IMPLEMENTATION OF SEISMIC STOPS IN PIPING SYSTEMS Fg J .

1.equivalent linearization option.INTRODUCTIONCommonwealthEdison (CE) has submittedaThe redesignand optimizationof pipingrequest 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 rode. BrookhavenNational Laboratory (13NL) 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 GAPPIPE code, aniud&pendent evaluation of the Byron/Braidwoodpiping using the non-linear time histoVcapability of the computer program ANSYS, astudy to veri& the non-linear capability of theANSYS code and bounding calculations for theByron/Braidwood piping using the linearresponse spectrum option of the ANSYS code.support 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 snubbersand 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 excessive seismicmotions, A passive device which has thesecharacteristics is a gapped pipe support. Ideallythe gap is large enoughto allowfree thermalexpansion while small enough to limit seismicmotions to acceptable levels.The sections that follow provide a descriptionand summary of the BNL studies.Gapped supports made up of box framessurrounding the pipe but with a clearance gaparound the entire circumference are used infossil fuel power plants. Commercial uni*designated “Seismic StopS” incorporatingclearance gaps sized for specific applicatio aremanufactured by Robert L. Cloud Associat%Inc. (RLCA) for use in the nuclear industry.These devices have the physical appearance of asnubber (Figure 1), and are designed to allowpin to pin snubber replacement.2. GAPPIPE METHODOLOGYDESCRIPTIONThe GAPPIPE computer program is a fullfeatur@ finite element piping analysis code. Itwas developed by RLCA by expanding andmodifyiig the public domain structural analysiscode SAPIV. A key feature of the code is theincorporation of an analysis algorithm designedspecifically to allow the dynamic evaluation ofpiping systems with gapped supports using linearelastic response spectrum methods. Themethodology is called equivalent linearizationanalysis.The adequacy of nuclear piping systems andtheir associated supports are typicd.lydemonstrated using linear elastic analysismethods. The gapped suppor 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 code istitled “GAPPIPE” and essentially has all thecomputational capabilities of a conventionalpiping analysis code while including theIn the method each gapped support orseismic stop in the mathematical model of thepiping systems is replaced with an equivalentlinear spring. The stiffness of the equivalentlinear spring is determined by mininMng themean difference of the support restoring forcebetween each equivalent spring and thecorresponding gapped spring. The mean1

The equivalent linearized stillhess isdetermined by ninimkhg the mean value of thesquare of the force difference, Eq. (1) over acycle. The mean square of the dtierence, D.over a cycle of vibration may be expressed axdifference is an average over time 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 following.(4)Figure 2 shows the force-displacementrelationship of a symmetric gapped support.Tle gapped support has a stiffness equal to 1 ,after the gap is closed. Let g be the gap siz Fbe the support force as a functionof the pipedisplacemen % in the direction of the suppo Kn be the equivalent linearized stifrness to bedetermined by a minimization process. ThefoUowing equation defines the dtierence, D,between the restoring forces of the gappedsupport and its equivalent linearized spring atany instance of time, t asD@(t)) F@@)) - Ii&r(t)and the minimizationrequireswhere klisthe linearized stiffnesscorresponding to quasi harmonic response andcan be seen as a constant over each cycle.(1)Using relations 1 and 4 Equation 5 provideswherem and Ix be used“ when 1 g:(tit)When lxI gk(2) -g)Jo’r- (’) w’]dt o(6)Incorporatingif d(t) constankI denotes that the absolute values ofJfi0For the case where the system is exhibitingquasi harmonic response the pipe displacementmay be expressed relation (3), and realizing thatd8/dt u, provides- A Co& F(x) k&2cot? 0 ]d&O(7)which yields(3)X(2) A(t)cosewheree (A (t)for the equimlent linearized stiffness associatedwith quasi harmonic response.and # is the phase angle.During a seismic even the pipe response isnot harmonic. Th due to the randomness indisplacement amplitudes in dynamic response,the minimization of the mean squared differenceneeds to be performed using the methods ofIn the abov% although the amptitude andphase angle are time dependen they vary slowlywith time and are assumed to be constant over acycle.2

random vibration. The minimization process ktherefore, applied to the expectation of themean square difference rather than to the meansquare itself.Althoughthe pipe response is not harmonicover the duration of the seistnicevent it can beSolving for Km yieldsassumed to be quasi harmonic over each cycle inthe response and to have a dtierent amplitudemagnitude associated with each cycle. Theresponse then would exhibit a spectrum ofdisplacement amplitudes and frequencies.TJh k1A2dtT To(13)Km Iim TA2&T-M TofThe expected value of the mean squareddifference can be expressed asor written in terms of the expectationoperatorKm and mhimhing this quantity with respect to theweighted average of the equivalent linearizedspring, Km, over the time duration requiresdKmEssentially this states that Km is theweighted average of kl(A) over all amplitudes AThe calculation of Km is carried out bynumerical means in an iterative manner untilconvergence in accordance with an acceptancecriteria is achieved In genera the procedurebegins assuming that all linearized stiffnesses arezero as if the gapped seismic stops are notpresent. The pipe displacement responses atgap location are then calculated using theconventional reponse spectrum method. Basedon these respons% a new set of linearizedstiffnesses are calculated using the linearizationprocedure described above. With this new set oflinearized stiftlesses added to the piping system,the response spectrum analysis procedurerepeats. The iteration continues until thechanges in the linearized stiffnesses for all gapsare within prescribed tolerances.“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 klwith Km provides after dtierentiation withrespect to Kw(11) xmXqt))dz]dt (14)E [A”J(lo)d EfDJ E [A* kl]This procedure is outlined step-by-step in thefollowing “o(1)(2)(3)Using equation 8 both expressions in thisequation can “be exprkssed in terms of theamplitude dependent equivalent linear springconstant for one cycle &l(A) and the amplitude3Assume a null [Kn].Add [Kn] to .Perform the response spectrum analysisto determine the maximum displacementamplitudes at gaps

(4)Use(5)Compare the old and new [Kw]’s to seeif the difference is within the prescribedtolerance for every gap. If alldtierences are within the tolerances, thesolution is converged.(6).the project monitor to RLCA.concerns wertxthe maximum d iacernentamplitudes to calculate a new [Km].If the tolerance is exceeded by at leastone gap, a new updated [Km] iscalculated for use in the next iterationusing the following formula[I& Updated] (l-b)[KW .D] b[Kw -]where b is a convergence factor, b s 1(7)The BNL.(a)will the iterative solution process remainstable when a large number of gappedsupports exist in the system,(b)conversely, is there a limit to how manygapped supports can be in a system,(c)what is the sensitivity of the solutionmode to the chosen acceptancetolerance an (d)if appropriate, would the solutionpredict or aliow supports to remainopen.Go to step (2) and process repeats.Following the literature review a visit wasmade to the RLCA offices in Berkeley,California. A thorough review of thedevelopment and current status of theThe whole solution process is a repetition ofthe response spectrum analysis procedure. ‘Ihenonlinearity is embedded in the linearizationprocedure and the interaction between gappedsupports is inherently accounted for through theiterative solution.GAPPIPEcode and the seismicstop concepttook piace. In the cmurse of the meetingdetaiied information cleating with the designconcept of the RLCA seismic stop and itsimpacton the nuclear industry,its mathematical3. MliiTHOD AND IMPLEMENTATIONfoundation and its implementation into theGAPPIPE code were discnssed. In addition,information on physical tests conducted withpiping systems incorporating seismic stops wasprovided. These included results of the @RSHAG, HDR-SHAM, and RLCA/EPRI tests. Afull listing of the information provided ispresented in Appendix A.As the first pha

piping systems with gapped supports using linear elastic response spectrum methods. The methodology is called equivalent linearization analysis. In the method each gapped support or seismic stop in the mathematical model of the piping systems is replaced with an equivalent linear spring. The stiffness of the equivalent