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DYNAPrint version ISSN 0012-7353

Dyna rev.fac.nac.minas vol.82 No.194 Nov./Dec Medellin. 2015

http://dx.doi.org/10.15446/dyna.v82n194.49731

DOI: http://dx.doi.org/10.15446/dyna.v82n194.49731

Estimate of stress induced During filling and

discharge of metallic silos for cement storage

Estimation of induced during filling and em ptyin g of metal silos for cement storage efforts

Wilmer Bayonne-Carvajal to & Jairo Useche-Vivero b

to Universidad Tecnológica de Bolívar, Cartagena, Colombia. b Faculty of Engineering, Universidad Tecnológica de Bolívar, Cartagena, Colombia.

[email protected]

Received: March 19 th , 2015. Received in revised form: June 1 rd ,

2015. Accepted: June 16 th , 2015.

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License .

AbstractThe present article show the structural analysis Realized to metallic silo for storage of cement through theparametric model development in the finite element software ASNYS APDL, the fill and discharge Pressures on

the silo wall applied is determined to Eurocode With the EN 1991-4 normative. The model is development withtype shell elements Allowing That the silo structure fits to the cylindrical and conical geometric of the silo. ItExplains each of the phases Having the development of the model and is made a detailed analysis of the resultsdelivered by the software; EVALUATED different models are changing the sheet thickness The most Appropriatefor select. Also the results are Analyzed be changing the tilting When the hopper and is reviewed the behavior of the silo When is Analyzed With its structure.

Keywords: Cement silos, structural analysis, finite element, parametric model, Eurocode EN 1991-4, ANSYSAPDL, type shell elements

SummaryThis article describes the structural analysis to a metal silo storing cement through a parametric modeldeveloped in the finite element software ANSYS APDL, pressure filling and emptying the material exerts on thewalls of the silo are determined based in the regulations of Eurocode EN 1991-4. The model is made with shellelements types allowing its structure fits the cylindrical and conical silo geometry. Each of the phases involvedin the development of the model is explained and a detailed analysis of the results produced by the softwareanalysis is done, different models are evaluated by varying the sheet thickness in order to select the mostappropriate. The results are also analyzed when the hopper silo changes its angle of inclination and behaviorthat has the silo when analyzed in conjunction with its support structure is reviewed.

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Keywords: Silo of cement, structural analysis, finite element parametric model, Eurocode EN 1991-4, ANSYSAPDL, type shell elements.

1. Introduction

The cement silo is responsible for storing the ready to pack and deliver to the consumer material, also servesas a reserve to cushion production changes and maintenance downtime, ensuring that all the time cement canbe delivered to the customer.

To make the design of a metal silo efficiently, they should take into account different variables that affect thebehavior of the material within it is essential to determine the loads that determine the structural behavior of the silo. Initially we must be clear that the material stored in the silo plays a critical role in the outcome of structural analysis to be performed, different physical characteristics of the material influence the resultant of the forces generated by the pressure on the sides of the silo [ 5,6].

Currently there are different regulations with which one can determine the pressure on the walls of the silos,however Eurocode EN 1991-4 has gained prominence because of its large application worldwide and withsatisfactory results in the designs [1]. Based on this methodology a spreadsheet involving each of the variablespresent in the calculation of the pressures and developed with standard regulations studied it develops. Todetermine some variables silo is necessary that its geometry defined, so that the spreadsheet must have asinputs the dimensions of the silo plus the material characteristics stored. With these values and the information

contained therein, they are obtained as a result of calculating the pressures both filling and emptying into thecylindrical portion and the silo hopper.

With certain pressures can perform finite element structural analysis, not without first seeking the most suitableto represent the metal element geometry of the silo. Shell elements types or more commonly known as shell-type elements are described in the development of this work and it is these elements that the silo models [4,7].

Structural analysis of the silo by means of a finite element computer model to determine the suitable wallthickness should have the silo. Initially two codes ANSYS-APDL commands are generated in two tabs of thespreadsheet; one for the model filling pressures and the other with drain pressure. Each code takes as input allvariables in the silo for parameterizing any desired geometry. Additionally, in this file you can change thecharacteristics of the screen to select the type, quantity and size of elements that it should have. The code islinked to the results of the pressures of filling and emptying obtained with the same worksheet. By two linksyou have the spreadsheet can be generated text files in txt format, containing the code that is inserted into the

command line ANSYS-APDL, there the program results run and evaluated and analyzed to get proper silo design[2,12].

variation of efforts has the silo when the inclination angle of the hopper changes its behavior and finally the silois evaluated when analyzed in conjunction with a structure that supports [13] is also analyzed.

With a model that can vary the properties of the stored material and adjust the geometric characteristics of thesilo, the designer will be able to assess the best condition for a given scenario, resulting in a suitable designthat meets the specific needs of a case .

2. Methodology

To determine the stresses and strains in the silo a first part determining working pressures both filling andemptying the cylinder and the hopper and a second part which is the model with finite element ANSYS-APDL.

2.1. Calculation of pressure based on the regulations of Eurocode EN 1991-4

2.1.1. geometric specifications silo

The Fig. 1 shows the geometry of the silo with the variables affecting the pressure curve and which are input forcalculating the silo [3,10].


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Where;

d c = diameter silo

h b = the height that has the material

h c = height of the material in the cylindrical portion

h h = It is the height that has the hopper

h s = height of the upper cone forming material

b = angle between the wall of the hopperand i = Eccentricity filling

and or = emptying runout

2.1.2. Properties of the granular materials in the calculation of the silo

The properties of the material that is contained in the silo and which are necessary for the calculation of thepressure on the walls of this are:

→ Specific material weight g→ Angle of repose with the horizontal f r→ effective internal friction angle f i→ l lateral pressure ratio→ angle of wall friction f w

The properties for different granular materials can be found in the Eurocode EN 1991-4 Annex E [3,10].

2.1.3. Calculating filling pressures in the cylinder and hopper

In Fig. 3 path shown zy pressures are involved in filling the silo in its cylindrical part [3.10].


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Where:

With:

A = area of the cross section of the silo.U = circumference of the circular section of the silo.R = Radius of the silo.

Z = Traversing the cylinder pressure = specific weight material. = Ratio of lateral pressure.

= coefficient of friction with the wall.

The calculation is performed free pressure by increasing the horizontal pressure by the following relation:

Where:

and i = eccentricity filling.

The total horizontal pressure is the sum of the two horizontal pressures determined previously fixed pressureand pressure free.

The horizontal filling pressure is given by:

And the horizontal pressure:

The Fig. 4 describes the trajectory xy pressures are involved in filling the silo in its conical part [3.10].


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Where:

With:

Where:

= specific weight of the material.

h h = height of the hopper, from the tip of the cone to the junction with the cylinder.x = Traversing the pressure in the hopper. h = coefficient of friction with the wall of the hopper.

= angle of the hopper.P vft = vertical pressure of the cylindrical section.

a = 0.8 for filling pressures.

2.1.4. Calculation of pressure in the cylinder and emptying hopper

The Fig. 5 shows the pressures involved in emptying the silo in its cylindrical part. Then equations [3,10].


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The Fig. 6 shows the pressures involved in emptying the silo in its conical part. Then equations.

Where;

s = coefficient of friction of hopper wall

wh = angle of wall friction of the hopper

i = effective angle of internal friction of solid material

2.2. Finite element model in ANSYS-APDL

For this project platform Mechanical APDL (language parametric design) it was chosen because it allows todevelop a code commands which are structured each of the phases of structural analysis and which can beparameterized geometric inputs, material characteristics, type and size element to be used, and detailedmeshing characteristics of the loads on the model, the model also allows to provide a curve of pressure, if it isnot possible in Worckbench as this allows only hydrostatic [2,12] pressures.

2.2.1. Method for generating meshing silo

Before performing the meshing variables geometric silo are named for the model are parametric, this part alsonamed the element type to use (shell 281, to be better curvatures silo setting), size element and materialproperties of the silo. The Fig. 7 shows these variables.


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Once variables geometry silo defined proceeds to locate strategic points in space (keypont) in order to draw thegeometry of the silo, with keypont lines are generated and when they rotate on the axis of the silo these linessilo surfaces are obtained, the Fig. 8 shows this result.

For meshing the different surfaces of the silo is selected and assigned the physical properties of the material,the thickness and size of the element in Fig. 9 you can see the mesh.

2.2.2. Load allocation model

The equations used in Section 2.1.3 and 2.1.4 are entered into a spreadsheet where pressures are determinedfilling and emptying the cylinder and hopper silo, hence the constant curve of the third order are determined to

show the pressure curves and can be seen in Fig. 10 . With these constants and relating the area where it isapplied pressure loads to the model nodes are assigned by two equations that vary with height; one for thecylindrical part and one for the tapered portion. The Fig. 11 represents the allocation of loads in the cylinder.


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Finally they are assigned boundary conditions to the nodes representing the base of the silo support preventingits movement in either direction. Once this code is copied to the command line ANSYS and SOLVE is typed, sothe program calculates the stresses and strains of the silo.

3. Results

3.1. Esfuerzo.sy deformations silo studied

The Figs. 12 and 13 show the effort Von Mises produced by the casting pressure, it is evident that the maximumvalue of 0.166Mpa is located in reinforcements belt, that is logical bearing in mind that the support of the silo islocated in this part and there supports all cargo


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Regarding the deformations of Figs. 14 and 15 show that the maximum value of 8.29mm is present in thehopper just below the belt reinforcements, phenomenon that occurs due to the restriction of movement issupported.

3.2. Selecting the most suitable model

6 models silos same geometry but different thicknesses analyzes were performed in order to evaluate which

offers better safety factor and is less heavy, this in order to reduce manufacturing costs and assembly. Is thatthe Model 5 is right because it throws safety factors of 1.51 for filling and emptying and 1.37 for weight is40256kg. The Table 1 shows the results.


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3.3. Analysis of an effort in a silo with different inclination hoppers

Taking the silo model May 2 analyzes are performed by changing the inclination angle of the hopper (value A1of Table 1 = 60 degrees), case 1 for hopper 70 degrees and 50 degrees 2 case.

The Figs. 16 and 17 show the Von Mises stress generated by the filling pressure in the case 1 and 2 respectivelyand in Figs. 18 and 19 for emptying loads.


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Note that for case 1 Von Mises effort is greater for emptying (0.146GPa vs 0.100GPa), this occurs because thehopper is more inclined and vertical forces are minor, opposite case occurs in case 2 where the effort von Misesis 0.197GPa for emptying 0.213GPa for filling.

3.4. Analysis of a silo structure

As seen in previous analyzes the silo showed their utmost efforts in belt and the maximum strains in thehopper, which is why an analysis of the silo is done contemplating a support structure 10 meters high, sizecommonly used for this type silos in the cement packing process. It is used as a base code ANSYS model 5adicionándole the geometry of the columns and beams of the structure.


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The Figs. 20 and 21 represent the Von Mises stress for filling and discharge pressures respectively and Figures22 and 23 deformations in the same cases.


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From the results it can be deduced that efforts in the silo are lower when analyzed in conjunction with itsstructure, this is due to the fact that the two different boundary conditions of each model is induced.

When the silo is only analyzes their fulcrums have no degree of freedom, while in the case silo structure thesesame points have degrees of freedom and its movement it depends on the rigidity of the structure.

4. Conclusions

The parametric model developed with a code and the finite element software ASNYS APDL allows the calculationof a silo with any geometry, size, sheet thickness and type of material, size and type of finite element to use.This model can be manipulated thicknesses of different sections of the silo for comparative analysis andevaluate the suitability of one or another design, allowing the calculista develop a suitable model that meets theconditions of manufacture and assembly of the silo.

In determining the pressures exerted by the material and are applied on the walls of the silo, in its cylindricalpart and the conical part is that there are two types of behavior in relation to the pressure in the conical part,finding that for hoppers with high pressure drain inclinations are notoriously higher than filling otherwise itoccurs in the hoppers with a small slope where the pressures of filling and emptying are similar.

Graphical environments, which are quite friendly but little manipulated, major finite element software do nothave the option to enter the model pressures with variation from a height, the closest they offer is applicationof hydrostatic pressure which is linear. As the pressure curves were determined are third order, it becomesnecessary to replace a code that pressure for routine application of equivalent forces on the nodes in each area,cylindrical portion and conical portion. This is another reason why APDL ANSYS was chosen as the software forfinite element analysis, the platform allows any type of load application.

Performed the structural analysis was found to not necessarily pressures drain can cause failures in a silo, iseasy skew this information as pressure casting are always higher in the silo, can in the hopper described aboveproviso is given, but the total silo is always higher. The specific event occurs in one of the important parts of the silo and often relegates; belt is in charge of attaching the silo structure. It was found that values the efforts

were greater when the fill was applied, this is because there is a balance between the loads of the hopper andthe cylinder just at that point, if the cylinder is lower the hopper begin to sag but this area, making greaterefforts at this point. Is important to note that the efforts in the body of the silo if older than emptying filling.

To describe the behavior of curved silo surfaces model develops most known type shell elements as "shell" asthese simultaneously displays bending stresses and membrane stresses, the first corresponding to the bendingstresses of a plate producing moments bending and torsional moments and the latter correspond to efforts planestress problem, which act tangentially to the middle surface and tangents produce forces in the membrane.

References

[1] Aguado, P., advanced calculation methods in agricultural silos pressures by finite element technique.

Emptying bins and walls of corrugated iron. PhD Thesis, School of Agronomists UPM, Spain. 1997. [ Links ]

[2] Ansys, Inc., Ansys Mechanical APDL Introductory Tutorials. Canonsburg, USA, 2013. [ Links ]

[3] CEN (European Committee for Standardization). Eurocode EN 1991-4. Brussels, Belgium. Actions onstructures - Part 4: Silos and tanks, 2005. [ Links ]


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[4] Cook, R., Malkus, D., Plesla, M. and Witt, R., Concepts and applications of finite element analysis,University of Wisconsin, Madison, 2001. [ Links ]

[5] Ding, S., Rotter, M., J. and Enstad Ooi, G., Development of standard pressure and frictional traction alongthe steep walls of a conical hopper During filling: Thin-Walled Structures 49, pp. 1246-1250, 2011. DOI: 10.1016

/ j.tws.2011.05.010 [ Links ]

[6] Ercoli, N, Ciancio, P. Massey, L., Evaluation of grain-wall interaction in the structural behavior of silos.Computational Mechanics XXVII, pp.161-180, 2007. [ Links ]

[7] Ercoli, N., Ciancio, N. and Berard, C., Analysis for designing a clinker silo and computationalimplementation, in: Buscaglia, G., Dari, E. and Zamonsky, O., ( Eds.), Computational Mechanics. XXIII, pp. 619-638, 2004. [ Links ]

[8] Jürgen, T. Assessment of Mechanical properties of cohesive particulate solids - Part 2. Particulate Scienceand Technology, 19, pp. 111-129, 2001. DOI: 10.1080 / 02726350152772065 [ Links ]

[9] Rodriguez, W. and Pallares, R., three - dimensional modeling of a dual pavement under load with finiteelements. DYNA Magazine, 82 (189), pp. 30-38, 2015. DOI: 10.15446 / dyna.v82n189.41872 [ Links ]

[10] Rotter, J., Guide for the economic design of a circular metal silos. CRC Press. London and New York, 2001.[ Links ]

[11] Ulrich, H. and Josef, E., Numerical investigations on discharging silos. Journal of Engineering Mechanics,110, pp. 957-971, 1984. DOI: 10.1061 / (ASCE) 0733-9399 (1984) 110: 6 (957) [ Links ]

[12] University of Alberta - ANSYS tutorials. Canada. [Online] - Available at:http://www.mece.ualberta.ca/tutorials/ansys/ [ Links ]

[13] Yanes, to., Fernández, M. and Lopez, P., Analysis of the distribution of static pressures in silos witheccentric cylindrical hopper by MEF influence of eccentricity and comparison with Eurocode 1. Reports of Construction, 52, 2001, 472 P. [ Links ]

Bayonne, W., received his BSc. in Electromechanical Engineering in 2004 at the Pedagogical and TechnologicalUniversity of Colombia, for more than 10 years he has worked in the area of mechanical design developedconceptual, basic and detail of different plants in the energy, metalworking, steel, cement sector engineeringand Petroleum. research areas of interest: stress and strain analysis by the finite element method, study thebehavior of fluids and powdered materials through computational fluodinámica, design of silos, tanks andpressure vessels. ORCID: 0000-0001-5799-5246

Useche, J., is a professor of mechanical engineering at the Technological University of Bolívar (UTB),Colombia, is coordinator of the Research Group of Materials and Structures Continuous UTB. Is PhD inMechanical Engineering from the State University of Campinas, Brazil. He received his BSc in MechanicalEngineering at the Technological University of Bolivar, Colombia and MSc. in Mechanical Engineering from theUniversity of the Andes, Colombia. research areas of interest: finite element method, boundary element methodand mesh - free methods for analysis of stress and strain, mechanical damage and residual life assessment.ORCID: 0000-0002-9761-2067

National University of Colombia at Medellin

Street 59A No 63-20Block 42 [email protected]
mailto:[email protected]://www.mece.ualberta.ca/tutorials/ansys/

estimate of stress induced during filling and discharge of metallic silos for cement storage

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