Forwards GE rept,'Seismic Analysis of Reactor Internals ...
40
Commonwea&diso·n One First Chicago, Illinois Address Reply to: Post Office Box 767 Chicago, Illinois 60690 : Mr. Paui' o :Project. Manager Operating Branch ..:. SEP BraDch u.s. Nuclear Regulatory Cormnission Washington, OC 20555 .· February 29, 1980 Seismic Analysis of Reactor Internals for Dresden 2 by General Electric 'NRC 'DOcket 'N0.'_;50..:.237 '·. '. ·. . · · · .. Dear Mr. O'Connor: Attached is one copy of a. re:r;or:t number 257HA 7-18 titled Seismic ·Analysis ·of ·:Reactor · · Internals for ·the ·Dresden ·rr··p1ant· dated . . ' .· _ ..... Attachment · ·very'truly yours, p Robert F. Janecek Nuclear Licensing Administrator Boiling Water Reactors Booaos 0
Transcript of Forwards GE rept,'Seismic Analysis of Reactor Internals ...
Commonwea&diso·n One First National~. Chicago, Illinois Address Reply to: Post Office Box 767 Chicago, Illinois 60690
: Mr. Paui' o ~Connor, :Project. Manager Operating Branch ..:. SEP BraDch u.s. Nuclear Regulatory Cormnission Washington, OC 20555 .·
February 29, 1980
~ubject: Seismic Analysis of Reactor Internals for Dresden 2 1per~o¥med by General Electric 'NRC 'DOcket 'N0.'_;50..:.237 '·. '. ·. . · · · ..
Dear Mr. O'Connor:
Attached is one copy of a. re:r;or:t number 257HA 7-18 titled Seismic ·Analysis ·of ·:Reactor · · Internals for ·the ·Dresden ·rr··p1ant· dated
. ~2:-24...:68. . ' .· _ .....
Attachment
· ·very'truly yours,
p
Robert F. Janecek Nuclear Licensing Administrator Boiling Water Reactors
Booaos0
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ABSTRACT
111c maximum seismic shears and manents of reactor internals for the nresden II due to their respective nesi.P.n Basis Earthquakes arc
. . detennined. The method used for these detenninations are detailed. The Tesults for those components with significant seismic loads arc ~iven in the following table.
Tahle I
Significant Seismic Shears and ~fanents - Dresden II Plant Reactor Internals.
Dresden II Vessel Skirt Moment (Kip - ft.) 12,800.0
Vessel Skirt Shear (Kips) 728.0
Top Guide Shear (Kips) 147.0
Shroud Support Moment {Kip - .ft.) S,36n.o
Total Fuel Moment (Kip - ft.) 700.0
Total CRD Housing Moment (Kip - ft.) 880.0
Stabilizer Force (Kips) 202.0
Notes: , 1. Dresden II Design Basis Earthquake: .1n g 1~4n F.l rentro Enrthquake
N-S Component.
3. For niaxi.?n1z.l credible earthquake values, rultiply the tabulated values hy:
· Dresden . 2. 00
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SEISMIC A'iA.LYSIS OF RF.ACTOR rr-,'I'ER'"iAJ..S FOR IBE nRF.SDEN II f>L~NI
I. . !~1'ROOOCTIO~
In order to insure safe operation and prevent unnecessary outage of nuclear boiler systems, seismic· responses of reactor internals. have to he determined. This report details the methods, apPr.oximations, and computer progra'llS which are being used at APED to o~tain such responses. It should he emphasized that the.se methods, approximations, and computer prop,Tams are constantly
. being updated. h'hat is reported her.e is current as of the analysis date.
In addition to the description of the method.used for determining seismic response, the,ma.xirnum seismic shears and moments for various reactor .internal components of tWo plants (Dresden II are also included in this report.
II. MA.nIDt.\TICAL t-nDEL.S OF ntE NUCLEAR PIAVI'S
The nuclear steam Stipply system of the Presden II plants were · modeled wi. th lwnped mass configurations as shown in Figures 1 and. 2. Several
features in each model carry the same assumptions in M01.folin~, hut each ~eel ·was generated by an individual author.*
The assumptions associate~ with each component of the nresden II model are given here. A discussion of each assumption is provided to indicate the degree of confidence associated with the entire model.
l. Vessel Head - ,The e.ntire weight of the vessel head is lumped at its center of gravi ~·. The flexibility of the vessel head is detennined from the curves given iri Reference 1 where ~ truncated hemispherical head shown below is analyzed. ~ ·
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SEISMIC ANALYSIS OF REACTOR I~'TER.'iALS FOR mE DRESDEN II PLANT
The element flexibility matrix is defined by the following matrix equation:
where:
er : Pntation nf the to~ of trunc~tP.n h~~i~phere
b = l~teral c\pf.lection
thus: £11 is the rotat,ion due to a unit moment M
and £12 is the lateral deflection due to a unit l110r.lCnt M, etc.
The distance d is ta."<en to be the distance from top of the flange to the center gravity of the shell portion of the vessel head.
z. Flanges - the weights of the two flanges are lumped at their center cf gravity. The stiffness of the flanges compared to that of the vessel is such that 't;he flanges move as a rigid body.
3. Dryer • The dryer is relatively light and is supported off the vessel. In no way does its response affect.those of the rest of the inte111als. For these reasons .its weight is ltnnped to that of the vessel.
4. Vessel - The vessel is divided into several sections. The weight within each section is lumped at its center qf gravity. The stiffness of these vessel sec:tions are taken equal to those of beams having the same crosssectional moment of inertia and area as the cylindrical vessel. A shear form factor of 2 is used for detennining the deflection due to shear.
S. Vessel skirt - The mass and stiffness matrices are treated in the same . manner as the vessel •
. 6. Bottom h~a4 - The mass and stiffness matrices are treatedL.the same manner
as the top head. . I REV
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J T•TL.E SEISMIC ANALYSIS OF REACTOR nrIER.~ FOR n£E DRESIEN rr PLPI~' ··-. ·,-------------------------------------------!
/l 7.
8.
9.
10.
Pedestal, Shield Wall, Building & Foundation - The treatment is the same as those given in· References 2 and 3.
Separators - The separators are modeled as beams for stiffness detennination with masses ltmiped at the center of gravity.
Standpipe - rue to the bracing between standpipes, the stiffness is very high and essentially rigid body motion results. As usual, the masses are lumped at the center of gravity.
Top Guide and Core Plate - These are treated as rigid bodies (for lateral motion) and their masses as included as part of the shroud mass. Part of the fuel mass is considered to be part of the top guide and core plate mass. See 12 below.
11. Shroud - The stiffness of the shroud is taken to be equal to that of a beam with the same moment of inertia and area. The shear fonn factor is taken to be 2. The. 1!'.asses are lumped at the center of mass.
The Dresden II plant . has the leg-type shroud support. This support is simulated by a hinge
and a torsion spring. This torsion spring rate is equal to the resistin~ moment per imit rotation of the shroud bottom. Contrihutions to this resisting moment comes fran: a. .Axial defol'lll3.tion (tension or compression) of the legs in direct -
proportion to.their distances from the rotation axis. b. Bending of the legs due to structural compatibility requirements. c. Bending stiffness of the shroud support plate assuming it to be an ·- - -annular plate with a rigid center· as shown.
a-~ .. -~' ~ 90\ of the stiffness contribution c~s from (a).
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of these corrq:>ooenti are needed, they can be determined after the system response has been found.
III. HYDROD~'ilC MASS
In order to properly account for the effect of the water enclosed in the pressure vessel on the d)11amic characteristic of nuclear steam supply system (NSSS), hydrodynamic (or virtual) mass has to be included in the. mass matrix. 1be hydrodynamic mass manifests itself as a dynamic coupling between the real masses and therefore should appear as off-diagonal as well as diagonal terms in the mass matrix. The hydrodynamic masses of the NSSS can be idealized as
those between three concentric cylinders. The inner cylinder representing the . fuel, guide tube, or standpipes: The second and third cylinders representing·
the shroud and pressure vessel. Based on this idealization, ·the method for
generating the mass matrix to include hydrodynamic mass tenns is derived in Appendix A. The method given in Appendix A. is used to generate the mass matrices for beth the !·ulls~one ~d Drezden plants •
IV. SYSJE.f FLEXIBILI1Y A.\'D LOAD MATRIX
ev
P..aving derived the indh-idual· element stiffness or flexibility matrices as described in II, the overall system stiffness or flexibility matrix can he
derived by either the matrix force method or·the matrix displacement method. Both methods are described in Reference s. ·111e matrix force method has heen chosen for this analysis due to the adaptibility of the computer program GE-OP-I ,(See Reference €) to this method. A brief description of the ioothod, follJ'""ing closely the exposition given in Reference S, is given below. The reader is referred to Reference 5 for the detailed logical proof of the
validity of the me~'iod. .
1. Derivation of the system flexibility matrix: If axial --deformations are
neglected for element a, the individual element flexibility matrix can be represented as:
Fa• f711
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12. Fuel - The fuel is modeled by thi:ee lumped masses. The three lumped masses are distributed such that the.three largest periods are approximately equal to the theoretical periods of a prismatic beam with uni.:. fonnly distributed mass. 11tl.s is accomplished by dividing the beam into 8 segments, with 1/8 of the mass ltD'Tlped at hoth supports. The rem:, :ning 3/4 of the mass equally distributed among the three masses. This :is
Sh""1 schematically in the figure below, r ~~:"' J. o--i::H
1 41-:-*"1 -~--..!...~ 8
The l/SM at both supports are lumped with the mass of the top guide and core plate onto• the shroud. The stiffness is taken to be that . of a beam with moment of inertia equal to that of the fuel channel alone.
13. Guide tube - .Again the lumped masses are distrfouted such that the fundaraental per~od is the same as the theoretical fundamental pe,riod. The effect of the axial load (due to the fuel weight) on the guide tube frequency is neglected. The jtistification being that the axial load is less than 1% of the critical buckling load. Hence, the frequer.cy cha..Tl.r.:e·
is extremely small. The guide tube is treated as a beam for stiffness calculations.
14~ CRD and CRD housing - The masses arc distributed such that the fundamental . natural frequency is approximately the same as t.~at determined from
experiments reported in Reference 4. The stiffness is taken to he that of the am housing alone..
Not included in the mathematical model are light components such as jet pump, in-core guide tube and housing, spargers and their supply headers. This is_ done in order to reduce the· CaT!IJlexity of the dynamic model. The just-. ification for this lies .in the .fact the response of these light canponents rlo
·not materially influence the overall system response. If the seismic responses
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SEIS.UC A'l.\LYSIS OF REACTOR I~1'ER'\ALS FOR nIE DRESDE.'I II P\..R~.,-
The individual element flexibility matrices is then fonned into a diagonally partitioned flexibility matrix, Fv,
~afb. l • • FsJ
.Fv =
For beam elements, this operation is done by the program GFJ~P-I automatically where the moment of inertia, effective area, length, Young's modulus, and
Poisson's ratio is given. For non-beam elements, the individual element flexibility matrix can be read in.
The next step is to remove redundant supports temporarily from the system to reduce it to a statically detenninate stn.icture. In most nuclear pla~ts, the redundancies can be chosen to be the stabilizers between the vessel and the shield \•;all, and hetwcen the shield wall and the building. Using th('
statically deterr..inate system, the ith colt.nm of a ~.latri.x Reis ohtained by
finding the moment a'1d shear at every mass point when the stn.icture is . subjected to the exteni.al fcrce F1 = 1 and all other external forces
Fj=O for j;1 The complete r.~trix Bo is fonneJ by varying i from 1 to ~, where N is the nur.iber of mass points. J\nother matrix B1 is formed in a ,
similar manner, except that the redundant force, Xi takes the place of the exteni.al force, F
1 Thus, the ith column of B1 is the moment and shear at
all mass points when the statically detenninate structure is subjected to X1=1, and all other redundant forces Xj:o for in. The complete n1 rotrix
is formed when i is varied between 1 and n, \,·here n is the degree of redundancy.
Given the three matrices, Bn, Fv, and Bl' the system flexibility matrix, f, is given by:
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where:
D oo .. 1h T R, · 1h D10 • BT ~ Jh n11 = B: I\, B1
BoT = transpose of B0 , etc. D -1 .. inverse of D ·
11 11
· PlA\11'
The fonnation of the matrix Fv and the necessary matrix multi plication and inversion are easily accomplished by using the program GE-OP-I.
·111e load matrix, the ith column of which gives the moment and shear at each I mass point when the system is subjected to F.,_=1 and~; =o when j~i, is given by: .
It should be noted that if the complete structure is statically determinate,
Ba ~·
Given the flexibility matrix, £,.the stiffness matrix, K, of the system can be found by a ~imple inversion. From the mass matrix (non-di~gonal in this
case) and the stiffness matrix, the tmda.'Tlped natural frequencies and mode shapes can easily be detennined from an eigenvalue routine. These capahilitics are again built-in in the GE\OP-I program. The modal matrix, 0, outputted by ·~OP-I is nonnalized such that: I
rtl 1·0 = I
and 0.T K0 • [' ~ n ' ] where Mis the mass;matrix
K is the stiffness matrix I is the identity matru
[' A n ']
:frequency squared.
is the diagonal matru of the eigenvalues, i.e., angular
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. - ·! TITl..E SEISMIC A'iALYSIS OF REACTOR INTERNALS FOR THE DRES~ II' PL~~'
VI. EQUA.TIO:-iS OF ~ICN
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The equations of motion in matrix fonn is as follows:
M . (X + Y) + c i + KX = 0
where: M • mass matrix, n x n (This· includes the hydrodynamic mass.)
X = column vector of displacement relative to ground (n x 1) C = damping matrix (n x n) K = stiffness matrix (n x n)
·y~. column vector of greund accelerations (n x 1)
···second derivative ~1th respect to time
Removing the ground acceleration vector to the right side of equation (1),
the equation reduces to the classical fonn: If I u
MX+ CX+ KX• • m:- (2)
In order to uncouple equation (2), we set:
x. ·01 (3)
Equation (2) then becanes:
M 0~' + c¢~ + K¢~ = • ~fl (4)
Pre·multiplying by the transpose of 0 and using the orthogonality conditions,·
we get: •. '/JT :.'1' + ~ aj + 0TK 0 q = ·~fl (5)
1•'/JTC04+0TK~ ... ·0TMY (6)
The above procedure for uncoupling the equation of mction by using the modal matrix of the undamped system must require that damping in the system be small. It Will be further assumed that the damping matrix C is such that 0TC0 is a diagonal matrix. The elements of this diagonal matrix &re the modal damping values!
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Wit~ the ahovc assunptions, erpi;:1.tion (6) n."\y !-1c ~'TittP.:i.:
.. + + - c: TT
~i s (t) (7)_
i a l,?. -- N
- da~~inz ratio for t~e ith ~of.e exr.ressP.rl as ~~rcent oF critic2l
ca~pin~
th wi = i natural angular frenuencie~ of thP systPn
th - nocal ~articipation factor for the i . r.ode
u g
T
QI i -sr~und accel~ration tine h1story
·th trans~ose of i rnde shape.
I = (:\ x 1) u
'r1e nodal da~ping ~iven 1-elo•-1.
l ter.?
value~ usually give.r. in the ~l~nt design Tahle II
a.
c.
e.
f.
Reinf orcec concrete structure
Wel~e.d structural assc:?nhlies
Bolted and riveted structural assP.n~li~s
Vital pipinz systen.
Punp, fan~, ~echanical equi~rnent
~cinforced or prcstressed concrete pric~ry con~~!n-
ment structures
a -~ T MI
s;iec.
u
s.o 1.0
1.0
.5
1.0
2.0
r-te accountable damping is, therefore, alPays less thar.. 5~ (B~ .OS). '!'he TespoMc error associated ~nth assU;~ing danping not chan~ing t~e resonant frequency or mode shapes is shol.'Tl in Figure 5 of Reference 7. This general curve sets the error in the response at less than 10 rercent (ln~ corre:~!'onds to S~~ carnpinz for the model~ng of the t~o powe:- plants undertaken herein).
For components not covered in the Table I (fuel and control rnrl drive), the 1~C'li.'!"in~ v~lue~_~re assigned (7~ for the fuel), and l? for the l.~D. '!'he darn;inr. factor for
the CRD ~as experirientally ci~terr.ined recently to hP. 3.S'o ("ef. 4). JJouevcr, ':'·'<;
t:as not reported earl? enour;rh for inclusion in the rresent ttr.alysi~. F;winz detcmined the dam!'ins values of. iru:!ividual cOMpone!'lt~, t"ie REv
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. SEISMIC A'iA.LYSIS OF REACTOR INTER'iALS FOR mE DRESIEN II ·Pl.A.VT
system modal damping value for each mode can be· easily detennined.
The approach taken is to examine the mode shapes. If in any particular mode only one component vibrated with the other components essentially stationary, then.the ~ing valu~ for that component is taken as the system modal.damping value. If more than one component vibrates, than a modal damping value is
·assigned based on the relative vibration amplitudes of these components. A
more refined energy balance technique of assigning modal damping is presently . being investigated and will be reported in RA-43. Presently, the procedure
described above, selecting modal\ damping frcm mode shape amplitude is considered within the accuracy of the model and with good engineering judgement, a quite acceptable procedure.
\11.
BY
RESPa-:SE CA.LCULATICNS
The system of one degree of freedom equations represented by eq. (7) suhjected to the initial conditions:
qi (0) .. 0
qi (0) .. 0
detennines the modal response q~ (t)Using eq. (7), the maximum seismic response (displacement, acceleration or load response) can be detennined by
one of the two methods described below:
1. Time History Method - In the time history method, the grmmd acceleration tiine· history is divided into small ti.Joo increments. For each of these
small time increme:nts, the modal response ~ (t), i = 1 ••. m, mfN, is detennined. The number of modes considered, m, is selected in such th~t
t.'1-ie response cf 1 i (t), 1 • m, ••• _N is negligible compared to the lower mode responses. . · · . .
HaVing fourid the modal responses, %. (t), ••• 1~a (t), the time history displacement and acceleration responses of indivi 1 mass points becomes:
x (t) • 0 rt) ·x ct) • 0 ft)
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where:
0 ...... 0 !
11. 1m l~t) 0 • 1 (t) = . . . . .
~1 ~ t (t) M
The tir..e history of the load response becomes L (t) = BK X (t}
where B is the previously defined load matrix K is the stiffness matrix.
The quantities of interest are usually the ma.xi.mum values of the displacerr:ent,
acceleration, and load responds. These quantities are easily. determined by finding the maximum values of X (t), X (t), and L (t). Of course, these maximum values need not occur at the same t.
2. Resnonse Snectrum Method
In the response spectrum method, the maximum modal response for each natilral frequency of interest is fmmd from response spectrum curves for the particular earthquake record under consideration. Response
spectrum curves for most strong motion earthquakes "'·hich have been recorded are given in Reference 8. The response spectrum curves in
Reference 8 have not been smoothed. It is a more conTilon practice to use smoothed curves such as those given in Reference 9. Response spectrum curves are essentially plots of the maxL'T!l..DTl responses of single-degrees-of-freedom systems described by eq. (7) with Si. ~ 1.0
against various natural periods or frequencies.
Haring found the maximum modal.responses, qi~ i. = 1, physical displacement for the ith mode is given by:
X1 • Si ~i 0 i
.. APPROVAL.I
m, the maxi.rrumt
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As pointed out in reference 10, the ~axinu~ nhy~ical r~~nonse. for e~ch ~nss
is tr.en usually ta!~en to he the i:;f!urrc root of the suMt=; C1f t~e squares of
each of the ~axL~UM resr-onses for each ~od~, iP.,
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=
L:!i . • . .
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The t:".&Xi.mum load response is again taY.en to he the square root of the sums
of the squares of each of the naximuM responses for each node, ie,
(Li)max • [~ ii~IZ i = l,·· · n
REV NO. 0
l--9-'------------------------~l--A_D_D_•_.o_v_._'-_• ______ _,,, ______________________ -t 2571~718 .H . · y I · 1 'i v. -
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e GENERAL~ ELECTRIC A ATOMIC POWER EQUIPMENT OEPARTMEN.,.,
ENGINEERING FORM 257?'.".71~ TITl.lt
9Y
~oth the time histoey methorl of analysi.s a"~ t~r. res!'onse spP.ctr1tT"I t~et~o~ of
' analysis can he perforr.ied hy GDJ~P-I.
VIII }(ASS .Mrct ELASTIC PROP'.~TJES C'.lF TH"" ~SS
The mass and elastiC properties of the ~!SS~ for the ~resden II
pl.,ant· are given in Ap~endices Ban~ r., respectively.
L'C
1. Dre5dcn II Plant
The shear and tTtomer.t dinp.ra!'.'s for the c'lesir,n hasic; carthciual:e · (.lne inun . F.l Centro, H-S compoii.ent) are sho~~ in Figures 3 to lf'l. :r~e s hP.ar an~.
monent values sho'm for the sc~arators, stanrl~i~es, fuel a~~ 8Uide tuhes
are total values. They should ce civideC: hy the apt'lror-riatr! Tlnnber to
o~tain individual elenent values. ~ere are 21° !':enarators and stR.r?d;'i~es,
724 fuel bundles, 177 ~ui~e tuhes and control rod drives. In ~11 t~~ fi~ure~, vessel "o" is used as reference for t11e ell'!vatinns.
x OISCUSSI0~ OF TRE R~SULTS
Of all com~onents in the nuclear boiler, the design of the follouing item~
may be significantly influenced by seisnic loads: sl~irt, stabilizer, top guide,
fuel, shroud support, c~n housing. Therefore, t':e load:'i on these conponP.nts
are tabulated in Tahle I. '!'hese loads sl'?oulcl he u.;ec:1. to deternir.e w'"?etlie::'." nr
AEV ... o. n
I APPl>OYAl.S L t--------------------------~l--------------------------------------U57Jt~ie
IUUEO ~ /;:l-:J.(/ -/, y CONT CN S"1EET _!.L sw "IO. l,L
i
., . .. .. e GENERAL~· ELECTRIC • ATOMIC POWER EOUIPMENT DEPARTMEN
ENGINEER!NG FORM 257!~\711'
not the col":io':lents arc adcciu<".tely c!esizT'\ed.
'!he r2tio of the t1axir:iur:i credible e<irt~quc:'!-<c load to t~e design ~arth'1uCI~:~,
load is coMronly tcil:en to !:-e C'!ual to t!"le ratio of tr..e t:taxir.:ur. ground
acceleration of the ~a::dnun creci~le eart1'1'!11nl~t? to that of the C.c:;i:n
eart!"i~ua!:e. T:1i~ is correct only E t~•P. structure rel"'!ained elastic anr1
hP.nce, line::tr. "!-'.<:'Pever, due to tlie difficulties of nonlinear analysis of
highly complex structures, no attempt has been made to determine the loads
when the structure goes into the inelastic ran<>e. Therefore, tl:e loads
for t~e naxir.um crcd !.blc ef'lrt:-.i:uab~ er~ ci~te:-ll'li!.P>'!it a.s if the struc::urP.s
r~na:t!"tec! elastic.
r!!portec! •. Also, only t"ose results corrP-sronc;iT'i to th~ PP.rthqua.l~es
spe.cif iec for the Dre~den II plcnt (~l Centro)
are giv:?n.· 'l'>rP. r~c:;nlts for ot~~l' e.art~i::ua~e~ <'.~r. t!":_e_ re;sults i:sir:g
the resronse s~ectrun n~thoc! 'rill b~ rerort~d i~ n futu~e PAR.
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• ENGINEERING FORM .TOMIC POWER ~QUIPMENT DEPARTMENT- l
TITI..&: ·
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.... 1a1uco
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1. C • P • Steels, n,:onsyr.:I'1etric !)e forna t ion of DOl'\P.-~1-.A nerl fi'he lls 0 f ~evolution", Journal of f.pnlied ''echnnics, June, 1~62.
., """•·· ·!arthcual:e ~nalysis of t~e ~eactor Pressur~ Vessel, ntesden II and TIT,
~:uclear Plar.t,. '">y Jo1-in ·"· Rlu;.ie ancl Associates, ;.~s~n~ers, FP.h. 24, l('\F~.
4. S. H. S!!!!.th, "Vibration Testing of a Pro.~~ctior.. r'ontr:ol r.or. nrive 1'ousin!'. Installed in the 30 11 Ve5sel in Buildir.c; G", TR-A3"l5, 257P.flf><')Q, ~fCS:U25. APEI' internal docucP.nt.
5. E •. c. Pestel, F. A. LeckiP., '"·tatrix :~ethods in Elasto-:·!echanics, 11
~k-Graw Hill Dock Co., Inc., ~!ew ~ort:, '1 %3. C~pters. 9 anc 10.
6. ·\1. ~. ~·!etzel, "G8:0P-I, A General ~tatrix Clperation Proeran", SAR-3f,, !!oveMher, 1%7.
7. ·r-r. Gurtin, "Vihration Analysis of Discrete ~ass Syster:is", P.eport ~;o. 59GL 75, General flectric COT'l?any, ~chenectady, N. Y., '1arch, lQSQ.
8.
n , .
G. l!. Pousner, et al, "Spect!"'JT'l Ari.::ilysis of Strong-~!otion i=:arthciual:es", Bulletin of the ~eisrnological ~ociety of ,1\nerica., Volume 43, ~~ut:l~er 2, April, 1953. .
"i:'uclear nC?actor and :i:'.arthquakes", TID7'1~4, .August, 1~63, U~AEC, Division of Technical Inf ornation.
10. R. W. Clough, "Earthquake Analysis i-.y RP.S?Onse Srectrum Superposition," Bulletin of the Seisl'lological Society of ,\r.:erica.,, VolumP. 52, ~1uTTlher 3, July, 1962.
A£V NO. " APPROVAi.i
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.ATOMIC POWER EQUIPMENT DEPARTMENT,.. 1' '' 2.57J'A71R . ,, ENGINEERING FORM
TITLE
APPF:~IDIX' A
~ * The basic fort:tulae used i~i this section t·~erc first derived hy John rorr ** . and .Ed Kiss • The formullle for hydrodyn:ir.ic Mnss· cP.rtved by thP.m •u~re
in terms of two concentric' cylinders. Recause the nuclear 1--oiler, for the ' '
purposes of hydrodynaMic ~~R~ analysis, cnn he thought of as conRisting
of T11any concentric cylinders, R sli3ht rnorlificRtion is ni:cessary. The
raodel chosen for the !'resent anRlysis is sho•'Tl in the fip.;ure heloP. ;1
The method for deriving thE! complete r.iass TTlatrix (hot!i . the real mass and
the hydrodyna:nic mass) i.$ E~ssentially as follo~·s:
I
1. Ohtain t'hP. kinetic ene,'rgy function in tems of tre lateral velocities
of the cylinders. Thi~ kinetic enerey function s~c~ld inclurle the
kinetic energy of the :real masses as t.Tell as the kinetic energy of the I
fluid masses. The ldni?tic enerey of the fl11:1.rl MRss is dP.termined hy ., assuoing incompressiblE? anr\ non-vi!'lcous flow.
2. Obtain the t:otential et'1:,ercy function in tern~ cf the lateral coorc1inate?3
and the real spring constants.
3. Use the Euler-La3range :equations to obtain the equations of motion. !i
4. Arrange coefficients of:,\the terms involving the second ti~e derivations
* ·John Corr, "Some New Re~1ults on Virtual ~~ass F.ffects for ~eactor Internal Vibration Analys.is", January ~. 1o~R, ~temo to T. Trocki, CoT:!ponP.nt Engineering., :'
** Ed Kiss, "Vibration in F:luids", ~(arch 20, 196i.
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I . ; \ . ' . e. GENERAL" ELECTRIC A ATOMIC POWER EQUIPMENT OEPARTME1'f
ENGINEERING FORM
TITLE
ISY
SEIS~!IC AN,~.!.Y'SIS OF Pr.ACTOR I INTrn.Nt.T.S .FOR Tl-ft DP..ES;>'GU II . PJ-~f\Si-
of the lateral coordinates into thP. na~s T".atrix er) such tr.at
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2571-IA718
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. +. 11.,·' :11:. -: .. 14~)
+11:) " •. , "/ '• ··. ~ ~ 4 -
-..~ .. -...
....
--- -····- ·-··--·-·. ·--····- .. -· ... '. ····· ~ ·,. ... "':.--_-:-;• - ·.· t _. (~) -fer"'~. 4,.e t}e-ro: -for_;, ~()) ,·.t.. _11·~~r(M.rA'1,~ ~-~A·f:(") c?;f{.s~l~J - ·- - ~ Jr•unJ ··- . - -- --~-, .. . .- .s_ - ~€7 ~a'. l ~._ . . ·'._!
l N ;.-: l'A ~"·~-__,( . \~..,.,,.. ~:;!.... ... ----- ·;_·.;.::-Afft·a- ----
.•': ... ~-~-- ___ .:..._:. ___ -- .. . ---- ·-- __ .... __ ·. - ~:-~ ...... .... :. ...... -
'· .... ~~.
,,-• .._.__,,...]""",A~_"";...::!r"'!..---. -~-~..,.._ .. ..,"!..~~ '•cJ. )i }. ;;::~~:C"'~·-~~. ~ .... ~-:·:-!J:.-· .... :-.. -~·';_-r. ·;.· ....... ·:.-_;:;~·: .. :··"·J·~·-.1·-.:- ... "i..·"~:t--;.~-:-·:.~·'"'<"·-.O:• -.. ~.-::: ... :,.-...,: ·- .- :• •.. ,.. .
I· • ._._/.
_____ _--._
... ·-. . ~·'..- ... ; ·~""'··~·. ~.·,,1 ... ·-1-...:- ..... ·:··· ... l"
_. (- 1 &Efi~R:.L ruefr.~ m ... ,_ · .__. - HtJCl~'llf Enor;-r Ohrl:tlOfl · -
INGIHHtfH~ CALC-"LATION sHm ·e DAT.._ ______ __. ______ ~-~
·SHOP OR.OU NO ____________ --------------------
__ · j_·-~-~- ·--~ ~ ·~1
I ~ .. - ~-o;:- --~ ....
. . . -· - -- ·'--:---~---~-----· ··--···· ..
. ---- --- -i---- -. -I-"---·~- -·- -
·~-- ..
. I -r -- -- --- -- ... ·- ··---~ .
~ ......... ~ -·~
. l:: ! .- ·- ·-·-·------·- ·-·-·· . . . ~
. - ----·-- _, ·---· -----· ··-· ·- -~--. ~-
~ ~ ~ ~ ..... ,........., ~ '+-~ ~
I ~ ~ .. ~ --~ - ~. . . ~ 1- . . .. '- . 'llfo. . . ' .
: ··---:-- --_- --~-- -~-· -~---··4loo~--- ---·
~--.. ~ _ _; - --~ .
i- .. '+. -~ ~1- ~
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"i-. ~ ~
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. . - - -- - - . --·- - .
_____ ...; _____ __.. _________ .... -- ....
. t
.-
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- ' . ; : ""
. "·.·. ··. "· _.·: - . . -. ..: . I ·.
_2 5 7 B t~ ''t 1 S. . _. JI'
C1:tttT !!'<I r~~~ • ti_/ l ~ lfC. I !.., - I
------------------------------------------~~~ ...... ...________ ~-~
\ ..
- -~
a GENERAL 0 ELECTRIC - ATOMIC POWER EQUIPMENT OEPARTM-
ENGINEERING FORM 2571'.A.718 TITL.£
av
ISSUEO
SEIS~!Ir. A~~ALY'SIS OF '?..F'..AC'l'OR l lNTF.r-~~.\LS 'f'()R THE Dr.ESP~: II p LPtl-ll
;..ppr.:;-.:nrx n
~~ass and Stiffness PronertiP.!; of the nresden II m;ss
The mass numhers and element i;tiffness or flexihiH_ty nunbers refer to tr.e
nunhers sho,.m in Figure 1.
I. "ass Properties
a. ~eal ~fi:tss
.t.PPRO'IAl..I
. 1 Ma~~ (10· slues)
1. 1i:i511
5.031115
3.54037
.83850
2.45341
l.70fl07
l.5:!173
REV NO • n
2571!..\ 71~ . l ~ . l ~ c::uT ON s..;cc~ ~ IH "40, ~
NCO - Ut ----------'-----------...-. ...... .,,,.,.--..,,..,.~---~-~-·-.--,..,.. ----..,-·-. --..,.-~~ ... ,...,_·.-.~-.·-....,,.,...-..,..,,_.
..
f ' '._)
. ' j. ..,;.'
ENGINEERING FORM
TITL.E
• GENERAL$ ELECTRIC al ATOMIC POWER EQUIPMENT OEPARTMENT9~S7l1J7lR
... _.,,_, _.._._..._,_, _.__, ....... -1 I
.Terns , .. 'i.th only one r.ass nun.'rer indicate diagonnl eler.P.nts; terms llith
t1-ro nass nuri'":ers iflcic:"it~ off-~iagonal terns.
1
2
3
4
5
6
APPROVAL.I
n.2J
10. 33
:?1. il3
n.'.!2 REV NC.
~.:.-.
n !. I
1--------------~---------------------1 i57J') 711' ISSUEC ..., ,. , / ti
I l n !1Q I
/"j,.~" /,f;,_,.'t-,o<f C:ONT ON 1 ... EET _ 1 _. _SH NC,--·
r:.·•·.-
•.•• : .;;. --ll e GENERAL~ ELECTRIC A ATOMIC POWER EQUIPMENT OEPARTMEN,., 257HA71R l E~GINEERING FORM
j
. TITl..E
I SEIS~IC A~tALYSIS OF REACTOR I !~.:"!'E't~ALS FO~ TITF. nP.r::snrN II PLJ:\l\)T
7 21. 73
8 25.1'3
9 ·n.r,4
10 in.r:4
11 '!... f, 7
12 L71
13 1.73
14 15. f,I')
15 J.7.71
16 17.9~
17 4 .115
l<'l 4.145
J.'l /,. t..5
20 .945
21 ' • 'Jl·~
22 1. 73
23 1. 73
24 1.SO
4-11 · -.2'21
4-12 -1.42
5-13 -14.09
6-14 -lt..oq
7-15 -lt..O{J
·~ 10-21 -'J.. 74
AEV n . NO .
!IY &PPA0,,&1..S. '
2.'.i71'l':.HR 111 .. s::i ~ /~-,.."~' c;n 1,0
C:ONT ON S .. EET ...,:___I .. NO. -
ENGINEERING FORM
e · GENERALO ELECTRIC 9 ATOMIC 'powER EQUIPMENT DEPARTMENT .
257P.A71R TITl..IC - sns·nc ~~ALYS!S OF P.F.Acton. I t:rrr:r.:v.L~ Fn~ '!'l'E nr..t.Sf'.1!7~ !I PLl\-\.n-
13-17 -.514
14-18 -.514
15-19 -.514
16-20 -.n1
16-21 ~.81
The mass natrix is symmetric. Therefore, ,_there are tP-rns in reverse orner
as those listed above in off-diagonal po~itions.
II. Elenent Stiffness Pro~erties
The elenent ntl1'lher corresponds to those shO'·'TI in Fi;ure 1. ':'h.e eler.er.t
flexibility matrix for the ~!esi;el '!'op l'~ad (~le~ent !fo. 1) is
fu .. (3.12 (l0-9) (n.p-ft)-1
f21 f 12 (2.704) (l0-8) . -1 - -- (Y..ip)
. (10-7) f22
.. (5.239) (ft/Kip)
I>efinition.s of £11 , £21, f 12 , t 22 is given on,pnge 4 The element
flexibility ?!Ultrix of the bottoa vessel head (element No. 12) is
.. · t ...
0 8Y APP,.OVAl..I
-1 en co .. T 0 .. IHl!:ltT ~ ... MO, -.J-
---·
~--
e GENERAL 0 ELECTRIC -ATOMIC POWER EQUIPMENT DEPARTMENT .
ENGINEERING FORM 257HA71A
TIT .. &:
f 11 (1.(\1) (10-Q) -1 .. (t<ip-f t)
f21 .. f 12 • (2.30) (10-~) (Jap)-1
f :?2 .. (2.55) (10:7) . I (ft/J~ip)
F.le!:!ent 19 re!'resents the shroud suriport which is riodeled as a torsion
spring Hith a flexibility constant of (2.~4) (lo-12) rad/in-lb •.
. -· ........ --...... ~
All other elenents are treade~ as heat:is with t~c ~fff"!ctive r.;oMent of inertia
shear· area, leneth, Yo~ne' s !-!odulus, ·and Poisson's ratio given in thP. tahle
o~ t~e followine page.
. .......
flt&:Y NO . 0 • ., I .... PROYA'-I
i------------..._.------·-----------r257HA71g ' 1U•&::: 63fpl /o:J. ,,;_y~ J" I CONT ON 9 .. &:&:T C\., 1>4 NO • ...s.:....
Nl:O - 1•t
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tJ ;i " ·: ·' ~~ ·.r
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I :.;::I
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Element ••• ~ 2. li
3 t 4
~ 5 6 '°\ 7
,. 8 .. 9· 11 lt 10 0 < 11 ,. r •
13
lit
15 16•
17
in
20 21
N 22 n U1 z lt I.I ":::! Oro 23 z < ... > 24 0 ~ :i: ~ 0 25 .. co x 26 "' !'I 27 ...
I 28 V> 29 '.,.)
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rLt:XIEULITY SEAH l:ONST ~NTS ( INPUT> ,..
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~ 0.!_28JOIJUOE: .. or: o.431~unor: 01 U,J::no"OOE 0 .l IJ. ,i64:t.!> _t)F. ;!C .. J!. '42·~onoQE_ o~. r N .... ):I \JI ·0,26lOllOOE Q.) 0,431 ·1JOOf: 01 ll • J 9 flu '0 Qt.:
0 '· 0, J.6416 °'iJF. :•7 P, 42 101.101)E 011 Fl ~
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