冷弯型钢C形截面受弯构件平面内稳定性能研究

为了研究冷弯型钢受弯构件平面内的稳定性能,对直卷边和斜卷边的冷弯型钢C形截面受弯构件分别进行了试验研究和有限元参数分析。试验研究和有限元分析均包含构件纯弯和非纯弯两部分。研究结果表明,多数构件在非纯弯作用下的抗弯承载力高于纯弯作用下的,但也有部分以局部和畸变相关屈曲为主的构件在纯弯作用下的抗弯承载力略高。屈曲模式是影响构件抗弯承载力的重要因素,构件以畸变屈曲为主时,非纯弯作用下的抗弯承载力明显高于纯弯作用下的。     

冷弯薄壁型钢C形截面构件受弯承载力试验研究

为了研究冷弯薄壁型钢构件的受弯性能,对卷边形式为直卷边、斜卷边和复杂卷边的冷弯薄壁型钢C形截面受弯构件进行了试验研究。共计24个试件,分为12组试验,其中纯弯试验和非纯弯试验各6组。试验结果表明,卷边形式是影响构件受弯承载力的重要因素。试验中出现了局部屈曲、畸变屈曲以及局部和畸变的相关屈曲。对比两种受弯状态下的承载力发现,非纯弯时试件的承载力比纯弯时均有所提高,但提高的幅度和试件的屈曲模式有关,当发生畸变屈曲时提高得较多,而发生局部屈曲时提高得较少。利用有限元程序ANSYS对试验进行模拟,模拟结果与试验结果吻合较好。     

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.     

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.     

Experimental and numerical investigation of cold-formed lean duplex stainless steel flexural members

Experimental and numerical investigation of cold-formed lean duplex stainless steel flexural members is presented in this paper. The test specimens were cold-rolled from flat plates of lean duplex stainless steel with the nominal 0.2% proof stress of 450 MPa. Specimens of square and rectangular hollow sections subjected to both major and minor axes bending were tested. A finite element model has been created and verified against the test results using the material properties obtained from coupon tests. It is shown that the model can accurately predict the behaviour of lean duplex stainless steel flexural members. An extensive parametric study was carried out using the verified finite element model. The test and numerical results as well as the available data on lean duplex beams are compared with design strengths predicted by various existing design rules, such as the American Specification, Australian/New Zealand Standard, European Code and direct strength method for cold-formed stainless steel. Reliability analysis was performed to evaluate the reliability of the design rules. It is shown that these current design rules provide conservative predictions to the design strengths of lean duplex stainless steel flexural members. In this study, modified design rules on the American Specification, Australian/New Zealand Standard, European Code and direct strength method are proposed, which are shown to improve the accuracy of these design rules in a reliable manner.     

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.     

带加劲冷弯薄壁型钢C形受弯构件有限元分析

采用有限元程序ANSYS,对带加劲肋的冷弯薄壁型钢C形截面受弯构件在纯弯和非纯弯两种受弯状态下的力学性能进行了有限元分析,分析结果表明:构件的卷边宽度是影响试件屈曲模式的重要因素,不同的屈曲模式在纯弯与非纯弯的条件下对极限承载力的影响不尽相同。     

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.     

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.     

冷弯薄壁复杂卷边槽钢受弯构件稳定性能分析

采用有限元软件ANSYS对3种加劲形式冷弯薄壁复杂卷边槽钢受弯构件的稳定性能进行了非线性分析,结果表明:加劲形式是影响构件屈曲模式和抗弯承载力的重要因素,构件在非纯弯状态下的抗弯承载力均大于纯弯状态下的抗弯承载力。     

Effect of imperfections on numerical simulation of instability behaviour of cold-formed steel members

The paper analyses the influence of imperfections on the behaviour of cold-formed steel members. Special attention is paid on the characterisation and codification of imperfections for non-linear FEM simulation. Based on the ECBL approach [2] and using an advanced non-linear inelastic analysis, the erosion of theoretical buckling strength, due to geometrical imperfections, in single and coupled instability modes is evaluated.     

Load-carrying capacities of cold-formed steel cut stub columns with lipped C-section

Cutting roll-formed steel lipped C-sections may produce different extent of cross section distortion along the lengths of the sections and may lead to additional initial geometric imperfections. Ten stub columns cut from two different sections were tested under axial compression. Flanges of the stub columns experienced distortional mode of failure, whereas the webs showed signs of local buckling failures. Ultimate compressive strengths obtained from the test results were 75–77% of the strengths estimated based on BS5950:Part 5. This indicates that geometric imperfections caused by cutting may significantly reduce the ultimate strength of stub columns.     

G550高强冷弯薄壁槽钢受弯构件力学性能与设计方法

为了研究高强冷弯薄壁槽钢受弯构件的力学性能和设计方法,对3种板件加劲形式的G550高强冷弯薄壁型钢槽形截面受弯构件进行了试验研究和有限元参数分析。结果表明,板件加劲形式对高强冷弯薄壁槽钢受弯构件屈曲模式和受弯承载力有显著影响,翼缘V形加劲比腹板V形加劲能够更有效地提高构件抗弯承载力,构件抗弯承载力的变化规律与屈曲模式有关。根据有限元参数分析结果,在已有直接强度法基础上回归出适用于高强冷弯薄壁槽钢受弯构件的直接强度法修正公式。     

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.     

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.     

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.     

Simplified design approach for cold-formed stainless steel compression members subjected to flexural buckling

The design criteria of stainless steel compression member are more complicated than those of carbon steels due to the nonlinear stress strain behavior of the material. In general, the tangent modulus theory is used for the design of cold-formed stainless steel columns. The modified Ramberg–Osgood equation given in the ASCE Standard can be used to determine the tangent modulus at specified level of stresses. However, it is often tedious and time-consuming to determine the column buckling stress because several iterations are usually needed in the calculation. This paper presents new formulations to simplify the determination of flexural buckling stress without iterative process. Taylor series expansion theory is utilized in the study for numerical approximations. The proposed design formulas are presented herein and can be alternatively used to calculate the flexural buckling stress for austenitic type of cold-formed stainless steel columns. It is shown that the column strengths determined by using the proposed design formulas have good agreement with those calculated by using the ASCE Standard Specification. A design example is also included in the paper for cold-formed stainless steel column designed by using the ASCE Standard equations and the proposed design formulas.     

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 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.     

Distortional buckling tests of cold-formed steel compression members at elevated temperatures

In recent times, light gauge cold-formed steel sections have been used extensively since they have a very high strength to weight ratio compared with thicker hot-rolled steel sections. However, they are susceptible to various buckling modes including a distortional mode and hence show complex behaviour under fire conditions. Therefore, a research project based on detailed experimental studies was undertaken to investigate the distortional buckling behaviour of light gauge cold-formed steel compression members under simulated fire conditions. More than 150 axial compression tests were undertaken at uniform ambient and elevated temperatures. Two types of cross sections were selected with nominal thicknesses of 0.60, 0.80, and 0.95 mm. Both low (G250) and high (G550) strength steels were used. Distortional buckling tests were conducted at six different temperatures in the range of 20-800 ^°C. The ultimate loads of compression members subject to distortional buckling were then used to review the adequacy of the current design rules at ambient and elevated temperatures. This paper presents the details of this experimental study and the results.