Thin-walled Structural Members Research Articles

The overall imperfection method for fire design situation

In this paper the Overall Imperfection Method, which is a well validated method for the assessment of the global stability resistance of thin-walled steel structural members with any load and supporting conditions, is used for fire design situation. The method uses equivalent initial geometrical imperfection in the shape of relevant elastic global buckling mode. The assessment of the global stability resistance is performed by geometrically nonlinear analysis and by checking of cross-sectional resistance using reduced elastic moduli in the analysis and reduced design strength for the cross-section checking. The validation of the method is carried out through the analysis of more thousands different structural members with hot-rolled I cross-sections. The reference values for the safety study are calculated by geometrically and materially nonlinear analysis with imperfections.

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.

Measurement and visualization of crack patterns in basalt fabric reinforced fine-grained concrete with different textile structures using high-speed photography and a cohesive finite element model

Textile reinforced fine-grained concrete (TRC) is a new type of construction material that can be used for lightweight thin-walled structural members, sandwich thermal insulation composite panels, reinforcement of concrete structures in harsh marine environments, etc. In this paper, the tensile and flexural properties of the basalt fabric with different mesh sizes, different angles of layer, and different warp and weft densities reinforced fine-grained concrete were investigated by using a universal material testing machine through 48 experimental specimens. The crack patterns of the specimens were recorded and analyzed using high-speed photography. A cohesive finite element model was proposed to simulate the flexural properties of basalt fabric reinforced fine-grained concrete. The results showed that as the mesh sizes of basalt fabric increased, its enhancement effect on the tensile and flexural properties of fine-grained concrete weakened. The basalt fabric with a layup angle of 45° exhibited little effect during the hardening stage. Since the weft yarns were arranged along the principal stress direction of the specimens, the weft yarn density presented a great influence on the tensile and flexural properties of basalt fabric reinforced fine-grained concrete, while the effect of warp yarn density on the tensile and flexural properties of basalt fabric reinforced fine-grained concrete was not obvious. When the basalt fiber content was sufficient, the stress could be transferred in time, and the composites illustrated evident strain-hardening and multiple-cracking phenomena when subjected to tensile load. This multiple-cracking mode and the evolution mode of the cracks were recorded by high-speed photography. The finite element analysis results corresponded to the experimental results, which indicated the accuracy and applicability of the established model.

Optimization cross-sectional dimensions for cold-formed steel lipped channel columns

Parametric optimization problem of cross-sectional sizes for cold-formed C-profiles subjected to central compression has been considered by the paper. Parametric optimization problem for cross-sectional sizes of cold-formed C-profiles has been formulated as follow: to define optimum cross-sectional sizes taking into account post-buckling behavior and structural requirements when stripe width and thickness as well as type of the cold-formed profile are constant and defined by the designer.
 Criterion of the profile load-bearing capacity maximization has been assumed as purpose function. The latter has been presented in the form of linear convolution of the resistance to central compression taking into account flexural, torsional and torsional-flexural buckling of thin-walled structural member determined according to the requirements EN 1993-1-3:2012 and EN 1993-1-5:2012. Searching for the optimum cross-sectional sizes has been performed taking into account a possibility of post-critical buckling behavior of the structural member based on the local buckling of the web and flanges and/or distortional buckling of the edge fold stiffeners.
 Formulated parametric optimization problem has been solved using software OptCAD. Update gradient method of the purpose function projection on the active constraints hyperplanes with simultaneous liquidations of the residuals in the constraints has been implemented by the software.
 As optimization results cold-formed C-profiles have been obtained. With the same stripe width optimum profiles have higher load-bearing capacity level taking into account buckling resistance under central compression comparing with the cold-formed C-profiles proposed by Ukrainian manufacturers. Besides, torsional-flexural buckling resistance of the cold-formed C-profile is determinative for all optimum cross-sectional decisions.

Mechanical properties of hybrid fibre reinforced polymer-timber veneer laminates

Hybrid fibre reinforced polymer (FRP)-timber (HFT) thin-walled structural members made out of thin-timber veneer and fibre reinforced polymer composite laminates are a sustainable alternative to light-weight steel and aluminium thin-walled structural members. Preliminary studies on HFT structures have demonstrated the potential of HFT thin-walled structures to be used as high performing structural members. This study is aimed at investigating the effect of manufacturing pressure and the fibre type on the mechanical properties of the HFT laminates. Two different manufacturing pressures and three types of FRPs were used in the investigation. Series of experiments were carried out to determine the tensile, compressive, shear, and flexural properties of the laminates. Best manufacturing pressure as well as the fibre type to use were found to be dependent on the type of loads (membrane and/or flexural) applied on the HFT laminate. Classical laminate theory was found to be accurate in calculating membrane properties of the HFT laminate, but was found to result in significant inaccuracies when calculating the flexural properties.

Constrained shell finite element method of modal buckling analysis for thin-walled members with curved cross-sections

The objective of this study is to develop a constrained shell finite element method (cFEM) for curved cross-sections based on a force-based approach and to enrich the elastic buckling analysis of these thin-walled members for a potentially broader engineering application. These curved thin-walled sections, with significant material efficiency, can experience very complex buckling behaviors that commonly exist for thin-walled members, namely global (G), local (L), and distortional (D) buckling. Given the limitations of the current constrained finite strip method (cFSM) and constrained finite element method for handling curved cross-sections, the cFEM method developed in this study provides a constrained approach to enable buckling mode separation for curved sections. This is a unified method not only applicable to curved sections, but also for straight wall sections. In this study, four criteria utilizing the displacement and force characteristics of modes are defined to separate these mode classes (i.e., G, D, and L). Constraint matrices of G, D, and L mode classes were then constructed and implemented based on the shell element formulations in ANSYS. Numerical examples are presented to demonstrate how the method’s capability in modal decomposition and identification can be applied to the stability analysis of thin-walled structural members, such as circular cylindrical tubes, elliptical cylindrical tubes, and open-branch lipped channel sections with and without rounded corners. All these numerical examples demonstrate the potential of the developed cFEM in advancing structural mechanics to provide an enriched structural analysis capability that can aid the design and enable broad applications of these members.

Theoretical Local Buckling Behavior of Thin-Walled UHPC Flanges Subjected to Pure Compressions.

To enhance structural performance of concrete and reduce its self-weight, ultra-high-performance concrete (UHPC) with superior structural performance has been developed. As UHPC members with 180 MPa or above of the compressive strength can be designed, a rational assessment of thin-walled UHPC structural member may be required to prevent unexpected buckling failure that has not been considered while designing conventional concrete members. In this study, theoretical local buckling behavior of the thin-walled UHPC flanges was investigated using geometrical and material nonlinear analysis with imperfections (GMNIA). For the failure criteria of UHPC, a concrete damaged plasticity (CDP) model was applied to the analysis. Additionally, an elastic-perfectly plastic material model for steel materials was considered as a reference to establish differences in local buckling behavior between the UHPC and steel flanges. Finite element approaches were compared and verified based on test data in the literature. Finally, this study offers several important findings on theoretical local buckling and local bending behavior of UHPC flanges. The inelastic local buckling behavior of UHPC flanges was mainly affected by crack propagation due to its low tensile strength. Based on this study, possibility of the local buckling of UHPC flanges was discussed.

Experimental study on the behaviour of hybrid fibre reinforced polymer–timber thin-walled Cee section columns

Hybrid fibre-reinforced polymer (FRP)-timber (HFT) think-walled structural members are a novel structural concept developed as a sustainable alternative to the steel and aluminium thin-walled structural members. HFT structures are made by combining thin-timber veneers with fibre reinforced polymer composites. Preliminary studies on HFT structures have shown promising results. However, studies into HFT structural members are still at a very early stage. This study aims to investigate the effects of fibre type, manufacturing pressure, and specimen length on the behaviour of HFT Cee section columns. Three different fibre types, namely glass FRP, natural FRP and natural FRP mat were used in the investigation, while two different manufacturing pressures, 0.1 MPa and 1 MPa were also considered. Two different specimen lengths, 280 mm and 1000 mm were considered in the investigation. In total thirty-three specimens were manufactured and tested under axial compression. In addition, material coupon tests were also carried out to determine the tensile and flexural properties of the laminates. Both membrane and flexural elastic modulus was found to increase with the manufacturing pressure. All the Cee section columns tested failed due to local buckling. Addition of FRP was found to significantly increase the load carrying capacity of the pure timber Cee section columns. HFT Cee section columns made using natural FRP mat were found to provide the highest load carrying capacity. HFT Cee section columns manufactured under 1 MPa pressure were found to perform better than the similar columns manufactured under 0.1 MPa pressure. HFT sections were also found to have a higher weight specific load capacity than similar ultra-thin-walled steel Cee section columns.

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.

The Bi-moment Analysis for Thin-wall Component under Non-uniform Torsion

Thin-walled steel structural members are commonly used in order to reduce the weight of the building. It might be influenced by bi-moment, which was induced by torsion. In designs, engineers would normally neglect the bi-moment and let bending moment be the key parameter. However, for some situations, stress due to bi-moment would be greater. This study focus on the stress induced by bi-moment under eccentric load, applying on the flange of I section, which aims to find the critical eccentric to decide whether the bi-moment could be neglected. The model focuses on the plastic state with no buckling, using the finite element software Strand7. The result shows that for the I beam, the bi-moment has to be taken into account if the eccentricity is over 0.4.

Hybrid FRP-timber thin-walled Cee section columns under axial compression: Numerical modelling

This study presents the first ever investigation aimed at accurate numerical modelling of the behavior of hybrid fibre reinforced polymer (FRP)-timber laminated (HFT) Cee section columns under axial compression. Existing numerical modelling approaches for modelling thin-walled structural members, such as modelling using composite laminate shell elements, orthotropic laminate shell elements with experimentally obtained properties, were found to either over-predict or under-predict the stiffness and capacity depending on the approach used. Existing modelling approaches fail to accurately capture the effects of possible interlaminar slips under combined flexural and axial loading. A new modelling approach using ABAQUS subroutine UGENS was proposed incorporating both in-plane stiffness matrix and bending stiffness matrix simultaneously, forming the general section stiffness matrix. Failure initiation criteria and a damage evolution law were incorporated in the subroutine to derive the damaged section stiffness matrix. The predictions from the proposed numerical model showed much improved agreement with the test results.

Fire resistance behaviour of LSF floor-ceiling configurations

Light gauge Steel Frame (LSF) floor-ceiling systems made of thin-walled cold-formed steel structural members deliver innovative, lightweight and cost effective solutions for many floor assemblies. However, the mechanical properties of cold-formed steel structural members deteriorate in fire. Hence fire rated gypsum plasterboard ceilings are required to protect them and avoid premature failures of floor assemblies. However, the behaviour of LSF floor-ceiling systems in fire is not well understood. Hence a series of small-scale standard fire tests was undertaken to investigate the fire resistance of cold-formed LSF floor-ceiling systems of varying configurations. Configurations included structural plywood as the subfloor, gypsum plasterboard ceilings, thin steel sheathing, different joist sections such as lipped channel beam and rivet fastened rectangular hollow flange channel beam and rockwool cavity insulation. The effects of these parameters on the fire resistance of LSF floor-ceiling assemblies are discussed in this paper. Fire resistance improvements of 21–32% were observed when steel sheathing was used in varying configurations. This shows the potential of using thin steel sheathing below the gypsum plasterboard that enhanced the insulation failure times by resisting gypsum plasterboard fall-off. However, cavity insulation led to reduced fire resistance times while plywood subfloors exhibited rapid decomposition and burning when the temperature exceeded 234°C. This paper presents the details of the small-scale standard fire tests of LSF floor-ceiling systems of varying configurations and the results in terms of time-temperature curves and fire resistance times.

Behavior of thin-walled beam-column modular connection subject to bending load

Abstract Steel modular construction has the potential to meet the growing infrastructure needs of the big cities and hence, the demand for modular construction is on the rise. This paper introduces a unique and innovative modular construction technique which involves the use of thin-walled hollow structural steel members and a state-of-the-art cast-steel connector, namely VectorBloc connector. The performance of the beam-column connections to be used in this modular construction largely determines its performance and success. In the present study, uniaxial and biaxial bending behavior of a typical corner beam-column connection made of thin-walled hollow structural steel members and VectorBloc connector was studied through full-scale tests and nonlinear finite element method. This beam-column connection will be used for constructing an assisted living facility. This study concludes that the design loads of the proposed assisted living facility can be safely carried by the VectorBloc connection. However, the weight of the VectorBloc connector can be reduced to 80% without compromising the design requirements of the assisted living facility. This study also concludes that the VectorBloc connection can be considered as a rigid connection. However, effective bracings against horizontal displacements must be provided in the structure in which the connection is intended to be used.

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.

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.

Searching for shear forces flows in arbitrary cross-sections of thin-walled bars: numerical algorithm and software implementation

Development of a general computer program for the design and verification of thin-walled bar structural members remains an actual task. Despite the prevailing influence of normal stresses on the stress-strain state of thin-walled bars design and verification of thin-walled structural members should be performed taking into account not only normal stresses, but also shear stresses.Therefore, in the paper a thin-walled bar of an arbitrary cross-section which is undergone to the general load case is considered as investigated object. The main research question is development of mathematical support and knoware for numerical solution for the shear stresses problem with orientation on software implementation in a computer-aided design system for thin-walled bar structures.The problem of shear stresses outside longitudinal edges of an arbitrary cross-section (including open-closed multi-contour cross-sections) of a thin-walled bar subjected to the general load case has been considered in the paper. The formulated problem has been reduced to the searching problem for unknown shear forces flows that have the least value of the Castigliano’s functional. Besides, constraints-equalities of shear forces flows equilibrium formulated for cross-section branch points, as well as equilibrium equation formulated for the whole cross-section relating to longitudinal axes of the thin-walled bar have been taken into account.A detailed numerical algorithm intended to solve the formulated problem has been proposed by the paper. The algorithm is oriented on software implementation in systems of computer-aided design of thin-walled bar structures. Developed algorithm has been implemented in SCAD Office environment by the program TONUS. Numerical examples for calculation of thin-walled bars with open and open-closed multi-contour cross-sections have been considered in order to validate developed algorithm and verify calculation accuracy for sectorial cross-section geometrical properties and shear stresses caused by warping torque and shear forces. Validity of the calculation results obtained using developed software has been proven by considered examples.

Modal decomposition of coupled instabilities: The method of the equivalent nodal forces

A solution to the ‘modal decomposition problem’ encountered within the context of the stability analysis of thin-walled structural members is presented. The proposed method achieves decomposition of a randomly deformed shape into a number of constituent modes, which have the physical meaning of the classical local, distortional and global buckling modes, augmented with two additional classes of shear and transverse extension modes. The basis vectors of these five classes are created by defining sets of nodal forces which, when applied to the member in a first order linear elastic problem, generate shapes commensurate with specific mechanical criteria defining the local, distortional, global, shear and transverse extension modes. In a second step the basis vectors of a given class are used to define a constrained stability problem, where the solution is restricted to a linear combination of these basis vectors, in order to obtain the buckled shapes under a given loading. The full set of buckling modes spanning the five classes forms an orthonormal basis of the complete deformation space. Consequently, decomposition can be achieved by projecting the shape which is to be decomposed onto the basis vectors. Two examples are provided to illustrate the method.

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.

Modal identification of thin-walled members by using the constrained finite element method

Thin-walled structural members have complex behavior. It is usual to interpret the complex behavior as the superposition of simpler behavior components, like global, distortional, local, in-plane shear and transverse extension. When the standard shell finite element method is employed for the analysis, the behavior components are not separated, and the results can be difficult to interpret due to the complexity of the deformations. The results are more meaningful if identified, i.e., if the participations of the behavior components are quantified. Methods for the formal identification of the deformations have already been proposed, by using either the modes of generalized beam theory, or the basis functions of the constrained finite strip method. In this paper a newer and more general method, the constrained finite element method is used. Since this method can handle a wide range of thin-walled members, including members with holes, or members with varying cross-sections, or even stiffened plates, the identification can readily be applied to various thin-walled members. In the paper some particularities of the identification method are highlighted, as well as several sample examples are presented and discussed.

Constrained Finite Strip Method with Rigid Corner Element for the Buckling Analysis of Thin-Walled Members with Rounded Corners

In this paper modal decomposition of the deformations of thin-walled structural members are discussed. Modal decomposition is a process which separates the characteristic behavior modes. If applied in buckling analysis, modal decomposition makes it possible to analyze pure global or pure distortional buckling or pure local-plate buckling. Ability to calculate critical loads to a pure buckling mode is highly useful in the design of thin-walled structural members, such as cold-formed steel beams or columns. 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 element method and generalized beam theory fail to lead to reasonable results if the rounded corners are directly modelled in the analysis. An extension to the constrained finite strip method is proposed and discussed. The proposal introduces rigid corner elements, which make 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. The formulation of the proposal is summarized, then the rigid-corner approach is studied by an extended parametric study.