NUREG/CR-6128 BNL-NUREG-52396 II I IImI IIII I I Iea I III I 11 II I I I Piping Benchmark Problems for the ABB/CE System 80 + Standardized Plant li IHI III II III IImI I I II I IIll II ",:r_ i?i" Manuscript Completed: May 1994 1.te Published: July 1994 Prepared by EBezler, G. DeGrassi, J. Braverman, Y. K. Wang Brookhaven NationalLaboratory Upton, NY 11973-5000 Prepared for Division of Engineering Office of Nuclear Reactor Regulation U.S. Nuclear Regulatory Commission Washington, DC 20555-0001 NRC FIN E2024 orr,ls,ocuMrEsU_,TUMi_ n ,, ABSTRACT To satisfy the need for verification of the computer programs and modelin_ techniques that will be used to perform the final piping analyses for the ABB/Combustion Engineering System I_0+ Standardized Plant, three benchmark problems were developed. The problems are representat/ve p/ping syst,;ms subjected to representative dynamic loads with solutions developed using the methods being proposed for anal_sis for the System 80+ standard design. It w/Ube required that the combined license licensees demonstrate that their solutions to these problems are in agreement with the benchmark problem set. o.o m CONTENTS PAGE ABSTRACT ........................................................................ iii LISTOF FIGURES AND TABLES ...................................................... vi EXECUTIVE SUMMARY ............................................................. vii 1.0 INTRODUCTION .............................................................. 1 1.1 Purpose ...................................................................... 1 1=2 Background ...... 1 13 BenchmarkProgramOverview ...................................................... I 2.0 PROJECT BACKGROUND ....................................................... 3 2.1 Mathematical Background ......................................................... 3 2.1.1 Uniform SupportMotion Response Spectrum Analysis .............................. 3 2.1.2 Modal Superposition T'nneHistoryAnalysis ...................................... 5 2.1.3 Direct IntegrationT'nneHistory Analysis........................................ 5 22, Input-Output Format ............................................................. 6 3.0 DESCRIFHON OF PIPING BENCHMARK PROBLEMS ............................... 11 3.1 BenchmarkProblem 1 ........................................................... 11 32 BenchmarkProblem 2 ........................................................... 14 33 BenchmarkProblem 3 ........................................................... 14 4.0 BENCHMARK ACCEPTANCE CRITERIA .......................................... 23 5.0 CONCLUSION .............................................................. 27 6.0 REFERENCES ............................................................... 29 APPENDIX A UNITS OF MEASURE .................................... '......................... A-ill BENCHMARK PROBLEM 1 -UNIFORM SUPPORT MOTION RESPONSE SPECTRUM ANALYSIS .. A-1 BenchmarkProblem 1-Lower Frequency Amplified Response ............................... A-13 BenchmarkProblem 1-HighFrequency Response (Rigid Response) .......................... A-39 BenchmarkProblem 1-Total R_nse ............................................... A-63 BENCHMARK PROBLEM 2 -DIRECT INTEGRATION TIME HISTORY ANALYSIS ............ A-73 BENCHMARK PROBLEM 3 -MODAL SUPERPOSITION TIME HISTORY ANALYSIS .......... A-159 LIST OF FIGURES PAGE Figure 1 Sign Convention for Forces and Moments ........................................... 8 Figure2 Feedwater Line ............................................................. 12 Figure3 F_dwater Line Isometric ...................................................... 13 Figure4 F_dwater Mode Shapes ....................................................... 15 Figure5 Pressurizer Surge Line ........................................................ 16 Figure6 Pressurizer Surge Line Isometric ................................................. 17 Figure7 Pressurizer Surge Line Mode Shapes .............................................. 18 LISTOF TABLF_ Table 1 Fe_dwater Piping Modal Analysis Results .......................................... 19 Table 2 Pressurizer Surge Line Piping Modal Analysis Results .................................. 20 Table 3 Acceptance Criteria .......................................................... 24 Table 4 Piping Segments ............................................................. 25 vi EXECIn'IVE SUMMARY The NRC staff has identified pipingandpipe support designas one technical areawhere engineering information in sufficient detail can not be provided for the ABB/Combustion Engineering System 80+ standard designto allow the staff to make a finalsafety decision under therulesof 10 CF, Part52. Forth/s andsimilar areas the staff willuse design acceptance criteria(DAC) verified byinspections, tests, analyses, andacceptance criteria(ITAAC) to enable the final safe_ determination. One element of the piping DAC requiresthe combined license (COL) licensee to verifythe sufficiencyof the computercodes andmodeling techniques to be used to complete its piping stress analyses. To provide the basisfor thisverification, the staff developed aSystem 80+ specific piping benchmarkprogram. The COL licensee willbe requiredto develop solutions to the benchmark problems andto demonstrate that those solutions meet the acceptance criteriaspecified in this benchmark program report. The benchmark program consists of three piping problems involvingtwo piping systems representalive of the System 80+ design. One system represents aportion of the Main Feedwater Line andthe other represents the Pressurizer SurgeLine. The problems provide analytical benchmarksfor three analysismethods, the uniform supportmotion response spectrum analysis method, the modal superposition time historyanalysis method, and the direct integration time historyanalysismethod. The response spectrum method andthe directintegration time history methods are applied to the Feedwater Line while the modal superposition time historymethod is applied to the SurgeLine. Inall analyses the excitation functions are representative for the System 80+ standard design. This report presents the benchmarkproblems andincludes all the informationneeded bythe COL . licensee to perform the analyses andevaluate the results. Acceptable analysis methods will estimate natural frequencies to within2%, maximumpipe moments to within5%,and supportreactions andmaximum displacements to within 10%of the benchmark results. A COL licensee having demonstrated this level of accuracymay use the benchmarked analysismethod without furtherreview. In instances where some deviations from the acceptance criteria occur,the results andjustification for suchdeviations shallbe documented and submitted to the staff for review andapprovalbefore initiatingpiping qualification analyses. vii L0 INTRODUCTION commitments was toverify the pipinganalysis modeling andthe computer code to be used bythe I.I Purpose COL licensee to complete its pipingstress analysis. The COL licensee willverify the sufficiency of the This report describesthe NRC benchmark computer code andmodeling techniques in programfor the verification of computer programs conjunction with the DAC. The NRC found this thatwill be used bycombined Hcense (COL) commitment acceptable providedthat the computer licensees to complete the design andanalysis of program and the modeling techniques willbe pipingsystems in the ABB/Combnstion Engineering evaluated using the NRC benchmark program. The (ABB/CE) System 80+ Standardized Plant. It staff concluded that once the COL licensee provides detailed descriptions of the benchmark successfal_ completes the DAC verifyingthat the problems including geometries, material properties, piping benchmark results arewithin the acceptable analytical methods, input loads and solutions. The range ofvalues specified inthe benchmark program, report also prov/des the acceptance criteriawhich there is reasonable assurance that the computer mustbe met to demonstrate thatthe COL licensee's code and analyticalmodeling techniques to be used solutions to the benchmark problems are acceptable to complete the System 80+ piping design and to NRC. analyses are adequate. 1.2 Background 1.3 Benchmark Program Overview In reviewing the design certification application The benchmarkprogram requires the COL for the ABB/CE System 80+ under the rulesof 10 licensee to construct mathematical models and CFR Part 52, Reference 1,the NRC staff identified perform dynamicanalyses of specified representative anumber of technical areasin whichthe applicant System 80+ pipingsystems using his own computer didnot provide design andengineering information program. When the analyses arecompleted, the in sufficient detail to make a finalsafety decision. COL licensee willcompare his resultsto those of the One of these areaswas piping andpipe support benchmark problems given in thisreport to ensure designwhere ABB/CE did not have the as-befit or that the results meet the range of acceptable values. as-procured information to complete the final Any deviations fromthese values, as well as, the design. To resolve this issue, the staff developed an justification for suchdeviations, shallbe documented alternate approach using design acceptance criteria and submitted to the NRC staff for reviewand (DAC). The DAC are aset of prescribed limits, approvalbefore initiating final certifiedpiping parameters, procedures, and attributes upon which analyses. This benchmarking willprovide assurance the NRC relies inmaking afinal safety that the computer program used to complete the determination to support a design certification. The System80+ pipingdesign and analyseswillproduce DAC are objective (measurable, testable, or subject results that are consistent with results considered to analysis using pre-approvedmethods), and must acceptable to the NRC staff. be verified as a partof the inspections, tests, analyses, and acceptance criteria (ITAAC) used to This report presents the benchmarkvroblems and demonstrate that the as-builtfacilityconforms to the gives all informationneeded bythe COL licensee to certified design. The combined license (COL) perform the analyses andevaluate the results. The ficensee will use the DAC to demonstrate Brookhaven National Laboratory(BNL), under conformance with the System 80+ standard design contract with the NRC staff, developed these duringconstruction. This will enable theN'RCstaff problems based on representative piping system to make a final safety determination throughthe designinformationprovided byABB/CE during the reviewof the COL licensee's satisfactory NRC technical reviewand evaluation of the System implementation andverification of the ITAAC. 80+ standard design. The benchmark problems represent aportion of the System 80+ Main The NRC staff's evaluation of ABB/CE's Feedwater Line and the Pressurizer Surge Line. proposed DAC approachfor the System80+ piping Although the piping benchmark problems are designwas documented in their final safety considered representati,,e System 80+ piping evaluation repolt. In that document the staff configurations andloadings, they are not intended to provided their evaluation of the ABB/CE certified be final designs. BNL constructed mathematical designcommitments andcorresponding ITAAC for models of these two piping systems using the the System 80+ piping design. One of these PSAFE2 piping analysisprogram. 1 NUREG/CR-6128 ABB/CE-SYSTEM 80+ This report provides a complete description of the inputparameters for each problem including pipingdimensions, material properties, weights, support stiffnesses and locations, load definitions anddampingvalues. The dynamicanalysis methods benchmarked include the uniformsupport motion response spectrum method, the modal superposition time historyanalysis method, and the direct integration time-history analysis method. The BNL solutions to each problem are presented inthis report. Specificguidelines for comparing COL licensee resultsto these published results and acceptance criteriato be satisfied inorder to demonstrate acceptability are alsogiven. HUREG/CR-6128 2 2.0 PROJECT BACKGROUND where [M] is the massmatrix,[C] is the damping The PSAFE2 program isa fullfeature, elastic matrix,and [K]is the stiffness matrixof the element piping analysis code based on the Finiteelement assemblage. The vectors (u}, {_}, and {ii} are the method. The program,amodified versionof the nodal displacements, velocities, andaccelerations, general purpose computer program SAP IV, respectively. {R(t)} can be avector of timevarying Reference 2,was developed byBNL to analyze loadsor of effective loads which result fromground pipingsystems subjected to both static anddynamic motion. The PSAFE2 programcan carryout time loading. Dynamic analysiscapabilities includeboth historyor response spectrum analysisfor the response spectrum and time history analysis for solution of thisequation. A brief description of the systems subjected to either uniformor independent methods used in these benchmark problem solutions supportmotions, is providedbelow. The PSAFE2 program anditsprecursor EPIPE, 2.1.1 Uniform Support Motion Response Reference 3, havebeen extensively tested and Spectrum Analysis verified against other pipingprograms andagainst physicaltest results. The programshave been In the case of groundmotion, ifit is assumed that applied to develop earlierNRC benchmarkproblem thepiping system isuniformly subjected to the solutions to confirmthe adequacy of programsused ground acceleration, ils,the equations of motion can bynuclear power plant license applicants be expressed as follows: (References 4 and 5). [M]{_,} . [C]{_,} * [KJ{u,} = -[MJ{tis} This report presents the solutions to piping benchmark problems with configurations that are where {u_}is the relative displacement of the system representative of ABB/CE System 80+ piping with respect to theground, {ur} = {u}- {us}. systems. The solution methods thatwere applied were not in their entirety included in earlierNRC The equations arethen expanded in terms of the benchmark studie_ They include the uniform systemmodal matrixandgeneralized coordinates: response spectrum method with high frequency mode responses, the modal superposition time [air][4_](_}.[C] [_] {_}+[K] [_] {q} = -[M] {z2s} historyanalysis method, andthe direct integration time history analysismethod. The following section where: provides abrief description of the analytical methods. [4_]= norma/_d moda/matr_ suchthat[0]r[.u3[_]= [rJ 2.1 Mathematical Background Since elastic piping analysis is awell established {q} --8eneralized coordinatea vector. procedure, onlya briefoutline of the theoretical considerations used in obtaining the dynamic solutions will be presented. A more detailed Multiplication bythe transpose of the modal description of the analysis methods andsolution matrixyields: schemes is given in Reference 2. {q}.[A]{_}.[_2] {q}=_[4_]r[M]{as} The analysis of apiping system is carriedout by use of the stiffness matrix method, in whichthe piping is represented by anetwork of basic elements, where: straightandcurved beams, and one-dimensional elements interconnected atthe nodes. The dynamic [t0_]= diagonal matrix of eigen-values response of the network isdescribed mathematically [A] ffi d/agonal matrix of modal damping bythe equation of motion: coefficients, where the damping is assumed to satisfythe modal orthogonality condition. This resultsin n [M]{a} + [C]{d) . [K](u} = {_(t)} uncoupled equations for the generalized coordinates. 3 NUREG/CR-6128 ABB/CE-SYSTEM 80+ The equation set can be solved for the maximum Reference 7,was implemented. This procedure is as modal response for each system degree of freedom follows: corresponding to excitation in each spatial d/rection as follows: For each degree of freedom (DOF) included in the dynamicanalysis, the fraction of DOF mass, 4, u,tj,_ = _ 4_,u,.L_ included in the summation of all of the modes up to 2 the cutoff frequency was calculated for each DOF as follows: N where: di ffi=E.Ln× 4)_ u_= maximumdisplacement of mth degree of freedom in the nthmode where: due to excitation in the ith spatial direction n is order of the mode under consideration, S_ = value of spectral acceleration N is the number of modes up to the corresponding to frequency _on,and cutoff frequency, the i-thspatial direction input _ is the nth natural mode of the system, response spectnun and L_ is the participation factor given by: L_ = modalparticipation factor for nth mode and ith spatial direction _o = nth system natural frequency L, = {_,}r[M]{_,} ¢_ = modal deflection oZdegree of freedom m in nth mode The fraction of DOF massnot included in the summationof these modes, e_,wasthen calculated m = degree of freedom index a_ n = modal index •t= _ "_j i = spatial index where_ is the Kronecker delta, whichis one if DOF i is inthe direction of the earthquake motion For the final solution, the maximummodal andzero ifDOF i is a rotation ornot in the responses are combined over the firstn modes upto direction of the earthquake input motion. the cutoff frequency (the lower frequency nodes) at which the spectral acceleration roughlyreturnsto Since higher modes can be assumed to respond the zero period acceleration (ZPA). For the in phase with the ZPA andthus, with each other, benchmarkproblem given in this report, the modal these modes s_ould be combined algebraically. This combination is performed in accordance with the is equivalent to pseudostatic response to the inertial grouping method as described in Section 1=2.1of forces fromthese higher modes excited at the ZPA. Regulatory Guide 1.92, Reference 6. These pseudostatic inertial forces for all higher modes for each DOF i are given by: Insome piping systems the r_wonses of modes above the cutoff frequency (the high frequency Pl = ZPA × Mt x •l modes) mayhave asignificant effect on the total response, especially on support reactions. In order where: to ensure that these high frequency mode effects are accounted for, an additional calculational procedure Ptis the force or moment to be applied to DOF based on the methodology descn'bedinAppendix A i. to Section 3.7.2 of the Standard Review Plan, NUREG/CR-6128 4 bitis the massor mass moment of inertia coordinates u andcombined algebraicallyat each associated with DOF i. time step to provide the total response of the piping system as afunction of time. Inorder to determine the maximumresponses associated with the high frequency modes, astatic 2.1.3 Direct Integration Time History Analysis analysisis performed by applyingthis set of pseudostatic inertial forces to allof the degrees of Inthis solution mode the equation of motion is freedom in the model. The total high frequency solved directly bynumerical integration. Eigen value mode responses are then combined bythe square- evaluations are not made andno simplification root-of-sum.of-squares method with the total associated with eigenvector orthogonaiity properties combined response from the lower-frequency modes is used. As such, no approximation associated with to determine the overall piping systempeak a modal assumption is introduced. The method is a responses, basic approach andis describedin any reference on numerical methods. References 2 and3 are 2.1.2 Modal Superposition Time History Analysis particularlyapplicable. The time history response of apiping system In the PSAFE2 program the Wilson 0 method subjected to aknown forcing function canbe is used to perform the numerical integration. The obtained by the modal superposition method. This advantage of thismethod is that itis unconditionally procedure requires the solution of the generalized stable. As a matter of good practice, the time step e/genvalue problem to determine the frequencies should be essentially 1/10 the shortest period of andmode shapes of the system. Ituses the same interest. In this method, Rayleigh dampingis modal transformation procedures descrPoedabove assumed suchthat the damping matrixis given by: for the response spectrum method. The general equations of motion in matrix form are expressed as follows: It] - _[M] + p[4 [_{a} .(C'lla}.(_{u} - {k(t)} Applying the transformation: Where a and 0 satisfythe following relation: ___ =p<+i {u} - [<l,]lq} {' - 2_,t The equations canbe expressed in termsof the generalized modal coordinate_ whereit isthe modal damping ratio corresponding [M][4_]{q} +[c][_] {_}+[_[_] |q} ={R(O} to naturalfrequency 04. Multiplication bythe transpose of the modal The a andI_constants may bedetermined fromthe matrixand application of the modal orthogonality above relationship by assigningaprescribed modal assumptions yields the following set of equations: damping ratio, +,to anytwo frequencies, o_xandw2 andsolving the following set of simultaneous {_p}+ [A]{+} + [m_fq} " [+]rlR(t)} equations: This set of decoupled differential equations is j[=_+ i__._2 2 solved numerically for asufficient number of modes needed to adequately characterize the dynamic response of the piping system. In selecting the _ = _ + 13 integration time step and the number of modes, the 2_o2 2 dynamiccharacteristicsof the systemas well as the forcing function mustbe considered. The PSAFE2 Once the c_and0 constants are established, the program uses the Wilson 0 numericalintegration modal damping ratio, _l,for each remaining mode of method which is anunconditionally stable step-by- vibrationwith naturalfrequency, 04,is determined step integration scheme. Finally, the modal from the equation given above. Thus, the damping responses are converted back togeometric ratio is afunction of frequency. This differs from 5 NUREG/CR-6128 II rl , i, , , , ,