ML20237K327

Intervenor Exhibit I-SC-7,consisting of Article Entitled, Seismic Response of Free Standing Fuel Rack Const to 3-D Floor Motion, in Nuclear Engineering & Design 80 (1984). Copyright Matl

ML20237K327
Person / Time
Site:	Diablo Canyon
Issue date:	06/17/1987
From:	Singh K, Soler A JOSEPH OAT CORP., PENNSYLVANIA, UNIV. OF, PHILADELPHIA, PA
To:
References
OLA-I-SC-007, OLA-I-SC-7, NUDOCS 8709040300
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Nuclear E.nganeenng and Deogn 80 (1984 31$-329 ^( F 'i : 315 North. Holland. Amsterdam

'87 Am 26 P4 :02 SEISMIC RESPONSE OF A FREE STANDING FUEL RAQK: CONSTRUCTION TO 3-D FLOOR MOTION N ,

Alan 1. SOLER Professor of Mechamcal Engmeerong and Apphed Mechames. Unwersary of Pennsylvama. Phdadelphua, Penns> hama. U.5 A Krishna P. SINGH

~

nce Presidem of Engmeerms. Joseph Oar Corpo.orron, Camden. New Jersey, USA Received January 1984 Seisrruc analysis of free standing submerged racks is complicated by the presence of water and structural non hncanoes such as fuel assembly cellimpact and floor interface inction. A direct ume integration techruque has been proposed to analpe this class of structures. Apphcauon of the ume integrauon techruque on a fourteen degree of freedom lumped mass rnodel of the rack reveals some heretofore unpubbshed quirks in the structure's behavior. The method of analysis is utihzed to conipare the seistrue response of some representative rack designs. Results show wide differences in the structural response, depending on the fabncauon details of racks.

1. Introduction prompted the evolution of the free standing high density racks storage concept. Increasingly, the new generation Subsequent to the US government announcement of high density racks are being designed for free standing an indefmite suspension of spent fuel reprocessing in installation. The structural analysis of such racks under 1977, the nuclear power industry has scrambled to postulated floor motions, referred to as Safe Shutdown increase its capacity for on site storage. The storage and Operating Basis earthquakes in the lexicon of the i

pools in most of the commercial reactors were initially nuclear power industry, is the subject of this paper.

designed to store li core worth of spent fuel. The Representative of other work in this area of interest is i

storage rack modules, built for storing the spent fuel in the rather qualitative paper by Habedank and co authors q' the pool, were typically of open lattice construction. [1].

The racks were anchored to the pool floor, and were A free standing rack module is a highly non-linear frequently braced to the side walls of the pool and to structure. During a seismic event the fuel assemblies can each other. Wide pitch (center to-center spacing) be- " rattle" inside their storage locations, and the module tween the storage locations ensured suberiticality of the itself may slide on the pool floor, Furthermore, the rack fuel array. Ostensibly, the most viable and cost effective may life off at one or more support feet locations procedure to increase fuel pool storage capacity lay in causing impact between pool floor and the rack support

, replacing these rack modules with the so-called high structure. Exigency of the market place calls for econo-density racks. The latest version of high density racks mies in design and construct on; however, reduction in consists of cellular storage locations arranged in a tight the rack structural strength can only be made after an pitch with neutron absorber materials interposed be- exhaustive analysis of the resultant non-hnear effects. In tween the cells to maintain nuclear suberiticabty, this paper we present a n:chnique which can be utihzed Matching of the new "high density rack supports" with to make such an analysis.

the original floor anchor locations is usually quite To illustrate the procedure, we consider two types of cumbersome, if not impossible. Moreover, it is desirable rack construction; one in which the storage cells are to mimmtze the in-pool installation time for personnel attached to each other along their long edges in a radiation safety. These considerations, among others, certain pattem (honey-comb construction) and another 0029-5493/84/$03.00 C Elsevier Science Publishers B.V.

(North-Holland Physics Publishing Division)

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1. NUCLEAR REGULATORY COMMIS$10N Decket No. 5 o-21'r-6L4 o,,isi , g, . ,,, M&1 ,

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316 AJ Soler, KP. Songh / Setsmsc resporue of a free standong fuel rock I

in which the connection between the cells is made only 2. Theory ,

at the top and bottom (end connected tube cons cuc- ,,

tion). The latter construction involves only a fraction of We consider 'a system govemed by absolute gener- ,

the welding of the former, and therefore is a far more alized coordmates p,(s), i- 1,2. .N,. All internal forces economical design. From a safety standpoint, the over- contributing to system deform 4 tion are associated with ,

riding concern relates to the increase in the rack stress generahzed extensions 6,(p,).1,mernajl orce clementsM levels and rigid body displacements as the inter cell may be non-hnear functions of the g& nth!Et@8MM longitidutinal welds are clindnated. It is necessary to tions p,(t) such as gap or inction elements. Lagrange's develop a methodology to address such concerns dunng  ; equations,-wntien in terms of generahzed forces Q,(ty land generalized external forces G,(t) are #

the initia' design and beensing effort. This psper is intended to provide such a tool.

A storage rack is a structure submerged in water d [ BT j BT .

which greatly compbcates its motion. Proper simulation dr\ap,f af, of rack dynamics requires consideration of hydraulic Since all of the p,(t) are independent, it is casily couphng and virtual mass effects. Such effects are m? demonstrated that ciuded in this analysis using simplified models.kincef

'our object herein is to establish a tool for comparisons N  %

purposes only, we propose a fourteen degrees-of-free- 0,(t)=[F[33 =' [ F B,, , 4 (2) dom model to simulate rack behavior. A more compre- A-1 *-1 l@nsive model has been employed by the authors in where the dot (-) indicates time derivative and B,i are smalyzing racks for individual plants [2]. It is important called coupling coefhcients [3). B,, relate the generahzed te emphasize that what we are demonstrating here as a velocitiesp,(t) and the generahzed extension ratesgi (r).

'atmpler version of what would be required to qualify an The system kinetic energy Tis written as wed 4mit; however, the methodology, employed to bopahe model is essentially the samec f'

(

• Comparison of different rack geometries on the basis I" 5 E' E M.> A.h - i (3) of their structural response is affected by three major '"3>"3 variables; (i) the acceleration time history, which vanes For a geometrically linear system (equilibrium equa-from plant to plant, (ii) the fraction of module storage tions based on the undeformed configuration), the gen-locations occupied, (iii) and the limiting static and eralized massa M,, are independer.t of coordmates p,.

dynamic coefficients of friction at the rack and pool Using eqs. (2) and (3) in eq. (1) yields the system floor interface. In order to drew tenable conclusions, equations of motion in the form analyses are performed using three arbitrary sets of earthquake time histories. Two conditions of rack load- lM](#}-[B}(F)+(G}, (4) ing (all or half of the locations occupied), and two .

values of the coefficients of hiction are also considered.

1. ' ** ' '* 'I I # b * * " P *8 *

• C* 8 m8 nx. er ,X o ( F ), (G) are column In all a total of six cases are utilized to infer characteris-matnces c ntaining N, r ws, and (F) is a column tics of the rack structural behavior.

ma cm g N, r ws. A set f inertially decoupled The three orthogonal seismic excitations are applied

• 9"* "** # * *4

coincidentally. The results reveal some striking peculiar-ities of the rack 3-D structural reponse. The marked {p}.[y)-1[p){y)+[y)-1gg) (3) increase m the rack stress levels and displacements predicted by this study as the design is varied from the Eq. (5) is solvable by direct integration techniques

" honey-comb" to "end connected" construction high- using a time history computer code described in ref. (3) lights the problem areas of the latter design. Perhaps (p. 336).

more important, beyond the numerical resu's pre-sented here, the analysis suggests a methodical tech-nique to evaluate candidate designs for a particular 3. Fuel rack model apphcation.

The following items should be considered in the development of any fuel rack-fuel assembly dynamic model:

~

? .

A.I. Soler, KP. Smgh / Sessmsc response of a free standmg fuel rack 31'l 0,4 3.1. Modellmg of the rack structure 0,,

l The rack structure may be modelled by clastic beam T - "~ ~ F~ .N"' - ~~"' T elements as long as appropriate cross section properties //^*

can be denved and as long as shear deformation and ,

rotatory inertia effects are included. In specific design i  ! //

applications, the authors have used four beam elements *ie j

and five nodal points to describe the rack structure. In /- ve

. y*

this paper, since the emphasis is on a comparison of two different rack geometries, we have adopted a simpler ., ";p,' g'5f'y' ,'g 8,5,58"M model for the rack structure involving only a single maar criara beam element. This simplification helps to focus atten-tion on the main differences between the two rack N configurations studied; namely, the significant dif. ,

ference in the shear resistance. j@. @}

e i 3.2. Modellmg of thefuelassemblies ,I ' $'

'a y' ,, - . . .

Each fuel assembly should be treated as an individ. /

ual distributed mass clastic element. In the actual fuel / ',

j rack, an element may be located anywhere, in the x-y .g Q.

plane and will impact with the fuel rack surrounding metal at one or more vertical locations. An assemblage - I a, ~II of fuel assemblies will certainly not move in phase j /

j' 4 during a seismic event. For the purposes of evdving a a conservative model, we have assumed that all of the fuel Fig.1. Rack model showing degrees of freedom.

assemblies move as a unit; thus, the impacts with the

( fuel rack are magnified leading to higher stress and load levels. In a detailed model where the rack is simulated supported at the four corners by rigid supports that may by five nodal points, impacts between fuel rack and fuel shde or lift off the pool floor. The pool floor is excited assemblies may oc:ur at different levels; in the simpler by a known ground acceleration in three orthogonal model used herein for comparison purposes, we assume directions.

that impact between fuel rack and fuel assemblies oc. Fluid coupling between rack cell walls and the en.

cuts only at the top of the rack, and that 50% of the fuel semble of fuel assemblies is simulated by introducing assembly mass is involved in any impact with the rack, appropriate inertial coupling terms into the system We emphasize that in any real design study, the possi. kinetic energy. Similar inertial coupling is introduced to bility of impacts at various heights should be included in the model For this illustrative comparison, we feel y' that the salient features of the behavior of each rack -!

type will be correctly demonstrated with the simpler 6

)

r7odel. ///

' /// '/ '

j Figs. I and 2 show the model considered in this /

/p//!

paper. The fuel rack metal structure is a single * -~n . '

i' I

clement whose end points have a general six degree of / '

freedom motion. The ensemble of fuel assemblies are '

j l' conservatively assumed to move in phase under seismic , // =d '

excitation, and their effect on the fuel rack is considered h hv- -

to have the potential of 50% of the effective mass h.

impacting the rack at the uppermost point. The offset of the lumped mass from the rack beam centerline enables simulation of a partially filled rack with induced tor-sional moments. The fuel rack base is a rigid plate, Fig. 2. Impact spnns onentation at top of rock g

h

-. _- g

318 A1. Soler, KP. Songh / Sessmuc response of a free standong fuel rock e

account for fluid structure effects between adjacent energy due to the rack base is racks. Fluid damping effects are neglected in this study. .

2 T2 = m , pi + m 3, pj + m ,pj + 1,p;, + 1,p;, + 1,p,2, As shown in fig. 2, potential irnpacts between the rack beam and the lumped mass representing the fuel assem- (9) bhes are accounted for by inclusion of appropriate gap elements. The fluid inertial coupling terns are based on where mg,1,, I ,1, f are the effective mass, and masi, moments of inertia of the base, includmg fluid mass nominal clearances in this investigation; however, it has effects.

been showfi f4) that inclusion of large deformation The contribution to system kinetic energy due to c!fects near the impact points may considerably affect fluid coupling between fuel rack and fuel assemblies is the results. fleres.Lwello~not include the' effects 'of gaf

. expressed by the 2 D model given in ref.15) The closure on (AP9M6'ome- necessity for accounting for 3 D fluid structure interac-

% tion is a question that merits future study. Using the co ,

" n co'mpu' ting kinetic energy contributions from the 2-D approximation, we obtain for the kinetic energy.

due to rack-assembly interaction.

rack, we use appropriate consistent mass matrices.

Therefore, the contribution to the system kinetic energy , .

due to the rack. T3, is given by

+ 2 A ,( p,p, + p,pio).

i (10) 27, = { p3,pi }T[Mg]f p + ( p. p:3 }'[M 7 ]f p',')f

~

j Similarly, the kinetic en due'td fhild cou e-p, MG!MPfiHMit!k"Aff6 ao a l M. , , ,u' <

+ { psop,,ps,pn,}'[M y } $'

a Blj'pj + Bl lip! + Bl{'p' + Bl lip' p:2 + 2BjySpiDi + 2Bjj192 O2 + 2B!I'pvOn p2 + 2Bjj 8p,D2 4 O(D,2,D'), 2 (11)

( + ( P2,99,- p4,- pii f(Ms} - ,

W MW3MEIMified'-p1 '*'

hr seisd

~

%otions.+ e " ^ '

Finally, the contribution to the system kinetic energs where [Mg), [M r] and [M ] are the appropriate mass due to the mass of the fuel assembly group is written a's matrices for extensional, torsional and flexural motions.

If A, I, are the rack cross section effective metal area 2T3 - AM( pj + pjo) + M( p3 + Y,p,- x,p3)2 and polar moment of inertia, respectively, then .,

+ (1 - A)M (( pi - Yap )' + ( pa + Xsp. )') .

[ Mt } " plAH 1 f. (12) 3 ,3 1

- M is the total fuel assembly mass and A is the mass

[y7) . # II- ,

(7) fraction assumed acting at the top of the rack in the l

3 ,f 1 horizontal plane. We have assumed that vertical move-ment of the fuel assemblies is equal to the vertical

' 13 9 11H 13H m vement of the rack base at fuel assembly centroid 35 70 210 420 location, and that the fuel assembly mass fraction (1 - A )

9 13 13H 11H M m ves with the base in the X-Y plane, in the study ,

70 35 420 210 herein, we have arbitrarily set A = 0,5 which implies

[ M,] . p*A H H2 y2 11H 13H that' 50% of the fuel assembly mass is involved in the 210 420 105 140 impact process and the impacts all occur at the top of

- 13H - 11H -# 2 g2 the rack. If more conservatism is desired A may be 105 , increased. It would be far better to include more degrees

. 420 210 140 of freedom and allow for the possibihty of impacts

} (g) below the top level, however, than to attempt to de-p* and p7 are effective mass densities accounting for termine a proper value for A. For the purposes of the fluid effects. The contribution to the system kinetic comparison simulation here,it is felt that the value of A

A.I. Soler, KP. Smgh / Sensmoc response of a free standmg fuel rock 319 used will not negate any conclusion developed as long hY as A is sufficient to induce significant impacts between . -

rack and assembbes. Eqs. (6)-(12) estabbsh the system IT III mass matrix [M] in eq (4) for the 14 x 14 model I RI I I I a (TYPa g considered herein. We introduce displacement coordi- p pp ppp i nates q,(t). relative to ground, defined as follows: ppy p p, = q, + U i ( th i = 1,7,8. ppp ppp i

p, = 9, + U2 ( r ); i = 2,9,10, ppp p p pigyg III T p, = 9, 4 Us( f ); i = 3,14' III l p, = g,; i = 4.5.6.11,12.13. o ,

4 The governing equations may be represented as follows: 4 ~ ~ ~~~~;

g tg  ; i.12 E= 9 u ~

e

[ M,,4, = Q,( t ) + G,( t ) - l a,,U, + a,2U+aU) 2 n2 yh f^ t, .,o4 4 3l P0t$0N

>-1 i = 1.2, . 14. (14)

" s l dnben l 9 30i r l t .

in what follows. we discuss briefly the computation of > -; V -

some of contributions to the elements of the set of ( j }{

equations [14]. f-

10.4 3,, -!

Fig. 3. Rack cross section and typical cell geometry - honey..

4. Fluid added mass effects comb construction.

Consider a typical cell with an internal fuel assembly i

shown in fig. 3. Assuming that the assembly and the cell The fluid mass that would fill the cell volume in the are vibrating, it is shown by Fntz [5] that the constant absence of the fuel assembly is denoted by M 2 in ref.

coefficients A,, of eq. (10) are given as [5); the effect of this virtual fluid mass is incorporated l directly in eq. (8) by defining an effective p*.

Aii = Mu ; At a " -(Mi + MH ); A22" Mi

• MH ,(15)

The effect of fluid inside of the rack structure has where Mi = fluid mass displaced by fuel assen bly, Mu W acc=M h 6 h Unne energy en W,,h

! !, = hydrodynamic mass. We use the Fritz model for i, n6w~ consider the effect of the11uid outsaeTof I concentric cylinders employing equivalent radii R3 , R 2 l - CEnl

l. defined as We consider fig.;4 which'shows'a vibrating 2

}e. . ertical wIll of width W and height R. Following case l, Ri = a*/6, R = b'/6, 2 (16) 13 of ret [5), we assume the hydrodynamic mass term as a* is the side length of the square fuel assembly and p,ws y w b* > o' is the inside dimension of a typical square cell;  ; u-  ; 4 = 1 + p. (19) l i.e. the nominal clearance between assembly and cell is'

( b* - a')/2. hen, in the fourteen degree of freedom simulation For a rack of heipt H, assuming all assemblies move .,

odel, the coefficients B ii Bi2 at each level are given in phase, we obtain ;s M i = orp,HRlf,, (17) =

h(20) where f, is the number of cells containing spent fuel itEW being tS value'apidoh$aYIor X or l' m tion assembbes. If the nominal gap g is defined as g =-(b* - The above discussion is concerned with fluid cou-a')/2, then ref. [5] suggests that the hydrodynamic pling effects induced by horizontal vibrations. To mass is account for fluid effects in vertical vibrations, we simply g 2 define an effective mass density for the base plate usmg .

\

Mu = 8JM i/(1 + 12R$/H ). (18) case 6 of ref. [5] and add it to the base plate metal mass. I l

l l

~

• E_______________________________________ _ _ . _

320 AJ Soler. KP. Smgh / Sessmse response of a free standmg fuelrack

11. Rock elasticity f6 elements) 4 NTORsloN " !(( '

AEXTENSION " A/H'

< 12E/ 12 Ela p EswtAn " g3g , ) ' + " gjff a

• K aENo No = E//H.

H '

(21)

The coefficient a represents the effect of shear deforma.

' tion, and I is the area moment of inertia of the cross section associated with beam bending. Note that one N '

shear and bending spring pair is needed for each plane of bending.

Fig 4. Fuel rack wall model used to obtain flud couptmg.

L2. Impact sprong rate f4 gap elements)

The potential impact between fuel assembly mass and fuel rack is simulated by incorporation of a Th2 total effective rnass density is then used in the Spring-gap combination. Each impact elements acts in computation of mg, I,, I, for the base plate. The effect CornPression only with spring constant given as of virtual fluid movements on the rack is simulated by defming an effective mass density pl in the matrix [ME ] X, =f,64wD/a2 ; D = Et)/12(1 - ,2), (22) in eq. (8). p; is computed by adding to the rack metal K iis determined by assuming that the impact is simu-mass, a mass equal to the mass of fluid displaced by the

/ rack. lated by a uniform pressure acting over a circular see-non of cell wall of radius a and thickness t. The radius a is taken as b'/6 where b* is the inside dimension of

5. Internal forces an individua? cell and f, is the number of cells contain-ing fuel assemblies.

The internal force elements representing system clas-

33. Support leg spring rate f4 gap elements) ticity, disappative friction and impact effects are simu.

lated by using standard spnng, friction and gap ele- The effect of support legs at each corner of the fuel ments described in ref. (3). The model shown in fig.1 rack base is simulated by four compression only gap contains 6 clastic spnngs to model two bending planes, elements to permit lift off of any or all supports. The extension, and torsion of the rack beam. The model local spring rate K, for a support of height A is contains four gap eiernents modelhng contact between the fuel assembly lumped mass and the top of the rack. ) 3 3 3

=-+-+

The model used four gap elements albgned in the verti. Ks K r Kor Ka, t (23) cal direedon and located at the x, y coordinates of the base plate supports to simulate the support behutor in where Kr = EAs/h; As a support leg cross section area, and the verucal direction and has sixteen friction elements to simulate support leg flexibility and the sliding poten. K t.7 = 1.05E,B/(1 - ,2); K t, = 1.0$ NEB /(1 - r2 ),

tial of the supports. Finally, eight rotational inctional ,

elements at the base supports are used to simulate (24) resisting moments due to floor-structure interaction. K or represents the local elasticity of the pool floor with Full details of the behavior of these elements and the E, being the Young's modulus of concrete and B being development of their associated couphng coefficients  ;

the width of the support leg pad [3). K ea represents the j are found in tel (3]; herein, we simply specify the spring rates associated with each of the elements. local elasticity of the rack just above the support leg; I the coefficient 9 is taken arbitrarily as equal to the ratio of the metal area of single cell to included area of single cell.

i

~_- ^

..- ]

A.J. Soler, KP. Snnah / Sersmuc response of a free standing fuel rock - 321

34. Floor rosassonal andfnction elements fY

- xi

~~

The effect of local floor elasticity on rocking motion

.{g ,

(support leg bending)is represented by rotational spnngs with spring rate ([3] p. 293). b}

I b! '

Kn = E,B /6(1 - r2 ).

3

-(25) n n n l These rotational springs are moment limited since if t, 0 0. L J L_J L_) _*

edging of the pad occurs, no further moment 4,an be [ -

] ]r resisted. '

9 Associated with each support leg compression ele- -

ment spring are two orthogonal friction elements located in the plane Z = -h (see fig.1). The friction element a

]  ;

F local spring rate is assumed as the spring constant of a o

support leg when considered as a guided cantilever beam of length h under an end load P. Therefore, from ,,

- T.J25 C4.30i ref. [6), assuming that the support has area moment of inertia 1, when considered as a beam, j 1-

' ** N9 305 12 El' 1 1* - 1*

K,-  ; ' = 8,52 - 4.157 .

p,s. 5. Rack cross section and typical ec11 geornetry, uncon.

3 4

nected tube construction.

l (26)

J f I' \ J V* " - b b V,e  !; N' " b E N,/ * '(27)

6. Application to typical units .

g f=1t # 4 jal i Figs. 3 and 5 show a cross section through a level of Castigliano's Theorem for the ith tube yields (assuming the rack structure of two practical rack constructions.

The first is n' fully connected honeycomb construction (HCC) which is considered as a beam-like structure with ' W' cross section dimensions b and a, having certain area and inertia properties; the second is an end connected _

T Y PIC AL CELL ND sube construction (ETC) which has no shear transfer N ll capability between tubes except at top and bottom of y, u

' ~ ~ ~ - - ], s,igNu 4 the rack. For the HCC rack, eq. (21) can be used lJ directly to model rack clasticity since the entire cross vg W y,

[

T section is capable of beam-like shear transfer; we need

p only examine the cross section details to derive expres- q j y, sio.ns for A,1,1,. For the ETC construction, however. - - - - - - - j y,-

since no shear transfer between cells can occur, we must s ,

! " M undertake additional analysis in order to arrive at the ty proper spring rates for eq. (21). ,

d) j+

Fig. 6 shows a free body of the rigid ring connecting -

' [

all of the tube-like cells at : - H and constrains them to move as a unit. If there are J cells at level xi, then

' *8 -

equilibrium requires that for a 2-D motion.- Ny M*= E ( M,, + y, N,,) ,

/-1

• Fig. 6. Free body analysis of end ring in ETC rack I

i i

o - -_----- _ -----_--_----_--_----- --_ - -- J

322 A I Soler, KP. Smgh / Seusmic response of a free standmgfuel rock a fixed ba.te) ,g g re . _12 El g>*. _6El *e, H) H2 lg ,,

lg M,, - + H'* + e' (28) C 2 c c j

, 0; . .,; 2,i E m,J c Also, bearing in trund the constraint of the end closure, ,s * *

,_L we have, 7 N,, - EA g ( U * + r, e * ) . (29) s ,

u U U lj in eqs. (28). (29) A. I refers to the properties of the individual cell, and we have neglected shear effects in (~ * 'l the bending of the individual cells. Using eqs. (28) (29), Fig. 7. HCC cross section for torsional ngidii> analysis.

in eq. (27) yields, for the case of n total cells in the unit,

y. . + 6E(nl)H 4E 7 7 d' pa, The torsional analysis for the HCC unit is based on l

H' N i 7 '~' 4 j the classical analysis of St Venant described in ref. (7) and applied to the cross section of fig. 7. By using the P' = + 12 Enl H'* + 6En/ e* , membrane analogy for the torsion problem,it can easily

1. 2 N' be shown that 1, for the HCC construction is simply g . . "fA p. (30) ([7h P. 278)

H

~

If we now replace eq. (30) by the corresponding equa- #)P Hec ' !d '

tions for an equivalent uniform beam acted upon by where Ki is a tabulated function of b/a, f end generahr.ed forces M*, F*, N", and having effec-An analysis of the end cross section of the ETC tive cross section area A*, inertia property /*, and shear construction using fig. 8, yields coefficient 4*, we can show that the A*, /*,4* [for use in eq. (21)) which correspond to the ETC unit are given y, , j , 24( r)j . y]). (34) 1 + 4, = nit A*=nA, ,y h w, n

I 3 (4 + 4* )l* = 4 nl + [ [ ~y A ' (31) Ghe

[r .

I** i

>-I li.hw, 3

so that i i I

1 * = nl + [ [y,3A; 4* = [ [y A/nl. {32) 6:

LE- -X The results for A*, / *,4* can be used in cq. (21)in heu I of A,1, (, it is clear that between the two geometries the only essential difference is in the magnitude of 4* T, I

The considerably larger value of 4' obtained using eq.

(32) for the ETC unit (as opposed to eq. (21) for the i j HCC unit) leads to a much smaller spring rate KsHE.AR being obtained for the ETC unit. It remains only to T* TOTAL CROSS SECTION TORQUE compute a value for 1, for both the HCC and the ETC 6 eANGLE OF TwlST/ UNIT LENGTH configurations, and then to apply the simulation to typical in service units. Fig. B. ETC end cross section under torsion 5 'i

A.J. Soler, K.F Smgh / Seumsc resporue of a free standmg fuel rack 325 where Ip, I are the area polar _ and bending inertia in the supports on the basis of_the formula, properties of ar. 'ndividual cell, and n is the total ,

' C2

'+

number of cells in the unit. o=-+ 2 A #8 12 (35)

It should be emphasized that in the above analysis, we have assumed that the ends of the individual tubes where A,1,,I. are , the appropriate geometric properties are assumed to be connected in such a manner as to. for the supports or for the entire rack cross section of enforce the requirement that plane sections remain the HCC unit. As noted previously, the use of the total plane. This req sirement may or may not be satisfied in cross section properties for rack stress. evaluation is any specific ETC design. justified for the HCC unit since the full cross section is available for shear transfer, The evaluation of stress in the ETC unit requires some additional analysis. The cell

7. Application to typical configuration whose centroid is at X,,1; in the cross section experi-ences a direct stress of the form w . We consider the configurations of figs. 3 and 5 for E

the case b = 124.128" (315.3 cm), o = 92.8125" (235.7 co = p((qi, q3) + Y r(qn q.)- X,(f12 95)) .

cm) having a 9 x 12 cell arrangement for a total of 108 cells. The support legs are assumed to be four B"x (36) 12"x 1" (20.4 cm x 30.5 cm x 2.54 cm) plate sections Due to bending of the cells in two planes, we have, for a p forming a box at each corner. Table 1 shows the sprmg cell of nominal cross section (c x c), at the base of the rates computed for the two units assuming that the . rack material is stainless eteel having a Young's modulus E = 28.3 x 10' psi (195 kPa) and the rack height 1/ = 20er , , 6E ,q y ,

161.12$ (409.26 cm). c H2 The seismic load-time histories used have statisti.

2E 6E 7

+ cally independent components in the global directions.

The particular records used are those from three differ-7(qn 94) 79 . (37)

I ent plant specifications. (See figs. 9-11 showing one 2ony

, horizontal component.) C H

, q,), };{ q ,q,)]

For the HCC unit, net beam forces and moments are . 2E 6E used to compute extreme fiber stresses in the rack and (38)

• 7(fu ~ fs) + 798 The maximum rack stress in any cell wall can be con-7g) structed, at any time instant, from the expression -

Spnng rates for model o =lod +la # lo 4 (39) item HCC UTC We emphasize that eq. (39) does not include any local hq,;

3; Area of cell 4.379 sq. in 4.652 sq. in stress effects induced by non-rigidity of the rack base, p, lcon = 35.55 in' 33.56 in' load transfer between supports and adjacent cells or g /f (urut) 616 926 in' 654 996 in' tubes, etc.

p 1,* (unit) 346 825 n' 367 993 in' For a given time history of stress in the supports, in the HCC rack cross section, or in the ETC individual ll uni

• 1 32 .8 m' 9 9 n' cell cross section, a determination of unit structural 2.35;1.322 179.71;100.53

+,,,;+$

Krons leq (21)J 7.520 x 10'm * / rad 1.009 x 10' m * / rad. integrity may be carried out. In accordance wi.h ref. [8),

Kgxygusiou 0.43D6 x 10' * /in 0.8818 x 10' s /in - structural integrity may be m, terpreted as setting limits 8

Ksu g4 n. , 0.1214 x 10 * /m 0.294 x 10' * /in on forces and moments acting separately or together on l

, Ksst., _ x 0.1214 x 10' at /m 0.294 x 10' a /in a defined cross section, For the HCC construction, the l K.,

0.1084 x10"in */ rad 0.1150x10"in w/ rad entire rack cross section can be used in the structural Key 0.0609 x 10" in * / rad 0.0646 x 10" in = / rad integrity evaluation; for the ETC construction, we must Kmper (fa - 108) 0.715 X 10' * /m 5.084 x 10' c/in examine the cross section of the critical cell.

s[ (25)} x1 m# rad x1 in *r rad -

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Table 2 ef the' mu,m ~ corner deflection of thegacgin either ,

Simulation studies frelc on asless than 50% of thepp#

- To assess the two rack constr(rcOEns, the" simulations Case Description Seismic load full rack; COF = 0.8 fig. 9 2 m #md %u d 6 M.

I cients of friction, 0.2 < COF < 0.8 are accepted upper (0.302 x 1.5 = max. g. level) and lower bound values. Simulations 1-5 are performed full rack; COF = 0.2 fig. 9 with the seismic input amplified by 1.5 on all three 2

(0.302 x 1.5 = max. g. level) input directions. Simulation 6 as performed with the 15 s. duration appropriate seismic inputs amplified by 2.5. Thus, case 3 full tack; COF = 0.8 fig.10 6, when compared to case 3 shows the effect of employ-(0.17 x 1.5 = max. 8. level) ing different amplifications on the same seismic event.

12 s. dwration Simulati*on 5 using a half loaded rack, highlights the 4 fult rack; COF = 0.8 fig.11 effect of rigid body rotation of the rack around the (0.15 x 1.5 = max. g. level) vertical axis. The half loaded cases assume that all cells 20 s. duration on one side of the unit diagonal are loaded. In all cases.

5 half rack load. COF = 0.8 same as case 1 structural damping of 2% is assumed at a frequency of 6 fult rack; COF = 0.6 O x 2.5 = max g. level) 20 Hz. Table 3 summarizes the results obtain:d for

(

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. 12 s. duranon stresses and table 4 shows the maximum corner dis-placements and maximum floor loads transmitted by

,,r.m- w r w - v m rn e , , the rack. We may define factors R, which are limited to e Q- f.;[, '.- U C ua _10" .f7q d P '- -

@f Aeeerst the value 1 or 2 for an OBE. or SSE event, respectively

[8).

of adjacent racks, inter-eack impact is; =' "-3 Table 3

[

CASE Honeycomb construction End connected tube construction Rack Support Rack Support R1 R4.R$ R1 R4.R5 R1 R4.R5 R1 R4 R5 1 0.002 0.081 0.385 1.46 0.200 1.21 0.613 1.896 2 0.001 0.038 0.182 0.356 0.104 0.642 0.232 0.548 3 0.001 0.068 0.322 0.964 0.155 0.955 0.372 1.27 4 0.001 0.065 0.319 0.957 0.180 1.12 0.406 1.35 5 0.003 0.127 0.485 1.93 0.123 1.004 0.294 1.082 6 0.002 0.061 0.513 1.664 0.204 1.322 0.499 1.50 Table 4 Maumum rack deflecnons/transnutted loads Case Honeycomb construcuon End connected tube construction l X Y Max. *' Sinpe Impact X Y Max.

• Single impact

! (m) (in) flr. Id. le8 Id. load (in) (in) fir. Id. les Id. load (Ibs) (1bs) (lbs) (Ibs) (Ibs) (lbs) 1 1.175 0.084 536 600 257 700 201 400 1.049 1.629 1 280 000 411 300 $78 500 j 2 0.573 0.489 232 600 121 000 138 300 1.624 1.55 345 700 156 100 241 800 3 0.187 0.086 402 200 215 900 49 370 0.499 0.753 809 400 257 700 357 800 4 0.111 0.064 334 800 211 600 113 100 0.624 0.568 772 700 297 700 350 500 5 1.35 1.62 496 300 340 900 79540 2.145 2.392 602 200 200 000 181 500 6 0.826 0.343 611 000 309 800 216 800 0.856 1.45 985 500 343 100 588 300

Staue load = 184 000se for Cases 1.2.3.4.6 l = 103 300sr ior Case 5.

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328 AJ. Soler, KL Smgh / Sessmic response of a free standing fuel rock Ri - direct stress on a net section/ allowable OBE rack stress levels in the thin walls of the cells.

tensile (compressive stress), . induced by gross dynamic motions remain low R 2" gross shear on a net section/ allowable OBE shear, enough so that stress raisers have minimal effect on l R 3= maximum bending stress in one plane / allowable urut performance. By the very nature of the con.

OBE value, struction, stress raisers should tend to be higher in R,- combined flexure and compression ratio, the ETC rack compared to what might be present in l

R3- additional combined flexure and tension (com- the HCC rack; therefore. gross stress levels (pnor to pression) rat o. inclusion of stress raisers)in the thin walled cells on It has been found from a large number of simula- the order of the allowable stress should be viewed tions of different HCC racks that factors R, or Rs with concern.

usually govern structural integrity in both rack and in (5) Because of its increased tendency to slide, the ETC support legs. In table 3, we show only values for Ri , and rack generally experiences greater horizontal die l

R, or R 3at the most critical location. placements. Y5r18fffE"87"!!iWinedlemanimtaiaiall

$^ ~5%$% '5h&Mnh 9

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8. Discussion arid conclusions MC_ _ spacmghetween adjacenvracks.

(6) The maximum load (static ~ plus dynamic impact)

From the simulation results, we can draw the follow- transmitted to the floor from the total number of

, ing conclusions:

support feet in contact at any instant is larger with

1) An accurate picture of the results can only be the ETC rack. This is attributed to the increased obtained using 3 D nonlinear time history analysis propensity of the ETC rack to lift off the pool floor.

, regardless of the rack modelled. A large contribu- possibly pivot on a single support leg. and subse-3 tion to the maximum rack horizontal displacements quently re-contact the floor with a substantial im-can be mede during an instant when the rack is only. pact.

L supported on one foot and the seismic loads cause a (7) The increased displacements found for the case of Q pivot of the rack about the only remaining contact the half loaded rack dramatically show the effect of 3 D motions and the potential for rigid body rota-d point.

{ p l) Maximum displacements, with a full rack, may be tions about the vertical axis. It is noted that this i found when the upper bound coefficient of friction effect is substantially affected by the initial assump.

. value is used. This can be explained by noting that tion on the amount of fuel assembly mass par-

! there is a greater tendency for an individual support ticipating in impacts with the cell walls.

leg to stick when in ground contact and therefore On the basis of the above results, we conclude that in the possibility of pivoting during an instant when a general, the HCC rack offers greater safety margins in j h single foot is in contact is increased. the rack body, is less prone to excessive displacement.

i

3) For the seismic events considered here, stress levels and results in lower dynamic loading on the pool floor.

l in the supports legs have the same order of magni- Although the model used herein is - vely simple, it tude in both HCC and ETC racks. does exhibit the features of the ?' stion and the i

(4) Stress levels in the rack cells, above the base, are expected impacts. In any real design e ation a more significantly higher in the ETC unit than in the elaborate model would be called for,

• accounts for HCC unit. The ratio of cell stress levels (ETC/HCC) impacts at different levels, additional 4 u degrees of is 10 to 20 in the simulations considered here. While freedom, etc.. In the study reported on here, however, the levels reported here due to beam type stress the simplest model is appropnate since we week only a resultants may not imply violation of gross failure comparison of results from two different constructions. g criteria, it is noted that effects near the supports. The numerical studies presented in the foregoing and construction details not modelled herein, will point up the significance of inter-cell welding. The ,

certainly induce stress raisers on the computed levels longitudinal welds connecting the cells in the honey-reported here. For example, any flexibihty at the comb construction are found to improve ths stress levels rack base plate will cause more load to be shif ted to and kinematic response of the rack significantly over I the outermost cells; also, local stress raisers will the end connected construction. The difference is cer-certainly be imposed on those cells nearest the sup- tain to be all the more important if consolidated pin ports. Therefore, it is prudent to ensure that the storage is contemplated.

l l

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• 5

• . . i kl. Soler. K.P. Smph / Seamic resporne of a free standmg fuel rock 329 Nomenclature / *, A *,4* l p* . equivalent tack properties .

for ETC unit .

c side length of a single fuel '

T system kinetic energy cell -

Q,, G, generalized internal, ex- t .

wall thickness of fuel cell ternal lorces R,(i = 1,2. 5) structuralintegrity factors p,, q, generalized coordinates E Young's Modulus of rack -

Np N, number of internal force metal elements, degrees of free- X, , Y, centroid of fuel assem-dom ' blies movmg tis a group ~

[B] coupling coefficient ma-trix

= [Mel,lMs);lMy] mass matrices for exten. References sion; bending; and tor-sion of rack [1] G. Habedank, LM. Habip and H. Swebm, Dynamic analy-g*,p* effective mass densities sis of storage racks for spent fuel assembbes, Nucl. Engrg-A;N rack cross section metal D'5 54 (1979) 379-383-area; rack height [2] Spent fuel pool modification for inerened storage capacity, i

• Quad Cities Units 1&2, Commonwealth Edison Company, m , ,1, ,1, ,1, mass and inertia proper.

N.R.C. Document No. 50-264,50 265 (June,1981).

ties of rack base

[3] S. Levy, and J.P.D. .Wilkinson, The Component Element DA i) specified seismic motion Method in Dynamics (McGraw Hill, New York,1976).

of pool floor M) A.1, Soler and K.P. Singh, Dynamic couphng in a closely M total mass of fuel assem- spaced two body system vibrating in a liquid medium: the bly case of fuel racks, 3rd Keswick Int. Conf. Vibration in 4 B,'f ', B,'j ), A ,, fluid coupling coefficients Nuclear Plants, May 1982, Keswick, United Kingdom.

( A

[egs. (10) and (11)1 defined in eq. (12)

[$) RJ. Fritt., The effect of liquids on the dynanue motions of .

immused solids, ASME J. Engrg. Industry (February.19721 MH 167-173 hydrodynamic mass [eq.

S.P TNW Str@ M Math Vol.1, 3rd Ed.

(McGraw Hill, New York) p.175.

f, number of cells in fuel

[7] 5.P. Timoshenko and J. Goodier, Theory e,f Elasticat3. 3rd rack ed. (McGraw Hill. New York,1951) pp. 258-315.-

. f, number of cells contain- [8] ASME Code, Section 111, Subsection NF, and Appenda ing fuel assembbes XVII (1980).

ii h height of rack support leg ,

A , ,1, metal area, metal inertia .

'g, of support leg cross sec.

6 tion j

Y.

l.

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____.r___m_m_m_-____________.________________________._ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ . . ._ - _ _____.__..__________._______.___.____________J

l . p Cn UNITED STATES

j. Af 'of ' ..

, .g NUCLEAR REGULATORY COMMISSION l 5 ;j WASHINGTON, D. C, 20555

% . . . . . +**

May 26, 1987 MEMORANDUM FOR: . John Hilligan Technassociates.

FROM: Emile:L. Julian #cting Chief Docketing and Service Branch

SUBJECT:

D m3Lo e EXHIBITS Any documents filed on the o)en record in the Braidwood pro-L ceeding and made a part of t1e official hearing record as.'an exhibit'is considered exempt from the provisions.of the' United i

States Copyright Act,-unless it was origina11yifiled under seal l with the court expressly because of copyright concerns.

All of~the documents sent to TI for processing fall within the exempt classification.

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