Showing papers in "Thin-walled Structures in 1989"

Web crippling strength of thin-walled steel members with web opening

Abstract: This paper is concerned with the effect of web openings on the web crippling strength of unreinforced cold-formed (thin-walled) steel members The influence of an opening has been examined through experimental research on C-shaped lipped channel sections subjected to interior one flange loading condition First, the web crippling provisions of various Canadian design codes have been reviewed Then, the results of the 103 laboratory tests undertaken by the authors are presented along with the description of test procedure The parameters covered in this investigation include web height to thickness ratio, opening height/web height and opening width/bearing length Experimental data corresponding to sections without opening have been compared to code estimations Based on the non-linear regression analysis of the test results a prediction equation for the influence of an opening has been established Until further results become available, the prediction equation proposed herein may be used in the web-crippling design of thin-walled steel members with web openings

Inelastic buckling analyses of beams, columns and plates using the spline finite strip method

Abstract: A method of inelastic buckling analysis of thin-walled structural members and plates is described. The method is based on the spline finite strip method of structural analysis. The analysis takes into account the non-linear material stress-strain properties, strain hardening and residual stresses. The plastic theories used in the study are the flow theory of plasticity and the deformation theory of plasticity. The method of inelastic buckling analysis is applied to a variety of instability problems including plates, cold-formed columns, hot-rolled columns and welded tee section beams. The buckling modes and loads computed are compared with theoretical values and test results.

Some thoughtd on mode interaction in thin-walled columns under uniform compression

Abstract: Interaction of nearly simultaneous buckling modes in the presence of imperfections is studied. The investigation is concerned with thin-walled trapezoidal columns under uniform compression. The asymptotic expansion established by Byskov and Hutchinson is also used here. The present paper is devoted to an improved study of the equilibrium path in the initial post-buckling behaviour of imperfect structures. The results obtained include the effect of interaction of the ‘primary’ local mode and a ‘secondary’ local mode having the same wavelength as the primary. In this paper the analysis of a few buckling mode interactions is presented.

Analysis of folded plate structures

Abstract: The new approximate method for the analysis of folded plate structures is based on Vlasov's theory of thin-walled beams where the folded plate is divided into longitudinal beams connected like a monolithic The two primary assumptions are the equilibrium of the forces in the longitudinal direction and the compatibility of the beams in the transverse direction On this basis the system of differential equations for the folded plate was derived and transformed into an eigenproblem Comparison of the present solution with the solution based on a known method is made to demonstrate the accuracy and efficiency of the present method

Postbuckling behaviour of rectangular plates under combined loading

Abstract: Postbuckling behaviour of perfect and imperfect rectangular plates under biaxial compression combined with lateral pressure is considered. Based on the nonlinear large deflection equations of von Karman plates, the lateral pressure is first converted into an initial deflection by the Galerkin method. The postbuckling behaviour of simply-supported rectangular plates under biaxial compression combined with lateral pressure is then studied using a perturbation technique, taking deflection as its perturbation parameter. Through comparison, it is found that a discrepancy exists between the two cases; with and without lateral pressure. In the case of rectangular plates under uniaxial compression combined with lateral pressure, it is seen that the results obtained from the present paper are quite in accord with other experiments.

Local buckling of thin-walled steel box columns

Abstract: The investigation presented in this paper is concerned with the ultimate strength of thin-walled steel box columns that are pinned at their ends and subjected to an eccentrically applied load. An effective width formula to account for local buckling and residual stresses is proposed and the formula along with the tangent stiffness method has been used to develop an analytical method for predicting the failure load of box columns. The accuracy of the present method is established by comparing the predicted values of failure loads with the corresponding experimental values and the results are presented in the form of design curves.

Buckling under compression of simple and multicell plate columns

Abstract: Results are presented from buckling tests carried out on some thin-walled simple and multicelled columns under axial compression. These tests have in turn been compared with predictions made from a computer program that is based on an existing theory. Agreement between the tests and the theory has been found to be good in the main. The problems associated with defining the buckling loads of practical columns and the comparison of test results with theory are discussed.

Torsional vibrations and buckling of thin-walled beams on elastic foundation

Abstract: The problem of free torsional vibration and buckling of doubly symmetric thin-walled beams of open section, subjected to an axial compressive static load and resting on continuous elastic foundation, is discussed in this paper. An analytical method based on the dynamic stiffness matrix approach is developed, including the effects of warping. The resulting transcendental equation is solved for thin-walled beams clamped at one end and simply supported at the other. A computer program is developed, based on the dynamic stiffness matrix approach. The software consists of a master program to set up the dynamics stiffness matrix and to call specific subroutines to perform various system calculations. Numerical results for natural frequencies and buckling load for various values of warping and elastic foundation parameter are obtained and presented.

Postbuckling analysis of circular cylindrical shells under external pressure

Abstract: The postbuckling behavior of circular cylindrical shells of finite length under uniform external pressure is analysed using the spline finite strip method. A Total Lagrangian formulation on the displacement dependent pressure load in the orthogonal curvilinear reference frame is derived. An improvement for the arc-length iteration method is presented. The postbuckling equilibrium path and the contour map of equal radial deflection computed are in good agreement with the experimental and analytical results reported in Esslinger, M. and Geier, B., Postbuckling Behaviour of Structures, Springer-Verlag, Wien, New York, 1975.

Buckling of circular cylindrical shells partially subjected to external liquid pressure

Abstract: Theoretical analyses are presented for the buckling of circular cylindrical shells partially subjected to external liquid pressure. The shells are assumed to stand vertically with the lower end clamped, and the upper end clamped or free. In the analyses, the Donnell equations are used for the basic equation, and prebuckling deformation as well as the membrane state of stress of the shell are taken into account. The Galerkin method is used, and the critical pressures at various liquid heights as well as the wave numbers, are obtained for a wide range of the geometrical parameters of the shell Z. A convenient chart which indicates the buckling liquid height for a given shell and liquid are presented. Experimental studies are also conducted by using test cylinders made of polyester film, and water. The theoretical and experimental results for the buckling liquid height, are in excellent agreement.

Two-dimensional upheaval buckling of a heavy sheet

Abstract: A large elastic sheet with a significant self-weight subject to biaxial in-plane compression while lying on a rigid horizontal plane may buckle. The buckles, circular areas which lift away from the rigid subgrade, are essentially a plate (two-dimensional) phenomenon, analogous to the widely discussed one-dimensional upheaval buckling of beams. It is shown that plate upheaval is relatively insensitive to subgrade friction, a fact which may simplify design against such buckling.

Post-buckling behaviour and imperfection sensitivity of spherical shells based on nonlinear elastic stability theory

Abstract: Using the nonlinear elastic stability theory and its applications to shells, we have investigated the post-buckling behaviour and imperfection sensitivity of spherical shells with amplitude modulation. For this purpose, we assume that the buckling modes have the form of legendre polynomials with an exponential function as a modulating factor. Since the expressions of the second and the third variation of the energy functional of the spherical shell in the fundamental state are too complicated to obtain a closed form, we use a numerical analysis technique with high precision. The amplitudes of the post-buckling modes and the critical loading factors of the spherical shell with various imperfection modes are presented.

Static and dynamic numerical analysis studies of hemispheres and spherical caps. Part I: Background and theory☆

Abstract: Shell-like structures are prevalent in nature. However, because of their slenderness they are prone to buckling, and to such an extent that this is often the dominant consideration in their design. Early attempts to determine buckling pressures were unsatisfactory. Although initial geometric distortions are now recognised as the cause of this, little comprehensive work has been conducted on doubly-curved shells, particularly hemispheres, subjected to external pressure and having asymmetric initial shapes. This paper presents the results of such a study, in two parts. In Part I, the background research on doubly-curved shells is briefly reviewed. The kinematic, equilibrium and constitutive equations used in the work are stated. The adopted numerical procedure which can generate static or dynamic solutions is described along with the results of convergence studies. In Part II, the effect of various initial shapes and their location will be described; the critical combination will be identified. The parameters selected to nondimensionalise the results will be indicated, followed by those of the study which primarily involve initial deformation magnitude and shell slenderness. Two strength formulations which conveniently represent the results of the study will be presented.

Local buckling behavior of stiffened curved elements

Abstract: A series of stub column and beam tests has been performed to determine the initial buckling stress of stiffened curved elements. A semi-empirical expression has been developed for the elastic, local buckling of stiffened curved elements subject to uniform axial compression. For inelastic buckling, the tangent modulus approach is employed. Also, methods have been developed to predict the interaction between the local buckling of flat and curved elements and to predict local buckling of curved elements subject to bending. The predicted buckling loads, based on these expressions, are compared to the test data.

A consistent theory for torsion of thin-walled bars

Abstract: A consistent theory for torsion of thin-walled bars with cross-sections of arbitrary shape (open, closed or mixed) is developed in this paper; it is an improvement on the classical torsion theory of thin-walled bars. All the basic relations, formulas and equations are derived and proved under the consistent assumptions. A torsional stiffness matrix for thin-walled bar elements is also formulated on the basis of the consistent theory. A computer program has been written which is applicable to the practical use of torsional analysis of thin-walled bar structures with arbitrary cross-sections.

Buckling of rings in column-supported bins and tanks

Abstract: Theories for the out-of-plane buckling of rings under uniform circumferential compression are well established. However these theories are not applicable to rings in column-supported bins where the circumferential stress in the ring varies significantly over the cross-section and around the circumference. This paper deals with the out-of-plane buckling of annular plate rings in column-supported bins and tanks. The stress distributions in such rings are first examined using a finite element shell analysis. A closed-form solution for the buckling of rings under non-uniform circumferential stresses is then derived. Numerical results from the closed-form solution are compared with those from a finite element shell buckling analysis, and close agreement is found. The significant effect of stress non-uniformity on the buckling predictions is demonstrated. Finally, simplified equations are given which are suitable for structural design purposes, and which closely model the predictions of the more rigorous solution.

Torsional post-buckling of thin-walled open section beams resting on a continuous elastic foundation

Abstract: The post-buckling behaviour of thin-walled beams of open section subjected to an axial compressive load and resting on a Winkler-type continuous elastic foundation is discussed. We assume the strains to be small and elastic, shear deformations and the in-plane cross-sectional deformations to be negligible. The post-buckling paths are determined for simply supproted and clamped beams with constant cross-section. The points of bifurcation in both cases are found to be symmetric and stable for various values of warping and foundation parameters.

Second-order and second-approximation theory in the statics and dynamics of thin-walled straight bars

Abstract: This paper concerns the analysis of lightweight structures and especially the single bars from which they are composed. It is a further development of the general thoery derived previously by the author and allows one to analyse the single thin-walled bar exactly by the second-approximation approach in the areas of statics, dynamics, stability, dynamical stability, as well as natural or forced vibrations. The theory is valid for bars with arbitrary cross-section and any boundary conditions. It can be applied to thin-walled bars of large dimensions, such as is used in bridges, viaducts, etc., and even to high buildings stiffened by shafts treated either as single units or as groups of thin-walled bars.

Static and dynamic numerical analysis studies of hemispheres and spherical caps. Part II: Results and strength predictions

Abstract: Shell-like structures are prevalent in nature. However, because of their slenderness they are prone to buckling, and to such an extent that this is often the dominant consideration in their design. Early attempts to determine buckling pressures were unsatisfactory. Although initial geometric distortions are now recognised as the cause of this, little comprehensive work has been conducted on doubly-curved shells, particularly hemispheres, subjected to external pressure and having asymmetric initial shapes. This paper presents the results of such a study, in two parts. In Part I, which was presented in the previous issue of Thin-Walled Structures, the background research on doubly-curved shells was briefly reviewed. The kinematic, equilibrium and constitutive equations used in the work were stated. The adopted numerical procedure which can generate static or dynamic solutions was described along with the results of convergence studies. In this Part, the effect of various initial shapes and their location is described: the critical combination is identified. The parameters selected to nondimensionalise the results are indicated, followed by those of the study which primarily involve initial deformation magnitude and shell slenderness. Two strength formulations which conveniently represent the results of the study are presented.

A mixed-mode method for analysing partially prismatic curved thin-walled structures

Abstract: A recently proposed combined finite strip/finite element analysis of partially prismatic structures is investigated in its application to horizontally curved bridge decks. Static and dynamic behaviour is considered and the method is illustrated with examples ranging from slabs with intermediate cross-beams to a three-span trapezoidal box.

On the plastic tripping of flatbar stiffeners

Abstract: A simple model for plastic tripping of the web of a stocky T-strut subjected to axial compression is presented and the complete collapse behaviour of the model is analysed. The model is an extension of the Shanley model which has been proved useful in the past in understanding several aspects of inelastic column buckling. The column material is assumed to be elastic perfectly plastic. A closed-form solution is obtained for the post-ultimate load shortening behaviour of the present model strut. This solution is compared with the available experimental results and the previous analytical predictions based on Murray's plastic mechanism approach. It is shown that the present results are in better agreement with the experimental results than the previous analytical solutions. The present model grasps the main features of the post-ultimate collapse phenomenon, including tripping of the web and elastic unloading in a part of the cross-section.

Flexural-torsional elasto-plastic buckling analysis of stiffened plates using dynamic relaxation. Part 2: Comparison with test results and other formulations

Abstract: Having described, in Part 1, the theoretical basis of the method used to study the lateral-torsional behaviour of stiffeners attached to flat plating, detailed comparisons with a series of tests and other theoretical formulations are presented in this paper.

DP-Sandwich—The utilization of thin high-strength steel sheets in compression

Abstract: Thin steel sheets are used in a variety of structures, but a major disadvantage is their sensitivity to buckling. To overcome this, stiffeners are used in order to decrease the slenderness ratio and thereby increase the buckling load. In the present paper, a structural element based on the sandwich principle is presented, which can utilize the properties of thin, high-strength steel sheets in compression. In this way, an element is obtained with buckling stress exceeding the compressive yield strength of the steel, even for relatively high slenderness ratios. Compressive stresses up to 860 MPa have been measured on a 1·2 mm thick steel sheet of 400 mm length. Furthermore, the element can absorb large amounts of energy in both static and dynamic loading situations. In comparison with a non-sandwich structure, the energy absorbed per unit weight is almost doubled. In addition, it is shown that fatigue tests on thin steel sheets with negative loads can be performed with this element.

Local buckling of thin-walled girders of triangular cross-section

Abstract: A theoretical study of the local buckling of thin-walled girders under compound loading is presented. Girders of triangular cross-section with one axis of symmetry are considered. The following load cases are examined: compression, eccentric compression, pure bending and bending with shear. A parabolic distribution of shear stress in the webs is assumed when lateral forces are present. The problem is solved using a semi-energy method, described in Jakubowski, S., Buckling of thin-walled girders under compound load, Thin-walled Structures,6 (1988) 129-50. Numerical results are presented in the form of diagrams. The analysis of buckling modes for the more complicated cases such as bending with shear has also been performed.

Further experimental studies of the collapse of welded aluminium plate girders

Abstract: This paper describes eleven tests which were conducted to study the collapse behaviour of welded 7020 series aluminium alloy girders. The girders were of varying proportions and were subjected predominantly to shear loads. It is observed that, although shear sway mechanisms develop in a similar manner to those in steel girders, the webs of the aluminium girders fracture within the heat-affected zones adjacent to the perimeter welds. This confirms earlier observations for girders fabricated from 6082 aluminium alloy. Comparisons of predicted and measured values show the tension field theory, originally developed for steel girders, to give a reasonable estimate of the shear capacity of 7020 aluminium alloy girders. An earlier modification of the tension field theory proposed for 6082 alloy girders is seen to lead to very conservative predictions for the 7020 alloy girders. It is concluded that an improved theory is required to represent the true collapse behaviour of all aluminium girders.

Compound strip method for the frequency analysis of continuous sector plates

Abstract: A finite-strip method is developed for the frequency analysis of linear elastic flat curved plate systems continuous over flexible supports The method presented incorporates the effects of support elements using a direct stiffness methodology Mass matrices for the support elements are derived and presented in the form of strip matrices These strip matrices add directly to the plate strip matrices at the element level This summation creates a substructure called a compound strip Curved multipanel plate systems are analyzed and the results are presented for illustration Natural frequencies and mode shapes obtained from the compound strip analyses compare closely to those obtained from the finite-element method

The effect of support interference on the behaviour of high-rise spherical inflatables☆

Abstract: The vertical deflection behaviour of high-profiled spherical inflatables, subjected to axisymmetric loading and undergoing very large displacements, is affected by constraints caused by the geometry of the structure/support. The effects of such ‘support interference’ on the overall deflection characteristics of such structures is treated and evaluated.

Fourier integral representation of curvilinear influence functions applied to surface structures

Abstract: The paper proposes the application of curvilinear influence functions represented by Fourier integrals to problems of surface structures. It investigates in detail characteristic properties of such integrals. Particular attention is called to differentiation of the integrals representing functions with curvilinear discontinuities, as in this case their distributional features are most visible. The problem is illustrated by an example of an infinite plate.

General analysis of asymmetric thin-walled members

Abstract: This paper presents the closed-form solution for the deflection and stresses of an asymmetric thin-walled member. The method is based on the assumption that the cross-section can deform out of plane when warping and shear-lag effects are significant. The out-of-plane deformation is represented by a linear warping function plus a truncated series of complete eigenfunctions. The differential equations are derived by using the principle of Minimum Potential Energy and solved by a symbolic manipulator. An example is used to illustrate the application of the method and the use of the closed-form solutions obtained. Results of the example are compared to the results of a finite element analysis and other approximate models. The comparison indicates that the maximum error of the proposed method is within 0·1% of the value obtained by the finite element method in lateral displacement and 0·2% in axial displacement.

Buckling of vibrations of shear-flexible orthotropic plates subjected to mixed boundary conditions

Abstract: An approximate technique is presented for the analysis of buckling and vibrations of free-form, orthotropic, shear-flexible (‘Mindlin’) plates subject to mixed boundary conditions. The method falls into the category of Rayleigh/ Ritz-techniques; however, by using Lagrangian multipliers to ‘relax’ the geometric boundary conditions, the selection of appropriate trial functions is made considerably simpler. Accuracy and reliability of the proposed technique is demonstrated on the basisof several sample problems.