GBT-based semi-analytical solutions for the elastic/plastic stability analysis of stainless steel thin-walled columns exposed to fire

The authors gratefully acknowledge the financial support of FCT (Fundação para a Ciência e a Tecnologia, Portugal), through Project “StaSteFi—Fire design of stainless steel structural elements”.This paper presents and illustrates the application of an efficient Generalized Beam Theory (GBT) semi-analytical solution procedure to determine elastic and plastic bifurcation loads (linear stability analysis) of stainless steel thin-walled members subjected to uniform compression and exposed to fire. Besides global (flexural or flexural-torsional) buckling, the proposed GBT formulation allows for cross-section deformation and therefore makes it possible to capture local and distortional buckling. The temperature effect is taken into account using the material law for stainless steel specified in Eurocode 3 part 1-4 (CEN 2006) and Annex C of part 1-2 (CEN 2009). For plastic buckling, the material tangent moduli are obtained using both J2 small-strain incremental and deformation plasticity theories. For illustrative purposes, the procedure is applied to columns with a lipped channel cross-section.authorsversionpublishe

On the Modeling of Thin-Walled Member Assemblies Combining Shell and GBT-Based Beam Finite Elements: the Linear and Bifurcation Case

In this paper, a general and efficient approach to model thin-walled members and frames with complex geometries (including tapered segments and holes). The approach combines shell and GBT-based (beam) finite elements, using each of them where it is most efficient: (i) shell elements in the plastic and geometrically complex zones, and (ii) GBT elements in the prismatic and elastic zones. To illustrate the capabilities and potential of the proposed approach, a set of numerical examples are presented, concerning linear, bifurcation (linear stability) and first-order plastic zone analyses. The examples analysed involve (i) members with tapered segments, (ii) members with holes and (iii) tapered beam-column assemblies. For validation and comparison purposes, full shell finite element solutions are provided and it is demonstrated that the proposed approach yields very accurate solutions in all cases, while involving much less DOFs

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

Non-linear Buckling Analysis of Thin-walled Metal Columns

Uniformly compressed cold-formed metal columns are susceptible to instability in a variety of modes. In the stability analysis of such a column, using any of the available numerical methods with the exception of the eigenvalue method, the perfect geometry of the column must be \u27 seeded\u27 with an imperfection in order to cause it to collapse. If the member buckles in a global mode, it is easy to introduce an appropriate imperfection in form of a suitable displaced shape. However, it is more difficult to define the imperfections for the distortional and local buckling modes due to the unknown nature of the critical buckling patterns. The eigenvalue method can be used to predict the bifurcation buckling of a perfect member and linear solutions of eigenvalue problems have been well developed and documented. However, because many members buckle in the nonlinear region, it is necessary to develop non-linear solutions for eigenvalues. In the authors\u27 studies, the eigenvectors from linear eigen-solutions have been introduced as the imperfections in non-linear finite element analysis using ABAQUS version 5.4. However, this may not always be sufficiently accurate because the patterns of linear buckling and non-linear buckling could be different. Unfortunately, if a problem with a large number of degrees of freedom is analyzed using the finite element method, the existing methods are expensive in terms of either time or memory consumption. In this paper, a non-linear solution of eigenvalue problems set up using the finite element method is developed. The method has been used to analyze some stability problems in the uniformly compressed uprights of steel pallet racks. The results from analyses and tests agree well [1]

Structural behaviour of cold-formed steel purlin-sheeting systems under uplift loading

This thesis provides an investigation into the structural behaviour of cold-formed steel zed- and channel-section purlins when subjected to uplift loading in purlin-sheeting systems. In pre-buckling, an analytical model is presented to describe the bending and twisting behaviour of partially restrained zed- and channel-section purlins when subjected to uplift loading. Formulae used to calculate the bending stresses of the roof purlins are derived by using the classical bending theory of thin-walled beams. Detailed comparisons are made between the present model and the simplified model proposed in Eurocode EN1993-1-3. In buckling, a numerical investigation is presented on the buckling behaviour of partially restrained cold formed steel zed- and channel-section purlins when subject to transverse distributed uplift loading. The buckling behaviour of zed- and channel-section purlins of different dimensions subjected to uplift loading under the influence of rotational spring stiffness applied on the middle line of the upper flange is examined. In the post-buckling, nonlinear finite element analysis models are created for the partially restrained cold-formed steel zed- and channel-section purlins subjected to transverse uniformly distributed uplift loading. The analyses are performed by considering both geometric and material nonlinearities, and corresponding design curves of zed- and channel-section purlins are established

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

New approaches for linear and nonlinear analyses of thin-walled members in the framework of Generalized Beam Theory

The Generalized Beam Theory (GBT) is a reliable tool for the linear and nonlinear analysis of thin-walled members (TWMs). Based on expressing the displacement field as a linear combination of assumed deformation fields (i.e., trial functions) and unknown amplitude functions (i.e., linear coordinates), it relies on two steps: (a) selection of the deformation fields (i.e., cross-section analysis); and (b) solution of an equivalent 1D problem (i.e., member analysis). This thesis proposes new approaches for the GBT-based analysis of TWMs, in particular: (a) a novel approach for the cross-section analysis, (b) a GBT formulation for the partial interaction analysis of multi-component TWMs, (c) a displacement - based GBT for composite perforated TWMs, and (d) a nonlinear GBT for the analysis of arbitrary TWMs. The novel cross-section analysis is based on the so-called dynamic approach (GBT-D) and relies on the solution of a very limited number of constrained eigenvalue problems. It is much simpler to use than the classic static approach, in addition to provide even better results from the point of view of accuracy and symmetry of obtained displacement fields. The proposed cross-section analysis is suited for developing a GBT-based formulation for the study of the linear-elastic behavior of multi-component TWMs. The novelty of the approach consists on its ability to accurately model the partial interaction between the different components forming the cross-section in both longitudinal and transverse directions. The displacement-based GBT for the analysis of composite TWMs is based on a variable transform which allows to express the unknown linear coordinates in terms of cross-section nodal degrees-of-freedom (DOFs). The proposed approach leads to a beam-like finite element equivalent to an assembly of flat quadrilateral shell elements. Finally, the nonlinear GBT is developed according to the nonlinear Galerkin method, which calls for the evaluation of nonlinear (passive) trial functions, to be used in conjunction with linear (active) ones, in describing the displacement field. Within this framework, equilibrium paths can be determined by using few linear (and corresponding passive) trial functions, supplying good results when compared with burdensome finite-element solutions

Linear and bifurcation analyses combining shell and GBT-based beam finite elements

This paper concerns a general and very efficient approach to model thin-walled members with complex geometries (including taper and/or connected through joints), which combines standard shell and GBT-based finite elements. This approach (i) allows a straightforward modelling of complex geometries and (ii) is very efficient from a computational point of view, as the shell model substructures can be condensed out of the global equilibrium equations. The capabilities of the proposed approach are demonstrated through several examples concerning the linear and bifurcation (linear stability) analyses of (i) members with tapered segments, (ii) members with holes and (iii) beam-column assemblies. The results obtained are compared with full shell finite element model solutions and an excellent match is obtained.The first author gratefully acknowledges the financial support of FCT (Fundac¸ ˜ao para a Ciˆencia e a Tecnologia, Portugal), through the doctoral scholarship SFRH/BD/130515/2017

The behaviour of curved hybrid girders

Includes bibliographical references.Curved girders are used in bridges to fit predefined alignment. Hybrid girders are an innovative use of high strength steel enabling optimising moment capacity. Previous studies of curvature and hybrid girder effects have been disjointed, focusing on curved homogeneous girders and straight hybrid girders. There are no generally accepted curved girder equations and this has implications in the study of curved hybrid girders since the hybrid effects become apparent in the inelastic range. Furthermore, the range of radius to span ratio where available analytical procedures can be applied is not known. A total of 48 girders are investigated, 12 of which are straight. The girders are all simply supported, un-braced and loaded at midspan. The load-deflection behaviour of curved hybrid girders is investigated. Stress plots of the girders are obtained at ultimate load. The radius to span ratio is varied from 5 to 50 for 5m span girders and from 5 to 30 for 8m span girders. Three steel grades are used to obtain hybrid girder configurations, with higher yield steel always used in the flanges. The web-flange yield steel combinations used are 350MPa/460MPa, 350MPa/690MPa and 460MPa/ 690MPa. A finite element model using ADINA version 8.4 is used to investigate curved girder behaviour. The collapse analysis option is used to trace behaviour as the load is incremented automatically to a prescribed displacement. Available experimental data is used to check the validity of the modeling assumptions. The presence of curvature radically modifies a girder's load pattern by causing additional lateral bending moments. Lateral bending moments reduce the vertical load carrying capacity of a girder and cause the flanges to be unequally stressed. For the girder and spans investigated, there is a reduction of 57% in ultimate load for radius to span ratio (R/L) of 5 compared to a straight girder of similar proportions and span. The effects of curvature reduce as R/L increases and this is observed in the 5m homogeneous girder with R/L of 50 which attained more than 91% of the straight girder load capacity. The 8m girder with R/1 of 30 attained more than 83% of the equivalent straight load girder capacity. The hybrid girders investigated had load-deflection curves close to corresponding homogeneous girders with flange steel grade, reaching more than 97% of the ultimate load capacity of reference homogeneous girders. The hybrid factors as proposed in the simplified design procedure are adequate and can be applied to analytical equations that predict curved homogeneous girder loads. The available analytical equations give conservative loads for both hybrid and homogeneous girders compared to the finite element method when R/1 is 5 and are unconservative for higher rations