Thin-walled Beam Theory Research Articles

Buckling resistance assessment of thin-walled open section element under pure compression

The paper deals with the problem of buckling resistance determination in case of perforated thin-walled elements. Depending on element slenderness the limit load in compression mode may be determined taking into account elastic (LBA analysis), elasto-plastic and plastic material properties (GMNA analysis). The limit load value is determined on the basis of thin-walled open section beam theory in case of elastic buckling and using Johnson-Ostenfeld approximation for elasto-plastic buckling. Obtained results are compared with finite element solutions derived using shell modelling and large deformation theory with Huber-Mises elasto-plasticity constitutive model without any geometrical imperfections. Some results of the carried out experiments are also shown.

Transient wave velocities in pre-stressed thin-walled beams of open profile with Cosserat-type micro-structure

In the present paper, a new wave theory of thin-walled beams of open profile with Cosserat-type micro-structure is suggested based on the approach proposed by Rossikhin and Shitikova [1] for pre-stressed spatially curved thin-walled beams of open profile. The aim of the authors is to create the theory of propagation of transient waves (surfaces of strong discontinuity) in thin-walled beams of open profile, which should be quite different from Timoshenko-like theories, resulting in the data comparable with those corresponding to transient wave propagation in the three-dimensional Cosserat continuum.

Flexural-torsional coupled vibration of anisotropic thin-walled beams with biconvex cross-section

This study investigates the flexural–torsional coupled vibration of thin-walled composite beams. We first derived the thin-walled beam theory for an arbitrary cross-section and applied it to a biconvex cross-section. The flexural–torsional coupled motion is generated featuring a symmetric lay-up composite configuration. The natural frequencies are determined by solving the eigenvalue problem, which are obtained both for the warping restraint and the free-warping models. The variations of the natural frequencies with respect to the ply angle orientation are computed for selected values of thickness, slenderness and aspect ratios. We find that the natural frequencies have a tendency to increase with increasing slenderness and thickness ratios, while they tend to decrease with increasing aspect ratio. We also observed that omission of the transverse shear effect, particularly at the ply angles between 60° and 120°, led to an overestimation of the natural frequencies of the first and the second modes for higher slenderness ratios, while overlapping results are obtained for any thickness or aspect ratios regardless of including/omission of transverse shear deformation. Overall, we point out that the geometrical aspects have a substantial influence on dynamic characteristics in the design of thin-walled composite beams.

The Influence of Lintel Beams and Floor Slabs on Natural Frequencies of the Tall Buildings Core - Numerical and Experimental Studies

This paper presents the analysis of influence of lintel beams and floor slabs on natural frequencies of tall buildings, braced by core walls. For that purpose a numerical procedure based on the Vlasov theory of thin-walled beams and transfer matrix method has been developed. In order to check the accuracy of the proposed method the calculated results are compared with those obtained by FEM and experiment. Based on these results the effects of the lintel beams and floor slabs on the natural frequencies of the tall buildings core are discussed.

A shear deformable theory for the analysis of steel beams reinforced with GFRP plates

A shear deformable thin-walled beam theory is developed for the analysis of steel beams reinforced with a GFRP plate to one of the flanges. Starting with the principle of stationary potential energy, the governing equilibrium equations and boundary conditions are formulated for the problem. The theory results in two sets of fully coupled systems of equilibrium equations. The first system describes the longitudinal-flexural response of the system and involves four generalized displacement fields and the second system governs the lateral-torsional response and involves six generalized displacement fields. The resulting coupled systems are then solved numerically for practical problems. Detailed comparisons with three dimensional and shell solutions under ABAQUS show that the present theory provides reliable predictions for displacements and stresses. A comparison with results from a non-shear deformable theory illustrates the necessity of incorporating shear deformation effects in cases involving predominantly twisting responses.

The Influence of Cross-Section Shape Changing on Work of Cold Formed Beam

The Necessity of taking into account the ability of cold-formed steel thin-walled profiles to gradually change its cross section shape proportionally to the load acting on it is considered. Free torsion constants Jt value for cold-formed profiles is justified. Underestimation of beam torsion due to ignoring of the cross-section contour deformation is assessed. The thin-walled Z and C-shaped cold formed steel sections recently are becoming more and more popular in the constructions of low-rise buildings. A characteristic feature of cold-formed thin-walled profiles in these structures is the need to consider not only the longitudinal and bending deformations, but also the deformations of torsion. Presently there are two approaches to analysis of structures of thin-walled cold-formed steel sections. One of them is based on the thin-walled beam theory designed by V.Z. Vlasov, another one is based on the super-critical load-carrying capacity theory. In the first approach the contour of the cross-section is non-deformable, in the second caseanalysis is carried out on the basis of a reduced cross-section, caused by local buckling of the compressed cross-section elements. Both approaches do not take into account the ability of cold-formed steel thin-walled profiles to change itscross section shape proportionally to the load acting on it. In this connection it is necessary to conduct theoretical and experimental studies of the cross-section deformation effect on behavior of cold-formed steel profiles.First of all,it is important to find out the range of section-length characteristics for cold-formed profiles in which the fact of not taking into account of contour deformation of the cross-section leads tothe significant, from an engineering point of view, error in the calculations. Also it is needed to estimatehowload types and connections applied on cross section influence on cross-section form changing.

Longitudinal analysis of concrete U-girder bridge decks

U-shaped prestressed concrete bridge decks, simply supported, are now being increasingly used in railways and highways. Simplified methods of analysis are commonly used in design practice. In the longitudinal direction, the U-girder is modelled as a beam. However, under eccentric loading, simple beam analysis is found to yield unconservative estimates of longitudinal forces, mainly due to torsional warping. An understanding of U-girder bridge deck behaviour under torsional loading is facilitated by the application of Vlasov's thin-walled beam theory. This theory can be easily invoked as a substitute for simple beam analysis, resulting in vastly improved predictions of longitudinal stresses. The two U-girder decks have also been modelled in Structural Analysis Program software using shell elements, and the results of three-dimensional finite-element analysis validate the thin-walled beam theory. The scope of the study is limited to a straight and thin-walled U-girder bridge deck of uniform section. The effects of variation in load position have also been studied, and it is established that the thin-walled beam theory is well suited to estimate and design the U-girder for longitudinal stresses.

Dynamic analysis of non-planar coupled shear walls with stiffening beams using Continuous Connection Method

In this paper, the dynamic analysis of non-planar non-symmetrical coupled shear walls on a rigid foundation has been considered. The analysis deals with coupled shear walls having a finite number of stiffening beams, whose properties vary from region to region along the height. In the analysis, Continuous Connection Method (CCM) and Vlasov׳s theory of thin-walled beams are employed to find the stiffness matrix of the structure. The system mass matrix has been found in the form of lumped masses at the heights where the unit forces have been applied. Following the free vibration analysis, uncoupled stiffness, damping and mass matrices have been found employing the mode superposition method. A time-history analysis has been carried out using Newmark numerical integration method to find the system displacement vector for every time step. Finally, a computer program has been prepared in Fortran language and an asymmetrical example has been solved. The results have been verified via comparisons with those of the SAP2000 structural analysis program using frame method and a perfect match has been observed.

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

A hybrid finite element formulation is developed by using the Hellinger–Reissner functional which is obtained from the complementary energy functional for pre-buckling and buckling analysis of thin-walled beams by introducing element equilibrium and force boundary conditions as auxilary conditions. Comparison to the complementary energy based formulation the current hybrid formulation is advantageous because it does not require the satisfaction of inter-element force equilibrium a-priori and therefore it is easily adaptable within the existing displacement-based thin-walled beam finite-element analysis codes for which the assemblage procedure is relatively easy. 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. In the current formulation, the effects of load position can also be easily captured by virtue of the freedom provided in the beam axis selection. Comparisons with solutions from literature and those based on shell element models are presented and an example is designated to illustrate the significance of shear deformation effect.

Vibration and Instability of Rotating Composite Thin-Walled Shafts with Internal Damping

The dynamical analysis of a rotating thin-walled composite shaft with internal damping is carried out analytically. The equations of motion are derived using the thin-walled composite beam theory and the principle of virtual work. The internal damping of shafts is introduced by adopting the multiscale damping analysis method. Galerkin’s method is used to discretize and solve the governing equations. Numerical study shows the effect of design parameters on the natural frequencies, critical rotating speeds, and instability thresholds of shafts.

A shear locking-free spatial beam element with general thin-walled closed cross-section

A new shear locking-free spatial beam element with general closed thin-walled cross-section is presented in this paper. Based on the Timoshenko beam theory and Benscoter thin-walled beam theory, the proposed element considers the effects of shear deformation, coupled flexure and torsion, and warping shear stress. The shear locking is avoided by introducing an interior node to the element and adopting two-node Hermitian interpolation functions for transverse displacements and torsional rotation and three-node Lagrangian interpolation functions for the flexural rotations and warping function. Several examples are analyzed to validate the accuracy and convergent efficiency of the proposed beam element, and the results are compared with theoretical and numerical solutions. The comparisons demonstrate that the proposed element is applicable to the analysis of a thin-walled beam with an arbitrary closed cross-section.

A higher order model for thin-walled structures with deformable cross-sections

A higher order model for the analysis of linear, prismatic thin-walled structures that considers the cross-section warping together with the cross-section in-plane flexural deformation is presented in this paper. The use of a one-dimentional model for the analysis of thin-walled structures, which have an inherent complex three-dimensional (3D) behaviour, can only be successful and competitive when compared with shell finite element models if it fulfills a twofold objective: (i) an enrichment of the model in order to as accurately as possible reproduce its 3D elasticity equations and (ii) the definition of a consistent criterion for uncoupling the beam equations, allowing to identify structural deformation modes.The displacement field is approximated through a linear combination of products between a set of linear independent functions defined over the cross-section and the associated weights only dependent on the beam axis; this approximation is not constrained by any ab initio kinematic assumptions. Towards an efficient application of the approximation procedure, the cross-section is discretized into thin-walled elements, being the displacement field approximated for each element independently of the displacement direction. The approximation is thus hp refined enhancing the “capture” of the 3D structural mechanics of thin-walled structures. The beam model governing equations are obtained through the integration over the cross-section of the corresponding elasticity equations weighted by the cross-section global approximation functions.A criterion for uncoupling the beam governing equations is established, allowing to (i) retrieve the classic equations of the thin-walled beam theory both for open and closed sections and (ii) derive a set of uncoupled deformation modes representing higher order effects. The criterion is based on the solution of the polynomial eigenvalue problem associated with the beam differential equations, allowing to quantify the Saint-Venant principle for thin-walled structures. In fact, the solution of the non linear eigenvalue problem yields a twelve fold null eigenvalue (representing polynomial solutions) that are verified to represent beam classic solutions and sets of pairs and quadruplets of non-null eigenvalues corresponding to higher order modes of deformation.

Mode I stress intensity factor for cracked thin-walled composite beams

In this paper, we present an analytical method to determine the mode I stress intensity factor for thin-walled beams made of laminated composites. The technique relies on the concept of crack surface widening energy release rate, which is expressed in terms of the G* integral and thin-walled beam theory. In the vicinity of the crack tip, a solution of the G* integral is obtained employing stress and displacement fields derived for materials with general orthotropy. The effect of warping is taken into account. This is a common feature in thin-walled beams which cannot be neglected, especially when flexural–torsional loads are present.The model shows a good agreement with finite element results. It is shown that, although the approaches developed for isotropic materials may be useful in the treatment of orthotropic problems, they may not yield good results for some typical lamination sequences.

Mode I stress intensity factor for cracked thin-walled open beams

A general analytical method to determine the mode I stress intensity factor for thin-walled beams is presented. This method is based on the concept of crack surface widening energy release rate, which is expressed in terms of the G* integral and the thin-walled beam theory. A distinctive aspect of this technique is the incorporation of the warping effect, which is a common feature in thin-walled beams that significantly influences in the stress distribution. This characteristic gives generality to the method, allowing the analysis of crack scenarios that have not been yet considered by other authors. The results show a good agreement with shell finite element solutions and other results available in the literature.

A conceptual wing-box weight estimation model for transport aircraft

AbstractThis paper presents an overview of an advanced, conceptual wing-box weight estimation and sizing model for transport aircraft. The model is based on linear thin-walled beam theory, where the wing-box is modelled as a simple, swept tapered multi-element beam. It consists of three coupled modules, namely sizing, aeroelastic analysis, and weight prediction. The sizing module performs generic wing-box sizing using a multi-element strategy. Three design cases are considered for each wing-box element. The aeroelastic analysis module accounts for static aeroelastic requirements and estimates their impact on the wing-box sizing. The weight prediction module estimates the wing-box weight based on the sizing process, including static aeroelastic requirements. The breakdown of the models into modules increases its flexibility for future enhancements to cover complex wing geometries and advanced aerospace materials. The model has been validated using five different transport aircraft. It has shown to be sufficiently robust, yielding an error bandwidth of ±3%, an average error estimate of -0·2%, and a standard error estimate of 1·5%.

Thin-Walled Rods With Semiopened Profiles

The analysis of thin-walled rods with semiopened cross-section is performed in this article. An essential characteristic for this class of thin-walled beamlike structures is their closed but flattened profile. The unusual shape of semiopened thin-walled beams allows the efficient optimization due to wide variability of shapes. One popular application of the theory of semiopened thin-walled beams is the twist beam of the semisolid suspension.

Free Vibration Analysis of Cross-Ply Laminated Thin-Walled Beams with Open Cross Sections: Exact Solution

AbstractThe objective of the present paper is to analyze the free vibrations of thin-walled beams with arbitrary open cross section, made of cross-ply laminates with midplane symmetry, by means of an exact solution. The theory of thin-walled composite beams is based on assumptions consistent with Vlasov’s beam theory and classical lamination theory. The governing differential equations for coupled bending-torsional vibrations were obtained using the principle of virtual displacements. To simplify the coupled system of differential equations, an ideal center of gravity and shear center were introduced. In the case of a simply supported thin-walled beam, the closed-form solution for the natural frequencies of free harmonic vibrations was derived. The frequency equation, given in determinantal form, is expanded in an explicit analytical form. To demonstrate the validity of this method, the natural frequencies of nonsymmetric thin-walled beams having coupled deformation modes are evaluated and compared with r...

Static analysis of non-planar coupled shear walls with stepwise changes in geometrical properties using continuous connection method

This paper describes the static analysis of non-planar coupled shear walls with stepwise cross-sectional changes, employing Continuous Connection Method (CCM) in conjunction with Vlasov’s theory of thin-walled beams. Furthermore, the change of wall cross-section, span length and the heights of the stories and connecting beams from region to region along the height are taken into consideration. In the analysis, the compatibility equation has been written at the midpoints of the connecting beams. The results of the proposed method are compared with those of the frame method using the SAP2000 structural analysis program.

Thin-walled rods with semi-open profile for semi-solid automotive suspension

A new type of thin-walled rods with a semi-open cross-section is suggested and the optimization performed. Descriptive of this class of thin-walled beam-like structures is the closed but flattened profile. In this work, an intermediate class of thin-walled beam cross sections is studied. The cross-section of the beam is closed, but the shape of the cross-section is elongated and curved. The walls that form the cross section are nearly equidistant. The principle application of the theory of semi-open thin-walled beams is the twist beam of the semi-solid trail arm axle. The analytical expressions for the effective torsion stiffness and effective bending stiffness of the twist beam are derived in terms of section properties of the twist beam with a semi-open cross section. Based on the stiffness coefficients of the twist beam, the roll rate, chamber and lateral rigidity of the suspension are derived.

Bending analysis of partially restrained channel-section purlins subjected to up-lift loadings

Cold-formed steel section beams are widely used as the secondary structural members in buildings to support roof and side cladding or sheeting. These members are thus commonly treated as the restrained beams either fully or partially in its lateral and rotational directions. In this paper an analytical model is presented to describe the bending and twisting behaviour of partially restrained channel-section purlins when subjected to uplift loading. Formulae used to calculate the bending stresses of the roof purlins are derived by using the classical bending theory of thin-walled beams. Detailed comparisons are made between the present model and the simplified model proposed in Eurocodes (EN1993-1-3). To validate the accuracy of the present model, both available experimental data and finite element analysis results are used, from which the bending stress distributions along the lip, flange and web lines are compared with those obtained from the present and EN1993-1-3 models.