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Prof. J. Thomas

Otto-von-Guericke U niversität M agdeburg Faculty of verfahrenstechniK und Systemtechnik Storage and F low of P articulate Solids Presented by : AHmad Gohari Calculation of reinforcement and wall thickness of concrete or metal silos. Prof. J. Thomas. Table of contents. 1. Introduction

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Prof. J. Thomas

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  1. Otto-von-Guericke Universität MagdeburgFacultyofverfahrenstechniK und SystemtechnikStorage andFlow ofParticulateSolidsPresentedby: AHmadGohariCalculation of reinforcement and wall thickness of concrete or metal silos Prof. J. Thomas

  2. Table of contents • 1. Introduction • 1.1. Whypressure in Silo Matter? • 1.2. Pressure in Silo, basictheory • 2. Wall thicknesscalculation • 3. The importanceofflowpatternsduringdischarge • 3.1. Eccentricdischargeanditsconsequence • 4. Structuraldamageanditscause, Reinforcment • 4.1. Steel and Aluminium Silo (metal) • 4.2. Concret Silos • 4.3. Reinforcement • 5. Summary

  3. 1. Introduction • 1.1 Whypressure in Silo Matter? • Pressure in Silo isdominatedbyFrictionalPhenomena • Therearemanymisleading on pressurecalculating , not unerstandingtheconditionof stress northecondictionwhichleadstofailure • Mtealandconcrete Silos behavevery different, different cricticalconsiderationshouldbetake on account (speakaboutit at 3.1)

  4. 1.2. PressureandTenstion in Silo, Basic theory • Horizontal pressure (N/m²) • Premeter (m) • Shear Stress (N/m²) • Bulkdensityof material (kg/m³) • Height (m) • smoothnessof wall Note: A smooth wall leadstohigherpressurethan a rough wall A slice ofthe wall

  5. Janssen Pressure Patern

  6. Pressure in hoppers • -}] • thevalueof n is just a number, simplification • depends on geometryand solid properties, canbeseen in particulargraphs Notes: 1.Most structurefailuresoccurebyrapture at transitionunderthe stress resultamt 2. The mostcriticalfeatureof a hooperis not the wall pressuredistribution but theoverequilibrium

  7. Simple structureconseptforShaft

  8. Pressurechangesduringdischargeofsolids(emptying) Force increase in horizontal direction Force increase in verticaldirection Note: Kp/Kf at firstconsideredtobeorderof 9 andthen 6, thismuchpressureincreasehadbeenneverreportedbefore, severaltheories(Arnold 1980, Jenke 1973) showedthatKp/Kfshouldbearound 2.5

  9. Pressurechangesduringdischargeofsolids (emptying) Note: The mostcriticalfindingforsilo design was thepatternofunsymmetricalpressures, both after fillingandduringdischarge. The ratioofthelargestsustainedpressuretothesmallest at a singlelevelcouldbe high as 2.8 understaticcondiction after fillingand 5.6 duringdischarge Pieper & Wentzel 1964, in Braunschweig, muchofthefollowingcomesfromtheirwork

  10. 2. Thicknesscalculation

  11. 2. Thicknesscalculation

  12. Parametes and coeficients we need for calculation

  13. 3. The importanceofflowpattern • A modern describtion(EN 1991-4 2007) dividesthepossibleflowpatternintothreemaincategoriesundersymetricalcondition

  14. 3. The importanceoffolwpattern Note: Structuralresearchestudieshaveshownthatfunnelflowis not critialtothestrenghtofmetalanditisindeedbeneficial(Rotter 1986a; Teng & Rotter 1991) • Itispossibletodeterminewithreasonableprecisionwetherthesilo will exhibitmassorfunnelflow

  15. 3. The importanceoffolwpattern Note: Here man canobviouslyseewhymassflowiscritical in design Typicalpatternofaveragesymetric wall pressure after fillingandduringemptying, for different flowchannel geometries

  16. 3.1. Eccentricdischargeanditsconsequence Flow channelgeometry, typicalpressurepatternandvertical wall stress duringeccentricdischarge

  17. 3.1. Eccentricdischargeanditsconsequence • The mostdamagingconditionformostsilosisunplannedoccourenceofunsymmetricalflowregimes, iftheflowchannelmakescontactwith Silo wall • Itismabyenecessarytohave off-center dischargeoutletforfunctionalreasonsandconditions in silo such asblockageofthefeeders, thermlormoistureorsegregationofcontent.

  18. 4. Structuraldamageanditscause, reinforcement • 4.1. Steel and Aluminium Silos • 1. Boltedandweldedconstruction: • The firstbigdiffernce in metalsilosarethe Joints thatisusedin metal Silos construction. The jointsarethelinesofweakness, so theshouldbemadestrongerthanisstrictlynecessary. • 2. Brustingofvertical wall: • Brustingfailursareveryuncommonandarealmost all found in boltedsiloswhere a jointdetailshasfailed. • 3. Axial compressionbulckingofvertical wall: • This failurisnot also so common but shouldbeseriouslyconsideredbecausethismodeoffailureisoftendramaticallycatastrophic. Itcanbe also resultofunsymmetricpressureagainstthesilo wall.

  19. 4. Structuraldamageanditscause Note: Bulking under axial compression occur at very low stresses compared with the material strength (perhaps at 20 Mpa in a metal with yield stress 250 Mpa)

  20. 4.1. Steel and Aluminium Silos • 4. Eccentricdischargebuckling of the vertical wall • This is the commonest cause of axial compression buckels, where the low pressure against the wall in the flow channel cause high vertical compressive stresses over part of the perimeter near the mid-height of the silo, in which the whole silo falls over in the direction of discharge outlet. • 5. External pressure buckling of the vertical wall • When a Silo is empty the thin wall is very sensitive to buckling under extreme wind. • 6. Shear buckling of the vertical wall • Unsymmetrical top pile producing different height of solid-wall contact • 7. Rupture, plastic deformation and buckling in hopper • Hoppers made in bolted constructions are sensitive to fracture.

  21. 4.1. Steel and Aluminium Silos • 8. Bucklingandyielding in transitation rings • The transitionissubjecteto high compresionsbecuasehopperhas a slop form. Bothbucklingandyieldingfailurecanoccur in these rings

  22. Silo Failure

  23. Structuraldamageanditscause • 4.2 Concrete Silos • GeneralyConcreteisgood in compression but cannot resisttensile stress at all . • Whenconcreteissubjectedtotension, itcracks at rightanglestothetension. • Concreteshouldbereinforcedforsure. • The simplesetwayistoprestressetheconcretewithsteel. Itcanavoidthetension. • Verticalcompressionsdoes not usuallycauseproblem • The thicknessandgoodcompressivestrength all contributetohave an exellentstrength

  24. 4.2 ConcreteSilos • 1. Ductiltyanddelamination • Concreteis a brittle material, but moststructural design relies on ductilemanner. In particularshearfailures in concrete wall cancauseseriouscracking. Withappropriatereinforcementconcretestructurebehave also likeductile.An otherbrittleproblemdelamination, layerofconcrete separate. • 2. Crackingunderbendingmoment: • The mainproblemofconreteiscrackingunderbendingmomentinducedbyunsymmetricpressure • 3. Crack observation: • care must betakenwetherthecracksarecausedbythrou-thicknesstension(veryserious) orexternalsurfacetension.

  25. Reinforcement

  26. Real Example of a Silo Reinforcement

  27. 5. Summary • Whypressure in Silo Matter? • Pressurein Silo, basictheory • Wall thicknesscalculation • The importanceofflowpatternsduringdischarge • Eccentricdischargeanditsconsequence • DifferencesofMetalandConcrete Silos • Differntwayofreinforcementofconcrete

  28. Questions?

  29. References • Silo and hopper design for strength • J. MICHAEL ROTTER • Teaching Notes • Dr.Ing.habil J. Thomas

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