Text

Forwards Revision 2 to Seismic Analysis of Waterford Ses Spent Fuel Storage Racks, Design Calculations for Reinforced Concrete Block Walls
	ML20003H742
Person / Time
Site:	Waterford
Issue date:	05/05/1981
From:	Pierson M; EBASCO SERVICES, INC.
To:	Rinaldi F; NRC
Shared Package
ML20003H743	List: ML20003H742; ML20003H745; ML20037D011;
References
	L-LOU-81-144, NUDOCS 8105070380
	Download: ML20003H742 (67)
	v • d • e

.

EBASCO SERVICES INCORPORATED EB6SCO Two World Trace Center. New York. N Y.10048 May 5, 1981 L-LOU-81-144 e

l$

TO:

F Rinaldi (NRC)

D FROM:

M A Pierson

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SUBJECT:

LOUISIANA POWER & LIGHT COMPANY p

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WATERFORD SES UNIT NO. 3

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STRUCTURAL ENGINEERING BRANCH N y f'

AUDIT FOLLOW-UP l

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Co As discussed at the Structural Engineering Branch Audit held in New York during the wcek of April 6, 1981, please find enclosed the following information:

1.

One copy of design calculations for reinforced concrete block walls and associated drawing G-765502.

2.

One copy of report on seismic analysis of Waterford SES spent fuel storage racks as prepared by Wachter Associates, Inc., Gibsonia, Pa.

3.

One copy of report on non-linear analysis for fuel impact, Waterford SES Unit No. 3 spent fuel racks as prepared by Wachter Associates, Inc., Gibsonia, Pa.

4 One copy of catalogue of design calculations submitted in two parts:

Part I - Civil Design Calculations of Reinforced Concrete Structures; Part II - Civil Design Calculations of Steel Structures.

Additionally, the following is enclosed for your information:

1.

FSAR Pages 3.8-63, 3.8-63a and 3.8-78, as submitted in Amendment 17, addressing masonry wall design on the Waterford-3 project.

/

2.

Draft revised responses to Questions 130.15, 130.17, 3o0 110.20, 130.23, 130.26 and 130.28 and page 3.5-18 as s

wi.1 be submitted in the forthcoming Amendment 18.

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We believe the forwarding of this information is in accordanceg i

with your verbal request.

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RS6 F:/s3 If there are any questions, please de not hesitate to call (2:2) 839-3805.

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MAP:eco f

o Enclosure cc:

(w/o encl) l S Kebiusek-Black (NRC)

P C Huang G Harstead 81050703TQ

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b WSF.S-FSAR-UNIT-3 Rolled Shapes, Bars and Plates A36-69 or A441-70, A533 Crade B, class 2

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High Sttength Bolts A325-70s or A490-67 Other Bolts A307-68 Stainless Steel A167. Type 304L Other types of eted were used in small quantities in the internal structures as required.

Mill test reports were obtained for structural steel materials used.

3.8.3.7 Testing and Inservice Inspection Beauirements There are no testing and inservice inspection program for the internal struc-tures.

3.8.3.8 Masonry Wall Design All concrete block masonry walls in the proximity of safety related piping or equipment and those enclosing stairwells and elevators are not classified seismic Category I but have been designed to withstand safe shutdown earth-quake.

The primary function of these concrete block masonry walls, Maich vary in thickness from 8 to 12 inches, is to act as a barrier or as a fire wall with a minimum fire rating of 2 hours2.314815e-5 days <br />5.555556e-4 hours <br />3.306878e-6 weeks <br />7.61e-7 months <br />. The hollow cores are filled with mortar every 4 feet on center and are reinforced with two #6 vertical bars on each face. Every second course (16 inches) is reinforced horizontally with extra heavyweight "Dur-O-Wal" trusses.

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The hollow concrete block load units conform to ASTM C-90, Grade N-1 and are 1f composed of normal weight aggregate conforming to ASTM C-33 with cinders unacceptable. The vertical reinforcing steel is deformed, intermediate grade, new billet steel conforming to ASTM A-615, grade 60.

The horizontal steel reinforcement conforms to ASTM A-116, Class 3.

The mortar is in com-pliance with ASTM C-476 having a minimum compressive strength of 2500 psi.

The laying of these blocks is in accordance with the recossmended practices for laying concrete block by the Forcland Cement Association. The hollow cells that are filled with mortar are throughly rodded every two courses to t

eliminate entrapped air voids. All concrete block masonry walls receive a full mortar bedding prior to embedding the horizontal reinforcement so as l

to obtain proper bonding and covered with an additional spread of mortar l

if necessary to insure full embeddoent.

One other function of the concrete block sesonry walls is to provide shield-ing. These are mainly multiple wythe walls with each individual wall hori-zontally reinforced with extra heavyweight "Dur-O-Wal" trusses at every The composite behavior of the walls is assured by connecting the l

course.

horizontal reinforcing between the individual walls with 16 gage bent straps at 6 inches on center horizontally in each course and 16 inches on center l

vertically in alternate courses. At the end supports the walls are inter-l connected with a mortar fill and the horizontal reinforcement is intercon-i (

nected with a continuous #4 reinforcing bar.

3.8-63 Amendment No.17, (4/81) l y

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r WSES-FSAR-UNIT-3 The shield walls resisting pressurization loads have a maximum span of 4 feet and those without pressure loading have a maximum span of 10 feet.

The shielding concrete blocks are the solid type with a maximum uniform dansity of 138 pounds per cubic foot and a minimum compressive strength of 4000 psi.

Although the concrete block masonry walls are not considered to be seismic Category I, these walls are designed so that in the event of a seismic g,*

cc:urrence or an accident condi' tion, all concrete block masonry walls in the proximity of safety related equipment, components or structures will remain intact.

There are no safety, related piping systems or equipment being supported directly or indirectly on the Waterford-3 concrete block masonry walls.

3.8-63a Amendment No.17, (4/81)

WSES-FSAR-UNIT-3

2) Variation from true circular section: not more than j; three in. in radius from vertical axis of vessel

3) Variation of wall thickness: not more than - 1/4 in. or more than + one in.

b)

Dome

1) Variation from true spherical section: not more than j; three in.

in radius

2) Variation in dome thickness: not more than + one in. or more than

-1/2 in.

3.8.4.6.1.5 Special Construction Techniques a)

Shield Building The three it. cylindrical portion of the Shield Building was constructed by using the slip form construction technique.

The dome was constructsi in two stages by first forming a thin layer of structural concrete supported by a form, which was in turn sup-ported by the does of the steel containment vessel. The second stage of the dome was supported on the thin dome, which was designed for its dead load, construction load and dead load of the second stage. A typical reinforcement of the Shield Building done is shown in Figure 3.8-41.

3.8.4.6.2 Reinforcing Steel

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See Subsection 3.8.3.6.2 3.8.4.6.3 Structural Steel See Subsection 3.8.3.6.3 3.8.4.7 Testing and Inservice Surveillance Requirerents Testing of structural materials during the preoperational and construction period is discussed in Subsection 3.8.4.6.

There are no planned systematic testing or surveillance programs for the seismic Category I structures af ter the plant has been placed in operation.

The structural steel framing and connections will be generally accessible to visual inspection.

3.8.4.8 Masonry Walt Desian 17 Refer to Subsection 3.8.3.8 3.8.5 FOUhDATIONS 3.8-78 Amendment No. 17, s4/81)

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Question No.

130.15 State the minimum thickness of concrete barriers (both walls and (3.5.3) roofs) provided for all Category I structures resisting the effects of the postulated tornado winds and missiles. These barriers should meet the requirements for design against locr8 penetration, scabbing, spalling and overall effects. Also, identify the minimum values of the concrete compressive strength ~

(f ') and the typical reinforcement details.

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Response

The minimum thickness of concrete barriers (both walls and roof s) provided for all seismic Category I structures resisting the effects of postulated tornado winds and missiles is 2 feet, as stated in FSAR Table 3.5-11.

The 28-day design compressive strength for all Category I concrete structures subject to tornado missile impact is 4000 psi minimum (refer to FSAR Subsection 3.8.4.6.1.2).

The typical reinforcement for the Category I buildings exterior walls and missile barrier walls varies from No. 6 reinforcement at 12 in. spacing to No.11 at 12 in. spreing at cach face of the wall.

The depths of penetration in concrete surfaces' calculated for the tornado missiles postulated for the site are given in FSAR Table 3.5-10.

To prevent spalling or scabbing, the minimum thickness of concrete barriers provided exceeds 3 times the depth of penetra-tion as calculated by the modified Petri formula except for the one in. diameter steel rod. For the steel rod, with velocity of t

317 fps at moment of impact (FSAR Table 3.5-10), the least thickness of concrete barrier is 2.92 the depth of penetration

, calcalated.#The thich:::: f:::ich:2 i: : ffici::, :::::lin; ::

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i; ;;ti;fied hy th; ;;;n;;; i_ :in thi:h:::::: :p::ified. For additional information on spalling and scabbi.ng, refer to l

I response to Question 130.14.

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Overall damage prediction for concrete barriers is discussed in FSAR Subsection 3.5.3.2.1.

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b WSES-FSAR-UNIT-3 Question No.

130.17 You have stated that Regulatory Guide 1.60 has higher response (3.7.1.1) in the low to intermediate frequency ranges than the responw spectra proposed for the structural / seismic analysis of Water-ford-3.

Identiff the Category I structures that fall in this low to intermediate f requency range. For each of these structures, select three key points, determine the safety margins available and compare them with the values determined in the current r

analysis.

Response

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free thr : :i:; th: ynth: tic !! : hi:::ry_ "; etili: ire 1:r::

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U Reference 37-5 Refer to FSAR Subsection 3.7.1.1.1 Tables 3.7-1 and Figures 4

3. 7-1 through 3.7-4 as amended.

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130.17-1 Amendment No. /,I (4rf9tt l

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In general, as depicted in revised Figures 3.7-1 through 3.7-4, the Regulatory Guide 1.60 spectral gurves fall below the Water-ford-3 synthetic time hitecry spectral curves.

The portions of R.G. 1.60 spectral curves exceeding the Waterford-3 synthetic time history spectral curves are all less than 10 percent in magnitude within the significant range of periods (See Tv;?c 130.17-1).

In comparisons of spectral and time history meth.sds, FSAR Tables 3.7-6 to 3.7-9 show that the structure responses using Waterford-3 design spectra have less than a 10 percent difference from those using the synthetic time history.

The as identified in Table 130.17-1 effects of spectral variances on structural responses are evaluated according to the magnitude of mode contributions under seismic excitation.

The mode frequencies of the combination structures are shown in Table 3.7-5.

Since the structure design is governed by the cases with a higher soil shear modulus (G) value, the mode frequencies considered herein are those of G=16,050 psi, i

The first mode frequency is 1.68 and 2.09 cycles per second (eps) for horizontal (E-W and N-S) and vertical earthquake respectively.

i The spectral value for frequencies smaller than 1.68 cps are not utilized in the design, therefore, their variances are insignificant.

Fk+cen V The few remaining negative variances are only related to higher modes with less than 10 variances.

Since no negative variances are found within the first mode frequency range, the positive gain in the first mode is more than enough to cover the negative loss of higher modes.

The Waterford-3 synthetic time history spectral acceleration near F=1.68 cps is larger than R.G.

1.60, with more than 15 percent positive variances.

1 In studies to ensure the inclusion of all significant modes, i

the magnitude of mode contributions has been determined.

The results indicate that the first mode has a dominant effect on the overall structural responses, approximately 60 and 90 percents respectively f or horizontal and vertical excita tions.

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a dominant effect with the positive spectral variduces of the first mode resulted in obtaining my more conservative structural The 4t//o'sgto'en *f response values for design.

0; tili;;;;31ower damping values in the Waterford-3 design,as compared to the damping values identified in R.C.

1,61 (see revised Table 3.7-1), tends to provide an additional conservativeness for the design; therefore, it is concluded that the small spectral variances as identified in Table 130.17-1 have no effect on the structural safety of the Category I structures.

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TABLE t 7-COMPARISONS OF SPECTRAL ACCELERATION (g)

(Waterford #3 Vs. R.G. 1.60) 10 fS D A Design Base Earthquake, 2% Damping (Refer Figure 3.7-1) 5 Point Number (1)

(2)

(3)

(4)

(5) 4#

Period (sec) 0.09 0.10 0.37 1.40 2.00 0.60 Frequency (eps) 11.11 10.00 2.70 0.71*

0.50*

1.68 Waterford #3 0.28 0.31 0.38 C.M 0.10 0.38 NRC R.G. 1.60 0.30 0.34 0.40 0.15 0.11 0.29 Difference

-0.02

-0.03

-0.02

-0.01

+0.09 Differnece in %

-6.67

- 8.8

-5.00

-7.1

-9.10

+31.0 6

1* ps#A Design Base Earthquake, 5% Damping (Refer Figure 3.7-2)

A Point Number (1)

(2)

(3)

(4) 74 #

Period (sec) 0.33 0.43 1.5 3.00 0.60 Frequency (cps) 3.03 2.33 0.67*

0.33*

1.68 Waterford #3 0.28 0.27 0.12 0.05 0.27 NRC R.C. 1.60 0.30 0.29 0.13 0.055 0.23 Difference

' -0.02

-0.02

-0.01

-0.005

+0.04 Difference in %

-6.67

-7.0

-7.69

-9.10

+17.4

64 A J

Operating Base Earthquake, 2% Damping (Refer Figure 3.7-3)

A Point Number (1)

(2) k#

Period (sec) 1.40 1.90 0.60 Frequency (cps) 0.71*

0.53*

1.68 Waterford #3 0.070 0.048 0.180

.3 NRC R.G. 1.60 0.075 0.055 0.155 Difference

- 0.005

- 0.007

+0.025 Difference in %

- 6.67

- 12.73

+16.1 is F9Y Operating Base Earthquake, 5% Damping (Refer Figure 3.7-4)

Point Number (1)

(2)

(3)

(4) f(M Period (sec) 0.11 0.34 0.41 3.00 0.60 Frequency (cps) 9.09 2.94 2.44 0.33*

1.68 i

Waterford #3 0.11

,0.155 0.15 0.025 0.13 NRC R.G. 1.60 0.12 0.160 0.16 0.028 0.11 Difference

-0.01

- 0.005

- 0.01

- 0.003

+0.02 Difference in %

- 8.30

- 3.10

- 6.30

- 10.7

+18.2

Those spectral variances in frequency range less than 1.68 cps sh

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WSES-FSAR-UNIT-3 Question No.

130.20 State if the time history response spectra envelopes the design (3.7.1.2) response spectra for all damping values used in design with no more than five (5) points f alling below (all within ten (10) percent) the design spectra.

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y gg Revised FSAR Figures 3.7-1 to 3.7-4 show clearly that the, time history spectra envelopes by a large margin the design response i II spectra for all damping values.

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Reference Refer to FSAR Figures 3.7-1 to 3.7-4 as amended.

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1 se csled 130.20-1 Amendeent No, % (+/01-)

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6 WSEE-FSAR-UNIT 3.

Question No.

130.23 State the criteria employed for system / subsystem decoupling. The (3.7.2.3) following criteria are acceptable for the staff:

(3.7.3.3) 1.

If R (.01, decoupling can be done for any Rg 2.

If, Al$ R,$.1, decoupling can be done if.82Rg21.25 3.

If R,).1, an appropriate model of the subsystem should be included in the primary systets model.

where:

R, = Total mass of the supported subsystem Mass that supports the subsystaa f = Fundamental frequency o f the supported subsystem a

R Frequency of the dominant support motion l

State if you comply with our criteria. If not, provide l

justification for your proper criteria.

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Response

j jM All major equipment,and subsystems f Waterford-3 satisfy the decoupling criteria stipulated in SRP 3.7.2, II.3.b.

The R 's are in the range of.02 to.05 and 0.8 2Rg21.25. Therefore,e4, M m__-_,r__

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3 WSES-FSAR-UNIT-3 Question No.

130.26 State if the fundamental frequency of subsystems is controlled (3.7.3.4) to be greater than twice or less t'aan one-half the dominant frequency of the supporting syster.

Response

The fundamental frequency of piping subsystems is less than one-half of the dominant frequency of the supporting system.

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130.26-1 Amendment,No. -it, (#91-)

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WSES-FNAR-UNIT =3 Question No.

130.28 State if you have considered accidental torsional effects in the (3.7.2) analysis of category I structures. Provide tt'e information related to the percent of accidental torsion considered in your analysis and the results of the analysis. It is the staff position that a minimum of 5 percent accidental eccentricity should be considered due to the facte that both construction tolerances and the internal structures would introduce some degree of eccentricity effect. This can be accomplished by evaluating the structures considering a 5 percent accidental eccentricity. That is the distance between the actual center of mass and the center of rigidity must be modified by the 5 percent eccentricity. This modification should consist of an addition of 5 percent and a subtraction of 5 percent from the center of mass, with the controlling case used for the actual design.

Response

FSAR Subsection 3.7.2.11 describes the torsional analysis.

Figure 3.7-21 shows the torsional model used for the analysis.

Table 3.7-10 lists the torsional responses of each structure.

Since torsional effect accounts for only approximately 5 percent

'of the total responses, the additional 5 percent accidental l

eccentricity will contribute only 1/4 of 1 percent of the total response. This is considered negligible.

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Refer to FSAR Subsection 3.7.2.11 as amended.

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130.28-1 Amendment No. 4+, W

WSES-FSAR-UNIT-3 SECTION 3.5: REFERENCES 1.

Salvatori, R., " Failure Angle of Disc," Westinghouse, May 24, 1971.

2.

Bush, S., " Probability of Damage to Nuclear Components Due to Turbine Failure," Nuclear Safety 14_, November 3,1973.

3.

" Full-Scale Tornado Missile Impact Tests," EPRI NP-148, April 1976.

4.

Russel, C.R., " Reactor Safeguards," Pergammon Press, New York,1962.

5.

" Concrete Manual" - Bureau of Reclamation, 8th Edition, 1975, p. 45.

6.

Recht, R.F. and Ipson T.W., " Ballistic Perforation Dynamics," Journal of Applied Mechanics, September 1963.

7.

Amirikian, A. " Design of Protective Structures" U.S. Navy Bureau of Tards and Docks, August 1950.

8.

" Introduction to Structural Dynamics" by J. Biggs, McGraw Hill Book Co, 1964.

1 9.

" Impact Effect of Fragments Striking S;_ructural Elements" by 1 A Williamson and R R Alvy; Holmes & Nerver Inc, November 1973.

10.

Air Force Design Manual

" Principles and Practices for Design of Hardened Structures" - Technical Document Report No.' AFSWC-TDR-62-138, December 1962.

11.

" Full-Scale Tornado Missile Impact Tests" EPRI NP-440, July 1977.

6 12.

"A Review of Procedures for the Analysis and Design of Concrete Structures to Resist Missile Impact Effects" by R P Kennedy; Holmes and Narver Inc., September,1975 13.

Norris, C H, etc., " Structural Design for Dyn-sic Loads" McGraw Hill, 1969.

14.

Rotz, J V. Symposium on Tornadoes; Assessment of Knowledge and In-plications for Man", Texas Tech University, Lubbock, Texas,1976.

17 15.

" Tornado-Borne Missile Speeds" NBSIR 76-1050 by Emir Simiu and Martin Cordes, April,1976 (prepared for the U.S. NRC).

16.

"A Report on a Pipe Missile Wall Shot Test" by MA Suarez February 15, 1973.

17.

" Structural Analysis and Design of Nuclear Plant Facilities" by ASCE, January 1976.

(Chapter 6 " Design against Impulse and Impact Loads).

/ T.

",J A -S T J -W =L y )C L.;eppt gp-,yg, r &p % s L c m,r 4 r aA y & M OJgth s

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W g d r/x. 3.5-18 Amendment No. +7, (W el l

s.

I. CIVIL DESIGN CALCULATIONS OF REINFORCED CONCRETE STRUCTURES i

l i

l l

l

t FILE NO.

TITLE 6W12-DA-001(Q)

Report on Dyn. Analysis Vol. 1

-002(Q)

Report on Dyn. Analysis Vol. 2

-003(Q)

Combined Structure Tortional Analysis

-004(Q)

Input Data

-005(Q)

Computer Output - Vol. 1

-006 (Q)

Computer Output - Vol. 2

-007 (Q)

Computer Output - Vol. 3 (Floor Spectrum Curves G=16050 PSI Original)

-008 (Q)

Computer Output - Vol. 4 (Comb. Str.

Tortional Analysis G=16050 PSI)

-009(Q)

Computer Output - Vol. 5 (Tortional Analysis G-6400 PSI)

-010 (Q)

Computer output - Vol. 6 Fl. Spectra.

(R/B Mass #8) G-16050 DBE(5%) OBE(2%)

-Oll(Q)

Computer output - Vol. 7 (Fl. Spectra Masses #17, 24, 31, 37, 39 DBE E-W j

G=5800, 8000, 16050)

-012(Q)

Computer Output - Vol. 8 (Response by Spectrum Method 5% G=5800, 6400, 8000, 16050 PSI)

-013 (Q)

Computer Output - Vol. 9 (Fl. Spectra 1% Mass #17, 24, 32, 38, 40 DBE Vert.

G=5800, 8000, 16050)

COMMON MAT 6W12-CM-001 (Q)

Stress Analysis - Vol.1

-002(Q)

Stress Analysis - Vol. 2

-003 (Q)

Stress Analysis - Vol. 3 (Dead Load)

-004 (Q)

Stress Analysis - Vol. 4 (Buoyancy) l

-005 (Q)

Stress Analysis - Vc). 5 (L.L. HOR. SOIL l

PRES OBE)

-006 (Q)

Stress Analysia

.Vol. 6 (DBE, FLOOD SOIL PRES) 1 1

-007 (Q)

Stress Analysis - Vol. 7 (EQUIP. LCAD, &

COMBINATION) l

-008(Q)

Stress Analysis - Vol. 8 (Load Combination)

-009(Q)

Stress Analysis - Vol.

9.- (Spring Constant)

-010 (Q)

Stress Analysis - Vol.10 (Cooling Tower Area)

I-l

l FILE NO.

TITLE 6W12-CM-Oll (Q)

Stress Analysis - Vol.11 (Foundation Design)

-012 (Q)

Stress Analysis - Vol. 12 (Heat of Hydration)

-013 (Q)

Stress Analysis - Vol. 13 (Finite Element Model)

REACTOR BUILDING 6W12-RB-001 (Q)

Design Calc - Vol. 1 (Shield Structure)

-002 (Q)

Design Calc - Vol. 2 (Secondary Shield Wall)

-003 (Q)

Design Calc - Vol. 3 (Secondary Shield Wall)

-004 (Q)

Design Calc - Vol. 4 (Primary Shield Wall)

-005 (Q)

Design Calc - Vol. 5 (Equip. Flexibility) r00G tQ):

Design Calc - Vol. 6 Shield Structure -

Block-out Stresses)

-017(Q)

Design Calc - Vol. 7 (Internal Structure -

Design)

-008 (Q)

Design Calc - Vol. 8 (Jet Impingement)

-009 (Q)

Design Calc - Vol. 9 (Steam Gen. Foundation)

-010 (Q)

Computer Input - Vol. 1 (Temperature)

-Oll(Q)

Computer Input - Vol. 2 (Temperature) l

-012 (Q)

Computer Input - Vol. 3 (Temperature)

-013 (Q)

Computer Input - Vol. 4 (Temperature) f

-014 (Q)

Computer Input - Vol. 5 (Pipe Restraint and Stop Loads)

-015 (Q)

Computer Input - Vol. 6 (Jet Impingement)

-016 (Q)

Computer Input - Vol. 7 (Jet Impingement)

-017 (Q)

Computer Input - Vol. 8 (Finite Element Model)

-018 (Q)

Computer Output - Vol. 1 (Shield Structure Geometry)

-019 (Q)

Computer output - Vol. 2 (Shield Structure Geometry)

-020 (Q)

Computer Output - Vol. 3 (Loading)

-021 (Q)

Computer Output - Vol. 4 (Loading)

-022 (Q)

Computer Output - Vol. 5 (Loading) l

-023 (Q)

Computer Output - Vol. 6 (Loading)

-024 (Q)

Computer output - Vol. 7 (Load Combination) l

-025 (Q)

Computer output - Vol. 8 (Load Combination)

I-2

FILE NO.

TITLE 6W12-RB-026 (Q)

Computer output - Vol. 9 (Load Combination)

-027 (Q)

Computer output - Vol. 10 (Load Combination)

-028 (Q)

Computer Output - Vol. 11 (Load Combination)

-029 (Q)

Computer Output - Vol. 12 (Load Combination)

-030 (Q)

Computer output - Vol. 13 (Penetration Analysis - Geometry)

-031(Q)

Computer Output - Vol. 14 (Penetration Analysis - Geometry)

-032 (Q)

Computer Output - Vol. 15 (Penetration Analysis - Loading)

-033 (Q)

Computer Output - Vol. 16 (Penetration Analysis - Loading)

-034 (Q)

Computer Output - Vol. 17 (Penetration Analysis - Loading)

-035 (Q)

Computer Output - Vol. 18 (Penetration Analysis - Loading)

-036 (Q)

Computer Output - Vol. 19 (Penetration Analysis - Loading)

-037 (Q)

Computer Output - Vol. 20 (Penetration Analysis - Loading)

-038 (Q)

Computer output - Vol. 21 (Penetration Analysis - Loading)

-039 (Q)

Computer Output - Vol. 22 (Penetration Analysis - Load Combination) l

-040 (Q)

Computer Output - Vol. 23 (Penetration Analysis - Load Combination)

-041 (Q)

Computer Output - Vol. 24 (Penetration Analysis - Load Combination) l

-042 (Q)

Computer Output - Vol. 25 (Penetration l

Analysis - Load Combination)

-043 (Q)

Computer Output - Vol. 26 (Penetration Analysis - Load Combination)

-044 (Q)

Computer Output - Vol. 27 (Penetration Analysis - Load Combination)

-045 (Q)

Computer Output - Vol. 28 (Penetration Analysis - Load Combination)

-046 (Q)

Computer Output - Vol. 29 (Coolant Pump Supp. Flexibilities)

-047 (Q)

Computer Output - Vol. 30 (Coolant Pump l

Supp. Flexibilities)

I-3 l

e s

FILE NO.

TITLE 6W12-RB-048 (Q)

Computer Output - Vol. 31 (Internal Structure-Geometry)

-049 (Q)

Computer Output - Vol. 32 (Internal Structure-Loading)

-050 (Q)

Computer Output - Vol. 33 (Internal Structure-Loading)

-051 (Q)

Computer Output - Vol. 34 (Internal Structure-Loading)

-052 (Q)

Computer Output - Vol. 35 (Internal Structure-Loading)

-053(Q)

Computer output - Vol. 36 (Internal Structure-Loading)

-054 (Q)

Computer Output - Vol. 37 (Internal Structure-Load Combination)

-055 (Q)

Computer Output - Vol. 38 (Internal Structure-Load Combination)

-056 (Q)

Computer Output - Vol. 39 (Internal Structure-Load combination)

-057 (Q)

Computer output - Vol. 40 (Internal Structure-Load Combination)

-058 (Q)

Computer Output - Vol. 41 (Primary Shield Wall)

-059 (Q)

Computer Output - Vol. 42 (Secondary Shield Wall - Coolant Pump Support)

-060 (Q)

Computer Output - Vol. 43 (Shield Structure -

Derrick Strut Load)

-061(Q)

Computer Output - Vol. 44 (Shield Structure -

Block Out Model)

-062(Q)

Computer Output - Vol. 45 (Shield Structure -

Block Out Model)

-063 (Q)

Computer Output - Vol. 46 (Shield Structure -

Shield Structure - Pilaster)

-064 (Q)

Computer Output - Vol. 47 (Inner Ring Girder and Dnbedded Ring)

-065 (Q)

Computer Output - Vol. 48 (Primary Shield Wall - Accident Pressurc)

REACTOR AUXILIARY BUILDING 6W12-RAB-001 (Q)

(Floor Slab) Design Calc - Vol. 1

-002 (Q)

Design Calc - Vol. 2 (Ext. Wall Design)

-003 (Q)

Design Calc.- Vol. 3 (Bemn Design)

-004 (Q)

Design Calc - Vol. 4 (Beam Design)

I-4

FILE NO.

'IITLE 6W12-RAB-005 (Q)

Design Calc - Vol 5 (Misc Design)

-006 (Q)

Design Calc - Vol 6 (Column Design)

-007 (Q)

Design Calc - Vol 7 (Beam Design)

-008 (Q)

Design Calc - Vol 8 (Beam Design)

-009 (Q)

Design Calc - Vol 9 (Wall Emb P1 Loading Review El - 35 to -4.0)

-010 (Q)

Design Calc - Vol 10 (Slab Emb Pl Loading Review E1 -4.0 to +21.0)

-Oll (Q)

Design Calc - Vol 11 (Wall Emb P1 Loading Review El 21.0)

-012 (Q)

Design Calc - Vol 12 Slab Emb P1 Loading Review El +21.0 to El 46.0)

-013 (Q)

Design Calc - Vol 13 (Slab Emb Pl Loading Review El +35.0)

-014 (Q)

Design Calc - Vol 14 (Slab Emb P1 Loading Review El +46.0)

-015 (Q)

Design Calc - Vol. lb (Wall Emb P1 Loading Review El _46.0 to 69.0)

-016 (Q)

Design Calc - Vol 16 (Slab Emb P1 Loading Review El +69.0)

-017 (Q)

Design Calc - Vol. 17 (Slab & Beam El +46.00)

-018 (Q)

Design Calc - Vol 18 (Slab & Beam El +69.00)

-019 (Q)

Computer Input - Vol 1

-020 (Q)

Computer Input - Vol 2

-021 (Q)

Computer Input -U1 3 (Pipe Impingement From Mech)

-022 (Q)

Computer Input - Vol 4 (Pipe Restraint Load)

-023(O)

Computer Input - Vol 5 (Ed3 Pl Load at El +35.0)

-024 (Q)

Computer Input - Vol 6 (Dd) P1 Load at El +46.0)

-025 (Q)

Computer Input - Vol 1 (Frame 2A)

-026 (Q)

Computer Output - Vol 2 (Frame 3A)

-027 (Q)

Computer Output - Vol 3 (Frame 4A)

-028 (Q)

Computer Output - Vol 4 (Frame 6A)

-029 (Q)

Computer Output - Vol 5 (Frame 7A) l

-030 (Q)

Computer Output - Vol 6 (Frame 8A)

-031 (Q)

Computer Output - Vol 7 (Frame 10A)

I-5 l

l

FILE NO.

TITLE 6W12-RAB-032 (Q)

Computer Output - Vol 8 (Frame 11A)

-033 (Q)

Computer Output - Vol 9 (Frame El)

-034 (Q)

Computer Output - Vol 10 (Frame H2)

-035 (Q)

Computer Output - Vol 11 (Frame J)

I

-036 (Q)

Computer Output - Vol 12 (Frame K)

-037 (Q)

Computer Output - Vol 13 (Frame K)

-038 (Q)

Computer Output - Vol 14 (Frame M2)

FUEL' HANDLING BUILDING 6W12-FHB-001(Q)

Design Calc - Vol 1

-002 (Q)

Design Calc - Vol 2

-003 (Q)

Design Calc - Vol 3 l

l

{

l l

l I-6 l

c

l d

II.

CIVIL DESIGN CALCULATIONS OF STEEL STRUCTURES i

I

FILE NO.

TITLE 8QL-1-1 Typical valve Suppcrt Connection Details 80L-1-2 Typical Seismic Support Models G-694 ard G-695 Series 8QL-1-3 Seismic Supports for HVAC Valves Dwg 694 S53; 54; S71; S72; S73 80L-1-4 Cable Tray & Duct Supports (Typical Details)

G-695 Series 80L-1-5 Design Calculation for Stop:

A B, D&E f

G-696 8QL-1-6 Design Calculation for Stop "C" G-696 80L-1-7 Coolant Pump Support Design G-696 S01 and S02 8QL-1-8 RCB RCS Pipe Stops - Model Records

[

l II-l

FILE NO.

TITLE 80L-1-9 Electrical Seismic Supports Type:

1; lLB; 2; 3; 4; 5 and 6 80L-1-10 Electrical Seismic Supports Type:

7; 8; 9; 10; 11; 12; 13 and 14 8QL-1-ll Electrical Seismic Supports Type:

15; 16; 17; 18; 19; 20 and 21 8QL-1-12 Electrical Seismic Supports Type:

22; 23-lb; 24; 25; 26; 27; 28; 29 and 30 8QL-1-13 Electrical Seismic Supports Type:

31; 32; 33; 34; 35; 36 and 37 80L-1-14 Electrical Seismic Supports Type:

38; 39; 40; 42; 43; 44 and 45 8QL-1-14 Electrical Seismic Supports Type:

46; 47; 48; 49; 50; 51; 52 and 53 80L-1-15 Electrical Seismic Supports Type:

54; 55; 56; 57; 58; 59; 60 and 61 8QL-1-16 Electrical Seismic Supports Type:

62; 63; 64; 65; 66 and 67 80L-1-17 Electrical Seismic Supports Type:

68; 69; 79; 71; 72 and 73 80L-1-18 Electrical Seismic Supports Type:

74; 75; 76; 77: 78; 79 and 80 l

80L-1-19 Electrical Seismic Supports Type:

81; 82; 83; 84; 85; 86 and 87 8QL-1-20 Electrical Seismic Supports Type:

88; 89; 90; 91; 92; 93 and 94 8QL-1-21 Electrical Seismic Supports Type:

95; 96; 97; 98; 99; 100; 101 and 102 80L-1-22 Electrical Seismic Supports Type:

103; 104; 105; 106; 107; 108 and 109 80L-1-23 Electrical Seismic Supports Type:

110; 111; 112; 113; 114; 115; 116 and 117 II-2

i FILE NO.

TITLE 8QL-1-24 Electrical Seismic Supports (Unistrat)

Type:

118; 120; 122; 124; 125; 126 and 127 80L-1-25 Electrical Seismic Supports (Reduced Steel)

Type:

118; 120; 122; 124; 125; 126 and 127 8QL-1-26 Electrical Seismic Supports (Exist Steel)

Type:

118; 120; 122; 124; 125; 126 and 127 80L-1-27 Electrical Seismic Supports Type:

119; 121; 123; 128 and 129 8QL-1-28 Electrical Seismic Supports Type:

131; 132; 133; 134; 135 and 136 8QL-1-29 Electrical Seismic Supports Type:

137; 138; 139; 140; 141; 142 and 143 80L-1-30 HVAC Seismic, Supports (Valba), Dwg G-694 S71; S72 and S73 80L-1-31 HVAC Seismic Supports (Valve) Dwg G-694 S71 and S73 8QL-1-32 HVAC Seismic Supports (Valve) Dwg G-694 S72 8QL-1-33 HVAC Seismic Supports (Valve) Dwg G-694 S54 80L-1-34 HVAC Seismic Supports (Valve) Dwg G-694 S54; i

S71; S72 and S73

(

I 80L-1-35 Seismic Conduit Supports (Static Analysis)

From "A" to "T"

8QL-1-36 Seismic Conduit Supports (Static Analysis)

C-1A; C-1B; C-lC; C-2A; C-2B; C-2C; JB-1A; JB-1B and X 8QL-1-37 Seismic Conduit Supports (Frequency Analysis)

H; J; L; Ml; M2; N; P; Q; R; S and T 80L-1-38 Seismic Conduit Supports (Unistrat)

Type:

W2U and W3U 8QL-1-39 Seismic Supports For Cable Tray Section E70; E47 and E2 II-3

FILE NO.

TITLE 80L-1-40 Seismic Supports for Cable Tray Section E39 80L-1-41 Seismic Supports For HVAC and Electrical Type:

78B; 79As 80; 97; 98A; 100; 121 and 122A 8QL-1-42 Seismic Supports With Bergen Paterson Loads CCRR-1283; 1287; 1364; 1282; 1287; 1420 and 1510 and 1442 4

8QL-1-43 Seismic Supports With Bergen Paterson Loads CCRR-1368; 1370; 1419; 1337; 1369; 1378 and 1365 80L-1-44 Cable Tray Seismic Supports w/Bergen Paterson Loads CCRR-1523; 1498; 1499; 1495; 1351; 1497; 1339; 1326 and 1492 8QL-1-45 Electrical Seismic Supports w/Bergen Paterson Loads Type:

E-148; H-ll54 8QL-1-46 None assigned 8QL-1-47 None assigned 80L-1-48

~

Tornado Missile Project Structure G-697 S01 and S02 80L-1-49 Construction Trestle Inside Cont Dwg G-699S01 and G-699S02 80L-1-49A Constructicn Trestle Inside Cont Dwg G-699 S03 8QL-1-50 Screen Safety Inj System G-702 80L-1-51 Pipe Restraints G-704 S01 8QL-1-52 Pipe Restraints G-704 S02 80L-1-53 Pipe Restraints G-704 S03 80L-1-54 Pipe Restraints G-704 SO4 and SOS 80L-1-55 Pipe Restraints G-704 S06 80L-1-56 Pipe Restraints G-704 S07 8QL-1-57 Pipe Restraint G-704 S08 8QL-1-58 Pipe Restraint G-704 SO9 8QL-1-59 Pipe Restraint G-704 S10 II-4

FILE NO.

TITLE 80L-1-60 Pipe Restraint G-704 S11 80L-1-61 Pipe Restraint G-704 S12 80L-1-62 Pipe Restraint G-704 S13 80L-1-63 Pipe Restraints G-704 S14 8QL-1-64 Pipe Restraints G-704 S15 80L-1-65 Intake Structure - Misc Steel G-705 8QL-1-66 Tornado Missile Protection Structure G-707 S01 and G-707 S02 80L-1-67 Pressurizer Support Structure G-711 80L-1-68 Safety Injection Tank Support Structure G-712 80L-1-69 Missile Shield Over Reactor G-713 S01 80L-1-70 Missile Shield Over Reactor G-713 SO2 8QL-1-71 Missile Shield over Reactor G-713 S03 8QL-1-72 Decontamination Area-Liner Plates and Misc Steel G-799 S03 80L-1-73 Reactor Bldg Misc Steel G-800 80L-1-74 Reactor Bldg Platforms G-801A and G-801B 80L-1-75 Reactor Bldg Platforms G-802A; G-802B and G-802C 80L-1-76 Reactor Bldg Platforms (Part I) G-802D; 802E and G-802F 80L-1-77 Reactor Bldg Platforms G-802D; 802E and G-802F (Part II) 8QL-1-78 Reactor Bldg Stairs G-803 and G-804 80L-1-79 Reactor Bldg Misc Steel G-805 8QL-1-80 Reactor Bldg Misc Steel'G-806 II-5

FILE NO.

TITLE 8QL-1-81 Reactor Bldg Elev Framing G-807 8QL-1-82 Reactor Bldg Steam Generator G-808A amd G-809A 8QL-1-83 Reactor Vessel Grillage Foundation G-810A&B (book #1) 80L-1-84 Reactor Vessel Grillage Foundation G-810A and 810B (bk #2) 8QL-1-85 Reactor Vessel Grillage Foundation Computer Input Form G-810 A&B (bk. #3) 80L-1-86 Reactor Vessel Grillage Foundation Computer Input Form G-810 A&B (bk #4) 8QL-1-87 Reactor Vessel Grillage Foundation Computer Input Form G-810 A&B (bk #5) 80L-1-88 Reactor Vessel Grillage Fo'2ndation Computer Input Form G-810 A&B (bk 16) 80L-1-89 Reactor Bldg:

Steam Generator Sliding Base G-812 8QL-1-90 Reactor Bldg:

Misc Steel G-813 8QL-1-91 Reactor Bldg:

COLUMN Schedule Anch Bolt Plan G-814 80L-1-92 Reactor Bldg:

Misc Steel G-815 80L-1-93 Reactor Bldg:

Canal Liner G-821A; G-822A and G-823A 80L-1-94 Reactor Aux Bldg:

Restraints (Book No. 1)

G-824A; G-825A and E-826A; B; G and E 80L-1-95 Reactor Aux Bldg:

Restraints (Book No. 2)

G-824A; G-825A and G-826A! B; C and E 8QL-1-96 Reactor Aux Bldg:

Restraints (Book No. 2)

G-826F 80L-1-97 Reactor Aux Bldg:

Restraints (Book No. 4)

G-826D 80L-1-98 Reactor Aux Bldg:

Pipe Restraint Steel G-829J and K; G-832A; B and C II-6

FILE NO.

TITLE 80L-1-99 Reac'ccr Bldg:

HVAC Duct Support G-834A; B and C 8QL-1-100 Framing Over Steam Generator G-838A; G-839A and G-839B 8QL-1-101 Framing Over Steam Generator Computcr Output 8QL-1-101A Framing Over Steam Generator Computer Output 8QL-1-102 Reactor Bldg:

Dome Access Stairs Platforms G-840 80L-1-103 Reactor Aux Bldg:

Stairs, Platf; Monorail and Missile Prot.

G-842B and G-842C 80L-1-104 Reactor Aux Bldg:

Stairs, Platf; Monorails and Missile Protection G-842D 80L-1-105 Fuel Handling Bldg Spent Fuel Pit Liner G-845; G-846 and G-847 80L-1-106 Fuel Handling Bldg:

New Fuel Storage Racks G-849 80L-1-107 Fuel Handling Bldg:

Misc Steel G-850 80L-1-108 Reactor Aux Bldg:

Misc Steel G-892 S01 80L-1-109 Reactor Aux Bldg:

Misc Steel G-892 S02 80L-1-110 Reactor Aux Bldg:

Misc Steel G-893 S01 thru S05 80L-1-lll Reactor Aux Bldg:

Misc Steel G-893 S06 80L-1-ll2 Reactor Aux Bldg:

Misc Steel G-893 S07 l

l 8QL-1-113 Reactor Aux Bldg:

Misc Cteel G-893 S08 80L-1-ll4 Reactor Aux Bldg:

Misc Sttel G-893 SO9 l

l 8QL-1-115

~;eactor Aux Bldg:

Misc Steel *:-893 S10 80L-1-ll6 Reactor Aux Bldg:

Stairs & Platforms G-894 S02 and S03 j

80L-1-ll7 Embedded Plates (Book No. 1) G-896 S01 II-7 I

FILE NO.

TITLE 8QL-1-ll8 Embedded Plates (Book No. 6) G-896 SO2 80L-1-119 Hatch Covers G-897 S01 80L-1-120 Hatch Covers G-897 S02 8QL-1-121 Cooling Tower Area Framing & Platforms G-904 S01 thru S07 8QL-1-122 Reactor Aux Bldg:

Refuel Pit Liner G-905; G-906 and G-907 8QL-1-123 MS & FW Pipe Anchorages G-908 S01 8QL-1-124 MS & FW Pipe Anchorages G-908 S02 80L-1-125 Reactor Aux Bldg:

Pipe Restraints G-912 80L-1-126 Plant Stack G-915 l

80L-1-127 None assigned 80L-1-128 Reactor Bldg:

Misc Steel G-937 80L-1-129 RB Reactor Cavity Grillage Foundation Computer Output G-810A and G-810B l

8QL-1-130 RB Reactor Cavity Grillage Foundation l

Computer Output G-810A and G-810B 80L-1-131 RB Reactor Cavity Grillage Foundation Computer Output G-810A and G-810B 80L-1-132 RB Reactor Cavity Grillage Founde. tion Computer Output G-810A and G-810B 3OL-1-133 RB Reactor Cavity Grillage Foundation Computer Output G-810A and G-810B 8QL-1-134 RB Reactor Cavity Grillage Foundation Computer Output G-810A and G-810B 8QL-1-135 RB Reactor Cavity Grillage Foundation Computer Cutput G-810A and G-810B 80L-1-136 RB Reactor Cavity Grillage Foundation i

l Computer Output G-810A and 810B l

II-8

FILE NO.

TITLE 8QL-1-137 RB Reactor Cavity Grillage Foundation Computer Output G-810A and G-810B 8QL-1-138 RB Reactor Cavity Grillage Foundation Computer Output G-810A and G-810B 8QL-1-139 Hard Restraints - Spring Rates G-704 Series 80L-1-140 Hard Restraints - Spring Rates G-704 Series 80L-1-141 Hard Restraints - Spring Rates G-704 Series 80L-1-142 Hard Restraints - Spring Rates G-704 Model 8QL-1-143 Hard Restraints - Spring Rates G-704 Model 80L-1-144 Hard Restraints - Spring Rates G-704 Model 8QL-1-145 Model Computer Output; Stop:

A, B, D and E G-696 S03 thru S06 80L-1-146 Safety Injection Tank - Computer Output G-712 80L-1-147 Safety Injection Tank - Computer Output G-712 8QL-1-148 Safety Injection Tank - Computer Output G-712 80L-1-149 Safety Injection Tank - computer Output G-712 80L-1-150 FW Pipe Restraints - Outside Ccnt G-826 Series-Computer Output 80L-1-151 FW Pipe Restraints - Outside Cont G-826 Series - Computer Output 80L-1-lS2 Steam Generator Sliding Base G-812 - Computer Output 80L-1-153 Steam Generator Sliding Base G-812 - Computer Output 80L-1-154 Reactor Bldg:

Steam Generator Upper Supports G-808A and 809A - Computer output l

80L-1-155 Reactor Bldg:

Steam Generator Upper Supports G-808A and G-809A - Computer Output II-9

FILE NO.

TITLE 8QL-1-156 Presturizer Supports Computer Output G-711 8QL-1-157 Pressurizer Supports Math Model G-711 80L-1-158 Steam Generator Lower Support Finite Element Model G-812 l

i II-10

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NON-LINEAR ANALYSIS FOR FUEL IMPACT WATERFORD SES UNIT NO. 3 SPENT FUEL RACKS LPL-T-149 f

Rev. O, November 1979

.%v.

1, April 1980 i

Prepared by [-

I!I!EO

/i Stokef/

W.

F.

M.

C 8['

Reviewed by e

E. R.

Frantz i

f

t NON-LINEAR ANALYSIS FOR FUEL IMPACT WATERFORD SES UNIT NO. 3 SPENT FUEL RACKS 1.0 OBJECTIVE The object of this analysis is to study the effects of the clearances between the fuel elements and the rack structure, and between the rack structure and the foundation, when the foundation is subjected to a seismic disturbance.

The rack structure is considered to be resting on the ground, and to slide when the friction force is insufficient to keep it moving with the ground.

The fuel elements are considered to rest in the rack at its center, with a simple support (hinge) between the two.

The space between the fuel element and the rack wall is filled with water se that as the fuel and the wall move relative to each other, hydrodynamic forces are set up due to the acceleration of the water.

These forces are exerted on the fuel and in the rack structure.

Methods described 1

2 by Fritz and Dong are used in this analysis to determine these hydrodynamic forces.

The input to the model is an acceleration time history

--having points at time intervals of 0.01 sec.

The displace-

- ment and velocity of the ground.are found by integrating l

the acceleration curve twice.

The ground' displacement is I

not tmed in any calculation.

^

i of Immersed Solids", Jour. Eng. for Ind., ASME (Feb. 1972), page 172.

2

Dong, R.C., " Effective Mass and Damping of Submerged Structures",

UCRL-52342, Lawrence Livermore Laboratory.

y

-,--e v

,,. ~.,

p.

,,g,---

c -

- s s

2.0 MATERIAL DESCRIPTION A mathematical uodel representing an 11 mass system is used.

This model is shown in Figure 1 and is similar to the model used in the finite element beam model (Appendix G, Seismic Analysis Report), except that the mass of the fuel is separated from the mass of the rack.

The numbered masses represent the following:

Mass No.

Parts 1

1/10 rack mass, 1/10 fuel mass, base mass 2-5 1/5 Rack mass 6

1/10 rack mass 7-10 1/5 fuel mass 11 1/10 fuel mass

- (Note:

The mass of the enclosed water is included in fluid coupling)

A stiffness formulation is used in finding the stiffness matrix, but the following are described as flexibilities.

Plexibility No.

1-5 Bending and shear flexibility of the rack 6-10 Bending flexibility of fuel a, b Compressive flexibility of seismic supports c thru 1 Local flexibility of the rack and fuel element where they meet.

c thru 1 have clearances, so that no force is exerted by the spring until the displacement of the parts exceeds this clearance.

i

t

3. 0' THEORY The governing equationa will be written explicitly for a two mass system, and then extended to a general multi-mass system in matrix form:

yy=471 1 12*2 + Psl + Fyyk + F yyh+F x4

+F (1}

mx y

Fl

2

2 " 'N21*l-k22*2 s2 + F 2+F22*2 + Iw2y + FF2

+

(2) 21 where g = mass i m

g = displacement of mass i x

kg3 = the force exerted by the structure on mass i by a unit displacement of mass j F ) = hydrodynamic force exerted on mass i due to g

a unit acceleration of mass j,

described in Fritz (loc. cit.). (F usually negative, gg others positive.)

F g = force exerted on mass i due to a unit acceleration of the wall; described in Appendix F.

Fyy = friction force acting on mass i (only F7 l

0 here) l F,g = force exerted on mass by gap spring l

y = ground displacement l

En matrix form equations (1) and (2) are i

i 1

-F "i-Fy1 12 4

1)=

11 ' 12

1 F,1 F

~

s1

+ 4 _.) y_+q.___ g yy

)

.(3) 4 *2 y+4

_- F21 "2-F

-k Fs2 Fw2 F

22

2 21 22,

~

F2 I

l l

l I

s Solving for the acceleration yields:

_t x

m -F

-F Fy y'

'F y

y yy 12 11 12

1 si yy i

i=

21 2

22

' 21 -b2 4 *2 :p+<

P

)+4

>y N

)

(4)

2

-F F

F

~

s2 w2 F2

~

/

i

~

For a multi-mass system, the matrix form of this equation is:

_1

-K{X} +{Fs}+{F,} h

+{F }

X=

M 7

(5)

{ } represents column matrices and M includes the hydrodynamic effects F ).

y In the F (fluid coupling) matrix, there are two effects considered, 1) coupling between the fuel and the rack walls, and 2) coupling between the rack walls and the pool walls.

For the mass elements representing the rack wall, the diagonal terms of the matrix include the following terms, (rack mass i and fuel mass j are opposite each other).

ii " Hj #

lj + M2i

NHWi (Sa) i l

'dhere MHj ydrodynamic mass of the fuel mass element.

=

M13 = mass of water displaced by fuel.

M

= mass of water that would be contained in the rack f

21 if no fuel was present.

These are the same as the terms in M f Eq (1), page C2 of H22 Appendix C.

MHwi = hydrodynamic mass of the rack mass element in the pool.

This term is the same as term M of the same equation.

ggy For the mass elements representing the fuel, the term F33 =

M the same as the first term in Eq. (Sa).

Hj, _-

.~

1 The off diagonal terms, which represent coupling between the-b fuel and the rack are, referring to term M f Eq. 1), App. C.

H12 F)=MHj + lj f

The effect of the ground motion on the rack is stored in the last column of the fluid matrix and is F y=MHwi - M,g (Sc) 1 Where M s defin'ed above Hwi W

mass of water displaced by the rack.

lwi Note that this matrix is simply an extension of Eq. (1), App.

C in which the rack mass is acted on by both the fuel and the wall by fluid coupling.

In the program, equation (5) is solved in the following order

-K {X} is calculated to give the force or each element due to the structure

{Fs}

is calculated and added to -K {X}

F is calculated for each clearance by first finding the 3

difference between the deflections of the masses involved. If l

this difference is less than the clearance, the force is zero.

l If it is greater than the clearance, the spring force is found by multiplying the spring deflection, (i.e. the above difference minus the cleacance) by the spring constant.

This spring force is added to the other structural forces applied to each of the masses involved.

{F }

is calculated, as described below p

~1

-1 {F,},which The product M

-K {X } + (F is calculated.M s

is constant and s+ sted, is multiplied by h and added to the

~

l l

above.

The product M~1 (Fp} is calculated and added.

l l

~r~'

=

The acceleration relative to ground is found by subtracting the ground acceleration.

The idealized coefficient of friction would be represented by the following diagram.

The static coefficient of friction di u, applies if there is no relative velocity vrel between the base of the rack and the ground.

For numerical reasons, it is assumed that if the velocity is less than a small value Vy,there is no relative velocity.

~

The factor '4 is used because most computers do not calculate zero for real numbers, even when a numerical calculation would indicate that to be the answer.

The value of V used v

/h is a very small velocity used to forestall this problem.

The actual value used is somewhat arbitrary, but the results are quite insensitive to the value, since it only comes into play occasionally, i.e., when the relative velocity is between zero and the value uced.

Friction Force between Base and Ground j

d a s l

A-l t

Yv V d l

Equation (1) is solved for F using predicted values of

~

py acceleration.

This calculation yields the force required to keep the base moving at the same velocity as the ground so that no relative motion occurs.

If F is less than u,N, the maximum py friction force, the calculated value is used.

If it is greater than u N, then Fpy = p N and relative motion may occur.

s s

gg

- 6.-

ev---

-g--s em-.-,

,,y v.

---7--

l If v is greater than V the following is used to repre-rel y

sent the friction.

h

)$ -

V Vrel g,g l

The rationale for this modification is that, because the normal force N between the base and the ground is much greater than the weight of the base, the maximum kinetic friction force could be large encugh (in the calculation) to change the sign of the relative velocity during the time interval.

Consider the following example :

N = 4Wy, where Wy is the weight of mass 1.

uk = 0.45 kinetic coefficient of friction.

At = 0.001 sec.

V - V, = Vrel g

= 0.3 ft/sec.

g The friction force acting on the mass would be db F

= p N = 4W x 0.45 = 1 8W p

k y

1 The acceleration that this would give to the mass, ignoring structural and fluid effects, is:

1.8W F

y a = I- =

W

= 1.8g = 1.8 x 386 = 695 in/sec 1

M 9

During the time interval At, this would cause a change of velocity.

AV = aat = 695 x.001 =.695 in/sec. _ - -.-

t Thus, after the time interval the relative velocity would be V - V, = Vrel

- AV = 0. 3

. 6 95 =

. 395 3

y i.e.,

the mass would be aoving to the right relative to the di ground.

Now, of course, the direction of the friction force would reverse.

Note, however, that as soon as the relative velocity changes sign, during the time interval, the direction of the force would ghange.

One method of overcoming this difficulty might be to shorten the time interval At, but this would require longer running times.

The method used was to assume that the maximum force, if v is less than v rel break' is approximately that required to bring v

EE#0*i""U"17 rel zero if no other forces, structural or fluid, are acting.

In the above example, the break. velocity would be about Vbr "

0.695 so that the friction force would be Y

00 I

FF = yk rel N = 0.45 4W

= 0.777W b

.695j i i 0.777W1 a=

= 0.777 x 386 = 300 g

1 g

l The chance of velocity is 0.300 during the time interval so that the relative velocity does not change sign due to the friction force alone.

I i

i l f v

~

w Y

w

[,

1I 6

no C

f lo S

t I

4 7

4 8

3 3

0 3

7 2

2 4 7

h z I

L b

a M

M I

Ytel.

bO O

Fy; '

FIGURE 1 Eleven mass model for analyzing fuel, rack, and wall impact forces during seismic events. _

4.0 PROGRAM INPUT r.he following conditions were analyzed for an 80 module rack for Waterford Unit 3.

(The 80 module rack produces higher wall loadings, forces, and moments than the 64 module rack.

In this sense, it is conservative to analyze the 80 module rack.)

Case No.

Seismic Wall Cap *

(in)

Fuel Gau (in) 1 SSE (E-W) 0.25 0.30 2

SSE (N-S) 0.25 0.30 3

+0BE (E-W) 0.25 0.30 4

SSE (E-W) 0 0.30 5

SSE (E-W) 0 0

as measured from spring "a".

The initial gap on the right side is zero.

+

taken as SSE x (2/3).

TABLE 1 Various cases studied for the non-linear impact analysis.

A total of 13 different runs were made to study the effects of the following:

b a.

changes in V from.0001 to.01 in/sec y

b.

extent of cycle duration from 5 to 20 seconds.

c.

variations in the natural frequency (3 and 6 cps) and d.

stiffness of the fuel bundle (base case and times 1/10, 5, and 10).

These runs differ as indicated in Tables 1 and 2. _

~

5.

K thru K

V

~ Cycle Length Fuel Stiffness g

y Case No.

6 (10 lb/in)

(in/sec)

(sec)

Katio*

u 1

1 0.3

.01 20

'l 2

1 1.0

.0001 20 1

3 1

1.0

.0001 20 0.1 4

1 1.0

.0001 20 5

5 1

1.0

.0001 20 10 6

2 0.3

.01 20 1

7 2

0.3

.0001 20 1

8 3

0.3

.01 5

1 9

3 1.0

.0001 20 1

10 4

0.3

.01 5

1 11 4

1.0

.0001 20 1

i 12 5

1.0

.01 5

1 13 5

1.0

.0001 20 1

Although these two columns are related, either one can be varied independently of the other.

The moment of inertia of the fuel assembly determines the fuel stiffness.

The base case EI is derived on page 13 (calculation sheet 2).

Further derivations are given on page 18.

TABLE 2 Summary of input variations used for the non-linear analysis.

l l

~,

NECNAMCAL-NT,t2EM DEJICM WACHTER ASSOCIATES. INC.

EA E*L

b-[i"*"

SHEET NO.

1 OF d 77 II #I SUBJECT IMII DATE s

WsW 4 J PROJ.NO-137 CHKD.SY ISF DATE'/7112 O A

v$r -

Ceed,w 4.0 :L P L-T-Mf, 4 _.

I

-h- ; ; ;-

_ =

[.

NN8 l

l

~ "^

-IL& o=I;;w -L t

-h k mA y.y~,.

5

' ~

~

v3 L M res un it + 3 sg kk p at..- t&&,

&m a

s r~

a4,.

ea,,a [

~~~

r n

a s._

2 a # 3.

( w.

r s4 m as cat +o k (zo

~ u as z.+)

Pew 21to JAt [ 3 3) 1 0

ISTD X to =

{20, no.r %d /22/./l9: 3d7 x f 3a.4.4. : %ed m: + t (237 * [477.2.,$r M, Mg^ %_c = 3.E99 - 7o r#1]r. = %-s-i-: b a ~I T-!- l ' '_ ' S-1r4% 3 g 4 4,j f = % t-9= (0 i m.,, .l

~,

n.7,, e ; zo. 36 = 7 izu. Br = _ L '. 7, i= = m,, - u ffhhh t f ~ p-a,..,-.y. -.7.-w- ,-.-m ,,--vm.

MECHANICAL-NUCl.E4R DdSIGN ' WACHTER ASSOCIATES. INC. MadDd-No*-l'* SHEET NOe 2 OF sy of FS o4TE 79fta/ sus >EcT (3)*N N 63 EK.F UIIL O PROJ. NO. I3I DATE + n's - CHKD.sY L.PL-T,141 i ' G 0 /n..;( & C--5); . _...&...es;. s k = 4 Juo l.{ Sm p l <.h- .[ .sfi ( & "spiys' a-4. L ) CM Sf.b C -b.4 5 i ~ b Ed- - w.Ad % <e f.4 3 eg. T' 4 - Lip Fa.h Er= WN Y h g z (,g,4.) 2. cc-0 i f/foo _.L h (I7'l ( z n 3)*' gye t7si Sysj qg,4p j Er = 3.I7 Et? { Jir lo ) n &<A L A Cw-80 : EZ= 254E+8 }b in ** /r h5 = 37 I 3ex 19 14 1%", -fu La. eMec4ius l< ~)k 2 y 3 7 '= 74 - k-4F EI 4 t(25 4 Ee 8) J.q'y (7+) 5 - = 3.oed.=g -t c. gy i IJev M ~l[ l ~ 1 cj.. E .%<f re.c k : I Sc CC t J.$r. + Da@ w k : 1 To A l cell by $d 54: W* la / = 1g psim w+% 2v sf/c =

27. t.14. /cde t 7 7. 2 A ls /ea n

' f r o.t k. : w&hys >. (ro;(177.0; 14tyc.dk I u s.s..s u a < : (su40)(M + su.e = 2sne Jk ( IEA) : *b dlr ud y;+ (2r7er) = 32.i2.Ar. a = .,,m w e .,,.y.

~ WACHTER ASSOC 1ATES. INC. MECHANKAL-NEXI. EAR DESIGN U k5 DATE 77//0/ SUBJECT b -M-/sh S By SHEET NO= OF CHKD. B'.' DATE 77//20 Mb fey - WMC 40 03 PROJ.NO. I31 u LPL-T- /ff {. 4* L 2 c$rfd wdev z' ($ {7G + 32I2. = 17.Mth Ncb k ( pord rees.)- irs tir-17317 x /4eas 31.

i F/"id I* %

ex .r. 4. =. l o & Ed 4WIe. [~' i 4 " a ' @ Z.4 X Io) (It) ? = A I S4 in3 V i.a Up p t-c). = (AIN/pgg) ~ 22 + inVia T & 37 ( Yrl9.) F W= ? L2 +)[32) =29 93 k. (718 2@ b. = to ur = 239+.)bs (A), = Wy= } W, = 3Geo Jjr. w+wu= Goc a Jhr b r? " InX n W, t ulu= 30s.llr I f '4 " l N 9 --j (to) (f.5] P ( ltfl 'Z'I [ 3.2 h ;.I I '... [ .,-., t.l. [ . I. ] ws t, 171i 'tr(> I,..l t J... W.= 7tro_ A.P 3 7 l IAz = 3325A..C,v-Ifli." ^ l

~

i nie c q.y ( see s.r) W " ' Y * $ r) { ,','. f) = w,. i+s+ n a. w $ m,= w% ( g',).= n /c.r sir. m

. 'WAC5YER ASSOCIATES, INC. MEOfAMC4L ~ NUCLEAR DESIGN sy ' (A) Fi DATE 79//o/ sus;Ecr Lod 'D A-h- /,W SHEET NO. 4 0F 0 CHKD.8Y 6D' DATE '19 //20 $~~r W a-M PROT.NO-13 i ~ f PL-T-.~lt1 I; ' ;- ~ i i ' ' h. 1.h.j [._ [ ; - riAJi W, pw-rec 4, m o.cl : ~ y Mr= h ( i+r413 +. T314T){Tyr)= .2.Cl'.A.brl*n.

i 37" +

n = (31)(2U) = 11/6 fle " l' ca ~~ ~ I d r,". wq. 4.prf,J$., ~ f~ t h LA/t / W C.k. [d3.[ K [J.0 ) Wa-t A = hML (le3.t)(e3.04-)= 3II Niy-tur F.Iuid 4 % : & mi-w= 475s Mr. g ng-tp,s Wu+ vi w: Gwo+ n/a+ 7tSD z e a ~ 23,7 4 f lls. = $( L3, W-) = IIf t3.)Ar., Wd M7 '- a + vi, = 957+ (Ar)(sti)= 107I2.Ala-m, w ? ? "t-r - -i 2.(is7/s) =.m, 2. I f z2./4,.__ i, g- ~]' -i jk7/z../lr] (y., nz,si ,l ru- - kyl.n (e-ua .J. - 4

- r r

mmc r + !_j I i; [kf sh T a .i i r. -w y y ---w-, ,,-,.,e_

l s . WACHTER ASSOCIATES,INC. NECHAMCAL-NLt2E1A DE#CN BY 3 F5' DATE 8 /l0/ SUBJECT E8' 1 Da#k - hlw SHEET NO-OF $ ~ CHKD.BY DATE 77H2O ('S - fAk d'M M 3 PROJ.NO. OI -T- /41 LPL t-j .t .__L .__.__i

(&c.. d i4 A _ E-w '.c%).' '... L; iy l

Pnght :4 v-s r= 2ct,(,u

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,i.

i b56b MU 'h.. %.5- [ 2(li7to) = I15lO Ar ) s q I. I e ~ ~T ' i s ._. i ' I.- _ e-m--nww-~- -wm - - -me w -w.s.- w ,,,w-w w, e -m w m-mm -,w ,-n -w

( - WAbSTER ASSOCIATES. INC. MEGIANICAL-NLt2 EAR DESIGN a5r V FS oarg_21U0/ SUBJECT b#*d D* N - [/ den F" d OFI SHEET NO. CHKD. BY ERF carg 79t/24 A%e.r_ w.-/e h 6 3 p g o;, n o, f3f _ _. _ L. P L -T- /f7 f 4. , ' Co< A red:. cP FatA g*I i 1 L: !' 1' t .i SMt ( l v'g w l A.01 Wu) ,4, n 0.Cb k.d (v 4 fw I >.of ia/44 ONT [' Fp, ( ga -l) - l &= (.+TX I40 m) O ie"* Alr. T. r1,+. Ng, = ((, 7 7 2. +- STf 2. = 22.324 lle. !~! r-xr-u s 4.u h b h -! - Fr, 4 w g srp : L _.

F Um

2. f2 2.

1

a. -

-W. -, z. 514 z ~' SQ yded : .c o l.c.u.. 4u

a. p of = (2..f 2t )( 3rc)(.ooi)= /. ors 3 m.

vA.k % k. v< L c.,'i " E I.2 i-/c.u. n g is u.r d is p ny - >j. U i F i -t

j: 4.. i..

H.; , 3 R. E. Lul9 ' c" Inveshjakim q h Clth bu) n ph s9 Allwp (A i ssLaa.w Lo +e< Lalv.'w4<d C u chie s, d G.3 *.i D a E. Repet-p GM T.,20, Tan,.194o, _.-y.- -_.--g ,,._,,9 w

~. On page 13 (calculation sheet 2), a natural frequency of 3 cps was assumed for the fuel bundle. A value of 2,5 is typical (based on Dong, UCRL-52342, pp 4, 62). If the fuel cladding and control rod guide tubes are assumed to determine the natural frequency, a lower bound on EI can be calculated based on the zircalloy wall thickness. For a thin ring of radius 'r' and 3 thickness ' t',. the section moment of inertia is wr t. For a 3 fuel rod.382 inch 0.D.,.025 inch wall, wr t = x (.18) 3 (.025) = 4 4 ~ .00046 in, and for 236 fuel rods per bundle, I =.11 in. The five guide tubes are.97 inch OD,.90 inch ID, so I a x (.47) 3 (.0 35) (5) =.06 in. The bundle inertia is then.17 4 4 6 2 in. With E = 13 x 10 lb/in for the zircalloy cladding, 6 2 EI a 2.2 x 10 lb/in This. lower bound is approximately one order of magnitude lower than the calculated value on page 13. An upper bound or EI can be obtained by assuming that the grids and tie plates are effective in transferring shear from ro'd to rod. With the zircalloy area of 2 2 2 2 { (.382 .332 )(236) + {(.970 .90 )5 = 7.13 in Taken uniformly over the 8.18 = 67 in bundle area, 4 I (8.181 7. 3' Iz = 4 0 in i 6 i 8 2 EI = 5.2 x 10 lb/in which is now one order of magnitude higher than the value assumed for the fuel bundle. The base case fuel stiffness matrix is based on EI = 3.17 x 107 2 8 2 lb/in for the bundle and 25 x 10 lb/in for the entire 80 l module rack. Since this value could be subject to large un-certainties, K thru K and the fuel stiffness ratio were varied g to cover the ranges expected. ___

= - - 5.0 RESULTS AND CONCLUSIONS Analyses were performed for the conditions shown in Section 4.0. The results of these are shown in the follow'ing table. The maximum bending stresses are found using the formula: o = M2 I where for the East-West direction L = 172,846 in' and c = 41.52 in, for the North-South direction L = 268,626 in" and c = 51.90 in. These stresses occur in the outer wall of the rack. The base shear stress is.tound by dividing the peak shear 2 force by the shear area of 148 in. The pool wall compressive b stress is found by dividing the peak contact force by the snubber area of 88 in. Output from run no. 1 (case no. 1) is attached to th s report. Peak Rack Pool Wall Run No. Case No. Bending Stress Time. Base Shear Time Compressive Time I (psi) (sec.) (psi) (sec.) Stress (psi) (sec.) 4 1 1 2730 12.5 650 1.8 680 10.3 2 1 3030 3.4 560 4.78S 580 4.790 3 1 3080 12.622 580 12.622 610 4.8 4 1 4400 4.7 610 9.6 610 3.1 i 5 1 3790 4.2 580 2.8 470 1.9 f 6 2 2380 10.481 590 10.483 630 12.3 7 2 2020 4.7 510 2.593 590 2.605 8 3 2620 3.6 520 4.2 240 3.8 9 3 2920 13.3 530 19.3 280 3.1 10 4 2590 4.7 740 4.179 850 4.193 11 4 4500 13.2 1100 9.670 1450 9.675 ~ '12 5 660 4.700 180 4.701 -0 13 5 660 4.699 180 4.700 ~0 TABLE 3 Comparison of rack and wall stresses for non-linear impact analysis. h

Runs 8 and 9 indicate that the assumed EW-OBE (SSE x 2/3) has slightly lower stresses than the EW-SSE runs 1 thru 5. Runs 2 and 9 have all variables the same except the spectrum amplification dh factor. The times of pes'; stress intensities differ radically and this tends to mask differences in the bending and shear stresses. However, the peak wall compressive stress for run 9 is approximately half of that for run 2. The stress for run 1 may be compared with a bending stress dh of 670 x 1.5 = 1005 psi given in Section G.4.2 of the seismic report. The factor of 1.5 is introduced because the calculations in Appendix G, are for an OBE, while the present calculations are for an SSE. For run 1,.then, the stress is increased by a factor of f005 = 2.72 because of the fuel rattle effect. These two stresses are based on similar stick models, with and without clearance between the fuel and the rack. If this factor is applied to the North-South and the East-West seismic stress for SSE, Table I of the Seismic Analysis Report, the vertical seismic and static loading stresses remaining the same, the following combined stress is obtained. S = 2.72 (1600+2500) + 500 + 2100 = 13,750 psi The corresponding factor of safety is ,00 l N = 13 50 = 1.45 These: calculations for the effect of fuel rattle should be quite conservative. Since all of the fuel is lumped together, it is assumed that in the actual rack all fuel elements are moving to-( gether, so that the effect of fuel impact occurs simultaneously for all fuel elements. In the actual rack, the impacts are probably - r -- -- o--- e v

k The time step used for all computations was one milli-second. litil ~ ~' ~ the possible exception of case 5 (without non-linear effects), the rack behavior is somewhat random and the three stresses tabulated do not in general occur at the same time. ~ The only parameter changed for case 2 (NS-SSE with fuel and wall gaps) was the value of V. Although both runs (6 and 7) were of y the same 20 second duration, stresses peaked during the 10 to 13 second interval for run 6 and. during the 2 to 5 second interval for run 7. The two ordar of magnitude reduction in Vy'may~ tend' ~ - -- to lower the peak forces slightly, but this (~10%) effect is more likely masked by the erratic response of the rack. In four of the ten 20 second runs, the three different stresses peaked during the first five seconds of the transient. There was a tendency for the bending stress to peak at (or soon after) 4.7 seconds, the time when maximum forces are predicted for case 5 (without non-linear elements). In many case, stresses peaked after 5 seconds, so running the full time history is preferable. A var.iation in the natural frequency of the fuel bundle (from 3 to 6 cps) is roughly equivalent to changing the spring constants (K thru K ) from 0.3 to 1.0 million lbs/in. Assuming the change g g in V, has little effect, changing this fuel to box wall spring constant does not significantly alter the peak stress predictions for runs 1 and 2 (EW-SSE, runs 10 and 11). There appears to be a significant increase in the peak stresses when the-fuel rattle effeui. is present without wall gaps and K thru K are increased.

However, g

g the increase in time history may have been responsible for these higher stress intensities. Increasing the fuel stiffness tends to increase the bending stress l (as noted by comparing runs 4 and 5 to runs 2 and 3). Changes l in the base shear and wall compressive stresses are not noted, l possibly due to the somewhat random rack behavior. l l.- --,w r--- -m

, '. ~, g i not simultaneous. It should also be' emphasized that the non-linsar analysis is based on zero damping. Including damping and the modeling of additional fuel masses will and to lower the stresses predicted here. However, these stresses are small enough so that these refinements are not necessary. The pool wall stress tabulated (peak contact force divided by 88 in snubber contact area) exceeds 1000 psi in only one run (no. 11, without wall gaps). For faulted or extreme loadings, the allowable stress is f'c = 4000 psi. This factor of 4. safety 4 margin for one rack sliding is sufficiently high to insure that the 4 x 4 rack array in the pool does not produce impact loadings that exceed the allowable compressive strength of the concrete walls. This conclusion is also supported by the variations in the time of peak wall impact, indicating that it will be un-likely for 4 racks to line up together and strike together and a-gainst the wall simultaneously. Therefore, the racks may (and should) be installed with gaps between adjacent racks and the seismic supports to allow for differential expansion of the fuel racks and tha pool walls. l l 2: I l 23-l ,.r-m = - -

- =. = _-- . = ", Nk rn, s 4 ' 's c O M T e* ~ M \\ v w O= J O O M cb>\\ =. '4 - 1 O = e O }' O T M O O =J O b + + J, las na .~ a O O O O e + =, O

=

0 O O = = O O O. O e T O O 64 O O O O + + taa W O O O O O O T O O. O V e O O f4 O O O O + + ta 4:J O O O.* O O O O y 3 O. O. Q 9

== O E EO O O O O N O O O Z O O 4 + + W isa taa o u 44 O O 4 + 000000000000 O O S C00000000000 O O OOOOO0000000 O = 2 9

=

000000000000 O O O O ina "a e e n m O

= = = * = = * = = = = = = = * = = = * = =

3 m

== 0 C e-Y

O O

naa 4.J + + S W daJ ua laa C. 0 0 0 0 0 0 0 0 0 0 0 E> O O t isa e e O O O Q% COOOCrOOOOOOO O O

- 4

=a O O O to 4 w r8 e f U 3UO O O 8 EEO O l E *= 9 QQT LE O Zse OO 00 at M OO OO Z ua 44 ++ t + ,j W 000000000000 WW ww

== 4A (A taa OOOOOOOOOOOO ua 3= 0 00 0O I 3 **

= *= 0 *= ('* O taa Z

O O O O O O O O O O O O- >e=== 0O OO l 44

a=

O O a= W" O h OOOOOOOOOOOO

====O OO OO a= 4 OdO O Z h 000000000000 E WU OO 00 ( 4A S =0 O Z 4

== 0 O M C1 (i n 44 Ei ti M M F8 Q et O O =

taa (A n
O 3

E n a= gg

== .a a OO OO 22 e= O== O 4

= W9 U

nas taa = c 2 O

== db w 4 O .a E> i e=== w J ts OO OO en en S O U en las UZ OO OO ~ 4 tas taa N 9

- U Z== Q
O

++ + + tas O .J** O 2 Q e-== E 40 4A taa us taJ &aJ to taa IA

== Z 44 4 OOOOOOOOOOOO laJ e= E v ' e= 0 O OO ~ O n= e. ats O M 4 ua E n O ti fi ti 69 6'. M ti si f4 44 > ZUw

2OO OO at 2 IA, Z tas taa IA ik W D

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