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316109
REPORT NO.
EERC 75-38
NOVEMBER 1975
PB 259 530
EARTHQUAKE ENGINEERING RESEARCH CENTER
NONLINEAR RESPONSE SPECTRA FOR PROBABILISTIC SEISMIC DESIGN AND DAMAGE ASSESSMENT OF REINFORCED CONCRETE STRUCTURES
by
MASA Y A MURAKAMI
JOSEPH PENZIEN
Report to the National Science Foundation
COLLEGE OF ENGINEERING
UNIVERSITY OF CALIFORNIA • Berkeley, California
BIBLIOGRAPHIC DATA \1. Report No. 12. SHEET EERC 75-38
3. Recipient's Accession No.
4. Title and Subtitle "Nonlinear Response Spectra for Probabilistic Seismic
5. Report Date
November 1975 Design and Damage Assessment of Reinforced Concrete J
Structures" 6.
7. Author(s)
Masaya 11urakami and Joseph Penzien 9. Performing Organization Name and Address
Earthquake Engineering Research Center University of California, Berkeley 1301 S. 46th Street Richmond, California 94804
12. Sponsoring Organization Name and Address
National Science Foundation 1800 G Street, N. W. Ivashington, D. C. 20550
15. Supplementary Notes
16. Abstracts
8. Performing Organization Rept. No. 75-38
10. Project/Task/Work Unit No.
11. Contract/Grant No.
NSF-GI-38563
13. Type of Report & Period Covered
14.
In the investigation reported herein, twenty each of five different types of artificial earthquake accelerograms were generated for computing nonlinear response spectra of five structural models representing reinforced concrete buildings. To serve as a basis for probabilistic design and damage assessment, mean values and standard deviations 6f ductility factors were determined for each model having a range of prescribed strength values and having a range of natural periods. Adopting the standard philosophy, i.e. only minor damage is acceptable unde~ moderate earthquake conditions and total damage or complete failure should be avoided under severe earthquake condi·tions, required strength levels were investigated for each model. Selected results obtained in the overall investigation are presented and interpreted in terms of proto-type behavior.
17. Key Words and Document Analysis. 170. Descriptors
17b. Identifiers/Open-Ended Terms
17c. COSATI Field/Group
18. Availability Statement
Release Unlimited
FORM NTIS-35 (REV. 3-72)
19 •. Security Class (This Report) . .
UNCLASSIFTEn 20. Security Class (This
Page UNCLASSIFIED
121. No. of Pages
USCOMM-OC 14952-P72
NONLINEAR RESPONSE SPECTRA FOR PROBABILISTIC SEISMIC DESIGN AND DAMAGE ASSESSMENT OF REINFORCED CONCRETE STRUCTURES
by
Masaya Murakami
Visiting Assistant Research Engineer, University of California, Berkeley and Associate Professor of Architectural Engineering, Chiba University, Japan.
Joseph Penzien
Professor of Structural Engineering, University of California, Berkeley
Prepared under the sponsorship of the National Science Foundation
Grant NSF-GI-38463
Report No. EERC 75-38 Earthquake Engineering Research Center
College of Engineering University of California
Berkeley, California
November 1975
i 6
ACKNOWLEDGMENT
This report covers one phase of the research program "Seismic
Safety of Existing School Buildings" sponsored by the National Science
Foundation under grant NSF-GI-38463 with Professor Boris Bresler serving
as principal faculty investigator.
Dr. Masaya Murakami's participation was under the program "U.S.
Japan Cooperative Research in Earthquake Engineering with Emphasis on the
Safety of School Building" sponsored by the U.S.-Japan Cooperative Science
Program administered jointly by the National Science Foundation and the
Japan Society for the Promotion of Science.
A portion of this report was presented at the review meeting of
the cooperative program "U.S.-Japan Cooperative Research in Earthquake
Engineering with Emphasis on the Safety of School Buildings," East-West
Center, University of Hawaii, Honolulu, Hawaii, August 18-20, 1975.
ii
ABSTRACT
In the investigation reported herein, twenty each of five
different types of artificial earthquake accelerograms were generated for
computing nonlinear response spectra of five structural models representing
reinforced concrete buildings. To serve as a basis for probabilistic
design and damage assessment, mean values and standard deviations of
ductility factors were determined for each model having a range of pre
scribed strength values and having a range of natural periods. Adopting
the standard philosophy, i.e. only minor damage is acceptable under
moderate earthquake conditions and total damage or complete failure should
be avoided under severe earthquake conditions, required strength levels
were investigated for each model. Selected results obtained in the over
all investigation are presented and interpreted in terms of prototype
behavior.
TABLE OF CONTENTS
ACKNOWLEDGEMENTS
ABSTRACT
TABLE OF CONTENTS
I. INTRODUCTION
II. GENERATION OF ARTIFICIAL EARTHQUAKE ACCELEROGRAMS
2.1 STOCHASTIC MODELS .
III.
2.2 TIME INTENSITY FUNCTIONS
2.3 HIGH FREQUENCY FILTER CHARACTERISTICS
2.4 LOW FREQUENCY FILTER CHARACTERISTICS
2.5 DISCUSSION ON ARTIFICIAL ACCELEROGRAMS
STRUCTURAL HYSTERETIC MODELS . . .
3.1 BASIC PARAMETERS OF MODELS
3.2 ORIGIN-ORIENTED SHEAR MODEL
3.3 TRILINEAR STIFFNESS DEGRADING FLEXURE MODEL
IV. SELECTION OF MODEL PARAMETERS
4.1 ORIGIN-ORIENTED SHEAR MODEL
4.2 TRILINEAR STIFFNESS DEGRADING FLEXURE MODEL
4.3 VISCOUS DAMPING MODEL
V. DYNAMIC RESPONSE ANALYSIS
VI. DUCTILITY RESPONSE SPECTRA .
6.1 LINEAR ELASTIC MODEL
6.2 ORIGIN-ORIENTED SHEAR MODEL.
6.3 TRILINEAR STIFFNESS DEGRADING FLEXURE MODEL
iii
i
ii
iii
1
3
3
4
4
5
6
9
9
9
10
13
13
13
14
15
17
17
18
19
iv
VII. USE OF DUCTILITY ~SPONSE SPECTRA FOR PROBABILISTIC SEI91IC DESIGN 21
7.1 SELECTION OF REQUI~ED DUCTILITY LEVELS 21
7.2 SELECTI0N OF REQUIRED STRENGTH LEVELS 23
VIII. CONCLUDING STATEMENT 28
IX. BIBLIOGR~PHY 29
TABLES. 30
FIGURES. 31
APPENDIX A 63
EARTHQUAKE ENGINEERING RESEARCH CENTER REPORTS 84
1
I. INTRODUCTION
The general philosophy of seismic resistant design in most
countries of the world, including Japan and the United States, is that
only minor damage is acceptable in buildings subjected to moderate earth
quake conditions and that total damage or complete failure should be
prevented under severe earthquake conditions. This philosophy serves as
the basic criterion for assessing the potential seismic performance of
existing buildings and for defining design criteria for new buildings.
Usually, the above philosophy is applied to performance assess
ments and to design in a deterministic manner. In this case, seismic
response analyses are carried out for fixed mathematical models using
fully prescribed ground motion excitations. It should be realized how
ever that many uncertainties exist in this method. The highly variable
characteristics of ground motions, even for a given site, is the major
cause of these uncertainties. However, other causes also exist such as
the variability of structural properties. For this reason, nondeterministic
methods which formally recognize uncertainties and which predict response
in probabilistic terms should be encouraged. Meanwhile every effort
should be made to reduce the uncertainties through experimental and
analytical research and through improved design and construction methods.
To carry out nondeterministic seismic analyses, an appropriate
stochastic model must be established for the expected ground motions. If
sufficient strong ground motion data were available this model could be
obtained by direct statistical analyses. However, due to the limited
data available, one is forced to hypothesize model forms and to use the
existing data primarily in checking the appropriateness of these forms.
The particular model used in this investigation is essentially
2
nonstationary filtered white noise as commonly used by many investigators
[1,2]. While this model is admittedly not perfect, it does reflect the
main statistical features of real ground motions; therefore, its use in
seismic response analyses leads to more realistic predictions than does
a single fully prescribed accelerogram.
Since it was the intent of this investigation to concentrate on
low-rise reinforced concrete buildings, two basic single degree of free
dom structural models were selected for dynamic analysis purposes, namely,
the so called "Origin-Oriented Model" and the "Trilinear Stiffness
Degrading Model" [3]. These models were selected to represent structures
which fail primarily in shear and flexure, respectively. Various strength
values were prescribed for these models and their initial stiffnesses
were varied to produce a wide range of fundamental periods.
Mean values and standard deviations of ductility factor were
generated using the five different classes of earthquake accelerograms
for each structural model having a prescribed period and assigned
strength values. These statistical quantities can be used as the basis
for probabilistic design and damage assessment.
Accepting the basic philosophy previously mentioned, namely
that only minor damage is acceptable under moderate earthquake conditions
and that total damage or complete failure should be avoided under severe
conditions, Umemura has proposed a basic criterion for seismic design
which has been adopted herein [3]. This criterion has been used in
probabilistic terms to establish appropriate strength levels for each
model consistent with the basic design philosophy.
A computer program which generates artiticial earthquake
accelerograms and nonlinear response spectra is presented in Appendix A.
3
II. GENERATION OF ARTIFICIAL EARTHQUAKE ACCELEROGRAMS
2.1 STOCHASTIC MODELS
Two basic types of nonstationary processes are commonly used to
represent earthquake ground motions, namely, nonstationary filtered white
noise and filtered shot noise [1,4,5]. Shinozuka and Sato suggest that
under similar conditions both types lead to essentially the same response
characteristics of linear systems [6].
In the present investigation, five specific types (Types A, B,
B02
' C, and D) of artificial accelerograms were generated using the
second of the above mentioned basic types. The computer program used for
this purpose was a modified version of the program (PSEQGN) developed by
Ruiz. It follows a procedure consisting of five phases, (1) stationary
wave forms are generated having a constant power spectral density function
(white noise) of intensity S o
over a wide range of frequencies starting
at zero frequency, (2) nonstationary shot noise is next obtained by
multiplying each stationary wave form by a prescribed time intensity
function, (3) each of the resulting wave forms of shot noise is then
passed through a second-order filter which amplifies the frequency con~
tent in the neighborhood of a characteristic frequency and attenuates
the higher frequencies, (4) next each of these filtered wave forms is
passed through a second second-order filter which eliminates the very
low frequency content, and finally (5) a baseline correction is applied
to the double filtered accelerograms in accordance with the procedure of
Berg and Housner [7]. Both second-order filterings are accomplished
digitally by solving numerically the second-order differential equations
relating filter outputs to their corresponding inputs [8]. These
4
solutions are obtained numerically by the standard linear acceleration
method using constant integration time intervals of 0.01 seconds. By
this procedure, final accelerograms are obtained in digitized form with
each having similar 0.01 second time intervals.
2.2 TIME INTENSITY FUNCTIONS
Five classes of earthquake accelerograms (Types A, B, B02
' C
and D) were generated using four different time intensity functions as
shown in Fig. 1. These intensity functions are the same as those used
previously by Jennings, et al [2]. Note that accelerograms of Types B
and B02 were generated using the same intensity function. All four
intensity functions consist of three phases (1) a parabolic or cubic
build-up phase, (2) a constant intensity phase, and (3) an exponential
decay phase. The total durations of these particular functions are 120,
50, 12 and 10 seconds, respectively; however, since the ends of the decay
phase do not affect maximum response of damped structural systems, they
were cut off at 75, 30, 10 and 5 seconds for Types A, B, C and D,
respectively.
2.3 HIGH FREQUENCY FILTER CHARACTERISTICS
As previously stated, the nonstationary shot noise wave forms
were obtained by multiplying each stationary wave form having a power
spectral intensity S by a prescribed time intensity function. o
The high frequency filtering procedure was then used to shape
the frequency content of the shot noise wave forms using the transfer
function (complex frequency response function [8])
2 2 3 [l + (4 E;, - 1) (w/w ) ] - 2i E;, (w/w )
000 (1)
5
This transfer function, previously suggested by Kanai and Tajimi for this
purpose [9,10], is usually written in the more familiar form
(2)
Jennings, Ruiz, and other investigators have also used this same transfer
function.
Parameters Wo and ~o appearing in the above filter function
may be thought of as some characteristic ground frequency and damping
ratio, respectively. Kanai has suggested 15.6 rad/sec for W o
and
for ~o as representative values for firm soil conditions. The fre-
0.6
quency transfer function in the form of Eq. (2)is plotted in Fig. 2a for
~o ~ 0.6. These same values of Wo and ~o were used in the present
investigation for four of the five classes of accelerograms, namely,
Types A, B, C, and D. AGcelerograms of Type B02 used the same value for
Wo ' i.e. 15.6 rad/sec., but a different value for ~o' namely, 0.2.
This damping value was selected for Type B02 accelerograms to study t.he
influence of a relatively narrow band excitation on structural response.
2.4 LOW FREQUENCY FILTER CHARACTERlSTICS
The low frequency filter used in this investigation had the
transfer function [2,8]
(W/Wf
) 2
[1 - (w/wf
)2] - 2i ~f(W/Wf)3 222 2
[1 - (w/wf
) ] + 4 ~f (w/wf
) (3)
or
( 4)
6
where and are the characteristic frequency and characteristic
damping ratio, respectively, for the filter. The damping ratio term ~f
was assigned the numerical value 1/1:2 which reduces Eq. (4) to
(5)
Introducing the period ratio T/Tf
, where T
Eq. (5) becomes
2n/w and Tf
= 2n/wf
,
1 (6)
In this investigation, Tf
equals 7 and 2 seconds for Types A, Band
B02 and for Types C and D, respectively. The square root of the function
given by Eq. (6) is shown in Fig. 2b.
2.5 DISCUSSION ON ARTIFICIAL ACCELEROGRAMS
The constant power spectral intensity S, used in generating o
the stationary wave forms, was assigned the value 0.08952 ft2/sec3
. Using
a family of 20 Type B accelerograms, this intensity resulted in a mean
peak acceleration of 0.300g with a standard deviation of 0.032g. In-
creasing the number of accelerograms to 40 gave a mean peak acceleration
of 0.308g and a standard deviation of 0.037g. Following the method of
Gumbel [11], it is estimated that for an infinite number of similar
accelerograms, the mean peak acceleration would be 0.309g and the standard
deviation would be O.041g. Therefore, in view of this mean peak accelera-
tion and the time intensity function used, the Type B accelerograms
closely represent that class of motions containing the N-S component of
acceleration recorded during the 1940 El Centro, California, earthquake
[2,4].
7
Table 1 lists the mean values and standard deviations for the
peak accelerations in all 5 classes of accelerograms, i.e. for Types Ai
B, C, D, and B02
' In obtaining these results, So was assigned the same
value 0.08952 ft 2/sec3
in each case. Notice that the mean peak accelera-
tion decreases as the duration of the constant intensity phase in the
motion decreases. This observation is, of course, consistent with the
theory of extreme values. Notice also that the standard deviations are
relatively small in each case.
Following the suggestion of Jennings, et. al. [2], the Type A
accelerograms are intended to represent the upper bound ground motions
expected in the vicinity of the causative fault during an earthquake
having a Richter Magnitude 8 or greater. The Type B accelerograms are in-
tended to represent the motions close to the fault in a Magnitude 7
earthquake, such as the 1940 El Centro, California, earthquake and the
1952 Taft, California, earthquake. The Type C accelerograms are intended
to represent the ground motions in the epicentral region of a Magnitude
5.5 shock, such as occurred during the 1957 San Francisco earthquake,
and the Type D accelerograms are intended to represent the motions present
in the immediate vicinity of the fault of a 4.5 to 5.5 Magnitude earth-
quake having a small focal depth, such as the 1966 Parkfield, California,
earthquake. If the artificial accelerograms generated as Types A, B, C,
and D are indeed to be representative of these conditions, then each
class of motions should be normalized by the appropriate factors to raise
the mean peak acceleration levels from 0.332g, 0.309g, 0.244g, and 0.189g,
respectively, to approximately 0.45g, 0.33g, O.lOg, and 0.50g.
Since the extreme values of response for all 5 structural models
used in this investigation were measured in terms of ductility factors,
the above mentioned normalization of accelerograms is not required. These
8
ductility factors are controlled by a structural model strength to ground
motion intensity ratio; i.e. p /mv where Ps is the significant s go
structural strength parameter, m is the mass of the single degree of
freedom system, and v go
is the mean peak acceleration. Allowing this
ratio to vary over a prescribed range of values is equivalent to allowing
and/or v go
to vary independently over restricted ranges.
Further, it should be recognized that the structural response
data generated for ground motions of Types A, B, C, D and B02 can be
interpreted in terms of structural response to other classes of motions.
For example, suppose one wished to interpret these response data for
similar classes of earthquake motions but for a change in the characteristic
ground frequency w o
to reflect a change in soil conditions. This
interpretation can be accomplished by considering a change in the time
scale of the accelerograms; thus, forcing corresponding changes in the
time intensity functions, the value of Tfl the value of w , o
and the
mean peak acceleration. Since the value of S representing the new o
classes of accelerograms is to remain unchanged, the mean peak accelera-
tions of the new motions will be changed exactly in proportion to the
square root of the ratio of the original time interval to the new time
interval. Specifically, suppose the time interval is considered to be
changed from 0.01 sec. to 0.005 sec. for the Type A accelerograms. In
this case, the total duration (as represented by OC, Fig. 1) is reduced
from 75 sec. to 37.5 sec., w 0
is increased from 15.6 rad/sec. to 31.2
rad/sec., Tf
is reduced from 7 sec. to 3.5 sec., and the mean peak
acceleration is increased from 0.33g to 0.46g (1:2·0.33 = 0.46).
9
III. STRUCTURAL HYSTERETIC MODELS
3.1 BASIC PARAMETERS OF MODELS
The single degree of freedom system shown in Fig. 3a was used as
the basic form for all structural models investigated. This model has
a linear viscous dashpot but a nonlinear hysteretic spring. The restor-
ing spring force is therefore some prescribed nonlinear function F(v)
of the relative displacement v(t). The principal quantities used to
characterize this function are Pc' P , v , y c and v
y as shown in Fig. 3b.
Loads and represent the spring restoring forces corresponding
to the concrete cracking strength and the ultimate strength, respectively.
Displacements v c
and v are the corresponding relative displacements 0
y
3.2 ORIGIN-ORIENTED SHEAR MODEL
One of the five structural models used in this investigation
was the so-called "Origin-Oriented" hysteretic model proposed by Umemura,
et. al. [3]. This model is shown in Fig. 4 where it is characterized by
v , sc
and v which represent the concrete shear cracking sy
strength, the ultimate shear strength, the relative displacement produced
by Psc' and the relative displacement produced by Psy' respectively.
Application of this model is restricted to those structural types where
the nonlinear deformations and failure characteristics are controlled
primarily by shear.
This model is defined such that the hysteretic behavior takes
place with increasing relative displacements greater than v sc
or
decreasing displacements less than -v sc
Reduction of loads from values
greater than Psc or less than -Psc follow linear paths always directed
through the origin, e.g. paths A'O and A"O in Fig. 4. Oscillatory
motions can, of course, take place along the linear paths such as A'OA'
10
and A"OA" without developing hysteretic loops provided the maximum
displacements do not exceed the maximum displacement previously developed.
The particular model plotted in Fig. 4 is for the case where p = 1.9 p , sy sc
v sy
10.0 and
3.3 TRILINEAR STIFFNESS DEGRADING FLEXURE MODEL
Four of the five structural models used in this investigation
were the so-called "Trilinear Stiffness Degrading" hysteretic model [3].
This model is shown in Fig. S where it is characterized by PBc' PBy' vBc
'
and vBy
which represent the load at which the concrete cracks due to
flexure, the load at which the main reinforcing steel starts yielding due
to flexure, the relative displacement produced by p , and the relative Bc
displacement produced by PBy' respectively. Application of this model
is restricted to those structural types where the nonlinear deformations
and failure characteristics are primarily controlled by flexure.
The trilinear model is defined such that linear elastic behavior
(without hysteretic loops) always takes place for oscillatory displace-
ments where the corresponding oscillator loads are in the range
p < PBc; however, hysteretic behavior occurs with every cycle of
-p < Bc
deformation which has load levels above or below During that
period of time between the initiation of loading and that instant at
which the relative displacement first increases above v or decreases By
below -vBy ' the trilinear model behaves exactly like the standard
bilinear hysteretic model having stiffnesses kl and k2 (QPOAB; Fig. Sa).
However, as soon as the relative displacement increases above or
decreases below -v ,a new bilinear hysteretic relation controls the By
response. For example, suppose the relative displacement for the first
time increases above to level v as represented by C in Fig. Sa. max
Upon decreasing the displacement from this level, the corresponding load
decreases along path CD which has a slope equal to ak1 , where
2 v By
v + V max By
As soon as the load drops by the amount
(7)
2p reaching point D in Fig. Bc
Sa, any further drop in load will follow the continuing path shown
11
having a slope ak2
. It should be noted that point D is located at load
level in Fig. Sa but only because the particular trilinear model
represented in that figure is for PBy/PBC = 3.0. If this ratio had been
assigned a different numerical value, the load level at point D would be
different from
The new bilinear hysteretic model controlling the continuing
motion is shown in Fig. Sb. Note that the origin of the skelton curve
is shifted from point 0, the origin of the original bilinear hysteretic
model, to point 0'. This point is the intersection point of line QC and
the abscissa axis in Fig. Sa; therefore 00' is equal to BC/2. The stiff-
nesses of the new bilinear model are akl
, and ak2
•
If during the period of response controlled by the second
bilinear model (Fig. Sb) the relative displacement should increase beyond
v (v = vB ,) as represented by point B' to a new level as max max y
represented by C', the continuing response would be controlled by a
third bilinear hysteretic model whose characteristics could be obtained
in exactly the same manner as the characteristics of the second model.
Also, if yielding of the trilinear model had taken place at load level
rather than load level the new bilinear model controlling
the continuing motion would be obtained by a similar procedure.
One characteristic feature of the trilinear stiffness degrading
model worth noting is that when subjected to full-reversal cyclic
displacements at a constant amplitude the bilinear hysteretic loops are
12
perfectly stable, i.e. each loop retraces the preceding one. The energy
absorbed during each successive cycle must therefore be equal. Using a
period T = 2'[ /m/k , 2 Y
where k Y
is an average stiffness as shown in
Fig. 6, one can calculate the equivalent damping ratio ~ for a linear
viscously-damped single degree system which represents the same energy
absorption per cycle of oscillation. This damping ratio is shown in
Fig. 6 for each of four different bilinear models.
13
IV. SELECTION OF MODEL PARAMETERS
4.1 ORIGIN-ORIENTED SHEAR MODEL
As previously defined, the origin-oriented hysteretic model
shown in Fig. 4 is completely characterized by any four of the seven
parameters kl
, k2
, k3
, P , P I V , V sc sy sc sy
Based on experimental
data [31, it has been determined that
1.9 p sc
(8)
v sy
10 v sc
(9)
which reduces the number of independent parameters to two. It is most
meaningful to let one of these two parameters be a stiffness parameter
and the other be a strength parameter. For this purpose, it is con-
venient to use period Tl = 2n Im/kl and the concrete cracking force
As shown later, is normalized by the force
is the mean peak ground acceleration.
4.2 TRILINEAR STIFFNESS DEGRADING FLEXURE MODEL
mv , go
where
The general trilinear stiffness degrading hysteretic model
shown in Fig. 5 is completely characterized by any four of the seven
v go
parameters k l , k 2 , k y ' PBc' PBy' vBc ' vBy ' Four specific models, which
were previously studied by other investigators [31, were selected for
this investigation,
1. kl 2k Y PBy 3PBC
2. kl 2k PBy 2PBc y (10)
3. kl ~y PBy 3PBC
4. kl 4k Y PBy 2PBC
14
These four models were chosen because k y
and are often found in
the ranges 2PBC < P < 3p , By Bc respectively, for
reinforced concrete members. For frame structures, these ranges are not
so well defined so that engineering judgment must be relied upon in
assigning values consistent with their overall nonlinear behaviors.
Having assigned numerical values to the ratios ky/kl and
PBy/PBC' only two independent model parameters remain. In this case it
is most convenient to select a stiffness parameter measured in terms of
Tl = 2~ Im/kl and a strength parameter measured in terms of PBy. Again,
the strength parameter selected (PBy) is normalized by the force
4.3 VISCOUS DAMPING MODEL
mv go
As shown in Fig. 3a, the single degree of freedom model used in
this investigation included a linear viscous dashpot having a variable
coefficient c. The coefficient used with the origin-oriented shear model
is defined by the relation c(t) = 2 ~l k(t)/w(t) where ~l is a con-
stant damping ratio, and k(t) and w(t) are variable stiffness and
natural circular frequency in accordance with the stiffness at time t,
respectively. The coefficient used with the trilinear stiffness degrad-
ing flexure model is defined by the relation c(t) = 2 ~l k(t)/wl
where
WI is a initial natural circular frequency. This coefficient becomes
smaller with a reduction or degradation of stiffness.
15
v. DYNAMIC RESPONSE ANALYSIS
The complete time history of dynamic response was generated for
the single degree of freedom system using the five different structural
models subjected seperately to the twenty artificially generated earth-
quake ground motions. The equation of motion governing this response is
the well known relation
. m vet) + c(t)v(t) + F(v) - m v (t)
g ell)
where F(v) is the nonlinear spring force defined by the hysteretic
model being considered; i.e. the spring force defined by either Fig. 4
or Fig. 5. Dividing through by
[
1 ] .. ~ go v (t)
mv (a constant) gives go
. v (t) +
F(v)
m v go
v (t) g
v go
(12)
Note that the third term on the left hand side of this equation is the
same force-displacement relation defined by the hysteretic model but with
the force normalized (as previously mentioned) by the constant
Knowing the numerical values assigned to constants VgO
' Sl'
- -.. ..
m v go
and
as well as the prescribed value of p 1m v (or PB 1m v ), one can sc go y go
solve Eq. (12) for the complete time history of response v(t). This
solution is obtained numerically using the standard "linear acceleration"
method. The time interval ~t generally used in the integration was
shortened to a subdivided value ~t' during short periods of time in
which the model stiffness changed value. The numerical values of ~t
and ~t' used for four different ranges of period Tl
, are shown in
Table 2.
16
The response quantity of primary interest is the ductility
factor ~ which is defined as v(t) Iv max sc
for the origin-oriented
model and as v(t) IVB
for the trilinear stiffness degrading model. max y
This factor was obtained for each of the five structural models when
subjected separately to each of the 20 ground motions generated for Types
A, B, C, D, and B02 ' The damping ratio ~l was assigned the value
0.05 for the origin-oriented model and 0.02 for the trilinear stiffness
degrading model. Since the ductility factor was desired for a range of
stiffnesses, period Tl was assigned 10 different numerical values as
given by
0.1(2)n/ 2 (n 0,1,2, ..• ,9) (13)
Using the origin-oriented model, ductility factors were
.. obtained for a range of values of p 1m sc
v , go
namely 0.50, 0.75, 1.00,
1.25, 1.50, 1.75, 2.00, 2.25, 2.50, and 3.00. Using the trilinear
stiffness degrading model, these values were obtained for p 1m v By go
equal to 0.50, 0.75, 1.00, 1.125, 1.25, 1.50, and 1.75.
17
VI. DUCTILITY RESPONSE SPECTRA
6.1 LINEAR ELASTIC MODEL
To characterize the five classes of earthquake motions (Types
A, B, C, D, and B02
) in most familiar terms, all 20 accelerograms of each
type were seperately used as the excitation applied to a linear, viscously
damped (~ = 0.05) single degree of freedom system. Mean absolute
acceleration response ratios a as defined by
a
;:t v (t)
max .. v
go
(14)
, where :-:t v (t) is the mean value of 20 maximum absolute accelerations
max .. t
[v (t) ] and where max
.. v
go is the peak mean value of ground accelerations,
were determined for each excitation over a range of periods T. The
coefficients of variation (ratio of standard deviation to mean value) of
··t v (t) were also determined for the 20 accelerograms in each type of max
excitation.
The results of the analyses for all five classes of earthquake
are shown in Fig. 7 where the mean absolute acceleration response ratios
and the coefficients of variation of ··t v (t) are plotted as func-
max
tions of period T. As would be expected, the values of a for the
five classes of earthquakes are widely seperated at the long period end
of the abscissa scale but converge together towards the low period end
of the scale. As the period goes to zero, a must of course, approach
unity. It is seen in Fig. 7 (excluding Type B02
) that a increases with
duration of the earthquake excitation. The very high peak shown in the
function of a for Type B02 is caused by the narrow band excitation in
the ground motion in the neighborhood of T = 0.4 sec.
18
The coefficients of variation of vt(t) decrease with max
duration of excitation and increase generally with period T. It should
be recognized that as T approaches zero the coefficients of variation of
··t v (t) approach the corresponding coefficients of variation of max
V (t) as given in Table 1. go max'
6.2 ORIGIN-ORIENTED SHEAR MODEL
-Mean ductility factors ~ and their corresponding coefficients
of variation were generated for the origin-oriented shear model using the
20 response time histories for each class of earthquake ground motions.
Values, as obtained over the period range 0.1 < Tl < 1.6 /:2 and over
the normalized load range 0.50 < S < 3.00 (where s
is defined as
the ratio p 1m v ), are shown in Figs. 8a-Se. c go For each type of
earthquake, these ductility factors generally increase with decreasing
period and the spread of ductility factors over the full strength range
increases with decreasing period. Also the ductility factors for a
fixed period increases with decreasing structural strength.
The trends of the coefficients of variation with period are
similar to those previously described for mean ductility factor,
particularly regarding strength level and strength variation. It is
most significant to note that the coefficients of variation are low
when the response is essentially elastic (~ < 1) but they can become very
large with increasing inelastic deformations.
When interpreting the results in Figs. 8a-8e, it should be
noted that the strength ratio ..
S = p 1m v can be expressed in the s c go
form
(p IW) I (v Ig) c go
(15)
19
where W is the weight of the single degree of freedom mass and g is
the acceleration of gravity. Therefore, this parameter can be considered
as the ratio of base shear to coefficient of mean peak ground acceleration.
If for any particular case one wishes to determine the mean
maximum relative displacement V (t) , max
this can be accomplished by
using the appropriate mean ductility factor ~ taken from Figs. 8a-8e.
By definition of ductility factor, one can state
V (t) max
v fl c
(16)
Making use of the definition of Ss given above, this equation can be
written in the form
V (t)
or
V (t)
max
max
v go
Equation (18) is the most convenient form for calculating
6.3 TRILINEAR STIFFNESS DEGRADING FLEXURE MODEL
(17)
(18)
V (-t) max
Mean ductility factors and their corresponding coefficients of
variation were generated for the four trilinear stiffness degrading
flexure models using the 20 response time-histories for each class of
earthquake ground motions. Values, as obtained over the period range
0.1 < Tl < 1.6 1:2 and over the normalized load range 0.50 < Sf < 1.75
(where is defined as the ratio p 1m v ), are shown in Figs. 9a-9d, y go
lOa-lad, lla-lld, 12a-12d, and 13a-13d for earthquake Types A, B, C, D,
and B02
' respectively.
20
The general trends of these results are very similar to those
previously described for the origin-oriented shear model. It is worth
pointing out again that the coefficients of variation of maximum response
are relatively low for cases of essentially elastic behavior but can
become very large for cases involving inelastic deformations.
As in the case of the origin-oriented model, mean maximum
response can be calculated using the relation
v(t) max =
..
[~][~] (19)
VII. USE OF DUCTILITY RESPONSE SPECTRA FOR PROBABILISTIC SEISMIC DESIGN
7.1 SELECTION OF REQUIRED DUCTILITY LEVELS
It is implied in the basic philosophy of design previously
21
stated that economical considerations do not permit the design of struc-
tures for zero risk of damage in high seismic regions. To minimize total
costs (initial costs, repair costs after earthquakes, etc.), damage is
often permitted to limited degrees under moderate to severe earthquake
conditions. It should be understood that permitting some damage to occur
in a well designed structure has the beneficial effect of limiting damage
to that same structure. This is due to the fact that the energy absorp-
tion associated with damage is effective in limiting the maximum levels
of oscillatory motion in the strucuture. Therefore, a good seismic
resistant structure should be designed for high energy absorption
capacity assuming it will experience controlled damage under severe to
moderate earthquake conditions. In terms of the hysteretic structural
models presented herein, this concept means that the ductility factor
should be limited to certain values consistent with the basic design
philosophy.
Assume for the moment that one prescribes two numerical values
of ductility factor for a given structural model. The smaller value was
chosen to be consistent with light damage under moderate earthquake
conditions and the large value was chosen to be consistent with heavy
damage (but not complete failure) under severe conditions. Two questions
come to mind (1) "What is the probability of these ductility factors
being exceeded during a single earthquake of Types A, B, C, D, or B02
?"
and (2) "What ductility factors are required, consistent with the design
22
philosophy?". To answer these questions, one must establish the
appropriate probability density or distribution functions.
Previous investigations have shown that the probability dis-
tribution function for extreme value of structural response for a single
earthquake follows closely the Gumbel Type I distribution [1,4]
exp {- exp [- a (~ - u)]} (20)
where ~ is the maximum response measured in terms of ductility factor,
and a and u are parameters which depend on the average and standard
deviation of ~. If only 20 sample values of ~ are available as in
this investigation, a and u can be obtained using the relations [11]
and
CL 1. 063/cr ~
u = ~ - 0.493 cr ~
(21)
(22)
where ]l and cr ]l
are the mean and standard deviation of the 20 sample
values of ~. Using these equations and expressing the standard deviation
of ~ in terms of its coefficient of variation (cr = c ~), Eq. (20) can ]l
be written in the nondimensional form
P (q)
where
exp {- exp [- 1.063 (q - 1 + 0.493c)]} c
q
This probability distribution function is plotted in Fig. 14 over a
range of values of c, i.e. over the range 0 < c < 1.5. Since the
probability distribution function is defined such that
( 23)
(24)
23
P (x) Probability [~ < x] (25 )
, the probability exceedance function is given by
Q(x) Probability [~ > x] 1 - P (x) (26)
The first question previously raised, namely, "What is the probability of
these ductility factors being exceeded during a single earthquake of
Types A, B, C, D, or B02
?" , can be easily answered using Eq. (26), Fig.
14 and the data provided in Figs. 8a-13d. The second question raised,
i.e. "What ductility factors are required consistent with the design
philosophy?", is more difficult to answer. Before attempting to answer
this question, one must realize that the basic design criteria cannot be
met in absolute terms, i.e. with 100% confidence. This complication is
due to the scatter of coefficient of variation of ductility factor
present for each family of earthquake excitations. The best one can do
is reduce the probability of exceedance associated with each of the two
ductility factors to an acceptable level. Deciding on an acceptable
level is complex as it involves economic, social, and political
considerations.
Suppose for example, it was decided that a 15 percent pro
bability of exceedance was acceptable, i.e. Q(~) = 0.15 and P(~) = 0.85.
Using Fig. 14 and the data provided in Figs. 8a-13d, one can easily
establish that ductility factor ~85 associated with P(~) = 0.85. This
has been done for all four trilinear stiffness degrading models sub
jected to Type A ground motions giving the results shown in Fig. 15.
7.2 SELECTION OF REQUIRED STRENGTH LEVELS
To establish the required strength levels of the various struc
tural models for each class of earthquake motions, one must first prescribe
24
basic criteria consistent with the basic design philosophy. In the
following discussion, 20, 15, 10 and 5 percent probabilities of exceedance
were selected as examples of acceptable risk and it was assumed that
moderate and severe earthquake conditions are represented by 0.30g and
0.45g, respectively, for the mean peak acceleration of ground motions.
Finally, the two ductility factors, consistent with light and heavy (but
controlled) damage, are chosen as 2 and 10 for the origin-oriented shear
model and 2 and 4 for the trilinear stiffness degrading model. The
values of peak accelerations and ductility factors selected above follow
the suggestions of Umemura, et ale [3].
Using data such as shown in Fig. 15 for each structural model
and for each type of earthquake motions, i.e. using curves of ~85 vs. Tl
,
one can easily obtain the required strength ratios (6 = plm v ) for go
discrete values of Tl
. Linear interpolation between the curves (~85 vs.
Tl
) for a fixed value of Tl can be used for this evaluation. The
resulting required strength ratios for each prescribed risk level can
then be plotted as functions of period Tl as shown in Figs. 16-19 for
the trilinear stiffness degrading flexure model Subjected to earthquake
Types A, B, C and D. Figures 20 and 21 show the required strength ratios
corresponding to ductility ratios ~80' ~85' ~90 and ~95 equal to 6.
Figs. 22 and 23 show similar results but with the ductility ratios equal
to 8. These results have no direct relation to the basic design criteria
but are of interest in showing the influence of high ductility on the
required strength level. One characteristic feature of all sets of
curves in these figures is that the four curves representing earthquake
Types A, B, C and D are quite close to each other, except for the case
of Type D earthquakes when 10 and 5 percent probability of exceedance is
prescribed. One finds the required strength ratios are significantly
25
influenced by the area of the hysteretic loop; see Fig. 6. The required
strength ratios for the trilinear model subjected to earthquake Type B02
are shown in Figs. 26 and 27.
One very significant feature to notice in these figures for all
five types of earthquakes is that generally, the required strength ratios
for the trilinear model in the range Tl > 0.2 sec. vary in a linear
manner with negative slopes along the log scale for Tl
. Converting to
a linear scale, the required strength ratios would vary in inverse pro-
portion to the square root of Tl
, i.e. s ~ (T )-1/ 2 1
for Tl > 0.2 sec.
This implies that buildings represented by the trilinear model which have
a shorter natural period than the predominant period in the ground motions
are likely to suffer excessive deformation, especially in a case of
earthquake Type B02
' because a lengthening of the period caused by
reduction and degradation of the stiffness brings the characteristic
period more in line with the predominant period in the ground motions.
The required strength ratios (S = p 1m v ) are shown in s c go
Figs. 24 and 25 for the origin-oriented shear model subjected to earth-
quake Types A, B, C and D. The results in Fig. 24 are obtained for the
basic criteria previously established; however, the results in Fig. 25
are for ductility factors ~ set equal to 1.5 and 5 which represent
brittle structures. These latter results show the influence of brittle-
ness on the required strength level. The four curves representing
earthquake Type A, B, C and D are quite close to each other similar to
the corresponding curves for the trilinear model. The required strength
ratios for the shear model subjected to earthquake Type B02 are shown in
Fig. 28. The results in Figs. 24, 25 and especially, in Fig. 28, show
a high tendency to peak at Tl = 0.4 sec. which corresponds with the
predominant period of the input ground motions. This tendency is most
26
significant in the case of lower ductility factors which correspond to
small degradations in stiffness. The required strength ratios vary in
inverse proportion to the square root of Tl for Tl > 0.4. As for the
shear model, the period at the peak of these curves becomes smaller with
the higher ductility factors which accompany the larger degradations of
the stiffness.
When judging which of the two prescribed ductility factors
control a particular design or damage assessment, one should be careful
not to base the decision on a direct comparison of the required strength
ratios as shown in Figs. 16-19, 24, 26 and 28 since these ratios have
different normalization factors. For example, consider a shear model
with Tl = 0.4 sec. as shown in Figs. 24c and 24d. Using the light
damage criteria, i.e., Vgo = 0.30 g and ~85 = 2, gives S = 2.2 and
p = 0.66 mg. c
Using the heavy damage criteria, i.e. v go
0.45g and
~85 = 10, gives S = 0.8 and p = 0.36 mg. c
Note that for these two
different levels of damage, the resulting values for S have a different
ratio to each other than do the two values for p. Obviously in this c
case, the light damage criteria requiring Pc 0.66 mg control the
design or damage assessment. Let us consider a second example of the
origin-oriented model with Tl = 0.15 sec. In this case the light damage
criteria give S = 1. 7 and p = 0.51 mg and the heavy damage criteria c
give S = 1.3 and Pc = 0.58 mg. For this particular structural model,
the heavy damage criteria requiring Pc = 0.58 mg control the design or
damage assessment. Making similar comparisons for the various trilinear
stiffness degrading models represented in Figs. 16-19 and 26, one finds
that the heavy damage criteria (v = O.45g and ~ = 4) always control . go 85
the design or damage assessment.
27
When using the results in Fig. 16-28 in accordance with the
above example calculations, one should remember that they are based on the
ground motion parameters w = 15.6 rad/sec (T = 0.4 sec) and ~ 000
which represent firm ground conditions. If one should have quite
different ground conditions, these parameters should be adjusted
appropriately. These adjustments shift the level of the predominant
frequencies in the ground motions and also change the mean intensity
-
0.6
level v go
With considerable experience and using engineering judgment,
certain modifications to the data in Figs. 16-28 can be made to reflect
these new conditions.
One should also keep in mind that these results do not include
the influence of soil-structure interaction which lengthens the natural
period and often increases damping in the overall system.
28
VIII. CONCLUDING STATEMENT
The response ductility factors and coefficients of variation
presented herein provide the necessary data for carrying out probabilistic
seismic resistant designs and for conducting damage assessments consistent
with basic design criteria and the statistical nature of earthquake
ground motions.
29
IX. BIBLIOGRAPHY
[1] Ruiz, P., and Penzien, J., "Probabilistic Study of the Behavior of Structures during Earthquakes," Earthquake Engineering Research Center, No. EERC 69-3, University of California, Berkeley, California, March, 1969.
[2] Jennings, P. C., Housner, G. W., and Tsai, N. C., "Simulated Earthquake Motions," Earthquake Engineering Research Laboratory, California Institute of Technology, Pasadena, California, April, 1968.
[3] Umemura, H., et. al., "Earthquake Resistant Design of Reinforced Concrete Buildings, Accounting for the Dynamic Effects of Earthquake," Giho-do, Tokyo, Japan, 1973, (in Japanese).
[4] Penzien, J., and Liu, S-C., "Nondeterministic Analysis of Nonlinear Structures Subjected to Earthquake Excitations," Proceedings of the 4th World Conference on Earthquake Engineering, Santiago, Chile, January, 1969.
[5] Amin, M., and Ang, A. H. So, "A Nonstationary Stochastic Model for Strong-Motion Earthquakes," Structure Research Series 306, University of Illinois, Urbana, Illinois, April, 1966.
[6] Shinozuka, M., and Sato, Y., "Simulation of Nonstationary Random Process," Proceedings, ASCE, Vol. 93, EM1, February, 1967.
[7] Berg, G. V., and Housner, G. W., "Integra ted Velocity and Displacement of Strong Earthquake Ground Motion," Bulletin of the Seismological Society of America, Vol. 51, No.2, April, 1961.
[8] Clough, Ro W., and Penzien, J., "Dynamics of Structures," McGraw Hill, 1975.
[9] Kanai, K., "Semi-Empirical Formula for Seismic Characteristics of the Ground," Bulletin of Earthquake Research Institute, University of Tokyo, Japan, Vol. 35, June, 1967.
[10] Tajimi, H., "A Statistical Method of Determining the Maximum Response of a Building Structure during an Earthquake," Proceedings of the 2nd World Conference on Earthquake Engineering, Tokyo, Japan, Vol. II, July, 1960.
[11] Gumbel, E. Jo, and Carlson, P. Go, "Extreme Values in Aeronautics," Journal of the Aeronautical Sciences, 21, No.6, June, 1954.
30
TABLE 1
MEAN VALUES AND STANDARD DEVIATIONS OF PEAK GROUND ACCELERATIONS
Type of Statistical Number of Earthquakes
Earthquake Quantity 20 40 Infinity
A Mean 0.327 0.331 0.332
Std. Deviation 0.023 0.036 0.040
B Mean 0.300 0.308 0.309
Std. Deviation 0.032 0.037 0.041
C Mean 0.240 0.243 0.244
Std. Deviation 0.022 0.035 0.039
D Mean 0.191 0.188 0.189
Std. Deviation 0.041 0.039 0.044
Mean 0.346 0.336 0.337 B02
Std. Deviation 0.048 0.049 0.055
TABLE 2
STANDARD TIME INTERVAL AND SUBDIVIDED TIME INTERVAL
Interval Type Natural Period T
1, sec.
0.1 and 0.14 0.2-0.4 0.57-1.13 1.6 and 2.26
Standard 0.005 0.01 0.01 0.01
Subdivided 0.000625 0.00125 0.0025 0.005
TY
PE
A
A
O
A:
EN
V(t
)=t
2 /16
B
B
C:
EN
V(t
)=e
xp
[-0
.03
57
(t-3
5)]
I.O~
!~
-I
: ------------_
__
__
__
__
_ ~C
>
: :
~ z ~
75
(S
EC
) w
0
4 3
5
TY
PE
B
AN
D
TY
PE
B
02
LO~
B
-::
OA
: E
NV
(t)=
t2 /16
~ ~ ~
Be
: E
NV
(t)=
ex
pto
.09
92
(t-
15
l]
o 4
15
30
(S
EC
)
TY
PE
C
1.0
' A
B
-o A
: E
N V
(t)
= t
2/4
~ Vi ~c
BC
: E
NV
(t)=
exp
[-
0.2
68
(t-4
D
o 10
(S
EC
) 2
4
TY
PE
D
:= 1.0~
AB
>
i z
II
C
W
II
o 2
2.5
5
OA
: E
NV
(t)=
t3 /8
BC
: E
NV
(t)=
exP
[-1
.60
6(t
-2.5
il
FIG
. 1
TIM
E
INT
EN
SIT
Y
FUN
CT
ION
S W
f-
'
(\j ]
1.0
...... -
:I:
o 1.
0
1.0
~
0.5
1 HI(
iw )1
2 (..
!:!L)2
1
+4
{o
Wo
-G+
(~)2
J2 +4~:(~)2
2.0
W/W
o
( a )
~o=
0.6
3.0
Tr
=1
/[1
+{T
/Tf)
4JI/
2
Tr =A
H 2(iW
)12
o ~I _
__
_ -L
__
__
-L
__
__
-L
__
__
-L
__
__
-L
__
__
-L
__
__
-J
1.0
2.0
T/T
f
( b )
3.0
FIG
. 2
FIL
TE
R T
RA
NSF
ER
FU
NC
TIO
NS
v(t
)
p
Py Pc
Vc
(0 )
( b
)
v'(
I)=
v(I
)+ v
g( t)
Vy
T=
27
T J
m1
k
( =
c 1
2 ./f
i1k
FIG
. 3
SIN
GL
E
DEG
REE
O
F FR
EED
OM
M
OD
EL
WIT
H
FOR
CE
-DIS
PLA
CE
ME
NT
R
EL
AT
ION
SH
IP
W
tv
-VSY
C A
ll /7
B
/
/
~
B/
P SY
I ~ k, ~~~/
P SC
rYtf/
-
Vs
c..
#l
VSC
Vsy
PSY
= I.
9 P
sc
Vsy
=
10.
0 Vs
c
-Psc
k
2 =
0.1
k
I
k3
=0
.19
kl
-P sy
FIG
. 4
OR
IGIN
-OR
IEN
TE
D
HY
STE
RE
TIC
M
OD
EL
All
C
OR
IGIN
S
KE
LE
TO
N
CU
RV
E
PB
y I
Bf
C
p ~ =
3
Psc
/ I
/ /f
ak
2
VB
y V
By
vm
ax
::: V
min
a=~
Vm
ox
-V
min
P
By
I 8
1/
Cl
/ r -P
By
;'
. / I
R
) Q
(0
)
,Ja
kl 1a
': /
I I
ak y
I
/ I
I ,I
I A
/l
ak
2 I
""/
///0
/ /
/
-VB
y
VS
y'
Y I
I
SK
EL
ET
ON
C
UR
VE
/
. /"
f I
AF
TE
R
YIE
LD
ING
j'
R ~Q
( b)
FIG
. 5
TR
I-L
INE
AR
HY
STE
RE
TIC
M
OD
EL
w
w
T 2
= {2
TI
PB
y=
2.0
PB
c
T2 =
{2
TI
PB
/ 3
.0 P
Bc
PS
y
PS
y
~ =
0.1
59
~ =
0.1
06
T2 =
2
T j
PB
y=
2.0
PB
c
T2
=2
1T
.Jm
/ ky
TI
=2
1T
Jm
/kl
T2
= 2
T\
PB
y =
3.0
PB
c
PS
y
~ = 0
.23
9
PS
y
~=0.
159
FIG
. 6
STA
BL
E
BIL
INE
AR
HY
STE
RE
TIC
L
OO
P FO
R
TR
ILIN
EA
R
ST
IFF
NE
SS
D
EG
RA
DIN
G
MO
DEL
w ~
LIN
EA
R
MO
DE
L
t=0
.05
5
.0 ,
I ------------,
~
4.0
1,\
o ~
a::
--
TY
PE
A
T
YP
E
8
TY
PE
C
T
YP
E D
TY
PE
8
02
'Jt(
l)m
ax
a
= -,--~.:..c..::c:.
·Vg
o
5 3
.0 ~
I ------;---+
----
f <t a::
w
--1
W
U
U
<t w 5
j (f
) f'
~
1.0
\:,~
,,~
a::
o 1
I )
I)
I )
I)))
) I
0.1
0.2
0
.5
1.0
2.0
T
(SE
C)
z o ~
LIN
EA
R
MO
DEL
t
=0
05
0
.5 "
-------,........-----,
\ I I
\
I
" , I
" y_
A
f
0.4
f-I -----~----
I ~ . ..
, I
"', ......
~~
/ \
I f /
i f
a:: :!
0.3
1
i\
...
lL
o f Z w
u 0
.2 I
.' .4
>.~2
'1
~~
lL
lL
W o u
0.1 o
I I
I )
I I
I I) Ii)
)
0.1
0.2
0
.5
1.0
2.0
T
(SE
C)
FIG
. 7
RE
SPO
NSE
ACCELERll~.TION
R).I
"TIO
S FO
R
LIN
EA
R
MO
DEL
TYPE
A
EAR
THQU
AKE
'1= 0.
05
p y
=1
.9P C
Vy
= 1
0.O
v e
fL'
v (I
)m
ax/
vc
20
0.0
1\
T, '2
."..
Jm!k
,
t, =
c/2.
./rT
iTk,
1.4
r' ---------
--Ii
: '0
.50
mV
go
1.3 ~
, 0
.75
,
1.0
0
10
0.0
!k
---'
\...
..--
l::l
0::
' 1.
25
0
IT '
1.50
f-
, 1.
75
U Lt
1.1
'2.0
0
, 2
.25
>-
, 2
.50
f-
1.0
'3.0
0
...J
20
.0
~
0::
0 f-1
0.0
u
g 0
.9
Cl
LL.
<[
LL.
o 0
.8
>- f- ...J
z 0 f-0
.7
<[
i=
u =>
Cl
~ 0
.6
>
Z
~ 0
.5
<[
W ~
f- r5 0
4
u iJ:::
0.3
L.!...
0.2
I 'g
I w
8 0.
2
0.1
1-1
----------1
0.
1
0.0
5 I
, )
! )
! !
) )
I ! I)
) I
0 0.
1 0
.2
0.5
1.
0 2
.0
0.1
0.2
0
.5
1.0
2.0
TI
(SE
C.)
TI
(S
EC
. )
FIG
. 8
a
MEA
N
DU
CT
ILIT
Y
FAC
TO
RS
AN
D
CO
RR
ESP
ON
DIN
G
CO
EF
FIC
IEN
TS
O
F V
AR
IAT
ION
FO
R
OR
IGIN
O
RIE
NT
ED
M
OD
EL
HA
VIN
G
DIF
FE
RE
NT
ST
RE
NG
TH
L
EV
EL
S w
V
1
w
0'\
TYPE
B
EAR
THQ
UAK
E TY
PE
C
EART
HQ
UAK
E e- I= 0
.05
p
= I.
9 p
v
=IO
.Ov
e- 1=0
.05
p
= 1
.9 p
v
= 1
0.O
v y
c y
c y
c Y
c
1.4
1.4
p. =
v (1
1mox
/ve
j --~ =
0.5
0m
Vgo
p
.=v(
11
mo
x/ve
--~ =
0.5
0 m
V90
T, =
217"
.Jm
ik,
20
0.0
T,
= 21
7".J
mik
, 1.
3 =
O. 7
5 1.
3 =
0.7
5
',=
e/2
.Jm
7k,
= 1
.00
" =
e/2.
Jm7k
, =
1.0
0
0::
= 1
.25
0::
= 1
.25
0 1.
2 =
1.5
0 0
1.2
= 1
.50
f-=
1.7
5 f-
= 1
.75
<..>
<..>
~
1.1
= 2
.00
5
0.0
~
= 2
.00
=
2.2
5 1.1
V
y =
2.2
5
>-=
2.5
0
>-=
2.5
0
I::i.
f- -.J
1.0
=3
.00
I:
:i.
f- :::::i
1.0
=
3.0
0
~
~
0::
g 0
.9
0::
g 0
.9
0 0
f-0
r-1
0.0
0
u u
~
~
0.8
<
! ~
0.8
IJ.
..
>-Z
>-
5.0
z
f-o
0.7
r-
o 0
.7
-.J
f--.
J f-
~
<!
~
<!
U
0::
0.6
u
2.0
~
0.6
::>
<
! ::>
0
>
0 >
Z
~
0.5
z
1.0
~
0.5
<
! <
! W
f-
w
f-:::!
: z
:::!:
~
0.4
w
0
.5
u u
iL:
0.3
iL:
0
.3
IJ...
IJ...
°T ~I w
w
8
0.2
0
.2
8 0
.2
0.1
0.1
0.
1
0::
' I
I I I
I I
I , I'
I ,
I 0
0.0
5
0 0.
1 0
.2
0.5
1.
0 2
.0
0.1
0.2
0
.5
1.0
2.0
0.
1 0
.2
0.5
1.
0 2
.0
0.1
0.2
0
.5
1.0
2.0
TI
(SE
C.
) TI
(S
EC
.)
TI
(SE
C.
) TI
(S
EC
. )
FIG
. 8
b
MEA
N
DU
CT
ILIT
Y
FAC
TO
RS
AN
D
CO
RR
ESP
ON
DIN
G
FIG
. 8
e
MEA
N
DU
CT
ILIT
Y
FAC
TO
RS
AN
D
CO
RR
ESP
ON
DIN
G
CO
EF
FIC
IEN
TS
O
F V
AR
IAT
ION
FO
R
OR
IGIN
-C
OE
FF
ICIE
NT
S
OF
VA
RIA
TIO
N
FOR
O
RIG
IN-
OR
IEN
TE
D
MO
DEL
H
AV
ING
D
IFF
ER
EN
T
STR
EN
GT
H
OR
IEN
TE
D
MO
DEL
H
AV
ING
D
IFF
ER
EN
T
STR
EN
GT
H
LE
VE
LS
LE
VE
LS
TY
PE
D
E
AR
TH
QU
AK
E
',= 0
.05
p
= I. 9
p
y c
v =
IO.O
v
y c
1.4
20
0.0
1
fL ~
v (
I )m
a,/
vc
j --~ ~0.50mOgo
T, =
2 "IT
.;;;;
7k,
1.3
= 0
75
~, =
c/2
,;m
7k,
=
1.0
0
10
0.0
I I
a::
= 1
.25
~,
, 1.
2 0
= 1
.50
f-=
'.7
5
U
50
.0 1
" V,
'.
.J
i1: =
2.0
0
I
I
1.1
Vc
Vy
=2
.25
>- f-
l:::l
~ \.
--
l 1.
0
i=
~
0.9
a::
0 f-
10
.0
0
U
LL
« o
0.8
LL
5.0
z
>-0
f-f-
--l
« i=
u
2.0
~
0.6
:::
J 0
>
z 1.
0 ~
0.5
« w
f-
::!!:
r5 0
.4
0.5
u iJ::
0
.3
LL
W
0.2
1
"I\(
?~\'
.I
8 0
.2
0.1
1
'\~~~ I
0.1
0.0
5 I
I
I I
I I
t I
I t I!!
I I -
I 0
0.1
0.2
0
.5
1.0
2.0
0.
1 0
.2
0.5
1.
0 2
.0
T,
(SE
C.
) T,
(
SE
C.)
FIG
0 8
d
MEA
N
DU
CT
ILIT
Y FACT~)RS
.A.N
D C
OR
RE
SPO
ND
ING
C
OE
FF
ICIE
NT
S
OF
VA
l:C
NI 'I
Oi'i
f FO
R.
OR
IGIN
·O
RIE
NT
ED
lv
(OD
EL
H?c
JIIl
·]G
D
IPF
ER
EN
'T
STR
EN
GT
H
LE
VE
LS
TY
PE
B
02
EA
RT
HQ
UA
KE
',= 0
.05
p
= 1.9
p
v =
10.O
v
y c
Y
c
1.4
fL ~
v (
t)m
ax/v
C
--~ =
0.5
0m
Ogo
2
00
.0
T, =
2 "IT
.;;;;
7k,
1.3
= 0
.75
~, =
c 1
2 ,;m
7k,
= '
.00
10
0.0
a:
: =
'.2
5
1.2
0 =
'.5
0
f-=
1.7
5 U
5
0.0
Lt
f =
2.0
0
1.1
Vy
, =
2.2
5
I >-
I =
2.5
0
l:::l
f-1.
0 ,
= 3
.00
--
l I
~
I
a::
I
g 0
.9 \
I
0 ,
f-1
0.0
0
, U
,
« L
L
LL
0
>-5
.0
z f-
~
0.7
--
l f-
~
« u
2.0
a:
: :::
J «
0 >
z
1.0
~
0.5
« W
f-
::!!:
r5 0
.4
0.5
u LL
0
.3
LL
w
0.2
8
0.2
0.1
t=
0.1
0.0
5 0.1
0.2
0
.5
1.0
2.0
0.
1 0
.2
0.5
1.
0 2
.0
T,
(SE
C.
) T,
(S
EC
.)
FIG
. 8
e
MEA
N
DU
CT
ILIT
Y
FAC
TO
RS
AN
D
CO
RR
ESP
ON
DIN
G
CO
EF
FIC
IEN
TS
O
F V
AR
IAT
ION
FO
R
OR
IGIN
O
RIE
NT
ED
M
OD
EL
HA
VIN
G
DIF
FE
RE
NT
ST
RE
NG
TH
L
EV
EL
S W
-..
J
w
TY
PE
A
E
AR
TH
QU
AK
E
00
TY
PE
A
E
AR
TH
QU
AK
E
{,o
:O.0
2
T 2 .. ./
2T
, p.
:: 2
p. y
c e-,
= 0
.02
T2=~T,
p =
3p
y
c
20
0.0
T.
= 21
f'../
m/k
7,
1.3
--
~ =
05
0 m
VQO
20
0.0
T2
= 2
7r.,
;m7k
2
'T --
Py=
0.5
0m
Vgo
1
00
.0 T
r-
T, =
27r.
jiTi7
k,
--
=0.
75
= 1
.00
T, =
2 7r
.jiTi
7k,
--
=0.
75
~,=
c/2
./rTi
Ik,
a:
1.2
= 1.1
25
10
0.0
~,
= c/2
./rTi
Ik,
~ 1.
2 =
1.0
0
~ =
1.25
=
1.12
5
50.0~-+
P Yk 4k ,
~ -( 1
= 1
.50
j'k,
/ =
1.25
U
I.
, 5
0.0
I,
--(
1
~
1.1
= 1
.50
/':;:
'k
fJ. =
, , m
ox Iv
y ~
= I. 7
5 /':
;:'k
fJ.
=v
I m
ox/v
y P,
/'-r z
/'-r 2
u.
=
I. 75
L_
--L
_
~
1.0
1::1..
Vc
Vy
I::l..
Vy
~
1.0
20
.0
-l
20
.0
:J
a:
t; 0
.9
a:
t 0
.9
0 .... 1
0.0
:::>
0
u 0
I-1
0.0
:::>
Lt u.
0
.8
u 0
0 ~
u.
0.8
>-5
.0
5.0
0
I-~
0.7
>-
~
0.7
I-
-l
i=
-l
i=
I-<t
0
.6
i=
u 2
.0
u <t
0
.6
:::>
a:
:::>
a:
0 <t
0
<t
Z
1.0
>
0
.5
z >
0
.5
<t
lI..
1.0
lI..
0 <t
0
LtJ
LtJ
~
I-0
.4
~
I-0
.4
0.5
z
0.5
z
LtJ
LtJ
U
0.3
U
0
.3
lI..
lI..
0.2
!---
lI..
0.2
lI.
.
~
0.2
~
0.2
U
U
°t:
0.1
0.1
0.1
0.0
5
I II
I
I I
I II
I I
I 0
.05
0
0.1
0.2
0
.5
1.0
2.0
0
.2
0.5
1.
0 2
.0
0.1
0.2
0
.5
1.0
2.0
0.
1 0
.2
0.5
1.
0 2
.0
TI
(SE
C.)
T,
(S
EC
.)
TI
(SE
C.)
TI
(S
EC
.)
FIG
. 9
a
MEA
N
DU
CT
ILIT
Y
FAC
TO
RS
AN
D
CO
RR
ESP
ON
DIN
G
FIG
. 9
b
MEA
N
DU
CT
ILIT
Y
FAC
TO
RS
AN
D
CO
RR
ESP
ON
DIN
G
CO
EF
FIC
IEN
TS
O
F V
AR
IAT
ION
FO
R
TR
ILIN
EA
R
CO
EF
FIC
IEN
TS
O
F V
AR
IAT
ION
FO
R
TR
ILIN
EA
R
ST
IFF
NE
SS
D
EG
RA
DIN
G
MO
DEL
H
AV
ING
D
IFF
ER
EN
T
ST
IFF
NE
SS
D
EG
RA
DIN
G
MO
DEL
H
AV
ING
D
IFF
ER
EN
T
STR
EN
GT
H
LE
VE
LS
STR
EN
GT
H
LE
VE
LS
TYPE
A
EA
RTH
QU
AK
E TY
PE
A E
AR
THQ
UA
KE
e- 1=O
.02
T
2 =
2T
I P
=
2 p
e- 1=
O.0
2
T2
= 2
TI
P
= 3
p
y c
y c
10
0.0
1
00
.0
T 2 =
2 ".
. ..,/i
TlTk
2
--
P. =
05
0 m
Vgo
T2
= 2"
....,/
iTlT
k 2
--
P. =
05
0 m
V90
50
.0 f
----
T, =
2 ".
...;m
7ii,
1.3
--
Y=0
.75
T, =
2 1T
..;m
7ii,
'l --
Y=
0.75
=
1.0
0 5
0.0
(,
=e/
2.jI
TiI
k,
= 1
.00
(, =
e/2
JIT
ilk,
= 1.
125
= 1.
125
a::
1.2
= 1
.25
~
1.2
= 1
.25
0 =
1.5
0 =
1.5
0 I-
20
.0 I-
--\-
0 \-;-
----...
-.:r;;
,LL =
v \!
)m
ax
I V
y -l
t)
I I
= 1
.75
20
.0
~
1.1
= 1
.75
~
u..
lo.ob
\
Vy
Vy
>-I:::
\...
.... ~
1.0
I:::
\...
10
.0
I-1.
0
--l
--l
a::
I-0
.9
a::
5.0
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0.9
0
5.0
t)
0 t)
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I-
:::>
t)
Cl
0.8
t)
Cl
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<t
u..
0.8
u.
. u..
u.
. 2
.0
0 2
.0
0 >-
>-I-
~
0.7
I-
~
0.7
--
l --
l
i=
10
I-
i=
1.0
l-
t)
<t
0.6
t)
<t
0.6
:::>
a::
:::>
a::
C
l <
t C
l 0
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<t
0.5
>
0.5
>
0
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z z
<t
u..
<t
u..
w
0 w
0
::!!:
I-0
.4
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0.2
z
0.2
z
w
w
t)
0.3
t)
0.3
0.1
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0.
1 u.
. u.
. u.
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0.2
~
0.2
0.0
51
t)
0.0
5
t)
0.1
0.1
0.0
2 !
, I
! I
I I
I I! III
I I
I 0
.02
0
0.1
0.2
0
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1.0
2.0
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0.5
1.
0 2
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0.1
0.2
0
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1.0
2.0
0.
1 0
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0.5
1.
0 2
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TI
(SE
C.
) T
I (
SE
C.)
T
I (S
EC
.)
TI
(SE
C.)
FIG
. 9
c
MEA
N
DU
CT
ILIT
Y
FAC
TO
RS
AN
D CO~RESPONDING
FIG
. 9
d
MEA
N
DU
CT
ILIT
Y
FAC
TO
RS
AN
D
CO
RR
ES
PO
ND
ING
C
OE
FF
ICIE
NT
S
OF
Vi',
RIA
TIO
N
FOR
T
RIL
INE
AR
C
OE
FF
ICIE
NT
S
OF'
V
AR
IAT
ION
F
OR
T
RIL
INE
AR
S
TIF
FN
ES
S
DE
GR
AD
ING
J'
:F);
':)E
;L
HA
VIN
G
DIF
FE
RE
NT
S
TIF
FN
ES
S
DE
GR
AD
ING
M
OD
EL
HA
VIN
G
DIF
FE
RE
NT
sr
J'RE
NG
rl'H
L
EV
EL
S
S'l'R
EN
GT
B
LE
VE
LS
w
\.0
I::i
..
lr
o I o Li: > I- ...J i=
o :::>
o z <X:
w
::E
TYPE
B
EA
RTH
QU
AK
E
'1=
0.0
2
T2 =
./2
TI
20
0.0
" -----------,
10
0.0
50
.0
T 2: 2
7f F
mTk2
T,
: 2
Tr.j
iTi7
k,
~,:
c/2
./iiiT
k,
Py~ /
jk,
~ _
I. 3k
/-
L: v
(tl
mo
x/V
y
~ ./,
2
"--
--V
c Vy
5.0
I
'< "\
2.0
I
.• '.
. \:,
\
0.5
1
".:c ....
. ' .....
. '" 1
0.2
1
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0.1
~I ------------------~
0.0
5!
I!
I I
[ I
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[ I
I t
I
0.1
0.2
0
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1.0
2.0
T,
(S
EC
.)
1.3
~
1.2
I- ~
1.1
IJ... >- t::
1.0
...J i=
o 0
.9
:::>
o IJ...
O.B
o ~
0.7
!i lr
<X:
0.6
>
0.5
IJ.
.. o I-0
.4
z w
o 0
.3
IJ...
IJ... w
0.2
o o
0.1
P =
2 P
y
c --
p. :0
.50
mVg
O
--
Y:0
.75
:
1.00
:
1.12
5 :
1.25
:
1.50
:
1.75
0.2
0
.5
1.0
2.0
T,
(SE
C.)
FIG
. lO
a
MEA
N
DU
CT
ILIT
Y
FAC
TO
RS
AN
D
CO
RR
ESP
ON
DIN
G
CO
EF
FIC
IEN
TS
O
F V
AR
IAT
ION
FO
R
TR
ILIN
EA
R
ST
IFF
NE
SS
D
EG
RA
DIN
G
MO
DEL
H
AV
ING
D
IFF
ER
EN
T
STR
EN
GT
H
LE
VE
LS
::i..
a::
o I o Lt > I- ...J
I o :::> a z <! w
::E
TYPE
B
EA
RTH
QU
AK
E
'1=
0.0
2
T2 =
./2
TI
20
0.0
" ------------,
1.0
0.5
1
"II,,'
..:"
' ...
...
"I
0.2
1
......
.. 1
0.1 cL~----------------~
0.0
5'
! I
, I!!
I I
!!
, I
I
0.1
0.2
0
.5
1.0
2.0
T,
(S
EC
.)
1.3
a::
1.2
o I- ~
1.1
~ '
1.0
...J i=
0.9
o :::>
o
0.8
IJ.
.. o ~
0.7
i=
~
0.6
lr
<X
: >
0.5
IJ.
.. o I-0
.4
z w
o IJ...
IJ...
W
0.2
o o
0.1
P y =
3 P
c --
p.:
0.5
0 m
Vgo
--
Y:0
.75
:
1.0
0
: 1.
125
: 1.
25
: 1
.50
:
I. 7
5
0.2
0
.5
1.0
2.0
T,
(S
EC
.)
FIG
. lO
b
MEA
N
DU
CT
ILIT
Y
FAC
TO
RS
AN
D
CO
RR
ESP
ON
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G
CO
EF
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IEN
TS
O
F V
AR
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ION
FO
R
TR
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R
ST
IFF
NE
SS
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EG
RA
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G
MO
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AV
ING
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EN
T
STR
EN
GT
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LE
VE
LS
~
o
TYPE
B
EAR
THQ
UAK
E 'I
=0
. 0
2
T2
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Tj
p =
2
P
Y
c
10
0.0
T2
= 2
7r,J
m7i
i2
1.3
--
p. =
05
0 m
V90
50
.0 ~ T,
=27
rJni
Tk,
--
Y=
0.7
5
= 1
.00
,,=
c/2
.,/m
7k,
rr
1.2
= 1.
125
PI j'k
, /
= 1
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0 =
1.5
0 y
I, _
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I-2
0,0
I--
\---
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~
1.1
= 1
.75
, LA
.. Y
c Y
y
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1
0.0
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rr
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0 5
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Cl
08
« LA
.. LA
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0
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0.6
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C
l 0
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« z
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0
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0.2
z w
u
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0.
1 I
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LL
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U
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0
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2 0
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1.0
2.0
TI
(SE
C.
) T
I (S
EC
. )
FIG
. lO
c
MEA
N
DU
CT
ILIT
Y
FAC
TO
RS
AH
D
CO
RR
ESP
ON
DIN
G
CO
EF
FIC
IEN
TS
O
F V
AH
IAT
I·JN
FO
R
TR
ILIN
EA
R
ST
IFF
NE
SS
D
EG
RA
DIN
G
MO
DEL
H
AV
ING
D
IFF
ER
EN
T
STR
EN
GT
H
LE
VE
LS
TYPE
B
EA
RTH
QUA
KE
'1=
0.0
2
T2 =
2 T
I P
=
3p
y
c
10
0.0
T2
= 2
7r..,
/ii17k
2
''t --
p. =
05
0 m
V90
T,
= 2
7r .J
rilTk ,
--
Y=
0.7
5
50
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" =
c/2.
,/m7k
, =
1.0
0
g 1.
2 =
1.12
5 =
1.2
5 =
1.5
0 2
0.0
~
1.I
= 1
.75
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Yy
~
1.0
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1
0.0
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rr
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0 5
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u I-
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u C
l 0
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0
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0 I-
u «
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C
l 0
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« z
> 0
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0
~
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0.2
z w
U
0
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LA.. ~
0.2
0.0
5
U
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0.0
2
0 0.
1 0
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0.5
1.
0 2
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0.1
0.2
0
.5
!.O
2.0
TI
(SE
C)
TI
( S
EC
)
FIG
. lO
d
MEA
N
DU
CT
ILIT
Y
FAC
TO
RS
AN
D
CO
RR
ESP
ON
DIN
G
CO
EF
FIC
IEN
TS
O
F V
AR
IAT
ION
FO
R
TR
ILIN
EA
R
ST
IFF
NE
SS
D
EG
RA
DIN
G
MO
DEL
H
AV
ING
D
IFF
ER
EN
T
STR
EN
GT
H
LE
VE
LS
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TYPE
C
EA
RTH
QU
AK
E
'1=
0.0
2
T 2=
V2
TI
P
= 2
P
y c
20
0.0
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271
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1.
3 --
R =
05
0 m
V90
100.0~ T
, =
271'
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k,
--
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1.0
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2 =
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25
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5 P y
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vy
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2
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Vy
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1.
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TI
(SE
C.)
TI
(S
EC
.)
FIG
. ll
a
MEA
N
DU
CT
ILIT
Y
FAC
TO
RS
AN
D
CO
RR
ESP
ON
DIN
G
CO
EF
FIC
IEN
TS
O
F V
AR
IAT
ION
FO
R
TR
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EA
R
ST
IFF
NE
SS
D
EG
RA
DIN
G
MO
DEL
H
AV
ING
D
IFF
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EN
T
STR
EN
GT
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LE
VE
LS
TYPE
C
EA
RTH
QU
AK
E
'I =
0.0
2
T =
./2
T
2 I
P
= 3
p
Y
c
20
0.0
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2 7
1'./i
TiTk
2
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R =
0.5
0 m
V90
T,
= 2
7T./ri
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--
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1
00
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= 1
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c/2
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1.
2 0
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50
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) U
1.
1 =
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0 /::
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fL =
v t
max
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75
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2
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10
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0.3
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0.2
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0.2
u
0.1
0.
1
0.0
5 0.1
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0
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2.0
0.
1 0
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0.5
1.
0 2
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TI
(SE
C.)
TI
(S
EC
.)
FIG
. ll
b
MEA
N
DU
CT
ILIT
Y
FAC
TO
RS
AN
D
CO
RR
ESP
ON
DIN
G
CO
EF
FIC
IEN
TS
O
F V
AR
IAT
ION
FO
R
TR
ILIN
EA
R
ST
IFF
NE
SS
D
EG
RA
DIN
G
MO
DEL
H
AV
ING
D
IFF
ER
EN
T
STR
EN
GT
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LE
VE
LS
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TYPE
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KE
TYPE
C
EA
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AK
E '1
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3 p
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c Y
c
10
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1
00
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Tr Jf
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2
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50
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125
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25
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1 0
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(SE
C.)
T
I (S
EC
.)
TI
l S
EC
.)
TI
( S
EC
.)
FIG
. ll
c
I~AN
DU
CT
ILIT
Y
FAC
TO
RS
AN
D
CO
RR
ESP
ON
DIN
G
FIG
. ll
d
MEA
N
DU
CT
ILIT
Y
FAC
TO
RS
AN
D
CO
RR
ESP
ON
DIN
G
CO
EF
FIC
IEN
TS
O
F V
AR
IAT
ION
FO
R
TR
ILIN
EA
R
CO
EF
FIC
IEN
TS
O
F V
AR
IAT
ION
FO
R
TR
ILIN
EA
R
ST
IFF
NE
SS
D
EG
RA
DIN
G
MO
DEL
H
AV
ING
D
IFF
ER
EN
T
ST
IFF
NE
SS
D
EG
RA
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G
MO
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H
AV
ING
D
IFF
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T
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EN
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H
LE
VE
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STR
EN
GT
H
LE
VE
LS
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PE
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ARTH
QUA
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TYPE
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EA
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QU
AK
E
e- 1=O
.02
T z =
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TI
p =
2 p
e- 1=
O.0
2
T Z =
../2
TI
P =
3p
y
c y
c
20
0.0
2
00
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T2 =
211'
Fm
Tk2
1.
3 -
R =
0.5
0 m
V90
T2 =
211'
Fm
Tk2
13~
--
R =
0.5
0 m
V90
10
0.0
c----
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= 2
11'
./rii7
k,
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5
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2 7
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--
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5
= 1
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1
00
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riiT
k,
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1.2
= 1
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gs 1.
2 \
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0
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50
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---
P y
u 1.1
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1.5
0 5
0.0
y
I, _
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0
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~ 1.
75
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max
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2
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8
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11
11
1
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(SE
C.)
T
I (S
EC
.)
TI
(SE
C.)
T
I (S
EC
.)
FIG
. 1
2a
MEA
N
DU
CT
ILIT
Y
FAC
TO
RS
AN
D
CO
RR
ESP
ON
DIN
G
FIG
. 1
2b
M
EAN
D
UC
TIL
ITY
FA
CT
OR
S A
ND
C
OR
RE
SPO
ND
ING
C
OE
FF
ICIE
NT
S
OF
VA
RIA
TIO
N
FOR
T
RIL
INE
AR
C
OE
FF
ICIE
NT
S
OF
VA
RIA
TIO
N
FOR
T
RIL
INE
AR
S
TIF
FN
ES
S
DE
GR
AD
ING
M
OD
EL
HA
VIN
G
DIF
FE
RE
NT
S
TIF
FN
ES
S
DE
GR
AD
ING
M
OD
EL
HA
VIN
G
DIF
FE
RE
NT
ST
RE
NG
TH
L
EV
EL
S ST
RE
NG
TH
L
EV
EL
S
TYPE
D
EAR
THQ
UAK
E ';1
=0
.02
T
2 =
2T
I P
=
2
P
y c
10
00
T2
= 27
1'..j
iii7k
2
1.3
--
P. =
0.5
0 m
V90
50
.0 f
---
T, =
271
'../ri
iTk,
--
Y=
0.7
5
',=
c/2
.Jm
7k,
= 1
.00
a::
1.2
= 1
.125
R~M
= 1
.25
0 2
0.0
f---;
/ '~
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I-=
1.5
0 ~
1.1
= 1
.75
C
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I 2
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LL
Vy
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1.0
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00
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it LL
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=>
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> 0
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0
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LL
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5 I
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0.0
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l II
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0.1
0.2
0
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1.0
2.0
TI
(SE
C.
) T
I (
SE
C.)
FIG
. 1
2c
MEA
N
DU
CT
ILIT
Y
FAC
TOR
.S
AN
D
CO
RR
ESP
ON
DIN
G
CO
EF
FIC
IEN
TS
O
F V
AR
I1\T
ION
FO
R
TR
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EA
R
ST
IFF
NE
SS
D
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A_D
ING
M
GO
BL
HA
VIN
G
DJ:
FF'E
R'E
NT
ST
RE
NG
TH
L
EV
EL
S
TYPE
D
EA
RTH
QU
AK
E ';
1=
0.0
2
T2
= 2
lj
P
= 3
p
y c
10
0.0
T2
= 27
1'..j
iii7k
2
'l --
p. =
05
0 m
V90
T,
= 2
71' ..
/riiT
k ,
--
Y=
07
5
50
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" =
c/2
Jm
7k,
=
1.0
0
I. 2
\ =
1.1
25
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, /'
a::
0
= 1
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I-=
1.5
0 2
0.0
C
,.)
1.1
= I.
75
./
,
2 <
! LL
Vc
Vy
>-
I:::i.
. 1
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,
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0 0.
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0 2
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0.1
0.2
0
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2.0
TI
(SE
C.
) T
I (S
EC
.)
FIG
. 1
2d
M
EAN
D
UC
TIL
ITY
FA
CT
OR
S A
ND
C
OR
RE
SPO
ND
ING
C
OE
FF
ICIE
NT
S
OF
VA
RIA
TIO
N
FOR
T
RIL
INE
AR
S
TIF
FN
ES
S
DE
GR
AD
ING
M
OD
EL
HA
VIN
G
DIF
FE
RE
NT
ST
RE
NG
TH
L
EV
EL
S
,):>.
U1
TY
PE
B
02
E
AR
THQ
UA
KE
~1=O
.O2
T2 =
..!2
TI
P
= 2
p
y c
20
0.0
T2
= 2
7T
.Jm
7k2
1.3
--
p. =
0.5
0 m
V90
I 00
. o
.l--
----
T, =
2 7r
...;m
7i<,
--
Y=
0.7
5
= 1
.00
~, =
cf 2
.,(rii
7k,
~
1.2
= 1.
125
0
P~~
I-=
1.2
5 ()
= 1
.50
50
.0 I
--\:
--Y
/
'%
ii =
" (t
) Iv
Li:
1.1
c.:Jk
m
ax
y =
1.7
5 /,
2
I::L
>- I-1.
0 2
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J ~
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()
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J ()
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O
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0.5
1.
0 2
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0.2
0
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1.0
2.0
TI
(SE
C.)
TI
(S
EC
.)
FIG
. 1
3a
MEA
N
DU
CT
ILIT
Y
FAC
TO
RS
AN
D
CO
RR
ESP
ON
DIN
G
CO
EF
FIC
IEN
TS
O
F V
AR
IAT
ION
FO
R
TR
ILIN
EA
R
ST
IFF
NE
SS
D
EG
RA
DIN
G
MO
DEL
H
AV
ING
D
IFF
ER
EN
T
STR
EN
GT
H
LE
VE
LS
TY
PE
B
02
E
AR
TH
QU
AK
E
e- 1=
O.0
2
T2 =
..!2
TI
p =
3p
y
c
20
0.0
T2 =
2 7
T.J
m7k
2
'T --
p. =
0.5
0 m
V90
T, =
2 7r
...;m
7i<,
:~ ~ -
-Y
=0.7
5 1
00
.0
~
= 1
.00
0 =
1.12
5 I-
jk,
/ ()
= 1
.25
50
.0
« =
1.5
0 I,
__
(
) u..
/
~k
I'-=
V 'm
ax
Ivy
= 1
.75
/T 2
>-
I::L
t: V
y ..
J 1.
0 2
0.0
;::
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g 0
.9
0 I-1
0.0
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()
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O.S
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0
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z 1
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0.5
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1
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0
0.0
5
I 0.
1 0
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0.5
1.
0 2
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0.1
0.2
0
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1.0
2.0
TI
(SE
C.)
T
I (S
EC
.)
FIG
. 1
3b
M
EAN
D
UC
TIL
ITY
FA
CT
OR
S A
ND
C
OR
RE
SPO
ND
ING
C
OE
FF
ICIE
NT
S
OF
VA
RIA
TIO
N
FOR
T
RIL
INE
AR
S
TIF
FN
ES
S
DE
GR
AD
ING
M
OD
EL
HA
VIN
G
DIF
FE
RE
NT
ST
FBN
GT
H
LE
VE
LS
"'" (j\
TYPE
B
02
EA
RTH
QU
AK
E ';1
= 0
02
T
2 =
2T
I P
=
2 P
y
c
10
0.0
T2
~27T
Fm7k
2 I
3 --
p. ~
0.5
0 m
V90
50
.0 f
----
T, ~
27T
./rTi
Tk,
--
Y~0.
75
~ 1.
00
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/2 J
m7k
, 1.
2 ~
1.12
5 a::
:
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~
0 ~
1.50
2
0.0
~
D f-
/ '~;'--jL:V(I)mox/Vy
l- <..)
1.1
:
1.75
./
,
2 <
{ -'-
----
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Vy
>-I:::
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10
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0
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0
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o 0
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u..
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0
>- I-~
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i=
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{ 0
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=>
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0 <
{ 0
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>
0.5
z <
{ u..
w
0
~
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0.2
z w
<
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0.3
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0.0
51
<
..)
0.1
0.0
2l
1 I
I I I
I
I "
I I I
I I
0 0.
1 0
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0.5
1.
0 2
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0.1
0.2
0.
5 1.
0 2.
0
TI
(SE
C.
) T
I (
SE
C.)
FIG
. 1
3c
lVlE
AN
DU
CT
ILIT
Y
Fli
Cl'
OR
S
l\~\
TD
CO
RR
ESP
ON
DIN
G
CO
EFE
'ICIE
N::'
:'S
OF
VIJ,
.R~~
.:::
TI(i
N FO
R
TR
ILIN
El-
1R
STIF
F)\1
ESS
DEGRAD~-i\iC
j'/iC
;')F
":
I-lA
ITTN
C D
TE"F
EREN
'? S'
l'REN
GTI
-I L
EV
EL
S
TYPE
B
02
EA
RTH
QU
AK
E ';
1=
0.0
2
T2
= 2
TI
P
= 3
p y
c
10
0.0
T2~27TFm
7k2
''t --
p. ~050 m
VgO
T, ~
2 7T
./rT
iTk,
--
Y~0.
75
50
.0
~ 1.
00
" :c
/2Jm
7k,
1.2
: 1.
125
a::
: 1.
25
0 :
1.50
I-
20
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:
I. 75
<
{ u..
Vy
>-1:
:1..
10
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0
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a::
i=
0.9
0
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<
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l-=>
<
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o 0
8
<{
u..
u..
.
2.0
0
>- I-~
0.7
--1
i=
1.0
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<{
0.6
=>
a::
0
<{
0.5
>
0
.5
z <{
u..
w
0
~
I-0
.4
0.2
z w
(3
0
.3
0.1
u..
u.. ~
0.2
0.0
5
<..
)
0.1
0.0
2
0 0.
1 0
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0.5
1.
0 2
.0
0.1
0.2
0
.5
1.0
2.0
TI
( S
EC
.)
T,
(SE
C.)
FIG
. 1
3d
M
EAN
D
UC
TIL
ITY
FA
CT
OR
S A
ND
C
OR
RE
SPO
ND
ING
C
OE
FF
ICIE
NT
S
OF
VA
RIA
TIO
N
FOR
T
RIL
INE
AR
S
TIF
FN
ES
S
DEG
RA
DIN
G
MO
DEL
H
AV
ING
D
IFF
ER
EN
T
STR
EN
GT
H
LE
VE
LS
"'" -...J
48
5.0~~~----~--~----~--~--~----~------~~
_ fL q =-=-
}L
1.4
4.0 t-----+-----+-----+-----+---+----j------+---+-f-+_ I. 3
1.2
1.1
1.0 o ~ 3.0~---+---~----~----+--4--~--~yy~+-~~~
c:: a:: o tU
~ >=
0.8
0.7
0.6
0.5 ~ 2.0t-----+---~----~----+_-4~~77~~~~~~~
0.4 -I
~ U :::> o
0.3
0.2
0.1
1.0 c= 0 =--r---+------+-----~ 0
0.1
0.2 0.3
0.4 0.5 0.6
0 0.05 0.2 0.4 0.6 0.7 0.8 0.9 0.95
PROBABILITY DISTRIBUTION FUNCTION, P(q])
FIG. 14 PROBABILITY DISTRIBUTION FUNCTIONS FOR DUCTILITY FACTOR RATIOS ON GUMBEL PLOTS
10
CD
::i..
0:: o t O ~
> t- -.-J 1=
o ::>
o
TYPE
A
EA
RTH
QU
AK
E
'=0
.02
T
=.I
2T
p
=2
p
I 2
lye
20
0.0
.-, ------------,
T, =
2 ...
.jffi
7k,
T, =
2 ... .J
rii7k,
e, = c
12 ../
riiIk,
jk,
//
Ir
T
_ I
0ik
, 1
'-.5
-v .
5
Vy
'/
I
Vy
0.5
1
"" ~'._ ...
... I
0.2f
--1 ---------1
0.1
f-I -----------1
0.0
51
[ I
! I
I I
I I
I , I!
I I
!
'=0
.02
T
=
-i2
T.
p =
3p
I
2 lye
--
R =
0.5
0 m
Vgo
--
Y=
0.7
5
L\
= 1
.00
=
1.1
25
= 1
.25
=
1.5
0 =
I. 7
5
0.1
0.2
0.5
1.
0 2
.0
0.1
0.2
0
.5
1.0
2.0
T
I (S
EC
.)
FIG
. 15
0.
RE
SPO
NSE
D
UC
TIL
ITY
Fl
,C'I'
OR
S FO
R
85
9 6
LE
VE
L
ON
PRO
B1.
l,13I
LI':
:'Y
DIS
TR
IBU
TIO
N
FUN
CT
ION
S
III ex>
::i..
0::
0 t- O
<t
ll.. >- t- -.-J i=
0 ::>
0
TYPE
A
EA
RTH
QU
AK
E
'1=
0.0
2
T2
=2
TI
Py =
2p c
10
0.0
,r-----------,
T, =
2 7T
.;;;
;7k,
50
.0
20
.0
10
.0 t\
\ ~ l(
/ -yk
, '~
lie
V
y
5.0
2.0
t-"',
1.0
0.5
0.2
0.1
0.0
5
0.0
2'
I I
I I!
I !
!! I!'
! I
'1=
0.0
2 T2
=2~
P y =
3P c
--
R =
0.5
0 m
Vgo
--
y=
0.7
5
I \
= 1
.00
\
= 1
.125
= 1
.25
=
1.5
0
= I.
75
0.1
0.2
0.5
1.
0 2
.0
0.1
0.2
0.5
1.0
2.0
TI
(S
EC
.)
FIG
. 1
5b
R
ESP
ON
SE
DU
CT
ILIT
Y
FAC
TO
RS
FOR
85
%
LE
VE
L
ON
P
RO
BA
BIL
ITY
D
IST
RIB
UT
ION
FU
NC
TIO
NS
..,. ~
50
CQ
~ I-« !l::
I l-e.!)
Z w !l:: I-(f)
0 w !l:: ::; 0 w !l::
CQ
~ I-« !l::
I I-(!)
z W !l:: I-(f)
0 w ~ ::> 0 w !l::
f1, =2 80 T2 = ./2T,
Py = 3 Pc
1.7 (0 )
1.6
1.5 /
/
\ 1.4
,
1.3
1.2
1.1
1.0.
0.9
0..8
0.7
0.6
0..5
fL80 = 2 T2 = .j2 T,
Py = 2 Pc
( b)
~ , , \
\
~~. / \\ \\
'\\ ~\ \\ \\
\\ \
\ I I I I j
fL80 .= 2
(c)
\ \ \
fL80 = 2
(d) -- TYPEA -- TYPE B -.- TYPE C
----- TYPE D
Py {3=--=
m Vgo
0..1 0..2 0.5 0..1 0..2 0..5 0.1 0..2 0..5 0..1 0..2 0..5
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0.
0..9
0..8
0..7
0..6
0..5
fL80= 4 T2 =./2 T,
Py = 3Pc
(0 )
~ '\~\
\\ '\~ \\~
\'~ .~
f\ \ \
[ [ [ 1[[
TI (SEC.)
fL80=4 T2 =./2T,
Py = 2 Pc
( b)
, , .~ ~ \
,\ \\ \\ \:~ . ..
I [ I 1\.1 I
fL80 = 4 T2 = 2T,
Py = 3 Pc
(c)
\
~ '\ '\ \\
\';\ \ \ .-
I \ I I II
fL80 =4 T2 = 2T,
Py = 2 Pc
(d) -- TYPE A -- TYPE B
1----.- TYPEe
----- TYPE D
I--- Py {3=~
I--- m Vgo
,
~ \'\\, \~l
\\ \~ \,
I \~I I I I I 0..1 0..2 0..5 0..1 0..2 0..5 0..1 0..2 0..5 0..1 0..2 0..5
TI (SEC.)
FIG. 16 REQUIRED STRENGTH RATIOS FOR STRUCTURAL MODELS, DUCTILITY FACTORS, PROBABILITY DISTRIBUTION LEVELS AND EARTHQUAKE TYPES INDICATED
en.
Q f-<l: a::: I f-(!)
Z w a::: f-en 0 w a::: :::J CI w a:::
52 ~ 0::
:r: I<.!l
j-L8s=2 T2 =J2T,
1.7 Py =3pc
( 0 )
1.6
,'I. I \
1.5
14
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.2 0.5 0.1
~8S=4 T2 =v'2T,
I. 5 .-___ --'P ,,-=_3_P...:.c-,
(0 ) 14 r---------j
1.3 1----------1
I. I v----'~----___I
j-L 8S=2 T2 = f2T, j-L8s=2 T2 = 2 T, j-L85 =2 T2 = 2 T,
Py = 2 Pc P y = 3 Pc Py = 2 Pc
(b) (c) (d)
-- TYPE A -- TYPE B
_.- TYPE C
----- TYPE D
f3=~ m Vgo
0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5
TI (SEC)
~8S=4 T2=f2T, P, =2P c .-___ P'-','--=_3_P...:.C -, P, = 2 Pc
(b) (C) (d) --TYPE A -- TYPE B _.- TYPE C
------ TYPE D
f3=+ m Vgo
I---------l ,
~ I.Or-----;h\r----j I 1--';--------: 0:: Ien o W 0::
0.9 r------1-\1r----j
::> 0.8 f----11\\-----1 c w 0::
0.7 r------\---'<------i
0.6 1----------1
O. 5 L---'---'-.LL...LL.LL~ 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5
T, (SEC)
FIG. 17 REQUIRED STRENGTH RATIOS FOR STRUCTURAL MODELS, DUCTILITY FACTORS, PROBABILITY DISTRIBUTION LEVELS AND EARTHQUAKE TYPES INDICATED
51
52
1.7
1.6
1.5
Ql. 1.4
0 i= 1.3 <t 0:
I 1.2 I-l? Z w 1.1 0: I-(f)
1.0 0 w I!: 0.9 :)
a w 0.8 0:
0.7
0.6
0.5
1'-90 =2
(0 )
f'.,
/ \ \
\
T2 =./2 T,
Py = 3 Pc
\ , \
1'-90 = 2 T2 = ./2 T,
Py = 2 Pc
( b)
'\ \.
\ .-'I' .. '
//-:y, /0;\\
V 1 -.... , ,
\ \ \\
,\\~
\ \
L 1 -' J J
1'-90 =2 T2 = 2T,
Py = 3Pc
(C)
, , \
\ \
0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2
Ql.
1'-90 =4 T2 = ./2T, Py = 3Pc
1.7 (0)
1.6 1--------1
1.5f------
o 1.4 f--------I
i= ~ 1.3 t---=------
I t; 1.2 I"-~'o------_I z W 0: 1.1 1---'"*----1 I(f)
o W 0:
1.0 1-------'cIt-----j
:) 0.9 f------I\\----I a w 0: 0.8 I----~+_---j
0.7 f-----+-;-\__-I
0.6 I-------'r'--I
0.5 '----'---.L....l....L.J...LLL1-U
TI (SEC.)
1'-90 =4 T2 =./2 T,
Py = 2 Pc
(b)
-"'\
..... \ ,/~ '\,
~\ '~,
\, '\ \\
\.
I I I I I
1'-90 =4 T2 = 2T, Py = 3Pc
(c)
\ \ \
~\\ \\\
~\ W' .~~
\\ I I ~ I II
I'- =2 gO T2 = 2 T,
Py = 2 Pc
(d) -- TYPE A
-- TYPE B -.- TYPE C
----- TYPE D
Py {3= ---.=;
mVgo
\ , ,
1'-90 =4 T2 = 2T,
Py = 2 Pc
(d) -- TYPE A
-- TYPE B r---___ TYPE C
----- TYPE D
r-- Py (3=---.=;
r-- mVgo
\ \ \
~\ \\~ ~
\\\ \~ \~ \\
I 1\ III 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5
TI (SEC)
FIG. 18 REQUIRED STRENGTH RATIOS FOR STRUCTURAL MODELS, DUCTILITY FACTORS, PROBABILITY DISTRIBUTION LEVELS AND EARTHQUAKE TYPES INDICATED
<l:l.
0 i= <[
0::
:r I-t9 Z w 0:: I-en 0 W 0::
~ 0 w 0::
<l:l.
0 I-<[ 0::
:r I-t9 z W 0:: I-en 0 w 0::
~ 0 w 0::
fL95 = 2 T2 =hT,
Py = 3Pc
1.7 (0) ...
\ \ \
1.6
/'1 \ 1.5
. ,
f 1.4
1.3
1.2
1.1
1.0
0.9
08
0.7
06
0.5 0.1 0.2 0.5
,u95=4 T2 = ./2T,
Py = 3 Pc
1.7 (0)
1.6 1--------1
1.5
1.4 /
1.3
1.2
1.1
1.0
0.9
08
0.7
0.6
0.5
fL95 = 2 T2 =hT, fL95 = 2 T2 = 2 T,
Py = 2Pc Py =3Pc
(b) (c)
, , , -..
\ , ~ ,
\ \
0.1 0.2 0.5 0.1 0.2 0.5 TI (SEC.)
,u95 =4 T2 =./2 T,
Py = 2 Pc
(b)
" / , \ \
N ' .. \
\~\
\~ ~ \0,\
1 1 1 1'1
fL95=4 T2=2~ Py = 3~
(c)
, , , , ,
~, " ~\
~\ . \ \
'\" . .. ,
\\ \ \~
1 1,\ I II
fL95 = 2 T2 = 2T,
Py = 2 Pc
(d) TYPE A
TYPE B
TYPE C
TYPE D
Py f3 = -----;0;
m Vgo , \
\ \ ,
0.1 0.2 0.5
,u95 =4 T2 = 2T,
Py = 2 Pc
(d) -- TYPE A
-- TYPE B -_.- TYPE C
----- TYPE D
c---- Py f3 = -----;0;
I--- mVgo
\ \
\
~\ \\~\
~~. .\
1 I ~ III 0.1 0.2 0.5 0.1 0.2 0.5 0.1 02 0.5 0.1 0.2 0.5
TI (SEC,)
FIG. 19 REQUIRED STRENGTH RATIOS FOR STRUCTURAL MODELS, DUCTILITY FACTORS, PROBABILITY DISTRIBUTION LEVELS AND EARTHQUAKE TYPES INDICATED
53
54
<Xl.
0 i= « a:: :I: ~ (!)
z w a:: ~ (/)
Q
w a:: S 0 w a::
en.
~ ~ « a:: :I: ~ (!) Z w a:: ~ (/)
Q w !!: :::> 0 w a::
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
1-'-80 = 6 T2 = .j2 T, Py = 3Pc
(0 )
~;~ \ \
''<\\ \\\ \\\
'~
I I I I II
1-'-80 = 6 T2 = .j2 T,
Py = 2 Pc
(b)
~ .~
.,
,~
\ "\ ..
I I I II I
1-'-80=6 T2=2T, Py = 3 Pc
(c)
~ \~
'\\ t\
\'
I \1 I, I I I
1-'-80 = 6 T 2 = 2 T, Py = 2 Pc
(d) - TYPEA
-- TYPE B --.- TYPEC
----- TYPE D - Py
f3=~ - m Vgo
:~ \\~ \~
1\ 1111 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
1-'-85= 6 T, = .j2 T,
Py = 3 Pc
(a)
~
\~~ '\ .. .
,,~~
\~ \\~ ~\\ "X I I) I' I
1-'-85 = 6 T, = .j2T,
Py = 2 Pc
(b)
~ '~ ~ .'
"~ \~
\
T, (SEC.)
1-'-85=6 T,=2T,
Py = 3 Pc
(c)
~ "\ .~
\ I I I I II I \ I I I I
I-'-85 = 6 T, = 2 T, Py = 2Pc
( d) - TYPEA -- TYPE B
1----.- TYPEC
----- TYPE D
- Py f3=~
- m Vgo
I~\
<:\ \\ \\ 1.\ I III
0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 T, (SEC.)
FIG. 20 REQUIRED STRENGTH RATIOS FOR STRUCTURAL MODELS, DUCTILITY FACTORS, PROBABILITY DISTRIBUTION LEVELS AND EARTHQUAKE TYPES INDICATED
~ I-« a: :r: I-e.!)
z w a: I-en a w !!: :J a w 0::
~ I-« 0::
:r: l-e.!)
Z w a: I-en a w a: :J a w 0::
1'-90; 6 T2 = -12 T,
Py = 3 Pc
1.7 (0)
1.6 f---------1
I 5 f----------1
IA
1.3
1.2
I I
1.0
0.9
0.8
0.7
0.6
0.5
1'-90 =6 T2 = -I2T, Py = 2Pc
(b)
,
~ ~\
... -
\,~ . , \~ \' ,
I I ~,~ I
1'-90 = 6 T 2 = 2 T,
Py ; 3 Pc
(c)
\ \
\
'.~~ '~\ \~
\ \
I "I I I 1 I
1'-90=6 T2 ;2T,
Py = 2 Pc
( d)
-- TYPE A
-- TYPE B f--_._ TYPEe
----- TYPE D
f-- Py {3= --;:;
I--- mVgo
f-.
\
~'. I\\!, \\\ \~
'\ 1 \~I 1,1 1 I
0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5
1'-95; 6 T2 =';-2 T,
Py = 3 Pc
1.7 "'(-"'0-'..) ____ -1
1.5 f--------j
IA
1.3
1.1
1.0
0.8
0.7
0.6
0.5
1'-95;6 T2 ; -I2T,
Py ; 2 Pc
(b)
, , )
F\\-~\ \~, \ \
\~ . \
\ '
\\
TI (SEC.)
1'-95;6 T2 =2T,
Py = 3 Pc
(c)
, ~, ~:, . ,
\ ,
\\ ~\ \~
I I .~ ~ I 11 I, I I I
1'-95 ; 6 T 2 = 2 T,
Py = 2Pc
(d) -- TYPEA -- TYPE B
f--- -.- TYPE C
----- TYPE D f-- Py
{3= --;:; I--- mVgo
, \
~, .~ . ,
\. \
\~ ,
1K \,
I \1 1 I II 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5
T, (5 EC.)
FIG. 21 REQUIRED STRENGTH RATIOS FOR STRUCTURAL MODELS, DUCTILITY FACTORS, PROBABILITY DISTRIBUTION LEVELS AND EARTHQUAKE TYPES INDICATED
55
56
at
Q I-et a:: :z: I-t!)
Z W a:: l-(/)
D w !!: ::::> 0 w a::
at
0 ~ <t a:: :z: l-t!)
Z W a:: l-(/)
D W
!!: => 0 w a::
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
fL80= 8 T2 = ../2T,
Py = 3 Pc
(a)
l:\ ." (.'\ '\,
\.
'1\ \ ~
\\ \'\
I I} I I I
fL80 = 8 T 2 = ../2 T,
Py = 2 Pc
(b)
~ \\ '~J
1).\\
\\ I "I \ I II
fL80 = 8 T2 = 2T,
Py = 3 Pc
( c )
~
~\ .\
. \~ \\~ \t ~ I I I I II
fL80=8 T2 =2T,
Py = 2 Pc
(d)
-- TYPEA -- TYPE B
I--- _._ TYPE C
----- TYPE D I--- Py
f3=~ I--- mVgo
\ \\ '~~ \ I I I II
0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5
L7
L6
1.5
14
1.3
1.2
1.1
LO
0.9
0.8
0.7
0.6
0.5
fL85=8 T2 =hT,
Py = 3 Pc
(0 )
~ "\\ '\
\\ f~ b\ ~\\
\ I I I 1 II
fL85 = 8 T2 =./2 T, Py = 2Pc
(b)
~ r-, \~ \~
'~\\
\\
TI (SEC.)
fL85 = 8 T2 = 2T,
Py = 3 Pc
(c)
~ \\
~'~\I\ .~
1 1,\ I 1 1 ,\ 1 1 1 1
fL85 = 8 T2 = 2T, Py = 2Pc
(d)
-- TYPEA
t--- - - TYPE B -.- TYPEC
----- TYPE D t--- Py
f3=~ t--- m Vgo
~ \'\
\~~ .~
I 1 I II i 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5
TI (SEC)
FIG. 22 REQUIRED STRENGTH RATIOS FOR STRUCTURAL MODELS, DUCTILITY FACTORS, PROBABILITY DISTRIBUTION LEVELS AND EARTHQUAKE TYPES INDICATED
<ll.
~ l-e:( a: J: I-<!> Z w a: l-I/)
Cl w a: :::l CI W a:
<ll.
~ l-e:( a: J: I-<!> Z w a: l-I/)
Cl w a: :::l CI w a:
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
fL.a= 8 T2 = ../2 T,
Py = 3 Pc
(a)
\~ f"\,,,\
'\\ ~ \~\ \~\\
.~
"~ .~
I I I I II
fL.a=8 T2 =../2T,
Py = 2 Pc
(b)
\
~ .", . \
\\\
'\ \i
\\ I I ,\~ I I I
fL.o =8 T2 = 2T,
Py = 3Pc
(c)
~~ \\ ,\ '\ 1,\ I III
fLgo
=8 T2 =2T,
Py = 2 Pc
(d) - TYPEA -- TYPE S
-_.- TYPEC
----- TYPE 0 - Py
(3=~ - mVgo
\
~~ \\ \~
\~
I I I I II 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
fL.; 8 T2 = ../2T,
Py = 3Pc
( c;J )
~ ~\
'\ "\ \\\ \\~ .\
\~ I I \ II II
TI (SEC,)
fL., = 8 T2 = ../2T,
Py = 2 Pc
(b)
\
:-l, ~
'\ '~\
\X\ \
\~
I I ~ I I I
fL'5
= 8 T2 = 2 T,
Py = 3 Pc
(c)
\ \
~\ \~\ '~
'\ \'
I ,~ I I II
fL'5
= 8 T2 = 2 T,
Py = 2 Pc
( d)
- TYPEA _-- TYPES
_.- TYPEC
----- TYPE 0 -
Py (3=~
- m Vgo
\
~\
I\~~, \ \ ~, '" \~ \ I \ I III
0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 TI (SEC.)
FIG. 23 REQUIRED STRENGTH RATIOS FOR STRUCTURAL MODELS, DUCTILITY FACTORS, PROBABILITY DISTRIBUTION LEVELS AND EARTHQUAKE TYPES INDICATED
57
58
<ll.
~ I-« n::: I l-t!)
Z W n::: I-en 0 w ~ ::J a w n:::
<ll.
~ I-« n::: I l-t!)
Z w n::: I-en 0 w ~ ::J a w n:::
3.0
2.5
2.0
(0 )
Py =1.9Pc Vy = lOVe
F-,r, ''.\ U ... \ \
,iY \\ \\ (} I. " \
1.5 r! 'I \,
1.0
0.5 0.1
3.0
2.5
2.0
\"\ \'iI. \ \\,\ \,\ .,
I I I I I I 0.2 0.5
fL90= 2 Py = 1.9 Pc
Vy = lOVe
(e)
fl. ./lY\\ r,r/ \ ~\
/l/ 'II \ \ i,// \\ \
/J/ ,,\ "\ ./ '~U
1.5 V \~\\ ~\\\ \~
"
1.0
0.5 I I I I I I
fLao =10 Py = 1.9 Pc
Vy = lOVe
(b)
;:~
IF'>---~\\ [;'~/A, ,\\
" \ \\ ,!, \~ ',\, \\.
I I I 1\1 I 0.1 0.2 0.5
1j
fL90= 10 Py = 1.9 Pc
Vy = 10 Ve
(f)
r\. I,F-"""", \
(1,0. , , :\\ I , \~
"'\ '\ \1-\\~~
"\\ I I I 1'1 I
(c)
Py = 1.9 Pc
Vy=IOVc
I~ .lL. \ \
fIt\ "\\ If/I '0.11
ijY ,,"\ \ \ r::l \\\\ II ,,\ \
I', \ \\\
\1" 1,\
I I II I I 0.1 0.2 0.5 (SEC.)
fL95 = 2 Py = 1.9 Pe Vy =IOVe
-.l g)
A r/I .~,
i''! / \ '\ /l/ \ 1\
/;// ~\'\' " Iii \\ \
... --f \~\ / ~
1/ l\ \
I I I I I I
fLa5 =10 Py = 1.9 Pc
Vy = 10 Vc
(d)
f---------- TYPEA
f----------- TYPE B --- TYPE C
f--------- ----- TYPE D f--------- Py I-- (3= -=-f--------- mVgo
7 •. --4'\ lf'l ',\\
/ ", \',,-'\ \. ~
.... \\ ~\~
\\" I -[ 11\1 I
0.1 0.2 0.5
fL95 = 10 Py = 1.9 Pe Vy = 10 Ve
(h)
f---'- TYPE A
I--- -- TYPE B _.- TYPE C
I--- _____ TYPE D
f--- Py f--- {3=~ I--- mVgo
~
//I'~ Il.?! \'\
I I
,,-..,-, " \'\
,,-~.~\
\\ ~
.~
I I I, I I I 0.1 0.2 - 0.5 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5
T, (SEC.)
FIG. 24 REQUIRED STRENGTH RATIOS FOR STRUCTURAL MODELS, DUCTILITY FACTORS, PROBABILITY DISTRIBUTION LEVELS AND EARTHQUAKE TYPES INDICATED
30
2.5 <!l.
~ I-« a:: I
2.0 l-e!)
Z W a:: l-(/)
1.5 0 w ~ :::l 0 W a::
1.0
0.5
f-Lao=1.5
(0 )
Py =1.9Pc,
Vy = 10 Vc
--
.1-... o'!~
l"f /\ \ I~ f// \1 '. \
d/J 'I". \ i / if I '. \ \ \
v"" ',\ \ I '.~\
~/ "1;\\ , ., 1,\
I I I I II
f-Lao=50 FY = 1.9 Pc
Vy = 10 Vc
( b)
~ i~A'\
1/ ~\\~
If ,.'-_, \ , , ,\ , ..... " \\
"'\\ \'\ ~ \:
I I I i I I
f-L = 1.5 a5
(c)
A
Py = 1.9 Pc
Vy=IOVc
riA. /j~ ~7 / \', '0-
/ / \., I " /"/1 I ~\\\
, )// \\ \\ f \\
1.1 \-\ r7 II
I I I I I I
f-La5=50 Py =1.9Pe Vy = 10 Vc
(d) ~- TYPEA
~ == ~~:~~ ~ ----- TYPE D ~ Py ~ f3=~ ~ m Vgo
/'~ 7/''::'''\-
C7.. \\ , / \ ,\ '0.,o
\\ ~\ \\\,\ ~ \'
I I I I I I 0.1 0.2 0.5 01 0.2 0.5 01 0.2 0.5 0 I 0. 2 0.5
3.0
~ 2.5 Cll.
~ I« a:: I 2.0 l-e!)
Z W a:: l-(/)
o w a:: :::l o W a::
1.5
1.0
0..5
f-L90= 1.5 Py = 1.9Pe Vy = 10 Ve
(e)
1\ I ,
1"/,1\ i 1/ Ii),
.1,/ f\ \\ I i / / \\\~
: / / \, \ \ I 11/ \\ 11 ,.~
/J '~ V
.' I I I II I
TI (SEC.l
(f )
Py = 1.9 Pc
Vy = 10 Vc
~
h~ .... ' "-/\ ,\
t1i,' \ \ \\ , .. \~\
'\\ .~~ .~~
~~\ '\ ~
I I I I II
, ,
Py = 1.9 Pc
Vy = lOVe
(a) " I' , , , , \ ,
'1/-"" \ ,. i' " \ :\j:;~ , 'I I 1\ ~ , ! ; I m , , ! i I \
11 j \~I if " II \i
1/ . ,
I I I, II I
(h)
Py = 1.9Pc Vy = 10 Vc
-'- TYPE A
--- TYPE B TYPE C
------ TYPE D - Py - f3=~ - m Vgo
~ 7 " \\ 1 \ -.\
I;" '" \\ -m ~ \\ ~ '~
'i
I I I I I I
0..1 0..2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 TI (SEC.)
FIG. 25 REQUIRED STRENGTH RATIOS FOR STRUCTURAL MODELS, DUCTILITY FACTORS, PROBABILITY DISTRIBUTION LEVELS AND EARTHQUAKE TYPES INDICATED
59
60
<n.
0 i= « a:: I: I-(9
Z w a:: I-m 0 w a:: ::>
" w a::
<n.
2 I-« a:: I: I-(9 Z w a:: I-m 0 W a:: ::>
" w a::
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
fL = 2 T2 = .j2 T,
Py = 3 Pc
(a) ,
I I I
I
1\
~\\ ~\ \~\ ~\
\\1
1 1 1 1 II
TYPE B02 EARTHQUAKE fL=2 T2 =.j2 T,
Py = 2Pc
(b) . , I
]/1'\ \ fh\l\
~/I \ I
V '1 1
I: ., Ii 11\:
!~\ \1
I ·1
I \ I
.1
1\\
~;\ \\ \\\
1 1 1 1 0
fL = 2 T2 = 2 T, Py = 3 Pc
(c)
l/ \ i -'\ \ I
\i l
\i\ ~(I III
·1
\\\ I .1
\1\ I I
II .1
~\ '1
~\ ,~
\ •
1 1 1111 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 0.1
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
I
fL = 4 T2 = .j2 T, Py =3Pc
• (a) I
I
....... ...,\
"-1,\1
IAil
V ~I\ ~\\ ~;\ ~\\ ~\\\
\1)
t \
~;\ ,~\
1 1 1 I~ 1
T, (SEC.)
TYPE B02 EARTHQUAKE fL = 4 T2 =.j2 T,
Py = 2 Pc
(b)
I , I ,
vA",
.\
\\ .\
fL = 4 T2 = 2 T, Py = 3 ~
(c)
, , ,
~\\ \ II \,1\
,~\ \\\
~~, ~\ \~ ~\ \ ~\
\ \
\
1 1 \~, 1 1 1
fL= 2 T2 = 2T, Py = 2Pc
(d) -- fLeo
-- fLe5
- - fLso
----- fLS5 -'\
Py (3= ---
m Vgo
fL=4 T2 =2T, Py = 2Pc
(d) -- fLeo
-- fLe5
- - fLso
----- fLS5
Py {3= ---
m Vgo
0.5 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5
T, (SEC.)
FIG. 26 REQUIRED STRENGTH RATIOS FOR STRUCTURAL MODELS, DUCTILITY FACTORS, PROBABILITY DISTRIBUTION LEVELS AND EARTHQUAKE TYPES INDICATED
1.7
1.6
<l'l. 1.5
0 IA I-« a: 1.3
::I: I- 1.2 l!)
Z W a: I I I-Cf)
Cl 1.0 w a: :::> 0.9 0 W a: 0.8
0.7
0.6
0.5
J1- = 6 T2 = .j2 T,
Py = 3 Pc
(0 )
\ /' \ /
\
i' ~11\
~\ \
!\ ~I
1\ \ '\ \
\ .\
~\ ~~ ~
I 1 1 III
TYPE B02 EARTHQUAKE J1- = 6 T2 = .j2 T,
Py = 2 Pc
(b)
-"-\
" h
K~i\ l~\
~\ ~\ t
~~\
't I 1 1 1 1 1
J1-=6 T2 = 2T,
Py = 3 Pc
(c)
\ \ \
\'. .\\
'i\ .\ ~~ ~\\ ~~\ \~\ .\ ~:~
1 'I 1 1 II
J1-=6 T2 =2T,
Py = 2 Pc
(d) -- J1-ao -- J1-a5
- - J1-90
----- J1-95
0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5
J1-=8 T2 =J2T,
Py = 3 ~
1.7 f-'(c.::0'-!)'---___ ----i
1.6 f---------1
I. 5 +-,----------1 \
" o 1.4 1+---".--
I« a: ::I: Il!) Z
~ 1.1 1---"'"*----] ICf)
Cl W a: :::> o w a:
0.7 i-----\W\-----i
0.6 1------\\\---]
0.5 '----L--'---l--L-J-LLLLLJ
T, (SEC.)
TYPE B02 EARTHQUAKE J1-=8 T2 =J2 T,
Py = 2 Pc
( b)
\
[\~." M\ \\'-\
'V il \11
h;\
\~ l
.\
\\ I'
I I ,~.I I
J1- = 8 T 2 = 2 T,
Py = 3 Pc
(c)
\ \
. \
~ \
l\ '\\ ,~ \
\ t\
\
\
1 'I 1 1 1 1
J1-=8 T2 =2T,
(d)
Py = 2 Pc
-- /Lao
-- J1-a5 - - J1-90
----- J1-95
Py {3= ---
m Vgo
0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 0.1 0.2 0.5 T, (SEC.)
FIG. 27 REQUIRED STRENGTH RATIOS FOR STRUCTURAL MODELS, DUCTILITY FACTORS, PROBABILITY DISTRIBUTION LEVELS AND EARTHQUAKE TYPES INDICATED
61
<U..
0 I- <t
Q: ::r:
I- (!) z W
Q:
I- en
Cl
w
Q:
:J
0 W
Q:
J-L
=2
3.0
(a
)
2.5
II
2.0
fl I /f til tl
1.5
if ,/
l ,.
1.0
Py=1.9~
Vy
= lO
Ve
, II
i /
iT I
ill
I i I
\ \ \; III 1\\\
\\.
\ \ \ .\
TY
PE
B
02
E
AR
TH
QU
AK
E
J-L
= 1
0 P y
= I.
9 P
e V
y =
lOV
e
( b )
--
J-L80
--
J-L85
_
. -
J-Ls
o ~
-----
J-LS
5 - -
P y (3
=--
-;:;
-
m V
go
-
/1
I 1
I \
.l~~·
\ /.V~~I
~
'\\ "
tt
l\ "
11\ ,~\ \~, t,\ ~~~
J-L
= 1
.5
(c)
I j j 1 1 -:1
~l
P y =
1.9
Pe
Vy
= l
OV
e
~ , ~\ ., , 1\
I·
' , .1 I I .\
, 1 I .\ 1
J-L
=5
( d )
, I /~
/f/
/'
I ,
P y =
1.9
~
Vy
= lO
Ve
, i,;
'~'
'/ '
!~~
1/,11
., f.
\ I.~
~ .
\ . , . , \ \ . , \ \ \\ ' t\
\\i\ ~ 1-:, ,(~, \h ~
0.5
0.1
I I
I I
I I
0.2
0
.5
0.1
I I
I I
I I J~
U_
I I
I I
I I
I I
I I
I I
I 0
.2
0.5
0.
1 0
.2
0.5
0.
1 0
.2
0.5
TI
(S
EC
.)
FIG
. 2
8
RE
QU
IRE
D
STR
EN
GT
H
RA
TIO
S FO
R
STR
UC
TU
RA
L
MO
DE
LS,
D
UC
TIL
ITY
F
AC
TO
RS
, P
RO
BA
BIL
ITY
D
IST
RIB
UT
ION
L
EV
EL
S A
ND
EA
RTH
QU
AK
E T
YPE
S IN
DIC
AT
ED
(})
to
63
APPENDIX A
COTvIPUTER PROGRA"1 "SHOCHU"
C C C C C C C C C C C C C C C C C C C C C C C C C
C
C
C
64
PROGRAM S~OCHU ( INPUT, OUTPUT, PUNCH
• • • • • • • • * • * • * ~ * • • * * • * * * * * * * *.* * * • *
INPUT DATA
MCONTL
MCONTL 0 1
" 2
'" ·3
,. 4
INDEA FO~ ~1~DS OF JuB
STOP PSEUDU EA~TH~UAKt ~tNEKATION
EARTHQUAKE ~tNE~AT1UN.AN0 ~ESPON~E ANALYSl~ UF ORIGIN-URIENTtD SHEAR MJOEL EAKTH(JUAII.E GENEKATION A,~,) KESPUN~E Ar"ALY~I~ UF TRI-LINtAR STi~FNES~ OE~RAOING FLEXJ~E ~COEL EARTHQUAKE GENERATIUN AN,) RESPUNSE A~ALY~lS ~F
BOTH ,.-IJDELS
• * * • • * • * * * * • * * * * * * • * * * * * * * * * * * * * * DATA ARE READ IN THE CORRESPONDING SUBROUTiNES ( PSEQGN , ORIGIN , OTR1Ll )
NSlEP 2 NUMBER OF INTERPULATION OF ACCELEkOGRAM
• * * • • • * • • * • • • • * * * * * * • • * * * • • * * * * * *
COM;-10N AA! 32000) COMMON ICNTRll NEQREC,T,DT,EAMAX,DA~P,Fu,Tl,TO,CE2,NUUTlo),HED(u) 1.NEQ,ISHAPE,ACC~AX(~J),VELMAXI40J,DiSMAXI401
COMMJN IGE~CI PI2,Nu,NI,NDEC,NTOT,AMPL,Ol,G2,u3,O~,wJ,o.c, 1 Al,A2,A3,A4,A5,Ao,A1,CL,OL,NACC,N~EL
1 READ 100, MCONTL
IFI MCONTl.EQ.O I GO TJ 2
C PSEUDO EART~~UAKE GENE~ATION
C CALL PSEQGN
C IF I MCONTL .E\.i. 1 ) GO TO 3
C C LINEAR INTERPOLATIUN uF tAKTH\.iUAKE ACCELERATIuN C
C
C
NSTEP"'Z NTOTZ=NSTEP*NTOT TH=DT/FLUATINSTEPI CALL ERIKO lAAINACCI,AAINVEL),NTOT,NSTEPI
IF I MCONTL .EQ. 3 ) GO TU 4
C RESPONSE ANALYSIS OF ORIGIN ORIENTED SHEAR MODEL C
CALL ORIGIN IAAIN~ELI,NTOT2,TH,ACCMAX(1)1 c
IF I MCONTL .EQ. Z ) GO TO 3 C C RESPONSE ANALYSIS Of TRI-L1NEAR STIFFNESS DEGRADING FLEXURE MODEL C
4 CALL DTRILI IAAIN~ELI,NTUTZ,TH,ACCMAXI1)1
- -- - -.---~-.
SHCH 1 StiCH 2 StiCH .l SHCH 4 SHCH 5 SHCH C>
SHCH 1 SHCH 8 SHCH 9 SHCH LO SHCH 11 SHCH 1.2 SHCH 1.3 SHCH l4 SHCH l~
~HCH 10 SHCH 11 SHCH 18 SHCH 19 SHCH 20 SHCH 2l SHCH .2l SHCH 23 SHCH 24 SHCH 2.:> SHCH ;'0
StiCH 21 SHCH 28 SHCH 29 SHCH 30 SHCH .H SHf-H 32 St:lCH h SHCH J4 SoHCH y, SHCH jb SHCH H SHCH 36 SH(.H .)'1 SHCH .. 0 SHCH 41 SHCH 't2 SHCH 43 SHCH 'tit SHCH 45 S,HCH 4b SHCH 47 SHGH 48 StiCH 't9 SHCH. )0 SHCH 5l SHCH 5, SHCH 53 SHCH 54 SHCH 55 SHCH 5b SHCH 51 SHCH 58 SHCH 59 SHCH 00
C
c
3 GO TO i 2 STOP
100 FOKMAT 15 I END
SUBROUTINE PSEQGN
c * * * * * * * * * * * * * * * * ~ * * * * * * * * * * * * * * * * C C PSEUDO EARTHQUAK~' GENERATIUN C C PROGRAMMERS •• P MUll AND J PENlIEN,UNIV OF CAllf,BEMKtlEY. 1969 C M00IFICATIONS •• NISEE 1972 C MODI~ICATIUNS •• M MURAKAMI 1975 C
C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ~ * * C
C
COMMLJIII /UHRl/ ~tQRI:c.,r,DT,I:AMA)(,JA:"f',FJ,TI,rJ,CEL"'OLJI (o),rlcU(bl 1 , "E tJ , i SHA PI::, AC C HA X ( .. 0) ,V t L ,~A X ( '> J) ,i) I S "lAX ( '+ \) ) CO""'1U,~ /GE,iC/ PIL,,·,c),Ni ,'~LitC"~rJT,AMPL,ul,[)2.,Uj,04,,,~,U,4,
1 Al,AL,A3,A4,A~,Au,A7,Cl,DL,NACC,NV~L
C * * * * ~ ~ * * * * * * * * * * * * * * * * * * * * * * * * * * * C C INPUT DATA C C ~EQKEC = NUMbER Ur EAkTH~UA~E RtCURDS C T = OURATJUN OF REC0MDS C TH = DT = TIMe INCKt~ENI C DENST z POWER SP~(.T~AL OlNSITY ICM**Z/StC**j) C NOUT=UUTPUT CUNTRuL ARKAY C C HIGH FREUUENCY FilTER PAkAMETERS C C DAMP· DAMPING ~ATIO C FO - UNDAMPED NATURAL FKL~UENCY (CPSJ C DENST z puwER SPECTKAL INTENSITY C C LOw FREQUENCY FILTER PARAMETERS C C DAMPl : DAMPING RATIU C FOL - UNDAMPED NATUNAL FReQuENCY '(CPSI C C SHAPiNG FUNCTION PARAMETERS C C Tl z DURATION OF INITIAL PAKAtiUliC dUllDUP C TO - Ti~E AT END OF STATIuNARY PUKTiON C CEZ - EXPONENTIAL OECAY CONSTANT C lSHAPE - 2 (PARABOLIC BUILD-UP PHASEI C • 3 (CUijIC 8UIlD-UPI C C • • * • • • • * * • * * * * * • * • * • * * * • * * * • • * * * * C C BLANK COMMON STOkAGE AlLO.CATllJN C SET COHMlJN AAINNNI AND NAA-NNN C
65
SHCH SHCH SHCH SHCH SHCH
SHCH SHCH SHCH SHCH SHCH StolCH SHCH SHCH SHCH ~H('H
SH('H ~HCH
SH(.H ~HCH
SH('H SliCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCM SHCH SHCH SHCH SH('H StiCH SHOi SHCH 5,HCl-I SHCH S~H
SHCH SHCH SHCH SHCH StiCH SHCH SliCH SHOt
01 02 03 64 05
60 07 od 09 70 71 U 13 1<+ 1':> 70 17 7;;) 79 tiO 01 dL dJ tl't tl:i 136 tJ I tid /j'J 'JU 'ill <02-93 941 95 ';16
~7
~8
99 100 11l! 102 hI.; 10«0 105 lOb 101 108 10'.1 lAO UJ. li..l 1.13 HI, 115 !.It>
66
C wHERE NNN EXCEEDS 3*NTOT+NI+NOEC C C wHERE NTDTsT/OT+l C NlsTI/DT+1 C NOECsNTOT-TO/OT C
C • • • • • * • * • • • • • * • * * • * * • * * • * • • * • * • • • C C NEQREC s 1 IS RE~UI~ED FOR RESPUNSE ANALYSIS. C IF LAST hlO CARl) ARE "BLANK", SUdRIJUTINE KETURI'4S TU MAIN. C
C * • * • * • * * * * • • • • * • * • * * * • • • • • • • * • • • • c
C
COMMON AA( 320001 NAA~320000
C READ SPECIFICATIONS C
C
C
READ 6, HEO,~E~K~C,T,TH,DcN~T IF (NtQREC.tQ.O) GO TU:) . DT=TH READ d, DA'IP,FO REAO 9, ISHAP" READ a, TI,TO,CEZ READ 8,DAMPl,FOl READ 9, NOUT PRINT 10, HtD,NtQKtC,U~N~r.T.OT,NGUT,FJ,UAMP.FJl,uAMPL.rl,I~HAP~.
lTO,CE2
NTUT=T/Df+1.000 1 NO=TO/OT+l.OOOl NI=TI/DT+l.uOOl NDEC=NTOT-NO+l MAA=3·NTOT+NDEC+~I+l IF (NAA-MAA) 2,3.3
2 PRINT 1. MAA STOP
3 CO"lTlNUE
C STORA~E ALLOCAT[ON C
c
~P:l
NP l:NP+NDEC r-IACC=NP1+NI NIJEL=NACC+NTUT NDI SPzNIJEL+NTlH
C GENERATE INTEN!>lTY-TIME FUNCTIO~ C
CALL SHA~E &AA(NPI,AA(NP1),NI.NOECI c C GENERAL CONSTANTS C
P 12"0.2831853 IIIOsPI2·FO 0-2 •• 0AMP.wO A2 s b./OT Al~A2IOT
. A3a3./OT 44"'OT/2.
SHCH 111 SHeH 11d SHeH 119 SHCH llO SHCH 12l SHCH 12~ StiCH 12l SHCH 121t SHCH 1~5 SHCH 120 StiCH 121 SHCH 12~ SHCH 129 SHCH 130 SHCH 131 SHCH 132 SHCH 1.;3 SHCH 1 . .H SHCH 135 SHCH Ull SHCH u1 SH~H US SHC.H LJ9 SHCH 140 SIiC H 141 !>HI.H l .. l SHCH 14J SHCH 144 SIiCH 14> SIiC ti 140 SIiCH 141 SHCH 1'08 SHCH 1 .. 9 SHCH 151) SHCH 151 SHCH 15l SHCH 153 SHCH 1H !>HCH I» SHCH 15ll SHCH 151 SHCH 15d SHCH 159 SHCH 100 SHCH 101 SH(.H l<>2 SHCH l<>j SHCH lb~ SHCH l&S SHCH 1<>6 .SHCH 1&1 SHCH lb8 StiCH 109 SHCH 170 SH(.H H1 SHCH 112 SHCH 113 SHCH 114 SHCH 115 SHCH 11~
C C C
C C
·c C C C C C
A1-A4 A5-A1*OT/3.Q Ao"Z.0*A5 C-Al+0*A3+WO*kojO WOL-PI2*FOL -Dl-2.*OAiI4Pl* .. 0l Cl·Al+Ol*A3+~Ol*wOL AMPL"PIZ*OENST/Ur AMP(-SQRTIAMPll 01'"OTIT 02'"01*01/T 03-02*01 04-03*01
GENERATE, PRINT AND PUNCH RECuRDS
DO 4 NEQ:l,NEO~EC CAll GEN IAAINPI,AAINPll,AAINACCI,AAINVill,AAINUlSPI) CALL OUT IAAINACC),AAINVEll,AAINOISPI,NfOTI
It CONTINUE GO TO 1
5 CONTINUE RETURN
o FOaMAT 18A4/l5,3FlO.OI 1 FORMAT IIIIZIH EXECUTIU~ TERMINATEOI -i 21H ••••• SEE USER ~UIDE fO SEf I 1 35H NAA AND-DIMENSIUN OF ARRAY AA )
8 FORMAT 18FIO.4) 9 FORMAT (6111
10 fORMATIIHI,8A411 132M NUMBER OF EARTH~UAKE RECORDS .Ijl 2 3ZM INTENSITY ICM*.2/SEC.*3) ,FIO.51 3 32H DURATION OF RECORDS IStes) ,FIO.51 4 32_H TIME INCRb"IENT (::>EC51 ,. ,FlO.,1 5 32H OUTPUT CUNT~Ul ARRAY z ,011/1/1 6 33H HI~H FREQUENCY FllTtR PKUPERTltS II 1 20H NATURAL FKtQUtNCY ;,FIO.jl 8 20H DAMPING RATIO ; ,FIO.51111 9 33H la .. FRE~Ui~CY ~llTER PKUPtRTIE~ II ~ 20H NATURAL FREJUENCY =,FIO.jl $ 20H OAMPING RATIO = ,FID.51/11 $ 28H SHAPING FU~CTIUN PARAMETEKS // ~ 32H DURATION OF SUllD-U~
$ 32H BUILD-UP CURVE $ 32H TIME AT ~iGINNING OF DECAY $ 32H EXPONENTIAL DECAY CUNSTANT
END
SUBROUTINE SHAPE (P,Pl,NI,NDEC)
• .. * • -* * * * • * * * * * .. .. .. * * .. *
- ,FIO.51 • ,IZI z ,FIO.51 z ,FIO.51111)
* * • .. * '" * •
SHAPING FUNCT ION FOR INITIAL PARAtiOLIC OR CUSIC BUILD-UP
• .. * * • • .. * * * * * .. * .. * * * * .. * * .. * * .. .. .. *
.. .. *' *
.. * * ..
67
SHCH SHCH SHCH StiCH StiCH StiCH SHCti SHCti SHl.H SHCH SHCti SHCH StiCH ~HCh
.sHCH SnCH StiCH SHCh SHCti StiCH StiCH SHCH ShiCh SHCH SHCH SHCH SHCH SHCH ShlCH SHCH SHCH ~H('H
StiCH SHCH SHCH SHCH SHCH StiCH :)HCh StiCH SHCH SHCH StH.H SHCH :iHCH SHCH SliGH :iHl;;H S,HCtI
SHLH SHCH StiCH SHCH StiCH StiCH SHCH
177 US .1.19 1!W un 182 183 1(1 ..
185 itlc lii7 188 Ul9 190 191 192 193 194 195 19b l'i7 198 19'» LOu .201 202 203 204 2Jj 200 2u1 2u8 2uS! 210 ZlJ. 212 213 21 .. n::. 21b 217 .lld 2!3 220 221 222 2n 224 us
Z26. 221 228 LZ9 230 LH L32
C
C C C
C C C C C C C
C C C
C
C C
68
CO~~JN ICNTRLI NEWKtC,T,OT.E4M4X,DAMP,FO,TI,rO,LE2,NGUrl~I,HED(8) 1,~EJ,ISHAPE,ACCMAXI401,VELMAXI.OI,OISMAXI401
DI'1E'.SlO'I PIlI,P1l1l IF PHI 3,3,1
1 CJEFF=IDT/TII**ISHAPE 00 2 ,,: 1, N I F='l**ISHAPE
2 PIOj)=f*CClEFF 3 CO'lT I We
SHAPING FUNCTION 1-01<. EXPJI<ENTIAL DECAY
IF IN:)cCI 0,0,4 4 CE2:-CE2*DT
OJ j lIl=l,NO"C F::,
5 P(N)=lXP(CE2*FI 6 RETUc<.N
E\j.)
SUo~0uT[\jE GEN IP,Pl,ACC,VtL,OI~PI
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * •
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * DI'lcNSILJ\j P(lI,PlIl),ACCIl),Vt::Lll),OISP(lI CO~M')N IGENel PI2,NO,~I,NUt::C,NTuT,AM~L,Dl,D2,03,D4,~u,0,c,
1 Al,A2,A3,A4,A5,Ao,A1,CL,OL,NACC,NVEL CJMMON I:NTI<.LI NEWI<.EC,T,OT,t:AMAX,DAMP,FO,Tl,TO,Ct2,NLJUTlol,HEOI81
l,NtJ,ISrlAPE,ACCMAX(401,VELMAXI4ul,OISMAX(401 .
INITIAL CONDITIONS
J= 1 £=,).0 lO=O.O £00=0.0 lL=.).O lDL=O.O lODL=O.O F=O.O AG1=0.0 v=').o Sl=').O 52=0.0 S3=.).0 OI:.PIll=O.O VEl(1):O.O ACc( 11-:0.0
DO iI N=2,NTOT
,mITE NOISE
SHCH lOHCH ~HCH
SHCH SHCH SHCH SHCH ~HCH
SHCH ~HCH
SHCH SHCH SHCH SHCH SI1CH SHCH SHCH SHCH SHCH SHCH
:'HCH SHCH SHCH SliCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SI1CH SIiCH S~H
StiCH StiCH StiCH SHeH SMCH SHC.H £HeH S~H
~H SHeW SH(.H
SHtH SHeH SHeH SHC.H 5H(;H
~H iNCH iHCH SHeH
lH 234 2:>5 231> 211 2.:i8 239 240 241 242 243 244 245 24~
241 248 2't~ 250 251 252
253 25.4 2SS 251> 257 2S8 259 2~0 2t.1 202 2t.3 2b'o 2t.5 2t.b 267 2t.1I 2t.9 270 271 272 27) 27. l1S 27t. lH 218 2H lllO 281 21112 lU 2" US 2h ll1· l ...
C (M) TO B,2J, J
C • • ~ • • • • • • * '* * * * * * * * * * * * * * * • C RANF IS THE CDC KANOUM NUMiiEk GENtkATIUN fUNCTiON C AT EACH CALL' IT RETURNS A RA~~0~ hUM~tR bET~EEh 0.0
C * • * * • * * * * * • • * • * * * * * * • * • * • *
C
1 lU-RANFtll.OI XZ-P 12*'RANF (0.0) U--ALOGtxll X 1-S~R TC Xl +X11 ifaXl*COStXl' J-Z
,GO TO 3 2 W"Xl*S'~(X21
J-1 3 COt.lTINUE
C SHAPE THE WHITE NJISE C
C
l-I\t-N I IF' U 4,5.5
it .-"*PllNI 5 CONTlI'o4UE
I-N-:-40, IF ", 1,l,b
b ,.-"*PCII
C fILTER THE SHOT NOISE C
C
1 A-Al*Z+A2*ZD+ZDQ+ZOO 8-A3*Z+ZO+ZO+A4*ZOO Z-tA-w+O*S'/C ZDo-A3*Z-B ZOOsAIH-A _-IIi+ZOO
C LO_ FREQUENCY FILTER C
c; C C
~-Al*ZL+A2*ZOL+ZJDL+ZDOL
8-A]*ZL+ZOL+ZOL+A4*ZDDL Zl-tA-ioI+QL*SI/CL ZOl-Aj*ZL-B ZOOl..-Al*ZL-A AGaZOOL
BASELINE CORRECTION FACTORS
C1a F+.5 C2-F/o.+.125 '3"'f/3.+5./24. Sl-S1+C1*V+(C2*AG+C3*AG11*OT fZ-F*F Cl-f2+F+l./3. C2-F2/6.+F/4.+0.1 C3-F2/J.+F/l.4+.15 S2-S2+C1*V+(Cl*AG+Cj*AG11*OT F3-F*Fl CI-F3+1.5*fl+F+.25 C2·f3/6.+.115*F2+.3*F+l~/12. C]-F3/3.+.bl5*F2+.45*F+l./bO.
69
'- --~-----..:..--
SHCH 289 SHCH 290
* * • * * * * £HI.H 291 SHCH 292
Ahu l..u SHCH 291 * * * * * * * StiCH 294
SHt;H 295 SHCH Z\ilt> ~CH 291 SHCH 298 SHCri .l"J9 SHCH 300 SHCH 301 SHCH 302 SHCH 303 SHCH 304 SHCH 30~ SHCH 300 SHCH 301 StiCH 308 SHCH )09 SHCH, .HO SHCH .H! SHeH 3!l SHCH 313 SHeH 31.4 SHCH 315 SHCH Jtb SHCH .Hl SHCH 318 SHCH 319 SHICH 320 SHtCH 321 SI1CH 32" SHCH 323 SHCH 32'> SHCH 325 SHCH 321> SHi;.H 321 SHCH 3.<:1:1 SHtCH ~29
SHi.H :no SH-CH 331 SHCH 332 SHCH 333 StK.H 33't SM,CH :ns S,HCH 330 S,H<CH 337 £I1CI1 3:18 SHICH 339 S!1CH 340 SHCH 341 SHCH H2 SI1CH 343 SHCH 344 SHCH 3 .. 5 SHCH 34b SHCH 3",7 !>HCH 348
c
70
Sl-Sl+Cl*V+{C2*AG+C3*AG1'*OT faf+l. Va V+IAG+AG lJ *AIt AG1 z AG ACCIN ,sAG
8 CONTINUE
C BASELINE COR~ECTION COEffiCIENTS C
c
Bl .. 02*51 B2·03*52 B3a 04*53 Clz-300.*Sl+900.*S2-630.*ti3 C2:1800.*81-5760.·82+4200.*83 C lz-1890." tll +6 300. *82-'0725. *S3
C BASELINE CORRECTIuNS AND MAXIMUM VALUES C
C C C C C C C
4CCMAXINEQ)=0.0 VElMAXINEQ)zO.O DISMAXINEQ)~O.O
Xl=O.O Ou 9 N=2,NTOT Xl=/(1+01 ACC(N)-(ACCIN)+Cl.C2·Xl.C3*Xl*Xl)*AM~L CAll AV0~AXIACC(NI,ACC~AXIN~WI) VElIN)-VElIN-1)+(4CCIW)+ACC(N-1))*Al C4ll AVUMAXI~ElIN),VtlMAX(NEWI) OlSprN)-DISPIN-1).V~lIN-1).DT+ACC(N-1)*Ab+ACCIN)*A5 CALL AVO~AX(DlSP(N),UIS~AXINtQII
9 CONTiNUE PKINT 10, NEQ
10 FORMATIIH ,11111 1 28H ACCELEKATION KECURU ~UMtl~R ,12)
PRINT 11,ACCMAX{NEU),VtLMAXINt~),OISMAX'NE~1 11 FURMATll.-i ,/
1 36ti MAXIMUM 1 36ti MAXIMU~ 1 36ti MAXIMU~
RETURN END
ACCElERATIOIIIICM/SEC**21 VELOCITYICM/SEC) DISPLACE MtN T I CMI
SUSRJUTINE OUT (ACC,VEl,OISP,NTOT)
,f7.~/
,F7.1I .f7.21
* * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * *
PRINT AND PUNCH RECOKOS
* • * * • * * * * * * * * * * * * • * * *.* * * * •• * * * • * *
COMMON ICNTRll NE~KEC,T,OT.EAMAX,DAMP,FO,TI,TO,CE2,NGUT{b'.HEO(dl 1.NE~,ISHAPE,ACCMAX(~UI,VElMAA'~OI,OISMAX'401 OIMENSIUN ACC{NTOTI,VElINTOT).UIS~(NTuT) OT5=5.*OT IF (NOUTlll.NE.O) GO TO 1 PRINT 7, HEO,NE~ CAll PRIN (ACC,NTOT,OT51
.$HeH SHeH 5H'H SHeH ~H SHeH SHCH SHeH SHeH SHCH SH(;H SHeH SHCH SHeH SI1CH SHeH SHeh StiCH SHCH SrtCH SHCH SHCH SHCH SHCH SHCH ~HCH
SHCH SHCH SHeH SHCH SHCH SHCH SHeH SHC" SHeH SHeH StiCH SHCH SHeH SHeH SHeH
SHe" SHCH SHC,H SHCH StiCH $HCH 5;HCH SHeH SHeH :.HC11 SHCH SHeH SttCtf $Ii'H SHCH
.~ '~'" 1
" ... , ;.
1~9 lsa lSi 352 lS.l n~
lSS l5Ct 351 lSi 359 l60 )61 102 103 361t 305 166 307 168 109 370 371 372 17J 311t 31!) 370 171 318 319 381l lSi 382 3&3 381t 3115 1116 381 lii 389
390 391 392 193 391t 39§ 19o 391 398 399 .. 00 ~l
~02 ~Ol
~O.
c
C C C C C C ,
;:
C
... .- --..... ------~---- .. --.- -_._------ -" - .
1 IF CNOUTC2).NE.O) GO TU 2 PRINT 8, HED,NE,;j CALL PRIN CVEl,NJOJ,Dlj)
2 IF INOUTC3).NE.O) GO TO) PRINT 9, liED,NE>! CALL PRIN IDISP,NTOT,DTS)
3 IF CNOUTI~).NE.O) GO TO 4 PUNCH 11, HED,NE~,NTUT,Or PUNCH la, IACCII).I·i,NT~TI
~ IF CNOUTIS).NE.OI GO TO ~ PUNCH 12, HEO,NEU,NTUT,JT PUNCH la, IVElIlI,l"l,NTUT)
5 IF lNOUT(bl.NE.OI GO TO 0
PUNCH 13. HED,NE>!,NTO~,DT PUNCH 10, lOISPIII,I-l,NTOTI
6 CONTINUE RETuRN
1 FORMAT 1
8 FORMAT 1
9 FORHAT 1
11Hl,8A~,;X,26HACC~LERATIUN KeCURO NUMdE~,1311 6X,~TIME,;I~X,lbHACCN (CM/SEC •• 2))1
IIH1,8A4,5X,22HVElOCITY' ~ECURO NUl4oEK,l~II 6X,~HTIME,518X,12HVEl (CM/SEC))) 11Hl,8A~,;X,lbHOISPlACcMENT RECURD NU~deR,I~11 6X,~HTl"E,511lX,9HDISP 'C~II)
10 FORMAT 11 FORMAT 12 FORMAT 13 FORMAT
18Fl0.~t 18A4,IZH 18A4,12H '8A~, lZH
A~CN RECORD,13,lH VEL RECO~D,13,lH
OlSP RECORD,13,7H
NPTS-,I; ,5H NPT!)",lj,5H NPTS",1),5H
DT .. ,F503) DT=,F5.31 Dl=,F5:JI
ENP
SUBROUTINE PRIN IA,NHl'T,OT51
• ... . • • . ... •••••• • • • • • • . ... ... . • • . ..... . . ... ... ... . PRINT RECORDS
... ... ... ... ... ... ... ... ... ... ... . ... . . ... . ... ... ... ... ... . ........ * ... • * ... • ... DIMENSION A'NrOT) Ni-i "'2'"'5 TT-O.
1 PRINT 2, TT,IAll),12Nl,N2) IF 'N2.EQ.NrOT. RETURi~
Nl"'Nl+5 NZ-NZ+5 TT-TT+OTS If INZ.GT.NfOll N2,aNTOT GO TO 1
2 FORMAT 'FlO.3 ,lP5E 20.3) END
SUBROUT1NE AVDMAX(A,81
71
SI1CH <t05 Sri!.H 4u6 !)I1CH 401 SHCI1. <t08 StiCH 4u9 SHCH 410 SHCti 'oil SHCti 412 SHCH 4U SHCH 41.4 SHCH 41:) StiCH 416 SHI.H 417 SHCH 4!8 SHI.H 419 StiCH ~20
SHCH 421 SHCH 422 StiCH 423 SHCH 424 SIiCH 425 SHCH 426 SHCIi 421 SHCH 't28 StiCH 429 SHCH 430 SHCH '+31 SHCH 432 SHCIi <t33
SHCH 't3't SHCH .. 35 ~Hl.H 't36 S,HCH '+37 SHCH 4.HI SHCH .. 39 SHCH 440 SHCH 441 !iHCH "~2 SHCH 443 SHCI1 4,,10 SHCH .. 't5 SHCH 446 StlCH 441 SHCH 4~8
StiCH 449 SHCH 450 SHCH '0:>1 SHCH 45.2 SHCH 453 SHCH 454 SHCH 45,
SHCH 450
72
---~-------~:- -- ._:.... ______ ~ __ .. __ ~ ___ .. _.~_ J ___ ...... _ • ..-...._~~
C C C C C C e
C C C C C C C C C. C C C C C C C C C C C C C C C C C C C C C C C C C C C C C
1000
• • • •• • • • • • • • • • • • ••••• • • • • * •. * * • • • • DETERMINAT ION OF MAXIMuM VALUE
• * • * • • • • * • * • • • • * ............ ~ . ... '. X:A8S1 A I IF!X.GT.BI S-=X RETURN END
SU8ROUTINE ORIGINIII,MJSKt,TH,IMAXI
• • • • • • 4< • • • • • • • • • • • • • • 4<.. • • • • ••.• • • •
NONLINEAR KESPONSE ANALYSIS fOR URIGIN-ORIENTtD MODEL
PROGRAMMER •• M.MURAKAMI 1975
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • INPUT OATA
NAME OF MODEL INITIAL NATURAL PERIOD ISEC)
NAMEI Jl X1STR X2SH DAMP AMAX 10
CRACKING STKEN~TH IN TEKMS OF SASE SHEAR COEFFiCIENT ULTIMATE SrREN~TH IN TERMS OF dASt SHEAR COEFFICIeNT DAMPING RATIO AVERAGE OF MAXIMUM ACCELERATION IN TERMS Of GRAViTY' NUMBtR uF Tl INCREASED IN GEO~crK1CAl RATlu I S:;)R Til. 0 II
• • • • • • • * * • • • • • • • • • • • • • • • • • • • 4< • • • •
zz MJSKE Th l~AX
81 XLI U X1l21
EARTHQUAKE ACCELEROGRAM NUMdER OF DATA uF EA,{THi,lUAKE ACCELERO"RAM T Ha: INCREMlNT MAXIMUM ACCELERATION
STIFFNESS Of EACH REGION C~AC~ING DISPLACEMENT YIELDING DI5PLAClMlNT
• • • • • • • • * • • * • * • • • • * * * * • • * • • • * * * * •
IF LAST CARD IS ~STOP"1COLU~N 1-41, SUBROUTINE RETuRNS TO MAIN.
• • • • • • • • • • • • • • • • * • * • * • • • * • * • • • • • •
DIMENSION NAME1IHI,BI1J),XI12),lllMJSKE),DXEI21 DATA ~AERE/4rlSTOP/
READ 100, NAMCI. IF lNAMElIll.EQ.II.AEKEI GO TO 9999 READ 102, Tl,XI5TR,DAMP,AMAX,lO X2STR=1.9*X1STR
SHCt+ S~H
SHC:H SHeH SHeH S",H SHtH SHeH SHC.H SHeH SHCH
SHeH StiCH SHCH SHeH SHeH SHeH SHeH SHeH StICH SHeH SHeH SHCH SHeH SHeH SHCH SHeH SHCH SHGH SriCH SHCH SHCH iHCH SH<:H SHCH SHCH SHeH ShCH SHCH SHCH SHeH SH(;H S~H
SHeH SHeH SHCH SHeH SHCH StiCH SHCH SHCH SHeH SHert SHCH SHCH SHeH
~51 . ItS8 ~S9 ·~O
'"1 ,"2 ItU .... •• s ." ltd
-.oi '"9 ~10
.11 ~12 ~B
~n ~lS
~1t. ~71 Hi ~N
~80
.81 ~82 'oal ~8. ~8S 'tab ~81
~tla
~8'i '090 ~91
1t92 ~9l '09'0 'o9~ 49(> ~91 ~98
~99 ,00 501 ,02 SOl ,04 ,0, ,06 SOl 508 S09 S10 ~Hl 512
C
REOUCT-O.19 00 1 11-1,10 IIRR"II-1 T1a Tl*SQkTCl.01*.IIRK PRINT 10~, NAMEl,AMAX,X1SrR,X2~TK,REOUCT,OAMP
81(1."C6.l8318,/T11**2 81(l."REOUCT*SI111 8X-980.*CXlSTR-X1STKI X1(1I a 980.*XlSTR/blCll X112.,,980.*XlSTK/b11Z1 81ll. s aX/CX1Cl'-Xlil" 81131:0.001*SI121 NSTEP"l IF(II.GI.lI ~STEP=2 OELTAT=TH*FLOATINSTtPI PRiNT 106, Tl,OELTAT,Xl Ad.,SlIll AR=2.*OAMP*SQRrlABI LLL=l IOA z 8 IFIll.liT.'>1 10A=" IFIII.GT.71 IOA=2 A2=O.O '12=0.0 02=0.0 '11/2=0.0 OUMAX=O .0 OXEI 1I=xl( 11 OXEI21=xlI21 K2"1 GGz lOA OTzOELT AT IGG
C RESPONSE ANALVSIS C
C
00 l la1,MJSKE,NSTEP A1 a A2 .
.'11-'12 01-0l VVl-VVl Kl-Kl IFCJ.NE.11 GO To 10 l.LZlllaZlC 11 GO TO 15
10 II la I-NS TEP llllllallCII-llI!111
15 CONTINUE 1.1.lllla980.*llllll*AMAXllMAX CALL RESPl IlllllZ,A2,AK,AS,Al,vl,Dl,uELTAT,VL,Ui,vl/i,LLL) lll-O IFC I-U 20,25,2J
20 CONTINUE
C JUDGE FOR CHANGE OF POSITION C
CAll MASA'VV1.VV2.D2,OXt,~1,LLLI IFClLll 30,2,,30
25 CONTINUE CALL AVOMAXC02.DOMAXI
GO TO l
73
StiCH ,13 -SHCH ,14 SHCH ,1'> SHCH ,1t. SHCH 511 SHCH ,Ab SHCH 519 SHCH 520 SHCH 5.!l SnCH '>22 SHCH 523 SHCH '>24 SHCH 5,,~
StiCH 520 SnCH 527 SHGH 5iB SHCH '>29 SHCH 530 SHCH 531 SHCH 532 SHCH 533 :'rlCH 534 StiCH 53:> SHCh 530 StiCH '>)7 ~tiCti 53d SHCH :'J'j StiCH 54lJ StiCH :'41. SHCH ~42
SHCH :.43 SHCH ~44
SHCH 545 SnCH 540 SHCH 5'01 SHCH 54d SHCH 5 .. 9 SHCH 550 SHCH 551 SHCH 552 ~HCH 553 SHCH 55<; SHCH 555 SHCH 556 StiCH 557 SHCH 551l SHCH '>5':1 SHCH '><>0 SNCH 50! SHCH 51>2 SHCH 503 SHCH ')6'0 SHCH '>05 SHCH 506 SHCH 561 SHCH 'Gd SHCH 5<>9 ~H('H ,10 :.HCH 571. SHCH 512
C C C
C C C
C C C C
74
30 ZZZZZZ&ZlZZlZ/GG
RESPONSE ANALYSIS fOR SUBOIVIDEO INTE~VAL
DO 3 (Aa 1 ,lOA (FIlA-II ~0,45,40
ItO CONTINUE AI-A2 Vl"V2 01-02 VVlaVV2 Kl"'Kl
45 CUNTINUE CALL RESPI IllZlZZ~Al,AR,A8,Al,Vl,Dl,DT
lLL=O .V2,Dl,VV2,LLU
JUOGE FOR CHANGE Of PQSITION ANU DETERMINATION OF STIFfNESS
CALL JUNKU(~l,A8.X2STR,VWl.VV2,OZ.DXE.Kl,K2,LLLI IFtLLLI 50.55,50
50 CONT INUE AR=2.*OAMP*SQRTIAdl CALL AVDMAXID2,DOMAXI GO TO 3
55 CONTINUE CALL AVO~AX(02,OJ~AXI
3 CONT INUE LLl=l
2 CONTINUE DUCT=DUMAX/XlIlI PRINT lu8, OQMAX,uUCT
1 CONTINUE GO TU 1000
100 FORMA T( 8A41 102 FORMAT(4F8.0,141 104 FORMAT (IHl,8A~11
1 35H AVERAGE OF MAAIMUM ACCELERATION 2 35H CRACKING 5HEA~ ST~ENGTH 3 35H ULTIMATE SHEAR STRENGTH 4 35H ~ATIO OF K2 TO Kl (REJUCTIUNI
,Fo.31 • ,fr..31 ~ ,fo.21
,Fo.31 5 35H DAMPING RATIU • ,F~.3IJ)
106 FORMAT (IH ,/ 1 25H NATURAL PERI00 '" ,F8.31 2 25H TIME INCREMENT • ,Fd.31 3 25H CRACKING DISPLACEMENT'" ,F8.3,2X,3HCM I 4 25H ULTIMATE DISPLACEMENT ,Fd.J,lX,3HCM III
108 FORMAT 11H ,/ 1 24H MAXIMJM DISPLACEMENT ,FIO.3,2X.3HCM I 2 24H DUCTILITY FACTUR NT - ,FIO.3111
9999 RETURN END
SUdROUTlNE JUNKO 'dl,Ad.X2~TR.V~.Vl.02,DXE.~l.K2.KI
• • • • • • • • • • * • • • • * • • • • • • • • • • . . .. SElECT ION llF STIFFNESS AT NEXT STEP
• • • •
SHeH SHc:H SHc:H
. SHc:H SHCH. SHCH SHCH SHCH SHeH StiCH SHCH StiCH SHeH SHC.H SHCH SrlcH StiCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SH('H SHCH SHCH SHCH SH<.H StiCH SHCH SHCH SHCH StiCH SHCH SHeH SHCH SHCH SHeH StiCH SHCH SHCH Sm;H SHcH StiCH SHCH SHCH SHeH
~KCH
SIiCH SIiCH $H'H ~H
S13 Slit
. ·575 510 S7I 518 5N 580 581 582 5i13 581t 585 58t. 581 5d8 5i1~
59U 591 592 593 594 59) 590 597 598 )9'1
600 toOL b02 603 oO~
605 00" b07 008 b09 010 011 612 613 ollt 615 t>lto 611 b18 tJl.9 blO 021 4>22 623
&l~
025 026 6U 628
c , c c c c C c c C C C C C C C C C C C
c c c c
INPUT DAU
IH X2STR '11 '12 02 DXE
K1
OUTPUT DAU
AS K2 K
STIFfNESS OF EACH REGION ULTIMATI: ;;TKENGTH I,~ TE'{MS OF liASt: SHtAk COI::FFICltNT INC'{EME~TAL Dis~lAC~MtNT AT LAST ~TEP INCRE~ENTAl DISPLACt:MENT ~l:lATIVE Ol~PLACI:MI:NT ORIGINAL Ok M~DIFIEU DI;;PlACE~t:NT CUKRI:SPONUING TU SREAI<.-PUINT INDeX full. POSITION
STIFFNES~ AT NEXT ~TEP
l.NDEX fUR POSITlO~ AT NEXT _STEP INDEX fOR CHANGE ~F PuSITION K=O NUN
• $ • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
Ol~NSION DXE(2),Bll3) Ifl'l1.V2) 10.1(1,20
10 IfCK1.E~.1) GO Tu 30 ZaASSlD2) IflKl-2J 40,40,50
40 ST-B1Il).OXEI1J GO TO bO
50 ST"'980.*X2STR 60 ST"'ST+Bl(Kl).(l-DXEIKl-ll.
AS-STIZ 811lJ-AB OXEll'·Z 1(2&1 K--l GO TO 10
20 IfIKl.NE.l) GO TO 70 Z--ASSl02) IFIZ.lT.DXEI1JI GO TO 30 IfCZ.GT.UXEll)) GO Tu dO AB--S1I2. K"Z K2-2 GO TO 10
70 IFIK1.EQ.l) GO TO 30 Z-ASS(D2) Ifll.lT.DXE(2)) GQ TO 30
80 K"l KZ-1 AS-S1I31
10 RETURN END-
SUSROUTINE MASA (Yl.V2,D2,OXE,Kl,l<.)
• • • • • • • • • • • • • • • • • • • • • • • • • • • * • * • * • JUDGE fOR CHAIlGE OF POSIT ION
75
SHCH 629 SHCH b3\) SHCH 631 SHCH b32 SH\:.H oj)
SHCH 034 SHCH bj)
SHCH 030 SHCH 031 StiCH 63d
- SHCH td9 SHCH 640 SHCt1 b41 SHCH 642 SliCH 6 .. 3 SHCH 64 .. SHCti 045 SHCH b'to StiCH 04-1 SHCH b48 SliCH 64'1 SHCH b50 SHCH oS! StiCH 05L StiCH b53 SHCH 054 SHCH b55 StiCH 65b SHCH 651 SttCH 6:i8 SHCH 659 SHCH boO SHCH bol SHCH 602 SkCH 6b3 SHCH bolo SHCH 06) SHCH 000 SHCH 067 SHCH bbd SHCH oog SHCI1 b ,u SKCH tdl SH\:.t-j 672 ShiCH 013 StJCH b 74 SrlCH 075 SHCH 076 SrlCH 671 SI-KH 6ra SI'li..H 019
St-ICH 6BO SHCH 681 SHCH 68L SHCH 683 Sl-ICH 6B4
76
------._----------
c c C 'C C C C C C C C C C C C C
C C C C C C C C C C C C C C C C C C C C C C C C C C C
,C
10
20
30
INPUT DATA
VI INCREMENTAL DISPLACEMENT AT LAST STEP V2 INCREMENTAL OISPLACt~ENT 02 RELATIVe DISPLACEMENT DXE OklGINAL OR MODIFIED DISPLACEMENT CORRESPONDING TU
BREAK-PO HH
JUTPUT DUA
Kl K
INDEX FOR PUSITION INDEX FOR CHANGE OF PUSITION K.Q NuN
• * • • • * * * * ~ * • * • * * * * * * * * • * * • • • • • • • •
DIMENSION DXE (2)
IFIVl*V21 10,10,20 IFIK1.EQ.1l GO TO 30 K= 1 GO TO 30 IF(Kl.E[~.31 Gll TO )0 .l= AB S (02 I IF Il.L T .DXEIKI I I GO 1U 30 K=2 RUUKN END
SUBROUTI~E DTRIlIlll,MJSKE,TH,lMAXI
• • * • • • • • • * * • • * • • • • * • • • * • • * • • * * * • *
NONLINEAR RESPONSE ANALYSIS FOR D~GRAUING TRI-LINEAR MODEL
ORIGINALLY PROGRAMED BY UMEMURA LABORATURY IUNl~EK~lTY OF TO~Yul MOOIFICATIUNS •• M.MURA'(AMI 1915
• * • * • • * • • • • • • * * • * • • • • * * • • • • * • • • • •
INPUT DATA
NAMEl Tl REDUCT
X1STR X2STR OM4P AMAX 10
NAME OF MO)El INITIAL NATURAL PERIOD ISECt RATlll OF Tl TU NATURAL PERIOD CURRESPUNDING fa YIELDING STIFFNtS$ CRACKING STRENGTH I~ TERMS OF SASE SHEAR COEFFICieNT YIELDING STRENGTH IN TtRMS uF SASE SHEAR COEFFICIENT DAMPING RATiO AVERAGE OF MAXIMUM ACCELERATION IN TERMS OF GRAVITY NUMBER UF Tl INCREASED IN GEOMETRICAL RATIU , SQR Tl2. u) •
• * •• * • * •• * ••• * •• * • * * * • * • * ••••••• -.'
ZZ MJSKE
EARTHQUAKE ACCElEROGRAM NUMBER OF DATA OF EARTH~UAKE ACCELER0GRAM
StiCH SHCH SHCH SHCH SHCH SHCH StiCH SHCH SHCH SHCH SHCH SHCH StiCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SItCH SHCH SHCH SHCH SHCH
SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SliCH SHCH SHCH SHCH SHtH SHCH SHCH SHCH SHCH SHCH StiCH SHCH StiCH ~H
SHCM SHCH SHCH StiCH SHCH
685 6do 687 688 b89 690 091 6'12 bY3 691t 695 696. b97 b98 699 700 101 702 Iv} 10 .. 105 106 101 70a 709 110 111
112 1-13 714 715 116 71.7 718 719 7l.U 7ll 7ll. 713 12.4 '125 no 721 na 7H 730 HI. 132 113 U" 115 11b 137 Ui 139 H>~
c c c c c c C c c c c c c
c c c
1000
TH ZHU
81 Xl( 1)
xlfz,
T IHE INCI(EHENT MAXIMUM ACCELERATIUN
STIFFNESS OF EACH R~GION CRACKING OISPLACEMENT YI~LOIN~ OI::oPLACE~ENT
• • • • • • • • • • • • • • • • • • • • * * * * • * • • * * * * •
IF LAST CARD IS "STUP"tCOlUMN L-~). ::oUSROuTIN~ RETURNS TO MAIN.
* • • * * • • • • • • • • • • • • • • * * * * • * •. • * * • • • *
DIMENSION NAMHldl. S1(3). x1(2) .ll(.'USt<.b) 04'A KAERE/4HSTUP/ REAO 100. NAMtl I~ INA~ELll).E~.KAEKE) GO TO 9999 READ 10Z. TL.XISTR.X2STR.~EDUCT.DAMP.AMAX.IO OOlllsl,lO IIRR-II-1 Tl-rl*SQRTIZ.O) •• IIRR PRINT 104, NAME1.AMAX.XISTR,X2STR,REoucr,OAMP RR a OAMP*Tl/1.14159 81'1'-'6.Z8118)/Tl).*2 ~1'Z)sREOUCT.~111)
BX-980.*'XZSTR-XISTRI Xl(1)-980 •• X1STR/BlI11 Xl(Z)-980 •• XZSTR/BlIZ) 811Z)-8X/IXIIZ)-X1111) 81(1)-0.001*SlI2) NsrEP-l Iflll.GT.Zl NSTEP-2 OELTAr-rH*fLOATINSTEP) PRINT 106, Tl,OfLTAT,Xl A8-811U AR""SlIU*RR lll-l IOA-8 Iflll.Gr.5) iOA 3 4 IfU I .GT.1I IOA~2 AZ-1).O vz-o.o OZ-O.O VVZ-O.O OOI4AX-O.O OI4AX-X1(Z) . DIUN--JUI ZI 001"0.0 002-0.0 DCE-Xl (11 DC-XlIlI Oy-xlIZ) AlPHs1.0 KZ-1 (;GaIOA DT-OELTATIGG
RESPONSE ANALYSIS
DO Z I-l,MJSKE.NSTEP
77
£HCH. SHCH SHCH SHCH SHCH SHCH SHCH SH("H SHCH SHCH SHCH ~HCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SHCH SrI(..H SHCH SHCH SHCH SHCH SHCH SHCH SHCH S~lCH
::oMCH S~,CH
SHCH SHCH SHCH SHCH SriCH SHCH SHCH SHeH SHCH SHCH
7'tl HZ 743. 7440 7't5 746 1'01. H8 749 751.1 HJ. 75Z 7)3 754 755 756 hl 75<:1 15'J 160 76!. 762 7,,3 71:>4 105 706 701 768 709 770 771. 712. 773 17'. 175 110 777 778 17 .... l8U 181 lci2 ld3 184 1115 100 787 188 789 7'10 791 HZ 793 794 7'1) 796 791 798 7'i9 800
C C C
c c C
C C C
C C C
78
A1=A2 V1:V2 01"'02 YV1=Vv2 K1 s K2 IFII.NE.11 GU TO 10 llZlll=LZl11 GO TO 15
10 Ill'" I-NSTEP ZZZZZZ=ZZIII-lZIIIII
15 CONTINUE ZZZLZZ=990.*ZZlLZZ*AMAX/ZMAX CAll kESPI (ZZllZl,AZ,AR.AB,Al,Vl.Dl,OElTAT,VZ,02~VV2,lll' IFIl-lI 20,25,20
20 CONTINUE DE=02-DOI-D02
JUOG~ FOR CHANGE OF POSITION
CALL KAlUIVVl.VVZ,D2,DMAX,OMIN,Dt,OCE.Kl,~2,LlL.JJJI IFILlLl JO,25,jO
25 COiH INJE CALL AVOMAXI02,OUMAXI
GU TO 2 30 lZllll=ZZLllllGG
RE~PONSE ANALYSIS FOR SUdDIVIDEO INTtKVAl
DO 3 I A= 1, lOA IFIIA-ll 40,45,40
40 CONTINUE Al=A2 V 1=\12 01=02 VVl=VV2 Kl=K2
45 CONTINUE CALL RESPI IZZZllZtAl,AR,A8,Al,~1.Dl,DT
lll=O OE"'02-DOI-002
JUDGE FOK CHAN~E OF POSITION
.Vl,Ol,VlJ2,llll
CALL KAZJ(VVl,VV2,D2,DMAX,OMIN,OE,DCE,Kl,K2,llL,JJJI IFILLLl 50,55,50
DETERMINATION OF STIFFNESS
50 CALL SHUBOOIBl,AB,lll,JJJ,OMAX,OMIN,DOI,D02,OCE,AlPH,OY,DC,021 AR=AB*RR CAll AVOMAX(D2,OOMAX) GO TO 3
55 CONTINUE CALL AVO~AX(D2,DJMAXI
3 CONTINUE llL=l
l CONTINUt DUC T=DUMAX/XUZ) PRINT 108. DOMAX,OUCT
1 CONTINUE
.. '
SHCH SHeH SHCH SHeH SHeH SHeH SHeH SHeH SHeH SHCH SHCH SHeH SHeH SHeH SHeH SHeH SHeH SHeH SHCH SHCH SHCH SH(;H SHCH SHeH SHeH SHCH SHeH SHCH SHCH SHeH SHeH SHCH SHCH SHeH SHeH SHeH SHeH SHeH SHeH SHeH
, SHeH SH(.H SHeH SHeH SHCH SI't(;H SH<:H SHeH SHeH iHCH SHeH SHeH SHeH SliCH SHC;H SHeH ~H SHC;H $tiCH Sri(;H
I 801 . 802 80) 80~ iO~
80~ 801 808 809 al0 811 812 813 8lit Cll~ 8lb 811 818 819 820 821 822 8£3 8;':4 825 dZt. 8n d28 8.t9 1130
·831 tU2 8ll 834 835 8l~
ill III a 8)9 8itO 8 .. 1 8~l a41 il41t 3 .. 5 3~~
s .. 7 848 849 850 a51 ·a52 a53 u .. iSS ase. as} as. .59
.hO
I .
C C C C C C C
c c c c c c c
, ,'------,---
coo 1:0 1000 100 FORMAT'SAIt) 102 fO~MATI6f8.0,l~1 104 FORMAT 11Hl,aA~11
1 35H AVERAG~ Of ~AXIMUM ACCELERATION a ,Fo.ll 2 35H CRACKING STR~~GTH - ',Fo.ll 3 35H YIELuiNG STR~MGTH a ,F6.31 It 351"1 RATIO Of K2 TU Kl 'K~OUCTIUN) - ,FoAJI 5 351"1 DAMPING KATIO ,. ,Fo.lll)
106 FORMAT 'lH ,I 1 25H NATU~AL P~KIJD % ,Fa.ll 2 25H TIME INCREM~NT = ,Fa.31 3 25H CKAC~ING OISPLACEMENT - ,Fd.3,lX,JHCM I It 25H YIELDING DISPLACtMtNT a ,Fd.3,2X.3HCM II)
108'FORMAT IlH ,I 1 241"1 MAXIMU~ DISPLACEMENT ,Fl~.J,2X,3HCM I 2 241"1 DUCTILITY fACTOR NT .. ,Flu.JIII
9999 RETURN
1
3 2
END
SU8ROUTI~E ERIKOIZ,ZZ,N,NSTEP)
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • LINEAR INTERPOLATION FOR EARTHQUAKE MuT ION
• •••• •••••• • • • • • • • • • • • * * * • * * * * * * *
DIMENSION Zll',Zlll' fN'"'NSTEP DO 1 J"'l,NSTEP ZZIJ'aZlll*FlOATIJI/FN CONTINUE 00 2 I a 2,N ll-NSTEP*II-li DO 3 Jal,NSTEP II 1-1-1 IIJJ-Il+J ZZIIIJJ'-IZII)-Zllll))*FLOATIJ)/FN+lIII1) CONTINUE CONTINUE RETURN ENO
• • • • • • • • • * • • • • • • * • * • • • * • • * • • * * • • *
LINEAR ACCELERATION METHOD
• • • • • * • • * • • • * * • * • • • * * • • * • • • • * * • • * IFIKKK.EQ.O) GO TO 100 OTZsDT /2.0
79
SHCH d61 StiCH 802
'SHCH li63 SHCH 86ft SHCH 8b5 SHCH 860 SHCH 861 SHCH 868 SHCH db9 SHCH 810 :)HCH all SHCH a 12 SHCH 813 StiCH 8H SHCH 1315 StiCH 81b StiCH 817 SHCH 818 SHCH 819
StiCH 880 SHCH aal StiCH 882 SHCH a8l SHeH 884 SnCH 885 SHCH b86 SHCH 887 SHeH 888 SHCH 869 SHCH 890 SHeH 891 SHCH 8n SHCH 8<,13 SHCH 89'<-SHCH 895 SHCH d~6
SHCH 897 SHCH a98 StiCH 8'>19 SHeH 900 StiCH 901 SHCH 902
SHCH 903 SHCH 90'0 SHCH 905 SHCH 900 SHCH 901 SHCH 90d SHCH 909 SHCH 910 SHCH 9il SHCH 912
c c C C C C C C C C C C C C C C C C C C C C C C
C
C
C
80
OT3 .. 0T**2/2.0 OTo .. OT3/3.0 51"'OT6*S+OTZ*A+l 5Z=OT3*6+0T*A 53:DT*S
100 AZz-(SZ*A1+S3*Vl+ZZI/Sl YVZsDT*Vl+OT3*Al+OTo*AZ 02a Dl+VVZ V2-Vl+0T*Al+DTZ*A2 AZ-..A1+AZ RETURN END
SUBROUTINE SHUSOO(S,B~,~,J.DMAX,OMIN,001,DOZ,OCE.ALFA,DY.OC,OZI
* * * * • * * * * * * • * * * • • * * * * * * * • • • • • • • • •
SELECTION OF STIFFNESS AT NEXT STEP
INPUT DATA B DC DY K J D2
OUTPUT OAT A B~
OMAX DMIN 001 DOZ OCE ALFA
ORIGINAL STIFFNESS Of EACM REGION ORIGINAL CRACKING UISPLACEMENT O~IGIN~L YIELDING UISPlACEMENI INDtX FUR CHAN~t Of PuSITION K~O NON INDEX FuR CHANGE OF SIGN OF VELOCITY J_O NuN RELATIVE OISPLACEMENT
STIFFNESS AT NEXT STEP YIELDING O~ MAXIMUM DISPLACEMENT NEGATIVE YItlDING OK MINIMUM UISPLACEMENT CENTER OF FIRST REGION CENTER OF SECOND REGION ORIGINAL OR MOOIFIEu CRACKING DISPLACtMENT RAHO QF fkUUCTlON IN RIGIDITY
• * • • • • • • * * * * • * * * • • • • * • • • • * • • * • * * •
DIMENSION st 31
GO TO (1000,ZOOOI,J
1000 GO TO IIIOO,1200,1300I,K 1100 BK=ALFA*BIll
GO TO 9000 lZ00 BK=ALFA*S(ZI
GO TO 9000 1300 BK=ALFA*B(31
GO TO 9000
2000 IF(KI 3000,3000,4000 C
3000 K=IABSIKI GO TO 16000,3200,3300I,K
3200 001=02-D02+0CE GO TO 6000
3300 OMIN=02
$titH SHCH ~H
SHCH SlitH SHeH SHCH SHeH SHeH SHeH ~CH SHCH
~HCH SHCH SHCH SHCH
f c}13 9H 'liS cU. 911 918' 919 920 921 922 923 920\
925 9Z6 927 '121l
SHCH --92<# SHCH 930 SHeH 9.31 SHCH 'IJ2 SHCH 933 ~HCH 9J't SHCH 935
- SHCH 93t. SHeH 937 SHCH 'HS SHCH 939 SHCH 9'00 SHCH 'HI SHCH 9102 SHCH 9'03 5HCH 91010 SHCH 9105 SHCH 91t6 SttCH 9'07 SttCH 9108 SttCH - 'lit 9 SttCH 9,0 SHCH 9~H StitH 952 SHC.H 9!j]
SHeH 9SIt S~H 955 SHeH 9,co StICH 951 SHCH 958 SHeH 959 SHC.H 9foO SHeH 901 SitCH 962 SiiCH 9U SHCH 9010 SKtH 9.S SHeH 9" SHeH 'jet 7 SHeH 9 foil
ll-DHAX-DMIN ZZ-DY-DC DGI--Zl*ZZ/12.0.0YI GO TO 5000
C 4000 GO TO IbOOO~.100,~LO~I,~
C
c c c C C C C C C C C C C C C C C C C C C
C
4100
.200
5000
6000 9000
001-1)2-002-DCE Go TO 6000 OMAXsOZ 1l-OMAX-0141N ZZ-Oy-OC 001-Zl*Z2/(2.0*OYI
Z3-IZ1-Z.0*OY)*d(3) Z.·S(11·0C+SI21*l2 ZS-2.0+Z31l.4 Al·FA-OY*l. 51 l.1 OOZ-(~AX+DMIN)/2.0
DC~-Zl.DC/2.0/0Y BK-ALFA*SI11 CONT INUE RETURN END
SU~RoutINE KAZUIY1,YZ,X,XI4AX,XMIN.XE,XCE,Kl,K2,K,JI
• • • • * • • • * * * • * • • • • • • • • • • • * • • • • * * * •
JUDGE FOR CHANG~ OF POSITION AND OErEKMINATIO~ OF POSITION
INPUT DATA V1 VZ X XMAX XMIN XE XCE Kl
OUTPUT DATA K2 K J
INCREM~NTAL OISPLACE~~~T
INC~EM~NTAL DI:'PLACb'1ENT UF LAST SrEf> KELATIYE DISPLACEMt~r
YIELDING Ok MAXIMUM uISPLAC~M~~T NEGATI~E YIELDING ~R MI~I~UM UI"PLA~EMENr
RELATIVE OISPLACEMtNT SHI~TED IN :>~tLtlG~ CURVE ORIGINAL OK MQUIFIE~ CRAC~lNG DISPLACt:Mt~r
INDEX FO~ POSITIUN
INDEX FOR PuSITION AT NEXT STEP INDEX FOR CHANGE Of PUSITIUN ~gJ NUN INDEX FOR CHANGE uF D1RECTIUN
• * • * * • • • • • * • * • • • • * • • • • • • * • * • * * * * * IF(Vl*Y2) 2000,2000,100
100 J.sl IFIY21 1000,110,110
110 IF'X-XMAX) 200,150,150 150 KZ s 3
GO TO 1600 200 IF(XE-XCE) 300,250,250 z~o K2 s 2
GO TO 1600 300 IFIXE+XCEI 9999,350,350
81
SHCH '>o~
SH('H 'i10 :>I1CH 911 :>HCH 912 SHCH '173 :,ra.H -if'+ SHCH '11') :>t1CH 'ITo SH(;H '117 :'r1CH ':178 :>riCH '17'> SHCH 980 SHCH 931 SHCH 9dL StiCH '>83 SHCH 9d4 SHCH 935 SHCH 98b SHCH ~81
SHCH 980 SHCH 989 SHCH 990 SHCH 991
St'lCH 99;(, SHCti 993 SnCH 994 SHCH 99j SHCH '>90 StiCH 9 'H SHCH .. 90 SHCH '1':19 :>HCH 1000 SI1~H 1u01 :>hCH 1u~2 SHCH 10,)3 SHCH 1u04 StiCH 100:. SHCH lUOo SliCH 1~0 1 :>HCH 1008 :iHCrl 1009 SHCH 1010 StiCH 1011 "HCH 1012 SnCH 1013 SHCH 101'+ SHCH 1015 SHCH 1016 SHCH 10 11 SHCH l.u18 SHCH 1019 SHCH lOLO SHCH 1021 SHCH LULL SliCH IJ23 SHCI1 10L4
C
C
C C
C
C C. C
82
350 K2=1 GO TO 1600
1000 IFIX-X,'IlN) 1150,1150,1200 1150 K2=3
GO TO lbOO 1200 IF (XE+XCE:) 1250,1250,1300 1250 K2=2
GO TO 1600 1300 (F I XE-XCE) 1350,1350,9999 1350 K2=1
GO TO 1600
1600 IF IK2-Kll 1620,1630,16l0 1610 K=Kl
GO TO 5000 1630 K=O
GO TO 5000
2000 J=l IFIV21 3100,3100,2100
2100 IF I X-AMINI 2150,L150, aoo 2150 K2=-3
GO TO 3500 2200 IF (xE+XCE) 22'>0,2250,4000 2250 1<.2=-2
GO TO :;500 3100 IF (X-XMAXI 3200,jI50dl:>O 3150 K2=3
GO TO 3500 3200 IF(XE-XCE) 4000,3250,3250 3250 K2=2
GO TO 3500 4000 Kl=l
IFIKl-Kll 3500,5500,35,)0 5500 K=O
GO TO 5000 3500 K=K2
j( 2=.1 GO TO 5000
9999 WRITEI6,8000) 3000 FORMATI//,5X,ldH**** LOGICAL MISTAKES * ••• //) 5000 COiH (NUE
4
RETURN END
DATA
D TYPE 15.0
EXAro1PLE
0.01 S.Ho.792 0.6 2.5 3 2.0 2.5 1.606
SHCH 1025 SHCH 1026 SHCH 1027 SHCH 1028 SHCH 1029 SHeH 1039 SHCH 1031 SHeH 1032 SHeH lOB SHCH 10.H SHCH 10:;5 SHCH 10J~
SHCH 1031 SHCH 1038 SHCH 1039 SHCH 1040 SHCH 10 .. 1 SHCH 1042 SHCH 1043 SHCH 1044 SHCH 104) SHCIf 1046 SHCH 10'07 SHCH 10lt8 SHCH l.049 SHCH 1050 :)HCH 1051 SHCH lI)2 SHCH 1053 SHCH 1054 SHCH 1055 SHCH 1056 SHCH 1057 SHCH 10)8 SHCH 1059 SHC"H lObO SHCH lObi SHeH 10b2 SHeH 10bJ ShCH 1064 SHCH lObS StiCH 10bc> SHCH 10b7 SHCH 10b8 SHCH 1009 SHCH 1070 SHCH 1011
SHCH 1012 SHCH lon StiCH 10H Sli(;H 1075 SHCH 1070 SHCH i1l7] StiCH 10./8 SHCH 1019 StiCH 1080
0.707113 0.5 011111
ORIGIN ORIENTED MODEL 0.1 u.50 u.o~ 1.0 STJP DEGRADING TRI-lINEA~ MUDEl 0.1 0.25 v.50 0.25 STOP
2
0.1.12 1.0 2
, 83
SHCH 1081 SHCH 108l SHCH lOiU SHCH 10114 SHCH 1u85 SHCH .l.Otlo SHCH 10tl7 SHCH 1088 SHCH lu89 SHCH 1090 SHCH 1u91
84
EERC 67-1
EERC 68-1
EERC 68-2
EERC 68-3
EERC 68-4
EERC 68-5
EERC 69-1
EERC 69-2
'EERC 69-3
EERC 69-4 •
EERC 69-5
EAR'l'HQUAKE ENGINEERING RESEARCH CENTER REPORTS
"Feasibility Study Large-Scale Earthquake Simulator Facility," by J. Penzien, J. G. Bouwkamp, R. W. Clough and D. Rea - 1967 (PB 187 905)
Unassigned
"Inelastic Behavior of Beam-to-Column Subassemblages Under Repeated Loading," by V. V. Bertero - 1968 (PB 184 888)
"A Graphical Method for Solving the Wave ReflectionRefraction Problem," by H. D. McNiven and Y. Mengi 1968 (PB 187 943)
"Dynamic Properties of McKinley School Buildings," by D. Rea, J. G. Bouwkamp and R. W. Clough - 1968 (PB 187 902)
"Characteristics of Rock Motions During Earthquakes," by H. B. Seed, I. M. Idriss and F. W. Kiefer - 1968 (PB 188 338)
"Earthquake Engineering Research at Berkeley," - 1969 (PB 187 906)
"Nonlinear Seismic Response of Earth Structures," by M. Dibaj and J. Penzien - 1969 (PB 187 904)
"Probabilistic Study of the Behavior of Structures During Earthquakes," by P. Ruiz and J. Penzien - 1969 (PB 187 886)
"Numerical Solution of Boundary Value Problems in Structural Mechanics by Reduction to an Initial Value Formulation," by N. Distefano and J. Schujman - 1969 (PB 187 942)
"Dynamic Programming and the Solution of the Biharmonic Equation," by N. Distefano - 1969 (PB 187 941)
Note: Numbers in parenthesis are Accession Numbers assigned by the National ~echnical Information Service. Copies of these reports rnay be ordered from the National Technical Information Service, 5285 Port Royal Road, Springfield, Virginia, 22161. Accession Numbers should be quoted on orders for the reports (PB --- ---) and remittance must accompany each order. (Foreign orders, add $2.50 extra for mailing charges.) Those reports without this information listed are not yet available from NTIS. Upon request, EERC will mail inquirers this information when it becomes available to us.
EERC 69-6
EERC 69-7
EERC 69-8
EERC 69-9
EERC 69-10
EERC 69-11
EERC 69-12
EERC 69-13
EERC 69-14
EERC 69-15
EERC 69-16
EERC 70-1
EERC 70-2
"Stochastic Analysis of Offshore Tower Structures," by A. K. Malhotra and J. Penzien - 1969 (PB 187 903)
"Rock Motion Accelerograms for High Magnitude Earthquakes," by H. B. Seed and r. M. Idriss - 1969 (PB 187 940)
"Structural Dynamics Testing Facilities at the University of California, Berkeley," by R. M. Stephen, J. G. Bouwkamp, R. W. Clough and J. Penzien - 1969 (PB 189 111)
"Seismic Response of Soil Deposits Underlain by Sloping Rock Boundaries," by H. Dezfulian and H. B. Seed - 1969 (PB 189 114)
"Dynamic Stress Analysis of Axisymmetric Structures under Arbitrary Loading," by S. Ghosh and E. L. Wilson - 1969 (PB 189 026)
"Seismic Behavior of Multistory Frames Designed by Different Philosophies," by J. C. Anderson and V. V. Bertero - 1969 (PB 190 662)
"Stiffness Degradation of Reinforcing Concrete Structures Subjected to Reversed Actions," by V. V. Bertero, B. Bresler and H. Ming Liao - 1969 (PB 202 942)
"Response of Non-Uniform Soil Deposits to Travel Seismic Waves," by H. Dezfulian and H. B. Seed - 1969 (PB 191 023)
"Damping Capacity of a Model Steel Structure," by D. Rea, R. W. Clough and J. G. Bouwkamp - 1969 (PB 190 663)
"Influence of Local Soil Conditions on Building Damage Potential during Earthquakes," by H. B. Seed and I. M. Idriss - 1969 (PB 191 036)
"The Behavior of Sands under Seismic Loading Conditions," by M. L. Silver and H. B. Seed - 1969 (AD 714 982)
"Earthquake Response of Concrete Gravity Dams," by A. K. Chopra - 1970 (AD 709 640)
"Relationships between Soil Conditions and Building Damage in the Caracas Earthquake of July 29, 1967," by H. B. Seed, I. M. Idriss and H. Dezfulian - 1970 (PB 195 762)
85
86
EERC 70-3
EERC 70-4
EERC 70-5
EERC 70-6
EERC 70-7
EERC 70-8
EERC 70-9
EERC 70-10
EERC 71-1
EERC 71-2
EERC 71-3
EERC 71-4
EERC 71-5
"Cyclic Loading of Full Size Steel Connections," by E. P. Popov and R. M. Stephen - 1970 (PB 213 545)
"Seismic Analysis of the Charaima Building, Caraballeda, Venezuela," by Subcommittee of the SEAONC Research Committee: V. V. Bertero, P. F. Fratessa, S. A. Mahin, J. H. Sexton, A. C. Scordelis, E. L. Wilson, L. A. Wyllie, H. B. Seed and J. Penzien, Chairman - 1970 (PB 201 455)
"A Computer Program for Earthquake Analysis of Dams," by A. K. Chopra and P. Chakrabarti - 1970 (AD 723 994)
"The Propagation of Love Waves across Non-Horizontally Layered Structures," by J. Lysmer and L. A. Drake -1970 (PB 197 896)
"Influence of Base Rock Characteristics on Ground Response," by J. Lysmer, H. B. Seed and P. B. Schnabel - 1970 (PB 197 897)
"Applicability of Laboratory Test Procedures for Measuring Soil Liquefaction Characteristics under Cyclic Lo'ading," by H. B. Seed and W. H. Peacock -1970 (PB 198 016)
"A Simplified Procedure for Evaluating Soil Liquefaction Potential," by H. B. Seed and 1. M. Idriss - 1970 (PB 198 009)
"Soil Moduli and Damping Factors for Dynamic Response Analysis," by H. B. Seed and I. M. Idriss - 1970 (PB 197 869)
"Koyna Earthquake and the Performance of Koyna Dam," by A. K. Chopra and P. Chakrabarti - 1971 (AD 731 496)
"Preliminary In-Situ Measurements of Anelastic Absorption in Soils Using a Prototype Earthquake Simulator," by R. D. Borcherdt and P. W. Rodgers -1971 (PB 201 454)
"Static and Dynamic Analysis of Inelastic Frame Structures," by F. L. Porter and G. H. Powell - 1971 (PB 210 135)
"Research Needs in Limit Design of Reinforced Concrete Structures," by V. V. Bertero - 1971 (PB 202 943)
"Dynamic Behavior of a High-Rise Diagonally Braced Steel Building," by D. Rea, A. A. Shah and J. G. Bouwkamp - 1971 (PB 203 584)
EERC 71-6
EERC 71-7
EERC 71-8
EERC 72-1
EERC 72-2
EERC 72-3
EERC 72-4
EERC 72-5
EERC 72-6
EERC 72-7
EERC 72-8
EERC 72-9
EERC 72-10
"Dynamic stress Analysis of Porous Elastic Solids Saturated with Compressible Fluids," by J. Ghaboussi and E. L. Wilson - 1971 (PB 211 396)
"Inelastic Behavior of Steel Beam-to-Column Subassemblages," by H. Krawinkler, V. V. Bertero and E. P. Popov - 1971 (PB 211 335)
"Modification of Seismograph Records for Effects of Local Soil Conditions," by P. schnabel, H. B. Seed and J. Lysmer - 1971 (PB 214 450)
"Static and Earthquake Analysis of Three Dimensional Frame and Shear Wall Buildings," by E. L. Wilson and H. H. Dovey - 1972 (PB 212 904)
"Accelerations in Rock for Earthquakes in the Western United States," by P. B. Schnabel and H. B. Seed -1972 (PB 213 100)
"Elastic-Plastic Earthquake Response of Soil-Building Systems," by T. Minami - 1972 (PB 214 868)
"Stochastic Inelastic Response of Offshore Towers to Strong Motion Earthquakes," by M. K. Kaul - 1972 (PB 215 713)
"Cyclic Behavior of Three Reinforced Concrete Flexural Members with High Shear," by E. P. Popov, V. V. Bertero and H. Krawinkler - 1972 (PB 214 555)
"Earthquake Response of Gravity Dams Including Reservoir Interaction Effects," by P. Chakrabarti and A. K. Chopra - 1972 (AD 762 330)
"Dynamic Properties on Pine Flat Dam," by D. Rea, C. Y. Liaw and A. K. Chopra - 1972 (AD 763 928)
"Three Dimensional Analysis of Building Systems," by E. L. Wilson and H. H. Dovey - 1972 (PB 222 438)
"Rate of Loading Effects on Uncracked and Repaired Reinforced Concrete Members," by S. Mahin, V. V. Bertero, D. Rea and M. Atalay - 1972 (PB 224 520)
"Computer Program for static and Dynamic Analysis of Linear Structural Systems," by E. L. Wilson, K.-J. Bathe, J. E. Peterson and H. H. Dovey - 1972 (PB 220 437)
87
88
EERC 72-11
EERC 72-12
EERC 73-1
EERC 73-2
EERC 73-3
EERC 73-4
EERC 73-5
EERC 73-6
EERC 73-7
EERC 73-8
EERC 73-9
EERC 73-10
EERC 73-11
EERC 73-12
"Literature Survey - Seismic Effects on Highway Bridges," by T. Iwasaki, J. Penzien and R. W. Clough -1972 (PB 215 613)
"SHAKE-A Computer Program for Earthquake Response Analysis of Horizontally Layered Sites," by P. B. Schnabel and J. Lysmer - 1972 (PB 220 207)
"Optimal Seismic Des ign of Multistory Frame s ," by V. V. Bertero and H. Kamil - 1973
"Analysis of the Slides in the San Fernando Dams during the Earthquake of February 9, 1971," by H. B. Seed, K. L. Lee, I. M. Idriss and F. Makdisi -1973 (PB 223 402)
"Computer Aided Ultimate Load Design of Unbraced Multistory Steel Frames," by M. B. EI-Hafez and G. H. Powell - 1973
"Experimental Investigation into the Seismic Behavior of Critical Regions of Reinforced Concrete Components as Influenced by Moment and Shear," by M. Celebi and J. Penzien - 1973 (PB 215 884)
"Hysteretic Behavior of Epoxy-Repaired Reinforced Concrete Beams," by M. Celebi and J. Penzien - 1973
"General Purpose Computer Program for Inelastic Dynamic Response of Plane Structures," by A. Kanaan and G. H. Powell - 1973 (PB 221 260)
"A Computer Program for Earthquake Analysis of Gravity Dams Including Reservoir Interaction," by P. Chakrabarti and A. K. Chopra - 1973 (AD 766 271)
"Behavior of Reinforced Concrete Deep Beam-Column Subassemblages under Cyclic Loads," by o. Kustu and J. G. Bouwkamp - 1973
"Earthquake Analysis of Structure-Foundation Systems," by A. K. Vaish and A. K. Chopra - 1973 (AD 766 272)
"Deconvolution of Seismic Response for Linear Systems," by R. B. Reimer - 1973 (PB 227 179)
"SAP IV: A Structural Analysis Program for static and Dynamic Response of Linear Systems," by K.-J. Bathe, E. L. Wilson and F. E. Peterson - 1973 (PB 221 967)
"Analytical Investigations of the Seismic Response of Long, Multiple Span Highway Bridges," by W. S. Tseng and J. Penzien - 1973 (PB 227 816)
EERC 73-13
EERC 73-14
EERC 73-15
EERC 73-16
EERC 73-17
EERC 73-18
EERC 73-19
EERC 73-20
EERC 73-21
EERC 73-22
EERC 73-23
EERC 73-24
EERC 73-25
EERC 73-26
"Earthquake Analysis of Multi-Story Buildings Including Foundation Interaction," by A. K. Chopra and J. A. Gutierrez - 1973 (PB 222 970)
"ADAP: A Computer Program for Static and Dynamic Analysis of Arch Dams," by R. W. Clough, J. M. Raphael and S. Majtahedi - 1973 (PB 223 763)
"Cyclic Plastic Analysis of Structural Steel Joints," by R. B. Pinkney and R. W. Clough - 1973 (PB 226 843)
"QUAD-4: A Computer Program for Evaluating the Seismic Response of Soil Structures by Variable Damping Finite Element Procedures," by I. M. Idriss, J. Lysmer, R. Hwang and H. B. Seed - 1973 (PB 229 424)
"Dynamic Behavior of a Multi-Story Pyramid Shaped Building," by R. M. Stephen and J. G. Bouwkamp - 1973
"Effect of Different Types of Reinforcing on Seismic Behavior of Short Concrete Columns," by V. V. Bertero, J. Hollings, O. Kustu, R. M. Stephen and J. G. Bouwkamp - 1973
"Olive View Medical Center Material Studies, Phase I," by B. Bresler and V. V. Bertero - 1973 (PB 235 986)
"Linear and Nonlinear Seismic Analysis Computer Programs for Long Multiple-Span Highway Bridges," by W. S. Tseng and J. Penzien - 1973
"Constitutive Models for Cyclic Plastic Deformation of Engineering Materials," by J. M. Kelly and P. P. Gillis - 1973 (PB 226 024)
"DRAIN - 2D User's Guide," by G. H. Powell - 1973 (PB 227 016)
"Earthquake Engineering at Berkeley - 1973" - 1973 (PB 226 033)
Unassigned
"Earthquake Response of Axisymmetric Tower Structures Surrounded by Water," by C. Y. Liaw and A. K. Chopra -1973 (AD 773 052)
"Investigation of the Failures of the Olive View Stairtowers during the San Fernando Earthquake and Their Implications in Seismic Design I" by V. V. Bertero and R. G. Collins - 1973 (PB 235 106)
89
90
EERC 73-27
EERC 74-1
EERC 74-2
EERC 74-3
EERC 74-4
EERC 74-5
EERC 74-6
EERC 74-7
EERC 74-8
EERC 74-9
EERC 74-10
EERC 74-11
EERC 74-12
"Further Studies on Seismic Behavior of Steel BeamColumn Subassernblages," by V. V. Bertero, H. Krawinkler and E. P. Popov - 1973 (PB 234 172)
"seismic Risk Analysis," by C. S. Oliveira - 1974 (PB 235 920)
"Settlement and Liquefaction of Sands under Multi-Directional Shaking," by R. Pyke, C. K. Chan and H. B. Seed - 1974
"Optimum Design of Earthquake Resistant Shear Buildings," by D. Ray, K. S. Pister and A. K. Chopra -1974 (PB 231 172)
"LUSH - A Computer Program for Complex Response Analysis of Soil-Structure systems," by J. Lysmer, T. Udaka, H. B. Seed and R. Hwang - 1974 (PB 236 796)
"Sensitivity Analysis for Hysteretic Dynamic Systems: Applications to Earthquake Engineering," by D. Ray -1974 (PB 233 213)
"soil-Structure Interaction Analyses for Evaluating Seismic Response," by H. B. Seed, J. Lysmer and R. Hwang - 1974 (PB 236 519)
Unassigned
"Shaking Table Tests of a Steel Frame - A Progress Report," by R. W. Clough and D. Tang - 1974
"Hysteretic Behavior of Reinforced Concrete Flexural Members with Special Web Reinforcement," by V. V. Bertero, E. P. Popov and T. Y. Wang - 1974 (PB 236 797)
"Applications of Reliability-Based, Global Cost Optimization to Design of Earthquake Resistant Structures," by E. Vitiello and K. S. Pister - 1974 (PB 237 231)
"Liquefaction of Gravelly Soils under Cyclic Loading Conditions," by R. T. Wong, H. B. Seed and C. K. Chan 1974
"Site-Dependent Spectra for Earthquake-Resistant Design," by H. B. Seed, C. Ugas and J. Lysmer - 1974
EERC 74-13
EERC 74-14
EERC 74-15
EERC 75-1
EERC 75-2
EERC 75-3
EERC 75-4
EERC 75-5
EERC 75-6
EERC 75-7
EERC 75-8
EERC 75-9
"Earthquake Simulator Study of a Reinforced Concrete Frame," by P. Hidalgo and R. W. Clough - 1974 (PB 241 944)
"Nonlinear Earthquake Response of Concrete Gravity Dams," by N. Pal - 1974 (AD/A006583)
"Modeling and Identification in Nonlinear Structural Dynamics, I - One Degree of Freedom Models," by N. Distefano and A. Rath - 1974 (PB 241 548)
"Determination of Seismic Design Criteria for the Dumbarton Bridge Replacement Structure, Vol. I: Description, Theory and Analytical Modeling of Bridge and Parameters," by F. Baron and S.-H. Pang - 1975
"Determination of Seismic Design Criteria for the Dumbarton Bridge Replacement Structure, Vol. 2: Numerical Studies and Establishment of Seismic Design Criteria," by F. Baron and S.-H. Pang - 1975
"Seismic Risk Analysis for a Site and a Metropolitan Area," by C. S. Oliveira - 1975
"Analytical Investigations of Seismic Response of Short, Single or Multiple-Span Highway Bridges," by Ma-chi Chen and J. Penzien - 1975 (PB 241 454)
"An Evaluation of Some Methods for Predicting Seismic Behavior of Reinforced Concrete Buildings," by Stephen A. Mahin and V. V. Bertero - 1975
"Earthquake Simulator Study of a Steel Frame Structure, Vol. I: Experimental Results," by R. W. Clough and David T. Tang - 1975 (PB 243 981)
"Dynamic Properties of San Bernardino Intake Tower," by Dixon Rea, C.-Y. Liaw, and Anil K. Chopra - 1975 (AD/A008406)
"Seismic Studies of the Articulation for the Dumbarton Bridge Replacement Structure, Vol. I: Description, Theory and Analytical Modeling of Bridge Components," by F. Baron and R. E. Hamati - 1975
"Seismic Studies of the Articulation for the Dumbarton Bridge Replacement Structure, Vol. 2: Numerical Studies of Steel and Concrete Girder Alternates," by F. Baron and R. E. Hamati - 1975
91
92
EERC 75-10
EERC 75-11
EERC 75-12
EERC 75-13
EERC 75-14
EERC 75-15
EERC 75-16
EERC 75-17
EERC 75-18
EERC 75-19
EERC 75-20
EERC 75-21
EERC 75-22
EERC 75-23
"Static and Dynamic Analysis of Nonlinear Structures," by Digambar P. Mondkar and Graham H. Powell - 1975 (PB 242 434)
"Hysteretic Behavior of Steel Columns," by E. P. Popov, V. V. Bertero and S. Chandramouli - 1975
"Earthquake Engineering Research Center Library Printed Catalog" - 1975 (PB 243 711)
"Three Dimensional Analysis of Building Systems," Extended Version, by E. L. Wilson, J. P. Hollings and H. H. Dovey - 1975 (PB 243 989)
"Determination of Soil Liquefaction Characteristics by Large-Scale Laboratory Tests," by Pedro De Alba, Clarence K. Chan and H. Bolton Seed - 1975
"A Literature Survey - Compressive, Tensile, Bond and Shear Strength of Masonry," by Ronald L. Mayes and Ray w. Clough - 1975
"Hysteretic Behavior of Ductile Moment Resisting Reinforced Concrete Frame Components," by V. V. Bertero and E. P. Popov - 1975
"Relationships Between Maximum Acceleration, Maximum Velocity, Distance from Source, Local Site Conditions for Hoderately Strong Earthquakes," by H. Bolton Seed, Ramesh Murarka, John Lysmer and I. M. Idriss - 1975
"The Effects of Hethod of Sample Preparation on the Cyclic Stress-Strain Behavior of Sands," by J. Paul Mulilis, Clarence K. Chan and H. Bolton Seed - 1975
"The Seismic Behavior of Critical Regions of Reinforced Concrete Components as Influenced by Moment, Shear and Axial Force," by B. Atalay and J. Penzien - 1975
"Dynamic Properties of an Eleven Story Masonry Building," by R. M. Stephen, J. P. Hollings, J. G. Bouwkamp and D. Jurukovski - 1975
"State-of-the-Art in Seismic Shear Strength of Masonry -An EVdluation and Review," by Ronald L. Mayes and Ray W. Clough - 1975
"Frequency Dependencies Stiffness Matrices for Viscoelastic Half-Plane Foundations," by Anil K. Chopra, P. Chakrabarti and Gautam Dasgupt.a - 1975
"Hysteretic Behavior of Reinforced Concrete Framed Walls," by T. Y. Wong, V. V. Bertero and E. P. Popov - 1975
EERC 75-24
EERC 75-25
EERC 75-26
EERC 75-27
EERC 75-28
EERC 75-29
EERC 75-30
EERC 75-31
EERC 75-32
EERC 75-33
EERC 75-34
EERC 75-35
EERC 75-36
EERC 75-37
EERC 75-38
"Testing Facility for Subassemblages of Frame-Wall Structural Systems," by V. V. Bertero, E. P. Popov and T. Endo - 1975
"Influence of Seismic History on the Liquefaction Characteristics of Sands," by H. Bolton Seed, Kenji Nori and Clarence K. Chan - 1975
"The Generation and Dissipation of Pore Water Pressures During Soil Liquefaction," by H. Bolton Seed, Phillippe P. Martin and John Lysmer - 1975
"Identification of Research Needs for Improving a Seismic Design of Building Structures," by V. V. Bertero - 1975
93
"Evaluation of Soil Liquefaction Potential during Earthquakes," by H. Bolton Seed, 1. Arango and Clarence K. Chan 1975
"Representation of Irregular Stress Time Histories by Equivalent Uniform Stress Series in Liquefaction Analyses," by H. Bolton Seed, I. N. Idriss, F. Makdisi and N. Banerjee 1975
"FLUSH - A Computer Program for Approximate 3-D Analysis of Soil-Structure Interaction Problems," by J. Lysmer, T. Udaka, C.-F. Tsai and H. B. Seed - 1975
"ALUSH - A Computer Program for Seismic Response Analysis of Axisymmetric Soil-Structure Systems," by E. Berger, J. Lysmer and H. B. Seed - 1975
"TRIP and TRAVEL - Computer Programs for Soil-Structure Interaction Analysis with Horizontally Travelling Waves," by T. Udaka, J. Lysmer and H. B. Seed - 1975
"Predicting the Performance of Structures in Regions of High Seismicity," by Joseph Penzien - 1975
"Efficient Finite Element Analysis of Seismic Structure -Soil - Direction," by J. Lysmer, H. Bolton Seed, T. Udaka, R. N. Hwang and C. -F. Tsai - 1975
"The Dynamic Behavior of a First Story Grider of a ThreeStory Steel Frame Subjected to Earthquake Loading," by Ray W. Clough and Lap-Yan Li - 1975
"Earthquake Simulator Study of a Steel Frame Structure, Vol. II - Analytical Results," by David T. Tang - 1975
"ANSR-I General Purpose Computer Program for Analysis of Non-Linear Structural Response," by Digambar P. Mondkar and Graham H. Powell - 1975
"Nonlinear Response Spectra for Probabilistic Seismic Design and Damage Assessment of Reinforced Concrete Structures," by Masaya Murakami and Joseph Penzien - 1975
