ML20199F553
| ML20199F553 | |
| Person / Time | |
|---|---|
| Site: | Waterford  |
| Issue date: | 03/31/1991 |
| From: | Singh K, Soler A HOLTEC INTERNATIONAL |
| To: | |
| Shared Package | |
| ML20070L320 | List: |
| References | |
| NUDOCS 9802040038 | |
| Download: ML20199F553 (8) | |
Text
- . - - - -
Technical Sp:cification Ch:nga l
e
- Requ:st NPF 38193 ATTACHMENT 8 SPENT FUEL STORAGE l
outside of the gamma shield. Tc amund 120t. Four tunnions are at- raic is estimated to be about 60 mrem /h, j neutron shield is enclosed by a thin tached to the cask body for lifting. with the dose rate at any location l outer shell. !n addition to containing the tiedow n and rotation. 'Two of the accenible to the public well within the i l resin, the aluminum also provides a trunnions are located near the top of the allowable limits.
conduction path for heat transfer from body and two near the lower end. The the cask body to the outer shell. lower trunnions may be used for rotat- UCENUNG The cak'is scaled using redundant ing the unloaded csk between vertical Work on the project began last autumn.
metallic seals. The cuk cavity is pr essur- and horizonial positioni. The completion date depends largely on '
ired above atmospheric pressure with The long term cask surface tempera- the licensing process. A saferv analviis helium to preclude air inicakage in the ture ha been calculated a being 19t*F. report ha been submitted by North'ern event of seal fadure. The short term ternperature on hot, States Power to the US NkC, whose The casks will be about 16.5ft tall and sunny days has been calculated as 233'F. review is expected to be completed 8.5ft wide. A fully loaded cak will weigh The maimum external contact dose around mid April.
Chin Shan analyses show advantages
- of whole pool multi-rack approach l
By KP Singh and A I Soler i Results from whole pool multi rack (WPMR) analyses at Chin Shan and Oyster Creek point up l the potential inadequacies ci single rack 3D analyses, and show just how important it is to carry out WPMR simulations, despite their abstruseness and high cost, Fuel storace racks are essentially thin- proaches (vit the response spectrum other with selocity u. The moving walled, ceilular structures of posmatic planes, for simphcity of this illustration, method) are predicated on the assumpl are assumed to be in6nitely long, such crou section. Ahhough the details of tion that the structure is linear. A fue rack. however, is the epitome of a that the motion of water exinng the design varv from one supplict to an-other, certain key physical attributes are non linear structure (de6ned as one in inter-plane space is in the plane of the common to all designt For example, all which the applied force does not have a page in the diagram below. For this rackt feature square cells of sut6cient linear relationship to the resulting dis- geometry, the velodry of water v is open ng sue and height to enable placement) The stored fuel usemblics, computed by direct volume balance insertion and withdrawal of the fuel which constitute over 60 per cent of the (continuity):
anembly. w eight oia fully loaded rack module. are The cells (or boxes") are arranged in free to rattle inside the storace cell in a time interval dt.
a square (or rectangular) pattern and are during a scismic event. The rack nmdule fastened to each other using suitable itselfis not attached to the fuel pool stab. w (2u)(dt) bd (dt) connectors and welds. The atrav of cells Furthermore, the Coulomb fnction re-is positioned in a sertical odentation sisting the sliding of the rack module on or vlu . w/d and is supported otTihe pool stab surface the pool surface is by de6nition, a by four or more support legs. The spent non linear force. This leads to the conclusion that the fuci pool is 611ed with the indhidual fuel '# E ***'# E # EY TIME INTEGRATION TECHNIQUES wld omes the selocity of c%e approach rnks. The plenum created by the support legs is cuential for proper in recognition of these highly non linear plane. In a typical spent fuel pool the p attributes of the dynamic behaviour of racks are about Moem (100 n) wide, cooling of the fuel assemblies smred in the rack, w hich relies on natural convec- fuel storage racks, their seismic simula- and are spaced at 4.5 '.5cm (2 3in) tive cooling to extract the heat emitred tion ha been carried out using time by the spent fuel. Howeser, it ha the integration techniques.The state of the-inialutary effcst of making it kinemati- art analnis technique invok es mod-cally lesi stable. Regulatory authorities require careful and comprehensive anal-elling a' single rack module as a o structure with features to capture the i
.' h v I
v.is of the response of the racks under fuel anembiv rauling. module diding. *"
o
'he t seismic motions postulated for the rocking and ' twisting motions.
,el. /
Despite the verutility of the m JL,.
pool dab.
seismic model, the accuraev of the single i Non hnerr structure. Such an analysis rack simulations ha been suspect due'to cannot be conducted m the manner of onc key element: namelv. hs drodtnamie anventional structural analyses for participation of water a'rou'nd the rackt ,
rmer planti, because the clanical ap- ibis cifect is understood hv considering l
the monon of water bemeen latee flat planes of width w at a bmalb distance d A Two submerged parallel flat planes T/va M.av enh #dm burman el 's approachmg eacn otner.
/am.Mrw Ov5 #di .s wt ira m apart, which are mming toward, each 9802040038 900129 n PDR ADOCK 05000302 P PDR >
I rack in rack (or task to pool walp wth- Shan analysin the s nm analyses yield:d 4 intervah. For the rack modules arranged a maumum kinematic duplacement of a I "ons dunny a setete senmic n ent.
m a rypical spent fuel pool. *
- ID"* 'l.anvan Power set out to determine the rack in the pool - 8.5 times the sing lc l and d' . 2in, w v/u . 30. Since kinenc rack analym prediction. The irnpact response to racks by a comprehenme energy is proportmnal to the squate of whole pool analyut kiads between rack suppore pedestah f vek>ary, ific water curing the inter r.uk Under a consulting contract with and the pool slah decreaed Mighth from (
space will have 200 nmes the specific the valun obtained from the ungle r,ak kmetic energy of the movmg rack Taiwan Power. Hohec International (USA) undertook to prepare a dynamic anahsa, in the Chin Shan analym, the This hydraulie energy a either drawn coctTicient of friction between pednral from or ' added to the mnving rack. modc' of the ennte auemblage of racks I (a total of 14 moduleo in the pool, with and dah was about 0.2. Esen though the modifving its submerged motion in a r wk displacements relative to the slah l significant manner, The dynamin of due conuderation of fluid couphng effects. Hohec's code mmct. which snowed a large incrtase over the single j one rack. therefore, affects the motion nf uses the component element method for rack results. no rack-to rack or rack to-all others in the pook A dynamic wall impacts were predicted.
simulation which trea s only one rack.or non.hnear dynamic analysis. and has '
a small grouping of racks, therefore, is been used in over a doien fue! rack MSW CREEV ANAMES intrinsically madequate to predict the hcensing proiects, was uwd for thi, l rnotion of rad nwdulo with any quan- purpose. Subsgent to the Chin Shan anal.,k, Hohec International completed some l tifiable level of accuracy. The resuhs of this first ner so called similar work for CPU Nucleari Onter l whole pool muhi rack (s nai analais EXPERIENCE lH TAlWAN punided fur;her inught into the in-p'ool Creek plant 'ocated near Torm iker. (
rack dynamic hchauour. Trasking of the New Jerser. The Oyster Creek analyses Taiwan - no stranger to schmk trem-inter rack gap showed that the prnense were performed using coeffwients of on - hai three nuclear instalianont friction of 0.2 and R in tha case, the l of warei has the e%ct of iniecimg a Kuosheng. Maanshan and Chin Shan. maimum dnplacement of any ratk in l Taiwan l ower Company procured racks cenain nmmein into the moin.n of adiacent r ac ks, although a certam the pool predwted b" the sm analnes l for the Clon %n ute from General uai 1.* timn the single rack anafysis Ucctne Compan3 in luso. Thne racks amount of out of-phase monon occun.
Comparnon with ungle rack ii) analy- predktion. In tha anahsis, the pedesta! l are of the so called honeycomb ton-struction, and were initially anahwed by se , howner, pointed to the rather to dah impaer loads predicted by the l unsculing conclusion that the ungle mm analysn are diphtly greater than l.
4 imple rask m senmu modek Recog- the value obtained from the single rack nuing the inadequacy of such a moJd to tack modeh do not hound the resulo of i the whole pool simulationt in the Chin analysis prognouicate the poiential hazard of i New storaae technolo w a Greifswald !
f By W Fischer, S Standhe, M hin and K Hochstrate
' I.
The Greifswald site in the former GDR boasts a large interim fuel store (as well as four i
now shut down WER 440s and four more in various stages of construction). In recent years the east Germans have been working towards expanding the capacity of the store by re racking the ponds using locally developed transport / storage baskets, j
l s ulh design (d hMkch to ,hiommodate centre to-ccm c diqarbe O[ 22 5mm ht-In IUM 114 .urangimshh for shipping aucmhhes with faikd demems Atounh tween the tud asmbhes.
spsnt fud trom Rhcinshcrp el X uin
- d and GrctIsuaId 11 X ss Ly,m) in pond as ts ,h a rew n c, s.tstern Cs tmans hask to the ( %R ucre
\t thy end of 1000. /\h somamed around 2@o spcnt iud aucmblic from %rk has been in pmgreu o npand ths thanpd prmoush. ihe speni fuel haJ hevn returncd atur toohng t'or three t he s s i n .e's and the ssinN hn v.
3 0ah at the pnuct 4.It oth, lo meet ths planthd that a turther 2300 Iud ,incm- , 3, cray blics stored in brettswald unih I to 4 l nine Ntvist r6t]uirement f or a in c s car cool. will he trarbt'ttred to / \ll af ter a sorihng D T Int time Ilk- interim storage facihh '-
[ \8 l/.wishcullper lur JNgshrannte time HIduce yeah. lha tratkisr h to hk - - ~ .;,, -- -] l pstformed udng ths Ikt + tail trath 4g l lJ ,
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j ulinothlot h pc h pA kages. j i MUi hs n s metal NO. llw bhmbho I IG hbm , .db3, bd I are stiers d m t his c pimds. s A h .h som- % n h t -di s t loth d fail h> L '
whc hoth e mw th for ths o sak Md em! p modating 42 hekct% enh somc spe I e shirap r Aks m thc / \B pimds lhh gg g , g g. ;
I j a i . M ,o,s s % ~6 4 da Moib tbg nesd to bandh dngk fad @7m bi !t o e. /. !c . %. 4 s .
.! (I nwmhho in the / \D lAilut l$A h
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heke sontams ,O t o u, .bw mh e' & CrCSS leCilon ot the ZAB interim ,
m 3, O I'lliV < I hs s nth ahn ah t s o! 's spent fuel Store at Greif swald m eastern sv9 m i n /* A, %,n a /ha , ii 69ttnany j t'on i o % (. h.blgi n Ahh scd bs hm ui; a NUCcEAR ENOtNEERING INTERNATIONAL 40
(. .e .8 A'ITACHMENT 9
d
.g ,
g Nuclear Issmeenns and Desi5n to (19s4) 31$ 329 315 North.llolland, Amsterdam .
i SEISMIC RESPONSE OF A FREE STANDING FUEL RACK CONSTRUCTION TO 3 D FLOOR MOTION Alan L SOLER Vice Pruideal of Enginaring, llohee lasernadonal Krishna P. SINGH heeldest, llohoe lacemstional 4
Received January 19s4 Seismic analysis of fra standing submerged racks is comphcated by the presence of water and structural non-lineanties such as fuel unembly cellimpact and floor interface incuon. A direct ume h..e6 ration technique has been proposed to analyze tius class of structures. Application of the tune integration technique on a fourteen degree of freedom lumped mass model of the rock reveals some heretofore unpublished quirks in the structure's behavior. De method of analysis is utthred to compare the smnuc response of some representative rack daigns. Resuhs show wide ddferences in the structural response, depending on is febncation details of racks.
b
- 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 tacks are being designed for free standing an mdefinite suspension of spent fuel reprocessing in installation. The structural analysis of such rocks under 1977, the nuclear power industry has scrambled to postulated floor motions, referred b as Safe Shutdown
, increase its capacity for on site storage. De shrage and Operating Basis earthquakes in the lexicon of the pools in most of the commercial reactors were initially nuclear power industry, is the subject of this paper, designed to store 1) core worth of spent fuel, ne Representative of other work in this area of interest is storage rack modules, built for storing the spent fuelin the rather qualitative paper by Habedank and co authors 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 nuemblies can .
each other. Wide pitch (center to-center spacing) be- " rattle" inside their storage locations, and the module e tween the storage locations ensured subcriticality of the itself may slide on the pool floor, Furthermore, the rack fuel array. Ostensibly, the most viable and cost effective may lift 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 4 replacing these rack modules with the so-called high structure. Exigency of the market place calls for econo.
density tacks. The latest version of high density racks mies in design and construction; 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- ethaustive analysis of the resultant non linear effects. In tween the cells to maintain nuclear suberiticality, this paper we present a technique which can be utilized Matching of the new "high density rock 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 ;
i to minimize the in-pool installation time for personnel attai hed to each other along their long edges in n )
radiation safety, hese considerations, among others, certain pattern (honey-comb construction) and another 1 Elsevier Science Publishers BN, 0029 Holland (North. 5493/84/503.00 Physics C, Publishing Division) Response to Questions on Technical Soecification Change Request NPF 38193 ATTACHMENT 9 QWYN jfl,
d 4 #
316 A1. Soler, K ! Sangh / Sensnue req <nue of a pre standung fuel rod in which the connection between the cells is made only 2. Deory at the top and bottom (end connected tube construc.
tion). he latter construction i. ilves only a fraction of We consider a system governed by absolute gener.
the weldmg of the former, and ti., efore is a far more alized coordinates p,(t),4 = 1,2,..N,. All internal forces economical design. From a safety standpoint, the over. contributing to system deformation are anociated with riding concern relates to the increase in the rack stress generalized extensions 8,(p,). Internal force elements F, levels and rigid body displacements as the inter. cell may be non. linear lunctions of the generalized defotma.
longitidulinal welds are climinared. It is necessary to tions p,(s) such as gap or friction elements. Lagrange's develop a methodology to address such concerns during equations, written in terms of generalir.ed forces Q,(t),
the initial design and licensing effort. This paper is and generalized external forces G,(f) are intended to provide such a tool.
A storage rack is a structure submerged in water 0,,T, which greatly complicates its motion. proper simulation .d, ds { Sp, } ,, Sp,8J-3 ,
=t ) d =' t 2. ,,N,.
,( s ) + G,( (1) of rack dynamics requires consideration of hydraulic couphng and virtual mass effects. Such effects are m. Since all of the p,(t) are independent, it is easily demonstrated that cluded in this analysis using simplified models. Smcc our object herein is to establish a tool for comparison "i 8A 0,(t)- E F purposes only, we propose a fourteen degrees-of. free- = E Fs B,s , (2) dom model to simulate rack behavior. A more compre. s-t ' A-1 hensive model has been employed by the authors in where the dat (-) indicates time derivative and B,s are analyzing racks for individual plants (2[ 11 is importt.nt called coupling coefficients l3). 8,s relate the generalized to emphasize that what we are demonstrating here is a veloc ties p,(s) and the generalized extension rates ha (f).
simpler version of what would be required to qualify an De system kinetic energy Tis wntten an actual unit; however, the methodology employed to develop the model is essentially the same. "* ".
) Comparison of different rack geometries on the basis T={E EAI,,Apf (3) of their structural response is affected by three major '"Il*'
variables; (1) the acceleration time history, which varies 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 erahzed masses V,j are independent of coordinates ps, dynamic coefficients of friction at the rack and pml Using eqs. (2) and (3) in eq. (1) yields the system floor interface. In order to draw tenable conclusions, equations of motion in the form analyses are performed using three arbitrary s*ts of earthquake time histories. Two conditions of rack load. l Af }( # } "l8)( F} + (G }' (4) ing (all or half of the locations occupied), and tw where [ Af] is of order N, x N,: (B), the coupling coeffi.
values of the coefficients of friction are also considered.
cients matrix, is of order N, x N,, ( p ), (G) are column in all a total of sis cases are utilized to infer charactens-tics of the rack structural behavior, matrices containing N, rows, and (F) is a column De three orthogonal seismic excitations are applied matria containing N, rows. A set o,'inertially decoupled equations evolved from eq. (5), is coincidentally. %e results reveal some striking peculiar.
ities of the rack 3 D stnictural reponse, ne marked ( p } . [3f }-8(gl(p} +[ Afl-'(G) increase in the rack stress levels and displacements (5) 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 results pre-sented here, the analysis suggests a methodical tech.
nique to evaluate candidate designs for a particular 3. Fuel rack model application.
De following items should be considered in the development of any fuel rack-fuel assembly dynamic model:
l A I Soler. K P So~gh / Senemic respoone of a ftre standmg furt vad 311
- 31. hfodellmg of the rmk structure w ,'
O i The rask structure may be modelled by clastic beam T-- F T'- "T clements as long as appropriate cross section properties , / /
can be derived and as long as shear defortnation and / -5 7
rotatory inertia effects are included. In specific design applications, the authors have used four beam elements j //
l -
+ *,o ard five nodal points to desenbe the rack structure. In F f-- 'e --
ik paper, since the emphasis is on a comparison of two e different tack geometries, we have adopted a simpler . 3g,'p,'g lg *l,jueo model for the rack structure involving only a single umuts etera beam element. His simplification helps to focus atten.
tion on the main differences between the two rack N configurations studied; namely, the significant dif. / ' l ference in the shear resistance.
/ j@ @!
/ '. l 3 2. himlellms of the fuelanemMn lj .i. 3* ,
,l rt;~'n - ' '
Each fuel nuembly hould be treated as an individ. / ** ,/ ' '
ual distributed mass clastic element, in the actual fuel '
rack, an element may be kicated anywhere, in the x-y [N tg Q, '
j plane and will impact with the fuel rack surrounding i metal at one or more vertical kications. An anemblage = I a, II of fuel ammblies will certainly not move in phase during a seismic event. For the purpmes of evohing a j
./ [ t conservative rnodel, wt have auumed that all of the fuel Fig.1. Rad model showmg degrecs of freedom.
assemblics move as a unit; thus, the impacts with the fuel tack are magnified leading to higher stress and load levels. In a detailed model where the rack is simulated supported at the four comers by rigid supports that may by five nodal points, impacts between fuel rack and fuel slide or hit off the pool Ikior. De pool floor is excited anembhes may occur at different levels; in the simpler by a known ground acceleration in three orthogonal model used herein for companson purposes, we assume directions.
that impact between fuel tack and fuel anemblics oe. 11uid coupling between rack cell walls and the en.
curs only at the top of the rack, and that 50% of the fuel semble of fuel assemblies is simulated by introducing auembly mass is involved in any impact with the rack. appropriate inertial coupling terms into the estem We emphasize that in any real design study, the possi. Linctic energy. Similar inertial coupling is introduced to bility of impacts at vanous heights should be included in the modet For this illustrative comparison, we feet that the salient feats res of the behavior of each rack d type wdl be correctly demonstrated with the simpler , . .
I r,
rnodel. /'//
f Figs. I and 2 show the model considered in this '
paper. De fuel rack metal structure is a single beam /[f[k'M / 0 I' !/ , g ,,
element whose end points have a general sit degree of
// ,/, i freedom motion. The ensemble of fuel anemblies sre f 1 consenatively assumed to move in phase under seismic h ' /,(
escitation, and their effect on the fuel rack is considered W " W A to have the potential of 50% of the effective mass y 7
impacting the rack at the upperrnost point. De offset of '
the lumped mass from the rack beam centerline enables !.
simulation of a partially filled rack with induced tor.
sional moments. De fuel rack base is a ngid plate, Fig. 2. Irnpact spnrig onentation at top of rack.
l l
l 11R A I. Soler, Kl' Songh / Seumte response of a free standnng fuel rark l account for Duid structure effects between adjacent energy due to the tack base is I racks. Fluid damping effects are neglected in this study. '
As shown in fig. 2, potential impacts between the rack II: " **ie! + M ,e} 6 + **,f} + 1,el + 1, Al + 1,bl.
beam and the lumped mass representing the fuel assem.
blies are accounted for by inclusion of appropriate gap (9) elements. The fluid inertial coupling terns are based on where mg,, I,, I,, /, are the effective mass, and mass nominal clearances in this investigation; however, it has moments of inertia of the base, including fluid mass been shown (4) that inclusion of large deformation effects.
effects near the impact points may considerably affect The contribution to system kineth energy due to the results. licrein, we do not include the effects of gap fluid coupling between fuel rack and fuel assemblies is closure on the fiuid inertia terms since there is some capressed by the 2.D model given in ref. l$J. The preliminary evidence [4] that neglect of the effects is necessity for accounting for 3.D fluid structure interac.
conservative, tion is a question that merits future study. Using the in computing Linetic energy contnbutions from the 2.D approsimation, we obtain for the kinetic energy rack, we use appropriate consistent mass matrices. due to tack-assembly interaction, Therefore, the contribution to the system Linctic energy due to the rack Ti ,is given by 2T-A:(p}+pH+Aii( pl + pl,)
3
+ 2 di > ( t,t. + p.ti.). 00) 2 r, - ( p,,pi,l'[ Ai,)/ l ea,s tp 1 + ( ps l pi,)'[ Ar,1 ets// p, \
Similarly, the Linetic energy due to fluid coupling be.
p, tween a fuel rack and adjacent structure is given as
+ ( et.hties eeis )*l Ms } p,' II *4 8lI'#! + 8ll'#} + 8lI'e! & 8lf'#I
- + 2 Bjj'piDi + 2 Bl{'),03 + 2 Bjj'p,Di pa + 2 Bl{'#,0, + O(D',D8).
) i (11)
+ ( es./,.-#4.- An )*lafs) - . (6) where U,U- l. 2,3) are specified pool floor seismic p motions.
Finally, the contribution to the system kinetic energy where [ Afg], [ Aft ) and l AI,l are the appropriate mass due to the mass of the fuel assembly group is written as matrices for extensional, torsior.al and fleaural motions.
If A I, are the rack cross section effective metal area 2T, = A Af( pl + p!,) + Af( p3 + Y,p - X,p3)'
and polar moment of inertia, respectively, then
+ (1 - A) Af f( pi - Y,p.)* + ( p, + X,p.)3),
l Afe l" p,iAll 'l f' 3
i 02)
,g g, M is the total fuel assembly mass and A is the mass
[ Ar,] . # # I 5 fraction assumed acting at the top of the rack in the 3
(7)
' ~.) 1 horizontal plane. We have assumed that vertical move.
13 9 1111 1311 - ment of the fuel assemblies is equal to the vertical 35 70 210 420 movement of the rack base at fuel assembly centroid 9 13 1311 1111 location, and that the fuel assembly mass fraction (1 - A) 70 35 420 210
- * "*' " E'"""" '*" Y
[ At* J . p+ Alt ' herein, we, have arbitrarely set A = 0.5 which implies 11H 13/I 118 1/3 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
- 1311 - 1111 - 118 118 the rack, if more conservatism is desired A may be
, 420 210 140 IO5 , increased. it would be far better to include more degrees of freedom and allow for the possibility of impacts (R) below the top level, however, than to attempt to de.
p* and p,* 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 nf A
o e,
A I, Soler, K!. Stegh / Stumse resprue ole free standmg fuel rock 319 used will not negate any conclusion developed as long hY as A is sufficient to induce significant impacts between - --
tack and suemblics. Eqs. (6)-(12) establish the system I rnass matris [ Af] in eq. (4) for the 14 x 14 model considered herein. We introduce displacement coordi.
(( I I I I nates g,(t), relative to ground, defined as follows: (( p p p p ~T p, = e, + Ui ( 0 ; f=1,7,8.
- pp pp ,
p,=g,+U,(s); i = 2,9,10, FFFFFI pppppp 3 , p, ,
p, = g, + Us(I); i = 3,14, p, = g,; i = 4,5,6,11,12,13, FFF FFF I
-k .
The governing equations may be represented as follows: ~~1 '
L 4
~
E Aldj " O (8) + G,(f) ~ [a,i Ui + a,3 U + a,3U] 3 3 ,[' N 1-t , a
- f. t =.049 A 060N i = 1,2, . . 14.
(14) '
' 'nY: no 9.30 4 '
In what follows, we discuss briefly the computation of :: -
some of contnbutions to the elemo.ts of the set of equations [14].
[VQM 10.4 5,, 5, ris. 3. Rad enas section and typical cell geometry - honey.
- 4. Hund added mais effects comb construcuon.
Consider a typical cell with an internal fuel nuembly I
shown in fig. 3. Assuming that the anembly and the cell are vibrating, it is shown by Fntz [5] that the constant The fluid mass that would fill the cell volume in the absence of the fuel anembly is denoted by Af3 in ref.
coefficients A,j of eq. (10) are given as
[5]; tha effect of this virtual fluid mass is incorporated A n = Ain ; A u = ' ( Afi + AfH )I A U
- AIl + AIH ,(15) Y M N N"8 "" ' 'O The effect of fluid inside of the rack structure has where Af = fluid mass displaced by fuel assembly, Afn been accounted for in the Linetic energy term T3 ( A,,).
= hydrodynamic mass. We use tia Fritz emdel for We now consider the effect of the fluid outside of the concentric cylinders employing equivalent rad,i Ri , R 3 rack (say between the rack being studied and adjacent defined as structures). We consider fig,4 which shows a vibrating
~
R = a'/[w , R -b'/s,'s, vertical wall of width H' and height #, Following case i 3 (16) 13 of ref. [5), we asume the hydrodyn.smic man term as o' is the side length of the square fuel assembly and n, b* > a' is the innde dimension of a typical square cell; Afn = p,g sy i 1.e. the norninal clearance between assembly and cell is 12 9 +"1+F (l')
( b' - a ' )/2. Then, in the fourteen degree of freedom simulation For a rack of height H, assuming all assei.ibhes move in phase, we obtam model, the coefficients, Bu,8u at each level are given as Af = FP.NRff , (17) Bn = Alu/2; Bn = -( Afn 4 p.HH't,)/2 (20) where f, is the number of cells containing spent fuel with M' being the value appropriate for X or l' motinn.
anemblies. If the nominal gap g is defined as g -(6* -
a')/2, then tef. [1] suggests that the hydadynamic The above discussion is concerned with fluid cou.
mass is pling effects induced by horizontal vibrations. To account for fluid effects in vertical vibrations, we simply define an effective mass density for the base plate using Afu " pI g
Ali /(1 + 12 3R p'H3). (18) case 6 of ref. [5] and add it to the I ase plate rnetal mass.
J20 A l Soler, K P Smsk / Saunut response <4 a free standong fuel rock
- 31. Ra<k rlastmty f6 elements) n Kwes,ou = Gip /fl.
%' Ktmusum=EA/II.
' 12 El 12 Ela
< A.
s l suran-ll*(1++); $='.Gall u ,
Ketumuo = E!/fl, (21)
H '
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 g% ,
shear and bending spring pair is needed for each plane
- of bending.
~
F88 1 Fuel rak wsil model used to obtain flud couphng. "I N# *#
ne potential impet between fuel assembly mass and fuel rock is simulated by incorporation of a The total effectre mass density is then used in the spring-gap c mbination. Each impact elements acts in coniputation of m.,, l.1, for the base plate. He effect compression only with spring constant given as of drtust fluid movements on the r.sck is simulated by def:ning an effective mass density p; in the matris [ Afg]
g ,f,4,pj,3; D = Et /12(1 - ,a).
1 3
(22) in eq. (8). p; is computed by adding to the rack metal K, is determined by assuming that the impact is simu.
maan, a mass equal to the mass of fluid displaced by the lated by a uniform pressure acting over a circular sec.
3 recit.
' tion of cell wall of radius a and thickness r. The radius a is taken as b'/6 where b* is the inside dimension of an individual cell and f, is the number of cells contain.
5, Internal forces ing fuel assemblics.
l'he internnl force elements representing system elas. 3.3. Support leg spesng rate M gay elements) ticily, disappative friction and impact effects are simu.
lated by using standard spring, friction and gap ele. He effect of arpport legs at each corner of the fuel ments described in ref. (3). He model shown in fig. I rack base is simulated by foer compression only gap cos.tains 6 elastic springs to model two bending planes, elements to permit hit off of any or all supports. De extension, and torsion of the rack beam, he model local spring rate K, foi a support of height A is cor.tains four gap elements modelling contact between g g j g the fuel assembly lumped mass and the top of the rack.
The model used four gap elements alligned in the verti. -~
As=Kr- + Ke - L+ K n , i (23) cal direction and located at the x, y coordinates of the where K, = EAs/h; As = support leg cross section area, base plate supports to simulate the support behavior in and the vertical direction and has sixteen friction elements to simulats support leg ficaibility and the slHing poten. K t, = 1.0$E,B/(1 - e8 ); K. a - 1.05g EB/(1 - el ),
tial of the supports. Finally, eight rotational frictional elements at the base supports are used to simulate (;,g) resisting moments due to floor-structure interaction. K t, represents the local elasticity of the pool floor with Full details of the behavior of these elements and the E, being the Young's modidus of concrete and B being developmer.t of their associated coupling coefficients the width of the support leg pad [3). Kom represents the are found in ref. [3); herein, we simply specify the local clasticity of the rack just above the support leg; spring rates associated with each of the elements. the coefficient g is taken arbitrarely as equal to the ratio of the metal area of single cell to included area of single cell.
1
I I
A 1 Soler, KP. 5,nsk / Stunne resmo of a fore stand,ng fuel red 321
$.4 Floor rotatwnalandfrsctuur elements Y g -xi ne effect of local floor elasticity on rocking me r
' (support leg bendi e,)is represented by rotational springs wiih ,p,ing ,aie . . p. 293).
~~(({]'""~l Kn- E,B 2/6(1 - e ). 8 000000 3 I' (25) nese rotational springs are moment limited since if OOOL_Jr 1r L_J1r- L_)7 I_* -
edging of the pad occurs, no further moment can be tO O 03 sicciated with each support leg cortipreuion ele-ment spring are two orthogonal friction elements krated in the plane Z = - A (see fig.1). He friction element kwal spring rate is anumed as the spring constant of a
((((((y -
.o- .e support leg when considered as a guided cantilever beam of length n under an end load I'. Therefore, from ref. l6). assuming that the support has area moment of '* *T. %
inertia 1, when considered as a beam, C.9. 304' 1
I*
9dO'S
]
K, = 12 Elg ; d = 8.$2 - 4.1$7 i
' ' %' 4 rig. 5, Rack crou action and typical cell geometry. uncon-nected tube construction.
(26)
' ) fi T J
- 6. Application to typical units P* " - E E V,f i N ' " E E N,j . (27) 1- 1 > n i >=t .
Figs. 3 and 5 show a cross section through a level of the rack structure of two practical rack constructions. Ce.stighano's neorem for the 4th ti.be yields (assuming De first is a fully connected h"Nycomb construction (llCC) which is considered as a beam-like structure with cross section dimensions b and o. having certain area and inertia properties; the second is an end connected 'W' tube construction capability between ttp(ETC) which has no shear transfer (TYPICAL CELL escept at top and bottom of r END the rack. For the HCC rack, eq. (21) can be used
__\
' n $ RING directly to model tack clasticity since the entire cross - ], gf " Nd -
r ya "
section is capable of beam-like shear transfer; we need [
only esamine the cross section details to derive espres. y; sions for A.1.1,, For the ETC construction, however, - m g,
since no shear transfer between cells can occur, we must - - - - - - - [g +-
undertake additional analysis in order to arrive at the "
proper spring rates for eq (21). ny E y +
Fig. 6 shows a free body of the rigid ring connecting,' , ,NJ all of the tube-like cells at : -Il and constrains them to ' N ,. Y 4 move as a unit. If there t.re / cells at level I, then equilibrium requires that for a 2-D motion. *j ' '
J ( j/ N M* = E E { M,, + y,N,,)
1"l 8 H
Nl Fig. 6, Free tufy analyus of end nns in IMC rack.
i l
322 A.I. Soler, K P. Smgh / Saumu resporue of a free staredsorg /snel rock a fixea base)
_jl V,, . 12 Elli '
g,, _ 6 El , C.) ' O Tl B
li' y p M,, = + W*+ 8*. C ~J (28) m 0;.,,J Bi.J Om,J e Also, bearing in mind the constraint of the end closure, ,I ,
we have, p a e
'J EA N,j = 7(U * + y,0 * ), (29)
In eqs. (28), (29), A, I refers to the properties of the
% u u lj indnidual cell, and we have neglected shear effects in
(,
the bending of the individual cells. Using eqs. (28), (29),
Fig. 7. HCC cross section for torsional n6idity analysis.
in eq. (27) yields, for the case of n total cells in the unit, y e . + 6E(nl)W* H 2 . fEn ' l + [ [ 4 ff
- , The torsional analysis for the HCC unit is based on g j , i the classical analysis of St Venant described in ref. [7]
and applied to the cross section of fig. 7. By using the V * * + 12 Enly W * + 6 Enl *d, membrane analogy for the torsion problem, it can easily be shown that I, for the HCC construction is simply N'= U* (30) (17). P 278)
If we now replace eq. (30) by the corresponding equa- #
P Hcc
~
d '
, tions for an equivalent uniform beam acted upon by where K, is a tabulated function of b/a.
end eneralized forces Af *, V*, N *, and having effec.
An analysis of the end cross section of the ETC
.4 e .: section area A*, inertia property l', and shear ca construction using fig. 8, yields
- +*, we can show that the A*, / *,9' [for use 4 (21)] s.hich correspond to the ETC unit are given , , , 24(
f, , f sr) j (y3r + 7 ), {34) l*
- = nit A*=nA, \;Lgj W' 1 + +* oY Hs i
(4 + $* )l* = 4n1 + [ [ y,23 ,
(31) GL.O r
+# >~t L
- i f- ~ Qw n se . hat I j
/* = nI+ { Ey 3; 9. . { { y,2A/nl.
2 (32)
L A- -X The results for A*, I*, +* can be used in eq. (21) in lieu I of A, I, +. It is clear that between the two geometries the only essential difference is in the magnitude of 4*. T, I The considerably larger value of +* obtained using eq. ,
(32) for the ETL unit (as opposed to eq. (21) for the i HCC umt) leads to a much smaller spring rate Ksnex, I being obtained for the ETC unit. It remains only to T * = TCTAL CROSS SECTICN TORQUE compute a value for I, for both the HCC and the ETC 0 = ANGLE OF TWIST / UNIT LENGTH configurations, and then to apply the simulation to typical in service units. Fig. 8. ETC end crou section under torsion, o
., +
A 1. Saler. K.P &ngh / Seamuc response of a free stanJng fuel rad 323 where I,, I are the area polar and bending inertia in the supports on the basis of the formula.
properties of an individual cell, and n is the total number of cells in the unit. o dd + M# '+ -
M 3, (35)
It should be emphasized that in the above analysis, 1 la we have assumed that the ends of the individual tubes where A,1,1 3 3are the appropriate geometric properties are assumed to be connected in such a manner as to for the supports or for the entire rack cross section of enforce the reqairement that planc sections remain the HCC unit. As noted previously, the use of the total plane. This requirement may or may not be satisfied in cross section properties for rack stress evaluation is any specific ETC design. justified for the llCC unit since the full cross section is avaihble for shcar transfer. The evaluation of stress in the ETC unit requires some additional analysis. The cell
- 7. Application to typical configuration whose centroid ir at X,, E in the cross section experi-I ences a direct stress of the form We consider the configurations of figs. 3 and 5 for E
the case b = 124.128" (315.3 ct$), a = 92.8125" (235.7 oo = p((fi cm) having a 9 x 12 cell arrangement for a total of 108 93) + M(9n - 94)- X.(fu 4s- cells. The support legs are assurwd to be four 8"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 forming a box at each corner. Table I shows the spring 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 . teel having a Young's modulus E = 28.3 x 10' psi (195 kPa) and the rack height # = 28e v , _6E , .y ,, 161.125" (409.26 cm). c n a The seismic load-time histories used have statisti' cally independent components in the global directions. 2E 6E The particular records used are those from three differ-7 [4a - 94}' y 44 (37) ent plant specifications. (See figs. 9-11 showing one 2a ar ,_ horizontal component.) C H 9,_9,),,y,49g_q,)) For the llCC unit, net beam forces and moments are 2E 6E used to compute extreme fiber stresses in the rack and + y(9u - 9s) + 7f 9s- (38) The maximum rack stress in any cell wall can be con-TabkI structed, at any time instant, from the expression spnns rates for model o = N +1od +1od. (39) Item HCC UTC Ares of cell We emphasize that eq. (39) does not include any local 4.379 sq. in 4.652 sq. in Ic.u stress effects induced by non-rigidity of the rack base,
= J5.55 in* 33.56 in*
ll (unit) 616 926 in* load transfer between supports and adjacent cells or 654 996 m* tubes, etc. 1l (unit) 346 825 in* 367 993 in' For a given time history of stress i, the supports, in
, (u it .8 in. the HCC rack cross section, or in the ETC individual
+ gg 2.35;1.322 179.71;100.53 cell cross section, a determination ot urut structural Kroas: [eq. (21)) 7.520 x 10'in #/ rad 1.009x 10'in #/ rad. integrity may be carried out. In accordance with ref. (81, K,xymsm 0.8306 x 10' # /in 0.8818 x 10' #/in structural integrity may be interpreted as setting limits Kan u a.y 0.1214 x 10' #/in 0.294 x 10' #/in or, forces and moments acting separately or together on Ksnun u 0.1214 x 10' # /in 0.294 x 10' #/in a defm' ed cross section. For the HCC construction, the Kox Key 0.1084x 10"in #/ rad 0.ll50 x 10" in # / rad entire rack cross section can be used in the structural 0.0609 x 10" in # / rad 0.0646 x 10" in #/ rad integrity evaluation; for the ETC construction, we must Km,wr (fa = 108) 0.715 x 10' # /in 5.084 x 10' # /in K s[eq. (23)l 0 c925 x 10' #/in examine the cross section of the critical cell.
0 0958 x 10' #/in Ku [eq (25)l 5.971 x 10' in # / rad In addition to stress limitations, adjacent racks must 5.971 x 10' in # / rad K,[eq (26)] 2.004 x 10 #/in 2.004 x 10 # /in not impact during a seismic event. In the simulation heirein, virtual mass effects from gaps between racks
324 A.I. Soler, K.P. Sangh / Sessmsc response of a free vanding fuel rack R 9 q- E L g T.
==
d
- ==
3a
" j C
f::::::=> 9 7 2
<- h q L)=
c.:, ,
's g
==
. b $
r' -- e
- i W
.2-o
_ -==- et 2
)
W o, *= l 9 1
-m .
4 I 4 d
- r-aus- 4 a
ar* y
,=S ==-- . .
._.-- -- ~
4 % m- .._ y T'
-- g
- y. =
9 Ie q d mm a1 m's um n;e svo so o oro ero- st 'e-(S-SI N0!1WTt3330 n 'o- m> 2 + ct T-6 s
f
+
A 1. Saler, K.P. Smgh / Seismic response of a free standmg fuel rack 325 d Nh -
'N ,
N O EF_ . .
-e 6
- " e d
e N N -
~
~--
%e m ._.
3
\ ~
d M _
-d
.=- .
mi
'N M N
..= ens ======.-- =
64 4e . -
- h. l
.mununumammung -. g h.
N S "M 9 9 O
-- e d
# w on M 3
... I
~_ -
4 . T I 3 s
=a uo oro mo are m' m o. c o. a (S-3) N0!11ATJ1333W C 1
l
4 4 326 A.I. Soler, K.P. Smgh / Seumsc response of a free standms fuelrack 4_ - k O o
. _. 2 O
-n o
d
. p:_.--- _
D
'Wh-i%
t Q E
=
4 - o
- N E
g 4-. Ow
=__ eg g m-
.Z
- = _
O
. ~ _ ~ _~ .-._ g
~.
O O
-N, m--~ e
._ _e-. N g
M p 6 O N . m 0 b e d
- . - .l~ _
N Ze o t .c- -g . . . I M a - St o st e at e ci o so o sa o so o co o aa ., i go.,,,,,,,,,.,,,,,,,,,,,,,,,,,,,,,,,," j (S-S) N0!1WW7ETJOU
e A 1. Soler, Kf, Smgh / Sounue respoout of a free standung ful rock 327 Table 2 if the maximum corner deflection of the rack in either Sirnulation studies direction is less than 50% of the rack spacing. To assess the two rack constructions, the simulations Cm %h See W given in table 2 are performed. Values used for coeffi-I full rack; COF = 0,8 fig. 9 (0.302 x 1.5 = inas. g. Iml) cients of friction, 0.2 < COF < 0.8 are accepted upper and lower bound values. Simulations 1-5 are performed 2 fult rack; COF = 0.2 fig. with the seismic input amplified by 1.5 on all three (0.302 x t.5 = max. g. level) input directions. Simulation 6 is performed with the 15 s. duration appropriate seismic inputs amplified by 2.5. Thus, case 3 fuu rack; COF = 0.8 fig.10 6, when compared to case 3 shows the effect of employ-(0.17 x 1.5 = mas. g. level) ing different amplifications on the same seismic event. 12 s. duration Simulati'on 5, using a half loaded rack, highlights the 4 fult rack; COF = 0.8 fig. it effect of rigid body rotation of the rack around the (0.15 x 1.5 = mas. 3. level) vertical axis. The half loaded cases astome 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 6 full rack; COF = 0.8 f O structural damping of 2% is assumed at a frequency of x2.5- w hl) 20 Hz. Table 3 summarizes the results obtained for , 12 s. duration stresses and table 4 shows the maximum corner dis-placements and maximum floor loads transmitted by the rack. We may define factors R, which are limited to have been included based on adjacent rack separation the value 1 or 2 for an OBE, or SSE event, respectively equal to 3" (76.2 mm). Therefore, assuming the worst IBl. motion of adjacent racks, inter rack impact is precluded I Table 3 CASE Honeycomb vonstruction End connected tube construction Rack Support Rack Support Rt R4,R5 R1 R4,RS R1 R4.R5 R1 R4,RS I 0.002 0.081 0.385 1.46 0.200 1.21 0.613 1.898 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 0.95) 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 Maximum rack deflections / transmitted loads Case lioneycomb construction End connected tube construction
,. X Y Max. Single Impact X Y Max.
- Single Impact (in) (in) 11r. Id. les Id. load (in) (in) fir. Id. les Id. load (Ibs) (lbs) (lbs) (lbs) (lbs) (lbs) 1 1.175 0.084 536 600 257 700 201 400 1.049 1.629 1 280 000 411 300 578 500 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 79 540 2.145 2.392 602 200 200 000 181 500 6 0.126 0.343 611 000 309 800 216 800 0.856 1.45 985 500 343 100 588 300
Statie load = 184 000 # for Cases 1,2,3.4.6,
, = 103 30a# for Case 5.
e
+
y 328 A.I. Soler, KP. 5sngh / Seemn response of a free standong fuelrock Ri = direct stress on a net section/ allowable OBE rack stress levels in the thin walls of the cells, tensile (compressive stress), induced by poss dynamic motions, remain low R = gross shear on a net section/ allowable OBE shear, enough so that stress raisers have minimal effect on R 3= maximum bending stress in one plane / allowable unit performance. By the very nature of the ron. 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 Rs = additional combined flexure and tension (com- the HCC rack; therefore, gross stress levels (prior to pression) ratio. . 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 R, 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 dis-R.orRs at the most eritical location. placements. For some of the simulations studied herein, inter rack impact may occur since the pre-dicted maximum displacements exceed fifty per cent
- 8. Discunnion and conclusions of the assumed spacing between adjacent racks.
(6) The maximum load (static plus dynamic impact) From the simulation ret.ults, we can draw the follow-ing conclusions: transmitted to the floor from the total number of 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. tion to the manmum rack horizontal displacements . quently re-contact the floor with a substantial im-can be made during an instant when the rack is only pact. supported on one foot and the scismic loads cause a (7) The increased displacements found for the case of I pivot of the rack about the only remaining contact the half loaded rack dramatically show the effect of point, 3-D motions and the potential for rigid body rota-(2) Maximum displacements, with a full rack, may be tions about the vertical axis. It is noted that this found when the upper bound coefficient of friction effect is substantially affected by the initial assump-value is used. His can be c~plained by noting that tion on the amount of fuel assembly mass par-t 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 single foot is in contact is increased. the rack body, is less prone to excessive displacement, (3) For the seismic events considered here, stress levels and results in lower dynamic loading on the pool floor. in the supports legs have the same order of magni- Although the model used herein is relatively simple, it tude in both HCC and ETC racks. does exhibit the features of the 3-D motion and the (4) Stress levels in the rack cells, above the base, are expected impacts. In any real design application a more significantly higher in the ETC unit than in the elaborate model would be called for, which accounts for HCC unit. The ratio of cell stress levels (ETC/HCC) impacts at different levels, additional rack 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 appropriate since we week only a resultants may not imply violation of gross failure comparison of results from two different constructions. 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 flexibility at the comb construction are found to improve the stress levels rack base plate will cause more load to be shifted to and kinematic response of the rack significantly over 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 consetidated pin ports. Therefore, it is prudent to ensure that the storage is contemplated.
4 A 1. Soler, Kf. Smgk / Stunue response of e jree standing luel rack 329 Nomenclature I *, A ',,*,1; equivalent rack 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 forces R,(i=1,2,,,5) structuralintegrity factors
/>,, q, generalized coordinates E Young's Modulus of rack N,, N, number of internal force metal elements, degrees of free- X,, Y, centroid of fuel assem-dom blies moving as a group
[B] coupling coefficient ma-trix [ Aft ],[ AI.];( AIrj mass matrices for exten- References sion; bending; and tor-sion of rack lll 0. Habedank, LM. Habip and H. Swebm, Dynanuc analy-p*,p,' effective mass densities sis of storage racks for spent fuel assemblies, Nuct Engrg. A;11 rack cross section metal D'8 34 (I'79) 379-383-area; rack height [2] Spent fuel pad modification for increased storage capacity, m % ,1,,1,,1, mass and inertia proper. Quad Cities Units 1&2, Commonwealth Edison Company, ties of rack base N.R.C Document No. 50-264,50 265 (June,1981), U,(t) specified scismic motion 13] S. Levy, and IP.D. Wdkinson, The Component Element Method in Dynamics (McGraw-Hill, New York,1976). of Pool fker M [4] A.I. Soler and K.P. Singh, Dynamic couphng in a closely - 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 Bl,", Bl[, A,, fluid coupling coefficients Nuclear Plants, May 1982, Keswick, United Kingdont [egs. (10) and (11)) [5] RJ. Fntt The effect of hquids on the dynamic motions of A defined in eq. (12) immersed solids, ASME J. Engrg. Industry (February,1972) Mn 167 hydrodynamic mass (eq. g p. henko, Strength of Materials, Vol.1, 3rd Ed. f, . number of cells in fuel (McGraw-Hill, New York) p.175. rack [7] S.P. 'limoshenko and J. Goodier, Theory of Elasticuy,3rd
/, ed. (McGraw Hill, New York,1951) pp. 258-315.
number of cells contain- [8] ASME Code, Section Ill, Subsection NF, and Appendix ing fuel assemblies XVII (1980). h height of rack support leg A . ,1, metal area, metal inertia of support leg cross sec-tion 1
. k ATTACHMENT 10
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. a
~
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= a :
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