ML083120308
| ML083120308 | |
| Person / Time | |
|---|---|
| Site: | Browns Ferry  |
| Issue date: | 10/30/2008 |
| From: | Kok S Structural Integrity Associates |
| To: | Office of Nuclear Reactor Regulation |
| References | |
| TAC MD5262, TAC MD5263, TAC MD5264, TVA-BFN-TS-418, TVA-BFN-TS-431 0006982.304 | |
| Download: ML083120308 (105) | |
Text
ENCLOSURE 6 TENNESSEE VALLEY AUTHORITY BROWNS FERRY NUCLEAR PLANT (BFN)
UNITS 1, 2, AND 3 TECHNICAL SPECIFICATIONS (TS) CHANGES TS-431 AND TS-418 EXTENDED POWER UPRATE (EPU)
CALCULATION PACKAGE 0006982.304 Attached is Calculation Package 0006982.304, "Extended Power Uprate Main Steam Line Strain Gauge Vibration Monitoring."
Structural Integrity Associates, Inc.
File No.: 0006982.304 CALCULATION PACKAGE Project No.: 0006982.00 PROJECT NAME:
Extended Power Uprate Main Steam Line Strain Gauge Vibration Monitoring CONTRACT NO.:
CWA P4463 CLIENT:
PLANT: Browns Ferry Units 1, 2 & 3 Tennessee Valley Authority (TVA)
CALCULATION TITLE:
Comparison Study of Substructure and Submodel Analysis using ANSYS Document Affected Project Manager Preparer(s) &
Revision Pages Revision Description Approval Checker(s)
Signature & Date Signatures & Date 0
1-97, Initial Issue A I-A4, Computer Files K. K. Fujikawa 10/30/08 S. B. Kok 10/30/08 R. Gnagne 10/30/08 M. Qin 10/30/08 Page.1 of 97 F0306-01 RO
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Table of Contents
1.0 INTRODUCTION
8 1.1 B ackground Inform ation.................................................................................................
8 1.2 V alidation M ethodology................................................
8 1.3 N om enclature..............................................................................................................
9 2.0 STRUCTURE DESCRIPTION AND MATERIAL PROPERTIES.....................................
10 3.0 FINITE ELEMENT MODEL DEVELOPMENT......................................................................
11 3.1 Model Descriptions and Boundary Conditions.............................................................
12 3.1.1 F ull Shell M odel................................................................................................................
12 3.1.2 F ull Solid M odel................................................................................................................
13 3.1.3 Shell Subm odel #1..............................................................................................................
14 3.1.4 Solid Subm odel #1............................................................................................................
15 3.1.5 Shell Submodel #2......................................................
16 3.1.6 Solid Submodel #2 18 3.2 So l
em e l #2.............................................
F.........em t.................................................
20 3.3 Stress Paths M esh..............................................................
22 4.0 L O A D C A SE S..........................................................................................................................
24 4.1 Static A nalysis Load C ases................................................................................................
24 4.2 Dynamic Analysis Load Cases......................................
25 5.0 STATI C ANALYSIS L TS........................................
ST TI.AAL........................................
26 5.1 Static Load Case #1R....................................................................
........ 26 5.1.1 Full Shell Finite Element Analysis........................................................................
...... 26 5.1.2 Full Solid Finite Element Analysis...............................................................................
27 5.1.3 Substructure Analysis Using Shell Submodel #1...............................................................
29 5.1.4 Substructure Analysis Using Shell Submodel #2........................................................ 30 5.1.5 Substructure Analysis Using Solid Submodel #1.............................
31 5.1.6 Substructure Analysis Using Solid Submodel #2..........................................................
33 5.1.7 Submodel Analysis Using Submodel #1.........................................................................
35 5.1.8 Submodel Analysis Using Submodel #2.......................................................................
40 5.2 Static L oad C ase #2.......................................................................................
....... 45 5.2.1 Full Shell Finite Element Analysis............................................
45 5.2.2 Full Solid Finite Element Analysis...............................................................................
46 5.2.3 Substructure Analysis Using Shell Submodel #1.........................................................
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5.2.4 Substructure Analysis Using Shell Submodel #2..........................................................
49 5.2.5 Substructure Analysis Using Solid Submodel #1..........................................................
50 5.2.6 Substructure Analysis Using Solid Submodel #2..........................................................
52 5.2.7 Submodel Analysis Using Submodel #1.......................................................................
54 5.2.8 Submodel Analysis Using Submodel #2.......................................................................
59 6.0 DYNAM IC ANALYSIS RESULTS......................................................................................
64 6.1 Structural M odal Frequencies......................................................................................
64 6.2 Structural Damping Values..........................................................................................
65 6.3 Time History Analysis Integration Time Step..............................................................
65 6.4 Dynamic Load Case #1................................................................................................
66 6.4.1 Full Shell Finite Element Analysis...............................................................................
66 6.4.2 Substructure Analysis Using Shell Submodel #2..........................................................
70 6.4.3 Substructure Analysis Using Solid Submodel #2..........................................................
72 6.4.4 Submodel Analysis Using Submodel #2..........................................................................
74 6.5 Dynamic Load Case #2.................................................................................................
79 6.5.1 Full Shell Finite Element Analysis...............................................................................
79 6.5.2 Substructure Analysis Using Shell Submodel #2..........................................................
83 6.5.3 Substructure Analysis Using Solid Submodel #2..........................................................
85 6.5.4 Submodel Analysis Using Submodel #2.......................................................................
87 7.0 SUMM ARY STRESS REDUCTION FACTORS................................................................
92 7.1 Static Analysis SRF.....................................................................................................
92 7.2 Dynamic Analysis SRF.................................................................................................
93 8.0 D ISC U S SIO N S...........................................................................................................................
94 8.1 S tatic A naly sis...................................................................................................................
94 8.2 Dynamic Analysis..............................................................................................................
95
9.0 CONCLUSION
S........................................................................................................................
96
10.0 REFERENCES
97 Appendix A - Computer Files............................................................................................................
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Structural Integrity Associates, Inco List of Tables T able 2-1 K ey D im ensions..................................................................................................................
10 Table 5-1 Full Solid Model Baseline Analysis SRF for Static Load Case #1........................... 28 Table 5-2 Substructure Analysis (Submodel #1) SRF for Static Load Case #1....................
32 Table 5-3 Substructure Analysis (Submodel #2) SRF for Static Load Case #1........................ 34 Table 5-4 Submodel Analysis (Submodel #1) SRF for Static Load Case #1............................. 39 Table 5-5 Submodel Analysis (Submodel #2) SRF for Static Load Case #1.................................
44 Table 5-6 Full Solid Model Baseline Analysis SRF for Static Load Case #2................................
47 Table 5-7 Substructure Analysis (Submodel #1) SRF for Static Load Case #2.............................
51 Table 5-8 Substructure Analysis (Submodel #2) SRF for Static Load Case #2.............................
53 Table 5-9 Submodel Analysis (Submodel #1) SRF for Static Load Case #2................................
58 Table 5-10 Submodel Analysis (Submodel #2) SRF for Static Load Case #2...............................
63 Table 6-1 Structural Vertical (Y direction) Modal Frequencies......................................................
64 Table 6-2 Structural Horizontal (Z direction) Modal Frequencies................................................
64 Table 6-3 Substructure Dynamic Analysis (Submodel #2) SRF for Dynamic Load Case #1......
73 Table 6-4 Submodel Analysis (Submodel #2) SRF for Dynamic Load Case #1.................... 78 Table 6-5 Substructure Dynamic Analysis (Submodel #2) SRF for Dynamic Load Case #2........ 86 Table 6-6 Submodel Analysis (Submodel #2) SRF for Dynamic Load Case #2..........................91 Table 7-1 Summary SRF for Static Load Case #1..........................................................................
92 Table 7-2 Summary SRF for Static Load Case #2........................................................................
92 Table 7-3 Summary SRF for Dynamic Load Case #1................................
93 Table 7-4 Summary SRF for Dynamic Load Case #2..................................................................
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Structural Integrity Associates, Inc-List of Figures Figure 3-1 Full Shell M odel...........................................................................................................
12 Figure 3-2 Full Solid M odel............................................................................................................
13 Figure 3-3 Shell Subm odel #1.........................................................................................................
14 Figure 3-4 Solid Subm odel #1.........................................................................................................
15 Figure 3-5 Shell Subm odel #2.......................................................................................................
16 Figure 3-6 Solid Subm odel #2.......................................................................................................
18 Figure 3-7 Shell Finite Elem ent M odel M esh...............................................................................
20 Figure 3-8 Solid Finite Elem ent M odel M esh...............................................................................
21 Figure 3-9 Solid Finite Element Model Stress Paths (Side View)................................................
22 Figure 3-10 Solid Finite Element Model Stress Paths (Top View).................................................
23 Figure 5-1 Full Shell Model Stress Plot for Case #1 (Full Shell Model Baseline Analysis)......
26 Figure 5-2 Full Solid Model Analysis Stress Plot for Load Case #1 (Full Solid Model Baseline A n aly sis)..................................................................................................................................
2 7 Figure 5-3 Substructure Analysis using Shell Submodel #1 Stress Plot for Load Case #1............ 29 Figure 5-4 Substructure Analysis using Shell Submodel #2 Stress Plot for Load Case #1............ 30 Figure 5-5 Substructure Analysis using Solid Submodel #1 Stress Plot for Load Case #1............... 31 Figure 5-6 Substructure Analysis using Solid Submodel #2 Stress Plot for Load Case #1........... 33 Figure 5-7 Submodel Analysis using Submodel #1 Applied Displacements for Load Case #1......... 35 Figure 5-8 Submodel Analysis using Submodel #1 Stress Profile Comparison for Load Case #1.... 36 Figure 5-9 Submodel Analysis using Submodel #1 Shell Model Stress Plot for Load Case #1........ 37 Figure 5-10 Submodel Analysis using Submodel #1 Solid Model Stress Plot for Load Case #1...... 38 Figure 5-11 Submodel Analysis using Submodel #2 Applied Displacements for Load Case #1....... 40 Figure 5-12 Submodel Analysis using Submodel #2 Stress Profile Comparison for Load Case #1..41 Figure 5-13 Submodel Analysis using Submodel #2 Shell Model Stress Plot for Load Case #1...... 42 Figure 5-14 Submodel Analysis using Submodel #2 Solid Model Stress Plot for Load Case #1...... 43 Figure 5-15 Full Shell Model Stress Plot for Case #2 (Full Shell Model Baseline Analysis).....
45 Figure 5-16 Full Solid Model Analysis Stress Plot for Load Case #2 (Full Solid Model Baseline A n aly sis).................................................................................................................................
4 6 Figure 5-17 Substructure Analysis using Shell Submodel #1 Stress Plot for Load Case #2.......... 48 File No.: 0006982.304 Page 5 of 97 Revision: 0 F0306-O1RO
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Figure 5-18 Substructure Analysis using Shell Submodel #2 Stress Plot for Load Case #2.......... 49 Figure 5-19 Substructure Analysis using Solid Submodel #1 Stress Plot for Load Case #2......
50 Figure 5-20 Substructure Analysis using Solid Submodel #2 Stress Plot for Load Case #2......
52 Figure 5-21 Submodel Analysis using Submodel #1 Applied Loads for Load Case #2................ 54 Figure 5-22 Submodel Analysis using Submodel #1 Stress Profile Comparison for Load Case #2.. 55 Figure 5-23 Submodel Analysis using Submodel #1 Shell Model Stress Plot for Load Case #2...... 56 Figure 5-24 Submodel Analysis using Submodel #1 Solid Model Stress Plot for Load Case #2...... 57 Figure 5-25 Submodel Analysis using Submodel #2 Applied Loads for Load Case #2................ 59 Figure 5-26 Submodel Analysis using Submodel #2 Stress Profile Comparison for Load Case #2... 60 Figure 5-27 Submodel Analysis using Submodel #2 Shell Model Stress Plot for Load Case #2...... 61 Figure 5-28 Submodel Analysis using Submodel #2 Solid Model Stress Plot for Load Case #2....... 62 Figure 6-1 Full Shell Model Dynamic Analysis Vertical Transient Displacement for Load Case #1 66 Figure 6-2 Full Shell Model Dynamic Analysis Nodal Stress Intensity for Load Case #1............ 67 Figure 6-3 Full Shell Model Dynamic Analysis Vertical Displacement Plot for Load Case #1 (Full Shell M odel Baseline A nalysis)..........................................................................................
68 Figure 6-4 Full Shell Model Dynamic Analysis Maximum Stress Plot for Load Case #1 (Full Shell M odel B aseline A nalysis)...................................................................................................
69 Figure 6-5 Substructure Analysis using Shell Submodel #2 Vertical Displacement Plot for Load Case
- 1.............................................................................................................................................
7 0 Figure 6-6 Substructure Analysis using Shell Submodel #2 Stress Plot for Load Case #1............ 71 Figure 6-7 Substructure Analysis using Solid Submodel #2 Stress Plot for Load Case #1........... 72 Figure 6-8 Submodel Analysis using Submodel #2 Applied Displacements for Load Case #1......... 74 Figure 6-9 Submodel Analysis using Submodel #2 Stress Profile Comparison for Load Case #1..... 75 Figure 6-10 Submodel Analysis using Submodel #2 Shell Model Stress Plot for Load Case #1...... 76 Figure 6-11 Submodel Analysis using Submodel #2 Solid Model Stress Plot for Load Case #1...... 77 Figure 6-12 Full Shell Model Dynamic Analysis Horizontal Transient Displacement for Load Case
- 2.............................................................................................................................................
7 9 Figure 6-13 Full Shell Model Dynamic Analysis Nodal Stress Intensity for Load Case #2.......... 80 Figure 6-14 Full Shell Model Dynamic Analysis Horizontal Displacement Plot for Load Case #2 (Full Shell M odel Baseline Analysis)................................................................................
81 Figure 6-15 Full Shell Model Dynamic Analysis Maximum Stress Plot for Load Case #2 (Full Shell M odel B aseline A nalysis)...................................................................................................
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Figure 6-16 Substructure Analysis using Shell Submodel #2 Horizontal Displacement Plot for Load C a se # 2.....................................................................................................................................
8 3 Figure 6-17 Substructure Analysis using Shell Submodel #2 Stress Plot for Load Case #2.......... 84 Figure 6-18 Substructure Analysis using Solid Submodel #2 Stress Plot for Load Case #2......
85 Figure 6-19 Submodel Analysis using Submodel #2 Applied Horizontal Loads for Load Case #2... 87 Figure 6-20 Submodel Analysis using Submodel #2 Stress Profile Comparison for Load Case #2... 88 Figure 6-21 Submodel Analysis using Submodel #2 Shell Model Stress Plot for Load Case #2...... 89 Figure 6-22 Submodel Analysis using Submodel #2 Solid Model Stress Plot for Load Case #2...... 90 File No.: 0006982.304 Revision: 0 Page 7 of 97 F0306-01 RO
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1.0 INTRODUCTION
1.1 Background Information This calculation addresses United States Nuclear Regulatory Commission (NRC) request for additional information (RAI) # 199/156 (Reference 3) pertaining to Tennessee Valley Authority (TVA) Browns Ferry Units 1 and 2 extended power uprate (EPU) licensing application.
In the stress assessment of the Unit 1 steam dryer, TVA has employed submodel analysis approach to determine a stress reduction factor (SRF) and apply it to the shell analysis stress in the full shell model steam dryer analysis. NRC has noted that the submodel analysis approach is different from a typical substructure analysis approach, as employed in the general purpose finite element code such as ANSYS (References 4 & 5). This calculation validates the submodel analysis approach by specifically addressing the following issues:
- 1. An analysis of the problem using a typical substructure analysis approach.
- 2. An analysis of the problem applying the submodel analysis approach, by applying "loads" to match the stress intensity along a line common to the full shell model and the shell submodel.
- 3. An analysis of the problem applying the submodel analysis approach, by applying "displacements" to match the stress intensity along a line common to the full shell model and the shell submodel.
- 4. A comparison of the results obtained in (1) using the typical substructure analysis approach with those in (2) and (3) using the submodel analysis approach.
1.2 Validation Methodology The submodel analysis approach will be validated using two analysis options: (1) static analysis and (2) dynamic time history analysis. In both the static and dynamic time history analyses, the submodel analysis approach will be compared with the typical substructure analysis approach.
In addition to the requested comparison of the two approaches, the following additional analyses are performed to provide more benchmark comparison:
- Perform a static analysis using a full solid model, which models in the detailed weld configuration. This full solid model analysis provides the most accurate information, since this does not include any inherent assumption or approximation associated with substructure or submodel analysis techniques.
In the static analysis, two submodels are developed: one submodel is 1/2 the size of the full model, and the other is 3/4 the size of the full model. The two different sized models will provide some additional data for comparison, and establish if the size of the submodel influences the analysis results.
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1.3 Nomenclature The key terminology used in the calculation is defined as follows.
Submodel This refers to a subpart of the full model that has been developed for use in either the substructure analysis or the submodel analyses.
Substructure Analysis Substructure analysis refers to a typical analysis approach, as employed in the general purpose finite element codes such as ANSYS. In this approach, the displacements from the full model analysis are interpolated and mapped onto the nodes on the appropriate submodel boundaries. These nodal displacements along the boundaries and any loads applied to the local region determine the solution of the submodel.
Submodel Analysis In a submodel analysis, two submodels are created: one is based on shell elements and the other solid elements. The shell submodel is used to match the stress profile in the submodel with the corresponding stress profile of the full shell model. This matching of stress profile is an iterative process. This is performed by applying loads or displacements, typically along a line. When a close match of the stress profile is achieved, the established loads or displacements can then be applied to the corresponding solid submodel stress analysis. Appropriate boundary conditions are required to be applied to the submodel boundaries. A stress reduction factor (SRF) is calculated by comparing the solid submodel result to the corresponding full shell model result. The SRF is then applied to the appropriate stresses in the full model shell analysis.
Stress Reduction Factor (SRF)
This refers to the ratio of the maximum solid submodel linearized stress intensity and the maximum full shell model stress intensity, at the location of interest. Mathematically, SRF is defined as "Solid Submodel Maximum Linearized Pm + Pb Stress Intensity (along solid submodel stress paths) / Full Shell Model Maximum Pm + Pb Stress Intensity".
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2.0 STRUCTURE DESCRIPTION AND MATERIAL PROPERTIES Structure Description With reference to Figure 3-1, the structure used for this study consists of:
A 10" x 40" x 1/2" thick vertical plate.
A 6" x 12" x 1/4" thick horizontal plate.
The 1/4" horizontal plate is welded to the 1/2" vertical plate using double-sided 1/4" fillet weld. The fillet weld is wrapped around at both ends of the horizontal plate.
The vertical plate is restrained at the top and at the bottom. The vertical edges of the vertical plate are not restrained.
A-240, Type 304 stainless steel material properties at 550'F (Reference 1) are assumed for all components.
Table 2-1 Key Dimensions Thickness / Size Modeled Dimensions (in)
(in x in)
Vertical Plate 1/2" 10" (width) x 40" (height)
Horizontal Plate 1/4" 6" (width) x 12" (long)
Weld (1) 1/4" Along the entire connection.
Note: (1) The fillet weld is modeled in the solid finite element models, on both sides.
Material Properties Modulus of Elasticity Poisson's Ratio
=
25.55E6 psi (Reference 2)
=
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Structural Integrity Associates, Inco 3.0 FINITE ELEMENT MODEL DEVELOPMENT There are a total of 6 finite element models used in this study:
- 1. The full shell model (see Figure 3-1). This model is used to establish the Shell Baseline Analysis.
- 2. The full solid model (see Figure 3-2). This model is used to establish the Solid Baseline Analysis.
- 3. The shell submodel #1 (see Figure 3-3). This shell submodel is 1/2 the size of the full shell model. This model is used in the submodel analysis to match the stress intensity along the weld line.
- 4. The solid submodel #1 (see Figure 3-4). This solid submodel corresponds to the shell submodel as shown in Figure 3-3. This model is used to establish the stress reduction factor (SmF.
- 5. The shell submodel #2 (see Figure 3-5). This shell submodel is 3/4 the size of the full shell model. This model is used in the submodel analysis to match the stress intensity along the weld line.
- 6. The solid submodel #2 (see Figure 3-6). This solid submodel corresponds to the shell submodel as shown in Figure 3-5. This model is used to establish the stress reduction factor (SRF).
A typical finite element mesh of the shell model is shown in Figure 3-7, and a typical finite element mesh of the solid model is shown in Figure 3-8.
Detailed weld configurations are modeled in the solid finite element models. The top two edges of the vertical plates are fixed, and the two vertical edges are free, i.e. not restrained(see Figure 3-1).
The boundary conditions are identified for each of the finite element model in the figures.
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3.1 Model Descriptions and Boundary Conditions 3.1.1 Full Shell Model EdgeA A
2(r Edge B
EdgA'/
Figure 3-1 Full Shell Model Boundary Conditions Edge A:
Fixed Edge B:
Free (i.e., not restrained)
Edge C:
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Ed~K 3.1.2 Full Solid Model mf
- Edge B EdgeB iEdge C Figure 3-2 Full Solid Model Boundary Conditions Edge A
Fixed Edge B:
Free (i.e., not restrained)
Edge C:
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3.1.3 Shell Submodel #1
-AN-Edge B 94W Figure 3-3 Shell Submodel #1 Substructure Analysis Boundary Conditions Edge A:
Edge B:
Edge C:
Applied Displacements Free (i.e., not restrained)
Applied Displacements Submodel Analysis Boundary Conditions Static Load Cases #1 Edge A:
Fixed Edge B:
Free (i.e., not restrained)
Edge C:
Applied Displacements Static Load Case #2 Edge A:
Restrained in X & Z translations Edge B:
Free (i.e., not restrained)
Edge C:
Applied Load.
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3.1.4 Solid Submodel #1 AM Ec1WB EdC EdeA'
/Edge A,
L.W Figure 3-4 Solid Submodel #1 Substructure Analysis Boundary Conditions Edge A:
Edge B:
Edge C:
Applied Displacements Free (i.e., not restrained)
Applied Displacements Submodel Analysis Boundary Conditions Static Load Cases #1 Edge A:
Fixed Edge B:
Free (i.e., not restrained)
Edge C:
Applied Displacements Static Load Case #2 Edge A:
Restrained in X & Z translations Edge B:
Free (i.e., not restrained)
Edge C:
Applied Load.
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3.1.5 Shell Submodel #2 AN jEdge C 15*
Figure 3-5 Shell Submodel #2 Substructure Analysis Boundary Conditions Edge A:
Edge B:
Edge C:
Applied Displacements Free (i.e., not restrained)
Applied Displacements Submodel Analysis Boundary Conditions Static Load Cases #1 Edge A:
Fixed Edge B:
Free (i.e., not restrained)
Edge C:
Applied Displacements Static Load case #2 Edge A:
Fixed Edge B:
Free (i.e., not restrained)
Edge C:
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Dynamic Load Cases #1 Edge A:
Fixed Edge B:
Free (i.e., not restrained)
Edge C:
Appfied Displacements Dynamic Load Case #2 Edge A:
Restrained in X & Z translations Edge B:
Applied Load Edge C:
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3.1.6 Solid Submodel #2 Ee j ;Ede A1 Ed-eB EdgeC~
Edge Figure 3-6 Solid Submodel #2 Substructure Analysis Boundary Conditions Edge A:
Edge B:
Edge C:
Applied Displacements Free (i.e., not restrained)
Applied Displacements Submodel Analysis Boundary Conditions Static Load Cases #1 Edge A:
Fixed Edge B:
Free (i.e., not restrained)
Edge C:
Applied Displacements Static Load case #2 Edge A:
Fixed Edge B:
Free (i.e., not restrained)
Edge C:
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Dynamic Load Cases #1 Edge A:
Fixed Edge B:
Free (i.e., not restrained)
Edge C:
Applied Displacements Dynamic Load Case #2 Edge A:
Restrained in X & Z translations Edge B:
Applied Load Edge C:
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3.2 Finite Element Mesh Shell Finite Element Model The shell finite element model is modeled using SHELL63 elements. A regular mesh size of 0.25" is used for the shell finite element models. The full shell model consists of approximately 7,800 nodes and 7,600 shell elements. The following Figure 3-7 shows the finite element mesh for the shell finite element models.
-AN I
Figure 3-7 Shell Finite Element Model Mesh File No.: 0006982.304 Page 20 of 97 Revision: 0 F0306-01 RO
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Solid Finite Element Model The solid finite element model is modeled using SOLID45 elements. The solid finite element models generally maintain the same element size of 0.25". In the transition regions around the weld, finer element sizes are used. Six layers of element are modeled across the plate thickness, therefore, providing adequate discretization through the plate thickness to capture the stress variations across the thickness. The entire model consists of approximately 86,000 nodes and 76,000 solid elements.
The following Figure 3-8 shows the finite element mesh for the solid finite element models.
I AN Figure 3-8 Solid Finite Element Model Mesh File No.: 0006982.304 Page 21 of 97 Revision: 0 F0306-O1RO
V Structural Integrity Associates, Inc 3.3 Stress Paths Linearization stress paths are taken from the weld root to the component surface in the vicinity of the high stress region. In addition, linearization stress paths are also taken from the weld toe to the opposite surface of the connected parts. The stress paths used for the stiffener solid model are shown in the following Figure 3-9 and Figure 3-10.
AN, 7
3 2
9
'10
- 11 4
5 A(
6 Figure 3-9 Solid Finite Element Model Stress Paths (Side View)
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15 16 Figure 3-10 Solid Finite Element Model Stress Paths (Top View)
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Structural Integrity Associates, Inc 4.0 LOAD CASES 4.1 Static Analysis Load Cases Two static load cases are applied:
- 1. Vertical Load A uniform vertical load of 24 lb is applied along Edge C (see Figure 3-1). This load will generate primarily bending stress on the horizontal plate. In the submodel analysis, applied displacements will be used to match the stress intensity along the weld line.
- 2. Horizontal Load A uniform horizontal load of 480 lb is applied along Edge C in the Z direction (see Figure 3-1).
This load will generate primarily membrane stress on the horizontal plate. In the submodel analysis, applied loads will be used to match the stress intensity along the weld line.
Static Analysis Objectives The two static load cases accomplish the following objectives:
- Applying Displacement in Submodel Analysis This is accomplished in the Load Case #1.
- Applying Load in Submodel Analysis This is accomplished in the Load Case #2.
- Full Solid Finite Element Baseline Analysis This analysis provides a direct comparison with the full shell finite elemnt baseline analysis.
This analysis removes any inherent approximation and assumption that is associated with the substructure and submodel analyses.
Submodel #1 and Submodel #2 Two submodels are used for substructure and submodel analyses. Submodel #1 is 1/2 the size of the full model, and submodel #2 is 3/4 the size of the full model. This different size will highlight the discrepancies, if any, in the substructure and submodel analyses.
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4.2 Dynamic Analysis Load Cases Two dynamic load cases are applied:
I. Vertical Load A harmonic uniform vertical load of 24 lb, applied along Edge C (see Figure 3-1). The freqeuncy of the load is set at 25 Hz. The maximum magnitude of this load is similar to the corresponding static analysis load case.
- 2. Horizontal Load A harmonic uniform horizontal load of 480 lb is applied along Edge C in the Z direction (see Figure 3-1). The frequency of the load is set at 25 Hz. The maximum magnitude of this load is similar to the corresponding static analysis load case.
Dynamic Analysis Objectives The two dynamic load cases accomplish the following objectives:
" Applying Displacement in Submodel Analysis This is accomplished in the Load Case #1.
- Applying Load in Submodel Analysis This is accomplished in the Load Case #2.
- Comparing the effectiveness of substructure analysis and submodel analysis.
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5.0 STATIC ANALYSIS RESULTS 5.1 Static Load Case #1 5.1.1 Full Shell Finite Element Analysis Stress Plot The maximum stress intensity is 5,189 psi, and the stress plot is provided in the following Figure 5-1. This analysis is the full shell model baseline analysis, and the maximum stress intensity of 5,189 psi is used to determine the SRF in the other analyses.
Figure 5-1 Full Shell Model Stress Plot for Case #1 (Full Shell Model Baseline Analysis)
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5.1.2 Full Solid Finite Element Analysis Stress Plot The maximum non-linearized stress intensity is 5,608 psi, and the stress plot is provided in the following Figure 5-2. This analysis is the full solid model baseline analysis.
Figure 5-2 Full Solid Model Analysis Stress Plot for Load Case #1 (Full Solid Model Baseline Analysis)
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SRF Table Table 5-1 Full Solid Model Baseline Analysis SRF for Static Load Case #1 Path #
Solid Shell SRF (psi)
(psi)
I 3,043 2
1,223 3
799 4
3,043 5
1,223 6
799 7
3,020 8
549 9
746 10 746 11 549 12 373 13 417 14 1,726 15 364 5,189 0.59 0.24 0.15 0.59 0.24 0.15 0.58 0.11 0.14 0.14 0.11 0.07 0.08 0.33 0.07 0.05 16 265 Maximum =
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5.1.3 Substructure Analysis Using Shell Submodel #1 With reference to Figure 3-3, the displacements along Edges A and C computed in the full shell finite element analysis (Section 5.1.1) are applied onto this shell submodel.
Stress Plot The maximum stress intensity is 5,198 psi, and the stress plot is provided in the following Figure 5-3.
The maximum stress intensity is the same as the full shell baseline analysis maximum stress intensity, and the stress contours are very similar (see Figure 5-1). This confirms that the shell substructure analysis produces the same stress results as the full shell baseline analysis.
Figure 5-3 Substructure Analysis using Shell Submodel #1 Stress Plot for Load Case #1 File No.: 0006982.304 Page 29 of 97 Revision: 0 F0306-O1 RO
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5.1.4 Substructure Analysis Using Shell Submodel #2 With reference to Figure 3-5, the displacements along Edges A and C computed in the full shell finite element analysis (Section 5.1.1) are applied onto this shell submodel.
Stress Plot The maximum stress intensity is 5,198 psi, and the stress plot is provided in the following Figure 5-4.
The maximum stress intensity is the same as the full shell baseline analysis maximum stress intensity, and the stress contours are very similar (see Figure 5-1). This confirms that the shell substructure analysis produces the same stress results as the full shell baseline analysis.
Figure 5-4 Substructure Analysis using Shell Submodel #2 Stress Plot for Load Case #1 File No.: 0006982.304 Page 30 of 97 Revision: 0 F0306-O1RO
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5.1.5 Substructure Analysis Using Solid Submodel #1 With reference to Figure 3-4, the displacements along Edges A and C computed in the full shell finite element analysis (Section 5.1.1) are applied onto this solid submodel.
Stress Plot The maximum non-linearized stress intensity is 7,033 psi, and the stress plot is provided in the following Figure 5-5.
Figure 5-5 Substructure Analysis using Solid Submodel #1 Stress Plot for Load Case #1 File No.: 0006982.304 Page 31 of 97 Revision: 0 F0306-O1RO
Structural Integrity Associates, cinc SRF Table Table 5-2 Substructure Analysis (Submodel #1) SRF for Static Load Case #1 Path #
Solid Shell SRF (psi)
(psi)
I 3,822 2
1,543 3
1,003 4
3,822 5
1,543 6
1,003 7
3,785 8
696 9
936 10 936 11 696 12 488 13 546 14 2,239 15 477 5,189 0.74 0.30 0.19 0.74 0.30 0.19 0.73 0.13 0.18 0.18 0.13 0.09 0.11 0.43 0.09 0.07 16 364 Maximum =
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5.1.6 Substructure Analysis Using Solid Submodel #2 With reference to Figure 3-6, the displacements along Edges A and C computed in the full shell finite element analysis (Section 5.1.1) are applied onto this solid submodel.
Stress Plot The maximum non-linearized stress intensity is 6,568 psi, and the stress plot is provided in the following Figure 5-6.
Figure 5-6 Substructure Analysis using Solid Submodel #2 Stress Plot for Load Case #1 File No.: 0006982.304 Page 33 of 97 Revision: 0 F0306-O1RO
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SRF Table Table 5-3 Substructure Analysis (Submodel #2) SRF for Static Load Case #1 Path #
Solid Shell SRF (psi)
(psi) 1 3,565 2
1,435 3
936 4
3,565 5
1,435 6
936 7
3,536 8
646 9
874 10 874 11 646 12 445 13 498 14 2,051 15 434 5,189 0.69 0.28 0.18 0.69 0.28 0.18 0.68 0.12 0.17 0.17 0.12 0.09 0.10 0.40 0.08 0.06 16 321 Maximum =
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5.1.7 Submodel Analysis Using Submodel #1 Matching Stress Profile The stress profile matching is performed along the weld line connecting the vertical plate to the horizontal plate. The matching is accomplished by imposing vertical displacements along the Edge C (see Figure 3-3) of the submodel. Fixed boundary condition is applied to the top and bottom edges. The applied displacements and the comparison of the stress profiles are shown in the following Figure 5-7 and Figure 5-8, respectively.
-0.0164
-0.0166
-0.0168
-0.0170 4)
E
-0.0172 4)
C.)
MA -0.0174
-0.0176
-0.0178
-0.0180
-0.0182 X Coordinate (in)
Figure 5-7 Submodel Analysis using Submodel #1 Applied Displacements for Load Case #1 File No.: 0006982.304 Page 35 of 97 Revision: 0 F0306-01 RO
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6,000 Shell Submodel Analysis 4,000 1,000 0
2 Figure 5-8 Submodel Analysis using Submodel #1 Stress Profile Comparison for Load Case #1 File No.: 0006982.304 Page 36 of 97 Revision: 0 F0306-01 RO
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Stress Plot Figure 5-9 Submodel Analysis using Submodel #1 Shell Model Stress Plot for Load Case #1 File No.: 0006982.304 Page 37 of 97 Revision: 0 F03 06-01 RO
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Figure 5-10 Submodel Analysis using Submodel #1 Solid Model Stress Plot for Load Case #1 File No.: 0006982.304 Page 38 of 97 Revision: 0 F0306-O1RO
Structural Integrity Associates, Inc.
SRF Table Table 5-4 Submodel Analysis (Submodel #1) SRF for Static Load Case #1 Path #
Solid Shell SRF (psi)
(psi)
I 3,543 2
1,443 3
929 4
3,543 5
1,443 6
929 7
3,495 8
645 9
865 10 865 11 645 12 456 13 499 14 2,084 15 437 5,189 0.68 0.28 0.18 0.68 0.28 0.18 0.67 0.12 0.17 0.17 0.12 0.09 0.10 0.40 0.08 0.07 0.68 16 367 Maximum =
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5.1.8 Submodel Analysis Using Submodel #2 Matching Stress Profile The stress profile matching is performed along the weld line connecting the vertical plate to the horizontal plate. The matching is accomplished by imposing vertical displacements along the Edge C (see Figure 3-5) of the submodel. Fixed boundary condition is applied to the top and bottom edges. The applied displacements and the comparison of the stress profiles are shown in the following Figure 5-11 and Figure 5-12, respectively.
-0.0380
-0.0385
-0.0390 4)
E 4)
C.)
o
-0.0395
-0.0400
-0.0405 X Coordinate (in)
Figure 5-11 Submodel Analysis using Submodel #2 Applied Displacements for Load Case #1 File No.: 0006982.304 Page 40 of 97 Revision: 0 F0306-O1RO
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Ful ZWO V
2 2
Figure 5-12 Submodel Analysis using Submodel #2 Stress Profile Comparison for Load Case #1 File No.: 0006982.304 Page 41 of 97 Revision: 0 F0306-O1RO
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Stress Plot Figure 5-13 Submodel Analysis using Submodel #2 Shell Model Stress Plot for Load Case #1 File No.: 0006982.304 Page 42 of 97 Revision: 0 F0306-O1 RO
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Figure 5-14 Submodel Analysis using Submodel #2 Solid Model Stress Plot for Load Case #1 File No.: 0006982.304 Page 43 of 97 Revision: 0 F0306-O1 RO
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SRF Table Table 5-5 Submodel Analysis (Submodel #2) SRF for Static Load Case #1 1
3,414 2
1-378 3
896
- 4.
3,4.14-5 1,378 6
896 7
3-481 8
618 9
- 8. 6 10 836 11 618 S...........................................,...........................................
12 4,22 13
- 472, 14-1-950 15 412 5-1189 0.66 0.27 0.17 066 0.27 0.17 0.65 0.12 0.16
,0.16 0.12 0.08 0.09 0.38 0(08 16 318
.I File No.: 0006982.304 Revision: 0 Page 44 of 97 F0306-O1RO
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5.2 5.2.1 Static Load Case #2 Full Shell Finite Element Analysis Stress Plot The maximum stress intensity is 6,579 psi, and the stress plot is provided in the following Figure 5-15. This analysis is the full shell model baseline analysis, and the maximum stress intensity of 6,579 psi is used to determine the SRF in the other analyses.
Figure 5-15 Full Shell Model Stress Plot for Case #2 (Full Shell Model Baseline Analysis)
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5.2.2 Full Solid Finite Element Analysis Stress Plot The maximum non-linearized stress intensity is 10,470 psi, and the stress plot is provided in the following Figure 5-16. This analysis is the full solid model baseline analysis.
Figure 5-16 Full Solid Model Analysis Stress Plot for Load Case #2 (Full Solid Model Baseline Analysis)
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SRF Table Table 5-6 Full Solid Model Baseline Analysis SRF for Static Load Case #2 Path #
Solid Shell SRF (psi)
(psi)
I 3,760 2
3,789 3
5,733 4
3,760 5
3,789 6
5,733 7
2,939 8
5,872 9
4,731 10 4,731 11 5,872 12 5,042 13 4,358 14 3,667 15 3,720 6,579 0.57 0.58 0.87 0.57 0.58 0.87 0.45 0.89 0.72 0.72 0.89 0.77 0.66 0.56 0.57 0.75 16 4,954 Maximum =
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5.2.3 Substructure Analysis Using Shell Submodel #1 With reference to Figure 3-3, the displacements along Edges A and C computed in the full shell finite element analysis (Section 5.2.1) are applied onto this solid submodel.
Stress Plot The maximum stress intensity is 6,579 psi, and the stress plot is provided in the following Figure 5-17.
The maximum stress intensity is the same as the full shell baseline analysis maximum stress intensity, and the stress contours are very similar (see Figure 5-15). This confirms that the shell substructure analysis produces the same stress results as the full shell baseline analysis.
Figure 5-17 Substructure Analysis using Shell Submodel #1 Stress Plot for Load Case #2 File No.: 0006982.304 Page 48 of 97 Revision: 0 F0306-O1 RO
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5.2.4 Substructure Analysis Using Shell Submodel #2 With reference to Figure 3-5, the displacements along Edges A and C computed in the full shell finite element analysis (Section 5.2.1) are applied onto this solid submodel.
Stress Plot The maximum stress intensity is 6,579 psi, and the stress plot is provided in the following Figure 5-18.
The maximum stress intensity is the same as the full shell baseline analysis maximum stress intensity, and the stress contours are very similar (see Figure 5-15). This confirms that the shell substructure analysis produces the same stress results as the full shell baseline analysis.
Figure 5-18 Substructure Analysis using Shell Submodel #2 Stress Plot for Load Case #2 File No.: 0006982.304 Page 49 of 97 Revision: 0 F0306-01 RO
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5.2.5 Substructure Analysis Using Solid Submodel #1 With reference to Figure 3-3, the displacements along Edges A and C computed in the full shell finite element analysis (Section 5.2.1) are applied onto this solid submodel.
Stress Plot The maximum non-linearized stress intensity is 10,789 psi, and the stress plot is provided in the following Figure 5-19.
Figure 5-19 Substructure Analysis using Solid Submodel #1 Stress Plot for Load Case #2 File No.: 0006982.304 Page 50 of 97 Revision: 0 F0306-O1RO
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SRF Table Table 5-7 Substructure Analysis (Submodel #1) SRF for Static Load Case #2 Path #
Solid Shell SRF (psi)
(psi) 1 2
3,874 3,904 3
5,909 4
3,874 5
3,904 6
5,909 7
2,965 8
6,036 9
4,861 10 4,861 11 6,036 12 5,207 13 4,456 14 3,768 15 3,825 6,579 0.59 0.59 0.90 0.59 0.59 0.90 0.45 0.92 0.74 0.74 0.92 0.79 0.68 0.57 0.58 0.78 16 5,109
+/- i Maximum =
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5.2.6 Substructure Analysis Using Solid Submodel #2 With reference to Figure 3-3, the displacements along Edges A and C computed in the full shell finite element analysis (Section 5.2.1) are applied onto this solid submodel.
Stress Plot The maximum non-linearized stress intensity is 10,673 psi, and the stress plot is provided in the following Figure 5-20.
Figure 5-20 Substructure Analysis using Solid Submodel #2 Stress Plot for Load Case #2 File No.: 0006982.304 Page 52 of 97 Revision: 0 F0306-01 RO
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SRF Table Table 5-8 Substructure Analysis (Submodel #2) SRF for Static Load Case #2 Path #
Solid (psi)
Shell (psi)
SRF 2
2 3,833 3,863 3
5,845 4
3,833 5
3,863 6
5,845 7
2,981 8
5,981 9
4,818 10 4,818 11 5,981 12 5,142 13 4,434 14 3,736 15 3,791 6,579 0.58 0.59 0.89 0.58 0.59 0.89 0.45 0.91 0.73 0.73 0.91 0.78 0.67 0.57 0.58 0.77 16 5,051 Maximum =
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5.2.7 Submodel Analysis Using Submodel #1 Matching Stress Profile The stress profile matching is performed along the weld line connecting the vertical plate to the horizontal plate. The matching is accomplished by applying a horizontal (Z) load along the Edge C (see Figure 3-3) of the submodel. The nodes at the top and bottom edges are restrained in X and Z translations. The applied loads and the comparison of the stress profiles are shown in the following Figure 5-21 and Figure 5-22, respectively.
25.0 20.0 M
15.0 0-J 10.0 5.0 0.0
-3
-2
-1 X do1ri2Q.t3in, l
Figure 5-21 Submodel Analysis using Submodel #1 Applied Loads for Load Case #2 File No.: 0006982.304 Page 54 of 97 Revision: 0 F0306-01RO
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Full Shell Model Analysis.
a 4,OW Ia I
U
- 1,OW Z"
)tCWaffdMat&O.*rji Figure 5-22 Submodel Analysis using Submodel #1 Stress Profile Comparison for Load Case #2 File No.: 0006982.304 Revision: 0 Page 55 of 97 F0306-O1RO
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Stress Plot Figure 5-23 Submodel Analysis using Submodel #1 Shell Model Stress Plot for Load Case #2 File No.: 0006982.304 Page 56 of 97 Revision: 0 F0306-OIRO
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Figure 5-24 Submodel Analysis using Submodel #1 Solid Model Stress Plot for Load Case #2 File No.: 0006982.304 Page 57 of 97 Revision: 0 F0306-O1 RO
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SRF Table Table 5-9 Submodel Analysis (Submodel #1) SRF for Static Load Case #2 Path #
Solid Shell SRF (psi)
(psi) 1 3,737 0.57 2
3,765 0.57 3
5,697 0.87 4
3,737 0.57 5
3,765 0.57 6
5,697 0.87 7
2,911 0.44 8
5,849 0.89 6,579 9
4,715 0.72 10 4,715 0.72 11 5,849 0.89 12 5,014 0.76 13 4,326 0.66 14 3,644 0.55 15 3,697 0.56 16 4,924 0.75 Maximum =
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5.2.8 Submodel Analysis Using Submodel #2 Matching Stress Profile The stress profile matching is performed along the weld line connecting the vertical plate to the horizontal plate. The matching is accomplished by applying a horizontal (Z) load along the Edge C (see Figure 3-5) of the submodel. The nodes at the top and bottom edges (i.e., Edge A) are fixed.
The applied loads and the comparison of the stress profiles are shown in the following Figure 5-25 and Figure 5-26, respectively.
35.0 30.0 25.0 0
20.0
- j.
15.0 10:0 5.0 0.0
-3
-2
-1 0
1 2
3 X Coordinate (in)
Figure 5-25 Submodel Analysis using Submodel #2 Applied Loads for Load Case #2 File No.: 0006982.304 Page 59 of 97 Revision: 0 F0306-OI RO
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// Shell Submodel Analysis 6,000 Full Shell Model Analysis 5,000 3,000 2,000 0
Figure 5-26 Submodel Analysis using Submodel #2 Stress Profile Comparison for Load Case #2 File No.: 0006982.304 Page 60 of 97 Revision: 0 F0306-OI RO
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Stress Plot Figure 5-27 Submodel Analysis using Submodel #2 Shell Model Stress Plot for Load Case #2 File No.: 0006982.304 Page 61 of 97 Revision: 0 F0306-01 RO
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Figure 5-28 Submodel Analysis using Submodel #2 Solid Model Stress Plot for Load Case #2 File No.: 0006982.304 Page 62 of 97 Revision: 0 F03 06-0 1 RO
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SRF Table Table 5-10 Submodel Analysis (Submodel #2) SRF for Static Load Case #2 Path Solid Shell SRF (psi)
(psi)
I 3,755 2
3,784 3
5,736 4
3,755 5
3,784 6
5,736 7
1,763 8
5,851 9
4,719 10 4,719 11 5,851 12 5,482 13 3,706 14 3,504 15 3,608 6,579 0.57 0.58 0.87 0.57 0.58 0.87 0.27 0.89 0.72 0.72 0.89 0.83 0.56 0.53 0.55 0.78 16 5,143 Maximum =
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VStructural Integrity Associates, Inc 6.0 DYNAMIC ANALYSIS RESULTS 6.1 Structural Modal Frequencies Modal analysis of the structure is performed to determine the fundamental frequencies of the system.
The following Table 6-1 and Table 6-2 summarize the major frequencies in the vertical (Y direction) and the horizontal (Z direction) directions, which correspond to the directions of the Load Cases #1 and #2, respectively.
Table 6-1 Structural Vertical (Y direction) Modal Frequencies Effetive Cumulative Mode # (1)
Frequency Period Participation MsEffective mass (Hz)
Factor Mass Faci Fraction 1
2.64 0.379 1.779 3.164 0.759 4
8.69 0.115 0.050 0.002 0.760 7
16.77 0.060
-1.000 1.000 1.000 10 28.24 0.035
-0.027 0.001 1.000 Note:
(1) Insignificant modes have been excluded from the table.
Table 6-2 Structural Horizontal (Z direction) Modal Frequencies Cumulative Mode # (1)
Frequency Period Participation Effective Mass (Hz)
Factor Mass Faci Fraction 2
2.82 0.354 6.604 43.614 0.848 6
15.80 0.063 2.798 7.827 1.000 Note:
(1) Insignificant modes have been excluded from the table.
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6.2 Structural Damping Values For the purpose of this study, assume that the structural critical damping value is 4%.
The damping used in the dynamic transient analysis is the Alpha and Beta damping, also known as the Rayleigh damping and is defined by Rayleigh damping constants x and P3. The damping matrix, C, is calculated by using these constants to multiply the mass matrix, M, and the stiffness matrix, K:
C = aM + P3K The values of a and P3 are calculated from modal damping ratio, 4i, which is the ratio of actual damping to critical damping for a particular mode of vibration, i. If oi is the natural frequency of the mode i, a and 03 satisfy the relation:
4i = a/2o~i + 3,oi/2 (Reference 4, Structural Analysis Guide, Section 5.9.3)
Therefore, given 4 and a frequency range between wi and coj, two simultaneous equations can be solved for ax and P3.
In this analysis, the frequency range is 2.0 Hz and 28.2 Hz, which cover the frequency range from mode #1 to mode #I0(see Table 6-1 and Table 6-2). The calculated values are:
ax
= 0.939 P = 4.216E-4 The calculations of ax and P3 are documented in the spreadsheet Damping.xls (described in Appendix A).
6.3 Time History Analysis Integration Time Step The accuracy of the transient dynamic solution depends on the integration time step. For the Newmark time integration used herein, it is recommended that using approximately twenty points per cycle of the highest frequency of interest results in a reasonably accurate solution. That is, iff is the frequency (in Hz), the integration time step (ITS) is given by:
= 1/(20J)
(Reference 4, Structural Analysis Guide, Section 5.9.1)
The modal analysis shows that the highest major mode is 28.2 Hz, in the vertical direction (see Table 6-1). The applied harmonic load frequency is set at 25 Hz (see Section 4.2). Therefore, conservatively use 50 Hz as the highest frequency of interest.
= 1/(20*50)
= 0.001 seconds File No.: 0006982.304 Page 65 of 97 Revision: 0 F0306-O1RO
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6.4 Dynamic Load Case #1 6.4.1 Full Shell Finite Element Analysis Transient DisDIacement Plot The maximum vertical displacement occurs at the edge node of the load application line. The following Figure 6-1 shows a plot of the nodal transient displacements.
0.002 0.000
- 0.
0.05 0.10 0.15 0
-0.002 E
0
-0.004 An
-0.006
-0.008
-0.010 Time (second)
Figure 6-1 Full Shell Model Dynamic Analysis Vertical Transient Displacement for Load Case #1 File No.: 0006982.304 Page 66 of 97 Revision: 0 F0306-O1RO
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Transient Stress Intensity Plot The maximum stress intensity occurs at one of the weld line nodes. The following Figure 6-2 shows a plot of the nodal transient stress intensities. The maximum stress intensity is 2,100 psi, which occurs at 0.048 seconds time step.
2,500 2,000 (A
1,500 1,000 500 0
0.00 0.05 0.10 0.15 0.20 Time (second)
Figure 6-2 Full Shell Model Dynamic Analysis Nodal Stress Intensity for Load Case #1 File No.: 0006982.304 Revision: 0 Page 67 of 97=
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Vertical Displacement Plot The following Figure 6-3 shows the vertical displacements at 0.048 seconds time step, when the maximum stress intensity occurs. The nodal displacements (for 6 degrees of freedom) at the submodel boundaries at this time step are used for subsequent substructure analyses.
NODAL SOLUTION STEP=48 SUB =1 TIME=.048 UY (AVG)
RSYS=0 DMX =.003813 SMN =-.003813 Figure 6-3 Full Shell Model Dynamic Analysis Vertical Displacement Plot for Load Case #1 (Full Shell Model Baseline Analysis)
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Maximum Stress Plot The maximum stress intensity is 2,100 psi, which occurs at 0.048 seconds time step. The stress plot at that time step is provided in the following Figure 6-4. This analysis is the full shell model baseline analysis, and the maximum stress intensity of 2,100 psi is used to determine the SRF in the other analysis.
NODAL SOLUTION STEP=48 SUB =1 TIME=.048 SINT (AVG)
DMX =.003813 SMN =.635E-06 SMX =2100 Figure 6-4 Full Shell Model Dynamic Analysis Maximum Stress Plot for Load Case #1 (Full Shell Model Baseline Analysis)
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6.4.2 Substructure Analysis Using Shell Submodel #2 With reference to Figure 3-5, the displacements along Edges A and C computed in the full shell finite element analysis (Section 6.4.1) are applied onto this shell submodel.
Vertical Displacement Plot The maximum vertical displacement plot is provided in the following Figure 6-5.
Figure 6-5 Substructure Analysis using Shell Submodel #2 Vertical Displacement Plot for Load Case #1 File No.: 0006982.304 Page 70 of 97 Revision: 0 F0306-O1RO
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Stress Plot The maximum stress intensity is 1,564 psi, and the stress plot is provided in the following Figure 6-6.
Figure 6-6 Substructure Analysis using Shell Submodel #2 Stress Plot for Load Case #1 Observation The maximum stress intensity of 1,564 psi is significantly lower than the full shell baseline analysis maximum stress intensity of 2,100 psi. The stress pattern is also different. The maximum stress intensity for the substructure analysis is located along the edge, not at the weld line.
In this analysis, only the displacements at the boundaries are mapped from the full shell model to the submodel. The shell internal displacements, influenced by the dynamic inertia effects, are not captured in the substructure analysis. Without imposing the dynamic characteristic displacements within the submodel boundaries, the substructure analysis is not able to duplicate the stress pattern of the full shell model.
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6.4.3 Substructure Analysis Using Solid Submodel #2 With reference to Figure 3-6, the displacements along Edges A and C computed in the full shell finite element analysis (Section 6.4.1) are applied onto this solid submodel.
Stress Plot The maximum non-linearized stress intensity is 1,596 psi, and the stress plot is provided in the following Figure 6-7.
1 Figure 6-7 Substructure Analysis using Solid Submodel #2 Stress Plot for Load Case #1 File No.: 0006982.304 Page 72 of 97 Revision: 0 F0306-O1RO
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SRF Table Table 6-3 Substructure Dynamic Analysis (Submodel #2) SRF for Dynamic Load Case #1 Path#1 Solid Shell (psi)
(psi)
I 711 2
297 3
186 4
711 5
297 6
186 7
780 8
133 9
173 10 173 11 133 12 124 13 144 14 567 15 107 2,100 0.34 0.14 0.09 0.34 0.14 0.09 0.37 0.06 0.08 0.08 0.06 0.06 0.07 0.27 0.05 0.04 16 93 i
i i
Maximum =
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6.4.4 Submodel Analysis Using Submodel #2 Matching Stress Profile The stress profile matching is perform along the weld line connecting the vertical plate to the horizontal plate. The matching is accomplished by imposing vertical displacements along the Edge C (see Figure 3-3) of the submodel. Fixed boundary condition is applied to the top and bottom edges. The applied displacements and the comparison of the stress profiles are shown in the following Figure 6-8 and Figure 6-9, respectively.
Figure 6-8 Submodel Analysis using Submodel #2 Applied Displacements for Load Case #1 File No.: 0006982.304 Page 74 of 97 Revision: 0 F0306-01 RO
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Shell Submodel Analysis Full Shell Model Analysis E
-2, 2
Figure 6-9 Submodel Analysis using Submodel #2 Stress Profile Comparison for Load Case #1 File No.: 0006982.304 Revision: 0 Page 75 of 97 F0306-01 RO
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Stress Plot NODAL SOLUTION STEP=1 SUB =1 TIME=1 SINT (AVG)
DMX =.008614 SMN =.221E-06 SMX =2100 Figure 6-10 Submodel Analysis using Submodel #2 Shell Model Stress Plot for Load Case #1 File No.: 0006982.304 Page 76 of 97 Revision: 0 F0306-O1 RO
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Figure 6-11 Submodel Analysis using Submodel #2 Solid Model Stress Plot for Load Case #1 File No.: 0006982.304 Page 77 of 97 Revision: 0 F0306-01 RO
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SRF Table Table 6-4 Submodel Analysis (Submodel #2) SRF for Dynamic Load Case #1 Path #
Solid Shell SRF (psi)
(psi) 1 1,351 2
550 3
351 4
1,351 5
550 6
351 7
1,512 8
233 9
325 10 325 11 233 12 213 13 256 14 1,073 15 207 2,100 0.64 0.26 0.17 0.64 0.26 0.17 0.72 0.11 0.15 0.15 0.11 0.10 0.12 0.51 0.10 0.08 0.72 16 158 i
i i
Maximum =
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6.5 Dynamic Load Case #2 6.5.1 Full Shell Finite Element Analysis Transient Displacement Plot The maximum horizontal displacement in the applied load Z direction occurs at the edge node of the load application line. The following Figure 6-12 shows a plot of the nodal transient displacements.
0.008 0.006 0.004 E
T.)
0._
a N
0.002 0.000
-0.002 Time (second)
Figure 6-12 Full Shell Model Dynamic Analysis Horizontal Transient Displacement for Load Case #2 File No.: 0006982.304 Revision: 0 Page 79 of 97 F0306-O1RO
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Transient Stress Intensity Plot The maximum stress intensity occurs at the one of the weld line nodes. The following Figure 6-13 shows a plot of the nodal transient stress intensities. The maximum stress intensity is 2,262 psi, which occurs at 0.031 seconds time step.
2,500 2,000 CL 50 0) 0.00 0.05 0.10 0.15 0.20 Time (second)
Figure 6-13 Full Shell Model Dynamic Analysis Nodal Stress Intensity for Load Case #2 File No.: 0006982.304 Page 80 of 97 Revision: 0 F0306-01RO
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Horizontal Disrlacement Plot The following Figure 6-14 shows the horizontal Z displacements at 0.031 seconds time step, when the maximum stress intensity occurs. The nodal displacements (for 6 degrees of freedom) at the submodel boundaries at this time step are used for subsequent substructure analyses.
NODAL SOLUTION STEP=31 SUB =1 TIME=.031 UZ (AVG)
RSYS=0 DMX =.004594 SMN =-.489E-03 SMX =.004594 AN
.002899
.004029 003464
.004594
.755E-04
.001205 Figure 6-14 Full Shell Model Dynamic Analysis Horizontal Displacement Plot for Load Case #2 (Full Shell Model Baseline Analysis)
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Maximum Stress Plot The maximum stress intensity is 2,262 psi, which occurs at 0.031 seconds time step. The stress plot at that time step is provided in the following Figure 6-15. This analysis is the full shell model baseline analysis, and the maximum stress intensity of 2,262 psi is used to determine the SRF in the other analysis.
Figure 6-15 Full Shell Model Dynamic Analysis Maximum Stress Plot for Load Case #2 (Full Shell Model Baseline Analysis)
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6.5.2 Substructure Analysis Using Shell Submodel #2 With reference to Figure 3-5, the displacements along Edges A and C computed in the full shell finite element analysis (Section 6.5.1) are applied onto this shell submodel.
Horizontal Displacement Plot The maximum horizontal displacement plot is provided in the following Figure 6-16.
NODAL SOLUTION STEP=1 SUB =1 TIMe-1 UZ (AVG)
RSYS--O DMX =.004231 SMN =-. 487E-03 SMX =.004231
-. 487E-03
.561E-03
.00161
.002658
.003707
.369E-04
.001085
.0
.003183
.004231 Figure 6-16 Substructure Analysis using Shell Submodel #2 Horizontal Displacement Plot for Load Case #2 File No.: 0006982.304 Page 83 of 97 Revision: 0 F0306-01 RO
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Stress Plot The maximum stress intensity is 948 psi, and the stress plot is provided in the following figure.
NODAL SOLUTION STEP=-1 SUB =1 TIME=1 SINT (AVG)
DMX =.004231 SMN =17.891 SMX =948.406 NX X
638.234 845.015 741.625 948.406 121.282 328.063 Figure 6-17 Substructure Analysis using Shell Submodel #2 Stress Plot for Load Case #2 Observation The maximum stress intensity of 948 psi is significantly lower than the full shell baseline analysis maximum stress intensity of 2,262 psi. The stress pattern is also different. The maximum stress intensity for the substructure analysis is located along the top edge, not at the weld line.
In this analysis, only the displacements at the boundaries are mapped from the full shell model to the submodel. The shell internal displacements, influenced by the dynamic inertia effects, are not captured in the substructure analysis. Without imposing the dynamic characteristic displacements within the submodel boundaries, the substructure analysis is not able to duplicate the stress pattern of the full shell model.
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6.5.3 Substructure Analysis Using Solid Submodel #2 With reference to Figure 3-6, the displacements along Edges A and C computed in the full shell finite element analysis (Section 6.5.1) are applied onto this solid submodel.
Stress Plot The maximum non-linearized stress intensity is 1,389 psi, and the stress plot is provided in the following Figure 6-18.
NODAL SOL STEP=Il SUB =1 TIMe--1 SINT DMX =.004 SMN =3. 97 SMX =13891 Figure 6-18 Substructure Analysis using Solid Submodel #2 Stress Plot for Load Case #2 File No.: 0006982.304 Revision: 0 Page 85 of 97 F0306-O1RO
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SRF Table Table 6-5 Substructure-Dynamic Analysis (Submodel #2) SRF for Dynamic Load Case #2 Path #
Solid Shell SRF (psi)
(psi)
I 500 2
503 3
762 4
500 5
503 6
762 7
239 8
777 9
627 10 627 11 777 12 730 13 496 14 469 15 482 2,262 0.22 0.22 0.34 0.22 0.22 0.34 0.11 0.34 0.28 0.28 0.34 0.32 0.22 0.21 0.21 0.30 16 686 Maximum =
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6.5.4 Submodel Analysis Using Submodel #2 Matching Stress Profile The stress profile matching is perform along the weld line connecting the vertical plate to the horizontal plate. The matching is accomplished by imposing horizontal forces along the two vertical edges (i.e., Edge B, see Figure 3-3) of the submodel. The nodes at the top and bottom edges (i.e.
Edge A) are restrained in UX and UZ translations. Fix boundary condition is applied to Edge C.
The applied loads and the comparison of the stress profiles are shown in the following Figure 6-19 and Figure 6-20, respectively.
4.0 3.5 3.0 2.5 0
0 1.5
'U-1.0 0.5 0.0
-15
-10
-5 v i 5
10 15
- '...UI eil IILI n)ll Figure 6-19 Submodel Analysis using Submodel #2 Applied Horizontal Loads for Load Case #2 File No.: 0006982.304 Page 87 of 97 Revision: 0 F0306-0IRO
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2,$W Sr 0
-2
- 2 2
3 Figure 6-20 Submodel Analysis using Submodel #2 Stress Profile Comparison for Load Case #2 File No.: 0006982.304 Page 88 of 97 Revision: 0 F0306-0 1 RO
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Stress Plot Figure 6-21 Submodel Analysis using Submodel #2 Shell Model Stress Plot for Load Case #2 File No.: 0006982.304 Page 89 of 97 Revision: 0 F0306-OI RO
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Figure 6-22 Submodel Analysis using Submodel #2 Solid Model Stress Plot for Load Case #2 File No.: 0006982.304 Page 90 of 97 Revision: 0 F0306-OI RO
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SRF Table Table 6-6 Submodel Analysis (Submodel #2) SRF for Dynamic Load Case #2 Path #
Solid Shell (psi)
(psi)
I 1,871 2
1,233 3
1,820 4
1,871 5
1,233 6
1,820 7
1,888 8
1,467 9
1,228 10 1,228 11 1,467 12 1,905 13 1,259 14 1,871 2,262 0.83 0.55 0.80 0.83 0.55 0.80 0.83 0.65 0.54 0.54 0.65 0.84 0.56 0.83 0.37 0.72 15 16 832 1,619 Maximum 0.84 File No.: 0006982.304 Revision: 0 Page 91 of 97 F0306-O1 RO
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7.0
SUMMARY
STRESS REDUCTION FACTORS 7.1 Static Analysis SRF Static Load Case #1 Table 7-1 Summary SRF for Static Load Case #1 Analysis Approach SRF Full Solid Model Baseline Analysis 0.59 Substructure Analysis (Submodel #1) 0.74 Substructure Analysis (Submodel #2) 0.69 Submodel Analysis (Submodel #1) 0.68 Submodel Analysis (Submodel #2) 0.66 Static Load Case #2 Table 7-2 Summary SRF for Static Load Case #2 Analysis Approach SRF Full Solid Model Baseline Analysis 0.89 Substructure Analysis (Submodel #1) 0.92 Substructure Analysis (Submodel #2) 0.91 Submodel Analysis (Submodel #1) 0.89 Submodel Analysis (Submodel #2) 0.89 File No.: 0006982.304 Revision: 0 Page 92 of 97 F0306-OIRO
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7.2 Dynamic Analysis SRF Dynamic Load Case #1 Table 7-3 Summary SRF for Dynamic Load Case #1 Analysis Approach SRF Substructure Analysis (Submodel #2) 0.37 Submodel Analysis (Submodel #2) 0.72 Dynamic Load Case #2 Table 7-4 Summary SRF for Dynamic Load Case #2 Analysis Approach SRF Substructure Analysis (Submodel #2) 0.34 Submodel Analysis (Submodel #2) 0.84 File No.: 0006982.304 Revision: 0 Page 93 of 97 F0306-O1RO
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8.0 DISCUSSIONS The comparisons of the SRF and the different analyses lead to the following observation and deduction.
8.1 Static Analysis Substructure Analysis Using Shell Submodels The substructure analyses using the shell submodels show that the results are the same as the full shell model. The maximum stress intensities from both the shell submodel and the full shell model analyses are the same. The stress plots of both the submodel and full model analyses also show that the stress patterns are the same.
Substructure Analysis Using Solid Submodels The substructure analysis using the solid submodel predicts higher SRF than the SRF computed in the full solid model baseline analysis (see Table 7-1 and Table 7-2). The reason that they are different is because the shell model is more flexible than the solid model, which models in the detailed weld configuration.
The local region of the solid model that models in the weld configuration becomes stiffer than the corresponding region in the shell model. When the displacements from the more flexible shell model analysis are applied onto the more rigid solid submodel, higher stresses are computed for the solid submodel.
To better predict the local stresses using the substructure analysis, the boundaries of the submodel need to be extended to a reasonable distance. This is evident when the submodel #1 and submodel
- 2 substructure analysis results are compared. When the boundaries are extended from submodel #1 to submodel #2, the SRF is lowered (see Table 7-1 and Table 7-2).
Submodel Analysis The study shows that when the matching of the stress intensity profile along the high stress weld line is achieved, the submodel analysis is a reasonable approach for calculating the SRF. For Load Cases
- 1 and #2, the submodel analyses have computed SRFs that show good agreement with the full solid model baseline analysis.
The SRFs computed using submodels #1 and #2 are very similar. This similarity in SRFs demonstrate that after satisfactory stress intensity profile matching, the computation of SRFs is not sensitive to the size of the submodel.
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8.2 Dynamic Analysis Substructure Analysis Using Shell Submodels The maximum stress intensity calculated using a substructure shell analysis is significantly lower than the maximum stress intensity computed using full shell baseline analysis. The stress patterns of the two analyses are also different.
In the substructure analysis, only the displacements at the boundaries are mapped from the full shell model to the submodel boundaries. The shell internal displacements, caused by the dynamic inertia effects, are not captured in the substructure analysis. Without imposing the dynamic characteristic displacements at regions within the submodel boundaries, the substructure analysis is not able to duplicate the stress pattern of the full shell model. This results in predicting lower shell submodel stresses at the weld line.
Substructure Analysis Using Solid Submodels Similar to the substructure analysis using shell submodel, the substructure analysis using. solid submodel also does not capture the internal displacements at regions within the submodel boundaries, and therefore the full dynamic inertia effects of the structure have not been accurately represented. This also results in predicting lower solid submodel stresses at the weld line.
Consequently, the SRF computed using the substructure analysis shows an unreasonably low value (see Table 7-3 and Table 7-4).
Submodel Analysis Similar to the static analysis, the study shows that when the matching of the stress intensity profile along the high stress weld line is achieved, the submodel analysis is a reasonable approach for the calculation of the SRF.
For both Load Cases #1 and #2, the SRFs computed using the submodel analysis are significantly higher than the SRFs computed using the substructure analysis. However, they demonstrate reasonable agreement with the SRFs computed in the static analysis.
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9.0 CONCLUSION
S The comparison study documented in this calculation fully addresses the issues identified in the RAI 199/156 from NRC (Reference 3).
Two Load Cases have been considered in this calculation:
Load Case #1 This load case examines the scenario where the weld is subjected to mainly bending action. To match the stress profile, imposed displacements are used. This is similar to the submodel analysis approach used to determine the stresses at the bottom of the skirt/drain channel junction.
Load Case #2 This load case examines the scenario where the weld is subjected to mainly membrane action. To match the stress profile, imposed loads are used. This is similar to the submodel analysis approach used to determine the stresses at the intersection between the bottom of the inner hood, stiffener and base plate.
Two analysis options have been evaluated: the static analysis and the dynamic time history analysis.
Together these analyses show that the SRFs computed using the TVA submodel analysis technique are accurate and acceptable.
In conclusion, this comparison study validates the submodel analysis approach adopted for the steam dryer stress analysis.
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10.0 REFERENCES
- 1. Email with attachments from George Nelson (TVA) to Marcos Herrera (SI) on 04/22/08 at 9:02 am, "Steam Dryer - Drain Channel," SI File No. BFN-15-224.
- 2. Email with attachment from Rick Cutsinger (TVA) to Soo Bee Kok (SI) on May 20, 2008 @9:02 am, "RE: Weld Structure Evaluation," SI File No. BFN-15-227P.
- 3. Email with attachments from Denzel Housley (TVA) to Soo Bee Kok (SI) on 10/29/08 at 7:31 am, "RE: Editorial Changes to EMCB.199.156 R2", SI File No. BFN-15-229.
- 4. ANSYS Mechanical, Release 11.0 (w/ Service Pack 1), ANSYS, Inc., August 2007.
- 5.
SI Calculation No. 0006982.302, Revision 0, "Project Specific Software Verification and Validation of ANSYS Release 11.0 (w/ Service Pack 1)"
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Appendix A - Computer Files File No.: 0006982.304 Revision: 0 Page A l of A4 F0306-O1 RO
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General Application Filename Description ShellFull.inp Full shell finite element model development input file.
ShellSubl.inp Shell submodel #1 finite element model development input file.
ShellSub2.inp Shell submodel #2 finite element model development input file.
SolidFull.inp Full solid finite element model development input file.
SolidSubl.inp Solid submodel #1 finite element model development input file.
SolidSub2.inp Solid submodel #2 finite element model development input file.
PPpath.mac Stress path generation macro.
Static Load Case #1 Application Filename Description TIE.inp Full shell model baseline analysis for Load Case #1 input file.
C1E.inp Substructure analysis using shell submodel #1 for Load Case #1 input file.
C2E.inp Substructure analysis using shell submodel #2 for Load Case #1 input file.
T2E.inp Substructure analysis using solid submodel #1 for Load Case #1 input file.
T2EPP.inp Substructure analysis using solid submodel #1 for Load Case #1 post processing input file.
T2EPP.xls Substructure analysis using solid submodel #1 for Load Case #1 SRF calculation spreadsheet.
T3E.inp Substructure analysis using solid submodel #2 for Load Case #1 input file.
T3EPP.inp Substructure analysis using solid submodel #2 for Load Case #1 post processing input file.
T3EPP.xls Substructure analysis using solid submodel #2 for Load Case #1 SRF calculation spreadsheet.
T4E.inp Full solid model baseline analysis for Load Case #1 input file.
T4EPP.inp Full solid model baseline analysis for Load Case #1 post processing input file.
T4EPP.xls Full solid model baseline analysis for Load Case #1 SRF calculation spreadsheet.
T5E.inp Submodel stress intensity matching analysis using shell submodel #1 for Load Case #1 input file.
T6E.inp Submodel analysis using solid submodel #1 for Load Case #1 input file.
T6EPP.inp Submodel analysis using solid submodel #1 for Load Case #1 post processing input file.
T6EPP.xls Submodel analysis using solid submodel #1 for Load Case #1 SRF calculation spreadsheet.
T7E.inp Submodel stress intensity matching analysis using shell submodel #2 for Load Case #1 input file.
T8E.inp Submodel analysis using solid submodel #2 for Load Case #1 input file.
T8EPP.inp Submodel analysis using solid submodel #2 for Load Case #1 post processing input file.
T8EPP.xls Submodel analysis using solid submodel #2 for Load Case #1 SRF calculation spreadsheet.
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Static Load Case #2 Application Filenarne Description Filename Description TID.inp Full shell model baseline analysis for Load Case #2 input file.
C1D.inp Substructure analysis using shell submodel #1 for Load Case #2 input file.
C2D.inp Substructure analysis using shell submodel #2 for Load Case #2 input file.
T2D.inp Substructure analysis using solid submodel #1 for Load Case #2 input file.
T2DPP.inp Substructure analysis using solid submodel #1 for Load Case #2 post processing input file.
T2DPP.xls Substructure analysis using solid submodel #1 for Load Case #2 SRF calculation spreadsheet.
T3D.inp Substructure analysis using solid submodel #2 for Load Case #2 input file.
T3DPP.inp Substructure analysis using solid submodel #2 for Load Case #2 post processing input file.
T3DPP.xls Substructure analysis using solid submodel #2 for Load Case #2 SRF calculation spreadsheet.
T4D.inp Full solid model baseline analysis for Load Case #2 input file.
T4DPP.inp Full solid model baseline analysis for Load Case #2 post processing input file.
T4DPP.xls Full solid model baseline analysis for Load Case #2 SRF calculation spreadsheet.
T5D.inp Submodel stress intensity matching analysis using shell submodel #1 for Load Case #2 input file.
T6D.inp Submodel analysis using solid submodel #1 for Load Case #2 input file.
T6DPP.inp Submodel analysis using solid submodel #1 for Load Case #2 post processing input file.
T6DPP.xls Submodel analysis using solid submodel #1 for Load Case #2 SRF calculation spreadsheet.
T7D.inp Submodel stress intensity matching analysis using shell submodel #2 for Load Case #2 input file.
T8D.inp Submodel analysis using solid submodel #2 for Load Case #2 input file.
T8DPP.inp Submodel analysis using solid submodel #2 for Load Case #2 post processing input file.
T8DPP.xls Submodel analysis using solid submodel #2 for Load Case #2 SRF calculation spreadsheet.
General Dynamic Analysis Application Filename Description THIE.inp Full shell model modal analysis input file.
Damping.xls Alpha and beta damping coefficient calculation spreadsheet.
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Dynamic Load Case #1 Application Filename Description TH2F.inp Full shell model baseline time history analysis for Load Case #1 input file.
TH2FPI.inp Full shell model baseline analysis for Load Case #1, 1st post processing input file.
TH2FP2.inp Full shell model baseline analysis for Load Case #1, 2nd post processing input file.
TH3F.inp Substructure analysis using shell submodel #2 for Load Case #1 input file.
TH6F.inp Substructure analysis using solid submodel #2 for Load Case #1 input file.
TH6FPP.inp Substructure analysis using solid submodel #2 for Load Case #1 post processing input file.
TH6FPP.xls Substructure analysis using solid submodel #2 for Load Case #1 SRF calculation spreadsheet.
TH4F.inp Submodel stress intensity matching analysis using shell submodel #2 for Load Case #1 input file.
TH5F.inp Submodel analysis using solid submodel #2 for Load Case #1 input file.
TH5FPP.inp Submodel analysis using solid submodel #2 for Load Case #1 post processing input file.
TH5FPP.xls Submodel analysis using solid submodel #2 for Load Case #1 SRF calculation spreadsheet.
Dynamic Load Case #2 Application Filename Description TH2G.inp Full shell model baseline time history analysis for Load Case #2 input file.
TH2GP1.inp Full shell model baseline analysis for Load Case #2, 1 st post processing input file.
TH2GP2.inp Full shell model baseline analysis for Load Case #2, 2nd post processing input file.
TH30.inp.
Substructure analysis using shell submodel #2 for Load Case #2 input file.
TH6G.inp Substructure analysis using solid submodel #2 for Load Case #2 input file.
TH6GPP.inp Substructure analysis using solid submodel #2 for Load Case #2 post processing input file.
TH6GPP.xls Substructure analysis using solid submodel #2 for Load Case #2 SRF calculation spreadsheet.
TH4G.inp Submodel stress intensity matching analysis using shell submodel #2 for Load Case #2 input file.
TH5G.inp Submodel analysis using solid submodel #2 for Load Case #2 input file.
TH5GPP.inp Submodel analysis using solid submodel #2 for Load Case #2 post processing input file.
TH5GPP.xls Submodel analysis using solid submodel #2 for Load Case #2 SRF calculation spreadsheet.
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ENCLOSURE 7 TENNESSEE VALLEY AUTHORITY BROWNS FERRY NUCLEAR PLANT (BFN)
UNITS 1, 2, AND 3 TECHNICAL SPECIFICATIONS (TS) CHANGESTS-431 AND TS-418 EXTENDED POWER UPRATE (EPU)
CDI AFFIDAVIT Attached is the CDI affidavit for the proprietary information contained in Enclosures 2, 3, 4, and 5.
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