Tank Shell Design According To Eurocodes And Evaluation Of .
Tank Shell Design According toEurocodes and Evaluation ofCalculation MethodsDimensionering av cisternvägg enligt Eurokod samt utvärdering avberäkningsmetoderMalin PlutoFaculty of Health, Science and TechnologyDegree Project for Master of Science in Engineering, Mechanical Engineering30 hpSupervisor: Jens BergströmExaminer: Pavel Krakhmalev2018-07-25
AbstractTanks are storage vessels for liquids. They can have different appearances; some are short and wide, othersare tall and slim, some are small, others are large. In this thesis a tank of 6 m in both diameter and heighthas been used to obtain numerical results of the stresses in the tank. Tanks are most often thin-walled withstepwise variable shell thickness with thicker wall sections at the bottom of the tank and thinner at the top.Since they are thin walled they are susceptible to buckling and there are conditions the shell construction mustmeet. The conditions that has to be met are determined by the laws and regulations that govern tank design.The National Board of Housing, Building and Planning (Boverket) is the new Swedish authority for rules oftank design and the Eurocodes are the new family of standards that should be followed. Sweco Industry ABis the outsourcer of this thesis and wants to clarify what rules that apply now when the Eurocodes are to befollowed. The thesis project has produced a calculation document in Mathcad for tank shell design accordingto the Eurocodes with stress calculations according to membrane theory and linear elastic shell analysis. Thisthesis has also produced a comparison of stresses calculated using membrane theory, linear elastic shell analysisand finite element method (FEM). The comparison has been made for numerical results given for an arbitrarilydesigned tank wall.The loads acting on the tank included in the description were self-weight, internal and hydrostatic pressureas well as wind and snow loads. The loads were described in accordance with the Eurocodes. Some assumptionshad to be made where the standard was vague or deficient in order to make calculations by hand possible. Forexample, the wind load had to be described as an axisymmetrically distributed load rather than an angularlyvarying. The stresses in the tank wall were calculated through creating free-body diagrams and declaringequations for force and moment equilibrium. The loads and boundary conditions were set in a correspondingmanner in the FEM software Ansys as in the calculation document in order to obtain comparable results. Whencompared, the stress results calculated with membrane theory and FEM were quite similar while the stressescalculated with linear analysis were a lot larger. The bending moments were assumed to be too large whichmake the results of the linear analysis dominated by the moments. The arbitrarily dimensions set for the tankdid thus not fulfill the conditions when linear analysis was used but did so for membrane theory and FE-analysis.Since the results calculated with membrane theory were very close to FEM in most cases, even withoutexpressions for local buckling, it was assumed to be an adequate method in this application. Expressions forlocal buckling are although needed for the meridional normal stress. The conclusions of the results obtained arethat membrane theory is a simple and adequate method in most cases. Linear analysis thus becomes redundantsince it is more complicated and more easily leads to faulty results. Furthermore it cannot be used for higherconsequence classes than membrane theory. FEM, with a computer software such as Ansys, is although themost usable calculation method since it can conduct more complicated calculations and is allowed to be usedfor all consequence classes.Keywords: Tank, Eurocode, Membrane theory, Linear elastic shell analysis, Finite element methodi
SammanfattningCisterner är behållare för lagring av vätska. De kan se ut på olika sätt; vissa är korta och breda, andra ärhöga och smala, vissa är små, andra är stora. I detta arbete har en cistern med 6 m i både diameter och höjdanvänts för att erhålla numeriska resultat av spänningarna i cisternen. Oftast är cisterner tunnväggiga medstegvis variabel manteltjocklek där väggen är tjockare nertill än upptill. Eftersom att de är tunnväggiga är deockså benägna att buckla, vilket det finns villkor som skalkonstruktioner ska uppfylla för att undvika. Vilkavillkor som ska uppfyllas bestäms av de lagar, regler och förordningar som finns för cisterner. Boverket är dennya myndigheten som skriver de förordningar som cisterndesign ska följa. Eurokoderna är den nya samling avstandarder som ska följas. Sweco Industry AB är uppdragsgivare till uppsatsen och vill reda ut vad som gälleri och med att Eurokoderna nu ska följas. Uppsatsen har tagit fram ett beräkningsdokument i Mathcad för cisternväggsdesign enligt Eurokoderna med spänningsberäkning enligt membranteori och linjärelastisk skalanalys.Uppsatsen har även framfört en jämförelse mellan spänningarna beräknade av membranteori, linjäranalys ochfinita elementmetoden (FEM). Jämförelsen har gjorts för numeriska resultat givna för en godtyckligt dimensionerad cisternvägg.Lasterna på cisternen som togs fram var egenvikt, inre tryck och hydrostatiskt tryck samt vind- och snölast.Lasterna togs fram i enlighet med Eurokoderna. En del antaganden fick göras där standarden var otydlig ellerför att göra handberäkning möjlig, bland annat att beskriva vindlasten som en jämnt fördelad last istället förangulärt varierande. Spänningarna i cisternväggen beräknades sedan genom friläggning och uppställning avkraft- och momentjämvikt. Laster och gränstillstånd bestämdes på liknande sätt i FEM-programmet Ansyssom i beräkningsdokumentet för att få jämförbara resultat. Vid jämförelse av resultatet var resultaten frånmembranteori och FEM ganska lika medan linjäranalys var mycket större. Momenten antogs vara alldeles förstora vilket gör att resultaten från linjäranalys dominerades av momenten. Den godtyckligt dimensioneradecisternen uppfyllde därför inte villkoren när linjäranalys användes medan den uppfyllde villkoren med råge förmembranteori och FE-analys.Eftersom membranteori i de flesta fall var mycket nära FEM, även utan uttryck för lokal buckling, antogs detdärför vara en tillräckligt bra metod i denna tillämpning. Det behövs dock förenklade uttryck för lokal bucklingför normalspänningen i generatrisled. Slutsatsen av de resultat som erhölls är att membranteori är enkelt attanvända och ger tillräckligt bra resultat i de flesta fall. Linjäranalys blir därför överflödig eftersom den är merkomplicerad och orsakar därför lättare fel, dessutom kan den inte tillämpas vid högre konsekvensklasser änmembranteori. FEM, med datorprogram som Ansys, är dock den mest användningsbara beräkningsmetodeneftersom att den kan utföra mer komplicerade beräkningar och får användas för alla konsekvensklasser.Nyckelord: Cistern, Eurokod, Membranteori, Linjärelastisk skalanalys, Finita elementmetodeniii
ContentsList of FiguresviList of TablesviiNomenclatureviii1 Introduction1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2 Eurocodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.3 Purpose, goal and method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11242 Theory2.1 Membrane theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.2 Linear elastic shell analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.3 Finite element analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55563 Method3.1 Actions . . . . . . . . . . . . . . . . . . . . .3.1.1 Self-weight . . . . . . . . . . . . . . .3.1.2 Internal and hydrostatic pressure . . .3.1.3 Wind load . . . . . . . . . . . . . . . .3.1.4 Snow load . . . . . . . . . . . . . . . .3.2 Limit states . . . . . . . . . . . . . . . . . . .3.2.1 Plastic limit condition . . . . . . . . .3.2.2 Buckling conditions . . . . . . . . . .3.3 Free body diagrams and force equilibrium . .3.4 Stresses calculated by membrane theory . . .3.5 Stresses calculated by linear analysis . . . . .3.6 Simulation with finite element method (FEM).78891011121212141818194 Results244.1 Membrane theory and linear analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.2 Finite element analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.3 Summary and comparison of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 Discussion5.1 Limitations of this thesis project . . . .5.2 Loads and assumptions . . . . . . . . .5.3 Comparison of obtained results . . . . .5.4 Comparison against the plastic limit and. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .buckling limit conditions.30303030316 Conclusions337 Acknowledgement348 References35AppendicesA1A Geometry of conical roofA1B The calculation documentB1v
List of 27282930313233343536373839404142A slim tank [5]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Cross section view of tank [6]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The inside of a large tank [7]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The outside of a large tank [7]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Membrane stresses and bending moments in a shell. . . . . . . . . . . . . . . . . . . . . . . . . .Transverse shear stresses in a shell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Sectioning of a model into finite elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Principial element of finite element method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The numerical dimensions of the tank used. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Numerical values of the stepwise variable shell thickness. . . . . . . . . . . . . . . . . . . . . . . .The internal pressure distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The hydrostatic pressure distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The wind distribution around a cylinder [24]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Wind distribution used. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The wind load distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The snow load distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Transformation of stepwise variable thickness to equivalent uniform thickness. . . . . . . . . . . .Actions on shell wall, seen in xr-plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Actions on the roof. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Sectioning of shell, seen in xr-plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Meridional stress resultant. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Meridional bending moment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Sectioning of shell, seen in xθ-plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Circumferential stress resultant. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Circumferential bending moment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The solid model of the tank. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Close-up on solid model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Close-up on shell model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Bonded edge contact between sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Symmetry condition limiting displacement in circumferential direction. . . . . . . . . . . . . . . .Symmetry condition limiting rotation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Boundary condition at the top. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Boundary condition at the bottom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The mesh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Close-up on the mesh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Self-weight. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Load from roof. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Hydrostatic pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Internal pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Wind action. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Meridional path. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Diagram of the circumferential design stress for the effective cylinder calculated with membranetheory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43 Diagram of the shear design stress for the effective cylinder calculated with membrane theory. . .44 Diagram of the circumferential design stress for the effective cylinder calculated with linear analysis.45 Diagram of the shear design stress for the effective cylinder calculated with linear analysis. . . .46 Equivalent von Mises stress result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47 Equivalent von Mises stress result with exaggerated deformation. . . . . . . . . . . . . . . . . . .48 Deformation of static structural analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49 Diagram of the equivalent stress. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50 Meridional design stress. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51 Diagram of meridional design stress. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52 Circumferential design stress for effective cylinder. . . . . . . . . . . . . . . . . . . . . . . . . . .53 Diagram of circumferential design stress in effective cylinder. . . . . . . . . . . . . . . . . . . . .54 Shear design stress in effective cylinder. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55 Diagram of shear design stress in effective cylinder. . . . . . . . . . . . . . . . . . . . . . . . . . .A.1 Geometry of a conically shaped roof for a tank. . . . . . . . . . . . . . . . . . . . . . . . . . . . .A.2 Diameter and height of insulation on a conically shaped roof . . . . . . . . . . . . . . . . . . . 8A1A1
List of Tables12345678910The family of Eurocodes . . . . . . . . . . . . . . . . . . . . . . . . . . . .The relevant standards for tank shell design . . . . . . . . . . . . . . . . .Thicknesses of roof, insulation and weather protection cover . . . . . . . .Material properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The density of the steels and insulation . . . . . . . . . . . . . . . . . . .Comparison of equivalent stresses for the three calculation methods . . . .Comparison of stresses for the three calculation methods . . . . . . . . . .Comparison of equivalent stresses and meridional stresses with conditionsComparison of stresses for effective cylinder with buckling conditions . . .Comparison of circumferential and shear stresses with buckling conditionsvii.337782929323232
NomenclatureFactors and other symbolslbLength of section b of the tank walllcLength of section c of the tank wallle f fEffective lengthljLength of section j of the tank wallsroofLine of the roof of which the lineloadsare appliedtaThickness of section a of the tankwalltbThickness of section b of the tankwallγFPartial factor for variable loads(safety factor)γGPartial factor for permanent loads(safety factor)γM 0Partial factor for resistance to plasticity (safety factor)γM 1Partial factor for resistance to buckling (safety factor)µiSnow load shape coefficientψhydCombination factor for hydrostaticloadtcThickness of section c of the tankwallψintCombination factor for internal pressuretjThickness of section j of the tank wallψsnowCombination factor for snow loadtaveAverage thickness of the tank wallψwindCombination factor for wind actiontcover,roofThickness of the weather protectionon the roofξweightReduction factor for self-weighttcover,shellCeExposure coefficientThickness of the weather protectionaround the shellCtThermal coefficienttins,roofThickness of the insulation on theroofcpe,roofPressure coefficient for external windpressure acting on the rooftins,shellThickness of the insulation aroundthe wallcpePressure coefficient for external windpressuretroofThickness of the roof plategGravitational accelerationVshellVolume of the steel plates of the shellqpPeak velocity pressurezHeight above the groundskCharacteristic value of snow load ongroundzeReference height for the externalwind acting on the tank wallze,roofReference height for the externalwind acting on the roofGeometrical dimensionsαroofAngle of the sloped roofAcover,roofSurface area of the weather protection on the roofAins,roofSurface area of the insulation on theroofFweight,roof,Ed Design value of force per unit widthoriginating from the total weightof the roof including insulation andweather protectionAroofSurface area of the roof plateFweight,roofDDiameter of the tankDoutOuter diameter of the tank including insulation and weather protection coverhHeight of the roofFweight,shell,Ed Design value of force per unit widthoriginating from the total weight ofthe shell including insulation andweather protection.H0Height of the tank wallFweight,shelllaLength of section a of the tank wallLoadsviiiForce per unit width originating fromthe total weight of the roof includinginsulation and weather protectionForce per unit width originating fromthe total weight of the shell includinginsulation and weather protection
PInternal and hydrostatic pressurecombinedρliquid,EdDesign value of the density of the liquidpHydrostatic pressureEpiInternal pressureStiffness of tank steel, Young’s moduluspEdDesign value of the hydrostatic pressurefyYield strength of tank steelfy kCharacteristic yield strength of tanksteelpi,EdDesign value of the internal pressuressnow,EdDesign value of the snow loadssnowSnow loadTbase,rStressesσθ,Ed,ef fCircumferential design stress for effective cylinderReaction force from the ground in radial directionσθ,EdjCircumferential design stres
tank design and the Eurocodes are the new family of standards that should be followed. Sweco Industry AB is the outsourcer of this thesis and wants to clarify what rules that apply now when the Eurocodes are to be followed. The thesis project has produced a calculation document in Mathcad for tank shell design according
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3- Differential surge tank: an orifice tank having a riser is called differential tank. 4- One- way surge tank: in a one way surge tank the liquid flows from the tank into the pipeline only when the pressure in the pipeline drops below the liquid level in the surge tank. 5- Closed surge tank: if the top of the tank is closed and there is
Shell TelluS S2 V 15 15 3.8 160 –42 871 Shell TelluS S2 V 22 22 4.8 190 –39 872 Shell TelluS S2 V 32 32 6.4 170 –42 872 Shell TelluS S2 V 46 46 8.2 210 –39 872 Shell TelluS S2 V 68 68 10.9 230 –36 877 Shell TelluS S2 V 100 100 14.7 176 –30 889 Shell TelluS S3 M 46 46 6.8 220 –33 865 Shell TelluS S4 Vx 32 33.8 9.93 100 –60 866
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prevent tank uplifting, the following are minimum requirements for different types of common tank supports and surfaces upon which the tank shall be placed. Tank Supports – Tank supports shall be either (a) types that are included under the tank Listing (steel saddles welded to tank), or (b) 1.25" diameter
