ML102871036
| ML102871036 | |
| Person / Time | |
|---|---|
| Site: | Crystal River  |
| Issue date: | 01/08/2010 |
| From: | Dyksterhouse D Progress Energy Co |
| To: | George T Office of New Reactors |
| References | |
| FOIA/PA-2010-0116 0102-0135-01, 0102-0135-jlh-2 | |
| Download: ML102871036 (29) | |
Text
Sengupta, Abhijit From: Dyksterhouse, Don [don.dyksterhouse@pgnmail.com]
Sent: Friday, January 08, 2010 8:17 AM To: Thomas, George Cc: Dyksterhouse, Don; Lake, Louis
Subject:
Approved calculations Attachments: 0102-0135-jlh-2 Radial Pressure at Tendons rOsigned.pdf; Approved January 6 0102-0135-01 effective elastic modulus rO.pdf
- George, will change as we place two approved MPR calculations. Please note that the numbers
-01;-Please find the calculations in the ProgresstheEnergy attached document control system.
0102-0135-jih-2 Radial Pressure at Hoop Tendons ý?CW I!
0102-0135-01 Reinforcement Ratio and Effective Modulus of Elasticity (P)/13
MPR Associates, Inc.
&M PR 320 King Street Alexandria, VA 22314 CALCULATION TITLE PAGE.
Client:
Progress Energy Page 1 of 15 Project: Task No.
CR3 Containment Calculations 0102-0906-0135
Title:
Calculation No.
Radial Pressure at Hoop Tendons 0102-0135-jlh-2 Preparer / Date Checker / Date Reviewer & Approver / Date Rev. No.
J. L. Hibbard Kevin Gantz Edward Bird 11-11-2009 11-11-2009 11-11-2009 QUALITY ASSURANCE DOCUMENT This document has been prepared, checked, and reviewed/approved in accordance with the Quality Assurance requirements of 10CFR50 Appendix B, as specified in the MPR Quality Assurance Manual.
MPR-QA Form QA-3.1-1, Rev. 1 a
MPR Associates, Inc.
OM PR 320 King Street Alexandria, VA 22314 RECORD OF REVISIONS Calculation No. Prepared By Checked By Page: 2 Aet PagesDescrip 0102-0135-jlh-2Rvsn Revision IAffected Pages Description 0 All Initial Issue Note: The revision number found on each individualpage of the calculation carries the revision level of the calculation in effect at the time that page was last revised.
MPR Associates, Inc.
320 King Street IM PR Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 3 0102-0135-jlh-2 , . - " Revision: 0 Table of Contents 1.0 Purpose........................................................................................................ 4 2.0 Sum m ary ...................................................................................................... 4 3.0 Background...................................................................................................... 4 4.0 Assum ptions ................................................................................................... 5 4.1 Unverified Assumptions ........................................................................................ 5 4.2 Other Assumptions ................................................................................................. 5 5.0 Calculation........................................................................................................ 6 5 .1 D ata ............................................................................................................................... 6 5.2 Radial Pressure from Hoop Tendon ........................................................................ 8 5.3 Radial Pressure in Concrete .................................................................................... 9 5.4 Radial Pressure at Reduced Area ........................................................................... 13 6.0 References ..................................................................................................... 15 MPR QA Form: QA-3.1-3, Rev. 0
60M PR MPR Associates, Inc.
Prepared By: Ž .. , -
Calculation No.:
0102-0135-jlh-3 Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: Page No.: 4 1.0 PURPOSE This calculation determines the radial pressure in the Crystal River 3 containment at the location of the hoop tendons. The radial pressure is determined for two values of the concrete elastic modulus, a nominal value based on the ACI correlation and the minimum value from CR3 design basis calculations.
The radial pressure is also determined for three area cases. This is the area that is assumed to carry the radial load. The first is the base case with no area reduction. The second removes the area of the horizontal tendon. The third removes the area of the horizontal and vertical tendons.
2.0
SUMMARY
The radial pressure at the location of the hoop tendons is provided in Table Ts.
'Area" "Nominal" "Minimum" )
"Reduction" "Modulus" "Modulus" Ill, "NoArea Removed" 28.2 27.1 Ec = 25x106psi "HorizontalConduit" 38.8 37.3 "Horizontal& Vertical Conduit" 45.6 43.8 Notes:
- 1. The radial pressure value does not account for stress intensification at the tendon conduits.
3.0 BACKGROUND
A project is underway at Progress Energy's Crystal River Unit 3 site to replace the steam generators.
As part of that project, an opening has been cut into the concrete containment above the equipment hatch. As this opening was being cut, cracking in the concrete wall was identified. The crack is around the full periphery of the opening and is in the cylindrical plane of the wall. The cracking is located at the radius of the circumferential tensioning tendons, and is indicative of a delaminated condition.
Calculation No.:
Prepared By: Ž ."- ,* 0102-0135-jlh-3 MPR Associates, Inc. Revision No.: 0 320 King Street C e k Be Alexandria VA 22314 Checked By: Page No.: 5 4.0 ASSUMPTIONS 4.1 Unverified Assumptions There are no unverified assumptions.
4.2 Other Assumptions
- 1. It is assumed that the tension in a tendon is T = 1635.kip based on Reference 2, p. 15. This is the tendon tension at lockoff.
- 2. It is assumed that there is negligible change in thickness of the concrete due to the radial pressure from the tendons. This is a reasonable assumption since the radial strain is negligible.
Calculation No.:
IM PR MPR Associates, Inc.
Prepared By: Ž .-. , 0102-0135-jlh-3 Revision No.:0 320 King Street C ek By R e No.: 0 Alexandria VA 22314 Checked By: , Page No.: 6 5.0 CALCU LATION 5.1 Data Containment ri:= 65.ft+ 0.375.in ri= 65.03 ft Concrete containment inside radius; Ref. 1.1 ro:= ri + 3.5.ft r= 68.53 ft Containment outside radius; Ref. 1.1 Containment concrete minimum strength; Ref. 2, p. 2 o-:= 5000.psi A scoping calculation shows the interface pressure is not sensitive to this input lb W:= 150. Containment concrete density; Ref. 2, p. 3 E ,l:= 33.psi. ( Nominal and low values of elastic modulus for concrete; Ref.
lb -ft' 4, p. 51 and Ref. 5, Page 1.01.7/6, Note 4 6
EC2 := 2.5.10 .psi 6
4.287 x 10i E,= 2.5 x 1 06 ps Tendons T =- 1635.kip Hoop tendon tension at lockoff; Assumption 4.2.1 rHT := 812.375.in rHT= 67.7 ft Hoop tendon radius at conduit centerline; Ref. 2, p. 15 (210.ft+ 6.75.in) - (181.ft+ 8.75.in) Average vertical spacing of hoop tendons at the Yt"= approximate elevation of the access opening for the steam 18 generator replacement; Ref. 1.2 Yt = 19.22.in
Calculation No.:
i MP R MPR Associates, Inc.
Prepared By:
ŽA- _ l 0102-0135-jlh-3 Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: Page No.: 7 rVT:= 807375.in rVT = 67.28 ft Vertical tendon radius at conduit centerline; Ref. 2, p. 15 Xt:=
L(+16 6060,I38+-I 9
4] deg-rVT Average horizontal spacing of vertical tendons at the approximate location of the access opening for the steam generator replacement; Ref. 1.2 Xt = 35.23.in d,:= 5.25.in Tendon conduit outside diameter; Ref. 2, p. 4 Containment Liner Es:= 29.106.psi Elastic modulus for steel; Ref. 3, Table 38, steel for bridges and buildings tl:= 0.375.in Containment liner thickness; Ref. 1.1
A MP R MPR Associates, Inc.
Prepared By: Ž ..-
- Calculation No.:
0102-0135-jlh-3 Revision No.: 0 320 King Street
- By Alexandria VA 22314 Checked By: Page No.: 8 5.2 Radial Pressure from Hoop Tendon The figure below is a free body diagram for a hoop tendon.
T T Hypothetical Hoop Tendon Free Body Diagram A force balance in the up/down direction as shown by the figure gives:
7r-0=-2.T-+2. Frsin(O).rtdO 0
Solve for the radial force per unit circumferential length of the tendon on the containment. Use the radius to the inner most point of the conduit as the effective radius for the hoop tendon.
rt := rHT - - rt = 809.75 .in 2
T Ibf Fr := - Fr = 24230.
rt ft The radial pressure on the containment created by all of the hoop tendons is Pr, which is equal to Fr (radial force per unit circumferential length for a single hoop tendon) divided by the average vertical spacing between hoop tendons.
' Fr PrY:= - Pr = 105psi Yt
Calculation No.:
6 M P R Prepared By: .*..\ % 1 0102-0135-jlh-3 MPR Associates, Inc. - Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: Page No.: 9 5.3 Radial Pressure in Concrete This section determines the radial pressure in the concrete at the radius of the inner most surface of the hoop tendon conduit. The figure below shows three cylinders, one for the containment concrete at a larger radius than the tendon, a second for the concrete at a smaller radius than the tendon, and a third for the containment liner.
Cylinder
- Cylinder 3 (Containment Liner) li Cylinder 2
Hoop /
Tendon Plan View of Containment Loads acting on the three cylinders are as follows:
- Cylinder 1. The radial interface pressure between Cylinders 1 and 2 exerts a radial inward pressure on Cylinder 1.
"Cylinder 2. The radial interface pressure between Cylinders I and 2 exerts a radial outward pressure on Cylinder 2. The tendon exerts a radial inward pressure on Cylinder 2. The radial interface pressure between Cylinder 2 and the containment liner exerts a radial outward pressure on Cylinder 2.
- Cylinder 3. The radial interface pressure between Cylinder 2 and the containment liner exerts a radial inward pressure on Cylinder 3.
Calculation No.:
SMPR Associates, Inc.
M P R Prepared By: Ž ._ . 0102-0135-jlh-3 Revision No.: 0 320 King Street Checked By:
Alexandria VA 22314 By: Page No.: 10 The net internal pressures acting on Cylinders 1, 2, and 3 as a function of the interface pressures are:
P1(PI.2) := -P1.2 P 2 (Pl.2 , P 2 .3) := -P, + P1.2 + P2.3 P3(P2.3) := -P2.3 where P1 = net internal pressure on cylinder 1 P2 = net internal pressure on cylinder 2 P3 = net internal pressure on cylinder 3 Pr = radial pressure from hoop tendons P1.2 = interface radial pressure between cylinders 1 and 2 P2.3 = interface radial pressure between cylinders 2 and 3 The radial displacements of the three cylinders are equal (Assumption 4.2.2).
Ar 1 = Ar 2 = Ar 3 Define a function to calculate radial displacement in a thin wall cylinder for an internal pressure (Ref 3, Equations 2.2.4 and 2.4.2 with a 1=O):
2 P.r Ar(r, P, t, E):=-
The parameters r and t for the three cylinders are:
rl:= rt r, = 67.48ft t:= ro - rt t1 = 1.05ft r2 := ri r2 = 65.03ft t2 := rt - ri t2 = 2.45ft r3 := ri - tl r3 = 65ft t 3 = 0.0312 ft
Calculation No.:
Prepared By: -\ A
- 0102-0135-jlh-3 MPR Associates, Inc. Revision No.: 0 320 King Street "- i. P e o 1 Alexandria VA 22314 Checked By:/ Page No.: 11 The radial displacements of the three cylinders as a function of the interface pressures are:
Arl(P.,, E,) := Ar(r,, P,(P,.2),tj,,Ec)
Ar2 (P 1. 2 , P 2 .3 , Er) := Ar(r 2 , P 2 (P,. 2 , P2.3 ), t2 , EC)
Ar3 (P2.3) := ,r(rj, P3(P2.3), t3 , E,)
Set the displacements equal to solve for the interface pressures. The initial guesses for the interface pressures are:
P 1 .psi P 2 .3 10:.psi Given Arl(P 1.2 , Ec) = zAr 2 (P,. 2 , P 2 .3 , Ec)
A6r 2 (P 1.2 , P 2 .3 , Ec) = 6r3(P2.3) mint(Ec) := Find(P,.2 , P 2 .3 )
Case 1-Nominal Modulus of Elasticity i:= 1 Ec. = 4.29 x 106 psi
.21>P I Pint(Eci) Pr2 &2 s
= ,611 Verify that the displacements are equal.
Arl ( P1.2I, Ec) = -0.342.in Ar 2 (PI.2,, P 2 .3j, Ec) = -0.342.in z4r 3 (P 2 .3) = -0.342.in
Calculation No.:
W M PR MPR Associates, Inc.
Prepared By: ŽA-..t.
,-\. - 0102-0135-jlh-3 Revision No.: 0 320 King Street Alexandria VA 22314 Checked By: Page No.: 12 Case 2-Minimum Modulus of Elasticity i:= 2 EC. = 2.5 x 106 psi I
LP1.2.i P2.3i. := Pint(Eci
- .i1 Ip (2711)ps
.321P y10 06 ,)
Verify that the displacements are equal.
Arl (P 1.2 i, Ec.) = -0.563.in Ar2(PI.2I., P2.3., Ec,)= -0.563.in
.6r 3 (P2.3) = -0.563-in
Calculation No.:
I M P R Prepared By: -. \_ 0102-0135-jlh-3 MPR Associates, Inc. . Revision No.: 0 320 King Street Checked By:
Alexandria VA 22314 Cc By: : Page No.: 13 5.4 Radial Pressure at Reduced Area The pressure P 1 .2 is the general membrane stress at the location of the inner most radius of the hoop conduit. Calculate the local membrane stress at a reduced area. The variable, Aratio, is the ratio of the reduced area to the area used for the calculation in Section 5.3.
Pm,(Arato) := 1 A ratio Consider two cases of reduced area in addition to the nominal case with no area reduction. One case is subtracting the area of the hoop conduit. The second case is subtracting the area of the hoop conduit and the vertical conduit.
17 yt- dc 1 Aratio := Yt Aratio = 0. 73 (y, d)- (x,-dc L0.62 yt'xt The pressure multipliers for these two areas are:
Pmult:= Pm(A.tjo) mmult = r 1 1.38 Y1.62)
The P 1 .2 interface pressures at the reduced areas are:
Case 1-Nominal Modulus of Elasticity 28.&22 I P12 1.2 .'mult P1.2,i = 38.83 psi
~45.63)
r M PR MPR Associates, Inc.
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Calculation No.:
0102-0135-jlh-3 Revision No.: 0 320 King Street CBN Alexandria VA 22314 Checked By:/ Page No.: 14 Case 2-Minimum Modulus of Elasticity i:=2 (2127 Pl2 1.: 12 .mult P1.2,i= 37.28 psi
ý.43.81)
Calculation No.:
Prepared By: Ž .L .. -w.., 0102-0135-jlh-3 MPR Associates, Inc. Revision No.: 0 320 King Street Checked B P o Alexandria VA 22314 By.cked By: Page No.: 15
6.0 REFERENCES
- 1. Crystal River Unit 3 Drawings:
1.1 Drawing No. SC-421-031, "Reactor Building Exterior Wall Concrete Outline," Revision 4.
1.2 Drawing No. 421-347, "Reactor Building Temporary Access Opening for SGR Vertical & Horizontal Tendon Positions," Revision 0.
- 2. Progress Energy, "Design Basis Document for the Containment," Revision 6.
- 3. J. F. Harvey, "Pressure Vessel Design: Nuclear and Chemical Applications," D. Van Nostrand Company, 1963.
- 4. ACI 318-63, "Building Code Requirements for Reinforced Concrete."
- 5. CR3 Reactor Building Shell Calc's, 4203-00-212, 1:01.4 to 1:01.11, Material Design, Book 2 of 5.
-4 MPR Associates, Inc.
OMPR 320 King Street Alexandria, VA 22314 CALCULATION TITLE PAGE Client:*
Progress Energy Page 1 of 13 Project: Task No.
CR3 Containment Calculations 0102-0906-0135
Title:
Calculation No.
Reinforcement Ratio and Effective Modulus of Elasticity 0102-0135-01 Preparer / Date Checker / Date Reviewer & Approver / Date Rev. No.
0 J. L. Hibbard Chris Bagley P. Butler 1-6-2010 1-6-2010 1-6-2010 QUALITY ASSURANCE DOCUMENT This document has been prepared, checked, and reviewed/approved in accordance with the Quality Assurance requirements of 10CFR50 Appendix B, as specified in the MPR Quality Assurance Manual.
MPR-QA Form QA-3.1-1, Rev. 1
MPR Associates, Inc.
- M P R 320 King Street Alexandria, VA 22314 RECORD OF REVISIONS Calculation No. Prepared By Checked By Page: 2 0102-0135-01 Revision Affected Pages Description 0 All Initial Issue Note: The revision number found on each individualpage of the calculation carries the revision level of the calculation in effect at the time that page was last revised.
MPR Associates, Inc.
OLM PR 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By Page: 3 0102-0135-01 4 Revision: 0 Table of Contents 1.0 Purpose........................................................................................................ 4 2.0 Sum m ary...................................................................................................... 4 3.0 Background...................................................................................................... 5 4.0 Assum ptions................................................................................................... 5 4.1 Unverified Assumptions ........................................................................................ 5 4.2 Other Assumptions ................................................................................................. 5 5.0 Calculation....................................................................................................... 6 5 .1 D ata ............................................................................................................................... 6 5.2 Reinforcement Ratio and Effective M odulus of Elasticity .................................... 10 6.0 References ..................................................................................................... 13 MPR QA Form: QA-3.1-3, Rev. 0
Calculation No.:
Prepared By: 0102-0135-01 MPR Associates, Inc. Revision No.: 0 320 King Street Be Alexandria VA 22314 Checked By Page No.: 4 1.0 PURPOSE This calculation determines the reinforcement ratio and the equivalent modulus of elasticity in selected concrete sections for the Crystal River Unit 3 containment. These results will be used in subsequent calculations supporting the repair of the containment to make informed decisions on how to address rebar in constructing finite element models of the containment. The selected sections are the containment locations of interest in the finite element model with potential for high stress.
2.0
SUMMARY
The reinforcement ratio and the equivalent modulus of elasticity of selected concrete sections are summarized in Table Ts. The equivalent modulus of elasticity is calculated with an area weighted average of the concrete and steel moduli of elasticities. This modulus of elasticity can be used to calculate the displacement of concrete sections in pure tension or compression. This modulus of elasticity will not provide accurate calculations of displacements for bending, because the reinforcing steel is not uniformly distributed in the concrete sections.
x
("Section" "Location" "Rebar" "Elevation" "Reinf." "Equiv." "Modulus" "Orientation" "(f)". ."Ratio" "Modulus" "Increase" "vertical" " t%1 1. E6.psi92
. .9%"
"'vertical"
.. .93 to 1031" 1.2 4.95 5.9 1 "Buttress" 2 "RingGirder" "hoop" "250 to 256" 0.3 4.76 1.8 3 "RingGirder" "vertical" "250 to 256" 1.5 5.03 7.6 4 "Containment" "vertical" "230 to 250" 1.7 5.08 8.6 5 "Containment" "vert & horiz" "103 to 250" 0.2 4.71 0.8 6 "Containment" "vertical" "93 to 103" 2.1 5.18 10.9 7 "UnderEq. Hatch" "vertical" "-103" 2.2 5.21 11.4 8 "SGRPlug" "hoop" "196" 0.8 4.88 4.3 9 "EquipmentHatch" "hoop" "116" 2.7 5.32 13.8 J Notes:
- 1. The reinforcement ratio is an approximation based on the total rebar area (tension and compression areas) divided by the concrete section area.
- 2. The equivalent modulus accounts for the steel and concrete.
- 3. The modulus increase is the increase in the equivalent modulus compared to the concrete modulus of E, = 4.675 x 106psi (calculated on p. 9).
7AMPR Prepared By: -ý A- -
o~oo o Calculation No.:
0102-0135-01 MPR Associates, Inc. A
- Revision No.: 0 320 King Street Cc B:ei7 w Alexandria VA 22314 Checked By Page No.: 5
3.0 BACKGROUND
A project is underway at Progress Energy's Crystal River Unit 3 site to replace the steam generators.
As part of that project, an opening has been cut into the concrete containment above the equipment hatch. As this opening was being cut, cracking in the concrete containment wall was identified. The crack is around the full periphery of the opening and is in the plane of the wall. The cracking is located at the radius of the circumferential tensioning tendons, and is indicative of a delaminated condition.
4.0 ASSUMPTIONS 4.1 Unverified Assumptions None.
4.2 Other Assumptions None.
Calculation No.:
I M P R Prepared By: Ž A-.- .hj...$.- 0102-0135-01 MPR Associates, Inc. Revision No.: 0 320 King Street Checked By:
Alexandria VA 22314 Checked By Page No.: 6 5.0 CALCULATION 5.1 Design Input Data for the calculation is input into arrays that contain entries, each of which corresponds to the section number in the table below. For the elevation of the SGR plug, see Reference 2.8.
"Section" "Location" "Rebar" "Elevation" "Orientation" 1 "Buttress" "vertical" "93 to 103" 2 "Ring Girder" "hoop" "250 to 256" 3 "Ring Girder" "vertical" "250to 256" Td:=
4 "Containment" "vertical" "230 to 250" 5 "Containment" "vert& horiz" "103 to 250" 6 "Containment" "vertical" "93 to 103" 7 "UnderEq. Hatch" "vertical" "1103" 8 "SGRPlug" "hoop" J
"196" 9 "EquipmentHatch" "hoop" "116" Standard rebar diameters from Reference 3, Table 12.3.1 are:
Rebar Rebar Dia.
No. (in.)
Odrebar :=
3 0.375 4 0.5 5 0.625 Define a function to return rebar diameter.
6 0.75 7 0.875 dr(n) := vlookup(n, Odrebar,2)l in 8 1 9 1.128 For example, 10 1.27 11 1.41 14 1.693 dr(18) = 2.257.in 18 2.257
[ M PR Calculation No.:
OILM P R MPR Associates, Inc.
Prepared By: 0102-0135-01 Revision No.: 0 320 King Street ed:7 Alexandria VA 22314 Checked By Page No.: 7 tcont 42.in Containment wall thickness; Ref. 2.1 tb = tcont + (2. ft + 4.in) tb = 70.in Buttress thickness; Ref. 2.1 trg =-tcont + (2. ft + 4.-in) Ring girder thickness at approximately the 250 ft trg= 70.in elevation; Ref. 2.1 Ro., 65.ft + 0.375.in + 42.in R.,= 68.53 ft Outside radius of containment; Ref. 2.1 Ro.rg Ro.c + (2. ft + 4.in) Ro.rg 70.86 ft Outside radius of ring girder; Ref. 2.1 70 / "Buttress" 70 "Ring Girder" Concrete thickness
-Ref. 2.1 70 "Ring Girder" -Ref. 2.1; conservative thickness 42 "Containment" -Ref. 2.1; conservative thickness
-Ref. 2.1 42 in lOc = "Containment"
-Ref. 2.1 42 "Containment" -Ref. 2.1; conservative thickness for Elev. = 93 ft
-Ref. 2.1; conservative thickness for Elev. = 93 ft 42 "UnderEq. Hatch"
-Ref. 2.1 42 "SGR Plug" -Ref. 2.6 83.625 S"Equipment Hatch")
12 ft Width of section considered; this is an arbitrary dimension, but references are provided to show the (255.ft+ 10.5-in) - (250.ft) dimension
- 30. deg .Ro.rg -Ref. 2.1
-Ref. 2.1 (11 + 15 + 60).deg.Ro., -Ref. 2.3, O° to 3300
-Ref. 2.2, Section 2-2, 110-15' section b:= 12.in -Ref. 2.2, Section 3-3 and Ref. 2.7 48.in -Ref. 2.2, this width was chosen to give an integer number of rebar for each layer 144.in -Ref. 2.2, this width was chosen to give an integer 132. in number of reba r for each layer
-Ref. 5; this width was chosen to give an integer 103.5.in number of rebar for each layer
-Ref. 2.6.
Calculation No.:
Prepared By: Ž ." , . 0102-0135-01 MPR Associates, Inc. J.A, Revision No.: 0 320 King Street C c Wy)P g e No:z Alexandria VA 22314 Checked By (.J Page No.: 8 144 "Buttress" 70.5 "RingGirder" 445.26 "RingGirder" 161.47 "Containment" 12 -in Ioc = "Containment" 48 "Containment" 144 "UnderEq. Hatch" 132 "SGR Plug" 103.5 \"Equipment Hatch" There are several layers of rebar through the depth of the sections. The data for the layers are input with 1 by x arrays below, with x being the number of layers. For example, the first entry in the array below is a 1 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))
Rebar diameter (dr(9) dr(9) dr(9) dr(9)) -Ref. 2.2, Section 1-1 and Ref. 2.5, Section 1-1 (dr(9) dr(9) dr(11) dr(11) dr(18)) -Ref. 2.3, Section 1-1 (dr(18) dr(18)) -Ref. 2.3, Section 1-1
-Ref. 2.2, Section 3-3 odr:= (d*(8) ) -Ref. 2.2, Section 3-3 and Ref. 2.7
-Ref. 2.2, Section 3-3 and Ref. 2.5, (dr(l1) d,(18) d,(18)) Section 1-1 (dr(11) dr(18) dr(18)) -Ref. 2.2, Section 3-3, Ref. 2.5, Section 1-1, and Ref. 2.4 (dr(8) dr(11) dr(11)) -Ref. 5
-Ref. 2.6 (dr(11) dr(18) dr(18) dr(11) dr(1l) dr(18) dr(11))
(1.41 2.257 2.257) "Buttress" (1.128 1.128 1.128 1.128) "RingGirder" (1.128 1.128 1.41 1.41 2.257) "RingGirder" (2.257 2.257) "Containment" odr = (1) -in Ioc = "Containment" (1.41 2.257 2.257) "Containment" (1.41 2.257 2.257) "UnderEq. Hatch" (1 1.41 1.41) "SGR Plug" (1.41 2.257 2.257 1.41 1.41 2.257 1.41) "EquipmentHatch"
MOM P MPR Associates, Inc.
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Calculation No.:
,0102-0135-01 Revision No.: 0 320 King Street Checked Alexandria VA 22314 By Page No.: 9 Number of rebar in section width, b (12 8 16) -Ref. 2.2, Section 1-1
-Ref. 2.3, Section 1-1 (there are four rebar in the (5 2 2 8) angle section of which two are credited and (59 59 33 33 59) assumed to align with the above rebar for ease of calculation)
(11 17) -Ref. 2.3, 00 to 3300 with spacing at mid-bay used (1) over buttress for Layer 1
-Ref. 2.2, Section 2-2 (4 3 6) -Ref. 2.2, Section 3-3 and Ref. 2.7 (16 9 18) -Ref. 2.2, Section 1-1
-Ref. 2.2, Section 1-1, Ref. 2.5, Section 1-1, and Ref.
(11 12 12) 2.4 (12 19 11 10 11 10 11) -Ref. 5
-Ref. 2.6 Misc.
- 6. Steel modulus of elasticity; Ref. 1, Section 1100 Es:= 29-10 . s Concrete minimum compressive strength; Ref. 4, fc':= 6720.psi Results Summary, Class 5000 concrete lb pc:= 144.- Concrete density; Ref. 7 ff, Pc Sil.
Elastic modulus for concrete; Ref. 1, Section 1102 Ec:= 33.psi.
Ec = 4.675 x 16psi
Calculation No.:
MOM P R MPR Associates, Inc.
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Alexandria VA 22314 Cc ByPage No.: 10 5.2 Reinforcement Ratio and Effective Modulus of Elasticity The area of rebar in each layer is:
(18.74 32.01 64.01)
(5 2 2 7.99)
(58.96 58.96 51.53 51.53 236.05)
(44.01 68.01)
.2
.In Asl1 = [r'flr(odr.)2] As 1 = (0.79)
(6.25 12 24.01)
(24.98 36.01 72.02)
(8.64 18.74 18.74)
(18.74 76.02 44.01 15.61 17.18 40.01 17.18)
The area of rebar at each section is:
114.76' 16.99 457.03 112.02
.i2 Asi 6 := As1 0.79 in 42.25 133.01 46.11
.228.74 j
Calculation No.:
O LM P R MPR Associates, Inc.
Prepared By: Ž, .- .* 0102-0135-01 Revision No.: 0 320 King Street C e Alexandria VA 22314 C d' Page No.: 11 The concrete area of each section is:
9965 4918 30711 6670 A, := (to.b - A,) 503 *.2 in A, =
1974 5915 5498
.8426 /
The reinforcement ratio is approximated with:
This is an approximation of the reinforcement 1.15 ratio,which is defined as (Reference 6, Section 4-1):
0.35 1.49 1.68 0.16 where As - reinforcement area at 2.14 tension face of beam b = width of the compression 2.25 face 0.84 d = distance from extreme compression fiber to centroid
,2.71 of tension reinforcement The area weighted equivalent modulus of elasticity is:
(4.95) 4.76 5.03 5.08 Ec.Ac + Es.As Eequiv ,+ A Eequiv = 4.71 .106.psi 5.18 5.21 4.88 S5.32
Calculation No.:
I MP R MPR Associates, Inc.
Prepared By: Ž .-.. *
- 0102-0135-01 Revision No.: 0 320 King Street Alexandria VA 22314 Checked By Page No.: 12 The percentage increase in the concrete modulus of elasticity accounting for the steel is:
- 5. z 1.79 7.63 8.6 Eequiv - Ec mmoduus.- Pmodulus = 0.81 10.91 11.44 4.33
.13.75)
Calculation No.:
Prepared By: Ž* .\_. , 0102-0135-01 MPR Associates, Inc. Revision No.: 0 320 King Street Alexandria VA 22314 Checked By Page No.: 13
6.0 REFERENCES
- 1. ACI 318-63, "Building Code Requirements for Reinforced Concrete."
- 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-421-040, "Reactor Building Exterior Wall - Equipment Access Opening Reinforcement Placing Details," Revision 3.
2.7 No. SC-421-032, "Reactor Building Stretch-out of Exterior Wall Buttress #2, #3, #4, & #5,"
Revision 8.
2.8 No. 421-347, Reactor Building Temporary Access Opening for SGR Vertical & Horizontal Tendon Positions," Revision 0.
- 3. E. Avallone & T. Baumeister, "Marks' Standard Handbook for Mechanical Engineers,"
McGraw-Hill Book Company, 9th Edition.
- 4. Florida Power Corporation Document Identification No. S-00-0047, As-built Concrete Strength for Class 1 Structures, Revision 0.
Subject:
Design Input for Calculation 0102-0135-01.
- 6. J. Wight and J. MacGregor, Reinforced Concrete Mechanics and Design, Pearson Education, Inc., 5th Edition.
Subject:
Concrete Density.