NUREG-0484

Rev. 1

Methodology for

Combining Dynamic Responses

R. K. Mattu

Office of

Nuclear Reactor Regulation

U.S. Nuclear Regulatory

Commission
Available from

GPO Sales Program

Division of Technical Information and Document Control

U.S. Nuclear Regulatory Commission

Washington, D.C. 20555

and

National Technical Information Service

Springfield, Virginia 22161
NUREG-0484

Rev. 1

Methodology for

Combining Dynamic Responses

Manuscnpt Completed: April 1980

Manuscript Completed: April 1980

Date Published: May 1980

R. K. Mattu

Division of Safety Technology

Office of Nuclear Reactor Regulation

U.S. Nuclear Regulatory Commission

Washington, D.C. 20555

ABSTRACT

The NRC has historically required that the structural/mechanical responses

due to various accident loads and loads caused by natural phenomena (such

as earthquakes) be combined when analyzing structures, systems, and components

important to safety. This requirement flows from lOCFR50, Appendix A, General

Design Criterion 2, which calls for an appropriate combination of the effects

of the above events to be reflected in the design bases of safety equipment.

This requirement has been implemented in various ways both within the NRC

and the Nuclear Industry. An NRR Working Group constituted to examine

load combination methodologies developed recommendations which were published

in September 1978 as NUREG 0484. NRC adopted the Working Group's recommendations which stated: "For the combination of the dynamic responses within the

Reactor Coolant Pressure Boundary (RCPB) and its supports which result from

the coincidence of an SSE and LOCA, the Square Root of the Sums of the Squares

(SRSS) technique is acceptable contingent upon performance of a linear

elastic dynamic analysis to meet the appropriate ASME Code, Section III,

Service Limit." Revision 1 of NUREG-0484 extends the conclusions of the

original NUREG-0484 on the use of SRSS methodology for the combination of

SSE and LOCA responses beyond RCPB to any other ASME Section III, Class

1, 2, or 3 affected system, component or support, and provides criteria for

the combination of dynamic responses other than SSE and LOCA.

iii

CONTENTS

Page

2. DYNAMIC RESPONSES AND COMBINATION METHODOLOGIES - (NUREG 0484),... 5

3. SSE AND LOCA RESPONSES - RCPB AND BALANCE OF PLANT ................ 14

4. CRITERIA FOR COMBINATION OF DYNAMIC RESPONSES OTHER

THAN THOSE OF SSE AND LOCA ......................... o.9.......... 19

5. CONCLUSIONS....... ............ . .o. . o. o o ...... .f ...... 23

6. BROOKHAVEN NATIONAL LABORATORY GENERIC STUDIES ON RESPONSE

COMBINATION METHODOLOGY STATUS................................... 24

APPENDIX A. DEFINITIONS ........ o ... ............... ................ 25

APPENDIX B. REFERENCES ..... . .... ....... oo .... . 27

V

1. INTRODUCTION

(A) Objective of Report

NUREG-0484 Revision 1, Methodology for Combining Dynamic Responses supersedes

NRC Staff Working Group Report NUREG-0484 published in September 1978. This

revision does not alter the conclusions of NUREG-0484. It extends the conclusions of NUREG-0484 on the use of SRSS methodology for the combination of SSE

and LOCA responses beyond the Reactor Coolant Pressure Boundary to any other

ASME Section III, Class 1, 2, or 3 affected system, component, or support,

and provides criteria for the combination of dynamic responses other than SSE

and LOCA.

(B) Background

The NRC has historically required that the structural/mechanical responses due

to various accident loads and loads caused by natural phenomena (such as

earthquakes) be combined when analyzing structures, systems, and components

important to safety. This requirement flows from 10 CFR Part 50, Appendix A,

General Design Criterion 2, which calls for an appropriate combination of the

effects of the above events to be reflected in the design bases of safety

equipment. The requirement has been implemented in various ways both within

the NRC and the Nuclear Industry.

Loads due to postulated accidents and natural phenomena often yield dynamic

responses of short duration and rapidly varying amplitude in the structures
and components exposed to the loads. For some loading phenomena, the accident

analysis provides a definitive time history response and allows a straightforward addition of responses where more than one load is acting concurrently.

In other cases, no specified time-phased relationship exists, either because

the loads are random in nature (e.g., vent chugging in pressure-suppression

containments) or because the loads have simply been postulated to occur

together (e.g., LOCA and SSE) without a known or defined coupling. Where a

defined time-phase relationship is lacking, system designers have utilized

several approaches to account for the potential interaction of the loads. One

approach, the so-called absolute or linear summation (ABS) method, linearly

adds the absolute values of the peak structural responses due to the individual dynamic loads. Babcock and Wilcox (B&W) and Combustion Engineering (CE)

use the ABS method to analyze the primary coolant system components and supports.

In general, the ABS method has also reflected the staff's conservative preference for the combination of dynamic load responses.

A second approach, referred to as SRSS, yields a combined response equal to

the square root of the sum of the squares of the peak responses due to the

individual dynamic loads. Depending on the relative magnitudes of the loads,

the SRSS value will vary between about 0.7 ABS and 1.0 ABS for the combination

of two dynamic loads. The SRSS method has been used by both General Electric

(GE) and Westinghouse in selected applications. The NRC staff has approved

the use of SRSS to combine certain modal responses caused by earthquakes' and

!Regulatory Guide 1.92, Combining Modal Responses and Spatial Components in

Seismic Response Analysis, February 1976.

-2-
to combine LOCA and SSE loads in the analysis of PWR fuel bundles. 2 The staff.

also has been requested to consider its application in Mark I and Mark II

containment pool dynamic loads evaluations.

The lack of a physical relationship between some of the loads has raised

questions as to the proper methodology to be used in the design of nuclear

power plants. The ABS approach may lead to overly conservative design requirements and may result in a system more rigid than that required

to provide an optimum response to the thermal stresses present in normal

operation. These overly conservative design requirements may also require

unnecessary modifications for operating plants (if reanalyzed) which were

licensed before promulgation of the present GDC 2. On the other hand, there

needs to be a technical basis for the use of the SRSS method.

An NRR Working Group was constituted in June 1978 to examine load combination

methodologies and to develop a recommendation concerning criteria or conditions

for their application. During the course of its deliberations, the Working

Group met with each of the NSSS vendors, and telephone calls were made to

solicit the views of a number of architect/engineering firms. A limited

amount of time was made available to this group so that the work reported in

NUREG-0484, published in September 1978, focused its attention on application

of the methodologies to the primary reactor coolant system. In this regard,

another consideration was the amount of information available at that time

regarding the design and response of various primary system components to

2 Memo, R. Meyer to R. Mattson, Use of SRSS Load Combination for'Fuel, dated

July 18, 1978.

-3-
dynamic loads. Emphasis was placed on an objective review of each methodology

and the development of a balanced judgment with regard to the information

available at that time. The Working Group efforts focused on the ABS and SRSS

methods and their evaluations of these methods are repeated in Sections 2(A)

and 2(B) of this report. No other combination methodology was identified by

the Working Group that warranted further investigation at that time. Although

not a specific task of the group, decoupling of LOCA and SSE loads was considered an inseparable part of the discussions and is discussed in Section 2(C):

(C) Report Content

Section 2 of this report summarizes the work done by the Working Group in 1978

for the combination of the dynamic responses within the Reactor Coolant Pressure

Boundary (RCPB) and its supports, which result from the coincidence of an SSE

and LOCA. Section 3 provides methodology and its rationale for combining

dynamic responses due to SSE and LOCA to any ASME Class 1, 2, and 3 affected

system, component, or support. Section 4 describes the criteria for combination of dynamic responses other than those of SSE and LOCA. The staff

conclusions are provided in Section 5. Sections 3, 4, and 5 reflect the staff

work and findings completed since the publication of NUREG-0484 in September

1978. Section 6 describes briefly continuation of generic effort on load/

response combinations.

-4-
2. DYNAMIC RESPONSES AND COMBINATION METHODOLOGIES - (NUREG-0484)

ABS and SRSS methods and their evaluation are discussed below. Also discussed

here are decoupling of LOCA and SSE loads/responses.

(A) Absolute or Linear Summation Method

Concept

In the design of nuclear power plant components when the time-phase relationship

between the responses caused by two sources of dynamic loading is undefined or

random, the use of the ABS methodology linearly adds the peaks of the individual

colinear responses to obtain the combined response. No consideration is given

to the probability of occurrence of either of the associated events that cause

the combined loading in arriving at the procedure for combining the randomly

phased responses. An example of a design equation using the ABS method for

the combination of SSE and LOCA loads is provided below (N represents normal

loads):

I NI+ISSEI+ILOCAI< Level D Service Limit

Advantages/Disadvantages

(1) The ABS method generally provides greater margin to failure as compared

to other methods considered, although it may be overly conservative given

the random dynamic nature of the responses. The extra margin to failure

-5-
obtainable by the ABS method in relation to the SRSS method is a function

of the relative magnitude of the dynamic responses. The maximum difference

between ABS and SRSS for combining two responses is approximately 30 percent

and occurs when the peak amplitudes of the dynamic responses which are

being added are equal.

(2) The ABS method is conceptually straightforward in that it attempts to

bound the combined response by adding the individual peak responses.

Application or justification of the method does not involve probabilistic

bases.

(3) The ABS method is acceptable to the NRC staff, although consideration has

been given to the use of SRSS on a case-by-case basis. Where SRSS has

been used in the design of existing plants or where new loading conditions

have been identified, application of ABS could require extensive and

sophisticated reanalyses or plant modifications in order that response

criteria be met.

(4) The use of the ABS method may result in more rigid systems which is not

beneficial when the design must consider thermal stresses.

(B) Square Root Sum of Squares Method (SRSS)

-6-
Concept

The SRSS approach of combining dynamic transients is to square the peak value

from each individual response, add the squared values, and take the square

root of the sum. The SRSS technique does not result from any explicit analytical approach but rather is a method to approximate the dynamic coupling of

random transients when the time phasing is unknown. Historically, SRSS

coupling of dynamic transients has been used in certain conventional building

designs and for the design of piping systems in the petrochemical and

aerospace industry. SRSS is also used in earthquake engineering, and limited

use has been accepted by the NRC in seismic design.

An example of a design equation using the SRSS technique for the combination

of SSE and LOCA loads is provided below (N represents normal loads):

N + (SSE) S 2 + (LOCA)Z < Level D Service Limit

Advantages/Disadvantages

The applicability of the SRSS method as a design tool for use in the design of

safety-related structures, systems, and components centers on two issues. The

first is the extent to which margins of safety inherent in the ABS method

could be reduced considering all other potential concerns such as the possibility of undetected flaws in piping. The second is the relative conservatism or

nonconservatism inherent in the SRSS technique to predict the random combination of two dynamic responses. The first of these considerations is largely a

-7-
matter of regulatory philosophy, i.e., should conservatism be incorporated in

the response combination methodology to compensate for other uncertainties in

the as-constructed system. The Working Group believed that the method of

response combination should be selected on its merits and divorced from what

are essentially extraneous factors. In addition, artificial conservatism in

the response combination can lead to arbitrary and uncertain margins in the

design that may or may not be appropriate for the intended purpose. In any

event, the regulatory approach of defense in depth is designed to encompass

errors or operational problems such as pipe cracks without the need for

arbitrary conservatism in the analysis tools. To address the second consideration, the group surveyed the studies conducted by General Electric and

Westinghouse to attempt to quantify the adequacy of the SRSS technique. The

General Electric studies were an effort to quantify the probability of exceeding the SRSS value. In its evaluation, GE selected 291 dynamic transients

from various events (a non-uniform population) such as LOCA, safety relief

valve (SRV) discharge, and earthquake (OBE and SSE). Each of these transients

contained random amplitudes and phases, relatively short time durations, and

were rapidly varying. A sensitivity study was conducted by GE to investigate

the effects on exceedance probabilities for variations in the amplitude ratios,

frequency content, and transient durations. This study concluded that the

exceedance probabilities are relatively insensitive to changes in these parameters. The transients selected by GE were elastically calculated responses

of different components and structures. The conservative assumption of using

elastic superposition of the time-phased response transients was also applied

in this study. GE reported that the SRSS value was not exceeded for approximately 86 percent of the combinations investigated, which include all of the

-8-
transient responses identified above. GE also reported that 95.5 percent of

the combinations exceeding the SRSS value did so by less than 10 percent of

the SRSS value.

Westighouse also conducted studies to quantify a basis for justifying SRSS.

Westinghouse looked at only LOCA and SSE response transients for the primary

coolant system of its PWRs. Westinghouse used elastically calculated responses

that were linearly superimposed by random time phasing. This study also

included the normalization of the peak response amplitudes to represeht the

largest difference between the ABS and SRSS approach. The transients selected

by Westinghouse represented three earthquakes (nine transients) and several

LOCAs (21 transients total). Westinghouse reported that 75 percent of the combinations investigated were less than the SRSS value.

Both the GE and Westinghouse evaluations of the SRSS method predict a finite

probability of exceeding the SRSS value and therefore raise the question of

the potential consequences of exceeding the SRSS value. General Electric

funded research to investigate and quantify the differences between the

response of a structure to dynamic loads and its response to static loads.

The study considered the response of a single degree of freedom model and

varied parameters such as fundamental frequency (5 and 16 Hz) and ductility

ratios (2 to 3). A multi-degree of freedom beam model was also used to demonstrate applicability of this study to multi degrees of freedom systems.

Typical earthquakes and SRV transients were used along with some other loading

cases such as a triangular load pulse. This study concluded that, even for a

worst case model (ductility ratio equal to two), a dynamic reserve margin

-9-
(OR•) existed that was 50 percent greater than the static reserve margin (SRM).

General Electric further concluded that because the allowable stress limits in

the ASME Code were developed based on static load considerations, the dynamic

reserve margin would more than compensate for excursions above the SRSS value

and the Code safety margin would not be reduced. The discussions in the GE

(Reference 1) and Westinghouse (Reference 5) reports could be summarized as

follows:

(1) SRSS has been accepted by the NRC staff in some applications such as

summing certain seismic modal responses (see Regulatory Guide 1.92).

(2) SRSS accounts for the rapidly varying changes in frequency content and

amplitudes of these dynamic events in a more realistic manner than the

ABS method.

(3) Use of SRSS in lieu of ABS offsets some of the conservatisms inherent in

doing an elastic analysis for structures that would be predicted to

behave inelastically. The conservatisms exist due to the energy absorption

characteristics of a structure in the inelastic range that are not

currently considered in the superposition of elastic responses.

(4) The probabilistic studies conducted by Westinghouse and General Electric

both predict a finite (i.e. small but not zero) probability of exceeding

the SRSS value.

- 10 -
(5) The probabilistic exceedance predictions contained conservative assumptions

but were based on a relatively small data base and, for the General

Electric study, on a non-uniform population.

(6) If the probability of the combined dynamic events is low, then the conditional probability that the actual peak combined response will exceed

the SRSS calculated peak response is also low and of less significance

than for higher probability events.

(7) The difference between the combination of two dynamic responses by ABS

and SRSS becomes small as one response peak becomes large with respect to

the other response peak. The actual percentage difference between design

values (with ABS and SRSS) will be something less than the difference

between the dynamic responses because the normal operating loads in the

design equations are always added absolutely.

(C) Decoupling of LOCA and SSE Loads

Although the charter of the NRC staff Working Group did not specifically include

the study of the interdependency of postulated accidents and natural phenomena,

the group's discussions with certain of the industry groups included consideration

of this subject. As discussed earlier in this report, the consideration of

combined accident and earthquake loads derives from GDC 2. It has been the

staff interpretation that systems important to safety be designed against LOCA

plus SSE loads although there has not been a clear articulation of the intent

- 11 -
of this requirement, i.e., is there intended to be an explicit physical

dependence between the LOCA and SSE? If the separate events are considered to

be statistically independent, then it can be shown that the probability of a

LOCA event and SSE event occurring in the same general time frame is extremely

low and that the probability of the peak LOCA response and peak SSE response

combining is exceedingly low and of a magnitude which would not be indicative

of a design basis event. On the other hand, calculations of the potential

coupling of the events, i.e., SSE causing a LOCA, also yield low probabilities

althouah the numbers are subject to considerable controversy (Reference 6).

At the time of NUREG-0484 report, Westinghouse had made the most visible progress

in developing a technical basis for decoupling LOCA and SSE loads, including submittal of a topical report (Reference 6) to the NRC. B&W and CE indicated that

low-level efforts were being maintained and that there was great interest in

whether the NRC would be receptive to further work in this area.

The Westinghouse studies investigated the likelihood of a large seismic event

causing a LOCA and concluded that an SSE could not reasonably be the initiator

of such an event. One analysis postulated an undetected flaw in the pipe wall

and showed that seismic loadings would not produce significant fatigue crack

growth. A further analysis postulated a large through wall flaw (which would

ordinarily be detectable) and showed that extension of the flaw due to

instability would not occur.

It was the consensus of the Working Group that the studies performed to date

(September 1978), such as by Westinghouse, are promising, although further work

- 12 -
is necessary to confirm an adequate technical basis for decoupling. The group

believed that pursuit of this additional work should be encouraged by the NRC.

(D) 1978 Working Group Recommendations - NUREG-0484

Based on studies of proposed response combination methodologies, the 1978 NRC

Working Group concluded that a limited application of the SRSS method could be

supported at that time, 3 and, therefore, they developed recommendations for

combining dynamic responses in the analyses of structures, systems, and

components important to safety. These were published in September 1978 in

NUREG-0484 (Reference 8).

NRC in September 1978 adopted the Working Group's recommendations which stated:

"For the combination of the dynamic responses within the Reactor Coolant

Pressure Boundary (RCPB) and its supports, which result from the coincidence

of an SSE and LOCA, the Square Root of the Sums of the Squares (SRSS)

technique is acceptable contingent upon performance of a linear elastic

dynamic analysis to meet the appropriate ASME Code, Section III, Service

Limits."

3This was in addition to the uses of SRSS that the NRC had already approved

prior to acceptance of NUREG-0484 recommendations.

- 13 -
3. SSE AND LOCA RESPONSES - RCPB AND BALANCE OF PLANT

The study described in NUREG-0484, dated September 1978, was limited to the

primary reactor coolant system because the Working Group focused only on the

available information regarding the design methods and responses of various

primary system components and dynamic loads. Since the publication of

NUREG-0484, the staff has considered the design and responses of ASME

Section III Class 2 or 3 systems, and compared the effects of applying SRSS

and Absolute Sum (ABS) methodologies to BWR applications for Operating

Licenses, The staff has obtained additional information from the work done at

General Electric Company 4 (Reference 9), the Mark II Owner's Group and their

consultants Dr. R. P. Kennedy and Dr. Nathan Newmark 4 (References 10 and 11).

The staff also has had the benefit of generic dynamic response combinations

studies at Brookhaven National Laboratoriess (Reference 12).

Evaluation of this information indicates that ABS method may result in a

design overly influenced by unlikely peak combinations rather than a design

which considers modes of operation. Design by using ABS method may make these

systems less reliable for normal operation, and is particularly a concern for

piping systems which are subjected to large thermal expansions and relative

motions that are best accommodated by flexibility. SRSS represents a method of

4 NEDE 24010-P, NEDE 24010-1, NEDE 24010-2, NEDE 24010-3 (including tapes of

various transients supplied by MK. II Owner's Group to NRC & BNL).

5NUREG/CR-1330.

- 14 -
designing a less rigid system than ABS and thus permits a degree of design

optimization when thermal stresses are present and excessive rigidity is not

desirable.

The evaluation of the 1978 Working Group recommendations (Section 2(D)) and

the technical bases (see paragraphs (A) thru (E)) has led the staff to the

conclusion that the SRSS methodology for combining responses6 due to

LOCAW and SSE can be extended to any ASME Class 1, 2, and 3 affected system,

component, or support.

In applying SRSS methodology, the responses should be calculated on a linear

elastic basis and the time-phase relationship among functions to be combined

should be random. Functions which are not independent such as those that

result from the same dynamic initiating event should not be combined by SRSS

methodology. In those cases for which the independence of the function cannot

be established (e.g., Annulus pressurization and jet impingement or reaction

loading which result from a postulated LOCA), absolute summation of responses

or the use of time-phased responses is required.

The technical bases for this extension of SRSS methodology to include any ASME

Class 1, 2, and 3 system, component, or support is summarized below in paragraphs (A) through (E), and is also supported by the work performed by

5The individual responses have rapidly varying amplitude and a limited number

of short duration peak responses with the proviso that the frequency content

of the associated forcing functions provide significant excitation of the

natural frequencies of the component.

7 Pipe breaks in RCPB that result in the maximum response in any component or

component support.

- 15 -
Brookhaven National Laboratories for NRC reported in NUREG/CR-1330. Due to

the lack of of comparable ductility for concrete structures, and procedural

differences between Divisions 1 and 2 of the ASME Section III Code in considering loads and load combinations, the application of SRSS methodology to

structures has not been accepted at this time.

(A) Low Probability of Occurrence.

The individual probabilities of occurrence of the SSE and LOCA are small. If

these two events are statistically independent, the probability of simultaneous

occurrence of these events would be very low. Alternatively, given the occurrence of an SSE, there is some finite probability that a LOCA could result.

Although difficult to quantify at this time, G.E. and Westinghouse studies

have indicated that this conditional probability is also low. Within this low

probability frame of reference, the possible excursions of the combined dynamic

response over the SRSS value are of less significance than would be the case

for higher probability events. (In this regard the use of low versus high

probability is intended to distinguish between design basis accidents as

contrasted to types of events that are anticipated to occur at least once in

the plant lifetime.)

- 16 -
(B) Engineering Judgment Indicates that SRSS Represents a More

Realistic Combination of Peak Dynamic Responses for Rapidly

Varying Frequencies and Amplitudes, Short Time Duration of

Peaks and Random Time Phasing

The nature of the dynamic response time histories, e.g., rapidly varying

frequencies and amplitudes, short time durations of peaks, and random time

phasing would indicate that an ABS combination is very unlikely, even though

this combination can be attained on a theoretical basis. In addition, the

techniques used to calculate SRSS nonexceedance probabilities conservatively

assume that peak responses superimpose linearly when the structure behaves

inelastically. This assumption does not account for the expected coupling

behavior for an inelastic structure that exhibits higher energy absorption

capabilities than would be predicted by the elastically calculated response.

Good engineering judgment is therefore supportive of the SRSS method as being

a more realistic combination of peak dynamic responses.

(C) Techniques Used to Calculate SRSS Nonexceedance Probabilities

Contain Conservative Assumptions

Both Westinghouse and General Electric utilized Probability Distribution

Functions (PDF) and Cumulative Distribution Functions (CDF) in their studies

to quantify SRSS nonexceedance probabilities. Examples of conservatisms

utilized in these techniques include normalization to 1.0 of each individual

response that yields the maximum difference between ABS and SRSS summation of

peak responses and random statistical superposition of the peak responses so

- 17 -
I

that the maximum sum of the absolute values of the peaks can he attained. In

addition, CDF parametric sensitivity studies were performed that demonstrated

that the nonexceedance probabilities of SRSS were relatively insensitive to

the parameters that could affect the CDF distribution.

(D) Conservatisms Inherent in Linear Elastic Dynamic Analysis

ASME Code, Section III, stress limits are equivalent static limits and therefore

do not account for the additional energy absorption capability of components

under short duration (dynamic) energy limited forcing functions. This fact is

generally recognized by the engineering community and is not unique to this

study. Work undertaken to quantify this additional energy absorption capability

has shown that for components exhibiting even moderately ductile behavior, the

Dynamic Reserve Margin (DRM) is generally much larger than the Static Reserve

Margin (SRM). Because the use of SRSS is contingent upon performance of a

linear elastic dynamic analysis, the additional dynamic design margin (i.e.,

DRM

R- ) appears to compensate for peak combined responses which could probabilistically exceed the SRSS value.

(E) Independence of Dynamic Response Combination Techniques from Other

Factors Affecting Design Margins

The design margins inherent in the fluid systems of nuclear power plants are

not only dependent upon reasonably accurate load definition and structural

analyses, but encompass material integrity programs, adequate fabrication and

examination techniques, effectiveness of inservice inspection and many other

- 18 -
factors. Periodically, operating experience also uncovers problems such as

snubber malfunctions, steam generator tube wastage, and flaws or cracks in

safety-related components that have some cumulative effect on overall design

margin. It has been contended that conservative assumptions should be made

regarding response combinations to provide additional design margin against

such contingencies. The staff believes that this is not a valid consideration, principally because the amount of margin achieved through the selection

of a particular load/response combination methodology is quite variable and

may or may not be appropriate. Therefore, the staff recommendation is based

on an assessment of the technical merits of how dynamic responses should be

combined, rather than the need or desirability of providing design margin,

against those contingencies.

4. CRITERIA FOR COMBINATION OF DYNAMIC RESPONSES OTHER THAN THOSE OF SSE

AND LOCA

General Electric Company, the Mark II Owner's Group and their consultants

presented information from their studies which concluded that there are several

bases (reliability, optimum design, dynamic margin and statistical basis) for

accepting the SRSS combination of peak dynamic responses. The Brookhaven

National Laboratories (BNL) under Technical Assistance Contract from NRC

studied the statistical basis and confirmed that the rules of SRSS methodology

are valid provided that the loads are conservatively defined and the

characteristics of response functions are carefully examined. NUREG/CR 1330

contains a series of demonstration analyses using simulated time functions and

- 19 -
actual Mark II response combination cases. All responses 8 received from

General Electric and the Mark II Owner's Group were evaluated.

These Mark II combinations evaluated were the dynamic responses to OBE, SSE,

combined-with SRV and CHUG load, for the RHR wetwell piping systems, the

feedwater piping, the main steam line piping, the reactor pressure vessel

skirt, the shroud support and the guide tube.

The results of these evaluations formed the bases for accepting SRSS

methodology and are as follows:

" The Non Exceedence Probability (NEP) for the SRSS combination of two

responses generally has a value greater than 0.50. Specifically,

30 percent of such combinations were greater than 0.90, 80 percent

greater than 0.60, 92 percent greater than 0.50, and 8 percent less than

0.50.

" For the cases where the NEP using SRSS was below 0.50, the difference

between SRSS and ABS was observed to be small, and the peak magnitude of

one of the responses was observed to be much larger than the peak magnitude of the other response. For such cases, the use of a multiplication

factor of 1.2, applied to the peak magnitude of the responses will result

in an adjusted combination value which will be in an acceptable range.

8A11 responses with the exception of those pertaining to the containment

structure.

- 20 -
Based on the staff study of the Newmark-Kennedy (N-K) Criteria (Reference 10),

its supporting document (Reference 11), and the Brookhaven National Laboratories work reported in NUREG/CR 1330, the staff has arrived at the following

position which is applicable to all mechanical systems, components, and supports

for combining responses to dynamic loads other than LOCA and SSE.

The SRSS method may be used when Conditions A and B are both satisfied.

Condition A

(i) The dynamic response time function is rapidly varying;

(ii) Duration of the strong motion portion of the function is short;

(iii) Function consists of a few distinct high peaks which are random with

respect to time;

(iv) Response is calculated on a linear elastic basis; and

(v) Time-phase relationship among functions to be combined is random.

Condition B

For loads which meet Condition A, the SRSS method may be used provided a nonexceedance probability (NEP) of 84 percent or higher is achieved for the

- 21 -
combined response. An acceptable method of attaining that goal is meeting all

the following requirements:

(i) Define loads at approximately the 84 percentile or 1.15 times the

median, whichever is greater.

(ii) The SRSS value of the response combination has an NEP > 50 percent

selected from a Cumulative Distribution Function (CDF) curve constructed on the assumption that individual response amplitudes are

known and only random time phasing defined by its probability density

function exists. The CDF curve may be developed using the procedures

of Appendix N of Section III of the ASME Code, or alternatively

methods developed by BNL (Reference 12), or Westinghouse in WCAP-9279

(Reference 5) using absolute (unsigned) values of response amplitude

may be used. The method selected shall be justified in the submission

for the application being analyzed.

(iii) 1.2 times the SRSS value of the response combination has an NEP >

85 percent from the CDF curve constructed as in (ii) above assuming

only random time phasing.

The confirmatory work in NUREG/CR 1330 (Reference 12) also has demonstrated

that the SRSS use of methodology accepted for the combination of SSE and LOCA

responses by both Sections 2 and 3 of this report will provide a non-exceedance

probability of 84 percent or higher. For the combination of LOCA and SSE

responses, it is not necessary to apply the procedure described in this section

- 22-
(Section 4) since we have determined that Condition A has been satisfied and

that the 84 percent NEP level has been satisfied.

Should a case not meet the response combination criteria stated in Conditions A

and B above, responses shall be combined by absolute sum, or alternatively

other methods may be used provided justification is furnished to the staff to

ensure that the 84 percent level for NEP of the response combination has been

met.

5. CONCLUSIONS

The staff considers the use of SRSS appropriate for:

(i) Combination of SSE and LOCA dynamic responses for all ASME Class 1,

2, or 3 systems, components, or supports. For dynamic responses

resulting from the same initiating event, when time-phase relationship between the responses cannot be established, the absolute

summation of these dynamic responses should be used.

(ii) Combining responses of dynamic loads other than LOCA and SSE provided

a non-exceedance probability (NEP) of 84 percent or higher is achieved

for the combined SRSS response. An acceptable method for achieving

that goal is outlined in Section 4, Condition A and Condition B,

paragraphs (i), (ii) and (iii).

- 23 -
6. BROOKHAVEN NATIONAL LABORATORY GENERIC STUDIES ON RESPONSE COMBINATION

METHODOLOGY STATUS

Brookhaven National Laboratory under contract from NRC is continuing its

work on response combination methodology beyond that documented in NUREG/CR 1330.

The second phase (Phase 2B of TAP B-6) 9 of the BNL work will investigate the

validity of several proposed "loading level" criteria reported in NUREG/CR 1330.

A "loading level" criterion that permits a determination of the applicability of

SRSS methodology to be made by simple inspection of the loading input is much to

be preferred over a "response level" criteria contained in the position outlined

in Section 5.

The broader subject of which dynamic events and natural phenomena require

combination, how responses in components, equipment, and structures should be

combined and the specification of suitable design margin for such combinations

is under active review within the scope of Task Action Plan B-6, "Loads, Load

Combinations and Stress Limits."

9Task Action Plan B-6, Section 2B.

- 24 -
Appendix A

DEFINITIONS

1. Cumulative Distribution Function (CDF): The integral of the Probability

Density Function over a range from 0 to X, i.e., CDF (x) = Xp(x)dx P 

2. Dynamic Design Margin (DDM): The ratio of the Dynamic Reserve Margin

(DRM) to the Static Reserve Margin (SRM), i.e., DDM = DRM SRM

3. Dynamic Reserve Margin (DRM): For dynamic loads DRM is the ratio of the

peak dynamic load to cause failure, calculated by dynamic elastic-plastic

analysis, to the peak dynamic load resulting in code stress limits calculated

by linear elastic analysis.

4. Juctility Ratio (p): Total allowable deformation of a structural system

divided by the effective yield deformation.

5. Probability Density Function (PDF): In the general case PDF is P(X) as a

function of X where X is defined as a time of event occurrence, response

magnitude, etc.

6. Static Reserve Margin (SRM): For static loads SRM is the ratio of the

static load to cause fuilure, calculated by elastic-plastic analysis, to

the static load resulting in Code stress limits calculated by linear

elastic analysis.

- 25 -

Appendix B

REFERENCES

1. NEDE-24010-P, Technical Bases for the Use of the Square Root of the Sum

of Squares (SRSS) Method for Combining Dynamic Loads for Mark II Plants,

July 1977.

2. Technical Bases for the SRSS Method of Combining Dynamic Responses,

General Electric Co., April 1978.

3. EDAC 134-240.7R, Combining Multiple Dynamic Responses by the Square Root

of the Sum of the Squares Method, May 1978.

4. Probability Evaluation for Dynamic Response Combinations, Nuclear Services

Corp., 1700 Dell Avenue, Campbell, CA 95008.

5. WCAP-9279, Combination of Safe Shutdown Earthquake and Loss-of-Coolant

Accident Responses for Faulted Condition Evaluation of Nuclear Power

Plants, March 1978.

6. WCAP-9283, Integrity of the Primary Piping Systems of Westinghouse Nuclear

Power Plants During Postulated Seismic Events, March 1978.

7. SDAR-78-02, Inherent Design Margins in Structures Subjected to Pulse Type

Loads, May 1978.

- 27 -
8. NUREG-0484, NRC Working Group Report, "Methodology for Combining Dynamic

Responses."*

9. NEDE-24010-1, Supplement 1, SRSS Application Criteria as Applied to

Mark II Load Combination Cases, October 1978.

10. NEDE-24010-2, Supplement 2, Bases for Criteria for Combination of Earthquake

and Other Transient Responses by the Square-Root-Sum-of-the-Squares

Method, December 1978.

11. NEDE-24010-3, Supplement 3, Study to Demonstrate the SRSS Combined Response

has Greater than 84 Percent Non-Exceedence Probability When the NewmarkKennedy Acceptance Criteria are Satisfied, August 20, 1979.

12. NUREG/CR-1330, Brookhaven National Laboratory Review of Methods and

Criteria for Dynamic Combinations in Piping Systems, Final Report, April

1980.*

Available for purchase from the NRC/GPO Sales Program, U.S. Nuclear Regulatory

Commission, Washington, D.C. 20555, and the National Technical Information

Service, Springfield, Virginia 22161.

- 28 -
NRC FORM 335 U.S. NUCLEAR REGULATORY CO#SSON 1. REPORT NUMBER (Assigned by DDC)

(7.77)

BIBLIOGRAPHIC DATA SHEET NUREG 0484, Revision 1

4. TITLE AND SUBTITLE (Add Volume No.. if appropriate) 2. (Leave blank)

Methodology for Combining Dynamic Responses 3. RECIPIENT'S ACCESSION NO.

7. AUTHOR(S) 5. DATE REPORT COMPLETED

MONTH j YEAR

April 1980

9. PERFORMING ORGANIZATION NAME AND MAILING ADDRESS (Include Zip Code) DATE REPORT ISSUED

(Unresolved Safety Issues Program) MONTH IYEAR

U. S. Nuclear Regulatory Commission May 1980

Office of Nuclear Reactor Regulation 6. (Leave blank)

Washington, D.C. 20555

8. (Leave blank)

12. SPONSORING ORGANIZATION NAME AND MAILING ADDRESS (Include Zip Code) Division of Safety Technology 10. PROJECT/TASK/WORKUNITNO.

Office of Nuclear Reactor Regulation

U. S. Nuclear Regulatory Commission 11. CONTRACT NO.

Washington, D.C. 20555

13. TYPE OF REPORT PERIOD COVERED (Inclusive dats)

Technical Report

15. SUPPLEMENTARY NOTES 14. (Leave blank)

16. ABSTRACT g200 words or less) Procedures in accordance with Appendix A of lOCFR50, GDC 2, call for an

appropriate combination of the effects of the accident loads and loads caused by natural

phenomena (such as earthquakes) to be reflected in the design bases of safety equipment. This

requirement of interaction of loads has been implemented in various ways both within the NRC

aiid the Nuclear Industry. An NRR Working Group constituted to examine load combination method- )logies developed reconmiendations which were published in September 1978 as NUREG-0484. NRC

dopted the Working Group's recommendations which stated: "For the combination of the dynamic

esponses within the Reactor Coolant Pressure Boundary (RCPB) and its supports which result

rom the coincidence of an SSE and LOCA, the Square Root of the Sums of the Squares (SRSS)

echnique is acceptable contingent upon performance of a linear elastic dynamic analysis to

eet the appropriate ASME Code, Section III, Service Limit." Revision 1 of NUREG-0484 extends

he conclusionsof the original NUREG-0484 on the use of SRSS methodology for the combination

f SSE and LOCA responses beyond RCPB to any other ASME Section III, Class 1, 2, or 3 affected

ystem, component or support, and provides criteria for the combination of dynamic responses

ther than SSE and LOCA.

17. KEY WORDS AND DOCUMENT ANALYSIS 17a. DESCRIPTORS

17b. IDENTIFIERS/OPEN-ENDED TERMS

18. AVAILABILITY STATEMENT 19. SECURITY CLASS (This report) 21. NO. OF PAGES

Unclassified Unlimited Availability 20. SEIVRIfY CL,, f~aispage) 22 PRICE I unc assi lea s

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