Thin-walled Open Section Research Articles

Educational Software for Stress Analysis of Open Thin-Walled Structures

Thin-walled structures are commonly employed in aerospace and automotive structures because of their high strength to weight ratio. Design and hence the stress analysis of thin-walled structures is tedious and time-consuming. An educational software which can aid students in stress analysis of thin-walled open sections will enhance the teaching-learning process. With the present available software, the number of sections that can be analysed is limited, hence in this work, a generalized section has been developed through which many new complex sections can be generated and analysed for stresses. The objective of the present work is to develop educational software that will provide a solution for the section properties like centroid, moment of inertia and shear centre, and the stresses on the section for a given loading. The software enables students to select different cross-sections which may be subjected to bending, shear or torsional loads and evaluate the stresses on it. Results obtained through this software have been validated against literature. The software has been developed using MATLAB with graphical user interface (GUI). The software is expected to be a useful tool for effective teaching learning process of courses on thin-walled structures, aircraft structures and advanced mechanics of materials.

Numerical Evaluation of Lateral Torsional Buckling of PFRP Channel Beams under Pure Bending

The use of pultruded fiber reinforced polymers (PFRPs) in strengthening and sustainable design of bridges and other structures exposed to corrosion and resistance reduction factors is growing rapidly. However, a comprehensive understanding of the structural behavior of these materials under various loading conditions is crucial to unlock their full potential and promote their wider use in diverse structural and industrial applications. Pultrusion profiles can be also used as beams in bridges. One important aspect of the structural behavior of PFRPs is their buckling behavior, particularly in thin-walled open cross sections. Lateral torsional buckling is a probable instability mode for beams with thin-walled open cross sections that are not laterally restrained along their span. Therefore, research on the buckling behavior of PFRP members is essential. In this study, the analytical responses of channel-shaped PFRP beams in bridges under pure bending are calculated using an equation in the Eurocode 3 regulation. The buckling behavior of these beams is then investigated through numerical modeling using the finite element package Abaqus. A total of 75 specimens of PFRP channel profiles with different thicknesses in various spans and lateral restraint conditions are studied for their lateral-torsional buckling behavior. This study uniquely explores the behavior of PFRP beams with lateral restraints, a novel aspect in the field of lateral-torsional buckling research of PFRP beams. The results show that the analytical equation used for these beams needs to be modified to more accurately estimate the buckling loads of FRP beams under the conditions studied in this paper.

Asymmetric Folded Plate with Parallel Edges in Validation of their Static Behavior by Combining Vlasov Torsion Theory with Bernoulli Bending Theory

Aims: A new hybrid procedure that combines the Vlasov torsion theory with the Bernoulli bending theory is presented herein, to demonstrate qualitatively and quantitatively the operation of asymmetric folded plates with parallel edges, which are loaded with gravity static loads. Background: A recently proposed technique based on Vlasov torsion theory is used for the exact calculation of the Principal Elastic Reference System in a reinforced concrete folded plate having an asymmetric thin-walled open cross-section with parallel edges. Moreover, the warping moment (or bi-moment) concept of the Vlasov theory is combined with the pure-bending around two axes, according to the Bernoulli bending theory, to determine the normal stresses along the longitudinal dimension of the folded plate. Methods: Τhe warping properties of a thin-walled open cross-section are determined by calculating: (a) the elastic characteristics (elastic center, principal axes) of the section, (b) the principal start point, the sectorial coordinates, the wrapping moment of inertia and the wrapping stiffness of the section. Finally, the normal stresses along the longitudinal dimension are calculated considering the bi-axes flexure with the bi-moment phenomenon. Results: Τhe exact solution of normal stresses at the middle section of an examined folded plate along the longitudinal dimension is found by combining the Bernoulli bending theory for prismatic beams and the Vlasov torsion theory for thin-walled open sections. Conclusion: The current procedure can be used as a benchmark analysis method of asymmetric folded plates in order to evaluate the reliability of the results of various analysis F.E.M. software, covering an open issue of the structural analysis of special structures.

ANALYSIS OF MECHANICAL CHARACTERISTICS OF KNOT CONNECTIONS IN BUILDING STRUCTURES BASED ON ANSYS SIMULATION

The most common cross-section – the joining of two symmetrical I-beams – is investigated in this work. The transmission of force on the node connection in the form of a multi-bolt connection, welded connection, welded connection through the lining is modeled. The effect of node connections on the stress-strain state of the spatial structure made of thin-walled open section rods, torsional effects depending on the fastening of the elements is studied. The calculation of the structure is reduced to the determination of the stresses and displacements in the fastening nodes, by which the change in the mechanical characteristics of steel is then determined.

Advances on kinematically exact rod models for thin-walled open-section members: Consistent warping function and nonlinear constitutive equation

This work proposes two advances on kinematically exact rod models for thin-walled open section members: (i) an explicit analytical expression for the cross-section warping function, including both primary and secondary warping for arbitrary section geometries, and (ii) a nonlinear elastic constitutive equation with all higher-order strain terms included, suitable for truly finite strains. By not neglecting any of the strain terms at the constitutive level, full bending, compression and torsional strain couplings are enabled. This improves the model performance in capturing buckling phenomena and describing the developed post-critical configurations. Since the stress-resultants end up with elaborate expressions, numerical rather than analytical integration over the cross-section is preferred for their computation, which explains the need for knowing a priori the warping function (and its directional derivatives) in the entire cross-section, including in the thickness direction. The advances are implemented in a 7-DOF (3 displacements, 3 rotations and one warping intensity) rod model available in an in-house finite element program. Validation is performed using existing results from the literature as well as solutions obtained with shell models from a commercial software. The proposed advances proved to fix pathological behavior of previous rod models in both torsional and lateral–torsional buckling problems, as well as numerical convergence issues in developed post-critical configurations.

Center of Stiffness, Principal Axes and Principal Start Point of Thin-Walled Open-Sections of Cores: A New Modified Calculation Technique Based on Vlasov Torsion Theory

The present paper deals with the exact calculation of the Principal Elastic Reference System of R/C Cores, which have thin-walled open section. A new modified technique based on Vlasov torsion theory is developed that examines the warping phenomenon of cores. The exact position of the elastic center (or shear center) of a core and the orientation of the principal axes of elasticity, as well as the exact calculation of warping constant, are special parameters since, on the one hand it strongly affects the in plan stiffness distribution of the building members, and on the other hand it affects the values of the building eigen-frequencies and mode-shapes. These parameters are particularly critical in seismic design of asymmetric multistorey buildings. Based on Vlasov torsion theory of cores with thin-walled open sections, a repetitive mathematical procedure about the calculation of the location of the elastic center of core and the principal start point of the section is proposed. This new modified technique can be applied to cores of any shape. Afterwards, the exact diagram of sectorial coordinates of the section, as well as the warping constant, are calculated. All the above-mentioned parameters are very useful in the simulation of the cores in numerical models that are going to use in linear and nonlinear seismic analysis of the structures. Knowing all mentioned parameters, the numerical accuracy of the finite element method on cores can be checked. Finally, a numerical example, where the proposed new modified technique is applied on a fully asymmetric core, is presented.

FINITE ELEMENT ANALYSIS FOR THIN-WALLED MEMBER SUBJECTED TO COMBINED LOADING

Thin-walled structures are widely used in various structural engineering applications due to their advantage of high bearing strength when compared to self-weight and used in a complex loading situation where subjected to combined loadings. When a thin-walled section is subjected to a combined load with restrained torsion, they are ineffective at resisting, resulting in a reduction in beam capacity due to torsion and additional warping stresses. A finite element calculation can be used to analyze a 3D bar of thin-walled structural sections. Different commercial software and studies commonly consider six degrees of freedom at each node of a member for a space frame without considering the effect of warping restraint at the member's ends. This paper presents a finite element calculation for thin-walled sections with restrained torsion using the 14x14 member stiffness matrix, which includes warping as an additional degree of freedom and is commonly used for open thin-walled sections. In this study, we considered two different methods for including the additional degree of freedom for the stiffness matrix, which are very close to each other for small values of characteristics number.

Experimental investigation of four-point bending of thin walled open section steel beam loaded and set in the shear center

Thin walled cold formed structures were, and still are, very popular structural elements used in mechanical engineering. Modern technology and the progress in materials engineering allow to fabricate various shapes of thin walled cold formed components. Therefore, combinations between technology possibilities, material properties, loads and engineering requirements are wide and unlimited for thin walled components. The aim of this paper is to perform an experimental study of cold formed C-channel steel beams under four-points bending loads based on the global and the local buckling phenomena. A test rig was developed with a specially designed support system to subject thin-walled steel beams to a four-point bending load, where the support and loads were applied to the shear center of the open section steel beam. It is shown that it is not possible to completely eliminate the torque load on a thin-walled beam with an open section where load and support are applied in the shear center because investigated beams weren’t ideal made. Thin walled open section beams are very sensitive for boundary conditions and geometrical accuracy. The force of gravity is also working. The presented research methodology can be improved and do test with other open section thin walled beams.

Exact solutions for thin-walled composite open section beams using a unified state space coupled field formulation

Thin-walled open section composite beams (TWOSCB) used extensively in aerospace structures exhibit several non-classical effects such as torsional warping, warping shear, material coupling, and shear deformation. Arbitrary cross-section and material coupling make the governing equations highly coupled and difficult to solve analytically. In this paper, a unified coupled-field formulation is developed to analyze TWOSCB accommodating all non-classical effects. Using the state-space method to derive analytical expressions for displacements and forces, Vlasov solutions of isotropic beams are recovered. Results obtained for arbitrarily laminated mono-symmetric composite channel and I-section beams subjected to bending and torsion loads show excellent agreement with available results in the literature.

Transformation Matrix for Combined Loads Applied to Thin-Walled Structures

This paper transforms combined loads, applied at an arbitrary point of a thin-walled open section beam, to the shear centre of the cross-section of the beam. Therein, a generalized transformation matrix for loads with respect to the shear centre is derived, this accounting for the bimoments that develop due to the way the combined loads are applied. This and the authors’ earlier paper (World Journal of Mechanics 2021, 11, 205-236) provide a full solution to the theory of thin-walled, open-section structures bearing combined loading. The earlier work identified arbitrary loading with the section’s area properties that are necessary to axial and shear stress calculations within the structure’s thin walls. In the previous paper attention is paid to the relevant axes of loading and to the transformations of loading required between axes for stress calculations arising from tension/compression, bending, torsion and shear. The derivation of the general transformation matrix applies to all types of loadings including, axial tensile and compression forces, transverse shear, longitudinal bending. One application, representing all these load cases, is given of a simple channel cantilever with an eccentrically located end load.

Seismic performance of ATLS modular house based on joint stiffness analysis

Modular buildings have developed rapidly in recent years due to the advantages of environmental protection, fast construction, and guaranteed construction quality. As a form of a modular structure, the assembled-type light steel (ATLS) modular house possesses the following additional features: it can be easily disassembled, transported, and the column can be separated from the top and bottom frames. The structural components of the modular unit adopt cold-formed open thin-walled sections; their connection is weak, which results in low structural integrity. Therefore, the connection performance and evaluation of the lateral stiffness have always been the focus of research. In this study, firstly, a two-story ATLS modular house is tested for quasi-static loading, and the finite element software ABAQUS is used to compare the test results. Then, to improve the analysis efficiency based on the modeling simplification, the stiffness analysis of the intra-modular connections and the inter-modular connections of the ATLS modular house was carried out. The simplified method of connections was then proposed. Finally, based on the developed simplified model, the seismic performance of the two-story ATLS modular house was obtained and validated with test findings. Results demonstrated that the structure showed a suitable degree of ductility and energy consumption. The simplification of intra-modular joints as semi-rigid, while inter-modular joints as rigid were found reasonable to adequately obtain the overall seismic response of the structure. Hence, the study provides a foundation for applying ATLS modular houses in temporary housing after the earthquake rehabilitation.

General Stiffness Matrix for a Thin-Walled, Open-Section Beam Structure

This paper is to review the theory of thin-walled beam structures of the open cross-section. There is scant information on the performance of structures made from thin-walled beam elements, particularly those of open sections, where the behavior is considerably complicated by the coupling of tensile, bending and torsional loading modes. In the combined loading theory of thin-walled structures, it is useful to mention that for a thin-walled beam, the value of direct stress at a point on the cross-section depends on its position, the geometrical properties of the cross-section and the applied loading. This applies whether the thin-walled section is closed or open but this study will be directed primarily at the latter. Theoretical analyses of structures are fairly well established, considered in multi-various applications by many scientists. However, due to the present interest in lightweight structures, it is necessary to specify where the present theory lies. It does not, for example, deal with compression and the consequent failure modes under global and local buckling. Indeed, with the inclusion of strut buckling failure and any other unforeseen collapse modes, the need was perceived for further research into the subject. Presently, a survey of the published works has shown in the following: 1) The assumptions used in deriving the underlying theory of thin-walled beams are not clearly stated or easily understood; 2) The transformations of a load system from arbitrary axis to those at the relevant centre of rotation are incomplete. Thus, an incorrect stress distribution may result in; 3) Several methods are found in the recent literature for analyzing the behaviour of thin-walled open section beams under combined loading. These reveal the need appears for further study upon their torsion/flexural behaviour when referred to any arbitrary axis, a common case found in practice. This review covers the following areas: 1) Refinement to existing theory to clarify those observations made in 1 - 3 above; 2) Derivation of a general elastic stiffness matrix for combined loading; 3) Calculation of the stress distribution on the cross-section of a thin-walled beam. A general transformation matrix that accounts for a load system applied at an arbitrary point on the cross-section will be published in a future paper.

Modeling of the Vibratory Tube Finisher Container

Abstract The paper is dedicated to the problem of modeling the container of vibratory tube finisher additive manufacturing technology. The aim of the research is to develop an engineering approach of designing a rational model of deformative oscillations of a big size container. A thin-walled open cross section cylindrical beam is used as a model of bend and rotation of the vibratory tube finisher container. A method of division of all components of a strain and deformative state into the main and secondary is used to evaluate variants of a model of the vibratory tube finisher container. A ratio of the principle dimension of a cross section and changing of the stress-strain state is used as a weight parameter of components of potential and kinetic energy. A shear model of a thin-walled beam can be used to study the dynamic deformations not only in the elongated containers but in containers with commensurable quantities of its specific dimensions, too. Accuracy regarding the main natural frequency will be satisfied (with error about 1 %) when the length of the container is two times greater than a specific dimension of a cross section. Conditions of the rational models of deformation vibrations of containers are presented in a graph form that is comfortable in engineering practice.

Thin-walled composite beam cross-sectional analysis using the mechanics of structure genome

Quick and accurate predictions of cross-sectional properties are required in the preliminary design of thin-walled composite beams. Existing literature provides accurate analytical solutions to the problem, albeit limited to open and single cell sections with stress continuity constraints imposed. Mechanics of structure genome has been used to develop an asymptotically correct model for thin-walled open, closed, single and multi-cell cross sections consisting of any arbitrary anisotropic material without imposing any additional conditions. In this paper, Euler-Bernoulli thin-walled beam cross-sectional model is developed in a finite element framework and demonstrated using several examples, followed by a comparison with existing approaches.

Dynamic Modeling of Metal Columns with Open Thin-Walled Sections

High-height columns become more economically viable when designed with thin-walled open cross-sections. For such structural release, there is the occurrence of the flexion-torsion phenomenon and the evident loss of lateral stiffness, which can be reduced with the presence of bracing by lintels spaced at height. In the case of road bridges and overhead cranes, there is a low traffic speed, characterizing internal forces that allow the use of cross-sections folded into C and Z-shaped sheet metal, as well as double-T-shaped welded metal sections. In this sense, this paper is intended to contribute to the advancement of the Continuous Medium Technique (CMT) formulation through the Wall Panel Theory (WPT) applied to the thin-walled columns. Through the WPT applied to thin-walled sections, it is possible to express the system of differential equations of the static problem, characterizing the rigidity of the core column via matrix [J] and bracing by matrix [S]. In item 2.3, the inclusion of the dynamic portion in the WPT is performed, thus providing the determination and characterization of the first seven vibration modes of the abovementioned column. Finally, this paper provides the structural engineer with a manual verification tool (via CMT) of static or dynamic modeling for thin-walled columns using commercial software. In this paper we used software ANSYS 2019 R1 (student version) for such numerical checks and validations.

Buckling resistance of steel H-section beam–columns: In-plane buckling resistance

Buckling resistance predictions resulting from flexural and flexural–torsional buckling of double tee section members subjected to compression and bending are considered. A novel analytical model is developed for establishing design criteria based on decomposition of the member buckling behaviour into in-plane and out-of-plane resistance. The former is based on second-order bending relationships of load effects of structural members with in-plane equivalent imperfections, while the latter is based on the stability theory of thin-walled open sections. First part of this study presents an analytical formulation of the in-plane buckling resistance of beam–columns. In this regard, further decomposition is postulated for the in-plane first-order bending moment diagram that results in the loading state to be the superposition of two components. The first component is related to symmetrical loading and the second to antisymmetric loading. To consider the second-order effects, prebuckling displacements generated by the abovementioned loading components are amplified with regard to the inversion of the residuum of the buckling force utilisation ratio in order to obtain approximate values of second-order displacements and internal moments. As a result, the in-plane interaction curve, expressed in dimensionless coordinates, that describes the beam–column in-plane flexural buckling resistance without considering lateral–torsional buckling effects, is obtained. The results of nonlinear finite element simulations are used for the verification of the developed analytical formulation. It is concluded that this proposal yields less conservative predictions than those based on the interaction relationships of clause 6.3.3 of Eurocode 3, Part 1–1.

Sectional constitutive model for the thin-walled steel H-section beam-column element

To evaluate the seismic performance of steel frames employing thin-walled open-section members, an accurate hysteretic model that considers the unfavorable coupling effects of plastic deformation and local buckling behavior is needed. The constitutive model for a steel H-section beam-column element considering the effect of local buckling can achieve both computational accuracy and efficiency and thus have great potential for nonlinear analyses. This constitutive model is therefore chosen as the basis for the macro calculative curves. Then, a sectional hysteretic model for H-sections subjected to cyclic loading, considering the deteriorations caused by local buckling, is proposed. By employing a validated finite element analysis model created using the software ABAQUS, an extensive parametric study involving 300H-sectional beam-columns with different plate width-thickness ratios and axial force ratios is conducted to identify the parameters for the H-sectional hysteretic model. The proposed model considering the effect of inelastic local buckling is indicated to accurately predict the nonlinear cyclic response of H-sections through the entire loading process.

Bifurcation and large-deflection analyses of thin-walled beam-columns with non-symmetric open-sections

Non-symmetric thin-walled open-sections are used extensively in metal structures. The behaviour of such sections is usually complex because their shear centre and centroid do not coincide, and as a result, they are often susceptible to lateral-torsional and/or flexural-torsional buckling. This paper develops an efficient and robust computational framework for practical application, including a refined beam-column element for non-symmetric sections, a cross-section analysis algorithm for determining pertinent properties of open-sections, and an Updated-Lagrangian (UL) solution method for large deflection analysis. Details of the derivation of element stiffness matrices and the related numerical procedures are provided. Several examples are given that demonstrate accurate results from its implementation within the educational structural analysis software MASTAN2.

Spectral Dynamic Analysis of Torsional Vibrations of Thin-Walled Open Section Beams Restrained Against Warping at One End and Transversely Restrained at the Other End

The present paper deals with spectral dynamic analysis of free torsional vibration of doubly symmetric thin-walled beams of open section. Spectral frequency equation is derived in this paper for the case of rotationally restrained doubly-symmetric thin-walled beam with one end rotationally restrained and transversely restrained at the other end. The resulting transcendental frequency equation with appropriate boundary conditions is derived and is solved for varying values of warping parameter and the rotational and transverse restraint parameter. The influence of rotational restraint parameter, transverse restraint parameter and warping parameter on the free torsional vibration frequencies is investigated in detail. A MATLAB computer program is developed to solve the spectral frequency equation derived in this paper. Numerical results for natural frequencies for various values of rotational and transverse restraint parameters for various values of warping parameter are obtained and presented in both tabular as well as graphical form showing the influence of these parameters on the first fundamental torsional frequency parameter.

Torsional Post-Buckling of a Simply Supported Thin-Walled Open-Section Beam Resting on a Two-Parameter Foundation

The problem of the post-buckling response of a simply supported thin-walled beam subjected to an axial compressive load and supported by the Winkler–Pasternak foundation is studied in this paper. The strains are assumed to be small and elastic. The shear deformations and the in-plane cross-sectional deformations are assumed to be negligible. The post-buckling paths of the simply supported beam are determined for different values of the Winkler and Pasternak stiffness parameters. Bifurcation points are found.