NL-22-0406, Request to Relax the Required Number of Fully Tensioned Reactor Pressure Vessel Head Closure Studs in Technical Specification Table 1.1-1, Modes

Request to Relax the Required Number of Fully Tensioned Reactor Pressure Vessel Head Closure Studs in Technical Specification Table 1.1-1, Modes

ML22231B055
Person / Time
Site:	Hatch
Issue date:	08/19/2022
From:	Gayheart C Southern Nuclear Operating Co
To:	Document Control Desk, Office of Nuclear Reactor Regulation
References
NL-22-0406
Download: ML22231B055 (104)

Text

3535ColonnadeParkway

 Cheryl A. Gayheart Birmingham,AL35243

Regulatory Affairs Director 2059925316 tel



2059927601 fax

 cagayhea@southernco.com

August 19, 2022 Docket Nos.: 50-321 NL-22-0406 50-366 10 CFR 50.90 U. S. Nuclear Regulatory Commission ATTN: Document Control Desk Washington, D. C. 20555-0001 Edwin I. Hatch Nuclear Plant - Units 1 and 2 Request to Relax the Required Number of Fully Tensioned Reactor Pressure Vessel Head Closure Studs in Technical Specification Table 1.1-1, MODES Ladies and Gentlemen:

Pursuant to the provisions of 10 CFR 50.90, Application for amendment of license, construction permit or early site permit, Southern Nuclear Operating Company (SNC) hereby requests a proposed license amendment to the Technical Specifications (TS) for Edwin I. Hatch Nuclear Plant (HNP) Units 1 and 2 Renewed Facility Operating Licenses DPR-57 and NPF-5, respectively. The proposed amendment would revise TS Table 1.1-1, MODES.

The amendment is considered a permanent change to allow operation of HNP Units 1 and 2 with the required reactor pressure vessel head closure studs fully tensioned. The required number of fully tensioned closure studs, which may be less than the total number, has been established by calculation that demonstrates operation of HNP Units 1 and 2 reactor pressure vessels with the required studs fully tensioned does not result in any component of the reactor pressure vessel closure flange exceeding the design basis ASME Code allowables. The calculation for HNP Unit 1 determined that any one closure stud may be less than fully tensioned. The calculation for HNP Unit 2 determined that any two closure studs may be less than fully tensioned as long as the two studs are separated by nine or more studs. Prudent operating and engineering principles are applied to maintaining all the head closure studs in service. Circumstances may arise that result in the need to safely operate HNP Units 1 and 2 with a head closure stud(s) not fully tensioned.

SNC has made several attempts to remove HNP Unit 2 reactor pressure vessel head closure stud #33 due to the identification of a circumferential flaw indication. Removal is necessary to perform an ASME Section V, Mandatory Appendix 6 (Liquid Penetrant) or Mandatory Appendix 7 (Magnetic Particle) Surface Examination. SNC is proposing changes to TS Table 1.1-1 to address the increased possibility that a reactor pressure vessel head closure stud may not be able to be fully tensioned and avert the possible need for an exigent or emergency license amendment during the Spring 2023 Refueling Outage. Therefore, SNC requests approval of the proposed license amendment by February 25, 2023. The amendment, if approved, will be implemented within 30 days of issuance.



U.S. Nuclear Regulatory Commission NL-22-0406 Page 2



 provides a description and assessment of the proposed change, including a no significant hazards considerations analysis, regulatory requirements, and environmental considerations. Attachment 1 to Enclosure 1 provides the existing TS pages marked to show the proposed change. Attachment 2 to Enclosure 1 provides the revised (clean) TS pages. provides the HNP Unit 1 calculation for operation with one closure stud out of service. Enclosure 3 provides the HNP Unit 2 calculation for operation with two closure studs out of service.

In accordance with 10 CFR 50.91, Notice for public comment, State consultation, paragraph (b), a copy of this application, with enclosures and attachments, is being provided to the designated Georgia Officials.

This letter contains no regulatory commitments. If you have any questions regarding this submittal, please contact Amy Chamberlain at 205.992.6361.

I declare under penalty of perjury that the foregoing is true and correct. Executed on the 19th day of August 2022.

Respectfully submitted, Cheryl A. Gayheart Regulatory Affairs Director Southern Nuclear Operating Company CAG/agq

Enclosures:

1. Evaluation of the Proposed Change

2. Calculation C-037-2201-00-01, Hatch Unit 1 Operation with One Stud Out of Service Evaluation

3. Calculation C-037-2201-00-02, Hatch Unit 2 Operation with Two Studs Out of Service Evaluation cc: NRC Regional Administrator, Region II NRC NRR Project Manager - Hatch NRC Senior Resident Inspector - Hatch Director, Environmental Protection Division - State of Georgia RType: CHA02.004





Edwin I. Hatch Nuclear Plant - Units 1 and 2 Request to Relax the Required Number of Fully Tensioned Reactor Pressure Vessel Head Closure Studs in Technical Specification Table 1.1-1, MODES NL-22-0406 Enclosure 1 Evaluation of the Proposed Change to NL-22-0406 Evaluation of the Proposed Change ENCLOSURE Evaluation of the Proposed Change

Subject:

Request to Relax the Required Number of Fully Tensioned Reactor Pressure Vessel Head Closure Studs in Technical Specification Table 1.1-1, MODES

1.

SUMMARY

DESCRIPTION

2. DETAILED DESCRIPTION 2.1 System Design and Operation 2.2 Current Technical Specification Requirements 2.3 Reason for Proposed Change 2.4 Description of Proposed Change

3. TECHNICAL EVALUATION

4. REGULATORY EVALUATION 4.1 Applicable Regulatory Requirements/Criteria 4.2 Precedent 4.3 No Significant Hazards Consideration Determination Analysis 4.4 Conclusions

5. ENVIRONMENTAL CONSIDERATION

6. REFERENCES ATTACHMENTS:

1. HNP Units 1 and 2 Technical Specifications Marked-up Pages

2. HNP Units 1 and 2 Technical Specifications Revised Pages E1-1 to NL-22-0406 Evaluation of the Proposed Change

1.

SUMMARY

DESCRIPTION Southern Nuclear Operating Company (SNC) is proposing to revise the Technical Specifications (TS) Table 1.1-1, MODES, for Hatch Nuclear Plant (HNP) Units 1 and 2.

The amendment is considered a permanent change to the Technical Specifications allowing operation of HNP Units 1 and 2 with the required reactor pressure vessel head closure studs fully tensioned. The required number of fully tensioned closure studs, which may be less than the total number, has been established by calculation that demonstrates operation of HNP Units 1 and 2 reactor pressure vessels (RPVs) with the required studs fully tensioned does not result in any component of the reactor pressure vessel closure flange exceeding the design basis ASME Code allowables. The calculation for HNP Unit 1 determined that any one closure stud may be less than fully tensioned. The calculation for HNP Unit 2 determined that any two closure studs may be less than fully tensioned as long as the two studs are separated by nine or more studs.

2. DETAILED DESCRIPTION 2.1 System Design and Operation The HNP Unit 1 reactor pressure vessel is designed, fabricated, inspected, and tested in accordance with ASME Boiler and Pressure Vessel Code,Section III, Nuclear Vessels, 1965 Edition and addenda to and including winter 1966 addenda, and the following additions:

x Low-alloy steel plate for pressure parts in accordance with ASME SA-533, Grade B, Class 1 material and Code Cases 133B-3 and 1339-2.

x Low-alloy steel forgings to pressure parts in accordance with ASME SA-508, Class 2 material, Code Case 1332-4.

x Inconel nozzles in accordance with SB-166 material, Code classes 1336 and 1359-1.

x Nozzle ends for austenitic pipe and flange ends for low-allow steel nozzles in accordance with SA-105 Grade II material, Code Case 1332-4.

x Studs, nuts, bushings, and washers in accordance with American Society of Testing Materials A-540, Grade 24 material and Code Case 1335.

x Shroud support legs, baffle plate, and ring in accordance with SB-168 material, Code Case 1336.

The HNP Unit 2 reactor pressure vessel is designed, fabricated, tested, inspected, and stamped in accordance with the ASME Boiler and Pressure Vessel Code,Section III, Class A (1968 edition plus summer 1970 addendum). The HNP Unit 2 reactor pressure vessel closure studs were examined in accordance with the requirements of ASME Section III, N-325. Bored blank nuts were ultrasonically examined by both the longitudinal E1-2 to NL-22-0406 Evaluation of the Proposed Change and shear wave methods. Shear wave examination of the nuts was performed in both the axial and circumferential directions.

The cylindrical shell and bottom head of the HNP Units 1 and 2 reactor pressure vessels are fabricated of low-alloy steel, the interior of which is clad with stainless steel weld overlay.

Internal surfaces of nozzles that connect to stainless steel pipe are also clad with stainless steel weld overlay.

Each reactor pressure vessel top head is secured to the reactor pressure vessel by studs and nuts. These nuts are tightened with a stud tensioner. The reactor pressure vessel flanges are sealed with two concentric metal seal-rings designed to permit no detectable leakage through the inner or outer seal at any operating condition, including heating to operating pressure and temperature at a maximum rate of 100°F/h and cold hydrostatic pressure testing at the pressure specified in the ASME Code. The reactor pressure vessel is described in the HNP Unit 1 Final Safety Analysis Report (FSAR) Section 4.2.4.1 (Reference 1) and Appendix I (Reference 2) and in the HNP Unit 2 FSAR Section 5.4.6.3.1.

(Reference 3).

Reactor vessel top head flange leakage detection is provided for both HNP Units 1 and 2.

A connection is provided on the reactor vessel flange into the annulus between the two metallic seal rings used to seal the reactor vessel and top head flanges. This connection permits detection of leakage from the inside of the reactor vessel past the inner seal ring.

The connection is piped to a pressure switch having an associated alarm in the main control room. The reactor vessel top head flange leakage detection is described in the HNP Unit 1 FSAR Section 7.8.5.5 (Reference 4) and in the HNP Unit 2 FSAR Sections 5.6.2.5 and 5.2.7.2.2.1 (Reference 5).

A Class 1 system leakage test in accordance with ASME Code IWB-5220 is conducted prior to each plant startup following a reactor refueling outage at a test pressure of 1045 psig.

Plant procedures provide the methodology for tensioning the reactor pressure vessel closure studs, and the studs at HNP Units 1 and 2 are typically tensioned four studs at a time in a four-fold symmetric pattern. If the reactor pressure vessel head is to be installed with an untensioned stud(s), the tensioning pattern will be reviewed to ensure that the sealing o-rings are fully compressed before the stud(s) not being tensioned is encountered in the pattern. The final tensioned condition of the studs is verified by an elongation measurement when all required studs have been tensioned. Elongations must be within acceptance criteria. The acceptance criteria for the final stud elongations are established to ensure that ASME Code stress limits are met for specified service loads for the worst-case flange and stud bending that result from various tensioning patterns, including an untensioned stud(s). The ASME Code examination requirements would also be reviewed to verify the requirements are being met or if relief is necessary.

E1-3 to NL-22-0406 Evaluation of the Proposed Change 2.2 Current Technical Specification Requirements HNP Units 1 and 2 TS Table 1.1-1, MODES, is provided below:

Table 1.1-1 (page 1 of 1)

MODES AVERAGE REACTOR COOLANT REACTOR MODE TEMPERATURE MODE TITLE SWITCH POSITION (°F) 1 Power Operation Run NA 2 Startup Refuel(a) or Startup/Hot NA Standby 3 Hot Shutdown(a) Shutdown > 212 4 Cold Shutdown(a) Shutdown 212 5 Refueling(b) Shutdown or Refuel NA (a) All reactor vessel head closure bolts fully tensioned.

(b) One or more reactor vessel head closure bolts less than fully tensioned.

Footnotes (a) and (b) specify the reactor head closure bolt requirements. For the purposes of this amendment request, reactor vessel head closure bolts as specified in the TSs, are equivalent to reactor pressure vessel head closure studs or studs.

2.3 Reason for the Proposed Change A flaw indication was found on HNP Unit 2 reactor pressure vessel head closure stud #33 during a code required volumetric examination during the spring 2017 refueling outage (2R24). The examination was completed in accordance with ASME Section XI Table IWB-2500-1, examination category B-G-1, Item B6.20, and met the examination volume requirements of Figure IWB-2500-12. During the lnservice Inspection (lSI) of the HNP Unit 2 closure studs (#1 through #56), a circumferential flaw indication was identified in the stud at location #33. The indication is located at a distance of 41.7 inches from the top of the closure stud. This correlates to just below or at the surface of the reactor vessel flange. The indication is approximately one inch (1") in length.

In accordance with IWB-3515.2(c), flaws detected by volumetric examination shall be investigated by a surface examination. Due to the location of the flaw indication at or slightly below the reactor flange, removal of reactor pressure vessel head closure stud #33 is E1-4 to NL-22-0406 Evaluation of the Proposed Change necessary to perform an ASME Section V, Mandatory Appendix 6 (Liquid Penetrant) or Mandatory Appendix 7 (Magnetic Particle) Surface Examination.

After discovery of the indication, various attempts were made to remove the closure stud prior to flooding the reactor cavity for fuel movement and after draindown for vessel reassembly in refueling outage 2R24. Two different methodologies (Basic Removal and Advanced Removal) were pursued to remove the stud. The first attempt to remove the stud utilized the Basic Removal Technique. This technique includes chasing the stud hole, applying an approved penetrant directly to the stud (includes soak time), installing a STAR adapter to the stud and attempting removal with an impact tool. The Advanced Removal (Full STAR Tooling) Technique was also utilized. This technique includes installing an adapter plate, pumping an approved penetrant down the elongation hole and back up the threads, using a vibrator to agitate the stud (attached to the STAR Adaptor) prior to utilizing an impact tool to remove the stud.

SNC submitted a Relief Request (Reference 6) from the surface examination requirement in the event reactor pressure vessel head closure stud #33 could not be removed for a code compliant surface examination. The Relief Request was subsequently approved by the NRC in Reference 7. Both of the attempts to remove the stud were unsuccessful.

During the HNP Unit 2 Spring 2019 refueling outage (2R25), several additional more aggressive attempts were made to remove the reactor pressure vessel head closure stud #33. These attempts were also unsuccessful. SNC submitted a Relief Request (Reference 8) to continue operation with a flaw indication on the reactor pressure vessel head closure stud #33. The Relief Request was subsequently approved by the NRC in Reference 9. There were no attempts to remove the stud during the 2021 refueling outage (2R26).

Since the attempts to remove reactor pressure vessel head closure stud #33 were unsuccessful, the stud remains in place, and is approved in a Code relief (Reference 9) to remain for the duration of the current 5th lSI Interval which is scheduled to end on December 31, 2025. This Code relief does not provide relief from the TS Table 1.1-1, MODES, which requires all reactor vessel head bolts to be fully tensioned. Reactor pressure vessel head closure stud #33 is fully tensioned at this time. However, if the indication on stud #33 becomes worse, or indication is found on another stud, there is a possibility that a stud(s) might be incapable of full tension.

The indication at HNP Unit 2 stud #33 is atypical of industry experience. Review of industry operating experience for degradation of reactor vessel closure studs was performed in support of Electric Power Research Institute (EPRI) Report 30020114589, Technical Basis for Optimization of the Volumetric Examination Frequency for Reactor Vessel Studs, (Reference 10). The review identified only one confirmed case of closure stud cracking, which occurred in 1989 and was traced to poor material conditions. Given this broader operating experience and the inspection history at HNP Units 1 and 2, there is no common cause associated with the examination indication.

As such, SNC is proposing changes to TS Table 1.1-1 to address the increased possibility that a reactor pressure vessel head closure stud may not be able to be fully tensioned and avert the possible need for an exigent or emergency license amendment during the E1-5 to NL-22-0406 Evaluation of the Proposed Change Spring 2023 Refueling Outage. During that refueling outage, stud #33 will be detensioned for reactor pressure vessel head removal and retensioned for operation, thereby increasing the possibility of its failure.

2.4 Description of Proposed Change HNP Unit 1 TS Table 1.1-1 defines the criteria for MODES 1 through 5. Reactor MODE Switch Position Refuel for MODE 2, MODE 3, Hot Shutdown, and MODE 4, Cold Shutdown, is annotated with footnote (a) which currently states:

(a) All reactor vessel head closure bolts fully tensioned.

The proposed change would revise the footnote to state:

(a) All required reactor vessel head closure bolts fully tensioned. The required number of head closure bolts is at least 51 of 52 bolts.

In addition, MODE 5, Refueling, is annotated with footnote (b) which currently states:

(b) One or more reactor vessel head closure bolts less than fully tensioned.

The proposed change would revise the footnote to state:

(b) One or more required reactor vessel head closure bolts less than fully tensioned.

HNP Unit 2 TS Table 1.1-1 defines the criteria for MODES 1 through 5. Reactor MODE Switch Position Refuel for MODE 2, MODE 3, Hot Shutdown, and MODE 4, Cold Shutdown, are annotated with footnote (a) which currently states:

(b) All reactor vessel head closure bolts fully tensioned.

The proposed change would revise the footnote to state:

(b) All required reactor vessel head closure bolts fully tensioned. The required number of head closure bolts is at least 54 of 56 bolts, with a minimum of nine bolts between the two out of service bolts.

In addition, MODE 5, Refueling, is annotated with footnote (b) which currently states:

(b) One or more reactor vessel head closure bolts less than fully tensioned.

The proposed change would revise the footnote to state:

(b) One or more required reactor vessel head closure bolts less than fully tensioned.

The addition of the word required and specifying the required number of reactor pressure vessel head closure studs in footnote (a) will avoid any confusion regarding the state of a closure stud(s) that may be out of service.

E1-6 to NL-22-0406 Evaluation of the Proposed Change For HNP Unit 1, the required number of fully tensioned closure studs is 51 of the 52 closure studs based on Calculation C-037-2201-00-01, Hatch Unit 1 Operation with One Stud Out of Service Evaluation, (see Enclosure 2).

For HNP Unit 2, the required number of fully tensioned closure studs is 54 of the 56 closure bolts, with a minimum of nine studs between the two out of service studs, based on Calculation C-037-2201-00-02, Hatch Unit 2 Operation with One Stud Out of Service Evaluation, (see Enclosure 3).

3. TECHNICAL EVALUATION Separate calculations were performed for HNP Units 1 and 2. The calculations analyzed reactor pressure vessel closure stresses, stud stresses, closure flange separation and fatigue.

The calculations demonstrated that applicable ASME Code allowable stresses are met. The calculations were performed using the design pressure of 1,250 psia. At HNP Units 1 and 2, the design pressure bounds the pressure for all Normal and Upset transients established in the design basis analysis. Stresses resulting from Emergency and Faulted transients were also considered.

HNP Unit 1 Calculation Results provides the Dominion Engineering, Inc. calculation supporting continued operation of the HNP Unit 1 reactor pressure vessel with one closure stud out of service. The average stresses in the studs due to primary load conditions were calculated with all studs meeting the ASME Code requirements for primary loads with one stud out of service. The maximum primary stud stress is calculated to be 35.48 ksi, which is less than the design stress-intensity value (Sm) allowable of 36.30 ksi.

Operation of the HNP Unit 1 reactor pressure vessel with any one stud out of service does not result in any component of the reactor pressure vessel closure flange exceeding the design basis ASME Code allowables. The closure stud out of service has little to no impact on the stresses associated with General Primary Membrane Stress Intensity, Primary Local Membrane plus Bending Stress Intensity, and Maximum Stress Intensity Range. Each of these stress values remain below the appropriate ASME Code allowable stresses.

The closure stud out of service has a modest impact on the stresses associated with the stud Maximum Membrane and Maximum Membrane plus Bending stress. Each of these stress values remain below the appropriate ASME Code allowable stresses.

The closure stud out of service causes an additional flange separation at the inner o-ring of 0.0079 inch. The flange separation is less than the o-ring minimum springback of 0.010 inch.

Due to rotation of the flanges under stud loading, the flange separation at the outer ring is less than the inner o-ring. Therefore, compression on the gasket is maintained, and the flange separation will not result in additional risk of leakage.

The closure stud out of service increases the maximum stress at: (1) the head flange/shell by 1.02 ksi, (2) the vessel flange/shell by 0.40 ksi and (3) the stud by 0.23 ksi; each of these increases are approximately 1-2% of the previous design basis stress. The fatigue usage values were calculated for the full service life of the component. The impact of a 2% increase in E1-7 to NL-22-0406 Evaluation of the Proposed Change stress for a single cycle of operation on these components is negligible. The calculation demonstrated for higher values of alternating stress that the number of allowable cycles is inversely proportional to the square of the increase in stress. Therefore, even if the components were operated for their full service life with the increase in stress resulting from one stud out of service, the increase in fatigue usage would be the square of the increase in stress, or 1.022 = 1.04 (4% increase). Increasing the fatigue usage by 4% results in fatigue usage that is well below the Code allowable of 1.0.

HNP Unit 2 Calculation Results provides the Dominion Engineering, Inc. calculation supporting continued operation of the HNP Unit 2 reactor pressure vessel with any two closure studs out of service. The average stresses in the studs due to primary load conditions were calculated with all studs meeting the ASME Code requirements for primary loads with two studs out of service. The maximum primary stud stress is calculated to be 34.74 ksi, which is less than the Sm allowable of 36.30 ksi.

Operation of the HNP Unit 2 reactor pressure vessel with two studs out of service, with a minimum of nine studs between them, does not result in any component of the reactor pressure vessel closure flange exceeding the design basis ASME Code allowables. The condition with two closure studs out of service has little to no impact on the stresses associated with General Primary Membrane Stress Intensity, Primary Local Membrane plus Bending Stress Intensity, and Maximum Stress Intensity Range. Each of these stress values remain below the appropriate ASME Code allowable stresses.

The condition with two closure studs out of service has a modest impact on the stresses associated with the stud Maximum Membrane and Maximum Membrane plus Bending stress.

Each of these stress values remain below the appropriate ASME Code allowable stresses.

The condition with two closure studs out of service causes an additional flange separation at the inner o-ring of 0.0066 inch. The total flange separation is less than the o-ring minimum springback of 0.010 inch. Due to rotation of the flanges under stud loading, the flange separation at the outer ring is less than the inner o-ring. Therefore, compression on the gasket is maintained, and the flange separation will not result in additional risk of leakage.

The condition with two closure studs out of service increases the maximum stress at: (1) the head flange/shell by 1.48 ksi, (2) the vessel flange/shell by 0.42 ksi and (3) the stud by 0.31 ksi; each of these increases are approximately 1-2% of the previous design basis stress. The fatigue usage values were calculated for the full service life of the component. The impact of a 2% increase in stress for a single cycle of operation on these components is negligible. The calculation demonstrated for higher values of alternating stress that the number of allowable cycles is inversely proportional to the square of the increase in stress. Therefore, even if the components were operated for their full service life with the increase in stress resulting from two studs out of service, the increase in fatigue usage would be the square of the increase in stress, or 1.022 = 1.04 (4% increase). Increasing the fatigue usage by 4% results in fatigue usage that is below the Code allowable of 1.0.

E1-8 to NL-22-0406 Evaluation of the Proposed Change

4. REGULATORY EVALUATION 4.1 Applicable Regulatory Requirements/Criteria x 10 CFR Part 50, Appendix A, General Design Criterion (GDC) 14, Reactor coolant pressure boundary, requires that:

The reactor coolant pressure boundary shall be designed, fabricated, erected, and tested so as to have an extremely low probability of abnormal leakage, of rapidly propagating failure, and of gross rupture.

The HNP design, fabrication, erection, and testing of the reactor coolant pressure boundary (RCPB) assure an extremely low probability of failure or abnormal leakage.

Allowing the required pressure vessel closure stud(s) to be fully tensioned during operation will still satisfy the requirements of GDC 14.

x 10 CFR Part 50, Appendix A, General Design Criterion (GDC) 30, Quality of reactor coolant pressure boundary, requires that:

Components which are part of the reactor coolant pressure boundary shall be designed, fabricated, erected, and tested to the highest quality standards practical. Means shall be provided for detecting and, to the extent practical, identifying the location of the source of reactor coolant leakage.

By utilizing conservative design practices and detailed quality control procedures, the pressure retaining components of the RCPB are designed and fabricated to retain their integrity during normal and postulated accident conditions. Accordingly, components which comprise the RCPB are designed, fabricated, erected, and tested in accordance with recognized industry codes and standards. Further product and process quality planning is provided to assure conformance with the applicable codes and standards and to retain appropriate documented evidence verifying compliance. The RCPB and the leak detection system are designed to meet the requirements of GDC 30. Allowing the required pressure vessel closure stud(s) to be fully tensioned during operation will still satisfy the requirements of GDC 30.

It is noted that HNP Unit 1 was not licensed to the 10 CFR 50, Appendix A, GDC. HNP Unit 1 was licensed to the applicable Atomic Energy Commission preliminary general design criteria identified in Federal Register 32 FR 10213, published July 11, 1967 (ADAMS Accession No. ML043310029). The applicable AEC proposed criteria were compared to the 10 CFR 50, Appendix A, General Design Criteria, as documented in the Hatch Updated Final Safety Analysis Report (UFSAR), Appendix F, Conformance to the Atomic Energy Commission (AEC) Criteria.

x U. S. NRC Regulatory Guide 1.65, Materials and Inspections for Reactor Vessel Closure Studs, is NRC guidance which defines materials and testing procedures acceptable for implementing these criteria for reactor vessel closure stud bolting.

(Reference 11)

E1-9 to NL-22-0406 Evaluation of the Proposed Change This regulatory guide is applicable only to HNP Unit 2. HNP Unit 2 design and inspection procedures are in conformance with the requirements of this regulatory guide except those in Regulatory Positions 2b, 2e, and 3.

Studs were examined in accordance with the requirements of American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code,Section III, N-325; (1968 Edition plus Summer 1970 Addendum in effect at the time of the contract). Bored blank nuts were ultrasonically examined by both the longitudinal and shear wave methods. Shear wave examination of the nuts was performed in both the axial and circumferential directions.

Regulatory Position 3 recommends provision for adequate corrosion protection during venting and filling of the vessel, and while the head is removed. General Electric (GE) supplies thread protectors which prevent stud damage, but stud holes are not plugged, and neither stud nor flange threads are protected from exposure to water. In practice, this has been found to be adequate, as exposure to applied loads and operating and servicing environments has not required the replacement of any boiling water reactor (BWR) studs or flange threads. No corrosion protection for studs is provided.

4.2 Precedent The proposed changes are similar to NRC-approved license amendment issued to:

x Braidwood Station Units 1 and 2 and Byron Station Units 1 and 2 on October 28, 2015, in Amendment Nos. 186 and 192, respectively (ADAMS Accession No. ML15232A441). These amendments approved the use of the methodology for developing the pressure and temperature limits reports and changed TS Table 1.1-1, MODES, footnote (b) to state: All required reactor vessel head closure bolts fully tensioned and footnote (c) to state: One or more required reactor vessel head closure bolts less than fully tensioned (emphasis added). The proposed license amendment request for HNP Units 1 and 2 is not requesting changes to the pressure and temperature limits methodology.

x Callaway Plant Unit 1 on May 28, 1999, in Amendment No. 133 (ADAMS Accession No. ML021640446). Amendment No. 133 converted the current TSs to the improved TSs. The amendment approved changes to TS Table 1.1-1 based on an NRC Safety Evaluation issued on May 26, 1988 (ADAMS Accession Nos. ML20155J379 and ML20155J490) associated with the operation of the Callaway Plant with stud #2 untensioned. Amendment No. 133 revised footnote (b) to state: At least 53 of 54 reactor vessel head closure bolts fully tensioned and footnote (c) to state: Two or more reactor vessel head closure bolts less than fully tensioned.

The approved TS changes are similar to the changes proposed in this amendment request.

E1-10 to NL-22-0406 Evaluation of the Proposed Change 4.3 No Significant Hazards Consideration Determination Analysis Southern Nuclear Operating Company (SNC) is proposing to revise the Technical Specifications (TS) Table 1.1-1, MODES, for Hatch Nuclear Plant (HNP) Units 1 and 2.

The amendment would allow operation of HNP Units 1 and 2 with the required pressure vessel head closure studs fully tensioned. The required number of closure studs, which may be less than the total number, has been established by calculation that demonstrates operation of HNP Units 1 and 2 reactor pressure vessels with the required studs fully tensioned does not result in any component of the reactor pressure vessel closure flange exceeding the design basis ASME Code allowables. The calculation for HNP Unit 1 determined that any one closure stud may be less than fully tensioned. The required closure studs continue to meet ASME Code requirements for primary loads with one stud out of service. The calculation for HNP Unit 2 determined that any two closure studs may be less than fully tensioned as long as the two studs are separated by nine or more studs. The required closure studs continue to meet ASME Code requirements for primary loads with two studs out of service.

SNC has evaluated whether or not a significant hazards consideration is involved with the proposed amendment(s) by focusing on the three standards set forth in 10 CFR 50.92, Issuance of amendment, as discussed below:

1. Does the proposed change involve a significant increase in the probability or consequences of an accident previously evaluated?

Response: No.

Overall protection system performance will remain within the bounds of the accident analyses, since no hardware changes are proposed. Since the stresses remain within ASME Code allowables, the proposed change will not affect the probability of any event initiators nor will the proposed change affect the ability of any safety related equipment to perform its intended function. There will be no degradation in the performance of nor an increase in the number of challenges imposed on safety related equipment assumed to function during an accident situation.

Therefore, the proposed change does not involve a significant increase in the probability or consequences of an accident previously evaluated.

2. Does the proposed change create the possibility of a new or different kind of accident from any accident previously evaluated?

Response: No.

There are no hardware changes nor are there any changes in the method by which any safety related plant system performs its safety function. The method of plant operation is unaffected. Leakage would be precluded since adequate compression remains.

Analysis demonstrates that any gap opening remains less than the springback recovery of the inner closure o-ring. Since stresses remain within ASME Code allowables, no E1-11 to NL-22-0406 Evaluation of the Proposed Change new accident scenarios, transient precursors, failure mechanisms, or limiting single failures are introduced as a result of this change.

Therefore, the proposed change does not create the possibility of a new or different kind of accident from any previously evaluated.

3. Does the proposed change involve a significant reduction in a margin of safety?

Response: No.

The proposed change does not affect any Safety Limits or controlling numerical values for a parameter established in the updated final safety analysis report or any specific values that define margin that are established in the plants licensing basis. ASME Section III stress limits for affected components are not exceeded. Plant specific evaluations indicate that the reactor vessels will continue to meet ASME Code allowable stress criteria with the required reactor pressure vessel closure studs fully tensioned.

The proposed change does not alter nor exceed the acceptance criteria for any analyzed event. There will be no effect on the manner in which safety limits or limiting safety system settings are determined nor will there be any effect on those plant systems necessary to assure the accomplishment of protection functions.

Therefore, the proposed change does not involve a significant reduction in a margin of safety.

4.4 Conclusions In conclusion, based on the considerations discussed above, (1) there is reasonable assurance that the health and safety of the public will not be endangered by operation in the proposed manner, (2) such activities will be conducted in compliance with the Commissions regulations, and (3) the issuance of the amendment will not be inimical to the common defense and security or to the health and safety of the public.

5. ENVIRONMENTAL CONSIDERATION SNC has determined that the proposed amendment would change a requirement with respect to installation or use of a facility component located within the restricted area, as defined in 10 CFR 20, Standards for protection against radiation, or would change an inspection or surveillance requirement. However, the proposed amendment does not involve (i) a significant hazards consideration, (ii) a significant change in the types or a significant increase in the amounts of any effluents that may be released offsite, or (iii) a significant increase in individual or cumulative occupational radiation exposure. Accordingly, the proposed amendment meets the eligibility criterion for categorical exclusion set forth in paragraph (c)(9) of 10 CFR 51.22, Criterion for categorical exclusion, identification of licensing and regulatory actions eligible for categorical exclusion or otherwise not requiring an environmental review. Therefore, pursuant to 10 CFR 51.22(b), no environmental impact statement or environmental assessment need be prepared in connection with the proposed amendment.

E1-12 to NL-22-0406 Evaluation of the Proposed Change

6. REFERENCES

1. HNP-1-FSAR, Edwin l. Hatch Nuclear Plant Final Safety Analysis Report, Revision 38, September 2020, Section 4.2.1.4, Reactor Vessel.

2. HNP-1-FSAR, Edwin I. Hatch Nuclear Plant Final Safety Analysis Report, Revision 38, September 2020, Appendix I, Reactor Pressure Vessel Design Information.

3. HNP-2-FSAR, Edwin l. Hatch Nuclear Plant Final Safety Analysis Report, Revision 38, September 2020, Section 5.4.6.3.1, Reactor Pressure Vessel.

4. HNP-1-FSAR, Edwin l. Hatch Nuclear Plant Final Safety Analysis Report, Revision 38, September 2020, Section 7.8.5.5, Reactor Vessel Top Head Flange Leakage Detection.

5. HNP-2-FSAR, Edwin l. Hatch Nuclear Plant Final Safety Analysis Report, Revision 38, September 2020, Section 5.6.2.5, RPV Top Head Flange Leakage Detection, and 5.2.7.2.2.1, Reactor Vessel Head Seal Leak Detection.

6. Letter from C. R. Pierce (SNC) to the Document Control Desk (NRC), Edwin I. Hatch Nuclear Plant - Unit 2 Relief Request Reactor Pressure Vessel Stud Inspection, dated February 17, 2017 (NRC ADAMS Accession No. ML17048A090).

7. Letter from M. T. Markley (NRC) to J. J. Hutto (SNC), Edwin I Hatch Nuclear Plant, Unit 2 -

Relief Request HNP-ISI-RR-05-01 Regarding Reactor Pressure Vessel Head Stud Inservice Inspection Requirements (CAC NO. MF9271), dated August 10, 2017 (NRC ADAMS Accession No. ML17205A345).

8. Letter from C. A. Gayheart (SNC) to the Document Control Desk (NRC), Edwin I. Hatch Nuclear Plant - Unit 2 Relief Request Reactor Pressure Vessel Stud HNP-ISI-RR-05-02, dated November 5, 2018 (NRC ADAMS Accession No. ML18309A272).

9. Letter from M. T. Markley (NRC) to C. A. Gayheart (SNC), Edwin I Hatch Nuclear Plant, Unit 2 - Relief Request HNP-ISI-RR-05-02 Regarding Reactor Pressure Vessel Head Stud Inservice Inspection Requirements (EPID L-2018-LLR-0137), dated February 6, 2019 (NRC ADAMS Accession No. ML19035A550).

10. EPRI Report 30020114589, Technical Basis for Optimization of the Volumetric Examination Frequency for Reactor Vessel Studs, November 2018.

11. U. S. NRC Regulatory Guide 1.65, Materials and Inspections for Reactor Vessel Closure Studs, October 1973.

E1-13

Edwin I. Hatch Nuclear Plant - Units 1 and 2 Request to Relax the Required Number of Fully Tensioned Reactor Pressure Vessel Head Closure Studs in Technical Specification Table 1.1-1, MODES NL-22-0406 Attachment 1 HNP Units 1 and 2 Technical Specifications Marked-up Pages

Definitions 1.1 Table 1.1-1 (page 1 of 1)

MODES AVERAGE REACTOR COOLANT REACTOR MODE TEMPERATURE MODE TITLE SWITCH POSITION (°F) 1 Power Operation Run NA 2 Startup Refuel(a) or Startup/Hot NA Standby 3 Hot Shutdown(a) Shutdown > 212 4 Cold Shutdown(a) Shutdown 212 5 Refueling(b) Shutdown or Refuel NA (a) All required reactor vessel head closure bolts fully tensioned. The required number of head closure bolts is at least 51 of 52 bolts.

(b) One or more required reactor vessel head closure bolts less than fully tensioned.

HATCH UNIT 1 1.1-7 Amendment No.

Definitions 1.1 Table 1.1-1 (page 1 of 1)

MODES AVERAGE REACTOR COOLANT REACTOR MODE TEMPERATURE MODE TITLE SWITCH POSITION (°F) 1 Power Operation Run NA 2 Startup Refuel(a) or Startup/Hot NA Standby 3 Hot Shutdown(a) Shutdown > 212 4 Cold Shutdown(a) Shutdown 212 5 Refueling(b) Shutdown or Refuel NA (a) All required reactor vessel head closure bolts fully tensioned. The required number of head closure bolts is at least 54 of 56 bolts, with a minimum of nine bolts between the two out of service bolts.

(b) One or more required reactor vessel head closure bolts less than fully tensioned.

HATCH UNIT 2 1.1-8 Amendment No.

Edwin I. Hatch Nuclear Plant - Units 1 and 2 Request to Relax the Required Number of Fully Tensioned Reactor Pressure Vessel Head Closure Studs in Technical Specification Table 1.1-1, MODES NL-22-0406 Attachment 2 HNP Units 1 and 2 Technical Specifications Revised Pages

Definitions 1.1 Table 1.1-1 (page 1 of 1)

MODES AVERAGE REACTOR COOLANT REACTOR MODE TEMPERATURE MODE TITLE SWITCH POSITION (°F) 1 Power Operation Run NA 2 Startup Refuel(a) or Startup/Hot NA Standby 3 Hot Shutdown(a) Shutdown > 212 4 Cold Shutdown(a) Shutdown 

5 Refueling(b) Shutdown or Refuel NA (a) All required reactor vessel head closure bolts fully tensioned. The required number of head closure bolts is at least 51 of 52 bolts.

(b) One or more required reactor vessel head closure bolts less than fully tensioned.

HATCH UNIT 1 1.1-7 Amendment No.

Definitions 1.1 Table 1.1-1 (page 1 of 1)

MODES AVERAGE REACTOR COOLANT REACTOR MODE TEMPERATURE MODE TITLE SWITCH POSITION (°F) 1 Power Operation Run NA 2 Startup Refuel(a) or Startup/Hot NA Standby 3 Hot Shutdown(a) Shutdown > 212 4 Cold Shutdown(a) Shutdown 212 5 Refueling(b) Shutdown or Refuel NA (a) All required reactor vessel head closure bolts fully tensioned. The required number of head closure bolts is at least 54 of 56 bolts, with a minimum of nine bolts between the two out of service bolts.

(b) One or more required reactor vessel head closure bolts less than fully tensioned.

HATCH UNIT 2 1.1-8 Amendment No.

Edwin I. Hatch Nuclear Plant - Units 1 and 2 Request to Relax the Required Number of Fully Tensioned Reactor Pressure Vessel Head Closure Studs in Technical Specification Table 1.1-1, MODES NL-22-0406 Enclosure 2 Calculation C-037-2201-00-01, Hatch Unit 1 Operation with One Stud Out of Service Evaluation

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Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 2 of 39 TABLE OF CONTENTS Last Mod.

Section Page Rev.

1 PURPOSE..................................................................................................................................... 5 0 2

SUMMARY

OF RESULTS ................................................................................................................. 5 0 3 INPUT REQUIREMENTS .................................................................................................................. 5 0 3.1 Analysis Inputs ............................................................................................................... 5 0 3.2 Acceptance Criteria ........................................................................................................ 6 0 4 ASSUMPTIONS .............................................................................................................................. 7 0 5 ANALYSIS..................................................................................................................................... 8 0 5.1 Stud Primary Stress with One Stud Out of Service ......................................................... 8 0 5.1.1 Average Stud Force ......................................................................................... 9 0 5.1.2 Calculation of Stud Force Distribution .............................................................. 9 0 5.1.3 Primary Stress Comparison ........................................................................... 11 0 5.2 Analysis of Closure Flange with Stud Out of Service .................................................... 11 0 5.2.1 Evaluation Methodology ................................................................................. 11 0 5.2.2 Reactor Vessel Closure Flange Model ........................................................... 11 0 5.2.2.1 Model Geometry ......................................................................... 11 0 5.2.2.2 Model Boundary Conditions ....................................................... 12 0 5.2.3 Analysis Cases............................................................................................... 13 0 5.2.4 Results Discussion ......................................................................................... 13 0 5.2.4.1 RPV Closure Stresses ................................................................ 13 0 5.2.4.2 RPV Stud Stresses ..................................................................... 14 0

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Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 4 of 39 LIST OF TABLES Last Mod.

Table No. Rev.

Table 1. FEA Model Inputs 0 Table 2. Calculation of Primary Stresses in Reactor Vessel Studs, One Stud Out of Service 0 Table 3. Stress Increase Due to Stud Out of Service 0 LIST OF FIGURES Last Mod.

Figure No. Rev.

Figure 1. Reactor Vessel Head Stud Geometry, One Stud Out of Service 0 Figure 2. Hatch Unit 1 RPV Closure Flange FEA Model Overall View [1] 0 Figure 3. FEA Model Node Numbering and Section Cut Line Locations [1] 0

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Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 5 of 39 1 PURPOSE Dominion Engineering, Inc. (DEI) originally provided optimized tensioning and detensioning procedures for Plant Hatch in April 2015 [1], along with design basis evaluations for expanded elongation tolerances. The purpose of this calculation is to provide an update to these evaluations that consider the effect of a single stud out of service. This analysis considers the stresses resulting from two conditions which bound the effects of a stud out of service: (1) operating with one stud left untensioned, and (2) the unlikely condition of a stud that is tensioned then fails in service.

2

SUMMARY

OF RESULTS The average stresses in the studs due to primary load conditions with one stud out of service were calculated using the methodology outlined in Section 5.1. As summarized in this section, all studs continue to meet ASME Code requirements for primary loads with one stud out of service.

The FEA model which was used to develop the current stud tensioning evaluations in DEI Report R-3937-00-02 [1] was used to perform an analysis of the closure flange with one stud out of service, as summarized in Section 5.2. The analysis results are summarized in Table 3. As demonstrated by the results in Table 3, operation of the Hatch Unit 1 RPV with one stud out of service does not result in any component of the RPV closure flange to exceed the design basis ASME Code allowables.

3 INPUT REQUIREMENTS 3.1 Analysis Inputs The following inputs are required to calculate the average stresses in the studs due to primary load conditions with one stud out of service:

1. The RPV design pressure is 1,250 psia and the design temperature is 575°F [1, Table 3-1].

2. The RPV inner o-ring radius is 111.0 inches [1, Table 3-3].

3. The RPV stud circle radius is 117.313 inches [1, Table 3-3].

4. The number of studs in the Hatch Unit 1 RPV is 52 [1, Table 3-1].

5. The stud shank OD is 6.0 inches, the stud shank ID is 1.0 inches, and the stud shank cross section area is 27.489 in2 [1, Table 3-1].

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Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 6 of 39 The following inputs are required for the FEA analysis of tensioning effects related to one stud out of service:

6. Reactor vessel head and closure flange dimensions. The geometry of the model developed for this analysis is identical to the one used in the Reference [1]. The model parameters used in this FEA model are detailed in Table 1; this table is identical to Table A-1 from Reference [1].

7. Reactor vessel head and closure flange low alloy steel material properties. The material properties of the model developed for this analysis are identical to those used in Reference [1].

8. ASME Code design basis summary. The design basis conditions for the RPV closure flange components, updated to include the analyses performed in the 2015 tensioning optimization stress report, are summarized in Table 2-1 of Reference [1]. Table 2-1 includes the updated stress values applicable to the conditions evaluated in the report. The following values from Table 2-1 are used in this calculation:

a. Closure head / head flange maximum stress intensity range: 66.5 ksi [1, Table 2-1]

b. Vessel closure shell / flange maximum stress intensity range: 50.1 ksi [1, Table 2-1]

c. Closure stud membrane stress, maximum service load: 46.2 ksi [1, Table 2-1]

d. Closure stud maximum stress, maximum service load: 101.5 ksi [1, Table 2-1]

e. Closure stud fatigue usage: 0.454 [1, Table 2-1]

f. Closure head / head flange fatigue usage: 0.080 [1, Table 2-1]

g. Vessel closure shell / flange fatigue usage: 0.268 [1, Table 2-1]

9. Primary stress design basis values. The conditions evaluated in the 2015 tensioning optimization stress report do not impact primary conditions, and therefore they were not included. Using the original closure flange design basis report [2] (referenced in the 2015 analysis), the following limiting primary stress values are obtained:

a. Closure head / head flange general membrane stress: 21.9 ksi [2, p. A-7]

b. Vessel closure shell / flange general membrane stress: 25.5 ksi [2, p. A-7]

c. Closure head / head flange local membrane + bending stress: 26.9 ksi [2, p. A-7]

d. Vessel closure shell / flange local membrane + bending stress: 35.0 ksi [2, p. A-7]

3.2 Acceptance Criteria The following acceptance criteria are applicable to this calculation:

1. The RPV closure components were designed according to the 1965 Edition with Winter 1966 Addenda of Section III of the ASME Boiler and Pressure Vessel Code [7].

2. The stresses in the closure studs are subject to the following requirements and allowable stresses:

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Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 7 of 39

a. Primary stress at 575°F design temperature: 36.3 ksi (Sm) [1, Table 3-3].

b. Maximum allowable average stress, evaluated at 550°F: 73.5 ksi (2Sm) [1, Table 2-1]

c. Maximum allowable stress, evaluated at 550°F: 110.3 ksi (3Sm) [1, Table 2-1]

3. The stresses in the closure head and vessel are subject to the following requirements and allowable stresses:

a. Closure head / head flange and vessel closure shell / flange [7, Paragraph N-414.1] general membrane allowable stress at 575°F design temperature: 26.7 ksi (Sm) [1, Table 3-3]

b. Closure head / head flange and vessel closure shell / flange [7, Paragraph N-414.3] primary local membrane + bending allowable stress at 575°F design temperature: 40.05 ksi (1.5Sm)

[1, Table 3-3]

c. Closure head / head flange and vessel closure shell /flange [7, Paragraph N-414.4]

maximum allowable stress intensity range, evaluated at 575°F design temperature:

80.10 ksi (3Sm) [1, Table 2-1]

4. The maximum allowable fatigue usage factor is 1.0 [7, Paragraph N-415.2(d)(6)].

5. The minimum o-ring springback is 0.010 inch [1, Table 3-2]. Although this is not an ASME Code criterion, it is a condition evaluated to demonstrate the flange opening will not result in additional risk of leakage. The design basis report does not calculate any o-ring opening at operating conditions [1, Table 3-2].

4 ASSUMPTIONS The following assumptions are used to calculate the average stresses in the studs due to primary load conditions with one stud out of service:

1. The reactor vessel and head are rigid. This is consistent with the usual treatment of primary loads which only considers net forces and moments and not localization of stress from geometry and compliance effects. A consequence of this assumption is that the distribution of stud forces varies linearly with the distance from the neutral axis.

2. The reactor vessel and head exert no contact forces on each other (i.e., the compression forces on the mating surfaces are neglected). These secondary forces serve to mitigate the redistribution of loads when studs fail, so this assumption conservatively maximizes the calculated maximum stud stress value.

3. As a simplifying assumption, each stud is individually treated as a point force. That is, each stud contributes no bending stiffness to the cross section as a whole. This assumption is appropriate given the small bending stiffness of the studs relative to the overall head cross section.

4. The design pressure is assumed to act out to the radius of the inner o-ring of the vessel. This is an appropriate assumption because leakage past the inner o-ring is not a normal operating condition.

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Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 8 of 39 The following assumptions are used for the FEA analysis of tensioning effects related to one stud out of service. These assumptions are consistent with analyses described in Reference [1].

5. All vessel elements were assigned material properties appropriate for low carbon steel at ambient temperature: E = 27.9E6 psi and = 0.3. All stud elements were assigned material properties appropriate for low alloy steel at ambient temperature: E = 29.9E6 psi and = 0.3. The differences caused by differential thermal expansion of the stud and vessel are negligible and are not considered.

6. The modulus of elasticity in the stud hole regions of the upper and lower flanges were de-rated by the ratio shown in Table 1 to account for the removed material in the stud holes.

7. The contact between the nut and the washer is assumed to occur at a single point location. This is considered a reasonable assumption since the nut and washer mate at a spherical surface, and therefore come into contact all at once.

8. Beam elements that are stiff in bending are used to impose flange rotation on the ends of the studs. Despite the presence of spherical washers between the nut and the upper flange, friction acts to "glue" the nut to the flange once the stud is preloaded. At full pressure load, a modest amount of friction (  0.1) has been demonstrated to be sufficient to transmit the bending stresses which arise from this boundary condition. Thus, the infinite friction assumption is concluded to be more realistic than the assumption of zero friction at the spherical washer.

9. The interface between the head and vessel flanges was simulated by a row of line elements connecting the head and vessel flanges. The location of these interface elements was selected to act at a reaction radius empirically determined in Reference [1] from the correlation between the model predictions and the actual stud elongation data using the original plant tensioning procedure.

10. All studs are assumed to be initially uniformly tensioned to the target stud elongation of 0.0432 inch, equivalent to a stud stress of 40.403 ksi [1, Table 3-1].

5 ANALYSIS 5.1 Stud Primary Stress with One Stud Out of Service The effect of a stud being out of service on the primary stress in the remaining studs is greater than simply increasing the design basis primary stress by the ratio of original to remaining studs. The change in restraint conditions caused by the inactive stud will tend to create a larger primary load in the studs adjacent to the inactive stud.

We treat the studs as a single cross section loaded in bending by the pressure on the reactor head.

Assuming one stud is out of service, and that the resulting force distribution in the studs is a linear

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Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 9 of 39 function of the distance from the neutral axis of the stud cross section, we enforce the static equilibrium equations on the studs. Note that the linear distribution assumption is a consequence of Assumption 1. An Excel spreadsheet is used to facilitate solution of the equations which are developed.

5.1.1 Average Stud Force Ignoring for a moment that the 51 remaining studs are not uniformly distributed around the RPV closure, we can compute the average force in the studs according to the following equation. Assuming that the design pressure (in psig) acts out to the location of the inner o-ring radius (characterized by radius Ri), we have:

(1235 psig)( x 111. 0 in )

= = = = 937.3 kips [5-1]

51 51 51 This value will be used in computing the actual force (and, from there, stress) distribution among the studs in a later section. For comparative purposes, we note that when all studs are intact and tensioned, the corresponding average force is (51/52)x937.3 = 919.3 kips.

5.1.2 Calculation of Stud Force Distribution Because the out of service stud is located symmetrically about the x-axis, the neutral axis of bending for the remaining studs (considered as a whole) must be oriented parallel to the y-axis in Figure 1. The offset G from the center of pressure is still an unknown at this point, however. The solution for G is achieved by writing the static equilibrium equations for the reactor head F F  PA z i h 0 i

[5-2]

Mn Fi x i  G  PAh (G ) 0 i

where Fz = net force in the direction parallel to the stud lengths

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Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 10 of 39 Mn = net moment about the neutral axis xi = x-coordinate of each stud per the axes in Figure 1 G  parallel offset of the neutral axis from the y-axis as shown in Figure 1

 $h = area of the reactor head on which the pressure force acts The coordinates xi can be written in terms of the bolt-circle radius (Ro) and Ti as defined in Figure 1.

27

= , where = x 2 [5-3]

52 At this point, we assume per Assumption 1 that the stud force varies linearly with its distance from the neutral axis. The mathematical form of the force distribution in the studs consequently may be expressed as follows, where f is a constant Fi F  f xi  G [5-4]

Substituting Eq. [5-4] into the first of Eqs. [5-2] and taking advantage of the fact that F PAh yields i

+ ( ) = 0 ( ) = 0 1 [5-5]

51 51 where Eq. [5-3] has been used for xi. Since G is now known, we can substitute Eq. [5-4] into the second of Eqs. [5-2], resulting in the following

+ ( ) ( ) () = 0

+ ( ) ( ) + = 0 [5-6]

+ 51

=

2 + 51

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Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 11 of 39 The values for f and G can be substituted directly back into Eq. [5-4], producing the force distribution for all studs. The final results appear in Table 2. Note that the highest stud force occurs at Stud Location Nos. 2 and 52, as might be expected since these are adjacent to the untensioned stud (No. 1).

5.1.3 Primary Stress Comparison The distributed primary stud forces are divided by the stud stress area of 27.489 in2 (Input 5) to calculate the primary stud stresses. The maximum primary stud stress is calculated in Table 2 to be 35.48 ksi, which is less than the Sm allowable of 36.3 ksi; therefore, this condition is satisfied.

5.2 Analysis of Closure Flange with Stud Out of Service 5.2.1 Evaluation Methodology The effect of one stud out of service on the ASME Code comparison stresses in the reactor vessel closure flange components is evaluated using the same model used in the 2015 tensioning optimization stress report. The approach used to evaluate these conditions is to: (1) determine the stresses in the studs and vessel for the intact case and for the case of a single stud out of service under preload plus design pressure conditions, (2) determine the increase in the stresses when going from the intact to single stud out of service condition, (3) add the calculated increase in stress to the stress given in the design report which includes the effect of plant design transients, and (4) compare the calculated single stud out of service condition stresses to ASME Code requirements.

5.2.2 Reactor Vessel Closure Flange Model The simulation was performed using the finite element analysis model described in Appendix A of Reference [1]. The modeling methods are summarized in this section; greater detail on the specifics of the model is described in Reference [1].

5.2.2.1 Model Geometry The vessel shell, head and flange regions were modeled using SOLID45 (3D structural solid) elements with each row of elements corresponding to one stud pitch. Studs were modeled using BEAM4 (3D beam) elements which resist tensile loads and bending moments. A three dimensional model of the

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Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 12 of 39 Hatch RPV closure flange was simulated as shown in Figure 2. The model considers half the circumference of the closure flange, with symmetry boundary conditions at the circumferential edges.

The 3-D BEAM4 elements used for the studs and tie bars require three real properties: area, moment of inertia, and thickness (used to calculate section modulus). The stud element real properties used in the analysis are reported in Reference [1]. Tie bar properties were selected so that the area is 100 times smaller than the area of the studs, and the moment of inertia is 100 times greater than that of the studs.

This has the effect of making the tie bars rigid in bending (as they are being used, the elements have no shear deflection), so that the rotation of the flanges is imposed on the ends of the studs without affecting the stiffness of the adjacent solid elements.

The interface between the head and vessel flanges was simulated by a row of LINK8 (3D spar) elements connecting the head and vessel flanges. The location of these interface elements was selected to act at a reaction radius empirically determined from the correlation between the model predictions and the actual stud elongation data using the existing tensioning procedure.

The case of an untensioned stud is simulated by deleting the beam element representing that stud and adjusting the initial strains on the studs adjacent to the untensioned stud to produce the specified preload. If the spar elements simulating the vessel to head contact have axial tensile stresses in the pressurized condition, these elements are deleted and the coupled circumferential and radial constraints at these nodes are removed to simulate the fact that there is no longer a frictional restraining force at this location.

5.2.2.2 Model Boundary Conditions The nodes at the bottom of the vessel shell were all fixed in the vertical and circumferential directions and allowed to move freely in the radial direction. Additionally, out of plane rotations (ROTX and ROTZ) were restrained on the nodes associated with the tie bar elements. The rotation of the flange was tied to the bending of the stud by coupling the rotational degree of freedom between the node at top of the stud beam element and the center node of the tie bar elements at the top of the flange.

As noted previously, symmetry boundary conditions were applied at the circumferential edges of the model. In addition, the stud and tie bar beam elements located at each end of the model (i.e., in the first and last planes) are assigned half of the area and moment of inertia as the rest of the studs because they

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Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 13 of 39 lie on a plane of symmetry. Similarly, the LINK8 elements representing flange contact located at each end of the model are given half the area of the rest of the flange contact elements.

5.2.3 Analysis Cases Six cases are evaluated as follows:

x Case A1 represents the preload condition with all studs intact x Case A2 represents the operating condition with the vessel at design pressure and with intact studs x Case B1 represents the case of one stud untensioned and with all other studs preloaded to the specified initial stress x Case B2 same as Case B1 with the vessel at design pressure x Case C1 represents the case of all studs preloaded to the specified initial strain with one stud assumed to fail in service x Case C2 same as Case C1 except the vessel is at design pressure 5.2.4 Results Discussion The results of the finite element analyses are summarized in Table 3. The increases in stress caused by the inactive stud are summarized, and the stresses are compared to the appropriate ASME Code allowables. The current design basis conditions for the closure flange and closure studs are defined in Inputs 8 and 9, and the associated ASME Code comparisons and allowables are defined in Section 3.2.

The following evaluations are considered:

5.2.4.1 RPV Closure Stresses As shown in Table 3, the stud out of service has little to no impact on the stresses associated with General Primary Membrane Stress Intensity, Primary Local Membrane plus Bending Stress Intensity, and Maximum Stress Intensity Range. Each of these stress values remain below the appropriate ASME Code allowable stresses.

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Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 14 of 39 5.2.4.2 RPV Stud Stresses As shown in Table 3, the stud out of service has a modest impact on the stresses associated with the stud Maximum Membrane and Maximum Membrane plus Bending stress. Each of these stress values remain below the appropriate ASME Code allowable stresses.

5.2.4.3 RPV Closure Flange Separation As shown in Table 3, the stud out of service causes an additional flange separation at the o-ring of 0.0079 inch. This increase does not impact an ASME Code allowable. The flange separation is less than the o-ring minimum springback of 0.010 inch per Section 3.2.

5.2.4.4 Fatigue Per Table 3, the stud out of service increases the maximum stress at: (1) the head flange/shell by 1.02 ksi, (2) the vessel flange/shell by 0.40 ksi and (3) the stud by 0.23 ksi; each of these increases are approximately 1-2% of the previous design basis stress. As noted in Input 8, the fatigue usage values in these components are as follows: (1) the head is 0.080, (2) the vessel is 0.268, and (3) the stud is 0.454.

These fatigue usage values were calculated for the full service life of the component.

The impact of a 2% increase in stress for a single cycle of operation on these components is negligible.

Referring to the fatigue curves in the design basis Code [7], Figures N-415A (vessel and head material) and N-416 (bolting material), it may be demonstrated for higher values of alternating stress that the number of allowable cycles is inversely proportional to the square of the increase in stress. Therefore, even if the components were operated for their full service life with the increase in stress resulting from one stud out of service, the increase in fatigue usage would be the square of the increase in stress, or 1.022 = 1.04 (4% increase). Increasing the fatigue usage by 4% results in fatigue usage that is well below the Code allowable of 1.0.

5.2.4.5 Emergency and Faulted Conditions Review of the design basis conditions evaluated in the original plant design basis report [2]

demonstrates that the design basis transients considered as part of the nominal analysis for normal and upset conditions included transients associated with emergency and faulted conditions (although not

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Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 15 of 39 specified as such). Therefore, the analyses performed here include consideration of emergency and faulted conditions.

5.2.5 ANSYS Input Listings The RPV closure flange stud tensioning analysis described in this section is performed using the ANSYS input listing files _HATCH1.RUNS, _MACROS.HATCH1, and _MACROS.DEI. The

_HATCH1.RUNS input listing defines parameters that are used by _MACROS.HATCH1 and

_MACROS.DEI to generate the geometry and run the stud out of service analysis cases. The input listings _HATCH1.RUNS and _MACROS.HATCH1 are provided in Appendix A.

_MACROS.DEI is a proprietary input listing developed outside of the scope of this work. It is retained as an electronic file on a data disk [6] along with other software usage QA records required by the DEI QA program [4]. The contents of this data disk are listed in Appendix B. This data disk is retained with the project file for this task (Task 037-2201) and is available for on-site review by Southern Nuclear personnel.

5.3 Quality Assurance Software Controls The RPV closure flange stud tensioning analysis described in this calculation was performed on the ANSYS-A Dell Precision R7910 workstation, using Windows Server 2012 R2 Standard 64-bit operating system and ANSYS Version 19.0 which was verified on March 13, 2022, as documented in Reference [3]. This software is maintained in accordance with the provisions for control of software described in Dominion Engineering, Inc.s (DEIs) quality assurance (QA) program for safety-related nuclear work [4]. 1 In addition to QA controls associated with the procurement and use of the ANSYS software (e.g., maintenance of the ANSYS Inc. as an approved supplier of the software based on formal auditing and surveillance; formal periodic verification of ANSYS software installation), QA controls associated with all ANSYS batch input listings are also carried out by DEI. These include independent checks of a batch input listing each time it is used; review of all ANSYS Class 3 error reports and QA notices to assess their potential impact on a batch input listing; and independent 1

DEIs quality assurance program for safety-related work (DEI-002) commits to applicable requirements of 10 CFR 21, Appendix B of 10 CFR 50, and ASME/ANSI NQA-1. This QA program is independently audited periodically by both NUPIC (the Nuclear Procurement Issues Committee) and NIAC (the Nuclear Industry Assessment Committee).

Dominion Engineering, Inc.

Title:

Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 16 of 39 confirmatory analyses 2 to ensure that the project-specific application of the analysis is appropriate. The review of ANSYS error reports and QA notices as well as the project-specific check calculations are documented formally in a QA memo to project file [5].

The stud primary stress calculations performed in Table 2 were generated using Microsoft Excel 365 on a Dell 5530 Precision Mobile Workstation with an Intel Core i7 processor and running Microsoft Windows 10. The one-time-use Microsoft Excel spreadsheet Hatch 1 Stud Primary Stress Calc v0.xlsx was prepared, checked, and reviewed in accordance with DEIs nuclear QA program manual

[4] and is archived on the data disk associated with this calculation [6].

6 REFERENCES

1. DEI Report R-3937-00-02, Rev. 0, Reactor Vessel Tensioning Optimization Stress Report -

Hatch Nuclear Plant Unit 1, April 2015.

2. Analytical Report for Hatch No. 1 Reactor Vessel for Georgia Power Company, Combustion Engineering Report No. CENC-1160, August 1971.

3. Dominion Engineering, Inc. Software Test Report No. STR-9898-00-31, ANSYS 19.0 Re-Verification on ANSYS-A.DOMENG.COM Software Test Report. Revision 0, March 2022.

4. Dominion Engineering, Inc. Quality Assurance Manual for Safety-Related Nuclear Work, DEI-002. Revision 18, November 2010.

5. Dominion Engineering, Inc. Memorandum M-037-2201-00-01, Revision 0, ANSYS Confirmatory Analysis and Review of Error Reports / QA Notices for C-037-2201-00-01, Rev. 0, June 2022.

6. Dominion Engineering, Inc. Data Disk D-037-2201-00-01, Revision 0, July 2022.

7. ASME Boiler and Pressure Vessel Code,Section III - Rules for Construction of Nuclear Vessels, 1965 Edition with Addenda through Winter 1966.

2 Confirmatory analyses for a given project may include comparison of model-computed stresses to theoretical closed-form solutions and other checks on model results.

Dominion Engineering, Inc.

Title:

Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 17 of 39 Table 1. FEA Model Inputs Parameter Units Hatch Unit 1 Stud and Vessel Parameters

- Number of Studs --- 52

- Stud Shank OD in 6.000

- Design Stud Stress Area in Shank in^2 27.489

- Calculated Stud Moment of Inertia in^4 63.568

- Membrane Stress, Preload Only ksi 40.59

- Corresponding Elongation in 0.0434

- Design Pressure psia 1,250

- Stud Effective Length in 31.972 Tensioning Parameters

- Max Tensioner Pressure (new) psi n/a

- Optimized Sequence Final Pressure (new) psi 7,250

- Resulting Stud Stress ksi 40.403

- Tensioner Coefficient, Kt psi/in 5.573 Bolting Dimensions

- Stud Circle Radius in 117.313

- Stud Hole Diameter in 6.750

- Spherical Washer Radius of Curvature in 27.000

- Modulus Ratio in Hole Region --- 0.63 Vessel Flange Dimensions

- Flange IR in 109.690

- Inner O-ring Mean Radius in 111.000

- Reaction Radius in 112.750

- Seating Surface Outer Radius in 113.750

- Flange OR in 122.625

- Z dim to ID Transition in -18.000

- Z dim to OD transition in -14.500 Vessel Shell Dimensions

- Shell IR in 110.373

- Shell thickness in 5.875

- Z dim to Bottom of Transition in -20.048 Head Flange Dimensions

- Flange IR in 109.250

- Flange OR in 122.625

- Flange Top Fillet Radius in 2.750

- Z dim to Top of Flange in 24.375

- Z dim to Recess (inner) in 0.375

- Z dim to Recess (outer) in 0.375 Head Shell Dimensions

- Shell IR in 109.500

- Shell thickness in 3.188

- Z dim to Head Coord. Sys. in -7.250

Dominion Engineering, Inc.

Title:

Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 18 of 39 Table 2. Calculation of Primary Stresses in Reactor Vessel Studs, One Stud Out of Service Design Pressure, P, psig 1,235 Bolt Circle Radius, Ro 117.313 in.

Inner o-ring Radius, Ri 111.000 Average force, Fbar 937.3 kips Studs Out of Service 1 Neutral axis offsd 2.300 in.

Stud Stress Area, A 27.489 Coefficient f -319.9 lb/in Number of Studs 52 Stud theta cos(theta) cos^2 (theta) Fi Stress (deg) (kip) (ksi) 1 -180 untensioned untensioned untensioned untensioned 2 -173 -0.9927 0.99 975.3 35.48 3 -166 -0.9709 0.94 974.5 35.45 4 -159 -0.9350 0.87 973.2 35.40 5 -152 -0.8855 0.78 971.3 35.33 6 -145 -0.8230 0.68 968.9 35.25 7 -138 -0.7485 0.56 966.2 35.15 8 -132 -0.6631 0.44 962.9 35.03 9 -125 -0.5681 0.32 959.4 34.90 10 -118 -0.4647 0.22 955.5 34.76 11 -111 -0.3546 0.13 951.4 34.61 12 -104 -0.2393 0.06 947.0 34.45 13 -97 -0.1205 0.01 942.6 34.29 14 -90 0.0000 0.00 938.1 34.13 15 -83 0.1205 0.01 933.5 33.96 16 -76 0.2393 0.06 929.1 33.80 17 -69 0.3546 0.13 924.8 33.64 18 -62 0.4647 0.22 920.6 33.49 19 -55 0.5681 0.32 916.8 33.35 20 -48 0.6631 0.44 913.2 33.22 21 -42 0.7485 0.56 910.0 33.10 22 -35 0.8230 0.68 907.2 33.00 23 -28 0.8855 0.78 904.8 32.92 24 -21 0.9350 0.87 903.0 32.85 25 -14 0.9709 0.94 901.6 32.80 26 -7 0.9927 0.99 900.8 32.77 27 0 1.0000 1.00 900.5 32.76 28 7 0.9927 0.99 900.8 32.77 29 14 0.9709 0.94 901.6 32.80 30 21 0.9350 0.87 903.0 32.85 31 28 0.8855 0.78 904.8 32.92 32 35 0.8230 0.68 907.2 33.00 33 42 0.7485 0.56 910.0 33.10 34 48 0.6631 0.44 913.2 33.22 35 55 0.5681 0.32 916.8 33.35 36 62 0.4647 0.22 920.6 33.49 37 69 0.3546 0.13 924.8 33.64 38 76 0.2393 0.06 929.1 33.80 39 83 0.1205 0.01 933.5 33.96 40 90 0.0000 0.00 938.1 34.13 41 97 -0.1205 0.01 942.6 34.29 42 104 -0.2393 0.06 947.0 34.45 43 111 -0.3546 0.13 951.4 34.61 44 118 -0.4647 0.22 955.5 34.76 45 125 -0.5681 0.32 959.4 34.90 46 132 -0.6631 0.44 962.9 35.03 47 138 -0.7485 0.56 966.2 35.15 48 145 -0.8230 0.68 968.9 35.25 49 152 -0.8855 0.78 971.3 35.33 50 159 -0.9350 0.87 973.2 35.40 51 166 -0.9709 0.94 974.5 35.45 52 173 -0.9927 0.99 975.3 35.48

Dominion Engineering, Inc.

Title:

Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 19 of 39 Table 3. Stress Increase Due to Stud Out of Service Shell Stresses (ksi) (1) Stud Stresses (ksi) Flange Stud Load Gen. Membrane Local Memb.+Bend. Maximum SI Max Memb+ Separation Load Condition Condition Case Head Vessel Head Vessel Head Vessel Membrane Bending (10^-3 in)

Preload Only Normal A1 0.08 0.33 27.00 22.12 27.89 22.41 40.41 93.02 13.9 Preload Only 1 Untensioned B1 0.11 0.34 27.02 22.13 27.90 22.42 40.41 93.05 14.0 Preload Only 1 Failed C1 0.10 0.33 27.01 22.13 27.90 22.42 43.77 93.04 14.0 Preload+Pressure Normal A2 22.12 23.36 37.70 36.89 37.53 36.39 37.79 104.94 17.6 Preload+Pressure 1 Untensioned B2 22.13 23.37 38.47 36.92 38.55 36.44 40.13 105.02 25.5 Preload+Pressure 1 Failed C2 22.12 23.37 37.97 37.28 38.06 36.79 42.77 105.17 23.3 Max. Increase from A2 (Cases B2 & C2) 0.01 0.00 0.77 0.39 1.02 0.40 4.98 0.23 7.9 Limiting Vessel Report Value 21.9 25.5 26.9 35.0 66.5 50.1 46.2 101.5 --

New Maximum Value 21.9 25.5 27.7 35.4 67.5 50.5 51.2 101.7 7.9 Code Stress Limit Sm = Sm = 1.5 Sm = 1.5 Sm = 3 Sm = 3 Sm = 2 Sm = 3 Sm =

26.7 26.7 40.1 40.1 80.1 80.1 73.5 110.3 (1) Local Membrane + Bending and Maximum SI taken at cut lines 2, 3, 4, 5, 6, and 7. General Membrane SI taken at cut lines 1 and 8. (See Figure 3).

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Title:

Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 20 of 39 y

13 14 15 12 16 11 17 10 18 9 19 8 20 7 21 6 22 5 23 4 24 3 25 Blackened Stud is 2 Out of Service 26 1 27 x 52 28 G

51 29 T

50 30 49 31 48 32 47 33 46 34 45 35 44 36 43 37 42 39 38 41 40 Neutral Axis Figure 1. Reactor Vessel Head Stud Geometry, One Stud Out of Service

Dominion Engineering, Inc.

Title:

Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 21 of 39 26,000's Nodal Plane 2000's Nodal Plane 1000's Nodal Plane 1's Nodal Plane Figure 2. Hatch Unit 1 RPV Closure Flange FEA Model Overall View [1]

Dominion Engineering, Inc.

Title:

Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 22 of 39 364 354 8 361 351 8

284 7

281 6

7 5

6 269 5

261 219 141 169 149 111 119 4 4 81 85 3 3 71 75 2 2 61 65 1 1 11 15 1 5 Figure 3. FEA Model Node Numbering and Section Cut Line Locations [1]

Dominion Engineering, Inc.

Title:

Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 23 of 39 A FINITE ELEMENT ANALYSIS INPUT LISTINGS A.1 File: _HATCH1.runs

/BATCH,LIST

/COM,

/COM, **********************************************************************************

/COM, Hatch Unit 1 Stud Out of Service Evaluation

/COM, **********************************************************************************

/COM,

/INP,_MACROS,HATCH1

/INP,_MACROS,DEI

/COM,

/COM, **********************************************************************************

/COM, PRE-RUN SETUP

/COM, **********************************************************************************

/COM,

/FILNAM,Tens-1

/SHOW,plots,grph

/TYPE,1,4

/PREP7

/TITLE, Hatch1 Reactor Vessel Tensioning

/COM, Define run parameters NT = 52  ! Total number of studs in model NV = 52  ! Total number of studs in real vessel NPMAX = 52*3  ! Max number of studs any sequence TENSMX = 7  ! Max number of Tens-* routines XS = 40403  ! Final stud stress target for old tensioner XP = 7250  ! Corresponding tensioner pressure Pmax = 8600  ! Tensioner pressure cap X1 = 0.98  ! Empirical correction factor (init guess)

X2 = 0.95  ! Empirical correction factor (init guess)

Kt = XS*X2/XP  ! Relate tensioner pressure to stud stress RLMAX = 54  ! Number of data items in RLIST (from ENDPOST macro)

• DIM,TENSAR,ARRAY,TENSMX,3

/COM,

• DIM,MPBTMPI,ARRAY,5

• DIM,MPBTMPC,ARRAY,5

• DIM,MPBTMPO,ARRAY,5

• DIM,TOTTMPI,ARRAY,5

• DIM,TOTTMPO,ARRAY,5

/COM,

/COM, *** TOGGLE TENSIONING ROUTINES ***

/COM,

/COM, To set tensioning routine I (Tens-I) to RUN, toggle TENSAR(I,1)=1

/COM, To set tensioning routine I (Tens-I) to OFF, toggle TENSAR(I,1)=0

/COM, TENSAR(I,2) is number of cyclic symmetry slices (=1 for full model) for Tens-I

/COM, TENSAR(I,3) is number of passes thru OPTLOOP for Tens-I (max of 7)

/COM, TENSAR(1,1)=1 $TENSAR(1,2)=1 $TENSAR(1,3)=1 RUNMORF = 1  ! RUNMORF=1 to run out of service stud cases

/COM,

• DIM,PLIST,ARRAY,NPMAX,4

• DIM,RLIST,ARRAY,NT,RLMAX

• DIM,RSAVE10,ARRAY,NV/2+1,RLMAX,6

/COM,

/COM,

/COM, **********************************************************************************

/COM, GEOMETRY FIGURES

/COM, **********************************************************************************

/COM,

/COM, Make 1/2 model to lay down 'Appendix A' plots NT = NV/2+1  ! Total number of studs in model

/COM, Clear the boundary conditions and re-do the geometry.

/PREP7

• USE,GEOM,0  ! Create geometry

/TITLE, Hatch1 Reactor Vessel Tensioning

/VIEW,1,1,1,1 ESEL,S,TYPE,,1 NSLE

/COLOR,NUM,BLAC,1

/TRIAD,OFF

Dominion Engineering, Inc.

Title:

Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 24 of 39

/DIST,1,1.5*HFOR

/FOCUS,1,-HFOR/4,-65,-HFOR/2.1 EPLO  ! FIGURE A-1 ESEL,S,ELEM,,41,290 ESEL,A,ELEM,,1041,1290 NSLE

/PNUM,MAT,1

/NUM,1

/AUTO EPLO  ! FIGURE A-2 ESEL,S,TYPE,,1 ESEL,R,ELEM,,1,1000 NSEL,S,NODE,,1,1000

/VIEW EPLO  ! FIGURE A-3

• DO,I,1,11

/COLOR,NUM,WHIT,I

• ENDDO

/NUM

/PNUM,ELEM,1 ESEL,S,ELEM,,502,506 ESEL,A,ELEM,,1502,1506

• REPEAT,4,,,,1000,1000 NSLE NSEL,U,NODE,,361,4361,1000

/VIEW,1,1,1,1

/AUTO EPLO  ! FIGURE A-4

/VIEW,1,-1,1,5

/NUM,2 ESEL,S,ELEM,,501 NSLE EPLO

/USER

/DIST,1,5.75 ESEL,S,TYPE,,1 ESEL,A,ELEM,,501 NSLE EPLO  ! FIGURE A-5 ALLSEL

/AUTO

/COLOR,DEFA

/NUM FINISH

/COM,

/COM,

/COM, **********************************************************************************

/COM, TENSIONING ROUTINE 1: INITIALIZE MODEL

/COM, **********************************************************************************

/COM,

/COM,

/PREP7 NT = 10  ! Total number of studs in model

• USE,GEOMCLUP

• USE,GEOM,0  ! Create geometry FINISH

/COM,

/COM, Do initial sets at final pressure to solve for X1 and X2

/COM, Tension all studs except in one set and then retension stud 10 PP = NT  ! Number of studs in each set NP = 2  ! Number of sets in this sequence TT = 1  ! Number of sets to achieve one-pass tens.

• USE,ZEROIT

• DO,I,1,NT PLIST(I,1) = I  ! Load PLIST column 1 with stud numbers PLIST(I,2) = XP  ! Load PLIST column 2 with ref. tens. press.

• ENDDO

• DO,I,NT+1,NT*2 PLIST(I,1) = 10  ! Load PLIST column 1 with stud numbers PLIST(I,2) = XP  ! Load PLIST column 2 with ref. tens. press.

PLIST(I,4) = 1.0  ! Load PLIST column 4 with retens. flag

• ENDDO

• IF,TENSAR(1,1),GT,0.5,THEN

• USE,GOSOLV,'Hatch1','Tens-1',1 ! Solve model X1 = X2*XS/RLIST(10,3)  ! X1 is ref. stress/av. stud stress - single stud X2 = X2*XS/RLIST(1,3)  ! X2 is ref. stress/av. stud stress - all studs

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Title:

Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 25 of 39 Kt = XS*X2/XP  ! Relate tensioner pressure to stud stress

• ENDIF

/COM,

/COM,

/COM, **********************************************************************************

/COM, TENSIONING ROUTINE 10: RUN MISSING OR FAILED STUD CASES

/COM, **********************************************************************************

/COM,

/COM,

/FILNAM,Tens-10

/COM, Change over to a half model for missing stud runs

/PREP7

• USE,GEOMCLUP NT = NV/2+1  ! Total number of studs in model

• USE,GEOM,0  ! Create geometry FINISH Kt = XS*X2/XP  ! Relate tensioner pressure to stud stress

/COM, Tension all studs in one pass PP = NT  ! Number of studs in each pass NP = 1  ! Number of passes TT = 1  ! Number of passes to achieve one-pass tens.

• USE,ZEROIT

• DO,I,1,PP PLIST(I,1) = I  ! Load PLIST column 1 with stud numbers PLIST(I,2) = XP  ! Load PLIST column 2 with ref. tens. press.

• ENDDO

• USE,GOSOLV,'Hatch1','Tens-10',1  ! Solve model - Case A1 SAVE,,A1

• DO,I,1,NT

• DO,J,1,RLMAX RSAVE10(I,J,1) = RLIST(I,J)

• ENDDO

• ENDDO

• USE,ZEROIT I=1

• USE,PSOLV,'Hatch1','A2',2.0,1235  ! Solve model - Case A2 SAVE,,A2

• DO,I,1,NT

• DO,J,1,RLMAX RSAVE10(I,J,2) = RLIST(I,J)

• ENDDO

• ENDDO

• USE,ZEROIT I=1

/COM, BEGIN SOLUTION PHASE

/SOLU ANTYPE,STATIC,REST SFDELE,ALL,ALL EKILL,502

/TITLE, Hatch1 Reactor Vessel - Case C1 - Preload Only TIME,3.0 SOLVE FINISH

/POST1 SET,,,,,3.0

• USE,POSTER

• USE,ENDPOST FINISH SAVE,,C1

• DO,I,1,NT

• DO,J,1,RLMAX RSAVE10(I,J,5) = RLIST(I,J)

• ENDDO

• ENDDO

• USE,ZEROIT I=1

• USE,PSOLV,'Hatch1','C2',4.0,1235  ! Solve model - Case C2 SAVE,,C2

• DO,I,1,NT

• DO,J,1,RLMAX RSAVE10(I,J,6) = RLIST(I,J)

• ENDDO

• ENDDO

/COM, Check for flange contact links which came out of compression LCHG = 0

• DO,I,1,NT

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Title:

Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 26 of 39

• IF,RLIST(I,10),GT,0,THEN LCHG = 1.0

/PREP7 EKILL,I*1000-499  ! EKILL 501 El. in row CPDELE,I CPDELE,100+I FINISH

• ENDIF

• ENDDO

• IF,LCHG,EQ,1.0,THEN

• USE,ZEROIT I=1

• USE,PSOLV,'Hatch1','C2',5.0,1235  ! Re-Solve model - Case C2 SAVE,,C2A

• DO,I,1,NT

• DO,J,1,RLMAX RSAVE10(I,J,6) = RLIST(I,J)

• ENDDO

• ENDDO

• ENDIF

/COM, Clear the boundary conditions and re-do the geom.

/PREP7 SFDELE,ALL,ALL

• USE,GEOMCLUP

• USE,GEOM,0  ! Create geometry FINISH

/FILN,Tens-10B

/COM, Tension all studs in one pass except stud 1 PP = NT-1  ! Number of studs in each pass NP = 1  ! Number of passes TT = 1  ! Number of passes to achieve one-pass tens.

• USE,ZEROIT

• DO,I,1,PP PLIST(I,1) = I+1  ! Load PLIST column 1 with stud numbers PLIST(I,2) = XP  ! Load PLIST column 2 with ref. tens. press.

• ENDDO

• USE,GOSOLV,'Hatch1','Tens-10B',1  ! Solve model - Case B1 SAVE,,B1

• DO,I,1,NT

• DO,J,1,RLMAX RSAVE10(I,J,3) = RLIST(I,J)

• ENDDO

• ENDDO

• USE,ZEROIT I=1

• USE,PSOLV,'Hatch1','B2',2.0,1235  ! Solve model - Case B2 SAVE,,B2

• DO,I,1,NT

• DO,J,1,RLMAX RSAVE10(I,J,4) = RLIST(I,J)

• ENDDO

• ENDDO

/COM, Check for flange contact links which came out of compression LCHG = 0

• DO,I,1,NT

• IF,RLIST(I,10),GT,0,THEN LCHG = 1.0

/PREP7 EKILL,I*1000-499  ! EKILL 501 El. in row CPDELE,I CPDELE,100+I FINISH

• ENDIF

• ENDDO

• IF,LCHG,EQ,1.0,THEN

• USE,ZEROIT I=1

• USE,PSOLV,'Hatch1','B2',3.0,1235  ! Re-Solve model - Case B2 SAVE,,B2A

• DO,I,1,NT

• DO,J,1,RLMAX RSAVE10(I,J,4) = RLIST(I,J)

• ENDDO

• ENDDO

• ENDIF

/COM, Check again for flange contact links which came out of compression

Dominion Engineering, Inc.

Title:

Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 27 of 39 LCHG = 0

• DO,I,1,NT

• IF,RLIST(I,10),GT,0,THEN LCHG = 1.0

/PREP7 EKILL,I*1000-499  ! EKILL 501 El. in row CPDELE,I CPDELE,100+I FINISH

• ENDIF

• ENDDO

• IF,LCHG,EQ,1.0,THEN

• USE,ZEROIT I=1

• USE,PSOLV,'Hatch1','B2',4.0,1235  ! Re-Solve model - Case B2 SAVE,,B2B

• DO,I,1,NT

• DO,J,1,RLMAX RSAVE10(I,J,4) = RLIST(I,J)

• ENDDO

• ENDDO

• ENDIF FINISH

/COM, Clear the pressure boundary conditions

/PREP7 SFDELE,ALL,ALL FINISH

• USE,ZEROIT

/COM,

/TITLE, Hatch1 Reactor Vessel Tensioning FINISH SAVE

/COM,

/COM, **********************************************************************************

/COM, PRINT RESULTS

/COM, **********************************************************************************

/COM,

/COM, Print contents of PSAVE and RSAVE arrays

/OUT,RESULTS,OUT

/NOPR

• IF,RUNMORF,EQ,1,THEN

• USE,PRINTENS,'PSAVE10','RSAVE10',6,'Stud OOS',0

• ENDIF

/OUT

/GOPR FINISH

/COM,

/COM, **********************************************************************************

/COM, RUN COMPLETE

/COM, **********************************************************************************

/COM,

/FILN,Tens-0 PARSAV,ALL

/COM, Do some file cleanup

/SYS, del CMMAKER

/SYS, del ENDPOST

/SYS, del GEOM

/SYS, del GEOMCLUP

/SYS, del GODETEN

/SYS, del GOSOLV

/SYS, del OPTLOOP

/SYS, del POSTER

/SYS, del POSTER2

/SYS, del POSTER3

/SYS, del PRINTOLR

/SYS, del PRINTENS

/SYS, del PSOLV

/SYS, del READSI

/SYS, del ZEROIT

/SYS, del NPL

/SYS, del linrept

/SYS, del *.dbs

/SYS, del *.stat

/SYS, del *.osav

/SYS, del *.PCS

Dominion Engineering, Inc.

Title:

Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 28 of 39

/SYS, del *.PVTS

/SYS, del *.BCS

/SYS, del *.full

/SYS, del file.log

/SYS, del Tens-1.*

/SYS, del Tens-10.e???

/EXIT

Dominion Engineering, Inc.

Title:

Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 29 of 39 A.2 File: _MACROS.HATCH1

/COM, --------------- MACROS.HATCH1, Revision 1, Created May 2022 ----------------

/COM, **********************************************************************************

/COM,

/COM,

/COM,

/COM, **********************************************************************************

/COM, **********************************************************************************

/COM, CREATE GEOMETRY MACRO

/COM, ----------------------------------------------------------------------------------

/COM,

• CREATE,GEOM

/COM, ------------------------------------------------------------------

/COM, GEOMETRY AND RUN PARAMETERS

/COM, ------------------------------------------------------------------

/COM, Loads and Material Properties Esteel = 27.9E6  ! Young's modulus (psi)

Ds = 6.000  ! Stud shank diameter (in)

As = 27.489  ! Stud area (in^2)

Is = 63.568  ! Stud mom. of I (in^4)

Ls = 31.972  ! Stud effective length (in)

Estud = 29.9E6  ! Tune Estud or Ls to get right effective L

/COM,

/COM, Bolting Dimensions SCR = 117.313  ! Stud Circle Radius (in)

NDs = 6.750  ! Stud Hole diameter (in)

SWRC = 27.00  ! Spherical Washer Rad. of Curvature (in)

Ehole = 0.63*Esteel  ! Derate in stud hole regions

/COM,

/COM, Vessel Flange Dimensions VFIR = 109.690  ! Vessel flange inner radius (in)

! CBIR = 0.000  ! Core Barrel groove inner radius (in)

IORR = 111.00  ! Inner O-Ring radius (in)

SSOR = 113.75  ! Seating Surface outer radius (in)

RR = 112.75  ! >>> TUNE REACTION RADIUS <<<

VFOR = 122.625  ! Vessel flange outer radius (in)

! ZVFS = 0.000  ! Z dimension to vessel flange surface (in)

! ZBCB =--0.000  ! Z dimension to bottom of Core Barrel groove ZVIT =-18.00  ! Z dim to vessel inside trans. (120's row)

ZVOT =-14.50  ! Z dim to vessel outside trans. (130's row)

/COM,

/COM, Vessel Shell Dimensions VSIR = 110.373  ! Vessel shell inside radius VSTH = 5.875  ! Vessel shell thickness ZVTR =-20.048  ! Z dimension to bottom of vessel transition

/COM,

/COM, Head Flange Dimensions HFIR = 109.25  ! Head flange inner radius HFOR = 122.625  ! Head flange outer radius HFFR = 2.750  ! Head flange top fillet radius ZTHF = 24.375  ! Z dimension to top of head flange ZHFRI = 0.375  ! Z dimension to head flange recess - inner ZHFRO = 0.375  ! Z dimension to head flange recess - outer

! /COM,

! /COM, Head Shell Flange Transition

! RTCS = 0.000  ! Radial dimension to Transition Coordinate System

! ZTCS = 0.000  ! Z dimension to Transition Coordinate System

! IRTR = 0.000  ! Inner radius of transition area

! ZUIC = 0.000  ! Vertical rise of OD Transition

/COM,

/COM, Head Shell Dimensions HSIR = 109.50  ! Head shell inner radius HSTH = 3.188  ! Head shell thickness ZHCS = -7.250  ! Z dimension to Head Coordinate System AHT = 19.0  ! Approximate start of head shell region

/COM,

/COM,

/COM,

/COM, At = As/100  ! Arbitrarily small tie bar area (in^2)

It = Is*100  ! Arbitrarily large tie bar mom. Of i (in^4)

Dt = Ds*100  ! Arbitrarily large tie bar diameter (in)

RLTH = 0.005  ! Reaction link thickness (in Z direction)

Ar = As*100*(RLTH/Ls)  ! Reaction link area tuned for stiffness

Dominion Engineering, Inc.

Title:

Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 30 of 39

! 100 times greater than stud (in^2)

/COM,

/COM,

/COM, ------------------------------------------------------------------

/COM, MATERIAL PROPERTIES

/COM, ------------------------------------------------------------------

/COM, Set types, mats, and reals

/COM, Element types ET,1,SOLID45  ! Solids - vessel (no associated real props)

ET,2,LINK8  ! Links - for reaction (REALS: AREA,ISTRN)

ET,3,BEAM4  ! Beams - studs (A,IZZ,IYY,TKZ,TKY,THETA,ISTRN)

/COM,

/COM, Material properties

/COM, Material 1 for GENERAL USE MP,EX,1,Esteel MP,NUXY,1,0.30

/COM,

/COM, Material 2 for STUD ELEMENTS MP,EX,2,Estud MP,NUXY,2,0.30

/COM,

/COM, Material 3 for STUD HOLES MP,EX,3,Ehole MP,NUXY,3,0.30

/COM,

/COM, REAL PROPERTIES

/COM, R,1,0  ! Real 1: Dummy real for solid elements R,2,Ar  ! Real 2: Reaction links R,3,Ar/2  ! Real 3: Cutting plane reaction links R,4,At,It,It,Dt,Dt,0  ! Real 4: Tie bars R,5,At/2,It/2,It/2,Dt,Dt,0  ! Real 5: Cutting plane tie bars R,11,As,Is,Is,Ds,Ds,0  ! Real 11:Stud elements

• REPEAT,NT,1  ! Assign different reals to each stud

/COM,

/COM,

/COM, ------------------------------------------------------------------

/COM, NODE DEFINITION

/COM, ------------------------------------------------------------------

/COM,

• AFUN,DEG

/COM, Establish coordinate systems LOCAL,20,0,0,0  ! Cartesian on lower mating surface LOCAL,21,1,0,0,0,0,-90,0  ! Cylindrical on lower mating surface (z up)

! LOCAL,22,1,RTCS,ZTCS  ! Cylindrical system 1 for head curvature LOCAL,23,1,0,ZHCS  ! Cylindrical system 2 for head curvature LOCAL,24,2,0,ZHCS  ! Spherical system for head stresses

/COM,

/COM, Define keypoints on theta = 0 plane CSYS,20 BOTZ=-100+ZVTR N,1,VSIR,BOTZ  ! SHELL I.R. AT BOTTOM OF MODEL N,5,VSIR+VSTH,BOTZ  ! SHELL O.R. AT BOTTOM OF MODEL N,81,VSIR,ZVTR  ! SHELL I.R. AT BOTTOM OF FLANGE N,85,VSIR+VSTH,ZVTR  ! SHELL O.R. AT BOTTOM OF FLANGE

/COM,

/COM, DEFINE FEATURES ON MATING SURFACE N,161,VFIR,0  ! Flange inner surface N,162,(VFIR+IORR)/2,0  ! "Core barrel groove inner surface" N,163,IORR,0  ! Inner o-ring radius N,164,RR,0  ! Reaction radius N,165,SSOR,0  ! Outer limit of seating surface N,166,SCR-NDs/2,0  ! Bolt hole inner edge N,167,SCR,0  ! Bolt circle N,168,SCR+NDs/2,0  ! Bolt hole outer edge N,169,VFOR,0  ! Flange outer surface flwdth = HFOR-HFIR  ! Flange width - head flwdtv = VFOR-VFIR  ! Flange width - vessel iormo = RR-IORR  ! Inner o-ring moment arm

/COM,

/COM, COPY FEATURES THROUGH VESSEL FLANGE NGEN,2,-10,161,169,1,0,(ZTHF-Ls)/2 ! Copy mating surf. thru lower flange (150's)

NGEN,2,-20,161,169,1,0,ZTHF-Ls  ! Copy mating surf. thru lower flange (140's)

NGEN,2,-50,161,169,1,0,ZVOT  ! Make 110's row for O.D. feature FILL,151,156,,,,2,-10  ! Even out 150's and 140's row FILL,111,117

Dominion Engineering, Inc.

Title:

Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 31 of 39 FILL,116,118 NGEN,2,-20,111,117,1,0,(ZVIT-ZVOT) ! Make 90's row for I.D. feature NMODIF,97,NX(85)

FILL,91,97 NGEN,2,10,91,97,1,0,-(ZVIT-ZVOT)/2 ! Make 100's row for transition FILL,111,141,2,121,10,9,1

/COM,

/COM, FILL IN REST OF NODES IN VESSEL FLANGE FILL,1,5 FILL,81,85 FILL,1,81,7,,,5,1,0.4  ! FILL IN VESSEL SHELL NODES

/COM,

/COM, ARRANGE HEAD FLANGE SURFACE NODES CSYS,20 NGEN,2,40,161,169,1,0,RLTH  ! COPY LOWER MATING SURF. TO UPPER FLANGE N,201,HFIR,RLTH  ! HEAD FLANGE INNER SURFACE FILL,201,203 NGEN,2,10,201,209,1,0,ZHFRI-RLTH  ! COPY UP THROUGH UPPER FLANGE NGEN,6,10,211,219,1,0,((ZTHF-ZHFRI)/5)! COPY FIVE ROWS UP THROUGH UPPER FLANGE FILL,221,226,,,,5,10  ! ALIGN 220'S ROW

/COM,

/COM, MOVE HEAD SHELL IR NODES CSYS,23 NMODIF,231,HSIR

• REPEAT,4,10 FILL,231,234,,,,4,10

/COM,

/COM, DEFINE NODES IN FREE HEAD CSYS,23 N,361,HSIR,90  ! TOP OF HEAD (INNER SURFACE)

N,364,HSIR+HSTH,90  ! TOP OF HEAD (OUTER SURFACE)

N,271,HSIR,AHT  ! LOCATE I.R. AT TOP OF FILLET RADIUS N,274,HSIR+HSTH,AHT  ! LOCATE O.R. AT TOP OF FILLET RADIUS FILL,271,361,8,,,,,2.5  ! FILL IN HEAD INNER RADIUS FILL,274,364,8,,,,,2.5  ! FILL IN HEAD OUTER RADIUS FILL,251,254,,,,12,10  ! FILL IN INTERIOR HEAD NODES

/COM,

/COM, SWEEP OUT AROUND 360 DEGREES CSYS,21 NGEN,NT+1,1000,ALL,,,0,360/NV,0  ! MAKE FULL SWEEP OF MODEL NROTAT,ALL  ! BRING CS'S INTO ACTIVE CS

/COM,

/COM, ------------------------------------------------------------------

/COM, ELEMENT DEFINITION

/COM, ------------------------------------------------------------------

/COM,

/COM, _____________________________________

/COM, MAKE SOLID ELEMENTS TYPE,1 MAT,1 REAL,1 EN,1,1,2,12,11,1001,1002,1012,1011 ENGEN,1,4,1,1,1,1  ! SWEEP ACROSS BOTTOM ROW ENGEN,10,8,10,1,4,1  ! SWEEP UP TO BOTTOM OF FLANGE SHPP,OFF  ! TEMPORARILY TURN OFF SHAPE WARNINGS EN,81,81,82,92,91,1081,1082,1092,1091 EN,82,82,93,92,92,1082,1093,1092,1092 EN,83,82,83,94,93,1082,1083,1094,1093 ENGEN,1,2,1,83 EN,85,84,96,95,95,1084,1096,1095,1095 EN,86,84,85,97,96,1084,1085,1097,1096 EN,91,91,92,102,101,1091,1092,1102,1101 ENGEN,1,6,1,91  ! make 91 - 96 ENGEN,10,2,10,91,96,1  ! make 101 - 106 ENGEN,10,2,10,101  ! MAKE 111 ENGEN,1,8,1,111,111,1  ! SWEEP RIGHT TO MAKE 112 - 118 ENGEN,10,5,10,111,118

/COM, EN,201,201,202,212,211,1201,1202,1212,1211  ! MAKE 201 ENGEN,1,4,1,201,201,1  ! SWEEP RIGHT TO MAKE 202 TO 204 ENGEN,10,2,10,201,201,1  ! SWEEP UP TO MAKE 211 ENGEN,1,8,1,211,211,1  ! SWEET RIGHT TO MAKE 212 TO 218 ENGEN,10,5,10,211,218,1  ! SWEEP UP TO TOP OF FLANGE ENGEN,10,10,10,251,253,1  ! SWEEP THROUGH SHELL EN,351,351,1351,1361,361,352,1352,1362,362  ! MAKE 351

Dominion Engineering, Inc.

Title:

Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 32 of 39 ENGEN,1,3,1,351,351,1  ! FIX UP LAST ROW

/COM,

/COM,

/COM, ASSIGN BOLT HOLE REGION ESEL,S,ELEM,,146,500,10  ! SELECT INNER SIDE OF BOLT HOLE ESEL,A,ELEM,,147,500,10  ! SELECT OUTER SIDE OF BOLT HOLE EMODIF,ALL,MAT,3  ! ASSIGN BOLT HOLE DIFFERENT MATERIAL ESEL,ALL ENGEN,1000,NT,1000,ALL  ! COPY AROUND CIRCLE

/COM,

/COM, _____________________________________

/COM, MAKE LINE ELEMENTS FOR STUD TYPE,2 REAL,2 EN,501,164,204  ! REACTION FORCE LINK TYPE,3 REAL,11 MAT,2 EN,502,147,267,361  ! STUD

/COM,

/COM, _____________________________________

/COM, MAKE LINE ELEMENTS FOR TIE BARS REAL,4 MAT,1 EN,503,146,147,207 EN,504,147,148,207 EN,505,266,267,207 EN,506,267,268,207  ! TIE BARS EN,507,162,163,204 EN,508,163,164,204 EN,509,164,165,204 EN,510,202,203,164 EN,511,203,204,164 EN,512,204,205,164  ! REACTION SURFACE ENGEN,1000,NT,1000,501,512,1  ! COPY REST OF WAY THROUGH

/COM,

/COM, _____________________________________

/COM, ASSIGN INDIVIDUAL REAL PROPERTIES TO EACH STUD

/COM, STUD REAL IS STUD NO. + 10

• DO,I,1,NT ESEL,S,ELEM,,I*1000-498 EMODIF,ALL,REAL,I+10

• ENDDO ESEL,ALL

/COM,

/COM, _____________________________________

/COM, DO SOME NODAL CLEANUP NSLE,U NDELE,ALL  ! DELETE UNUSED NODES NSEL,ALL NUMMRG,NODE,0.001  ! MERGE OVERLAPPING NODES

/COM,

/COM,

/COM, ------------------------------------------------------------------

/COM, APPLY BOUNDARY CONDITIONS

/COM, ------------------------------------------------------------------

/COM, CSYS,21

/COM, _____________________________________

/COM, COUPLE UPPER AND LOWER FLANGE AT REACTION RADIUS

• DO,I,1,NT CP,I,UX,164+(I-1)*1000,204+(I-1)*1000 CP,100+I,UY,164+(I-1)*1000,204+(I-1)*1000

• ENDDO

/COM, APPLY DISPLACEMENT BOUNDARY CONDITIONS NSEL,S,LOC,Z,BOTZ  ! SELECT BOTTOM OF MODEL D,ALL,UY  ! APPLY ZERO VERT DISP D,ALL,UZ  ! APPLY ZERO VERT DISP NSEL,ALL ESEL,S,REAL,,4  ! SELECT TIE BAR ELEMENTS NSLE  ! SELECT TIE BAR NODES NSEL,U,NODE,,207,99207,1000  ! DESELECT CENTER NSEL,U,NODE,,361  ! DESELECT TOP OF FLANGE D,ALL,ROTX,0,0,,,ROTZ  ! HOLD ROTATIONS ON TIE BARS ESEL,ALL NSEL,ALL

Dominion Engineering, Inc.

Title:

Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 33 of 39

/COM,

/COM, _____________________________________

/COM, APPLY PRYING FORCES DUE TO CORE BARREL SPRING AND CORE SUPPORT LOAD

• IF,Fspr+Fcsl,GT,1.0,THEN

• DO,I,1,NT F,131+(I-1)*1000,FZ,-(Fspr+Fcsl)/2 F,132+(I-1)*1000,FZ,-(Fspr+Fcsl)/2 F,201+(I-1)*1000,FZ,+Fspr/2 F,202+(I-1)*1000,FZ,+Fspr/2

• ENDDO

• ENDIF

/COM,

/COM, _____________________________________

/COM, PUT SPECIAL BOUNDARY CONDITIONS ON VESSEL FOR PARTIAL MODELS

• IF,NT,LT,NV,THEN

• IF,ARG1,LT,0.5,THEN  ! USE MIRROR SYMMETRY B.C.s

/COM, DELETE EXTRA ELEMENTS AND NODES BEYOND LAST STUD EDELE,(NT-1)*1000+1,(NT-1)*1000+499

/COM, DO SOME NODAL CLEANUP NSLE,U NDELE,ALL NSEL,ALL

/COM, CHANGE REALS ON CUTTING PLANES ESEL,S,ELEM,,501 ESEL,A,ELEM,,501+(NT-1)*1000 EMODIF,ALL,REAL,3 ESEL,S,ELEM,,503,512 ESEL,A,ELEM,,503+(NT-1)*1000,512+(NT-1)*1000 EMODIF,ALL,REAL,5 ESEL,ALL NSEL,S,NODE,,1,1000 NSEL,A,NODE,,1+(NT-1)*1000,NT*1000 NSEL,U,NODE,,164,99164,1000 NSEL,U,NODE,,204,99204,1000 D,ALL,UY NSEL,ALL

• IF,Fspr+Fcsl,GT,1.0,THEN F,131,FZ,-(Fspr+Fcsl)/4 F,132,FZ,-(Fspr+Fcsl)/4 F,201,FZ,+Fspr/4 F,202,FZ,+Fspr/4 F,131+(NT-1)*1000,FZ,-(Fspr+Fcsl)/4 F,132+(NT-1)*1000,FZ,-(Fspr+Fcsl)/4 F,201+(NT-1)*1000,FZ,+Fspr/4 F,202+(NT-1)*1000,FZ,+Fspr/4

• ENDIF

• ELSE  ! USE CYCLIC SYMMETRY B.C.s

/COM, GET RID OF EXCESS ELEMENTS EDELE,(NT-1)*1000+1,(NT-1)*1000+350

/COM, SWING LAST PLANE AROUND TO 0 DEGREES NSEL,S,NODE,,NT*1000+1,(NT+1)*1000 CSYS,21 NMODIF,ALL,,0 NSEL,A,NODE,,1,1000 NSEL,U,NODE,,164,204,40 NROTATE,ALL CPINTF,ALL,0.001 NSEL,S,NODE,,NT*1000+1,(NT+1)*1000 NMODIF,ALL,,NT*360/NV NSEL,ALL NROTATE,ALL

/COM, BRING BACK LAST PLANE OF ELS.

ENGEN,(NT-1)*1000,2,(NT-1)*1000,1,350,1  ! COPY AROUND CIRCLE

/COM, FIX UP COUPLES ON EDGE PLANES CP,1,,NT*1000+164,NT*1000+204 CP,101,,NT*1000+164,NT*1000+204 CP,1501,UZ,164,NT*1000+164 CP,1502,UZ,204,NT*1000+204

• ENDIF

• ENDIF

/COM, Define a few components for later use

• USE,CMMAKER,201,500,'NHEAD','EHEAD'

• USE,CMMAKER,1,200,'NVESSEL','EVESSEL'

• USE,CMMAKER,221,500,'NHEADR','EHEADR'

/COM, Define pressure surfaces for PSOLV macro

Dominion Engineering, Inc.

Title:

Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 34 of 39 NSEL,S,NODE,,1,99999,10

/COM, Include nodes in core barrel groove and up to inner o-ring NSEL,A,NODE,,161,99999,1000 NSEL,A,NODE,,162,99999,1000 NSEL,A,NODE,,163,99999,1000 NSEL,A,NODE,,201,99999,1000 NSEL,A,NODE,,202,99999,1000 NSEL,A,NODE,,203,99999,1000 CM,PSURF,NODE NSEL,ALL SHPP CHECK

• END

/COM,

/COM, ----------------------------------------------------------------------------------

/COM, END GEOMETRY MACRO

/COM, **********************************************************************************

/COM, **********************************************************************************

/COM,

/COM,

/COM,

/COM, **********************************************************************************

/COM, **********************************************************************************

/COM, CREATE CMMAKER MACRO

/COM, ----------------------------------------------------------------------------------

/COM,

• CREATE,CMMAKER NSEL,NONE ESEL,NONE

• DO,I,0,(NT-1)*1000,1000 NSEL,A,NODE,,ARG1+I,ARG2+I

• IF,I,EQ,(NT-1)*1000,THEN

• IF,NT,LT,NV,EXIT

• ENDIF ESEL,A,ELEM,,ARG1+I,ARG2+I

• ENDDO CM,ARG3,NODE CM,ARG4,ELEM NSEL,ALL ESEL,ALL

• END

/COM,

/COM, ----------------------------------------------------------------------------------

/COM, END CMMAKER MACRO

/COM, **********************************************************************************

/COM, **********************************************************************************

/COM,

/COM,

/COM,

/COM, **********************************************************************************

/COM, **********************************************************************************

/COM, CREATE GEOMCLUP MACRO

/COM, ----------------------------------------------------------------------------------

/COM,

• CREATE,GEOMCLUP CPDELE,ALL CMDELE,NHEAD CMDELE,EHEAD CMDELE,NVESSEL CMDELE,EVESSEL CMDELE,NHEADR CMDELE,EHEADR EDELE,ALL NDELE,ALL

• END

/COM,

/COM, ----------------------------------------------------------------------------------

/COM, END GEOMCLUP MACRO

/COM, **********************************************************************************

/COM, **********************************************************************************

/COM,

/COM,

/COM,

/COM, **********************************************************************************

/COM, **********************************************************************************

/COM, CREATE ENDPOST MACRO

Dominion Engineering, Inc.

Title:

Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 35 of 39

/COM, ----------------------------------------------------------------------------------

/COM, RLIST columns as follows:

/COM, RLIST(J,1) = Flange Displ. last pass

/COM, RLIST(J,2) = Stud Initial Elongation Real Constant

/COM, RLIST(J,3) = Stud Final Membrane Stress

/COM, RLIST(J,4) = Stud Max. Membrane+Bending Stress

/COM, RLIST(J,5) = Maximum Membrane Stress during any pass

/COM, RLIST(J,6) = Pass Number at which Max. Membrane Stress Occurs

/COM,

/COM, RLIST(J,7) = Angular Rotation of Upper Flange (radians)

/COM, RLIST(J,8) = Angular Rotation of Lower Flange (radians)

/COM, RLIST(J,9) = Inner O-ring separation

/COM,

/COM, RLIST(J,10) = Force on Contact Link Element

/COM, RLIST(J,11) = Global X Shear Force on Coupled Set

/COM, RLIST(J,12) = Global Z Shear Force on Coupled Set

/COM,

/COM, RLIST(J,13) = Mu Required to Prevent Flange Mating Surf. Slide

/COM, RLIST(J,14) = Mu Required to Prevent Flange Stud Washer Slide

/COM,

/COM, Cut Plane Stress Intensities:

/COM, Line 1 - Vessel Far Field Cut Plane (RLIST(J,15) to RLIST(J,19))

/COM, RLIST(J,15) = Linearized SI at Inner Surface

/COM, RLIST(J,16) = Linearized SI at Center of Surface (Membrane SI)

/COM, RLIST(J,17) = Linearized SI at Outer Surface

/COM, RLIST(J,18) = Total SI at Inner Surface

/COM, RLIST(J,19) = Total SI at Outer Surface

/COM,

/COM, Line 2 - Vessel Local Cut Plane - Lower (RLIST(J,20) to RLIST(J,24))

/COM, Line 3 - Vessel Local Cut Plane - Middle (RLIST(J,25) to RLIST(J,29))

/COM, Line 4 - Vessel Local Cut Plane - Upper (RLIST(J,30) to RLIST(J,34))

/COM, Line 5 - Head Local Cut Plane - Lower (RLIST(J,35) to RLIST(J,39))

/COM, Line 6 - Head Local Cut Plane - Middle (RLIST(J,40) to RLIST(J,44))

/COM, Line 7 - Head Local Cut Plane - Upper (RLIST(J,45) to RLIST(J,49))

/COM, Line 8 - Head Far Field Cut Plane (RLIST(J,50) to RLIST(J,54))

/COM,

• CREATE,ENDPOST

/COM, Finish by loading results in RLIST

• DO,J,1,NT ENUMB = J*1000-498  ! El. no. of subject element

• GET,RLIST(J,3),ELEM,ENUMB,ETAB,MEMBSTRS  ! El. membrane stress

• GET,DUMBOT,ELEM,ENUMB,ETAB,MAXM+BI  ! El. membrane+bend stress (I)

• GET,DUMTOP,ELEM,ENUMB,ETAB,MAXM+BJ  ! El. membrane+bend stress (J)

RLIST(J,4) = DUMBOT > DUMTOP

/COM, RSYS,21 NNUM1 = (J-1)*1000+151  ! Node 151 NNUM2 = (J-1)*1000+159  ! Node 159 NNUM3 = (J-1)*1000+211  ! Node 211 NNUM4 = (J-1)*1000+219  ! Node 219 RLIST(J,7) = (UZ(NNUM4)-UZ(NNUM3))/flwdth  ! Upper Flange Rotation (radians)

RLIST(J,8) = (UZ(NNUM2)-UZ(NNUM1))/flwdtv  ! Lower Flange Rotation (radians)

NNUM1 = (J-1)*1000+164 NNUM2 = (J-1)*1000+204 RLIST(J,9) = UZ(NNUM2)-UZ(NNUM1)+iormo*(RLIST(J,8)-RLIST(J,7))

/COM, ENUMB = (J-1)*1000+501  ! El. no. 501

• GET,RLIST(J,10),ELEM,ENUMB,ETAB,FORCE  ! El. Force CMSEL,S,EHEAD NSEL,S,NODE,,(J-1)*1000+204 FSUM ESEL,ALL NSEL,ALL

• GET,RLIST(J,11),FSUM,,ITEM,FX  ! Global X-Shear Force

• GET,RLIST(J,12),FSUM,,ITEM,FZ  ! Global Z-Shear Force

! RLIST(J,13) is resultant shear divided by link membrane force

• IF,RLIST(J,10),LT,-1.0,THEN RLIST(J,13) = -SQRT(RLIST(J,11)**2+RLIST(J,12)**2)/RLIST(J,10)

• ELSE RLIST(J,13) = -1  ! Trap divide by zero

• ENDIF SLIPCNST = 2*Is/(Ds*SWRC*As)  ! Constants in washer slip calc

• IF,RLIST(J,3),GT,1.0,THEN RLIST(J,14) = SLIPCNST*(RLIST(J,4)-RLIST(J,3))/RLIST(J,3)

• ELSE RLIST(J,14) = -1  ! Trap divide by zero

Dominion Engineering, Inc.

Title:

Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 36 of 39

• ENDIF

/COM,

/COM, Cut Lines:

• USE,READSI,11,15,21,15,J  ! Cut 1: Nodes 11 to 15 in CSYS 21

• USE,READSI,61,65,21,20,J  ! Cut 2: Nodes 61 to 65 in CSYS 21

• USE,READSI,71,75,21,25,J  ! Cut 3: Nodes 71 to 75 in CSYS 21

• USE,READSI,81,85,21,30,J  ! Cut 4: Nodes 81 to 85 in CSYS 21

• USE,READSI,261,264,24,35,J  ! Cut 5: Nodes 261 to 261 in CSYS 24

• USE,READSI,271,274,24,40,J  ! Cut 6: Nodes 271 to 274 in CSYS 24

• USE,READSI,281,284,24,45,J  ! Cut 7: Nodes 281 to 284 in CSYS 24

• USE,READSI,351,354,24,50,J  ! Cut 8: Nodes 351 to 354 in CSYS 24

• ENDDO

• END

/COM, ----------------------------------------------------------------------------------

/COM, END ENDPOST MACRO

/COM, **********************************************************************************

/COM, **********************************************************************************

/COM,

/COM,

/COM,

/COM, **********************************************************************************

/COM, **********************************************************************************

/COM, CREATE PRINTENS MACRO

/COM, ----------------------------------------------------------------------------------

/COM,

/COM, PRINTENS arguments as follows:

/COM, ARG1 = PSAVE Text

/COM, ARG2 = RSAVE Text

/COM, ARG3 = Loop Ending No.

/COM, ARG4 = Free Text Field (e.g., 'Existing')

/COM, ARG5 = Sequence Print Flag (1 = Print Sequence)

/COM,

• CREATE,PRINTENS

• DO,K,1,ARG3

• VWRITE,K

('-----',/,'Tensioning Sequence Iteration ',F2.0)

• VWRITE,ARG4

('-----',/,A,' Procedure Results -')

• VWRITE (2/,'Stud Stress Summary',/)

• VSCFUN,MAXCOL1,MAX, %ARG2%(1, 3,K)

• VSCFUN,MINCOL1,MIN, %ARG2%(1, 3,K)

• VSCFUN,AVECOL1,MEAN,%ARG2%(1, 3,K)

• VSCFUN,MAXCOL2,MAX, %ARG2%(1, 4,K)

• VSCFUN,MINCOL2,MIN, %ARG2%(1, 4,K)

• VSCFUN,AVECOL2,MEAN,%ARG2%(1, 4,K)

• VSCFUN,MAXCOL3,MAX, %ARG2%(1, 5,K)

• VSCFUN,MINCOL3,MIN, %ARG2%(1, 5,K)

• VSCFUN,AVECOL3,MEAN,%ARG2%(1, 5,K)

• VSCFUN,MAXCOL4,MAX, %ARG2%(1,14,K)

• VSCFUN,MINCOL4,MIN, %ARG2%(1,14,K)

• VSCFUN,AVECOL4,MEAN,%ARG2%(1,14,K)

/COM, MEMBRANE MEMB+BEND MAX. MEM. REQUIRED

/COM, STRESS STRESS STRESS WASHER MU

• VWRITE,'MAXIMUM',MAXCOL1,MAXCOL2,MAXCOL3,MAXCOL4 (A7,3X,3(F9.0,3X),3X,F7.4)

• VWRITE,'MINIMUM',MINCOL1,MINCOL2,MINCOL3,MINCOL4 (A7,3X,3(F9.0,3X),3X,F7.4)

• VWRITE,'AVERAGE',AVECOL1,AVECOL2,AVECOL3,AVECOL4 (A7,3X,3(F9.0,3X),3X,F7.4)

• VWRITE (2/,'Head and Head Flange Cut Planes Stress Summary',/)

• VSCFUN,AVECOL1,MEAN,%ARG2%(1,51,K)

• VWRITE,AVECOL1

('General Membrane Stress Intensity ',F6.0)

• VSCFUN,MAXCOL1,MAX,%ARG2%(1,36,K)

• VSCFUN,MAXCOL2,MAX,%ARG2%(1,41,K)

• VSCFUN,MAXCOL3,MAX,%ARG2%(1,46,K)

MAXCOL4 = MAXCOL1 > MAXCOL2 > MAXCOL3

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Title:

Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 37 of 39

• VWRITE,MAXCOL4

('Maximum Local Membrane Stress Intensity ',F6.0)

• VSCFUN,MAXCOL1,MAX,%ARG2%(1,35,K)

• VSCFUN,MAXCOL2,MAX,%ARG2%(1,40,K)

• VSCFUN,MAXCOL3,MAX,%ARG2%(1,45,K)

MAXCOL4 = MAXCOL1 > MAXCOL2 > MAXCOL3

• VSCFUN,MINCOL1,MAX,%ARG2%(1,37,K)

• VSCFUN,MINCOL2,MAX,%ARG2%(1,42,K)

• VSCFUN,MINCOL3,MAX,%ARG2%(1,47,K)

MINCOL4 = MINCOL1 > MINCOL2 > MINCOL3

• VWRITE,MAXCOL4 > MINCOL4

('Maximum Local Mem + Bend Stress Intensity ',F6.0)

• VSCFUN,MAXCOL1,MAX,%ARG2%(1,38,K)

• VSCFUN,MAXCOL2,MAX,%ARG2%(1,43,K)

• VSCFUN,MAXCOL3,MAX,%ARG2%(1,48,K)

MAXCOL4 = MAXCOL1 > MAXCOL2 > MAXCOL3

• VSCFUN,MINCOL1,MAX,%ARG2%(1,39,K)

• VSCFUN,MINCOL2,MAX,%ARG2%(1,44,K)

• VSCFUN,MINCOL3,MAX,%ARG2%(1,49,K)

MINCOL4 = MINCOL1 > MINCOL2 > MINCOL3

• VWRITE,MAXCOL4 > MINCOL4

('Maximum Local Stress Intensity ',F6.0)

• VWRITE (2/,'Vessel and Vessel Flange Cut Planes Stress Summary',/)

• VSCFUN,AVECOL1,MEAN,%ARG2%(1,16,K)

• VWRITE,AVECOL1

('General Membrane Stress Intensity ',F6.0)

• VSCFUN,MAXCOL1,MAX,%ARG2%(1,21,K)

• VSCFUN,MAXCOL2,MAX,%ARG2%(1,26,K)

• VSCFUN,MAXCOL3,MAX,%ARG2%(1,31,K)

MAXCOL4 = MAXCOL1 > MAXCOL2 > MAXCOL3

• VWRITE,MAXCOL4

('Maximum Local Membrane Stress Intensity ',F6.0)

• VSCFUN,MAXCOL1,MAX,%ARG2%(1,20,K)

• VSCFUN,MAXCOL2,MAX,%ARG2%(1,25,K)

• VSCFUN,MAXCOL3,MAX,%ARG2%(1,30,K)

MAXCOL4 = MAXCOL1 > MAXCOL2 > MAXCOL3

• VSCFUN,MINCOL1,MAX,%ARG2%(1,22,K)

• VSCFUN,MINCOL2,MAX,%ARG2%(1,27,K)

• VSCFUN,MINCOL3,MAX,%ARG2%(1,32,K)

MINCOL4 = MINCOL1 > MINCOL2 > MINCOL3

• VWRITE,MAXCOL4 > MINCOL4

('Maximum Local Mem + Bend Stress Intensity ',F6.0)

• VSCFUN,MAXCOL1,MAX,%ARG2%(1,23,K)

• VSCFUN,MAXCOL2,MAX,%ARG2%(1,28,K)

• VSCFUN,MAXCOL3,MAX,%ARG2%(1,33,K)

MAXCOL4 = MAXCOL1 > MAXCOL2 > MAXCOL3

• VSCFUN,MINCOL1,MAX,%ARG2%(1,24,K)

• VSCFUN,MINCOL2,MAX,%ARG2%(1,29,K)

• VSCFUN,MINCOL3,MAX,%ARG2%(1,34,K)

MINCOL4 = MINCOL1 > MINCOL2 > MINCOL3

• VWRITE,MAXCOL4 > MINCOL4

('Maximum Local Stress Intensity ',F6.0)

• VSCFUN,MAXCOL1,MAX,%ARG2%(1,9,K)

• VWRITE,MAXCOL1 (2/,'Maximum Inner O-Ring Separation is ',F7.5,' inches.')

• VSCFUN,MAXCOL1,MAX,%ARG2%(1,13,K)

• VWRITE,MAXCOL1

('Required Mating Surface Mu to Prevent Slip is ',F7.5,'.')

• IF,ARG5,EQ,1,THEN

• VWRITE,ARG4

('-----',/,A,' Procedure - Sequence Listing',/)

/COM, SET NO. STUD NO. PRESSURE RETEN. FLAG

• VWRITE,SEQU,%ARG1%(1,1,K),%ARG1%(1,2,K),%ARG1%(1,4,K)

(4(F9.0,3X))

• ENDIF

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Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 38 of 39

• VWRITE,ARG4

('-----',/,A,' Procedure Results - Stud Stresses',/)

/COM, MEMBRANE MEMB+BEND MAX. MEM. ACHIEVED REQUIRED

/COM,STUD # STRESS STRESS STRESS @ SET NO. WASHER MU

• VWRITE,SEQU,%ARG2%(1,3,K),%ARG2%(1,4,K),%ARG2%(1,5,K),%ARG2%(1,6,K),%ARG2%(1,14,K)

(F5.0,5X,4(F9.0,3X),2X,F7.4)

• VWRITE,ARG4

('-----',/,A,' Procedure Results - Flange Contact Forces',/)

/COM, GLOBAL GLOBAL REQUIRED

/COM,STUD # LINK FORCE X SHEAR Z SHEAR FLANGE MU

• VWRITE,SEQU,%ARG2%(1,10,K),%ARG2%(1,11,K),%ARG2%(1,12,K),%ARG2%(1,13,K)

(F5.0,3X,3(E11.4,2X),2X,F7.4)

• VWRITE,ARG4

('-----',/,A,' Procedure Results - Flange Deflections',/)

/COM, UPPER FLANGE LOWER FLANGE O-RING

/COM,STUD # ROTATION ROTATION SEPARATION

• VWRITE,SEQU,%ARG2%(1,7,K),%ARG2%(1,8,K),%ARG2%(1,9,K)

(F5.0,4X,3(E11.4,4X))

CLNO = 0

• DO,L1,15,50,5 CLNO = CLNO+1 L2 = L1+1 L3 = L1+2 L4 = L1+3 L5 = L1+4

• VWRITE,ARG4,CLNO

('-----',/,A,' Procedure Results - Cut Line ',F2.0,/)

/COM, INNER CENTER OUTER INNER OUTER

/COM,STUD # LIN. S.I. LIN. S.I. LIN. S.I. TOT. S.I. TOT. S.I.

• VWRITE,SEQU,%ARG2%(1,L1,K),%ARG2%(1,L2,K),%ARG2%(1,L3,K),%ARG2%(1,L4,K),%ARG2%(1,L5,K)

(F5.0,2X,5(F9.0,3X))

• ENDDO

• ENDDO

• END

/COM, ----------------------------------------------------------------------------------

/COM, END PRINTENS MACRO

/COM, **********************************************************************************

/COM, **********************************************************************************

/COM,

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Title:

Hatch Unit 1 Operation with One Stud Out of Service Evaluation Calculation No.: C-037-2201-00-01 Revision No.: 0 Page 39 of 39 B SOFTWARE USAGE RECORDS The following table lists the Software Usage Records for the ANSYS analyses performed in support of this calculation. These records are included on the Data Disk D-037-2201-00-01 [6] in their native electronic formats. This data disk is retained with the Task 037-2201 project file and is available for on-site review by Southern Nuclear personnel.

File Name Description

_HATCH1.RUNS Input file which sets run parameters and performs the closure flange evaluation cases.

_MACROS.HATCH1 Input file which sets the finite element model geometry and boundary conditions specific to the Hatch Unit 1 RPV model.

_MACROS.DEI Input file which performs stud tensioning and closure flange analyses.

RESULTS.OUT Formatted output file which contains the stud stress results for the closure flange analysis cases.

HATCH1.out Full output file generated automatically which includes every ANSYS operation performed throughout the analysis.

HATCH1.err Automatically generated error file which includes all warnings generated during the analysis.

Hatch 1 Stud Primary Stress Microsoft Excel spreadsheet used to perform stud primary stress Calc v0.xlsx calculations.

Edwin I. Hatch Nuclear Plant - Units 1 and 2 Request to Relax the Required Number of Fully Tensioned Reactor Pressure Vessel Head Closure Studs in Technical Specification Table 1.1-1, MODES NL-22-0406 Enclosure 3 Calculation C-037-2201-00-02, Hatch Unit 2 Operation with Two Studs Out of Service Evaluation

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Title:

Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 2 of 41 TABLE OF CONTENTS Last Mod.

Section Page Rev.

1 PURPOSE..................................................................................................................................... 5 0 2

SUMMARY

OF RESULTS ................................................................................................................. 5 0 3 INPUT REQUIREMENTS .................................................................................................................. 5 0 3.1 Analysis Inputs ............................................................................................................... 5 0 3.2 Acceptance Criteria ........................................................................................................ 7 0 4 ASSUMPTIONS .............................................................................................................................. 7 0 5 ANALYSIS..................................................................................................................................... 9 0 5.1 Stud Primary Stress with Two studs Out of Service........................................................ 9 0 5.1.1 Average Stud Force ......................................................................................... 9 0 5.1.2 Calculation of Stud Force Distribution .............................................................. 9 0 5.1.3 Primary Stress Comparison ........................................................................... 11 0 5.2 Analysis of Closure Flange with Two Studs Out of Service .......................................... 11 0 5.2.1 Evaluation Methodology ................................................................................. 11 0 5.2.2 Reactor Vessel Closure Flange Model ........................................................... 12 0 5.2.2.1 Model Geometry ......................................................................... 12 0 5.2.2.2 Model Boundary Conditions ....................................................... 13 0 5.2.3 Analysis Cases............................................................................................... 13 0 5.2.4 Results Discussion ......................................................................................... 14 0 5.2.4.1 RPV Closure Stresses ................................................................ 14 0 5.2.4.2 RPV Stud Stresses..................................................................... 14 0

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Title:

Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 4 of 41 LIST OF TABLES Last Mod.

Table No. Rev.

Table 1. FEA Model Inputs 0 Table 2. Calculation of Primary Stresses in Reactor Vessel Studs, Two Studs Out of Service 0 Table 3. Stress Increase Due to Two Studs Out of Service 0 LIST OF FIGURES Last Mod.

Figure No. Rev.

Figure 1. Reactor Vessel Head Stud Geometry, Two Studs Out of Service 0 Figure 2. Hatch Unit 2 RPV Closure Flange FEA Model Overall View [1] 0 Figure 3. FEA Model Node Numbering and Section Cut Line Locations [1] 0

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Title:

Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 5 of 41 1 PURPOSE Dominion Engineering, Inc. (DEI) originally provided optimized tensioning and detensioning procedures for Plant Hatch in January 2015 [1], along with design basis evaluations for expanded elongation tolerances. A subsequent calculation performed for Hatch Unit 2 in February 2017 [3]

demonstrated the acceptability of operating Unit 2 with one stud out of service. The purpose of this calculation is to provide an update to these evaluations that considers the effect of two studs out of service. This analysis considers the stresses resulting from two conditions which bound the effects of studs out of service: (1) operating with two studs left untensioned, and (2) the unlikely condition of two studs that are tensioned then fail in service. The analysis of record for operating with one stud out of service should remain the original analysis performed in February 2017 [3].

2

SUMMARY

OF RESULTS The average stresses in the studs due to primary load conditions with two studs out of service were calculated using the methodology outlined in Section 5.1. As summarized in this section, all studs continue to meet ASME Code requirements for primary loads with two studs out of service.

The FEA model which was used to develop the current stud tensioning evaluations in DEI Report R-3937-00-01 [1] and DEI Calculation C-3944-00-01 [3] was used to perform an analysis of the closure flange with two studs out of service, as summarized in Section 5.2. A further restriction is placed on operating with two studs out of service: the two studs must be separated by nine or more studs (e.g., studs 1 and 10 out of service would meet this restriction). The analysis results are summarized in Table 3. As demonstrated by the results in Table 3, operation of the Hatch Unit 2 RPV with two studs out of service, with a minimum of nine studs between them, does not result in any component of the RPV closure flange to exceed the design basis ASME Code allowables.

3 INPUT REQUIREMENTS 3.1 Analysis Inputs The following inputs are required to calculate the average stresses in the studs due to primary load conditions with two studs out of service:

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Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 6 of 41

1. The RPV design pressure is 1,250 psia and the design temperature is 575°F [1, Table 3-1].

2. The RPV inner o-ring radius is 111.0 inches [1, Table 3-3].

3. The RPV stud circle radius is 117.313 inches [1, Table 3-3].

4. The number of studs in the Hatch Unit 2 RPV is 56 [1, Table 3-1].

5. The stud shank OD is 6.0 inches, the stud shank ID is 1.0 inches, and the stud shank cross section area is 27.489 in2 [1, Table 3-1].

The following inputs are required for the FEA analysis of tensioning effects related to two studs out of service:

6. Reactor vessel head and closure flange dimensions. The geometry of the model developed for this analysis is identical to the one used in the Reference [1]. The model parameters used in this FEA model are detailed in Table 1, which is reproduced from Table A-1 of Reference [1].

7. Reactor vessel head and closure flange low alloy steel material properties. The material properties of the model developed for this analysis are identical to those used in Reference [1].

8. ASME Code design basis summary. The design basis conditions for the RPV closure flange components, updated to include the analyses performed in the 2015 tensioning optimization stress, report are summarized in Table 2-1 of Reference [1]. This table includes the updated stress values as well as the appropriate ASME Code comparison and allowable stress value. The following values from Table 2-1 are used in this calculation:

a. Closure head / head flange maximum stress intensity range: 64.0 ksi [1, Table 2-1]

b. Vessel closure shell / flange maximum stress intensity range: 47.4 ksi [1, Table 2-1]

c. Closure stud membrane stress, maximum service load: 45.3 ksi [1, Table 2-1]

d. Closure stud maximum stress, maximum service load: 95.4 ksi [1, Table 2-1]

e. Closure stud fatigue usage: 0.846 [1, Table 2-1]

f. Closure head / head flange fatigue usage: 0.178 [1, Table 2-1]

g. Vessel closure shell / flange fatigue usage: 0.679 [1, Table 2-1]

9. Primary stress design basis values. The conditions evaluated in the 2015 tensioning optimization stress report do not impact primary conditions, and therefore they were not included. Using the original closure flange design basis report [2] (referenced in the 2015 analysis), the following limiting primary stress values are obtained:

a. Closure head / head flange general membrane stress: 22.5 ksi [2, p. A-16]

b. Vessel closure shell / flange general membrane stress: 23.8 ksi [2, p. A-16]

c. Closure head / head flange local membrane + bending stress: 37.9 ksi [2, p. A-7]

d. Vessel closure shell / flange local membrane + bending stress: 37.5 ksi [2, p. A-7]

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Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 7 of 41 3.2 Acceptance Criteria The following acceptance criteria are applicable to this calculation:

1. The RPV closure components were designed according to the 1968 Edition with Summer 1970 Addenda of Section III of the ASME Boiler and Pressure Vessel Code [8].

2. The stresses in the closure studs are subject to the following requirements and allowable stresses:

a. Primary stress at 575°F design temperature: 36.3 ksi (Sm) [1, Table 3-3].

b. Maximum allowable average stress, evaluated at 550°F: 73.5 ksi (2Sm) [1, Table 2-1]

c. Maximum allowable stress, evaluated at 550°F: 99.2 ksi (2.7Sm) [1, Table 2-1]

3. The stresses in the closure head and vessel are subject to the following requirements and allowable stresses:

a. Closure head / head flange and vessel closure shell / flange [8, Paragraph N-414.1] general membrane allowable stress at 575°F design temperature: 26.7 ksi (Sm) [1, Table 3-3]

b. Closure head / head flange and vessel closure shell / flange [8, Paragraph N-414.3] local membrane + bending allowable stress at 575°F design temperature: 40.05 ksi (1.5Sm)

[1, Table 3-3]

c. Closure head / head flange and vessel closure shell /flange [8, Paragraph N-414.4]

maximum allowable stress intensity range, evaluated at 575°F design temperature:

80.10 ksi (3Sm) [1, Table 2-1]

4. The maximum allowable fatigue usage factor is 1.0 [8, Paragraph N-415.2(e)(6)].

5. The minimum o-ring springback is 0.010 inch [1, Table 3-2]. Although this is not an ASME Code criterion, it is a condition evaluated to demonstrate the flange opening will not result in additional risk of leakage. The design basis report maximum o-ring opening is 0.0015 inch [1, Table 3-2].

4 ASSUMPTIONS The following assumptions are used to calculate the average stresses in the studs due to primary load conditions with two studs out of service:

1. The reactor vessel and head are rigid. This is consistent with the usual treatment of primary loads which only considers net forces and moments and not localization of stress from geometry and compliance effects. A consequence of this assumption is that the distribution of stud forces varies linearly with the distance from the neutral axis.

2. The reactor vessel and head exert no contact forces on each other (i.e., the compression forces on the mating surfaces are neglected). These secondary forces serve to mitigate the redistribution of

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Title:

Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 8 of 41 loads when studs fail, so this assumption conservatively maximizes the calculated maximum stud stress value.

3. As a simplifying assumption, each stud is individually treated as a point force. That is, each stud contributes no bending stiffness to the cross section as a whole. This assumption is appropriate given the small bending stiffness of the studs relative to the overall head cross section.

4. The design pressure is assumed to act out to the radius of the inner o-ring of the vessel. This is an appropriate assumption because leakage past the inner o-ring is not a normal operating condition.

5. Stud primary membrane stress is calculated by conservatively assuming the two out-of-service studs to be adjacent to each other.

The following assumptions are used for the FEA analysis of tensioning effects related to two studs out of service. These assumptions are consistent with analyses described in Reference [1].

6. All vessel elements were assigned material properties appropriate for low carbon steel at ambient temperature: E = 27.9E6 psi and = 0.3. All stud elements were assigned material properties appropriate for low alloy steel at ambient temperature: E = 29.9E6 psi and = 0.3. The differences caused by differential thermal expansion of the stud and vessel are negligible and are not considered.

7. The modulus of elasticity in the stud hole regions of the upper and lower flanges were de-rated by the ratio shown in Table 1 to account for the removed material in the stud holes.

8. The contact between the nut and the washer is assumed to occur at a single point location. This is considered a reasonable assumption since the nut and washer mate at a spherical surface, and therefore come into contact all at once.

9. Beam elements that are stiff in bending are used to impose flange rotation on the ends of the studs. Despite the presence of spherical washers between the nut and the upper flange, friction acts to "glue" the nut to the flange once the stud is preloaded. At full pressure load with all studs active, a modest amount of friction (  0.1) has been demonstrated to be sufficient to transmit the bending stresses which arise from this boundary condition. Thus, the infinite friction assumption is concluded to be more realistic than the assumption of zero friction at the spherical washer.

10. The interface between the head and vessel flanges was simulated by a row of line elements connecting the head and vessel flanges. The location of these interface elements was selected to act at a reaction radius empirically determined from the correlation between the model predictions and the actual stud elongation data using the existing tensioning procedure.

11. All studs are assumed to be initially uniformly tensioned to the target stud elongation of 0.0397 inch, equivalent to a stud stress of 37.146 ksi [1, Table 3-1].

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Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 9 of 41 5 ANALYSIS 5.1 Stud Primary Stress with Two studs Out of Service The effect of two studs being out of service on the primary stress in the remaining studs is greater than simply increasing the design basis primary stress by the ratio of original to remaining studs. The change in restraint conditions caused by the inactive studs will tend to create a larger primary load in the studs adjacent to the inactive studs.

We treat the studs as a single cross section loaded in bending by the pressure on the reactor head.

Assuming two adjacent studs are out of service, and that the resulting force distribution in the studs is a linear function of the distance from the neutral axis of the stud cross section, we enforce the static equilibrium equations on the studs. Note that the linear distribution assumption is a consequence of Assumption 1. An Excel spreadsheet is used to facilitate solution of the equations which are developed.

5.1.1 Average Stud Force Ignoring for a moment that the 54 remaining studs are not uniformly distributed around the RPV closure, we can compute the average force in the studs according to the following equation. Assuming that the design pressure (in psig) acts out to the location of the inner o-ring radius (characterized by radius Ri), we have:

(1235 psig)( x 111. 0 in )

= = = = 885.3 kips [5-1]

54 54 54 This value will be used in computing the actual force (and, from there, stress) distribution among the studs in a later section. For comparative purposes, we note that when all studs are intact and tensioned, the corresponding average force is (54/56)*885.3 = 853.6 kips.

5.1.2 Calculation of Stud Force Distribution Because the out of service stud is located symmetrically about the x-axis, the neutral axis of bending for the remaining studs (considered as a whole) must be oriented parallel to the y-axis in Figure 1. The

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Title:

Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 10 of 41 offset G from the center of pressure is still an unknown at this point, however. The solution for G is achieved by writing the static equilibrium equations for the reactor head F F  PA z i h 0 i

[5-2]

M F n i x i  G  PAh ( G ) 0 i

where Fz = net force in the direction parallel to the stud lengths Mn = net moment about the neutral axis xi = x-coordinate of each stud per the axes in Figure 1 G  parallel offset of the neutral axis from the y-axis as shown in Figure 1

 $h = area of the reactor head on which the pressure force acts The coordinates xi can be written in terms of the bolt-circle radius (Ro) and Ti as defined in Figure 1.

Note that the axes are arranged to split the gap between two studs that are out of service, accounting for an additional one-half stud pitch in the coordinate calculation.

(28 + 0.5)

= , where = x 2 [5-3]

56 At this point, we assume per Section 4 that the stud force varies linearly with its distance from the neutral axis. The mathematical form of the force distribution in the studs consequently may be expressed as follows, where f is a constant Fi F  f xi  G [5-4]

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Title:

Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 11 of 41 Substituting Eq. [5-4] into the first of Eqs.[5-2] and taking advantage of the fact that F PAh yields i

+ ( ) = 0 ( ) = 0 1 [5-5]

54 54 where Eq. [5-3] has been used for xi. Since G is now known, we can substitute Eq. [5-4] into the second of Eqs. [5-2], resulting in the following

+ ( ) ( ) () = 0

+ ( ) ( ) + = 0 [5-6]

+ 54

=

2 + 54 The values for f and G can be substituted directly back into Eq. [5-4], producing the force distribution for all studs. The final results appear in Table 2. Note that the highest stud force occurs at Stud Location Nos. 2 and 55, as might be expected since these are adjacent to the untensioneds stud (Nos. 1 and 56).

5.1.3 Primary Stress Comparison The distributed primary stud forces are divided by the stud stress area of 27.489 in2 (Input 5) to calculate the primary stud stresses. The maximum primary stud stress is calculated in Table 2 to be 34.74 ksi, which is less than the Sm allowable of 36.3 ksi; therefore, this condition is satisfied.

5.2 Analysis of Closure Flange with Two Studs Out of Service 5.2.1 Evaluation Methodology The effect of two studs out of service on the ASME Code comparison stresses in the reactor vessel closure flange components is evaluated using the same model used in the 2015 tensioning optimization

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Title:

Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 12 of 41 stress report. The approach used to evaluate these conditions is to: (1) determine the stresses in the studs and vessel for the intact case and for the case of a two studs out of service under preload plus design pressure conditions, (2) determine the increase in the stresses when going from the intact to the two studs out of service condition, (3) add the calculated increase in stress to the stress given in the design report which includes the effect of plant design transients, and (4) compare the calculated two studs out of service condition stresses to ASME Code requirements.

The two studs out of service are not adjacent to each other in this evaluation. In order to meet all defined acceptance criteria, the two out of service studs must be separated by at least nine tensioned and in service studs.

5.2.2 Reactor Vessel Closure Flange Model The simulation was performed using the finite element analysis model described in Appendix A of Reference [1]. The modeling methods are summarized in this section; greater detail on the specifics of the model is described in Reference [1].

5.2.2.1 Model Geometry The vessel shell, head and flange regions were modeled using SOLID45 (3D structural solid) elements with each row of elements corresponding to one stud pitch. Studs were modeled using BEAM4 (3D beam) elements which resist tensile loads and bending moments. A three dimensional model of the Hatch 2 RPV closure flange was simulated as shown in Figure 2. The model considers half the circumference of the closure flange, with symmetry boundary conditions at the circumferential edges.

The 3-D BEAM4 elements used for the studs and tie bars require three real properties: area, moment of inertia, and thickness (used to calculate section modulus). The stud element real properties used in the analysis are reported in Reference [1]. Tie bar properties were selected so that the area is 100 times smaller than the area of the studs, and the moment of inertia is 100 times greater than that of the studs.

This has the effect of making the tie bars rigid in bending (as they are being used, the elements have no shear deflection), so that the rotation of the flanges is imposed on the ends of the studs without affecting the stiffness of the adjacent solid elements.

The interface between the head and vessel flanges was simulated by a row of LINK8 (3D spar) elements connecting the head and vessel flanges. The location of these interface elements was selected

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Title:

Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 13 of 41 to act at a reaction radius empirically determined from the correlation between the model predictions and the actual stud elongation data using the existing tensioning procedure.

Untensioned studs are simulated by deleting the beam element representing that stud and adjusting the initial strains on the studs adjacent to the untensioned stud to produce the specified preload. If the spar elements simulating the vessel to head contact have axial tensile stresses in the pressurized condition, these elements are deleted and the coupled circumferential and radial constraints at these nodes are removed to simulate the fact that there is no longer a frictional restraining force at this location. The condition for two studs out of service is simulating by considering stud number 6 in the model as out of service; because of model symmetry (see Section 5.2.2.2), this condition represents both stud 6 and stud 54 being out of service.

5.2.2.2 Model Boundary Conditions The nodes at the bottom of the vessel shell were all fixed in the vertical and circumferential directions and allowed to move freely in the radial direction. Additionally, out of plane rotations (ROTX and ROTZ) were restrained on the nodes associated with the tie bar elements. The rotation of the flange was tied to the bending of the stud by coupling the rotational degree of freedom between the node at top of the stud beam element and the center node of the tie bar elements at the top of the flange.

As noted previously, symmetry boundary conditions were applied at the circumferential edges of the model. In addition, the stud and tie bar beam elements located at each end of the model (i.e., in the first and last planes) are assigned half of the area and moment of inertia as the rest of the studs because they lie on a plane of symmetry. Similarly, the LINK8 elements representing flange contact located at each end of the model are given half the area of the rest of the flange contact elements.

5.2.3 Analysis Cases Six cases are evaluated as follows:

x Case A1 represents the preload condition with all studs intact x Case A2 represents the operating condition with the vessel at design pressure and with intact studs x Case B1 represents the case of two studs untensioned and with all other studs preloaded to the specified initial stress. The two untensioned studs are separated by nine tensioned studs.

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Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 14 of 41 x Case B2 same as Case B1 with the vessel at design pressure x Case C1 represents the case of all studs preloaded to the specified initial strain with two studs assumed to fail in service. The two studs are separated by nine tensioned studs.

x Case C2 same as Case C1 except the vessel is at design pressure 5.2.4 Results Discussion The results of the finite element analyses are summarized in Table 3. The increases in stress caused by the inactive studs are summarized, and the stresses are compared to the appropriate ASME Code allowables. The current design basis conditions for the closure flange and closure studs are defined in Inputs 8 and 9, and the associated ASME Code comparisons and allowables are defined in Section 3.2.

The following evaluations are considered:

5.2.4.1 RPV Closure Stresses As shown in Table 3, the condition with two studs out of service has little to no impact on the stresses associated with General Primary Membrane Stress Intensity, Primary Local Membrane plus Bending Stress Intensity, and Maximum Stress Intensity Range. Each of these stress values remain below the appropriate ASME Code allowable stresses.

5.2.4.2 RPV Stud Stresses As shown in Table 3, the condition with two studs out of service has a modest immpact on the stresses associated with the stud Maximum Membrane and Maximum Membrane plus Bending stress. Each of these stress values remain below the appropriate ASME Code allowable stresses.

5.2.4.3 RPV Closure Flange Separation As shown in Table 3, the condition with two studs out of service causes an additional flange separation at the o-ring of 0.0066 inch. This increase does not impact an ASME Code allowable. The resulting total flange separation in Table 3 is less than the o-ring minimum springback of 0.010 inch cited in Table 3-2 of Reference [1].

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Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 15 of 41 5.2.4.4 Fatigue Per Table 3, the condition with two studs out of service increases the maximum stress at: (1) the head flange/shell by 1.48 ksi, (2) the vessel flange/shell by 0.42 ksi and (3) the stud by 0.31 ksi; each of these increases are approximately 1-2% of the previous design basis stress. According to Table 2-1 of Reference [1], the fatigue usage values in these components are as follows: (1) the head is 0.178, (2) the vessel is 0.679, and (3) the stud is 0.846. These fatigue usage values were calculated for the full service life of the component.

The impact of the 2% increase in stress for a single cycle of operation on these components is negligible. Referring to the fatigue curves in the design basis Code [8], Figures N-415A (vessel and head material) and N-416 (bolting material), it may be demonstrated for higher values of alternating stress that the number of allowable cycles is inversely proportional to the square of the increase in stress. Therefore, even if the components were operated for their full service life with the increase in stress resulting from two studs out of service, the increase in fatigue usage would be the square of the increase in stress, or 1.022 = 1.04 (4%. increase). Increasing the fatigue usage by 4% results in fatigue usage that is well below the Code allowable of 1.0.

5.2.4.5 Emergency and Faulted Conditions Review of the design basis conditions evaluated in the original plant design basis report [2]

demonstrates that, for the RPV closure flange components, meeting the ASME Code requirements for normal and upset conditions described in previous sections of this calculation bounds the requirements for emergency and faulted conditions. This is demonstrated on pages A-11 through A-30 of Reference [2] as follows:

x The emergency condition evaluated in Reference [2] is a vessel overpressure event. The evaluated pressure is 1,350 psia, or a factor of 1.08 greater than the normal condition design pressure, but the stress allowables for emergency conditions are at least 1.2 times the normal condition allowables.

x The faulted condition evaluated in Reference [2] is a pipe rupture event. The evaluated pressure is 1,000 psia, which is lower than the normal condition design pressure.

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Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 16 of 41 5.2.5 ANSYS Input Listings The RPV closure flange stud tensioning analysis described in this section is performed using the ANSYS input listing files _HATCH2.runs, _MACROS.HATCH2, and MACROS.DEI. The

_HATCH2.runs input listing defines parameters that are used by _MACROS.HATCH2 and MACROS.DEI to generate the geometry and run the stud out of service analysis cases. The input listings _HATCH2.runs and _MACROS.HATCH2 are provided in Appendix A.

MACROS.DEI is a proprietary input listing developed outside of the scope of this work. It is retained as an electronic file on a data disk [7] along with other software usage QA records required by the DEI QA program [5]. The contents of this data disk are listed in Appendix B. This data disk is retained with the project file for this task (Task 037-2201) and is available for on-site review by Southern Nuclear personnel.

5.3 Quality Assurance Software Controls The RPV closure flange stud tensioning analysis described in this calculation was performed on the ANSYS-A Dell Precision R7910 workstation, using Windows Server 2012 R2 Standard 64-bit operating system and ANSYS Version 19.0 which was verified on March 13, 2022, as documented in Reference [4]. This software is maintained in accordance with the provisions for control of software described in Dominion Engineering, Inc.s (DEIs) quality assurance (QA) program for safety-related nuclear work [5]. 1 In addition to QA controls associated with the procurement and use of the ANSYS software (e.g., maintenance of the ANSYS Inc. as an approved supplier of the software based on formal auditing and surveillance; formal periodic verification of ANSYS software installation), QA controls associated with all ANSYS batch input listings are also carried out by DEI. These include independent checks of a batch input listing each time it is used; review of all ANSYS Class 3 error reports and QA notices to assess their potential impact on a batch input listing; and independent confirmatory analyses 2 to ensure that the project-specific application of the analysis is appropriate. The review of ANSYS error reports and QA notices as well as the project-specific check calculations are documented formally in a QA memo to project file [6].

1 DEIs quality assurance program for safety-related work (DEI-002) commits to applicable requirements of 10 CFR 21, Appendix B of 10 CFR 50, and ASME/ANSI NQA-1. This QA program is independently audited periodically by both NUPIC (the Nuclear Procurement Issues Committee) and other nuclear industry vendors.

2 Confirmatory analyses for a given project may include comparison of model-computed stresses to theoretical closed-form solutions and other checks on model results.

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Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 17 of 41 The stud primary stress calculations performed in Table 2 were generated using Microsoft Excel 365 on a Dell 5530 Precision Mobile Workstation with an Intel Core i7 processor and running Microsoft Windows 10. The one-time-use Microsoft Excel spreadsheet Hatch 2 Stud Primary Stress Calc v0.xlsx was prepared, checked, and reviewed in accordance with DEIs nuclear QA program manual

[5] and is archived on the data disk associated with this calculation [7].

6 REFERENCES

1. DEI Report R-3937-00-1, Rev. 0, Reactor Vessel Tensioning Optimization Stress Report -

Hatch Nuclear Plant Unit 2, January 2015.

2. Analytical Report for Hatch No. 2 Reactor Vessel for Georgia Power Company, Combustion Engineering Report No. CENC-1232, April 1975.

3. DEI Calculation C-3944-00-01, Rev. 0, Hatch Unit 2 Operation with One Stud Out of Service Evaluation, February 2017.

4. Dominion Engineering, Inc. Software Test Report No. STR-9898-00-31, ANSYS 19.0 Re-Verification Software Test Report. Revision 0, March 2022.

5. Dominion Engineering, Inc. Quality Assurance Manual for Safety-Related Nuclear Work, DEI-002. Revision 18, November 2010.

6. Dominion Engineering, Inc. Memorandum M-037-2201-00-02, Revision 0, ANSYS Confirmatory Analysis and Review of Error Reports / QA Notices for C-037-2201-00-02, Rev. 0, June 2022.

7. Dominion Engineering, Inc. Data Disk D-037-2201-00-02, Revision 0, July 2022.

8. ASME Boiler and Pressure Vessel Code,Section III - Rules for Construction of Nuclear Vessels, 1968 Edition with Addenda through Summer 1970.

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Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 18 of 41 Table 1. FEA Model Inputs Parameter Units Hatch Unit 2 Stud and Vessel Parameters

- Number of Studs --- 56

- Stud Shank OD in 6.000

- Design Stud Stress Area in Shank in^2 27.489

- Calculated Stud Moment of Inertia in^4 63.568

- Membrane Stress, Preload Only ksi 35.58

- Corresponding Elongation in 0.038

- Design Pressure psia 1,250

- Stud Effective Length in 31.937 Tensioning Parameters

- Max Tensioner Pressure (new) psi n/a

- Optimized Sequence Final Pressure (new) psi 7,100

- Resulting Stud Stress ksi 37.15

- Tensioner Coefficient, Kt psi/in 5.232 Bolting Dimensions

- Stud Circle Radius in 117.313

- Stud Hole Diameter in 6.750

- Spherical Washer Radius of Curvature in 27.000

- Modulus Ratio in Hole Region --- 0.60 Vessel Flange Dimensions

- Flange IR in 109.690

- Inner O-ring Mean Radius in 111.000

- Reaction Radius in 113.250

- Seating Surface Outer Radius in 113.750

- Flange OR in 122.625

- Z dim to ID Transition in -18.000

- Z dim to OD transition in -14.500 Vessel Shell Dimensions

- Shell IR in 110.720

- Shell thickness in 5.875

- Z dim to Bottom of Transition in -21.090 Head Flange Dimensions

- Flange IR in 109.250

- Flange OR in 122.625

- Flange Top Fillet Radius in 2.750

- Z dim to Top of Flange in 24.375

- Z dim to Recess (inner) in 0.375

- Z dim to Recess (outer) in 0.375 Head Shell Dimensions

- Shell IR in 109.500

- Shell thickness in 3.188

- Z dim to Head Coord. Sys. in -7.250

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Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 19 of 41 Table 2. Calculation of Primary Stresses in Reactor Vessel Studs, Two Studs Out of Service Design Pressure, P, psig 1,235 Bolt Circle Radius, Ro 117.313 in.

Inner o-ring Radius, Ri 111.000 Average force, Fbar 885.3 kips Studs Out of Service 2 Neutral axis offsd 4.338 in.

Stud Stress Area, A 27.489 Coefficient f -581.1 lb/in Number of Studs 56 Stud theta cos(theta) cos^2 (theta) Fi Stress (deg) (kip) (ksi) 1 -177 untensioned untensioned untensioned untensioned 2 -170 -0.9859 0.97 955.0 34.74 3 -164 -0.9609 0.92 953.3 34.68 4 -158 -0.9239 0.85 950.8 34.59 5 -151 -0.8752 0.77 947.4 34.47 6 -145 -0.8156 0.67 943.4 34.32 7 -138 -0.7456 0.56 938.6 34.14 8 -132 -0.6663 0.44 933.2 33.95 9 -125 -0.5787 0.33 927.2 33.73 10 -119 -0.4837 0.23 920.8 33.50 11 -113 -0.3827 0.15 913.9 33.24 12 -106 -0.2768 0.08 906.6 32.98 13 -100 -0.1675 0.03 899.2 32.71 14 -93 -0.0561 0.00 891.6 32.43 15 -87 0.0561 0.00 884.0 32.16 16 -80 0.1675 0.03 876.4 31.88 17 -74 0.2768 0.08 868.9 31.61 18 -68 0.3827 0.15 861.7 31.35 19 -61 0.4837 0.23 854.8 31.10 20 -55 0.5787 0.33 848.3 30.86 21 -48 0.6663 0.44 842.4 30.64 22 -42 0.7456 0.56 836.9 30.45 23 -35 0.8156 0.67 832.2 30.27 24 -29 0.8752 0.77 828.1 30.13 25 -23 0.9239 0.85 824.8 30.00 26 -16 0.9609 0.92 822.3 29.91 27 -10 0.9859 0.97 820.6 29.85 28 -3 0.9984 1.00 819.7 29.82 29 3 0.9984 1.00 819.7 29.82 30 10 0.9859 0.97 820.6 29.85 31 16 0.9609 0.92 822.3 29.91 32 23 0.9239 0.85 824.8 30.00 33 29 0.8752 0.77 828.1 30.13 34 35 0.8156 0.67 832.2 30.27 35 42 0.7456 0.56 836.9 30.45 36 48 0.6663 0.44 842.4 30.64 37 55 0.5787 0.33 848.3 30.86 38 61 0.4837 0.23 854.8 31.10 39 68 0.3827 0.15 861.7 31.35 40 74 0.2768 0.08 868.9 31.61 41 80 0.1675 0.03 876.4 31.88 42 87 0.0561 0.00 884.0 32.16 43 93 -0.0561 0.00 891.6 32.43 44 100 -0.1675 0.03 899.2 32.71 45 106 -0.2768 0.08 906.6 32.98 46 113 -0.3827 0.15 913.9 33.24 47 119 -0.4837 0.23 920.8 33.50 48 125 -0.5787 0.33 927.2 33.73 49 132 -0.6663 0.44 933.2 33.95 50 138 -0.7456 0.56 938.6 34.14 51 145 -0.8156 0.67 943.4 34.32 52 151 -0.8752 0.77 947.4 34.47 53 158 -0.9239 0.85 950.8 34.59 54 164 -0.9609 0.92 953.3 34.68 55 170 -0.9859 0.97 955.0 34.74 56 177 untensioned untensioned untensioned untensioned

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Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 20 of 41 Table 3. Stress Increase Due to Two Studs Out of Service Shell Stresses (ksi) (1) Stud Stresses (ksi) Flange Stud Load Gen. Membrane Local Memb.+Bend. Maximum SI Max Memb+ Separation Load Condition Condition Case Head Vessel Head Vessel Head Vessel Membrane Bending (10^-3 in)

Preload Only Normal A1 0.07 0.28 23.85 18.14 24.63 18.50 37.15 81.68 15.2 Preload Only 1 Untensioned B1 0.09 0.28 23.87 18.12 24.65 18.52 37.15 81.72 15.2 Preload Only 1 Failed C1 0.08 0.28 23.86 18.12 24.64 18.51 40.13 81.70 15.2 Preload+Pressure Normal A2 22.13 23.49 36.94 34.20 37.03 33.97 34.96 98.04 21.4 Preload+Pressure 1 Untensioned B2 22.13 23.50 38.40 34.30 38.51 34.07 36.93 98.22 28.0 Preload+Pressure 1 Failed C2 22.13 23.49 37.61 34.62 37.70 34.39 39.27 98.35 26.1 Max. Increase from A2 (Cases B2 & C2) 0.00 0.01 1.46 0.42 1.48 0.42 4.31 0.31 6.6 Limiting Vessel Report Value 22.50 23.80 37.90 37.50 64.00 47.40 45.30 95.40 1.5 New Maximum Value 22.50 23.81 39.36 37.92 65.48 47.82 49.61 95.71 8.1 Code Stress Limit Sm = Sm = 1.5 Sm = 1.5 Sm = 3.0 Sm = 3.0 Sm = 2 Sm = 2.7 Sm =

26.7 26.7 40.1 40.1 80.1 80.1 73.5 99.2 (1) Local Membrane + Bending and Maximum SI taken at cut lines 2, 3, 4, 5, 6, and 7. General Membrane SI taken at cut lines 1 and 8. (See Figure 3).

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Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 21 of 41 y

13 14 15 16 12 17 11 18 10 19 9 20 8 21 7 22 6 23 5 24 4 25 3 26 2 Blackened Studs are 27 Out of Service 1 28 x

56 29 55 G 30 54 31 T 53 32 52 33 51 34 50 35 49 36 48 37 47 38 46 39 45 44 41 40 43 42 Neutral Axis Figure 1. Reactor Vessel Head Stud Geometry, Two Studs Out of Service

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Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 22 of 41 28,000's Nodal Plane 2000's Nodal Plane 1000's Nodal Plane 1's Nodal Plane Figure 2. Hatch Unit 2 RPV Closure Flange FEA Model Overall View [1]

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Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 23 of 41 354 8 364 361 351 8

284 7

281 6

7 5

6 269 5

261 219 141 169 149 111 119 4 4 81 85 3 3 71 75 2 2 61 65 1 1 11 15 1 5 Figure 3. FEA Model Node Numbering and Section Cut Line Locations [1]

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Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 24 of 41 A FINITE ELEMENT ANALYSIS INPUT LISTINGS A.1 File: _HATCH2.runs

/BATCH,LIST

/COM,

/COM, **********************************************************************************

/COM, Hatch Unit 2 Stud Out of Service Evaluation

/COM, **********************************************************************************

/COM,

/INP,_MACROS,HATCH2

/INP,_MACROS,DEI

/COM,

/COM, **********************************************************************************

/COM, PRE-RUN SETUP

/COM, **********************************************************************************

/COM,

/FILNAM,Tens-1

/SHOW,plots,grph

/TYPE,1,4

/PREP7

/TITLE, Hatch2 Reactor Vessel Tensioning

/COM, Define run parameters NT = 56  ! Total number of studs in model NV = 56  ! Total number of studs in real vessel NPMAX = 56*3  ! Max number of studs any sequence TENSMX = 7  ! Max number of Tens-* routines XS = 37146  ! Final stud stress target for old tensioner XP = 7100  ! Corresponding tensioner pressure Pmax = 8500  ! Tensioner pressure cap X1 = 0.98  ! Empirical correction factor (init guess)

X2 = 0.95  ! Empirical correction factor (init guess)

Kt = XS*X2/XP  ! Relate tensioner pressure to stud stress RLMAX = NT+1  ! Number of data items in RLIST (from ENDPOST macro)

• DIM,TENSAR,ARRAY,TENSMX,3

/COM,

• DIM,MPBTMPI,ARRAY,5

• DIM,MPBTMPC,ARRAY,5

• DIM,MPBTMPO,ARRAY,5

• DIM,TOTTMPI,ARRAY,5

• DIM,TOTTMPO,ARRAY,5

/COM,

/COM, *** TOGGLE TENSIONING ROUTINES ***

/COM,

/COM, To set tensioning routine I (Tens-I) to RUN, toggle TENSAR(I,1)=1

/COM To set tensioning routine I (Tens-I) to OFF, toggle TENSAR(I,1)=0

/COM, TENSAR(I,2) is number of cyclic symmetry slices (=1 for full model) for Tens-I

/COM, TENSAR(I,3) is number of passes thru OPTLOOP for Tens-I (max of 7)

/COM, TENSAR(1,1)=1 $TENSAR(1,2)=1 $TENSAR(1,3)=1 RUNMORF = 1  ! RUNMORF=1 to run out of service stud cases

/COM,

• DIM,PLIST,ARRAY,NPMAX,4

• DIM,RLIST,ARRAY,NT,RLMAX

• DIM,RSAVE10,ARRAY,NV/2+1,RLMAX,6

/COM,

/COM,

/COM, **********************************************************************************

/COM, GEOMETRY FIGURES

/COM, **********************************************************************************

/COM,

/COM, Make 1/2 model to lay down 'Appendix A' plots NT = NV/2+1  ! Total number of studs in model

/COM, Clear the boundary conditions and re-do the geometry.

/PREP7

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Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 25 of 41

• USE,GEOM,0  ! Create geometry

/TITLE, Hatch2 Reactor Vessel Tensioning

/VIEW,1,1,1,1 ESEL,S,TYPE,,1 NSLE

/COLOR,NUM,BLAC,1

/TRIAD,OFF

/DIST,1,1.5*HFOR

/FOCUS,1,-HFOR/4,-65,-HFOR/2.1 EPLO ESEL,S,ELEM,,41,290 ESEL,A,ELEM,,1041,1290 NSLE

/PNUM,MAT,1

/NUM,1

/AUTO EPLO ESEL,S,TYPE,,1 ESEL,R,ELEM,,1,1000 NSEL,S,NODE,,1,1000

/VIEW EPLO

• DO,I,1,11

/COLOR,NUM,WHIT,I

• ENDDO

/NUM

/PNUM,ELEM,1 ESEL,S,ELEM,,502,506 ESEL,A,ELEM,,1502,1506

• REPEAT,4,,,,1000,1000 NSLE NSEL,U,NODE,,361,4361,1000

/VIEW,1,1,1,1

/AUTO EPLO

/VIEW,1,-1,1,5

/NUM,2 ESEL,S,ELEM,,501 NSLE EPLO

/USER

/DIST,1,5.75 ESEL,S,TYPE,,1 ESEL,A,ELEM,,501 NSLE EPLO ALLSEL

/AUTO

/COLOR,DEFA

/NUM FINISH

/COM,

/COM,

/COM, **********************************************************************************

/COM, TENSIONING ROUTINE 1: INITIALIZE MODEL

/COM, **********************************************************************************

/COM,

/COM,

/PREP7 NT = 10  ! Total number of studs in model

• USE,GEOMCLUP

• USE,GEOM,0  ! Create geometry FINISH

/COM,

/COM, Do initial sets at final pressure to solve for X1 and X2

/COM, Tension all studs except in one set and then retension stud 10 PP = NT  ! Number of studs in each set NP = 2  ! Number of sets in this sequence TT = 1  ! Number of sets to achieve one-pass tens.

• USE,ZEROIT

• DO,I,1,NT PLIST(I,1) = I  ! Load PLIST column 1 with stud numbers PLIST(I,2) = XP  ! Load PLIST column 2 with ref. tens. press.

• ENDDO

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Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 26 of 41

• DO,I,NT+1,NT*2 PLIST(I,1) = 10  ! Load PLIST column 1 with stud numbers PLIST(I,2) = XP  ! Load PLIST column 2 with ref. tens. press.

PLIST(I,4) = 1.0  ! Load PLIST column 4 with retens. flag

• ENDDO

• IF,TENSAR(1,1),GT,0.5,THEN

• USE,GOSOLV,'Hatch2','Tens-1',1 ! Solve model X1 = X2*XS/RLIST(10,3)  ! X1 is ref. stress/av. stud stress - single stud X2 = X2*XS/RLIST(1,3)  ! X2 is ref. stress/av. stud stress - all studs Kt = XS*X1/XP  ! Relate tensioner pressure to stud stress

• ENDIF

/COM,

/COM,

/COM, **********************************************************************************

/COM, TENSIONING ROUTINE 10: RUN MISSING OR FAILED STUD CASES

/COM, **********************************************************************************

/COM,

/COM,

/FILNAM,Tens-10

/COM, Change over to a half model for missing stud runs

/PREP7

• USE,GEOMCLUP NT = NV/2+1  ! Total number of studs in model

• USE,GEOM,0  ! Create geometry FINISH Kt = XS*X2/XP  ! Relate tensioner pressure to stud stress

/COM, Tension all studs in one pass PP = NT  ! Number of studs in each pass NP = 1  ! Number of passes TT = 1  ! Number of passes to achieve one-pass tens.

• USE,ZEROIT

• DO,I,1,PP PLIST(I,1) = I  ! Load PLIST column 1 with stud numbers PLIST(I,2) = XP  ! Load PLIST column 2 with ref. tens. press.

• ENDDO

• USE,GOSOLV,'Hatch2','Tens-10',1  ! Solve model - Case A1 SAVE,,A1

• DO,I,1,NT

• DO,J,1,RLMAX RSAVE10(I,J,1) = RLIST(I,J)

• ENDDO

• ENDDO

• USE,ZEROIT I=1

• USE,PSOLV,'Hatch2','A2',2.0,1235  ! Solve model - Case A2 SAVE,,A2

• DO,I,1,NT

• DO,J,1,RLMAX RSAVE10(I,J,2) = RLIST(I,J)

• ENDDO

• ENDDO

• USE,ZEROIT I=1

/COM, BEGIN SOLUTION PHASE

/SOLU ANTYPE,STATIC,REST SFDELE,ALL,ALL EKILL,5502

/TITLE, Hatch2 Reactor Vessel - Case C1 - Preload Only TIME,3.0 SOLVE FINISH

/POST1 SET,,,,,3.0

• USE,POSTER

• USE,ENDPOST FINISH SAVE,,C1

• DO,I,1,NT

• DO,J,1,RLMAX RSAVE10(I,J,5) = RLIST(I,J)

• ENDDO

• ENDDO

• USE,ZEROIT

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Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 27 of 41 I=1

• USE,PSOLV,'Hatch2','C2',4.0,1235  ! Solve model - Case C2 SAVE,,C2

• DO,I,1,NT

• DO,J,1,RLMAX RSAVE10(I,J,6) = RLIST(I,J)

• ENDDO

• ENDDO

/COM, Check for flange contact links which came out of compression LCHG = 0

• DO,I,1,NT

• IF,RLIST(I,10),GT,0,THEN LCHG = 1.0

/PREP7 EKILL,I*1000-499  ! EKILL 501 El. in row CPDELE,I CPDELE,100+I FINISH

• ENDIF

• ENDDO

• IF,LCHG,EQ,1.0,THEN

• USE,ZEROIT I=1

• USE,PSOLV,'Hatch2','C2',5.0,1235  ! Re-Solve model - Case C2 SAVE,,C2A

• DO,I,1,NT

• DO,J,1,RLMAX RSAVE10(I,J,6) = RLIST(I,J)

• ENDDO

• ENDDO

• ENDIF

/COM, Clear the boundary conditions and re-do the geom.

/PREP7 SFDELE,ALL,ALL CPDELE,ALL EDELE,ALL NDELE,ALL

• USE,GEOM,0  ! Create geometry FINISH

/FILN,Tens-10B

/COM, Tension all studs in one pass except stud 6 PP = NT-1  ! Number of studs in each pass NP = 1  ! Number of passes TT = 1  ! Number of passes to achieve one-pass tens.

• USE,ZEROIT

• DO,I,1,5 PLIST(I,1) = I  ! Load PLIST column 1 with stud numbers PLIST(I,2) = XP  ! Load PLIST column 2 with ref. tens. press.

• ENDDO

• DO,I,6,PP PLIST(I,1) = I+1  ! Load PLIST column 1 with stud numbers PLIST(I,2) = XP  ! Load PLIST column 2 with ref. tens. press.

• ENDDO

• USE,GOSOLV,'Hatch2','Tens-10B',1  ! Solve model - Case B1 SAVE,,B1

• DO,I,1,NT

• DO,J,1,RLMAX RSAVE10(I,J,3) = RLIST(I,J)

• ENDDO

• ENDDO

• USE,ZEROIT I=1

• USE,PSOLV,'Hatch2','B2',2.0,1235  ! Solve model - Case B2 SAVE,,B2

• DO,I,1,NT

• DO,J,1,RLMAX RSAVE10(I,J,4) = RLIST(I,J)

• ENDDO

• ENDDO

/COM, Check for flange contact links which came out of compression LCHG = 0

• DO,I,1,NT

• IF,RLIST(I,10),GT,0,THEN LCHG = 1.0

Dominion Engineering, Inc.

Title:

Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 28 of 41

/PREP7 EKILL,I*1000-499  ! EKILL 501 El. in row CPDELE,I CPDELE,100+I FINISH

• ENDIF

• ENDDO

• IF,LCHG,EQ,1.0,THEN

• USE,ZEROIT I=1

• USE,PSOLV,'Hatch2','B2',3.0,1235  ! Re-Solve model - Case B2 SAVE,,B2A

• DO,I,1,NT

• DO,J,1,RLMAX RSAVE10(I,J,4) = RLIST(I,J)

• ENDDO

• ENDDO

• ENDIF

/COM, Check again for flange contact links which came out of compression LCHG = 0

• DO,I,1,NT

• IF,RLIST(I,10),GT,0,THEN LCHG = 1.0

/PREP7 EKILL,I*1000-499  ! EKILL 501 El. in row CPDELE,I CPDELE,100+I FINISH

• ENDIF

• ENDDO

• IF,LCHG,EQ,1.0,THEN

• USE,ZEROIT I=1

• USE,PSOLV,'Hatch2','B2',4.0,1235  ! Re-Solve model - Case B2 SAVE,,B2B

• DO,I,1,NT

• DO,J,1,RLMAX RSAVE10(I,J,4) = RLIST(I,J)

• ENDDO

• ENDDO

• ENDIF

/COM, Check again for flange contact links which came out of compression LCHG = 0

• DO,I,1,NT

• IF,RLIST(I,10),GT,0,THEN LCHG = 1.0

/PREP7 EKILL,I*1000-499  ! EKILL 501 El. in row CPDELE,I CPDELE,100+I FINISH

• ENDIF

• ENDDO

• IF,LCHG,EQ,1.0,THEN

• USE,ZEROIT I=1

• USE,PSOLV,'Hatch2','B2',5.0,1235  ! Re-Solve model - Case B2 SAVE,,B2C

• DO,I,1,NT

• DO,J,1,RLMAX RSAVE10(I,J,4) = RLIST(I,J)

• ENDDO

• ENDDO

• ENDIF

/COM, Check again for flange contact links which came out of compression LCHG = 0

• DO,I,1,NT

• IF,RLIST(I,10),GT,0,THEN LCHG = 1.0

/PREP7 EKILL,I*1000-499  ! EKILL 501 El. in row CPDELE,I CPDELE,100+I FINISH

Dominion Engineering, Inc.

Title:

Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 29 of 41

• ENDIF

• ENDDO

• IF,LCHG,EQ,1.0,THEN

• USE,ZEROIT I=1

• USE,PSOLV,'Hatch2','B2',6.0,1235  ! Re-Solve model - Case B2 SAVE,,B2D

• DO,I,1,NT

• DO,J,1,RLMAX RSAVE10(I,J,4) = RLIST(I,J)

• ENDDO

• ENDDO

• ENDIF FINISH

/COM, Clear the pressure boundary conditions

/PREP7 SFDELE,ALL,ALL FINISH

• USE,ZEROIT

• ENDIF

/COM,

/TITLE, Hatch2 Reactor Vessel Tensioning FINISH SAVE

/COM,

/COM, **********************************************************************************

/COM, PRINT RESULTS

/COM, **********************************************************************************

/COM,

/COM, Print contents of PSAVE and RSAVE arrays

/OUT,RESULTS,OUT

/NOPR

• IF,RUNMORF,EQ,1,THEN

• USE,PRINTENS,'PSAVE10','RSAVE10',6,'Stud OOS',0

• ENDIF

/OUT

/GOPR FINISH

/COM,

/COM, **********************************************************************************

/COM, RUN COMPLETE

/COM, **********************************************************************************

/COM,

/FILN,Tens-0 PARSAV,ALL

/COM, Do some file cleanup

/SYS, del CMMAKER

/SYS, del ENDPOST

/SYS, del GEOM

/SYS, del GEOMCLUP

/SYS, del GODETEN

/SYS, del GOSOLV

/SYS, del OPTLOOP

/SYS, del POSTER

/SYS, del POSTER2

/SYS, del POSTER3

/SYS, del PRINTOLR

/SYS, del PRINTENS

/SYS, del PSOLV

/SYS, del READSI

/SYS, del ZEROIT

/SYS, del NPL

/SYS, del linrept

/SYS, del *.dbs

/SYS, del *.stat

/SYS, del *.osav

/SYS, del *.PCS

/SYS, del *.PVTS

/SYS, del *.BCS

/SYS, del *.full

/SYS, del file.log

/SYS, del Tens-1.*

/SYS, del Tens-10.e???

Dominion Engineering, Inc.

Title:

Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 30 of 41

/EXIT

Dominion Engineering, Inc.

Title:

Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 31 of 41 A.2 File: _MACROS.HATCH2

/COM, --------------- MACROS.HATCH2, Revision 2, Created May 2022 ----------------

/COM, **********************************************************************************

/COM,

/COM,

/COM,

/COM, **********************************************************************************

/COM, **********************************************************************************

/COM, CREATE GEOMETRY MACRO

/COM, ----------------------------------------------------------------------------------

/COM,

• CREATE,GEOM

/COM, ------------------------------------------------------------------

/COM, GEOMETRY AND RUN PARAMETERS

/COM, ------------------------------------------------------------------

/COM, Loads and Material Properties Esteel = 27.9E6  ! Young's modulus (psi)

Ds = 6.000  ! Stud shank diameter (in)

As = 27.489  ! Stud area (in^2)

Is = 63.568  ! Stud mom. of I (in^4)

Ls = 31.937  ! Stud effective length (in)

Estud = 29.9E6  ! Tune Estud or Ls to get right effective L

/COM,

/COM, Bolting Dimensions SCR = 117.313  ! Stud Circle Radius (in)

NDs = 6.750  ! Stud Hole diameter (in)

SWRC = 27.00  ! Spherical Washer Rad. of Curvature (in)

Ehole = 0.60*Esteel  ! Derate in stud hole regions

/COM,

/COM, Vessel Flange Dimensions VFIR = 109.690  ! Vessel flange inner radius (in)

! CBIR = 0.000  ! Core Barrel groove inner radius (in)

IORR = 111.00  ! Inner O-Ring radius (in)

SSOR = 113.75  ! Seating Surface outer radius (in)

RR = 113.25  ! >>> TUNE REACTION RADIUS <<<

VFOR = 122.625  ! Vessel flange outer radius (in)

! ZVFS = 0.000  ! Z dimension to vessel flange surface (in)

! ZBCB =--0.000  ! Z dimension to bottom of Core Barrel groove ZVIT =-18.00  ! Z dim to vessel inside trans. (120's row)

ZVOT =-14.50  ! Z dim to vessel outside trans. (130's row)

/COM,

/COM, Vessel Shell Dimensions VSIR = 110.72  ! Vessel shell inside radius VSTH = 5.875  ! Vessel shell thickness ZVTR =-21.090  ! Z dimension to bottom of vessel transition

/COM,

/COM, Head Flange Dimensions HFIR = 109.25  ! Head flange inner radius HFOR = 122.625  ! Head flange outer radius HFFR = 2.750  ! Head flange top fillet radius ZTHF = 24.375  ! Z dimension to top of head flange ZHFRI = 0.375  ! Z dimension to head flange recess - inner ZHFRO = 0.375  ! Z dimension to head flange recess - outer

! /COM,

! /COM, Head Shell Flange Transition

! RTCS = 0.000  ! Radial dimension to Transition Coordinate System

! ZTCS = 0.000  ! Z dimension to Transition Coordinate System

! IRTR = 0.000  ! Inner radius of transition area

! ZUIC = 0.000  ! Vertical rise of OD Transition

/COM,

/COM, Head Shell Dimensions HSIR = 109.50  ! Head shell inner radius HSTH = 3.188  ! Head shell thickness ZHCS = -7.250  ! Z dimension to Head Coordinate System AHT = 19.0  ! Approximate start of head shell region

/COM,

/COM,

/COM,

/COM, At = As/100  ! Arbitrarily small tie bar area (in^2)

It = Is*100  ! Arbitrarily large tie bar mom. Of i (in^4)

Dominion Engineering, Inc.

Title:

Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 32 of 41 Dt = Ds*100  ! Arbitrarily large tie bar diameter (in)

RLTH = 0.005  ! Reaction link thickness (in Z direction)

Ar = As*100*(RLTH/Ls)  ! Reaction link area tuned for stiffness

! 100 times greater than stud (in^2)

/COM,

/COM,

/COM, ------------------------------------------------------------------

/COM, MATERIAL PROPERTIES

/COM, ------------------------------------------------------------------

/COM, Set types, mats, and reals

/COM, Element types ET,1,SOLID45  ! Solids - vessel (no associated real props)

ET,2,LINK8  ! Links - for reaction (REALS: AREA,ISTRN)

ET,3,BEAM4  ! Beams - studs (A,IZZ,IYY,TKZ,TKY,THETA,ISTRN)

/COM,

/COM, Material properties

/COM, Material 1 for GENERAL USE MP,EX,1,Esteel MP,NUXY,1,0.30

/COM,

/COM, Material 2 for STUD ELEMENTS MP,EX,2,Estud MP,NUXY,2,0.30

/COM,

/COM, Material 3 for STUD HOLES MP,EX,3,Ehole MP,NUXY,3,0.30

/COM,

/COM, REAL PROPERTIES

/COM, R,1,0  ! Real 1: Dummy real for solid elements R,2,Ar  ! Real 2: Reaction links R,3,Ar/2  ! Real 3: Cutting plane reaction links R,4,At,It,It,Dt,Dt,0  ! Real 4: Tie bars R,5,At/2,It/2,It/2,Dt,Dt,0  ! Real 5: Cutting plane tie bars R,11,As,Is,Is,Ds,Ds,0  ! Real 11:Stud elements

• REPEAT,NT,1  ! Assign different reals to each stud

/COM,

/COM,

/COM, ------------------------------------------------------------------

/COM, NODE DEFINITION

/COM, ------------------------------------------------------------------

/COM,

• AFUN,DEG

/COM, Establish coordinate systems LOCAL,20,0,0,0  ! Cartesian on lower mating surface LOCAL,21,1,0,0,0,0,-90,0  ! Cylindrical on lower mating surface (z up)

! LOCAL,22,1,RTCS,ZTCS  ! Cylindrical system 1 for head curvature LOCAL,23,1,0,ZHCS  ! Cylindrical system 2 for head curvature LOCAL,24,2,0,ZHCS  ! Spherical system for head stresses

/COM,

/COM, Define keypoints on theta = 0 plane CSYS,20 BOTZ=-100+ZVTR N,1,VSIR,BOTZ  ! SHELL I.R. AT BOTTOM OF MODEL N,5,VSIR+VSTH,BOTZ  ! SHELL O.R. AT BOTTOM OF MODEL N,81,VSIR,ZVTR  ! SHELL I.R. AT BOTTOM OF FLANGE N,85,VSIR+VSTH,ZVTR  ! SHELL O.R. AT BOTTOM OF FLANGE

/COM,

/COM, DEFINE FEATURES ON MATING SURFACE N,161,VFIR,0  ! Flange inner surface N,162,(VFIR+IORR)/2,0  ! "Core barrel groove inner surface" N,163,IORR,0  ! Inner o-ring radius N,164,RR,0  ! Reaction radius N,165,SSOR,0  ! Outer limit of seating surface N,166,SCR-NDs/2,0  ! Bolt hole inner edge N,167,SCR,0  ! Bolt circle N,168,SCR+NDs/2,0  ! Bolt hole outer edge N,169,VFOR,0  ! Flange outer surface flwdth = HFOR-HFIR  ! Flange width - head flwdtv = VFOR-VFIR  ! Flange width - vessel iormo = RR-IORR  ! Inner o-ring moment arm

/COM,

/COM, COPY FEATURES THROUGH VESSEL FLANGE

Dominion Engineering, Inc.

Title:

Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 33 of 41 NGEN,2,-10,161,169,1,0,(ZTHF-Ls)/2 ! Copy mating surf. thru lower flange (150's)

NGEN,2,-20,161,169,1,0,ZTHF-Ls  ! Copy mating surf. thru lower flange (140's)

NGEN,2,-50,161,169,1,0,ZVOT  ! Make 110's row for O.D. feature FILL,151,156,,,,2,-10  ! Even out 150's and 140's row FILL,111,117 FILL,116,118 NGEN,2,-20,111,117,1,0,(ZVIT-ZVOT) ! Make 90's row for I.D. feature NMODIF,97,NX(85)

FILL,91,97 NGEN,2,10,91,97,1,0,-(ZVIT-ZVOT)/2 ! Make 100's row for transition FILL,111,141,2,121,10,9,1

/COM,

/COM, FILL IN REST OF NODES IN VESSEL FLANGE FILL,1,5 FILL,81,85 FILL,1,81,7,,,5,1,0.4  ! FILL IN VESSEL SHELL NODES

/COM,

/COM, ARRANGE HEAD FLANGE SURFACE NODES CSYS,20 NGEN,2,40,161,169,1,0,RLTH  ! COPY LOWER MATING SURF. TO UPPER FLANGE N,201,HFIR,RLTH  ! HEAD FLANGE INNER SURFACE FILL,201,203 NGEN,2,10,201,209,1,0,ZHFRI-RLTH  ! COPY UP THROUGH UPPER FLANGE NGEN,6,10,211,219,1,0,((ZTHF-ZHFRI)/5)! COPY FIVE ROWS UP THROUGH UPPER FLANGE FILL,221,226,,,,5,10  ! ALIGN 220'S ROW

/COM,

/COM, MOVE HEAD SHELL IR NODES CSYS,23 NMODIF,231,HSIR

• REPEAT,4,10 FILL,231,234,,,,4,10

/COM,

/COM, DEFINE NODES IN FREE HEAD CSYS,23 N,361,HSIR,90  ! TOP OF HEAD (INNER SURFACE)

N,364,HSIR+HSTH,90  ! TOP OF HEAD (OUTER SURFACE)

N,271,HSIR,AHT  ! LOCATE I.R. AT TOP OF FILLET RADIUS N,274,HSIR+HSTH,AHT  ! LOCATE O.R. AT TOP OF FILLET RADIUS FILL,271,361,8,,,,,2.5  ! FILL IN HEAD INNER RADIUS FILL,274,364,8,,,,,2.5  ! FILL IN HEAD OUTER RADIUS FILL,251,254,,,,12,10  ! FILL IN INTERIOR HEAD NODES

/COM,

/COM, SWEEP OUT AROUND 360 DEGREES CSYS,21 NGEN,NT+1,1000,ALL,,,0,360/NV,0  ! MAKE FULL SWEEP OF MODEL NROTAT,ALL  ! BRING CS'S INTO ACTIVE CS

/COM,

/COM, ------------------------------------------------------------------

/COM, ELEMENT DEFINITION

/COM, ------------------------------------------------------------------

/COM,

/COM, _____________________________________

/COM, MAKE SOLID ELEMENTS TYPE,1 MAT,1 REAL,1 EN,1,1,2,12,11,1001,1002,1012,1011 ENGEN,1,4,1,1,1,1  ! SWEEP ACROSS BOTTOM ROW ENGEN,10,8,10,1,4,1  ! SWEEP UP TO BOTTOM OF FLANGE SHPP,OFF  ! TEMPORARILY TURN OFF SHAPE WARNINGS EN,81,81,82,92,91,1081,1082,1092,1091 EN,82,82,93,92,92,1082,1093,1092,1092 EN,83,82,83,94,93,1082,1083,1094,1093 ENGEN,1,2,1,83 EN,85,84,96,95,95,1084,1096,1095,1095 EN,86,84,85,97,96,1084,1085,1097,1096 EN,91,91,92,102,101,1091,1092,1102,1101 ENGEN,1,6,1,91  ! make 91 - 96 ENGEN,10,2,10,91,96,1  ! make 101 - 106 ENGEN,10,2,10,101  ! MAKE 111 ENGEN,1,8,1,111,111,1  ! SWEEP RIGHT TO MAKE 112 - 118 ENGEN,10,5,10,111,118

/COM,

Dominion Engineering, Inc.

Title:

Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 34 of 41 EN,201,201,202,212,211,1201,1202,1212,1211  ! MAKE 201 ENGEN,1,4,1,201,201,1  ! SWEEP RIGHT TO MAKE 202 TO 204 ENGEN,10,2,10,201,201,1  ! SWEEP UP TO MAKE 211 ENGEN,1,8,1,211,211,1  ! SWEET RIGHT TO MAKE 212 TO 218 ENGEN,10,5,10,211,218,1  ! SWEEP UP TO TOP OF FLANGE ENGEN,10,10,10,251,253,1  ! SWEEP THROUGH SHELL EN,351,351,1351,1361,361,352,1352,1362,362  ! MAKE 351 ENGEN,1,3,1,351,351,1  ! FIX UP LAST ROW

/COM,

/COM,

/COM, ASSIGN BOLT HOLE REGION ESEL,S,ELEM,,146,500,10  ! SELECT INNER SIDE OF BOLT HOLE ESEL,A,ELEM,,147,500,10  ! SELECT OUTER SIDE OF BOLT HOLE EMODIF,ALL,MAT,3  ! ASSIGN BOLT HOLE DIFFERENT MATERIAL ESEL,ALL ENGEN,1000,NT,1000,ALL  ! COPY AROUND CIRCLE

/COM,

/COM, _____________________________________

/COM, MAKE LINE ELEMENTS FOR STUD TYPE,2 REAL,2 EN,501,164,204  ! REACTION FORCE LINK TYPE,3 REAL,11 MAT,2 EN,502,147,267,361  ! STUD

/COM,

/COM, _____________________________________

/COM, MAKE LINE ELEMENTS FOR TIE BARS REAL,4 MAT,1 EN,503,146,147,207 EN,504,147,148,207 EN,505,266,267,207 EN,506,267,268,207  ! TIE BARS EN,507,162,163,204 EN,508,163,164,204 EN,509,164,165,204 EN,510,202,203,164 EN,511,203,204,164 EN,512,204,205,164  ! REACTION SURFACE ENGEN,1000,NT,1000,501,512,1  ! COPY REST OF WAY THROUGH

/COM,

/COM, _____________________________________

/COM, ASSIGN INDIVIDUAL REAL PROPERTIES TO EACH STUD

/COM, STUD REAL IS STUD NO. + 10

• DO,I,1,NT ESEL,S,ELEM,,I*1000-498 EMODIF,ALL,REAL,I+10

• ENDDO ESEL,ALL

/COM,

/COM, _____________________________________

/COM, DO SOME NODAL CLEANUP NSLE,U NDELE,ALL  ! DELETE UNUSED NODES NSEL,ALL NUMMRG,NODE,0.001  ! MERGE OVERLAPPING NODES

/COM,

/COM,

/COM, ------------------------------------------------------------------

/COM, APPLY BOUNDARY CONDITIONS

/COM, ------------------------------------------------------------------

/COM, CSYS,21

/COM, _____________________________________

/COM, COUPLE UPPER AND LOWER FLANGE AT REACTION RADIUS

• DO,I,1,NT CP,I,UX,164+(I-1)*1000,204+(I-1)*1000 CP,100+I,UY,164+(I-1)*1000,204+(I-1)*1000

• ENDDO

/COM, APPLY DISPLACEMENT BOUNDARY CONDITIONS NSEL,S,LOC,Z,BOTZ  ! SELECT BOTTOM OF MODEL D,ALL,UY  ! APPLY ZERO VERT DISP

Dominion Engineering, Inc.

Title:

Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 35 of 41 D,ALL,UZ  ! APPLY ZERO VERT DISP NSEL,ALL ESEL,S,REAL,,4  ! SELECT TIE BAR ELEMENTS NSLE  ! SELECT TIE BAR NODES NSEL,U,NODE,,207,99207,1000  ! DESELECT CENTER NSEL,U,NODE,,361  ! DESELECT TOP OF FLANGE D,ALL,ROTX,0,0,,,ROTZ  ! HOLD ROTATIONS ON TIE BARS ESEL,ALL NSEL,ALL

/COM,

/COM, _____________________________________

/COM, APPLY PRYING FORCES DUE TO CORE BARREL SPRING AND CORE SUPPORT LOAD

• IF,Fspr+Fcsl,GT,1.0,THEN

• DO,I,1,NT F,131+(I-1)*1000,FZ,-(Fspr+Fcsl)/2 F,132+(I-1)*1000,FZ,-(Fspr+Fcsl)/2 F,201+(I-1)*1000,FZ,+Fspr/2 F,202+(I-1)*1000,FZ,+Fspr/2

• ENDDO

• ENDIF

/COM,

/COM, _____________________________________

/COM, PUT SPECIAL BOUNDARY CONDITIONS ON VESSEL FOR PARTIAL MODELS

• IF,NT,LT,NV,THEN

• IF,ARG1,LT,0.5,THEN  ! USE MIRROR SYMMETRY B.C.s

/COM, DELETE EXTRA ELEMENTS AND NODES BEYOND LAST STUD EDELE,(NT-1)*1000+1,(NT-1)*1000+499

/COM, DO SOME NODAL CLEANUP NSLE,U NDELE,ALL NSEL,ALL

/COM, CHANGE REALS ON CUTTING PLANES ESEL,S,ELEM,,501 ESEL,A,ELEM,,501+(NT-1)*1000 EMODIF,ALL,REAL,3 ESEL,S,ELEM,,503,512 ESEL,A,ELEM,,503+(NT-1)*1000,512+(NT-1)*1000 EMODIF,ALL,REAL,5 ESEL,ALL NSEL,S,NODE,,1,1000 NSEL,A,NODE,,1+(NT-1)*1000,NT*1000 NSEL,U,NODE,,164,99164,1000 NSEL,U,NODE,,204,99204,1000 D,ALL,UY NSEL,ALL

• IF,Fspr+Fcsl,GT,1.0,THEN F,131,FZ,-(Fspr+Fcsl)/4 F,132,FZ,-(Fspr+Fcsl)/4 F,201,FZ,+Fspr/4 F,202,FZ,+Fspr/4 F,131+(NT-1)*1000,FZ,-(Fspr+Fcsl)/4 F,132+(NT-1)*1000,FZ,-(Fspr+Fcsl)/4 F,201+(NT-1)*1000,FZ,+Fspr/4 F,202+(NT-1)*1000,FZ,+Fspr/4

• ENDIF

• ELSE  ! USE CYCLIC SYMMETRY B.C.s

/COM, GET RID OF EXCESS ELEMENTS EDELE,(NT-1)*1000+1,(NT-1)*1000+350

/COM, SWING LAST PLANE AROUND TO 0 DEGREES NSEL,S,NODE,,NT*1000+1,(NT+1)*1000 CSYS,21 NMODIF,ALL,,0 NSEL,A,NODE,,1,1000 NSEL,U,NODE,,164,204,40 NROTATE,ALL CPINTF,ALL,0.001 NSEL,S,NODE,,NT*1000+1,(NT+1)*1000 NMODIF,ALL,,NT*360/NV NSEL,ALL NROTATE,ALL

/COM, BRING BACK LAST PLANE OF ELS.

ENGEN,(NT-1)*1000,2,(NT-1)*1000,1,350,1  ! COPY AROUND CIRCLE

/COM, FIX UP COUPLES ON EDGE PLANES CP,1,,NT*1000+164,NT*1000+204

Dominion Engineering, Inc.

Title:

Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 36 of 41 CP,101,,NT*1000+164,NT*1000+204 CP,1501,UZ,164,NT*1000+164 CP,1502,UZ,204,NT*1000+204

• ENDIF

• ENDIF

/COM, Define a few components for later use

• USE,CMMAKER,201,500,'NHEAD','EHEAD'

• USE,CMMAKER,1,200,'NVESSEL','EVESSEL'

• USE,CMMAKER,221,500,'NHEADR','EHEADR'

/COM, Define pressure surfaces for PSOLV macro NSEL,S,NODE,,1,99999,10

/COM, Select additional nodes which form crevice between flanges out to the

/COM, inner o-ring NSEL,A,NODE,,161,99999,1000 NSEL,A,NODE,,162,99999,1000 NSEL,A,NODE,,163,99999,1000 NSEL,A,NODE,,201,99999,1000 NSEL,A,NODE,,202,99999,1000 NSEL,A,NODE,,203,99999,1000 CM,PSURF,NODE NSEL,ALL SHPP CHECK

• END

/COM,

/COM, ----------------------------------------------------------------------------------

/COM, END GEOMETRY MACRO

/COM, **********************************************************************************

/COM, **********************************************************************************

/COM,

/COM,

/COM,

/COM, **********************************************************************************

/COM, **********************************************************************************

/COM, CREATE CMMAKER MACRO

/COM, ----------------------------------------------------------------------------------

/COM,

• CREATE,CMMAKER NSEL,NONE ESEL,NONE

• DO,I,0,(NT-1)*1000,1000 NSEL,A,NODE,,ARG1+I,ARG2+I

• IF,I,EQ,(NT-1)*1000,THEN

• IF,NT,LT,NV,EXIT

• ENDIF ESEL,A,ELEM,,ARG1+I,ARG2+I

• ENDDO CM,ARG3,NODE CM,ARG4,ELEM NSEL,ALL ESEL,ALL

• END

/COM,

/COM, ----------------------------------------------------------------------------------

/COM, END CMMAKER MACRO

/COM, **********************************************************************************

/COM, **********************************************************************************

/COM,

/COM,

/COM,

/COM, **********************************************************************************

/COM, **********************************************************************************

/COM, CREATE GEOMCLUP MACRO

/COM, ----------------------------------------------------------------------------------

/COM,

• CREATE,GEOMCLUP CPDELE,ALL,ALL CMDELE,NHEAD CMDELE,EHEAD CMDELE,NVESSEL CMDELE,EVESSEL CMDELE,NHEADR

Dominion Engineering, Inc.

Title:

Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 37 of 41 CMDELE,EHEADR EDELE,ALL NDELE,ALL

• END

/COM,

/COM, ----------------------------------------------------------------------------------

/COM, END GEOMCLUP MACRO

/COM, **********************************************************************************

/COM, **********************************************************************************

/COM,

/COM,

/COM,

/COM, **********************************************************************************

/COM, **********************************************************************************

/COM, CREATE ENDPOST MACRO

/COM, ----------------------------------------------------------------------------------

/COM, RLIST columns as follows:

/COM, RLIST(J,1) = Flange Displ. last pass

/COM, RLIST(J,2) = Stud Initial Elongation Real Constant

/COM, RLIST(J,3) = Stud Final Membrane Stress

/COM, RLIST(J,4) = Stud Max. Membrane+Bending Stress

/COM, RLIST(J,5) = Maximum Membrane Stress during any pass

/COM, RLIST(J,6) = Pass Number at which Max. Membrane Stress Occurs

/COM,

/COM, RLIST(J,7) = Angular Rotation of Upper Flange (radians)

/COM, RLIST(J,8) = Angular Rotation of Lower Flange (radians)

/COM, RLIST(J,9) = Inner O-ring separation

/COM,

/COM, RLIST(J,10) = Force on Contact Link Element

/COM, RLIST(J,11) = Global X Shear Force on Coupled Set

/COM, RLIST(J,12) = Global Z Shear Force on Coupled Set

/COM,

/COM, RLIST(J,13) = Mu Required to Prevent Flange Mating Surf. Slide

/COM, RLIST(J,14) = Mu Required to Prevent Flange Stud Washer Slide

/COM,

/COM, Cut Plane Stress Intensities:

/COM, Line 1 - Vessel Far Field Cut Plane (RLIST(J,15) to RLIST(J,19))

/COM, RLIST(J,15) = Linearized SI at Inner Surface

/COM, RLIST(J,16) = Linearized SI at Center of Surface (Membrane SI)

/COM, RLIST(J,17) = Linearized SI at Outer Surface

/COM, RLIST(J,18) = Total SI at Inner Surface

/COM, RLIST(J,19) = Total SI at Outer Surface

/COM,

/COM, Line 2 - Vessel Local Cut Plane - Lower (RLIST(J,20) to RLIST(J,24))

/COM, Line 3 - Vessel Local Cut Plane - Middle (RLIST(J,25) to RLIST(J,29))

/COM, Line 4 - Vessel Local Cut Plane - Upper (RLIST(J,30) to RLIST(J,34))

/COM, Line 5 - Head Local Cut Plane - Lower (RLIST(J,35) to RLIST(J,39))

/COM, Line 6 - Head Local Cut Plane - Middle (RLIST(J,40) to RLIST(J,44))

/COM, Line 7 - Head Local Cut Plane - Upper (RLIST(J,45) to RLIST(J,49))

/COM, Line 8 - Head Far Field Cut Plane (RLIST(J,50) to RLIST(J,54))

/COM,

• CREATE,ENDPOST

/COM, Finish by loading results in RLIST

• DO,J,1,NT ENUMB = J*1000-498  ! El. no. of subject element

• GET,RLIST(J,3),ELEM,ENUMB,ETAB,MEMBSTRS  ! El. membrane stress

• GET,DUMBOT,ELEM,ENUMB,ETAB,MAXM+BI  ! El. membrane+bend stress (I)

• GET,DUMTOP,ELEM,ENUMB,ETAB,MAXM+BJ  ! El. membrane+bend stress (J)

RLIST(J,4) = DUMBOT > DUMTOP

/COM, RSYS,21 NNUM1 = (J-1)*1000+151  ! Node 151 NNUM2 = (J-1)*1000+159  ! Node 159 NNUM3 = (J-1)*1000+211  ! Node 211 NNUM4 = (J-1)*1000+219  ! Node 219 RLIST(J,7) = (UZ(NNUM4)-UZ(NNUM3))/flwdth  ! Upper Flange Rotation (radians)

RLIST(J,8) = (UZ(NNUM2)-UZ(NNUM1))/flwdtv  ! Lower Flange Rotation (radians)

NNUM1 = (J-1)*1000+164 NNUM2 = (J-1)*1000+204 RLIST(J,9) = UZ(NNUM2)-UZ(NNUM1)+iormo*(RLIST(J,8)-RLIST(J,7))

/COM, ENUMB = (J-1)*1000+501  ! El. no. 501

• GET,RLIST(J,10),ELEM,ENUMB,ETAB,FORCE  ! El. Force CMSEL,S,EHEAD

Dominion Engineering, Inc.

Title:

Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 38 of 41 NSEL,S,NODE,,(J-1)*1000+204 FSUM ESEL,ALL NSEL,ALL

• GET,RLIST(J,11),FSUM,,ITEM,FX  ! Global X-Shear Force

• GET,RLIST(J,12),FSUM,,ITEM,FZ  ! Global Z-Shear Force

! RLIST(J,13) is resultant shear divided by link membrane force

• IF,RLIST(J,10),LT,-1.0,THEN RLIST(J,13) = -SQRT(RLIST(J,11)**2+RLIST(J,12)**2)/RLIST(J,10)

• ELSE RLIST(J,13) = -1  ! Trap divide by zero

• ENDIF SLIPCNST = 2*Is/(Ds*SWRC*As)  ! Constants in washer slip calc

• IF,RLIST(J,3),GT,1.0,THEN RLIST(J,14) = SLIPCNST*(RLIST(J,4)-RLIST(J,3))/RLIST(J,3)

• ELSE RLIST(J,14) = -1  ! Trap divide by zero

• ENDIF

/COM,

/COM, Cut Lines:

• USE,READSI,11,15,21,15,J  ! Cut 1: Nodes 11 to 15 in CSYS 21

• USE,READSI,61,65,21,20,J  ! Cut 2: Nodes 61 to 65 in CSYS 21

• USE,READSI,71,75,21,25,J  ! Cut 3: Nodes 71 to 75 in CSYS 21

• USE,READSI,81,85,21,30,J  ! Cut 4: Nodes 81 to 85 in CSYS 21

• USE,READSI,261,264,24,35,J  ! Cut 5: Nodes 261 to 261 in CSYS 24

• USE,READSI,271,274,24,40,J  ! Cut 6: Nodes 271 to 274 in CSYS 24

• USE,READSI,281,284,24,45,J  ! Cut 7: Nodes 281 to 284 in CSYS 24

• USE,READSI,351,354,24,50,J  ! Cut 8: Nodes 351 to 354 in CSYS 24

• ENDDO

• END

/COM, ----------------------------------------------------------------------------------

/COM, END ENDPOST MACRO

/COM, **********************************************************************************

/COM, **********************************************************************************

/COM,

/COM,

/COM,

/COM, **********************************************************************************

/COM, **********************************************************************************

/COM, CREATE PRINTENS MACRO

/COM, ----------------------------------------------------------------------------------

/COM,

/COM, PRINTENS arguments as follows:

/COM, ARG1 = PSAVE Text

/COM, ARG2 = RSAVE Text

/COM, ARG3 = Loop Ending No.

/COM, ARG4 = Free Text Field (e.g., 'Existing')

/COM, ARG5 = Sequence Print Flag (1 = Print Sequence)

/COM,

• CREATE,PRINTENS

• DO,K,1,ARG3

• VWRITE,K

('-----',/,'Tensioning Sequence Iteration ',F2.0)

• VWRITE,ARG4

('-----',/,A,' Procedure Results -')

• VWRITE (2/,'Stud Stress Summary',/)

• VSCFUN,MAXCOL1,MAX, %ARG2%(1, 3,K)

• VSCFUN,MINCOL1,MIN, %ARG2%(1, 3,K)

• VSCFUN,AVECOL1,MEAN,%ARG2%(1, 3,K)

• VSCFUN,MAXCOL2,MAX, %ARG2%(1, 4,K)

• VSCFUN,MINCOL2,MIN, %ARG2%(1, 4,K)

• VSCFUN,AVECOL2,MEAN,%ARG2%(1, 4,K)

• VSCFUN,MAXCOL3,MAX, %ARG2%(1, 5,K)

• VSCFUN,MINCOL3,MIN, %ARG2%(1, 5,K)

• VSCFUN,AVECOL3,MEAN,%ARG2%(1, 5,K)

• VSCFUN,MAXCOL4,MAX, %ARG2%(1,14,K)

• VSCFUN,MINCOL4,MIN, %ARG2%(1,14,K)

• VSCFUN,AVECOL4,MEAN,%ARG2%(1,14,K)

/COM, MEMBRANE MEMB+BEND MAX. MEM. REQUIRED

/COM, STRESS STRESS STRESS WASHER MU

Dominion Engineering, Inc.

Title:

Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 39 of 41

• VWRITE,'MAXIMUM',MAXCOL1,MAXCOL2,MAXCOL3,MAXCOL4 (A7,3X,3(F9.0,3X),3X,F7.4)

• VWRITE,'MINIMUM',MINCOL1,MINCOL2,MINCOL3,MINCOL4 (A7,3X,3(F9.0,3X),3X,F7.4)

• VWRITE,'AVERAGE',AVECOL1,AVECOL2,AVECOL3,AVECOL4 (A7,3X,3(F9.0,3X),3X,F7.4)

• VWRITE (2/,'Head and Head Flange Cut Planes Stress Summary',/)

• VSCFUN,AVECOL1,MEAN,%ARG2%(1,51,K)

• VWRITE,AVECOL1

('General Membrane Stress Intensity ',F6.0)

• VSCFUN,MAXCOL1,MAX,%ARG2%(1,36,K)

• VSCFUN,MAXCOL2,MAX,%ARG2%(1,41,K)

• VSCFUN,MAXCOL3,MAX,%ARG2%(1,46,K)

MAXCOL4 = MAXCOL1 > MAXCOL2 > MAXCOL3

• VWRITE,MAXCOL4

('Maximum Local Membrane Stress Intensity ',F6.0)

• VSCFUN,MAXCOL1,MAX,%ARG2%(1,35,K)

• VSCFUN,MAXCOL2,MAX,%ARG2%(1,40,K)

• VSCFUN,MAXCOL3,MAX,%ARG2%(1,45,K)

MAXCOL4 = MAXCOL1 > MAXCOL2 > MAXCOL3

• VSCFUN,MINCOL1,MAX,%ARG2%(1,37,K)

• VSCFUN,MINCOL2,MAX,%ARG2%(1,42,K)

• VSCFUN,MINCOL3,MAX,%ARG2%(1,47,K)

MINCOL4 = MINCOL1 > MINCOL2 > MINCOL3

• VWRITE,MAXCOL4 > MINCOL4

('Maximum Local Mem + Bend Stress Intensity ',F6.0)

• VSCFUN,MAXCOL1,MAX,%ARG2%(1,38,K)

• VSCFUN,MAXCOL2,MAX,%ARG2%(1,43,K)

• VSCFUN,MAXCOL3,MAX,%ARG2%(1,48,K)

MAXCOL4 = MAXCOL1 > MAXCOL2 > MAXCOL3

• VSCFUN,MINCOL1,MAX,%ARG2%(1,39,K)

• VSCFUN,MINCOL2,MAX,%ARG2%(1,44,K)

• VSCFUN,MINCOL3,MAX,%ARG2%(1,49,K)

MINCOL4 = MINCOL1 > MINCOL2 > MINCOL3

• VWRITE,MAXCOL4 > MINCOL4

('Maximum Local Stress Intensity ',F6.0)

• VWRITE (2/,'Vessel and Vessel Flange Cut Planes Stress Summary',/)

• VSCFUN,AVECOL1,MEAN,%ARG2%(1,16,K)

• VWRITE,AVECOL1

('General Membrane Stress Intensity ',F6.0)

• VSCFUN,MAXCOL1,MAX,%ARG2%(1,21,K)

• VSCFUN,MAXCOL2,MAX,%ARG2%(1,26,K)

• VSCFUN,MAXCOL3,MAX,%ARG2%(1,31,K)

MAXCOL4 = MAXCOL1 > MAXCOL2 > MAXCOL3

• VWRITE,MAXCOL4

('Maximum Local Membrane Stress Intensity ',F6.0)

• VSCFUN,MAXCOL1,MAX,%ARG2%(1,20,K)

• VSCFUN,MAXCOL2,MAX,%ARG2%(1,25,K)

• VSCFUN,MAXCOL3,MAX,%ARG2%(1,30,K)

MAXCOL4 = MAXCOL1 > MAXCOL2 > MAXCOL3

• VSCFUN,MINCOL1,MAX,%ARG2%(1,22,K)

• VSCFUN,MINCOL2,MAX,%ARG2%(1,27,K)

• VSCFUN,MINCOL3,MAX,%ARG2%(1,32,K)

MINCOL4 = MINCOL1 > MINCOL2 > MINCOL3

• VWRITE,MAXCOL4 > MINCOL4

('Maximum Local Mem + Bend Stress Intensity ',F6.0)

• VSCFUN,MAXCOL1,MAX,%ARG2%(1,23,K)

• VSCFUN,MAXCOL2,MAX,%ARG2%(1,28,K)

• VSCFUN,MAXCOL3,MAX,%ARG2%(1,33,K)

MAXCOL4 = MAXCOL1 > MAXCOL2 > MAXCOL3

• VSCFUN,MINCOL1,MAX,%ARG2%(1,24,K)

Dominion Engineering, Inc.

Title:

Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 40 of 41

• VSCFUN,MINCOL2,MAX,%ARG2%(1,29,K)

• VSCFUN,MINCOL3,MAX,%ARG2%(1,34,K)

MINCOL4 = MINCOL1 > MINCOL2 > MINCOL3

• VWRITE,MAXCOL4 > MINCOL4

('Maximum Local Stress Intensity ',F6.0)

• VSCFUN,MAXCOL1,MAX,%ARG2%(1,9,K)

• VWRITE,MAXCOL1 (2/,'Maximum Inner O-Ring Separation is ',F7.5,' inches.')

• VSCFUN,MAXCOL1,MAX,%ARG2%(1,13,K)

• VWRITE,MAXCOL1

('Required Mating Surface Mu to Prevent Slip is ',F7.5,'.')

• IF,ARG5,EQ,1,THEN

• VWRITE,ARG4

('-----',/,A,' Procedure - Sequence Listing',/)

/COM, SET NO. STUD NO. PRESSURE RETEN. FLAG

• VWRITE,SEQU,%ARG1%(1,1,K),%ARG1%(1,2,K),%ARG1%(1,4,K)

(4(F9.0,3X))

• ENDIF

• VWRITE,ARG4

('-----',/,A,' Procedure Results - Stud Stresses',/)

/COM, MEMBRANE MEMB+BEND MAX. MEM. ACHIEVED REQUIRED

/COM,STUD # STRESS STRESS STRESS @ SET NO. WASHER MU

• VWRITE,SEQU,%ARG2%(1,3,K),%ARG2%(1,4,K),%ARG2%(1,5,K),%ARG2%(1,6,K),%ARG2%(1,14,K)

(F5.0,5X,4(F9.0,3X),2X,F7.4)

• VWRITE,ARG4

('-----',/,A,' Procedure Results - Flange Contact Forces',/)

/COM, GLOBAL GLOBAL REQUIRED

/COM,STUD # LINK FORCE X SHEAR Z SHEAR FLANGE MU

• VWRITE,SEQU,%ARG2%(1,10,K),%ARG2%(1,11,K),%ARG2%(1,12,K),%ARG2%(1,13,K)

(F5.0,3X,3(E11.4,2X),2X,F7.4)

• VWRITE,ARG4

('-----',/,A,' Procedure Results - Flange Deflections',/)

/COM, UPPER FLANGE LOWER FLANGE O-RING

/COM,STUD # ROTATION ROTATION SEPARATION

• VWRITE,SEQU,%ARG2%(1,7,K),%ARG2%(1,8,K),%ARG2%(1,9,K)

(F5.0,4X,3(E11.4,4X))

CLNO = 0

• DO,L1,15,50,5 CLNO = CLNO+1 L2 = L1+1 L3 = L1+2 L4 = L1+3 L5 = L1+4

• VWRITE,ARG4,CLNO

('-----',/,A,' Procedure Results - Cut Line ',F2.0,/)

/COM, INNER CENTER OUTER INNER OUTER

/COM,STUD # LIN. S.I. LIN. S.I. LIN. S.I. TOT. S.I. TOT. S.I.

• VWRITE,SEQU,%ARG2%(1,L1,K),%ARG2%(1,L2,K),%ARG2%(1,L3,K),%ARG2%(1,L4,K),%ARG2%(1,L5,K)

(F5.0,2X,5(F9.0,3X))

• ENDDO

• ENDDO

• END

/COM, ----------------------------------------------------------------------------------

/COM, END PRINTENS MACRO

/COM, **********************************************************************************

/COM, **********************************************************************************

/COM,

Dominion Engineering, Inc.

Title:

Hatch Unit 2 Operation with Two Studs Out of Service Evaluation Calculation No.: C-037-2201-00-02 Revision No.: 0 Page 41 of 41 B SOFTWARE USAGE RECORDS The following table lists the Software Usage Records for the ANSYS analyses performed in support of this calculation. These records are included on the Data Disk D-037-2201-00-02 [7] in their native electronic formats. This data disk is retained with the Task 037-2201 project file and is available for on-site review by Southern Nuclear personnel.

File Name Description

_HATCH2.runs Input file which sets run parameters and performs the closure flange evaluation cases.

_MACROS.HATCH2 Input file which sets the finite element model geometry and boundary conditions specific to the Hatch Unit 2 RPV model.

_MACROS.DEI Input file which performs stud tensioning and closure flange analyses.

RESULTS.OUT Formatted output file which contains the stud stress results for the closure flange analysis cases.

_HATCH2.out Full output file generated automatically which includes every ANSYS operation performed throughout the analysis.

HATCH2.err Automatically generated error file which includes all warnings generated during the analysis.

Hatch 2 Two-Stud Primary Microsoft Excel spreadsheet used to perform stud primary stress Stress Calc v0.xlsx calculations.