Local-plate and Distortional Post-buckling Behavior of Cold-formed Steel Lipped Channel Columns with Intermediate Stiffeners

This paper reports the results of an investigation concerning the local-plate and distortional post-buckling behavior of cold-formed steel lipped channel columns with web and flange intermediate stiffeners. They have all been obtained through geometrically non-linear analyses based on a recently developed and implemented Generalized Beam Theory (GBT) formulation that incorporates (i) conventional (shear undeformable), (ii) shear (non-linear warping) and (iii) transverse extension deformation modes. These results, some of which are compared with values yielded by shell finite element analyses performed in the code ABAQUS (mostly for validation purposes), provide the evolution, along a given local-plate or distortional post-buckling equilibrium path, of the column deformed configuration and relevant displacement profiles and/or stress diagrams. In order to assess the influence of the member end support conditions, one also compares the distortional post-buckling behaviors of columns having pinned/free-to-warp and fixed/warping-prevented end sections. Taking full advantage of the GBT unique modal features, all the above results are discussed in great detail and it becomes possible to unveil, explain and/or shed some new light on several interesting and scarcely known behavioral aspects. In particular, one is able to provide very clear and structurally meaningful explanations for the qualitative differences existing between the local-plate and distortional post-buckling behavior of lipped channel columns with and without intermediate stiffeners

On the Direct Strength Design of Continuous Cold-formed Steel Beams

The work reported in this paper concerns an ongoing investigation aimed at developing an efficient methodology to design continuous cold-formed steel beams failing in modes that combine local, distortional and global features. At this stage, it is intended to assess how accurately can the load-carrying capacity of lipped channel continuous (two and three-span) beams subjected to non-uniform bending be predicted by means of the current Direct Strength Method (DSM) design curves. “Exact” ultimate strength values yielded by geometrically and materially non-linear shell finite element analyses are compared with estimates provided by the DSM equations and, on the basis of this comparison, it is possible to identify some features that must be included in a DSM approach applicable to continuous cold-formed steel beams

GBT-based Distortional Buckling Formulae for Thin-walled Channel Columns and Beams

After a brief outline of the Generalized Beam Theory (GBT) fundamentals and linear stability analysis procedure, the main concepts and steps involved in the derivation of GBT -based fully analytical formulae are described and discussed. Such formulae provide distortional bifurcation stress estimates in cold-formed steel channel columns and beams with arbitrary sloping single-lip edge stiffeners and pinned/free-to-warp or fixed/warping-free end sections. The application of the proposed formulae is illustrated in detail and, in order to assess their accuracy and validity, results concerning several specific channel columns and beams are presented. In particular, the GBT-based analytical estimates are compared with exact numerical results and, whenever possible, also with values yielded by the formulae developed by Lau & Hancock, Hancock and Schafer

Using Generalized Beam Theory (GBT) to Assess the Buckling Behavior of Cold-formed Steel Structural Systems

This paper deals with the application of beam finite element models based on Generalized Beam Theory (GBT) to analyze the buckling behavior of three cold-formed steel structural systems, namely (i) beams belonging to storage rack systems, (ii) portal frames built from rectangular hollow section (RHS) profiles and (iii) roof-supporting trusses, exhibiting different support conditions and subjected to various loadings. In particular, taking advantage of the GBT unique and structurally clarifying modal features, it is possible to assess how different geometries and/or bracing arrangements affect (improve) the local, distortional and/or global buckling behavior of the above structural systems. The accuracy of the GBT-based buckling results is assessed through the comparison with values yielded by rigorous shell finite element analyses carried out in the code ANSYS. In spite of the disparity between the numbers of degrees of freedom involved, which are orders of magnitude apart, there is a virtual coincidence between the critical buckling loads and mode shapes provided by the GBT (beam) and ANSYS (shell) finite element analyses

Using Generalized Beam Theory to Assess the Behavior of Curved Thin-Walled Members

In this work, the first-order behavior of naturally curved thin-walled bars with circular axis, without pre-twist, is assessed with the help of the Generalized Beam Theory (GBT) formulation previously developed by the authors. With respect to the previous work, which dealt with simple cross-sections, the present paper presents a method to obtain the deformation modes for arbitrary flat-walled cross-sections. Despite the complexity involved in this generalization, the standard GBT kinematic assumptions are kept, since they are essential to (i) subdivide the modes in a meaningful way and (ii) reduce the number of DOFs necessary to obtain accurate solutions. It is shown that the curvature of the bar influences significantly the deformation mode shapes. Furthermore, a standard displacement-based finite element (FE) is employed to solve several examples that highlight the peculiar behavior of curved members. For validation and comparison purposes, results obtained using shell FE models are provided. Finally, the superiority of a mixed GBT-based FE format is demonstrated

Proposal for Codification of a DSM Design Approach for Cold-Formed Steel Short-to Intermediate Angle Columns

This paper presents a proposal for the codification of an efficient design approach for cold-formed steel short-to-intermediate equal-leg angle columns, consisting of a slight modification of a design approach developed by Dinis & Camotim (2015) and based on the Direct Strength Method (DSM). After (i) collecting the available experimental and numerical failure load data, comprising fixed-ended and pin-ended columns with several geometries (cross-section dimensions and length) and reported by various researchers, and (ii) briefly reviewing the mechanical reasoning behind the proposed procedures, the search for new/simpler expressions to provide the DSM design curves is addressed. Their merits are assessed through (i) the quality of the estimates of the available failure load data and (ii) the determination of the corresponding LRFD resistance factors. Concerning the latter, it is shown that the value recommended, for compression members, by the North American Specification (NAS) for the Design of Cold-Formed Steel Structural Members (AISI 2012), namely Φc =0.85, can also be adopted for angle columns

Proposal to Improve the DSM Design of Cold-Formed Steel Angle Columns: Need, Background, Quality Assessment and Illustration

This paper presents a proposal for the codification of an efficient design approach, based on the Direct Strength Method (DSM), for cold-formed steel equal-leg angle columns with short-to-intermediate lengths, i.e., those buckling in flexural-torsional modes. Initially, the available experimental failure load data, comprising fixed-ended and pin-ended (“cylindrical hinges”) columns with several geometries (cross-section dimensions and lengths) and tested by various researchers, are collected and used to show that the currently codified DSM design provisions are not able to handle adequately short-to- intermediate angle columns and that a specific DSM-based design approach is needed to estimate the failure loads of such columns. Then, the paper presents a brief overview of the structural reasoning behind the DSM-based design approach proposed by Dinis & Camotim (2015, 2016). Next, the quality (accuracy and reliability) of the failure load estimates obtained with this design approach is assessed through the comparison with the above experimental failure load data and also a fairly large number of numerical failure loads. This merit assessment includes the determination of the LRFD resistance factors concerning the failure-to-predicted load ratios -- it is shown that the value recommended, for compression members, by the North American Specification (AISI 2016), Φc=0.85, can also be adopted for short-to-intermediate angle columns designed with this DSM-based approach. Finally, the paper presents and discusses a few numerical examples, which illustrate the application of the proposed design approach and provide evidence of its advantages and benefits, when compared with the currently codified one

Recent Developments in the GBT-Based Numerical Modeling of Steel-Concrete Composite Beams

This paper presents the latest developments concerning the numerical modeling ofsteel-concrete composite beams using GBT-based (beam) finite elements. In particular, it is shown that GBT makes it possible to assess, accurately and with computational efficiency, the buckling (bifurcation) behavior of steel-concrete composite beams subjected to negative (hogging) bending. Two relevant buckling phenomena are considered, namely (i) local buckling of the web (plate-like), possibly involving the torsional rotation of the compression flange, and (ii) distortional buckling, combining a lateral displacement/rotation of the lower flange with cross-section transverse bending. The determination of the buckling loads is performed in two stages: (i) a pre-buckling analysis is first carried out, accounting for shear lag and concrete cracking effects, and (ii) an eigenvalue buckling analysis is performed next, on the basis of the calculated pre-buckling stresses, allowing for cross-section distortion and plate bending. Several numerical examples are presented, illustrating the application of the proposed GBT-based finite element and providing clear evidence of its capabilities and potential.info:eu-repo/semantics/publishedVersio

Local buckling of RHS members under biaxial bending and axial force

The authors of this paper gratefully acknowledge the financial support provided by the Research Fund for Coal and Steel project RFCS-2015-709892, “Overall Slenderness Based Direct Design for Strength and Stability of Innovative Hollow Sections – HOLLOSSTAB”.This paper aims at providing an in-depth analysis of the local plate buckling coefficients for thin-walled rectangular hollow sections (RHS) subjected to biaxial bending and/or axial force. For the determination of these coefficients, a computational efficient Generalised Beam Theory formulation is implemented in a MATLAB code, capable of calculating accurate local buckling loads with a very small computational cost and, therefore, making it possible to conduct extensive parametric studies in a very short period of time. Taking advantage of the small longitudinal half-wavelength nature of the local buckling mode, semi-analytical solutions using sinusoidal half-wave amplitude functions may be employed for the GBT cross-section deformation modes. The code then computes the lowest local buckling load by varying the member length and using the “golden-section search” algorithm. Although most of the paper is devoted to cross-sections without rounded corners, the code is also capable of handling rounded corners and a preliminary study concerning its effect on the buckling coefficients is also presented.publishersversionpublishe