ML18029A931

Speech Entitled, Flora:Program for Direct Generation of Floor Response Spectra.

ML18029A931
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Site:	San Onofre
Issue date:	03/29/1985
From:	ABB IMPELL CORP. (FORMERLY IMPELL CORP.)
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FLORA: A Program for the Direct Generation of Floor Response Spectra Presented by:

IMPELL CORPORATION 350 Lennon Lane Walnut Creek, Cal $ forn$ a 94598 (415) 943-4500 8504020i55 850329 PDR ADOCK 0500020h P,

0 1.0 Intr oduct$ on 2.0 Methodology 3.0 FLORA Features 4.0 Exampl es 5.0 Lkst of Projects 6.0 FLORA User's Manual

0 1.0 Impell Corporation has developed a computer code> FLORA (Floor Response Spectr a Analysis) > to efficiently generate secondary and tertiary response spectra directly from ground response spectra or any other primary spectra.

FLORA uses random vibration techniques and perturb bation analysis to generate the in-structure response spectra. The methodology on which FLORA is based was fiist developed by Der Kiureghian et al f13 at the University of California> Berkeley> and then expanded by Impell Corporation f23.

s nd c FLORA has been developed to replace the cumbersome time-history analysis procedure with a more direct> flexible and less costly approach. With

.the FLORA technology> no time-histories are ever required; FLORA can accurately generate any requi-red output response spectr um directly in terms of the input spectrum and the dynamic properties of a given system. The analytical approach employed by FLORA requires substantially less computer time than a standard time-history analysis.

More importantly> it el iminates the need to generate synthetic motions and reduces the subsequent engineering effort associated with a dynamic anal ysi s.

Proven applications of FLORA include generation of secondary spectra to resolve licensing and backfit issues> and greatly improve efficiency in any design modification or requalification efforts. Typical examples include:

o Building analysis (or reanalysis) to generated required in-structure response spectra.

o Subsystem or component analysis to generate the Required Response Spectrum (RRS) for equipment qualification and testing purposes.

FLORA is particul arly useful in those situations where time-histories were not generated originally or may no longer be valid because of design modifications. It can also be used to evaluate a new component which must be added to an existing system without the necessity of altering the existing model of that system. As an aid in choosing optimum equipment attachment points> FLORA can generate spectra at any.

number of equipment attachment points with a single run.

o FLORA can generate secondary response spectra at any nunber of locations and for any number of damping values at each location>

directly frcm an arbitrarily shaped set of input ground or floor response spectra. FLORA uses the dynamic properties of the primary structure as input. These properties may be supplied by a standard finite element code or fran modal test data.

"i

o FLORA can employ either of two main solution algorithms. The "wide-band" option is used when the input spectrum varies smoothly over a wide range of frequencies. The "narrow-band" option is used when the input spectrum has'a relatively high amplitude in one or more frequent bands.

o FLORA can take into account the effect of interaction between the primary structure and the mass of the attached secondary system (piping> equipment> etc.). Typically> the effect of this interaction is to reduce the spectra at the secondary system locations contributing to its qualification potential.

o FLORA is ideally suited for probabil istic applications. Any number of synthetic time-histories could be generated to match a given input spectrum; each would result in a different secondary response. FLORA automatically accounts for this and can provide the complete probability distribution on response amplitude, in addition to the mean response value which is used in standard applications.

The narrow-band solution technique in FLORA deserves further comment.

Other direct generation codes require the input spectrum to be wide-banded. This either restricts the use of those codes to the few cases where this criterion is met, or it produces very conservative results when the input is not wide-banded. FLORA has no such limitation; the code provides a very accurate proediction of response, regardless of the characteristics of the input motion. Since the large majority of practical problems involve narrow-banded input spectra> this unique capability of FLORA greatly increases the potential appl ications of the direct generation approach.

Either option in FLORA requires only that the dynamic properties of the primary structur e be available.

FLORA has been fully verified in accordance with the Impell Qual ity Assurance Program and requirements of 10CFR50.

'll L13 A. Der Kiureghian> J. L. Sackman and B. Nour-Omid> "Dynamic Response of Light Equipment in Str uctures>" Report Number UCB/EERC-81/05> EERC> University of California> Berkeley, CA>

April 1981.

L23 G. V. Miller> H. Uyei. W. F. Hahn> and M. Ratiu. "Comparison of Secondary Spectra Genet ation Techniques>" 4th National Congress on Pressure Vessel and Piping Technology> ASIA, Portland> Oregon, June 1983.

.r 0

2.0 The methodology incorporated $ n FLORA is briefly explained $ n the attached two documents: "Comparison of Secondary Spectra Generation Techniques" by Mufller et al and "FLORA: Mathenatfcal Formulation":

Impell~s internal document. More $ nformat$ on about the theory can be found $ n the references 1 usted $ n the above-mentioned documents.

o' v

INTRODUCTION Dynamic analysis of many structural systems can most conveniently be performed by the response spectrum method. Until only recently, secondary spectra, i.e.

the spectra of structural response at any arbitrary location in a structure due to an input spectr a applied to the base. <<ere generated by the time history method.

CONPARISION OF SECONDARY SPECTRA Briefly, one or more time histories were derived from GENERATION TECHNI(UES the specified base spectra. Next, a time history analy-by sis of the structure resulted in secondary time histo-ries at the point of interest. Finally, the resulting (1) (2) time history is converted to a response spectrum by Greg V. Hiller , Ha5ime Uyei sub5ecting a single-degree-of-freedom oscil'lator with a varying natural frequency to the output time history.

(3) (4) Several methods have recently been presented that Malter F. Hahn , and Hicea Ratiu derive secondary spectra directly from the input spec-(1) Principal Engineer, EOS Nuclear Inc., tra. Among the most widely used are methods by Singh 350 Lennon Lane, Malnut Creek, California [1] and Oer Kiureghian [2]. These methods generally (2) Technical Specialist, EOS Nuclea~ Inc. give very good results when the input spectra are 350 Lennon Lane, Malnut Creek, California smoothly varying with wide-banded Power Spectral (3) Supervising Engineer, EOS Nuclear Inc. Density (PSO) functions.

350 Lennon Lane, Malnut Creek, California This paper compares three direct generation (4) Technical Specialist, EDS Nuclear Inc. methods. They do not represent all the available meth-350 Lennon Lane, Malnut Creek, California ods. However, the three used here represent three dif-ferent levels of approximation and, as such, can give the Jeader an idea of each of the methods'pplication.

The first two are based on Oer Kiureghian's L23 results. The third method was derived by the authors and computes secondary spectra for general, arbitrarily banded inputs.

Following is a brief review of the first two ABSTRACT methods. The reader should refer to the origin paper This paper compares the accuracy and efficiency for details. Next we present a brief description of of thr ee methods of direct generation of secondary the exact method, which uses elements of the first response spectra from known input response spectra and methods but with a more rigorous computational tech-structure modal properties. In order of degree of nique. Finally, response spectra plots for each of approximation, these are: 1) a method which assumes a the two numerical examples illustrate their relative smooth input and only a weak coupling between modal accuracy with respect to the time-history-generated responses; 2) a similar method except that a much more secondary spectra.

complete modal coupling is included; and 3) an "exact" MIDE BAND METHODS approach good for arbitrary inputs. Two numerical examples compare the results of each of the above methods to results obtained from the traditional time Der Kiureghian used random vibration theory to history approach. derive his direct generation methods. In [2], he derives a closed-form solution for the secondary response spectra. This solution relates the secondary spectral ordinate to a modal combination of weighted input spectral ordinates. The equation is:

n n 1/2 R . E E p, i)<i4,s)k) iaO gsO where po,i~ is an expression for the cross-correlation between mo8es and ticipation factor and fi and Si represent the ith mass par-the input spectral ordinate eval-uated at node i. The zero mode corresponds to the out-put frequency ordinate. The closed form expression for p iyy for a white noise input with small modal dampings po,

0 29) is given in [23 as where we have set 1 2 cd~ kgj r$ f [(>i+> ) (fi+l ) + (o)i4) (t$ -f )3

~o,ij 2 jj 4(i-+j) + (gi+gj) ( i+ j) (2} (6)

Equation (1) is valid if the frequencies of the

~ca 1

~

modes making dominant contributions to the response are not very widely spaced, and when the response itself is jjjkgj k~Pk jk not extremely narrow-banded. This method is the first method in the comparison.

same The second method uses this expression, but with a substantial refinement,

~cj p)) ~ k IH( jk where given also by Der Kiureghian [3]. Briefly, an addi-tional weighting factor is introduced as the ratio of a process peak factor to modal peak factors p2/pipj. Ajk ~

T)

(Br j(~k 1

/jr)[(1-r ) -4r(f> ~k )(~kk j These peak factors are computed from a closed form jk equation which assumes white noise input.

a Bjk ~j2(1-r 2 )[4r 4 1

~kr ~k ~Jr)-(1-r )

2 2

]j The equation for the secondary spectra is then n n 2 1/2 Djk Br [(pj+pk)(l-r ) ~k ~j ~j ~k ~+

(3)

(1 r2)4 Equation (3) is the second spectra gener ation with r >~k~.

method included in this comparison. Note that equa- Note that Ajk 1. Bjk Djk 0 for k-j.

tion (1) with p2/plpj 1 is,always conservative compared to equation (3).

Substitution of (5) into the equation for spectral moments of the PSD (8), we have NARROW BAND METHOD The authors derived an exact solution for the out-put response spectra by dropping the assumption that jd GR (Cj) djd; m ~ 0, 1, 2 0

the input is wide-banded. The essential difference is that the peak factors p, defined above, are calculated using the exact spectral moments (see Appendix I) of '

cpPR )[j+t)d()Q>>'2 ) 9.) 4 (9) the output Power Spectral Density (PSD) function, m,j GR(~)

first use Sundararaian's method To derive these,

[4] to calculate

, response spectra, G(o)).

we the PSD of the actual input Next, we combined the expres-

~2 if sion for the output PSD (see for example [1]), where m

o) G cu des GR(fd) E ) C)ct [jdI44+4[ (tjdpcjd (lo)

)2 y 4 J

+ 2iu+M Qkgjmjfk)j Hj(N) Hk(<)G(() are calculated in Appendix II. Once the spectral moments }GO, }),1, and }92 are found by equation (9),

with Vanmarke's [5] simplification of the real part of the exact peak factor may be calculated. This peak the transfer function, Re[Hi([o)Hk*(u))j. cj is the factor is then used to relate the mean of the peak structure's jth effective participation factor. kith some algebraic manipulation, we write this combination response, 7wherto the standard deviation of the response as R ~o9

~2 r peR GR(jd) ~ G(jd)[ Z c)jd) iG)(jd( [1<<) + (1 - Q) 92]

(5)

+ 4 L')[)Jic){jd)iV(ldc)+(\ - Q)4>))

V 0

p gi FLOOR SPECTi@ IN REACTOR BUILDING where, Figure 1 illustrates the finite element model of an auxiliary building associated with a nuclear power installation. The input spectrum is applied to the base (oJ'-cJ') +g$ 'u) ~ (13) and the output is calculated at node 24. The input

'I.C I

spectra is shown in Figure 2 and is an NRC Regulatory Also, Guide 1.60 seismic spectrum. Figure 3 illustrates the comparison of the time history results with the three 6a III ~

4p - 'uJ Q(ICI LI L direct generation results. Execution times on a CDC Cyber 170 were as follows: 39 seconds for method 1, 72 Cu~ -MJ ' '(14) seconds for method 2, and 268 seconds for method three, the latter using 50 PSD iteration points. The time The substitution of Equation (14) into (13) results in:

history approach required approximately 750 seconds.

All spectra are evaluated with two percent damping.

SPECTRA ON A PIPE LINE ti)

[(I, (C);) - )'. (IC(.) ]-

Figure 4 illustrates the discretized ax)del of a small piping system. The input spectrum is applied to all supports and is a narrow-banded floor spectrum.

This spectrum is given in Figure 5. Node C3A is the where, location of the output spectra and is the location of a non-rigid valve. Figure 6 compares the time-history-CJ i IE u"j Ciao

~

generated response spectrum with each of the direct ( )

generation methods. (ou uJ') CV (l6)

J CONCLUSIONS The necessary integrals Km( ) for the calculation of the spectral moments of the response PSOF are evaluated Clearly, the time history approch to spectra gen- analytically, and are given by:

eration is made obsolete by these recent direct genera-tion techniques. It also may be concluded that the ~- ~~~"+

choice of generation technique will be controlled by the judgement of the engineer based on the bandedness 4 + 'J4((I'~rll-~BALI' l f

)

(

z g<-~~g>

RA% [

~+z~i-g.J ~cv+q" J

of the input spectra (which strictly speaking requires a look at the Power Spectral Density function), the accuracy desired, and cost constraints. Mith a compe-C L 4,,'II ~l') L'j(17) tent computer program, the pr eparation time will be the same for each of the direct methods.

The narrow band method is expensive compared to ttOu) cqf 4 4o-<In[(o)'-w') ~4(.u*aJ'g +

the wide band approches. Yet not, only are the results J J J reliably correct, but,more information about the input (18) process is available. Specifically, since the method solves for the exact input PSO and can calculate the i-z5 CI -(I ((I)C-C output PSD via a transfer function, both of these PSDs 'IS~IS. 2(L ~l- g.

are available for further use. Additionally, if the input is the result of a random excitation, it should be expressed in terms of a PSO and, as such, the PSO can be input directly.

APPENDIX I: SPECTRAL NOHENTS t ( I ~II-~I-( Ll' -I~CI ll-, III'J T(L The power spectral density function, G(o)), of the input accele~ation is assumed to be defined at discrete freqency points i, i ~ 0, 1, 2, N+1 and composed of a straight line segment between the specified frequency points o)i and coi+1. The PSOF value is zero outside the interval MO('M< MN+I,, with GD ~ G~l ~ 0.

Thus, D

y~p i7 0

(22) ACKNOWLEDGEHENTS The authors would like to thank Kim Hoang for her technical assistance and useful suggestions.

REFERENCES

[1] Singh, H. P., "Generation of Seismic Floor Spectra," Journal of the Engineering Hechanics Division, ASCE Vol. 101, No. EH5, Proc. Paper 11651, October 1975, pp. 593-607.

APPENDIX II: NOTATION [2] Oer Kiureghian, A., Sackman, J. L., and Nour-Omid, B., "Dynamic Response of Light Equipment in Struc-The following symbols are used in this paper: tures," Report No. UCB/EERC-81/05, Earthquake Engineering Research Center, University of gk, Bgk, ~ factors which depend on period and dampin9 California, Berkeley, California, April 1981.

Dgk values of modes g and k;

[3] Oer Kiureghian, A., "Structural Response to Sta-c, ~ effective participation factor of equip- tionary Excitation," Journal of the Engineering ment for node i; Hechanics Division, ASCE, Vol. 106, No. EH6, Proc.

Paper 15898, December 1980, pp. 1195-1213.

one-sided power spectral density of input process [4] Sundarara)an. C., "An Iterative Hethod for the Generation of Seismic Power Spectral Density Func-

~ one-sided power spectral density of equip- tions," Second ASCE Conference on Civil Engineer-ment process; ing and Nuclear Power, Knoxville, Tennessee.

September 1980.

H> (cu) complex frequency-response function for mode $ ; [5] Vanmarcke, E. H., "Properties of Spectral Moments with Application to Random Vibration," Journal of function used for calculation of spectral the Engineering Hechanics Division, ASCE, Vol. 98.

moments;. No. EM2, Proc. Paper 8822, April 1972, pp.

425-446.

~ peak factor; t5, g3, ~ coefficients which depend on dynamic rdo sd properties and participation factors; R mean of the peak equipment response over time

~ response spectrum ordinate at frequency and damping c; i-th modal damping coefficient

~ m-th spectral moment Poe ib cross>>correlation coeff icient between modal responses; eR standard deviation of equipment response; cubi

~ i-th modal frequency

~ i-th modal mass participation factor

a r

Y(E'-W)

(o oo) 8 (N-S)

FIGURF X. 8 0 Bb'ILO/NG MOOEL

- R& -/.6'0 Spectrum 0.4 oO 0/ OZ P.S /. 2'. S /0 B7. P7.

r~z uzucv cps) 8'/SL/EE 'Z. /iVPgj RESPONSE SPECTRA (z% Damping)

o)

l. EBEN':

PYide Bund Improved PVide Eund ( ">~+" ~)

Time History Narrow Bund 1)

I, I

J I

//

lQ

~ 4 ~

/I

~

i REQVEIVCY (CPSj FIGUR'E 8. SECOA/OAEY EESPOhSE SPECTRA- ZS OHMIC

C3A FIGURE +: 86iler Feed Line

~ 1 lo

~ AO z

0

~ AO C

K llI

~ > L~

c 0.10 LI 0.5 5, L fo.,

NATURAL FREQUENCY (CPS)

FIGURE 5 - INPUT SEISMIC SPECTRA FOR 1% DAMPING

U 22.5C I CQ LEGEND:

Wide Band Improved Wide Band Narrow Band

-"---- Time

~

History

0. C~ S.

FREQUEN GY (GP S)

FIGURE B. SECONDARY RESPONSE SPECTRA qg DAMPING

0 0

FLORA: NTHENTICAL FORNULATION

"~

v 0

("i

FLORA PROCEDURE MODAL PROPERTIES MODAL PROPERTIES N DOF BUILDING OSC ILLATOR Wa Z>4 ~oi fi M PERTURBATION ANALYSIS MODAL PROPERTIES N+1 DOF SYSTEM ZO WIDE BAND NARROW BAND

'APPROACH 'APPROACH

r j )t

},

p C op

~PELLg+y~

HIDE BAND APPROACH GROUND RESPONSE MODAL PROPERTIES

'PECTRUM N+1 DOF SYSTEM FLOOR RESPONSE SPECTRUM ORDINATE

'8+1 8+1 P2 S

R '1j1~

(~o,g)=LQ g~p, -o'sj h

f.*f."S(M.*,

s j s

' Z.*)S(W.*, Z.*)j J J I II \

/I h I I la I

I Cd CiJ p

NEXT ~O

WIDE BAND APPROACH FLOOR RESPONSE SPECTRUM 1

p . -: CORRELATION COEFFICIENT BETWEEN RESPONSES I AND J fl)

OF MODES MEAN MA IMUM E R SPONSE PEAK FACTOR TANDARD EV IATION ESPONSEfl),f21 P-*:

1 EFFECTIVE PARTICIPATION FACTOR DER KI UREGH IAN> A g STRUCTURAL RESPONSE TO e

STATIONARY EXCITATION'" JOURNAL OF THE ENGINEERING MECHANICS DIVISION> ASCE> VOL. 106'O EM6r PROC. PAPER 15896> DECEMBER'980>

PP, 1195-1213

[2] DAVENPORT> AsG i NOTE ON THE DISTRIBUTION OF

'OF THE LARGEST VALUE A RANDOM FUNCTION WITH APPLICATION TO GUST LOADING ~ PROCEEDINGS INSTITUTION OF CIV IL ENGINEERS'ONDON'8'87-196'964.

0 NARROW BAND APPROACH GROUND RESPONSE SPECTRUM MODAL PROPERTIES N+1 DOF SYSTEM POWER SPECTRAL DENSITY OF INPUT W>> Z>> 0>>

Gg POWER SPECTRAL DENSITY OF RESPONSE G

SPECTRAL MOMENTS OF RESPONSE Xm~ f O

a) G S

do)

FLOOR RESPONSE NEXT ~O SPECTRUM ORDINATE YR(u),g) ~ P~

YR CO

~o

a 0

1

PERTURBATION ANALYSIS Frequency Oscillator (1 Mode)

M1 M~

- ,Hz Frequency Building (7 Modes) gk gk Frequency 8+1 DOF System (8 Modes)

REFERENCE l DER KIUREGHIAN A a SACKMAN J L > AND NOUR-ONID B r DYNAMIC RESPONSE OF LIGHT EQUIPMENT IN STRUCTURES'" REPORT NO, UCB/EERC-81/05'PR I L 1981

0

~PELLgy~

EVALUATION OF POWER SPECTRAL DENSITY OF INPUT GROUND RESPONSE SPECTRUN

~ SUNDARARAJAN'S NETHOD flf

~ ITERATIVE PROCEDURE TRIAL SOLUTION Go POWER SPECTRAL DENSITY OF RESPONSE OF AN OSCILLATOR GR =H (M) Go STANDARD DEVIATION OF RESPONSE OF THE OSCILLATOR cr = G de 0

MAXIMUM PEAK RESPONSE (SPECTRUM)

So

= P<R COMPARE S AND GIVEN GROUND SPECTRUM S(~) .

AT EACH Fl4Q UEN CYz DEFINE IMPROVED TRIAL.

G>(~;) = C; Go(u<)

fl] SUNDARARAJANp Car AN ITERATIVE NETHOD FOR THE GENERATION OF SEISMIC POWER SPECTRAL DENSITY FUNCTIONSi" SECOND ASCE CONFERENCE ON CIVIL ENGINEERING AND NUCLEAR POWERS 15-17> 1980, KNOXVILLE'ENNESSEE'EPTEMBER

l 0

~PELLONER SPECTRAL DENSITY OF RESPONSE N+1 8+1

• ip.* H<(~) *(~) G~(~)

s

() =

gg,, g ip 3 J H

H<(~) COMPLEX FREQUENCY-RESPONSE FUNCTION FOR MODE H -"i~):

3 COMPLEX CONJUGATE OF H~(~)

G,. <>) INPUT POWER SPECTRAL DENSITY FUNCTION CLOUGH'oMea AND PENZIENs J! i DYNAMICS OF STRUCTURE MCGRAW-HILL, INC. 1975,

r

~PELLg+p~

SPECTRAL MOMENTS OF THE RESPONSE P

R R MEAN OF THE PEAK RESPONSE R

STANDARD DEVIATION OF RESPONSE R

aR POWER SPECTRAL

- MOMENT OF ORDER 0 OF THE RESPONSE

,DENSITY FUNCTION

~ill 0 S NEEDED FOR EVALUATING PEAK FACTOR P DER KIUREGHIAN A,r SACKMAN> J L,i AND NOUR-OMIDi B "DYNAMIC RESPONSE OF LIGHT EQUIPMENT IN STRUCTURES."

REPORT NO. UCB/EERC-81/05, APRIL, 1981, VANMARCKEi Es Hog "PROPERTIES OF SPECTRAL MOMENTS WITH OF THE APPLICATION TO RANDOM VIBRATIONS JOURNAL EM2i ENGINEERING MECHANICS DIV I SION'SCEz VOL 98> NO PROC, PAPER 8822> APRIL 1972> 025-446

V \ I 3.0 FLORA> version 3A> is a computer program developed to generate secondary response spectra and power spectral density functions (PSD) directly from known primary response spectra and the structure's modal properties, without an explicit time-history analysis. The program was developed by Impell Corporation and is written in standard FORTRAN 77.

It is written to be absolutely system independent; it may be installed In addition> with on any system possessing a FORTRAN 77 compiler.

it trivial modifications can execute on most 8 and 16 bit micro computers. FLORAL'ersion 3A> is the result of an effort to replace the expensive and deterministic time-history method of response spectrum generation with a less costly probabil istic> random vibr ation based direct method. The code contains several features which make FLORA superior to current "direct generation" codes. These features are:

The user has complete control in specifying the probability of exceedance on each output response spectra. The spectra are calculated such that each ordinate represents the response for a constant exceedance probability. Spectra calculated with multiple time histories and even spectt a calculated by other direct methods yield responses with unknown exceedance levels.

2. Another unique feature is that the restricting> universal assumption of wide banded input excitations is unnecessary. While most seismic input excitations can be considered wide-banded>

in-structure equipment qualification analyses have narrow-banded floor spectra as the input. FLORA~s optional narrow-band algorithm calculates actual. probabil istic responses> el iminating the unnecessary conservatism inherent in the wide band solutions of these problems. FLORA also allows the user to specify a wide-band solution algorithm for those situations where the input is clearly wide banded. This results in significantly shorter execution time and is quite adequate when the input is not sharply peaked at one or a few frequencies.

3 ~ The program can take into account interaction effects between the structure and the mass of a potential item of equipment. The equipment item need not be present in the or iginal dynamic test or finite element analysis of the structure once the structure e~s dynamic properties are obtained FLORA can internally modify then for any proposed spectra generation location and associated small equi pment mass. The equipment mass~ s ef feet is typical ly to reduce the spectra at its location> contributing further to its if qual ication- potential. Conventional floor spectr a are obtained by setting the equipment mass to zero and disabling the exceedance level calculations.

f ~ ~

4~ The program accepts structural modal properties from a specified neutral data file. Thus FLORA may read the properties from any finite element code> or by hand prepared files> or from modal test data. Modal test data can completely describe the structure's propet ties if Impell's computer program MPFGEN is used to generate the structure's mass participation factors from the test data.

5. FLORA can generate all three translational direction response spectra resulting frcea single direction input spectr a. For two or three directional simultaneous analysis> items only necessary to run the two or three executions of FLORA and then for each output direction simply combine the results of the two or three FLORA runs by the SRSS method for the total response.

4 Several other features of the code are:

The Nuclear Regulatory Guide R.G. 1.60 seismic response spectrum curves are built in and available for use as the input spectra.

The defining parameters ate horizontal/vertical input and zero period acceleration. The spectra internally contain damping as a pa rameter.

2. A single run can generate any number of output spectra for any number of equipment attachment points in any or all three directions at each point. The equipment mass is specified for each direction at a given point thus the interaction effects can be different for each direction at the attachment point. To generate responses at each of the three directions for one attachment point, one speci fies three attachment degrees-of-freedom in FLORA~s input.

3 ~ Four restart options are available when using the narrow-band option. The user may:

a) execute the compl ete secondary spectr um cal cul ation b) generate the PSD of the input and save it c) refine the PSD through further iteration d) use the saved PSD and complete the execution 4 ~ The code can run on any computer possessing a standard FORTRAN 77 compiler. A slightly different version exists that runs on most 8 and 16 bit micro computers.

e l ~

4.O BEHELD Three numerical examples are presented. f The two f rst examples compare

$ n-structure response spectr a generated using t1me history analyses and by using computer code FLORA. The third example shows the generation of a floor response spectrum for SONGS-l. t In th$ s example $ 1s shown that t

the direct generation appr oach ranoves conservatism kmpl $ c$ $ n the generation of floor response spectra by using a time history input which spectrum envelopes the smooth design spectrum. t Also $ $ s shown the possible addftkonal reduction of the spectral ord$ nates 1f Interaction is considered.

~1 1 Qa EXAMPLE'PROBLEM 1 - 3/D BUILDING MODEL, VERTICAL ANALYSIS FREQUENCY MASS PARTICIPATION HODAL DA."P IHG

~HZ. FACTOR 4) 1 0 F 005 0 ~ 012 10.0 2 0 '07 10.0 3

4 2

6

'1

'0 21.0 4 ~0 5 6 '8 lo40 4 0 6 12.36 0 ~ 54 4 ~8 7 13 ~ 24 58ol 4 ~0 8 15+28 0 ~ 41 4.0 9 16 ~ 54 30 ~ 01 4 0 ll 10 12 17054 19 ~ 80 20+10 21 07

-15 ~ 17 1.55 4 ~0 4 0 0

13 14 21 21 22 ~ 94 0 '8 0%11 4.0 4.0 15 23 84 11.43 0 16 23 ~ 97 3e26 4~0 17 18 24.13 27+91 9 '6 0+19 4 0 0

19 29 '4 0 '9 4~1 20 30 24 0 15 4+0 21'2 31 '5 32o78 6 38 1~56 4 0 4.0 23 32o83 10 ~ 08 0 24 33 ~ 15 0 ~ 89 4 0 25 34e33 0 '7 4 ~0 TABLE 1: EXAMPLE PROBLEM HO. 1 - MODAL PROPERTIES

~a Pa Mlat Iyeeea u+t ~

~a

~ .t Lt O.t t.t ta ~ .e tta FOEOVEttCV ICFSI EXAMPLE PROBLEH I- INPUT RESPONSE SPECTRA (2S DAMPING)

~la ala

~ al o

tlat ~

~ sl

~ J boa

~a

~ tt lta Sla Ãa FOEOVEttCV tCFSI EXAHPLE PROBLEN I- COHPARISON UF SECONDARY RESPONSE SPECTRA AT NODE 24 (2'X DAttPING) 2ta W

~I eta K

o~ Ml illa ~

~l 1J h'ta ca F.tt ta tta w\ lta fltEOMENCF tCFS)

EXA'APLE PROBLEM I- CO'APARISON OF SECONDARY RESPONSE SPECTRA AT NODE 26 (2>> DA!1PING)

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