ML18029A933

Speech Entitled, Correlation Coefficients for Combination of Piping Responses.

ML18029A933
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Site:	San Onofre
Issue date:	03/29/1985
From:	ABB IMPELL CORP. (FORMERLY IMPELL CORP.)
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CORRELATION COEFFICIENTS FOR COMBINATION OF PIPING RESPONSES Presented by:

Impell Corporation 350 Lennon Lane Walnut Creek, California 94598 (41 5) 943-4500

I h TABLE OF CONTENTS 1.0 Introduction 2.0 Methodology 3.0 References 4.0 Example

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1. 0 INTRODUCTION 0 One of the staff in December 1984 recommendations

[lj on Response Combinations in the Report of the U.S. Nuclear Regulatory Commission, Piping Review Committee published is that "the independent suppor't motion response spectrum method should be allowed as an option in calculating the response of multiply supported piping with independent inputs." The staff also recommends rules for the combination of the individual group level responses, individual modal responses and directions (see attachment).

These rules do not properly consider the modal correlation and the correlation between support motions.

Impell Corporation proposes to use the multiple level response spectrum (MLRS) approach but using the corresponding and appropriate correlation coefficients to combine group, modal and directional responses. The methodology, based on random vibration theory, was developed by A. Asfura et al [2, 3, 4, 5j and it has been incorporated in Impell's computer program SUPERPIPE (RV-SUPERPIPE).

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2.0 METHODOLOGY A detailed explanation of the methodology 'is beyond the scope of this document. References 2, 3, 4, and 5 give all the theoretical background for the generation of the correlation coefficients and the derivation of consistent combination rules. A brief summary of the combination rules for the dynamic and pseudostatic component of the response is presented.

2.1 ~i R  : Total dynamic response.

R.k ik ..Maximum dynamic response of mode i (with proper sign) due to the excitation at group level k.

n  : Number of considered piping modes.

na  : Number of group levels.

pikjl  : Correlation coefficient which account for the correlation between modes i and j and the correlation between group levels k and l.

This correlation coefficient is given by:

where Ordinate of the acceleration cross-cross response spectrum for modes i and j and group levels k and 1 [2, 31.

Ordinate o f the accel erati on floor response Sk(, <,.)

spectrum for mode i at group level k.

These correlation coefficients are function of the modal properties of the building, the design ground spectra and the modes of the piping.

In the correlation coefficients, the directional correlation can be included defining each direction at a support group location as a "different" group level.

2.2 Pseudostatic Com onent na na z z k=1 1=1 k 1 kl j Total pseudostatic component.

Pk . Response due to static displacement Uk of group level K.

bkl . Correlation coefficient between the displacement of group levels k and l.

This coefficient is given by bkl kl IUkl IU1 l 4

Ckl .. Term proportional to the corariance of the displacements of the group levels k and 1 f4, 53 which is given by:

N N C

kl

= Z Z "' 0 IJ g

( II) g J I=1 J=l where N  : Number of considered building modes.

~I  : Effective building participation factor.

S g

(W I ): Ordinate of the design ground response spectrum for building

'requency WI.

Po IJ Correl ation coefficient for cl osely spaced building modes (C(}C type coefficients).

The coefficients bkl are function of the modal properties of the building and the design ground spectra. Again the correlation between directions can be included directly in these coefficients.

2.3 ~1R Standard procedures. Absolute sum or SRSS of R and P depending on the case.

3.0 REFERENCES

0 [13 Report of the Committee.

U.S. Nuclear Regulatory Commission, Piping Review Evaluation of Other Dynamic Loads and Load Combinations.

NUREG-1061, Volume 4, December 1984.

[21 A. Asfura and A. Der Kiureghian, "A New Floor Response Spectrum Method for Seismic Analysis of Multiply Supported Secondary Systems," Report No. UCB/EERC-84/04, EERC, University of California, Berkeley, California, June 1984.

[3j A. Asfura and A. Der Kiureghian, "Floor Response Spectrum Method for Seismic Analysis of Multiply Supported Secondary Systems," paper submitted to Earthquake Engineering and Structural Dynamics.

[4] A. Asfura and A. Der Kiureghian, "Correlation Coefficients for Modal Combination of Multiply Supported Secondary System," in preparation.

' [53 A. Asfura, "A June 1985.

New Combination Rule Systems," paper submitted to the for ASME Seismic Analysis of Piping PVP Conference, New Orleans, 4,0 EXAMPLE This example represents a real pipe line (line AC-03 at SONGS-1) which is attached to a building comp'osed of three different structures. Figures 1 and 2 show the models of the buiding and the pipeline respectively, and Table 1 and 2 lists the modal properties of them. The building represents a reactor building. For analysis purposes, the building was considered responding in only two directions (X and Y directions). The input ground excitation corresponds to a R.G. 160 design ground spectra scaled to 0.4G ground acceleration applied in the x-direction. The pipe line is a three-dimensional system which is attached to two different structures in the building (see figure 1 and 2). The support levels are located at elevation 35.9'n the containment and at elevations 30.0'nd 45.0'n the interior structure. It is noted (Figure 2) that each support level consists of a group of piping supports which are considered to have the same input motion. Because the piping system is connected to two different structures, the pseudostatic component of its total response are considered. Time history and multiple response spectrum analyses are performed. For the response spectrum analysis, the following combination rules are used.

Combination 1:

Dynamic Response Level Combination: Absolute sum.

Modal Combination: Grouping Method (R.G. 1.92)

Pseudostatic Response: Absolute sum of the responses due to the static displacement of each support level.

Total Response: Absolute sum of the dynamic and pseudostatic response.

Combination 2:

Dynamic Response: Use of correlation coefficients.

Pseudostatic Response: Use of correlation coefficients.

Total Response: Absolute sum of the dynamic and pseudostatic response.

For this example, only the bending stresses and the support loads are presented. The maximum bending stresses evaluated using time history analysis and response spectra analysis are presented in Figures 3 and 4, respectively, for 54 points along the pipe. Figure 3 shows the dynamic component of the response using time history analysis. Figure 4 shows equivalent curves for the total responses.

It can be observed that the proposed combination rules accurately predict the dynamic and total responses along the pipeline. It is also observed that the use of this new combination technique= may result in an important response reduction with respect to results obtained by the standard methods currently used by the nuclear industry. for this example, on an average, the reduction is approximately 25 percent for the dynamic component of the bending stresses and 9 percent for the total bending stresses. Tables 3 and 4 present similar results for the reaction at the supports.

'I It is observed that the new methodology is in agreement (for design purposes) with the time history analysis. Also, these tables give the average reduction obtained in the support loads by using the proposed combination rules instead of the standard combination rules. This example shows that the combination rules given herein can become powerful tools in the requalification of existing piping systems for a hiqher level of seismicity and for snubber reduction evaluations.

In this example, the dynamic component and the'pseudostatic component were always combined using absolute sum. Results were also obtained by combining them using the SRSS rule. In this case, these results were in general unconservative and so, are not presented herein.

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MODE FREQUENCIES NODAL PART DAMP I NG (CPS) FACTORS RATIOS (5) 3,25 -1777,30 13,0 3.84 -24,43 3,0 6.39 -1266,60 13.0 36.74 2.0 19.45 -4.11 4,0 1q,79 85,94 7,0 33,46 5,47 4.0 36,30 -0,0025 4,0 TABLE I ~ BUILDING .PROPERT'I ES i'10DE FREQUENC I ES NODAL PART FACTORS DA'1P ING (CPS) RATIOS (X) 4,69 -0.0048 0.0029 -0,0204 5,0 7;19 -0,0386 0,0038 0,0043 5,0 11.65 0,0097 0.0328 0,0020 5,0 12,83 -0.0035 -0,0003 -0.0351 5,0 13,66 0,0059 -0,0222 0,0012 5,0 17, 78 0,0090 0,0008 -0,0116 5,0 2l.05 0,0191 0.0010 -0,0065 5,0 25,69 -0,0042 -0,0044 -0,0192 TABLE 2. PIPING PROPERTIES

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Nodal Type of Force {lb) Time Combination Comb 1 PV-SUPERPIPE RV SUPERPIPF Point Support or Moment History rm (lb-ft) 23 Anchor Fx 133.60 179. 66 1.34 192. 75 1.44 Fy 77.22 104.18 1.35 108.00 1.40 Fz 47. 83 75. 73 1. 58 47.47 0. 99 Mx 132.81 241. 87 1.82 150.61 1.13 My 94.33 139.51 1.48 94. 75 1.00 Mz 293.92 394.64 1.34 356.96 1. 21 60 Anchor Fx 83.25 83. 76 1.01 83. 34 1.00 Fy 35.82 35.64 0. 99 31. 73 0. 89 Fz 73.31 114.86 1. 57 85. 06 1. 16 Mx 86.36 140.91 1.63 94.68 1. 10 My 114.51 148. 17 1.29 121.87 l. 06 Mz 34.32 42.25 1.23 43.50 1.27 35 Single Fy 29. 85 39. 39 1.32 29. 21 0- 98 Fz 46.65 94.19 2. 02 54. 82 1.18 110 S ing 1 e Fy 52.78 121. 90 2.31 96.49 1.83 Fz 76.92 127. 79 l. 66 100. 71 1.31 115 Single Fx 985. 67 1319.93 1.34 940.37 0. 95 Mean ratio 1.49 1.17 Standard Deviation ratio 0.34 0.23 Average reduction 21. 5'X TABLE 3. DYNAMIC SUPPORT LOADS

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1 0

Nodal Point 23 Type Support Anchor of Force or (lb)

Moment (lb-ft)

Fx Time History 287. 80 Combination 1

316.45

~

Comb.

1.10

~

1 RV-

$ [lpppD[Dp 329.61 RV-SUPERPEPEo

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1.15 Fy 168.44 172.86 1. 03 177.22 1.05 Fz 92.56 120. 28 1.30 92.37 1.00 Mx 221.79 323.02 1.46 231. 78 1.05 My 82. 50 149. 26 1.81 104. 69 1. 27 Mz 671 48 710.68 1.06 673.03 1.00 I

60 Anchor Fx 148. 34 222.79 1.50 222.70 1.50 Fy 100.20 78.29 0. 78 75.16 0.75 Fz 138. 47 187.29 1.35 157.74 1.14 Mx 96.00 159.11 1.66 113. 99 1. 19 My 269.29 369. 60 1.37 370. 84 1.38 Mz 103.38 124.35 1.20 126. 00 1. 22 35 Single Fy 57. 67 64.66 1.12 54. 70 0. 95 Fz 76. 04 122.28 l. 61 83. 00 1. 09 110 Sing 1 e Fy 53. 59 123.46 2.30 97. 88 1.83 Fz 76. 86 127. 79 1. 66 100. 71 1. 31 115 Singl e Fx 978. 91 1331.42 1.36 951.84 0. 97 Mean ratio '.39 1.17 Standard Deviation ratio 0.36 0.25 Average reduction 15. 8X TABLE 4. TOTAL SUPPORT LOADS

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CONTAINMENT STICK El. 177 8'l.

12+0'EGEND: ~ MASS LOCATIONS BEAM El EMENTS TRUSB ELEMENTS RIQID BEAM ELEMENTS 1

EL.

85.5'NTERIOR STRUCTURE STICK 80.5'TEAM

'L. QENERATOR STICK EL.

70.2'L.

GENERATOR SNUBBER RESTRAINT EL 81.$ dd.0'TEAM EL. 85.II'L 80.0'l..

15.0'L.

SII.S'L.

2i.d'L.

10.5'BASEMAT)

VWf Kx Kg SOIL BPRINQS Ky'IGURE

1. BUILDING MODEL

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SLl: E lev. 35. 9 'ontainment SL2: Elev. 30.0'nterior Structure SL3: Elev. 45.0'nterior Structure

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('g Qg Cw(p Gp g

0

.5

's 4he 82'O 8

pe (zZ) gr2 FIGURE 2 . PIPING MODEL (AC-03 SOH65-1)

~ COQSOIATIOII 'I I TIM'C IOOTOIIY RV IVPIRPIPTOIIC NISTORT Q>>

0.0 T.o 0.0 OT.TIN TI.TO I I 0.000 TRAIT 0 0 P 0 Ii.ooo ROOKIIO:

I 0.000 lL COIIOOIATIOII I I LOOO 4 TIIIO IIIOTOOY

'IIANO I 0.000

~ .000 PI ~ .OOO P.OOO CI Z

o ~ .ooO Z

~ .000 O.OOO FIGURE 3 ~ DYNAMIC BENDING STRESSES

0.0

~ COVOIIIATIOIII I TIME INOTOIIY

~ Ry tUPKRPI Pl~I IRI IIISTIR y a.o I.O-e.o 14.400 0 O O

t 4.040 14,444 g colleoIATIott I 14,449 0 iy SLOIRPIPI 0 Tete 104TOIIT 1 TABOO to,000

~ .Ooo 0.000 nAI T.ooe Z

IR 0.040 X

Ql

~,040 0,000 t,ooo t,ooo FIGURE 4. TOTAL BENDING STRESSES

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ATTACHMENT NUREG-1061, Yolume 4 December 1984 0 2. STAFF RECOMMENDATIONS ON RESPONSE COMBINATIONS

2. 1 Introduction This section of the Task Group report treats questions regarding the use of independent support motion (ISM) methods in place of the presently approved uniform response spectrum (URS) techniques specified in SRP Section 3.9.2. Additionally, issues relating to the sequence of combinations between directional and modal components and to the treatment of high frequency modes are included.

2.2 Historical Develo ment of Technical Issues The NRC position on multiply supported piping with independent seismic inputs was developed at a time (during the early 1970's) when the urgency to establish criteria did not allow for a complete assessment of the problem. As a consequence, criteria were selected that would provide conservative results without, however, indicating the effect that these criteria might have on overall reliability. These criteria were based on the following conservative assumptions:

A single uniform response spectrum that enveloped all the independent response spectra applied to the different support groups was used.

~ z. With peak group displacements occurring at the same moment, these peak displacements were combined in the most unfavorable way to calculate the seismic anchor motion (pseudostatic) component of seismic response.

3. The inertial and pseudostatic response was absolutely combined to obtain the total response.

Recent studies have indicated that, in most cases, analyses based on these assumptions can considerably overestimate the seismic response when compared to time-history solutions that do not embody these conservatisms.

An item that was not addressed during the early *1970's is the combinational sequence between modal and directional components of piping response. This combinational sequence is a consideration only when closely spaced modes comes into play, under which conditions combining directional components first will give a more conservative result. This issue is not addressed in the SRP or in regulatory guides but is treated in branch technical, positions. Recent studies have shown that in some situations the, choice of one sequence over another leads to maximum differences in response estimates of about 20 percent. However, in the majority of practical cases where this item was addressed, the results show only minor differences in final responses. Therefore, present thinking is that this issue is more an academic one than an issue seriously impacting safety.

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Difficulties with combining high frequency modes by the square root of the sum of the squares -(SRSS) approach were pointed out in 1979 in the course of responding to Task Action Plan A-40. Mere high frequency modes means modes beyond the maximum input excitation frequency where dynamic amplification's essentially zero. For this situation, the high frequency modes are all nearly 'in-phase with the input motion, and, as a result, in-phase with each other. This implies that the algebraic combination of

. high frequency modal responses is appropriate..

2.3 Su+var and Assessment of Available Information Brookhaven National Laboratory (BNL) in a report prepared for the Nuclear Regulatory Conmission entitled "Alternate Procedures for the Seismic Analysis of Multiply Supported Piping Systems,'" NUREG/CR-3811, May 1984, recommended that "The independent support motion response spectrum method should be certified as acceptable for the evaluation of the dynamic component of response." This recommendation was endorsed by this Task Group's consultant and the NRC staff however, with a significant exception. BNL (with support from NUTECH) advocated that combinations between support groups be by the use of the SRSS rule. The NRC staff and our consultant recotanended the absolute sum rule instead. Westinghouse offered the view that absolute su+nation should be implemented "unless the groups are from different structures (or if from the same structure, they can be shown to be phase uncorrelated), then SRSS should be used." For the dynamic and pseudostatic component of response, our consultant and BNL both endorse a newly developed procedure called grouping by attachment points (BNL offers an additional option, grouping by elevations, for preliminary design). In this grouping procedure, structural support points that are attached to a rigid floor or structure (so that the same translationary motion, without rotation, is experienced) are considered as one group of supports. Supports should not be considered rigid for any frequency. After the individual group responses .are determined, they are combined by the absolute sum method. The aforementioned BNL NUREG report demonstrates that significant reductions in predicted responses can be achieved without leading to unconservatisms. It is the consensus of all parties that the total response should be obtained by combining the inertial and pseudostatic responses by the SRSS rule, which would be a relaxation over the present absolute sum rule.

Evaluations of the issue on the sequential combination of directional and modal components indicate that it is relatively insignificant and our receanendations reflect this observation.

Available evidence also strongly supports the algebraic summation .of

.high 'frequency modes or a procedure,equiva'lent to. algebraic summation; After the high frequency modes are combined by algebraic su+nation, this quantity's combined with the response to lower frequency modes by the SRSS rule to obtain the total response.

2.4 Recomnendations for Revisions to Present NRC Criteria There are three principal recommendations for the material of this section as follows:

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. Inde endent Su The ort Notion Nethod independent support motion response spectrum method should be allowed as an option in calculating the response of multiply supported piping with independent inputs. This method should be implemented under the following rules for response combination.

a. For Inertial or Dynamic Components (1) Group responses for each direction should be combined by the absolute sum method.

(2) Nodal and directional responses should be combined by the SRSS method without considering closely spaced frequencies.,

b. For the Pseudostatic Components (1) For each group, the maximum absolute response should be calculated for each input direction.

(2) These should then be combined by the absolute sum rule.

(3) Combination of the directional responses should be by the SRSS rule.

c. For the Total Response Dynamic and pseudostatic responses should be combined by the SRSS rule.

2. Se uence of Combinations Any sequence may be selected between spacial and modal components, that is, modes may be obtained first or spacial components may be combined first. The reason is that consideration of closely spaced frequencies need not be taken into account.

3. Hi h Fre uenc Nodes Algebraic combinations should be used for high frequency modes as described in the position paper on Response Combinations in Section B.2 of Appendix B to this report. The high frequency modes should be combined with low frequency modes by the SRSS rule.

. The procedure for independent support motions should be added to SRP Section 3.9.2. Regulatory Guide 1.92 should bq modified to reflect the inclusion of the high frequency modal effects.

2.5 Recommendations for Additional Stud The studies delineated below reflect the Task Group's view as to fruitful fields of future effort.

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o Investigations should be undertaken to establish the transition frequency between high and low frequency when implementing the algebraic suaeation rule for high frequency modes.

o Additional effort on phase correlation between groups and the impact on the BNL recomnendations is needed. BNL, using the Lawrence Livermore National Laboratory (LLNL) data from Zion, were unable to quantify the influence of phase correlations.

Thus, uncertainties exist as to potential limitations on the recomnendations.

o Additional effort is warranted on appropriate methods for calculating the effect of closely spaced modes.

2.6 alitative Value Im acts of Recoaeended Revisions The revisions discussed above regarding multiply supported piping with independent inputs will lead to more accurate and more realistic estimations of piping behavior. Significant predicted reductions in response (by a factor of two or more) can be expected in general for all response quantities. Adoption of these procedures could lead to the removal of pipe supports from operating plants without violating code allowables. On the other hand. for very stiff piping systems, -the high frequency mode combination recommendation could result in higher response predictions under certain conditions. The degree to which these response predictions increase depends on the importance of the high frequency modes in deciding the total response.

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