Recent Highlights of X-ray Magnetic Scattering Studies from SurfacesBNL 66109

G.M. WATSON 1,Doon GIBBS2, and G.H. LANDER3

‘ Department of Physics, University of Mavlandj Baltimore County, 1000 Hilltop Circle, Baltimore, MD 212502 Department of Physics, Brookhaven National Laboratory, Upton, New York 11973-50003 European Institute of Transuranium Elements, Postjach 2340, D- 76125 Karlsruhe, Germany

In this work, recent studies of surface magnetism, as observed by x-ray scattering techniques, are described. Theexperiments were concerned with uranium dioxide crystals for which x-ray resonance effects enhance the small magneticsignal from the surface. The main result is that, in contrast to the bulk which exhibits a discontinuous magnetic orderingtransition, both the (001) and (1 11) surface layers order continuously. This is reminiscent of the general phenomenon ofsurface wetting, but had not been previously observed for magnetic materials. Magnetic reflectivity studies show fhrther thatthe near-surface magnetic layers are more disordered than layers deep in the bulk, even at low temperatures.

Keywords: surface magnetism, X-ray scattering

1. Introduction

During the last 10 years, x-ray magnetic scatteringtechniques using synchrotrons radiation have blossomed,especially in studies of rare earth metals and actinides,including bulk materials, thin films and compounds. Thesestudies have especially benefited ffom the use of theresonance and polarization properties of the cross sectionwhen the incident x-ray energy is tuned near as L or Mabsorption edge. Brief reviews of these techniques andrecent applications may be found in references 1 and 2.Non-resonant magnetic scattering has also continued todevelop, most notably in studies of transition elementmagnetism using incident photons of a 40 keV3) and instudies of the separation of the orbital and spinmagnetization densities.4) In the former case theenhancement to the signal comes ii-em the increasedpenetration (up to ems) possible with high energy photons.Although the strengths of x-ray magnetic scatteringtechniques sometimes overlap those of neutron diffraction,they are generally complementary, and include high Qresolution, sensitivity to lattice modulations, small beamsize and useful polarization and resonance properties.

For these reasons, x-ray magnetic scattering studies ofthe magnetic structure of rare earth and actinide materials(including thin films) have ahnost become routine?-’) Arecent review of x-ray scattering studies of rare-earth metalshas been given by McMorrow, Gibbs and Bohr (1998).10)New kinds of experiments have been concerned with criticalproperties, characterized near magnetic orderingtransformations 1’12)and with the use of circularly polarizedincident beams.]3) In addition, these techniques have beenextended to surfaces and interfaces. 14’15) Very recently,

resonant scattering techniques have been applied to thedirect observation of orbital ordering in transition metaloxides. 16)

In the following, we briefly describe recent efforts toprobe long-ranged magnetic order at surfaces by x-ray and

17-26)follow~g many earlierneutron diffi-action techniques,studies by low energy electron diffraction.27) The mainmotivation has been to discover how bulk magneticstructures are modified near a surface, where the crystalsymmetry is broken. Some basic questions of interestinclude: Does the magnetization profile at the surfacefollow that of the electronic charge density? Does themagnetic critical behavior near a surface differ from that inbulk? What is the relationship between chemical andmagnetic interracial roughness?

Neutron diffraction has been the traditional probe ofmagnetic structure, and was first applied to surfaces byFelcher, et al.18)to obtain magneticdepth profiles of v~ious

materials using reflectivity techniques. Subsequently, Al-Usta et al.24)observed weak magnetic signals at glancinginci~ence in MnF2. Enormous, related progress has beenmade in studies of interracial magnetism through the use ofmultilayers (see e.g., ref. 12) although the interracial strainand bilayer coupling introduce additional complexities.

In this work, x-ray scattering studies of magneticordering have been carried out on the (001) and (1 11)surfaces of U02. 17’]9’20)The initial aim was simply toobserve a pure magnetic truncation rod (defined below) and,if possible, to then explore the near-surface magnetismdirectly. The motivation for choosing UOZ was two-fold:fwst, to take advantage of the large resonant enhancementsof the magnetic cross-section which occur when the incidentphoton energy is tuned near the uranium w absorptionedge.29) This work follows earlier observations of the

and complements magnetic circular dichroism studies,which are centered at zero momentum transfer.3031)

By way of background, UOZhas the face-centered cubicfluorite lattice and a triple-Q antiferromagnetic structure(T.=30.2K). The surface diffraction pattern consists of a setof rods of scattering (called truncation rods) which passthrough all of the allowed bulk Bragg points, and lie parallelto the surface normal direction.32) The variation of the x-rayintensities along the chemical truncation rods is determinedby the decay of the electronic charge density near thesurface, and may be used to model the surface structure.Magnetic truncation rods may be defined similarly, with theintensity variation now determined by the magneticstructure near the surface.26)

Scans of the (O1L) magnetic truncation rod taken alongthe surface normal direction of a U02(001 ) crystal areshown in Fig. 1 for temperatures increasing from 10 to 30.2r, I7)K.

I f

1.2I

(a) ~ o1OK

PI● 26K❑ 129K= 30.2 K

I

I Io 0.05 0.10 0.15 0.20

L [Units of c*] ‘

Fig. 1. Temperature dependence of the (O1L) magnetictruncation rods of U02 (001 ).

The L-dependence of the Iineshape is characteristic of atruncation rod of the chemical lattice with the peak atL=0.07 corresponding to the critical angle. Separateexperiments monitoring the energy and polarizationdependence of these profiles have shown that they arisefrom pure magnetic scattering. This is also consistent withthe temperature dependence of the scattering whichdecreases with increasing temperature, until it disappears atTN=30.2 K. Signal rates as high as 1000/sec have beenobserved at the critical angle using undulator and wigglerbeamlines. More exciting, recent improvements in actinidesurface preparation techniques 19)suggest that increases byas much as a factor fifteen are readily available!

Fig. 2 shows the temperature dependence of the magneticscattering intensity obtained at two positions along the(OIL) magnetic truncation rod, and at the bulk (001)reflection. *7)The discontinuity observed at T=30.2 K for

5 10 15 20 25 30 35

Temperature [K]

Fig. 2. Temperature dependence of the magnetic scatteringof bulk (001) reflection (closed symbols) and of the (O1L)truncation rod at two values of L. Inset: Log-log pilot ofthe rod intensity vs. reduced temperature.

the scattering at the (001) reflection is characteristic of bulkbehavior. In contrast, the magnetic scattering intensitiesobtained along the truncation rods fall more slowly to zeroas TN is approached from below-indeed, they appearcontinuous. This behavior is reminiscent of the generalphenomenon of surface-induced disorder, wherein apartially disordered layer of crystalline phase wets the near-surface volume below Tc and grows logarithmically inthickness as T approaches T..33) Similar results have beenobserved earlier in x-ray structural studies of the order-disorder transition in CUSAU,34)however, this is the firstsuch observation for a magnetic material. Within Landautheory, these theories predict that the temperaturedependence of the order parameter should follow a powerlaw in reduced temperature under specific conditions.3~)Fits of the magnetic scattering intensity to a power-law formare shown for two values of L by the solid lines in Fig. 2.The fits are satisfactory, and yield exponents increasingbetween (1/2) and 1, depending on L. This behavior isqualitatively consistent with surface induced disorderprovided the diffuse scattering at the interface is describedwithin the Gaussian approximation-which is a satisfactoryapproximation for these data.

Measurements of the magnetic specular reflectivity allowfurther insight into the interracial magnetic structure. Thisis illustrated in Fig. 3, which shows the pure magneticreflectivity obtained from a UOZ(OO1) surface in the

NOTICE

This report was prepared as an accoont of work sponsored by the United States Government.Neither the United States nor the United States Department of Energy, nor any of theiremployees, nor any of theircontractnmsubcontractor or their employees, makesany warranty,express or implied, or assumesany legal liability or responsibility for the accuracy, completeness,or usefulness of any information, apparatoq product or process disclosed, or represents that itsuse would not infringe privately owned rights. Reference herein to any specific commercialproduc~ process, or service by trade nam%tradema~ manufacture, or otherwise, does notnecessarily constitute or imply its endoraemen~ recommendation, or favoring by the UnitedStates Government or any agency, contractor, or subcontractor thereof.

Tbe views and opinions of authors expressed herein do not ❑ecessarily state or reflect those ofthe United States Government or U.S. Nuclear Regulatory Commission.

,:,

IMPLEMENTATION OF SEISMIC STOPS

IN PIPING SYSTEMS

P. Bezler, N. Simos, Y.K Wang

Brookhaven National LaboratoryUpton, NY

Februaxy 1993

.

Comrnonweaith Edison has submitted a request to NRC to replace the snubbers in the ReactorCoolant Bypass Line of Byron Station -Unit 2 with gapped pipe supports. llte specific supports intendedfor use are commercial units designated “SeismicStop< manufactured by Robert L. Cloud Associat-Inc. (RLCA). l%ese devices have the physical appearance of snubbers and are essentially spring supportsincorporating clearance gaps sized for the Byron Station application. Although the devices have anonlinear stiffness characteristic%their design adequacy is demonstrated through the use of a proprietarylinear elastic piping analysis code “GAPPLPE”developed by RLCA The code essentialityhas all thecapabilities of a conventional piping analysis code while including an equivalent linearization technique toprocess the nonlinear spring elements.

Brookhaven National Laboratory (BNL) has amkted the NRC staff in its evaluation of the RLCAimplementation of the equivalent linearization technique and the GAPPIPE code. Towards this endBNL performed a detailed review of the theoretical basis for the metho4 an independent evaluation ofthe Byron piping using the nonlinear time history capability of the ANSYS cmmputer code and by resultcomparisons to the RLCA developed result% an amessment of the adequacy of the response estimatesdeveloped with GAPPKPE. Associated studies included efforts to veri~ the ANSYS analysis results andthe development of bounding calculations for the Byron Piping using linear response spectrum methods.

...nt

CONTENTS

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6.

7.

Abstract . . . . . . . . . . . . .

Lkt of Figures and Tables

Executive Summmy

iNTRODUC’IION

METHODOLOGY

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METHOD AND IMPLEMENTATION REVIEW

VERIFICATION ANALYSES . . . . . . . . . . . . . .

A. ANSYSNon-Linear Analysis . . . . . . . . .. . . . .B. ANSYS Liiear. Analysis . . . . . . . . . . . . . . . .C. Follow On . . . . . . . . . . . . . . . . . . . . . . . . . .D. Observations . . . . . . . . . . . . . . . . . . . . . . . . .

ANSYS VERIFICATION ANALYSIS . . . . . . . . .

CONCLUSIONS

REFERENCES

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PROVIDED FOR STAFF REVIEW . . . . . A-1

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LXSTOF TABLES

Table 1Table 2Table 3Table 4Table 5Table 6Table 7Table 8Table 9

Figure 1Figure 2Figure 3Figure 4Figure 5Figure 6Figure 7Figure 8Figure 9Figure 10Figure 11Figure 12F~ure 13Figure 14F~ure 15Figure 16Figure 17Figure 18Figure 19Figure 20Figure 21Figure 22AFigure 22BFigure 23AFigure 23BFigure 24

Reactor Coolant Bypass Line Model Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . ..I2Comparison of Natural Frequency Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..13Seismic Stop Parameters ..,...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14No&l Displacements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...15Reaction Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...16Max. Pipe Stresses ofEach Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...18Max. No&l Displacements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...19Reaction Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Anchor Forces Comparison for Hovgoard Model . . . . . . . . . . . . . . . . . . . . . . . . . . .24

LISTOFFKWRES

Seismic Stop Pipe Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........o.o.~Force-Displacement Relationship of asymmetric Support . . . . . . . . . . . . . . . . . . . . . 26Example lConvergence, Stopll. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...27Example l, Piping System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..~Byron Station-Unit 2 Reactor Coolant Bypass . . . . . . . . . . . . . . . . . . . . . . . . . . ...29Byron Station-Unit 2RCS2RC19f14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...30SEX. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...31SSE Y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...32SUE Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...33SEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...34SSEY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...35SUE Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...36SSEXMAX PSD VALUE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...37SSEYMAX PSD VALUE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...38SSEZMAX PSD VALUE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...393D Piping System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...403DPiping System Gmputational Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...41Applied Forcing Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...42Spring Force Node 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...43Spring Force Node 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...44Spring Force No&l O. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...45Cantilever Beam Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...46Ground Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...46Displacement Tiie History Acceleration Input . . . . . . . . . . . . . . . . . . . . . . . . . . ...47Displacement Time Histo~ Force Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...47Displacement Time History Pseudo Force Analysis . . . . . . . . . . . . . . . . . . . . . . . ...48

v

EXECUTIVE SUMMARY

A request to allow the replacement of snubbers in the Reactor Coolant Bypass Line of ByronStation - Unit 2 with commercially produced gapped pipe supports was submitted to NRC ‘l%e.firnrnm.ci~lwomm~rtm;meQltmnn.tcav- ~eeium~tedag%;ctnkqtmmdf%mt-1Dre m~nasf.x.tawd hv Rnhar? T-—.., . . . . ~.yy..a y.y. “.yy. . w . . “ ..-.&A....-- ---—” .---y. ---- -. w CAS.-.wvww.w. ..U .J ..VVV.. “.

Cloud Associates, Inc. (RLCA). A description of the evaluations performed by Brookhaven NationalT .hnr.tnru (RNT ) tn acdet tha NRC ctnff tn r~crmnrl tn thic rm-m~et k nrmntd—. . . . . J \-& ‘-] ●V --=- ---- . . . . . w...= -v . 7--- -“ .-” . “y..-. . ~. —..—.

i%nnd nirw ~Imnnrt.a ran rmhme ninina viirati”nns hv limitina the amnlhwb nf frma vi%ratinnc fiu~-.-== -- =.y - ..-y~-- - — ------ ~.r--~ . . . . . . . . . -J ...-....~ --- -.-.r ----- ~. -- . . . . . . . . . .

Seismic Stops incorporate engineered gaps in mechanical devices to me@ this purpose. Although theserlw”ce.Qc+xhl%it nnnlimmr chamderi~kx RT rA hm ~~v~~q~~ ~ pK#~t&t ~~a_r ~!@c nininu anatvck------- -. —--- --- —-— -- —------- -= .—— - -— ~ -~ —~ —.J “-.

code, “GAPPiPE,” to demonstrate the design adequacy of the devices in piping systems. BNL performeda detafled review of the them-etical b~s1sfar G.A_PPmE. COde and in&pendent eW-&Iat~CMLSof the re.snmw+----- .—. —-. —.—. --. —-- --_r -—--

of the Byron Piping with gapped supports using nonlinear time histoxyanalyses and bounding linearre.soonse smztrurn..ana!yses.=.—- .’------

Based on the eva!uation~ it was COnc!udedthat Drorbedvde..imed Izarmedsunnort.. muld effective‘. -r.-., -.-–-w—–—~- ~= -— .—=K. ..- . . .-.— –_– _._. –-,txxttrol seismic motions. The GAI?PIPE code was determined to provide estimates of piping systemresponse with an accuracy consistent with the response spectrum methodology. Further: in reneral. the~-—.–..–,code can.be expected to provide consewative estimates of the time averaged support forces.

.

vi

1. INTRODUCTION equivalent linearization option.

The redesign and optimization of pipingsupport systems has received considerableattention in recent years. A primary aim ofthese redesign efforts is to reduce the number ofsnubbers used in the support system. Snubberreduction is desirable since it directly reducesthe time consuming and costly inspection andmaintenance operations required for snubberaand the likelihood of adverse system responseassociated with snubber malfunctions. Suchredesign efforts are referred to as snubberreduction programs.

One approach to snubber reduction is tosimply replace each snubber with an alternatesupport device. To be comparable to a snubbersuch a device must accommodate thermalexpansions while restricting excessiveseismicmotions. A passive device which has thesecharacteristics is a gapped pipe support. Ideallythe gap is large enough to allow free thermalexpansion while small enough to limit seismicmotions to acceptable levels.

Gapped supports made up of box framessurrounding the pipe but with a clearance gaparound the entire circumference are used infossil fuel power plants. Commercial unimdesignated “SeismicStop~” incorporatingclearance gaps sized for sp* appikatiox aremanufactured by Robert L. Cloud Asaociat%Inc. (RLCA) for use in the nuclear industry.llese devices have the physical appearance of asnubber (Figure 1), and are designed to allowpin to pin snubber replacement.

The adequacy of nuclear piping systems andtheir associated supports are typicallydemonstrated using linear elastic analysismethods. The gapped suppor4 however, is anon-linear element and its inclusion in a systemposes computational complexities. In order tomarket the seismic stop, RLCA has developed aproprietary linear-elastic piping analysis codewhich uses equivalent linearized properties tosimulate these restraints. The RLCA mde istitled “GAPPIPE” and essentially has all thecomputational capabilities of a conventionalpiping analysis mde while including the

Commonwealth Edison (CE) has submitted arequest to replace the snubbers in theByron/Braidwood units with seismic stops. Theactual calculations to determine the requiredsizes and number of restraints was performed byRLCA using the GAPPIPE coda BrookhavenNational Laboratory (BNL) has assisted the staffin its evaluation of the RLCA linearizationmethodology and the application of themethodology to the analysis of theByron/Braidwood piping systems with seismicstops Specifically,BNL performed a detailedreview of the theoretical basis for themethodology, a review of the implementation ofthe methodology in the GAPPKPE code anindependent evaluation of the Byron/BraidWoodpiping using the non-linear time historycapability of the computer program ANSYS, astudy to verify the non-linear capability of theANSYS code and bounding cakulations for theByron/Braidwood piping using the linearresponse spectrum option of the ANSYS code.

lle sections that follow provide a descriptionand summary of the BNL studies

2. GAPPIPE METHODOLOGYDESCRIPTION

lle GAPPIPE computer program is a fullfeatura ftite element piping amlysi$ code. Itwas developed by RLCA by expanding andmodifying the public domain structural analysiscode SAPIV. A key feature of the code is theincorporation of an analysis algorithm designedspecitlcally to allow the dynamic evaluation ofpiping systems with gapped supports using linearelastic response spectrum methods. Themethodology is called equivalent linearizationanalysis

In the method each gapped support orseismic stop in the mathematical model of thepiping systems is replaced with an equivalentlinear spring. lle stiffness of the equivalentlinear spring is determined by mkbizing themean difference of the support restoring forcebetween each equivalent spring and thecorresponding gapped spring. The mean

1

difference is an average over t@e across theresponse duration and is derived based onrandom viiration concepts. A summary of thedetailed formulations of the method asimplemented in GAPPIPE is provided in theUser’s manual for the code and is presented inthe foUowing.

Figure 2 shows the force-displacementrelationship of a symmetric gapped support.The gapped support has a stiffness equal to ~after the gap is closed. Let g be the gap sizq Fbe the support force as a function of the pipedisplacement L in the direction of the supporqKm be the equivident linearized stiffness to bedetermined by a minimization process. The

. following equation defines the difference, D,between the restoring forces of the gappedsupport and its equivalent linearized spring atany instance of time, t as

D@(t)) = F@(t))- g~t) (1)

where

k

“ when, lxI< g (2)fix) = ~(x(~ -g) when Ixl %

and I I denotes that the absolute values ofx be used.

For the case where the system is exhibitingquasi harmonic response the pipe displacementmay be expressed ax

x(t)

wheree = d +$(t)

= A(t)cd(3)

and tp is the phase angle.

In the abmq although the amplitude and :phase angle are time dependen~ they vary slowlywith time and are assumed to be constant over acycle.

The equivalent linearized stiffness isdetermined by minhhing the mean value of thesquare of the force difference, Eq. (1) over acycle. ‘l%emean square of the difference, D.over a qcle of vibration may be expressed a~

D.= ;@W)yd (4)

where T = 2 irfw

and the minimization requires

(5)

where kl is the linearized stiffnesscorresponding to quasi harmonic response andcan be seen as a constant over each cycle.

Using relations 1 and 4 Equation 5 provides

+J:[-m’)+%x’, d+ (6)

Incorporatkg relation (3), and realizing thatif d(t)= constan~ d6/dt=~, provides

J?- A Cod F(x) + k#2d 0 ]dO=O(v

●

which yielckx

for the equivalent linearized stiffness associatedwith quasi harmonic response.

During a seismiceven~ the pipe response is .not harmonic. Thus due to the randomne~ indisplacement amplitudes in dynamic response,the minimkmtionof the mean squared differenceneeds to be performed using the methods of

2

random vibration. The minimization process ktherefore, applied to the expectation of themean square difference rather than to the meansquare itself.

Although the pipe response is not harmonicover the duration of the seismic event it can beassumed to be quasi harmonic over each cycle inthe response and to have a different amplitudemagnitude associated with each cycle. ‘Iheresponse then would exhl%ita spectrum ofdisplacement amplitudes and frequencies.%

The expected value of the mean squareddifference can be expressed as

and minimizing this quantity with respect to theweighted average of the equivalent linearizedspring, Ku, over the time duration requires

If it is assumed that the response is astationary, narrow banded proc~ K.. can bedetermined using the value of D. given byequation 4. Using Equation 4 and replacing kl

with Km provides after differentiation withrespect to Km

d aDJ

(iKW = TE. + p’ [+ Jo’(-2dt)F(x)

(11)

+2KW Xlt))dqdt ● = o

Using equation 8 both expressions in thisequation can be expressed in terms of theamplitude dependent equivalent linear springconstant for one cyclekl(A) and the amplitude

(12)

%lving for Ku yields

or written in terms of the expectationoperator

Km =E [A2 kJ

E [A’1

(13)

(14)

Essentially this states that Km is theweighted average of lq(A) over all amplitudes A.

The calculation of Km is carried out bynumerical means in an iterative reamer untilconvergence in accor&nce with an acceptancecriteria ia achieved In general the procedurebegins aasuming that all linearized stiffnesses arezero as if the gapped -“smic stops are notpresent. ‘he pipe displacement responses atgap location are then calculated using theconventional reponse spectrum method. Basedon these respo~ a new set of linearizedstiffnesses are calculated using the linearizationprocedure described above. With this aew set oflinearized stiffnesses added to the piping .ystem,the reqcmse spectrum analysis procedurerepeats. The iteration continues until thechanges in the linearized stiffnesses for all gapsare within prescrii tolerances.

his procedure is outlined step-by-step in thefollowing

(1) Assume a null [Kw].(2) Add [Kw] to ~.(3) Perform the response spectrum analysis

to determine the maximum displacementamplitudes at gaps

(4)

(5)

(6)

Use the maximum displacementamplitudes to calculate a new [Ku].

Compare the old and new [KW]’Sto seeif the difference is within the prescribedtolerance for every gap. If alldifferences are within the toleranc~ thesolution is converged

If the tolerance is exceeded by at leastone gap, a new updated [Kw] iscalculated for use in the next iterationusing the followingformulrx

[Km Updated] = (l-b)[KW .m] + b[Kw -]where b is a convergence factor, b s 1

(7) Go to step (2) and process repeats.

The whole solution process is a repetition ofthe response spectrum analysis procedure. Thenonlinearity @embedded in the linearizationprocedure and the interaction between gappedsupports is inherently accounted for through theiterative solution.

3.METHOD AND IMPLEMENTATION

As the first phase of the evaluation a reviewwas made of the literature for the equivalentlinearization method It was found that. themethod had clearly been investigated by manyauthors (l-5). Of particular interest were thepapers by W.D. Iwan (5-7) of CALTE@L Headvanced applications of the method to estimatethe seismic response of systems supported bynonlinear elements using response spectrummethods. llte rhethod as implemented inGAPPIPE ($10) closelyparalleled theprocedures advanced by W.D. Iwan. Based onthe review, it was concluded that there was atheoretical basis for the metho~ it could provideacceptable approximations of system responseand its basic implementation in GAPPIPEfollowed the procedures recommended by arecognized researcher in the field

Although the opinion of the method wasessentially positive, several questions regardingits application to piping systems were raised.These were formulated and transmitted through

the project monitor to RLCA. The BNLconcerns were:

(a)

(b)

(c)

(d)

wiIl the iterative solution process remainstable when a large number of gappedsupports exist in the system,

conversely, is there a limit to how many .

gapped supports can be in a syste~”

what is the sensitivity of the solution .mode to the chosen acceptancetolerance and

if appropriate, would the solutionpredict or allow supports to remainopen.

Following the literature review a.vish waa-made to the RLCA oftlces in-Berkeley,California. A thorough review of thedevelopment and current status of theGAPPIPE code and the seismic stop concept.took place. In the course of the meetingdetailed infonpation dealing with the design-concept of the RLCA seismic stop and itsimpact on the nuclear industry, its mathematicalfoundation and its implementation ihto theGAPPIPE code were discussed. In additio~information on physical tests conducted withpiping systems incorporating seismic stops wasprovided These included results of the HDR-SHAG, HDR-SHAM, and RLCA/EPRI tests. Afull listing of the information provided ispresented in Appendix A.

Discussions and the information providedduring the visit“broughta resolution to each ofthe BNL concerns. Examples demonsttitingthat stable solutions were achieved for systemsincorporating numbers of seismic stops ofengineering interest were provided.

Figure 3 illustrates one such example. Itshows how the predcted or estimated value ofthe linearized spring constant (IQ and theresultant calculated value of the linearizedspring constant converge to a“value withiri theconvergence “toleranm. The illustration.corresponds to the wnvergence of one gappedelement in a piping system F~re 4,incorporating 16 gapped elements. Each cyclecm-responds to making,an estimate of ~ from

4

the prior results (shown by 0 symbol) andcalculating Kti corresponding to this estimatebased on a response spectrum solution for theentire piping system (shown as a + symbol).For the example shown, more than 50 iterationswere required to establish ~ for the .speci&elemenq and iterations would proceed untilconvergence within tolerance for all gappedelements was achieved

In the example% instances where theconverged solution corresponded to thecondition that a gap remained open were shown.As a practical matter, in such - the supportwould be removed from the t“utaldesign as itsinclusion in the system offered no benefit.

The complexity of the interaction is related tothe number of gapped supports in the system. Ithas been obsemxi that the number of iterationsto achieve convergence is proportional to thisnumber and computational time increasesaccordingly. Regarding the convergencecriterion, a tolerance of 10% of the linearizedstiffness is used. This criterion appeara toprovide estimates of piping system response withan accuracy consistent with that associated withresponse spectrum methods.

The physical tests for which results wereprovided were carried out over the years underthe sponsorship of RLCA and EPRI. ‘Ihey wereconducted to investigate seismic stopperforman~ demonstrate their capacity tocontrol vibrations and to allow a comparison oftheir performance to other seismic motionrestraining mechanisms. For most testscomputations using the GAPPIPE code weremade to demonstrate the adequaq of itsresponse predictions,

In the 1988 RLCAfEPRI tests the seismicresponse of a piping ~stem supported andexcited by a multi-story frame was investigatedllvo sequences of tests were conducted In one,the piping was restrained by snubbers andsupper% in the other it was restrained byseismic stops and supporta. The measuredresponses demonstrate that seismic stops provideas much control of system response as dosnubbers.

In the HDR-SHAG and HDR-SHAM tests apiping SYSkmin the shutdown HDR nuclearplant was subjected to operating level and highlevel simtdated seismic =Citations. In each testseries alternate support systems were used in asequential fashion to support and restrain thepiping. ‘Thesupport systems included a fkdde(SC@SYWUILa rigid (stiff) system incorporatingsnubbew a qstem using energy absorbers inplace of snubbers and a .ystem using seismicstops instead of snubbers For all testscorresponding analytical estimates of systemresponse were developed. The test results againdemonstrated that the seismic stops controlsystem viitions as well as other supportelements. The post tem analytical resultsdemonstrated that the estimates of systemresponse dewelopedwith GAPPIPE were asacxwrateas the estimates of system responsedeveloped for the other systems usingconventional analysis methods.

It was concluded after this review that theseismic stop represented an acceptablealternative to conventional restraint devic~that the equivalent Iinea&ation methodolo~was solidiybased and its implementation byRLCA in the GAPPIPE computer codeappeared theoretically correct and competentlyperformed

4.VERIFICATIONANALYSES

From the outset of the evaluation effort itwas intended that the performance ofindependent analyses to confirm the adequacy ofthe seismicstops in the proposed applicationwould be a major element of the evaluation.Further, it was also intended that theindependent verification be performed using thenon-linear time history capability of thecomputer program ANSYS. Using a recognizedcomputer axle in this applicatio~ it wasthough$ vmuld enhance the credllility of theverification analysis results and prechtde theird~editation if they were ur.tfhvorable.

‘fhe problem selected for the verificationstudy was the Reactor Coolant Bypass Line forByron Station-Unit 2. This is the exact line forwhich Commonwealth Ediin requestedapproval for the application of seismic stops. Asketch depicting the ~em and showing key

5

nodal points in the finite element model for thesystem is shown in Figure 5.

‘he system consists of 8 inch, 1 In inch, and3/4 inch SCH 160 type 304 stainless steel pipinglSystem pressure is 2425 psi while system”temperatures range from 12@’Fto 6180F withthe majority of the piping being at atemperature 55&F. The system includes onerefief valve, three check valves and four stopvalves. The system terminates at fiie anchorpoints and is supported by five rod hangers.The support system includes eight ieis!nic stopsreplacing thirteen snubbers to provide seismicrestraint.

The finite element model consists of 294 ~nodes and 379 elements. llte 8 inch pipeextends from node 203 to 235 the 1 1L2inchpipe from node 72 through node 180 to”node212 and the 314inch pipe, in two segmen% fromnode 7 to node 180 and from node 1 to node115. Anchors exist at nodes 1,7,72,203, and238 while vertical support is provided at nodes49, 102117, 162 and 171. ‘Ihe eight seismicstops are located at nodes 39, 44, 55, 98, 147,151, 157, and 170. The stops at nodes 55,98,and 170 provide restraint in the Z coordinatedirection, the one at 151 in the Y direction,those at 39, 147 and 157 in the X and Zdirections and the one at 44 in the X and Ydirections. A sununmy of model parameters arepresented in Table 1.

All key parameters of the finite model wereselected to be identical to those used by RLCAin their qualification calculations for this system.Towards this end BNL requeste@ and RLCAdid provide, a complete description of the finiteelement model used in their evaluations. TheGAPPIPE input file listing (SAP V format) forthe dead weight analysis for the system satisfiedthis request. The parameters extracted from thislisting included geometry, piping temperature,pressur~ section properties and weighg valvesection properties and weighg support stifb~orientation and gap characteristic.

To proof test the BNL model both a deadweight and natural frequency run were made.Table 2 provides a comparative listing of thenatural frequencies for the system. A can beseen, there is excellent agreement for the thirty

6

natural frequencies computed. Although notshown, the level of agreement between the BNLand RLCA estimates of displacements for thedead weight loading was also excellent. Theseresults substantiated that the ANSYS model wasan equivalent to the GAPPIPE model.

In the frequency determina tion abov% springshaving location and orientation identical to theseismic stops were included in the model. Thesesprings were assigned stifbsses equal to theestimates of linearized stiffness predicted byGAPPIPE. Given th@ the model test alsoassured that the lbcation and orientation of theseismic stops were correct. For the non-lineartime histoxy analysis with ANSYS these locationsand orientations were retained but the true gapand stiffness properties of the seismic stops weremodeled, A listing of the seismic stopparameters including the GAPPIPE estimate ofthe equivalent linearized stiffness is presented inTable 3.

‘Ihe next phase of the evaluation was todefine the time history forcing fimctiom The “evaluations performed with GAPPIPE wereenvelope response spectrum evaluations basedon N+ll damping and SSE input levels. Assuch, the loading was defined by three envelopeacceleration spectra for the three coordinatedirections, Figure 6. For the ANSYS analysistime history definitions of the systemaccelerations were required. Accordingly, arequest was made to RLCA for the timehistories cmrespondmg to the SSE spectra.Unfortunately, BNL was advised that the desired.time histories were not available.

.

.

To accimunodate the analysis needs synthetictime histories consistent with the SSE responsespectra were developed. This was accomplishedusing a modiEed version of the CAREScomputer code. The code was mod?kdspecificallyfor this evaluation to allow it to -accommodate the N411 definition of dampinginherent in the design spectrz ‘Ihe resultantsupport SSE acceleration time history recordsfor the three coordinate directions are shown inFigures 7,8, and 9.Aswillbenoted eachrecord is 15 seconds long and the peakacceleration levels are 1.01, 0.98 and 0.78 for theX, Y, and Z dwections respectively.

.

lltree checks of the adequacy of the timehistory records were performed. These includeda comparison of the spectra derived from thetime histoty records with the target (Byron SSE)Spectrz a determination of the power spectraldensity (PSD) cutves for the time histories and adetermination of the degree of correlation thatexists between the time histork

The comparison of sp=tra derived from thetime histories (the generated spectmm) and thedesign spectra are shown in Futues 10, 11, and12. As can be seen, the level of agreement isgood with the generated spectra exceeding thedesign spectra to only a nominal amount ‘IlePSD curves corresponding to the time historiesare shown in Figures 13, 14, and i5. As can beseen, there is content throughout the frequencyrange. Finaiii, the correlation calculationindicated the correlation coefficient between X-Y as 0.04, “betweenY-Z as 0.03 and “betweenX-2 as 0.003. In summary, the time histories werefound to “muncorreiate@ to have aczeptaidePSD’Sand to provide spectra which match thecieaignspectra to a satisfactory degree.

.,,... .* . ---- 3–, .—J .L. .- —--A c.. -,.. —w m me moaei ana tne rnpru Lorcmg

function defineq the last piece of input.—r——-–.:.—mmmauon mX@ring >~ecifkiiikm ‘w-astimdefinition of damping. In the response spectrum--l —.I_.:--- =1A+ 4 —-4-1 2- —-:-- .-.-- ..-->GarGUuruuus 11-A 1 rrluual rurrrlpurg wits Uacu.

That deftition of damping could not be used in.~- -__-_ --> A W1@V@ ___. L.-._ T_.A__A C-- .L _LUV ~1 UPUMXI till O 1 Cl ilUdlyMS. lllWCil+ LUI UK

non-linear analysis two Coefficient%a and /3,-.L:-l- -.. --.:C. --. -— -—-:-- -- - r..-.-:-- -cWUKU quiiuuly Sys!crrr dilrllprrg am a Lrrm.uurr U1

the system mass and stiffness matric~ must beJ..C-.-A Il... ..-.. CC-....*. -. . ..A d ..,----- “A-*-AUGUUCU. LUG WGALlbLGU~ U dUU ~ WG1 G X1=LCU

to match N-411 damping at the fkquencies of7.7 ~ and 20 ~. ‘his provided a reasonablebut not exact correspondence to N-411 dampingover the frequency range 7 through 30 ~ withthe ANSYS damping being greater than 5% atlower fhquencies and less than 2% at higherfrequencies. me selected values for a and /3were 4.8 and 0.0000143 respectively.

L ANSYS Non-Linear Analysis

With all model and forcing functionparameters define4 the non-linear time historyanalysis was performed. In the analysis thefollowing parameters and options were used. Asolution time step of 0.0005 sec. (should be

sufGcient to capture a 200 ~ event). TheNewmark implicit direct integration suMouoption with 6=0,5 and 6=0.25 (~numerical damping). The Newtott Rap&minitial stiffness optio% KAY(9)=3 (stifksamatrix is only reformed when the status of anygap element is changed). KEYOPT(3) - toone to account for the additional flexiMhy ofbend elements. The plasticity conve~criterion was set at 0.01. This criterioa &finesthe allowed global system force un~ aftereach iteration and was selected after ~ trialruns.

‘Theoutput results were quite ext~Selected displacements force and stres resultswitit comparisons to the correspondingGAPPIPE response spectrum results arepresented in Tabies 4, 5, and 6.

Tinedisplacement resuis Tatile 4, arepresented corresponding to each piping suctionas defined in Taiie i. For each sectiomd~lacements are presented for each node for.*. *wmcn a maximum displacement was prcsk$.ed in

the RLCA GAPPIPE solution. Maxinmma foreach coordinate diraiioit are presented h thetable the number in parenthesis is the--—-—-—J:-- ..- 1--- 4?-—— .I_- TIT -A —Ll.-. f--wrrcspuuuurg viuw Mum urG mA.A umard Uuu.As can be seen, the ANSYS and GAPPIPE_--.1.- --—----- ..--. --.. LL.-.-11 c-- .L- v --A v1 GMuui Wuq.mr G 1 mariuuauy WGU lUI LUG A arlu 1

coordinate directions but less well for tk Z--,.-A:--*- A:--..*:---1 ULUCILG Urr G+uuu.

T.t.l- c ------- . 1:.4: -- . . ●L..—---A Caulc’J plcsarm a Ilaullg UL LUG —

value of each component of reaction fau for. ..I. “..---+ .1.-.. * :. ●I.. -“.+.- p=G-U W~~L b GN21UGUL UJ LUG 0yCW2UA.

includes the five ancho~ the five rod ~ersand the eight seismic stops The cm-respmdingGAPPIPE estimates are listed in the cokmnheaded RLCA. For the seismic stops the RLCAestimates are impact forces computed W onthe cakulated disphwements at the stops and thetrue stop spring stiffnessea (i.e. not thelinearized approximations). A review of rktable will indicate that the degree ofcorrespondence between the ANSYS adGAPPPIPE results are poor. Except fcwtheseismic stopsj the ANSYS estimates of-ionforce exceed the GAPPIPE estimates of reactionforce by factors ranging from 50% to a order ofmagnitude. For the seismic stops the trcd isreversed with the GAPPIPE estimates exmeding

7

the ANSYS estimates by as much as a factor offive.

Table 6 completes the result presentationwith a summary of the maximum predicted pipestresses for each section. The stresses werecomputed as indicated with no correction forstress intensification. As with displacement@ thelisting is for those locations where the GAPPIPEcode predicted a maximum. A review of thetable will indicate that the correspondence ofresults is fair with the GAPPIPE estimate of thepeak stress exceediig the ANSYS estimate bylo%.

The great diiarity of reaction force resul~and in particular, the fact that the GAPPIPEestimates of these were so low, was a greatconcern. The ANSYS input data fdes weresearched in detail for errors but none werefound Discussions were held with the ANSYScomputer aid semice but they could onlyrecommend that the calculation be repeatedusing an entirely dtierent approach. The use ofdifferent computer codes was also considered.The last two options were rejected as they wouldrequire large new investments of resources whichcould not be accommo&ted. Finally, a copy ofthe ANSYS job deck was transmitted to theANSYS computer aid service for their review.

B. ANSYS Linear Analysis

Given the significant disparities noted it wasdecided to augment the ANSYS non-linearanalysiswith linear analyses performed using theANSYS model. In particular, two responsespectrum calculations were made. In onecalculation all the seismic stops were eliminatedfrom the model. In the other calculation, all theseismic stops were included with their stiffnessset to the closed gap stiffness. The twocalculations then bounded the operatingconfigurations of the seismic stops.

The results for the response spectrum runsare shown in Tables 7 and 8. Table 7 providesthe d~lacement results while Table 8 providesthe reaction force results. These tables alsoinclude a listing of the GAPPIPE and ANSYSnon-linear time history results presented earlier.In the table, the column headed RLCA are theGAPPIPE results, the column headed T.H. are

the ANSYS non-linear time history resulm thecolumn headed RSR are the response spectrumresults with all seismic stops closed, and thecolumn headed RST are the response spectrumresults with all seismic stops open.

A review of Table 7 shows that the tworesponse spectrum estimates of maximumdisplacement typicallybound or are inreasonable agreement with the GAPPIPE andT.H. results A revitnvof Table 8 shows thesame level of agreement between the responsespectrum estimates of reaction force and theGAPPIPE estimates for those forces. Theagreement with the T.H. esiimates of thereaction force are poor. In.many instances theT.H. estimates exceed the response spectrumresults by large amounts. The disparities are infact comparable to the d~arities noted etilierbetween the GAPPIPE and T.H. results andwhich were the source of concern. Theseresponse spectrum results lend Credl%ilityto theGAPPIPE results and d~edit the ANSYS non-linear analysis resul~ at least for the estimatesof support forces.

C Follow On

At a later date the ANSYS computer aidservice group advised BNL as follows:

a) A mn made using the BNL ANSYS filereproduced the BNL results includingthe high reaction force estimates.

b) Using a small subsection of the modeland the same computational parametersagain resulted in high reaction forceestimates.

c) Using the subsection model andprogressively smaller time step sizesproduced estimates of the reactionforces which were progressively smaller.

A reduction of the time step size by afactor of 250 produced a reduction ofthe original force estimate by a factor of100.

d) Based on the above, the time step usedin the BNL analysis was far too coarse.

8

\

e) The difficulty in part lies in the fact thatANSYS U* the-enforced grounddisplacement as input. Specification ofenforced displacements is notrecommended when using the NewmarkBeta method since this methodintroduces discontinuities inacceleration.

f) The model should be reordered tominimize the wavefront. Reorderingcould reduce the CPU time by a factorof 100.

D. Observations

The estimates of support force developed inthe ANSYS non-linear time histmy analysis arenot considered reliable. The reduction inintegration time step size apparently needed todevelop reliable results would burden thecomputing capacity at BNL and is consideredimpractical. The estimates of piping systemdisplacements and the resultant stressespredicted with this analysis are comparable tothose predicted with the response spectrummethods and may be more reliable.

The response estimates developed with thetwo bounding linear response spectrum analysesshow good agreement with the responseestimates developed with the GAPPIPE code.For many response quantities the GAPPIPEresult was bounded between the two responsespectrum estimat- For those instances wherethe GAPPJPE estimates fell out of the boundsof the two response spectrum solutio~ thecorrespondence between solutions were stillrelatively close. Tbe good correlation achievedin this phase of the study lend confidence in theadequacy of the GAPPIPE response estimates.

S. ANSYSVERIFICATION ANALYSIS

Owing to the poor response predictionsdeveloped with ANSYS it was decided toperform some analysis to verify the capability ofthe ANSYS non-linear time history analysisoption with gapped spring elements. A problemselected for this purpose was a threedimensional pipe bend supported by two anchorsand restrained by three gapped springs. lhisproblem was used by researchers at

Westinghouse (11), RLCA and BNL (12) to testanalysis options based on the pseudo forcemethod of analysis. The results developed bythe three organizationa were esaentialty identicaland can save as a benchmark.

A sketch of the system is shown in Fiiure 16.A computer generated isometric of the finiteelement model of the system is shown in Figure17. As shown, the three gapped springs arelocated at nodes 4, 6, and 10 and each acts in adifferent coordinate direction. The excitation isintroduced by three time vatying forces acting atnodes 4, ~ and 10 in line directions to close thegaps. The time history traca of the appliedforces are shown in F~e 18. The gap size andspring stiffness at the three gapped sptigs are0.250 in./2.OE+06 lb./in., 0.125 in./3.OE+06lb./ii. and 0.062 in./l.5 E+06 Ib./ii. for nodes 4,6, and 10 respectively.

The predicted spring force versus time foreach of the gapped spring elements are shown inFiiures 19, 20, 21. ‘Thesewere developed usingthe same time step (0.0000625) as was used inthe pseudo force test runs. Each figure shows infact two time history t- one correspondingto the ANSYS run and one corresponding to theBNL pseudo force m% overlayed on oneanother. As will be not~ very little indicationthat there are two traces is apparent indicatingthe good agreement of results achieved for thegapped spring forces.

Table 9 shows the corresponding comparisonfor anchor forces. The agreement for theseparameters is not quite as good. Difference inboth the times of peak Occurrence and themagnitudes of peaks is apparent. Although thedifferences are not great they may be indicativeof the type of disparity noted in the seismic stopanalysis. Unfortunately, the data base foranchor forces is only the BNL pseudo forceresults and their reliability as benchmark valuesis less clear.

In summary, for this problem the ANSYSestimates for gap spring forces are in excellentagreement with the “Benchma# results. Foranchor forces the agreement is only fair to g~but certainly much better than obtained in theseismic stop problem. The discrepanci~however, may indicate that one m“ght expect

9

larger disparities for more complex ~tems.

lle development of a solution for a secondsimpler, verification problem was also attempted.This problem was a cantilever beam who% freeend displacements are restricted by gappedsprings. TM problem was also one of the setuskd by several researchers to test, theirimplementation of the pseudo force analysismethod.

Figure 22 shows a sketch of the problem andthe ground acceleration loading function. The20 inch long beam was modeled with 20”equallength beam elements and 2 gapped springelements on each side of the beam ena asdepicted in Figure 22A. The material andstructural properties of the, beam were taken W,Young’s modulus, 30 x 106psi, Poison’s ratio,03; cross section, 2“ x 3“; moment of ineitix 2in4;and mass density of 0.0042 lb/st@ii. Thegap clearance was 05x 10S in., and the springstiffness was 2 x 1~ lb/ii. The excitation wasthe ground motion acceleration time hikorydepicted in Figure 22B.

Several attempts were made to develop asolution to this problem. In the ti attemp~the ground motion acceleration record was usedas input and the integration time step was takenas 0.00003125 seconk the value used byresearchers in the pseudo force investigations.Since poor results were achieved the initialattempt was followed by several more each witha finer integration time step, ending when a timestep 1/10 the origina~ or 0.000003125 Seconbwas used The results still being defkien~another tact was then followed In these newattempts the input excitation was defined as timevarying forces acting on each mass pokt withthe vahms of the force being derived from theacceleration record. This series of calculationswas performed for the same time step sizes asused in the initial series. Again, poor resukswere achieved. Efforts were concluded whencalculations with a time step reduced by anotherorder of magnitude yielded different results.

The predicted relative dwkicement withrespect to gxound at the cantilever free end forthe last and equivalent calculation in each seriesis shown in Figure 23, with the upper figurecorresponding to the acceleration input option

and the lower figure corresponding to the forceoption. Clearly, they are different. ‘The ,predcted d~lacement at the free enddeveloped with the pseudo force methtipresumably the correct solution, is shown inFigure 24. As can be seen, there is littleapparent correspondence between the solutionsdeveloped with ANSYS and the pseudo forceresult. Close examination reveals that the forceinput solution at least shows correspondence ofthe number of peaks and valleys in the solutionas compared to the pseudo force solution.

For this problem the verification a~emptswere all a failure. Possi%ly,if the attempts hadbeen continued with finer and finer integrationtime steps an improvement in results mighthave been achieved However, that option wasimpractical given the resources available.

This verillcation problem represented a closerparallel to the Reactor Coolant Bypass line thanthe first problem in that the forcing func$ion wasa ground motion acceleration time history.lltese poor results coupled with the poor resultsobtained for the bypass line may be indicative ofa deficiency in ANSYS for this mode okexcitation.

6. CONCLUSIONS

‘Ihe evaluation followed two phases; a reviewof the theoretical basis for the equivalentlinearization method and its implementation intothe GAPPIPE computer code”and verification ofGAPPIPE through confirrnatoiy analy~. It wasdetermined that the method had beeninvestigated by many researchers whoestablished a theoretical basis for the metho~explored its range of applicability and quantifiedthe accuracy to be expected in its application.The adequacy of its implementation “intotheGAPPIPE code was demonstrated by the facilitywith which the code could handle variousproblems and the coimspondence of its responsepredictions with test results. The confirmatoryevaluatio~ although compromised to some .

extent by the poor performanti in the non-linear calculational mode, confirmed that theGAPPIPE code did provide acceptable estimatesof system response.

10

Based on the evaluatio% the followingobservations and conclusions are made:

. Properly designed seismic stops (gappedsupports) can be as effective as snubbers incontrolling seismic motions.

. Acceptable estimates of the response ofsystems incorporating gapped supports can bemade using an equivalent Linearizationmethodology.

. ‘fhe implementation of the linearizationmethodology into the GAPPIPE computercode appeared correct and competentlyperformed.

. Response estimates developed withGAPPIPE should exhibit an accuracyconsistent with the response spectrummethodology.

. l%e support force estimates developed withGAPPIPE should be interpreted as timeaveraged approximations of these quantiti~

. Accurate estimates of instantaneous or peaksupport forces or support force estimates thatare in global equilibrium should not beexpected from GAPPIPE.

. In genera~ the method can be expected toprovide czmsewative estimates of supportforces.

7. REFERENCES

1. Caughey, T.K9 “Equivalent LinearizationTechniqu~” Journal of the Acoustical Societyof Ametia, Vol. 35, No. 11, 1963, pp. 1706-1711.

2. Iwan, W.D., “A Generalization of the Methodof Equivalent Linearization,” InternationalJournal of Nordinear Mechan@ Vol. 8, 1973,pp. 27%287.

3. Lute% L.DV and Takemiy~ H. “RandomVibration of Yielding Oscillator: J~/ ofthe Engineering Mechanics DivirionProceeding ASC& Vol. 100, No. EhQ Apr.1974, pp. 343-358.

4. Weu Y.K., ‘Method for Random Vibrationof Hysteretic System” Journal of EngineeringMechania &&&Wl Ptvceedin& ASCc Voi.IQ No. EhQ Apr. 197$ pp. 249-263.

5. Spanoq P.T. and Iwan, W.D., “On theExistence and Uniqueness of SolutionsGenerated by Equivalent Linearization“International Journal of Nonlinear Mechanics,vol. 13, No. ~ 197$ pp. 71-78.

6. Iwan, W.D., “Ibe Earthquake Design andAnalysis of Equipment Isolation Syste~”Eadquake Ehgineenkg and StructuralDynamkr, Vol. 6, 1978, pp. 523-534

7. Iwan, W.D., “Application of Non-linearAnrdysisTechniqu~” Applied Mechanics inEarthquake Engineering AMD-Vol. 3, ASWN.Y., 1974, pp. 135-162

8. Ck@ R.L, Andersom P.H., and Leung,J.S.M., “SeismicStops vs. Snubbers; AReliable Altemative~ Nuclear Engineaing and_ 107, 198&pp. 205-213.

9. Leun~ J.S.M., Tang, Y.K., Yang, M.SV

“Analysis of Pping Systems with GappedSupports Using the Response SpectrumMethod”.

10. RL@ GAPPIPE User Manual.

11. Molnar, AJw Vasl@K.M., and Gay, C.W.,“Application of Normal Mode Theory andPseudo Force Methods to Solve Problemswith Noxdinearities”,Journal of PressureVessel Technology, May 1976,pp. 151-156.

12. Bezler, P., PrachuktaW S., and Hartzman,M9 “Nordinear Dynamic Analysis of PipingSystem Using the Pseudo Force Method”,BNL-NUREG-27834, January 1980.

11

REACTOR COOLANT EYPASS LINE MODEL PARAMETER

2A.EL!U

PIPE SIZE # OF VERTICAL SEISMICSEC (INCHES) NODE FROM RANGE TO ELEMENTS ANCHOR SUPPORT STOPS

1 3/4 1 6a 67 1* 49- 39, 44855

2 1 1/2 68 120 53 72 117 98

3 3/4 121 177 ’57 7 171, 162, 151, 147,102 157, 170

4 1 1/2 178 202 25 I

“5 8 203 238 28 203,238

●

* Pipe node where support, anchor,. or se~smi.c stop is located.

, ,, 1

TABLE 2.

.

.

CowAuSoI”?OFNMmALmQuENcr8oImIorBFOBRBACTOBCOOLAN SYSTEM BYPASSLINE (LOOP4)CALCULATEDFROMTWODIFFBMNTComr12RPROGRAM

B.N.L B.C.L.A(ANsYs) (GAmPB)

MODE FRBQUBNCY(crcLBs/sBc)“

:3456.7a91011121314151617181920

z2324252627282930

5.0525.8406.2667.6237.7918.9909.77010.44911.05814.14814.69415.16015.91416.84617.47018.81319.28519.96620.24520.83721.40623.05623.84826.47828.69127.76729.84331.22532.44634.555

5.052~S.8406.2667.5387.8178.9909.77110.45811.06114.18614.70115.16715.92416.97917.47018.85419.32419.98920.27820.84221.41323.06123.87126.47826.6S627.76729.82631.22432.44734.570

.

13

..

TABLE 3

@EISMIC STOP PARAMETERS

NODE LOCATION SUPPORT STIFFNESS STOP STOP GAPPIPE4STOP CLOSED LEFT SIDE RIGliT SIDE LINBAR ESTINATE(LB,/INo) GAP (IN.) GAP (IhJa) (LB/IMs)

39 . 15,000 0.400 # 0.000” 1042

44 5,000 0.000 0.810 518

55 2,800” 0.000 1.250 200

98 5,000 0.000 0.910 421

147 15,000 10160 0.000 “ 1311 ~

151 15,000 0.000 0.100 1160

157 2,800 0.000 0.830 200

170 2,800 00000 le384 246’

*

* ‘ .

. .

.

.

.

.

TABLE4 - NODAL D1SPTJ4CEMENTS (IN .)

SEC NODE x Y z

1 47 0.84 (0.92)*

45 0.13 (0.14)

58 0.95 (0.78)

2 100 0.49 (0.50)

105 0.05 (0.1)

105 0.95 (0.35)

3 161 0.60 (0.52)

121 0.12 (0.20)

155 0.63 (0.45)

4 183 0.25 (0.22)

188 0.15 (0.13)1.01 (0.37)

177

5 221 0.13 (0.14)

217 0.11 (0.10)

220 0.17 (0.16)

* Max. nodal displacement (in inches) values in parenthesis areRLCA results.

15

. ..

TABLE 5 ‘- REACTION FORCES(lbs. or in./lbs.)

TYPE NODE COMPONENT RLCA BNL

ANCHOR 1 ‘x 76 2,229’

xx 548 728

Y 3,20 179

YY. 3,402 7,501

z 91 265

Zz 4,695 6,027.

ANCHOR 7 x 82 846

xx 4,098 4,385

Y. 133 3.45

YY 3,376 6,666

.. z 34’ 1,950

Zz 2;8S7 2,220

ANCHOR ,72 x 119 2,407

Y’ 119 2,045

z 134 2,003

xx 4,920 17,130

YY 4,890 7,025-

Zz 6,130 21,660

ANCHOR 203 x 2,615 115,100

Y 3,091 28,540

z 1,494 110,80,0

xx 167,373 493,600

YY 152,435 890,200

Zz 132,556 540,900

.

.

16

.

.

.

BLE S REACTION FOR ESc(lbs’.-or in./lbs. )

TYPE NODE COMPONENT RLCA BNL

ANCHOR 238 x 3,328 34,730

Y 5,018 11,530

z 3,862 18,940

xx 177,701 177,800

YY 383,289 521,500

Zz 335,763 471,100

VERTICAL 49 74 340SUPPORT

102 163 503

117 316 412

162 35 ‘“ 182

171 111 427

SEISMIC STOP 39 506 91

44 407 113

55 453 181

98 618 470

147 208 134

151 116 158

157 267 148

170 452 281

17

.

TA BLE 6 - MAX. PIPE STRESSES OF EACX SECTION

.

SEC IELEMENT NUMBER STRESS (Icsi)

BNIJ

II STRAIGHT PIPES1 I i

r

1 67J 18.5 I 22.6

2 1121 10.8 9.4

1 3 I 177J I 20.7 I 22.s

1 4 I 1941 I 15.8 I 10.8

I 5 I 235J I 14.1 I 9.3

ELBOWS

2 101 16.8 I 15.8

2 95M 10.5 8.2

,3 145M 10.7 “13.1

4 193ti 18.0 10.8

5 2091 9.6 3.2

stress intensification

s = (M$ + M+ +“ M=2)1f2

z

factor applied.

.

18

. ● * .

LE 7 MAX . NODAL DISPLA CEM~TS (IW

.~OOKHAVEN NATI ONAL LABORATOR~

SEC NODE COMPONENT RLCAm’ Kdl W

1 47 x 0.92 .84 0.33 0.88

45 Y 0.14 .13 0.12 0.74

58 z 0.78 .95 0.54 1.09

2 100 x .50 .49 0.53 0.65

105 Y .10 .05 0.35 0.06

105 z .35 .95 0.11 1.40

3 161 x .52 .60 0.34 0.83

121 Y .20 ● 12 0.17 0.2

155 z .45 .63 0.53 1.0

4 183 x .22 .25 0.22 “ 0.21

188 Y ● 13 .15 0.13 0.13

177 z .37 1.01 0.09 1.51

5 221 x 014 ,13 O*14 0.12

217 Y ● 10 .11 0.1 0.1

220 z .16 .17 0.17 0.16

.

.

TYPE

ANCHOR

ANCHOR

TABLE 0 - REACTION FORCES

NODE

1

7 ‘

COMPONENT

x

“Y

z

xx

YY

Zz

x“.“

Y

i

xx

YY

Zz

(lbs. or in.\lbs. )

RLCA

76

120

91

548

3,402

4,695

82

133

34

4,098

3,376

2,857

BROOKHAV

T.H.

2,229

179

265

728

7,501

6,027

e46

145

1,950

4,385

6,666

2,220

1 NATIONAL LABORATORYI

142 I i55

54 I 136

589I

458

1,843’ I5,700

87 I 159

87 I 200

2,468I

5,720

3,463I13,285 “

2,196 I 2,937

* * >

* .

‘YPEIN*DE IC*MP*NENT

ANCliOR 72 x

Y

z

xx

YY

Zz

ANCHOR 203 x

Y

z

xx

(lbs.or in./lbs.)

-.,

RLCA

119

119

134

4,920

4,890

6,130

2,615

3,091

1,494

167,373

152,435

132,556

PR00K~

T.H.

2,407

2,045

2,003

17,130

7,025

21,660

115,100

28,540

110,800

493,600

890,200

540.900

RSR

144

122

150

5,865

5,355

6,510

2,546

3,007

1,496

105,400

149,000

130,600

171

184

273

7,216

11,050

9,250

2,005

2,416

1,492

142,840

125,594

106,103

..

m“IQ

TA BLE a - REACTION FORCES(lbs. or i.n./lbs.)

‘#

TYPE NODE COMPONENT RLCA BROOKHAVEN NATIONAL LABORATORY

T.H. RSR RSF

ANCHOR 238 x 3,328 34,730 3,294 2,980

Y.’ 5,018 11,530 5,007 4,776

z 3,862 18,940 3,826 .3,746

xx 177,7Ql 177,800 177,600 166,994 “

YY 383,289 521,500 379,600 365,677

Zz 335,763 471,100 33.3,600 296,811

VERTICAL 49 Y 74 340 62 66SUPPORT

102 Y 163 503 181 154

117 Y, 316 412 280 314

162 Y 35 182 39 75

171 Y 111 427 102 163

1 ,

.

.

., ,

a REA TI N FORCESbs.-or fn./?bs.)

TYPE NODE COMPONENT RLCA j3R00KHliVEN NATIONAL LAB ORATORY

T.H. RSR RSF*

SEISMIC 39 x&Y 506 91 92 0STOP

44 x&Y 407 113 103 0

55 z 453 181 144 0

98 z 618 470 387 0

147 x&z 208 134 202 0

151 Y 116 158 100 0

157 x&z 267 148 101 0

170 z 452 281 198 0

* The spring elementsare removed in this case,

iMULL Y “,

.

ANCHORFORCE$ COMP~SON F R H(IVGOAo RD MODEL

PSEUDO FORCE METHOD ANSYS

ANCHOR NODE FORCE COMP. VALUE TIME (SEC) VALUE TIME (SEC)

1 FX ,. 1.72E6 0.275 1.80E6 0.283

Ff 1.17E6 0.231 ‘ 1.3oE6 0.101

FZ 0.57E6 0.262 0.59E6 0.216

MX 0.07E6 0.193 0.09E6 0.271

MY 0.67E6 0,,156 0.79E6 0.216

~z 1.56E6 0.231 1.71E6 0.101

12 FX 1.07E6 0.2 1.25E6 0.203

FY 0.65E6- 0.268 0.88E6 0.224

FZ’. 1005E6 0.193 1.09E6 0.261

MX 0.19E6 0015 1,19E6 0.224

MY 1.39E6 00193 1.64E6 0.277

Mz 100E6 0,268 0.21E6’ 0.246—-

.

,

, , ,

SEISMIC STOP PIPE SUPPORT

DESIGN DESCRIPTION.

/

/

2/43

,lwmr 07/08a5KJ -w

RobutL auwf&Assudut4?%k

\

I-

r ~—

I,’

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Figure 2 Farce-Displacement Relationship of ASymmetric Gapped Support

.

.

26

,.

.

0x\

0035

0.3

0.25

0.2

0.15

0,1

0,05

EXAMPLEI CONVERGENCE, STOP 11KG=1OO,OOOLBS/lNCH

1 1 1 A 1 Ill 1 1 I 1

“

0.52 0,56 0.6 0,64 O*68 0,72 0,76 0.0

DISPLACEMENT (INCH)

. .

.

0:s

.-,,

.

28

.

.

.1-/ .

.,

29

R4V&WPl! = NORTI1-SOLM1—.3.5

3.0- (7

2.s “

2.0

\1.s

1.0

0.5/

0.0, 1 ,0 -w

m2Qusr4ff(Ilz)

BYRON UNIT 2 - RCSFIGURE 6

40

2RC19/04

.

30

x.

umm

ZI

5q--—I

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i

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(3 ) No I luwlmw

31

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66”0 99”0

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‘G

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LEGEND

GENERFITEOSPECTRUM#

.DESIGN SPECTRUM........................................*...........

,,

,’ ,.

,, ::.;**:,:,

1 I i I 1 i I I I t I s I 8 I I I I 1

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FIGURE 10,

*. .

a .

aa

nm

C.9u

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v .

ITER. NO. 5

LEGEND

GEtW?fiTEOSPECTRUM

DESIGN SPECTRUM....................................................

\,.“*“.*:;●. . .

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ff?EOUENCY(HZ)10’

FIGURE 11

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GENERRTED SPECTR(JIM.———————DESIGN SP,ECTRUIM P

1

................................................................

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~-l——— -r--r-l-l-f-y I I I I I I n~—— -—l—— 77“1 1C)a 10’

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umm

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FIGURE 16

40

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AFPLIED”FORCING FUNCTIONS

.

SEC

FIGURE18

42

— —— —

l’”

NT.0.400E+0

0.360E+0

0.320E+0

o.280Rl+o

0.240E+0I

0.200E+

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400000

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SPRING FORCE NODE 4

0

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ANsnSW 30 .14:353 -PLOT NPOS?26

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r“*. ——-—-— - .-—_—.——.—.—— ————-—-—-----.————.——1-—.. — - — — —— -—. — -—. ----- .- ---- ~—— —- —-— ——- —.-.

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<-”____-- —-4i

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FIGURE 21

$PRING FORCE NODE 10

WC.m I I Io I 0.0s I km I o,2d I 0.32 I 0.9

.. .. . . ...——— —.. ———— --—— ----- —— . —.-.-. —.- —— --- .- —-.— --------

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FIGURE22A,DISPLACEMENTTIMEHISTORY, ACCELERATIONINPUT

.0 :sJs. *g V*E

# ●*S I 9.-7s 1 ~.,, I :..,:s

●

FIGURE236,OISPLACEI’+ENT

● .W*ZS ● .00*?s ●.01;2s

TIMEHISTORY,FORCEINPUT

47

n

..

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isplacement

1

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—, —, .

—

}

—

—

—

—

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. .

...

.-●

✎

i

PACKAGES OF INFORMATION PROVIDED

A.

B.

c.

D.

E.

F.

G. ‘

H.

I.

J.

FOR STAFFREVIEWOF COMPUTER PROGRAM - GAPPIPE

GAPPIPE User Manual and instruction for using GAPPII?E on thesystem.

RLCA VAX Computer

CECO PipingApplicationcalculationPackage, including piping description, model dam andGAPPIPE input/output listings (RLCA &lC. No. P182-1/112Rev. A).

sHDR S~G post-test analysis data fdes and calculation reports on the comparison of GAPPiPEanalysis results with test data for both Seismic Stop and Snubber support configurations.

Preliminary HDR-SHAM post-test calculation reports. (RLCA Calc. No. P101-1OL21Draft).

Copy of SHAM post-test technical paper by C. Kot, et al, at the 16th Water Reactor SafetyMeeting (taken from NUREG/CP-0097).

RLCA calculation”reportontheimplementationofNonlinearTimeHktoryAnalysisusingthePseudo-force Method in GAPPIPE (RLCA Calc. No. P94435).

ANSYS model data and analysis comparison with the 19S5 RLCA/EPRI Shake Table Tests.

Data plots of snubber and Seismic Stop responses from the 19SSRLCA/EPRI Shake TablePiping System Tests.

Input/output printout and plots of GAPPIPE analysis of sample piping systems illustrationsolution convergence and gap behavior.

Copy of ASME/PVP paper on the Pilot Study of Seismic Stop Pipe Supports at Millstone Unit 3.

e

A-1