Showing papers in "Thin-walled Structures in 1984"
TL;DR: In this paper, an approximate method of predicting the ultimate load carrying capacity and the postbuckling behavior of perforated plates typically used in engineering structures is presented, based on a mechanism solution, used in conjunction with an elastic loading path derived from energy methods.
Abstract: An approximate method of predicting the ultimate load carrying capacity and the post-buckling behaviour of perforated plates typically used in engineering structures is presented. The theory is based on a mechanism solution, used in conjunction with an elastic loading path derived from energy methods. Experiments have shown that a good approximation of the loading and unloading paths for simply supported plates containing square and circular openings has been obtained by the suggested theoretical treatment. Curves suitable for the use of designers have been proposed and can be employed to determine the ultimate capacity of approximately square plates containing centrally placed holes.
83 citations
TL;DR: In this paper, a nonlinear finite strip method of analysis is described for the post-local buckling of geometrically imperfect plate assemblies, which is used to provide an accurate alternative to the Winter effective width formula for obtaining the effective section of a simply supported I-beam.
Abstract: A nonlinear finite strip method of analysis is described for the post-local buckling of geometrically imperfect plate assemblies. The method is used to provide an accurate alternative to the Winter effective width formula for obtaining the effective section of a simply supported I-beam in the post-local buckling range of structural response. The effective section of a locally buckled beam with thin flange outstands is used to investigate the resistance of the beam to flexural-torsional buckling. The analytical methods developed to assess the nonlinear interaction of local and lateral buckling are compared with experimental tests performed by Cherry.
80 citations
TL;DR: Theoretical analyses for the linear free vibration of a clamped-free cylindrical shell partially filled with an incompressible, inviscid liquid are presented in this paper.
Abstract: Theoretical analyses are presented for the linear free vibration of a clamped-free cylindrical shell partially filled with an incompressible, inviscid liquid. For the vibration of the shell itself, the dynamic version of the Donnell equations was used and the problem was solved with the modified Galerkin procedure, taking the effect of the axisymmetric deformation due to the static liquid pressure into consideration. Concerning the vibration relevant to the liquid motion, the solution for the velocity potential was assumed as a sum of two sets of linear combinations of the suitable harmonic function, the unknown parameters of which were imposed to satisfy both boundary conditions along the wetted shell wall and the free liquid surface in a sense of appropriate series expansions. The procedure stated in the foregoing leads to a determinantal equation for the determination of the natural frequencies of the present shell-liquid system. To compare with the experimental results which will be stated in a companion paper, 14 detailed numerical results will be presented in another companion paper 13 on the free vibration characteristics of the two test cylinders partially filled with water.
50 citations
TL;DR: In this article, a finite element solution for the buckling and geometrically nonlinear elasto-plastic collapse of perforated plates is presented, which is in close agreement with existing approximate and semi-empirical solutions.
Abstract: Finite element solutions for the buckling and geometrically nonlinear elasto-plastic collapse of perforated plates are presented. Triangular elements are used to model the plates and the elasto-plastic stress-strain relationships are based on Ilyushin's approximate area yield function assuming full plastification of the entire thickness of the plate for stress states on the yield surface. Solutions are presented for square plates with central square and circular holes subjected to uniaxial compression, biaxial compression and pure shear, and are shown to be in close agreement with existing approximate and semi-empirical solutions which have been verified by test results.
46 citations
TL;DR: In this article, the free vibration of a clamped-free cylindrical shell partially filled with liquid was analyzed by exciting the shell wall with two small shakers located at diametrically opposite positions and observing the resonant responses of the shell with a noncontacting proximeter utilizing fiberglass optics.
Abstract: To compare with the theoretical results presented in Parts I and II, 1,2 detailed experimental results have been obtained on the free vibration of a clamped-free cylindrical shell partially filled with liquid. Two polyester test cylinders with radius 100 mm, thickness 0·25 mm, and lengths 114 and 227 mm were used, and the filling ratio of the contained water was varied from 0 to 1·0 stepwise by 0·25 increments. Experiments were carried out by exciting the shell wall with two small shakers located at diametrically opposite positions and by observing the resonant responses of the shell with a noncontacting proximeter utilizing fiberglass optics. Excellent agreement between theory and experiment was demonstrated for the natural frequencies and the corresponding wave numbers concerning the lower-order natural vibrations dominated by the shell wall response. Variations of the mode shape with the circumferential wave number and the liquid depth were also examined, and were found to compare favourably with those predicted theoretically.
44 citations
TL;DR: In this paper, the buckling coefficient for square and rectangular cut-outs and subjected to shear has been investigated and approximate formulae for the use of designers have been suggested for the practical cases where the hole dimension is generally not greater than half the width of the plate.
Abstract: Finite element studies aimed at computing the buckling coefficient for plates containing cut-outs and subjected to shear are reported. The cases considered are: 1. 1. Square and rectangular plates with central circular cut-outs. 2. 2. Square plates with centrally placed rectangular cut-outs. 3. 3. Square plates with eccentrically placed circular cut-outs. 4. 4. Square plates with reinforced circular cut-outs. 5. 5. Square plates with reinforced rectangular cut-outs. Simply supported plates as well as clamped plates have been studied and approximate formulae for the use of designers have been suggested for the practical cases where the hole dimension is generally not greater than half the width of the plate.
37 citations
TL;DR: In this paper, a geometric non-linear analysis of prismatic thin-walled structures is presented, which is based on the moderately large displacement assumption, giving nonlinear strain-displacement relations, but linear curvaturedisplacements relations.
Abstract: The geometric non-linear analysis of prismatic thin-walled structures is presented. The theory is based on the moderately large displacement assumption, giving non-linear strain-displacement relations, but linear curvature-displacement relations. The corresponding non-linear equilibrium equations are produced by the principle of stationary potential energy using the finite strip discretisation. The equilibrium equations are solved using incremental and incremental-iterative numerical methods. Thus for the simple case of the square plate in edge compression, the self-correcting incremental method gives satisfactory results. For more complex examples of loading and structural type, a variable load incremental-iterative method is adopted. It is shown that the finite strip method used in conjunction with this method can be applied in particular to problems containing load maxima.
26 citations
TL;DR: In this paper, the problem of free vibrations of clamped-free circular cylinders has been analyzed in detail using the first-order thin shell theory of Budiansky and Sanders, and two simple linear relationships for the frequency parameter are given by incorporating an interrelationship among displacement components in two different ways.
Abstract: The problem of free vibrations of clamped-free circular cylinders has been analysed in detail using the first-order thin shell theory of Budiansky and Sanders. Two simple linear relationships for the frequency parameter are given by incorporating an interrelationship among displacement components in two different ways. For the variations in wave numbers, radius-to-thickness ratio and length-to-radius ratio the comparison with the exact frequencies and the frequencies due to various approximate formulae has been extensively studied. Strain and kinetic energy considerations are put forward to explain the apparent difference between linear and the cubic frequency approximations. In the case of two typical cylinders the theoretical results are shown to be in reasonable agreement with the observed frequencies and also with the results calculated by using Flugge shell theory equations.
16 citations
TL;DR: In this article, an analytical method for calculating the frequencies of laminated orthotropic cylindrical shells, based on the well-known Rayleigh-Ritz procedure, is presented.
Abstract: Vibration characteristics of laminated orthotropic cylindrical shells are investigated. The analysis, based on the Love-Timoshenko theory, can deal with shells composed of an arbitrary number of bonded layers each with a different thickness and different eleastic orthotropic properties. The analytical method, which is derived and applied here for calculating the frequencies of laminated orthotropic cylindrical shells, is an application of the well-known Rayleigh-Ritz procedure. In applying the Rayleigh-Ritz procedure the expression of strain and kinetic energies in general form for laminated orthotropic cylindrical shells have been used. The results obtained compared very well with some available experimental and analytical results.
14 citations
TL;DR: In this article, the finite strip method is applied to study the behavior of cold-formed steel beams including webs with longitudinal stiffeners, and the effect of variable core stiffnesses on the buckling strength is quantified and presented.
Abstract: The finite strip and finite layer methods are powerful tools for the analysis of thin-walled structures. In this paper, the finite strip method is applied to study the behavior of cold-formed steel beams including webs with longitudinal stiffeners. Comparisons are made with AISI specifications and published data. The finite layer method is used to investigate the buckling behavior of sandwich panels with thin facings and rigid foam cores. Effects of variable core stiffnesses (due to uneven curing, etc.) on the buckling strength are quantified and presented.
14 citations
TL;DR: In this paper, a model for the elastic lateral buckling of a continuous cold-formed roof purlin whose top flange is prevented from deflecting laterally, and which is braced against lateral deflection and twist at the supports and intermediate bridge points is developed.
Abstract: A simple model is developed for the elastic lateral buckling of a continuous cold-formed roof purlin whose top flange is prevented from deflecting laterally, and which is braced against lateral deflection and twist at the supports and intermediate bridge points. The effects of cross-section distortion are neglected, but so are the torsional restraints provided by roof sheeting against twisting. Local buckling is ignored, and must be designed against separately. The model is analysed by a finite element computer program, and predictions of the maximum moment in a segment at elastic buckling under either uplift or gravity loading are presented graphically. A simple method of using this elastic buckling information to determine the design working load capacity of a roof purlin is then presented, and this is illustrated by a worked example. An improved method is also presented which allows the restraining effects which occur between adjacent segments during elastic buckling to be estimated. Strength predictions obtained from the improved method are compared with test results.
TL;DR: In this article, a nonlinear finite element computer program was developed to analyze thin-walled metal structural members, which has the ability to handle both geometrical and material nonlinearities so that the postbuckling behaviour and ultimate strength of members can be predicted.
Abstract: A nonlinear finite element computer program has been developed to analyse thin-walled metal structural members. The program has the ability to handle both geometrical and material nonlinearities so that the post-buckling behaviour and ultimate strength of members can be predicted. A bending-membrane rectangular element with six degrees of freedom at each node forms the basic type of element used in the program. Marguerre's shallow shell theory is adopted for the strain-displacement relationships and hence the bifurcation point at buckling can be bypassed by providing an initial inperfection. The finite element formulation is based on the total Lagrange coordinate system and the flow theory of plasticity. Explicitly shown in the paper is the formation of the tangent stiffness matrix and the tridiagonal block form of solution procedure. Two problems of a square tube and a channel section beam subjected to pure bending were tested and found to be in close agreement with previous theoretical work.
TL;DR: In this article, a mechanism approach is presented for determining the collapse behavior of ring-stiffened cylindrical shells subjected to axial compression and external pressure, and failure loads are calculated as an upper bound of elastic and mechanism responses.
Abstract: A mechanism approach is presented for determining the collapse behaviour of ring-stiffened cylindrical shells subjected to axial compression and external pressure. It extends previous work of Alexander,5 and Andronicou and Walker,6 incorporating the effect of pressure and calculates failure loads as an upper bound of elastic and mechanism responses. Comparison with recent experiments and a lower bound analysis are given. The paper also discusses the relevance of the results to offshore design.
TL;DR: In this paper, the Kirchhoff-love assumptions are used together with deep thin shell finite elements to develop a number of 20 degrees of freedom rectangular and 15 degrees offreedom triangular cylindrical shell elements.
Abstract: The method of forming thin cylindrical shell finite element displacement functions by initially developing the strain function is presented. The Kirchhoff-Love assumptions are used together with deep thin shell finite elements to develop a number of 20 degrees-of-freedom rectangular and 15 degrees-of-freedom triangular cylindrical shell elements. The elements are tested on an extended range of barrel vault roof problems and results are presented. Only in the very specific case of N φ for the free straight-edged barrel vault using the triangular elements are the results found to be inaccurate. In all cases where the displacements and stresses can be analytically checked, the strain approach gives accurate results.
TL;DR: In this article, a method for obtaining directly the stresses in the ring beam and shell of a cooling tower is presented, where the stresses assuming a continuous base support are corrected by means of self-equilibrating base loads to give the actual discrete column support.
Abstract: A method for obtaining directly the stresses in the ring beam and shell of a cooling tower is presented. The stresses assuming a continuous base support are corrected by means of self-equilibrating base loads to give the actual discrete column support. The circumferential variation of the highly discontinuous base loads is represented by Fourier series. A careful study of the nature of the series involved leads to an explicit determination of significant terms and an assessment of accuracy when the series are truncated. The consequent savings in computation are shown to give the method practical viability. Examples of results for typical cooling towers are presented, together with typical computer times. It is shown that the method has clear advantages over present methods of determining ring beam stresses.
TL;DR: In this paper, the effective length of a column in a frame restrained by roof sheeting is calculated using a set of formulae, and an example is given to illustrate the advantages resulting from the use of these formularies.
Abstract: Formulae have been derived for the calculation of the effective length of a column in a frame restrained by roof sheeting. An example is given to illustrate the advantages resulting from the use of these formulae.
TL;DR: In this paper, the elastic analysis of clad pitched roof portal frame structures is presented, first neglecting the stiffening effect of sheeting and then according to the rules of stressed skin design.
Abstract: This paper deals with the elastic analysis of clad pitched roof portal frame structures. A practical structure is analysed, first neglecting the stiffening effect of sheeting and then according to the rules of stressed skin design. The differences between both analyses are shown. Different aspects of stressed skin design analysis are investigated, namely: 1. 1. The fact that some vertical loads mobilize the diaphragm effect, whereas others do not. 2. 2. The modification of axial forces in the columns, due to the influence of diaphragm action. 3. 3. The assumption that shear forces are transmitted from sheeting to the eaves of the frames.
TL;DR: In this article, an approximate value of the elasto-plastic flexibility of screwed fastenings is derived for a very thin-walled steel structure. But the analysis may be made more accurate by taking into account the elastic flexibility.
Abstract: Normal calculations of flexibility as a deformation characteristic of fastenings disregard the plastic response of screwed fastenings of very thin-walled steel structures. Preliminary tests have, however, shown that, unlike bolted fastenings in thick-walled steel structures, in screwed fastenings of very thin-walled steel structures the occurence of considerable plastic deformations can be observed from the beginning of loading. These should not be generally neglected in establishing the design characteristics of fastenings, i.e. design strength and design flexibility. This paper deals with cases in which an approximate value of ‘elastic flexibility’ can be used with sufficient accuracy, and how the analysis may be made more accurate by taking into account ‘elasto-plastic flexibility’. Extensive experimental research into the behaviour of screwed fastenings of very thin-walled steel structures subjected to non-repeated loading, repeated fluctuating and reversed loading, and multi-level loading simulating wind loading has been carried out, and ‘elastic flexibilities’ of selected fastenings have been established. At the same time, conditions for their application taking into account the elasto-plastic behaviour of fastenings subjected to repeated loading have been determined.