Software to Calculate Pressures in Cylindrical Metal Silos

This paper presents a software to calculate pressures in cylindrical silos with all products mentioned by BS EN 1991-4, which are very common used on farms and cooperatives. Properties of products vary widely, and consequently pressures, in magnitude, distribution and stability. The study of pressures is important to avoid unpredictable peak pressures which can cause serious damage. This software was developed in Python and refers extensively to the provisions of the developed European standards for silo pressures (EN 1991-4 2006) for slender, squat and intermediate slenderness silos, with and without filling or discharge eccentricities. The program was developed to be fast, safe, modular, structured and easy to handle. The software interface is simple for interaction between the data provided by the user and the results of the pressures must be presented clearly. It has application examples and analysis of results in metallic cylindrical silos of different types of walls: slippery, smooth, raspy and irregular. It is expected to provide an important tool for designers and have more efficient silo designs, reducing structural faults,collapses and waste of material. Index Terms — Silo, computer program, pressures


A. General Consideration
Silos are storage structures, capable of retaining itens of thousand of tonnes of different products and have a great economic importance for countries to invest in agriculture and industry.The main economic advantage of the storage of the products is to control the use of production, reducing imports and market price fluctuations.Rotter (2010) [1] recalls that a silo disaster is a significant financial burden, both in terms of the destruction of the structure, the loss of the material stored inside and the halt in productivity at the facility.Beside that, it is necessary to assure the quality of products in storage units.Calil Jr. and Cheung (2007) [2] showed the advantages of a technically designed silo and well conducted to obtain a better preserved product: rational, safe and economical storage, without insects and rats attacks, transport economy and reduction of impurities.
Silos can store bulk and granular products.These products transmit shear stresses of friction between the grains and the walls very different from those developing in a tank that contains fluid, so there is complexity and importance of the study of the actions in silos.Rotter (2010) [1] explains that fluid pressures depend uniquely on the head, and in most fluid storages flow velocities are so low that dynamic effects are small.By contrast, pressures in silos are dominated by frictional and there are few analogies between fluid and solid storage that are either valid or practically useful.
Silos are classified according to the cross-sectional shape in a plan section, however most silos are circular.Pressures are calculated according to the slenderness of the silo, what is the ratio between the height (H) and diameter (D), determined according to the Table I.Operating processes in a silo: loading, filling and discharge, require specific structural analysis.These analyzes should be calculated taking into account the geometric structure of the silo, the properties of the products stored and eccentricities in both processes.
Properties of the products used in the study of pressures are unit weight (γ), angle of repose, angle of internal friction, lateral pressure ratio (K), patch load solid reference factor and wall friction coefficient.The latter changes according to the type of wall: slippery, smooth, raspy and irregular.Values are shown by most international standards (AS 3774 1996 [4], DIN 1055-6 2006 [5], EN 1991EN -4 2006 [3] [3]) for all these properties , and there is the conversion factor which can determine the upper and lower characteristic values used for determining the magnitude of higher pressures.
No experimental tests were performed to characterize the properties of particulate solids, then it was used the values proposed by EN-Part 4 in Annex E, as shown in Fig. 1.
These properties of the stored product can also be determined by laboratory tests, the most widely used equipment is the "Jenike Shear Tester", created by Jenike (1964) [6] which determines the properties by direct shear test on a compressed cell.In addition to determining the product properties and the physical dimensions, EN 1991-4 [3] divides silos into classes, showed in Table II, according to the mass of product stored and consequently the risk of collapse that can occurs in the structure.Rotter (2010) [1] recalls that small silos does not present structural challenges and can be designed using fairly simple calculations, however very large silos need great attention to many details.
As proposed by EN 1991-4 [2], there are values of horizontal pressure (Phf), wall friction traction (Pwf) and vertical pressure (Pvf) distributed in depth (z), indicated in Fig. 2, for both cases of filling and discharge, and may be symmetrical or asymmetrical, global and local.In case of filling slender silos, pressures are calculated based in the theory of Janssen (1895) [7] according to the expressions below.
(1 tan ) (1 / ) They differ in the distribution of pressures slender silos to be zero at height z = 'ho'.In other words, at the contact point between the wall and the grain shown, and not at height z = 0, according to Fig. 3.In order to obtain the highest values for pressures, it should be adopted the best combination of upper and lower characteristic values of the physical properties of the stored product (μ, K and φ_i) in classes 2 and 3.For class 1, it is not necessary to check the combination of values because average values of these physical properties are used.
When the silo is being emptied, Ketchum (1907) [12] experimented and found that the pressures often increased.By EN-Part 4, symmetrical discharge pressures on vertical walls of slender silos, horizontal pressure (Phe) and wall frictional traction (Pwe), are calculated from the values obtained in the filling case weighted by discharges factors Ch e Cw shown in Table III, which is the pressure increment and according to the expressions below.
In case of squat silos, symmetrical discharge pressures are taken by the same filling pressure.For intermediate slenderness silos, symmetrical discharge pressures are calculate by the same expressions of slender silo, but the discharge factor changes which is shown on Table IV.The software was programmed in Python, a high-level programming language, object-oriented and compatible with operating systems: Windows, Linux and Mac.Python needs few lines of code compared to the same program in other programming languages and it is easy to learn.The graphical interface allows user interaction through pre-existing Python graphic objects.
Finally, application examples and analysis of the results will be developed according to cylindrical silos of corrugated sheet meal, usual in farms and cooperatives.

IV. RESULTS AND DISCUSSION
The graphical interface of interaction with the user of the program called "Eurosilo" is shown in Fig. 4 below.They were made numerous simulations with different implemented products early mentioned, varying geometric properties of the silo, classes, eccentricities and wall types.However, as an example, they will only be presented results of the horizontal pressures for soybeans, in filling case.Graph ordinate refers to the depth (z).
In first case, the silo is slender and geometrical values used were: height of 10 meters and a diameter of 5 meters without eccentricities of filling and discharging, raspy metal sheet wall, ranging all the three classes.Results are shown in the Fig. 5 below.It was concluded that not much has changed in this case with the pressures for classes 1, 2 or 3.In second case, silo is medium intermediate slenderness or squat and geometrical values used were: height of 19 meters and diameter of 12 meters, without eccentricities of filling and discharging, class 3, varying the wall characteristics.Results are shown in the Fig. 6 below.It was concluded that the wall characteristic changes significantly pressure results.Then, as expected, the smoother the wall the greater the horizontal pressure, as the surface roughness increases the friction between the wall and the stored product.
In general, it is noted that the horizontal pressure by filling in all cases has an exponential trend, which can be represented by Janssenś pressures model (1895) [7].
Journal of Advances in Information Technology Vol. 8, No. 1, February 2017 intermediate slenderness or squat silos, also in case of filling, pressures are calculated according to the expressions below.
This paper has a descriptive study of the calculation model proposed by EN-Part 4 with all the assumptions and formulations and was developed a software for design pressure in cylindrical silos.

TABLE II .
DISCHARGE FACTOR VALUES FOR SLENDER SILOS

TABLE IV :
DISCHARGE FACTOR VALUES FOR INTERMEDIATE SLENDERNESS SILOS