Study of buckling in steel silos under eccentric discharge flows of stored solids

The most serious loading condition for slender thin-walled metal silos has long been recognized to be the condition of discharge, with eccentric discharge causing more catastrophic failures than any other. Two key reasons for this high failure rate are the difficulties in characterizing the pressure distribution caused by eccentric solids flow, and in understanding the associated unsymmetrical stresses in the silo wall. Few studies have addressed either the linear elastic behavior of such a silo or its buckling failure under eccentric discharge. In this study, the eccentric discharge pressures are characterized using the new rules of the European Standard EN 1991-4 on Silos and Tanks. This novel description of unsymmetrical pressures permits a study of the structural behavior leading to buckling during eccentric discharge, including the critical effects of change of geometry and imperfection sensitivity, to be undertaken using geometrically and materially nonlinear computational analyses. The mechanics of the behavior are found to be quite complicated. A silo which is safe under axisymmetric loading is found to be susceptible to catastrophic stability failure under eccentric discharge. © 2010 ASCE

Full plastic resistance of tubes under bending and axial force: exact treatment and approximations

The full plastic resistance under a combination of bending and axial force of tubes of all possible wall thicknesses, from thin cylinders to circular solid sections, does not ever seem to have been thoroughly studied, despite the fact that this is a relatively simple analysis. The first part of this paper pres ents a formal analysis of the state of full plasticity under longitudinal stresses in a ri ght circular tube of any thickness free of cross-section distortions. The derivation leads to relatively complicated algebraic expressions which are unsuitable for design guides and standards, so the chief purpose of this paper is to devise suitably accurate but si mple empirical descriptions that give quite precise values for the state of full plastici ty whilst avoiding the complexity of a formal exact analysis. The accuracy of each approx imation is demonstrated. The two limiting cases of a thin tube (cylindrical shell) a nd circular solid section are shown to be simple special cases. The approximate expressions are particularly useful for the definition of the full plastic condition in tension members subject to sma ll bending actions, but also applicable to all structural members and steel buil ding structures standards, as well as to standards on thin shells where they provide the full plastic reference resistance. These expressions are also useful because they give simple definitions of the orientation of the plastic strain vector, which can assist in the development of analyses of the plastic collapse of arches and axially restr ained members under bending

On the gradient of the yield plateau in structural carbon steels

New design methodologies are being developed to allow stocky steel members to attain and exceed the full plastic condition. For theoretical validation, such methods require a characterisation of the uniaxial stress-strain behaviour of structural steel beyond an idealised elastic-plastic representation. However, the strain hardening properties of carbon steels are not currently guaranteed by the standards or by any steel manufacturer. Assumptions must thus be made on what values of these properties are appropriate, often based on limited information in the form of individual stress-strain curves. There is very little consistency in the choices made. This paper first illustrates, using an example elastic-plastic finite element calculation, that a stocky tubular structure can attain the full plastic condition at slendernesses comparable with those defined in current standards and supported by experiment when using only a very modest level of strain hardening, initiated at first yield. It is then hypothesised that the yield plateau in the stress-strain curve for structural carbon steels, classically treated as flat and with zero tangent modulus, actually has a small but statistically significant positive finite gradient. Finally, a robust set of linear regression analyses of yield plateau gradients extracted from 225 tensile tests appears to support this hypothesis, finding that the plateau gradient is of the order of 0.3% of the initial elastic modulus, consistent with what the finite element example suggests is sufficient to reproduce the full plastic condition at experimentally-supported slendernesses

Bending of rectangular plates subject to non-uniform pressure distributions relevant to containment structures

Rectangular planform silos are often used where there is need for simple construction or space restrictions. The flexibility of the flat plate walls leads to a horizontal variation in wall pressure across each wall, with much reduced pressures at the mid-side. There is a clear and systematic relationship between the wall flexural stiffness relative to the stiffness of the stored solid and the pressure pattern on the wall which is now well proven. Since the centre of each wall is subject to significantly reduced pressures, it may be expected that the bending moments in the wall will much lower, permitting the use of a thinner wall. In turn, the thinner wall is then more flexible and leads to a further redistribution of the pressures. This paper is the first to examine the structural consequences of these pressure changes. The horizontal variation of the wall pressure is well captured by a hyperbolic form, with much reduced mid-side pressures and raised corner pressures, characterised by a single parameter “alpha” that determines the strength of this redistribution. This parameter is naturally dependent on the relative wall and solid stiffness. In this study, the value of is varied between the uniform pressure condition = 0 and a high value (=3). The highest values occur when a stiff solid is stored in a silo with very flexible walls. Wall plates of different aspect ratio are investigated representing conditions in a square or rectangular silo. The finite element predictions show that great savings can be made in the design of these structures by exploiting the reduced deflections and reduced stresses that arise when realistic patterns of pressure are adopted. The results presented here are suitable for transformation into design rules for the Eurocode standards EN 1993-1-7 [1] and EN 1993-4-1 [2]

Cylindrical shells under uniform bending in the framework of Reference Resistance Design

The resistance of cylindrical shells and tubes under uniform bending has received significant research attention in recent times, with a number of major projects aiming to characterise their strength through both experimental and numerical studies. However, the investigated cross-section slenderness ranges have mostly addressed low radius to thickness ratios where buckling occurs after significant plasticity and the influence of geometric imperfections is relatively minor. The behaviour under uniform bending of thinner imperfection-sensitive cylinders that fail by elastic buckling was largely omitted, as was the influence of finite length effects. The value of such resistance models that are only useful for thicker cylinders is therefore somewhat limited. This paper offers the most comprehensive known characterisation of the buckling and collapse resistance of isotropic cylindrical shells and tubes under uniform bending. Expressed within the modern framework of Reference Resistance Design (RRD), it holistically incorporates the effects of material plasticity, geometric nonlinearity and sensitivity to realistic and damaging weld depression imperfections. The characterisation was made possible by the authors' recently-developed novel methodology for mass automation of nonlinear shell buckling finite element analyses. A modification of the RRD formulation is proposed which facilitates its application to systems of low slenderness, and offers a compact algebraic characterisation of all potential imperfection amplitudes for this common shell structural condition. A reliability analysis is also performed