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.     

局部屈曲或局部和畸变屈曲综合作用下冷弯型钢梁的有限元模拟

有限元法可以解决冷弯钢梁复杂的相关联屈曲问题,其中包括很多重要的关键因素:几何缺陷、材料非线性和后屈曲等。也是该方法与其他分析方法的不同之处。根据特定的冷弯Z型钢梁的材料和几何非线性建立了两类研究屈曲性能的有限元模型。其中,一个模型用于分析局部和畸变屈曲综合作用,而另一个仅用于分析局部屈曲。通过先前的四点弯曲试验证实了有限元模型的有效性。利用ABAQUS软件,模拟了一个简化的试验装置。在局部屈曲有限元模型中,通过在梁翼缘角部设置弹簧以防止畸变屈曲。由于更多的模型与试验结果相吻合,证实了对承载力和变形的预测。未来的研究将优化有限元模型,以得到侧向受约束的冷弯型钢梁不同的屈曲形式,如:局部,畸变或局部与畸变综合作用。     

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.     

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.     

卷边加强冷弯型钢梁局部和畸变屈曲

设计时,应重点考虑冷弯型钢构件的屈曲特性及其导致的有效性损失,以保证结构的经济性。数值模型改进后,能够反映考虑几何缺陷、材料非线性特性、后屈曲性能等因素的冷弯型钢梁的真实屈曲特性。针对侧向约束下冷成型Z型钢梁,采用已有的有限元模型,研究钢梁卷边及其与受压翼缘的相互作用对后屈曲特性的影响。利用卷边翼缘宽度比以及卷边倾角,观测局部屈曲、畸变屈曲和局部/畸变屈曲相互作用下截面抗弯刚度的变化。评估了EC3中适用于冷成型Z型钢梁局部和畸变屈曲的设计方法的有效性。总体而言,采用EC3计算的截面抗弯刚度并不保守。指出其中的不足并提出改进建议,改善卷边受压翼缘的失稳系数。     

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.     

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.     

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.     

受压翼缘外带卷边和中间加劲肋的冷弯型钢梁的局部和扭转屈曲特性

采用数值模型分析受压翼缘含卷边和中间加劲肋的冷弯型钢梁的屈曲特性。通过一系列非线性有限元分析,研究了由局部或扭转屈曲导致失稳的两侧翼缘处均含卷边和中间加劲肋的冷弯Z型钢的弯曲性能。研究了中间加劲肋的尺寸和位置以及卷边加劲肋和中间加劲肋的相互作用对型材的屈曲特性和极限强度的影响。有限元分析结果常可用来检验用欧洲设计规范在预测这类断面极限强度时的精确度。     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Bending strength of hybrid cold-formed steel beams

For the purpose of determining the load-carrying capacity of cold-formed steel structural members, the effective width approach has been used. Since most studies were limited only to the structural members, which were assembled from the same material in a given section, this investigation was concentrated on a study of structural strength and behavior of hybrid cold-formed steel beams subjected dynamic loads. An investigation was also conducted to study the validity of effective design width formulas for the design of these specimens. The materials used in this study were 25 AK and 50 SK sheet steels. A total of 72 spot-welded closed-hat sections were tested under different strain rates. The results showed that the structural strengths including yield moment and ultimate moment of hybrid cold-formed steel beams increase with increasing strain rates. In the determination of the strength of hybrid sections, the effective cross-sectional area calculated on the basis of the dynamic yield stresses can be employed. A design procedure was also developed to compute the member strength of hybrid beams.     

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.     

Design of cold-formed steel unequal angle compression members

Cold-formed steel unequal angles are non-symmetric sections. The design procedure of non-symmetric sections subjected to axial compression load could be quite difficult. The unequal angle columns may fail by different buckling modes, such as local, flexural and flexural–torsional buckling as well as interaction of these buckling modes. The purpose of this study is to investigate the behaviour and design of cold-formed steel unequal angle columns. A nonlinear finite element analysis was conducted to investigate the strength and behaviour of unequal angle columns. The measured initial local and overall geometric imperfections as well as the material properties of the angle specimens were included in the finite element model. The finite element analysis was performed on fixed-ended columns for different lengths ranged from stub to long columns. It is demonstrated that the finite element model closely predicted the experimental ultimate loads and the behaviour of cold-formed steel unequal angle columns. Hence, the model was used for an extensive parametric study of cross-section geometries. The column strengths obtained from the parametric study were compared with the design strengths calculated using the North American Specification for cold-formed steel structural members. It is shown that the current design rules are generally unconservative for short and intermediate column lengths for the unequal angles. Therefore, design rules of cold-formed steel unequal angle columns are proposed.