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Summary of 871124 Meeting W/Util & Holtec in Bethesda,Md Re Reracking of Spent Fuel Pool.Meeting Agenda & List of Attendees Encl
	ML17221A548
Person / Time
Site:	Saint Lucie
Issue date:	12/09/1987
From:	Tourigny E; Office of Nuclear Reactor Regulation
To:	; Office of Nuclear Reactor Regulation
References
	TAC-65587, NUDOCS 8712210108
	Download: ML17221A548 (75)
	v • d • e

December 9,

1987 Docket No. 50-335 DISTRIBUTION NRC 8 Local PDRs LICENSEE: Florida Power and Light Company (FP8L)

PD22 Reading H. Berkow FACILITY: St. Lucie Plant, Unit No.

1 E. Tourigny D. Miller

SUBJECT:

SUMMARY

OF'OVEMBER 24, 1987 MEETING BETWEEN OGC-Bethesda FP8L AND NRC STAFF REGARDING THE RERACKING E. Jordan OF THE SPENT FUEL POOL (TAC NO. 65587)

J. Partlow ACRS

( 10)

INTRODUCTION B. Troskosk i J. Ridgely H. Ashar The NRC staff met with FP8L personnel,'on November 24, 1987 in Bethesda, Maryland to discuss the licensee's proposal to rerack the spent fuel pool.

The licensee and the staff had their consultants present.

The scope of the meeting focused on the questions that were sent to the licensee.

Enclosure 1

identifies the meeting attendees.

Enclosure 2 provides the questions that were discussed.

SUMMARY

The licensee provided to the staff a draft of their answers to the structural questions.

The draft document is provided as Enclosure 3.

In regard to Enclosure 3, the licensee requested the following disclaimer:

"The enclosed draft responses to questions on the FP8L rerack proposal were provided by FP8L as a basis for discussion with the staff in this meeting.

FP8L pointed out that these are draft proposed responses and that they have not completed de-tailed technical and management review.

As a result, FP8L stated that they do not represent FP8L's docketed responses to these questions."

The staff felt that the draft structural answers were adequate in some cases, but that additional information should be provided in other cases.

The licensee did not have available a draft of their answers to the plant sys-tem questions.

However, the licensee's representatives discussed how they planned to answer each question.

The licensee plans to submit the final answers to the questions in the next few weeks.

Enclosures:

As stated cc w/enclosur es:

See next page E.

G. Tourigny, Project Manager Project Directorate II-2 Division of Reactor Projects-I/II L

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Mr. C. 0. Woody Florida Power 5 Light Company St. Lucie Plant CC:

Mr. Jack Shreve Office of the Public Counsel Room 4, Holland Building Tallahassee, Florida 32304 Resident Inspector c/o U.S.

NRC 7585 S.

Hwy AlA Jensen Beach, Florida 34957 State Planning 8 Development Clearinghouse Office of Planning 5 Budget Executive Office of the Governor The Capitol Building Tallahassee, Florida 32301 Harold F. Reis, Esq.

Newman

& Holtzinger 1615 L Street, N.W.

Washington, DC 20036 John T. Butler, Esq.

Steel, Hector and Davis 4000 Southeast Financial Center Miami, Florida 33131-2398 Administrator Department of Envir onmental Regulation Power Plant Siting Section State of Florida 2600 Blair Stone Road Tallahassee, Flor ida 32301 Mr. Weldon B. Lewis, County Administrator St. Lucie County 2300 Virginia Avenue, Room 104 Fort Pierce, Florida 33450 Mr. Charles B. Brinkman, Manager Washington - Nuclear Operations Combustion Engineering, Inc.

7910 Woodmont Avenue

Bethesda, Maryland 20814 Jacob Daniel Nash Office of Radiation",Control Department of Health and Rehabi litative Services 1317 Winewood Blvd.

Tal lahassee, Florida 32399-0700 Regional Administrator, Region II U.S. Nuclear Regulatory Commission Executive Director for Operations 101 Marietta Street N.W., Suite 2900 Atlanta, Georgia 30323

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NRC/FPAL MEETING ST.

LUCIE PLANT, UNIT NO.

1 SPENT FUEL POOL EXPANSION NOVEMBER 24, 1987 ENCLOSURE 1

E. G. Tourigny J.

N. Ridgely H. Ashar G. DeGrassi M. R. Bloor T. J.

Vogan M. A. MacLeod M. F. Brannen E. J. Meinkam A. Soler AFFILIATION NRC PM for St. Lucie Plant NRC/NRR/DEST/PSB NRC/NRR/DEST/SGB NRC/BNL

'FPKL/Power Plant Engineer FPAL/Power Plant Engineer, Project Manager FP8L/Power Plant Engineer FPKL/Power Plant Engineer FPAL/Nuclear Licensing Holtec

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I ENCLOSURE 2 MEETING AGENDA - Pg.

1 of 2 PLANT SYSTEMS QUESTIONS 1.

Answer question 7, part 3 of the 7/16/87 RAI, especially related to the safety factors.

2.

Provide the results of the faflure of the temporary crane's hook, assuming that it is lifting the heaviest rack at the maximum carrying height.

3.

Provide the stress levels in the temporary crane when the heaviest rack is dropped onto ft from the maximum carrying height associated with the cask handling crane.

{Ifthe cask handling crane is single-failure proof, then dropped means the maxfmum possible lowering velocity associated with the cask handling crane).

I'.

Does Figure 1 {September 8, 1987 submittal) represent the locations occu-pied by the spent fuel before the temporary crane fs installed?

5.

Provfde the results of a light load drop analysis which includes a list of the objects considered, their weight and their maximum carrying height, as well as the same information related to the referenced load.

As an alter-native, provide a discussion of the effects of having the new racks on a previously approved light load drop analysis.

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MEETING AGENDA - Pg.

2 of 2 STRUCTURAL QUESTIONS 2.

,~

Provide the results of the multi-rack seismic analysis for racks (modules) Al, A2, Bl, and B2.

Explain how the increased load of the spent fuel pool due to the re-racking changes the safety laargin on the liquefaction 'potential of the soils beneath the fuel handling building?

3.

Demonstrate that in developing the simulated seismic excitation for the pool floor, the spectra enveloping requirement of SRP 3.7.1.11.a is met.

4.

Was pool wall flexibilityconsidered in the fuel rack analysis model?

5.

Provide a description of the EBS/NASTRAN and the POSBUKF programs and sample outputs.

Discuss how these programs were verified.

Also, provide a list of values of modeling parameters used in the pool structure ana lysis.

6.

How was fuel assembly structural integrity demonstrated under seismic and impact load conditions?

7.

How was the structural integrity of the Boraflex material and its cover plate demonstrated under all design conditions?

8.

How was the leak-tight integrity of the pool liner evaluated?

Mas consideration given to potential punching or 'tearing of the liner due to rack-to-floor impacts?

gi7v QUESTION fl:

Provide the results of the multi-rack seismic analysis for racks (modules) Al, h2, Bl, and B2.

RESPONSE fl: [The multi-rack seismic analysis is in the development stage.

The results of the analysis will be provided upon completion.]

DRAFT 0113L/0023L

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QUESTION f2:

Explain hov the increased load of the spent fuel pool due to the re-racking changes the safety margin on the liquefaction potential of the soils beneath the fuel handling buildingP RESPONSE f2:

We increase in the veight of the building resulting"'from the re-racking of the spent fuel pool villnot reduce the safety margin against the liquefaction potential of the soils beneath the Fuel Handling Building.

'Ihe fuel handling building is founded on structural backfill which had been sub)ected to strict QC inspecti'on to meet the design intent of providing adequate bearing capacity and dynamic strength to resist seismically induced loadings and liquefaction potential.

Me re-racking of the spent fuel pool within the Fuel Handling Building will result in an increase in the weight of the building. &is increase willnot reduce the safety margin on the liquefaction resistance of the soils beneath the Fuel Handling Building, but to the contrary, may actually improve or increase the subsoil liquefaction resistance because this resistance is directly proportional to the effective mrerburden pressure.

'%is phenomenon vas presented by Seed and Idriss and others in the publication, Li uefaction of Soils Duri

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that soils subJected to static shear stresses prior to an earthquake willhare a higher resistance to liquefaction compared to soils sub)ected to free field shaking.

Under the increased building might, the static shear stresses in the soils will increase, thereby maintaining or even imprering this lique faction resistance.

DRAPE" 0113L/0023L

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QUESTION >3:

Demonstrate that in developing the simulated seismic excitation for the pool floor, the spectra enveloping requirement of SRP 3.7.1.II.a is met.

RESPONSE f3:

SRP 3.7.1 specifies that where.... "a recorded or.specified time history is not available as input motion for seismic system

analysis, an artificial time history may be generated from the design response spectra for the purpose of carrying out a time history analysis".

It further requires that the response spectra obtained from such artificial time history of motion should "generally" envelope the design response spectra for the damping value used.

Purthermore, the SRP requires that the response spectra corresponding to the time histories should not fall below the design response spectra at more than five points separated by increments of not more than 10 percent of the coincident frequency.

"3he time histories produced for use in the St Lucie Unit 1 rack analysis meet this requireaent within the margin of visual interpolation errog.

QUESTION f4:

Was pool wall flexibilityconsidered in the fuel rack analysis model2 RESPONSE f4:

Pool wall flexibilitywas not considered in the ana1ysis of the spent fuel racks since the analysis demonstrates that rack-to-wall impacts do not occur.

0113L/0023L

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QUESTION 45:

Provide a description of the EBS/NASTRAN and the POSBUKF programs and sample outputs.

Discuss how these programs were verified.

Also, provide a list of values of modeling parameters used in the pool structure analysis.

RESPONSE

S5:

(a)

EBS/NASTRAN X)RAPT EBS/NASTRAN is an enhanced NASTRAN program developed by Ebasco.

It not only has all the NASTRAN capabilities in structural and mechanical analyses, but also has many additional features.

One of the additional features is the ability to perform concrete

. cracking analysis.

This feature incorporates a special plate element which consists of a user specified number of layers, each having a different proportion of steel to concrete area, representing the presence of reinforcing steel.

Each layer vill crack or re-close according to the stress-strain relationships of the concrete and steel.

Thus a cracking pattern and stress redistribution can be determined.

One of the verification problems listed in EBS/NASTRAN Verification Manual is included as Attachment 1.

The feature verified in the example is the plate bending formulation of the non-linear cracking analysis by comparing analytical results with experimental data.

Sample output from EBS/NASTRAN for the verification problem is also included in the Attachment.

(b)

POSBUKF POSBUKF is a program developed by Ebasco to examine the elastic post-buckling behavior of a flat plate sub)ected to thermal and lateral loading using an energy method approach.

The program determines the deflected shape of a buckled plate by mini-mixation of potential energy, and from this calculates plate stresses utilixing strain&isplacement and stress-strain relationships for the particular case under study.

For a detailed description and verification of the program, as well as sample output, see Attachment 2.

Modeling parameters used in the pool structural analysis may be found in Subsection 4.6.1.2 of the,St Lucie Plant Unit No 1 S ent Fuel Store e Facilit Modification, Safety Analysis Report, transmitted via'etter L&7-245 dated June 12, 1987.

n 0113L/0023L

QUESTION f6:

How was fuel assembly structural integrity demonstrated under seismic and impact load conditionsP RESPONSE f6:

The concept of integrity of the fuel assembly in the context of spent fuel storage implies that the fuel rods do not-crush or crack under impact loading.

The maximum fuel assembly to cell wall impact load at a typical spacer grid location is less than 2300 lbs, which is an order of magnitude less than the fuel rod crushing or impact resistance.

In experiments conducted on comparable fuel assemblies, failure of even the spacer grids is known to require much greater loads.

0113L/0023L

QUESTION 47:

How was the structural integrity of the Boraflex material and its cover plate demonstrated under all design conditional RESPONSE f7:

The Boraflex material is held in the vertical orientiition by a stainless sheathing which provides full lateral support to the Boraflex sheet.

Both the sheathing and the Boraflex material are removed from any load paths that develop in the rack during mechanical or seismic loadings.

Therefore, the integrity of the Boraflex material is unaffected by the seismic or other postulated load conditions.

DRAPE'113L/0023L

QUESTION $8:

How vas the leak-tight integrity of the pool 1iner evaluated'as consideration given to potential punching or tearing of the liner due to rack-to-floor impact>>

RESPONSE f8:

We leaktight integrity of the pool liner plate is'"confirmed by the fact that liner stresses and strains under design conditions are within allowable values.

See Table 4-3 of the St Lucie Plant Unit No 1 S nt Fuel Stor e Facility Modification, Safety Analysis Report, transad.tted via letter L-87-245 dated June 12, 1987.

Possible punching or tearing of the liner plate due to localized impact forces will not occur since the 1-1/4 inch thick base plates (ai.nimua 13 inches square) provided under the rack support feet (9-1/2 inch dialleter) will distribute such loads and prevent direct contact between the rack feet and the liner plate.

0113L/0023L

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ATTACHMENl Page 1 of 7

EBS/NASTRAN VERIFICATION MANUAI, 1.

Name:

CA20 burns and Seiss'eam - leading approach 2 ~

~Pur ose:

To verify the noa-linear cracking analysis of reinforced concrete beam by using Burns aad Seiss's beam.

The Burns and Sciss's beam is a simply supported beam vith a concentrated load acting at the center of thc beam.

The physical configuration of the beam are shovn in Pigure 1.

h finite element model is constructed by using 10 CQDCA elements vith each element divided iato 10 layers.

Note that at each cross-section only one element is used.

The bending stiifaess of the element is used to resist the external load P.

The finite element model and its idealisation is shovn in Pigurc 2 vith the folloviag material properties:

ft ~ 546 psi Ec ~ 3.8 z 106 p Es ~30x 106 ps Vc ~ 0.15 4 ~

Method of Verification The verification is accomplished by comparing the analytical results from EBS/NASTRAN aad the experimental results of burns and Sciss's beam.

5 Rcsu~ lt Table 1 compares the displacemcnts ot the beam's center obtained from thc analytical and experimeatal results.

6.

References Burns, N.H. and Siess, C.P., "Load<<Deformation Characteristics of Beam-Column Connections in Reinforced Concrete," Civil Engineering

Studies, SRS No. 234, University of Illinois, Urbane, Illinois, January 1962.

The EBS/NASTRAN input data deck listing is shovn in'Table 2.

j The EBS/NASTRAN analytical displacement results are showa in Table 3.

CA20-1

Page 2 of 7 EbS/NhSTRhN VERIFICATION MhNUhL Magnitude of P Analytical Kxperiaeatal "P

32000 lbs 24000 lbj 16000 Ibj 8000 lbs Oo 27 0.19 0.11 0.03 0025 0.18 0010 0.03 Table 1 - Coaparison of Results Ch20 <<2

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SS/NASTRAN VKRZFZCATIC5 MANUAL p 'g NUN+I

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I

hs iAvn.'Lc."i Page 7 of 7 E)S/NA)TRhH VERIFIC)TZSI Hkll

+~@V.~

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Beom 5)~ll 6

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9 11 13 15 17 19 21 Top'iew-Model TA I

CV

~

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5 7

9 ll 13 15 17 h

10 8 7.2 i 72 Side View-Model

,'19."~

Figure 1 - Burne and Siesa Beam. Information and Finite Element Model CA20-7

ATTAC/RENT 2 Page 1 of 33 PROGRAM 2628 USER'S MANUAL FOR CALCULATION OF ELASTIC POST-bUCKLING OF k PLAT PLAIX JANUARY 1981 FIELD OF INTEREST:

PROGRAMMING 1hNGUAGE:

PROGRAM NAME:

STRUCTURAL ENGINEERING FORTRAN POSSUKF2628 0,

PREPARED SY:

S J Chen/F Bettiager HQGRAM 3%RZFICATION 3Y:

R Leveat User Administrator

~~

~

Implemcnte tioa Manager PH~~ 8" O te i-9-8'I Copy No.

Iaaued to:

EBASCO SERVI CES INCORPORATED TWO WORLD TRADE CENTER HEY YORK, HER YORK 10048

page i oc CONTENTS PURPOSE hND SCOPE

~

o

~

B

~ hBSTRACT

~

fg,

~

~ p ij<</0-

~

II - PROGRAM DESCRIPTION h - PROBLEM SThIKMENT

~

II I B - SOLUTION METHODS

~

II-1

-~l h ~ INPUT UhIQhSLES

~

o

~

III~1 B ~ OUTPUT

~

~ " ~

~

III~1 h - PROGRAM OPERATING CHARACTERISTICS

~

~.

~

ZV-1 Cf jw p<<j\\ y I.

,hPPENDI CES a - ShMPLE PROBLEMS 6 PROGRAM VERIFIChTION

page 3 ~f 33 CAWCUV,nOr OF ElASTlC POST-CKlZNC OF h F1AT PlATE I

~IRIARY g~. Wi Igy h

PURPOSE hND SCOPE This compu ter program a flat plate sub)ected to analysis of this behavior examines the elastic post buckling behavior of thermal and static lateral pressure loads.

The is based on an energy method approach.

s - msxsacr The first step of analysis assumes a buckled deflected shape.

For this deflected

shape, an expression involving total potential energy is established, and by minimising this potential energy the magnitude of the buckled plate deflections is determined.

By utiliring strain<isplacement and stress-strain relations the buckled plate stresses are readily cal-culated.

Since the program assumes that the imperfection in the plate is infinitesimal, any effect of significant imperfection should be considered separately either by ~ safety factor or by manual calculation.

f S

gA k

g't

~ page 4 nf ZZ -

ROt;an DESCRIPTION g

ERE" This program determines the elastic post-buckling behavior of a flat plate subjected to thermal loads and static lateral prasaure loads.

B <<SOLUTION METR)DS hssumed Dis lacement Functions

~

Clamped Edges

~

I I

I

~

i I I,'

I

'I

~

I i

~

v

~ f (1+cos b ) (1+cos

)

u

~

C2ain (1+ cos ~)

2@x b

a v

~

C sin~ (1+ cos

)

2 TX 1

a b

1

Page 5 of 33 2,

Strain-Dis lacement Rtlationshi s

- In middle plane during bending:

bu 1

Bv 2

a ct>>

2 8>>

Bv 1

v 2

0 a

+

ily 2

8y

.u c}v

~ ~v ay ax a>> ay

- Sending Strains (x i +4) 2 2'a.'h gv a ~

~'.

ay

+

8 v 2h 5x by 3.

Stress-Strain Relatienshi s

= In middle plane:

ex - aT

(<x -<<ey) 1 E

0

~ aT

+ ~ (iy ~<<fg) 1 E

vxy/C or/

C

~

E/2(1 + <<)

[ex +

<<ted (1 + r)aT]

X x

1 r

[<y +

<<cg (1+r)aT) 2 1 r C 't

)

hTThGHNENT 2

page 5 oi 33

- Sending sx 0'y Stress &lationships

~(h) 2 1

+ ~(2)

B'v h

+

a By 2

2

+

B v 2

-Gh-Bx By

~v 2

By2 B v 2

o'x2 vhere: '2

.2 f (1 + cos ~) cos ~

2 2

e b

Bx B2 2 f (1 + cos ~) cos ~

B2 2

b a

2

2. sfn sin ~

Bv r

vx ab b

I 4.

Calculation of the Totcl Potential Ener V

V U +U2+U3 1

U

~

Middle p4ne aembrane strain energy 1

U2

~

Sending and tvisting strain energy U3

~

cwork done by 4teral pressure

~

b 1

U i h

{r

~

+ r

~

+ r y

)

E o E (s

+ s

)

d 1

n c

y y

scy cy E(1-s)

X Subs titute e e Relationships a

b C h 2

2

+t

+2f(

s +- (1 v) 1 1

1 f

sx y

x y

2

~

b 2(1+r) aT (c

+ ~ )

X (E

- ~

P4gt 7 of 33

~

U 8

2

- M ~+M

+M dx dy y

}

aXaxay rxax ay

<<g <<b x

ay SubstitutsaS s

<<Q (

s

<<Q (

a}f e

a b

U2 ~ 2 9

<<g <<b 8 v/Bx +.8 v/By )

2 2

8 v/By + r8 v/Bx) 2 2

2 2

b '(1-r) 8 v/ c} x By, 2

2 2

+ ~

+

8 v v

Bx By 2

2 E h /12 (1-r )

3 2

8 v 8 v 2

2 2

'r

2 2+ 2(l r) dz dy (E

8 Bx By Bxay I

b U

~

p vdxdy 3

<<g

<<b (Eq x ansien of Ex ression for U1 Substituting Eqs 1 tata Eq 4-I b" Bu 1

Bv 2

+

ax I

Bx.

+ ohkR ~

+

Bz Qz

- ay 1

Bv 4

2

+

~

~ ~

+ ~ ~

+ 2 r Bv Bv By 2

By Bx 4

Bx By au av 1

Bu

+~~

Bx8y 28x

+-(1 <<)

1 2

Bv 2

By Bv 2

Bv Bu

+

Bx Bx By Bv Bv Bv au 2

+2 +

+2-Bu ax Bz ay By ay 2

2 (1+r) a T ++-

Bu Bv 1

Bv Bx By 2

c}x

~v ~v Bv Bx ay Bx Bv 2

+ 2 dz dy

~v 2

By (Eq V;

hTThCHMENT 2

page 8 of 33 g1 (Conc'd) 2sx u i C

sin {1+ cos ~)

.Bu/ Bx

> {2r/b)C {1+ cos ry/a) cos 2rx/b 2

Bu/By

(-r/a)C (ain 2sx/b)ain ry/a (Eqs 4) v i C sin~ (1+cos

)

2 's SZ

~

1

~

b Bv/Bx

~ ( r/b)C (sin 2ry/a)ain rx/b 1

Bv/By Or/a)C (1+ cocrx/b) cos 2ry/a 1

(Eq. 9) v

~ f (1 + cos

) (1 + cos ~)

b Bv/ B x

< (-r/b)f (1 + cos ry/a) ain rx/b Bv/8 y

~ (-r/I)f (1+ cos rx/b) sin ry/I (Eqs.1(

Substituting Eqs 8, 9, 10 into Eq 7 a

b U1 0

JJ eg eb 4r 2

C (1+ cos

)

cos +-

rv 2 2 2sx b2 2

~

I b

(Eq 11) s 4

4 rv 4 rz 2r 3 3

rv 2rx 2

+.

f 1 + cos ~

sin

+

C x

1 + cos ~

coa sin 4'4 4

4 b

4r 2

2 rz 2

4 2 2 1 r rz 4

4 rv

+

C 1+ cos cos ~+ r 1+ coa ain 2

1 b

a 4

4 b

0 4

2S 3 rz 2r 2

r 3.

+

C f 1+ ccs ccs ~ sic 3

1 b

I I

Sr

+

C C

ab 1

2 2

3

+

C 2b 2

I b

(

'x

'2rz.

2rv 1+ cos ~

1+ coc cos,'woc 4

b (i"b,

~

4

(

sv rx

~2rz 2 rv 1 + cos ~

1 + cos coc sin 4

b b.

4

h h

Page 9 cf g

(Cont 'd)

VX C'X

+ 2f r rx C

1 ltcoo-b2 1

b eb e

r 4

2

+- f 1+ coc ~

2 2

2 S

2 1 + cos ~

e 1+ cos rx b

2rv 2

rx cos ~win b

ein ain.

2

<<x 2'

a Ql/f 2

2 b2 1

4

~1-o o

f4 1

2a b

2

~2r 2

rx

~l~i 2

2

+ cos ~

1+ cos rx I

b C2 ein I

2 rx "2

)

ain ain b

sin 2rx 2

g b

a 2

+ (1-r)

C C

ain

~ b 1

2 r3

- (1-f')

C 2 ain b

2

eXn sin-2rx 2 rv rx b

a b

I + cos ~ " 1 + cos-rv r x b /

ein ain ain ~

2r rx 2rx r

a b

b I

3 fl-o)

C f ofc r

2 1

a b

~1+i aT C il o b

cos ~I 2 r-x cos b

ein "ain~

e b

I 1+ cos ~

I rx il+ coc-b a

2 c

il+~i aTw f'f 1+

~c 1 T oa 1

b I3 V

\\ ~

Iw&4c +

%10 4 r 1+a NT C

1 ix

~2r 1

b C

1 + cos cos I 2 A 2

1+i a T r x

1+ cos rx ain2mr I

4 d

a$ '."

No@ integrate

AlTh Page 10 of 33 final Expressions for Ul>> UZ>> U3 ~ V U1 1

v

< 2 2

12b

~1

~ a 1

a 2b

+<2 2

12a+~1

~ b 2

2a 3f (1+~)eTr b+

+ ~ f r 3

+

3+

a b

1 4

4 105a

'105b 50 5b a ~1-.3>>

2 2b a

CZf r 5a + ~l-3>>

bZ 2e Q

s abf D

2 2

+

3 3

2 4

4 2bZ a

a b

U

+

4abpf 3

V U1 + UZ U3 5 ~

CalcuIatfon of Post-Suc'klfa behavior Mined.se total potential energy BV Gh g}C1 1-~

2C1 s 2 12b a ~1->> a a

Zb f'a 3 Sb a ~1-3>>

2 2b a

~0 (Eq

>>ak" bV gh 2CZ s 2 12a

~1~b b

2a

&+ &1~31 0

(Eq b2 2a 2

a b

1 P 4

105a 105b jO b

a 16 b3 3

ab 8V ~ G aa gf (1+~)c2Ts'

-2C fs

+

3 Sb 1-3>>

3 1

2 2b

- 2CZ fi 5a a ~13>>

2a

+ t abS 4

I

+ +

3 3

2 b4 4

2 b2 a

a

+ 4 abp,~'~0

~%I@

ATTACHNEiiT 2 Page 11 of 33 Eqs 12-14 can be expressed as fo11ms:

C n f 0/h 1

C2

~ f J/C 2

ff+f0+I n

0

@here:

h, b, C, F, J

~

Fct (Geometry)

Fct (Geometry, Temp)

I

~

Fct (Geometry, Pressure)

(Eq 12')

(Eq 13')

(Eq 14')

Cnnnidnr Eq 14': f + f (0/f) + Zlf n

0 n

f +fK+L n 0

Zf Pressure P i 0; f+f Hn0 ~ fn ~alp 2

2 3

3 2

0

+ +-

b4 4

2 b2 nnr f n

0~ Tcr 1

1 b2 36 (1+i)a +-

a gc aT E

2E n

8 8

cr (1-i) 36 (1 2) b 2

b 4

2 3+2

+3 h

e

e 4

~'

Page 12 of 33 f

ressure P

0 - (normal at the plate)

D wQP a

When T g T

~ buckling does not occur vith downvard pressure.

cr h

When 2 8 T end f(1/4)h

+Q/27)K d ) 0 huo'klfnd does not ooous 2

3 E

There is only one real root for the expression,gn the brackets, and it is negative.

c - When T P T and fQ/4)L +(1/27)K 3 < 0 buckling occurs because 2

31 there is a physically meaningful real root.

When there fs buckling,

. the value of f which fs physically meaningful is:

(see paragraph below for determination of f) 2

- cos 4'/3 vhere 1 R cos x

-1 3

-L/2

/27

then, Cl e

2 2/4 C2-dc/C K

R 8/F

'L R I/j

- While this is a theoretical solution nevertheless ft accurately predicts the actual buckling situation.

So knockdoMn factors are required as hg shells and curved plates.

Using f, Cl and C2, the displacements u, v and v can be determined.

partfal derivatives of the displacenents can be used to calculate strains and these strains can fn turn be used to detennfned stresses at any point on the plate.

s s page 13 oi 33 Derivition of Value of f from Cubic E Ation 14':

The expression for f vas deternined in the folloving manner frocn Equation 14' f (8/F)

+ I/F

~

0 3

f

+ f (K)

+

L

~

0 (Eq 14')

3

~'

M I

t Zf fO/4)L +(1/27)K 3- 0 roots are:

2 31 cf

~

2

-X/3 cos 4/3 1

f2 u

2 ~K/3 cos (o/3 + 2r/3) f3 n 2~2/3 eos (d/3+ 4/3r) sshere +denotes

(+) root end el 4 ~

cos for L u + (dounserd pressure)

-L/2

-K /27 Values of

@ versus f are-@harn in table belov:

antit fL/2~K/3 0

1.0

'F 2 0.866 0,5 3%'

2F 0.5 22/2 ~K/3 0.5 0.866 1.0 i0.866

~ 0.5 f3/2 ~i/3

'.5 0.5 W.866 1.0

.Sy observation 3 different roots are possible bastien 0 and s'/2.

Also 3 roots are possible betveen s and 2

's Values of J from 0 to e yield the sane values of i as those for 1 from e ro 2e.

1harafore ve anly need to lnvestlt at a~the h~aL-Sttegoenoa af f values for 4 fram 0 to r.

I I

Since L is pasitive, g can vary from v/2 to 3+/2 only. ~Therefore ve only need to consider 4 from r/2 to v.

values of f /2 ~63 oen be altotnatad slots they ere negative Therefare if P ~ 0, Equation 14 reduces to f + f (8/F) ~ 0, and its roots 3

are, i ~ 0 f ~ -

-HIF

~ ~ <<~ ~e

<<e

~e~Os

~ e ~

~,

e~~m v

~o e e

When P 0 0 and pressure ia down, the effect of pressure on curve (1) is ta reduce the value of f for P > 0 and 0 > </2.

The solution f is not physically aeaningful, in tenus of the effects 3

of pressure on those due to temperature alone.

Therefore fl is the only valid solution.

st.

INPUT VARIABLES ATlACH.)E'NT 2 ge 15 of 33 III -

NPUT/OUT

~i ~

The FORTRAN source deck of this program is available from the User hdmfnistrator aad Implementation Manager.

The follovfng describes the program input aad format:=

CARD 1 CARD 2 COL 2-72 COL 1 10 11-20 21-30 31%0 41-50 COL 1 15 COL 16-30 31<5 46-60 COL 1-10 11-20 TITLE GA PLA'5 HALF ltlDTH (IN.)

'CB PLATE HALF-LENGTH (IN.)

GH - PQLTK THICKNESS (IN.)

M, NO.

OF DIVISIONS OF HALF-IZNGTH N, NO, OF DIVISIONS OF HALF WIDTH EMOD MODUIlJS OF RUSTICITY, E (PSI)

SMOD - SHEAR MODULUS, G (PSI)

PRATIO ~- POISSONS RATIO hLPHAT-- COEF OF THEM EXPANSION DELTAT DELTA TEMPERATURE (DEG F)

PRES - APPLIED UNIFORM IhIXRAL PRESS.

(PSI) 18A4 F10,0 F10. 0 F10.0 I10 Ilo F15.0 F15.0 F15.0 F15.0 F10.0 F10.0

~~Several problems msy be run in one aubmfssfoa simply by stacking sets of data Cards 1 to 4.

Place tvo (2) blank cards at ead of total data deck.

ht requested locatioas, strains aad stresses are prfWed out as ahovn ia sample output on hppendix Page h-ll. ht each location, the first line ahovs middle plane strains and stresses; the second line shovs bending strains

'I and stresses.

hlso printed ia the critical buckling temperature and corres-ponding critical stress, as showa oa Appendix Page h-10.

hTThCHNENT 2

Page 1l'f ~

h -

ROGRAN OPERATING CHARACTERISTICS 1.

Core Estimate:

Minimum 2.

Peripberalc Required:

Disk - Pull time if program ia copied to diak Magentic Tape - Wquired if NASTRhN output ia atored on tape Card Reader Full time Card Punch - Sot required Printer - Full time 5-1

Page 17 of 33 APPENDIZ k SAMPLE PROBLEMS HtOGRAM VHQPIChTI($

J lt fP a

~

tltiiit 11 Si 11 11 11 1I 1111111

$ 4 11 11 11 11 11 11 11 11 11111 111 11 1$

ll 1'I

$ 1 11111111 i(

$ 1 I 1 1'I 11111111 11 11 1 I

'I 1'

)lliII I 11 11

~l 11 11

~ 1 1$ 1 11

$ 1 11 4$

~ S 11 11$

11 11 11

~ 1 5i, 1'I 11 1111111

$ $'1

~ ~

l Verification of POSSUKt2628 (Test lan for $1hich Hand Calculations ere Provided) v

~ I

~.

aI

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Page 27 of 33 CHECKOUT OF PROGRAM FOR FI)ZD-ENDED P~TE ShHPLE R1$ NO. 2:
b -
83.28",
a 27,72",
t
,25 M
N
~ 30 x 10
psi, G >
12 x 10 psi, i 0 0 36 o
% 6 5 g 10 / F 6
-6 o
)AT
~ 80 F, p ~ 8.9 psi 0
~w. 4 cr 36 ~1+) a +
1 2
2 a
2
.252 ~ +
+
83,28 27.72 83.28 27.72 36.
(1.3)(6.3 x 10
)
2
+
2]
-6 1
1
~
83. 28
27. 72 T
~
7.74 F
cr T > T 3
proceed vith ana lysis cr t
as a check, submit above data vith T i 3.
F-)Program should terminate 0
It does; see ShHPLE RUN NO.
3 Calculate -
L
+
1 2
1 33 4
27 L
~ I/F X
a/F 246 +~1-i a
a b
B r
Sb
+
1 33'4s
+ ~1-v 6
b a
hT1 AvH."4r..'i i Page 28 of 33 E
Elastic Modulus r4 F
16 2B 2
105a 105b so b
3 ab h
a 2Jr2 C
G
~
Shear Modulus of Elasticity 8
8 (2+v)aTg
+
+
+ +
2 a
b (1-v)r b5 3
~
2 b
a G b b4 4
2b2 a
a b G h E b 3 U (1-
~
)
0.7 4
27.72 83.28 8.9 (U x 10 )(.25) 6 6
3 12 (.91) 0
. 0192 8 ~ -6 (1.3)(6.5 x 10
)(80) r
-6 2
27.72 83.28 83.28 27,72 0.7 r 27 72 83.
8 4
3 x 10 5 487 10-6 4
4 6
(U x 10 )(.25) 8
~ -.134 +.0144
~
-.1196
+
~ r
.543 +
~ 0006
~
1.71 83 28 (27.72) 2 (83.28)
+~
722
+
222 7228
27. 72
83. 28
~24 27 72 4 ~783.28 8 8+ 2 2
2p 2
83. 28
27. 72
~527. 72 (83. 28)
L (83. 28)
.020 +.0018 i
.0685
.1 2 (27.72)
(27,72)
(27.72) (83.28)
72. 33 lp. 1
4 F a
.00504
+
.410
+
.0217
.798
~
.0092 16 F
2.66
.798
.0092 1.853 0192 L
I/F ~
~ 01037
1. 853
- ~1196
l. 853
-.0645 4L +27K a
i@ >0,
(.01037)
+ (
~ 0645)
~,0000269 -.00000994
~ +.00001696 1
2 1
3 4
27 no buckling k-20
~
4 g', i8 (63 (9
9 Calculate case for p i 0:
I ~ 0, L i 0, a11 other values same as
above, This is SA.PLE RUN NO.
1
-L/2 s
a0 cos 4
-R /27 4
~
-1 900 cos
(-0) 4 /3 ~
30 i 0.523 radians
1. 57 radians 99]
8 2 ccs -
2 q~
ccc (30 )
(0.2932)(.866) 0.234
-K 4
0645 0
1 3
FF2 e f 2
cos
( t 240 )
~
( ~ 2932)
( 0 )
-K a
0 2
3 3
~ f B/h
(.254)
(1.71)/72.33
.00153 2
2 11 1
~ f J/C
~
(.254)
(.0685) /10. 1
~
~ 000437 FF2 C12 f? B/A
~
0 2
C
~f> J/C 0
Solution l FF1 ~ 0.254 C1
~.00153 C
~.000437 2
Solution 2
FF2 i 0 C1 '~0 C2
~0
~ 6 0 f7
)
80LUIIOX 1 ps ggg$
I w P~
~P-X Location Pl Calculation of
< 'a 6
e 's at x
% b
% 83.28) y
% a
% 27.72 (Point P )
1 a
x 0
E 30 x 10
-6 6
~
+ vs
- (I + ~ ) a I 91
- (1.3)(6.5 x 10
)(80)j 2
x ax
-223DD. p)1 E
y 2
y x
(1+
8 ) o T
% -22300. pai T
%Go 0,
xjj For location P, Solution 2
% Solution 1
1'OLUTION 1
Location P x
% b
% 83.28, y
% 0 2
~
(. 000437)-(2) (1)j
+
0
. 000066 X
83.28
~
0
~
0 30 10 e
".M0066 + 0 - (1.3)(6.5 x 10
)(80)j 2180 - 22300
-20,120. )s(
x
.91 30 10 a
0+.3 (.OOD0614) - (1.3)(6.5 x 10
)(80)]
y
.91 654 - 22300
% -21)646.
0 h-22
k G
<t 1
II
A62nv(I ~ 4%44 page 32 of 33 80101109 I 3 x'0 y<<a <<2772" (i
I A
c
<<0 x
(.00153) (2) (1)
+ 0
.000694 y
L 27.72 c
<<0 xjj Ox 10
[.3 (.000694)j
- 22300.
6860. - 22300.
-15440, ysi x
.91 30 x 10 6 9
.91
<<0 xy Location 4
x b
(83 28) 33 31 5
5 x << 0.4 y <<
rv cos ~ << cos a << (27.72)
<< 11,09 2
2 5
5
(,4r ) <<,309, cos ~ <<
+<<0.4
-.81, sin ~
.951, ain ~
.588 r
2r SOLUTION 1
(.000437) (1.309) (.81)
+ -
~
(.254) (1.309) (. 951) 4 83.28 2
L 83.28
~ x
~
y
~ 0000349 +. 000071
.0000361 t
(. 00153) (l.309) (-. 81)
+ I
(. 254) (l.309) (. 951)
27. 72 2 i 27.72
~ 000278 xy 83 28
~
~
~
27 72
~
(. 00153) (. 588) (. 951)
(. 000432) (. 588) (. 951)
+
28 27 72
( 254)
(1 309) (1 309) ( 951) ( 951)
~
<< -,0000323
.0000277 +. 000428
+
~ 000368 xy
page 33 of 33 30x 10 y
88
'. 0000361 +,3 (,000278)
-22300, X
3600.;2230D.
-18700.
Dc2 d
91
. 000278 +
. 3 ( ~ 0000361)
-22300.
9540 22300
- 12760, 30 x 10
~ (12 x 10 )(.000368)
~
+ 4420 t3si 6
XJJ k-24
4 f
'k~
i4
~/
I

v t e Letter Sequence Meeting
TAC:65587, (Approved, Closed)
Initiation Acceptance... Administration Meeting, Meeting, Meeting, Meeting, Meeting Questions 20 August 1987 1 September 1987 21 September 1987 25 November 1987 Answers Results Approval, Approval, Approval Other: ML17221A357, ML17221A482
MONTHYEAR1987-12-09 [Table View]

ML17221A548

Text

SUBJECT:

SUMMARY

SUMMARY

Enclosures:

RESPONSE

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