FH-AnhaltMasterProgramMembraneStructures

MandatoryModuleCM05

SemesterTaskWS2017/2018

StructuralAnalysesReport

Prepared by: Thomas Dührsen

SID: 4065604

March 2018

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1. Basics.................................................................................................................................32. Generalinformation..........................................................................................................32.1. Basicdata..................................................................................................................32.2. Membrane.................................................................................................................32.3. Cables........................................................................................................................4

3. Projectdescription............................................................................................................43.1. Membranesytem......................................................................................................43.2. Computersoftware...................................................................................................43.3. Units..........................................................................................................................43.4. Coordinates...............................................................................................................43.5. Codes.........................................................................................................................4

4. Geometry..........................................................................................................................54.1. Groundplanview......................................................................................................54.2. Sideelevations..........................................................................................................64.3. Isometricviews..........................................................................................................64.4. Details........................................................................................................................7

5. Loadassumptions............................................................................................................105.1. Generalnotes..........................................................................................................105.2. Selfweights/deadloads.........................................................................................105.3. Pre-stress(membrane)............................................................................................105.4. Pre-Stress(cables)...................................................................................................105.5. Snowloads..............................................................................................................105.6. Windloads...............................................................................................................11

6. Resistance(material)side–membrane..........................................................................146.1. Materialproperties.................................................................................................146.2. Reductionfactorsonresistanceside–membranematerial...................................146.3. Membraneallowablestresses.................................................................................15

7. Membraneloads/loadcases–Overview......................................................................157.1. Loadcombinations..................................................................................................15

8. Analysesofmaximalmembranestresses.......................................................................168.1. ServiceabilityLimitState(SLS).................................................................................168.2. Stress-Verifications(Sd<=Rd).................................................................................168.3. UltimateLimitState(ULS).......................................................................................17

9. Analysesofmaximaldeflections.....................................................................................189.1. ServiceabilityLimitState(SLS)(Sd<=Rd)...............................................................18

10. Waterpondinginvestigation.......................................................................................1911. Steelwork(mastsandcables)......................................................................................2011.1. Analysisofaxialstress.........................................................................................2011.2. Masts...................................................................................................................2111.3. Cables..................................................................................................................21

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1. Basics The report in hands comprises the structural analyses of the membrane structure for the above-mentioned project. It consists of the following topics:

• descriptionofthestructuralsystem• overviewdrawingswithdimensions• loadassumptionsaccordingtoEurocodesEN1090/EN1991etseq.• structuralanalysesofthemembrane• structuralanalysesofallcables• structuralanalysesofthemastwiththehigheststresses

2. Generalinformation 2.1. BasicdataLocation(country,city,street,no.) Germany,StadtparkDessau

Coveredarea(groundplanprojection) 28.4m²

Materialsofprimarystructure(steelstructure) HighstrengthsteelgradeS355

Utilizationofthemembraneconstruction Shadingcanopyincitypark

Absolutealtitudeabovesealevel 63m

Hightofeavesabovetheground 2.36m

Hightofridge/vertexabovetheground 6.1m

Pitchoftheroof(min) 0°(saddlepoint)

Pitchoftheroof(max) 31.5° 2.2. Membrane

Numberoflayers 1layer

Membranematerial ValmexFR700Mehatop

Furtherusedmembranematerials -

FireClassification CLASSBs2d0

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2.3. CablesCable-types Edge, guy and stay cables

Cable-materials Unalloyedqualitysteel

Cable-products Pfeifer PG Open Spiral Strand - GALFAN

Cable-amounts4edgecables4staycables2guycables

Cable-diameters 10.1mmforallcables

Cable-fittingsPG980openswagedfittingPG984turnbucklewithopensocketPG988swagedfittingwiththread

3. Projectdescription 3.1. MembranesytemImportant notes: - 3.2. Computersoftware

Membrane RhinoGrasshopperTensArcLibrary(ownimplementation) ixCube4.10Steel-Structureoverall ixCube4.10SteelMembers MicrosoftExcelAnchors HiltiPROFISAnchor2.7.5CAD Rhino3DV5,RhinoGrasshopper3D-Visualization Rhino3DV5Renderer

3.3. Units

forces [kN]forcespermeter [kN/m]stress [N/mm²]dimensions [m]

3.4. Coordinates All coordinates depend on the global system of coordinates “X”, “Y” and “Z”. If local coordinates are given, than as small letters: “x”, “y” and “z”. The „right-hand“ rule has been applied. 3.5. Codes

• BS_EN_1991-1-1_2002:Actionsonstructures–ImposedLoads• BS_EN_1991-1-3_2003:Actionsonstructures–Snowloads• BS_EN_1991-1-4_2005:Actionsonstructures–Windactions• BS_EN_1993-1-8_2005: Design of steel structures – Joints

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4. Geometry 4.1. Groundplanview

Figure 1: Plan View

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4.2. Sideelevations

Figure 2: Front View

Figure 3: Side View 4.3. Isometricviews

Figure 4: 3D View

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4.4. Details

Figure 5: Location of details 4.4.1. Detail1–masthead

Figure 6: Detail 1

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Detail2–mastfoot

Figure 7: Detail 2 4.4.2. Detail3–staycablesgroundconnectorstype1

Figure 8: Detail 3

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4.4.3. Detail4–staycablesgroundconnectorstype2

Figure 9: Detail 4 4.4.4. Detail5–membranecornerdetailUniversal cornerplate suitable for different membrane corner angles.

Figure 10: Detail 5

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5. Loadassumptions 5.1. GeneralnotesApplied codes:

• Eurocode1-EN1991-1-1:2002:Actionsonstructures–Part1-1:Generalactions–Densities,selfweight,imposedloadsforbuildings

• Tensinet-EuropeanDesignGuideforTensileSurfaceStructures

5.2. Selfweights/deadloadsMembrane: Valmex FR 700 Mehatop weighing 0.830 kg/m2 Steel: High-strength steel weighing 7850 kg/m3 Own weights are automatically calculated by the analysis program. 5.3. Pre-stress(membrane)Prestress warp: 1.0 kN/m Prestress weft: 1.0 kN/m 5.4. Pre-Stress(cables)Prestress for membrane Edge cables: 6.0 kN/m

Figure 11: Cable and mast pre-stress values 5.5. SnowloadsApplied codes:

• Eurocode1-EN1991-1-3:2003:Actionsonstructures–Part1-3:Generalactions–Snowloads

• Eurocode1–NationalAppendixforGermany

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Figure 22: Snow map of Germany with location of Dessau marked

Figure 13: snow load coefficients 𝑠" = 𝜇"×𝑠' à Range for 𝑠" = 0.68 to 1.02 kN/m2 5.6. WindloadsApplied Codes:

• Eurocode1-EN1991-1-4:2005:Actionsonstructures–Part1-4:Generalactions–Windactions

• Eurocode1–NationalAppendixforGermany

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Figure 14: Map of basic Windspeed and terrain category, Eurocode 1 – National Appendix for Germany

Location/County Dessau,Germany

10minutemeanvelocityat10maboveground 𝑣),+ = 25

𝑚𝑠

directionalfactor 0.1=dirc

seasonalfactor 0.1=seasonc

basicwindvelocity 𝑣) = 𝑐0"1×𝑐234256×𝑣),+ = 25𝑚𝑠

Terraincategory 3

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Referencepressureqref 0.39kN/m2

BuildingheightZ 6.0m

Windpressureqz qz=1.5xqref=0.59kN/m2

5.6.1. windloadcoefficients

Figure 15: Values of external pressure coefficients cp for hypars according to the European Design Guide

for Tensile Surface Structures - Tensinet The cp values listed above apply to a closed sided structure with a shape ratio of 4.7. The structure to analyze has a ratio of 10 / (6.1 – 2.2) = 2.56 The structure to analyze has open sides. à Since the applicable codes do not provide any values for the structure under analysis, the roof area of 28m2 is rather small and wind tunnel testing is too expensive, a simplified approach is considered: A cp value of -0.7 (suction) for the main wind direction is applied to the whole membrane area. A cp value of -0.7 compares well to the value of -0.65 for the largest sections C and K of the table above.

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6. Resistance(material)side–membrane 6.1. Materialproperties

Figure 16: Physical properties of the membrane material, Low & Bonar 6.2. Reductionfactorsonresistanceside–membranematerial Factor Description Value 0A biaxial exposure on site / uniaxial tested material properties 1.2

1A long term / permanent exposure 1.5

2A environmental conditions (e.g. UV radiation) 1.2

3A high temperature conditions 1.4

4A inaccuracy in fabrication 1.0

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6.3. Membraneallowablestresses For permanent loads, Resistance = 3000/50/6.3 = 9.5 kN/m in both directions For all other cases, Resistance = 3000/50/4.5 = 13.3 kN/m in both directions

7. Membraneloads/loadcases–Overview Loads and load cases (according to EN 1990): g = self-weight v0 = pre-stress / pre-tension w = wind loads - acting downwards (pressure) and/or upwards (uplift) s = snow load 7.1. Loadcombinations SLS_01:1.0g+1.0vSLS_02:1.0g+1.0v+1.0wSLS_03:1.0g+1.0v+1.0sSLS_04:1.0g+1.0v+1.0w+1.0sULS_01:1.35g+1.35vULS_02:1.35g+1.35v+1.50w(uplift)ULS_03:1.35g+1.35v+1.50sULS_04:1.35g+1.35v+1.50s+(0.6*0.9)w(downwards)

Figure 17: Load case combinations

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8. Analysesofmaximalmembranestresses 8.1. ServiceabilityLimitState(SLS)

Figure 18: SLS max stress warp direction

Figure 19: SLS max stress weft direction 8.2. Stress-Verifications(Sd<=Rd) As shown in the above figures, the maximum stresses (6.9 kN/m) are less than the minimum allowable (9.5 kN/m) → S < R

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8.3. UltimateLimitState(ULS)

Figure 20: ULS max stress warp direction

Figure 21: ULS max stress weft direction

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9. Analysesofmaximaldeflections

Figure 22: SLS max deflection Z-axis 9.1. ServiceabilityLimitState(SLS)(Sd<=Rd) The maximal deflection should be approx. +/- L/20 with L = span width of the membrane [m] Span width (mast - mast): 10.3m Max deflection: 0.201m Allowable deformation: 10.3m / 20 = 0.515m à max deflection of 0.201m < 0.515m à ok

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10. Waterpondinginvestigation Shape: Hypar / saddle form with a shape ratio 2.56 (see above) Contour lines: no closed contour lines à Waterponding is not an issue.

Figure 23: Contour lines

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11. Steelwork(mastsandcables)11.1. Analysisofaxialstress

Figure 24: Max axial stress of masts and cables

Figure 25: Max axial stress of masts and cables

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11.2. Masts Steel of quality 355, circular hollow section, outer diameter 114.3mm, thickness 8mm.

Figure 26: Results of steel member check 11.3. Cables Cables are selected according to the recommendations of Pfeifer / technical brochure „Pfeifer Tension Members”. Cable fittings are selected to match the individual cables sizes accordingly. Position Count Max tension Size / Type (Pfeifer) Diameter Mast stay cables 4 x 41 kN PG 10 10.1 mm Membrane guy cables 2 x 46 kN PG 10 10.1 mm Membrane edge cables 4 x 41 kN PG10 10.1 mm

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Figure 27: Overview cable properties, Pfeifer technical brochure “Tension Members”