ML20102A330

Responds to Structural & Geotechnical Engineering Branch Draft SER Open Item Re soil-structure interaction.Kausel- Whitman,three-stem Method Accounts for Effects of Soil Layer & Geometric Effects of Structure on Vibratory Motion

ML20102A330
Person / Time
Site:	Beaver Valley
Issue date:	02/01/1985
From:	Woolever E DUQUESNE LIGHT CO.
To:	Knighton G Office of Nuclear Reactor Regulation
References
2NRC-5-015, 2NRC-5-15, NUDOCS 8502080302
Download: ML20102A330 (32)

Text

{{#Wiki_filter:* o 'Af 4 ) 78 5 41 Nuclear Construction Division Telecopy Robinson Plaza, Building 2 Suite 210 Pittsburgh, PA 15205 February 1, 1985 United States Nuclear Regulatory Commission Washington, DC 20555 ATTENTION: Mr. George W. Knighton, Chief Licensing Branch 3 Of fice of Nuclear Reactor Regulation

SUBJECT:

Beaver Valley Power Station - Unit No. 2 Docket No. 50-412 Response to NRC Structural and Geotechnical Engineering Branch's Draf t SER Open Item on Scil-Structure Interaction Gentlemen: This letter provides our response to the NRC Structural and Geotech-nical Engineering Branch's (SGEB) Draft SER open item on Soil-Structure Interaction (Item SRP 3.7.3 [ Audit Action Items 4, 7, and 23]). This submit-tal supplements our response to NRC Structural Design Audit Action Item 7, which was provided in Reference (a), and addresses the discussion of that response at our November 30, 1984, meeting with the SGEB (Reference [b]). In Action Item 7, the SCEB reviewers requested that additional soil-structure interaction analyses be performed for the containment and int ake structures in order to demonstrate that BVPS-2 meets the intent of SRP 3.7.2.11.4. No further analyses were perfo rmed for the intake structure because, as stated in References (a) and (b), the adequacy of this structure was. addressed under the BVPS-1 docket. To demonstrate that BVPS-2 meets the intent of SRP 3.7.2.11.4, DLC's response to Action-Item 7 provided an alternate soil-structure interaction analysis for the containment structure. As discussed in FSAR Section 3.7.2, the original' soil-structure interaction analysis for the containment used the finite element method (PLAXLY computer code), in which the soil was modeled as finite elemen*.s ~ and the structure as a lumped mass elastic beam. The alternate soil-structure interaction analysis, provided in the Action Item 7' response, was based on the three-step solution developed ~ by Kausel and Whitman. This analysis used the same. lumped mass elastic be am model to represent the containment structure;.the soil was modeled as. a half-space using the frequency-dependent compliance function method of anlaysis. The design earthquake input motion was defined to occur at the ground surface in .the free field. Kinematic interaction was used to transform the purely .translational motion at the ground surface into combined translational and rotational motion at the foundation level. At our meeting with the SGEB on November 30, 1984, our response to -Action Item 7 was discussed. The SCEB reviewers ; requested that a further soil-structure interaction analysis be performed by using either a simplified 8502080302 800291 {DRADOCK05(V g( l j

p c).' ;!Unitsd. States Nuclear._Ragulatory Commission - Mr.,Gaorgs W. Knighton, Chief. PageL2 s Wh itman-type soil spring approach or a freq uency-de pendent impedance approach.~ = For'. either approach, the SGEB reviewers specified that the free- . field ground surf ace earthquake input motion was to be applied at the founda-L tion -level of L the - structure. DLC agreed to perform an analysis for the containment. structure ithat : uses the frequency-dependent impedance approach _ with-the free-field ground surface motion applied at the foundation level. lUpon further - consideration of > the SGEB reviewers' request, we con-cludef that. such an analysis would yield results which are neither physically representative. of the actual site conditions nor_ technically appropriate. The,SGEB reviewers' suggested' analysis neglects two physical phenomena which are_well-recognized by professionals in the field of seismic analysis (Refer-ence> [c } ) and are very impo rt ant to specifying the ap propriate vibratory _ ground' notion to be applied at the foundation' level' of the structure, consis- -tent Lwith the' requirements of 10CFR100, Appendix A. These two phenomena ~ .are: (1)'the soil layer _ between the ground surface and foundation -level 3 modifies ~the foundation level vibratory motion compared with the

ground surface'_ vibratory motion; and

-(2) -the gsometric ef fects of the structure also modify the vibratory motion l at the foundation level relative to - the ground surface + vibratory motion. s The' Kausel-Whitman three-step. analytical ' method, usedt in our Action -Item 17 L response, has ~ a. sound engineering basis and accounts for both - the : i ef fec'ts. of the; soil layer and 1the geometric ef fects of the structure on the vibratory motion at ' the foundation level compared 1 with the ground. surf ace , vibratory aotion. We believe that '. the results of the analysis presented in ' L .our Act' ion. Item. 7 response -are physically' consistent with these 'well-recog-nized ' principles _ of soil-structure interaction and are therefore) technically ,appropr a e. Attachment A provides; a : detailed description of the:Ka'usel ' it

Whitman three-step analytical method.

~ '.' Attachment Bipresents a c'omparison of the one-percent: dimping curve's e

of f both i theEBVPS-2 design' response spectra and' those L resulting - froo f the i w;.Kausel-Whitman three-step method for several~ typical locations.- 'Both spectra-

~

compare < J favorably with 7only'; minor.exceedances~ which' are insignificant?

%considering the iconservative ;value -(one percent) used for equipment 1 damping.- 4 Thisidemonstrates that BVPS-2' meets the: intent of SRP 3;7.2.II.4.. J [In DLC'sf application ~ for th'e BVPS-2. Construction Permit, thei soil-- C J

structure interaction' Ewasi analyzed ' as directed by c yourJ staff. ' ' (See PSAR

~ ~ , Question 2 3.19, _ Amendment }7,7 July 9, '1973.) : In the ' course f offthe present. / Operating. License' Application review,1 the ; docket has, been : augmented with s aE s i ~ indicates th at - BVPS-2'- Jg ' - presponsive,gtechnically. appropriate analysis E which 1 = ne'ets Ethe intentiof ~SRP-3.7.2.11.4 of NUREG-0800, the; most: recent formal NRC - guidan' e :' concerning ' thisfissue.: - Therefore, we - beiievei that the BVPS-2 PSAR,. 1;e 4 FSAR, j the _ supplemental information provided in - the response - to' NRC' Structural c (Design'. Audit Action. Item 7, and this letter provide a complete record for, the . satisf actory closure of.. this. issue. DLC isiwilling to again. meet. with the a t r L g ^^ p

n: - Unitsd States Nuclear Ragulctory _ Conusiosion Mr.'Gacrga W..Knighton, Chief =Page:3 J SGEB ' staf f. ~ to : clarify any. points in this or previous submittals. If such a ~ meeting.: is desired,. DLC requests - that' the Assistant Director for Licensing , participates to. ensure involvement ~of. appropriate NRC management personnel. However,- DLC.. believes that-further requests for analyses utilizing alt e rn a-tive methodologies will of fer no meaningful additions to.the existing record. Therefore,LDLC is.- requesting.. that further requests fo r information on this issue : be addres' sed : by the. NRC staff as a backfit in accordance with the ~ provisions 'of s10CFR50.109, GNLR 84-08, and NRC Manual Chapter 0514. DUQUESNE LIGHT COMPANY By . fr-. E. 5. Woolever d' Vice President sJD0/wjsi _ Attachmen't s '- cc:- Mr.lB. K. Singh,. Project' Manager (w/a) Mr. G. Walton, NRC. Resident Inspector (w/a) Mr.1G. E. Lear, NRC.SGEB Chief (w'/a) ~ l

References:

(a)-Letter 2NRC-4-080, dated June 15, 1984 t

(b) Letter '2NRC-4-207, = dated December 17; 1984 . (c).NUREG/CR-1780, : " Soil-Structure Interaction: The. Status of. _ Cur rent -- Analysis - Methods and ' Research" prepared._for U.S. = Nuclear. RegulatoryI Commission - by ~ Lawrence Livermore Labora- ^ Jtory,-October 1980 3 m COMMONWEALTH OF PENNSYLVANIA. ) ~ .-). 'SS: f l COUNTY' 0F ALLEGHENY, )J y /975~ , before me,.'s JOn this ,424 2 day of~ j r . Notary l Publiez in and :- forf asid a Commonweafth and ? County, personally 1 appeared c ,E.'J. Woolever, to - beio, duly.. sworn, deposed ' and said - that.-(1). he is Vice } President 4ofi Duquesne. Light, (2) lhe i isiduly ' authorized ? to executeiand f file 4

the jforegoing SubmittalJ on behalf of a ssid

Company, fand _-(3).the statements s

set ' forth'in the Submittal are true and scorrect to

-the best;of.1his knowledge..

s Mij g f _.6 .;/, E . I u v' ; . - Notary Public' ,.^ - ANITA ELAINE REITER; NOTARY;FOBLIC - ' ROBINSON TOWNSHIP ALLEGHENY COUNTY : 1 ^, ~; - MY COMMISSION _ EXPIRES 'OCTO'OER 20,1986.- 3.. ,f' a 9 (._- N

C

~=- ^ -,

ATTACHMEM A I. DESCRIPTION OF THE THREE-STEP ANALYSIS The solution of soil-structure interaction problems can be reduced to the following three steps: 1. Calculations of frequency-dependent soil stiffnesses 2.- Modification of the specified surface motion to account for structure ~ embedment-3. Interaction Analysis -These steps are illustrated in Figure I-1 (see Reference 2). I.1.11 Frequency-Dependent Soil Stiffness The. frequency-dependent stiffnesses of.a rectangular footing founded at the ) p surface of a layered medium are computed with the program REFUND, discussed in Section II. The program solves the problem of forced vibration of a rigid plate on a viscoelastic, layered stratum using numerical solutions to .the generalized problems. of Cerruti and Boussinesq (see Figure I-2). The effects of unit harmonic horizontal and vertical point loads are combined by superposition to produce the behavior of a rectangular plate. LSolutions to the problem of a point load on the surface of continuum require ' an assumption about the behavior of tpydium directly under the load; for example, see ' Timoshenko and Goedier. In REFUND, a ' solution ' directly under the. load is achieved by employing a colusuun of elements for which a' linear displacement function is assumed. Away from this central column, in the "far-field," the solution for. a viscoeleastic layered medium is obtained

(see Figure I-3).

If the central column under - the point load is removed and replaced by: equi-valent distributed forces. corresponding to the internal stresses, the dyna-mic equilibrium of the far field is preserved. Since no other prescribed forces act on the far field, the displacements at the boundary (and any other point:in the far field) are uniquely defined in terms of these bound-ary forces. The_ problem is thus to find the relations between these bound-ary forcesand the corresponding boundary displacements. LB4-12241-7772 1

4 4 In REFUND's cylindrical coordinates, loads and displacements are expanded in Fourier Series around the axis: oo oo n n Ur E u cos ne Pr - E p cos n e o o = n y u cos nO Py : I p" cos n O U n n U E-u sin ne pe = E - pe sin n e e e o o For the problem at hand, only the first two components of the series are needed. The (unit) vertical force case corresponds to the Fourier component of order zero (n = 0), and the horizontal unit force case corresponds to the Fourier component of order one (n = 1). The cartesian displacement (flexi-bility) matrix (F) at a point then follows from the cylindrical displacement components-. (uf +u )+f(u'r ug)cos 20 f(u -ug) sin. 20 l u cosO e r u cos e uy u'y sin e y O 2(Ur+ug)-[(u -u g)cos 29 1 l (u -u sin 29 u sin O r p w s and the displacement vector for arbitrary loading is U = FP where 3 e m u px x P-i p f U=< u y y 9 i> uc B4-12241-7772 2 ~

U is the displacement vector at a point (x,0,z), while P is the load vector at (0,0,0). The coordinate system is illustrated in Figure I-4. - For points along the free surface, the reciprocity theorem requires that US-Uh. Hence, F is chessboard syuumetric/antisyuumetric. REFUND then com-putes the cylindrical displacement, components for the two loading cases, and determines the cartesian flexibility matrix F under the load (axis) at the boundary and at selected points beyond the boundary. j To compute the subgrade stiffness functions for a rigid, rectangular plate, the program discretizes the foundation into a number of points and computes l the global flexibility matrix F from the nodal subnatrices F using the technique just described. Imposing then the conditions of unit rigid body displacements and rotations, it is possible to solve for the global load vector from the equation FP = U where U is the global displacement vector satisfying the : rigid body condi-tion. It follows that U is of the form U = TV (6 x 1) vetor containing the rigid body translations or rota-where V is a - tions of the plate. and T is the linear transformation matrix assembled with the coordinates of the nodal points. The stiffness functions are then obtained fron l t Z=TP L' l ( which corresponds formally to f-T z=TP1 Tv i B4-12241-7772 3 . ~..... ..~.

A comparison of' REFUND results with another method is shown in Section II.1. I.1.2 Embedment Correction '= The effects of foundation embedment on the impedancesgre included by employing correction factors described by Kausel et. al. These corree-tion factors are determined from parametric studies of embedded foundations and are of the form C =(1+C h )(1+C )(1+C3 ) g 1 in which .C R R., = foundation radius E- = embedment depth N = depth to bedrock Cg = constants, different values for each degree of freedom. The frequency-dependent stiffnesses, K, determined by REFUND, are modified to become s .K1.=KxCR I.1.3 Kinematic Interaction In the second step of the analysis shown in Figure I-1, " kinematic inter-action" modifies the purely translational input specified at the surface of the stratum to both a translational and rotational motion at the base of the rigid, massless foundation. The existence 'of.the additional input can be - - inferred from Figure I-5. In a stratum undergoing translational motion only,' the boundary conditions at the." excavation" require the foundation to-rotate. Ignoring the rotational component would result in an unconservative solution. Note that the modified motion at the. base of the foundation is not equivalent to a~ deconvolution. The solution to -the -kinematic _ interaction portion of the analysis. is based on Kausel's adaptation of Iguchi's (1982) ' generalized weighted averaging technique. In essence, the method requires solving the 6 x_1 equation U H^[A T U*d A + K^ [A T T T 3* dA f '84-12241-7772 4 G

4 4 where: c (Z-Zo)-(Y-Yo)k T= 1 0 0 0 ' O 1 0 -(Z - Zo) 0 (X - Xo) O O 1 .(Y - Yo) -(X - Xo) 0 (Xo,Yo,Zo) = coordinates of the centroid of the foundations contact area (X,Y,Z) = coordinates of foundation / soil interface A = surface area of foundation U* = U*(X,Y,Z) = the free field displacement vector 'along the foundation / soil' interface (before excavation) S = S*(X,Y,Z) - the free field tractions vector at -the foundation / soil interface i f' T . T TdA u = *A K. = Foundation impedance matrix U = matrix of transfer functions for motion of the f massless foundation 1 To-obtain the actual motion to be used as support motion.in the three-step _ method, the transfer functions must be convolved with the Fourier transforms of the accelerations of ' the. surface earthquakes, resulting in the.following solution: E (t)-= IFT (F(O) u} / ~ (F(O)4) .5 (t)'s IFT F(O) = Fourier Transform 'of surface motion / IFT = Inverse Fourier transform [ _ cos(PE) 2E{ sin (PE) },_ 77 PR (l. ) sin (PE) R PE 4 t 2E (GG +g it 0.6i PR) g i ^R 84-12241-7772 5-

e 4o (f c:s (PE))+ (% sin (PE))-( E )f(Sa'(@ ;I+3 y(l.v) 'r ' luos(PE) ph sm(PE)' 4 s (Pf) 8 2 g y (PR)y i. R PE R-PR l+ { 4(f)4 '[ R = foundation radius l+ E h (3-IS P = s E = foundation embedment depth V = Poisson's ratio G = shear modulus of soil adjacent to foundation y G = shear modulus of soil below foundation 2 h = height of the foundation's area center of gravity above the base of the foundation c, = shear wave velocity I.1.4 Interaction Analysis i The third step of the procedure illustrated schematically in Figure I-1 is the analysis o_f the structural model supported on the frequency-dependent springa from Step 1 for the modified seismic input from Step 2. The solu-tion is achieved using the program FRIDAY. I- -FRIDAY evaluates the dynamic response of an assembly of cantilever struc-tures supported by a common met and subjected to a seismic excitation. - The l support of the est can be rigid, or it can consist of frequency-dependent / j independent _ springs and dashpets faubgrade stiffnesses). The equations of motioc are solved in the frequency domain, determining response time histor-c ies by convolution of the transfer functions and the Fourter transform of the input escitation. The dynamic equilibrium equations can be written in matrix notation as: MO+C + KY= 0 (1) where M, C, and K are the mass, damping, and stiffness matrices, respec-tively,, and : U,' Y are the absolute and relative (to the moving support) dis- . placement vectors. These two vectors are related by: U = Y + EU (2) B4-1224'.-7772 6

where U is the base excitation vector (three translations and three rota-tions), and E is the matrix: e m I T1 .O I I T2> <O I I Tn O I .s J (3) where I is the (3 x 3) identity matrix, O is the null matrix, and 9 O Zj Zo -(Yj - Y ) o T; = i - (Z -Z ) 0 o X;- Xo Yj-Yo MXj-X ) o o u J with x, y, z being the coordinates of the corresponding mass point; x,, t y,, z, are the coordinates of the common support. In the frequency response method, the transfer functions are determined by setting, one at a time, tge ground motion components equal to a unit har-monic of the form u =e It follows then that U, Y are also harmonic: 84-12241-7772 7

O= H eiwt j Y = (Hj - Ej) eiwt C-{i iwt I 'H iwt w je y = g(H;-Ej)e iWt iwt Hje y-(H;-Ej)e U.- 3 (4) . vgre -H inpuk groun(d. motion, and Ethe vector contain gs the transfer functions for the =H w) is g j is the j column of E in Equation.3. Sub-g .stitution of. Equation 4 into Equation 1 yields: s '(-w M + iwC.+ K)H = (iwC + K)E) (5) If the damping' matrix is of the form C = h D, which corresponds to a linear hysteretic damping situation, the equation reduces to: 2 -(-w M + K + iD)H) = (K.+ iD)E (6) In view of the correspondence principle, it is possible to generalize the-equation of motion allowing at'this stage elements in the stiffness matrix K with an' arbitrary variation with frequency. This enables the use of frequency-dependent stiffness functions or impedance (the inverse of-flexi- .bility. functions or-compliances). I Defining.the dynamic'etiffness matrix: -K = K-+ iD'- m M ~(7) 2 d The. solution'for the transfer functions follows formally from: B4-12241-7772 8 E-

Hj a - K'g' (K + iD) Ej 2 s -(I + w K7 M)Ej (8) Note that the dynamic stiffness matrix K does not depend,on the loading cor.dition E. Also, for m = 0, H (0) = E. g g Having found the transfer functions, the acceleration time-histories follow then from the inverse Fourier transformation: e U*h Hj fj ] e *dw I s., -e (9) f (w) is the Fourier transform of the j input acceleration where, f =- component: T fj = y e*I* dt a B4-12241-7772 9 e ye e-,-

(10) The procedure consists then of determining the dynamic stiffness matrix K ' d solving Equation 6 for the six loading conditions H = {H }, determining the six Fourier transforms of the input components F which corres{p hds formally to:f {, and p = ing the inverse transformation (Equation 9), e 0 a g Mr.* 4. -e The dynaiac equations are solved in FRIDAY by Gaussian elimination, and the Fourier transforms are computed by subroutines using the Cooley-Tuckey FFT (fast Fourier transform) algorithm. A comparison of the results of FRIDAY with another solution is shown in Section II.3. I.2 REFERENCES 1. Timoshenko & Goodier, Theory of Elasticity, Third Editiori, McGraw-Hill Book Co., pp. 97-109. 2. Kausel, Whitman, Morray, & Elsabee, The Spring Method for Embedded Foundations. Nuclear Engineering and Design 48(1978): 377-392. 3. Michio Iguchi, An Approximate Analysis of Input Motions for Rigid Embedded Foundations. Trans of A.I.J. No. 315 May 1982. B4-12241-7772 10

II. DESCRIPTION OF COMPUTER PROGRAMS II.1 REFUND AND EMBED The computer program REFUND is used for computation of the dynamic stiffness functions (impedance funcitons) of a rigid, massless, rectangular plate welded to the surface of a viscoelastic, layered stratus. The subgrade stiffness matrix is. evaluated for all six degrees of freedom for the range of frequencies specified by the user. Embedment effects are applied subse-quently by the program EMBED. The program reads the topology and material properties, assembles the sub-grade flexibility matrix, and determines the foundation impedances by inver-sion. The subgrade flexibility matrix is determined with discrete solutions to the problems of Cerruti and Boussinesq. A cylindrical column of linear elements is joined to a consistent transmitting boundary, and the flexibil-i ity coefficients found by applying unit horizontal and vertical loads at the axis. The rectangular plate is discretized into a number of nodal points, and the global flexibility matrix found using the technique just described. The foundation stiffnesses are then determined solving a set of linear equa-tions which result from imposing unit-rigid body translations and rotations to the plate. Since REFUND is restricted to surface-founded plates, the effects of embed-ment are included by adjusting the REFUND results with the program EMBED. The theoretical bases of these programs and their application to the ' solu-tion methodology are described in Section I.1.2. The results of REFUND compare very well with published results. The com-parisons shown in Figures II.1-2 through II.1-7 are based upon " Impedance Functions for a Rigid Foundation on a Layered Medium," J. E. Luco, Nuclear Engineering and Design, Vol. 2, 1974. Of the various solutions presented by Luco, the following was selected for comparison (see Figure II.1-1): Layer 1 Layer 2 Shear wave velocity 1 1.25 Specific weight 1 1.1764 1 Poisson's ratio 0.25 0.25 The comparisons shown are of the coefficients k and c f rom which the verti-cal, translational, and rocking impedances can be expressed: K = Ko [k + iso c] in which ao is a ' dimensionless - measure of frequency and Ko is 'a zero-frequency stiffness. The minor - differences shown between the REFUND result and Luco's analysis l can be attributed to the use of an " equivalent" rectangu la r plate in the REFUND analysis (Luco's is circular) and to dif ferences in boundary condi-tions at the footing (rough vs. smooth). B4-12241-7772 'I1

II.2 KINACT 2 1 KINACT is a computer program used in the three-step solution of soil-structure interaction problems. Briefly, the program modifies the specified translational time history at the surface to tranlational and rotational time histories at the base of a rigid, massless foundation. i The theoretical basis for the program is derived from wave propagation theory as described in Section I.1.3. II.3 FRIDAY 4 The computer program FRIDAY is used for dynamic analysis of structures sub-jected to seismic loads, accounting for soil-structure interaction by means of frequency-dependent complex soil springs. i The structure is idealized as a set of lumped masses connected by springs or linear members, and attached to. a common support, the mat. The latter is supported by soil springs or impedances, which may or may not be frequency-dependent. Alternatively, the sat may rest on a rigid subgrade. The structure may be three-dimensional, but cannot be interconnected; each structure has to be simply connected. Fourier transform techniques are used i to determine time histories; cutoff frequency is prescribed internally to l 15 Hz. f The theoretical basis and implementation of ' the program is described in .Section I.1.4. A comparison of FRIDAY with a public domain program, STAR-DYNE, for the seismic response of a fixed-base, multi-mass, cantilever model is shown in Figure II.3.-l. The model is shown in Figure II.3-2. i B4-12241-7772 12 4 .m ,m_,yr,,,..--,,,,..,.._,,...-,,,,,.,7 ,,,.,,,,,,..,y-,% ,,,,,,,m,,, ,.-..m---,, 9-

4 i i j. i \\ i y(t) (K],,, y(t) I-l A f(t) O u gh Q <u(t),f(t) ft Q j f" ~ F. G(t) + 3E \\ WM '**VW snerwr n1 W [K] nxn FREQUENCY KINEMATid INTERACTION ~' DEPENDENT INTERACTION ANALYSIS STIFFNESS REFUND KINACT FRIDAY 4 I I. FIGUREI-l ,~ THE THREE STEP SOLUTION i

Z ~ / lat V=e L \\) i l ~ \\ / My BOUSSINESQ Z / ~ }r \\ n..tas X \\ ( \\ ~. 1 l I fy CERRUTI FIGURE I-2 l THE 800SSINESO AND CERRUTI PROBLEMS

E vi%a \\ s \\ \\_ i CENTRAL l i-COLUMN N \\, X ,,4w-awe,4w FIGURE I-3 IDEALIZATION OF THE BASIC 'REFOND' SOLUTION FOR CONCENTRATED LOADS F l I 4 U Um i UY r Z 0 e X l l FIGURE I-4 ' REFUND COORDINATE SYSTEM i

t i, l l 11 y n A ( Y ( Y ) h L b y ( ey E 1 j( bV V J 5' I E tiu G I F Y A ' A{ f A I a . I A j "I N A O I A A a T / I TA AON A NU I ( i O O F I N T l ~ AS O - = I I RS T ) ) E E t A g ( L L R g ES E u CS CA L A M E C L C = D A AI NG OI L R A I T N AF O LO I S T NE A AS T RA O TB R = = l ) l t i ( sf u e lIll1I ?! l ill14!! j1 i lj1i

d J I t 4 i i I i I UNIT-RAOlus ~ l sssssssssssssssst >a at 3eala t i t l I I l. I h ( - I' r FIGURE X.1-1 LUCO'S TWO-LAYER PROBLEM i l I

~ h P J i h Luco --- Ruuse t.o as - / \\ / \\ t es p / g / as / at - i l a o 1 2 3 4 s a 7 e o 4 f i

t. -

I l 1 i l-f FIGURE H.1-2 ROCKING STIFFNESS COMPARISON - L REAL PART m _..._.,. _ _._ ~ _,,, _, _ _,. _,,,,,,.,,,,,,,.., _,,,.,,,, _,,.

a.AA* 4 -...,.d.-.6 A _ +, _. s L-. .m g w__ 9 0 0 t W 4 f i l Ce Luco asruno SD = i-D 9 Y Q up M 42 = e 1 9 9 9 9 9 9 g-0 1 1 3 4 S. 8 7 8 g / f + 1 ( g e p l. t h N t l-FIGURE II.1-3 ROCKING STIFFNESS C(MPARISON - ~ -IMAGINARY PART y ,,., - -..... -..--.,.........~, _---.~............. m.-... ._.,45s..,.__--._._,

s_. ~ - . _.. ~ 's d' 4 t 4

e

.,.p. ? J j - 4 . kg J L 4 - LUCO I g

---

agruuo t.s -

tt i to g 1 1 i 1.2 = g [ O \\ t \\ \\ \\ \\ [ as s. t / \\ I \\ l an + t g i f- \\ l' 44 i I az e i i i e i e o-1 2 3 4 s s 7 e g, i f i i l-FIGURE R.$-4 0 HORIZONTAL STIFFNESS COMPARISON -- REAL PART p l-i l l t- .j re -....,...,,,,,....,,......... _.... -.... ~.. _ _,...... _. - _ -...

4 D 4 1 1 5 l l i' e l i C, H LUC 0 ~ ~ REFUND >s 4 as -

• = =

M = E esp f e i 0 9 1 1 3 4 5 's y 3 So + r e O 6 9 FIGURE I.1-5 HORIZONTAL STIFFNESS COMPARISON - IMGINARY PART J e ,.+ ,,-e-- w e-w-e ,...-,w-,...,. ,-,.,-,,,,,-,.,--,...,,.mw-r.,,,-.., . - _. - ~.. -. - - -.. -,, _....,.,, -,.. - - -.. -

+ A .m -a a a, .a, 4 6 G O 4 s a I O ? I g j LUC 0 13 ngPUND t i ,/ tg \\ j e M = Od = g \\ ,N 4 s ,9..,. a 9 F U t 6 FIGURE II.1-6 VERTICAL STIFFNESS COMPARISON - REAL PART .... - _. _ _.~.. _.,.. _ _. _ _ _. -.. _ _. _...

4 4 C, A Luco

=== RtFUND to - 68 - f,a ,'s N as g ^ as IQ# I p I i' e i I g O 1 3 4 3 g y. 3 r !l-l FIGURE R.1-7 1 VERTICAL STIFFNESS COMPARISON - [ IMAGINARY PART 5 9 y-,- 5w. -e,~-m-- .,-.,-..,.,-,..e--, .~,.,%-ww... w-, n -r, ..---.,.-..,,-..,-,..,--.m.,,..-,eb.,.,,---,

I. 4 -.. l d-14 s = FR304Y i~

===== STAnoYIst g3.0 a _ son a E as 4a: W.s sa w 5'n ( e a,o T i o a.1 c.a os o.4 os o.s o.7 o.s os .ts PERIOD (SECONDS) ~ FIGURE II.3-1 COMPARISON OF ' FRIDAY' AND 'STARDYNE'-ARS AT THE ROOF 1 l

q l at so' 1 q i i 1 i I gL es' 2-l 2 4' I EL as' 3 3 EL 24' 4 4 2L ta' 5 Ya u ' Xe 5 ge ////4f//// 6 FIGURE H.3-2 '5TARDYNE' MODEL i

• i w

e,wme or-,,, ...,,r v,..w.,,,,.ye-e m w..w w..., ,.y..,.,..ww--w- -.w..,me ..is.,-w--.r---c..-,e-..-,,,--e.w-eme.-- .w...-v.-r-+we.,,m... ...w-w

9 'h e 1 3 r _, - - - l DESIGN SPECTRA ^ g 3 STEP METHOD SPECTRA 8 b I i 3 i i j i 8, I l g L7 1 / i d# o 1 W I i A i i 1 8 I l r-1,-/ L__ j l i i - ) 6 / =g a x x m 8 2 d s.n c.n c.m c.m c. c.m c.m g.,w, j.g c.n .a c.n c.n c.n c. c.n 4 W BVPS-2 CONTAINNENT STRU CTUR E EL 854.0 (TOP OF D0ME) l HORIZONTAL SSE 1% EQUIPMENT DANMNG i

1 7 $ gnzEm2 3S2m ab se 's. A R TC m E 's. P .AS R D T o O s C 's. .E H P T SE M es N ) P 'n. G L E I ST L ES A e W D3 s 's. E N A s R e. C 's F O t i s PG e d. ON T 7 't l ( P g

0. M J.

. 8 DA L 1 7I g 8 l L g. T E N EE s e.'s RM U P TI CU e s. U Q 'e R E T i S e e. T% 's N1 E 1 1 M e s. N E / 'e S. I AS. T pl NL s e. I I l fg 'e OA l I 1 I . CT N o O 2 Z n r i. SI 9 / P R V O e B H s Q" q-3 t~ I-g. 8# s 5i ,f aUE F l' I! i ii .l liiliIq!:1l I,'i: I

ATTACHMENT 8 FIGUR E 8.3 4 h 0 Y. IE 8 o x W > kW I 2 xg E. W m> W W O m ,E i I ,E i I s.: p.- - S l

• i rJ

~ la o i 1 e m Mz r- - - j s Dr a 'dE w2 I E [ o 8 W l d EH m z l >w -o E a.&_ g rg __a

== i z# 1 J w-I ~2 l 1 _E W l-I '4 # L----_______ 3 5.J d 'O(. ~ U>z e i I

• E

>O ,\\ 8 -e z ee 's es'e en e es 's se f ee< s . ee e ee 'e es 'e ee e g'y . _.. ~.... -...,

i >agagm2 T sc=, O l A R c. T C EP = S c. A RD TO C H = ET c. PE S M NP = IGE c. S T S E D3 c. c. )T ,L A M E 7' SAB g. ( g G N { g

0. lP I

g M 48 g. A 8 D L ET N E E R M U P I FI TU C9 UE R M'r T% SI t T 7t N E ES MS I[I N I A L T A N T O N C O iZ t -SI PR VO BN 5:. q'" 34 5i 5 3* 34 E-5s o y ,4 l:i~ ): ji , : i ! 1 I!

i :i Ii I

!i r}}