Thin-walled Members Research Articles

The polarisation method and the method of equivalent nodal forces: A comparison with other modal decomposition methods in the analysis of coupled instabilities

The objective of this paper is to validate the newly proposed polarization method (PM) and the method of the equivalent nodal forces (NFM) and to highlight their distinctive features by comparing them with some more established modal decomposition methods, including mainly the generalized beam theory (GBT) and the constrained finite strip method (cFSM). Modal decomposition methods analyse the deformed shapes of a buckled thin-walled structural member by decomposing them into a linear combination of constituent modes (classical local, distortional and global buckling) augmented with shear and transverse extension modes. An overall comparison of the methods is provided, including practical aspects such as how the buckling modes are generated, and the versatility of these methods when applied to various cross-sectional shapes. Specific technical details are discussed for each method, along with numerical examples focusing on the buckling behaviour of thin-walled structural members under compression. Moreover, considerable attention is paid to the discrepancies between the results yielded by different methods, namely the critical stresses associated with pure local, distortional and global buckling. The numerical examples demonstrate that, in spite of the fact that these four methods stem from different theories, they provide essentially the same extended capabilities for examining and understanding thin-walled member stability. Reasons for the discrepancies between the results are discussed and the conclusion is reached that they are attributed to the differences in the criteria adopted in the various methods of mode generation, particularly in the handling of the membrane strains and stresses. In addition, through this comparison features of the newly proposed methods are unveiled such as greater mesh sensitivity, significantly lower critical stress at extremely short half-wavelengths, and different output regarding distortional buckling of hollow-flange sections.

Buckling Behavior of Aluminum Alloy Thin-Walled Beam with Holes under Compression Loading

Thin-walled members are increasingly used in structural applications, especially in light structures like in constructions and aircraft structures because of their high strength-to-weight ratio. Perforations are often made on these structures for reducing weight and to facilitate the services and maintenance works like in aircraft wing ribs. This type of structures suffers from buckling phenomena due to its dimensions, and this suffering increases with the presence of holes in it. This study investigated experimentally and numerically the buckling behavior of aluminum alloy 6061-O thin-walled lipped channel beam with specific holes subjected to compression load. A nonlinear finite elements analysis was used to obtain the buckling loads of the beams. Experimental tests were done to validate the finite element results. Three factors namely; shape of holes, opening ratio D/Do and the spacing ratio S/Do were chosen to study their effects on the buckling strength of the channel beams. Finite elements results were obtained by using Taguchi method to identify the best combination of the three parameters for optimum critical buckling load, whereas determining the contribution of each parameter on buckling strength was implemented by using the analysis of variance technique (ANOVA) method. Results showed that the combination of parameters that gives the best buckling strength is the hexagonal hole shape, D/Do=1.7 and S/Do= 1.3 and the opening ratio (or size of holes) is the most effective on buckling behavior.

Shear-deformable hybrid finite-element formulation for lateral-torsional buckling analysis of composite thin-walled members

A shear deformable hybrid finite element formulation is developed for the lateral-torsional buckling analysis of fibre-reinforced composite thin-walled members with open cross-section. The method is developed by using the Hellinger–Reissner functional. Comparison to the displacement-based formulations the current hybrid formulation has the advantage of incorporating the shear deformation effects easily by using the strain energy of the shear stress field without modifying the basic kinematic assumptions of the thin-walled beam theory. Numerical results are validated through comparisons with results based on other formulations presented in the literature. Examples illustrate the effects of shear deformations and stacking sequence of the composite layers in predicting bucking loads.

Semi-Analytical Solutions for the Uniformly Compressed Simply Supported Plate with Large Deflections

The thin plane plates are largely used in practice as single elements or as components of the thin-walled structures, and their behavior under compression is characterized by large post-buckling load-carrying capacity. Various semi-analytical solutions of the uniformly compressed simply supported plate with large deflections were formulated almost a century ago, mainly solving the fundamental equations governing the deformation of thin plates, or using classic energy methods. Due to several shortcomings, none of these solutions were introduced in the design codes of thin-walled members. This paper presents new semi-analytical solutions based on classic energy methods. The main innovation is brought by the considered displacement field which is far more accurate than the ones used by the previous formulations. The initial geometric imperfections are considered, and the proposed solutions are validated against numerical solutions and experimental data. The validation is also supported by a publicly available software application.

Experimental investigation of composite floor system with thin-walled steel trussed beams and partially prefabricated concrete slab

The present investigation addresses the structural behavior of steel and concrete composite floor systems, composed of thin-walled trussed members, usually adopted in the steel frame constructional technology. The floor systems of typical light-weight frame constructions are generally constituted by thin-walled beams (or open-web joist), wood-based panels (Oriented Strand Boards – OSB) and self-drilling screws connecting both materials (steel and wood). In some situations, concrete slabs are cast over the OSB panels and no shear connectors are adopted to ensure the composite action between the steel members and the concrete. In this context, one of the objectives of this work aims at presenting three new innovative solutions for shear connectors, composed of thin-walled members and attached to the top chord of the trusses by means of self-drilling screws (4.2 mm diameter). A series of experimental tests were performed in the Structures Laboratory of Federal University of Rio de Janeiro (COPPE/UFRJ), in order to provide reliable information in terms of shear strength, deformation capacity and mechanisms of collapse associated with eight push-out test specimens, according to recommendations established by Eurocode 4. Also, the performance of the referred connectors was investigated with the help of three full-scale bending tests, which revealed important characteristics regarding the structural behavior of the composite floor systems in terms of bending capacity, flexural stiffness, degree of interaction between the steel trusses and the concrete slabs, as well as strain distribution at mid-section.

Geometric and material nonlinear analysis of thin-walled members with arbitrary open cross-section

Abstract This paper describes the formulation of a thin-walled beam finite element for arbitrary open cross-sections, including doubly-, singly- and non-symmetric cross-sections. The formulation is developed within the co-rotational framework of OpenSees – an open source program available for the simulation of structural and geotechnical systems. The formulation accounts for eccentricity between the shear centre and the centroid of the cross-section, as well as warping. Both elastic and inelastic material behaviour is considered. The stiffness relation for the displacement-based beam element is established based on the Green-Lagrange strain. A local cross-section transformation matrix is derived to relate the end actions with the axial force acting at the centroid to the end actions with the axial force acting at the member axis system. The elastic and inelastic performance of the beam finite element is demonstrated through a series of instability problems comprising doubly-, singly- and non-symmetric sections subjected to compression, bending, and torsion. The buckling and post-buckling behavior predicted by the beam element is shown to be in close agreement with the results of shell finite element models, thereby demonstrating its reliability.

Static Strength of Square T-Joints Reinforced with Collar-Plates under Axial Compression or In-Plane Bending

In typical square tubular joints, the most common failure mode is local yielding or buckling of the chord at the brace/chord intersection. Thus, in the current paper, a collar-plate, as external reinforcement, is welded around the weld toe to increase the stiffness of the chord surface. Firstly, theoretical formulas, based on the yield line principle which is often used to examine thin-walled members suffering from local collapse mechanisms, for calculating the capacities of the collar-plate-reinforced square tubular T-joints under axial compression and in-plane bending are deduced. Then, experimental tests and finite element (FE) simulations are carried out on square tubular T-joints reinforced with collar-plates. The experimental results showed an improvement in the bearing capacity of SHS joints reinforced with collar-plate by 78 and 89% compared with the corresponding un-reinforcement joints. The FE results, as well, proved that using the collar-plate reinforcement is an efficient method to improve the static strength of a square tubular T-joint under either axial compression or in-plane bending. Finally, through the comparison between the FE results and the theoretical formulas, the validation range of the formulas for predicting the strengths of the collar-plate-reinforced square tubular T-joints is specified. For the joints under axial pressure, the validation range of the proposed formula is 0.45 ≤ βc ≤ 0.8, 2γ ≥ 20 and τc ≥ 1.5, while for the joints under in-plane bending is βc ≤ 0.8, 15 ≤ 2γ ≤ 30 and τc ≥ 1.50.

Combining shell and GBT-based finite elements: Linear and bifurcation analysis

This paper proposes a general and efficient approach to model thin-walled members with complex geometries and/or connected through joints, by combining shell and standard GBT-based (beam) finite elements. It is shown that this approach is (i) very versatile, in the sense that complex geometries can be modelled quite easily, and (ii) computationally efficient, since the shell model substructures are condensed out of the global equilibrium equations. To show the capabilities of the proposed approach, several illustrative examples are presented and discussed, concerning the behaviour of (i) members with tapered segments, (ii) members with holes and (iii) complex beam-column assemblies. For validation purposes, full shell finite element model solutions are provided, showing that an excellent match is obtained. This paper deals exclusively with the linear (first-order) and bifurcation (linear stability) analysis cases, but the proposed approach will be extended to other analysis types.

A simplified-but-general nonlinear thin-walled beam finite element model with independent interpolated axial displacement

This paper presents a study performed on the simplified thin-walled beam finite element model that takes into account the effects of shear deformation and higher-order axial displacement. Without using the torsion-related warping function derived from classical theories, the axial displacement field over the cross-section is constructed by using independent Langrage interpolation polynomials. Then, the effect of shear stress distribution can be reasonably included and the beam model is dedicated to thin-walled members with arbitrary cross-section. The expressions of the Green-Lagrange strain components are derived. The element elastic stiffness matrix and geometrical stiffness matrix are obtained to perform static and buckling analyses. Numerical examples are employed to demonstrate the effectiveness of the proposed model and discuss the probable accuracy-loss from different deformation assumptions and nonlinear strain definitions. As revealed by the results, the transverse shear deformation and higher-order axial displacement could exert significant effects on solution accuracy for static and buckling analyses under the circumstances of small slenderness and unsymmetrical cross-section. In addition, the nonlinear strain terms related to torsion and quadratic terms of the transverse shear deformation are found to be crucial to stability analysis, for which they ought to be included in a simplified strain definition. • A thin-walled beam finite element with interpolated axial displacements is developed. • The expressions of the Green-Lagrange strain components are derived. • Effects of shear deformation and higher-order axial displacement are discussed. • A simplified strain definition for flexural-torsional buckling analysis is suggested.

Numerical investigation of web crippling in fastened aluminium lipped channel sections under two-flange loading conditions

Aluminium alloys have recently been utilised in the fabrication of thin-walled members using a roll-forming technique to produce purlins, floor joists and other structural bearers. Such members are often subjected to transversely concentrated loads which may possibly cause a critical web crippling failure. Aluminium specifications do not explicitly provide clear design guidelines for roll-formed members subjected to web crippling actions. Therefore, this study was conducted to investigate the mechanism of web crippling for roll-formed aluminium lipped channel (ALC) sections with flanges attached to supports (fastened) under two-flange loading conditions. Based on the experimental works presented in a companion paper, numerical simulations were conducted including an extensive parametric study covering a wide range of ALC geometrical dimensions, bearing lengths, and 5052 aluminium alloy grade with H32, H36 and H38 tempers. The acquired web crippling data were then used to investigate the influence of the flange restraints on the web crippling mechanism of the ALC sections. Furthermore, a detailed assessment of the consistency and reliability of the currently available design rules used in practice was carried out. The predictions of the web crippling design guidelines given in the Australian, American and European specifications were found to be unsafe and unreliable, whereas a good agreement was obtained between the predictions of our recently proposed design guidelines and acquired web crippling results. Further a suitable Direct Strength Method (DSM)-based design approach was developed in this study with associated equations to predict the elastic bucking and plastic loads of fastened ALC sections under two-flange loading conditions.

Comparison of FEA for Different Type Element Models of Open Thin-Walled Member

Open thin-walled beam is widely used in civil engineering. The open-walled section model is significantly different from closed section model because the torsional stiffness is small. In order to select an appropriate analytical model for the open-walled section member, three different type element models (beam element model, shell element model and solid element model) for open-walled section members are adopted in ABAQUS/Standard and the low-frequency cyclic loading is used in the analysis process in this paper. The hysteretic curves and skeleton curves of the different element model are obtained using above method, and the bearing capacity, stiffness and the computation time are compared. The analysis results show that the results of three type element models are in good agreement, and the computational efficiency of the three type element models varies significant differences. Hence, it can be concluded that the accuracy of computation results can be guaranteed using those three type element models, and the beam element model has the highest computational efficiency.

A GBT-based mixed finite element for curved thin-walled members with circular axis

Abstract In this paper a mixed finite element based on Generalised Beam Theory (GBT) is proposed to analyse the first-order behaviour of naturally curved beams with circular axis (without pre-twist) and having deformable thin-walled cross-sections. The element applies the assumed strain concept to the longitudinal strains terms that are not present in straight members and cause locking. The additional strain DOFs are condensed out and therefore the stiffness matrix of the mixed element shares the DOFs of the standard (displacement-based) GBT finite element. The superior predictive capacity of the proposed mixed element with respect to the standard element with reduced integration is demonstrated through several examples involving complex global-distortional-local cross-section deformation.

An efficient finite strip procedure for initial post-buckling analysis of thin-walled members

An efficient procedure based on the semi-analytical finite strip method with invariant matrices is developed and applied to analyze the initial post-buckling of thin-walled members. Nonlinear strain–displacement equations are introduced in the manner of the von Karman assumption for the classical thin plate theory, and the formulations of the finite strip methods are deduced from the principle of the minimum potential energy. In order to improve the computational efficiency, an analytical integral of the stiffness matrix is transformed into matrix multiple calculation with introducing invariant matrices which can be integrated in advance only once. Three commonly employed benchmark problems are tested with proposed method and other state-of-the-art methods. The corresponding comparison results show that: (1) this finite strip method is proved to be a feasible and accurate tool; (2) compared with the calculation process of the conventional finite strip methods, the proposed procedure is much more efficient since it requires the integration of the stiffness matrix only once no matter how many iterations are needed; and (3) the advantage of time-saving is greatly remarkable as the number of iterations increases.

A Study on the Behaviour of Cold Formed Built - Up Steel Compression Member

The use of cold-formed thin-walled steel structural members has increased in recent years. Especially, Cold-formed steel columns are widely used in the construction industry due to their lightweight, easy installation, erection and economy. The strength and efficiency of cold-formed steel profiles depends on the cross-sectional shape, which controls the three fundamental buckling modes: local, distortional and global. As most of their sections are open with only one symmetrical axis, they would likely fail by twisting and interacted with the other buckling modes such as local and distortional buckling. In order to improve the ultimate strength of columns, a built-up column section with distinct shape was selected from the detailed study of Literatures and three specimens of thickness 1.6mm were fabricated with different lengths 500mm, 600mm and 700mm. Consequently, buckling behaviour of built up steel members was investigated theoretically with Direct Strength Method (with the help of CuFSM) as well as experimentally and the results were compared with the buckling modes obtained numerically using ANSYS software and it is found that the ultimate load carrying capacity of the column increases with the decrease of slenderness ratio and finally a new innovative and economical column element was presented.

Constrained shell finite element method for elastic buckling analysis of thin-walled members

Abstract The objective of this paper is to develop a constrained shell Finite Element Method (cFEM) based on a force approach for elastic buckling analysis of thin-walled members. The new cFEM is able to separate the general deformation of thin-walled members into the three fundamental deformation mode classes, namely Global (G), Distortional (D), and Local (L), to enable the modal decomposition and identification. In this paper, four force-based mechanical criteria are defined to separate these mode classes. These mechanical criteria are implemented with the general shell finite element formulation without any special treatment of the element formulation. The constraint matrices of the G, D, and L mode classes are then constructed. Numerical examples are presented to demonstrate the capabilities of the new cFEM in modal decomposition and identification. In particular, the modal decomposition and identification results are compared with the cFSM solutions. Applicability of the new cFEM to other shell FE formulation and different loading conditions are illustrated. All these numerical examples demonstrate the potential of the developed cFEM in taking advantages of the modeling capability of the existing shell FE method.

Study of Concrete Filled Coldformed Corrugated Steel Tubular Columns under Axial Loading

Concrete filled steel tube columns have many advantages such as high strength, high stiffness and high ductility. In recent years, cold formed thin walled stainless-steel members have become popular due to their high corrosion resistance, light in weight and highly controllable quality. Corrugated steel sheets have higher stiffness than flat steel sheets. This study investigates the effectiveness of corrugated steel sheets in concrete filled tubular columns as the confining outer tubes. An experimental program was conducted on CFST with corrugated steel tube and is compared with CFST with plain steel tube. Non-linear FE analysis was conducted to study the various parameters such as no: of corrugation, angle of corrugation, spacing of corrugation, depth of corrugation and slenderness ratio which affects the performance of column.

Web crippling behaviour and design of aluminium lipped channel sections under two flange loading conditions

Aluminium alloys have recently drawn significant attention in structural applications due to its outstanding mechanical characteristics. Thin-walled members fabricated by aluminium alloys can be more competitive in construction industries than the conventional cold-formed steel sections, particularly in areas with high humidity and severe environmental conditions. Nevertheless, they are more vulnerable to various types of instability due to their relatively low elastic modulus compared to steel. Applying high concentrated load transversely on thin-walled members can cause critical damage to the web of the cross section called web crippling. Although a large number of studies has been performed to investigate the web crippling mechanisms on different types of sections, the existing studies are primarily of the empirical nature and thus merits further investigations. To fill the research gap, this study was thus performed based on our previously conducted experimental work to further comprehend the web crippling phenomenon of the roll-formed aluminium lipped channel (ALC) sections under the loading conditions of end-two-flange (ETF) and interior-two-flange (ITF). This was done through numerical investigations followed by a parametric study which are reported herein in details. A wide range of roll-formed ALC sections covering web slenderness ratios ranged from 28 to 130, inside bent radii ranging between 2 mm and 8 mm, bearing lengths ranged from 50 mm to 150 mm, and three sheeting aluminium alloy grades (5052-H32, 5052-H36 and 5052-H38) were considered in the parametric study. The acquired web crippling database was then used to assess the consistency and accuracy of the current design rules used in practice. It was found that the web crippling capacity determined by the current international specifications are unsafe and unreliable, whereas the predictions of the recently proposed equations agree very well. Furthermore, a Direct Strength Method (DSM)-based capacity prediction approach was proposed and then validated against the web crippling database acquired here as well as the experimental and numerical data for cold-formed steel lipped channel sections used in the literature.

Experimental analysis of the effect of dent variation on the buckling capacity of thin-walled cylindrical shells

Tanks, silos, and most large steel-shell structures consist of smaller pieces connected together during the manufacturing process. This causes several types of malformations on the shell walls. Furthermore, thin-walled members can be easily deformed in wall surfaces owing to the thickness of the structure. Fourteen thin-walled cylindrical shell specimens in two groups with different dent depths and various longitudinal dent numbers subject to hydrostatic pressure were tested in the present work. The models were designed to demonstrate how repairing dents by using carbon-fibre-reinforced polymer can recover lost capacity. The results of testing under different theories and codes were compared. This study shows the decreasing effects of the longitudinal dent number on the buckling capacity of the shells. Using carbon-fiber-reinforced polymer strips resulted in softening or stiffening behaviour in the models. Furthermore, to obtain the initial and overall buckling according to theoretical formulas, coefficients were predicted to obtain the initial, overall, and collapse buckling without an experiment for the models that were beyond the scope of the theories.

Geometrically nonlinear Hessian eigenmode decomposition for local stability analysis of thin-walled structures

A nonlinear geometric formulation based on position and unconstrained vector is originally proposed to evaluate the local stability of thin-walled members. The Hessian is decomposed into linear and geometric equivalent installments. As the Hessian matrix exhibits a definite positive quadratic form, stability condition for large displacements requires that the Hessian matrix positivity be verified at each load small steps. This condition must be established by evaluating the smallest eigenvalue signal at the critical point imminence. The positional finite element method is formulated from a total Lagrangian reference. The mechanical system equilibrium is guaranteed by the total potential energy stationary principle. The constitutive law of Saint–Venant–Kirchhoff is obtained from the linear relationship between the second Piola–Kirchhoff stress tensor and Green–Lagrange deformation tensor. Some examples demonstrate the applicability of the methods.

Modal buckling analysis of thin-walled members with rounded corners by using the constrained finite strip method with elastic corner elements

In this paper modal decomposition of thin-walled structural members with rounded corners is discussed. Modal decomposition is a process which separates the characteristic behaviour types. If modal decomposition is applied in buckling analysis, pure uncoupled buckling modes can readily be analysed, such as pure global buckling, pure distortional buckling or pure local-plate buckling. Ability to calculate critical loads to a pure buckling mode is highly beneficial in the design of thin-walled structural members, for example in the design of cold-formed steel beams or columns. However, cold-formed steel profiles are always produced with rounded corners, and earlier studies showed that the now-used modal decomposition techniques of the constrained finite strip/element method sometimes fail to lead to reasonable results if the rounded corners are directly modelled in the analysis. In this paper a special version of the constrained finite strip method is presented and discussed. The proposed method introduces elastic corner elements, which makes it possible to perform the modal decomposition by the same process used for members with sharp corners, even if the rounded corners are directly modelled, still the results of pure buckling modes satisfy the engineering expectations. The theoretical background of the proposal is briefly summarized, then the elastic-corner approach is discussed by detailed analysis of sample examples as well as by an extended parametric study.