The application of plastic flow theory to inelastic column buckling

The paper presents a theory of inelastic column buckling which is consistent with the principles of plastic flow theory. The theory accounts for flexural, torsional and flexural-torsional modes. While the use of the tangent modulus to describe inelastic flexural buckling has been common place for a long time, efforts to comprehensively unite the torsional and flexural-torsional modes with the principles of plastic flow theory have so far been hampered by the ‘plastic buckling paradox’. New theoretical developments presented in this paper provide a way to achieve this goal. The solution hinges on the derivation of the inelastic shear stiffness while considering an infinitesimal solid element embedded within the column at a stage immediately past the point of buckling. The proposed inelastic column theory is verified against selected experimental data pertaining to aluminium and stainless steel columns of various cross-sections. Particular attention is paid to the torsional buckling problem of the inelastic cruciform section column

Experimental investigation of local-flexural interactive buckling of cold-formed steel channel columns

This paper presents the results of a comprehensive experimental programme aimed at studying the interaction of local and overall flexural buckling in cold-formed steel (CFS) plain and lipped channels under axial compression. The results were further used to verify the accuracy of the current design procedures in Eurocode 3, as well as to evaluate the effectiveness of a previously proposed optimisation methodology. A total of 36 axial compression tests on CFS channels with three different lengths (1 m, 1.5 m and 2 m) and four different cross-sections were conducted under a concentrically applied load and pin-ended boundary conditions. The initial geometric imperfections of the specimens were measured using a specially designed set-up with laser displacement transducers. Material tests were also carried out to determine the tensile properties of the flat parts of the cross-sections, as well as the cold-worked corner regions. A comparison between the experimental results and the Eurocode 3 predictions showed that the effective width approach combined with the P–M interaction equation proposed in Eurocode 3 to take into account the shift of the effective centroid consistently provided safe results. However, the Eurocode 3 procedures were also quite conservative in predicting the capacity pertaining to local-global interaction buckling, especially for plain channels. Furthermore, the experimental data confirmed the results of an optimisation study and demonstrated that the optimised CFS columns exhibited a capacity which was up to 26% higher than the standard channel with the same amount of material taken as a starting point

The capacity of grade C450 cold-formed rectangular hollow section T and X connections: An experimental investigation

The paper presents the results of an experimental program which consists of 15 T and X truss joints fabricated from grade C450 cold-formed rectangular hollow sections (RHS). The aim is to study the effect of the increased yield stress and the somewhat reduced ductility resulting from the cold-working process on the static capacity of these joints. The experimental program was designed to include the full range of possible failure modes and covers a comprehensive spectrum of geometries, including commercially available sections which fall outside the CIDECT limits in terms of wall slenderness ratios. In a next step, the results are compared to the current CIDECT design rules where applicable. In particular, the need for a reduction factor of 0.9 on the capacity of grade C450 connections, imposed by both the CIDECT rules and the Eurocode, is evaluated

Sidewall Buckling of Equal-width RHS Truss X-Joints

This paper presents a new design methodology for equal-width rectangular hollow section (RHS) X-joints failing by sidewall buckling. In the new approach, a slenderness parameter is defined based on the elastic local buckling stress of the sidewall, idealized as an infinitely long plate under patch loading. A Rayleigh-Ritz approximation is thereby used to obtain a closed-form solution. The proposed design equation is verified against experimental results over a wide range of wall slenderness values obtained from the literature and complemented by a brief experimental program carried out by the authors. It is demonstrated that the new design equation yields excellent results against the experimental data. Finally, a reliability analysis is performed within the framework of both the Eurocode and the AISI standards to ensure that the proposed design equation possesses the required level of safety. The newly proposed equation strongly outperforms the current Comité International pour le Développement et l’Etude de la Construction Tubulaire (CIDECT) design rule for sidewall buckling and also further extends the range of applicability to a wall slenderness ratio of up to 50

Local buckling in cold-formed steel moment-resisting bolted connections : behavior, capacity and design

The research presented in this paper aimed to investigate local buckling failure occurring adjacent to moment-resisting bolted connections in cold-formed steel back-to-back channel beams connected to a gusset plate through their webs. This failure is a result of a complex stress state originating from the transfer of both shear and bending moment through the web, combined with important shear lag effects. Experimentally validated finite-element models were used, accounting for material nonlinearity, geometric imperfections, and nonlinear bolt bearing behavior. The effects of the cross-sectional shape and thickness of the beam, the bolt group configuration, and the bolt group length were investigated. It was discovered that the detrimental effect of local buckling exponentially decreases when a longer bolt group length is used, when the load is introduced at the connection with a smaller eccentricity relative to the centroid, and when the thickness of the beam is increased. The results of the investigation were employed to develop a practical design equation with a wide range of applicability. Finally, a reliability analysis was performed within the framework of various standards

Experimental study of cold-formed steel built-up columns

A comprehensive experimental programme was contrived with the aim of investigating the behaviour and the capacity of cold-formed steel built-up columns with particular emphasis on the effects of connector spacing and contact between individual components. A total of 24 built-up columns, including four different cross-sectional geometries, were tested between pin-ended boundary conditions, while applying the load with nominal eccentricities of L/1000 or L/1500. The columns were designed to fail by interaction of cross-sectional buckling of the components, possible global-type buckling of the components between connectors and global buckling of the whole column, and all these failure modes were successfully achieved. The built-up sections were fabricated from flat plates, plain channels and lipped channels and were assembled with either bolts or self-drilling screws. The connector spacing was varied between specimens of the same cross-sectional geometry. Tensile coupons were taken from the flat portions and the corners of the sections in order to determine their material properties, while detailed measurements of the geometric imperfections of each specimen were also carried out using a specially designed measuring rig. In addition, the isolated behaviour of both the bolts and the screws used in the specimens was investigated through single lap shear tests. It was observed that the buckling patterns in the built-up specimens were affected by contact between the various components and by the spacing between the connectors. However, in the cases where global buckling of the components in between connector points was not critical, the connector spacing had a minor influence on the ultimate capacity of the columns

Behavior and design of cold-formed steel bolted connections subjected to combined actions

Cold-formed steel (CFS) moment connections are often formed by bolting the webs of the connecting elements to a stiffened gusset plate, and local buckling of the web adjacent to the connection typically governs their capacity. This paper aims to study this failure mode in case the connection is subject to combined axial compression, shear and bending moment. In a first step, the case of pure compressive loading was investigated. Validated GMNIA Finite Element (FE) models were used to investigate the effects of different design variables, including the cross-sectional geometry and thickness, the bolt group configuration and the bolt group length. The results were then used to develop design equations for the compressive capacity of CFS bolted connections. In a next step, the FE models were used to assess the capacity of CFS bolted connections subject to combined bending and shear, and combined axial compression, bending and shear. Suitable interaction equations were proposed and reliability analyses were performed within the framework of both the Eurocode and the AISI standards. It was concluded that a linear equation accurately captures the interaction between bending moment and axial force, while the effects of a shear force smaller than half of the shear capacity on the bending moment capacity can be neglected

Development of More Efficient Cold-Formed Steel Channel Sections in Bending

Cold-formed steel (CFS) cross-sections can be optimised to increase their load carrying capacity, leading to more efficient and economical structural systems. This paper aims to provide a methodology that would enable the development of optimised CFS beam sections with maximum flexural strength for practical applications. The optimised sections are designed to comply with the Eurocode 3 (EC3) geometrical requirements as well as with a number of manufacturing and practical constraints. The flexural strengths of the sections are determined based on the effective width method adopted in EC3, while the optimisation process is performed using the Particle Swarm Optimisation (PSO) method. To allow for the development of a new ‘folded-flange’ cross-section, the effective width method in EC3 is extended to deal with the possible occurrence of multiple distortional buckling modes. In total, ten different CFS channel cross-section prototypes are considered in the optimisation process. The flexural strengths of the optimised sections are verified using detailed nonlinear finite element (FE) analysis. The results indicate that the optimised folded-flange section provides a bending capacity which is up to 57% higher than standard optimised shapes with the same amount of material

Predicting the buckling behaviour of thin-walled structural elements using machine learning methods

The design process of thin-walled structural members is highly complex due to the possible occurrence of multiple instabilities. This research therefore aimed to develop machine learning algorithms to predict the buckling behaviour of thin-walled channel elements subjected to axial compression or bending. Feed-forward multi-layer Artificial Neural Networks (ANNs) were trained, in which the input variables comprised the cross-sectional dimensions and thickness, the presence/location of intermediate stiffeners, and the element length. The output data consisted of the elastic critical buckling load or moment, while also providing an immediate modal decomposition of the buckled shape into the traditionally defined ‘pure’ buckling mode categories (i.e. local, distortional and global buckling). The sample output for training was prepared using a combination of the Finite Strip Method (FSM) and the Equivalent Nodal Force Method (ENFM). The ANN models were subjected to a K-fold cross-validation technique and the hyperparameters were tuned using a grid search technique. The results indicated that the trained algorithms were capable of predicting the elastic critical buckling loads and carrying out the modal decomposition of the critical buckled shapes with an average accuracy (R2-value) of 98%. The influence of the various channel parameters on the output was assessed using the SHapley Additive exPlanations (SHAP) method