recommendations for shape ofearthquake response …

WASH-1254

RECOMMENDATIONS FOREARTHQUAKE RESPONSE SPECTRASHAPE OF

February 1973

Directorate of LicensingU.S. Atomic Energy Commission

Washington ,D.C.

LEGAL NOTICETM5 report %, prep.,rej js 4n 4%:%ount 3f '&otk %ponioted by tilt UnitedSt~ate% C~o~etniient. %:itlivr tile United States not the~ United States AtomicEnergy Cummimmion. nof An of their cmplo)cc%. not any of theirciontractfe.%, subt;ont rj,:tots. or their employees. makes, any wajrrnty.expre,.% or implied, or anumcs any troM~ hbiabyI3 or responsibility for thej~xurjcy. completenci% or uwefilness ot ny information. .ippiritus. pfodialor pro%:rs% disdowcd, or reprewenih that its uwe *ould nut inritnge privitclyowned riplit%

I

WASH-1254uc-1i

RECOMMENDATIONS FOR SHAPE OF EARTHQUAKE RESPONSE SPECTRA

prepared by

JOHN A. BLUME & ASSOCIATES, ENGINEERS

for the

DIRECTORATE OF LICENSINGUNITED STATES ATOMIC ENERGY COMMISSION

UNDER CONTRACT NUMBER AT(49-5)-3011

-w

February 1973

,it onit 1-y th. utu,rintnilont n o Dti) umonts. U.S. (u•'vrnmo.nt I nrsn ig: tlirt .

ACKNOWLEDGEMENTS

Assistance of Dr. A. G. Brady of California Institute

of Technology, Mr. D K. Jephcott of the State of Cali-

fornia Office of Artritecture and Construction, arid

Mr. V. Perez of the ieismological Field Survey, NOAA,

San Francisco, is ackno&wledged for supplying the punched

card decks of the digitized accelerograms. Mr. D. Lange

and Dr. K. Kapur of the Mechanical Engineering Branch,

Directorate of Licensing, AEC provided helpful comments

during review of a preliminary draft of this report.

- i I -

J

RECOMMENDAT IONS

FOR

SHAPE OF EARTHQUAKE

RESPONSE SPECTRA

LONTENTS

I. SUMMARY OF MAJOR FINDINGS AND RECOMMENDATIONS ----------------

A. Scope ----------------------------------------------------

B. Data Used ------------------------------------------------

C. Analytical Approach ------------------------------------

0. Major Findings and Observations --------------------------

E. Recommendations----------------------------------------

II. INTRODUCTION -----------------------------------------------

A. General ------------------------------------------------

B. Scope ---------------------------------------------------

III. RESPONSE SPECTRUM SHAPES -------------------------------------

A. Introduction -------------------------------------------

B. Selection of Historic Earthquakes-----------------------

C. Analytical Aspects of a Response Spectrum

D. Response Spectrum Shapes from Historic Earthquakes-------

IV. STATISTICAL ANALYSES OF SPECTRUM SHAPES---------------------

A. Introduction ---------------------------------------------

B. Statistical Analysis Techniques --------------------------

C. Statistics of Spectrum Shape Ensemble --------------------

D. Statistics of Grouped Spectrum Shapes-------------------

1. General -----------------------------------------------

2. Maximum Ground Acceleration -------------------------

Paqeý

2

4

7

78

9

9

91014

17

17

17

18

20

20

21

- iii -

CONTENTS (Cont'd)

Page

3. Soil Characteristics---------------------------------

4. Epicentral Distances of Recording Stations------------

Geographic Grouping of Spectrum Shapes--------------------

Summary of Findings---------------------------------------

E.

V. EFFECTS OC EARTHQUAKE DURATION-------------------------------

A. General-------------------------------------------------

B. Analytical Approach--------------------------------------

C. Pat Plot Studies and Results ------------------------------

D. Observations --------------------------------------------

E. Summary of Major Findings ---------------------------------

VI. RECOMMENDED SPECTRUM SHAPES----------------------------------

22

25

26

28

39

39

39

40

40

41

48

48

48

50

53

54

65

A.

B.

C.

D.

Introduction -------------------------------- ------

Recommended Spectrum Shapes-------------------------------

!. Probability Estimation for DAF -----------------------

Major Findings-------------------------------------------

Recommendations -----------------------------------------

VII. REFERENCES--------------------------------------------------

TABLES

I Salient Characteristics of Selected Accelerograms---------

2 Grouping of Accelerograms According to Maximum GroundAccelerations -------------------------------------------

3 Grouping of Accelerograms According to the Soil Impedanceat the Recording Stations--------------------------------

4 Grouping of Accelerograms According to Epicentral Distanceof the Recording Stations--------------------------------

5 Geographic Group 1: San Fernando Valley Earthquake -------

6 Geographic Group I[: Southern California -----------------

16

31

32

3334

35

- iv -

TABLES (cont'd)

Page

7 Geographic Group III: California ----------------------------- 36

8 Geographic Group IV: Western U.S.A.- -------------------------- 37

9 Strong Motion Durations 3 of the Accelerograms Selectedfor the Pat Plot Studies --------------------------------------- 43

10 Results from Pat Plot Studies of El Centro, 1940, NS ----------- 44

11 Results from Pat Plot Studies of El Centro, 1940, EW ----------- 44

12 Results from Pat Plot Studies of Taft, N21 0 E ------------------ 45

13 Results from Pat Plot Studies of Taft, S690E ------------------ 45

14 Results from Pat Plot Studies of Helena, NS ------------------- 46

15 Results from Pat Plot Studies of Helena, EW -------------------- 46

16 Results from Pat Plot Studies of Golden Gate Park, NIO°E -------- 47

17 Results from Pat Plot Studies of Golden Gate Park, NSO*W 47

18 Numerical Data for Recommended Spectrum Shapes ---------------- 56

FIGURES

I Single-Degree-of-Freedom System -------------------------------- 11

2 An Snsemble of n Response Spectrum Shapes for a Damping Ratio - 38

3 Basic Spectrum Shape ------------------------------------------ 52

4a Recommended Spectrum Shapes for Large (50%) Probability ofExceedance --------------------------------------------------- 57

4b Recommended Spectrum Shapes for Large (50%) probability ofExceedance ---------------------------------------------------- 58

5a Recommended Spectrum Shapes for Small (15.8%) Probab~ility ofExceedance ---------------------------------------------------- 5)

5b Recommended Spectrum Shapes for Small (15.8%) Probability ofExceedance ----------------------------------------------------- 60

6a Recommended Spectrum Shapes for Negligible (2.3%) Probabilityof Exceedance -------------------------------------------------- 61

6b Recommended Spectrum Shapes for Negligible (2.3%) Probability

of Exceedance ----------------------------- 62

7 Recommended Spectrum Shapes ----------------------------------- 63

8 Spectrum 16:ape Comparisons; Damping Ratio = 0.02 --------------- 64

" V "

APPENDICES

A Response Spectrum Shapes

B Ensemble Spectrum Statistics

C Group Spectrum Statistics

D Period-Amplitude-Time (PAT) Plots

F Spectrum Shapes Based on Log Normal Distribution

- vi -

I. SUMMARY OF MAJOR FIND!NGS AND

RECOMMENDATIONS

A. SCOPE

The major objectives of the studies described in this repor. were to analyse

and evaluate a numhbr of significant earthquake records and to utilize the re-

sults to develop "standardized" design snectrum shapes to be used in the seis-

mic design of nuclear power plant facilities. Because earthquak-s are complex

phenomena, and since it is not possible to exactly predict the nature of seis-

mic ground motions, statistical analyses of recorded ground motions must be

used. The major findings and recommendations from the studies based on such

statistical analyses, along with brief discussions of the data and the ana-

lytical approaches used, are discussed in this chapter.

B. DATA USED

Response spectrum shapes for thirty-three significant and different accelero-

grams generated by twelve major earthquakes were developed for damping ratios

of 0.005, 0.01, 0.02, 0.05, 0.07, and 0.10. The California Institute of Tech-

nology prepared most of the accelerogram digitizations, which are consistent

and reliable reproductions of the actual qround motions. The remaining digit-

izations were obtained from the State of California Office of Architecture and

Construction, Los Angeles, and the Seismological Field Survey, NOAA, San fran-

cisco. The thirty-three accelerograms for purposes of this study are termed

the ensemble.

The response spectrum shapes were studied as an ensemble and as groups cate-

gorized according to peak gro-nd accelerations, site soil characteristics,

epicentral distances, and geographical locale of the recording stations.

These studies were made to determine the influence of the various character-

istics on the shape of the response spectra. Pertinent literature was

searched to collect the most reliable available data concerning these earth-

quakes and their recording stations.

C. ANALYTICAL ADPROACH

The following approach was used for the statistical analyýes:

- I -

" Spectrum shape statistics, such as mean, median, and standard de-

viation were developed for the ensemble of all accelerograms and

for each of the groups to provide indications of the central ten-

dencies and uncertainties associated with the corresponding groups.

" A statistically acceptable probability model suitable for the com-

plete ensemble of spectrum shapes was determined. Smooth "stan-

dardized" design spectrum shapes were derived on the basis of this

probability model.

" Comparisons were made between the recommended spectrum shapes and

the current Atom!c Energy Commission (AEC) regulatory criteria,

Newmark, Housner, and Blume F-factor spectrum shapes.

" Period-time amplitude plot studies of eight accelerogranis generated

by four important earthquakes were made to investigate the effects

of earthquake duration.

The probabilistic approach was used because it was considered to be most

rational, realistic, and appropriate for seismic design, especially of crit-

ical installations such as nuclear power plants. Previous studies end pre-

dictions of the frequency characteristics of seismic ground motions have usu-

ally been based on the analysis of only a few records. The results of the

present studies are particularly significant for the following reasonis:

" The studies are based on the analyses of thirty-three different

accelerorrams, a larger number than used in other studies.

" The accelerogram digitizations are the most reliable ones available.

" The studies are comprehensive because they include the effects of a

number of parameters, detailed statistical analyses, and effects of

earthquake duration.

0. MAJOR FINDINGS AND OBSERVATIONS

The following major findings resulted from the studies:

- 2 -

o Statistical predictions of spectral characteristics of future-seis-

mic ground motions are plausible and desirable.

* Smooth "standardized" design spectrum shapes can be used to represent

probable severity of seismic motions. Recommended spectrum shapes de-

veloped from these studies are presented in Figures 4 through 6 for

large, small, and negligible probabilities of being exceeded.

* The approach of using spectrum shapes derived from analyses of the

ground motion with peak acceleration normalized to unity was vali-

dated because there was low correlation between the peak ground ac-

celerations and the spectrum shape values. Separate treatment of

these two as independent variables in these studies was therefore

appropriate.

The followitig significant observations can be made from the results of group

analyses:

* Various seismic parameters appear to influence response spectrum

shape.

o Larger spectral amplifications can be expected to occur at a softer

site. The predominance of long period motion for softer sites and

of short period motion for firmer sites was not confirmed or rejected.

* Distance from epicenter did not appear tc irnfluence spectrum shape.

Predominance of long period motion at longer epicentral distances did

nfrt seem conclusive. Neither, however, was there sufficier,t basis to

reject this possibility.

* The studies by geographic grouping revealed minor variations in the

central tendencies as indicated by the means and medians, although

there were significant variations in the standard deviations or un-

certainties. The ensemble represented a wide-range of frequency con-

tent much better than any other group and thus, it was adopted as the

basis for the recommended spectrum shapes.

-3-

The followring observationý can be made from the comparisons between the rec-

ommended spectrum shapes and the AEC. Newmark, Housner, and Blume F-factor

shapes for a 2% damping ratio:

" The current AEC design spectrum shape is below the small probability

of exceedance shape for periods shorter than 0.5 sec, and those

longer than 0.9 sec.

" Tla Newmark spectrum shape is consistently above the small probabil-

ity of exceed.ince shape, except for a short interval in the vicinity

of zero perioo.

" The Housner spectrum shape is below the large probability of exceed-

once shape for periods shorter than 0.4 sec, and it is above the

latter for longer periods.

" The Blume F-factor spectrum shape for a standardized normal variable

value of 1.0 is consistently higher than the small probability of ex-

ceedance shape.

From the period-ampiltude-time studies, the following observations can be

made:

e The earthquake duration effect on the response spectrum shape is

small for periods shorter than 0.5 sec, the period ringe significant

for the nuclear power plant structures. The dynamic amplification fac-

tor (OAF) at longer periods, however, would generally tend to bc iigher

for long duration motions than for those of short duration.

E. RECOMMENDATIONS

Because risk. minimization is Zhe basic rationale for the seismic design of

critical installations such as nuclear power plants, the seismic load criteria

should consider risk variability with such factors as regional seismicity,

geotectonics, etc.. Thus, design spectrum shapes representing variable -.evvr-

ity of seismic loadings should be specified to achieve appropriate minimiza-

tion of the cotal risk.

-4 -

'hfe follor..ing rLcommendations.pert nent tu the design spectrum sha,.cs are con-

skstent witO this seisr'ic design objective. Other ground motion character-

istics, surh is peak grournd acceleration .-:sd strong r.i-tion duratior (in the

case of time-history analyse! should oe thoroughly considered to fully satisfy

the seismic desion objective. The curves in Figures 4 through 6 are soectrum

shapes, not responst: speLtra theimselves. To derive pseudo absolute accelera-

tion response spectra, it is necessary to evaluate the joint probabilities for

peak ground accelerations and the sdectrum shape va!ues.

" The large probability of exceedance spectrum shapes shown in Fig-

ure 4 should be considered as lower bo'jnd spectrum :hapes.

" For sites associated withrelatively low risk!, e.g., located in

lowi seismic 'y areas, the design spectru',i shapes for different

damoing ratios should not he !o>.ier than the s,:iali probab;lity of

exceedance spectrum shapes shc.4n in Figure 5.

" For sites associated with relatively high risks, e.g., located in

high seismicity areas, the design spectrum ,hapes for different

damping ratios should not be lo.ver than the neg'iqible protability

of exceedance spectrum shapes shown in Figure 6.

It must be noted, howe-'er, that the negligible exceedance prob-

ability spectrum shapes represent extreme ground motion amplific.-

tion. An inappropriate use of these shapes could result in an ex-

tremely low probability seismic exposure and the corresponding de-

sign could be ultraconservative. For example, if a very high peak

ground acceleration estimated deterministically c,:, the basis of an

extreme earthquake expected to occur at a very short distance (say,

at a point on the nearby fault) from the site were to be combined

with the neS;igible probability shape, ar extremely low orobability

seismic exposure wcjld result. The corresponding design would be

ultraconservative because the risk considerations would then be un-

necessarily duplicated by first assuming a highly improbable earth-

.quake occurrence (because the probability of Pn extreme earthquake

occurring i a given Doint is extremely small) and then. determ nis-

tically combining the estimated peak ground acceleration with the

spectrum 5hape. ]h,1refore, it is rec ti:tl.,nded that for the sites

associ atvd with rc I at •,e 1 y hii h risk!., lý'c above rc•;ortmcndatiof

for tht neyl 9i b Ic probability shape b. applied in LIonjunct i cn

wlith an appropriate procedure for probabilistically estimating

the total seismicexposure.

* For sites judged to be significantly responsive to ground motion

compcmno:,ts with periods longer than 0.5 seconds, the above shapes

should riot be used without appropriate mudifications for the par-

ticular it:,. conridhiurns.

-6-

II. INTRODUCTION

A. GENERAL

Earth.quakes are complex phenomena that impose severe loadings on engineered

structures. The earthquake phenomena primarily consisL of large energy

releases in limited volumes of the earth's crust and propagation of signif-

icant parts of these released energies as seismic body and surface waves.

Engineered structures located in the propagation path of these waves re-

spond with vibratory motions. These vibrations generate forces in the struc-

tures which have to be safely resisted. Instances of inadequate structural

resi3tance to seismic loadings with disastrous consequences occur frequently.

Some of the major earthquakes that caused considerable damage are: San Fer-

nando (1971), Tokachi-Oki (1968), Lima (1966), Alaska (1964), Kern County

(1952), El Centro (1940), Long Beach (1933), San Francisco (1906), Charles-

ton (1885), and New Madrid (1811-12).

The severity of vibratory structural response to seismic motion largely de-

pends on the seismic ground motion characteristics and the structure's dy-

namic cuaracteristics. Some of the important grt)und motion characteristics

are the ptak motion parameters, such as acceleration, velocity, and displace-

ment, and the frequency content of the ground motion. The ground motion fre-

quency content can be generally described as a measure of relative predomi-

nance o` different fr..quencies present in the ground motion. Spectrum shapes

are one of the measures of the ground motion frequency content and are im-

portant in estimating seismic structural response.

Nuclear powJer plants are critically important structures, and as such must

be designed for appropriate seismic conditions. Because earthquakes are

complex phenomena and exact predictions of seismic ground motions are not

possible, it is appropriate to base the seismic design criteria on statis-

tical predictions of these motions. Various ground shaking intensity

levels and the probabilities of their being exceeded should be established.

and the seismic levels associated with appropriate probabilities of exceed-

ance should be used in the design.

-7-

One approach to developing statistical predcctiuns of seismic loadings is

to determine probabilities of occurrence of ground motion frequercy char-

acteristics.

The study described herein analysed the frequency ditribution of ground mo-

tions.generated by a number of major %arthquakes. The results were then used

to develop "standardized" design spectrum shape-.

B. SCOPE

The studies in this report were oriented ioward the delineation of appro-

priate shapes of earthquake response spectra to be recommended for seismic

design purposes, based on the rationale described above. The project was

authorized in the USAEC Division of Reactor Standards letter dpted August

18, 1971. The major steps in the studies were as follows:

* Develop response spectrum shapes for !he hr, izontal ground motion

components of a number of selected major earthquakes.

e Study the effect of earthquake duration on spectrum shape by de-

termining the relationship between the spectrum shape and nu.iber of

cycles at predominant periods.

* Perform statistical studies of the spectrum shapes, including group-

ing of the spectra according to various earthquake and site charac-

teristics.

" Recoinmend spectrum shapes appropriate for seismic design and evalua-

tion of nuclear paer plant facilities.

" Compare the results of the above analyses with the current AEC seis-

mic design review procedures.

Studies of each of the above items and the results are discussed in the follow-

ing text.

-8-

Ill. RESPONSE SPECTRUM SHAPES

A. IUT 7%CULIO1It

A number of important and reliable earthquake records of horizontal ground

motion components were selected, response spectrum shapes developed, and sta-

tistical studies made of the ensemble of response spectrum Fhapes. A fairly

large ensemble was used to derive significant results from the studies. The

development or the spectra shapes and the statistical studies are discussed

in this chapter. A number of important and reliable earthquake records of

horizontal ground motion components were selected and response spectrum shape

were developed. The ensemble of response spectrum shapes developed from the

selected earthquake accelerograms and the corresponding statistical studies

are presented in this chapter. To derive significant results from the sta-

tistical studies, a fairly large ensembie of important ground motions was

analysed.

8. SELECTION OF HISTORIC EARTHQUAKES

A total of thirty-three accelerograms generated by twelve different major

earthquakes with peak ground accelerations exceeding O.g were selected

for the analysis (Table 1). Oifferent magnitude ratings for an earthquake

are sometimes reported in the literature because the values reported are usu-

ally averages cf the values estimated at several recording stations. The mag-

nitudes given in Table I were selected because they have been quoted most fre-

quently. The rationale for selecting the earthquake records was as follows:

0 The accelerograms were considered to be reliable records of the

ground motions because most were recorded recently. Those not

recorded recently, such as El Centro and Helena. have been ex-

tensively and reliably documented.

* The accelerograms were associated with fairly intense ground shaking.

* A wide-range of response spectra characteristics was represented by

the selected accelerograms. The Linia and Hachinohe records were in-

cluded because the Lima records contain a predominant high-frequency

Q9

content and the Hachinohe records a predominant low-frequency con-

tent. Inclusion of these records Lhus increased the range of dif-

ferent spectrum shape characteristics.

" The accelerograms included eight different and important records

from the 1971 San Fernando earthquake.

" The accelerograms comprise a reasonably large ensemble, thus yield-

ing a higher degree of confidence and reliability to the studies.

" The effect3 of geographical variations were included because the

accelerograms were recorded at a number of different geographical

locales.

C. ANALYTICAL ASPECTS OF A RESPONSE SPECTRUM

A response spectrum is defined as a plot of the maximurn values of a response

parameter of a family of linearly elastic single-degree-of-freedom systems

with different frequency characteristics and with a given ratio of system

dai•ping to critical damping wher, subjectcd to a ground motion time-history

versus the frequency characteristics (such as natural periods or frequencies)

of the systems.

For the purposes of this report, the pseudo absolute acceleration response

spectrum shapes for damping ratios of 0.005, 0.01, 0.02, 0.05, 0.07, and 0.10

were developed for the selected accelerograms.

Figure I shows a model of a single-degree-of-freedom system. The spring is

linearly elastic with stiffness k and the dashpot indicates a viscous damper

with a damping coefficient c.

- 10 -

kg

FIGURE 1. SINGLE-DEGREE-OF-FREEDOM SYSTEM

The equation of motion of this system is:

m)n +c; + kx -i (1)

in which

m = mass

x = displacement relative to the ground [L]

d_ velocity relative to the ground [LT- 1 ]it

- d x• acceleration relative to the ground [Lf iId t

c = damping constant [;.IT- ]

k = spring constant [ MT- 2 ]

x = ground motion acceleration [LT" 2 ]g

. [!] indicates the dimension of the quantity. The basic dimensions

are mass, M; length, L; time, T.

Equation (I) can be rewritten as:

+ "+ - . (2)

in which

4-k = circular frequency Tm[t]C -

-2rr= damping ratio

The solution of Equation (2) is given by

tX(tI, - - f h(t-r) T () J

in which

h(T) = impulse rusponse function [T]

and

w damped circular frequency ( T-' ]

==

For a moderate amount of damping, w nearly equi-Is w. As example, for

a relatively high damping value of 20%, w is equal to 0.98;. Because

the damping values for most of the dynamic analyses of nuclear power

plant elements are considerably less then 20%, the difference between

w and w is negligible. Thus, w will be u3ed in place of w. The

system spring force, F, at an instant, t, is given by

F(t) = K.(t) _ mw2 (t) (5)

Let z (t) = W2X(t) (6)p

Then F(t) = m i (L) (7)

'"has the dimensions of acceleration, (LT-], and is termed pseudo

absolute acceleration. Comparison of Equation (6) with Equation (2)

indicates the reason for this quantity being termed "pseudo", namely,

- 12 -

the magnitude of P differs from that of the real absolute acceleration by

a quantity, 2cwý. The pseudo relative velocity, p, is defined by

x 2 [L11 (8)

ppThen, accepting •••

P ( t• = t (• .:t) (9 )

In accordance with the definition of a response spectrum, the pseudo absolute

acceleration response spectrum, S z is given by

0) I .0)

in which

n= atural period [:3

depends on the system period, , the system damping ratio, ,, and the in-

put ground motion, . Equation (1l) is derived from theoretical considera-

tions and Equation

Thus, for a rigid system =, 0), the pseudo absolute acceleration spectrum

value equals the maximum ground acceleration, a. This is one reason why nor-

malization of ground motion by peak ground acceleration is convenient. The

spectrum value generated from the ground motion normalized by the peak accel-

eration is actually the dimensionless ratio of the pseudo absolute acceleration

spectrum value to the peak ground acceleratior anJ is termed dynamic amplifica-

tion factor (DAF) for pseudo absolute acceleration.

- 13 -

Let D(T,,,) = dynamic amplification factor (OAF) for pseudo

absolute acceleration

(T •.- )

Then 1)(1 "") r_ (12)

and C)((;,.. ) = 1., (131

Thus, for zero period, equals 1.'].

0. RESPONSE SPECTRUM SHAPES FROM HISTORIC EARTHOUAKES

IThe obj~'ctive of the studies was to analyze the shapes of the respon.•e s.pec-

tra, not the response spectra themselves. To facilitate the c'amp'arison of

the spectrum shapes, the accelerograms w!re riormalized to a peak gruund a.:cel-

eration of 1.0g. i'hus, the spectral vaiues obtained are dimensiconless ratios

o'f spectral acceleration to peak 4"rouod acceleration, or dynamic'amplification

factors (DAF). The response spectra generated from such normalized ground

motions are term.td response spectrum shapes, or OAF. The response spectrom

shapes are useful for comparing the relative predominance of different fre-

quencies in an individual arcelerogram and for different accelerograr.s. Accel-

erograms can be normalIzed by several different methods. For t'ýe purposes of

his study, normalization by peak ground acceleration was co:widered most use-

ful and convenient, especially for the stotistical predictions of response

spectrum shapes.

A recursive algorithm' was used to compute the response spectrum shapes of

the selected historic earthquakes for damping ratios of 0.005, 0.01, 0.02,

0.05, 0.07, and 0.10. Because the method of digitizLiion of accelererjrams

significantly affects the response spectra,' the nwst receat and most reli-

able accelerogram digitizations were used in ihe in-jly-ses.

The spectrum shapes were computed for a period range: of 0.04 sec to 2.5 sec,

or a freqLency range of 0.4 cps to 25 cps. which was considere."- sufficient

to encompass the frequency characteristics of nuclear power plant components.

This range of frequency characteri,ýtics was discretized by us;g 108 points

to obtain good frequency resoiution of the spectra.

- 14 -

The Fourier content of digitized accelerogram data may be accurate up to

about 25 cps, 8 and thus the upper bound on the frequency range of the ýpc-

tra was set at 25 cps. Most of the accelerogram data were as described in

Reference I and hence the accelerogram corrections, such as smoothing of the

fixed trace, smoothing of the timing marks, and the root-mean-square minimi-

zation of acceleration were applied to the data. Generally, the accelero-

grams are also corrected by shifting and/or rotating the base line or using

a band-pass filter. Such corrections are necessary only for computing ground

motion velocities and displacements. Because they do not significantly af-

fect the computition of the pseudo absolute acceleration response,•,• these

corrections were not considered necessary.

Linear plots of the spectrum shapes are presented with period as abscissa and

alternatively with frequency as abscissa in Appendix A as Figures Al through

A66. These two way!. of plotting complement each other, representing the spec-

trum details more fully. Frequency-plots were used in determining the spectral

values for the high-frequency elements and period-plots were used for the long

period elements.

- 15 -

TABLE 1SALIENT CHARACTERISTICS OF

SELECTED ACCELEROGRAMSPeak GroundAcceleration,

Magnitude Component g UnitsEarthquake

El Centro

El Centro

Kern County

Olympia

Helena

San Francisco

Year Recording Station

1940 El Centro,Californi3

1934 El Centro,California

1952 Taft,CalifLrnia

1949 Olympia,Wasnington

1935 Helena,Montana

1957 Golden Gate Park,California

1966 Cholame-Shandon # 2,California

19%6 Chnlame-Shandon 0 5,California

Parkfield

Parkfield

Tokachi-Oki 1968 !!.chinohe,Japan

1966 Lima, Peru

7.0

6.5

7.7

7.1

6.0

5.3

5.6

5.6

7.8

7.5

6.6

6.6

6.6

6.6

6.6

6.5

5.6

N2 P ES69*E

S860W

UIS

1180 0W

UW5ES25OW

N5'1 W14115u 11

NSEW

EW

0.51Not Recorded

0.400.47

0.330.22

0.260.18

0.180.16

0.190.31

C. 130.16

0.110.13

IUSEW

Lima

San Fernando

San Fernando

San Fernando

San Fernando

Eureka

Olympia

Parkfield

1971 Castaic, ORR,California

1971 Bank of Calif.,California

1971 Universal-Sheraton, Calif.

1971 V.N. HolidayInn, California

1954 Eureka,California

196ý Olymoia,Washington

1966 Temblor,California

N8*°EN82 0W

N210 ES69°E

N11 0 EN79 0W

NSEW

NSEW

g790 E

S4 E

S860W

N650WN250 E

0.190.23

0.420.27

0.340.29

0.230.14

0.180.13

0.280.15

0.260.18

0.200.16

0.280.33

NOTE: Information presented in the above table is compiled from

References 1, 2, 3, 4, and 5.

- 16 -

IV. STATISTICAL ANALYSES OF SPECTRUM SHAPES

A. INTRODUCTION

The analyses in this chapter were oriented toward statistical predictiors of

the characteristics of future ground motions. Spectrum shape statistics such

as mean, median, and standard deviation were computed for the complete en-

semble of spectrum shapes discussed in Chapter Ill. These statistics were

also computed for the accelerograms grouped irn four differen: ,ýays:

" max;mum ground acceleration.

" so-l characteristics at the recording site,

" epicentral distance, and

* geographical locale of the recording stations.

The median and mean values indicate the central tendency of a sample. The

standard deviation measures uncertainty associated with the sample. In most

of the cases, the combination of either the mean or me-dian and the standard

deviation suffices for statisLical predict;ons.

B. STATISTICAL ANALYSIS TECHNIQUES

In an ensemble of r response spectrum shapes, shown in Figure 2, let i:f(!.,-)

denote the spectral ordinate of the ith spectrum shape for the period. , nd

the damping ratio, %. Then, the mean, -•.(T ,,)0 and standard deviation,

are computed by the following equations:

i( 1

r ,-" , II, ( Ss (T*~ -1- fT ) I!

- .17 -

The median of the ensemble, ry.)(T-,.), is determined as follows: First, the

spectral values, D.(Lt., i 1, 2 . ,are rearranged in a descending

order. Then, if ni is an even number,

7:) (16a)- J

If n is an odd number,

M, 0 •6b)

The mean spectrum shape, m,'(G'A, the median spectrum shape, , , and the stan-

dard deviation spectrum shape. , are constructed by computing means, me-

dians, and standard deviations for 108 periods in the period range under con-

sideration. The mean and median spectrum shape values For zero period equal

unity and the standard deviation spectrum value fer zero period equals zero be-

cause the DAF value for zero period is constant and equals unity. From Equa-

tions (14) and (16). the actual values of the mean and redian shapcs will not

be equal, if there is a skew in the data.

C. STATISTICS OF SPECTRUM SHAPE ENSEMBLE

The mean. median, and ýtandard dev;ation response spe,:trum shapes for the corn-

plete ensemble of the selected accelerograms and for all damping ratios were

computed as described above and are presented in Appendix B as Figures 81

through BIB. The following observatiuns regarding these spectrum shap o-.are

pertinent:

* Th,: mean and median spectrum shapes, indicators of the central ter;-

dency of the ensemble. are similar for each damping ratio. Th,.

small quantitative difference between these two s5atistics i'dicltes

that the DAF data his ,omv, -,kewnesý. See Chapt-r VI for a detailed

discussion of the DAF distributicon,.

* The mean arid median spectrum shapes are srmooth. As expected, the

smoothness increases with the damping ratios.

- 1 -

*A's the period approacnes zu-o the rmean ar'd rx!<;ar' jhpe ie

approach unity and thie s~andard deviat oni approaches zerc. as

expt2c ted . The s t.3toddrd Jvv i Is oar, dec rcta;e s a s t~ hep: n-r-j,*,

Tha 5 dec rea S tow * ,- r , ir s much smai I Ier t hav the cor rt~svo-e- .nq cc-

creije in the riwjr. arl:j lc~ ~ hu, *:" 'he it e~ne

in the OA-F increases w~itt t~e periodI. ese~al for ztcricds longer

mhan 0.25 -,cc For ;,v,-c,v,. i(~r'(er thr' 0.C9 sec. * " rvltjlt: .vJ-

certainty is st~s:ar't ialIlv larger t. i~ar for zhe shc~r te r per; wl

a ýa.i ri1- rap i ta~ trend Zk.nt ; nues tý 2 .5 ýt~c per; -;C.

The mo n reanor,~ fr.r '.!t: rc.c in xct.rt a nt,.. t per io

thle cl*,sLeml Ie Con' a ins sev..-,-I! I Lce I crc r.vr'. .,tr va !le~ Sricr t .4r

long s Y rong q -io iin a i&. . de~ .*i -~ r* f jte Ii

C e r tI i thv s ta)r u ura a o t: r r , is > ,ho- pr.* : ý i, ma r ir,C u

short per iods onl If *nrv- ~Ch~ t h Ifanq Jur at or~n 0-c thi. r~rv-

jo~r~i nance of both, short ar~d Ifloq 7a " WS . ts Mt' CV er-tr

dc ncy o tM hfe en bem b s a cc t!r. t u, i vs in th ) S~r IvE erat r arq t

an c unt i e r ab uItv mUe c~t 1 or J ;cfri k r lr.ge c Dus Ut. -I f-

t aI veIy l a r e d v v t i un~ 5f D£AF i i t rti v Inn tr~ r an t:. n j, %

ttv re iat vt uncur aart in tna. rant-e gr (r.'.t4'r *han (or

S h ()r tp t:riod r , jn ge

* The r~eafl and rmed ian spec ,rur, shapes dec reast: -. rL a~t ? ttr .tih

inc~reasing dam~pi ng rat ios . we;c ;nd;Cdte- reliti;vely qrvater dvc

crease fo. the ',hor t 'vtri od. t han for ihe Ir'nq per o(dS . The %tan-

dard deviation spectrum shav'ý,z also decreoae ane boeconeS flat*.?ýr ~..th

increasinq dam-inq ratio. This, dj~rre.se i, ia r hf-wt.~'er.t:K~

in the mea, and median and ;., e.spLuciaily t ruc for t~heŽ Ionq :)eriod!,

w.hich result,~ in great-.-r fIatnes.-. Thu0 5 * t he r-! 1 i vu wncer t a nt y

i n OAF va lues rumia ins PractLi ca I I i nd ifferent to t ho change', i T

d,,mping ratio. Increarer camping tend% to at.Cnuatv retpon-,L. more-

for sh.crt periods thanz fur long period',.

- '9

D. bkiAVSTICS OF GROUPED SPECTRUM SHAPES

I. General

The rationale of the grouping approach will be briefly discussed first

so that the group statistics may be appropriately interpreted.

A number of earthquake characteristics could influence response spectrum

shapesu Grouping of the records by a selected characteristic helps to

investigate and estimate the influence of such characteristics on re-

sponse spectrum shapes. Such an investigation has maximum sigificance

if performed under the ideal condition that only the characteristic under

consideration is varied wHile others are kept constant. It is apparent

fron. the sparsity of the available ground motion data, however, that this

is not fcs;ble. It is helpful, nevertheless, to understand what infor-

mation could be obtained from the grouping approach under ideal conditions.

Assume that a seismic characteristic, s, in the range, s; S < G, favors

a frequency range, f < f < f,,, over other frequencies. Then, the mean,

median, and standard deviation spectrum shapes for the accelerograms in

the group, s .: <, would be expected to display the following char-

acterisLics:

* In the frequency range, f < f : f the mean and median spectrum

values for this group will be generally higher than those for the

other groups, indicating the preference of this group. The same be-

havior will be expected when the ensemble mean and median are com-

pared with the group mean and median.

0 In the frequency range, f < f < f 2# the standard deviation spectrum

shapes will be generally lower than those for the other groups, in-

dicating a smaller degree.of uncertainty associated with the spectrum

values for the preferred frequencies. The same behavior will be ex-

oected when the standard deviation shapes of the ensemble are compared

with those of the group.

Higher spectrum shape values for the preferred frequency range will be

more probable than for the other frequencies. The reliability of such

- 20 -

an interpretaticn depends on two factors, nameiy, the number of accel-

erogram samples in the group, and the range of seismic parameter values

defining the group. The reliability will increase with an increase in

the number of samples, and decrease with an increase in the range of

seismic parameter values.

Statistics of the spectrum shapes grouped in four different ways were com-

puted to investigate the influence of different earthquake characteristics

on the response spectra. The accelerograms were grouped according to:

* the maximum recorded ground acceleration (Table 2),

* the soil characteristics at the recording station (Table 3),

* the epicentral distan.e of the recording station

(Tabie 4), and

* the geographical locale of the recording stations (Tables 5, 6, 7,

and 8).

The specific details of the groups and the analytical results are signif-

icant. Different values for a characteristic ef an earthquake are some-

times reported in the literature. In such cases, an apparently reason-

able value of the characteristic was adopted in the analyses without

further investigating the allthenticity of the value. It would be worth-

while, however, to c.)nduct such an investigation to improve the reliabil-

ity of the available information.

2. Maximum Ground Acceleration

Table 2 lists a grouping of accelerograms according to maximum ground ac-

celerations. This grouping of accelerograms described below achieves a

reasonable balance between group size and range of accelerations.

Maximum Number ofGroup Ground Acceler4 .. tion, a Accelerograms

Al a > O3g 8

A2 0.2g9 a < 0.g 10

A3 a < 0.29 15

21 -

The frean, median, and standard deviation spectrum shapes for the three

groups of accelerograms for a 0.02 damping ratio are presented in Appen-

dix C as Figures Cl through C9. The following are pertinent observations

regarding these spectrum shapes:

* The Group Al mean and median shapes are generally somewhat lower than

the mean and median shapes of the Groups A2 and A3 (Figures Cl, C2,

C4, C5, C7, and C8). The Group Al standard deviation spectrum shape

for periods longer than 1.0 second is considerably lower than the ones

of the other groups for the same period range (Fiqures C3, C6, and

CC). This means that higher OAF values for Group Al are less probable

than they would be for Groups A2 and A3. This is particularly true

for periods longer than 1.0 second; in other words, higher OAF values

occur for accelerograms with a 0.3,g.

* No cluar trends are apparent for the Groups A2 and A3.

In spite of the first observation above, the maximum ground accelerations

of the accelerograms generally have low correlation with the correspond-

ing OAF values. Thus, probabilities for the DAF values, as discussed in

Chapter VI, may be considered independent of those for the ma.6mum ground

accelerations. This conclusion leads to this important result:

From Equation (12),

Sa(T_~r,;j D U.(,•• (17)

Thus, the probabilities of exceedance for the spectral ordinate, 2 used

for computing response of structures, can be derived by a rather simple

combination of the probabilities for the peak ground acceieration, a, and

the DAF for pseudo absolute acceleration, D. This method of combination

of probabilities is discussed further in Chapter VI.

3. Soil Characteristics

The following site characteristics could influence the response spectrum

shape:

- 22 -

* Soil density

" Soil layering

" Layer thicknesses

• Depth to firm rock

* Water table elevation at the site

* Soil moisture content

" Shear and compressional wave velocities in the soil

* Nature of soil behavior -- linear or nonlinear

It is apparent from the above list that the influence of the soil char-

acteristics on the response spectrum shape is a complex phenomenon. In-

vestigation of this phenomenon is asid has been treated as an independent

field. 1 1 Thus, the subject can be treated only in an approximate way in

the present analysis.

It was shown 11,12 that the soil impedance, 1, is determined by Equa-

tion (18) is one of the factors of considerable importance in this kind

of analysis.

I (18)

in which

P = specific soil density

V = velocity of shear wave in soils

In the present analysis, soil impedances of the top layrrs at the record-

ing stations were used as the basis for grouping of the accelerograms.

In the case of a site with a number of shallow soil layers, an overall

average value of impedance was used. For the selected accelerograms, in-

formation on the soil characteristics at various recording sites is sparse

and contains a high degree of uncertainty. More detailed soil, geological

and geophysical investigations of various recording station sites are

needed to form a Firm basis for the kind of analysis described in Sub-

section I of this chapter.

- 23 -

The grouping of accelerograms according to their site impedance in

Table 3 can be condensed as follows:

Number ofLrm Impedance, I, (ft/sec)xlO Accelerograms

81 4.0 < I < 5.5 13

82 1 < 3.9 16

The accelerograms recorded at Helena and Temblor are not included in

these groups because the estimated impedance values for these sites,

based on the available data, are considerably higher than those of the

other sites and could result in Pn anomalous influence on the analysis.

The mean, median, and standard dev.iation spectrum shapes for the accel-

erograms in these two groups for 0.02 damping ratio value are presented

in Appendix C as Figures CIO through C15.

The following are pertinent observations regarding these spectrum shapes:

" The mean and median shapes for each group are generally similar

to each other.

* The mean shape of the Group BI is generally lov.ier than that of the

Group B2.

" No clear trend is seen in the standard deviation shapes.

It has been foundl 2 that the accelerograms recorded at firmer site5 gen-

erally show lower DAFs than those for the accelerograms recorded at

softer sites. This is indicated by the second observation above. It

would seem reasonable that ground motions recorded at soft sites would

show a predomitance of lower frequencies and those recorded at firm

sites would have higher predominant frequencies. Such a trend was not

strongly indicated by the results of this analysis because of the uncer-

tainty associated with the soil characteristics data, however, these re-

sults should not be considered as a negation of this belief.

- 24 -

4. Epicentral Distances of Recording Stations

The accelerograms were arranged according to the epicentral distances

of the recording stations as follows (Table 4):

Epicentral Distance, D Number of

Group Miks Arcel erog rams

Cl 15 < D < 45 14

C2 L < 15 15

The accelerograms recorded at Hachinohe and Lima were not included in

the analysis because the reported epicentral distances for these rec-

ording stations are much longer than those for the other stations and

hence could have an anomalous influence on the analysis.

The mean, median, and standard deviation spectrum shapes for the accel-

erograms in the Groups CI and C2 for a 0.02 damping ratio are in Appen-

dix C as Figures C16 through C21. The following are pertinent observa-

tions regarding these spectrum shapes:

* The mean and median shapes for each group are similar to each other.

* The mean shapes for both the groups are approximately equal.

* The standard deviation shape for the Group Cl is considerably lower

than for the Group C2 for periods longer than 0.5 second.

Although the comparisons of the median spectrum shapes do not clearly in-

dicate predominance of lower frequencies for accelerograms recorded 3t

longer epicentral distances or predominance of higher frequencies in

records with shorter epicentral distances, the third observation above

would tend to confirm these effects. As other parameters, such as soil

characteristics, would also influence the response spectrum shapes, the

absence of ciear trends in this grouping are not unexpected. In addition,

epicentral distance per se may not be a significant factor with respect

to the response spcctrum shapes. This may be rarticularly true for earth-

quakes associated with fairly Ior:ng aul breaks. In such cases, the

- 25 -

distance between the station and the nearest point of surface rupture

might be more appropriate. Also, the reported epicentral distances may

not be the actual ones because epicenters cannot be located exactly.

E. GEOGRAPHIC GROUPING OF SPECTRUM SHAPES

The selected accelerograms were recorded at a number of different geographical

locales in seismically active areas of the world. The accelerograms were gen-

erated by earthquakes that originated in different geological settings and per-

haps by different earthquake source mechanisms.

In all, spectrum shapes for five different geographic groups of accelerograms,

including the ensemble, were statistically analyzed as follows:

Number of

Group Geographical Locale Accelerograms

I San Fernando Valley 8earthquake

II Southern California 19

III California 23

IV Western U.S.A. 29

V Worldwide 33

The salient characteristics of the thirty-three accelerogram ensemble are

listed in Table I (Chapter III); those for the remainder of the above groups

are reproduced in Tables 5 through 8.

Mean, median, and standard deviation spectrum shapes for Groups I through IV

for 0.02 damping ratio are presented in Appendix C as Figures'C22 through

C33. Ensemble spectrum shape statistics for 0.02 damping ratio (Group V) are

in Appendix B as Figures B7 through B9.

A number of pertinent observations regarding comparisons of the spectrum shape

statistics for a geographical grouping can be made:

0 The mean and median shapes for each group are similar to each other.

The mean shapes are generally smoother than the median shapes.

- 26 -

" The Group I mean spectrum shape is generally higher than those for

the other groups, especially for the period ranges of 0.? - 0.4 sec

and 0.7 - 2.5 sec. In the latter period range, this shape is sub-

stantially higher than those for the other groups which indicates

a strong predominance of long period motion. In the short period

range, 0.04 - 0.02 sec, the Group I shape is slightly lower than

the Group V mean shape.

* The Group II mean spectrum shape is somewhat higher than those for

Groups III, IV,.and V. This tendency is more pronounced for the

longer period range (greater than 0.5 sec). This shape is slightly

lower than the Group IV and V shapes in the short period range, 0.04

- 0.2 sec.

* The mean spectrum shapes for Groups Ilt, IV, and V are close to each

other.

* The standard deviation spectrum shapes show more variations than the

mean shapes.

" The Group I standard deviation spectrum shape is higher than those

for the other groups in the period ranges of 0.2 - 0.4 sec and 1.0

- 2.5 sec, with the exception that the Group V shape is substantially.higher in the range of 1.0 - 1.25 sec but lower than the others in

the remaining period ranges.

* The Group II and IIl standard deviations are similar. Both are sub-

stantially lower than those for Group IV and V in the short period

range, 0.04 - 0.1 sec.

The Group IV standard deviation shape is similar to that for Group

V except it is lower than the latter in the period ranges of 0.04 -

0.1 sec and 0.8 - 1.2 sec.

* The ground motions recorded in Califor•iia are predominant in the

period ranges of 0.2 to 2.5 sec. This is particularly true for

the accelerograms generated by the San Fernane.dA earthquake. Incor-

poration of the spectrum shapes from the other parts of the western

U.S.A. and worldwide results in predominant dynamic amplification

in the short period range, 0.04 - 0.2 sec.

- 27 -

It appears appropriate to develop standardized design spectrum shapes on

the basis of the ensemble spectrum statistics for the following reasons:

0 The ensemble mean and standard deviation spectrum shapes appear to

encompass broader ranges of frequency content than those of any

other group. Thus, the predictions based on the ensemble statistics

would better represent the conditions not yet recorded in local areas

in addition to those recorded.

0 The reliability of the statistical measures and the predictions

based on them Increases with the sample size. The ensemble consists

of more earthquake records than any other group. Therefore, the

ensemble statistics and predictions based on them would be more re-

liable than those for any other group.

F. SUMMARY OF FINDINGS

Statistical analyses of the ensemble of response spectrum shapes and the

grouped spectrum shapes were presented in this chapter. The spectrum shapes

were grouped in four ways; by maximum ground acceleration, by epicentral

distance, by soil characteristics, and by geographical locales. The major

findings were:

& The mean and median spectrum shapes for the groups are smooth In com-

parison with the shapes for individual accelerograms, and they are

similar to each other. The median shape is less smooth than the

mean and shows small quantitative variations from the mean, indica-

ting some skewness in spectrum shape data.

• The mean and median shape values decrease for longer periods and

higher d'mping. The rate of decrease with longer periods, however,

decreases with higher damping, resulting in flatter shapes for

higher damping.

The standard deviation spectrum shapes show greater variations than

the mean and median, indicating greater variability of uncertainty.

- 28 -

" The standard deviation shapes also generally decrease with longer

period and higher damping. However, tI, rates of decrease are rela-

tively smaller than those for the means and medians, indicating in-

creased relative uncertainty for longer periods and an indifference

of relative uncertainty with respect to .1iping.

" The influences of various seismic parameters on response spectrum

shape were indicated from the grouping approach. The significance

of the results of this part of the study, however, would be enhanced

if the followiing conditions could be met:

I. The uncertainties associated with some of the available data

are investigated and minimized.

2. A large number of reliable accelerograms are available so as to

allow variation of only one parameter while the others are kept

constant.

Because reliable ground motion data are sparse, it is difficult to satisfy the

second condition. The following significant observations, however, can be made

from the results of group analyses:

* The approash of using spectrum shape derived from the ground motion

analysis by normalizing the peak ground motion to u.nity was confirmed

because the peak ground accelerations and the spectrum shape values

had low correlation. Separate treatment of these two as independent

variables was therefore appropriate.

" Spectral amplification at a soft site can be expected to be larger

than at a firm site. The expected long period predominance for soft

sites and short period preaominance for firm sites were not confirmed

or rejected.

N The influence of epicentral distance on spectrum shape diminishes

with the increasing epicentral distances. Tne expected long period

predominance at longer epicentral distances was not indicated; nei-

ther was the rejection of this belief indicated.

- 29 -

* The results of the geographic grouping revealed that the central ten•-

dencies of the groups, indicated by means and medians, do not vary

significantly with different geographical locales. Although the un-

certainties or standard deviations did show significant variations,

the ensemble represented a wide-range of frequency content much bet-

ter than any other group. Thus, the ensemble was adopted as the

basis for the recommended spectrum shapes.

- 30 -

TABLE 2

GROUPING OF ACCELEROGRAMS ACCORDING TO MAXIMUM GROUND

ACCELERATIONS

Number

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

Accelerogram

Parkfield #2

Parkfield #5

Lima

Parkfield #5

Castaic ORR

El Centro, 1940

Temblor

Olympia, 1949

Castaic ORR

V.N. Holiday Inn

Temblor

Lima

El Centro, 1934

Eureka

Hachinohe

Bank of California

El Centro, 1940

Olympia, 1965

Olympia, 1949

Hachinohe

El Centro, 1934

Taft

Universal-Sheraton

Eureka

Taft

Helena

Olympia, 1965

V.N. Holiday Inn

Bank of California

Helena

Golden Gate Park

Universal-Sheraton

Golden Gate Park

Component

N65°E

U85°E

118° E

N 50W

N210E

NS

N250 E

S860W

S690E

NS

tN65 0W

N820W

NS

N79 0 E

EW

N110E

EW

S4°E

N4°W

NS

EW

N210E

NS

N11IW

S69 0 E

EW

S86 0 W

EW

N790W

NS

N80OW

EW

NIO0 E

- 31 -

Maxi mum GroundAcceleration,

g Units

0.51

0.47

0.420.40

0.34

0.33

0.33

0.31

0.29

0.28

0.28

0.27

0.26

0.26

0.23

0.23

0.22

0.20

0.19

0.19

0.18

0.18

0.18

0.18

0.16

0.16

0.16

0.15

0.14

0.13

0.13

0.13

0.11

Group AI

Group A2

;roup A3

TABLE 3

GROUPINGOF ACCELEROGRAMS ACCORDING TO T11E

SOIL I1*EDAdCE AT THE RECORDING STATIONS

Numbe

12

3

4r

6

7

8

9

10

11

12

13

14

15

Recording Station Impift

Helena

Temblor

Golden Gate Park

Cholame-Shandon r2

Cholame-Shandon r5

Ilachinohe

Castaic, ORR

Eureka

Lima

Van Nuys Holiday Inn

Olympia

Bank of California

Universal-Sheraton

Taft

El Centro

Note: Information presented in the aboveand/or compiled from References 5,16, 17, 18 and 19.

edance, I

x IO•

19.1

10.3

5.4

4.34.3

4.3 Group B1

4.3

4.3

4.2

3.0

2.1

1.6 Group B2

1.6

1.3

1.1

table is deduced11, 13, 14, 15,

- 32 -

TABLE 4

GROUPING OF ACCELEROGRAMS ACCURDING TO

EPICENTRAL DISTANCE OF THE RECORDING STATIONS

Number

1

2

3

45

6

7

8

9

10

11

12

13

14

15

16

17.

Recording Station

Hachi nohe

Li ra

Taft

Olympia, 1965

Olympia, 1949

El Centro, 1934

Castaic ORR

Bank of California

Uni versdl-Sheraton

Eureka

El Centro, 1940

Van Nuys Holiday Inn

Golden Gate Park, S.F.

Helena

Temblor

Cholame-Shandon #5

Cholame-Shandon "2

Epi centralDistance,

M~iles

.100

10G

44

35

31

20 Group Cl

18

18

15

13

13

84 Group C2

43.3*

O.Ob*

* Shortest distance from the San Andreas fault

Note: Information presented'in the above tablefrom References 2, 3, 4, 5, 13, and 14.

is compilea

- 33 -

TABLE 5

GEOGRAPHIC GROUP I:

SAN FERNANDO VALLEY EARTHQUAKE

Peak GroundAcceleration,

q UnitsEarthquake

San Fernando

San Fernando

San Fernando

San Fernando



1971 Bank of California,California


1971 V.11. Holiday,Inn, California

Magnitude Component

6.6

6.6

6.6

6.6

N21°ES69"E

N179°W

NSEW

NSEW

0.340.29

0.230.14

0.180.13

0.280.15

- 34 -

TABLE 6

GEOGRAPHIC GROUP II:

SOUTHERN CALIFORNIA


g UnitsEarthquake Year Recording Station Magnitude Component

El Centro

El Centro

Kern County

Parkfield

Parkfield

San Fernando

San Fernando

San Fernando

San Fernando

Parkfield

1940

1934

1952

1966

1966

1971

1971

1971

1971

1966

El Centro,California


Taft,California

Cholame-Shandon #2California

Cholame-Shandon #5California

Castaic, ORRCalifornia

Bank of Califor'da,California

Universal-Sheraton, Calif.

V.N. Holiday.Inn, California

Temblor,California

7.0

6.5

7.7

5.6

5.6

6.6

6.6

6.6

6.6

5.6

NSEW

NSEW

N21°E$69°0E

U65 0ENot Recorded

N5°WN850E

N21°E$69°E

NIl 0EN70°WUS

EW

NSEW

N650WN25=E

0.330.22

0.260.18

0.180.16

0.51

0.400.47

0.340 .29

0.230.14

0.180.14

0.280.15

0.280.33

- 35 -

TABLE 7

GEOGRAPHIC GROUP III:

CALIFORNIA

Earthquake

El Centro

El Centro

Kern County

San Francisco

Parkfield

Parkfield

San Fernando

San Fernando

San Fernando

San Fernando

Eureka

Parkfield


1940 El Centro,California

1934 El CentroCalifornia

1952 Taft,California

1957 Golden Gate Park,California

1966 Cholame-Shandon #2,California

1966 Cholame-Shandon #5,California


1971 Bank of California,California


1971 V.N. Holiday,Inn, California

1954 Eureka,California

1966 Temblor,California

Magnitude

7.0

6.5

7.7

5.3

5.6

5.6

6.6

6.6

6.6

6.6

6.6

5.6

Component

NSEW

NSEW

N210ES69°E

N1O0 EN90OW

N65°ENot Recorded

N50WN85°E

N210ES69°E

N11 0 EN79 0W

NSEW

NSEW

N79 0 EN11°W

N65 0WN25°E


gi Units

0.330.22

0.260.18

0.180.160.110.13

0.51

0.400.47

0.340.29

0.230.14

0.180.14

0.280.15

0.260.18

0.280.33

- 36 -

TABLE 8

GEOGRAPHIC GROUP IV:

WESTERN U.S.A.

Earthquake

El Centro

El Ce',tro

Kern County

Olympia

ielena

San Francisco

Parkfield

Parkfieild

San Fernando

San Fernando

San Fernando

San.Fernando

Eureka

Olympia

Parkfield

Year

1940

1934

1952

1949

1935

1957

1966

1966

1971

1971

1971

1971

1954

1965

1966

Recording Station



Taft,California

Olympia,Washington

Helena,Montana

Golden Gate Park,California

Cholame-Shandon 62,California

Cholame-Shandon #5,California

Castaic, ORR,California

Bank of California,California

Universal-Sheraton., Calif.

V.N. Holiday,Inn, California

Eureka,California

Olympia,Washington

Temblor,California

Magni tude

7.0

6.5

?. 1

7.1

6.0

5.3

5.6

5.6

6.6

6.6

6.6

6.6

6.6

6.5

5.6

Component

NSEW

NSEW

U21°E569 0 E

N40 WS860 W

NSEW

N 10 0 EN801 W

N65°ENot Recorded

N50 W1485o E

N210ES690 E

N11 0EN790W

NSEW

NWEW

N79 EN11°W

S40ES860W

N650WN250 E


Units

0.330.22

0.260.18

0.180.16

0.190.31

0.130.16

0.110.13

0.51

0.400.47

0.340.29

0.230.140.180.130.280.150.260.18

0.200.16

0.280.33

- 37 -

D1

-41.0

D2

1.0

Di

-1.

1. 0

DI (Tj, i)

T . Period, T (sec)

D 2 (Tj, r')

T .3 Period, T (sec)

D- (T.,

"j,

T.3 Period, T (sec)

(Tj, )

I 3T Period, T (sec)

FIGURE 2. ENSEMBLE OF n RESPONSE SPECTRUM SHAPES

- 38 -

V. EFFECTS OF EARTHQUAKE DURATION

A. GENERAL

It is generally thought that long duration shaking is more damaging to build-

ings than short duration shaking, even though the amplitues may be equal. Al-

though the duration of strong shaking may not directly affect the onset of

damage, damage could be increased by continued strong motion. Thus, it seems

reasonable to postulate that damage potential of an earthquake is directly

dependent on the response levels induced and their duration. For this reason

the effects of- duration of strong seismic motion were included in this study.

The response spectrum, which is normally used to define seismic input motion,

is a plot of the maximum values of a specified response paramLter. The re-

sponse spectrum permits ready evaluation of the frequency content of the

seismic input motion. However, the duration of the maximum responses and

their frequency of occurrence are not discernible from the spectrum curve.

It is therefore possible that response levels smaller than the maximums may

exist, which might induce greater structure damage. The study was structured

so as to investigateresponse levels, in addition to the maximums, that might

be significant from thp-viewpoint of potential damage, and how these levels

and their duration are affected by the earthquake duration.

Detailed information regarding the relationship between building damage and

structural response levels and durations is not available. Attempts, however,

are being made to estimate the influence of structural response level and its

duration on building damage by low-cycle fatigue. 2 0

B. ANALYTICAL APPROACH

A recently developed technique of period-amplitude-time (PAT) contour mapping21

of response time-histories was used in these studies.

The pseudo absolute acceleration response time-histories of a family of single-

degree-of-freedom systems with different natural periods and 2% damping

ratio subjected to a ground motion were generated and the response amplitudes

enveloped to obtain response envelope time-histories. The response envelopek

- 39 -

contours corresponding to a number of response levels were then plotted on a

period-elapsed time plane. The PAT plots thus generated were advantageous in

studying the duration of various response levels for each earthquake. The num-

ber of cycles at a given response level were approximately determined by first

obtaining the total time extent of the response level contour for a given per-

iod and then taking the ratio of the time extent to the period.

C. PAT PLOT STUDIES AND RESULTS

Eight different accelerograms generated by four important earthquakes were

selected for the PAT plot studies (Table 9). The PAT plots for these accel-

erograms, normalized to a 1.Og maximum ground acceleration, for a 0.02 damp-

ing ratio are in Appendix 0 as Figures nl through D8. It can be seen from

Table 9 that the El Centro and Taft acc(elerograms have a fairly long strong

motion duration and the Helena and Goldtn Gate Park have relatively short dura-

tions. The PAT plot studies of these accelerograms are indicative of the dura-

tion effects of a range of strong motion durations.

The results of the PAT plot studies of the selected accelerograms are sum-

marized in Tables 10 through 17. The predominant periods for these accel-

erograms are those with fairly large DAFs (see the response spectrum shapes

in Appendix A). The total durations of different response levels for each

period were scaled from the PAT plots. The DAF values corresponding to the

periods are also listed.

D. OBSERVATIONS

* Although Helena and Golden Gate Park records are dominant in the 0.10

to 0.20 sec period range, El Centro (NS) is also strong in this

range.

* All records participate in the 0.10 to 0.50 sec period range.

* El Centro and Taft are dominant for periods longer than 0.5 sec.

* The number of cycles decreases with period, as expected.

* Normalized responses as S-eat as 4.0 or more appear out to 0.5 sec

period.

- 40 -

The above observations lead to the following interpretation:

* Both the short and long duration motions show significant and compar-

able dynamic amplification for periods shorter than 0.4 sec. Thus,

the duration effect on the response spectrum shape for periods shorter

than 0.5 sec -- a significant period range for nuclear power F:.int

structures -- can be considered relatively small. For longer periods,

however, the short duration records show significantly smaller dyna-

mic amplification than the long duration records. The spectrum shapes

for longer periods would thus generally tend to be higher for long

duration motions than the. short duration motions. This trend is reason-

able because short duration shaking cannot contain significant long

period motion nor permit the longer response build-up times renuired

for major response of long period structures.

o The total durations of various normalized response levels for a given

period are generally longer for the long duration accelerograms than

those for short duration motion. This indicates that the almost-

free vibrations that ensue after the strong shaking are quickly

damped out and thus would not result in a prolonged large-amplitude

response.

The above observations confirm the higher overall damage potential of

long duration earthquakes because they would excite structures over a

much wider range of frequencies. Large-amplitude structural responses

would be more prolonged for long duration earthquakes, and damage once

started, would tend to progress.

SUMMARY OF MAJOR FINDINGS

* The e3rthquake duration effect on the response spectrum shape for

periods shorter than 0.4 sec -- a significant period range fnr nuclear

power plant structures -- is small. The shape for longer periods,

however, would generally tend to be higher for long duration motions

than for short duration motions.

- 41 -

* Long duration earthquakes could be potentially more damaging than

those of short duration because of the following reasons:

1. Long duration earthquakes would excite structures and structure

components over a much wider range of frequencies.

2. Large-amplitude structural responses would be more prolonged

for long duration earthquakes, and once damage is started, it

would tend to progress.

3. Short duration earthquakes appear to induce significantly fewer

cycles of damaging response for periods less than 0.4 sec, than

do longer duration earthquakes. For the purpose of this compari-

son, response accelerations greater than 0.5g are assumed to be

damaging.

4. Long duration earthquakes also induce a significant number of

cycles of damaging response in periods greater than 0.4 sec.

- 42 -

TABLE 9

STRONG MOTION DURATIONS 3 OF THE ACCELEROGRAMS

SELECTED FOR THE PAT PLOT STUDIES

Number Accelerogram ComponentStrong MotionDuration, sec

I

2

3

4

El Centro, 1940

Taft

Helena

Golden Gate Park, S.F.

NSEW

N21°ES69 0E

NSEW

NlO*EN90gW

24

17

4

3

- 43 -

TABLE 10

RESULTS FROM1 PAT PLOT STUDIES

OF EL CENTRO, 1940, NS

Number

I

PredominantPeriod. sec

0.136

2 0.248

3 0.451

4 0.551

S 0.900

NormalizedResponse in

Excess of

1.02.03.0

1.02.03.0

1.02.03.C

1.02.03.0

1.0

Total Duration.sec

2.900.900.15

4.100.900.20

10.005.001.10

6.804.400.70

8.5

No. ofCycles

217

1

1741

22

212

OAF

3.63

3.55

3.49

3.43

2.12

12q

10

TABLE 11RESULTS FROM PAT PLOT STUDIES

OF EL CENTRO, 1940, EW

Number

1

2

3

4

5

6

PredominantPeriod, sec

O.k:48

0.302

0.451

0.551

0.744

1.226

NormalizedResponse InExcess of

1.02.03.04.0

1.02.0

1.0

1.02.03.0

1.02.0

1.02.0

1.0

Total Duration,sec

17.47.02.70.8

21.13.3

12.4

7.76.72.5

16.75.6

18.13.7

8.5

No. ofCycles

7028113

7011

28

14125

22.8

15

3

4

OAF

4.36

2.90

3.84

3L79

2.27

2.25

1.477 2.10

- 44 -

TABLE 12

RESULTS FROM PAT PLOT STUDIES

OF TAFT, N210E

NormalizedPredominant Response in

Number Period, sec Excess of

1

2

0.244

0.369

0.499

0.673

0.822

1.02.03.0

1.02.03.04.0

1.02.0

1.02.0

1.02.0

Total Duration,sec

9.62.21.2

10.35.03.20.3

9.02.0

11.80.8

18.12.9

No. ofCycles

43105

281491

OAF

3.67

4.30

2.87

3.28

2.3

3

4

184

181

224

5

TABLE 13

RESULTS FROM PAT. PLOT STUDIES

OF TAFT, S69 0E

Number

1

2

3

4

S

PredominantPeriod, sec

0.203

0.334

0.451

0.609

0.822

NormalizedResponse inExcess of

1.02.03.0

1.02.03.04.0

1.02.03.04.0

1.02.0

1.02.0

Total Duration,sec

12.28.80.8

18.15.31.20.2

12.44.02.20.6

10.70.7

7.21.8

No. ofCycles OAF

6043

4

541641

28951

181

3.58

4.25

4.58

2.10

2.1192

- 45 -

TABLE 14


OF HELENA, NS

PredominantNumber Period, sec

I 0.111

Normal izedResponse inExcess of

1.02.03.0

1.02.03.04.0

1.02.0

Total Duration,sec

3.61.60.1

3.81.91.10.6

5.41.7

No. ofCycles DAF

3.33

2 0.150

32141

251374

134

5.09

3 0.408 2.45

TABLE 15


OF HELENA, EW


1 0.183


1.02.03.0

i.02.03.0

1.02.03.0

Total Duration,sec

3.52.50.5

3.21.30.8

5.11.90.6

No. ofCycles DAF

2 0.274

19133

1253

14S2

3.86

3.64

3.283 0.369

- 46 -

TV.BLE 16


OF GOLDEN GATE PARK, tIO 0 E


1 0.111

0.150


1.J2.0

1.02.03.0

1.U2.03.0

2

Total Duration,sec

3.01.3

2.61.80.5

3.82.41.2

No. ofCycles

2711

17123

15105

2.97

3.74

3. 71

OAF

3 0.248

TABLZ 17


OF GOLDEN1 GATE PARK, N80 0 W


1 0.136

Normal izedResponse inExcezs of

1.02.03.04.0

1.02.03.04.0

1.0

Total Duration,ScC

1.61.31.00.6

4.12.01.10.5

2.3

No. ofCycl es OAF

1210

74

18952

4.78

2 0.244 4.32

3 0.408 6 1 .54

- 47 -

VI. RECOMMENDED SPECTRUM SHAPES

A. INTRODUCTION

Nuclear power plants are structures of ý._fmrnount :iportance because they are

sources of power and because enurmous'potential risks are involved in the

case of partial or total structural failure due to inadequate scismic resis-

tance. Ideally, statistical predictions of seisn.ic forces, structural be-

havior, and potential damage and loss should form a basis for design optimi-

zation to achieve mininum potential risk. 2 2 Designs of nuclear ptwer plant

structures, based on seismic design conditions having sufficiently low prob-

abilities of exceedance considerably reduce or eliminate the risks of struc-

tural failure.

Pseudo atsolutc acceleration respon•e spectra are quite important ir- reprvtent-

ing the severity and Frequency content ..f the seismic ground motions. As rioted

prevt.'usly. they are also useful in determining the seismic forces inc,.ced in

a structure. Statistica' ,'redictions of pseudo absolute acceleratin respont,e

spectra should therefore provide a rational basis for probabilistically esti-

mating the seismic input motion for structural designs.

Selection of spectrum shapes (i.e., pseudo absolute acceleration response'

spectra for ground motions normalized by the peak ground acceleration) is oat

important step in deriving the pseudo absolute acceleration response spectra.

Recommendations for the use of spectrum shapes for damping ratios 0.005, 0.01,

0.02, 0.05, 0.07, and 0.10 are presented at the end of this chapter. The

recommended spectrum shapes are based on the probabiiity distributions consi-

dered suitable for the spectrum shape ensemble data.

B. kuCOHMENDED SPECTRUM SHAPES

In view of the relationship between the pseudo absolute acceleration spectrum

and the DAF, probabilistic estimation of the peak ground accelerations and the

spectrum shape values is necessary for predicting the pseudo absolute accelera-

tion spectra. Such peak ground accelerations and spectrum shapes then shou!d

be combined probabilistically to derive the spectra. It must be noted that

deterministic estimates of very high peak ground accelerations based on a

- 48 -

postulated extreme earthquake occirrence when directly combined with spectrum

shapes representing fairly '.vei probab;lIties of exceedance could result in ex-

treme seismic conditions 3nd erence unduly conservative designs. Pseudo abso-

lute acceleration response sp-ctra, " for different probabilitriLs of exceed-

ance can be derived by using pribat-ility density functions (:cO) of peak

ground accelerations (0) and £Ais (..:) as discussed herein.

Let random variables ., ., and Y represent a, , and D, respectively. Then,.j

Equation (17) can ve rewritten as:

' = v .(19)

Because of the low correlation between and Y noted in Chapter IV. these

variables can be considered independent and their joint r,,:f can be derived

by Equation (20).

f V y) = ,C.) , (201

in which

f , y) = joint rdf' of X and Y

f x(A) = pOf of ;0 . :

.fy i) -- P f of Y, y 0 ,

tNow, the z.df of ., f,(;:) can be derived by Equation (21).I-

?2(z) t ' f (rfn) ,i•, d] , C (21)

in which

].',n =dummy variables of integration

The oCf of Z or 3a can be used to derive different probabilities for S..

- 49 -

Probabilistic estimation of tlhe peak ground accelerations is not within the

scope of the present study. Probability estimation for DAFs are presented

below.

0 Probability Estimation for DAF

As liscussed in Chaoter III, the spectrum shape ensemble statistics, such

as mean, median, and standard deviation were computed for 108 different

periods in the period range under consideration. The coefficient of skew-

ness, or third moment, and the coefficient of kurLosis, or fourth mment,

were also determined for these periods. It is not surprising that the

third and fourth moments varied considerably from period to period in

view of the nature of response spectrum shapes, which tend to have pro-

nounced peaks and valleys, especially at low damping values.

The skewness coefficients are positive, which indicates a distribution

with a pronounced tail to the right, in this case away from the zero

value. This is acceptable because response spectra are constructed with

absolute peak values. The values of s':ewness vary widely between the

general limits of 0 and 4. However, the middle period range of, say

0.02 to 0.75 seconds, has skewness values much less than either the shorter

or longer periods, indicating for this range that the distribution is

closer to the normal distribution symmetry. Over a range of damping val-

ues, the skewness coefficient averages about 0.3 to 0.4 for periods from

0.10 to 0.75 seconds and about 1.00 to 1.40 for other periods. The co-

efficient of Ljrtosis or flatness also is less in the middle period range

with average values of about 2.3. This indicates more peaked'distribu-

tion than normal. At the other periods, however, the kurtosis coefficient

averages greater than 3, indicating flatter than the normal peaks.

These data, plus comparisons of mean and median values, indicate that

there is more variation in the short and Ionq period ranges than between

0.20 and 0.75 seconds. In general, a skewed distribution, with a 'ero

lower limit, occurs over the whole period range of interest.

It is apparent from these observations that any one of several distri-

butions would be effective. Three of these distributions, namely normal

or Gaussian with appropriate truncation in view of the postulated abso-

- 50 -

lute value for OAF, log normal, and extreme type II, were tried on the

OAF ensemble for 0.02 damping ratio. All of these distributions are

statistically acceptable within the range of the data.

The log normal distribution, given by Equation (22), was considered the

most desirable because it is convenient to use and has been found effec-

tive for ground motions generated by underground explosions.23

D (T., C; y) = 'M (T.,i.) (T., Y (22)

in which

y = standardized normal variable

p(Ti., r,) = geometric deviation for period, Ti., and damp-

ing ratio, C

r'D(Tj, 4) = median OAF for period, T., and damping ratio,

4, computed by using the mean and standard

deviation of OAF (as shown below). It differs

only slightly from the median described in

Chapter III

D (T., C; y) -OAF for period, T., and damping ratio, ., asso-J J'

ciated with the standardized normal variable, y.

The parameters, i"'M zd B are computed by using the ensemble mean and stan-

dard deviation as shown in Equations (23) and (24).

5T0 , T mD (Tj,r,) exp [- ½sD(T.,)] (23)

= exp n ( -. ,L)) 2 + i (24)

in which

rr D(T ,) = mean OAF for period, TV, and damping ratio, r,

- 51 -

SD(TJi) standard deviation DAF for period, Ti., and dampingratio, C

n= natural logarithm

exp = exponentiation

The parameters, mffD and 6 were computed for all 108 different periods to

derive the spectrum shapes for different y values of 0.0, 1.0, 1.645,

and 2.0 corresponding to probabilities of exceedance of 50%, 15.8%, 5%

and 2.3%, and for all damping ratios. These spectrum shapes are pre-

sented In Appendix E as Figures El through E6. Equation (22) shows

that the y = 0 curve is the median shape.

These spectrum shapes are smooth when compared with spectrum shapes of

individual accelerograms and form the basis for the recommended spec-

trum shapes.

The spectrum shapes in Appendix E for the above y values consistently

follow a basic shape shown in Figure 3.

DAF, D b

1"0

Period, T sec

FIGURE 3. BASIC SPECTRUM SHAPE

- 52 -

A moderate amount of smoothing was required to derive smooth spectrum

shapes from those in Appendix E. The amount of smoothing decreased rap-

idly with smaller y values, longer periods, and higher damping ratios.

It is noted that these spectrum shapes were not obtained by enveloping

b-tt by appropriate visual fitting to the different ,-value curves.

Three spectrum shapes, defined as large (50%), small (15.81), and neg-

ligible (2.39) probabilities of being exceeded, were developed corre-

sponding to y-values of 0.0, 1.0, and 2.0 and are presented in Figures

4 through 6. Four-way log plots of the shapes are presented in Fig-

ure 7. In addition, numerical data for the shapes, including the con-

trol points, A, 8, and C, and parameters b and -3 are listed in Table

18 to facilitate the reconstruction of these curves. The curves in the

vicinity of point A are extrapolaticns of the ..- curves in Appendix E

because the original shapes, due to limitation of the input data, were

computed to 25 cps frequency or 0.04 sec period. These extrapolations,

however, do not result in any significant errors.

Comparisons of the recoinmended spectrum shapes for a 0.02 damping ratio

with the current AEC criteria and other shapes proposed by Newmark."',

Housner2 5 , and Blume are presented in Figure 8.

The usefulness of the recommended spectrum shapes is demonstrated"F by

the fact that a time-history generated to match a spectrum curve for one

damping-ratio shape matches quite well with the curves for other damping

ratios. Such matching of spectrum shapes for different damping ratios

by a single time-history has not been satisfactorily obtained so far

and indicates the appropriateness of the recommended shapes with respect

to damping ratio relationships.

C. MAJOR FINDINGS

The major findings from these analyses are:

0 The log normal, truncated normal, and extreme type II probability

distributions were found statistically acceptable for the spectrum

shape ensemble data. The log normal distribution was adopted for

the further analyses because it is the most convenient to use.

- 53 -

0 The current AEC design spectrum shape for a 2% damping ratio is

below the small probability of exceedance shape for periods shorter

than 0.4 sec and for periods longer than 0.9 sec.

* The Newmark spectrum shape is consistently above the small probabil-

ity of exceedance shape, except for a short interval in the vicinity

of zero period.

a The Housner spectrum shape is below the large probability of exceed-

ance shape for periods shorter than 0.4 sec, and it is above the latter

for longer periods.

* The Blume F-factor spectrum shape for a 2% damping ratio and stan-

dardized normal variable value of 1.0 is consistently higher than

the small probability of exceedance shape.

D. RECOMMENDATIONS

To minimize risk in the seismic design of important installatiuns, such as

nuclear power plants, the seismic load criteria should incorporate such fac-

tors as regional seismicity, geotectonics, etc. The following recommenda-

tions, pertinent to the spectrum shapes described herein, are intended to

partly achieve the seismic design objective. Other ground motion charac-

teristics, such as peak ground acceleration and strong motion duration, in

the case of time-history analyses, should be given thorough consideration

to fully satisfy the design objective. The following are recommended:

* The curves shown in Figure 4 should be considered as lower bound

spectrum shapes for any site.

* For sit-s associated with relatively low risks, e.g., sites lo-

cated in low seismicity areas, the design spectrum shapes for

different damping ratios should not be lower than the small

probability of exceedance spectrum shapes shown in Figure 5.

* For sites associated with relatively high risks, e.g., sites lo-

cated in high seismicity areas, the design spectrum shapes for

- 54 -

differcnt damping ratios should not be,lcr.-er than the negligible

probability of cxceedancc spectrum shoaps -.hown In Figure 6. Be-

cause these curves represent extreme ground motion amplification,

their use should be carefully coordinated with the selection of

the peak ground acceleration. Care must be exercised to ensure

that the total seismic exposure for a site is compatible with the

risk exposure involved and not unduly conservative.

* For sites judged to be significantly responsive to ground motion

components with periods longer than 0.5 seconds, the above shapes

should not be used without appropriate modifications for the par-

ticular site conditions.

- 55 -

TABLE 18

NUMERICAL DATA FOR RECOMMENDED SPECTPUM SHAPES

Probabilityof BeingExceeded

Large

(50•;")

Smal 1

(15. 8;)

DampingRatio

0.005

0.01

0.020.05

0.07

0.10

0.005

0.01

0.02

0.05

0.07

0.10

Point A

T OAF

Point B

T DAF

Poi nt C

T DAF

0.03

0.032

0.034

0.036

0.038

0.040

0.028

0.029

0.030

0.031

0.032

0.033

0.025

0.026

0.027

0.028

0.029

0.030

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

0.12

0.12

0.12

0.12

0.12

0.12

0.11

0.11

0.11

0.11

0.11

0.11

0.09

0.09

0.09

0.09

0.09

0.09

3.22.8

2.5

2.0

1.851.7

5.1

4.1

3.5

2.6

2.2

2.0

0.350.35

0.35

0.35

0.35

0.35

0.35

0.35

0.35

0.35

0.35

0.35

0.35

0.35

0.35

0.35

0.35

0.35

4.03.5

2.9

2.3

2.0

1.75

6.2

5.0

4.2

3.1

2.6

2.3

Parameters for,the curve, bT

b o

1.20 1.46

1.08 1.16

0.93 1.075

0.76 1.053

0.67 1.038

0.59 1.032

2.342.00

1.73

1.35

1.13

1.02

4.32

13.68

3.12

2.40

2.03

1.77

0.928

0.872

0.843

0.794

0.790

0.776

0.761

0.692

0.604

0.511

0.489

0.470

Negligible

(2.3-4)

0.0050.01

0.02

0.05

0.07

0.10

1.0

1.0

1.0

1.0

1.0

1.0

8.16.2

4.8

3.2

2.6

2.3

9.67.6

5.9

4.1

3.4

2.9

- 56 -

8 1 t.

7.1---61-i-~--

U,

I

5 dl, €-

4

3.

2-

6•

Damping Ratios: 0.005, 0.01, 0.02,0.05, 0.07, 0.10

1 -- .. . - -

IiiS -4-~----- I ~-~-~-- 4 ~ I P 4*-* 4

v ii - I N -- 4 - -- -.----- 4 ~ F ~ A~ ~ I 4 1

IJ gJ I

114 I t 4

0.0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.0O 2.25 2.50

Period, T sec

FIGURE 4a. RECOMMENDED SPECTRUM SHAPES FOR LARGE (50%) PROBABILITY OF EXCEEDANCE

Damping Ratios:5.

4-

0.005, 0.01, 0.02,0.05, 0.07, 0.10

PCo

I

3

2

m I

SLL.

NY

I

0IF

l ~I. -I I-

I t I I I 4

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0

Frequency, cps

FIGURE 4b. RECOMMENDED SPECTRUM SHAPES FOR LARGE (50Z) PROBABILITY OF EXCEEDANCE

8

7

0 0

Damping Ratios: 0.005, 0.01, 0.02,0.05, 0.07, 0.10

~JI

5.--

LL 4.

0.0 0.25 0.50 0.75 1.00 1.25 1.50 .75 2.00 2.25 2.50

Period, T sec

FIGURE 5a. RECOMENDED SPECTRUM SHAPES FOR SMALL (15.8%) PROBABILITY OF EXCEEDANCE

6-Damping Ratios: 0.005, 0.01, 0.02

0.05, 0.07, 0.10

3

I _ _ _ _ _ _ ____ _ _ _ _ _ _

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0

Frequency, cps

FIGURE 5b. RECOMMENDED SPECTRUM SHAPES FOR SMALL (15.8%) PROBABILITY OF EXCEEDANCE

10

9

7 - Damping Raties: 0.005, 0.01, 0.02,0.05, 0.07, 0.10

- ., .

1 -

4- I.5- _

0.0 0.25 0.50 0.75 1.00 ±.25 1.50 1.75 2.00 2.25 2.50

Period, T sec

FIGURE 6a. RECOMMENDED SPECTRUM SHAPES FOR NEGLIGIBLE (2.3%) PROBABILITY OF EXCEEDANCE

10

8 i

__ -Damping Ratios: 0.005, 0.01, 0.02,0.05, 0.07, 0.10

9. .. i - .- ..-.4 . ......... _ ___ _LL.

- i .

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0

Frequency, cps

FIGURE 6b. RECOMMENDED SPECTRUM SHAPES FOR NEGLIGIBLE (2.3%) PROBABILITY OF EXCEEDANCE

0.00s002 /Dampi ng

0:01 Ratiosto. 0

i IityExceedance

I-,-..-

K -Small Probabilityof Exceedance

r...

V. Ju

Large Probabilityof Exceedance

t

0.01 0.10

FIGURE 7.

Period, T so.

RECOMIIMENI DE D- 63 -

SPECTRUM SHAPES

10.0

10

9

8

Probability of4 Exceedance

S..Negligible

- Recommended Shapes

------ tNewmark1 Blume

--.-- Current AEC

------ Housner

La..

5

4

3

2

1

0

Large[l

0.25 0.5 0.75 1.00 1.25 1.50 1.75 2.0 2.25

Period: T s ec

2.50

FIGURE 8. SPECTRUM SHAPE COMPARISONS; DAMPING RATIO = 0.02

VII. REFERENCES

I. "Strong Motion Earthquake Accelerograms, Digitized and Plotted Data,"

Volume I, Parts A (July 1969) and B (October 1970), Earthquake Engi-

neering Research Laboratory, Calirornia Institute of Technology, Pasa-

dena, California.

2. "Response of Earth Dams to Strong Earthquakes," N. N. Ambraseys and

S. K. Sarma, Geotechnique, Volume XVII, Number 3, September 1967.

3. "Intensity cf the Ground Shaking Near the Causative Fault," G. W.

Housner, Proceedings of the Third World Conference on Earthquake Engi-

neering, Volume I, New Zealand, 1965.

4. "The Peru Earthquake of October 17, 1966," C. Lomnitz and R. Cabre,

S. J., Bulletin of Seismological Society of America, Volume 59, No.

2, April 1968.

5. "The Tokachi-Oki Earthquake, Japan, May lb. 1962, A Preliminary Report

on Damage to Structures," Report NIo. 2, International Institute of

Seisriology and Earthqudke Engineering, Japan, June 1968.

6. "Evaluation of Response Routines." R. E. hunroc, John A. Blume , Asso-

ciates Research Division, San Francisco, A Letter Report to Nevada

Operat ions ()ffice. AEC. September 1371.

"nalysis-of Strong i.ctiun *,ccvltcr,9rrap.h Records," D. E. Hisdon. N. L.

Nigan:, and 11. D. Tril'unac, Proceeding% uf the Fourth World Cocr,'r.;.ct'

of L,,rthqtjaý.- Engineering, Volure' I, Santiago, Chile. 19 6'i.

6. "High Frequency Errors and Instrument Correction, of Strong Motion

Accelerooram.s,' If. D. Trnfunac, F. E. UL-!wadia and A. G. Brady, Earth-

quake Engineering Research Laboratory, California Institute of Tec!!-

nolnny, Pasadena, California, July 197!.

- 65 "

9. "Low Frequency Digitization Errors and a New Method for Zero Baseline

Correction of Strong Motion Accelerograms," M. D. Trifunac, Earthquake

Engineering Research Laboratory, California Institute of Technology,

Pasadena, California, September 1970.

10. "Elementary Seismology," C. F. Richter, W. '-4. Freeman and Company, 1958.

I1. "Site Characteristics of Southern California Strong Motion Earthquake

Stations," C. M. Duke and b. 0. Leeds, Report No. 62-65, Department of

Engineering, University of California, Los Angeles, November 1962.

12. "Earthquake Ground Motion and Engineering Procedures for Important In-

stallations near Active Faults," John A. Blume, Proceedings of the Third

World Conference on Earthquake Engineering, Volume III, New Zealand, 1965.

13. "Studies on the Parkfield, California Earthquakes of June 1966," Bulletin

of Seismological Society of America, Volume 57, No. 6, December 1967.

14. "Strong Motion Instrumental Data on the San Fernando Earthquake of

February 9, 1971,11 D. E. Hudson, Editor, EERL, CAL TECH and Seismological

Field Survey, NOAA, U.S. Department of Commerce, September 1971.

15. Files of Seismological Field Survey, NOAA, San Francisco.

16. Geophysical Investigation of Recording Station Site, made by John A.

Blume & Assorates, Engineers, San Francisco, California.

17. "Report of a Foundation Investigation, Sheraton-Universal Site, Universal

City, California," L. T. Evans, Inc., Los Angeles, California, September

1966.

18. "Report of Foundation Investigation, Proposed Office Building and Parking

Structure, Ventura Boulevard East of Sepulveda Boule'ard, Sherman Oaks

Gistrict, Los Angeles, California," Le Roy Crandall and Associates, Los

Angeles, California, February 1969.

- 66 -

19. "Report of Foundation Investigation, Proposed Seven Story Motel, Roscoe

Boulevard and Orion Avenue, Panorama City, Los Angeles, California,"

Dames and Moore, Los Angeles, California, February 1966.

20. "Low-Cycle Fatigue Failure of Seismic Structures," I. Kasiraj and J.T.P.

Yao, Technical Report CE-li(68) NJSF-065, University of 1le* e Mexico, Albu-

querque, flew Mexico, 1968.

21. "Production of Time Dependent Response and Bond Pass Filter Spectra,"

JAB-99-10, K. F. Schopp, R. E. Scholl, Prepared for Nevada Operatians

Office, USAEC.

22. "Damage aid Risk Analysis for the Greater San Francisco Bay Area due to

Earthquake Loadiiig," Hiaresh C. Shah arid Jaiat S. Dalal, Coisference on

Microzonation, Seattle, Washington, 1972.

23. "Respot'se of High-rise Buildings to Ground Motion from Underground

Nuclear Detonations," John A. Blum'e, Bulletin of Seimological Society

of America, Volume 59, December 1969.

24. "Seismic Design Criteria for lucll•,r Reactor Facilities," N. M. tNcwmark

and W. J. Ilal], Proceedings of tlhc Fourth World Conference of Earth-

quake Engineering, Santiago, Chile, 19b9.

25. "Behavior of Structures During Eart!,iuakes," G. W. Houns.ner, Proceed-

ings of Air.erican Society of Civil En(.'ne,_,rs, Voi. 85, EM4, October 1959.

26. "Civil, Mechanical, and Electrical Aspectc, of.Se ismic De.,iyn of tNuclear

Power Plants," Roland L. Sharpe, Presented at Joint Po..jer Conference

(ASME, IEEE, ASCE), [Uo.ton, Mas-,.cht,-,wtt,-, 11112.

- 67 -

APPENDIX A

Response Spectrum Shapes

Figures Al through A66

0

-j

CLJ

a

Lfd

12 .C

RESPO]NSEEr-L CENTRo>DAMhP. ICT IDS --*

SPECTRRI19e40

.010!.070o

.020

.100

GROUND MOTION NORMALIZED TO 1.0 G

- :~-"-t-.----.-

4L .~• .0 1 •2 .0

FIGURE Al p L R, I V) ci I SN L- c

I.-

crU.,-jI

Cf

-LJ

4r,

cr

LlU

I S . C0 RESPONSEEL CENTRGWDAMP. RPTIOS =

GROUND MOTION NORMALIZED

SPEC1940.O0s,.OO,07

TO I.OG

TRO9 EW.0101.0701

.020

.10012 . a

9.4

S.G

. • -.i

o ._ iI_______________- - -.- -I

.0 1.0 2.0 2.5

FIGURE A2 PERtODrY SEC

7-4

cr.

U'

C-)

03

:3CrJ

1 r . ( RESPONSEEL CENTRIT]DPi:P RflTI1JS _

SPECTRR11934.00,o.Osol

~NSr.)10,0 0?01

.020

.100

i C+GROUND MOTION NORMALIZED TO I.2G

9 .

6.rk

3

0

V.-........ t -

p

4..--~ + ... ........ .t, ... .......... . ... --t.

0.0 .E 1 .0 1 .S 2.0 2,5

FIGURE A3 PERIOD' SEC

ci

I.

CLi

t-J

cli

al

CL

(~) 4

ifýI

RE.-SPFiNGEEL CENTRF[19D~4r1p. RflTIOc z

SPEC1934.005?.OSO7

~EW~.020.100

GROUND MOTION NORP.ALIZED TO 1.0 G

1I

-...- -. - -.-----------1 ----- "----*-.-----------* --

A

t

* ~- - - -4-~ .*j *I* . -~

.: 1.0 1 .£ 2.0 2.S

FIGURE A4 FUERI 00i SEC

1 -

TFqFT 49~2)

C2 T; RJ PT

r* )C~JLJ

G-ROUD MOTION NORMALIZED TO 1.0 G

I---

P A

t

*1*1.*

- -F.

1.'~- I .cl 2 .C 2 .

FIGURE A5

IL°I •"*

7

c-j

-j

U

-- 4

ti

'a-,

-'a,

L.

VqF, E P)L2NT~1~ (fl*FwT

'DC.

rwn.r13

GROUNMD MOTIONJ NOP.iALIZED TO 1.0 G

2

-F

C. -I

6.

.4.

1.0 2.C2 .~

FIGURE A6 F-R .IEC

-z

.1. .

~ A1 [71

GROU14D MOTION NQR.4A1LIZED TO 1.0 G

TB414 n0*').~** I ~**

-j

1..

D

12

.2

IT

( .

1.4-~.-*-

....*... . ...... ,...........

-; ~) (**, r-, £:

FIGURE A7f r

it: ~

~1. R~ESP ENSIE SPEC49:•S

rj"_, I •

1 640-.(

u.£ ~..

U I

.020

GROUND MOTI ON NOW1ALIZED TO 1.0 C

D .C~

,- (I.

It'

1 m -') (":

FiCURE A8 PICE k I EA8 )ý PEFU ',-

GOr1) ?YYION NrJORMALiZED TO 1.00

*~~ ...... ..- .. .. .

FIGURE A9 . I

2.0

tie

RES)PfNSE PEW

GROUND MOTIONI NOR?4ALIZED TO 1 .0 G

J

i . 132* 100

44.

"I

I II JI

ls

•__, II†- ~l

1.0 V. 2 .0

FIGURE A1O

n RESPOILSEGOLDEN C_-D P M R n T I E,06J'J

S PE C"'T RPF

Li

-J

-4

1.1 1

cL2

LA

0 c9

.070

N10E020'Co

•. ; -,

GPOU-ND W)TIOM NORMALIZED TO 1.0 G

2 -

I

'2 Ci.--0.0 f 21 2.S

FIGURE All PERIOD" SEC

1 -C-' rP [N, SE SPECTRPGOLLDEN I-F1hI5~iG

0,17 0 .0?Oý .1-00

GROUJD) M.OTION NORMALIZED TO 1 .0 G

FIUE A2P R LE E

? .0

Is .rJf RESPONSEPPRKFIELD-DAMP. RATIOS =

SPECTRP

.-J

CL

V1,co

2 5.19,00,5,.O0SO: 0

ISG.9.010* 070

NGSE.020.,100

1 2 .(*GROUND t4OT ION NORMALIZED TO I .0 G

3.O0

09 .( %.# 1 .0 1.5 2.0

FIGURE A13 PERIODSEC

I- III I I I I I _,.

<RESPO]NSE GPETF?PPRKF'iFLD- sI 6 3 5J

A M Fs . n, 020

r1 2 GROUNDU I4OT I ON NOR?.IAL IZED TO 1 .0 G

CL

~~~1~~ L..a. . r.0

FIGURE A14ER2, E

F E R 127 ýý- 3 Sl E C

iS .G RESPONSEPPRKFIELD-DAMP. RATIOS =

C3

I-

Li

a

cm

CL

SPECTRP51 IG~i N,00S3 .0103.0503 .0?0)

B5E.020.100

12 .01GROUND MOTION NORMALIZED TO 1.0 G

iII

I

II

I

2.0A t - - - -

irl ý ----- 4---.

2.0

FIGURE AIS FIGURE AlS ERIdD)G EC

is .0 R E S-1P GN SEHiPCHIINDHE 5C, f? Cý. P, Af IC,- =

SP E CT RP

U j

196. O0'n-Osc,

El5NS.- 020

.10012 P+

GROUND 14OTlO .i NOF%.¶ALIZED TO 1.0 G

t

I.C0

UDLxJ

r .4,,p.) •. - .r - --- r -r - +

.5 1.S 2.0

FIGURE A16 PERIF)]5 SEC

1 :.Cli. r~SL~ S PPECT R ý7:

Li

crncrEl

HlCHINLHE9 9•962wLi .IP. rIzS = .D -

GROUND- MOTIOON NORMALIZED TO I.0 G

.070).020.100

12 . C+

9 -4

1-

I

!

0I- .n I I

L)•I-• S1.0 2.0 2. S


C-

z

ci_LLI

LUJ

ci

RESPTINSE SPELLINfll 19669 NBEDAMP. RlrIos = .. 0053

.0s0,

GROUND MOTION NOPRALIZED TO 1.0 G

.0101 .020

.070, .10012.

9.

L;J

mcr

6.

CL 3.

i.0 2.0 2.S

FIGURE A)8 PERIOD3 SEC

u-.

ciLii-j

CL

E7.

'12

R E-S)P NIiNS -E SPEO TRiL I N ýqo n~ rl1 ~.

ý 19 G., N 132 W. 010 Iq .020

* 100

GROUND ?4OTION NORMALIZED TO 1.0 G

4L*

S

...

.2 2'. 0

FIGURE A19 R I L"i S) E.

Luj

LJ

-i]

I-

Cfa2.4

PESP~jNSE71,ACPS5T PTC 5 19

R qr 1 ci z-

TRA21E.010,

.070,, lor .020.100

GROUND 1.101 I,1 "N NO•MALIZED TO I .0 G

*I r\ f~ .---- _______ ______

I

.- '~--

1.0 I.S 2.0

FIGURE A20 PERIrJCJ.SEC

r~EF': N SShSET q T C , 1~)

S P E

*rJos.0 :5 0

CC'

TR qG9r'DE.010o. 13 7 0!( -I

C

.020

.100L 1 . -

GP t',. T.TIOIN N1ORMALIZED TO 1 .0 G

2 . 'it

Li

ti

I.,'-I

IV- ** * *; --

-I- lr1 4" 4-

r9~rj 1 {i.0 , .%rr -~ ~.* '7)

FIGURE A21 p 1 .' 1 ,1 _

---- --- ----

u-

-7D

uj

is.

12.

3'.

C.

0.

RESPINSEEBP1N K [I F -CF PDAMPF'. R nrFI C S -m


Al

SPECTRflL IF -19 7 1 Ni11E7

.CO0, .('110 C'20

TO 1 .0 G

It

i I

0 .G 1.0 1 . S:

FIGURE A22 PERIC0 i SEC.

Li-

L;

w

-J

a_

is. RE SPOJN SE8BP NKDAMP~.

0 FR A' 11 1

SPECCALTF

,OO5,.OS0- .0-10)

N 7 N9'LJ

-i

7

GROUND MOTION NOW4ALIZED TO 1.0 G

r-. (

hi

I I

IJ0. --N

0.0 z.0 I...S 2 . 0

PE.RllJUD ECFIGURE A23

LA-

7-

r-3

ILi

:I~ Z , 0

:L 2

RE SP0NSE SPEUNIUL SHERPTODAMP .RATIOS-) .00S

0 G


.N0 10 ý070?

02NS.0201 00

'C"T R

ILlý

m

CL

r

K ~ (~ I

3*9 K -- -.-.-...

-~------ - I

I..) 1 ,0 1 -S 22.0

FIGURE A24 PERIOD) LEC

C3

cz'-j

adu

t Li

C3

C)

:DwI(1)a_

2 .cr

12.0

9.0

6.0

RE SPOiN SEUNIU .OF P. RP

S'HE RTIO'E =

SPECTRPA TEN5 197

00: , .010•.050) .0?0,

1L•,EH.020.100


3 Cl4 I.70.0 . C 2.0 2., e

PERIDD. S)ECFIGURE A25

u-

13

0

0

mi

1s .0& RESPDNSE SPECTRPU.N. HLILIDF1Y IDANri. RATIOlS .00s

o~ol

NN5 I.0107.0703

971.020.100

12 0ý---

9.%

GROUNI) MOTION NOVEALIZED TO 1.0 G

6 .0w

3.0

0 C0.0 . 1.0 1 .5 2.0

FIGURE A26 PERIODOSEC

U- is. RESPONSE

2:u-

ai

U .N~DAMP.

HU0LI DRAlTIOS =

SPECTRAPY INN919719EW.OOS, .0107 .020.•OSO .070, .100

12. GROUND MOTION NORMALIZED TO 1.0 G

9.

CIE

f--

-J0

O0

Dnw

U._

G

3.

0.

Jýv

1 <7if~ -. ~-.1

0.0 .S I .0 1.5 2.0 2. S

FIGURE A27 PERIODI'SEC

a

C-)

ci

C1)cr.

15.

12.

RESPONSEEUREODMP.

•KR 5 195RATIOS =

SPECTRP4,N79E. 006, .010, .020.050, .070, .100


9

G.

U')CL

3.

0. +

0.0 1.5 2.0 2.5


1S .O%u-

aw-J.wL)U.

Lii

C3

RESPONSE SPECEUREKPA 19S34 .NIDAMP. RATIIJS =.00

.050,


TRAI.w..010".070. .020

.10012.0

9.0

6.0

3.0

0 .0 I I -~-- -~I0.0 1.0 1.s

I

2.0I

2'.5

FIGURE A29 PERIODi SEC

U-

I.

IdC-)u-cr.ui

c-J

0

a-

IS.

12.

9.

6.

3.

0.

RESPONSE SPE(OLLYMPIP9 19;G5DAMP. RATIOS .00s,

.050:GROUND MOTION NORMALIZED TO 1 .0 G

CTRAS04E

.010, .020

.070) .100

0.0 1.0 1.5 2.0 2.5

FIGURE A30 PERI00~ SEC

10

0ý

CE)

'LI

0

LU

a.

Is Gcr RE SP UN S)ElULYM'PTP3,1-9DAMIP. RATIOS =

SPECTRFP65938GW.0051 .010).0s0, .0702

.020

.1001' c• CROUND MOTION NORMALIZED TO 1.0 G

64

3.C4

0. a OL,

0.0 1.0 2.0


U-

0-

LIi

C-Jw3

0

a-

iS .0C,

12.0

RESPONSETEMBL.F]R i19DAMP. RATIOS =

S PIECJRPPGG qN.00sl.0s0l

.0101 .020.100


.G .14-

7~~1

0.00.0 1.0 1.5 2.0

. FIGURE A32 PERIOD, SEC

IL

Lit

cr

-J

10.

is5 ,C RESPONSETEMBLUR5 19DAMP. RATIOS =

SPECTRPG65N25E.005, .010,.050, .070,

.020

.100

12 .%1 GROUND MOTION NORMALIZED TO 1.0 G

9.0

6,.0ý

3.i~c~

0 C4.. -

0 . 1 .0 2.0 2. S

FIGURE A33 PERIOODSEC

7iiI~TI

K:

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I j Au*1 lift

-~ fv~+ ti1~4~(iII ~II~~Jl

-r 1 pj'

U- Ivci

CI I

RESP[I Ns E P F C T R qzL

D A INC L--~

1Ills1j cl r) *,Io

. C f:

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it!

*1-

V.2V »A

f!

10 . 0 4. t

FgCURE A34 1'ý U y r

-77-- - 7 ' I

ý- i i~ ~ \' K... <' ,j ~..

a-

I f_ __ 11KL A.

L'

1 ) ~~

1T' R*

0 9.~cC '. "D

? ,2C GROUND) MOT I ON 1,10fý!.1AL 1 1-[!) TO I .0 G

S .44-

3 .6CJ .- '

1 ..BC

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0.0 5.0 10.0 15.0 20.0 25.0

F RE 0U E NC Y, C PSFIGURE A35

U. I'I:

L1I

ICl

12 .Cn

91.6.

iEL CENTR~iD IMhP. RATFIOS

RE,-SPDNS-E

? .2


iJ

SPECTRA19345NS.0D5S 1 .0i0, .020.0 ,- .070, .100

TO 1.0 G

Lii.

D-J

LAcnci

00:2Li

(1.

I

4.F•.

t2.4 ........

Vit!|

1-C' I

25.00 .0 f'-" . 0 10.0 15.0 20.0

FIGURE A36 FREQUENCYiCPS

10.0

0

Cr

CL

G..0

4.0

2.0

0.0

0.0 5.0 " 10.0 20.0 25.0

FIGURE A37 FREQUENCY)CPS

9.LL.

0i

2u0

F-3

ma

U3crwD

RESPONSE SPE[TAFT 1952 9.N211 2DIPN. RPTIOS- .00,


ZT!RP

.01'0,'20.0701 .100

5.4

3.6

1.8

-. 0

0.0 10.0 1, 20.0 25.0

FIGURE A38 FIGUIE A38FREOUENCY, CPS

z

ci

ILl

cr.

0

02

0-

7

6~.

RESPONSE SPEIKTqFT, 2952, S691

I. . OPMP. RprIos = .00S,

iGROUIND MOTION NORMALIZED TO 1.0 G

.0101 .02-0

.0?0) .100

3.0

0.0

0.0

I,iI

0.0 10.0 isl0 20.0 23 .0

FIGURE A39 F REQUENCY, CPS

ILI

(I

0

0:D

Li)

12.

9.2

4.

2.

0.0 6.0 10.0 16.0 2-0.0 25.0

FIGURE A40 FIGURE MOFRELUENCY, CPS

0L

z03

a

w

LiiI-

-LJu

Uf)

cr

13

U)0(.

7 .5s

6.0

4.5

3.0

I.S

RESPONSE SPECOLYMPIAh I9499 £ODMP. Rerios = .0051

.050,


VVRRB86W.0iO! .020

.100

0.0 .5.0 10.0 15.0 20.0 25.0

FIGURE A41FREQUENCYCPS

0

V1-4

ciw

(-j

ci

Lii

-J

Cr;

a..

10.0

8.0•

6.0

4.0

S2 .0

0.;0

0.0 10.0 IS.0 20.0 2S.0

FIdURE A42 FREQUENCYsCPS

0L

2

.-1wuuu

-LJD

I?fn

0

a.=

6.0.1

4.E

3.6

2.4

1.2

-. 00.0 10.0 IS .0 20.0 25.0

FIGURE A43 FIGURE A43REOUENCYICPS.

ci

w

LUJuu

ci0-w

6.0

4 .Ei

3.61

2 .4i1

1.2'

-. 00.0 [0.0 1: .0 20.0 .2S.0

FIGURE A43 FIGUR A43FREQUENCY~ OPS

0L

z0

a

a

V;

Z)w

CL!

s.0

413

3.6

2.4

I

0.0 10.01 15.0 20.0 2S.0

FIGURE A44 FIGURE A41.FREQUENC~i~CPS

C3o

z

I]

CLi

w

ci

cr

0U)I

4'.

3.

0.

0.

5.0 10.0 15.0 20.0 25.0

FIGURE A45 FREQUENCYCPS

z0

a

0ý.

w

I

-J

w

'n

U

C-

0E

w

tIJ

6.0

4.8

3.6

2.4

1.2

RESPONSE SPECPPRKFIELD- "2 , 19DAMP . RPTIOS = .00O,


T R(S6 1 N tD^5E.0101 .020.0701 .100

0.0 5.0 10.0 15.0 20.0 25.0

FIGURE A46 I E .F QUENNY, C PS

6.00.-

w

.0alii _

, I

10.0 1 5 .0 20.0

.FIGURt A47 FREQUENrYCPS

RESP[ONSE ~SFECTVRP

PARKFILELD--Sl9GtSN~HE2 O~~~DPP . rI 10nS .rf~ Cv.0~20

S 4 H- GROUND) MOTION NORMAL IZEID TO 1 .0 G

-IJ

F IGURE 14. ý7 C.:--H

r ~

7 RE S P' NS ..

cr

tit

cr

~1:

CI

CL

HPCHINL]HE)onriD. Pnrin's -- .301"-, .010, .020

6.01

4 .S

0.0

- GROUND MOTION NORMALIZED TO 1.0 G

K ~

, .......... '.'t-

0.0 5.0 10.0 15.0 .20.0 25.0

FIGURE A49 FIGU~E 49 REOUENCYI CPS')

.9 - - I

U-J 9.0

z0

cr

wY

cr

cc)

00

Lu('0)a-

RESPONSE SPECHPCHINLHE9 196[DAMP. RATIOS .OOs,


:T RP15 EL

.0109 .020

.0?0) .100

3.6

1_.8

0.0 £5.0 10.0 15.0. 20.0 25.0

FIGURE -A50 FREQUENCYiCPS

2< -2. RESPONSE SPECTRALIMlqi 1%9G NBE

z DAMP. RPTIOS = .005, .OlO, .020n .050, .070, .100

.c" GROUND MOTION NORM4ALIZED TO 1.0 G

ww I

LI.-

J I i ___

o 4 E •

a_

r. C 5.C 00 16 c 20.

FREQUENCY. CPS

.. * 'x_..-)

LL-

z

w-LJ

wr

12.

9.

cD00

6.

3 .

0 ,10 .0 16.0 20.0 2S.0

FIGURE A52 FIGUR A52FREQUENCYi CPS

4-

LL

CI

I-

C

C

h

L1

Li

L)

ooJ

Li

FI UE 5

S .0 10.0 1S.0 20.0 25.0

FREQUENCYCPS

.oo1-t- RESPONSE SPECTRAI CPSTPIC,19 iSG9E

_ DAMI RAnIn r .OO:, .010 .020

cI* 4 [.80 -](GROUND MOTION NORMALIZED TO 1.0 G

-J

U I

L 2 .

CIIN

ui 2 40--

2OL --- -.-. ....

o.0 .O .10.0 nS.0 20.0

FIGURE A54 FREQUENCY., CPS

u-

0

1-4

-JIQuar

Ld1I-

-JCl

co:

00.0Li)(U3a-

9.0

5.4

3,6

1.8

'-. 0

RESPONSE SPEBPNK [IF CPLIFOrMP . R rIioS = .005

.050


CTRP•,1971, NI-E

, .010, 020.0701 .100

Vtq N

0.0 5.0 10.0 15.0 20.0 25.0

FIGURE A55 FREQUENCYi CPS

La-

z

Ld-i

Ld

C3

CL

i 2 RESPONSE SPE(BPNK OF CPLIFCAMP. RPTICS = ,C0S,


.070, .ico

4.

2.

0.0 10.0 15.0 20.0 25.0


cr..

0

cil

-juii

E3

(LLa--

C_

Iw(na.

0 RESPONSE SPECTRA

4.. e a --

A

UNIVDIMP .

SHERRATIOS =

P"l VEN.005N.0OOS,

, 1971, NS.0101 .020.070, .100

"'tROUND MOTION NORMALIZED TO 1.0 G

I3.60

2.40

? ?.q

- 4 J - ~~~I .44..L~it.4.~.J...II I

C'~AWIW

rýUAA'

1

/W - fmc-t td~~~t ~ -4-A~'4 ~ + 4 1 - -

11(\ ý Výjjj

Nv V

1IiKP,.-, .

04~y- '- t i +p - -A I I I

-r * I I I.

0.0 I0.0 20.0 25 .0


<0 0.0(

z0

9- .01a

Lu

S6.01

w

o3 4.0'

cr_

C30

w 2.0CL

0.0

LINSE SPEC. SHERPTON

RATIOS = .00S.050

ION NORMALIZED TO 1 .0 G

0.0 5 .0 I0 .0 .15.0 20.0 25.0

FIGURE A~58 FREQUENCYCPS

La3 12.

z

crwL

-Jua

RESPONSE SPEU .N, HOLIDPYDAMP. RArIOs =.OOS,

S.050'GGROUND MOTION NORMALIZED TO 1.0 G

CTRAINN,• I 19 NS

.010, .020

.070, .100

6

.

7 .

El)mcr.4.

0. 2.

0. ,0 10.0 20.0 25.0

FIGURE A59 FIG~fE A59FREQUENCY) CPS

0

CLL

-JLuu

LUI

0Z)

a-

12. RESPONSE SPECU N. HOLIDOY IDAMP. RATIOS = .005,

.0501


TRFANN, 19?1? EW.010Y .020.070, .100

0

4.

)

0.0 10.0 15.0 20.0 25.0

FIGURE A60 FREQUENCYi CPS

?b .so •RESPONSE SPECTRPEUREKA, 1954) N79E

Z DAMP. RATIOS = .005, .010C .02C3 ".0s0. .0C,? .100

6.0cCE GROUND MOTION NORMALIZED TO 1.0 G

wL-

u

w_J

S3.00

cr.CN

0

r-,i

C . .0 20.0 25.0

FIGURE A61 rmmuur-Nt-Tlur;D

RE SPONSEFEUREKPiI I9jDFPhP. RPT0DS

S PE C: U41N-1h

*r00S, .010.-0 C) ,rj100

Lu

CL

C-1

-J

Lu

S10201 00

6.0GRO1111D ?,TIO I N NORMALIZED TO 1.0 G

3 .0

1..5

- +- - I- -+ . -

0 0- , 15. 0 2" .0

FIGURE. A62 FIGURE A62 '. IEGDEflC~r'iCO

Pill

LMi

LJ

CL

12.

RE S PFNSE SPECTRAL1LYMP1PI5 1965~ 5S04EorqMp. ~RPIoS .005) .0105

.3S0' .0701.020.100

0 . 10.0 15.0. 20.0 25.0

FIGURE A63 FREQUENC'Yi CPS

*c 12.

z

CY

LJ

DJLU

D.(I

C3

a-

9.

4.

2.

0.0 5.0 10.0 15.0 20.0 25.0

FIGURE A64 FiGUR A64FREQUENCY5 CPS

6.0

pDrMP. R Is IS . o005, .010, .0200 •. O0SO .070, .100' 4 .1 -0 GROUND MOTION NOFRALIZED TO 1.0 GCT-

IL.

LuI

Il

--C• 2.40

LU 1.20U)

-. 0.

0.0 5.0 10.0 15.0 20.0 25.0

FIGURE A65 1r'l:ncnKmrv roDC

6.0

z0

I-wuj

a

RE SPO[NSE SPETEMBLOR915i66i

DPrMP. RPTIOS C005.050

GROLU4D MOTION NORMALIZED TO 1.0 G

N25E .2

S.07C, .1004. .84

3 .6C

-J

0

0

2.4

1.2

-. C0.0 5.0 10.0 15.0 20.0 25.0

FIGURE A66 FREOUENCY, CPS

APPENDIX B

Ensemble Spectrum Statistics

Figures B1 through B18

ci

i S . r M E'qNrDqmpI I

RE S PONSENG R PIT1

SPEC TRUM~01005


12 .

C3

0

0 31)

00.0 1.0 2.0 2.

FIGURE 81 PERIOD) SEC

z

C3

a:

-j

an

LlJcna..

IS .0Ot N1EDIPN RESPOflHP. RPTILI

ONS5E SPEC TRUM'= nOOS


12 .C

9.q

6.%

.q

0.C

0.0 1.0 'I.s 2.0

FIGURE 82 FIGUE 82PERIDOD£EC

MEMO Wý

0L

z

w-J

I

a

0

U)CL

STD., DEU. RESPONSE SPECTRU[1

2.0

1.s

DFhP1 R -PTID[


.006

IZ"/N

0.0 .0 1.0 I.S 2.0

FI GURE . 3 PERIOOSEC

C3

cr

-j

F-i

a03

0L

15.

12.

9'

6.

MEPN RESPONSEDAMPING RPTIU

SPECTRUM= 0.010


I!

I

~~~1_

0.0 I .5 2.0 2.5

PERIODiSECFIGURE 84

I-

-J

ci

0

mI

a.

15.

S.

rEDIqN RESPON.D1MP. RPTIO =


E ISPECTRUM.010

3.

0.0.0 .S 1.0 2.0

FIGURE B5 PERIC02 SEC

L&.

z

'-4

a

V-)

-LJ

STID. DEU RESPOINSE SPECTRUMDAMP, RATIOI 1C010

GROUND MOTION NORMALIZED TO 1.0 G2.00

i .Sa

fMLA iII Oa I

.4' - '-*- _______ 6

/illI

K "I14- I I I I 4 4 ~ 4- -. ~---- I .~-.----- 4-

I

r~Li .UI - -, I I ------- ~-------------~-

T

c.0 1.0 2.0*1-

FIGURE B6 PERI00d SEC

ILL

z

0ý

wIJ

wu

clw

C-

0

a-

15;.(

12 .1

9.

6.

3,

0.

MEAN RESPONSEDAMPING RFITID


SPECTRUM= 0.020

0.0 .5 1.0 1.5 2.0

FIGURE 87 PERICDi SEC

.-

w-Jl

Lu

L!I--

-J

U)

cc:CE

CL

MEDIRN RESPONSEDPMP, RPTIO =


SPECTRUM020

12 .0

9.0

- 1r

01.0.0 . 1.0 1.S 2.0

FIGURE B88 PERIOD0GEC

C . ] STD DLYE' L RESPONSE SPECTIRUM

DP[P. RPP1I.. . ,020ZC3


2LU Ij .

.Jm

LU

C7,

C3

rri i • _ _ ____ ___ ___

-- ---- -- --- --

. .0S2.0

FIGURE 13 PE-RI00YSEC

2.5

L.-

0-- 1 . C- M1E: PN R E SPflNE ý- c) SP E CT Rulm0o.osor !'RIN RPqT Lr-i

7-

(2

Lu

Li

C:J

C,

.Ci


12.0

6 . j

2 ,.0

0 ,.0"1-

"[ I 1

1.0 2,0 C-

PERIQDSECFIGURE BIO

UY-4:

-jwuscu(-3arwd

W40

maC3

0~

toa.)

I1EDIE N RESPONSE -SPECTRUMD P M P RPTI Dl - 'OoD

12.0GROUND MOTION NORMALIZED TO 1.0 G

_1 --- , --.-. ...

6 qQ

3 G

I ic - 1. - r -9 1 r

0.0 .5 1.0

PERIO~iJSEC

2.0 2.5

FIGURE 811

U-H

a-4

ULU

Il---

cr'

CJ30

m

CL.

a..

2 .S

2.0

1 .Si

1 ,O1

STD. DEU. RESFDAMP. RPTI =


>ONSE SPECTRUM.OSO

0.00.0 1.0 2.0 2.5

FIGURE 812 PERIBODSEC

<5.r MEPN RESPONSE SPECTRUMDPfMPING RPTIO - .070

U7-

12. GROUND MOTION NORALIZED TO 1.0 G

Lu .uF--Cu- 9 G

cl

S, .0 1 CE 2.0 2 S

...... ... PERIGDiSECIIUUIL U0I.

z

Y-4

LUI

cr

wL

U)m

0

Ld

I3)

MEDIAN RESPONSEDPMP, RPTII --


SPECTRUM070

12.

9.

6.

3.

0.0.0 1.0 1.5 2.0 2.5

FIGURE 814 PERIODOSEC

t.-4

a3

wr-I

wJuu

0

0

wUJ

2 .50 STD.DfrPMP

rDEt RESPDNSE SPECTRUMRP~TIO .070

2 .OCGGROUND MOTION NOWtALIZED TO 1.0 G

I .

.s

r. r

Q.C 1.0 1.S 2.0 2.5

FIGURE B15 FERIG0D SEC

16

FMEAN RESPONSE SPECTRUM,DPMPINC RPTIEJ = 0.100

GROLND MOTION NORMALIZED TO 1.0 G

clLu

LU

uj

c:LI

LLJLU)

C-J I.x

:IuJLU

C. C1.01.52.0 2.S

FIGURE B16 PERIOD, SEC

C3

z

w-JLua

ui

a

0

U)Cl

15 .01 MEDIAN RESPONSE SPECTRUMDPMP. RATIO = .100

GROUND MOTION NORMALIZED TO 1.0 G12 .a

9.C

e.01

3.0 - 4-.----~-..-.. . - __________ - I -

I I I

I_I i -

O. 1.4' 9 1 -v 1 I

0 .0 .S 1.0 1.5 2.0

PERIODSECFIGURE 817

u-I

<- 2.0

a

Ii-JLuU

ciLLuI-

c3

Q-

0 L

00

FIG3o81

STD. DEUL. RESfDPAMP. RPTI-


PDNSE SPECTRUM.100

.0 1.0 :. .5 2.0

PERIOCiSEC

APPENDIX C

Group Spectrum Statistics

Figures Cl through C33

I0

I

MEPN RESPLNSEDAMPING RATIIOGROUP Ali


SPECTRUM= 0O.020

Z

-JLU

Lii

I-

CImcl

(L.

12.

6.

3.

0.0.0 .5 1.0 ._1.5 2.0 2,5

FIGURE CI PERIOD, SEC

u- 16 .q GROUP P.. READPIP., RPTIO

MEDIAN

S PONSE= ,020

SPECTRUN

zC

LU-JLu

Ua

12 2c

GROUND tIOTION NORMALIZED TO 1.0 G

LU

a-

G . r*

3 ). cit I

t

0 . S.0 1 .5 2.0 2.5

FIGURE .C2 PERICDE SEC

LL

2.5 GROUP PI RESPONSE SPECTRUMDP' R:PTIlIO : .020STPNCPRi C EUI,, r~ircN

S2.00-CI GROUND MOTION NORMALIZED TO 1.0 GLi"

-J

0.J

LLi

1.0

Z)

•-"m i "ci

LI I "

o. I " I I

It:

0 .0 .. .- . ._._2 0.

0.0 .0 .0. 1. 2.0 2.5

FIGURE C3 PERIOD, SEC

.4

c3

LA

Lii

rl-]

L7i

.D

12.4

MEqN RESPOINSEDAMP1PING RPTIWGROUP A2


SPECTRUM= 0 0420

S.) -

'1rts

-.

4

[

I

II-,-,-

-4

..., -- --t- , , , :- * '- - .- --t - - - - - --

I n0 S -~ 2.0 r

PEriC SEFIGURE C4

U.

0 I5 ,0. GROUP P2 RESPONSE SPECTRUMI DFPMP. RPTID

M E D It AN

'-I

Z0

c1

-LJ

Lii

ci

U]

Cl

ml

ci:

0~

12 .CtGROUND MOTION NOF•.ALIZED TO 1.0 G

6.

3.

0.0 1.0 1.5 2.0 2.5

FIGURE C5

C73

z1-l

ci

-LJwu

1*-

0

0

0-

GROUP P2 RESPEUPHP. RPTIO =STPNDARD DEUIATION

GROUND MOTION NORWALIZED TO 1.0 G

]NSE SPECTRUMo020

2 .0

.i .,:

1.0

0 10

I I

0.0 1 .0 i.5 2.0 2.5

FIGURE c6 PERIDDSEC

I -

IL

z

ciCL

000Lii

co(I

1 S oi.

12 .•

9.C

6.C

3n5

M1I N RE-SPOINSE SPECTRUMDiMPING RPTIOGROUP A3


0 , 02 0

C" 1.0 2.0 2.5

FIGURE Q7 PERIODSEC

z0

cr

c-4

Lu

U-)

a.i

I£,

12.

9.

6.

3.

0.

GROUP P.3 RESPODPAP. RATIO =


NSE SPECTRUM.020

0.0 .s 1.0 1.5 2.0 2.5

FIGURE C8 PERIDDsSEC

hL

AC 2.

a

C3

co

C-)ci

LU

a.

FIUR

GROUPOAMP,,STPNOPqRD

q ý,ý p r-- cr r, i *

SPECTRUM

RATJIO .020

DEUIPTION

NORM1ALIZED TO 1.0

G

I• r-1 L , ,-• _

GROUND MOT I ON

I .

I .&j

.s1.0

C9

1.,, r

2.0

PERIOD, SEC

cIs FIEAN RESPONSE SP

DPAMPING RPYT] =z GROUP Bi

12 .0 GRJUND MOTION NORMALIZED TO 1.0 GCL

.-JLu.

ci

_L1

•'-r' 1 . . 1'-

C1

1.0 1.

PERIODDSEC

IC T R U M),,020

2.0

FIGURE CIO

FIIT~ I I ml

L.Is .Oi GROUP

DPMPMEDIPN

Bi RESPONSE SPECTRUMR PT 10i = 020

cr

F-

0

in

0

U)(m

12 0 GROUND MOTION NORMALIZED TO 1.0 G

6.0

3.0

0.0

0.0 .5 1.0 1.5 2.0 2.5

PERIODSECFIGURE C1I

GROUP BI RESPONSE SPECiDAMP. RATIO = .020

z STfNDPRC CEUIPTICN

2 0 GROUND M)OTION NORMALIZED TO 1.0 G

w=-Jw

a

1 .0

ciI I

U) II'

0.0 1E 00J . 2.0

PERIODSEC

rRUN

2.5

FIGURE CI1

IL

.MEPN RESPONSE SPECTRUM

DFr[NPING RPTIL = E C020GRCUP B2

H1S12.6

GROUD 1OTION NORMALIZED TO 1.0 G

uj

-J6.,

Il-Cr_

w 3j,0-

0.. .5 1,0 1.5 2.0 2.E

PERICCSEC

0-Is . 0ý GROUP B2 RESPONSE SPECTRUN

z

H

I--

-J

L)uJ

uj

F-

C-L)

.LJU)

Q

0.

DAMP, RATIO =.020MEDIAN

GROUND MOTION NORMALIZED TO 1.0 G12

9

c

01

6.%

3.G

0 .c0.0 1.0 1.5 2.0

PERIOD, SECFIGURE C14

LLJ

I-i

L*J

I-

0

cnr

Q..

2 .SO GROUPDPMP.STANDPRD

B2 RESPONSE SPECTRUMRATIODEUIATION

= .020

GROUND MOTION NORMALIZED TO 1.0 G2 .0a

I. .50

1 .00

C.0G

0 oG0.0 I.0 1.S 2.0 2.5

FIGURE C15 PERIODSEC

u-

CL

w-LJ

Lii

C3

CL

NEPN RESPENSEDPMPING RPT-IfGROUP Cl

GkOUND MOTION NORM$ALIZED TO 1.0 G

SPECTRUM= 0 .020

12.

9.

6.

3.,

0.0 .S 1.0 1.5 2.0 2.5

PERIOD)SECFIGURE C16

Lj~

frI

cruIcl

Cf

cc:u

(AJ

Is . 0- GROUPDPM'P.MIEDIAN

C.I RESPONSE SPECTRUMRPTID = .020

12 OýGROUND MOTION NORMALIZED TO 1.0 G

9 r.

6 ,C-

.A I

o .c0

iI

.0 . .. 1.0

PERIOOSEC

2.0

FIGURE C17

,ý V,ý . ý . k. . . .I I . I I ýý ! , . , - . - - - $1 .7L .* - . . -)ILL - i, - I- *. I ý ý . 11

L-

CD)

~ .•C+ G REJ UP 1Z R PE P FN SPEC T RUMR PTIT 1-

£Tflnr-4RD 51:U I Pi F'NO20

-~U-

GRCUIJIU M.OT ION NINM.ALIZED TO 1 .0 0ý

I . ~Ci

- . U'

i

/*. ,

-1~

2 . 0 2 .S

FIGURE C18

I 4*1

MEPN RESPONSED P MP.ING RPT ILGRCUP C2

GF;OUND A. OTION NORM- ALIZED TO I .0 G

SP ECTRUM0 .020

I.

1.0 1.5 2.0 2.5

'::": " !9 PERIODSEC

i GROUPDPMPMEDIAN

C2RA

R'ESPOT 10 =

NSE SPECTRUM,020


'4

\1.

4'

1.0 2.0 2 .,

"-z ! ' ',; 1". , C 2 0 PERIOD) SEC

G.ROUPOTMP .STANDARRD

C2 RESPRLATIONOEUIPr IoN

LINSE.020

SPECTRUrM

'4-

:, .0 .5 1.0 2.0 2.5

PERICOD SECF ~(WUR C21

.MEPN RESPONSE SP[DE MPING RPTID = (GROUP I

,I 2 '• - . GROUND MOTION NORMALIZED TO 1.0 G

1 . i

_______iO__

". I I

I I I

iI I

0.0 ." 1.0 1.5

•-,,,o• ,.,-,PERIODS SEC

-CTRUMD .020.

2.0 2.5

' UVINL L.LL

I .1- I'MEDIPN RESPONSEIl DMPING RPTIDL

GROUP

_ GROUND MOTION JORI.IALIZED TO 1.0 G

C3

cr'

1 .Lu24

J .

1E60

0.00 1 + ÷

0.0 .5 .0 1,5J

FIGURE c23. PERIDDSEC

SPECTRUMS.020

2.0 2 .E

UL-

0

arw-LJ

I

-LJ

0..L

4 .01

3.2'

2.4

1.6

.8

0.0

RESPONSE SPECTRUNRATIlO = 0.020DAMPIN

STPNDARDGROUP I

OEUIATION'


\AI0.0 .5 1.0 2. n 2.5

FIGURE C24 PERIODiSEC

Fr

.4.0 "HMEPN RESPONSE SPECTRUMDAMPING RATII = 0.020

.z GROUP II

'- 3.20 OG

a " GROUND MOTION NORMALIZED TO .3 G

ujLli

J..U: i I--II.cx

I • . .

-J 1

0.0 .5 2.0 1." 2.0 2.5

PERIBDSEC:'IGURE C;25

z1-4

L±J-Jw

C-J

0

co:(I

4.0

3-,,

2.4

1.6

0.0

MrEDITN RESPFINSDPMPING RqTITGROUP II

GROUND MOTION NORMALIZED TO 1-.0 G

E SPECTRUM= 0.,020

0.0 1.0 2.0

FIGURE C26 PERIODD SEC

S4. 0 RESPONSE SPECTRUI

DPMPING RPTIO =z STANDARD DEUIPTION

&GROUP IIc 3.2 GROUND MOTION N•ORMALIZED TO 1.0 G

wu, 2 .40

w

L.i ____

? 1.'6 -_._

cr

Cl'

0 .001I.0.0 1.0 1.5

PERIOD)SEC

D . 020

2.0

FluvKh LZr

IL

7-)

cr

4.0c

3 . .

VILHN <Lz

I DP MP I NGI GROUP III

SP [N, S E.R PT 101

SPEC- 0

TRU0020

2 .4r

CLI . 6C

C0

LW

a-

0.n 1.0 I.S 2.0

FIGURE C28 PERIODD SEC

z0

y-I

u- 3.ci

w1--

(-3

C:

00

Z)

0L

0.0.0 1.0 2.0

FIGURE C29 PERIDO) SEC

!I

u-

-r

L-2

Lli

4 .0O RESPONZE SPECTRUMDPMPING RPTID 0,,020STrNDRD OEUIPTIONGROUP III

Gr,3UND MOTIOIN NORMALIZED TO 1.0 G

2 .40a . ,- -r

1.60

0.0o..0 1.0 1.5 2.0 2.5

FIGURE C30 PERIOD, SEC

4 .O0

cr

LUj

I-01

ILf

n)

1=~HEPN RESPONSEDOrPING RPTIOGROUP Iu

SPECTRUM= 0.020

3 . 201. GROMND IAT IOt1 NORM4AL I ZED TO I .0 G

i

.1=.2 . C[

DL .6

ft

0.0

I

I II I

0 .0 1.0 -I . 2.0

FIGURE C31 PERIODJSEC

'C

z

y-IL.I

ci

C-

4 .01

3.2,

2.4

1.6

.8

0.0

MEDIPN RESPLNSEDPMPING RPTIO =GROUP IU


SPECTRUM0 .020

0.0 1 . 0 1.5 2.0 2.S

PERIOCiSECFIGURE C32

U-

0

z

Y-JLUJ

a

Iy-

c,-)m-

4.01

3 2

2.6

0.0

,MEDTPN RESPLNSDAMPING RATIDGROUP IU

GROUND MOTION NORI4ALIZED TO 1.0 G

E SPECTRUM= 0o020

0.0 1 .0 1.6 2.0

PERIODOSECFIGURE C32

LL.

z

'-4

Li

LJ(1-

cr-

00

Li(i:)

CL

4,0•

3.20

2.40

1.6G

RESPONSE SPECTRUMDAMPING RPTIOSTANDARD DEUIATIONGROUP IU

GROUND W-TION NORMALIZED TO 1.0 G

=O0 20

.0.0 I.S 2.0

PERIODi SECFIGURE C33

APPENDIX D

Period-Ampli tude-Timne (PAT) Plots

Figures DI through DC

J DHN A. E31. UMEc + q''SOCI A FE:: ./ENt IN.E 1 -N E E R ýS

rD A m -ni m c R P.r 14- .G2 0

Pc-EuDf nFl

CO NT SJU

S,~; fCCEL.

LE U EL S

.6000E+01

.ýO00E+oi

" sGOnGE+0i

" 20C'0E +01

* I000E.101

.600.'DE+00

.2 0,C0 E + Cl

RES~p DNS E E I: Lý' EL 1 P ~ESV rlqp

E L 'C'ENW7 [],' 1 '9 -! C"I H s


IFIGURE Dl

i , , . i i i i I ! i i i i i i ! .- --4- I I I - - - i i

I- It -

- -'S

-'S

a* . ~ o*

J~-

> b A

___ 'V ~o *'

In~ a ~ ~

~ ~. -'-.-.-

p __

-~~r ~r-Z... LI

6K>* .c~nZtŽ~-~ *I~1

v'I ~ . J ~I~

o ~ r~ ~~ ( ~V- _ N~1V

- --

c ~ ciiQ ~ (0Ia,.

~ .z,. ~r-'L~" I -z~~ ~ - -~

r~-~ ~ C) •0-.------.------.. '--------- -S

-~

I -.- - ,z~ -~ Y

~

a

~-~-'N~ 3IS4 3'

Q ---.I.

I 4

/

6

JOHN A. BLUME + ASSOCIPAES / EN6INEERS

DIPIN1PINC' RFTI O= .020

ACCEL.PSEUDO ABS.

CONTOUR LEUELS

.0oc0E+O1

.SOOOE+O1

.4000E+Oi

.3000E+Oi

*2000F+OI

.IO00E+OI

.6000E+O0

.2000E+O0

RESPCNSE EN'JELOPE SPECTRA (RES) MAP

EL CENTRDi. 19409 EIWGROUND MOTION NORMALIZED TO 1.0 G

FIGURE D2

263

LIW

'44

,73

1,4

U4

ISO

C1.2

Css

c-Li

04 X.4 J,

.9~~M1 .1UP P~1 ~ ii ~4~I NhJ r, ~fillIAA.L~~k ~~o HI I~flv' I

C. .. .0 10~ .1 1.0 e.u ' 1. IL.C. it1.0 L2.C 13-C 14 .- IS -C ±l-C 1V.C 18.l0 -'D0 "IX 2. Z2.C .. I c ±4. -,.116 z1I.0 2.1. Z, -H,.C

'CIIE ESECC:413..Fl

JOHN A. BLUME + PSSOCIfrES / ENGINEERS

DNPING RPrfIC = .02C

PSEUDO ABS. qCCEL.

CONTOUR LEUELS

.60CCE+OI

.5CCOE+O1* d000E+OI

.3000E+Oi

.2000E+Oi

.1000E+01

.6O00E+O0

.2000E+O0

RESPONSE EN'JEL OPE SNPECIRP (RES') MOcP

TqFT 19525 N21ECROUND N4OTION NOR•ALIZED TO 1:.0 G

FIGURE D3

0.4ý

Al 0 0,zc

ACA)

.0 i.c Z. .C 4.C S.0 6 .0 ?.0 ea 1. 1 CA ! I X 12 c I a. CS Isc tC . c U .C e.0 2.. zr C ±c a. 2 S.C Jt' . 1. 2?c Mnc

C It-;

F T

PS ELDE r) C4 6 ý-,. , q'ý '- E L -

CnNTqiUR LEk.ELS

t2 EC CE f C.1

E* C COE -4-01

2 D Cir;-i~ E

*6 c .C,§F KKC217 C- E C' I-

j E N J E L D PE SPIN ON

Yý r Ir 4 I-. /~ ~ Li

GROU.,D MOT ION NORMAL IZED TO ,..0 G

FIGURE D4

W -A

-- --- - -- --

..... .. D .6. ...

< ~ (K K

'I* zl ýA

.6 1 ____

3,:c )., ý.z 5, c C.. a .c 10 2.0 11.0 12.C L3.G 1. .S .. C IC..C O~.f 19.0 &9.1 ZCG 21.C :2.C ,].Z .. .~S-C .0C 21.C 20.

OAPMING RATIO = .020

PSEUDO ABS. PCCEL.

CONTOUR LEVELS

.6000E+01

* £OOOE+OI

* 4000E+Oi.

.3000E+01

.2000E+01

.1000E+01

* 6000E+00

* 2000E+00

4

rcJi3K ()9

(~ 0 a6•> RESPONSE ENUELGPE SPECTRP (RES) mnP

HEILENP2 193S5 NS

GROUND MOTION tJ(N6.ALIZED TO 1.0 G

(IME I&6CM10f.1 F I

/

OPrIRING- RAFTIO -- .0J20

PSEUDO PBSZ. LJCCEL.

0

CCNTOUR LEVELS

.6000E+O1

.SOO E.*O1

.400OE+OI

3000E+o1

.2000E+OI

.IO00E÷01

.6000Ec-O+

.200UE+r0

RESPONSE ENVELOPE SPECTRA (RES

HELENMP 19353 Eý

GROUND MOTION INOIALIZED TO 1.0 G

60.

P)

Cr3

a u.. ý wf.. A - 1 1 -- t-- --h -.-- f-- -t- - --t-'1---I---+- t-- --- $- i i i -.0 .0.2.c V~C 4.&3 S.O 6!G ?.a0 .0 3.c 10,011. ±2.0L s 1.1.0 14-' 1s.C .t6.0 17.0 10.0 19.2 n0 c 21.0 22.c 13.0 Z4.z 25.0 26.0 27. 20.0trflE hSECCOWS1

DAMrPING, RATIOD .0-L0

PSEUDS PBS. PCCEL.

CONTOUR LEVJELS

k-EY9S0 E +401

* 5000E+01

.4000E+01

.3000E+01

.2000E+0!

.1000E+0!

.6000DE+00

.2000E+00

"•1>

6RESPONSE ENUELOPE SPECTRA (RES) M'

GOLDEN GP'TE9 195 7 N10GR~OUNlD PtJTIotl NORMALIZED TO 1.0 G

r IM E ScoliCs) F Irime

DPIIPING RATIO =.020

PSEUDO PBS. QCCEL.

CON~TOUR LEUELS

.6000E+01

.500!9E+01

* '400E+Oi

.3000E+01

* 2000E+01

.1000E+01

*G0O0E +00

.2000E+00

C,~vRESPONSE ENUELOPE SPECTRA (RES) MAP

GL!_DEN GWTE 19E? I N8O1ý

GROUND IAOTIC-11 !,nORMALIZED TO 1.0 G

I I II* -+------.---4-~Io ~ 3. Z. 30 4. ~. .0 0 90 10.0 It1.0 12.C 13.0 1,. 1. 1,;.0 17.0 18.0 19.C 7:.C JL.C J2.9 ?3-G --2 Z.0 Zt .0 ? !0.0 'q

ul"E IsECalIDSt F I GU

APPENDIX E

Spectrum Shapes Based on Log NJormal:Distribution

Figures El through E6

LA.

z

Ir-

a

U)

0-

Is.0

12.4

RESPONSE SPECTDPMPING RPTIOMEDIAN) Y=N I Y=T.04SG

GROUND MOTION NORMALI ZED TO 1.0 G

R P0 .00O5

Y=2

9 . 1ý

G.O%

3

n ri - 1-r

0.c

-r

1.c 2.0 2. G

FIGURE El PERICCSEC

U-

z'-4I-

ci:w~~2wU

1±1

-J

cr~

c:JI LIU)a-

i~Lor RESPUNSE SPECTRPDPMPING RPTIZ zMEDIA:N) Y=z, Y=z1.645, Y=

GROUND MOTIO ON NORMALIZED TO I .0 G

0 .010

12 oi.

Itr• V

- -- ~ - -

L. 1.0 I .C 2.0 2.S

FIGURE E2 FIGURE E2 F £. RJii [~S E C

- w -

CL

(-I

LU

'is£~ ~E~;[NE3'L

D P INP PiW 'P" iTL IJI2M U~r~ P. Y -j 0..eP. 4Eýý Y

1.?

t3.d!34

GROUJr~ .'orio~j Pj.jR~.¶AI.t7j~ To I .0 t3

N

~''~N

N -'- - ------.- *-.--- --------- -

~-.--~

S.-.--.-..... -. ---.- .~-..- -~1-------------+4---

t" - Al n= a - P%

;IGURE t3 K;m .. r., - - C

z

a

LuaJ

15 aG

12 .O

9.0

RESPONSE SPECYRPDAMPING RPTIO-- 0ME DIRNfl Y=1, Y=i.6463 Y=2


16.%

3.0,-

0. w, I

0.0 I.0 2.0T -r

FIGURE E4 PERIOD)SEC

LL

z3

c-JwýUL

ci-w

C12

02

ci0)aL

IS. I0 RESPONSE SPECTRADAPPING RPTIE0MEDIRN3 Y=1. Y=1.645)GROUND MOTION NORMALIZED TO 1.0 G

0.0~70Y=2

12 .0[

9.%

6;. +

3.0

0 #,,,-I--r

0.1-r

.5T

0 1 S 2.0

PERIfJO, SEC.FIGURE E5

Ld

cc:

-JMti

1s ,q RESPOFNSE SPE.CTRPDPfMPING .RAT ID = t0.1O0MEDIAN• Y=I,.. Y.=1.645 Y=2

GROUND MOTION NORMALIZED TO i .0 G

12 ,. r

9.0-

6. C+

11. (1j.

PERIOIJ)SECFIGURE. E6

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