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

Dr. Mukti L. Das

Seattle, WashingtonNovember 13-16, 2012

Dynamic Analysis of Nuclear Containments Using Shear

Deformation Shell

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”.

Kirchhoff – Love Classical Shell Theory

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

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

Software Used

Kirchhoff – Love: GT STRUDL (SBHQ6)

Mindlin – Reissner: GT STRUDL (SBMITC, IPSQQ); ANSYS (SHELL43), STAAD (SHELL)

Experiment with a 20′X20′ Fixed-Fixed Plate

Deflection at Plate Center

E= 3,605.0 ksi

Poisson= 0.3

Uniform load = 1.0 ksf

Experiment with a 20′X20′ Fixed-Fixed Plate (cont’d)

Moment at Plate Center

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.

Experiment with a Benchmark Reference Cylinder (Cont’d)

Diameter = 4 m

Height = 8 m

Internal Pressure = 1.0 Kg/cm2

E = 2.1 x 105 Kg/cm2

= 0.2

The reference used a cylinder with the following data to demonstrate the theory that was developed in the reference.


Fixed End Moment


Fixed End Moment

Experiment with a Containment

Major Design Parameters for Typical Nuclear Plants

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

Typical Power Plant Model in 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)

Experiment with a Containment (Cont’d)A Typical Containment Model for this Study

Experiment with a Containment (Cont’d)Experiment with a Containment (Cont’d)

Patch Load on the Base Mat

Patch Load:1379.46 kN/m² on21.34m X 21.34m

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

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

Load

X

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

X


Deformed Shaped due to Accidental Internal Pressure


Mid Point Deflection of Base Mat due to Accidental Internal Pressure

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

Accidental Internal Pressure

X


Moment about X-Axis at Elv 6.47 m due to Accidental Pressure

X


Moments about X-Axis at Elv 30.1 m And 52.55 m due to Accidental Pressure

X


Moment at Elev. 63.17m Due to Accidental Internal Pressure

X


Moment about Y-Axis at Location “A” on Base Mat due to Wind Load

Wind Direction

Location A

Y

Eigenvalue Analysis of 10′ Diameter Eigenvalue Analysis of 10′ Diameter Steel Plate With Fixed EdgeSteel Plate With Fixed Edge

Eigenvalue Analysis of 10′ Diameter Eigenvalue Analysis of 10′ Diameter Steel Plate With Fixed EdgeSteel Plate With Fixed Edge

Eigenvalue Analysis of ContainmentEigenvalue Analysis of ContainmentWith Fixed BaseWith Fixed Base

Dome: 1.0 mCylinder: 1.5 mMat Slab: 4.0 m




SBHQ6: 4.3 HzSBMITC: 4.3 HzSTAAD: 4.3 Hz

SBHQ6: 4.8 HzSBMITC: 4.8 HzSTAAD: 4.8 Hz

SBHQ6: 4.8 HzSBMITC: 4.8 Hz STAAD: 4.8 Hz

SBHQ6: 4.3 HzSBMITC: 4.3 HzSTAAD: 4.3 HZ

First Mode Mass Participation

SBHQ6: 66.1 %SBMITS: 60.7 %STAAD: 65.5 %

SBHQ6: 71.2 %SBMITC: 62.5 %STAAD: 69.4 %



First Mode Frequency

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