ML102870560
| ML102870560 | |
| Person / Time | |
|---|---|
| Site: | Crystal River  |
| Issue date: | 01/23/2010 |
| From: | Hibbard J MPR Associates |
| To: | Office of Information Services |
| References | |
| FOIA/PA-2010-0116 | |
| Download: ML102870560 (126) | |
Text
MPR Associates, Inc.
320 King Street OMPR Alexandria, VA 22314 CALCULATION TITLE PAGE Client:
Progress Energy Page 1 of 12 plus Attachment Project: Task No.
CR3 Containment Calculations 0102-0906-0135
Title:
Calculation No.
Concrete Modulus of Elasticity and Specified Compressive Strength 0102-0135-02 Preparer / Date Checker / Date Reviewer & Approver / Date Rev. No.
J. L. Hibbard Chris Bagley P. Butler 1-16-2010 1-16-2010 1-16-2010 QUALITY ASSURANCE DOCUMENT This document has been prepared, checked, and reviewed/approved in accordance with the Quality Assurance requirements of 10CFR50 Appendix B, as specified in the MPR Quality Assurance Manual.
MPR-QA Form QA-3.1-1, Rev. 1 PIDIq
MPR Associates, Inc.
320 King Street WMPR Alexandria, VA 22314 RECORD OF REVISIONS Calculation No. Prepared By Checked By Page: 2 0102-0135-02 ._. k A- . .. /
Revision Affected Pages Description 0 All Initial Issue Note: The revision number found on each individual page of the calculation carries the revision level of the calculation in effect at the time that page was last revised.
I MPR QA Form QA-3.1-2, Rev. 0
MVPR Associates, Inc.
320 King Street 50 M PRAlexandria, VA 22314 Calculation No. Prepared By Checked By Page: 3 0102-0135-02 Revision: 0 Table of Contents 1.0 Purpose.................................................................................. 4 2.0 Summary ................................................................................ 4 3.0 Background............................................................................. 5 4.0 Assumptions......................... .................................................. 5
- 4. 1 Unverified Assumptions.................................................................... 5 4.2 Other Assumptions.......................................................................... 5 5.0 Approach ............... ................................................................. 6 6.0 Calculation .............................................................................. 8 6.1 Design Inputs ................................................................................ 8 6.2 Modulus of Elasticity ....................................................................... 9 7.0 References .............................................................................. 1 Attachment................................................................................... 13 MPR QA Form: QA-3.1-3, Rev. 0
Calculation No.:
YR MPR Associates, Inc.
Prepared By: S. , 0102-0135-02 Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: Page No.: 4 1.0 PURPOSE This calculation determines the concrete elastic modulus and the concrete specified compressive strength for original concrete and for new concrete for the Steam Generator Replacement construction opening plug and containment repair for Crystal River Unit 3.
2.0
SUMMARY
The elastic modulus and the specified concrete compressive strength for the new and existing concrete for maintenance conditions, design basis return to service conditions, and design basis end of life conditions are summarized in Table Ts.
"Concrete" 'Applicable" "Elastic" "Specified Comp."
"Conditions" "Modulus" "Strengthfor"
'Allowable"
......... "psi
- E06" "psi" "Original" "Maint./ Repair" 4.03 6720 TS I'O i ( "Design Basis Return to Service" 4 "Original" k( "DesignBasis End of Life" 4.03 5000 "New" "Maint./ Repair" 5.12 6000
("Design Basis Return to Service")
"New" I 5.12 5000 "e "Design Basis End of Life" )
Notes:
- 1. 6000 psi is the 5-day specified compressive strength of the new concrete.
- 2. 5000 psi is the specified compressive strength of the containment concrete in the FSAR. 7000 psi is the 28 day specified compressive strength of the new concrete. 7000 psi can be used instead of 5000 psi for new concrete if the FSAR is revised.
- 3. This note applies to the column titled, "Elastic Modulus." The elastic modulus is for analytical use. The concrete compressive strength (psi) used for the calculation of the elastic modulus is:
n "Original" 5000)
= "New" 7000)
Calculation No.:
- Prepared By: * .. . 0102-0135-02 MPR Associates, Inc. Revision No.: 0 320 King Street B /hecke Alexandria VA 22314 Checked By: Page No.: 5
3.0 BACKGROUND
A project is underway at Progress Energy's Crystal River Unit 3 site to replace the steam generators.
As part of that project, an opening has been cut into the concrete containment above the equipment hatch. As this opening was being cut, cracking in the concrete containment wall was identified. The crack is around the full periphery of the opening and is in the plane of the wall. The cracking is located at the radius of the circumferential tensioning tendons, and is indicative of a delaminated condition.
4.0 ASSUMPTIONS 4.1 Unverified Assumptions None.
4.2 Other Assumptions None.
Calculation No.:
&I i'iiPrepared By:
MPR Associates, Inc.
. ,\... , 0102-0135-02 Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: Page No.: 6 5.0 APPROACH The concrete modulus of elasticity is calculated with the correlation provided in ACI 318-63 (Reference 1.1, Sections 301 and 1102). ACI 318-63 is the design code for the Crystal River Unit 3 containment (Reference 13, Section 5.2.3.1).
=. L where Ec = static modulus of elasticity of concrete, psi 3
Pc = density of concrete, lb/ft fc = specified compressive strength of concrete, psi The source of the correlation in ACI 318-63 is a paper by Pauw (Reference 5, p. 686 and Reference 1.2, Section 8.5). The correlation is based on a best fit to experimental data as shown in the following figure from Pauw's paper, Reference 5, Figure 2.
-i I I I r
at a K* JA L -7 1
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t...4 pm - - as-.;.. 4 a",
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ata pm
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- .5
- 51 Ii - pt~ta a f.t~a4 O.a...sat.
I'Nf I
- j ........
I ..... ... ... . .
,Z*AW '.0'0W q ,.2-CO"l6 ossnJ Wes" dnat
Calculation No.:
Prepared By: ' ,\-- - 0102-0135-02 MPR Associates, Inc. Revision No.: 0 320 King Street Checked/By Alexandria VA 22314 Checked By: Page No.: 7 The Pauw correlation was based on lower strength concretes than are used today. The suitability of the ACI 318-63/Pauw correlation for high strength concretes is established in Reference 9, Conclusions Section, Reference 10, Figure 1, Reference 11, Figure 1 and Table 9, and Reference 12, Conclusion 3.
The concrete strength parameter in ACI 318-63 is fc', the specified compressive strength (Reference 1.1, Sections 1102 and 301). The concrete strength parameter in the Pauw correlation is the concrete strength at the time of the test (Reference 5, p. 681). The effect of this difference in definition of concrete strength on the calculated modulus of elasticity is evaluated in Section 6.2.
O IM PR Prepared By:. . .%-.,,--
Calculation No.:
0102-0135-02 MPR Associates, Inc. Revision No.: 0 320 King Street Checked B Alexandria VA 22314 Cc Page No.: 8 6.0 CALCULATION 6.1 Design Inputs Original concrete compressive strength.
"Specified & Design Basis" -Ref. 2, p. 2 fc.ng: 6720)'s case 1 -Ref. 3, Results Summary, Class 5000
. "5-year" concrete 5000 New concrete compressive strength.
j
-Ref. 2, p. 2 fc'.nw -60001"psi case2:= -Ref. 6 and Ref. 7, Table 1 117000) -Ref. 6 and Ref. 7, Table 1
'Concrete density Oi giNew" c 15-144). fflb case3:= ( "Original" -Ref. 4
(" "New" ) -Ref. 6 and Ref. 8, p. 6; Ref. 8 provides the theoretical density and measured density for two mixes, Options 1A and 2A. A density of 151 lb/ft3 is representative of the theoretical and measured densities of the two mixes.
core :=
"core 16-1" 3.75"106 Measured modulus of elasticity from CR3 concrete "core 16-2" 4.05" 106 cores "core 40-1" 3.15'106 -Ref. 14 for all cores but Core 59
-Ref. 15 for Core 59 "core 40-3" 2.95'106 "core 65-2" 2.7" 106 "core 66-2" 3.1.106 "core 63-2" 3.3" 106 "core 59" 3.35"06 Ec~meas :=core(2).psi
Calculation No.:
Prepared By: A.-- ,-' ,d -q - 0102-0135-02 MPR Associates, Inc. Revision No.: 0 320 King Street CekdyA, Alexandria VA 22314 Checked By: Page No.: 9 6.2 Modulus of Elasticity Original Concrete The modulus of elasticity for the original concrete is determined based on the core measurements, and is also calculated for the specified compressive strength ( fc.Ogl = 5000psi ) and 5-year compressive strength (fc,.og 2 = 6720psi ). A comparison of the results and selection of the concrete modulus is at the end of the section.
The average modulus of elasticity for the original concrete from measurements of cores taken from the CR3 containment is:
Ec.avg.m:= mean(Ec.meas) Ec.avg.m = 3.29 x 106psi 3.75 4.05 3.15 2.95 6 where Ec.meas = *10 *psi 2.7 3.1 3.3 3.35, The calculated modulus of elasticities for the specified compressive strength and the 5-year compressive strength are:
.( PCl *1.5 fc.origi Ecorijg.:= 33-psi. P, FI11i9
- 3) p Ylb ýf (4.03 x 106 p. case1 = ("Specified & Design Basis" E 4 .6 7 x 10 K "5-year" lb (5000 ) . & Design Basis" )
where pc1 =144- I = \ "Specified"5-year casecase1 ff3 f 6720J g
Calculation No.:
Prepared By: * .s.. . -. m.- 0102-0135-02 MPR Associates, Inc. Revision No.: 0 320 King Street 1JL ')/
Alexandria VA 22314 Checked By: Page No.: 10 The above results show that the elastic modulus ranges from a low of Ec.avg.m = 3.29 x 106 psi to a 6
high of Ec.oog2 = 4.67 x 10 psi based on the 5-year compressive strength. It is concluded that the modulus of elasticity based on the specified compressive strength best represents this range. This calculated modulus is consistent with ACI 318-63, the design basis for the CR3 containment. The elastic modulus for the original concrete is:
Ec.ongI = 4.03 x 106psi This elastic modulus is for the original concrete from the current time to the end of plant life.
New Concrete The concrete modulus of elasticity is calculated with the ACI 318-63 correlation in Reference 1.1, Section 1102.
KP 2 1.5 ~~e Ec.new:= 33.psi.
- PSI.
Ylb ff )
Ecnew = 5.12 x 106psi lb where pc2 = 151 - fc,.new 3 = 7000psi This elastic modulus is for the new concrete from the time the concrete reaches at least its 5-day strength of 6000 psi to the end of plant life. Use of a single modulus for this time period is justified based on the scatter in results for the elastic modulus correlation shown in the figure in Section 5.0.
Calculation No.:
Prepared By: .
A- 0102-0135-02 MPR Associates, Inc. Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: Page No.: 11
7.0 REFERENCES
- 1. American Concrete Institute, "Building Code Requirements for Reinforced Concrete."
1.1 ACI 318-63 1.2 ACI 318-05
- 2. Progress Energy, "Design Basis Document for the Containment," Revision 6.
- 3. Florida Power Corporation Document Identification No. S-00-0047, As-built Concrete Strength for Class I Structures, Revision 0.
Subject:
Concrete Density.
- 5. A. Pauw, "Static Modulus of Elasticity of Concrete as Affected by Density," Journal of the American Concrete Institute, Vol. 57, 1960, pp. 679-687.
Subject:
Comments Calculation 0102-0135-02.
- 7. Progress Energy Specification CR3-C-0003, "Specification for Concrete Work for Restoration of the SGR Opening in the Containment Shell," Revision 0.
- 8. S&ME Phase II Test Report Trial Mixture Testing for Crystal River Unit 3 Steam Generator Replacement Project," S&ME Project No. 1439-08-208, January 13, 2009.
- 9. F. Oluokun, E. Burdette, and J. Deatherage, "Elastic Modulus, Poisson's Ratio and Compressive Strength Relationships at Early Ages," ACI Materials Journal, Jan.-Feb. 1991, pp. 3-10.
- 10. T. Shih, G. Lee, K. Chang, "On Static Modulus of Elasticity of Normal-weight Concrete,"
Journal of Structural Engineering, Vol. 115, No. 10, October 1989, pp. 2579-2587.
- 11. P. Gardoni, D. Trejo, M. Vannucci, and C. Bhattacharjee, "Probabilistic Models for Modulus of Elasticity of Self-Consolidated Concrete: Bayesian Approach," Journal of Engineering Mechanics, April 2009, pp. 295-306.
Calculation No.:
Prepared By: S. 0102-0135-02 MPR Associates, Inc. Revision No.: 0 320 King Street By:
ed e Alexandria VA 22314 Checked By: Page No.: 12
- 12. G. Washa, J. Saemann, and S. Cramer, "Fifty-year Properties of Concrete made in 1937," ACI Materials Journal, July-August, 1989, pp. 367-371.
- 13. Progress Energy Final Safety Analysis Report (FSAR), Containment System & Other Special Structures, Chapter 5, Revision 31.3.
- 14. S&ME Document Transmittal No. 09-208-03, S&ME Project No. 1439-08-208, November 16, 2009.
- 15. S&ME Document Transmittal No. 09-208-05, S&ME Project No. 1439-08-208, November 24, 2009.
Calculation No.:
Prepared By:
- 0102-0135-02 MPR Associates, Inc. Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: Page No.: 13 Attachment The attachments are:
" Email from Mr. J. Holliday (PE) to Mr. K. Gantz (MPR), 12-30-2009, 10:35 AM,
Subject:
Concrete Density.
" Email from Mr. J. Holliday (PE) to Mr. J. Hibbard (MPR), 1-7-2010, 3:42 PM,
Subject:
Comments Calculation 0102-0135-02.
Message Page 1 of 1 Hibbard, Jim From: Holliday, John [John.Holliday@pgnmail.com]
Sent: Wednesday, December 30, 2009 10:35 AM To: Gantz, Kevin; Knott, Ronald Cc: Hibbard, Jim; Dyksterhouse, Don
Subject:
RE: Concrete Density
- Kevin, The reference will be EC 75218, RB Delamination Repair Phase 2- Detensioning The unit weight is 144 lbs cu ft.
From: Gantz, Kevin [mailto: kgantz@mpr.com]
Sent: Wednesday, December 30, 2009 10:01 AM To: Knott, Ronald; Holliday, John Cc: Hibbard, Jim
Subject:
RE: Concrete Density John and Ron, I don't think there was ever a follow-up sent to this email. Could you provide us with the reference. I did not see it in SOO-0047.
Kevin
---Original
-- Message -----
From: Knott, Ronald [1]
Sent: Wednesday, December 16, 2009 10:15 AM To: Holliday, John Cc: Gantz, Kevin
Subject:
FW: Concrete Density John, Can you direct Kevin to the density reference. I don't know where the original data came from for density. I was only quoting what I heard in the meeting. I assumed it was in the 500-0047 attachments.
From: Gantz, Kevin [2]
Sent: Tuesday, December 15, 2009 6:22 PM To: Knott, Ronald Cc: Dyksterhouse, Don; Holliday, John; Bird, Edward; Butler, Patrick
Subject:
Concrete Density Ron, During our previous meeting you received some original information on the concrete density. I remember you saying later that the concrete density was 144 or 145 pcf. Do you have a reference or an actual number so that I can make sure I have the correct modulus calculated?
Thanks, Kevin 12/30/2009
Page 1 of 1 Hibbard, Jim From: Holliday, John [John.Holliday@pgnmail.com]
Sent: Thursday, January 07, 2010 3:42 PM To: Hibbard, Jim Cc: Dyksterhouse, Don; Knott, Ronald
Subject:
RE: comments calculation 0102-0135-02 Attachments: Z25R5 Concrete spec CR3-C-0003.pdf; Z43R3 Phase II Test Plan.pdf; Z44R3 Phase II Test Report.pdf
- Jim, The following inputs are approved by Progress Energy as being acceptable for use by MPR:
The 5 and 28 day minimum concrete compressive strengths for the new concrete for the SGR access opening and repair of the delamination are 6000 and 7000 psi respectively. This requirement for the new concrete is contained in Attachment 1 of specification CR3-C-0003 and in S&MEs phase IITest Plan. Additionally, the theoretical unit weight of the new concrete is 151 pcf as reported in the S&ME Phase IITest Report.
- Regards, John Holliday From: Hibbard, Jim [3]
Sent: Thursday, January 07, 2010 2:47 PM To: Holliday, John
Subject:
comments
- John, Could you give me a call to discuss your comments on the -02 calc? At present I do not have your number, although I may get it from Ed or Patrick.
Jim 1/8/2010
MPR Associates, Inc.
- M PR 320 King Street Alexandria, VA 22314 CALCULATION TITLE PAGE Client:
Progress Energy Page 1 of 47
(+ Att. A)
Project: Task No.
CR3 Containment Calculations 0102-0906-0135
Title:
Calculation No.
Tendon Tension Calculation 0102-0135-03 Preparer / Date Checker I Date Reviewer & Approver I Date Rev. No.
1/18/2010 1/18/2010 1/18/2010 Kevin Gantz Adrian Trif Jim Hibbard 0 QUALITY ASSURANCE DOCUMENT This document has been prepared, checked, and reviewed/approved in accordance with the Quality Assurance requirements of 10CFR50 Appendix B, as specified in the MPR Quality Assurance Manual.
MPR-QA Form QA-3.1-1, Rev. 1
MPR Associates, Inc.
WIMPR 320 King Street Alexandria, VA 22314 RECORD OF REVISIONS Calculation No. Prepared By Checked By Page: 2 0102-0135-03 - , ( -
Revision Affected Pages Description 0 All Initial Issue Note: The revision number found on each individual page of the calculationcarries the revision 1 level of the calculation in effect at the time that page was last revised. I MPR QA Form QA-3.1-2, Rev. 0
MPR Associates, Inc.
50MPR 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 2 0102-0135-03 ),, (j/*'- Revision: (
Table of Contents 1.0 Purpose......................................................................................................... 4 2.0 Sum m ary....................................................................................................... 4 3.0 Assumptions .................................................................................................... 6 3.1 Unverified Assumptions ........................................................................................ 6 3.2 Verified Assumptions ............................................................................................. 6 4.0 Methodology ............. o................................. 8 5.0 Calculation....................................................... .................................................. 9 5 .1 D ata ............................................................................................................................... 9 5.2 Dome Tendons - 60 Years After Initial SIT ......................................................... 13 5.3 Vertical Tendons - 60 Years After Initial SIT ....................................................... 16 5.4 Horizontal Tendons - 60 Years After Initial SIT ................................................... 29 5.5 Dome Tendons - After SGR Completion ............................................................ 37 5.6 Vertical Tendons - After SGR Completion .......................................................... 40 5.7 Horizontal Tendons - After SGR Completion ..................................................... 43 6.0 References ..................................................................................................... 46 A Reference 23 ............................................. A-1 MPR QA Form: QA-3.1-3, Rev. 0
Ql RPrepared By: 0102-0135-03 MPR Associates, Inc. 4** Revision No.: 0 320 King Street Chce y Alexandria VA 22314 Checked By: Page No.: 4 1.0 PURPOSE This calculation determines the dome, vertical, and horizontal tendon tension immediately following the Steam Generator Replacement (SGR) Project completion (33 years) and at end of plant life (60 years) in the Crystal River Unit 3 containment. The values of tendon tension calculated herein will be used in structural analyses of the containment for ages 33 and 60 years after the Structural Integrity Test (SIT).
2.0
SUMMARY
Average dome, vertical, and horizontal tendon losses from the following four mechanisms were calculated:
" Elastic Shortening
- Concrete Shrinkage
" Tendon Steel Relaxation
- Concrete Creep The above mechanisms are described in Reference 22. Tendon losses were calculated individually for different groups. For the dome tendons, the tension in all tendons is not modified during the SGR project.
For the vertical tendons, some of the tendons are detensioned and subsequently retensioned, and some of the tendons are not modified at all. Losses are calculated separately for these two groups. For the horizontal tendons, several tendons are detensioned and subsequently retensioned and other tendons are not modified at all. For the detensioned and retensioned tendons, several tendons pass through replacement concrete that fills the SGR opening plug and replaces the delaminated concrete, and others do not pass through the replacement concrete. Tendon losses are calculated individually for these two groups of detensioned and retensioned tendons as well as the tendons that are not modified during the SGR project.
Concrete shrinkage and concrete creep are dependent on the material properties of the concrete that the tendons pass through. By calculating tendon tension losses separately depending on the tendon location (as explained above), the effects of local concrete material differences are accounted for. However, for tendons that are detensioned and subsequently retensioned that pass through or near the repaired SGR opening, the tendon losses are calculated as if the tendon passes directly through the repaired SGR opening. Tendon steel relaxation losses are not dependent on the tendon location, and they are treated the same for all tendons. Elastic shortening losses are unique to each tendon based on the sequence with which the tendons are tensioned. An average elastic shortening loss is calculated based on tendon orientation (dome, vertical, or horizontal) so that every tendon does not have to be tensioned individually in the containment structural analyses.
The tension in each group of tendons is reported as the average tension along the tendon length.
LPrepared By: 0102-0135-03 MPR Associates, Inc. Revision No.: 0 320 King Street By:AP N Alexandria VA 22314 Checked By: Page No.: 5 The tendon tension at the end of the SGR Project (33 years):
Dome Tendons:
All Dome Tendons: Tensiond.33 = 1376kip Vertical Tendons:
Detensioned and Retensioned Tendons: Tensionv.33 .mod = 1603 kip Unadjusted Tendons: Tensionv.3 3 .unmod = 1474 kit Horizontal Tendons:
Detensioned and Retensioned Tendons Passing Tensionh33modSGR = 1573 kip through SGR Opening Bay:
Detensioned and Retensioned Tendons not Passing TenSionh.33.md 1573kip through SGR Opening Bay:
Unadjusted Tendons: Tensionh.33.unmod = 1398ki The tendon tension at the 60 year end of life:
Dome Tendons:
All Dome Tendons: Tensiond.6O = 1353kip Vertical Tendons:
Detensioned and Retensioned Tendons: Tensionv 60.ood = 1539 kip Unadjusted Tendons: Tensionv.60.unmod = 1464 k*p Horizontal Tendons:
Detensioned and Retensioned Tendons Passing Tensionh60.modSGR = 1498 kip through SGR Opening Bay:
Detensioned and Retensioned Tendons not Passing Tensionh.60 mod through SGR Opening Bay:
Unadjusted Tendons: Tensionh.60.oumod = 1380kiip
Calculation No.:
P M PR Prepared By: * - 0102-0135-03 MPR Associates, Inc. Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: Page No.: 6 3.0 ASSUMPTIONS 3.1 Unverified Assumptions There are no unverified assumptions.
3.2 Verified Assumptions
- 1. The thickness of the concrete replacing the delaminated concrete is approximately 10 inches, the width spans the entire span between buttresses 3 and 4, and the height spans between the top of the equipment hatch to approximately 10 feet below the bottom of the ring girder. These dimensions are consistent with the measured extents of the delamination with only the tendons that pass through the Steam Generator Replacement (SGR) opening detensioned (see Figure 1).
- 2. The end of plant life is assumed to be 60 years after the containment Structural Integrity Test (SIT) in November 1976 (Reference 7, page 10). This assumption has been confirmed by Progress Energy (see Lead Reviewer comments to this calculation).
- 3. The replaced concrete in the patch and the outer portion of the delamination will not be prestressed until 5 days after pouring. This assumption has been confirmed by Progress Energy (see Lead Reviewer comments to this calculation).
- 4. The concrete that is used to plug the SGR opening and replace the outer portion of the delamination will have improved shrinkage properties (less shrinkage) compared to the existing concrete when it was first placed. This assumption has been confirmed by Progress Energy (see Lead Reviewer comments to this calculation).
No.:
E MP R MPR Associates, Inc.
Prepared By: )v
,-2,14
ýý
-;ýV -Calculation a a0102-0135-03 Revision No.: 0 320 King Street Alexandria VA 22314 Chckd By:y Checked Page No.: 7 A ¢ E Ht Equipment Hatch Figure 1. Delamination Boundary (Delamination shown in red)
Calculation No.:
UAM PR MPR Associates, Inc.
Prepared By: )c~~0102-0135-03 Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: Page No.: 8 4.0 Methodology The dome, vertical, and horizontal tendon losses are determined by considering losses from four different mechanisms:
" Elastic Shortening - Shortening of concrete as prestress is applied
" Concrete Shrinkage - Decrease in concrete volume
" Steel Relaxation - Stress relaxation in the prestressing steel
" Concrete Creep - Strain of the concrete over time due to sustained loads Each loss has been determined at 40 years after the Structural Integrity Test (SIT) in various Crystal River Unit 3 calculations (References 2, 3, and 7). These losses are used as a basis for determining the losses at the end of steam generator replacement and at 60 years after SIT. The methodology for this calculation is similar to that of Progress Calculation S08-0008 (Reference 14).
Calculation of the increase in tendon tension during an accident which increases containment pressure is not included in this calculation.
// / Calculation No.:
- MIMPR MPR Associates, Inc.
Prepared By: )~ ~0102-0135-03 Revision No.: 0 320 King Street Cek B Alexandria VA 22314 Checked By: Jill Page No.: 9 5.0 CALCULATION 5.1 Data 2
A,:= 9.723in Total cross section area of 163 wires in a single tendon; Ref. 1, page 6.
E,:= 4.03 x 106psi Elastic modulus of existing concrete; Ref. 16, page 4.
E,:= 29x 10 6psi Elastic modulus of steel; Ref. 4, Table 38.
hopen := 27ft Height of SGR opening; Ref. 5.
Eltop.SGR:= 210ft Elevation of the top of the SGR opening; Ref. 5.
Wopen;= 25ft Width of SGR opening; Ref. 5.
tdelam lOin Approximate thickness of the delaminated concrete; Assumption 3.2.1.
Eltop.eq.hatch := 157ft + lOin Eltop.eq.hatch = 157.83ft Elevation of the concrete at the transition to 3'-6" wall thickness above the equipment hatch; Ref. 9.
Elbot.ring.girder:=250ft Elevation of the bottom of the ring girder; Ref. 9.
Eltop.ring.girder:=267. 5ft Elevation of the top of the ring girder; Ref. 9.
Ldelam.ring.girder"= lOft Approximate distance from the bottom of the ring girder to the top of the delamination boundary; Assumption 3.2.1.
Elbot.containment := 80.5ft Elevation of the bottom of containment; Ref. 15.
Eltop basemat:= 93.Oft Elevation of the top of the containment basemat; Ref. 9.
abuttress := 60deg Radial angle between adjacent buttresses; Ref. 9.
Wbuttress := 12ft + 4.125in Wbuttress = 12.34ft Average buttress width; Ref. 9.
tbuttress := 2ft + 4.5in Buttress thickness increase beyond containment wall thickness; Ref. 9.
Rliner := 65ft Radial distance to liner inside surface; Ref. 9
Calculation No.:
- M PR MPR Associates, Inc.,*,
Prepared By: )~~~-0102-0135-03 Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: Page No.: 10 tliner 0.375in Nominal liner thickness throughout most of the containment; Ref. 9.
t Wall thickness between buttresses (undelaminated);
wa, := 3.5ft Ref. 9.
Stressd.creep.40:= 13.85ksi Loss in dome tendon stress due to creep at 40 years life; Ref. 2, page 4.
Stressd.shrink.40 := 2.90ksi Loss in dome tendon stress due to concrete shrinkage at 40 years life; Ref. 2, page 4.
StresSdeshort.40 := 5.50ksi Loss in dome tendon stress due to elastic shortening at 40 years life; Ref. 2, page 4.
Forced relax.40 := 48.5kip Loss in dome tendon force due to steel relaxation at 40 years life; Ref. 7, Att. F, page F2.
Forced relax.35 := 48.2k'p Loss in dome tendon force due to steel relaxation at 35 years life; Ref. 7, Att. F, page F2.
rd.axial:= 1530psi Average concrete compressive prestress in dome, in direction of tendon length; Ref. 3, page 49. As a check of this value from Ref. 3 a scoping comparison was made to finite element analysis results for the CR3 containment. It was concluded that this is an appropriate stress for this calculation.
-6 1 Basic creep for dome tendon loading beginning 180 Creepd.basic.60 := 0.35x 1 psi days after pouring, at 60 years life; Ref. 7, Aft. G, page G5.
-6 1 Creepv.basic.6 := 0.25 x I1 Basic creep for vertical tendon loading beginning 834 psi days after pouring, at 60 years life; Ref. 7, Att. G, page G5.
6 1 Basic creep for horizontal tendon loading beginning Creeph.basic.60 := 0.24 x 10 psi 964 days after pouring, at 60 years life; Ref. 7, Aft. G, page G5.
6 1 Basic creep for dome tendon loading beginning 180 Creepd.basic.33 := 0.30x 10 psi days after pouring, at 33 years life; Ref. 7, Att. G, page G5.
-6 1 Basic creep for vertical tendon loading beginning 834 Creepv.basic.33= 0.215x 10 .-
psi days after pouring, at 33 years life; Ref. 7, Aft. G, page G5.
// / Calculation No.:
- M PR MPR Associates, Inc.
Prepared By: 0102-0135-03 Revision No.: 0 320 King Street Chckd y Alexandria VA 22314 Checked By: Page No.: 11
-6 1 Basic creep for horizontal tendon loading beginning CreePh.basic.33:=0.205 x 10 .spsi 964 days after pouring, at 33 years life; Ref. 7, Aft. G, page G5.
Stressv.shrink.40 := 2.90ksi Loss invertical tendon stress due to concrete shrinkage at 40 years life; Ref. 2, page 2.
Forcev.reda.40:= 48.5kip Loss in vertical tendon force due to steel relaxation at 40 years life; Ref. 7, Aft. F, page F2..
Forcerrelax.35:=48.2kip Loss in vertical tendon force due to steel relaxation at 35 years life; Ref. 7, Aft. F, page F2..
Vu'patch := 1.14 Ultimate creep coefficient for concrete in plug; Ref. 6.
StresSh.shrink.40 := 2.90ksi Loss in horizontal tendon stress due to concrete shrinkage at 40 years life; Ref. 2, page 3.
Forceh.rela.40:=48.2kip Loss in horizontal tendon force due to steel relaxation at 40 years life; Ref. 7, Aft. F, page F2..
Forceh.rela.35:=47.9kip Loss in horizontal tendon force due to steel relaxation at 35 years life; Ref. 7, Aft. F, page F2..
GUTS7 0 := 1635kip Tendon lock off tension, equal to 70% of the Guaranteed Ultimate Tensile Strength (GUTS) per tendon; Ref. 1, page 14.
nv,,endon :=144 Total number of vertical tendons; Ref. 1, page 14.
Ageoutage : 33yr Ageoutage = 12053 day Age of original concrete at SGR outage, starting from the date of containment Structural Integrity Test; Ref. 7, page 10 and Ref. 8, page 7.
Age ,,:
0 6Oyr Ageo01 = 21915day Age of original concrete at end of plant life, starting from date of containment Structural Integrity Test; Assumption 3.2.2 A:= 75 Relative humidity for the containment outside environment, in percent; Reference 17.
- Calculation No.:
MPR Associates, Inc. Revision No.: 0 320 King Street : P-e N .: 1 Alexandria VA 22314 Checked By: ,Page No.: 12 Forcehreaxo:= 47.6kip Horizontal tendon steel relaxation load at 30 years; Ref. 7, Aft. F, page F2.
Forcevrehu.30:= 47.8kip Vertical tendon steel relaxation load at 30 years; Ref. 7, Aft. F, page F2.
Forced.relda.33:= 48.Okip Dome tendon steel relaxation load at 33 years; logarithmically interpolated from Ref. 7, Att. F, page F2.
Forceh.relax.33.unmod := 47.8k'p Horizontal tendon steel relaxation load at 33 years; logarithmically interpolated from Ref. 7, Aft. F, page F2.
Forcev.relax.33.unmod := 48.Okip Vertical tendon steel relaxation load at 30 years; logarithmically interpolated from Ref. 7, Aft. F, page F2.
Elavg.tend.space.bot:= 183ft + 10. 75in Bottom horizontal tendon elevation used to calculate average horizontal tendon spacing; Ref. 20.
Elavg.tend.space.top:= 212ft+ 8.25in Top horizontal tendon elevation used to calculate average horizontal tendon spacing; Ref. 20.
navg.tend space := 19 Number of tendons spanning between El avg.tend. space.bot and Elavg.tend.space.top, inclusive; Refs. 20 and 21.
rh.tendon := 67ft + 8.625in Horizontal tendon placement radius; Ref. 24.
nbuttress := 6 Number of buttresses in the containment; Ref. 9.
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MPR Associates, Inc. Revision No.: 0 320 King Street Cek BPgN:
Alexandria VA 22314 Checked By: Page No.: 13 5.2 Dome Tendons - 60 Years After Initial SIT The dome tendons will not be detensioned or retensioned during the Steam Generator Replacement (SGR) outage. The tendon tension at 60 years after the Structural Integrity Test (SIT) of November 1976 (Reference 7, page 10) is determined by scaling the predicted tension at 40 years after SIT. The individual losses in the dome tendons at 40 years after SIT from creep, steel stress relaxation, elastic shortening, and concrete shrinkage are as follows (see Section 5.1 for references):
Stressd.creep.40 = 13850psi StresSdeshort.40 5500psi StresSd.shrink.40 = 2900psi Forced.relax.40 Stressd.relax.40 At Stressd.relax.40 = 4988psi where Forced.relax.40= 48.5kip A, = 9.723 in2 Elastic Shortening The dome tension losses due to elastic shortening do not change over time. The elastic shortening losses at 60 years after SIT are:
Stressd eshort.60 := Stressdteshort.40 StresSdeshort.60 = 5500psi Concrete Shrinkage Industry experience shows that the majority of concrete shrinkage occurs in the early life of the containment. Since the containment was constructed over 30 years ago, nearly all of the shrinkage has already taken place. At this point, shrinkage is essentially time-independent, and the concrete shrinkage at 60 years will be approximately equal to the concrete shrinkage predicted at 40 years.
Stressd.shrink.60 := Stressd.shrink.40 StreSSd.shrink.60 ý 2900psi
Calculation No.:
5 M PR MPR Associates, Inc.
Prepared By: 0102-0135-03 Revision No.: 0 320 King Street Alexandria VA 22314 Chce Checked By: y * *Page No.: 14 Steel Relaxation The steel relaxation losses at 40 years have been calculated previously (Reference 7, AUt. F, Page F2). Based on Figure 5-26 of Reference 10, steel relaxation is linear with time on a logarithmic scale. The losses calculated at 40 years will be extrapolated to 60 years based on the last two data points from Reference 7, Att. F, page F2.
Forcedrelax40 - Forced relax 35 t Forced.relax.6 0 := log(40) - 1og(35) .(60) - Iog(35)) + Forcedrelax.35 Forcedrelax.60 = 49.4kip Forced relax.60 StresSd.relax.60 := Stressd relax.60 = 5082psi A,
where
.2 Forced.relax.40= 48.5kip Forced.relax.35= 48.2kip A= 9.723 in Creep The basic creep determined from testing extrapolated to 60 years is (see Section 5.1 for reference):
-71 Creepd.basic.60 = 3.5 x 10 --
psi The average prestress in the dome in the axial direction of the tendons is (see Section 5.1 for reference):
adQaxial = 1530psi The reasonableness of this value has been confirmed using finite element analysis.
The tendon prestress lost due to creep is calculated based on Page 4 of Reference 2:
Stressd.creep. 60 := U7d.axiarCreepd.basic.6 0 .E, Stressd creep.60 = 15529psi where Es is the steel elastic modulus and is equal to:
7 E~2.9 x 10psi
U 00 M PRPrepared PR By: *Calculation PrprdB:0102-0135-03 No.:
MPR Associates, Inc. Revision No.: 0 V 22314 320 King Street Alexandria VA 3e Checked By: Ba Pae/o. o 1 Total 60 Year Loss The total tendon stress loss after 60 years is:
Stressd total.60 : StreSSdeshortM60 + StresSd.shrink.60 + Stressd.relax.60 + StreSSd.creep.60 Stressd total.60 = 29011 psi Converting the stress lost into a force per tendon that is lost:
Forced.total.60 := Stressdtotal60. At Forced.total 60 = 282. 1kip where At = 9.723 in2 The design tension per tendon, excluding losses, is (see Section 5.1 for reference):
Forcedesign := GUTS70 Forcedesign = 1635kip The remaining tension in the dome tendons at 60 years is:
Tensiond.60 := ForCedesign- Forced.total.60 Tensiond6O = 1352.9kip
'// /Calculation No.:
- M P R Prepared By: ) ,v 0102-0135-03 MPR Associates, Inc. Revision No.: 0 320 King Street C c d yP e o 1 Alexandria VA 22314 Checked By: : - Page No.: 16 5.3 Vertical Tendons - 60 Years After Initial SIT Some of the vertical tendons near the SGR opening will be detensioned and retensioned during SGR while the tension in some other tendons will not change at all. The tendon tension at 60 years will be calculated for each of the two sets of tendons individually. When calculating tendon losses, all of the vertical tendons that are detensioned and retensioned will be considered to pass directly through the SGR opening since cutting and repairing the opening will affect the region both inside and around the SGR opening. The tendon tension at 60 years after the Structural Integrity Test (SIT) of November 1976 (Reference 7, page 10) is determined by scaling the predicted tension at 40 years after SIT. The individual losses in the vertical tendons at 40 years after SIT from steel stress relaxation and concrete shrinkage are as follows (see Section 5.1 for references):
StreSsv.shrink.40 = 2900psi Forcev.relax.40 Stressv relax.40 - A Stressv.relax.40 = 4988psi where 2
At = 9.723 in Force,.relax.40 = 48.5kip Elastic Shortening The total vertical force in the containment due to the vertical tendons tensioned to lock off load is:
Forcev.axial := nv.tendon*GUTS70 Forcev.,axial = 235440kip where nv.tendon = 144 GUTS7 0 = 1635 kip The horizontal cross sectional area of concrete at approximately the mid height of the containment is:
2 Av.contain ýT'f(Rliner + tliner + twall) - (Rliner + tliner)2] + nbuttress'Wbuttress'tbuttress Av.contain = 236807.3 in2 where Rliner = 65ft t liner = 0.375 in twall = 3.5ft Wbuttress = 12.34ft tbuttress = 2.38ft nbuttress = 6
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? s-0102-0135-03 Calculation No.:
Revision No.: 0 Alexandria VA 22314 Checked By: Page No.: 17 The horizontal cross sectional area of the liner at approximately the mid height of the containment is:
2 Av.iiner := lr'[(Rliner + tliner) - Rliner2]
Av.liner = 1838.3 in2 The average elastic shortening losses for the vertical tendons are calculated based on the equations found in Section 2.1 of Reference 22. The vertical tension losses due to elastic shortening do not change over time. Note that the proportion of load in the tendon conduit is conservatively neglected from the calculation.
-/ GUTS7o Forcev~eshort.60.unmod 2-. er"neno*A~
(Av.contain - nv.tendon'A)'Ec + Avliner'Es 5 fv.tendon'Es" At
+ nv.tndonAt'Es Forceveshort.60. unmod = 31.84 kip Forcev.eshort.60.unmod StreSsv.eshort.60.unmod At Stressveshort.60,unmod = 3274 psi where GUTS70 = 1635 kip Ec= 4.03x 106psi E, = 2.9 x 10 7psi 2
A, = 9.723 in nv.tendon = 144 This loss of stress applies to tendons that were not detensioned during the SGR.
For tendons that are adjusted during SGR, the elastic shortening stress losses will be affected by the material properties of the concrete used to replace the plug and the delaminated concrete. A diagram with the different areas of concrete represented as springs with different stiffnesses is presented in Figure 2. For a unit width along the circumference of the wall passing through the SGR opening, the equivalent spring stiffness would equal:
Eeq"t I LE L3 1 L5 Ee'-tf Ee' te+Ed-td Ep' tf Ee..t e+Ea td Ee' tf L2 L4
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0102-0135-03 Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: Page No.: 18 Existing Wall L, Delamination L2 SGR L
Open L3 L4 1,5 Figure 2. Spring Diagram for Vertical Stiffness of a Section of Unit Width Passing through the Reconstructed SGR Opening.
Ee = Existing concrete elastic modulus Ed - Delamination concrete elastic modulus Ep = Plug concrete elastic modulus tf - Full concrete wall thickness (between buttresses) te = Existing concrete thickness in area of delamination, inner portion td - Delaminated concrete thickness, outer portion L# = Vertical length as defined in Figure 2
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MPR Associates, Inc. Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: /'/7, Page No.: 19 Alexndri 231 VA The value of each of the variables in the equation are defined below from inputs defined in Section 5.1:
If:" twall tf = 3.5 ft LI := Eltop.ring.girder - Elbot.ring.girder + Ldelam.ring.girder L1 = 27.5ft L2 Eltop.ring.girder - L1 - Eltop.SGR L2 = 30ft L3 hopen L3 = 27ft L4 Eltop.ring.girder- L 1 - L2 - L3 - Eltop.eq.hatch L4 = 25.17ft L5 := Eltop.eq.hatch - Elbot.containment Ls = 77.33ft
- td:= tdelam t d= 0. 83ft te := tf-- td t, =2.67ft Note that the wall thickness from the top of the ring girder to the bottom of the containment basemat (the entire span of the vertical tendons) is treated as a constant twal = 3.5ft even though the wall is much thicker in the ring girder, basemat, and lower portion of the containment wall. By not accounting for the stiffness of the thicker walls, this calculation will be conservative.
The ratio of the equivalent elastic modulus of the containment in the vertical direction passing through the SGR opening compared to the modulus of the existing concrete is calculated. The calculation is based on a modulus of elasticity that is 25% higher in the plug and delamination compared to the existing concrete. This calculation will determine the relative significance of the plug material properties on the effective elastic modulus used for scaling the elastic shortening losses. The 25% increased modulus is' not intended to be a definitive estimate of the new concrete properties but, rather, an estimate of the maximum difference in modulus of elasticity between new and old concrete. Based on Reference 16, 25% is a reasonable value for the difference in elastic moduli.
Ee := 1 Reference Factor Ed:= 1.25.Ee Ed= 1.25 Ep : 1.25-Ee EP = 1.25
Calculation No.:
&IM PR MPR Associates, Inc.
Prepared By: )A f0102-0135-03 Revision No.: 0 320 King Street By :
Alexandria VA 22314 Checked By: Page No.: 20 L, + L2 3+ L4 + L 5 E~q K 1 L3 L5 '
Eeq 1.05 If the modulus of elasticity for the patch and delamination replacement concrete were 25% greater than the existing concrete, the equivalent elastic modulus for the wall would be 5% greater than the modulus of the existing concrete. The same percentage decrease in the equivalent elastic modulus would be expected if the modulus of the patch and the delamination were 25% less than the existing concrete. This is a small increase in modulus. To determine the elastic shortening losses for the detensioned and retensioned tendons, the predicted loss for the existing concrete would be scaled by the same percentage. Since the exact properties of the replaced concrete are not known, the elastic shortening losses for the detensioned and retensioned tendons will be conservatively estimated to equal those of the unmodified tendons.
Stres&veshort.60.mod := Stressveshort.60.unmod Stressveshort.60.mod = 3274psi Concrete Shrinkage The majority of concrete shrinkage occurs in the early life of the containment. Since the containment was constructed over 30 years ago, nearly all of the shrinkage has already taken place. At this point, shrinrlage is essentially time-independent, and the concrete shrinkage at 60 years will be approximately equal to the concrete shrinkage predicted at 40 years.
StreSsvshrink.60.unmod := StreSSv.shrink.40 StreSsv.shrink.60.unmod = 2900psi This loss of stress applies to tendons that were not detensioned during the SGR.
The tendons that are detensioned and retensioned during SGR will only experience shrinkage in the concrete that replaces the SGR opening plug and that replaces the delamination. The replacement concrete is low-shrinkage concrete (Reference 11), but the shrinkage losses in this region will conservatively be set equal to the shrinkage losses of the original concrete at 40 years.
However, the results will be scaled based on the ratio of the new concrete height to the entire height of the containment (The entire span of vertical tendons).
Calculation No.:
RO P RPrepared MPR Associates, Inc.
By: 0102-0135-03 Revision No.: 0 320 King Street By :
Alexandria VA 22314 Checked By: Page No.: 21 The total height of the containment is:
htotaI := Eltop.ring.girder- Elbot.containment htotai = 187 ft where Eltop,ring.girder= 267.5ft Elbot.containment = 80.5ft The height of the SGR opening is (see Section 5.1 for reference):
hopen = 27ft The height of the delamination, excluding the height of the SGR opening, is:
hdelam Elbot.ring.girder - Ldelam.ring.girder- Eltop.eq.hatch - hopen hdelam = 55.17 ft where Elbot.ring.girder= 250ft Ldelam.ring.girder = lOft Eltop.eq.hatch = 157.83ft The ratio of the delaminated thickness to the entire wall thickness is:
tdelam Ratiotdelam :=- Ratiot.delam = 0.24 twall where tdelam = lOin tw.1 1 = 3.5ft The shrinkage loss for the tendons that are detensioned and retensioned around the SGR opening is equal to:
hopn hdelam ."*
Stre'Sv.shrink.60.mod =hpen + "-la'Ratiot.delmlStreSSv.shrink.40 p
m htotal htotal Stre'"v.shrink.60. mod =622psi
SM PR
// P/ Calculation No.:
MPR Associates, Inc.
Prepared By: )~ ~ 0102-0135-03 Revision No.: 0 320 King Street Alexandria VA 22314 Chce Checked By: yT,*.Page No.: 22 Steel Relaxation The steel relaxation losses at 40 years have been calculated previously (Reference 7, AUt. F, Page F2). Based on Figure 5-26 of Reference 10, steel relaxation is linear with time on a logarithmic scale. The losses calculated at 40 years will be extrapolated to 60 years based on the last two data points from Reference 7, AUt. F, page F2.
Forcevrejax4o - Forcev.relax.35 Forcev.reiax.6 0 : log(40)(60) - log3) + Forcev.reax.3 5 Forcev,,relax.60 = 49.4kip Forcev.relax 60 Stressv.relax.60.unmod - Stres&vrelax.60.unmod = 5082psi where Forcev.relax.40 = 48.5kip Forcev.relax.35 = 48.2kip At = 9.723in2 The detensioned and retensioned tendons will be active for the following number of years before the 60 year end of life is reached:
Agereten := AgeeoI - Ageoutage Agereten = 27yr Conservatively using the tendon steel relaxation loss at 30 years from Reference 7, Attachment F, Page F2:
Forcev.relax. 60.mod := Forcev.relax.30 Forcev.relax.60.mod = 47.8kip Converting the force loss to a prestress loss in the tendon:
Forcev.relax.60.mod Stressv relax.60.mod := Stressv.relax.60.mod = 4916psi
Calculation No.:
SMM PR MPR Associates, Inc.
Prepared By: 0102-0135-03 Revision No.: 0 320 King Street fZ Alexandria VA 22314 Checked By: Page No.: 23 Creep The basic creep for the existing concrete determined from testing and extrapolated to 60 years is (see Section 5.1 for reference):
2 -7]
Creepy.asic.60= .5 x 10 7 psi The ratio of the concrete stiffness to the total stiffness of the horizontal cross-section is calculated based on the equations in Section 2.1 of Reference 22.
Av.contain'Ec Rati~vonc 0 stif~f (Av.contain - nv tendon.At).EC + Avliner'Es + nv.tendon'At'Es Ratiov.concstiff = 0.92 where 2
Av.contin = 236807.3in Ec=4.03x 106psi nv.tendon = 144 2 2 At =9.723in Aviiner = 1838.3 in E, = 2.9 x 10 7psi The average vertical prestress was calculated earlier in this section. For the stress contributing to creep, elastic shortening and shrinkage losses are subtracted because they occur early in the life of the containment.
Forcev.axiat - nv.tendon' (Stressveshort.60.unmod + StreSsv.shrink,4 0)"At ....
UTv.axial.creep := ALUluvconc.stiff Av.contain Qv.axiat.creep = 877 psi where Forcev.axia = 235440kip Stressv.shrink.40 = 2900psi Stressv.eshort.60.unmod = 3274 psi 2 2 A, = 9.723 in in Acontin = 236807.3
MOEP Prepared By: 0102-0135-03 MPR Associates, Inc. Revision No.: 0 320 King Street Cc By :
Alexandria VA 22314 . Page No.: 24 The tendon prestress lost due to creep is calculated based on Page 4 of Reference 2. This value is applicable to tendons that were not detensioned during the SGR:
Stressv.creep.60. unmod := (v.axiaLcreep Creepv.bas ic.6o'Es Stressv.creep.60. unmod = 6356psi where E, is the steel elastic modulus and is equal to:
Es=2.9x 10 psi Creep losses for the tendons that pass through the patch are calculated separately by taking into account the creep properties of the replacement concrete. The ultimate creep coefficient of the new concrete is (see Section 5.1 for reference):
Vu.patch = 1.14 The ultimate creep coefficient must be adjusted for non-standard environmental and geometrical properties in accordance with Reference 12, Section 2.5. There are also correction factors associated with concrete composition, but these have a smaller effect than geometrical and environmental properties and are neglected (Reference 12, Section 2.6).
The correction fitor for the ultimate creep coefficient due to the relative humidity is expressed by (Reference 12. v;,.ection 2.5.4):
A =75 Relative Humidity, (%)
YA:= 1.27 - 0. t, 1 yA = 0.767 The vole," ratio of the plug and the delamination is calculated as follows. The wie" .... i.:inatiol.l is delam " . ...... cr wall - _ Wbuttress we58.9r where abuttress = 60deg Rliner = 65ft t liner = 0.38 in t
ta = 3, 5 f delam = lOin Wbuttress = 12.34ft
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Prepared By: ) 0102-0135-03 Revision No.: 0 320 King Street Cc BPgN:
Alexandria VA 22314 Checked By: Page No.: 25 The volume of the new concrete is:
Vnew : Wopen'twall'hopen + (Wdelam'hdelam - Wopen hopen).tdelam 3
Vnew = 4511.7ft where Wopen = 25ft twi,, = 3.5ft hopen =27ft Wdelam = 58.99ft hdelam = 55.17ft tdelam = 10 in The only surface exposed to the environment for the new concrete is the outside surface of the containment. This area is equal to:
2 Snew Wdelam"hdelam Snew = 3254.04ft where Wdelam = 58. 99ft hdelam = 55.17ft The volume to surface area ratio is:
Vnew Ratio ,s.- Snew Ratio,, = 16.64 in The correction factor to the ultimate creep coefficient for the volume to surface ratio is (Reference 12, Section 2.5.5b):
54-Ratiovs--in rVS := Z -( I + 1. 13. e- 0. rv, = 0.667 3
A correction factor must also be applied for operating temperature other than 70'F. Based on Reference 23, operating temperature correction will have a small effect on the concrete creep rate and is, therefore, neglected.
A correction factor is also to be applied when load is applied other than 7 days after concrete placement from Reference 12, Section 2.5.1. However, the ultimate creep coefficient was calculated based on a loading age of 5 days, and the load is assumed to be applied at 5 days in this calculation (see Assumption 3.2.3), so no correction for loading age is applied.
Calculation No.:
Prepared By: 0102-0135-03 MPR Associates, Inc. Revision No.: 0 320 King Street Checked By:
Alexandria VA 22314 Page No.: 26 The resulting creep correction factor accounting for relative humidity, volume to surface ratio, and operating temperature effects is (see definition of y in Reference 12):
2 Ycreep :
7 "vs"Y.ý creep = 0.512 The new concrete will be under load for Age,,,, = 27yr. The creep coefficient at the end of this time is (Reference 12, Equation 2-8):
(Agereten + day) 0.6 vt:= -Vu.patch" Ycreep V1 =-. 561 0 6 10+ (Agereten + day)
Note that this equation is applicable to Types I and Ell concrete. The concrete is Type I in accordance with Reference 6, page 3.
The tendon tension lost due to creep of the new concrete is scaled based on the tension lost due to elastic shortening. Elastic shortening is a short term loss and creep is a long term loss. The creep loss can be scaled from the elastic shortening loss by the effective short term and age-adjusted elastic moduli. The age-adjusted elastic modulus accounts for additional strain due to long term loads (Reference 12, Section 5.2). The short term losses (elastic shortening losses) can be scaled using the following equation (this equation was used in Reference 14, but was not derived in Reference 14. It is derived here for clarity.):
Feshort Eeshort LossEcreep = LOSSeshort - LOSSeshort = LOSSeshort l --
Ecreep Ecreep where Eeshort is the instantaneous modulus of elasticity (used for short term loads), Ecreep is the effective modulus of elasticity for long term loads, and Losseshort is the tendon elastic shortening loss.
The ratio of the effective modulus of elasticity for a short term load to a long term load minus one is determined by rearranging equation 5-1 of Reference 12.
Est
- - I = Xvt Elt where Est = Modulus of elasticity for short term loads Elt = Effective modulus of elasticity for long term loads X = Aging coefficient vt = Creep coefficient
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Calculation No.:
~~0102-0135-03 Revision No.: 0 320 King Street C k BP N:
Alexandria VA 22314 Checked By: Page No.: 27 Looking at the aging coefficients in Table 5.1.1 of Reference 12, the maximum this value can be is 1 and the minimum value is 0.5. Conservatively assuming a value of 1 for X, the tendon loss due to creep in the new concrete can be calculated as follows based on combining the previous two equations:
Losscreep = LOSSeshort Vt The total loss in the new concrete is scaled based on the proportion of the height and cross-sectional ratio of the new concrete to the height and total thickness of the containment wall.
The remaining concrete will creep following the same trend from the measured data in Reference 3, page 45. The creep experienced by the existing concrete up to the beginning of the SGR outage (33 years) is:
StreSsv.creep.33.unmod (Tv.axial.creep Creepv.basic.33.Es Stressv.creep.33.unmod - 5466psi The total creep loss in the vertical tendons at 60 years is:
h open " h delam Stress, creep. 60.mod := Lope!. (StreSsv.eshort.60.mod Vt) + R.gatiot.delamh (Stressv.eshort.60.mod. Vt) ".
,htotal htotaa htotai - hopen hdelam
+ -tta htta Ratio,dcelam (Stressv. creep. 60. unmod StreSSv. creep. 33. unmod)
Stressv creep. 60.mod = 1093psi where hopen = 27ft htotaI = 187 ft StreSSveshort.60.mod = 3274psi Vt = 0.561 hdelam = 55.17ft Ratiot.delam = 0.24 Stressv.creep.60.unmod = 6356psi
Calculation No.:
MlkM P R MPR Associates, Inc.
Prepared By: 0102-01.35-03 Revision No.: 0 320 King Street C k yg .
Alexandria VA 22314 Page No.: 28 Total 60 Year Loss The total tendon stress loss after 60 years is calculated.
Unadjusted Tendons:
Stressvtotal.60.unmod := StreSsveshort.60.unmod + Stressvshrink.60.unmod + Stressv.relax.60.unmod + Stressv.creep.60.unmod Stressv.totaL 60.unmod 17612psi Detensioned and Retensioned Tendons:
Stressv.totaL60.mod := StreSSv.eshort.60.mod + Stressv.shrink.60.mod + StresSv.relax.60.mod + Stressv.creep.60. mod Stressv.total.60.mod 9906psi Converting the stress lost into a force per tendon that is lost:
Forcev.total60unmod Stressv.total.60.unmod At Forcev.total60.unmod = 171.2kip Forcev.totaL60.mod := Stressv.totaL.60.mod.At Forcev.totaL60.mod = 96.3kip where At = 9.723 in2 The design tension per tendon is (see Section 5.2 for original calculation):
Forcedesign = 16351'kp The remaining tension in the vertical tendons at 60 years is:
Tensionv.60.unmod := Forcedesign - Forcev.totaL60.unmod Tensionv.60.unmod = 1463.8kip Tensionv.60.mod := Forcedesign - Forcev.total.60.mod Tensionv.60.mod = 1538.7 kip
Calculation No.:
- kM P R MPR Associates, Inc.
Prepared By: )ý - 0102-0135-03 Revision No.: 0 320 King Street Ak!. Page No.: 29 Alexandria VA 22314 Checked By:
5.4 Horizontal Tendons - 60 Years After Initial SIT Some of the horizontal tendons near and away from the SGR opening will be detensioned and retensioned during SGR while the tension in some other tendons will not be changed. The tendon tension at 60 years will be individually calculated for the detensioned and retensioned tendons that pass through the SGR opening bay, the detensioned and retensioned tendons that do not pass through the SGR opening bay, and the tendons that are not detensioned. The tension losses for the tendons that pass through the SGR opening bay will be calculated considering all of these tendons to pass directly through the SGR opening since cutting and repairing the opening will affect the region both inside and around the SGR opening. The tendon tension at 60 years after the Structural Integrity Test (SIT) of November 1976 (Reference 7, page 10) is determined by scaling the predicted tension at 40 years after SIT. The individual losses in the horizontal tendons at 40 years after SIT from steel stress relaxation and concrete shrinkage are as follows (see Section 5.1 for references):
StresSh.shrink.40 = 2900psi StresSh. relax.40 := Forcehreax40 Stressh.relax.40 = 4957 psi A,
where A, = 9.723 in 2 Forceh.relax.40= 48.2kip Elastic Shortening The total circumferential force from a single horizontal tendon tensioned to lock off load is:
Forceh.axial:= GUTS70 Forceh.axial = 1635 kip where GUTS70 = 1635kip The average spacing between horizontal tendons near the containment mid-height is:
Sh.avg := Elavg.tend space.top - Elavg.tend space.bot Sh avg = 19.19 in navg.tendspace- 1 where Elavg.tend.space.top = 212.69ft Elavg.tend.space.bot = 183.9ft navg.tend.space = 19
Calculation No.:
50M PR MPR Associates, Inc.
Prepared By: )~ ~ 0102-0135-03 Revision No.: 0 320 King Street it/,
Alexandria VA 22314 Checked By: Page No.: 30 The average elastic shortening losses for the horizontal tendons are calculated based on the equations found in Section 2.1 of Reference 22. The horizontal tension losses due to elastic shortening do not change over time. These losses are applicable for the tendons that are not detensioned during the SGR. Note that the proportion of load in the tendon conduit is conservatively neglected from the calculation.
1 Forceh.axial Forceh~eshort.6ounmod := --.-
2 (Sh.avg'twa/i - At)'Ec + Sh.avg'tliner'Es + At'Es s Forceh.eshort.60.unmod 62.29kip Forceh.eshort.60.unmod StresSh.eshort.60.unmod A, StresSh.eshort.60.unmod = 6407psi This loss of stress applies to tendons that were not detensioned during the SGR.
For tendons that are adjusted during SGR, the elastic shortening stress losses will be affected by the material properties of the concrete used to replace the plug and to replace the outer portion of the delaminated concrete. As demonstrated in Section 5.3, the effect of the plug stiffness has a small effect on the elastic shortening losses, so the elastic shortening losses are estimated to be the same for all tendons.
StresSh.eshort.60.mod := StresSh.eshort.60.unmod Stressh.eshort.60.mod = 6407psi StresSh.eshort.60.mod.SGR := StresSh.eshort.60.unmod StresSh.eshort.60.modSGR = 6407psi Concrete Shrinkage The majority of concrete shrinkage occurs in the early life of the containment. Since the containment was built over 30 years ago, nearly all of the shrinkage has already taken place. At this point, shrinkage is essentially time-independent, and the concrete shrinkage at 60 years will be approximately equal to the concrete shrinkage predicted at 40 years.
Stressh.shrink.60.unmod := StresSh.shrink.40 StresSh.shrink.60.unmod = 2900psi This loss of stress applies to tendons that were not detensioned during the SGR.
Calculation No.:
- M PR MPR Associates, Inc.
Prepared By: 0102-0135-03 Revision No.: 0 320 King Street Ce dB Alexandria VA 22314 Checked By: Page No.: 31 The tendons passing through the SGR opening bay that are detensioned and retensioned during SGR will only experience shrinkage in the concrete that is replaced in the plug and that replaces the delamination. The replacement concrete is low-shrinkage concrete (Assumption 3.2.4), but the shrinkage losses in this region will conservatively be set equal to the shrinkage losses of the original concrete at 40 years. However, the results will be scaled based on the proportion of the span of new concrete to the entire span of the containment wall.
The total circumferential length of a horizontal tendon is:
2 Wtotal :=- abuttress'rh.tendon + Wbuttress Wtotal = 154.17 ft where abultres, = 1.05 rad Wbuttress = 12.34ft rh.tendon = 67. 72ft The span of the SGR opening is (see Section 5.1 for reference):
Wopen ý 25ft The circumferential length of the repaired delamination, excluding the span of the SGR opening, is:
Wdelam..ub.SGR := abuttress.rh.tendon - Wbuttress - Wopen Wdelam-sub.SGR = 33.57ft where abuttress = 1.05 rad Wbuttress = 12.34ft Wopen = 25ft rh.tendon = 67. 72ft The ratio of the thickness of the repaired delamination to the entire wall thickness is (see Section 5.3 for original calculation):
Ratiot.delam = 0.24 The shrinkage loss for the tendons that are detensioned and retensioned around the SGR opening is equal to:
(Wpn Wdelam sub.SGRm"Srshhin.4 Stressh shrink 60modSGR := Wopen + "Ratiot.dela Wtotal Wtotal .
Stressh,shrink.60. mod.SGR = 621psi
Calculation No.:
W M PR MPR Associates, Inc.
Prepared By:
Id.
0102-0135-03 Revision No.: 0 320 King Street Chckd.y Alexandria VA 22314 Checked By: Page No.: 32 The detensioned and retensioned tendons that do not pass through the SGR opening bay will not experience any shrinkage since there is no new concrete in the span of these tendons.
StresSh.shrink.60.mod := 0 Steel Relaxation The steel relaxation losses at 40 years have been calculated previously (Reference 7, Att. F, Page F2). Based on Figure 5-26 of Reference 10, steel relaxation is linear with time on a logarithmic scale. The losses calculated at 40 years will be extrapolated to 60 years based on the last two data points from Reference 7, Att. F, page F2.
Forceh'relax'40- Forceh'relax'35 3
Forceh.relax.6 0 := log(40) - log( "(log( 60) - Iog( J) + Forceh.relax.35 Forceh.relax.60 49.1 kip Forceh.relax.60 Stressh.relax.60. unmod "- Stressh. relax.60. unmod = 5051 psi where 2
Forceh-relax.40 = 48.2kip Forceh.relax.35 = 47.9 kip At = 9.7 3in2 The detensioned and retensioned tendons will be active for the following number of years before the 60 year end of life is reached (see Section 5.3 for original calculation):
Agereten = 27 yr Conservatively using the tendon steel relaxation loss in the horizontal direction at 30 years from Reference 7, Attachment F, Page F2:
Forceh relax.60.mod.SGR := Forceh relax.30 Forcedi.relax.60.mod.SGR =47.6kip Converting the force loss to a prestress loss in the tendon:
Forceh.relax.60.rmod. SGR StresSh.relax.60.mod.SGR := Stress h.relax.60.mod.SGR = 4896psi At tes
No.:
- M PR MPR Associates, Inc.
Prepared By:
'// /Calculation 0102-0135-03 Revision No.: 0 320 King Street By:P Alexandria VA 22314 Checked By: , Page No.: 33 This loss is also appropriate for the detensioned and retensioned tendons that do not pass through the SGR opening bay.
StreSSh.relax 60.mod := StreSSh.relax 60.mod.SGR StresSh.relax.60.mod = 4896psi Creep The basic creep for the existing concrete determined from testing and extrapolated to 60 years is (see Section 5.1 for reference):
-71 Creeph.basic.60 = 2.4 x 10 -7 psi The ratio of the concrete stiffness to the total stiffness through the cross-section of the containment wall is calculated based on the equations in Section 2.1 of Reference 22.
Sh.avg twall'Ec Ratioh.cocI.stiff := (Sh.avgtwali - At)'Ec + Sh.avg'tliner'Es + At'Es Ratioh.concstiff= 0.88 For the stress in the concrete contributing to creep, elastic shortening and shrinkage losses are subtracted because they occur early in the life of the containment.
GUTS70 - (Stressh'eshort.60"unmod + StresSh'shrink'40)"At .
07h.axiaL.creep := A""UL h.conc.stiff t
Sh.avg wall - At Yh.axial.creep = 1703psi where StresSh.eshort.60.unmod = 6407 psi StresSh.shrink.40 = 2900psi 9 72 At = . 3in2 Sh.vg = 19.19in twall = 3.5ft GUTS70 = 1635 kip
Calculation No.:
- OM P R Prepared By: )-. 0102-0135-03 MPR Associates, Inc. Revision No.: 0 320 King Street B :PaeN.3 Alexandria VA 22314 Page No.: 34 The tendon prestress lost due to creep is calculated based on Page 4 of Reference 2. This value The tendon prestress lost due to creep is calculated based on Page 4 of Reference 2. This value is applicable to tendons that are not detensioned during the SGR:
StresSh.creep. 60.unmod := Th. axial.creep Creeph.basic.60.Es StresSh.creep. 60.unmod = 11850psi where Es is the steel elastic modulus and is equal to:
Es=2.9x 10 psi Creep losses for the tendons that pass through the patch are calculated separately by taking into account the creep properties of the replacement concrete. The creep properties have been calculated in Section 5.3 of this calculation. The creep coefficient for end of life is:
v, = 0.56 The total loss in the new concrete is scaled based on the proportion of the width and cross-sectional ratio of the new concrete to the horizontal tendon lateral span and total thickness of the containment wall. The remaining concrete will creep following the same trend from the measured data in Reference 3, page 45. The methodology used here is duplicated from Section 5.3 of this calculation. The creep experienced by the existing concrete up to the beginning of the SGR outage (33 years) is:
Stressh.creep.33.unmod := (Th.axial.creep Creeph.basic.33Es StresSh.creep.33.unmod = 10122psi where
-71 x 10 -7 Creeph.basic.33 = 2.05 psi The total creep loss in the horizontal tendons at 60 years is:
StresSh.creep.60. mod.SGR := Wopen(StresSh.eshort.60.mod" Vt) + Wdelam.sub.SGR Ratiot.delam,(Stressh.eshort.60.mod'V) ) ..
Wtotal Wtotal (Wtotal - Wopen Wdelam.sub.SGR .Ratiodela (Stressh.creep.60.unmod - StresSh.creep.33.unmod)
\ Wtotal Wtotal M
Calculation No.:
00M PR MPR Associates, Inc.
Prepared By:
0102-0135-03 Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: Page No.: 35 Stressh.creep.60. od.SGR = 2127 psi where Wopen = 25ft Wtotal = 154.17 ft StresSh.eshort.60. mod = 6407 psi v, = 0.561 Wdelam.sub.SGR = 33.57ft Ratiot.delam = 0.24 StresSh.creep.60.unmod = 11850psi The total creep loss for the horizontal tendons that do not pass through the SGR opening bay is:
StresSh.creep. 60.mod : StresSh.creep. 60.unmod - StresSh.creep.33.unmod StresSh.creep.60.mod = 1728psi Total 60 Year Loss The total tendon stress loss after 60 years is calculated.
Unadjusted Tendons:
Stressh.total.60.unmod = StresSh.eshort.60.unmod + StresSh.shrink.60.unmod + StresSh.relax.60.unmod + StresSh.creep.60.unmod Stressh.total.60.unmod = 26208psi Detensioned and Retensioned Tendons that do not Pass through SGR Opening:
Stressh.total.60.mod StresSh.eshort.60.mod + StresSh.shrink.60.mod + StresSh.relax.60.mod + StresSh.creep. 60.mod Stressh.total.60mod 13031psi Detensioned and Retensioned Tendons that Pass through SGR Opening:
Stressh.total.60.mod.SGR := StresSh.eshort.60.mod.SGR + StresSh.shrink.60.mod.SGR + StresSh.relax.60.modSGR + StresSh.creep.60.mod.SGR Stressh.total.60.modSGR 14050psi
Ol RPrepared
- M P RPrepred y: *.0Caclt102-0135-03N° By: ~Calculation No.:
MPR Associates, Inc. Revision No.: 0 320 King Street VkP Alexandria VA 22314 Checked By:.A/', Page No.: 36 Converting the stress lost into a force per tendon that is lost:
Forceh.total.60.unmod := Streskhtotal.60.unmod.At ForCeh.total.60.unmod = 254.8ic'p Forceh.totaL60.mod := Stressh.total60.mod.At Forceh.total.60.mod = 126. 7kip Forceh.total 60.mod SGR := Stressh.totaL60.mod.SGR.At Forceh.total.60.mod.SGR = 136.6kip where 2
A, = 9.723 in The design tension per tendon is (see Section 5.2 for original calculation):
Forcedesign = 1635 kip The remaining tension in the horizontal tendons at 60 years is:
Tensionh.60.unmod := Forcedesign - Forceh.total, 60.unmod Tensionh.60.unmod = 1380.2 l'p Tens ionh.60.mod := Forcedesign - Forceh.total.60.mod Tensionh.60.mod = 1508.3 l'p Tensionh.60.modSGR := Forcedesign - Forceh.totaL60.mod.SGR Tensionh.60.mod.SGR = 1498.4kip
- M P RPrearedBy:Calculation No.:
MPR Associates, Inc. Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: *i/ . .
- . Page No.: 37 5.5 Dome Tendons - After SGR Completion After the Steam Generator Replacement Project is completed, the containment will only have experienced 33 years of its 60 year life. The tendon losses are expected to be less at this time compared to the losses after 60 years. The total losses after SGR completion are calculated Elastic Shortening The elastic shortening losses are not time dependent. The elastic shortening losses after 33 years will be equal to the elastic shortening losses calculated for 60 years in Section 5.2.
Stressd.eshort.33 " Stressdeshort.60 StresSdeshort33 = 5500psi Concrete Shrinkage The concrete shrinkage losses will be essentially independent of time after 33 years. Therefore, the concrete shrinkage losses calculated for the 60 year end of life calculated in Section 5.2 are appropriate for the 33 year losses.
Stressd.shrink.33 := Stressd.shrink.60 StresSdcshrink.33 = 2900psi Wire Relaxation The wire relaxation losses are interpolated from Reference 7, Appendix F, Page F2. The wire relaxation loss at 33 years is:
Forced.relax.33 = 48kip Converting this load into a stress loss in the tendon:
Forced.relax.33 Stressd.relax.33 := Stressdrelax.33 r = 4937 psi
Calculation No.:
I MP R MPR Associates, Inc.
Prepared By: 0102-0135-03 Revision No.: 0 320 King Street CcdyPeo3 Alexandria VA 22314 Checked By:.-l. Page.No.: 38 Creep The tendon tension loss due to creep can be calculated using the basic creep at 33 years. The basic creep at 33 years is defined in Section 5.1:
-71 Creepd basic.33 = 3.00 x 10 -
psi The stress in the dome in the direction of the dome tendons is (see Section 5.1 for reference):
d~axial = 1530psi The creep loss at 33 years is:
Stressd.creep.33 := Creepd.bas ic .33
- d.axiaflEs Stressd.creep.33 = 13311 psi where Es = 2.9 x 10 7psi Total Loss at 33 Years The total tendon stress loss after 33 years is:
Stressd.total.33 StresSd.eshort.33 + StresSd.shrink.33 -+ StreSSdrelax.33 + Stressd.creep.33 Stressd total 33 = 26648psi Converting the stress lost into a force per tendon that is lost:
ForCed.total.33:= Stressdtotal33. t Forcedtotal.33 = 259.1 kip where 2
At = 9.723in The design tension per tendon is (see Section 5.2 for original calculation):
Forcedesign = 1635 kip
O ~IL PR MPR Associates, Inc.
Prepared By:
Calculation No.:
0102-0135-03 Revision No.: 0 320 King Street Cy Alexandria VA 22314 Checked By: Page No.: 39 The remaining tension in the dome tendons at 33 years is:
Tensiond.33 :=Forcedesign - ForCed.tofaI.33 Tensiond 33 = 1375.9 kip
Calculation No.:
&IMPR MPR Associates, Inc.
Prepared By: )~ 4 -
~ 0102-0135-03 Revision No.: 0 320 King Street Checked By:
Alexandria VA 22314 /Page No.: 40 5.6 Vertical Tendons - After SGR Completion After the Steam Generator Replacement Project is completed, the containment will only have experienced 33 years of its 60 year life. The tendon losses are less at this time compared to the losses after 60 years. The total losses after SGR completion are calculated Elastic Shortening The elastic shortening losses are not time dependent. The elastic shortening losses after 33 years will be equal to the elastic shortening losses calculated for 60 years in Section 5.3. These losses are applicable to both tendons that are detensioned and retensioned and those that are not.
StreSSv.eshort.33.unmod := StreSSv.eshort.60.unmod StreSSv.eshort.33.unmod = 3274psi Stress&eshort.33.mod := Stres&veshort.60.mod Stres&veshort.33.mod = 3274psi Concrete Shrinkage For the existing concrete, the concrete shrinkage losses will be essentially independent of time after 33 years. Therefore, the concrete shrinkage losses calculated for the 60 year end of life calculated in Section 5.3 are appropriate for the 33 year losses for these tendons. For the tendons that are detensioned and retensioned, the new concrete will not have experienced any significant shrinkage immediately after the tendons are retensioned.
StreSSv.shrink.33.unmod := StreSsv shrink.60. unmod StreSsv.shrink.33.unmod = 2900psi StreSsv shrink.33.mod := 0 Wire Relaxation The wire relaxation losses are interpolated from Reference 7, Appendix F, Page F2. These losses are applicable for the tendons that are unadjusted during SGR. The tendons that are detensioned and retensioned will not experience any significant relaxation immediately after they are retensioned.
Forcev.relax.33.unmod = 48.Okip
M P R Prepared ByCalculation No.:
MPR Associates, Inc. Revision No.: 0 320 King Street CekdB Alexandria VA 22314 Checked By: Page No.: 41 Converting this load into a stress loss in the tendon:
reax 33 umod:=Forcev.relax.33.unmod Str,5 Stresvreax~snmodA, Stressvrelax.33.unmod = 4937 psi Stressv.relax. 33. mod := 0 Creep The tendon tension loss due to creep of the existing concrete can be calculated using the basic creep at 33 years. This calculation was performed in Section 5.3. The creep loss in the tendons that are unadjusted is equal to this value. The tendons that are detensioned and retensioned do not experience any significant creep immediately after retensioning.
Stressv.creep.33.unmod = 5466psi Stressv.creep.33.mod := 0 Total Loss at 33 Years The total tendon stress loss after 33 years is:
Stressv.total.33.unmod Stressv.eshort.33.unmod + StresSv.shrink.33.unmod + StresSv.relax.33. unmod + Stressv.creep.33.unmod Stressv.total.33. unmod 16577psi Stressv.total.33. mod Stressv.eshort.33. mod + StreSSv.shrink.33. mod + Stressv.relax.33.mod + Stressv.creep.33. mod StreSSv.total 33 .mod = 3274psi Converting the stress lost into a force per tendon that is lost:
Forcev.total.33.unmod := Stressv.total.33.unmod"At Forcev.total.33.unmod = 161.2kip Force,. total.33.mod := Stressv.total33.mod'At Forcev.total.33 mod = 31.8kip where 72 A, = 9. 3 in2
Calculation No.:
M P Inc.
- MPR Associates, R Prepared By: 0102-0135-03 Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: '* Page No.: 42 The design tension per tendon is (see Section 5.2 for original calculation):
Forcedesign = 1635 kip The remaining tension in the vertical tendons at 33 years is:
Tensionv.33.unmod := Forcedesign - Forcev.total33.unmod Tensionv.33.unmod = 1473.8 kip Tensionv.3 3.mod := Forcedesign - Forcev total.33.mod Tensionv.3 3.,mod = 1603.2 kip
ROM P R Prepared By: 0102-0135-03 MPR Associates, Inc. Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: Page No.: 43 5.7 Horizontal Tendons - After SGR Completion After the Steam Generator Replacement Project is completed, the containment will only have experienced 33 years of its 60 year life. The tendon losses are less at this time compared to the losses after 60 years. The total losses after SGR completion are calculated Elastic Shortening The elastic shortening losses are not time dependent. The elastic shortening losses after 33 years will be equal to the elastic shortening losses calculated for 60 years in Section 5.3. These losses are applicable to both tendons that are detensioned and retensioned and those that are not.
StresSh.eshort.33.unmod := Stressh.eshort 60.unmod StresSh.eshort.33.unmod = 6407 psi Stressh,eshort.33.mod := Stressh.eshort.60.mod Stressh eshort.33 mod = 6407 psi StresSh.eshort.33.mod.SGR := StresSh.eshort.60.mod.SGR Stressh.eshort.33.mod.SGR = 6407psi Concrete Shrinkage For the existing concrete, the concrete shrinkage losses will be essentially independent of time after 33 years. Therefore, the concrete shrinkage losses calculated for the 60 year end of life in Section 5.3 are appropriate for the 33 year losses for these tendons. For the tendons that are detensioned and retensioned, the new concrete will not have experienced any significant shrinkage immediately after the tendons are retensioned.
Stressh.shrink.33.unmod := StresSh.shrink.60.unmod Stressh.shrink.33.unmod = 2900psi StresSh. shrink.33.mod := 0 Stresh.shrink.33. mod.SGR := 0 Wire Relaxation The wire relaxation losses are interpolated from Reference 7, Appendix F, Page F2. These losses are applicable for the tendons that are unadjusted during SGR. The tendons that are detensioned and retensioned will not experience any significant relaxation immediately after they are retensioned.
Forceh~relar.33unmod 47.8kip
// / Calculation No.:
UMP R MPR Associates, Inc.
Prepared By:
474 0102-0135-03 Revision No.: 0 320 King Street Cc B IPg .
Alexandria VA 22314 4 Page No.: 44 Converting this load into a stress loss in the tendon:
Forceh.relax.33.unmod StreSSh.relax.33.unmod : Stressh.relax.33.unmod = 4916 ps'i StresSh.relax.33. mod := 0 Stressh.relax.33.mod.SGR := 0 Creep The tendon tension loss due to creep of the existing concrete can be calculated using the basic creep at 33 years. This calculation was performed in Section 5.3. The creep loss in the tendons that are unadjusted is equal to this value. The tendons that are detensioned and retensioned do not experience any significant creep immediately after retensioning.
Stressh.creep.33.unmod = 10122psi StresSh.creep.33.mod := 0 StresSh.creep.33. mod.SGR := 0 Total Loss at 33 Years The total tendon stress loss after 33 years is:
Stressh.totaL.33.unmod := Stressh.eshort.33.unmod+ Stresh.shrink.33.unmod + StresSh.relax.33.unmod + StresSh.creep.33.unmod Stressh.totaL33.unmod = 24345psi Stressh.total.33. mod StresSh.eshort.33. mod + StresSh.shrink.33.mod + Stressh.relax.33.mod + Stressh.creep.33.mod Stressh. total 33.mod = 6407psi Stressh.total.33.modSGR := StresSh.eshort.33.mod.SGR + StresSh.shrink.33.modSGR + StresSh.relax.33.modSGR + StresSh.creep.33.mod.SGR Stressh.total.33.modSGR = 6407 psi
Calculation No.:
M M PR MPR Associates, Inc.
Prepared By: 0102-0135-03 Revision No.: 0 320 King Street ChcedB :
Alexandria VA 22314 Checked By: Page No.: 45 Converting the stress lost into a force per tendon that is lost:
Forceh.total33.unmod := Stressh.totaL33.unmod At Forceh.total.33.unmod = 236.7 kip ForCeh.total.33.mod := Stressh.total 33. mod. A, Forceh.total 33. mod = 62.3kip Forceh.total.33.mod.SGR := Stressh.totaL33.mod.SGR.At Forceh.total.33.mod.SGR = 62.3kip where 2
A, = 9.723 in The design tension per tendon is (see Section 5.2 for original calculation):
Forcedesjgn = 1635 kip The remaining tension in the horizontal tendons at 33 years is:
Tensionh.33.unmod := Forcedesign - Forceh.total.33.unmod Tensionh.3 3.unmod = 1398.3 kip Tensionh.33.mod := Forcedesign - Forceh.total.33,mod Tensionh.3 3 .mod = 1572.7 kip Tensionh.33.mod.SGR := Forcedesign - Forceh.total.33.mod.SGR Tensionh.33.mod.SGR = 1572.7 kip
Calculation No.:
&MM PR MPR Associates, Inc.
Prepared By: )v 41/4 0102-0135-03 Revision No.: 0 320 Kin g S tre e t C e k B :a No 4 Alexandria VA 22314 Checked By: Page No.: 46
6.0 REFERENCES
- 1. Crystal River Unit 3, "Design Basis Document for the Containment," Revision 7.
- 2. Gilbert Associates Inc. Calculation 1.01.19.
- 3. Gilbert Associates Inc. Calculation 1.01.7.
- 4. Roark, Raymond J. and Warren C. Young, Formulasfor Stress and Strain, McGraw Hill, 5th Ed., 1975.
- 5. Progress Energy Drawing 421-347, Sheet 1, "Reactor Building Temporary Access Opening for SGR Vertical & Horizontal Tendon Positions," Rev. 0.
- 6. S&ME, Inc., "Phase UII Test Report Mix Acceptance Testing for Crystal River Unit 3 Steam Generator Replacement Project," June 19, 2009.
- 7. Florida Power Calculation S-95-0082, "6th Tendon Surveillance - Generation of Tendon Force Curves," Revision 3.
- 8. Progress Energy Calculation S06-0004, "Containment Shell Analysis for Steam Generator Replacement - Properties of New Concrete for Access Opening and Number of Hoop and Vertical Tendons to be De-tensioned," Revision 0.
- 9. Florida Power Corporation Drawing SC-421-031, "Reactor Building Exterior Wall - Concrete Outline," Rev. 4.
- 10. Crystal River Unit 3 Final Safety Analysis Report, Rev. 31.3.
- 11. Gilbert Associates Inc. Calculation 1.01.8.
- 12. American Concrete Institute Standard ACI 209R-92, "Prediction of Creep, Shrinkage, and Temperature Effects in Concrete Structures," 1992.
- 13. Prescon DWG 5EX7-003, Sheet P9, "Hoop Tendon Placement 60'-120', EL. 94'-5 3/4" -
143'-9 3/4"", Rev. 4.
- 14. Progress Energy Calculation S08-0008, "Containment Shell Analysis for Steam Generator Replacement - Evaluation of Restored Shell at 60-year Design Life," Revision 1.
- 15. Gilbert Associates Drawing SC-421-003, "Reactor Building Foundation Mat Concrete Outline,"
Revision 1.
IM PR Calculation No.:
MPR Associates, Inc. Revision No.: 0 320 King Street Checked By: /
Alexandria VA 22314 Page No.: 47
- 16. MPR Calculation 0102-0135-02, "Concrete Modulus of Elasticity and Minimum Compressive Strength."
- 17. Relative Humidity Data from January 2004 to September 2006 at Brooksville, FL, University of Florida IFAS Extension, Florida Automated Weather Network, fawn.ifas.ufl.edu.
- 18. Not Used
- 19. Not Used
- 20. Florida Power Corporation Drawing S-425-007, "IWE/IWL Inspection Hoop Tendon "53" Layout," Revision 1.
- 21. Florida Power Corporation Drawing S-425-006, "IWE/IWL Inspection Hoop Tendon "42" Layout," Revision 1.
- 22. USNRC Regulatory Guide 1.35.1, "Determining Prestressing Forces for Inspection of Prestressed Concrete Containments," July 1990.
- 23. Email from J. Holliday (Progress Energy) to K. Gantz (MPR), Subj: FW: Temperature Effect on Creep, January 7, 2010, 6:14 AM (Provided as Attachment A).
- 24. Prescon Drawing 5EX7-003, Sheet P9, "Hoop Tendon Placement 60'-120' El. 94'-5 3/4" -
143' - 9 3/4"," Revision 4.
MPR Associates, Inc.
M PR 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: A-i 0102-0135-03 "- ,Revision: 0 A
Reference 23 From: Holliday, John [John.Holliday@pgnmail.com]
Sent: Thursday, January 07, 2010 6:14 AM To: Bird, Edward; Gantz, Kevin Cc: Dyksterhouse, Don; Knott, Ronald
Subject:
FW: Temperature Effect on Creep Gentlemen, Attached e-mail is from Prof. Domingo Carreira the Chairman of the sub-committee that prepared ACI 209 and specifically authored the section that addresses the effects of temperature on creep, he is also the individual who designed the concrete mix for CR3 SGR. Based on his observations I believe we can exclude operating temperature as a factor in determining the creep ratio.
- Regards, John Holliday From: CHRIS.A.SWARD@sargentlundy.com [4]
Sent: Wednesday, January 06, 2010 1:10 PM To: Holliday, John
Subject:
Fw: Temperature Effect on Creep
- John, Domingo's reply follows. I think some of his discussion relates only to the patch concrete but in general I think he provides enough basis for not applying a temperature adjustment.
Chris Sward Project Manager Sargent & Lundy 312-269-7426 Forwarded by CHRIS A SWARD/Sargentlundy on 01/06/2010 12:08 PM -----
From: DOMINGO CARREIRA <domingocarreira@sbcglobal.net>
To: CHRIS.A.SWARD@sargentlundy.com Date: 01/05/2010 11:21 PM
Subject:
Re: Temperature Effect on Creep MPR QA Form: OA-3.1-3, Rev. 0
MPR Associates, Inc.
FIM PR 320 King Street Alexandria, VA 22314 Calculation No. Prepared By 0102-0135-03 / -
//A Chris:
Testing may recollection is a little bit risky, however the question is on a subject that I am familiar with, plus it was a good idea to send me the CR3 report to refresh what we did in 2007.
As you well said, ACI 209 Report discuss briefly the subject of the temperature effects on creep and shrinkage and gives some estimates but no factor is given to quantify it. I must confess that I personally wrote this portion of the report at the request of the late Jim Rhodes.
The same limitation on the effects of temperature on creep and shrinkage occurs with the other 3 methods of predictions given in the latest revision of ACI 209-2R recently published. The reason is the same for the four methods in ACI 209-2R, we don't have enough information to evaluate it and to propose an acceptable coefficient for correction. In addition, we say in the introduction of ACI 209-2R that a departure of +
or - 30% from actual test data could be expected when using the proposed our methods. This sad admission was approved by the authors of the other 3 methods in ACI 209-3R, that is, Bazant, Gadner, and Muller. Branson the author of the original 209 method is no longer a member of this committee, he retired some years ago.
In the case of CR3 concrete replacement I am of the opinion that temperatures higher than 70 F will not be of concern for the following reasons:
- 1. Despite the temperature of the concrete during operating conditions as well as the exterior temperature in Florida will be higher than 70F, this higher temperature will not increase significally concrete creep and shrinkage, since their values from the standard testing temperature are very low compared with the majority of the concrete on which the prediction methods are based on.
- 2. The operating temperature will be by far lower than the initial accelerated autogenous curing temperature from the cement heat of hydration. This high autogenous temperature is not present in the standard testing methods for creep and shrinkage.
- 3. Most of the effect of high operating temperatures on creep and shrinkage is caused by the driving out of the concrete the water uncombined with cement. Approximately MPR QA Form: QA-3.1-3, Rev. 0
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320 King Street 0M PR Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: A-3 012-13 -0 Revision: 0 the mass of water corresponding to 20% of the mass of cement will combine with it.
That is, a w/c ratio of 0.20 will be chemically combined with the cement. The remaining of the mixing water may evaporate from the concrete This problem is drastically reduced by the fact that in our concrete the free evaporable water is low compared with most concretes. Also, and most important, by the very high volume-to-surface ratio of the walls (48 inches) compared with that of the test specimens (3 inches), and by the use of fly ash and silica fume that will combine chemically with some portion of the evaporable water that will not chemically combine with cement.
- 4. The high modulus of elasticity and the high initial strength of the CR3 concrete mixture are conditions that help to reduce the effects of temperatures higher than the testing temperatures. We know that some of the high strength concretes have lower creep and shrinkage than normal strength concretes because of the lesser free water in these concretes.
- 5. The higher operating temperatures will mostly affect the top portion of the containment away from the replacement concrete.
I could continue elaborating on this subject, but I think that the given reasons make sense..
I will return to Chicago from California tomorrow January 6, 2010 and could visit you the coming Thursday or Friday.
My best wishes in this 2010, Domingo From: "CHRIS.A.SWARD@sargentlundy.com" <CHRIS.A.SWARD@sargentlundy.com>
To: Domingo Carreira <carreira@iit.edu>; domingocarreira@sbcglobal.net Sent: Tue, January 5, 2010 10:55:08 AM
Subject:
Temperature Effect on Creep Domingo, Happy New Year.
I need to test your recollection. The attached study was included with one of the calcs that we did for the CR3 containment analysis. Part of the study works through the computation of effective modulus based on creep. The creep coefficient computation (following ACI-209R) applies a number of adjustments for nonstandard conditions. ACI 209R discusses temperature as a factor although it does not provide a specific adjustment factor. Our temperature during operation will be somewhat above the standard 70 degF. Do you recall why we did not include a temperature adjustment?
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320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: A-4 0102-0135-03 Revision: 0 Chris Sward Project Manager Sargent & Lundy 312-269-7426 MPR QA Form: QA-3.1-3, Rev. 0
MPR Associates, Inc.
- M PR 320 King Street Alexandria, VA 22314 CALCULATION TITLE PAGE Client:
Progress Energy Page 1 of 20 Project: Task No.
CR3 Containment Delamination 0102-0906-0135
Title:
Calculation No.
Finite Element Model Description 0102-0135-04 Preparer / Date Checker / Date Reviewer & Approver / Date Rev. No.
1-21-2010 1-121 1-21-2010 Kevin Gantz 1-21-2010 Edward Bird 0 Peter Barrett QUALITY ASSURANCE DOCUMENT This document has been prepared, checked, and reviewed/approved in accordance with the Quality Assurance requirements of IOCFR50 Appendix B, as specified in the MPR Quality Assurance Manual.
MPR-QA Form QA-3.1-1, Rev. 1
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UM PR 320 King Street Alexandria, VA 22314 RECORD OF REVISIONS Calculation No. Prepared By Checked By Page: 2' 0102-0135-04t I Revision IAffected Pages Description 0 All Initial Issue Note: The revision number found on each individualpage of the calculation carries the revision level of the calculation in effect at the time that page was last revised.
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&IMPR 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 3 0102-0135-04 Revision: 0 Table of Contents 1.0 Introduction..................................................................................................... .4 1.1 Background .......................................................................................................... 4 1.2 Purpose .... ...................................................................................................... 4 1.3 Reactor Building Description ................................................................................. 4 2.0 Sum m ary of Results and Conclusions.......................................................... 5 3.0 Methodology ..................................................................................................... 5 3.1 Finite Element M odel Description .......................................................................... 5 3.1.1 Containm ent W all .......................................................................................... 6 3.1.2 Ring Girder and Dome ................................................................................. 7 3.1.3 Tendons ......................................................................................................... 9 3 .1.4 L in er .................................................................................................................. 11 3.2 Boundary Conditions ................................................................................................ 12 4.0 Design Input................................... .................................................................. 12 4.1 Geometry .................................................................................................................... 12 4.2 M aterial Properties ............................................................................................... 14 5.0 M odel Benchm arking Results....................................................................... 15 6.0 Assum ptions................................................................................................... 19 7.0 Computer Codes........................................................................................... .. 20 8.0 References ..................................................................................................... 20 MPR QA Form: QA-3.1-3, Rev. 0
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FIM PR 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 4 0102-0135-04 Revision: 0
1.0 INTRODUCTION
1.1 Background A project is underway at Progress Energy's Crystal River Unit 3 (CR3) site to replace the steam generators. As part of that project, 10 vertical and 17 horizontal tendons were detensioned and an opening was cut into the concrete containment above the equipment hatch. As this opening was being cut, cracking in the concrete wall was identified around the full periphery of the opening in the cylindrical plane of the wall. The cracking is located at the approximate radius of the circumferential tendon conduits, and is indicative of a delaminated condition. Progress Energy plans to remove the delaminated concrete and replace it.
1.2 Purpose This calculation documents an ANSYS finite element model of the Crystal River Unit 3 (CR3)
Containment Building. The model was developed to analyze containment restoration and design basis loading conditions. Limited results from the model are provided for benchmarking. Results of repair and design basis analyses performed with the model, including the detensioning sequence, are documented elsewhere.
1.3 Reactor Building Description Reference 1, Chapter 5.2, provides the following description of the Crystal River Containment.
The CR3 Reactor Building is a concrete structure with a cylindrical wall, a flat foundation mat, and a shallow dome roof. The foundation slab is reinforced with conventional mild-steel reinforcing. The cylindrical wall is prestressed with a post-tensioning system in the vertical and horizontal (hoop) directions. The dome roof is prestressed utilizing a three-way post-tensioning system. The inside surface of the reactor building is lined with a carbon steel liner to ensure a high degree of leak tightness during operating and accident conditions. Nominal liner plate thickness is 3/8 inch for the cylinder and dome and 1/4 inch for the base. (Note that the liner plate is thicker around the equipment hatch.)
The foundation mat is 12-1/2 feet thick with a 2 foot thick concrete slab above the bottom liner plate. The cylindrical portion of the containment building has an inside diameter of 130 feet, wall thickness of 3 feet 6 inches, and a height of 157 feet from the top of the foundation mat to the spring line. The shallow dome roof has a major radius of 110 feet, a transition radius of 20 feet 6 inches, and a thickness of 3 feet.
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IM PR 320'King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 5 0102-0135-04 -, Revision: 0 2.0
SUMMARY
OF RESULTS AND CONCLUSIONS This calculation documents the development of the CR3 Containment finite elempent model for restoration and design basis analyses. The benchmarking results provided in Section 5 show a favorable comparison between the finite element membrane stresses and a handcalculation of membrane stresses for the intact containment.
3.0 METHODOLOGY A three-dimensional finite element model is developed for the CR3 containment restoration and design basis analyses. The model includes linear-elastic material behavior with the exception of the steel liner which is modeled as elastic-plastic. The effects of concrete creep on prestress are represented in the finite element model by a reduction of tendon tension through time (Reference 7). Concrete creep strains are not considered in this calculation.
3.1 Finite Element Model Description The finite element model of the Crystal River 3 Containment for restoration and design basis analyses includes the following features:
- The model represents a symmetric portion of the building (1800) with the symmetry plane passing through the center of the steam generator replacement opening and center of the equipment hatch.
- The hoop and vertical tendons are modeled explicitly.
- The equipment hatch is modeled with a simplified representation.
- The model has the ability to remove individual tendons (hoop or vertical) and has the ability to vary an individual tendon's force (hoop or vertical).
- The prestress from the dome tendons is modeled using equivalent forces.
- The delaminated portion of concrete on the containment wall is explicitly modeled as well as the concrete that is still intact.
The following finite element types are used in the model:
- 1. 3-D, 8 node brick elements are used to model the concrete building.
- 2. 1-D truss elements are used to model the tendons.
- 3. 3-D Shell elements are used to model the steel liner.
- 4. 1-D spring elements are used to link the boundary between the concrete added to fill the steam generator opening and the containment wall as well as the boundary between the delaminated concrete and the intact concrete in the plane of the cylindrical Wall. The MPR 1 QA Form: QA-3.1-3, Rev. 0
MPR Associates, Inc.
FIM PR 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 6 0102-0135-04 6 . , Revision: 0 stiffness of these elements is varied to represent the delamination or continuous bond of the intact and repaired building
- 5. Surface-to-surface contact elements are used to model the delamination stage in the containment wall. Contact elements are also used to bond the SGR plug to the existing concrete.
These elements are discussed in more detail below.
3.1.1 Containment Wall Brick elements are used to model the containment wall since they can predict a nonlinear through-thickness stress distribution that cannot be captured using conventional shell modeling.
Using the element birth and death features of ANSYS, these brick elements can accurately represent the incompatibility of the stress-free concrete used for repairs and the pre-loaded building deformation pattern.
The cylindrical portion of the wall is modeled as 42-inch thick concrete, with the exception of the wall that contains the opening for the steam generator replacement. This portion of the wall is modeled in two separate sections, a 10-inch thick delaminated portion on the outside surface of the wall, and the remaining intact 32-inch thick portion of the wall. The portion of the wall that is modeled as delaminated is the area bounded laterally by the two adjacent buttresses, and vertically by the transition to a 42-inch thick wall above the equipment hatch and a horizontal line at elevation 240 ft (approximately 10 feet below the bottom of the ring girder). This rectangular area surrounds the opening used for steam generator replacement and is somewhat greater than the actual delaminated area. 1-D springs are added to the interface surfaces of the delamination to either free the delamination or bond the delamination to the intact concrete, depending on the intent of the analysis. For the load steps including delamination, very soft springs eliminate tensile load transfer across this boundary.
The area in the containment wall that was removed to form an opening for steam generator replacement is modeled using independent elements which have coincident nodes with the edges of the containment. Prior to removal of the section, the model uses stiff springs to bond the elements to the containment wall. Element birth and death is used to kill the elements in the opening simulating the plug being cut. The plug region remains in the model but carries no stiffness or loads and when replaced appears as stress and strain-free material. After the tendons around the opening are detensioned and the new concrete is installed, the springs at the interface are eliminated (set to a negligibly small stiffness) and contact elements are used to bond the interface surfaces. A similar technique is applied for the delaminated concrete.
Brick element edges are aligned with the tendons such that the tendon (truss) element nodes are coincident with the containment (brick) concrete element nodes. These coincident nodes allow MPR QA Form: QA-3.1-3, Rev. 0
MPR Associates, Inc.
320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 7 0102-0135-04 6 *._ Revision: 0 for direct coupling between the concrete and tendon elements in the two directions normal to the tendon. The truss elements are described in more detail below.
Figure 3-1 shows the 1800 model. The buttresses are modeled with brick elements to capture their eccentric stiffness and to provide tendon attachment points. The basic dimensions of the containment model are presented in Section 4.1. The personnel hatch and other localized geometry, with the exception of the equipment hatch, were not modeled since they are remote from the steam generator opening. A scoping submodeling analysis of the equipment hatch showed that the hatch modeling shown below is adequate for performing repair and design basis analyses. The regions remote from the opening are unaffected by the steam generator replacement; their presence will not affect the global model results near the SGR opening and delamination.
3.1.2 Ring Girder and Dome In the finite element model, the ring girder and dome are represented by uniform areas swept about the vertical axis of the containment. This representation is exact for the dome and nearly exact for the ring girder. The dome and ring girder elements are joined by constraint equations rather than by shared nodes. The dome delamination and repair are considered to have a negligible effect on the purpose of this calculation and therefore are not represented in the finite element model. All of the dome tendons are considered to be fully tensioned.
MPR Associates, Inc.
- M P R 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 8 0102-0135-04 )_- " Revision: 0 Figure 3-1 Finite Element Model of CR3 Containment Building MPR QA Form: QA-3.1-3, Rev. 0
MPR Associates, Inc.
320 King Street
- M PR Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 9 0102-0135-04 Revision: 0 3.1.3 Tendons Truss elements are used to model the vertical and hoop tendons to provide flexibility in evaluating variations in tendon loads (de-tensioning and re-tensioning) during the repair process.
Hoop tendon truss element nodes are defined at coincident locations of the brick elements of the containment wall where load transfer is required between hoop tendons and the containment wall. Vertical tendons are each modeled as a single truss element with nodes at the top of the ring girder and at the bottom of the basemat. Rigid beam elements areused at the buttresses for the hoop tendons, and at the top of the ring girder and bottom of the basemat for the vertical tendons to connect the ends of the tendons to the containment. This modeling distributes the tendon support loads to the concrete brick elements without modeling the anchorages explicitly.
Coupling in the radial and vertical directions between the tendon elements and the containment wall is used to transfer load between the hoop tendons and the containment wall. The axial degrees of freedom of the tendons are fixed, but are not tied to the containment wall. The fixed axial displacement allows for an initial strain tobe used to define the tendon forces in these elements. Forces are derived directly from the stresses and tendon areas. However since the building deformation effects the stress, the strain required to define the tendon forces requires an iterative approach to ensure the proper tendon force is applied. Thus, each element is given a different initial strain to produce the current tendon loads. Tendon de-tensioning and future re-tensioning is performed by scaling these strains.
Table 4-2 provides basic tendon spacing. There are 144 evenly spaced vertical tendons (2.5 degree spacing). There are 94 tendon hoops, each hoop consisting of three individual tendons.
The hoop tendons are arranged in pairs. The two tendons in the pair are separated by 12.75 inches (typically) whereas pairs are typically separated by 38.12 inches (Reference 12).
Tendons are initially tensioned to 80% of Guaranteed Ultimate Tensile Strength (GUTS) and then the load is reduced to 70% of GUTS. For horizontal tendons, this procedure results in a tendon force curve that is best represented by a uniform tendon tension along the length of the tendon. Consequently, a uniform tension was applied to the horizontal tendons (Reference 9).
The tension applied accounts for loss of tension through time (Reference 7).
Vertical tendons only transfer load between the tendon and containment wall at the anchorages.
The vertical tendon loads are defined using initial strains similar to the hoop tendons. The strains are adjusted via an iterative approach to account for the building stiffness. During tendon de-tensioning, adjacent tendons that are not de-tensioned automatically capture the additional forces caused by load re-distribution. The re-distribution of load also occurs during the de-tensioning of hoop tendons.
MPR Associates, Inc.
FIM PR 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 10 0102-0135-04 )_ * /*,*- Revision: 0 Tendon material and structural properties are defined below. Figure 3-2 illustrates the vertical and hoop tendons in the model.
The dome tendons are modeled in a similar manner as the vertical and hoop tendons, but since there is no detensioning required, the dome tendons are removed in the final model with prestress applied to the dome using equivalent forces. The dome tendons are modeled with an independent truss element mesh with coincident nodes aligned with the dome brick elements. In the process of constructing the model, these independent nodes are constrained in all directions and the tendon preload is applied using initial strains as described above. Reaction forces are calculated at all of the common nodes, and these forces are explicitly applied to the dome elements. The dome tendon truss elements are then removed. The dome tendon ring girder forces are distributed to the concrete elements via stiff beams. Modeling the dome tendons explicitly is not necessary since these tendons will not be detensioned. Dome tendon forces are adjusted to account for loss of tendon tension due to aging phenomenon (e.g. concrete creep) in a manner analogous to the process for the hoop and vertical tendons (Reference 7).
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FIM P]R 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 11 0102-0135-04 Zt Revision: 0 Figure 3-2 Hoop and Vertical Tendons for the 1800 Model 3.1.4 Liner The liner is included in the model to account for the structural interaction between it and the concrete containment. The liner plate is modeled as a single layer of four-node shell elements on the inside face of the containment building. The liner is modeled as %-inch thick on the inside surface of the cylindrical portion and dome and 1/4-inch thick on the bottom surface of containment (Reference 2, page 34). The liner plate thickness is increased to 1.125 inches around the equipment hatch.
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FIM PR 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 12 0102-0135-04 Revision: 0 3.2 Boundary Conditions Displacement boundary conditions are defined to prevent rigid body motion of the containment building and to simulate the reflected portion of the building modeled with the symmetry plane.
The vertical support of the building is modeled as an elastic foundation.
Symmetry boundary conditions are applied to constrain all nodes at the centerline of the model to have zero displacement in the normal (global z) direction. For the tendon nodes that have been rotated into a cylindrical coordinate system the symmetry constraint is applied to the local hoop or y direction.
A single point at the center of the foundation is constrained in the lateral "x" direction to prevent rigid body motion. This does not prevent rocking type motion that would occur in the building and the reaction force at this node is negligible.
Vertical support of the building is achieved using an elastic foundation. The elastic foundation stiffness is defined using a layer of surface effect elements placed under the basemat. The foundation stiffness defined in the model is 395 lbs per cubic inch (680 kips per cubic foot)
(Reference 1, Figure 5-20).
4.0 DESIGN INPUT The design input used to develop the finite element model is provided below.
4.1 Geometry The key dimensions used to model the CR3 containment are listed in Tables 4-1 and 4-2.
Table 4-1 Key Containment Concrete Dimensions Dimension Value Reference Containment Concrete ID 130 ft 0.75 in Reference 10 Containment Wall Thickness (excluding buttresses) 3 ft 6 in Reference 10 Basemat Thickness 12 ft 6 in Reference 11 Basemat OD 147 ft 0.75 in Reference 10 Dome Radius of Curvature (Cyl. To Dome 20 ft 6.375 in Reference 10 Transition)
Dome Radius of Curvature (Dome Middle) 110 ft 0.375 in Reference 10 Dome Thickness 3 ft Reference 10 MPR QA Form: QA-3.1-3, Rev. 0
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320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 13 0102-0135-04 d Revision: 0 Dimension Value Reference Ring Girder Vertical Thickness 16 ft 4 in Reference 10 Ring Girder OD 141 ft 8.75 in Reference 10 Height (Top of Basemat to Springline) 157 ft Reference 10 Buttress Wall Thickness 5 ft 10 in Reference 10 Buttress Height (Top of Basemat to Bottom of Ring 158 ft 2 in Reference 10 Girder)
Steam Generator Opening Height 27 ft Reference 12 Steam Generator Opening Width 25 ft Reference 12 Top of Basemat to Bottom of Opening 90 ft References 11 and 12 Top of Basemat to Equipment Hatch Centerline 39 ft Reference 10 1
Equipment Hatch Opening IR 11 ft 4.5 in Reference 10 Equipment Hatch Centerline Vert. Distance to 3.5 ft Thick Cyl. WallThik yl Wll25 ft 10 in Reference 10 Transition Radius of Curvature from Cyl. To 20 ft 0.375 in Reference 10 Basemat Slab Thickness 2 ft Reference 10 Note 1: The equipment hatch is modeled as a square opening with an equivalent area of the circular opening prescribed in the table.
Table 4-2 Miscellaneous Component Dimensions Dimension Value Reference 1
Hoop Conduit Placement Radius 67 ft 8.375 in Reference 2, Page 14 Vertical Conduit Placement Radius 67 ft 3.375 in Reference 2, Page 14 Tendon total area (163 wires) 9.723 in2 Reference 2, Page 6 Nominal Liner Thickness, Excluding Base 0.375 in Reference 10 Liner Thickness Near Equipment Hatch 1.125 in Estimated from Reference 10 Base Liner Thickness 0.25 in Reference 10 Number of Vertical Tendons 144 Reference 2, Page 14 Number of Tendon Hoops 94 Reference 2, Page 14 MPR QA Form: QA-3.1-3, Rev. 0
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UM PR 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 14 0102-0135-04 _ , Revision: 0 Dimension Value Reference Number of Tendons per Hoop 3 Reference 2, Page 14 Total Number of Hoop Tendons 282 Calculated from Reference 2, Page 15 Number of Prestressed Dome Tendons 123 Reference 2, Page 14 Note 1: The hoop conduit placement radius is listed as 67 ft 8.625 on Prescon DWG P10-A.
The difference in placement radius between the DBD (Reference 2) and the Prescon drawing is less than 1% of the total wall thickness and is less than 5% of the conduit diameter. The difference in results for the global model is judged to be insignificant.
4.2 MaterialProperties The linear elastic material properties used in the finite element model are elastic modulus, density and Poisson's ratio. There is a unique elastic modulus applied to concrete that has existed for the entire life of the plant and for concrete that is used to replace the delamination and the SGR opening. Concrete properties are listed below.
Elastic modulus Existing Concrete 4.03 x 106 psi Reference 3, page 4 Replacement Concrete 5.12 x 106 psi Reference 3, page 4 Poisson's Ratio All Concrete 0.2 Reference 2, page 3 Density All Concrete 150 lb/ft3 Reference 2, page 3 Thermal Expansion Coefficient All Concrete 4.25 x 10-6 in/in/°F Reference 6, Table 2.2.38 The liner is made of ASTM A283 Grade C carbon steel with a minimum yield strength of 30.0 ksi (Reference 2, page 34). The tendon wire in all post-tensioning conduit is ASTM A421-65 steel with a yield strength of 240 ksi (Reference 2, page 5). The typical density, stiffness, and Poisson's ratio of steel are used for these materials, taken from Reference 4, Table 38. The MPR QA Form: QA-3.1-3, Rev. 0
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- M PR 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 15 0102-0135-04 Oil Revision: 0 coefficient of thermal expansion is taken from Reference 5, Table TE-1 and is only applied to the liner.
Elastic modulus 29 x 106 psi Reference 4, Table 38 Poisson's ratio 0.27 Reference 4, Table 38 Density 0.283 lb/in 3 Reference 4, Table 38 Thermal Expansion Coefficient 6.83 x 10-6 in/in/°F Reference 5, Table TE-1 (Avg. from 70'F to 281OF)
Minimum Yield Strength Liner 30 ksi Reference 2 page 34 Tendon Wire 240 ksi Reference 2, page 5 The yield strength of the liner is incorporated directly into the liner material properties in the model so that if it becomes overstressed, the liner will yield and relieve itself of load. The yield point of the material is modeled as 1.2 times the minimum yield strength (Reference 2, page 26).
5.0 MODEL BENCHMARKING RESULTS To benchmark the finite element model, stress results for the intact containment model considering 95% of the deadweight plus tendon preload (1474 kips for the vertical tendons and 1398 kips for the hoop tendons) are compared to hand calculations. The linearized hoop and vertical membrane stresses were obtained at the SGR opening mid-height elevation. Figures 5-1 and 5-2 show color contour plots of hoop and vertical stress respectively. The linearized stresses are tabulated below.
Hoop membrane stress: 1630 psi Vertical membrane stress: 977 psi A hand calculation of hoop and vertical stress is provided below for comparison. The hand calculated hoop stress is 1560 psi; the hand calculated vertical stress is 957 psi. The hand calculated hoop stress is within 5% of the finite element result; the hand calculated vertical stress is within 3% of the finite element result.
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M P R 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 16 0102-0135-04 _ 'c7 ,-*- Revision: 0 h 157,ft Containment height ri :65.ft+ 3in Containment concrete inside radius (Reference 8) 8 ri= 65.031 ft ro =ri + 42. in Containment concrete outside radius (Reference 8) ro 68.531 ft tb 28.in Buttress thickness (Reference 8)
Lb:- 12.ft + 4.125.in Average buttress width (Reference 8)
Nb:= 6 Number of buttresses (Reference 8)
Nv:= 144 Number of vertical tendons (Reference 2, page 14)
Nh := 94 Number of hoop tendons (282 total/ 3 per loop = 94 loops.
Reference 2. page 14)
Tv := 1474000.lbf Vertical tendon tension (Reference 7, page 5, unadjusted tendon)
Th := 1398000.lbf Hoop tendon tension (Reference 7, page 5, unadjusted tendon) bf p:= 150. Concrete density (Reference 2, page 3) ft3 tdome := 3.ft Dome thickness (Reference 2, page 1) hrg := 16,ft+4-in Ring girder height (Table 4-1, above) 27 hsgro 90-t+2f Mid-height of the SGR opening (Table 4-1, above) hsgro =103.5ft 3.
tiner:= in Liner thickness (Reference 10)
Ec 4.03-106.psi Concrete elastic modulus (Reference 3, page 4)
E = 29-106 .psi Liner elastic modulus (Reference 4, Table 38)
The approximate concrete area of a vertical section through the full height of the containment wall is calculated below:
2 ah:= h.(rO - ri) ah = 549.5ft MPR QA Form: QA-3.1-3, Rev. 0
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IM P 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 17 0102-0135-04 - ( Revision: 0 The approximate steel liner area of a vertical section through the full height of the containment wall is calculated below:
alh := h'tliner alh = 4.906ft2 The average hoop stress in the containment wall is calculated below considering the effect of the liner:
Nh.Th ah-Ec ah ah.Ec+ alh.EI The area of a horizontal section through the containment is calculated below. The area contribution of the buttresses is included. The area contribution of the vertical conduits is not deducted because the conduits are not represented in the finite element model.
2 aa:= r.(ro2-ri2) + Nb-Lb'tb aa= 1641ft The average vertical stress due to tendon tension is calculated below considering the effect of the liner:
The approximate steel liner area of a vertical section through the full height of the containment wall is calculated below:
alv 2.-ritliner alv = 12.769ft2 Nv.Tv aa-Ec 85 a *a Ea = 0psi aa aa. c + alv EI The deadweight of the concrete above the mid-height of the SGR opening is estimated below.
The buttress is approximated by a rectangular section, the dome is approximated by a flat disc and the ring girder is approximated as a cylindrical section. (Note that the deadweight is a small contribution to the vertical stress. Consequently, these approximations are considered acceptable.)
Wshell := pc.(h hsgro).aa Wshell = 13.17 x 106 lbf W hr= . [(ro I tb 2- ri2] Wrg= 6.102x 10 6 lbf Wdome := Pc'tdome. ,-ri2 Wdome = 5.979 x 106 lbf The average vertical stress due to deadweight of the concrete above the mid-height of the SGR opening is estimated below Wshell + Wrg + Wdome
= aaw dw = 107 psi a.
The total vertical stress due to tendon tension and deadweight at the SGR opening mid-height is calculated below:
aa_tot := "a + adw aa-tot = 957 psi MPR QA Form: QA-3.1-3, Rev. 0
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FIM PR 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 18 0102-0135-04 Revision: 0 Stress results linearized through the wall thickness at the mid-height of the SGR opening MMSYS PLOT 11.0sPI ND. I NAL SC[TUIN STEP-1 SUB -1 TTW~-1 SY (AVG)
RSYS-5 EM -1. 194 SM -4767 SMC-3661 I -2500
- -2000
-1500
-1000 A500 500 1000 1500 2000 Figure 5-1 Hoop Stress MPR QA Form: QA-3.1-3, Rev. 0
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FIM PR 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 19 0102-0135-04 Revision: 0 Stress results linearized through the wall thickness at the mid-height of the SGR opening P2MYS II.OSPI PLOTNO. 2 NIIAL SCLTIaM STEP-1 SUB-1 TInE-I SZ (AW)
TOP RSYS-5 U-M -1.194 SMN-3186 SMW-1398
-2500
-2000
-1000 EJ 1500 500 500 1500 2000 Figure 5-2 Vertical Stress 6.0 ASSUMPTIONS
- 1. The tendons are assumed to be symmetric about the 150 degree azimuth through the center of the SGR opening. This assumption is reasonable because of the staggered design of the hoop tendons, the load application they apply to the building is nearly uniform radial compression which would make the loading symmetric about the centerline of each buttress. For the intact building cases, the response predicted in the finite element model is the same between each buttress set. Since the hatch and SGR opening are centered between buttresses 3 and 4, symmetry can be applied via the centerline of the model in this area.
MPR Associates, Inc.
FAMPR 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 20 0102-0135-04 0 _',, Revision: 0 7.0 COMPUTER CODES This analysis was performed with the ANSYS general purpose finite element program, Version 11.0 SP 1. The analysis was performed on a Sun v40z server running the Suse Linux 9.0 operating system. The ANSYS installation verification is documented in QA- 110-1.
8.0 REFERENCES
- 1. Final Safety Analysis Report, Progress Energy Florida, Crystal River 3, Revision 31.3.
- 2. Progress Energy, "Design Basis Document for the Containment," Revision 7.
- 3. MPR Calculation 0102-0135-02, Rev. 0, "Concrete Modulus of Elasticity and Minimum Compressive Strength."
- 4. Roarke, Raymond J. and Warren C. Young, Formulasfor Stress and Strain, 5 th Ed.,
McGraw-Hill, 1975.
- 5. ASME Boiler and Pressure Vessel Code,Section II, Part D - Properties, 1992 Edition.
- 6. National Cooperative Highway Research Program, Guidefor Mechanistic-EmpiricalDesign of New andRehabilitatedPavement Structures, March 2004.
- 7. MPR Calculation 0102-0135-03, Rev. 0, "Tendon Tension Calculation."
- 8. FPC DWG SC-421-031, Rev. 4, "Reactor Building, Exterior Wall - Concrete Outline."
- 9. CR3-LI-537934-31-SE-007, Revision B, Attachment C, January 6, 2010, DRAFT Follow-Up Input to Technical Issues Discussed at 3rP Party Review Meeting at MPR on December 8 &
9, 2009.
- 10. Drawing No. SC-421-031, "Reactor Building Exterior Wall Concrete Outline," Revision 4.
- 11. Drawing No. SC-421-003, "Reactor Building Foundation Mat Concrete Outline," Revision 4.
- 12. Drawing No. CR3 DWG 421-347, "Reactor Building Temporary Access Opening for SGR Vertical & Horizontal Tendon Positions," Revision 0.
- 13. Computer output file 0102-0135-04-1 and 0102-0135-04-2.
MPR Associates, Street Inc.
FIM PR. 320 King MR Alexandria, VA 22314 CALCULATION TITLE PAGE Client:
Progress Energy Page 1 of 15 Project: Task No.
CR3 Containment Delamination 0102-0906-0135
Title:
Calculation No.
Conduit Local Stress Analysis 0102-0135-05 Preparer / Date Checker / Date Reviewer & Approver / Date Rev. No.
1-20-2010 1-20-2010 1-20-2010 Edward Bird Erin Tindall Robert Keating 0 QUALITY ASSURANCE DOCUMENT This document has been prepared, checked, and reviewed/approved in accordance with the Quality Assurance requirements of 10CFR50 Appendix B, as specified in the MPR Quality Assurance Manual.
MPR-QA Form QA-3.1-1, Rev. 1
MPR-Associates, Inc.
WMPR 320 King Street Alexandria, VA 22314 RECORD OF REVISIONS Calculation No. Prepared By Checked By Page: 2 0102-0135-05 24. LY Revision Affected Pages Description 0 All Initial Issue I I Note: The revision number found on each individualpage of the calculation carriesthe revision level of the calculation in effect at the time that page was last revised.
I MPR QA Form QA-3.1-2, Rev. 0
MVPR Associates, Inc.
UAMPR 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 3 0102-0135-05 4--e-* x ,%: 1 ,l ,C' Ica1, Revision: (
Table of Contents 1.0 Purpose.................................................................................. 4 1.1 Background .................................................................................. 4 1.2 Purpose....................................................................................... 4 2.0 Summary of Results and Conclusions.............................................. 5 3.0 Methodology ............................................................................ 5 4.0 Design Inputs ........................................................................... 7 4.1 Geometry .................................................................................... 7 4.2 Material Properties.......................................................................... 7 4.3 Boundary Conditions........................................................................ 8 5.0 Assumptions........................................................................... 10 6.0 Computer Codes ...................................................................... 11 7.0 Results.................................................................................. 11 8.0 References............................................................................. 14 MPR QA Form: QA-3.1-3, Rev. 0
MPR Associates, Inc.
FIM PR 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 4 0102-0135-05 Revision: 0 1.0 PURPOSE 1.1 Background A project is underway at Progress Energy's Crystal River Unit 3 (CR3) site to replace the steam generators, As part of that project, 10 vertical and 17 horizontal tendons were detensioned and an opening was cut into the concrete containment above the equipment hatch. As this opening was being cut, cracking in the concrete wall was identified around the full periphery of the opening in the cylindrical plane of the wall. The cracking is located at the radius of the circumferential tensioning tendons, and is indicative of a delaminated condition. Progress Energy plans to remove the delaminated concrete and replace it.
1.2 Purpose The concrete repair and restoration of the steam generator opening may require detensioning additional tendons. The purpose of this calculation is to determine if the absence of either the vertical or horizontal compressive load results in a more limiting stress condition around the tendon conduits than the case with both vertical and horizontal compression applied. If a more limiting stress condition is predicted for the case with either vertical load only or hoop load only, this calculation will provide a basis for the detensioning sequence.
A local axisymmetric finite element analysis of the hoop tendon conduits was performed to evaluate the principal stress magnitude and orientation around the hoop conduits for three combinations of vertical and hoop compression. The three cases are:
- Both vertical and hoop tendons tensioned
- Vertical tendons only tensioned
" Horizontal tendons only tensioned.
MPR Associates, Inc.
- M P R 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 5 0102-0135-05 ,L, , *g,. ," G Revision: 0 2.0
SUMMARY
OF RESULTS AND CONCLUSIONS Figures 7-1, 7-2 and 7-3 show color contour plots of maximum principal stress (S1) in the concrete for the three post-tension loading conditions evaluated. The maximum principal stress for the three cases is listed below:
- Horizontal + Vertical Tendon Load: 1,041 psi
- Vertical Tendon Load Only: 919 psi
- Horizontal Tendon Load Only: 237 psi The results show that with either vertical only or horizontal only tendon loads, the maximum principal stress is less than the case with both loads applied simultaneously. Therefore, this calculation does not provide a basis for the detensioning sequence.
3.0 METHODOLOGY An axisymmetric finite element model of the local geometry around the hoop tendons was developed with the Ansys finite element program. The axis of symmetry for the model is the vertical centerline of the containment. The model represents an un-delaminated section of the containment wall. Linear-elastic, static structural analyses were performed for three loading conditions.
Figure 3-1 shows the axisymmetric model developed for the local stress analysis. The model represents a vertical slice through the containment wall between vertical tendons and includes the liner and two conduits.
MPR Associates, Inc.
AIMPR 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 6 0102-0135-05 ... ,¢ . ,/ Revision: 0
/3/8 inch Thick Liner 5.25 inch OD Conduit 42 inch Thick Concrete Containment Wall Figure 3-1 Hoop Conduit Axisymmetric Finite Element Model MPR QA Form: QA-3.1-3, Rev. 0
MPR Associates, Inc.
- MPR 320 King Street Alexandria, VA 22314 Calculation No.
0102-0135-05 4.0 DESIGN INPUTS 4.1 Geometry The basic geometric parameters used for the model are listed in Table 4-1.
Table 4-1. Local Model Dimensions Dimension Value Reference Containment Liner Inside Radius 65 ft Reference la and Reference 2, pg 35 Containment Wall Thickness 42 in Reference la Hoop Conduit OD 5.25 in Reference 2, Page 4 Hoop Conduit ID 5.125 in Assumption 1 Hoop Conduit Spacing 13 in Reference 2, Page 14 Hoop Conduit Placement Radius 67 ft 8.625 in Reference lb Liner Thickness, Excluding Base 0.375 in Reference 1a The model is 39 inches high, which represents the nominal distance between tendon pairs.
4.2 MaterialProperties The linear elastic material properties used in the conduit local stress analysis are elastic modulus, density and Poisson's ratio. The values used for concrete are listed below:
Elastic Modulus: 4.03x 106 psi Reference 3, page 4 (uncracked)
Density: 150 lb/ft3 Reference 2, page 3 Poisson's ratio: 0.2 Reference 2, page 3 The liner is made of ASTM A283 Grade C carbon steel with a yield strength of 30.0 ksi (Reference 2 page 34). Typical values for the elastic modulus, density and Poisson's ratio are taken from Reference 4, Table 38.
Elastic Modulus: 29 x 106 psi 3
Density: 0.283 lb/in Poisson's ratio: 0.27 MPR QA Form: QA-3.1-3, Rev. 0
MPR Associates, Inc.
FWM PR 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 8 0102-0135-05 .' Ica, Revision: 0 4.3 Boundary Conditions The boundary conditions applied to the model include displacement restraints and applied forces that represent post-tension loads only. As shown in Figure 4-1, along the lower edge of the model, displacements of the concrete and liner normal to the edge are restrained. At the upper edge of the model, the concrete and liner displacements normal to the edge are coupled to one another such that all nodes have the same vertical displacement. This condition forces the upper edge of the model to remain horizontal and represents a symmetry condition across the edge. A pressure corresponding to the vertical compression load was applied at the upper edge.
Three hoop tendons, each spanning 120 degrees, form a complete 360 degree circle around the containment. In the axisymmetric model, at each tendon conduit, the tendon load is represented by the total (360 degree) radial load. For the case with vertical load only, both hoop tendons in the model are detensioned. The hoop tendon load and vertical pressure are calculated below.
Note that because the liner is explicitly included in the model with steel material properties, the prestress load is shared between the steel liner and concrete wall.
MPR Associates, Inc.
- MPR 320 King Street Alexandria, VA 22314 Calculation No.
0102-0135-05 3.
ri :=65.ft+-.in Containment concrete inside radius (Reference la) 8 ri= 65.031 ft ro = ri +42. in Containment concrete outside radius (Reference 1 a) ro= 68.531 ft tb 28.in Buttress thickness (Reference 1a)
Lb 12.ft Buttress length (Reference 1a)
Nb:= 6 Number of buttresses (Reference 1a)
Nv:= 144 Number of vertical tendons (Reference 2, page 14) dc := 5.25.in Tendon conduit outside diameter (Reference 2, page 4)
TV:= 1474000.1bf Vertical tendon tension (Reference 5, page 5, unadjusted tendon at the end of the SGR project, 33 years)
Th := 1398000.1bf Hoop tendon tension (Reference 5, page 5, unadjusted tendon at the end of the SGR project, 33 years)
The vertical tendon load is reacted by the cross section area of the containment wall and buttresses less the area of the vertical tendon conduits.
aa := 7.(r 2 ri 2 )+ Nb.Lb.tb- Nv.4.dc 2 aa= 1615ft2 Nv-Tv Ga := aa aa = 913 psi Each hoop tendon has a tension of Th and exerts a unit radial force of Th / r on the containment. The Ansys code requires that the radial load be applied on a 360 degree basis. The total radial load is then (Th / r) x 2 pi r = 2 pi Th.
Fhoop :ý 2 .7r.Th Fhoop = 8.784 x 106 lbf MPR QA Form: QA-3.1-3, Rev. 0
MPR Associates, Inc.
- M P R 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 10 0102-0135-05 . ,:;,
- j/ Revision: 0 Along the upper edge, displacements normal to the A uniform pressure of 913 edge are coupled to one psi is applied to the upper another resulting in this line edge representing the remaining horizontal vertical tendon load A force equal to 2 -r Th is applied to each conduit Along the lower edge,----
- displacements normal to the edge are restrained Figure 4-1 Local Conduit Model Boundary Conditions 5.0 ASSUMPTIONS
- 1. The DBD provides both a minimum wall thickness of 1/16 inch for the hoop conduits and an inside diameter of 5 inch which leads to a thickness of 1/8 inch (Reference 2, page 4).
The conduit wall thickness used in the analysis is 1/16 inch.
MPR Associates, Inc.
tMPR 320 King Street Alexandria, VA 22314
): 11 0102-0135-05 Revision: 0 4ý'
6.0 COMPUTER CODES This analysis was performed with the ANSYS general purpose finite element program, Version 11.0 SP 1. The analysis was performed on a Sun v4Oz server running the Suse Linux 9.0 operating system. The ANSYS installation verification is documented in QA- 110-1.
7.0 RESULTS Figures 7-1, 7-2 and 7-3 show color contour plots of maximum principal stress (S 1) in the concrete for the three post-tension loading conditions evaluated. Positive (+) stress values are tensile. The maximum principal stress for the three cases is listed below:
Horizontal + Vertical Tendon Load: 1,041 psi Vertical Tendon Load Only: 919 psi Horizontal Tendon Load Only: 237 psi The results show that with either vertical only or horizontal only tendon loads, the maximum principal stress is less than the case with both loads applied simultaneously.
MPR Associates, Inc.
- M PR 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 12 0102-0135-05 Revision: 0 Maximum Principal Stress Type: Maximum Principal Stress - TopiBottom Unit: psi lime: 1 1/19/2010 11:16 AM 1041.3 Max 856.27 671.22 486.16 301.1 116.04
-69.015
-254.07
-439.13
-624.19 Min Figure 7-1. Concrete Maximum Principal Tensile Stress - Vertical + Horizontal MPR QA Form: QA-3.1-3. Rev. 0
MPR Associates, Inc.
- M PR 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 13 0102-0135-05 /d , Revision: 0 Manzn Primil Stress Type: Maximum Prinxpal Stress - TopiBottom Urit: ps lime: 1 1/19/2010 11:17 AM 919.03 Max 788.94 658684 528.75 398.65 268.56 138.46 8.3636
-121.73
-251.83 Mi Figure 7-2. Concrete Maximum Principal Tensile Stress - Vertical Only MPR QA Form: QA-3.1-3, Rev. 0
MPR Associates, Inc.
IMP M 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 14 0102-0135-05 x,* Revision: 0 Maxklm Pdnc" stress Type: Maximum Prrc" Stress - TopiBottom Urdt: psi lime: 1 1/19/2010 11:16 AM 237.23 Max 207.9 178.57 149.25 119.92 90.592 61.265 31.937 2.6096
-26.718 Mi Figure 7-3. Concrete Maximum Principal Tensile Stress - Horizontal only
8.0 REFERENCES
- 1. Drawings:
- a. FPC DWG SC-421-031, Rev. 4, "Reactor Building, Exterior Wall - Concrete Outline.
- b. Prescon Drawing P 10-A, Rev. 1, "Horizontal Tendon Detail Between 120' - 180*."
- 2. Progress Energy, "Design Basis Document for the Containment," Revision 7.
- 3. MPR Calculation 0 102-0135-02, Rev. 0, "Concrete Modulus of Elasticity and Specified Compressive Strength."
MPR Associates, Inc.
P R 320 King Street
- M Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 15 0102-0135-05 1O. Revision: 0
- 4. Roarke, Raymond J. and Warren C. Young, "Formulas for Stress and Strain," 5th Ed.,
McGraw-Hill, 1975.
- 5. MPR Calculation 0102-0135-03, Rev. 0, "Tendon Tension Calculation."
- 6. Computer output files 0102-0135-05-1, 0102-0135-05-2 and 0102-0135-05-3.
MPR Associates, Inc.
- M PR 320 King Street Alexandria, VA 22314 CALCULATION TITLE PAGE Client:
Progress Energy Page 1 of 23 plus Attachment Project: Task No.
CR3 Containment Calculations 0102-0906-0135
Title:
Calculation No.
Seismic, Wind, and Tornado Evaluation and Delamination Depth Evaluation for Detensioned State 0102-0135-08 Preparer / Date Checker / Date Reviewer & Approver / Date Rev. No.
0 J. L. Hibbard M. Oghbaei E. Bird 1-23-2010 1-23-2010 1-23-2010 QUALITY ASSURANCE DOCUMENT This document has been prepared, checked, and reviewed/approved in accordance with the Quality Assurance requirements of 10CFR50 Appendix B, as specified in the MPR Quality Assurance Manual.
MPR-QA Form QA-3.1-1, Rev. 1
MPR Associates, Inc.
PR 320 King Street
- M Alexandria, VA 22314 RECORD OF REVISIONS Calculation No. Prepared By Checked Bv Page: 2 0102-0135-08 1 .k...-Vom. - S4. H.
Revision L1Affected Pages Description 0 All Initial Issue Note: The revision number found on each individualpage of the calculationcarriesthe revision level of the calculation in effect at the time that page was last revised.
I MPR QA Form QA-3.1-2, Rev. 0
MPR Associates, Inc.
MIL M PR320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 2 0102-0135-08 . , Revision: (
Table of Contents 1.0 Purpose.................................................................................. 4 2.0 Summary ................................................................................ 4 3.0 Background............................................................................. 9 4.0 Assumptions............................................................................ 9 4.1 Unverified Assumptions.................................................................... 9 4.2 Other Assumptions.......................................................................... 9 5.0 Approach............................................................................... 10 6.0 Calculation............................................................................. 12 6.1 Design Inputs............................................................................... 12 6.2 Deadweight Stress ......................................................................... 15 6.3 Seismic and Deadweight Stress........................................................... 17 6.4 Tornado and Deadweight Stress.......................................................... 21 7.0 References............................................................................. 23 Attachment................................................................................... 24 MPR QA Form: OA-3.1-3, Rev. 0
Calculation No.:
Prepared By: I .A-.- 0102-0135-08 MPR Associates, Inc. Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: /1 . .Page No.: 4 1.0 PURPOSE This calculation evaluates the containment building for three design basis loads due to natural phenomena that might occur while the containment building is detensioned for repair. The load cases are: 1) deadweight and Safe Shutdown Earthquake (SSE), 2) deadweight and wind, and 3) deadweight and tornado. The containment is evaluated for membrane plus bending stress at two sections through the containment: 1) the bottom of the containment at Elevation 93 ft, and 2) at the bottom of the SGR (Steam Generator Replacement) opening at Elevation 183 ft. For the evaluation at the bottom of the SGR opening, the containment is assumed to have no concrete between Buttresses 3 and 4 between Elevations 183 feet and 210 feet. These are the bottom and top elevations respectively, of the SGR opening.
2.0
SUMMARY
Membrane plus bending stress in the containment shell at two sections for two load cases are provided in the table below. The deadweight plus wind load case is bounded by the results for the deadweight plus tornado load case.
"Load" "Section" "M + Bit "Stress" "Result" "Case... t. "Stress" "Limit" fill lift lfti t il, I'll fips
=( "Bottom of Cont." * (139 600 ("No Failure"1 "Deadweight& SSE" Q'Bottom of SGR Opening" ) . 19) 6 ."No Failure")
"Deadweight& Tornado" "Bottom of Cont.i" -103) 600 ("No Failure" k("Bot'tom of SGR Opnn" -95)"oFiu"J Notes:
- 1. Column with heading M + B is the membrane plus bending stress. Plus is tensile and minus is compressive.
- 2. SSE is Safe Shutdown Earthquake.
- 3. SGR is Steam Generator Replacement
- 4. The stress limit prevents a tensile failure per Reference 4. It is conservative to compare a compressive stress to a tensile stress limit.
- 5. The section at the bottom of containment is at Elev. Esect = 93 ft . The section at the bottom of the SGR opening is at Elev. Esect = 183ft 2
Calculation No.:
Prepared By: SA_..- ..-
- ., a, -,- 0102-0135-08 MPR Associates, Inc. Revision No.: 0 320 Kin g Stre et C ed yP a No :
Alexandria VA 22314 Checked By: 6(.P4'&" Page No.: 5 Conclusions from these evaluations are:
" The containment building is not expected to fail catastrophically while the building is detensioned for repairs due to the following load combinations: 1) deadweight and SSE, 2) deadweight and wind, and 3) deadweight and tornado.
- Delamination depths greater than nominal will not result in a catastrophic failure of the containment building for the load cases listed above. The basis for this conclusion is the analysis result at the section at the bottom of the SGR opening. This section is assumed to have no concrete between Buttresses 3 and 4 for the height of the SGR opening. This configuration bounds a case in which the delamination depth is greater than nominal. Delamination depths greater than nominal above and below the SGR opening are considered acceptable based on judgement The basis is that the SGR opening with a width of 25 feet and extending the full thickness of the containment wall will bound any thinned sections above or below the opening.
rAMPR MPR Associates, Inc.
,AP Prepared By: I A.- . O~o=o~.
Calculation No.:
0102-0135-08 Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: Vl. Page No.: 6
'~~r '~
I" Section at Bottom of SGR Opening (Elev. 183 ft) duw 't Bottom of Containment (Elev. 93 ft)
Figure 1. Containment Building
Calculation No.:
Prepared By: S A,- - 0102-0135-08 MPR Associates, Inc. Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: ,-g. Page No.: 7 11 N
V.
Xf I.
/
Section at Bottom of Containment (Approximate)
'7
/
\I
/
/
7 Section at Bottom of SGR Opening (Approximate)
Figure 2. Sections
Calculation No.:
Prepared By: SA'.- - 0102-0135-08 MPR Associates, Inc. Revision No.: 0 320 King Street Checked BY:
Alexandria VA 22314 Checked By: Af. Page No.: 8 I- 1~~ SConfiguration for this I Calculation ka
- MlA* I
> 1 1w >=a
>_ _ _ _ _ _ _ _ 4
>K Ow n_ _ 1
>=W-4
.4 ACCS~OPU0d AZ SGR Opening Figure 3. Configuration of Containment for Section at SGR Opening
Calculation No.:
FA MRPrepared By: S*~- 0102-0135-08 MPR Associates, Inc. Revision No.: 0 320 King Street ChekedBy:Pag No:.
Alexandria VA 22314 CekdB: /1 aeN.
3.0 BACKGROUND
A project is underway at Progress Energy's Crystal River Unit 3 site to replace the steam generators.
As part of that project, an opening has been cut into the concrete containment above the equipment hatch. As this opening was being cut, cracking in the concrete containment wall was identified. The crack is around the full periphery of the opening and is in the plane of the wall. The cracking is located at the radius of the circumferential tensioning tendons, and is indicative of a delaminated condition.
4.0 ASSUMPTIONS 4.1 Unverified Assumptions None.
4.2 Other Assumptions
- 1. It is assumed that the thickness of the ring girder is tg = £83 ft . This is a reasonable estimate of the concrete in the ring girder considered as an equivalent rectangular section (see Ref. 2. 1). The thickness is used to calculate the mass of the ring girder. A comparison was made of the mass of the ring girder and dome determined in this calculation to the mass calculated by the finite element model used in this project. There was good agreement between the mass calculation in this calculation with that from the finite element model.
Calculation No.:
Prepared By: S.'-. , 0102-0135-08 MPR Associates, Inc. Revision No.: 0 320 King Street Checked By:
Alexandria VA 22314 Page No.: 10 5.0 APPROACH This calculation is an approximate evaluation to assess the potential for a catastrophic failure of the containment when the containment is detensioned for repair. Approximate analysis techniques are used. The analysis considers effects that are considered to be important to the assessment. This is a bounding evaluation rather than a comprehensive evaluation. Effects that are considered to have less than a 20% effect on the final answer are not considered. This is justified based on the large margin to failure in the results.
This calculation considers three load cases: 1) deadweight and SSE, 2) deadweight and wind, and 3) deadweight and tornado. A best estimate is used for the deadweight load. The SSE, wind, and tornado loads are the design basis loads as defined by the FSAR (Reference 3). No load factors are used in the analysis. This is appropriate for a catastrophic failure assessment.
The static coefficient method for seismic analysis specified in Reference 7, Section 6.3 is used.
The static coefficient method applies a factor of 1.5 to peak response acceleration to account for potential closely spaced modes. The peak seismic response is from the ground acceleration spectrum from Reference 1. The seismic assessment considers horizontal acceleration and a simultaneous vertical acceleration in the up direction. The vertical up acceleration increases the tensile stress due to the horizontal acceleration, which is a conservative approach.
The analysis calculates the mass of the containment for deadweight and for seismic using the intact configuration of the containment. The effects of removing concrete for the delamination and removing the concrete for the SGR opening are not significant within the framework of this approximate analysis. The mass is based on cylinders and does not include the mass of the buttresses (the buttress mass is less than 1%of the total mass).
The acceptance criterion is that the containment wall membrane plus bending stress be less than the tensile failure stress criterion established in Reference 4 (o en = 600psi ). The containment wall membrane plus bending stress is a near uniform tensile stress across the containment wall thickness at the extreme tension fiber. Use of a tensile stress criterion is appropriate.
The analysis calculates membrane plus bending stress at two sections through the containment as shown on Figures 1 and 2.
The first section is at the bottom of the containment at elevation 93 feet. The nominal containment wall thickness is 3.5 feet. At elevation 93 feet, the containment wall is thicker than the nominal thickness. For conservatism and simplicity, the nominal containment wall thickness is used for the evaluation at this section.
Calculation No.:
AIM P R MPR Associates, Inc.
Prepared By: S.A.-. -,, -, 0102-0135-08 Revision No.: 0 320 King Street Cece H ,y:
Alexandria VA 22314 Checked By: it."".9, Page No.: 11
- The second section is at the bottom of the SGR opening at Elevation ESGR.b = 183 ft . The SGR opening dimensions are hSGR = 27 ft high by WSGR = 25 ft wide (Reference 2.2). The analysis assumes a configuration for the containment in which there is no concrete for an angular extent of a = 60.deg for the height of the SGR opening. Figure 3 shows the configuration used for the analysis. For reference, the angular extent of the SGR opening is qSGR = 20.9.deg.
Some vertical and hoop tendons will be detensioned for the repair. Detensioning vertical tendons reduces the containment resistance to an overturning moment such as might occur in a seismic, wind, or tornado event. The vertical tendons strengthen the containment in the longitudinal direction and keep the containment concrete in longitudinal compression. Without all the vertical tendons, the capacity of the containment to resist an overturning moment is reduced. This calculation uses the conservative approach that all vertical tendons are detensioned.
The containment building is reinforced with a significant amount of vertical rebar at the 93 foot elevation. This rebar connects the containment shell to the basemat. This calculation takes no credit for this rebar.
The center of gravity of the dome and ring girder are offset from the neutral axis for the analysis at the section at the SGR opening. The moment created by the offset increases the compressive stress due to deadweight at the SGR opening. No credit is taken for this effect in the analysis.
Calculation No.:
Prepared By: \ **.* b' 1' 0102-0135-08 MPR Associates, Inc. Revision No.: 0 320 King Street C:P Alexandria VA 22314 Checked By: Al. Page No.: 12 6.0 CALCULATION 6.1 Design Inputs Containment Cylinder tq =_42.-in Containment wall thickness; Ref. 2.1 Buttress additional thickness beyond thickness of tb a 2.ft+ 4.in tb = 28.in cylinder, Ref. 2.1 tamer 0.3 75.in Liner thickness; Ref. 2.1 Inside diameter of containment concrete wall; idcy' a 2.(65.ft + t&ier) idcy, = 130.06 ft Ref. 2.1 Odcy- idcyd + 2"tcy, odcy= 137.06 ft Outside diameter of containment; Ref. 2.1 Ecylb := 93ft Elevation of bottom of containment cylinder; Ref. 2.1 Ecyl.t := 250.ft Elevation of top of containment cylinder; Ref. 2.1 aa- 60.deg Angle between Buttresses 3 and 4; Ref. 2.1 and discussion in Section 5.0 SGR Opening ESGR.b 183.ft Elevation of bottom of SGR opening; Ref. 2.2 ESGR.t 210. ft Elevation of top of SGR opening; Ref. 2.2 WSGR - 25.ft Width of SGR opening; Ref. 2.2 WSGR OSGR --- aSGR = 20.9 .deg Angular extent of SRG opening hSGR - ESGRt - ESGR.b hSGR = 27 ft Height of SGR opening
Calculation No.:
Prepared By: ' *'--- 0102-0135-08 MPR Associates, Inc. Revision No.: 0 320 King Street Checked By:
Alexandria VA 22314 Page No.: 13 Ring Girder 2 Outside diameter of ring girder, Ref. 2.1 odrg:= odcy + .tb odrg = 141.73 ft Estimate of ring girder thickness for mass calculation; trg= tCy + tb + 3.ft trg = 106.in Ref. 2.1 and Assumption 4.2.1 idrg: odg trg idrg = 124.06 ft Inside diameter of ring girder Lrg:= 175-ft Height of ring girder; Ref. 2.1 Dome Dome thickness; Ref. 2.1 tdome:= 3-ft Ldome := (35.ft + 4.5.in) - Lrg Ldome = 1788ft Height of dome; Ref. 2.1 Concrete lb pc:= 144.-- Concrete density; Ref. 6 ftt 0-ten =-600.posi Concrete tensile strength; Ref. 4 Seismic SSE static equivalent acceleration; the peak in the ah := 1.5-2-0.135.g ah = 0.405.g OBE ground response spectra is from Pages 97 and 98 of Attach ment E to Ref. 1 at 2% damping; damping for the reactor building shell is from Ref. 3, Section 5.2.4.1.2, Page 36; SSE is a factor of 2 times OBE based on Ref. 3, Section 5.2.1.2.9; the 1.5 factor accounts for potential closely spaced modes per Ref. 7, Section 6.3 2 SSE vertical ground acceleration; Ref. 3, Section av:= - ah av = 0.27.g 5.2.1.2.9 3
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Calculation No.:
0102-0135-08 MPR Associates, Inc. Revision No.: 0 320 King Street Checked By: POageN:
Alexandria VA 22314 C 0' Page No.: 14 Wind Vwind := 179.mph Wind speed fbrdesign basis accident; Ref. 3, Section 5.2.1.2.5 Tornado Tornado wind speed for design basis accident; Ref.
Vtomado:= 300.mph 3, Section 5.2.1.2.6 Tornado internal to external pressure drop for design Pxt4 := 3.psi basis accident; Ref. 3, Section 5.2.1.2.6 Air lb Pair,:= 071 . Density of air; the air temperature to obtain density is 10OF for simplicity, Ref. 9, Table A-3
/lr=1.285.l0-5_Ib rft. sec Viscosity of air, the air temperature to obtain viscosity is 10OF for simplicity, Ref. 9, Table A-3 Misc.
Drag coefficient for a cylinder at Reynolds Number Cd.E6:= 0.38 greater than 10A; Ref. 8, Figure 5-78 Drag coefficient for a cylinder at Reynolds Number of Cd.E5:= 1.2 10d; Ref. 8, Figure 5-78
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o,,o~.
Calculation No.:
0102-0135-08 Revision No.: 0 320 King Street Cc B Alexandria VA 22314 Checked By: At'. Page No.: 15 6.2 Deadweight Stress Stress will be calculated at two sections at elevations:
EcG.b Esec
=[EGR.b Es (183 ) ft The length of the containment cylinder above each section for the analysis is:
Lcyl := Ec.t - Esect L~ =67) c 157 ft Esect = 93) ft The mass of dome, ring girder, and cylinder are:
7r 2 tdome "-4 . dcyl 4
The mass of the dome is calculated with a simplified massl,i:= Pc. L,*' .(od'2 - dg2) id:= approach in which the dome is a circular plate.
Lcy,
. r (d -1 idc,2)
T Esect = (93 183) ft 5.7 x106' 5.74x, 106' mass 9.29x 106t 9.29x 106 [lb id =
.,3.32 x 107, ,1.42x 10x7J The total mass is:
r4.82 x 10(93 masstot := Z massl, i masstot = Ib Esect = f K2.92 x 10 7
Calculation No.:
A M PR MPR Associates, Inc.
Prepared By: S , 0102-0135-08 Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: /i. Page No.: 16 The cross section area at the two sections is:
AC=7r.( 0 dC2 _ d,42) 4 Ody + icy, rmean : - rmean = 66.78 ft Ac2 := Ac - atrmean-tcyI Ac = 933 ' ft
('~183) h1.76 x csse The compressive stress is:
O'dw :=
masstot,l.g A 'dw C-228.1')
-*.-165.7 )psi E = Ic 183 ft
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Calculation No.:
0102-0135-08 Revision No.: 0 320 King Street CekdB Alexandria VA 22314 Checked By: A(. Page No.: 17 6.3 Seismic and Deadweight Stress Horizontal The length from the mass cg to the elevation for the section is:
Lcgl, i := Lcyi + Lrg + 2 L+yli + 2 T
8 t = (93 183) ft Ese
=
S183.44 165.75 (93.44'1 7 ft id =
L 78.5 ) . 33.5 ,
4I Dome c.g.
The moment due to horizontal seismic is: 4 Ring Girder c.g.
3 Msi: ah'* l: [(massl, i)i'(Lcglji)JI 4 Cylinder c.g.
Esect = 93ft Ms= (2.11 x 19 *.ft.Ibf 183
- 695 x 1o8)
The moment of inertia for the intact containment is:
6=4
Calculation No.:
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- A- -,.*-6 *.444 0102-0135-08 MPR Associates, Inc. Revision No.: 0 320 King Street CBN Alexandria VA 22314 Checked By: , y. Page No.: 18 The moment of inertia for the C shaped segment of containment about the containment centroid is calculated below. The neutral axis of the C shaped segment is defined as:
basic statics, no reference required T y dA =0 Define a function to calculate the integral.
7r a 22 f(y"8 ): 2. rmean-tc},i.(rMean-sin(OT - Yna) dO fIr 2
where y = rmean'sin(O)- Yna dA = rmean-tyj-~dO The neutral axis is:
Yna:= Yguess + 0 Yna = -12.75 ft I root(f(yguess), Yguess)
Verify the solution:
10 3 f(Yna) = 9.93 x 107 1.n which is approximately zero.
The moment of inertia about the containment centroid is:
Icentroid = y 2 dA Ref. 5, Formula j 100 r aI 2
rmean.tcyi.(rmean.sin(O)f d0 Icentroid = 4.72 x 010. in4
'centrodd: 2.
2 where Y = rmean -Sin ( )
dA = rmean -tcy,- dO
Calculation No.:
AM MPR Associates, Inc.
Prepared By: S.. 0102-0135-08 Revision No.: 0 32 0 Kin g Stre et l . 0 6 ,P a e N . 1 Alexandria VA 22314 Checked By: /1f'. Page No.: 19 The moment of inertia about the neutral axis is:
'C / .centroid
+ A c2Yna Ic = 5.14 x 1010.in4 Ref. 5, Formula p 19 2
where A 02 = 176232.in The distance from the neutral axis to the extreme tension fiber is:
2 1 cc.,,. = 72.1 ft where _ _ Yna =56.ft odcyl odcyi-sin7r - 2 Y = 72.1 ft 21= 2 (2 2 ,)Yn1a The moments of inertia for the two sections are:
=6.8 x 1010 -i4 Isect :=I( t~l/I 'sect = 1 5.14 x 1010 Esect =,183)
The distances to the extreme tension fiber are:
Csect :=
_ rod0 j= 2m cma I 2*.
Csect =
683 " f1 I72. Esect C83 )ft The bending stress is:
Cs~h:=
Ms" Csect
'sect O's.h =
(305.83)
( 14 0 .4 2 )PS Esect C (3 f
Calculation No.:
Prepared By: S A-.- 0102-0135-08 MPR Associates, Inc. Revision No.: 0 320 King Street Checked By: I .
Alexandria VA 22314 . Page No.: 20 Vertical The vertical seismic stress is:
v (61.5s8 sv : dw .44.74 Esect= (,183) 93 ft Deadweight and Seismic Stress The deadweight and seismic stress is:
(139.3 Ohdw.s := 05h + O's.v + OTdw 1833 ft
'~183)
Compare the stress to the concrete tensile strength.
("No Failure" check, I := if(Uodw.si < O'ten, ok, nok) check1 =,"No Fai Ese= ft 183
0 Calculation No.:
AM P R MPR Associates, Inc.
Prepared By: S,,h..* 0102-0135-08 Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: ('. Page No.: 21 6.4 Tornado and Deadweight Stress The drag on the containment building is (Ref. 8,,y-axis of Figure 5-78):
1 F
where Cd drag coefficient Pair air density Ap projected area Vtomado air velocity due to tornado The projected area of the containment including the projection of the buttresses and ring girder is:
Ap= 3.93x 166.in2 (93)ft Ap:= [odr.(LcI,+ Lg + Ldome)] sE.t= 1 8 3 )
.2.09 x 106)
The drag coefficient is a function of the Reynolds Number.
Pair Vtomado "Odrg Re:= Re = 3.45 x 108
/Pair The drag coefficient for a cylinder at Reynolds Number greater than 166 is Cd.E6 = 0.38 . For conservatism, use a drag coefficient of Cd.E5 = 1.2 at a Reynolds Number of about 105. The drag load is:
6.99 x 106 d= 1 Fd:= Cd.E5- -Pair'Ap'Vtomado 2
d=3.72 x 106 )
(931)f Esect = (,183 )
2 The bending moment due to the tornado is:
Mtomado [=Fd~ (L,, + Lrg + Ldme) 6"72x 108 (93)'~f Mtomado = . 1 ft./bf Esect = 18 3 )ft 1.9 x 108)
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Calculation No.:
0102-0135-08 MPR Associates, Inc. Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: It,'. Page No.: 22 The bending stress is:
Mtomado"Csect O'lomado - sect Ortomado = .49 )psi Est= ft 183 Coincident with the tornado wind is a local depressurization. The internal to external pressure drop across the containment wall is P.0 = 3psi . The longitudinal stress in the containment due to the pressure is:
7r 2 4 Esec =(893 )f "t=(2Z14 ext= 32.57 PS
~183}
Deadweight and Tornado Stress The deadweight and tornado stress is:
O'dwt = 103.3 ) ps O'w.t := (tOtomado + 'ext + Oidwr Esect = I 93)
(.-94.6J \.183}
Compare the stress to the concrete tensile strength.
check2 =*"oFiue "NoFailure" check 2 : if(o'dw.yI < atn, ok, nok)
E=183 )
Calculation No.:
Prepared By: .*\ 0102-0135-08 MPR Associates, Inc. Revision No.: 0 320 King Street Checked B AP Alexandria VA 22314 Page No.: 23
7.0 REFERENCES
- 1. Progress Energy Specification SP-5209, "CR-3 Seismic Qualification," Revision 0.
- 2. Progress Energy Drawings:
2.1 No. SC-421-031, "Reactor Building Exterior Wall Concrete Outline," Revision 4.
2.2 No. 421-347, "Reactor Building Temporary Access Opening for SGR Vertical & Horizontal Tendon Positions," Revision 0.
- 4. Letter from WJE (Mr. J. Fraczek) to Progress Energy (Mr. D. Dyksterhouse),
Subject:
CR3 Containment Limiting Tensile Stress, WJE No. 2009.4690, January 11, 2010.
- 5. K. Gieck, "Engineering Formulas," McGraw-Hill Book Company, 3rd Edition, 1979.
Subject:
Concrete Density.
- 7. Institute of Electrical and Electronics Engineers, Inc. (IEEE) Standard 344-1987, "IEEE Recommended Practice for Seismic Qualification of Class IE Equipment for Nuclear Power Generating Stations."
- 8. Perry & Chilton, "Chemical Engineers' Handbook," McGraw-Hill, 5th Edition.
- 9. F. Kreith, "Principles of Heat Transfer," International Textbook Company, 1964.
Calculation No.:
A M PR MPR Associates, Inc.
Prepared By: SA'- - 0102-0135-08 Revision No.: 0 320 King Street C k yg .
Alexandria VA 22314 Checked By: /1. Page No.: 24 ATTACHMENT Email from Mr. J. Holiday (PE) to Mr. K. Gantz (MPR), 12-30-2009, 10:35 AM,
Subject:
Concrete Density.
Message Page I of 1 Hibbard, Jim From: Holliday, John [John.Holliday@pgnmail.com]
Sent: Wednesday, December 30, 2009 10:35 AM To: Gantz, Kevin; Knott, Ronald Cc: Hibbard, Jim; Dyksterhouse, Don
Subject:
RE: Concrete Density
- Kevin, The reference will be EC 75218, RB Delamination Repair Phase 2- Detensioning The unit weight is 144 lbs cu ft.
From: Gantz, Kevin [5]
Sent: Wednesday, December 30, 2009 10:01 AM To: Knott, Ronald; Holliday, John Cc: Hibbard, Jim
Subject:
RE: Concrete Density John and Ron, I don't think there was ever a follow-up sent to this email. Could you provide us with the reference. I did not see it in SOO-0047.
Kevin
---Original
-- Message -----
From: Knott, Ronald [6]
Sent: Wednesday, December 16, 2009 10:15 AM To: Holliday, John Cc: Gantz, Kevin
Subject:
FW: Concrete Density John, Can you direct Kevin to the density reference. I don't know where the original data came from for density. I was only quoting what I heard in the meeting. I assumed it was in the S00-0047 attachments.
From: Gantz, Kevin [7]
Sent: Tuesday, December 15, 2009 6:22 PM To: Knott, Ronald Cc: Dyksterhouse, Don; Holliday, John; Bird, Edward; Butler, Patrick
Subject:
Concrete Density Ron, During our previous meeting you received some original information on the concrete density. I remember you saying later that the concrete density was 144 or 145 pcf. Do you have a reference or an actual number so that I can make sure I have the correct modulus calculated?
Thanks, Kevin 12/30/2009