Text

Rev 0 to C-003, USI A-46 HCLPF Evaluations for Contaminated Condensate Storage Tank
	ML17191A589
Person / Time
Site:	Dresden
Issue date:	05/29/1996
From:	; STEVENSON & ASSOCIATES
To:	;
Shared Package
ML17191A588	List: ML17191A587; ML17191A589; ML17191A591; ML17191A613; ML17191A614; ML17191A615; ML17191A616;
References
	REF-GTECI-A-46, REF-GTECI-SC, TASK-A-46, TASK-OR C-003-01, C-003-R00, C-3-1, C-3-R, NUDOCS 9804160302
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93C2806.4-C-OO~

Commonwealth Edison Calculation No.

C-003

Title:

USI A-46 and HCLPF Evaluations for Contaminated Condensate Storage Tank l /.

I Project:

Dresden USI A-46 / IPEEE Seismic Evaluation Method:

EPRl-6041, Revision 1, Appendix H Acceptance Criteria:

EPRl-6041, Revision 1, Appendix H

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Remarks:

REVISIONS No.

Description By Date 0

Original Issue MSL\\

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JOB NO. 93C2806.04

SUBJECT:

Dresden USI A-46/ IPEEE Calculation No. C-003 Stevenson & Associates USI A-46 and HCLPF Evaluations for a structural-mechanical Contaminated Condensate Storage Tank consulting engineering firm Table of Contents

SHEET #1of13 Revision 0 By MSL 5/29/96 Chk. TMT 5/29/96

1. OBJECTIVE............................................................................................................................................... 2

2. ANALYSIS INPUT...................................................................................................................................... 2

3. ASSUMPTIONS........................ :................................................................................................................ 2

4. ANALYSIS........................ ".'.~....................................................................................................,................. 7 4.1 ANALYSIS CRITERIA................................................................................ *****.............................................. 7 4.2 CAPACITY CHECKS.................................................................................................................................... 7 4.3 MATERIAL STRENGTHS....... '....................... :........ ;.:........... :.. :... :..,......... :~...........,........... ;.*.. ;........................... 8-4.4 SEISMIC RESPONSE.................................................................':................................................................. 8 4.5 BOLT PULLOUT CAPACITY.............................................. :...............,.......................................................... 10

4. 5. 1 Yielding of Bolt..........................,...................... _............................................................................... 1 O

4.5.2 Failure of Shear Cone........................................................................ :............................................ 10 4.5.3 Ring Foundation and Minimum Reinforcement......................................................... :..................... 10 4.6.ANCHORAGE CONNECTION CAPACITY :.............................................................................. :....................... 11

4.6.1 Top Plate....................,..................................................................................................................... 11 4.6.2 Tank Shell Stress.................................................................'~........................................................... 11 4.6.3 Vertical StiffenerPlate................................,................................................ ::***********1....................... 11 4.6.4 Chair-to-Tank Wall Weld..'............................................................................................................... 11 4.7 BASE MOMENT AND SHEAR CAPACITIES..................... :............................................................................. 12 4.8 SLOSH HEIGHT**********~**********************************************************************'****************************************************** 12

5. CONCLUSION............ :..................,.:....................................................................................................... 12

6. REFERENCE........................................................................................................................................... 13 Appendix A - MathCad Works~eets for Tank Subjected to A-46 SSE Input.

Appendix B - MathCad Worksheets for Tank Subjected to IPEEE SME Input.

JOB NO. 93C2806.04

SUBJECT:

Dresden USI A-46/ IPEEE Calculation No. C-003 Stevenson & Associates USI A-46 and HCLPF Evaluations for a structural-mechanical.

Contaminated Condensate Storage Tank consulting engineering firm

1. Objective SHEET #2of13 Revision 0 By MSL 5/29/96 Chk. TMT 5/29/96 This calculation assesses the adequacy of the Dresden Nuclear Power Plant Contaminated Condensate Storage Tanks for Safe Shutdown Earthquake (SSE) loads. The tank has been designated as a GIP outlier because of the ring foundation [7]. This calculation also assesses the HCLPF value of the IPEEE seismic margin.

2. Analysis Input Configuration

The CST contains water and is 32 feettall and 37 feet in diameter. Its maximum water level is 28.5 feet (High Level Alarms) [3]. The tank shell material is 5454-0 and 5154 H112 aluminum. The tank base material is 3003-F aluminum and its bolt chair material is 6061-T6 aluminum. It is located outside at grade and anchored by 20 1-1 /4'~ diamete.r cas_t-in-pta_ce bolt~. R~f_ereoces ~ an_d 2 detail. the ~ank configuration, bolt schedule and foundation. A sketch of the tank configuration is shown in sheet 3.

Seismic Demand Seismic demand for Dresden USI A-46 evaluation is per the ground response spectrum of Safe Shutdown Earthquake (SSE) provided in Reference 4 and shown in Figure 1. Seismic demands for Dresden IPEEE evaluation are per the ground response spectra of Seismic Margin Earthquake (SME) provided in Reference 5 and shown in Figure 2 and 3.

3. Assumptions The following assumption was employed in this Cjlnalysis. This assumption is considered reasonable and/or conservative.

Strength values for 3003-F aluminum base material are 90% of 3003-0 aluminum (see "Criteria")

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JOB NO. 93C2806.04

SUBJECT:

Dresden USI A-46/ IPEEE Calculation No. C-003 SHEET #4 of 13 Revision 0 Stevenson & Associates a structural-mechanical -

consulting engineering firm USI A-46 and HCLPF Evaluations for Contaminated Condensate Storage Tank By MSL 5/29/96 Chk. TMT 5/29/96 1

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JOB NO. 93C2806.04

SUBJECT:

Dresden USI A-46/ IPEEE Calculation No. C-003 SHEET #5of13 Revision 0 Stevenson & Associates a structural-mechanical consulting engineering firm USI A-46 and HCLPF Evaluations_ for Contaminated Condensate Storage Tank By MSL 5/29/96 Chk. TMT 5/29/96 2

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JOB NO. 93C2806.04

SUBJECT:

Dresden USI A-46/ IPEEE Calculation No. C-003 SHEET #6of13 Revision 0 Stevenson & Associates a ~tructural-mechanical consulting engineering firm USI A-46 and HCLPF Evaluations for Contaminated Condensate Storage Tank By MSL 5/29/96 Chk. TMT 5/29/96 1

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JOB NO. 93C2806.04

SUBJECT:

Dresden USI A-46/ IPEEE Calculation No. C-003 Stevenson & Associates USI A-46 and HCLPF Evaluations for a structural-mechanical Contaminated Condensate Storage Tank consulting engineering firm

4. Analysis SHEET #7 of 13 Revision 0 By

. MSL 5/29/96 Chk. TMT 5/29/96 This analysis generally follows the conservative deterministic failure margin (CDFM) approach as defined.

in EPRI NP-6041 [6], except that seismic demand is based on the design basis spectrum as noted. The

,detailed procedure defined in Appendix H of that report is the basis for tank base moment and shear capacity determination.

4.1 Analysis Criteria The tank was analyzed for the maximum water level of 28.5 feet. This level is three and half feet below the tank shell height. The tank and its contents are at atmospheric pressure and temperature of 150 degree F.

The tank is analyzed for extreme seismic loading conditions. Consistent with the CDFM philosophy, irielas,~~ m~teria! defOJIJlatiQn is alloweo._Fe1ilure occ1,1(s when the tank.can_not contain its contents.

Because of uncertainty in post-buckling or post-sliding behavior, buckling or sliding is assumed to result in tank failure.

4.2 Capacity Checks These capacity checks are performed.

Buckling of tank wall

Global overturning moment capacity

Sliding of the tank Sloshing of water against the tank dome will also be addressed.

JOB NO.. 93C2806.04

SUBJECT:

Dresden USI A-46/ IPEEE Calculation No. C-003 Stevenson & Associates USI A-46 and HCLPF Evaluations for a structural-mechanical Contaminated Condensate Storage Tank consulting engineering firm 4.3 Material Strengths SHEET #8 of 13 Revision 0 By MSL 5/29/96 Chk. TMT 5/29/96 The material strengths are listed. in the table below. Allowable stresses and loads are based on the guidance in reference 6. The strength values of the 3003-F aluminum shell were set equal to 90% of 3003-0 aluminum specified minimums. The -F condition is "as fabricated" with no heat treatment and minimum properties are not specified. The -0 condition is "annealed", with the lowest specified strength properties for the alloy (also not heat treated).

Item Strength 1-Basis Tank shell Sm= 8.0 ksi, Fy = 18 ksi, Fu= 32 ksi Reference 9 for 5154 H112 Aluminum Fba = 2.4*Sm = 19.2 ksi sheet Fva = 0.42*Fu = 13.44 ksi Tank base Sm= 2.61 ksi, Fy = 4.1 ksi, Fu= 11.7 ksi Reference 9 for 3003-F Aluminum Fba = 2A*Sm.= 6.264 ksi -

sheet,-where 0.90 reduction factor Fva = 0.42*Fu = 4.914 ksi applied for -F condition {see above)

Bolt chair Fy = 35 ksi, Fu = 42 ksi Reference 9 for 6061-T6 Aluminum stiff.en er, sheet Fillet Welds Fva = 1.7*7 ksi = 11.9 ksi Reference 10 for parent materiel 5454-0 Aluminum sheet and filler alloy E-5554 (minimum expected shear strength of E-5554 is 17 ksi)

I Where Sm = allo,wable stress intensity, Fy = nominal yield stress, Fu = ultimate stress, Fba = allowable bending stress, and Fva = allowable shear stress.

4.4 Seismic Response Assumed dynamic behavior of the tank is based on reference 6. The seismic respon.se of significant tank modes is obtained from the corresponding ground response spectra. If no vertical ground response spectra is provided, 213 of horizontal ground response spectra is used. Supporting cal~ulations for modal frequenci,es are on following sheet and also in MathCad worksheet. A +/-10% frequency uncertainty was considered in determining the spectral acceleration in each case.

Motion Mode Freq (Hz)

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JOB NO. 93C2806.04

SUBJECT:

Dresden USI A-46/ IPEEE Calculation No. C-003 Stevenson & Associates USI A-46 and HCLPF Evaluations for a structural-mechanical Contaminated Condensate Storage Tank consulting engineering firm 4.7 Base Moment and Shear Capacities SHEET #12 of 13 Revision O By MSL 5/29/96 Chk. TMT 5/29/96 The tank base moment and shear capacities are analyzed using MathCad worksheets [14]. Two cases were studied

1. Tank subjected to SSE (Appendix A)

2. Tank subjected to SME (Appendix B)

The MathCad worksheets automatically calculate all the results except in the calculation of the impulsive mode frequency and the response spectral valves, where the user must supply the valves from the tables or graphs.

r 4.8 Slosh Height Per GIP Section 7* [7], hs = 0.837 RSar For SSE, Sar = 0.07 g, and for SME, Sar = 0.17 g, I

Max. hs-= 0.837x18:5' x0_.17 = 2.63' < Freeboard clearance= 3.5' (O.K.)

5. Conclusion This calculation has determined that the Dresden Nuclear Power Station Contaminated Condensate

St9rage Tank holds its integrity during the event of Safe Shutdown Earth. The CDFM capacity has shown to be 0.26g PGA for SSE input. Capacity is governed by the base moment capacity of th_e tank. Thus, the outlier is resolved.

The IPEEE HCLPF value is 0.2g forSME input.

/

JOB NO. 93C2806.04

SUBJECT:

Dresden USI A-46/ IPEEE Calculation No. C-003 SHEET #13of13 Revision o Stevenson & Associates USI A-46 and HCLPF Evaluations for By MSL 5/29/96 Chk. TMT 5/29/96 a structural-mechanical Contaminated Condensate Storage Tank consulting engineering firm

6. Reference

1.

Nooter Corp. Drawings for 37' l.D. x 32' Contaminated Condensate 'Storage Tank, Job No. D-4943, Rev. C.

2.

Dresden Drawing, "Miscellaneous Outdoor Foundations, Sheet 1", B-480, Rev. B.

3.

COMED Nuclear Design Information Transmittal, "Information Needed for the SQUG/IPEEE Project", NDIT No. SEC-DR-96-003, S&A Log No. 93C2806.04-DC-013.

4.

Sargent & Lundy, "Seismic Design Criteria for D.resden Station - Units 2 and 3, Reactor-Turbine Building", Project No. 7355-00, DC-SE-002-DR, Rev. 2, December 5, 1988.

5.

Sargent & Lundy, "In-structure Seismic Response Spectra for SMA, Dresden Nuclear Power Station

6.

7.

8.

9.

10.

11.

12.

13.

14.

Units 2 & 3, Quad Cities Nuclear Power Station, Units 1 & 2", Project No. 09630-016, SL-8.11.6-2, Rev. O,*May 1995...

Reed, J.W., et al, "A Methodology for Assessment of Nuclear Power Plant Seismic Margin",* Rev. 1, Electric Power Research Institute, August 1991: EPRl-NP-6041-SL.

"Generic Implementation Procedure for Seismic Verification of Nuclear Plant Equipmenf', Seismic Qualification Utility Group, February 1992.

Czarnecki, R. M., "Recommended Approaches for Resolving Anchorage Outliers", Electric Power Research ln~titute, Final Report, June 1994. EPRl-TR-103960, Project 2925-01.

ASME Boiler and Pressure Vessel Code, Section Ill Division 1, 1980 Edition..

Aluminum Associates, "Specifications for Aluminum Structures", Section 7, Welded Construction,*

1972.

_J Haroun and Housner, "Seismic Design of Liquid Storage Tank", Journal of the Technical Councils of ASCE, Vol. 107, No. T~1. 1981, pp. 191-207.

ASCE Standard, "Seismic Aralysis of Safety-Related Nuclear Structures and Commentary onr Standard for Seismic Analysis of Safety Related Nuclear Structures", ASCE 4-86, September 1986.

I Roark & Young, "Formulas for Stress and Strain", 5th Edition..

MathSoft, Mathcad, Version 6.0 Plus, 1995.

S&A 93C2806.04 Dresden A-46/IPEEE Calculation C003 Appendix A A-46 SSE Page A-1 Revision O By MSL 5/29/96 Chk. TMT 5/29/96 Dresden Contaminated CST, NP-6041 Appendix' H Procedure, SSE Input R := 222*in H := 342*in H s := 384*in H d := 13.875-in ts := 0.46* in th:= 0.1875*in ta := 0.302* in t b := 0.25* in Es := 9800* ksi v := 0.3 Radius Fluid Height

Shell Height Dome Height Shell thickness Head shell thickness Average shell thickness Bottom plate thickness Shell Young's modulus Poisson's ratio Pefinitions kip := 1000* lb ksi := kip in2 lb psi:=-

in2 lb pcf := 3 ft minx(x,y) := if(x>y,y,x) maxx(x,y) := if(x>y,x,y)

K := 300*ksi Fluid 'bulk modulus, Mark's Standard Handbook, 9th Ed., Table 3.3.2 a ys' := 18*ksi a us := 32* ksi a yb := ?.264* ksi a ub := 12.6*ksi Yf := 62.4*pcf y s *:~ 165* pcf Yf Pf:= -g Ys Ps - -g

( '

Shell yield stress Shell ultimate stress Bottom plate yield stress Bottom plate ultimate stress Fluid weight Shell weight.

1 b = 12-(1 _ v2)

I b = 0.001431 *in3 Av = 0.133* g 2/3 ZPA of Dresden SSE ground spectra PGA = 0.26* g Assumed, must iterate so that the demand M5h is close to the capacity Msc SSE = 0.2*g..

PGA Scale.- SSE

ZPA of* Dresden SSE ground sp~ectra

S&A 93C2806.04 Dresden A-46/IPE::EE Weight Summary Hd XH := Hs+2 Hs Xs:=2 Impulsive Mode ta R = 0.00135 Cw1 := 0.104 f1=5.583*Hz S Al := 0.33*g Calculation C003 Appendix A A-46 SSE X H = 390.9*in w s = 15*kip Ww = 1912*kip H

R = 1.541 Frequency coefficient from Haroun and Housner (1981)

C LI= 0.06 0.9* f I = 5.025 *Hz 1.1*f1=6.141 *Hz From Dresden SSE Ground Spectra 5% Damping, peak of the spectra s Al := Scale*S Al

s Al= 0.429*g

(

~\\

H w 1 :=

1 - 0.436*.. -y*Ww if R<!:1.5

. (0.764*Ww) if ~<1.5 W1=1371 *kip

x I = 129.3 ;in*_

Page A-2 Revision O By MSL 5/29/96 Chk. TMT 5/29/96

.I

('

y S&A 93C2806.~

Dresden A-46/IPEEE SAi V I := -g-* cw H + W s + W 9 SAi MI:= -g-*(WH*X H + Ws*Xs + WrX 9 Sloshing Mode Calculation C003 Appendix A A-46 SSE VI= 596*kip MI= 6480*kip*ft ft f c '" 1.S*~*tanh[ 1.835{~ l f c ~ 0.284*HZ S Ac := 0.07*g Dresden SSE Ground Spectra @0.5% Damping at 0.5 Hz

sAc := Scale*SAc S-Ac =0.091*g w£ "046~tanh[1.B3s(~)Jww Xe:=

H cash 1.835*R - 1 1" -

H

H 1.835*R*sinh 1.835*R Vertical Mode 1

1 [

(. 2* R.

1) ]-2

. f v := 4* H. pf \\ts* Es + K fv = 7.49*Hz W c*= 567 *kip X c = 234.5*in v c = 52*kip Mc= 1008*kip*ft 0.9*fv = 6.741 *Hz 1.1*fv = 8.24*HZ S Av := 0.21 *g 2/3 Horizontal, 5% Damping, 10% shift S Av := Scale* S Av Demand SRSS{x,y) := Jx2 + y2 V sh := *sRSS(V I* V c)

M sh := SRSS(M 1.M c)

S Av = 0.273 *9 V sh= 598*kip M sh = 6558 *kip* ft PageA-3 Revision O By MSL 5/29/96 Chk. TMT 5/29/96

S&A 93C2806.04 Dresden A-46/IPEEE Pressures

(

)

y := ( H - 126* in), H.. H p st(Y) := YfY SAc 0.267*Ww*-- cosh g

in psi psi psi. psi 1~~111~:~~11~~~11~:~~11~:;:1 Pep:= Pst(H) + Psh(.H) + 0.4*Pv(H)

Elephant Foot Buckling R

S1 :=--

400*t s s 1 = 1.207 Calculation C003 Appendix A A-46 SSE

/

Pi= 2.153*psi P sh(Y) := SRSS(P i, P c(y))

P srri(Y) := SRSS(P sh(Y),P v(Y))

psi 1~:;~~1 P cp = 15.583*psi Pcm= 13.425*psi P tm = 9.117 *psi Pa= 11.271 *psi cr ye := cr ys cr ye = 18

ksi

.

s cj:>>

1 36* ksi

. (

cr ye )

0'6 E [

(p R) 2

] (

)

S 1 + --

ap'"W*1-aye*ls

1-1.12+S1'*'*

Sp1

_cr p*= 4597~psi lb C Be= 1903*.,-m PageA-4 Revision O By MSL 5/29/96 Chk. TMT 5/29/96

\\ /

S&A 93C2806.04 Dresden A-46/IPEEE Diamond Shape Buckling1 1 IE cj>,:= 16'~1§ cl>= 1.373 y := 1 - 0.73{1 - e-~)

y =.0.455 I

Calculation C003 Appendix A A-46 SSE

=0.319 Pcm ~R) 2 Es ts.

Page A-5 Revision 0 By MSL 5/29/96 Chk. TMT 5/29/96

!J..y := 0.17 Manually from Figure Figure 6 of NASA SP-8007 based on Pc-Es a cb '" (

0.6*y + Ay)* ~R) ts C Bd :=er cb*ts Fluid Hold Down Force P.:= P st(H) - 0.09*P sh(H) - 0.4*P y(H)

P = 11.077*psi E s*ts3 K := -12_-(_1 --v2~)

2*K*K

. Ks :=-R-L := Hn,2*in.. 30*in Ks*L*

F(L) := 1 + 2*E s*l'b lb C Bd = 4138*.,-

m lb CB= 1903*.,-m Average pressure for fluid hold-down calculation Coefficient of Psh must match (1 +cosb)/2 at end of c~lc.

K =.28.24 K = 7279*1b*ft Ks = 22222* lb MF= 334*1b

( ) \\

S&A 93C2806.04

(

Dresden A-46/IPEEE

(

t 2 t 2)

M pb :=minx CJ us*+,CJ ub*+

)

lculatlon C003 Appendix A A-46 SSE M pb = 0. 197. ki~* in in

' kip F H = 0.172*-.

in 3000 0.5 o e( L) 2000 T e{L)

', T m{L)

T e(L)

L o e(L}

lb in in

. in 1

-0.002 192.949 Te( L)

~

~")

1000 0 0 0.5 i := 0.. 30

o. := o e(0.2*i*in + 7*in)

I Ti:= T e{0.2*i*in + 7*in)

T eO := intercept{ o, T)

T e1 := slope{o,T}

70 60 T eO + T e1*1i e(L)

~~)

50 1

L Page A-6 Revision O By MSL 5/29/96 Chk. TMT 5/29/96 L

1.5 2

2.5

\\

lb T eO = 61.487 *.,....

in lb

, T e1 = 126.796*-

in2

.. o e( L).*

in

I S&A 93C2806.04 Dresden A-46/IPEEE L limit:= 13.B*in o eO := o e(L limiy h c := 6.75*in LH e := T e1 *0 eO o eO = 0.401 *in

(

Scale*Av\\

W te := (W H +.w s)" 1 - 0.4*

9

)

C. ( ) *-

1 + cos( p).

1 P.- sin(p) + (7t - p)-cos(p)

C ( ) := sin(p)-cos(p) + 7t - p 2 p 1 +cos( p)

Calculation C003 Appendix A A-46 SSE C

=

sin(P) - P*cos(p)

_ 1 + cos(p) 3(P)

sin(p) + (7t - p)-cos(p) 1 - cos(p)

C ( ) := P-sin(p)-cos(p) 4 p 1 - cos( p) p1 := 2.54 Initial Guess Nb:= 20 i := 1,2.. Nb A b := 4.0* in2

. 360 d a.:= 1*-* eg I

Nb cos fa~ - cos( p1) o *- o 0. _

_.~

'.J. ___ _

ei.-

e 1 - cos(p1)

T bi:= maxx(minx(o e_i*K b,T sc)'O*kip)

/

p d* := 2 '2.1.. 3 h a := 33.0* in 2.2 Wte = 17 *kip p*ageA-7 Revision 0 By MSL 6/29/96 Chk. TMT 5/29/96 Tse:= 10.57*kip.

2.4 2.6 2.8.

3

-r~

S&A 93C2806.04 Dresden A-46/IPEEE J3 = 2.629 1 + cos( J3) 0 c := 0 eo*....,..1---c-o-s(.,.-13....,..)

\\I

(

Es*ts*Oc

\\

C m := minx h c

, C B}

Calculation C003 Appendix A A-46 SSE 1 + c~s( 13 ) = 0.064 lb Cm = 1903*.,-m MSC := c m*C 2< J3 )* R2 t-L:T bi" R cos( a~ t-T eo*R2*2*sin( J3) t-Li T e*C 4( J3 )* R2 I

M sc = 6554*kip*ft COF := 0.7 v SC:= COF-W ve V SC= 1233 *kip

~

MSC V SC)

HCLPF := minx ~

~

PGA sh sh HCLPF = 0.26

g Page A-8 Revision 0 By MSL 5/29/96 Chk. TMT 5/29/96

S&A 93C2806.04 Dresden A-46/IPEEE Calculation C003 Appendix B IPEEESME Page B-1 Revision O By MSL 5/29/96 Chk. TMT 5/29/96 Dresden Contaminated CST, NP-6041 Appendix H Procedure, SME Input R := 222*in H := 342*.in H s := 384*in H d := 13.875*in ts := 0.46* in th:= 0.1875*in ta:= 0.302*in tb := 0.25*in

Es := 9800*ksi

. v := 0.3 K := 300*ksi CJ ys := 18*ksi CJ us := 32* ksi CJ yb := 6.264* ksi CJ ub := 12.6*ksi yt := 62.4* pct.

rs:= 165*pcf Yf Pf:= -g Ys Ps := -g Radius Fluid Height Shell Height Dome Height Shell thickness Head shell thickness Average shell thickness Bottom plate thickness S.hell Young's modulus Poisson's ratio Definitions kip := 1000* lb ksi kip

.- in2 lb psi:= -

in2 lb pcf := 3 ft minx(x,y) := if(x>y,y,x) maxx(x,y) := if(x>y,x,y)

Fluid bulk modulus, Mark's Standard Handbook, 9th Ed., Table 3.3.2 Shell yi.eld stress Shell ultimate stress Bottom plate yield stress Bottom plate ultimate stress Fluid weight Shell weight Av = 0.2* g ZPA of Dresden SME vertical ground spectra PGA. = 0.20* g Assumed, must iterate so that the demand Msh is close to the capacity Msc

~SE = 0.3*g

. PGA Scale. : = SSE ZPA'ot Dresden SME ground spectra before reduction

S&A 93C2806.04 Dresden A-46/IPEEE Weight Summary Hs Xs:=2 2

. Ww := 7t*R *H*yf Impulsive Mode ta R = 0.00136 Calculation C003 Appendix B IPEEE SME X H = 390.9 *in w s = 15*kip Ww=1912*kip H R = 1.541 C WI := 0.104 Frequency coefficient from Haroun *and Housner (1981)

J°.127'p s c u := c wr c u = o.oa Pf Cu ~s f1*=--* -

. 2*7t*H Ps 0.9* f I = 5.025 *Hz 1.1*f1=6.141 *Hz f1=5.583*Hz" S Al := 0.64* g From Dresden SME Ground Spectra 5% Damping, peak of the spectra S Al :; Scale* S Al S Al = 0.427 *g

_\\

W1,o (1 - 0.436*~*Ww W ~>1.5 (0.764*Ww) if ~<1.5 WI = 1371 *kip x

1 o [(as -o 188* ~)HJ it ~>15

~0304 H :7) ff~< 15

.. XI= 129.3'*in Page B-2 Revision O -

By MSL 5/29/96 Chk. TMT 5/29/96

S&A 93C280J r Dresden A-46/IPEEE SAi V I := -g-"(W H + W s + W 9 SAi M 1 :~ T*(WH*X H + Ws*Xs + wrx 9 Sloshing Mode Calculation C003 Appendix B IPEEE SME VI= 593*kip

. MI= 6445*kip*ft ft f c ** 1.5*f'. tanh[ 1.835{~) ]

f c = 0.284. Hz S Ac:= 0.17*g From Dresden SME Ground Spectra 0.5% Damping at 0.35 Hz S Ac := Scale* S Ac

'S Ac = 0. 1-13

g w

c ** 0.46-~*tanh[ 1.835*~) Jww H..

cosh 1.835*R - 1 X c :=

1 -;-.

H

H 1.835*R*sinh 1.835*R SAc.

Vc:=--*Wc g

SAc Mc:=-g-*Wc*Xc, Vertical Mode fv**4 1H(;f~::. *~)f~

fv = 7.49*H.z w c = 567*kip X c ='234.5 *in v c = 64*kip Mc= 1256*kip*ft

. /

0.9*fv = 6.741 *HZ 1.1*fv = 8.24*Hz Page B-3 Revision 0 By MSL 6/29/96 Chk. TMT 6/29/96 S Av := 0.427

g From Dresden SME Vertical Ground Spectra 5% Damping,, peak of the spectra S Av := Scale* S Av S Av = 0.285

g Demand I 2 I 2 SRSS(x,y) :=.JX + y v sh :~-* SRSS~cv: I* v

~).

V sh= 596*kip Msh := SRSS(M 1.M c)

M sh = 6566 *kip* ft

S&A 93C2806.04 Dresd.en A-46/IPEEE Pressures

)

y := (H-126*in),H.. H Calculation C003 Appendix B IPEEESME P st(Y) := YfY SAi WrXr-P i :=

92 1.36*RH Pi= 2.141 *psi SAc 0.267*Ww*-- cosh g

S Av (rc H - y)

P v(Y) :~ 0.8*rrH*-.-9-*cos,.f-H-*

P sh(Y) := SRSS(P i,P c(Y))

P sm(Y) := SRSS(P sh(Y),P v(Y))

psi l~:~~cil Pep:= Pst(H) + Psh(H) + 0.4*Pv(H)

Pcm:= Pst(H) + Psh(H)- 0.4*Pv(H)

\\

Ptm := Pst(H)- Psh(H)- 0.4*Pv(H)

Pa:= P st(H) - 0.4*P v(H)

Elephant Foot Buckling R.

S 1 := 400*ts a ye:= a ys a p = 4593*psi C Be := 0.9*cr p*t s s 1 = 1.207 a ye= 18 *ksi lb C Be= 1901 *.,-m P cp = 15.618*psi Pcm= 13.368*psi P tm = 9.082 *psi Pa= 11.225*psi Page B-4 Revision 0 By MSL 5/29/96 Chk. TMT 5/29/96

\\ J S&A 93C2806.04 Dresden A-46/IPEEE

Diamond Shape Buckling

$ := 1~*r.

$ = 1.373 y := 1 - 0.73* (1 - e-~)

y = 0.455 I

Calculation C003 Appendix B IPEEE SME

= 0.318 Pcm ~R) 2 Es ts Page B-5 Revision O By MSL 5/29/96 Chk. TMT 5/29/96 6.y := 0.17 Manually from Figure Figure 6 of NASA SP-8007 based on Pc-Es a cb '~ (0.6-y + "r)* ~R) ts C Bd := cr cb*ts CB := minx(C Be,C Bd)

Fluid Hold Down Force P := Pst(H)- 0.09*Psh(H)- 0.4*Pv(H)

P = 11.032*psi E s*t s 3 K := -12~-(-1 --v2~J 2*K-K Ks :=-R-L := 1*in,2*in.. 30*in Ks*L F ( L) := 1 + 2 E I

s* b lb C Bd = 4138*.,-m lb Cs=1901*.,-m Average pressure for fluid hold-down calculation Coefficient of Psh must match (1 +cosb)/2 at end of calc 1C = 28.24 K = 7279*1b~ft Ks= 22222*1b MF= 333*1b

( ) \\

S&A 93C2806.04

(

Dresden A-46/IPEEE M pb ** minx(a us:

1 2

,o ub*

1

')

}.

L in 1

5 e{L) in.

-0.002 T 0 {L)

( )

)

j lculatlon C003 Appendix B IPEEE SME M pb = 0.197. ki~* in m

/

0.5 Se(L)

Page B-6 Revision O By MSL 5/29/96 Chk. TMT 5/29/96 kip F H = 0.172*-.

m 0 1---------

T m{L)

~'

93./64.

93.. 09 93.022 92.984 92.998 93.093 93.302 93.663 94.216 95.007 96.082 97.487 99.271 101.477 104.145 107.312 111.007 115.253 120.066 125.457 131.431 137.988 145.125 152.835 161.112 169.945 179.325 189.241 199.685 210.645

--0.5 0 3000 2000 T e(L) 1000 0 0 0.5

. i := 0.. 30 oi := o e{0.2*i*in +?*in)

Ti:= T 0 {0.2*i*in +?*in)

T eO := intercept{ o, T)

T e1 := slope{ 5, T)

T e(L) 70

~

j'._")

60 T eO + T e1*Se(L)

~~)

50.

2 L

1.5 2

2.5, L

lb T eO = 61.236*in lb

/\\.

T e1 = 126.796 *-

in2 40L-------'-----L----~

0 0.1 0.2 0.3 Se(L) in **

S&A 93C2806.04 Dresden A-46/IPEEE L limit:=* 13.S*in o eO = o e (L limi9 h c := 6.75*in AT e := T e1* 0 eo o 00 =0.4*in W

te * (W H

+ W s} (1 -o 4* Seal; Av) 1 +cos( p)

C 1CP) := sin(p) + (7t - p)-cos(p) sin(p)-cos(p.) + 7t - p C2(P) :=

1 + cos(p)

Calculation C003 Appendix B IPEEE SME sin(p) - P*cos(p) 1 + cos(p)

C,3(p) := sin(p) + (7t - p)-cos(P>° 1 - cos(p) p - sin(p)-cos(p)

C 4(P):=

1-cos(p) p1 := 2.54 -

Initial Guess i := 1,2.. Nb T bi:= maxx(minx(o ei*K b,T sc),O*kip) p d := 2 '2.1.. 3

Nb:= 20 A b := 4.0* in2 ha := 33.0* in Wte = 17 *kip Page B-7 Revision 0 By MSL 6/29/96 Chk. TMT 6/29/96 T BC := 10.57*kip

/

S&A 93C2806.04 Dresden A-46/IPEEE p = 2.629 1 + cos( p) 0 c := 0 eo*-1---c-o-s(_p_)

M sc _= 6S49 *kip* ft COF := 0.7 2

Wve := Wte + P a*7t*R v SC:= COF*W ve

\\I

(

MSC V SC)

HCLPF := minx ~

~

PGA sh sh Calculation C003 Appendix B IPEEE SME 1 + c;s(p) = 0.064 lb Cm = 1901 *.,.-m V SC= 1229 *kip HCLPF = 0.199*9 Page B-8 Revision O By MSL 5/29/96 Chk. TMT 5/29/96

\\

ML17191A589

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