Thin-walled Beams Research Articles

Experimental, Numerical and Analytical Evaluation of Load-Bearing Capacity of Cold-Formed S-Beam with Sectional Transverse Strengthening

The article provides information about strengthening cold-formed thin-walled steel beams made of the sigma profile. An innovative concept for sectional transverse strengthening of thin-walled beams subjected to concentrated forces was investigated. The proposed solution’s novelty lies in attaching the sectional transverse strengthening to the beam’s cross-section, employing a point crimping technique. This technique requires a specific modification of the cross-section edges, necessitating double-lipped flanges. This strengthening method is innovative, as it has not been previously applied to cold-formed structures. Typically, strengthening is achieved using other cold-formed elements or materials, such as timber, lightweight concrete, or CFRP tapes. The laboratory experimentally validated the proposed method using short- and medium-length beams. The experimental results were then compared with the results of the numerical analyses and the conventional design approach described in EC3. The results demonstrated the feasibility of implementing this type of strengthening, its reliability under load, and the confirmation of an increase in the load-bearing capacity of the experimental samples by 11–24%.

Integrated Dynamic Analysis of Thin-Walled Beams: Coupled Bidirectional Bending, Torsion, and Axial Vibrations Under Axial Loads

This paper proposes a beam model integrating the Timoshenko beam theory with Vlasov beam theory to capture the coupled behavior of bidirectional bending, torsion, and axial vibration in thin-walled beams subjected to axial loads. Our model incorporates the effects of shear deformation, rotational inertia, and axial loads, offering a comprehensive approach to complex dynamic behaviors. By utilizing Hamilton’s principle, we derived a complete set of coupled dynamic equations and boundary conditions. The highlight of this model is its capacity to accurately predict the dynamic response of thin-walled beams under multifaceted loading conditions, surpassing traditional models by integrating coupled axial vibrations. This research significantly advances the understanding of the dynamic behavior of thin-walled beams, providing a precise analytical tool for structural design and safety assessment. The robustness and accuracy of the proposed model were validated through extensive theoretical analysis and empirical validation, equipping engineers with critical insights to optimize the design of engineering structures subjected to complex dynamic loads.

Beam finite element models with node dependent kinematics and arbitrary displacement fields over the cross-section

The present paper proposes new, improved one-dimensional finite elements that use the node-dependent kinematics method, i.e. each node may adopt a different expansion over the cross-section without using a special coupling method. Furthermore, the presented method is able to choose independent models for each of the three displacement variables. In particular, Taylor-based and Lagrange-based functions have been chosen as expansions for the cross-sections. These two outcomes are possible through the use of the Carrera Unified Formulation, which subdivides the three-dimensional displacement field into a cross-section domain and an axis domain. Starting from the principle of virtual displacements, the governing equations and finite element matrices are obtained. In numerical results, compact and thin-walled beams have been studied and subjected to various loading conditions, including bending and torsion-bending. The selected cases are compared with existing literature or with high-refined CUF-based solutions. The accuracy of the models presented is assessed for both displacements and stress components. The results show that the choice of the ‘best’ computational models in terms of accuracy vs degree of freedom is problem-dependent. Finally, the Node-dependent kinematics method permits the selection of the most suitable expansions for each cross-section.

Numerical investigation on bending characteristic and ductile fracture of AA7075 thin-walled beam using advanced orthotropic plasticity and fracture models

Thin-walled structures manufactured from the 7075 aluminum alloy are gaining tremendous attention in the automotive industry for their potential to reduce vehicle weight. However, the bending characteristics and rupture behavior of the AA7075 thin-walled beams under unexpected collision events have not been extensively studied. This study aims to fill that gap through a detailed numerical investigation of the bending deformation and failure mechanism of AA7075 thin-walled beams under quasi-static three-point bending at room temperature. Full-size, three-dimensional numerical simulations of laboratory-scale AA7075-T6 hat-shaped beam were conducted using the ABAQUS/Explicit solver. The material elastic–plastic response is described by a rate-independent constitutive description, incorporating advanced non-quadratic orthotropic plasticity and anisotropic ductile fracture criteria via VUMAT subroutines. Results indicate that the simulations accurately reproduced experimental observations, including the loading-displacement curves and deformation patterns. The bending behavior of the AA7075-T6 thin-walled beams aligns with typical bending collapse mechanisms, consistent with Kecman’s theory. The rupture process exhibits ductile fracture characteristics, with heterogeneous stress distribution across the material thickness affecting crack initiation rates between the upper and lower surfaces. Notably, the stress state at the fracture’s half-thickness section approximates an equi-biaxial tension condition. These findings provide essential insights into the bending deformation and failure mechanisms of AA7075 thin-walled structures under unexpected impact loading.

Asymptotic Numerical Method for dynamic buckling of shell structures with follower pressure

Asymptotic Numerical Method (ANM) is applied to non-linear dynamics of thin-shells subjected to conservative and non-conservative loads such as follower pressure. ANM is decomposed into several stages: the finite element discretization of the non-linear equations of motion of the shell dynamics, a homotopy transformation of the semi-discrete non-linear equations, a perturbation technique to expand the quantities into Taylor series according to the homotopy parameter and the time integration scheme to solve the series of linear problems resulting from the perturbation technique. ANM is applied here with the 7-parameter shell elements thanks to the Enhanced Assumed Strain (EAS) concept and implicit Newmark integration. In the case of non-conservative force, follower pressure also requires to be decomposed in either Taylor series or rational Padé approximants. The academic case of the cylindrical roof with dynamic snap-through phenomenon is investigated for the purpose of comparing ANM strategies and the classical Newton–Raphson (NR) method. Two engineering cases including an I-shaped thin-walled beam and a closed thin-shell cylinder under dynamic external follower pressure are also investigated. ANM turns out to be accurate, robust and efficient in terms of computation time, providing an alternative method to the well-established Newton–Raphson method.

Local-global buckling interaction in steel I-beams—A European design proposal for the case of fire

This paper presents a comprehensive review of the developments leading to the proposal of European fire design rules for steel beams with thin-walled I-sections. Thin-walled beams are favoured in steel construction due to their structural efficiency, however they are prone to buckle when subjected to in-plane loads, phenomenon which requires a thorough investigation. The focus lies on addressing the interaction between local and global buckling in these members. This study discusses modifications to the Effective Width Method at elevated temperatures, aiming to rectify underestimation of section capacity on certain cross-sections. Additionally, an overview of lateral-torsional buckling resistance is provided, being a new Effective Section Factor proposed to account for its interaction with local buckling. The paper revisits the European fire design proposal, comparing the improvements of the existing Eurocode 3 Part 1–2 (EN1993-1-2:2005) relative to the recent second generation of Part 1–2 of Eurocode 3 (FprEN1993-1-2:2023) through an extensive numerical study. Limitations and future research directions are also discussed, such as dependency on the section classification and broadening the application scope of these rules to higher steel grades.

A simple but accurate FEM for lateral-torsional buckling loads of mono-symmetric thin-walled beams considering pre-buckling effects

This study intends to present a simple but accurate FE buckling analysis procedure in order to determine lateral-torsional buckling (LTB) loads of mono-symmetric steel beams considering pre-buckling effects. For this, a nonlinear co-rotational FEM for lateral-torsional post-buckling of a thin-walled beam system with non-symmetric cross sections is summarized in which all displacement parameters are defined at centroid. After that, an iterative LTB analysis method is newly proposed with consideration of in-plane deformations due to external loads. Through numerical examples, it is demonstrated that buckling solutions by this method are very well matched with those by lateral post-buckling analysis of the steel beam with lateral imperfections. Finally, numerical results on LTB of simple/cantilever beams under conservative moments, simple beams under gradient moments, simple beams under eccentric compression, a cantilever beam with an un-symmetric channel section, and a cantilever right-angle frame with I-section are presented using conventional LTB, iterative LTB, and post-buckling analysis methods.

Nonlinear free vibrations of a structurally tailored anisotropic pre-twisted thin-walled beam subjected to large deformations

It is essential to understand the nonlinear free vibration behaviour of a thin-walled composite structure as they find their applications in harsher environments prone to large deformations. Further, these structures made of fibrous materials, have directional properties for different fibre orientations resulting in a diversified and a complex nonlinear behaviour. In this regard, present work provides a comprehensive mathematical formulation on nonlinear vibration of pre-twisted thin-walled anisotropic box beam. The mathematical model is derived as coupled (flap-lag-extension-torsion) model considering shear deformation and green's strain tensor for large displacements in order to study the influence of nonlinear couplings on the dynamic behaviour. The derived energy equations are presented depending on degree of nonlinearity. These nonlinear equations those derived are nondimensionalized and solved with in the frame work of energy method using classical Ritz approximation. An iterative method is used to solve the nonlinear equations pertaining displacement terms. This nonlinear behaviour is evaluated for two important types of structural tailoring techniques available for thin-walled composite beams namely Circumferentially Asymmetric Stiffness (CAS) and Circumferentially Uniform Stiffness (CUS). It is found that CAS layup experiences significantly severe nonlinear effects compared to CUS due to the presence of 3rd degree nonlinear coupling terms. The variation of nonlinear frequency ratios over different ply angles showing the influence of nonlinearity on fibres orientation is presented for the first time for the two ply lay ups. The influence of degree of nonlinearity on the accuracy of the nonlinear frequencies is evaluated and presented. Moreover, the impact of nonlinearity on the pre-twisted beam is presented for different pre-twist angles.

Damage detection in composite and plastic thin-wall beams by operational modal analysis: An experimental assessment

The detection and localization of different damage features in thin-wall beam composite and plastic beams using Operational Modal Analysis (OMA) has been demonstrated experimentally. The detection of small damage features using modal analysis techniques is an emerging field, with few experimental OMA-based assessments having been reported so far. The proposed method is based on OMA combined with Stochastic Subspace Identification (SSI) and the enhancement of damage features by Continuous Wavelet Transforms (CWT). A composite thin-wall beam (CTWB) structure in two measurement configurations and a PVC tube in a free-free configuration have been tested. Damage features detected include extra masses attached to the beam, with a range from 9.5 % to 14.0 % of the beam mass, and small cracks perpendicular to the beam axis with lengths of about 4 % of the perimeter of the cross section. Calibration curves relating the strength of the damage signal with the weight of the attached masses have been constructed. Two simultaneous cracks or two masses could be detected as well. The quantification and localization of damage feature along the beam was possible through the use of Gaussian fit surface applied to damage maps obtained with the CWT technique. The width of the Gaussian fit curve was of the order of the distance between accelerometers, but the accuracy, estimated to be around 3 % of the beam length, was found to have sub-grid resolution. The proposed method was shown to work reliably with a relatively coarse measurement grid, potentially allowing for cost-effective Structural Health Monitoring (SHM) approaches.

Bending-torsional vibration response of modified Timoshenko thin-walled beams under moving harmonic loads

In this paper, a new method is proposed for calculating the bending-torsional vibration response of modified Timoshenko thin-walled beams under moving harmonic loads. The boundary conditions of the beams are considered to be simply supported at both ends. By using Fourier and Laplace transformations, analytical solutions for vibration responses are derived. For the validation of the proposed method, the results obtained using the proposed method are compared with those acquired by the finite element method (FEM). Through the parametric analysis, the effects of cross-sectional properties as well as the load magnitude, velocity, and eccentricity are further investigated. The results indicate that: (1) compared to the method that ignores shear rotary inertia, the vertical displacement of the beam at the midspan calculated by the proposed method shows an accuracy improvement of up to 6.87%; (2) the bending-torsional vibration frequency increases with the growth of the torsional moment of inertia; (3) when the velocity increases from 20 m/s to 80 m/s, the difference in the maximum displacement at the midspan is essentially within 5%; (4) the bending-torsional vibration response is significantly influenced by the load magnitude and eccentricity, whereas the vibration frequency of the beam remains unaffected by these variations; (5) an increase in load velocity does not always lead to a greater response from the beam, which can be explained from the perspective of resonance.

Coupling Effects and Resonant Characteristics of Rotating Composite Thin-Walled Beams in Hygrothermal Environments

Coupling Effects and Resonant Characteristics of Rotating Composite Thin-Walled Beams in Hygrothermal Environments

A one-dimensional higher-order dynamic modeling method for thin-walled beams with circular cross-sections

This paper addresses the construction of a dynamical model for a thin-walled beam with circular cross-section in the framework of one-dimensional higher-order beam theory. And a method for pattern recognition of circular thin-walled structures is proposed based on principal component analysis. Initially, a set of equal length linear segments are defined to discretize the mid-line of a circular section. Preliminary deformation modes of thin-walled structures, defined over the cross-section through kinematic concept, are parametrically derived through changing the discretization degree of the section. Next, the generalized eigenvectors are derived from the governing equations, and the characteristic deformation modes of circular sections with different discretization degrees are solved based on principal component analysis. In addition, a reduced higher-order model can be obtained by updating the initial governing equations with a selective set of cross-section deformation modes. The features include further reducing the number of degree of freedoms (DOFs) and significantly improving computational efficiency while ensuring accuracy. For illustrative purposes, the versatility of the procedure is validated through both numerical examples and comparisons with other theories.

Nondimensional triply coupled free vibration analysis of the axially layered thin-walled beams with nonsymmetric open cross sections and its application to the frequency optimization

Nondimensional triply coupled free vibration analysis of the axially layered thin-walled beams with nonsymmetric open cross sections and its application to the frequency optimization

Non-Uniform Torsion Behavior of Thin-Walled Beams According to the Finite Element Method

Non-Uniform Torsion Behavior of Thin-Walled Beams According to the Finite Element Method

Optimization Method of Floating Fixture Layout for Distortion Control of Low-Stiffness Thin-Walled Beams.

The aim is to reduce the elastic deformation of the web and side walls of low-stiffness thin-walled beams when the floating fixture method is used. This paper takes the number and position of fixture points as the optimization variables, establishes a calculation model of elastic deformation, and constructs the objective function of maximum total elastic deformation. An optimized solution utilizing the augmented multiplier method is employed, which forms the basis for the fixture layout optimization method to reduce the elastic deformation of low-stiffness thin-walled beams. A theoretical calculation, simulation analysis, and the fixture layout optimization of total maximum elastic deformation were completed using an aluminum alloy low-stiffness thin-walled beam as an example. The results show that based on the optimized layout, the average relative error between the calculated value and the simulated value of total maximum elastic deformation is 17.43%, and the simulated value of maximum elastic deformation is reduced by 48.49% after optimizing the fixture layout. The measured value is reduced by 0.02 mm on average, and deformation is reduced by 74.07%, which verifies the effectiveness of the floating fixture layout optimization control of machining elastic deformation proposed in this paper.

Hermite element for vibration analysis of thin-walled beams with higher-order beam theory

Hermite element for vibration analysis of thin-walled beams with higher-order beam theory

A coupled model to analyse dynamic behaviour of non-prismatic rotating anisotropic thin-walled beams

The current research presents a dynamically coupled mathematical model considering the energy method and employing the classical Ritz-approximation method for a thin-walled anisotropic tapered rotating box beam. The novelty of this work lies in presenting the effect of circumferentially uniform stiffness (CUS) ply layup to investigate the reverberations of not considering bending-shear couplings toward vibration behavior. The current model is formulated by considering transverse shear and cross-sectional warping of order primary and secondary. The repercussions of not including non-classical effects like Coriolis-force, centrifugal-acceleration and warping, inertial-warping is explored. Mode switching arising for change in geometry and centrifugal stiffening is presented for various ply angles and rotational speeds.

Analytical solutions for the vibration response of thin-walled beams under bidirectional moving random loads

Analytical solutions for the vibration response of thin-walled beams under bidirectional moving random loads

Coupled axial-torsional free vibration analysis of a rotating thin-walled composite beam in hygrothermal environments

ABSTRACT The coupled axial-torsional vibrations of a composite beam in hygrothermal environments are studied. In the existing literature, most studies investigated the torsional/axial-bending vibrations of rotating composite beams. Few works considered the axial-torsional vibrations in hygrothermal environments. By considering this, the coupled axial-torsional vibration characteristics of composite thin-walled beams in hygrothermal environments are studied. Vibration characteristics are solved using the Rayleigh-Ritz method. The accuracy of the calculation results is verified using the finite element method. The following conclusions are obtained: (1) The frequencies decrease with the hygrothermal factors and mounting angle. (2) Compared to temperature, moisture has a smaller impact on frequencies. (3) The influence of rotating speed and mounting angle is minimal and can be ignored. (4) The influences of ply angle on frequencies are more significant than other parameters. (5) The axial inertia force decreases torsional frequencies when the ply angle is 15°~75°. (6) The influences of temperature, moisture, rotating speed, and mounting angle on the first two modes are very small and can be ignored.

A NUMERICAL MODEL FOR ANALYZING CROSS LAMINATED TIMBER UNDER OUT OF PLANE LOADING

This paper targets the validity of a novel numerical model for analyzing CLT under out of plane loading. This numerical model was initially developed for determining the shear lag effect that appears in laminated thin walled composite beams. A parametric study was conducted in order to determine the influence of orientation of layers in CLT panels on bending strength and deflection. For confirming the accuracy of the proposed model, the results from the numerical model are compared with the external results of the computer software Ansys. The differences in bending stress vary from 0.27% to 1.69% depending on the orientation of layers and for deflection the differences are ranged from 2.25% to 7.42%. A numerical study was conducted and obtained data corresponds to results obtained from experimental study. It was concluded that the proposed numerical method can enough precisely predict the behavior of CLT under out of plane loading.