Showing papers in "Thin-walled Structures in 1987"

Asymmetric interactive buckling of thin-walled columns with initial imperfections

Abstract: In this paper the effect of the interaction between two or more simultaneous buckling modes on the postbuckling behaviour of uniformly compressed thin-walled members (TWM) is analysed by means of the general theory of elastic stability. The analysis is restricted to third-order terms of the energy expansion and therefore can be fruitfully applied to the investigation of structures with asymmetric postbuckling behaviour only. Initial imperfection effect is taken into account. A simplified procedure is suggested for solving the nonlinear equations relative to the evaluation of the bifurcated paths. By using the finite strip method an extensive parametric analysis is performed. It is found that when the flexural-torsional (FT) buckling interacts with a local symmetric and antisymmetric mode, sensitivity to initial inperfections is remarkable and is comparable to the one arising from the interaction between the Euler (E) and any local buckling.

Static and transient response of rectangular plates

Abstract: Static and transient analysis of composite plates is presented using a recently proposed shear deformation theory. The dynamic response is obtained by employing the numerical time integration scheme due to Newmark. The results obtained by using the classical plate theory (CPT) and the Mindlintype shear deformation theory (SDT) are compared with those obtained by using the proposed theory. The comparison studies reveal that the linear stress distribution, as assumed in CPT and SDT, differs considerably from the predicted nonlinear distribution of the proposed theory.

Nonlinear elastic response of locally buckled thin-walled beam-columns

Abstract: A theory is described which combines the finite strip method of nonlinear elastic analysis of locally buckled thin-walled sections with the influence coefficient method of analysis of beam-columns. The theory combines the advantages of both methods of analysis to produce a computationally efficient procedure for the estimation of the overall nonlinear elastic response of locally buckled thin-walled beam-columns. The theory is used to predict the previously reported measured behaviour of I-section test specimens of Bijlaard and Fisher. The theory is also compared with theoretical responses of eccentrically loaded thin-walled beam-columns analysed by an asymptotic theory. An example of a locally buckled thin-walled beam-column is studied in detail and some observations are made concerning the nonlinear response of members of this type.

Static and transient response of cylindrical shells

Abstract: Static and transient analysis of composite cylindrical shells is presented using a recently proposed shear deformation theory. The dynamic response is obtained by employing the numerical time integration scheme due to Newmark. The results obtained by using classical shell theory (CST) and Mindlin-type shear deformation theory (SDT) are compared with those obtained by using the proposed theory. The comparison studies reveal that the linear stress distribution, as assumed in CST and SDT, differs considerably from the predicted nonlinear distribution of the proposed theory.

Mode interaction in thin-walled trapezoidal column under uniform compression

Abstract: Interaction of nearly simultaneous buckling modes in the presence of imperfections is studied. The investigations is concerned with thin-walled trapezoidal columns under uniform compression. In these structures two modes are of particular interest, namely a local short-wave and an overall long-wave buckling mode of the whole structure, respectively. The asymptotic expansion established by Byskov and Hutchinson is also used here. The present paper is devoted to the study of equilibrium paths in the advanced post-buckled region of imperfect columns. The bifurcation stress is determined analytically and the asymptotically exact expansion is obtained for the initial post-bifurcation behaviour. The calculations are carried out for several types of rectangular and trapezoidal columns.

Torsion of closed cross-section thin-walled beams: The influence of shearing strain

Abstract: In this study a theory of rectangular closed cross-section thin-walled beams subject to torsion is presented, with express consideration being given to the shearing strain. The equations of equilibrium (in weak form) of the elastic system subjected to twisting distributed loads and to bimomental loads, in the unknown θ (angle of rotation by torsion) and βw (average shearing strain in the webs)—or ψw (distorsional angle)—are derived from the variational method of Minimum Potential Energy. The problem of Shear Lag in torsion is posed when non-canonical torsional contraint, which does not distribute the torque uniformly between the elements of the beam, is present. Particular emphasis was given to the case in which the geometry of the section is such that pure torsion warping is identically zero ( w = 0 and J w = 0) , an aspect which is not usually considered in classic Non Uniform Torsion (NUT). The differential equation in θ derived from the proposed theory is formally identical to the NUT equation; however, the singularity in the coefficient of θiv for ψ → 1 is no longer present. It is shown that the present theory, including the known results, determines, depending on the actual constraints conditions, the shearing stress which can differ considerably from the results predicted by the NUT. The paper concludes with a numerical study of a bimomental distorsion at the ends and also suggests possible improvements of the model.

Strength of damage ring and orthogonally stiffened shells—part I: Plain ring stiffened shells

Abstract: This paper is the first of two parts describing the procedure of, and results from, a series of tests on ring and orthogonally stiffened thin-walled shells. The primary purpose of the work was to investigate the collapse behaviour of the shells subjected to simulated damage and then tested under a combination of external pressure and axial compressive loading. The test specimens consisted of two five-bay cylinders stiffened with plain ring stiffeners; two three-bay cylinders stiffened with T-ring stiffeners and two three-bay orthogonally stiffened cylinders, one with 20 stringers, and the other with 40. This Part I deals with the tests on the plain ring stiffened cylinders. A major conclusion that can be drawn from the results of these few tests is that although the design of the plain rings was adequate to prevent general buckling of the undamaged shells, they were ineffective in limiting the area of initial damage when the shell was subjected to pressure loading.

Nonlinear flexural vibrations of rectangular plates subjected to in-plane forces using a new shear deformation theory

Abstract: Recently developed shear deformation theory is used to analyse large amplitude, flexural vibrations of laminated rectangular plates subject to in-plane forces. Single mode approach, in conjunction with the Galerkin method, is used to reduce the five coupled equilibrium equations to a single second order ordinary differential equation in time variable by ignoring certain inertia terms. This reduced equation involves quadratic and cubic nonlinearities and the solution of which is obtained by the method of Multiple Scales. Numerical results are presented in tabular form for various parameters of the rectangular plate considered.

Local buckling and inelastic cyclic behavior of tubular sections

Abstract: Moment-curvature relationship of a circular tubular section under reversed loading conditions is obtained. A simple kinematic model, proposed previously by the authors, is used here to obtain the local buckling branch of the moment-curvature relationship. Three types of closed form expressions are proposed to approximate the reversed loading branch of the computed moment-curvature curve of the locally buckled section. These expressions can be used to obtain the load-deflection relationship of a long circular tubular member/brace.

Effect of boundary conditions and rigidities on the buckling of annular plates

Abstract: The buckling analysis of multi-annular plates, with different properties, is presented. The geometry may include ring stiffners at the common joints and the plate may be supported in various manners, simple supports, clamped supports, etc., at the loaded outer edge. The loading is uniform radial compression and static. Several parametric studies are performed in order to assess the effect of geometry, material properties of the annular sections and of the ring stiffness. Moreover, when rings are present, the ring geometry is modeled both as a curved beam and as an annular plate, for comparison purposes.

The collapse of welded aluminium plate girders—an experimental study

Abstract: Twenty-two tests conducted to study the collapse behaviour of welded aluminium girders are described. The girders are of varying proportions, have transverse or longitudinal web stiffeners and are subjected to different combinations of shear and bending loads. It is observed that, although shear sway mechanisms similar to those for steel girders do develop, the webs of aluminium girders may fracture in the heat affected zones adjacent to the perimeter welds. These fractures develop at some stage during the formation of the collapse mechanism and are the consequence, rather than the cause, of failure. It is shown that the tension field theory, originally developed for steel girders, may overestimate the shear-carrying capacity of aluminium girders and it is concluded that the theory requires some modification before it can be applied with confidence to aluminium girders.

The effects of initial imperfection and changing support conditions on the vibration of structural elements liable to buckling

Abstract: The effects of initial imperfection and support conditions which change during the loading process on the vibration of structural elements liable to buckling are discussed. Typical experimental results reported in the literature are presented. Simplified one-degree-of-freedom models which reproduce stability characteristics of columns, plates and cylindrical shells are used. Damping is not included in the analysis.

A folded plate method of analysis for profiled steel sheeting in composite floor construction

Abstract: Composite flooring systems incorporating cold formed profiled steel sheeting as both permanent formwork and tensile reinforcement are becoming widely adopted for high rise buildings. Research has shown that the performance of the sheeting alone in supporting the weight of wet concrete during construction frequently governs the design. This paper concentrates upon this aspect of the behaviour and describes the application of the elasticity method, derived from folded plate analysis. The method allows the important deformations due to ponding and transverse bending to be taken into account accurately; such deformations are treated empirically, or ignored, in current design codes. Comparisons with the summarised results of many tests establish the accuracy of the folded plate method and indicate the limitations of the codes. Folded plate analysis is also used to illustrate several aspects of behaviour, particularly the possible movements at the lapped joints between adjacent sheets.

Compound strip method for the buckling analysis of continuous plates

Abstract: A special finite strip method is developed for the analysis of linear buckling of flat plate systems that are continuous over non-rigid supports. This approach incorporates the effect of support elements in a direct stiffness methodology. The stiffness contribution of the support elements adds directly to the plate strip stiffness matrices at the element level prior to assembly. This summation of plate and support stiffness contributions forms a substructure, which is termed a compound strip. The compound strip methodology may be readily employed for the enhancement of computer programs based on traditional finite strip procedures. The validity of the compound strip method for elastic buckling analysis is demonstrated in two examples. The critical loads based on compound strip methodology compare favorably with those obtained with the finite element method.

A direct method of evaluating the warping properties of thin-walled open and closed profiles

Abstract: The indirect method of evaluating the warping function and warping constant of a thin-walled profile involves a large number of steps in their calculations. Separate techniques are required for open, single-celled and multi-celled profiles. Not only is the method tedious but arithmetical errors are difficult to avoid. In the method described here the warping function and location of the shear centre are obtained in one step and the warping constant is then easily evaluated. The method is independent of the choice of axes it does not require the calculation of the location of the centroid and the principal axes.

Stresses in Thin Spherical Shells with Imperfections. Part I: Influence of Axisymmetric Imperfections

Abstract: A finite element model of axisymmetric geometry is used to obtain stress and moment fields in the region of an imperfection in thin, spherical shells. In Part I the studies are restricted to axisymmetric imperfections with a cosine variation along the meridian. Parametric studies are carried out to identify the main parameters controlling the response for internal pressure and gravity load. The results show that the behaviour of the shell is similar to the imperfect cylindrical shell with the same radius as in the spherical shell.

Shallow spherical shell on Pasternak foundation subjected to elevated temperature

Abstract: Nonlinear static behaviour of clamped shallow spherical shell at elevated temperature and resting on Pasternak type elastic foundation is examined, using Berger's approximation. Variation of non-dimensional central deflection with foundation parameters for a given thermal loading is investigated.

Stability in the elasto-plastic range of rectangular plates subjected to uniaxial compression, with unloaded edges clamped

Abstract: The post-buckling behaviour of a rectangular plate, with unloaded edges clamped, is analysed using the Rayleigh-Ritz variational principle, involving plasticity. The method is a combination of analytical and numerical solutions.The stress-strain relations are derived from a plastic flow theory. Results of numerical calculations, such as load-shortening curves and spread of plastic regions for square plates, are presented in illustrations.

Stresses in thin spherical shells with imperfections. Part II: Influence of local imperfections

Abstract: The changes in stress resultants in thin spherical shells, associated with a local imperfection introducing curvature errors in all directions, are investigated. An axisymmetric finite element model of the shell and imperfection is employed to carry out the linear elastic analysis. Parametric studies have been performed, to identify the main parameters controlling the response, for the case of internal pressure. The results are compared with those obtained in Part I for axisymmetric imperfections, and bounds for maximum elastic stress resultants are established to cover the possibility of both local and axisymmetric imperfections.

Lateral instability of monosymmetric beams with initial curvature

Abstract: A theoretical study of the flexural-torsional, or lateral, instability of monosymmetric beams is presented. The analysis is based on beam theory and energy considerations and incorporates the influence of pre-buckling displacements and initial curvature in the plane of major axis bending. Closed form solutions are obtained for simply supported beams subjected to uniform moment, central concentrated and uniformly distributed loads, which are valid for a wide range of section properties. Where the closed form solutions become inaccurate due to the complexity and variability of the buckled shape, numerical results are presented.

Dynamic analysis of partially prismatic thin-walled structures

Abstract: A mixed-mode method is investigated for the dynamic analysis of partially prismatic structures, such as box girders with intermediate diaphragms and supports, or with variable-depth webs. Thus the prismatic ‘main structure’ is discretised by finite strips, and the non-prismatic ‘sub-structure’ by finite elements. After dynamic reduction of the finite element degrees of freedom, advantage may be taken of the finite strip harmonic expansions in determining mode shapes. The method is tested by a variety of examples. Thus for structures with transverse substructures (e.g. diaphragms), the method is shown to be successful, being up to an order of magnitude faster than finite elements. However, for structures with longitudinal substructures (e.g. variable-depth webs) the method is shown to be unreliable. This is because for such structures, approximations in the dynamic reduction procedure are found to be significant.

An oriented finite element model for shearwall analysis

Abstract: Generally, loadbearing wall structures exhibit some regularity along the height. This regularity is exploited by cutting the building into typical slices. Each slice is obtained from the assemblage of basic structural units. The finite element method supports the calculation of the boundary stiffness matrices of these components which are stored in a user-defined structural library. Evaluation of structural response is based on a frontal process. The resulting program is runable on a minicomputer at low cost. Torsion of a model core illustrates the application of the method.

Large-deformation and collapse behaviour of underground aluminum piping

Abstract: In designing thick-walled underground tubing, a linearized analysis is usually satisfactory for predicting stresses and deformations in such pipes. For thin-walled flexible tubing, linearization and associated approximations are not admissible since relatively large deflections can occur which may significantly affect the pipe-soil interaction and lead to a reduction in the pipe's load carrying capacity and to its collapse. This paper presents an approximate geometrically and materially non-linear analysis of the large deformation and collapse behaviour of buried flexible tubing. The tube material was assumed to have a typical bilinear elastic-strain hardening curve with material constants taken from commercial aluminum tube specifications. The soil was assumed to exert a vertical, active pressure, q v , on the pipe whereas a lateral resistance or passive pressure is assumed to be proportional to the horizontal deflection of the tube, with a soil resistance coefficient k. The deflected shape was taken to be symmetrical in form, arrived at from the originally circular shape by isometric deformations, leading to flattening of the pipe. The upper and lower bounds of the load-flattening characteristics are determined by applying kinematically and statically admissible fields. The present non-linear solution clearly differs significantly from the linear one, both in magnitude and characteristics. It shows that as a result of plastification of the tube wall there exists a maximum value of q v , referred to as the critical pressure, q cr , beyond which dynamic collapse of the tube will occur.

A more accurate evaluation of buckling loads of thin-walled members in torsion and torsion-bending

Abstract: The objective of this paper is to present a more accurate evaluation of torsional and torsional-flexural buckling loads of thin-walled members. Numerical examples, which exhibit the accuracy of the formulae obtained in the buckling analysis of thin-walled members, are given.

Isolines of internal forces in circular spherical panels weakened by circular holes and subjected to nonlinear deformation and buckling

Abstract: A special modification of the finite difference scheme is used to study the nonlinear deformation of circular spherical segments having circular cutouts. Isolines of internal forces T 11 , T 12 , T 22 , M 11 , M 12 and M 22 are analysed.

Buckling and vibration of plate assemblies of non-constant thickness

Abstract: This paper considers the well-known generalized method of analysis in which the stability and natural response of plate systems are obtained on the basis of a closed-form solution for the transverse modal shape of each component plate. It is shown that, while this solution can be taken to be the same for all plates provided the thickness is uniform throughout the system, other shapes for the transverse deflections of some of the components may have to be employed in cases where the thickness (and/or the applied axial stresses) are not common to all elements.