Institute of Structural Analysis

Dieser Beitrag zeigt die exemplarische Anwendung alternativer Beulbemessungsprozeduren, wie sie in der neuen Europäischen Schalenbeulnorm EN 1993, Teil 1.6 “Festigkeit und Stabilität von Schalen aus Stahl” eingeführt sind, und zwar auf eine baupraktische dünnwandige kreiszylindrische Stahlsilokonstruktion. Die wichtigsten charakteristischen Eigenschaften dieser Bemessungsprozeduren sowie einige charakteristische Besonderheiten der baustatischen Modellbildung werden dargestellt. Anschließend werden die aus der Anwendung dieser alternativen Beulbemessungsprozeduren auf die betrachtete versteifte Schalenkonstruktion erhaltenen Resultate miteinander verglichen und kritisch bewertet.Buckling design of discretely supported thin-walled steel silo structures according to EN 1993-1-6.This paper deals with the exemplary application of alternative buckling design procedures, as introduced by the new European Standard on buckling of steel shells, to a practical thin-walled steel silo structure. First the general features of these design procedures as well as relevant issues of structural modelling are outlined. Then the outcomes of the different buckling design procedures are compared to each other and critically evaluated.

In the paper, the expressions for membrane forces in an axisymmetric steel silo structure at filling and discharge with a particulate solid material are presented. Graphical plots of these expressions are given. They can be used for a quick and easy estimate of membrane forces distribution in all parts of a silo structure. The plots are valid for any silo geometry and for any material stored. The influence of silo geometry and stored material properties on the size and distribution of membrane forces can be thus checked. The paper completes with an illustrative example where actions (pressure loads) at filling and discharge on the walls of a silo are computed and the corresponding membrane forces are evaluated.

In this paper a new computer program (NLBEAM3D) is presented for nonlinear Finite Element analysis of general skeletal structures. The theoretical background is represented by a consistent quadratic approximation of the geometrically exact finite rotation beam equations (moderate rotation approach). Cross-sectional warping and geometrical imperfections are accounted for in a consistent way. Nonlinear material behaviour including initial residual stress conditions may be prescribed for the individual parts of parametrically defined cross sections. Practical examples demonstrate the basic completeness of the presented element formulation and the modelling capability of the developed computer program.

Technical thin–walled axisymmetric shell structures usually consist of several segments, including ring– stiffeners, which are connected to each other at circumferential shell junctions. The stress state in the interior of these shell segments is primarily governed by membrane action, however, additional secondary bending stresses occur at these shell junctions due to compatibility requirements. Linear elastic stress analysis of such meridional discontinuities in thin–walled axisymmetric shells is an important pre–requisite for the proper design of these components, i. e. with respect to assessing the ultimate plastic limit state and the ultimate limit states of cyclic plasticity and fatigue in particular. In this paper a general and elegant approach to the analysis of axisymmetric stress states of arbitrary shell junctions is presented which is based on a newly developed effective–ring analogy model. The axisymmetric elastic stiffness of this "analogous" effective ring is...

Liquid-filled conical shells can typically be found in a steel water tower where the conical vessel acts as a water reservoir. The presence of the liquid in the thin-walled steel shell leads to compressive stresses in meridional direction and tensile stresses in circumferential direction. This meridional compressive stress increases rapidly along the generators of the cone between the liquid surface and the base of the cone. If this compressive stress surpasses a certain critical level, the shell buckles despite the stabilising effect of the tensile hoop stresses. This elastic buckling phenomenon entails the failure of the entire structure. The combination of the meridional compressive stress and the hoop stress can also lead to a second type of failure, i.e. yielding of the shell wall and thus plastic failure. For this failure phenomenon both stress components act together. In the past, a number of water towers have collapsed due to these failure phenomena. This was the incentive f...

Thin-walled shell structures of a circular cylindrical shape are widely used in structural engineering to serve in applications such as silos, tanks or chimneys. The design of such structures poses some considerable challenges to structural engineers as the load carrying behaviour of cylindrical shells is quite complex, especially for non-axisymetric load cases. Very often a comprehensive analysis causes considerable expenses and the vast amounts of results which are typically generated make it hard to understand the underlying load-carrying principles of the structure. The introduction of an engineering method to handle two typical non-axisymetric load cases on circular cylindrical thin-walled shell structures is the goal of this paper. The proposed method offers a quick way to generate critical section forces and displacements. The load cases discussed herein are wind-loading and foundation-settlement. Ground support for many cylindrical steel structures is often realised by ancho...

In this paper the elastic stability and imperfection sensitivity of axially loaded cylindrical shells on narrow discrete supports is explored. This is done by parametric geometrically nonlinear finite element analyses of the perfect and imperfect cylinders up to the critical load maxima. In addition, classical buckling eigenvalues are computed for reference purposes. The obtained numerical results are plotted in a systematic unified way and related curve-fit expressions are developed for the critical load maxima in dependency of the geometrical parameters of the problem. The support width, the shell slenderness and the type of local support, i.e. flexible versus rigid local support conditions, are varied. The present basic investigation is restricted to shells with linear-elastic material behaviour. The study of the buckling behaviour for narrow local supports, including the limiting case of point supports is of special concern. Strictly speaking, point supports exist only in the mathematical limit, since the stress singularities which occur in this case are mere artefacts and have no direct physical significance. But it turns out that the local buckling behaviour, like shape and evolution of buckles, magnitude of buckling loads etc. tends to an invariant typical limiting scenario, which is surprising but understandable at the same time. This typical local mono-modal buckling scenario, which is also investigated and presented in this paper, may be viewed as the counterpart to the well-known multimodal characteristic global buckling scenario which occurs under uniform axial compression.

Cylindrical steel containments, like silos and tanks, frequently rest on column-supports, which induce high local axial forces into the shell. This causes pronounced stress concentrations, which might impair the shell by local yielding or buckling failure above the support. The load-carrying behaviour of such axially loaded cylindrical shells has been investigated in recent years resulting in proposals for design rules. However, in many practical cases the axial loading acts in combination with internal pressure caused by the filling medium of the containment, which induces circumferential (hoop) stresses in the shell. The effect of these stresses on the load-carrying capacity is the objective of this paper. The study was carried out on the basis of numerical investigations, which were verified by experimental results of steel models. The calculations, based on geometrically nonlinear analyses, include the effects of geometrical imperfections as well as material plasticity. The scope of the paper covers unstiffened cylinders with a radius/thickness ratio of 500 and the steel grade Fe 360 resting on four local supports.

This paper deals with practical problems encountered in the design of seismically loaded liquid-filled vertical tanks. Global stability, buckling under combined action of axial compression and internal pressure and the effect of flexible boundaries on axial buckling are studied. The question of the mutual interaction of global and local failure modes is considered. Numerical studies on the basis of finite element-discretized-shell models are carried out which show the typical features of the different failure modes. Both the effect of internal pressure on axial buckling (elephant foot failure) as well as the flexibility of the base ring results in noteworthy reductions of the axial buckling resistance. Global stability effects turned out to play no major role in the present tank design.

The basic equations of stationary heat conduction in shells of revolutiontaking into accountsurfaceheat exchangeat the boundarysurfacesare derived and further specified for the practically important axisymmetric case. A structural mechanics analogy is then established to the problem of out-of-plane loading and deformation of a plane grillage structure, consisting of shear-flexible beams on continuous elastic foundation, with the axes given by the meridians of the shell parts.This analogy provides an elegant and easy way of qualitative and quantitative understanding of the complicated thermal states in these components which are usually unfamiliar to the practisingcivil engineer.General and some specific solutions of the basic equations for practically important types of ring stiffened shells are worked out and presented in diagram form. The analysis procedure is demonstrated by an illustrative example.