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B E C E l v e o BY TJC JUN 1 3 1 9 8 4

NUREG/CR-3805Vol.1

Engineering Characterizationof Ground Motion

Task I: Effects of Characteristics ofFree-Field Motion on Structural Response

Prepared by R. P. Kennedy, 8. A. Short, K. L. Merz, F. J. Tokarz/SMAII. M. Idriss, M. S. Power, K. Sadigh/WCC

Structural Mechanics Associates, Inc.

Woodward-Clyde Consultants

Prepared for _ -^ ^ « - . . - -

^c^,.!^^Z"•"""""' K ) NOT MICROFILM1 ^ ^ COVER

M A S J E l l

D 1S T W B 8T O » 9 m W C M IH IT IS W l H i T a

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w e t

^ NOTICE

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NUREG/CR—3805-Vol

DE84 901344

Engineering Characterizationof Ground iViotion

Tasl< I: Effects of Characteristics ofFree-Field Motion on Structural Response

Manuscript Completed: February 1984

Date Published: May 1984

Prepared by

R. P. Kennedy, S. A. Short, K. L. Merz, F. J. Tokarz, Structural Mechanics Associates, Inc.

I. M. Idriss, M. S. Power, K. Sadigh, Woodward-Clyde Consultants

Structural Mechanics Associates, Inc.

Newport Beach, CA 92660

Under Contract to:

Woodward-Clyde Consultants

Walnut Creek, CA 94596

Prepared forDiv is ion of Engineer ing TechnologyOf f ice of Nuclear Regulatory ResearchU.S. Nuclear Regulatory Commiss ionW a s h i n g to n , D.C. 20555

NRC FIN B6680 DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United StatesGovernment. Neither the United States Government nor any agency thereof, nor any of theiremployees, makes any warranty, express or implied, or assumes any legal liability or responsi

bility for the accuracy, completeness, or usefulness of any information, apparatus, product, orprocess disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark,manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The viewsand opinions of authors expressed herein do not necessarily state or reflect those of the

United States Government or any agency thereof.

J o l s l i l e a t a l i a W l l t f .

O is ii iiBinioi Of m mcuMEJiT is UNLIMITED

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FOREWORD

This report presents the results of the first task of a two-task

study on the engineering characterization of earthquake ground motion for

nuclear power plant desig n. The overall objec tive of this study is to

develop reco mmendations for methods for selecting design response spectra

or accel eratio n tine histories to be used to characterize motion at the

foundation level of nuclear power plant s.

Task I of the study, presented h erein , develops a basis for

selecting design response spe ctra, taking into account the characteris

tics of free-field ground motion found to be significant in causingstructural d ama ge. Task II of the stu dy , to be completed later in 1984,

will provide recomm endations for methods for selecting response spectra

and time histories incorporating wave passage and soil-structure inter

action effects and Task I results.

This study is being conducted under Contract No. NRC 04-80-192

with the U.S. Nuclear Regulatory Commission ( U S N R C ) . Woodward-Clyde

Consultants (WCC) is the prime contractor for the project. Task I has

been carried out primarily by Structural Mechanics Ass oci ate s, Inc.

( S M A ) , as a subcontractor to WCC.

In additio n to the listed aut hors o f this repo rt, several

individuals made important contribu tions to the study. These individuals

included T. R. Kipp and H. Banon of SMA ; and C.-Y. Chang and R. R.

Youngs of WCC. Project consult ants, W. J. Hall of the University of

Illinois, Champaign ; J. E. Luco of the University of Cali fornia, San

Diego; J. M. Roesset of the University of T e x a s , Austi n; H. B. Seed ofthe University of Californ ia, Berkeley; and N. C. Tsai of NCT Engi

neering, I nc., Lafay ette, Californi a, provided a detailed review of

draft versions of the report and made many useful com ments . J. F.

Costello provided overall technical guidanc e and review in his role

as technical representativ e of the USNRC for this research project.

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TABLE OF CONTENTS

Section Title Page

1 INTR ODUC TION 1-1

1.1 Backgrou nd (Literatu re Revi ew) 1-1

1.1.1 Effect ive Ground Acce lera tion for

Ancho ring Elastic Spectra 1-3

1.1.2 Effect of Duration on Damage Capability . . . . 1-8

1.2 Conclus ions Reached from a Review of Structural

Damag e from Past Earthquake s 1-11

1.3 Charac teriza tion of Struct ure Damage 1-14

1.4 Obj ect ive of this Study 1-17

1.5 Stud y Appr oach 1-19

1.6 Repo rt Out lin e 1-20

2 ENGINEERING CHARACTERIZATION OF GROUND MOTION

FOR RECORDS STUDI ED 2-1

2.1 Energ y, Power and Duration Content 2-3

2.2 Frequency Conten t 2-6

2.2.1 Respon se Spectra 2-6

2.2.2 Cumulative Power Spectral DensityFunctions 2-9

2.2.3 Moments of the Spectral Density

Function 2-11

2.2.4 Frequency Content Summary and

Conclusions 2-13

2.3 Engineering Characterization needed for

Elastic Respon se 2-15

2.4 Engineering Characterization of Ground

Motion Summary 2-22

3 TECHNICAL APPROACH FOR NONLINEAR STRUCTURAL

RESPONSE ANALYSES 3-13.1 Representative Nonlinear Structural

Response Resistance Functions 3-1

3.2 Detailed Descrip tion of Shear Wall Model 3-4

3.2.1 Rules for Construct ing Shear Wall

Resist ance Function Model 3-4

3.2.2 Resist ance Function Properties Used

in this Study 3-8

3.2.3 Dynamic Propertie s Used in this Study 3-10

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TABLE OF CONTENTS (Continued)

Section Title Page

3.3 Simplified Methods to Approxim ate

Nonlinear Structural Response 3-12

3.3.1 Equivalent Linear Resistance

Function Models 3-13

3.3.2 Inelastic Spectra Deamplification

Factors 3-16

4 NONLINEAR STRUCTURAL RESPONSE ANALYSIS RESULTS

AND COMPARISON TO PREDICTION EQUATIONS 4-1

4.1 Input Scale Factor Results for Ground

Motion Studied 4-2

4.1.1 Dura tion Effects 4-2

4.1.2 Freque ncy Effects 4-3

4.1.3 Influence of Frequency Shift from

Elastic to Secant Frequency 4-3

4.2 Number of Strong Nonlinear Response Cycles 4-5

4.3 Comparison of Computed Scale Factors withthose Predicted by Equivalent Linear

Response Models 4-7

4.4 Comparison of Computed Scale Factors with

those Predicted by Inelastic Response Spectra 4-12

4.5 Conclusions on Predicting Inelastic Response 4-17

5 GROUND MOTION CHARACTERIZATION FOR NONLINEAR RESPONSE . . . 5-1

5.1 Inela stic R.G. 1.60 Spec tra 5-1

5.2 Predicted Inelastic Spectra for Real

Time Histori es 5-3

5.3 Comparison of Inelastic Spectra to

R.G. 1.60 Inelasti c Spectr a 5-4

5.4 Ground Motio n Characterization for

Nonlinear Response Summary 5-8

6 MEASURE OF RELATIVE STRENGTH OF GROUND MOTION

RECORDS 6-1

6.1 App roa ch 6-1

6.2 Relative Strengths of Ground Motion

Records Studied 6-3

6.3 Relative Strength SUMMARY 6-6

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TABLE OF CONTENTS (Continued)

Section Title Page

7 CONCLUSIONS 7-1

7.1 Engineer ing Charact erizat ion of

Ground Motion 7-1

7.2 Predict ion of Inelastic Spectral

Deamplification Factors and

Inelastic Response Spectra 7-6

7.3 Measur e of Relative Strength of

Ground Moti on Records 7-15

8 REFER ENCES 8-1

APPENDICES:

A LITERATURE REVIEW: EARTHQUAKE STRUCTURAL DAMAGE A-1

B INPUT GROUND MOTION DATA B-1

C TECHNICAL BACKGROUND ON EQUIVALENT LINEAR

RESISTANCE FUNCTION MODELS C-1

D PARAMETER STUDIES TO DETERMINE SENSITIVITY OF

NONLINEAR RESPONSE RESULTS TO PROPERTIES OF

THE RESISTANCE FUNCTION MODEL . D-1

E STRUCTURAL EVALUATION OF EL CENTRO STEAM PLANT

UNIT 4 SUBJECTED TO TH E 1979 IMPERIAL VALLEY

EARTHQUAKE E-1

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1 . INTRODUCTION

This re po rt pro vides a summary of the re su lts obtained du ring

the f i r s t phase of an ongoing pro jec t with the ob jec t ive o f pr ovid ing

guidance and the development of procedures fo r the ch ar ac te riz at io n of

earthquake ground motion used for design of nuclear power plant struc

t u r e s . The ov er all study e ff o r t is divide d in to two separate tasks :

I : The development of a bas is fo r se le ct in g design responsespectra based on f r e e -f ie ld mo t ion.

I I : The development of recommendations for methods forselect ing design response spectra and t ime histories to beused as input motions at the foundation level.

This re po rt is concerned w ith the Task I e f fo r t o nl y. The work performed

co nsis ts of (1 ) the development of a procedure fo r e stim atin g redu ction

factors that provide equal-damage effect ive response spectra, (2) the

comparison of ground motions on the basis of equal structural damage

po te n tia l and (3) a review of the design basis and observed behavior o f

actual structures due to past damaging earthquakes.

1 .1 BACKGROUND (LITERATURE REVIEW)

The ground motion in pu t fo r the seism ic ev alu ati on and design of

nuclear power plants is ge ne ra lly de fined i n terms of a design response

spectrum fo r which the stru ct u re is expected to remain e la s ti c . The

design response spectrum is generally a broadbanded spectrum with broad

frequency con ten t. I t expresses the peak lin e a r response of a whole

ser ies of s ingle-degree-of- f reedom o sc i l l at or s at a spe ci f ied damping

l e v e l . Either site-independent or site-dependent response spectra are

s p e c i f i e d . A site-independent sprectrum uses a broad standard spectrum

shape which is considered ap plic ab le to a wide range of loc al geo logic

and seismological condit ions, while a site-dependent spectrum tends to be

less broadbanded as i t depends at lea st in pa rt on p a rt ic u la r loc al s it e

co nd it ion s. F igure 1-1 presents a repres entat ive s i te- independent

1-1

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response spectrum which has been commonly used for nuclear power plants

in the United States [USNRC ( 1 9 7 3 a ) ] . This s pectr um (as well as most

other site-independent spectra) is anchored to a design ground acceler

ation with the entire spectrum normally being defined in terms of this

one ground motion para mete r. Newmark (1973) states that in the frequency

region of interest (approxima tely 1.8 to 10 Hz) for stiff nuclear power

plant s tructure s, the design spectra are most appropria tely anchored to

the design ground accel erati on. Th us , as a minimum the ground motion

parameter which must be defined is the design ground accele ration .

Seismologists have tended to concentrate on defining ground

motion in terms of an instrumental peak acc elera tion, which represent s

the absolute peak acceleration recorded during the entire earthquakemotion by a reliable strong-moti on instrument situated at the free ground

surface (i.e., not significan tly influenced by soil-stru cture interaction

or local topographic con dit ion s). This parameter represents a relatively

easily determined quantitative value not strongly influenced by subjective

judg ment s. Unfortunately, as illustrated by many studies (e.g., see

Hoffman , 1 974; Page and ot hers, 1972; Housner, 1975, 1979; Housner and

Jennings , 1977; Newmark, 1975; Blume, 1979; Nuttli, 1979 , Kennedy, 1 9 8 0 ) ,

the instrumental peak accel eration is, by itsel f, a poor measur e of the

damaging potential of earthqua ke ground mo tio ns. It has been noted, par

ticularly in connection with near-source motions due to low-to-moderate-

magnitude earthqu akes, that structures have performed much better during

earthq uakes than would be predicted co nsidering the instrumental peak

acceleration to which the structures were subj ecte d. Examples of this

behavior may be seen from the 1966 Parkfield eart hqu ake , the 1971 Pacoi ma

Dam earthquake record, the 1972 Ancona earthquak es, and the 1972 Melendy

Ranch Barn earthqu ake reco rd. These earthq uake record s had instrumental

peak accel erations of between 0.5 and 1.2g and ye t, only minor damageoccurred in the vicinity of the recording sit es. In these cases and

others, the differences in measured ground moti on, design levels, and

observed behavior is so great that it cannot be reconciled with typical

safety factors associated with elastic seismic analyses used for design .

This subject is discussed in more detail in Newmar k and Hall , 1982 .

1-2

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The problem with instrumental peak acceleration is twofold.

First, a limited number of high freq uency spikes of high acceleration but

yery short duration have little effect on the elastic response spectra

within the region of primary interest (1.8 to 10 H z ) . This problem can

be corrected throu gh the use of a design ground ac celeration value that

is often called "effect ive peak a ccel erat ion" and is defined herein as

that accele ration at which the design resp onse spectrum is anchored at

zero-period (or y &ry high f r e q u e n c y ) . The design ground acceleration can

be defined by the methods reviewed by Kennedy (1980, 1981) if the purpose

is to anchor an elastic response spectrum for computing peak elastic

structural resp onse. Howeve r, the second problem is that an elastic

respo nse spectrum anchored to any of these design ground acceleration

values or to the instrumental peak a ccelera tion does not provide a goodmeasu re of damage to struct ures. Elastic response spectra describe

elastic response while structure damage is related to structures being

strained into the inelas tic r ange in which the duration of motio n or the

number of cycles of straining as well as the nature of such cycles sub

stantially influence the damage. The elastic spectrum ignores the effect

of duration and unde rest imate s the effect of the number of cycles of

near-peak excursions on damage.

1.1.1 Effective Ground Accelerat ion for Anchoring Elastic Spectra

Much research has been conducted for the purpose of defining

"effecti ve" design ground accelerations to use as anchor accelerations

for elastic design spectra. In gen eral , the elastic response spectrum

used in design should have a broad freq uenc y content and should be smooth

(i.e., not contain large differences in spectral amplitude for minor

shifts in natural f r e q u e n c y ) . This is required because the specific

frequency content of a future ea rthquake ground motion cannot be accu

rately specified and two different ground motions recorded at the samesite may have different frequency conten t. Howeve r, recorded instrumental

ground motions often lead to elastic response spectra with narrower fre

quency content than smooth design spectra and with many peaks and valleys

(i.e., substantial differences in the spectral response for minor shifts

in natural f r e q u e n c y ) . The narrow frequency content of the spectra and

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the differe nces in amplitudes between peaks and valleys increases as the

effective duration of the motion decr ease s. Th us , real spectra derived

from actual short duration earthq uake re cords dif fer more from the broad

idealized design spectra than do spectra derived from the recorded long

duration reco rds . Yet normal ly, it may not be prudent in design to take

advantage of the narrow frequency content and large differences between

the amplitudes of peaks and valleys associated with these short duration

spectra be cause their frequen cy content could vary over a wide range for

different eart hqua kes. One often proposed solution to this problem is to

anchor the broad design spectrum to a reduced "effec tive" ground accel

eration such that "on the ave rage" the broad freq uenc y, smooth design

spectrum will predict about the same elastic respo nse as would be pre

dicted by the actual spec tra.

Even within the higher frequenc y range (1.8 to 10 Hz) the elasti

response spectrum values are primaril y influenced by the energy contained

within a number of cycles of ground motion and are little influenced by a

few spikes of very high acceler ation. Blume (19 79) has shown that

clipping the highest 3 0% off the measured acceleration time histor y

(using only 7 0% of the re cord, in an absolute sen se, closest to the zero

line) produced only about a 5% reduction in the elastic resp onsespectrum. Similar results have been shown by Schnabel and Seed (1973)

and Ploessel and Slosson ( 1 9 7 4 ) . Newmark (1976) has shown that the

elastic response spectrum from the 1.25g Pacoima Dam record can be

conser vative ly enveloped wit hin the freque ncy range of interest by a

broadbanded design spectrum anchored to a design ground acceleration of

0.75g. These fin dings have led to a number of recommendations for

defining an effective design acceleration, A Q , including the use of

sustained or repeatabl e peak acceleration (Nutt li, 1 9 7 9 ) , the use of an

equivalent cycl ic motion (Whitman, 1 9 7 8 ) , and the use of filtered time

histories in which high freque ncy spikes are removed by passing the

measured time histor y through an 8 to 9 Hz cutoff frequ ency filter (Page

and othe rs, 1972 ; Ploessel and Slosso n, 1 9 7 4 ) . Based upon a review of

these recom menda tion s, Kenned y (1980) has suggested that the effective

design acceleration, Ap for elastic response might be defined by:

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AQ = 1.25 * A3P (1 -1 )

where A^p is the third highest peak acceleration from the f i l tered t ime

h is to ry re co rd . The f i l t e r chosen by Page (1972) which is centered at

8.5 Hz w ith a value of 1.0 at 8.0 Hz and 0.0 at 9.0 Hz appears t o be a

reasonable f i l t e r approach. Th is d e f in i t i on is i l l u s t ra te d us ing the

1.25g Pacoima Dam re co rd . Figure 1-2 presents the u n fi l t e re d and f i l t e r e d

Pacoima Dam rec ord . The t h ir d h ighest peak, A^p, from the f i l t e r e d

record is 0.62g as opposed to an u n fi l t e re d peak acce lera tion of ap pro xi

m ately 1 .2g. The Ap from Equation 1 -1 is 0.78g which agrees w ith

Newmark's (1976) recommendations fo r th is re co rd . On the othe r hand, fo r

the 1940 no rth -so uth El Centro reco rd i n which there were several lower

frequency near-peak excursions the design ground acceleration, Ar,, wouldbe e ss e n tia l ly equal to the instrum en tal peak acce lera tion of Q.35q by

t h i s d e f i n i t i o n .

Another approach to de f in in g an ef fe ct ive "e la st ic " design

ground motion is in terms of the energy conten t of the earthquak e. Ar ias

(1970) and Housner (1975) have suggested that E(T) given by:

. / ' - " ' . .E(T) = J a'=(t)dt (1-2)

to

can serve as a measure o f t h e total energy between time t a n d time

tg + T Q . T h e Arias Intensity i s proportional t o E ( T ) . In Equation

1-2, a(t) represents t h e instrumental acceleration at time t , a n d Tr, is

the duration o f strong motion. T h e average rate of energy input (earth

quake power) i s then given b y :

P = E(T)/T[j ( 1 - 3 )

A lt e r n a te ly , M ortgat (1 97 9), and McCann and Shah (1979) have suggested

the root-mean-square acceleration, rms, as the ground motion parameter of

in te re st . This rms acc elera t ion is g iven by:

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rms = V P (1-4)

Both the powe r, P, and rms acceleration are heavily influenced by the pro

cedure used to select the duration of strong mot io n, T Q . Often the

duration of strong motion has been selected as the time between the first

and last excursion of the absolute acceleration above a selected percent

age of the peak accelerati on (such as 10 or 20 percen t) or the time

between the first and last crossing of a particul ar acceleration level

(such as 0.05g). Such definitions give anomalous results for durat ion,

power, and rms acceler ation for a record such as the 1940 El Centro record

which appears to consist of three distinct zones of strong motion during

the time history . Kenn edy, (1980) has suggested that the cumulative time

the ground motion exce eds a selected percentage (such as 10 perce nt) of

the peak acceleration provides a more consistent estimate of the strong

motion durati on, power , and rms acceleration for a number of reco rds.

Duration defined in this manner is referred to as T^ in this report.

In the analytical studies reported in later chapters of this

report, the strong du ration , T^ is defined by:

"""[) = """M - ''"0.05 wh er e T ^ = ma x { " T ^ } (1-5)

where T Q 75 and T Q 05 represent the time at which 75 % and 5%, respec

tively, of the total energy as measured by / a^ dt has been reached. If

the time of maximum positive or negative ground acceleration occurs after

^0.75» *'^®" ^^^ ^^""^ ^pa °^ ^^^ first zero crossing after the time of

peak acceleration is used in lieu of T Q 75. The reasons for the use of

this definitio n of duration are described in Chapter 2. Strong durati ons

by this definition are shown in Tab le 2-3. For the San Fernando recordswith peak ground accelera tions in exce ss of 0.2g, the strong durations

T Q were generally 5 to 6 seconds while T Q was generally 9 to 10

seconds. T h u s , these records might be said to have 5 to 6 seconds of

strong dura tion, or 9 to 10 seconds depending upon the strong duration

definition. By some other definiti ons, these records would have strong

durations of about 12 seco nds. The reported strong duration can differ

by more than a factor of 2 depending on the defini tion.

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Use of the rms acceleration as the basis for the design ac celera

t i o n , A Q , has many attracti ons. It is an easily computed quantity once

a definition for T Q is accepted. As shown by Mortgat ( 1 9 7 9 ) , it

enables a design acc eleration to be selected at any desired pro bability

of excee danc e. A design acceleration defined in this fashion can be usedto define the elastic r esponse spectru m with a given probabilit y of

exce edanc e. The design acceleration is related to the rms acceleration

by:

A Q = Kp * rms (1-6)

where K is a function of the acceptable exceedance probability for each

individual peak of the time hist ory. Consider ing the design acceleration

as a median estimate of the maximum acceleration over the duration of

strong motion for a stationary random Gaussian mo tion , Vanmarcke and Lai

(1980) have determined K„ to be:

Kp = v/2 an ( 2. 8 T Q / T ^ ) ( 1- 7)

except K is not less than ^ / ^ wh ere T Q is the predominant period of

the ground motion which can be taken to be between 0.2 and 0.4 seconds

for most r ecor ds. Kenn edy (1980) has reported that Equations 1-6 and 1-7appear to work well for defining a design acceleration to which elastic

response spectra can be anchored.

The usage of Equat ions 1-2 thro ugh 1-7 can be illustrated using

the 0.7g 1972 Melend y Ranch recording (Figure 1-3) and the 0.18g 1952 Taft

recording (Figure 1-4) . Both records contain relatively similar total

energy content despite the nearly fourfol d greater instrumental peak

acceleration for the Melendy Ranch record. The Melendy Ranch record has

a much shorter strong motion duration ( T Q ) of about 1.5 seconds versus

about 16 seconds for the Taft record. With these durat ions, the design

accelerations given by Equations 1-6 and 1-7 are 0.34g for the Melendy

Ranch record and 0.14g for the Taft reco rd. The design acceleration

ranges from less than 50 percent of the instrumental peak acceleration

for Melend y Ranch to 70 percent for Taft which illustrates the expected

effect of the short duration for Melendy Ra nch.

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For several earthquake r eco rds . Table 1-1 compares i nstrumental

peak acce lera tio ns, and design ac celerat ions given by Equatio ns 1-1 or 1-6

and 1-7 (T^ = 0.3 seconds ) based on a duration , T Q . Also presented

is the strong motion duration, T Q . In each case, the design accelera

tion from E quatio ns 1-1 or 1-6 and 1-7 is judged to be a consistent basis

for anchoring the design response spectrum for the purpose of computing

elastic response in the 1.8 to 10 Hz frequency range. One can note the

influence of duration on the rati o of A Q to Ajp (instrumental peak

accele ration ) for elastic respo nse.

Either the approach of Equation 1-1 or Equations 1-6 and 1-7 have

been reported by Kennedy (1980) to provide reasonable estimates of

"effective" design accelerations to be used to anchor elastic design

response spectra for elastic anal yses. Howe ver, it was already mentioned

that compa risons of elastic resp onse do not provide a good description of

relative damage from two different ground mot ion s. Ther efor e, neither

method of defining a design acceleration provides an adequate characteri

zation of the damage capability of earthquake ground motion in every case.

1.1.2 Effect of Duration on Damage Capa bili ty

There are energy absorbing mechanisms that occur during seismicresponse of structures that limit the resisting force levels such that a

limited number of cycles of very high acceleration input ground motion

might result in only minor damage and not affect the prim ary function of

the structural system. Such energy absorbing mechan isms include concrete

cracki ng, minor bond slip of reinforcement bars, friction at bolted

connections and other locations, and other mech anis ms. These energy

absorbing mechanisms cause nonlinear behavior of sufficient amount to

considerably reduce required design force levels from those calculated

assuming totally elastic behavio r. For each cycle of earthquake motion,

energy absorptio n has a small d eterio rating or degrading eff ect on the

structure; for sufficient numbers of cycles these degrading effects would

eventually accumulate to produce noticeable structural da mage . For

exa mpl e, when a reinforced concrete shear wall is subjected to sufficient

transverse shear forces during an earthqua ke, the concrete will crack

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even though the steel continues to behave elastical ly. This would const i

tute acc eptabl e beha vior even for a critical facil ity such as a nuclear

power plant. Such a memb er in shear would exhibit softer unloadin g

stiffness and degrading stiffness during reloading because the concrete

cracks do not heal during unloading and the concrete begins to deterio

rat e. For a limited number of cycles of seismic response such that the

energy of the seismic excitation was less than the energy absorption

capaci ty of the struc ture , such a structur e as that described would shake

down to pseudo -elas tic behavior possibly at a reduced stiffness and

possibly with some permanent set but the structure would be stable and

safe and would not have experienc ed significant damage (Figure 1- 5) . On

the other ha nd, for a strong earth quake in which the number of cycles o ^

seismic response is such that the energy of the seismic excita tionexceeds the energy absorption capacit y of the structure, such a structure

as that described above would reach displa cement amplitudes correspo nding

to significant structural damage and possibly total collapse (Figure 1 -6 ) .

The effect of the duration of strong motion or number of cycles

of strong inelastic response is not incorporated into the low-damped

elastic response spectrum. Thu s, a given elastic spectral response would

correspond to greater damage capabil ity for a long duration earthquake

than for a short duration eart hqua ke.

Furt herm ore , it was mentioned in the previous subsection that

short duration earthquake records have narrower frequency content and

greater differences between the spectral responses at peaks versus

valleys than do longer duration reco rds . Thes e longer duration records

are richer in a broad range of frequenc y content and tend to be

smoothe r. The abilit y of structures to withstand ea rthquake ground

motions which result in elastic response spectra substant ially higherthan the elastic design response spectrum is greater for spectra which

have narrow frequ ency co ntent and ma ny peaks and valleys than it is for

smooth, broad frequency content spectra. Basically, if the elastic

structure is in resonance with the ground moti on at a frequenc y of one of

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the peaks of the elastic spect rum, small inelastic behavior of the

struct ure will shift the structure freque ncy off the resonan t peak and

into a valley. As will be shown in subsequent chapt ers, the level of

inelastic response is more consistently predicted by the average spectral

response over a broad frequency range to the soft (lower frequenc y) side

of the elastic natural frequenc y. The difference between this frequency

averaged spectral response and the elastic natural frequency spectral

response is significantly greater for narrow frequency band elastic

spectra with large peaks and valleys than it is for broad fr equen cy

conte nt, smooth elastic spectra of the type used in design.

When one ignores duration and considers only the elastic

resp onse spectra or the design acceleration defined by Equations 1-1 or1-6 and 1-7, one would conclude that the Melendy Ranch record was more

severe than the Taft record for structures with natural frequen cies

greater than 3 Hz (see Figure 1-7 ), and the 1966 Parkfield Cholame #2

record was more severe than the 1940 El Centro record at all frequencie s

(see Figure 1-8 ). Both conclusions would be incorrect and illustrate the

inadequacy of the elastic response spectrum to define the damage

capability of an earthquake. The problem is that the elastic response

spectrum values are related primar ily to the power of the earthquake

(Equation 1-3) , or the rms acceleration (Equation 1-4 ), or the design

acceleratio n (Equations 1-1 or 1-6 and 1- 7) , whi le the d amage capability

is probably more related to the total energy fed into structure s

(Equation 1-2 ). Housner (1975) has proposed that this dilemma be solved

by a two-parame ter definition of the ground shak ing in which one para

meter could be any of the parameters relating to the power of the earth

qua ke such as the design acce lera tion fr om Equ ation s 1-1 or 1-6 and 1-7.

the other parameter should be strong motion dura tio n, T^.

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Short (1980a and 1980b ) and Kenned y (1981a) have studied the

effect of a high a ccelerat ion, short duration record such as the Melendy

Ranch (1972, 0.52g corrected accelera tion) record on a nuclear power

plant structure designed for a long dur ati on, much lower acceleration

record like the Taft (1952, 0.18g correc ted acc ele rat ion ) recoi'd. The

shear wall-typ e structure was designed to ultimate strength for a broad

banded design spectrum anchored to 0.2g. The structure was subjected to

shaking characterized by the Melendy Ranch record. Concrete elements

were defined to have highly degrading stiffness characteristi cs. The

Mele ndy Ranch record shows maxim um 5% damped spectral acceleration in

exce ss of 1.5g in the 5 to 6 Hz frequen cy range and the str ucture was

designed to have a fundamental frequency within this range. The

nonlinear response of this structure was found to be highly stable with a

single inelastic excursion followed by pseudo-elastic behavior with a

slightly degraded st iffnes s. T h u s , a highly degrading structure designed

for a design response spectrum anchored to an "effective" ground

accelerati on of 0.2g shows per fectly satisfa ctory behavior when subjected

to the Melendy Ranch record. Ther efore , this record should be taken to

have a design acceleration value of 0.2g o r less as opposed to the

nominal values of 0.5g. In sum mar y, ignoring duration and considering

only the elastic response spectrum would lead one to conclude that the

Melendy Ranch record was more severe than the Taft record; however, this

would be an incorrect co nclusion which illustrates the inadequacy of the

elastic response spectrum to alone define the damage capability of an

earthquake.

1.2 CONCL USION S REACHED FROM A REVIEW OF STRUCTURAL DAMAGE

FROM PAST EARTHQUAKES

Appendix A summarizes the results of a literature review on

structural damage from past ear thq uak es. The primary purpose of this

review was to summarize the avai lable data on whether or not elastic

computed forces could be used to estimate the onset of significant

structural dam age. Whenever po ssible, the elastic computed forces were

compared with the design forces and/or the estimated ult imate ca pacity of

the structures reviewe d.

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The conclusion of this review is that the inelastic energy

absorption capability of the structure, and the duration of strong ground

motion both influence structural performance and one cannot totally rely

on the elasti c computed force s in determini ng structural perf orma nce.

The onset of significant structural damage for structures which had some

seismic design was predominantly due to either:

1. Inadequate design, detailing, or construction necessary toachieve a ductile design. In other word s, the structurehad features which do not meet a strict interpretation ofthe intended provisions in the current Uniform BuildingCode for achieving a ductile design.

2 . The structure contained "weak links" such that inelastic

energy absorption was not spread throughout the structurebut was very localized. In other words , the ratio ofelastic computed forc es (dema nd) to estimated ultimatecapacity was far from uniform throughout the struct ure.

These factors appear to have at least as much and prob ably more influe nce

on the ground motion level at which significant structural damage occurs

than does the average ratio of elastic computed demand to estimated

ultimate capacity.

As discussed in Appendi x A, the ratio of elastic computed demand

to capacity was evaluated for a number of structures for the 1971 San

Fernando ea rth qua ke. So long as the structu re did not suffer from one of

the above two defi cie nci es, minor structural damage did not appear to

occur at elastic demand to capacity ratios less than about 1.5.

Similarly, significant structural damage did not appear to occur at

elast ic demand to capa city ratios less than about 2.5. These estima tes

represen t lower bounds and were s ignifi cantly exceede d in some cases

witho ut the corres pondin g dam age. For inst ance , in the case of the

Veterans Administration Hospital Building #4 1, the elastic demand to

capacity ratio exceeded 3 with essentially no structural damage.

Howe ver , this lack of even minor damage appears to be heavily influ enced

by beneficial nonlinear soil-structure interaction effects.

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The ratio of elastic demand to capacity will be referred to as

the reduction factor or the input scale facto r, F, in subsequent chapters

of this repoi^t. This fact or F represents th e factor by which the ela stic

computed re sponse must be divided before being compared with the yieldingcapacity for the purpose of predicting a given level of structural d amag e.

Alt ern ate ly, F represent s a scale factor by which the ground motion can

be increased beyond that which corresponds to an elastic response equal

to the structural yielding capacity.

The reduction factor, F, associated with the onset of significant

structural damage appears to be influenced by the duration of strong

shak ing. The follo wing statem ents are keyed to durations T Q defined by

Equation 1-5 for con siste ncy. It was noted above that for the 1971 San

Fernando records ( T Q « 5 to 6 sec onds) the reduction facto r, F, corres

ponding to the onset of significant structural damage was at least 2.5.

Simi larl y, F corres pondin g to the onset of significant structural damage

would also appear to have been at least 2.5 for the 1952 Kern County

( T Q « 10 seconds) and the 1972 Managua earthqu akes. However, correla

tion with the onset of structural damage for well-designed buildings would

appear to require larger F factors for the 1978 Santa Barbara ( T Q « 3

s e c o n d s ) , the 1979 Imperial V alle y (generally T Q between 3 and 5 secondsfor records exceeding 0 . 2 g ) , the 1966 Parkfield ( TQ < 2 s e c o n d s ) , an d

the 1972 Ancona ( T Q < 2 second s) earthquak es. The sketchy nature of

the data does not enable the increase in F to be quantitatively defined.

Howe ver, the summation of damage data strongly suggest that F corres

ponding to the onset of significant structural damage is larger for

records with strong durations less than about 5 seco nds. Strong dura

tions less than about 5 seconds reduce the damag e potential of a given

level of ground shaking.

In summary, the literature review clearly indicates that the

characte rizatio n of ground motion by low-damped (10% and lesser dampin g)

elastic response spectra is insufficient to define the structural damage

potential of the ground mot ion . One must also consider the inelastic

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energy absorption capability of the structure and the strong duration of

the ground motion particularly for records with strong durations by

Equation 1-5 of less than 5 seco nds. The inelastic energy absorption

reduction factor, F, appears to be at least 2.5 prior to the onset of

significant structural damage for well-designe d structures and eart hquake

strong durations greater than 5 seco nds. These observations form the

impetus for the analytical studies reported in subsequent ch apters .

1.3 CHARACTERIZAT ION OF STRUCTURE DAMAGE

This study concentrates on predicting nonlinear response of

stiffness degrading shear wall and braced frame structures with

fundamental f req uenc ies in the amplified spectral acceleratio n region

from 1.8 to 10 Hz . These structure types and fundamental frequencies are

typical of those found in nuclear power pl ants .

Representative shear force versus deformation diagrams for shear

walls and braced frames unde rgoing multiple cyc les of deformation are

shown in Figure 1-9. The structural elemen t retains its initial st iff

ness and strength characteristics up to the first nonlinear cycle. After

the first nonlinear cycle, the structure loses stiffness and streng th.

Thus , each subsequent nonlinear cycle ratchets the structure to greater

total nonlinear defor matio ns. A short duration ground motion is likely

to result in only one nonlinear cycle . With a long duration record ,

multiple nonlinear cycles occur and each subsequent cycle results in

greater deformation . Th us, one effect of a longer duration ground motion

is to result in greater total de formati ons than occur from a short

duration ground motion for a stiffness and strength degrading struc ture.

For this study, a quantitative description of damage was

required. Basically, damage can be generally related to:

1. Displacement ductility which is defined as the ratio ofmaximum deformation to yield deforma tion.

2 . Total hysteretic energy absorbed during nonlinear cycles.

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For moment frames and in e la s t i c hinge ro ta t i o n s , the to ta l

hysteretic energy absorbed during nonlinear cycles probably best accounts

fo r the c um ulative damage th a t may occur as a re s u lt of reverse d

ine las t ic deformat ions.

However, fo r degrading s ti ff n e s s and degrading stre ng th shear

wa lls and braced frames, the displacement d u c t i l i t y also de scribes

cumulative damage because each nonlinear cycle results in increased

deformation or displacement duct i l i ty over the previous nonlinear cycle

(see Figures 1 -5, 1 -6 and 1 -9) . Thus, the maximum displacement d u c t i l i t y

reached prov ides a measure of the cum ula tive damage up to t ha t p o in t.

Furthermore, a study of m u lt ip le cycle forc e-d eform ation diagrams such as

those shown in Figure 1-9 tends to indicate that strength degradation isminor u n t i l a ce r ta in displacement d u c t i l i t y is reached. Beyond the dis

placement duct i l i ty , s t rength degradat ion increases rapidly wi th add i

t io n a l nonlinear cycles. This displacement d u c t i l i ty at which st rength

degrad ation tends to increase r a p id ly w ith subsequent cycles can be

considered to represent the onset of signif icant structural damage.

Thus, i f the onset of s ig n if ic a n t st ru ct ur a l damage is considered to

represent the l i m it of acceptable st ru ct ur a l per formance, the displace

ment d u c t i l i t y probably represents the bet ter des cr iptor of permissibledamage. Collapse would ge ne rally re qu ire a dd it io na l non linear cycles

resu l t ing in substant ia l s t rength degradat ion af ter the permiss ib le d is

placement d u c t i l i t y is reached. The refore, hy ste ret ic energy absorpt ion

for nonl inear cycles af ter the permissible displacement duct i l i ty is

reached probably provides the best descriptor of collapse for shear walls

and braced frames. Ad dit i on al research is necessary on th is su bj ec t.

For nuclear power plan t s tr u c tu re s , deformations beyond the onset

of s ig n if ic a n t st ru ct u ra l damage would ge ne rally not be considered

acceptab le . Therefore, w i th in th is s tudy, a l i m i t on permiss ib le

displacement d u c t i l i t y is used as a measure of acceptable st ru c tu ra l

performance.

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The use of permissible displacement ductility as the descriptor

of structural performance introduces some conservative bias to this study

for short duration rec ord s. A short duration ground motion could result

in the permisible displacement ductili ty being reached without the ground

motion time history having sufficient rema ining strong motion duration to

lead to the rapid strength degradation from subsequent nonlinear cycles

necessa ry for collap se. Th us , the short duration record could lead to

the permissible displacement ductility being reached without the structure

being at the onset of collapse because of insufficient duration to the

ground motion recor d. On the other hand, for a long duration reco rd,

reaching the permissibl e displacement ductil ity would indicate the

structure was at the onset of collapse from rapid strength degradation

during subsequent nonlinear cycles.

In other wo rds , the use of a permissible displacement ductility

as a measure of damage may overem phasize the ability of short duration

ground motion records to damage shear wall and braced-frame structures.

Howe ver, this potential conservatis m in evaluatin g the effect of short

duration records was judged desirable because of the lack of understanding

on the relat ive importance of hysteretic e nergy absorption versus

displacement ductility in leading to dama ge. Even so, the reader should

note that this study ma y overempha size the ability of short duration

earthqua kes to damage shear wall and braced- frame str uctu res.

The response of nonlinear systems can be best represented graphi

cally by means of a modified respon se spectrum to reflect the effect of

nonlinear behavior (called herein an inelastic yield s p e c t r u m ) . * Consider

the structural resistance function (or primary load-deflection c u r v e ) , as

shown in Figure l - l O ( a ) . In this c ase , the total deforma tion of the

system is specified as a multi ple of the yield deform ation , 6 = \i 6

The term "inelastic yield spectrum" is somewhat of a misno mer butwill be used herein because of its common usage in the lite ratu re.

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The fa ct or y represents the displacement d u c t i l i t y . For the response of

a s ingle-degree-of- freedom system, the y ie ld level sp ectra l acc elera t ion ,2

SA = 0) 6 m ul t ip l ie d by the mass, gives the yi e ld resistance le v e l,

Vy = Mco 6 = K6y. The in e la s ti c y ie ld spectrum is a p lo t of the

yield level spectral acceleration versus the corresponding system elastic

freq uen cy, as ind ica ted i n Figure l- lO ( b ) . I f the system had remained

li n e a r, then the system response would be the e la s ti c de form atio n, <S

and the corresponding spe ctra l ac ce ler ati on lev el would be given by2

SA = w 6 g . jh e yield level spectral acceleration m a y then b e considered

as a reduced elastic level response or, SA = SA/F, where F is t h e

reduction factor (Application A ) . I f 6 ^ i s considered t o b e t h e elastic

response level associated with t h e input motion y , then & = M 6 i s

the response level which results from t h e scaled input moti on, y x F

(Application B). Thus, F m a y b e viewed as either an input scale factor

(Application B ) o r a s a reduction factor (Application A ) depending upon

application viewpoint. It should b e noted that t h e inelastic yield spec

trum is associated with a given level of peak deformation as specified b y

the ductilit y ratio (Application A ) . Given a deformation damage measure,

the inelastic yield spectrum o r input scale factors provide t h e format

for comparing input motion s o n t h e basis o f equal inelastic structural

r e s p o n s e . T h u s , f o r a permissible displacement o f ductility, t h e inelas

tic yield spectrum represents th e "effective" response spectrum. T h e

definition o f equal-damage response spectra allows t w o records with t h e

same effective spectral acceleration at a structural natural frequency t o

cause t h e same level of nonlinear structural response.

1.4 OBJECTIVE OF THIS STUDY

In t h e previous subsections it w a s shown that t h e low-damped

elastic spectral response does not provide a consistent descriptor o f

damage f o r short duration versus long duration ground motion records.

The elastic spectral response would indicate much greater damage t o a 5 H z

structure from t h e ^ e r y short duration Melendy Ranch record than from t h e

long duration Taft record (see Figure 1 -7 ). Yet, a detailed nonlinear

analyses o f a nuclear power plant structure showed that if this plant w a s

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designed for the 0.18g Taft record, the structure would not be ser iously

damaged by th e 0.52g Melendy Ranch record because i t on ly undergoes one

cycle of nonl inear deform ation. There is in s u ff ic ie n t energy content in

the shor t d urat ion record to ratche t a degrading s t i f f ne ss s tru ctu re tof a i l u r e .

The objective of this study was to determine what ground motion

ch a ra ct e ri st ic s do provide a good de sc rip to r of damage fo r degrading

sti f fness ducti le structures such as those found in nuclear power plants.

Thus, th is s tudy w i l l def ine a procedure fo r developing " e f fe ct iv e"

spectral responses such that two ground motion records with the same

"e ff e ct iv e" spec tra l responses at the s tructures natura l f requency w i l l

lead to the same displacement d u c t i l i t y . Thus, us ing the "e f f e ct iv e "

response spectra as input to an e la st ic analysis and design w i l l re su lt

in the permissible system displacement ducti l i ty being reached for both

ac tua l t ime h is to r ies .

These "e f f e c t iv e " response spec tra then serve as a means of

des cr ibing the re la ti v e damage ca p a b il i ty of di ff e re n t ground motion t ime

h is to ri e s and thus serve as a means of p ro vid ing an eng ineering ch ara cte r

iz at io n of the ground mo tion. The ch ara cte r iza tio n of the ground motionby "e ff e c ti v e " s pec tral responses provides a be tter en gineering chara cter

iz at io n of the ground motion than does the instrume ntal peak a cc el er at io n,

or the elastic spectral responses.

I t w i l l be shown th at the "e f fe c t iv e " spe ctra l responses can be

approximated by the highly-damped average sp ec tra l ac ce le ra tio n over a

frequency range to the soft ( f lex ib le) s ide of the e last ic natura l

frequency. Thus, the highly-damped spe ctral ac cele ration w ith in t h is

frequen cy range can serve as a method of p ro vi d in g an en gin ee ring charac

te r i z a ti o n of the ground mo tion. De tai ls w i l l be presented in subsequent

chapters .

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This study is concerned with the in e la s t i c response of st ru ct ur a l

systems (braced frames and shear w a lls ) and the concept of " e ff e c ti v e "

sp ec tra l response is considerd va li d fo r such systems. The re su lts of

th is study can also probab ly be ex trap ola ted to d u c ti le passive equipmentwhose f r a g i l i t y is governed by st ru ct u ra l fa i l u r e modes. However, the

study is probably not appropriate for act ive equipment.

1.5 STUDY APPROACH

The study effort was subdivided into three major subtasks:

(1) a na lyt ic al s tudies to develop an est ima t ion procedure fo r in e la st ic

y ie ld spe ctra; (2) a demonstration of "e f fe ct iv e " ground motion compari

sons on the basis of equal damage; and (3) a literature review to documentand evaluate the observed performance of structures during past damaging

earthquakes. The major study e ff o rt was associated with the a n al yt ic al

subtask. The a na ly t ic al studies were fu rt h e r subdivided in to the

fol lowing study increments:

(a) The se le cti on and ev alu atio n of a group of stron g motion\ e c o r d s which encompass a wide range of poss ible f r e e - f i e l d

input mot ions.

(b) A review of the in e la s ti c beh avior of primary power plantst ru ct u ra l co nf ig ura t ion s and components.

(c) The d e f i n i t io n of a set of represe ntat ive st r uc tu ra l systemmodels with the overall nonlinear response behaviorat t r ibuted to power plant st ructural types.

(d) The development of an an alys is procedure fo r de term inatio nof reduct ion factors based upon input scaling.

(e) The determ inat ion and ev alu at io n of a set of input scalefactors (reduct ion factors) which correspond to two

d if fe re n t damage (deforma tion) le ve ls .( f ) The development and co rr e la ti o n of an inp ut scale fa ct or or

reduct ion factor est imation procedui^e.

(q) The development of "e ff e c t i v e " spe ctra using th is reduc t ionfactor procedu<^e.

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1.6 REPORT OUTLINE

The ground motion r ecor ds used in this study are described in

Chapter 2. Engineering characterizat ion defining both the time and

frequency characteristics of these records are presented and discussed.Minimum engineering characterizations to define elastic response of these

records are discussed.

The structural mo dels and analytical approach used in this study

are presented in Chapter 3. The primary structural model used consisted

of a degrading st iffn ess, degrading s trengt h, pinched behavior shear wall

model developed to closely approximate the shear wall behavior shown in

Figure 1-9. This model was specified as having 7 percent elastic damping.

Nonlinear response of such mode ls with initial (elastic ) natural freque n

cies of 2.1, 3.2, 5.3, and 8.5 Hz was studied . These natural frequencie s

are approximately equally-spaced within the frequency range from 1.8 to 10

Hz which covers the range of fundamental frequencies for the majority of

nuclear power plant building stru ctur es. The study concentrated on pre

dicting the nonlinear reduction factor, F, associated with ductility

ratios of 1.85 and 4.3. These ductility ratios were considered to repre

sent lower bounds on the onset of minor s tructura l damage and the onset

of significant structural damage, respectively.

Model parameter variation studies were also conducted (Appendix

D ) . For a few ca ses, damping was reduced to 3 percent elastic damping to

determine the effect of elastic damping on the reduction facto r. The

nonlinear force-deformation characteristi cs were modified to study the

effect of such charac teri stic s. Lastly , a few cases were also analyzed

for a nonlinear model representing the braced-frame characteris tics in

Figure 1-9.

The study results are presented in Chapter 4 in terms of

response reduction fact ors, F, obtained from a series of nonlinear

analyses using the ground motions and structure models described in

Chapters 2 and 3. Statistical studies performed on these reduction

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factors are prese nted. A method to derive these reduction factors from

the characteristics of the elastic response spectra and the structural

model is present ed.

A method to define an "effecti ve" resp onse spectrum using the

results of Chapt er 4 is presen ted in detail in Chapt er 5. This meth od

requires only a knowledge of the nonlinear ch aracteristics of the

struc ture model and the elast ic response spect>-a. "Effect ive" response

spectra are presented for the ground motion time histories studied.

The relative strengths of the ground motion records used in this

study in terms of ela stic (y = 1.0) and i nelas tic (y = 1.85 and 4.3)

structural response for stiff structures (f = 1.8 to 10 Hz) are describedin Chapte r 6.

Lastly, conclusions from these analytical studies are summarized

in Chapter 7.

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TABLE 1-1

INSTRUMENTAL PEAK VERSUS DESIGN ACCELER ATIONS

Earthquake Records

Melendy Ranch N61E

N29W

Parkfield, Cholame #2 N65E

Temblor S25W

Pacoima Dam N76W

Hollywood Storage SOOW

PE Lot N90E1

El Centre 1940 NS

Olympia N86E

Taft S69E

1*

Instrumental Peak Accel

Aip (g)

Uncorrected

.50

.70

.51

.41

1.25

.19

.22

.37

.31

.20

Corrected

.48

.52

.49

.35

1.07

.17

.21

.35

.28

.18

Elastic Response

Design Accel .

A , (g)

1.25*A3p

0.40

0.45

0.500.26

0.78

0.150.21

0.30

0.21

0.14

K *RMSP

0.36

0.34

0.41

0.26

0.78

0.15

0.19

0.28

0.21

0.14

Strong Duration

T[3"(Sec)

1.2

1.5

4. 4

4. 2

5.7

9.3

9.0

13.1

13.1

16.1

* As reported by California Institute o f Technology

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S.0 ro 1JI

PERIOD. IN SECONDS

as 02 0.1 aos 0.02 0.01

1000

100

10

0.3

\

V/ "

/

^

^

/

' ^ ••

1 \p i tnp in

yt2

'

\

factor(ptfo

^

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V/ ^

nU

K:

\

^

f/'(c)

1

^ 1

1 \

~ \ \

l \ \ /

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A11

1

A

f/

)

v

i" ^

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1 \

^

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y

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a i OJ 0.5 10 20 so 100

FREQUENCY, IN HERTZ

FIGURE 1-1. SITE-INDEP ENDENT HORIZONTAL RESPONSE

SPECTRUM SCALED TO l.Og [USNRC (1973a)]

1-23

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UNFILTERED

A V V< ^ < '* »»i * i « t y o i w V v M ^ •

I

ro

^

5Q :UJ- IUJoo<

FILTERED (/'c*8.5 Hz)

FIGURE 1 - 2 . UNFILTERED AND FILTERED ACCELEROGRAMS OF THE 1971 SAN FERNANDO EARTHQUAKE FROM THE S . 74 " W.ACCELEROGRAPH COMPONENT AT PACOIMA DAM. RESPONSE OF F ILTER I S 1 . 0 A T FREQUENCIES LESS THAN

8 HZ AND 0 . 0 AT FREQUENCIES GREATER THAN 9 HZ WITH A HALF-WAVE COSINE TAPER FROM 8 TO 9 HZ.(PAGE AND OTHERS, 1972) .

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1972 Bear Valley Earthquake

Melendy Ranch Recording

Component N29W

i^'yhl/^'rA*/^ ^'v '^.^' '\j < » . * » ' • - n -

0.02

~ T~ • - 1 1 " - T '

-i L-

2.5 5.0 7.5 10.0 12.5 15.0 1 7.5 20.0 22.5 25.0Time (seconds)

FIGURE 1-3. ACCELE RATION A N D VARIATION O F CUMULATIVE ENERGY

WITH TIME F O R T H E 1972 BEAR VALLEY EARTHQUAKERECORDING A T MELENDY RANCH

1-25

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co

ou

<

u

CM

I

•a

(0

- 0 . 1 -

>a>c

LU

- 0 . 2

0.04

o.m

0 . 0 } '

aoi'

1952 Kern County Earthquake

Taft. ACXM, Component S69E

""{ i f^ i^ ' i^^^^A^^^^ '^VgwV^

15 20 25 30

Time (seconds)

35 40 45 50 55

FIGURE 1-4 ACCELEROGRAM A N D VARIATION OF CUMULATIVE ENERGY WITH

TIME FOR THE 1952 KERN COUNTY EARTHQUAKE RECORDING A T TAFT

•

1-26

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Resistance

0 - (D Init ial UncrackedConcrete Stiffness

(D - (?) Pseud o-ElasticStif fness

5. SEISMIC SHEAR FORCE-DISPLAC EMENT RELATION F OR STRUCTURAL

MEMBER WHICH SHAKES DOWN T O PSEUDO-ELASTIC BEHAVIOR

1-27

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Deformation Associated

FIGURE 1-6. SEISMIC SHEAR FORCE-DISPLACEMENT RELATION FOR STRUCTUR E MEMBER WHICH

PROGRESSIVELY CYCLES TO DEFORMATION CORRESPONDING TO SIGNIFICA NT DAMAGE

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1 0 " ' 2 3 y 5 6 7 8 9 J 0°1 1 — I — I I I I I r

2 3 y 5 6 7 8 9 J 0 '_ i — I I I 1 I r

2 3 y 5 6 7 8 9 j 0 '- 1 i I I I I I 1 "

- r2

TAFT

DAMPING 0.07

MELENDY RANCH

y " \

^^^•\

J

-r3

1 — I — 1 1 1 1 — r r I 1 1 — I — 1 1 1 1 — r5 6 7 8 9 ' l 0 2 3 y 5 6 7 8 9 ' l 0 T

0.52g

O.lSg

-r-3

T — I 1 1 ' I I f ,

y 5 6 7 8 'l 00-'FREQUENCY (HERTZ)

FIGURE 1-7. COMPARISON OF MELENDY RANCH A N D TAFT RESPONSE SPECTRA

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0.6

-0.6

0.3

t 1 1-

Parkfield

^w^A^v*^

4 6 8 10 12

Time (sec)

•0.3 -

Time (sec)

(a) Accelerograms

(/> «uQ .

>, 60+ ->

( J

° 40OJ

>

-g 203QJ

^ 0

1 1 1

Damping 0.05

A ^ P a r k f i e l d

y / ^' {\ / ^-^-^^IAL V / ^ ' • ^ ^11 \ > x ^ ^1/ v ^ ' ^

- / / ^ — s ^ A El Centre'//

3 1 2 3

~ ~ n

\

\

\

4Period (sec)

GROUND RESPONSE CHARACTERISTICS FROM PARKFIELD CHOLAME #2

(1966) AND EL CENTRO (1940) EARTHQUAKE RECORDS

1-30

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1l-S.

}M

•O t

(w) (Km)

no o

800-

aooi

4 0 0

25 0

« o o l J A

M /

m^^^^TZ/jfil fi

»-too

»1 -W / AW y^^ «

-MO

• ^ I

"^^jpy

^Hr'^l

u^^^±

^J»

Vl\\/^

n 1

HI //y^^ ^

\*mt iM i

1*

•••••««-

IM'! l

J.«ao

Vl/

/ /

/

/« IMO)

0 1

• . ? _ . v

»

11'

t m . . . ,

u i 1ITI1 *

_

I

L-p""I

(a) Shear force-shear distortion diagram f o r structuralconcrete wall test (Wang, Bertero, Popov; 1975)

H(ton)P=70t p

A (cm)

(b) Lateral force-displacem ent diagram f o r braced-steelframe (Wakabayashi; 1973)

FIGURE 1-9. CYCLIC LOAD-DEFLE CTION BEHAVIOR O F REPRESENTATIVE POWER PLANT STRUCTURAL ELEMENTS

1-31

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M

— r

mm

T/7 - 7

^ ^ _ , U

711 f fj

2 K

M H M

Factored Seismic Input

e nO

3

II

A p p l i c a t i o n ( B )

Mu + K u =-My X 1 —*. 6

Mii + K u =- My x F —» . 6

Mli + V (u ) = -My X F — ^ y6

Appl icat ion (lO

Mli + K u = - ^

F

M u + K u = -M y

M u + V( u ) = - My y6

« m = ^ « y

(a) Structural Resistance Function f o r Single-Degree-of-FreedomRepresentation o f Overall Structural Behavior

I A = FSA (Application B)

SA =0)2$ (Application A)

• B)^Elas tic Spectrum

Inelastic Yield

Spectrum

(log f )

f = 1.8 Hz f = 10 Hz rigid

Range o f Interest f o rNuclear Structures

(b) Inelastic Yield Spectrum

FIGURE 1-10. DEFINITION O F STRUCTURAL RESISTANCE FUNCTION

AND CORRESPONDING INELASTIC YIELD SPECTRUM

1-32

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2 . ENGINEERING CHARAC TERIZATION OF GROUND MOTION

FOR RECORDS STUDIED

Eleven real earthquake ground motion time histories and one

artificial ea rthqu ake time history were used in this study. The eleven

real records used are defined in Table 2-1 . Througho ut the study , the

record will be designated by the underlined name in Table 2-1 . On some

fig ure s, an abbreviat ed symbol will be used for each reco rd. The names

and symbols used for these 11 records a re: Taft ( T) , Olympia (0 ), El

Centro No. 12 ( E C 1 2 ) , El Centro No. 5 ( E C 5 ) , Pacoima Dam (P D) , Hollywood

Storage (H S) , Coyote Lake (C L) , Parkfield ( P A 2 ) , Gavilan College (GC),

Goleta (G) , and Melendy Ranch (MR ). The Artificial (A) time history was

a 0.2g ground motion which approximated, at low damping, the NRC Regula

tor y Guide 1.60 resp ons e spect rum a nchored to 0.2g and had a duration of

approximately 20 seco nds. It is typical of some of the more realistic

artificial time histories used in nuclear power plant dynamic ana lys es.

Table 2-1 presents the earthquake name and da te, the local

magnitu de. M L , the surface-wave magnitude , Ms , the recording station, its

distance from the fault trace on which the earthquake was located, and

the corrected peak ground accelerati on, a, and velocity, v. All time

history inputs utilized herein have been corrected and processed using

the routine processi ng procedures outlined by Hudson ( 1 9 7 9 ) . The

corrected peak ground velocity reported was obtained by integrating the

corrected acceleration record.

These real earthquake records were selected in order to have a

wide variation in ground motion charact erist ics. Local magnitudes range

from 4.7 to 7.2 with fault rupt ure dista nces ranging from less than 1 Km

to 40 Km. The corrected peak accel erati ons vary between 0.14 and 1.17g

with corrected peak velocities ranging from 1.6 to 44.6 in/sec. Figure

2-1 present s a ccelera tion time history plots of these 11 real records

2-1

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plus the artificial recor d. All time histories have been normalized to a

peak acceleration of 0.5g in Figure 2-1 in order to make dur ation compari

sons easie r. These plots are ordered by decreasing du ration of strong

motion . The Olympia, Taft, El Centro #12, and Artificial records repre

sent long strong motion duration r eco rds . The Pacoima Dam, HollywoodStorage, El Centro #5, and Goleta records are of moderate d uration. The

Coyote Lake, Parkfield, Gavilan College and Melendy Ranch records have

short strong motion dura tio ns. The generally expected range of strong

motion durations of earthquakes with magnitudes from 4.5 through somewhat

over 7.0 are covered by the 12 tim e histories used in this stud y. The

very long strong motion durations which might occur from great earth

quakes with surface wave magnitudes greater than 8.0 are not covered by

this study.

Plots of the followin g detailed ground motion charact eristi cs

are presented in Appendix B for each of these 12 reco rds :

1. Acceleratio n time history

2 . Cumulative energy

3. 7, 10, 15, 20 and 25% damped-elastic response spectra

4. Elastic response time histories for 2, 5, and 8 Hz , 7%damped oscillator

5. Fourier spectra for the strong motion portion of theaccelerogram

6. Cumulativ e spectral densi ty functio ns for the strong motionportion of the records.

These plots fully define the time duration, frequency characteris tics,

elastic response characteristics, and energy characteristics of these

rec ord s. A careful study of these plots will show the wide variation of

ground motion charac terist ics in the 2 to 8 Hz frequ ency range included

in this study. All of these plots are ordered in descend ing order from

the longest duration record (Olympia) to the shortest duration record

(Melendy R a n c h ) . Data presented in these plots will be discussed in

subsequent subsections.

2-2

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2 .1 E N E R G Y , P O W E R , A N D D U R A T I O N C O N T E N T

T h e t o t a l e n e r g y E ^ ( m o r e c o r r e c t l y d e f i n e d a s t h e F o u r i e r

e n e r g y ) of t h e r e c or d i s d e f i n e d b y E q u a t i o n 1 -2 i n t e g r a t e d o v e r t h e f u l l

d u r a t i o n o f t h e r e c o r d . A c u m u l a t i v e e n e r g y p l o t i s s i m p l y a p l o t o f E ( T )

v e r s u s t i m e , T , w h e r e E ( T ) is de f i n e d b y E q u a t i o n 1 -2 i n t e g r a t e d f r o m t i m e

z e r o t o t i m e T .

H o u s n e r a n d J e n n i n g s ( 1 9 7 7 ) , h a v e d e m o n s t r a t e d t h a t j E ^ m a y b e

i n t e r p r e t e d as t h e " f r e q u e n c y e n s e m b l e w o r k " a nd i s a m e a s u r e o f t h e

c a p a c i t y o f t h e g ro u nd m o t i o n t o d o w o r k o n an i d e a l i z e d u n i f o r m p o p u l a

t i o n o f s t r u c t u r e s o f aVI_ n a t ur a l f r e q u e n c i e s . F o r t h i s r e a s o n . A r i a s

( 1 9 7 0 s u g g e s t e d u s i n g ^ E^^ as a m e a s u r e o f s ei s m i c i n t e n s i t y an d s u ch

is de f i n e d a s t h e A r i a s I n t e n s i t y . O n e m i g h t t h u s c o n s i d e r E,^ o r A r i a sI n t e n s i t y t o b e a m e a s u r e o f t h e d a m a g e p o t e nt i a l o f a g r o u n d m o t i o n

r e c o r d f o r a u n i f o r m p o p u l a t i o n o f s t r u c t u r e s o v e r a l l f r e q u e n c i e s . A s

c an b e s ee n f r o m t h e p l o t s i n A p p e n d i x B , t h e t ot a l e n e r g y , E ^ , i s v e r y

p o o r l y c o r r e la t e d w i t h t h e p e a k g r o un d a c c e l e r a t i o n , a . T h i s i s o n e o f

t h e r e a s o n s w h y p e a k g r o u n d a c c e l e r a t i o n a l o n e d o e s n o t p r o v i d e a g o o d

m e a s u r e of d a m a g e . F o r i n s t a n c e , F i g u r e 2 -2 c o m p a r e s t h e Ol y m p i a a n d

M e l e n d y R a n ch r e c o r d s . M e l e n d y R a n c h h a s a c o r r e c t e d p e a k a c c e l e r a t i o n

1 .8 5 t i m e s t h a t o f O l y m p i a . Y e t , t h e t o t al e n e r g y f o r M e l e n d y R a n ch is

o n l y 5 6 % o f t h at f o r O l y m p i a .

T h e m o st c om m o n d e f i n i t i o n o f s t r o n g m o t i o n d u r a t i o n i s t h at d u e

t o T r i f u n a c a nd B r a d y ( 1 9 7 5 ) . B y t h i s d e f i n i t i o n , t h e s t r o n g m o t i o n

d u r a t i o n i s d e f i n e d a s :

^ D " ^ 0 . 9 5 • ^ 0 . 0 5 ^ ^ ' ^ ^

where TQ gg represents the time at which E (T)/E^ = 0.95 and T Q Q S i^epre-

sents the time at which E(T)/En, = 0.0 5. Thus, t h is du rat ion window

inclu des 90% of the t o ta l cum ulative en ergy. The time T^ can be defined

as the f- f ra c t io n Husid t ime since i t represents the t ime at which the

f- f ract ion of the tota l energy has occurred.

2-3

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Howe ver, for stiff structures (1.8 to 10 Hz) such as those in

nuclear power plants. Equation 2-1 provides too long of an estimate of

strong motion duration for many re cord s. Many records contain a long tail

of oscillatory ground motion with lesser accelerations at the end of the

record which c ontinues to input energy but at a substa ntiall y lesser rate

than the earlier portion of the record. This situation is illustrated

for the Taft record in Figure 2-3. Based upon Equation 2- 1, the duration

of the Taft record would be considered to be 28.1 sec ond s. Yet, 70 % of

the total energy is input in a duration T Q of only 9.9 s econ ds. Reporti ng

the duration of the Taft record as 28.1 seconds would severely misrepre

sent its effect ive dura tion at least for stiff structur es with frequ encie s

over 2 Hz. Figure 2-4 compares the time histo ry acceleration resp onse of

an example set of simple, damped-elastic oscillators (7% damping) obtained

for represent ative long and short duration input mo tio ns . The example

oscillators were tuned to 2, 5 and 8 Hz to encompass the range of ela stic

structure frequency considered in the study. The time of peak respons e,

T , and the times, T Q Q ^ and T Q 75 are indicated for each example

oscillator respon se shown in Figure 2-4. For the records and freque ncies

considered in Figure 2-4, the time of peak res ponse, T„ ,^ , falls

between T Q Q ^ and T Q 75. Thus , at least for stiff s tructures, a more

appropriate and shorter definition of strong duration than that given by

Equation 2-1 is needed.

In order to determine a more a ppropriat e definition of strong

duratio n, a study of the time of maximum respons e was conducted for all

twelve earthquake time histories considered herein. The time of maximum

response for both elastic and nonlinear s tructures represent ative of

degrading stiffness and degrading strength shear walls was cons idered .

Shear wall st ructur e mod els with initial (elas tic) natural freq uencie s of

2.14, 3.20, 5.34, and 8.54 Hz and 7% elast ic damping were used. The time

of maxi mum dis pla cem ent res pon se, T ^^^^ for elast ic resp onse (y = 1.0) and

two levels of nonlinear response (y = 1.9 and y = 4.3) was determined for

all four natural fre que nci es. The upper bound of maximum re sponse time ,

T „ , ^ , noted for the entire set of oscilla tors w ithin a frequenc y ran ge

from 2.14 to 8.54 Hz (i.e., T ^ ^ ^ y ^ = max {TJJ,3J^>.J) can be compared to

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v a r i o u s H u s i d r a t i o t i m e s as t a b u l a t e d in T a b l e 2-2 for e a c h of the 12

s e l e c t e d e a r t h q u a k e r e c o r d s . In T a b l e 2 - 2 , the t i m e T 0 . 9 5 , T Q . S S * T 0 . 7 5 .

T Q Q 5 are the t i m e s a s s o c i a t e d w i t h 9 5 % , 85 % 75% and 5% of the t o t a l

c u m u l a t i v e e n e r g y . The t i m e , Tpg , is the t i m e a s s o c i a t e d w i t h the f i r s t

z e r o c r o s s i n g of the a c c e l e r o g r a m f o l l o w i n g the m a x i m u m p o s i t i v e or

n e g a t i v e a c c e l e r a t i o n , w h i c h e v e r o c c u r s l a t e r in t i m e . F r o m T a b l e 2 - 2 , it

c a n be s e e n t h a t an u p p e r b o u n d on the t i m e of m a x i m u m r e s p o n s e can be

r e a s o n a b l y a p p r o x i m a t e d by:

|;:.'1^ =ma x { , -'-^ } (2-2)

I n no c a s e , was the a c t u a l u p p e r b o u n d on the t i m e of m a x i m u m r e s p o n s e

m o r e t h a n 6% g r e a t e r t h a n t h a t g i v e n by E q u a t i o n 2-2.

T h u s , E q u a t i o n 2-1 was m o d i f i e d to p r o v i d e the f o l l o w i n g

d e f i n i t i o n of e f f e c t i v e s t r o n g m o t i o n d u r a t i o n for s t i f f s t r u c t u r e s :

Ti = T M - T O . 0 5 (2-3)

E q u a t i o n 2-3 p r o v i d e s a b e t t e r d e f i n i t i o n of the r e l a t i v e l e n g t h of

s t r o n g d u r a t i o n for s t i f f s t r u c t u r e s t h a n d o e s E q u a t i o n 2-1.

W i t h the s t r o n g d u r a t i o n d e f i n e d by E q u a t i o n 2 - 3 , the H o u s n e r

p o w e r ( a v e r a g e r a t e of e n e r g y i n p u t ) d u r i n g t h i s t i m e can be d e f i n e d by:

P= f (2-4)

' D

where AE represents the cumulative energy between time TQ Qg and T|v|.

Except for Olympia and Pacoima Dam, AE is equal to 70% of E , since

T = TQ 7c. For Olympia and Pacoima Dam, Tpg exceeds TQ 75 and thus T j,

exceeds TQ 75. For Olympia and Pacoima Dam, AE equals 85%, and 82%,

respectively, of E^.

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The d ur a tio ns , TQ and TQ, peak ground a cc el e ra tio n s, a, peak

ground velocity, v, effect ive total energy, AE, and average power, P, are

tab ula ted in Table 2-3 fo r a l l 12 records stu die d. The records are

ordered i n terms of decrea sing du ra tio n , TQ . One should note the

reasona bly poor c o rr e la ti o n between TQ and TQ. These records would have

been in a su b st a n t ia l ly d if fe re n t order i f they had been ordered by TQ

ra th e r than TQ . Thus, TQ does not serve as a good measure fo r th e

ef f ec t ive du rat ion of s t rong shak ing fo r s t i f f s t ru c tu res .

If the power of the cumulative energy plot is assumed to be

approximately constant during the effect ive durat ion window, then the

root-mean-square-accelerat ion, a^j j ,^, is also approximately constant

durin g th is in te rv a l and can be given by:

a = / P ~ ( 2- 5)rms '

A review o f t h e cumulative energy plots given in Appendix B f o r t h e 1 2

records considered in this study indicate that t h e assumption of constant

power during t h e interval defined by Equation 2 - 3 i s re as on ab l e . T h e r m s

accelerations ar e tabulated in Table 2 - 3 .

For stiff structures, t h e q u an t it i es T Q , a , v , A E , a n d P listed

in Table 2 - 3 a r e judged to provide an adequate characterization o f t h e

ground motion i n t h e time domain. It should b e noted that only t w o o f

t he q u a n t it i es T Q , A E , a n d P need b e defined. T h e third quantity follows

automatically from Equation 2 - 4 .

2.2 FREQUENCY CONTEN T

2.2.1 Response Spectra

Structural analysts a re most familiar with t h e frequency content

of ground motion records being defined b y their low-damped elastic

response spectra. Elastic response spectra f o r a l l 1 2 records a r e

presented in Figures B - 2 o f Appendix B . I t i s most informative t o group

these records into t h e following three groups in accordance with their

effective duration:

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1. Long Duration: T Q > 9 sec.

2 . Intermediate Duration: 2.5 sec- < T Q 9 sec.

3. Short Duration: T Q < 2.5 sec.

This study considers four records in each grou p. The 7% damped elastic

response spectra normalized to Ig ground acceleration are plotted in

Figure 2-5 for each of the four records in each of the three groups and

compared to the Regulatory Guide 1.60 response spectrum.

Table 2-4 lists the 7% damped spectral accelerations at 2.14,

3.20, 5.34, and 8.54 Hz for each of the recor ds. In addition. Table 2-5

lists the v/a ratio s, the maximum 7% damped spectral acceleration

amplific ation fac tor (SA^^/a) and the freq uen cy (f^) at which th isamplification occ urs , the maximum 7% damped ve locity amplification factor

(SV /v ) and the frequ ency (f ) at which it ocu rs, and the corner

freq uenc y* (f,„) between the amplified acceleration and amplifieda V

velocity regio ns. This corner frequen cy was defined by:

^av = 2 ^ - (2-6)

m

The relationship between the corner freque ncy and the frequencies at which

the spectral acceleration and spectral velocity peak is shown schemati

cally in Figure 2-6. For short duration records such as Melendy Ranch,

the spectral acceleration and spectral velocity peak at the same

freque ncy. In this cas e, the corner frequ ency is equal to the frequency

at which both spectral responses pea k. For the longer duration recor ds,

the frequ ency, fg, at which the spectral acceleration peaks is generally

a factor of 2 or more gre ater than the frequ ency f^ at which the spectralvelocity peaks. In these ca ses, the corner frequenc y is not as

distinctly locate d. The corner frequency estimated by Equation 2-6 lies

about midway between f^ and f^.

* As used herein, the term "corner frequen cy" refers to the

interact ion of the amplified spectral acceleration and amplifiedspectral vel ocity regi ons. This definition is not the same as thatused by seismologists.

2-7

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Equa tion 2- 3. Such spe ctra are presen ted in Figure B-4 throu gh B-5 of

Appendix B fo r the 12 t ime h is to r ie s stu die d. The sin gle -sid ed Power

Spec tra l Dens ity fu nc t io n , G ' ( f ) , i s re la ted to the Four ie r ampl i tude,

F' ( f ) , by:

G ' ( f ) = ^ ,2 -7)I Q V /

where t h e primes are used to indicate that these functions are only

evaluated within t h e time window defined by Equation 2-3. T h e Cumulative

Spectral Density function (Cum G ( f ) ) is obtained b y integrating G'(f)

from zero t o t h e frequency f .

The differing frequency characteristics o f t h e short duration

records versus t h e long duration records is clearly indicated b y t h e

Fourier spectra in Figure B - 4 o r th e Cumulative Spectral Density plots of

Figure B-5. Table 2- 6 lists t h e fre quen cie s, fj^Q, f^Q, and fgQ, at which

1 0 , 5 0 , a nd 9 0 % , r e s p e c t i ve l y , o f t h e cumulative power occurs f o r t h e 1 2

records studied. T h e range from f , Q t o f g Q represent t h e frequency range

within which 80% o f t h e power is located. T h e frequency f g Q represents

the median frequency.

The five records with durations T Q from 9.6 seconds t o 3 . 4

seconds (El Centro # 1 2 through El Centro #5) all have median frequencies

between 2 . 1 5 a n d 3 . 3 H z a n d contain significant power between at least

0.8 and 6.55 H z . T h e t w o longest duration records (Olympia and T a f t )

have similar median frequencies but do have slightly lesser frequency

bandwi dths. Even so, these records cover frequency bands from at least

1.2 t o 5 .5 H z .

As shown in Table 2-6, all five o f t h e records with strong

durations T ' o f 3 . 0 seconds and less are missing some o f t h e frequency

content o f t h e longer duration record s. Coyote Lak e, Gavilan College,

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and Melendy Ranch are missing f requency content below the 2.5 to 3.6 Hz

r a n g e . Parkfield is missing frequency content below 1.2 Hz . Both Goleta

and Parkfield are missing high freque ncy content above about 3 Hz.

Because of either missing low or high frequency content, Goleta, Coyote

Lake, Parkfield, and Melendy Ranch have \/ery narrow amplified regions for

their response spectra as demonstrated in the previous section. The

breadth of the frequency bandwidth for Gavilan College is nearly as large

as those for Olympi a and Taft but is much less than for the other longer

duration record s. Furthermor e, the median frequency for this record

differs substan tially from that of the longer records having a much

higher median freque ncy because low frequ ency content is missing fr om

this record.

2.2.3 Moments of the Spectral Densit y FunctionVanmarcke (1972, 1975) has suggested that the moment s of the

spectral density function can be utilized to provide a measure of the

freque ncy content of a given input mo tio n. The terms X Q , XJ and ^2

denote , resp ecti vely , the zero, first, and second moment of the spectral

density function as given by:

/

oo

G'(a3)da) ( 2 - 8 )

700

coG'(a))daj ( 2 - 9 )

X' = 2nd mome nt = J a3^G'(u))dto (2-10)0

It should be noted that {x^/Z-n) serves as an alternate means of

describing the power P listed in Tabl e 2-3. Given the zero, firs t, and

second mome nt s, the central fre quency (mean f r e q u e n c y ) , fi', and

dispersion (coefficient of v a r i a t i o n ) , 6', are given by:

^' s central freque ncy (Hz) = o-^ /^ ^/x ^ (2-11 )

s * = dispersio n parameter = >il- (xp /^2'^Q (2-12)

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Thus the frequency standard deviation, o^, is:

0^=6'^' (2-13)

The mean frequency and frequency standard deviations f o r each o f t h e 1 2

records are also listed in T a b l e 2 - 6 .

The mean frequencies, ^', all exceed t h e m e d i a n f r e q u e n ci es, f g Q ,

as o n e would expect. F o r t h e 7 longer duration records, t h e mean

frequencies l i e between 3 . 6 a n d 4 . 7 H z . T h e lower frequency f ^ g ^"• ^

1.25 t o 1 . 4 5 standard deviations below t h e mean while f g g lies from 0 . 9 5

to 1 . 2 0 standard deviations above t h e m e a n . T h u s , f o r records with

durations T p greater than about 3 s e c o n d s , t h e records c a n b e described

as having 80% o f their power within a range from -1.35 t o +1.05 standard

deviations from t h e m e a n . In t h e s e c a s e s , fi' nd a | serve as good

descriptors o f t h e frequency conten t. However, it should also b e noted

that one m a y n ot need to describe t h e specific frequency content of t hese

r e c o r d s . A l l o f these records c a n b e reasonably f i t i n t h e 1 . 8 t o 1 0 H z

range b y a single design spectrum such a s Reg. Guide 1 . 6 0 anchored t o a

design acceleration . Thu s, their frequency content i s n o t sufficiently

different from each other to require a record specific description o f t h e

f r e q u e n c y c o n t e n t .

For t h e 5 short duration records (TA < 3 . 0 s e c o n d s ) , t h e mean

f r e q u e n c y , a' , tends t o serve a s a reasonable description o f t h e central

f r e q u e n c y . H o w e v e r , t h e dispersion statistic (either a | o r 5') appears

to overpredict t h e breadth of f r e q u e nc i e s f r om f J Q t o f g g i n some cases.

For instance, f , Q lies at o n l y - 1. 0 6 , - 1 . 1 , and -0.92 standard deviations

below t h e mean frequency f o r G o l e t a , C o yo te L a k e , and Parkfield, respec

tive ly, rather than at the -1.25 t o -1.45 standard deviation range

applicable f o r t h e longer reco rds. Similarly, f g g lies at only 0.49,

0.85 a n d 0 . 3 3 standard deviations above t h e mean frequency f o r Go let a,

Coyote Lake and Parkfield, respectively, rather than at t h e 0 . 9 5 t o 1 . 2 0

standard deviation range applicable f o r t h e l on g er r e c or ds . T h u s , o n e

must be cautious in using this dispersion statistic f o r t h e short

duration records with T Q o f 3 seconds or less.

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2.2.4 Frequ ency Content Summary and Conclus ions

The seven long duration spectra can be reasonab ly approximated

at about an 84th percent no n-exce edance probability by a Reg. Guide 1.60

spectrum or some other "smooth-design" spectrum without introducing undue

conser vatism . Th us , the concept of a smooth design spectrum is compatible

with these rec ord s. The problems with a "smooth -design " spectrum become

serious with the four short duration (Tp < 2.5 secon ds) reco rds. These

four records apparently do not have sufficient duration to develop broad

freque ncy content. Each record shows high spectral amplification only

within a narrow frequency ran ge. They cannot be fit over any broad

freque ncy range by any Reg. Guide 1.60 spectrum anchored to any design

ground accel erat ion. In fac t, the ensemble of these four records cannot

be fit by any "smooth-d esign" spec trum. If the four spectra were

avera ged, a smooth broad spectrum would result . However, this resulting

smooth spectrum would be unrepresentative of any one of the four

individual spectra which contain only narrow frequency content. Each

spectrum shows high amplification in a different frequenc y range so that

averaging the four would lead to a broad frequency content and the loss

of the frequency characteristics of the individual records.

It will be shown that breadth of the amplified r espon se regionof the elastic respons e spectra has a majo r influence on both linear and

nonlinear response of stru cture s. A narrow frequency spectrum will only

strongly excite one or two modes of a structure while a broad freque ncy

design spectrum excites many mo de s. Use of a broad frequency design

spectrum is likely to overpredict elastic response because of this

combination of modes . As a structure goes nonlinear, its "effective"

frequ ency is lowered. With a broad respo nse spectrum, this shifting of

frequen cy has only a small effect on the nonlinear respon se. On the

other hand, with a narrow response spect rum, this shifting of frequency

often has a major effect in reducin g the nonlinear resp onse . Artificial

broadenin g of the frequ ency content will lead to an overpre diction of the

damage capabil ity of this record . The most significant single conclusion

of the entire study is that any engineeri ng characterizatio n of these

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short duration records must retain the record's narrow frequency content.

Hope ful ly, this conc lusion will not be lost because of the maz e of data

presented herein.

The most apparent solution to the above dilemma for records with

strong durati ons, Tn, less than about 3 seconds is to define a narrow-

frequ ency c ontent design spectrum and then to vary the frequ ency at which

this spectrum peaks over the range of frequenc y uncertainty for the site.

An engineering characteriza tion of the frequency content of the

records can be provided by the frequency range from f,Q to fgQ over which

8 0 % of the power is distributed and by a mean freq uency ^'. All seven of

the records with durations Tp greater than 3.0 seconds contained

freq uenc y content between at least 1.2 to 5.5 Hz . The elasti c respon se

spectra for all of these records can be reasonably fit by a single design

spectrum within the 1.8 to 10 Hz ran ge. Thu s, for these rec ords , it

appears to be unnecessary to specify the frequency content except in

terms of a standard design spectrum.

On the other hand , all short duration rec ord s, with Tp less than

about 3.0 seconds included in this study are missi ng fre quen cy conten t in

eith er the high or low range of freq uenc ies between 1.2 and 5.5 Hz. All

of these records either do not contain power below 2.5 Hz or above 3.1 Hz.

A single broadbanded design spectr um cannot be used even within the 1.8 to

10 Hz range to adequately approximate these records which miss frequency

content either below 2.5 Hz or above 3.1 Hz . These records with duration s

less than about 3 seconds should be represented by narrow frequency con

tent design spectra based upon ground motion record with similar frequency

content as defined by the frequency range from f^g to fgg. Thu s, CoyoteLake, Gavilan Colle ge, and Melendy Ranch could probably be approximated

in the 1.8 to 10 Hz range by a single nar row frequ ency design spectrum

which does not contain power below about 2.6 Hz . Parkfield and Golet a

could pr obably be approximated in the 2 to 8 Hz range by a different

narrow frequency design spectrum which doesn't contain power above about

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3.0 Hz. For these reco rds , uncertainty in the central f requency should

be accommodated by the use of multiple narrow frequency content design

spectra with differing central frequencies rather than by a single broad

banded spectrum which will result in overcomputing damag e.

2.3 ENGINEERING CHARACTERIZATION NEEDED FOR ELASTIC RESPONSE

In order to define a design spectrum for elastic response of

structures in the 1.8 to 10 Hz freque ncy ran ge, records should be

classified as having either broad or narrow frequency content. A record

classified as having a broad frequ ency content should have at least a

freque ncy range from 1.2 Hz to 5.5 Hz needed to develop 80 % of the

cumulative power of the record. All of the records considered in this

study with effective durat ions, Tp, from Equations 2-2 and 2-3 of greater

than 3.0 seconds meet this require ment. The elastic response spectra

within the 1.8 to 10 Hz frequenc y range for these records can be approxi

mated by a single broad frequency content design spectrum such as Reg.

Guide 1.60 anchored to an "effective" accele ration. The shape of the

design spectrum and the specification of an "effective" acceleration is

sufficient to provide an engineering char acterization of these records

for computing elastic response of structures in the 1.8 to 10 hz

frequency ran ge. The concept of an "effective" acceleration is valid for

elastic response with these recor ds. Such statements cannot be made for

the five records with T Q durations of 3.0 seconds or less. None of these

records can be fit over t he 1.8 to 10 Hz frequ ency range by a broad

freque ncy content design spectrum such as Reg . Guide 1.60. For these

reco rds , the concept of an "effectiv e" anchor acceleration is not very

meaningful until narrow frequency content design spectra are developed

and specified.

To demonstrate these po ints , the 7% damped Reg . Guide 1.60

spectrum anchored at an "eff ecti ve" accelera tion is compared with the 7%

damped spectra for the 11 real earth quake time histo ries over the

frequency range from 1.8 to 10 Hz in Figures 2-7(a) through 2 - 7 ( c ) . The

"effective" acc eleration , A Q ^ , for anchoring the elastic Reg . Guide 1.60

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spectrum was set so that 8 4% of the actual re cords spectral accelerat ions

between 1.8 and 10 Hz would lie below the Reg. Guide spect ra. In other

w o r d s , the Reg. Guide spectra is exceeded at 16% of the frequencies

between 1.8 and 10 Hz . Based upon this definiti on, the "effective"elastic anchor ac celerat ions, Apr* were determined and are shown in Table

2-7 for the 11 real rec ords . Table 2-7 also presents the maximum,

me dia n, and minimum ratios of the actual spectral accelerat ions to Re g.

Guide 1.60 spectral acceleration within the frequency range from 1.8 to

10 Hz . These ratios are defined as (SA^/SA^ g o ) ^ ^ ^ . (SA^/SA^ g Q ) ^ ^ ^ ^ ^ ^ ,

and (SA /SA, ^n) ,• . resp ecti vely . All of these ratios are reported fora 1.60 min '

the Reg. Guide spectru m being anchored at the "eff ectiv e" elastic design

acceleration. Ape*

The six real ground motion records with T Q greater than 3.0

second s (Olympia throug h El Centro #5) are all re asona bly fit by th e Reg.

Guide 1.60 spectrum anchored at Apr. For these 6 reco rds, the maximum

amount by which the actual spectral acceleration exceeds t he Reg. Guide

spectral accelerat ions between l.S and 10 Hz varies from 1.08 to 1.23

with a median -maxim um value of 1.12. The median ratio of actual spectral

acceleration to Reg. Guide spectral acceleration varies from 0.84 to 0.90

with a median-median of 0.88. Thus on the a verage, the Reg. Guide

spectrum introduc es a factor of conserva tism of (1/0.8 8) = 1.14. The

minimum ratio of actual spectral accelerati on to Re g. Guid e spectral

acceleration varies from 0.45 to 0.70. Thu s, for these 6 recor ds,

between 1.8 and 10 Hz the Reg. Guide spectrum anchored to A Q ^ ranges from

1.23 unconservative to (1/0.45) = 2.22 conse rvative with a median factor

of conservatism of 1.14. The Reg. Guide spectrum anchored to A Q ^

represents an adequate characterization of these 6 records for elastic

structural response.

The four short duration records with T Q less than 3.0 seconds

(Coyote Lake through Melendy Ranch) are clearly inadequately represented

by the Reg. Guide s pectrum anchored to A Q ^ . The maximum-maximum factor

of unconservatism is 1.66 while the minimum-minimum factor of conserva

tism is (1/0.08) = 12.5 whi le the media n-med ian factor of conserva tism is

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(1/0. 64) = 1.56. The scatter band is simply too large when those records

are attempted to be fit by the Reg. Guide spectrum even within the 1.8 to

10 Hz frequen cy ra nge . The Reg. Guide spectrum does not serve as an

adequate representation of these records.

The Goleta record ( T Q = 3.0 sec ond s) could be placed in either

group . The fit to the Reg. Guide spectrum is better than for the four

shorter duration records but not as good as for the six longer duration

records. It is judge d tha t the fit is not adeq uate and the Goleta record

is placed with the four shorter duration records.

Development of narrow frequency design spectra would require the

considerat ion of many more records than the five short duration records

used in this study. How eve r, these five records can be utilized to

illustrat e some pro ble ms. If all five of these short duration records

were used to develop a design spectrum, the resulting spectrum would have

a broad frequency content and would represent each individual record

nearly as poorly as does the Reg. Guide 1.60 spectrum. In order to

develop narrow frequency content design sp ectrum, one must separate these

short duration records by their freque ncy conte nt. The freque ncy range

fjQ to fgQ over which 80 % of the cumulati ve power is contained canprobabl y be used for this purp ose. It might be appropria te to segregat e

these records into a high freque ncy group of records in which f J Q exceeds

2.5 Hz (Coyote Lake , Gavilan Col lege , and Melend y Ranch would belong to

this group) and a low frequency group in which fgg is less than 3.5 Hz

(Parkfield and Goleta would belong to this g r o u p ) . A mid-frequency group

of short duration records would probably also be needed to cover those

records which do not fall into either the high or low freque ncy gr oup.

Once narrow frequency design spectra are developed for these records with

T Q less than about 3.0 sec ond s, the resulting design spectrum needs to be

compared to the spectrum of the individual records similar to the

comparisons made in this study for the longer duration records and the

Reg . Guide 1.60 spectrum. It is believed that these narrow frequency

design spectrum will provide an adequate engineering characterization for

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elasti c response of those short duration reco rds when anchored to an

appropriate "effective " accelera tion. Uncertai nties in frequency content

should be covered by requiring the central freq uen cy of these narrow

frequency design spectrum to be varied over the range of uncertaintyrather than by broadening the design spectrum.

It should be noted from the 11 real recor ds in this study that

the characteristics of narrow frequency content appears to be directly

correlat ed to short durati ons T Q of about 3.0 secon ds and less as defined

by Equation 2-2 and 2-3. Furthe rmore , the duration T Q also appears to be

hig hly co rrelated with the local ma gni tud e, M L » i'or records with ground

accelerations of 0.14g and greate r. The five records with T Q of 3.0

seconds and less all have M L of 5.7 and l ess. The six records with T Q

greater than 3.0 seconds all have M L of 6.4 and grea ter. Th us, one might

tentat ively conclude that the Reg. Guide 1.60 spectrum provides an

acceptable engineering characterization for elastic response for records

from earthq uakes with M L of about 6.0 aiid greater and does not provide an

adequate characterization for records with M L less than about 6.0. It

appears likely that records with both ground accele ratio ns of 0.14g and

greater and M L of 6.0 or less can only be characterized by narrow

frequency design spectrum and the standard usage of broad design spectra

anchored at the 84th percent ile will likely lead to substanti al

inaccuracy and generally excessive conservatism in these cas es. Note

that the SSE ground motion for nuclear power plants east of the Rocky

Mountains generally correspon ds to records with ground accelerations of

0.14g or greater and M L of 6.0 or less and thus fal ls into this cate gory .

For reco rds with broad frequ ency con tent (at least 1.2 to

5.5 H z ) , it was shown that the Reg. Guide 1.60 spectrum anchored to A Q ^provides an adequate characterization for elastic response . The next

step is to define A Q E in terms of characteristics of the ground mot ion .

Several likely candidates exist for defining A Q E * These are corrected

peak ground accel eratio n, a, rms accele ration, a ^ms . and spectrum

intensity, SI.

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The rms acc ele ratio n over the du ratio n TQ is repo rted in Table

2-3. A median estimate o f the design acce lera tion fo r e la st ic response

is then pro vided by Equ ation 1-6 and 1-7 where the du ra tio n TQ is

subs t i tu ted fo r J^ and the predominant p e ri o d , T , i s given by:

T^ = l / f j ' (2-1 4)

in which f2' represents the central frequency from Equation 2-11 and is

l i s te d in Table 2-6 . The re su lt is an e ff ec ti ve e la s ti c rms based anchor

acce lera t ion AQ^J given by:

AQ^T = (yz SLr){2.8J^n')) Vms (2-15)

Housner (1952) has suggested that spectrum intensity could serve

as a measure o f t h e ground motion severity. Within t he frequency domain,

spectrum intensity is defined b y :

. S „ ( 6 , f )

SKB.f^-f^)= I - ^ df (2-16)

w h e r e S ^ represents the spectral velocity, e represents the appropriate

damping, f represents frequency, a nd f , t o f ^ represents t h e frequency

range o f interest. For elastic response of nuclear power plant

s t r u c t u r e s , an elastic spectrum intensity SI will be defined b y t h e 7 %

damped spectrum between 1 . 8 a n d 1 0 . 0 H z . T h u s :

SIg = S I (0.07, 1 . 8 - 10.0) (2-17)

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With this definition, an effective elastic SI based anchor acceleration

A Q C O for anchoring the Reg. Guide 1.60 spectra can be defined as:

'DE2 18(2-18)

w h e r e A Q £ 2 is in fraction of g ra v it y un i t s, Slg is obtained from

integrating spectral velocities in inch-per-second units over a fre qu ency

range in Hz u n i t s . The factor in the denominator of Equation 2-18 has

been empirically determined by this study to achieve a mean A Q £ / A Q £ 2

ratio near unity.

T a b l e 2-7 p r e s e n t s , for each of the 11 records studied, the

corrected ground acceleration, a, the rms based acceleration, A Q ^ J , and

SIg based acceleration, A Q £ 2 for comparison with AQE obtained from

fitting the Reg. Guide Spectrum to actual ground motion spectra from 1.8

to 10 H z . All three definitions for "effective" elastic design

a c c el e r a ti o n a g r ee c l o s e l y w i th A Q £ f o r the six records (Olympia through

El Centro # 5) which can be represented by the Reg. Guide spectrum. For

these six r e c o r d s :

Ratio

AQE/a

'^DE/'^DEI

DE''' DE2

Max.

1.10

1.17

1.17

Mean

0.87

1.06

0.99

Min.

0.73

0.96

0.85

c o v 1

0.15

0.08

0.12

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All mean ratios are close to unity and have low coefficients of

va ria tio n (COV). The use of corre cted ground ac ce le ra tio n, a, introduc es

a mean fa ct or of con servatism of (1/0 .87 ) = 1.15 and has the la rg es t

COV. Intr od uc tion of added conse rvatism in defin ing AQ^ is undesirable

since the use of the Reg. Guide 1.60 already generally introduces conser

vatism in th e 1.8 t o 10 Hz freque ncy range when compared w ith s pe ct ra from

the actual reco rds . The rms based "ef fec t ive " a cc ele rat ion , AQ^J, i n t r o

duces a mean fa c to r of u nco nse rva tism of 1.06 and has th e lowes t COV.

This mean unconservatism is negligible when one considers the conserva

tism introd uce d by the use of the Reg. Guide 1.60 spe ctrum . The SIg

based "ef fec t ive" a cce lera t ion , ADE2» tends to overemphasize the

impo rtance of the lower fre qu en cie s (near 1.8 Hz) wh ile underemp hasizing

the importance of the highe r frequ enc ies (near 10 Hz). For th is rea so n,i t has a s li g h tl y hig her COV than does A Q E I .

It is concluded th at an rms based effec tive ac ce le ra tio n, AQ^J,

defined by Equation 2-15 provides a good definition of the anchor

acceleration for the Reg. Guide 1.60 spectrum for the six longer duration

re a l r ec or ds s tu d ie d . When the Reg. Guide 1.60 spectrum i s anchored to

A Q £ J , with in t he 1.8 to 10 Hz frequency range of i n t e r e s t , th e maximum

r a t i o of (SA^/SAj gg) rang es from 1.29 to 1.05 with a median-maximum

ra ti o of 1.20 for the six records stud ied. Si m ilar ly , the median ra t i o

ran ge s from 1.05 to 0.8 3 w ith a median-median of 0 .88 wh ile th e minimum

r a t i o ra ng es from 0.76 to 0 .49 with a median-minimum of 0 .5 9. This

performance is just as good as that obtained from the empirically

determined AQ^.

For broad frequency content records (frequency content from 1.2

to 5.5 Hz) associated with duration TQ greater than 3.0 seconds, the

elast ic response character ist ics of the ground motion for structures with

freq uen cies from 1.8 to 10 Hz can be adequate ly c ha rac ter ize d by th e Reg.

Guide 1.60 spe ct ra anchored to an rms based "e ffe ct iv e" ac ce le ra tio n

defined by Equation 2-1 5. For th e si x reco rd s st u d ie d , the maximum

factor of unconservatism introduced was only 1.29, the median factor of

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conservatism was (1/0.88) = 1.14 and the largest factor of conservatism

was (1/ 0.49) = 2.04. These uncertainties are certainl y tolera ble

considering the simplicity of this engineering characterization of the

ground motion.

2.4 ENGINEE RING CHARACTERIZATIO N OF GROUND MOTION SUMMARY

Eleven real earthquake ground motion time histories and one

artificial earthquake time history have been cons idere d. Charact eristic s

of these ground motion records have been evaluated including energy, power

and duration as well as frequency content by mean s of frequency breadth

and a central freq uenc y. Section 2.1 recommends that the strong motio n

durat ion, T Q , for stiff structures be computed from Equations 2-2 and 2-3

using cumulative energ y plots (Figure 2 - 3 ) . It is shown that this dura

tion corres ponds to the time of steepest slope (i.e., greatest power and

greatest rms acce ler atio n) from these energy plo ts. It is also shown

that T Q corr elate s well with the longest tim e to reach maximum structural

response (both for elastic and inelastic re spo nse ) for stiff structures

(1.8 to 10 Hz ) . The breadth of the range of freque ncy content can be

defined by the freq uenc y range from fjg to fgg wher e 1 0% of the cumul ative

power lies at freque ncies below fjg and 90 % of the cumulative power lies

at frequencies below fgg. Thu s, the frequency range from fjQ to fgg

contains the central 80 % of the cumulative power of the strong motion

portion ( T Q duratio n) of the record. Central frequency, fi' is defined in

accordance with Equation 2-11 in terms of moments of the spectral density

function.

The 11 real e arthqua ke ground motion s can be divided into two

groups (Group 1: Taft, Olympia, El Centro #12 , El Centro #5, Pacoima Dam

and Hollywood Storage; Group 2: Coyote Lake, Parkfield Cholame #2,

Gavilan College , Goleta and Melendy Ranc h) as foll ows:

1. Strong duration, T Q . All the Group 1 records have strongdurations of 3.4 seconds and greater while all the Group 2records have durations of 3.0 seconds and less.

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2. Local magnit ude. M L . All the Group 1 records are from

earthq uakes with local magnitu des of 6.4 and greater while

all the Group 2 records are from- earthquakes with local

magnitudes of 5.7 and less.

3. Frequency breadth. All the Group 1 records have motionsrich in frequency content (fjQ to fgg) from at least 1.2 to5.5 H z. Each of the Group 2 records has narrower freque ncycontent than the above range (i.e., f^Q to fgg does notcover the range from 1.2 to 5.5 H z ) .

An adequate engineering characterization for elastic structural

response for stiff str uctures (1.8 to 10 Hz ) subjected to any of the 6

longer duration (Group 1) records is provided by the Re g. Guide 1.60

spectrum anchored to an "effect ive" peak accelera tion. It is shown in

Section 2.3 that this "effective" peak accel eration, A Q ^ ^ , can be definedas an rms based acceleration given by Equation 2-15. This conclusion is

not applicable to the 5 shorter duration (Group 2) rec ord s. Elastic

response from any of the five Group 2 records cannot be adequately approx

imated by the Reg . Guide 1.60 spectrum or by any other broad frequency

content spectrum . The most adequate way to characterize these records is

by a narrow-banded design spectrum obtained by averaging records with

similar central frequ encie s, Q \ and frequency bands, f^g to fgg. Uncer

tainties in central freq uenc y, n', should be covered by shifting the

central frequ ency of a narrow-banded design spectrum throughout the range

of uncert ainty and not by the use of a broad frequency content design

spectrum for stiff structures subjected to Group 2 type records.

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T A B L E 2-1

C H A R A C T E R I S T I C S O F T H E S E L E C T E D A C C E L E RO G R A M S

ro

EARTHQUAKE

21 July

13 April

15 Oct.

15 Oct.

09 Feb.

09 Feb.

06 Aug.

27 June

28 Nov.

13 Aug.

04 Sept.

1952

1949

1979

1979

1971

1971

1979

1966

1974

1978

1972

Kern County, CA

Olympia, WA

Imperial Valley, CA

Imperial Valley, CA

San Fernando, CA

San Fernando, CA

Coyote Lake , CA

Parkfield, CA

H o i lister, CA

Santa Barbara, CA

Bear Valley, CA

MAGNITUDE

\

7.2

7.0

6.6

6.6

6.4

6.4

5.7

5.6

5.2

5.1

4.7

^S

7.7

7.0

6.9

6.9

6.6

6.6

5.6

6.4

4.5

5.6

4.3

RECORDING STATIONAND COMPONENT

Taft Lincoln School (S69E)

Highway Test Lab (N86E)

El Centro Array No.12(140)

El Centro Array No.5 (140)

Pacoima Dam (S14W)

Hollywood Stg.P.E.Lot(N90E)

Gilroy Array No.2 (050)

Cholame-Shandon No.2 (N65E)!

Gavilan College (S67W)

UCSB Goleta (180) !

Melendy Ranch (N29W)

SYMBOLS

T

0

EC12

EC5

PD

HS

CL

PA2

6C

G

MR

FAULTDISTANCE

(km)

40

29

18

1

3

21

7

< 1

13

4

6

a

(g)

0.180

0.281

0.142

0.530

1.170

0.211

0.191

0.490

0.138

0.347

0.520

V

(in/sec)

7.0

6.7

6.9

17.3

44.6

8.3

4.0

10.4

1.6

15.7

5.4

8/22/2019 6848574


TABLE 2-2

COMPARISON OF UPPER BOUNDS ON PEAK ELASTIC AND INELASTIC DEFORMATION

RESPONSE TIME WITH HUSID RATIO TIMES

E a r t h q u a k e R e c o r d

( C o m p o n e n t )

1

2

3

4

5

6

7

8

9

10

11

12

O l y m p i a , W A . , 1949

( N 8 6 E )T a f t , K e r n C o . , 19 5 2

( S 6 9 E )

El Centro Array N o . 12

I m p e r i a l V a l l e y , 197 9, (140)

A r t i f i c i a l

(R.G. 1.60)

P a c o i m a D a m

S a n F e r n a n d o , 1971 ( S1 4 W )

H o l l y w o o d S t o r a g e P E L o t ,

S a n F e r n a n d o , 1971 ( N 9 0 E )

El C e n t r o A r r a y N o . 5I m p e r i a l V a l l e y , 197 9, (140)

U C S B G o l e t aS a n t a B a r b a r a , 197 8 (180)

G i l r o y A r r a y N o . , 2 , C o y o t e L a k e

1979, ( 0 5 0 )

C h o l a m e A r r a y N o . 2 , P a r k f i e l d

1966 (N65E)

G a v i l a n C o l l e g e

H o l l i s t e r , 1974 ( S 6 7 W )

M e l e n d y R a n c h B a r n , B e a r V a l l e y

1 9 72 ( N 2 9 W )

^ 0 . 9 5

( s e c )

21.7

31.8

2 5 . 0

15.0

10.0

13.5

12.7

13.6

10.0

12.4

3.4

4.1

^ 0 . 8 5

( s e c )

19.8

18.3

18.3

13.2

8.5

8.9

8.7

8.7

6.9

5.3

3.0

2.6

"•^0.75

( s e c )

19.2

14.0

16.0

11.4

8.2

7.2

7.9

6.9

4.7

4.6

2.9

2.3

^ 0 . 0 5

( s e c )

4.4

3.7

6.4

2.0

2.6

1.8

4.5

3.9

2.5

3.2

1.8

1.5

( s e c )

2 0 . 0

6.7

11.0

10.3

8.7

3.4

5.7

4.9

3.1

4.0

2.3

1.9

E l a s t i c

( y =1 . 0 )

19.9

9.9

12.0

11.5

8.6

5.1

8.2

5.1

4.5

4.5

3.0

2.3

N o n l i n e a r

^ y =1 . 9 & 4 . 3 )

T m a x ( ^ ^ ^ )

19.9

9.2

16.6

10.6

8.6

7.6

8.3

5.1

3.5

4.8

2.9

2.1

T = Upp e r bou n d on tim e of ma x i m u m res p o n s e thr o u g h o u t fre q u e n cy ran g e , f = 2.1-8.5 H z , at 7 % dam p i n g

^ ^^ and for the following du ctilit ies: Elastic (y = 1.0) and Nonlinear (y = 1.9 and 4.3)

8/22/2019 6848574


TABLE 2-3

COMPARISON OF DURATION MEASU RES. PEAK GROUND ACCELERATION. PEAK GROUND VELOCITY.

ENERGY. AVERAGE POWER A N D R M S ACCELERATION OF SELECTED INPUT ACCELERATIONS

roIroat

1 Earthquake Record(Component)

1

1 2

3

4

5

6

7

8

9

10

11

12

Olympia. WA.. 1949(N86E)

Taft, Kern Co., 1952(S69E)

El Centro Array No. 12Imper ia l Val ley, 1979, (140)

A r t i f i c i a l(R.G. 1.60)

Pacoima DamSan Fernando, 1971 (S14W)

Hollywood Storage PE Lot,San Fernando. 1971 (N90E)

El Centro Array No. 5Imper ia l Val ley, 1979. (140)

UCSB GoletaSanta Barbara. 1978 (180)

Gilroy Array No. 2, Coyote Lake,

1979. (050)Cholame Array No. 2, P ar kf ie ld1966 (N65E)

Gavi lan CollegeH o l l is te r . 1974 (S67W)

Melendy Ranch Barn, Bear Valley1972 (N29W)

TD

(sec)

15.6

10.3

9.6

9 .4

6 .1

5.4

3.4

3. 0

2.2

1 .4

1 .1

0.8

TD

(sec)

17.3

28.1

18.6

13 .0

7.4

1 1 . 7

8 .2

9.7

7.5

9.2

1 .6

2.6

a(g )

0.281

0.180

0.142

0.200

1.170

0.211

0.530

0.347

0.191

0.490

0.138

0.520

AE

( i n / s e c ) K f t V s e c ' ' )

6 .7

7.0

6.9

1 1 . 3

44.6

8 .3

17 .3

15.7

4 .0

10 .4

1 .6

5.4

64.2

27.4

18.6

44.2

466.8

30.0

78.1

57.3

13 .3

86.1

2 .1

29.8

P

( g ^ x i o - 2 )

3.97

2.57

1.88

4.54

74.0

5.37

22.2

18.5

5.86

59.4

1.80

36.0

RM S Ace. 1

Vms(9)

. 0 6 3 1

. 0 5 1 1

. 0 4 3 1

. 0 6 7 1

. 2 7 2 1

. 0 7 3 1

. 1 4 9 1

.136

.077

.244

. 0 4 2 1

.190

T Q = Strong Duration (from Equation 2-3 )

AE = Fourier Input Energy E (T^)-E(T o5),E (T) = / " a ^d t

P = Average Fourier Input Power = A E / T A

T Q = Trifunac-Brady Duration = 5 - 9 5 % Range f o r / a d

8/22/2019 6848574


TABLE 2-4

ELASTIC 7 PERCENT DAMPED SPECTRAL ACCELERATION

Earthquake Record

(Component)

1

2

3

4

5

6

7

8

9

10

11

12

Olympia, WA., 1949

(N86E)Taft, Kern Co., 1952

(S69E)

El Centro Array No. 12

Imperial Valley, 1979, (140)

Artificial(R.G. 1.60)

Pacoima 0am

San Fernando, 1971 (S14W)

Hollywood Storage PE Lot,

San Fernando, 1971 (N90E)



UCSB GoletaSanta Barbara, 1978 (180)

Gilroy Array No., 2, Coyote Lake1979. (050)

Cholame Array No. 2, Parkfield1966 (N65E)

Gavilan CollegeHollister, 1974 (S67W)

Melendy Ranch Barn , Bear Valley1972 (N29W)

SA(g)

2.14 Hz

0.487

0.395

0.218

0,430

1.623

0.263

0.741

0.641

0.203

1.404

0.088

0.158

3.20 Hz

0.595

0.375

0.270

0.549

1.614

0.431

0.880

0.642

0.443

0.813

0.118

0.435

5.34 Hz

0.443

0.323

0.327

0.477

1.673

0.626

1.136

0.585

0.656

0.533

0.204

1.491

8.54 Hz

0.440

0.214

0.248

0.454

1.589

0.512

1.106

0.490

0.390

0.557

0.241

0.951

8/22/2019 6848574


T A B L E 2-5

COMPARISON O F RESPONSE SPECTRA PARAMETERS

Earthquake Record

(Component)

1

2

3

4

5

6

7

8

9

10

11

12

Olympia, WA., 1949(N86E)

Taft, Kern Co., 1952

( S 6 9 E )

El Centro Array No. 12Imperial Valley, 1979, (140)


Pacoima DamSan Fernando, 1971 (S14W)

Hollywood Storage PE Lot,San Fernando, 1971 (N90E)


UCSB GoletaSanta Barbara, 1978 (180)

Gilroy Array No. , 2, Coyote Lake1979. (050)

Cholame Array No. 2 , Parkfield

1966 (N65E)


Melendy Ranch Bar n, Bear Valley1972 (N29W)

^/ a

in/sec/g

24.0

38.7

48.5

(56.5)

38.1

39.4

32.7

45.4

21.0

21.3

11.4

10.4

m

a

2.24

2.58

2.42

2.83

2.13

3.06

2.16

2.44

3.45

2.96

2.79

3.03

f, (Hz)

3.12

2.30

5.00

2.50

2.60

5.50

5.88

1.33

5.26

2.30

10.5

5.50

m

v

2.52

1.97

2.29

1.91

1.74

2.78

2.29

2.57

2.18

5.34

1.83

3.19

fv (^ )

1.61

1.18

0.45

0.45

0.83

0.25

0.36

1.20

3.30

1.52

2.60

5.50

fav (" '

2.3

2.1

1.3

1.6

2.0

1.7

1.8

1.3

4.6

1.6

8.3

5.5

S A ^ = M a x . Spectral Acceleration

"' 7% Damping

SV = M a x . Spectral Velocity, 7 % Damping

•

8/22/2019 6848574


TABLE 2-6

COMPARISON O F FREQUENCY DOMAIN PARAMETERS

1

2

3

4

5

6

7

8

9

10

11

12

Earthquake Record(Component)


T a f t , K e r n C o . , 1 9 5 2(S69E)



Pacoima Dam




UCSB Goleta

S a n ta B a r b a r a , 1 9 7 8 ( 1 8 0 )Gilroy Array No. , 2, Coyote Lake1979, (050)



Melendy Ranch Barn, Bear Valley1972 (N29W)

Frequency Range (Hz)

fio

1.20

1.10

0.55

0.60

0.75

0.75

0.80

0.80

2.70

1.20

2.55

3.55

^50

3.05

2.70

3.05

2.15

2.60

3.30

2.75

1.40

4.70

1.80

6.35

5.60

^90

6.10

5.50

7.50

6.55

6.70

7.90

6.75

3.05

6.90

2.75

11.35

8.20

Mean Freq.

n' (Hz)

3.90

3.61

4.52

3.91

4.19

4.68

4.12

2.34

5.12

2.34

7.67

6.11

Std. Dev.

a f (Hz)

1.99

1.89

2.80

2.58

2.56

2.71

2.51

1.45

2.10

1.24

3.30

2.08

8/22/2019 6848574


T A B L E 2-7

'EFFECTIVE" ELASTIC DESIGN ACCELE RATION

1

2

3

4

5

6

7

8

9

10

11

Earthquake Record(Component)


Taft, Kern Co., 1952

(S69E)



Pacoima Dam


Hollywood Storage PE Lot,

San Fernando, 1971 (N90E)



UCSB Goleta

Santa Barbara, 1978 (180)

Gilroy Array No., 2, Coyote Lake1979, (050)



Melendy Ranch Barn , Bear Valley1972 (N29W)

(SA^/SAj_gg)*

Max.

1.12

1.23

1.09

1.08

1.14

1.11

1.33

1.15

1.16

1.66

1.14

Medi an

0.90

0.89

0.86

0.84

0.86

0.90

0.82

0.77

0.48

0.58

0.69

Min.

0.70

0.61

0.61

0.55

0.45

0.60

0.69

0.25

0.37

0.26

0.08

Effective

ElasticAcceleration

A Q , (g)

0.219

0.149

0.128

0.856

0.233

0.471

0.283

0.233

0.562

0.105

0.573

Ground

Accel.

a (g)

0.281

0.180

0.142

1.170

0.211

0.530

0.347

0.191

0.490

0.138

0.520

RMS Based

Accel.

A Q E I (g)

0.202

0.155

0.133

0.795

0.213

0.404

0.332

0.202

0.514

0.106

0.435

Spectral

Intensity

Based Accel.

% 2 (9)

0.253

0.175

0.128

0.879

0.200

0.442

0.324

0.154

0.564

0.060

0.221

* Ratios of Actual to R e g . Guide 1.60 S p e c tr a l Acc e l e r a t i o n s are reported for the

frequency range of 1.8 to 10 Hz.

8/22/2019 6848574


oLP

6 . 0 0 1 2 . 0 0 18.00 2 4 . 0 0 3 0 . 0 0 3 6 . 0 0TIME (SECOND)

oLP

6 . 0 0 1 2 . 0 0 18.00 2 4 . 0 0TIME (SECOND)

3 0 . 0 0 3 6 . 0 0

oLP

O

0 . 0 0 6.00


Imperial Vall ey, 1979(140;

1 2 . 0 0 18.00 2 4 . 0 0TIME (SECOND)

3 0 . 0 0 3 6 . 0 0

FIGURE 2-1. EARTHQUAKE TIME HISTORY RECORDS (NORMALIZED TO 0 . 5 g )

2-31

8/22/2019 6848574


oLP

0 . 0 0 6.00 1 2 . 0 0

r iME

1 8 . 0 0 2 4 . 0 0

(SECOND)

3 0 . 0 0 3 6 . 0 0

aLP

0 . 0 0 6.00

< y \ ^ , v V L I t,, >...ii , t^f I,..

Pacoima Dam

San Fernand o,1971 (S14W)

^^•4\fv •—

1 2 . 0 0 18 .00 2 4 . 0 0

TIME (SECOND)

3 0 . 0 0 3 5 . 0 0

oLP

0 . 0 0 6.00 1 2 . 0 0 18.00 2 4 . 0 0 3 0 . 0 0 3 6 . 0 0

riME (SECOND)


(Continued)%

2-32

8/22/2019 6848574


oIP

Ooo

LLJ

C JC J

cr. oLP

o .0 . 0 0 6 . 0 0

El Cent ro Array No. 5

I m p e r i a l V a l l e y , 1979 (140)

^ / ^ J \ ^ ^ y v r ^ ^ V ^ ' / ' ' V ^ - ^ i > V ' ^ V " " ~ " v '

1 2 . 0 0 18 .00 2 4 . 0 0

TIME (SECOND)

3 0 . 0 0 3 6 . 0 0

oLP

O

CD

oo

LUC JC J

L P

0 . 0 0 6 . 0 0

UCSB GoletaSanta Barbara. 1978 (180)

A . S, yr y * f t ^ y \ ^ . - r t ^ n.^ »fV^

1 2 . 0 0 18 .00 2 4 . 0 0

TIME (SECOND)

3 0 . 0 0 3 6 . 0 0

oLP

0 . 0 0

Gilroy Array N o . 2Coyote Lake. 1979 (050)

6 . 0 0 1 2 . 0 0 18 .00 2 4 . 0 0

TIME (SECOND)

3 0 . 0 0 3 6 . 0 0


(Continued)

2-33

8/22/2019 6848574


oLP

O

oo

CJCJC E O

LP

0 . 0 0 6 . 0 0

Cholame Array No.2

Parkfield. 1966 (N65E)

y/V'^'v'^' -V- ••'' ' ^ -''• ' ' ""•

12.0 0 18.00 24. 00 30. 00 36 .0

TIME (SECOND)

oLP

O

I

0.00

^•WW^NWyw^'V"*'*"

G a v i l a n C o l l e g e

H o l l i s t e r . 1 9 7 4 ( S 6 7 W )

e'. 00 12.0 0 18.0 0 24. 00

T I M E ( S E C O N D )3 0 . 0 0 3 6 . 0

oLP

o

CJ

oo

LJ J

C JC J

c n oLP

o_t

" W n lIW|PlfV^^"'^'^' • ^ " •"

1 • 1

Melendy Ranch Barn

Bear Valley. 1972 (N29W)

1 1 1

0. 00 6.0 0 12.0 0 18. 00 24. 00 30. 00 36. 0

TIME (SECOND)

F I G U R E 2 - 1 . E A R T H Q U A K E T I M E H I S T O R Y R E C O R D S ( N O R M A L I Z E D TO 0 . 5 g )( C o n t i n u e d )

•

2 - 3 4

8/22/2019 6848574


• • • S.O 10 .0 IS.O !•• n.o M.eTIHE (SECSI

M .O 4 0 .0 4 i . a « . *

OL YM PIA . WASHINGTON HIGHWAYTEST L AB. N8 6 E

1 0 - 0 t S . O 2 0 . 0

Tine I SEC)

MELENDY RANCH N29W

FIGURE 2-2 . COMPARISON O F ACCELEROGRAM AND VARIATION O F CUMULATIVE ENERGYWITH TIME F O R REPRESENTATIVE LONG.AND SHORT DURATION MOTIONS

8/22/2019 6848574


FIGURE 2-3. ACCELEROGRAM AND VARIATION OF CUMULATIVE ENERGY WITH TIME

FOR THE 1952 KERN COUNTY EARTHOUAKE RECORDING AT TAFT

•

2-3'6

8/22/2019 6848574


1 0 .0 l e . o ZO.O 28 .0 30 .0

TIME I S E C )

fe = 5 Hz

^ 0 5 ^ '•^^ max75

0 S .b 10.0 IB .O 20.0 21.0 30.0

TItlE (SEC)20.0 29.0

ri ME ISE C)

(a) SDOF Oscillator (7% Damping) Response D u e t o Taft Record

o

e

a

-1

•j":

^

m

•

^.05

\ 7 5

\m MMAhMttfLAfiJi tu^ MJU-

1max

0 I.ll lo'.o is'.oTIHE ( SE C)

f = 2 Hze

•

•

lo' .o n' .o 30 0

,05

T

f»0H,»f »

max

fe = 5 Hz

l.o ' r S ioTo iJTo ioTo 2«'.oT i n E ( S E C )

O.o s.b lo'.o is'.oTIHE ( SE C)

20.0 2S .0

(b) SDOF Oscillator (7% Damping) Response D u e t o Melendy Ranch Record

fIGURE 2-4. ELASTIC RESPONSE O F DAMPED OSCILLATOR D U E T O REPRESENTATIVE LONG A N D SHORT DURATION MOTIONS

8/22/2019 6848574


t » T T 1 I 'I I I I I I '» ' ' f -" f f 1 I I I

T|! j>9 Sec

W

DHMPINC 0.070

EC12

- I 1 y — T — I — I I I I

F R E Q U E N C Y I H E R T Z )

1 3 i 6 7 " * 1 0 '

o.

tx>

^ H)

3 ^Z =^

cror.UJ V

JUJo- J

lU """

- -3 «. J t^

ID un( T

C3Qn »iUJV I

" -

o

'

-

•iff

2 5

-T

Sec

n

^ T ^ ^ 9 Sec

'V>/ ^y/ -^ {

Z ' A ^Jf\ /^_^^\J \l

/ IF / / \ /

li fv ^^Im^ '^ J

" C ECS

I ns^ i i t f

DflMPlNC

' ^ P D

: \ \ \ \ Ti i ' l t f ;

0.070

A .

M «

! M T

f f 1 »J

•j

1

J

JJ

•H

- i

]

^

H

^

1 TJTI

F R E Q U E N C Y I H E R T Z )

- J r~

OO3 "

I I I I I—I I I I

T^< . 2 . 5 Sec

PA2

-T 1 f — 1 — r - - I r — I — I — I I I

DflMPlNC 0.010

s0-^—:—r-rrTTT7Trf—;—mrTTTTtf—J—i <! i \\\\\o-F R E Q U E N C Y I H E R I Z )

FIGURE 2-5. COMPARISON OF NORMALIZED (l.Og) RESPONSESPECTRA SHAPES ASA FUNCTION OF DURATION

2-38

8/22/2019 6848574


«/1

O

o

s-

oo<

< t3

s-+ ->o(UQ.

CO

av 2TrSV.

1 1

Frequency (log f )

(a) Representative Long Duration Input Motion

o

co

(O

s-O)

oo•a:

s-

o

Q .00

Frequency (log f)

(b) Representative Short Duration Input Motion

FIGURE 2-6. GROUND MOTION PARAMETERS

2-39

8/22/2019 6848574


(J j lO_ lIxJ u^

C_)(_) 3-

cr

o1/1C O

cr_,

Q ' " '-D 07UJ CO

to c~

a .lO

in

T 1 1 1 1—I I » - I 1 r — I — I I I T 1 r — 1 — r — I — j — r

DflMPINC 0.070

Olympia WA, 1949(N86E)

~I 1 1—I—I—TT n

n s s 1 Q °\ff—\ 1 [ — I — I — i — T T — r

3 ij 5 6 7 8 9 ' l 0-1 1 1 —I—I—r—r

3 4 s e v e s hO"FREQUENCY (HERTZ)

T [ 1 — ( — I — t — r - 1 ( 1 — I — [ — I — r — r - 1 1 1 1 — I — I — r — r

- ^ ID

o

r ^ "cr

UJ cv_ lU JC_)CJ

cr o

lO

U JI - <"= ) "O

.-I r-OLOca uicr

3"

o

Q

U J

to

D fiM P IN C 0 . 0 7 0

T af t ,K e rn CO, 1952(S69E)

I I — I — I — [ — r"T n • 1 1 1 1 1—TT"! r

3 14 5 6 7 8 9 1 0 2 3 IJ 5 6 7 8 9 1 0

- I 1 1 — I — I I r -

3 II 5 6 7 8 90'FREQUENCY (HERTZ)

(a) Long Duration Records (!!> 9.0 S e c )

FIGURE 2-7a. COMPARISON OF REAL GROUND MOTION SPECTRA WITH REG.GUIDE 1.60SPECTRA ANCHORED T O "EFFECTIVE" ACCELERATI ON, A p ^

2-40

8/22/2019 6848574


n 1 1 1—I—I I I - | 1 1 1 — I — I — n - T 1 1 1—I—I—r

CJ

O

cra :UJ .>;_ lUJC JC J „

U J

U3

ID to

O

t oCO m I-cn

o

aU J

to

O R M P I N C 0 . 0 7 0

El Centro Array N o. 12Imperial Valley, 1979 (140)

"T 1 1 1—I—r—TT n ' 1 1 ' 1 '—'"T-l T

3 y 5 6 7 8 9 ' l O 2 3 y S 6 7 8 9 ' l O

FREQUENCY (HERTZ)

- I ( — I — I — I — r ~ T

3 y 5 6 7 8 9 1 0 'iG-

(a) Long Duration Records (Tp> 9 .0 S e c )(Continued)

FIGURE 2-7a. COMPARISON O F REAL GROUND MOTION SPECTRA WITH REG,SPECTRA ANCHORED T O "EFFECTIVE" ACCELERATION, A ^ ^

GUIDE 1.60

2-41

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3. TECHNICAL APPROACH FOR NONLINEAR STRUCTURAL RESPONSE ANALYSES

Chapter 2 presented the minimum engineering characterization of

the ground motion required for the deter mina tion of elastic structural

respons e. However , as noted in Chapter 1, elastic structural response

does not provide a good measure of structural dam age. Potential quan tita

tive meas ures of structural damage and their relative pros and cons were

presented in Section 1.3. Throu ghout this study, the ratio of peak

displacement to elastic yield displace ment (ductility ratio, y) is used

as a measur e of damage for the reasons given in Section 1.3. Aga in, it

should be noted that this measure of damage may overstate the damage capa

bility of short duration ground moti ons . However, this damage measure is

used because of uncer taint y concer ning other meas ures of damage and

because it serves as a conservative damage m easu re.

The purpose of this chapter is to provide technical background

material for the computation and prediction of inelastic structural

response . Results of inelastic structural response analyses will be

presented in Chapter 4. Ground motion characterizations for inelasticrespons e will be described in Chapt er 5.

3.1 REPRESENTATIVE NONLINEAR STRUCTURAL RESPONSE RESISTANCE FUNCTIONS

Several representative nonlinear structural response resistance

functi ons are shown in Figure 3-1. Thes e are a) Bilin ear, b) Take da, and

c) Shear Wall.

The bilinear model represents the resistance function for intrin

sically duct ile, nondeteriorating systems such as shear members and

unbraced mom ent-resi sting steel frames primarily deforming in flexure with

only moderat e axial loads. In this mo de l, the structure loads with an

initial stiff ness, K, until the yield capaci ty, V is reached. Further

loading occurs along a reduced sti ffn ess , sK. Unloading occurs on the

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initial st iffne ss, K. Cycles are stable without any dependence on the

number of previous nonlinear cycl es. The elasto-plas tic model represents

a subset of this bilinear model in which the second s lope , sK, is zero.

The Takeda model generally represents the appropriate model for

properly reinforced concrete structures pr imarily loaded in flex ure.

Init iall y, the Takeda model loads and unl oads in the same man ner as the

bilinear mo de l. However, nonlinear deformations are accompanied by

concrete cra cking. Upon returning to zero force , the presence of these

cracks softens reloading in either direct ion. Future loading cycles are

always toward the point of maximum previous defo rmatio n. The Takeda model

thus incorporates stiffness degradation due to concrete cr ackin g.

Experimentally determined resistance functions (Figure l-9a) for

low-rise concrete shear walls predominantly deforming in shear exhibit

certain characteristics not incorporated into the previously described

Takeda mode l. These are:

a) Unloading on a softer stiff ness, Ky, than the initialloading stiffness.

b) A substantial pinched behavior upon loading in the oppositedirection until disp lacements return to zero.

c) After zero displacements are reached, further loading istoward a point of greater displac ement than that reached inany prior deformation cycle.

d) Once a certain ductility lev el, ^niax* ^s reache d, futureloading cycles are accompanied by rapid str engthdegradation.

The shear wall model shown in Figure 3-lc in corpora tes Items ( a) through( c ) . Strength degradation should be precluded by limiting the permissible

upper bound ductility, v^^^^ to leve ls less than that at which subst an

tial strength degradation occ urs . Th us , it was judged to be unnecessary

to incorporate strength degradation into this shear wall model.

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Low-rise shear walls predominantly deforming in shear represent

the primary seismic load carrying e lements for most nuclear plant struc

ture s. Th us , the shear wall resistance func tion model is used for most of

the nonlinear analyses in this study. This model was chosen because:

1. It is more representat ive of the major ity of nuclear plants t r u c t u r e s .

2 . Its use is conservative relative to either the bilinear orT a k e d a m o d e l s .

The shear wall model has less hysteretic energy dissipation per cycle

than does either the bilinear or Takeda mo del . Thu s, for a given ground

motion time hist ory, the maximum computed ductility l evel, P, will be

larger from this model tha n from either the Takeda or bilinear mo de l. A

short parame tric analysis is presented In Appendi x D to demonstra te that

this shear wall model does lead to greater ductility levels than does the

T a k ed a m o d e l .

The other primary lateral load carrying systems often found in

nuclear plants are steel-braced fram es. A representative nonlinear

resistance function for such braced frames was shown in Figure l-9b. Thisbraced frame resistance function also shows pinched behavior similar to

that for shear wa ll s. Howe ver, the pinching is not generally as severe

so that a typical braced frame nonlinear re sponse cycle will generally

contain more hysteretic energy dissipation than does a similar shear wall

nonlinear response cycl e. Th us , again , the shear wall model will

generally conservatively overestimate the ductility le vel, y, for a

braced frame subjected to a given ground motion when both model s have the

same yield capac ity and elastic stiffne ss, K. This point is also demon

strated by a short braced frame paramet ric analysis presented in

Appendix D.

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In surmiary, it is judge d that r esult s and c oncl usi ons prese nted

in this study based upon the shear wall model can be conservatively used

for structures exhibiting bilinear, Takeda, shear wal l, or braced-frame

resistance functions.

3.2 DETAILED DESCRIPTION OF SHEAR WALL MODEL

3.2.1 Rules for Constructing Shear Wall Resistan ce Function Model

Reinforced c oncret e wall s resist shear through various

mec hani sms. Initially, the wall is elastic and shear resistance is

developed according to elastic beam theor y. Inclined shear cracks develop

when the principal tensile stresses exceed the concrete tensile strength.

Once shear cracks o pen , the shear force is resisted m ain ly by the reinforcing bars and aggregate inte rlock. Other mecha nisms such as dowel

action, truss action, and the flexural compression zone also contribute

to the shear resi sta nce . The opening and closing of cracks under load

reversals causes the pinching behavior noted in the hysteresis loops.

Also, as shear cracks open wider and damage to the concrete increases,

the contribution of concr ete, through aggregate in terlock , to shear

resistance decrease s. This effect causes,strength degradation under large

displacement cyc les. A shear force-shear distortion diagram obtained

during a structural wall test was shown in Figur e l-9a whic h illustrate s

the reverse cycle loading behavior characterized by stiffness degradation

and pinching of the hysteresis loo ps. Relatively few reversing load tests

of low-rise walls have been reported. Fiorato and Corley (1977) have

summarized the laboratory testing conducted on low-rise walls with

typical reinforcement rati os, in the range of 0.25 - 0.5%, which are more

typical of commerical building construction (Shiga, 1973; Barda, 1976;

Cardenas, 1973; Paulay, 1977; Park, 1975; Alexander, 1 9 7 3 ) . Much of the

structural wall testing (Wang, 1975) conducted at the Univers ity of

Calif ornia , Berkeley, provides useful information on the behavior of low-

rise wall segments which has been recently summarized by Bertero (1977)

and Popov ( 1 9 8 0 ) . Cyclic load testing of low-rise box structures with

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reinforc ement ratios in the range of 0.6 - 1.6% has been limited to model

structures and conducted p rimaril y in Japan (Umemura, 19 77, 1980 : Uchi do,

1980; Fukada, 1 9 8 1 ) .

The primary or envelope loading curve assumed for inelastic shear

elements representing the shear flexibility of low-rise reinforced

concre te walls is defined by a bilinear approximation of the deformation

behavior of low aspect ratio walls under mono tomi call y increasing load.

The consideratio n of a bilinear curve consisting o f two linear segments

is based on the work by Umemura (1977, 1980) interpreted in terms of the

Araka wa formula (Kubota, 1978) for shear strength of reinforced concrete

mem bers . The slope of the first segment represents the effective shear

stiffness of the uncracked concrete wall secti on, whi le the slope of the

second segment rep resents the effecti ve stiffness of the reinforcing steel

after cracking has occurred.

The hystere sis behavior for the shear element is defined by a

set of 10 ru les . These rules are described bel ow, and they are also

shown by their corre sponding numbers in Figure 3-2.

Rule 1: The shear deformat ion curve, defined by a linearstiffnes s, K, is elastic up to the yield shear force,Vy.

Rule 2: Once the yield point in any direction is exceeded,loading continues on the second slope defined by asofter linear stiffness para meter , sK.

Rule 3: Unloading is initiated when the direction of loadingchanges. A degrading unloading stiffness feature isbuilt into the mo de l. This is shown in Figure 3-3a.Therefore, if the system unloads from Rule 2, instead

of unloading parallel to the elastic s tiff ness , K, toa recov ery point such as 6,1, unlo adin g is towards anew recovery point, 6p, such that

\ = (i-cc)6; (3-1)

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wher e a is the unloading stiffness paramet er. Thereduced unloading slope is used for subsequentunloading as long as the maximum deformation is notexceed ed. If the recov ery point, 6p, is reache d,

loading in the opposite dire ction is according toRule 4. Reloading from this part is according toRule 8.

Rule 4: Once the unloading is fini shed, the system wouldinitially exhibit a low stiffness in the opposit edirec tion . This 1s a typical pinching behavior whichis observed in shear wall tes ts. The pinched behavio ris due to opening and closing of cracks under cyclicloads. Loading s tiffness for this point is assumed tobe the same as the second slope of the primary curve,sK. Once zero deformation is reached , loading will beaccording to Rule 7. Unloading from this part is

according to Rule 5.

Rule 5: Unloading from Rule 4 is parallel to the unloading(Rule 3) slope on the same deformation sid e. Oncezero shear force is reached, loading in the oppos itedirection is according to Rule 8. If the direction ofloading chan ges , loading is according to Rule 6.

Rule 6: If the direction of loading changes while in Rule 5,loading will be on the same line until the point whereunloading was initiated is reached (Point A In Figure3 - 2 c ) . Loading is according to Rule 4 there after. On

the other hand, unloading from this part is accordingto Rule 5.

Rule 7: Once the cracks are closed (6 = 0 In Rule 4 ) , loadingbegins toward the previous point of maximumdeformatio n. In addition, a strength degradingfeature is built into the mod el. This is shown inFigure 3-3b. Th us , instead of loading towar ds theprevious point of maximum (Point A in Figur e 3 - 3 b ) , anew target point such as 5 Is defined such that

-Sg = ^~^/y (3-2)

wher e Y Is the strength degradation paramet er. Oncepoint B is reached, loading starts on the second slopeagain (Rule 2 ) . Unloading from this part is accordingto Rule 3.

%

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Rule 8: This rule assures that any loading from Rule 3 will betowar ds the previous intermedi ate point (Points B andC in Figure 3 - 2 c ) . Once tKis point is reach ed, loadingis according to Rule 7 (Point C in Figure 3 - 2 c ) .However, for a point such as B in Figure 3-2c, loadingfrom Rule 8 is on the second slope (Rule 2 ) .

Unloading from this part is according to Rule 9.

Rule 9: Unloading from Rule 8 is parallel to the last minimumunloading slope (Rule 3 ) . Once unloading is finished,loading in the other direction is according to Rule 4.A change of direction in load would cause the systemto follow Rule 10.

Rule 1 0: Loading from Rule 9 is on the same slope until theprevi ous Inter mediate point (Point D in Figure 3-2c)is reached. Loading is according to Rule 8 thereafter .Unload ing from this part is according to Rule 9. Thesmall am plitude or shakedown behavior of the shear

hystere sis model is shown in Figure 3-3c.

The 10 rule hyst eretic model defined above is based on quas i-

static cyclic load tests of shear wall elements representative of nuclear

plant box-type reinforced concrete st ructur es. The model is similar to

the shear models used by Banon (1981) and Saiidi ( 1 9 7 9 ) . Except for shear

pinching and strength degr adat ion, the model is very similar to the mod i

fied Takeda model (Kanaan, 1975) used to represent the hystereti c behavior

of reinforced concrete in flexure . Comparison of the model behavior with

avail able cyclic load test data Ind icates that the model provides good

agreement with test results when large displacement cycles are considered

up to displacements associated with the onset of substantial strength

degradation (typically occurring at ductility levels ranging from 4.3 to

6 . 0 ) . The shakedown behavior (i.e., behavior after peak deformation is

reached as shown in Figure 3-3c) used in this model is unverified because

of insufficient experimental data on cyclic behavior after peak response

is reached. However, proper modeling of this shakedown behavior is

unimportant so long as a peak displacemen t (ductility rat io) crite ria is

used as a measure of damage. The proper modeling of this shakedown

behavior is very Important If a total hys teretic energy absorption

criterion had been used as a meas ure of dama ge. The lack of experiment al

data on shakedown behavior Is one of the prima ry drawbacks to the use of

a total hysteretic energy absorption criteria as a measure of damage.

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3.2.2 Resistan ce Function Properties Used in this Study

The follo wing resista nce functio n par ameters were used in this

study:

a) Slope parameter of post-yield loading curve , s = 0.1

b) Unloading stiffness param eter, a = 0.35

c) Strength degradation param eter, Y = 0.95

The second slope of the loading curve is shallow compared to the initial

stiffn ess, K, for most structural elem ents , with s typically ranging fro m

about 0.03 to 0.15. The value chosen for this study (s = 0.1) is

considered repres entative for shear walls with large reinforcement ratios

(approximately one percent stee l) typical of nuclear plant struct ures.The second slope increases with steel perc entag e and s would be less than

0.1 for steel percentages less than about one percent. A very limited

parame ter study is presented in Appe ndix D to show that the computed

ductili ty level, y, decreases slightly as s is increased above 0.1. The

resul ts presented herein are reas onab le for the case of 0 < s < 0.1 and

become conservative for cases where s » 0.1.

The unloading stiffness and strength degradation pa ramet ers, a

and T, respectively, have been chosen to be realistic (slightly conserva

tiv e) for duc tility levels up to about 4.3 which is the maximum ductility

level considered in this study. The unloading stiffness parame ter, a =

0.35, results in an unloading stif fness , K^^, of approximately two-th irds

of the initial loading (elas tic) stiffness at a duct ility level of 3.0

which is slightly greater unloading sof tening than shown by most e xperi

mental dat a. Howeve r, Appendix D shows results are not sensitive to a.

Simila rly, the strength degradation param eter, y = 0.95, is repr esentative

of the very slight strength degrad ations which occur at duct ilit y levels

less than 4.3. Howeve r, this strength degradation is substantially too

small if the ducti lity level is increased signif icantl y beyond about 4 .3.

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The elastic yield capacity, V ^ , f o r each analysis w a s estab

lished b y :

V = m S ( f . B ) * ( 3 - 3 )y o

where m is the mass of the s tr u c tu ra l elem ent, and S /^ g\ is the

spectral acc elera t ion fo r the given ground mot ion at the e la st ic natura l

freque ncy, f , and the e la s t ic damping r a t i o , 3 , where:

f = f A / T (3-4)27r Y m

represents t h e frequency at t h e initial (elastic) stiffness, K . I n other

w o r d s , all structures were placed a t t h e onset o f yielding when subjected

to t h e ground motions defined in Chapter 2 .

This study was conducted a t t h e following t w o ductility levels:

Low: y|_ = 1. 8 5

High: y ^ = 4 . 2 7

Inelastic response o f shear walls begins a s soon as extensive

concrete cracking occurs. F o r heavily reinforced shear walls (steel

percentages o f about o n e percent ) typical o f those found in nuclear

plants, this inelastic behavior occurs before t h e code specified minimum

ultimate capacity is reached . Based upon o u r review o f a number o f shear

wall designs, a ductility level o f about 1 . 8 5 represents o u r best estimate

of t h e inelastic deformations which would occur in a shear wall designed

for static lateral loads t o t h e ACI-349 code capacity. T h e current

elastic design analysis method when carried t o code ultimate capacities

is judged t o lead t o roughly this level o f inelastic deformation f o r

S (f, B) used here is equivalent t o S A i n Chapter 1 a n d Figure 1 - 1 0

for Application B (determination o f input scale f a c t o r s ) .

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static lateral loads. In other wor ds, ^^^ of 1.85 is judged to corres

pond to code capacity pseudo-elast ic behav ior. This situation is illus

trated in Figure 3-4. This means that the recomm endatio ns and conclusions

of this study for the low ductil ity case ( y = 1.85) are consid ered to be

approp riate for shear wall structur es designed to remain ess entia lly

elastic for the design earthquake.

The high ductility level, y^ = 4.27, represents a conservative

lower bound on the deformations which correspond to significant strength

degradation under a small number (3 to 5) of strong nonlinear respo nse

cycles which might occur during strong ground shaking. In other wor ds,

this d uctility level represents our best judgment of a conservative lower

bound on the onset of significant structural d ama ge.

T h u s , the low (1. 85) and high (4.27) ducti lity l evels considered

in this study are believed to bound the ductility range of interest for

nuclear plant shear wall type structures.

3.2.3 Dynamic Proper ties Used in this Study

This study is concerned with the engineering characterization of

ground motion responses of stiff structures repre sentative of those innuclear plants . Such structures tend to have fundamental elastic

frequenci es in the 1.8 to 10 Hz ran ge, i.e., the amplified acceleration

response rang e. There fore, this study is Intended to cover structures,

with fundamental elastic frequen cies from 1.8 to 10 Ht. Results of this

study can probabl y be extrapola ted to frequ encie s beyond this range but

this was not verified by studying structures with elastic frequencies

outside of this ran ge. Shear wall structural elements with the follow ing

elastic natural frequencies were used in this study:

f = 2.14 Hz; 3.20 Hz; 5.34 Hz; 8.54 Hz

to represent the frequency range from 1.8 to 10 Hz . Elastic stiff nesses,

K, for the shear wall resist ance func tion were then computed from

Equation 3-4.

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Energy dissipation due to the elastic component of response was

modeled by a viscous damping coefficient, c, given by:

c = (i f) K, (3-5)

where 6 represents the fraction of critical damping within the elastic

range of r esp ons e, and K-,. repr esen ts the tangent stiffness at any point

on the resistance functio n. The damping coef ficient, c, was made propo r

tional to the tangent stiffness as opposed to the initial stiffness to

avoid double-counting the hysteretic energy dissipation within the inelas

tic ran ge. Energy dissipation primarily occurs during nonlinear respons e

due to the hysteresis loop of the resis tance funct ion. This energydissipation is already accounted for by the use of resistance functions

with hysteretic loops and would be double-counted to some extent if the

damping coeff icien t, c, were not reduced durin g nonlinear res pons e.

«

Damping is a term which is utilized to account for various mecha

nisms of energy dissipation which occur when a structure is subjected to

dynamic loads . Within the elastic range, damping is normally considered

to be visco us and it is defined as a perc enta ge of critical dam ping . Itis usually difficult to estimate the viscous damping in a structure,

because it depends on many factors such as material type (i.e., reinforced

concrete or steel ) and stress level. Damping values used in structural

analyses are usuall y conservative estimates based upon experimental dat a.

A detailed survey of studies on damping in nuclear facilities has been

recently compiled by Stevenson ( 1 9 8 0 ) . Test results indicate that a

conservative estimate of damping in concrete structures (mainly shear

wal ls) varies from 5 percent for stress values below 0.5 yield to 10

percent for stress values close to yiel d. Regulato ry Guide 1.61 (USNRC,

1973) suggests a 7 percent damping value be used for shear wall type

structures under SSE condi tions . This value has been used in this

study. Thus:

e = 0.07

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A small paramet ric study was performed with a lower elast ic

damping value of B = 0.03 and the results are presented in Append ix D.

This study shows that the results and conclusions of this study on

reduction factors to be applied to elastic spectra to obtain inelastic

spectra are slightly conservative when the elastic damping value used for

the elastic spectra is less than 7 perce nt. Thu s, the results of this

study are usable for elastic spectra with 7 percent and less damping.

This study is not Intended to address the question of what value

of damping should be used when per forming nonlinear analyses of shear

wall struc tures. There are advocates of damping values ranging from

about 3% to 10 % as well as advocates for both initial stiffness and

tangent stiffnes s proportional d amping . More research needs to beperformed on these Issues. Howe ver, the conclusions of this study are

insensitive to these Issues.

3.3 SIMPLIFIED METHODS TO APPROXIMATE NONLINEAR STRUCTURAL RESPONSE

Simplified metho ds to predict nonl inear structural r espon se from

elastic response spectra consist generally of one of the following

a p p r o a c h e s :

1. Replace the nonlinear resistance function by an equivalentlinear resistance function which has a lesser stiffness,K e , and increased damping, 3e. This equivalent linearresistance function is then used with the elastic re sponsespectra to compute maximum displacement res pon se, 6^ = y<s .

2 . Modify the elastic response spectra to create reducedequivalent inelastic response spectra for use with theinitial elastic stiffn ess, K, and elastic range damping, B,to compute the yield displacement r espon se, Sy and Vy.

Each of these general methods is discussed in greater detail in the

following subsections.

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3.3.1 Equivalent Linear Resistance Function Models

An equivalent linear resistance function model is developed t o

replace t h e actual resistance functions (Figure 3 -1 ). This equivalent

model should be capable o f approximating t h e average reduced stiffness

(or frequency) and average increased damping which occur during t h e

nonlinear response cycles which occur prior t o peak response. T h e secant

stiffness represents t h e minimum effective stiffness during nonlinear

response a nd f o r t h e resistance functions shown in Figure 3-1 this

stiffness is given b y :

V ^ ' I ± f ^ (3.6)

The secant freque ncy, f^, is obtained from Equation 3-4 by s u b st itu t in g

Kg fo r K. Thus:

f g/ f = N/K^/K (3-7)

The effective frequency, f ^ , represents the frequency associ

ated with some "average" nonlinear response cycle a n d t h e effective

damping, e^, represents t h e s u m o f elastic, 6, and hysteretic, 3 ^ ,

damping associated with this "average" nonlinear response cycle.

Appendix C provides technical background suggesting that t h e effective

frequencies and damping c a n b e approximated b y :

f ; / f = ( i-A) + A(f^/ f )

3 H = C,(l-f^/f)

3-13

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where A and C^ are empirically determined coefficients selected to

provide a good fit of the peak responses computed by nonlinear time

histor y analy ses. One would expect A to be approximately 0.5 for the case

of N=l (one strong nonlinear response cycle) and to increase toward 1.0 as

N became large with the pinched shear wall resistance funct ion. Further

m o r e , the coefficient A should increase with Increasing ductility, i.e.,

with reducing (fg/f) ratios . The coefficient C ^ is expected to be

less than 0.55 for N=l, less than 0.38 for N=2, and less than 0.32 for N=3

and 4 for the pinched shear wall resistance function (See Appendix C ) .

How eve r, both A and C ^ will be empirica lly dete rmine d.

Previous inv estigators have made attempts to estimate the average

effective frequency and damping for nonlinear structural res ponse . Based

upon a study of Takeda resistance function models for reinforced

concrete struc tures, Sozen (Gulkan and Soz en, 19 74; and Shibata and

Sozen, 1976) has suggested:

(Sozen) f K fe s

3 ' « 3 + 0.2(1-f /f) (3-9)

" s

Note that Equ ation 3-8 would be Identical to Equation 3-9 if A=1.0 and

Cf = 0 .2 0.

Simila rly, based upon a study of bilinear resistance functions

and of resistance functions which approximate those for braced frames

(Figure l - 9 b ) , Iwan (1980) has suggested the effective freq uen cy be given

by:

f

( ^ " ^; = 1 +0 . 1 2 1 ( y - 1 ) 0 - 9 3 9

B ; = 3 + 0.0587(y-1)°-3 7^ (3-10)

3-14

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T h e eq u i v a l e n t l i n ea r r e s p o n s e c o e f f i c i e n t s , A a n d C| ^, w i l l be

d e t e r m i n e d i n C h a p t e r 4 t o p r o v i d e a g o o d f i t o f t h e n o n l i n e a r t i m e

h i s t o r y m a x i m u m r e s p o n s e r e s u l t s . T h e n , E q u a t i o n s 3 - 8 , 3- 9 , a nd 3 - 1 0

w i l l e a c h b e us ed t o p r e d i c t t h e n o n l i n e a r r e s p o n s e f a c t o r , F , w h i c h w i l l

b e c o m p a r e d w i t h t h e a c t u al c o m p u t e d n o n l i n e a r r e s p o n s e f a c t o r f o r al l 12

e a r t h q u a k e t i m e h i s t o r i e s and 4 e l a s t i c f r e q u e n c i e s at y , = 1 . 8 5 a n d

v ^ = 4 . 2 7 i n t h e ne x t c h a p t e r . F i s t h e s c a l e f a c t o r b y w h i c h t h e

g r o u n d m o t i o n m u s t b e i n c r e a s e d o v e r t h a t c o r r e s p o n d i n g t o s t r u c t u r e y i e l d

c a p a c i t y i n or d er t o a c h i e ve a g i v e n l e ve l o f n o n l i n e a r r e s p o n s e , y.

W i t h e a ch o f t h e s e e q u i v a l e n t l i n e ar m o d e l s , t h e m a x i m u m

n o n l i n e a r s t r u c t u r a l r e s p o n s e d i s p l a c e m e n t , <5 is g i v e n b y :

m= '/ \o ( 3 - 1 1 )*" (2TTf')2

whereas, the yield displacement, <5 is given by:

6y= 'f (3-12)

or

S , ( f , 3 )6 = ^ 1 — (3-13)^ (2Trf)2

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T h u s , t h e i n p u t s c a l e f a c t o r , F , is g i v e n b y :

F = y ( f : / f ) ^y 6

S ^ ( f , 3 )( 3 - 1 4 )

i n o r d e r to a c h i e v e a d u c t i l i t y l e v e l y . It i s t h e s e p r e d i c t e d f a c t o r s ,

F , w h i c h w i l l b e c o m p a r e d w i t h 1

f a c t o r s , F , i n t he n e x t c h a p t e r .

F , w h i c h w i l l b e c o m p a r ed w i t h t h e a ct u a l n o n l i n e a r a n a l y s i s c o m p u t e d

3 .3 .2 I n e l a st i c S p e c t r a * D e a m p l i f i c a t i o n F a c t o r s

I n l i e u of c o n s t r u c t i n g a n e q u i v a l e n t e l a s t i c s t r u c t u r e m o d e l t o

a c co u nt f o r i n e l a s t i c r e s p o n s e , o n e c an s i m p l y m o d i f y t h e e l a st i c s p e c t r umt o o b t a i n an I n e l a st i c r e s p o n s e s p e c t r u m f o r u s e w i t h t h e e l a s t i c

s t r u c t u r e m o d e l . T h e I n e l a s t i c s p e c t ra l r e s p o n s e t o u se at t h e e la s t i c

f r e q u e n c y i s o b t a i n e d b y d i v i d i n g t h e e l a s t i c s p e ct r a l r e s p o n s e a t t h a t

f r e q u e n c y b y an i n e l a s t i c d ea m p l i f i c a t i o n f a c t o r , F ^ , i . e . :

S , ( f , 3 ) **

s w f « ^ = - ^ r - ^ ( 3 - 1 5 )

ay(f,3) F^

T h e n t h e r e q u i r e d y i e l d c a p a c i t y , V ^,^ , o f t h e s t r u c t u r e t o a c h i e v e a

g i v e n d u c t i l i t y l e v e l , y , i s o b t a i n e d b y u s i n g t h e i n e l a s t i c s p e ct r a l

a c c e l e r a t i o n , S . i n E q u a t i o n 3 -3 i n l i eu o f t h e e l a s t i c s p e c t r al

a c c e l e r a t i o n , S , .a

* M o d i f i e d s p e c t r a t o r e f l e c t n o n l i n e a r b e h a v i o r

** F o r t h e p u r p o s e of c o m p u t i n g s p e c t r a d e a m p l i f i c a t i o n f a c t o r s ( A p p l i

c at i o n A ) , S , ( f , 3 ) as u s e da

C h a p t e r 1 a nd F i g u r e 1 - 1 0 .

c at i o n A ) , S , ( f , 3 ) as u s ed i n t h i s s e c t i o n c o r r e s p o n d s t o S A o fa

•

3 - 1 6

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•

One method to predict t h e inelastic deamplification factor is

through t h e u s e o f Equation 3-14. If this equation is used, t h e

technique o f using an inelastic response spectrum and an elastic

structure model will produce identical results a s a r e obtained from t h e

use of an equivalent elastic structu re model with t h e elastic response

spectrum so long a s t h e same effective frequency and effective damping

are used in Equation 3 - 1 4 t o determine F .

Alte rnat ely, investigators have developed estimates of F

directly from a combination of theoretical considerations and empirical

studies. T h e inelastic deamplification factor is different i n t h e

amplified spectral acceleration frequency range (generally about 2 t o 8

Hz) than it is in the amplified spectral velocity frequency range

(generally about 0 . 2 5 t o 2 H z ) . N ew m a r k ( 1 9 7 8 ) has suggested that:

Acceleration Region

^ = a = ^^^^ (3-16)

Velocity Region

^ = ^ v = ^ (3-17)

More recently, Riddell and Newmark (1979) have suggested t h e following

improvement on these factors:

• ; = ( ( q - i ) ^ - q ) ' (3-18)

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where :

Acce le ra t ion Reg ion

q = q = 3.06•0.30

r = r = 0.48B-0.08

(3-19)

V e l o c i t y R e g i o n

q = q^ = 2.7B

r = r^ = 0.66B

- 0 . 4 0

- 0 . 0 4 ( 3 - 2 0 )

When using Equation 3 - 1 9 o r 3-20, B is elastic damping in percent of

critical. F o r y = 1. 8 5 a n d 4.27, these t w o approaches yield (B = 7 % ) :

1 ^

1.854.27

Acceleration, F ^ ^

Newmark

1.64

2.75

Riddell

1.632.55

Velocity, F ^ ^

Newmark

1.854.27

Riddell

1.923.65

The Riddell equations will be used herein f o r comparison with t h e time

history computed F, factors.

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A n i n e l a s t i c s p e c t r al r e s p o n s e c o r n e r f r e q u e n c y i s sp e c i f i e d b y :

fsavMr^K.v ( 3 - 2 1 )

w h e r e f ^ ^ r e p r e s e n t s t h e c o r n e r f r e q u e n c y b e t w e e n e l a s t i c s p e c t r a l

v e l o c i t y a nd a c c e l e r at i o n a s l i s t ed i n T a b l e 2 - 5 f o r e a c h of t h e g r o u n d

m o t i o n s c o n s i d e r e d i n t h i s s t u d y . A t f r e q u e n c i e s b e l o w f . , „ . t h e

v e l o c i t y d e am p l i f i c a t i o n f a c t o r , F ^ ^ , i s us ed t o s p e ci f y t h e i n e l as t i c

s p e ct r a l a c c e l e r a t i o n , S g b y E q u a t i o n 3 - 1 5 . A t f r e q u e n c i e s a b o v e f ^ g y

t h e a c c e l er a t i o n d e a m p l i f i c a t i o n f a c t o r , F g , i s u s e d . H o w e v e r , w i t h i n

t h e a m p l i f i c a t i o n a c c e l e r a t i o n r e g i o n , t h e i n e l a s t i c s p e c t r al a c c e l e r a

t i o n i s no t a l l o w e d t o d r o p b e l o w :

A c c e l e r a t i o n R e g i o n

y

a s p e r t h e s u g g e s t i o n o f R i d d e l l a n d N e w m a r k ( 1 9 7 9 ) .

•

3 - 1 9

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a) Bilinear b) Takeda

6 = y6

m ^"y

c) Shear Wall

FIGURE 3-1. REPRESEN TATIVE NONLINEAR RESISTANCE FUNCTIONS

3-20

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1

h

1

I

L

V

/

/

/

/1

w «

"11

1f

I1

COIro

^^ ^ / / / / / / /

I* Hw I

(a) Reinforced ConcreteShear Wall

Structure Mass, M

I

TTTf f "f }

Seismic Excitation

(?) Model Rules

^ 6

(b) Structure Model (c) Shear Deformation Hysteretic Behavior

FIGURE 3-2. SHEAR WALL STRUCTURE MODEL AND CORRESPONDINGHYSTERETIC DEFORMATION BEHAVIOR

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-5^ = (l-a)6V

6 6

r r

a6'

B = V y

(a) Unloading stiffnessparameter a

(b) Strength degradationparameter y

*- 6

(c) Shakedown behavior

FIGURE 3-3. CHARACTERISTICS OF THE HYSTERESIS MODEL ANDIDENTIFICATION OF MODEL PARAMETERS

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ACI-349 Capacity

(wl.09 V )

1.85 (6 )

y

FIGURE 3-4. REPRESENTATIVE RELATIONSHIP BETWEEN ACTUAL NONLINEAR RESISTANCEFUNCTION AND ACI -349 CODE CAPACITY FOR SHEAR WALL WITH ABOUTONE PERCENT REINFORCEMENT STEEL

3-23

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4. NONLINEAR STRUCTURAL RESPONSE ANALYSIS RESULTS AND

COMPARISON TO PREDICTION EQUATIONS

As noted in Chapter 3, the structural model yield capa citi es,

V , were determined from the elastic spectral acceleratio n, Sg (f ,3 ) ,

at the models elastic freq uency, f, and elastic damping B , of 7 percent.

Next, the input ground motion was scaled by an input amplitude scale

facto r, F, and the maximum inelastic response (ductility factor,y ) was

computed by time history nonlinear structural response analys es. Note

that with a scale factor of un ity, the elastic yield response (y = 1.0)

will occur and with F factors greater than unity, inelastic response

( y > 1 . 0 ) will occu r. A sufficient number of analyses were performed

with different F factors to enable the F factors corresponding to y. =

1.85 and y ,^ = 4.27 to be accurat ely determi ned by interpolation for each

ground motion time history and elastic natural freq uency, f, considered .

Thus, F represents an input scale factor by which the ground

motion must be increased over that corresponding to the structure yield

capacit y in order to achieve a given level of nonlinear respon se,y .

Alterna tely, F is also equal to the spectral deamplification factor needed

to convert an elastic spectral ac celerati on to a ducti lity of y. This

inelastic spectral acceleration then defines the yield capac ity, V p,

required in order to limit the ductili ty level to y when the structure is

subjected to the actual unsealed time histor y. Both definition s for F are

equivalent to each other. Thu s, the input scale factors, F, corre s

pondi ng to y|_ = 1.85 and ^^ = 4.27 as com puted by time h ist ory

nonlinear structural response analyses can be directly compared to the

inelastic deamplification fact ors, F , predicted by Equations 3-14 and

3-16 through 3-20 to evaluate the accuracy of these prediction methods.

4-1

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4.1 INPUT SCALE FACTOR RESUL TS FOR GROU ND MOTION STUD IED

Tabl e 4-1 pres ents the input scale fac tor s, F^ and Fr ,

corr espon ding to y^ = 4.27 and \ = 1.85, respectively, for the time

histories and elastic frequencies studied. Mean valu es, standard devi atio ns, and coeffici ents of variation of these scale factors are also

present ed for each earthq uake ground motion and for each freq uen cy studied

as well as overall composite val ues . The trends for the high duc tili ty

and low ductility scale factors are similar. There fore, only the high

ductility scale factor results will be discussed.

One sho uld not infer t hat the mea n F| and F^ value s s hown in

Tabl e 4-1 of 2.62 and 1.54, respe cti vel y, can be used as aver age

inelastic scale fact ors . The inelastic scale factor is sensitive to

durat ion, frequen cy, and the smoothness of the elastic spectrum and a

single average number should not be used for any partic ular cas e.

4.1.1 Duration Effects

The high d uctil ity sc ale fac tor , F^^, is plotted in Figur e 4-1

against strong motion duration, Tp, for each of the cases studied.

Very large data scatter exis ts. In fact , the coefficient of variation

for F^ is 0.49. This large data scatter tends to mask strong motion

duration eff ects . For durations Tp greater than 2.5 seco nds, the

scatter band on F^ is from 1.25 to s lightl y less than 4.0 with a mean

of 2.28 and a coefficie nt of variation of 0.29. For durati ons less than

about 2.5 seco nds , the lower bound on F, remains about 1.25 whil e the

upper bound rapidl y increases with decreas ing dura tion . The result is

that the mean increases for these short duration record s to 3.29 but the

coefficient of variation also increases to 0.57 or approximately double

what it was for the longer duration rec ord s.

The only conclusion which can be reached from the comparison is

that in some cases F| is sub sta nti all y g reater for the short dura tion

records than it is for the long duratio n records but in some other cas es,

^H does not appear to be increased by short duration.

4-2

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4.1.2 Frequency Effects

Table 4-1 shows a definite trend of increasing F M with

decreasing elastic natural freq uenc y. Howe ver , there is substantial data

scatter which also tends to increase with decreasing natural frequency.

Obv iou sly , there is a freq uenc y effect but it is being partiall y masked

by some other important eff ects .

4.1.3 Influence of Freque ncy Shift from Elastic to Secant Frequency

As structures go nonlinear, their effective frequency gradually

shifts from the elastic frequency toward the softer secant frequency (see

Section 3.3.1 for a discuss ion of this e f f e c t ) . As this effect occurs,

energy is fed into the structure over the frequenc y range from f to f

and thus one could postulate that the average spectral acceleration over

this frequency range is a better descriptor of nonlinear structural

response than is the elastic spectral accele ration . Th us , if the average

spectral acceleration within this frequency range is less than the

spectral acceleration at the elastic frequenc y then Fn would be high,

whil e if the average spectral acceleration is less than the spectral

accelera tion at the elasti c freq uen cy, then FM would be low (see Figure

4-2 for a schematic^ pict ure of the c o n c e p t ) .

Figures 4-3a through 4-3c plot the relationship between averagespectral acceleration and elastic frequen cy spectral a cceleration for

each of the 12 records and 4 frequ encie s con sidere d. FM exceeds 2.7 in

each of the following cases:

' ^ H ^ 2 . 7

Olympia - 2.14 Hz

Taft - 2.14 Hz

Artificial - 3.20, 2.14 Hz

Pacoima Dam - 2.14 Hz

El Centro #5 - 2.14 Hz

Coyote Lake - 5.34, 3.20, 2.14 Hz

Gavilan Co llege - 8.54, 5.34 , 3.20, 2.14 Hz

Melendy Ranch - 5.34, 3.20, 2.14 Hz

4-3

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All of these 16 cases have average spectral accel eratio ns between f and

fg less than the spectral accele ration at f. Simi larl y, F^ is less

than or equal to 1.7 in each of the following case s:

' H ^ 1 - 7

Olympia - 8.54, 5.34 Hz

Taft - 8.54, 5.34 Hz

El Centro #12 - 8.54 Hz

Pacoima Dam - 8.54 Hz

Goleta - 8.54 Hz

Coyote Lake - 8.54 Hz

Parkfield - 8.54, 5.34, 3.20 Hz

All of these 11 cases have average spectral accele rations between f and

fg greater than the spectral acceleration at f.

It is clear that the average spectral accelerat ion between f and

fg has a more sig nifican t influence on inelastic res ponse than does the

spectral acceleration at the elastic frequenc y, f. This factor accounts

for the large variation in F^. This spectral avera ging effect is the

overriding dominant effect influencing inelastic structural response.

The spectral averagin g effect is much more important than the

apparent duration effect described in Subsecti on 4.1. 1. In fac t, it is

this spectral averaging effect which creates most of the apparent duration

effect on F| . As noted in Chapter 2, short duration recor ds ( T Q <

3.0 seconds) appear to have narrow frequency content with a narrow

frequency range of highly amplified spectral a ccele ratio ns. When the

elastic frequency lies from about 1.4 to 2.0 times the frequency at which

these narrow frequency content spectra have maximum spectral accelerati on,

the F| fa cto r is low (less than 1 . 7 0 ) . On the other ha nd, when the

elastic frequency is less than 1.2 times the frequency of maximum

spectral acce lera tion , the F, factor is higher (greater than 3 . 0 ).

T h u s , one should ex pect very large data scatter on the FM factor for

these short duration records.

4-4

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The conclusion is that one must retain the narrow frequency

content band-width on spectral amplification for these short duration

records in any engineering characterization of the record for nonlinear

structural resp ons e. All of the comments made in Chapter 2 on the

importance of freq uency conte nt band-width are even more important for

nonlinear structural res pon se. Short duration records (Tr, < 3.0

seco nds) should not be averaged to gether in a way which increases their

freque ncy content band-width in order to obtain a design spectrum. Such

averaging will destroy ones ability to accurately compute nonlinear

structure response using the averaged design spectrum.

4.2 NUMBER OF STRONG NONLINEAR RESPONS E CYCLES

So long as the duc tility leve l, y , is used as a measure of

dama ge, the spectral averaging effect described in the previous subsection

will have the predominant influence on the ductility level reached and

thus on dama ge. The strong motion duration , Tp, primar ily effects the

spectral averaging process because short duration records have narrower

frequen cy conten t. How eve r, duration also has a very direct influence on

the number of strong nonlinear cycles, N, and thus the hysteretic energy

dissipation per cycle (see Subsection 3.3.1 for a technical discussio n of

this e f f e c t ) . This number of strong nonlinear cycles appears to haveonly a minor influence on the maximum ductility level , y, reached. Thu s,

so long as the duct ility level is used to describe da mage , this duration

effect on damage will be much less important than the spectral averaging

effect described previo usly. However, if the total hysteretic energy

dissipation were used to descri be dama ge, then this duration effect on

the number of strong nonlinear cycles would be \/ery important. Thus , the

following discussions on the number of strong nonlinear cycles is

warranted even though N has only a minor effect on the ductilit y level

reached.

Figure 4-4 shows a plot of nonlinear structural response versus

time for a 5.34 Hz structure subjected to the Olympia record scaled to an

input level to produce a ductil ity level of 4.35 . Initially, the

4-5

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structure oscil lates at an elastic frequency of about 5.3 Hz . Just prior

toT O t h e first nonlinear excursion occur s. Due to the strong nonlinear

cycle r i j - (z j , the effective frequency is reduced to about 4.1 Hz . A

second strong nonlinear cycle is associated with M ^ - M J - Q T ^ . Due tothis cycle, fg is further reduced to about 3.7 Hz. The next strong

nonlinear cycle is ^ 6 ^ - (Vj. During this tim e, the effective frequency

gradually lowers from 3.6 to 3.1 H z. The last nonlinear cycle is ( s ) -

Q g j and peak d uctility, y = 4.35, is reached at ^ ¥ ) . Olympia results in

essentially 4 strong nonlinear cycles through the time of peak

displ aceme nt. The effect of previous nonlinear cycles is to reduce the

hysteretic energy dissipation during the last cycle ( V ) -r 9) be lo w that

which would have occurred at this ductili ty if the precedin g cycles had

not occ urred. Th us, the peak ductility, y, is somewhat greater than would

have occurred with this same fac tor, F, if the preceding cycles had not

occurred.

The influence of strong duration, Tp^ on the number of strong

nonlinear cycles is illustrated by comparisons of the nonlinear resistance

vers us deformation plots for Taft (Tp = 10.3 s e c o n d s ) , Parkfield (T^ =

1.4 seconds), and Melendy Ranch {l^^ = 0.8 s e c o n d s ) . These resistance

versus deformation plots are shown in Figures 4-5 through 4-7 for a 5.34Hz structure at ductility levels of approximately 1.9 and 4.3. Note that

the number of strong nonlinear cycles does not appear to be sensitive to

the ductility leve l. This conclusion was found to be generally true for

all cases studied. Nex t, Figures 4-8 and 4-9 present the resistance

deformation diagrams for Taft and Melendy Ranch scaled to produce

ductility levels of approximately 4.3 for elastic frequencies of 2.14,

5.34, and 8.54 H z. These plots show that the number of strong nonlinear

response cycles does vary somewhat with frequen cy. However , no consistent

trends were observed. Sometimes N increased as f decreased and sometimes

N decreased as f decreased. Generally, the differences were one cycle .

4-6

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T a b l e 4 -2 p r e s e n t s t h e r e la t i o n s h i p b e t w e e n s t r o n g d u r a t i o n ,

T Q , a nd t h e n u m b e r o f s t r o n g n o n l i n e a r r e s p o n s e c y c l e s , N , g e n e r a ll y

o b s e r v e d i n t h i s s t u d y . A l s o p r e s e n t e d i n t h i s t a b l e ar e f r e q u e n c y a nd

d a m p i n g c o e f f i c i e n t s , Cp a n d Cf j, w h i c h w i l l b e d i s c u s s ed i n t h e n e x t

s e c t i o n .

4 .3 C O M P A R I S O N O F C O M P U T E D S C A L E F A C T O R S W I T H T H O S E P R E D I C T E D B Y

E Q U I V A L E N T L I N E A R R E S P ON S E M O D E L S

T h e s c a l e f a c t o r s , F , b y w h i ch t h e g r o u nd m o t i o n a m p l i t u d e s m u s t

b e i n c r e a s e d t o a c h i e v e a d u c t i l i t y r a t i o o f y, = 1 .8 5 o r PLI = 4 . 2 8

a re l i st e d i n T a b l e 4 - 1 . T h e s e f a c t o r s w e r e c om p u t e d b y p e r f o r m i n g

n o n l i n e a r t i m e h i s t o r y a n a l y s e s . I t w o u l d b e d es i r a b l e t o be a b l e t o

p r e d i c t t h e s e s c a l e f a c t o r s s i m p l y f r o m c h a r a c t e r i s t i c s o f t h e e l a st i c

r e s p o n s e s p e ct r a w i t h o u t h a v i n g t o p e r f o r m n o n li n e a r t i m e h i s t o r y

a n a l y s e s . O n e m e t h o d t o a c h i e v e t h i s g oa l w o u l d b e t o c on v e r t t h e

n o n l i n e a r r e s i s t a n c e f u n c t i o n f o r t h e s t r u c t u r e t o an e q u i v a l e n t l i n e ar

r e s i s t a n c e f u n c t i o n w i t h an e f f e c t i v e f r e q u e n c y , f ' a nd e f f e c t i v e

d a m p i n g , B g . T h i s e q u i v a l e n t l i n e ar m o d e l i s u s ed w i t h t h e e l a s t i c

s p e c t r a l a c c e l e r a t i o n at f r e q u e n c y f ^ a n d d am p i n g 6 ^ t o c o m p u t e p e a k

r e s p o n s e . B y t h i s a p p r o a c h , t h e p r e d i ct e d s c al e f a c t o r , F , i s g i v e n b y

E q u a t i o n 3 - 1 4 . T h e n , t h e r a t i o , R , g i v en b y :

R = - f ( 4 - 1 )

r e p r e s en t s t h e r a t i o o f t h e p r e d i c t e d t o t i m e h i s t o r y c o m p u t e d s c al e

f a c t o r . I f R e x c e e d s 1 . 0 , t h e e q u i v a l e n t l i n e a r m o d e l o v e r p r e d i c t s

( u n c o n se r v a t i v e ) t h e s c a le f a c t o r . C o n v e r s e l y , i f R i s le ss t ha n u n i t y ,

t h e e q u i v a l e n t l i n e a r m o d e l u n d e r p r e d i c t s ( c o n s e r v a t i v e ) t h e s ca l e f a c t o r .

T h e d e s i r e i s t o f i n d a m e t h o d t o d e f i n e t h e e q u i v a l e n t l i n e a r m o d e l s o

t h a t t h e m e an v a l u e o f R w i l l b e c l o s e t o u n i t y w i t h a s m a ll c o e f f i c i e n t

o f v a r i a t i o n .

4-7

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Subsection 3.3.1 suggested that the effective frequency, f'

and effective damping, B^, could be defined by Equation 3-8 in terms of

two empirical coef fici ents , A and C^. jhe coefficient A was varied

from 0 to 1.0 in 0.1 increments while the coeffi cient C» was varied

from 0 to 0.5 in 0.1 in crem ents . For each specific set of A and C ^

coef ficie nts, the ratio R of predicted to computed scale factors was

determined for the four elastic frequen cies , f, the two ductilitie s,y ,

and the twelve time histories studied . It was found that a mean R value

close to unity with a low coefficient of variation could be achieved when

A was defined by:

' = ^F (1- (f s/ f) ) ^ 0 . 8 5 (4-2)

with the coefficients Cp and C^ defined in Table 4-2 as functions of

the number of strong nonlinear cycles N.

One should note that as A increase s, the effec tive frequ ency,

fg* is shifted clos er to the secant fr equen cy (A = 1.0) and away from

the elastic frequ ency (A = 0 ) . It was found that A increases withincreases in the number of strong nonlinear cycles and with decreases in

the ratio ( f g / f ) , i.e., increases in the ductility ratio,y . However,

A should not exceed 0.85. Th us, the effective frequency (Equation 3-8)

does not shift more than 85 % of the difference from the elastic frequency

to the secant freque ncy. The lowest A found in this study was 0.35 for

Melen dy Ranch ( N=l) at the low ducti lity y= 1.85 (f^/f = o . 7 7 ) . T h u s ,

in this study, the effective frequency was found to range from 3 5% to 85%

of the difference from the elastic frequency to the secant frequency.

Table 4-3 lists the ratio of (f^/f) as obtained from Equations 3-8 and

4-2 and the Cp valu es in Table 4-2 for N=l through 4 for the low and

high ductility cases studied.

4-8

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The hyster etic damping coe ffi cie nts , Cj^, listed in Table 4-2

range from 32 % to 55 % of the values listed in Equation C- 10 of Appendix C

for C ^^ associated with the largest nonlinear response cycle. This

coefficient C ^ decre ases subst antia lly as N is increased from 1 to 2 and

only slightly with further increases in N. Table 4-3 presents the

effective damping percentages Bg , which results from the use of these

C i value s in Equation 3-8 for the cases s tudi ed. Damping p ercent ages

are rounded to the closest 0.5%. One should note that the effective

damping percenta ges, Bg , are only slightly increased over the elastic

damping ( B= 7%) for the low ductilit y (y^ = 1.85) case with N of 2 and

great er. Significantl y higher effective damping percentages result for

the high duct ility cases (y^ = 4.27) and for the case of N=l.

Also shown in Table 4-3 are effective frequency and damping

percen tages as defined by the Sozen proced ure (Equation 3-9) and the Iwan

procedure (Equation 3 - 1 0 ) . The effective frequencies obtained by the

method recommended in this study generally lie between those obtained by

the Sozen and Iwan me th od s. For N=l, the method recommended herein give s

an effective frequency yery similar to that from the Iwan method.

However, as N incre ases, the recommended method produces an effective

frequency lower than that from the Iwan method and higher than that fromthe Sozen method.

The effective damping percentages obtained from the recommended

method are substantially lower than those obtained from the Sozen and Iwan

met hod s. The reasons for this lower effective damping are twofold:

1. The shear wall resist ance functions used in this study havea more extreme pinched behavior (more conservative) than

the resistan ce functio ns used in the Sozen and Iwan stud ies .It is believed that the resistance functions used in thisstudy are more re alisti c for shear wall structu res and areconservative for other structural systems where theresistance functions used by Sozen and Iwan are likely tobe more re alistic.

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2 . The elastic d amping,B , was made proportional to the tangentstiffness at any time in this study whereas the elasticdamping was held proport ional to the initial stiffn ess inthe Sozen and Iwan stud ies . Thu s, within this study, theeffective elastic damping was much reduced during nonlinearresp onse . The reasons for making elastic damping proportional to the tangent stiffness are given in Subsection3.2.3.

Tables 4-4 through 4-6 present the ratios R of predicted to

computed scale factors obtained from effective linear models defined by

the recommended, Sozen, and Iwan methods, respectively.

Table 4-4 shows that an effective linear model with effective

frequenc y and effective damping defined by the recommended procedure

accurate ly predicts the scale facto r. The ratio of predicted to computed

scale factors has a mean of 0.98 (2% conse rvati ve) for the high ductility

case and a mean of 1.02 (2% unco nser vati ve) for the low ductility cas e.

Furthermore, the COV about these means are only 0.12 and 0.09 for the

high and low ductility cases, respectively. At the worst extrem es, the

rat io of predicte d to computed scale factors ranged from 0.75 to 1.29 for

the high ductility case and from 0.85 to 1.26 for the low ductility case.

This agreement is considered to be exceptional ly good. Furth ermor e, no

consistent errors are obse rved . The agreement is equally good throughout

the frequency range covered (approximately 1.8 to 10 H z ) . The agreement

is good for all 12 time histories co nside red. Figure 4-10 demonstrates

that the ratio R of predicted to computed scale factors is independent of

the strong motion dur ation, T Q , and the ductility level,y . In other

w o r d s , no consistent bias exists with either of these param ete rs. The

worst COV are for the Coyote Lake record but are only 0.20 and 0.15 for

the high and low ductility cas es, respe ctive ly. The most severe uncon-servatism occurs for the Taft and El Centro #12 records where the

predicted scale factors are 6 to 10% unconservative on the avera ge. The

most severe conservatism occurs for the El Centro #5 and Pacoima Dam

records where the predicted scale factors are 5 to 1 2% conservati ve on

the average.

4-10

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The Sozen method (Table 4-5) also performs well on the average

for defining an effective linear structure model to be used to predict

peak resp ons e. How eve r, it does not perform as well as the recommended

proc edur e. On the average, the Sozen model introduces slight conservatism

( 2 % for the high ductility case, and 6% for the low ductility c a s e ) . How

ever , the COV are from 150 % to 2 00 % of those for the recommended

proc edur e. Thus , the scatter band is larger with the ratio of predicted

to computed scale factors ranging from 0.66 to 1.43 for the high ductility

case and from 0.60 to 1.37 for the low ductility cas e. Furthermore,

consistent errors are observ ed. The method tends to introduce consistent

conservative bias (ratios of predicted to computed scale factors less

than unit y) when the elastic frequ ency lies to the stiff side of the

frequency at which the elastic spectra peak . The basic problem appears

to be that the method o verpredicts the softening of the structure. Thus,

the method tends to overpredict the peak displacement (ductility)

respons e of the structure for a given level of ground mot ion . On the

other hand, the method also tends to overe stima te the effecti ve damping

for the shear wall resistance functions used in this study and this tends

to underpredict peak respons e. On the average, this overprediction and

underprediction cancel each other and thus the mean ratio of predicted to

computed scale factors is close to unity. However , for structures withan elastic frequency on the stiff side of the frequency at which spectral

accelerations pe ak, the overprediction of displacement (ductility) due to

too large a freque ncy shift is subs tant iall y greater than the under

prediction due to the use of too large of an effective damping and the

net result is significant overprediction of peak response.

The Iwan method (Table 4-6) does not perform well in defining an

effective linear structure model for the shear wall resistance functions

used in this study . The ratio of predicted to computed scale factors for

a given ductility ratio is consistent ly greater than unity. This means

that for a given ground motion lev el, the Iwan method will c onsist ently

unconservatively underpredict the peak displacement (ductility) response .

This unconservatism results from both an underestimate of frequency shift

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and an overestimate of the effective damping. This unconservatism is

signi ficant ly greater for the long duration r ecor ds (N=3 and 4) than for

Melendy Ranch (N=l) for which the Iwan method works reasonably wel l. In

gene ral, the Iwan method should not be used to generate effect ive linear

structure models for shear wall type structures.

The conclusion is that an equivalent linear model can be used to

accurately predict peak nonlinear response of structures at least within

the elastic frequency range from 1.8 to 10 Hz studied herein. For shear

wall type struc tures , the procedure recommended herein should be used to

define the effective f requency, fg , and effec tive damping, ^e » of the

equivalent linear mo de l. This procedure requires that the number of

strong nonlinear response cycle s, N, be defined . Table 4-2 can be used

to define N as a function of the strong duration T Q . This procedure

will be conservative for other types of structural resistance functions

where the pinching behavior is less severe than for the shear wall

resistance function models used in this study.

4.4 COMPARISON OF COMPUTED SCALE FACTORS WITH THOSE PREDICTED BY

INELASTIC RESPONSE SPECTRA

As noted in Section 3.3.2, in lieu of constructing an equivalentelastic structure model to account for inelastic respo nse, one can simply

modify the elastic spectrum to obtain an inelastic response spectrum for

use with the elastic structure mo de l. The inelastic spectral response

associated with the elastic frequency, f, and elastic damp ing,B , is

obtained by dividing the elastic spectral respo nse at this frequency and

damping by an inelastic deamplifi cation fac tor , F , as shown in Equation

3 - 1 5 .

One method to define F is through the use of Equation 3-14

together with the effective elastic frequency, fg , and effective damping

B g . defined in the preceding section for the equivalent elastic

structure mo de l. Another method to define F is through the use of the

Riddell procedure described in Subsection 3.3.2. Lastly, F might be

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defined by some average spectral acceleration within a frequency range

bounded by the elastic freq uency , f, and the secant frequency, f^.

Thus:

where S (f^ - f ,B ' ) represents the average spectral acceleration

between an upper frequ ency , f^, and the secant frequ ency, fg, at an

average effective dam pin g, B^g , and fga represents an average

effective frequency within the frequency band from f^ to fg. Intui

tive ly, it would seem that this averaging proces s would provide a mor e

accurate estimate of F than that obtained by Equation 3-14 wherein only

a single effective f requency, fg, is used.

Many different forms of spectral averaging were tried. These

included:

1. Averagin g spectral accelera tions with a uniform weighting

of spectral accelerations at all frequencies between f and

f . "

s

2. Averaging spectral accelerations with a linear increase in

weighting of spectral accelerations as frequencies were

decreased from f (zero weighti ng) to f <. (unity w e i g h t i n g ) .

u -'

3. Uniform weighted averaging of spectral velocities at all

freque ncies between f and f^,

u s

It was found that M ethods (2) and (3) did not produce better accuracy in

estimating F than could be obtained with Method (1) . There fore , onlythe method based on uniform weighted averaging of spectral accelerations

will be described he rein .

Sg(f,B)(4-3)

.1-13

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T h e u p p e r f r e q u e n c y , f , w a s d e f i n ed b y :

{ - j - ) = ( 1 -B ) + B ( - f ) ( 4 -4 )

a nd f or u n i f o r m w e i g h t e d a v e r a g i n g , t h e av e r a g e e f f e c t i v e f r e q u e n c y

w i t h i n t he f r e q u e n c y b a nd f r o m f t o f i s :

f + f cf = - ^ - ^ ( 4 - 5 )e a c

T h e n t h e a v e r ag e e f f e c t i v e d a m p i n g w a s d e f i n ed b y :

ea( 4 - 6 )

N o t e t h a t E q u a t i o n s 4 -4 a n d 4- 6 a r e i d en t i c a l i n f o r m a t t o E q u a t i o n 3 -8

w h i c h w a s r ec o m m e n d e d f o r d e v e l o p i n g a s i n g l e f r e q u e n c y e q u i v a l e n t

e l as t i c s t r uc t u ra l m o d e l . T h e c o e f f i c i e n t , B , w a s v a r i ed f r o m 0 (f jj = f )

t o l (f = f ) i n 0 .1 i n c r e m e n t i n t e r v a l s w h i l e t h e c o e f f i c i e n t C M w a s

v a r i e d f r o m 0 t o 0. 5 i n 0 . 1 i n c r e m e n t s . F o r ea c h s p e c i f i c s e t of B a nd

C|^ c o e f f i c i e n t s , t h e r a t i o R o f p r e d i c t e d t o c om p u t e d d e a m p l i f i c a t i o n

f a c t o r s w a s d e t e r m i n ed f o r t h e f o u r e l a st i c f r e q u e n c i e s , f , t h e t w o

d u c t i l i t i e s , y , and t h e 1 2 t i m e h i s t o r i e s s t u d i e d .

•

4 - 1 4

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Mean R values close to unity with a low coefficient of variation

could be achieved when:

B = r2Cp(l- (f5/f)) j-l (4-7)

except

0 < B < 0.70

with the coefficie nts Cp and C^ being identical to those defined for

the effe ctiv e elastic structural model in Table 4-2 . It should be noted

that with B defined by Equation 4 -7, the average effective frequen cy, fgg,

is identical to the equivalent elastic fr equen cy, fg, defined by Equations

3-8 and 4-2 for all cases where A from Equ ation 4-2 exceeds 0.5 since B =

( 2 A - 1 ) . How eve r, when A is less than 0 .5, B is limited to a lower bound

of zero (f^j = f ) and f' is less than f'. For those ca ses where f g^ is

less than f', the average effective damping , Bg^, from Equation 4-6 is

slightly greater than B ' from Equation 3- 8. Otherwise , these two

effective damping ratios are identica l. Table 4-7 lists the frequency

ratios ( f , , / f ) , and (f' /f ) and the average ef fectiv e damping perce ntage ,

6 !=.» found from Equation 4-4 through 4-7 together with Table 4-2 for all

cases stu died . Note that average effe ctiv e damping has been rounded to

the nearest 0.5 percent.

The ratio of the predicted inelastic deamplification factor

(identical to scale fact or) using Equation 3-14 together with the

effective frequency, fg , and effective damping, Bg, to the computed

facto r has alread y been given in Tabl e 4-4 since this method is identi cal to the use of an equivalent elastic structure mod el. The ratio of

the predicted inelastic deamplification factor using the spectral

averaging approach defined by Equations 4-3 through 4-7 to the computed

factor is given in Table 4-8 . The ratio of the predicted inelastic

deampl ificat ion factor obtained by the Riddell method (Equations 3-18

through 3-22) to the computed factor is given in Table 4-9.

4-15

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By comparing Tabl e 4-8 and Ta ble 4-4, one notes that the spectral

averaging approach recommended in this section does only trivially better

than the simpler equivalent elastic freq uency approach of the previou s

secti on. The mean ratios of predicted to computed deamplification factors

are essen tially identical from the two app roa che s. The spectral averaging

approach shows only a negligible reduc tion in an already low coefficien t

of vari atio n. Howe ver, the spectral a veraging approach does reduce the

extrem e bounds of this ratio of predicted to computed deamplification

factors. Wher eas, for the high ductility case the equivalent elastic

model produced a scatter band for this ratio ranging from 0.75 to 1.29,

the spectral averaging approach reduces this band to a range from 0.75 to

1.19. Simil arly, for the low ductili ty case, the equivalent elastic

model scatter band ranged from 0.85 to 1.26 while the spectral averaging

approach scatter band ranged from 0.85 to 1.14. Response spectra contain

a number of small local peaks and valleys even at damping rat ios as high

as 12 %. The equivalent elastic model approach can place the effective

frequency at one of these local valleys or peak s. The spectral averaging

approach smooths these local valleys and peaks and thus reduces the

possi ble extremes in the ratio of predicted to computed deamplifi cation

f a c t o r s . This smoothing represents a minor im provem ent. It is unclear

whether this minor improvement warr ants the substantial increase in compu

tational work entailed by the spectral averagi ng ap proach .

The mean ratio of the predicted to computed inelastic dea mpl ifi

cation factor for the Riddell method is 1.10 (10% unco nser vati ve) for both

the high and low ductili ty cases stud ied. This mean unconserv atism is due

to the extreme pinched behavior of the shear wall resistance functions

used in this study. Such pinching was not considered in the Riddell

study . This slight unconserva tism of the Riddell method could be accommodated in design by the use of sligh tly lower acceptable duc tilit y levels

in des ign. Howe ver, the Riddell method also shows COV for the ratio of

predicted to computed deamp lification factors which range from 1 40% to

2 0 0 % of those obtained for the spectral ave raging method recommended in

this study. For the high ductility cas e, the scatter band ranges from

4-16

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0 . 4 3 t o 1 .7 8 w h i c h i s j u d ge d t o b e e x c e s s i v e l y l a r g e w h e n c o m p a r e d t o a

s c a t t e r b a n d o f 0. 75 t o 1 .19 f o r t h e s p e c t r a l a v e r a g i n g m e t h o d . T h e

p r o b l e m o f a l a r g e s c a t t e r b a n d i s n o t a s s e v e r e f o r t h e l ow d u c t i l i t y

c a s e w h e r e i t r a n g e s f r o m 0 . 8 8 t o 1 .4 7 f o r t h e R i d d e l l m e t h o d a s c o m p a r e d

w i t h 0 .8 5 t o 1.1 4 f o r th e s p e c t r a l a v e r a g i n g m e t h o d . T h e R id d e l l m e t h o d

i s a v e r y e a s y m e t h o d t o g e n e r a t e a n i n e l a s t i c r e s p o n s e s p e c t r u m .

H o w e v e r , t h i s s t u d y s h o w s i t s h o u l d b e u s e d w i t h s o m e c a u t i o n b e c a u s e o f

t h e p o t e n t i a l l y l a r g e u n c e r t a i n t i e s a s e x p r e s s e d b y t h e w i d e s c a t t e r b a n d s

d e m o n s t r a t e d h e r e i n . I t s h o u l d b e n o t e d t h a t t h e N e w m a r k m e t h o d d e s c r i b e d

i n S ub s e c t i o n 3 .3 .2 w o u l d b e s l i g h t l y l e s s a c c u r a t e t h a n t h e R id d e l l

m e t h o d s o t h e s e s a m e c o m m e n t s a p p l y t o t he N e w m a r k m e t h o d .

4 .5 C O N C L U S I O N S O N P R E D I C T I N G I N E L A S T I C R E S P O N S E

I t i s c o n c l u d e d t h a t t h e i n e l a s t i c s p e c t r a l r e s p o n s e , S , i f „ \ ,apkT,3;

a s s o c i a t e d w i t h a n e l a s t i c s t r u c t u r al f r e q u e n c y , f , e l a s t i c d a m p i n g , 3 ,

a n d d u c t i l i t y f a c t o r , y , c a n b e a c c u r a t e l y a p p r o x i m a t e d b y e i t h e r :

P o i n t E s t i m a t e A p p r o a c h

S f f ' 8 ' )

' ^ y(f;/f)2

s p e c t r a l A v e r a g i n g A p p r o a c h

S (f - f , 6 ' JS , ( f . 3 ) = ' ' ' 2 ' ' ( 4 - 9 )

w h e r e f ' a n d g ' r e p r e s e n t t h e b e s t e s t i m a t e e f f e c t i v e f r e q u e n c y a n d

e f f e c t i v e d a m p i n g r a t i o s a s d e f i n e d b y E q u a t i o n s 3 - 8 , a n d 4 -2 w i t h

c o e f f i c i e n t s d e f i n e d b y T a b l e 4 - 2 . S i m i l a r l y , S ^ ^ ^ u ' ^ s ' ^ e a ^ r e p r e s e n t s

t h e a v e r a g e s p e c t r a l a c c e l e r a t i o n b e t w e e n f r e q u e n c i e s f ^ a n d f ^ f o r a n

a v e r a g e e f f e c t i v e d a m p i n g , 3 ' , a n d f ' r e p r e s e n t s t h e m i d p o i n t f r e q u e n c y

b e t w e e n f a n d f w h e r e t h e s e t e r m s a r e d e f i n e d b y E q u a t i o n s 4- 4 t h r o u g h

4 -7 w i t h c o e f f i c i e n t s f r o m T a b l e 4 - 2 .

4 - 1 7

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Within this study, the spectral a veraging approach shows only a

slight improvement in accuracy over the point estimate approac h. Both

approaches are very accurate with a COV of only 0.12 at v ^ = 4.27, and a

COV of only 0.09 at v , = 1.85 for the point estimate approach withslightly lower COV for the spectral averaging appr oach. The spectral

averaging approach requires substantially greater computational effort.

However, it does smooth out local peaks and valleys in the spectral

responses and this smoothing is desir able. The ref ore , for an elastic

response spectrum which contains significant local peaks and valleys at

damping values of 7.5 to 12.5%, the spectral averaging approach would be

slight ly prefera ble. If the elastic response spectrum does not contain

significant local peaks and valleys at these higher damping level s, the

point estimate approach would be equally a ccura te.

It should be noted that both approaches require knowledge of the

elastic response spectrum at the appropriate damping values which range

from 7.5 to 12.5 % for the ductili ty levels considered in this study. In

addition, both methods require an approximate knowledge of strong motion

duratio n, T Q , since the freq uenci es fg, fg^, and fjj and the effective

damping value s, g' and 3' depend slig htly on Tp particularl y when T Q

becomes moderate ly short (7 seconds and l e s s ) . These properties represent

the minimum engineering characteriz ation of the ground motion required for

predicting inelastic structural response.

The approache s defined by Equation 4-8 and 4-9 for predi ctin g

inelastic spectral response and the approach described in the previous

section for defining an equivalent elastic structural model were developed

for shear wall type resistance functions with elastic damping of 7%.

Howe ver, based upon the parameter studies described in Appendix D , these

approaches can be conservatively used for braced frames and other

structu ral or equipme nt systems so long as the structural system does not

have a resistan ce-deform ation function which shows greater stiffness

degr adat ion and pinchin g behavio r than that used in this study for shear

w a l l s .

4-18

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The brief parametric studies in Appendix D demonstrate :

1. Equation 4-6 can be used to estimate the average effectivedamping equally well for an elastic damping of 3% as for anelastic damping of 7%. The prediction procedure worksequall y well at 3% elastic damping as at 7% elastic damp ing.

2 . The frequency shift and hysteretic damping coefficient, Cpand C| , in Table 4-2 we re d evelo ped for a shear wallresistance function mode l. Use of these coefficients willintroduce only a slight conservatism for the Takeda model.The shear wall model overestimates the stiffness degradationand pinching behavior for braced-frame and bilinearresistance function mod els . Therefor e, these coefficientsoveremph asize the importance of N and T Q for suchm o d e l s . The input scale factor (inelastic spectral

deamplification factor) for the braced-frame and bilinearresistance function models studied in Appendix D lay midwaybetween the scale factors predicted using the Cp and C ^given in Table 4-2 for the appr opriate T Q and the scalefact or predi cted using Cp = 1.5 and C^ = 0.30 whic h aregiven for N=l. Averagin g the results obtained from the useof t hese two dif fer ent sets of Cp and C|\j va lu es wi llimprove the prediction accuracy for braced-frame andbilinear models when TQ is greater than 1.0 seconds.

4-19

8/22/2019 6848574


TABLE 4-1

STATISTICAL EVALUATION O F SCALE FACTOR DATA

(a) Scale Factors (Fu) for High Ouctnity Ratio (p - 4.27)

i1 (Co^p)

10

111

lu

Olynpla, UA., 1949(N86E)

Ta ft . Kern Co .. 1952(S69E)

El Centro Array No. 12Imperia l Val ley . 1979. ( 140)

A r t i f i c i a l(R.6. 1.60)

Pacolma DamSan Fernando. 1971 CS14W)

Hollywood Storage PE L ot .San Fernando. 1971 (N90E)

El Centro Array No. 5.Imperia l Val ley . 1979. (140)

UCS8 GoletaSanta Barbara. 1978 (180)

Gllroy Array No. 2. Coyote Lake.1979. (050)

Cholame Array No. 2. Parkfleld1966 (N65E)

Gavllan CollegeHoi l is ter . 1974 (S67H)

Melendy Ranch Barn. Bear Valley.1972 (N29U)

Model Stru ctu re Frequency ]

8.54 Hz

1.56

1.25

1.56

1.89

1.70

1.94

2.38

1.52

1.56

1.55

2.84

1.89

5.34 Hz

1.54

1.65

2 . 29

1.88

1.86

2.50

2.66

2.05

3 . 85

1.29

2.97

5.48

3.20 Hz 1

2 . 61

2.05

2 . 10

2.84

2.67

2.60

2.33

2.05

4.36

1.48

2 . 71

1 5.16

2.14 Hz 1

3.75

3.38

2.14

2.75

3.89 1

2.05

3.45

1.96

3.03

2.65

8.49

3.36

Meanj<F>

2.37

2.08

I7.O2

2.34

2.53

2.27

12.71

1.90

3.20

1.74

| 4 .25

I3.97

swqOev.

a \

1.05

0.92

0.32

0.53

1.00

0.33

0.52

0.25

1.22

0.61

2.83

1 1.67

C.O.V.<J/<F>

0.44

0.44

0.16

0.23

0.40

0.15

0.19

0.13

0.38 1

0.35

0.67

0.42

1 Mean,< F>

Std. D e v . . a

1 C.O.V., a/<r>

1. 8

0.43

0.24

2. 5

1.17

0.47

2.75

1.03

0.37

3.41 1

1.73

0.51

Overal l:

<F> -

0 •

1 C.O.V. •

2.62

1.28

0.49

(b) Scale Factors (F^) for Low Du cti lity Ratio {y^^ ' 1.85)

r«y>t-hniiak« OATAMI„ . „ . , „ _ „ , . .

2

3

4

5

6

7

8

9

[1 0

11

| l 2

Olynpla. WA.. 1949(N86E)

Taft. Kern C o.. 1952(S69E)

El Centro Array No. 12Imperial Valley. 1979. (140)

A r t i fi c i a l(R.6 . .1 .60)

Pacolma DamSan Fernando. 1971 (S14U)

Hollywood Storag e PE Lot.San Fernando. 1971 (N90E)

El Centro Array No. 5.Imperial Valley. 1979. (140)

UCSB Go le USanto Barbara. 1978 (180)



Gavllan CollegeHoi11 star. 1974 (S67H)

Melendy Ranch Bam. Bear Valley.1 1972 (N29W)

Model Structu re Frequency |

8.54 Hz

1.36

1.20

1.34

1.50

1.25

1.45

1.58

1.35

1.36

1.22

1.61

1 1.45

5.34 Hz

1.11

1.25

1.56

1.33

1 .38

1.65

1.60

1.65

1.93

1.21

1.55

1 1.96

3.20 Hz 1

1.49

1.50

1.29

1.60

1.26

1.58

1.34

1.41

2.00

1.21

1.62

1 2 . 1 8

2.14 Hz 1

1.70

1.78

1.48

1.73

2.19 1

1.39

1.51

1.49

1.86

1.59 1

1.93 1

1 ^-^

Mean<F>

1.41

1.43

1 .42

1.54

1.52

| l . 5 2

1.51

1.48

1.79

1.31

| l . 6 8

1.89

SM. 1Dev .

0

0.25

0.27

0.12

0.17

0.45

0.12

0.12

0.13

0.29

0.19

0.17

0.31

C.O.V.a/<F>

0.18

0.19

0.08

0.11

0.29

0.08 1

0.08

0.09 1

0.16

0.15

0.10 1

I 0 . 16

1 Mean.<F>

Std. D ev . . 0

1 C.O.V.. o ^ F >

1.39

0.13

0.09

1.52

0.27

0.18

1.54

0.29

0.19

1.72 1

0.24

0.14

4-20

Overal l :

< F> -

a •

1 C.O.V. •

1.54

0.26

0.17

8/22/2019 6848574


TABLE 4 - 2

CORRELATION BETWEEN DURATION (T|!j), EFFECTIVE NUMBER O F STRONG NONLINEAR CYCLES (N ), FREQUENCY SHIFT

COEFFICIENT (Cp), A N D HYSTERETIC DAMPING COEFFICIENT (C ^) *

I

Strong Duration

T,!) (S ec .)

less than 1.0

1.0 - 7.0

9.0 - 11.0

greater than 15.0

Effective Number of Strong

Nonlinear Cycles, N

1

2

3

4

Frequency Shift

Coefficient, Cp

1.5

1.9

2.3

2.7

Hysteretic DampingC o e f f i c i e n t , C^ .

0.30

0.15

0.11

0.11

These frequency shift an d hysteretic damping coefficien

model. Howev er, based upon parameter studies in Append

bilinear, Takeda, a n d braced-frame resistance function

a slight conservatism f o r t h e Takeda model. T h e shear

pinching behavior f o r braced-frame and bilinear resista

overemphasize t h e importance o f N a n d T n f o r such model

fication factor) for t h e braced-frame a n d bilinear resis

between t h e scale factors predicted using the Cp and Cfjscale factor predicted using C p = 1.5 an d Cf^ = 0.3 0 wh i

ts were developed f o r a shear wall resi

ix D , they c a n also b e conservatively umodels. U s e o f these coefficients will

wall model overestimates t h e stiffness

nee function models. Therefore, these

s. T h e input scale factor (inelastic stance function models studied in Append

given in Table 4 - 2 f o r t h e appropriate

ch a r e given f o r N = l .

stance functio

se d f o rintroduce onl

degradation a n dcoefficients

pectral deampli

ix,D l i e midwa

T Q a n d t h e

8/22/2019 6848574


TABLE 4-3

COMPARISON O F EFFECTIVE FREQUENCY A N D EFFECTIVE DAMPING A S OBTAINED B Y VARIOUS METHODS

I

Ductility

y

1.85

4.27 1

Secant Frequency

Ratio, (f^/f)

0.77

0.56

N*

1

2

3

4

1

2

3

4

Recommend

( f ; / f )

0.92

0.90

0.87

0.85

0.71

0.63

0.62

0.62

ed Method

^e (° )

10

7.5

7.5

7.5

12.5

10.5

9.5

9.5

Sozen Method

{ f ; / f )

0.77

0.56

3 ; {% )

11.5

16

Iwan Method

( f ; / f )

0.91

0.73

Bg (%)

12.5

16

Number o f Strong Nonlinear Cycles

8/22/2019 6848574


TABLE 4-4

RATIO O F PREDICTED T O COMPUTED SCALE FACTOR FOR RECOMMENDED METHOD T O

DEFINE EFFECTIVE LINEAR MODEL

High Ductility Case (nu • 4.27)

(Corap)

1

2

3

4

5

6

7

8

9

10

11

12

Olympla, WA.. 1949(N86E)

Ta ft. Kern Co .. 1952(S69E)

El Centro Array No. 12Imperia l Val ley , 1979, (140)


Pacolma DamSan Fernando. 1971 (S14W)

Hollywood Storage PE Lo t.San Fernando. 1971 (N90E)

El Centro Array No. 5,Imperia l Val ley . 1979. (140)

UCSB GoletaSanta Barbara, 1978 (I80)

G11roy Array No. 2. Coyote Lake.1979, (050)

Cholame Array No. 2, Pa rk fle ld1966 (N65E)

Gavllan CollegeHolllster, 1974 (S67H)

Melendy Ranch Barn. Bear Valley,1972 (N29H)

Model Struc ture Frequency |

8.54 Hz

1.09

1.01

.9 0

1.00

1.01

.8 4

.7 5

1.11

.8 3

1.16

.8 4

.9 0

5.34 Hz

1.01

.9 9

1.C2

.8 7

1.13

1.11

.8 7

.95

.7 7

.9 8

1.09

1.02

3.20 Hz

.9 3

1.02

1.29

.9 2

.8 8

1.17

.9 9

.8 4

1.19

.7 7

1.13

1.06

2.14 Hz

1.01

1.02

1.03

.9 1

.9 0

1.05

.9 1

.7 8

1.01

1.03

1.01

1.01

Mean<F >

1.01

1.01

•1.06

.9 3

.9 8

1.04

.8 8

.9 2

.9 5

.9 9

1.02

1.00

Std.

D e v .0

.0 7

. 0 1

.1 6

.0 5

.1 2

.1 4

.1 0

.1 4

.1 9

.1 6

.1 3

.0 7

C.O.V.o/<F>

.0 6

.0 1

.1 6

.0 6

.1 2

.1 4

. 1 1

.1 6

.2 0

.1 6

.1 3

.0 7

Mean,<F>

Std. Dev., a

C.O.V., oA:F>

.9 5

.1 3

.1 4

.9 8

.1 1

.1 1

1.02

.1 6

.1 5

.9 7

.0 8

.0 8

Ov e ra l l :

< F> «

0 =

C.O.V. •

.9 8

.12

.1 2

Lo w Ductility Case (y = 1.85)

1 ( C o m p )

1

2

3

4

5

6

7

8

9

10

U

12

Olympla. MA.. 1949(N86E)

Ta ft . Kern Co .. 1952(S69E)

El Centro Array No. 12Imperia l Val ley . 1979, (140)


Pacolma DamSan Fernando, 1971 (S14W)


El Centro Array No. 5,Imperia l Val ley , 1979, (140)

UCS8 Goleta

Santa Barbara, 1978 (180)Gllroy Array No. 2, Coyote Lake,1979. (050)

Cholame Array No. 2, Parkfleld1966 (N65E)

Gavllan CollegeHolUstor. 1974 (S67H)

Melendy Ranch Barn, Bear Valley,1972 (N29U)

Model Stru ctu re Frequency |

8.54 Hz

.9 7

1.10

.9 6

.8 9

.9 6

1.07

1.06

1.16

1.00

1.13

1.01

1.00

5.34 Hz

1.05

1.01

1.04

1.17

.9 0

1.11

.9 5

1.06

.9 0

1.19

1.03

1.05

3.20 Hz

.9 3

1.09

1.04

1.00

1.00

.8 9

1.00

1.01

1.02

.9 2

.8 5

.9 7

2.14 Hz

.9 5

1.20

1.09

.8 5

.94

1.05

.9 8

.8 5

1.26

.9 9

1.07

1.06

Mean<F >

.9 8

1.10

•1.03

.9 8

.9 5

1.03

1.00

1.02

1.05

1.06

.9 9

1.02

S to .

D e v .

0

.0 5

.0 8

.0 5

.1 4

.0 4

.1 0

.0 5

.1 3

.1 5

.1 2

.1 0

.0 4

C.O.V.a/<F>

.0 5

.0 7

.0 5

.1 5

.0 4

.0 9

.0 5

.1 3

.1 5

.1 2

.1 0

.0 4

Mean,<F>

Sto. Dev. , 0

C.O.V.. o/<F>

1.03

.0 8

.0 6

1.04

.0 9

.0 9

.9 8

.0 7

.0 7

1.02

.1 2

.1 2

O v e r a l l :

< F> •

0 •

C.O.V. -

1.02

.0 9

.0 9

4-23

8/22/2019 6848574


TABLE 4-5

RATIO O F PREDICTED T O COMPUTED SCALE FACTOR FOR SOZEN METHOD T O

DEFINE EFFECTIVE LINEAR MODEL

High Duc t i l i ty (y > 4 .2 7 >

Earthauake Record

(Comp)

1

2

3

4

5

6

7

8

9

10

U

12

Olympla. UA., 1949

(N86E)

Taft. Kern Co .. 1952(S69E)




Pacolma Dam

San Fe rnando, 1971 (S14W)

Hollywood Storage PE Lot,San Fern ando, 1971 (N90E)

El Centro Array No. 5,

Imperial Valley. 1979, (140)

UCSB Goleta

Santa Barb ara, 1978 (180)

Gllroy Array No. 2 , Coyote Lake,

1979. (050)Cholame Array No . 2. Parkfleld1966 (N65E )

Gavllan College

Holllster, 1974 (S67W)

Melendy Ranch Barn, Bear Valley,

1972 (N29 W)

Model Structure Frequency

8.54 Hz

.91

.95

1.12

.93

.82

.84

.68

1.09

.82

.88

.80

.79

5.34 Hz

.87

.98

.98

.92

.90

1.11

.90

.77

.92

.66

.93

1.30

3.20 Hz

.96

1.31

1.11

.97

1.15

1.11

1.19

.68

1.43

.78

1.33

1.19

2.14 Hz

1.13

.91

1.05

1.18

.67

.91

.86

.74

.96

1.32

1.13

.90

Mean

<F >

.97

1.04

1.07

1.00

.89

.99

.91

.82

1.03

.91

1.05

.97

Sto.

Oev.a

.11

.18

.06

.12

.20

.14

.21

.18

.27

.29

.23

.17

C.O.V.o/<F>

.12

.18

.06

.12

.23

.14

.23

.22

.26

.32

.22

.18

Mean, <F >

Sto. Dev.. 0

C.O.V.. a/cF>

.89

.13

.14

.94

.16

.17

1.10

.22

.20

.98

.19

.19

Overall:

< F> -

o «

C.O.V. -

.98

.19

.19

Low Du ctility (p - L as')

11 (Comp)

Olympla. UA.. 1949(N86E)

Taft. Kern C o.. 1952(S69E)

El Centro Array N o. 12

Imperial Vall ey. 1979 . (140)


Pacolma Dam

San F ernando. 1971 IS14U)

Hollywood Storage PE L ot.San Fern ando, 1971 (N90E)

El Centra Array No. 5.

Imperial Val ley. 1979. (140)

UCSB GoletoSanto Barbara. 197 8 U S O )


Cholame Array No. 2 . Parkfleld

1966 ( N65E)

Gavllan CollegeHolllster. 1974 (S67U)

Melendy Ranch Barn. Bear Valley.

1972 (N29 U)

Model Structure Frequency |

8.54 Hz

.85

.91

.82

.81

.91

.91

.76

.74

.80

.85

.84

.60

5.34 Hz

1.04

.96

1.09

.89

.91

.82

.81

.85

.85

.80

1.15

1.12

3.20 Hz

1.00

.88

1.02

.86

.82

1.08

1.11

.98

1.30

.62

.83

.97

2.14 Hz

.89

1.15

.90

1.01

1.17

1.06

1.37

.68

1.16

.86

1.35

.90

Mean<F >

.95

.98

• .96

.89

.95

.97

1.01

.81

1.03

.78

1.04

.90

Sto.

Dev.0

.09

.12

.12

.09

.15

.12

.28

.13

.24

.11

.25

.22

C.O.V.o/<F>

.09

.12

.13

.10

.16

.13

.28

.16

.24

.14

.24

.24

Overall:

< F > •

a •

C.O.V. •

.94

.17

.18

Mean,< F>

Sto. Dev.. 0

C.O.V.. oA F>

.82

.09

.11

.94

.13

.14

.96

.17

.18

1.04

.21

.20

4-24

8/22/2019 6848574


TABLE 4-6

RATIO O F PREDICTED T O COMPUTED SCALE FACTOR FOR IWAN METHO D T ODEFINE EFFECTIVE LINEAR MODEL

High D uc t i l i t y (u •= 4 . 27>

rarthniialfA Rornrvi

(Comp)

1

2

3

4

5

6

7

8

9

10

1 1

12

Olympla. UA.. 1949

(N86E)

Taf t . Kern Co. , 1952(S69E)

El Centro Array No. 12I mper ia l Va l l ey . 1979 . ( 140)



Hol lywood Storage PE Lot ,San Fernando. 1971 (N90E)

El Centro Array No. 5,I mper ia l Va l l ey , 1979 , ( 140)

UCSB GoletoSanto Barbara. 1978 (180)

Gl l roy Array No. 2, Coyote Lake.

1979. (050)Cholame Array No. 2, Park f le ld1966 (N65E)

Gav l lan Col legeHo l l l s t e r . 1974 (S67U)

Melendy Ranch Bam. Bear Val ley .1972 (N29U)

Model St ru ctu re Frequency |

8.54 HZ

1.83

1.88

1.64

1.63

1.54

1.55

1.14

1.53

1.62

1.55

1.21

1.10

5.34 Hz

1.72

1.68

1.90

1.47

1.64

1.42

1.19

1.59

1.15

1.61

1.45

1 . 10

3.20 Hz

1.38

1.48

1.60

1.30

1.14

1.65

1.63

1.44

1.43

1.23

1.34

1 . 12

2.14 Hz

1 . 11

1.49

1.52

1.62

1.42

1.60

1.42

1.26

1.68

1.39

.8 1

1.15

Mean<F>

1.51

1.63

•1.67

1.51

1.44

1.56

1.35

1.46

1.47

1.45

1.20

1.12

SM .Dev.o

.3 3

.19

.1 6

.1 6

.22

.1 0

.2 3

.14

.24

.17

.2 8

.0 2

C.O.V.o/<F>

.22

.12

.1 0

.10

.1 5

.06

.17

.10

.16

.12

.2 3

.02

Mean.<F>

Sto. Dev.. 0

C.O.V.. aAF>

1.52

.2 5

.16

1.49

.2 5

.17

1.40

.1 8

.1 3

1.37

.25

.1 8

Overa l l :

< F> -

a «

C.O.V. -

1.44

.2 3

.1 6

Low Ductility (p > 1 . 8 5 )

! (Comp)

1

2

3

4

S

6

7

8

9

10

1 1

12

Olynv la . UA. . 1949(N86E)

Ta f t . Kem Co. . 1952(S69E)

El Cent ro Array No. 12I mper ia l Va l l ey . 1979 . ( 140)



Hol lywood Storage PE Lot .San Fernando. 1971 (N90E)

El Cent ro Array No. 5.I mper ia l Va l l ey . 1979 . ( 140)

UCSB GoletoSanto Barbara. 1978 (180)

Gl l roy Array No. 2. Coyote Lake.1979. (050)

Cholame Arr«y No. 2. Pa rk f le l d1966 (N65E)

Gav l l an Co l l egeHo l l l s t e r . 1974 (S67H)

Melendy Ranch B a m . Bear Va l l ey .1972 (N29U)

Model St r uc to re Frequency |8.54 Hz

1.37

1.32

1.35

1.15

1.13

1.32

1.14

1.22

1 . 18

1.27

1.26

1.02

5.34 Hz

1.33

1.42

1.37

1.53

1 . 12

1.25

1.09

1.30

1 . 15

1.25

1.27

1 . 17

3.20 Hz

1.22

1.39

1.43

1 . 31

1.28

1 . 19

1 . 41

1.30

1.32

1 . 13

1.03

1.03

2.14 Hz

1.21

1.35

1.37

1.23

1.20

1.28

1.35

1 . 01

1 . 41

1.21

1.25

1.12

Mean<F>

1.28

1.37

1.38

1.31

1.18

1.26

1.25

1.21

1.27

1.22

1.20

1.09

SM .Oev.

0

.08

.0 4

.03

.1 6

.07

.05

.1 6

.14

.12

.06

.12

.07

C.O.V.o/<F>

.06

.0 3

.0 3

.1 3

.06

.04

.1 3

.1 1

.1 0

.05

.1 0

.07

O v e r a l l :

<F> -

a "

C.O.V. •

1.25

.1 2

.1 0

Mean.<F>

SM . Oev. , 0

C.O.V., o/tF>

1.23

.1 1

.0 9

1.27

.1 3

.1 0

1.25

.1 4

.1 1

1.25

.1 1

.0 9

4-25

8/22/2019 6848574


TABLE 4-7

EFFECTIVE FREQUENCY RANGES A N D AVERAGE EFFECTIVE DAMPING

Ductility

y

1.85

4.27

Secant FrequencyRatios, (fg/f)

0.77

0.56

Number of Strong Nonlinear

Cycles, N

1

2

3

4

1

2

3

4

(f,/f)

1.00

1.00

0.98

0.94

0.86

0.70

0.69

0.69

(^a/^)

0.88

0.88

0.87

0.85

0.71

0.63

0.62

0.62

B ; , (%)

10.5

8

7.5

7.5

12.5

10.5

9.5

9.5

8/22/2019 6848574


TABLE 4-8

RATIO OF PREDICTED TO COMPUTED INELASTIC DEAMPLIFICATION FACTOR FORRECOMMENDED SPECTRAL AVERAGING METHOD

High Ductility Case (p - 4.27)

1 (Component)

1

2

3

4

5

6

7

8

9

10

U

12

Olympla. UA.. 1949(NOeE)

Ta f t , Kem Co. . 1952(S69E)

El Centro Array No. 12I mper ia l Va l l ey , 1979 . ( 140)



Hol lywood Storage PE Lot ,San Fernando. 1971 (N90E)

El Centro Array No. 5,I mper ia l Va l l ey , 1979 , ( 140)

UCSB GoletoSanta Barbara, 1978 (180)

Gi l roy Array No. 2, Coyote Lake,1979, (050)

Cholame Array No. 2, Pa rk f le l d1966 (N65E)

Gav l l an Co l l egeHo l l l s t e r , 1974 (S67H)

Melendy Ranch Barn, Bear Valley,1972 (N29W)

Model St ruc tur e Frequency |

8.54 Hz

1.04

.9 6

.9 2

.9 9

1.01

.8 7

.7 5

1.06

.8 6

1.15

.8 0

.9 5

5.34 Hz

1.00

1.02

1.04

.8 8

1.06

1.05

.87

.9 1

.8 1

.9 6

1.07

1.00

3.20 Hz

.92

1.03

1.17

.9 1

.89

1.17

1.05

.8 2

1.19

.77

1 . 11

1.02

2.14 Hz

.98

.94

1.01

.93

.9 0

1.02

.90

.76

1.01

1.05

.95

1.09

Mean<F >

.9 9

.9 9

•1.04

.9 3

.97

1 .03

.8 9

.89

.97

.9 8

.9 8

1 .02

Std.

Oev.0

.05

-04

.1 0

.05

.08

.1 2

.12

.1 3

.17

.16

.1 4

.06

C.O.V.a/<F>

.05

.04

.1 0

.05

.09

.1 2

.14

.1 5

.1 8

.1 6

.1 4

.06

Mean,< F>

St d . D e v . . 0

C . O . V . . o/<F>

.9 5

.1 1

.1 2

.9 7

.09

.09

1 . 0 0

.14

.1 4

.9 6

.09

.09

O v e r a l l :

< F> -

0 »

C.O.V. •

.97

.1 1

.1 1

Lo w Ductility Case (p • 1.85)

ravfh/ i t iaka DArnwt

(Component)

1

2

3

4

5

6

7

8

9

10

U

12


Ta f t . Kem Co. . 1952(S69E)

El Centro Array No. 12I mper ia l Va l l ey . 1979 . ( 140)

A r t i f i c i a l( R . G . , 1 . 6 0 )

Pacolma DamSan Fernando, 1971 (S14H)

Hollywood Storage PE Lot,San Fernando. 1971 (N90E)

El Cent ro Array No. 5.I mper ia l Va l l ey , 1979 , ( 140)

UCSB GoletoSanto Barbara, 1978 (180)

Gl l roy Array No. 2, Coyote Lake.1979, (050)

Cholame Array No. 2, Pa rk f l e ld1966 (N65E)

Gav l lan Col legeHo l l l s t e r , 1974 (S67H)

Melendy Ranch Barn. Bear Valley,1972 (N29W)

Model Structure Frequency

8.54 Hz

.9 6

1 . 11

1.00

.9 0

1.00

1.08

1.00

1.04

.9 9

1.09

1.01

.8 9

5.34 Hz

1.02

1.04

.9 9

1.12

.9 5

1.00

.9 4

1.02

.8 8

1.12

1.09

1.06

3.20 Hz

.95

1.03

1.06

.95

.95

.94

1.12

1.05

1.05

.8 9

.87

.95

2.14 Hz

.9 2

1.12

1.07

.89

.98

1.09

1.10

.85

1.14

.97

1.08

1.04

Mean

<F >

.9 6

1 .08

•1 .03

.9 7

.97

1 .03

1 .04

.9 9

1 . 0 2

1 . 0 2

1 .01

.9 9

St d .

D e v .

0

.04

.05

.04

.1 1

.02

.07

.08

.09

.1 1

.1 1

.1 0

.08

C.O.V.

o/<F>

.04.

.04

.04

.1 1

.0 3

.07

.08

.1 0

.1 1

.1 1

.1 0

.0 8

Mean,<F>

Std. Dev. . 0

C.O.V.. o A F >

1.01

.07

.0 7

1.02

.0 7

.0 7

.9 8

.0 8

.0 8

1.02

.1 0

.09

O v e r a l l :

< F> •

o •

C.O.V. •

1.01

.0 8

.0 8

4-27

8/22/2019 6848574


TABLE 4-9

RATIO O F PREDICTED T O COMPUTED SCALE FACTOR FOR RIDDELL METHOD T ODEFINE EFFECTIVE LINEAR MODEL

High Ductility Ca3e (p ' 4.27)

11 (Component)

1

2

3

4

5

6

7

8

9

10

11

12

Olympla, UA., 1949

(N86E)Taft , Kem Co. , 1952(S69E)

El Centro Array No. 12Imperia l Val ley , 1979, (140)


Pacolma DamSan Fernando, 1971 (S14U)

Hollywood Storage PE L ot ,San Femando, 1971 (N90E)

El Centro Array No. 5,Imperia l Val ley . 1979, (140)


Gllroy Array No. 2, Coyote Lake,

1979, (050)Cholame Array No. 2, Parkfleld1966 (N65E)

Gavllan CollegeHol l ls ter , 1974 (S67U)

Melendy Ranch Bam, Bear Valley.1972 (N29U)

Model Str uc tor e Frequency |

8.54 Hz

1.21

1.15

1.35

1.35

.9 6

1.31

1.06

1.13

1.58

.8 8

1.29

1.17

5.34 Hz

1.23

1.32

1.11

1.36

.9 3

1.02

.96

1.00

.9 5

1.02

1.23

.6 7

3.20 Hz

1.40

1.23

1.10

.9 0

.6 3

.9 5

.8 6

1.09

.8 4

1.35

1.35

.7 1

2.14 Hz

.9 7

1.08

.8 6

1.33

.9 4

1.78

1.06

1.14

1.20

1.38

.4 3

1.09

Mean<F >

1.20

1.20

1 .1 0

1.24

.8 6

1.26

.9 8

1.09

1.14

1.16

1 .08

.9 1

• S M .O e v .

.1 8

.1 0

.20

.2 2

.1 6

.3 8

.1 0

.0 6

.3 3

.25

.4 3

.26

C.O.V.o/<F>

.1 5

.08

.1 8

.1 8

.1 9

.3 0

.1 0

.06

.29

.22

.4 0

.2 9

Mean.<F>

S M . O e v . . o

C . O . V . . o/cF>

1.20

.1 9

.1 6

1.07

.1 9

.1 8

1.03

.26

.25

1.10

.3 2

.29

O v e r a l l :

< F > •

a "

C.O.V. •

1 . 1 0

.25

.2 3

Lo w Duct ili ty Cas e (p •= 1.85)

1r .M.fc .# . . .a l . . . DA. .M.W4

(Component)

1

2

3

4

5

6

7

8

9

10

11

12


Ta ft . Kem Co . . 1952(S69E)

El Centro Array No. 12Imperia l Val ley . 1979, (140)


Pacolma DamSan Femando, 1971 (S14U)

Hollywood Storage PE Lo t.San Femando, 1971 (N90E)

El Centro Array No. 5,Imperia l Val ley . 1979. (140)




GavHan CollegeHol l ls ter . 1974 (S67U)

Melendy Ranch Barn, Bear Valley,1972 (N29U)

Model Stru ctu re Frequency |8.54 Hz

1.20

1.08

1.22

1.09

1.18

1.12

1.03

1.13

1.20

1.01

1.19

1.12

5.34 Hz

1.47

1.30

1.04

1.23

1.12

.9 9

1.02

.9 9

.9 9

.9 8

1.24

.9 8

3.20 Hz

1.09

1.09

1.26

1.02

1.19

1.03

1.22

1.16

.9 6

1.35

1.19

.8 8

2.14 Hz

1.13

1.08

1.10

.9 4

.8 8

.97

1.01

1.09

1.03

1.03

.9 9

.9 7

Mean<F >

1.22

1.14

1.16

1.07

1 .09

1 .03

1.07

1 .09

1.04

1.09

1.15

.9 9

S td .

D e v .0

.1 7

.1 1

.1 0

.1 2

.1 4

.07

.1 0

.07

.1 1

.1 7

.1 1

.1 0

C.O.V.a/<F>

.1 4

.1 0

.09

.1 1

.1 2

.07

.09

.06

.1 1

.1 6

.1 0

.1 0

Mean,<F>

S M . D e v . . a

C . O . V . . o/tF>

1 . 1 3

.07

.0 6

1 . 1 1

.1 6

.1 4

1 . 1 2

.1 3

.1 2

1.02

.07

.07

4-28

O v e r a l l :

< F> -

0 -

C.O.V. -

1 1 0

.1 2

.1 1

8/22/2019 6848574


C 6

o

o(O

(U

oC O

5 .

OI 4

0

00

2 •0

0

©

© O

Upper Bound of Data

2©

@ ®

© /^ Lower Bound0 0 V of Data

Q 5§

6 8 10 12

Stro ng Du ra tio n, TJI, (se c.)

14 16 18

FIGURE 4-1. SCALE FACTOR, F^ VERSUS DURATION, TJ

4-29

8/22/2019 6848574


\—I—I—I I 1 I — ry 5 6 7 8 9 ' ! 0 2 3 y 5 6 7 8 9 'l O'

FREQUENCY

I 1

FIGURE 4 - 2 . EFFECT OF FREQUENCY SHIFT DUE TO NONLINEAR RESPONSE

4-30

8/22/2019 6848574


J or ' 2 3 « S 6 7 8 9 J G r 2 3 a 5 6 7 8 9 J 0 ' 2^ • • • 1 • • r I . I I I I I I I r 1_

3 « 5 6 7 8 9 J ( f- I 1 I ' ' ' > '

a. •»•0 1 r-bJ

U

taJn

a '

in-

O L Y M P I P

f

DAMPING 0.070

R a n g e off r e q u e n c y s h i f t~ f o r d e g r a d i n g s y s t e m w i t h11 = 4.3

• , ' I ' I I l i i i i i ' . ' ' — r , T,—f '11 r—I I II I—r-1 0 ' 2 3 y 5 6 7 8 9 ^ 0 " ?! 3 l < J 5 i 6 7 8 p ' l 0 '

FREQUENCY (HERTZ)

T 1 1 i I I I I • ,

2 3 < S 6 7 89| | ( j '

E l a s t i c s t r u c t u r e fr e q u e n c y , f 2.14 3.20 5'. 34 8.54

IQT' 2 3 V 5 6 7 8 9 j a r 2 3 « S 6 7 8 9 J 0 '

n , I t i_i I I I I r I I I I I I I I r

» - <»

en •»

0 1 c-

l U u>

(_)

omma.

o

aZJl i j

IO0 .

tv -

fc»• ^ .

0 ) -» •

e»-

in-

3 M S 6 789 J O *- I I I—i 1 1 1 ^

TflFT

DAMPING 0.070

-\ R a n g e off r e q u e n c y s h i f t

f o r d e g r a d i n g s y s t e m w i t h

M = 4.3

— . , i ' I I — I — I — r I I I—J ' I I 1 I I I I I ' I I — : 1 T 1 —I I I I I • _ ,

10 2 3 i | S 6 7 8 9 ' l 0 ' 21 3 l > l 5 | 6 7 e | 9 ' l 0 ' 2 3 1 5 6 7 8 9 1 0 ^

FREQUENCY (HERTZ)

I i I I

E l a s t i c s t r u c t u r e f r e q u e n c y , f - 2.14 3.20 5.34 8.54

FIGURE 4-3a. ELASTIC RESPONSE SPECTRA FOR 7% DAMPING ( T ^ > 9 S ec )

4-31

8/22/2019 6848574


ICT' ? 3 ^ 5 Blf>9}tf 2 3 f 5 6 7 8 ? j Q- 2 3 < 5 6 7 8 j j t f

2 -*IT mo t "»0 1 I-U J

I ] "U

^ '

UJ n

CD

ac

o toQ ~*3 <nUJ OB

W p.

in

EL CENTRO. ARRAY NO. 12

f

DAMPING 0. 070

Ra nge of f r e q u e n c y s h i f t" f o r d e g r a d i n g s ys te m w i t hu • 4.3

10- i 3 4 s iUs\(f 5 T T T T T J I WFREQUENCY (HERTZ)

2.14 sizo s'.34 8',s4

"T 1 .1 i I I 1 I • .

2 3 <i $ 6 7 8 9 1 0 '

Elastic ttructur * frtqutncy. f •

IGT' 7 3 i | 5 6 7 8 9 J C r

2°P o,CE •0 1 (-

UJ in

tn

CE

O ^3 •>UJ •>

in -

A R T I F I C I A L

3 U S 6 7 8 9 J 0 '• • I I I I i r — j__LJ_iillll<'

. ^ ^ 1 : - J

DRMPING 0.070

Range of frequency shiftfor degrading system withy ' 4.3

^» J—i 4 i ni i ^ t f l\ ii 4 siiUji',0' 5 T T T T T nFREQUENCY IHERTZ)

E l a s t i c s t r u c t u r e f r e q u e n c y , f2 . 1 4 3.20 5.3» 8 54

FIGURE 4-3a. ELASTIC RESPONSE SPECTRA F OR 7% DAMPING (T^> 9 S e c )(Continued)

•

4-32

8/22/2019 6848574


10-'

»-( T

0 1UJ_ lUJ

uu( E

UJ

»—3- 1O

«oI Q<E

O

a3U J

«n0 .

OJ.

m

f -I D

in

n

N

•o

O)

<D

t~

in

2 3 U S 6 7 8 9 J G ^ 2 3 t 5 6 7 8 9 J 0*t • 7 ? ? . . . r I 1—I—I I I I I r—

2 3 « 5 6 7 8 9 JCf

PACOIMA DAMDRMPING 0.070

Range of frequency shiftfo r degrading system w i t hy ' 4.3

10- 1 3 4 i iUi\(f' 2 i 4 5 r 7 8 9 ' | 0 ' I i 4 i iU 9\(fFREQUENCY, (HERTZ)

• tr1>i I'lV 5 6 7 89

u„w. . JHERTZ) I

E l a s t i c s t r u c t u r t f r t q u t n c y . f • 2.14 3.Z) s'.SH 9,54

' « ^ ' 1 ? It ^ ? 7 ? ? K I ? ! ? «???. '0 ' ? 3 f, 8f T f j J t f

h -CE0 1U J- 1

tuuuaU it-3- 10

«nCD( E

0

3U J

in0 .

O I

•>t -

•0

in

M

N -

b

O I

»^10

HOLLYUOOO STORAGE

f

10"* 2 i M^TTTeTToT

DAMPING 0.070

Range of f r e q u e n c y s h i f tf o r d e g ra d in g s y s te m w i thu ' 4. 3

1— nmuvitfFREQUENCY (HERTZ)

I I IE l a s t i c s t r u c t u r t f r t q u t n c y . f • 2.14 3.20 5.34 8

54

FIGURE 4 - 3 b . ELASTIC RESPONSE SPECTRA F O R 7 % DAMPING (2.5 Sec* T' ^ 9 S e c )

4-33

8/22/2019 6848574


l o r ' 3 3 « S 6 7 8 9 J ( f 2 3 4 5 6 7 9 9 J 0* 2 3 « 5 I 7 8 ? Q^ • ' f • • i i i i i i i 1 I i i i i i T .

t c •0 1 f

s 'UJ nh -3- IO «i nCOa.o fc)a -* •3 atUJ *>

in p.

EL CENTRO. JAMES ROADDAMPING 0.070

R a ng e o f f r e q u e n c yf o r d e g r a d i n g s y s t e i iu = 4 . 3

i F 2 3 4 5 6 7 89h ( f 2 I i j 4 i | ^7 e|9 "l 0*FREQUENCY (HERTZ)

i—rTTTTTn(j '

E l a s t i c s t r u c t u r e f r e qu e n c y• ' ' 2.14 s'.ZO 5.34 8.54

ICT' 2 3 l | S 6 7 B 9 J a r 2 3 q 5 6 7 8 9 j | 0 ' 2 3 « 5 6 7 8 a ( f, 1 1 1—I—I I I I r I X L _ j I I I i r ' • . . i i . T '"

(E s

UJ „

a:lu nh -3- IO «in03(C

o fc>a - *•

3 o>U J OB'in r..

GOLETA

/ "

DAMPING 0.070

R an ge o f f r t q u t n c y s h i f t• f o r d e g r a d i n g s y s t e m w i t h

u - 4 . 3

' . , I ' I I I I I I I L -« * I '* '1

10 2 3 « 5 6 7 8 9 ' l 0 r 2 3 " !FREQUENCY (HERTZ)

«TTTeTYtf" 1 — r T T H T P I t f

Elastic structurt frtqutncy

r [\I:.UUI:RI. I i n [ ; i \ i c ) i

. f ' t\u l ! » S'.3» $.8 4

FIGURE 4-3b. ELASTIC RESPONSE SPECTRA 7 % DAMPING ( 2 . 5 S e c « T ^ < 9 S e c )

(Continued)

4-34

8/22/2019 6848574


) 0 " 2 3 « S 6 7 a 9 j a r 2 3 « 5 6 7 8 9 J 0 ' 2 3 « S S 7 a 9 J 0 '• I 1 1— I i 1 11 I I I I I I TI r 7 1 T 1 t , T f f

DAMPING 0. 07 0

Range of f r e q u e n c y s h i f tf o r deg rad i ng sys t em w i t hV ' 4.3

Iff' 5 T T T T T a l W 2 1 ii4 5id7eJ9'io'FREQUENCY (HERTZ)

E l a s t i c s t r u c t u r t f r t q u t n c y , f •2;i4 3.20 5.34 8.54

1 4 i i 7 islio'

J LJLLLLUiO'

• -(E

acU I- 1U i

uuaU if-3- 1

ai n

oas

0

a3U ii n

ft,

Ofa -fto

rn-

OK

•»•

IM '

to

"at-0 -r-

le-in-

PRRICFIELDDAMPING 0.070

Range of f r e q u e n c y s h i f tf o r deg rad i ng sys t em w i t hu -4.3

T^» 5—TTTTTnTtfiTilTTlTTTTO 3 — i H iiUi\(fFREQUENCY (HERTZ)

E l a s t i c s t r u c t u r t f r t q u t n c y , f •2.14 3.20 5.34 8. SI

FIGURE 4-3c, ELASTIC RESPONSE SPECTRA F O R 7 % DAMPING (T,!)<2.5 S e c )

4-35

8/22/2019 6848574


• b i o " 3 M

0 1

(_) - 1

03.

OQ =''(X

mOQ

UJ (MIO0 -

5 6 7 8 9 J tf• I • • • r

2 3 1 1 5 6 7 8 9 | 1 0 '-x • • 1 • • • • •

3 <» S 6- I t.

7 8 9 JO *I I I I

HOLLISTER DAMPING 0. 07 0

•at

-•o

R a n g e of f r e q u e n c y s h i f tf o r d e g r a d i n g s y s t e m w i t hu • 4.3

-O)

' ; 1 1 I I I — I r I I , I I 1 I I — I ' l l — r

1 0 2 3 « S 6 7 8 9 ' l O ^ 2 3 q 5 5 7 8 9 ' l 0FREQUENCY IHERTZ)

—1 1—I—1—I I I ,

3 1 s e v e g i o

E l a s t i c s t r u c t u r t f r t q u t n c y , f • 2.14 3.29 5.34 ^_^^

\ff* 2 3 l i 5 6 7 B 9 J Q r 2 3 U S 6 7 e 9 J 0 ' 2 3 « S S 7 8 9 0 f• • ' • • • I • r I • • • • I I • r • • . . i I T T **

a. «»m c-UJJ "U i inO

UJ n» —3

intoa

o t>a "*

U i B

in ,-

MELENDY RANCHDAMPING 0. 07 0

Range of f r e q u e n c yf o r d e g r a d i n g s y s t eli = 4. 3

10 -I I I I I I I—tV 5 6 7 8 9 ^ o r sTrTiTTTTO!- \—TXTTTTHO'

FREQUENCY (HERTZ)

E l a s t i c s t r u c t u r e f r e q u e n c y , f * 2 . 1 4 3 1 2 0 5:34 8'.54

FIGURE 4 - 3 c . ELASTIC RESPONSE SPECTRA F O R 7 % DAMPING (T J^ 2.5 S e c )(Continued)

t4-36

8/22/2019 6848574


V = R(u)

M

/ J

/ R

1/ / t / / / }

r r—»6

/1rf*\l •> •

5.34H2

f =3.1Hze

0 . 0 0 y . o o 8 . 0 0

( a ) Tim e H i s t o r y R e s p o n s e

1 2 . 0 0 1 6 . 0 0 2 0 . 0 0 2 4 . 0 0

T I M E

0 3 0 a .^0 a 10

OEfOR^I f iTJON

(b) Reaction Force - Displacement Response

FIGURE 4 - 4 . MODEL STRUCTURE RESPONSE FOR OLYMPIA EARTHQUAKE

(N86E , 1949) FOR f = 5.34 H z , y = 4.35

4-37

8/22/2019 6848574


\/T

1

(a) f = 5.34 Hz

e = 0.07

y = 1.9

0.00 0.39 0.16

DEFORMfiTlON

0.40

(b) f = 5.34 Hz

6 = 0.07

y = 4.3

- 0 . 6 0 - 0 . 4 a -0.20 O.aO 0.20 0.40

OEFORMflTlON0.60 o . e o

FIGURE 4-5. MODEL STRUCTURE RESPONSE TO KERN CO. EARTHQUAKE(TAFT, S69E, 1952) for f = 5.34 H z, y = 1.9-4.3

4-38

8/22/2019 6848574


(a) f = 5.3 4 Hz

3 = 0.07

y = 1 .9

0 38 3 30 0 38

DEFORMATION

(b) f = 5.34 Hz3 = 0.07

y = 4 .3

0 eo 9 30 0 iO 0 -taDEFORMATION

•

FIGURE 4-6. MODEL STRUCTUR E RESPONSE TO PARKFIELD EARTHQUAKE (CHOLAME

ARRAY NO. 2 , N65E , 1966) f o r f = 5 . 34 H z , y = 1.9-4.3

4-39

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ooo

OQ

Q•M.

aoo .to

oc:c tl i jX H

a

ooQto.

aaQ

§ao

/ f(a) f = 5.34 Hz

3 = 0.07

y = 1.9

0 36 0 30 0 38

DEFORMflTiaN

J

J - _ , ,

0r 1 ' " T 1

(b ) f = 5.34 Hz

3 = 0.07

y = 4.3

0 90 0 20 0 i<0

DE f^O RM P TlO N

FIGURE 4 - 7 . MODEL STRUCTURE RESPONSE TO BEAR VALLEY EARTHQUAKE (MELENDYRANCH, N29W, 1 972) fo r f . = 5.34 H z, y = 1.9-4.3

•

4-40

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0 60 -0 to -0 20 0.0 0 0.^0 O.VO 0 $0DEFORHflTION

v.oo

0.)0 1 00

(a) f = 2.14

6 = 0.07

y = 4.3

(b) f = 5.34 Hz

B = 0.07

M = 4.3

(c) f = 8.54 Hz

B = 0.07

y = 4.1

-0 6 -0 08 0' 00 0" oa 3 6 am 0 3 j

FIGURE 4-8. STRUCTURE RESPONSE TO KERN CO. EARTHQUAKE (TAFT,

S 6 9 E , 1952) for f = 2-9 Hz , y = 4.1 - 4.3

4-41

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0.00 O.OS 0.10DCFORNRTION

o V . s ^ 2 0 O.ZS

(a) f^ = 2.14 Hz

Bg = 0,07

y = 4.3

(b) f^ = 5.34 Hz

Bg = 0.07

y = 4.3

(c) fg = 8.54 Hz

Bg = 0.07

4.3

FIGURE 4-9. MODEL STRUCTURE RESPONSE TO BEAR VALLEY EARTHQUAKE (MELENDY RANCH,

N29W, 1972) for f^ = 2-9 H z , y = 4.3

8/22/2019 6848574


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8/22/2019 6848574


5. GROUND MOTION CHARACTERIZAT ION FOR NONLINEAR RESPONSE

Chapter 2 described the engineering characteriz ation of ground

motion for elastic structural resp onse . This chapter will extend that

engineering characterization of ground motion to the prediction of

nonlinear structural response using the procedure recommended by Chapter 4

for predicting nonlinear response.

The nonlinear response cha racteriza tion of ground motion can be

defined in terms of the inelast ic spec tral r esp ons e, S ^ ( f , B ) , which can

be obtained by the spectral averaging approach of Equation 4-9, This

inelastic spectral response can be obtained for either an average design

spectrum such as R.G. 1.60 or for actual ear thquake spec tra. It was shown

in Chapter 2 that the R.G. 1.60 spectrum anchored to an "eff ective" acce l

eration could be used as an engineering characterization of the ground

motion for longer duration ( T Q > 3.0 rec ord s) broad frequency content

(1.2 to 5.5 Hz) records when predicting the elastic response of stiff

structures (natural frequenc ies of 1.8 to 10 H z ) . There fore, the

inelastic spectral respo nses will first be shown for the R.G. 1.60spectrum.

5.1 INELASTIC R.G. 1.60 SPECTRA

Figures 5-1 and 5-2 show the inelastic response spectra from 1.0

to 10.0 Hz correspo nding to y = 1.85 and y = 4.27 for the 7% damped R .G.

1.60 spect rum. All spectra are anchored to a l.Og ground acc eleration .

The inelastic spectra were developed using Equations 4-4 through 4-7 and

4-9 together with the coefficients of Table 4-2. The inelastic deamplifi-

cation factors for a given d uctility are a constant throughout the ampli

fied acceleration frequency range and another constant throughout the

amplified spectral velocity regi on. These constants are a function of the

number of strong inelastic cycles (i.e., a function of the strong

durat ion) decreasing with an increasing number of cycl es. One can compare

5-1

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these constant F factors found from this study for shear wall resistant

function models with the Riddell factors reported in Section 3.3.2 as

follows:

V

1.85

4.27

N

1

2

3

4

1

2

3

4

Inelastic Deamplification

Factor for Acceleration

Reg ion , F^a

Recommended

1.74

1.52

1.44

1.36

3.68

1.93

1.81

1.81

Riddell

1.63

2.55

Inelastic Deamplification

Factor for Velocity

Regi on, F^y

Recommended

1.92

1.69

1.63

1.58

3.60

2.91

2.75

2.75

Riddell

1.92

3.65

One should note that the Riddell F values are greater than the F

values found in this study for the longer duration records (N=2 through 4)for which the R.G. 1.60 spectrum was an adequate characterization of the

ground moti on. The shear wall resistance function models used in this

study have significantly lower effective damping Bg than the models used

in the Riddell study for the same elas tic damping of 755.

#

5-2

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The conclusion is that the inelastic deamplification factors

proposed by Riddell are unconservative for the shear wall r esistance

function models used in this study. This unconservatism increases with

duc tili ty level from a factor of about 1.15 at y = 1.85 to about 1.37 atP = 4.27 .

Secondl y, one should note that for Tp > 3.0 seconds (N=2

through 4 ) , the F^j factor is rather insensitive to N. One could use the F^

values for N=3 with a maximum error of about + 6%. The refo re, for broad

frequency content ground motion s associated with T Q > 3,0 seconds for

which the R.G. 1.60 spectrum is a reasonable characterization of the

ground motion, it is unnecessary to estimate T Q ' or N. It is adequate

to assume N=3 for the purpose of predic ting the ductility level y .

5.2 PREDICTED INELASTIC SPECTRA FOR REAL TIME HISTORIES

Figures 5-3 through 5-13 present the inelastic spectra predicted

within the frequency range from 1.0 to 10.0 Hz for the 11 real time

histories included in this study using the prediction methods of Chapter 4

and ductilitie s of 1.85 and 4.2 7. Several points should be noted from

these figures:

1. The peak inelastic spectral accelerations always occur atfrequencies higher than those at which the peak elasticspectral accelerations occur. This situation occurs becauseinelastic response of these higher frequency structuresshifts the effective frequency downward into the range ofpeak elastic response.

2 . The inelastic deamplification factors associated withfrequencies equal to or less than that at which the elasticspectr um peaks are much gr eater than those for higherf r e q u e n c i e s .

These points are most dramatica lly illustrated by the Parkfield

Cholame Array #2 spectra (Figure 5 - 1 1 ) . The elastic spectral amplifica

tions are very high from 1.2 to 3.0 Hz and drop off very rapidly at both

higher and lower freq uenc ies. The largest inelastic deamplification

5-3

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factors are associated with elastic frequencies less than 3.0 Hz since

inelastic response will shift these frequencies lower and markedly reduce

respo nse. Structures with frequen cies of 3.0 Hz and less could be

designed to yield at spectral acc elera tions much less than those indicatedby the elastic spectra for Parkfield without severe damag e. However , for

the Parkfield record one must be very careful not to reduce the e lastic

spectral accelerations for structures in about the 3.5 to 5.0 Hz ran ge.

These str uctures should be designed to remain elastic for the Parkfield

record. Inelastic response of such structures will shift their effective

frequencies into the frequency range (1.2 to 3.0 Hz) within which the

power of the input is predominantly con centrat ed. For such stru cture s,

inelastic responses would rapidly increase because of this frequency

shift . For records with narrow frequency co ntent , such as Parkfield, one

should be very careful about taking any credit for inelastic re spons e for

structures which lie slightly to the stiff side of the predominant

frequency range of the record. On the other hand, for even stiffer

structures (elastic frequencies greater than 5.0 Hz) the inelastic

deamplification factors are again significant although not as large as

for structures with frequencies below 3.0 Hz .

5.3 COMPARISON OF INELASTIC SPECTRA TO R.G. 1.60 INELASTIC SPECTRA

In Section 2.3, the 7% damped elastic R.G. 1.60 spectrum

anchored at an "effective" acceleration w as compared to the 1 % damped

elastic spectra for the 11 real earthquake time histories over the

frequency range from 1.8 to 10 Hz . The "effective" acceleration, A^c ,

was set so that 8 4% of the actual spectral accelera tions between 1.8 and

10 Hz would lie below the R.G. 1.60 spectr um. In other wor ds, the R.G.

1.60 spectrum wa s exceeded at 16 % of the frequenc ies b etween 1.8 and 1 0

H z . This process has been repeated for the inelastic spectra corresponding to y = 1.85 and 4.27. The corresponding "effective" acc eleration,

^Dy» ^^"^ inelastic response are shown in Table 5-1.

5-4

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Figure s 5-3 through 5-13 c ompare the y = 1.0, 1.85, and 4.27

spectr a for the 11 actual reco rds studied to the correspondin g R.G. 1.60

spectra anchored to the effective design ac celerati ons, A^ , for these

same ductility levels for frequencies fr om 1.0 to 10 Hz . The R.G. 1.60spectrum used depends upon the number of strong nonlinear cycl es, N. The

N = 4 spectrum wa s used for O lympi a; N = 3 for Taft and El Centro #12;

N = 1 for Melendy Ranc h; and N = 2 for the other 7 recor ds. Table 5-2

presents the maxim um, med ian , and minimum ratio of actual inelastic

spectral accel eration to R.G. 1.60 inelastic spectral acceleration

(SA,, /SA,, ) fo r the fre que ncy range fro m 1.8 to 10 Hz conside red in• a ^1.60

this study.

The six real ground motion records with T^ > 3.0 seco nds

(Olympia through El Centro #5) are all reasonably fit by the R.G. 1.60

spectrum anchored at A Q for y = 1.0 (elastic), 1.85, and 4.27. Actuall y,

the fit is even be tter for the inel astic R eg. Guide spectra to the

inelastic actual spectra than it is for elastic spectra (y = 1.0 ). There

f o r e , the conclusio n of Section 2.3 that the R.G. 1.60 spectrum anchored

to an "effective" acceleration provides an adequate engineering character

ization of the ground motion for the six longer duration records for

elastic response of structures with elastic frequencies between 1.8 and10 Hz can be easil y extended to inelastic response at least up to

duct ility levels of 4.3. The reason that the R.G. 1.60 spectrum works

even better for inelastic resp onse than for elastic response is that

inelastic response spectra are smoother than elastic spectra and thus can

be better fit by a smoot h, broad frequency design spectrum such as R.G.

1.60.

Simil arly, the conclusion of Section 2.3 that the elastic R.G.

1.60 spectrum does not provide an adequate engineering characterization

for the 5 shorter duration records (Tp ^ 3.0 seconds) for elastic

response can also be extended to inelastic response.

5-5

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For t h e s i x records with broad frequency content a nd T ^ > 3 . 0

seconds (Olympia through El C e n t r o # 5 ) , t h e "effective" design accelera

t io ns , A Q ^ , f o r y = 1.0, 1.85, a nd 4 . 2 7 a r e compared in Table 5 - 1 t o t h e

corrected instrumental ground acceleration,a , t h e r m s

based design accel

e r a t i o n , A p ^ j ^ , a n d t h e Spectral Intensity based design acceleratio n,

^DE2» described in Section 2.3. F o r these s i x records, all three accel

erations could serve a s a basis f o r defining "effective" acceleration t o

anchor t h e R.G. 1 . 6 0 spectrum. F o r these s i x records:

y

1 .0

1 . 8 5

4 . 2 7

Ratio

^Dy^^DEl

' Dy/' DE2

^Dy/'^DEl

^Dy ' DE2

^ D y / ^

' Dy/ DE2

Max.

1 . 1 0

1 . 1 7

1 . 1 7

1 . 1 3

1 . 2 1

1 . 1 9

1 . 1 9

1 . 3 1

1 . 2 6

Mean

0 .8 7

1 .06

0 .99

0 .87

1 .06

0 . 9 9

0 . 9 1

1 .10

1 .03

Min.

0 .73

0 .96

0 .85

0.71

0 . 9 4

0 . 8 3

0 .70

0 .95

0 .85

COV

0.15

0 .08

0 .12

0 .17

0 .09

0 .14

0 . 1 9

0 . 1 2

0 . 1 6

The rms-based "effective" acceleration, Ap^^, h a s t h e lowest

COV. However, it also introduces a mean factor o f unconservatism o fbetween 1 . 0 6 a t t h e lower ductilities t o 1 . 1 0 a t y = 4.27. Considering

the conservative bias introduced b y u s e of t h e R.G. 1 . 6 0 spectrum ( s e e

Table 5- 2) , this slight factor o f unconservatism is unimportant. When t h e

R.G. 1 . 6 0 spectrum is anchored t o Ap^^, within t h e 1 . 8 t o 1 0 H z range,

the following ratio o f ( SA / S A ) a r e obtained f o r t h e 6 records

considered: ^ ^-^^

5-6

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y

1.0

1.85

4.27

(SA /SA )^a ^1.60

Maximum

Range

1.29-1.05

1.24-1.00

1.32-1.03

Median

1.20

1.10

1.12

Med i urn

Range

1.05-0.83

1.15-0.85

1.06-0.84

Median

0.88

0.99

0.98

Minimum

Range

0.76-0.49

0.88-0.51

0.82-0.56

Median

0.59

0.64

0.67

For broad frequency content records (frequency content at least

throughout the range from 1.2 to 5.5 Hz) associated with durations TI

greater than 3.0 seconds, both the elastic (y = 1.0) and inelastic

response chararacteristics of the ground motion for structures with

elastic frequencies from 1.8 to 10 Hz can be adequately characterized by

the R.G. 1.60 spectra anchored to an rms based "effective" acceleration

defined by Equation 2-15. For the six records studied with these charac

t e r i s t i c s , the maximum factor of unconservatism obtained at a n y frequency

from 1.8 to 10 Hz for ductilities from 1.0 to 4.3 was 1.32 while the

maximum factor of conservatism w a s (1/0.49) = 2.04. The median factor of

conservatism ranged from (1/0.88) =1 . 1 4 f o r elastic response (y = 1.0) to

(1/0.99) = 1.01 for inelastic response. In other words , at t h e w o r s t ,

this method of defining the engineering characterization ofground motion

can range from a 1.3factor of unconservatism to a 2.0 factor of conserva

tism with a slight conservative bias on the average. Considering the

uncertainties in the ground motion, this range of accuracy is very

tolerable.

5-7

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5.4 GROU ND MOTION CHARACTERIZATION FOR NONLINEAR RESPONSE SUMMARY

In this cha pter , inelastic spect ra are predicted by the spectral

averaging approach presented in Chapter 4 for the 11 real e arth quake

ground motion records considered in this study. In addition, inelastic

Re g. Guide 1.60 spectra have been constructed by the same approac h. The

actual ea rthqua ke spec tra and the Reg. Guide spectra are utilized to

establish "effective" accelera tion, Ap , for inelastic response as the

value the Reg. Guide spectrum must be anchored such that 84 percent of

the actual earthquake inelastic response spectral accelerations between

1.8 and 10 Hz would lie below the Reg. Guide 1.60 spectr um. It is shown

in Tabl e 5-2 that the inel astic spectra for all the longer du ration

records studied are reasonab ly fit by the Reg Guide 1.60 spectra anchored

to Ap but this is not the case for the 5 shorter duration r ec or ds. It

is also shown in this chapter t hat the rms based definiti on for

"eff ectiv e" acc eler atio n, Ap^j^ as given by Equation 2-15 pr ovid es a good

match with the empirically determined "effective" acceleration, Ap^.

In Chapter 2 it was demonstrated that an adequate engineer ing

characterization for elastic structural response for stiff structures

(1.8 to 10 Hz) subjected to any of the six real ground motion records

with Tp > 3.0 seconds is provided by the Reg . Guide 1.60 spectrum anchored

to an "effectiv e" peak acceleration, Apni as given by Equation 2-15. In

this ch apte r, it is demonstr ated that this conclusion can be extended to

inelastic response at least up to ductility levels of 4.3. Similar ly,

the conclusion of Chapter 2 that the elastic Reg. Guide 1.60 spectrum

does not provide adequate engineering characterization for the 5 shorter

duration records (Tp ^ 3.0 secon ds) for elastic response can also be

extended to inelastic response.

5-8

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TABLE 5-1

"EFFECTIVE" DESIGN ACCELERATIONS FOR INELASTIC RESPONSE

( C o m p o n e n t )

1

2

3

5

6

7

8

9

10

11

12

O l y m p i a , WA., 1949

N 8 6 E )

T a f t , Kern Co., 1952

( S69 E )

El Cent r o Arra y No. 12


PaCOima Dam

S a n Fern a n d o , 1971 (S14W)

H o l l y w o o d Stor a g e PE Lot,

S a n Fern a n d o , 1971 ( N 9 0 E )

El Cent r o Arra y No. 5,


UCSB Go!eta

S a n ta B a r b a r a , 1978 (180)

Gil r o y Arra y No. 2, C o y o te L a k e ,

1979, (050)

C h o l a m e Arra y No. 2, Parkfield

1966 (N65E

Gav i l a n Coll e g e

Hoi l i s t e r , 1974 ( S67W)

M e l e n d y Ranc h Barn , Bear Valle y ,

1972 (N29 W )

'E f f e c ti v e"D es i g n Acc e l e r a t i o n ,

y = 1.0

0.219

0.149

0.128

0.856

0.233

0.471

0.283

0.233

0.562

0.105

0.573

y = 1.85

0.216

0.145

0.129

0.825

0.238

0.487

0.272

0.241

0.516

0.101

0.631

y = 4.27

0.223

0.148

0.135

0.820

0.251

0.528

0.402

0.243

0.625

0.093

0.620

Ground

A c c e l .

a (g)

0.281

0.180

0.142

1.170

0.211

0.530

0.347

0.191

0.490

0.138

0.520

RMS-Based

A c c e l .

ApEi (g)

0.202

0.155

0.133

0.795

0.213

0.404

0.332

0.202

0.514

0.106

0.435

Spectral

Intensity

B a s e d Acce l .

ApE2 (g)

0.253

0.175

0.128

0.879

0.200

0.442

0.324

0.154

0.564

0.060

0.221

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TABLE 5- 2

COMPARISON O F ACTUAL SPECTRAL ACCELERATIONS T O R.G. 1.60 SPECTRAL ACCELERATIONS ANCHORED TO A,

Earthquake Record

(Component)

1 ^ '1 ^1 ^

5

1 ^1 7

1 ^1 ^10

1 ^12

Olympia, WA. , 1949(N86E)

Taft, Kern Co., 1952(S69E)


Pacoima Dam




UCSB Goleta

Santa Bar bara, 1978 (180)

Gilroy Array No. 2, Coyote Lake1979 (050 )

Cholame Array No. 2, Parkfield1966 (N65E )

Gavilan CollegeHolliste r, 1974 (S67W)

Melendy Ranch Barn, Bear Valley1 1972 (N29W)

(S A / SA ) * 1^ a ^ 1 . 6 0 1

y = 1.0 1

Max.

1.12

1.23

1.09

1.08

1.14

1.11

1.33

1.15

1.16

1.66

1.14

Median

0.90

0.89

0.86

0.84

0.86

0.90

0.82

0.77

0.48

0.58

0.69

M i n . 10 . 7 0 1

0 . 6 1 1

0.61 1

0.55

0.45 1

0 . 6 0 1

0 . 6 9 1

0.25

0.37 1

0.2 6 1

0 . 0 8 1

1 y = 1.85 1

1 M a x .1 1.08

1 1.12

1 1.03

1 1.02

1 1.02

1 1.03

1 1.65

1.04

1.40

1 1.26

1 1.03

Median

0.94

0.92

0.88

0.93

0.91

0.95

0.89

0.80

0.53

0.84

0.80

M i n . 10 . 8 2 1

0 . 6 8 1

0.70

0 . 4 9 I

0.51 1

0 . 5 4 1

0.76

0.27 1

0.46

0 . 1 8 1

0.09 1

1 y = 4.27 1

1 M a x .1 1.07

1 1.10

1.01

1 1.03

j 1.02

1 1.01

I 1.35

1.01

1 1.15

1 1.09

1 1.01

Median

0.94

0.95

0.83

0.91

0.87

0.81

0.64

0.77

0.49

0.57

0.61

M i n . 10 . 6 1 1

0 . 8 6 1

0 . 7 0 1

0 . 5 4 1

0.50

0.51

0.53

0.27 1

0 . 4 2 1

0.11

0.10

* Ratios o f Actual t o R e g . Guide 1.60 Spectral Accelerations a r e reported

fo r t h e frequency range of 1.8 to 10 Hz

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T 1 1 1 1—r n \ 1 1—r

7% Damping

N

N

N

N

= 1.0

1.85

TJ (Sec)

< 1.01.0 - 7.0

9 .0 - 11.0>15.0

N

12

34

•^y

1.75 Hz

1.921.69

1.631.58

6.0 Hz

1.741.52

1.441.36

T 1—r - I — I — I — I — r7 8 9 'l 0'

1 ^

6 7 8 9 '1 0

FREQUE NCY (HERT Z

FIGURE 5 - 1 . INELASTIC REG. GUIDE 1.60 RESPONSE SPECTRA - LOW DUCTILITY

8/22/2019 6848574


o" T — I — r 1 1 1—r

1% Damping

y = 1.0

N = 3 & 4,N = 2 Vy = 4.27

N = 1

T^ (Sec)

1 < 1 . 01.0 - 7.09.0 - 11.0

>15.0

N

1234

^ 11.75 Hz

3.602.912 . 7 52.75

6.0 Hz 1

2.68 11.931.811.81

6"1 1— r7 8 9 '1 0" 3

-r -5


9 '10^

FIGURE 5-2. INELASTIC REG. GUIDE 1 . 6 0 RESPONSE SPECTRA - HIGH DUCTILITY

8/22/2019 6848574


1 r 1 1—r

u = 1 .0

^ = 1.85

n = 4.27

Dashed lines areR.G. 1.60 spectra

n —3

-I 1 1 — i — r1 1 — r

6 7 8 9 10"

FREQUENCY (HERTZ)

6 7 8 9 1 0

FIGURE 5-3. COMPARISON O F OLYMPIA SPECTRA WITH REG. GUIDE 1.60 SPECTRA

ANCHORED T O "EFFECTIVE" DESIGN ACCELER ATION, A^ .

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CD

CM

o

O I -

Z «° -O r~- -

CL LD -

Ql

L U 3. -

_ JU JCJ ro -

CJCC

L UCM -

0COOD

cr

0

L JZ )

ii 1COCL.

0

—'O I

00

r-

eo

U )

T 1 1—I—r -1 1—I—r

C M V

3

// = 1.0

- B — n = 1.85_

~e— u = 4.27

Dashed 1ines are

R.G. 1.60 spectra

- 1 1 1 1 — I — I — ; ;

5 6 7 8 9 l 02

-T 1—r27 8 9 1 0

FREQUENCY (HERTZ)

FIGURE 5-4. COMPARISON OF TAFT SPECTRA WITH REG. GUIDE 1.60 SPECTRA

ANCHORED TO "EFFECTIVE" DESIGN ACCELERATION, Ap

8/22/2019 6848574


-I 1 1 1 1 — r "T 1 1 — r

A = 1.0

^ = 1.85

H = 4 . 2 7


3- I — r - 1 1 1 — I — 1 r

6 7 8 9 'l 0^ 38 9 1 0"1^

2

FREQUENCY (HERTZ)

FIGURE 5-5. COMPARISON OF EL CENTRO #12 SPECTRA WITH REG. GUIDE 1.60 SPECTRAANCHORED TO "EFFECTIVE" DESIGN ACCELERATION, Ap^

8/22/2019 6848574


T 1—I—r 1 1 — r

^ = 1 .0

|/-= 1.85

^ = 4.27Dashed lines are

G. 1.60 spectra

- i — I — I — r37 8 9 'lO° 2 3 4 5

FREQUENCY (HERTZ)6 7 8 9 '1 0

FIGURE 5-6. COMPARISON O F PACOIMA DAM SPECTRA WITH REG. GUIDE 1.60 SPECTRA

ANCHORED T O "EFFECTIVE" DESIGN ACCELERATION, ADii

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1 1 1 1 1 — r 1 1 — r

^ = 1.0

n = 1.85

Ii = 4.27

Dashed lines a r e

R.G. 1.60 spectra

1 1 — r5 6 7 8 9 'lO°

- I -

3- 1 1 1 — I — 1 r

6 7 8 9 'l 0— I

3

FREQUENCY (HERTZ

FIGURE 5-7. COMPARISON O F HOLLYWOOD STORAGE SPECTRA WITH REG. GUIDE 1 . 6 0SPECTRA ANCHORED T O "EFFECTIVE" DESIGN ACCELERATION. A p ^

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LD

3 *

roC J

GD

ct: oLU —^— I mUJ COC JC Jcn u3

c^

U l

n

LU

COQQCE

OCD

L J J „CO O

cn -CD

r~ [-

iD -

T T 1 r

/ i = 1 .0

- Q — M = 1 . 8 5

— 8 — n = 4.27

Dashed lines a r eR.G. 1.60 spectra

-| 1 1 — r -1 1 1 — I — I — r

6 7 8 9 'l O'8 9 '10" 2 3 4 5

FREQUENCY (HERTZ)

FIGURE 5-8. COMPARISON O F E L CENTRO # 5 SPECTRA WITH RE G. GUIDE 1.60 SPECTRA

ANCHORED T O "EFFECTIVE" DESIGN ACCELERATION, AD//

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-| 1 \—r - r — r - | r -

H = 1. 0

O — p = 1.35

— e — U = 4.27


-| 1 — r2 3

-1 1 1 — I — I r

6 7 8 9 1 08 9 1 0


FIGURE 5-9. COMPARISON OF GOLETA SPECTRA WITH REG. GUIDE 1.60 SPECTRAANCHORED TO "EFFECTIVE" DESIGN ACCELERATION, Ap

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^ 2m

Z ^ -O r~ -I— I

h - ^

(X Ln -

LU :3._ JL ULJ ro -

CJCC

L U 'M -

CO oCQ ^cr cn

QO

g -=) lo

LU(O ^CL.

1 1 1—r - | 1—r

'M r3

- r5 6

1 — r

^ = 1 .0

— Q — u = 1.85

— 8 — n = 4 . 2 7Dashed lines a r eR.G. 1.60 spectra

3 5-1 1 — I — I — r

7 8 9 1 08 9 '10

F R E QU E N C Y ( H E R T Z i

%

FIGURE 5-10. COMPARISON O F COYOTE LAKE , GILROY SPECTRA WITH REG. GUIDE 1.60SPECTRA ANCHORED T O "EFFECTIVE" DESIGN ACCELERAT ION, A p ^

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LD- | 1 1—r 1 — r

CJ

D

L U_ JL UCJCJ

cr

o'—'cn

00

O)

L U

OCDQQCC

OauL J U _

fO

CM

cnCL. oen

OD

-T 1 1 1 1 1 fT

5 6 7 8 9 1 0

fl = 1 .0

- o — ^ = 1.85

- 8 — ^ = 4.27

— j S - : : i . - - .

Dashed 1ines a r eR.G. 1.60 spectra

5- 1 1 1 — I — I r

6 7 8 9 1 0FREQUENCY (HERTZ)

FIGURE 5-11. COMPARISON O F PARKFIELD, CHOLAME SPECTRA WITH REG. GUIDE 1.60SPECTRA ANCHORED T O "EFFECTIVE" DESIGN ACCEL ERATION, A p

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on 1—r -| 1—r

^ = 1.0

- Q — n = 1.85

- 9 — ^ = 4.27


5 2 3•T 1 — r

6 7 8 9 1 0

FREQUENCY (HERTZ)

7 8 9 1 0 2

FIGURE 5-12. COMPARISON O F GAVILAN COLLEGE SPECTRA WITH REG. GUIDE 1.60 SPECTRA

ANCHORED TO "EFFECTIVE" DESIGN ACCELERATION, A p ^

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IroCO

O ^

I—I e n

in ^

LU

O ^

c r M

L U -

t - bI D ^—I OTO CO

COm to

CC ^

O

CO

Q_ ,

O

CD -

U3

1 — r

U = 1 .0

-G // = 1.85

^ — H = 4 . 2 7

Dashed lines a r eR.G. 1.60 spectra

T5 7 8 9 'l 0 4 5

1 -

6 -r -9 '10'

FREQUENCY (HERTZ)

FIGURE 5-1 3. COMPARISON O F MELENDY RANCH SPECTRA WIT H REG. GUIDE 1.60SPECTRA ANCHORED T O "EFFECTIVE" DESIGN ACCELERATION, A n

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6. MEASURE OF RELATIVE STRENGTH OF GROUND MOTION RECORDS

6.1 APPROACH

One method to define the relative strength of a ground motion

record is in terms of the resulting maximum structural r espo nse. Within

this s tudy, the maximum structural res ponse is defined in terms of

ductil ity levels reach ed. The study has considere d shear wall resistance

function structures with elastic behavior (y = 1. 0) , nearly elastic

behavior (y = 1 . 8 5 ) , and a conservative lower bound on the onset of

significant structural strength degradation (y = 4 . 2 7 ) . The relative

strength of a ground motion record can then be defined by the inelastic

spectral acceleration, S^^^^^gj, corresponding to an appropriate

ducti lity level, y, for a structure with an elastic freque ncy, f, and

elastic damping, 6.

Figures 6-la through 6-ld present the relative strengths of each

of the 12 records studied as defined by S^^/^ ^j for ductilities of 1.0,

1.85, and 4.27 for 1 % damping and elastic frequencies of 8.54, 5.34, 3.20,

and 2.14 Hz, resp ectiv ely. These frequen cies are considered representa

tive of the frequenc y range from 1.8 to 10 Hz which is typical for stiff,

nuclear power plant structures.

Several ground motion relative strength zones are defined on

Figures 6-la through 6-ld. These zones are defined in terms of the zero

period ground acceleration (ZPA) for which a plant must be designed to

remain elastic using the R.G. 1.60 spectrum in order to prevent the

ductility level from exceeding 4.27 (conservative lower bound for onset

of significant strength deg rada tion ) when subjected to the actual r ecord.

For y = 4.27 these zo nes are defined by:

6-1

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Zone

Very Severe

Severe

Moderate

Low

Requi red Elastic Design ZPA Range (g)

> 0 . 3

0.2 - 0.3

0.1 - 0.2

< 0 . 1

In other word s, if the plant must be designed to remain elastic for a R.G .

1.60 spec trum anchored at a ZPA greater than 0.3g in order to prevent the

ductility from exceeding 4.27 for the actual record, this record is

considered to be very severe . Similarl y, if the elastic design ZPA must

be between 0.2 and 0.3g to prevent the ductility from exceeding 4.27 for

the actual record, the record is considered to be sev ere . For y = 1.0

and y = 1.85 these zones are defined in terms of a mul tip le of th e

spectral acceleration at y = 4.27. The following multiples are used:

^^1 .0 = 1-9 Sa4.27 f > 4 Hz

S a ^ Q = 2.7 Sa4 27 f < 4 Hz

^^1.85 = 1-^ Sa4.27 f > 4 Hz

^^1.85 = 1-7 Sa4.27 f < 4 Hz

These intercepts were selected so as to enable these lesser ductility

spectral accelerations to be a reasonable prediction of the severity of

the ground motion at y = 4.27.

As an example , at a frequency of 8.54 Hz, the Reg . Guide 1.60

spectral amplification factor is 2.29. Ther efor e, the intercept between

the ve ry severe and the severe zones for y = 4.27 at f = 8.54 Hz is 2.29

times 0.30g = 0.69g. The other interc epts fo r y = 4.27 and f = 8.54 Hz

are at 0.46g and 0.23g. Thes e zone interce pts for y = 4.27 are drawn on

6-2

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Figure 6-la (f = 8.54 H z ) . The int ercepts for y = 1.0 and y = 1.85 are

then at 1.9 and 1.4 tim es , respe ctive ly, the correspon ding intercept at

y = 4.27. Thu s, the intercept between the very severe and severe zones

is at 1.31g and 0.97g for y = 1.0 and 1.85, respectively, on Figure

6-la. A similar approach was used to define these intercepts on the

figures for other frequencies.

6.2 RELATIVE STREN GTHS OF GROUN D MOTION RECORDS STUDIE D

The Pacoima Dam record represents a wer y severe ground motion by

this definition for structures with elastic frequencies greater than about

4 Hz . This record represents sever e ground motio n for structures with

natural f requencies of about 2.5 to 4 Hz and only moderate ground motion

for structures with natural frequ encies less than about 2.5 Hz. The

elastic spectral acceleration (y = 1.0) properly describes the relative

severity of this record for structures with natural freque ncies greater

than about 2.5 Hz but overstates the relative severity of the record for

structures with natural f reque ncies less than 2.5 Hz .

The elastic spectral accelera tions (y = 1.0) would lead one to

believe that the Melendy Ranch and El Centro #5 records would be severe

to very severe records for structures with natural frequencies from about4 to 10 Hz . Howev er, the severit y of these records based upon the onset

of significant strength degradation is seriously overstated by the elastic

spectral accelerat ion. Based upon significant strength degrad ation , both

records are barely severe records for structures with elastic frequencies

of about 8.5 Hz . El Centro # 5 is only a mode rate record for structures

with natural frequencies from about 2.2 to 8.0 Hz and is a low severity

record for structures with frequencies below 2.2 Hz despite its high

elast ic spectral accel erati on. The severity of Melendy Ranch drops off

even more rapidly as the structure frequencies are reduced. Melendy Ranch

is a moder atel y severe record for structures with natural frequenc ies of

5 to 8 Hz and has low severity for structures with natural frequencies

less than 5 Hz despite its very high elastic spectral acceleration at

frequencies above 4 Hz.

6-3

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The Parkfield record shows elastic spectral accelerations

(y = 1.0) of 0.5 to 0.6g for frequ enci es above about 5 Hz . Thes e

elastic spectral accelerations increase to about 0.8g at a frequency of

3.2 Hz and in crease to 1.4g at 2.1 Hz . Th us , based upon the elastic

spectral acceleration, one would judge the Parkfield record to be of

moderate severity for structures with natural frequenci es above about 2.5

Hz increasing to a severe record for structures with natural frequenc ies

less than about 2.5 Hz. The elastic spectral ac celera tions appear to

underestimate the relativ e severity of the Parkfield record for structures

in the 2.5 to 3.5 Hz ran ge. Based upon the onset of significant streng th

degradat ion, the Parkfield record represents a severe ground motion for

structures with natural frequencies of 1.8 to 3.5 Hz.

El Cent ro No. 12, Taft, and Gavilan College represent low

severity ground motions throughout the frequency range from 1.8 to 10 Hz

whethe r defined by the elastic spectral accele ration or by the onset of

significant strength degrad ation. Howev er, Gavilan College is of partic

ularly low severity for ductilities associated with the onset of signifi

cant strength d egradati on (y = 4.27) and this parti cula rly low severi ty

is not fully indicated by the elastic (y = 1.0) spectral acc eler ati ons .

Because of its high frequency content. Coyote Lake is of moderate

severity for frequencies above about 7.5 Hz. For frequencies between 4.5

and 7.5 Hz , the elas tic (y = 1.0) spectral accel erati ons would indicate

moderat e severity for Coyote Lake. Howeve r, because of its short

duration , this record has a narrow frequency content and is missing the

lower frequency content . Thu s, based on the onset of significant strength

degradation, this record has low severity for structures v/ith elastic

freq uenc ies less than 7.5 Hz despite the high elastic spectral accel era

tions down to 4.5 Hz.

Based on the onset of significant strength degradation, Goleta

represents a mode rate severity ground motio n for structures througho ut

the frequency range from 1.8 to 10 Hz because of its low frequency content

(similar to Parkfield in this regar d) and moderatel y high ground accelera

t i o n .

6-4

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For structures with elastic frequencies between about 1.8 and

3.5 Hz, only Pacoima Dam, Parkfiel d, El Centro # 5, and Goleta represent

moderate or severe ground motions based upon the onset of significant

strength d egra dati on. Pacoi ma Dam and El Centro #5 are in this category

because of their broad frequ enc y content (at least 0.8 to 6.7 H z ) , longer,

strong durations (greater than 3.0 s e c o n d s ) , and high ground accelerations

(greater than 0 . 5 g ) . Goleta and Parkfield are in this category despi te

their shorter durations (3.0 seconds or less) because of their predomi

nately low frequency content (essentially no frequencies above 3.0 Hz)

and yet moderately high ground acceleration (at least 0 . 3 5 g ) . To obtain

this high a ground acceler ation without fre quen cy content abov e 3.0 Hz

requir es substantial velo city content in the 1.8 to 3.5 Hz rang e.

In summary, from this study only Pacoima Dam is clearly capable

of causing very severe structural damage (possibly collapse) for struc

tures with natural fr eque nces greater than 4 Hz that have been designed

to remain elastic for the R.G. 1.60 spectrum anchored to 0.2g. This

damage ca pabili ty is due to the high acceler ation ( 1 . 1 7 g ) , longer strong

duration (6.1 s e c o n d s ) , and broad freq uency content (0.75 to 6.7 Hz)

associated with this record. Even so, this record would be expected to

resu lt in only severe damage (ductiliti es sli ghtly greater than 4.3 and

some significant strength degr adati on) for structures with frequencies

between 1.8 and 2.5 Hz when these str ucture s are designed to remain

elastic for a 0.2g R.G. 1.60 spectrum.

In addition, Parkfield might result in severe damage (ductilities

slightl y greater than 4.3 but no colla pse ) for such structures with elas

tic frequencies from 2.0 to 4.0 Hz because of its low frequency content

(approximately 1.0 to 3.0 Hz) and high acceleration ( 0 . 5 g ) . Similarly,

El Centro #5 and Melendy Ranch might result in severe damage to similarly

designed structures with frequency content above 7.5 Hz because of their

high ground acc elerat ion (0.5 g) and higher freque ncy content (up to at

least 7 Hz ) . None of the other records are capable of resulting in more

than moderat e damag e (ductil ities less than 4.3) for a 0.2g R. G. 1.60

designed structure.

6-5

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Basically , this study indicates that 0.5g short duration records

such as Parkfield and Melendy Ranch are capable of causing severe damage

(short of collapse) to 0.2g designed struct ures within a narrow fre quency

range from about 1.8 f ^ to 1.3 fy where fg is the freque ncy at which

the spectral accele ration peaks and f^ is the frequenc y at which the

spectral velocity peaks (see Table 2-5 for these freque ncie s). Outside

this narrow frequency range which lies on the stiff side of the peak

elastic spectral r espo nses , these short duration records should not result

in severe damage despite th eir ground accelerations being 2.5 times the

elastic design acceleration.

Even the above may overestimate the damage capability of these

high acceleration ground motio ns. This phase of this study has not

considered the reduced structural responses which might result from

soil-structure intera ction, wave passage effects and wave scattering

effe cts. Secondly, in this study, damage is defined in terms of the

maximum duct ility factor rather than total hysteret ic energy ab sorpti on.

The ductility descriptor of damage results in less benefit of short

duration than would a hysteretic energy descriptor of damag e. Third ly,

only single-degree- of-freedom structural resp onse is considered in the

measures of relative strength presented herein which tends to overestimatethe damage capability of narrow frequency content rec ords as compared to

broad frequency content records capable of exciting multiple frequen cies

simultaneously in multi-degree-of-freedom structures. Lastly, potential

overcapaci ty of the structure has been ignored. Genera lly, a structure

has greater capacity than indicated by the minimum design re quir emen ts.

6.3 RELA TIVE STRENGTH SUMMARY

If a structure of elastic fre quency , f, and elastic damping, e,

is designed to be at the onset of yield ing fo r spectral accele ration

S^ (f.3) which is the inelastic spectral acceleration for any grounday

motion considered, then the structure will respond to ductility level, y,

when subjected to that ground motion record . Thu s, comparing S^ (f,3)ay

for the various ground motion records considered in this study provides a

6-6

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measure of the relative strength of the records . A ground motion record

with a large S^ (f,6) requi res the struct ure to be designed at a largeay

yield level to limit respo nse to a given duct ility and is more s evere

than a record with a small S^ (f,6) which req uires the structure to be

designed at a small yield level to limit resp onse to the same duct ility

l e v e l . In this chap ter, the inelastic spectral acceleration values are

compared for the 12 ground motio n re cords co nsidere d in this study at 3

duc tili ty level s (y = 1.0, 1.85 and 4. 27) at 4 freq uenc ies (f = 8.54,

5.34, 3.20 and 2.14 Hz and one damping value (6 = 7 p e r c e n t ) ) .

Relative strength zones (i.e., very severe, sev ere, moderate and

low strengths) are defined in terms of the acceleration level for which a

structure must be designed to remain elastic using the Reg. Guide 1.60

spectrum in order to prevent seismic response exceeding ductility levels

of 4.27 when subjected to the actual earthquake ground moti on. Similar

relative strength zones for y = 1.85 and 1.0 are obtained by scaling the

zone levels for y = 4.27 . The inelastic spectral accelera tions and

relati ve strength zones are presente d in Figu res 6-la through 6-ld for

the 4 frequencies consider ed.

Based upon the data presented in Figur es 6-la through 6-ld, itis concluded that only the Pacoima Dam record is a very severe ground

motion in terms of potential damage for structures with frequencies

greater than 4 Hz. At below 4 Hz, this record is a severe ground motion

at about 3 Hz and a moder ate ground motion at about 2 Hz. At 8.5 Hz , the

Mele ndy Ranch and El Centro #5 records are in the severe categor y. At

below 4 Hz, the Parkfield record is within the severe category. All

other ground motion records fall in the low or mod era te categories at all

freq uenc ies. Note that reasons are outlined in this chapter as to why

the damage capability of high accelera tion, short duration earthquakes

such as Mele ndy Ranch and Parkf ield ma y be oversta ted by the metho ds used

to assess relative strengths of the ground mot ion .

6-7

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PD

EC S

MR

1.59* PD _- 1.27*

1.11

0.95

EC 5

MR

0.70

0.65

0.47

1.0 1.85

PD

MR

EC 5

PA 2

0 . 9 4*

0.50

0.47

0.37

y 4.27

s-

>

> >s-a>

s-

>

0)

LEGEND

A

CL

ECS

EC12

G

GC

HS

MR

0

PAZ

PD

T

Artificial (0.2g)

Coyote Lake

El Centro #5

El Centro #12

Goleta

Gavilan College

Hollywood Storage

Melendy Ranch

Olympia

Parkfield

Pacoima Dam

Taft

•Values shown are inelastic

spectral acceleration S.

for y = 1.0, 1.85, and '

4.27

ay

FIGURE 6-la.f= 8.54 Hz

MEASURE OF RELATIVE STRENGTH OF GROUND MOTION RECORDS A S DEFINED BY Sau(f,7%)

#

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y = 1.0 y = 1 . 8 5 y = 4.27

PD _

MR -

EC5 -

CLHS

G -

PA2 -

A

0

E C 1 2 _T -

GC

_ 1 . 6 7 *

- 1 . 4 9

- 1 . 1 4

_ 0 . 6 6- 0 . 6 3

- 0 . 5 8

- 0 . 5 3

_ 0 . 4 8

- 0 . 4 4

- 0 . 3 3- 0 . 3 2

- 0 . 2 0

PD _

MR

EC5 _

PA2 -

0| S

CL

T

E C 1 2 -

GC

- 1 . 2 2 *

- 0 . 7 6

- 0 . 7 1

- 0 . 4 4

E8:|§0 . 3 4 ^

- 0 . 2 6

f - 0 . 2 1

r o . i 3

PD

EC 5PA 2

0

§R

' HS

T

CL

E C 1 2

GC

4

- 0 . 9 1 *

V

V

>)

^1)

i1

c

1)

>

o

- 0 . 4 3- 0 . 4 2

a>fO

s-

_ 0 . 2 9 :m£

._

. 2 5 1- 0 . 2 0

_ 0 . 1 7

- 0 . 1 4

5

_ 0 . 0 7 - 3

LEGEND

A

CL

ECS

EC12

GGC

HS

MR

0

PA2:

PD:

T:

A r t i f i c i a l ( 0 . 2 g )

: Coyote Lake

El Centro #S

El Centro #12

Goleta

Gavi lan College

Hollywood Storage

Melendy Ranch

Olympia

P a r k f i e l d

Pacoima Dam

Taf t

*Values shown a r e inelastic

spectral accelerations Sfor y = 1.0, 1.85 and

4.27

ay

FIGURE 6-lb.f = S.34 Hz

M E A S U R E O F RELATIVE STRENGTH O F GROUND MOTION RECORDS A S DEFINED BY Sa y ( f , 7 % )

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PD - - 1.61*

ECS

P A2

G

O

H ST

E C12 --0.27

G C

0.88

0.81

0.64

.0.60

.0.55

•M i0.43•0.38

.0.12

PD

E C SP A 2

O

A

H S

5L Z ILEC12.M R •

G C

1.28*

,0.660.66

•0.46

•0.400.35

0.27'0.25.0.23•0.21"0.20

.0.07

y = 4 . 2 7

LEGEND

A:

CL:

ECS:

EC12:

G:

GC:

HS:

MR:

0:

P A 2:

PD:

T:

Artificial (0.2g)

Coyote Lake

El Centro # 5El Centro # 12

Goleta

Gavilan College

Hollywood Storage

Melendy Ranch

Olympia

Parkfield

Pacoima Dam

Taft


spectral accelerations Sfor y = 1.0, 1.85 and "^4.27

y = 1.0 p = 1.8S

f = 3.20 Hz

FIGURE 6 -lc. MEASURE O F RELATIVE STRENGTH O F GROUND MOTION RECORDS A S DEFINED BY Sa y ( f , 7 % )

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7. CONCLUSIONS

Many conclusions are reached in the individual sections as data

are presen ted. Only the more significant con clusio ns will be summarized

h e r e .

7.1 ENGINEERING CHARAC TERIZAT ION OF GROU ND MOTION

The 11 real e arthq uake ground motion time histories studied

(listed in Table 2-1) can be divided into two groups . Group 1 consists

of the 6 longer duration records (Taft, Olympia, El Centro # 12 , El Centro

# 5 , Pacoima Dam, and Hollywood Storage ) while Group 2 consists of the 5shorter duration reco rds (Coyote Lake, Parkfield Cholame #2 , Gavilan

College, Goleta, and Melendy R a n c h ) . Both elastic and inelastic struc

tural response of stiff struct ures (1.8 to 10 Hz) subjected to the Group

1 recor ds can be adequate ly approxi mated by the use of the Reg. Guide

1.60 spectrum anchored to an "ef fect ive" peak accel erati on. In fac t, it

is shown in Section 2.3 that for elastic r espon se between 1.8 and 10 Hz ,

the maximu m ratio of actual spectral acceleration to Reg. Guide 1.60

spectral acceleration (SA^/SA^ gg) ranges from 1.29 to 1.05 with a

median maximum ratio of 1.20 for the six records studied. In other

wor ds, the Reg. Guide 1.60 spectrum anchored to an "effe ctive" peak

acceleration never introduces more than a factor of 1.29 unconservatism.

The median ratio ranges from 1.05 to 0.83 with a median median of 0.88,

or a factor of (1/0.88) =1 . 1 4 conservatism. The minimum ratio ranges

from 0.76 to 0.49 with a median minimum of 0.59. Thu s, the Reg. Guide

1.60 spectrum anchored to an "effective" peak acceleration never intro

duces more than a factor of (1 /0.49) = 2.04 conservat ism for these six

rec ords . Section 5.3 shows similar results for inelastic response out to

ductility ratio of 4.3 (the highest ratio s t u d i e d ) . The maximum factor

of unconservatism never exceeded 1.32 for ductilities from 1.0 to 4.3 and

elasti c frequencies from 1.8 to 10 Hz . Withi n this same rang e, the factor

of conservatism never excee ded 2.04 and the med ian fact or of conservatism

7-1

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ranged from 1.14 for elastic r esponse (y = 1.0) to 1.01 for inelastic

response (y = 1.8 to 4. 3 ) . Considering the uncertainti es in the ground

motion , this performance is excellent.

In other words, an adequate engineering characterization for both

elastic and inelastic structural response for stiff structures (1.8 to 10

Hz ) subjected to any of the 6 longer du ration (Group 1) records is

provided by the Re g. Guide 1.60 spectrum anchored to an "eff ectiv e" peak

acce lera tion . It is shown in both Section 2.3 (elastic resp onse ) and 5.3

(inelastic respo nse) that this "effect ive" peak accelerati on, Apci, can

be defined as an rms-ba sed acceleratio n given by Equation 2 -15. It can

be seen from Equation 2-15 that the "effective" acceleration increases

with increasing strong motion duration, T Q , and increasing mean (central)

frequency, n'. In addition, the rms acceleration, a^.^^, used to define

'^DEl ^^ heavily influenced by the method used to define the strong

motion duratio n, Tp (see Section 1.1.1 for a further di sc us si o n ) .

T h u s , to establish an "effective" a ccelera tion, one must define a method

to quantify Tp and one must define a central f req uen cy, Q'. The

central fre quen cies computed for each of the 11 real records and for an

artificial R eg. Guide 1.60 time history are given in Table 2-6. The

central freq uency for the six Group 1 (longer d uratio n) records plus theartificial record ranges from 3.6 to 4.7 Hz. For all of these reco rds,

this central fre quency can be approximated as 4.0 Hz without introducing

more than a 6% error in the computed "effect ive" peak accelerat ion.

Section 2.1 recommends that the strong motion duration, Tp,

for stiff structures be computed from Equations 2-2 and 2-3 using cumula

tive energy plots (Figure 2- 3) . It is shown that this duration corres

ponds to the time of steepest slope ( i.e., greates t power and greates tRMS acceler ation) from these energy plo ts. It is also shown that Tp

correla tes well with the longest time to reach maxi mum structural respo nse

(both for elastic and inelastic resp onse) for stiff structures (1.8 to 10

H z ) . The strong motion durati ons, Tp, given by Equations 2-2 and 2-3

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are tabulated in Table 2-3 for the 11 real and one artificial record

studi ed. It should be noted that Equati ons 2-2 and 2-3 often lead to

much shorter estimates of strong duration than do other commonly used

metho ds. However , it is recommended that the short durations given by

Equation s 2-2 and 2-3 correlate better with the longest time of maximu m

respons e for stiff structures and with the duration of maximum rms accel

erat ion . The strong duration for the six Group 1 records range from 15.6

seconds (Olympia) to 3.4 seconds (El Centro #5 ) . The strong duration for

the five Group 2 records range from 3.0 seconds (Goleta) to 0.8 seconds

(Melendy R a n c h ) . Increasing str ong duration from 3.4 seconds to 15.6

seconds increases th e "effec tive " peak acceler ation by a factor of 1.50

given identical rms acceleration s. Ther efor e, strong duration has a

moderately significant influence on the "effective" peak acceleration and

must be reasonably app roximated.

The previous concl usion that the Re g. Guide 1.60 spectrum

anchored to an "effective" acceleration provides an adequate characteriza

tion of both elastic and inelastic structural response for stiff struc

tures (1.8 to 10 Hz ) is not applicable to the five Group 2 records.

Neither ela stic nor inelastic r espon se from any of these five records can

be adequately approx imated by th e Reg. Guide 1.60 spectrum or by any

other broad frequency content spectrum. T h u s , one must define the

distinguishing differences between the Group 1 and Group 2 record s. The

most obvious differences are :

1. Strong dur ati on, Tp . All the Group 1 recor ds have strongdurations of 3.4 seconds and greater while all the Group 2records have durations of 3.0 seconds and less.

2. Local magnit ude. M L . All the Group 1 records are from

earthquake s with local magnitud es of 6.4 and greater whileall the Group 2 reco rds are from eart hquakes w ith local

magnitudes of 5.7 and less.

However, these differences do not appear to be the primary

reason why the Reg. Guide 1.60 spectrum is inadequate for predicting the

response of stiff structures. The primary reason is related to differ-

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ences in the breadth of the range of freque ncy co ntent. This breadth of

the range of freq uenc y content can be defined by the frequency ran ge from

f^O to fgo where 10% of the cumulative power lies at frequencies below

f]^0 and 90 % of the cumula tive power lies at freq uenc ies below fg Q.

T h u s , the frequency range from f^Q to fgo contains the central 80 % of

the cumulative power of the strong motion portion (Tp duratio n) of the

rec ord . Table 2-6 defin es the frequenc y range from f^^Q to fgo for

the 11 real records and one artificial record studied. The six Group 1

records for which the Reg. Guide 1.60 spectrum provides an adequate

engineering charact erization from 1.8 to 10 Hz all have frequency bands

(f]^0 t° fgo) ^^^'"^ ^* least 1.2 to 5.5 Hz . None of the five Group 2

records for which the Reg. Guide 1.60 spectrimi does not provide an

adequate engineering characterization cover the entire frequency band

from 1.2 to 5.5 Hz . Coyote Lake , Gavilan Co lleg e, and Melendy Ranch are

missing frequency content below about 3 Hz . Goleta and Par kfield-Ch olame

#2 are missing fr equency content above about 3 Hz . This missing frequency

content and resultant narrow-banded response spectra has a strong in

fluence on both elastic and inelastic structural response even for these

stiff structures.

The conclu sion is that the Reg . Guide 1.60 spectrum or other

broad frequency content spectra anchored to an "effective" acceleration

should only be used even for stiff str ucture s (1.8 to 10 Hz) to char ac

terize ground motion records which contain significant power between at

least 1.2 to 5.5 Hz as defined by the range from f^Q to fgn . Recor ds

which do not contain significant power throughout this frequency range

should be characterized by narrower frequency design spectra .

The standard practi ce of averaging a number of real recor ds

together irrespective of their relative frequency content to produce a

design spectrum will always lead to a broad freq uenc y content de sign

spectr um even when all the individual reco rds are narrow bande d. For

instance , averaging the five Group 2 spectra will lead to an average

spectrum which contains frequency content from at least 1.3 to 7 Hz .

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Such a spectrum will be narrower than the Re g. Guide 1.60 spectrum which

contains f requen cy content from 0.6 to 6.4 H z , but for stiff structures

(1.8 to 10 Hz) the differences will be mino^-. These differen ces wou ld

only be significant for structures with freq uenci es less than 1.8 Hz .T h u s , a design spectr um obtained by averaging the five Group 2 spectra

would not provide an adequate engineering characterization for either

elastic or inelastic response of stiff structu res subjected to any one of

these five record s. The only adequate way to characterize these records

is by a narrow-banded design spectrum obtained by averaging records with

similar central freq uen cie s, ^', and frequency bands, fng to fgn . For

inst ance , Parkfield Cholame #2 and Goleta can be averaged to obtain a

narrow-banded, low-frequency spectrum representative of either record.

Possibly , Melendy R anch , Gavilan Coll ege, and Coyote Lake could be

averaged to obtain a representative high frequency spectrum. Uncertain

ties in central f requ ency, i', hould be covered by shifting the central

frequenc y of a narrow-banded design spectrum throughou t the range of

uncertainty and not by the use of a broad freque ncy content design

spectrum for stiff structures subjected to Group 2 type record s.

A strong correlatio n appears to exist between local magnit ude

and strong dura tion, Tp , for records with instrumental acceleratio ns, a,

of 0.14g and gre ate r. Reco rds with M _ of 5.7 and less and values of a

of O . H g a n d greater all had Tp of 3.0 seconds and less. Conversel y,

the rec ords with M|_ of 6.4 and greater all had Tp greater than 3.0

secon ds. It appears that earthquakes with M, less than about 6.0 ma y

not have sufficient energy content to be capable of producing both high

accelerations (greater than 0.14g) and longer dur ation s (Tp > 3.0

seconds). Sec ond ly, a strong correlation exists between Tp and the

breadth of the frequency band of significant power . None of the records

with Tp < 3.0 seconds had significant power throu ghout the freque ncy

range from 1.2 to 5.5 Hz whil e all of the recor ds with Tp > 3.0 seconds

contained power throughout this frequency ra nge. A tentative conclusion

woul d be that the design respo nse spect rum for ear thqu akes with M|_ < 6.0

and ground ac celerations of 0.14g and greater should be a narrow-banded

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spectrum obtained by averaging only records with similar central

fr eq ue nci es , f^', and similar freq uenc y ban ds, f^^Q to fgn. This

conclusion would have wide ranging effects since the SSE design earth

quake for nuclear plants east of the Rocky Mountains would generally

correspond to these condit ions . The conclusion is only tentative because

not enough records were stud ied.

7.2 PREDICTION OF INELASTIC SPECTRAL DEAMPLIFI CATION FACTORS AND

INELASTIC RESPONSE SPECTRA

A represent ative nonlinear lateral force-def ormation resistance

function for shear wall type structures was presented in Chapter 3. In

each an alys is, the yield cap acity of this model was set equal to the

capacity associated with the elastic spectral acceleration at the

structur e's elastic natural frequency for each earthq uake record. Th us ,

the structure was at the onset of yielding (ductility, y, of unity) when

subjected to the ground motion record. Next, a series of nonlinear time

history analyses were performed in which the record time history had

ampli tudes scaled up by an input scale fac tor , F. For a given F, the

maximum resultant ductili ty, y, was determined. By this me an s, the input

scale fact ors , F, corresponding to a low ductil ity (v. = 1.85) and a

high ductility (y^ = 4.27) were de termine d. Table 4-1 presents these

input scale factors for the 12 records studied at four natural

frequenci es between 1.8 and 10 Hz . The low ductility is intended to

correspond to minor i nelastic behavior while the high ductili ty

corresp onds to a conservative estimate of the onset of significant

strength degradation.

It should be noted that these input scale factors, F, are equal

to the inelastic spectral deamplificatio n factor by which the elastic

spectral acceler ation must be divided to obtain an inelast ic spectral

accele ratio n. If the structure were designed to have a yield capacit y

corresponding to this inelastic spectral acceleration at the elastic

natural freque ncy, then the structure would undergo a ductilit y, y, when

subjected to the actual recorded time history. As illustrated in Figure

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3-4, a shear wall elastically designed to ACI -349 code ultimate capac

ities for static lateral loads is permitted some inelastic deformation.

Input scale factors or inelastic spectral deampli fication factors are

based on the yield capacity which is less than the code ultimate cap acity .

It was found that these input scal e factors (inelastic spectral

deamplification fact ors ) were not constant for a given ductility factor , v.

The F factors w ere hea vily influenced by the ratio of spectral accele ra

tions on the soft (lower freque ncy) side of the elastic frequency to the

spectral accelerations at the elastic frequenc y. When the spectral accel

erations on the lower frequ ency side were much less than the spectral

acceleration at the elastic frequ ency, F was high . Conversel y, when these

lower frequency spectral accelerations were much higher than the elastic

frequency spectral acceler ations , F was low. This effect can be con

sidered to be either a spectral averaging ef fect or can be considered to

be an effective frequency shift to lower frequ encie s. For simplicity, it

will be called a spectral averagin g effe ct. This effect is discussed in

more detail in Sectio n 4.1.3.

This spectral averaging effe ct was by far the most substantial

factor influencing the computed F fact ors. For the broad frequency

content Group 1 reco rds {Jj^ > 3.0 seconds), the F factors were fairly

uniform and showed a gradual increase as frequ encie s were reduc ed. On

the other hand , the F factors for the narrow frequency Group 2 records

( T Q < 3.0 se cond s) were far from uniform. T h u s , for the short duration

records, th e F factor could be either very large or could be low depending

upon where the structure's elastic frequency lay relative to the frequency

of maximum spectral acceleration. Except within a narrow frequency band,

the F factors fo r thes e short duration records are greater than for the

longer duration recor ds. Howe ver, within this narrow frequency ban d, the

F factors for the short duration records are about equal to or may be

slightly less than those for the longer duration records . Figure 4-1

shows this increase in scatter for F as TA is reduced.

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In addition to the spectral averaging ef fec t, a smaller duration

effect was also noted. The predomi nant duration effect is accounted for

by the spectral av eragi ng. The lesser duration effect is related to the

number of strong nonlinear response c ycl es. It is clear that the number

of strong nonlinear response cycles inceases with duration and ranges

from 1 for Melendy Ranch (Tp =0 . 8 seconds ) to 4 for Olympia (Tp =

15.6 s e c o n d s ) . Other than for Olympia and Melendy Ran ch, the records

generally showed 2 or 3 strong nonlinear response cycles . In every case,

the total number of strong nonlinear response cycles was low (4 or l e s s ) .

On the aver age, the duration effect on the F factors was small once the

spectral averaging effect was accounted for.

One effect of increasing the number of strong nonlinear response

cycles from 1 to 4 was to reduce the effective structural natural fre

quency toward the secant frequenc y and away from the elastic fr eque ncy.

With one strong nonlinear cycl e, the effective frequency lay about midway

between the secant and the elastic frequenc ies. With more nonlinear

response cyc les, the effective frequency more closely approached the

secant fre quency. However, the effective frequency was never as low as

the secant frequen cy. A second effect was to reduce the effective damping

percentage with increasing numbers of nonlinear cycles for the shear wallresistance function s. The technical basis for this reduced damping is

described in Appendi x C. Both the freque ncy shift and effective damping

reduction we re most not iceabl e when increasing the number of strong

nonlinear cycles from 1 to 2. These effects were much smaller when

increasing the number of strong nonlinear cycles from 2 to 4 (see Table

4 - 3 ) . Thus , within about 1 0% accuracy on the predicted F fact or, one

could assume 3 strong nonlinear response cycles when evalua ting th e

effective frequency and effective damping except when Tp is less than

one second in which cas e, one should assume 1 strong nonl inear respo nse

cycle . There fore, other than for the spectral averaging e ffect, it is

really only necessary to estimate whether Tp is greater or less than

one second for predicting the inelastic spectral deamplification factor,

F^. The effect of Tp and the number of strong nonlinear resp onse

c y c l e s , N, on the F factor is shown for the Reg. Guide 1.60 spectrum in

Figures 5-1 and 5-2.

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It was found that the inelastic structural response of singl e-

degree-of-freedom structural mod els , the inelastic spectral deamplifica-

tion factor (F ) , and the inelastic spectral acceleration (Sg^) could all

be accurate ly predicted from char acteri stics of the moderate ly damped (7

to 15% damp ing) elastic r esponse spectrum and an approximate knowledge of

Tp . Either of two meth ods could be used.

1. The nonlinear resistance function model can be replaced by

an equivalent linear resistance functio n with a lesser

effective frequency (lesser effective stiffness) and

increased effective damping than the elastic frequency

(elastic stiffnes s) and elastic damping. This equival ent

linear model is then used with the elastic respo nse

spectrum to compute maximum displacement response s,

2 . The elastic res ponse spectrum is reduced to obtain an

inelastic response spectrum for use with the elastic

frequ ency and damping in order to compute the yield

displac ement, *y , and required yield capaci ty, Vy, needed

to hold the structure to a duct ilit y, y. At a given

frequency and damping v alue , the inelastic spectral accel

eration is given b y:

S j f , 3 )

Say(f'^) = ^ (7-1)

y

whe re F^ is the predicted inelast ic spectral deamplificationfactor.

In the first method, and effective fre quency, f' and an

effective damping ratio , 3^, must be estimated. It is recommended that

Equations 3-8 and 4-2 be used together with coefficients fr om Table 4-2

to make these esti mate s. This effective frequenc y and effective damping

estimate can also be used together with the elastic r esponse spectra to

predict F by Equation 3-14 for use in the second meth od. This approach

for predictin g F is called a point estima te approach since it is based

upon a single point estimate of fg, and Bg. When this point esti

mate approach is used to predict F^, the first and second approxim ate

nonlinear analysis methods described above produce identical results.

The ref ore , further comparisons can be made based upon the accuracy with

which F is predicted compared to the time history computed F fac tor s.

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It was found that the recommen ded point estimat e approa ch (based

on an estimat ed f^ and 3g) provided an excellent estim ate of F^^. The

ratio of predicted to time history computed scale facto rs (F /F) are shown

in Table 4-4 to have mean values of 0.98 and 1.02 and coefficients of

vari atio ns (COV) of only 0.12 and 0.09 for ducti lit y levels of u^ = 4.27

and \i^ = 1.85, resp ecti vely. At the worst ext reme s, the ratio F^/F

ranged from 0.75 to 1.29 for y^ and from 0.85 to 1.26 for \ .

Other methods also exist for predicting an effective fr equency

fg , and an effective damping rat io, 3g. Two common metho ds defined

as the Sozen method and the Iwan method are described in Section 3.3.1.

These methods were not developed for shear wall type resistance functions

but were used in this study for comparison with the recommended methodfor predicting an effective frequency and an effective dampin g. Table 4-3

compares the effectiv e freque ncies and effective damping percenta ges

predicted by the three me tho ds . One should note that the Sozen method

predicts lower effective frequen cies while the Iwan method predicts

higher effective frequencies than does the recommended method . In other

wo rd s, the Sozen method softens the structure more while the Iwan method

softens the structure less than the method recommended by this study .

Both the Sozen and the Iwan meth ods predict substa ntiall y higher effective

damping percentages than the method recommended by this study for shear

wall res istance func tio ns. The reasons for this difference are given in

Section 4.3. Tables 4-5 and 4-6 compare the predicted to computed scale

factor s (F /F) when the effective frequ encies and effective damping are

computed by the Sozen and Iwan met hod s, resp ecti vely . The Sozen method

introduces a slight conse rvative bias while the Iwan method introduces a

significant u nconservative bias for the mean ratios . Both methods result

in substan tially higher COV than the recommended meth od. The conclusion

is that the recommended proced ure p rovide s a better estim ate of the

effective frequency and effective damping for shear wall type structures

than does either the Sozen or Iwan methods.

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It was judged that a spectral a veragi ng approach should provide

a better estimate of F than the best point estimate approach . Spectral

avera ging smooths out local peaks and valle ys in the response spectru m

and is expected to be more stable. The ref ore , a number of spectral

averaging approaches to estimate F were also investigated. A simple

approach given by Equations 4-3 through 4-7 together with Table 4-2 is

recomm ended. This approach averages the spectral accelerations between

f^j and the secant fre que nc y, f^, whe re f^ lies between the elas tic and

secant freque ncies as shown in Table 4-7. The ratios of predicted to

computed scale factors (F /F) as obtained by this spectral averaging

approach are shown in Table 4-8. One should note that the spectral

averaging approach provides only marginal improvement over the recom

mended point estimate approach (Table 4 - 4 ) . It is not clear that thismarginal improvement is worth the consid erable increase in computational

effort requir ed. Howe ver, if the elastic response spectrum contains

significant local peaks and valleys at about 10 % dampin g, the spectral

averaging approach would be expected to provide some improvement over the

point estimate approa ch. The data indicates that the spectral averaging

approach does reduce the maximum factor of unconserva tism (maximum ratio

of F / F ) . This maximum ratio of F /F is 1.29 for the point estimate

y y ^

approach and only 1.19 for the spectral avera ging approach at yj, = 4.2 7,

and is lowered from 1.26 to 1.14 for y. = I.35.

Other commonly used approache s for estimating F^ are the Newmark

method and the Riddell method described in Section 3.3.2. These method s

give similar results for F with the Riddell method being a slight

improvement over the Newmark method . Table 4-9 shows the predicted to

computed scale facto rs (F /F) when the Riddell method is used. One should

note that for the shear wall res istan ce fu ncti on model used in this stu dy,

the Riddell method introduces a slight factor of unconservatism on the

averag e. Furt hermo re, the COVs range from 14 0% to 200% larger than those

obtained for the spectral averaging approach recommended in this study

(Table 4 - 8 ) . For y^ = 4.27 , the extre me range of (F /F) ranges from

0.43 to 1.78 for the Riddell approach as compared to a range of 0.75 to

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1.19 for the recom mende d spectral aver agin g me th od . At y|_ = 1.8 5, the

extr eme ra nge for the Riddell meth od is not as severe but still ranges

from 0.88 to 1.47 as compared to 0.85 to 1.14 for the recommended spectral

averaging method.

It is concluded that either the point es timat e approach or the

spectral averaging approach rec ommended in this study provide excell ent

predi ctions for F out to ducti liti es of at least 4.3. Either approach

provides significantly more accurate estimates for F^ than do other

commonly used approaches for shear wall type resistance fun ctio ns. It

should be noted that F fact ors presented in this report are not intended

to be specifically used for the design of fac ilit ies . These factors have

been evaluated on the basis of a limited number of ground motion records

and at a limited number of structural fr equenc ies and ductili ty lev els .

Instead, the purpose of this work is to present the methodol ogy by which

inelastic spectral deamplification factors may be developed such that

permissible levels of inelastic deformation may be incorporated into

designs using simplified elastic analytical tech nique s.

Although this study was predominantly concerned with shear wall

resistance fun ctio ns, other inelastic resistance fu nctions and the

influence of various parameter variations were also studied and the

results are summarized in Appendix D. The basic conclusion of these

parameter variation studies was that the approaches recommended in this

study can be conse rvat ively used for braced-f rames and other structural

or equipme nt systems so long as thes e systems do not have re sist ance -

deformation functions which show greater stiffness degradation and

pinching behavior than that used in this study for shear wal ls. The

authors do not know of any other structural system used in nuclear power

plants which would have more severe stiffness degradation or pinching

behavi or and so they genera lly believe that the recommended approaches

from this study could be cons erva tive ly applied to all structural and

equipm ent systems in a nuclear power plant. Some other conclusio ns of

these parametric studies are:

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1. Equation 4-6 can be used to esti mate the average effective

damping equally well for an elastic damping of 3% as for an

elastic damping of 1%. The prediction procedure works

equally well at 3% elastic damping as at 7% elastic d amping.

2 . The frequency shift and hysteretic damping coefficie nt, Cpand Cfj, in Tabl e 4-2 were developed for a shear wall

resistance function mo de l. Use of these coefficients willintroduce only a slight conservatism for the Takeda mod el.

The shear wall model overes timates the stiffness degradationand pinching behavior for braced-frame and bilinear resistance function mod els . There fore, these coefficients over

emph asiz e the importance of N and T[) for such mo de ls .

The input scale factor (inelastic spectral deamplification

fac tor ) for the braced-fra me and bilinear resistance

function models studied in Appendix D lay midway between

the sc ale fac tors predicted using the Cp and Cfj given

in Tabl e 4-2 for the appropriate T Q and the scale factorpred icte d usin g Cp = 1.5 and Cfj = 0.30 wh ich are given

for N=l . Averagi ng the results obtained from the use of

these two d ifferent sets of Cp and C M values will

improve the prediction accuracy for braced-frame and

bilinear mod els when T Q is greater than 1.0 seconds and

thus will reduc e the conserv atism introduced by the

recommended approach for these mod els .

Figures 5-3 through 5-13 present the inelastic spectra predicted

with in the fre quen cy r ange fro m 1.0 to 10.0 Hz for the 11 real time

histor ies included in this study using the spectral averaging prediction

meth ods of Chapter 4 and duct ilit ies of 1.85 and 4.27 . Several points

should be noted from these figu res:

1. The peak inela stic spectral accelerat ions always occur at

frequencies higher than those at which the peak elasticspectral accelerations occur. This situation occurs

because inelastic response of these higher frequencystructures shifts the effective frequenc y downward into the

range of peak elastic respon se.

2 . The inelastic deamplification factors associated with

frequenc ies equal to or less than that at which the elastic

spectrum peaks are much greater than those for higher

frequencies.

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These points are most dramatically illustrated by the Parkfield-

Cholame Array #2 spectra (Figure 5 - 1 1 ) . The elastic spectral amplifica

tions are very high from 1.2 to 3.0 Hz and drop off very rapidly at both

higher and lower fre que nci es. The largest inelasti c deamplification

factors are associated with elastic frequencies less than 3.0 Hz since

inelastic respon se will shift these frequenci es lower and marke dly reduce

resp ons e. Struc tures with frequ encie s of 3.0 Hz and less could be

designed to yield at spectral acce leration s much less than those indicated

by the elastic spectra for Parkfield without severe damag e. However , for

the Parkfield reco rd, one must be very careful not to reduce the elast ic

spectral accele ratio ns for structu res in about the 3.5 to 5.0 Hz ran ge.

These str uctures should be designed to remain elas tic for the Parkfield

record. Inelastic response of such structures will shift their effective

freque ncies into the frequency ran ge (1.2 to 3.0 Hz) with in which the

power of the input is predominantly conc entrated. For such struct ures,

inelastic responses would rapidly increase because of this frequency

shift. For records with narrow frequency co ntent , such as Parkfield, one

should be very careful about taking any credit for inelastic response for

structures whi ch lie slightly to the stiff side of the p redominant

freq uency range of the rec ord. On the other hand, for even stiffer

structures (elastic frequencies greater than 5.0 Hz) the inelastic

deamplification factors are again significant although not as large as

for structures with frequencies below 3.0 Hz .

This study is concerned with the inelastic response of

structural systems (braced frames and shear walls) and the concept of

"effective" spectral response is considered valid for such system s. The

results of this study can also probably be extrapo lated to ductile

passive equipment w hose fragil ity is governed by structural failure

m o d e s . Howeve r, the study is probably not appropriat e for activeequipment.

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This study was conducted using single-degree-of-freedom (SDOF)

str uc tu ra l models. I t is bel ieved that the res ul ts should also be a p p l i

cable f o r m ul ti-d eg re e- of -fre ed om (MDOF) models. However, when used w ith

MDOF mo dels, one must keep in mind these re s u lt s are to be used w it h a

system d u c t i l i t y . In the case of loc al iz ed nonl inear behavior , the story

d r i f t d u c t i l i t y is o f ten about tw ice the system d u c t i l i t y and e lement

d u c t i l i t y w i l l exceed s to ry d r i f t d u c t i l i t y . Thus, i f one needs a

sp ec i f ic c on trol on ei th er element or s t o r y d r i f t duc t i l i t y , t he s y s t em

d u c t i l i t y must be he ld to lesser l im i t s . Th is top ic w i l l be d iscussed

fu rt h e r in a fo llo w -o n study which extends the SDOF re s u lt s to MDOF

models.

7.3 MEASURE OF RELATIVE STRENGTH OF GROUND MOTION RECORDS

I f a st ru ctu re of el a st ic f reque ncy, f , and el a st ic damping, S,

is designed to be at the onset of y ie ld in g fo r s pe ctral ac cele rat io n

Sg ( f ,3 ) which is the in e la st ic s pec tral ac cele rat ion for any ground

mot ion cons idered, then the s t ruc ture wi l l respond to duct i l i t y leve l , y ,

when sub jected to th a t ground motion rec o rd . Thus, comparing Sg^ (f, P )

for the various ground motion records considered in this study provides a

measure of the re la t i v e stre ng th of the rec ord s. A ground motion record

w ith a large S^^ (f ,3 ) req uire s the str uc tu re to be designed at a largey ie ld level to l im it response to a given du c t i l i t y and is more severe

than a record with a small S^^ (f ,S ) which requ ires the s tru ctu re to be

designed at a small y ie ld lev el to l im it response to the same d u c t i l i t y

l e v e l . In Chapter 6, the inelast ic spectral accelerat ion values are

compared fo r the 12 ground motion records considered in th is study at 3

d u c t i l i t y lev els (y = 1 .0, 1.S5 and 4.27) at 4 f requencies ( f = 8.54,

5.34 , 3.20 and 2.14 Hz and one damping value ( 3 = 7 p e rc e n t) ).

Relat ive strength zones ( i . e . , very severe, severe, moderate and

low streng ths) are def ined in terms of the a cce lera t ion lev el f o r which a

structure must be designed to remain elastic using the Reg. Guide 1.60

spectrum in order to prevent seismic response exceeding duct i l i ty levels

of 4.27 when subjected t o the actua l earthquake ground m otio n. Sim ilar

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rel ativ e s trengt h z ones for y = 1.85 and 1.0 are obtained by scalin g the

zone levels for y = 4.27. The inelastic spectral ac celerations and

relative strength zones are presented in Figure s 6-la through 6-ld for

the 4 frequencies considered.

Based upon the data presented in Figu res 6-la through 6-ld, it

is concluded that on ly the Pac oima Dam record is a very severe ground

motion in terms of potential damage for structures with frequenci es

greater than 4 Hz . At below 4 Hz , this record is a severe ground motion

at about 3 Hz and a moder ate ground motion at about 2 Hz . At 8.5 H z , the

Melen dy Ranch and El Centro #5 records are in the severe categ ory. At

below 4 Hz , the Parkfield record is within the severe categor y. All

other ground motion records fall in the low or mode rate categories at all

fre que nci es. Note that reasons are outlined in Chapter 6 as to why the

damage capability of high accelera tion, short duration earthquakes such

as Melendy Ranch and Parkfie ld may be overstated by the methods used to

assess relative strengths of the ground mot ion .

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8. REFERENCES

Alexander, C. M., Heiderbrecht, A. C , and Ts o, W. K. ( 1 9 7 3 ) , "Cyclic LoadTests on Shear Wall Pan els ", Proceedings of the Fifth World

Conference on Earthquake Engine ering, Ro me, pp. 1116-1119.

A r i a s , A . ( 1 9 7 0 ) , "A Measure of Earthquake Intensity", Seismic Design for

Nuclear Power Plant s, MIT Pres s, Cambridge, Massachusetts.

Banon, H., Bi ggs , J. M., and Irvine , H. M. ( 1 9 8 1 ) , "Seismic Damage in

Reinforced Concrete Frame s", Journal Structural Division, ASC E, Vol.1 0 7 , ST 9, pp . 1713-1729, Septem ber.

Barda, F., Hanson, J. M., and Corley, W. G. ( 1 9 7 6 ) , "Shear Strength of

Low-Rise Walls with Boundar y Ele ment s", Proceedings of the SixthWorld Conference on Earthquake Engineer ing, New Delhi.

Bertero, V. V., et. al. , ( 1 9 7 7 ) , "Seismic Design Implications of

Hysteretic Behavior of R/C Structural W al ls" , Proceedings of the

Sixth World Conference on Earthquake Engineering , New Delh i.

Blume, J. A., ( 1 9 7 9 ) , "On Instrumental versus Effective Acceleration andDesign Coeff icien ts", Proceedings of the Second U .S. NationalConference on Earthquake Engineeri ng", Stanford, Califo rnia, Augus t.

Cardenas, A. E. , Hanson, J. M. Corley, W. G., and Hognestad, E. ( 1 9 7 3 ) ,

"Design Provisions for Shear W all s", ACI Journal, Proc. Vol. 70 ,

N o . 3, pp. 221-230, March .

Dobry, R., Idriss, I. M., Ng , E. ( 1 9 7 8 ) , "Duration Characteristics of

Horizontal Components of Strong-Motion Earthquake Recor ds", Bulletin

°^ ^!?^-^^J^'?9^°g^^^.^ Soc iet y o f A me ri ca , Vo l. 6 8 , No . 5 ,p p . 1487-1520, Octob er.

Fiorato, A. E . and Corley, W. G. ( 1 9 7 7 ) , "Laboratory Tests of Earthquake-Resistant Structural Wall Systems and E lemen ts", Workshop onEarthquake-Resistant Reinforced Concrete Building Construction,University of California, Berkeley, pp. 1388-1429, July.

Fukada, Y., Hirashima, S. and Shobara, R. ( 1 9 8 1 ) , "Experimental Study on

One-Thirtieth Scale Model of Reinforced Concrete Reactor Build-UnderCyclic Lateral Loadi ng", Tran s. Sixth International Conference of

Structural Mechanics in Reactor Tec hnolog y, Volume K, paper K15/1,

August.

Gugerli, H. and Goe l, S. C. ( 1 9 8 0 ) , "Large Scale Tests for the HysteresisBehavior of Inclined Bracing Memb ers ", Proceedings of the SeventhWorld Conference on Earthquake Engineering , Istanbul, pp . 87-94.

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REFERENCES (Continued)

Gulkan, P. and Sozen, M. A. ( 1 9 7 4 ) , "Inelastic Responses of ReinforcedConcrete Structures to Earthquake Moti ons" , ACI Journal, Vol. 71,N o . 12, pp. 604-610, December.

Hoffman, R. B. ( 1 9 7 4 ) , "State-of-the-Art for Assessing Earthquake Hazardsin the United Stat es; Factors in the Sp ecification of Ground Mo tionsfor Design Earthquakes in California", Miscellaneous Paper S-63-1,U . S . Army Engineers Waterways Experiment Station, Vicksburg,M i s s i s s i p p i , J u n e .

Housner, G. W. ( 1 9 5 2 ) , "Spectrum Intensities of Strong-Motion Earthq u a k e s " , Proceedings of the Symposium on Earthquake and Blast Effec tson Struct ures", Earthquake Engineering Research Institute, Los

Angeles, California, June.

Housner, G. W. ( 1 9 7 5 ) , "Measures of Severity of Earthquake Ground

Shaki ng", Proceedings of the U. S. National Conference on Ear thquakeEngineering, EER I, Ann Arbor, Michigan, pp . 25-33., June.

Housner, G. W., and Je nnings, P. C. ( 1 9 7 7 ) , "Earthquake Design Criteriafor Struc tures", Report No. EERL 77-06, EERL, California Instituteof Technology, Pasadena, November.

Housner, G. W. ( 1 9 7 9 ) , "Statistics of Pulses on Strong Motion Accelerog r a m s " , Proceedings of the NSF Seminar Workshop on Strong Ground

M o t i o n .

H u d s o n, D . E . ( 1 9 7 9 ) , Reading and Interpreting Strong Motion Accel erograms , EERI Monograph, EERI, Berkeley.

Husid, R. ( 1 9 7 3 ) , Terremotos-Earthquakes, Editorial Andres Bello,Santiago, Chile.

Iwan, W. D . and Gate s, N. C. ( 1 9 7 9 ) , "Estimating Earthquake Response ofSimple Hysteretic S ystem s", Journal of the Engineering Mec hanicsD i v i s io n , A S C E , V o l . 1 0 5 , N o . E M 3 , p p . 3 9 1 - 4 0 5 , J u n e .

Iwan, W. D. ( 1 9 8 0 ) , "Estimating Inela stic Response Spectra from Elast ic

Spectra", Earthquake Engineering & Structural Dynamics, Vol. 8, pp.375-399.

Jain, A. K. and Goel , S. C. ( 1 9 7 8 a ) , "Hysteresis Models for Steel MembersSubjected to Cyclic Buckling or Cyclic End Moments and Buckling(User's Guide for Drain - 2D: EL9 and E L I O ) " , Report No. UMEE 78R 6,Department of Civil Engi neers, University of Michigan, December.

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Jain, A. K., G oel , S. C. and Hanson, R. D. (1978b ) , "Inelastic Responseof Restrained Steel Tub es" , Journal of Structural Division, ASCE ,S T 6 , Vol. 104, pp. 897-910, June.

Jain, A. K. and Goel, S. C. ( 1 9 7 9 ) , "Cyclic End Moments and Buckling inSteel Members", Proceedi ngs of the Second U .S . National Conferenceon Earthquake Engineerin g, Stanford, pp. 413- 422.

Jain, A. K., Goel, S. C. and Hanson, R. D. ( 1 9 8 0 ) , "Hysteretic Cycles ofAxially Loaded Steel Mem bers ", Journal Structural Di vision, ASCE ,S T 8 , Vol . 106, pp. 1777-1795, August.

Jennings, P. C. and Housner, G. W. ( 1 9 7 7 ) , "The Capacity of ExtremeEarthquake Motions to Damage Struc tures ", Structural and GeotechnicalMechanics, Prentice-Hall, Englewood Cliffs, New Jersey, pp. 102-116.

Kanaan , A. E. and Powel l, G. H. (1973, 1 9 7 5 ) , "DRAIN- 2D, General PurposeComputer Program for the Dynamic Analysis of Inelastic PlaneStruct ures", EERC Report No . 73- 6, Earthquake Engineering ResearchCenter, University of California, Berkeley, April, 1973 (Revised1 9 7 5 ) .

Kennedy, R. P. ( 1 9 8 0 ) , "Ground Motion Parameters Useful in StructuralDesign", presented at Conference on Evaluation of Regional SeismicHazards and Risk , Santa Fe , New Mexico, Octo ber.

Kenned y, R. P.\, Short, S. A. and Newmar k, N . M. ( 1 9 8 1 a ) , "The Response ofa Nuclear Power Plant to Near-Field Moderate Magni tude Earthquakes",Sixth International Confer ence on Structural Mechani cs in ReactorTechnology, Paris, France, August 17-21.

Kennedy, R. P. ( 1 9 8 1 b ) , "Peak Acceleration as a Measure of Dama ge",

presented at Fourth In ternational Seminar on Extreme- Load Design ofNuclear Power Facil ities , Paris, France, August.

Mahin, S. A. and Bertero, V. V., "An Evaluation of Inelastic SeismicDesign Spectra", Journal Structural Division, ASCE, Vol. 107, ST9,

p p . 1777-1795, September.

Maison, B. F. and Popov, E. P. ( 1 9 8 0 ) , "Cyclic Response Prediction forBraced Steel Fr ames ", Journal Structural Division , ASC E, Vol 106,S T 7 , pp. 1401-1416, July.

McCann, M. W., J r. and Sh ah, H. C. ( 1 9 7 9 ) , "RMS Accele ration for SeismicRisk Analys is: An Overview" , Proceedings of the Second U .S . NationalConference on Earthquake Engineerin g, Stanford Un iversit y,p p . 883-897 , August 2 2 - 2 4 .

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Mortgat, C. P. ( 1 9 7 9 ) , "A Probabilistic Definition of Effective

Acce lera tion ", Proceedings of the Second U. S. National Conference onEarthquake Engineering, Stanford University, pp. 743-752,August 22-24,

Newmark, N. M. ( 1 9 7 0 ) , "Current Trends in the Seismic Analysis and Designof High Rise Structur es, Chapter 16, in Earthquake Engineering,edited by R. Wiegel, Prentice-Hall, Inc., Englewood Cliffs, NewJersey, pp. 403-424.

Newmark, N. M. ( 1 9 7 3 a ) , "A Study of Vertical and Horizontal Earthqu akeSpectra", WASH-1255, Directorate of Licensing, U. S. AEC, Washing ton.

Newmark, N. M. and Hall , W. J., ( 1 9 7 3 b ) , "Procedures and Criteria forEarthquake Resistant Design", Building Practices for DisasterMitigation, National Bureau of Standards (Washington, D . C . ) ,

Building Sciences Series 46 , Vol. 1, pp. 209-236, February.

Newmark, N. M. ( 1 9 7 5 ) , "Seismic Design Criteria for Structures and

Faciliti es: Trans-Alaska Pipeline System", Proceedings of the U.S.National Conference on Earthquake Engineering, Ann Arbor , Michigan.

Newmark, N. M. ( 1 9 7 6 ) , "A Rationale for Development of Design Spectrafor Diablo Canyon Reactor Facil ity" , N. M. Newmark Consulti ng

Engineering Servi ces, Urbana, Illinoi s, September.

Newmark, N. M. and Hall , W. J. ( 1 9 7 8 ) , "Development of Criteria forSeismic Review of Selected Power Plant s", NUREG/CR-q098 , NewmarkConsulting Engineering Serv ices, Urbana , Illinois, May.

Newmark, N. M., and H all , W. J. ( 1 9 8 2 ) , "Earthquake Spectra and Design",Earthquake Engineering Research Institute Monograph.

Nuttli, 0. W. ( 1 9 7 9 ) , "State-of-the-Art for Assessing Earthquake Hazardsin the United S tat es: The Relation of Sustained Maximum GroundAcceleration and Velocity to Earthquake Intensity and Magnitude",Miscellaneous Paper S-73-1, Report 16, November, 1979, U.S . Army

Engineers Waterways Experiment Statio n, Vicksburg, Missi ssip pi.

Page, R. A., Boore, D. M., Joyner, W. 8., and Cou lter, H. W. ( 1 9 7 2 ) ,

"Ground Motion Values for Use in the Seismic Design of theTrans-Alaska Pipeline System", USGS Circular No. 672, Washin gton.

Park , R. and Paul ay, T . ( 1 9 7 5 ) , Reinforced Concrete Structures, JohnWiley and Sons, New York, pp. 610-66 2.

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P a u l a y , T . ( 1 9 7 5 ) , "Earthquake Resistant Structural Walls" , Workshopon Earthquake-Resistant Reinforced Concrete Building Construction,University of California, Berkeley, pp. 1339-1365, July.

Ploessel , M. R., and Slosson, J. E. ( 1 9 7 4 ) , "Repeatable High Ground

Accelerations from Earthquak es", California Geology, Vol. 27, No. 9,pp. 195-199, September.

Popov, E. P., Zayas, V. A. and Mahin , S. A. ( 1 9 7 9 a ) , "Cyclic InelasticBuckling of Thin Tubular Colu mns", Journal Structural Division,ASCE, Vol. 105, STll, pp. 2261-2277, November.

Popov, E. P. ( 1 9 7 9 b ) , "Inelastic Behavior of Steel Braces Under CyclicLoad ing", Proceed ings of the Second U. S. National Conf erence onEarthquake Engineering, Stanford, pp. 923-932.

Popov, E. P. ( 1 9 8 0 ) , "Update on Simulated Seismic Tests on ReinforcedConcrete and Structural Steel As sembli es", Proceedings of the 1 980Annual Convention of the Structural Engineeri ng Association ofCalifornia, Monterey, pp. 15-35, October.

Popov, E. P. and Black, R. G. ( 1 9 8 1 ) , "Steel Structures Under Severe

Cyclic Load ings", Journal Structural Division, ASCE, Vol. 107, ST9,p p . 1857-1881, September.

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Saiidi, M. and Sozen, M. A. ( 1 9 7 9 ) , "Simple and Complex Models for

Nonlinear Seismic Response of Reinforc ed Concrete Stru ctures ", CivilEngineering Studies, Structural Research Ser ies, No. 465, Universityof Illinois, Urbana, August.

Schnabel, P. 8. and Seed, H. B. ( 1 9 7 3 ) , "Accelerations in Rock forEarthquakes in the Western United States", Bulletin of the

Seismological Society of Americ a. Vo l. 62, April.

Shibata, A. and S ozen, M. A. ( 1 9 7 6 ) , "Substitute-Structure Method forSeismic Design in R/C" , Journal Structural Division, ASCE, Vol . 102,STl, pp. 1-18, January.

Shiga, T., Shibata, A. and Ta kahas hi, J. ( 1 9 7 3 ) , "Experimental Study onDynamic Properties of Reinforced Concrete Shear Walls", Proceedingsof the Fifth World Conference on Earthquake Engineering, Rome,Paper 142.

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Short, S. A., Kennedy, R. P., and Newmark, N. M. ( 1 9 8 0 a ) , "PWR ReactorBuilding Response from High Acceleration, Short DurationEarthquakes", Seventh World Conference on Earthquake Engineering,I s t a n b u l , Turkey, September.

Short, S. A., Kennedy , R. P., Ne wmark, N. M., and Sozen, M. A. ( 1 9 8 0 b ) ,"Nonlinear Response of Nuclear Plant to Moderate Magnitude, NearField Earthqu ake", ASCE Specialty Conference on Civil Engineeringand Nuclear Power, Knoxvil le, Tennessee, September.

Singh, P. ( 1 9 7 7 ) , "Seismic Behavior of Braces and Braced Steel Fram es",UMEE 77 R1, Department of Civil Enginee ring, University of Mich igan,July.

Stevenson, J. D. ( 1 9 8 0 ) , "Structural Damping Values as a Function of

Dynamic Response Stress and Deformation Lev els" , Nuclear Engineeringand Design. Vol. 60, pp. 211-23 7.

Trifunac, M. D. and Brady, A. G. ( 1 9 7 5 ) , "A study of the Duration ofStrong Earthquake Ground Motion", Bulletin of the SeismologicalSociety of America, Vol. 65, pp. 581- 626.

Uchida, T. et. al., ( 1 9 8 0 ) , "Structural Test and Analysis on the SeismicBehavior of the Reinforced Concrete Reactor Building", Proceedingsof the Seventh World Conference on Earthquake Engineering, Istanbul,

p p . 2 1 7 - 2 2 4 .

Umemura, H. and Tanaka, H. ( 1 9 7 7 ) , "Elasto-Plastic Dynamic Analysis ofReactor Bu ildin gs", Proceedings of the Sixth World Conference onEarthquake Engineering., New Delhi, India, pp. 8-51/8-56.

Unemura, H. et. al., ( 1 9 8 0 ) , "Restoring Force Characteristics of R.C.Walls with Openings and Reinforcing Meth ods" , Proceedings of theSeventh World Conference on Earthquake Engineering, Istanbul,p p . 209-216.

USNRC ( 1 9 7 3 a ) , "Design Resonse Spectra for Seismic Design of NuclearPower Plan ts', Regulatory Gu ide 1.60 (Revision 1 ) , Office of

Standards Development, USNRC, Washington, D.C., December.

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Vanmarcke, E. H. ( 1 9 7 2 ) , "Properties of Spectral Moments with Applicationsto Random Vibrat ion", Journal of the Engineering Mechanical Division,A S C E , V o l . 9 8 , N o . E M 2 , p p . 4 2 5 - 4 4 6 , A p r i l .

Vanmarcke, E. H. ( 1 9 7 5 ) , "Structural Response to Earthquakes", Chapter 8in Seismic Risk and Engineering Decis ions, C. Lomnitz andE . Rosenblueth, eds. , Elsevier Publishing Co., New York.

Vanmarcke, E. H., and Lai, S. P. ( 1 9 8 0 ) , "Strong Motion Duration and RMSAmplitude of Earthquake R eco rds ", Bulletin of the SeismologicalSociety of America, Vol. 70, No. 4, pp. 1293-1307, August.

Wang, T. Y., Bertero, V. V. and Popov, E. P. ( 1 9 7 5 ) , "Hysteretic Behaviorof Reinforced Concrete Framed W all s", Report No . EERC 75-23, EERC,University of California, Berkeley.

Wakabayashi, M. et. al., ( 1 9 7 3 ) , "Inelastic Behavior of Steel FramesSubjected to Constant Vertical and Alternating Horizontal Load s",Proceedin gs of the Fifth World Conf erence on Earthquake Eng ineering,Rome, Vol. I, pp. 1194-1197.

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Subjected to Horizontal Load due to Earthquakes ", Proceedings of theSixth World Conference on Earthquake Engineering, New Delhi, India,V o l . Ill, pp. 3188-3193.

Whitman, R. V. ( 1 9 7 8 ) , "Effective Peak Acceleration", Proceedings of theSecond International Conf erence on Micro zonat ion, San Francisc o,Califo rnia, Vo l. Ill, pp. 124 7-125 5, November 26 - December 1.

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P D

P A 2

E C 5

- G

AT

H S -EC12.C L -M R -

G O -

1.62*

1.40

0.74

0.64-

0.49

0.430.40

•0.260.220.20

0.16

0.09

y = 1.0

P A 2 _ _ 0 . 8 8 *

P D

E C S

0.74

0.50

__ 0.43

0

A

TH S

EC12

C L

M R

G C

y

f

_ 0.28

- 0 . 2 5

- 0 . 2 2- 0 . 1 9

_ 0 . 1 5

_ 0 . 1 1

- 0 , 0 8

_ 0 . 0 5

= 1.85

2.14 H z

y = 4.27

LEGEND

A

CL

ECS

EC ! 2

GGC

HS

MR

0

PA2

PD:

T:

• Artificial (0.2g)

Coyote Lake

El Centro #5

El Centro # 12

Goleta

Gavilan College

Hollywood Storage

Melendy Ranch

Olympia

Parkfield

Pacoima Dam

Taft


spectral accelerations Sfo r y = 1.0, 1.85 and4.27

ay

FIGURE 6-ld. MEASURE O F RELATIVE STRENGTH O F GROUND MOTION RECORDS A S DEFINED B Y Say(f,7%)

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APPENDIX A

LITERATURE REVIEW: EARTHQUAKE STRUCTURAL DAMAGE

Seismic design criteria for nuclear power plants are normally

expressed in the form of elastic response spectra anchored to an instru

mental peak acceleration or some "reference acceleration for seismic

design" coupled with an elastic structural a nalys is. Numerous studies

have suggested that the predicted performance (i.e., damage or lack of

damag e) of structures obtained using such design spectra anchored toinstrumental peak ground motion and elastic analysis does not correlate

well with the observed perf orman ce of real stru ctur es. Namel y, the

analyses generally overestimate earthquake force levels and thus predict

that damage would be more severe than is actually observ ed. One such

invest igatio n has been perfor med as part of this study for the El Centro

Steam Plant subjected to the 1979 Imperial Valley earth quake . The

results of the steam plant evaluation are reported in Appendix E. These

studies indicate that in order to better correlate both design conditions

and predicted structural response with the actual observed performance

(i.e., damage or lack of damage) of structures, design parameters must

not only reflect peak acceleration and the frequency characteristics of

the earthquake motion, but also must consider factors such as duration of

strong motio n, the number of peak cyc les, etc., as well as the energy

absorption capac ity of the structures and soil-structure interaction

effe cts. It has also been suggested that the problem is further compli

cated when dealing with near-source ground motions due to low-to-moderate

magnitu de eart hquakes wh ose motions are characterized by very high peak

accelerations, and short duration of strong shaking.

The purpose of this task was to conduct a literature review of

available data and document the performance of real structures subjected

to strong ground shaking from past eart hqua kes. The primary objective was

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to use the assembled information to judge how well the predicted struc

tural perfo rma nce , based on design motions such as those currently defined

for nuclear power pla nts ( namely , design motio ns based on elastic spectra

anchored to peak acceleration from recorded motions coupled to an elastic

response analysis) correlates with the actual observed behavior of real

structures in past earth quakes. A second objective was to identify, from

the cases reviewe d, ground motion and structural characteris tics that

strongl y influenced the actual observed respo nse behavior of the

structure.

A.l SCOPE

There are many papers describing damage to structures re sulting

from earthquakes. By far , most of these papers focus on architecturaland cosmetic damag e. There are only a limited number that discuss

performance (i.e., structural damage or lack of structural d amage ) wher e

the level of ground shaking is known. This review focuses on such papers

as much as poss ible . The review concentrates on the performance of

structures subjected to near-s ourc e, strong ground motions from low-to-

modera te size eart hqua kes. It also emphasizes the structural performance

of those structures located in close proximity to recorded motion . For

completeness and comparisons sake, the review includes data from larger-

size earthquakes and for structures located at more distant rang es. In

all cases, structures which had dynamic response characteristics similar

to those of nuclear power plant structures were sought.

The review addresses and documents in detail the performance of

a wide variety of structure-types subjected to strong motion from ten

different ear thqu akes . The damage noted in 18 additional earthquakes is

addressed in brief. Table A-1 lists all of the earthquakes reviewed and

structure-type s reported . Table A-2 provides additional details on these

earthquakes and distance to pertinent struc tures . The earthquake s cover

a wide Richter magni tude ran ge, 2.7 to 8.3. The majo rity fall in the low-

to-moder ate range of 4.5 to 6.5. Esse ntial ly, all structures discussed

are located near-source and t h u s , were subjected to high accelerations.

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The performance of a wide range of structure-t ypes is noted and

includes residen tial, commer cial, and industrial bui ldings . Discusse d,

for exampl e, are older to newer structures; low-rise to high-rise

buildings; office building s; mobile homes and office traile rs; private

and commercial ho usin g; sch ool s; bri dge s; and general commercial

buildings. Industrial facility structu res include those associated with

refineries, steam pla nts, pumping station s, cycling p lan ts, water tanks

(elevated and ground l e v e l ) , a research/experimental laboratory, a

thermal pla nt, steel st ack s, hydro/geothermal pla nts , and nuclear power

plants. The review focused on the performance of engineered structures

where attempts were made to reconcile pr edicted re sponse beha vior with

actual observed behavior.

Earthquake design considerations of the reported struct ures

covered a wide range. On the one ext reme , there were structures which

incorporated the latest concepts in earthquak e resist ance desi gn. Such

structures employed good provisio ns for accommodating both lateral and

vertical earthquake for ce s, had good lo ad-carryin g continui ty between

major structural elements (e.g., beam s, flo ors , wal ls, e t c . ) , were

well-anchored to well-designed found ations , were designed to be flex ible ,

and had good energy absorbing capacit y. Well-de signed structu res were

built under quality control guidel ines. Scho ols, hos pita ls, and nuclear

power plants have even more strict earthquake pr ovision s placed on them

than conventional facilities designed to the Uniform Buildin g Cod e. At

the other extre me, many reported structures did not incorporate any

earthquake design pr ovisio ns, lacked any structural continuity between

major load-carrying mem be rs , and had few or no quali ty control or quality

assurance requirement s.

A detailed study of the El Centro Plant subjected to the 1979

Imperial Valley earthqua ke was conducted for this proje ct. This plant

was designed for a horizontal force coe fficient of 0.2 and was subjec ted

to actual earthquake ground motion estimated to be about 0.5g and

experienced no significant structural d amage . It was also a case in

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which building drawings as well as measur ed ground motion close to the

site was availabl e. The results of the El Centro Steam Plant evaluation

are sutmari zed in Section A.3 .5 and presente d in detail in Appendi x E.

A.2 ASSESSMENT PROCEDURE

The following is a brief description of the assessment procedure

employed to meet the review object ives . For each eart hqua ke, the litera

ture was reviewed to identify structures that were subjected to strong

ground shaking and whose observed structural performan ce is repor ted.

The structure's capacity was then established by defining the earthqu ake

force level associated with the onset of structural damage and/or the

force level associated with the onset of col lap se. At the lower cap acit y

level , one would expect only minor yielding and inelastic behavior of

structural me mbers . At the higher capacity level, one would expect sig

nificant damage, yielding and inelastic behav ior. Next , the earthq uake

force level in the structure was estimated by means of an elastic respon se

analysis using either recorded or estimated ground motion to define the

struc ture i nput. The estimat ed force level was then compared with the

structure's capacity in order to predict perf orma nce. This final compar

ison was employed to assess how well the predicted structural perf orma nce,

using elastic structural analysis methods based on elastic response spectra and peak accelerations from recorded moti on, correlated with actual

observed behavior.

Most published observatio ns of performance fo cus on conventional

structures designed to Uniform Building Code (UBC) pro vis ion s. For such

stru ctur es, the expected performance can be expressed as a function of

code design level . For exam ple, past observations suggest that on the

aver age, a properly designed structure should survive major shakin g to

earthquake force levels more than 4 to 6 times design v al ues . Under such

force levels , the structure can be expected to behave inel astic ally,

exhibi ting large , plastic deformations and some structural dama ge, but

without collap se. At force levels at about 2 to 3 times code design

leve ls, onset of yielding can be expected with some inelastic behavior but

only minor structural dama ge.

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Figure A-1 taken from Referen ce A -6 0, gives an example of

observed data from the 1971 San Fernando earthquake for multi-sto ry rein

forced concrete structures constructed since 1964. The figure supports

the above capaci ty level of 2 to 3 times code design levels for the onset

of dama ge. The authors suggest that margin of safety against collapse of

these structures was not tested by the San Fernando earthq uake, but the

data suggests that responses equivale nt to five or more times design base

shear could have been resisted with out co lla pse , though severe damage

would probably have resulted.

A.3 RESULTS OF REVIEW

Over 150 papers (listed at the end of this Appendix) have been

reviewed ; most of which describe the nature of structural damage resulting

from past earth quake s. Based on information presented in these pap ers ,

the performance of structures during ten different earthquakes is reported

in more det ail . Published data from the other earthquakes is generally

too limited to draw significant con clus ions . Table A-1 lists the earth

quakes chronologically and identifies the types of structures which are

discussed along with cited refe renc es. Other earthquakes investigated

but not discussed in any detail are the 1933 Long Beac h, 1949 Olymp ia

(A-140, A-152, A - 1 5 5 ) * , 1964 Alask a ( A - 5 5 ) , 1967 C aracas , Venezuela(A-110, A - 1 4 8 ) , 1974 Lima Peru (A-65, A - 1 4 6 ) , 1976 Fr iuli , Italy (A-80,

A-145) 1977 Roma nia , 1980 Mammoth Lakes (A-156) and 1980 Trinid ad-Offshore

(Eureka) (A-123, A - 1 2 4 ) .

For each of the cases pr esen ted, a brief description of the size

and location of the earthquake and the general extent of strong ground

shaking is first inclu ded. Nex t, the types of affected structures are

identified and the level of ground motion to which they were subjected is

estimat ed. The actual performance of the structures is then described

and compared with that which would be predicted using elastic dynamic

analysis procedure s.

Numbers in parentheses refer to the Research Bibliography reference

number.

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A.3.1 San Fernando, California Earthquake, 1971 (A-58, A- 60 , A-6 6,

A - 6 7 , A - 7 6 . A - 8 4 . A - 8 7 , A - 1 5 7 , A - 1 5 9 , A - 1 6 2 , A - 1 6 3 )

The San Fernando ear thquake occurred on February 9, 1971 at the

northern edge of the Los Angel es metropolitan area. The earthquake was

of mod era te mag nit ude (M|_ = 6.4, M5 = 6. 6 ). Its hypoce nter was located

at the southern edge of the San Gabriel M ountains at a depth of 8.4 km.

The focal mechanism for the San Fernando fault consists of thrust with a

significant left-lateral movement along a fault dipping north-northe ast

at an angle between 35° and 50 °. The aftershock locations indicate

that rupture was limited to a disc-shaped region approxim ately 20 km

across. The rupture extended to the surface along an irregular fault

z o n e .

The San Fernando earthquake occurred near the center of the

largest concentration of strong motio n recording instruments in the world.

As a resu lt, more usable strong-motion accelerometers were recorded than

from all previous earthquakes combi ned. The highest ground motion was

1.2g horizo ntal mo tion recor ded on the Paco ima Dam abutment located on the

upthrust block 8 km from the epic ent er. Peak horizontal accelerat ions from

0.15 to 0.40g were recorded in the area surrounding the fault ruptu re.

Strong motion lasted some 12 sec onds . The major ity of the recordings

were obtained in the Los Angeles area approximately 30 km to the south of

the rupture zo ne. Many of these instruments were installed at various

levels of high-rise buil ding s. The site conditions at the recording

stations range from crystalline basement rocks to the north and east

through older sedimentary rocks to deep deposits of unconsolidated and

consolidated alluvium in the valleys to the south. The majo rity of the

recor dings obtained in the Los Angeles area are from buildings founded on

thick. Pliocene deposits.

Modified Mercalli (MM) intensitie s ranging from VIII to XI

occurred in a 190 square mile area in the region s urrounding the fault

rup tur e. Extensive damage to residential buil dings , streets and

utilities occurred along the zone of surface fault ing. Two hospitals

suffered major collapses due to ground shaking. Forty-nine people were

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killed in the collapse of olde r, unreinforced ma sonr y buildings at the

San Fernando Vetera ns Admini strati on Hospital and three additional people

were killed (2 due to to life support fail ure ; 1 due to structural

fai lur e) in a modern reinforced concrete hosp ital . Severe damage toother residential and commerical buildings and highway bridges occurred

in this area. Major landslides were caused by ground shaking, inc luding

the near failure of the Lower Van Norman Dam and severe damage to the

Upper Van Norman Dam.

Outside of the immediate area of strongest shaking , damage was

mai nly restricted to older stru ctur es. Most of the urban areas were

constructed since 1933 when the first earthq uake design requirements were

incorporated into the local building codes and most modern buildings

performed well.

Although only of moderate size, the earthquake provided a real

test for many types of building st ruct ures . Many engineering studies were

conducted of earthqu ake-res istant structures to determine the adequacy of

present design criteri a. These studies included (a) tall buildings that

contained three stro ng-motion instruments (b) major structures in the

heavily shaken ar eas , most which happened to be medical facilities

(c) modern one-st ory industrial and commercial stru ctur es, (d) public

schools because these represented both non-earthquake and earthquake

resistant designs and (e) some old, unreinfor ced mas onry structures (e.g.,

the Veterans Administration H o s p i t a l s ) .

The majority of the structures studied (except for tall buildings

in downtown Los Ange les ) suffered modera te to severe damage and even

colla pse. Engineering studies focused on damaged structures rather than

undamaged structures subjected to strong mo tio ns. The discussion included

herein of Building 41 of the Veterans Administr ation Hospital complex is

an exception.

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Veterans Administration Hospital Building 4 1 . - The Veterans

Adminis tration Hospital Buildi ngs 41 and 43 provid e what is probably the

best examp le in the San Fernando earthquake of structures designed to

resist nominal loads, yet surviving intense shaking and suffering only

minor structural dama ge. A study (A-163) was conducted of Building 41 to

reconcile the observed behavior with the level of strong shaking experi

enced during the earthqu ake.

Building 41 and the Olive View Hospital (which was severely

dama ged) were located near the major surface faulting and about 1-1/4

miles southwest of the Pacoima Dam where peak acceleratio ns over Ig were

recorded. Other buildings at the Veterans Administration sit e, which

accounted for most of the earthquake's cas ual tie s, were not designed to

resist earthquakes.

There were no actual strong-motion accelerometers in the vicinity

of the building site and t h u s , it is impossible to reconstruct the high-

frequency components of the ground motion which are important towards the

response of the building. The range of peak acceleration values measure d

or inferred from nearby sites is rather wide ; 0.5g to 1.2g. Mor eov er,

the peak acceleration is not as important as the freque ncy content of the

record in the range of structural freq uenc ies. Reasonab le estimates of

spectral amplit udes in the period rang e of inter est are 0.7g to 1.5g.

Building 41 was designed in 1937 and built in 1938 . It was four

stories hi gh, about 51 x 20 0 feet in plan with a centrally-located

pent hous e. The vertical and lateral load-carr ying system consisted mainly

of reinforced concrete shear walls supported on spread foo tin gs. There

wer e six shear walls in the transverse direction and three longitudinal

walls. Due to the sloping ter rai n, the ground story (or basem ent) was

half-buried on the north s ide , whe rea s, it was nearly on grade on the

south eleva tion. The basement floor slabs were cast on gra de, and, as

suc h, were not load-carrying. The other three floor slabs and the roof

slabs were ribbed. These slabs were supported on beams spanning between

columns and bearing w a l l s . The building had structural symmetry.

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The building was designed for a lateral load coefficient of

appro ximate ly 10 percent its weight (at workin g s t r e s s e s ) . The UBC code

in force today would lead to a base shear coefficient of 0.28.

In view of the apparent strength of the longitudinal wal ls, the

study focused on the transverse response onl y. The lateral load capacity

was first estimated on the basis of conventional code (current) oriented

proc edur es. The results indicated that with a fixed base , the structure

could resist lateral loads implied by a lateral load coefficient of about

0.4g; the limiting factor being the tensile strength of concrete in the

w a l l s .

A complete three- dimension al model of the entire structure was

dynamicall y analyzed for a flat acceleration spectrum . The most important

result from the analysis was that the inferred level of ground accelera

tion as indicated by a spectral accel erati on of about 0.5g is still quit e

low compared with credible lower bound estimates of the spectral accelera

tion to which this building was subject ed. This implies that the struc

ture had a capacity signif icantly in excess of that revealed by the

fixed-base elastic analy sis. Conside ring linear soil-structure inter

action in the analysis d oes not necess ari ly lower the level of internalforces in the structure compared with the fixed-base analysis (i.e.,

spectral acceleration m ay rise steeply with inc reasing period even though

damping is increas ed. Th us , a nonlinear soil-str ucture interaction

analysis was performed to help resolve the discrepancy between observed

behavior and capacity estimates.

The need for a nonlinear analysis stemmed m ainly from the fact

that at relat ively low levels of exci tati on, partial uplift of the

structure was already suggeste d. The reduced contact area between the

base and the soil leads to lowering the rocking and lateral rigidities of

the founda tion , and with increasing sepa rati on, may lead to partial

yielding of the soil. A two-dimension al analysis was conducted using the

1971 Pacoima Dam (S 16E) and the Holida y Inn (Orion Blvd., N OOW) records

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norm a l i zed t o a 0 .5g peak ac ce le ra t i o n . Th i s leve l i s com pa t i b l e w i t h

the lower est ima tes of ground mo t ion at the s i t e . Both reco rds gave a

base shear o f appro x ima te ly 0 .9 g .

The r e s u l t s c l e a r l y show t h a t n o n li n e a r s o i l - s t r u c t u r e i n t e r

ac t io n e f f e c ts lead to lower shear forc es and moments and to h ig he r

com press ive ax ia l f o r ces i n t he conc re te w a l l s . A l l these e f f e c t s t end

t o in c r e a s e t h e a b i l i t y o f t h e s t r u c t u r e t o s u r v i v e s t r o n g s h a k i n g . The

key to the su cce ssfu l response of the bu i ld in gs was found to be in the

com bined e f f e c t s o f two f a c to r s : ( a ) t he l a rge s t r en g th bu i l t i n t o the

s t r u c t u r e a t t a i n e d th r o ug h p ro p e r d e t a i l i n g and ( b) t h e b e n e f i c i a l e f f e c t s

o f n o n li ne a r s o i l - s t r u c t u r e i n t e r a c t i o n .

Ear thquake fo rc es based on l in ea r e la s t i c an a ly s is es t im ate

forc es grea ter than 10 t imes des ign or a t lea s t 3 t imes the es t ima ted

c a p a c i t y . A t such f o r c e l e v e l s , y i e l d i n g and i n e l a s t i c r es p on s e b e h a v io r

lea din g to severe damage would be p re d ic te d . The ac tu al per formance o f

t he bu i l d i n g was one o f es se n t i a l l y no dam age. Th e re fo re , t he l i n ea r

ana l ys i s ove res t im a ted t he ac tua l ea r thquake f o r ces by a s i g n i f i c a n t

amount.

Thus, VA Bu i l d i n g 41 rep rese n ts a s t r uc tu r e wh i ch , a t l i n ea r

e l a s t i c c a l c u l a t e d fo r c e s o f a t l e a s t 3 t im e s t h e e s t im a t e d c a p a c i t i e s ,

expe r ienced e ss e n t i a l l y no dam age.

H igh -R i se Bu i l d i ngs - There were 66 h i gh - r i se bu i l d i n gs i n t he

major Los Ange les area th a t were ins t rum ented w i th s t ro ng -mo t ion ac ce l

erometers at the t ime of the Feb ruary 9, San Fernando ea r thq ua ke. En gi

nee r ing s tud ie s were conducted and are rep or te d on 11 o f these bu i ld in gs

(A -60 ) . A l l had th re e s t rong -m ot ion ins t rum ents and were des igned by

ap p l i ca b le b u i ld in g codes. S tudy re su l ts were used to rev iew ear thquake

des ign procedures and eva lua te ac tu a l sa fe ty fac to rs in the m in imum

des ign requ i rem en ts sp ec i f i e d by t he bu i l d i n g code .

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The buildings are the Sheraton-Universal Hote l, Bank of

Califo rnia, two Holiday Inn s, Bunker Hill Tow er, KB Valley Cen ter , Muir

Medical Cent er, Kajim a International Building , Certified Life Building,

Union Bank (Los Angeles), and 1901 Avenue of the Stars Building . All of

the buildings w ere located 13 to 26 mile s from the epicen ter.

The buildings ranged from 7 to 42 stories in height. Construc

tion mater ials we re either reinforced concrete or structural st eel.

Lateral force systems employed ductile moment resisting frame s, moment -

resisting fra me s, flat slab and parameter f ram e, ductile frame (tube

s y s t e m ) , shear wall, and X-braced fra me.

Fundamental periods of the buildings ranged from 0.7 seconds to

over 4.0 seco nds . Design base shear values varied from 2.6 to 7.3 percent

of gravity . Peak record ground acceleration values at the different

building sites ranged from 10 to 26 percen t gravit y.

All of the 11 buildings ex perience d calculated force levels

greater than code design values . For the Sheraton-Universal Hote l, KB

Valley Cente r, Union Ban k, Muir Medical C ent er, Kajima International

Build ing, Certified Life Building and the 1901 Avenue of Stars Buildin g,

dynamic elastic analyses using the recorded ground motion would predict

forces from about 1 to 2 times their design level s. Even so, no damage

was observed. For the Bunker Hill Tower and the Bank of California

bui ldi ng, calculated forces were 2.5 to 3.0 times their design loads and

there fore, some yieldi ng, inelastic behavior and minor strutural damage

might be expected. However , no significant structural damage was

observed in these buildi ngs. Minor damage to structural elements was

observed in the form of cracking and spall ing of concrete and local

yielding of rein forc emen t. The structural r esponse of the Bunker Hill

Tower was nonlinea r and could not be described or modeled very well by

linear-elastic dynamic analysis techn iqu es. The analysis of the two

Holiday Inns indicated ear thquak e force levels 4 to 5 times design

values. T h u s , predicted performance would suggest significant yieldi ng,

inelastic behavior and structural da mag e. Beam and slabs would be

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expected to y ie ld and columns to remain w it h in el a s t i c l i m i t s . Observa

t io ns did show signs of beam y ie ld in g and su bs tan tial no ns truc tura l

damage. No serious column damage was obse rved . Beam damage was less

severe than would be predicted from the calculated forces.

Thus, fo r these 1 1 h ig h -r is e b u il d in g s , no damage was observed

at e l a st ic calcu lated forces up to 2 times th e ir design le ve ls . Only

minor c rac kin g, concrete s p a l l in g , and re inforcement y ie ld in g was observed

fo r e la s t ic calcu lated forces up to 3 t imes the design le v e ls . Stru ctu ral

y ie ld in g and su bs tan tial no ns truc tura l damage was observed at e la s t i c

ca lcu la ted fo rces 5 times design, but w i thout s i gn i f ic an t s t ru ctu ra l

damage.

Olive View Ho spital (A-1 62) - An extensive f i e l d and an al yt ic al

inv es t ig at i on of the str uc tu ra l performance of the main bui ld ing of th e

O live View H os pita l M edical Treatment and Care F a c i l i t y was conducted.

This modern, engineered building suffered such severe structural and

no ns tru ctu ra l damages th at i t had to be demolished aft er the earthqua ke.

The observed st ru c tu ra l damages were compared w ith those pr ed ic te d by

e la s t i c and nonlinear dynamic an al ys is .

The main bu i ld in g was a re la t i v e ly massive, 6-story re in forc ed

concrete stru ct ur e. The bu i ld in g ' s ground stor y was considerably larger

in p lan than the upper f ive stor ies; approximately 1 /3 of the bui ld ing 's

to ta l weight was concentrated at the f i r s t f l o o r . The upper por t ion

consisted of fou r recta ngu lar stru ctu res connected to each other at r ig h t

angles and en clo sin g an open co u rt ya rd . A st ai rt o w e r appendage was

located at the end of each wing.

The entire Olive View Medical Center was designed according to

the p ro vi sio n of the 1964 UBC fo r a la te ra l base shear of appro xima tely 8

percent g ra v it y . The main bu ild in g had a complex s tr u c tu ra l system

inco rpo rat ing a wide va r ie ty of st ru ctu al e lements. The pr imary v er t ic a l

loa d-c arr yin g system used in the bu ild in g consisted of columns and f l a t

slabs with drop panels.

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Two di f fe re n t types of la te ra l lo ad -re sis t in g st ru ctu ra l systems

were used. In the upper fo u r s t o r i e s , numerous shear w al ls were provided

to re s is t l a te ra l loads . These w a lls , however, did not extend through

the f i r s t and ground st o r ie s , so th at the slabs and columns of the lower

two stor ies formed a relat ively f lex ible, moment-resist ing space f rame.

Essentially all observed damage is attributed to ground shaking

( i . e . , none due to permanent ground displa ce m en ts) . No ground mo tion

records were obtained near the bu ild in g si t e . Several accelerograms were

numerically simulated or taken from recordings obtained at other sites in

order to perform the analyses . The Olive View f a c i l i t y was located about

six miles southwest of the epicenter, a MM intensity of XI has been

assigned to the s i t e . According to Reference A-1 62, the dura t ion of the

severe ground motion in the general v i c i n it y of the s it e was est imated tobe about 8 seconds and the peak ground acceleration was estimated to be

0.65g. Acc elera t ion t ime h is to ry used in the e la st ic analysis was the

Pacoima Dam base rock motion norma lized to 0 .65g . The no nl ine ar dynamic

analysis used several d i f f e re n t acce lerat ion t ime hist or ie s scaled to

peak values ranging from 0.4g to l.Og.

Damage to the building was particularly severe in the bottom two

s t o r i e s , \lery large, permanent deformations were observed, including

sub stan t ia l in e la st ic deformat ion in s labs and columns, and the fa i l u re

of numerous t ied-co lum ns. The t ied-columns ge ne rally fa i l e d in shear,

re su lt i n g in the collapse of three of the stair tow ers and much of the

sin gl e- sto ry po rt ion of the ground st or y. In te rs to ry deformation in the

upper st o ri es were small due to the presence of the shear w a ll s . In

genera l , damage to upper stories was relatively minor.

E la s t ic analys is res u l ts were ab le to detec t b r i t t l e fa i lu re s o f

the tied-columns (when the results were compared with estimated shearca pa cit ie s) and the co nce ntra tion of deforma tion in the bottom two

s to r i e s. However, id e n t i f i c a t i o n of many of the deta i ls of the response,

such as the sev er i ty and d is t r ib u t i o n of in el a st ic deformat ions, and the

s ig n if ic a n t increase i n l a te ra l displacements when an in e la s t i c mechanism

formed, was not poss ible from the res ul ts of the various e la st ic analysis

performed.

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The in e la s t i c ana lyses revea led th a t the b u i ld in g was des igned

to be very s t r o n g i n co m p ar is o n w i t h b u i l d i n g cod e s p e c i f i c a t i o n s , b u t

th a t fo r some members (no ta b ly , the t ied-c o lum ns and f l a t s labs in th e

b o tt om tw o s t o r i e s ) t h e r e q u i r e d i n e l a s t i c d e f o r m a t i o n s were l a r g e r t h an

t h e y c o u ld d e ve lo p a c c o r d i n g t o t h e i r d e t a i l i n g . The i n e l a s t i c a n a ly s e sa l s o i n d i c a t e d t h a t t h e r e l a t i v e l y s m a l l s t r e n g t h and s t i f f n e s s o f t h e

bo ttom two s t o r ie s re su l te d in a p a r t i a l s idesway co l la pse mechan ism

w h ic h c o n c e n t r a te d d r i f t s and i n e l a s t i c d e f o r m a t i o n s i n t h es e tw o s t o r i e s .

The d i sp l a ce m e n t s p r e d i c t e d b y t h e i n e l a s t i c a n a l y s e s , a l th o u g h g e n e r a l l y

la rg e r than those p re d ic ted by the e la s t i c a na ly ses , were sm a l le r than

the permanent d isp lace me nts observed in the b u i l d in g . On the o ther hand,

the i n e la s t i c response was found to be ve ry se ns i t i ve to the g round

m o t io n r e c o r d u s e d , a n d , i n p a r t i c u l a r , t o r e c o r d s t h a t c o n t a i n s e v e r e ,

l o n g - d u r a t i o n a c c e l e r a t i o n p u l s e s .

Base shears o f the b u i ld in g were ca lcu la t ed us ing e la s t i c an a ly

s i s w i th re su l t s i n d ic a t i n g va lues a t l ea s t 12 t imes des ign va lue . F rom

s uc h a l a r g e c a l c u l a t e d base s h e a r , one w o u ld g e n e r a l l y p r e d i c t t o t a l

c o l l a p s e o f th e m ain b u i l d i n g p a r t i c u l a r l y , when one c o n s i d e rs t h e l o c a l

c o n c e n t r a t i o n o f n o n l i n e a r i t i e s a t t h e b o tt om tw o s t o r i e s . Maximum s t o r y

shears were a lso ca lc u la ted f rom non l inea r dynamic analyses fo r d i f fe re n t

g round ac ce le r a t i on t im e h is to r i e s and found to be s i m i la r i n magn itude

desp i te o f the fac t tha t the t ime h is to r ies were sca led to peak acce le ra

t i o n va lues rang ing f rom 0 .4g to l .O g . From non l inea r a na ly s i s , the base

shear in the bo ttom two s to r ie s were ca l cu la t ed to be 4 t imes la r ge r than

the work ing s t re ss l ev e l s used in the des ign o f the b u i l d in g . The in e la s

t i c s he a rs w ere s i g n i f i c a n t l y s m a l le r t h a n t h e s t o r y s he a r f o r c e s p r e d i c t e d

us ing e l a s t i c methods. Th is base shear va lue o f 4 t ime s des ign appeared

to be more com pat ib le w i th the observed be ha v io r , nam e ly , s ig n i f i c a n t

dam age, y i e l d i n g and i n e l a s t i c b e h a v io r r e s u l t i n g i n n ea r c o l l a p s e .

Thus , the O l i ve V iew Ho sp i ta l rep re sen ts a case where e la s t i c

computed fo rc es were a t l eas t 12 t imes th e i r des ign va lue s . Fu r the rmo re ,

n o n l i n e a r i t i e s w ere c o n c e n t r a t e d at t h e lo w e r tw o s t o r i e s . V e ry s e ve r e

damage resu l ted .

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Holy Cross Hospital - The Holy Cross Hospital was located in the

area heavily shaken by the earthquake approximately nine miles from the

ep ice nte r. The main bu i ld ing has a 7-s tory towe r, a 3-s tory wing to the

north and 1-story wings to the east and we st. A s in g le -s to ry basementwas b u i l t under the main tow er. The main fram ing of the 7-s to ry tower

consisted of concrete joists framed to beams or to walls along inter ior

column line s and to spandrels on the ex te ri o r column li n e s . On the n ort h

and south e xt e r io r w a ll s, spandrels were located on the in side edge of

the columns. The 1-story and 3- st or y wings were of s im ila r j o i s t and beam

con stru ctio n fo r f loo rs and ro o fs . The la te ra l force system consisted of

concrete shear w all s in each d ir e c t io n . As most shear wa lls were not

continuous from top to bottom, reliance also was placed on the concrete

fl o o r j o i s t and slab system actin g as a diaphragm to tra ns fe r shears at

po ints of d is c o n ti n u it y . The ho sp ita l was designed to a base shear of

approx imately 8 percent g ra v i ty .

Damage to the s tr u c tu ra l system of the main b u ild in g was qu ite

genera l , but more pronounced on the f i r s t 4 s to ri e s . The west shear w all s

were dis co ntin uo us below the second f l o o r . The diaphragms were inadequate

to re d is tr ib u te hor iz on ta l loads on the 2nd, 3rd and 4th f l o o r s , and were

damaged se ve rely in t h is are a. One of the west w al l columns was sha tte redat the t h i r d f l o o r . Each of the west shear wa ll elements exh ibit ed

cra ck ing . The lo ng itu di na l shear wa lls had numerous X-pa ttern f a i l u re s

over door op en ings . Excessive no ne la st ic movement of shear w al ls p ro

duced deforma tions large enough to cause po rtio ns of the ve rt ic a l load

fram ing system to act as a moment frame so th a t columns were ca rry in g

earthquake shears and moments. Due to de form ations in the tra ns ve rse

d ire ct io n s, the columns ex hib i ted shear crac k ing . In the lon gi tu din al

d ir e c ti o n , many ex te r io r spandrels were crushed in f le xu ra l compression

and the column covers were sh a tt e re d .

There were no accelerometers in or near the Holy Cross Hospital

complex. However, i t s loc at ion ind ica tes th at the ground shaking would

be between the in st ru m en ta l mo tion at th e Pacoima Dam and at th e Holid ay

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Inn on Orion Bl vd. Peak ground ac celera tion at these sites were 1.2g and

0.25g, respe ctivel y. Using this information plus the observed perform

ance of the building itsel f, a peak ground accelerati on of 0.4g to 0.5g

was estimated for the site (Reference A - 6 7 ) .

Calculated earthquake forces for the main building using an

elastic model of the building indicate a base shear of app roxima tely

0.55g. As with the Indian Hills Medical C enter , respons e spec tra of the

Pacoima Dam (S74W) and the Holiday Inn, Orion Blvd. (NS) records were

scaled to the peak ground a cceler ation estim ates and were used to account

for spectral amp lification. In addition , ultimate capacities of several

critical shear walls were computed in the main tower struct ure. These

capacity calcula tions suggest a 15 percent gravity base shear would be

associated with major c rackin g.

Elasti c calculated ear thquake forces were 3 to 4 times ultimate

capacity and 6 to 8 times design. From such high forc es, one would

predict significant yielding , inelastic be havior, and structural dama ge.

Although significant damage was obser ved, collapse was not imminent. The

buildi ng met the basic intent of the code (i.e., no collapse under heavy

s h a k i n g ) . The shattered columns gave indication that damage would have

been greater had the high intensity of shaking occurred over a longer

time interval.

Thu s, the Holy Cross Hospital represents a case where significant

damag e, but no collapse occurred for elastic calculated forces 6 to 8

times design and 3 to 4 times ultimate capac ity.

Indian Hills Medical Center - The Indian Hills Medical Center

was located in the heavily shaken area, some nine miles from the

epic ente r. The building is a reinforced concret e structure of seven

storie s, about 80 x 170 feet in plan, with a complete load-carrying frame.

Concrete beams run north and south across the building. Typical floor

slabs span between girde rs. The exterior walls are light, curtain-wall

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construction ex cept where concrete shear wall s are located. These shear

walls are concentrate d toward the ends of the building. The building was

designed per the 1966 edition of the Los Angles code for a lateral base

shear of 4.5 percent gravity.

Some damage to shear walls was observed as cracks forming at the

horizontal co nstruct ion joints of floor lin es. There was evidence of

slight horizontal movement although these cracks were not related

directly to shear. The slabs, in some case s, also showed cracks. The

ends of shear walls were designed as columns and thu s, were subjected to

both shear and axial l oad s. Concret e in the splice area crumbled. All

shear walls in lower levels cracked in the typical X-pattern indicating

high shear stress. Damage was noted at interse ctions of girders and

w a l l s .

No strong-motion records were available at the building site.

However, based on the building location relative to the epicent er, the

nearby buildings studi ed, and its own observed p erfo rmanc e, the peak

ground motion was estimated to be between 0.4 and 0.5g (Reference A - 6 7 ) .

A linear elastic dynamic analysis was conducted of the building

to estimate earthquake force s. Time history motions considered were the

Pacoima Dam (S74W) and the Holiday Inn, Orion Blvd. (NS) records scaled

to the peak estimated acceleration for the site. This analysis,

accounting for spectral eff ect s, result ed in a calculated base shear of

35 percent gravity . In addi tion , ultimate ca pacities of several of the

critical shear walls in comp ressi on, tension and shear were computed

establishing an ultimate capacit y limit of about 10 percent gravit y or 2

times the design values.

Thu s, elastic calculated earthquake forces are 3.5 times

ultimate capacit y and 7 times design. From such high for ces , one would

predict significant yi eldi ng, inelastic be havior , structural damage, and

possibly the onset of collapse. Howev er, observations suggest the

building was not near collapse.

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Medical B ui ld in gs Near Hansen Lake - Four med ical b ui ld in g s

loc ate d near Hansen Lake were s tu d ie d . These are the Fo o th i ll Medical

Center, the Pacoima Lutheran Medical Center, the Golden State Community

Mental Health Center and the Pacoima Memorial Lutheran H o s p it a l. A ll are

loca ted about 8 to 9 m iles from the earthquake e pice nter and less than 1

m ile south of the nearest f a u l t break . There were no stro ng motion

instrum ents at any of the b ui ld in g s it e s . However, peak ground motion is

estimated to be about the same as that at Holy Cross Hospital and Indian

H il ls Medical Center ( i . e . , in the 0.4 to 0.5g range).

A ll four f a c i l i t i e s were designed to a base shear of about 13

percent g ra v it y . Except fo r the Golden State Center, a l l of the medical

bu ild ing s included design and co ns truc t ion fe ature s not consideredadequate under str ict interpretat ion of the Los Angeles Building Code.

These features were directly responsible for the type of damage observed

in the stru ctu re s. For example, a closer study of the Fo o th i l l Medical

Center showed tha t a 7 percent g ra vi ty l a te ra l load would be s u ff ic ie n t

to cause the f i r s t fa i l u r e of i ts bracing system.

The Golden State Center is considered to be properly designed in

tha t i t met the in te nt of the bui ld in g code. Calculated forces (viae la s t i c a nalys is and peak ground ac ce lera t ion ) would re s u lt in an ea rth

quake fo rc e le ve l perhaps 2 to 3 times th e Golden Sta te Center design

va lue . One would, th us , pre dic t onset of y ie ld in g , minor in el a st ic

beha vior, and ne g lig ib le s tr uc tu ra l damage except at the lo ca tio n of

improper design and con struct io n fea tur es . This pred ict io n is consistent

with the observed performance.

Low-Rise In d u s tr ia l and Commercial Bu ild in gs - The performance

of f i f te e n low -r ise i n du st r i a l and commercia l bui ld in gs were stud ied.

Th irtee n are one-story bu ildi ng s w ith wood roof systems, one is a

f i v e -s to ry mon ol i th ic concrete bu i ld in g, and one is a one-story bu i ld in g

wi th precast concrete roof and w al ls . A l l f i f te e n b ui ld ing s were located

between 8 and 17 mile s from the epic ente r and were b u i l t since 1 958. A ll

were designed by ap pli ca ble b ui ld in g codes. No reco rding s of the motion

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at the b u il d in g s it e s were made. Peak ground mo tion was estim ated to have

been between 20 and 40 percent gravity with most buildings subjected to

40 perce nt g r a v i ty (Reference A -6 7) . P ri n c ip a l damage was due to heavy

v ib ra ti o n altho ug h th er e was some permanent ground disp lace m ent. The

la te r a l design for ce s f o r most bu ild in gs was about 13 percent of dead

l oad . Calculated forces using e last ic analysis procedure ( i . e . , response

spectra anchored to the peak acceleration estimates) would suggest

earthquake forces at least 3 to 6 times design . Thus, s ig n if i ca n t

y i e l d i n g , in e la s t i c beha vior, and s ig n if ic a n t damage would be predicted

from the ca lcu la te d loa ds . Observed performance var ied from moderate

damage to complete c oll ap se of the s tr u c tu re s . Much of the damage was

the resu l t o f lack o f cont inu i ty ( i . e . , stre ng th cap acity ) between the

w al l and the ro of systems. Several w all shear fa il u r e s were caused by

lack of a b i l i t y to re s is t out-of-p lane earthquake for ce s. Performance of

the bu i ld ing s was stro ng ly inf luenc ed by th e ir capacity fo r energy

absorp t ion and duc t i l i t y .

Implications - The San Fernando earthquake subjected a variety

of structures to ground accelerat ions that equaled or exceeded their

design v alue s. Many en gin ee rin g analyses were performed to compare both

ca lcu lat ed and actua l respon ses. In those cases where an e la s ti canalysis calculated base shear forces only moderately greater than the

structures design values, good correlation was seen between predicted and

observed beha vior. Both pre dic ted and ac tual performances of these

structures ranged from no damage to moderate cracking and yielding of

s t ructura l e lements.

In those cases where an e la s ti c an aly sis ca lcu lat ed base shear

forces much grea ter than the str u ct u re 's design valu e, the p redicte dexte nt of damage s i g n i f i c a n t l y exceeded observed response. Tota l

collapse would be pre dic ted f o r some st ru ct u re s , yet actua l performance

ranged from no damage (VA Building 41) to signif icant yielding and

in e l as t ic response (O l ive V iew, Ho ly Cross, Ind ian H i l l s ) .

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Ine last ic ana lys is incorpora t ing non l inear mater ia l p roper t ies

were performed on several stru ctu res in an e ff o r t to rec on cile the

diffe ren ce s between ca lcu late d el a s t i c response and actual b ehav ior. The

in e l a s t i c an aly sis method produced lower base shear for ce s and gave a

bet ter corre lat ion with observed structural performance.

In the absence of design or construct ion deficiencies which

would resu l t in reduced duct i l i t y o r energy absorp t ion capab i l i t y , the

fo llo w in g general observations could be made:

1 . For the Veterans Ad m inistra t ion H ospita l Bui ld ing #41 ,e s s e n ti a l l y no s tr u ct u ra l damage occurred even though thef ixed base, l inear e last ic calculated forces exceededdesign forc es by a fa c to r grea ter than 10 and exceeded theestimated ul t im ate capa cit ies by a fa ct or greater than 3.This st ru ctu re was a s t i f f st ru ctu re (s im i la r to manynuclear power p lant st ructures) subject to substant ia lnon l inear so i l s t ruc ture in te ra ct io n e f fe ct s . Thebene f ic ia l e f fec t of non linea r so i l - s t ru c tu re in te rac t ionef fe cts and pa r t ic u l a r l y good st r uc tur a l de ta i l in g havebeen judged to be responsible for the very good performanceat high fo rce l ev e l s .

2. High-r ise bui ld ings (not s imi lar to nuclear power p lants)

tended to show no damage at elastic calculated force levelsup to 2 t imes t h e ir design le v e ls ; minor s tr uc tu ra l damageat e la s t i c calcuated forces up to 3 t imes des ign; andst ru ct ur al y ie ld in g and su bs tant ia l no n-s truc tura l damagebut no su bs tan t ia l st ru ct ur al damage at e l a st ic calc ulate dforc es 5 t imes d esig n. I t should be noted tha t the designca pa city is based on working s tres s design and th a t t heest imated actual u l t imate capacity is general ly about twicethe design ca pa ci ty . Thus, minor s tr u c tu ra l damage mightbe expected at 1.5 t imes the ult imate capacity, while nosu b st an tia l s tr u c tu ra l damage would be expected at 2.5times ul tim at e ca pa ci ty . The Holy Cross Ho sp ital showeds ig n if ic a n t s t ru ct ur al damage but no col lapse at e la s t i ccalc ulate d forces 3 to 4 t imes the u l t ima te cap acity .However, collaps e is l i k e l y to have re su lte d i f theduration of strong shaking had been longer.

3. Very s ig n if ic a n t str uc tu ra l damage occurred at the O liveView Hospital at elast ic calculated forces greater than 12times d esig n. However, th i s damage was he av ily influ en ce dby the fact that nonlinear behavior was concentrated at thelower two floors as opposed to being spread uniformlythroughout .

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The S a n Fernando data illustrate t h e importance of designing

adequate ductility into the structural system and the importance o f n o t

overdesigning t h e strength of a portion o f t h e structure s o a s t o

concentratet he

nonlinearities into localized "weak-link" regio ns.So

long as these principles are obse rved , these data illustrates that t h e

onset o f significant structural damage should not occur at elastic

calculated force levels less than 2.5 times t h e ultimate capacity f o r

ground motion similar to that recorded f o r t h e S a n Fernando earthquake.

Because of nonlinear soil-structure interaction, t h e actual performance

might be substantially better than indicated by this 2.5 factor. These

data clearly illustrate that elastic response cannot be correlated with

damage unless the inelastic energy absorption capability (ductility) o f

properly designed structures is considered. T h e elastic computed

response must be reduced by a factor o f approximately 2 .5 o r greater if

it is to be compared with t h e ultimate c apacity for t h e purposes of

predicting t h e onset of significant structural damage f o r a properly

designed structure subjected t o S a n Fernando type ground moti on.

A.3.2 Managua , Nicaragua, Earthquake, 1972

(A-26, A - 3 0 , A - 4 0 , A - 4 2 , A- 111, A-112. A-113)

On December 23 , 1972, a moderate magnitude earthquake (M^ = 6.2 )

occurred i n Managua. Loss of l i f e approached 10,000 , appro ximate ly 57

percent of the city's 450,000 occupants were rendered homeless, property

damages are estimated to be about $1 b i l l i o n . The hypocenter of th e main

shock was located in an area approximately coinciding with downtown

Managua at a depth of 2 to 8 ki lo m e te rs . Only one accelerometer rec ord

was obtained at the ESSO r e f in e r y which was app roxim ately 3 m iles from

the f a u l t tra ces and the ci t y of Managua. Peak recorded ac ce ler atio ns

were 0.39g EW, 0.33g NS and 0.31g v e r t i c a l .

From the re su lts of seismoscope records throughou t the c i t y ,

ob se rva tion of damage, and the estimated lo ca tio n of the hypocenter, i t

fo llo w s th a t the ground motion in ce nt ra l Managua was more inten se than

th at recorded at the r e fi n e r y . Peak ac ce ler atio ns have been estimated at

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0.5 to 0.6g. A maxi mum MM intensit y of nearl y IX was estimated in the

central downtown area where much damage was observed. Other areas of

concentrated damage were the heavily populated northwestern part of the

city and in the popula ted, industrial areas to the northea st. In the

vicinity of the ESSO refine ry, intensity values of V to VI were estima ted.

Structures in Managua were predominan tly one-to-two stories with

some taller buildings up to eight stories in height. The type of con

struct ion in the city can be describ ed accordin g to height rather than

func tion . Low-rise structures were dominated by taquezal type construc

tion - adobe bricks filling a light timber frame work . Suburban hou sing

typically consisted of reinforced maso nry or concrete walls with heavy

reinforced concrete roof slabs. One-st ory factori es and wareh ouses were

also constructed in this man ner . Taller structures consisted primaril y

of reinforced c oncre te. The range of actual base shear strength

coefficients was wide . On one extreme were institutional bui ldin gs,

heavy but with considerable wall area. At the other extreme were light,

modern buildings.

Severe damage and collapse were generally confined to those

structures with taquezal, concrete, and unreinforced masonry construction

that lacked adequate lateral force resi sta nce . These buildings are

inherently quite weak and heavy enough to generate large lateral forces

under earthqua ke shaking. There were examples of moment resist ing

unbraced frame structures for which the structure endured the ea rthquak e

without severe damage but experienced motions great enough to cause

extensiv e proper ty losses and loss of func tiona lity . Shear wall frame

buildings were much stif fer; the limited deformations resulted in very

little property loss or loss of funct iona lity. Howe ver, some of these

showed sufficient structural damage to question their safety for an

earthquake of equal intensity but longer dura tion.

A variet y of industrial fac ilities were located in Man agu a.

Damage to these facilities varied with dista nce from the fau lt, type of

const ructi on, and the extent to which earthqua ke-resi stive details were

engineered into their desig n.

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ESSO R e fin er y - The ESSO R ef in e ry was designed and b u i l t in two

d if fe re n t stages in the mid 1950's and ea rly 1 960's. Plant stru ctu res

include v e rt ic a l vessels of various h eights and slenderness, pumps,

generators, heat exchangers, p ip ing systems, tanks, foundat ions, etc.

The design met requirements of the Uniform Bu ild in g Code. A ll d e ta il in g

ref lected the U.S. design procedures in effect at the t ime of design.

All equipment was tied to its foundation, piping systems were braced,

et c . In 1968, a smaller earthquake caused some d i f f i c u l t i e s at the

p la nt . Consequently, port io ns of the pla nt were redesigned to withs tand

a peak ground ac ce le ra tio n o f 0.2 g. On the a verage, however, the design

base shear c oe f f ic ie nt at the f a c i l i t y was about 0.10 to 0.1 3g.

The peak recorded ac ce le ra tio n a t the si t e was 0.3 9g. The highamplitude portion of the motion lasted for about five seconds with a

nominal acc ele ra tio n value of about 0.2 g. Ground motion of a lon g-p erio d

nature fo ll o w e d . Much of the equipment and low-h eight str uc tur es at the

s i te have re la t i v e ly h igh natura l f requencies. The t a l l f ra ct io na t ing

tow ers, rea ct or s, and o i l heaters are cha racte rized by low freq ue ncie s.

The nature of the ground shaking was such that most structures and

equipment would see some response amplification over the ground

a cc e le ra tio n. The peak ground ac ce ler at ion was over 3 times the average

design base shear c o ef f i c i e n ts . Consider ing spec tra l am pl i f i ca t io n, the

e la s t i c computed for ce s would be expected to have been at le as t 6 times

the average design base shear and at l ea st 3 times the yi e ld ca pa cit y.

Damage at the r e fi n e ry was minimal and lim it e d pr im arl y to

grouted pads, concrete block w a ll s , and some ste el cross brac ing . A fte r

performing analyses, Blume (A-26) noted that even when the earthquake

demand on the p la nt was over t hr ee times y ie ld capac it y , damage was

i n s i g n i f i c a n t .

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ENALUF Thermal Pla nt - The ENALUF f a c i l i t y is a thr ee u n i t ,

o i l - f i r e d p lant with a to ta l c apa city of 90 MW(e). At the s i te were

modern tu rb ine gen era tors, a,group of six dies el gen erators of

app roxim tely 1 MW(e) each, a 138/69-KV transm ission su bs ta t io n, a

69/13.8-KV d is t r ib u t i o n sta t io n and an indoor switching s ta t i o n . The

pla nt was rep or ted ly designed to a la te ra l force of O.lOg.

The ENALUF f a c i l i t y was located w ith in 0.15 miles of th e

p r i n c ip a l f a u l t . A peak ground acc elera t ion at the s i t e was est imated at

0.6g - si x t imes the design le v e l. Any e la s t i c ana lysis techniques based

on the ground excitat ion would give calculated forces much greater than

yi e l d capa ci ty . S ig n i f ic an t y ie ld ing wou ld be pred ic ted .

O ve ra ll damage to the plan t was s l i g h t . Some of the wors t

damage occurred to unanchored equipment which was free to displace or

f a l l . Equipment attached to the floor was not affected by the

earthquake. Piping throughout the pla nt struck platform s or equipment.

U su al ly, the pip e's lagging and thermal in su la t io n were crushed , but the

pipe i t s e l f was undamaged.

Im p li ca ti ons - Both the ESSO R ef in er y and the ENALUF the rm alplant provides examples of engineered structures subjected to strong

ground sh ak ing . Ca lcula ted earthquake forc es based on ground acc ele ra

t io ns w ould fa r exceed estimated ca pa cit ie s (by fac tor s of 3 to 6 or

more) . Aga in , e l a st ic ana lys is w i thout accounting fo r the i ne la st ic

energy absorpt ion c ap ab i l i ty would re s u lt i n a poor co rr e l at io n between

pre dic ted and observed s tr u c tu ra l performance.

A.3 .3 Kern County, C a li fo rn ia Earthquake, 1952

(A-32, A-137, A-138, A-139, A-140)

The Kern County area of C a li fo rn ia was sub jecte d to stro ng

ground shaking from the major J ul y 2 1 , 1952 Kern County (Arv in-Te hac hap i)

earthquake ( M L = 7 .2 , Ms = 7.7) and a se ries of r e la te d earthquakes and

aftersho cks tha t fol l ow ed . The epice nter was located about 26 miles

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south of B ak er sf ie ld and 4 m iles west of Wheeler Ridge . The shock was

f e l t over 160,000 square m ile s. Another stron g shock, August 22, 1952,

had a more loc al e f f e c t . I t caused cons iderable damage to B ake rsfie ld

and immediate v i c i n i t y and was f e l t over 40,000 square m ile s.

There were no strong motion accelerometer stations in the

ce n tra l area to record the ground m otio n. The nearest s ta tio n was at

T af t about 25 m iles from the f a u l t ru p tu re . The maximum peak

ac ce lera tio n was 0.20 g. Strong motion (>0.1 g) la ste d more than 12

seconds. The instru m en t s it e has been assigned a MM i n t e n s i t y o f V I I .

In areas of higher intense shaking (MM in te n s it y V I I I and IX ), c lose r to

the fa u l t ru pt ur e, the ground mot ion is est imated to be s ig n i f ic a n t l y

greater than 0.20g.

The earthquake occu rred near a pop ulated a rea . Con seque ntly, a

la rge var ie ty o f res id e n t i a l , pu b l ic , commercia l and ind us t r ia l s t ruc tures

were af fe ct ed . Co nstruction m ate r ial used in these stru ctu res included

wood, both reinforced and unreinforced masonry and concrete, and steel.

In g en era l, damage to b u i ld in g s, e levated water tan ks, and other str uc

tur es fol lo we d the patt ern t ha t stru ctu res performed we ll when earthquake

prov isions were incorpo rated i n th e ir design . Poorly designed and con

stru cte d bui ld ings were the f i r s t to su ffe r severe damage or co l lap se .

Relatively few wood frame structures were seriously damaged.

Those th a t were h ea vi ly damaged were thrown o ff fou nd atio ns because of a

lack of brac ing or su ff ic ie n t bo l t in g to foundat ion w al ls . In the region

of stron gest sh aking, un reinforce d b r i ck , concrete block and adobe stru c

tures were severely damaged; however, the performance of reinforced

concrete block and re in fo rc e d , grouted br ick was good. Small ste el

structures such as gasoline stations suffered no damage, although somehigh-r ise steel structures suffered minor damage.

There were several r e fi n e r i e s subjected to strong shaking. The

o v e ra ll behavior of re fi n e ri e s was good and damage was s l i g h t . This can

be attr ibuted to the general use of steel piping and good anchorage of

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equipment. Most p ip ing breaks occurred due to lack of f l e x i b i l i t y or use

of cast i r o n . Breakage in ste el underground pip in g was li m it e d to a few

cases in very poor s o i l .

Kern County Steam Plan t - The Kern County Steam Pla nt was b u i l tin 1947-48 and has a capacity of 175 MW in two un i ts . The pr in c ip a l

bu ild in g is construc ted of stee l frames and concrete w a ll s . The pla nt

b ui ld in g and associated equipment re prese nt a wide range of fundamental

f requ enc ies. A l l st ruc tures w ith in the p lant were designed fo r a la te ra l

for ce of 20 percent g ra v i ty . For th is design le v e l, the onset of

y ie ld in g is est imated at base shears of 40 to 60 percent of i t s we ight.

This p lant i s located about 15 miles from the fa u lt ru pt ur e. Att h i s lo c a ti o n , peak ground motion was estim ated t o be between 0.3 and

0.4 g. The fundamental frequ enc ies of the plan t str uc tu re s should cover a

wide range. Estimated earthquake forc es using e la s t i c response (spectrum)

analysis should re su lt in some plant st ru cture s having a calc ulated forc e

of at least two to three times greater than the above estimated yield

le v e ls . Y ie ld in g of major st r uc tu ra l e lements in the p lant would then be

pr ed ic te d. However, damage to the build ing s was ne g lig ib le suggesting

th a t i f an e la s t i c analys is had been used to ca lcu lat e earthquake fo rc es ,

the loads would have been signif icant ly overest imated.

Elevated W ater Tanks - A water tank at th e Maricopa Seed Farms,

100,000 gallo ns in c apa city and 100 fe e t in h ei gh t, was sub ject to stron g

shaking estimated to be about 0.25 to 0.3 g. This tank was loca ted about

20 m iles from the f a u l t r u p tu re . The tank was designed to a value of

O. lg . Even ignor ing poss ib le spect ra l am pl i f ic a t io n e las t ic ana lys is

would re su lt i n calcu lated forces in the tank fa r greater than i t s design

ca pa city . S ig ni f ic a n t damage would be pr ed ic te d; y e t, none occ urre d. A

similar tank at nearby Di Giorgio Farms, designed to 0.12g and subjected

to strong shaking a lso suf fered l i t t l e damage. For both tank s, e la s t ic

analysis would overestimate earthquake forces actually seen by the

s t ru c t u re s .

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Implications - The overall pe rformance of structures during this

earth quake points to the importance of energy absorption and ductility in

the response behavor of structures (e.g., brittle structures suffered the

greatest d a m a g e ) . The observed performance of the Kern County steam

Plant and elevated tanks show that calculated earthquake forces based on

elastic analysis overestimate actual forces. Thus, their predicted

performance did not correlate with observed behavior.

A.3.4 Santa Barbara , California Earthqu ake, 1978

(A-64, A-119, A-120, A-160)

A moderate earthquake ( M L = 5.1, Ms = 5.6) struck the Santa

Barbara-Goleta area on August 13, 1978. The earthquake was centered in

the Santa Barbara Cha nne l, 5 to 8km south of downtown Santa Barbara. The

resulting ground motion displayed a marked directional asymmetry which

had an important bearing on overall effects of the earthq uake. This

asymmetry caused the mos t intense ground moti on in the Goleta area even

though Santa Barbara is closer to the epicen ter. A maximum MM intensity

of VII is reported near the Universit y of Califor nia Santa Barbara (UCSB)

campus located in Gole ta. The focal depth was estimated at about 13km.

The fracture apparently propagated from the epicenter laterally west -

northwest toward Goleta for a rupture length of about 8km with a terminus

about 4km from the UCSB campu s.

Several strong motion accelerometers recorded the ground

mot ion . In Santa Bar bara , strong motion was recorded at the base of the

Freitas Building and also the Santa Barbara Courtho use. A peak value of

0.23g was recorded . A Goleta Substation of the Southern California

Edison Company recorded 0.29g. Two recordi ngs were made on the UCSB

campus near Building 340 and at the base of North Hall. The recorded

accel erati on at North Hall had a peak value of 0.42g. Duration of

strongest shaking was about 2 to 3 seconds.

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As would generally be expected because of the more severe

shaking, structures in Goleta suffered more damage than those in Santa

Barbara . Most of the major stru ct ur es loca ted i n Goleta are on or near

the UCSB campus. These inclu de d a number of re in fo rc e d c oncre te shear

w all bu i lding s up to 8 sto rie s in h eight locate d on the campus, several

larg e s te el frame hangars and a co nt ro l tower at the adjacent m unicip al

a i r p o r t , a pa i r o f h igh -r ise re in forced concrete shear wal l dorm i tor ies

west of campus, and a number of long low -r is e (1 -3 st o ri e s ) commercial

bu ildin gs n or th of campus. The major rema ining buil din gs i n the Goleta

area co ns ist of co nve ntiona l 1-3 s to ry wood frame apartment bu ildin gs and

duplexes locate d in the area west of campus. F in a l l y , there are several

mob ile home parks i n the area loca ted e as t, n o rt h and west of campus.

Except f o r a few o ld wood frame and adobe st ru ct u re s (m os tly farm houses)

the bui ld ing s in Goleta are r e la t iv e ly modern. The m aj or i ty have been

constructed wi th in the la st 20 to 30 yea rs.

Several of the m u l t i - s t o ry , reinfo rce d concrete bu i ld ings on the

UCSB campus rece ived moderate diagonal cra ck ing of shear wa lls in the

lower st o r ie s . Some of the ro o f- to p mechanical equipment were sev ere ly

a f f e c t e d , and instruments and supplies were destroyed in some

lab or ato r ies . Damage to l ig h t f i x tu re s , ce i l i n g s , and p las ter occurredthrou ghout the campus. The t o t a l ea rthquake damage to s truct u re s and

bu ild in gs on the UCSB campus was estimated at $3.4 m i l l i o n . Of th is

t o t a l , only approximately $300,000 was a tt ri b u te d to s tr u ct u ra l damage.

Just no rth o f the UCSB campus ther e are n ea rly 100 bu il d in g s .

The bui ldin gs comprise a m ixture of hangars and sin gle sto ry o ff ic e

service b u i ld in g s. The m a jo ri t y of the bu i ldin gs are wooden and of World

War I I v in ta ge . Most of the damage was a r c h it e c tu r a l. The most nota bles tr u c tu ra l damage was lim it e d to two hangars and the a ir p o rt co nt ro l

tow er. Both are ste el frame st ru c tu re s . They su ffe re d permanent

deform ations. With these exceptions., the remaining st ru ct u ra l damage

consisted of cracked concrete f loor slabs in two bui ldings and shifted

wood columns i n one o f them. There was e s s e n t ia ll y no damage to

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el ec t r i ca l serv ice f a c i l i t i e s . S t ruc tures in the Santa Barbara area

disp lay a wider va r ia t io n of a rc hi te ct ur e , and con struct ion than those in

Go leta . However, damage to these stru ctu re s was com paratively m inor.

North Ha ll (UCSB) - North H all is a rectan gu lar th re e- sto ry

re in forced concrete shear wal l s t ru c ture o r i g in a l l y b u i l t w i th a

de f ic ien cy in i t s la te ra l res istan ce . Thus, concrete shear wa l ls were

'added to make the structure meet the 1976 edit ion of the Uniform Building

Code. As previously indicated, the bui ld ing was inst rumented with

strong-mo tion accelerometers during the earthquake. The base ac ce lera t ion

in the tran sve rse d ir e c ti o n was about .40 g. There was also another

intrument w hich measured approximately .65g on the t h ir d f l o o r , and the

ro of rec ord reached I g . These motions im ply a base shear of 50 to 70

percent of the weight of the s tr u c tu re ; yet the damage to the bu ild in g

consisted only of l ight - to-moderate X-cracking in the concrete shear

w a l l s .

Im plic at io ns - Although the lev el of ground shaking was quit e

h i g h , l i t t l e s t r uc tur a l damage occurred to engineered s t ruc ture s .

Performance pre dic t ion s based on earthquake forces lev els from e la s t i c

ana lysis would have pre dicte d much grea ter damage. In p a rt ic u la r,calculated earthquake forces at North Hall based on the measured

acceleration would clearly have predicted damage, yet none was observed.

Second ly, the damage was less at G oleta f o r 0.25 to 0.45g ground

ac ce lera tion s than occu rred in San Fernando w it h in these same ground

acc elerat ion regio ns. Thus, the in e la s t ic energy absorpt ion ef fec ts

indi ca ted by the San Fernando da ta , would have to be even grea ter at

Go leta to account fo r the sma ll amount of observed damage. In oth erwords, the shorter duration Goleta records resulted in less damage than

the longer du ra tio n San Fernando reco rd s, fo r the same ground

ac c e le r a t i on .

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A.3.5 Impe ria l Va l ley , C a l i fo rn ia , Earthquake, 1979

(A-35, A-36. A-37, A-38, A-125, A-127, A-128, A-129)

On October 1 5, 1 979, a moderate earthquake ( M L = 6.6, Ms = 6.9)

shook the Impe ria l Val ley of C a l i f o rn ia . The cen tra l region of Im peria l

Valley extending from Brawley to Calexico is estimated to have had ground

motion associated w ith a maximum MM V I I . The d is tr ib u ti o n of strong

ground shaking was about the same in El Centro, Imperial, Calexico, and

Brawley, the four communities most affected by the earthquake.

The area was w el l instru me nted by a network of str on g-m otio n

accelerometers. In several instanc es, peak v e rt ic a l a ccele rat ions were

considerably higher than horizontal accelerat ion values (for example, at

S ta tio n No. 2, a 1.74g ve r ti c a l ac ce ler ati on was re co rd ed ). The maximumpeak recorded horizontal acceleration was 0.81g at Bonds Corners which is

loca ted about 2km from the ep ice nter and caus ative fa u l t . El Centro

experienced ground motion in the 0.2 to 0.5g range. Im pe rial Va lley

College 0.52g , Brawley 0.22g , H o lt v i l le 0.26 and Calexico 0.28. Sta t ion

No. 9 in El Centro is the same location where the 1940 El Centro record

was take n. I t is 6km west of the Im pe rial Fa ul t and also 1km from the El

Cen tro Steam P la n t. Peak acce le ra tio ns were 0.40g NS, 0.27g EW, and 0.38

v e r t i c a l . About 0.83km SE of the p la nt another str on g-m otio n instru m ent

recorded 0.51 g NS, 0.37g EW and 0.93 v e r t i c a l . With onl y a few excep

t i o n s , pa rt ic u la r l y tha t at Bonds Corners, the durat ion of st rong shaking

( i . e . , grea ter than O.lg) was very sh o rt . Bonds Corners stro ng shaking

la st ed about 13 seconds.

Earthquake damage and e ffe ct s in the Imp eria l V al le y va ried

gr ea tly in th e ir occurrence and d is tr ib u ti o n . The damage consisted of

par t ia l ly co l lapsed unre in forced br ick wa l ls ; cracked corn ices, parapets

and gab les ; a few damaged chimne ys; d is p la y windows broken or sh a tt e re d ;

plas ter cracked and f a l l e n ; sect ions of suspended c e i l in g t i l e s d isplaced

or fa l l e n ; shelves, and considerable q ua nt i t ie s of g lassware, d ishes , and

small objects f a ll e n and broken.

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Wood frame stucco d w e ll in g s , some as clo se as 30 to 150 meters

from the f a u l t ru pt ur e had ve ry minor damage. The most he av ily damaged

modern building was the Imperial County Services Building in El Centro, a

six-story reinforced concrete frame shear wall structures designed under

the 1967 pro vis ions of the UBC. Excluding th is b u il d in g , the most severe

damage in Brawley, Calexico, El Centro, and Imperial was to low-rise

unreinforced b r ick bui ld ings and to a few low-r ise re in forc ed concrete

frame buildings constructed before the 1940 El Centro earthquake.

The Im pe ria l Va lle y College had a rec ord ing of 0.52g . The

m aj or i ty of bu i ld ing s on campus are low, one-s tory stru ctur es with

rei nfo rc ed concrete block w alls and metal deck ro o fs . Bu ildings are of

recent c o ns tru c t io n, probably less than 10 years o ld . St ruc tur al damage

was minor and t y p ic a l of damage observed in prev ious earthq uakes.

There was some ele va ted w ater stora ge tanks in or near the

c i t i e s of Brawley, Im pe ria l, El Centro and Ca lex ico . Most experienced no

damage. Two suf fe re d mino r t o moderate damage in the form of buckled

braces and to rn gusset p la te s ; one tank colla pse d and ru p tu re d. Ground

supported ste el storage ta nk s, in g en era l, performed very we ll except fo r

those with height to diameter rat io s grea ter than one. As these tankswere not anchored down, the y rocked and l i f t e d o ff th e ir foun datio n pads

re su lt i n g in seam ru ptu re s, p ip ing fa i l u r e s , and compression buck l ing.

Imperial County Services Building - Although the intensity of

shaking in El Centro was V I I , the Im pe rial County Service s B uil din g was

assigned an in te n s it y IX. Completed in 1971 , the si x- st o ry re in force d

concrete frame and sh ea r-w all st ru ct ur e was designed per UBC (probab ly

fo r a base shear of about 13 percent gr a v it y ) . Although seve relydamaged, the b ui ld in g did not c ollap se but was subsequ ently demolished

because of the ea rthquake damage. The major damage to the b u il d in g was

the fa il u r e of the four re info rc ed concrete support columns on the east

sid e of the b u il d in g . The con crete a t the base of the columns on one

side of the b ui ld in g was sha ttered and the v e rt ic a l rei nfo rc ed beams were

seve rely bent. The p a rt ia l colla pse of the support columns allowed

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the eastern extr em ity of the bu i ld in g to sag about 1 f o o t . In the upper

leve ls of the b u i ld in g , the south ex te r io r w al l was ex ten sive ly cracked

near the window fram es. A ls o , the re was p a r t ia l se pa ratio n between

f loors , wal ls , and ce i l ings ; fa l len suspended ce i l ing t i les ; damage to

in te r io r w a l l s ; and o f f i ce fu rn i tu re sh i f ted o r over tu rned . A shear wa l l

system was used to r e s i s t NS motion and a frame system used fo r EW

fo rc e s . At the east and west ends of the b u ild in g above the second

f lo o r , the ex te r io r consisted of rein forc ed concrete shear w al ls . The

ground st or y had fou r w al ls r e s is t i n g NS fo rc e s. The second f l o o r slabs

tra ns fe rre d shear forc es from the end w alls in the second stor y t o

in te r i o r w al ls in the ground st or y. A thi ck er s lab at the second f l o o r

was used to aid the shear tr a n s fe r. The foun datio n con sisted of p i l e

caps re st in g on tapered p i l e s .

Sixteen accelerat ion records were obtained at the bui ld ing

s i t e . Three were f r e e - f i e l d . Peak ground acce lera tions were 0.29g NS

and 0.32g EW. Mo tion measurements in d ic a te d b u il d in g pe riod s were 0.62

seconds i n th e EW d ir e c t io n , 0.44 seconds in t he NS d ir e c ti o n and a

to rs io n mode pe riod at 0.35 seconds. Much in e la s ti c behavior was also

noted. Peak measured roof acc el er a tio n was 0.48g EW.

El C entro Steam P lant (See Appendix E) - The El Centro Steam

Plan t i s located i n the no rtheast po rt io n o f El Cen tro, about 25km from

the ep icenter and 5km from the causa tive fa u lt fo r the 1979 earthquake .

The NS component of the ac ce ler at ion rec ord fro m USGS re co rd ing s ta ti o n

5165 which was lo ca ted less than 1km from the steam pla n t had a peak

recorded acc ele ra tio n of 0.49g NS. In sp ite of the high ground

acce lerat ions at the plant s i t e , no s ig n i f i c a n t s tr uc tu ra l damage

occurred to the plant.

The El Centro Steam Plan t has fou r u ni ts th at burn o i l or

na tu ra l g as. U nits 1 , 2, and 3 were designed by Gibbs and H i l l and b u i l t

in 1 949, 1952 and 1 957, re sp e ct iv e ly . U nit 4 , the newest and larg es t

w i th a 80-MW e le c tr ic ou tpu t, was designed by Fluor co rp ora t ion , L t d . ,

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and b u i l t i n 1968 . Combined ou tpu t of a l l fo u r u ni ts i s 174 MW. Each

un it of the p lant i s s t r u c tu ra l l y independent and contains three st ru c

tu r es : a tu rb in e bu i ld in g , a tu rb in e pedesta l and a bo i le r s t r uc tu re .

So il at the s it e con sists of very deep a l lu v i a l deposits composed of

s t i f f to hard c lays in te r l a in w i th laminat ions o f s i l t y c lay loam.

Un its 3 and 4 were o pe ratin g when the earthquake o cc urr ed .

Un its 1 and 2 were down fo r maintenance. The op era ting un its tri pp ed o ff

l in e when s ta t io n power was l o s t . Un it 3 was restore d to servic e w it h in

15 minutes a fte r the main shock. U nit 4 was resto red to se rvice w ith in

two hours. Several of the references c ite d rep ort the de tai led ea rth

quake ef fe ct s on the p la n ts . In ge ne ra l, only minor damage was observe d.

There was a great deal of motion at the s i t e , and vario us tr ac es of the

motion were observable, e.g., skid marks of reheater feet, bent seismic

sto ps , e tc . There were"some equipment f a i l u r e s ; leaks occurred in the

water supply for the hydrogen coo lers ; a two- inch pipe f a i l e d ; a buckl ing

fa i l u r e occurred in an o i l storage tan k; o ld wooden forced dra f t coo l ing

towers sustained damage to the wooden structure; and a l ightning arrester

broke o ff a tran sfo rm er. St ru ct ur al damage was l im ite d to buck ling of

bracing members in the bo ile r st ru ct ur e s.

The seism ic design basis of U nits 1 , 2 and 3 is unknown. Review

of the pro je ct s pe ci f ic a t io ns f o r U n i t 4 ind ica tes tha t the s tee l f raming

was designed fo r a la te ra l s ta t i c eq uiva lent seismic load ing of 0.2g

(dead and l i v e loa ds ). The Un it 4 tur b in e bu i ld i ng is a mom ent-resist ing

ste el frame w ith rei nfo rce d concrete shear w al ls on 3 si de s. The boi le r

st ru ctu re is a braced ste el frame wh ile the turb ine pedestal is a r e i n

forced concrete frame tha t supports the tu rb in e ge nerator. The pedestal

shares a box-girder foundat ion with the turb ine bui ld ing and boi lers t r u c t u r e .

Analyses o f U nit 4 o f the steam pla nt have been re po rte d i n

References A-37 and A-1 28. Both analyses of th e Unit 4 st ru ct u re were not

conducted for the expressed purpose of correlat ing predicted structural

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damage w ith observed s tr u c tu ra l damage. The an aly sis pre sented i n

Reference A-37 was conducted for the purpose of estimating equipment

response le ve ls , th us , the st ru ct ur al model was gr ea t ly s i m p l i f ie d . The

an alysis presented in Reference A-128 u t i l iz e d a general three-dim ensiona l

repre sen tat ion of the Uni t 4 st ru ct u re , but considered the founda t ion to

be f ix ed -bas e , t hus , i gno ri ng s o i l - s t ru c tu r e i n t e rac t i on e f f e c t s . I t

should be noted that the purpose of the analysis conducted in Reference

A-128 was to demonstrate th at a p a rt ic u la r set of con serva tive design

c r i t e r ia would y ie ld analysis res ul ts which would grea t ly overpredic t the

observed st ru ct u ra l response leve ls of the Un i t 4 st ru ct u re .

Since por t ion s of the Un it 4 str uc tu re were designed fo r a

s t a t ic 0.2g la te r a l forc e and yet the observed damage fo r a recordedground mot ion, character ized by a 0.5g peak accelerat ion, was s l ight, the

Un i t 4 str uc tur e was selected to be inve st igate d in de ta i l as part of

th is stud y. This inv es t ig at ion is described in Appendix E. In ge ne ral ,

the resul ts of this study indicate that the concrete shear wal ls , which

were not considered as part of the design lateral force system, actual ly

ca rr ie d much of the la te r a l fo r c e . Thus because of the presence of these

shear wal ls, the basic response of the turbine bui lding remained within

code l i m it s fo r the 0.5g ground motion due to the p a rt ic ip a ti o n of thesew alls in the ov e ra l l l a te ra l response. However, the re were loc al regions

in which the calculated seismic response of the turbine bui lding steel

frame was nearly double the plastic moment capacity and in which horizon

t a l diagonal bra cing members exceeded y ie ld by a fa c to r of 4 due to the

lack of ef fe ct ive diaphragms in some reg ions . In the bo i le r st ru ct u re ,

e la s t ic a l l y ca lcu late d seismic response would also in dic at e more damage

than was a c tu a ll y obs erved. For members damaged du rin g the e arth quak e,

the rat io of calculated seismic response to ul t imate capaci ty is 4.0 or

gr ea te r. For the members w ith no observed buckl ing fol lo w in g the ea rt h

quake, the rat io of calculated seismic response to ul t imate capaci ty is

4.9 or le ss . Hence, i t may be concluded th a t for the Im pe rial V al ley

earthquake and the steam plant st ru ct u re , the onset of s i g n i f i ca n t

st ru ct ur a l damage should not occur at el a s t i c a l l y c alcu lated force leve ls

less than about 4 t imes the code sp ec if ie d u lt im ate ca pa city . The

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investigation of the El Centro Steam Plant demonstrates that the plant

had significantly more capacity than the design level of 0.2g due to the

additional turbine building shear walls as well as other factors such

that it may be concluded that seismic capaci ty cannot be directly

inferred from the design level earthquake acceleration . In addit ion,

this investigation also demonstrates that elastic analyses using

instrumental earthquake ground motion predicts much more damage than

actually occurs during an earthquake even if all seismic resistant

mechan isms for the structure and code specified ultimate capacities are

accounted for. This investigation points out the need for including

inelastic energy absorption capability, wave scattering phenomena,

repeatable acceleration peaks , duration of strong shaking, etc ., in

design analyses of critical facilitie s such that analytical results

realistically reflect potential levels of structural damage.

1940 versus 1979 Earthquakes - There are man y similarities

between the May 18, 1940 and the October 15, 1979 Imperial Val ley

earthquakes. Ground rupture from the 1979 event followed the same

pattern as the 1940 ev en t, and showed man y of the same features and

chara cteri stics . The similarity also exten ds to the distribution and

types of damage. Their magnit ude, about 6.5, and felt areas are

approximately the s ame , yet damage from the 1940 earthquake was much

greater if damage to the Imperial County Services Building in El Centro

is excluded in the c omparis on.

It should be noted that the maximum acceleration recorded at the

same site in El Centro during the 1940 and 1979 earthquake s were 0.36 and

0.40g, resp ecti vely . This suggests that the levels of maximum horizontal

acceleration in El C ent ro, were not marked ly different in the two earth

quakes, but the duration of strong shaking differs by a factor of at

least thr ee. The differenc e in damage levels suggest that the greater

duration of shaking during the 1940 shock might be the reason for the

greater damage.

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Implication - The general lack of damage (excluding the Imperial

County Services Building) during the 1979 Imperial Valley earthquake for

0.3 to 0.6g ground mo tion ind ica te s the importance of ground motion dura

t i o n i n est im ating damage p o te n t ia l and the need fo r in e la s t i c energy

absorpt ion capabi l i ty in the design of st ructures to mit igate damage.

C e rt a in ly , one would have expected grea ter damage i f these str on g ground

ac ce lera tion s had been asso ciated w ith long er d ura tion re cord s such as

those recorded in the 1971 San Fernando or in the 1952 Kern County

earthquake.

A.3.6 P ar k f i e l d , C al i fo rn ia Earthquake, 1966

(A-32. A-33, A-115 through A-118)

The Parkf ield-Cholame area of California was subjected to veryhigh ground acc ele rat ion s from a moderate earthquake ( M L = 5. 6 , Ms = 6.4 )

on June 27 , 1966. The epice nte r was locate d on the San Andreas f a u l t

approxim ately 5 miles northwest of P a rk f ie ld or 20 miles northwest of

Cholame. A maximum in t e n s it y V II was assigned to a sm all area in and

near the San Andreas fa u lt zone, extending sou thea ster ly from a few miles

no rth of P a rk f ie ld to a few miles south of Cholame. Five strong motion

instrum ents and f i f t e e n seismoscopes recorded the ground m oti on . The

maximum recorded a cc ele rat io n was 51 percent g ra vi ty (S ta t io n 2) locate dabout 200 fe et of the f a u lt t r a c e . Other peak ac ce lera t ion values were

47 (Stat ion 5 ) , 28 (Sta t ion 8) and 7 (Sta t ion 12) percent gr a vi t y a t

distan ce of 3, 6 and 9 m il e s , res p ec t iv e ly . The accelerometer at Temblor

also located about 6 mi les f rom the f a u l t recorded 41 percent g ra vi ty .

Although 0.5g was recorded at the f a u l t , the ground motion attenuated

ra p id ly w ith distance and at 10 m iles from the fa u l t the maximum

ac ce lera t ion was reduced to about one -tenth of i t s near fa u lt va lue . At

Cholame Sta t ion 2, the motion cons isted p rim a ri l y of a si n gl e pulse wi th

stro ng motion less than 2 seconds. However, ground mo tion recorded at

f u r ther d is tance los t t h i s pu lse - l i ke charac te r i s t i c .

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Despite the large ac ce ler at ion s, very l i t t l e damage was caused

by the earthqua ke. In ge ne ra l, the area was spa rsely populated and the re

were no m u lt i- s to ry b u ild in g s. However, th er e were a number of sm all

s tr u ctu re s, a couple of o i l company pumping p lan ts, an e le ct r i ca l t ra ns

former s ta ti o n , several br idg es , and houses, e tc . A pump st at io n near

Shandon was subjected to ground motion e stimated at 25 percent g r a v it y .

No damage occured to the b u il d in g or t o a st eel st ac k. Another pump

st a tio n loca ted closer to the fa u lt and subjected to higher ground shaking

also saw no damage.

In Cholame and v i c i n i t y , a domestic water tank con tain ing

approximately 4500 gallons of water saw an estimated 0.4g acceleration.

Although th er e was evidence of s l i g h t base movement, no damage was

observed. At a Standard O il S ta ti o n , some metal forms bu ckled .

The f i r e s ta t ion b ui ld in g in Pa rk f ie ld is located w i th in l im i ts

of the fa u lt and was subjected to an estimated acc elera tion greater than

0 .4g . The sta t io n is a on e-s tory , rein for ce d br ick bu i ld in g presumably

constructed according to UBC requirem ents. A conse rvative estimate of

the design base shear would be about 0.1 5g . Given the high le ve l o f

ground m otio n, some y ie ld in g would have been pre dic te d. The st a ti o n ,however, was not damaged.

Implications - The observed performance of the Parkfield f i re

stat ion indicates that elast ic calculated earthquake forces would

su b st an t ia l ly overestimate actual fo rce s. Co rrela t ion between e la st ic

predicted and observed behavior would not be good.

Reference A-33 states in general, judging from the effects ofthe main shock on structures, the recorded maximum acceleration appar

e n tly lacked damage p o te n ti a l . Probable reasons are (a) short dur ation

of the maximum ground ac c e le ra ti o n , (b) predominent pe rio d of the ground

accelerat ion out of range of the natural periods of exist ing structures,

and (c) few structures of engineering s igni f icance located in the v ic ini ty

of the maximum recorded ac ce le ra tio n s.

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A.3.7 Bear Valley Earthquake, 1972 (A-34)

The Bear Valley earthquake occurred on September 4, 1972 in San

Benito Coun ty, Cali forni a. The earthq uake was of small size

( 13 = 4.6 , M|_ = 4 . 7 ) . The hyp oce nte r wa s locat ed at a dept h of 5km,

approxi mately 1km southwest of the most re cent ly active trace of the San

Andreas fau lt. The aftershock locations define a vertical plane 3km in

width and 4km in length parallel to the San Andre as fault . Recent work

indicates that there may be a systematic bias to the west for the location

of the earthqua ke in the reg ion . Movement of the aftershock z one, a few

kilometers to the east, would place the zone direc tly on the San An dr ea s.

Three strong moti on instruments wer e located within 10km of the

calculated epicenter. The stations, recorded peak horizontal accelera

tions and calculated epicentral distances are: the Stone Canyon

Geophysical Observatory, peak acceleration 0.23g, distance 3km; Melendy

Ranch Barn, peak recorded acceleration 0.70g, (0.52g c o r r e c t e d ) , distance

9km; Bear Valley Fire Station, peak acceleration 0.17g, distance 10km.

Eastward movement of the rupture zone to place it on the San Andreas

fault would result in the distance from the rupture zone to each of the

three stations being only a few kilome ters . All three instruments are

located on relatively shallow deposits of recent alluvium.

The earthquak e occurred in a sparsely populated region. The

principal effect of the earthquake pertained to numerous rockfalls along

the steep banks of the San Benito Riv er. The epicentral region was

assigned an intensity VI with only slight damage repor ted. The damage

was reported at the Bear Valley Fire Station at a distance of approxi

mately 9km from the epicenter. At the fire station, cinder block walls

developed fine crack s, a fire truck rocked noticeably from side-to-side,

and a vertical pip e from a water heater exten ding through the ceiling

crushed the sheet rock. At Melendy Ranch, approximately 8km from the

epi cen ter , small landslide s occurre d, small objects fell and vehicles

rocked.

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Implications - A s n o major eng ineered structures were located

within t h e region affected b y t h e Bear Valley earthquake (the design

basis f o r t h e Bear Valley Fire Station is unknown) no significant

statement c a n b e made concerning t h e effect o f high ground acceleration

earthquake motions on engineered structures from this earthquake.

A.3.8 Coyote Lake Earthquake, 1979

(A-105, A-106, A-107, A-108, A-109)

On August 6, 1979, a ma gnitud e, M[_ = 5.7 , earthquake occu rred

at a depth of 10km in the Calaveras f a u l t zone at Coyote Lake ap pr ox i

ma tely 50 km southeast of San Jose or 10km no rth- no rthe as t of G il ro y ,

C a l i f o r n i a .

Because of the high seismic act iv i ty in the Gi l roy-Hol l is ter

area, there were a number of strong motion instruments in the area which

recorded the ground mo t ions. A l l s tat io ns in the G i l ro y array are wit hi n

16km of the epice nter and extend from a rock si te through an a l l u v ia l

va l le y to another rock s i t e . The sta t ion s in the Bear Va l ley array

loca ted between 50 and 75km from the e pic en ter recorded ac ce lera tion s

gre ater than 0.05 g. A maximum ho riz on ta l ac ce lera tion of 0.42g was

recorded at st at io n 6 located on rock wi th in 1km of the fa u l t t race andto the southeast of the epicenter.

The earthquake caused wery l i t t l e damage in the ep icen tral area,

which is mountainous and spa rsely p op ula ted . A stron g motion instrum ent

at Coyote Dam recorded a ho riz on ta l ac ce le ra tio n of 0.23 g. The highe st

MM in te n s it y values of V II were observed in the G ilro y and San Fe lipe

Lake areas . In te n s it i e s were higher in these areas due to deep, a l l u v i a l -

f i l l e d val leys and the dire ct io n of earthquake energy propaga t ion.

Reports f rom G i l roy and H o l l is te r ind icated no s ign i f ic an t

st ru c tu ra l damage. Minor cosmetic damage co ns ist in g of pla ste r c rac kin g,

some pounding between adjacent b u il d in g s , and glass breaking occ urre d.

In g en e ra l, the le ve l of damage was ve ry low.

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Imp l icat io ns - Although the earthquake af fec ted a va r ie ty of

commerc ia l s t ructures in both G i l ro y and H o l l is te r , in s uf f ic ie n t

published data describing the performance of specif ied structures

e x is ts . Consequently, no co rr el at io n between pred icted and observeds tr u c tu ra l performance can be made.

A.3 .9 O ro v i l le , C al i fo rn ia Earthquake, 1975 (A-147)

The O ro v il le earthquake occurre d on August 1 , 1975, near

O r o v il le , C a li fo rn ia . The earthquake was of medium size (M| = 5. 7,

M^ = 5.6) w ith a hypocenter depth of 8km.

Five str on g motion instrum ents were loca ted w it h in 35Km of the

earthquake epice nter . The O ro vi l le Dam seismograph st a t i o n , a rock s i t e ,

recorded a peak ho riz on tal ac ce lera t ion o f O.llg and a peak vert ical

ac ce lera t ion of 0.1 4g. Two instrumen ts were on alluvium and recorded

peak accelerations of 0.08g and 0.07g while the remaining two instruments

were on rock, one recording a peak acceleration of 0.03g and the other

not be ing t r iggered.

Twelve strong motion instruments were installed in the

ep ic en tra l area a fte r the occurrence of the main shock. Over 100 stro ng

motion recordings were obtained for aftershocks in the magnitude range

\ = 3.0 to 5.0 at e pic en tra l distances ge ne rally less than 12km.

The O ro vi l le Medical Center is a one -story wood frame st ru ct ur e

wi th a two -sto ry p ort io n on a side h i l l . The building is located on

approximately 100 fe et of Cenozoic terr ac e gra ve ls. Peak ho riz on tal

ac ce ler atio ns between 0.04g and 0.39g were recorded fo r afters hoc ks in

the magnitude range M|_ = 4.0 to 4.9 a t hyp ocentra l dista nce s of 7km to11km. Damage cons isted p ri m a ri ly of no ns truc tura l pla ste r damage.

With in the ci ty of Orovi l le , where the peak hor izontal accelera

ti o n s may have been of the orde r o f O.lOg to 0.1 5g , bu il d in g damage con

sis ted p ri m a ri ly of broken windows, cracked plas ter and broken c e il in g

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tiles. Very little structural damage occurred in modern building s. Only

minor damage w a s observed in any o f t h e several Sta te Water project

facilities i n t h e area, including t h e O r o v i l l e D a m a n d t h e associated

power plant.

Implications - T h e only engineered structures o f significance in

the epicentral area were t h e State Water Project facilities at Oroville

Dam and Thermal ito Afte rbay . These facili ties experienced peak horizon

tal accelerations o f t h e order o f O . l g during the main shock with only

slight damag e. This low level o f shaking d i d n o t allow an effective

assessment o f t h e correlation between predicted an d observed behavior.

A.3.1 0 Greenvi lle, California Earthqua ke. 1 9 8 0

(A-141, A - 1 4 2 , A - 1 4 3 )

In January, 1980, the Livermore Valley area of California was

shaken by a se rie s of earth qua kes . Most of the damage was the r e s u lt of

shocks which occurred on January 24th. The largest shock was a ML = 5.5

loc ate d 12km no rth of t he Livermore V al le y and 20km northwe st o f th e

Lawrence Livermore National Laboratory (LLNL) along the Greenville

f a u l t . In ad di t io n to the main shock, the re was a foreshock ML = 2.7 a

minute and a ha lf e a rl ie r and an aftersh ock ML = 5. 2, loca ted again onthe Gre env i l le fa u lt 14km to the south of the f i r s t pr i nc ipa l shock. The

second principal shock caused essentially no damage.

There were no strong motion instruments in the Livermore Valley

or at LLNL. The clos es t instru me nts were at Del V a ll e Dam and Ve teran 's

H os pit a l , south of General E le ct r ic Va l le ci to s Plant (Pleasan ton), Kodak

F a c il i t y (D ub lin ), and Trac y. Peak ground ac ce lera t ion recorded were

0.26g, 0.1 8g, O . ll g , 0.15g and 0.09g. Estimates fo r ground motion at theLLNL Site were 0.2 to 0.3g.

In general, damage to structures in the Livermore vicinity was

very l i g h t . A few chimneys were cracked and seve ral u nre inforc ed br ick

se rpe ntin e w al ls were to p p le d . The abutment on G re e nv ill e Road Overpass

on Int er sta te 580 which passes almost d ir e c t l y over the Gree nvi l le fa u lt

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had one abutment drop 6 to 10 inches i n te rr u p ti n g t r a f f i c . There was

some in si g ni f ic a nt minor cracking in the concrete s tru ct ur e. The

Livermore City H a l l , a f a i r l y new re info rced concrete b u i ld in g , had no

s t ru c tu ra l damage; however, the re was ex ten siv e damage to the suspended

T-bar ce il in g s . Elsewhere in Livermo re, there was very l i t t l e damage tostructures except for occasional broken glass.

Most of the damage was concentrated in the eastern portion o^

the v a ll e y , damage was noted p r in c ip a l ly to a mob ile home pa rk. A high

percentage of mo bile homes f e l l o ff t h e i r stands and sus taine d damage.

No damage was rep orte d to an e l e c t r i c a l su bs ta tio n or any equipment which

was located 1 m ile west of Gre en vil le f a u l t . Two wine ries are located

about 2 to 3 kil om ete rs south east of Live rm ore . One su ffe re d no damageto any s tr u c tu re , wh ile exte nsiv e damage was sustain ed by an elevated

water tank and wine tanks i n the oth er . An e la s ti c e stimated base shear

c o e ff ic ie n t of 35 percent of g ra v it y was estima ted to have caused the

observed damage. Ty pic al damage to the small wind fi b e rg la s s lin ed ste el

tanks was top p lin g due to broken leg s . No ru pt ures occurred and damage

was not s ig n if ic a n t . The larger tanks (sta in le ss st ee l) suf fered more

damage. There were fa il u re s to anchorage, loc al bu ck lin g, concrete

s p a ll in g of support base, and permanent ov er al l d efor ma tions . Only onetank rup ture d. Total do l la r value fo r re pairs was est imated at $1 to 1 .5

m i l l i o n .

The Lawrence Livermore National Laboratory occupies an area of

ap pro xim ate ly one square m ile loc ate d about 2 m iles east of downtown

Liverm ore. I t contains some 147 bu ildin gs and 975 t r a i l e r un its (re pre

sent ing about 3.5 m i l l i o n square fee t of f lo o r a rea). Design c r i t e r i a

f o r LLNL f a c i l i t i e s va ri es co n side rab ly . C r i t i ca l f a c i l i t i e s ( i . e . , those

with radioactive materials) were designed or evaluated using dynamic

an aly sis w ith peak ground motion values o f 0.5 to 0 .8 g; lase r and magnetic

fusio n experimental f a c i l i t y (with h igh ca pita l c ost) employs a 0.25g

ground acc elera t ion w ith a dynamic an aly sis ; o f f i c e bui ld ings vary f rom

no seismic design to the Uniform Bui ldin g Code with an equ ivalen t s ta t i c

c o e ff ic ie n t of about 0. 2; equipment and fu rn is h in g also v aries from no

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seismic design to a greater than l.Og s ta t i c c o e ff ic ie n t. Damage to

equipment and f a c i l i t i e s were est imated at $10 m il l io n . A large part of

the cost was fo r s t ruc tur a l repa i rs to th ree adm in is t ra t ive bu i ld in gs ,

fo r the repa ir of a rc hi te ct ur al - ty pe damage, and for esse nt ia l improve

ment to meet upgraded seismic sa fe ty stan dard s. The to t a l d o ll a r co st

fo r both re p a ir and improvements was es tim ate d a t between $15 and $20

m i l l i o n .

There was no st ru ct ur al damage to c r i t i c a l f a c i l i t i e s at LLNL

and on ly minor cosmetic or arc hi te ct ur al damage. These f a c i l i t i e s are

ty p ic a l l y o f very s t i f f low r is e shear wa l l type o f con st ruc t ion . In

genera l , bu i ld ing fa c i l i t y damage was p r im ar i l y to f i ve no n -c r i t i c a l

bui ld ing s a l l o f which are moment re s is t i n g st ru ctu re s. The in te r i o r

fur nis hin gs were most af fe c te d . Connections between t i l t - u p concrete

slabs and th e ir support ing s tru ct ur al stee l frames were af f ec ted . Core

walls had considerable cracking in some buildings.

The 975 in d iv id u a l t r a i l e r un its at LLNL are assembled in to 216

complexes. Eighty-seven were t ie d down. In ge ne ral, there was l i t t l e

damage to t r a i l e r s . In complexes not ti e d down, one t r a i l e r was badly

damaged (w alls cra cke d, e tc .) and fo ur were mod erately damaged ( i n t e r i o rce i l i n g t i le s and l i g h t f ix tu re s d isp lace d) . No st r uc tur a l damage

occurred to t ra i lers t ied down.

In ge ne ra l, much of the a ctu al cost of rep ai r at LLNL res ult ed

from cosmetic damage. T a ll bookcases th a t were not anchored tip pe d ov er ,

damaging wa lls and breaking i n te r io r gla ss . Sheetrock p a rt it io n s were

cracked in many bu i ld in gs . Ce i l ing t i l e s , l ig h t f ix tu re s , and a i r

d if fu s e rs (not anchored) f e l l to the flo o r and broken water pipes causedwater damage.

Im pli ca tio ns - The engineered s tru ct ur es behaved as would be

expected of st ru ct ur es designed in accordance wi th UBC code design

provisions which resist moderate earthquakes without structure damage but

allow nonstructural damage.

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A.3 .1 1 Other Earthquakes

In addition to the above included cases, numerous other examples

e x is t where obs erv ations have been made of st ru ct ur es sub jecte d to

r e la t i v e ly st rong ground mot ions. Although not included in d e t a i l , they

a re wor th c i t ing .

The lack of damage in the vicinity of the ground accelerat ions

due to the 1972 Ancona, It a l y earthquakes i s noted in Reference A-1 3.

The 1 972 earthquakes magnitude o f 4 to 5.0 produced reco rded maximum

ac ce ler atio ns of 0.6g at Rocca (roc k) and 0.4g at Palombina (s ed im en t).

Ep ice ntra l distances to these st at io ns were about 7 and 15km, respec

t i v e ly . I t a l i a n se ismolog is ts and engineers (A-39) repor t the re la t i v e ly

small damage and the fac t th at bu ild ing s designed w ith seismic c o e f f i cients of about 0.07g in accordance with the recently adopted Ital ian

earthquake code, su ffe re d no damage. This con clusion again in di ca te s

tha t short durat ion records and in e la s t i c energy absorpt ion c a p ab i l i ty of

st ru ctur es l i m it actual damage. Without accounting fo r these fa c to rs ,

e la s t i c computed force s compared to u lt im ate ca pa cit ie s would gr ea tly

overpredict damage.

References A-140, A-154 descr ibe b r i e f l y s t ru ct ur al performance during the 1940 Imperial Valley (El Centro) earthquake which caused

con side rable damage. References A-1 52, A-155 des cribe e ffe c ts from the

1949 Olympia ear thqu ake . Reference A-55 describ es th e damage to

s tr u c tu re s caused by the 1 964 Alaska earth qu ake . There were no reco rded

motions fo r the 1 964 Alaska ea rthquake.

References A-26 and A-40 address the damage th a t the 1906 San

Franc isco earthquake (magnitude 8.3) brought on the C it y o f San Fr an cis co .

The e pice nt er of the 1906 earthquake was about 17km from downtown San

Franc isco on the San Andreas f a u l t . There were no ground motion r e

co rd ing s. References A-26 and A-40 suggest th at cu rre nt procedures would

estimate peak ac cele rat io ns exceeding l.Og in downtown. Fu rth er , sp ec tral

ac ce le ra t io ns , i f based on the peak ac ce lera t ion va lue , w it h reasonable

damping ratios and at the fundamental frequencies of major buildings of

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the e ra , would be 2.0g or more. The papers in di ca te th at the re were 52

major b uild ing s in San Fra ncis co, none of which were sp e c if ic a ll y designed

to re s is t earthquake s. The ir resi sta nc e to earthquakes was a by-product

of th e ir wind design and no n- str uc tur al facades and p a rt it io n s . None of

the b uild ing s collap sed and a l l but seven were repair ed and return ed to

use. Most are s t i l l in use today. A few of the su rvi vin g b uildin gs

include the 19-story Central Tower, the Fairmont Hotel, the old port ion

of the S t. F rancis H o te l, the post of fi c e at Seventh and Mission S tree ts

and the Ferry B u il d in g . None of these bu ild ing s would meet cu rre nt code

requ irem ents . The referenc es in di ca te tha t an average base shear c o e ff i

ci en t of 0.4 would be a generous estimate of the y ie ld -l e v e l stres s

capaci ty fo r these bu i ld ings.

A number o f obs ervation s have been made reg ard ing the e ff e c t of

more di st an t earthquakes on st ru ct ur es . References A-11 0, A-146, A-148,

A-149, and A-150 discuss the 1967 Caracus, Venezuela, 1974 Lima, Peru,

and the 1977 Romania earthquakes whose ep icen te rs were fa r removed from

i t s hig hly affec ted are as. Structure s with longer periods were more

inf luenced and so i l cond it ions p layed a larger ro le .

Another more distant earthquake series, the 1960 Chile earthquakes, caused con side rab le damage and is f a i r l y well-documented in

References A-151 , A-26, A-40, A-43, and A-88. Of pa rt ic u la r note, is the

behavior of the Huachipato Steel Plant located near Concepcion in Central

C h i l e . This plan t was subjec ted to stron g mo tions . The pla nt was b u i l t

in 1947-1960. The f a c i l i t y includes a b las t furna ce, stee l product ion

plant and blooming, merchant and rev ers ing m il ls and a fa b ri c a ti n g shop.

There are also many v e r ti c a l stacks and seve ral e levate d water tan ks . In

genera l , the plant was designed using allowable stress values associated

with st at ic la te ra l c oe f f ic ie nt s bel ieved to be in the range of 0.10 to

0.3 0. An ex tens ive stu dy of the plan t was conducted in order to develop

the most l i k e l y sp ec tral response ac ce ler at i on s. The actual damage, or

lack of damage, was then used to r ec on str uc t the p robable response p at ter n

and then to determine the base shears and an approximate spectral diagram

fo r the pl an t. The probable spe ctral ac cele rat io n at the period and

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damping of the most c r i t i c a l stru ctu res is 1 .2g. Damage pr ed ict ion s based

on earthquake force s developed from such sp ec tral acc eler at ion s c le a rl y

would suggest s ig n if ic a n t damage. Very l i t t l e damage was observed.

Agadir, Morocco was severely damaged by an earthquake on February29, 1 960. The earthquake was assigned a magnitude of 5 .8 , w it h e stim ates

ranging from 5.5 to 6 .0 . The epic ente r of the earthquake was w ith in 2 to

3 kilo m ete rs of the center of the c i t y of Ag ad ir. Damage obs ervation s

suggest a depth of focus no more than 2 or 3 ki lo m e te rs . The rad ius of

s ig n if ic a n t damage was very con fine d, w it h in a 5km radiu s of the e p i

cente r. In te ns it i es of X and XI were assigned to th is cen tra l c i t y

area. No stro ng motion data are a v a il a b le . Damage evidence (A-U O)

str on gly suggests tha t the ground motion consisted l a rg e ly of a sin gleprimary ac ce lera t ion pulse of short du ra tio n. There were several types

of s tru ct ur es in Agadir at the time of the earthq uake . The most preva

lent was constructed with unreinforced or poor ly re inforced masonry.

Nearly all such structures nearest the quake epicenter collapsed or were

damaged beyond repair.

Another principal type of structure employed reinforced

co nc ret e. Many had concrete columns and beams fo r ca rry in g v e r ti c a l

loads; however, th e j o i n t s between members lacked both moment and shear

resistance c a p a b i l i t y . When subjected to la te ra l sha king, the beam-

column connections f a i l e d . The lack of c o n tin ui ty between the various

s tr u c tu ra l elements did not allow a re d is tr ib u ti o n of loads and many such

st ru ct ur es co lla ps ed . I t was ge ne ra lly observed th at even in cases where

s t ruc tu res had s ig n i f i ca n t s ta t i c res is tance to la te r a l f o rce s , the i r

earthquake performance was poor due to a lack of d u c t i l i t y and energy

absorpt ion capacity.

References A-44, A-121 and A-122 report on the June 8, 1975,

earthquake ( M L = 5. 2, M^ = 5.7) th at occured in the Ferndale region of

Northern C a l i fo rn ia . The epicenter was located 4 miles south and s l i g h t l y

west of Fernd ale . The Humboldt Bay Power Pl an t is lo ca ted south of Eureka

and adjacent to the bay. The plan t con sists of two un its of fo s s il fu el

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powered gen erato rs and a nuc lear powered gen erato r u n it (U nit 3 ). Both

fossi l fuel units were operating at the t ime of the earthquake while the

nuclear un it was out of ser vice f o r a scheduled re fu e l i n g , maintenance

and m o d if i ca tio n . The only strong motion accelerograms recorded during

the earthquake were those obtained at the power plant site located 12

miles from the epice nter of the earthquake. A MM i n tens i t y o f V i s

assigned to the pla nt s i t e . Un it 3 was instrume nted w ith three strong

motion instr um en ts. At these sensor lo c a tio n s, the large st peak acc elera

t io n was recorded in the (tran svers e) EW d ir e c ti o n . Peak (c orre cted )

values were 0.35g, 0.25g and 0.1 6g, fo r f r e e - f ie ld (storage b u i ld in g ),

ground leve l ins id e the ref ue l ing bu i ld in g and reactor caisson (78 fe et

below grade ), re sp e c tiv e ly . Strong shaking was about 3 to 5 seconds.

The corresponding ac ce ler at ion response sp ectra f o r 2 percent dampingind ica tes tha t maximum sp ec tra l values occurred fo r both instrumen ts in

th e Refu eling B ui ld ing between 2 to 3Hz and fo r the Storage B uild ing

between 2 to lOHz. The e ff e c t of the earthquake was to t r i p the generator

o i l c i r c u i t breakers and the aux i l ia ry t ransformer fo r both fo ss i l u n i ts .

On the nuclear u n i t , the on ly abnormal co n di tio n caused by the earthquake

invo lved spu rious ac tion s on one of a pa ir of redundant rela ys i n the

ref ue l ing bui ld in g h igh d i f fe re n t i a l pressure protec t ion system. Small

waves (9 to 12 inches) were observed in the spent fuel poo l . Nos ig n if ic a n t earthquake re la te d damage was observed .

References A-1 1 4, A-123 and A-124 re po rt the ef fe ct of a

November 8, 1980 ear thquake on the Humboldt pl a n t . Th is earthquake had a

surface wave magnitude of 7.0 and occured o ff the coast of C a lif o rn ia

west of Eureka and the Humboldt pl a n t. F re e -f ie ld peak ground motion

estimates were 0.15g to 0.25g . The e ff e ct s of the earthquake on pla nt

s tr u c tu re , pi p in g , equipment and components were m inim al. The on lys tr u ct u ra l damage was permanent de form ation of a re in fo rc ed masonry w all

of the pl a n t' s on e- sto ry cold machine shop. The w all is 18 fe e t high and

spans ho ri z o n ta ll y 70 to 80 fe e t between cross w a ll s . Movement at the

base of thre e w ater stora ge tanks was eviden ced , but the re was no damage

to the tank or attached p ip in g . Effe cts on pip ing and mechanical

equipment were e ss e n t ia l ly n i l .

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References A-45, A-97 and A-144 discuss earthquake effects on

two nuclear power p la n ts . F ir s t is the Fukishima Nuclear S ta tio n which

was subjected to strong motion from the 7.4 magnitude Miyagi-Ken-Oki,

Japan earthquake o f June 1978 loc ate d about 140km from the s t a t i o n . Peakground mo tion was ap pro xim ate ly O .lg w ith a maximum response ac ce le ra tio n

o f about 0.25g . OBE design motion was 0.1 8g . The on ly damage repor ted

fo r the power complex was breakage of some n o n - c r it ic a l e le c t r ic a l i nsu

l a t o r s . The second is the Wm. H. Zimmer Station, Moscow, Ohio which was

subjected to ground motion from the July 27, 1980 Sharpsburg, Kentucky

earthquake. Magnitude of th is event was 5.1 w ith i t s e picen ter located

46 mi les south-southeast of the st a t i o n . Peak acc elera t ion at the s i te

was 0.0 4g , below the OBE of O .l g . There was no v i s i b l e damage to any

structures at Zimmer.

References A-13 4, A-135 and A-136 ind ica te th at the V i r g i l C.

Sumner Nuclear Station, located near Parr, South Carolina was subjected

to ground mo tion from sev era l nearby magnitude earthquakes in 1 978. The

strongest event occurred on August 27, 1978 and had a local magnitude of

2.8 . The epicenter on th is even t, ca l led Monti ce l lo R eservoir Earth

quake, was about 6500 fe et northwest of the nuclear s ta ti o n . The fo ca l

depth is estimated at 100 to 500 m eters. The nearest rec ord ing i n s tr u

men t, a USGS stro ng motion accelerometer was locate d on a s tr a ig h t l i n e

between the pl an t and the e pic en te r and at a dis tan ce of about 4400

f e e t . Peak recorded h or izo nt al components of the acc ele ra tion s were

0.27g and 0.2 1 g, and 0.08g fo r the ve r ti c a l component. The du ra tion o f

stron g shaking was very shor t (les s than 1 second). A con serva tive

estim ate o f 0.lOg to 0.18g i s made fo r the ground motion a t the pla nt

s i t e . No damage was observed. In fa c t , the event was e s se n ti a l ly u n fe lt

by personnel at the p la n t.

Cloud (A-41) discusses the seismic performance of power piping

by examin ing the in t r in s ic ch ara cte r is t ic s of p ip ing that are b u i l t - in due

to designed co ns tru ct io n p ra ct ic e and also by examining the performance

of comparable pip in g in past earthqu akes. Discussed are power p lan t

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pip ing be havior d urin g seven past earthqua kes . These are the 1979

Imp eria l V a ll ey , the 1978 Miya gi-Ke n-O ki, the 1972 Managua, the 1971 San

Fernando, the 1964 Alas ka , the 1952 Kern County (T a ft ) and the 1933 Long

Beach. Observations include the seismic performance of piping in the El

Centro Steam Pla nt in th e Im pe ria l V a ll e y , th e Fukushima Nuclear Power

P la n t , and the ESSO R efinery Complex and the ENALUF Power P la nt in

Managua. San Fernando Valley Power Plant, the Kern County Steam Station,

and the Long Beach Steam S ta t io n . In summary. Cloud ind ic at es th a t based

on the ava ilab le data and observations pe rta inin g to the behavior of

power piping during actual earthquakes, even for power plants experiencing

severe ground motion the p ipin g remains in ta c t.

A .4 CONCLUSIONS

The objec t ives of the review e f f o rt were tw ofo ld. F ir s t , t o

assess how we ll pred icted s tr u c tu ra l performance, based on el a s t i c

an aly sis procedures tha t employ e la s ti c response spec tra derived from

recorded ground mo tion, cor rela tes with ac tual observed str uc tu ra l

behavior durin g past earthquak es. Second, to id e n ti fy ground motion and

st r uc tura l ch ara cte r is t ic s tha t s t rong ly in f luence a s t ru ctu re 's response

behavior.

To meet these ob je ct iv e s, an extensive l i te ra tu re review was

conducted and a data base es ta bl is hed th a t documents the performance o f

structures subjected to strong ground shaking from past earthquakes.

When po ss ib le , those cases were id e n ti f i e d where a d ir ec t comparison

between observed behavior and predicted performance based on calculated

earthquake for ce s cou ld be made.

The literature review and damage documentation presented,he r e in , lead to the fo l lowing conclusions:

1 . When the level of ground motion was such that the observedove ra l l s t ru ctu ra l behavior was es se nt ia l ly e l a s t i c , thepredicted behavior based on calculated earthquake forcesusing e la st i c ana lys is cor re la ted we l l w i th observat ion .Note, structures were observed to often exhibit suchove ra l l behav io r and s t i l l e xh ib i t loca l y ie ld ing .

A-49

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When the le ve l of ground motion caused the actua l st ru c tu reto respond in e la s t i c a l l y , the e la s t i c analysis method gavecalculated earthquake forces which signf icant ly overestimated the actual force level which occurred producingthe observed damage. In these cases where the cal cul a te d

e l as t ic fo rce leve ls wou ld be genera l ly ind ica t ive o fs ig n if ic a n t s tru ct ur al damage, the pred icted performancedid not corre late with observed behavior.

Several factors were ident i f ied which inf luence theresponse behavior of we ll-de sig ne d s tr u c tu re s . Among theseare the duration of strong shaking, the energy absorptionor d u c t i l i t y capa city of a g iven str uc tu ra l system, and thee f fec ts o f so i l - f ounda t ion in te ra c t i on . In genera l , t hedocumentation assembled qualitat ively supports the beliefthat such factors must be included in the develoment ofdesign ground motion c r i t e r ia i f p red ic ted s t ru ctu ra lbehavior is to accurately correlate with actual observed

performance.

There are some documented cases where sho rt du ra tio nmotions have not caused any significant damage, even tonon-engineered structures, in spi te of the fact that thesh ort du rat ion motions had equal or higher peak ac ce lera t ions than long durat ion mot ions which resulted in significant damage.

A-50

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TABLE A-1

LIST OF EARTHQUAKE/STRUCTURE-TYPES

INCLUDED IN REVIEW/DAMAGE DOCUMENTA TION

EARTHQUAKE STRUCTURE-TYPE REFERENCES

Cases with Damage Documentation

1952 Kern County, CA

i»

en1—'

1966

1971

1972

1972

1975

1978

1979

1979

1980

Other

1906

1940

1949

1960

1960

1964

Parkfield, CA

San Fernando, CA

Bear Vall ey, CA

Managu a, Nicaragua

O r o v i l l e , CA

Santa Barb ara, Ca

Coyote Lak e, CA

Imperial Valley , CA

Greenville, CA

Cases Reviewed

San Francisco, CA

Imperial Valley, CA

Olympia, WA

Agadir, Morocco

Chile

Alaska

General, Kern County Steam Plant ,

Elevated Tanks

General

General Medical Facilities,

High-Rise Buildings , Industrial,

0. View, VA

General

Ge n e r a l , ESSO Refiner y, ENALUF

Thermal Plant

Ge n e r a l , State Water Project

General

General

General, El Centro Steam Plant

General, LLNL

Major High-Rise Buildings

General

General

General

Huachipato Steel Plant

General

137-140, 32

3 2 , 33 , 115-118

5 8 , 6 0 , 6 6 , 6 7 , 7 6 , 8 4

8 7 , 157, 158, 159, 162

34

2 6 , 3 0 , 4 0 , 4 2 ,111-113

147

6 4 , 119, 120 , 160

105-109

35-38, 125-129

141-143

26, 3 0, 99, 155

154, 140

140, 152, 155

110

26, 4 0 , 4 3 , 8 8 , 151

5 5 , 110

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TABLE A-1 (Continued)

LIST OF EARTHQUAKE/ST RUCTURE-TYPES

3sI

Other

1967

1967

1972

1974

1975

1976

1977

1978

1978

1980

1980

1980

EARTHQUAKE

Cases Reviewed (Con tinued)

Caracas, Venezuela

Koyna, India

Ancona, Italy

Lima, Peru

Ferndale, CA

Friuli, Italy

Romania

Miyagi-Ken-Oki, Japan

Monticellor Reservoir

Mammoth Lake , CA

Eureka, CA

Sharpsburg

INCLUDED IN REVIEW/DAMAGE DOCUMENTATIO^

STRUCTURE-TYPE

General, High-Rise

Koyna Dam

General

General

General, Humboldt Bay, Nuclear

General

General

Fukushima Nuclear Power Plant

Virgil C. Summer Nuclear Plant

General

General, Humboldt Bay, Nuclear

Wm. Zimmer Nuclear Power Plant

1

Power

Power

Plant

Plant

REFERENCES

110, 148

130-133

1 3 , 39

6 5 , 146

4 4 , 121,

8 0 , 145

6 2 , 149,

4 5 , 97

134-136

156

114, 123,

144

122, 85

150

, 124

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TABLE A-2

SUMMARY EARTHQUAKES , MAXIMUM RECORDED ACCELER ATIONS, STRUCTURE-TYPES AND

LEVEL OF MOTION AT STRUCTURE SITE

Magnitude

M MEarthquake

Maximum DistanceRecorded CausativeAcceleration Fault

3»Icn

18 April

18 May

21 July

29 Feb.

21 May

26 July

27 June

10 Dec.

9 Feb.

14/21 June

4 Sept.

23 Dec.

6 Oct.

7 June

1906

1940

1952

1960

1960

1963

1966

1967

1971

1972

1972

1972

1974

1975

12 June 1978

13 Aug. 1978

27 Aug. 1978

15 Oct. 1979

San Francisco

Imperial Valley

Kern County

Agadir, Morocco

Chile

Skopje, Yogoslavia

Parkfield

Koyna, India

San Fernando

Ancona, Italy

Bear Valley

Managua, Nicaragua

Acapulco, Mexico

Ferndale

6.9

6.4

7.2

5.6

6.0

6.4

4.9/4.4

4.7

5.2

Miyagi-Ken-Oki

Sabta Barbara

Monticello Reservoir

Imperial Valley 6.6

5.1

2.8

6 Aug. 1979 Coyote Lake

24 Jan. 1980 Greenville

27 July 1980 Sharpsburg

5.7

5.9

5.1

8.3

7.1

7.7

5.8

7.5

6.0

6.4

6.5

6.6

4.3

6.2

4.8

5.7

7.4

5.6

6.9

5.6

5.9

0.39

0.20

0.50

0.63

1.2

0.60/0.40

0.70

0.39

0.53

0.35

0.10

0.45

0.25

0.81

0.42

0.17

10 km

40

<1

7

3

7/15

6

5

35

20

140

4

<1

7

16

Structure-Type

High Rise Buildings

General

General

General

Hauchipato Steel Plant

General

General

Koyna Dam

General

General

General

General

ESSO Refinery

ENALUFGeneral

General

Humbolt Bay Power Plant 0.35

Fukushima Nuc. Power Plant 0.10

Level of Motion

Structure Site

Duration ofStrong Shaking

(>-ig)

Up to l.Og EST

0.2 - 0.5 EST

>0.1

0.06 - 0.50

0.63

Up to 0.5 (?)

0.60/0.40

<0.6 EST0.390.6 EST

0.53

General

Virqil C. Summer NPP

General

El Centro Steam Plant

General

Livermore Valley/LLNL

Wm. Zimmer NPP

0.45

<0.1 EST

0.2 - 0.4

0.49

0.42

0.2 - 0.3 EST

<0.1

IX-X

VIII-IX

X-XI

VI I

VI I

VI-XI

VI

IXV-VIVII-VIII

VI-VII

V

VI I

VI IVI I

VI I

[long]

25 sec.

>12

single pulse

[short]

short

<2 single puls

6

[<7]

<2

<3

[>io310

[>10]

1-2

VI

[<4]<4

[short]

2-3

<1

<13

7

<2

[short]

[short]

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60

40

20 -

&«n

1—

zU J

oH-1L l.U .L UOO

^U J3 :o i

U JCO

CO

10

8

6

4

2 -

—

[—

—

1—

1 1,

j—

• ^

1 ^

1—

L_

1 1 1 1 1 1 1

dd

o oo

o

D off

o

EJn

D D

1 1

cfo

D

D

O

D DO

C i r c l e s r e p r e s e n t t h e i Mx ii wu i f i r s t - m o d e b a a * s h e a r se i ^ e r l e n c e d d u r i n g t h e e a r t h q u a ke , t i c k e d c i r c l e s r e p r e s e n ts t r u c t u r e s t h a t h a d s a n e d a m a ge ; s qu a r e s r e p r e s e n t t h e n o m i n a lc o d e v a l u e s o f b a s e s h e a r s f o r w hi c h t h e b u i l d i n g s w e r e d e s i g n e d .T he p e r i o d s a r e t h o s e o f t h e f u n d a m e n ta l mo d e s o f v i b r a t i o n .B a s e s h e a r c o e f f i c i e n t i s e q u a l t o b a s e s h e a r d i v i d e d b y t o t a lw e i g h t o f s t r u c t u r e .

t

1 1 1 1 1 1 1 1 1

— j

-1

-\

—H

_J

- j

^^

-\

-J

0.4 0 .6 1 .0

OBSERVED PERIOD ( s e c . )

FIGURE A - 1 . BASE SHEAR COE FFICIENTS OF MULTI-STORY CONCRETE BUILD INGS SUBJECTEDTO STRONG GROUND SHAKING DURING 1 9 71 SAN FERNANDO EARTHQUAKE

( R e f e r e n c e A - 6 0 )

A-54

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RESEARCH BIBLI OGRAPHY FOR THE EARTHQUAKE STRUCTURAL DAMAGE

LITERATURE REVIEW

1 J. A. Blume , The Effect of Arbitr ary Variations in Peak GroundAcceleration on Spectral Response, Diablo Canyon Nuclear PowerPlant, URS D-11 30 , May 9, 1977.

2 P. B. Shnab el, and H. B. Seed, "Accelerations in Rock for Earthquakes in Western U . S . " , Bulletin of the Seismological Societyof America, Vol. 6 3, Nos. 2, 1973.

3 M. R. Ploes sel, and J. E. Slosson, "Repeatable High GroundAccelerations from Earthq uakes ", California Geology, September,1974.

4 R. A. Page , D. M. Boore , W. B. Joyner and H. W. Coulte r, "GroundMotion Values for Use in the Seismic Design of the Trans-AlaskaPipeline System", Geological Surve y Circular, 672. Washin gton,D.C., 1 9 7 2 .

5 R. B. Hoffm an, "State-of-the-Art for Assessing Earthquake Hazardsin the United States; Factors in the Specification of GroundMotions for Design Earthquakes in Califo rnia", MiscellaneousPaper S-63-1, U.S. Army Engineers Water ways Experiment Stat ion,Vicksburg, Miss., June, 1974.

6 0. W. Nutt li, "State-of-the-Art for Assessing Earthquake Hazards

in United S tate s; The Relation of Sustained Maximum GroundAcceleration and Velocity to Earthquake Intensity and Magnit ude",Miscellaneou s Paper S- 73-1, Report 16 , November, 1979, U.S. ArmyEngineer Waterways Experiment Station , Vicksburg, Miss., 1979.

7 C. P. Mort gat, and H. C. Shah, "A Bayesian Approach to SeismicHazard Mapping; Develo pment of Stable Design Para meters" , TheJ. A. Blume Earthquake Engineering C enter , Report No. 28, Dept.of Civil E ngr., Stanford Universit y, 1978.

8 C. P. Mortg at,, "A Probabilistic Definition of Effective Acce leration", Proce edings of the 2nd U.S . National Conference onEarthquake Engi neering, Stanford Univ ersity , August 22-24 , 1979,

pp. 743-752.

9 E. H. Vanmarcke and S. P. Lai , "Strong Motion Duration ofEarthq uakes" , M. I.T . Dept. of Civil Engineering Research ReportR 7 7 - 1 6 , 1 9 7 7 .

10 T. C. Hanks , "Measures of High-Frequency Strong Ground Motion" ,Proceedings of the NSF Seminary Workshop on Strong Ground Motion,1978.

A-55

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RESEARCH BIBL IOGRAPHY FOR THE EARTHQUAKE STRUCTURAL DAMAGEL I T E R A T U R E f t E V T E f f

(Continued)

A - U T. C. Hanks, "Seismological Aspects of Strong Motion Seismology",Proceedings of the 2nd U.S. National Conference on EarthquakeEngineerin g, Stanford University , August 2 2-24, 1979, pp.8 9 8 - 9 1 2 .

A-12 M. W. McCann , Jr., and H. C. Shah, "RMS Acceleration for SeismicRisk Artalysis: An Over view ", Pro ceedi ngs of the 2nd U. S. NationalConference on Earthquake Engineering, Stanford University,August 22-24, 1979, pp. 883-897.

A-13 N. M. Newmark, "A Rationale for Development of Design Spectrafor Diablo Canyon Reactor Facili ty", N. M. Newmark ConsultingEngineering Service s, Urbana, Illi nois, September, 1976.

A- 14 R. P. Ken ned y, "Ground Motion Paramet ers Useful in Structural

Design", Structural Mechanics Associates, Inc., Presented at theConference on Evaluation of Regional Seismic Hazards and Risk,Santa Fe, New Mexico, October 21, 1980.

A-1 5 H. Yam aha ra, "Ground Motion During Earthquake and the Input Lossof Earthquake Power to an Excitation of Buildings", Soils andFoundation, Vol. 10, No. 2, 1970, pp. 145-161, Tokyo.

A-1 6 N. M. Newm ark, W. J. Hall and J. R. Mor gan , "Comparison ofBuilding Response and Free-Field Motion in Earthquakes",Proceedings of the 6th World Conference on EarthquakeEngineering, New Delhi, India, 1977.

A-1 7 R. H. Scan Ian, "Seismic Wave Effects on Soil- Struc ture-Interaction", Earthquake Engineering and Structural Dynamics,V o l . 4, 1976, pp. 379-338.

A- 18 N. Ambr asey s, "Character of Strong Ground Motion in the Near

Field of Small Magnitude Earthquakes", Invited Lecture, 5 Conf.European Committee for Earthquake Engineering, Istanbul,September, 1975 .

A-1 9 J. R. Whitel y, J. R. Morgan, W. J. Hall , and N. M. Newmark "BaseResponse Arising from Free-Field Mo tion s", Transactions of the4th SMiRT Conference, Vol. K(a ), 1977.

A-20 D. Ray and D. P. Jhaveri , "Effective Seismic Input Through RigidFoundation Filtering", Transactions of the 4th SMiRT Conference,V o l . K ( a ) , 1 9 7 7.

A-56

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RESEARCH BIBLIOGRAPHY FOR THE EARTHQUAKE STRUCTURAL DAMAGELITERATURE REVIEW

(Continued)

A-21 W. J. Hall , J. R. Morgan and N. M. Newmark , "Traveling SeismicWaves and Structural R esp ons e", Proceedings of the SecondInternational Conference on Microzo nati on, Vol. Ill, SanFrancisco, California, November, 1978.

A-22 Reduction in Free-Field Ground Motion Due to the Presence ofStru ctur es, Submitted to: Southern California Edison Company byTERA Corporation, August, 1980.

A - 2 3 C. B. Crou se, "Prediction of Free-F ield Ear thquake Ground

Motion s" Proceeding s ASCE Conferen ce on Earthquake Eng r. & SoilDynamics, 1978.

A - 2 4 G. W. Housner, "Statistics of Pulses on Strong Motion Accelerograms", Proceedings of the NSF Seminar Workshop on Strong GroundM o t i o n , 1 9 7 9 .

A-25 G. W. Housn er, "Spectrum Intensities of Strong Motion Earthq u a k e s " , Proceedin gs of the Symposium on Earthquake and BlastEffects on Stru ctures, EERI, June, 19 75, pp. 20-36.

A-26 J. A. Blume , "Instrumental Versus Effective Acceleratio n",Report D - U 26, Final Safety Analysis Report, Units 1 and 2,

Diablo Canyon Sit e, Amendment N o. 50 . "Seismic Evaluation forPostulated 7.5M Hosgri Earthquak e", U.S. Nuclear RegulatoryCommission Docket No s. 50-275 and 50-23 2, 1977.

A-27 R. V. Whitman, "Effective Peak Acceleration", Proceedings of the2nd International Conference on Microzonation, San Francisco ,V o l . Ill, 1578, pp. 1247-1255.

A-28 S. A. Short, R. P. Kennedy, et al, "Nonlinear Response of a

Nuclear Plant to a Moderate Magn itude , Near-Field Earthquake",ASCE Specialty Conference on Civil Engineering and Nuclear Power,K n o x v i l l e , T e n n e s s e e , S e p t e m b e r , 1 9 8 0 .

A-29 G. W. Housner, "Measures of Severity of Earthquake GroundShaking", Proceedings of the U. S. National Conference onEarthquake Engineering, EERI, Ann Arbor, Michigan, June, 1975,p p . 25-33.

A-30 J. A. Blume , "On Instrumental Versus Effective Acceleratio n andDesign Coeffici ents", Proceedings of the 2nd U. S. NationalConference on Earthquake Engineerin g, Stanford, California, 1979

A - 5 7

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RESEARCH BIBLIOGRAPHY FOR THE EARTHQUAKE STRUCTURAL DAMAGEL I T E f t A T U f t E R E Y T b r

(Continued)

A-3 1 S. H. Harz ell, J. N. Brune and J. Princ e, "The October 6, 1974 ,Acapulco Earthquake; An Example of the Importance of Short-PeriodSurface Waves in Strong Ground Motion", Bulletin of theSeismological Society of America, Vol. 68, December, 1978 , pp.1 6 6 3 - 1 6 7 7 .

A-32 6. W. Housner, "Earthquake Research Needs for Nuclear PowerPlants", Journal Power Divisi on, Proceedings ASCE, Vol. 97,1 9 7 1 , pp. 77-91.

A-33 W. K. Cloud, "Intensity Map and Structural Damage, Parkfield,Californi a Earthquake of June 2 7, 1966 ", Bulletin of theSeismological Society of America, V ol. 57, No. 6, 1967, pp.1 1 6 1 - 1 1 7 8 .

A-3 4 J. F. Lander, Editor, Seismological Notes, Bulletin ofthe Seismological Society of America, Vol. 62, No. 5,January-February, 1972, pp. 1360-1362.

A-35 C. Rojah n, Selected Papers on the Imperial Valle y, Californi aEarthquake of October 15, 1979, U.S. Geological Survey, OpenFile Report 80- 1094, 1980.

A-36 6. E. Brandow, et al. Reconnaissance Report, "Imperial County,California Earthquake of October 15, 1979", EarthquakeEngineering Research Institute, February, 1980.

A-37 R. C. Murray, T. A. Nelson, et al, "Response of El Centro SteamPlant Equipment During the October 15 , 1979, Imperial Va lleyEarthquake", Lawrence Livermore Laboratory, NUREG/CR-1665,UCRL-53005, September, 1980.

A-38 Reconnaissance Reports - Imperial Valley Earthquake, October 15,1 9 7 9 , USNRC Earthquake Team Report, November, 1979.

A-39 R. Console, F. Peronaci, A. Sonaglia, Relazione Sue FenomeniSismica Dell 'Anconitano, 197 2, Annali di Geofi stica , Vol . 26,Supplement, 197 3, Rome .

A-4 0 J. A. Blume, "Performance of Industrial and Power Facilities inMajor Earthquakes", Report D-11 34, Final Safety AnalysisRepo rt, Units 1 and 2, Diablo Canyon Site , Amendment No . 50,"Seismic Evaluation for Postulated 7.5M Hosgri Earthquake",Nuclear Regulatory Co mmission, Docket N os. 50-275 , and 50-232,1 9 7 7 .

.V58

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RESEARCH BIBLIOGRAPHY FOR THE EARTHQUAKE STRUCTURAL DAMAGELITERATURE klJWH

(Continued)

A-41 R. L. Cloud, "Seismic Performance of Piping in Past Earthquakes",

ASCE Specialty Conference on Civil Engineering and Nuclear Power,Knoxville, Tennesee, September, 1 9 8 0 .

A-42 J. F. Meehan, H. J. Degenkolb, e t a l , "Managua, NicaraguaEarthquake of December 2 3 , 1972", Earthquake EngineeringResearch Institute, M a y , 1 9 7 3 .

A-43 J. A. Blume, A Structural Dynamic Analysis of Steel PlantStructures Subjected t o t h e M a y , 1 9 6 0 , Chilean Earthquakes,

Bulletin of the Seismological Society of America, V o l . 5 3 ,February, 1 9 6 3 , p p . 4 3 9 - 4 8 0 .

A - 4 4 0 . Steinhardt, Report on Magnitude 5.7 Ferndale Earthquake of

June 7 , 1 9 7 5 , PG&E Company.

A-45 P. I. Yanev, T . A . Moore and J. A. Blume, "Fukushima NuclearPower Station, Effect and Implications o f t h e June 1 2 , 1 9 7 8 ,Miyagi-Ken-Oki, Japan, Earthquake", U R S Reconnaissance Report,Copy 6 6 , January, 1 9 7 9 .

A-46 R. P. K e n n e d y , W . H . Tong and S. A. Short, "Earthquake DesignGround Acceleration Ver sus Instrumental Peak Ground Accelera

tion", Report SMA 12501.01, Structural Mechanics Associates,Inc., Newport Beach, 6a^lifornia, October, 1 9 8 0 .

A-47 J. A. Blume, "On the Attenuation of Ground Motion by Large

Foundations", Report D - L L 3 9 * , J . A . Blume, M. R. Somerville,an d R. M. Czarnecki, "A Comparison of Observed and EstimatedPeak Ground Accelerations and Their Probabilities", Report D-LL3 6 * , J. A. Blume, A . S . Kiremedjiian, "Recurrence Relationshipsby Fault Units", Report D - LL 3 7 * , 1 9 7 7 .

A-48 J. A. Blume, "A Busy Start for the New Decade", Newsletter,

EERI, V o l . 1 4 , N o . 2 , March, 1 9 8 0 .

A-49 J. A. Blume and M . H. Stauduhar, ( e d s . ) , "The Thessaloniki,Greece Earthquake of June 2 0 , 1978", EERI, January, 1 9 7 9 .

* Final Safety Analysis Report, Units 1 and 2, Diablo Canyon Site,Amendment N o . 5 0 , "Seismic Evaluation for Postulated 7.5M HosgriEarthquake", 1 9 7 7 , USNRC, Docket N o s . 50-275 and 50-232.

A-59

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RESEARCH BIBLIOGRAPHY FOR THE EARTHQUAKE STRUCTURAL DAMAGELITERATURE REVIEW '

(Continued)

A-5 0 J. A. Blume, "The Motion and Damping of Building Relative to

Seismic Response Spec tra", Bulletin of the Seismological Societyof America, 60:231-249, Febru ary, 1970.

A-51 J. A. Blume , "Allowable Stresses and Earthquake Perfo rman ce",Proceedings of the 6th World Conference on EarthquakeEngineering, New Delhi, 1977 .

A-52 J. A. Blume, "Structural Dynamics in Earthquak e-Resist ant

Design",Journal of the Structural Div ision, ASCE, July, 1958 .

A-5 3 B. A. Bolt and R. A. Hansen , "The Upthrow of Objects in

Earthquakes", Bulletin of the Seismological Society of America,V o l . 67, No. 5, October, 1977, pp. 1415-1427.

A- 54 R. L. Cloud, "How Nuclear Piping Code Rules Will Influence PipingDesign Today and Tomorrow", Heating, Piping & Air Condi tions,J u n e , 1 9 7 0 , p . 6 9 .

A-55 W. K. Cloud, The Great Alaska Earthquake of 1964, Engineering,National Academy of Sci ences, Washington, D. C., 1973.

A-56 C. A. Cornell and N. M. Newma rk, "On the Seismic Rehab ility ofNuclear Power Plants", Proc. Topical Mtg . on ProbabilisticAnalysis of Nuclear Reactor Safety, Vol. 3 ANS, 19 78, pp.XXIVI-1 to 1-14.

A-5 7 N. C. Donova n, B. A. Bolt and R. V. Whit man, "Development ofExpectancy Maps and Risk Analy sis", Jour nal, StructuralDivision, Proceedings, ASCE, 1978.

A-5 8 K. V. Steinbrugge , et. al ., "San Fernando Earthquake, February 9,1971", Pacific Fire Rating Bureau, San Francisco, California,1971.

A-59 W. J. Hall, B. Mohr az and N. M. Newmark, Statistical Studies ofVertical and Horizontal Earthqua ke Spectr a, prepared for USNRC,Report NUREG-0003, January, 1976.

A-6 0 G. W. Housner, and P. C. Jenning s,, "Earthquake Design Criteriafor Structures", Report No. EERL 77-06, EERL, CaliforniaInstitute of Technology, Pasadena, November, 1977.

A-61 Jungmann, "Documentation of the Earthquake in the SchwabiacheAlb on 3 September 1978" , Kraftwerk Union, October 11, 1978.

A - 6 0

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(Continued)

A-62 D. L. Leeds, ( e d . ) , "Earthquake in Roma nia, March 4, 1977",EERI, V o l . 1 1 , N o . 3 B , M a y , 1 97 7.

A-6 3 R. K. McGuir e and T. P. Bernard, "The Usefulness of GroundMotion Duration in predicting t he Severity of Seismic Shak ing,"Proceedi ngs of the 2nd U. S. National Conference on EarthquakeEngineering, Stanford University, August 22-24, 1979.

A-6 4 R. K. Miller and S. F. Felszegh y, "Engineering Features of the

Santa Barbara Earthquake of August 13, 1978", EERI, UCSB-ME-78-2,

December, 1978.

A-65 D. Moran, G. Ferver, et al, "Engineering Aspects of The Lima,Peru Earthquake of October 3, 1974", E E R I , M a y , 1 9 7 5 .

A-66 J. L. Mulloy, "San Fernando Earthquake of February 9, 1971",

Effects on Power System Operation and Facilities, Department ofWater and Power, City of Los Angeles, October 1974.

A-67 L. Murphy, "San Fernando , California Earthquake of February 9,1971", Sci-Coord., U .S. Dept. of Commerce, NOAA, 3 Vols.,Washington, D.C., 1973.

A-6 8 N. M. Newmark , Testimo ny Before the Atomic Licensing AppealBoard USNRC, Pacific Gas and Electric Company (Diablo CanyonNuclear Power Plant Units No s. 1 and 2 ) , Docket No s. 50-275 and50-323.

A-6 9 N. M. Newmark , W. J. Hall and B. Mo hra z, "A Study of Verticaland Horizontal Ea rthqua ke Spectra, " Directorate of Licensi ng,U. S. Atomic Energy Commission Report W ASH-1255, April, 1973.

A- 70 N. M. Newmark , J. R. Morgan and W. J. Hal l, "Response Spectra ofCombined Translation and Torsion For A Traveling Seismic Wave,Prepared for NRC, Contract NRC-04- 058, September, 1978.

A-71 N. M. Newmar k, "Interpretation of Apparent Upthrow of Objects inEarthquakes", Proceedings of the 5th World Conference onEarthquake Engineering, Rome, Vol. 2, 1974, pp 2338-2343.

A-7 2 N. M. Newma rk, "Seismic Design Criteria for Structures andFacilities: Trans-Alaska Pipeline System", Proceedings of theU.S. National Conference on Earthquake Engineering, Ann Arbor,Michigan, 1975.

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(Continued)

A-73 R. A. Page, J. A. Blume and W. B. Joyner, "Earthquake Shaking

and Damage to Build ings", Science Vo l. 189, No. 4203, August 22 ,1975.

A-74 C. Rojahn, B. J. Merri ll, et. al , "The Island of Hawaii Earthquake", EERI, Vol. 10, No. 18, February, 1976.

A-75 J. 8. Savy, "Determination of Seismic Design Parameters: AStochastic Approach", M . I . T . , Cambridge, Massachusetts.

A-7 6 A. I. Snyder , "Damage to Mechanical Equipment as the Result ofthe February 9, 1971 Earthquake in San Fernando, California,"Seismic Design and Analysis, American Society of MechanicalEngineers, 1971.

A-77 0. W. Steinhardt, "Protecting A Power Lifeline AgainstEarthquakes", Journal of the Technical Councils of ASCE,November, 1978.

A-78 0. W. Steinhardt, "Low-Cost Seismic Strengthening of a PowerSystem", ASCE Preprint 80-076, April, 1980.

A-79 J. M. Stephenson , "Earthquake Damage to Anchorage Area

Utilities", U. S. Naval Civil Engineering Laboratory, June, 1954.

A-80 J. L. Stratta and L. A. Wyll ie, Jr., "Reconnaissance Report,Friuli, Italy Earthquakes of 1976", EERI, January, 1979.

A-81 J. L. Stratta, T. J. Canon, et al, "Reconnaissance ReportMindana o, Phillippines Earthquake, August 17, 1976", E E R I ,August, 1977.

A-8 2 W. F. Swig er, "Notes on Plants Designed by Stone & Webster WhichHave Experienced Large Earthquakes", 1979 (unpublished).

A-83 J. M. Tanaka, "Airports and Air Traffic Control Facili ties",U . S . Army Corps of Engineers District, Alaska, 1967.

A-84 A. Rutenberg, P. C. Jennings and G. W. Housner, "The Response ofVeterans Hospital Building 41 in the San Fernando Earthquake",EERI Report 80-03, May, 1980.

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LU'ERATURE REVIEW

(Continued)

A-85 J. E. Valer a, H. B. Seed, C. F. Tsai and J. Lysmer, "Seismic

Soil-St ructure Interaction Effects at Humboldt Bay Power Plant",Journal of the Geotechnical Engineering Division, ASCE, Vol.103, No. GTIO, October, 1977.

A-8 6 E. H. Vanmarc ke and S. P. La i, "Strong-Motion Duration and RMSAmplitude of Earthquake Records", Bulletin of the SeismologicalSociety of America, Vol . 70, No. 4, August, 1980, pp 1293-1307.

A-87 H. S. Lew, E. V. Leyendecke r, and R. D. Dikkers, "Engineering

Aspects of the 1971 San Fernando E arthq uake ", U.S. Department ofCommmerce, National Bureau of S tandard s, Washingt on, D.C., 1971.

A-8 8 R. Vignola and E. Arz e, "Behavior of a Steel Plant Under MajorEart hqua kes" , Proceedi ngs of the 2nd World Conference onEarthquake Engineering, Japan, 1960.

A-89 H. M. Waldr on, R. P. Miller and S. 0. Wer ner , "GeotechnicalInvestigations at Nuclear Power Plant Site s", NuclearEngineering and Design , North Holland Publishing Company, Vol.3 6 , 1976, pp. 397-405.

A-90 S. D. Werner , "Engineering Characteristics of Earthquake GroundMotions," Nuclear Engin eering and Design , North HollandPublishing Company, Vol . 36, 1976, pp.367-395.

A-91 S. D. Wern er, "Procedures for Developing Vibrato ry Ground MotionCriteria at Nuclear Power Plant Si tes ", Nuclear Engineering andDesign, North Holland Publishing Company, Vo l. 36, 1976, pp.4 1 1 - 4 4 1 .

A-92 P. I., Yanev , Draft Paper on "Behavior of Power Plants and OtherIndustrial F aciliti es in Past Eart hqua kes" , URS, April 2 8, 198 0.

A-9 3 T. Zsutty and M. Dehe rra, "A Statistical Analysis of Accelerogram

Peaks Based Upon the Exponential Distribution Mode l", StanfordUniversity, Palo Alto, California.

A-94 Letter, N. Hirata, San Francisco District Mgr., Toshiba International Corporation, to T. Mcllraith , Pacific Gas & Electric Co.,San Francisco, California, April 9, 1979.

A-95 Ministry of Power Engineering and Electriciation, "ProvisionalDesign Standards for Nuclear Power Plants in Seismic Regions",Minehnergo, USSR.

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(Continued)

A-96 CIT Reports Published 1 951 , Dynamics Lab orato ry Disa sterResearch Center, EERL, 1980.

A-97 P. I . Yanev, ( e d . ) , "Reconnaissance Re po rt, M iyag i-Ke n-O ki,Japan Earthquake", EERI, June 12, 1978.

A-98 H. Bo lton Seed and John Lysmer, "The S ig ni fic an ce of S it eResponse in Soi l -Structure Interact ion Analyses for NuclearF a c i l i t i e s " , ASCE Sp ecia l ty Conference on C iv i l Engineering andNuclear Power, Knoxvil le, Tennessee, September, 1980.

A-99 T a ll B u ild in g C r i t e r ia and Loa ding , Monograph on Planning andDesign of Tall Buildings, Volume CL, ASCE, 1980.

A-lOO D. E. Hudson, "S tro ng Mo tion Earthquake Measurements i nEpicentral Regions", Proceedings of the 6th World Conference onEarthquake Eng inee ring, New D e lh i, 1 977.

A-1 01 E. H. Vanmarcke, "Random V ib ra ti o n Approach to So il DynamicsProblems", The Use of P ro b a b i l i t ie s in Earthquake En gine ering ,ASCE P re p ri n t 291 3, ASCE F a ll Co nve ntion , San Fran cis co ,C a l i f o rn i a , 1977 .

A-102 "Damage to Pumping and Power S ta ti o n s ", C a li fo r n ia DWR B u ll e ti nNo. 166-3, June, 1967.

A-103 J . Prince and L. Alons o, "The R e la ti v e ly Li gh t Damage Producedby Two Strong Motion Earthquakes in Southern Mexico", Proceedings of the 7th World Conference on Earthquake Engineering,September, 1980.

A-104 J . P rin ce , L. Alon so, and I . Na varro, "Procasamiento deAcelerogramas Obtenidos en 1974, "Reporte del Instituto deIn g e n ie ri a , Universida d Nacional Autonoma de Mexico, Fe brua ry,1976.

A-105 R. B. Ma tthiesen and J . Ragsdale, "P re lim ina ry Report of Stro ng -Motion Data from the August 6, 1979 Coyote Lake Earthquake",USGS, 1979.

A-106 G. Dean, et a l , "1979 Coyote Lake (G ilr o y) Earthq uake ", EERINewsletter, September, 1979.

A-107 R. K. Reitherman , "Notes on No n-S truc tura l Features of theAugust 6, 1979 Coyote Lake Earthquake", EERI Newsletter,November, 1979.

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A-108 F. L. M el lo n, "Report of Post-Earthquake In ve st ig at io n TeamCoyote Lake Earthquake o f August 6 , 1 97 9" , CALTRANS O ff ic e o fStructures Design.

A-109 C. F. Arm stro ng , "Coyote Lake Ea rthqu ake , 6 August 1 979",California Geology, November, 1979.

A -l lO Earthquakes - Ag ad ir, Morocco, February 1 9, 1 960, Skop je,Yugoslavia, July 26, 1963; Anchorage, Alaska, March 27, 1964;Caracas, Venezuela July 1967, American Iro n and Steel I n s t i t u t e ,1975.

A-1 1 1 Managua, Nicaragua Earthquake of December 23. 1972. EERIConference Proceedings, San Fran cisc o, C a l i fo rn ia , Vo l. I & I I ,November 29 & 30, 1973.

A-11 2 B u il d in g Performance i n the 1972 Managua Earthqu ake , NBSTechnical Note 807, U.S. Department of Commerce, November, 1973.

A-11 3 M. A. Sozen and R. B. M at th ie se n, "En gin ee ring Report on theManagua Earthquake of 23 December 1973", "National Academy ofSciences, Washington, D.C., 1975.

A-11 4 H er rin g, K. S. et a l . "Reconnaissance Repo rt: Effe cts ofNovember 8, 1980 Earthquake on Humboldt Bay Power Plant andEureka, California Area", NUREG-0766, USNRC, June, 1981.

A-115 G. W. Housner and M. D. T ri fu n a c , "An al ys is of Accelerogram -Parkf ie ld Earthquake", Bul let in of the Seismological Society ofAmerica, Vol. 57, No. 6, December, 1967, pp. 1193-1220.

A-11 6 W. K. Cloud and V. Perez , "Accelerograms - P a rk fie ld Earthquake ",Bullet in of t l ie Seismological Society of America. Vol. 57. No. 6,December, 1967, pp. 1179-1192.

A-11 7 Un ited Sta tes Earthquakes 1966, U.S. Dept. of Commerce, ESSA,

A-11 8 G. B. Oakes hott, "Geologic Hazards P ar kf ie ld Earthquakes",C a li fo rn ia D iv isi on of Mines and Geology. July 1 3, 1966.

A-11 9 J . F. Meehan, "Reconnaisance Report Santa Barbara EarthquakeAugust 13, 1978", Off ice of the State Architect, Sacramento,C a l i f o r n i a .

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(Continued)

A-120 United States Earthquakes, 1978, U.S. Dept. of In te ri o r Ge ological Survey and U.S. Department of Commerce, NOAA, Golden,Colorado. 1980.

A-121 J . H. Gates, "A Note on the Fe rnda le, C a li fo rn ia Area Earthquakeof June 7. 1975", (personal correspondence).

A-122 United States Earthquakes. 1 975, U.S. Department of In t e r i o r ,Geo logica l Survey and U.S. Department o f Commerce, NOAA.Boulder. Colorado. 1977.

A-123 "Seismic Report Post-Earthquake In ve s tig a tio n Team. Eureka,California (Trinidad-Offshore) Earthquake of November 8, 1980",CALTRANS, O ff ic e of St ru ct ur es De sign.

A-124 "T rin ida d-O ffsh ore , C a li fo rn ia Earthquake November 8, 1 980",EERI Newsletter, Vol. 15, Part B, January. 1981.

A-125 R. Nason, "Seismic In te ns ity Studies in the Impe ria l V al le y" ,(d ra f t re po rt ) U. S. Geological Survey, Menio Park. C a l i fo rn ia ,1980.

A-126 "Seismic Report Post-Earthquake In ve st ig at io n Team, "Im pe rialV a lle y . C a li fo r n ia , Earthquake of October 1 5, 19 79", CALTRANS,Off ice of Structures Design.

A-127 C. Re al, R. D. McJunkin, and E. Le iva s, "Eff ec ts of Im pe rialVa lley Earthquake 15 October 1 979". Imp erial County. Ca li fo rn ia .California Geology, December, 1979.

A-128 "Ana lysis of the El Centro Steam P la n t" , (d ra ft re po rt) submittedto PG&E by URS/John A. Blume, May, 1 98 1 .

A-129 J . M. Pauschke, C. S. O li v e ir a , H. C. Shah and T. C. Z u tt y . "APreliminary Investigation of the Dynamic Response of the ImperialCounty Services Building During the October 15, 1979 ImperialValley Earthquake", J. A. Blume Earthquake Engineering Center,S tanford Un ive rs i ty , January. 1981 .

A-130 A. K. Chopra and P. C ha kr ab ar ti, "Analy sis of the EarthquakePerformance o f Koyna Dam". Paper No. 1 2 1 , B u l l e t in ISET, V o l. 9 ,No. 2, June, 1972, pp. 49-60.

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A-131 A. K. Chopra and P. C ha kr ab a rt i, "The Koyna Earthquake and theDamage to Koyna Dam", Bulletin of the Seismological Society ofAmerica. V o l. 63, No. 2, A p r i l , 1 973, pp. 380-397.

A-132 G. V. Be rg, Y. C. Das, K. Gokhale, and A ., V. S e tl u r, "TheKoyna. India Earthquakes". Proceedings of the 4th WorldConference on Earthquake En gin eer ing, San tiago . Ch il e , 1969.

A-1 33 UNESCO Committee o f E xpert s , "Koyna Earthquake of December 1 1 ,1967", Re port, New D e lh i. 1 968.

A-1 34 Dames and Moore Rep or t: Comparison of August 27, 1 978,Monticello Reservoir Earthquake Response Spectra to theOperating Basis Earthquake Response Spectra for the Virgil C.Summer Nuclear Station, submitted to South Carolina Electric &Gas Company, 1980.

A-135 "F ina l Report - Sig nif ic an ce of the M on tice llo ReservoirEarthquake o f August 27 . 1978 to th e V i r g i l C. Summer NuclearS t a t i o n " , prepared f o r South Ca rol ina E le c tr ic & Gas Company,Dames and Moore Report 5182-068-09, May, 1980.

A-136 Personal Communication w it h Robert Whorton, South Ca roli naE le c tr ic and Gas Company, May, 1 981 .

A-137 United Sta tes Earthquakes 1 952, S e ri a l No. 773, U. S. Departmentof Commerce, Coast and Geodetic Survey, Washington, 1954.

A-138 K. V. Steinbrugg e and D. F. Moran, "An Eng inee ring Study of theSouthern C a li fo rn ia Earthquake of J uly 2 1 , 1952 and I t s A ft e rshocks", Bullet in of the Seismological Society of America, Vol.44, No. 2b A p r i l , 1954.

A-139 Earthquakes in Kern County, C a li fo rn ia During 1952, State ofCalifornia, Department of Natural Resources, Division of Mines,SF, Bu l le t in 1 71 , 1955.

A-140 C. F. Ri ch te r. Elementary Seismo logy, W. H. Freeman and Company.San Francisco and London, 1958.

A-1 41 "The LLNL Ea rthqu ake". Impact Ana lysi s Committee Report on theLivermore, California, Earthquakes of January 24 and 26, 1980,UCRL-52956, July 15, 1980.

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(Continued)

A-142 G re en vil le (D iablo -Live rm ore ) Earthquakes of January 1 980, EERINewslet ter, Vol . 14, No. 2, March, 1980.

A-143 "Seismic Report Post-Earthquake In ve st iga tio n Team, G re en vi l le ,C a li f o rn ia Earthquake of January 24, 1 980", CALTRANS, O ffi ce ofStructures Design.

A-144 "E ffe cts of Sharpsb urg, Kentucky Earthquake of Ju ly 27, 1 980, onWm. Zimmer Station Moscow, Ohio", Report prepared for theCincinnati Gas and Electric Company. Cincinnati , Ohio, Sargent

and Lundy Engineers and Fugro, I n c . , Janu ary, 1 981 .

A-145 C on trib utio n to the Study of F r i u l i Earthquake of May^ } ^ ^ ^ *CNEN-ENFL Commission on Seismic Problems Associated with theInstal lat ion of Nuclear Plants, November, 1976.

A-146 P. Re pe tto, I. Aranzo and H. B. Seed, "In flu en ce of S ite Con ditions on Building Damage During the October 3, 1974 Lima Earthquake", Report No. UCB/EERC-80/41. September. 1980.

A-147 "O ro vi l le , C a l i f o rn ia . Earthquake. August. 1 975", Special Report124, C a li f o rn ia D ivis ion of Mines and Geology, 1975.

A-148 H. B. Seed, I . M. Id r is s , and H. D e zf ul l ia n, "R elat ions hipBetween Soil Conditions and Building Damage in the CaracasEarthquake of Ju ly 1 9, 1 967", Report No. EERC 70 -2 , F ebruary ,1970.

A-149 S. S. Tezcon, V. Y e r l i c , and H. T. Du rgunoglu, "A ReconnaissanceReport f o r th e Romanian Earthquake of 4 March 1 977 ", EarthquakeEngineering and S tru ct ur al Dynamics. Vo l. 6. 1 978, pp. 397-421.

A-150 Earthquake in Romania, ^^gi ch 4 . 1 977, An Engine ering Re po rt.National Research Council and EERI, 1980.

A-1 51 "Sp ecial Issue - An Eng ineering Report on the Ch ilean Earthquakesof May, 1960". Bul let in of the Seismological Society of America.Vol. 53. No. 2, February, 1963.

A-152 United Sta tes Earthquakes 1949, S e ria l No. 748, U. S. Departmentof Commerce, U.S. Coast and Geodetic Survey, Washington, 1951.

A-153 Un ited State s Earthquakes 1 928-1 935. U.S. Department of Commerce,Environmen tal Science Services A d m in is tr a tio n , Coast and GeodeticSurvey, Washington, 1969.

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A-154 Un ited Sta tes Earthquakes 1 936-1 940, U.S. Department of Commerce,Environmental Science Services Administrat ion. Coast and GeodeticSurvey, Washington, 1969.

A-155 Earthquakes and Blas t E ffe ct s on S tr uc tu re s, Proceedings ofSymposium, Los Angeles, June, 1952, Sponsored by EERI andUniversi ty of Cal i forn ia, September, 1952.

A-156 A. G. S yl ve st er , "The Mammouth Lakes, C a li fo r n ia , Earthquakes,25-31 May 1 98 0", Department of Geo log ica l S cien ce s, U.C. SantaBarb ara, May 3 1 , 1 980.

A-157 P. C. Je nn ings , En gine ering Feature s of the San FernandoEarthquake February 9, 1971 , C a l i f or n i a I n s t i tu te of Technology,EERL 71-02, 1971.

A-158 Un ited Sta tes Earthquakes 19 71 , U.S. Department of Commerce,NOAA, Boulder, Colorado, 1973.

A-159 G. Howard, et a l , "Earthquake Ef fec ts at Nuclear F a c i l i t ie s -San Fernando Earthquake of February 9. 1971 " , U.C. Los Angeles,UCLA ENG-7215, February, 1972.

A-160 S. H. Mendes, "Earthquake Re sistance of Modern B ui ld in gs - ACase Stu dy", The 50-Year Ev en t, Proceed ings of the 1980 SEADCConvention, Monterey, October 2-4, 1980.

A-161 M. A. Lars on, "Needed Improvements i n A Seismic De sig n", Stru ct u r a l Moments, SEAOC p u b li c a ti o n , Feb ruary, 1 980.

A-162 S. A. Ma hin, e t . a l , "Response of the O live View H os pita l MainB u il d in g D uring th e San Fernando Ea rthq ua ke ", EERC 76 -22 .Un ivers i ty o f Ca l i fo rn ia . Berke ley, October . 1976.

A-163 A. Ru thenberg . P. C. Je nn ing s, and G. W. Housner. "The Response

of the Veterans Hospital Building 41 in the San FernandoEarthquake". Earthquake Engineering Research Laboratory, ReportEERL 79-03, C a li fo rn ia In s t i tu te of Technology, Pasadena,C a l i f o rn ia , 1 9 7 9 .

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FIGURE B-la. ACCELEROGRAM AND CORRESPONDING CUMULATIVE ENERGYFOR THE OLYMP IA, WA., 1949 (N86E) RECORD

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B-12

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? ? t ^ ^ T t ^ j t f I ? ? < M ? ? ? ^ " * ? 3 1 S » 7 « 9 J 0 '

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0. 100

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10"' ! 3 « 5 6 7 « a J C f ! i I | 5 6 7 e 9 l 0 ' J J l | S « 7 a 9 | l C f—I 1 1—I—u-i—I I r 1 1 1 1 I I • • ' I I ..n

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0. 100

0.150

0.200

0.250

TTTTTTTTo i 3— rTTTTTTTt f i—TTTTTTJlo'FREOUENCr (HERTZ)

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B R T I F I C I B L

FIGURE B-2a. ELASTIC RESPONSE SPECTRA (T||j > 9 SEC.)

8/22/2019 6848574


D OI

10"'

2 ffi.

? ? « ? I'Uf ? ; '! ? «?«»J°' ? ? '• M?!>lO"

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0.100

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0-200

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1 — m T T T T r t f

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To ^— r - rX TTTS TTo ' 3 rTTTTTTTt f "FREQUENCT (HERTZ)

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F IG Ur .E B - 2 b . E L A S T I C R E S P O N S E S P E C T R A (2.5 SEC. < T^ < 9 SEC.)

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ft-

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— !«.d • -oc ,„.UJ- • J » .

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T - T T T T U T ^

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D R M P I N G 0.070

0. 10 0

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0.200

0.250

10' i — T T T T r n W i—r TTTTTTTtf-FREQUENCT IHERTZI

MELENOT RRNCH

T r~rTTTaTt'B'

FIGURE B-2c. ELASTIC RESPONSE SPECTRA (T;^ < 2 .5 S E C . )

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.l>»M»iV<VV •

J O 0 0 2 0 0 0 9 0 0 0 q o 0 0 s o 3 0 « 0 0 0 1 0 3 0 K O 0 0 3 0 3 0 1 0 0 3 0 1 1 0 3 0

T I H E I S E C O N O l

FIGURE B -3 a . ELAS TIC RESPONSE OF It DAMPED, 2 , 5 AND 8 HZ OSCILLATORSTO THE OLYM PIA, WA ., (1 9 4 9 ) EARTHQUAKE (N8 6E )

B - 1 6

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v | < 4 ' ^ / i f > ^ | i f 4 | # ^ ' ^ ' V v > ' W i J W w r ' ^ v \ i \ r ^

D 30 S 00 1 0 3 0 I S 0 0 2 0 3 0 2 5 3 3 30 0 3 3' 30 110 30 IS 0 0 5 0 3 0 S 5 0 0

riME ISECOND)

IK^W^^ A.' l».uV^^> .

'=^ 0 s''oc JO 30 IS 00 20 30 2S~03 30 00 ?-" l^ lib 33 JTo o So lo Ss 00

FIGURE B -3 b . EL ASTIC RESPONSE OF 7 % DAMPED, 2 , 5 AND 8 HZ OSCILLATORSTO THE TAFT, KERN CO., 1952 EARTHQUAKE (S69E)

B-17

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3 3 3 <4 :iD

" ** N ^ ' [iM|lfiftw/yA^v^-yi j i r " 'A H-V fcj " *'•••u • •

3 0 0 1 3 3 • 33 J2 33 16 33 20 30 24 33 2S 30 3 33 J 30 <I0 33 >1J 33. IME 'SECOND'

FIGURE B-3c. ELASTIC RESPONSE O F 1% DAMPED, 2 , 5 A N D 8 H Z OSCILLATORS T O T H EEL CENTRO ARRAY NO. 12 , IMPERIAL VALLEY , 1979 EARTHQUAKE (140) •

B-18

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riHE 'SECOND!

30 3 . 00 3- 30 'JO 30 IJt) 33

»' 00 l ' 00 12 00 le 00 21) 00 2\l 00 21 30 } '. 30 j ' t 00 10 30 VI 30

TIME ISECOND)

FIGURE B - 3 d . ELAS TIC RESPONSE OF 7 % DAMPED, 2 , 5 AND 8 HZ

OSCILLATORS TO THE NRC AR T IF IC IA L EARTHQUAKE

B-19

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3 3 3 V 3 0 I 0 0

3 30 U 0 0 a 0 0

1 1 1 ^ ^ 1 ^ . p^iM »•»> H f..i*>i S ¥m~^

l' 00 1 2 0 0 J « 0 0 2 0 0 0 J T o O 2'« 30 92 00 i't DO t'o 30 W 3 0

T I M E ' S E C O N D )0 00 « o o

FIGURE B -3 e . ELA STIC RESPONSE OF 7% DAMPED, 2 , 5 AND 8 HZ OSCILLATORS TOTHE PACOIMA DAM, SAN FERNANDO, 1 9 71 EARTHQUAKE (S1 4W)

B-20

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l^A * '"/'^ ''* •**" ''• '•W'. W-~-it- * r—

•;^ 1 r r 1 10 . 3 3 • 3 3 li 33 2<J 33 3 . . 3 3 1 0 .3 0 116 3 0

riNE ISECOND)

fmnnfi^^'fUvt'' - K

? 1 1 —

0 . 3 0 3 3 0J« 30 MTOO J'^ .OO 43 .00 I j' s 30 S6 .3 0 f iV 00 72.0 0 I 'o . 30 M . 00

f lNE 'SECOND)

y^ivytJo^-i^f*

3 3 0 t o o I t 3 0 2 ^ 3 0 l i 3 0 1 0 . 3 0 1 1 3 0 l \ 00 t \ 30 I 'j 30 10

(IKE ISECOND)0 . 3 0 I S 3 0

B - 3 f . ELAS TIC RESPONSE OF 7% DAMPED, 2 , 5 AND 8 HZ OSCILLATORS TO THEHOLLYWOOD STORAGE P .E . LO T, SAN FERNANDO, 1 971 EARTHQUAKE ( N90E )

B-21

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iVyVV^V^.. </y,J^, "AV

3 33 1 33 t 33 T 2 33 15 33 20 33 2'J 30 28 30 3. 30 3 30 1330 11 30

TIME 'SECOND)

<»Hwy"iif'*» • • /*• O'»• 1 ^

J 2 . 0 3 16 30 2 0 . 0 0 M O O 2« 30 ^ 0 0 9C 00 «b . 0 0 11 30

( IH E IS ECO ND !

3 . 0 0 1 33 t 30

> » y v * i | i f V ' ~ ^ ' » " - . I"

i IKE 'SECOND)

FIGURE B-3g. ELASTIC RESPONSE OF 7 % DAMPED, 2 , 5A N D 8H Z OSCILLATORS T O T H G

EL CENTRO ARRAY NO. 5 , IMPERIAL VALLEY, 1979 EARTHQUAKE (140)

B-22

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3 30 J 30

is /A/y-<y-» .\ V i * •' "^' •• •'^'

" T 1

a 30 V 0 0 « 00 12 00 16 "oij 20 00 2^ 30 3S 30 3*^ 33 3G 33 v'o 30 «1| 3 0T I M E ' S E C O N D )

V-*<rfV*S/*w* • ^ ^ - ^ . . . . T u * .

•' 00 ?2 30 j 's 00 30 00 2^ 30 28 00 3\ 30 3'^ 00 40 00 Ijl* 30

T I M E ( S E C O N D )0 0 0 q 30

B -3 h . ELAST IC RESPONSE OF 7 % DAMPED, 2 , 5 AND 8 HZ OSCILLATORS TOTHE UCSB GOLE TA, SANTA BARBARA, 1 97 8 EARTHQUAKE (1 8 0 )

B-23

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3 3 0 1 3 0

^.i'"ii«'i<iym<*'i".

•' 0 0 J 2 3 0 I'e 3 0 2 0 3 0 2 ^ 3 0 2 1 3 0 9 2 0 0 9'c 3 0 1 0 0 0 1 1 3 0T I M E ' S E C O N D )

0 30 1 30

iA\/*^'** ^*/"i*''u'*'*w''~'^'v"" •

1 30 T o o 12 00 I'c 00 20 30 JT oO 2'« 30 92 00 9C 00 10 30 Hj 30

T I M E 'SECO N D )

FIGURE B - 3 i . ELAS TIC RESPONSE OF 7% DAMPED, 2 , 5 AND 8 HZ OSCILLATORS TO THEGILROY ARRAY NO. 2 , COYOTE LA KE , 1 97 9 EARTHQUAKE (0 5 0 )

B-24

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A / V > -

3 00 T's o TT o 12 33 16 33 20 30 21 33 2'« 30 9'. 33 9 0 0 10 33 iV 30r i M E ' S E C O N D )

^\M»'^""'^w>"'"' > . '.v^ . i ^ * * "

12 00 I'e 00 2b 30 l \ 30 21 30 92 33 96 00 t'o 00 t \ 30

riME 'SECOND)0 30 1 30 I 00

» " Y > \ » » ^ , ^ ' H J ^ ^ . • •VUv '^ . . * •••".••

12 00 16 00 2 0 0 0 2^ 00 2'l 30 9' 30 9V 00 vb 00 11 30

i INE 'SECOND)

3 30 1 00 I 00

B - 3 i ELAS TIC RESPONSE OF 7 % DAMPED, 2 , 5 AND 8 HZ OSCILLATORS TO THECHOLAME ARRAY NO. 2 , PA RK FIE LD , 1 96 6 EARTHQUAKE (N 65 E)

B-25

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" • -yvy^ u—v^vT ' - / '

3 30 2 30 1 0 3 6 3 0 I 03 10 00 12 33 j l j 00 16 00 J'B 30 20 30 22 33

, I M E 'SECO N D!

. r < ^ " ^ » - i ^ m ^

2* 00 l' 0 0 f i ' 0 0 •' 0 0 J O 0 0 j'2 0 0 1 ^ 0 0 1 6 0 0 I S 3 0 2 0 0 0 2 2 0 0

( I M E I S E C O N D )

FIGURE B -3 k . EL ASTIC RESPONSE OF 7 % DAMPED, 2 , 5 AND 8 HZ OSCILLATORS TOTHE GAVILAN COLLEGE, HOLLISTER, 1974 EARTHQUAKE (S67W)

B-26

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i^.M--^vyvw'.' /

0 00 1 30 8 30 12 33 16 30 20 00 21 33 26 03 3* 30 3 03 10 00 11 30

TIME ' S E L O N D '

3 30 1 00

"" 10 0 Too 12 00 JS 00 jb 00 JToO 2< 00 92 00 96 00 IQ 00 ill 00

T I M E I S E C O N D )

FIGURE B - 3 L . ELA STIC RESPONSE OF 7 % DAMPED, 2 , 5 AND 8 HZ OSCILLATORS TOTHE MELENDY RANCH BARN, BEAR V ALLE Y, 1 97 2 EARTHQUAKE (N29W)

B-27

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=b'. 0 0 y . 0 0 9 . 0 0 J 2 . 0 0 1 6 . 0 0

FREQUENCY ( C P S )2 0 . 0 0 2 4 . 0 0

=^'. GO tt. 0 0 e .O O 1 3 . 0 0 1 6 . o o

FREQUENCY ( C P S )3 0 . 0 0 214. OO

(a) T^> 9 sec ,

FIGURE B-4a. FOURIER SPECTRA O F EFFECTIVE ACCELEROGRAM

SEGMENT DEFINED B Y T i = T „ - T ^ .

D m ,05

B-28

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E l C e n t r oNo. 12

=%'. oo B. 00 1 2 . O O J 6 . O O

F R E Q U E N C Y ( C P S )

'=b'. o o 1 4.0 0 a . 0 0 1 2 . o o l e . o o

F R E Q U E N C Y ( C P S J

(a) T '> 9 sec .

(Continued)

FIGURE B-4a. FOURIER SPECTRA O F EFFECTIVE ACCELEROGRAM

SEGMENT DEFINED B Y T ^ = T^ - T Q ^

B-29

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U -IC D

a::

ik1 i W\

Pacoima Dam

=b'. 0 0 4 . 0 0 e . 0 0 1 2 . 0 0 1 6 . 0 0F R E Q U E N C Y ( C P S )

=b'. 0 0 <J. 0 0 e . 0 0 1 2 . 0 0 1 6 . 0 0F R E Q U E N C Y ( C P S ) s y . 0 0

(b) 2.5 sec$ Tp $9 sec.

FIGURE B-4b. FOURIER SPECTRA O F EFFECTIVE ACCELEROGRAMSEGMENT DEFINED B Y T ^ = T ^ - T ^

B-30

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= b ' . 0 0 B . 0 0 1 2 . 0 0 1 6 . 0 0

F R E Q U E N C Y ( C P S )2 0 . 0 0 2 y . 0 0

^b.ooI J. OO S . o o 1 2 . O 0 1 6 . 0 0

F R E Q U E N C Y ( C P S )2 0 . o o 2 4 . 0 0

(b ) 2.5iT^'69 sec .

(Cont inued)

F I G U R E B - 4 b . F O U R I E R S P E C T R A O F E F F E C T I V E A C C E L E R O G R A MS E G M E N T D E F I N E D B Y T J = T ^ - T Q ^

B - 3 1

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= ^ . 0 0 8 . 00 1 2 . 0 0 1 6 . OOF R E Q U E N C Y ( C P S )

=%. 00 <i. 0 0 6 . 0 0 1 2 . 0 0 1 6 . 0 0F R E Q U E N C Y ( C P S )

214 . 0 0

Co) T ^< 2 .5 sec .

FIGURE B-4c. FOURIER SPECTRA O F EFFECTIVE ACCELEROGRAM

SEGMENT DEFINED B Y T ' = T „ - T c

D m .Do

B-32

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"=b.oo 8 . 0 0 1 2 . 0 0 16 . oo

FREQUENCY (CPS)

2 0 . 0 0 214 . OO

= * . 0 0 8 . OO 1 2 . 0 0 1 6 . 0 0

FREQUENCY (CPS)2 0 . 0 0 2 14 .O O

(,c) T|!j<2.5 s e c .

CContinued)

FIGURE B-4c. FOURIER SPECT RA O F EFFECTIVE ACCELEROGRAM

TEGMENT DEFINED BY Tjj = T^.05

B-33

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'%' . 00 14 . o o B . 0 0 1 2 . 0 0 1 6 . 0 0


2 0 . 0 0 2 4 . 0 0

=T3'. OO 14. OO 6 .O O 1 3 . 0 0 1 6 . 0 0

F R E Q U E N C Y ( C P S )3 b . 0 0 3 \ l . 0 0

Ca) T^>9 sec.

FIGURE B -5 a . CUMULATIVE SPECTRAL DENSITY FUNCTIONS OF EFFE CTIVEACCELEROGRAM SEGMENT DEFINED BY T^ = T ^ - T Q^

B-34

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E l C e n t r e

N o . 1 2

=^'.00 <4. 0 0 a . 0 0 1 2 . 0 0 1 6 . 0 0F R E Q U E N C Y ( C P S )

2 0 . 0 0 2 ) 4 .0 0

' ^ ' . 0 0 a . 0 0 1 3 . o o 1 6 . 0 0F R E Q U E N C Y ( C P S )

3 0 . OO 314 . 0 0

( a ) T p > 9 s e c .

( C o n t i n u e d )

FIGURE B -5 a . CUMULATIVE SPECTRAL DENSITY FUNCTIONS OF EFFECTIVE

ACCELEROGRAM SEGMENT DEF INED BY TA = T - T ^ ^D m . 0 5

B-35

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• ^b .o D y . o o 8 . 0 0 1 2 . 0 0 1 6 . 0 O

F R E Q U E N C Y ( C P S )3 0 . 0 0 2 4 . 0 0

^ b . 00 < i . o o 8 . 0 0 1 2 . 0 0 1 6 . 0 0

F R E Q U E N C Y ( C P S )3 0 . 0 0

Cb) 2.5 sec<T^^9 sec.

FIGURE B-5b. C U M U L A T I V E S P E C T R A L D E N S I T Y F U N C T I O N S O F E F F E C T I V EA C C E L E R O G R A M S E G M E N T D E F I N E D B Y T Jj = T^^ - T Q ^

B - 3 6

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c

E l C e n t r oNo. 5

' ^ . 0 0 4 . 0 0 e . 0 0 1 2 . 0 0 1 6 . 0 0F R E Q U E N C Y ( C P S )

2 0 . 0 0 2 4 . OO

^ . 0 0 4 . 0 0 e . O O 1 3 . 0 0 1 6 . 0 0


3 0 . 0 0

( b ) 2 . 5 se c^ T^ i9 se c .

(Continued)

FIGURE B-5b. CUMULATIVE SPECTRAL DENSITY FUNCTIONS O F EFFECTIVEACCELEROGRAM SEGMENT DEFINED BY T ^ = T„ - T .

B-37

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^ . 0 0 B . 0 0 1 2 . 0 0 1 6 . 0 0

F R E Q U E N C Y ( C P S )2 0 . 0 0 2 4 . 0 0

• ^ . 0 0 4 . 0 0 6 . 0 0 1 3 .O O 1 6 . 0 0F R E Q U E N C Y ( C P S ) 3 0 . 0 0 3 4 . 0 0

(c ) T | l j<2 .5 sec .

FIGURE B-5c. CUMULATIVE SPECTRAL DENSITY FUNCTIONS O F EFFECTIVEACCELEROGRAM SEGMENT DEFINED B Y T ^ = T^ - T ^^

B-38

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APPENDIX C

TECHNICAL BACKGROUND ON EQUIVALENT LINEAR RESISTANCE

FUNCTION MODELS

An equivalen t linear resistance functi on model is developed to

replace the actual resistance function (Figure 3- 1 ). This equivalent

model should be capable of approximating the reduced stiffness and

increased hys teretic loop damping associated with a nonlinear response

cycl e. Figure C-1 shows one such nonlinear cycle from peak negative

displacement to peak positive displac ement . During this cycle , the

equivalent stiffness is K given by:

K. 2 + S(y„ + y . - 2)e

^^n ^n*'(C-1)

where (Vp^y) is the n-cycle peak nonlinear displa cement in one direction

and (y *S )"is the preceding peak nonlinear displacement in the opposited i r e c t i o n .

With the equivalent linear resistance function app roach, one must

also estimate an effecti ve damping rati o. With c defined by Equation 3-5,

the total energy dissipat ion, E within a half-cycle oscillation (i. e.,

from peak response in one direction to peak response in the other

dire ction ) as shown in Figure C-1, can be given by:

9 7

TTK e(y + y +) 6

E„ - ° " 7 '' * 4E„ (C-2)

C-1

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where K i s t h e effective linear stiffness from peak-to-peak, y „ i s t h e

ductility level i n o n e direction f o r that response cycle, yp*is t h e

immediately preceding ductility level i n t h e opposite direction, & i s t h e

yield displacement and A E ^ i s t h e half-cycle hysteretic energy dissipation

as defined b y Figure C-1 . This total energy dissipation in a half-cycle

can b e rewritten in terms of an effective inelastic damping, & -

2 . 2^K^6„(y„ + y „ * ) 6

e e (C-3)

where t h e effective damping is given b y :

(C-4)

in which e ^ represents an equivalent viscous damping to account f o r t h e

one-half cycle hysteretic energy dissipation as given b y :

4 A E .

"n

IfK^d^r, + tJ^*) 5 y

(C-5)

e"^n n'

For t h e shear wall resistance function shown in Figure C-1, t h e

half-cycle hysteretic energy dissipation c a n b e obtained from:

2

yAE„ = K S ^ C l - s ) ! ( y ^ + y ^ * - 2 X )

-h -^ + y „ * (Y + 1 ) - ( 2X + Y )

(C-6)

l-s(l-a)(y„* - 1 )

C-2

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where

1 + (s + a - Sa)(y^* - 1)

1 + S(y * - 1)

Y = (1 - a) (1 - S)

and a and Y are the unloading stiffness parameter and strength degradation

parameter, respectively, as defined in Figure 3 - 3 .

A large number ofnonlinear resistance-deformation diagrams were

developed f o r t h e 4 frequencies and 12 earthquake time histories

considered in this study at various maximum ductility ratios, y , from 1.5

to 5. A limited number ofthese diagrams are shown in Figures 4 -4 through

4-9. Based upon these resistance-d eformation d iagr ams, it w a s observed

that:

P, - (y) "/'

~ / J n - 1 ) / N ^ " ^

v i - ^ ^ )* ^ (,)(n-0.5)/N

^n

where N is the number of strong nonlinear cycles through t h e time of

maximum ductility, y . With these approximation s, the effective stiffness

and effective damping associated with any individual nonlinear cycle can

be estimated by use of Equations C-1 through C-6. The effective

frequency, f , can be obtained by substituting K- f o r K in Equation 3 - 4 .

The cycle with the lowest effective stiffness. K g , and effective

frequency, f , and the largest effective damping, 6 corresponds to the

last strong nonlinear cycle at which y is reached ( n = N ) . Table C-1

presents estimates f o r t h e secant and effective frequency ratios, and

C-3

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hysteretic and effective damping percentage for this largest nonlinear

cycle as a function of number of strong nonlinear c ycle s, N, based upon

the approximations of Equation C-7 . Note that the effective frequency

associated with the maximum nonlinear response cycle reduces only slightly

as the number of strong nonli near cycles through the maximum cycle (N) isincreased from one to fou r. Even with only one strong nonlinear cycle,

the effective frequency associated with the maximum nonlinear cycle is

onl y 1 1% greater than the secant fre quency for y = 4.27 and approache s

the secant frequency closer as N increas es. Thu s, for the maximum

nonlinear cycle, the secant frequency only slightly underestimates the

effective frequency.

The hysteretic damping percenta ges,6u , and total effectiveNdamping perc enta ges, 6„ , associated with the maximum nonlinear response

Ncycl e increase as N is reduced from 4 to 1. For N=l, the hyst eretic

damping is considerably greater than for N of 2 and mor e.

The effective frequenc y and hysteretic damping in Table C-1 for

the largest nonlinear r esponse cycle (n=N) can be approxim ated by:

(*)••§ (C-8)

6 H , = ' = N N O - (fs/f)) (C-')

where

SN = 0.55

CNN = 0.38

NN - 0-34

(N=l)

(N=2)

(N=3 and 4)

(C-10)

c-4

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Similarly , for elastic response cycles ( n = 0 ) :

(f / f) = 1.0 (C-11 )

^ e 'o

s, = 0 (C-12 )

For any intermediate response cycles ( 0 < n < N ) , the effective frequency lies

between the elast ic and the secant fre que ncy and the hystere tic dam ping B|

lies between Q ^, and zero.

" N

The equivalent linear resistance function model used for

computing peak response must represent some average of the effective

frequencies for the various linear and nonlinear cycles loading up to peak

respo nse. One might define this average effective frequency, f', by:

^ = (1-A) + A(l- f3/f ) ^ - ^

where A is an empirically determined coefficient which lies between 0

(elastic) and 1.0 ( s e c a n t ) . This coefficient would be expected to be

about 0.5 for N=l (midway between the frequency of the elastic cycles and

the one strong nonlinear cyc le) and should increase with increasing

numbers of nonlinear cycles. Further more, the coefficient A is expected

to increase with increasing ductility ratios.

The equivalent linear resistance function model should retain

the same energy dissipation capability as the actual mod el. Using

Equation C-3 to define the energy dissipation capability of each mod el,

the equivalent elastic model must have an effect ive dampi ng, B g , given by:

C-5

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, I

e ' SN^^' ^ / f ) ] (C-14)

to be equivalent to the largest nonlinear cycle of the actual model when

both go from a displacement of - y t o +y. Equation C-14 can be rewritten

a s :

' S N ^ I - f,/f) (C-15)

by noting that (K /K' ) = (f / f r . Actually , Equation C-15 will ove rstate B ' because the last nonlinear c ycle has the greatest hystere tic

damping while 6' should express an average damping level during the strong

portion of the response time history leading up to the time of peak

respo nse. To correct this deficienc y. Equation C-15 should be replaced

by :

I - ^ 6 + C^(l- f 3 / f ) ] (C-16)

where Cj^ is an empirical ly de termined coefficien t which should have a

va lu e less than C ^ ^ (Eq uat ion C - 1 0 ) .

•

C-6

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#

TABLE C-1

SECANT A N D EFFECTIVE FREQUENCY RATIO A N D HYSTERETIC A N D TOTAL EFFTrTIVE DAMPING PERCENTAGE

(SHEAR WALL RESISTANCE FUNCTION - LARGEST N O N L K ' ^ A K CYCLE)

Number of StrongNonlinear Cycles, N

1

2

3

4

y = 1.85 1

y'

0.77

0.77

0.77

0.77

(Vf)N

0.81

0.79

0.78

0.78

BM (%)

" N

13

9

8

7

3e (%)^N

20

16

15

14

y = 4.27

V^

0.56

0.56

0.56

0.56

< V " N

0.62

0.59

0.58

0.57

Bn (%)

" N

24

17

15

14

3g (%)^H

31

24

22

21

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F I G U R E C - 1 . H A L F - C Y C L E H Y S T E R E T I C E N E R G Y A B S O R P T I O N

C - 8

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A P P E N D I X D

P A RA M E T E R S T U D I E S T O D E T E R M I N E S E N S I T I V I T Y O FN O N L I N E A R R E S P O N S E R E S U L T S T O P RO P E R T I E S O F T H E

R E S I S T A N C E F U N C T I O N M O D E L

T h i s a p p e n d i x p r e s e n t s t h e re s u l t s o f a f e w s e n si t i v i t y s t u d i e s

p e r f o r m e d t o d e t e r m i n e t h e s e n s i t i v i t y o f n o n l i n e a r r e s u l t s t o p r o p e r t i e s

o f t h e r e s i s t a n c e f u n c t i o n m o d e l . T h e p u r p o s e o f t h e s e a n al y s e s i s t o

d e m o n s t r a t e t h a t t h e s h e a r w al l r e s i s t a n c e f u n c t i o n p r o p e r t i e s u s ed i n

t h i s s t u d y t e n d t o c o n s e r v a t i v e l y u n d e r e s t i m a t e t h e i n p u t s c a l e f a c t o r

( i n e l a s t i c d e a m p l i f i c a t i o n f a c t o r ) , F . T h e r e f o r e , t h e r e s u l t s p r e s e n t e d

i n C h a p t e r 4 t e n d t o b e c o n s e r v a t i v e f o r o t h e r m o d e l p r o p e r t i e s . T h i s

a p p e n d i x w a s w r i t t e n w i t h t h e a s s u m p t i o n t h a t t h e r ea d e r h a s c a r e f u l l y

r e v i e w e d C h a p t e r s 3 a nd 4 an d d o e s n ot r e p e a t d i s c u s s i o n s c o n t a i n e d i n

t h o s e c h a p t e r s .

D . l I N F L U E N C E O F N O N L I N E A R R E S I S T A N C E F U N C T I O N T Y P E

F i g u r e 3 -1 c o m p a r e s t h e b i l i n e a r , T a k e d a , a nd s h e a r w a l l

r e s i s t a n c e f u n c t i o n s . I t c an b e s ee n t h a t f o r t h e s a m e d u c t i l i t y l e v e l ,

t h e T a k e d a a n d s he a r w a l l m o d e l d i s s i p a t e l e ss h y s t e r e t i c e n e r g y i n a

g i v e n n o n l i n e a r c y c l e t h a n d oe s t h e b i l i n e a r m o d e l . T h u s , o n e w o u l d

e x p e c t t h e T a k e d a a nd s h e a r w a l l m o d e l s t o h a v e s i m i l a r i n p u t s c a l e

f a c t o r s , F , f o r a g i v e n d u c t i l i t y l ev el a nd f o r t h e b i l i n e ar m o d el t o

h a v e a s i g n i f i c a n t l y h i g h e r i n p u t s c a l e f a c t o r , F . T o d e m o n s t r a t e t h i s

e x p e c t a t i o n , t h e F f a c t o r s w e r e d e t e r m i n e d f o r t h e P a r k f i e l d r e co r d f o r

l ow a nd hi g h d u c t i l i t y f a c t o r s o f y = 1 . 8 5 , an d y = 4 . 2 7 , r e s p e c t i v e l y ,

f o r a 5 . 3 4 H z s t r u c t u r e m o d e l w i t h b i l i n e a r , T a k e d a , an d s h e a r w a ll

r e s i s t a n c e f u n c t i o n s . F o r a ll t h r e e r e s i s t a n c e f u n c t i o n s , t h e s l o p e

p a r a m e t e r o f t h e p o s t - y i e l d l o ad i n g c u r v e w a s s = 0 . 1 . F o r t he T a k e d a

a nd s h e a r w a l l r e s i s t a n c e f u n c t i o n s , t h e u n l o a d i n g s t i f f n e s s p a r a m e t e r

D - 1

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was a = 0.35, and the strength degradation parameter wa s Y = 0.95. The

only difference between the Takeda and shear wall resistance functions

was the pinched behavior of the shear wall mo de l. The resulting F

factors were:

Ductility Level

Input Sca le Fac tor, F

Bi 1i near

1.85 1.29

4.27 1.51

Takeda

1.24

1.33

Shear Wall

1.21

1.29

The conclus ion is that the shear wall resi stan ce funct ion model

conservati vely underestima tes the input scale fact or, F, for the Takeda

and bilinear models.

D.2 COMPARISON OF NONLINEAR RESPONSE FOR SHEAR WALL VERSUS

BRACED-FRAME MODEL

Diagonal bracing elements are the primar y lateral force-carrying

elements in braced-steel fr ame s. For nuclear struct ures , such elements

are usually angle s, wide flange sections or standard we ight or extra-

strong steel pipe with diameters ranging from 6-12 inche s. The limiting

behavior of braced elements with adequate con nections is governed by

yielding in tension and inelastic buckling in comp ress ion. When employed

as frame bracing elements for resisting reversin g lateral loads, the

braces can become subjected to severe axial cyclic loading causing the

braces to sequentially buckle and stretch ine lastica lly. Tests indicate

that the overall lateral force-d isplacement behavior of a braced frame is

also characterized by pinched hysteresis loo ps. The degrad ing, pinched

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character of these loops is due primarily to the inelastic behavior of

the individual brac es under cyclic loading. During a cycle, once the

tension diagonal has inelastically lengthened and while the compression

brace has buckled upon load rev er sal , the system is softened until the

buckled braced is restr aighte ned and its axial stiffness is reco vere d.

The axial sti ffness of a buckled brace is smaller than the stiffness of a

straight membe r. The capacity of a member in compression is also greatly

reduced, either due to its bowed shape or previous inelastic strain

hist ory. A lateral load-displacement diagram obtained during a structural

frame test is shown in Figure l-9b which illustrates the reverse cycle

hysteretic behavior characterized by stiffness degradation and pinching

of the resulting hysteresis loops.

The number of investigations involving reversing load tests of

braced-fra me systems is very limited. Wakabayashi (1973, 1 9 7 7 ) * has

summarized the laboratory testing conducted on braced frames in Japan.

Maison (1980) and Popov (1980) have reported testing on half-scale and

one-sixth scale model braced fra mes . The hysteresis behavior of bracing

membe rs under cyclic axial loading has been reported by several inv esti

gators (Jain, 1980, 1978b; Gugerli, 1980; Popov, 1979, 1 9 8 1 ) .

To investigate the effect of the braced-frame resistance

function, an example, one-story, single bay, braced-steel-frame was

defined, as indicated in Figure D-1 . The example structure was modeled

directly with DRAIN-2D, utilizing the hysteresis model for steel members

developed by Jain (1979) and included in the DRAI N-2D program (Jain and

G o e l , 1 9 7 8 a ) . Buckling elem ent, EL 9, developed originally by Singh

( 1 9 7 7 ) , and modified by Jain ( 1 9 7 8 a ) , was utilized to model the yielding

and post-buckling behavior of the pin-connected bracing element (8"

diameter pip e) defined for the example braced frame . The cyclic loading

behavior of the frame model , obtained using DRAIN- 2D, is also shown in

Figure D- 1. As can be noted, the model reflec ts the pinched, degrading

stiffness behavior noted in testing of braced-fr ame str uctur es.

* All refer ence s in this appendi x are listed in the Refere nce list forthe main body of this repo rt.

D-3

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Input scale f act ors , F, were obtained for both the shear wall

and the braced-frame resistance function models with a 5.34 Hz elastic

frequency and 7% elastic damp ing. The following input scale factors were

obtained for the Taft, Parkfield, and Melendy Ranch records.

Record

Taft

Parkfield

Melendy Ranch

Computed Input Scale Fac tor , F, for5.34 Hz Structure

y = 1.85 1

Shear Wall

1.25

1.21

1.96

Braced Frame

1.49

1.21

2.04

1 y = 4.27 1

Shear Wall

1.65

1.29

5.48

Braced Frame

2.17

1.40

5.44

One may note that for the Melendy Ranch record, t he input scale

factors are essentially identical for the shear wall and br aced-fra me

m o d e l s . Howev er, for the Taft reco rd, the braced -fram e model results in

significantly greater input scale factors than does the shear wall model.

Basica lly, the braced-frame model does not show as much degradation in

stiffness or pinched behavior as does the shear wall model.

In Chapter 4, it was shown for shear walls that the predicted

input scale factor (inelastic deamplification f a c t o r ) , F^, was influenced

by the number of strong nonlinear response cycles, N, and thus by the

strong motion durati on, T Q . It was recommended that F^ could be bestpredicted by Equation 4-3 for shear wal ls. This equation depends upon

the estimate of an effective frequency and an effective damping using

D-4

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coefficient C p a n d C ^ from Table 4-2. These coefficients ar e shown t o b e

a function o f N f o r s he a r walls . Howev e r , f o r braced-frame and bilinear

m o d e l s , t h e F y does n o t appear t o b e a s much influenced b y N . T o investi

gate this effec t, t h e coefficients Cp = 1-5 and C^ = 0 . 30 f o r N = l were

used f o r t h e Taft and Parkfield re cord s. T h e predicted scale factors, F y ,

for t h e recommended procedure (Equation 4-3 and Table 4-2) f o r shear walls

is compared with t h e predicted scale factors obtained f o r 1 ) Equation 4-3

and C p = 1.50 and Cf^ = 0.30, 2 ) t h e Iwan Method , a nd 3 ) t h e Sozen Method .

Record

T a f t

Parkfield

Melendy Ranch

Predicted Input Scale Factor, F,

for 5.34 Hz Structures

y^ = 1.85

Eqn. 4-3 andTable 4-2

1.30

1.36

2.08

Eqn. 4-3 andCp = 1.50; C^ = 0.30

1.58

1.38

2.08

Iwan

1.78

1.51

2.29

Sozen

1.20

0.97

2.20

Record

Taft

Parkfield

Melendy Ranch

Predicted Input Scale Fact or, F,

for 5.34 Hz Structures

y|_ = 4. 27

Eqn. 4-3 and

Table 4-2

1.68

1.24

5.48

Eqn. 4-3 and

Cp = 1.50; C,^ = 0.30

2.38

1.77

5.48

Iwan

2.77

2.08

6.03

Sozen

1.62

0.85

7.12

D-5

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E x c e p t f o r t h e l ow d u c t i l i t y ( y ^ = 1 . 8 5 ) P a r k f i e l d r e c o r d c a s e ,

t h e F y p r e d i c t e d b y E q u a t i o n 4 - 3 an d T a b l e 4 -2 u n d e r e s t i m a t e s t h e

n o n l i n e a r t i m e h i s t o r y a n al y s i s c o m p u t e d F v a l u e s f o r b r ac e d f r a m e s a nd

b i l i n e a r s t r u c t u r e s f o r t h e T a f t a n d P a r k f i e l d r e c o r d s . F o r M e l e n d yR a n c h , E q u a t i o n 4 - 3 an d T a b l e 4 - 2 a c c u r a t e l y p r e d i c t t h e t i m e h i s t o r y

c o m p u t e d F v a l u e s f o r b r a c ed f r a m e s . O n t h e o t h e r h a n d , t h e u s e o f

E q u a t i o n 4 - 3 w i t h t h e N = l v a l u e s o f C p = 1 .5 0 a n d C N = 0 . 3 0 c o n s i s t e n t l y

o v e r p r e d i c t s t h e t i m e h i s t o r y c o m p u t e d F v a l u e s f o r b r a ce d f r a m e s f o r t h e

T a f t and P a r k f i e l d r e c o r d s . T h i s b r i e f s t u d y s u g g e s t s t h e F v a l u e s f o r

b r a c ed f r a m e s a nd b i l i n e ar s t r u c t u r e m o d e l s l i e a p p r o x i m a t e l y m i d w a y

b e t w e e n t h e F y v a l u e s p r e d i c t e d u s i n g t h e C p a nd C M v a l u e s o f T a b l e 4 - 2

a n d t h o s e p r e d i c t e d w i t h C p = 1 . 50 a nd C ^ = 0 . 3 0

T h e I w a n m e t h o d c o n s i s t e n t l y s e v e r e l y o v e r p r e d i c t s ( u n c o n s e r v a -

t i v e ) t h e t i m e h i s t o r y c o m p u t e d F v a l u e s f o r b r a c e d f r a m e s f o r t h e r e a s o n s

d i s c u s s e d i n C h a p t e r 4 . T h e S o z e n m e t h o d i s l es s a c c u ra t e t h a n E q u a t i o n

4 - 3 a n d T a b l e 4 - 2 i n p r e d i c t i n g F v a l u e s f o r b r a c e d f r a m e s f o r t h e r e a s o n s

d i s c u s s e d i n C h a p t e r 4 .

T h e c o n c l u s i o n o f t h i s b r i e f s t u d y i s t h a t t h e C F a n d C N v a l u e s

g i v e n i n T a b l e 4 - 2 f o r s h ea r w a l l s t r u c t u r e s o v e r e m p h a s i z e t h e i m p o r t a n c e

o f s t r o n g m o t i o n d u r a t i o n , T p , o n F u f o r b r a c e d - f r a m e a nd b i l i n e a r

s t r u c t u r e m o d e l s . F o r t h i s r e a s o n , t h e u s e o f C p an d C N v a l u e s f r o m

T a b l e 4 - 2 w i l l t e n d t o u n d e r p r e d i c t ( c o n s e r v at i v e b i a s ) t h e F y v a l u e s f o r

t h e l o n g er d u r a t i o n r e c o r d s (N i 2 ) . T h i s u n d e r p r e d i c t i o n o c cu r s b e c a u s e

t h e b r a c e d - f r a m e a nd b i l i n e a r m o d e l s d o no t h a v e a s s e v e r e o f s t i f f n e s s

d e g r a d a t i o n a nd p i n c h e d b e h a v i o r a s d o t h e s h ea r w a ll m o d e l s u s ed i n t h i s

s t u d y . F o r b r a c e d - f r a m e a nd b i l i n e a r m o d e l s , a b e t t e r e s t i m a t e o f F y c an

b e o b t a i n e d b y a v e r a g i n g t h e F y v a l u e s o b t a i n e d f o r C p a n d C ^ v a l u e s f r o mT a b l e 4 - 2 w i t h t h o s e o b t a i n e d f o r C p = 1 . 50 a n d C^j = 0 . 3 0 .

J k D - 6

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D . 3 I N F L U E N C E O F R E S I S T A N C E F U N C T I O N C O E F F I C I E N T S a A N D s

T h e d e t a i l e d s h a p e o f t h e s h e a r w a ll r e s i s t a n c e f u n c t i o n i s

s i g n i f i c a n t l y i n f l u e n c ed b y t he c o e f f i c i e n t s a a nd s w h e r e s r e p r e s e n t s

t h e r a t i o o f t h e p o s t - y i e l d i n g s t i f f n e s s t o t h e i n i t i a l s t i f f n e s s ( F i g u r e3 - 1 ) an d a r e p r e s e n t s t h e d e g r a d a t i o n i n s t i f f n e s s o n u nl o a d i n g ( F i g u r e

3 - 3 ) w i t h a = 0 i n d i c a t i n g n o u n l o a d i n g s t i f f n e s s d e g r a d a t i o n a n d

i n c r e a s i n g a i n d i c a t i n g i n c r ea s e d u n l o a d i n g s t i f f n e s s d e g r a d a t i o n .

M o s t r e a l s t r u c t u r a l s y s t e m s h a v e a n s r a t i o b e t w e e n a b o u t 0 . 0 3

a nd 0 . 1 5 . P r e v i o u s s t u d i e s h av e i n d i c a t e d v a r i a t i o n s o f s b e t w e e n 0 . 0 3

a nd 0 . 1 5 h a s l i t t l e e f f e c t o n t h e c o m p u t e d d u c t i l i t y l ev el s o l on g a s y i s

l e s s t h a n a b o u t 5 . F o r t h i s r e a s o n , s = 0 . 1 0 w h i c h i s m i d w a y w i t h i n t h i s

n o r m a l r a n g e w a s us ed i n t h i s s t u d y . F o r a g i v e n d u c t i l i t y , t h e i n p u t

s c a l e f a c t o r , F , i s no t e x p e c t e d t o i n c r e a s e s i g n i f i c a n t l y f o r s f r o m 0 . 0 3

t o 0 . 1 5 . H o w e v e r , a s s i n c r e a s e s b e y o n d a b o u t 0 . 1 5 , t h e F v a l u e is

e x p e c t e d t o b e g i n t o i n c r e a se s i g n i f i c a n t l y f o r a c o n s t a n t d u c t i l i t y

r a t i o . T h i s i s d e m o n s t r a t e d b y t h e f o l l o w i n g t a b l e w h i c h t a b u l a t e s t h e

t i m e h i s t o r y F v a l u e s r e q u i r e d t o d e v e l o p y , = 1 .8 5 f o r a s h e a r w a l l

r e s i s t a n c e f u n c t i o n s t r u c t u r a l m o d e l w i t h a n el a s t i c f r e q u e n c y o f 5 . 3 4 H z

a nd v a r i o u s s v a l u e s s u b j e c t e d t o t h e P a r k f i e l d r e c o r d .

s

0

0 . 0 3

0 . 1 0

0 . 1 5

0 . 2 0

0 . 5 0

1 . 0 0

F

1 . 1 6

1 . 1 7

1 . 2 1

1 . 2 6

1 . 3 2

1 . 5 4

1 . 8 5

D - 7

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I t i s c o n c lu d e d t h a t s = 0. 10 g i v e s i n p u t s c a l e f a c t o r s , F , w h i c h

a r e a c c u r a t e f o r t h e r a n g e O f s l O . 1 5 . H o w e v e r , t h e F v a l u e s o b t a i n e d f o r a

r e s i s t a n c e f u n c t i o n w i t h s = 0 . 10 w i l l b e i n c r e a s i n g l y c o n s e r v a t i v e l y l o w

a s s i s i n c r e a s e d b e y o n d 0 . 1 5 .

N e x t , t h e i n f l u e n c e o f s t i f f n e s s d e g r a d a t i o n o n u n lo a d i n g w a s

s t u d i e d . F o r t h i s s t u d y , a w a s a s s i g n e d v a l u e s o f 0 . 0 , 0 . 3 5 , a n d 0 . 5 0

w h i c h c o v e r s t h e r a n g e f r o m no u n l o a d i n g s t i f f n e s s d e g r a d a t i o n t o v e r y

s e v e r e u n l o a d i n g s t i f f n e s s d e g r a d a t i o n . T h e s h e ar w a l l r e s i s t a n c e

f u n c t i o n m o d e l w i t h a n e l a s t i c f r e q u e n c y o f 5 . 3 4 H z w a s s u b j e c t e d t o t h e

P a r k f i e l d r e c o r d w i t h a n i n p u t s c a l e f a c t o r o f 1 .2 1 a nd t h e f o l l o w i n g

d u c t i l i t y r a t i o s w er e o b t a i n e d :

a

0

0 . 3 5

0 . 5 0

y

1 . 8 8

1 . 8 5

1 . 8 4

I t w a s c o n c l u de d t h a t i n c r e a s e s i n u n l o a d i n g s t i f f n e s s d e g r a d a

t i o n a c t u a l l y r e s u l t e d i n a t r i v i a l r e d u c t i o n i n t h e d u c t i l i t y f a c t o r .

T h e u s e o f a n u n l o a d i n g d e g r a d a t i o n c o e f f i c i e n t o f a = 0 .3 5 p r o d u c e s

r e s u l t s w h i c h a r e r e p r e s e n t a t i v e f o r t h e f u l l p r a c t i c a l r a n g e o f

0 i a l 0 . 5 0 .

D . 4 I N F L U E N C E O F E L A S T I C D A M P I N G

R i d d e l l ( 1 9 7 9 ) h a s sh o w n i n c r e a s es i n e l a s t i c d a m p i n g r e s u l t i n ar e d u c t i o n i n t h e i n e l a s t i c s p e c t r a l d e a m p l i f i c a t i o n f a c t o r , F . T h e

m e t h o d s r e c o m m e n d e d i n t h i s r e p o r t ( E q u a t i o n s 3 -1 4 o r 4 - 3 ) w i l l a ls o

r e s u l t i n a l e s s e r F y v a l u e w i t h i n c r e a s e d e l a s t i c d a m p i n g . T h i s

s i t u a t i o n r e s u l t s b e c a u s e b o t h e l a s t i c d a m p i n g a nd i n e l a s t i c r e s p o n s e a re

e n e r g y d i s s i p a t i o n m e c h a n i s m s a nd a b s o l u t e a d d i t i o n o f t h e t w o e f f e c t s

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will overstate the total reduction in res pons e. Ther efor e, the input

scale factors (inelastic deamplification fac tors ) presented in Chapter 4

for 7 percent elastic damped structures are conserva tively low for struc

tures with less than 7% damp ing. This point is illustrated by computingthe input scale factors, F, for ductilities of 1.85 and 4.27 for an

elastic structural freque ncy of 5.34 Hz with 3% elastic damping for the

Taft, Artificial, and Melendy Ranch record s. These 3% damped F values

are compared with tho se shown in Tab le 4-1 for 7 % damping:

Ductility

1.85

4.27

Record

Taft

Artificial

Melendy Ranch

Taft

Artificial

Melendy Ranch

Input Scale Factors DeamplificationFactors) 5.34 Hz

7 % Damping

Computed,

F

1.25

1.33

1.96

1.65

1.88

5.48

Predicted(Eq. 4- 3) , Fy

1.30

1.49

2.08

1.68

1.65

5.48

3% Damping

ComputedF

1.53

1.48

2.07

2.19

2.38

6.25

Predicted(Eq. 4- 3) , Fy

1.54

1.59

2.21

2.20

1.95

6.14

The above table also shows the inelastic deamplification factors

predicted by Equation 4-3 with coeffici ents from Table 4-2. The effective

damping val ues , B' * obtained from Equation 4-6 and Table 4-2 are:

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Record

Taft

Artificial

Melendy Ranch

Effective Damping, 3^^ {% )

y = 1.85

e = 7 %

7. 5

7.5

10.5

3 = 3%

4.5

4.5

7.5

y = 4.27

B = 7%

9.5

9.5

12.5

B = 3%

6.5

6.5

10.0

Note that for these six cases (2 duct iliti es, 3 recor ds, 1

frequ ency) which represent a subset of the 96 cases (2 ductiliti es, 12

reco rds, 4 frequencie s) studied in Chapter 4 to develop Equation 4-3 and

Table 4- 2, the recommended prediction approach does as good a job of

predicti ng the computed F values at 3% elast ic damp ing as it did at 7 %

elastic damping. At 7% elastic damping, the ratio of predicted to

computed F values has a mean of 1.02 and a COV of 0.08 for these six

cases. At 3% elasti c dampi ng, this ratio has a mean of 0.99 and a COV of

0.09 for these six cases.

Two conclusions are reached from this brief study:

1. The inelastic deamplific ation factors are larger at 3%elastic damping than at 7 % elastic damping. Thus, Ffactors generated for 7% elastic damped structural modelscan be conservatively used for structures with damping

values less than 7% .

2 . The recommended prediction method (Equation 4-3 and Table4-2) works equally well for structures with 3% elasticdamping as it does for 7% elastic damping.

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W 18 x 50

W 21 x 44

8 " *

( r

14.7 in^

13.0

8.4

2.94in, -^-

I

802 in.^

971

72.5

26.9 x 12

2.94O l O )

/6 = 714 x kips

(a) Struct ure Model Definition

b) Cyclic Loading Behavior Using DRAIN-2D Bracing Element 9 (Jain, 1978a)

F I G U R E D - 1 . B R A C E D - F R AM E S T R U C T U R E M O D E L

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* — •

2 o

Gavilan

College

'^.aa V I . O O a . 0 0 1 2 . D O 1 6 . o o

F R E Q U E N C Y tC P S )2 0 . O O 2 4 . O O

u . 0 0 a . 0 0 1 3 . 0 0 1 6 . 0 0

F R E Q U E N C Y ( C P S J

( c ) T , l) < 2. 5 s e c .

( C o n t i n u e d )

F I G U R E B - 5 c . C U M U L A T I V E S P E C T R A L D E N S I T Y F U N C T I O N S O F E F F E C T I V EA C C E L E R O G R A M S E G M E N T D E F I N E D BY T ' = T - T Q ^

B - 3 9

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•

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APPENDIX E

STRUCTURAL EVALUATION OF EL CENTRO STEAM PLANT UNIT 4

SUBJ ECTE D TO THE 1979 IMPERIAL VALLEY EARTHQUAKE

E.l INTRODUCTION

The El Centro Steam Plant located in the northeast portion of

El Centro , was subjected to peak horizontal ground acc elerations est imated

to be about 0.5g (Reference E-1) as a result of the 1979 Imperial Vall ey

earthq uake. This plant consists of four uni ts. The seismic design basis

for Units 1, 2 and 3 built in 1949 , 1952 and 195 7, resp ecti vel y, is

unknown. Howeve r, review of the project specifications for Unit 4, which

was built in 196 8, indic ates that the steel fra ming was designed for a

lateral static equivalent seismic loading of 0.2g (dead and live l o a d s ) .

Even though the El Centro Steam Plant was subjected to earthquake ground

motion that was about 2.5 times the design seismic loadin g, there was

only minor damage observed at the plant following this earthquake. The

purpose of this evaluation is to correlate predicted structural damage

with observed structural damage for the El Centro Steam Plant Unit 4

subjected to the 1979 Imperial Valley earth quake.

Analys es of Unit 4 of the steam plant have been reported in

References E-1 and E-2 . Howev er, neither of these evaluations were

conducted for the express purpose of correlating predicted and observed

structural da mage. The analysis presented in Reference E-1 was performed

for the purpose of estimating equipment response levels and was based on

a simple structural mo de l. There was no evaluation of structural res ponse

and capacities in this refer ence. The analysis presented in ReferenceE-2 was conducted to demons trate that a particular set of conservative

design criteria would produce analytical results which would overpredict

observed Unit 4 structural resp onse . This analysis was based on a

detailed three- dimen sional model of the Unit 4 struc ture but which ignored

soil-structure interaction eff ect s. Data from each of these references

have been used in the preparation of this report.

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The evaluation of the El Centro Steam Plant as presented herein

is based on a relat ivel y detailed structural model whi ch incorporate s

soil-structure interaction effects . Structural response is calculated

with this model by an elastic response spectrum ana lys is. The seismic

excitations are taken from response spectra computed from measured accel

eration time histories recorded close to the steam plant site. The calcu

lated structural resp onse is then compared to code-s pecifi ed ultimate

capacities (i.e., from AISC Part 2 and ACI building codes ) of structural

members and elements to assess predicted structural beh avior. The pre

dicted structural behavi or is then , in turn , compared with o bserva tions

of the plant following the earthquake in order to demonstrate how behavior

calculated from an elastic structural analysis based on elastic spectra

anchored to peak acceler ation from recorded motio ns corre lates with actual

observed behavior of this structu re.

E.2 DESCRIPTION OF THE STRUCTURE

The El Centro Steam Plant consists of four units that generate

power by burning oil or natural gas (Figure E- 1 ) . Units 1, 2 and 3 were

designed by Gibbs and Hill and built in 1949, 1952 and 19 57, resp ect ivel y.

Unit 4, the newest and largest with an 80 MW electri c ou tpu t, was designed

by Fluor Corpor atio n, Ltd. and built in 196 8. Combined output of all four

units is 174 MW. Each unit of the plant is stru ctur ally inde pendent and

contains three structur es: a turbine building, a turbine pedestal and a

boiler str uctu re. Each of these structures is founded on a single 12.2

foot-thick h ollow, honeycomb-like reinforced concrete foundation with

plan dimensi ons of 96 by 207 fee t. Soil at the site consists of very

deep alluvial deposits composed of stiff to hard clays interlain with

laminations of sllty clay loam and sandy loam (Reference E-1). Cross

sections of Unit 4 are shown in Figures E-2 and E-3 and a plan view of

the ground floor is shown in Figure E- 4.

The Unit 4 turbine building is a moment-r esisting steel f rame

with reinforced concrete shear walls cast monolithically with the exterior

steel frames on the eas t, west and south sides of the buildin g. The

turbin e building has plan dimen sions of 93 feet by 128 feet and a maxim um

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height of 55 feet . As shown in Figures E-3 and E- 4, the turbine building

has four bays: auxil iary, heater, turbine and service. An operating

floor 20 feet above the ground floor extends through all four bays. This

floor contains a large opening for the turbine pedestal struc ture. There

is also a floor in the heater bay 14 feet a bove the opera ting flo or.

Both the operating and heater bay floors are constructed of metal d ecking

and concrete fi ll . Covering the a uxiliar y and heater bays is a roof of

metal decking and concrete fill . The roof covering the turbine and

service bays is composed of gypsum decking and composition roof ing.

The Unit 4 turbine pedestal is a reinforced concrete frame that

supports the turbine g enera tor. The pedestal is located within the

turbine buildin g but is isolated from the buildi ng by a one-inch expansion

joint at the operating floor . The pedestal has plan dimensions of 68

feet by 23 feet and is 20 feet hig h.

The boiler structure for Unit 4 is a braced-steel frame with

plan dime nsions of 31 by 51 feet and a height of 97 fee t. The boiler

structure and the turbine building are connected along Column Line G

between Colum n Lines 15 and 16 . The boiler is suspended from girders at

the top of the steel fra me . Lateral s upport for the boiler is provided

by seismic stops at various elevations of the fram e. The boiler

structure also supports a steel stack.

E.3 EARTHQUAKE GROUN D MOTION

On October 15, 1979, a strong earthqua ke shook the Imperial

Valley of California . As reported in Refer ence E -1 , this earthquake had

a local magni tude M^^, of 6.6 and a surface wav e mag nit ude , M^, of

6.9. The earthquake produced 30 km of predomi nantly strike-slip rupturealong the Imperial Fault (Figure E- 5 ) . There were many aftersh ocks,

three of which exceeded M, = 5 within the first 8 hour s.

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As a result of the 1940 El Centro earthquake and other smaller

ear thq uak es, the Imperial Val ley was extensiv ely instrumented by a network

of strong motion a ccel erom eter s. A 13 station linear array straddling

the fault and passing through El Centro is shown in Figure E-5 . Included

in this array is Station No. 9, the original instrument that recorded the

1940 El Centro ground motion re cord. Also of interest , is a digital

recording differential array installed by the U. S. Geological Survey about

two weeks before the 1979 earthqu ake in a large vacant lot near Unit 4 of

the El Centro Steam Plant. Unfortunate ly, there were several malfunctions

in the operation of this system such that useful data was not obtained

from most of the instruments in this array. How ever , a good record was

obtained from the instrument labeled No. 5165 El Centro Differential

Array installed in a small building at the south end of the array.

The El Centro Steam Plant is located between Sta tions N o. 8,

No. 9 and the Differential Array as shown on Figures E-5 and E-6.

Stations 8, 9 and 5165 are about 4,000, 3,800 and 2,400 feet from Unit 4

with Station 8 closest to the Imperial Fault and Station 9 furthest from

the fault. Station 5165 is located at about the same distance from the

fault as the steam plant although this instrument is closer to the earth

quak e epic ente r. Good ground motion records were obtained for this

earthqu ake at Stations 8 and 516 5. Because of the age of Station No. 9,

there was difficulty in obtaining a complete time history from this

instrument. Also , there are questions about the free-field nature of

Station N o. 9 because it is situated on a large fo unda tio n.

For this evaluation, a digitized corrected version of the

recorded time history from Station 5165 was used as input excitation for

the analysis of the El Centro Steam Plant Unit 4 as reported herei n. Itis believed that this record is a reasonab le estima te of the ground motion

at the steam plant site for the following reasons:

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a. The steam plant appears to be within a zone along theImperial Fault wher e ground motio n is relativ ely con stan t.Large at tenuation of the ground motion is not seen untilStation No. 10 located much further away from the fault.Recorded ground motion for the 1979 Imperial Valley Earth

quake at Statio ns 7 throug h 10 and 5165 are summarized inTable E-1.

b . A Wilmot Seis mosco pe with a period of 0.75 se c. situated atthe bottom floor of the steam plant itself registered amaxim um re sponse displacement of 6.57 cm and a maximumresponse velocity of 55 cm/s ec. These are approximatelyequivalen t to the maximum respon ses at 0.75 sec. period and1 0 % damping computed from the horizontal time histories atStation 5165 . The seismosco pe is believed to have adamping of about 10%.

The critical elements of the Unit 4 structure are primarily

sensitive to horizontal lateral forces and thus this evaluation considered

only the horizontal components of earthquake ground motion. The time

histories and response spectra of the north-south and east-west components

from Station 5165 are illustrated in Figures E -7 , E- 8, and E-9 . Note

that in Figures E-7 and E- 8, the 7 percent damped s pectra from Station

5165 and Reg. Guide 1.60 (Reference E- 6, anchored to the peak accele ration

from Station 51 65) are compare d. The spectra from the recorded eart hquake

motion general ly fall below the Reg. Guide 1.60 spectra with the exception

of the region between about 5 and 9 Hz where t he east-west moti on spectrum

from Station 5165 is greater than the Reg . Guide spect rum. The strong

motion dura tion , Tfj, defined in the mann er described in Chapte r 2 (i.e.,

"•"[) " "laximum of Tp ^ or T0 .7 5 m in us T0 .0 5 wh er e T Q . Q S and T0.75

are the times associated with 5 and 75 percent of the total cumulative

ener gy for the record and Tp^^ is the time a ssociate d with the first

zero crossing of the accelerog ram follow ing the maximum positive or

negative acceleration, whichever occurs later in time) are 2.8 seconds

for the north-south motion and 3.7 seconds for the east-west motion.

Qualitat ively, the Station 5165 motions are moderate duration records.

E-5

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E.4 EARTHQUAKE DAMAGE

An NRC reconnaissance team visited the steam plant shortly after

the earthquake struck. Lawrence Livermore National Laboratory (LLNL)

personnel visited the site on March 18 , 1980 . At the request of LLN L, a

representative of Structural Mechanics Associates, Inc. (SMA) inspected

the plant and examined the plant log book for the day of the earthquake

and for the following day in Augus t, 19 80. Based upon the data gathered

from these site vis its , a record of the damage incurred at the steam

plant during the earthquake was presented in Reference E -1 . A brief

summary of the observed damage extracted from this reference is presented

in this section.

When the earthquake occur red. Units 3 and 4 of the El Centro

Steam Plant were operating and Units 1 and 2 were shut down for maint en

anc e. The operating units tripped off line when station power was lost

because of a short circui t res ulting from a broken ins ulator in a light

ning rod in Unit 1. Unit 3 was restored to service within 15 minut es

following the main shock and Unit 4 was restored to service within 2

hours . Much of the time was spent by plant personnel inspecting for

dam age . Later in the day and during the follow ing day, both Units 3 and 4

were removed from service to repair piping.

No significant structural damage was observe d. Minor concrete

cracking was generally apparent throughout the plant. More significant

cracki ng, on the order of 1 in. , was observed at a junction of a floor

diaphragm high in the structure and the turbine building shear wa ll . In

addition, concrete cracks were observed at upper elevations between the

various units , where larger deflections would be expected. However , in

all c ase s, this cracking was local in nature and overall structural

integrity was mainta ined. Structural steel, for the most part, was not

permanently deformed as a result of the earthquake. Significant stressing

wa s apparent on some members through obs ervati ons of cracked paint on

structural sections and the gouging of metal near conn ectio ns.

E-6

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One of the few areas wher e structural damage was observed was the

Unit 4 boiler, which is hung in a pendulum fashion using rods supported

by a braced fram e. Lateral seismic restraints are mounted on the braced

frame to minimize excessive motion of the freely supported boiler.

Travel through the rest raint gap was evidenced by paint chipping in the

area and permanent deformation of the restr aint . In addition, four

diagonal bracing members on the boiler frame buckled (Figure E - 1 0 ) ,

apparently due to excessive compressive loads . These diagonals were

later replaced.

E.5 ANALYTICAL APPROACH

The structural evaluation of El Centro Steam Plant Unit 4 has

been conducted using an analytical approach which is consistent with that

used for the design of many critical faci liti es. The structural model

consists of beam elements and lumped masses representing the stiffness

and inertial charac teristi cs of the struc ture . Soil springs and radiation

damping have been used to account for soil-structure inte raction. Seismic

response has been computed by a response spectra dynamic analysis

employing modal superposition using the SMA version of computer program

MOD SAP . The computed respo nse is compared with code specified ultimate

capacities (i.e., ACI or AISC Part 2) to evaluate predicted behavi or.Details of the analytical method are briefly described b elow.

The structural model consisting of 44 nodes , 67 beam elements

and 5 spring elements is illustrated in Figure E- 11. This model is

capable of considering both north-south and east-west input motions

simulta neously. As mentioned pre viously , because the critical elements

of this structure are primarily sensitive to horizontal loads , neither

vertical d ynamic loads nor dead and live loads were consi dere d. In the

model shown in Figure E-11 , Beam Elements 1 through 19 represent the

boiler stru cture. Beam Element 44 represents the turbine pedestal and the

remaining beam elements represent the turbine building with Beam Elements

1 7 , 18 and 19 at the structural connection of the turbine building and

the boiler structure. Spring Elements 1 through 5 represent transla-

tional and rotational soil sti ffn ess es. Nodal coord inate s and beam

E-7

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se ctio n prop ert i es and co nn ec tiv it i es are given on Tables E-2, E-3 and

E-4. Lumped masses and ro ta ti o n a l in e rt ia s are presented in Table E-5.

These inc lud e weights of s tr u c tu ra l members and equipment t r ib u ta r y to

each node. Un its are kip s and inches fo r these ta b le s . Note th at the

coo rdinate system used is shown in Figure E-1 1 , X = eas t-we st, Y = no rth -

sou th and Z = ve r t i ca l .

For north-south seismic exci tat ion, the re inforced concrete shear

w al ls at Column Lines A and G and the st ee l frame along Column Lines B, E,

F and H^ are rep rese nted by v e r t i c a l beam elements and diaphragms

provided by f l o o r s , ro ofs and ho riz on tal braced frames are represented by

ho riz on ta l beam elements at the app ropriate ele va tion s c onnecting no rt h -

south column l ines together s t r uc tu ra l ly . In th is manner, the d is t r ib u

t ion of seismic-induced forces along each column line accounting for

re la t i v e r ig id i t ie s and to rs ion is Inc luded in the model.

For east-west se ismic ex c i ta t io n , the Un i t 4 tu rb ine bu i ld in g

and b oi le r st ru ct ur e are a symmetrical mom ent-resist ing stee l frame and a

braced steel f rame, respect ively, with the except ion of the shear wal l

along Column Line 17 on the south side of the t ur bi ne b u il d in g . As a

r e s u l t , the v e r ti c a l beam elements at Column Lines A through H^ havelumped pro pert ie s fo r east-west d ir ec t io n ex ci ta t io n corresponding to the

cumulative st if fness of the structural steel members In the turbine

bu ild in g (columns) and b oi le r str uc tur e (braced frame) of Column Linds

1 4, 1 5, 16 and 1 7. In ad d it io n , v e rt ic a l beam elements repre sen ting the

south shear wall are included in the model at a southward offset from the

elements representing the steel members equal to one-half the building

wid t h . For east-west motion, horizontal members represent diaphragms

structural ly connect ing the shear wal l to the steel f rame and girders

runn ing in the east-west d i re c t io n . Note tha t to rs io na l s t i f fn es s o f the

bo i le r s t ruc ture is included in th is model. For east-west shaking, the

st ructura l mode l p roper ly accounts fo r the re la t ive r ig id i ty and to rs ion

of the steel frame and south shear w a l l .

E-8

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The boiler is suspended from the top of the boiler structure and

will act as a pendul um under lateral seismi c moti on with little effect on

structural resp onse prior to impact with seismic restrai nts. When the

combined displ acem ents of the boiler and suppo rting structure are

sufficient to overco me the seismic gaps p rovided, the lateral respons e of

the boiler will influence the response of the struc ture. The boiler did

impact and damage the seismic restraints and the mass of the boiler has

been lumped to various nodes of the boiler structure for this evaluation.

Energy dissipation within the structures due to material and

structural damping has been represen ted by specify ing equival ent vi scou s

damping in accordance with the U. S. NRC Regulatory Guide 1.61 (Reference

E-7) used for design of nuclear power pla nt s. For the evaluat ion of

seismic-induced loads throughout the struc ture , 7 percent of critical

damping has been utilized. From the Regu lato ry Guid e, this damping is

appropriate for reinforced concrete (predominant behavior of turbine

building and turbine pedestal) and bolted steel structures (boiler

struct ure) subjected to Safe Shutdown Earthqua ke (SSE) mot ion . Soil

damping is predominantly the loss of energy through propagation of elas

tic waves from the immediate vicinity of the foundation (i.e., radiation

of energy from the structure to the surrounding s o i l ) . Radiation dampinghas been evaluated in the mann er descri bed bel ow.

In this evaluation of the El Centro Steam Plant, soil-structure

interaction is accounted for in an identical manner to that used in

Reference E- 1. By this approac h, the soil was treated as an elastic

half-space and soil springs and dashpots were developed using the rela

tions in Reference E- 3. The complex-shaped foundation was transformed to

an equivalent rec tangle with equal area for calculational pu rpo ses. Soilstiffnesses and dampings are based on soil she ar wave veloci ty of 650 fps

and shear modulus of 1600 ksf as average strain-compatible values over a

depth equal to the foundation width as reported in Reference E -1 . The

resul ting soil stiff nesse s evaluated by this approach are represent ed in

the analytical model by soil spring eleme nts attached to the rigid ground

E-9

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f loo r-fo un da t ion elements as shown on Figure E-1 1 . Values fo r so i l s t i f f

nesses are presented i n Table E-6 fo r s o il sp ring element 1 through 5.

The re su lt i n g s o i l dashpot constants repre sen ting so i l ra d ia tio n damping

are Incorporated in to th is evaluat ion by ca lcu lat in g the f ra c t io n of

c r i t i c a l damping fo r each so il response mode ( i . e . , s l i d ing , rock ing and

to rs io n) and u t i l iz in g these so i l damping values along w i th st ru ct ur al

damping to determine modal damping values such that a response spectrum

dynamic ana lys is maty be pe rform ed . Soil damping r a ti o s are evaluated

from the assumption of a r ig id stru ctu re re st in g on an e la st ic hal f -space

such th at the so i l s t i f fn e ss and st ru c tu ra l mass are used to convert s o i l

dashpot constants to f ra c t io ns of c r i t i c a l damping. Frac t ions of c r i t i c a l

damping in each soil response mode ( i . e . , associated w i th so i l spr ing

elements 1 throug h 5) are presented in Ta ble E-6.

The so i l - s tr u ct u re in te ra ct io n approach employed fo r t h is e valua

ti o n of th e El Centro Steam pla nt is an approximate method i nc lu d in g

several s im p li fy in g assumptions. The treatment of the s o i l as an e la s ti c

hal f -space Ignores layering in the underly ing soi l which could poten

t i a l l y reduce the rad iat ion damping from that corresponding to an ela st ic

h al f-s p ac e. The fou nd atio n fo r th e El Centro steam pla nt is embedded

about 12 f e e t. Embedment ef fe ct s on s o i l -s tr u c tu re in te ra c tio n have beenignored he re in. A lso , f requency-independent re la t io ns for s o i l s t i f f ne ss

and damping are provided in Reference E-1 which are approxim ations w it h in

a c e rt a in frequency band since these so il Impedance fu nc tio ns vary wit h

frequ enc y. Furthermore, the conversion from so i l dashpot value to fr a c

t io n of c r i t i c a l damping depends upon an assumed fre qu en cy . As mentioned

above, this conversion was accomplished at frequencies corresponding to

s ing le-degree-of- f reedom o sc i l la to rs in which the r ig id s t r uc tur a l mass

or ro tat ion al in e r t ia is supported by the var ious so i l spr ing s t i f fn es se s.

In sp i te of the s im pl i f i ca t ion s employed fo r so1 1 -s t ruc ture I n te rac t ion

in th is e va lua t ion , i t is judged tha t adequate est imates of so i l s t i f fn es s

and damping at the frequencies of the soi l-structure system ( i . e . , at

frequencies between 3.5 and 5 Hz) have been obtained for this evaluation

of the steam plant.

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For response spectrum dynamic an aly se s, i t is necessary to

evalu ate modal damping. To determ ine e qu iva len t modal damping, beam

elements were assigned 7 percent of c r i t i c a l damping and s o il sp rin g

elements were assigned the radiation damping values listed in Table E-6.

Composite modal damping values were then computed by an approach assuming

that element damping is proportional to the element stiffness for each

ele men t. However, modal damping values were not pe rm itt ed to exceed 20

percent of c r i t i c a l damping. Use of an upper l i m i t modal damping is

commonly used fo r the design of c r i t i c a l f a c i l i t i e s to obta in conservat ive

ca lc ula te d se ismic respo nse. Composite modal damping values wit h ve ry

high so il ra di at io n damping evaluated by the element st i f fn e ss we ighting

technique can be uncon servative w ith ou t an upper cu to ff because s tr u c tu ra l

response of combined soil-structure modes can be over-damped due to

smearing of s o il and s tr uc tu re damping. I t is our judgment th at an upper

c u t- o ff on damping w i l l lead to more accurate seismic response from

ca lcu lat io ns based on the approximate so i l -s t r u ct u re in ter ac t io n approach

used in t h i s stu dy . The ca lc u la te d modal damping values and the modal

damping values used in the response spectrum analysis are presented in

Table E-7 for all modes considered.

The freq ue nc ies of s tr u c tu ra l modes and the percentage of massp a r ti c ip a ti n g in each mode are presented in Table E-7. About 94 percent

of the to ta l st ru ct ur al mass is accounted fo r by the f i r s t 10 modes

ranging in frequency from 1.40 to 5.14 Hz. The f i r s t 10 modes are q u a li

t a t i v e l y d escribed i n Table E-8. By the 1 7th mode at 7.70 Hz, over 99

percent of the to ta l s tr u c tu ra l mass has been inc lud ed . T h ir ty -s ix modes

in c lu d in g frequen cies up to 1 8.63 Hz have been used fo r ev alu atin g s tr u c

tu ra l response in order to inclu de a l l loc al seismic vib ra t io n modes.

This number of modes enabled at least 98 percent of the mass for eachhorizontal degree of freedom to part icipate in the seismic response.

In di vi d ua l modal responses are combined to give a to t a l response for each

d ir e c t io n of e x c it a t i o n . Responses fo r each di re c t io n are then combined

t o giv e t o t a l seism ic resp onse . Modes are combined i n accordance wi th

Reg. Guide 1.92 Sec tion 1 .2.2 (Ten Percen t Method) which takes the abso

lu te sum of closely-space d modes and then sq ua re- roo t-of- the -su m -of- the -

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squares (SRSS) combination of other modes and summed closely-spaced modes.

To ta l se ism ic response was ev aluate d by SRSS com bina tion of combined

responses for each ex c i ta t ion d i r e c t io n .

E.6 ANALYTICAL RESULTS

Maximum seismic response displacements and accelerations are

prese nted i n Figure s E-12 and E-1 3. From Fig ur e E-1 2, i t may be seen

th a t maximum displacements are at the top of the b o i le r str uc tu re w ith

maximum values of 3.6 inches i n the ea st-wes t d ir e c ti o n and 5.5 inches in

the nor th-south d i r e c t io n . D isplacement of the turb ine bu i ld ing s tee l

frame at the top of the bui lding 1s 1.6 inches in the east-west direction

and from 1 to 2 Inches between Column Lines B and F in the no rth -s ou th

d ir e ct io n . North-south displacements of the concrete shear wa l ls at

Column Lines A and G and eas t-we st displacem ents of the concrete shear

w all along Column Line 17 are less than 0.5 Inch es. The large d i f f e r

ences in displacements and in accelerations as shown in Figure E-13, are

due to the large d i f ferences i n r ig id i t ie s of the var ious s t ru c tu ra l

components making up th is steam p la n t. The b o il e r s tr u ct u re is ve ry

f l e x ib le such th at large response displacements occur whi le the tu rb ine

bu i ld ing shear wa l ls are very s t i f f and have r e la t i v e ly low seismic

response d isp lacements . The f l e x i b i l i t y o f the turb ine bui ld ing s tee l

frame l ie s between th at of the bo i le r st ru ct ur e and the concrete shear

w a ll s . Based on the computed disp lace m en ts, i t is concluded th a t Un it 4

would not impact Unit 3 and the tu rb in e pede stal would not Impact the

operat ing f loor dur ing th is ear thquake.

Peak ac ce le ra tio n s, as shown in F igure E-1 3, are about 3 to 4g

in the n orth -sou th d ir e c tio n at the w al l along Column Line B in the upper

po rtio n of the turb in e b ui ld in g and at the heater bay f l o o r . Maximum

accelerat ion of the bo i ler s t ru c ture is about 2 .4g. I t i s In te re s t in g to

note th a t the maximum ac ce ler at ion of the fo un da tion is about 0.56g and

0.47g in the east-west and nor th-south d i re c t io n s, re sp ec t ive ly , wh i le

the maximum earthquake ground accelerations ( i . e . , ZPA va lues) are 0.35

and 0.49g in the east-west and north-sou th d i r e c t i o n s , re sp ec t ive ly.

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Thus, there has been a si gn if i c an t am pl i f ic at ion f rom the ground accelera

t i o n fo r east-west earthquake shak ing. This am pl if ic at io n is due to s o i l -

stru ctu re i nt er ac t io n e f fec ts as t rea ted by th is an aly t ica l model and may

be an in di ca tio n of some overconservatism in t h is treatm ent. As state d

pr ev io us ly , the approach employed is th at t y p ic a ll y used fo r design

a nalyse s o f many c r i t i c a l f a c i l i t i e s .

In Figure E-13, i t is a lso in te re s t in g to note tha t the no rth -

south accelerat ions of the upper port ion of the boi ler st ructure a long

Column Line G are grea ter than those a long Column Line H^. At f i r s t

in sp ec tio n, i t would be expected tha t H^ response accelera t ions would

be grea ter since to rs io na l response should be greatest at th is column li n e

which is near the edge of the bu il d in g and because the bo il er st ru ct ur eis supported by the turb ine bu i ld ing shear wal l in th i s d i re ct ion a long

Column Line G. Closer ins pe ctio n reve als th at the no rth-s ou th response

o f Column Line H^ occurs at a frequ ency o f 1 .4 Hz and the no rth -s ou th

response of Column Lin e G occu rs at about 2 .7 Hz (See Tab le E-8) . At

frequencies of 1.4 and 2.7 Hz, the nor th-s ou th spe ctral acc elera t ions are

about 0.7 and l.O g, re sp ec tiv el y as shown in Figure E-7. This di ffe re nc e

in spectral accelerat ion is the reason that the seismic response accelera

t ion s at the upper po rt io n of the b o il e r str uc tur e along Column Line 6are la rge r than at the correspo nding ele va tio ns along Column Line H^.

The calculated seismic response moments and shears have been

used to e valu ate th e pr ed icte d performance o f El Centro Steam Pla nt U ni t

4. In the following discussion, the calculated seismic response and the

est imated ul t imate capacity for the structural e lements of the boi ler

st ru ct u re , turb ine bu i ld i ng and tur b in e pedestal are compared.

E.6.1 Bo ile r St ru ctu re Response

For the boiler structure, seismic response shears are obtained

from the beam element model shown in Figu re E -1 1 . The c r i t i c a l elements

are the diago nal braces along Column Lines 1 5, 1 6, G and H^ which car ry

lateral seismic loads from upper elevations to lower elevations of the

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boiler structure and horizontal bracing member s which enable transfer of

seism ic loads in the north-south direction from Column Line H^ to G at

each elevation of the boiler stru ctur e. Shears in Elements 1 through 6

and 14 through 19 must be carried by diagonal braces which transfer

lateral seismic loads between various eleva tions of the boiler stru ctur e.

Shears in Elements 7 through 12 must be carried by horizontal bracing mem

bers which transfer north-south seismic loads between Column Lines H^

and G. For single diagonal br ace s, two shear capacities are provided

depend ing on whether the diagonal member is in tension or compre ssion.

The shear capac ity of an element in which lateral seismic resistan ce

consists of a single diagonal brace is the horizontal component of the

diagonal membe r force corres ponding to yield level for tension and

ultima te buckling capaci ty (AISC Part 2 criterion as given in Refere nce

E-4) for compression. For k-bracing or x-bracing, only a single shear

capa city has been evaluated. This shear capacity is the sum of the

horizontal components of the diagonal membe r forces corresponding to the

ultima te buckling capacit y for compression members and the ultimate

tensile capacity for tension mem ber s. For k-braces, the ultimate tensile

capacity is the lesser of the yield level or the maximum tensile force

which can be supported by the horizontal beam member whi ch must resist

the unbalanced load occurring if the forces in each of the k-brace

members are unequal .

The elastically computed seismic-induced shears and ultimate

shear capacities for diagonal members along Column Lines 15 and 16 in the

boiler structure are summarized in Figure E-1 4. For the diagonal members

between Elevations 1011 and 1031, the elastically calculated seismic-

induced shear is about 4.8 times the code specified ultimate shear

capacity and as shown in Figure E -1 0, these members did buckle as a

resul t of the 1979 Imperial Valley ear thq uak e. For most of the other

diagonal mem bers along Column Lines 15 and 1 6, the calculated load also

exceeded the capac ity but by a lesser amount . There was no evidence of

buckling for these members as a result of this earthquake including the

member s between Elevations 9 98 and 1011 for which the elast icall y

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computed seismic exceeded the ultimate shear capacity by a factor of

about 3.5. Buckling of diagonal members subjected to oscillator y loading

such as earthquake excitation may not be apparent from post-earthquake

observat ions. For the boiler structure memb ers, the capacities are

governed by elastic buckling and during several cycles of seismic

resp ons e, the diagonal member might buckle and then straingten out under

tensile load. Only members which undergo significant deformation into

the inelastic range would remain permanently displaced such that their

buckling could be detected followi ng the earthqua ke. Furth ermor e, for

k-braces or x-braces in which one member is always in tensio n, the

deformations of a buckled member would be limited by the tensile mem ber .

As a result, it is possible that some of the diagonal members whose

calculated seismic response exceeded the code specified ultimate capacity

mao' have actually buckled during this earthquake even though there was no

evidence of buckling following the earthquake.

The elastically computed seismic-induced shears and ultimate

capacities for diagonal members along column Line H^ are summarized in

Figure E-1 5. Between Elevations 1031 and 1046 , the computed load/

capacit y ratio was 3.9 with no observed buckling and between Elevati ons

1011 and 103 1, the computed load/cap acity ratio was 4.0 and one of these

members was observed to have buckled followin g the 1979 eart hqua ke. All

other diagonal members along Column Line H^ had computed load/capac ity

ratios ranging from 1.4 to 2.6 with no buckling of these members observed

following the earthquake.

The calculated seismic shears and ultimate capacities for

diagonal members along Column Line G are shown in Figure E-16. There was

no buckling of these members observed fo llowi ng the 1979 earthquak e even

though the elastically computed seismic-induced shears exceeded the code

specified ultimate shear capaci ty by as much as a factor of 4.9.

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At severa l e levat ions of the boi ler s t ruc ture, there are

horizontal braced frames acting as horizontal diaphragms as shown in

Figure E-1 7. At Elev ation 998, which is at the top of the r ein for ce d

concrete shear wall along Column Line G, the seismic-induced diaphragm

loads are the gr e at es t. The computed shears in t h is ho riz o nt a l braced

frame and the ult im ate shear ca pa cit ie s fo r the bo i le r st ru ct ur e diaphragm

at th is e leva t ion are summarized in Figure E-17. The e la s t i c a l l y ca lcu

la te d seismic-induced loads are as much as a fa ct o r of 3.9 grea ter than

the ultimate capacity although no buckling of these members was observed

at any e levat ion of the boi ler s t r uc tu re .

The columns throughout the boi ler structure are al l below their

y ie ld or buc kl ing capa cit ies based on th e ir ca lcula ted seismic response

f o r t he 1 979 Im pe ria l V al le y ea rthquake. No damage to these columns was

observed fol lowing the earthquake.

E.6 .2 TURBINE BUILDING RESPONSE

For the turbine bui ld ing reinforced concrete shear wal ls cast

m o no l i th ic al ly wi th the ex te r io r stee l frame on the so uth, east and west

s ides of the turb ine b u i ld in g , the u l t ima te shear capa ci ty has been

eva luate d in accordance w ith the ACI code (Reference E-5 ). For these

w a l l s , the seismic-induced shear load is carried by both the reinforced

concrete wa l l and the steel f ram e. Based on the re la t i v e r ig id i t ie s of

the w al l and fram e, 80 to 90 percen t of the shear load i s ca rr ie d by the

w all and 10 to 20 percent of the shear load is ca rr ie d by the fram e.

On Figure E -1 8, the elements in the s tr u c tu ra l model are

gra ph ica l ly represented on e leva t ion v iews of the turb ine bu i ld ing w a l ls .

Also shown on this figure, are the seismic-Induced shear loads and theult imate shear capacit ies from the ACI code for each of these elements.

A l l but one of the elements is below the ulti m at e ca pa city although the

seismic-induced loads are si g n if ic a n t such th at some crack ing might be

expected. For Element 19, at the lower region of the west w a l l , the

elastical ly computed seismic-induced load exceeds the code specif ied

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ult im ate ca pacity by 11 pe rcen t. However, i t is recognized tha t the

ult imate capacity for shear walls as specif ied in the ACI code is conser

vat ive re la t i v e to labo rato ry tests on shear w al ls . Furthermore, the

ul tim at e ca pa city rep orte d i n Figure E-18 is based on minimum s pe ci fie d

ma teria l strengths and the actual s treng th of the concrete and re in fo rc in g

ste el f o r the tu rb in e bu ild in g w alls is l i k e l y to be more than the minimum

value s. As a r e s u l t , fo r the small amount of ca lcu lated seismic overload

in Element 1 9, no s ig n if ic a n t damage would be expec ted. I t should be

noted that shear stress in these walls are calculated to be generally

greater than UO psi ( i . e . , about 2 v f ^ such tha t some concrete cra ckin g

would be expected. The highest c alc ula ted shear stress fo r the tu rb ine

bu ild in g w alls is 255 ps i fo r element 19. A ll other wall elements have

ca lcu late d shear stresses less than about 200 p s i.

The tu rb in e b ui ld in g ste el frame is designed predominantly fo r

lateral forces in the east-west direct ion as the columns are loaded about

th e i r s t rong ax is fo r th is d i re ct i on mot ion . In ad d i t ion , the shear wa l l

a long the south side of the turb ine bu i ld ing c arr ie s a si gn if i ca n t po rt ion

of the east-west la t er a l fo rce s. As a re s u l t , the tu rb ine bu i ld ing

moment-resisting steel frame responds to the east-west component of the

1979 Imperial Valley earthquake below the yield stress level.

For la tera l fo rces in the nor th-south d i rect ion , the tu rb ine

bu ild in g ste el columns are loaded about th e ir weak axis but la te ra l

forces in th is d i re ct io n are ca rr ied by the re inforc ed concrete shear

wa lls along the east and west sides of the turb ine b u il d in g . There is a

problem in th is d irect ion in that the only ef fect ive d iaphragms for

t ra ns fe rr in g seismic- induced loads f rom the in te r i o r stee l frame to the

ex te rio r concrete w alls is the ope rating f l o o r which is 20 fe et above theground f loor and the concrete roof over the heater and auxil iary bays.

The roofs over the turbine and service bays are composed of gypsum

decking and composition roofing and are not as effective in diaphragm

action as the concrete f lo o rs and roo fs (see Figure E-1 9).

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As a re su lt of the lack of ef fe ct iv e d iaphragms for t ra ns fe rr i ng

loads from the interior steel frame to the exterior concrete walls, some

of the frame elements above the o pe ra tin g f l o o r are computed to be

strained into the plast ic range when subjected to the north-south compo

nent of the 1979 Im pe ria l Va lle y earthquake . Along Column Line B, the re

is a shear wa ll as shown i n Figure E-19 fo r which seism ic response ac cel

era t ions of about 4 g's in the north-sou th di re c t io n (see Figure E-13) are

computed. The i n e r t i a l loads from t h is shear w al l must pass down through

the p ort ion of the ste el frame represented by Element 49 in the st ru ct u ra l

model to the operating floor and then out to the east shear w a l l . The re

s u lt in g seismic response moments in the s tee l columns at t h i s lo ca tio n are

about a fa ct o r of 1 .9 gre ate r than the p la s ti c moment ca pa city fo r these

column se c ti o n s . At Column Line s E and F, the heater bay f l o o r is com

puted to have seism ic response acc ele ratio ns of about 3 g's in the no rt h-

south d i re ct io n (see Figure E-13). The corresponding in e r t i a l loads for

the heater bay f l o o r must be tra ns fe rre d through the p or t io n of the s tee l

frame represented by Elements 27, 28 and 38 to the roo f or op era ting fl o o r

and out to the west shear w a l l . The resulting seismic response moments

in the s tee l columns at these lo ca tion s are from a fa c to r of 1 .2 to a

factor of 1.8 greater than these column sections as indicated in Figure

E-19. As mentioned p re v io u sl y , there was no s ig n if ic a n t damage in thetu rb in e b ui ld in g as a re s u lt of the 1979 Imp erial V all ey earthquake even

though the calculated seismic moments exceeded the plastic moment capacity

f o r some of the s te el columns by ne ar ly a fa c to r of 2.

The op era ting f l o o r , heater bay f l o o r and the roo f over the

a u x il ia r y and heater bays are e ff e c ti v e diaphragms made of metal decking

and concrete f i l l . The shear stresses calculated in the elements of the

structural model representing these diaphragm elements are summarized inTa ble E-9. The maximum shear s tre ss o f 253 ps i is i n Element 23 , which

transfers the roof loading from east-west shaking between the turbine

bu ild in g ste el frame and the south concrete shear w a l l . No s ign i f i can t

damage would be expected for any of the computed shear stresses shown in

Table E-9 although some concrete cracking might be expected for shear

stresses in excess of about UO psi ( i . e . , a b o u t 2 v / TT ) .

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other less effective diaphragm action occurs at the roof of the

tu rb ine bay and se rvic e bays (Elements 41 and 52 fo r no rth- so uth m otion

and Elements 46 and 47 for east-west motion as shown in Figure E-11).

The primary load carrying elements of these diaphragm elements are single

angle x-br acin g in the ho rizo nta l plane . The ca lcula ted seismic-induced

loads i n these diago nal members are as much as 4 times th e y ie ld ca pa city

o f the member. However, th ere was no damage in the roof observed f o l

low ing the 1979 ea rthq uake. I t should be noted th a t some of the diaphragm

loa din g could have been tr a n sf e rr ed by the ro o f d ec king. The more complex

load pa tte rn of p ar t of the load through ro of decking and pa rt of the

load through horizontal bracing has not been considered herein.

E.6.3 Turbine Pedes tal ResponseThe turbine pedestal is calculated to respond to the 1979

Impe rial Val ley earthquake at a r e la t i v e ly low stress le v e l . Calculated

stres ses correspond to the e la s ti c behavior ran ge . There was no damage

observed at the turbine pedestal fo l lowing this earthquake.

E.7 SUMMARY AND CONCLUSIONS

The El Cen tro Steam Plant was subjec ted t o the Im pe ria l Val ley

earthquake which occurred on October 15, 1 979. I t is estimated th a t themaximum ho riz on ta l earthquake ground ac ce ler atio n at the p lan t s it e was

about 0.5g . The ste el fram ing throug hout U nit 4 of the plan t was designed

fo r an equiva lent la te ra l seismic loading of 0.2g although the plant had

ad di t ion al capaci ty due to turbine bu i ld in g rein force d concrete shear

w alls which are capable of re s is t i n g la te ra l seismic load ings . Because

of the lack of si g n if ic a n t damage at the plant as a re su lt of th is ea rth

quake even though earthquake motion spectral acceleration exceeded design

leve ls by a fa c to r of as much as 5 to 6 as shown in Figu res E-7 and E-8,a de tai le d s tr u ct u ra l eva luatio n of the El Centro Steam Plant subjected

to the 1979 Imperial Valley earthquake was performed and is reported

he rein as part of the NRC research p ro je ct on Eng ineering Cha racter

iz a ti o n of Ground M otio n. The purpose of t h is work was to dem onstrate,

fo r th is case, whether or not an e la s ti c an alys is based on recorded

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earthquake ground motion would predict damage in excess of observed damage

fo l lo win g the ear thquake. In ad d i t io n , i t is o f in t er es t to eva luate the

fa ct or by which e la s t i c a l l y ca lculate d seismic response leve ls exceed

ult im ate ca pa cit ies . For example, studies of several st ruc tures s ubjected

to the 1 971 San Fernando earthquake ind ic at ed th a t the onset of s i g n if

ica nt s t ru ct ur al damage should not occur at e la s t i c a l l y ca lculate d forc e

le ve ls less than 2.5 t imes the u lt im ate ca pa city for San Fernando ea rth

quake ground m otio n. I t was expected th at th is ev alu atio n of the El

Centro Steam Plan t would provid e f u rt h e r evidence fo r the need to develop

a reasonable des ign and ana lys is bas is fo r c r i t i c a l f a c i l i t i e s wh ich

accounts fo r the "e f f e c t i v e " repeatable ground mot ion ac ce ler at io n, the

dur ation of the strong ground motion and the in e la s t i c energy ab sorption

ca p a b i l i t y o f d u c t i l e s t r u c t u re s .

Un it 4 of the El Centro Steam Plan t c on sis ts of a ste el braced

frame bo i le r st ru ctu re at tached to the tur b in e b ui ld ing which is a ste el

mom ent-resistant frame w ith three ex te rio r re inf or ce d cont:rete shear

wa l ls and a s tr u c tu ra l l y Independent re info rce d concrete frame tu rb ine

pede stal a l l on a common foun datio n mat. The un de rly ing s o il co ns ists of

deep al luvium.

The October 15, 1979 Imperial Valley earthquake had a local

magnitude of 6.6 . Ground motion measurements in the v i c i n i t y of th e

El Centro Steam Pla nt inclu ded Sta tion s 8 and 9 of the Im pe rial Vallfey

l ine ar array and Sta t ion 5165 of the USGS d if fe re n t i a l arra y. I t is

judged tha t S tat ion 5165 located about 2,400 fe et from Unit 4 provides a

reasonable estimate of the ground motion at the pla nt s it e and a di g it iz e d

version of th is recorded t ime h is to ry has been used fo r th is st ru ct ur al

eva luatio n of the steam p la n t. For the north-s outh component of m otio n,

the maximum ac ce ler at io n is 0.49g and the d ura tio n o f stro ng m oti on , T^,

is 2.8 seconds. For the east-w est component of m o ti o n , the maximum a ccel

er at io n is 0.35g and the du ratio n of strong m otio n, TA, is 3.7 seconds.

Thus, the El Centro Steam Plant was subjected to high a cc ele rat io n ea rth

quake ground shaking of moderate duration.

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Ther e was no significant structural damage of the plant as a

result of the 1979 ear thqu ake . Most nota ble damage was at upper eleva

tions of the boiler structure where four diagonal bracing members buckled

and there was permanent deformation of boiler seismic rest rain ts. Other

damage noted was minor concrete cra cking. These structures were in no

danger of collapse as a result of the earthquake and, in fact, were

returned to operation on the same day of the earth quake . The buckled

diagonals were replaced.

A beam element , lumped mass structural model of Unit 4 was

developed for this evalu ation . So11-s tructu re interaction was accounted

for by soil springs attached to the foun dati on. Reg. Guide 1.61 damping

values for structural e lemen ts and calcu lated radiation damping for soil

elements were used to evaluate composite modal damping val ues . An upper

limit of 20 percent of critical dam ping was imposed in a mann er consi stent

with man y design analyses of critical faci liti es. Seismic respo nse was

evaluated by an elastic respo nse spectrum analysis using spectra from

Station 5165 horizontal recorded ground mot ion . Calculated seismic

response was then compared to code specified ultimate capacities to assess

analytically predicted structure behavior based on elastic analysis and

instrumental ground motion.

Based upon this evaluation of the El Centro Steam Pla nt, there

are two general conclusions which can be ma de :

1. The seismic capacit y or resistance of a structure cannot,in general , be directl y Inferred from the design levelearthquake motion.

2 . Elastic structural calculation s based upon Instrumentalground motion which are typically used for design analysesof many critical fac ilities do not lead to good correlationbetween calculated and observed structure be havior .

The seismic design basis for the El Centro Steam Plant was an

equivale nt lateral seismic coefficient corresponding to 0.2g. This

horizontal force coeffi cient was applied to live and dead loads and was

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used to design the building steel frami ng. Detail s of the design approach

are unknown but because the design was performed around 1 968 , it is likely

that the design criterion correspond to working stress values plus one-

third increase for dynamic loading as allowabl e stress limits. In addi

tio n, exterio r reinforced concrete shear wall s on three sides of the

turbine building were added to the turbine building steel fra me which had

already been designed for the horizontal force coefficient of 0.2. As a

result of the above fac tor s, it may be seen that seismic re sistance cannot

be directly inferred from the design level earthquake mot ion . Although

the steam plant Unit 4 structure was designed for a horizontal forc e

coefficient of 0.2, that does not mean that structural failures or damage

would be expec ted for earthquake ground moti on greater than 0.2g. The

lateral force coefficient ignores dynamic amplification during seismicresponse of the structure such that inertial loads at higher elevations

in the structure for a 0.2g earthqu ake can be much greater than that

correspondin g to 0.2g. On the other hand, application of the lateral

coefficient to live loads as well as the usage of very conserva tive

allowable stress criteria enable the structure to resist seismic loads

signi fican tly greater than that correspon ding to a 0.2g ear thq uak e.

However, a primary reason that the steam plant can resist motion

exceeding 0.2g is the exterior concrete shear walls around the turbine

buildi ng. These walls are signific antly stronger than the steel frame

such that they actually dominate the seismic resistance capacity of the

turbine building even though they are additional to the basic lateral

resistance accounted for by the Unit 4 des ign er.

From the combination of factors described abo ve, it may be seen

that it is Impossible to infer the seismic capacity of the El Centro

Steam Plant Unit 4 from the design earthquake leve l. In this cas e, the

structure has considerably greater capacity than that corresponding to an

earthquake with peak acceleration of 0.2g due primarily to the presence of

additional con crete shear walls . It is our judgment that this situation

is not abn orm al. Most structures have additional c apacity above that

accounted for by the designer due to the existence of alternate load paths

E-22

8/22/2019 6848574


not expl ic i t ly accounted for in the design, due to strength provided by

non-structural elements such as part i t ions, wal l c ladding, equipment or

p i p i n g , e t c . , and due to the usage of cons ervative design c r i t e r i a . These

fa c to rs may be one of the reasons th a t the conclusion s of Appendix A

( i . e . , th a t str uc tu re s behave much be tte r du ring actu al earthquakes than

would be expected based on their design cri teria) are seen.

Based upon the evaluation of El Centro Steam Plant Unit 4

repo rted h er ein , i t is a lso demonstrated tha t even i f the above fa cto rs

are accounted fo r by con side ring a ll s tr u c tu ra l re sist an ce mechanisms

a va i la b le , using code sp ec i f ied u l t ima te stren gth l im i t s and using re

corded earthquake motion at the si te of the structure considered, analyt

ic a l approaches which are ty p ic a l l y used fo r the design of many c r i t i c a l

f a c i l i t i e s such as nuclear power plants s t i l l underestimate the seismic

re sist an ce ca pa city o f the st ru ct ur e and p re d ic t more damage than was

seen during an actual earthquake.

The analyt ical ly predicted structural performance of the various

components of t he El Centro Steam Pla nt U nit 4 st ru ct u re is summarized i n

Table E-10 in terms of the ratio of seismic response to ult imate capacity

or by q u a l i t a t i v e d e sc rip tio n . The only damage occ urring to the steampl ant as a r e s u lt of the 1979 earthquake was bu ck ling of d iagona l members

at upper eleva t ions of the bo i le r str uc tu re . This represents lo cal ize d

minor damage which was e a s il y re p a ir a b le . Based upon pos t-earthq uake

examination of the structure, the steam plant was not in danger of

co l lap se . Ye t, based upon the e la s t ic a l l y calc ula ted seismic response as

summarized i n T able E-1 0, much more s ub s ta n ti a l damage than was observed

would be ex pe cted. For the members damaged du rin g the e arthq uake , the

r a ti o of ca lcu late d seismic response to ult im ate cap acity is 4.0 org re a te r. For the members undamaged du rin g the ea rthqu ake , the r a t i o o f

ca lcu late d seismic response to ult im ate cap acity is 4.9 or les s. Hence,

i t may be concluded th at fo r the Im pe rial V alle y earthquake and the steam

plant s tr uc tu re , the onset of s ig n i f i ca n t stru ctur e damage should not

occur at el a s t i c a l l y calcu lated force leve ls less than about 4.0 t imes

the u l t imate capac i ty .

E-23

8/22/2019 6848574


A prim ary reason f o r the lac k of damage at the steam p la nt as a

re s u l t of the 1979 earthquake was tha t the str uc tur e had s ub st a nt ia l ly

greater capacity than the 0.2g design level for the steel frame because

of the e xt e rio r concrete shear wal ls on three sides of the tu rb ine

b u i l d i n g . However, the calculated seismic response based on recorded

motions from the 1979 earthquake of in d iv id u a l s tr u c tu ra l members exceeds

th e ir code sp ec if ie d ult im ate cap acit ie s by as much as a fa ct or of 4.0 or

more w itho ut any s ig n if ic a n t s tr u ct u ra l damage. Based upon e la s ti c a l l y

ca lcu lat ed seismic respo nse, b uck ling of more members of the b o ile r

st ru ct u re and some tu rb in e b u ild in g damage would have been pre dic ted fo r

the 1979 ear thqu ake . There are a number of reasons fo r th e lack of

damage seen in the bo i le r str uc tu re and tu rb ine bu i ld ing ste el framing

i n c l u d i n g :

1 . Inelast ic energy absorpt ion capabi l i ty is not accounted forby e la s t i c ana lys i s .

2. Foundation l ev el motion may be less than i s ca lcu lat ed bythe analysis performed due to:

a. sp at ia l va r ia t io n of ground mot ion over the founda t ionarea.

b. wave sc at te rin g or kinem atic in te ra ct io n phenomena.

c . more complex so i l - s t ru c t ur e In te rac t ion ef fe c ts thanassumed fo r t h is an aly sis in cl ud in g some embedmente f f e c t s .

3. The an al yt ica l technique of employing an upper l i m i t cu to ffto composite modal damping may not f u l l y account fo r s o ilradiation damping and thus give overly conservative seismicresponse.

I t is not known which of the above fac to rs are the mostimpo rtant reasons fo r diff er en ce s between ca lcu lat ed and observed

behavior of the El Centro Steam P la n t. In our judgment, a l l of these

fac tors are probably s ig n i f i ca n t .

E-24

8/22/2019 6848574


I t is shown by th is ev alu atio n of th e El Centro Steam Plant th a t

the seismic resistan ce capa ci ty cannot be d i r e c t l y in fe rre d from the

design earthquake le v e l. Factors such as conservatism in the al lowa ble

stress c r i t e r io n and streng th of the str uc tur e which, fo r some reason, i s

not accounted for in the structural design, cause the structure to becapable of withsta nd ing higher ground motion than the design le v e l. I t

is b el ieve d tha t the steam pla nt is not abnormal in th is regard and th a t

th is conclusion is genera l ly t r u e . Another important conclusion to note

is tha t the an aly t ica l approach employed fo r th is ev alu at io n, which is

ge ne ra lly ty p ic a l of th at used fo r design analyses of many nuclear power

f a c i l i t i e s u t i l i z i n g e la s t i c ana lys i s and inst rumenta l ground mo t ion ,

does not lead to good co rr e la ti o n between ca lcu late d and observed seism ic

beh avior. This method of ev alu atio n und erpre dicts the seismic cap acityof the El Centro Steam Plan t by more than a fa c to r of 4. Hence, i t is

concluded th a t some or a l l of the fa ct o rs such as in e la s ti c energy absorp

t i o n ca p a b i l i t y wave sca tte r in g phenomena, more complex so i l - s tr u c tu re

in te ra c t i o n , e tc . should be Incorpora ted in to the approach used fo r design

analyses of nuclear power plants or other cr i t ical fac i l i t ies such that

r e a l i s t i c designs may be achieved.

E-25

8/22/2019 6848574


Table E-1

PEAK ACCELERATIONS RECORDED DURING THE

1979 IMPERIAL VALLEY EARTHQUAKE

S t a t i o n

7

1 ^

1 5165

1 ^

1 °

A z i m u t h *

230

140

V e r t i c a l

230

140

V e r t i c a l

3 6 0

27 0

V e r t i c a l

3 6 0

0 9 0

V e r t i c a l

0 5 0

3 2 0

V e r t i c a l

U n c o r r e c t e d

.47g

.34g

.63g

.48g

.62g

.48g

.49g

.35g

.75g

, 4 0 g * *

. 2 7 g * *

. 3 8 g * *

.18g

.23g

• iig

C o r r e c t e d

• 4 6 g 1.33g

•51g

.47g 1

.61g

.41g

.49g 1

.35g

.66g

—

.17g

.23g

• iig

* Numbers are horizontal angle from north measured clockwise

** Estimated Values

E-26

8/22/2019 6848574


Table E-2

NODE COORDINATES

C E N E R A T E O N O D A L C A T A

NOCEItUHBER

123

*967

a910

1112131415161718192021222324292b

2728

2 9303132333135363738394 0

41

42434 4

4S

BCUNOARVX00000000

c000

c0000000

c0

c000

c0

0000

c00000

c0

cc00

1

Y00000000

000000000000

c00

c0000

0000000000

c0

0

000

1

CONCITiON20

c0

cc00

c00

c0000c0000

c0

c000

c0

000010

c00c00

1000

1

XX00000000

00000000000000000000

000000000000

0000

1

CCCESYY

0

cc

220

ccc000

c0c0000

c0000000000000

0000

c00000

cc

0C 00 c0 0

1

NCOALX

Z1480£*0415360E*04214eOE*0419360E*0421480E«041S360£*0421480Et0421480E*04

21480E*04214eOE*0415360E40415360E«0419360E*0415360E'»04132C0E«0413200E*041C200£*0413200E«041C200E«0413200E*04I32C0E«0413200E*041C2C0£«04132C0E*0410200E«04132C0£*043tO0OEt033600CE*03

13200E»0418O00£«03I8000E*033tOCO£*03.7e0C0£«03.36000E*03.3t00CE«03.ieC0OE«O3.1800CE«03.180C0E*03.ieOOO£*03.36C00E*03

.780C0E*03

.7aOOOE*03

ROI»T COCRCINATES

0 .0 .0 .0 .0 .0 .0 .0 .

0 .0 .0 .0 .0 .0 .0.0 .0 .0 .0 .

0 .

0 .

o !

0.

-,

0 .0.0 .

-,0 .0 .0 .

0 .0 .0 .0 .

sseooE

Y

»C3

95800E*C3

55eO0E*C3

5)aOOE 03

S5800E*C3

S580CE*C3S5800E*C399800E*C3

55800ES5800E

>C3>C3

S5800E*C3

10000E*03

2.11640E*04.11640E*a4.9840CE*03.98400E*03.744C0E*03.74400E*03.S9640E*03.456C0E*O3

.240C0E*030 .

.59640E*03

.45600E«03

.240C0E*030 ..59640E*03.40aOOE*03.40a0OE*03

0 ..S9640E*03.S9640E*03.24000E*03.40aOOE*03.24000E«03.240COE*03

0 .C ..5964CE*03.99640E*03

.24000E«03

.24O00E*030 .C .C ..38040E«03.3a040E*03.38040E*03.24000E*03.240COE*03

C ..240C0E*O3

.27000E*03

.38040E*03

. ^ 4 0 C o e * e ^0 .

c.

* 0 - free

1 - fi xed

Note: Units a r e inches

E-27

8/22/2019 6848574


Table E - 3

BEAM PROPERTIES

3 / C E A P E L E M E N T S

NUNBER OF BEAPS • 67NUMBER OF GEOPETRIC PROPERTY S E T S * 5 2NUPBER OF FIXEC ENO FORCE SETS - CNUMBER OF MATERIALS • 2

PATERIAL PROPERTIES

PATERIAL

NUMBER

YCUNC*SMCOULUS

.3C00£*C5

.31CCE*C4

POISSCN»SRATIO

.3C00

.2500

PASSDENSITY

HEIGHTDENSITY

0 .

0 .

0 .

c .

tEAP GEOMETRIC PROPERTIES

SECTIONNUMBER

12

34

!6789

IC1112131415It1718192C21

22232425262728293C313233343 !363738

394C414243444546474849909192

AXIAL AREAA ( l )

.1C0CE*C5

.100CE«09

.100CE*C5

.10CCE*05

.1CCCE«C5

.10CC£*C5

.1C0CE405

.100CE*C5

.100CE«C5

.1C0CE«CS

.10CCE*05

.100C£«C5

.1CCC£*C5

.1CCCE*C5

.1CCCE*C5

.1000E*C9

.1C0CE«09

.100CE*C5

.1C0CE«C5

.1C0CE«C9

.1C0CE«C9

.100CE*09.1C0CE4C5

.1C0CE*C5

.1CCCE*C5

.1000E«09

.100CE*C9

.1C0CE*05

.1000E«C9

.100CE*05

.1CCCE*C9

.IC0CE*09

.1CCCE4C5

.1C0CE4C5

.1C0CE*09

.1C0CE*C5

.tCCCE*C5

.100CE*09

.1CCCE«C5

.100CE*05

.10CCE«05

.100CE*CS

.1C0CE«09

.1C00E*C5

.1CCCE«C5

.1C0CE«C5

.100CE4C5

.10CCE4C9

.1000E*C9

.100CE»09

.100CE«05

.1C0CE*C9

SPEAR AREAA(2I

C ..1CC0E*02

.77O0E*Ol

.990CE*01

.1C0CE*02

.194CE«02

.1970E*02

.1CCCE*02

.770CE«01

.9900E*C1

.9CC0E«02

.173CE«03

.176CE«030 .C .C .C .C .C .C .0 .

c.C .C ..3140E»04.314CE«04.4870E*04

C .0 .C .C .0 ..134CE*05

C .C .0 ..115C£*04

C .

C .C ..276CE«04.1610E*04

0 .C .C ..£26CE*03.:76CE»03

C .0 .

c.c.c.

SHEAR AREAAI3I

0 ..1380E*02

.1COO£«02

.1110E«02

.2210E402

.2C40E«02

.1340E«02

.7700E401

.7400E*01

.9100E401

.8930E«04

.6400E404

.8930E«04

.2CaOE*03

.2C30E*03

.8810E«03

.4a00E*03

.8260E*03

.1460E401

.18a0E*Ol

.1660£«01

.20aOE*03.2030E403

.2C30E*030 .0 .0 ..1700E«01.2140E401.3560£«01.4700E«01

0 ..2C00E*O9.1930E*03.3730E«01.2500E*01.1710E«04.4600E*01

.2C30E*03

.2C30E*030 .0 ..5760E«03.6700E*04.6700E404

0 .0 ..7e00E*01.4600E*01

0 ..2750E«01.9C00E*01

TORSIONJill

.1000E«10

.3460E«C6

.2660E*06

.3430E4C6

.346CE*CE

.671CE«06

.6820E*06

.346CE*06

.266CE'»06

.3430E«C6

.311CE«C7

.6C4CE*C7

.614CE*C7

.1000E*00

.lOOOEtCO

.100CE*00

.1000E*00

.1C00E*00

.1C0OE4CO

.1000E«00

.1COOE«CO

.1000E«00.1Q0CE*C0

.1COOE*00

.1C00E«CC

.1000E«OC

.100CE«00

.1000E«CO

.1COCE*00

.1C00E*C0

.100CE«CO

.1COCE*00

.100CE*10

.1COOE«CO

.1C0CE«00

.1C0CE«C0

.100CE4CC

.10006*00

.1C0CE«CC

.1000E«00

.100CE«C0

.1000E«00

.1000E«00

.100CE4CC

.1000E*00

.1000E41C

.1C00E*10

.1000E«00

.1000E*00

. i c o c E * c e

.100CE*CO

.1000E«CO

INERTIA1(2)

.1000E*10

.1700E*07

.1700E*07

.2400E*07

.2400E*07

.9000E*07

.5000E407

.9000E*06

.1400£*07

.1400£*07

.1C00E«10

.1000E*10

.1000E*10

.1000E*10

.1000E«10

.100CE410

.1000E*10

.1COOE*10

.1C00E*10

.1000E410

.1000E*10

.1COOE*10.1000E*10

.1COOE«10

.1C00£*02

.1000E«02

.1000E«02

.1C00E410

.1CC0E*10

.1C00E*10

.1CC0£*10

.1000E*02

.1COOE*10

.1C00E*10

.1000E*10

.1COOE*10

.1000E*10

.1000E*10

.1C00E«10

.1000E*10

.1000E*02

.1000E*02

.1000E410

.1000E*10

.1000E*10

.1000E*02

.1000£*02

.1000E410

.1000E410

.3T90E*0»

.2C00E«0t

.4000E*06

INERTIA1(3)

.1000E*10

.35C0E407

.4100E407

.41C0E4C7

.94C0E4C7

.77C0E407

.1270E*0a

.39C0E407

.4100E4C7

.41C0E*07

.4a60E*ca

.6930E*C8

.1143E*09

.a3COE*04

.1450E*a9

.10COE*02

.1000E402

.10COE402

.97C0E404

.9700E*a4

.9700E404

.1020E4Q9.2340E4CS

.4030E*C5

.1000E*10

.1000E410

.10COE410

.16COE*04

.2390E4C5

.3640E*05

.16I0E4C5

.3750E*09

.10COE«10

.16C0E*04

.2350E*09

.3640E*09

.10C0E41C

.9aC0E*04

.4510E409

.4910E409

.10C0E410

.10C0E*10

.1000E*02

.4T00E*C9

.4700E*09

.10C0E410

.10C0E*10

.10C0E402

.1000E*02

.1CC0E4C2

.1CCOE*02

.1CCOE*02

Note: Units a r e kips a n d inchesE-28

8/22/2019 6848574


Table E-4

BEAM CONNECTIVITY

3 /0 BEAM ELEPE NT DATA

B E A M

N U P B E R

123456789

1 0

111 21 31 419161 71 819

2 02 12 22 32 42 52 62 72 82 93 03 13 23 33 43 53 6J718

3 94 041S24 34 44 94 64 7

4 84 95 05 15 2S 35 45 55 69 7

5 85 96 06 16 26 36 46 56 66 7

N C C E- I

1357S9

13

«7

89

1 0246

1 11 21 3

1 11 31 4

1 5162 11 8

1 51 62 11 91 62 11 82 02 22 41 91 7

2 32 01 92 42 54 13 32 73 42 73 44 0

2 83 44 C3 83 23 9

3 9

3 63 C3 83 94 24 32 62 12 93 7

N O D E- J

35789

1 024

6

111 21 31 446

1 11 21 31 4

1 52 11 82 02 22 42 61 62 11 81 91 72 32 52 22 42 61 72 3

2 92 82 73 03 33 33 22 83 93 44 C3 2

3 94 23 84 33 94 43 6

3 03 13 C3 14 34 43 12 93 73 8

N O C E P A T E R I A L- K N U M B E R

1 6 21 5 21 9 21 5 1

2 8 22 8 22 8 2

3 5 1

2 0 1

3 9 12 8 1

2 0 2

2 0 1

2 0 22C 23 1 23 0 1

1 21 2

2 0 13 7 22 1 12 1 2

S E C T I O NN L M B E R

234567

5 15 2525 25 25 2189

1 0111 213

1 41 51

161 71 81

1 92 02 12 22 32 41

2 92 62 72 82 9

3 013 13 21

3 31

4 84 93 43 53 63 73 83 94 011

r

4 14 24 31

4 44 51

4 65 04 7

E L E M E N TA

00000000000000C0000

0000000

000000000000

0000000000000000000

0000

000000

B

00000000

00000000000

0000000000000000000

0000

000000000000000

0000

000000

E N C L O A D S

c

0

ccccccc0

c0

cccc000

cc0cc0

ccccc0

cc0

cc0

cc0c000

cc00

c0

c0000

cc0

cccccccccc

0

0000000000000000000

000

0000000000000000

0000000000000000000

0000000000

E N C C O D E S- I

00000000

0000

c0

00000

1100000

000000000000

01 1 1

00000000000000000

0000000000

- J

0000000000000000000

0000000000000000000

01 100000000000000000

0000000000

B A N

1 81 81 81 21 21 21 21 2

1 23 03 03 03 01 81 83 61 21 21 2

3 05 43 03 64 22 45 4

1 23 62 43 01 21 84 81 81 81 81 84 2

1 89 49 44 29 35 21 11 21 24 74 2S 34 7S 31 83 54 73 91 2

4 11 25 35 31 21 23 65 45 31 2

E-29

8/22/2019 6848574


Table E - 5

LUMPED MASSES A N D ROTATIONAL INERTIA

N 0 C A L L C « C S ( S T A T I C ! 0 R P A S S E S ( C Y K A C I C I

KQCEhUrtBER

123

S

6789

111213ISIS161719202122232425262728293031333435

3637384041424344

LCACCASE

C0ccc0ccccCc

ccCccccc0cccccccccc

c0cc0

c0G0

X-AXISFORCE

.29300E«OC0 ..13570E«C1.1C9C0E40C.13(O0E«Ol.114C0E4CC.966COE*0C.12430E«C1.1S150E«01.143C0E4C1.39t00E*CC.242tOE4Cl.15C90E«0C

.33440E4CC

.39540E«CC

.14930E«CC

.2t7eOE«OC

.28350E«0C

.StS'iOE + CC

.28360E«0C

.1C270E«CC

.432SQE«0C0 ..18420E«CC.19e50E40C.e99C0E-01.ieC40E«0C.36390E4CC.1CC30E«0C.4S3C0E«02.17320E*0C.t82C0E-Cl.S23C0E-01.22200E40C.16920E«CC.71600E-C1.49870E*01.lie40E*0C

.3iceoE*cc

.21S80E*0C

Y-AXISFORCE

.613CCE*C0

.2StOCE*00

.4C00CE*C0

.3e<>0CE*00

.8700CE*C0

.6CC0CE«C0

.8950CE*CO

.8870CE«C0

.S910CE*C0

.1773CE*01

.9440CE*00

.3192CE+01

.19e6CEvC0

.3344CE»00

.3954CE*CC

.24C3CE400

.3ei4CE*00

.1365CE*C0

.6722CE*00

.1218CE*00

.4201C£*00

.5970CE«C0

.9460CE-01

.4190CE-01

.19e5CE*00

.8990CE-01

0 ..7940CE-01.4C9CCE-C1.4530CE*02.1732CE*00.7290CE-C1

0 .0 ..24C4CE*00.3833CE*00.4987CE*01.1591CE«00.4404CE«00.27e2CE*00

Z-AXISFORCE

.4530CE«00

.12eC0E«00

.87900E«G0

.2S300E*C0

.1115CE«Q1

.357CCE+00

.931CCE*00

.lCt5CE*01

.1C;30E*01

.15aC0E*01

.63500E*00

.2772CE*01

.1SC90E«C0

.3344CE»00

.39:40E4CO

.1493CE«00

.26760E*C0

.283S0E*C0

.62C8C£*0C

.2836CE«C0

.2CtOCE*00

.4325aE«C0

0 ..18420E*00.19eSCE*00.8990CE-01

C ..36390E*00.10C30E*00

0 ..17320E*C0.68200E-01

.S2300E-010 ..2CS0CE*00.23990E«00

0 ..1184CE«Q0.328SCE*C0.21880E«00

X-AXISnor<EKT

c .c .c .c .c .c .c .c .c ..10300E*05.16300E*05.17600E+05.116C0E*05

0.C.C .C .c.c.c.c.c.c.c..17200E«05

C .C .C .C ..48000E*07.16300E*05

C .

C .C .C .C .

.327Q0E406

.870a0E*04

.17500E*05

.16800E*05

Y - A X I SHCfENT

0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .

0 .0 .0 .

.SO00OE*O4

.143CCE«0S0 .

.14900E«0S0 .

.2210CE*0S0 .

.1910CE«0S0 .

.8600CE*030 .

.42900E+04

.2840CE*04

.2200CE*080 .

.470CCE*03

.17500E*040 .0 .0 .

.3690CE«0S0 .0 .0 .

Z-AXU

HCEHT

0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .

0 ..1180CF«05

0 .0 .

.35000F*04

.1030CF*05

.11000^*040 .

. 3 5 0 0 0 F * C ^0 .0 .0 .0 .0 .0 .0 .

.26000F*Oe0 .0 .

0 .0 .0 .0 .

.36400F«060 .0 .0 .

T O T A L P A S S

X-OIRECTIOh Y - D I R E C T I C I t 2-DIRECTIOfi.6t9t7E«02 .67487E*C2 .16e86E«02

Note: Units are k ips , inches and seconds

E-30

8/22/2019 6848574


T a b l e E-6

SOIL ELEMENT PROPERTIES

ElementNumber

(See FigureE-11

1

23

4

5

Node(See Figure

E-11

33

3333

33

33

D i r e c t i o n *

x - T r a n s l a t i o n

y - T r a n s l a t i o nR o t a t i o n A b o u t x

Ro ta t i on Abou t z

R o t a t i o n A b o u t y

Spr ingS t i f f n e s s

( k / i n )

4.74 X 10^

5.32 X 10^2.32 X 10^°

3.47 X 10^°

5.46 X 10^°

Rad ia t i onDamping

( F r a c t i o no f C r i t i c a l )

0.89

0.950.78

0.49

0.69

* x = E a s t - W e s t

y = North-South

z = Vertical

E-31

8/22/2019 6848574


T a b l e E-7

SUMMARY OF M O D E S . M A SS P A R T I C I P A T I O N AND M O D A L D A M P I N G

Mode

1 11 21 31 41 b

678

1 9

1 101 111 121 13

1 141 15

1 161 171 181 19

1 201 211 22

I 231 24

1 261 261 27

1 281 291 30

1 311 32

1 331 34

1 3536

Summat

F r e q . ( H z )

1.401.652M3 .02'i.223.653.974 .614 . 8 2

6.145.736.006 . 1 76 . 5 36 .627.247.70B . I 88 .708 . 8 59 . 6 /9.70

10.2610 . 6 011.1011.1612 . 0 712 . 2 41 4 . 1 615 . 6 015.$017.0917.5717.95

18.4318.63

. ion =

P e r c e n t of S t r u c t u r ei Mass P a r t i c i p a t i n g

N-S(Y)

6.261.66J .byU.U9y.U4

12.312.48

35.2916.65

8 .650.090.010 . 153 .350.210.291.480.230.020 .030.010.01

o.oz0

0.06000

0.01000

0000

100.00

E-W(X)

2.20

1 l & . O I1 u1 II.yy1 U.341 5.231 0.371 10.301 36.67

15.710.590.020.030.020 . 160.100.07

00.08

u0

O.OZ

0.030

0.02000

00.01

000 i

0.04 1

0 10

100.00

Modal DampingF r a c t i o n of C r i t i c a l I

C a l c u l a t e dVa lue

.0831 .099

1 .089

1 .1211 .105

. 178

.091

.489

.627

.360

.563

.080

.077

.152

.079

.086

.192

.0991 .1261 .073

.073

.072

.322

.070

.163

.071

.081

. 12 7

.084

. 13 8

.291

.091

.070

.085

.135.073

Value Used inResponse Analys s

.0 71 .10 1

1 .10 1

1 .10 1.10 1.1 5.1 0

1 .20 1.2 0.20.2 0.0 7

1 .07 1.1 5.0 7.07 1.20.1 0.10 1.0 7.0 7.0 7

.2 0

.07 1

.15 1

.07

.0 7

.1 0

.0 7

.1 5

.2 0

.1 0

.0 7

.0 7

.1 5

.0 7

Total Mass - N-S (Y) = 67.487 k-sec'/inE-W (X) = 66.987 k-sec2/ in

E - 3 2

8/22/2019 6848574


T a b l e E - 8

D E S C R I P T I O N O F S I G N I F I C A N T M O D E S

M o d e

1

2

3

4

5

6

7

8

9

10

F r e q u e n c y ( H 2 )

1.40

1.65

2 . 6 8

3 . 0 2

3 . 2 2

3 . 6 5

3 . 9 7

4.61

4 . 8 2

5.14

P r e d o m i n a n t B e h a v i o r

N - S r e s p o n s e o f B o i l e r S t r u c t u r e a l o n gd o l u m n l i n e H - 9

E - W r e s p o n s e o f B o i l e r S t r u c t u r e a nd

T u r b i n e B u i l d i n g S t e e l F r a m e

N - S r e s p o n s e o f u p p e r B o i l e r S t r u c t u r e

a l o n g c o l u m n l i n e G

2 n d M o d e f o r E - W r e s p o n s e o f B o i l e r

S t r u c t u r e a n d T u r b i n e B u i l d i n g S t ee l

F r a m e

2 n d M o d e f o r N - S r e s p o n s e o f B o i l e r

S t r u c t u r e a l o n g c o l u m n l i n e H- 9

N - S r e s p o n s e a l o n g c o l u m n l i n e s E a n d F ,s o m e so il r e s p o n s e

N - S r e s p o n s e a l o n g c o l u m n l i n e B

N - S s oi l r e s p o n s e , N - S r e s p o n s e o f

c o l u m n l i n e s B , E an d F

E - W s o i l r e s p o n s e

N - S r e s p o n s e o f c o l u m n l i n e B

H i g h e r M o d e E -W T u r b i n e B u i l d i n g B o i l e r

S t r u c t u r e r e s p o n s e , so il r e s p o n s e

E ' . 3 3

8/22/2019 6848574


T a b l e E - 9

S H E A R S T R E S S E S IN

METAL DECK-CONCRETE FILL DIAPHRAGM ELEMENTS

Element

(see Figure 11)

20

30

23

24

31

21

32

53

54

25

60

65

67

Direction

N-S

N-S

E-W

E-W

N-S

N-S

N-S

N-S

N-S

E-W

E-W

E-W

E-W

Description

heater and

auxiliary bay

roof

heater bay

floor

operating

floor

Elasticilly

Calculated

Shear Stress

(DSi)

83

55

253

103

45

14 5

55

122

127

158

81

114

119

E«34

8/22/2019 6848574


Table E-10

SUMMARY OF CALCULATED SEISMIC BEHAVIOR

FOR EL CENTRO STEAM PLANT UNIT 4 SUBJECTED TO

THE 1979 IMPERIAL VALLEY EARTHQUAKE

Structure

1. Boiler Structure

a. Diagonal Bracing

b . Horizontal BracingDiaphragm

c. Boiler StructureColumns

2 . Turbine Building

a. Concret e ShearWalls

b . Steel Frame

c. Diaphragms

3. Turbi ne Pedestal

Calculated Behavior

For members that actually buckled duringthe earthquake, the response/capacityratio ranged from 4.0 to 4.8. For members

which did not buckle, response/capacitywas as high as 4.9 in one case, butbut generally below 4.0

Response/capacity ratios were as large as3.9 with no observed damage.

Elastic behavior below ultimate bucklingcapacity for seismic loading.

Elastic re sponse/capa city ratio was 1.11 at

bott om of west wall and below 1.0 for allo t h e r w a l l s .

Elastic behavio r for east-west exc itatio n.Seismic response nearly double plasticmoment capacity for weak axis bending ofinterior columns subjected to north-southexcitation with no observed damag e.

Concrete diaphragms have shear stressesranging from about 50 to 250 psi. Horizontal bracing angles exceed yield by asmuch as a factor of 4.0 with no observedd a m a g e .

Elastic behavior.

E-35

8/22/2019 6848574


North

U Transformer yard

Pump No. 1

houses No. 2

Oil tanks

No. 4 o

No. 5

• '

o] i 1

\J^

FIGURE E-1 . PLOT PLAN O F T H E E L CENTRO STEAM PLANT (REFERENCE E - 1 )

E-36

8/22/2019 6848574


E U t

1045-

1 0 3 0 -

Boiler

1 0 1 0 -

/ \ N —

DeaeratorTop of crane rail

9 8 3 -

9 6 9 -

( Evaporator IM l i l- i

fe^H U ^im

H. P. heater no. 4-3

Steam jetair ejector

9 4 9 -

- Turbine oilreservoir tank

©F I G U R E E - 2 . E L E V A T I O N D R A W I N G , L O OK I N G W E S T A T C O L U M N L I N E B , O F T H E

E L C E N T R O S T E A M P L A N T , U N I T 4 ( R E F E R E N C E E - 1 )

E - 3 7

8/22/2019 6848574


1COCO

0- 2 6 -

Stackbay-o

Stack

El. 1 0 4 5

El. 1030

El. 1 0 1 0

El. 98 7

5s=sE!.949

- 5 1 -Boiler bay

-iG]

Elevations and di

mensions in feet

Auxiliary

18 (F >

liary bay I

25 0 -— bay V

55Turbine ba y

30 -

Servicebay •<?

High-pressurefeedwater heaters

rr * g"

•.' i • • • .1 r

g » t

. - - . — • - - , • .

• " • • ' • - • « ' - ••

Evaporator

Soiler feedwater pumps

• ' • • • • • •- • •• •

FIGURE E-3. ELEVATION DRAWING, LOOKING NORTH, O F T H E E L CENTRO STEAM PLANT, UNIT 4 (REFERENCE E - 1 )

8/22/2019 6848574


I00I D

(C y —25—^Stack bay

I

51 -

Boiler bay

(G)—18 * ( ? ) ^ 25 ^ T )

Dimensions in ft

INI

Key

Auxiliarybay

Heater bay

M T ) Column line

Z Z : ^ Concrete shear wall

H - c r Steel column and f raming

Turbine pedestal

Generator pedestal

'M k ^» .

Base slab outline

V////A Reinforced concrete

G R O U N D F L O O R(El. 949)

31

®

31

FIGURE E-4 . SCHEMATI C PLAN VIEW O F T H E UNIT 4 GROUND FLOOR ( E L 9 4 9 FT) ( REFERENCE E-1)

8/22/2019 6848574


115°45'W II B 'S C W

33°15'N -

Salton Sea

33''00'N

32''45'N

Nlland |

Calipatria Q I i ' I ' i 'i — H r

• Strong motionground stations

^ Differential array

Kilometers0 101^—1.—t-^

0 5

Miles

/

i W estmoreland

El Centre Steam Plant imperial ( )(USGS Station No. 5165)

Epicenter

10/15/79

FIGURE E-5 . MAP OF THE IMPERIAL VALLEY, CALIFORNIA, SHOWS THE IMPERIALFAULT AND THE EL CENTRO STEAM PLANT SITE . ALSO SHOWN ISTHE STRONG MOTION ARRAY THAT STRADDLES THE FAULT. (REFERENCEE

E-40

8/22/2019 6848574


^ Indio 82 mi

iW»t«f rank' 1 _ 'J Sch_ ' __

\ _Imperial ygl lev ', _ i

C e n tral — •* j " ^ ^ | '^SSir^eT • . j ' i '

C

IWi'unn Sch ,

Harding

N M C pP l J l t I ;?—f—

:7 School

4

Radio S t *

• ^ K X O

3 2 ° 4 7 '

. • C E f ^ r / T A L

115° 34' C ol.i.co 9.6 n,.. ji 11 503 3' 115° 3 2

2 0 0 0 4 0 0 0

Scale in feet

El Centro - Terminal Substotion Q

USGS TopographicQuadrangle: El Centro, Cal i fo rnia .

Coordinotes; 3 2 ° 47 ' 4 2 " N115° 32 ' 5 5" W

Lo cation: N.W. corner of inters ectio n of

Third St. and Comm ercial Ave.

Stru cture : T *o story , heav y, reinforced concretebuilding.

S T A T IO N L O C A T I O N P L A N

- E L C E N T R O -

FIGURE E -6 . STEAM PLANT AND ADJACENT GROUND MOTION INSTRUMENT STATIONS

E-41

8/22/2019 6848574


10 15 20 25 30

Time (s)

35

10 1 1—I I I I II I \ 1—I I I I 1 1—I I I M td

7 % Damping

0.01 J I I I I I I I I 1 I I I M i l l I I f I I I I

0.1 1 10

Frequency (Hz)

100

FIGURE E -7 . NORTH-SOUTH GROUND MOTION TIME HISTORY A N D RESPONSESPECTRUM F O R T H E OCTOBER 15, 1 9 7 9 IMPERIAL VALLEYEARTHQUAKE RECORDED A T U.S . GEOLOGICAL SURVEY STATIONNO. 5 1 6 5 (REFERENCE E - 1 )

E-42

8/22/2019 6848574


lOp

0.01

" 1 1 — I I I I 1 1 T 1 — I I I I l l | 1 1 — I M M I d

7% Damping

R.G. 1.60

0.35 g-

' I i I I I i i I I I I I I 1 1 1 I 1 I I I I I I

0.1 1 10 100

Frequency (Hz)

FIGURE E-8 . EAST-WEST GROUND MOTION TIME HISTORY AND RESPONSE

SPECTRU M FOR THE OCTOBER 15, 1979 IMPERIAL VALLEY

EARTHQUAKE RECORDED AT U .S. GEOLOGICAL SURVEY STATION

MO. 5165 (REFERENCE E-1)

E-43

8/22/2019 6848574


10- 5 6 7 89 iCT—I I • I I r 4 5 6 7 8 9 1 0

_i 1 I I I I r3 11 5 6 7 8 9 , 1 0 '

- I I I I • • ' "

O 1 0

UJoO mcr

o(n-co ocr -1.

°'UJ 10.

(n

DAMPING 0.070

0.100

0. 150

0.200

0.250

-CD

-in

10- 2—TTTTTnTrf I i i U H ^ o 'FREQUENCY IHERTZ)

EL CENTRO 19 7 9 . N-S

1 r^TTTTIPI^

10- 4 5 6 7 8 9 , 1 ofI I I r

3 4 5 6 7 8 9 1 0 ' 2_ i I i__i I I I r i_

3 4 5 6 7 8 9 1 0 *_ l 1 1 — I 1 I I - m

e-b

zo. — «

caU J_i

L U

<_)(_)crLLJ

(—r j_iC3in

CDcc

UJin0 .

w-iOD-l

f^-l

<D-|

*" 1

:»-l

<n-|

™ 1

~O^ ^0 ) - J

IO-4

in-

DAMPING 0 . 0 7 0

0 . 1 0 0

0 . 1 5 0

0 . 2 0 0

0 . 2 5 0

-i n

i^' I i~TTTTiiTtf 1 r m n T T FFREQUENCY (HERTZ)

EL CENTRO 1979. E-W

oOI

1 TTTTTH

44 FIGURE E-9 . ELASTIC RESPONSE SPECTRA, DIFFERENTIAL ARRAY (USGS STATION5165) IMPERIAL VALLEY EARTHQUAKE, OCTOBER 15,1979

8/22/2019 6848574


1-PiCJ1

©

Buckled

Members

•

9I E l . 1 , 0 i * 6 '

/

/ E I . 9 9'7- /r

y ^

y .v

7- i r r ?

( j s ) (Js)

I E l . 1,0^6' j

Buckled

Members

T T T T yT T T

Column LineQ^ Column Line(T5) Column LinelH

FIGURE E-IO. DIAGONAL MEMBERS I N T H E UNIT 4 BOILER STRUCTURE WHICH BUCKLED DURING T H E 1979 IMPERIALVALLEY EARTHQUAKE

8/22/2019 6848574


16 - Node Number

^ 9 ) - Beam Element

iTl- Soil Spring Element

Z (V e r t i ca l )

Y (N-S) \1 X (E-W)

nrp—(g

FIGURE E-11 . STRUCTURAL MODEL

8/22/2019 6848574


Legend

(3.6, 2.9) =

•

3.6 inch max east-w est

displacement and 2.9

inch max no rth-south

displacement

1

--J

(N-S)

\1 •(E-W)

(0.3,1.9)

(3.6,2.9) (3.6,5.5)

(3.3,4.6)

•Maximum displacement of all foundation nodes

FIGURE E-12. MAXIMUM ELASTICALLY CALCULATED SEISMIC RESPONSE DISPLACEMENTS

8/22/2019 6848574


Legend

(1.57,1.79) = 1.57g max imum east-west

acceleration and 1.79g

maximum north-south

acceleration

(N-S

M (E-W)

(0.63,4.02)

o5 (0.62,3.16)

(0.61,0.45)

(0.81,0.48)

(1.57,2.39)

(0.63,0.92)

.04.4.02)

(0.62,3.

(1.04,1

1.32,3.95) (0.90,2.92)

(Q.62,0.52)

(0.81,0.78)

(n ^fi.n A7)*

•Maximum acceleratio n of all foundation nodes

(1.57,1.79)

(1.29,1.20)

(1.21,1.05)

(1.04,1.07)

(0.67,1.08)

(0.76,0.85)

FIGURE E-13. MAXIMUM ELASTICALLY CALCULATED SEISMIC RESPONSE ACCE LERATION S

t

8/22/2019 6848574


Calculated

Seismic

Response

V(kips)

131.8

548.1

723.9

545.4

630.6

676.6

Ultimate

Capacity

V^^y. (kips)

9 2 . 7 ( C ) *

283.0(T)

113.2

206.5

393.8

634.8

865.6

V/V

1.4(C)

0.5(T)

4.8^

3.5

1.4

1.0

0.8

Column L i n e ( l 5 ) & @

•Buckled Members

••(C) = Compression(T) = Tension

FIGURE E-14. SEISMIC RESPONSE SHEARS & SHEAR CAPACITI ES FOR COLUMN

L I N n s @ a n d < T | ) I N B OIL ER S TR UC TU RE

E-49

8/22/2019 6848574


EL 1046

EL 1031

EL 9491

[CalculatedSeismic

Response1 V(kips)

378.2

5 10 . 9

564.6

578.2

699.6

726.5

753.4

UltimateCapacity

V cr

97 .1

126 .6

216 .4

330.7

5 1 1 . 1

477.8

520.0

V/V" ' " c r

3 .9

4 . 0 ^

2 .6

1 .7

1 .4

1 .5

1 .4

• B u c k l e d M e m b e r

C o l u m n L i n e v H - >

F I G U R E E - 1 5 . S E I S M I C R E S P O N S E S H E A R S & S H E A R C A P A C I T I E S F O R C O L U M NL I N E @ I N B O I L E R S T R U C T U R E

E - 5 0

8/22/2019 6848574


EL 1046

EL 1031

EL 1 0 1 0

EL 9 9 8

CalculatedSeismic

ResponseV(kip§)

210.7

419.5

563.5

UltimateCapacityVj,^(kips)

78.5

85.0

224.1

V/Vcr 1

2.7

4.9

2.5

C o l u m n L i n e ^ )

FIGURE E-16. SEISMIC RESPONSE SHEARS & SHEAR CAPACITIES F O R COLUMNLINE(G)IN BOILER STRUCTURE

E-51

8/22/2019 6848574


Calculated

Seismic

Response

V(fcips)

70.3

70.3

70.3

UltimateCapacityV^.^(kips)

1 9 . 7 ( C ) *54.9(T)

31.8(C)57.7(T)

17.8(C)45.6(T)

V/V"'"cr

3.6(C) *1.3(T)

2.2(C)1.2(T)

3.9(C)

i:5(T)

•(C) = Compression(T) = Tension

ST6W18

FIGURE E-17. SEISMIC RESPONSE SHEARS & SHEAR CAPACITIES FOR BOILERDIAPHRAGM BRACING AT EL 998 #

E-52

8/22/2019 6848574


6" w a l l ,

#4 @ 12" e.w.

eater Bay

South Elevation

®

perating

Floor

1

•

[-1

el. 62

el.63

1 1

0

I—I

1

b. East Elevation

®

6" w a l l ,

#4 @ 12'

e.w.

Seismic Loads and

Ultimate Capacities

(kips)

el.

3435365158

5948/51

6263171819

V

457430795244246

287338162734989

1201

2205

frame

5358935234

6424188164107305

^wall

404372702192212

223314144653925

ri094

1900

^u

623623967228548

3208708238231706

1222

1706

^wall

Vu

0.65

0.60

0.73

0.84

0.39

0.700.36

0.18

0.79

0.54

0.90

1.11

34

(16;

West Elevation

frame

wall

- Element number of

structural, model

(see Figure 11)

- Total calculated

seismic shear

- Shear carried by

steel frame

- Shear carried by

concrete wall

- Ultimate shear

capacity(ACI Code )

FIGURE E-18. TURBINE BUILDING CONCRETE WALL LOADS AND CAPACITIES

E-53

8/22/2019 6848574


^ -^Boi ler

ire-vt ructure-

WestShearWall

C o n c r e t e R o o f O v e rH e a t e r & A u x i l i a r yB a y s

T u r b i n e Bay R o o f

: \

el

el.

n

I Z e l . 3 3

z peratingFloor

'Shear Wall

•Heater Bay Floorr

^

© © ©

"•7.z

T u r b i n e P e d e s t a l

S h e a r W a l l

S e r v i c e B ay R o o f

e l . 4 9

) p e r at i n g F l o o r j j. ,,

E a s tS h e a r

T u r b i n e B g i l d i n g L o o k i n g N o r t h

e l e m e n t

49

38

27

28

S e i s m i c I n d u c e d M o m e n t

P l a s t i c M o m e n t C a p a c i t y

1.9

1.2

1.4

1.8

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REFERENCES

E-1 T. A. Nels on , R. C. M ur ra y, e t a l , "Response of El Cen tro SteamPlant Equ ipment Dur ing the October 15 , 1979, Imper ia l Va l leyEarthquake" , Lawrence Livermore Laboratory, NUREG/CR-1665,UCRL-53005, September, 1980.

E -2 " An a l ys i s o f t he E l Cen t ro S team P la n t " , ( d ra f t r e po r t ) subm i t tedto PG&E by URS/John A. Blum e, May, 1 9 81 .

E-3 R ic h a r t , F. E.> J . R. Ha l l and R. 0. Woods, V ib ra t io ns o f S o i ls andF o u nd a tio n s P r e n t i c e - H a l l , I n c . , E n gle wo od C l i f f s , New J e r s e y , 1 9 7 0.

E -4 Am erican I n s t i t u te o f S tee l Co ns t ru c t i o n , M anual o f S tee l Cons t ruc t i o n , Eighth Edi t ion, 1980.

E-5 Bu ildin g Code Requirements fo r Reinforced Concrete (ACI 31 8-77 ),American Concrete Inst i tute, 1977.

E-6 USNRC Reg ula tory Guide 1 .60 , "D esign Response Spectra fo r Seism icDesign of Nuclear Power Pl a n ts ", Re vision 1 , December, 1973.

E-7 USNRC Regula tory Guide 1 .6 1 , "Damping Values fo r Se ismic Design ofNuclear Power Plant", October, 1973.

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