Email - From: Dyksterhouse, Don [don.dyksterhouse@pgnmail ...

_ _e

Sengupta, Abhijit

From:Sent:To:Subject:Attachments:

Dyksterhouse, Don [[email protected]]Wednesday, January 27, 2010 7:57 AMLake, LouisDesign Basis Calculations0102-0135-02 concrete strength and elastic modulus rO final.pdf; 0102-0135-03_rO0final.pdf;0102-0135-04 FE Model Description signed.pdf; 0102-0135-05 Conduit Local Stress Analysissigned (2).pdf; 0102-0135-07 concrete moment capacity load rO (2).pdf; 0102-0135-08seismic wind tornado rO.pdf

Lou,Sorry about that.

From: Dyksterhouse, DonSent: Saturday, January 23, 2010 3:34 PMTo: Thomas, George'Cc: Dyksterhouse, Don; Miller, GarrySubject: Design Basis Calculations

George,Please find attached the following calculations: For your information, the attached MPR signed calculations

have the number listed in the left column. The calculation numbers in the red are the Progress Energy Calculationnumbers. I expect the Tendon Detensioning Calculation to be approved early next week and will trans nit thecalculation to you after approval. -,

0101-0135-jlh-20101-0135-010101-0135-020101-0135-030101-0135-040101-0135-050101-0135-060101-0135-070102-0135-08Detensioned State

S09-0054 Radial Pressure at Hoop Tendons (provided on 1/8/10)S09-0055 Reinforcement Ratio and Effective Modulus of Elasticity (provided 1/8/10)S09-0056 Concrete Modulus of Elasticity and Minimum Compressive StrengthS10-0001 Tendon Tension CalculationS10-0002 Finite Element Model DescriptionS10-0003 Conduit Local Stress AnalysisS10-0004 Tendon Detensioning Calculation (not approved at this time)S10-0005 Bending/Tension Interaction Diagrams for Selected SectionsS10-0006 Seismic Wind, and Tornado Evaluation and Delamination Depth Evaluation for

From: Thomas, George [mailto: [email protected]]Sent: Friday, January 22, 2010 1:27 PMTo: Dyksterhouse, DonSubject: Design Basis Calculations

Hello Don,

Do you have any more Design Basis calculations ready for NRC review. If you do, please email them to me, orlet me know when they would be available.Thanks.

George ThomasCR-3 Containment Delamination SIT

1

PI-28

[email protected]

2

MPR Associates, Inc.

0MPR 320 King StreetAlexandria, VA 22314

CALCULATION TITLE PAGE

Client:

Progress Energy Page 1 of 30

Project: Task No.CR3 Containment Calculations

0102-0906-0135

Title: Calculation No.Interaction Diagrams for Selected Sections 0102-0135-07

Preparer / Date Checker / Date Reviewer & Approver / Date Rev. No.

J. L. Hibbard Chris Bagley D. Werder1-19-2010 1-19-2010 1-19-2010

QUALITY ASSURANCE DOCUMENTThis document has been prepared, checked, and reviewed/approved in accordance with the Quality Assurance

requirements of 1OCFR50 Appendix B, as specified in the MPR Quality Assurance Manual.

MPR-QA Form QA-3.1-1, Rev. 1


*M P R 320 King StreetAlexandria, VA 22314

RECORD OF REVISIONS

Calculation No. Prepared By Checked By Page: 2

0102-0135-07 . .. . C1&s')

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.

MPR QA Form QA-3.1-2, Rev. 0

MPR Associates, Inc.0M P R 320 King Street

Alexandria, VA 22314


0102-0135-07 .1 . Revision: 0

Table of Contents

1.0 Purpose ................................... ..................................................................... 4

2.0 Sum m ary ..................................................................................................... 4

3.0 Background ...................................................................................................... 5

4.0 Approach ..................................................................................................... 5

5.0 Assum ptions ...................................................................................................... 7

5.1 Unverified Assumptions ......................................................................................... 7

5.2 Other Assumptions ................................................................................................. 7

6.0 Calculation ....................................................................................................... 8

6 .1 D ata ............................................................................................................................... 8

6.2 Rebar Distance to Compression Face and Rebar Area ......................................... 13

6.3 Interaction Diagram Functions ............................................................................ 14

6.4 Interaction Diagrams for Sections ................................. 18

7.0 References ..................................................................................................... 30

MPR QA Form: QA-3.1-3, Rev. 0

Calculation No.:7AW M P R Prepared By: S .'. 0102-0135-07MPR Associates, Inc. Revision No.: 0320 King Street Ch ckd/yAlexandria VA 22314 Checked By: Page No.: 4

1.0 PURPOSE

This calculation provides interaction diagrams for selected sections of the Crystal River Unit 3containment. These results will be used in subsequent calculations to determine the acceptability ofcontainment locations that have high stress. The sections were selected based on preliminary finiteelement model results.

2.0 SUMMARY

Interaction diagrams are calculated for selected sections of the Crystal River Unit 3 containment. Thefigure below shows the interaction diagram for all the sections. Individual interaction diagrams andnumerical results are in Section 6.4.

-Section 1-Section 2

m 0• o Section 3

- -- Section 4

* * @*Section 5

... - Section 6• 0 0 oSection 7

1000

6

.4

Notes:1. These results are applicable

to uniaxial bending andtension/compression.

2. See Section 6.4, Section 4 fora limitation on use of theSection 4 interaction diagram.

3. Section 6 applies betweenButtresses 1&2, 2&3, 4&5,and 5&6.

S 4. Section 7 applies betweenButtresses 3&4.

Failure

laI)jI . - _________________ -

- 1000 0 1000 2000

Moment (fi*kip/ft)

("Section" "Location" "Tension" "Rebar"

1

2

"Buttress"

"Buttress"

Td = 3 "Ring Girder"

4 "Ring Girder"

5 "Containment"

6 "Containment"

"Surface" "Orientation"

"OD" ".vertical"

"OD" "vertical"

" O D .... "h o o p "

"OD" "vertical"

"OD" "vertical"

"OD" ".vertical"

"OD" "vertical"

"Elevation"

I1(ft)Il

"93 to 103"

"230 to 250")

"250 to 256""250 to 256"

"230 to 250"

"93 to 103"

"93 to 103"7 "Under Eq. Hatch"

Calculation No.:7iM Prepared By: S . • 0102-0135-07MPR Associates, Inc. Revision No.: 0320 King Street Checked By:Alexandria VA 22314 CekdB: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 equipmenthatch. As this opening was being cut, cracking in the concrete containment wall was identified. Thecrack is around the full periphery of the opening and is in the plane of the wall. The cracking is located atthe radius of the circumferential tensioning tendons, and is indicative of a delaminated condition.

4.0 APPROACH

This calculation develops interaction diagrams for selected sections of the Crystal River Unit 3containment. The approach used is that provided in Reference 4, which is a explicit approach consistentwith ACI criteria and methodology (Reference 1.2, Sections 10.2 and 10.3). A comparison ofrequirements from ACI 318-63 to those in a later edition of the code is provided on the following page.

This analysis evaluates the capacity of the containment concrete plus reinforcement without the effect ofprestressing forces. Prestress loads, deadweight load, and other loads can be evaluated with thecalculated interaction diagrams.

The approach in Reference 4 is based on application of axial load and bending to a column. Thisapproach is adapted to sections of interest in the Crystal River containment. The sections of interest canbe simplified to rectangular beams similar to a column. The loading on the beam is uniaxialtension/compression and bending. For example, the ring girder in the hoop direction is treated as astraight column with bending and tension/compression loads. Ultimate strength tensile loads andmoments are calculated per unit width of the beam. The width of the beam, b, is arbitrary and is selectedfor convenience in determining the reinforcement cross section area.

Reference 4, Equation 11-8b gives a limit on axial compression to account for accidental moments, suchas might occur in columns supporting a building. Since the results of this calculation are applied to thecontainment and to moments calculated with ANSYS there are no accidental moments. Accordingly,this limit is not included.

spColumn is commercial software for calculating interaction diagrams. spColumn was used to calculatean interaction diagram for Section 1, the buttress. The results of the calculation with spColumn and theresults below in Section 6.4 are nearly identical. This was done to confirm the calculation method.spColumn results are not included in this calculation because spColumn is not QA software.

Calculation No.:Prepared By: • . 0102-0135-07

MPR Associates, Inc. Revision No.: 0320 King Street Cc B: / 7/Alexandria VA 22314 Checked By: Page No.: 6

As stated above, the approach used in this calculation is consistent with a later edition of the ACI Code.Reference 4 does not specify the ACI 318 Code year used, but it is later than 2002 (Reference 4, p.492). For the purpose of a comparison, the 2005 edition of ACI 318 was used below.A comparison was made of the requirements in ACI 318-63 to ACI 318-2005. Results of thecomparison are as follows:

The following sections of ACI 318-63 and ACI 318-2005 are equivalent:

ACI 318-631503(c)1503(d)1503(f)1503(g)

1602(e)1604(a)

ACI 318-200510.2.310.2.410.2.610.2.7 (except that there is a lower limit of 0.65 for concrete with compressive

strengths greater than 8,000 psi, which is not a factor for this analysis)10.3.210.3.1

The reinforcing steel strain limits of ACI 318-2005 in 10.3.4 and 10.3.5 are not addressed in ACI318-63.

The capacity reduction factors in ACI 318-2005, 9.3.2 are equivalent to or more conservative than inACI 318-63, 1504.

Based on the above, it was concluded that the approach in this calculation is consistent with and suppliesresults at least as conservative as that in ACI 318-63.

Calculation No.:RIM P R Prepared By: • *_.-,• 0102-0135-07MPR Associates, Inc. Revision No.: 0320 King Street Chce y 7/•Alexandria VA 22314 Checked By: Page No.: 7

5.0 ASSUMPTIONS

5.1 Unverified Assumptions

None.

5.2 Other Assumptions

1. It is assumed that the rebar cover depth for vertical rebar at the OD face of the ring girder(Ref. 2.3) is dovor = 2.25.in . This is a reasonable assumption because the same rebar cover

depth is used at other locations as shown on Reference 2.2.

IMPRMPR Associates, Inc.320 King StreetAlexandria VA 22314

Calculation No.:Prepared By: ,L,, • 0102-0135-07

Cheke ByRevision No.: 0Checked By: EPage No.: 8

6.0 CALCULATION

6.1 Data

This calculation determines the moment capacity of the concrete at the locations specified in the followingtable. Data for the calculation is input into arrays that contain entries, each of which corresponds to theSection number in the table below.

"Section" "Location" "Tension" "Rebar" "Elevation"

"M Surface" "Orientation" "Y(f)"

1 "Buttress" "OD" "vertical" "93 to 103"

2 "Buttress" "OD" ".vertical" "230 to 250"

Td := 3 "Ring Girder" "OD" "hoop" "250 to 256"

4 "Ring Girder" "OD" "vertical" "250 to 256"

5 "Containment" "OD" "vertical" "230 to 250"

6 "Containment" "OD" . " vertical" "93 to 103"

7 "Under Eq. Hatch" "OD" "vertical" "93 to 103"

tcont =- 42 in

tb =-tont + (2. ft + 4. in)

trg - 6nt + (2. ft + 4. in)

R., 65.ft + 0.375.in + 42.in

Ro.rg= Re.,+ (2.ft + 4.in)

fy := 40ksi

fc':= 5000.psi

tb =70.in

trg 70.in

Ro., = 68.53 ft

Ro.rg n

Containment wall thickness; Ref. 2.1

Buttress thickness; Ref. 2.1

Ring girderthickness at approximately the 250 ftelevation; Ref. 2.1

Outside radius of containment; Ref. 2.1

Outside radius of ring girder; Ref. 2.1

Rebar minimum yield strength; Ref. 3 Section 5.2.2

Concrete specified compressive strength; Ref. 7, p. 2

Calculation No.:PN M Prepared By: * ,'_,. , 0102-0135-07MPR Associates, Inc. Revision No.: 0320 King Street Cheicked/ByAlexandria VA 22314 Checked By: Page No.: 9

Standard rebar diameters from Reference 5, Table 12.3.1 are (rebar diameter is in inches):

Odrebar '=34

5

6

7

8

9

10

11

14

18

0.3750.5

0.625

0.75

0.875

1

1.128

1.27

1.41

1.693

2.257

Define a function to return rebar diameter.

dr(n) := vlookup(n,fOdrebar,2)1.in

For example,

dr(18) = 2.257.in

tc b=

b :=

70

70

70

70

42

42

K42,

in bOc =

12.ft

12.ft

(255.ft + 10.5 .in) - (250.f

30.deg.Ro.rg

(11 + 15 ÷ 60).deg.Ro.,

48.in

144. in

"Buttress"

"Buttress"

"Ring Girder"

"Ring Girder"

"Containment"

"Containment"

"Under Eq. Hatch"

")

"Buttress"

"Buttress"

"Ring Girder"

"Ring Girder"

"Containment"

"Containment"

"Under Eq. Hatch"

Concrete thickness-Ref. 2.1-Ref. 2.1-Ref. 2.1; conservative thickness-Ref. 2.1; conservative thickness-Ref. 2.1-Ref. 2.1; conservative thickness for Elev. = 93 ft-Ref. 2.1

Width of section considered (see discussion inSection 4); this is an arbitrary dimension, butreferences are provided to show the dimension-Ref. 2.1-Ref. 2.1-Ref. 2.1-Ref. 2.3, 00 to 3300-Ref. 2.2, Section 2-2, 11 *-15' section-Ref. 2.2, this width was chosen to give an integernumber of rebar for each layer

-Ref. 2.2, this width was chosen to give an integernumber of rebar for each layer

144

144

70.5

445.26

161.47

48

144

-in Ioc =

Calculation No.:Prepared By: A- *._. . 0102-0135-07

MPR Associates, Inc. Revision No.: 0320 King Street Checked By:Alexandria VA 22314 Checked By Page No.: 10

There are several layers of rebar through the depth of the sections. The data for the layers is input with 1by x arrays below, with x being the number of layers. For example, the first entry in the array below is a1 x 3 array with the three entries corresponding to the three layers of rebar in the buttress (one layer of#11 at the OD face and two layers of #18 near the ID face).

(dr(11) dr(18) dr(18))

(dr(11) dr(18))

(dr(9) dr(9) dr(9) dr(9))

odr:= (dr(9) dr(9) dr(11) dr(11) dr(18))

Re bar diameter-Ref. 2.2, Section 1-1 and Ref. 2.5, Section 1-1-Ref. 2.2, Sections 2-2 and 3-3-Ref. 2.3, Section 1-1-Ref. 2.3, Section 1-1-Ref. 2.2, Section 3-3-Ref. 2.2, Section 3-3 and Ref. 2.5, Section 1-1-Ref. 2.2, Section 3-3, Ref. 2.5, Section 1-1, and Ref.2.4

(dr(18) dr(18) )

(dr(11) dr(18) dr(18))

(dr(11) dr(18) dr(18))

(1.41 2.257 2.257)

(1.41 2.257)

(1.128 1.128 1.128 1.128)

"Buttress"

"Buttress"

"Ring Girder"

"Ring Girder"

"Containment"

"Containment"

odr= (1.128 1.128 1.41 1.41 2.257) Iin bOc =

(2.257 2.257)

(1.41 2.257 2.257)

(1.41 2.257 2.257) ý"Under Eq. Hatch"j

nr :=I

(12 8 16)

(12 13)

(5 2 2 8)

(59 59 33 33 59)

(11 17)

(4 3 6)

(16 9 18)

bOc =

"Buttress"

"Buttress"

"Ring Girder"

"Ring Girder"

"Containment"

"Containment"

"Under Eq. Hatch"

Number of rebar in section width, b-Ref. 2.2, Section 1-1-Ref. 2.2, Sections 2-2 and 3-3, and Ref. 2.6-Ref. 2.3, Section 1-1 (there are four rebar inthe angle section of which two are creditedand assumed to align with the above rebarfor ease of calculation)

-Ref. 2.3, 00 to 3300 with spacing at mid-bayused over buttress for Layer 1

-Ref. 2.2, Section 2-2-Ref. 2.2, Section 1-1-Ref. 2.2, Section 1-1, Ref. 2.5, Section 1-1,and Ref. 2.4

dcover =- 2.25.in

a:= atan(2-52

Cover depth for OD face rebar; Ref. 2.2, Sections 1-1and 3-3

Angle with respect to vertical of ID face rebar at aboutElevation 93 feet; Ref. 2.5, Section 1-1a= 15.15.deg

MR ,Calculation No.:& IM P R Prepared By: A .-- --- 0102-0135-07MPR Associates, Inc. Revision No.: 0320 King Street cke B:7/,Alexandria VA 22314 Checked By: Page No.: 11

Radial distance of rebar layer from OD face-Ref. 2.2, Section 1-1 and Ref. 2.5, Section 1-1-Ref. 2.2, Sections 1-1, 2-2, and 3-3-Ref. 2.3, Section 1-1, scaling for Layers 2 and 3, and Assumption 5.2.1-Ref. 2.3, Section 1-1, scaling for Layers 2, 3, and 4, and Assumption 5.2.1-Ref. 2.2, Section 3-3-Ref. 2.2, Section 3-3 and Ref. 2.5 Section 1-1-Ref. 2.2, Section 3-3, Ref. 2.5, Section 1-1, and Ref. 2.4

rr:=

dcover + 1.5-dr(11) 70.375.in - (7.5 + 2.5).in n0.37.5. 5in

_ cos(a) cos(a)

[dcover + 1.5.dr(11) 70.in - (7.in + dr(11) + 0.5.dr(18))]

[dcover + 0.5.dr(9) 12.5.in 22.in (70- 8.25).in- 0.5.dr(18) - 0.5.dr(9)]

[dcover+1.5.dr(9) 35in 47.in 51in (70-8.25).in]

[dcover + dr(11) + 0.5.dr(18) 42.in - (7.in + dr(11) + 0.5.dr(18))]

S(7.5 + 2.5).in 7.5.-in1

L4.25in 42.375.in- cos(a) 42.375.in cos(a)

[425-i1 42.375*in- (7.5+ 2.5).in 7 7.5.in

4I cos(a) cos(a)

I(4.365 60.015 62.605)

(4.365 60.462 )

rr =

(2.814 12.5 22 60.057)

(3.942 35 47 51 61.75)

(4.788 32.462 )

(4.25 32.015 34.605)

(4.25 32.015 34.605)

-in bOc =

"Buttress"

"Buttress"

"Ring Girder"

"Ring Girder"

"Containment"

"Containment"

K"Under Eq. Hatch")

Calculation No.:• Prepared By: Ž *_. . L sQ. .-.,9 . 0102-0135-07MPR Associates, Inc. Revision No.: 0320 King StreetAlexandria VA 22314 Checked By: Page No.: 12

Misc.

ec:= 0.003 Concrete compressive strain limit; Ref. 4, Page 496

Steel modulus of elasticity; Ref. 1.1, Section 1100ES.:= 29.106.psi

0.65 if -0.002 < £s <_0.003

2500.65+ - 0.002).- if -0.005 < e, -0.002

0.9 if es _-0.005

S 0.8..... .... .... ...

" 0.7

0.6'

Capacity reduction factor; Ref. 4, Table 11-1

The sign convention in this calculation ispositive is compressive and negative istensile, consistent with the sign convention inReference 4.

0.8 -0.6 -0.4 -0.2 0 0.2 0.4

Steel Strain (%)

Calculation No.:Prepared By: • .- . 0102-0135-07

MPR Associates, Inc. Revision No.: 0320 King Street CheckAedByAlexandria VA 22314 Checked By Page No.: 13

6.2 Rebar Distance to Compression Face and Rebar Area

The radial distance of the rebar layer center to the extreme compression fiber is:

d :=( - rr

(65.635 9.985 7395)

(65.635 9.538)

(67186 57.5 48 9.943)

(66.058 35 23 19 8.25)

(37212 9.538)

(37.75 9.985 7395)

(37.75 9.985 7395)

-in Rebar center to extremecompression fiber

The area of rebar in each layer is:

A,. := [nri'[ '(Odr.)2]

(18.74 32.01 64.01)

(18.74 5201 )

(5 2 2 799)

(58.96 58.96 51.53 51.53

(44.01 68.01 )

(6.25 12 24.01)

(24.98 36.01 72.02)

?36. 05) .in2 Re bar area

1M P R Calculation No.:1,vA Prepared By: A- -'.. , 0102-0135-07

MPR Associates, Inc. Revision No.: 0320 King Street CheckedAlexandria VA 22314 By.kedBy:Page No.: 14

6.3 Interaction Diagram Functions

The interaction diagram is calculated with the approach in Reference 4. In Reference 4 and in thiscalculation, compressive strain, compressive load, and compressive stress are positive.

The concrete compressive strain limit is:

= 0.003

The reinforcement strain at yield strength is:

= yS5 : .

e/= 0.1379.%

The distance from the compression face to the neutral axis is a function of arbitrary parameter Z.

d1C

(Z ) E -Y(iRef. 4, Equation 11-9

The strain in the reinforcement is:

c(Z,' - (di) lj.Es(Z,i,j) :"Co

c (Z, 1

The stress in the reinforcement is:

fs(Z,i,j):= *-Es-es(Z,ij)

-fy if f, < -fyIi y if f, > fy

Ref. 4, Equation 11-10


The factor P1 used to calculate the size of the stress block is:

,31 := 0.85 if fc <-4000.psi

fc,- 4000.psi0.85 - 0.05. if 4000.psi < f. <- 8000.psi

1 000 .psi0.65 if f0. > 8000.psi

Ref. 4, Equation 4-14a, b, and c

01 = 0.8

Calculation No.:P re p a red B y : * .L .. bo.-i,- 0 10 2-0 135-07

MPR Associates, Inc. Revision No.: 0320 King Street Checked ByAlexandria VA 22314 Cek ByPage No.: 15

The depth of the concrete stress block is:

a(Z,i) /,31-C(Z,f)Ref. 4, Paragraph below Equation 11-11, andFigure 11-14(c)

The compressive force in the concrete per unit width is:

Cc(ZJ):= 0.85-fc-a(Zi) Ref. 4, Equation 11-12

The force in the reinforcement per unit width is:1

Fs(Z,i,j): -. fs(Z,i,j).(As)' if a(Z,i)bi - 0j

(fs(Z, i,j ) - O.85"fc')'(A.ijj

(d')l,j

otherwise

Ref. 4, Equations 11-13a and 11-13b

The axial load capacity per unit width of the beam including the capacity reduction factor is providedbelow. Reference 4, Eq. 11-8b gives a limit on the axial compression to account for accidentalmoments. Since the results of this calculation are applied to the containment and to moments calculatedwith ANSYS there are no accidental moments. Accordingly, this limit is not included.

cols( di)

P,,(Z,I): q5(eS(Z~i,1)) .rC,(Z,i) + FZ~~ Ref. 4, Equation 11-14

The moment capacity per unit width of the beam including the capacity reduction factor is:

Mn(Z,I)= tAeZi1)rc(Z' i){ - a(Zi)~ +

cols( d1) IZ [Fs(Zl i~I) L [2 - (di)1 J'j

j =

Ref. 4, Equation11-15a

The pure axial tension capacity including the capacity reduction factor is:

Pnt(Z, i) -(E, (Ii,1 1)) cols(d,)j=l


Calculation No.:Prepared By: S 0102-0135-07

MPR Associates, Inc. Revision No.: 0320 King Street ChceAlexandria VA 22314 Checked By: Page No.: 16

The unbalanced moment for pure axial tension is calculated based on the discussion in Reference4, the paragraphs above and below Equation 11-16. The concrete section is cracked completelythrough. Equation 11-15a from Reference 4 is modified to account for the steel only and to use asteel stress of minus yield strength (-ty) in the tension layer.

1 col•d,) [ Ft0. 1]gnt(l) := b-I . ] cofY'(ASi)l,j'J .'c - (di),,

j =I

Define a function to calculate the value Z for the case of pure bending, i.e., the tension is 0.

Zbend(•) Zg - -10

Iroot(Pn (zg, i), zg)

Define a function to calculate the values of Z for the case of pure bending and pure tension. The value ofZ for the case of pure tension is arbitrary since the interaction curve between these two cases will bedetermined from linear interpolation.

ZS(I := Zb <- Zbend(i)

Zb Zb -2)

Calculation No.:Prepared By: • *_.. , 0102-0135-07

MPR Associates, Inc. Revision No.: 0320 King Street Checked By: Page No.: 17Alexandria VA 22314 'PgNo:1

The interaction diagram in the tension region is approximately linear as shown in Reference 4, Figure11-18. The interaction diagram will be calculated with a linear interpolation in the tension region of theinteraction diagram. This is a conervative approach.

Define functions to calculate the axial load capacity and the moment capacity.

Pn 2 (Z,i):= Ze -- ZS(I)

Pn(Z,') if Z>Ze

linterpfz:2j I' ,1 i) , 7] otherwise

Mn2 (Z,I):= Ze--zS(i)

Mn(Z,i) if Z>Ze

linterp rz 2, ,"rZ otherwiseE' Il gn(zel '

Calculation No.:7dMPRPrepared By: * A.- . 0102-0135-07

MPR Associates, Inc. Revision No.: 0320 King Street e&b 7,Alexandria VA 22314 Checked By: Page No.: 18

6.4 Interaction Diagrams for Sections

Section i:= 1L !i Section"

"Location" "Tension"

I'l "Surface"

"Buttress" "OD"

"Rebar"

"Orientation"

"vertical"

"Elevation" >"(ft)"

"93 to 103"

9/I/1(}

1500

1000

500

0

-500

7 IIt[t)

-•1000- 500 0 500 1000 1500 2000 2500 3000

Moment (ft*kip/ft)

Calculation No.:AW M PR Prepared By: S . 0102-0135-07MPR Associates, Inc. Revision No.: 0320 King Street Checked/ByAlexandria VA 22314 Checked By: Page No.: 19

"Z " "P.nt"I'll. "kip/if'

"M.n"

"'kip"

I'l

"iFs"

"kip/ft"

I'll

"C. c"

"kip/ft"I'l

"in"

Tchk () =

(00 1926.6 1683 95.35

1.190.71,

-31.23'

-0.5 1580.9 2076.5 95.35

Y190.71)

-62.46

-1 13377 2208.7 95.35

Y.190. 71 )

(-62.46

-3 11173 2521.5 95.35

.190.71)

-62.46

-20.69 0 387.1 -106.69

-85.59

(-62.46

-22.69 -344.3 -553.8 -106.69

-

2677.9 52.51

21774 42.69

1834.5 35.97

1125.5 22.07

If 111

0

40

40,

40

40S40)40

40

40

40

"e.s"

0

0.25

0.27)L-0.07'0.24

0.26 )-0.14)

0.23

0.25 )-0.410.19

0.22 J

"in"

65.64

53.37

44.96

27.59

6.24

5.74

1" -40 -28254.7 4.99 -40 -0.18

-16.05 ) -0.06,

40 (-3.13234.3 4.59 -40 -0.6 2

-25.06 : -0-09)

Notes:1.

2.

3.

Positive P, are compressive forces.

Positive M, are compressive at the ID face.

Entries that are arrays provide results for each of the layers of reinforcement. Thefirst entry in the array is for the layer nearest the OD, the second for the secondlayer, and so on.

IMPRMPR Associates, Inc.320 King StreetAlexandria VA 22314

Calculation No.:Prepared By: S _. k 0102-0135-07

Revision No.: 0Checked By: (E /4J•7/A/ Page No.: 20

Section i:= 2 L(O=L 2'

"Buttress"

"Tension" "Rebar" "Elevation"

"Surface" "Orientation" ".(ft)"

"OD" "vertical" "230 to 250"

I~nnJ~

1506

1006

506

6

- 1000- 500 0 500 1000 1500 2000 2500

Moment (ft*kip/fit)

Tchk () =

liZIt

0

-0.5

-1

-3

-22.52

-24.52

",P.n"

"kip/ftl"

1841.4

1495.7

1252.5

1008.7

0

-212.2

"Mn"

1482.3

1875.8

2008.1

2265.8

390.6

-208.4

"F.s"

"kipftl"

15 4.9 5 )

5-31.23)

154.95)

-62.46

154.95)

-62.46)

(154.95)C-62. 46-173.37)

-62.46

-173.37)

IC.cc

"kip/ft"

2677.9

2177.4

1834.5

1125.5

235.8

218.2

"a"

"in"

52.51

42.69

35.97

22.07

4.62

4.28

"ksi"

0°)4C20D40

C -2040

40

(40

ý-40

(-40

"~e.s"I

C.-0.07(0.25)C-0. 14(0.24)C-0. 41

0.26

-3.11)

C-0.2)-3.38

-0.24)

"in"

65.64

53.37

44.96

27.59

5.78

5.35

Calculation No.:Olk M P R Prepared By: -ý A- - 0102-0135-07

MPR Associates, Inc. Revision No.: 0320 King Street ed eAlexandria VA 22314 Checked By: Page No.: 21

Section i:= 3

2000

1500

1000

L~500

""Section"

3

"Location" "Tension" "Rebar"

.... ."Surface" "Orientation"

"Ring Girder" "OD" "hoop"

"Elevation"

"2(ft)"

"1250 to 256")

2500

Moment (ft*kip/ft)

Calculation No.:

Prepared By: S *_. . 0102-0135-07MPR Associates, Inc. Revision No.: 0320 King Street ,J6.4)"'Alexandria VA 22314 Checked By: Page No.: 22

1711 IIP.n"

I'll Xiplftlf

I'll "it

"Est,

"kiplft"

III,

"C.¢"~

"kip/ft"

III

"a"

Tchk (i) =

(0

4.270 1820.7 1262.4 I I

7.01

.48.65),

-17.01

-1.56-0.5 1470.6 1682.5 | 3

3.59

K 48.65

(-34.02

-7.38-1 1224.5 1822.7 -12

-1.27

K 48.65

(-34.02'

-13.61-3 943.7 2077.8 -1 I

-13.61

K 48.65 )(-34.02'

-13.619.37 0 309.8 _13 I-13.61

,-54.43)

(-34.02

-13.611.37 -104.1 178 -16

-13.61

K-54.43)

2741.2 53.75

2228.8 43.7

1877.8 36.82

1152.1 22.59

115.7 2.27

111.3 2.18

0

12.54

24.84

40 )L-20-4.57

10.56

40)

-40L-21.69-3.73

40)

"-40'L-40-40

,40)L-40,-40

-40

-40)L-40-40

-40

-40)

Ie.sl

0

0.04

0.09

,.0.26)L-0.07-0.02

0.04

0.25 )-0.14

-0.07

-0.01

0.24 )-0.41

-0.31

-0.21

0.19L-6.81-5.78

-4.78

-0.75)

-7.09

-6.02

-4.98

-0.79

"C"

"in"

6719

54.63

46.03

28.24

2.83

2.73

-4

-5

Calculation No.:Prepared By: 'ý A\-. •-4boa-- 0102-0135-07

MPR Associates, Inc. Revision No.: 0320 King Street Cekdya &Alexandria VA 22314 Checked By Page No.: 23

Section i:= 4 "Section"L(J) toll

4

"Location" "Tension"

I'll "Surface"

"Ring Girder" "OD"

"Rebar"

"Orientation"

"vertical"

"Elevation"

"250 to 256"

zUUU•

150t

1006

506

6

- 506

............... ..........

................................. ................. ............................

- 1000- 500 0 500 1000 1500 2000 2500 3000

Moment (ft*kip/ft)

Note:The rebar configuration shown in Section 1-1 of Reference 2.3 was used tocalculate the interaction diagram for the ring girdervertical rebar in thiscalculation. As shown in Section 1-1 of Reference 2.3, there is no verticalrebar at the OD face of the ring girder that spans the construction joint atElevation 255 ft -10.5 in. This above interaction diagram does not applyabove above the construction joint at Elevation 255 ft - 10.5".

Calculation No.:M M P R Prepared By: • *-. . 0102-0135-07MPR Associates, Inc. Revision No.: 0"320 King Street C e dB /lAlexandria VA 22314 Checked By: Page No.: 24

IIZI1 "Ent'

"It "kiplft"

fill I'll

WWI"

"kip"

Tchk () =

0 2001.2 1656.9

-0.5 1643 2062.6

-1 13871 2201.8

-3 1087.8 2476.8

-17.24 0 629.1

-19.24 -443.4 -532.4

"kipift"

0

5681

49.65

49.65

\22743

-31.78

41.41

49.65

49.65

122743J

-63.56

24.57

49.65

49.65

,227.43

-63.56

-36.03

20.73

32.23

,22743)

-63.56'

-63.56

-55.55

-55.55

,-63.66)

-63.56

-63.56

-55.55

-55.55

-12722

"kipIft"I'll

2695.2 52.85

2191.4 42.97

1846.3 36.2

1132.8 22.21

301.9 5.92

,273.7 5.37

0

40

40

40

,40J

-20

30.31

40

40

40

-40

19.71

40

40

40

-40

-22.68

14.93

2746

40

-40

-40

-40

-40

,-10.01

-40

-40

-40

-40

,-20)

"in"

0

0.14

0.2

0.21

(0.26

-0.07,

0.1

0.17

0.19

,0.25

-0.14

0.07

0.15

0.17

(0.25

-0.41

-0.08

0.05

0.09

0.21

-2.38

-1.12

-0.63

-0.47

-0.03,

-2.65

-1.27

-0.73

-0.55

-0.07)

66.06

53.71

45.25

27.76

74

6.71

C.

"in"

Calculation No.:7 Prepared By: • 0102-0135-07MPR Associates, Inc. Revision No.: 0320 King Street Checked B,Alexandria VA 22314 C Page No.: 25

Section i:= 5 "Section"

"Location"

"Containment"

I JtU.

1006

0

506

"Tension"

"Surface"

"OD"

"ksi"

III,

"Rebar"

"Orientation"

"vertical"

"Elevation"II (ft)II

6

.1U)-500 0 500

Moment (ft *kip/fi)

"Z7. "P.n"

I'll V'kip/lft

,I'l I'll

"Mn"

"tki"

"iFs"

"Xip/ft"I'll

"IC.cI"

"W•p/ft"' Ila"'in"l

I'l

Tchk () =

0 1104.3 615.1 (180.7)

-0.5 877.3 764.6 -1 5.47 )

(-130.82

-1 708.5 835.7 130.7 I

K180.7)C -130.82-3 544.4 914.4 130.82)

(150.07)(-130.82

-9.33 0 416.3 -1 56.3

K-156.3)(9-130.82)-11.33 -299.7 -16.4 I.221

1518.2 29.77 I00K0 40)

1234.4 24.2 (-204

1040 20.39 (4040

638.1 12.51 -40

K33.94)

287.1 5.63 (-0.

K -30.92)

244.6 4.8 -0

"le.s",

C 0.072)

0.21 )-0.14

0.19)

-0.41)

0.12 )

-1.56(-O0.18

"'in''

mll

37.21

30.26

25.49

15.64

7.04

5.99

Calculation No.:Prepared By: ' 0102-0135-07

MPR Associates, Inc. Revision No.: 0320 King Street edBy:Alexandria VA 22314 Checked By: Page No.: 26

Section i:= 6

cation" "Tension"

lilt "Surface"

ainment" "OD"

"Rebar"

"Orientation"

"vertical"

"Elevation"

"9(ft)1"

"93 to 103"16 "Conti

I JUU

1000

0

500

0

- JLUL-500 0 500 1000 1500

Moment (ft*kip/ft)

Calculation No.:Prepared By: • . , 0102-0135-07

MPR Associates, Inc. Revision No.: 0320 King StreetAlexandria VA 22314 Checked By: Page No.: 27

"Z71 "Pn"IM. ."kip/if'

I'll IMw

"M. n"

"kip"

" F.s""VP/ff"

III,

Tchk (1) =

(0

0 1210.3 714.3 107.27

,214.55)

-31.23

-0.5 1002.9 842.1 107.27

,214.55)

-62.46

-1 854.4 887.8 107.27

t,214.55

(-62.46

-3 731.6 992.1 84.01

p214.55)

(-62.46

-10.62 0 260.3 -120.03

-79.41

-62.46

-12.62 -380.3 -295.1 -120.03

Y,-173.46)•

"Cc" "a" "f.s"

"kiplft" "into "ksi"

(0

1540.2 30.2 40

,40,

(-20o

1252.3 24.56 40

40

-40

1055.1 20.69 40

40

(-40

647.3 12.69 32.25

40 )

"e.s"

L0 N0.22

0.24)(-0.07 N0.2

0.23)L-0.14 N0.18

0.21)

-0.41 NL0.16)

ICl

"in"

37.75

30.69

25.86

15.87

6.42

5.55

1-40 146261.9 5.14 -40 -0.17

,-13.23, -0.05

226.5 4.44 -40 -0.24

\-28.9 k,-0.1 )

Calculation No.:O M P R Prepared By: S .- - 0102-0135-07

MPR Associates, Inc. Revision No.: 03 2 0 K in g S tre e t C e k B yP g,. 2Alexandria VA 22314 Checked By: Page No.: 28

Section i:= 7"Section"

"Location" "Tension" "Rebar" "Elevation"

..... "Surface" "Orientation" . .(fi)"

"Under Eq. Hatch" "OD" "vertical" "93 to 103"

S1J00

1 000

ZI 500

0

- 500 0 500

Moment (ft*kip/ft)

1000 1500

Prepred y: kk--Calculation No.:TVMPR °'°-°Prepared By: P R k, 0102-0135-07

MPR Associates, Inc. Revision No.: 0320 King Street e OJ6Pg .Alexandria VA 22314 Checked By: Page No.: 29

1"71 IPn"... .kip/if'

"Mn"

"kip"t

"F.st

"kipift'I'll

Tchk () =

(0

0 1210.3 714.3 107.27

,214.55)

(-41.64'

-0.5 996.1 851.6 107.27

1,214.55)

(-83.28

-1 840.9 906.7 10727

Y214.55)

(-83.28

-3 714.4 1016.2 84.01

Y,214.55s)

-83.28

-10.31 0 308.8 -120.03

-65.01

-83.28

-12.31 -399 -266.1 -120.03

-159.06)

"C1c"l "all I"fs1""tkip/fl" "..in" .. .. si"

(0

1540.2 30.2 40

,40,

1252.3 24.56 40

40

(-40

1055.1 20.69 40

40

(-40

647.3 12.69 32.25

0 40

268.3 5.26 -40

K-10.83)(-40

231.3 4.53 -40

-26.5)

"e.s"

0

S0.22

-0.07

S0.2

0.23)L-0.140.18

0.21)L-0.41'01.11

0.16)L-1.42'-0.16

-0.204

(-1.7

-0.23

-0.09)

lClIVn"in"l

I'lll

37.75

30.69

25.86

15.87

6.58

5.67

Calculation No.:YR Prepared By: Ž• .'_.. i-,-.• 0102-0135-07MPR Associates, Inc. Revision No.: 0320 King Street ed By:Alexandria VA 22314 Checked By: Page No.: 30

7.0 REFERENCES

1. ACI 318, "Building Code Requirements for Reinforced Concrete"

1.1 ACI-631.2 ACI-83

2. Progress Energy Drawings:

2.1 No. SC-421-031, "Reactor Building Exterior Wall Concrete Outline," Revision 4.2.2 No. SC-421-036, "Reactor Building External Wall Sections and Details," Revision 10.2.3 No. SC-421-301, "Reactor Building Ring Girder Plan & Sections," Revision 8.2.4 No. SC-421-039, "Reactor Building Exterior Wall Equipment Access Opening, Reinforcement

Placing," Revision 5.2.5 No. SC-421-006, "Reactor Building Foundation Mat Anchor Bolt and Dowels," Revision 4.2.6 No. SC-421-032, "Reactor Building Stretch-out of Exterior Buttress #2, #3, #4, and #5,"

Revision 8.

3. Florida Power FSAR, Containment System & Other Special Structures, Revision 31.3.

4. J. Wight and J. MacGregor, Reinforced Concrete Mechanics and Design, Pearson Education,Inc., 5th Edition.

5. E. Avallone & T. Baumeister, "Marks' Standard Handbook for Mechanical Engineers,"McGraw-Hill Book Company, 9th Edition.

6. Florida Power Corporation Document Identification No. S-00-0047, As-built ConcreteStrength for Class 1 Structures, Revision 0.

7. Progress Energy, "Design Basis Document for the Containment," Revision 6.


&I*M PR 320 King StreetAlexandria, VA 22314


Client:

Progress Energy Page 1 of 23plus Attachment


0102-0906-0135

Title: Calculation No.Seismic, Wind, and Tornado Evaluation and Delamination Depth 0102-0135-08Evaluation for Detensioned State


0J. L. Hibbard M. Oghbaei E. Bird

1-23-2010 1-23-2010 1-23-2010


requirements of 1 OCFR50 Appendix B, as specified in the MPR Quality Assurance Manual.




RECORD OF REVISIONS

Calculation No. Prepared By Checked Bv Page: 2

0102-0135-08n_[__Afecte Page Dsrtion


0 All Initial Issue




MPR Associates, Inc.Q0 M PR 320 King Street



0102-0135-08 , ,1 f h~z.- Revision: 0

Table of Contents

1.0 Purpose ......................................................................................................... 4

2.0 Sum m ary ....................................................................................................... 4

3.0 Background ...................................................................................................... 9

4.0 Assum ptions .................................................................................................... 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 1..................................................................................................... 15

6.3 Seismic and Deadweight Stress .............................................................................. 17

6.4 Tornado and Deadweight Stress .......................................................................... 21

7.0 References ..................................................................................................... 23

Attachm ent .................................................................................................................. 24


Calculation No.:60 Prepared By: A -.. . 0102-0135-08MPR Associates, Inc. Revision No.: 0320 King Street C kAlexandria VA 22314 Checked By:. Page No.: 4

1.0 PURPOSE

This calculation evaluates the containment building for three design basis loads due to naturalphenomena that might occur while the containment building is detensioned for repair. The load casesare: 1) deadweight and Safe Shutdown Earthquake (SSE), 2) deadweight and wind, and 3) deadweightand tornado. The containment is evaluated for membrane plus bending stress at two sections throughthe 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 theSGR opening, the containment is assumed to have no concrete between Buttresses 3 and 4 betweenElevations 183 feet and 210 feet. These are the bottom and top elevations respectively, of the SGRopening.

2.0 SUMMARY

Membrane plus bending stress in the containment shell at two sections for two load cases are providedin the table below. The deadweight plus wind load case is bounded by the results for the deadweightplus tornado load case.

"Load" "Section" "M + B"t "Stress" "Result"

"Case ." "Stress" "Limit"

liltof tl oni" 139 lt Failure"

Ts "Deadweight & SSE" "Bottom of Cont.i" 19 600 ("No Failure"( "Bottom of Cont." )(-103 ("No Failure"

"Deadweight& Tornado" 'Bottom of SGR O " -103) 600 ("No Failure"\.."Bot'tom of SGR Opnng (~-95) "No Failure")

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 Replacement4. 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. Esect2 = 183ft .

Calculation No.:

ON M Prepared By: • A-.. • 0102-0135-08MPR Associates, Inc. Revision No.: 0320 King Street C d.P.N :Alexandria VA 22314 Checked By: /'. Page No.: 5

Conclusions from these evaluations are:

* The containment building is not expected to fail catastrophically while the building is detensioned forrepairs 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 containmentbuilding for the load cases listed above. The basis for this conclusion is the analysis result at thesection at the bottom of the SGR opening. This section is assumed to have no concrete betweenButtresses 3 and 4 for the height of the SGR opening. This configuration bounds a case in which thedelamination depth is greater than nominal. Delamination depths greater than nominal above andbelow the SGR opening are considered acceptable based onjudgement. The basis is that the SGRopening with a width of 25 feet and extending the full thickness of the containment wall will boundany thinned sections above or below the opening.

Calculation No.:Prepared By: A .- , 0102-0135-08

MPR Associates, Inc. Revision No.: 0320 King Street Checked By:Alexandria VA 22314 Checked By: A(. ,yr Page No.: 6

-~ 41

I.

at Bottom of SGR Opening(Elev. 183 ft)

~1-

-F

a •.... .. . L..:• •. .: , .. • .. ,

-L

Section at Bottom of Containment(Elev. 93 ft)

Figure 1. Containment Building

Calculation No.:1 M P R Prepared By: * . 0102-0135-08MPR Associates, Inc. Revision No.: 0320 King Street Ch ck dyAlexandria VA 22314 Checked By: H1. Page No.: 7

I

N

'~1

Ii~...

/

///

/

"7

Section at Bottom of Containment (Approximate)

... ...... ; £•• . : " • . . .

"-'7

I!

/y

'I'

i/>

Section at Bottom of SGR Opening (Approximate)

Figure 2. Sections

Calculation No.:Prepared By: Žý A--. 0102-0135-08

MPR Associates, Inc. Revision No.: 0320 King Street C e dB HAlexandria VA 22314 Checked By: /41. Page No.: 8

4. BU~tTT•ES8

• Configuration for this-r - Calculation I

,, SGR Opening

Figure 3. Configuration of Containment for Section at SGR Opening

Calculation No.:I M R Prepared By: • . L--,-. 0102-0135-08MPR Associates, Inc. Revision No.: 0320 King StreetAlexandria VA 22314 Checked By: A(. Page No.: 9

3.0 BACKGROUND


4.0 ASSUMPTIONS


None.


1. It is assumed that the thickness of the ring girder is trg = 8.83 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 comparisonwas made of the mass of the ring girder and dome determined in this calculation to themass calculated by the finite element model used in this project. There was goodagreement between the mass calculation in this calculation with that from the finiteelement model.

SM PR Calculation No.:Prepared By: • .. . 0102-0135-08

MPR Associates, Inc. Revision No.: 0320 King StreetAlexandria VA 22314 Checked By: Page No.: 10

5.0 APPROACH

This calculation is an approximate evaluation to assess the potential for a catastrophic failure ofthe containment when the containment is detensioned for repair. Approximate analysistechniques are used. The analysis considers effects that are considered to be important to theassessment. This is a bounding evaluation rather than a comprehensive evaluation. Effects thatare considered to have less than a 20% effect on the final answer are not considered. This isjustified 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 tomado loads are the design basis loads as defined by the FSAR (Reference 3). Noload 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 forpotential closely spaced modes. The peak seismic response is from the ground accelerationspectrum from Reference 1. The seismic assessment considers horizontal acceleration and asimultaneous vertical acceleration in the up direction. The vertical up acceleration increases thetensile 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 theintact configuration of the containment. The effects of removing concrete for the delaminationand removing the concrete for the SGR opening are not significant within the framework of thisapproximate analysis. The mass is based on cylinders and does not include the mass of thebuttresses (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 thanthe tensile failure stress criterion established in Reference 4 (oten = 600psi ). The containmentwall membrane plus bending stress is a near uniform tensile stress across the containment wallthickness 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 containmentas shown on Figures 1 and 2.

The first section is at the bottom of the containment at elevation 93 feet. The nominalcontainment wall thickness is 3.5 feet. At elevation 93 feet, the containment wall is thickerthan the nominal thickness. For conservatism and simplicity, the nominal containment wallthickness is used for the evaluation at this section.

Calculation No.:

AA M P R Prepared By: • A.- - 0102-0135-08MPR Associates, Inc. Revision No.: 0320 K ing S treet C c- . a qg N 1Alexandria VA 22314 Checked By. All V Page No.: 11

The second section is at the bottom of the SGR opening at Elevation ESGR.b = 183ft . TheSGR opening dimensions are hSGR = 27 ft high by WSGR = 25 ft wide (Reference 2.2). Theanalysis assumes a configuration for the containment in which there is no concrete for anangular extent of a = 60.deg for the height of the SGR opening. Figure 3 shows theconfiguration used for the analysis. For reference, the angular extent of the SGR opening isaSGR = 20.9. deg.

Some vertical and hoop tendons will be detensioned for the repair. Detensioning vertical tendonsreduces 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 longitudinaldirection and keep the containment concrete in longitudinal compression. Without all the verticaltendons, the capacity of the containment to resist an overturning moment is reduced. Thiscalculation 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 footelevation. This rebar connects the containment shell to the basemat. This calculation takes nocredit for this rebar.

The center of gravity of the dome and ring girder are offset from the neutral axis for the analysisat the section at the SGR opening. The moment created by the offset increases the compressivestress due to deadweight at the SGR opening. No credit is taken for this effect in the analysis.

Calculation No.:Prepared By: • 0102-0135-08

MPR Associates, Inc. Revision No.: 0320 King Street Cc BAlexandria VA 22314 Checked By: /1, Page No.: 12

6.0 CALCULATION

6.1 Design Inputs

Containment Cylinder

tcyl=- 42 in

tb =- 2.ft+ 4.in

tliner 0.3 75.in

idyI, 2.(65. ft + tiner)

o dcyI= idcyl + 2. tcy

Ecyl.b 93.ft

Ecyl.t =250.ft

a =- 60.deg

SGR Opening

ESGR.b 183.ft

ESGR.t- 210.ft

WSGR 25"ft

WSGRoaSGR =

odcyl + 2

hSGR ESGRt - ESGR.b

tb 28.in

idcyj = 130.06 ft

Odyt =137.06 ft

qSGR = 20.9. deg

hsGR = 2 7 ft

Containment wall thickness; Ref. 2.1

Buttress additional thickness beyond thickness ofcylinder; Ref. 2.1

Liner thickness; Ref. 2.1

Inside diameter of containment concrete wall;Ref. 2.1

Outside diameter of containment; Ref. 2.1

Elevation of bottom of containment cylinder; Ref. 2.1

Elevation of top of containment cylinder; Ref. 2.1

Angle between Buttresses 3 and 4; Ref. 2.1 anddiscussion in Section 5.0

Elevation of bottom of SGR opening; Ref. 2.2

Elevation of top of SGR opening; Ref. 2.2

Width of SGR opening; Ref. 2.2

Angular extent of SRG opening

Height of SGR opening

Calculation No.:

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MPR Associates, Inc. Revision No.: 0320 King StreetAlexandria VA 22314 Checked By: P7. Page No.: 13

Ring Girder

odrg := od0y + 2. tb odrg = 141.73 ft Outside diameter of ring girder; Ref. 2.1

trg = tcyl + tb + 3. ft

idrg := Odrg - 2 .trg

trg = 106.inEstimate of ring girder thickness for mass calculation;Ref. 2.1 and Assumption 4.2.1

idrg = 124.06 ft Inside diameter of ring girder

Height of ring girder; Ref. 2.1Lrg:= 17.5.ft

Dome

tdome := 3ftDome thickness; Ref. 2.1

Height of dome; Ref. 2.1Ldome := (35.ft + 4.5.in) - Lrg Ldome = 17.88 ft

Concrete

lbpc:= 144-.

f' 0

O-tn =-600.psi

Concrete density; Ref. 6

Concrete tensile strength; Ref. 4

Seismic

ah:= 1.5.2.0.135.g ah = 0.405.gSSE static equivalent acceleration; the peak in theOBE ground response spectra is from Pages 97 and98 of Attachment 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 timesOBE based on Ref. 3, Section 5.2.1.2.9; the 1.5factor accounts for potential closely spaced modesper Ref. 7, Section 6.3

SSE vertical ground acceleration; Ref. 3, Section5.2.1.2.9

2av:= - ah

3av = 0.27.g


MPR Associates, Inc. Revision No.: 0320 King Street Checked By:Alexandria VA 22314 Page No.: 14

Wind

Vwinld:= 179.mph Wind speed fordesign basis accident; Ref. 3,Section 5.2.1.2.5

Tornado

Vtornado:= 300.mph

Pext:= 3.psi

Tornado wind speed for design basis accident; Ref.3, Section 5.2.1.2.6

Tornado internal to external pressure drop for designbasis accident; Ref. 3, Section 5.2.1.2.6

Air

lbPair: 0.071.-

P-air := 1.285.107 5 lb

ft.sec

Misc.

Cd.E6:= 0.38

Cd.E5:= 1.2

Density of air; the air temperature to obtain density is10OF for simplicity; Ref. 9, Table A-3

Viscosity of air; the air temperature to obtain viscosityis 10OF for simplicity; Ref. 9, Table A-3

Drag coefficient for a cylinder at Reynolds Number

greater than 10 6; Ref. 8, Figure 5-78

Drag coefficient for a cylinder at Reynolds Number of

105; Ref. 8, Figure 5-78


MPR Associates, Inc. Revision No.: 0320 King Street Checked By:Alexandria VA 22314 C Page No.: 15

6.2 Deadweight Stress

Stress will be calculated at two sections at elevations:

Ecyl.bEsect:= ESGR.b Esect • ft1

The length of the containment cylinder above each section for the analysis is:

Lcyl := Ecy t - Esect

L 157"fL/ •67) Esect ý ( 93 ) ft183

The mass of dome, ring girder, and cylinder are:

mass1, i:= Pc"

tdome-1 dcy

Lrg (odrrg- Idrg2)

4

Lcy.. 7r(od cY,2 -idcyl2)

id:= 2 The mass of the dome iscalculated with a simplifiedapproach in which the dome is acircular plate.

TEsect = (93 183 ) ft

5.74xx610 5.74x 106

mass=!9.29 x 0 6 9.29x 106 lb

L\3.32 x 107 Y.1.42 x 107

id = 2The total mass is:

masstot := I mass,' ip4.82 x 107

masstot = lb<2.92 x 107)

=93 )fEsect= C183)

Calculation No.:Prepared By: S . 0102-0135-08

MPR Associates, Inc. Revision No.: 0320 King Street Ch.cke ..ByAlexandria VA 22314 Checked By: .€.* Q Page No.: 16

The cross section area at the two sections is:

A, l -. (od y'2 - id0yl2)4

odcyl + idcylrmean :-

Ac2 := AI - aormean-tcyI

2.11 x 1051 2

Ac = .in

\1.76 x 105

The compressive stress is:

rmean = 66. 78 ft

(93>E sect = 183)ft183

masst0 t-1 g'7dw := - A

S-228.1)O'W -165.7 )ps

Esect C 1893 ) ft

Calculation No.:Prepared By: S *\._ , 0102-0135-08

MPR Associates, Inc. Revision No.: 0320 King Street Checked By: Pg N .Alexandria VA 22314 C. Page No.: 17

6.3 Seismic and Deadweight Stress

Horizontal

The length from the mass cg to the elevation for the section is:

SLcyl, + Lrg + Ldome + 2 ]

L Lcgl, i :=j TLcg1 Lcyl. + rg 2

Lcyl1 i + 2

TEsect = (93 183) ft

L 183.441 (93.441] "dome"

Log = 165.75 75.75 ft = "ring girder"

L 78.5 ) Y. 33.5)] "cylinder" )

The moment due to horizontal seismic is:

3Msi: ahj- Yl [(massl, )i -j(Lcgj,,ijj

44

4

Dome c.g.Ring Girder c.g.

Cylinder c.g.

2.11 x 109Ms = • ft.lbf

k.6.95 x 108)

93 ftEsect C 183)

The moment of inertia for the intact containment is:

cyI = -(odcyl idc) cy = 6.8 x 10olin4

7P Calculation No.:Prepared By: • 0102-0135-08

MPR Associates, Inc. Revision No.: 0320 King Street C e dBAlexandria VA 22314 Checked By: /'. Page No.: 18

The moment of inertia for the C shaped segment of containment about the containment centroid iscalculated below. The neutral axis of the C shaped segment is defined as:

f ydA =0

basic statics, no reference required

Define a function to calculate the integral.

ir a

f(Yna) 2

2

2

where y

dA

rmean'tcy,.(rmean'sin(O) - Yna) d9

=rmean-Sin(O - Yna

=rmean, tcyl, d9

The neutral axis is:

Yna = Yguess +- 0

root( f(Yguess) , Yguess)

Yna = -12. 75 ft

Verify the solution:

f(Yna) = 9.93x 1- 10.in which is approximately zero.

The moment of inertia about the containment centroid is:

cetod= I'y ~2 Ref. 5, Formula j 100

7r a2 2

Icentroid := 2* rmean, tcyl .(rmean. sin (0) 2 dO

2

1centroid = 4. 72 x 10 10.n4

where y = rmean-sin(69

dA = rmean -tcyl -d9

Calculation No.:AU M P R Prepared By: • .... , 0102-0135-08MPR Associates, Inc. Revision No.: 03 2 0 K i n g S t r e e t C e k d B :a e N . 1Alexandria VA 22314 Checked By: /H*., ' Page No.: 19

The moment of inertia about the neutral axis is:

2Ic:'centroid + A02"Yna 10 . 4/c,= 5.14 x10 .ifl Ref. 5, Formula p 19

where Ac2 = 176232.in2

The distance from the neutral axis to the extreme tension fiber is:

- 2 I2 Yna

C C ~m a x = m a x _I(a Y a2d~ .n2i -2)Yn

CC.max = 72.1 ft

where2 Yna 56.ft2 =

S2 f . iV - _Yna =72.1 ft21K 2) 1=

The moments of inertia for the two sections are:

Isect:=cy/.c6.8x 1010 4

Isect = t5.14 x 1010i Esect = (93)1ftC183)The distances to the extreme tension fiber are:

:(°d 0 y'+2"j (68.53"I

Csect := jCCm + Csect = 68.1 ) ftKcc~max ) K72.1)

Esect = (9 Jft183

The bending stress is:

MS. CsectO's.h.=- Isect (~~7 1 4 0.4 2 ps Esect = 9 ft183

Calculation No.:50M PR Prepared By: . 0102-0135-08MPR Associates, Inc. Revision No.: 0320 King Street CcdAlexandria VA 22314 Checked By: Page No.: 20

Vertical

The vertical seismic stress is:

av )61.58O 'S.v : =: - - O 'd w '- _ _'S.V = 4 . 4 p s i

S 1-g} (44.74)

Deadweight and Seismic Stress

The deadweight and seismic stress is:

Esect = ft183

O-dw.s :ýO.h + 0 'S.V + 0~dw -dw's C 139.3 ) psi(19.5)Ps

Esect = ft183

Compare the stress to the concrete tensile strength.

checkI:= if(o-dw.s I .oten, ok, nok)= ("No Failure"

("No Failure"Esect = 83 )ftC183)

Calculation No.:t Prepared By: • 0102-0135-08

MPR Associates, Inc. Revision No.: 0320 King Street C dP oAlexandria 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 2Fd = Cd . "Pair'Ap Vtomado

2

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:= [odrg.(Lcyl + Lrg + Ldome) Ap = .09 X9113k\2.09 x 106) Esct= 83), f

The drag coefficient is a function of the Reynolds Number.

Pair" Vtornado "od rg8

Re := Re = 3.45 x 10/1air

The drag coefficient for a cylinder at Reynolds Number greater than 106 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:

1 2 (6.99x10o6> 93"

Fd:= Cd.E5" I "Pair'Ap"Vtomado Fd = I 6 Ibf Esect 93jft23.72 x 10 6,183

The bending moment due to the tornado is:

Mtornado [Fd - (Lyi + Lrg + Ldome)]

Mtomado = x .ft.Ibf Esect =(3)ft

1.9x 8 183

Calculation No.:Prepared By: • *'- , 0102-0135-08

MPR Associates, Inc. Revision No.: 0320 King StreetAlexandria VA 22314 Checked By: At'. Page No.: 22

The bending stress is:

Mtomado * Csect

'ornado - sect tornad° 938.49 ) psi(ondo=38.49)s

Esect ( ft183

Coincident with the tornado wind is a local depressurization. The internal to external pressuredrop across the containment wall is Pext = 3 psi . The longitudinal stress in the containment due to

the pressure is:

1?- 2Pext, dy

40-,t: - AC

C27.14)°'ext = 32.57 )psi

Esect = ( 93 fty183j

Deadweight and Tornado Stress

The deadweight and tornado stress is:

Jdwt:= (Ctomado + O7ext + O'dwt -103.3)

d -94.6)Esect = ft

183

Compare the stress to the concrete tensile strength.

cheC" 21 if ( Odwt, •ý O'ten, ok, nok)("No Failure"

check2 ("'No Failure)Esect = ft

183

Calculation No.:Prepared By: '% *"-. , 0102-0135-08

MPR Associates, Inc. Revision No.: 0320 King Street CyAlexandria VA 22314 Checked By: ,'?. 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.

3. Florida Power FSAR, Containment System & Other Special Structures, Revision 31.3.

4. Letter from WJE (Mr. J. Fraczek) to Progress Energy (Mr. D. Dyksterhouse), Subject: CR3Containment Limiting Tensile Stress, WJE No. 2009.4690, January 11, 2010.

5. K. Gieck, "Engineering Formulas," McGraw-Hill Book Company, 3rd Edition, 1979.

6. Email from Mr. J. Holliday (PE) to Mr. K. Gantz (MPR), 12-30-2009, 10:35 AM, Subject:Concrete Density.

7. Institute of Electrical and Electronics Engineers, Inc. (IEEE) Standard 344-1987,"IEEE Recommended Practice for Seismic Qualification of Class 1E Equipment for NuclearPower 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.:7 P R Prepared By: A - 0102-0135-08MPR Associates, Inc. Revision No.: 0320 King Street C e dBAlexandria VA 22314 Checked By: A(. Page No.: 24

ATTACHMENT

Email from Mr. J. Holliday (PE) to Mr. K. Gantz (MPR), 12-30-2009, 10:35 AM, Subject: ConcreteDensity.

Message Page 1 of I

Hibbard, Jim

From: Holliday, John [[email protected]]

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: [email protected]]Sent: Wednesday, December 30, 2009 10:01 AMTo: Knott, Ronald; Holliday, JohnCc: Hibbard, JimSubject: 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 itin SOO-0047.

Kevin

---- -Original Message -----From: Knott, Ronald [mailto: [email protected]]Sent: Wednesday, December 16, 2009 10:15 AMTo: Holliday, JohnCc: Gantz, KevinSubject: FW: Concrete Density

John,Can you direct Kevin to the density reference. I don't know where the original data came from fordensity. I was only quoting what I heard in the meeting. I assumed it was in the 500-0047 attachments.

From: Gantz, Kevin [mailto:[email protected]]Sent: Tuesday, December 15, 2009 6:22 PMTo: Knott, RonaldCc: Dyksterhouse, Don; Holliday, John; Bird, Edward; Butler, PatrickSubject: Concrete Density

Ron,

During our previous meeting you received some original information on the concrete density. I rememberyou saying later that the concrete density was 144 or 145 pcf. Do you have a reference or an actualnumber so that I can make sure I have the correct modulus calculated?

Thanks,

Kevin

12/30/2009


*M PR 320 King StreetAlexandria, VA 22314


Client:


Project: Task No.CR3 Containment Delamination

0102-0906-0135

Title: Calculation No.Conduit Local Stress Analysis 0102-013505


1-20-2010 1-20-2010 1-20-2010Edward Bird Erin Tindall Robert Keating 0

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requirements of IOCFR50 Appendix B, as specified in the MPR Quality Assurance Manual.




RECORD OF REVISIONS


0102-0135-05 .-. ' ,- ,

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0 All Initial Issue

Note: The revision number found on each individual page of the calculation "carries the revision



MPR Associates, Inc.50MPR 320 King Street



0102-0135-05 Revision: C

Table of Contents

1.0 Purpose ........................................................................................................ 4

1.1 Background .......................................................................................................... 4

1.2 P u rp o se ......................................................................................................................... 4

2.0 Sum m ary of Results and Conclusions .......................................................... 5

3.0 Methodology ..................................................................................................... 5

4.0 Design Inputs ................................................................................................... 7

4.1 Geometry ........................................................................................................... 7

4.2 M aterial 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 Associates, Inc.FIM PR 320 King StreetAlexandria, VA 22314


0102-0135-05 . , -,,-1c, . 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 steamgenerators. As part of that project, 10 vertical and 17 horizontal tendons were detensioned and anopening was cut into the concrete containment above the equipment hatch. As this opening wasbeing cut, cracking in the concrete wall was identified around the full periphery of the opening inthe cylindrical plane of the wall. The cracking is located at the radius of the circumferentialtensioning tendons, and is indicative of a delaminated condition. Progress Energy plans toremove the delaminated concrete and replace it.

1.2 Purpose

The concrete repair and restoration of the steam generator opening may require detensioningadditional tendons. The purpose of this calculation is to determine if the absence of either thevertical or horizontal compressive load results in a more limiting stress condition around thetendon conduits than the case with both vertical and horizontal compression applied. If a morelimiting 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 toevaluate the principal stress magnitude and orientation around the hoop conduits for threecombinations 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.320 King StreetAlexandria, VA 22314


0102-0135-05 . , lc,-"G, Revision:(

2.0 SUMMARY OF RESULTS AND CONCLUSIONS

Figures 7-1, 7-2 and 7-3 show color contour plots of maximum principal stress (S 1) in theconcrete for the three post-tension loading conditions evaluated. The maximum principal stressfor 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 maximumprincipal stress is less than the case with both loads applied simultaneously. Therefore, thiscalculation 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 wasdeveloped with the Ansys finite element program. The axis of symmetry for the model is thevertical centerline of the containment. The model represents an un-delaminated section of thecontainment wall. Linear-elastic, static structural analyses were performed for three loadingconditions.

Figure 3-1 shows the axisymmetric model developed for the local stress analysis. The modelrepresents a vertical slice through the containment wall between vertical tendons and includesthe liner and two conduits.





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


*MPRMPR Associates, Inc.320 King StreetAlexandria, VA 22314

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 l a

The model is 39 inches high, which represents the nominal distance between tendon pairs.

4.2 Material Properties

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:

Density:

Poisson's ratio:

4.03x 106 psi Reference 3, page 4 (uncracked)

150 lb/ft3

0.2

Reference 2, page 3

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 aretaken from Reference 4, Table 38.

Elastic Modulus:

Density:

Poisson's ratio:

29 x 106 psi

0.283 lb/in3

0.27





0102-0135-05 . , •C'1CdG. Revision: 0

4.3 Boundary Conditions

The boundary conditions applied to the model include displacement restraints and applied forcesthat represent post-tension loads only. As shown in Figure 4-1, along the lower edge of themodel, displacements of the concrete and liner normal to the edge are restrained. At the upperedge of the model, the concrete and liner displacements normal to the edge are coupled to oneanother such that all nodes have the same vertical displacement. This condition forces the upperedge of the model to remain horizontal and represents a symmetry condition across the edge. Apressure 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 thecontainment. In the axisymmetric model, at each tendon conduit, the tendon load is representedby the total (360 degree) radial load. For the case with vertical load only, both hoop tendons inthe 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, theprestress load is shared between the steel liner and concrete wall.


MPR Associates, Inc.*M PR 320 King Street



0102-0135-05 ,. ,. ,,. - Revision: 0

ri:= 65.ft+-in8

ri= 65.031 ft

ro =ri + 42.in

ro= 68.531 ft

tb := 28.in

Lb 12.ft

Nb:= 6

Nv := 144

dc:= 5.25.in

TV:= 1474000.lbf

Th := 1398000.lbf

Containment concrete inside radius (Reference la)

Containment concrete outside radius (Reference la)

Buttress thickness (Reference 1a)

Buttress length (Reference la)

Number of buttresses (Reference 1 a)

Number of vertical tendons (Reference 2, page 14)

Tendon conduit outside diameter (Reference 2, page 4)

Vertical tendon tension (Reference 5, page 5, unadjusted tendon atthe end of the SGR project, 33 years)

Hoop tendon tension (Reference 5, page 5, unadjusted tendon at theend of the SGR project, 33 years)

The vertical tendon load is reacted by the cross section area of the containment wall andbuttresses less the area of the vertical tendon conduits.

aa :=r.(ro2- ri2)+ Nb.Lb.tb- Nv.4.dc2 aa = 1615 ft2

Nv.TvGa :- aa cra = 913 psi

Each hoop tendon has a tension of Th and exerts a unit radial force of Th / r on thecontainment. The Ansys code requires that the radial load be applied on a 360 degreebasis. The total radial load is then (Th / r) x 2 pi r = 2 pi Th.

Fhoop := 2 .7rTh Fhoop = 8.784 x 106 lbf


MPR Associates, Inc.* M P R 320 King Street



0102-0135-05 . , ý',m f,-.- Revision: 0

A uniform pressure of 913psi is applied to the upperedge representing thevertical tendon load

Along the lower edgedisplacements normal tothe edge are restrained

Along the upper edge,displacements normal to theedge are coupled to oneanother resulting in this lineremaining horizontal

A force equal to2 rr Th is appliedto each conduit

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 andan 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.


IMPR


11

0102-0135-05 4 ,%•Iý Revision: 0

6.0 COMPUTER CODES

This analysis was performed with the ANSYS general purpose finite element program, Version11.0 SP1. The analysis was performed on a Sun v40z server running the Suse Linux 9.0operating 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 theconcrete for the three post-tension loading conditions evaluated. Positive (+) stress values aretensile. The maximum principal stress for the three cases is listed below:

Horizontal + Vertical Tendon Load:

Vertical Tendon Load Only:

Horizontal Tendon Load Only:

1,041 psi

919 psi

237 psi

The results show that with either vertical only or horizontal only tendon loads, the maximumprincipal stress is less than the case with both loads applied simultaneously.





0102-0135-05 1,, Revision: 0

Maximum Principal StressType: Maximum Principal Stress -Top/BottomUnit: psiTime: 11/19/2010 11:16 AM

1041,3 Max856.27671.22486.16301.1116.04-69.015

S-254.07

-439.13-624.19 Min

Figure 7-1. Concrete Maximum Principal Tensile Stress - Vertical + Horizontal




0102-0135-05 Revision: 0

Mlaxirnumn Principal StressType: Maximum Principal Stress -Top/BottomUrit: psilime: 11/19/2010 11:17 AM

919.03 Max738.94658.84528.75398.65268.56138.468.3636-121.73-251.83 Mki

Figure 7-2. Concrete Maximum Principal Tensile Stress - Vertical Only




0102-0135-05 Revision: 0

Maxknim Principal StressType: Maximum Prindpal Stress - Top/BottomUnit: psiTime: 11/19/2010 11:16 AM

237.23 Max207,9178.57149.25119.9290.59261.26531.9372,6096-26.718 4in

Figure 7-3. Concrete Maximum Principal Tensile Stress - Horizontal only

8.0

1.

2.

3.

REFERENCES

Drawings:

a. FPC DWG SC-421-031, Rev. 4, "Reactor Building, Exterior Wall - Concrete Outline.

b. Prescon Drawing P10-A, Rev. 1, "Horizontal Tendon Detail Between 1200 - 180°."

Progress Energy, "Design Basis Document for the Containment," Revision 7.

MPR Calculation 0102-0135-02, Rev. 0, "Concrete Modulus of Elasticity and SpecifiedCompressive Strength."





0102-0135-05 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.





Client:

Progress Energy Page 1 of 47(+ Att. A)


0102-0906-0135

Title: Calculation No.Tendon Tension Calculation

0102-0135-03


1/18/2010 1/i8/2010 1/18/2010

Kevin Gantz Adrian Trif Jim Hibbard 0


This document has been prepared, checked, and reviewed/approved in accordance with the Quality Assurance



MPR Associates, Inc.0M PR 320 King StreetAlexandria, VA 22314

RECORD OF REVISIONS


0102-0135-03


0 All Initial Issue







0102-0135-03 - (/• - • Revision:

Table of Contents

1.0 Purpose ......................................................................................................... 4

2.0 Sum m ary .............................. ........................................................................... 4

3.0 Assum ptions .................................................................................................... 6


3.2 Verified Assumptions ............................................................................................. 6

4.0 M ethodology ................................................................................................... 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


M PRPrearedBy:~ ~Calculation No.:MPR Associates, Inc. Revision No.: 0320 King Street C eP NAlexandria VA 22314 ecked By:/

1.0 PURPOSE

This calculation determines the dome, vertical, and horizontal tendon tension immediately following theSteam 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 instructural 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 werecalculated:

* Elastic Shortening* Concrete Shrinkage* Tendon Steel Relaxation* Concrete Creep

The above mechanisms are described in Reference 22. Tendon losses were calculated individually fordifferent 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 ofthe tendons are not modified at all. Losses are calculated separately for these two groups. For thehorizontal tendons, several tendons are detensioned and subsequently retensioned and other tendons arenot modified at all. For the detensioned and retensioned tendons, several tendons pass throughreplacement concrete that fills the SGR opening plug and replaces the delaminated concrete, and othersdo not pass through the replacement concrete. Tendon losses are calculated individually for these twogroups of detensioned and retensioned tendons as well as the tendons that are not modified during theSGR project.

Concrete shrinkage and concrete creep are dependent on the material properties of the concrete that thetendons 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, fortendons that are detensioned and subsequently retensioned that pass through or near the repaired SGRopening, the tendon losses are calculated as if the tendon passes directly through the repaired SGRopening. Tendon steel relaxation losses are not dependent on the tendon location, and they are treatedthe same for all tendons. Elastic shortening losses are unique to each tendon based on the sequence withwhich the tendons are tensioned. An average elastic shortening loss is calculated based on tendonorientation (dome, vertical, or horizontal) so that every tendon does not have to be tensioned individuallyin the containment structural analyses.

The tension in each group of tendons is reported as the average tension along the tendon length.

A ý-- Calculation No.:OILM PR Prepared By: )~ ~-0102-0135-03MPR Associates, Inc.,Revision No.: 0

320 King Street Checked By:

Alexandria VA 22314 Checked By: ,/k/el.... Page No.: 5

The tendon tension at the end of the SGR Project (33 years):

Dome Tendons:

All Dome Tendons: Tensiond33 = 1376kip

Vertical Tendons:

Detensioned and Retensioned Tendons: Tensionv.33 .mod = 1603 kip

Unadjusted Tendons: Tensionv.33.unmod = 1474k,

Horizontal Tendons:

Detensioned and Retensioned Tendons Passing Tensionh.33.mod.SGR = 1573

through SGR Opening Bay:

Detensioned and Retensioned Tendons not Passing Tensionh3 3 mod = 1573]kp


Unadjusted Tendons: Tensionh.33.unmod = 1398ki

The tendon tension at the 60 year end of life:

Dome Tendons:

All Dome Tendons: Tensiond.6O = 1353 kip

Vertical Tendons:

Detensioned and Retensioned Tendons: Tensionv.6O.mod = 1539kip

Unadjusted Tendons: Tensionv.60.unmod = 1464 ki

Horizontal Tendons:

Detensioned and Retensioned Tendons Passing Tensionh.60.mod.SGR = 1498

'through SGR Opening Bay:

Detensioned and Retensioned Tendons not Passing Tensionh.60.mod = 1508kip


Unadjusted Tendons: Tensionh.6O.unmod = 1380kl

ip

kip

ip

p

kip

p

Calculation No.:MlkM PR Prepared By: )~ ~ 0102-0135-03MPR Associates, Inc. Revision No.: 0320 King StreetAlexandria VA 22314 Checked By: A" Page No.: 6

3.0 ASSUMPTIONS


There are no unverified assumptions.

3.2 Verified Assumptions

1. The thickness of the concrete replacing the delaminated concrete is approximately 10 inches, thewidth spans the entire span between buttresses 3 and 4, and the height spans between the top ofthe equipment hatch to approximately 10 feet below the bottom of the ring girder. Thesedimensions are consistent with the measured extents of the delamination with only the tendons thatpass 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 ProgressEnergy (see Lead Reviewer comments to this calculation).

3. The replaced concrete in the patch and the outer portion of the delamination will not beprestressed 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 thedelamination will have improved shrinkage properties (less shrinkage) compared to the existingconcrete when it was first placed. This assumption has been confirmed by Progress Energy (seeLead Reviewer comments to this calculation). '

Calculation No.:EAM PR Prepared By: 0102-0135-03MPR Associates, Inc. Revision No.: 0320AlxndraV 2 Checked By: Page No.: 7Alexandria VA 22314ChceByPaeN.7

A

C

Equipment Hatch

Figure 1. Delamination Boundary (Delamination shown in red)

Calculation No.:*OM P R Prepared By: 0102-0135-03

MPR Associates, Inc. Revision No.: 0320 King Street Checked By:Alexandria VA 22314. Page No.: 8

4.0 Methodology

The dome, vertical, and horizontal tendon losses are determined by considering losses from fourdifferent 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 RiverUnit 3 calculations (References 2, 3, and 7). These losses are used as a basis for determining the losses atthe end of steam generator replacement and at 60 years after SIT. The methodology for this calculation issimilar to that of Progress Calculation S08-0008 (Reference 14).

Calculation of the increase in tendon tension during an accident which increases containment pressure isnot included in this calculation.

-;ý" ýýCalculation No.:S M PR Prepared By: 0102-0135-03MPR Associates, Inc. Revision No.: 0320 King Street C e e B:ioa No.: 9

Alexandria VA 22314 Page By: 9

5.0 CALCULATION

5.1 Data

A,:= 9.723in2

E,:= 4.03 x 106 psi

E,:= 29x 106 psi

hopen := 27ft

Eltop.SGR:= 210ft

Wopen := 25ft

tdelam := lOin

Eltop.eq.htch := 157ft + lOin Eltop.eq.hatch 157.83ft

Elbot.ring.girder:- 250ft

Eltop.ring.girder := 267.5ft

Ldelam.ring.girder := loft

Elbot containment := 80.5ft

Eltop.basemat:= 93.Oft

Total cross section area of 163 wires in a singletendon; Ref. 1, page 6.

Elastic modulus of existing concrete; Ref. 16, page 4.

Elastic modulus of steel; Ref. 4, Table 38.

Height of SGR opening; Ref. 5.

Elevation of the top of the SGR opening; Ref. 5.

Width of SGR opening; Ref. 5.

Approximate thickness of the delaminated concrete;Assumption 3.2.1.

Elevation of the concrete at the transition to 3-6" wallthickness above the equipment hatch; Ref. 9.

Elevation of the bottom of the ring girder; Ref. 9.

Elevation of the top of the ring girder; Ref. 9.

Approximate distance from the bottom of the ringgirder to the top of the delamination boundary;Assumption 3.2.1.

Elevation of the bottom of containment; Ref. 15.

Elevation of the top of the containment basemat;Ref. 9.

Radial angle between adjacent buttresses; Ref. 9.

Average buttress width; Ref. 9.

Buttress thickness increase beyond containment wallthickness; Ref. 9.

Radial distance to liner inside surface; Ref. 9

abuttress:= 60deg

Wbuttress:= 12ft + 4.125in

tbuttress := 2ft + 4.5in

Rliner := 65ft

Wbuttress = 12.34ft

Calculation No.:* M PR Prepared By: )~ ~ 0102-0135-03MPR Associates, Inc. Revision No.: 0320 King Street By :PAlexandria VA 22314 Checked By: Page No.: 10

tiner 0.375in

tw~al :3.5ft

Stressdcreep.40:= 13.85ksi

Stressd.shrink. 40 2.90ksi

.. rt.40 5.50ksi

48. 5kip

d~a.i.ai := l530psi

Nominal liner thickness throughout most of thecontainment; Ref. 9.

Wall thickness between buttresses (undelaminated);Ref. 9.

Loss in dome tendon stress due to creep at 40 yearslife; Ref. 2, page 4.

Loss in dome tendon stress due to concreteshrinkage at 40 years life; Ref. 2, page 4.

Loss in dome tendon stress due to elastic shorteningat 40 years life; Ref. 2, page 4.

Loss in dome tendon force due to steel relaxation at40 years life; Ref. 7, Aft. F, page F2.

Loss in dome tendon force due to steel relaxation at35 years life; Ref. 7, Aft. F, page F2.

Average concrete compressive prestress in dome, indirection of tendon length; Ref. 3, page 49. As acheck of this value from Ref. 3 a scoping comparisonwas made to finite element analysis results for theCR3 containment. It was concluded that this is anappropriate stress for this calculation.

Basic creep for dome tendon loading beginning 180days after pouring, at 60 years life; Ref. 7, Att. G,page G5.

Basic creep for vertical tendon loading beginning 834days after pouring, at 60 years life; Ref. 7, Att. G,page G5.

Basic creep for horizontal tendon loading beginning964 days after pouring, at 60 years life; Ref. 7, Aft. G,page G5.

Basic creep for dome tendon loading beginning 180days after pouring, at 33 years life; Ref. 7, Att. G,page G5.

Basic creep for vertical tendon loading beginning 834days after pouring, at 33 years life; Ref. 7, Aft. G,page G5.

Creepd basic. 60 :- 0.35 x 10-61

psi

-6 1Creepv.basic.6 :60 0.25 x 10 .-

psi

CreePh.basic.60 :- 0.24 x

Creepdbasic.33 := 0.30 x

-6 110 .1

psi

-6 110 .-

psi

-6 1Creepv.basic.33:= 0.215x 10 .-

psi

Prepard By:Calculation No.:Prepared By: 0102-0135-03

MPR Associates, Inc. Revision No.: 0320 King Street ....Alexandria VA 22314 Checked By: ',/Y Page No.: 11

CreePh~basic33 :ý0. 205 x

Stressv~shrink.40: 2.90ksi

ForCev~reI..40 48.5kip

ForcevreI.35: 48.2kip

Vu.path := 1. 14

StreSSh~shrink.40: 2.90ksi

Forceh~relax40: 48.2kip

Forceh~rdea.35 47.9kip

GUTS 70 := 1635kip

-6 110 .spsi

Basic creep for horizontal tendon loading beginning964 days after pouring, at 33 years life; Ref. 7, Att. G,page G5.

Loss in vertical tendon stress due to concreteshrinkage at 40 years life; Ref. 2, page 2.

Loss in vertical tendon force due to steel relaxation at40 years life; Ref. 7, Aft. F, page F2..

Loss in vertical tendon force due to steel relaxation at35 years life; Ref. 7, Aft. F, page F2..

Ultimate creep coefficient for concrete in plug; Ref. 6.

Loss in horizontal tendon stress due to concreteshrinkage at 40 years life; Ref. 2, page 3.

Loss in horizontal tendon force due to steel relaxationat 40 years life; Ref. 7, Att. F, page F2..

Loss in horizontal tendon force due to steel relaxationat 35 years life; Ref. 7, Att. F, page F2..

Tendon lock off tension, equal to 70% of theGuaranteed Ultimate Tensile Strength (GUTS) pertendon; Ref. 1, page 14.

Total number of vertical tendons; Ref. 1, page 14.

Age of original concrete at SGR outage, starting fromthe date of containment Structural Integrity Test;Ref. 7, page 10 and Ref. 8, page 7.

Age of original concrete at end of plant life, startingfrom date of containment Structural Integrity Test;Assumption 3.2.2

Relative humidity for the containment outsideenvironment, in percent; Reference 17.

nv.tendon :ý144

Ageoutage := 3 3yr

Ageeo0 : 60yr

Ageoutage = 12053day

Ageeol = 21915day

;L:= 75

Calculation No.:50 M PR Prepared By 0102-0135-03MPR Associates, Inc. Revision No.: 0320 King Street CekdB:Pg o:1Alexandria VA 22314 Pg o:1

Forceh.relax.30 := 47.6k1p

Forcev.relax.30 47.8kip

Forced. relax. 33 48. Okip

Forceh.relax.33.unmod 47.88kip

Forcev.relax.33.unmod 48.Okip

Elavg.tend.space.bot:= 183ft + 10. 75in

Elavg. tend.space. top:= 212ft+ 8.25in

navg.tendspace := 19

rh.tendaon := 67ft + 8.625in

Horizontal tendon steel relaxation load at 30 years;Ref. 7, Att. F, page F2.

Vertical tendon steel relaxation load at 30 years;Ref. 7, Att. F, page F2.

Dome tendon steel relaxation load at 33 years;logarithmically interpolated from Ref. 7, Att. F,page F2.

Horizontal tendon steel relaxation load at 33 years;logarithmically interpolated from Ref. 7, Att. F,page F2.

Vertical tendon steel relaxation load at 30 years;logarithmically interpolated from Ref. 7, Att. F,page F2.

Bottom horizontal tendon elevation used to calculateaverage horizontal tendon spacing; Ref. 20.

Top horizontal tendon elevation used to calculateaverage horizontal tendon spacing; Ref. 20.

Number of tendons spanning betweenEl avg.tend. space. bot and Elavg.tend.space.top, inclusive;

Refs. 20 and 21.

Horizontal tendon placement radius; Ref. 24.

Number of buttresses in the containment; Ref. 9.nbuttress := 6

U M PRPrepred y: ~Calculation No.:

MPR Associates, Inc. Revision No.: 0320 King Street By:P1Alexandria VA 22314 Page No.: 13

5.2 Dome Tendons - 60 Years After Initial SIT

The dome tendons will not be detensioned or retensioned during the Steam GeneratorReplacement (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 at40 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 5.1for references):

Stressd.creep.40 = 13850psi

Stressdeshort.40 = 5500psi

StresSdshrink.40 2900psi

Forced relax.40StresSd~relax. 40 "At

where

Forced rea. 40 = 48.5kip At = 9.723 in 2

Stressdrelax.40 = 4988psi

Elastic Shortening

The dome tension losses due to elastic shortening do not change over time. The elastic shorteninglosses at 60 years after SIT are:

Stressd eshort.60 := StreSSdeshort. 40 Stressd.eshort.60 = 5500psi

Concrete Shrinkage

Industry experience shows that the majority of concrete shrinkage occurs in the early life of thecontainment. Since the containment was constructed over 30 years ago, nearly all of the shrinkagehas already taken place. At this point, shrinkage is essentially time-independent, and the concreteshrinkage at 60 years will be approximately equal to the concrete shrinkage predicted at 40 years.

StresSd shrink. 60 := StreSsd shrink. 40 Str"Sdshrink.60 = 2900psi

Calculation No.:M M P R Prepared By: 0102-0135-03MPR Associates, Inc. Revision No.: 0320 King Street ecked By:Alexandria VA 22314 Page No.: 14

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 alogarithmic scale. The losses calculated at 40 years will be extrapolated to 60 years based on thelast two data points from Reference 7, Att. F, page F2.

Forcedrelax.40 - Forced.relax. 35Forced.relax.6 0 := log(40) - log(35) (log(60) - log(3 5)) + Forcedrelax.35

Forced relax.60 = 49.4 kip

Forced relax. 60Stressd relax. 60 "-A, Stressd.relax.60 = 5082psi

where

Forced.relax.40 = 48.5kip Forced.relax.35 = 48.2kip At = 9.723in2

Creep

The basic creep determined from testing extrapolated to 60 years is (see Section 5.1 forreference):

-7]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 forreference):

Udaxial = 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 := od.axial'Creepd. basic.60" Es Stressd creep. 60 = 15529psi

where Es is the steel elastic modulus and is equal to:

Es = 2.9 x 10 7psi

Calculation No.:OI M P R Prepared By: ) 0102-0135-03MPR Associates, Inc. Revision No.: 0320 King StreetAlexandria VA 22314 Checked By: Page No.: 15

Total 60 Year Loss

The total tendon stress loss after 60 years is:

Stressd. total. 60 := StresSd.eshort.60 + Stresd.shrink.60 + Stressd.relax.60 + StreSSd. creep. 60

Stressd.totl.6 0 = 29011 psi

Converting the stress lost into a force per tendon that is lost:

Forced. total.60 Stressdtotal.6 0 .At Forced.total60 = 282. I kip

where

A, = 9.723in2

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.6 0 := Forcedesign - Forced.totaL.60 Tensionda60 = 1352.9 kip

Calculation No.:*IM P R Prepared By: ) 9 '-0102-0135-03

MPR Associates, Inc. Revision No.: 0320 King Street CPAlexandria 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 duringSGR while the tension in some other tendons will not change at all. The tendon tension at 60years will be calculated for each of the two sets of tendons individually. When calculating tendonlosses, all of the vertical tendons that are detensioned and retensioned will be considered to passdirectly through the SGR opening since cutting and repairing the opening will affect the region bothinside and around the SGR opening. The tendon tension at 60 years after the Structural IntegrityTest (SIT) of November 1976 (Reference 7, page 10) is determined by scaling the predictedtension at 40 years after SIT. The individual losses in the vertical tendons at 40 years after SITfrom steel stress relaxation and concrete shrinkage are as follows (see Section 5.1 for references):

StreSkshrink.40 = 2900psi

Forcev.relax.40Stressv. relax. 40 A,

where

Stressv.relax.4O = 4988psi

At= 9.723in2 Forcev.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.axiaI := nv.tendon GUTS7 0

where

Forcev~xial = 235440kip

nv.tendon = 144 GUTS 70 = 1635kip

The horizontal cross sectional area of concrete at approximately the mid height of the containmentis:

Av.contain 7r'[(Riiner + tiner + twall)2

- (Rliner + tliner)2] + n buttress*Wbuttress'tbuttress

Av.contain = 236807.3in2

where

Rliner = 65ft tliner = 0.375 in t wall = 3.5fi

Wbuttress = 12.34ft Wbntrss 1.34fttbuttress =2 .3 8 ft nbuttress = 6

Calculation No.:*MI P R Prepared By: )v 0102-0135-03MPR Associates, Inc. -. ;: Revision No.: 0320 King Street Checked By:lAlexandria VA 22314 Page No.: 17

The horizontal cross sectional area of the liner at approximately the mid height of the containmentis:

Avliner 7r'I(Rliner + tfiner)2 - Rtiner2]

Avliner 1 838.3 in2

The average elastic shortening losses for the vertical tendons are calculated based on the equationsfound in Section 2.1 of Reference 22. The vertical tension losses due to elastic shortening do notchange over time. Note that the proportion of load in the tendon conduit is conservativelyneglected from the calculation.

1 GUTS70Forcev'eshort'60"unmod := 2 (Av.contain - nv,tendon'At)'Ec + Av.liner'Es + nv.tendon'At'Es

Forcev.eshort.60.unmod = 31.84k'p

Forcev.eshort. 60. unmodStreSSv.eshort.60.unmod A,

Stressv.eshort.60.unmod = 3274psi

where

GUTS 70 = 1635kip E, =4.03x 10 6psi E, =2.9 x 10 7psi

A,= 9.723in2 ntendon = 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 bythe material properties of the concrete used to replace the plug and the delaminated concrete. Adiagram with the different areas of concrete represented as springs with different stiffnesses ispresented in Figure 2. For a unit width along the circumference of the wall passing through theSGR opening, the equivalent spring stiffness would equal:

Eeqtf 1

Ft 1 L3 1 L5Ee- tf Ee- te+Ed- td Ep-tf Ee..-te+Eartd Ee'tf

L2 L 4

Calculation No.:M M P R Prepared By: - , /,0102-0135-03MPR Associates, Inc. Revision No.: 0320 King Street Checked By: ,Alexandria VA 22314 Page No.: 18

Existing Wall L,

Delamination L2

SGR L

Open L3

L4

L5

Ee

EdEp

tf

te

td

L#

Figure 2. Spring Diagram for Vertical Stiffness of a Section ofUnit Width Passing through the Reconstructed SGR Opening.

= Existing concrete elastic modulus= Delamination concrete elastic modulus

= Plug concrete elastic modulus

= Full concrete wall thickness (between buttresses)

= Existing concrete thickness in area of delamination, inner portion

= Delaminated concrete thickness, outer portion

= Vertical length as defined in Figure 2

'// --. Calculation No.:&IM PR Prepared By: er0102-0135-03MPR Associates, Inc. I-;,J, Revision No.: 0320 King Street CPAlexandria VA 22314 Checked By: Page No.: 19

The value of each of the variables in the equation are defined below from inputs defined in Section5.1:

tf:= twall t f= 3 .5ft

L1 := Eltop.ring.girder - Elbot.ring.girder + Ldelam.ring.girder

L2:= Eltop.ring.girder - L1 - Eltop.SGR

L3 := hopen

L1 = 27.5ft

L2 = 30ft

L3 = 27ft

L4 = 25.17ft

L5 = 77.33ft

L4 Eltop.ring.girder - L1 - L2 - L3 - Eltop.eq.hatch

L 5 := Eltop.eq.hatch - Elbot. containment

td:= tdelam

te:= tf- td

td = 0.83ft

te= 2.67ft

Note that the wall thickness from the top of the ring girder to the bottom of the containmentbasemat (the entire span of the vertical tendons) is treated as a constant twal = 3.5ft eventhough the wall is much thicker in the ring girder, basemat, and lower portion of thecontainment wall. By not accounting for the stiffness of the thicker walls, this calculationwill be conservative.The ratio of the equivalent elastic modulus of the containment in the vertical direction passingthrough the SGR opening compared to the modulus of the existing concrete is calculated. Thecalculation is based on a modulus of elasticity that is 25% higher in the plug and delaminationcompared to the existing concrete. This calculation will determine the relative significance of theplug material properties on the effective elastic modulus used for scaling the elastic shorteninglosses. The 25% increased modulus is not intended to be a definitive estimate of the new concreteproperties but, rather, an estimate of the maximum difference in modulus of elasticity between newand old concrete. Based on Reference 16, 25% is a reasonable value for the difference in elasticmoduli.

Ee:= I

Ed:= 1.25.Ee

Ep := 1.25.Ee

Reference Factor

Ed= 1.25

Ep= 1.25

Calculation No.:* M P R Prepared By: 0102-0135-03MPR Associates, Inc. Revision No.: 0320 King StreetAlexandria VA 22314 Checked By: Page No.: 20

L1 + L2 + L3 + L4 + L5Ee: '.et le LEdt _L3 EeL+Etl "5'f

ty "- + + E-t + +

L2 L4

Eeq= 1.05

If the modulus of elasticity for the patch and delamination replacement concrete were 25% greaterthan the existing concrete, the equivalent elastic modulus for the wall would be 5% greater than themodulus of the existing concrete. The same percentage decrease in the equivalent elastic moduluswould be expected if the modulus of the patch and the delamination were 25% less than theexisting concrete. This is a small increase in modulus. To determine the elastic shortening lossesfor the detensioned and retensioned tendons, the predicted loss for the existing concrete would bescaled by the same percentage. Since the exact properties of the replaced concrete are notknown, the elastic shortening losses for the detensioned and retensioned tendons will beconservatively estimated to equal those of the unmodified tendons.

StreSSveshort.60.mod := Stressveshort.60.unmod StresSv.eshort.60.mod = 3274psi

Concrete Shrinkage

The majority of concrete shrinkage occurs in the early life of the containment. Since thecontainment was constructed over 30 years ago, nearly all of the shrinkage has already takenplace. At this point, shrinkage is essentially time-independent, and the concrete shrinkage at 60years will be approximately equal to the concrete shrinkage predicted at 40 years.

Stressv.shrink.60.unmod := StreSSv.shrink 40 StreSSv.shrink.60.unmod = 2900psi


The tendons that are detensioned and retensioned during SGR will only experience shrinkage inthe concrete that replaces the SGR opening plug and that replaces the delamination. Thereplacement concrete is low-shrinkage concrete (Reference 11), but the shrinkage losses in thisregion 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 entireheight of the containment (The entire span of vertical tendons).

M P PrearedBy:0102-0135-03

MPR Associates, Inc. Revision No.: 0320 King Street ,Alexandria VA 22314 Checked By: Page No.: 21

The total height of the containment is:

htotaI := Eltop.ring.girder - Elbot.containment htotal = 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

Ratiot.delam := - Ratiotdelam = 0.24

where

tde/am = loin twa/1 = 3.5ft

The shrinkage loss for the tendons that are detensioned and retensioned around the SGR openingis equal to:

(h opn h dl"

StreSsv. shrink. 60. mod := + o d Ratio.,shrink 40.htotal htotai M)

StreSSv. shrink. 60. mod 622psi

// / Calculation No.:&I M P R Prepared By: ) 0102-0135-03MPR Associates, Inc. Revision No.: 0320 King StreetAlexandria VA 22314 Checked By: ; Page No.: 22

Steel Relaxation

The steel relaxation losses at 40 years have been calculated previously (Reference 7, Att. F, PageF2). Based on Figure 5-26 of Reference 10, steel relaxation is linear with time on a logarithmicscale. The losses calculated at 40 years will be extrapolated to 60 years based on the last twodata points from Reference 7, Att. F, page F2.

Forcev.relax.40 - Forcev.relax.35Forcev.relax.6 0 : ("(log((g(60) -log(35)) + Forcevreax.3 5

Forcev.relax.60 = 49.4 kip

Forcev.relax. 60Stressv. relax. 60. unmod"-Stressv-relax.60.unmod = 5082psi

where

Forcev.relax.40 = 48. 5kip Forcevrelax.3s = 48.2kip At= 9.723in2

The detensioned and retensioned tendons will be active for the following number of years beforethe 60 year end of life is reached:

Agereten := AgeeoI - Ageoutage Agereten = 27 yr

Conservatively using the tendon steel relaxation loss at 30 years from Reference 7, Attachment F,Page F2:

Forcev. relax. 60.mod := Forcevrelax.30 Forcev. relax.60.mod = 47.8 kip

Converting the force loss to a prestress loss in the tendon:

Forcev. relax. 60.modStressv relax. 60.mod :=

Stressv.relax.60.mod = 4916psi

RPrepared By: 0102-0135-03

MPR Associates, Inc. Revision No.: 0320 King StreetAlexandria VA 22314 CekdB:I/I.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):

-7]Creepv.basic.60 = 2.5 x 10 --

psi

The ratio of the concrete stiffness to the total stiffness of the horizontal cross-section is calculatedbased on the equations in Section 2.1 of Reference 22.

Av.contain'Ec(Av.contain - nv.tendon At)'Ec + Av.iiner"Es + nv.tendon" At'E

RatiOv.concstiff = 0.92

where

Av.contain = 236807.3 in2

At = 9.723 in2

Ec = 4.03x 10 6psi

2Aviliner = 1838.3 in

nv.tendon = 144

E, = 2.9 x 107 psi

The average vertical prestress was calculated earlier in this section. For the stress contributing tocreep, elastic shortening and shrinkage losses are subtracted because they occur early in the life ofthe containment.

Forcev'axial - nv.tendon'( Stressv'eshort'60.unmod + Stressv'shrink'40)'At __...C7v.axial.creep := "lW(-Lv.conc.sliff

Av.contain

Crv.axialcreep = 8 77 psi

where

Force.axiaI = 235440kip StreSSv.shrink. 40 = 2900psi

Av.contain = 236807.3in2

Stressv.eshort.60.unmod = 3274psi

At = 9.723 in2

'// /Calculation No.:M P R Prepared By: 0102-0135-03

MPR Associates, Inc. ;, Revision No.: 0320 King StreetAlexandria VA 22314 Checked By: /ir Page No.: 24

The tendon prestress lost due to creep is calculated based on Page 4 of Reference 2. This valueis applicable to tendons that were not detensioned during the SGR:

Stressv. creep. 60. unmod := 0

7v.axial.creep* Creepv. bas ic.60"Es Stressv.creep.60. unmod = 6356psi


Es=2.9x 10 7psi

Creep losses for the tendons that pass through the patch are calculated separately by taking intoaccount the creep properties of the replacement concrete. The ultimate creep coefficient of thenew concrete is (see Section 5.1 for reference):

Vu.patch = 1.14

The ultimate creep coefficient must be adjusted for non-standard environmental and geometricalproperties in accordance with Reference 12, Section 2.5. There are also correction factorsassociated with concrete composition, but these have a smaller effect than geometrical andenvironmental properties and are neglected (Reference 12, Section 2.6).

The correction factor for the ultimate creep coefficient due to the relative humidity is expressed by(Reference 12, Section 2.5.4):

A = 75 Relative Humidity, (%)

y, := 1.27 - 0.0067.A L = 0.767

The volume to surface area ratio of the plug and the delamination is calculated as follows. Thewidth of the delamination is:

telamWdelam .= abuttress" Rliner + tliner + twall- 2 Wbuttress

Wdelam = 58. 99ft

where

aObuttress = 60deg Rliner = 65ft tliner = 0.38 in

twal! = 3.5ft tdelam = 10 in Wbuttress = 12.34ft

Prepard By:Calculation No.:SM PR PrprdB:) ~-0102-0135-03MPR Associates, Inc. Revision No.: 0320 King Street By: Pae o. 2Alexandria VA 22314 Checked By: Page No.: 25

The volume of the new concrete is:

Vnew := Wopen'twall'hopen + (Wdelam'hdelam - Wopen~hopen).tdelam

Vnew = 4511.7 ft3

where

Wopen = 25ft twa,, = 3.5ft hopen 27fl

tdelam 10 inWdelam = 58.99ft hdelam = 55.17ft

The only surface exposed to the environment for the new concrete is the outside surface of thecontainment. This area is equal to:

Snew:= Wdelam'hdelam

where

Wdelam = 58.99ft

Snew = 3254.04f 2

hdelam = 55.17ft

The volume to surface area ratio is:

WnewRatiovs -=

SnewRatiovs = 16.64 in

The correction factor to the ultimate creep coefficient for the volume to surface ratio is (Reference12, Section 2.5.5b):

2(s:= 0 + 1 0. 54.Ratiovs in)7 := •1 1.3 .e y, = 0.667

A correction factor must also be applied for operating temperature other than 70'F. Based onReference 23, operating temperature correction will have a small effect on the concrete creep rateand is, therefore, neglected.

A correction factor is also to be applied when load is applied other than 7 days after concreteplacement from Reference 12, Section 2.5.1. However, the ultimate creep coefficient wascalculated based on a loading age of 5 days, and the load is assumed to be applied at 5 days inthis calculation (see Assumption 3.2.3), so no correction for loading age is applied.

Calculation No.:MM W PR Prepared By: )~ ~ 0102-0135-03MPR Associates, Inc. Revision No.: 0320 King StreetAlexandria VA 22314 Checked By: 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):

Ycreep := Yvs'rl rcreep = 0.512

The new concrete will be under load for Ageretn = 27yr. The creep coefficient at the end of

this time is (Reference 12, Equation 2-8):

(Agereten + day) 0.6

Vt "= Vu.patch"Ycreep Vt = 0.561

10-+ (Agereten + day)0.6

Note that this equation is applicable to Types I and I1 concrete. The concrete is Type I inaccordance with Reference 6, page 3.

The tendon tension lost due to creep of the new concrete is scaled based on the tension lost dueto elastic shortening. Elastic shortening is a short term loss and creep is a long term loss. Thecreep loss can be scaled from the elastic shortening loss by the effective short term andage-adjusted elastic moduli. The age-adjusted elastic modulus accounts for additional strain dueto 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 notderived in Reference 14. It is derived here for clarity.):

Eeshort - os Eeshort "

Losscreep = LOSSeshort Feshor = LOSSeshort" E-- 1r'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 loadminus one is determined by rearranging equation 5-1 of Reference 12.

-- 1 = XvtEl,

where

Est = Modulus of elasticity for short term loads

Elt = Effective modulus of elasticity for long term loads

X = Aging coefficientvt = Creep coefficient

Calculation No.:JAW M P R Prepared By: 0102-0135-03MPR Associates, Inc. Revision No.: 0320 King Street CiAlexandria 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 is1 and the minimum value is 0.5. Conservatively assuming a value of 1 for X, the tendon loss -dueto creep in the new concrete can be calculated as follows based on combining the previous twoequations:

Losscreep = LOSSeshort* Vt

The total loss in the new concrete is scaled based on the proportion of the height andcross-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 inReference 3, page 45. The creep experienced by the existing concrete up to the beginning of theSGR outage (33 years) is:

Stressv.creep. 33. unmod := Crv.axiaL creep CreePv. basic.33.Es Stressv.creep.33. unmod = 5466psi

The total creep loss in the vertical tendons at 60 years is:

hopen h delam

Stressv.creep.60.mod := "(StreSSv.eshort.60.mod* V) + .R (S 1)...htotal htotal

+ -ohopen _ " Ratiodetam} (StreSSv.creep.60.unmod - Stressv.creep.33.unmod)k. htotal hltotal M)

Stress, creep. 60.mod = 1093psi

where

hopen = 27ft htota = 187 ft Stressv.eshort.60. mod = 3274psi

vt = 0.561 hdelam = 55.17ft Ratiodelam = 0.24

Stressv. creep. 60.unmod = 6356psi

Calculation No.:UM PR Prepared By: ) • 0102-0135-03MPR Associates, Inc. Revision No.: 0320 King Street ChceyAlexandria VA 22314 Chce By: Page No.: 28

Total 60 Year Loss

The total tendon stress loss after 60 years is calculated.

Unadjusted Tendons:

Stressv.total.60.unmod StresSv.eshort.60.unmod + StreSSv.shrink.60.unmod + StreSS. relax. 60. unmod + StreSsv.creep. 60. unmod

Stressv.total60.unmod = 17612psi

Detensioned and Retensioned Tendons:

Stressv. total. 60.mod "= Stressv.eshort.60.mod + StreSSv.shrink.60.mod + Stressv.relax.60.mod + Stressv.creep. 60.mod

Stressv.total. 60.mod 9906psi


Forcev.total.60.unmod := Stressv. total. 60. unmod. At Forcev.total60.unmod = 171.2kip

Forcev. total. 60.mod := Stressv.total60.mod At Forcev. total 60.mod = 96.3kip

where

A, = 9.723 in2

The design tension per tendon is (see Section 5.2 for original calculation):

Forcedesign = 1635kip

The remaining tension in the vertical tendons at 60 years is:

Tensionv.6 0.unmod := Forcedesign - Forcev.total.60.unmod Tensionv.60.unmod = 1463.8kip

Tensionv.6O.mod:= Forcedesign - FOrce. total. 60.mod Tensionv.60.mod = 1538.7 kip

Calculation No.:80M P R Prepared By: )cA~0102-0135-03MPR Associates, Inc. Revision No.: 0320 King Street Checked BY: Page No.: 29Alexandria VA 22314

5.4 Horizontal Tendons - 60 Years After Initial SIT

Some of the horizontal tendons near and away from the SGR opening will be detensioned andretensioned during SGR while the tension in some other tendons will not be changed. The tendontension at 60 years will be individually calculated for the detensioned and retensioned tendons thatpass through the SGR opening bay, the detensioned and retensioned tendons that do not passthrough the SGR opening bay, and the tendons that are not detensioned. The tension losses forthe tendons that pass through the SGR opening bay will be calculated considering all of thesetendons to pass directly through the SGR opening since cutting and repairing the opening willaffect the region both inside and around the SGR opening. The tendon tension at 60 years afterthe Structural Integrity Test (SIT) of November 1976 (Reference 7, page 10) is determined byscaling the predicted tension at 40 years after SIT. The individual losses in the horizontal tendonsat 40 years after SIT from steel stress relaxation and concrete shrinkage are as follows (seeSection 5.1 for references):

StresSh.shrink.40 = 2900!psi

Forceh~relax.40

Stressh. relax.40 Stressh.reax.40 = 4957 psiAt

whereAt = 9. 723 in2 Forceh.rea.40 48.2kip

Elastic Shortening

The total circumferential force from a single horizontal tendon tensioned to lock off load is:

Forceh.axia; := GUTS70 Forceh.axial = 1635 kip

where

GUTS70 = 1635kip

The average spacing between horizontal tendons near the containment mid-height is:

Elavg.tendspace.top - Elavg.tendspace.botSh~avg := agtedsce-. sh.avg = 19.19in

navg.tendspace

where

Elavg.tend.space.top = 212.69ft Elavg. tend space. bot= 183.9ft navg.tend.space = 19

'// /Calculation No.:S M P R Prepared By: 0102-0135-03

MPR Associates, Inc., . Revision No.: 0320 King Street V 1k :NAlexandria VA 22314 Checked By:j? . Page No.: 30

The average elastic shortening losses for the horizontal tendons are calculated based on theequations found in Section 2.1 of Reference 22. The horizontal tension losses due to elasticshortening do not change over time. These losses are applicable for the tendons that are notdetensioned during the SGR. Note that the proportion of load in the tendon conduit isconservatively neglected from the calculation.

1 Forceh~aial

Forceh~eshort.60unmod .och~xa -.-

2 (Sh.avg'twall - At)'Ec + Sh.avg'tliner'Es + At'Es

Forceh.eshort.60.unmod = 62.29kip

ForCeh~eshort. 60. unmod

StresSh.eshort.60.unmod A,

A,

StresSh.eshort.60.unmod = 6407 psi


For tendons that are adjusted during SGR, the elastic shortening stress losses will be affected bythe material properties of the concrete used to replace the plug and to replace the outer portion ofthe delaminated concrete. As demonstrated in Section 5.3, the effect of the plug stiffness has asmall effect on the elastic shortening losses, so the elastic shortening losses are estimated to be thesame 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 thecontainment was built over 30 years ago, nearly all of the shrinkage has already taken place. Atthis point, shrinkage is essentially time-independent, and the concrete shrinkage at 60 years will beapproximately equal to the concrete shrinkage predicted at 40 years.

StresSh.shrink.60.unmod := StresSh.shrink. 40 Stressh.shrink.60.unmod = 2900psi


Calculation No.:& M P R Prepared By: 0102-0135-03

MPR Associates, Inc. Revision No.: 0320 King Street C BAlexandria VA 22314 Checked By: Page No.: 31

The tendons passing through the SGR opening bay that are detensioned and retensioned duringSGR will only experience shrinkage in the concrete that is replaced inthe plug and that replacesthe delamination. The replacement concrete is low-shrinkage concrete (Assumption 3.2.4), butthe shrinkage losses in this region will conservatively be set equal to the shrinkage losses of theoriginal concrete at 40 years. However, the results will be scaled based on the proportion of thespan of new concrete to the entire span of the containment wall.

The total circumferential length of a horizontal tendon is:

Wtotal ý 2abuttress'rh. tendon + Wbuttress wtot = 154.17 ft

where

abuttres, = 1.O5rad Wbuttress = 12.34ft rh.tendon = 67. 72ft

The span of the SGR opening is (see Section 5.1 for reference):

Wopen = 25ft

The circumferential length of the repaired delamination, excluding the span of the SGR opening, is:

Wdelam.sub.SGR abuttress'rh.tendon - Wbuttress- Wopen

Wdelam.sub.SGR 33.57ft

where

abuttres, = 1.O5rad 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 Section5.3 for original calculation):

Ratio,.delom = 0.24

The shrinkage loss for the tendons that are detensioned and retensioned around the SGR openingis equal to:

StreSshshrnk.60mod.SGR ' + .aRatsoudGml Stressh'shrink.40Wtotal Wtotal

St re~ksshrink. 60.mod.SGR = 621 psi

Calculation No.:&IM PR Prepared By: ) f0102-0135-03MPR Associates, Inc. Revision No.: 0320 King Street Cek By:Alexandria VA 22314 Checked By: Page No.: 32

The detensioned and retensioned tendons that do not pass through the SGR opening bay will notexperience 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, PageF2). Based on Figure 5-26 of Reference 10, steel relaxation is linear with time on a logarithmicscale. The losses calculated at 40 years will be extrapolated to 60 years based on the last twodata points from Reference 7, Att. F, page F2.

Forceh'relax"40 - Forceh'relax'35Forceh.relax.6 0 log(40) - log( .(Iog(60) - log(35)) + Foreh relax35

Forceh.relax.60 = 49. 1 kip

Forceh.relax.60Stressh. relax. 60. unmod := StresSh. relax. 60. unmod = 5051 psi

where

Forceh.relax.40 = 48. 2kip Forceh.relax.35 = 47.9kip A, = 9.723in2

The detensioned and retensioned tendons will be active for the following number of years beforethe 60 year end of life is reached (see Section 5.3 for original calculation):

Agereten = 27yr

Conservatively using the tendon steel relaxation loss in the horizontal direction at 30 years fromReference 7, Attachment F, Page F2:

Forceh.relax.60.modSGR := Forceh.relax.30 Force,

Converting the force loss to a prestress loss in the tendon:

Forceh relax. 60.mod.SGR

Stressh. relax. 60. mod.SGR -= StressA,

hz.relax. 60. mod.SGR = 47.6kip

h.relax.60.modSGR = 4896psi

*~~Z /~ rpae y Calculation No.:&I M PR PrprdB:0102-0135-03MPR Associates, Inc. , Revision No.: 0320 King Street /hecke BAlexandria VA 22314 Checked By: •/s, Page No.: 33

This loss is also appropriate for the detensioned and retensioned tendons that do not pass throughthe 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):

-71Creeph.basic .60 = 2.4 x 10 -

psi

The ratio of the concrete stiffness to the total stiffness through the cross-section of the containmentwall is calculated based on the equations in Section 2.1 of Reference 22.

Ratihonc~flstiff :Sh.avg'twallEc

(Sh.avgtwall - At).Ec + Sh.avg'tliner'Es + At'Es

Ratioh.conc.stiff = 0.88

For the stress in the concrete contributing to creep, elastic shortening and shrinkage losses aresubtracted because they occur early in the life of the containment.

GUTS70 - (Stressh'eshort.60"unmod + StresSh'shrink.40)"At _Uh.axial creep := " KatlOh.conc.stiff

Sh.avgltwall - At

Uh.axial creep = 1703psi

where

StresSh.eshort.60.unmod = 6407 psi StresSh.shrink.40 = 2900psi

A, = 9.723 in2

5h.avg = 19.19 intwall = 3.5ft

GUTS70 = 1635 kip

Calculation No.:S M PR Prepared By: 0102-0135-03MPR Associates, Inc. Revision No.: 0320 King Street Checked By:Alexandria VA 22314 Page No.: 34

The tendon prestress lost due to creep is cacltdbsdonPg .fRfrec .Ti au

The tendon prestress lost due to creep is calculated based on Page 4 of Reference 2. This valueis applicable to tendons that are not detensioned during the SGR:

Stressh. creep. 60. unmod : h. axiaL creep Creeph.basic. 6 0Es Stressh.creep. 60. unmod = 11850 psi


Es=2.9x 10 7psi

Creep losses for the tendons that pass through the patch are calculated separately by taking intoaccount the creep properties of the replacement concrete. The creep properties have beencalculated 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 andcross-sectional ratio of the new concrete to the horizontal tendon lateral span and total thicknessof the containment wall. The remaining concrete will creep following the same trend from themeasured data in Reference 3, page 45. The methodology used here is duplicated from Section5.3 of this calculation. The creep experienced by the existing concrete up to the beginning of theSGR outage (33 years) is:

StresSh. creep.33. unmod := 'h.axial.creep Creeph. basic.33Es Stressh.creep.33.unmod = 10122psi

where

-71Creeph.basic.33 = 2.05x 10 -7

psi

The total creep loss in the horizontal tendons at 60 years is:

StresSh. creep. 60. mod. SGR := Wop'(StresSh.eshort.60.mod" V) + Wdelam.sub.SGR atiot.delam'(Stressh.eshort. 60.mod V)Wtotal Wtotal

+ Wtotal - Wopen - Wdelam.sub.SGR .Ratiotdejam) (Stresshcreep60unmod - Stresshcreep33unmod)

Wtotal Wtopo,

// / Calculation No.:M'IM P R Prepared By: )A 0102-0135-03MPR Associates, Inc. Revision No.: 0320 King Street CcdyIPgN:Alexandria VA 22314 Checked By- Page No.: 35

Stresh creep. 60.modSGR 2127 psi

where

Wopen = 25ft 154.17 ft Streskheshort.60.mod = 6407psi

vt = 0.561 Wdelam.sub.SGR = 33.57ft Ratiotdetam = 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:

Stresshtotal.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.totaL60.mod StresSh. eshort. 60.mod + Stressh.shrink. 60.mod + Stressh.relax. 60. mod + Stressh. creep. 60. mod

Stressh.total.60.mod 13031 psi

Detensioned and Retensioned Tendons that Pass through SGR Opening:

Stressh.totaL60.mod.SGR := StresSh.eshort.60.modSGR + Stresh.shrink.60. mod SGR + Stressh.relax.60.mod.SGR + StresSh.creep.60.modSGR

Stressh.total. 60.modSGR = 14050psi

Calculation No.:* M PR Prepared By: 0102-0135-03MPR Associates, Inc. Revision No.: 0320 King Street ChckdiyAlexandria VA 22314 Checked By: Page No.: 36


Forceh. total. 60. unmod := Stressh.total.60.unmod.At Forceh. total. 60. unmod = 254.8kip

Forceh.total.60.mod := Stressh.total.60.mod At Forceh. total. 60. mod = 126. 7kip

Forceh. total. 60.mod.SGR := Stressh. total 60.mod.SGR. At Forceh.total.60.mod.SGR = 136.6kip

where

At = 9.723 in2


Forcedesign = 1635 kip

The remaining tension in the horizontal tendons at 60 years is:

Tensionh.60.unmod := Forcedesign - Forceh.total60.unmod TensiOnh.60.unmod = 1380.2koip

Tensionh.60.mod := Forcedesign - Forceh.total.60.mod Tensionh.60.mod = 1508.3kip

Tensionh.60.od.SGR := Forcedesign - Forceh.total60.mod.SGR Tensionh.60.modSGR = 1498.4kip

Calculation No.:

W MRPrepared By: 0102-0135-03MPR Associates, Inc. Revision No.: 0320 King Street Cc :PAlexandria VA 22314 Checked By: Page No.: 37

5.5 Dome Tendons - After SGR Completion

After the Steam Generator Replacement Project is completed, the containment will only haveexperienced 33 years of its 60 year life. The tendon losses are expected to be less at this timecompared 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 yearswill be equal to the elastic shortening losses calculated for 60 years in Section 5.2.

StreSSd eshort.33 : StresSd.eshort. 60 Stressd.eshor,.33 = 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 areappropriate for the 33 year losses.

StresSd.shrink.33 := StresSd.shrink.60 StreS~csdhrilk.33 = 2900 psi

Wire Relaxation

The wire relaxation losses are interpolated from Reference 7, Appendix F, Page F2. The wirerelaxation loss at 33 years is:

Forced.relax.33 = 48kip

Converting this load into a stress loss in the tendon:

Stressd.relax.33 Forcedrelax StresSd.relax.33 = 4937 psiA,

&I M R Prpare By:0102-0135-03

MPR Associates, Inc. Revision No.: 0320 King Street Checked By:Alexandria VA 22314 C. Page No.: 38

Creep

The tendon tension loss due to creep can be calculated using the basic creep at 33 years. Thebasic creep at 33 years is defined in Section 5.1:

-71Creepd.basic.33 = 3.00 x 10 -7

psi

The stress in the dome in the direction of the dome tendons is (see Section 5.1 for reference):

Ud.axial = 1530psi

The creep loss at 33 years is:

Stressd. creep.33 := Creepd. basic. 33. d.axial'Es Stressd.creep.33= 13311 psi

where

Es = 2.9 x 10 7psi,

Total Loss at 33 Years


StreSsd. total.33 := StreSSd. eshort. 33 + StresSd.shrink.33 + StresSd.relax.33 + Stressd.creep.33

Stressd total.33 26648psi


Forced.total.3 3 := Stressd total.33"At Forced.total.33 = 259. 1kip

where

At = 9.723 in2


Forcedesign = 1635 ip

Calculation No.:

MR A P R Prepared By: 0102-0135-03MPR Associates, Inc.ReionN.0320 King Street Checked By:

Alexandria VA 22314 Checked By: Page No.: 39

The remaining tension in the dome tendons at 33 years is:

Tensiond.3 3 := Forcedesign - Forced.total.33 Tensiond.33 = 1375.9 kip

Calculation No.:*OM P R - Prepared By: 7 A 0102-0135-03

MPR Associates, Inc. Revision No.: 0320 King Street Checkd ByAlexandria VA 22314 Checked By: Page No.: 40

5.6 Vertical Tendons - After SGR Completion

After the Steam Generator Replacement Project is completed, the containment will only haveexperienced 33 years of its 60 year life. The tendon losses are less at this time compared to thelosses 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 yearswill be equal to the elastic shortening losses calculated for 60 years in Section 5.3. These lossesare 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

Stressv.eshort.33. mod := StreSSv.eshort.60. mod Stressv.eshort.33. mod = 3274psi

Concrete Shrinkage

For the existing concrete, the concrete shrinkage losses will be essentially independent of timeafter 33 years. Therefore, the concrete shrinkage losses calculated for the 60 year end of lifecalculated in Section 5.3 are appropriate for the 33 year losses for these tendons. For thetendons that are detensioned and retensioned, the new concrete will not have experienced anysignificant shrinkage immediately after the tendons are retensioned.

StreSSvshrink.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 lossesare applicable for the tendons that are unadjusted during SGR. The tendons that are detensionedand retensioned will not experience any significant relaxation immediately after they areretensioned.

Forcev.relax.33.unmod = 48.0 kip

Calculation No.:* M P R Prepared By: 0102-0135-03MPR Associates, Inc.4. Revision No.: 03 2 0 K in g S tre e t e ....



StrS~. elx. 3.unod:ýForcev~relar33.unmodStresvre~33umodA,

Stressv.relax.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 basiccreep at 33 years. This calculation was performed in Section 5.3. The creep loss in the tendonsthat are unadjusted is equal to this value. The tendons that are detensioned and retensioned donot experience any significant creep immediately after retensioning.

Stressv.creep. 33.unmod = 5466psi

Stress, creep. 33.mod := 0



Stressv.total.33.unmod Stressv.eshort.33.unmod + StreSSv.shrink.33.unmod + StreSSv.relax.33.unmod + Stressv.creep.33.unmod

Stressvtotal.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


Forcev.totaL.33.unmod := Stressv. total. 33. unmod" At

Forcev.total.33.mod := StreSsv total.33.mod A,

Forcevtotal.33.unmod = 161.2kip

Forcev.totaL 33.mod = 31.8kip

where

At= 9.723in2

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-nsion per tendon is (see Section 5.2 for original calculation):

635 kip

ig tension in the vertical tendons at 33 years is:

od := Forcedesign - Forcev.total33.unmod Tensionv.33.unmod = 1473.8 klp

Forcedesign - Forcev. total.33.mod Tensionv.33.mrod = 1603.2 kip

ing the basicin the tendons-tensioned do

v.creep.33. unmod

!.mod

// / Calculation No.:* M PR Prepared By: ~ -0102-0135-03MPR Associates, Inc. Revision No.: 0320 King StreetChceByAlexandria 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 haveexperienced 33 years of its 60 year life. The tendon losses are less at this time compared to thelosses 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 yearswill be equal to the elastic shortening losses calculated for 60 years in Section 5.3. These lossesare applicable to both tendons that are detensioned and retensioned and those that are not.

Stresh.eshort.33,unmod := Stresheshort.60.unmod

Stressh.eshort. 33.mod := StresSh. eshort. 60.mod

StresSh eshort.33.modSGR := Stressh.eshort.60.mod.SGR

StresSh.eshort.33.unmod = 6407psi

Stressh.eshort.33. mod = 6407 psi

StreSSheshort.33.mod.SGR = 6407psi

Concrete Shrinkage

For the existing concrete, the concrete shrinkage losses will be essentially independent of timeafter 33 years. Therefore, the concrete shrinkage losses calculated for the 60 year end of life inSection 5.3 are appropriate for the 33 year losses for these tendons. For the tendons that aredetensioned and retensioned, the new concrete will not have experienced any significant shrinkageimmediately after the tendons are retensioned.

StresSh,shrink.33.unmod := Stressh.shrink.60.unmod Streshshrink.33.unmod = 2900psi

Streshshrink.33. mod := 0

Streshshrink.33.mod.SGR := 0

Wire Relaxation

The wire relaxation losses are interpolated from Reference 7, Appendix F, Page F2. These lossesare applicable for the tendons that are unadjusted during SGR. The tendons that are detensionedand retensioned will not experience any significant relaxation immediately after they areretensioned.

Forceh.relax. 33.unmod = 47.8kip

Calculation No.:OI M P R Prepared By: 0102-0135-03MPR Associates, Inc. Revision No.: 0320 King Street Checked By: PIaAoAlexandria VA 22314 Page No.: 44


Ste8/t rla. 3.unod:-Forceh.relax.33. unmodStreshrel~~unA, Stressh.relax.33.unmod = 4916psi

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 basiccreep at 33 years. This calculation was performed in Section 5.3. The creep loss in the tendonsthat are unadjusted is equal to this value. The tendons that are detensioned and retensioned donot experience any significant creep immediately after retensioning.

Stressh.creep.33.unmod = 10122psi

StresSh. creep. 33. mod := 0

StresSh. creep. 33. mod. SGR := 0



Stresshtotal.33.unmod := Stressh.eshort.33.unmod + StresSh.shrink.33.unmod + Stresrh.relax.33.unmod + Streskhcreep.33.unmod

Stressh.total.33.unmod = 24345psi

Stressh. total 33. mod := StresSh.eshort.33.mod + Stressh.shrink.33. mod + StreSSh.rel.33. mod + StresSh.creep.33. mod

Stressh.total.33.mod 6407 psi

Stresshtotal.33.modSGR := Stressh.eshort.33.modSGR + StresSh.shrink.33. mod SGR + StresSh.relax.33.modSGR + StresSh.creep. 33.modSGR

Stressh. total 33. mod.SGR = 6407 psi

// Calculation No.:*OM P R Prepared By: )v 0102-0135-03

MPR Associates, Inc. ,Revision No.: 0320 King StreetAlexandria VA 22314 Checked By: Page No.: 45


Forceh. total.33.unmod := Stressh.totaL33.unmod At Forceh. total.33. unmod = 236. 7kip

Forceh. total. 33.mod := Stressh. total 33 mod* At Forceh.total.33.mod = 62.3 kip

ForCeh.total.33.mod.SGR := Stressh.total.33.modSGR At Forceh.totaL.33.mod.SGR = 62.3kip

where

At = 9.723 in2


Forcedesign = 1635 kip

The remaining tension in the horizontal tendons at 33 years is:

Tensionh.33.unmod := Forcedesign - Forceh.total33.unmod Tensionh.33.unmod = 1398.31kip

Tensionh.3 3 .mod := Forcedesign - Forceh total.33.mod Tensionh.33.mod = 1572.7 kip

Tensionh.33.modSGR := Forcedesign - Forceh. total 33. mod.SGR Tensionh.33.modSGR = 1572.7 kip

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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, Formulas for Stress and Strain, McGraw Hill, 5thEd., 1975.

5. Progress Energy Drawing 421-347, Sheet 1, "Reactor Building Temporary Access Opening forSGR Vertical & Horizontal Tendon Positions," Rev. 0.

6. S&ME, Inc., "Phase I Test Report Mix Acceptance Testing for Crystal River Unit 3 SteamGenerator Replacement Project," June 19, 2009.

7. Florida Power Calculation S-95-0082, "6th Tendon Surveillance - Generation of Tendon ForceCurves," Revision 3.

8. Progress Energy Calculation S06-0004, "Containment Shell Analysis for Steam GeneratorReplacement - Properties of New Concrete for Access Opening and Number of Hoop andVertical Tendons to be De-tensioned," Revision 0.

9. Florida Pow :, Corporation Drawing SC-421-03 1, "Reactor Building Exterior Wall - Concrete

Outline," Rev. 4.

10. Crystal Riv .:,A 3 Final Safety Analysis Report, Rev. 31.3.

11. Gilbeft 2-I.•,sociates Inc. Calculation 1.01.8.

12. A,-erican Co - . -iJ -ýc 'tandard ACI 209R-92, "Prediction of Creep, Shrinkage, and-ifure i`ffects in Concrete Structures," 1992.

13. Prescon .WG 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 GeneratorReplacement - 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.

Calculation No.:* M PR Prepared By: ) /-0102-0135-03MPR Associates, Inc. evision No.:0320 K ing S treet C hecked By:

Alexandria VA 22314 Page No.: 47

16. MPR Calculation 0102-0135-02, "Concrete Modulus of Elasticity and Minimum CompressiveStrength."

17. Relative Humidity Data from January 2004 to September 2006 at Brooksville, FL, University ofFlorida 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/1WL Inspection Hoop Tendon "42"Layout," Revision 1.

22. USNRC Regulatory Guide 1.35.1, "Determining Prestressing Forces for Inspection ofPrestressed Concrete Containments," July 1990.

23. Email from J. Holliday (Progress Energy) to K. Gantz (MPR), Subj: FW: Temperature Effect onCreep, 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.

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AReference 23

From: Holliday, John [[email protected]]Sent: Thursday, January 07, 2010 6:14 AMTo: Bird, Edward; Gantz, KevinCc: Dyksterhouse, Don; Knott, RonaldSubject: FW: Temperature Effect on CreepGentlemen,Attached e-mail is from Prof. Domingo Carreira the Chairman of the sub-committee that prepared ACI209 and specifically authored the section that addresses the effects of temperature on creep, he is alsothe individual who designed the concrete mix for CR3 SGR. Based on his observations I believe we canexclude operating temperature as a factor in determining the creep ratio.

Regards,

John Holliday

From: [email protected] [mailto:[email protected]]Sent: Wednesday, January 06, 2010 1:10 PMTo: Holliday, JohnSubject: 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 Ithink he provides enough basis for not applying a temperature adjustment.

Chris SwardProject ManagerSargent & Lundy312-269-7426

----- Forwarded by CHRIS A SWARD/Sargentlundy on 01/06/2010 12:08 PM -----

From: DOMINGO CARREIRA <[email protected]>

To: [email protected]

Date: 01/05/2010 11:21 PM

Subject: Re: Temperature Effect on Creep


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Calculation No. Prepared By

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Chris:

Testing may recollection is a little bit risky, however the question is on a subject that Iam familiar with, plus it was a good idea to send me the CR3 report to refresh what wedid in 2007.

As you well said, ACI 209 Report discuss briefly the subject of the temperature effectson creep and shrinkage and gives some estimates but no factor is given to quantify it. Imust confess that I personally wrote this portion of the report at the request of the lateJim Rhodes.

The same limitation on the effects of temperature on creep and shrinkage occurs withthe other 3 methods of predictions given in the latest revision of ACI 209-2R recentlypublished. The reason is the same for the four methods in ACI 209-2R, we don't haveenough information to evaluate it and to propose an acceptable coefficient forcorrection. 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 ourmethods. This sad admission was approved by the authors of the other 3 methods inACI 209-3R, that is, Bazant, Gadner, and Muller. Branson the author of the original 209method 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 higherthan 70 F will not be of concern for the following reasons:

1. Despite the temperature of the concrete during operating conditions as well as theexterior temperature in Florida will be higher than 70F, this higher temperature will notincrease significally concrete creep and shrinkage, since their values from the standardtesting temperature are very low compared with the majority of the concrete on whichthe prediction methods are based on.

2. The operating temperature will be by far lower than the initial acceleratedautogenous curing temperature from the cement heat of hydration. This highautogenous temperature is not present in the standard testing methods for creep andshrinkage.

3. Most of the effect of high operating temperatures on creep and shrinkage is causedby the driving out of the concrete the water uncombined with cement. Approximately


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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. Theremaining of the mixing water may evaporate from the concrete This problem isdrastically reduced by the fact that in our concrete the free evaporable water is lowcompared 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 (3inches), and by the use of fly ash and silica fume that will combine chemically withsome 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 concretemixture are conditions that help to reduce the effects of temperatures higher than thetesting temperatures. We know that some of the high strength concretes have lowercreep and shrinkage than normal strength concretes because of the lesser free water inthese concretes.

5. The higher operating temperatures will mostly affect the top portion of thecontainment away from the replacement concrete.

I could continue elaborating on this subject, but I think that the given reasons makesense..

I will return to Chicago from California tomorrow January 6, 2010 and could visit youthe coming Thursday or Friday.

My best wishes in this 2010, Domingo

From: "[email protected]" <[email protected]>To: Domingo Carreira <[email protected]>; [email protected]: Tue, January 5, 2010 10:55:08 AMSubject: 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 theCR3 containment analysis. Part of the study works through the computation of effective modulus basedon creep. The creep coefficient computation (following ACI-209R) applies a number of adjustments fornonstandard conditions. ACI 209R discusses temperature as a factor although it does not provide aspecific adjustment factor. Our temperature during operation will be somewhat above the standard 70degF. Do you recall why we did not include a temperature adjustment?


MPR Associates, Inc.SM PR 320 King StreetAlexandria, VA 22314

Calculation No. Prepared By Checked By Page: A-4

0102-0135-03 ,, <'/ - Revision: 0

Chris SwardProject ManagerSargent & Lundy312-269-7426





Client:


Project: Task No.

CR3 Containment Delamination0102-0906-0135

Title: Calculation No.

Finite Element Model Description 0102-0135-04


1-21-2010 1-21-2010 1-21-2010Peter Kevin Gantz Edward Bird 0Peter Barrett






RECORD OF REVISIONS


0102-0135-04

Revision IAffected Pages Description

0 All Initial Issue

Note: The revision number found on each individual page of the calculation carries the revisionlevel of the calculation in effect at the time that page was last revised.



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Table of Contents

1.0 Introduction ...................................................................................................... 4

1.1 Background .......................................................................................................... 4

1.2 P u rp o se ......................................................................................................................... 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 G eom etry .................................................................................................................... 12

4.2 M aterial Properties ............................................................................................... 14

5.0 Model Benchmarking Results .................................. 15

6.0 Assumptions .................................................................................................... 19

7.0 Com puter Codes ............................................................................................. 20

8.0 References ..................................................................................................... 20





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1.0 INTRODUCTION

1.1 Background

A project is underway at Progress Energy's Crystal River Unit 3 (CR3) site to replace the steamgenerators. As part of that project, 10 vertical and 17 horizontal tendons were detensioned and anopening was cut into the concrete containment above the equipment hatch. As this opening wasbeing cut, cracking in the concrete wall was identified around the full periphery of the opening inthe cylindrical plane of the wall. The cracking is located at the approximate radius of thecircumferential tendon conduits, and is indicative of a delaminated condition. Progress Energyplans 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 designbasis loading conditions. Limited results from the model are provided for benchmarking. Resultsof repair and design basis analyses performed with the model, including the detensioningsequence, 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-steelreinforcing. The cylindrical wall is prestressed with a post-tensioning system in the vertical andhorizontal (hoop) directions. The dome roof is prestressed utilizing a three-way post-tensioningsystem. The inside surface of the reactor building is lined with a carbon steel liner to ensure ahigh degree of leak tightness during operating and accident conditions. Nominal liner platethickness is 3/8 inch for the cylinder and dome and 1/4 inch for the base. (Note that the linerplate 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 linerplate. 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 tothe spring line. The shallow dome roof has a major radius of 110 feet, a transition radius of 20feet 6 inches, and a thickness of 3 feet.





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2.0 SUMMARY OF RESULTS AND CONCLUSIONS

This calculation documents the development of the CR3 Containment finite element model forrestoration and design basis analyses. The benchmarking results provided in Section 5 show afavorable comparison between the finite element membrane stresses and a hand calculation ofmembrane stresses for the intact containment.

3.0 METHODOLOGY

A three-dimensional finite element model is developed for the CR3 containment restoration anddesign basis analyses. The model includes linear'-elastic material behavior with the exception ofthe steel liner which is modeled as elastic-plastic. The effects of concrete creep on prestress arerepresented in the finite element model by a reduction of tendon tension through time (Reference7). 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 basisanalyses includes the following features:

* The model represents a symmetric portion of the building (1800) with the symmetry planepassing through the center of the steam generator replacement opening and center of theequipment 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 thesteam generator opening and the containment wall as well as the boundary between thedelaminated concrete and the intact concrete in the plane of the cylindrical wall. The


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stiffness of these elements is varied to represent the delamination or continuous bond of theintact and repaired building

5. Surface-to-surface contact elements are used to model the delamination stage in thecontainment wall. Contact elements are also used to bond the SGR plug to the existingconcrete.

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 nonlinearthrough-thickness stress distribution that cannot be captured using conventional shell modeling.Using the element birth and death features of ANSYS, these brick elements can accuratelyrepresent the incompatibility of the stress-free concrete used for repairs and the pre-loadedbuilding deformation pattern.

The cylindrical portion of the wall is modeled as 42-inch thick concrete, with the exception ofthe wall that contains the opening for the steam generator replacement. This portion of the wallis modeled in two separate sections, a 10-inch thick delaminated portion on the outside surfaceof the wall, and the remaining intact 32-inch thick portion of the wall. The portion of the wallthat is modeled as delaminated is the area bounded laterally by the two adjacent buttresses, andvertically by the transition to a 42-inch thick wall above the equipment hatch and a horizontalline at elevation 240 ft (approximately 10 feet below the bottom of the ring girder). Thisrectangular area surrounds the opening used for steam generator replacement and is somewhatgreater than the actual delaminated area. 1 -D springs are added to the interface surfaces of thedelamination 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 softsprings eliminate tensile load transfer across this boundary.

The area in the containment wall that was removed to form an opening for steam generatorreplacement is modeled using independent elements which have coincident nodes with the edgesof the containment. Prior to removal of the section, the model uses stiff springs to bond theelements to the containment wall. Element birth and death is used to kill the elements in theopening simulating the plug being cut. The plug region remains in the model but carries nostiffness or loads and when replaced appears as stress and strain-free material. After the tendonsaround the opening are detensioned and the new concrete is installed, the springs at the interfaceare eliminated (set to a negligibly small stiffness) and contact elements are used to bond theinterface 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 arecoincident with the containment (brick) concrete element nodes. These coincident nodes allow





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for direct coupling between the concrete and tendon elements in the two directions normal to thetendon. The truss elements are described in more detail below.

Figure 3-1 shows the 1800 model. The buttresses are modeled with brick elements to capturetheir eccentric stiffness and to provide tendon attachment points. The basic dimensions of thecontainment model are presented in Section 4.1. The personnel hatch and other localizedgeometry, with the exception of the equipment hatch, were not modeled since they are remotefrom the steam generator opening. A scoping submodeling analysis of the equipment hatchshowed that the hatch modeling shown below is adequate for performing repair and design basisanalyses. The regions remote from the opening are unaffected by the steam generatorreplacement; their presence will not affect the global model results near the SGR opening anddelamination.

3.1.2 Ring Girder and Dome

In the finite element model, the ring girder and dome are represented by uniform areas sweptabout the vertical axis of the containment. This representation is exact for the dome and nearlyexact for the ring girder. The dome and ring girder elements are joined by constraint equationsrather than by shared nodes. The dome delamination and repair are considered to have anegligible effect on the purpose of this calculation and therefore are not represented in the finiteelement model. All of the dome tendons are considered to be fully tensioned.


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Figure 3-1 Finite Element Model of CR3 Containment Building



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3.1.3 Tendons

Truss elements are used to model the vertical and hoop tendons to provide flexibility inevaluating 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 thecontainment wall where load transfer is required between hoop tendons and the containmentwall. Vertical tendons are each modeled as a single truss element with nodes at the top of thering girder and at the bottom of the basemat. Rigid beam elements are used at the buttresses forthe hoop tendons, and at the top of the ring girder and bottom of the basemat for the verticaltendons to connect the ends of the tendons to the containment. This modeling distributes thetendon 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 containmentwall is used to transfer load between the hoop tendons and the containment wall. The axialdegrees of freedom of the tendons are fixed, but are not tied to the containment wall. The fixedaxial displacement allows for an initial strain to be used to define the tendon forces in theseelements. Forces are derived directly from the stresses and tendon areas. However since thebuilding deformation effects the stress, the strain required to define the tendon forces requires aniterative approach to ensure the proper tendon force is applied. Thus, each element is given adifferent 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 (2.5degree 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 12.75inches (typically) whereas pairs are typically separated by 38.12 inches (Reference 12).

Tendons are initially tensioned to 80% of Guaranteed Ultimate Tensile Strength (GUTS) andthen the load is reduced to 70% of GUTS. For horizontal tendons, this procedure results in atendon force curve that is best represented by a uniform tendon tension along the length of thetendon. 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 strainsare 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 forcescaused by load re-distribution. The re-distribution of load also occurs during the de-tensioning ofhoop tendons.




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Tendon material and structural properties are defined below. Figure 3-2 illustrates the verticaland hoop tendons in the model.

The dome tendons are modeled in a similar manner as the vertical and hoop tendons, but sincethere is no detensioning required, the dome tendons are removed in the final model withprestress applied to the dome using equivalent forces. The dome tendons are modeled with anindependent truss element mesh with coincident nodes aligned with the dome brick elements. Inthe process of constructing the model, these independent nodes are constrained in all directionsand the tendon preload is applied using initial strains as described above. Reaction forces arecalculated at all of the common nodes, and these forces are explicitly applied to the domeelements. The dome tendon truss elements are then removed. The dome tendon ring girder forcesare distributed to the concrete elements via stiff beams. Modeling the dome tendons explicitly isnot necessary since these tendons will not be detensioned. Dome tendon forces are adjusted toaccount for loss of tendon tension due to aging phenomenon (e.g. concrete creep) in a manneranalogous to the process for the hoop and vertical tendons (Reference 7).




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----------------------

-------------- -

Figure 3-2 Hoop and Vertical Tendons for the 180' Model

3.1.4 Liner

The liner is included in the model to account for the structural interaction between it and theconcrete containment. The liner plate is modeled as a single layer of four-node shell elements onthe inside face of the containment building. The liner is modeled as %-inch thick on the insidesurface of the cylindrical portion and dome and 'A-inch thick on the bottom surface ofcontainment (Reference 2, page 34). The liner plate thickness is increased to 1.125 inchesaround the equipment hatch.


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3.2 Boundary Conditions

Displacement boundary conditions are defined to prevent rigid body motion of the containmentbuilding 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 fodindation.

Symmetry boundary conAditions are applied to constrain all nodes at the centerline of the modelto have zero displacement in the normal (global z) direction. For the tendon nodes that have beenrotated into a cylindrical coordinate system the symmetry constraint is applied to the local hoopor y direction.

A single point at the center of the foundation is constrained in the lateral "x" direction to preventrigid body motion. This does not prevent rocking type motion that would occur in the buildingand the reaction force at this node is negligible.

Vertical support of the building is achieved using an elastic foundation. The elastic foundationstiffness is defined using a layer of surface effect elements placed under the basemat. Thefoundation 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


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 10Transition)

Dome Radius of Curvature (Dome Middle) 110 ft 0.375 in Reference 10

Dome Thickness 3ft Reference 10





0102-0135-04 Revision: 0


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 10Girder)

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 Basematto Equipment Hatch Centerline 39 ft Reference 10

Equipment Hatch Opening IR1 11 ft 4.5 in Reference 10

Equipment Hatch Centerline Vert. Distance to 3.5 ft 25 ft 10 in Reference 10Thick Cyl. Wall

Transition Radius of Curvature from Cyl. To 20 ft 0.375 in Reference 10Basemat

Slab Thickness 2 ft Reference 10

Note 1: The equipment hatch is modeled as a square opening with an equivalent area of thecircular opening prescribed in the table.

Table 4-2 Miscellaneous Component Dimensions


Hoop Conduit Placement Radius1 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


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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 isless than 1% of the total wall thickness and is less than 5% of the conduit diameter. Thedifference in results for the global model is judged to be insignificant.

4.2 Material Properties

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 hasexisted for the entire life of the plant and for concrete that is used to replace the delamination andthe SGR opening. Concrete properties are listed below.

Elastic modulus

Existing Concrete

Replacement Concrete

4.03 x 106 psi

5.12 x 106 psi

Reference 3, page 4

Reference 3, page 4

Poisson's Ratio

All Concrete

Density

All Concrete

0.2

150 lb/ft3

Reference 2, page 3

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 30.0ksi (Reference 2, page 34). The tendon wire in all post-tensioning conduit is ASTM A421-65steel with a yield strength of 240 ksi (Reference 2, page 5). The typical density, stiffness, andPoisson's ratio of steel are used for these materials, taken from Reference 4, Table 38. The


MPR Associates, Inc.FIM PR 320 King StreetAlexandria, VA 22314


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coefficient of thermal expansion is taken from Reference 5, Table TE-l and is only applied to theliner.

Elastic modulus 29 x 106 psi Reference 4, Table 38

Poisson's ratio 0.27 Reference 4, Table 38

Density 0.283 lb/in3 Reference 4, Table 38

Thermal Expansion Coefficient 6.83 x 10-6 in/in/0F Reference 5, Table TE-1(Avg. from 70'F to 281°F)

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 themodel so that if it becomes overstressed, the liner will yield and relieve itself of load. The yieldpoint 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 modelconsidering 95% of the deadweight plus tendon preload (1474 kips for the vertical tendons and1398 kips for the hoop tendons) are compared to hand calculations. The linearized hoop andvertical membrane stresses were obtained at the SGR opening mid-height elevation. Figures 5-1and 5-2 show color contour plots of hoop and vertical stress respectively. The linearized stressesare 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 handcalculated hoop stress is 1560 psi; the hand calculated vertical stress is 957 psi. The handcalculated hoop stress is within 5% of the finite element result; the hand calculated vertical stressis within 3% of the finite element result.





0102-0135-04 Revision: 0

h 157.ft

3ri:= 65.ft + 3-in

8

ri 65.031 ft

ro =ri + 42.in

ro 68.531 ft

tb 28.in

Lb 12.ft+4.125.in

Nb:= 6

Nv:= 144

Nh 94

TV 1474000.lbf

Th 1398000.4bf

Pc:= 150. lbf

ft3

tdome := 3.ft

hrg := 16.ft + 4.in

27hsro90,ft +-2fthsgro 103.5ft

3.tliner:= in

Ec 4.03.106.psi

EI .29:106 psi

Containment height

Containment concrete inside radius (Reference 8)

Containment concrete outside radius (Reference 8)

Buttress thickness (Reference 8)

Average buttress width (Reference 8)

Number of buttresses (Reference 8)

Number of vertical tendons (Reference 2, page 14)

Number of hoop tendons (282 total 1 3 per loop = 94 loops,Reference 2, page 14)

Vertical tendon tension (Reference 7, page 5, unadjusted tendon)

Hoop tendon tension (Reference 7, page 5, unadjusted tendon)

Concrete density (Reference 2, page 3)

Dome thickness (Reference 2, page 1)

Ring girder height (Table 4-1, above)

Mid-height of the SGR opening (Table 4-1, above)

Liner thickness (Reference 10)

Concrete elastic modulus (Reference 3, page 4)

Liner elastic modulus (Reference 4, Table 38)

The approximate concrete area of a vertical section through the full height of thecontainment wall is calculated below:

ah := h.(ro - ri) ah = 549.5ft2





0102-0135-04 4iJ- - Revision: 0

The approximate steel liner area of a vertical section through the full height of thecontainment wall is calculated below:

alh := h-tliner alh = 4.906ft2

The average hoop stress in the containment wall is calculated below considering theeffect of the liner:

NhTh ah-Ecah ah.Ec+ alhEi

The area of a horizontal section through the containment is calculated below. The areacontribution of the buttresses is included. The area contribution of the vertical conduits is notdeducted because the conduits are not represented in the finite element model.

aa:= -r 02 - ri2) + Nb.Lbtb aa = 1641ft2

The average vertical stress due to tendon tension is calculated belowconsidering the effect of the liner:

The approximate steel liner area of a vertical section through the full height of thecontainment wall is calculated below:

alv = 2 -n.ritliner alv = 12.769ft

2

Nv.TV aa.Eca a= va = 850psi

aa aa• Ec + alv. El

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 discand the ring girder is approximated as a cylindrical section. (Note that the deadweight is asmall contribution to the vertical stress. Consequently, these approximations are consideredacceptable.)

Wshell := Pc' (h - hsgro),aa Wshell = 13.17 x 106 lbf

Wrg := Pc.•.hrg'[(ro+tb)2- ri2j Wrg= 6.102 .106 lbf

Wdome:= Pctdomeri Wdome = 5.979 x 106 lbf

The average vertical stress due to deadweight of the concrete above the mid-height ofthe SGR opening is estimated below

Wshell + Wrg + Wdome 7•dw:= dw 107 psiaa

The total vertical stress due to tendon tension and deadweight at the SGR opening

mid-height is calculated below:

Cajot:= ca + "dw %a tot = 957 psi





0102-0135-04 Revision: 0

Stress results linearized through the wallthickness at the mid-height of the SGR opening

=NSYS 11.0SPIPLOT No. 1NCI9AL SCILUTIJNSTEP-1SUB =1TINE-1SY (AVW)TCPRSYS-5EMX =1.194SPIN -4767SMX -3661

-2500- -2000

-1500

0500

-10001500

2000

Figure 5-1 Hoop Stress


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Stress results linearized through the wallthickness at the mid-height of the SGR opening

AMIYS 11.0SPIPLOT NO. 2N[]DAL S=•3ICNSTEP-1SUB -1

sz (A\A)TlOPRSYS=5

-MX =1. 194SMt =-3186SW4 -1398

-2500I -2000

-1500-1000-500~0

S500100015002000

Figure 5-2 Vertical Stress

6.0 ASSUMPTIONS

1. The tendons are assumed to be symmetric about the 150 degree azimuth through the center ofthe SGR opening. This assumption is reasonable because of the staggered design of the hooptendons, the load application they apply to the building is nearly uniform radial compressionwhich would make the loading symmetric about the centerline of each buttress. For theintact building cases, the response predicted in the finite element model is the same betweeneach 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.





0102-0135-04 Revision: 0

7.0 COMPUTER CODES

This analysis was performed with the ANSYS general purpose finite element program, Version11.0 SPI. The analysis was performed on a Sun v40z server running the Suse Linux 9.0operating 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.


3. MPR Calculation 0102-0135-02, Rev. 0, "Concrete Modulus of Elasticity and MinimumCompressive Strength."

4. Roarke, Raymond J. and Warren C. Young, Formulas for 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, Guide for Mechanistic-Empirical Designof New and Rehabilitated Pavement 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-UpInput to Technical Issues Discussed at 3 rd 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 SGRVertical & Horizontal Tendon Positions," Revision 0.

13. Computer output file 0102-0135-04-1 and 0102-0135-04-2.





Client:

Progress Energy Page 1 of 12plus Attachment

Project: Task No.

CR3 Containment Calculations0102-0906-0135

Title: Calculation No.

Concrete Modulus of Elasticity and Specified Compressive Strength 0102-0135-02


L0J. L. Hibbard Chris Bagley P. Butler

1-16-2010 1-16-2010 1-16-2010


This document has been prepared, checked, and reviewed/approved in accordance with the Quality Assurancerequirements of 1 OCFR50 Appendix B, as specified in the MPR Quality Assurance Manual.



OM PR 320 King StreetAlexandria, VA 22314

RECORD OF REVISIONS


0102-0135-02 Ž .


0 All Initial Issue




MPR Associates, Inc.OLM PR 320 King Street



0102-0135-02 Revision: 0

Table of Contents

1.0 Purpose ......................................................................................................... 4

2.0 Sum m ary ............................................................................................................... 4

3.0 Background ...................................................................................................... 5

4.0 Assumptions ................................................................................................... 5


4.2 Other Assumptions .................................................................................................. 5

5.0 Approach ....................................................................................................... 6

6.0 Calculation ........................................................................................................ 8

6.1 Design Inputs ........................................................................................................... 8

6.2 M odulus of Elasticity .................................................................................................... 9

7.0 References .................................................................................................... 11

Attachm ent .................................................................................................................. 13


Calculation No.:0 Prepared By: S 0102-0135-02

MPR Associates, Inc. Revision No.: 0320 King Street

//1J6,;


1.0 PURPOSE

This calculation determines the concrete elastic modulus and the concrete specified compressivestrength for original concrete and for new concrete for the Steam Generator Replacement constructionopening 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 concretefor maintenance conditions, design basis return to service conditions, and design basis end of lifeconditions are summarized in Table Ts.

"Concrete" 'Applicable"

"Conditions"

"Original" "Maint. / Repair"

i "Design Basis Return to Service")

"Original" k. "Design Basis End of Life" )"New" "Maint. / Repair"

(" Design Basis Return to Service""New" ( "Design Basis End of Life" J

"Elastic"

"Modulus"

"psi * E06"

4.03

4.03

5.12

5.12

"Specified Comp."

"Strength for"

'Allowable"

'Ipsi"l

6720

5000

6000

5000

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 usedinstead 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 analyticaluse. The concrete compressive strength (psi) used for the calculation of the elastic modulus is:

("Original" 5000n3 = "New" 7000)

Calculation No.:00 Prepared By: A .- , 0102-0135-02MPR Associates, Inc. Revision No.: 0320 King Street //I. i/ .Alexandria VA 22314 Checked By: Page No.: 5

3.0 BACKGROUND


4.0 ASSUMPTIONS


None.


None.

Calculation No.:

Prepared By: • . 0102-0135-02MPR Associates, Inc. Revision No.: 0320 King Street CW6A} A,


5.0 APPROACH

The concrete modulus of elasticity is calculated with the correlation provided in ACI 318-63 (Reference1.1, 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).

Ec = 33.Pc1"5.-If;

where Ec = static modulus of elasticity of concrete, psi

PC = density of concrete, Ib/ft 3

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 Reference1.2, Section 8.5). The correlation is based on a best fit to experimental data as shown in the followingfigure from Pauw's paper, Reference 5, Figure 2.

- 1F-- --4.,.-OF-- ]zIE ,:z~q .t"

. . . . . . ... . ....' t •. r..v ,l 14

Fig. 2--Corr.iation of teat Meta

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The Pauw correlation was based on lower strength concretes than are used today. The suitability of theACI 318-63/Pauw correlation for high strength concretes is established in Reference 9, ConclusionsSection, 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 (Reference1.1, Sections 1102 and 301). The concrete strength parameter in the Pauw correlation is the concretestrength at the time of the test (Reference 5, p. 681). The effect of this difference in definition of concretestrength on the calculated modulus of elasticity is evaluated in Section 6.2.

V~U~ Calculation No.:&IA M P R Prepared By: • ,'.. ,.A1'-,-==-. 0102-0135-02MPR Associates, Inc. Revision No.: 0320 King Street Checked7ByAlexandria VA 22314 Checked By: Page No.: 8

6.0 CALCULATION

6.1 Design Inputs

fe~orig 5000).si

fe~new 600*psi

cSpecified & Design Basis" Icase1 :=\ "5-year

Original concrete compressive strength.-Ref. 2, p. 2-Ref. 3, Results Summary, Class 5000concrete

case2:= I New concrete compressive strength.-Ref. 2, p. 2-Ref. 6 and Ref. 7, Table 1-Ref. 6 and Ref. 7, Table 1

c 144) lb151)t3 case3 C"Original"(s "New" )Concrete density-Ref. 4-Ref. 6 and Ref. 8, p. 6; Ref. 8 provides thetheoretical density and measured density for two

mixes, Options 1A and 2A. A density of 151 Ib/ft 3

is representative of the theoretical and measureddensities of the two mixes.

Measured modulus of elasticity from CR3 concretecores-Ref. 14 for all cores but Core 59-Ref. 15 for Core 59

core :="core 16-1" 3.75"10 6

"core 16-2" 4.05'106"core 40-1" 3.15"106"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"106

Ec.meas := core (2)psi

Calculation No.:I M P R Prepared By: S A-- . 0102-0135-02

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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 ( f,,.orig = 5000psi ) and 5-year

compressive strength (fo,.oig 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 takenfrom the CR3 containment is:

Ec.avg.m := mean(Ec.meas) Ec.avg.m = 3.29 x 10 6psi

where Ec.meas =

3.75

4.05

3.15

2.95

2.7

3.1

3.3

3.35,

.106 psi

The calculated modulus of elasticities for the specified compressive strength and the 5-year compressivestrength are:

.Pc1 1.5 fc'.orig.,Ec rigi.:= 33"psi. Pc,+ ) " pIlb -ft3) Ps

4.03 x 10 6

Ec.orig = psi

p4.67 x 1 06

"Specified & Design Basis"

case1 = \ "5-year"

wherelb

pc 144-

1 ff3

(5000 .

( 6 72 0 )case = "Specified & Design Basis"

"5-year"

Calculation No.:M M P R Prepared By: • . 0102-0135-02MPR Associates, Inc. Revision No.: 0320 King Street bJ/674Alexandria 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 106psi to a

high of Ec.orig2 = 4.67 x 106psi 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. Thiscalculated modulus is consistent with ACI 318-63, the design basis for the CR3 containment. Theelastic modulus for the original concrete is:*

Ec.orig = 4.03 x 106 psi

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.

Ec~ew:=Pc2 Ffc'.new3

lb+f psi

Ec.new = 5.12 x 106 Psi

lb

where pc2 = 151 lb fcnew3 7000psi

ff,

This elastic modulus is for the new concrete from the time the concrete reaches at least its 5-day strengthof 6000 psi to the end of plant life. Use of a single modulus for this time period is justified based on thescatter in results for the elastic modulus correlation shown in the figure in Section 5.0.

Calculation No.:Prepared By: • ."- • 0102-0135-02

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7.0 REFERENCES

1. American Concrete Institute, "Building Code Requirements for Reinforced Concrete."

1.1 ACI 318-631.2 ACI 318-05


3. Florida Power Corporation Document Identification No. S-00-0047, As-built ConcreteStrength for Class 1 Structures, Revision 0.

4. Email from Mr. J. Holliday (PE) to Mr. K. Gantz (MPR), 12-30-2009, 10:35 AM, Subject:Concrete Density.

5. A. Pauw, "Static Modulus of Elasticity of Concrete as Affected by Density," Journal of theAmerican Concrete Institute, Vol. 57, 1960, pp. 679-687.

6. Email from Mr. J. Holliday (PE) to Mr. J. Hibbard (MPR), 1-7-2010, 3:42 PM, Subject:Comments Calculation 0102-0135-02.

7. Progress Energy Specification CR3-C-0003, "Specification for Concrete Work for Restorationof 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 GeneratorReplacement 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 CompressiveStrength 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 ofElasticity of Self-Consolidated Concrete: Bayesian Approach," Journal of EngineeringMechanics, April 2009, pp. 295-306.

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12. G. Washa, J. Saemann, and S. Cramer, "Fifty-year Properties of Concrete made in 1937," ACIMaterials Journal, July-August, 1989, pp. 367-371.

13. Progress Energy Final Safety Analysis Report (FSAR), Containment System & Other SpecialStructures, Chapter 5, Revision 31.3.

14. S&ME Document Transmittal No. 09-208-03, S&ME Project No. 1439-08-208, November16, 2009.

15. S&ME Document Transmittal No. 09-208-05, S&ME Project No. 1439-08-208, November24, 2009.

Calculation No.:Prepared By: Ž 0102-0135-02

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Attachment

The attachments are:

0 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: CommentsCalculation 0102-0135-02.

Message Page 1 of 1

Hibbard, Jim


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:[email protected]]Sent: Wednesday, December 30, 2009 10:01 AMTo: Knott, Ronald; Holliday, JohnCc: Hibbard, JimSubject: 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 itin SOO-0047.

Kevin

---- -Original Message -----From: Knott, Ronald [mailto:[email protected]]Sent: Wednesday, December 16, 2009 10:15 AMTo: Holliday, JohnCc: Gantz, KevinSubject: FW: Concrete Density

John,Can you direct Kevin to the density reference. I don't know where the original data came from fordensity. I was only quoting what I heard in the meeting. I assumed it was in the S00-0047 attachments.

From: Gantz, Kevin [mailto:[email protected]]Sent: Tuesday, December 15, 2009 6:22 PMTo: Knott, RonaldCc: Dyksterhouse, Don; Holliday, John; Bird, Edward; Butler, PatrickSubject: Concrete Density

Ron,

During our previous meeting you received some original information on the concrete density. I rememberyou saying later that the concrete density was 144 or 145 pcf. Do you have a reference or an actualnumber so that I can make sure I have the correct modulus calculated?

Thanks,

Kevin

12/30/2009

of I

Hibbard, Jim


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 TestReport.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 openingand repair of the delamination are 6000 and 7000 psi respectively. This requirement for the new concrete iscontained in Attachment 1 of specification CR3-C-0003 and in S&MEs phase II Test Plan. Additionally, thetheoretical unit weight of the new concrete is 151 pcf as reported in the S&ME Phase II Test Report.

Regards,

John Holliday

From: Hibbard, Jim [mailto:[email protected]]Sent: Thursday, January 07, 2010 2:47 PMTo: Holliday, JohnSubject: 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

Email - From: Dyksterhouse, Don [don.dyksterhouse@pgnmail ...

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