip Method as the method for determining the elastic buckling stresses. Several different models were developed to represent the effect of the web perforations. The capacities predicted using the Direct Strength Method for the limit states of distortional and local buckling were compared to capacities calculated using the equations contained in the AISI Specification [American Iron and Steel Institute (AISI). North American Specification for the Design of Cold-Formed Steel Structural Members 2001 Edition with Supplement 2004 (AISI/COFS/NASPEC 2004) and Commentary (AISI/COFS/NASPEC 2004), Washington, DC; 2004]. The limit state of longwave buckling is considered in a companion paper [Sputo T, Tovar J. Application of direct strength method to axially loaded perforated cold-formed steel studs: Part 1. Longwave buckling. Thin Walled Struct, submitted for publication]. The validity of the results is discussed and recommendations are made for the use of the Direct Strength Method for these members.     

Compression tests of high strength cold-formed steel channels with buckling interaction

This paper describes a series of compression tests conducted on cold-formed simple lipped channels and lipped channels with intermediate stiffeners in the flanges and web fabricated from high strength steel plate of thickness 0.6 and 0.8 mm with the nominal yield stress 560 MPa. A range of lengths of lipped channel sections were tested to failure with both ends of the column fixed with a special capping to prevent local failure of column ends and influence from the shift of centroid during testing. The high strength cold-formed steel channel sections of intermediate lengths generally displayed a significant interaction between local and distortional buckling. A noticeable interaction between local and overall buckling was also observed for the long columns. A significant post-buckling strength reserve was shown for those sections that showed interaction between local and distortional or overall buckling. Simple design strength formulas in the Direct Strength Method for the thin-walled cold-formed steel sections failing in the mixed mode of local and distortional buckling have been studied. The strengths predicted by the strength formulas proposed are compared with the test results for verification.     

Application of direct strength method to axially loaded perforated cold-formed steel studs: Longwave buckling

A study to develop methods of analyzing perforated, axially loaded, cold-formed steel studs using the provisions of the Direct Strength Method [3] was undertaken using the Finite Strip Method as the method for determining the elastic buckling stresses. Several different models were developed to represent the effect of the web perforations. The capacities predicted using the Direct Strength Method for the limit state of longwave buckling were compared to capacities calculated using the equations contained in the AISI Specification [3]. The limit states of local and distortional buckling are considered in a companion paper [12]. The validity of the results is discussed and recommendations are made for the use of the Direct Strength Method for these members.     

Genetic programming-based formulation for distortional buckling stress of cold-formed steel members

The main purpose of the research is to develop formulations for estimating the Elastic distortional buckling stress (EDBS) of cold-formed steel member under compressive loading using Genetic programming (GP) which has not been applied so far. The required data used for the training and testing is collected from the literature. Two GP-based formulations are proposed to predict the elastic distortional buckling of cold formed steel C sections. The results of proposed GP formulations are compared with experimental and analytical results of different researchers and methods and found to be accurate. The results obtained from the formulas have shown that GP is a promising technique for predicting EDBS of cold-formed steel C sections.     

Effective Width Method for determining distortional buckling strength of cold-formed steel flexural C and Z sections

This paper proposes a design method, based on the Effective Width Method, for determining the nominal distortional buckling strength of typical cold-formed steel C and Z sections subjected to bending. The method can be integrated into the classic effective width design provisions specified in AISI S100, and it allows the conventional design approach to cover more comprehensive limit states. The proposed method is calibrated by the flexural distortional buckling strength predicted by the Direct Strength Method. Comparison with experimental results indicates that the proposed method yields reasonable predictions for the flexural distortional buckling strength of industrial standard C and Z sections. The method offers the same level of accuracy and reliability as the Direct Strength Method.     

A parametric study for distortional buckling stress on cold-formed steel using a neural network

The process of prediction of distortional buckling stress of cold-formed steel members is often cumbersome and it is also difficult to perform parametric studies in this field to investigate the effect of geometric parameters on Elastic Distortional Buckling Stress (EDBS). To overcome this difficulty a neural network based model and formulation which was presented in a companion paper by the author [Pala M. A new formulation for distortional buckling stress in cold formed steel members. Journal of Constructional Steel Research 2006;62:716-22] is proposed as an alternative approach to investigate the effect of geometric parameters on distortional buckling stress. The model considers the effect of web height, flange width, angle of lip, lip length and flange thickness. The results of the Neural Network model are quite satisfactory and are consistent with the literature.     

Strength design curves and an effective width formula for cold-formed steel columns with distortional buckling

Distortional buckling mode of cold-formed steel thin-walled member is an unstable behavior, and in some cases it may govern the load-carrying capacity of the member. The source, evolution and performance of the formulas and test data for the two strength design curves developed by Hancock are studied, for predicting the load-carrying capacity in the distortional mode. A proposed strength design curve based on available test data and Hancock׳s strength design curves are then compared with the current design methods, the Direct Strength Method and the Effective Width Method, which are incorporated in the “North American specification for the design of cold-formed steel structural members” (AISI-NAS: 2007), “cold-formed steel structures” (AS/NAS 4600: 2005), and the Chinese “Technical specification for low-rise cold-formed thin-walled steel buildings” (JGJ 227-2011). The results indicate that the current design standards adopted the two strength design curves for the DSM and EWM, but they have some differences at the partial extent. A novel formula is proposed for dealing with this problem. The range of applicability of the proposed strength equation is extended from that in AS/NZS 4600 and is shown to be more accurate than AS/NZS 4600 when compared with that in the NAS S100.     

A new formulation for distortional buckling stress in cold-formed steel members

Distortional buckling of compression members usually comprises rotation and translation of each flange and lip about the flange-web connection in opposite directions. The present procedures for the calculation of elastic distortional buckling stress in the literature are very complex, cumbersome and have long expressions. In this paper a new neural network (NN) based formula is proposed for the determination of the elastic distortional buckling stress of cold-formed steel C-sections with both end sections pinned. The focus of this study is on the distortional buckling, for which existing results are for sections subjected to pure compression and/or pure bending only. The data used for training and testing NNs is taken from Schafer’s report. The NN-based estimates are compared with the experimental, numerical and analytical results of different researchers and methods. It was found that the proposed NN based-formula is practical in predicting the elastic distortional buckling stress of cold formed steel C-sections.     

Coupled instabilities with distortional buckling in cold-formed steel lipped channel columns

The paper addresses the elastic post-buckling behaviours of cold-formed steel lipped channel simply supported columns affected by mode interaction phenomena involving distortional buckling, namely local/distortional, distortional/global (flexural-torsional) and local/distortional/global mode interaction. The results presented were obtained by means of Abaqus shell finite element analyses adopting column discretisations into fine 4-node element meshes. In order to enable a thorough assessment of all possible mode interaction effects, the column lengths and cross-section dimensions were carefully selected to ensure similar local, distortional and/or global buckling loads. One analyses otherwise identical (elastic) columns having initial geometrical imperfections (i) with various configurations (combinations of the competing critical buckling mode shapes) and (ii) sharing the same overall amplitude.     

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.     

The direct strength method for stainless steel compression members

The paper presents a complete set of direct strength equations for stainless steel members and sections in compression. The direct strength equations are based on recent research on the local, distortional and member bucking of stainless steel compression members, including the interaction of local and member buckling. The paper summarises the underlying research and presents the direct strength equations in a consistent format using a notation similar to that used in the North American Specification and the Australian Standard for (carbon) steel structures. Direct strength equations are proposed for local, distortional and combined local and member buckling, which fit within the framework of the Australian, North-American and European standards for stainless steel.     

Multiobjective optimization of cold-formed steel columns

The optimal design of cold-formed steel columns is addressed in this paper, with two objectives: maximize the local-global buckling strength and maximize the distortional buckling strength. The design variables of the problem are the angles of orientation of cross-section wall elements—the thickness and width of the steel sheet that forms the cross-section are fixed. The elastic local, distortional and global buckling loads are determined using Finite Strip Method (CUFSM) and the strength of cold-formed steel columns (with given length) is calculated using the Direct Strength Method (DSM). The bi-objective optimization problem is solved using the Direct MultiSearch (DMS) method, which does not use any derivatives of the objective functions. Trade-off Pareto optimal fronts are obtained separately for symmetric and anti-symmetric cross-section shapes. The results are analyzed and further discussed, and some interesting conclusions about the individual strengths (local-global and distortional) are found.     

Study on distortional buckling performance of cold-formed thin-walled steel flexural Members with stiffeners in the flange

This paper presents a finite strip program CUFSM used to calculate and analyze the elastic distortional buckling of cold-formed thin-walled steel flexural members with stiffeners in the flange, which has different sectional geometric parameters. According to the classical buckling stress formula, the distortional buckling coefficient of the flange can be calculated so as to analyze the influence of changed sectional geometric parameters on it. On this basis, this study provides a simplified formula of distortional buckling stress to calculate 40 members with different sections which are selected from the Technical Code of Cold-Formed Thin-Wall Steel Structures of China but not contained in this paper. Compared with the analysis results of CUFSM, it shows that the two simplified formulas have quite high accuracy and wide applicability for general members provided by the specification. So it is suggested that they can be used for engineering design and standard revision.     

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.     

Distortional buckling formulae for cold-formed steel C- and Z-section members: Part II—Validation and application

General GBT-based fully analytical formulae have been derived in a companion paper, which provides distortional bifurcation stress estimates in cold-formed steel C- and Z-section members acted by arbitrary applied stress distributions and displaying four end support conditions. This paper (i) addresses the implementation of the above general formulae, (ii) illustrates their application in detail, (iii) validates them, by means of comparisons with exact results, and (iv) compares their estimates with values yielded by other formulae available in the literature. After considering a wide range of (i) cross-section geometries and lengths and (ii) applied stress distributions, it is concluded that the GBT-based formulae are both accurate and universal.     

Buckling analysis of thin-walled cold-formed steel structural members using complex finite strip method

In this paper, a generalised complex finite strip method is proposed for buckling analysis of thin-walled cold-formed steel structures. The main advantage of this method over the ordinary finite strip method is that it can handle the shear effects due to the use of complex functions. In addition, distortional buckling as well as all other buckling modes of cold-formed steel sections like local and global modes can be investigated by the suggested complex finite strip method. A combination of general loading including bending, compression, shear and transverse compression forces is considered in the analytical model. For validation purposes, the results are compared with those obtained by the Generalized Beam Theory analysis. In order to illustrate the capabilities of complex finite strip method in modelling the buckling behavior of cold-formed steel structures, a number of case studies with different applications are presented. The studies are on both stiffened and unstiffened cold-formed steel members.     

Analyses of distortional buckling of cold-formed sigma purlins using EN1993-1-3

This technical note presents a study on the calculation of the critical stress of distortional buckling of cold-formed sigma purlins using EN1993-1-3. The discussion is focussed on the determination of the spring stiffness of the stiffened element, a problem which has not yet been addressed in most design codes. Different support conditions at both the tension and compression ends of the web are employed and their influences on the critical stress of distortional buckling of sigma purlins are investigated. Comparison with finite strip analysis indicates that the model having a fixed support for the tension end and a roller support for the compression end of the web provides the best fit to the finite strip analysis.     

Strength and behaviour of cold-formed steel offset trusses

Thirteen full-scale truss specimens fabricated with cold-formed steel C-sections were tested to study various practical strengthening techniques in order to achieve a desired behaviour and an increased capacity. Specimens were subjected to concentrated panel point loading simulating the realistic loading condition of a roof truss. Results revealed that local buckling of the top chord (LBTC) adjacent to the heel plate was the predominant failure mechanism. In instances where the heel plate was not adequately stiffened, the distortion or crippling of the plate occurred at failure. For the investigated pitches, an increase in specimen pitch resulted in an increase in the capacity. Strengthening both the top chord adjacent to the heel plate and the heel connection with both a shallow member and a heel plate stiffener resulted in the most significant increase in the capacity compared with the original truss configuration. Beam-column analysis of the top chords in the failure region was performed using both the conventional interaction design equations and the direct strength method as suggested in CSA S136-07.     

Experimental and numerical investigation on cold-formed steel C-section flexural members

This paper presents an experimental and numerical investigation on the bending strength and behavior of cold-formed steel C-section flexural members with upright, inclined and complex edge stiffeners. A total of 24 specimens that divided into 12 tests including 6 pure bending tests and 6 non-pure bending tests have been conducted. Local buckling, distortional buckling and interaction between local and distortional buckling were observed in the tests. The experimental results show that the edge stiffener and buckling mode have great influence on member’s bending strength. Comparison of the bending strengths under the two bending states show that the bending strength under non-pure bending is higher than which under pure bending, but the increased magnitude is related to the buckling modes. Moment gradient effect has only a minor influence on local buckling, but has great influence on distortional buckling. The tests were simulated by finite element program of ANSYS and the simulated results show good agreement with the experimental results in terms of bending strength and buckling mode.