Text

Rev 0 to CE-0081, Review of Augmented ISI Frequency for Reactor Coolant Bypass Lines
	ML20249C403
Person / Time
Site:	North Anna
Issue date:	04/23/1996
From:	Dwivedy K, Hennessy M, Sorrell C; VIRGINIA POWER (VIRGINIA ELECTRIC & POWER CO.)
To:	;
Shared Package
ML20249C401	List: ML20249C400; ML20249C403; ML20249C405;
References
	CE-0081, CE-0081-R00, CE-81, CE-81-R, NUDOCS 9806290212
	Download: ML20249C403 (58)
	v • d • e

Attachment 1 Reactor Coolant System Loop Bypass Augmented inspections Virginia Electric and Power Company North Anna Power Station Units 1 and 2 9006290212 980623 #

PDR ADOCK 05000338 G PDR l-- _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Reactor Coolant System Loop Bypass Augmented inspections Section 3.6.2.3 (1), of the UFSAR at North Anna currently requires, an augmented inservice inspection program for the reactor coolant loop bypass lines at branch connection points and the weld points at the terminal ends. The examinations are performed as an alternative to modifications that had been identified for mitigation of the consequences of pipe rupture in the area due to pipe whip or jet impingement.

! These modifications were deemed impractical to implement.

The reactor coolant loop bypass lines are 8-inch nominal lines, located between the main reactor coolant loops (hot and cold legs) inside the containment. This piping is subject to the Class 1 inspection requirements of ASME Section XI Code as well as the augmented program noted above. Examinations performed to date have yet to identify any structural integrity problem with the bypass piping on either unit.

These examinations require significant personnel exposure to complete. An exposure estimate was calculated for both units assuming a ten-year interval and constant area dose rates. The estimate of approximately 28 person-rem for both units includes support personnel as well as the actual examiners. Since the examination history to date has shown no structural integrity problems and the exposure to complete the examinations is significant, as indicated by the above exposure estimates, an evaluation and reanalysis of the reactor coolant loop bypass lines was performed to determine the continued need for the augmented inspection.

The analysis used a Leak-Before-Break (LBB) methodology to justify the elimination of the current ~ required augmented inspection. The results of this analysis are documented in the attached Civil Engineering Technical Report entitled, " Review of Augmented ISI Frequency for Reactor Coolant Bypass Lines." The report's conclusion states that, " Based on the results of LBB analysis it is concluded that the dynamic effects of postulated pipe rupture can be excluded from the design basis of RCS loop

. bypass lines'at North Anna Units 1 and 2."

The ASME Section XI program will continue to require NDE examination (at the i

reduced frequency) and pressure testing of the affected lines assuring continued structuralintegrity of the piping.

Based upon the results of the Leak-Before-Break reanalysis of the reactor coolant loop bypass piping, the continuation of the required ASME Section XI inspection program, and the estimated high exposure requirement, we request your review and approval of the Leak-Before-Break reanalysis and our proposal to eliminate the current UFSAR commitment for the augmented inspection requirement of the reactor coolant loop bypass line piping for both Units 1 and 2.

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Review of Augmented ISI Frequency for Reactor Coolant Bypass Lines Civil Engineering Technical Report CE-0081 North Anna Power Station Units 1 and 2 h waamurons
Civil Engineering Technical Report CE-0081 Revision O Review of Augmented ISI Frequency for Reactor Coolant Bypass Lines North Anna Power Station Units 1 and 2 NP-2952 Prepared by: M. 8. b -
Date: 4 1 4 i K. K. Dwivedy &
Reviewed by: N. (.14pezersh __ Date: 4 / 2 3/96 M. C. Hennessy [/
Reviewed by: -.7 b O I ' Date: 4/s.&/T&
J.1. Ref ai Approved by: bC. E. Sorrell m Date: A -25%
Engineering Mechanics Design Engineering and Support i
~~Nuclear Engineering Services Virginia Power l l~~
April 1996 l
! Safety Related Key Words:- Reactor Coolant System, Augmented Inservice Inspection, Leak Before Break (LBB), Reactor Coolant Loop Bypass Lines.
t
I l-Table of Contents C o v e r s h eet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Table o f c o ntents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.0 I nt rod uctio n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.0 Background ...................................... 3-4 l
3.0 Evaluation ......................................4-12
>, 3.1 Analysis Method 3.2 Material Properties 3.3 Applied Loadings 3.4 Leakage Flow Rate 3.5 Limit Load Analysis 3.6 Crack Stability Analysis 4.0 LBB. NRC Computer Program . . . . . . . . . . . . . . . . . . . . . . . . 12-13 5.0 Summary of Results, Conclusions, and Recommendations . . . . . . . 13 6.0 R e f ere nce s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Appendix A: Analysis of Typical Configuration of RCS loop bypass line. . . A1 Appendix B: Limit Load Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Appendix C: Crack Stability Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . C1 i
Page 2 of 14
1.0
~~Introduction:~~
The purpose of this technical report is to establish Leak Before Break analysis (LBB) for the Reactor Coolant System (RCS) bypass lines using fracture mechanics method so that the dynamic effects of postulated ruptures in the lines can be eliminated from the design basis. Therefore, no additional protection will be needed for the mitigation of the dynamic effects. Then, the Augmented Inservice Inspection (All) instituted for the lines can be eliminated and the lines will only be inspected per the requirements of the applicable version of the ASME section XI'73 code.
RCS bypass lines are being inspected per the "All" program stated in section 3.6 of North Anna UFSAR. However, the records of inspection at a higher frequency have not shown any indication in the piping. The inspection is not helping in enhancing the safety of the plant. Therefore, it was decided to eliminate this unnecessary inspection if it can be verified by analysis that there is adequate technical basis that the ' weld locations in the system will provide enough warning prior to a catastrophic failure such that the operators can take appropriate steps to safely shutdown the plant. This can be achieved by performing a deterministic LBB analysis. It is considered that this verification process provides more deterministic assurance of safety than the "All" currently being performed.
An analysis of the RCS bypass lines was performed using the methodology detailed in the section 3.0 of this report. The results of the analysis show that LBB can be established for the RCS bypass lines and there is adequate technical basis to eliminate from the design basis the dynamic effects of postulated pipe rupture in RCS bypass lines. As a result, the preventive protection taken in the form of "All" is no longer required.
~~2.0 Background~~
General Design Criterion 4 (GDC-4) requires postulation of breaks in high energy piping in Nuclear Power plants and protection of safety related equipment and structures from the dynamic and other effects of the postulated pipe rupture. Section 3.6 of the North Anna UFSAR"' provides the protection measures taken in the plant to mitigate the effects of the postulated pipe ruptures to assure a safe shutdown and to prevent offsite dosages in excess of the limits as stated in 10CFR100. Reports 11715-RUP-1$ and 12050-RUP-28) document the applicable break and protection criteria, the piping systems subject to pipe rupture and the systems, components, equipment, structures, conduits and instrumentation requiring protection. Each postulated rupture point was investigated for potential damage to all essential targets.
Protective measures implemented include the rerouting of piping, electrical conduits, and instrumentation lines, the redesign of piping systems and supports, the installation of pipe whip restraints and jet impingement shields, and the implementation of a program of Augmented inservice Inspection (All).
Pago 3 of 14
The 8 in. diameter reactor coolant loop bypass lines are routed between the hotleg and coldleg of each loop and are used when required to bypass the loop -
isolation valves. During normal operating condition the valve in the bypass line is closed. The loop bypass lines, (Unit 1: 8-RC-11,8-RC-12, and 8-RC-13; Unit 2 : 8-RC-411, 8-RC-412, and 8-RC-413) contain borated water at 547'F which is normally pressurized to 2235 psig. Since the lines are ASME code class 1 piping, breaks ~are postulated at terminal points and at intermediate points where the ASME section til subsection NB"' paragraph 3653 equation 10 stresses exceed 2.4 S, or the cumulative usage factor exceeds 0.1. Several essential targets were considered in the references 2 and 3 in order to examine the effects of pipe rupture. Reports indicated that a substantial support structure would have to be constructed through the cubicle to protect components from pipe whip and jet impingement. An extensive design and analysis effort prior to plant start up indicated that this approach was not feasible.
Therefore, it was decided to provide assurance by conducting an "All" at postulated weld locations. It was judged that the implementation of "All" will assure that piping defects will be detected prior to propagation into a break. This approach has been accepted by the NRC.
For the last several years the RCS loop bypass lines have been inspected at a
' frequency three times the frequency of the normal 10 year inspection. As a result, these welds are being inspected almost during every refueling outage at a large expenditure of man power and radiation exposures. Re'sults from inspection, to date, have not shown any indication in the piping. Therefore the increased frequency of inspections have not achieved anything from the resources expended during the "All".
During this period, the regulatory position on the selection of intermediate weld location has been somewhat relaxed per generic letter 88-11*. The GDC-4* has been revised to eliminate dynamic effects due to postulated pipe rupture if a leak-before-
. break (LBB) can be established for the piping. In other words, protection does not have to be provided to mitigate dynamic effects, if LBB can be established for the piping by use of fracture mechanics analysis.
~~3.0 Evaluation~~
3.1 Analysis Method The. LBB methodology applied in this analysis is shown in the flow chart presented in Figure 3.1-1. A representative configuration of the RCS bypass lines (Unit 1: 8-RC-11, 8-RC-12, and 8-RC-13; Unit 2 : 8-RC-411, 8 RC-412, and 8-RC-413) is shown in Figure 3.1-2. Each step of the analysis is further detailed in the following sections.
Page 4 of 14 )
- - . _ . - - _ . _ - . . . - . ~ _ _ _ - _ . _ _ . . . - _ - - - . . . - . - -- ~ _ --. -..J
C E Technical Report C E-0081 LBB M ethodology Flowchart l Calculate Applied Normal Loads l v
Calculate Crack Size to Deliver 10 gpm Leakage Y
Calculate Applied Load Plus D B E; C alculate Limit Load Y
Mat a YES NO D u ctile O M etal NO yYES A p plie d y Double Calculated Load Less Double Calculated ! Lim t Crack Length Load?
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i l NO C ra c YES S ta bility -
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Y ~y LBB NOT LDB C PROVEN j PROVEN Fig 3.1-1 Page 5 of 14
REACTOR COOLANT LOOP BYPASS (Line Typical For all Loops)
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The LBB.NRC computer program used to calculate crack opening area (COA), leakage flowrate, and the applied crack extension potential (J ,,) is published in NUREG/CR-4572 <s' as an estimation procedure used by the NRC for reviewing Leak-Before-Break submittals. It is based on J-tearing theory and utilizes a conservative approximation .
technique which is an alternative to more elaborate and time consuming finite element I techniques. Subsequent comparisons of various estimation scheme presented in NUREG/CR-4853 concludes that LBB.NRC methodology generally gives good predictions at crack initiation and maximum loads. {
J The Crack Opening Area calculated by the LBB.NRC program uses the equation given on page 77 of NUREG/CR-3464 (10) without the effects of strain hardening but using the effective crack angle. The effective crack angle includes the effects of yielding at the crack tip.
COA = ( rr S, R I, e ) *
[ S, + S. ( 3 + Cos e.) ]
E 4 {
E = Modules of Elasticity 1, = Compliance Function R = Mean Pipe Radius S. = Normalized Pipe Bending Stress 4 S, .= Normalized Pipe Axial Stress S, = Material Flow Stress (Take as Average of Yield and Tensile) e, = Effective Half Crack Angle 1
The normalized crack driving parameter (J) differs from NUREG/CR-3464 (10) in that the total stresses rather than just the bending stresses are used in the integration formula. The predicted results from the refined equation have been shown to compare
_ quite well with experimental data.
! J estimations are calculated using the following equations:
J = J, + J, _
I, = TT 0, [ So F 8, + S, F, 0,12 J, = 4 F.
O. I 8b + I I / F )3 S, l d $,
t (S, + S) t Page 7 of 14
(
F. = Geometry Factor for Bending
- F, = - Geometry Factor for Tension F, = Factor Derived in NUREG/CR-3464 S,- = Applied S,
[
0, = Effective Half - Crack Angle
) $, = Plastic Component of Relative Kink Angle 3.2 Material Properties The material properties used in the LBB analysis reflect properties which are applicable of the specified materials used in fabrication. A summary of material properties used in this analysis is provided in Table 3.2-1.
Since the thermal expansion and internal pressure loading is accorapanied by elevated system temperatures, it is prudent to use material properties at operating temperatures for the LBB analysis. Most published data on the fracture mechanics properties of these materials is available at 550 F. Based on observed trends, the properties at this temperature are assumed to be sufficiently close to the bypass line material properties at operating temperatures. The review of material properties shows that the properties of weld materials are governing for LBB analysis.
Table 3.2-1 : Material Properties Base Metal SMAW Weld Metal Material (pipe) A376 TP316 SS Type 308 SS (Fittings) A182 F316 SS Type 304 SS A403 WP316 SS Yield Stress S (ksi) 18.7 48.1 Tensile Stress S,(ksi) 71.8 63.05 Modules of Elasticity E- 25,500 25,500 (ksi)
Flow Stress S, (ksi) 45.3 55.5 Ramburg-Osgood Parameters . et 12.1 9.0 n 3.1 9.8 J,c (in-lb/in-in) 3850 990 l Page 8 of 14
i Note: Ramburg-Osgood Stress Strain Parameters allow the true stcess strain curve to be idealized by a logarithmic estimation schedules
[ e/ e, = s/s, + a t s / s o)"
e - Strain I s = Stress s, = Yield Stress e, = Yield Strain n, cx = Ramburg-Osgood True Stress Strain Curve fit Parameters Reference Stress: Base Metal 33.2 ksi Weld Metal 49.4 ksi 3.3 Applied Loadings The piping loads applied in the analysis are listed in Table 3.3-1. An analysis of a typical configuration of the RCS loop bypass lines was performed using NUPIPE computer program to determine forces and moments in the piping system due to pressure, deadweight, thermal expansion and thermal anchor movements, and seismic DBE (inertia and anchor movement loadings). The details of the analysis are presented in Appendix A. Piping loads were reviewed to determine locations where the loadings are severe. Loads are listed at three different weld locations which were considered as the most severe (See Table 3.3-1). Normal loads are applied to a postulated crack in order to determine the c ack opening area needed to obtain a flow rate of 10 gpm. Normal plus 1.4 times the DBE loading is used in performing the limit load and fracture mechanics analysis. Analysis is also performed to check the stability of a crack about 2 times the 10gpm leakage crack when subjected to normal operating plus DBE loadings. This was established by determining the largest stable crack which will remain stable when subjected to normal plus faulted loading.
i Page 9 of 14
TABLE 3.3-1 TECHNICAL REPORT CE-0081, REV. O DATA POINT 10:
<- LOAD CASE i i~AXtAL FORCE l BENDING MOMENTS (IN.LBS):; ; RESULTANT s
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PRESSURE (Pr) 91250 - - -
DEAD WEIGliT(DW) -139 -15201 823 -
TiiERMAL (TliRM) 10316 -11654 21758 -
DBE (TOTAL)(DBET) 2876 134915 128322 -
NORMAL (Pr + DW + THRM) 101705 26855 22581 35087 FAULTED (NORMAL + DBET 104581 161770 150903 221227 FAULTED 105771 217625 204028 298309 (NORMAL + 1.414 DBET)
DATA POINT 45:
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LOAD C'ASE e (: AXIAL FORCE ':: D ING M'OMENTS(IN.LBS)'
. BEN' iRESULTANT{
c (F,i2 (LBS.):: .. MOMENTJ L M,1; xM,f j Mr = (M,8 + M,8)H PRESSURE (Pr) 91250 - - -
DEAD WElGHT(DW) -162 162 35414 -
THERMAL (THRM) 11615 -28178 713516 -
DBE(TOTAL)(DBET) 1672 14379 42630 -
NORMAL (Pr + DW + THRM) 103027 28340 748930 749466 FAULTED (NORM.AL + DBET 104699 42719 791560 792712 FAULTED 105391 48672 809209 810671 (NORMAL + 1.414 DBET)
Page 10 of 14
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TABLE 3.3-1 cont, TECHNICAL REPORT CE-0081, REV. 0 f
l DATA POINT 70:
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PRESSURE (Pr) 91250 - - -
DEAD WEIGHT (DW) .162 464 20286 -
THERMAL (THRM) -11615 20607 788014 -
DBE(TOTAL)(DBET) 1542 11259 54434 -
NORMAL (Pr + DW + THRM) 103027 21071 808300 808575 FAULTED (NORMAL + DBET 104569 32330 862734 863339 FAULTED 105207 36991 885270 886042 (NORMAL + 1.414 DBET) 3.4 Leakage Flow Rate North Anna UFSAR Section 5.2.4.1 discusses leakage detection, sensitivity and the extent to which Regulatory Guide 1.45 is met. A review of the leakage detection system during implementation of design change packages DC-86-09-1 and DC-86-10-2 showed that there is adequate confidence that a 1 gpm leak from the reactor coolant system can be detected with desirable accuracy in order to take appropriate action to operate the plant safely. In order to establish
' LBB for the RCS bypass lines stability of a 10 gpm crack is studied to assure a more than adequate margin of safety.
.Using the normal operating axial (tensile) and moment loading the crack size
. required to deliver 10 gpm of leakage is calculated. The crack opening area is .
- calculated using the equation listed in section 3.1. This equation is described on page 77 of NUREG/CR-3464. It is utilized without the effect of strain hardening, but using the effective crack angle which accounts for yielding near the crack
.tip. The calculation is performed by applying the LBB.NRC computer program l
presented in NUREG/CR-4572 (see section 3.1 for description of computer I program). A leakage rate of 350 gpm/inais applied to the crack opening area in the analysis ~ This value is conservatively less than 364 gpm/in2 reported by Westinghouse in EPRI report NP-4971. For the three limiting locations evaluated Page 11 of 14
here, the calculated crack lengths that would deliver 10 gpm were 4.36",
4.52" and 7.83".
3.5 Limit Load Analysis.
Limit load analysis is performed for the three critical locations. Elastic and full plastic analysis is performed with flow stress equal to the intermediate value between yield and ultimate stress. The details of analysis are provided in Appendix B.
3.6 Crack Stability Analysis The crack stability is established by both limit load analysis and fracture mechanics analysis. Due to the magnitude of applied loadings and the ductility of the base and weld materials, it is necessary to apply Elastic Plastic Fracture
\ Mechanics (EPFM) techniques in determining the stability of the postulated through-wall crack. LBB is proven if the applied crack driving potential J,,, is less than Jac which is the material property defining the crack driving potential required to initiate crack extension. J,,,is calculated using the LBB.NRC method presented in NUREG/CR-4572. If J,,, exceeds the Ji c the material resistance to unstable crack extension is determined by calculation of the applied tearing modulus T.,, and comparing it to material tearing modulus T , at any specific J level. Where J.,,2. J,e , unstable crack extension will not occur when:
,pp $ mat T ,, is determined from the slope of the J versus crack extension curve (J-R curve) and T.,,is calculated by determining the differential increment of J.,,,
( dJ )needed to produce a specified differential increment of crack ( da )
extension in a specific load and crack state.
T,,, = (dJ/da) ( E/S,2 )
Where, E = Modulus of Elasticity S, = Flow stress taken as the average of yield and ultimate tensile stress The allowable value of J is then based on the point where the T.,, curve intercepts the Tm, curve. The corresponding allowable moment for the location is determined by using the J - Moment curve plotted from the results of analysis using LBB.NRC. Details of crack stability analysis including the computer output are included in Appendix C.
4.0 LBB. NRC Computer Program:
LBB.NRC computer program was developed by NRC contractor Battelle's Columbus Division. The listing of the program is documented NUREG/CR-4572. The listing of the program is included in Appendix C . The program is based on NRC-NRR (Klecker) method, which is based on procedure of NUREG/CR-3664 except for the Page 12 of 14
modification on strain hardening. The program listing is in BASIC language and was
) recoded into a PC for use in the analysis. The program was verified against the sample j example in the NUREG/CR-4572 for accuracy. The sample run was made every time the program was reused. The program was stored in the PC as LEAKBEF. BAS.
i 5.0 Summary of Results and
~~Conclusions:~~
For the three critical weld locations examined here, the sizes of crack that yield
) 10 gpm are 4.36",4.52" and 7.83". The third crack size is large compared to the other two because the location is subjected to relatively smaller thermal loading than the other two locations. A limit load analysis at this location shows a margin of safety greater than 4.0 when subjected to normal plus 1.4 times the DBE load.
Results of limit load analysis are presented in Appendix B, Tables B-1 and B-2 for three criticallocations for normal plus DBE and normal plus 1.4 times DBE loadings respectively. The two most highly loaded locations have at least a margin of 2.0 and the other location has a margin greater than 4.0.
Results of the crack stability analysis are presented in Appendix C . The stable crack sizes for the two most highly loaded locations are 11.21" and 11.29" compared to 10 gpm crack of 4.36" and 4.52" respectively. The stable crack size for the other location is 14.75". Therefore, there is high level of confidence that there will be no unstable crack extension.
The PWR reactor coolant system has many years of satisfactory service experience. The portion of the system being examined here is butt welded 8" sch.160 pipe and fittings. The system is not subjected to corrosion or erosion. The system does not experience any significant pressure transient loading at the loop bypass line. The system is designed according to ASME section ill class 1 rules and was installed with preservice examination. The system is subjected to inservice examination per ASME section XI requirements in addition to "All". Therefore, it is highly unlikely that a crack will develop in the piping. Even if an undetectable flaw is left at a location, it is unlikely to grow into a through wall crack. Results of the analysis clearly indicate that there is high level of confidence that if a leak develops at a location it can be detected timely and steps can be taken to bring the plant to a safe condition.
Based upon the above results of LBB analysis it is concluded that the dynamic effects of postulated pipe rupture can be excluded from the design basis of RCS loop bypass lines at North Anna Units 1 and 2. Since the dynamic effects of postulated rupture can be excluded from the design basis, no protection device or program is needed to mitigate those effects. "All" was stipulated for these lines because it was not possible to install protection devices. Since it is established that no protection device is needed, the stipulated "All" can be eliminated. However, the routine ISI per ASME section XI will continue. The elimination of "All" will not cause any reduction of margin of safety. The "All" was verifying protection for an accident condition periodically, whereas this deterministic evaluation has verified up front that there is inherent toughness in the system and adequate margin exist against such accident.
Page 13 of 14
L 5.0
~~References:~~
~~1. North Anna Updated Final Safety Analysis Report Section 3.6~~
~~2. Pipe Rupture inside Containment, North Anna Power Station Unit 1,11715-RUP-1, Revision 1, Stone and Webster Engineering Corporation, 8-12-1977 l~~
~~3. - Pipe Rupture inside Containment, North Anna Power Station i. hit 1,12050-~~
~~' RUP-2, Revision 0, Stone and Webster Engineering Corporation,1980~~
~~4. ASME Boiler and Pressure Vessel Code Section 111, Subsection NB, ASME, New York,1971 Edition~~
~~- 5. Relaxation in Arbitrary Intermediate Pipe Rupture Requirements Generic Letter 87-11, Nuclear Regulatory Commission Washington, D.C. June 1987~~
~~6. 10 CFR Part 50 Appendix A, General Design Criterion 4, " Environmental and Missile Design Basis".~~
~~7.' ASME Boiler and Pressure Vessel Code Section XI, ASME, New York,1986 Edition~~
~~8. ~ Klecker, R., Brest, F. and Walkowski, G., "NRC leak-Before-Break (LBB.NRC)~~
~~' Analysis Method for Circumferential Through wall Cracked pipe under Axial plus Bending Loads, NUREG/CR-4572, May 1986~~
~~9. Brust, F. " Approximate Methods for Fracture Analysis of Through-wall Cracked Pipes", NUREG/CR-4853,' February 1987~~
10. Paris, P.C. and Tada, H. "The Application of Fracture Proof Design Methods Using Tearing Instability Theory to Nuclear Piping Postulated Circumferential Through Wall Cracks", NUREG/3464, September 1983.
~~11. Electric Power Research Institute, " Toughness of Austenitic Stainless Steel Pipe Welds", EPRI NP-4768 February 1982.~~
.12. .WCAP-11163, " Technical Basis for Eliminating Large Primary Loop Pipe
~ Rupture as a Structural Design Basis for North Anna Power Station Units 1&
2 Westinghouse Propriety class 2, Westinghouse, Pittsburgh August 1986 Page 14 of 14
CE Technical Report CE-0081 APPENDIX A 1
Analysis of a Typical Configuration of RCS Loop Bypass Line i
~~Purpose:~~
The purpose of this analysis is to generate forces and moments at critical weld locations of Loop bypass lines for verification of Leak Before Break j (LBB).
Math Model: The loop bypass lines (Unit 1: 8"-RC-11, 8"-RC-12 and '8"-RC-13; Unit 2: 8"-RC-411, 8"-RC-412,8"-RC-413) are represented in the Figure A-1. The piping class 1502 consists of 8" sch.160 pipe.
The support configuration is shown in the math model.
Computer Program:
QES, Inc. Piping Analysis program NUPIPE-II, Version 3.0.0 on Virginia Power SUNSPARC Station 20 is used in the analysis.
Method of Analysis:
The basic method of analysis used in NUPIPE-Il is th< finite element stiffness method. In accordance with this method, the continuous piping is mathematically idealized as an assembly of elastic structural members connecting discrete nodal points. Nodal points are placed in such a manner as to isolate particular types of piping elements, such as straight runs of tubing, elbows, valves etc., for which force-deformation characteristics can be categorized. Nodal points are also placed at all discontinuities, such as tubing supports, concentrated weights, branch lines and changes in cross section. System loads, such as weights, Earthquake inertia forces are applied at the nodal points. Stiffness characteristics of the interconnecting members are related to the effective shear area and moment of inertia of the pipe.
For seismic analysis NUPIPE-II's automatic option for selecting the
' dynamic degrees of freedom to generate mass distribution consistent with a cutoff frequency of "33 Hz" was used. An option was also used to perform the " Missing Mass Correction."
Loading Conditions:
Analyses are performed for Deadweight, Therrnal and Seismic DBE (inertia and anchor movements) cases. Pipe dead weight was modeled with pipe full of water and the weight of 3.5" thick insulation. The branch of the bypass line from the hot leg side up to the valve is subjected to a temperature of 640' F and the branch from the cold leg side up to the valve is subjected to a temperature of 580' F. Thermal movements from the loop were collected from calculation # 14938.22-Appendix A-1
NP(B)-001-X, Rev. 2 and were applied at the main header points. DBE analysis was performed using Code Case N-411 spectrum of " Reactor Containment Internal, envelope of elevations 204', 239', 261' and 291'"
.The seismic anchor rnovements were taken from calculation # 14938.22-NP(B)-001-X, Rev. 2.
Results:
Analysis results are shown in microfiche. Three critical weld locations (Node Points 10,45 and 70) were selected for tabulation of forces and mon ents for LBB.
w Appendix A-2
REACTOR COOLANT LOOP BYPASS (Line Typical For all Loops)
Mei f.$
l n x k
b
'4 N >k 2/ M N -
% .g h -
O " e.
k h ,! . i/
+'
~~/c Ti~~
'f .
a #C o
x ,<"
?% vl.P.EL.15C!= S u;,
'p, ts s .
to t
~Q e
'r f.q,
,. Appendix A-3 .
CE Technical Report 0081 Appendix A Microfichie ofNUPIPE Computer Outout Appendix A-4
h APPENDIX B Limit Load Analysis
Appendix B Limit Load Analvsis The limit load analysis is performed using Elastic - Full plastic material behavior. A
. flow stress to the mid point of yield stress and ultimate stress was used in the analysis The limiting moment is given by equation ( Reference 12)
M = 2 o R2 t (2 Cos S - Sin 0) where o = Flow stress R = Pipe mean radius t = Pipe wall thickness 0 = Half of crack angle S = Angle form Centerline of pipe which defines neutral axis is given by i
S = ( 0 / 2 ) + ( F / (4 o R t ))
where F = Axial Tensile force due to allloading including Pressure Margin with respect to limit load is determined by taking ratio of the limiting moment to applied moment.
R = mean radius = ( D - t ) / 2 M = Limit moment Ma = Applied Moment Margin = M / Ma Summary of results t = 0.906 inches D = 8.625 inches o = 55.5 ksi Appendix B 1
Appendix B Limit Load Analvsig Table: B - 1 Normal + DBE Loading 0 (in rad.) F M (Kin) Ma Margin 29' 104.569 2.047 x 10' 863.3 2.371 30' 104.699 2.014 x 10' 4 792.7 2.541 52 104.581 1.312 x 10' 221.2 5.929 Table: B - 2 Normal + 1.4 DBE Loading 8 (in rad.) F M (Kin) Ma Margin 29' 105.207 2047 885.2 2.312 30* 105.391 2014 810.7 2.484 52' 105.771 1312 298.3 4.398 kppendix B-2
CE Technical Report 0081 AppendbcB Fully Plastic Stress Distribution l
, 0, 20 l
~
( Neutral Ms NU -
o, = Flow Stress Fig. g.3
==
)
1 APPENDIX C Crack Stability Analysis 4
4
Appendix C-1 Crack Stability Analvsis The LBB.NRC Computer program is used in the analysis. A listing of the program is
! included in this Appendix. The computer output for different loading cases for three selected node points are also included in this Appendix and the output shows the details of the results. Crack Potentials are plotted with applied bending moments. (See Figures C-1 thru C-6)
The Tearing modulus is calculated at situations where J.,, exceeded the value of J,c.
J.,,is plotted with applied Tearing modulus T ,,along with the material J-T Curve for the weld material to determine allowable (J,n ) at the location. Fig C-7 shows the results.
Appendix C-1
10 REM LEAK BEFORE BREAK 20 REM *Seel Automated Plotting Using LOTUS
30 REM (LBB,NRC version 11 12-85) 31 REM The leak.before-break program is coded based on the NRC-NRR 32 REM (Klecker) method, which is based on the procedure of WUREG/
33 REM CR*3464 except for the modifications on strain hardening.
34 REM For reference of the coding, read the IBM Basic manual.
35 REM * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * * * - - - * - - - - * *
~~51 REM Lines 70 and 90 define default input parameters. The parameters 52 REM can be changed by the user using the EDIT mode.~~
~~53 REM 70 AL = 9: N1 = 9.8: SIGR = 49.4 SIGF = 55.52 TH0 = 50: F = 101.705: TT = .906~~
90 E = 25500

RR = 4.3125: LRC = 350: AMB = .035 110 REM ** --- --=-=** -==- = =-==* *-* == ** - =* = -
~~120 REM Parameter definition and data format preparation 125 REN * - --- -= -- -**-** - - -= ** =*--*-*=-** - *-~~
130 DIM a(20), aS(20), f(13, 2), B(13, 2), CS(10), W(50) 150 DIM A1(5), A2(5), A3(5), x(50), f(50), Z(50) 170 aS(1) = " 1 STRAIN HARDENING alpha = AL ="
190 as(2) = " 2 STRAIN HARDENING n = N="
210 as(3) = " 3 REFERENCE STRESS (ksi) SIGR="
230 a5(4) = " 4 FLOW STRESS (ksi) SIGF="
250 aS(5) = " 5 INITIAL HALF CRACK ANGLE (deg) TH0="
l 270 as(6) = " 6 AxlAL FORCE (kips) F="
l 290 aS(7) = " 7 ELASTIC M00ULUS (ksi) E="
310 eS(8) = " 8 PIPE OR VESSEL RADIUS (in) R="
330 as(9) = " 9 P!PE OR VESSEL THICKNESS (in) T="
350 as(10) = "10 LEAK RATE CONSTANT (g;n/si) LRC="
370 as(11) = =11 APPLIED BENDING MOMENT (kk*in) AMB="
390 Wit = "#N.NN ": W2s = "##N.#N ": W3s="NN.#N ": W/.S = "NN.N "
410 W55 = " ##N.#": W6S = " N.#N ": W75 = "#N.*W" 412 a(1) = AL: a(2) = Nis a(3) = SIGR a(4) = SIGF: a(5) = THO: a(6) = F: a(7) = E 413 a(8) = RR: a(9) = TT: a(10) = LRC: a(11) = AMB Appendix C-2 Computer Program s .,
===*-- - ----- *- - - - -- ----
~~420 RE% *---- - -- -* - - -----~~
421 REM The following are coefficients for F functions from Sander's 422 REM analysis of circunferentially cracked pipe under tension and 423 REM bending. The radius to thickness ratio (R/t) is limited to 424 REM between 4 and 16. The coefficients Listed are for unit 425 REM increments of R/t.
426 REM **----*---------*--------*--------*
430 DATA 3.488, -7.453, 24.792, 1.760, -1.512, 9.470 450 DATA 4.606, 10.402, 28.235, 2.778, -4.120, 12.034 470 DATA 5.566, -12.936, 31.195, 3.653, -6.362, 14.238 490 DATA 6.413, 15.171, 33.804, 4.424, 8.339, 16.181 510 DATA 7.173, -17.178, 36.147, 5.117, 10.114, 17.926
. 530 DATA 7.865, 19.005, 38.280, 5.748, 11.730, 19.514 550 DATA B.501, -20.685, 40.242, 6.328, -13.216, 20.975 570 DATA 9.092, 22.244, 42.062, 6.866, -14.594, 22.330 590 DATA 9.643, 23.700, 43.761, 7.368, -15.882, 23.596 610 DATA 10.161, 25.067, 45.358, 7.840, 17.091, 24.758 630 DATA 10.650, -26.358, 46.865, 8.286, 18.233, 25.907 650 DATA 11.114, 27.581, 48.293, 8.708, -19.314, 26.791 670 DATA 11.554, -28.744, 49.651, 9.110, -20.343, 27.982 671 FOR R = 0 TO 12: FOR C = 0 TO 5 672 IF C < 3 THEN READ T(R, C) ELSE READ B(R, C - 3) 673 NEXT C, R 690 REM *----*----*--*------*-**--------*
700 REM Input form the keyboard 711 REM * -- - --
721 CLS 730 PRINT SPC(32); " LEAK BEFORE BREAK": PRINT SPC(29); TIMES; SPC(4); DATES 731 INPUT " Do you want to use LBB.NRC M00: 7 or 8 (enter 7 or 8) "; ANS 732 INPUT " Facility Name"; CS(2) 733 INPUT " Pipe system"; CS(3) 740 REM * -- - - --
741 REM Open data file LBBOUT.PRN for Lotus plotting input 742 REM Open files MOO.PRN and PLANT.PRW for titles in plotting 743 REM Open file LBBOUT.P!C for storage of Lotus generated picture 744 REM *==---*-- -- - - - **-- =* -= - -* -*---===*
761 OPEN "0", #1, "A:M00.PRN" 762 PRINT #1, " LEAK BEFORE BREAK (LBB.NRC M003"; ANS; ")"
763 CLOSE #1 764 OPEN "0", #1, "A: PLANT.PRW" 765 PRINT #1, CS(2); " "; CS(3) 766 CLOSE #1 767 OPEN "0", #1, "A:LBBOUT.PIC" 768 CLOSE #1 769 OPEN "0", #1, "A:LBBOUT.PRN" i 770 PRINT : PRINT SPC(12); "The current default INPUT PARAMETERS are:": PRINT 800 FOR I = 1 TO 11 PRINT SPC(10); eS(l); a(I): NEXT 1: PRINT 810 PRINT SPC(12); "Do you want to change any of these parametersT" 811 INPUT " Enter y for yes, n for no"; 25: PRINT 820 IF ZS = "y" GOTO 830 ELSE GOTO 930 830 PRINT SPC(5); "To change any parameter, enter its line number, a comme, "
840 PRINT SPC(5); "and then the new parameter va.tue. For example, enter "
850 PRINT SPC(5); "7,25890 to change the etastic modulus to 25890 ksi.": PRINT 860 INPUT ; I, M: a(1) = M: CLS : GOTO 770 861 REM *-- - - - ---- --
862 REM Select the appropriate Sander's F-function coefficients 863 REM depening on R/t.
-*- -- --- ---- =~*-* - - - - *--- * --
~~864 REM ** - -- --- -~~
865 PEM If R/t is less than,4,,it is assumed to be 4 866 REM If R/t is greater than 16, it is assumed to be 16 Appendix C-3 run,,w wm
930 ROT = a(8) / a(9): ROTF = FIX(ROT) 940 IF ROT >= 4 THEN GOTO 960 ELSE ROT a 4 950 ROTF = 4 960 IF ROT == 16 THEN GOTO 980 ELSE ROT = 16 9 70 ROTF = 16 9 72 REM Interpolate Sander's F function coefficients for R/t 9 73 REM between integer values.
980 FOR R = 0 70 12 990 R0 = R + 4 1000 IF R0 <> ROTF THEN GOTO 1060 1010 FOR C = 0 70 2 1020 C1 = c + 12: C2 = c + 15 1030 a(C1) = f(R, C) + (ROT - ROTF) * (f(R + 1, C) - T(R, C))
1D40 a(C2) = B(R, C) + (ROT - ROTF) * (B(R + 1, C) - B(R, C))
1050 NEXT C 1060 NEXT R 13 70 R E M * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
~~1390 REM Print out the top part of the output page 1410 R E M* - - - - - - - - - - - - - - - - - - - - - - - - - - -~~
~~1430 N = 2: DOSus 4210: LPRlWT DATES; 1450 LPRINT TAB (25);~~
N = 24: GOSUB 4210: LPRINT " LEAK BEFORE BREAKS 1470 N = 24: GOSUB 4210: LPRINT SPC(30); "LBB.NRC MOD:"; : LPRINT ANS 1490 N = 24: GOSUB 4210: LPRINT SPC(25); " FACILITY "; LPRINT CS(2) 1510 N = 24: GOSUB 4210 LPRINT SPC(25); " PIPE SYSTEM: "; a LPRINT C$(3): LPRINT 1530 N = 24: GOSUB 4210: LPRINT SPC(30); "!NPUT PARAMETER $"
~~1550 N = 8 GOSUB 4210~~
~~1570 FOR I = 1 To 11 l 1590 LPRINT SPC(16); LEFTS (astl), 39) + "="; a(I) 1610 NEXT Is LPRINT 1630 A115 = " SIGT= Axial Stress SIGBssending Stress MB= Bending Moment "~~
1650 A125 = " PHl= Kink Angle" 1670 N s 8: GOSUB 4210: LPRINT A115 + A125 1690 A135 = " J=J Integret coa = Crack Opening Area LR= Leak Rate "
1710 A14S = " ST=SICT/SIGF" 1720 A155 = " SB=SIGB/SIGF CLetrack Length" 1730 LPRINT A13S + A14S: LPRINT SPC(20); A15$
1750 A4$ s "*** NORMALIZED *** "
1770 A5 S = "*********
ENGINEERING UNITS ***********
1790 A6S = " ff*SB PHI J "
1810 A7S = " $1GB MB PHI J COA LR" 1811 ABS = " -- -- - "
1831 A95 = " (ksi) (kk-in) (deg) (k/in) (si) (opm)"
1851 LPRINT : N s 24: GOSUB 4210: LPRINT A4s + A5$
1871 N = 8: GOSUB 4210: LPRINT A6$ + A7S 1891 LPRINT CHR$(27); " 1"; ABS + A95; CHR5(27); "-0" 1900 N = 2: GOSUB 4210 1910 REM * * *- - - --- - --- ---* - * - - - -- -* - - -
~~1930 REM Start the calculation 1952 REM * - - ----- - ------ --- --- - -- - -- --- ---- --~~
l 1970 AL s'a(1): W1 e a(2): SIGR = a(3): SIGF = a(4): TH0 = a(5): F = a(6): E = a(7) 1990 RR e a(8): TT = a(9): LRC = a(10): AMB = a(11): AT = a(12): BT = a(13): CT = a(14) 2010 AB = a(15): BB = a(16): CB = a(17) 2012 REM Define constants and normalization constants 2090 ALP = AL * (SIGF / SIGR) ^ (N1 1) l 2110 P1 = 3.141593: TH0 = TH0
~~PI / 180: MM = 0: PHIM = 0: JM = 0: COAM = 0: ST = 0 4~~
~~2150 CL = 2~~
RR
~~THO: MM = PI~~
~~TT * $1GF~~
~~RR ^ 2: PHIM = (180 / PI)~~
~~SIGF / E 2170 JM = RR * $1GF ^ 2 / E 2190 COAM = P1~~
~~SIGF~~
~~RR ^ 2 / Et ST = F / (2~~
PI
RR
~~TT * $1GF) 2230 SP s 4 / P1 * (COS(THQ ,/ 2 + PI~~
~~ST / 2) - $1N(THO) / 2) 2250 FJ s SIN (IMO / 2 + PI / 2~~
~~ST) + COS(THO): H = FJ / (SP + ST)~~
Appendix C-4
___ ca m anese @ea m e
2 290 R E M * - - - - - - - - - * * * * * - - - - - - - - - - - - - -
~~2292 REM Determine THF, the final crack angle at the limit load.~~
2294 REM * - - -- -c--- -- ** - - - -* - -- -- - **
2310 THF = TH0 + .36 2330 TH s THF GOSUB 3810: GOSUB 3890 2360 TH01 s THF * (FD / (FB
~~SP + ST~~
~~FT + FD)): DELTA = TH01 - TH0 2370 IF ABS (DELTA) > .000002 THEN THF = THF - DELTA: Goto 2330 2401 REM Calculate BETA from THF 2410 BETA = (SP~~
~~FB + ST~~
~~FT)~~
~~2 / (1 - TH0 / THF) 2430 TH s THos GOBUB 3810: GOBUS 4010 g 2450 FB0 m FB: FTO s FT ISO s IB: ITO s IT 2460 REN *---- -=-=*------=== =*--* = -*--=**= =-=-- - ---- -~~
2461 REM Angle TH is increased from TH0 to the final angle THF in ever 2462 REM increasing step sizes. It is assumed that the ex{al stress is 2463 kEM graoually applied w to the specified value with no bending.
2464 REM The angle at this point is cetted THQ. Then, while holding the 24o5 REM axial stress at the specified value, the bending stras is l 2466 REM gradually applied up to the limit load (or angle THF). Axist 2467 REM and bending stresses (ST,$8) are calculated for each step of TH.
2468 REM Then, LBB.NRC M00:7 and MOD 8 depart. For MOD 7, subsequent 2469 REM output values are based on inittet crack angle THO. For M00:8 2470 REM subsequent output values are based N effective crack anBle TH.
24 71 R EM * - -
2490 NC e 0: SB a 0 THQ = TH0 + .1: GOTO 2590 2491 REM increment angle TH for specified exist stress and increasing 2492 REM bending stress 2510 TH s TH + .001714 * (NC + 1) 2530 IF TH >= THF THEN TH s THF 2550 GOSUB 3810: GOSUB 4010 2570 SB e ((BETA * (1 TH0 / TM)) * .5 ST
~~FT) / FB: GOTO 2690 2580 REM Determine THQ by iteration 2590 TH = THQ: GOSUB 3810 2610 THot a TH * (BETA - (ST~~
~~FT)~~
~~2) / BETA 2630 DELE 8 THol~~
TH0 2650 IF ABS (DELE) > .000002 THEN THQ = THQ - DELE: GOTO 2590 2670 ST = 0: TH s THO: FB s FS0: FT = FTo: IB a 180 IT = ITO 2680 REM Calculate elastic kink angle 2690 IF ANS s 8 THEN PHIE = SB
~~IB + ST~~
~~IT ELSE PHIE = SB~~
~~IB0 + ST~~
~~ITO 2710 ASTSB = ABS (ST~~
~~SB) 2720 REM Introduce strain hardening to the kink angle 2730 PHI e PHIE * (1 + ALP * (SB + ST)~~
~~ASTSB ^ (N1 - 2))~~
~~2750 PHIP = PHI~~
~~PHIE 2810 IF ANS = 8 THEN GOTO 2830 ELSE GOTO 2850 2820 REM Calculate elastic J integral 2830 JE~~
PI
~~TH * (SB~~
~~FB + ST~~
~~FT)~~
~~2: XF = FT / FB: GOTO 2870 2850 JE a PI~~
~~TH0 * (SB~~
~~FB0 + Si~~
~~FTO)~~
~~2: XF s FTO / FB0 l 2870 IF FL = 1 GOTO 2910 ELSE FL s 1 l~~
~~2880 REM Calculate plastic J integret by runerical integration l 2890 JP = .6~~
~~H * (SB + XF~~
~~ST)~~
~~PHIP GOTO 2930 2910 JP s JP + H * .5 * (SB~~
YF
ST + SBS) * (PHIP - PHIPS) 2920 REM Total elastic ptastic J integret 2930 J s JE + JP 2940 REM Calculate crack opening area }
~~2950 coa = IT * (ST + SB * (3 + COS(TM)) / 4) 2960 REM Rewrite in engineering units 2970 SBS s SB + XF~~
~~ST: PHIPS a PHIP: SBA = SB~~
~~SIGF MBA = SB~~
~~MM / 1000: PHIA = PHI~~
~~PHIM 2980 REM Calculate leak rate also l i 2990 JA a J~~
~~JM COAA = CDA~~
~~C0AM: LR s LRC~~
~~CDAA l '~~
t 3010 IF NMB > 0 OR AMB s 0 THEN GOTO 3173 3030 A3(0) = SBA: A3ft) '= PHIA: A3(2) s JA: A3(3) = COAA: A3(4) s LR Appendix C-5
, a- ~ -
I 3050 IF MBA < AMB THEN GOTO 3150 ELSE NMB = 1 3060 REM Interpolate to the applied berding moment 3070 FY = (AMS PMBA) / (MBA - PMBA) 3090 FOR I = 0 TO 4 I
3110 A1(!) = A2(1) + (A3(I) A2(I))
~~FY l y~~
3130 NEXT 1: GOTO 3170 3150 A2(0) = SBA: A2(1) = PHIA: A2(2) = JA: A2(3) = C0AA: A2(4) = LRs PMBA = MBA 3170 W(NC) = MBA: X(NC) = PHIA: Y(NC) = SBA: 2(NC) = JA: NC = NC + 1 3180 REM Print out on paper calculated values 3190 LPRINT USING W18; (ST + $B); e LPRINT USING W2$; PHl; i LPRINT USING W35; J; 3210 LPRINT USING W48; SBA; MBA; PHIA; JA; LPRINT USING W2$; COAA; 3230 LPRINT USING W5$; LR 3235 REM saving data on disk file up to J of 10 (1000 in lb/(in-in))
3236 REM (only the bending moment ord J are saved for plotting) 3240 IF JA > 10 GOTO 3250
> 3245 PRINT #1, MBA, JA 3249 REM If angle TH <THQ, return (exist stress Will increase) 3250 IF THQ > TH COTO 3330 3260 REM pfangleTHreachesthelimitloadangleTHF,itisattdone.
3261 REM Otherwise, THe<TH<THF, return (berding stress will increase) 3270 IF TH = THF GOTO 3510 ELSE GOTO 2510 3310 REM Increment angle TH for zero Dending but increasing axlat stress 3330 TH = TH + .001714 * (NC + 1) 3350 IF TH >= THQ GOTO 3410 3370 GOSUB 3810: GOSUB 4010 3390 ST = (BETA * (1 TH0 / TH)) * .5 / FT: GOTO 2690 3410 TH = THQ: NC = 0: GOTO 3370 3420 CLOSE #1 3430 REM
~~3450 REM Print out the bottom of the output page~~

~~- - * - = --~~

~~1470 REM * -- - - * -- -~~
3490 N = 8 3510 N = 8: GOSUB 4210. x$ = STRINGS (27, 45) 3520 REM Print out results at the applied bending moment 3530 LPRINT XS; "RESULTS AT APPLIED LOAD *"; XS: LPRINT " SIGT= ";
3550 LPRINT USING W65; ST
~~SIGF; : LPRINT "ksi, CL="; I LPRINT USING W6$; CL; 3570 LPRINT "in., AMB="; LPRINT USING W4$; AMB; LPRINT #kk in, Js";~~
3590 LPRINT USING W7$; A1(2); i LPRINT "k/in, *; I LPRINT " StGB=";
3610 LPRINT USING V7$; A1(0); : LPRlWT "ksi, PHl="; : LPRINT USING W68; A1(1);
3612 LPRINT "deg, C0A="; I LPRINT USING W6$; A1(3); LPRINT "si, LR=";
l 3630 LPRINT USING W4$; A1(4); : LPRINT "spm" 3730 N = 2: GOSUB 4210: LPRINT CHR$(12) 3740 PRINT "** Calculation Completed **"
3750 END
- - - * - - - - - = * - - = = * - - - - === =* - - -*
l 3770 R E M * * = =
3790 REM Subroutines l
l 3791 REM * -- - - - --- -- - -- -
! 3800 REM Calculate functions FT and FB l 3810 FT = 1 + (TH / PI)
~~1.5 * (AT + BT * (TH / PI) + CT * (TH / PI) ^ 2) 3830 FB = 1 + (TH / PI) a 1.5 * (AB + BB * (TH / PI) + CB * (TH / PI) ^ 23: RETURN 3850 REM * ---*-- -*----*--- -----*-*-~~
~~3880 REM Calculate function FD containing derivatives of FT and FB 3890 FD1 = 3 * (AB~~
~~SP + ST~~
~~AT) 3910 FD2 = 5 * (BB~~
~~SP + ST~~
~~BT) * (THF / PI) 3930 FD3 = 7 * (CB~~
~~SP + ST~~
~~CT) * (THF / PI)~~
~~2 3950 FD = (THF / PI)~~
~~1.5 * (FD1 + F02 + FD3): RETURN 3970 REM * - * --* -* -*- - - -~~
4000 REM Calculate compliances 18 and IT
{ 4010181 = AB / 7 + BB / 9 * (TH / *PI) + CB / 11 * (TH / PI)
~~2 4030 IB2 = AB~~
~~2 / 2.5 + AB~~
~~BB / 1.% * (TH / PI) + (2~~
AB
~~CB + BB ' 2) / 3.5 * (TH / PI)~~
~~2 Appendix C-6~~
' ~ ~ ~ _
4050 IB3
BB
~~CB / 2 * (TH / PI)~~
~~3 + C8 ^ 2 / 4.5 * (TH / PI)~~
~~4 6070 IS = 2~~
TH
~~2 * (1 + 8 * (TH / PI)~~
~~1.5~~
~~IB1 + (TH / PI)~~
~~3 * (182 + IB3))~~
~~6090171 * (AT + AB) / 7 + (BT + BB) / 9 * (TH / PI) * (CT + CB) / 11 * (TH / PI) ^ 2 4110172 = AT~~
~~As / 2.5 + (AT~~
~~BS + A8~~
~~BT) / 3 * (TH / PI) + (AT~~
~~CB + BT~~
~~BB + AB~~
~~CT) / 3.5 ? (TH / P1)~~
~~2 4130 IT5 * (BT~~
~~Cs + r,s~~
~~CT) / 4 * (TH / P1)~~
~~3 + CT~~
~~Cs / 4.5 * (TH / PI) ^ 4 4150 IT~~
2
~~TH ^ 2 * (1 + 4 * (TH / PI) a 1.5~~
~~IT1 + (TH / PI) ^ 3 * (IT2 + IT3)): RETURN I 4170 R EM~~
~~j 4190 REM This subroutine is to emphasize the lettering of the output 4192 REM characters. For more information, see EPSON printer manual,~~
~~) 4210 LPRINT CHR5(27); *l*; CHR5(N); RETURN~~
~~ppendix C-7 Computer Program~~
02*14 1996 LFAK BEFORE BREAK L88.NRC MOD: 8 Node 10 FACILITT: North Anna units 1 and 2 PIPE SYSTEM: RCS Bypass INPUT PARAMETERS 1 STRAIN HARDENING alpha == 9
< 2 STRAIN HARDENING n= 9.8 3 REFERENCE STRESS (ksi) = 49.4 l 4 FLOW STRESS (ksi) = 55.5 5 INITIAL HALF CRACK ANGLE (deg) = 52 6 AXIAL FORCE (kips) = 101.705 7 ELASTIC MODULUS (ksi) = 25500 8 PIPE OR VESSEL RADIUS (in) = 4.3125 l ! 9 PIPE OR VESSEL THICKNESS (in) = .906 j 10 LEAK RATE CONSTANT (opm/si) = 350 j 11 APPLIED SENDING MOMENT (kk in) = .035 SIGT= Axial Stress S!G8= Sending Stress M8=8ending Moment PHl= Kink Angle JsJ Integral COA = Crack opening Area LR= Leak Rate ST=SIGT/$1GF
$8sSIG8/SIGF CL= Crack Length
NORMALIZED *** ********** ENGINEERING UNITS ""******
ST*S8 PHI J SIGS M8 PHI J COA LR 0
0.0000 0.000 0.000 0.00 0.00 0.00 0.00 0.000 0.0
] 0.0746 0.200 0.041 0.00 0.00 0.02 0.02 0.025 8.9 j j 0.1178 0.308 0.092 2.39 0.13 0.04 0.05 0.039 13.7 j O.1627 0.426 0.170 4.89 0.26 0.05 0.09 0.054 18.8 l 0.2076 0.549 0.274 7.38 0.39 0.07 0.14 0.069 24.3 j 0.2518 0.678 0.403 9.83 0.52 0.08 0.21 0.086 30.0 0.2947 0.815 0.559 12.21 0.65 0.10 0.29 0.103 35.9 0.3360 0.959 0.741 14.50 0.77 0.12 0.39 0.121 42.2 0.3754 1.114 0.950 16.69 0.88 0.14 0.50 0.139 48.8 0.4128 1.284 1.189 18.76 0.99 0.16 0.62 0.160 55.9 0.4478 1.474 1.462 20.71 1.10 0.18 0.76 0.181 63.4 0.4804 1.693 1.776 22.52 1.19 0.21 0.93 0.204 71.4 0.5103 1.950 2.140 24.18 1.28 0.24 1.11 0.229 80.0 l 0.5374 2.258 2.568 25.68 1.36 0.28 1.34 0.255 89.2 0.5616 2.628 3.071 27.03 1.43 0.33 1.60 0.283 99.2 0.5828 3.070 3.661 28.20 1.49 0.38 1.91 0.314 109.9 0.6010 3.586 4.344 29.21 1.55 0.45 2.26 0.347 121.5 0.6159 4.175 5.116 30.04 1.59 0.52 2.67 0.383 134.0 0.6278 4.825 5.963 30.70 1.62 0.60 3.11 0.422 147.6 0.6364 5.515 6.856 31.18 1.65 0.69 3.57 0.464 162.3 0.6418 6.219 7.762 31.48 1.67 0.78 4.04 0.509 178.2 0.6441 6.910 8.641 31.61 1.67 0.86 4.50 0.559 195.6
( 0.6442 7.070 8.843 31.61 1,67 0.88 4.61 0.571 199.9 l . . . . . . . . . . . . . . . . . . . . . . . . . - - RE sutT S AT APPt ! ED t0AD . . . . . - . - - - - . - - - - -
SIGT= 4.143 ksi, CL= 7.828 in., AM8= 0.04 kk in, Ja 0.029k/in, SIG8= 0.661ksi, PHl= 0.029 deg, COA = 0.029 si, LR= 10.22 ppm Appendix C-8 Computer Output i c.
02 14 1996 LEAK BEFC E BREAK LBB.NRC MOD: 8 FACILITY North Anna Units 1 and 2 PIPE SYSTEM: RCS Bypass Node 10 INPUT PARAMETERS 1 STRAIN HARDENING alpha == 9 l 2 STRAIN HARDENING n= 9.8 3 REFERENCE STRESS (ksi) = 49.4
. 4 FLOW STRESS (ksi) = 55.5
! 5 INITIAL HALF CRACK ANGLE (deg) = 52 6 AxlAL FORCE (kips) = 105.771 7 ELASTIC MODULUS (ksi) = 25500 i 8 PIPE OR VESSEL RADIUS (in) = 4.3125 9 PIPE OR VESSEL THICKNESS (in) = .906 10 LEAK RATE CONSTANT (spn/si) = 350 11 APPLIED BENDING MOMENT (kk in) = .298 SIGT= Axial Stress StGB= Bending Stress MB= Bending Monent PHl= Kink Angle f
! JsJ Integral COA = Crack opening Area LR= Leak Rate ST=$1GT/SIGF SB=SIGB/SIGF CL= Crack Length
~~*** ********** ENGINEERING UNITS **********~~
NORMALIZED ST+SB PHI J SIGS MB PHI J COA LR l' *0 O.0000 0.000 0.000 0.00 0.00 0.00 0.00 0.000 0.0 I
0.0776 0.208 0.044 0.00 0.00 0.03 0.02 0.026 9.3 0.1196 0.314 0.096 2.33 0.12 0.04 0.05 0.040 13.9 0.1640 0.430 0.174 4.79 0.25 0.05 0.09 0.054 19.0 0.2086 0.553 0.278 7.27 0.38 0.07 0.14 0.070 24.4 0.2525 0.682 0.407 9.71 0.51 0.09 0.21 0.086 30.1 0.2953 0.818 0.563 12.08 0.64 0.10 0.29 0.103 36.0 0.3365 0.962 0.746 14.37 0.76 0.12 0.39 0.121 42.3 0.3758 1.117 0.955 16.55 0.88 0.14 0.50 0.140 48.9 0.4131 1.287 1.195 18.62 0.99 0.16 0.62 0.160 56.0 0.4481 1.477 1.469 20.56 1.09 0.18 0.77 0.181 63.5 0.4806 1.696 1.783 22.37 1.18 0.21 0.93 0.204 71.5 0.5105 1.954 2.149 24.02 1.27 0.24 1.12 0.229 80.1 0.5376 2.262 2.577 25.53 1.35 0.28 1.34 0.255 B?.4 0.5617 2.633 3.082 26.87 1.42 0.33 1.61 0.284 99.3 0.5829 3 .0 75 3.675 28.04 1.48 0.38 1.91 0.315 110.1 0.6010 3.592 4.360 29.05 1.54 0.45 2.27 0.348 121.7 0.6159 4.180 5.134 29.88 1.58 0.52 2.67 0.383 134.2 0.6277 4.829 5.982 30.53 1.62 0.60 3.12 0.422 147.8 0.6363 5.518 6.877 31.00 1.64 0.69 3.58 0.464 162.5 0.6417 6.221 7.784 31.30 1.66 0.78 4.05 0.510 178.5 0.6439 6.909 8.662 31.43 1.66 0.86 4.51 0.559 195.8 0.6440 7.054 8.846 31.43 1,66 0.88 4.61 0.571 199.8
. . . . . . . . . . . . . . . . . . . . . . . . . . . R E SULT S AT APPL I ED LOAD -
SIGT= 4.309 kai, CL= 7.828 in., AMB= 0.30 kk in, J= 0.109k/in, StGB= 5.630ksi, PHI = 0.059 deg, COA = 0.060 si, LR= 20.86 spm Appendix C-9 Computer Output t
i 4
02-14 1996 LEAK BEFORE BREAK LSB.NRC MOD: 8 FACILITY: North Anna Units 1 and 2 P2PE SYETEM: RCS Bypass Node 10 INPUT PARAMETERS 1 STRAIN HARDENING alpha == 9 2 STRAIN HARDENING ns 9.8 j 3 REFERENCE STRESS (kst) = 49.4 4 FLOW STRESS (ksi) = 55.5 5 INITIAL HALF CRACK ANGLE (des) = 98 6 AXIAL FORCE (ktps) = 104.581 7 ELASTIC MODULUS (ksi) = 25500 8 PIPE OR VESSEL RADIUS (in) = 4.3125 l 9 PIPE OR VESSEL THICKNESS (in) = .906 10 LEAK RATE CONSTANT (spintsi) = 350
, 11 APPLIED BENDING MOMENT (kk-in) = .221 SIGT=Axlet Stress $1G3= Bending Stress MB= Sending Moment PHl= Kink Angle JmJ Integral COA = Creek opening Area Lk= Leak Rate ST=SIGT/$1GF j SS=SIGB/SIGF CL= Crock Length
~~NORMALIZED * **** * *** ENGINEERING UNITS ******* "~~
ST+SB PHI J SIGB MS PHI J COA LR 4
0 0.0000 0.000 0.000 0.00 0.00 0.00 0.00 0.000 0.0 0.0219 0.549 0.039 0.00 0.00 0.07 0.02 0.070 24.4 0.0343 0.874 0.096 0.00 0.00 0.11 0.05 0.111 -38.9 i 0.0455 1.182 0.176 0.00 0.00 0.15 0.09 0.150 52.6 0.0559 1.489 0.274 0.00 0.00 0.19 0.14 0.189 66.3 0.0658 1.801 0.392 0.00 0.00 0.22 0.20 0.229 80.2 0.0749 2.123 0.529 0.00 0.00 0.26 0.28 0.270 94.5 0.0768 2.191 0.560 0.00 0.00 0.27 0.29 0.279 97.5 0.0801 2.284 0.599 0.19 0.01 0.28 0.31 0.290 101.5 0.0848 2.419 0.658 0.45 0.02 0.30 0.34 0.306 107.2 0.0906 2.594 0.736 0.77 0.04 0.32 0.38 0.328 114.7 0.0972 2.804 0.834 1.13 0.06 0.35 0.43 0.353 123.6 l 0.1042 3.048 0.951 1.52 0.08 0.38 0.50 0.383 134.0 0.1115 3.323 1.088 1.93 0.10 0.41 0.57 0.417 145.8 0.1187 3.629 1.245 2.33 0.12 0.45 0.65 0.454 158.8 0.1257 3.966 1.421 2.72 0.14 0.49 0.74 0.495 173.2 0.1324 4.333 1.617 3.09 0.16 0.54 0.84 0.540 188.9 0.1385 4.732 1.833 3.43 0.18 0.59 0.95 0.589 206.0 0.1440 5.166 2.068 3.73 0.20 0.64 1.08 0.642 224.6 0.1487 5.637 2.322 4.00 0.21 0.70 1.21 0.699 244.7 0.1527 6.148 2.597 4.22 0.22 0.77 1.35 0.762 266.6 0.1559 6.702 2.891 4.39 0.23 0.84 1.51 0.830 290.4 0.1581 7.306 3.204 4.52 0.24 0.91 1.67 0.904 316.3 0.1595 7.963 3.537 4.59 0.24 0.99 1.84 0.985 344.6 l 0.1600 8.681 3.890 4.62 0.24 1.08 2.03 1.0 73 375.5 0.1600 8.717 3.907 4.62 0.24 1.09 2.04 1.077 377.1
...........................RESULTS AT APPLIED LOAD - ----- -----= * * -**=
i SIGT= 4.260 ksi, CL=14.752 in., AMs= 0.22 kk-in, Ja 1.326k/in, SICBs 4.175ksi, PHl= 0.755 des, COA = 0.750 si, LR= 262.52 spm Appendix U-10 Com$wter Output
02 14 1996 LEAK BEFORE BREAK LBS.NRC MOD: 8 FACILITT: North Anna Units 1 and 2 PIPE SYSTEM: RCS Bypass Node 10 to INPUT PARAMETERS 1 STRAIN NARDENING alpha == 9
! 4 2 STRAIN MARDENING ns 9.8 i 3 REFERENCE STRESS (ksi) = 49.4 4 FLOW STRESS (ksi) = 55.5 5 INITIAL MALF CRACK ANGLE (des) = 98.5
, 6 AX!AL FORCE (kips) = 104.581 7 ELASTIC MODULUS (ksi) = 25500 8 PIPE OR VESSEL RA01US (in) = 4.3125 9 PIPE OR VESSEL THICKNESS (In) = .906 10 LEAK RATE CONSTANT (spm/st) = 350 l 11 APPLIED BENDING MOMENT (kk In) = .221 SIGT=Anlet Stress $100=8ending Stress MB=8ending Moment PN!= Kink Angle J=J Integral COA = Creek opening Area LR= Leek Rate ST=SIGT/SIGF
$8=$1G8/$1GF CL= Crock Length
~~NORMALIZED *** * * * * * * * "~~
ENGlWEERING UNITS "********
ST+SS PHI J $1G5 MB PHI J C04 LR 0
0.0000 0.000 0.000 0.00 0.00 0.00 0.00 0.000 0.0 0.0214 0.552 0.039 0.00 0.00 0.07 0.02 0.070 24.6 0.0336 0.878 0.097 0.00 0.00 0.11 0.05 0.112 39.1 0.0446 1.187 0.174 0.00 0.00 0.15 0.09 0.151 52.8 0.0549 1.496 0.271 0.00 0.00 0.19 0.14 0.190 66.6 0.0645 1.810 0.387 0.00 0.00 0.23 0.20 0.230 80.6 0.0735 2.134 0.523 0.00 0.00 0.27 0.27 0.271 95.0 0.0768 2.260- 0.580 0.00 0.00 0.28 0.30 0.287 100.6 0.0799 2.352 0.619 0.18 0.01 0.29 0.32 0.299 104.5 0.0844 2.486 0.677 0.42 0.02 0.31 0.35 0.315 110.2 0.0899 2.659 0.754 0.73 0.04 0.33 0.39 0.336 117.6 0.0962 2.869 0.851 1.08 0.06 0.36 0.44 0.362 126.5 0.1029 3.112 0.967 1.45 0.08 0.39 0.50 0.391 136.9 0.1099 3.387 1.103 1.84 0.10 0.42 0.57 0.425 148.6 0.1168 3.693 1.258 2.22 0.12 0.46 0.66 0.462 161.7 0.1236 4.030 1.432 2.60 0.14 0.50 0.75 0.503 176.1 0.1299 4.398 1.626 2.95 0.16 0.55 0.85 0.548 191.8 0.1358 4.799 1.839 3.28 0.17 0.60 0.96 0.597 209.0 0.1411 5.235 2.072 3.57 0.19 0.65 1.08 0.650 227.7 0.1456 5.708 2.323 3.82 0.20 0.71 1.21 0.708 247.9 0.1494 6.221 7.595 4.03 0.21 0.78 1.35 0.771 270.0 0.1524 6.780 2.885 4.20 0.22 0.85 1.50 0.840 294.0 i 0.1545 7.387 3.195 4.32 0.23 0.92 1.66 0.914 320.1 l 0.1558 8.049 3.525 4.39 0.23 1.00 1.84 0.996 348.6 0.1562 8.741 3.859 4.41 - 0.23 1.09 2.01 1.081 378.4
, . . . . . . . . . . . . . . . . . . . . . . . . . . . RE SULT S AT APPL I ED LOAD- - - -
SIGT= 4.260 ksi, CL=14.828 in., AMe= 0.22 kk in, J= 1.482k/in, SIGs= 4.175ksi, PN!= 0.836 des, COA = 0.830 si, LR= 290.61 opm Appendix C-11 Comp, uter Output
' =
02 14 1996 LEAK BEFORE BREAK LBS.NRC MOD: 8 FACILITY:
PIPE SYSTEM: Node 45 INPUT PARAMETERS 1 STRAIN HARDENING alphe == 9 2 STRAIN NARDENING ns 9.8 3 REFERENCE STRESS (ksi) = 49.4 4 FLOW STRESS (ksi) = 55.5 5 INITIAL NALF CRACK ANGLE (des) = 30 6 AX1AL FORCE (kips) = 101.705 7 ELASTIC MODULUS (ksi) = 25500 8 PIPE OR VESSEL RADIUS (in) = 4.3125 9 PIPE OR VESSEL THICKNESS (in) = .906 10 LEAK RATE CONSTANT (spm/st) = 350 11 APPLIED SEMOING MOMENT (kk in) = .749 SIGT=Axlel Strees $!G8= Sending Stress Mengending b eent PHI = Kink Angle t JsJ Integral COA = Crack opening Area LR= Leek Rate ST=SIGT/$1GF
$3=SIGB/SIGF CL=C'eck r Length l
= *" * * " * * " *
ENGINEERING UNITS *** * ****
NORMALI2ED ST+$8 PHI J SIGS MB PWI J COA LR 0
0.0000 0.000 0.000 0.00 0.00 0.00 0.00 0.000 0.0 O.0747 0.051 0.014 0.00 0.00 0.01 0.01 0.007 2.3
! 0.1560 0.106 0.058 4.51 0.24 0.01 0.03 0.014 4.7 0.2288 0.158 0.123 8.55 0.45 0.02 0.06 0.020 7.1 l*
0.2979 0.211 0.211 12.39 0.66 0.03 0.11 0.027 9.4 0.3640 0.267 0.321 16.06 0.85 0.03 0.17 0.034 11.9 0.4273 0.330 0.454 19.57 1.04 0.04 0.24 0.042 14.6 0.4875 0.407 0.615 22.91 1.21 0.05 0.32 0.050 17.5 0.5445 0.513 0.815 26.08 1.38 0.06 0.42 0.059 20.6 0.5981 0.680 1.081 29.05 1.54 0.08 0.56 0.068 24.0 0.6480 0.958 1.461 31.82- 1.68 0.12 0.76 0.079 27.7 0.6942 1.425 2.037 34.38 1.82 0.18 1.06 0.091 31.8
0.7365 2.188 2.928 36.73 1.94 0.27 1.53 0.104 36.3 0.7749 3.374 4.290 38.86 2.06 0.42 2.23 0.118 41.3 0.8092 5.120 6.303 40.77 2.16 0.64 3.28 0.134 46.7
' 42.45 2.25 0.94 4.76 0.151 52.8 O.8395 7.551 9.144 0.8658 10.755 12.953 43.91 2.32 1.34 6.75 0.170 59.5 0.8880 14.754 17.791 45.14 2.39 1'.84 9.27 0.191 66.8 j 0.9062 19.478 23.598 46.15 2.44 2.43 12.29 0.214 74.9 0.9204 24.752 30.174 46.94 2.48 3.09 15.72 0.239 83.8
, 0.9306 30.300 37.168 47.50 2.51 3.78 19.36 0.267 93.6 I
0.9368 35.759 44.107 47.85 2.53 4.46 22.98 0.298 104.3 0.9392 40.718 50.445 47.98 2.54 5.08 26.28 0.331 116.0 l 0.9392 41.219 51.088 47.98 2.54 5.14 26.61 0.335 117.4
! . . . . . . . . . . . . . . . . . . .. . . .. . . .REsul.T S AT APPL I ED LOADa -- -- -- - -- - - -
1 SIGT= 4.145 ksi, CL= 4.516 in., AMs= 0.75 kk-In, Ja 0.137k/in, SIG8= 14.150ksi. PNl= 0.030 deg, C0A= 0.030 si, LR= 10.64 spm Appendix C-12 Computer Output 6
o_________________________________
02 14 1996 LEAK BEFORE BREAK LBB.NRC M00: 8 FACILITY: North Anna Units 1 & 2 P!PE STSTEM: RCS BYPASS Node 45 INPUT PARAMETERS 1 STRAIN HARDEN!NC alphe == 9 2 STRAIN HARDENING ns 9.8 3 REFERENCE STRESS (ksi) = 49.4
! 4 FLOW STRESS (ksi) = 55.5 5 !NITIAL HALF CRACK ANGLE (deg) = 30 6 AXIAL FORCE (kips) = 105.391
. 7 ELASTIC MODULUS (ksi) = 25500 8 PIPE OR VESSEL RADIUS (in) = 4.3125 9 PIPE OR VESSEL THICKNESS (in) = .906 10 LEAK RATE CONSTANT (spm/st) = 350 11 APPLIED BENDING MOMENT (kk in) = .811 SIGT=Axist Stress SIGB= Bending Stress MB= Bending Moment PH1= Kink Angle
, JsJ Integret COA = Crack Opening Area LR= Leak Rate ST=SIGT/SIGF SB=SIGB/SIGF CL= Creek Length
NORMALI2ED *** **"****** ENGINEERING UNITS * *******
ST*SB PHI J StGB MB PHI J COA LR 0
0.0000 0.000 0.000 0.00 0.00 0.00 0.00 0.000 0.0
. 0.0774 0.053 0.015 0.00 0.00 0.01 0.01 0.007 2.4 i 0.1574 0.107 0.059 4.44 0.24 0.01 0.03 0.014 4.8
! 0.2298 0.158 0.125 8.46 0.45 0.02 0.06 0.020 7.1 0.2987 0.211 0.212 12.28 0.65 0.03 0.11 0.027 9.5 0.3648 0.268 0.322 15.95 0.84 0.03 0.17 0.034 12.0 0.4281 0.331 0.456 19.46 1.03 0.04 0.24 0.042 14.6 0.4883 0.408 0.617 22.80 1.21 0.05 0.32 0.050 17.5 0.5453 0.515 0.819 25.97 1.37 0.06 0.43 0.059 20.6 0.5988 0.682 1.086 28.94 1.53 0.09 0.57 0.069 24.0 0.6487 0.963 1.469 31.71 1.68 0.12 0.77 0.079 27.7 0.6949 1,435 2.050 34.27 1,81 0.18 1.07 0.091 31.8 0.7373 2.205 2.951 36.62 1.94 0.27 1.54 0.104 36.3 0.7756 3.401 4.329 38.75 2.05 0.42 2.26 0.118 41.3 0.8100 5.163 6.366 40.66 2.15 0.64 3.32 0.134 46.8 0.8404 7.616 9.241 42.34 2.24 0.95 4.81 0.151 52.9 l 0.8666 10.848 13.096 43.80 2.32 1.35 6.82 0.170 59.5 0.8888 14.880 17.990 45.04 2.38 1.86 9.37 0.191 66.9 0.9070 19.642 23.863 46.04 2.44 2.45 12.43 0.214 75.0 0.9212 24.956 30.510 46.83 2.48 3.11 15.89 0.240 83.9 0.9313 30.542 37.577 47.39 2.51 3.81 19.57 0.268 93.7 0.9375 36.035 44.582 47.74 2.53 4.49 23.22 0.298 104.4 0.9399 41.018 50.974 47.87 2.53 5.12 26.55 0.332 116.2 0.9399 41.477 51.564 47.87 2.53 5.17 26.86 0.335 117.4
. . . . . . . . . . . . . . . . . . . . . . . . . . . R E SULT S AT APPL I ED LOAD - - - - - - - - - - - - -
j SIGT= 4.296 ksi, CL= 4.516 in., AMB= 0.81 kk in, Ja 0.158k/in, l SICB= 15.321ksi, PHl= 0.032 deg, COA = 0.033 si, LR= 11.54 opm Appendix C-13 Computer Output 4
02 14-1996 LEAK BEFORE BREAK LBB.NRC M00: 8 FACILITY: North Anna Units 1 and 2 PIPE SYSTEM: RCS BYPASS Node 45 INPUT PARAMETERS 1 STRAIN HARDENING alpha as 9 2 STRAIN HARDENING ns 9.8 3 REFERENCE STRESS (ksi) = 49.4 j 4 FLOW STRESS (ksi) = 55.5 5 INITIAL HALF CRACK ANGLE (des) = 59.5 l
6 AXIAL FORCE (kips) = 104.699 7 ELASTIC MODULUS (ksi) = 25500 8 PIPE OR VESSEL RADIUS (in) ' = 4.3125 9 PIPE OR VESSEL THICENESS (in) = .906 l 10 LEAK RATE CONSTANT (spm/si) = 350 l
11 APPLIED SENDING MOMENT (kk in) = .793 SIGT= Axial Stress S!GBsBending Stress MBrBending Moment PHl= Kink Angle JsJ Integral COA = Crack Opening Area LRsLeak Rate STsSIGT/SIGF SB SIGB/SIGF CLecrack Length
~~*** ********** ENGINEERING UNITS **********~~
NORMALIZED ST*SB' PHI J StGB MB PHI J C0A LR 0
0.0000 0.000 0.000 0.00 0.00 0.00 0.00 0.000 0.0 I
0.0712 0.280 0.053 0.00 0.00 0.03 0.03 0.036 12.5 O.0768 0.303 0.062 0.00 0.00 0.04 0.03 0.039 13.5 0.1095 0.422 0.115 1.81 0.10 0.05 0.06 0.053 18.7 0.1458 0.559 0.195 3.83 0.20 0.07 0.10 0.070 24.6 0.1832 0.707 0.301 5.90 0.31 0.09 0.16 0.039 31.1 0.2204 0.863 0.434 7.97 0.42 0.11 0.23 0.108 37.9 0.2568 1.028 0.593 9.99 0.53 0.13 0.31 0.129 45.1 0.2921 1.203 0.780 11.95 0.63 0.15 0.41 0.150 52.6 0.3258 1.388 0.993 13.82 0.73 0.17 0.52 0.173 60.6 0.3578 1.586 1.234 15.59 0.83 0.20 0.64 0.197 69.1 0.3878 1.800 1.505 17.26 0.91 0.22 0.78 0.223 78.0 0.4156 2.033 1.807 18.80 1.00 0.25 0.94 0.250 87.6 0.4410 2.290 2.143 20.21 1.07 0.29 1.12 0.279 97.8 0.4640 2.576 2.518 21.49 1.14 0.32 1.31 0.311 108.7 0.4844 2.895 2.935 22.62 1.20 0.36 1.53 0.344 120.4 0.5021 3.251 3.396 23.60 1.25 0.41 1.77 0.380 133.0 0.5170 3.646 3.903 24.43 1.29 0.45 2.03 0.419 146.5 0.5292 4.080 4.454 25.11 1.33 0.51 2.32 0.460 161.1 0.5385 4.550 5.041 25.62 1.36 0.57 2.63 0.505 176.9 0.5450 5.052 5.657 25.98 1.38 0.63 2.95 0.554 194.0 0.5487 5.579 6.291 26.19 1.39 0.70 3.28 0.607 212.6 0.5496 6.032 6.821 26.24 1.39 0.75 3.55 0.655 229.1
. . . . . . . . . . . . . . . . . . . . . . . . . ..R E SUL T S AT AP PL I ED L OAD SIGT = 4.265 ksi, CL= 8.957 in., AMB= 0.79 kk in, J= 0.600k/in, StGB* 14.981ksi, PHl= 0.189 deg, COA = 0.189 si, LRs 66.15 spm Appendix C-14 Computer Output
l-t I
02 14 1996 LEAK BEFORE BREAK l
' LSB.NRC MOD: 8 FAclLITY: North Anna Units 1 and 2 PIPE SYSTEM: RCS syPASS l
Node 45 l
INPUT PARAMETERS 1 STRAIN HARDENING alphe ass 9
+
2 STRAIN HARDENING n= 9.8 !
= 49.4 3 REFERENCE STRESS (ksi) 4 FLOW STRESS (ksi) = 55.5 l 5 INITIAL HALF CRACK ANGLE (des) = 60 6 AXIAL FORCE (kips) = 104.699 l
7 ELASTIC MODULUS (ksi) = 25500 8 PIPE OR VESSEL RADIUS (in) = 4.3125 l 9 PIPE OR VESSEL THICENESS (in) = .906 10 LEAK RATE CONSTANT (spn/si) = 350 ,
11 APPLIED BENDING MOMENT (kk in) = .793 PHl= Kink Angle SIGT=Amiel Stress SIGB= Bending Stress MB= Bending Moment J=J Integral COA = Crack Opentne Area LR= Leak Rate ST=SIGT/SIGF SB=$1GB/SIGF CL= Crack Length
~~NORMALIZED~~
*******"* ENGINEERING UNITS MB PHI J COA LR ST+%B PMI J SIGB l
0 0.00 0.00 0.00 0.00 0.000 0.0 l 0.0000 0.000 0.000 0.00 0.00 0.04 0.03 0.036 12.6 0.0703 0.284 0.053 0.00 0.04 0.03 0.039 13.8 0.0768 0.311 0.064 0.00 0.09 0.05 0.06 0.054 19.0 0.1089 0.430 0.117 1.78 0.20 0.07 0.10 0.0 72 25.1 0.1447 0.568 0.197 3.76 0.31 0.09 0.16 0.090 31.6 0.1815 0.718 0.303 5.81 7.85 0.42 0.11 0.23 0.110 38.5 0.2183 0.876 0.436 9.85 0.52 0.13 0.31 0.131 45.7 0.2544 1.043 0.596 0.62 0.15 0.41 0.152 53.4 0.2892 1.220 0.782 11.79 0.72 0.18 0.52 0.176 61.4 0.3226 1.407 0.995 13.64 l 15.39 0.81 0.20 0.64 0.200 70.0 0.3542 1.608 1.237 0.90 0.23 0.79 0.226 79.0 0.3838 1.823 1.307 17.04 0.98 0.26 0.94 0.253 88.7 /
0.4113 2.058 1.808 18.56 1.06 0.29 1.12 0.283 99.0 0.4365 2.316 2.144 19.96 1.12 0.32 1.31 0.314 110.0 0.4592 2.602 2.517 21.22 1.18 0.36 1.53 0.31 8 121.8 0.4793 2.921 2.930 22.34 1.23 0.41 1,76 0.384 134.5 0.4968 3.275 3.387 23.31 1.28 0.46 2.03 0.423 148.2 0.5116 3.667 3.888 24.13 1.31 0.51 2.31 0.466 163.0 ,
0.5235 4.097 4.430 24.79 25.30 1.34 0.57 2.61 0.511 178.9 f 0.5327 4.563 5.009 l 1.36 0.63 2.93 0.561 196.2 0.5391 5.060 5.,615 25.65 1.37 0.70 3.25 0.614 214.9 0.5426 5.584 6.240 25.85 1.37 0.75 3.51 0.660 231.1 0.5435 6.020 6.747 25.90
. . . . . . . . . . .. ... . . ... .. ... . . RESULT S AT APPLI ED LCAD-- -
4.265 ksi, CL= 9.032 in., AMB= 0.79 kk in, Ja 0.615k/in, SIC 1=
[
LR= 67.97 spm StGB= 14.981ksi, PM1= 0.195 deg, COA = 0.194 si,
) l Appendix C-15
{ Computer Output I
02 14-1996 LEAK BEFORE BREAK LBB.WRC MOD: 8 FACILITY North Anna Units 1 and 2 PIPE SYSTEM: RCS Bypass Node 45 INPUT PARAMETERS 1 STRAIN HARDEN!NG alpha am 9 2 STRAIN HARDENING n= 9.8 3 REFERENCE STRESS (ksi) = 49.4 4 FLOW STRESS (ksi) 55.5 5 INITIAL HALF CRACK ANGLE (des) = 75 6 AXIAL FORCE (kips) a 104.699 l 7 ELASTIC MODULUS (ksi) = 25500 8 PIPE OR VESSEL RADIUS (in) = 4.3125
! 9 P!PE OR YESSEL THICKNESS (in) = .906 1 10 LEAK RATE CONSTANT (spm/si) = 350 11 APPLIED BENDING MOMENT (kk*in) = .793 SICTsAxial Stress SIGBeBending Stress MB= Bending Moment PHisKink Angle JsJ Integral COA = Crack Opening Area LR= Leak Rate STsSICT/SIGF SB=SIGB/SIGT CL= Crack Length
"* NORMALIZED *** ***"*"** **""**
ENGINEERING {tNITS ST*SB PHI J $1GB MB PHI J CDA LR
-0 0.0000 0.000 0.000 0.00 0.00 0.00 0.00 0.000 0.0 0.0475 0.395 0.052 0.00 0.00 0.05 0.03 0.050 17.6 0.0745 0.629 0.130 0.00 0.00 0.08 0.07 0.080 28.0 0.0768 0.650 0.139 0.00 0.00 0.08 0.07 0.C83 28.9 O.0935 0.776 0.191 0.92 0.05 0.10 0.10 0.098 34.3 0.1143 0.938 0.269 2.08 0.11 0.12 0.14 0.118 41.3 0.1372 1.125 0.3 74 3.35 0.18 0.14 0.19 0.141 49.3 0.1609 1.331 0.504 4.66 0.25 0.17 0.26 0.166 58.1 0.1847 1.552 0.661 5.99 0.32 0.19 0.34 0.193 67.6 0.2080 1.738 0.843 7.28 0.39 0.22 0.44 0.222 77.7 0.2305 2.039 1.052 8.53 0.45 0.25 0.55 0.253 88.4 0.2518 2.305 1.287 9.71 0.51 0.29 0.67 0.285 99.8 0.2718 2.588 1.548 10.82 0.57 0.32 0.81 0.320 111.9 O.2902 2.890 1.835 11.84 0.63 0.36 0.96 0.356 124.7 0.3070 3.213 2.149 12.77 0.68 0.40 1.12 0.395 138.4 0.3220 3.559 2.489 13.60 0.72 0.44 1.30 0.437 153.0 0.3351 3.930 2.857 14.33 0.76 0.49 1.49 0.482 168.7 0.3462 4.329 3.251 14.95 0.79 0.54 1.69 0.530 185.5 0.3553 4.759 3.671 15.45 0.82 0.59 1.91 .0.582 203.6 0.3623 5.224 4.119 15.85 0.84 0.65 2.15 0.638 223.2 0.3674 5. 72 7 4.592 16.12 0.85 0.71 2.39 0.698 244.3 0.3704 6.272 5.092 16.29 0.86 0.78 2.65 0.763 267.2 l
0.3714 6.863 5.616 16.35 0.87 0.86 2.93 0.835 292.1 0.3714 4.869 5.621 16.35 0.87 0.86 2.93 0.835 292.4
. . . . . . . . . . . . . . . . . .. . . . . .. . .RE SUL T S AT APPL I ED LOAD ---- - - - -- --- -
l $!GT= 4.265 ksi, CL=11.290 in., AMB= 0.79 kk in, J= 1.708k/in,
! StGB= 14.981ksi, PHl= 0.543 deg, COA = 0.533 si, LR= 186.72 spm Appendix C-16 Computer Output f
02 14 1996 LEAK BEFORE BREAK LBB.NRC M00: 8 FACILITT: North Anna Units 1 and 2 PIPE SYSTEM: RCS Bypass INPUT PARAMETERS Node 45 1 STRAIN HARDENING alpha == 9 2 STRAIN HARDENING n= 9.8 3 REFERENCE STRESS (ksi) = 49.4 I
4 FLOW STRESS (ksi) = 55.5 5 INITIAL HALF CRACK ANGLE (des) = 75.5 6 AXIAL FORCE (kips) = 104.699 7 ELASTIC MODULUS (ksi) = 25500 i
1 8 PIPE OR VESSEL RADIUS (in) = 4.3125 9 PIPE OR VESSEL THICKNESS (in) = .906 10 LEAK RATE CONSTANT (spm/st) = 350
' = .793 11 APPLIE0 BENDING MOMENT (kk In)
SIGT=Axist Stress SIGB= Bending Stress MB=BendinB Moment PNisKink Angle JsJ Integral COA = Crack Opening Area LR= Leak Rate ST=SIGT/SIGF SB=$1GB/SIGF CL= Crack Length
"* * """"* ENGINEERING UNITS '"*"""
NORMAll2ED ST*SB PHI J SICB MB PH! J CDA LR 0
0.0000 0.000 0.000 0.00 0.00 0.00 0.00 0.000 0.0 0.0468 0.399 0.052 0.00 0.00 0.05 0.03 0.051 17.8 0.0734 0.635 0.130 0.00 0.00 0.08 0.07 0.081 28.3 0.0768 0.666 0.143 0.00 0.00 0.08 0.07 0.085 29.6 0.0931 0.792 0.195 0.90 0.05 0.10 0.10 0.100 35.0 0.1134 0.954 0.273 2.03 0.11 0.12 0.14 0.120 42.0 0.1358 1.142 0.377 3.27 0.17 0.14 0.20 0.143 50.1 0.1591 1.349 0.507 4.57 0.24 0.17 0.26 0.168 58.9 l 0.1823 1.572 0.663 5.87 0.31 0.20 0.35 0.196 68.5 l 0.2055 1.810 0.845 7.14 0.38 0.23 0.44 0.225 78.6 0.2276 2.062 1.053 8.37 0.44 0.26 0.55 0.256 89.4 0.2486 2.331 1.288 9.53 0.50 0.29 0.67 0.288 100.9 0.2683 2.616 1.548 10.62 0.56 0.33 0.81 0.323 113.1 0.2864 2.921 1.835 11.63 0.62 0.36 0.96 0.360 126.0 l
0.3029 3.246 2.148 12.55 0.66 0.40 1.12 0.399 139.8 0.3177 3.594 2.487 13.37 0.71 0.45 1.30 0.442 154.6 0.3305 3.968 2.853 14.08 0.75 0.49 1.49 0.487 170.4 0.3414 4.371 3.246 14.69 0.78 0.55 1.69 0.535 187.3 0.3504 4.804 3.665 15.18 0.80 0.60 1.91 0.587 205.6
' 0.3573 5.2 73 4.111 15.57 0.82 0.66 2.14 0.644 225.3
! 0.3622 5.780 4.583 15.84 0.84 0.72 2.39 0.705 246.6 0.3651 6.329 5.001 16.00 0.85 0.79 2.65 0.TT1 269.8 0.3661 6.914 5.594 16.05 0.85 0.86 2.91 0.841 294.4
. . . . . . . . . . . . . . . . . . . . . . . . . . . R E SULT S AT APPL I ED LOAD -
i SIGT= 4.265 ksi, CL=11.365 in., AMB= 0.79 kk in, J= 1.821k/in,
' LR= 198.22 spm SICBs 14.981ksi, PHl= 0.577 deg, COA = 0.566 si, Appendix C-17 Computer Output c ,
02 14-1996 LEAK BEFORE BREAK LSB.NRC MOD: 8 FACILITY North Anna Units 1 and 2 P!PE SYSTEM: RCS Bypass INPUT PARAMETERS
, 1 STRAIN MARDENING alpha == 9 Node 70 2 STRAIN HARDENING ns 9.8 3 REFERENCE STRESS (ksi) = 49.4 4 FLOW STRESS (ksi) = 55.5 5 INITIAL HALF CRACK ANGLE (deg) = 29 6 AX1AL FORCE (kips) = 103.027 7 ELASTIC MODULUS (ksi) = 25500 8 PIPE OR VESSEL RADIUS (in) = 4.3125 9 PIPE OR VESSEL THICKNESS (in) = .906 l 10 LEAK RATE CONSTANT (opWal) = 350 11 APPLIE0 BENDING MOMENT (kk-in) = .809 {
i
$1GT=Axlat Stress $1GB= Bending Stress MB= Bending Moment PHl= Kink Angle !
JsJ Integret COA = Crack Opening Area LR= Leak Rate ST=SIGT/$1GF SB=SIGB/SIGF CL= Crack Length
NORMALIZED *** ********** ENGINEERING UNITS **********
ST+SB PHI J SIGS MB PHI J COA LR 0
0.0000 ~0.000 0.000 0.00 0.00 0.00 0.00 0.000 0.0 0.0757 0.048 0.014 0.00 0.00 0.01 0.01 0.006 2.1 0.1588 0.100 0.057 4.62 0.24 0.01 0.03 0.013 4.5 l 0.2330 0.149 0.122 8.73 0.46 0.02 0.06 0.019 6.7 0.3034 0.199 0.209 12.64 0.67 0.02 0.11 0.026 8.9 0.3707 0.253 0.317 16.38 0.87 0.03 0.17 0.032 11.3 i
0.4351 0.313 0.449 19.95 1.06 0.04 0.23 0.040 13.8 l 0.4963 0.388 0.609 23.34 1.24 0.05 0.32 0.047 16.6 0.5541 0.496 0.811 26.55 1.41 0.06 0.42 0.056 19.5 0.6084 0.668 1.082 29.57 1.57 0.08 0.56 0.065 22.8 l 0.6590 0.963 1.477 32.38 1,71 0.12 0.77 0.075 26.4 l 0.7058 1.465 2.085 34.97 1.85 0.18 1.09 0.087 30.3
? 0.7486 2.290 3.038 37.35 1.98 0.29 1.58 0.099 34.6 O.7874 3.577 4.507 39.50 2.09 0.45 2.35 0.113 39.4 j 0.8221 5.477 6.687 41.43 2.19 0.68 3.48 0.128 44.7 J 0.8527 8.126 9.773 43.12 2.28 1.01 5.09 0.145 50.6 0.8792 11.620 13.919 44.60 2.36 1.45 7.25 0.163 57.1 l O.9016 15.983 19.192 45.84 2.43 1.99 10.00 0.183 64.2 O.9199 21.143 25.531 46.86 2.48 2.64 13.30 0.206 72.1 0.9342 26.913 32.719 47.65 2.52 3.36 17.04 0.231 80.8 0.9445 32.992 40.379 48.22 2.55 4.11 21.03 0.258 90.3 0.9508 38.990 47.999 48.57 2.57 4.86 25.00 0.288 100.7 0.9532 44.457 54.984 48.70 2.58 5.54 28.64 0.321 112.2 0.9532 45.056 55.752 48.70 2.58 5.62 29.04 0.325 113.7
. . . . . . . . . . . . . . . . . . . . . . . . . . . RE SULT S A T APPL I ED L DAD - - - - - - - - * - - - + - - -- - -
SIGT= 4.199 ksi, CL= 4.366 in., AMB= 0.81 kk In, J= 0.149k/in, SIGB= 15.283ksi, PHl= 0.030 deg, CoAs 0.030 si, LR= 10.61 gpm Appendix C-18 I
Computer Output
==,
e
02 14 1996 LEAK BEFORE BREAK LBB.NRC MOD: 8 FACILITY: North Anna Units 1 and 2 PIPE SYSTEM: RCS Bypass l INPUT PARAMETERS Node 70 1 STRAIN HARDENING alpha == 9 2 STRAIN HARDENING n= 9.8 3 REFERENCE STRESS (ksi) = 49.4 4 FLOW STRESS (ksi) = 55.5 5 INITIAL HALF CRACK ANGLE (deg) = 29 6 AXIAL FORCE (kips) = 105.207 7 ELASTIC MODULUS (ksi) = 25500 8 PIPE OR VESSEL RADIUS (In) = 4.3125 t
9 P!PE OR VESSEL THICKNESS (in) = .906 10 LEAK RATE CONSTANT (spm/si) = 350 11 APPLIED BENDING MOMENT (kk-in) = .886 SIGT=Axist Stress $1GB= Bending Stress MB= Bending Moment PHl= Kink Angle JsJ Integral COAsCrack opening Area LR= Leak Rate ST=SIGT/SICF
, SBsSICB/SIGF CL= Crack Length
" NORMAllZED *** * ****
ENGINEERING UNITS *** * *
ST+SB PHI J SICB MB PHI J CDA LR j 0 0.0000 0.000 0.000 0.00 0.00 0.00 0.00 0.000 0.0 0.0773 0.049 0.014 0.00 0.00 0.01 0.01 0.006 2.2 0.1597 0.100 0.058 4.57 0.24 0.01 0.03 0.013 4.5 0.2336 0.149 0.123 8.68 0.46 0.02 0.06 0.019 6.7 0.3039 0.200 0.209 12.58 0.67 0.02 0.11 0.026 8.9
, 0.3712 0.253 0.318 16.31 0.86 0.03 0.17 0.032 11.3 0.4355 0.314 0.450 19.88 1.05 0.04 0.23 0.040 13.9 0.4967 0.389 0.611 23.28 1.23 0.05 0.32 0.047 16.6 0.5545 0.497 0.813 26.49 1.40 0.06 0.42 0.056 19.6 0.6089 0.670 1.085 29.50 1.56 0.08 0.57 0.065 22.8
. 0.6595 0.967 1.482 32.31 1.71 0.12 0.77 0.075 26.4 0.7062 1.471 2.094 34.91 1.85 0.18 1.09 0.087 30.3 0.7491 2.301 3.053 37.28 1.97 0.29 1.59 0.099 34.7 0.7878 3.595 4.532 39.44 2.09 0.45 2.36 0.113 39.5 0.8226 5.505 6. 728 41.36 2.19 0.69 3.50 0.128 44.8 0.8532 8.169 9.836 43.06 2.28 1.02 5.12 0.145 50.7 0.8797 11.681 14.012 44.53 2.36 1.46 7.30 0.163 57.1 0.9021 16.067 19.322 45.78 2.42 2.00 10.07 0.184 64.3 0.9204 21.252 25.705 46.79 2.48 2.65 13.39 0.206 72.2 0.9347 27.048 32.941 47.59 2.52 3.37 17.16 0.231 80.8 0.9449 33.154 40.649 48.16 2.55 4.13 21.18 0.258 90.4 0.9512 39.175 48.314 48.50 2.57 4.89 25.17 0.288 100.8 0.9536 44.659 55.336 48.64 2.57 5.57 28.83 0.321 112.3 0.9536 45.232 56.071 48.64 2.57 5.64 29.21 0.325 113.7
...........................RESULTS AT APPLIED LOAD-* -- -----*---** --*- -- -
SIGT= 4.288 ksi, CL= 4.366 in. , AMB= 0.89 kk in, Ja 0.174k/in, SICBs 16.738ksi, PHI = 0.032 deg, COA = 0.033 si, LR= 11.62 spm Appendix C-19
! Computer Output s '.
I i
L 02 14 1996 LEAK BEFORE BREAK LSB.NRC MOD: 8 FACILITY: North Anna Units 1 and 2 PIPE SYSTEM: RCS Bypass INPUT PARAMETERS gg 1 STRAIN NARDENING slphe == 9 l
2 STRAIN HARDENING n= 9.8 l 3 REFERENCE STRESS (kst) = 49.4 l 4 FLOW STRESS (ksi) = 55.5
! 5 INITIAL NALF CRACK ANGLE (deg) = 58
! 6 AXIAL FORCE (ktps) = 104.569 7 ELASTIC MODULUS (ksi) = 25500 8 PIPE OR VESSEL RADIUS (In) = 4.3125 9 PIPE OR VESSEL THICKNESS (in) = .906 10 LEAK RATE CONSTANT (Bpen/st) = 350 i
11 APPLIED BENDING MOMENT (kk-in) = .863 SIGT=Axlal Stress SIGB= Bending Stress MB= Bending Moment PN!= Kink Angle i JsJ Integral COA = Crack Opening Aree LR= Leak Rate ST=$lGT/SIGF SBsSIGB/SIGF CL= Crack Length f
m * **** * *** ENGINEERING UNITS * ** * **
~~NORMALIZE 0 ST*SB PHI J StGB MB PHI J C0A LR 0~~
0.0000 0.000 0.000 0.00 0.00 0.00 0.00 0.000 0.0 0.0737 0.269 0.053 0.00 0.00 0.03 0.03 0.034 12.0 0.0767 0.280 0.057 0.00 0.00 0.03 0.03 0.036 12.5 0.1112 0.397 0.110 1.91 0.10 0.05 0.06 0.050 17.6 0.1492 0.531 0.190 4.02 0.21 0.07 0.10 0.067 23.4 0.1880 0.674 0.296 6.18 0.33 0.08 0.15 0.085 29.7 0.2266 0.825 0.428 8.32 0.44 0.10 0.22 0.104 36.3 0.2643 0.984 0.587 10.41 0.55 0.12 0.31 0.123 43.2 0.3008 1.152 0.773 12.43 0.66 0.14 0.40 0.144 50.5 O.3356 1.331 0.986 14.37 0.76 0.17 0.51 0.166 58.2 0.3(86 1.524 1.227 16.20 0.86 0.19 0.64 0.190 66.4 0.3996 1.732 1.497 17.92 0.95 0.22 0.78 0.214 75.0 0.4283 1.961 1.801 19.51 1.03 0.24 0.94 0.241 84.3 0.4547 2.215 2.141 20.97 1.11 0.28 1.12 0.269 94.1 0.4785 2.500 2.523 22.30 1.18 0.31 1.31 0.299 104.7 0.4996 2.823 2.951 23.47 1.24 0.35 1.54 0.332 116.0
! 0.5180 3.186 3.429 24.49 1.30 0.40 1.79 0.366 128.2 0.5336 3.593 3.958 25.35 1.34 0.45 2,06 0.404 141.4 0.5463 4.043 4.536 26.06 1.38 0.50 2.36 0.444 155.6
' 26.60 1.41 0.56 2.69 0.488 170.9 O.5561 4.531 5.155 .
0.5630 5.050 5.804 26.99 1.43 0.63 3.02 0.536 187.5 0.5670 5.593 6.469 27.21 1.44 0.70 3.37 0.587 205.5 0.5681 6.100 7.076 27.27 1.44 0.76 3.69 0.638 223.2
...........................RESULTS AT APPLIED LOAD ~~~~-
SICT= 4.260 ksi, CL= 8.731 In., AMB= 0.86 kk in, J= 0.647k/in,
? SICBs 16.303ksi PHI = 0.192 deg, coAs 0.191 si, LR= 66.88 gpm Appendix C-20 Computer Output 6
02 14-1996 LEAK BEFORE BREAK LBB.WRC MOD: 8 FACILITY: North Anna Units 1 and 2 PIPE SYSTEM: RCS Bypass Node 70 INPUT PARAMETERS 1 STRAIN HARJENING alpha == 9 2 STRAIN HARDENING n= 9.8 3 REFERENCE STRESS (ksi) = 49.4 l 4 FLOW STRESS (ksi) = 55.5 5 INITIAL HALF CRACT ANGLE (des) = 74.5 6 AXIAL FORCE (ktps) = 104.569 7 ELASTIC MODULUS (ksi) = 25500 l
3 PIPE OR VESSEL RADIUS (in) = 4.3125 9 PIPE OR VESSEL THICKNESS (in) = .906 10 LEAK RATE CONSTANT (spm/st) = 350 11 APPLIE0 BENDING MOMENT (kk in) = .863 I
SIG1=Axist Stress StGB= Sending Stress M8=5ending Moment PMl= Kink Angle JsJ Intwgret COA = Crack opening Area LR= Leak Rate ST=SIGT/SIGF Sp=SIGB/SIGF CL= Crack tength
NORMALIZE 0 '" ********** ENGINEERING UNITS *****"***
Sivs8 PHI J $1GB MB PHI J C04 LR 0
0.0000 0.000 0.000 0.00 0.00 0.00 0.00 0.000 O.0 0.0482 0.392 0.052 0.00 0.00 0.05 0.03 0.050 17.4 O.0756 0.623 0.131 0.00 0.00 0.08 0.07 0.079 27.7 0.0767 0.633 0.135 0.00 0.00 0.08 0.07 0.081 28.2
! 0.0938 0.760 0.187 0.95 0.05 0.09 0.10 0.096 33.6 0.1151 0.922 0.266 2.13 0.11 0.11 0.14 0.116 40.6 0.1384 1.108 0.370 3.42 0.18 0.14 0.19 0.139 48.6 0.1626 1.313 0.501 4.77 0.25 0.16 0.26 0.164 57.3 0.1868 1.532 0.658 6.11 0.32 0.19 0.34 0.191 66.8 0.2105 1.767 0.841 7.42 0.39 0.22 0.44 0.219 76.8 0.2333 2.015 1.050 8.69 0.46 0.25 0.55 0.250 87.4 J 0.2550 2.279 1.285 9.89 0.52 0.28 0.67 0.282 98.7 )
0.2753 2.560 1.547 11.02 0.58 0.32 0.81 0.316 110.7 0.2941 2.860 1.835 12.06 0.64 0.36 0.96 0.353 123.4 0.3111 3.180 2.150 13.01 0.69 0.40 1.12 0.391 137.0 0.3263 3.523 2.491 13.85 0.73 0.44 1.30 0.433 151.5 0.3396 3.891 2.859 14.59 0.77 0.49 1.4v 0.477 167.0 0.3509 4.287 3.255 15.22 0.81 0.53 1.70 0.525 183.7 0.3602 4.714 3.677 15.73 0.83 0.59 1.92 0.576 201.6 l l 0.3674 5.176 4.126 16.13 0.85 0.65 2.15 0.631 221.0 O.3726 5.675 4.601 16.42 0.87 0.71 2.40 0.691 241.9
. 0.3757 6.215 5.102 '6.5% 0.88 0.78 2.66 0.756 264.7 1 0.3767 6.802 5.628 16.65 0.88 0.85 2.93 0.827 289.3 0.3767 6.825 5.649 16.65 0.88 0.85 2.94 0.829 290.3
. . . . . . . . . . . . . . . . . . . . . . . . . . . R E SUL T S AT AP PL I ED LOAD * * = * -
SIGT= 4.260 ksi, CL=11.215 in., AMB= 0.86 kk in, Ja 2.297k/in, StGB= 16.303ksi, PHl= 0.683 deg, COA = 0.667 si, LR= 233.49 spm Appendix C-21 Computer Output
~~e. l I~~
02 14-1996 LEAK BEFORE BREAK L88.NRC MOD: 8 FACILITY: North Anna Units 1 and 2 PIPE STSTEM: RCS Bypass INPUT PARAMETERS alpha == 9 Node 70 1 STRAIN HAltDENING 2 STRAIN HARDENING n= 9.8 3 REFERENCE STRESS (ksi) = 49.4 e & FLOW STRESS (kst) = 55.5 5 INITIAL HALF CRACK ANGLE (des) = 75 l 6 AXIAL FostCE (kips) = 104.569 l 7 ELASTIC MODULUS (kst) = 25500 8 PIPE OR VESSEL RADIUS (in) = 4.3125 9 PIPE OR VESSEL THICKNESS (in) = .906 i
10 LEAK RATE CONSTANT (spn/st) = 350 i 11 APPLIED BENDING MOMENT (kk-in) = .863 I
I SIGT=Axlat 3 tress SIG8= Sending Stress MB= Sending Moment PHl= Kink Angle J=J Integral COA = Crack Opening Area LR= Leak Rate ST=$lGT/SIGF
' CL= Crack Length
$8= SICS /SICF NORMALIZE 0 *** ********** ENGINEERING UNITS **********
ST+SB PHI J $1GB MB PHI J COA LR 0
0.0000 0.000 0.000 0.00 0.00 0.00 0.00 0.000 0.9 i 0.0475 0.395 0.052 0.00 0.00 0.05 0.03 0.050 17.6 0.0745 0.629 0.130 0.00 0.00 0.08 0.07 0.080 28.0 0.0767 0.649 0.139 0.00 0.00 0.08 0.07 0.083 28.9 0.0934 0.775 0.191 0.92 0.05 0.10 0.10 0.098 34.3 0.1142 0.938 0.269 2.08 0.11 0.12 0.14 0.118 41.3 0.1371 1.125 0.3 73 3.35 0.18 0.14 0.19 0.141 49.3 0.1609 1.331 0.504 4.67 0.25 0.17 0.26 0.166 58.1 0.1847 1.552 0.660 5.99 0.32 0.19 0.34 0.193 67.6 0.2080 1.788 0.843 7.28 0.39 0.22 0.44 0.222 77.7 l
0.2305 2.038 1.051 8.53 0.45 0.25 0.55 0.253 88.4 0.2518 2.305 1.286 9.72 0.51 0.29 0.67 0.285 99.8 0.2718 2.588 1.547 10.82 0.57 0.32 0.81 0.320 111.9 0.2902 2.890 1.835 11.85 0.63 0.36 0.96 0.356 124.7 0.3070 3.213 2.148 12.78 0.68 0.40 1.12 0.395 138.4 0.3220 3.558 2.489 13.61 0.72 0.44 1.30 0.437 153.0 0.3351 3.929 2.856 14.34 0.76 0.49 1.49 0.482 168.7 0.3462 4.329 3.250 14.95 0.79 0.54 1.69 0.530 185.5 0.3553 4. 75 9 3.671 15.46 0.82 0.59 1.91 0.582 203.6
! 0.3624 5.224 4.118 15.85 0.84 0.65 2.15 0.638 223.1 0.3674 5.727 4.592 16.13 0.85 0.71 2.39 0.698 244.3 0.3704 6.2 72 5.091 16.30 0.86 0.78 2.65 0.763 267.2 0.3714 6.863 5.616 16.35 0.87 0.86 2.93 0.8I5 292.1 0.3714 6.870 5.622 16.35 0.87 0.86 2.93 0.835 292.4
. . . . . . . . . . . . . . . . . . . . . . . . . . . R E SUL T S A T A PPL I ED L OAD-- -- - - - -- - -- - - - - -- - -
SIGT= 4.260 ksi, CL=11.290 in., AM8= 0.86 kk in, Ja 2.'80k/in, 6
l SICBs 16.303ksi, PHl= 0.790 deg, COAs 0.771 si, LR= 269.76 ppm Appandix C-22 Computer Output
?
l North Anna Units 1 & 2 RCS Loop Bypass Line (Location 10) 2.5 - -
c m
2 a
R
< c
.b E 1 .5 r c
x
/ /
8 W
1
?
.s y 0.5
~M
, s ~
c #
o 0.1 0.15 0.2 0.25 0 0.05 Bending Moment Mb (1000 in-kip)
Fig. C-1 l
Appendix C-23
i l
l l
North Anna Units 1 & 2 RCS Loop Bypass Line (Location 10) 2.5 2 a g c:
"c
~~P J~~
Q 1.5
.E 3
=
.c f
0.5
, < ~
c#
0 0 0.05 0.1 0.15 0.2 0.25 Bending Moment Mb (1000 in-kips)
Fig. C-2 l
l l
.. Appendix C-24
~~c. _ _ _ . _ _ _ _ _ - _ _ _ _ - _ _ _ _ - - _~~
i t
I I
l-North Anna Units 1 & 2 RCS Loop Bypass Line (Location 45) i 3
2.5
+
R h2 f e
1.5
-O [
.E 1
A M
c 0.5 '
'~
a /
gg M' 0 0.2 0.4 0.6 0.8 1 Bending Moment Mb (1000 in- kips)
Fig. C-3
~~' Appendix C-25 l~~
North Anna Units 1 & 2 RCS Loop Bypass Line (Location 45) 3 o
Q3 2.5 '
R
}2 e 3
}
1 E.5 /
1 x
k W 0.5 0[
0 0.2 0.4 0.6 0.8 1 Bending Moment Mb (1000 in -kips)
Fig. C-4 l
,. Appendix C-26
l North Anna Units 1 & 2 RCS Loop Bypass Line (Location 70) l 3
a 3
~ 2.5 R
. G 2 l
b
. 5 TD 1
1.5 0
y /
[ I
$1
.G / \
m M f
0.5 '
- /
0' O 0.2 0.4 0.6 0.8 1 Bending Moment Mb (1000in - kips)
Fig. C-5 l
l Appendix C-27
North Anna Units 1 & 2 RCS Loop Bypass Line (Location 70) 3 f
2.5
+
R f "c 2 E
c
[
1.5 e /
.s 1
a M
r 0.5
'~
- d g M 0 0.2 0.4 0.6 0.8 1 Bending Moment Mb (1000in-kips) l l Fig. C-6 Appendix C-28 L _ _ _ _ _ _ _ _ _ _ _
Appendix C
[
Crack Stability Analvsis Aeolied Tearina Modulus
_ Node Point 10 Site of 10 gpm crack = 7.828" (obtained by trial @ 10.22 gpm)
T.,, = dJ/da * ( E / S,2) dJ = 1.482 - 1.326 k/in = .156 k/in da = 14.828" - 14.752" = .076" T.,, = (.156 / .076 ) (25,000/ 55.52) = 16.99 J.,, = 1482 lb/in J . ( See Fig C-7) 14.828" crack is stable Node Point 45 Size of 10 gpm crack = 4.516" dJ = 1.821 - 1.708 khn = .133 k/in da = 11.365" - 11.290" = .075" T.,,. = (.133 / .075 ) (25,000/ 55.52) = 14.68 J.,, = 18211b/in 11.365" crack is stable Node Point 70 Size of 10 gpm crack = 4.366" dJ = 2.680 - 2.297 k/in = .383 k/in da = 11.290" - 11.215" = .075" T,,, = (.383 / .075 ) (25,000/ 55.52) = 42.3 J,,, = 2680 lb/in 11.290" crack is stable Appendix C-29
J - T Curve for Material 6000 5500 5000 4500
{4000r\ \
.5 3500 >s s
G 3000 [ f a ,l Node 70 p q 2500 x
.5 v
f ff '
// / x
,2000 Node 45 N_
1500 j gNode 10 , x
//# C 1000 ll/
500 I
y,II I
O O 50 100 150 200 250 300 T
Fig. C-7 Appendix C-30
.'

ML20249C403

Text

Introduction:

2.0 Background

3.0 Evaluation

Conclusions:

References:

Purpose:

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