冷弯薄壁梁的屈曲及优化设计综述

介绍了冷弯薄壁梁的整体-局部屈曲和优化,包括:简化分析与计算、数值分析及试验。详细阐述了薄壁梁翼缘和腹板的屈曲问题。采用质量检测方法,对不同横截面薄壁梁进行比较。     

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.     

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.     

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.     

A unified energy formulation for the stability analysis of open and closed thin-walled members in the framework of the generalized beam theory

Generalized beam theory—GBT—is among the most adequate tools for the analysis of thin-walled prismatic elements. It enables the analysis of the distortion of the element cross-section and local buckling of individual walls in a unified manner that incorporates the results from classical bending theory. The basis of this theory was developed in the 1960s by Schardt for first and second order elastic behaviour of thin-walled members.Open and closed thin-walled members present the distinctive difference of the unknown shear flow that characterizes the latter. More specifically, shear strains must follow an elasticity law, as opposed to the simplifying assumptions for open cross-sections.It is the purpose of the present paper to present a unified energy formulation for the non-linear analysis of both open and closed sections in the framework of GBT, able to deal with all modal interaction phenomena between local plate behaviour, distortional behaviour and the more classical global (flexural, torsional and flexural–torsional) response. Finally, an application to the stability analysis of a compressed thin-walled column is presented and discussed.     

工字型卷边冷弯薄壁梁的屈曲性能试验研究

开口截面的冷弯薄壁钢梁在工业建筑中被广泛应用。这类梁截面的形状使得它们很容易产生局部屈曲。归纳了对卷边工字型梁进行试验的研究结果。梁上作用荷载有弯矩和集中力。此外,还将试验中获得的临界荷载数值与有限元分析和其他理论分析中得到的数据进行了对比。     

Stub column tests of thin-walled complex section with intermediate stiffeners

A series of stub column tests on complex sections with intermediate stiffeners is presented in this paper. Initial geometric imperfections and material properties of the test specimens were measured. It is shown that the intermediate stiffeners could effectively enhance the local buckling stress of thin-walled sections. The test strengths are compared with the design strengths calculated using the direct strength method in the North American Specification and Australian/New Zealand Standard for cold-formed steel structures. It is shown that the direct strength method using finite strip method to obtain the buckling stresses is very conservative. Therefore, finite element method was used to predict the elastic buckling stresses. It is shown that the design strengths calculated using direct strength method based on the buckling stresses obtained from finite element analysis results generally agree with the test results well.     

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.     

Finite strip elastic buckling solutions for thin-walled metal columns with perforation patterns

Approximate finite strip eigen-buckling solutions are introduced for local, distortional, flexural, and flexural-torsional elastic buckling of a thin-walled metal column with perforation patterns. These methods are developed to support a calculation-based strength prediction approach for steel pallet rack columns employing the American Iron and Steel Institute׳s Direct Strength Method, however they are generally posed and could also be useful in structural studies of thin-walled thermal or acoustical members made of steel, aluminum, or other metals. The critical elastic global buckling load including perforations is calculated by reducing the finite strip buckling load of the cross-section without perforations using the weighted average of the net and gross cross-sectional moment of inertia along the length of the member for flexural (Euler) buckling, and for flexural-torsional buckling, using the weighted average of both the torsional warping and St. Venant torsional constants. For local buckling, a Rayleigh–Ritz energy solution leads to a reduced thickness stiffened element equation that simulates the influence of decreased longitudinal and transverse plate bending stiffness caused by perforation patterns. The cross-section with these reduced thicknesses is input into a finite strip analysis program to calculate the critical elastic local buckling load. Local buckling at a perforation is also treated with a net section finite strip analysis. For distortional buckling, a reduced thickness equation is derived for the web of an open cross-section to simulate the reduction in its transverse bending stiffness caused by perforation patterns. The approximate elastic buckling methods are validated with a database of 1282 thin shell finite element eigen-buckling models considering five common pallet rack cross-sections featuring web perforations that include 36 perforation dimension combinations and twelve perforation spacing combinations.     

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.     

Lateral buckling strengths of cold-formed Z-section beams

This paper is concerned with the inelastic lateral buckling strengths of cold-formed Z-section (CFZ) beams. The point symmetry of the cross-section of a CFZ beam introduces characteristics that are not encountered in a doubly symmetric I-beam. Firstly, the effective section rotates after yielding, so that a CFZ beam under in-plane bending about the geometrical major principal axis is subjected to bending moments about the effective minor axis and bimoments. Secondly, the minor axis bending and warping strain distributions and therefore the lateral inelastic buckling behaviour and strengths of CFZ beams are related to the twist rotation and minor axis displacement directions. The stress–strain curves, residual stresses, initial imperfections, and lipped flanges of CFZ beams are all different to those of hot-rolled I-beams. This paper develops a realistic finite element model for the analysis of CFZ beams and uses it to investigate the elastic lateral-distortional buckling, inelastic behaviour, and strengths of CFZ beams with residual stresses and initial imperfections. The results of the study are used to develop improved design rules which are suitable for CFZ beams. The effects of moment distribution and load height on the lateral buckling strengths are also studied.     

Global optimum design of cold-formed steel hat-shape beams

Using the computational neural network model developed recently by the authors, a comprehensive parametric study is performed for global optimization of cold-formed steel hat-shape beams based on the AISI Specifications. Design curves are presented for global optimum values of the thickness, the web-depth-to-thickness ratio, and the flange width-to-thickness ratio for unbraced beams having steel yield strengths of 250 and 345 N/mm². The computational neural network model guarantees a local optimum solution. The global optimum is found by an exhaustive search that is guided by a heuristic approach to reduce the search effort. An extensive parametric study yielded insights into the behavior of cold-formed steel beams that are then used as rules to reduce the search space and guide the exhaustive search. The procedure for finding the global optimum design of cold-formed steel beams is presented in a few recursive steps. The optimum design curves presented in this article can be of great value to structural design engineers.     

Elastic buckling analysis of perforated thin-walled structures by the isoparametric spline finite strip method

This paper presents the application of the isoparametric spline finite strip method to the elastic buckling analysis of perforated folded-plate structures. The general theory of the isoparametric spline finite strip method is introduced. The kinematics assumptions, strain–displacement and constitutive relations of the Mindlin plate theory are described and applied to the spline finite strip method. The corresponding matrix formulation is utilised in the equilibrium and stability equations to derive the stiffness and stability matrices. A number of numerical examples of flat and folded perforated plate structures illustrate the applicability and accuracy of the proposed method.     

On the mechanics of distortion in thin-walled open sections

This paper addresses the distortional kinematics and mechanics of thin-walled sections and provides clear definitions of cross-section properties that characterise the distortional deformation, as it is usually done for conventional modes (axial, bending and torsion). In particular, a procedure to build the distortional displacement field of a given thin-walled section is described. The first part of the paper describes the essentials of distortion in comparison with the conventional modes of classical beam theories. It is shown that primary warping is the key factor that controls the distortion of thin-walled sections. Then, an analytical procedure to determine the distortional warping displacement distribution of a given cross-section is described, on the basis of orthogonality conditions existing between the distortional and conventional modes. Next, an overview of the kinematical assumptions underlying the distortional deformation is presented and a simple procedure to build distortional displacement fields of thin-walled sections is provided. This procedure is then applied to obtain the distortional displacement field of C-sections and general expressions of distortional cross-section properties are given. Finally, a simple example is presented to illustrate how the distortional displacement field of a C-section is built, on the basis of simple kinematics principles. The distortional critical stress and half wavelength are determined and good agreement with exact numerical estimates is found.     

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.     

Optimization of mono- and anti-symmetrical I-sections of cold-formed thin-walled beams

Subject of the study includes mono- and anti-symmetrical open I-sections of cold-formed thin-walled beams with double flanges. The beams under uniformly distributed vertical load are simply supported at both ends. Geometric properties of each of the I-sections are separately described by dimensionless parameters. Strength, global and local buckling conditions are defined for these beams. A dimensionless objective function is assumed and formulated on the grounds of the optimization criterion. Numerical study of a family of thin-walled beams is carried out. Results of the study are presented graphically.     

Mechanics of shear deformable thin-walled beams made of composite materials

In this paper, a new theoretical model is developed for the generalized linear analysis of composite thin-walled beams with open or closed cross-sections. The present model incorporates, in a full form the shear deformability by means of two features. The first one may be addressed as a mechanical aspect where the effect of shear deformability due to both bending and non-uniform warping is considered. The second feature is connected with the constitutive aspects, and it contemplates the use of different hypotheses adopted in the formulation. These topics are treated in a straightforward way by means of the Linearized Principle of Virtual Works. The model is developed by employing a non-linear displacement field, whose rotations are formulated by means of the rule of semitangential transformation. This model allows studying many problems of static's, free vibrations with or without arbitrary initial stresses and linear stability of composite thin-walled beams with general cross-sections. A discussion about the constitutive equations is performed, in order to explain distinctive aspects of the effects included in the theory. This paper presents the theoretical formulation together with finite element procedures that are developed with the aim to obtain solutions to the general equations of thin-walled shear deformable composite beams. A non-locking fourteen-degree-of-freedom finite element is introduced. Numerical examples are carried out in several topics of static's, dynamics and buckling problems, focusing attention in the validation of the theory with respect to experimental data and with 2D and 3D computational approaches. Also, new parametrical studies are performed in order to show the influence of shear flexibility in the mechanics of the thin-walled composite beams as well as to illustrate the usefulness of the model.     

Buckling of a thin-walled cylindrical shell with foam core under axial compression

This paper investigates the effect of partially filled foam core on the behavior of buckling in a thin-walled cylindrical shell. Previous studies have focused on 100% infill or simply used a fixed thickness of foam core. However, this may not be the optimum arrangement in terms of design. To further investigate this, a theoretical analysis is carried out using the Rayleigh–Ritz approximation, and a new formula is proposed to predict the critical buckling stress of an infill ranging from 0% up to 100% rigid. The proposed formula agrees well with works reported in the literature. It also shows that filling a foam core in a thin-walled cylindrical shell can enhance its resistance to buckling failure. Meanwhile, a simplified formula is provided to the practicing engineer. The paper concludes that an excessive increase in foam core thickness beyond 10% of outer radius is inefficient due to extra cost and weight.     

Influence of lateral restraint on lateral-torsional buckling of cold-formed steel purlins

In this paper, the influence of the lateral restraint provided by cladding on the lateral-torsional buckling of zed-purlin beams is investigated in detail. The analysis is performed using the energy method. The influence of the lateral restraint on the critical load is discussed for beams with various different boundary conditions, loading positions, with and without interval anti-sag bars.