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Showing papers in "Thin-walled Structures in 1992"


Journal ArticleDOI
TL;DR: In this paper, a series of quasti-static cyclic loading tests on unstiffened steel plate shear panels, with centrally placed circular openings, was described, and all the panels tested exhibited adequate ductility and stable S-shaped hysteresis loops, with the energy absorbed per cycle increasing with the maximum amplitude of the shear displacement.
Abstract: A series of quasti-static cyclic loading tests on unstiffened steel plate shear panels, with centrally placed circular openings, is described. All the panels tested exhibited adequate ductility and stable S-shaped hysteresis loops, with the energy absorbed per cycle increasing with the maximum amplitude of the shear displacement. The strength and stiffness of the panels decreased approximately linearly with increasing size of opening. Experimental results are compared with a previously developed theoretical model for predicting the hysteretic characteristics of unstiffened plate shear panels, which incorporates the influences of shear buckling and plastic yielding of the plate, and an assumed linear reduction in stiffness and strength to allow for openings.

179 citations


Journal ArticleDOI
TL;DR: In this article, the buckling behavior of symmetric angle-ply laminates having clamped edges and subject to a uniform temperature rise is investigated and the exact solution to the coupled differential equations is obtained using the general double Fourier series approach.
Abstract: The buckling behavior of moderately thick symmetric angle-ply laminates having clamped edges and subject to a uniform temperature rise is investigated. Transverse shear deformation is accounted for by employing the Reissner-Mindlin theory. The exact solution to the coupled differential equations is obtained using the general double Fourier series approach. Calculated values of the critical temperature are compared with corresponding finite element results.

44 citations


Journal ArticleDOI
TL;DR: In this paper, the vertical buckling of a pipeline encountering a point irregularity on an otherwise perfectly flat seabed, the so-called "prop case", is investigated. And the assumption that buckling is symmetric about the prop is tested.
Abstract: Submarine pipelines often carry products which are much hotter than the surrounding seawater. The potential thermal expansion is restrained by friction between the pipeline and the seabed, causing the development of large compressive axial forces in the line, which can lead to buckling of the pipeline. This paper takes a fresh look at the vertical buckling of a pipeline encountering a point irregularity on an otherwise perfectly flat seabed, the so-called ‘prop case’. Some approximations and assumptions in earlier work in this area are reexamined and their effects are calculated. Most importantly, the assumption that buckling is symmetric about the prop is tested. Asymmetric results are found, at a lower critical temperature than the symmetric mode, a fact which may have significant implications for design.

31 citations


Journal ArticleDOI
TL;DR: In this article, a detailed comparison of nonlinear analyses of thin-walled channel section columns with tests is presented, where the columns are analysed as beam-columns having nonlinear constitutive relationships.
Abstract: The paper presents a detailed comparison of nonlinear analyses of thin-walled channel section columns with tests. The columns are analysed as beam-columns having nonlinear constitutive relationships. The constitutive relationships are obtained firstly, by assuming elastic material behaviour and allowing local buckling of both flanges and web, and secondly, by assuming elastic-plastic material behaviour and confining local buckling deformations to the web. Based on the comparison, including theoretical and experimental load-shortening and load-deflection curves, it is concluded that the nonlinear theory generally closely agrees with the tests. The paper also investigates the applicability of combining an elastic nonlinear analysis with a spatial plastic mechanism analysis to describe the structural behaviour both before and after the ultimate load. The question of when this combination can be expected to accurately describe the column behaviour over the full loading range is discussed. A separate section compares theoretical ultimate loads with test strengths. The nonlinear analyses employed in the paper provide ultimate loads which agree with the test strengths to within 2% on average where primary local buckling occurs in the web of the channels, and 11% on average where primary local buckling occurs in the flanges of the channels.

28 citations


Journal ArticleDOI
TL;DR: In this paper, the linear bifurcation buckling behavior of column-supported thin elastic perfect cylinders using the finite element method was studied, and the effects of varying several shell parameters were examined.
Abstract: Large elevated silos and tanks are generally supported on a number of columns. The discrete supports of the columns give rise to high stresses adjacent to the column terminations. In particular, very high meridional compressive stresses arise above each column termination and these can lead to buckling of the shell at a load much lower than that for a uniformly supported shell. This paper presents a study of the linear bifurcation buckling behaviour of column-supported thin elastic perfect cylinders using the finite element method. Cylinders on both rigid and flexible column supports are studied, and the effects of varying several shell parameters are examined. The effects of the top and bottom edge boundary conditions are also investigated. It is well recognised that the linear bifurcation load is only an upper bound on the actual elastic buckling load, because the effects of large deflections and initial imperfections are ignored. Nevertheless, our understanding of the buckling behaviour of these structures is so limited that the results obtained here provide a significant starting point from which more elaborate studies may follow.

27 citations


Journal ArticleDOI
TL;DR: In this paper, a simple computational model of a thin-walled prismatic column is developed, which describes a transition from the postbuckling to the postfailure and crushing deformation phase.
Abstract: A simple computational model of a thin-walled prismatic column is developed, which describes a transition from the postbuckling to the postfailure and crushing deformation phase. Energy methods are used to analyze the elastic post-buckling response of the column. Ultimate strength is calculated, using the first yield criterion. Limit analysis methods, properly generalized to large displacement and rotation problems, are employed in the postfailure range. The new model explains, with some realism, the process of strain localization and the formation of a plastic folding mechanism in the column. It also leads to a prediction of the entire load-deformation characteristics up to the internal touching and stiffening.

24 citations


Journal ArticleDOI
TL;DR: In this paper, a finite element model is developed to investigate the elastic stability of eccentrically stiffened rectangular plates, where the plate and beam elements form a structural system in which the neutral surfaces for bending in the x-z and y-z planes may not coincide.
Abstract: A finite element model is developed to investigate the elastic stability of eccentrically stiffened rectangular plates. The plate and beam elements form a structural system in which the neutral surfaces for bending in the x-z and y-z planes may not coincide. The additional forces resulting from the eccentricity of the middle surface of the plate and the centroids of the beams is taken into account in deriving the element stiffness and geometric matrix. The formulation is based on the behaviour of the plate-stiffener system and not on the behavior of the separate components. The results of this study clearly show the limitations of the equivalent orthotropic plate theory.

19 citations


Journal ArticleDOI
TL;DR: In this paper, the authors used the strut on an elastic foundation theory for studying elastic buckling of axial loaded thin cylinders and showed that the shape of the stress-strain curve has an important influence on buckling behavior.
Abstract: The well-known ‘strut on an elastic foundation’ theory for studying elastic buckling of axial loaded thin cylinders is reworked so that it can be used to study buckling of pipes during cold field bending. This operation involves straining of the material well into the plastic range so any buckling will be post-elastic. In order to use the theory, the moduli in the circumferential and longitudinal directions have to be selected and the considerable experimental evidence from pipes of widely differing geometry and materials support the choice as Young's modulus, E, for the modulus in the circumferential direction and the tangent modulus in the longitudinal direction. A simple graphical method enables both the stress and strain at buckling and the peak-to-peak distance between buckles to be predicted. The paper concludes with observations about the important influence that the shape of the stress-strain curve has upon buckling behaviour.

17 citations


Journal ArticleDOI
TL;DR: In this paper, the effects of changing edge constraints on the frequencies of shallow shells with rectangular planforms were studied, focusing on a single edge, with the other three edges remaining completely free.
Abstract: The effects of changing edge constraints upon the frequencies of shallow shells with rectangular planforms are studied. Attention is focused upon a single edge, with the other three edges remaining completely free. For that edge clamped, simply supported, and free edge conditions are imposed; however, each of these has four possibilities depending upon the existence of either or both types of membrane constraint along the single edge. The Ritz method, assuming algebraic polynomials as displacement functions, is used to obtain accurate results. Frequencies for three types of shallow shells (circular cylindrical, spherical, hyperbolic paraboloidal) are obtained, for two shallowness ratios and two thickness ratios each. Careful attention is paid to the number of rigid body modes (zero frequencies) present, for these enter quite strongly into considerations of the effects of changing edge constraints.

14 citations


Journal ArticleDOI
TL;DR: In this article, a dynamic stiffness method is introduced to analyse thin-walled structures to reduce spatial discretisation errors, where harmonic oscillation is also eliminated to give an exact solution in a classic sense.
Abstract: A dynamic stiffness method is introduced to analyse thin-walled structures to reduce spatial discretisation errors. Where harmonic oscillation is concerned, time discretisation errors are also eliminated to give an exact solution in a classic sense. Constant axial forces and in-plane moments are included for dynamic buckling analysis. When warping effects are included, the governing differential equations correspond to a matrix polynomial eigenproblem of order 3 matrices and degree 4. The determinant equation is expanded analytically to give a scalar polynomial equation of degree 12 providing 12 integration constants for the 12 nodal displacements of the thin-walled beam member (excluding the uncoupled axial displacements). The generalised nodal forces are related to the nodal displacements analytically resulting in the exact dynamic stiffness matrix. Numerical examples show that the interaction diagram of natural frequency against the constant in-plane moment do not have monotonic change of slope. This is due to the fact that the constant in-plane moment softens the flexural modes while hardening the torsional modes. Examples on frames are also given.

13 citations


Journal ArticleDOI
TL;DR: In this article, an experimental investigation of lateral buckling behavior of thin-walled beams of narrow rectangular and I-section containing web openings and subjected to a single concentrated load applied at the centroid of the cross-section is concerned.
Abstract: This paper is concerned with an experimental investigation of lateral buckling behaviour of thin-walled beams of narrow rectangular and I-section containing web openings and subjected to a single concentrated load applied at the centroid of the cross-section. Experiments carried out to determine the effect of openings on the elastic critical load are described. Parameters such as support conditions, size, shape, location and number of openings are considered in the investigation. Experimental critical loads are compared with those obtained numerically using the energy approach. Good agreement between the results has been observed.

Journal ArticleDOI
TL;DR: In this article, the Rayleigh-Ritz energy method is used to obtain the magnitude of the assumed deflection functions of a flat plate and a simplified imperfection analysis is applied to examine certain cases.
Abstract: The buckling and post-buckling behaviour of thin, rectangular, simply supported flat plates subjected to end compression which varies linearly in the direction of loading and simultaneously loaded in shear is the subject of this paper. Part 1 presents a theoretical analysis of the problem. In this analysis the Rayleigh-Ritz energy method is utilised, and numerical minimisation of the total potential energy is applied to obtain the magnitude of the parameters of the assumed deflection functions. These are then used to define and describe other post-buckling characteristics of the plate. A simplified imperfection analysis is used to examine certain cases. The wide range of results presented covers many aspects of plate post-buckling behaviour.

Journal ArticleDOI
TL;DR: In this paper, a closed-form, compact and easily programmable formulae for the complete determination of internal actions and deformations stemming from arbitrary flexural and shearing actions uniformly distributed along the edges of a nonshallow thin-walled spherical-shell frustum was presented.
Abstract: This paper presents closed-form, compact and easily programmable formulae for the complete determination of internal actions and deformations stemming from arbitrary flexural and shearing actions uniformly distributed along the edges of a nonshallow thin-walled spherical-shell frustum. The shell edges are assumed to be sufficiently close to each other for bending-disturbance interaction to occur between them. The ensuing influence-coefficient expressions bring out the interaction component more explicitly than existing formulae. Unlike previous work on problems of spherical-shell frusta, the present study quantifies decoupling errors as continuous functions of a single fundamental parameter β. Edge-effect decoupling criteria are established for various error tolerances.

Journal ArticleDOI
TL;DR: In this paper, the linear elastic shell theory problem of the three-point bending of a curved pipe is considered, and summaries are given for solutions to this problem based on the Mushtari-Vlasov-Donnel (MVD) and Sanders linear shell theories.
Abstract: In this paper the linear elastic shell theory problem of the three-point bending of a curved pipe is considered. Such a loading arises in the industrial pipe ram bending process. Summaries are given for solutions to this problem based on the Mushtari-Vlasov-Donnel (MVD) and Sanders linear shell theories. Numerical results for displacements and stresses are obtained using the two shell theories, and these are compared with results from the finite element method (FEM). The present study gives practical information about the behavior of curved pipes subjected to ram bending. As well it provides information about the solution characteristics of thin-shell theories in toroidal coordinates.

Journal ArticleDOI
TL;DR: In this article, the effect of strain hardening on the behavior of a mild-steel pin-ended column was studied. But the authors focused on the effect on relatively long columns, and not on short columns, like those which form parts of a local plastic mechanism in a thin-walled structure.
Abstract: This paper is essentially a study of the effect of strain hardening on the behaviour of a mild-steel pin-ended column. A perfectly elastic-perfectly plastic column can develop theoretically a plastic hinge with infinite curvature at its midpoint. Strain hardening ‘blocks’ the development of sharp kinks. Instead, the central part of the column has a finite curvature. While this phenomenon is probably not important for relatively long columns, in the short columns, like those which form parts of a local plastic mechanism in a thin-walled structure, the effect is to increase the load-carrying and energy-absorbing capacities of the structure by a large factor. The analysis is carried out by using numerical techniques, and the results compare quite favourably with experimental measurements. Finally, a study of the sensitivity of strut behaviour to changes in the shape of the strain-hardening stress-strain diagram is carried out.

Journal ArticleDOI
TL;DR: In this article, an experimental investigation was carried out in order to verify the theoretical results obtained in Part 1. The experimental examination of the problem considered theoretically was performed using two separate experiments in which two different approaches have been employed to fulfil loading and boundary conditions at the plate edges.
Abstract: This experimental investigation was carried out in order to verify the theoretical results obtained in Part 1. The experimental examination of the problem considered theoretically was performed using two separate experiments in which two different approaches have been employed to fulfil loading and boundary conditions at the plate edges. The aspect ratio of the plate specimens examined in both cases was λ = 1.4 . The results are presented in graphical form and the conclusions are drawn from the comparison of the experimental and theoretical findings.

Journal ArticleDOI
TL;DR: In this paper, a spline finite strip method using computed shape functions in the transverse direction is presented for the analysis of right box girder bridges, which results in a relatively narrow band matrix which requires little computational effort to solve.
Abstract: A spline finite strip method using computed shape functions in the transverse direction is presented for the analysis of right box girder bridges. The shape functions for a few selected degrees of freedom necessary for the analysis are first obtained from the conventional finite strip analysis of a hypothetical simply supported span of the bridge using only the first harmonic of the Fourerr sine series. The displacement function of the bridge is then expressed as a product of longitudinal B 3 -spline expressions and the above-mentioned computed shape functions. As the number of shape functions adopted in the proposed method is much smaller than the total number of degrees of freedom in each cross-section, it results in a relatively narrow band matrix which requires little computational effort to solve. Numerical results are compared with other available analytical and numerical solutions.

Journal ArticleDOI
W.F. Chen1
TL;DR: In this article, the authors give designers an insight into the recent developments of the design criteria of steel beam-columns in the USA, including the ultimate strength of columns and beams, secondary effects (P-δ and P-Δ ), and simplified computer-based second-order elastic and inelastic analysis methods.
Abstract: This paper attempts to give designers an insight into the recent developments of the design criteria of steel beam-columns in the USA. The important features include (1) the ultimate strength of columns and beams that are special cases of beam-columns, (2) the secondary effects ( P-δ and P-Δ ) that should be considered in the ultimate strength design of beam-columns, and (3) the simplified computer-based second-order elastic and inelastic analysis methods that are suitable for adoption in the practical design for beam-columns in rigid frames. Recommended and proposed ultimate strength design interaction equations in the USA for different categories of beam-columns are presented. Important features of these equations are summarized. Several illustrative examples are given. Directions of further research are indicated.

Journal ArticleDOI
TL;DR: In this paper, an analytical solution for the stability and free vibration of the cross-ply laminated thin circular cylindrical shells which are simply supported at both ends and subject to axial and lateral pressure is presented.
Abstract: An analytical solution is presented for the stability and free vibration of the cross-ply laminated thin circular cylindrical shells which are simply supported at both ends and subject to axial and lateral pressure. Based on the principles of virtual work and a nine-term higher order transverse shear and transverse normal deformable displacement field, a set of governing equations for thermal buckling of thin circular cylindrical shells together with the associated boundary conditions are derived. Navier double series method is then applied to find the closed-form solutions. Effects of important parameters such as degree of orthotropy, ratio of length to radius, ratio of radius to thickness, etc., are studied.

Journal ArticleDOI
TL;DR: In this paper, a finite element buckling analysis was carried out to determine the critical shear stress of flat rectangular plates with two opposite edges free, and the results showed that the in-plane displacement normal to the loaded edges is restrained either at one or at both of those edges.
Abstract: A numerical investigation is carried out by means of a finite element buckling analysis to determine the critical shear stress of flat rectangular plates with two opposite edges free. Plate sizes and the boundary conditions at the two edges loaded in shear are the parameters considered in this study. Results of the investigation show a considerable difference in the buckling strength of plates if the in-plane displacement normal to the loaded edges is restrained either at one or at both of those edges. The in-plane flexibility of the supports is, therefore, an important parameter to be accounted for in the structural design of such plates. Finally, the numerical investigation is also extended to the shear buckling strength of flat rectangular plates with only one free edge.

Journal ArticleDOI
TL;DR: In this article, a displacement method based on the potential variational principle and the shear lag phenomenon is presented. But the method is not suitable for the case of thin-walled members.
Abstract: The classical theory of thin-walled members is unable to reflect the shear lag phenomenon since it is based on the assumption of no shear deformation. This paper presents a displacement method based on the potential variational principle and discusses the shear lag phenomenon. Compared with the mixed method, the displacement method is simpler in the analysis process and hence is easier to apply and to be combined with the finite element method. Numerical examples show that quite good results can be obtained. The solution also includes the results from the classical theory.

Journal ArticleDOI
TL;DR: In this paper, the effect of shear on collapse characteristics during the bending of cylindrical tubes was investigated both experimentally and theoretically, and the theoretical and experimental results were found to be in good agreement.
Abstract: Crashworthiness analysis has become an integral part of the automotive design cycle. Since oblique impacts and vehicle rollover are common vehicle accidents, further studies investigating frame collapse due to bending loading are needed. The main focus of this paper is to study both experimentally and theoretically the effect of shear on collapse characteristics during the bending of cylindrical tubes. Theoretical and experimental results were found to be in good agreement.

Journal ArticleDOI
TL;DR: In this paper, the authors presented the first elastic buckling analysis of a compound hyperbolic paraboloidal (hypar) shell under a uniformly distributed load, where the buckling modes of the shell are either symmetrical or antisymmetrical about both axes of symmetry.
Abstract: This paper presents the first elastic buckling analysis of a compound hyperbolic paraboloidal (hypar) shell under a uniformly distributed load. The compound shell is composed of four hypar panels of rectangular ground plan. A special feature of this analysis is the use of the pulse function to deal with the curvature discontinuities at the ridges. The stability-governing equations are derived from the general equations of Reissner for the linear elastic buckling of hypobolic paraboloidal shells, taking into account the curvature discontinuities at the ridges. These equations are then solved in an approximate manner by assuming trigonometric variations of the buckling deformations. Numerical results are presented, which show that the buckling modes of the shell are either symmetrical or antisymmetrical about both axes of symmetry. For antisymmetric buckling, the critical load of the compound shell is the same as that for a single hypar panel.


Journal ArticleDOI
TL;DR: In this article, the flexural and torsional properties of doubly symmetric core shear walls, with lintel beams providing bracing across the openings at each storey level, are described.
Abstract: A theoretical and experimental investigation of the flexural and torsional properties of doubly symmetric core shear walls, with lintel beams providing bracing across the openings at each storey level, is described. Such structures are used in tall buildings to support gravity loads and to resist horizontal forces induced by wind and earthquakes. The theoretical model developed is based on an equivalent closed section and is consistent with established open section and closed section behaviour at the two extremes of bracing. For intermediate bracing, the model incorporates the influences of bending and shear deformation of the bracing beams, out-of-plane bending of the side walls and continuousshear flow around the contour of the assumed equivalent closed section. The theoretical model is validated by a series of tests on perforated aluminium tubes, covering a wide range of lintel beam and effective side wall stiffnesses. The results indicate clearly that side wall distortion can reduce the torsional stiffness of such sections very significantly.

Journal ArticleDOI
TL;DR: In this paper, the authors present a study on the influence of the mode of geometrical imperfections on the maximum reduction in the load-carrying capacity of cylindrical shells due to stability failure.
Abstract: This paper presents a study on the influence of the mode of geometrical imperfections on the maximum reduction in the load- carrying capacity of cylindrical shells due to stability failure. The shells are made of multi-layered fibre-reinforced plastic material. The analysis of stability is based on Timoshenko's geometrically non-linear theory. The critical mode is obtained by non-linear optimal programming using a gradient method. Numerical results are obtained for a wide range of parameters of the geometry of the shells and the shape and magnitude of initial geometrical imperfections.

Journal ArticleDOI
TL;DR: In this article, the authors derived a model of a pretwisted thin-walled bar undergoing warp deformation and a moderately large twist about the elastic axis and derived closed-form torsional frequencies and mode shapes from the linear terms of the resulting nonlinear equations.
Abstract: Theoretical natural frequencies are determined for the first three modes of torsional vibration of pretwisted cantilevers with thin-walled open profiles. The equation of motion and boundary conditions are derived from a multifilament model of a pretwisted thin-walled bar undergoing warp deformation and a moderately large twist about the elastic axis. Closed-form torsional frequencies and mode shapes are derived from the linear terms of the resulting nonlinear equations. As the length-to-leg ratio ( L/b ) and leg-to-thickness ratio ( b/t ) of typical open-profile cantilevers are varied, the individual and collective effects of warping and pretwist on the torsional frequencies are qualitatively defined. The refined derivation and closed-form solutions presented here reveal significant destiffening of the torsional frequencies due to warping-pretwist coupling in cantilevers having pretwisted unsymmetrical open-profiles. These coupling effects, which have been ignored in thin-walled bar vibration theories heretofore, are brought out by the Wagner effect and warping shear stresses acting on the profile.

Journal ArticleDOI
TL;DR: In this article, a method, using a new surveying technique, is used for the measurement of the geometric initial imperfections in box girder diaphragms, accurate to ± 0·1 mm.
Abstract: A method, using a new surveying technique, is used for the measurement of the geometric initial imperfections in box girder diaphragms. The method, accurate to ±0·1 mm , may be used on diaphragms contained in a box girder where contact with the surface of the diaphragm is difficult or impossible or inadvisable due to the presence of strain gauges.

Journal ArticleDOI
TL;DR: In this article, the sensitivity analysis of the critical load of torsional buckling of thin-walled I-columns resting on a Winkler-type elastic foundation is presented.
Abstract: The sensitivity analysis of the critical load of torsional buckling of thin-walled I-columns resting on a Winkler-type elastic foundation is presented. The column behaviour is described according to the theory of a thin-walled beam with non-deformable cross-section. The first-order variation of the critical load due to the design variable variations is derived. The cross-section dimensions, except for the web height, the column material constants and the foundation stiffness, are assumed to be the design variables. The single eigenvalues are only discussed. Finally, a numerical example dealing with a simply supported I-column is presented. The accuracy of the approximation of the critical load change, caused by the design variable variations by means of its first-order variation, is also investigated.

Journal ArticleDOI
TL;DR: In this article, the effect of the initial imperfection in the dynamic response of thin-walled structures exhibiting asymmetric postbuckling behavior is discussed and the equilibrium characteristics are presented in terms of the equilibrium paths, which relate the applied load and the transverse displacement.
Abstract: The dynamic response of thin-walled structures exhibiting asymmetric post-buckling behaviour is investigated. The effect of the initial imperfection in the dynamic response of such structures is discussed. The equilibrium characteristics are presented in terms of the equilibrium paths, which relate the applied load and the transverse displacement. The dynamic response is illustrated by the characteristic curves which relate the applied load and the square of the correponding natural frequency of vibration. The dynamic response corresponds to the linear vibration around non-linear equilibrium configurations. The work is done in the scope of elastic stability and conservative systems. Damping is not included in the analysis.