ML15280A309
| ML15280A309 | |
| Person / Time | |
|---|---|
| Site: | Davis Besse  |
| Issue date: | 09/03/2014 |
| From: | FirstEnergy Nuclear Operating Co |
| To: | Advisory Committee on Reactor Safeguards |
| Shared Package | |
| ML15280A293 | List: |
| References | |
| L-15-310, TAC ME4640 C-CSS-099.20-63, Rev 1 | |
| Download: ML15280A309 (71) | |
Text
FirstEnercw Page i
CALCULATION NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 INITIATING DOCUMENT CA-2011-03346-15
[ ] VENDOR CALC
SUMMARY
VENDOR CALCULATION NO.
D BV1 D
BV2 DB D
PY Title/
Subject:
Shield Building Design Calculation Category Active Historical
Study Classification U Tier 1 Calculation Safety-Related/Augmented Quality Nonsafety-Related Open Assumptions?
Yes No If Yes, Enter Tracking Number System Number DB-SUB099.20 Functional Location N/A Commitments:
None (Perry & Davis-Besse Only)
Calculation Type:
N/A Referenced In Atlas?
Yes No (Perry Only)
Referenced In USAR Validation Database
[] Yes D No Computer Program(s Program Name Version
/ Revision Category Status Description ANSYS 13.0 Active Finite Element
- Analysis, validated under Bechtel's QA Program MathCAD 15.0 Active Mathematical computation Revision Record Rev.
000 Rev.
001 Rev.
002 Affected Pages All Originator (Print, Sign & Date)
Signatures on File Reviewer/Design Verifier (Print, Sign & Date)
Signatures on File Description of Change:
Initial issue Approver (Print, Sign & Date)
Signatures on File Initiating Document:
Describe where the calculation will be evaluated for 10CFR50.59 applicability:
RAD/Screen 13-00918 Affected Pages Body:
i-iv, vi,
- vii, 1-12, 17, 23-24, 44, 52, 62 Att. A:
1-3, 11-12, 16 Att.
I: ALL Att. J:
11 Att.
N: 4, 5, 6 Att. O: ALL Originator (Print, Sign & Date)
Thomas A. Henry Reviewer/Design Verifier (Print, Sign & Date)
Richard N. Bair Description of Change: Incorporation of Addendum 01 & changes due to crack propagation Approver (Print, Sign & Date)
Initiating Document:
CA-2013-14097-003 Describe where the calculation will be evaluated for 10CFR50.59 applicability.
RAD/Screen 13-00918 Revision 2 Affected Pages Originator (Print, Sign & Date)
Reviewer/Design Verifier (Print, Sign & Date)
Description of Change Approver (Print, Sign & Date)
Initiating Document:
Describe where the calculation will be evaluated for 10CFR50.59 applicability.
FirstEnercjv CALCULATION Page NOP-CC-3002-01 Rev. 03 CALCULATION NO.
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VENDOR CALCULATION NO.
TABLE OF CONTENTS COVERSHEET:
OBJECTIVE OR PURPOSE SCOPE OF CALCULATION
SUMMARY
OF RESULTS/CONCLUSIONS LIMITATIONS OR RESTRICTION ON CALCULATION APPLICABILITY IMPACT ON OUTPUT DOCUMENTS DOCUMENT INDEX CALCULATION COMPUTATION (BODY OF CALCULATION):
ANALYSIS METHODOLOGY ASSUMPTIONS ACCEPTANCE CRITERIA COMPUTATION RESULTS CONCLUSIONS ATTACHMENTS:
A. Evaluation of the Seismic Load Considering the Observed Laminar Cracking of the SB B. P-M Interaction Curves C. Thermal Moments D. Strength Design Check of the Shield Building E. Reinforcement / Concrete Stresses and Crack Width F. Tornado and Wind Loads G. ANSYS Static Analysis Input and Output H. ANSYS 13.0 Validation Report I. In-Plane Shear Check J. Shield Building Sectional Analysis K. Evaluation of Temperature Rise in a Concrete Wall Exposed to High Energy Line Breaks L.
ACI Code Compliance of Shield Building with Observed Laminar Cracking M. Memos from Outside Industry Experts N. Comment Resolution to Comments from 3rd Party Reviewers
- 0. Memo of Review for Revision 1
SUPPORTING DOCUMENTS (For Records Copy Only)
DESIGN VERIFICATION RECORD CALCULATION REVIEW CHECKLIST DESIGN INPUT RECORD DESIGN INTERFACE
SUMMARY
DESIGN INTERFACE EVALUATIONS 50.59 DOCUMENTS (RAD/50.59 No. 13-00918)
OTHER:
i iv iv iv iv iv V
3 9
9 12 25 62 58 32 14 1
212 4
1 8
2 29 4
13 5
6 4
1 Page 3 Pages 4 Pages 7 Pages 2 Pages 31 Pages
FirstEnerav CALCULATION Page NOP-CC-3002-01 Rev. 03 CALCULATION NO.
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VENDOR CALCULATION NO.
EXTERNAL MEDIA? (MICROFICHE, ETC.) (IF YES, PROVIDE LIST IN BODY OF CALCULATION)
M YES
NO TOTAL NUMBER OF PAGES IN CALCULATION (COVERSHEETS + BODY + ATTACHMENTS)
NOTES:
464 PAGES
FirstEnerav CALCULATION Page iv NOP-CC-3002-01 Rev. 03 CALCULATION NO.
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OBJECTIVE OR PURPOSE:
The purpose is to develop a new design calculation for the existing Shield Building (SB) including the cylindrical
- wall, the dome and the springline
- area, for the design basis events in wake of the observed laminar cracking, which are documented in Refs.
19a~19e, 25, and 27-35.
This calculation accounts for the observed laminar cracking as described in Section 3.0.
SCOPE OF CALCULATION/REVISION:
In this calculation, the analysis is performed with a three dimensional (3D) linear elastic Finite Element (FE) model of the Shield Building using ANSYS.
The model represents the entire Shield Building structure including the cylindrical wall, dome and the spring line area.
The Shield Building is modeled using a fixed base boundary condition at Elevation 565' without the basemat being included.
The model is created using shell elements SHELL181(Ref.12).
As such, membrane, shear and bending forces reported by shell elements are calculated using elastic shell theory, which is consistent with the analytical techniques specified in USAR Section 3.8.2.2.
The new calculation does not replace the existing design evaluations for the areas near the penetrations and permanent openings, and the foundation.
The effect of the observed laminar cracking is incorporated into the analysis and design per Section 3.0.
This section addresses the effect of the laminar cracking on stiffness, strength, serviceability and long-term durability of Davis-Besse Shield Building for use in this design-basis calculation.
All applicable design loads and load combinations specified in the USAR are included in the finite element analysis. Thermal stresses are calculated per ACI 307-69 and combined with stresses resulting from mechanical loads. The design of the Shield Building is carried out in accordance with ACI 307-69 and ACI 318-63.
A sectional analysis is also performed following the methodology of ACI 307-69 and ACI 318-63 to address the construction sequence and influence of Reactor Vessel Closure Head (RVCH) and Steam Generator Replacement (SGR) openings.
The original tornado missile impact (penetration) analysis, which is described in USAR Subsection 3.5.8 and listed in Ref.
1, Table 3.3-2 and Ref.
2, Table I.D.3.2-3, is still valid.
In this calculation, the SB wall is checked against the maximum penetration depth listed in Ref.
1, Table 3.3-2 and Ref.
2, Table I.D.3.2-3 assuming conservatively that the outer concrete cover affected by the laminar cracking does not provide any resistance against tornado missiles.
SUMMARY
OF RESULTS/CONCLUSIONS:
This calculation presents new design calculation for the existing Shield Building including the cylindrical wall, the dome and the springline
- area, under the design basis events for the observed laminar
- cracking, which are documented in Refs. 19a~19e, 25 and 27-35.
It is concluded that the Shield Building with observed laminar cracking meets all design requirements specified in USAR and will perform its USAR described design functions.
LIMITATIONS OR RESTRICTIONS ON CALCULATION APPLICABILITY:
The use of this calculation is limited to Davis-Besse Shield Building with the observed cracking condition, which are documented in Refs. 19a~19e, 25, and 27-35. The effect of construction openings and their closures are also addressed in the calculation. See also Section 2.0.
IMPACT ON OUTPUT DOCUMENTS:
No system descriptions are affected by this calculation.
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DOCUMENT INDEX DIN No.
1 2
3 4
56 7a 7b 7c 7d7e7f7g 7h 7i8a8b 8c8d8e Document Number/Title UpdatedSafetyAnalysisReport(USAR)forDavis-Besse NuclearPowerStationNo.1 Davis-BesseNuclearPowerStationUnit1Design CriteriaManual BechtelLetter/FileNo.
25539-000-TCM-GEG-00015,17 Mid-CycleOutageand18RFOConstructionOpening Dimensions BechtelLetter/FileNo.
25539-000-TCM-GEG-00040, ContainmentVesselandShieldBuildingOpeningSizesinSupportofTornadoDepressurizationAnalyses NRCReg.Guide1.29,SeismicDesignClassification NRCReg.Guide1.76,Design-BasisTornadoand TornadoMissilesforNuclearPowerPlants DrawingNo.7749-C-109,ShieldBuildingRoofPlan&
DetailsSheet1 DrawingNo.7749-C-110,ShieldBuildingRoofPlanWall Section&Details DrawingNo.7749-C-111,ShieldBuildingWall Development DrawingNo.7749-C-112,ShieldBuildingDetailsSheet1 DrawingNo.7749-C-113,ShieldBuildingDetailsSheet2 DrawingNo.7749-C-115,ShieldBuildingBlockout Details DrawingNo.C-0112A,ShieldBuildingTemporary ConstructionOpeningRestorationDetails DrawingNo.7749-A-8,Shield,Turbine,Auxiliary,Off.BLDGS.GeneralFloorPlanEL643'-0" DrawingNo.7749-C-230,AuxiliaryBuilding SuperstructureSectionC&Details OriginalCalculationNo.VC01/B01-01,ShieldBuilding-ThermalStresses-ShieldWall FENOCCalculationNo.VA08/B001-001,Structuraleffectsofhighenergylineruptures(Compartment pressurizationanalysis)
OriginalCalculationNo.VS01/B01-03,SeismicAnalysisoftheContainmentStructure OriginalCalculationNo.VC03/B01-04,ShieldBuildingWallatBaseFloorFENOCCalculationNo.C-NSA-000.02-016,36InchMainSteamLineBreakinRooms601and602 Rev.2 Rev.0 Rev.6 Rev.6 Rev.11 Rev.10 Rev.11 Rev.4 Rev.0 Rev.20 Rev.9 Rev.0,ApprovalDate10/01/1976 Rev.O Rev.0,ApprovalDate10/04/1976 Rev.0,ApprovalDate10/06/1976 Rev.00 Reference IS IS D
Input D
IS M
IS
El E
IS Output
D
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8f FENOC Calculation No.
C-NSA-000.02-005, Main Feedwater Line Breaks and Cracks in the Auxiliary Building Rev.02
8g FENOC Calculation No.
C-NSA-000.02-006, Steam Generator Blowdown Line Breaks in the Auxiliary Building Rev.01 8h FENOC Calculation No. C-NSA-000.02-007, Main Steam to AFW Pump Turbine Line Breaks and Cracks In the Auxiliary Building Rev.02
8i FENOC Calculation No.
C-NSA-000.02-009, Auxiliary Steam Line Breaks and Cracks in the Auxiliary Building Rev.02
8j FENOC Calculation No.
C-NSA-000.02-012, Auxiliary Building HELB Pressure Analysis Using Gothic 7.0 Rev.01
8k FENOC Calculation No.
60.013, Shield Bldg.
Annulus Pressure Drop Due to Cold WTR Pipe Rupture Rev.
1
9a ACI 307-69, Specification for the Design Construction of Reinforced Concrete Chimneys and 1969
9b ACI 318-63, Building Code Requirements for Reinforced Concrete 1963
9c ACI 349-76, Code Requirements for Nuclear Safery Related Concrete Structures 1976
9d ACI 349.1 R-07, Reinforced Concrete Design for Thermal Effects on Nuclear Power Plant Structures 2007 10 ASCE Paper No. 3269, Wind Forces on Structures 1961
11 FENOC Calculation No.
C-CSS-099.20-045, Evaluation of Shield Building for the Construction Opening - SGR-RVCH replacement Rev.O
12 ANSYS manual Version 13.0
13 Park and Paulay, 1975. Reinforced concrete structures 1975
14 ASME Section III Code, Articles I-2, I-3 and I-7 1968
15 ECP-10-0458, SGR-17M-Shield Building Construction Opening Rev.O
16 ACI Publication SP-20, Causes, Mechanism and Control of Cracking in Concrete 1968
17 FENOC Design Input Record and Design Interface Evaluation for Shield Building Design Calculation C-CSS-099.20-063 7/17/2013
18 Not Used
D 19a FENOC CR-2011-03996, Extent of Condition for Shield Building Fracture Indications Rev. 0 19b FENOC CR-2011-04402, Fractured Concrete Found at 17M Shield Building at Main Steam Line Penetration Rev. 0 19c FENOC CR-2011-04507, Isolated Crack Indication Identified by Impulse
Response
Testing of the Shield Building Rev. 0
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19d FENOC CR-2011-04648, Shield Building IR Indications above Elevation 780 Rev. 0 D
D 19e FENOC CR-2011-03346, Fractured Concrete Found at 17M Shield Building Construction Opening Rev. 0
19f FENOC CR-2013-09122, Design Criteria Manual Discrepancy Rev. 0
20 Commentary on Building Code Requirements for Reinforced Concrete (ACI 318-63)
21
- Ferguson, P.M.,
and
- Thompson, J.N.,
"Development Length of High Strength Reinforcing Bars in Bond," ACI
- Journal, Proceedings V.
59, No.
7, July
- 1962, pp.
887-922 1962
22
- Ferguson, P.M., and Matloob, F.N., "Effect of Bar Cut-off on Bond and Shear Strength of Reinforced Concrete Beams,"
- Journal, Proceedings V.
56, No.
1, July 1959, pp. 5-24 1959
23 Watstein, D., and Mathey, R.G., "Investigation of Bond in Beam and Pull-out Specimens with High Yield Strength Deformed Bars," ACI Journal, Proceedings V. 57, No. 9, March 1961, pp. 1071-1090 1961
24 Bechtel Report 25593-000-G83-GEG-00016, Effect of Laminar Cracks on Splice Capacity of No.
11 Bars based on Testing Conducted at Purdue University and University of Kansas for Davis-Besse Shield Building 2012 25 Doc No. 25593-000-GQT-GEG-00001, Shield Building Exterior Elevation IR Test Data Through 24 July 2012 7/24/2012
26 U.S. Army, Manuals-Corps of Engineers, EM 1110 2502 1961
27 FENOC CR-2013-13782, Shield Building Core Bore S5-666.0-10 findings Rev. 0 D
28 FENOC CR-2013-13854 Shield Building Core Bore S7-666.0-7 findings Rev. 0
29 FENOC CR-2013-13860 Shield Building Core Bore S7-666.0-7 findings Rev. 0
30 FENOC CR-2013-14097 Shield Building laminar crack extends Rev. 0
31 FENOC CR-2013-14623 Shield Building Core Bore S13-633.0-11 findings Rev. 0
32 FENOC CR-2013-16204 Shield Building Core Bore S15-646.5-8 findings Rev. 0
33 FENOC CR-2013-16210 Shield Building Core Bore S15-674.5-3 findings Rev. 0
34 FENOC CR-2013-14961 Shield Building Core Bore S4-773-16 findings Rev. 0
35 FENOC CR-2013-16211 Shield Building Core Bore S15-777-3 findings Rev. 0
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- NOTE:
In this calculation, reference indices presented in Section 6.0 are used in lieu of the document index (Dl) listed above.
FirstEnergy CALCULATION COMPUTATION Page 1
NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 TABLE OF CONTENTS COVER SHEET i
TABLE OF CONTENTS 1
LIST OF ATTACHMENTS 2
1.0 PURPOSE OF CALCULATION 3
2.0
SUMMARY
OF CONCLUSION 3
3.0 METHODOLOGY 3
4.0 ASSUMPTIONS 9
5.0 ACCEPTANCE CRITERIA 9
6.0 DESIGN INPUTS / REFERENCES 10 7.0 BODY OF CALCULATION 12 7.1 Description of the Shield Building 12 7.2 Material Properties 12 7.3 Finite Element Model 14 7.4 Design Loads and Load Combinations 15 7.5 Finite Element Analysis Results 25 7.6 Thermal Moments 28 7.7 P-M Interaction Diagram and Demand to Capacity Ratios 30 7.8 Reinforcement and Concrete Stresses Evaluation 44 7.9 Shear Evaluation 51 7.10 Maximum Concrete Crack Width 52 7.11 Tornado Missile Impact Evaluation 52 7.12 Construction Sequence and Sectional Analysis 52
8.0 CONCLUSION
62
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001 LIST OF ATTACHMENTS Att.
A B
C D
E F
G H
I J
K L
M N
0 Evaluation of the Seismic Analysis Loading Considering the Observed Laminar Cracking of the Shield Building P-M Interaction Curves Thermal Moments Strength Design Check of the Shield Building
(*)
Reinforcement / Concrete Stresses and Crack Width Tornado and Wind Loads ANSYS Static Analysis Input and Output (*)
ANSYS 13.0 Validation Report (*)
In-Plane Shear Check Shield Building Sectional Analysis Evaluation of Temperature Rise in a Concrete Wall Exposed to High Energy Line Breaks ACI Code Compliance of Shield Building with Observed Laminar Cracking Memos from Outside Industry Experts Comment Resolution to Comments from 3rd Party Reviewers Memo of Review for Revision 1
No. of Pages 58 32 14 1
212 4
1 8
2 29 4
13 5
5 4
Revision 001 000 000 000 000 000 000 000 001 001 000 000 000 001 000
- Note:
CD is provided for Attachments D, G and H
RrsflEnergy CALCULATION COMPUTATION Page 3 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 1.0 PURPOSE OF CALCULATION The purpose of this document is to develop a
new design calculation for the existing Shield Building (SB)
(including the cylindrical wall, the dome and the springline area), for the design basis events to include the effect of the observed laminar cracking.
During the removal of concrete in the Shield Building for Reactor Vessel Closure Head replacement at the Davis-Besse nuclear plant, laminar cracking was observed in the plane of the outer reinforcement mat consisting of No.
10 vertical bars and No.
11 hoop and vertical bars.
A detailed condition assessment was carried out to determine the extent of cracking as described in Refs. 19a~19e and 25.
This evaluation indicated that cracking is present in most of the architectural flute shoulders, two steam line penetration areas and within several locations of the top 20 ft of the Shield Building cylinder.
During inspections of the Shield Building as part of Long-Term Monitoring of this condition, it was determined that the laminar cracking condition propagated in several shoulder regions of the structure. This is documented in References 27-35.
2.0
SUMMARY
OF CONCLUSION A new design calculation is performed for the existing Shield Building that includes the cylindrical wall, the dome and the springline area, with observed laminar cracking for all design basis loads.
In the new design calculation, the Shield Building with the observed laminar cracking meets the acceptance criteria described in Section 5.0 as follows:
Methodologies applied in this calculation are consistent with those specified in the ACI codes, Design Criteria Manual (DCM) and USAR.
Load combinations are in accordance with DCM and USAR requirements.
Results are demonstrated to meet the code requirements specified in ACI 318-63 and ACI 307-69. Code compliance details are summarized and presented in Table 42 and Attachment L.
It is concluded that the Shield Building with observed laminar cracking meets all design requirements specified in USAR and will perform its USAR described design functions.
The identified crack propagation consisted of cracks with widths bounded by the previously identified cracking.
The planer limits of cracking have also been determined to be bounded by the previously considered cracking.
Therefore, these additional areas of cracking do not adversely affect the existing structural evaluation.
The limiting factors within this calculation with respect to crack propagation are the structural stiffness calculations of Attachment A, and the analyzed conditions of DIN 24 "Bechtel Report 25593-000-G83-GEG-00016, Effect of Laminar Cracks on Splice Capacity of No.
11 Bars based on Testing Conducted at Purdue University and University of Kansas for Davis-Besse Shield Building". Since the cracking widths are bounded by the previously identified cracking, the rebar splice capacity does not require modification. Additionally, since the planer limits of cracking are bounded by the previously considered
- cracking, there is no modification required to the stiffness and seismic loading distributions documented in Attachment A.
3.0 METHODOLOGY 3.1 Laminar Cracking
FirstEnerav CALCULATION COMPUTATION Page 4 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 During the removal of concrete in the Shield Building for Reactor Vessel Closure Head (RVCH) replacement at Davis-Besse nuclear plant, laminar cracking was observed in the plane of the outer reinforcement mat consisting of No.
10 vertical bars and No.
11 hoop and vertical bars.
A detailed condition assessment was carried out to determine the extent of cracking as described in Refs. 19a~19e and 25.
During inspections of the Shield Building as part of Long-Term Monitoring of this condition, it was determined that the laminar cracking condition propagated in several shoulder regions of the structure, specifically, Shoulders 4, 5,
7, 13, 15 have extended cracks (i.e.
crack propagation) in the plane of the outer main steel reinforcement mat of the building. This is documented in References 27-35.
Initially detailed technical evaluation was carried out to determine the effect of laminar cracking on the structural capacity of the Shield Building to resist its design basis loads as described in Section 4 of Ref.24.
This technical evaluation concluded that effect of laminar cracking on the structural capacity of the Shield Building to resist its design basis loads should be minimal, if any.
Two concrete industry experts Prof. Sozen and Prof. Darwin were retained to provide an independent opinion on the effect of laminar cracking on the structural capacity of the Shield Building.
Both experts agreed with the technical evaluation but recommended that the only issue to be further evaluated would be the effect of laminar cracking on the lap splices of No.
11 bars especially for the outer hoop reinforcement (Ref. 24).
The above recommendations by the outside industry experts were investigated by developing a detailed testing program as described in Ref. 24.
In order to ensure a
reliable set of
- results, Prof.
Mete Sozen of Purdue University and Prof.
David Darwin of University of Kansas were engaged to carry out a series of lap splice tests independently.
The test programs involved the following:
Purdue test program (Ref.
24) involved 6
beams with 79 inches lap splices and 6
beams with 120 inch lap splices.
In order to simulate laminar cracking in the plane of the bars, the splices were placed at 6 in spacing with a side cover of 3 inches.
A laminar crack of 0.01 inches or larger was initiated by loading of up to yield and subsequent unloading.
Kansas test program (Ref.
24) involved 3
beams with 79 inches lap splices and 3 beams with 120 inch lap splices.
The first beam with 79 in splice was cast monolithically as a benchmark.
In order to simulate laminar cracking in the plane of the bars, the remaining 5 beams were cast in two lifts; one up to the center of the bars and the second pour the next day to complete the casting to top of the beam.
This process allowed formation of a cold joint in the plane of the bars which would serve as a weak plane and help initiate a laminar crack at the designated location during testing. The reinforcement cover of 3 inches was maintained both on the sides and to the top surface of the beam.
The laminar crack of 0.010 inches or larger was initiated in the specimen by loading and subsequent unloading.
Both Purdue and Kansas beams had 2 reinforcement splices side by side (i.e. non-staggered) within 6 inches of spacing which presents a
conservative condition and likely to give lower bound capacity results.
Note that splices in the Shield Building are actually staggered by at least 12 inches.
Also, the splices in the Shield Building conform to the curvature of the building which provides an additional confinement effect not included in the straight beam tests.
In both test programs at Purdue and Kansas, an effort was made to simulate the concrete mix of the Shield Building to the extent possible.
Since it was practically impossible to exactly match the concrete strength given the age of the
- plant, every effort was made to test at relatively lower (conservative) compressive strength and tensile strength values to produce conservative bond capacity values.
Note that compressive strength and more importantly, tensile strength of concrete are recognized to be the key parameters of influence for bond strength of reinforcement in concrete.
Moreover, Kansas tests were carried out at an age of only 7
days which resulted in lower bound compressive and tensile strengths thus giving very conservative or lower-bound results.
The average 28 day compressive strength from original concrete construction of the Shield Building was 5836 psi. The average compressive strength of recent in-place concrete tested using cores taken during the Shield Building evaluation in 2011 was 7571 psi.
The corresponding tensile strength of in-place concrete was determined to be 918 psi.
In contrast, the compressive strength of the beams
FirstEnejgv CALCULATION COMPUTATION Page 5 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
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001 tested in Purdue varied from approximately 4500 to 6000 psi; while the compressive strength of the beams tested in Kansas varied from approximately 4300 to 5300 psi.
The testing at Purdue confirmed that No.
11 bars with a crack in the plane of the bars will be able to develop their full yield both for 79 inches splice as well as 120 inches splice.
This is despite the fact that beams were pre-cracked with 1st cycle loading and had splices next to each other (not staggered) at only 6 inches spacing.
The testing at University of Kansas confirmed that No.
11 bars with a simulated crack (involving a cold joint that is pre-cracked) will be able to develop near yield (57 and 62 ksi) for 79 inches splice and full yield for 120 inches splice.
It should be noted that these results are based on a conservative test condition of splices next to each other at 6 inches spacing (actual spacing for splices is larger).
Furthermore, Kansas tests were carried out at a concrete age of only 7 days with concrete strengths much lower than concrete in actual structure.
As indicated in Prof.
Darwin's memorandum (see Section 8.8 of Ref.
24),
as the spliced bar reaches its full
- capacity, the adjacent continuous bar with yield of 67 ksi (larger than specified 60 ksi for Shield Building) is likely to pick up the remainder load and continue to carry it until yield and beyond.
This will obviously increase the load capacity of the group of spliced bar and continuous bar adjacent to it to beyond 60 ksi on an average basis.
From the independent test programs carried out at two separate labs under the direction of two industry experts it was concluded that No.
11 bars with a crack in the plane of the bars will develop their full yield capacity.
3.2 Effect of Laminar Cracking on Shield Building STIFFNESS -
Detailed inspection and Impulse
Response
(IR) testing of the Shield Building confirmed that observed cracking is laminar and generally runs along the outer reinforcement mat, occasionally meandering in and out of the outer rebar mat and generally affecting 3 inches of cover thickness.
The cracking is tight (of the order of 0.013 inches or less) and exists only in the flute shoulder areas, the two steam penetration areas and in portions of the shell above El 780 ft for about 20 ft of the building height.
Based on this and the fact that load-deflection curves in Ref.
24 do not indicate any significant change in reloading stiffness of specimen after introduction of the laminar crack, it can be safely concluded that the effect of laminar cracking on the overall stiffness of the Shield Building will be minimal and can be neglected.
Note that for the controlling load combinations involving the design basis safe shutdown earthquake, the cylinder will tend to behave like a
cantilever where most of the forces are transferred through in-plane shear and very little through out-of-plane bending of the shell.
The laminar cracking will have no impact on in-plane stiffness of the shell, which will carry the majority of seismic forces.
For thermal and tornado loading producing hoop tension and moment, again the laminar cracking is of no significance as the concrete shell is assumed to be cracked through-thickness unable to resist tension forces.
These tension forces are primarily resisted by the hoop reinforcement in the shell. Based on above, it is concluded that no changes need to be made to the model in order to account for the effect of laminar cracking on stiffness of the Shield Building.
Furthermore in Attachment A,
different FE models with different levels of the laminar concrete cracks are examined based on the latest IR test results (Ref. 25). Attachment A, Revision 0 considered the laminar cracking condition was passive.
Given the findings of References 27-35 this is no longer applicable.
Based on the calculated natural frequencies and mode shapes for each FEM, it is demonstrated that the effect of observed laminar cracks identified in reference 25 on the dynamic behavior of the SB is insignificant.
Based on the locations of the crack propagation, the effect on the existing model is not impacted.
It is documented in Attachment A,
Revision 1
that the identified areas of crack propagation are located in areas previously considered to be cracked and they are enveloped in this model..
STRENGTH - As indicated in the detailed technical evaluation (Ref.
24), the effect of laminar cracking on the structural capacity of the Shield Building to resist its design basis loads should be minimal, if any.
The only issue to be confirmed was to evaluate the effect of laminar cracking on the splices of No.
11 bars; especially for the outer mat of hoop reinforcement.
Note that vertical splices are staggered and also confined by the outer hoop
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001 reinforcement.
Therefore, the vertical splices are inherently capable of performing better than splices located in the outer mat of hoop reinforcing steel.
In other words, the outer hoop splice locations represent the critical elements (relative to the cracking) in the structure and were chosen to be tested and evaluated for any possible strength reduction effects.
However, and as indicated above, testing carried out at Purdue (Ref. 24), confirmed that maximum reinforcement stresses in the test girders loaded to failure after having been loaded to develop bursting (laminar) cracks and then reloaded; reached their design yield strength despite the conservative test conditions simulated compared to that in the actual structure.
Testing at Kansas (Ref. 24) indicated that in the presence of laminar cracks, it would be conservative to conclude that lap-spliced No.
11 bars with a 79 inch splice length can achieve bar stresses on the order of 55 ksi or more and lap-spliced No.
11 bars with a 120 inch splice length can achieve yield with bar stresses in excess of 60 ksi.
- Again, this result was based on a
conservative test simulation as compared to the actual condition present in the Shield Building structure (Ref.
24).
Based on above discussion, and to remain conservative, it is prudent to use a stress limit of 55 ksi for the 79 inches outside mat horizontal reinforcement splices in the cracked regions (refer to Prof. Darwin's memo in Ref.
24),
between EL.
569' and EL.
780' of the Shield Building wall.
This would result in a
capacity reduction of approximately 8%
at these locations.
All other splices will have their full specified yield strength available for design as demonstrated by the testing results.
SERVICEABILITY AND CRACK CONTROL - Per applicable Codes (ACI 307-69 and ACI 318-63), serviceability essentially relates to crack control under service load conditions.
Service life of the structure can be affected by the
- nature, extent and width of cracking present on the surface of the structure that may provide a path for moisture penetration resulting in reinforcement corrosion.
The cracking could be due to shrinkage which has no structural consequence but could result in leak tightness issues and also long-term corrosion problems.
For cracking induced by applied loads such as flexure or hoop tension, the primary objective is to limit the crack width to less than 0.01 inches per USAR in order to limit potential moisture paths that lead to corrosion of reinforcing steel.
The detailed condition assessment of Shield Building did not indicate any unusual surface cracking due either to shrinkage or flexure that would provide a potential path for moisture to penetrate and cause reinforcement corrosion.
Any surface cracks observed were much tighter than 0.01 inches.
The concrete near the outer rebar mat did not show any unusual levels of carbonation or moisture infiltration.
Also, the outer reinforcement mat of the shell in the access opening was inspected and no unusual corrosion activity was detected. The moisture identified as part of the laminar cracking propagation has been analyzed under DIN 30 and determined to have a
high pH value.
The exposure of to high pH water is not conducive to generate corrosion in the rebar.
This is due to the passivizing nature of high alkaline environments.
Therefore, serviceability of the Shield Building is not affected and the laminar cracks will not have any impact on serviceability.
Note that the Shield Building has been coated to prevent moisture infiltration.
LONG-TERM DURABILITY - Most of the cracking below EL. 780' is in the flute shoulders.
The flute shoulders serve as additional concrete cover for the reinforcement at regular intervals around the main cylindrical shell.
Laminar cracks observed inside and outside the shoulder regions in the cylindrical shell are all tight (of the order of 0.013 inches or less) and do not seem to provide a path to the surface for potential air/moisture migration.
There was no evidence of any significant cracking on the surface of the shell or any noticeable corrosion on the reinforcement located in the cracked regions.
With the exception of the laminar cracking propagation identified in
- 2013, the initial laminar crack condition observed is believed to have existed for a number of years within the thickness of the concrete in the flute shoulder regions without any significant corrosion.
Based on observations and rebar embedment in
- concrete, there is no loss of protection for the reinforcement against environmental corrosion (Ref 30).
It is again noted that the Shield Building was recently coated for protection against moisture infiltration.
Refer to Reference 30 for additional discussion on Shield Building coatings.
3.3. Discussion on Code Compliance
FirstEn&gy CALCULATION COMPUTATION Page 7 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 The laminar cracking observed in the SB is an unusual situation where the crack exists in the plane of the outer reinforcement layer. Although there is a significant amount of test data on reinforcement bond development which forms the basis of the current ACI Code criteria, the effect of such laminar cracking on the bond transfer capacity of the reinforcement has not been evaluated.
In order to understand and evaluate the bond transfer capacity of reinforcement with a crack in the plane of the rebar, a detailed test plan was developed to determine the bond transfer mechanism and capacity of reinforcement with a simulated crack in the plane of the reinforcement. The confirmatory tests were carried out using the same procedure, means, and methods as are typically used for testing of reinforcement and bond transfer capacity that forms the basis of the ACI Code provisions. The tests were performed at well renowned laboratory facilities under the guidance of well-known subject matter experts. These tests are considered routine development and bond tests and are considered "confirmatory" in the sense that they follow the same process and procedures that are typically used for development and bond of reinforcement and are intended to confirm the effect of one of the aspects (cracking) on behavior and capacity.
The commentary to ACI 318-63 (Ref. 20) includes References 21-23 as supporting documentation for the description of the basis for the ACI 318-63 Code provisions related to bond and tension splices, and References 21-23 describe the test methods and procedures used to establish the bond transfer capacity of reinforcement.
Based on a thorough review of References 21-23, it is concluded that the methods and procedures used to perform the confirmatory tests are consistent with those described in References 6-8 and comply with the ACI 318-63 Code provisions. Therefore, the confirmatory tests carried out are deemed to be acceptable from the Code perspective, as are the development and bond tests that form the basis for the ACI Code provisions. The level of quality associated with the testing is acceptable for the test data to be used as design input to a safety-related calculation.
Purdue testing indicated that No.
11 spliced bars develop their nominal yield of 60 ksi and actual yield which is well above 60 ksi even with a simulated crack present in the plane of the bars.
However, Kansas testing, where a cold joint was formed in the plane of the bars indicated that under aggressive test conditions (of a preformed crack after first cycle at the cold
- joint, early age testing of less than 7
days after casting of concrete and conservative test set up involving two spliced bars next to each other) indicated that the some bars may not reach their specified yield.
The strength limit of 55 ksi was chosen as a
lower bound value based on Prof.
Darwin's memo and recommendation.
As indicated
- above, these tests were performed using a
bond and development test procedure that is typically used for such tests and forms the basis for the Code equations.
Note that the Code specified value of 60 ksi is to provide a general limiting strength for design.
The actual yield is generally higher and is not used in the design.
In that sense, the 55 ksi limit provides a similar but an even lower limit for design that was developed conservatively using the acceptable test protocol and is thus consistent with the Code.
Note that this lower bound value of 55 ksi actually only applies to outside layer hoop bars with 79 inches splices where the spliced region is cracked.
The fact is that hoop bar splices in the Shield Building are staggered so that no two splices are next to each other as simulated in the test set up.
Since the alternate bars are actually continuous, they are expected to go beyond their specified yield of 60 ksi and achieve their actually yield which is much higher (-67 ksi) based on Purdue testing.
Therefore, on the average any set of two bars next to each other (one spliced and other continuous) will achieve at least their specified yield of 60 ksi per Code but to be on a conservative side, only 55 ksi is used for design.
The identification of laminar cracking propagation does not impact the test methods or procedures used to establish the bond transfer capacity of reinforcement.
Therefore there are no changes to the analysis as a result of this finding.
3.4 Summary Position The laminar cracking will not affect the in-plane stiffness of the
- shell, which is the primary force transfer mechanism for the design basis seismic (SSE) and wind loadings.
- Further, the laminar cracking observed is tight enough and will be able to transfer whatever little out-of-plane moment is generated due to these lateral loads.
For thermal and tornado loads that produce hoop tension and moment, again the laminar cracking is of
Page 8 CALCULATION COMPUTATION NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 no significance as the concrete shell is assumed to be cracked though-thickness thus unable to carry any tension loads.
The tension force is essentially carried by the hoop reinforcement that is present in the shell.
Based on above, it is concluded that no changes need to be made to the Shield Building finite element model in order to account for the effect of laminar cracking on stiffness of the Shield Building.
The detailed condition assessment, testing and technical evaluation indicate that laminar cracking in the plane of the outside reinforcement mat will not impact the behavior or performance of the Shield Building.
The detailed testing carried out at Purdue and Kansas labs indicate that No.
11 splices with laminar cracking are expected to carry their full specified yield strength.
Because of the conservative test conditions simulated at
- Kansas, the capacity of some of the 79 inches lap-splices tested for horizontal hoop reinforcement in cracked region was reported to be in the range of 55-57 ksi.
Accordingly, and based on Prof.
Darwin's recommendations, the capacity of 79 inch horizontal lap-splices in cracked regions will be limited to 55 ksi (about 8% less than original design capacity) at splice locations between EL. 569' and EL. 780' of the Shield Building wall.
The design stress limit of 55 ksi is both a
lower-bound as well as conservative value.
Correspondingly, allowable stresses of aforementioned No.
11 lap spliced bars will be reduced by 8%.
All other splices will have their full specified yield strength available for design as demonstrated by testing.
Based on observed cracking on the surface being much tighter than the threshold limit of 0.01 inches and the fact that there is no path for moisture migration to laminar cracking, the Shield Building is expected to continue to meet its serviceability requirements and the observed laminar cracking has no adverse impact on it.
This conclusion is further reinforced by the added protection provided by the coating system applied to the Shield Building exterior surface to prevent possible moisture infiltration.
The long-term durability is not likely to be impacted as long as there is no path for moisture penetration.
Surface coating and periodic monitoring of the cracked regions and carbonation levels will help ensure long-term durability.
A code compliance summary table of computed result is presented in Section 8.0. A section-by-section code compliance evaluation of the SB per ACI 318-63 and ACI 307-69, with observed laminar
- cracking, is documented in Attachment L.
The limiting factors within this calculation with respect to crack propagation are the structural stiffness calculations of Attachment A, and the analyzed conditions of DIN 24 "Bechtel Report 25593-000-G83-GEG-00016, Effect of Laminar Cracks on Splice Capacity of No.
11 Bars based on Testing Conducted at Purdue University and University of Kansas for Davis-Besse Shield Building".
3.5 Methodology for Analysis In this calculation, the analysis is performed with a three dimensional (3D) linear elastic Finite Element (FE) model of the Shield Building using ANSYS.
The model represents the entire Shield Building structure including the cylindrical wall, dome and the spring line area.
The Shield Building is modeled using a fixed base boundary condition at Elevation 565' without the basemat being included.
This is consistent with original design basis calculations which listed in Section 1.0. The model is created using shell elements SHELL181 (Ref.12). As such, membrane and bending stresses reported by shell elements are calculated using elastic shell theory, which is consistent with the analytical techniques specified in DCM Section II.H.2.5.1.5 and USAR Section 3.8.2.2.
As described in USAR Section 3.8.2.2.2 and 3.8.2.2.5, additional reinforcement, including diagonal bars at each
- corner, is provided around permanent openings and major penetrations to strengthen these areas. The analytical methods and results described in USAR Section 3.8.2.2 and original calculations for the evaluation of the stress concentration effects at the permanent openings and major penetrations are still applicable since the cracking is
RrstEnergy CALCULATION COMPUTATION Page 9 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 not present in these areas (Ref.
25), except for the main steam line penetrations 39 and 40. At the main steam line penetrations 39 and 40, the cracking is located outside of the blockout around penetrations. As discussed above, the potential effect of laminar cracks on reinforcement is limited to lap splice capacity of circumferential reinforcement.
Review of the cracking map with consideration of crack propagation (Ref.
25, 27-35) and rebar drawing 7749-C-112 (Ref.
7d) indicates that additional reinforcements provided to strengthen these two openings, including diagonal bars at each corner, are not impacted by laminar cracking and as such no adverse impact is anticipated.
All design loads and load combinations specified in the USAR are included in the finite element analysis.
Thermal stresses are calculated per ACI 307-69 as specified in USAR and combined with stresses resulting from mechanical loads. The design of the Shield Building is carried out in accordance with ACI 307-69 and ACI 318-63.
A sectional analysis is also performed following the methodology of ACI 307-69 and ACI 318-63 to address the construction sequence and influence of Reactor Vessel Closure Head (RVCH) and Steam Generator Replacement (SGR) openings.
The original tornado missile impact (penetration)
- analysis, which is described in USAR Subsection 3.5.8 and listed in Ref.
1, Table 3.3-2 and Ref.
2, Table I.D.3.2-3, is still valid.
In this calculation, the SB wall is checked against the maximum penetration depth listed in Ref.
1, Table 3.3-2 and Ref.
2, Table I.D.3.2-3 assuming conservatively that the outer concrete cover affected by the observed laminar cracking does not provide any resistance against tornado missiles.
4.0 ASSUMPTIONS There is no unverified assumption made in this calculation. Other assumptions are specified in the body of the calculation with appropriate justification.
5.0 ACCEPTANCE CRITERIA The existing SB was originally designed in accordance with the procedures presented in ACI 307-69 (Ref. 9a) and ACI 318-63 (Ref.
9b),
together with the acceptance criteria provided in References 1
and 2.
In this calculation, the same acceptance criteria are maintained.
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C-CSS-099.20-063 REVISION:
001 6.0 DESIGN INPUTS
/ REFERENCES (Design inputs are annotated with an asterisk *)
1.
Updated Safety Analysis Report (USAR) for Davis-Besse Nuclear Power Station No.
1, Rev. 29 2.
Davis-Besse Nuclear Power Station Unit 1
Design Criteria Manual, Rev. 32 3.
Bechtel Letter/File No. 25539-000-TCM-GEG-00015 dated 8/27/2010, 17 Mid-Cycle Outage and 18RFO Construction Opening Dimensions 4.
Bechtel Letter/File No.
25539-000-TCM-GEG-00040 dated 12/8/2010, Containment Vessel and Shield Building Opening Sizes in Support of Tornado Depressurization Analyses 5.
NRC Reg. Guide 1.29, Seismic Design Classification, Rev. 2 6.
NRC Reg. Guide 1.76, Design-Basis Tornado and Tornado Missiles for Nuclear Power Plants, Rev. 0 7.
Drawings:
(a)* 7749-C-109, Rev. 6 "Shield Building Roof Plan & Details Sheet 1" (b)* 7749-C-110, Rev. 6 "Shield Building Roof Plan Wall Section & Details" (c)
- 7749-C-111, Rev.
11 "Shield Building Wall Development" (d) 7749-C-112, Rev. 10 "Shield Building Details Sheet 1" (e) 7749-C-113, Rev.
11 "Shield Building Details Sheet 2" (f) 7749-C-115, Rev. 4 "Shield Building Blockout Details" (g) C-0112A, Rev. 0 "Shield Building Temporary Construction Opening Restoration Details" (h)* 7749-A-8, Rev. 20, Shield, Turbine, Auxiliary, Off. BLDGS. General Floor Plan EL643'-0" (i)
- 7749-C-230, Rev.
9, Auxiliary Building Superstructure Section C & Details 8.
Original Design Calculations:
(a) *VC01/B01-01, Approval Date 10/1/1976, Rev.
0, "Shield Building-Thermal Stresses-Shield Wall" (b) VA08/B001-001, Structural effects of high energy line ruptures (Compartment pressurization analysis), Rev 0 (c)
- VS01/B01-03, Approval Date 10/4/1976, Rev.
0, "Seismic Analysis of the Containment Structure" (d)
- VC03/B01-04, Approval Date 10/6/1976, Rev. 0, "Shield Building Wall at Base Floor" (e)
- C-NSA-000.02-016, 36 Inch Main Steam Line Break in Rooms 601 and 602, Rev.O (f) C-NSA-000.02-005, Main Feedwater Line Breaks and Cracks in the Auxiliary Building, Rev.02 (g) C-NSA-000.02-006, Steam Generator Blowdown Line Breaks in the Auxiliary Building, Rev. 01 (h) C-NSA-000.02-007, Main Steam to AFW Pump Turbine Line Breaks and Cracks In the Auxiliary Building, Rev. 02 (i)
C-NSA-000.02-009, Auxiliary Steam Line Breaks and Cracks in the Auxiliary Building, Rev. 02 (j)
C-NSA-000.02-012, Auxiliary Building HELB Pressure Analysis Using Gothic 7, Rev. 01 (k)
- 60.013, Shield Bldg. Annulus Pressure Drop Due to Cold WTR Pipe Rupture, Rev.
1 9.
American Concrete Institute (ACI) codes:
(a) ACI 307-69, Specification for the Design and Construction of Reinforced Concrete Chimneys (b) ACI 318-63, Building Code Requirements for Reinforced Concrete (c) ACI 349-76, Code Requirements for Nuclear Safety Related Concrete Structures (d) ACI 349.1R-07, Reinforced Concrete Design for Thermal Effects on Nuclear Power Plant Structures 10.
ASCE Paper No. 3269, Wind Forces on Structures, 1961 11.
FENOC Calculation No. C-CSS-099.20-045, Evaluation of Shield Building for the Construction Opening
- SGR-RVCH replacement 12.
ANSYS Manual Version 13.0 13.
Park and Paulay, 1975.
Reinforced concrete structures 14.
ASME Section III Code, 1968 15.
ECP-10-0458, SGR-17M-Shield Building Construction Opening.
16.
ACI Publication SP-20, Causes, Mechanism and Control of Cracking in Concrete, 1968 17.
- FENOC Design Input Record and Design Interface Evaluation for Shield Building Design Calculation C-CSS-099.20-063, 7/17/2013 18.
Not Used 19.
Condition Reports (a) FENOC CR-2011-03996, Extent of Condition for Shield Building Fracture Indications
FirstEnemv CALCULATION COMPUTATION Page 11 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 (b)FENOC CR-2011-04402, Fractured Concrete Found at 17M Shield Building at Main Steam Line Penetration (c)FENOC CR-2011-04507, Isolated Crack Indication Identified by Impulse
Response
Testing of the Shield Building (d)FENOC CR-2011-04648, Shield Building IR Indications above Elevation 780 (e) FENOC CR-2011-03346, Fractured Concrete Found at 17M Shield Building Construction Opening (f) FENOC CR-2013-09122, Design Criteria Manual Discrepancy 20.
Commentary on Building Code Requirements for Reinforced Concrete (ACI 318-63), ACI Publication SP-10 21.
- Ferguson, P.M., and Thompson, J.N., "Development Length of High Strength Reinforcing Bars in Bond,"
ACI Journal, Proceedings V.
59, No.
7, July 1962, pp. 887-922 22.
- Ferguson, P.M.,
and
- Matloob, F.N.,
"Effect of Bar Cut-off on Bond and Shear Strength of Reinforced Concrete Beams," ACI Journal, Proceedings V. 56, No.
1, July 1959, pp. 5-24 23.
- Watstein, D., and Mathey, R.G., "Investigation of Bond in Beam and Pull-out Specimens with High Yield Strength Deformed Bars," ACI Journal, Proceedings V. 57, No.
9, March 1961, pp. 1071-1090 24.
Bechtel Report 25593-000-G83-GEG-00016, Effect of Laminar Cracks on Splice Capacity of No.
11 Bars based on Testing Conducted at Purdue University and University of Kansas for Davis-Besse Shield Building 25.
Bechtel Doc No. 25593-000-GQT-GEG-00001 (provided by FENOC),
Shield Building Exterior Elevation IR Test Data Through 24 July 2012, July 24, 2012 26.
U.S. Army, Manuals-Corps of Engineers, EM 1110-2-2502, 1961 27.
FENOC CR-2013-13782, Shield Building Core Bore S5-666.0-10 findings 28.
FENOC CR-2013-13854 Shield Building Core Bore S7-666.0-7 findings 29.
FENOC CR-2013-13860 Shield Building Core Bore S7-666.0-7 findings 30.
FENOC CR-2013-14097 Shield Building laminar crack extends 31.
FENOC CR-2013-14623 Shield Building Core Bore S13-633.0-11 findings 32.
FENOC CR-2013-16204 Shield Building Core Bore S15-646.5-8 findings 33.
FENOC CR-2013-16210 Shield Building Core Bore S15-674.5-3 findings 34.
FENOC CR-2013-14961 Shield Building Core Bore S4-773-16 findings 35.
FENOC CR-2013-16211 Shield Building Core Bore S15-777-3 findings NOTE:
Reference numbers in this section match the Dl numbers in Pages v & vii.
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C-CSS-099.20-063 REVISION:
001 7.0 BODY OF CALCULATION 7.1 Description of the Shield Building Davis-Besse nuclear containment structure consists of two components:
concrete Shield Building (SB) & steel Containment Vessel (CV)
(Ref.1).
The SB is separated from the steel CV, and there are no structural links between two components except at the bottom.
Figure 1
shows the overall SB outline with new and old construction openings.
The SB has a cylindrical reinforced concrete wall and a shallow spherical dome. The SB is supported by a
reinforced concrete foundation ring which bears on bedrock (Ref.
1).
Overall geometry information of SB is described as follows:
The thicknesses of the concrete wall and dome are 30" and 24", respectively.
The radii to the inner surfaces of the concrete wall and dome are 69'- 6" and 123'- 3.5", respectively.
The base elevation of the cylindrical wall used in this design basis calculation is set at 565'.
The top elevations of the concrete wall and dome are 809'- 6" and 824'- 6", respectively.
The ground elevation at the SB location is 584.0'.
For information only, the size of the original construction opening is 53 ft (width) x 46.5 ft (height), located at 305°52'13" (azimuth) and 579 ft (bottom elevation).
See Ref. 7c for details.
Similarly, the size of the RCVH/SGs opening is 26.3 ft (width) x 35.5 ft (height),
located at 323°15' (azimuth) and 603 ft (bottom elevation).
See Refs. 3 & 4 for details.
During the removal of concrete in the SB for Reactor Vessel Closure Head (RVCH) replacement at Davis-Besse nuclear plant, laminar cracking was observed in the plane of the outer reinforcement mat consisting of No.
10 vertical bars and No.
11 hoop and vertical bars.
A detailed condition assessment was carried out to determine the extent of cracking, and nature of observed propagation as described in Refs. 19a~19e, 25, and 27-35.
This assessment indicated that cracking is present in
- most, if not
- all, of the architectural flute shoulders, two steam line penetration (#39 & 40) areas and in most of the top 20 ft of the Shield Building cylindrical wall.
7.2 Material Properties Material parameters used in this calculation are based on Davis-Besse Design Criteria Manual (Ref.
2,Section II.H.2.5.1), as summarized in table below. The stress-strain diagrams (Ref.
- 13) for concrete and steel rebar used in the strength design are shown in Figure 2.
Material parameters (based on Ref. 2)
Concrete Compressive strength, fc (ksi)
Elastic modulus, Ec (ksi)
Specific weight, yc (Ibf/ft3)
Poisson's ratio, vc Thermal coefficient, etc (1/°F) 4 3,600 150 0.25 0.0000055 Steel Yield strength, fy (ksi)
Elastic modulus, Es (ksi)
Specific weight, Vs (Ibf/ft3)
Poisson's ratio, vs Thermal coefficient, as (1/°F) 60*
29,000 490 0.30 0.0000065
- Note: due to observed laminar cracking, design strength of outer hoop reinforcement is 55 ksi. See Section 3.0.
BrstEnergrv CALCULATION COMPUTATION Page 13 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 EL. 801-0 EL. 565'-0
/
\\
1 n
i CO f
1 t
13',
l l
1 i
RCVH/SGs l
ope 26.3 ning i
i i
i RPVHR opening 23.5'xl8.5' i
i i
i i
i Original Construction opening 53'x46.5' i
i i
i i
i EL 638'-6" EL 625'-6" EL 603'-0" EL 579'-0" I
I 323°15' 319° 305°52'13" 144 ft Figure 1
Shield building (SB) outline w/ new and old construction openings (Refs.
1 & 3) fc 5000
/c(l.2-10OEc) 100O/c-£c-(l-25OEc) 0.001 0.002 0.003
/y[ksi]
0.001 0.002 0.003 (a) Parabolic concrete compression stress-strain curve (Ref. 13)
(b) Rebar stress-strain curve Figure 2 Concrete and rebar stress-strain curves used in evaluation
FirsflEhergrv CALCULATION COMPUTATION Page 14 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 7.3 Finite Element Model Model Description A 3D linear elastic FE model is developed using ANSYS version 13.0 (Ref.
12) to represent the SB in its as designed condition.
Figure 3a shows the 3D FE model used in this calculation, input files for the generation of this Model are reported in Att. G.
The FE model consists of about 7,600 shell elements and 7700 nodes.
The SB includes a 2.5 ft thick cylindrical wall and a 2 ft thick spherical dome.
All cylindrical wall and spherical dome are modeled at the mid sections of the wall and dome using SHELL181 elements. SHELL181 is a 4-node shell element with 6 degree of freedoms (DOFs) at each node:
3 translational (x,
y, and z) and 3 rotational DOFs (Rx, Ry, and Rz).
Per Ref.
12 Section elementary
- library, this type of element is well-suited for
- linear, large
- rotation, and/or large strain nonlinear applications of thin to moderately thick shell structures, which is appropriate for the purpose of this calculation.
As shown in Figure 3a, the bottom of the FE model is located at EL.
565'-0", which is considered as a fixed boundary condition due to the large rigidity of the foundation ring.
This is consistent with the original design basis calculations as specified in Section 1.0. For validation purpose, the vertical membrane compressive stress due to dead load only at the bottom of the structure is evaluated in ANSYS Graphical User Interface (GUI) and result is presented in Figure 3b. The maximum membrane stress is found to be 44.24 ksf at EL. 565'. On the other hand using the closed form membrane theory per Ref.
14, the maximum membrane stress due to dead load is calculated as 49400 kip / (tt x 2 x 70.75ft x 2.5ft) =
44.45 ksf, note 49400 kip is the total weight of the SB FEM.
A good agreement is demonstrated between these two results.
In this FE model, a typical element (mesh) size of 4 ft (width) x 5 ft (height) is used to model the concrete wall, as shown in Figure 3a.
See Table 1
for the material properties used in this calculation.
Given the overall dimensions and structural characteristics of the cylindrical
- wall, this element size is sufficient to reflect the structural responses of the SB for all applicable design loads.
ELEMENTS
^^fiH pres-inrm sazsgwro:
IB Iff nXr
ntr
But Zt But ;
-TjTTfi UWa zz-M-.-.W::: \\
x 34
--4--
--jr"1
- " jj i
ij
I iBBI iife:
=!!! 1 gill; =1$*
AN FEB 2
2013 15:21:03 Figure 3a Three-dimensional (3D) FE model
FirstEnergy CALCULATION COMPUTATION Page 15 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 1
KI3ERI.
SOUJTIOH sna
=1 TIKE=1 SI UHEj HTDMZ OiX
=.018173 SKE
=-<<4.2i52 SUE
.001289 M
^.
-25.490S
-u<<.6S0S AN JCl 2J 201i 10:20:52 J31Q5
-.0C12S5 Figure 3b Vertical membrane stress for dead load 7.4 Design Loads and Load Combinations 7.4.1 Independent loads Per Ref.
1 Section 3.8.2.2.4 and Ref. 2 Section II.G., independent loads that need to be considered for the SB in its original as designed condition are: dead,
- live, seismic, wind, tornado, external
- missile, soil, high energy line break and temperature loads. These loads are described below (Refs 1 & 2):
Dead Load (D)
Dead loads (D) include self-weights of the SB and service equipment permanently attached to the SB, and any other loads considered as dead loads in the original SB design. Since architectural flutes are not modeled, a 10%
weight increase is also applied in the model to account for those flutes and other non-structure components. The 10% weight adjustment is determined by comparing the total weight of the FE model with the total weight specified in the original stick-mass model (Ref. 8c) used for seismic analysis.
Live Load (L)
Live load on the dome is uniformly applied to the top surface of dome at an assumed value of 40 psf (Ref 1 Section 3.8.2.2.4).
Temperature Load (To and Ta)
For the original as designed condition, there are two applicable thermal loads. They are generated due to the temperature difference between the inside and outside of the Shield Building.
During the normal operating
FirstEnerav CALCULATION COMPUTATION Page 16 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 condition, the maximum temperature difference at the inner and outer surfaces of SB is 78 °F (To),
based on Refs. 8a. For the Loss of Coolant Accident (LOCA) condition, the maximum temperature gradient is 125 °F(Ta).
Tornado Load (W)
Tornado loads are calculated consistent with the original design basis Ref.
1 and Ref.
2, which refers to Ref.
10 for calculation of wind and tornado
- effects, as detailed in Attachment F.
In particular, the pressure drop associated with tornado funnel (3psi) is applied to act concurrently with the force due to a 300 mph wind, per USAR Section 3.3.2.2 and DCM Section I.D.2; and a degree of conservatism is added to the tornado model by applying constant tornado wind velocities from the ground elevation to the dome (DCM Section I.D.2 and USAR Section 3.3.2.1.1).
Wind Load (W)
Wind loads are calculated consistent with the original design basis Ref.
1, which refers to Ref.
10 for calculation of wind and tornado effects, as detailed in Attachment F. This results in 90-mph basic wind at 30 ft above grade (EL 584' +
30J).
External Missiles The Shield Building is designed to withstand a tornado driven missile as described in Ref.
1, Section 3.8.2.2.4.
The evaluation of the structure integrity of the Shield Building to withstand a
design basis external missile is carried out in Section 7.11 using the procedure described in Ref.2,Section I.D.3.
High Energy Line break load (HELB or Rp)
Per Refs. 8f to 8j, there are High Energy Line Break (HELB) accidents either in the Aux Building or in the annulus that may impose pressure loads and associated temperatures to the SB cylindrical wall.
These accidents are:
- 2) Steam Generator (SG) Blowdown Line Break
- 3) Main Steam (MS) Line Break Information related to HELB loads are presented in Refs. 8e thru 8j.
Att. K discusses the thermal effect on the wall associated with these line break accidents, and concludes that the elevated temperature only penetrates a few inches (<=3") for the 30" thick SB wall, because of short duration of the high temperature. As such, the thermal effect on the 30" wall is very small and can be ignored for structural evaluation of the wall.
Review of Refs.
8f & 8g indicates that the MFW line break and SG Blowdown line break will cause a transient internal pressure of about 1 psi in the Annulus, which will be enveloped by the tornado induced internal pressure (3psi).
Review of Refs. 8b & 8e indicates that the only governing HELB effect on the SB wall is an external pressure of 6.8 psi in the main steam line rooms 601 and 602 (EL.
643' to EL.
660',
roof is 1.5' thick) during the MSLB.
Therefore, a 6.8psi external pressure is applied to the SB wall corresponding to the locations of rooms 601 & 602 (from EL. 643' to EL. 658.5', and approximately in a range of 180 degrees out of 360 degrees in plan view).
To be conservative, the pressure load is applied in the same direction as the seismic load to create maximum load effects.
FirstEnerav CALCULATION COMPUTATION Page 17 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 Ref 8k identifies that under a pipe rupture within containment a maximum differential pressure across the SB of negative 0.81 psi (14.4 psi outside the shield building, and 13.59psi in the annulus) may be experienced. This is conservatively assumed to act concurrent with the 6.8psi external pressure due to the Main Steam Line Break described in Section 7.4.1. See Section 7.4.2 for additional evaluation.
Seismic Load (E/OBE & E7SSE)
The inertial seismic forces (vertical and horizontal) reported in the original design of the SB (Ref.
8c) are used herein to calculate the seismic demand of the SB with the laminar cracks.
An evaluation is carried out to consider the effect of the laminar cracks to the original seismic analysis results (i.e.,
seismic loading inputs of the calculation).
Different FE models with different levels of the laminar concrete cracks are examined based on IR test results (Ref.
25, 27-35). Based on the calculated natural frequencies and mode shapes for each FEM, it is demonstrated that the effect of observed laminar
- cracks, to the extent identified and accounted for in Attachment A on the dynamic behavior of the SB is insignificant. Therefore, the same seismic loads considered in the original SB design are used in the calculation.
See Att. A for details of this evaluation.
It must be noted that per Ref.
2, the Davis Besse Maximum Possible Earthquake with a 0.15g Peak Ground Acceleration (PGA),
E',
is consistent with NRC RG 1.29 definition of SSE; while the Maximum Probable Earthquake with a 0.08g
- PGA, E,
is consistent with the definition of Operating Basis Earthquake (OBE).
Safe Shutdown Earthquake (SSE or E')
SSE inertial loads reported in Ref.
8c are provided
- below, with both the horizontal E'xy and vertical E'z components.
In this calculation, the seismic shear, bending moment and axial load (V),
M),
P'j)
) are derived from the maximum horizontal and vertical inertial forces (Exyi Ez) acting simultaneously, which is conservative since the maximum inertial responses are not always in phase.
Elevation (ft) 812.77 801.05 774.52 748.00 720.00 692.00 660.00 646.50 643.00 609.00 603.00 589.50 570.75 Horizontal Inertial force
£',,(kip) 2442.90 2688.80 2511.90 2171.20 1828.20 1587.00 882.00 271.00 579.00 332.00 140.00 145.00 25.00 Vertical Inertial force
£'.-(kip) 1167.40 1344.20 1399.10 1348.20 1254.60 1177.70 711.93 223.46 469.29 321.00 135.29 174.73 144.34
FirsiEhefgv Page 18 CALCULATION COMPUTATION NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 800" Elevation (ft)
Elevation (tt) 0 5000 I0O00 15000 20000 SSE Shear Force (kip) 637.5 0
1000000 2000000 3000000 SSE Bending Moment (kip.ft)
Elevation (ft) 2000 4000 6000 8000 10000 SSE Vertical Force (kip)
Figure 4: Shear, Bending Moment and Axial Seismic Demands for Safe Shutdown Earthquake (SSE or E')
Operating Basis Earthquake (OBE or E)
OBE inertiai loads reported in Ref.
8c are provided
- below, with both the horizontal Erv and vertical
£,
components.
In this calculation, the seismic shear, bending moment and axial load (V,-, M(-,
/>,-) are derived from the maximum horizontal and vertical inertiai forces (E^, Ez) acting simultaneously, which is conservative since the maximum inertiai responses are not always in phase.
BrsflEhergrv CALCULATION COMPUTATION Page 19 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 Elevation (ft) 812.77 801.05 774.52 748.00 720.00 692.00 660.00 646.50 643.00 609.00 603.00 589.50 570.75 Horizontal Inertial force Exy (kip) 1544.40 1699.20 1585.20 1367.70 1150.60 1000.30 557.20 172.00 367.10 211.90 89.30 92.50 15.40 Vertical Inertial force E: (kip) 808.33 931.55 971.52 935.68 869.68 813.14 486.98 152.19 318.75 210.14 88.32 107.82 77.52 800" Elevation (ft) 800 V Elevation (ft) 0 5000 10000 OBE Shear Force (kip) 0 500000 1000000 1500000 2000000 OBE Bending Moment (kip.ft)
FirstEner^v CALCULATION COMPUTATION Page 20 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 800" Elevation (ft) 700"-
I
'l I
\\
637.5
- i 604 0
2000 4000 6000 8000 OBE Vertical Force (kip)
Figure 5: Shear, Bending Moment and Axial Seismic Demands for Operating Basis Earthquake (OBE or E)
FirsiEhergy CALCULATION COMPUTATION Page 21 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 Soil Load Static soil load (treated as part of Dead Load per USAR and PCM, "D")
The static active and passive lateral earth pressure load is described in Davis Besse Design Criteria (Ref.2),
Section II.G.2.4 and USAR (Ref.1), Section 3.8.1.4.4. The calculation should follow Manuals-Corps of Engineers, U.
S.
- Army, EM 1110-2-2502.
In particular, the static backfill pressure has been calculated using Coulomb's theory below (USAR Section 3.8.1.4.4). Further detail of the Coulomb's theory is presented in Manuals-Corps of Engineers, U. S. Army, EM 1110-2-2502 (Ref. 26).
For the case of Shield Building, the static backfill pressure has been calculated using Ps = kar'h In which y' is the effective unit weight of soil and h is the depth of soil. The coefficient of active earth pressure ka is given by Coulomb's theory as (Ref.1 Section 3.8.1.4.4 and Ref. 26 equation 3-15, note the equation below may be deducted from the one presented in Ref.
1):
1 - sin (p q>
ka =
- = tan2 (45° - £)
a l + smcp v
2J As indicated in the equation, it is obvious thatO <ka< 0.5.
EM1110-2-2502 provides values of internal friction angle cp for various backfill materials.
Particularly for coarse grained materials used for
- backfill, internal friction angle <p is between 25 to 40 degrees.
Conservatively applying that <p = 25° thus ka =0.405. A more conservative
- value, ka =0.5 is used in this calculation.
Excavation for the containment and auxiliary buildings generally reaches EL 530' and EL 540', respectively (Ref.2 Section II.F.1.1). The structural backfill material consisted of crushed rock obtained on-site and was compacted to 98% of the maximum dry density (Ref.1, Appendix 2C.6.3).
Unit weight of soils are listed in DCM,Section II.D.10-1 and USAR 2.5.8.1 as follows:
Bedrock: 150 pcf Till Deposit: 132 pcf Glaciolacustrine: 125 pcf Conservatively use y =150 pcf for unit weight of backfill.
Per USAR, Section 3.4.2.1, the maximum probable static water level is at EL. 583.7'. All seismic class I structures are designed for a
max probable static water level of El.
584',
thus a
triangularly distributed saturated soil pressure should be applied to span between EL.565' and EL.
584',
for static soil
- loading, i.e.
[USAR, Section 3.4.2.1]
Therefore, y' = y - yw =87.6 pcf, with yw =62.4 pcf is the unit weight of water.
At EL.565, use h = 19 ft, the static soil pressure and water pressure are Ps = kay'h =0.833 ksf Pw = Ywh =1.186 ksf Soil surcharge loading is described in DCM II.G.2.4.2.1 as q = 250 psf (0.25 ksf) for the Shield Building.
RrsHEheruv NOP-CC-3002-01 CALCULATION NO.
C-CSS-099.20-063 Page CALCULATION COMPUTATION Rev. 03 REVISION:
001 22 Total resultant forces between EL. 565' and EL 584' are:
Ps = 2k*Y'h2 = 7.91 kip/ft Pw=-ywh2 = 11.27 kip/ft Q = kaqh = 2.375 kip/ft Dynamic soil load (Treated as part of Live Load per USAR and DCM, "L")
Per Ref.1, Section 3.8.1.4.4, "additional pressures due to earthquakes were used in accordance with Manuals-Corps of Engineers, U.
S.
- Army, EM 1110-2-2502".
Therefore, the Mononobe-Okabe approach is used for calculating additional soil pressure due to earthquake effect per EM 1110-2-2502.
SSE Earthquake kh ;= 0.15 horizontal acceleration (g), Ref. 8c 2-(tan((f)-kh) c2:=
a := atanl AP kh-tan(<p) tan((f)-kh kh-tan(tp))
c,
+ 4-c2 Ref. 26, eqn 3-60
= 0.634 Ref. 26, eqn 3-61
= 0.506 Ref. 26, eqn 3-59 2AP AE 2-ten (a)
QBE Earthquake AE ft h
= Q.lllksf
9 a
\\v
"\\
\\
Com pressior
- X 1
- \\\\
X
\\\\
X
'x Tension Cl C2
C3 D]
D2 D3
&C4
-60
-44
-28
-12 4
20 36 52 84 100 Membrane force (kip/ft)
Figure 10 Thermal moment as a function of mechanical membrane force (meridional, normal operation temperature)
FifStEhergv CALCULATION COMPUTATION Page 30 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 140 126 112 84 Moment (kip.ft/ft) 70 56 42 2S 14 0
\\
x
>\\
Com pressiojiN.
\\
1 A
Tension Cl C2
---C3&C4 Dl D2 D3
-58
-36
-14 8
30 52 74 96 118 140 Membrane force (kip/ft)
Figure 11 Thermal moment as a function of mechanical membrane force (meridional, accident temperature) 7.7 P-M Interaction Diagram and Demand to Capacity Ratios The requirements and notations from Ref.
9(b) are followed for evaluating the capacity of the SB cylinder wall.
The following steps are taken:
1.
Interaction diagrams are calculated in both circumferential and meridional directions for each element of each zone of the Shield Building, as detailed in Attachment B. Also see Figure 12 for an example. The interaction diagrams are obtained following standard procedures as described in Ref.13 Chapter 5. Per Section 3, the design strength of rebar in outside face circumferential reinforcement within cylindrical wall are conservatively reduced by 8% per Ref.24; while per Ref.
1, Section 3.8.2.3.4 the following strength reduction factors
(<l>) are used:
(a) Flexure, without axial load 0.90 (b) Axial tension, and axial tension with flexure 0.90 (c) Axial compression, and axial compression with flexure 0.70 2.
Calculate the design moment Mua and axial force Pu for each element as (also see Figure 6)
Circumferential direction Pu=-Nu Meridional direction Pu= - N22
FirstEnergy CALCULATION COMPUTATION Page 31 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 800
[Kip]
I
- '*uf U
-75
-200
- 300
- 200
- 100 0
100
- T, [Kip-ft]
200 300 400 Figure 12 Typical Interaction Diagram 3.
Superimpose thermal moment MT calculated in Attachment C to mechanical demands Mue obtained in Step 2 to obtain the total moment demand Mu= Mue + Mr 4.
Compare total demand (Mu, Pu) against capacity {<pPn, <f>Mn) at element basis for the Shield Building by plotting of (Mu, Pu) for all 7,600 elements in both circumferential and meridional directions for Ultimate Strength Design (USD) load combinations (LC101-LC404) in appropriate P-M interaction diagrams in Figure 13 thru Figure 20. Tabulated comparisons are also presented in Att.
D.
5.
Verify that the maximum Demand-Capacity-Ratio (DCR) at each region for each load combination is not larger than 1.0 for all ultimate strength load combinations (LC101-LC404). The DCR for each combination of moment and axial force are calculated as MJ<pMn.
It is understood that in engineering practices, for P-M interaction check, DCR could either be based on moment (with a given axial force), or based on axial force (with a given moment), or based on some sort of combination of moment and axial force. For ultimate strength design, regardless of which type of DCR is used, DCR <1 is sufficient to indicate that the demand is enveloped by the P-M diagram. Maximum DCRs are reported in Table 4 thru Table 19.
6.
For Working Stress Design (WSD) load combinations (LC 501-LC803), P-M interaction diagrams and DCRs are only used as a tool to identify the most critical case which will be further checked in terms of rebar and concrete stresses in Section 7.8. Detail information is presented in Att. D.
CALCULATION COMPUTATION Page 32 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 1M. [kip.ft]
-5 JO
-400
-300
-2O0
-100 200 300 400 590 Circumferential P-M interaction diagram; LC 101
-400
-300
-20C 200 300 400 Circumferential P-M^nteractiori diagram: LC 201-Meridional P-M interaction diagram: LC 201-206 0
-400
-300
-200
-100 200 300 400 5
0 areumferentialP-M'ifrteracttondiagram: X 301-302, MeridionaiP-M interaction diagram: LC 301-302
-400
-300
-200 200 300 400 SCO GrcumferentialP-Minteractiondagram:LC 401-404 Meridional P-M interaction diagram: LC 401-404, Figure 13 P-M Interaction diagram check USD: All elements in Region C1
CALCULATION COMPUTATION Page 33 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 Orcumferentiai P-ftFmtefaction diagram: LC 101
-1DC1 CircumferentialP-Minteractiondiagram:LC 201-206
-5 0
-400
-300
-200
-100 200 300 400 51 0 Circumferential P-M interaction diagram: LC 301-302 4>Mn [klp.ftl
-S 0
-400
-300
-200
-100 200 300 400 500 Circumferential P-M interaction diagram: LC 401-1 Meridional P-wRnteractiondiagram LC 101 Meridional P-M Interaction diagram: LC 301-302 Mend ionalP-M interaction diagram: LC 401-404 Figure 14 P-M Interaction diagram check USD: All elements in Region C2
FirstEnerav CALCULATION COMPUTATION Page 34 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001
-S(JO
-400
-300
-200
^1*^^
Q
- 200 200 300 400 500 Circumferential P%l interaction diagram: LC 101 DO
-400
-300
-200 OMnfkip.ft]
200 300 400 SOQ Meridional P-M interaction diagram LC 101
-*Pnfktpl 200 300 400 5
0 Circumferential P-M interaction diagram; LC 201-206
-SCO
-400
-300
-200 200 300 400 500 Meridional P-M interaction diagram: LC 201-206
-400
-300
-2O0 200 300 400 51 D
Circumferential P-M interaction diagram: LC 301-302
-500
-400
-300 Meridional P-M interaction diagram: LC 301-302 500
-400
-300
-200 200 300 400 5*0 MeridionalP-MirtteractlQndiagram:LC 401-404 Circumferential P-M interaction diagram: LC 401-404 Figure 15 P-M Interaction diagram check USD: All elements in Region C3
FirstEneray CALCULATION COMPUTATION Page 35 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 Ciraimfe rental P^Sfnteraction diagram: LC101
- 5 0
-400
-300
-200 ZOO 300 400 590 Meridional P-M^meraction diagram IX 101 Circumferential P-M interaction diagram: LC 201-206 MerWIonalP-M mteractiondiagram: LC 201-206 Circumferential P-interaction diagram: LC 301-302 Meridional P-M interaction diagram: LC 301-302 0
-400 DO
-400
-300
-200 QMn [kip.ft]
200 300 400 5<<0 Circumferential P-M interaction diagram: LC 401-404 MeridionalP-M interaction diagram: LC 401-404 Figure 16 P-M Interaction diagram check USD: All elements in Region C4
FirstEnergv CALCULATION COMPUTATION Page 36 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 S
0
-400
-300^^200
-100 300 400 S00 Orujmf* rental P^nteracttondiapamiLC 101
- 400
-300
-200 200 300 400 500 P-M interact'diagr>>m IX 101
-400
-300 \\-2O0
-100 I
100 100-^
300 400 5*0 Circumferential P-M interaction diagram: LC 201-206 MerldionalP-M interaction diagram: LC 201-206 ClrcumferentlalP-IVffiteracrtondiagram:LC 301-302 Meridional P-M interactiondiasram: LC 301-302 1000 oPn [kip]
-5 10
-400
-300^X1200 300 400 500 Circumferential P-M interaction diagram: LC 401-404
-5 0
-400
-300
-200 200 300 400 500 MendwnalP-M interaction diagram: LC 401-404 Figure 17 P-M Interaction diagram check USD: All elements in Region C5
FirsttEhergv CALCULATION COMPUTATION Page 37 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 1
0
-200
-ISO
-100 100 150 200 2
0 Grcumfe rental P-interaction diagram: LC 101
-2 0
-200
-ISO
-100 100 150 200 2
0 alP-M*nteractton diagram LI
-2 >0
-200
-ISO
-100 100 150 200 2!
Circumferential P-Minteractiondiagram:LC 201-206 MeridionalP-M interaction diagram: LC 201-206 Circumferential P-M*interaction diagram: LC 301-302 0
-200
-ISO
-100 100 150 200 2
0 MeridJonalP-M interaction diagram: LC 301-302
-150
-100 j^
^^J^^IOO loolr 200 2
D Circumferential P-M interaction diagram: LC 401-404 MerldionalP-M Interaction diagram: LC 401-404 Figure 18 P-M Interaction diagram check USD: All elements in Region D1
FirstEhegav CALCULATION COMPUTATION Page 38 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001
-300
-200
'"^4^
100 360 CircumferentalP-M interaction diagram: LC 101 ssas&i rwionjl P-M interaction diagram LC 101 QrcumfenentialP-M interaaiondiagram: LC 201-206, MeridionalP-Miiiteraawndiagram: LC 201-206 aroimferentialP-M^ri?eractiondiaBram;LC 301-302 600
/
500 W
400 f
300
\\w 200 It 100 0
-200
-100 ^V
-100"*
OPirftW 1
'<<L
\\
\\
\\
<<*n[kip-ft]
r
- ^
Vrf^
200 3i Meridional P-M interaction diagram: LC 301-302 Circumferential P-[^interaction diagram: LC 401-404 MeridionalP-M interaction diagram: LC 401-404 Figure 19 P-M Interaction diagram check USD: All elements in Region D2
FirsSEneray CALCULATION COMPUTATION Page 39 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 Circumferential P-M interaction diagram: LC 101 70&
/
+
400 1
300 300
^S_
100 10
-200
^^MO
^m_-ioo
-200
- Pnlkip]
^*i).Mn[kip.ftl J*° 200 3
Meridtonal P-M interaction diagram LC 101 0
-300
-200 300 4
0 Circumferential P-M*interaction diagram: LC 201-206
-200 Meridional P-M interaction diagram: LC 201-206 Circumferential P-M*interaction diagram: LC 301-302 OPntkipl 200 3<(HD Meridional P-M interaction diagram: LC 301-302 0
-300
-200 Circumferential P-M interaction diagram: LC 401-404
-3 0
-100 200 I
0 Meridional P-M interaction diagram: LC 401-404 Figure 20 P-M Interaction diagram check USD: All elements in Region D3
FfrsfEnefgv CALCULATION COMPUTATION Page 40 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
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001 Table 4 Maximurr Load Combinations LC101 LC201-206 LC301-302 LC401-404 Mue kip*ft/ft
-7.90
-4.09 13.67
-5.45 DCRs: Region C1, Circumferential direction Mu kip*ft/ft
-7.90 95.40 48.52 125.54 Pu kip/ft 72.37 85.99
-59.59 88.12
<t>Mn kip*ft/ft
-148.26 230.25 99.27 232.16 4Pn kip/ft 753.30 733.48
-106.08 693.88 Max DCR 0.05 0.41 0.49 0.54 Table 5 Maximum DCRs: Region
(
Load Combinations LC101 LC201-206 LC301-302 LC401-404 Mue kip*ft/ft
-31.59
-16.34 9.16
-21.64 Mu kip'ft/ft
-31.59 251.71 272.12 307.56 Pu kip/ft 161.84 308.64 301.75 327.37 D1, Meridional direction 4>Mn kip*ft/ft
-284.20 414.61 418.84 403.14
<<>Pn kip/ft 786.10 570.77 544.12 497.85 Max DCR 0.11 0.61 0.65 0.76 Table 6 Maximum DCRs: Region C2, Circumferential direction Load Combinations LC101 LC201-206 LC301-302 LC401-404 Mue kip*ft/ft
-0.16
-0.33 24.18
-1.91 Mu kip*ft/ft
-0.16 44.65 56.26 99.52 Pu kip/ft 2.69 13.72
-53.13 53.26 kip*ft/ft
-85.48 165.23 105.08 200.80 0Pn kip/ft 753.30 753.30
-99.02 728.08 Max DCR 0.00 0.27 0.54 0.50 Table 7 Maximum DCRs: Region C2, Meridional direction Load Combinations LC1O1 LC201-206 LC301-302 LC401-404 Mue kip*ft/ft
-0.64
-1.59
-2.50
-2.50 Mu kip*ft/ft
-0.64 218.63 230.27 257.16 Pu kip/ft 46.46 224.42 239.06 239.06 0Mn kip*ft/ft
-131.20 338.71 351.87 351.87 4>Pn kip/ft 750.70 570.55 555.34 520.23 Max DCR 0.00 0.65 0.65 0.73
ftfStEhengy CALCULATION COMPUTATION Page 41 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 Table 8 Maximurr Load Combinations LC101 LC201-206 LC301-302 LC401-404 Mue kip*ft/ft
-1.88
-0.65 17.03 1.21 DCRs: Region C3, Circumferential direction Mu kip*ft/ft
-1.88 43.86 32.07 71.65 Pu kip/ft
-0.47 14.41
-58.29 17.18
<CMn kip*ft/ft
-153.36 166.77 101.23 169.27
<]>Pn kip/ft
-156.39 775.60
-127.73 775.60 Max DCR 0.01 0.26 0.32 0.42 Table 9 Maximum DCRs: Region C3, Meridional direction Load Combinations LC101 LC201-206 LC301-302 LC401-404 Mu9 kip*ft/ft
-7.49
-2.23
-2.57
-2.57 Mu kip*ft/ft
-7.49 82.46 81.29 101.81 Pu kip/ft 38.26 57.81 56.83 56.83
<l>Mn kip*ft/ft
-201.41 219.04 218.16 218.16
<]>Pn kip/ft 784.30 784.30 784.30 770.95 Max DCR 0.04 0.38 0.37 0.47 Table 10 Maximum DCRs: Region C4, Circumferential direction Load Combinations LC101 LC201-206 LC301-302 LC401-404 Mue kip*ft/ft 9.55
-0.64 7.89 0.52 Mu kip*ft/ft 9.55 69.92 75.39 109.16 Pu kip/ft
-66.03 10.93 7.20 14.00 0Mn kip*ft/ft 236.90 306.85 303.46 309.64 kip/ft
-304.73 865.80 865.80 863.17 Max DCR 0.04 0.23 0.25 0.35 Table 11 Maximum DCRs: Region Load Combinations LC101 LC201-206 LC301-302 LC401-404 Mu9 kip*ftffi 38.15 43.25 40.56 40.56 Mu kip*ft/ft 38.15 102.57 97.96 118.40 Pu kip/ft 24.64 28.20 25.96 25.96 C4, Meridional direction
<t>Mn kip*ft/ft 189.12 192.34 190.31 190.31 Pn kip/ft 784.30 770.04 775.63 750.85 Max DCR 0.20 0.53 0.51 0.62
FirstEnergy CALCULATION COMPUTATION Page 42 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
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001 Table 12 Maximum DCRs: Region C5, Circumferential direction Load Combinations LC101 LC201-206 LC301-302 LC401-404 Mue kip*ft/ft 2.14 2.87
-7.58 3.40 Mu kip*ft/ft 2.14 2.87
-7.58 3.40 Pu kip/ft
-72.90
-100.82
-3.80
-94.58 4>Mn kip'ft/ft 227.17 202.35
-288.60 207.90
<t>Pn kip/ft
-311.78
-311.05
-306.29
-310.51 Max DCR 0.01 0.01 0.03 0.02 Table 13 Maximum DCRs: Region Load Combinations LC101 LC201-206 LC301-302 LC401-404 Mue kip*ft/ft 8.49 10.48
-14.61 10.41 Mu kip*ft/ft 8.49 10.48
-14.61 10.41 Pu kip/ft 2.44 2.55 1.40 2.22 C5, Meridional direction 0Mn kip*ft/ft 169.09 169.19
-168.16 168.89 4>Pn kip/ft 784.30 784.30 784.30 784.30 Max DCR 0.05 0.06 0.09 0.06 Table 14 Maximum DCRs: Region D1, Circumferential direction Load Combinations LC101 LC201-206 LC301-302 LC401-404 MU8 kip*ft/ft
-47.12
-0.71
-28.94 0.84 Mu kip*ft/ft
-47.12 39.34
-18.26 58.17 Pu kip/ft 100.11 38.51
-31.08 42.37
$Mn kip*ft/ft
-148.08 112.44
-48.93 115.19 4)Pn kip/ft 605.10 605.10
-68.86 589.91 Max DCR 0.32 0.35 0.37 0.51 Table 15 Maximum DCRs: Region Load Combinations LC101 LC201-206 LC301-302 LC401-404 Mue kip*ft/ft
-14.94 3.10 2.54 2.54 Mu kip*ft/ft
-14.94 47.28 43.07 57.72 Pu kip/ft 44.20 44.97 39.27 39.27 D1, Meridional direction 4>Mn kip*ft/ft
-105.82 117.04 112.98 112.98
<f>Pn kip/ft 605.10 605.10 605.10 590.66 Max DCR 0.14 0.40 0.38 0.51
F*rst£herqy CALCULATION COMPUTATION Page 43 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
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001 Table 16 Maximum DCRs Load Combinations LC101 LC201-206 LC301-302 LC401-404 Mu9 kip*ft/ft
-4.68
-2.71
-2.44
-2.50
- Region D2, Circumferential direction Mu kip*ft/ft
-4.68 42.89 43.36 61.85 Pu kip/ft 8.53 36.00 36.32 36.19
- Mn kip*ft/ft
-90.94 153.09 153.32 153.23
^Pn kip/ft 622.80 622.80 622.80 601.09 Max DCR 0.05 0.28 0.28 0.40 Table 17 Maximum DCRs: Region D2, Meridional direction Load Combinations LC101 LC201-206 LC301-302 LC401-404 Mu8 kip'ftm
-10.09
-5.55
-4.88
-4.89 Mu kip*ft/ft
-10.09 43.20 41.31 59.15 Pu kip/ft 36.04 41.45 37.41 37.37 0Mn kip*ft/ft
-96.29 156.98 154.09 154.07 4>Pn kip/ft 622.80 622.80 622.80 605.98 Max DCR 0.10 0.28 0.27 0.38 Table 18 Maximum DCRs: Region D3, Circumferential direction Load Combinations LC101 LC201-206 LC301-302 LC401-404 MuS kip*ft/ft
-5.08 7.40 7.04
-1.93 Mu kip*ft/ft
-5.08 42.33 41.79 74.77 Pu kip/ft
-4.63
-72.32
-71.20 18.86
- Mn kip*ft/ft
-126.88 193.25 194.04 257.51
<^Pn kip/ft
-178.05
-241.00
-240.29 655.34 Max DCR 0.04 0.22 0.22 0.29 Table 19 Maximum DCRs: Region D3, Meridional direction Load Combinations LC101 LC201-206 LC301-302 LC401-404 Mu6 kip*ft/ft 29.73 33.32 31.16 31.16 Mu kip*ft/ft 29.73 69.94 66.81 89.69 Pu kip/ft 25.90 29.99 27.80 27.80 4>Mn kip*ft/ft 146.82 149.69 148.15 148.15
<!>Pn kip/ft 647.20 625.60 630.71 593.39 Max DCR 0.20 0.47 0.45 0.61
FirstEnerqv CALCULATION COMPUTATION Page 44 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 As indicated in Figure 13 thru Figure 20 as well as in Table 4 thru Table 19 (also see Attachment D for further detail),
the P-M demands for various regions of the Shield Building for Ultimate Strength Design (USD) load combinations (LC101-LC404) are enveloped by available capacities. The maximum DCR = 0.76 (highlighted in Table 5) occurs in meridional direction in region C1 close to the basemat elevation under the load combination D
+ L +
E' + RP + Ta. On the other hand, the maximum DCR in circumferential direction (note that laminar cracks only affect capacity in circumferential direction) within the cracked region is found to be 0.54 (Highlighted in Table 6).
Note that these DCR's are localized maxima based on the 4ft x
5ft element sizes.
The demands outside/away from elements representing such maximum demands drop significantly (see Figure 13 thru Figure 20 and Attachment D),
indicating a sufficient overall design margin for the SB.
The P
- M Figures 13-20 and Tables 4 to 19, do not include the "Shield Building Annulus Pressure Drop Due to Cold Water Pipe Rupture" identified in Ref.
8k.
Following review of the Figures, and Tables it is confirmed that additions of these compressive forces to Figures 13-20 (detailed data are in Att.
D) will not cause any appreciable changes in the DCRs tabulated in Tables 4 to 19.
Given the design margins shown in Tables 4 to 19, the Shield Building will still meet the design basis requirements.
7.8 Reinforcement and Concrete Stresses Evaluation The purpose of this section is to calculate stresses in reinforcement (tension and compression) and concrete (compression) for Working Stress Design (WSD) load combinations (LC501-803).
Therefore, hoop rebar stresses reported in this section are derived using strain compatibility (no slip between concrete and rebar) and equilibrium concepts, as detailed in Attachment E.
Note that Attachment E also presents stress evaluation for Ultimate Strength Design (USD) load combinations (LC101-404) for information only.
To be consistent with References 9(a) and 9(b), the following criteria are used for the derivations:
Plane sections before bending remain plane after bending The stress strain behavior of concrete and steel is known Reinforcement and concrete stresses (negative as tension) are calculated for various regions of the SB, and the Demand-Allowable-Ratios (DAR) is tabulated in Table 20 thru Table 35.
In particular, the allowable stresses for the circumferential Outer Face (OF) rebar within regions C1-C5 (cylinder wall) are reduced by 8% compared to ones applied to inner face (IF)
- rebar, as discussed in Section 3.0.
Concrete and reinforcement stresses for ultimate strength design load combinations (LC101~404) are also provided in Attachment E for information.
Table 20 Stress Evaluation at Maximum DAR, Region C1, Circumferential direction Load Combinations LC501-502 LC6O1 LC701-702 LC801-803 Stress Demand Concrete (psi) 737 106.9 81.2 932.7 OF Rebar (ksi)
-9.3 0.7 0.3
-7.5 IF Rebar (ksi) 3.3 0.5 0.5 4.9 Allowable stresses Concrete (psi) 1600 1000 1500 2680 OF Rebar (ksi) 22.1 13.8 16.6 30 IF Rebar (ksi) 24 15 18 32.4 Demand to Allowable Ratio (DAR)
Concrete 0.46 0.11 0.05 0.35 OF Rebar 0.42 0.05 0.02 0.25 IF Rebar 0.14 0.03 0.03 0.15
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001 Table 21 Stress Evaluation at Maximum DAR, Region Load Combinations LC501-502 LC601 LC701-702 LC801-803 Stress Demand Concrete (psi) 1294.9 339.4 0
2182.9 OF Rebar (ksi)
-9.4 2.4
-in
-n.i IF Rebar (ksi) 7.3 1.6
-15.8 14.3 C1, Meridional direction Allowable stresses Concrete (psi) 1600 1000 1500 2680 OF Rebar (ksi) 24 15 18 32.4 IF Rebar (ksi) 24 15 18 32.4 Demand to Allowable Ratio (DAR)
Concrete 0.81 0.34 0.00 0.81 OF Rebar 0.39 0.16 0.15 0.34 IF Rebar 0.30 0.11 0.88 0.44 Table 22 Stress Evaluation at Maximum DAR Load Combinations LC501-502 LC601 LC701-702 LC801-803 Stress Demand Concrete (psi) 459.7 33.5 13.4 554.1 OF Rebar (ksi)
-10.8 0.2 0.1
-10.3 IF Rebar (ksi) 1.2
-0.3 0.1 1.9
, Region C2, Circumferential direction Allowable stresses Concrete (psi) 1600 1000 1500 2680 OF Rebar (ksi) 22.1 13.8 16.6 30 IF Rebar (ksi) 24 15 18 32.4 Demand to Allowable Ratio (DAR)
Concrete 0.29 0.03 0.01 0.21 OF Rebar 0.49 0.01 0.01 0.34 IF Rebar 0.05 0.02 0.01 0.06 Table 23 Stress Evaluation at Maximum DAR, Reqion Load Combinations LC501-502 LC601 LC701-702 LC801-803 Stress Demand Concrete (psi) 1196.7 95.4 0
2008.1 OF Rebar (ksi)
-10.4 0.7
-2.7
-13.4 IF Rebar (ksi) 6.4 0.6
-5.9 12.4 C2, Meridional direction Allowable stresses Concrete (psi) 1600 1000 1500 2680 OF Rebar (ksi) 24 15 18 32.4 IF Rebar (ksi) 24 15 18 32.4 Demand to Allowable Ratio (DAR)
Concrete 0.75 0.10 0.00 0.75 OF Rebar 0.43 0.05 0.15 0.41 IF Rebar 0.27 0.04 0.33 0.38
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001 Table 24 Stress Evaluation at Maximum DAR Load Combinations LC501-502 LC6O1 LC701-702 LC801-803 Stress Demand Concrete (psi) 431.1 31.6 0
525.7 OF Rebar (ksi)
-10.3 0.1
-1.7
-9.8 IF Rebar (ksi) 1.1
-0.3
-2.7 1.8 Region C3, Circumferential direction Allowable stresses Concrete (psi) 1600 1000 1500 2680 OF Rebar (ksi) 22.1 13.8 16.6 30 IF Rebar (ksi) 24 15 18 32.4 Demand to Allowable Ratio (DAR)
Concrete 0.27 0.03 0.00 0.20 OF Rebar 0.47 0.01 0.10 0.33 IF Rebar 0.05 0.02 0.15 0.06 Table 25 Stress Evaluation at Maximum DAR, Region Load Combinations LC501-502 LC601 LC701-702 LC801-803 Stress Demand Concrete (psi) 706.3 103.8 133.9 855.4 OF Rebar (ksi)
-10.2 0.7 0.9
-10 IF Rebar (ksi) 3 0.3 0.5 4
C3, Meridional direction Allowable stresses Concrete (psi) 1600 1000 1500 2680 OF Rebar (ksi) 24 15 18 32.4 IF Rebar (ksi) 24 15 18 32.4 Demand to Allowable Ratio (DAR)
Concrete 0.44 0.10 0.09 0.32 OF Rebar 0.43 0.05 0.05 0.31 IF Rebar 0.13 0.02 0.03 0.12 Table 26 Stress Evaluation at Maximum DAR Load Combinations LC501-502 LC601 LC701-702 LC801-803 Stress Demand Concrete (PSi) 558.6 0
0 615.3 OF Rebar (ksi)
-10.2
-7.2
-12.4
-9.9 IF Rebar (ksi) 2
-4.9
-9.5 2.4 Region C4, Circumferential direction Allowable stresses Concrete (psi) 1600 1000 1500 2680 OF Rebar (ksi) 22.1 13.8 16.6 30 IF Rebar (ksi) 24 15 18 32.4 Demand to Allowable Ratio (DAR)
Concrete 0.35 0.00 0.00 0.23 OF Rebar 0.46 0.52 0.75 0.33 IF Rebar 0.08 0.33 0.53 0.07
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001 Table 27 Stress Evaluation at Maximum DAR, Region C4, Meridional direction Load Combinations LC501-502 LC601 LC701-702 LC801-803 Stress Demand Concrete (psi) 880.7 296.2 387.3 1061.8 OF Rebar (ksi)
-18.1
-3.2
-4.2
-21 IF Rebar (ksi) 3 1.4 1.8 3.8 Allowable stresses Concrete (psi) 1600 1000 1500 2680 OF Rebar (ksi) 24 15 18 32.4 IF Rebar (ksi) 24 15 18 32.4 Demand to Allowable Ratio (DAR)
Concrete 0.55 0.30 0.26 0.40 OF Rebar 0.75 0.21 0.23 0.65 IF Rebar 0.13 0.09 0.10 0.12 Table 28 Stress Evaluation at Maximum DCR Load Combinations LC501-502 LC601 LC701-702 LC801-803 Stress Demand Concrete (psi) 0 0
0 0
OF Rebar (ksi)
-7
-7.2
-12.6
-12.6 IF Rebar (ksi)
-6.3
-6.2
-11.4
-11.4 Region C5, Circumferential direction Allowable stresses Concrete (psi) 1600 1000 1500 2680 OF Rebar (ksi) 22.1 13.8 16.6 30 IF Rebar (ksi) 24 15 18 32.4 Demand to Allowable Ratio (DAR)
Concrete 0.00 0.00 0.00 0.00 OF Rebar 0.32 0.52 0.76 0.42 IF Rebar 0.26 0.41 0.63 0.35 Table 29 Stress Evaluation at Maximum DAR, Region Load Combinations LC501-502 LC601 LC701-702 LC801-803 Stress Demand Concrete (psi) 61.1 76 98.9 98.9 OF Rebar (ksi)
-1
-1.4
-1.8
-1.8 IF Rebar (ksi) 0.2 0.3 0.3 0.3 C5, Meridional direction Allowable stresses Concrete (psi) 1600 1000 1500 2680 OF Rebar (ksi) 24 15 18 32.4 IF Rebar (ksi) 24 15 18 32.4 Demand to Allowable Ratio (DAR)
Concrete 0.04 0.08 0.07 0.04 OF Rebar 0.04 0.09 0.10 0.06 IF Rebar 0.01 0.02 0.02 0.01
FirstEnejTiv CALCULATION COMPUTATION Page 48 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
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001 Table 30 Stress Evaluation at Maximum DAR Load Combinations LC501-502 LC601 LC701-702 LC801-803 Stress Demand Concrete (psi) 733.4 65.2 111.8 846.6 OF Rebar (ksi)
-8.4 0.5 0.8
-8.4 IF Rebar (ksi) 2.8 0.4 0.7 3.5 Region D1, Circumferential direction Allowable stresses Concrete (psi) 1600 1000 1500 2680 OF Rebar (ksi) 24 15 18 32.4 IF Rebar (ksi) 24 15 18 32.4 Demand to Allowable Ratio (DAR)
Concrete 0.46 0.07 0.07 0.32 OF Rebar 0.35 0.03 0.04 0.26 IF Rebar 0.12 0.03 0.04 0.11 Table 31 Stress Evaluation at Maximum DAR, Region Load Combinations LC501-502 LC601 LC701-702 LC801-803 Stress Demand Concrete (psi) 602.3 87.4 112.6 681 OF Rebar (ksi)
-8.6 0.6 0.7
-8.1 IF Rebar (ksi) 1.9 0.4 0.4 2.5 D1, Meridional direction Allowable stresses Concrete (psi) 1600 1000 1500 2680 OF Rebar (ksi) 24 15 18 32.4 IF Rebar (ksi) 24 15 18 32.4 Demand to Allowable Ratio (DAR)
Concrete 0.38 0.09 0.08 0.25 OF Rebar 0.36 0.04 0.04 0.25 IF Rebar 0.08 0.03 0.02 0.08 Table 32 Stress Evaluation at Maximum DAR Load Combinations LC501-502 LC601 LC701-702 LC801-803 Stress Demand Concrete (psi) 645.4 46.9 98.1 768.3 OF Rebar (ksi)
-8.5 0.3
-0.2
-7.8 IF Rebar (ksi) 2.2 0
-3.8 3.1
, Region D2, Circumferential direction Allowable stresses Concrete (psi) 1600 1000 1500 2680 OF Rebar (ksi) 24 15 18 32.4 IF Rebar (ksi) 24 15 18 32.4 Demand to Allowable Ratio (DAR)
Concrete 0.40 0.05 0.07 0.29 OF Rebar 0.35 0.02 0.01 0.24 IF Rebar 0.09 0.00 0.21 0.10
FirstEnerctv CALCULATION COMPUTATION Page 49 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
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001 Table 33 Stress Evaluation at Maximum DAR, Region Load Combinations LC501-502 LC601 LC701-702 LC801-803 Stress Demand Concrete (psi) 614.5 123.1 167 684.8 OF Rebar (ksi)
-7.2 0.8 1
-6.6 IF Rebar (ksi) 2.3 0.2 0.3 2.8 D2, Meridional direction Allowable stresses Concrete (psi) 1600 1000 1500 2680 OF Rebar (ksi) 24 15 18 32.4 IF Rebar (ksi) 24 15 18 32.4 Demand to Allowable Ratio (DAR)
Concrete 0.38 0.12 0.11 0.26 OF Rebar 0.30 0.05 0.06 0.20 IF Rebar 0.10 0.01 0.02 0.09 Table 34 Stress Evaluation at Maximum DAR Load Combinations LC501-502 LC601 LC701-702 LC801-803 Stress Demand Concrete (psi) 609.7 0
0 276.3 OF Rebar (ksi)
-9
-5.9
-10
-17.4 IF Rebar (ksi) 1.9
-7.4
-15
-1.8 Region D3, Circumferential direction Allowable stresses Concrete (psi) 1600 1000 1500 2680 OF Rebar (ksi) 24 15 18 32.4 IF Rebar (ksi) 24 15 18 32.4 Demand to Allowable Ratio (DAR)
Concrete 0.38 0.00 0.00 0.10 OF Rebar 0.38 0.39 0.56 0.54 IF Rebar 0.08 0.49 0.83 0.06 Table 35 Stress Evaluation at Maximum DAR, Region Load Combinations LC501-502 LC601 LC701-702 LC801-803 Stress Demand Concrete (psi) 912.2 349.3 453.3 1099 OF Rebar (ksi)
-15.4
-3.2
-4
-17.6 IF Rebar (ksi) 2.5 1.4 1.9 3.4 D3, Meridional direction Allowable stresses Concrete (psi) 1600 1000 1500 2680 OF Rebar (ksi) 24 15 18 32.4 IF Rebar (ksi) 24 15 18 32.4 Demand to Allowable Ratio (DAR)
Concrete 0.57 0.35 0.30 0.41 OF Rebar 0.64 0.21 0.22 0.54 IF Rebar 0.10 0.09 0.11 0.10 As indicated in Tables 20-35, both concrete and reinforcement stresses are less than specified allowable stresses for working stress load combinations (LC501-803).
In particular, maximum Demand-Allowable-Ratio (DAR) for concrete and steel stresses is 0.81 and 0.88 (highlighted in Table 21),
which occur in meridional direction in region C1 close to the basemat elevation under load combinations D+E+To and D+E, respectively.
On the other hand, the maximum DAR in circumferential OF rebar within cracked regions (i.e., below EL 801')
is found to be 0.75(highlighted in Table 27).
Note that these DAR's are localized maxima based on the 4ft x 5ft
RrsfEhergy CALCULATION COMPUTATION Page 50 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
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001 element sizes.
- Again, the demands outside/away from elements representing such maximum demands drop significantly (see Attachment D), indicating a sufficient overall design margin for the SB.
In order to investigate impact of observed laminar cracks on the structure integrity, which is of the particular interest of this calculation, results of maximum DCRs and DARs in circumferential direction (note that laminar cracks only affect capacity in circumferential direction) within various cracked regions are identified in Figure 21, utilizing the cracking map provided in Ref. 25. Note that SB is considered an axisymmetrical structure in general and lateral load due to seismic (E or E') or wind
/ tornado (W or W) may come from any direction.
For a given seismic / wind / tornado lateral load direction, aforementioned maximum DCR / DARs occur at particular angles with respect to the lateral load direction.
In Figure 21, lateral seismic
/ wind forces are assumed at illustrated direction (approximate 240 degrees) for demonstration, in order to identify locations of maximum DCRs and DARs accordingly.
Based on the evaluations above, it is concluded that the SB is structurally adequate for combined axial and moment effects for all design load combinations.
DCR = 0.42 (D+E'+Rp+TA, C3, Table 8)
DCR = 0.35 (D+E'+Rp+T DAR in OF rebar = 0.52 (D+W, C4, Table 26) 1, Table 10)
DAR in OF rebar = 0.75(D+E, C4, Table 26)
DAR in IF rebar = 0.53 (D+E, C4, Table 26)
DCR = 0.50 (D+E'+Rp+TA, C2, Table 6)
.54 (D+L+W'+To, C2, Table 6)
Seismic / Wind Direction Figure 21 Maximum DCRs and DARs in circumferential direction within cracked regions
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001 51 7.9 Shear Evaluation Allowable shear stresses within the Shield Building, conservatively neglecting contribution of reinforcements, are given by 2q>s[f~c for ultimate strength design (LC101-LC404) and \\.\\JT~c\\qx working stress design (LC501
~
LC803) per ACI 318-63.
In which,
> Stage-1 Stage-2 Stage-3 Stage-4 Stage-5 Stage-6 Effect of previous openings in construction sequence for RVCH/SGs construction opening Figure 22: Construction sequence for creation and restoration of RVCH/SGs construction opening. CALCULATION COMPUTATION Page 55 NOP-CC-3002-01 Rev. 03 CALCULATION NO. C-CSS-099.20-063 REVISION: 001 L Strain due Total Strain under vertical Initial Strain overturning moment and lateral load (a) Strain profile showing strain concentrations near opening 1 Strain d ue Total Strain under vertical Initial Strain overturning moment and lateral load (b) Strain profile neglecting strain concentrations near opening Figure 23: Compressive strain profile after closure of construction opening. The capacity of the SB after restoration of the RVCH/SGs opening under vertical and seismic loads is investigated here per the requirements of ACI 307-69 (Ref. 9a) & ACI 318-63 (Ref. 9b), which is consistent with the original design of the SB. In particular the following criteria are used (see supplement to Ref. 9a and Section 1503 of ACI 318-63, Ref. 9b): (a) The capacity of the section under bending and axial load is based on the applicable principles of equilibrium and strain compatibility. (b) The strains in the concrete are assumed directly proportional to the distance from the neutral axis. In other words, plane sections before bending remain plane after bending. (c) The maximum strain at the extreme compression fiber is limited to 0.003. (d) The rebar stresses are calculated as Eses, as shown in Figure 2(b); where Es = 29000 ksi and es is the rebar strain, which is limited to be less than the yield strain ey (i.e., ss<ey). In other words steel yielding is not allowed. (e) A parabolic stress-strain curve is used for concrete under compression per Ref. 13, as shown in Figure 2(a). RrstEnergy CALCULATION COMPUTATION Page 56 NOP-CC-3002-01 Rev. 03 CALCULATION NO. C-CSS-099.20-063 REVISION: 001 Figure 24 shows a section of the Shield Building across the proposed RVCH/SGs opening location. As can be seen, the external moment (M) and axial force (P) are resisted by internal concrete (C) and steel forces (F), as given by Eqs. 2 and 3. Referring to Figure 24, the internal forces and their locations are calculated per Eqs. 4 and 5, using the concrete and steel stress-strain relationships provided in Figure 2(b). In general, for a given demand {M and P), the location of the neutral axis c must be solved by iteration, until the equilibrium Eqs. 2 and 3 are satisfied, as summarized in the following steps. Detailed calculations are provided in Attachment J. (a) For a given design load combination, determine the bending moment (M) and axial force demand (P) at the building section or elevation of interest. (b) Calculate the initial rebar strain per Eq. 1, where A is the area of the cross section without including the area of the proposed opening and original construction opening. (c) Guess the location of the neutral axis c and the bending strain in the outermost compressive fiber £m. (d) Calculate the concrete compression force (C) using the relations provided in Eq. 4. (e) Calculate the rebar forces (F,-) for each rebar location (di) using the relations provided in Eq. 5. (f) Repeat steps (c), (d) and (e) until equilibrium of Eqs. 2 and 3 are satisfied. This approach is equivalent to the solution of Equations 2 and 3 for the unknown £c (compressive strain) and c (neutral axis location). P=C + I W Force Equilibrium Eq.2
- -fl-:
- "f*w Fy b{y)dy
y0
Ata (0,c A) i>(rf) :
0 if d> h Moment Equilibrium Calculation on internal compressive force C Compressive strain ec at location y-Distance from the neutral axis to the first concrete fiber under compression, where h = 144 ft is the SB diameter.
Width (b) of the concrete section
-i at location d, where Re = 72 ft (d - Re)2\\
if 2.5ft <d<h-2.5ft and /?,= 69.5 ft are the external and internal radius of the SB.
Eq.3 Eq.4 y'b=c~~c Location of concrete compression resultant
FirstEnercty Page 57 CALCULATION COMPUTATION NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 Fs\\Asi'fsi-drc):=
REVISION:
001 fsi -Asi Force resultant at rebar i
Eq. 5 ifsi -O.*Sfc)-Asi if di<C Es£si fysign(zsl) if Esesi
>f Stress resultant at rebar i Es{c'di'£cm'ao'd£o) :=
c-e cb cm
£cm cb~di cb f.l Strain in rebar i L
initial Bending Total strain stress Internal Forces External Forces Figure 24: Shield building section showing strain, stress, and force distribution under axial and bending demands Thermal moments are calculated herein using the considerations of ACI 307-69 as described in Section 7.6.
In this section, load combinations LC403: D + L+
E' + Ta+ Rp (Vertical E' upward)
, LC 702: D + E (Vertical E upward) and LC803: D + To + E (Vertical E upward) are selected and used as the most governing load case for evaluation of construction sequence and dead load redistribution.
7.12.2 Sectional Analysis Results Sectional analysis calculations are detailed in Attachment J, the summarized results are provided next.
It must be noted that the structural integrity of the SB opening is checked at elevations affected by creation and closure of aforementioned temporary openings.
FirstEn&riv CALCULATION COMPUTATION Page 58 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
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001 Global Section Capacity V.S. Demand (D + E' + Rp)
In this section, the bending capacity of the SB is calculated for the elevations affected by creation and closure of temporary construction openings.
Results are presented in Figure 25.
Figure 25 shows the SB moment as a function of the maximum rebars tensile strain. Note that 0.9ey is also indicated in these figures, where 0.9 is the strength reduction factor for flexure.
For the sake of clarity, only elevations 602',
619.3',
629.25' and 638.5' are plotted. For comparison purposes the maximum SSE moment demands (also see Att. J) at elevations 602' (2.4 X 10s kip-ft) and 638.5' (1.7 X 106 kip-ft) are included in the plots. As can be seen these moment demands are well below the moment capacity of the SB.
Furthermore, no yielding of the rebar (emax <
ey) takes place for these maximum demands.
In fact the SSE bending moment demand will have to be increased by a
factor of approximately 2 before rebar yields. Therefore, it can be concluded that the SB has a large moment and ductility capacity reserve against the design SSE.
7.0x10 EL. 602' EL. 619.30' EL. 629.25' EL. 638.50' Normalized tensile strain esmax/ey Figure 25: Maximum rebar strain versus section moment for different elevations along the SGR opening.
Ultimate Strength Design Check The ultimate capacity of the SB is checked at the elevations affected by creation and closure of temporary construction openings for the governing load combination LC403:
D
+
E'
+
Rp +
Ta considering the vertical component of the earthquake acting upwards (LC1 in Attachment J). Note the live load is conservatively ignored in Attachment J because it reduces tension in the critical region of interest.
The response due to D +
RP +
E' is calculated here
- first, since this input is required to determine the thermal stresses.
Figure 26 below shows the distribution of rebar strains through the SB cross-section for different elevations along the SGR opening height for D + E' + Rp. As expected, the maximum tensile strains take place at the SGR opening location (i.e., d > 128.8'). Note that in this figure tensile strains are plotted positive.
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CALCULATION NO.
C-CSS-099.20-063 Page CALCULATION COMPUTATION 03 REVISION:
001 59 D + Rp+ E' (Vertical component of E' acting upwards) c ra XI 6x10 4x10 2x10
-2x10
-4x10
-4 A
0
-4
-4 E.L. 579
- E.L. 602
E.L. 615.2 E.L. 619.3 E.L. 623.4 E.L. 627.5 E.L. 629.5 E.L. 631.5 E.L. 635.5 EL. 638.5
&02 Large tensile strains inside the opening If 0
25 50 75 100 125 Rebar location d measured from location of maximum compression fiber
[ft]
150 Figure 26: Rebar strain through the SB cross section along the SGR opening (D + E' + Rp)
Maximum rebar tensile and concrete compressive stresses for D
+
Rp +
E' loading are reported in Table 38 (Attachment J). Note that the vertical component of E' is acting upward for this case. As can be seen the rebar tensile stresses are about 23% (14/60=0.23) of the yield stress.
Similarly, the concrete compressive stresses are about 23%(918.5/4000 = 0.23) of the concrete compression strength. Therefore the SB remains elastic during the site SSE.
Maximum rebar tensile stresses including thermal effects (D +
E' + Ta+ Rp) are reported in Table 39 (Attachment J), as can be seen the rebar stresses are about 32%(19.3/60=0.32) of the nominal yield stress. Per Ref.
1 Section 3.8.2.3.4, the
<l> factor for flexure is 0.9. Similarly, the concrete compressive stresses are about 52%(2083/4000 =
0.52) of the concrete compression strength.
Therefore the SB remains elastic for the most governing loading combination (LC403).
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C-CSS-099.20-063 REVISION:
001 Table 38: Maximum rebar tensile and concrete compressive stresses (D + Rp + E')
(E'verticai upward)
(Positive means compression, negative means tension)
Elevation (ft) 579.00 602.00 615.20 619.30 623.40 627.50 629.25 631.50 635.50 638.50 Maximum rebar tensile stress (ksi)
Outside face O.F. d = 143.6 ft
-14
-11.1
-9.3
-8.9
-8.4
-8
-7.8
-7.7
-9
-6.9 Maximum concrete compressive stress (psi)
Outside face O.F. @ d = 0 ft 918.5 782.9 704.5 681 657.5 633.9 623.8 606.4 624.8 572.1 Table 39: Maximum rebar tensile stresses for LC 403 (D+ E' + Rp + Ta)
(E'venicai upward)
(Positive means compression, negative means tension)
Elevation (ft) 579.00 602.00 615.20 619.30 623.40 627.50 629.25 631.50 635.50 638.50 Maximum rebar tensile stress (ksi)
O.F. @d = 143.6 ft
-19.3
-16.6
-15.3
-15.1
-14.9
-14.7
-14.6
-14.8
-15.2
-14.5 Maximum concrete compressive stress (psi)
Outside face O.F. @ d = 0 ft 2083.1 1928.3 1833.5 1804.1 1774.3 1744 1730.9 1717.9 1742.7 1670.7 Working Stress Design Check The working stress capacity of the SB is checked for the governing load combination LC702 (D + E) and LC803 (D + E + To). The critical loading condition for this check occur when the vertical component of the site OBE is acting
- upward, which results in maximum tensile stresses and thus maximum cracking (see discussion in
CALCULATION COMPUTATION Page 61 NOP-CC-3002-01 Rev. 03 CALCULATION NO.
C-CSS-099.20-063 REVISION:
001 Section 7.12.1). Under this scenario, the section capacity is checked at two critical locations, EL. 629.25' and EL.
579'.
Note that, for the reinforcement pattern above the opening the maximum bending moment takes place at EL.
629.25'.
Similarly, for the reinforcement pattern below EL.
629.25' the maximum bending moment takes place at EL.
579'.
In
- addition, to reduce the compressive
- stresses, the dead load from elevation 638.5' is conservatively used for both critical sections.
Maximum rebar tensile and concrete compressive stresses for D + E are reported in Table 40. As can be seen the rebar tensile stresses are about 13.6%
(4.4/32.4=0.136) of the allowable
- stress, while the concrete compressive stresses are about 19.8% (530.8/2680 = 0.198) of the concrete allowable compression stress.
Maximum rebar tensile and concrete compressive stresses for D + E + To load combination are reported in Table
- 41. As can be seen the maximum rebar tensile stress is 8.9 ksi, which is much lower that the admissible tensile stress of 32.4 ksi per Ref.
1, Sect.3.8.2.2.6.
Similarly, the maximum concrete compressive stress is 1839
- psi, which is lower that the admissible compressive stress of 2680 psi per Ref.
1, Sect.3.8.2.2.6.
Table 40: Maximum rebar tensile and concrete compressive stresses LC 702 (D+ E)
(Positive means compression, negative means tension)
Elevation (ft) 579 629.25 Maximum rebar tensile stress (ksi)
O.F. @d = 143.6 ft
-4.4
-1.7 Maximum concrete compressive stress (psi)
O.F. @ d = Oft 530.8 381.3 Table 41: Maximum rebar tensile stresses and concrete compression stresses LC 803 (D+ E + To)
(Positive means compression, negative means tension) (opening area uplift)
Elevation (ft) 579 629.25 Maximum rebar tensile stress (ksi)
O.F. @d = 143.6 ft
-8.9
-8.0 Maximum Concrete compression stress (psi)
@ d = Oft 1839.2 1628.5 Based on the evaluations in this section, it is concluded that the regions of SB, which are affected by creations and restorations of temporary openings and dead load redistribution, also meet the acceptance criteria described in Section 5.0.
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C-CSS-099.20-063 REVISION:
001
8.0 CONCLUSION
A new design calculation was performed for the existing Shield Building (SB) that includes the cylindrical wall, the dome and the springline
- area, with observed laminar cracking for the design basis
- loads, under all the design basis events, which are documented in Refs. 19a~19e, 25 and 27-35.
Methodologies applied in this calculation are consistent with ACI 318-63 and ACI 307-69 as specified in USAR.
The structure was evaluated using the acceptance criteria established in Section 5.0.
In particular, the Shield Building is evaluated for the following items:
P-M Interaction Diagram and Demand to Capacity Ratio (DCR) for combined axial and bending demands Reinforcement and concrete stresses Out-of-plane and in-plane shear Maximum concrete crack width Tornado Missile Impact Sectional analysis to address the dead-load redistribution effects due to temporary openings' creations and restorations A summary of code compliance for computed results is provided in Table 42.
Based on the
- results, it is concluded that the Shield Building meets all design requirements specified in USAR and will perform its USAR described design functions. A section-by-section code compliance evaluation is also conducted and documented in Attachment L, which indicates the SB meets all applicable requirements of these codes.
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001 Shield Build Table 42: Code Compliance Summary of Computed ng Evaluation Ultimate strength evaluation for bending plus axial load Thermal moment analysis Allowable working stress (D + To, To),
bending plus axial load Allowable working stress (D + W),
bending plus axial load Allowable working stress (D + E),
bending plus axial load Allowable working stress (D + To + W, D + To + E),
bending plus axial load Out-of-plane shear evaluation Global shear evaluation (in-plane) meridional rebar circumferential rebar concrete meridional rebar circumferential rebar concrete meridional rebar circumferential rebar concrete meridional rebar circumferential rebar concrete Ultimate strength design Allowable stress design Ultimate strength design Allowable stress design Cracking width Code Provision ACI 318-63 Section 1503 Supplement to ACI 307-69:
Derivation of Equations ACI 307 -69 Section 4.9 ACI 307 -69 Section 4.9 ACI 307 -69 Section 4.9 ACI 307 -69 Section 4.9 ACI 307 -69 Section 4.9 ACI 307 -69 Section 4.9 ACI 307 -69 Section 4.9 ACI 307 -69 Section 4.9 ACI 307 -69 Section 4.9 ACI 307 -69 Section 4.9 ACI 307 -69 Section 4.9 ACI 307 -69 Section 4.9 ACI 318-63, Section 1701 ACI 318-63, Section1201 ACI 318-63, Section1701 1703 ACI 318-63, Section1201-1203 ACI 318-63, Section 1508 Criteria Demand to Capacity Ratio (DCR) no larger than 1.0 Result Maximum DCR = 0.76 Computed thermal moments are presented in Figures 8 thru 11, and incorporated in the ultimate strength evaluation Allowable stress
= 24 ksi Allowable stress
= 22.1 ksi*
Allowable stress
= 1600 psi Allowable stress
= 15 ksi Allowable stress
= 13.8 ksi*
Allowable stress
= 1000 psi Allowable stress
= 18 ksi Allowable stress
= 16.6 ksi*
Allowable stress
= 1500 psi Allowable stress
= 32.4 ksi Allowable stress
= 30 ksi*
Allowable stress
= 2680 psi Allowable stress
= 107.5 psi Allowable stress
70 psi Required As
1.574 in2 / ft Required As
=1.515 in2/ft 0.01 in 18 ksi 10.8 ksi 1295 psi 3.2 ksi 7.4 ksi 349 psi 15.3 ksi 15 ksi 453 psi 21 ksi 17.4 ksi 2182 psi 39 psi 24 psi Provided As
= 2.35 in2/ft Provided As
=2.35 in2/ft 0.086 in Results Code Compliance Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Note P-M interaction diagrams reported in Figures 13 thru 28, ultimate strength reported in Tables 4 thru 19.
Methodology to perform thermal analysis Carried out at the bottom of the SB under SSE Carried out at the bottom of the SB under OBE "Usage of reduced ultimate strengths and allowable stresses for OF circumferential reinforcements, and its compliance with ACI 318-63 code is discussed in Section 3.0.