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Abstract Structural design formulae for beam-columns require accurate end points (i.e. accurate resistance predictions for pure compression and pure bending), should be of suitable form to capture the interaction between the different components of loading and should take due account of the influence of a moment gradient along the member length. However, existing design rules for stainless steel beam-columns do not fully capture the interaction responses observed in experiments and numerical simulations, and are often tied to inaccurate end points; the adopted equivalent uniform moment factors can also be unconservative in the case of high moment gradients. As a consequence, previous comparisons of stainless steel beam-column experimental and finite element results with codified strength predictions have often revealed a rather high degree of scatter. This prompted the present research, to develop improved design proposals for stainless steel square hollow section (SHS) and rectangular hollow section (RHS) beam-columns under moment gradients. To this end, revised design approaches are proposed firstly through the derivation of more accurate design interaction curves for stainless steel SHS and RHS beam-columns under uniform bending moment and then through the employment of more suitable equivalent uniform moment factors, underpinned by and validated against over 1500 test and numerical data points. The new design approaches are shown to lead to improved (safe-sided, accurate and consistent) resistance predictions for stainless steel SHS and RHS beam-columns under moment gradients over the current codified design rules. Finally, statistical analyses are performed to demonstrate the reliability of the proposed approaches, according to the requirements specified in EN 1990. Highlights • Current codified design rules for stainless steel beam-columns under moment gradients were briefly reviewed. • Shortcomings in the existing design codes were identified, and methodologies for overcoming them were described. • Improved design approach for stainless steel beam-columns under moment gradients was proposed. • Assessment of the new proposal indicates a higher level of design accuracy and consistency. • The reliability of the new proposal has been confirmed by means of statistical analyses. [ABSTRACT FROM AUTHOR]

This paper presents experimental and numerical investigations of the buckling behaviour and resistance of S960 ultra-high strength steel slender welded I-section beam–columns under combined compression and minor-axis bending moment. An experimental programme, including initial geometric imperfection measurements and eight beam–column tests, was firstly conducted. The test procedures, setups and results were fully reported. Following the experimental programme, a numerical modelling programme was carried out, with finite element models initially developed and validated against the test results and then employed to conduct parametric studies to generate further numerical data. On the basis of the test and numerical data, the relevant design interaction curves, as provided in the European code, Australian standard and American specification, were evaluated for their applicability to S960 ultra-high strength steel slender welded I-section beam–columns. The evaluation results revealed that all three codified design interaction curves lead to conservative resistance predictions, mainly owing to the conservative end points (i.e. column buckling strength and cross-section minor-axis bending resistance). Finally, a revised Eurocode design interaction curve, with improved compression end point determined from more accurate column buckling curve and bending end point determined from the direct strength method, was finally proposed, and shown to result in more accurate resistance predictions for S960 ultra-high strength steel slender welded I-section beam–columns than the codified design interaction curves. • The buckling behaviour of S960 ultra-high strength steel slender welded I-section beam–columns is studied. • Eight beam–column tests on S960 ultra-high strength steel slender welded I-sections are conducted. • FE models are developed and validated against the test results and then used to perform parametric studies. • The applicability of the relevant codified design interaction curves is assessed, revealing inaccuracy. • A new design interaction curve is proposed, resulting in more accurate failure load predictions. [ABSTRACT FROM AUTHOR]

For flexural thin-walled section beams, the ultimate strength is significantly affected by the interaction of different local buckling modes associated with combined bending and shear stresses. This paper provides a comprehensive analytical and numerical study of elastic buckling of thin-walled channels subjected to different combinations of bending and shear stresses. The commercial ABAQUS software package using Finite Element Method (FEM) has been used to perform the elastic buckling analyses of the channel sections. The results are benchmarked against those from the Semi-Analytical Finite Strip Method (SAFSM) for the cases of pure bending and shear only. Two typical types of channels with and without lips are selected for investigation. To study the effect of different combinations of bending and shear on the buckling stresses, different normal stress distributions and equilibrating shear stresses are applied at two end cross-sections of the channels to maintain static equilibrium. Different types of interactions which occur during the buckling analyses are studied by varying the ratios of bending moments resulting from the modelled longitudinal stresses. A new concept for the elastic local buckling interaction based on the Average Bending Moment (ABM) at buckling is provided. In addition, an explicit approach for local buckling loads of channels under different combinations of bending and shear is also introduced for the practical design use. The results from this explicit solution for elastic buckling can be used as direct inputs for an explicit Direct Strength Method (DSM) design of members under combined bending and shear. • A comprehensive study of elastic buckling of thin-walled channels under combined bending and shear stresses is performed • ABAQUS software package using FEM is used to conduct elastic buckling analyses of thin-walled channel sections • Results are benchmarked against those from the Semi-Analytical Finite Strip Method for the cases of pure bending and shear only cases • A new concept for elastic local buckling interaction based on the Average Bending Moment (ABM) at buckling is provided • Results from the explicit solution for elastic buckling analyses can be used in the Direct Strength Method (DSM) of design [ABSTRACT FROM AUTHOR]

Abstract: Trapezoidal sheeting of thin-walled steel is applied frequently for roofing and cladding. As such, it is loaded by a concentrated load (at the support) and a bending moment. A recently developed model to predict the sheeting's failure behaviour leaves the question open whether mode jumping (the phenomenon where a plate dynamically changes its buckling mode during an increasing load) should be taken into account in the model. This article presents the analytical and finite element modelling of square and long plates, which, depending on the boundary conditions, may represent the compressed flange of trapezoidal sheeting. The analytical modelling is based on the combination of several displacement functions and using the principle of minimal potential energy. Hereafter the stability of each part of the resulting equilibrium curves is determined. A spin-off of the analytical model is an analytical expression for a current curve-fitted based prediction formula for the post/pre-buckling stiffness ratio by Rhodes. Furthermore, the accuracy range of a solution by Williams and Walker for the far-post buckling behaviour can be confirmed. The finite element modelling has been carried out by implicit dynamic, and explicit (dynamic) simulations. Both for the load levels and the buckling mode sequences, the analytical and finite element models give equivalent results. It is concluded that for the specific boundary conditions that represent the situation of a compressed flange for trapezoidal sheeting, it is very likely that mode jumping will not occur. [Copyright &y& Elsevier]

Abstract: In a recent paper (Gonçalves and Camotim, 2013 [1]), the authors presented an investigation concerning the buckling (bifurcation) behaviour of uniformly compressed thin-walled tubes with regular polygonal cross-sections (RCPS). The present paper complements the previous work by addressing the local and distortional buckling behaviour of RCPS members subjected to bending or torsion and aims at providing a novel insight into these phenomena. In particular, the specialization of Generalized Beam Theory (GBT) for RCPS, as recently proposed in Gonçalves and Camotim (2013) [2], is employed to obtain closed-form analytical solutions and also to carry out parametric studies by means of numerical analyses which are both computationally efficient (due to the small number of d.o.f. involved) and clarifying (due to the modal decomposition features of GBT). For validation purposes, solutions taken from the literature and also standard shell finite element model results are employed. [Copyright &y& Elsevier]

The global buckling behaviour of hot-rolled stainless steel channel section beam–columns under combined compression and minor-axis bending moment has been studied based on testing and numerical modelling and reported in this paper. A testing programme was conducted on ten hot-rolled austenitic stainless steel channel section beam–columns, with five buckling towards webs and the other five buckling towards flange tips. This was followed by a numerical modelling programme, in which finite element models were firstly developed and validated against the test results and then used to perform parametric studies to generate further numerical data over a wide range of cross-section dimensions, member effective lengths and loading combinations. The test and numerical results were adopted to assess the current design interaction curves given in the European code and American guide, both of which were found to result in inaccurate and scattered failure load predictions. The inaccuracy of the codified design interaction curves stems from the inaccurate end points (i.e. the member resistances under pure compression and pure bending) and the inappropriate shape. To address these shortcomings, a new design interaction curve was developed firstly through the adoption of more accurate end points and secondly through the derivation of a more proper shape. The proposed design interaction curve was shown to yield accurate and consistent failure load predictions for hot-rolled stainless steel channel section beam–columns. The reliability of the new proposal was also confirmed by means of statistical analyses. • The buckling behaviour of hot-rolled stainless steel channel section beam–columns is studied. • Ten beam–column tests were conducted. • FE models were firstly developed and validated against the test results and then adopted to perform parametric studies. • The codified design interaction curves were assessed, indicating inaccuracy. • A new design interaction curves was proposed, with the accuracy and reliability demonstrated. [ABSTRACT FROM AUTHOR]

Abstract: For the coupled static and dynamic buckling of thin walled beam subjected to various forces, such as axial force, uniform bending moment, and bending moment due to concentrated and distributed lateral forces, the spline finite element method is employed to obtain the dynamic stiffness matrix. Second order effects of the axial force and moment are considered. A doubly symmetric cantilever beam with uniform cross-section is investigated. Extensive static and dynamic interaction diagrams are plotted. The effects of warping rigidity, torsional rigidity, axial tension and compression on moment buckling, moment on axial buckling compression, higher buckling modes are discussed in detail. The spline finite element method is proved to be very efficient for the present problem and many interaction diagrams can be plotted easily. Some new results are presented. The methodology is based on finite element formulation and therefore it can be easily extended to analyze structural frames. [Copyright &y& Elsevier]

This work presents an investigation on the compressive strain capacity of resisting buckling on an X80 steel corroded pipeline subjected to a bending moment using nonlinear finite element analysis (FEA) validated by full-scale tests. The modelling results indicate that the existing strain-based assessment method is not suitable for pipelines with deep corrosion and has certain application limitations. Consequently, a new evaluation method based on far-field strain was developed to predict the buckling failure of corroded pipelines subjected to bending loads. The influence of the corrosion shape type, corrosion size (i.e., depth d , length L , and width w), pipe geometry, and internal pressure on the critical buckling strain capacity and critical buckling moment of the pipeline were studied using parameter sensitivity analysis to verify the proposed strain criteria. The results illustrate that the variation trends between the critical buckling strain and the critical buckling moment with each factor were consistent, indicating that the proposed novel strain-based evaluation method is effective and applicable. In addition, the buckling resistance of a pipeline with rectangular corrosion is relatively weaker than that with a semi-spherical corrosion pit or cylindrical grooved corrosion under the same defect size. Further, the critical compressive strain capacity of a corroded pipeline is primarily affected by the depth and width of the corrosion, whereas the effect of the corrosion length is relatively insignificant. Moreover, the critical length and width of the corrosion defect affecting the bending capacity of resisting buckling were determined as L / D t = 20 and w / π D = 0. 5 , respectively. • A novel strain-based assessment method of local buckling of corroded pipelines. • Determined the effect of defect geometry on critical compressive strain capacity. • Determined the critical defect size that affect the pipe buckling strain capacity. [ABSTRACT FROM AUTHOR]

The current slenderness limits are significantly different in international design codes for cold-formed Circular Hollow Sections (CHS) under pure bending. This paper aims to use the Finite Element (FE) method to understand the behaviour of cold-formed CHS under pure bending and to propose new design rules. The model is calibrated by comparing its predicted load-deflection curves with previously published experimental data. In total, 21 specimens were modelled with diameter-to-thickness ratios ranging from 13 to 122. The current slenderness limits in the present international steel specifications were examined using the FE model and their suitability for cold-formed CHS is discussed. The effect of section slenderness on rotation capacity has been examined where the predicted variation of rotation capacity against section slenderness has been compared to the experimental results. A new equation for the amount of initial geometrical imperfection as a function of section slenderness has been developed and proposed for design purposes. The ovalisation deformation ratio and the critical strain at local buckling were determined and compared for compact, non-compact and slender sections. The progressive bending deformations of CHS at 10 critical steps have been presented and compared for the three cross sectional types, in particular at the maximum moment and bending rotation. In general, a good agreement has been obtained between the predicted strengths and ductilities using the current FE models and those of the experimental data of cold-formed CHS. • Using finite element method to determine the slenderness limit of cold-formed steel tubes and compared to the previous experimental results. • The effect of geometrical imperfections on the deformation cold-formed CHS has been examined. • The rotation capacity has been presented for CHS. • The ovalisation of compact, non-compact and slender section has been analysed. • The buckling mechanism has been analysed by using strain analysis, the critical strain at maximum moment has been determined and compared to the theoretical results. [ABSTRACT FROM AUTHOR]