Literature and the Eurocodes
Some Previous Research
Traditionally, silos have been designed for the fully-filled state based on the pressure values defined by the Janssen theory. Rotter (2001) points out in his earlier studies that the process of discharging can lead to much greater pressures, or specifically pressure differentials, caused by locally low pressures which can produce more serious conditions for the silo. There has been extensive research carried out to better the understanding of pressures exerted on silo walls with concentric hoppers, but limited research considering eccentric discharge, while most rules in silo loading are concerned with symmetrical pressures and pay little or no attention to unsymmetrical pressure conditions (Rotter, 2001). It is now accepted that eccentric discharge has the potential to create even greater pressures and pressure differentials than concentric discharge
Ayuga et Al. (2001) conducted research to analyse the pressure distributions in grain silos for both the discharge and static conditions with outlet eccentricity ranging from 0% (central) to 100% (outlet tangential to silo cylinder).They used a base model of cylinder height 8m and hopper height 2.5m with a cylinder radius of 3m. Their findings supported previous research for concentric discharge that the peak pressures occurred at the transition between the cylinder and the hopper for mass flow (the condition under which all particles of the particulate solid are in motion when the silo is discharging from the full condition) but at the intersection between the slip line and the vertical wall for funnel flow (a flow pattern in which solid adjacent to some part of the wall remains stationary whilst other parts move, when the silo is effectively in the full condition).
It was observed that for eccentric discharge the normal pressures on the wall increase by up to 11.4% for an eccentricity of 60% (which was 0.25 times the diameter in this case) with a greater gradient of pressures taking place in the transition. As eccentricity increases pressures decrease slightly on the side where discharge occurs but increase considerably on the other side, thus creating a large pressure differential. Lateral pressures obtained by the researcher’s finite element method are compared to those obtained from adherence to the Eurocode. The Eurocode considers pressures proposed to be valid up to an eccentricity of 0.25 times the diameter (EN 1991-4:2006, Section 5.3.3). However, as a result of the pressure differentials involved, Ayuga et Al. (2001) suggested that a more conservative calculation should be used in the Eurocode. Rotter (2001b) reports an analysis of eccentric discharge which measured the variation of vertical membrane stresses resultants and found them to be massively greater than the simple buckling criterion at ultimate limit state. The location for potential buckling on the silo wall was found to be very high (Rotter, 2001b).
In more recent developments, Vidal et Al. (2005) claim to be the first researchers to use a dynamic 3D finite element model to analyse wall pressures during filling and discharge of cylindrical silos with eccentric hoppers. The research analysed and compared static and dynamic pressures on the silo wall with maximum eccentricity. It also studied the influence of hopper eccentricity on discharge pressures at various points and performed a parametric analysis to define the influence of the friction coefficient and Poisson’s ratio on the silo with maximum hopper eccentricity. Their findings supported and further developed previous research concluding that the strongest influence of eccentricity was at the transition between the silo cylinder and the hopper with pressure differentials observed in the lower 20% of the cylinder.
The Eurocodes top Δ
The Structural Eurocodes which are produced by the Comité Européen de Normalisation (www.cen.eu) are a set of unified international codes of practice for designing building and civil engineering structures. There are ten Eurocodes (EC 0 – EC9) each of which are split up into constituent parts and dealing with a specific area of design and are gradually replacing national codes within the EU (British Standards Institute).
Eurocodes with direct relevance to this research
- Eurocode 0
- EN 1990: 2002 Eurocode 0: Basis of Structural Design
Gives material-independent guidance which must be consulted when using EC 2 to EC 9. It provides partial factors for actions, load combinations expressions for ultimate and serviceability limit states (British Standards Institute).
- Eurocode 1
- EN 1991-4:2006 Action on Structures. Part 4: Silos and Tanks (Sept. 2006).
The scope of this part includes the following:
- General principles and actions for the structural design of silos for the storage of particulate solids and tanks for the storage of liquids.
- Provisions for actions which are not just associated with the stored material (eg. Thermal differentials or differential settlement).
Certain restrictions are in place in terms of silo dimensions with an ability to accept minor variations with structural consequences considered:
- Overall height is less than 100m
- The ratio of overall height to inside dimension is less than 10
- Inside dimension is less than 60m
The scope contains restrictions to:
- Silos with limited eccentricity of inlet and outlet, with minor impacts caused by filling
- Silos designed for a defined range of particulate solid, which is free flowing and has low cohesion.
- Tanks which store liquids at normal atmospheric pressure (EN 1990).
Loading conditions outside the scope of EN 1991-4 such as eccentric discharge, local loadings due to aeration or unsymmetrical flow are provided for in EN 1993-1-6 (Rotter, 1998).
- Eurocode 3
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EN 1993-1-6 Design of Steel Structures. Part 1.6 General – Strength and Stability of Shell Structures (Expected: November 2006).
EN 1993-1-6 governs the design of steel structures which take the form of a thin shell of revolution. These could be towers, masts, chimneys, silos, tanks or pipelines. Each category also has its own specific Eurocode section and thus EN 1993 Part 4.1 (for silos) is also of interest to us. Ultimate limit state design is the primary concern in terms of plastic limit, cyclic plasticity, buckling and fatigue
The main provisions apply to axisymmetric shells and associated circular or annular plates, and also to ring beams and stiffeners which form part of the structure. Cylindrical and conical panels are not explicitly covered, but with appropriate boundary conditions the same provisions may be applied. With the appropriate material properties taken into consideration it can also be applied to other metallic shells as well as steel. The standard does not cover the eventuality of leakage of stored contents.
(CEN, prEN 1993-1-6:2006)
EN 1993-4-1 Design of Steel Structures. Part 4.1: Silos, Tanks and Pipelines. Silos (Expected: November 2006).This Eurocode standard governs the structural design of vertical metal silos (cylindrical and rectangular) for the storage of bulk solids at and above ambient temperature and is concerned primarily with the requirements for resistance and stability. The standard differentiates between silo classes and attempts to provide rules which can be understood by industrial manufacturers, where the limit state design method is not traditionally appreciated (Rotter, 1998).
A structural reliability class has been adopted in EN 1993-4-1 to make allowances for different sizes and complexity presenting very different challenges to the designer.
Table 1: Structural reliability classes.
Reliability Class Description 3 Ground supported silos or silos supported on a complete skirt extending to the ground with capacity exceeding 5000 tonnes†.
Discretely supported silos with capacity exceeding 1000 tonnes†
Silos with capacity exceeding 200 tonnes† in which any of the following design situations occur:- Eccentric discharge
- Patch loading
- Unsymmetrical filling
2 All silos covered by Eurocode 3 Part 4.1 and not placed in another class 1 Silos with capacity between 10 tonnes and 100 tonnes. † The values given here may be changed by National Application documents. (Reproduced from Rotter 1998, Rotter 2001 and EN 1993-4-1)
EN 1993-4-1 replaces previous National codes which were only concerned with the definition of pressures on the silo wall. This new code contains well over 100 equations governing silo design from granular solids testing to solid flow patterns, wall pressures, structural analysis and structural design (Rotter, 1998).
The scope of EN 1993-4-1 does not include:
- Resistance to fire
- Silos with internal subdivisions and internal structures
- Silos with capacity less than 10 tonnes
- Cases where special measures are required to limit the consequence of accidents.
(CEN, prEN 1993-4-1:2005)