ML20237D580

Rev 1 to Calculation 083-248-CBS-01, Shroud Finite Element Evaluation

ML20237D580
Person / Time
Site:	Oyster Creek
Issue date:	07/16/1998
From:	Lane B, Mccurdy W, Swanner C MPR ASSOCIATES, INC.
To:
Shared Package
ML20237D567	List: ML20237D566 ML20237D569 ML20237D571 ML20237D573 ML20237D576 ML20237D578 ML20237D580
References
083-248-CBS-01, 083-248-CBS-01-R01, 83-248-CBS-1, 83-248-CBS-1-R1, NUDOCS 9808270013
Download: ML20237D580 (45)

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I MPR Associites,Inc.

320 King StrEt Alexandria,VA 22314 CALCULATION TITLE PAGE Client GPU Nuclear

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-r Appendices Project Task No.

Shroud Vertical Weld Evaluation 083-9601-248-0 Title Calculation No.

Shroud Finite Element Evaluation 083-248-CBS-01 Preparer /Date Checker /Date Reviewer / Approver Date Rev. No.

,C. Sw nner B. Lane W. McCurdy Am h&

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MPR Associtt*.s, Inc.

MPR 320 King Str:ct Alexandria, VA 22314 RECORD OF REVISIONS Calculation No.

Prepared By C ecked By 083-248-CBS-01

%6 Page 2 Revision Dep%

0 InitialIssue 1

Revised seismic loads based on updated transient dynamic analyses.

Removed results for 10 wedges because only 8 wedges will be installed.

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f 1.0 PURPOSE i

The purpose of this calculation is to determine the flaw tolerance of the verticalwelds in the section between circumferential welds H5 and H6A in the Oyster Creek core shroud.

The vertical weld evalucion was originally performed in Reference 1. This calculation considers the effect ofinstalling wedges between the core plate and the shroud wall. A finite element model of the shroud section is developed to evaluate the effects.

The finite element model is also used to determine the leakage path flow area through the cracked vertical weld during normal operating conditions.

2.0

SUMMARY

OF RESULTS The maximum stresses in the shroud section between circumferential welds H5 and H6A are summarized for the limiting load cases in Table 2-1. Stress contours for each load case are presented later in this calculation. As shown, these stresses meet the requirements of Subsection NB of the ASME Boiler and Pressure Vessel Code,1989 Edition. The evaluations are performed with eight core plate wedges installed. All circumferential welds and the vertical welds in the H5/H6A shroud section are assumed to be completely failed.

The evaluations show that the load through the vertical welds can be reacted by taking credit for compression across the failed circumferential welds due to tie rod preload.

For the MSLB case, if only welds H5 and H6A are failed with all other circumferential welds intact, compression could no longer be maintained across both welds H5 and H6A.

Consequently, some amount of the vertical weld is required to react the hoop load from the differential pressure. Results of the evaluation performed in Appendix A show that if there is ten inches of intact vertical weld, the stresses in the H5 and H6A meet the requirements of the ASME Code.

The maximum leakage path flow area through a fully-cracked vertical weld in the H5/H6A 2

shroud segment during normal operating conditions is 4.67 in. This flow area will be used elsewhere to evaluate the effect of reactor coolant flow that bypasses the core through the cracked vertical weld.

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l 12iBMPR MPR Asiocitt.o,Inc.

Efn"ect223a Calculation No.

Prepared By C cked By 083-248-CBS-01 Page 4

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j Table Summay of Maximum Stresses in the Shroud Shell Between Circumferential Welds H5 and H6A Stress Calculated Allowable Stress Stress Type Limit Stress (ksi)

Stress (ksi)

Ratio

@}gy leg ijidaidisikUNBrsa$cplSSdfdShbidown*Ea$tkb5NO SeMIMsiM NW

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s Primary Membrane pim 3.6Sm 31.7 60.0 0.53 Bending (Pm+Pb) i

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Primary Membrane plus

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3.6Sm 44.5 60.0 0.74 l

Bending (Pm+Pb)

Note:

1.

The calculated stresses tabulated are for the locations at the wedges. The maximum stress shown in the stress contours presented in Section 4 are at the intersection of horizontal weld H5 and the vertical weld. These stresses are considered seconday since they are a result of the structural discontinuity at this location. Consideration of secondary stresses is not required for Service Level D loading.

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Alexandria, VA 22314 Calculation No.

Prepared By C

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3.0 DISCUSSION 3.1 Shroud Confleuration The design function of the core shroud is to provide lateral support for the nuclear fuel and to provide a flow partition within the reactor vessel. A developed view of the Oyster Creek reactor is shown in Figure 3-1. The shroud is divided into a number of cylindrical section by its circumferential welds designated H1 through H7. Each of these shroud sections has two vertical welds which join individual rolled plates to form the cylinders.

The shroud configuration is further modified by installation of the core shroud repair. The core shroud repair consists of ten tie rod restraint assemblies that structurally replace all the circumferential welds (H1 through H7). Figure 3-1 shows the location and positioning of each tie rod assembly. Note that each shroud segment between two adjacent circumferential welds has radial restraints to react lateral loads.

3.2 Applied Loads The following applied loads are reacted by the shroud cylinders.

Differential Pressure: The pressure difference across the shroud creates a hoop load (stress) in the shroud which must be reacted through vertical welds in each shroud cylinder. The differential pressures from Appendix A of Reference 5 are used in this calculation.

l Seismic Bumper Loads: The reactor vessel, shroud, and fuel are excited in the horizontal direction by an earthquake. Relative motion between the shroud and reactor vessel causes the radial restraints to contact the shroud resulting in lateral loads in the shroud shell.

l Seismic FuelLoads: The reactor vessel, shroud, and fuel are excited in the horizontal direction by an earthquake. Motion of the fuel causes lateralloads normally reacted through the core support ricg and the top guide.

Lateral RLB Loads: A recirculation line break (RLB) causes lateral loads on the shroud shell. Lateralloads are transmitted into the shroud barrelwhen the shroud contacts the radial restraints.

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MPR Associ;t:s,Inc.

MPR 320 King Strzt Alexandria, VA 22314 Calculation No.

Prepared By ecked By 083-248-CBS-01

&W Page 6 m-m During accident events, lateral loads are transmit om the fuel to the core plate. The original plant load path is through the core plate holddown bolts into the core support ring (between H6A and H6B) and out through the shroud. The core shroud repair structurally replaces all shroud horizontal welds with an alternative load path. For lateral loads, the alternative load path used in the analysis (Reference 2) was through the core support ring and directly into seismic restraints into the reactor vessel.

Oyster Creek plans to install eight wedges between the core support plate and the shroud cylinder between horizontal welds H5 and H6A. The wedges are designed to bypass the l

core plate holddown bolts thereby precluding the need to inspect and maintain the bolt I

preload. The wedges react the lateral fuel load from the core plate directly into the shroud.

This alternative load path was not analyzed as part of the original flaw tolerance evaluation or the core shroud repair design.

3.3 Calculation Method The acceptable flaw lengths in the vertical welds of the Oyster Creek core shroud were l

determined in Reference 1. The evaluation was based on the shroud loadings and load paths used in the analysis of the core shroud repair (Reference 2). The evaluation used a limit load approach by determining the amount of weld length required to maintain the limiting stresses within the ASME Code limits.

This calculation develops a finite element model to analyze the shroud cylinder between welds H5 and H6A with the core plate wedges installed. Specifically, this calculation will address the effect of potential cracking in the vertical welds on the structuralintegrity of the shroud cylinder between H5 and H6A. In all evaluations, both H5 and H6A are assumed to be cracked through wall, all the way around the shroud. This is the most limiting condition for the vertical welds because intact ligament in the horizontal weld provides an alternate load path around the vertical welds for hoop loads in the shroud cylinder.

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EMPR MPR Associtt s,Inc.

320 King Street Alexandria, VA 22314 Calculation No.

I Prepared By C

cked By 083-248-CBS-01 gg Page 7 m,W 3.4 Service Loadines The core shroud repair is designed to react loads arising from the following shroud service conditions (see Reference 5).

Table 3-1. ASME Code Service Limits ASME Load ASME Allowable Service Load Combination Primary Membrane Case Limit Stress Intensity (Note 1)

Upset Level B Upset differential pressure (AP)

Sm OBE Level B Operating basis earthquake (OBE) loads plus Sm normal AP SSE +

Level D Main steam line break (MSLB) AP plus safe Lesser of 2.4 Sm MSLB shutdown earthquake (SSE) loads or 0.7 Su SSE +

Ievel D Recirculation line break (RLB) loads plus normal Lesser of 2.4 Sm RLB AP plus SSE loads or 0.7 Su Notes:

1.

The allowable stresses are from Section NB-3220 of Reference 3. Specifically, the limits for design loads from NB-3221 are applied to Level B loads, and the limits from NB-3225 and F-1331 are applied to Level D loads. Primary membrane plus bending stress limits are 1.5 times the primary stress limit. Also, note that Sm is the allowable stress of the material at design temperture and Su is the ultimate tensile strength of the material at design temperature.

The controlling se'rvice loadings for comparison with the stress limits can be determined by examining.the load components for each service condition. From Reference 4, the RLB load case is most limiting for the H5/H6A shroud segment in terms of required vertical weld. The differential pressure associated with the MSLB case also causes vertical loads in the shroud large enough to separate potentially cracked horizontal welds. This results in different boundary conditions for the H5/H6A shroud section. As a result, this calculation I

investigates only the MSLB + SSE and RLB + SSd load cases.

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j 4.0 FINITE ELEMENT MODEL The input for each model used in this analysis are contained in the Appendix C.

4.1 Loadine Conditions 1

Loading conditions for the evaluation of the H5/H6A shroud cylinder are summarized

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below in Table 4-1.

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Table 4-1. Loading Conditions Loading Value Reference MSLB + SSE:

, Steam line break differential pressure across shroud wall 19.0 psi 5

l SSE seismic bumper load 74 kips (Note 1)

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SSE seismic fuelload 40 kips (Note 1) i RLB + SSE:

Normal operating differential pressure across shroud wall 4.34 psi 5

SSE seismic bumper load 74 kips (Note 1)

SSE seismic fuelloa:1 40 kips (Note 1)

I Lateral recirculation line break load 41.3 kips (Note 2)

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1.

The most limiting case for the vertical welds in the H5/H6A shroud section is when j

both horizontal welds are broken. The seismic load case corresponding to this condition is the multiple weld break case. The maximum bottom bumper load and l

maximum bottom fuel load for the multiple break case are taken from Reference 6.

2.

The lateral!oad due to an RLB is determined from the shroud shear distribution given in Reference 7. The load applied to the H5/H6A shroud section is calculated as the difference in shear loads at horizontal welds H5 and H6A.

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l 4.2 Material Properties The material properties of the shroud are summarized in Table 4-2 below. These l

properties are obtained from Appendix I of Reference 3 at the design temperature of 575'F (Reference 5).

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MPR Associatis,Inc.

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320 King Strut l

Alexandria, VA 22314 l

Calculation No.

Prepared By Ch ked By 083-248-CBS-01 gy Page 10 A vv mm Table 4-2. Material th Properties Material Properties Component Material Property Value Allowable Stress (Sm) 16.675 ksi

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Shroud (Reference 8)

Ultimate Strength (Su) 63.5 ksi

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Modulus of Elasticity (3) 25,40(/ ksi j

Note that a Poisson's ratio (v) of 0.3 and a density of 0.29 lb /in'is assumed for all m

materials in this calculation.

4.3 Model Geometry To evaluate the vertical welds in the H5/H6A shroud cylinder, the shroud sections between horizontalwelds H4 and H6B are modeled. The additional sections are modeled te include j

the effect of compression across horizontal welds from tie rod preload in the evaluation of the vertical welds. The core plate wedges and the radial restraints are also included in the finite element model. The geometric data used to construct the finite element model of the I

shroud is shown in Figure 4-1. The three-dimensional, finite element model of the shroud is shown in Figure 4-2.

The shroud is modeled with ANSYS SOLID 45 elements. These are 8-node, brick elements with three displacement degrees of freedom at each node. Bearing between the shroud and the core plate wedges and between the shroud and the radial restraints is modeled by coupling the bearing surface to the shroud. Both vertical welds in the shroud section are assumed to be completely cracked.

4.4 Imads and Boundary Conditions Three individual ANSYS runs for the two load cases are performed for this evaluation. For each load case (MSLB + SSE and RLB + SSE), the differential pressure is run separately from the lateral loads. The results of the two runs are combined by superposition to determine the net state of stress in the shroud.

For the differential pressure cases, the differential pressure is applied to all nodes on the inside surface of the shroud. For the lateralload case, the seismic fuel load is assumed to l

be directed at the vertical weld located at 165*. This results in the highest shroud shell bending stresses locally near the vertical weld.

MMPR l274 & "

Alexandria, VA 22314 Calculation No.

Prepared By C

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Page 11 083-248-CBS-01 The seismic fuelload is reacted to the shroudpr e wedges. The core plate is assumed to be infinitely rigid. This is modeled by coupling all the wedges to a node at the center of the shroud. The seismic fuelload is then applied to the center node and directed

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toward the vertical weld at 165'. It is assumed that there is no gap between the shroud and 1

the wedges. Accordingly, the wedges are directly coupled in all degrees of freedom to the j

shroud.

The seismic bumper load is conservatively assumed to be directed at the vertical weld at l

165*. Nominally, there is a 0.375" total gap between the radial restraints, the shroud I

outside diameter, and the reactor inside diameter. Because the restraints are located at l

various positions around the shroud, only several restraints will carry load when the shroud l

is loaded in a given direction. Initial scoping analyses have been performed to show that only the three restraints closest to the vertical weld are loaded when the lateral load is applied in the 165* direction. In this analysis, it is assumed that there is no gap between the restraints and shroud. This is modeled by directly coupling the restraints to the shroud in all degrees of freedom.

The RLB lateralload is directed toward the recirculation nozzle with the faulted pipe. This -

l analysis conservatively assumes that the RLB lateral load is directed at the vertical weld at l

165*. Since the seismic bumper load and RLB lateral load are assumed to act in the same direction, they are applied to the model as a combined uniform acceleration. The acceleration is determined by subtracting the seismic fuel load from the total lateral load (seismic bumper plus RLB lateral load) and then dividing by the total model mass.

The follo' wing model boundary conditions are applied to all the models:

The vertical welds in the H5 and H6A shroud section are assumed to be completely failed. Since the welds tend to open up due to pressure, this is modeled by uncoupling the nodes on either side of the weld.

All circumferential welds are considered completely failed. The tie rod preload keeps l

the entire shroud in compression during normal operation. The differential pressure during an RLB is bounded by normal operating conditions. Consequently, there is compression across all the failed circumferential welds during the RLB + SSE load case. During a MSLB accident the differential pressure across the shroud is significantly increased. This results in a large upload applied to the core plate due to l

differential pressure. Since it is assumed a weld below the core support ring is failed, the large core plate upload and the restraining loads from the tie rods keep all the circumferential welds above the core support ring in compression. Since there is compression across each of the failed circumferentialwelds, H5 and H6A are modeled as pinned joints, i.e. they can carry shear but not moment. (Note that if only H5 and l

H6A are failed during an MSLB event, the H5/H6A shroud segment becomes free.

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MPR Associ:1:2, Inc.

l 320 King Strat t

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Calculation No.

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Page 12 083-248-CBS-01 vv v- ~ ~

This case is examined more closely in App A.)

The pinned joints are modeled by coupling the nodes on the inside diameter of the weld of the two adjacent cylinders in all three transnational directions. The circumferential welds at H4 and H6B are away from the analysis area of interest and are considered free (i.e., no applied boundary conditions).

The modelis restrained vertically at the node in the center of the core plate.

i The outside surface of the radial restraints are restrained from motion in the radial direction.

4.5 Finite Element Analyses Results For each loading condition, the stresses are evaluated using a finite element model of the shroud (see Section 3.5). Stress analysis results are obtained using finite element methods and the ANSYS finite element program. The ANSYS evaluations are performed on a Sun UltraSPARC Workstation with the Solaris 2.5 operating system. The ANSYS installation verification was performed in QA-53-3.

The finite element model of the H5/H6A shroud section is evaluated for loading conditions described in the previous sections. Analysis results for the SSE + MSLB and the SSE +

RLB load cases are shown in Figures 4-3 and 4-4. Stress results are summarized and compared to the allowable stresses in Table 2-1.

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1

MPR Assoclit:s,Inc.

A ex dla,V 22314 Calculation No.

Prepared By C

ked By 083-248-CBS-01 hM P g e 17

/

5.0 REFERENCES

1.

MPR Report 1762, " Oyster Creek Nuclear Generating Station, Evaluations of the Upper Shroud Ledge and Shroud Vertical Welds," October 1996, Revision 0.

2.

MPR Report, " Oyster Creek Nuclear Generating Station, Core Shroud Repair, Design Report," October 1994, Revision 1 (Two Volumes).

3.

ASME Boiler and Pressure Vessel Code,Section III, Subsection NB,1989 Edition.

4.

MPR Calculation 083-224-03, " Required Intact Weld Length for Vertical Welds Based Upon a Limit Load Analysis," Revision 0.

5.

MPR Specification 083-9403-001, " Design Specification for Oyster Creek Nuclear Generating Station (OC) Core Shroud Repair," Revision 0.

6.

MPR Calculation 083-261-BRL-2, " Transient Dynamic Evaluation of OC Shroud v<ith Vertical Welds Failed," Revision 0.

7., MPR Calculation 083-205-13, " Tie Rod Assembly Loads for Recirculation Line Break," Revision 0.

8.

GE Drawing 105E1413B, " Oyster Creek, Shroud Data," Sheet 1, Revision 1.

9.

GPUN Letter E520-98-008 from A. Collado to P. Kasik (MPR), " Oyster Creek Core Shroud Vertical Welds Evaluation with Core Plate Wedges," Dated February 18,1998.

10. GPUN Drawing 3E-222-29-1002, " Reactor Vessel Shroud,16R Inspection Report,"

Revision 1, f

MPR As ocirt s,Inc.

320 King Stt:ct Alexandria, VA 22314 I

Calculation No.

Prepared By Ch ked By 083-248-CBS-01 Page A-1 bh l

1 l

l APPENDIX A MSLB + SSE Load Case With Only H5 and H6A Failed 1

l I

l l

MPR Associtt:s,Inc.

320 King Strnt Alexandria,VA 22314 Calculation No.

Prepared By ecked By Fage A-2 083-248-CBS-01 g

, [

A.1 PURPOSE The purpose of this appendix is to evaluate the effect of failed vertical welds in the H5/H6A shroud segment for the MSLB + SSE load case if only circumferential welds H5 and H6A are completely failed. This appendix accounts for the effect of the core plate wedges installed between the core plate and the shroud shell between H5 and H6A.

A.2 RESULTS If any ten inches of both vertical welds are intact, then the stresses in the H5/H6A shroud segment meet the requirements of the Subsection NB of the ASME Code during the MSLB + SSE load case.

l e

i

MPR Associates,Inc.

320 King Street Alexandria, VA 22314 Calculation No.

Prepared By C

ked By

/

083-248-CBS-01 g

Page A-3 A.3 FINITE ELEMENT MODEL The H5/H6A section of the Snite element model described in the main body of this calculation is used in this evaluation. The differences in loading and boundary conditions are described below:

During a MSLB, the differential pressure loads are sufficient to overcome the tie rod preload. If only welds H5 and H6A are failed, the shroud could potentially separate at both welds H5 and H6A. As a result, the assumption, used in the main body of the' calculation, that there is compression across failed circumferential welds is no longer valid. This condition is considered in this appendix by only modeling the shroud section between H5 and H6A. The shroud is given no constraint at the failed welds.

Because there is no longer compression across the failed circumferential welds, some portion of each vertical weld has to be intact to react the hoop load in the shroud due to pressure. Ten inches of weld ligament at the top of each vertical weld is assumed to be intact. (Note that the weld ligament is assumed to be at the top because this results in the highest bending stresses in the weld ligament from the seismic bumper load.)

Loads are applied to the model in the same way as described in the main body of this calculation. One case is run with the MSLB differential pressure of 19.0 psi. Another case is run with a seismic fuelload of 40 kips. The bumper load is also 40 kips because the horizontal welds are not capable of carrying shear and will not transfer an additional lateral load through the shroud sections to the bumper. Stresses are combined by direct summation.

The ANSYS runs have been performed with the following key stress results. The maximum membrane plus bending stress at the bumper contact is 52 ksi compared to an allowable stress of 60 ksi. The maximum membrane stress in the intact vertical weld is about 7 ksi compared to an allowable stress of 40 ksi, and the maximum membrane plus bending stress in the shroud section is 28 ksi compared to an allowable stress of 60 ksi.

The stress contour for the evaluation is shown in Figure A-1. The ANSYS analyses are documented References A-1 and A-2.

A.4 REFERENCES l

A-1.

ANSYS Output File " press 8.out", 7/10/98,10:13.

A-2.

ANSYS Output File "slbsse8a.out",7/10/98,08:57.

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9 O9 1838375319753 5

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1151511223445 S11 L=

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MPR Associtt s,Inc.

MMP 320 King Street Alexandria, VA 22314 Calculation No.

Prepared By C eked By 083-248-CBS-01 Page B-1 S&

'^' : =

/

APPENDIX B Leakage Path Flow Area During Normal Operation i

l 1

l l

I 4

l I

L______-_________________

____-.__-j

WMPR TA"erstfr

Alexandria, VA 22314 Calculation No.

Prepared By

. eked By 083-248-CBS-01 Page B-2 0%

+-

,n

~~

~

B.1 PURPOSE The purpose of this appendix is to determine the maximum leakage path flow area through a Dawed vertical weld during normal operation. This appendix accounts for the effect of the core plate wedges installed between the core plate and the shroud shell between H5 and H6A.

B.2 RESULTS The leakage path Dow area during normal operating conditions through a single, fully-cracked vertical weld in the H5/H6A shroud segment is 0.495 in,

z 1

I J

l l

l

?

l l

MPR Assoclita,Inc, M M P.

320 King Street Alexandria, VA 22314 I

l Calculation No.

Prepared By C

eked By 083-248-CBS-01 Page B-3 6

A_.. _ _,

[

B.3 CALCULATION The maximum leakage path flow area through a flawed vertical weld in the H5/H6A shroud segment is determined using the finite element model developed in this calculation. As in Section 3, the vertical weld is assumed to be completely cracked. During normal operating conditions, the only load that opens the cracked weld is differential pressure. The normal l

operating differential pressure is 4.34 psi (Reference 5). With this load, using the same boundary conditions as in Section 3 (except that the core support ring is assumed to be intact), the finite element model is re-solved to examine the displaced shape at the crack.

The totalleakage path Dow area can be determined by examining the circumferential displacement of selected nodes relative to the corresponding nodes on the opposite side of the crack face. The trapezoidal flow area between the nodes is determined using the following formula:

A (Z.i - Z ) [ (UY st i - UYurs ;) + (UY u ht i+i - Wuri,i+1) U 2

=

i i

i is Where:

Flow area between the ich and (i+1)* nodes (in )

2 A;

=

Z Distance along verticalweld (in)

=

UYur, Circumferential displacement of node on left crack face (in)

=

UY%3, Circumferential displacement of node on right crack face (in) j

=

The totalleakage path Dow area is the sum of the individual flow areas between adjacent nodes. The calculation is summarized in Table B-1. The ANSYS analysis is documented in Reference B-1.

B.4 REFERENCES 1

B-1.

ANSYS Output File " press 1.out",5/22/98,12:53.

1 l

MPR As:oci;tm,Inc.

l A ex ndri, VA 22314 Calculation,No.

Prepared By Ch ked By Page B-4 1

083-248-CBS-01 WW JAin=

Table B-1. Total Leaka h Flow Area Left Crack Face Right Crack Face Z (in) 2 Flow Area (in )

Node Number UYun (in)

Node Number UYa;g (in) 0.00 17732 0.00004 17732

-0.00004 l

4.00 17734

-0.00008 17734

-0.00008 0.000 7.00 17751

-0.00125 17851 0.00120 0.004 10.87 17796

-0.00233 17939 0.00229 0.014 14.16 17795

-0.00318 17938 0.00316 0.018 16.95 17794

-0.00383 17937 0.00382 0.020 19.32 17793

-0.00432 17936 0.00433 0.019 21.34 17792

-0.00470 17935 0.00471 0.018 23.05 17791

-0.00498 17934 0.00500 0.017 24.50 17738

-0.00519 17833 0.00522 0.015

)

1 26.00 17742

-0.00539 17827 0.00542 0.016

)

l 27.44 17757

-0.00554 17865 0.00558 0.016 l

29.55 17758

-0.00573 17866 0.00577 0.024 32.64 17759

-0.00590 17867 0.00596 0.036 37.18 17760

-0.00592 17868 0.00599 0.054 43.85 17761

-0.00547 17869 0.00553 0.076 53.64 17762

-0.00391 17870 0.00402 0.093 68.00 17756 0.00004 17756

-0.00004 0.057 Total Leakage Path Flow Area:

0.495 L

l MPR Assoclitis,Inc.

320 King Strett Alexandria, VA 22314 Calculation No.

Prepared By C

eked By 083-248-CBS-01 Page C-1 W

-;4^% x

~

Appendix C ANSYS Input Files t

Ulf C bl A4 hrtek TyOlp h e, N k - 1d 6 b it%b l, 3 gd 1.~. a am a.m :t m. a'm uitn um 3-

.; t.,

r lM

. i.

6ttp.J.-(e..pjjl}$,

,,.p e

/ batch, list

/filnam,recsse8a

/ title,0yster Creek Shroud Vertical Weld Evaluation

/psearch,/do/blane/ wedges /

/ prep 7 fapplied=40000

! applied load from core (1bs) flateral=34000+41300 t lateral load from shroud (1bs) thf=165 I angle of applied load thbo=75 t 1/2 angle over which bumpers participate thw0=100 1 1/2 angle over which wedges participate hintact1=.1 I intact length at bottom of weld hintact2=.1 I intact length at top of weld mod 146b8 fresume, mesh,db,/dO/blane/ wedges /

mp,ex,1,25.4e6 inp, nuxy,1,0. 3 mp, dens,1,0.29 mp,ex,2,25.4e6 mp,nuxy,2,0.3 mp, dens,2,0.001 bnds46b fini

/ solu antype, static solve aave l

\\

i l

l L

1

H 4 - t% b encd.1, f x M4l/) kaN btAA bMk N Vc4 kO(-

. m..,...o. m.. - ;se.y m o m,s h

4e-(9.h-(99HpHj.'

M., M ( :..e

/ batch, list

/filnam,sibsseBa

/ title,0yster Creek $hroud Vertical Weld Evaluation

/psearch,/dO/blane/ wedges /

/ prep 7 fapplied=40000 t applied load from core (1bs) flateral=34000 1 lateral load from shroud (1bs) _

thf=165 I angle of applied load thb0=75

! 1/2 angle over which bumpers participate thw0=180 l 1/2 angle over which wedges participate hintact1=.1

! intact length at bottom of weld hintact2=.1 I intact length at top of weld mod 146b8 f resume, mesh, db, /dO/blane/ wedges /

mp, ex,1,2 5. 4 e 6 mp, nuxy,1,0. 3 mp, dens,1,0.29 mp,ex,2,25.4e6 mp,nuxy,2,0.3 mp, dens,2, 0. 001 bnds46b fini

/ solu ant ype, static solve save e

l I

Mn Skam L,u-Gma k Svddoo, H S-Hr6e model,3 u dcycm y.;, a i,;.. ss, 0,m,mxm a us.uy, m.,

Mi]6G.. 'n 4) ilu.jr 10 tlf ilji; I

/ batch, list

(

/filnam,sibsse8a r

/ title,0yster Creek Shroud Vertical Weld Evaluation l

/psearch,/dO/blane/ wedges /

l

/ prep 7 i

i fapplied=40000 t applied Icad from core (1bs)

I flateral=0 t lateral load from shroud (1bs) l thf=165 t angle of applied load thb0=75 1 1/2 angle over which bumpers participate thwo=180 t 1/2 angle over which wedges participate hintact1=.1 1 intact length at bottom of weld hintact2=10 t intact length at top of weld mod 156a8

! resume, mesh,db,/dO/blane/ wedges /

I mp,ex,1,25.4e6 mp,nuxy,1,0.3 mp, dens,1,O.29 l

i beds $6a 1

fini l

/ solu antype, static solve save e

l l

l t

l I

r

inSema \\ pn:ssort eva \\ued,as, (54-t% 6 m od.al, 9 map 1*G M ) Y/C J pi Vit ht. W:hIj lmhiy -

8 RHiU 1 kb 4th ji 'l'; dd43)

/ batch, list

/filnam, press 8

/ title,0yster Creek Shroud Vertical Weld Evaluation

/psearch,/dO/blane/ wedges /

/ prep 7 thf=165 thb0=75 thw0=180

~

hintact1= 1 I intact length at bottom of weld hintact2= 1

! intact length at top of weld mod 146b8 1 resume, mesh,db,/dO/blane/ wedges /

mp, ex,1,2 5. 4 e 6 mp,nuxy,1,0.3 mp, dens,1,0.29 mp,ex,2,25.4e6 mp,nuxy,2,0.3 mp, dens,2,0.0.01 pres 46 fini

/ solu antype,atatic csys,1 I dp=4.34 cmsel,s, shroud asly Isla 1sel,r, loc,x,rl.01,rl+.01 as11,s,1 sfa,all,, pres,4.34 allsel csys,0 solve csys,1 t dp=19.0 cmsel,s, shroud asiv Isla j

1sel,r, loc,x,rl.01,rl+.01 as11,s,1 l

sfa,all,, pres,19.0 allsel csys,0 solve save 1

1 l

l I

1 1

1

l i

/ batch;11st

/filnam, press 8

/ title,0yster Creek Shroud Vertical weld Evaluation

/psearch,/do/blane/ wedges /

/ prep?

l thf=165 l

thbo=75 thw0=180 i

hintact1=.1 i intact length at bottom of weld l

hintact2=10 t intact length at top of weld mod 156a8

! resume, mesh,db,/dO/blane/ wedges /

mp,ex,1,25.4e6 mp,nuxy,1,0.3 mp, dens,1,0.29 prss56a fini

/ solu antype, static

!csys,1 1 dp=4.34 1cmsel,s, shroud las1v 11sla 11sel,r, loc,x,rl.01,rl+.01

!asil,s,1 l

I Isfa,all,, pres,4.34

!allsel i

! solve csys,1 i dp=19.0 cmsel,s, shroud l

asiv isla l

1sel,r, loc,x,r1.01,r1+.01 I

as11,s,1 I

sfa,all,, pres,19,0 1

1 allsel csys,0 solve save i

i l

i I

i l

l

I oyster creek shroud (h4 to h6b)

/ prep 7

• afun,deg i shroud dimensions r1=176/2 I ID r2=rl+1.5 1 CD r3=r2-8.75 t tD of core support ring z6b=0 t h68 weld elevation 26a= 6b+4

! h6A weld e?evation z5=t6a+64

? h5 weld elevation z4-z5+B9.875 t h4 weld elevation thl=164 1 vertical weld 1 th2=345 1 vertical' weld 2 I bumper dimensions zblaz6b I bottom of lower bumper zb2=z6a+3

! top of lower bumper dbw=2 I width of bumper drb=4 I radial thickness thbw=2

• a sin (dbw/ (2

• r2 ) ) I angular width of cumper nbumpers=7 I number of bumpers

• dim,thb, array,nbumpers ! bumper angular locations thb(1)=10,70,100,160 thb(5)=220,280,310 t wedge dimensions zwl=z6a+20.5 I bottom of wedge zw2=z6a+22 f top of wedge dww=4 I width of wedge drw=2.4 1 radial thickness thww=2*asin(dww/(2*rl)) ! angular wid*h of wedge nwedges=8 t number of wedges

• dim,thw, array,nwedges t wedge angular locations thw(1)=24-thww/2,60+thww/2,96-thww/2,172+thww/2 thw(5)=204+thww/2,240-thww/2,276+thww/2,312-thww/2 I

Geometry wprota,0,90.

rectng,rl,r2,z6a,z5 rectng,rl,r2,z6a,zb2 rectng,rl,r2,zwl,zw2

• 1f,hintactl,gt,0,then rectng,rl,r2,z6a,36a+hintacti

• endif

• if,hintact2,gt,0,then rectng,ri,r2,z$-hintact2,z5

• endif movlap,all rectng,rl,r2,z5,24 cectng,r3,r2,z6b,z6a wpstyl,defa numemp,all theurr=0 windx=1 bindx=1

• dim,thbl, array,nbumpers*2+1

• dim,thwl, array,nwedges*2+1

• do,ii,1,nbumpers,1 thb1(2*ii-1)=thbtiil-thbw/2 thb1 (2 *ii) =thb (ii) +thbw/2

• enddo

• do,ii,1,nwedges,1 thwl(2*ii-1)=thw(ii)-thww/2 thwl(2*ii)=thw(ii)+thww/2

• enddo thb1(2*nbumpers+1)=1000 thwl(2*nwedges+11=1000 k,1000,0,0,z6a k,1001,0,0,25 i

l

!L__-_-______-___-_-___-__

Wei, H 1 Ry M i ; U '. N. f.U.1. J,. qqp hi,i( ;. - a 4; ob.). In 4 pp :6fl.3 local',11,1,0,0, 0, 0,18 0, 0 esys,11

• do,11,1,2*(nbumpers+nwedges),1

• 1f, thbl (bindx),1t, thwl (windx), then asel, s, loc, y, thcurr.. 01, theurr+.01

• if,thb1(bindx)-theurr,gt,5,then vrotat,all,,,,,,1001,1000,thb1(bindx)-theurr,2

• else vrotat,all,,,,,,1001,1000,thb1(bindx)-thcurr,1

• endif theurr=thb1(bindx) bindx=bindx+1

• else asel, s, loc, y, theurr.01, theurr+. 01

• if,thwl(windx)-theurr,gt,5,then vrotat,all,,,,,, 1001,1000,thwl(windx)-theurr,2

• else vrotat,all,,,,,,1001,1000,thwl(windx)-theurr,1

• endif theurr=thwl (windx) windx=windx+1

• endif

• enddo asel,s, loc,y,theurr.01,theurr+.01 vrotat,all,,,,,, 1001,1000,360-theurr,2 csys,0 vsel,s, loc,z,z6b,z(a asiv i

1sla ksil nummrg,kp vsel, s, loc, z, z 6a,25 asiv Isla ksil nummrg,kp vsel,s, loc,z,z5,ze asiv Isla ksil numarg,kp numcmp,all I

cut the shroud at the vertical welds wpstyl,defa wprota,-thl,90 esys,11 vsel,s,1ce,y,th1-10,thl+10 vsbw,all,sepo l

wpstyl,defa i

wprota,-th2,90 l

vsel,s, loc,y,th2-30,th2+10 vsbw,all,sepo wpsty1.defa

! join shroud at the vertical welds as appropriate l

csys,11

~~'

"'a l

vsel, s, loc,z -z5,-z6a i

asel,s, loc,y,thi l

asel,a, loc,y,th2 i

asiv,r w

Isla 1sel,r, loc,z,-z6a+.01,-(26a+hintactl) as11,s,1 ks11 nummrg,kp asel,s, loc,y,thi asel,a, loc,y,th2 asiv,r Isla 1sel,r, loc,z,-(zS-hintact2),-z5.01 as11,s,1 ks11 nummrg,kp

• 1f.hintactl,ge,0,then vsel s,1?c, z,-z6b,-z6a asel,s, loc,y,thi asel,a, loc,y,th2

JE*is i(] \\'V MJ. i Pet lib gDF) '.!: hire y (,,

h1al1 J W Y h (6 ?l*ll':[k};

asiv,r Isla ks11 nummrg,kp

• endif vsel,s, loc,2,-ze,-z5 asel,s, loc,y,thi asel,a, loc,y,th2 asiv,r Isla ks11 nummrg,kp

! join shroud at horizontal welds as appropriate csys,1 vsel none asel,none

• 1f hintact1,1t,0,then 1sel,s, loc,x,r2.01,r2+.01 1sel,r, loc,y,-thi,-th2 1sel,r, loc,z,z6a ks11 nummrg,kp 1sel.inve 1sel,r, loc,x,r2.01,r2+.01 1sel,r, loc,z,z6a kc11 nummrg, kp

• else 1sel,s, loc,x,r2.01,r2+.01 1sel,r, loc,z,z6a ks11 nummrg,kp

• endif 1sel,s, loc,x,r2.01,r2+.01 1sel,r, loc,z,zS ks* 1 nege g, kp csys,0 l

allsel cm. shroud,volu 1

Mesh et,1,so11d45 type,1 eshape,2 csys,1 vsel,s, loc,z,z6a,z5 asiv Isla 1sel,r, loc,x,rl+.01,r2.01 lesize,all,,,4 l

vsel,s, loc,z,z5,z4 asiv Isla 1sel,r, loc,x,rl+.01,r2.01 lesize,all,,,1 allsel l

csys,1 ksel,all kesize,all,15 ksel,s, loc,z,2wl.1,zw2+.1 kosize,all,1.5 ksel,s, loc,1,zbl.1,zb2+.1 kesize,all,4 1sel,s, loc,z,zb2+.1,zwl.1 isel,a, loc,z,zw2+.1,z5.1 lesize,all csys,11 L11sel kesize,all,8 ksel,s, loc,y,thf-thwo,thf+thwo f

kesize,all,4

'do,ii,1,nwedges,1

8)Meit d 1.C 'i '.f.(

V '. M.lifi r.;.P_. Q.h 1 J.

AihM M@ NN $ 9.ti.dijnd10 a ;,;

4 vsel,s, loc,y,thd(ii)-thww/2,thw(ii)+thww/2 vsel,r, loc,z,-zwl,-zw2 vsel,r, loc,y,bhf-thw0,thf+thw0 l

asiv Isla ks11 kesize,all,1.5

• enddo csys,1 ksel,s, loc,z,25-1,z4+.1 kesize,all,15 411sel csys,1 allsel vse),s, loc,z,z6b,z5 mat,1 vmesh,all vsel,s, loc,z,z5,zt mat,2 vmesh,all 1

add the wedges vsel,none wpstyl,defa wprota,0,180,0 1

• do,ii,1,nwedges,1 cylind,rl-drw,rl,-zwl,-zw2,thw(ii)-thww/2 thw(ii)+thww/2

• enddo i

wpstyl,defa l

cm. wedges,volu csys,0 allsel add the bumpers vsel,none wpstyi.defa wprota,0,180,0

• do,ii,1,nbumpers,1 cylinde r2, r2+dtb,-zbl,-zb2, thb (ii)-thbw/2, thb (ii) +thbw/2

• enddo wpstyl,defa cm, bumpers,volu csys,0 allsel esize,2 vmesh,all allsel i

csys,0 l

l i

i l

1

b fot%#-

w H 5 - H 6 c.

mo da t (.~ 4 7 x dp

• )$eff H 1.GM).1 P 5hi f FpMilRif1ht.i -

.; ' ?.

' ce !.3 l

hDi{li j yL9.h. l' 'lth YUJ

.. O r.-

j k

oyster creek shroud (h5 to h6a) j 1

/ prep 7

• afun,deg 1 shroud dimensions rl=176/2 t 1D r2=rl+1.5 1 00 26a=0 t h6A weld elevation 25-z6a+64 I h5 weld elevation thl=164 I vertical weld 1 th2=345

! vertical weld 2 I bumper dimensions zb2=3 1 top cf bumper elevation dbw=2 t width of bumper drb=4 i radial thickness thbw=2*asin(dbw/(2*r2)) I angular width of bumper nbumpers=7 1 number of bumpers

• dim,thb, array,nbumpers I bumper angular locations thb(1)=10,70,100,160 thb(5)=220,280,310 1 wedge dimensions zwl=20.5 t bottom of wedge elevation zw2=22 i top of wedge elevation dww=4

! width of wedge drw=2.4 1 radial thickness thww=2*asin(dww/(2*rl)) I angular width of wedge nwedges=8' t number of wedges

• dim,thw, array,nwedges I wedge angular locations thw(1)=24-thww/2,60+thww/2,96-thww/2,132+thww/2 thw(5)=204+thww/2,240-thww/2,276+thww/2,312-thww/2 Geometry wprota,0.90 rectng,rl,r2,z6a,25 rectng,rl,r2,z6a,zb2 rectng,rl,r2,zwl,zw2

• if,hintact1,gt,0,then rectng,rl,r2,z6a,z6a+hintacti

• endif

• if hintact2,gt,0,then

)

l rectng,rl,r2,z5-hintact2,z5 j

• endif f

wpstyl,defa movlap,all numemp,all thcurr=0 windx=1 i

bindx=1 1

• dim,thbl. array,nbumpers*2+1 I

• dim,thwl, array,nwedges*2+1 I

• do,ii,1,nbumpers,1 thb1 (2 *ii-1) =thb (iil -thbw/2 thb1 (2*ii) =thb (ii) + thbw/2

• enddo l

• do,ii,1,nwedges,1 j

J l

thwl(2*ii-1) =thw (ii) -thww/2 f

thwl(2*ii)=thw(ii)+thww/2

• enddo 4

thb1 (2 *nbumpers +1) =1000 thwl(2*nwedges+1)=1000 k,1000,0,0, z 6a k,1001,0,0,z5 local.11,1,0,0,0,0,180,0 7

l csys,11 l

'do, ii,1,2 * ( nbumpe rs+nwedges ),1 l

• 1 f, thb1 (bindx),1t, thwi t windx), then asel,s, loc,y,theurr.01,theurr+.01

• 1 f, thb1 (bindx) -theurr, gt,5, then l

l L___________

J

p%'s ii bG 1 f J JiMM VLIGlM.t].pgly y,,'

MS O h.i<1 Mi'Frk V W M]u

.,(..

vrotat,all,,,,,,1001,1000,thb1(bindx)-theure,2

• else vrotat,all,,,,,,1001,1000,thb1(bindx)-theuer,1

• endif theurr=thb1 (bindx) bindx=bindx+1

• else asel,s, loc,y,theurr.01,theurr+.01

• 1 f, thwl (windx ) -theurr, gt,5, then vrotat,a11,,,,,,1001,1000,thwl(windx)-theurr,2

• else vrotat,all,,,,,,1001,1000,thwl(windx)-theurr,1

• endif l

theurr=thwl(windx) windx=windx+1

• endif

• enddo asel,s, loc,y,theurr.01,theurr+.01 vrotat,all,,,,,,1001.1000,360-thcurr,2 csys,0 allsel nummrg,all numemp,all' cut the shroud at the vertical welds wpstyl,defa wprota,-thl,90 csys,11 vse;,s, loc,y,th1-10,thl+10 vsbw,all,sepo wpstyl,defa wprota,-th2,90 vsel,s, loc,y,th2-30,th2+10 vsbw,all,aepo wpstyl,defa

! join shroud at the vertical welds as appropriate csys,11 asel,s, loc,y,th1 asel,a, loc,y,th2' 1sla 1sel,r, loc,z,-z6:+.01,-(z6a+hintactl) as11,s,1 ks11 nummrg,kp as el, s, loc, y, th1 asel,a, loc,y,th2 1sla 1sel,r, loc,z,-(z5-hintact2),-15.01 as11,s,1 ks11 nummrg,kp csys,0 l

allsel wpstyl,defa cm, shroud,volu Mesh et,1, solid 45 type,1 eshape,2 ksel,all csys,11 vsel,s, loc,y,thf-thw0,th!+thw0 kesize,all,4 ksel,inve kesize,all,8

• do,ii,1,nwedges,1 vsel,s, loc,y,thw(ii)-thww/2,thw(ii)+thww/2 l

vsel,r, loc,z,-zwl,-zw2

)

vsel,r loc,y,thf-thwo,tht+thw0 I

asiv l

1sla ksil

)

D.$yH 1.C4 CfJiP'l 1'14Tu@ ; l#6Ur T,'..

pi.,

751 0 tj W F M,, it*.Fj!Kf;T $

, ' ;'a kesize, all,1. 5 j

• enddo

)

es ys,1 l

la el, s, loc, x, r1+.01, r2.01 I

les ize, all,,,4 l

allsel mat,1 vmesh,all 1

add the wedges I

vsel,none wpstyl,de f a l

wprota,0,18 0,0 l

• do,11,1, nwedge s,1 I

cylind, rl-drw, rl,-zwl, -zw2, thw (ii) -thww/2, thw (ii) +thww/2

• enddo wps tyl,de f a cm, wedges, volu csys,0 allsel 1

add the bumpers vs el, none wpsty1.def a wp rota,0,18 0,0

• do,11,1, nbtunpe rs,1 cylind, r2, r2+drb,-z 6a, -zb2, thb (iil -thbw/2, thb t ii) + thbw/2

• enddo l

wpstyl,defa cm, bumpe rs, volu csys,0

{

allsel esize,2 vmesh,all 1

1

\\

f 4

i I

r I

I

(O A ' b 5 b kd b k kOcM (dits, H -H6 6 modtis l

l boundary condition macro

! couple wedges and shroud csys,11

'do,ii,1,nwedges,1 asel,s, loc,x,rl.01,rl+.01 l

asel,r, loc,y,thw(ii)-thww/2,thw(ii)+thww/2 asel,r, loc,z,-zwl,-zw2 nsla,s,1 epintf,all,.1

• enddo allsel l

csys,0 l

) couple bumpers and shroud csys,11

• do,ii,1,nbumpers,1 as el, s, loc, x, r2. 01, r2 +. 01 asel,r, loc,y,thb(ii)-thbw/2,thb(ii)+thbw/2 asel,r, loc,z,-zbi,-zb2 nsla,s,1 epintf,all,.1

• enddo allsel csys,0

! create rigid core plate and apply load

• get. nmax, node,, num, max n,nmax+1,0,0,(zwl+zw2)/2 et,2, mass 21 type,2 r,1,.01 real,1 e,nmax+1 csys,11 nsel none cm,ntmp, node

• do,ii,1,nwedges,1 nsel,all nsel, s, node,, node ( rl-drw, thw (ii), - ( zwi+ zw2 ) /2 )

cmsel,a,ntmp cm,ntmp,noce

'enddo nsel,a, node,,nmax+1 cerigid,nmax+1,all,uxyz csys,0 i

]

allsel d,nmax+1,uz,0 d,nmax+1,totx,O d,nmax+1,roty,0 f,nmax+1,fx,fapplied*cos(-thf)

)

f,nmax+1,fy,fapplied' sin (-th!)

l t apply constraint at lower bumpers csys,11 I

nsel,none

)

cm,ntmp, node

• do,ii,1,nbumpers,1 i

nsel,all nsel, s, node,, node ( r2+drb, thb (ii), -zbl/2 )

i l

cmsel,a,ntap

]

cm,ntmp,pode J

• enddo ns el, r, loc, y, thf-thb0, thf + thb0 cm,ntmp, node n1=nodetr2+ deb,thf,-zbl/2) t leading bumper nrotat.nl d,ni,ux,0 deltlead=. 375 /cos (thf-ny (n1) )

nsel,u, node,,n1 1 trailing bumpers cm,ntmp, node i

l

• get,nnum, node,, count n1=0 J

l l

sJC.orj a ;.cy :.J.; & 'it

.V.jity i @,dir a:.

MihiQ i dM b?.*h * 'j'J f 4 hc

• do,11,1,nnum,1 n1=ndnext(n1) protat nl I

d, ni, ux,. 37 5-deltlead*cos ( thf-ny tni) )

d,n1,ux,0

• enddo esys,0 allsel 1 apply constraint at intermediate bumpers

• 1 f, s kip, eq,1, then

• dim, thbmid, array,3 thbmid (1) =100,22 0,350 csys,11

• do,ii,1,3,1 nsel, s, loc, x, r2.01, r2+. 01 ns el, r, ) oc, y, thbmid t iil -thbw/2, thbmid t ii) +thbw/2 nsel, r, loc, z, -z5 nsel,r, loc,y,thf-thb0,thf+thb0 n ctat,all d,all,ux,0 nsel, s, loc, x, r2.01, r2+. 01 ns el, r, loc, y, thbmid (iil -thbw/2, thbmid (ii) +thbw/2 nsel, r, loc, z, -z 4 ns e l, r, loc, y, thf-thb0, thf + thb0 I

nrotat,all d,all,ux,0

• enddo allsel csys,0

• endif

^

! apply additional lateral load as an acceleration l

I cmsel,s, shroud l

vsel,r, loc,s,t6b,z5 l

vs u.m

• ge t, voltot, volu,, volu

• get,voldens, dens,1 mass 1=voltet*voldens vsel,inve vsum

• ge t, volto t, volu,, volu

• get,voldens, dens,2 mass 2=voltot*voldens l '

accel-flateral/ (massl+ mass 2) acel,-accel *cos (-thf),-accel' sin (-thf),0 esys,0 allsel k

j bd Condsh m E br ((Jbok (CKd CG M N $ ~ b ba //MO b

.w.o g m s.o u.3, m,.o.a m.

@. v. :r 1 M..h b;. ELV ilij bouncary condition macro

'! couple wedges and shroud csys,11

'do,ii,1,nwedges,1 asel,s, loc,x,rl.01,r1+.01 l

as el, r, loc, y, thw (111 -thww/2, thw (ii) + thww/2 asel,r, loc,z,-zwl,-zw2 nala,s,1 epintf,all,.1 i

• enddo I

allsel csys,0 t couple bumpers and shroud csys,11

• do,ii,1,nbumpees,1 asel,s, loc,x,r2.01,r2+.01 asel,r, loc,y,thb(ii)-thbw/2,thb(ii)+thbw/2 asel,r, loc,z,-zbl,-ze2 nsla,s,1 epintf,all,.1

• enddo allsel csys,0 I create rigid core plate and apply load

• get,nmax, node,,num, max n, nmax+1,0,0, (zwl+ zw2 ) /2 et,2, mass 21 type,2 r,1. 01 real,1 e,nmax+1 csys,11 nsel,none cm,ntmp, node

• do,ii,1,nwedges,1 nsel,all nsel, s, node,, node ( rl-drw, thw (ii), - ( zwi+ zw2 ) /2 )

emsel,a,ntmp cm,ntmp, node

'enddo nsel,a, node,,nmax+1 cerigid,nmax+1,all,uxyz csys,0 allsel d,nmax+1,ut,0 d,nmax+1,rotx,O d,nmax+1,roty,0 f, nmax+1, fx, f applied *cos (-thf) f,ncax+1,fy,fapplied* sin (-thf) t apply constraint at lower bumpers csys,11 nsel,none cm,ntmp, node

'do,ii,1,nbumpers,1 nsel,all ns el, s, node,, node ( r2+drb, thb (ii), -zbl /2 )

emsel,a,ntmp cm,ntmp, node

• enddo nsel,r, loc,y,thf-thb0,thf+thb0 cm,ntmp, node n1= node (r2+ deb,thf,-61/2)

! leading bumper nrotat,n1 d,nl,ux,O deltlead=.375/cos(thf-ny(n1))

nsel,u, node,,n1

! trailing bumpers em,ntmp, node l

• get,nnum, node,, count n1=0

MVp 10,V1 & L1 P M tU l.MIM. hull +

E J?<

' ~ '

',.diMPF MM& 'I'/ d!1kilM

,?1MI. ", a.,

• do,11,1,nnum,1 nl=ndnext(nl) nrotat,n1

! d,ni,ux,.375-deltlead*cos(thf-ny(n1))

d,nl,ux,0

• enddo csys,0 allsel

! apply constraint at intermediate bumpers

• if, skip,eq,1,then~

• dim,thbmid, array,3 thbmid (1) =100,220,350 csys,11

• do,ii,1,3,1 nsel,s, loc,x,r2.01,r2+.01 nsel,r, loc,y,thbmid(ii)-thbw/2,thbmid(ii)+thbw/2 nsel,r, loc,z,-z5 nsel,r, loc,y,thf-thb0,thf+thb0 nrotat,all d,all,ux,0 nsel,s, loc,x,r2,01,r2+.01 4

nsel,r, loc,y,thbmid(ii)-thbw/2,thbmid(ii)+thbw/2 j

nsel,r, loc,z,-zt nsel,r, loc,y,thf-thb0,thf+thb0

)

nrotat,all d,all,ux,0 i

• enddo j

.allsel 1

csys,0

• endif t apply additional lateral load a. an acceleration casel,s, shroud vsel,r, loc,z,26a,25 vsum

• get,voltot,volu,,volu

• get,voldens, dens,1 mass 1=voltot*voldens accel =flateral/massi acel,-accel

• cost-thf),-accel

• sin (-thf),0 csys,0 allsel l

f I

i i

i

Younawy condkuc (or passure eva L& hon, {44 -QG m Q gejj 9, y.g ;.. ; i,. t,;.1.y.;, ; j.., g y Ni dLiir.if i 4M sjt 'l's ml! M k

,I

i I

11 boundary condition macro for applied pressure case I couple wedges and shroud csys,11

• do,ii,1,nwedges,1 asel, s, loc, x, rl.01, r1+. 01 as el, r, loc, y, thw (ii) -thww/2, thw (ii) +thww/ 2 asel,r, loc,z,-zwl,-zw2 nsla,s,1 epintt,all, 1

• enddo allsel csys,0

!. couple bumpers and shroud csys,11

• do,ii,1,nbumpers,1 asel,s, loc,x,r2.01,r2+.01 a sel, r, loc, y, thb t ii) -thbw/2, thb (ii) + thbw/2 asel,r, loc,z,-zbl,-zb2 nala,s,1 epintf,all,.1

• enddo allsel csys,0 I restrain vertically at h4 csys,0 asel,s, loc,z,z4 nsia,s,1 d,all,uz,0 allsel I

! restrain circumferential1y and radially at h4 csys,11 nn1= node (rl,thl,-24),

nn2= node (rl,th2,-zt),

nsel,s. node,,nni i

nsel,a, node,,nn2 nrotat,all i

d,all,uy,all allsel d,nn2,ux,all I

! add dummy node for adding loadcases l

allsel t

• get,nmax, node,,num, max n,nmax+1,0,0,0 et,2, mass 21 type,2 l

r,1,.bul real,1 e,nmax+1 ep, next, all, nmax+1, node (rl,0,0) csys,0 allsel

I pressure boundary condition macro I couple wedges and shroud csys,11

• do,ii,1,nwedges,1 asel,s, loc,x,rl.01,rl+.01 asel,r, loc,y,thw(iil-thww/2,thw(ii)+thww/2

~

asel,r, loc,z,-zwl,-zw2 nsla,s,1 epintf,all,.1

• enddo allsel csys,0 t couple bumpers and shroud esys,11

• do,ii,1,nbumpers,1 asel,s, loc,x,r2.01,r2+.01 asel,r, loc,y,thb(ii)-thbw/2,thb(ii)+thbw/2 asel,r, loc,z,-z6a,-zb2 nala,s,1 epintf,all,.1

• enddo allsel csys,0

• if, skip,eq,1,then I apply constraint at lower bumpers csys,11 nsel,none em,ntmp, node

• do,ii,1,nbumpers,1 nsel,all nsel,s, node,, node (r2+drb,thb(ii),-z6a/2) emsel,a,ntmp em,ntmp, node

• enddo nsel,r, loc,y,thf-thb0,thf+thb0 cm,ntmp, node n1= node (r2+ deb,thf,-z6a/2)

! leading bumper nrotat,n1 d,ni,ux,0 l

deltlead=.375/cos(thf-ny(n11) nsel,u, node,,n1 f trailing bumpers em,ntmp,noce

• get,nnum, node,, count n1=0

• do,ii,1,nnum,1 n1=ndnext(ni) nrotat,n1

! d,ni,ux,.375-Jeltlead*cos(thf-nytni))

d,ni,ux,0 l

• enddo csys,0 allsel I apply constraint at intermediate bumpers

• dim,thbmid, array,3 thbmid(1)=100,220,350 csys,11 i

l

• do,ii,1,3,1 nsel,s, loc,x,r2.01,r2+.01 r.s el, r, loc, y, thbmid (ii) -thbw/2, thbmid (ii) +thbw/2 nsel,r, loc,z,-z5 nsel, r, loc, y, thf.-thbO, thf +thb0 nrotat,all d,all,all,0

• enddo

• endif 1 displacement constraints csys,1 nsel,s, loc,z,z5.1,z$+.1 nrotat,all d,all,uy,0

syteif j(1.sli:.{. j pilagig )}pi41-M pigJJ3 fil0<. :io t hih je $ 'Juhlik d, all,'uz,0 l add dummy node

• and mass element for adding load cases allsel

• ge t, raa x, node,, num, ma x n, raax+1,0,0, (zwl+ w2) /2 et,2, mas s 21 t ype,2 1

r,1,.01 1

real,1 e, nmax+1 cp, next, all, nmax+1, node ( el,0,0) allsel csys,0 e

9 L_____

- - - - - - - -