Keywords: steel silo, structural modelling, buckling design, nonlinear analysis.

An archetypal silo structure consists of a cylindrical upper part (barrel) and a conical lower part (hopper) in order to facilitate natural discharge by gravity action. In this case the silo structure is placed in elevated positions in order to enable easy access beneath the vessel. Ground support is provided either by continuous cylindrical skirts extending the barrel to the ground level, yielding an axisymmetric overall silo structure, or by discrete equidistant column supports around the circumference, yielding a non-axisymmetric overall silo structure. Discrete supports of thin-walled metal silos deserve special care in design. Depending on the magnitude of overall silo loading the provision of various types of stiffening measures is common practice, such as increased wall thickness, or ring stiffeners, or stringer stiffeners at the support meridians, or combinations of those measures. Since silo structures are mainly loaded vertically and are ground-supported, in a continous or discrete way, the cylindrical silo walls are exposed to axial compression stresses which have their peak values usually in the immediate region above the supports or above the vertical termination of stringer stiffeners. Apart from the primary problem of proper support design against the plasticity limit state this constitutes a latent secondary problem of proper design of the shell wall segments and stringer stiffeners against the buckling limit state (see references [1,2,3]). Since we have to deal with a great variety of constructional solutions in response to the magnitude of overall silo bulk solid loading, we are looking for a uni.ed method which can handle all these different situations. Such uni.ed design procedures for thin-walled general shell-of-revolution steel shell structures can be found in the new European Standard EN 1993-1-6 [4], which proposes three buckling design methods: 1. Membrane-stress based buckling design for elementary cases and for general cases, based on global linear shell analysis (LA), 2. simpli.ed global analysis design based on linear buckling eigenvalue analysis (LBA) and materially nonlinear limit load analysis (MNA) for reference purpose and 3. advanced global analysis design, based on geometrically and materially nonlinear shell analysis (GNiA) including imperfections, for the most general cases [5]. Important features and comparison of these design methods cannot be discussed here due to limited space. It is the purpose of this paper to apply these complementary buckling design methods to a practical discretely supported steel silo structure and to compare them with each other and to work out guidelines for the quick and easy application of these methods for such types of structures.

In this paper some basic aspects of modelling of thin-walled metal silo structures are also discussed. As basic result of our investigations the rule can be deduced, that structural modelling should be as realistic as possible in order to reduce the potential range of scatter of the resulting buckling load factors. This means for example, that the introduction of too sophisticated constraint equations or transformed displacement coordinate systems should be treated with great care or completely avoided. Structural modelling decisions are required for the silo support, the cylinder-cone transition junction, the stringer stiffeners at the supports, the ring stiffeners, the circumferential lower and upper shell edges and for the connections of the shell segments. The connection of eccentric beam-like stiffeners to the shell wall turned out complicated and error-prone. The stiffener modelling turned out easy and convenient if the thin-walled parts of the stiffener cross-sections, in a consistent way, were represented by strips of thin-walled shell elements.

The effects of different modelling assumptions in connection with the proposed buckling design procedures is demonstrated on a practical example of a stiffened silo structure with U-shaped ring stiffeners and U-haped stringer stiffeners at the supports. It turned out that vertical U-shaped stringer stiffeners at the supports have a bene.cial effect since the two distant stiffener webs essentially act as two isolated mono-stiffeners which results in a considerable increase in buckling load bearing capacity. Such advanced effects can only be utilized if consistent shell modelling, instead of beam modelling, is carried out.

1

C.J. Brown, J. Nielsen (Eds), "Silos - fundamentals of theory, behaviour and design", E&FN Spon, Routledge, London, 1998.

2

J.M. Rotter, "Guide for the Economic Design of Circular Metal Silos", Spon Press, London, 2001.

3

W. Guggenberger, R. Greiner, J.M. Rotter, "Cylindrical shells above local supports", in: Buckling of Thin Metal Shells, chapter 3, Eds: Teng, J.G. & Rotter, J.M., Spon Press, London, 88-128, 2004.

4

EN 1993-1-6, "Eurocode 3: Design of Steel Structures, Part 1.6: General Rules: Supplementary Rules for Shell Structures", CEN, Europ. Committee for Standardisation, Brussels, 2004.

5

J.M. Rotter, "Shell Buckling and Collapse Analysis for Structural Design - The New Framework of the European Standard", Festschrift Prof. C.R. Calladine, Cambridge, UK, September 2002.

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