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Dr. Mukti L. Das Seattle, Washington November 13-16, 2012

Dynamic Analysis of Nuclear Containments Using Shear Deformation Shell. Dr. Mukti L. Das Seattle, Washington November 13-16, 2012. Plates And Shell Theories.

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Dr. Mukti L. Das Seattle, Washington November 13-16, 2012

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  1. Dynamic Analysis of Nuclear Containments Using Shear Deformation Shell Dr. Mukti L. Das Seattle, Washington November 13-16, 2012

  2. Plates And Shell Theories To idealize a structure as a mathematical model, there is a need for a structural element that has a small third dimension compared to other two dimensions. This idealization resulted to various plates/shell theories that approximate equations of three dimensional quantum mechanics. Two commonly used theories are, a) Kirchhoff-Love theory and b) Mindlin - Reissner theory In this presentation, all plates/shell theory will be referred as “Shell Theory”.

  3. This theory is an extension of Euler – Bernoulli beam theory. The following assumptions are made in this theory: • Straight lines initially normal to the mid-surface remain straight and normal after deformation • Thickness of shell remain unchanged during the deformation process Kirchhoff – Love Classical Shell Theory

  4. Mindlin – Reissner Moderately Thick Shell Theory This theory is based on following assumptions: Straight lines initially normal to the mid-surface remain straight but may not remain normal after deformation Thickness of shell remain unchanged during the deformation process

  5. Software Used Kirchhoff – Love: GT STRUDL (SBHQ6) Mindlin – Reissner: GT STRUDL (SBMITC, IPSQQ); ANSYS (SHELL43), STAAD (SHELL)

  6. Experiment with a 20′X20′ Fixed-Fixed PlateDeflection at Plate Center E= 3,605.0 ksi Poisson= 0.3 Uniform load = 1.0 ksf

  7. Experiment with a 20′X20′ Fixed-Fixed Plate (cont’d)Moment at Plate Center

  8. Experiment with a Benchmark Reference Cylinder The article, “Consideration of Shear Deformation in the Analysis of Unsymmetrical Bending of Moderately Thick Shell of Revolution” published in the Transaction of 3rd SMiRT Conference, September 1975, is adopted as an experimental benchmark.

  9. Experiment with a Benchmark Reference Cylinder (Cont’d) The reference used a cylinder with the following data to demonstrate the theory that was developed in the reference. Diameter = 4 m Height = 8 m Internal Pressure = 1.0 Kg/cm2 E = 2.1 x 105 Kg/cm2n= 0.2

  10. Experiment with a Benchmark Reference Cylinder (Cont’d)Fixed End Moment

  11. Experiment with a Benchmark Reference Cylinder (Cont’d)Fixed End Moment

  12. Experiment with a ContainmentMajor Design Parameters for Typical Nuclear Plants Typical Power Plant Model in Study Diameter of Cylinder = 100′– 130′ 147′ Thickness of Cylinder = 3′ 6″ – 3′ 9″ 3′ 9″ Thickness of Dome = 2′ 6″ – 3′ 6″ 3′ 3″ Thickness of Slab = 8′ 6″ – 10′ 6″ 3′ 3″ to 26′ 3″ Height of Cylinder = 100 ′ – 169′ 137′ 6″ Soil Class = Sand – Hard rock Loose sand ( Ks=48 k/ft3 ) Accidental Pressure = 60 psi – 200 psi 143 psi

  13. Experiment with a Containment (Cont’d) A Typical Containment Model for this Study Geometry: Slab Diameter =48.25 mCylinder Diameter =45.25 mCylinder Height =39.40m Total Height =59.00 mCylinder Thickness = 1.2 m (Constant)Dome Thickness =1.0 m (Constant)Base Mat Thickness = 1m, 2m, 4m, 8m & 12m (One Particular Thickness at a time) Support:Soil Supported, Modeled as Winkler Spring Loading:1) Self Weight2) Patch Load On Base Mat: 1379.46 kN/m2 (21.3mx21.3m)3) Accidental Internal Pressure: 1000 kN/m2 4) Wind Load of 7 kN/m2 (141 km/h)

  14. Experiment with a Containment (Cont’d)Patch Load on the Base Mat Patch Load: 1379.46 kN/m² on 21.34m X 21.34m

  15. Experiment with a Containment (Cont’d)Mid Point Deflection of Base Mat due to Patch Load

  16. Experiment with a Containment (Cont’d)Moment About X-Axis on a Mid Point Element of Base Mat due to Patch Load X

  17. Experiment with a Containment (Cont’d)Moment about X-Axis at Elv 6.47 m due to Patch Load X

  18. Experiment with a Containment (Cont’d)Deformed Shaped due to Accidental Internal Pressure

  19. Experiment with a Containment (Cont’d)Mid Point Deflection of Base Mat due to Accidental Internal Pressure

  20. Experiment with a Containment (Cont’d)Moment About X-Axis on a Mid Point Element of Base Mat due to Accidental Internal Pressure X

  21. Experiment with a Containment (Cont’d)Moment about X-Axis at Elv 6.47 m due to Accidental Pressure X

  22. Experiment with a Containment (Cont’d)Moments about X-Axis at Elv 30.1 m And 52.55 m due to Accidental Pressure X

  23. Experiment with a Containment (Cont’d)Moment at Elev. 63.17m Due to Accidental Internal Pressure X

  24. Experiment with a Containment (Cont’d)Moment about Y-Axis at Location “A” on Base Mat due to Wind Load Wind Direction Y Location A

  25. Eigenvalue Analysis of 10′ Diameter Steel Plate With Fixed Edge

  26. Eigenvalue Analysis of 10′ Diameter Steel Plate With Fixed Edge

  27. Eigenvalue Analysis of ContainmentWith Fixed Base First Mode Frequency First Mode Mass Participation SBHQ6: 4.8 Hz SBMITC: 4.8 Hz STAAD: 4.8 Hz Dome: 1.0 m Cylinder: 1.5 m Mat Slab: 4.0 m SBHQ6: 66.1 % SBMITS: 60.7 % STAAD: 65.5 % SBHQ6: 71.2 % SBMITC: 62.5 % STAAD: 69.4 % SBHQ6: 70.7 % SBMITC: 61.4 % STAAD: 69.4 % SBHQ6: 66.1 % SBMITC: 60.7 % STAAD: 65.5 % Dome: 2.0 m Cylinder: 2.0 m Mat Slab: 4.0 m SBHQ6: 4.3 Hz SBMITC: 4.3 Hz STAAD: 4.3 HZ Dome: 4.0 m Cylinder: 4.0 m Mat Slab: 4.0 m SBHQ6: 4.3 Hz SBMITC: 4.3 Hz STAAD: 4.3 Hz SBHQ6: 4.8 Hz SBMITC: 4.8 Hz STAAD: 4.8 Hz Dome: 1.00 m Cylinder: 1.50 m Mat Slab: 12.0 m

  28. Thank You!

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