Vlasov's Theory Of Thin-walled Beams Research Articles

Elastic compressive buckling resistance for back-to-back double angle assemblies

The present study investigates the elastic buckling resistance of compression members consisting of non-slender hot-rolled double angles connected back-to-back with discrete interconnectors. Towards this goal, the study (a) formulates a thin-walled beam finite element buckling solution that treats both angles as independent members away from the intermediate connector locations while constraining the displacements for both angles at interconnector locations, and (b) develops an extension of the Vlasov thin-walled beam theory, originally intended for monolithic members, to determine the effective torsional/warping sectional properties for back-to-back double angle members. The validity of the thin-walled beam finite element model is then verified against experimental results and shell finite element models and its predictions are shown to asymptotically converge to the Vlasov theory extension developed in the present study as the number of interconnectors is increased. A systematic parametric study consisting of 1250 finite element runs is then conducted and the database of results generated is used to propose a simple equation to predict the elastic compressive buckling resistance of double angle compression members.

Nonlocal Analysis of the Flexural-Torsional Stability for FG Tapered Thin-Walled Beam-Columns.

This paper addresses the flexural–torsional stability of functionally graded (FG) nonlocal thin-walled beam-columns with a tapered I-section. The material composition is assumed to vary continuously in the longitudinal direction based on a power-law distribution. Possible small-scale effects are included within the formulation according to the Eringen nonlocal elasticity assumptions. The stability equations of the problem and the associated boundary conditions are derived based on the Vlasov thin-walled beam theory and energy method, accounting for the coupled interaction between axial and bending forces. The coupled equilibrium equations are solved numerically by means of the differential quadrature method (DQM) to determine the flexural–torsional buckling loads associated to the selected structural system. A parametric study is performed to check for the influence of some meaningful input parameters, such as the power-law index, the nonlocal parameter, the axial load eccentricity, the mode number and the tapering ratio, on the flexural–torsional buckling load of tapered thin-walled FG nanobeam-columns, whose results could be used as valid benchmarks for further computational validations of similar nanosystems.

Nonlocal elasticity theory for lateral stability analysis of tapered thin-walled nanobeams with axially varying materials

The lateral-torsional buckling behavior of functionally graded (FG) non-local beams with a tapered I-section is here investigated using an innovative methodology. The material properties are supposed to vary continuously along the longitudinal direction according to a homogenization procedure, based on a power-law function, whereas the nanobeam is modeled within the framework of a Vlasov thin-walled beam theory. The flexural-torsional governing equations of the problem are derived based on the Eringen's nonlocal elasticity theory and the energy method. The system of lateral stability equations is, thus, reduced to a fourth-order differential equation in terms of the twist angle by uncoupling the equilibrium differential equations. The buckling loads are finally determined using the differential quadrature method (DQM), which is here applied as numerical tool to solve directly the differential equations of the problem in a strong form. A systematic investigation checks for the influence of some parameters such as the power-law index, tapering ratios, loading height parameter, boundary conditions and non-local parameter, on the lateral stability resistance of the tapered I-nanobeams. The numerical outcomes of this paper can be used as benchmarks for further studies on nanoscale tapered thin-walled beams.

Lateral-Torsional Stability Analysis of a Simply Supported Axially Functionally Graded Beam with a Tapered I-Section

A lateral buckling analysis of simply supported web- and/or flange-tapered I-beams made of axially functionally graded materials and subjected to a uniformly distributed load is performed. The properties of beam material vary continuously along the beam axis, depending on the volume fraction of constituent materials, according to an exponential or power law. Considering the coupling between the lateral displacement and twist angle, equilibrium equations are derived via the energy method in association with the Vlasov thin-walled beam theory. For simply supported beams with free warping, the system of equilibrium equations is transformed into a differential equation in the twist angle. The differential quadrature method is then used to numerically solve the resulting fourth-order differential equation with variable coefficients and to determine the lateral buckling loads. A numerical example is finally considered to study the influence of different parameters — the axial variation of material properties, tapering ratios, and load eccentricities — on the lateral stability of the beams considered. The numerical results of this paper can be used as benchmarks for future studies on axially functionally graded nonprismatic I-beams with pinned-pinned end conditions.

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.

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.

Buckling analysis of thin-walled open members—A complementary energy variational principle

This first of two companion papers develops a new variational principle for the buckling analysis of thin-walled members based on the principle of stationary complementary energy. Some of the aspects of the Vlasov thin-walled beam theory (the rigid cross section assumption, and the stress expressions) are postulated to describe the behavior of members while other aspects of the theory (i.e., the zero shear strain assumption at mid-surface) are discarded. Koiter's formulation based on polar decomposition theory in finite elasticity is adopted to formulate expressions for statically admissible stress resultant fields. The stationarity conditions of the complementary energy expression are then evoked to yield the conditions of neutral stability and associated boundary conditions in which the rotation fields appear explicitly. The formulation seamlessly incorporates shear deformation effects and load position effects. Also, the Wagner effect and the mono-symmetry property which arise in displacement based formulations arise in the present formulation in a natural way.

Torsion analysis of thin-walled beams including shear deformation effects

The first part of the paper develops a theory for the torsional analysis for open thin-walled beams of general cross-sections which accounts for shear deformation effects. Statically admissible stress fields are postulated in agreement with those resulting from the Vlasov thin-walled beam theory. The principle of stationary complementary energy is then adopted to formulate the governing field compatibility condition under the stress fields postulated. The naturally arising boundary terms are found to relate the warping deformations to the internal force fields. A torsion beam example is solved using the new theory in order to illustrate its applicability to practical problems. The second part of the paper implements the solution numerically in a force-based finite element context. Two finite elements are developed by assuming linear and hyperbolic bimoment fields. The FEA solutions are shown to provide lower bound representations of the stiffness when compared to those based on conventional beam theories founded on postulated kinematic assumptions.

Nonorthogonal solution for thin-walled members – applications and modelling considerations

In a companion paper (R.E. Erkmen and M. Mohareb. 2006. Canadian Journal of Civil Engineering, 33: 421–439.), three finite elements based on the Vlasov thin-walled beam theory were formulated using a nonorthogonal coordinate system. Although the associated derivations are more elaborate than in more conventional solutions based on orthogonal coordinates, the new elements offer more modelling capabilities and flexibility in modelling structural steel members, a feature that is illustrated in this paper. In this context, the current paper presents four details in steel construction that were conveniently modelled within the new solution scheme. The applications involve thin-walled members with coped flanges, rectangular holes reinforced with longitudinal stiffeners, and eccentric supports. Comparisons with established shell finite element models using ABAQUS suggest the validity of the new solution. Key words: open sections, finite element analysis, thin-walled members, coped flanges, rectangular holes, eccentric supports.

Nonorthogonal solution for thin-walled members – a finite element formulation

Conventional solutions for the equations of equilibrium based on the well-known Vlasov thin-walled beam theory uncouple the equations by adopting orthogonal coordinate systems. Although this technique considerably simplifies the resulting field equations, it introduces several modelling complications and limitations. As a result, in the analysis of problems where eccentric supports or abrupt cross-sectional changes exist (in elements with rectangular holes, coped flanges, or longitudinal stiffened members, etc.), the Vlasov theory has been avoided in favour of a shell finite element that offer modelling flexibility at higher computational cost. In this paper, a general solution of the Vlasov thin-walled beam theory based on a nonorthogonal coordinate system is developed. The field equations are then exactly solved and the resulting displacement field expressions are used to formulate a finite element. Two additional finite elements are subsequently derived to cover the special cases where (a) the St.Venant torsional stiffness is negligible and (b) the warping torsional stiffness is negligible. Key words: open sections, warping effect, finite element,thin-walled beams, asymmetric sections.

Free vibration of core wall structure coupled with connecting beams

In this paper, a core wall structure coupled with connecting beams is discretized and modeled as an equivalent thin-walled member with closed section, while the connecting beams between openings are replaced by an equivalent shear diaphragm. Then, a numerical method (finite member element method, FMEM) for dynamic analysis of the core wall structure is proposed. The numerical method combines the advantages of the FMEM and Vlasov's thin-walled beam theory and the effects of torsion, warping and, especially, the shearing strains in the middle surface of the walls are considered. The results presented in this paper are very promising compared with the ones obtained from finite element method.

A shear-flexible element with warping for thin-walled open beams

A new finite element for the analysis of thin-walled open beams with an arbitrary cross section is presented. Combining Timoshenko beam theory and Vlasov thin-walled beam theory, the derived element includes both flexural shear deformations and warping deformations caused by the bimoment. By adopting an orthogonal Cartesian co-ordinate system, one can obviate the ad hoc introduction of St. Venant stiffness. The derived block stiffness matrix is comparable but more general than the one given by earlier researchers. The versatility and accuracy of the new element are demonstrated by comparing the numerical results with the classical solutions or other numerical results available in the literature. © 1998 John Wiley & Sons, Ltd.

Refined analysis of curved thin-walled multicell box girders

The generalized Vlasov's thin-walled beam theory was combined with the finite element technique to develop a new curved thin-walled multicell box girder finite element which can model extension, flexure, torsion, torsional warping, distortion, distortional warping and shear lag effects. For multicell box girders, several distortional modes were introduced to describe the complete distortional behaviour of the cross-section. Interaction between the longitudinal and transverse deformations of the box girder was also accounted for. The element is one dimensional, it has three nodes and employs the conventional polynomial shape functions. For modelling flexure, Timoshenko beam theory was used to take account of shear deformations. A computer program was developed based on the proposed element for the analysis of single and multicell curved box girder bridges. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed element. Compared to the standard finite element method, the proposed method needs substantially less computer time, memory and input data. The output is also in a form which can be used in design without further manipulation.

Analysis of a mono-symmetric core wall structure coupled with connecting beams

An open mono-symmetric core wall coupled with connecting beams is analysed under lateral loading, using Vlasov's thin-walled beam theory. Shearing deformations in the plane of the wall are taken into account, considering geometric compatibility. Coupling beams are treated as a medium with an equivalent stiffness property. Effect of connecting beam stiffness and of shearing deformations on the rotation of the whole system are presented. Inclusion of shearing deformations increases rotation of the structure; this effect being more outstanding in core walls with mono-symmetrical cross-section and those with very stiff connecting beams.

A finite element with exact shape functions for shear lag analysis in multi-cell box girders

Vlasov's thin-walled beam theory is combined with special shear lag warping functions to derive a box beam finite element with exact shape functions which can be used to analyze single- and multi-cell box girders. The fundamental theory of this model is rigorous and the governing differential equations are solved exactly. A computer program based on the proposed model has been developed for the analysis of single- or multi-cell box girder bridges. Examples are presented which compare the proposed method with the facet shell finite element analysis, with good agreement between the two sets of results.

Elasto-plastic analysis of perforated core structures subjected to applied torque

This paper presents a method of analysis, based on Vlasov's thin-walled beam theory in conjunction with the continuum approach, for investigating the elasto-plastic behaviour of perforated core structures subjected to torsional loading. A closed section analogy is utilized in the analysis. It is assumed that the plastic hinges form at the ends of the lintel beams and the lintel beams will fail prior to any yielding of the walls when the limiting rotational ductility is reached. The analysis enables the behaviour of a perforated core structure to be traced from working load to ultimate condition.