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A Report on Research Sponsored by NATIONAL SCIENCE FOUNDATION
(ASRA) Grant No. ENV77-l5333
STRUCTURAL WALLS IN EARTHQUAKE-RESISTANT BUILDINGS
Dynamic Analysis of Isolated Structural Walls
REPRESENTATIVE LOADING HISTORY
by
Arnaldo T. Derecho Mohammad Iqbal
Satyendra K. Ghosh Mark Fintel
w. Gene Corley
Submitted by RESEARCH AND DEVELOPMENT
CONSTRUCTION TECHNOLOGY LABORATORIES PORTLAND CEMENT ASSOCIATION
5420 Old Orchard Road Skokie, Illinois 60077
August 1978
Any opinions, findings, conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
I
50272 -101 3. Recipient's Accession No. REPORT DOCUMENTATION II:.-REPORT NO. 1
2 .
1--___ P_AG_E _____ L-_N-=-SF-.-:/_R_A_-7_8_0_2_55 ____ .. ___ ----'-_____ --t-:=-=--~---------l 4. Title and Subtitle 5. Re.l'°urtguD8stet 1978
Structural Walls in Earthquake-Resistant Buildings, Dynamic f\
Analysis of Isolated Structural Walls - Representative Loadinrt-6.--------------------~ Historv, Final Report ----------.. - ----.-------------- .. ---------------1
7. Author(s) A.T. Derecho, M.~bal. S.K. Ghosh et al
9. Performing Organization Name and Address Portland Cement Association 5420 Old Orchard Road Skokie, Illinois 60077
B. Performing Organization Rept. No. PCA Ser. 1589
--~----------------~ 10. Project/Task/Work Unit No. --------.---------~
11. Contract(C) or Grant(G) No. (C)
(G) ENV7715333 t-:-::-::--~---:---:------------------------------.-- .... ---- -----.---------------12. Sponsoring Organization Name and Address 13. Type of Report & Period Covered
Applied Science and Research applications (ASRA) Final National Science Foundation 1 1 1800 G Street, N.W. __ 2.74 ---- 978 ___ -.---
14.
Washington, DC 20550 1------=----'------------------.-----.-------------.----- --- -.------------------I
15. Supplementary Notes
1-----------------·_-_· __ · --.-.- ---.---. - .. _._-_._ .. _-------------16. Abstract (limit: 200 words)
An analytical investigation attempts to estimate the maximum forces and deformations that can reasonably be expected in critical regions of structural walls subjected to strong ground motion. This document deals with the qualitative description of "a representati ve 1 oadi ng hi story" wh i ch can be used in testi ng i sol ated structural wall specimens under slowly reversing loads. One hundred and seventy rotational response histories, representing a broad range of parameter values, are examined. The representative loading history is described in terms of the magnitude of the largest rotational deformation that can reasonably be expected in the hinging region of isolated walls, the total number of cycles of such large -amplitude deformations, and the sequence in which these large-amplitude deformations occur relative to deformations of lesser amplitude. Also considered are the forces (moments and shears) that can accompany these deformations. For the isolated walls considered in this study, the maximum number of large-amplitude cycles that can reasonably be expected for a 20-second duration of strong ground motion is six. A significant result is the fact that the first large-amplitude cycle of deformation can occur early in the response, with hardly any inelastic cycle preceding it.
r--------------------------------------------------------~ 17. Document Analysis a. Descriptors
Earthquakes Earth movements Earthquake resistant structures
b. Identifiers/Open·Ended Terms
c. COSATI Field/Group lB. Availability Statement
NTIS
(See ANSI-Z39.1B)
Seismic waves Critical frequencies Des i gn cri teri a
Dynamic response Dynamic structural analysis
19. Security Class (This Report) 21. No. of Pages 1.31.
20. Security Class (This Page)
See Instructions on Reverse
I
/ .. -fL
OPTIONAL fORM 272 (4-77) (Formerly NTIS-3S) Department of Commerce
TABLE OF CONTENTS
SYNOPSIS
BACKGROUND
INTRODUCTION
DESCRIPTION OF DATA
Parameters Represented
Basic Data
ANALYSIS OF DATA
Maximum Amplitude of Rotational Deformation and Accompanying Shears
Shear Stress Levels
Number of Cycles of Large Amplitude Corresponding to 20 Seconds of
Strong Ground Motion
Sequence of Large-Amplitude Cycles
REPRESENTATIVE LOADING HISTORY - AN EXAMPLE
Number of Fully-Reversed Large Amplitude Cycles and Sequence
Maximum Rotation, e max ' and Maximum Shear
COMMENTS ON CHARACTER OF SHEAR LOADING
SUMMARY
REFERENCES
TABLES
FIGURES
APPENDIX A
Page No.
ii
1
6
9
13
28
32
35
40
43
48
84
SYNOPSIS
Although structural walls have a long history of satis
factory use in stiffening buildings against wind, there is in
sufficient information on their behavior under strong earth
quakes. Observations of the performance of build ings dur ing
recent earthquakes have demonstrated the superior performance
of buildings stiffened by properly proportioned and designed
structural walls - from the point of view of safety and espe
cially from the standpoint of damage control.
The primary objective of the analytical investigation, of
which the work reported here is a part, is the estimation of
the maximum forces and deformations that can reasonably be ex
pected in critical regions of structural walls subjected to
strong ground motion. The results of the analytical investiga
tion, when correlated \vith data from the concurrent experi
mental program, will form the basis for the design procedure to
be developed as the ultimate objective of the overall investi
gation.
This is the fourth part of the report on the analytical
investigation. It deals mainly with the qualitative des
cription of "a representative loading history" which can be
used in testing isolated structural wall specimens under slowly
reversing loads. A total of 170 rotational response histories,
representing a broad range of parameter values, are examined.
The representative loading history is described in terms of the
magnitude of the largest rotational deformation that can rea-
-ii-
sonably be expected in the hinging region of isolated walls,
the total number of cycles of such large-amplitude deformations
and the sequence in which these large-amplitude deformations
occur rela ti ve to deformations of lesser amplitude. Also con
sidered are the forces (moments and shears) that can accompany
these deformations.
It is shown that, for the isolated walls considered in this
study, the max imum number of large-amplitude cycles that can
reasonably be expected for a 20-second duration of strong ground
motion is six. A significant result is the fact that the first
large-amplitude cycle of deformation can occur early in the
response, with hardly any inelastic cycle preceding it.
-iii-
Dynamic Analysis Of Isolated Structural Walls
REPRESENTATIVE LOADING HISTORY
by
A. T. Derecho(l) , M. Iqbal (2), S. K. Ghosh (3)
. (4) (5) M. Flntel ,W. G. Corley
BACKGROUND
Although structural walls (shear walls) * have a long his-
tory of satisfactory use in stiffening multistory buildings
against wind, not enough information is available on the be-
havior of such elements under strong earthquake conditions.
Observations of the performance of buildings subjected to
earthquakes dur ing the past decade have focused attention on
the need to minimize damage in addition to ensuring the general
safety of buildings during strong earthquakes. The need to con-
trol damage to both structural and nonstructural components dur-
ing earthquakes becomes particularly important in hospitals and
other facilities which must continue operation following a major
disaster. Damage control, in add i tion to 1i fe safety, is also
economically desirable in tall buildings designed for residen-
(1) Manager, Structural Analytical Section, Engineer ing Development Department, (2) Structural Engineer, Structural Analytical Section, Engineering Development Department, (3)Senior Structural Engineer, Advanced Engineering Services Department, (4)Director, Advanced Engineering Services Department, and (5)Director, Engineering Development Department.
*In conformi ty with the nomenclature adopted by the Applied Technology Council (1) and in the forthcoming revised edition of Appendix A to ACI 318-77, Building Code Requirements for Re inforced Concrete (2), the term "structural wall II is used in place of "shear wall".
-1-
tial and commerc ial occupancy 1 since the nonstructural compo-
nents in such buildings usually account for 60 to 80 percent of
the total cost.
There is Ii ttle doubt that structural walls offer an effi-
cient way to stiffen a building against lateral loads. When
proportioned so that they possess adequate lateral stiffness to
reduce interstory distortions due to earthquake-induced motions,
walls effectively reduce the likelihood of damage to the non
structural elements in a building. When used with rigid frames,
walls form a structural system that combines the gravity-Ioad
carrying efficiency of the rigid frame wi th the lateral-Ioad
resisting efficiency of the structural wall.
Observations of the comparative performance of rigid frame
bu ild ings and bu ild ings st i ffened by structural walls dur ing
recent earthquakes, (3,4,5) have clearly demonstrated the su
perior performance of buildings stiffened by properly propor
tioned and designed structural walls, from the point of view of
safety and especially from the standpoint of damage control.
The need to minimize damage dur ing strong earthquakes, in
add i tion to the pr imary requirement of I ife safety (1. e., no
collapse), clear ly imposes more str ingent requirements on the
design of structures. This need to minimize damage provided the
impetus for a closer examination of the structural wall as an
earthquake-resisting element. Among the more immediate ques-
tions to be answered before a rational design procedure can be
developed are:
-2-
1. What magnitudes of deformation and associated forces
can reasonably be expected at critical regions of
structural walls corresponding to specific combina
tions of structural and ground motion parameters? How
many cycles of large deformation can be expected in
critical regions of walls under earthquakes of average
duration?
2. What stiffness and strength should structural walls in
typical building configurations have relative to the
expected ground mot ion in order to limit the deforma
tions to acceptable levels?
3. What design and detailing requirements must be met to
provide walls with the strength and deformation capa
cities indicated by analysis?
The combined analytical and experimental investigation, of
which this study is a part, was undertaken to provide answers to
the above questions. The ultimate objective of the overall in
vestigation is the development of practical and reliable design
procedures for earthquake-resistant structural walls and wall
systems.
The analytical program undertaken to accomplish part of the
desired objective consists of the following steps:
(a) Characterization of input motions in terms of the sig
nificant parameters to enable the calculation of cri-
tical or 'near-maximum' response using a minimum num
ber of input motions(6).
-3-
(b) Determination of the relative influence of the various
structural and ground motion parameters on dynamic
structural response through parametr ic stud ies (7) .
The purpose of this study is to identify the most sig-
nificant variables.
(c) Calculation of estimates of strength and deformation
demands in critical regions of structural walls as
affected by the significant parameters determined in
Step (b). A number of input accelerograms chosen on
the basis of information developed in Steps (a) and
(b) are used (8) .
(d) Development of procedure for determining design force
levels(8) by correlating the stiffness, strength and
deformation demands obtained in Step (c) with the cor-
responding capacities determined from the concurrent
experimental program(9).
The first phase of this investigation is concerned mainly
with isolated structural walls. A detailed consideration of
the dynamic response of frame-wall and coupled wall structures
is planned for the subsequent phases of the investigation.
This is the fourth part of the report on the analytical
investigation. It describes a procedure for defining a "repre
sentative loading history" which can be used in testing lab-
oratory specimens under slowly reversing loads to simulate
earthquake load ing. The representative loading history, for a
particular set of structural and ground motion parameters, is
described in terms of the magnitude of the largest rotational
deformation that can reasonably be expected in the hinging
-4-
region, the total number of cycles of such large-amplitude
deformations and the sequence in which these large-amplitude
deformations occur relative to deformations of lesser amplitude.
Also considered are the forces (moments and shears) that can
accompany these deformations. To determine the number and
sequence of large-amplitude cycles, a total of 170 rotational
response histories of the critical region at the base of iso
lated structural walls, were examined. These represent a broad
range of parameter values.
The first part of the report on the analytical investiga
tion(6) dealt mainly with the characterization of input mo
tions in terms of duration, intensi ty and frequency content,
with particular regard to the effects of these on dynamic in
elastic response. The second part of the report (7) discussed
the results of parametric studies designed to isolate the most
signif icant structural and ground motion parameters. A proce-
dure for determining design force levels for isolated structural
walls is developed in the third part of the report on the ana
lytical investigation(8).
-5-
INTRODUCTION
A major objective of the analytical investigation is the
determination of the force and deformation demands in structures
corresponding to particular combinations of the significant
structural and ground motion parameters. Since design attention
will have to be focused on the critically stressed regions in
structures, these demands will have to be defined mainly in
relation to the hinging regions in elements. A complete char
acterization of these demands would include not only the maximum
amplitude but also the number of large-amplitude cycles that
can reasonably be expected, the sequence of such large-amplitude
cycles relative to cycles of lesser amplitude, and associated
forces. The development of a "representative loading history"
for critical regions in structures which can be used in testing
large-size specimens under slowly applied reversing loads is
one of the more important results that can be obtained from
dynamic inelastic analyses.
In developing a procedure for determining design force lev
els discussed in Ref. 8, the correlation between calculated
demands and measured capacities is based on critical (maximum)
values. It was implicitly assumed, in undertaking the correla
tion, that the loading program used in the laboratory to obtain
capacity values was either representative of or more conserva
tive than the loading associated with dynamic response to strong
ground motion. The loading program used in testing the first
ser ies of isolated wall specimens was character ized by loading
cycles of progressively increasing amplitude, with the moment,
-6-
shear and rotation all in phase. This type of loading has been
commonly used(9-29) to simulate earthquake loading conditions.
A preliminary examination of response histor ies indicated,
however, that the sequence of load cycles used in this loading
program was not typical of the deformation history of the hing-
ing region in isolated walls subjected to strong ground motion.
In undertaking the correlation, it was thus necessary to assume
that any difference between this loading and earthquake loading
had no significant effect on the behavior of the isolated wall
specimens. This assumption relates mainly to the number of
large-amplitude deformation cycles and the sequence in which
these cycles are applied to a specimen. It is worth noting that
the cumulative measures of deformation discussed in Ref. 8* re-
flect, to some degree, the number of cycles of significant am-
plitude. However, they do not provide a definite indication of
the number of such large-amplitude deformations which can be
used as a basis for laboratory tests.
In view of the importance of ensuring that the loading pro-
gram used in laboratory tests represent realistic loading con-
ditions, it was decided early in the investigation to develop a
representative loading history. Such a loading history, to be
used in the laboratory testing of isolated structural walls
under slowly reversing loads, would have to be based on analyt-
ical dynamic response data.
*i.e. cumulative rotational ductility and cumulative rotational energy.
-7-
The principal objective of this study is the character
ization of the typical response history of the cr i tical region
at the base of isolated structural walls in quantitative terms,
particularly as these affect structural behavior. The deforma
tion of major interest is the total rotation occurr ing in the
hinging region of walls. An adequate characterization of the
deformation history will have to include the following:
(1) The maximum ampli tude of deformation that can be ex
pected for a particular combination of structure pe
riod and yield level and earthquake intensity.
(2) The number of such large-ampl i tude cycles that can be
expected for a reasonable duration of the ground mo
tion; and
(3) The sequence of such large-ampli tude cycles re lati ve
to cycles of lesser amplitude.
Of equal importance as the deformation history are the ac
companying forces, i. e., moments and shears, and the ir var ia
tion relative to the deformation.
-8-
DESCRIPTION OF DATA
Parameters Represented
The raw data used for this study include results of dynamic
response analyses undertaken in connection with the work re
ported in Refs. 7 and 8.
The dynamic response data used correspond to multistory
isolated structural walls ranging from 10 to 40 stories in
height and subjected to 10 different input motions. Figure 1
shows the type of structure considered and the lumped 12-mass
model used in the analysis of 20-story walls. Note that the
masses are spaced closer together near the base of the model.
This was done in order to obtain a better indication of the
deformation in the critical region near the base. Corres-
ponding models for the 10-, 30- and 40- story walls are shown
in Fig. 2.
Table 1 gives the ranges of values of the different struc
tural parameters characterizing the isolated wall models as well
as the ground motion parameters used in this study. A detailed
descr iption of these parameter var ia tions is given in Refs. 7
and 8.
The basic moment-rotation relationship assumed for the
hinging regions in the walls is a bilinear idealization of the
pr imary curve typical of re inforced concrete structures. The
hysteresis loop is characterized by unloading and reloading
branches whose slopes decrease for response cycles subsequent
to yield. Th is is shown in Fig. 3a, where the unloading and
reloading parameters are denoted by ex. and S ,respectively. An
-9-
example of a moment-rotation loop for an isolated wall with
fundamental period, = 1.4 sec., a = 0.10, and S = 0, is
shown in Fig. 3b.
Of the ten different input motions used, six were of
10-second duration. The other four had 20-second durations.
These were synthesized by repeating the first 10-second strong-
motion portion of four records. In all cases, the input motion
was assumed applied directly to the base of the structure.
The six IO-second accelerograms used for most of the analy-
ses are shown in Fig. 4. These include the first 10 seconds of
five recorded motions, as digitized at the California Institute
of Technology (30) and one artificially generated accelerogram
obtained by using the program described in Ref. 31. The acce-
lerograms shown have been normali zed wi th respect to intensity
so that the spectrum intens i ty* of each one is equal to 1. 5
times the spectrum intensity corresponding to the first 10 sec-
onds of the N-S component of the 1940 El Centro record (denoted
here by SI f)' re • The 5%-damped velocity response spectra for
these six accelerograms are shown in Fig. 5. The four 20-second
composite accelerograms used are shown in Fig. 6, and the cor-
responding 5%-damped velocity response spectra are shown in
Fig. 7. The portions of each record used for the second ten
seconds of the composite accelerograms are indicated in Table
2. Also shown in Table 2 are the corresponding 5%-damped spec-
trum intensities.
*Spectrum intensi ty - defined as the area under the relative velocity response spectrum (for a single-degree-of-freedom system) corresponding to the first 10 seconds of ground motion, between periods 0.1 and 3.0 seconds.
-10-
The dynamic inelastic analyses were carr ied out using the
computer program DRAIN-2D(32) developed at the University of
California, Berkeley, as modified at the Portland Cement Asso
't' (33) C1.a 1.on •
Basic Data
Of the information necessary to describe a loading history
for a particular set of structural and ground motion parame-
ters, the maximum amplitude of deformation and the accompanying
shears and moments are discussed in detail in Ref. 8. Some 300
analyses were used as bases for these. The major question con-
sidered here concerns the number of large-amplitude cycles of
deformation in the hinging region as well as the sequence of
such large-amplitude cycles relative to cycles of lesser am-
plitude.
The data considered consist of response history plots of
the total rotation in the hinging region at the base of each
wall. The rotational deformation in the hinging region is taken
as equal to the nodal rotation at a height above the base re-
presenting the hinging length, as shown in Fig. 8.
Rotation histories for nodes at the first and second floor
levels of a particular 20-story wall subjected to the first 10
seconds of the E-W component of the 1940 El Centro record are
shown in Fig. 9. Note the similarity in shape between the re-
sponse history curves for nodes located at the first and second
floor levels. This is generally true for nodes near the base of
the wall and is due mainly to the predominance of the fundamen-
-11-
tal mode of response. Also shown in this figure is the hori
zontal displacement history for the floor at midheight.
Examples of the rotational response histories considered in
this investigation are shown in Appendix A. These plots were
examined to determine the number and sequence of such large
amplitude cycles. For this particular purpose, the rotation
history of any node near the base of the wall will provide
essentially the same information with respect to number of
cycles and sequence. The plots shown in Appendix A all
correspond to the node nearest to the base in the models of
Fig. 2.
-12-
ANALYSIS OF DATA
Maximum Amplitude of Rotational Deformation and Accompanying
Shears
In Ref. 8, the critical value of rotational ductility de
mand is obtained as a function of the fundamental period and
the flexural yield level, for selected values of ground motion
intensity and wall height. Plots such as Fig. 10 give the ro
tational ductility, 11 r' that has to be developed at the base
of an isolated wall of a particular height, fundamental period,
Tl , and flexural yield level, My' when subjected to an input
motion of specific intensity.
The tendency of the ductili ty demand to decrease with an
increase in the assumed hinging length, as indicated in Fig.
11, should be noted. This figure shows the calculated duc-
tility ratios based on nodal rotations at the first and second
floor levels for 20-story walls, both divided by the corre-
spond ing value at the second floor level (F ig. 1). The data
points are shown connected by straight lines, on the assumption
of a linear variation of the ratio between the two assumed
hinging lengths from 20.75 ft to 12.0 ft. Results of ex-
periments on isolated walls(9,36) suggest a hinging length,
i. e., the length over which most of the inelastic deformation
in a member occurs, equal to the width of the wall.
Another important set of results of the study reported in
Ref. 8 are plots, such as shown in Fig. 12, giving the critical
shear at the base of isolated walls as a function of Tl and
My' for particular values of the input motion intensity.
-13-
Since the rotational ductility of a reinforced concrete wall or
other element can be significantly affected by shear, this fac-
tor has to be considered in developing a loading program. It
will be noted in Fig. 12 that the critical shear at the base
increases wi th increasing yield level, My' but does not vary
significantly wi th chang ing values of the fundamental per iod,
Plots of cr i tical rotational ductility demand and shears
for other wall he ights are also shown in Figs. lOb, c,d and
l2b,c,d. All these plots correspond to a ground motion inten-
sity of 1.5 SI f Response data for input motion intensities re .
of 0.75 SIref
and 1.0 SI ref have also been generated(S).
The maximum amplitude of deformation and the accompanying
shears to be used in any loading program will depend on the
range of values of the structure per iod, yield level, he ight
and earthquake intensity represented by the loading program.
It is evident from the charts shown in Figs. 10 and 12 that the
greater the ductility demand used in a loading program, the
broader the range of parameter combinations that can be con-
sidered as 'represented' by the test. In Fig. 10, for example,
a maximum loading amplitude corresponding to a rotational duc-
tility ratio of 5, would represent the demand on all 20-story
isola ted walls having combinations of the fundamental per iod,
Tl , and yield level, My' for which the associated curves
lie below the hor i zontal line II r = 5.
It will be noted from Figs. 10 and 12 that while an in-
crease in yield level generally results in a decrease in duc-
tili ty demand, it is also accompanied by an increase in the
-14-
maximum shear force. Experiments (9,36) have indicated that
the presence of high shears can limit the rotational capaci ty
(or ductili ty) of the hing ing reg ion in walls subjected to re
versed loading.
Shear Stress Levels. In determining the magnitude of the
rotational deformation requirements associated with response to
strong ground mot ions, it is important to ascerta in the magni-
tude of the accompanying shear forces. These can have a sig-
nificant effect on both the flexural strength and deformation
capacity of reinforced concrete elements. Results of experi
ments on beams(16,17)and walls(9,lO,34,36) have clearly de-
monstrated the major influence that shear can have on the
behav ior of re inforced concrete structures. This is particu-
larly true of structures subjected to reversed loading with de
formations well into the inelastic range.
An indication of the level of the maximum nominal shear
stress that can be expected for earthquakes with intens i ties
equal to 1.5 (SI ref ), is given in Tables 3a and 3b. Table 3a,
for example, shows the maximum nominal shear stress corres-
pond ing to rectangular wall sections of var ious he ights. The
walls considered were chosen such that their initial fundamental
per iod would each be equal to 0.6 N, where N is the number of
stor ies in the bu ild ing. The section dimensions shown in the
table were calculated on the basis of the gross areas of the
sections. The wall stiffnesses corresponding to each value of
the fundamental period were determined using the curves of Fig.
13. Flexural yield level (My) values were chosen for each
-15-
section corresponding to a rotational ductili ty demand at the
base equal to 4.0. For th is purpose, curves such as shown in
Fig. 14 (based on Fig. 10), determined on the bas is of dynamic
inelastic analyses (8), were used. The cr i tical shear values
corresponding to each structure were obtained from Fig. 15
(based on Fig. 12), also developed in Ref. 8. Similar data for
flanged sections are shown in Table 3b.
Tables 3a and 3b show the maximum nominal dynamic shear
stress in terms of I:fI for f' = 4000 psi and f' = 6000 psi. c c c
The results shown in these tables indicate that for the
range of fundamental per iod and ductility demand considered,
maximum nominal dynamic shear stress values in the range of
4.0 ~ to 7.0 ~ can be expected.
It is important to note, however, that there is a signifi-
cant difference between the dynamic shear force and the shear
normally associated with quasi-static laboratory tests to simu-
late earthquake loading. The major difference lies in the var-
iation of the shear force wi th time, particularly in relation
to the accompanying moment and rotation. This is discussed in
detail under "Comments on Character of Shear Loading."
Number of Cycles of Large Amplitude Corresponding to 20 Seconds
of Strong Ground Motion
As discussed in Ref. 6, a duration of 20 seconds of the
strong-motion portion of an accelerogram should provide rea-
sonably conservative estimates of cumulative deformation re-
quirements. This observation applies similarly to the number
of large-amplitude cycles of response. Since the number of ap-
-16-
plications of reversed cycles of loading can significantly
affect the behavior of reinforced concrete elements, a reliable
assessment of this aspect of the deformation demand is
important.
To estimate the number of large-ampli tude cycles of res
ponse to strong ground motion, response history plots of the
nodal rotations of the first two nodes closest to the base, as
shown in Fig. 2 were prepared and examined. An example of these
response plots is shown in Fig. 9. Since the response of the
wall is dominated by the first or fundamental mode, in which all
parts of the wall remain on the same side of the original
vertical position at any instant, the calculated rotations of
nodes near the base represent essentially the total rotations
occurr ing in the segments of wall between the base and the
part icular nodes (F ig. 8). Because the response histor ies for
the two nodes closest to the base are generally similar and
yield essentially the same information with respect to number
of cycles of response, as shown in Fig. 9, only the response of
the node closest to the base was considered in detail. Plots
of rotation history for the node closest to the base for some
170 cases considered in Refs. 7 and 8 were examined. The cases
considered represent a broad range of values of the significant
structural and ground motion parameters, as indicated in Table
1. Figure 15 shows examples of rotational response history
plots. The nodal rotations in these plots have been normalized
by dividing these by the corresponding yield rotations. A
-17-
number of normalized rotation history plots representing sam
ples from the 170 cases considered have been assembled in
Appendix A.
Most of the analyses, and hence response plots, were done
using a 10-second duration of the input motion. However, to
allow for motions of longer duration, particularly as these
affect cumulative response quantities such as the number of
large-amplitude cycles, a few analyses were performed using
20-second composite accelerograms. As mentioned earlier, these
accelerograms were synthesized from the same records that pro-
vided the 10-second motions of Fig. 4. This was done by ap-
pending to the latter another 10 seconds of the strong-motion
portion of the corresponding accelerogram. The four compos i te
accelerograms used in this study are shown in Fig. 6. The cor
responding 5%-damped velocity response spectra are shown in
Fig. 7. The portion of each record used for the second ten
seconds of the composi te accelerograms is indicated in Table
2. Also shown in Table 2 are the corresponding calculated
5%-damped spectrum intensities.
Comparison of the cumulative measures of deformation for
the 20-second analyses and the 10-second analyses indicated
that a good estimate of the 20-second cumulative rotational
ductility could be obtained from 10-second analyses by multi
plying the results of the latter by a factor of 2.0. (9)
Figure 16 shows that when the response is inelastic, the
amplitude of deformation rarely remains the same for both half
cycles of a response cycle. In recognition of this fact and to
-18-
have a basis for classifying response cycles according to their
relative severity, the following definitions were introduced:
Relative Amplitude of Peaks
a. A "large-amplitude" peak is an inelastic half-cycle of
deformation having a magnitude between 0.75 and 1.0 of
the corresponding calculated maximum amplitude;
b. A "moderate-amplitude" peak is a deformation between
0.50 and 0.75 of the corresponding maximum.
Large-Amplitude Cycles:
a. "Fully reversed" cycles are complete cycles (+ and -)
with at least one large-amplitude peak and the other
peak, on reversal, of at least moderate amplitude.
This is illustrated in Fig. 16a;
b. "Partially reversed" cycles are cycles with one large
amplitude peak and the other 0.50 or less of the cal
culated maximum amplitude. This is illustrated in
Fig. 16b.
"Moderate" ampli tude cycles are those with one peak
value between 0.50 and 0.75 of the maximum (i.e., mod
erate amplitude) and the other 0.50 or less.
In the plots of nodal rotation history, shown in Fig. 15 and
Appendix A, the rotations have been normalized by dividing these
by the corresponding nodal rotation when yielding first occurred
at the base. Thus, the two horizontal dotted lines on each side
of the zero axis (Le., through ordinates +1.0 and -1.0) repre-
sent the initial yield rotation for all cases. Rotations ex-
-19-
ceed ing the initial yield values on each side of the zero axis
were considered inelastic.
The procedure used in determining the number of fully re
versed and partially reversed large-amplitude cycles can best
be explained with reference to a particular nodal rotation his-
tory, such as shown in Fig. 17. In this figure, the maximum
calculated amplitude of deformation is denoted bye max. A
deformation cycle in which one peak was inelastic (either of
large or moderate ampli tude) and the other less than the yield
amplitude was counted as 1/2 of an inelastic cycle. A few cases
where the maximum amplitude was only slightly greater than the
yield amplitude or cases of cycles in which both peaks were
elastic (Le., less than the yield amplitude) but which would
otherwise qualify as either large or moderate amplitude peaks
relative to the maximum, were also counted as 1/2 of an in
elastic cycle.
Results of the examination of response histories to deter
mine the number of large-amplitude cycles, etc. are listed in
Table A-I of Appendix A. Included in the tabulation are the
maximum amplitude of deformation, the total number of large and
moderate amplitude peaks, the number of fully reversed and par
tially reversed cycles and the total number of inelastic cycles.
The "Total No. of Inelastic Cycles" listed in the last column
of Table A-I include both "large-amplitude" and "moderate
amplitude" cycles.
Figure 18a shows a histogram indicating the distribution of
cases, in terms of the percentage of the total number con-
-20-
s ide red , having a spec if ic number of fully reversed cycles.
Another way of presenting the data of Fig. 18a is the percentage
exceedance plot shown in Fig. 18b, which is the complement of
the associated cumulative frequency plot. This plot gives the
percentage of the total number of cases having fully reversed
cycles exceeding a specific number (as indicated in the
abscissa) .
It is significant to note in Fig. 18 that for the broad
range of parameter values represented, the number of fully re
versed cycles corresponding to 20 seconds of strong ground
motion rarely exceeds six. Figure 18b indicates that for more
than 95% of the cases considered, the number of fully reversed
large-amplitude cycles of response is less than 4.
Histograms and percentage exceedance plots for the number of
"large-amplitude" peaks (i.e., half cycles) and the total number
of inelastic cycles (not necessar ily all "large-amplitude" as
defined above) are given in Figs. 19 and 20, respectively.
These figures indicate that for the range of parameter values
considered, both the number of large-amplitude peaks and the
total number of inelastic cycles of response under a 20-second
strong motion excitation rarely exceed ten. Figure 20b also
indicates that for more than 95% of the cases considered, the
number of inelastic cycles of response, corresponding to 20
seconds of strong ground motion, is less than eight.
The values plotted in Fig. 18 through 20 correspond to a
20-second duration of strong ground motion. As mentioned, most
-21-
of the analyses used only 10 seconds of input motion. The re-
suIts of these 10-second analyses (i. e., those relating to
cumulative measures of deformation) were then multiplied by 2.0
to obtain values for the 20-second input motions. The factor of
2.0 \vas based on a comparison(S) of the cumulative rotational
ductility for a limited number of cases analyzed using the
20-second composite accelerograms shown in Fig. 6, with the
corresponding 10-second values. Table 4, from Ref. S, shows
the average ratios of the cumulative cyclic rotational ductility
and the cumulative rotational energy (these terms are defined in
Fig. 21) associated with the 20-second composite accelerograms
to the corresponding 10-second results. Ratios for nodal rota-
tions at the first and second floor levels are listed in Table
4. The ratios listed represent the average of 12 cases, all for
20-story walls, with fundamental periods ranging from O.S sec.
to 2.4 sec. and yield levels from 500,000 to 1,500,000 in.-kips.
A total of some 170 cases were considered in preparing
Figs. lS through 20. These represent fundamental period values
from 0.5 to 3.0 seconds, yield levels from 300,000 to 2,500,000
in.-kips and wall heights from 10 to 40 stories. Six input
motions with intensities varying from 0.75 to 1.5 of the refer-
ence intensity, S1 f were considered. re .
Sequence of Large-Amplitude Cycles
To obtain detailed data on specimen behavior for design ap-
plications, the loading program most commonly used in tests of
large-size spec imens under slowly reversed loads consists of
deformation cycles of progressively increasing amplitudes until
-22-
failure occurs(9-29). This type of loading program is shown
schematically in Fig. 22. The maximum forces and deformations
sustained are then noted as ind ica ting capac i ty. It has been
suggested by Bertero(37-38) that such a loading program may
not be as conservative as a program in which the peak defor
mation is imposed early in the test.
An examination of response histories of nodal rotations
near the base of isolated walls indicates that in many cases,
the maximum amplitude, or an amplitude of deformation close to
the maximum, occurs early in the response, with hardly any in-
elastic cycle preceding it. Large-ampli tude cycles also occur
later in the response. This is evident in Fig. 15, which shows
nodal rotation histories for walls having different fundamental
periods, yield levels and stiffness degrading characteristics
subjected to the E-W component of the 1940 El Centro record.
Because this observed early occurrence of the maximum amplitude
cycle differs from the usual sequence of loading, it was decided
to examine the response histories obtained in the course of this
investigation(8) in greater detail. Rotation histories were
obtained for the two nodes closest to the base of the models
used, as well as the horizontal displacement histories of nodes
located at or near midheight of the walls. Figure 9 shows a
plot of all three response quant it ies for a particular case.
Since the time variation of these three response quantities are
very similar, it was decided to consider in detail only the
rotation history of the node closest to the base.
-23-
In examining the sequence of large-amplitude cycles, atten
tion was focused on the first response peak of large amplitude,
i.e., with a value between 0.75 and 1.0 of the calculated maxi
mum. Particular emphasis was placed on the number and relative
magnitude of the inelastic cycles preceding this large-amplitude
peak.
For the purpose of this examination, the deformation cycles
preceding the first large-amplitude peak are referred to as "B
cycles". "Fully reversed cycles", in relation to B-cycles, are
defined as complete cycles (+ and -) with the amplitude of the
greater peak denoted by B and the other, on reversal, between
0.5 and 1.0 of B. "Partially reversed cycles" are cycles with
one peak amplitude equal to at least 0.75 of B and the other 0.5
or less of B.
The results of this examination are listed in Tables A5
through AS for the 170 cases considered. Data on "fully re
versed" and "partially reversed" inelastic B-cycles preceding
the first large-amplitude response peak are listed under the
last two columns of these tables.
For the purpose of determining the number of fully reversed
and partially reversed
peak was inelastic and
inelastic B-cycles, a cycle where one
the reverse cycle was elastic (Le.,
with amplitude less than the initial yield rotation) was con
sidered as equivalent to one-half of an inelastic cycle. Cycles
where both peaks were elastic were not counted. However, even
when the only B-cycles occurr ing were all elastic (i. e., No.
of inelastic B-cycles = 0), the ratio of the amplitudes, B/A,
-24-
was still noted. In this case, B is the largest applicable
amplitude. In Fig. 23 for example, the ratio of the amplitude,
B, of the inelastic cycle preceding the first large-amplitude
peak, A (here, A is equal to the maximum), is 3 e /7 e = y y
0.43. In this case, the number of fully reversed B-cycles is
zero and of partially reversed cycles is 1/2, since the B-cycle
does not reverse itself. It will be noted in Tables A5 through
A8 that in most of the cases considered, there are no fully
reversed inelastic B-cycles.
The data on number of inelastic B-cycles listed in Tables
AS through A8 are summarized in Fig. 24. The abscissa in Fig.
25 indicates the sum of fully reversed and partially reversed
inelastic cycles noted in the last two columns of Table A5
through A8. In Fig. 24, data points along the vertical line
corresponding to zero inelastic B-cycles represent cases where
the largest amplitude B-half cycle was elastic. The figure
shows that in the major i ty of cases, there are no inelastic
cycles preceding the first large-amplitude response peak. In a
number of cases, mainly for those where the first large-
amplitude peak, A, is itself close to the yield amplitude,
(indicating low ductility demands), the ratio B/A exceeds 0.50.
The information relating to the number of inelastic
B-cycles preced ing the first large-amplitude peak in Fig. 24
has been replotted in the form of a histogram in Fig. 25. The
important thing to note in Figs. 24 and 25, with particular
reference to the question of sequence of load cycles, is that
in many instances, the maximum deformation (or a deformation
-25-
close to the maximum) can occur early in the response, with
hardly any inelastic cycle preceding it. Because of the prob-
able sensi ti vi ty of structural behavior under reversed loading
with high shears to the manner in which the maximum deforma
tion is approached, i.e., whether through progressively in
creasing ampli tudes of loading or by a relatively sudden in
crease to the maximum, this observation is significant and
should be considered if a realistic loading program is to be
developed.
Preliminary results of tests at peA to verify the effect of
sequence of loading (36) indicate that under shearing stresses
of the order of 8 If~ or greater, a loading program where the
maximum deformation is imposed early in the test can be more
severe than when the loading is progressively increased to the
maximum.
The tests involved two companion isolated wall specimens.
The first of these was loaded following the usual program of
progressively increasing amplitudes of deformation as shown in
Fig. 26a and 26b. The second, essentially identical specimen,
was loaded using a program based on the results of this study
as shown in Fig. 26c and 26d. For this specimen, the maximum
deformation was imposed early in the test, with only one small
inelastic cycle preceding it.
Results indicate that the first specimen could sustain a
particular maximum deformation through at least three cycles
when this maximum deformation was imposed after a ser ies of
progressively increasing load cycles. However, the second,
-26-
essentially identical, specimen could not sustain the same
maximum deformation through three cycles when the maximum defor-
mation was applied early. Deta ils of the tests are descr ibed
in Ref. 36. While no definite conclusions can be drawn on the
basis of a compar ison of only two specimens, this subject is
certainly one that merits further investigation.
The observed difference in behavior between the two speci
mens can be explained in major part by the greater deformation
capacity under the same lateral load, or the lesser stiffness,
of a specimen that has been appreciably cracked and "softened"
by earlier cycles of loading when compared to a "stiff" speci
men that has only a few cracks. A specimen with well-distri
buted flexural and diagonal cracks produced by earlier cycles
of loading can accommodate a particular total rotation by in
elastic deformations over a longer hinging length than a speci
men that has less cracking. In one case, the rotat ion in the
critical region is spread over a longer hinging length. In the
second case the inelastic rotation tends to be concentrated
over a much shorter length with consequent high curvatures and
strains.
-27-
REPRESENTATIVE LOADING HISTORY - AN EXAMPLE
The procedure for selecting a loading program to be used in
testing isolated structural wall specimens under slowly reversed
loads will be illustrated below. Such a loading can be consid
ered as "representative" of conditions associated wi th struc
tures having fundamental periods and yield levels within certain
ranges when subjected to a particular ground motion intensity.
The loading is representative in the sense of being as severe or
more severe than the response that might be expected in a par
ticular group of structures to the specific ground motion
intensity.
Number of Fully-Reversed Large-Amplitude Cycles and Sequence
It was shown in the preceding section that for a 20-second
duration of strong ground motion and a wide range of values of
the fundamental per iod and yield level, the number of "fully
reversed" cycles of response (or loading) rarely exceeds six.
The maximum total number of inelastic cycles, both large and
small, is ten. For over 95% of the cases considered, the cor
responding values are four and eight, respectively. Examina
tion of a large number of response histories also showed that
the occurrence of the first large-amplitude cycle very early in
the response is a very strong possibility. In view of the ad
verse effect that early occurrence of a large-amplitude cycle
can have on the behavior of reinforced concrete walls, a repre
sentative loading history for use in testing should incorporate
this aspect of response.
-28-
Figure 27 shows a rotational deformation loading program for
the hinging region of isolated walls incorporating aspects of
response relating to number and sequence of large-amplitude
cycles.
Examination of a rotation response history such as shown in
Fig. 16 shows that the positive and negative peaks of any re
sponse cycle generally are not of the same amplitude. Also, the
"fully-reversed" cycle as defined in this study may have the
higher peak ranging from 0.75 to 1. 0 of the calculated maximum
deformation. The other peak, on reversal, may be anywhere bet
ween 0.50 and 1. 0 of the maximum. To re flect these var iations
in amplitude of response cycles, the five fully-reversed cycles
in Fig. 27 have been divided into three cycles with amplitudes
equal to the maximum deformation and two cycles with amplitude
equal to 0.80 of the maximum. The first large-ampli tude cycle
occurs after a single inelastic cycle wi th amplitude close to
yield. Smaller inelastic cycles equal to about 1.5 to 2 times
the yield amplitude occur between the fully-reversed large
amplitude cycles. The effect of these small-amplitude inelastic
cycles
(9,36)
on structural behavior is generally not significant
In all cases, the cycles are made up of positive and
negative peaks of the same amplitude.
The loading program shown in Fig. 27 applies generally to
the entire range of isolated walls considered in this study.
It is important to note, however, that a particular loading
history, in all its details, cannot be thought of as being
-29-
generally applicable. The actual magnitude of the maximum rota-
tion, emax ' as well as the maximum shear, will vary depending
upon the combination of parameter values represented by the
loading. These parameters include earthquake intensity and
structure period and yield level.
Maximum Rotation, emax ' and Maximum Shear
To determine the value of the rotational ductility require-
ment, j.l = e / e . Id' to be used in a part icular load ing max Yle
program, a decision has to be made on the range of values of the
structure per iod and yield level as well as the earthquake in-
tensity represented by the test. Referring to Fig. la, for in-
stance, a maximum rotational ductility of 4.0 would represent or
cover 20-story isolated walls with periods ranging from about
1.0 sec. or greater and yield levels of about 1,500,000 in.-kips
or greater when subjected to an earthquake with intensity SI =
Also covered are walls with periods ranging
from about 1. 7 sec. or greater and yield levels of 1,000,000
in.-kips or greater. Walls with M = 750,000 in.-kips will y
be covered by the same ductility requirement provided the period
is 1.8 sec or greater. It is clear from Fig. 10 that the higher
the ductility ratio used in a test, the broader the range of
parameter values represented or covered by the results.
Similar observations apply to the maximum shear which should
accompany the imposed deformations. Figure 12 can be used as a
guide in selecting the appropriate shear force. Here again, the
distinction must be made between the maximum dynamic shear and
-30-
the shear applied to speci.mens in quasi-static tests which is
in phase with the accompanying moment and rotation. As indi
cated in the subsequent section on "Comments on Character of
Shear Loading," some adjustment may be required in either the
dynamic shears or the shear capacity obtained from quasi-static
tests before a valid compar ison can be made between these two
quantities.
Laboratory tests using a loading program based on dynamic
analysis results, such as shown in Fig. 27, with specific values
of 9 max and the accompanying maximum shear, will have the
character of proof tests. A specimen that sustains such a load
ing program without significant loss of strength can be said to
be adequate with respect to design and details for the particu
lar combination or range of values of the significant parameters
represented by the loading program.
-31-
COMMENTS ON CHARACTER OF SHEAR LOADING
In correlating capacity values obtained from experiments
with demands estimated from dynamic inelastic analyses (8), it
is essential that the capacity values be derived under condi-
tions closely approximating those prevailing under dynamic con
ditions. This, of course, assumes that the mathematical ideal
ization used in the dynamic analyses represents a realistic
approximation of the actual structure, i. e., with the signif i
cant variables adequately modelled.
The need for close correspondence between laboratory test
conditions and those obtaining under dynamic conditions is
particularly important wi th respect to factors that have sig
nificant influence on the behavior of reinforced concrete ele-
ments. The validity of any correlation between demand as
determined from analysis and capacity as obtained from labora-
tory tests will depend on how representative the test condi-
tions are of actual dynamic response. While there are many
aspects to the problem (38), only one, related to loading his
tory as used in quasi-static tests to simulate earthquake load-
ing, will be discussed here. This has to do with the time
variation of the shear force relative to that of the accom-
panying moment and rotational deformation. The question is im
portant because of the significant influence shear can have on
specimen behavior.
As far as the shear force used in tests is concerned, two
aspects have to be considered. First is the magnitude of the
maximum shear force. The second is its var iation with time,
-32-
and particularly in relation to the accompanying moment and
deformation. Most quasi-static tests that have been conducted
to date have been concerned mainly with the magnitude of the
expected shear forces. The loading imposed on test specimens
has been characterized by the moment, shear and deformation in
the critical region being all in phase. This results from the
application of a single horizontal load or a series of propor
tionally changing horizontal loads to a specimen.
Dynamic response studies of isolated structural walls
undertaken at PCA(8), however, indicate that the shear in the
critical region at the base is more sensitive to higher mode
response and thus fluctuates more rapidly with time than either
the moment or the rotation. This is illustrated in Fig. 28a
through 28d which show time-history plots of the shear, rota
tion and moment in the first story of an isolated wall subjected
to four different input motions.
It is significant to note in Fig. 28 that the shear force
in the critical region fluctuates more rapidly than either the
moment or the rotation. The maximum shear generally acts over
a shorter duration relative to the accompanying moment. In
addition, the direction of the shear force reverses itself
several times during a single half-cycle of moment and rota
tional response.
The behavior of the shears shown in Fig. 28 may be partly
due to the fact that the model of the hinging region allowed
yielding in flexure only, ''''hile remaining linearly inelastic
with respect to shear throughout the response. Experimental
studies (9 ,36) have shown that thi.s is generally not the case.
-33-
The shear distortion in the hinging region can be significant
and contributes appreciably to the total displacement at the
top (9,36) even before the onset of flexural yield ing. What-
ever the effect of this modelling assumption may be*, it is
important, in correlating experimental data on capacity with
analytical data on demand, to allow for any differences in the
manner in which shear is induced under dynamic response condi-
tions and in the typical quasi-static test. It is believed
that a shear force that fluctuates rapidly and reaches its peak
value only for very short durations relative to the associated
moment and rotation represents a less severe loading condition
than one in which the shear, moment and deformation are all in
phase.
The quest ion involved here re lates not only to the effects
of out-of-phase forces but also possible shear strain-rate
effects on the behavior of reinforced concrete members. The
determination of the sensitivity of reinforced concrete member
behavior to these differences in loading needs further investi-
gation. An indication of significant effects would suggest an
adjustment either in the dynamic shear demand or in the quasi-
statically determined shear capacity in order to allow a valid
comparison.
*A model which will allow yielding in shear in the hinging region, based on uncoupled behavior relative to moment, has been developed to study this and related questions concerning shear yielding.
-34-
SUMMARY
A total of 170 rotational response history plots for
isola ted walls, represent ing a broad range of structural and
ground motion parameter values, were examined in this study.
The primary objective of the examination was to determine the
number and sequence of large-amplitude cycles of rotational
response in the hinging region of isolated structural walls.
Response corresponding to 20 seconds of strong ground motion is
suggested as adequate for the purpose of establishing design
requirements. This information is essential in developing a
representative loading program for testing laboratory specimens
under slowly reversed loads to simulate earthquake loading.
Such a loading program can be considered as representative of
the response of a particular group of structures to ground
motions of specific intensity.
In add i tion to the number and sequence of large-ampli tude
cycles of rotation, other equally important parameters char
acterizing the response history are the magnitudes of the total
rotation in the hinging region and the accompanying shear. In
formation on the latter two parameters has been developed in
detail in Ref. 8. The relevant results have been reproduced
here for completeness.
Significant observations made in this study are summar ized
below. These apply strictly to isolated walls having properties
within the ranges indicated in Table 1.
1. An estimate of the maximum
deformation, i.e., rotational
-35-
amplitude of rotational
ductility requirement,
that can be expected for a particular earthquake in-
tens i ty and combination of structure per iod and yield
level may be obtained from charts such as shown in
Figs. lOa to lOde These charts were developed in Ref.
8. For 20-story structural walls with fundamental
period of 0.8 sec. or greater, for example, a maximum
ductility requirement of about 5 is indicated provided
the yield level at least 1,500,000 in.-kips (170,000
kN .m) •
2. The maximum dynamic shears corresponding to a particu-
lar combination of earthquake intensity and structural
parameters (i.e., period and yield level) may be
estimated using Figs. l2a to l2d, also developed in
Ref. 8. For a rotational ductility demand of 4 and a
structure period equal to 0.06 N, where N is the number
of stor ies, the maximum nominal shear stress at the
critical section near the base can vary from 4 1fT to c
7.5~. These values correspond to an earthquake in
tensity 8I = 1.5 (SI ref .) and yield level values
ranging from 600,000 to 2,350,000 in.-kips.
Because the critical shears shown in Figs. 12a to
12d are often produced by ground motions that are not
the same as those producing the critical ductility
demand shown in Figs. lOa to 10d, a conservatism
beyond that associated with using the largest value
for each response quantity is implied when using both
quantities and assuming that they occur simultaneously.
-36-
3. The maximum number of "fully-reversed cycles of large
* amplitude" that can be reasonably expected for
strong ground motions of 20-second duration is six.
The maximum total number of inelastic cycles, of small
and large ampl i tude, for the same duration of strong
ground mot ion, is ten. More than ninety-five percent
of the cases considered had less than four fully re-
versed cycles of large amplitude. The corresponding
number of inelastic cycles was eight.
4. The study relating to sequence of loading indicates
that a realistic loading program must reflect the fact
that in a large number of cases, the first maximum
amplitude of deformation can occur fairly early in the
response, with hardly any inelastic cycles preceding
it.
5. A loading program incorporating conclusions (3) and (4)
is shown in Fig. 27. The value of the maximum rotation
in the h ing ing reg ion, e ,and the maximum dynamic max
shears corresponding to a particular earthquake inten-
si ty and combinations of structure per iod and yield
level may be obtained from Fig. 10 and Fig. 12 respec-
tively. In application, laboratory tests using a
loading history such as developed in this study will
have the character of proof tests. A spec imen that
sustains such a loading program without significant
*See page 24 and Fig. 16 for definition.
-37-
loss of strength can be said to be adequate with re
spect to strength and deformation capacity for the
particular combination or range of values of the sig
nif icant design var iables represented by the loading
program. These variables include earthquake inten
sity, structure period and yield level.
6. A loading character izedby moments, shears and rota
tions all occurring in phase, such as is commonly used
in laboratory tests under slowly reversed loading,
differs from typical dynamic inelastic response in re
spect to the variation of the shear force with time.
Under dynamic conditions, the shears, which are more
sensitive to the higher modes of response, change
direction much more rapidly with time than the moment
and rotation. It is believed that in this particular
respect, the commonly used laboratory program repre-
sents a more severe loading condition when compared to
typical dynamic response.
Because of the difference in character of the
that ob-shear loading
ta ining under
adjustment may
under dynamic
commonly used
be required
conditions and
quasi-static tests, some
in either the estimated
dynamic shears or the shear capacities determined from
tests using slowly reversed loading berore a valid
comparison can be made between these two quatities.
-38-
ACKNOWLEDGEMENT
The combined analyt ical and exper imental program of wh ich
this investigation is a part has been supported in major part
by the National Science Foundation through Grant No.
ENV77-lS333.
Any opinions, findings and conclusions expressed in this
report are those of the authors and do not necessarily reflect
the views of the National Science Foundation.
-39-
REFERENCES
1. Applied Technology Council, Recommended Comprehensive Seismic Design Provisions for Buildings, Final Review Draft, ATC-3-05, Applied Technology Council, Palo Alto, California, January 7, 1977.
2. Appendix A, Building Code Requirements for Reinforced Concrete (ACI 318-77), Amer ican Concrete Institute, P. O. Box 19150, Redford Station, Detroit, Michigan 48219.
3. The Behavior of Reinforced Concrete Buildings Subjected to the Chilean Earthquakes of May 1960," Advanced Engineering Bulletin No.6, Portland Cement Assoc ia tion, Skokie, Illinois, 1963.
4. Fintel, M. I "Quake Lesson from Managua: Revise Concrete Building Design?" Civil Engineering, ASCE, August 1973, pp. 60-63.
s. Anonymous, "Managua, If Rebuilt on Same Site, Could Survive Temblor," Engineering News Record, December 6, 1973, p. 16.
6. Derecho, A.T., Fugelso, L.E. and Fintel, M., "Structural Walls in Earthquake-Resistant Buildings Analytical Investigation, Dynamic Analysis of Isolated Structural Walls
INPUT MOTIONS," Final Report to the National Science Foundation, RANN, under Grant No. ENV74-14766, Portland Cement Association, November 1977.
7. Derecho, A.T., Ghosh, S.K., Iqbal, M., Freskakis, G.N. and F intel, M. , "Structural Walls in Earthquake-Res istant Buildings - Analytical Investigation, Dynamic Analysis of Isolated Structural Walls - PARAMETRIC STUDIES," Final Report to the National Science Foundation, RANN, under Grant No. ENV74-14766, March 1978.
8. Derecho, A.T., Iqbal, M., Ghosh, S.K. and Fintel, M., "Structural Walls in Earthquake-Resistant Buildings Analytical Investigation, Dynamic Analysis of Isolated Structural Walls - DEVELOPMENT OF DESIGN PROCEDURE - DESIGN FORCE LEVELS," Final Report to the National Science Foundation, RANN, under Grant No. ENV74-14766, Portland Cement Association, (in preparation).
9. Oesterle, R.G., Fiorato, A.E., Johal, L.S., Carpenter, J.E., Russell, H.G. and Corley, W.G., "Earthquake-Resistant Structural Walls - Tests of Isolated Walls," Report to the National Science Foundation, RANN, Portland Cement Association, November 1976, 44 pp. (Append ix A, 38 pp., Append ix B, 233 pp.).
-40-
REFERENCES (cont'd.)
10. Popov, E.P. and Bertero, V.V., "On Seismic Behavior of Two RIC Structural Systems for Buildings," Paper No.8, Structural and Geotechnical Mechanics, W.J. Hall, Ed., Prentice-Hall, Inc. 1977.
11. Paulay, T., "Simulated Seismic Loading of Spandrel Beams," Proc. Paper No. 8365, Journal of the Structural Division, ASCE, Vol. 97, No. ST9, September 1971, pp. 2407-2419.
12. Barney, G.B., Shiu, K.N., Rabbat, B.G. and Fiorato, A.E., "Earthquake-Resistant Structural Walls - Tests of Couplings Beams," Progress Report to the National Science Foundation, Portland Cement Association, Skokie, Illinois, October 1976.
13. Bouwkamp, J.G. and Kustu, 0., "Experimental Study of Spandrel Wall Assemblies," Proc. Paper No. 89, Fifth World Conference on Earthquake Engineering, Rome 1973.
14. Higashi, Y., Okubo, M. and Iida, K., "Elasti-Plastic Behavior of Reinforced Concrete Beams with Spandrel Walls under Anti-symmetric Cyclic Loads," Proc. Paper No. 140, Fifth World Conference on Earthquake Engineering, Rome 1973.
15. Bertero, V.V., Popov, E.P. and Wang, havior of Reinforced Concrete Flexural Web Reinforcement," Report No. EERC California, Berkeley, August 1974.
T., "Hysteretic BeMembers with Special 74-9, University of
16. Popov, E.P., Bertero, V.V. and Krawinkler, H., "Cyclic Behavior of Three R.C. Flexural Members with High Shear," Report No. EERC 72-5, University of California, Berkeley, October 1972.
17. Hanson, N.W. and Conner, H.W., "Seismic Resistance of Reinforced Concrete Beam-Column Joints," Proc. Paper 5537, Journal of the Structural Division, ASCE, Vol. 93, No. ST5, October 1957, pp. 553-560.
18. Hanson, N.W., "Seismic Resistance of Concrete Frames with Grade 60 Re inforcement," Proc. Paper 8180, Journal of the Structural Division, ASCE, Vol. 97, No. ST6, June 1971, pp. 1685-1700.
19. Park, R. and Paulay, T., "Behavior of Re inforced Concrete External Beam-Column Joints under Cyclic Loading," Paper No. 88, Proceedings of the Fifth World Conference on Earthquake Engineering, Rome, 1973.
20. Megget, L .M. and Park, R., "Re in forced Concrete Exter ior Beam-Column Joints under Seismic Loading," New Zealand Engineering (Wellington), Vol. 26, No. 11, Nov. 15, 1971, pp . 341- 3 5 3 .
-41-
REFERENCES (cont'd)
21. Renton, G.W., "The Behavior of Reinforced Concrete BeamColumn Joints under Cyclic Loading," M. Eng. Thesis, Univ. of Canterbury, Christ Church, New Zealand, 1972, 163 pp.
22. Uzumeri, S.M. and Seckin, M., "Behavior of Reinforced Concrete Beam-Column Joints Subjected to Slow Load Reversals," Publication No. 74-05, Department of Civil Engineering, University of Toronto, March 1974, 84 pp.
23. Paulay, T., and Spurr, D.D., "Frame-Shear Wall Assemblies Subjected Simulated Seismic Loading," Proc. Prepr ints Vol. 3, Sixth Wor Id Conference on Earthquake Eng ineer ing, Ne\v Delhi, India, ,Jan. 1977, pp. 3-221 to 3-226.
24. De Paiva, H.A.R. and Zaghlool, E.R.F., "Seismic Resistance of Flat Plate Corner Connections," Transactions, Canadian Society for Civil Engineering, Vol. 56, No.9, September 1973, pp. I-X.
25. Carpenter, ,J.E., Kaar, P.H. and Corley, W.G., "Design of Ductile Flat Plate Structures to Resist Earthquakes," Proc. Paper No. 250, Fifth World Conference on Earthquake Engineering, Rome 1973.
26. Hawkins, N. M., "Slab-Column Connect ions Subjected to High Intensity Shears and Transferring Reversed Moments," Report SM 76-2, Department of Civil Engineering, University of Washington, Seattle, Washington, 1976, 150 pp.
27. Wight, J.K. and Sozen, M.A., "Shear Strength Decay in Reinforced Concrete Columns Subjected to Large Deflection Reversals," Report No. SRS 403, Department of Civil Engineering, University of Illinois, Urbana, August 1973, 290 pp.
28. Wight, J.K. and Kanoh, Y., "Shear Failure of Reinforced Concrete Columns Subjected to Cyclic Loading," Proc. Paper No. 94, Fifth World Conference on Earthquake Engineering, Rome 1973.
29. Hirosawa, M., Ozaki, M. and Wakabayashi, M., "Experimental Study on Large Models of Reinforced Concrete Columns," Proc. Paper No. 96, Fifth World Conference on Earthquake Engineering, Rome 1973.
30. Analysis of Strong Motion Earthquake Accelerograms, Vol. II, Corrected Accelerograms, Pat"ts A, B, C, Reports EERL 72-79, California Institute of Technology, Earthquake Engineering Research Laboratory, 1972, 1973, 1974.
-42-
REFERENCES (cont'd.)
31. Gasparini, D., "SIMQKE: A Program for Artificial Motion Generation," Internal Study Report No.3, Department of Civil Engineering, Massachusetts Institute of Technology, January 1975.
32. Kanaan, A.E. and Powell, G.H., "General Program for Inelastic Dynamic Response tures," (DRAIN-2D), Report No. EERC 73-6, neering Research Center, University Berkeley, April 1973.
Purpose Computer of Plane StrucEarthquake Engiof California,
33. Ghosh, S.K. and Derecho, A.T., "Supplementary Output Package for DRAIN-2D, General Purpose Computer Program for Dynamic Analysis of plane Inelastic Structures," Supplement No. 1 to an Interim Report on the PCA Investigation, "Structural Walls in Earthquake-Resistant Structures," NSFRANN Grant No. GI-43880, August 1975.
34. Noor, F.A., "Inelastic Behavior of Reinforced Frames," Magazine of Concrete Research, Vol. 28, December 1976, pp. 209-224.
Concrete No. 97,
35. Bertero, V.V., Popov, E.P. and Wang, T.Y., "Seismic Design Implications of Hysteretic Behavior of Reinforced Concrete Elements under High Shear ," Proceedings of the Review Meeting, U.S.-Japan Cooperative Research Program in Earthquake Eng ineer ing wi th Emphas is on Safety of School Build ings, August 18-20, 1975, Honolulu, Hawaii, The Japan Earthquake Engineering Promotion Society, Tokyo, Japan, 1976.
36. Oesterle, R.G., Aristizabal, J.D., Fiorato, A.E., Russell, H.G. and Corley, W.G., "Earthquake-Resistant Structural Walls - Tests of Isolated Walls - Phase II," Report to the National Science Foundation, RANN, Portland Cement Association, November 1977.
37. Bertero, V.V., "Experimental Studies Concerning Reinforced, Prestressed and Partially Prestressed Concrete Structures and Their Elements," Symposium on Resistance and Ultimate Deformabili ty of Structures Acted On by Well Defined Repeated Loads sponsored by the International Association for Bridge and Structural Engineering, Lisbon, Portugal, 1973.
38. Bertero, V.V., "Identification of Research Needs for Improving Aseismic Design of Building Structures," Report No. EERC 75-27, University of California, Berkeley, September 1975.
-43-
TABLES AND FIGURES
APPENDIX A
This Appendix presents tables giving detailed data obtained
from an examination of the 170 response histories considered in
this investigation. The compiled data relate mainly to the
number and sequence of large-amplitude cycles of response.
Also included is a sampling of the normalized rotation
h istor ies for 10-, 20-, 30- and 40-story isola ted walls. The
plots are for rotations of the nodes closest to the base in
each of the lumped-mass models shown in Fig. 2 of the main body
of this report. In each plot, the calculated nodal rotation
has been divided by the corresponding rotation at first yield.
In Tables Al through A8, the following abbreviations are
used under the column "Earthquake Input" to denote the corres
ponding input accelerograms:
EC-E - 1940 E1 Centro, E-W component (IO-sec. duration)
EC-E** - 20-second composite acce1erogram based on EC-E
EC-N - 1940 E1 Centro, N-5 component (lO-sec. duration)
EC-N** - 20-second composite accelerogram based on EC-N
P.D. - 1971 Pacoima Dam, S16E component (lO-sec. duration)
P.D.** - 20-second composite acce1erogram based on P.D.
H.O. - 1971 Holiday Orion, E-W component (lO-sec. duration)
H.O.** - 20-second composite acce1erogram based on H.O.
T - 1952 Taft, S69E component (IO-sec. duration)
51 - Artificially generated accelerogram
The intens i ty factor, f, shown in the tables, represents
the ratio of the 5%-damped spectrum intensity of the particular
-44- {L
input motion to the reference spectrum intensity, SI f' reo • i. e. ,
the 5%-damped spectrum intensity - between periods 0.1 and 3.0
seconds corresponding to the first 10 seconds of the N-S
component of the 1940 E1 Centro record.
-45-
I I
Table 1 Values of Parameters Characterizing Isolated Wall Models
Parameter I Value
= = = =
I I
= d I r I STRUCTURAL
=1 =
I I I I I
I I I I I I I I
I
No. of Stories
Fundamental Period, Tl
Yield Level, 1-1 y
Yield Stiffness Ratio, r * y
Parameters characterizing Hysteretic ~-e Curve:*
Unloading parameter, a Reloading parameter, S
Damping (stiffness-and massproportional)
Stiffness Variation with Height
Strength Variation with Height
Base Fixity Condition
INPUT MOTION
Intensity
Frequency Characteristics ("peaking" and "broad band")
Duration
*See Figure 3.
10 - 40
0.5 - 3.0 sec.
16,950 - 339,000 kN'm (150,000 - 3,000,000 in-kips)
0.05 for most
0.10 for most 0.0 for most-
0.05 of critical for initial first and second modes
Uniform for most
Uniform, except for adjus~~ents to reflect effect of axial load
-for most
Fully fixed
SI = 1.5 (SI ref .)* for most
1940 El Centro, E-W 1940 El Centro, N-S 1971 Pacoima Dam, S16E 1971 Holiday Orion, E-W 1952 Taft, S69E Artificial rlccelerogram, Sl
10 sec. for most 20 sec. for some
(reference spectrum intensityl=area under 5% damped velocity response spectrum, between periods 0.1 and 3.0 seconds, corresponding to the first 10 seconds of the N-S component of the 1940 El Centro reccrd.
i I I
I ..:
:,:
--:t
Tab
le
2 C
om
po
siti
on
an
d In
ten
sit
y o
f 2
0-S
eco
nd
C
om
po
site
A
ccele
rog
ram
s
Com
posi
tio
n
spec
tru
m In
ten
sit
y,
(in
.) @
Basi
c A
ccel
ero
gra
m
Fir
st
10 S
ec.
1st
Part
2n
d P
art
S
IlO
1940
E
l C
en
tro
, E-
W
Fir
st
12
.48
sec.
From
0
.98
to
8.5
se
5
5.9
7
as
reco
rded
*
of
reco
rd*
1940
E
l C
en
tro
, N
-S
Fir
st
10
.08
se
c.
From
2
.90
se
c.
to
70
.15
' as
re
cord
ed*
1
2.8
2 s
ec.
of
reco
rd*
1971
Ho
lid
ay O
rio
n,E
-W
Fir
st
10
.08
se
c.
From
1
.70
sec.
to
32
.67
as
re
cord
ed*
1
1.6
2 s
ec.
of
reco
rd*
1971
Pac
oim
a D
am,
S16
E
Fir
st
10
.08
se
c.
From
2
.42
sec.
to
17
7.2
5
as
'rec
ord
ed*
1
2.3
4 se
c.
of
reco
rd*
·See
Ref
eren
ce
30
. @
Bas
ed
on
5%-d
ampe
d v
elo
cit
y
spec
tru
m,
for
peri
od
ra
ng
eO
.l·t
o
3.0
se
con
ds.
~Reference
spec
tru
m in
ten
sity
, S
I f
re
•
20
-Sec
on
d
SI 20
68
.16
77 .4
4
42
.86
20
6.0
7
SI r
ef
• S
IlO
x
1.5
0
1.8
8
1.5
3.2
2
0.5
94
SIr
ef.
S
I 20
x 1
.50
1.5
4
1. 3
6
2.4
6
0.5
11
..l... ~
.c
Tab
le
3a
-A
pp
rox
imate
N
om
inal
S
heari
ng
str
esses fo
r D
iffe
ren
t W
all
H
eig
hts
Iso
late
d S
tru
ctu
ral
Wall
s -
Recta
ng
ula
r S
ecti
on
s
I S
ecti
on
N
om
inal
S
hear
I
Dim
ensi
on
s S
tress
-x~
I
Eff
ecti
ve
Eff
ecti
ve
Fle
xu
ral
Co
rresp
on
din
g
Cri
tical
No.
o
f F
un
dam
enta
l M
omen
t S
hear
Are
a y
ield
R
ein
forc
em
en
t S
hear
Sto
ries
Peri
od
, T
l o
f In
ert
ia*
T
hic
kn
ess
w
idth
==
0
.8h
!w
I.
eve1
, ,
Rati
o
P@
at
Bas
e fl
==
4
f~
== 6
I
Ie
h (i
n.)
tw
(f
t)
My
(kip
s)
c (s
ec)
(1n
.2)
ksi
(i
n.4
) x
l0G
in-k
10
0
.6
23
x 10
6 10
2
5.2
2
42
0
0.5
1
0.0
5
932
6.1
20
1
.2
77
x 10
6 1
2
35
.4
4080
1
.15
.0
)9
14
40
5
.6
30
1.8
1
63
x
106
14
4
3.2
5
81
0
1.6
6
$ .0
21
$
17
45
4
.8
$ (1
. 90
) ( .
03
3)
(19
08
) $
(5.2
)
40
2.4
2
85
x
106
16
49
.8
76
50
2
.45
$
.01
8
$ 2
31
5
4.8
$
(2 .
92
) (.
03
3)
(25
92
) $
(5.4
)
* Ie
b
ased
on
g
ross
are
a
of
secti
on
. E
c as
sum
ed
=
36
00
k
si
in calc
ula
tin
g
Tl
•
I M
y ch
ose
n
to co
rresp
on
d
tQ
a ro
tati
on
al
du
cti
lity
dem
and
of
ab
ou
t 4
at
the
base
u
nd
er
an
eart
hq
uak
e
inte
nsit
y,
SI
== 1
.5
(SI e
ef.)
. S
ee F
ig.
ksi
5.0
4.6
3.9
$
(4.3
)
3.9
$
(4.4
)
@ R
ela
tiv
e
to
an
assu
med
"fl
an
ge
are
a"
at
each
en
d o
f th
e secti
on
eq
ual
in
len
gth
to
0
.10
1
bas
ed
on
fy
==
60
ksi
an
d f~
== 4
ksi.
w
T
hu
s,
p A
S/h
(O.l
w
',
$ C
orr
esp
on
d
to
AC
I C
ode
req
uir
em
en
ts
for
min
. ste
el
are
a
in
shear
wall
s.
No
te:
1 in
. =
25
.4
mm
: 1
ft
a 0
.30
5
m:
1 k
ip =
4.4
5
kN
I I ~ I I I
I ~
-..J I h--
' .J
Tab
le
3b
-
Ap
pro
xim
ate
N
om
inal
S
heari
ng
S
tresses
for
Dif
fere
nt
Wall
H
eig
hts
Iso
late
d S
tru
ctu
ral
Wall
s -
Fla
ng
ed
S
ecti
on
s
Eff
ecti
ve
Secti
on
Dim
ensi
on
s E
ffecti
ve
Fle
xu
ral
Cor
res-
Cri
tical
No.
o
f F
un
dam
enta
l M
omen
t S
hea
r A
rea
yie
ld
po
nd
ing
S
hea
r S
tori
es
Peri
od
, T
l o
f In
ert
ia·
To
tal
Web
F
lan
ge
'" 0
.8h
tw
L
ev
el,
•
Rein
-at
Bas
e Ie
D
epth
T
hic
k-
My
forc
emen
t (k
ips)
(s
ec)
2 (i
n.4
) o
f n
ess
W
idth
T
hic
kn
ess
(i
n.
) x
I06
in-k
R
ati
o
Secti
on
(i
n.
) (i
n.
) (i
n.
) p@
(ft)
10
0.6
23
x
106
24
.2
10
14
20
23
20
0
.51
.0
71
93
2
20
1.2
77
x
106
34
.4
12
16
22
3960
1
.15
.0
74
1
08
3
-
30
1.8
16
3 x
106
42
.2
14
18
24
5670
1
. 66
0
.56
1
74
5
40
2.4
28
5 x
106
48
.9
16
20
26
75
10
2.4
5
$ 0
.05
$
23
15
(2
.65
) (.
06
2 )
(24
14
) $
* Ie
b
ased
on
g
ross
are
a
of
secti
on
. E
c as
sum
ed =
360
0 k
si
in calc
ula
tin
g
Tl
•
# M
ch
ose
n
to co
rresp
on
d
to
a ro
tati
on
al
du
cti
lity
dem
and
of
ab
ou
t 4
at
the
base
u
nd
er
an
eart
hq
uak
e
inte
nsit
y,
y 5
1 =
1.5
(5
1
f).
See
F
ig.
re
•
@ R
ela
tiv
e
to
an
assu
med
"f
lan
ge
are
a"
at
each
en
d
of
the
secti
on
.
S C
orr
esp
on
d
to
AC
I C
ode
req
uir
em
en
ts
for
min
. ste
el
are
a
in
shear
wall
s.
No
te:
1 in
. =
25
.4
mm
i 1
ft =
0.3
05
m
i 1
kip
=
4.4
5
kN
No
min
al
ShE
''.Ir
I
Str
ess
-x
./fl
c i
fl
'" 4
c f~
= 6
k
si
ksi
6.4
5
.2
!
5.7
4
.7
I I I
4.9
4
.0
I
4.9
$
(5.1
) 4
.0
$1 (4
.2)
I ""- 00
I
Tab
le
4 -
Av
era
ge
Rati
os*
o
f M
axim
um
an
d
Cu
mu
lati
ve
Resp
on
se V
alu
es
Co
rresp
on
din
g to
2
0-
an
d
10
-Seco
nd
D
ura
tio
n In
pu
t M
oti
on
s 2
0-S
tory
Is
ola
ted
S
tru
ctu
ral
Wall
s
Av
era
ge R
ati
o,
R2
0/R
IO
Resp
on
se P
ara
mete
r Y
ield
L
ev
el,
M
y (i
n-k
ips)*
*
50
0,0
00
1
,00
0,0
00
1
,50
0,0
00
Defo
rmati
on
M
easu
res
Base
d
on
N
od
al
Ro
tati
on
s at
1st
flo
or
lev
el
Cum
. C
ycli
c R
ota
tio
nal
Du
cti
lity
, L
]lrl
·2
.33
2
.14
1
.99
Cum
. R
ota
tio
nal
En
erg
y,
L:A
rl
2.1
S
1.9
7
1.7
8
Defo
rmati
on
Measu
res
Base
d
on
N
od
al
Ro
tati
on
s at
2n
d F
loo
r L
ev
el
Cum
. C
ycli
c R
ota
tio
nal
Du
cti
lity
, Ll
1 rc
2 2
.32
2
.11
2
.00
Cum
. R
ota
tio
nal
En
erg
y,
L:A
r2
2.1
S
1.9
5
1.S
2
* U
sin
fo
ur
dif
feren
t acce1
ero
gra
rns
as in
pu
t w
ith
S
I =
1.5
(S
Iref)
. F
un
dam
en
ta
l p
eri
od
ra
ng
e:
O.S
to
2
.4
sec.
**
1 in
-kip
=
0.1
12
97
92
k
i1o
new
ton
'rn
ete
r (k
N.r
n)
A
Structural Wall A
6 @ 24'-0" = 144'-011
(6 @l 7.3m = 43.9 m)
PLAN
-~ E _, I'-
~ g II II
=0) E - I I'-: co (\J
@@J 0) 0) - .::::::.
Floor level
Base
bE _, r0 o . W CO -
12- MASS MODEL
Fig. 1 Twenty-Story Building with Isolated Structural Walls
-49-
FLOOR LEVEL
40----1..-
36
32
30
28 27
24 24
21 39 Floors @ 8
1-9"
20 20 = 3411-3"
18 18
16 16 15
14
12 12 12
10 10 9
8 8 8 7
6 6 6 5
4 4 4 3
2 ,2 2 I 1 121-{)" BASE BASE BASE BASE
10 STORY 20 STORY 30 STORY 40 STORY t 13 Nodes 13 Nodes 15 Nodes 13 Nodes 10 Mass Model 12 Mass Model 14 Mass Model 12 Mass Model
Fig. 2 Lumped-Mass Models of Isolated Walls Investigated
-50-
Fig. 3a Unloading and Reloading Parameters a. and S Characterizing Hysteretic Loop of Decreasing Stiffness Model
10 ~----------------------------------------------~
- 8 "b )(
II) 6 Co :;:
I c: ::;
..... 4 z w :lE
2 0 :?! Cl
aJ 0 a:: w ~ -2 :?!
-4
TI = 1.4 sec.
My = 500,000 in-k
1940 El Centro, E-W
SI = 1.5 (Sl ref.)
-6 ~--~~----~----------------------+-----~----~--~ 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 2.5
NODAL ROTATION (radians x 103)
Fig. 3b Base Moment versus Nodal Rotation at First Floor Level - 20 Story Isolated Wall
-51-
100
50
o
-50
I lJ1
N I
I i" J h
~~iMJ~ "A~ di\
IJliM
! A.A J~ I
J: 'I
~ ~ -1
0
50
w
.J ~ -
20
19
40
El
Cen
tro
. E
-W x
1
.88
_5
0
r t b II
I ~I.JA~ .
~tl~l!kt
:'''1
Z
G
• r'\
I _IF
:I
-4
0.
~ :I
~ ....
50
: -1
0 ... iil ~
~20
20
·0 ~
'0
'" "- u u '" 0
~ ~
-,0
.. .. a: ~ -
:!o
~ -3
0
-40
1940
E
l C
entr
o.
N-S
x
1.5
0
'I ,-
.... ~
·J¥l
II
,. J
k'l
\b
1971
P
aco
ima
Dam
. S1
6E
x 0
.59
4
_~o
50
-2~
-5C
J
-75
••
1_
'00
0 3
..
~
6 7
8 ~
'0
-0
20
is
50
i ':L4I
AA.~~~
~~Lb/~
! IHt~
~!~ ["I
&l '" i ~ .... ~
-10
"' ~ ~ -2
0
1971
Hol
iday
Ori
on.
E-W
x
3.2
2
__ ~o
1':1. II.
M!h ~ IU
h~~ 11~~h
l~UA~ 1:"
i 5
0
~ .. ~
·to
... iil
~ -2
0
-50
1952
T
aft
. S
69E
x
3.15
20
5
0
·0
is '0
~ 2~
~ 0
-"/"
-Arn
r,lil
llllll
iii l'
i!!iL
i:n fi
Ji ili lll
lillli
i:IJl
ll:f:1
1,lll
.lllll
li 1!:
i~',II
+ ~ ~
-10
~ ~ -2
0
~ -30
A
rtif
icia
l A
ccel
erog
ra.m
. 51
x
1.6
6
-75
-40
I
I -1
00
o ,
..
5 I>
a
9 Le
TIN
E
SE
CO
ND
S
TIN
E
SE
CO
ND
S
Fig
. 4
Ten
-Seco
nd
D
ura
tio
n N
orm
ali
zed
A
ccele
rog
ram
s
'I U1 w 1
80
70
60
-() <U
If) 2
50
~
>- I- 0 g 40
W
>
X
<!
30
~
1940
EIC
en
tro
. E
-W
x 1
.88
------
19
40
El
Cen
tro
, N
-S
x 1
.50
---'-
19
11
Pac
oim
a D
am,
SIb
Il:
" 0
.59
4
_ ..
_ ..
-19
1'1
Ho
lid
ay O
rio
n.
E-W
x
3.Z
2
--
-19
52 T
aft,
S
69
E
x 3
.17
..
....
....
....
.. A
rti£
ic1
ill
Accelc
rog
ram
, S1
x
1.6
6
/\
i \"
~ i
\ A
I"
I /\
,·_· ......
. 1/
\ 1
\ l
\!
\.
I
, \
I ,'7'
. \
1'"
,-..
...'
rA!'"
•
\ "'
•• ,
" 'f\
."
. I
....
.. ,
I \
I I
I .'1
...1.
....
'\,'
.''\
... ...
( \,
/ I Ii'
.r .
'.l.
, ,,,
" •
\ ,
J \
!:.
. \'
....
l
.... ,
r ... ~
n .1;
), ...
I ...
. Y/;o'
.. ..../.. '
.,1
/
-...
. ~
J. ',.1 \
r" .. : \
'o/K
\ \. :
. . .
... ~l .. ,.~.
I /
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,\, .
. .
.., -...:
'~ ...
. .
: .'
~ I
~.
,.'
, ....
..... ~ .... ~
~_
", '.
! I: '..
y,
/
~,
..... J
..
..
~. N
.'
, ~
,-.J
"o.
...
f .
I'
\ ... -
-'
V.,
...
....
~
: . :
~
/',.
/ \
/ "'..
. .....
. _._.-
.-._.
f,"/ \
/ I:
\ ..
. .1
' ..
:, ,
J \
........
20
00
1500
1000
20
111
V
\ I
"-"-
"_M
_
:. I
ill ~!1'
\/
+ 50
0
10 ,.
Jf I
50/0
Dam
ping
. o
r 1
o Fig
. 5
1.0
2.0
PER
IOD
(se
cond
s)
3.0
4.0
Rela
tiv
e V
elo
cit
y
Res
po
nse
S
pectr
a fo
r F
irst
lO-S
eco
nd
s o
f N
orm
aliz
ed
Inp
ut
Mo
tio
ns
-() <U
If) ..... E
E
--.;
>- I- 0 0 ...J w
>
X
<! ~
aOT
T
50
2
0
50
--0
25
-§
10
IS
10
OS
~ ~
.....
.....
~ Ii!
'" ~
0 ~
0
6 6
l-I-
! c II
:
~ -1
0 ~
-10
V
,u.,J,
A i~
I~I I!Jj~~!
! ~ li1r
. rJ1
11 III1
,ll~~H.~ ~,~ 'I
I 111
1 r.~
, W
~ I'
If i i:lIP
i1l j W' . I
1\11: ,!'II
! 11i1l
'V11
I
25 N
O
o x E
.. ~ .....
25
I
-"1
19
40
E
1
Cen
tro
. E
-W
x 1.
88
~o
-20
-:-3{
1 -7
' -5
0
50
971
Paco
ima
Dam
. S
16
E
x 0
.59
4
L5
I U"1
I .;
:.
2°T
T 50
-"J
I
-0
IS 10
2'-
"& 10
~ ~
.....
.....
~o
u
~ olL
III
NO
C
0
o 8 u '"
6 ..
6 .....
U
I-
tl
I-
~ .....
~
OJ
-25
I
i -10
~ -1
0
-20
-5
0
-20
-~o
19
40
E
l C
en
tro
, N
-S
x 1
.50
-'0 l
I I
I I
I I
I I
I L~
-3
0
I)
2 4
• •
10
12
14
16
18
20
0
1971
H
oli
day
O
rio
n,
E-W
x
3.2
2
I I
I I
I I
1-7
5
2 4
• •
10
12
14
16
..
20
TN
SE
CO
ND
S T
N
SEC
ON
DS
Fig
. 6
No
rmali
zed
2
0-S
eco
nd
D
ura
tio
n
Co
mp
osi
te A
ccele
rog
ram
s
80
5"
/t D
amp
lni
70
'0
60
(J
)
~
c: =
>-5
0
I- u 0 4
0
--1
w >
I U1
U1
x 3
0
I <
! 2
20
+
iiI I
't
/' I
10
I .'
/;,'
o o F
ig.
7
!
\ t 20
00
~i
A
\ (
-t 150
0
/\ ~
I \
'
~\ \
" \
/"
'::---"
\
/"
'~\
" "
"/
~---
...... ,-
-,
./
' .... /
"
' ...
./"
.... ''-'
".
,/
1940
El
Cen
tro
. ll!
·W
x 1
.88
------
1940
El
Cen
tro
. N
-S
x 1
.50
-'-
'-1
97
1 P
aco
ima
Dam
, S
16
E
x 0
.5H
_
.. _
to
.
197'
1 H
oli
day
Ori
on
, E
-W
x. 3.2~
1.0
2.0
3
.0
PE
RIO
D
(sec
onds
)
Rela
tiv
e V
elo
cit
y
Resp
on
se S
pectr
a fo
r N
orm
ali
zed
2
0-S
eco
nd
C
om
po
site
A
ccele
rog
ram
s
10
00
t 5
00
4.0
-' u (J)
(/)
........
E
E
--- >- I- U 9 W
>
X
<! ~
hinging length
/ / / I I
/ /
/ / /
"1;-
/ /
/
/ /
/
8, nodal rotation
Plastic hinge (in model )
Fig. 8 Nodal Rotation as a Measure of Total Rotation in Hinging Region
-56-
5 .
3 r-
12
20
F
LOO
R L
EV
EL
4+
.1.
,n
/\
I
\ ~-IO
No
dal
Ro
tati
on
s
Flo
or
Lev
el
2 1 ~"I
\ 2 ~8
12
-3
If')
'Q
-III ><
G>
6 .t
::
lIo
r.
Dis
pla
cem
en
t u
III
c:
c:
:.:;.
0 u 2
Flo
or
Lev
el
10
t-
o Z
...
W
.....,
4 z
~
0 w
U
I
~ c:
{ U
l -N
-I
-.I
12 -
MA
SS
M
OD
EL
0 u..
I
0 2
(f)
0::
><
(5
-.J
E
0::
« E
0
0 I
0 0
0 z
l\
I It !
A',
T 1
=
1.
4 se
c.
M
= 5
00
,00
0
in-k
J-
-2
-I +
\\ ~ II
"
v Y
1
94
0 E
l C
en
tro
. E
-W
SI
= 1
.5 (
SI re
f. )
-11"4
-2 0
2.0
4.0
6.0
8.0
10.0
TIM
E (
seco
nds)
Fig
. 9
No
dal
R
ota
tio
n
and
H
ori
zo
nta
l D
isp
lacem
en
t H
isto
ries o
f N
od
es at
Dif
fere
nt
Heig
hts
fr
om
B
ase
-
20
-Sto
ry Is
ola
ted
W
all
... ::s.. 0 z c:t :E w 0
>-... ..J j:: (.) ::::J 0
..J c:t Z 0 j::
~ 0 0::
a
7
6
5
4
3
2
o o
I 1 10 Stories SI = 1.5 (SI ret) I in-k = 0.113 kN-m
Duration: 10 sec.
LEGEND Mv(in-k) Symbol
~OO,ooo 0
1,000,000 0
(~ / My: 500,000 in-k
_\ '\ \ ~/
Ir-/,OOO,OOO
f\.
'" l(\ -
" Based on Nodal Rotations at 1st Floor Level
0.5 1.0 1.5 2.0 2.5 3.0
FUNDAMENTAL PERIOD, TI (sec.)
Fig. lOa Critical Rotational Ductility Ratio at Base as a Function
of Fundamental Period, TI' and Yield Level, My
IO-Story Isolated Structural Walls
-58-
~
:i.. 0 Z <t :E LIJ C
> I-::::i i= c..> :::l Q
..J <t Z 0
~ ~ a::
20 Stories SI = 1.5 (Sl ref.)
Duration = 10 sec. 8~----~-----+-+-------+------~------------~
LEGEND My(in-k) Symbol
1~------+------ti-------+-------1 7~OOO 0
6
1,000,000
5
4
3
2
1,000,000 c .1,sOO,OOO A
Based on Nodal Rotations at 2nd Floor Level
o~----~------~--------------------------~ 0.0 0.5 1.0 1.5 2.0 2.5 3.0
FUNDAMENTAL PERIOD, T (sec.)
Fig. lOb Critical Rotaional Ductility Ratio at Base as a Function
of Fundamental Period, TI , and Yield Level, My
20-Story Isolated Structural Walls
-59-
· o Z 4: ::e l.IJ o >t--I i= (.;) :J o -I 4: Z o i= ~ o ct:
a
7
6
5
4
2
1
° O.S.
I I 30 Stories
I in-k = 0.113 kN-m SI = 1.5 (SI ref) Duration = 10 sec.
q , 1\ l.EGEND
My(in-k) Symbol
1,000,000 0
T~ ~500,000 c
My= 1,000,000 2,Qoo,ooo t::.
~ ~
\ ~
~ I
/ /1,500,000
c
\ ~l ~
'" ~ V- 2,000,000
I ~
Based on Nodal Rotations at 3rd Floor Level
1.0 1.5 2.0 2.5 3.0 3.5
FUNDAMENTAL PERIOD, TI (sec.)
Fig.IOc Critical Rotational Ductility Ratio at Base as a Function
of Fundamental Period, TI , and Yield Level, My
30-Story Isolated Structural Walls
-60-
~
=so. -0 z
ct ::e LLI 0
>-.... -..J .... 0 ;:) c ..J ct Z 0 i= ~ 0 Q:
40 Stories S I = 1.5 (SI ret)
Duration = 10 sec. I in-k "" 0.113 kN- m
8~--~1----+---~--~--------~
7 c
6
5 c
4
3
2
1,~Oo,OOO 0
2,000,000 C
:3,000,000 ~
My= 1,500,000 in-k
2,000,000
I
3,000,000
Based on Nodal Rotations at 4th Floor Level
OL-________ ~ ____________ ~ ____________ ~ ________ ~ ____________ ~ ______ ~ 1.0 1.5 2.0 2.5 3.0 3.5
FUNDAMENTAL PERIOD, TI (secJ
Fig. lOd Critical Rotational Ductility Ratio at Base as a Function
of Fundamental Period, TI' and Yield Level, My
40-Story Isolated Structural Walls
-61-
1.5 20-Story Isolated Walls
Tl = 0.8-2.4 sec.
~\ = 750,000-1,500,000 in-kips 1.4
SI = 1.5 (SIref • )
'\
" Duration = 10 sec.
" 1.3 , , , , , , , " :t. 1.2 Mean
..... .. a:: 0 t-U
Lt I.i
Fig. 11 Variation of Ductility Demand with Assumed Hinging Length
-62-
-(/)
0-:.;: --w (f)
<I: m
~ w u 0:: 0 l..!...
0:: <I: w J: en x « ~
2800 I I I I I I I I I I I I I I I I 10 Stories !
SI = 1.5(Slref.) I 2400
Duration = 10 sec. I ....
I-------Elastic I
II
2000
1600
1200
I
~ ..,
1,000,000 I \ ~ ~ e 1
---u
I ->-- 150~,OOO
I 0 I -,
9
7
5
800 '- /My -'"'= 150,000 in - k - 3
0
400 Based on Nodal Rotations -
at 121 Story Level I I I , I I I , J 1 L II I J I I 1 I L II JI I I
0.5 1.0 1.5 2.0 2.5 3.0
FUNDAMENTAL PERIOD, T, (sec)
Fig. 12a dyn Critical Base Shear, VT ,as a Function of
Fundamental Period, TI , and Yield Level, My
IO-Story Isolated Walls
-63-
-E I
Z ~ -
-en
20 Stories SI = 1.5 (SI ref)
Duration = 10 sec. 2800 ~---+--~~----~----r---~----~
~2400 ~----+-----~----~----~~----+-----~ -~
M = 1,500,000 in.-k y
d5 2000 ~_-t_~OL+===~~=~~-\---l----1-~
12
10
-w U
8 Z ::2:
0:: 1600 ~ 0:: c::x: ~ 1200 en
X c::x: ::E 800
400
750,000
Based on Nodal Rotations at 2nd Floor Level
6
4
~~~~~~~~~~~~~~~~~~~~ 2 o 0.5 1.0 1.5 2.0
FUNDAMENTAL PE RIOO 1j
2.5
( SEC.)
3.0
Fig. 12b Critical Base Shear, v~yn, as a Function of
Fundamental Period, TI , and Yield Level, My
20-Story Isolated Walls
-64-
-
-en 0..
32 --w (f)
<t c::u
~ w u 0::: 0 LJ..
0::: <t Lw J: (f)
x <! :2
3800
3400
I 30 Stories I I I I I I I I ! I I I I I I I I
I 0 ElaSli:~ SI = 1.5(Slref.} -4 Duration = 10 sec.
I ,
\ --;
16
3000 -1 14
2600 I I I -
0 12
2200
1800
1,501,000\ .--2,000,000
9 -I "..1 I ::.:r\
--- ~ I My = 1,000,000 in-k
I 0 I
0 r
10
8 Based on Nodal Rotations
at 2nd Floor Level
1400 I I "4 6
I
1000 o
I
I I I I I I I , I I II , I I I I I , I I I I I I i
Fig. 12c
0.5 1.0 1.5 2.0 2.5 3.0 FUNDAMENTAL PERIOD, TI (sec)
dyn Critical Base Shear, VT ,as a Function of
Fundamental Period, TI
, and Yield Level, M y 30-Story Isolated Walls
-65-
-z :2 -
6 -,.., 0 )(
en 5 0. :;: -w Cf)
<l: 4 co
7 i I I I I I I I I I I I I I I I I I I I I I I l----rT"
r 1
LL I , i
t ;
I 40 Stories I i I 51 = 1.5 (51 ref) Elastic \ t I 0 . I t i uratlon = 10 sec. I --.t -; f ...
\ I i
i t ! 0 i 1
...,
t ~ ! I
28
24
20
~ w
f My = 3,000,000 In.-k ________ I
! t-.. 0 ~J 16 -Z u 0::
~ 0:: c:t lLJ ::I: en x c:t ~
3 I I I I
2 ! I
I I
I I
i i I I
I ! o o
I
I I I
I v
8 l i
2,000,000 ~ l' !
12 ("l,
I I v _t V
Based on Nodal Rotations 1,500,000 /
at 4th Floor Level
8
I
I I I I I
IU I I I I ! I ! I I I I I ! I I I I !
4
0.5 1.0 1.5 2.0 2.5 3.0
FUNDAMENTAL PER 100, TI (sec)
Fig. 12d Critical Base Shear, v~yn, as a Function of
Fundamental Period, TI , and Yield Level, My
40-Story Isolated Walls
-66-
~ -
2.0
2.8
10 S
torie
s ~.
I 2
0 S
torie
s Ii
u
ClJ
Cll
~
.!!!
2ft.
1--
1.5
1--
0 0
2.0
0 0
n:
a::
w
w
n.
1.0
a..
1.6
...J
...J
~
~
z z
1.2
llJ
w
~
05
~
<{
<{
0 0
0.8
1 z
20
(kN
-m2
X
lOll
) z
(kN
-m2
X
10'2
) :J
10
:J
5
10
u..
LL
0 0
4
0 .2
5 .5
0
75
1.
00
1.25
0
10
· 2.
0 3.
0 4.
0 5.
0 6.
0 7.
0
E' (
k -
i n2
){ 10
' I) E
I (k
-in
2 x
10'1
)
I 0'\
-.
J I
3.0
3.5
d 3
0 S
torie
s d
I 4
0 S
tori
es
ClJ
Cll
~
~
3.0
2.5
1--
1--
0 0
0 0
2.5
0::
20
0::
w
w
n.
n.
...
J ..J
~
1.5
~
2.0
z z
w
w
:E
~
<{
1.0
(kN
-m2
x lO
ll)
<{
1.5
0 0
z z
I 6
0 (k
N-m
2x
10
'2)
:J
20
4
0
60
:J
2
0
40
LL
LL
0.5
1.0
0 5
10
15
20
2
5
30
35
0
10
20
3
0
40
E/ (
k-in
2 x
lO")
E
l(k-
in2
x lO
ll)
Fig
. 1
3
Sti
ffn
ess F
acto
r,
El,
v
ers
us
Fu
nd
am
en
tal
Peri
od
fo
r th
e
Fo
ur
Dif
fere
nt
Wall
H
eig
hts
C
on
sid
ere
d
-.lIC I
.5
~ .:.
.s &>. ~ --I I.U > UJ -I
Q -I UJ >=
~ I.U a:: Z 2
Fig. 14
1.8 200
1.6 175
1.4
150
1.2 -e 125 I Z
~ -1.0
100
0.8
75
0.6
50
20 Stories 51 = 1.5 (51 ref)
Duration = 10 sec.
LEGEND Ii!: Symbol
~ 0
4 CI
5 A
6 •
0.4~-----r------~-----r------~----~----~
0.2 25 o 0.5 1.0 1.5
Based on Nodal Rotations at 2nd Floor Level
2.0 2.5
FUNDAMENTAL PERIOD, T. (sec.)
3.0
min Minimum Yield Level, My , Required at Base as a "Function
of Available Rotational Ductility Ratio, ~~,
and Fundamental Period, Tl - 20-Story rsolated Walls
-68-
12
10
8
6
4
Z 0 2
Z t-O <l: 0
~-t- O
'" 0:: t- -2 0 0 0:: ..J
w -4 >-
-6
II
9
7
II
9
7
5
z 3 0 Z t-o <l: .... t-
o <l: 0: .... 0 0 -I 0:: ..J
W
>- -3
-s
-7
-9 0
Parameter: FUNDAMENTAL PERIOD, Tl
11 • 0.' ace.
Parameter: YIELD LEVEL, My
M • 500,000 ., • 750,000 !n-k---f-.o
• 1,000,000
• 1.500,000 In-k
M - 500,000 in-k y
1940 E1 Centro, E-W; SI = 1.5 SIref.
T1 = 1.4 sec.
1940 El Centro, E-W; SI = 1.5 SIref •
Parameter: DECREASING STIFFNESS RELOADING PARAMETER a
1.0 2.0 3.0
'St.!)l .. ' loop
T1
My = 500,000 in-k
1940 El Centro, E-Wi SI = 1.5 SIref •
5.0 6.0 7.0 B.O 9.0 10.0 4.0
TIME (seconds)
Fig. 15 Samples of Normalized Nodal Rotation History Plots
-69-
1 >~ 8max -4 . ""11,---
e
I ~ 28max
!
(a) II FULLY REVERSED" CYCLE
~ 43 8max. -,.r-----8y
I <2' e max.
i
(b) '·PARTIALLY REVERSED" CYCLE
Fig. 16 "Fully Reversed" and "Partially Reversed" Large Amplitude Cycles of Rotational Deformation Defined
-70-
z 0 ~
t-=
0 a:: :1 W
>- " z I
0 -..
J
~
...... I
r 0 a::
No
dal
Ro
tati
on
at
1st
Flo
or
Lev
el
10
T 1
:;:
1.
4 sec.
8 6 T
-M
y ;:;
50
0,0
00
in
-kip
s
1940
El
Cen
tro
,E-W
i S
I :;:
1.5
(S
l re
f)
4 2'
By
Bm
ax
I 1-
··.· .
....
...
I 2 4 6 8 10
12
14 0
2 3
....
....
....
....
..
No
. o
f la
rge-a
mp
litu
de
peak
s (0
.75
8 m
ax ~
t ~
1.0
8 m
ax)
:;: 2
No
. o
f m
od
era
te-a
mp
litu
de
peak
s (0
.50
8 m
ax ~
m <
0
.75
6 m
ax)
:;:
1
Larg
e-
{ N
o.
of
full
y re
vers
ed
cy
cle
s
am
pli
tud
e
cy
cle
s
No
. o
f p
arti
all
y re
vers
ed
cy
cle
s
No
. o
f m
od
era
te-a
mp
litu
de cy
cle
s
To
tal
Nu
mb
er o
f In
ela
sti
c C
ycle
s
45
6
TIM
E
(se
con
ds)
7 8
=:.
0
:;:
2 1
=
3
9 10
Fig
. 1
7
Ex
amp
le
Sh
ow
ing
D
ete
rmin
ati
on
o
f F
ull
y
Rev
ers
ed
an
d P
art
iall
y
Rev
ers
ed
C
ycle
s o
f D
efo
rmati
on
100 TOTAL NO. OF CASES = 170 T, = 0.5 --- 3.0 sec.
No. of stories = 10,20, 30,40 If)
80 10 input mot ions ( 20 sec duration) W If)
<t U
...J 60
~ 0 l-
lL. 40 0
~ 0
20
o 2 4 6 8 10 12 NO. OF FULLY REVERSED CYCLES
100 TOTAL NO. OF CASES = 170
- T, = 0.5 -.. 3.0 sec. x
80 No. of stories = 10, 20, 30,40 (!) z 10 input motions (20 sec. duration) 0 w w 60 u x W
...J
~ 40 0 l-
lL. 0 20 ~ 0
o 2 4 6 8 10 12 NO. OF FULLY REVERSED CYCLES (X)
Fig. 18 Distribution of Number of Fully Reversed Large-Amplitude Cycles
-72-
(f) w (f) <[
100
80
u 60 ....J <[ f-o f-
LL o
x
<.!> Z
40
20
o w w 60 u x w
TOTAL NO. OF CASES = 170
T, = 0.5 -- 3.0 sec.
No. of stories = 10, 20, 30,40
10 input motions (20 sec. duration)
o 4 6 8 10 12
NO. OF RESPONSE PEAKS OF LARGE AMPLITUDE
TOTAL NO. OF CASES = 170
ij = 0.5 - 3.0 sec.
No. of stories = 10,20,30,40
10 input motions (20 sec. duration)
...J 4 a -f:·'.: ..... ·.···l .• · •. ··· .•• · .• ::;··l··.·.·!:· ~ o
~ 2011l1l~~~ ?f!.
o o 2 4 6 8 10 12 NO. OF RESPONSE PEAKS OF LARGE AMPLITUDE (X)
Fig. 19 Distribution of. Number of Peaks of Large Amplitude
-73-
(f)
w (f)
<l:
100
80
u 60 ....J
g I-
LL o
x
40
100
o
- 80 -Wi::! }:··:h:! ·,,\1 (!) z
2
TOTAL NO. OF CASES = 170
Tl = 0.5 -... 3.0 sec.
No. of stories = 10, 20, 30,40
10 input motions (20 sec. duration)
4 6 8 10
NO. OF INELASTIC CYCLES
12
TOTAL NO. OF CASES = 170 1i = 0.5 ---- 3.0 sec. No of stories = 10,20,30,40 10 input motions (20 sec. duration)
~ 60 J~i~illl~'~!!ll!:i~I~:~lll u b~~ __ X :4H~nUI
W
....J « 4 0 --I.;, ••• : •• , ••.• :.: ..• :.:
b l-
LL o 20 (/!.
o o 2 4 6 8 10
NO. OF INELASTIC CYCLES (X)
12
Fig. 20 Distribution of Total Number of Inelastic Cycles
-74-
I --.J
U1 I
M
Bmax.
c
I-I
Bmax.
...1
My
.~
rcccca
t
t 8
~
I I
Mea
sure
s o
f D
efor
mat
ion:
rota
tiona
l d
uct
ility
, fL
r =
B ma
x
By
cycl
ic r
ota
tion
al
du
ctili
ty,
}-Lrc
"cum
ulat
ive
rota
tiona
l d
uct
ility
,
c 8 max
.
-By
"2. }-L
re =
LB~
ax
By
cum
ula
tive
a
rea
cum
ulat
ive
rota
tion
al
ener
gy,
"2.A
r =
unde
r M
-e l
oops
~ M
yBy
hing
ing
leng
th
'on
~i~~.A
IOSIiC
hinge
lin m
odel
)
Fig
. 21
D
iffe
ren
t M
easu
res
of
Ro
tati
on
al
Defo
rmati
on
in
H
ing
ing
R
eg
ion
.. z o (!) w a: (!) 2: (!) 2: :r: 2:
z o ~ r o a:
-- ,..",.-",.---- e max .
u
Fig. 22 Typical Sequence of Loading Used In Testing Specimens Under Slowly Reversed Loads
-76-
10
8
z 6
0 ~
r 4
0 ~
2 Q
I
---' w
>-I
.......
2 z
I 0
-...J
~
4 -..
.J I
5 ~ 6 8 10
12
14 0
No
dal
R
ota
tio
n at
1st
Flo
or
Lev
el
Tl
= 1
.4
sec.
M
50
0,0
00
in
-kip
s
y
T-
19
40
E
l C
en
tro
, E
-Wi
SI
=
1.5
(S
Iref.
>
A :
: Bma
x.
......
......
.....
No
. o
f 'f
ull
y re
vers
ed
',
B cy
cle
s
=
0
No~
of
'parti
all
y r
ev
ers
ed
'#
B cy
cle
s
=
1/2
i S
ee fo
otn
ote
in
T
ab
le
A -
for
defi
nit
ion
of
full
y re
vers
ed
an
d p
art
iall
y re
vers
ed
B
cy
cle
s.
2 3
4 5
6 7
8 9
TIM
E
(sec
onds
)
Fig
. 23
E
xam
ple
S
ho
win
g
Dete
rmin
ati
on
o
f In
ela
sti
c C
ycle
s P
reced
ing
L
arg
e-A
mp
litu
de
Resp
on
se
Peak
10
CD «
I. 00 .------.----.----r------.----rl---,.---I-----rl----, 170 CASES
. 90
6 INPUT MOTIONS
1j = 0.5 - 3.0 sec . 1-----+--4 ---+----+---+ My = 500,000 - 2,500,000 in-kips -
~
.80 I-----+--~-~L~---+--~----r---+--~
I
I~
.70 I----je.l~b-.. ----+. ---::l:~::-----+----+---+-----+-----l
.60 ~-~~~l~-4_-~-~~--_+--~--+---~4.--~ ,.~ ~ ~~ j ..
.50 t------i ... '""':h--____ --r_--+--~--+_---t--~
... ~~ "'lb.,
~~ 4 .40 I---~~~;~-~---~--+---~---~---+--~
.30 I----~~~---~+.----~--~-----r----+---+--~ 1" ~¢~. a r
.20 ~-----I------!-- ®f~ q. ®
vv I .10 I---~ 8jl6.-rr----+---+--
...... If ~
TIME
-
-
O~~ __ ~~ __ I~~L~_l~~l~~ o 2 3
NO. OF INELASTIC (8) CYCLES PRECEDING FIRST " LARGE -AMPLITUDE II RESPONSE PEAK (A)
Fig. 24 Number of Inelastic (B) Cycles Preceding First Large-Amplitude Response Peak (A),
versus Ratio B/A
-78-
U) w
U)
<{
U
....J ;:! g
I LL
-...
.J 0
~
I ~
0
10
0 .
., TO
TAL
NO
. O
F C
AS
ES
= 1
70
1. =
0.5
---
3.0
sec.
No.
o
f st
ori
es
= 1
0, 2
0,
30
,40
80.
10 i
nput
m
otio
ns
(20
sec
. d
ura
tion
)
60
1::'::::
::::::':::
::;)1
e 4
0
B
t r \
/ \
I I
I -T
IME
20
o F
':':':
';"}"
;':"':
'"
o 2
3 4
5
NO.
OF
INE
LAS
TIC
(8
) C
YC
LES
P
RE
CE
DIN
G
FIR
ST
LA
RG
E
AM
PLI
TU
DE
R
ES
PO
NS
E
PE
AK
(A
)
6
Fig
. 2
5
Dis
trib
uti
on
o
f In
ela
sti
c
(B)
Cy
cle
s P
reced
ing
F
irst
Larg
e-A
mp
litu
de
Resp
on
se
Pea
k
(A)
I co
o I
°mo
x'--
-------------
-----
8y~~t-mlHl
~IIIIII' t'
, ' ,
(0 )
I
I I I, .:
r=
_._
---
8 mox
'---
I I
(el
-L rB
Mom
ent
8'1
----'7'h'7~/' b~
... 0
( b
)
Mom
ent
" 7
IV
/ I
7:7
8
8 max..
~
( d
)
Fig
. 26
E
ffect
of
Seq
uen
ce o
f A
pp
licati
on
o
f L
arg
e-A
mp
litu
de D
efo
rmati
on
s o
n
Sp
ecim
en
B
eh
av
ior
.. z o (.!) W 0:: (.!) Z (.!) z :c z z o ..... ~ o a:
Fig. 27 Representative Deformation History for Hinging Region of Isolated Walls
-81-
I ex>
N I
24
r
19
40
E
L C
EN
TR
O.
N-S
My
= 7
50
.00
0 i
n-k
2
0 I-
Tj
= 1.
4 se
c.
r5
(NO
DA
L R
OTA
TIO
N
.., 9
0
16 I
-2.
0
i 7
0
I: ~
l~ fA
J;\-"'V
'"A
A r
f ~50
N-
l()
0 0
10
x ><
x
30
en
4~
N: Illft
NHi\
, NH
J u-\
(!~
f .1\ ~\
.
ti
..:.::
.e-.5
f
..:.::
0 ... c
10
0 0
0 w
I-
u Z
0:
: 0
-10
z w
0
I-:2
lJ.
.. -4
I
-.5
<t
0
0::
,\ I
.....
-30
:2
<
t I
0 W
0:
: (.
!)
:r:
-8
-1.0
.J
z
(/)
5 <t
-5
0
Z
0 w
-1
2 l
-V
\!
, \I
Y
~ -1
.5
0 O
J z
I ki
p =
4.45
kN
V
-7
0
-16
I
in-k
ip"
0.11
3 kN
·m
-2.0
J
-90
-20
-2
.5
0 2
4 6
8 10
TIM
E
(sec
onds
)
Fig
. 2
8a
Rela
tiv
e V
ari
ati
on
w
ith
T
ime
of
Sh
ear,
M
om
ent
an
d R
ota
tio
n in
H
ing
ing
R
eg
ion
-
20
-Sto
ry Is
ola
ted
W
all
I 00
w
I
24
20
16
12
-(\
J o 8
)(
II) ~
4
19
40
E
L C
EN
TR
O,
E-W
M
y =
750
,00
0 in
k
~
= 1
.4 s
ec.
SH
EA
R _
__
_ n
/NO
OA
L
RO
TATI
ON
~ 1\
f
\ r:
I I"
\
I \
__
__
_ M
OM
EN
T I
I I
\ \
L. I
2.5
2.0
1.5
1.0
.5
-f{
) '0
)(
1:i o
W
0 J<
'" •
'to
,..
. I
1,(0
0,
I f\}
, \
~
• )1
\ 1/
,,1\
.11 §
n.
\
, ' 'II
H I
f 11\
!Z
' ,
~ ,
\ .II
V' u
n
IV
kI
" I~ 0
I I
~ a J
--4
0:
: « w m -8
-12
-16
I ki
p ..
4.4
5
kN
I in
-kip
a
0.11
3 kN
'm
-.5
g 0::
-1.0
...
J « o o -1
.5
z
-2.0
-20
•
-2.5
o
2 4
6 8
10
TIM
E
(se
con
ds)
90
70
50
to
o
30
10 o -10
-30
)(
..or: I ~
I Z
W ~ :E
(!) z 5
-50
z w
m
-70
-90
Fig
. 2
8b
R
ela
tiv
e V
ari
ati
on
w
ith
T
ime
of
Sh
ear,
M
om
ent
an
d
Ro
tati
on
in
H
ing
ing
R
eg
ion
-
20
-Sto
ry Is
ola
ted
W
all
I 00
"'" I
23
r
1971
H
OLI
DA
Y
OR
ION
, E
-W
My
= 7
50
,00
0 i
n-k
..
,5
19 I
-T,
=
1.4
sec.
-15
4
til
(\)
I
0 0
)(
II
~~NODAL
3 )(
10
r-S
HE
AR
I \
R
OTA
TIO
N
0 en
~MOMEN~
\ -c
i 1 1
0 a.
\ 2
0 x
~
7 ~
\ \ I
z 6
..:.c
w
~ \
I u
3 \
\ 0
c a::
I-
0 (
, lL
I
\ ~
2 a::
I
0 0
0 I-
<t
-I
I a::
z
w
, -2
w
:c
I
-J
::2
C/)
l
<t
0 -5
-I
0
::2
I 0
I ki
p =
4.45
kN
z
-6
(!) z
-9 i
-I
In-k
ip =
0.113
kN
'm
-2
0 z -1
0
w
m
-13
I
I =I
-3
0 2
4 6
8 10
TIM
E
(sec
onds
)
Fig
. 2
8c
Rela
tiv
e V
ari
ati
on
w
ith
T
ime
of
Sh
ear,
M
omen
t an
d R
ota
tio
n in
H
ing
ing
R
eg
ion
-
20
-Sto
ry Is
ola
ted
W
all
15 T
19
71
PA
CO
IMA
D
AM
, SI6
E
115
NO
DA
L R
OTA
TIO
N
My
= 7
50
,00
0
in. -
k 3
MO
ME
NT
TI
= 1.
4 se
c .--
.. -1
-10
N~ 1°1
S
HE
AR
rt
')
'0
2 L
()
><
0 (/
) ><
c
9-5
-a
-5
.::£
.
.::£.
..
I -0
I
a c
L.
W
f-<
..)
Z
I 0:
: I
0 Z
~
W
00
0
0 I
o ~
0 lJ
1 LL
r
---r
l-'~-;
::z
I I
0 0:
: I
<I:
I I'
'" 0
::z
w
, \
r \
r I
I {
0::
I I
{ (9
I
-I
....J
z (f
) -5
. I
kip
= 4
.45
kN
I
<I:
-5
0 I I
0 z
I in
-kip
:: 0
.113
kN
·m
I 0
W
I -2
z
IT)
I I
-10 t
rj
,1 -3
.L -
10
\,1
I I
t I
0.0
1.
0 2.
0 3.
0 4.
0 5.
0 6.
0 7.
0 8
.0
9.0
10.0
TIM
E
(sec
onds
)
Fig
. 2
8d
R
ela
tiv
e V
ari
ati
on
w
ith
T
ime
of
Sh
ear,
M
om
ent,
an
d
Ro
tati
on
in
H
ing
ing
R
eg
ion
-
20
-Sto
ry Is
ola
ted
W
all
APPENDIX A
This Appendix presents tables giving detailed data obtained
from an examination of the 170 response histories considered in
this investigation. The compiled data relate mainly to the
number and sequence of large-amplitude cycles of response.
Also included is a sampling of the normalized rotation
histor ies for 10-, 20-, 30- and 40-story isolated walls. The
plots are for rotations of the nodes closest to the base in
each of the lumped-mass models shown in Fig. 2 of the main body
of this report. In each plot, the calculated nodal rotation
has been divided by the corresponding rotation at first yield.
In Tables Al through A8, the following abbreviations are
used under the column "Earthquake Input" to denote the corres
ponding input accelerograms:
EC-E - 1940 El Centro, E-W component (lO-sec. duration)
EC-E** - 20-second composite accelerogram based on EC-E
EC-N - 1940 El Centro, N-S component (lO-sec. duration)
EC-N** - 20-second composite accelerogram based on EC-N
P.O. - 1971 Pacoima Dam, S16E component (lO-sec. duration)
P.D.** - 20-second composite accelerogram based on P.O.
H.O. - 1971 Holiday Orion, E-W component (lO-sec. duration)
H.O.** - 20-second composite accelerogram based on H.O.
T - 1952 Taft, S69E component (lO-sec. duration)
Sl - Artificially generated accelerogram
The intens i ty factor, f, shown in the tables, represents
the ratio of the 5%-damped spectrum intensity of the particular
-86-
input motion to the reference spectrum intensity, 5I f' i.e., re •
the 5%-damped spectrum intensity - between periods 0.1 and 3.0
seconds corresponding to the first 10 seconds of the N-5
component of the 1940 El Centro record.
-87-
z a Ia: ;a e::: o , ~
z ::;
le: Io cr::: o -.J W
>...... ~ le: Ia a:::
lO-STCRY S7RUCT~RRL WRLL s- T1 = .5 SEC.
My = 1.0 ~IL. IN-KIPS
BF.SE P.CC- 1\)'10 EL ct."iTRO (N-S1 1.5 (SI) FE
WI \ I V \ I
_.i __________ IL ___________________ V ___________________ -----------• I J
I I I
-2~·-----------,~--~~----,----~----~----~,~--_;~--~~--~, o 2 3 4 S 6 7 S 9 :0 T~ME IN SECDNDS
Fig. Al
20 T
17j 13 ,
10-ST(jRY STRUCTURRL W?'LL T 1 =.5 S;::C. :1y = .1S M:l..._ :!'!-KIPS
SASE ACC- l11'lO EL CI'".J\TRO n:-I<l 1.5 (SI) R;J'
i I
'0 I . r !
6~ I
3t ------------n----
:r---~-I-----7t V -1~~1----~----~~--~------,~--~----~1----~1----~1 ----_, ____ ~I o 2 3 ~ 5 6 7 S 9 10
TIME IN SECDi\OS
Fig. A2
-88-
z a fe: fa e:::: o ...J W
>:::::: a 0-
fa: fa u::
z a 0-
f-e: f-a e:::: 0
u:i :::-"-:z: In
I-e: f-r!')
!l:::
2 3
Fig. A3
0
I I I
456
TI r:E ! N SECDNDS 7
1 G-STQRY STRUCTURRL ~:R:. .. L T 1 =.5 SEC. My 1.0 ~rL. IN-KI?S
BRSE Ace - 1940 EL CEt\TRO {~~-S l 1.5 (SD R~i'
s 9
lO-STORY STRUCTURRL wRLL T! =.6 ~EC.
My .5 MIi.. IN-KIPS
BASE RCC- 197! PR:~!M.q O~ .. '1 :51S::) 1.5 ISIl R~
-lr--------------------------------------------------------------
-2' f I o 1 2 3 ~ 5 6 7 8 9 10 TIME IN SECONDS
Fig. A4
-89-
z Cl
l-e: l-e cr::: 0 ...J W
>-"-..,.. a l-e: I-0 c.:;:
>.... :z c.
'1 2+
2 3
Fig. AS
2
Fig. A6
~ 5 6 7
TIME IN SECONDS
I I I
~ 5 6 7
TI ME IN SECClNDS
-90-
lO-STORY STRUCTURRL WRLL Tl =.8 SEC.
:':y =.5 roll. IN-KlPS
BRSE RCC- lS~O EL C'ENTRO IE-~) 1.5 lSI) R£F
10
10-ST~RY STRUCTURRl WRLl T 1 =.9 ;::C. My = .5 ~!L. l>.i-K!PS
8A~ Fk."C- 1971 HeLIDRY CRlON tE-ln 1.5 LSI) REI'
3 9 10
fa: C~ e:::: CI .....J W
>':z o fc: fa e::::
Fig. A7
J 1 J 1
3t I
2
I 1------------------
I l------
3 456 T!ME IN SECONDS
7
lO-STORY STRUCTUR~L WRLL T 1 =.e SEC. My =.5 "m .• 1:-:-~r?S
BASE ACC- 1940 EL CENrR~ (N-S) . 1.S (SIl R£f
s 10·
lO-STORY STRUCTUP,Rr.. j-iRLL Tl = 1.4 SEC.
My .2 M:L. I'I-l<lPS
E!=!SE Ace.. 19~C EL :::~HRC !£-Wl 1.S (SIlREF
--------J-----~ \ \
-3~'------------~----~,------------------~-----,-------------,----~, o 2 3 4 (; 6 7 8 9 10
TI ME I N SECONDS
Fig. A8
-91-
z: a fe: Ia ~
o I W >"'z a le::
~
z a "Ie:: ... o ~
a -l w
>"'z o
10-STC~Y STRJCTURRL ~RLL i l 1-'4 ~C.
My .:5 Mil. 1~-KlPS
BR3:: Rec - 1952 iAFT. sca::
1.5 (51) ~EF
-7~1-------------1------1~----------~1 ____ ~------~I----~I------______ _
:;
o 2:; 'ISS 7 S 9 10
TIME IN SECuNDS
Fig. A9
lO-STORY STRUCTURRL WRLL T\ 1.4 SEC. My = .:5 ~Hl. r~-K!~
BASE RCC- 1971 H~LlDR,( ORION (f.-Ill 1.5 151l REF
2 ______________________________________________________ ~ O+-~~~~~-c~~~~~~--~--~----_+------r_----r_----~-+----
-1 ------------------------------- --- ------------ -------------
::~I-------------~I------~I ----~I------~I----~I------~,------'~----~I--____ , o 2:; 4 5 6 7 e 9 10
TI ME I N SECONDS
Fig. AID
-92-
z a --f-a:: f-Q c::: a -l w .~
"-z 0
1--e: f-e> u:;
z a
I)
6
2
7
t= 5 fa c:::
:3 3 w >"z
o
Fig. All
a 1 ----------fe: fa c:::
,
2 3 q 5 6 7
Tlr-:E IN SECONDS
20-STDRY STRUCTURRl ~ALL = .8 S::C.
= .75 MIL. IN-KIPS
BASE ACC- 19~O EL CENTR'J !N-Sj I.S I SIl REF
8 9
20-STORY STRUCTUR~L WRlL Tl =.8 SEC. l1y = .75 till. IN-iGI'S
SilSE ACC- 19,0 EL IDiR:) IE-oI) 1.5 Isn REF
-5cO-------~------------3------~~~----~5~----~~--------~7~-----~8-------~g-------lO
TI ME I N SECONDS
Fig. Al2
-93-
5 20-STORY STRUCTURAL Wrill T 1 : .8 SEC. My : l.5 roIL. IN-KIPS
BASE ACt - 1 SS2 TAFT ($SSE)
1.5 (SI! REF
3
:t----------------------0 1 .
-2
-3
~~o----~~----~a------~3------4------~5----~6------~7----~a------+9----~10
TIME IN SECONDS
Fig. AI3
20-STORY STRUCiURRL J..IRLL
'I Tl :: 1.'1 SEC.
My = .75 MIL. IN-KIPS
BASE ACC- 19'71 P;:;CC;Xt1!l 0;;.'1 (Sl6C:) 1.5 (SIl REF
z ,I 0
~ a: ~ 0 3 Ct::
0 -l W
>-"-Z 0
~ a: I-0 ::::
-3
-S~O----~~----+2------~3------'1------~5----~6-------7------a~----~.9------10
TIME IN ·SECONDS
Fig. AI4
20-STORY STRUCTURi1L ~;Rl..L
Tl = 1.~ SEC. My = .75 MIL. IN-KIPS
BRSE ACC- IS71 HOLlDRY CRICN (E-'O 1.5 lSI) REF
Z II o f-a: o et::
C --l Ld
;.-
2
---- ------ -~---- --~ ~ O+-~~~~~--o-~~~~~~~~~~----~----~------+_----+_--~---C
fa:
Z o ;a: ;-o a::: a ....l w >...... Z o ;-
~t--------------------------------
1
~j -64:-1 ----':'" ---.----____ -~-~___=-___=_---<I o 2 3 II 5 S 7 S 9 10
TI ME I N SECONDS
Fig. A15
20-ST~RY STRUCTURRL ~;,LL Tl 1.4 stC.
lIy = .75 I1IL. IN-KiPS
3 WE ACC- 1552 TAFT (., 1.5 (SUW
2
1 ------- . -
O~~----~-----+------~--~----~----~----~--~----~--_H~----
:::= -2 o c.::
-3
:1 ... ----_,--__ --.... , ___ . __ -+, ___ "" __ -+0, --_, ____ ---., o 1 2 3 II 5 S 7 6 9 10
TIME IN SECONDS
Fig. A16
-95-
z a l-e;: I-a Cl::
Cl ....J W
>-...... z 0 --I-a: I-a 0:::
le:: "'"" a 0:::
CI ....J W
>"z: a Ia: Ia 0:::
2 20-SiGRY STRUCTURRL WRLl Tl = 1.~ ~C. My = 1.5 :':rI.;. IN-KIPS
SASE RCC- 51 (R.'lTlFIC:RL .R::C.l 1.5 (SO REF
l~------------ ----------------- ------- -----------------------
O.
-2~h------~----------~3----~*------~5------6~----~7------8~----~S----~1·0
n ME IN SECDNDS
Fig. A17
2
20-STDRY STRUCTURRL WRLl
.75 M!t.. IfI.:-KIP'S
B"S=: RCC - 1!NO EL ctNTRJ (N-S I 1.5 :SIl REF
1 -------------------------- ------------ - --------------------
O~~--~------~~----_+--------~------4_----4_------~4_------~
-1 -----------------
-2
-3~O----~------~2------3~----~~------~5------S------·7------8~----~S------lO
TI ME I N SECONDS
Fig. A18
-96-
z 0
;-a: ;-0 C<::
CI ....J W
>-...... z 0
;-a: r-0 C<::
z o le: lI!:) 0::
a -..l w ....
"
2
0
20-ST~RY STRUCTURRL WALL T 1 = 2.0 SEC.
My = 1.0 MIL. IN-KiPS
BASE ACC- lSll PIlC:::M; O<'.~ (S:SEl 1.S (SO REi"
-----------------~
-2~------~------~1---------1~------~------~------~--------~------~/-----------------~1 o 2 J .. 5 5 7 8 S 10
TIME IN SECDNOS
Fig. A19
20-STDRY STRUCTURAL WRLL Tl = 2.'1 SEC. K.,. = 1.0 :-Ill. It;-KIPS
'I 1~---------------------------
BASE ACC- 31 (AATIFICIRl.. ~.) 1.5 (SI) REF
--------------- -----------~
~ O+---~~~---------r4~-----~~-----------~-----~---------~~----~------z I!:)
le: lI!:) 0::
~ ----------------- --------------------------------------------
-2~------~-----~--------~------~-----~-----~~-----~------~------~------~ o 2 3 'I 5. 6 7 8 9 10 . n ME I N SECONDS
Fig. A20
-97-
z CJ
z o Ia:: Io c:: Cl -l W
>...... Z o le;: Io c:: .
I f
2 ~ 5 S 7
TI ME I N SECONDS
Fig. A21
S
~f-------------------
30 -STORY STRUCiURSL ;'!RLL Tl :: 1.4 S::C.
MV :: 1.0 ~IL. HI-KIPS
eRSE ACC- Sl (ARTIFICIAl. ACC. J
1.5 (SlJP.EF
8 9 10
3D-STuRY STRUCTURRL WALL Tl = 1.Q SEC.
My = 1.0 ~IL. I1':-KIPS
BnSE liCC- 1371 HO .. :n;;y JR:~o,: fE-oil 1.5 ISl) REF
-_-'e"I'
~-O----~----~I~----~~-----+'I----~I~----~I ----~----~I------------, 2 " " 5 6 7 S 9 10
TI ME ! N SECONDS
Fig. A22
-98-
z o
Cl 1
c:
z o
:I .j I
2t t------------------------------------
°1 V r-----------------------------------I
-2 i
I
-·1
30 -STORY STRUCTURRL. 1·!RL.l T 1 = 1.4 eEC. My .: !.S M:L. r~;-K!~
8RSE RCC- 1971 HCL!:AY GR:n~: (E-~l
1.5IS!lREf
-6~1------~------~--------~1--------,------~--------~1 _______ ,----__ ,----__ ,~--__ , o 2 3 'l 5 5 7 8 9 10
Fig. A23
r at
'I J I ~
20i t---------------------
TIME IN SECONDS
3D-STORY STRUCTURAL ~!RLL T t = !.~ :;EC.
Mv = 2.0 MIL. :N-Klf'S
SASE ACC- 197t PA~:~.f! DP.~ (St6El 1.5 ISll REf
ct---------~--~~--~----4_--4_----+_--+_----~~~~-------
-2
1 -~~I-------------,-------~----*-----~I-------~,------~,----------------~I------~I o 2 'I 5 6 7 a 0 10
Tt ME I N SECONDS
Fig. A24
-99-
z o
a .....J !.1J
>'-2:. o
z o le:: I--
a rr:;
:::l .....J ;.cJ
>'Z Q
le: IQ c::
30 -STORY STRUCTURR~ ~JRLL
J T 1 = 2.0 SEC. ~V = 1.0 ~llL. IN-KIPS
BASE ACC- 51 (ARTIFICIAL RCC. 1.5 (SII REF
,t--------- ----------1-I Or---~~~------~~--------~--------~~--~~----~----------+_
-2+
-, j
-6~--~1------------------~1----~1------+1------~----*'------~1 ----~I o 1 2 3 Ij 5 6 7 8 9 to . T I t-1E I N SECON~S
Fig. A25
3D-STORY STRUCTURRL WRLl T 1 = 2.0 SEC.
1.5 MIL. IN-K!PS
BASE RCC- 1940 EL CENTf:" W-S) 1.5 (SIl REF
Orl~--~~----~4-----~------~------4-----~--------------~
-1 --------- - --- ----
-2
-3~0------------+2------3~----~~------~5------6------+7------8~.----~9------10
TIME IN SECONDS
Fig. A26
-100-
z o le:: 1-:<.::> c:::
2 s
Fig. A27
J j
31
,~------------------------i
-It-----------------
I -31
r -5 I I 023
Fig. A28
I 1
456
TIME IN S::CONDS
I
'156
TI ME I N SECONDS
-101-
30-STeRY STRUCTURhl WRll T 1 = .2.0 SEC. My = 2.0 MIL. IN-K!PS
SRSE P.CC- :S,O EL ~'nK~ (N-Sl 1.5 (S!lREF
7 a 9
30-STCRY STRLiCTURAL. ~!R!..L
T 1 = 2.'1 SEC. My = 1.0 MI~. I~-!(:P$
I I I I
7 S 9 10
Z Q -l-
30-STORY STRUCTUR8L WhLL Tl = 2.4 SEC.
My = 1.5 ~rL. !1\-Krp3
BRSE A:C- SI I~RT!f!r.r~L Ace.)
1.5 ISllRE."
e: 2 I-
>":z o Ia: o I V j
-3~G----~~----~2------3~-----'~------~5----~$~----~7----~S~----~~------10
TIME IN SECONDS'
Fig. A29
3D-STORY STRUCTURAL W2LL Tl = 2.4 SEC. /'Iy = 2.0 ~IL. n:-KIPS·
BilSE ACC- IS~O EL CENTRO Ii':-SJ
1.5 ISll REf
2.1-
I ,l ___________________ _
Or---~~~------~----------~~--~--------~~~~--------------
-1 ' --------------------------------------------------------------
-2~1-------~----~----~1 ----~I------~I------------+I------~' ----________ , o 2 3 " 5 5 7 a 9 10 TIME IN SECONDS
Fig. A30
-102-
z o
z ::::;
fG: f::::; 0:::
C! .....J W
>'. Z o fer fa 0:::
:J
J I T-------------------------
40-STORY STPUCTURRL WM~L Tl = 1.4 SEC.
M.,. = 2.0 I':IL. IN-KIf'S
BASE ACC- 1~...2 TAFT (SS9El 1.5 (Sll RE!'
f\., ________ 1lI __ _
Orl----~~~~---~~------~-----Hr------_r---+_---~r_---+_---_+----
-------------------I
I
] I
t -6c!------~---------~------~-------+r--------~r ______ ~r~-----~I--------r~------~I----~1 o 2:: ~ 5 6 7 S 9 10
Fig. A31
'I 2~
I I
or------- --~ ! \ t-----------~---
~j
TIME IN SECONDS
40-SmRY STR:..JCTUR:':;L. WRLl Tl = 1.4 SEC.
11'1' = 2.0 MIL.. I'H<!?S
BASE ACC - 1940 EL CZ~-:-RO (~I-S I 1.5 (S!lRE."
~~!------~I----~-------------~'------r~----~I-----+I------------~r--__ ~I o 1 2 3 '4 5 Ii 7 e 9 10
T H1E I N SECONDS
Fig. A32
-103-
le:: Io r.;
o W >" z o le:: Io C<::
z o
"j :1 -j 2~ ________________________ _
40-ST~RY STRUCTURAL WRLL Tt = l.q SEC.
My = 2.0 MIL. I'l-KIPS
eASE RCC- 1971 H:lLICAY ::1<;0:.1 IE..;,j) 1.5 ISll REF
O~~~~~~~~~~~~r-----~~--~~--~~--~~--~--~---
t--------------------2 t
~1 -5 I
C 2 3 , I
~ 5 6
TI ME I N SECONDS
Fig. A33
7
5
1 ---~-----------------
: r----------------
I
7 I
a 9 I 10
40-STORY STRUCTURAL WALL = 1.q SEC.
= 3.0 MIL. IN-KIPS
BASE ACC- 1971 PRCCI~.M OR~ I S16El 1.5 (SII REF
-51~----------~1------------~1----~1----~1~----~1------,------,~ __ ~I o 2 "5 6 7 8 9 . 1" TIME IN SECONDS
Fig. A34
-104-
:z a ....... ~
c: fa e::::: a ..J W
::":z o
5
:1 ________________________ _
40-STORY STRUCTURAL WRLL T: = 2.0 SEC.
My = 2.0 MIL. IN-KIPS
BASE ACC- 51 IARTIF!CIR:.. ACC.I 1.5ISIIREF
~ ~ -------------------------f-a e:::::
..,. a
-'I -5~!----~------·!------~----~1------~----~1------------~1~----~1------o 2 II 5 6 7 a 9 10
TIME IN SECONDS
Fig. A35
40-STCIRY STRUCTURRL I-:RlL Tl = 2.'1 SEC.
My = 1.5 M1L. IN-KIPS
BASE ACe - 19ijO E!. CEN7P.O IE-WI 1.5 ISll REF
-7~I----~~----*'------~1 ----~I------~ __________ _+,------________ ----_, C 2 3 4 5 €i 7 a 9 10
TIME IN SECONDS
Fig. A36
-105-
'IT
3
z
40-STORY STRUCTURRL WRLL = 2.'1 SEC.
= 2.0 M:L. IN-KIPS
SASE ACC- 1971 H::UDilY eRICH (E-1I1 1.5 (SIl R'"..f
2 2 fa: fa a::: o .....J W
>"z: o l
e:: I-
b ~
z o "I-
e:: Io a::: o .....J W
>"z o "-I-,..., >= o a:::
~r---------------------------------- -
:~1 ____ ~, _____ , ___________ , _____ ,----__ --__ '----~'~--__ ,--___ ' o 1 2 3 'I 5 'G 7 8 S 10
Fig. A37
:1
l---------
~i-----------------I
TI ME I N SECONDS
40-STORY STRUCTURAL WALL TI = 2.'1 SEC.
11" = 2.0 I1Il. It.:-KIPS
BASE ACe- Sl (ARTJFICIPl. ACC.) 1.5 (S1) REF
~------ -- --------- -------,-------~---
::1 ~o----~~----*2------~3------'1------~5----~6------~7------e~----~9------10 TIME IN SECONDS
Fig. A38
-106-
z o
z o -'-
'1 ~l I
,j
40-STDRY 5TRUCT0RR~ ~RLL Tl = 3.0 SEC. My = 1.5 M!t.. IN-K:PS
BASE ACC- 1340 EL CENTRO IE-W) 1.5 (SrJ REF
r-------------------- ----------------------------------- -----°1 1 _______ _ I
-2..-I 1
-~ 1 1 I
-6~------~----~,~----~----~,------~,------·,------~,------~,------I~----~ o 2 3 Y 5 6 7 B 9 10 TIME IN SECONDS
Fig. A39
40-STORY STRUCTURRL WRLL Tl = 3.0 SE::. My = 2.0 M:L. IN-KZ?S
BASE ace -. 1952 TAFT (SS9!:: I 1.5 (SI) REF
Ir--------------------------------------------------------------
Or'--~~~~~~-------~--------r_----_rr+------------_r----~~r_-
I \ r -I ,------------------------- ------------V:
-2
I I
-3.,------+-----~1------~1 ----~I~ ____ ~I ______ ~I------~, ______ ~,------+I----__ , o 2 3 .. 5 6 7 e S 10
TIME IN SECONDS
Fig. A40
-107-
I I-'
o CO
I
Tab
le
Al
Data
o
n
Num
ber
of
Cy
cle
s B
ased
o
n
No
dal
R
ota
tio
ns at
Mid
heig
ht
of
1st
Sto
ry
10
-Sto
ry Is
ola
ted
S
tru
ctu
ral
Wall
s -
10
-sec.
Du
rati
on
In
pu
t M
oti
on
s
Yie
ld
Max
imum
N
o.
of
CY
CLE
S O
F lu
np
litu
de
To
tal
No.
o
f P
eak
s LA
RGE
Al>
iPLI
TUO
E N
o.
of
Run
F
un
dam
ent"
l L
evel
, In
ten
sity
o
f O
ofo
r-cy
cle
s T
ota
l N
o.
Ear
thq
uak
e F
acto
J:,
f m
atio
n
(in
o
f In
ela
sti
c
No.
P
eri
od
, T
I M
y/10
6 te
rms
of
Lar
ge
Mo
der
ate
Fu
lly
P
art
iall
y
Mo
der
ate
Cy
cles
S
I ..
C
orr
esp
dg
R
ever
sed
R
ever
sed
A
mp
litu
de
in-k
ips)
i-In
pu
t f
x S
I ref
• V
alu
e at
Am
pli
tud
e @
Am
pli
tud
e'
Cy
cles
C
ycl
es
l~W-
(sec. )
F
irst
Yie
ld)
-1
00
3
0.5
.1
5
EC
-E
1.5
1
1.
4 4
2 1
1~
2 4~
10
37
0
.5
.15
P
.O.
1.5
1
9.9
1
1 1
0 0
1
10
10
0
.5
.50
E
C-E
1
.5
4.0
1
2 1
0 1
2
10
36
0
.5
.50
V
.D.
1.5
1
.9
4 6
2 ~
2 4~
10
07
0
.5
1.0
E
C-E
1-
.5
2.1
2
3 0
1 1
2
i02
4
0.5
1
.0
Sl
1.5
2
.3
5 5
3 0
2 5
-10
31
0
.5
1.0
P
.O.
1.5
1
.3
1~
2~
~ 0
0 ~
10
04
0
.8
.15
E
C-E
1
.5
8.7
2
1 1
1 0
2
10
38
0
.8
.15
P
.O.
1.5
1
0.5
2
0 1
0 0
1
10
09
0
.8
.50
E
C-E
1
.5
1.9
2
7 1
0 0
1
10
35
0
.8
.50
P
.O.
1.5
2
.0
1 7
0 ~
3~
4
10
02
1
.4
.15
E
C-E
1
.5
6.6
2
1 0
1 1
2
10
34
1
.4
.15
P
.O.
1.5
5
.6
1 2
1 0
1 2
10
41
1
.4
.20
E
C-E
1
.5
3.9
2
1 0
1~
~ 2
10
40
1
.4
.25
E
C-E
1
.5
1.9
2
1 1
~ 0
1~
10
33
1
.4
.50
P
.O.
1.5
1
.5
2 3
1~
0 ~
2
--_
_
0 _
_ -_
-
+
-I
in.-
kip
a
O.l
ll
kN'm
.
@
"Lar
ge"
am
pli
tud
es a
re
tho
se in
ela
sti
c d
efo
rmat
ion
s b
etw
een
0
.75
-1
.0 o
f th
e c
orr
esp
on
din
g m
axim
um
am
pli
tud
e.
I "M
od
erat
e"
amp
litU
des
aJ
:e
tho
se b
etw
een
0
.50
-0
.75
of
the c
orr
esp
on
din
g m
axim
um.
"Fu
lly
rev
ers
ed
cy
cle
s" o
f la
rge a
mp
litu
de
are
co
mp
lete
cy
cle
s C+
an
d -)
w
ith
at
least
on
e p
eak
valu
e b
etw
een
0
.75
-
1.0
of
the m
axim
um
amp
litu
de
and
th
e o
ther
-o
n r
ev
ers
al
-b
etw
een
p.5
0 -
1.0
of
the m
axim
um.
"P
art
iall
y r
ev
ers
ed
c~cles"
are
cy
cle
s w~th
on
e la
rge a
mp
litu
de
pea
k
and
th
e o
ther
0.5
0 o
r le
ss o
f th
e m
axim
um.
"Mo
der
ate
amp
litu
de
cy
cle
s" are
th
ose
w
ith
on
e p
eak
v
alu
e b
etw
een
0
.50
-
0.7
5 o
f th
e m
axim
um
wh
ile
the o
ther
is
0.5
0 o
r le
ss.
I I i I
I I-'
o \.0
I
Tab
le A
2 D
ata
o
n
Num
ber
of
Cy
cle
s B
ased
o
n
No
dal
R
ota
tio
ns
at
1st
Flo
or
Lev
el
20
-Sto
ry Is
ola
ted
str
uctu
ral
Wall
s -
lO-s
ec.
Du
rati
on
In
pu
t M
oti
on
s
'~"-'-"'---
Yie
ld
Hax
imum
N
o.
of
CY
CLE
S O
F l\
mp
litu
de
To
tal
No.
o
f P
eak
s LA
RGE
MIP
LIT
UO
E
No.
o
f R
un
Fu
nd
amen
tal
Lev
el,
Inte
nsi
ty
of
Oef
or-
cy
cle
s T
ota
l N
o.
Ear
thq
uak
e F
acto
r,
f m
atio
n
(in
o
f In
ela
sti
c
No.
p
eri
od
, T
l M
y/l
06
te
rms
of
Lar
ge
Mo
der
ate
Fu
lly
P
art
iall
y
Mo
der
ate
Cy
cles
5
1
'"
Co
rres
pd
g
Rev
erse
d
Rev
erse
d
Am
pli
tud
e
(in
-kip
s)+
In
pu
t f
x S
I ref
. V
alu
e at
Am
pli
tud
e @
Am
pli
tud
e'
Cy
cles
C
ycl
es
ISI~-
(sec.)
F
irst
Yie
ld)
1 0
.8
.5
EC
-E
1.5
9
.6
2 2
1 1
~ 2~
11
6
0.8
.5
P
.O.
1.5
1
2.6
1
1 1
0 0
1
15
6
0.8
.5
P
.D.*
*
1.5
1
2.3
1
1 1
0 0
1
16
9
0.8
.5
P
.O.
.75
5
.8
2 1
1 0
1 2
7 0
.8
.75
E
C-E
1
.5
5.9
4
1 1
2 1
4
11
5
0.8
.7
5
P.O
. 1
.5
7.9
2
0 1
0 0
1 1
17
0
.8
.75
P
.O.
.75
4
.6
1 2
0 1
2 3
12
1
0.8
.7
5
P.O
. 1
.0
6.0
1
1 1
0 0
1
13
5
0.8
.7
5
H.O
. 1
.5
7.6
3
1 2
0 0
;2
14
3
0.8
.7
5
Sl
1.5
3
.3
2 9
2 0
3 5
14
9
0.8
.7
5
T
1.5
5
.3
2 4
1 1
1 3
4 0
.8
1.0
E
C-E
1
.0
1.4
3
1 1
~ 0
l~
5 0
.8
1.0
E
C-E
1
.5
4.0
3
4 2
1 3
!i
, I I ~
6 0.
·8
1.0
E
C-E
1
.5
3.0
5
3 3
0 1
4 I
90
0
.8
1.0
E
C-E
**
1
.5
4.4
1
6 1
0 2~
]~J
+
1 in
._k
ip =
O.l
ll k
N·m
.
@
NL
arge
-am
pli
tud
es are
th
ose
in
ela
sti
c d
efo
rmati
on
s b
etw
een
0
.75
-
1.0
of
the co
rresp
on
din
g m
axim
um
am
pli
tud
e.
t "M
od
erat
e"
am
pli
tud
es
are
th
ose
bet
wee
n
0.5
0 -
0.7
5 o
f th
e c
orr
esp
on
din
g m
axim
um.·
.. -
"Fu
lly
rev
ers
ed
cy
cle
sN
of
larg
e a
mp
litu
de
are
co
mp
lete
cy
cle
s (+
an
d -)
w
ith
at
least
on
e p
eak
valu
e b
etw
een
0
.75
-
1.0
of
the m
axim
um
amp
litu
de
and
th
e o
ther
-o
n r
ev
ers
al
-b
etw
een
0
.50
-
1.0
of
the m
axim
um
"P
art
iall
y r
ev
ers
ed
cy
cle
s"
are
cy
cle
s w
ith
on
e la
rge .
. uA
pli
tud
e p
eak
an
d
the
oth
er
0.5
0' o
r le
ss o
f th
e m
axim
um.
uH
od
erat
e am
pli
tud
e cy
cle
s·
are
th
ose
wit
h o
ne
pea
k
valu
e
bet
wee
n
0.5
0
-0
.75
of
the m
axim
um w
hil
e
the o
ther
is
0.5
0 o
r le
ss •
20
sec.
du
rati
on
in
pu
t m
oti
on
s.
I I-'
I-'
o I
Tab
le
A2
(co
nt'
d.)
D
ata
o
n
Num
ber
of
Cy
cle
s B
ased
o
n
No
dal
R
ota
tio
ns
at
1st
Flo
or
Lev
el
20
-Sto
ry Is
ola
ted
S
tru
ctu
ral
Wall
s -
10
-sec.
Du
rati
on
In
pu
t M
oti
on
s
-~-
--.~~ --------
Yie
ld
Max
imum
N
o.
of
CY
CLE
S O
F A
mp
litu
de
To
tal
No.
o
f P
eak
s LA
IlOE
AH
PLIT
UO
E N
o.
of
Run
F
un
dam
enta
l L
evel
, In
ten
sity
o
f O
efo
r-cy
cle
s T
ota
l N
o.
Ear
thq
uak
e F
acto
r,
f m
atio
n
(in
o
f In
ela
sti
c
No.
p
eri
od
, T
l H
y/l
06
te
rms
of
Lar
gll
Mo
der
ate
Fu
lly
P
art
iall
y
Mo
der
ate
Cy
cles
S
I ..
C
orr
esp
dq
R
ever
sed
R
ever
sed
A
mp
litu
de
in-k
ips)
'"
Inp
ut
f x
SI r
ef
. V
alu
e at
Am
pli
tud
e @
Am
pli
tud
e.
Cy
cles
C
ycl
es
ISW
-(s
ec. )
F
irst
Yie
ld)
91
0.8
1
.0
T**
1
.5
4.1
3
2 1
1 1
3 1
03
0
.8
1.0
E
C-E
1
.5
4.1
2
3 2
0 1
3 1
04
0
.8
1.0
E
C-E
1
.5
4.0
3
2 2
1 0
3 1
05
0
.8
1.0
E
C-E
1
.5
3.7
3
4 0
2~
2 4~
11
0
0.8
1
.0
P.D
. 1
.5
5.5
2
0 1
0 0
1
12
5
0.8
1
.0
EC
-E
1.5
2
.8
2 2
1 ~
~
2 I
15
3
0.8
1
.0
EC
-N
.75
2
.8
4 2
2 2
0 4
15
7
0.8
1
.0
P.D
.**
1
.5
3.8
1
2 1
0 1
2 2
0.8
1
.5
EC
-E
1.5
2
.7
3 3
1 1
2~
4h
3
0.8
1
.5
EC
-N
1.5
3
.0
3 3
3 1
0 4
10
9
0.8
1
.5
P.D
. 1
.5
4.2
1
0 0
1 0
1
13
9
0.8
1
.5
EC
-E
1.5
1
.0
5 1
~
0 0
~
14
2
0.8
1
.5
EC
-E
1.5
1
.1
4 4
~ 0
0 ~
14
7
0.8
1
.5
EC
-N**
1
.5
2.5
3
5 3
0 1
4
15
4
0.8
1
.5
P.D
.**
.7
5
1.3
4
Vl
1 1
0 1
- ... 1
in.-
kip
•
0.1
13
kN
·m.
@
·Lar
gc"
am
pli
tud
es are
th
ose
in
ela
sti
c d
efo
rmat
ion
s b
etw
een
0.7
5 -
1.0
of
the c
orr
esp
on
din
g m
axim
um
am
pli
tud
e.
I "M
od
erat
e"
amp
litu
des
are
th
ose
bet
wee
n
0.5
0
-0
.75
of
the c
orr
esp
on
din
g m
axim
um.,
"Fu
lly
rev
ers
ed
cy
cle
s· o
f la
rge a
mp
litu
de
are
co
mp
lete
cy
cle
s ( ..
. an
d -)
w
ith
at
least
on
e p
eak
v
alu
e b
etw
een
0
.75
-
1.0
of
the m
axim
um
amp
litu
de
and
the o
ther
-o
n r
ev
ers
al
-b
etw
een
0.5
0
-1
.0 o
f th
e m
axim
um
"P
art
iall
y r
ev
ers
ed
cy
cle
s" are
cy
cle
s w
ith
on
e la
rge a
lApU
tude
p
eak
an
d
the o
ther
0.5
0'o
r le
ss o
f th
e m
axim
um.
"Mo
der
ate
amp
litu
de
cy
cle
s" are
th
ose
wit
h o
ne
p-ea
k v
alu
e
bet
wee
n
0.5
0 -
0.7
5 o
f th
e m
axim
um
wh
ile
the o
ther
is
0.5
0 o
r le
ss •
.. -20
sec.
du
rati
on
in
pu
t m
oti
on
s.
I I I
I I---'
I---'
I---' I
Tab
le
A2
(co
nt'
d.)
D
ata
o
n
Nu
mb
er o
f C
ycle
s B
ase
d
on
N
od
al
Ro
tati
on
s at
1st
Flo
or
Lev
el
20
-Sto
ry Is
ola
ted
S
tru
ctu
ral
Wall
s -
10
-sec.
Du
rati
on
In
pu
t M
oti
on
s
'-'--
Yie
ld
Max
imum
N
o.
of
CY
CLE
S O
F lu
np
litu
de
To
tal
No.
o
f P
eak
s LA
RGE
AM
PLIT
UD
E N
o.
of
Run
F
un
d.l
men
tal
Inte
nsi
ty
of
DC
lfor
-cy
cle
s 'r
ota
l N
o.
Lev
ol,
E
arth
qu
ake
,"acto
r,
f m
atio
n
(in
o
f In
ela
sti
c
No.
P
eri
od
, T
l M
y/l
06
te
rms
of
Lar
ge
Mo
der
ate
Fu
lly
P
art
iall
y
Mo
der
ate
Cy
cles
51
..
Co
rres
pd
q
Rev
erse
d
Rev
erse
d
Am
pli
tud
e
in-k
ips)
'"
Inp
ut
f x
5I r
ef
, V
alu
e at
Am
pli
tud
e il
Am
pli
tud
e •
Cy
clo
s C
ycl
es
ISW
-(s
ec. )
F
irat
Yie
ld)
12
1
.4
.5
H.O
. 1
.5
4.7
3
2 2
0 1
3
13
1
.4
.5
EC
-E
1.5
7
.0
2 1
0 2
1 3
14
1
.4
.5
Sl
1.5
6
.2
3 3
1 l~
~ 3
15
1
.4
.5
P.O
. 1
.5
7.0
1
2 1
0 1
2
16
1
.4
.5
EC
-E
1.5
4
.7
2 2
1 0
1 2
18
1
.4
.5
EC
-E
1.5
2
.5
2 1
0 1
~
1~
21
1
.4
.5
EC
-E*
*
1.5
6
.0
3 3
1 2
2 5
22·
1.4
.5
E
C-E
1
.0
5.0
2
1 1
1 0
3
23
1
.4
.5
EC
-E
.75
2
.8
3 0
1 1
0 2
24
1.4
.5
E
C-E
1
.5
7.5
3
0 0
3 0
3
25
1
.4
.5
EC
-E
1.5
7
.5
2 1
0 2
1 3
26
1
.4
.5
EC
-E
1.5
7
.5
2 1
0 2
1 3
27
1
.4
.5
EC
-E*
*
1.5
8
.9
5 2
1 4
1 6
42
1
.4
.5
EC
-E
1.5
8
.5
. 2
2 1
1 1
3
45
1
.4
.5
EC
-E
1.5
7
.0
2 1
0 2
1 3
---
-~-
-~-------
... 1
in.-
kip
0
.11
1
kN·m
.
@
"Lar
geR
am
pli
tud
es
are
th
ose
in
ela
sti
c d
efo
rmati
on
s b
etw
een
0
.75
-
1.0
of
the c
orr
esp
on
din
g m
axim
um
am
pli
tud
e.
• "M
od
erat
e"
am
pli
tud
es
arc
th
ose
bet
wee
n
0.5
0
-0
.75
of
the c
orr
esp
on
din
g m
axim
um.
"Fu
lly
rev
ers
ed
cy
cle
s·
of
larg
e
amp
litu
de
are
co
mp
lete
cy
cle
s , ..
. an
d -)
w
ith
at
least
on
e p
eak
valu
e b
etw
een
0
.75
-
1.0
of
the m
axim
um
amp
litu
de
and
th
e o
ther
-o
n re
vers
al
-b
etw
een
0
.50
-
1.0
of
the m
axim
um
·Part
iall
y r
ev
ers
ed
cy
cle
s" are
cy
cle
s w
ith
on
e la
rge
alA
pli
tud
e p
eak
an
d
the o
ther
0.5
0· o
r le
ss o
f th
e m
axim
um.
"Mo
der
ate
am
pli
tud
e c
ycle
s· are
th
ose
wit
h o
ne
·pea
k
valu
e
bet
wee
n
0.5
0
-0
.75
of
the m
axim
um
wh
ile
the o
ther
is
0.5
0 o
r le
ss •
••
-20
se
c.
du
rati
on
in
pu
t m
oti
on
s.
I I-'
I-'
tv
I
Tab
le
A2
(co
nt'
d.)
D
ata
o
n
Nu
mb
er o
f C
ycle
s B
ase
d
on
N
od
al
Ro
tati
on
s at
1st
Flo
or
Lev
el
20
-Sto
ry Is
ola
ted
S
tru
ctu
ral
Wall
s -
10
-sec.
Du
rati
on
In
pu
t M
oti
on
s
Hax
imum
N
o.
of
CY
CLE
S O
F Y
ield
A
mp
litu
de
To
tal
No.
o
f P
eak
s LA
RGE
AM
PLIT
UD
E N
o.
of
Run
F
unda
men
tAl
Inte
nsi
ty
of
Def
or-
cy
cle
s 'r
ota
l N
o.
Lev
el,
Ear
thq
uak
e l"
acto
r,
f m
atio
n
(in
o
f In
ela
sti
c
No.
P
eri
od
, T
l H
y/l
06
te
rms
of
Lar
ge
Mo
der
ate
Fu
lly
P
art
iall
y
Mo
der
ate
Cy
cles
S
I ..
C
orr
esp
dg
R
ever
sed
R
ever
sed
A
mp
litu
de
in-k
ips)
'"
Inp
ut
f x
Sl r
ef
• V
alu
e at
Am
pli
tud
e @
Am
pli
tud
e I
Cy
cles
Cyc~es
151'
1-(s
ec.)
F
irst
Yie
ld)
46
1
.4
.5
EC
-E
1.5
7
.8
2 1
0 2
1 3
50
1
.4
.5
EC
-E
1.5
3
.3
'3
1 1
1 0
2 5
1
1.4
.5
E
C-E
1
.5
2.8
2
1 1
~
~
2 8
0
1.4
.5
E
C-E
1
.5
11
.0
2 1
0 1J
:z J:z
2 1
06
1
.4
.5
P.O
. .7
5
4.5
1
3 1
0 1~
2J:z
12
6
1.4
.5
E
C-E
1
.5
7.1
1
1 0
1 0
1 1
30
1
.4
.5
EC
-E
1.5
7
.5
2 1
0 1
1 2
13
3
1.4
.5
E
C-E
1
.5
2.2
1
1 0
1 0
1 1
41
1
.4
.5
EC
-E
1.5
2
.8
2 2
1 0
~ 1J
:z 1
51
1
.4
.5
P.O
. .7
5
2.0
1
3 1
0 1
2 1
71
1
.4
.5
Sl
.75
3
.2
2 2
1 1
1 3
11
1
.4
.75
E
C-E
1
.5
5.1
2
1 1
1 0
2 1
23
1
.4
.75
P
.O.
.75
3
.2
2 1
0 1
J:z 1~
12
4
1'.
4
.75
P
.O.
1.0
3
.2
1 2
0 1
1 2
12
7
1.4
.7
5
P.O
. 1
.5
4.9
2
1 1
0 1
2 -
--~
---_
... _.---~--~ ~----~~~~-'-~~--
... 1
in.-
kip
=
0.1
11
kN
·m.
@
"Lar
geR
am
pli
tud
es
are
th
oso
in
ela
sti
c d
efo
rmati
on
s b
etw
een
0
.75
-
1.0
of
the co
rresp
on
din
g m
axim
um
am
pli
tud
e.
t "M
od
erat
o·
am
pli
tud
es
arc
th
ose
bet
wee
n
0.5
0
-0
.75
o
f th
e c
orr
esp
on
din
g m
axim
um.,
"Fu
lly
rev
ers
ed
cy
cle
s·
of
larg
e am
pli
tud
e arc
co
mp
lete
cy
cle
s (+
an
d -)
w
ith
at
least
on
e p
eak
valu
e
bet
wee
n
0.7
5
-1
.0 o
f th
e m
axim
um
amp
litu
de
and
th
e o
ther
-o
n re
vers
al
-b
etw
een
0
.50
-
1.0
of
the m
axim
um
"P
art
iall
y r
ev
ers
ed
cy
cle
s"
arc
cy
cle
s w
ith
on
e lo
lrg
e al
Ap
litu
de
pea
k a
nd
th
e o
ther
0.5
0'o
r le
ss o
f th
e m
axim
um.
NM
oder
ate
am
pli
tud
e c
ycle
s· are
th
ose
wit
h o
ne
pea
k
valu
e b
etw
een
0
.50
-
0.7
5 o
f th
e m
axim
um
wh
ile
the o
ther
is
0.5
0 o
r le
ss.
**
-20
se
c.
du
rati
on
in
pu
t m
oti
on
s.
J ......
I-'
w
J
Tab
le A
2 (c
on
t'd
.)
Yie
ld
RU
Il
Fu
nd
amen
tal
Lev
el,
No.
p
eri
od
, T
l M
y/l
06
ISW
-(a
ec.)
(i
n-k
ips)
'"
12
8
1.4
.7
5
13
1
1.4
.7
5
13
2
1.4
.7
5
14
6
1.4
.7
5
16
5
1.4
.7
5
10
1
.4
1.0
1
13
1
.4
1.0
1
48
1
.4
1.0
1
52
1
.4
1.0
2
0
1.4
1
.5
11
4
1.4
1
.5
16
2
1.4
1
.5
31
2
.0
.5
Data
o
n
Nu
mb
er
of
Cy
cle
s B
ased
o
n
No
dal
Ro
tati
on
s at
1st
Flo
or
Lev
el
20
-Sto
ry Is
ola
ted
S
tru
ctu
ral
Wall
s -
10
-sec.
Dti
rati
on
In
pu
t M
oti
on
s
Max
imum
N
o.
of
CY
CLE
S O
F II
mpl
ituc
le
To
tal
No.
o
f P
eak
s LA
RGE
AH
PLIT
UO
r::
No.
o
f In
ten
sity
o
f O
ofo
r-cy
cle
s T
ota
l N
o.
Ear
thq
uak
e F
acto
r,
f m
atio
n
(in
o
f In
ela
sti
c
term
s o
f L
arg
e M
od
erat
e F
ull
y
Part
iall
y
Mo
der
ate
Cy
cles
51
..
C
orr
esp
dg
R
ever
sed
R
ever
sed
A
mp
litu
de
Inp
ut
f x
5I r
ef
• V
alu
e at
Am
pli
tud
o
@ A
mp
litu
de
• C
ycl
ea
Cy
cles
F
irst
Yie
ld)
..
H.O
. 1
.5
4.5
2
3 1
0 1
2 S
l 1
.5
3.3
2
2 1
~
~ 2
EC
-E
1.5
2
.5
1 4
1 0
1~
3 T
1
.5
3.9
3
2 1
2 1
4 S
l .7
5
1.9
3
5 3
0 1
4 E
C-E
1
.5
3.0
3
0 1
1 0
2 P
.O.
1.5
4
.5
1 3
1 0
2 3
P.D
.**
1
.5
4.5
1
3 1
0 1
2 P
.O.
.75
1
.0
2Jj
1 ~
0 0
~ E
C-E
1
.5
1.1
4
1 ~
0 0
~
P.O
. 1
.5
3.2
2
1 0
1 1:
l
1~
P.D
.**
1
.5
3.5
2
1 0
1~
~
2 E
C-E
1
.5
6.4
1
2 0
1 1
2
! I I I I
34
2
.0
.5
EC
-E
1.5
3
.5
1 3
1 0
1~
2~
I
-~
35
' 2
.0
.5
EC
-E
1.0
2
.9
3 1
0 2~
~
~-~-~ ~~---.
----
-------L
-_
. __
__ ~_. _
__
_
------~
... I
in.-
kip
~
0.1
13
kN
·m.
@
"Lar
ge"
am
pli
tud
es
are
th
ose
in
ela
sti
c d
efo
rmati
on
s b
etw
een
0
.75
-
1.0
of
the c
orr
esp
on
din
g m
axim
um
am
pli
tud
e.
• * -
"Mo
der
ate"
am
pli
tud
es
are
th
ose
bet
wee
n
0.5
0
-0
.75
o
f th
e c
orr
esp
on
din
g m
axim
um.'
"Fu
lly
rev
ers
ed
cy
cle
s"
of
larg
e
amp
litu
de
are
co
mp
lete
cy
cle
s (+
an
d -I
w
ith
at
least
on
e p
eak
valu
e
bet
wee
n
0.7
5
-1
.0 o
f th
e m
axim
um
amp
litu
de
and
th
e o
ther
-o
n r
ev
ers
al
-b
etw
een
0
.50
-
1.0
of
the m
axim
um
"P
art
iall
y r
ev
ers
ed
cy
cle
s" are
cy
cle
s w
ith
on
e la
rge
alA
pli
tud
e p
eak
an
d
the o
ther
0.5
0' o
r le
ss o
f th
e m
axim
um.
"Mo
der
ate
am
pli
tud
e c
ycle
s· are
th
ose
wit
h o
ne
pea
k
valu
e
bet
wee
n
0.5
0
-0
.75
of
the m
axim
um
wh
ile
the o
ther
is
0.5
0 o
r le
ss •
20
sec.
du
rati
on
in
pu
t m
oti
on
s.
I I--'
I--' "'" I
Tab
le
A2
(co
nt'
d.)
D
ata
o
n
Nu
mb
er o
f C
ycle
s B
ase
d
on
N
od
al
Ro
tati
on
s at
1st
Flo
or
Lev
el
20
-Sto
ry Is
ola
ted
str
uctu
ral
Wall
s -
10
-sec.
Du
rati
on
In
pu
t M
oti
on
s
-~.--.-
--M
axim
um
No.
o
f C
YC
LES
OF
Yie
ld
Am
pli
tud
e T
ota
l N
o.
of
Pea
ks
LA
RG
E
1IM
l'LIT
UO
E N
o.
of
Run
F
un
dam
enta
l L
evel
, In
ten
sity
o
f O
p.fo
r-cy
cle
s 'r
ota
l N
o.
EA
rth
qu
ake
f'acto
r,
f m
ilti
on
(i
n
of
Inela
sti
c
No.
p
eri
od
, T
l M
y/10
6 te
rms
of
Lar
ge
Mo
der
ate
Fu
lly
P
art
iall
y
Mo
der
ate
Cy
cles
S
I ..
C
orr
esp
dg
R
ever
sed
R
ever
sed
Pu
np li tu
de
in-k
ips)
'"
Inp
ut
f x
SI r
ef
• V
alu
e at
Am
pli
tud
e @
Am
pli
tud
e'
Cy
cles
C
ycl
es
ISW
-(s
ec. )
F
irst
Yie
ld)
36
2
.0
.5
EC
-E
1.5
4
.2
2 .
2 1
0 1
2
15
0
2.0
.5
H
.O.
.75
2
.9
2 0
1 0
0 1
16
3
2.0
.5
E
C-E
1
.5
5.0
2
1 O.
1
0 1
32
2
.0
.75
E
C-E
1
.5
3.0
3
1 0
2 ~
2~
11
9
2.0
.7
5
EC
-E
.75
1
.4
1 3
0 0
0 0
12
0
2.0
.7
5
EC
-E
1.0
2
.7
1 0
0 0
0 0
12
9
2.0
.7
5
T
1.0
2
.7
1 4
1 0
1~
2~
13
6
2.0
.7
5
Sl
1.5
2
.9
2 1
1 ~
0 l~
13
7
2.0
.7
5
H.O
. 1
.5
3.6
2
1 1
0 1
2
14
0
2.0
.7
5
P.O
. 1
.0
2.3
1
2 1
0 ~
1~
16
7
2.0
.7
5
H.O
. .7
5
. 1
.8
1 1
. 0
~
~
1
33
2
.0
1.0
E
C-E
1
.5
2.5
1
2 0
1 1
2
III
2.0
1
.0
H.O
. 1
.5
3.1
1
1 1
0 0
1
16
4
2.0
1
.0
H.O
.**
1
.5
2.9
2
0 1
0 0
1
11
2
2.0
1
.5
H.O
. 1
.5
1.7
1
1 0
k 2 ~
1
... 1
in.-
kip
a
O.l
ll
kN·m
.
@
"Lar
ge"
am
pli
tud
es
are
th
ose
in
ela
sti
c d
efo
rmat
ion
s b
etw
een
0
.75
-1
.0 o
f th
e co
rres
po
nd
ing
max
imum
am
pli
tud
e.
• "M
od
erat
e"
amp
litu
des
are
th
ose
b
etw
een
0
.50
-
0.7
5 o
f th
e c
orr
esp
on
din
g m
axim
um.
"Fu
lly
rev
ers
ed
cy
cle
s" o
f la
rge a
mp
litu
de
are
co
mp
lote
cy
cle
s (+
an
d -)
w
ith
at
least
on
e p
eak
valu
e b
etw
een
0
.75
-
1.0
of
the m
axim
um
amp
litu
de
and
the o
ther
-o
n r
ev
ers
al
-b
etw
een
0
.50
-1
.0 o
f th
e m
axim
um
"P
art
iall
y r
ev
ers
ed
cy
Cle
s" are
cy
cle
s w
ith
on
e la
rge a
mp
litu
de
pea
k a
nd
the o
ther
0.5
0·o
r le
ss o
f th
e m
axim
um.
-Mo
der
ate
amp
litu
de
cy
cle
s· are
th
ose
wit
h o
ne
pea
k
valu
e
bet
wee
n 0
.50
-0
.75
of
the m
axim
um
wh
ile
the o
ther
is
0.5
0 o
r le
ss.
** -
20 se
c.
du
rati
on
in
pu
t m
oti
on
s •.
I i , i i , , , i I I i
I ......
......
U1 I
Tab
le
A2
(co
nt'
d.)
D
ata
o
n
Num
ber
of
Cy
cle
s B
ased
o
n
No
dal
Ro
tati
on
s at
1st
Flo
or
Lev
el
20
-Sto
ry Is
ola
ted
str
uctu
ral
Wall
s -
10
-sec.
Du
rati
on
In
pu
t M
oti
on
s
------------
Hax
imw
n N
o.
of
CY
CLE
S O
F Y
ield
A
mp
litu
de
To
tal
No.
o
f P
eak
s LA
RGE
AH
PLIT
UD
E N
o.
of
Run
F
un
dam
enta
l In
ten
sity
o
f O
efo
r-cy
cle
s T
ota
l N
o.
Lev
el,
Ear
thq
uak
e F
acto
r,
f m
atio
n
(in
o
f In
ela
sti
c
No.
P
eri
od
, T
l M
y/l
06
te
rms
of
Lar
ge
Mo
der
ate
Fu
lly
p
art
iall
y
Mo
der
ate
Cy
cles
5
1
..
Co
rres
pd
g
Rev
erse
ci
Rev
erse
ci
Am
pli
tud
e
in-k
ips)
+
Inp
ut
f x
SI r
ef
• V
alu
e at
Am
pli
tud
o
@ A
mp
litu
de'
Cy
cles
Cyc~es
151'
1-(s
ec. )
F
irat
Yie
ld)
40
2
.4
.5
EC
-E
1.5
5
.0
2 2
1 1
~ 2~
15
8
2.4
.5
E
C-E
**
1
.5
5.1
2
1 1
0 0
1
10
2
2.4
.7
5
EC
-E
1.5
4
.1
1 2
0 ~
~ 1
12
2
2.4
.7
5
EC
-E
1.0
1
.6
2 2
2 0
0 2
13
4
2.4
.7
5
Sl
1.5
2
.1
4 2
2 ~
0 2~
13
8
2.4
.7
5
P.O
. 1
.5
1.5
2
3 0
~ ~
1 1
44
2
.4
.75
H
.O.
1.5
' 1
.9
3 2
2 0
0 2
14
5
2.4
.7
5
T
1.5
1
.3
1~
3 ~
0 0
~ 1
07
2
.4
1.0
E
C-E
1
.5
2.1
2
2 1
~ 0
1~
15
9
2.4
1
.0
EC
-E*
*
1.5
1
.5
2 1
~ l:
2
0 1
17
6
2.0
.2
5
Sl
.75
4
.0
4 1
2 ~
0 2~
17
4
2.4
.2
E
C-E
.7
5
5.2
3
0 1
0 0
1 1
75
2
.4
.2
T
.75
2
.8
2!:i
4 1
0 1
2 1
73
2
.4
.25
T
.7
5
2.8
3
4 1
1 1
2~
--------
+
-1
in.-
kip
a
0.1
1]
kN·m
.
@
"Lar
geN
am
pli
tud
es are
th
ose
in
ela
sti
c d
efo
rmat
ion
s b
etw
een
0
.75
-1
.0 o
f th
e c
orr
esp
on
din
g m
axim
um
am
pli
tud
e.
I "M
od
erat
e"
amp
litu
des
are
th
ose
bet
wee
n 0
.50
-0
.75
of
the c
orr
esp
on
din
g m
axim
um.,
** -
"Fu
lly
rev
ers
ed
cy
cle
s" o
f la
rge a
mp
litu
de
are
co
mp
lete
cy
cle
s (+
an
d -)
w
ith
at
least
on
e p
eak
valu
e
bet
wee
n
0.7
5
-1
.0 o
f th
e m
axim
um
amp
litu
de
and
the o
ther
-o
n re
vers
al
-b
etw
een
0.5
0
-1
.0 o
f th
e m
axim
um
"P
art
iall
y r
ev
ers
ed
cy
cle
s· are
cy
cle
s w
ith
on
e la
rge a
mp
litu
de
pea
k a
nd
th
e o
ther
0.5
0'o
r le
ss o
f th
e m
axim
wn.
-M
od
erat
e am
pli
tud
e cy
cle
s"
are
th
ose
wit
h o
ne
pea
k
valu
e
bet
wee
n 0
.50
-0
.75
of
the m
axim
wn
wh
ile
the o
ther
is
0.5
0 o
r le
ss.
20 se
c.
du
rati
on
in
pu
t m
oti
on
s.
i I
I .....
.....
0'\
I
'fab
Ie
A3
Data
o
n
Num
ber
of
Cy
cle
s B
ased
o
n
No
dal
R
ota
tio
ns
at
1st
Flo
or
Lev
el
30
-Sto
ry Is
ola
ted
S
tru
ctu
ral
Wall
s -
10
-sec.
Du
rati
on
In
pu
t M
oti
on
s ----~-
---
- Max
imum
N
o.
of
CY
CLE
S O
F Y
ield
A
mp
litu
de
To
tal
No.
o
f P
eak
s LA
RGE
AM
PLIT
UD
E N
o.
of
Run
F
un
dam
enta
l In
ten
sity
o
f D
cfo
r-cy
cle
s T
ota
l N
o.
Lcv
el,
Ear
thq
uak
e t'
acto
r,
f m
atio
n
(in
o
f In
elas
tic:
:
No.
P
eri
od
, T
l te
rms
of
Lar
ge
Mo
der
ate
Fu
lly
P
art
iall
y
Mo
der
ate
Cy
cles
M
y/l
06
5
1
-C
orr
esp
dg
R
ever
sed
R
ever
sed
A
mp
litu
de
(in
-kip
s)t
Inp
ut
f x
SIr~
f.
Val
ue
al:
Am
pli
tud
a @
A
mp
litu
de.
Cy
ole
s C
ycl
es
151'
1-(s
ec. )
F
irst
Yie
ld)
30
04
1
.4
1.0
E
C-E
1
.5
4.2
3
1 1
~
0 l~
30
13
1
.4
1.0
P
.O.
1.5
6
.3
1 1
0 1
1 2
30
08
1
.4
1.5
E
C-E
1
.5
3.3
2
1 1
0 0
1 3
01
4
1.4
1
.5
P.O
. 1
.5
5.8
2
0 1
0 0
1 3
01
2
1.4
2
.0
EC
-E
1.5
3
.9
3 1
1 1
~
2~
30
15
1
.4
2.0
P
.O.
1.5
5
.5
1 2
1 0
1 2
30
05
2
.0
1.0
E
C-E
1
.5
6.7
2
1 1
0 0
1 3
01
7
2.0
1
.0
P.O
. 1
.5
4.1
2
3 1~
0 ~
2 3
00
6
2.0
1
.5
EC
-E
1.5
4
.0
3 1
0 2
~
2~
30
1S
2
.0
1.5
P
.O.
1.5
2
.3
1 2
1 0
~ 1~
30
07
2
.0
2.0
E
C-E
1
.5
2.6
1
5 0
0 3
3 3
01
9
2.0
2
.0
P.O
. 1
.5
1.S
1
1 0
~ ~
1 3
00
9
2.4
1
.0
EC
-E
1.5
7
.0
2 1
1 0
0 1
30
21
2
.4
1.0
P
.O.
1.5
4
.2
1 2
0 1
1 2
30
10
2
.4
1.5
E
C-E
1
.5
5.2
1
2 0
1 1
2 3
02
2
2.4
1
.5
P.O
. 1
.5
1.4
1
~
0 ~
0 ~
30
11
2
.4
2.0
E
C-E
1
.5
3.2
2
1 0
1~
0 l~
30
23
2
.4
2.0
P
.O.
1.5
1
.3
1 1
0 ~
0 ~
---
-----
--
------
--_
.. --~---
-----
t 1
in.-
kip
•
0.1
11
kN
'm.
@
"Lar
geU
am
pli
tud
es are
th
ose
inelas~ic
def
orm
atio
ns
bet
wee
n
0.7
5 -
1.0
of
the c
orr
esp
on
din
g m
axim
um am
pli
tud
e.
"Ho
der
atc·
am
pli
tud
es are
th
ose
b
etw
een
0
.50
-
0.7
5 o
f th
e c
orr
esp
on
din
g m
axim
um.
"Fu
lly
rev
ers
ed
cy
cle
s" o
f la
rge a
mp
litu
de
are
co
mp
lete
cy
cle
s (+
an
d -)
w
ith
at
least
on
e p
eak
valu
e
bet
wec
n
0.7
5
-1
.0 o
f th
e m
axim
um
amp
litu
de
and
th
e o
ther
-o
n re
ver6
al
-b
etw
een
p.S
O
-1
.0 o
f th
e m
axim
um.
"P
art
iall
y r
ev
ers
cd
c~cles"
are
cy
cle
6
wit
h o
ne
larg
e a
mp
litu
de
pea
k a
nd
th
e o
ther
0.5
0 o
r le
ss o
f th
e m
axim
um.
"Mo
der
ate
amp
litu
de
cy
cle
s· are
th
ose
wit
h o
ne
pea
k
valu
e b
etw
een
0.5
0
-0
.75
of
the m
axim
um w
hil
e
the o
ther
ia
0.5
0 o
r le
ss.
I -
I I-'
I-'
-...J J
Tab
le
A4
Data
o
n
Num
ber
of
Cy
cle
s B
ased
o
n
No
dal
R
ota
tio
ns
at
2n
d F
loo
r L
ev
el
40
-Sto
ry Is
ola
ted
str
uctu
ral
Wall
s -
10
-sec.
Du
rati
on
In
pu
t M
oti
on
s
-
Max
imum
N
o.
of
CY
CLE
S O
F Y
ield
/l
mp
litu
de
To
tal
No.
o
f P
eak
s LA
RGE
AM
PLIT
UD
E N
o.
of
RUIl
Fu
nd
amen
tal
Inte
nsi
ty
of
On
for-
eye
leu
L
evu
l,
Ji:a
rthq
uake
~·ilctor.
t m
atio
n
(in
o
f N
o.
Peri
od
, T
l H
y/l
06
te
rms
of
Lar
ge
Mo
der
ate
Fu
lly
P
art
iall
y
~Ioderate
SI
-C
orre
sp<
ig
Rev
erse
d
Rev
erse
d
Am
pli
tud
e
(in
-kip
s)+
In
pu
t f
x S
I ret
• V
alu
e at
Am
pli
tud
a @
A
mp
litu
de'
Cy
clo
s C
ycl
es
ISW
-(s
ec. )
F
irst
Yie
ld)
40
08
1
.4
1.0
E
C-E
1
.5
9.2
1
2 1
0 0
40
21
1
.4
1.0
S
l 1
.5
15
.0
2 2
2 0
0
40
34
1
.4
1.0
P
.D.
1.5
1
2.2
2
0 0
l~
0 4
00
1
1.4
1
.5
EC
-E
1.5
9
.5
2 1
0 2
~ 4
03
9
1.4
1
.5
P.D
. 1
.5
9.0
1
1 0
1 0
40
06
1
.4
2.0
E
C-E
1
.5
3.4
2
1 0
1~
~
40
45
1
.4
2.0
P
.D.
1.5
7
.0
1 2
1 0
1
40
51
1
.4
2.5
E
C-E
1
.5
5.7
2
1 1
1 0
40
16
2
.0
1.0
E
C-E
1
.5
4.4
2
0 1
0 0
40
22
2
.0
1.0
sl
1.5
6
.5
2 2
2 0
0 4
04
3
2.0
1
.0
P.D
. 1
.5
8.5
2
1 0
~ 0
40
15
2
.0
1.5
E
C-E
1
.5
4.2
1
1 1
0 0
40
24
2
.0
1.5
S
l 1
.5
5.7
5
4 0
2 0
0 4
04
0
2.0
1
.5
P.D
. 1
.5
5.1
2
0 0
1 0
40
46
2
.0
2.0
P
.D.
1.5
3
.2
2 1
1 ~
0
~~ ~-~--~----
+
1 in
.-k
ip •
0
.11
1
kN'm
.
@
OILarge~
amp
litu
des
are
th
ose
in
ela
sti
c d
efo
rmat
ion
s b
etw
een
0
.75
-
1.0
of
the c
orr
esp
on
din
g m
axim
um
am
pli
tud
e.
-Mo
der
ate·
am
pli
tud
es are
th
ose
bet
wee
n
0.5
0 -
0.7
5 o
f th
e c
orr
esp
on
din
g m
axim
um.
To
t,il
H
o.
Inela
sti
c
Cy
cles
1 2 1~
2~
1 2 2 2 1 2 ~ 1 2 1 1~
~.~=
"Fu
lly
rev
ers
ed
cy
cle
s·
of
larg
e a
mp
litu
de
are
co
mp
lete
cy
cle
s (+
an
d -)
w
ith
at
least
on
e p
eak
valu
e b
etw
een
0
.75
-
1.0
of
the m
axim
um
amp
litu
de
and
the o
ther
-o
n re
vers
al
-b
etw
een
p.5
0
-1
.0 o
f th
e m
axim
um.
"P
art
iall
y r
ev
ers
ed
cy
cle
s" are
cy
cle
s w
ith
on
e la
rge a
mp
litu
de
pea
k
and
the o
ther
0.5
0 o
r le
ss o
f th
e m
axim
um.
"Mo
der
ate
amp
litu
de
cyC
les"
are
th
ose
wit
h o
ne
pea
k
valu
e b
etw
een
0.5
0 -
0.7
5 o
f th
e m
axim
um
wh
ile
the o
ther
1&
0.5
0 o
r le
ss.
.
I I i I
I I-'
I-'
co
I
Tab
le A
4 (c
on
t'd
.)
Yie
ld
Run
F
un
dam
enta
l L
evel
,
No.
P
eri
od
, T
l H
y/l
06
I5W
-(s
ec. )
in
-kip
s)+
40
50
2
.0
2.0
4
00
9
2.4
1
.0
40
23
2
.4
1.0
4
04
2
2.4
1
.0
40
20
2
.4
1.5
4
02
7
2.4
1
.5
"404
1 2
.4
1.5
4
00
4
2.4
2
.0
40
47
2
.4
2.0
4
01
2
3.0
1
.0
40
31
3
.0
1.0
4
03
8
3.0
1
.0
40
05
3~0
1.5
40
32
3
.0
1.5
4
03
7
3.0
1
.5
40
03
3
.0
2.0
40
48
3
.0
2.0
+
1 in
.-k
ip •
O
.lll
kN
·m.
Data
o
n
Num
ber
of
Cy
cle
s B
ased
o
n
No
dal
R
ota
tio
ns
at
2n
d
Flo
or
Lev
el
40
-Sto
ry
Iso
late
d str
uctu
ral
Wall
s -
10
-sec.
Du
rati
on
In
pu
t M
oti
on
s
Max
imW
ll N
o.
of
CY
CLE
S O
F A
mp
litu
de
To
tal
No.
o
f P
eak
s LA
RGE
AM
PLIT
UD
E N
o.
of
Inte
nsi
ty
of
Dcf
or-
cy
cle
s T
oti
ll 1
'10.
Ear
thq
uak
e ~'actor,
f m
atio
n
(in
o
f In
ela
sti
c
term
s o
f L
arg
e M
od
erat
e F
ull
y
Part
iall
y
Mo
der
ate
Cy
cles
5
1
..
Co
rres
pd
g
Rev
erse
d
Rev
erse
d
Am
pli
tud
e In
pu
t f
x S
I ref
• V
alu
e at
Am
pli
tud
a @
Am
pli
tud
e.
Cy
cles
C
ycl
es
Pir
st
Yie
ld)
EC
-E
1.5
5
.6
2 2
1 ~
~ 2
EC
-E
1.5
5
.7
1 2
1 0
0 1
Sl
1.5
6
.3
3 1
2 0
0 2
P.O
. 1
.5
6.3
2
0 0
~
0 ~
EC
-E
1.5
6
.5
3 0
1 0
0 1
Sl
1.5
6
.8
3 0
1 1
0 2
P.O
. 1
.5
3.8
1
1 0
0 1
1
EC
-E
1.5
5
.4
2 1
1 0
0 1
P.O
. 1
.5
3.2
1
2 0
1 1
2
EC
-E
1.5
4
.6
1 2
1 0
0 1
Sl
1.5
6
.7
2 1
1 1
0 2
P.O
. 1
.5
3.3
1
1 0
~
h 2 1
EC
-E
1.5
5
.8
2 1
1 0
~ 1~
Sl
1.5
5
.4
1 1
1 0
0 1
P.O
. 1
.5
2.1
1
2 0
0 0
0
EC
-E
1.5
3
.3
2 1
1 0
0 1
P.O
. 1
.5
2.0
1
1 0
~ ~
1
--~-----' ----
@
"Lar
ge"
am
pli
tud
es a
re t
ho
se in
ela
sti
c d
efo
rmat
ion
s b
etw
een
0
.75
-1
.0 o
f th
e
corr
esp
on
din
g m
axim
um
am
pli
tud
e.
• "M
od
erat
e"
amp
litu
des
are
th
ose
bet
wee
n
0.5
0
-0
.75
of
the
corr
esp
on
din
g m
axim
um •
•• D
.
"Fu
lly
re
vers
ed
cy
cle
s·
of
larg
e a
mp
litu
de
are
co
mp
lete
cy
cle
s (+
an
d -)
w
ith
at
least
on
e p
eak
valu
e
bet
wee
n
0.7
5
-1
.0 o
f th
e m
axim
um
amp
litu
de
and
th
e o
ther
-o
n r
ev
ers
al
-b
etw
cen
p.5
0
-1
.0 o
f th
e m
axim
Wll.
"P
art
iall
y r
ev
ers
ed
cy
cle
s"
are
cy
cle
s w
ith
One
la
rgc a
mp
litu
de
pea
k a
nd
th
e o
ther
0.5
0 o
r le
ss o
f th
e m
axim
um.
"Mo
der
ate
amp
litu
de
cy
cle
s· are
th
ose
wit
h o
ne
pea
k
valu
e b
etw
een
0.5
0 -
0.7
5 o
f th
e m
axim
Wll
wh
ile
the o
tho
r 18
0
.50
or
less.
I
I I-'
I-' ~
I
~able
AS
Data
o
n
Nu
mb
er
an
d
P.e
lati
ve H
ag
nit
ud
e o
f C
ycle
s P
reced
ing
F
irst
Larg
e-A
mp
litu
de
Resp
on
se
Pea
k
Bas
ed
on
N
od
al
Ro
tati
on
s at
Mid
heig
ht
of
1st
Sto
ry
10
-Sto
ry Is
ola
ted
S
tru
ctu
ral
Wall
s -
10
-sec.
Du
rati
on
In
pu
t M
oti
on
@
®
Yie
ld
Fir
s t
Lar
ge
1\.m
pli t
ud
e ®
N
o.
of
No.
o
f ®
Cy
cles
il
Illt
oll
ilit
y
I\In
pli t
ud
e o
f L
LU
"lJe
st
Pea
ks
Run
F
un
dam
enta
l L
evel
, F
acto
r,
f R
esp
on
se
Tim
e to
D
isp
lst.
b
etw
een
E
arth
qu
ake
pea
k
~.
Max
imum
p
rece
dil
lg
-O
-sec
. N
o;
peri
od
, T
l H
y/l
06
S
I ..
(in
te
rms
of
Dis
pls
t.
Max
. A
®
and
Ta
nxd
f x
SIr
ef.
C
orre
spd<
J.
Am
pli
tud
e (i
n
term
s o
f F
ull
y
Part
iall
y
(in
-kip
s)·
Inp
ut
Val
ue
at
TlIIX
d o
f Y
ield
am
pli
tud
e R
ever
sed
R
ever
sed
.
ISW
-(s
ec. )
F
irst
Yie
ld)
Am
pli
tud
e)
to@
' C
ycl
es
Cy
cles
10
03
0
.5
.15
EC
-:-E
1.5
9
.4*
1
.6
3.8
0
.40
1
0 ~
10
37
0
.5
.15
P
.D.
1.5
1
4.0
*
3.0
2
.3
0.1
6
1 0
~
10
10
0
.5
.50
E
C-E
1
.5
2.9
*
1.6
1
.6
0.5
5
1 1
0
10
36
0
.5
.50
P
.D.
1.5
1
. 7*
3.4
0
.8
0.4
7
1 0
~
10
07
0
.5
1.0
E
C-E
1
.5
2.1
2
.1
1.0
0
.47
~
0 0
10
24
0
.5
1.0
S
l 1
.5
1.9
*
4.1
1
.6
0.8
4
2 2
0
10
31
0
.5
1.0
P
.D.
1.5
1
.3
8.6
0
.9
0.6
9
1~
a 0
10
04
0
.8
.15
E
C-E
1
.5
8.0
*
3.4
4
.5
0.5
6
1 a
1
10
38
0
.8
.15
P
.D.
1.5
1
0.5
3
.0
0.9
0
.09
~
a a
10
09
0
.8
.50
E
C-E
1
.5
1.1
*
2.7
0
.97
0
.88
~
0 0
10
35
0
.8
.50
P
.D.
1.5
2
.0
3.4
1
.0
0.5
0
~ a
a 1
00
2
1.4
.1
5
EC
-E
1.5
6
.1*
3
.5
2.0
0
.33
1
0 1
10
34
1
.4
.15
P
.D.
1.5
5
.6
3.1
0
.4
0.0
7
~ 0
a 1
04
1
1.4
.2
0
EC
-E
1.5
3
.9
3.6
1
.0
0.2
6
1~
~
a 1
04
0
1.4
.2
5
EC
-E
1.5
1
.9
3.2
0
.6
0.3
2
~ a
0
10
33
1
.4
.50
P
.D.
1.5
1
.5
3.7
0
.8
0.5
3
~ 0
0 ~
-... --
+
1 in
.-k
ip •
0
.11
3
kN.m
.
$ eq
ual
to c
alc
ula
ted
max
imum
re
spo
nse
pea
k,
ex
cep
t w
her
e n
ote
d.
wit
h
amp
litu
de
equ
al to
at
least
0.8
5 o
f th
at
of ®
. ,
-@
-
"Fu
lly
rev
ers
ed
cy
cle
s'
are
co
mp
lete
cy
cle
s (+
an
d -
) w
ith
at
least
on
e p
eak
valu
e
bet
wee
n 0
.75
-
1.0
of
the a
mp
litu
de o
f@an
d
the o
ther
-o
n re
vers
al
-b
etw
een
0
.50
-1
.0 o
f@
. M
part
iall
y r
ev
ers
ed
cy
cle
s· are
cy
cle
s w
ith
on
e p
eak
am
pli
tud
e eq
ual
to a
t le
ast
0.7
5 o
f ®
and
th
e o
ther
0.5
0 o
r le
ss o
f ®
. .
* 7
5'
of
max
imum
am
pli
tud
e o
f d
efo
rmati
on
.
I i I
I I-'
I\..
)
o I
Tab
le A
6 D
ata
o
n
Nu
mb
er
and
R
ela
tiv
e M
ag
nit
ud
e o
f C
ycle
s P
reced
ing
F
irst
Larg
e-A
mp
litu
de
Resp
on
se
Pea
k
Bas
ed
on
N
od
al
Ro
tati
on
s at
1st
Flo
or
Lev
el
20
-Sto
ry
Iso
late
d S
tru
ctu
ral
Wall
s -
10
-sec.
Du
rati
on
In
pu
t M
oti
on
s
@
®
!
Yie
ld
Fir
!lt
r.ar
go
A
mpl
ituc
lo
®
No.
o
f 1'1
9.
of
® C
ycl
es I
i .
Inlc
nu
ity
A
lllp
lilu
de
of
1 • ..t
J:(J
csL
P
eak
s T
illi
e to
b
etw
een
R
un
t'und
<lm
enta
l L
ev
el,
fa
cto
r,
f R
esp
on
se
Dis
pls
t.
Ear
th'l
uak
e P
eak
~ M
axim
um
Pre
ced
ing
--
O-s
ce.
No.
P
eri
od
, '1'
1 M
y/lO
G
SI
-(i
n
term
s o
f D
iap
lst.
M
ax.
A
@
and
'fm
xd
f x
SIr
ef.
Corn~lipu~ •
A
mp
litu
de
(in
lc
rlll
lJ
of
Fu
lly
P
ilrt
i .. l1
1y
(in
-kip
s) *
Inp
ut
Val
ue
at
TIIIX
Q
of
Yie
ld
amp
litu
de
Rev
erse
d
Rev
erse
d
ISW
-(a
ec. )
F
irst
Yie
ld)
Am
pli
tud
e)
to@
' C
ycl
es
Cy
cles
1 0
.8
.5
EC
-E
1.5
9
.4*
3
.4
5.8
0
.62
1
0 ~
11
6
0.8
.5
P
.D.
1.5
1
2.6
3~0
1.1
0
.09
1
0 ~
15
6
0.8
.5
P
.D".
1
.5
12
.3*
*
3.0
1
.2
0.1
0
1 0
1
16
9
0.8
.5
P
.D.
.75
4
.4*
3
.0
0.4
0
.09
~
0 0
7 0
.8
.75
E
C-E
1
.5
4.5
*
2.4
1
.4
0.3
1
1 0
1
11
5
0.8
.7
5
P.D
. 1
.5
7.0
*
3.0
0
.6
0.0
9
~
0 0
11
7
0.8
.7
5
P.D
. .7
5
4.6
3
.5
2.0
0
.43
1
0 !:
i
12
1
0.8
.7
5
P.D
. 1
.0
6.0
3
.6
4.0
0
.67
1
0 ~
13
5
0.8
.7
5
H.O
. 1
.5
6.1
6
.8
4.8
0
.79
2
1 0
14
3
0.8
.7
5
Sl
1.5
3
.3
2.4
2
.4
0.7
3
1 0
~
14
9
0.8
.7
5
T
1.5
4
.2*
1
.3
3.6
0
.86
1
~
0
4 0
.8
1.0
E
C-E
1
.0
1.0
*
2.3
0
.4
0.4
0
1~
0 0
5 0
.8
1.0
E
C-E
1
.5
4.0
2
.3
1.0
0
.25
2
~
0
6 O
.B
1.0
E
C-E
1
.5
3.0
2
.3
1.0
0
.33
2
~
0 9
0
0.8
1
.0
EC
-N
1.5
4
.4*
2
.9
2.9
0
.66
2
1 0
I --'
+
-1
in.-
kip
5
0.1
11
kN
·m.
$ eq
ual
to c
alc
ula
ted
max
imum
re
spo
nse
p
eak
, ex
cep
t w
her
e n
ote
d.
• w
ith
am
pli
tud
e eq
ual
to
at
lease
0
.85
of
that
of ®
. @
"F
ull
y r
ev
ers
ed
cy
cle
s"
are
co
mp
lete
cy
cle
s It
and
-)
w
ith
at
least
on
e p
eak
valu~ b
etw
een
p.7
S -
1.0
of
the
amp
litu
de
of@
an
d
the o
ther
-o
n r
ev
ers
al
-b
etw
een
0
.50
-
1.0
of@
. -P
<lr
ti<
llly
rev
e.rs
ed c
ycle
s-are
cy
cle
s w
ith
on
e p
eak
<
lmp
litu
de
e'lu
<ll
to
<
It
least
0.7
5 o
f ®
and
the o
ther
0.5
0 o
r le
ss o
f ®
. .
* 1
5\
of
max
imum
am
pli
tud
e o
f d
efo
rmat
ion
•
.. -~o
sec.
du
rati
on
in
pu
t m
oti
on
a.
;
I f-'
l'V
I-' I
Tab
le
A6
(co
nt'
d.)
D
ata
o
n
Nu
mb
er
and
R
ela
tiv
e
Mag
nit
ud
e o
f C
ycle
s P
reced
ing
F
irst
Larg
e-A
mp
litu
de
Resp
on
se
Peak
B
ase
d
on
N
od
al
Ro
tati
on
s
at
1st
Flo
or
Lev
el
20
-Sto
ry
Iso
late
d S
tru
ctu
ral
Wall
s -
10
-sec.
Du
rati
on
In
pu
t M
oti
on
s
--
@
®
Yie
ld
Fir
s t
l.ar
ge
Am
pli
tud
e @
N
o.
of
No.
o
f ®
Cy
cles
il
Inte
nsi
ty
Am
pli
tud
e o
f L
arg
est
P
eak
s R
un
Fu
nd
amen
tal
Lev
el,
Facto
r,
f R
esp
on
se
Tim
e to
D
isp
lst.
b
etw
een
E
arth
qu
ake
Pea
k
$ M
axim
um
Pre
ced
ing
-
O-s
ec.
No.
P
eri
od
, T
l M
y/lO
Ci
51
-
(in
te
rms
of
Dis
pls
t.
Max
. A
®
ilnd
Tm
xd
f x
SIr
ef.
C
orr
esp
dg
. A
mp
litu
de
(in
te
rms
of
Fu
lly
P
art
iall
y
(in
-kip
s) +
In
pu
t V
alu
e at
Tmxd
o
f Y
ield
am
pli
tud
e R
ever
sed
R
ever
sed
I5
W-
(sec. )
F
irst
Yie
ld)
Am
pli
tud
e)
to@
' C
ycle
&
Cy
cle
.
91
0
.8
1.0
T
1
.5
4.1
**
4
.1
0.9
0
.22
~
0 0
10
3
0.8
1
.0
EC
-E
1.5
4
.1
2.3
1
.0
0.2
4
2 ~
0
10
4
0.8
1
.0
EC
-E
1.5
4
.0
2.3
1
.0
0.2
5
2 ~
0
10
5
0.8
1
.0
EC
-E
1.5
3
.7
2.3
1
.0
0.2
7
1~
~
0
11
0
0.8
1
.0
P.D
. 1
.5
4.5
*
3.0
0
.4
0.0
9
k 2 0
0
12
5
0.8
1
.0
EC
-E
1.5
2
.8
2.3
0
.8
0.2
9
2 0
0
15
3
0.8
1
.0
EC
-N
.75
2
.8
2.3
0
.9
0.3
2
~ 0
0
15
7
0.8
1
.0
P.D
. 1
.5
* 2
.8*
*
3.0
0
.3
0.1
1
~
0 0
2 0
.8
1.5
E
C-E
1
.5
2.1
*
2.3
0
.8
0.3
8
1~
0 ~
3 0
.8
1.5
E
C-N
1
.5
3.0
2
.3
1.5
0
.50
1
0 ~
10
9
0.8
1
.5
P.D
. 1
.5
4.2
3
.5
1.8
0
.43
1
0 ~
13
9
0.8
1
.5
EC
-E
1.5
0
.9*
3
.2
0.5
0
.56
~
0 0
14
2
0.8
1
.5
EC
-E
1.5
1
.1
3.1
0
.5
0.4
5
1~
0 0
14
7
0.8
1
.5
EC
-N
1.5
*
2.4
**
2
.4
1.4
0
.58
1
0 ~
15
4
0.8
1
.5
P.D
. .7
5
1.3
**
2
.8
0.8
0
.62
~
0 0
-
+
1 in
.-k
ip •
O
.lll
kN
·m.
$ eq
ual
to c
alc
ula
ted
max
imum
re
spo
nse
p
eak
, ex
cep
t w
her
e n
ote
d.
* w
ith
am
pli
tud
e eq
ual
to at
lease
0.8
5 o
f th
at
of ®
. "
DF
ull
y
rev
ers
ed
cy
cle
s·
are
co
mp
lete
cy
cle
s (+
an
d -)
w
ith
at
least
on
e p
eak
valu
e b
etw
een
0.1
5
-1
.0 o
f th
e am
pli
tud
e o
f@an
d
the o
ther
-o
n re
vers
al
-b
etw
een
0.5
0
-1
.0 Of
QD.
·Part
iall
y r
ev
ers
ed
cy
cle
s-are
cy
cle
s w
ith
on
e p
eak
am
pli
tud
e eq
ual
to at
least
0.1
5 o
f@an
d th
e o
ther
0.5
0 o
r le
ss o
f@.
.
* 1
5\
of
max
imum
am
pli
tud
e o
f d
efo
rmati
on
.
**
-ZO
se
c.
du
rati
on
in
pu
t m
oti
on
s.
I ......
N
N I
Tab
le A
6 (c
on
t'd
.)
Data
o
n
Num
ber
an
d R
ela
tiv
e
Mag
nit
ud
e
of
Cy
cle
s P
reced
ing
F
irst
Larg
e-A
mp
litu
de
Resp
on
se
Peak
B
ased
o
n
No
dal
R
ota
tio
ns
at
1st
Flo
or
Lev
el
20
-Sto
ry
Iso
late
d S
tru
ctu
ral
Wall
s -
10
-sec.
Du
rati
on
In
pu
t M
oti
on
s
®
®
Yie
ld
~'ir
s t
1 .. :1
I:ge
Am
p li tu
de
®
No.
o
f In
ten
oit
y
Am
pli
tud
e o
f L
urq
ost
P
eak
s N
o.
of
® C
ycl
es fI
R
un
Fu
nd
amen
tal
Lev
el,
Facto
r,
f R
esp
on
se
Tim
e to
D
isp
lst.
b
etw
een
E
arth
qu
ake
Pea
k
$ M
axim
um
Pre
ced
in'J
-
O-s
ec.
No.
P
eri
od
, T
l M
y/l0
6
51
..
(i
n
term
s o
f D
iap
15
t.
Max
. A
an
d
Tmxd
f
x S
Iref.
C
orr
espd
9.
Am
pli
tud
e (i
n
term
s ®
o
f F
ull
y
Part
iall
y
(in
-kip
s)+
In
pu
t V
alu
e at
'1'lI\
Xd
of
Yie
ld
amp
litu
de
Rev
erse
d
Rev
erse
d
ISW
-(&
ee
.)
Fir
st
Yie
ld)
Am
pli
tud
e)
to@
. C
ycl
es
Cy
cles
12
1
.4
.5
H.D
. 1
.5
3.6
*
5.5
2
.0
0.5
6
1 0
~
13
1
.4
.5
EC
-E
1.5
7
.0
3.5
3
.0
0.4
3
1 0
~
14
1
.4
.5
Sl
1.5
6
.2
2.1
0
.4
0.0
6
~
0 0
15
1
.4
.5
P.O
. 1
.5
7.0
3
.0
0.5
0
.07
~
0 0
16
1
.4
.5
EC
-E
1.5
4
.7
3.5
2
.4
0.5
1
1 0
~
18
1
.4
.5
EC
-E
1.5
2
.5
3.5
1
.0
0.4
0
1 0
~
21
1
.4
.5
EC
-E
1.5
6
.0*
*
3.6
1
.8
0.3
0
1 0
!;2
22
1
.4
.5
EC
-E
1.0
5
.0
3.5
1
.0
0.2
0
1~
0 ~
23
1.4
.5
E
C-E
.7
5
2.8
3
.3
0.7
0
.25
~
0 0
24
1.4
.5
E
C-E
1
.5
7.5
3
.5
3.2
0
.43
1
0 ~
25
1
.4
.5
EC
-E
1.5
7
.5
3.5
3
.2
0.4
3
1 0
~
26
1
.4
.5
EC
-E
1.5
7
.5
3.5
3
.2
0.4
3
1 0
~
27
1.4
.5
E
C-E
1
.5
* 7
.4*
*
3.6
3
.1
0.4
2
1 0
~
42
1
.4
.5
EC
-E
1.5
8
.5
3.4
4
.2
0.4
9
1 0
~
45
1.4
.5
E
C-E
1
.5
7.0
3
.5
3.2
0
.46
1
0 ~
+
1 in
.-k
ip »
0
.11
3
kN·m
.
$ eq
ual
to c
alc
ula
ted
max
imum
re
spo
nse
p
eak
, ex
cep
t w
her
e n
ote
d.
a w
ith
am
pli
tud
e eq
ual
to
at
least
0.8
5 o
f th
at
of ®
. !l
-Fu
lly
rev
ers
ed
cy
cle
s"
are
co
mp
lete
cy
cle
s (+
an
d -)
w
ith
at
least
on
e p
eak
valu
e b
etw
een
0
.75
-1
.0 o
f th
e
amp
litu
de
of@
an
d
the o
ther
-on
re
vers
al
-b
etw
een
0.5
0 -
1.0
ofQ
D.
·Part
iall
y r
ev
ers
ed
cy
cle
s·
are
cy
cle
s w
ith
on
e p
eak
am
pli
tud
e eq
ual
to at
least
0.1
5 o
f@an
d
the o
ther
0.5
0 o
r le
ss o
f@.
-
* 1
5\
of
max
imum
am
pli
tud
e o
f d
efo
rmati
on
.
*. -
20
sec.
du
rati
on
in
pu
t m
oti
on
li.
I .....
I\.)
w
I
Tab
le
A6
(co
nt'
d.)
Yie
ld
Run
F
un
dam
enta
l L
evel
,
Data
o
n
Nu
mb
er
an
d
Rela
tiv
e
Mag
nit
ud
e o
f C
ycle
s P
reced
ing
F
irst
Larg
e-A
mp
litu
de R
esp
on
se
Peak
B
ase
d
on
N
od
al
Ro
tati
on
s
at
1st
Flo
or
Lev
el
20
-Sto
ry Is
ola
ted
str
uctu
ral
Wall
s -
10
-sec.
Du
rati
on
In
pu
t M
oti
on
s
-
®
®
.'ir
st
J,ar
ge
1\m
pli t
ud
e ®
N
o.
of
No.
o
f ®
C
ycl
es jI
In
tcil
ait
y
lunp
lilu
c.lo
o
f L
.lr<
jest
P
eak
s F
acto
r,
f R
esp
on
se
Tim
e to
D
isp
lst.
b
etw
een
E
arth
qu
ake
pea
k
$ M
axim
um
Pre
ced
ing
-
O-s
ee.
No.
P
eri
od
, '1'
1 M
y/lO
Ci
51
a
(in
te
rms
of
Pis
pls
t.
Max
. A
®
ilnd
Tm
xd
, I
of
Fu
lly
P
art
lall
y
I f
x S
Iref.
C
orr
csl'
d'l
' A
mp
litu
do
(i
n
t:crl
llu
lin
-kip
s)T
In
pu
t V
alu
e at
'1'm
xd
of
Yie
ld
amp
litu
de
Rev
erse
d
Rev
erse
d
ISW
-(s
ec. )
F
irst
Yie
ld)
Am
pli
tud
e)
to®
"
Cy
cles
C
ycl
es
46
1
.4
.5
EC
-E
1.5
7
.8
3.5
3
.2
0.4
1
1 0
~ 5
0
1.4
.5
E
C-E
1
.5
3.3
3
.5
1.8
0
.55
1
0 k 2
51
1
.4
.5
EC
-E
1.5
2
.8
3.5
1
.3
0.4
6
1 0
~
80
1
.4
.5
EC
-E
1.5
1
1.0
3
.5
5.2
0
.47
1
0 ~
10
6
1.4
.5
P
.D.
.75
4
.5
3.8
2
.7
0.6
0
1 0
Ji
12
6
1.4
.5
E
C-E
1
.5
7.1
3
.5
3.0
0
.42
2
0 ~
13
0
1.4
.5
E
C-E
1
.5
7.5
3
.5 .
3
.1
0.4
1
1 0
L "2
13
3
1.4
.5
E
C-E
1
.5
2.2
3
.5
1.1
0
.50
1
0 ~
14
1
1.4
.5
E
C-E
1
.5
2.8
3
.5
1.5
0
.54
1
0 ~
15
1
1.4
.5
P
.D.
.75
2
.0
3.8
1
.1
0.5
3
1 0
~ 1
71
1
.4
.5
Sl
.75
2
.5*
1
.9
0.3
0
.12
1
0 0
11
1
.4
.75
E
C-E
1
.5
5.1
3
.5
1.1
0
.22
1
0 ~.
12
3
1.4
.7
5
P.D
. .7
5
3.2
3
.7
0.9
0
.28
~
0 0
12
4
1.4
.7
5
P.D
. 1
.0
3.2
3
.7
1.5
0
.47
1
0 ~
12
7
1.4
.7
5
P.D
. 1
.5
4.5
*
3.1
0
.3
0.0
7
~
0 0
--
-----~-'--
T
1 In
.-k
ip·
0.1
13
kN
·m.
$ eq
ual
to c
alc
ula
ted
max
imum
re
spo
nse
p
eak
, ex
cep
t w
her
e n
ote
d.
• w
ith
am
pli
tud
e eq
ual
to
at
lease
0.B
5 o
f th
at
of ®
. tl
-"F
ull
y r
ev
ers
ed
cy
cle
s"
are
co
mp
lete
cy
cle
s (t
and
-)
wit
h a
t le
ast
ono
pea
k v
alu
e b
etw
een
0
.75
-
1.0
of
the
amp
litu
de
of@
an
d
the o
ther
-on
re
vers
al
-b
etw
een
0
.50
-
1.0
ofQ
D.
·Part
iall
y r
ev
ers
ed
cy
cle
s· are
cy
cle
s w
ith
on
e p
eak
am
pli
tud
e eq
ual
to at
least
0.7
5 o
f@an
d
the o
ther
0.5
0 o
r le
ss o
f@
. .
* 7
5'
of
max
imum
am
pli
tud
e o
f d
efo
rmati
on
.
*. -
20 se
c.
du
rati
on
in
pu
t m
oti
on
s.
J I i I I I J
I I-'
N ~
I
Tab
le
A6
(co
nt'
d.)
D
ata
o
n
Num
ber
and
R
ela
tiv
e M
ag
nit
ud
e o
f C
ycle
s P
reced
ing
F
irst
Larg
e-A
mp
litu
de
Resp
on
se
Pea
k
Bas
ed
on
N
od
al
Ro
tati
on
s
at
1st
Flo
or
Lev
el
20
-Sto
ry Is
ola
ted
str
uctu
ral
Wall
s -
10
-sec.
Du
rati
on
In
pu
t M
oti
on
s
®
Yie
ld
.'i r
s t
I,ar
ge
Inte
nsi
ty
Am
pli
tud
e R
un
Fu
nd
amen
tal
Lev
el,
F
acto
r,
f R
esp
on
se
'rim
e to
E
arth
qu
ake
Pea
k $
Max
imum
N
o.
81
..
D
isp
lst.
P
eri
od
, T
l M
y/l0
6 (i
n
term
s o
f f
x S
Iref.
C
orr
esp
dg
. A
mp
litu
de
(in
-kip
s) +
In
pu
t V
alu
e at
ISW
-(a
ec. )
F
irst
Yie
ld)
12
8
1.4
.7
5
H.O
. 1
.5
4.2
*
13
1
1.4
.7
5
Sl
1.5
3
.1*
1
32
1
.4
.75
E
C-E
1
.5
2.5
14
6
1.4
.7
5
T
1.5
3
.9
16
5
1.4
.7
5
Sl
.75
1
.9
10
1
.4
1.0
E
C-E
1
.5
3.0
11
3
1.4
1
.0
P.O
. 1
.5
4.5
14
8
1.4
1
.0
P.O
. 1
.5
4.5
**
15
2
1.4
1
.0
P.O
. .7
5
1.0
20
1
.4
1.5
E
C-E
1
.5
.96
*
11
4
1.4
1
.5
P.O
. 1
.5
3.2
16
2
1.4
1
.5
P.O
. 1
.5
3.5
**
3
1
2.0
.5
E
C-E
1
.5
6.4
34
2
.0
.5
EC
-E
1.5
3
.5
·35
2
.0
.5
EC
-E
1.0
2
.6*
~ .. -
.. -.-
-----
t 1
in.-
kip
•
O.l
ll
kN·m
.
$ eq
ual
to
calc
ula
ted
max
imum
re
spo
nse
pea
k,
ex
cep
t w
her
e n
ote
d.
wit
h a
mp
litU
de
equ
al
to at
leas
!:
0.8
5 o
f th
at
of ®
.
~mxd
6.3
1.8
6
.1
4.3
2
.4
3.3
3
.9
3.8
3
.8
3.2
3
.7
3.7
3
.5
3.4
3.4
®
Am
pli
tud
e ®
N
o.
of
No.
o
f ®
Cy
cles
~
of
L.l
rycs
t P
eak
s D
isp
lst.
b
etw
een
p
rece
din
g
--
O-s
ec.
Max
. A
®
and
'rm
xd
(in
te
rms
of
Fu
lly
P
art
iall
y
of
Yie
ld
amp
litu
do
R
ever
sed
R
ever
sed
A
mp
litu
de)
to
®,
Cy
cles
~ycles
1.6
0
.38
1
0 ~
0.3
0
.10
!2
0
0 1
.6
0.6
4
3 0
1~
2.3
0
.59
2
1 1- 2
1.0
0
.53
1
0 ~
0.7
2
0.2
4
1 0
0
2.6
0
.58
1
0 ~
2.7
0
.60
1
0 k 2
0.5
0
.48
~
0 0
0.5
0
.52
~
0 0
0.9
0
.28
~
0 0
1.0
0
.29
1
0 ~
3.1
0
.48
1
0 ~
1.9
0
.54
1
0 ~
1.0
0
.38
1
0 ~
@
"Fu
lly
rev
ers
ed
cy
cle
s"
are
co
mp
lete
cy
cle
s (t
and
-)
wit
h a
t le
ast
ono
pea
k v
alu
e b
etw
een
0
.75
-1
.0 o
f th
e
amp
litu
de
ofG
Dan
d
the o
ther
-o
n re
vers
al
-b
etw
een
0
.50
-1
.0 O
fQD.
·P
art
iall
y r
ev
ers
ed
cy
Cle
s· are
cy
cle
s w
ith
on
e p
eak
am
pli
tud
e eq
ual
to at
least
0.7
5 o
f ®
ilnd
. th
e o
ther
0.5
0 o
r lo
ss o
f ®
. 7
5'
of
max
imum
am
pli
tud
e o
f d
efo
rmat
ion
•
••
-20
aec.
du
rati
on
in
pu
t m
oti
on
s.
, I I I I
I .......
IV
U1 I
Tab
le
A6
(co
nt'
d.)
D
ata
o
n
Nu
mb
er
an
d R
ela
tiv
e M
ag
nit
ud
e o
f C
ycle
s P
reced
ing
F
irst
Larg
e-A
mp
litu
de
Resp
on
se
Peak
B
ase
d
on
N
od
al
Ro
tati
on
s
at
1st
Flo
or
Lev
el
20
-Sto
ry Is
ola
ted
S
tru
ctu
ral
Wall
s -
10
-sec.
Du
rati
on
In
pu
t M
oti
on
s
@
Yie
ld
Fir
st
I,arg
e
Inte
nll
ity
A
mp
litu
ue
Run
F
lln
dam
enta
l L
evel
, F
acto
r,
f R
esp
on
se
Tim
e to
E
arth
qu
ake
Pea
k $
Max
imum
N
o.
SI
..
Oio
pls
t.
Peri
od
, T
I M
y/10
6 (i
n
term
s o
f f
x S
Iref.
C
orr
esp
dg
. A
mp
litu
de
lin
-kip
s)"
Inp
ut
Val
ue
at
ISW
-(s
ec. )
F
irst
Yie
ld)
36
2
.0
.5
EC
-E
1.5
4
.2
15
0
2.0
.5
H
.O.
.75
2
.2*
16
3
2.0
.5
E
C-E
1
.5
5.0
32
2
.0
.75
E
C-E
1
.5
2.5
*
11
9
2.0
.7
5
EC
-E
.75
1
.4
12
0
2.0
.7
5
EC
-E
1.0
2
.7
12
9
2.0
.7
5
T
1.0
2
.7
13
6
2.0
.7
5
Sl
1.5
2
.9
13
7
2.0
.7
5
H.O
. 1
.5
3.2
*
14
0
2.0
.7
5
P.O
. 1
.0
2.3
16
7
2.0
.7
5
H.O
. .7
5
1.8
33
2
.0
1.0
E
C-E
1
.5
2.5
III
2.0
1
.0
H.O
. 1
.5
2.3
16
4
2.0
1
.0
H.O
. 1
.5
* 2
.2*
*
11
2
2.0
1
.5
H.O
. 1
.5
1.7
-
~-~--
~~~ -~--
.. 1
in.-
kip
•
0.1
13
kN
·m.
$ eq
ual
to c
alc
ula
ted
max
imum
re
spo
nse
p
eak
, ex
cep
t w
her
e n
ote
d.
wit
h a
mp
litu
ue
eq
ual
to a
t le
ast
0.8
5 o
f th
at
of ®
.
'l'mxd
7.5
6
.6
3.5
3
.3
9.4
9.5
3
.1
3.1
6.4
4.0
7.5
9.5
6.6
6
.6
7.5
-
®
Am
pli t
uu
e ®
N
o.
of
No.
o
f ®
Cyc
le::
; il
, o
f L
ilry
cst
Pea
ks
Dis
pls
t.
bet
wee
n
Pre
ced
ing
-
O-s
ec.
Max
. A
®
and
Tm
xd
(in
te
rms
of
Fu
lly
p
art
iall
y
of
Yie
ld
amp
litu
de
Rev
erse
d
Rev
erse
d
Am
pli
tud
e)
to®
' C
ycl
es
Cy
cles
. 3
.2
0.7
6
3 1
1
1.0
0
.45
ll:
z l:z
0
2.5
0
.49
1
0 l:z
1.0
0
.40
1
0 l:z
0.8
0
.57
3
0 0
1.1
0
.41
5
2 0
1.5
0
.56
1
1 0
1.5
0
.52
1
0 l:z
2.0
0
.63
1
1 0
1.3
0
.57
1
0 l:z
0.9
0
.49
1:
"2 0
0
1.2
0
.48
6
3 0
1.1
0
.48
1
0 1
1.0
0
.45
l~
l:z 0
0.8
0
.47
1
0 0
@
"Fu
lly
rev
ers
ed
cy
cle
s"
are
co
mp
lete
cy
cle
s (+
an
d -)
w
ith
at
least
on
e p
eak
valu
e
bet
wee
n
0.7
5 -
1.0
of
the a
mp
litu
de
of@
an
d
the o
ther
-on
re
vers
al
-b
etw
een
0
.50
-1
.0 o
fQD
. ·p
art
iall
y r
ev
ers
ed
cy
cle
s" are
cy
cle
s w
ith
on
e p
eak
am
pli
tud
e eq
ual
to a
t le
ast
0.7
5 o
f@'a
nd
th
e o
ther
0.5
0 o
r le
ss o
f@.
.
* 7
5\
of
max
imum
am
pli
tud
e o
f d
efo
rmat
ion
•
••
-20
se
c.
du
rati
on
in
pu
t m
oti
on
s.
I I-'
tv
0"\
I
Tab
le
A6
(co
nt'
d.)
Yie
ld
Run
F
un
dam
enta
l L
ev
el,
Data
o
n
Nu
mb
er
and
R
ela
tiv
e M
ag
nit
ud
e
of
Cy
cle
s P
reced
ing
F
irst
Larg
e-A
mp
litu
de
Resp
on
se
Peak
B
ase
d
on
N
od
al
Ro
tati
on
s
at
1st
Flo
or
Lev
el
20
-Sto
ry Is
ola
ted
S
tru
ctu
ral
Wall
s -
10
-sec.
Du
rati
on
In
pu
t M
oti
on
s
®
®
Fir
st
l.il
rqe
Am
pli
tud
e ®
N
o.
of
No.
o
f ®
Cy
cles
fI
Intc
nu
ity
A
mpl
i tu
dQ
of
L4
r,)c
sl
PC
4ks
Facto
r,
f R
esp
on
se
Tim
e to
D
isp
lst.
b
etw
een
E
arth
qu
ake
Pea
k $
Max
imum
p
rece
din
g
-O
-sec
. N
o.
Peri
od
, '1
'1
My
/l0
6
SI
.. (i
n
term
s o
f D
ilip
lst.
M
ax.
II
®
and
Tm
xd
t x
SIr
ef.
C
Ol."
cesp
dq.
l\m
pli
tud
Q
(in
te
rln
s o
f F
ull
y
Pi!
rtia
lly
I
(in
-kip
s) ...
In
pu
t V
alu
e at
'l'mxd
o
f Y
ield
am
pli
tud
e
Rev
erse
d
Rev
erse
d
ISW
-(s
ec. )
F
irst Y~eld)
l\m
pli
tud
e)
to®
, C
ycl
es
Cyc
le!>
40
2
.4
.5
EC
-E
1.5
5
.0
3.5
2
.2
0.4
4
1 0
0
15
8
2.4
.5
E
C-E
1
.5
5.1
**
3
.5
2.9
0
.57
1
0 ~
10
2
2.4
.7
5
EC
-E
1.5
4
.1
3.5
1
.1
0.2
7
1 0
~
12
2
2.4
.7
5
EC
-E
1.0
1
. 5
*
3.5
0
.7
0.4
7
~ 0
0
13
4
2.4
.7
5
Sl
1.5
1
. 7*
2
.9
1.3
0
.76
1
0 ~
13
8
2.4
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5
P.O
. 1
.5
1.5
8
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1.2
0
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2
1 0
14
4
2.4
.7
5
H.O
. 1
.5
1.6
*
5.8
1
.3
0.8
1
1 ~
0
14
5
2.4
.7
5
T
1.5
1
.3
3.5
0
.9
0.6
9
2 1
0
10
7
2.4
.7
5
EC
-E
1.5
2
.1
3.5
0
.8
0.3
8
~
0 0
15
9
2.4
1
.0
EC
-E
1.5
1
.5*
*
3.5
0
.5
0.3
3
~ 0
0 .
17
6
2.0
.2
5
Sl
.75
3
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1
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0.2
0
.06
~
0 0
17'4
2
.4
.2
EC
-E
.75
4
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2
.1
0.2
0
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~
0 0
17
5
2.4
.2
T
.7
5
2.8
4
.5
1.9
0
.68
2
1 0
17
3
2.4
.2
5
T
.75
2
.1*
2
.2
1.3
0
.62
1
~ 0
---_
..... _
----
---------
... 1
In.-
kip
a
O.l
ll
kN·m
.
$ eq
ual
to c
alc
ula
ted
max
imum
re
spo
nse
pea
k,
ex
cep
t w
here
n
ote
d.
, w
ith
am
pli
tud
e eq
ual
to a
t le
as!:
0
.85
of
that
of ®
. i!
-Fu
lly
re
vers
ed
cy
cle
s"
are
co
mp
lete
cy
cle
s C
... an
d -I
w
ith
at
least
on
e p
eak
v
alu
e b
etw
een
0
.15
-
1.0
of
the
amp
litu
de
of
®
and
th
e o
ther
-on
re
vers
al
-b
etw
een
0
.50
-
1.0
ofQ
D.
·Part
iall
y r
ev
ers
ed
cy
cle
s"
are
cy
cle
s w
ith
on
e p
eak
am
pli
tud
e eq
ual
to at
least
0.7
5 o
f@an
d
the o
ther
0.5
0 o
r le
ss o
f@).
• 7
5\
of
max
imum
am
pli
tud
e o
f d
efo
rmat
ion
•
• * -
20
sec.
du
rati
on
in
pu
t m
oti
on
s.
I I i I i I ! j
I I-'
N
-...J I
Tab
le A
7 D
ata
o
n
Nu
mb
er
and
R
ela
tiv
e
Mag
nit
ud
e o
f C
ycle
s P
reced
ing
F
irst
Larg
e-A
mp
litu
de
Resp
on
se
Peak
B
ase
d
on
N
od
al
Ro
tati
on
s at
1st
Flo
or
Lev
el
30
-Sto
ry Is
ola
ted
S
tru
ctu
ral
Wall
s -
10
-sec.
Du
rati
on
In
pu
t M
oti
on
s
@
®
Yie
ld
Fir
st
J,il
rgc
Am
pli t
ud
e ®
N
o.
of
No.
o
f ®
Cy
cles
ii
Inte
nsi
ty
Am
pli
tud
e o
f L
ury
est
P
eak
s R
un
Fu
nd
amen
tal
Lev
el,
Facto
r,
f R
esp
on
se
Tim
e to
D
isp
lst.
b
etw
een
M
axim
wn
Pre
ced
ing
-
a-s
ec.
Ear
thq
uak
e P
eak
$ N
o.
Peri
od
, T
l M
y/l
06
5
1
..
(in
te
rms
of
Dis
pls
t.
Max
. A
®
and
Tm
xd
Part
iall
y
I f
x S
Iref.
C
orr
esp
dg
. A
mp
litu
de
(in
te
rms
of
Fu
lly
R
ever
sed
I
(in
-kip
s)'"
In
pu
t V
alu
e at
TlIlX
d o
f Y
ield
lil
llP li t
ud
e
Rev
erse
d
1SW
-'s
ec. )
F
int
Yie
ld)
Am
pli
tud
e)
to®
•
Cyc
lelO
C
ycl
es
---
30
04
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0 0
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. 1
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4
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~
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02
1
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. 1
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2
1 0
30
10
2
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C-E
1
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0
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~
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2
.4
1.5
P
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1
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11
2
.4
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C-E
1
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0 0
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L 0
0 '2
I.----.
.. __ .-
----
--. ----
---.-
---.-
... 1
in.-
kip
= O
.lll
kN
·m.
$ eq
ual
to
calc
ula
ted
max
imum
re
spo
nse
pea
k,
ex
cep
t w
her
e n
ote
d.
wit
h
amp
litu
de
equ
al
to a
t le
ast
0.8
5 o
f th
at
of ®
. I
-
@
--F
ull
y re
~ers
cd c
ycle
s-are
co
mp
lete
cy
cle
s (+
an
d -)
w
ith
at
least
on
e p
eak
valu
e b
etw
een
0.7
5
-1
.0 o
f th
e a
mp
litu
de
ofQ
Dan
d
the o
ther
-on
re
vers
al
-b
etw
een
0.5
0 -
1. a
o
f ®
. ·P
art
iall
y r
ev
ers
ed
cy
cle
s·
are
cy
cle
s w
ith
on
e p
eak
am
pli
tud
e eq
ual
to a
t le
ast
0.7
5 o
f ®
and
the o
ther
0.5
0 o
r le
ss o
f ®
. *
75
' o
f m
axim
um
amp
litu
de
of
def
orm
atio
n.
I I i I I I
I I-'
IV
CO
I
Tab
le
AB
Data
o
n
Num
ber
and
R
ela
tiv
e M
ag
nit
ud
e o
f C
ycle
s P
reced
ing
F
irst
Larg
e-A
mp
litu
de
Resp
on
se
Peak
B
ased
o
n
No
dal
R
ota
tio
ns
at
2n
d F
loo
r L
ev
el
40
-Sto
ry Is
ola
ted
S
tru
ctu
ral
Wall
s -
10
-sec.
Du
rati
on
In
pu
t M
oti
on
s
®
®
Yie
ld
Fir
st
J.ol
rge
J\m
pli
tud
o
®
No.
o
f N
O.
of
® C
ycl
es ~
lnte
llu
ity
A
mp
litu
de
of
Lill
-CjO
st
POilk
s R
un
Fu
nd
amen
tal
Lev
el,
Facto
r,
f R
esp
on
se
Tim
e to
o
isp
lst.
b
etw
een
E
arth
qu
ake
Pea
k $
M
axim
um
Pre
ced
ing
--
O-s
cc.
No.
P
eri
od
, '1'
1 My
11 0
6 5
1
..
(in
to
rms
of
Dia
pIs
t.
Max
. A
®
and
'l'r
nxd
f x
Slr
et.
C
orr
esp
dg
. A
mp
litu
de
(in
te
rms
of
Fu
lly
P
art
iall
y
(in
-kip
s) +
In
pu
t V
alu
e at
TlIIX
d o
f Y
ield
am
pli
tud
e R
ever
sed
R
ever
sed
IS
W-
(sec. )
F
irst
Yie
ld)
Am
pli
tud
e)
to@
1
Cy
cles
C
ycl
ea
40
08
1
.4
1.0
E
C-E
1
.5
9.2
3
.5
6.1
0
.66
1
0 ~
40
21
1
.4
1.0
S
l 1
.5
15
.0
2.1
1
.2
O.O
B
1 0
~
40
34
1
.4
1.0
P
.O.
1.5
1
2.2
3
.1
O.B
0
.06
~
0 0
40
01
1
.4
1.5
E
C-E
1
.5
9.5
3
.5
4.5
0
.47
1
0 ~
40
39
1
.4
1.5
P
.O.
1.5
9
.0
3.1
0
.5
0.0
6
~
0 0
40
06
1
.4
2.0
E
C-E
1
.5
3.4
3
.5
1.4
0
.41
1
0 ~
40
45
1
.4
2.0
P
.O.
1.5
7
.0
3.1
0
.4
0.0
6
~
0 0
40
51
1
.4
2.5
E
C-E
1
.5
5.7
3
.5
1.6
0
.2B
2
0 1
40
16
2
.0
1.0
E
C-E
1
.5
4.4
2
.1
0.2
0
.05
~
0 0
40
22
2
.0
1.0
S
l 1
.5
6.5
2
.1
0.3
0
.05
~
0 0
40
43
2
.0
1.0
P
.O.
1.5
8
.0*
3
.0
0.4
0
.05
~
0 0
40
15
2
.0
1.5
E
C-E
1
.5
4.2
3
.5
2.7
0
.64
1
0 ~
40
24
2
.0
1.5
S
l 1
.5
5.7
5
2.1
0
.3
0.0
5
~ 0
0
40
40
2
.0
1.5
P
.D.
1.5
4
.B*
3
.1
0.2
0
.04
~
0 0
40
46
2
.0
2.0
P
.O.
l.5
3
.2
3.1
0
.2
0.0
6
~
0 0
'---
._-_
.-+
1
in.-
kip
a
0.1
11
kN
·m.
$ eq
ual
to
calc
uli
lted
max
imum
re
spo
nse
pea
k,
ex
cep
t w
her
e n
ote
d.
wit
h a
mp
litu
de
eq
ual
to a
t le
ast
0.8
5 o
f th
at
of@
).
. - @
-"F
ull
y r
ev
ers
ed
cy
cle
s·
are
co
mp
lete
cy
cle
s (+
an
d -)
w
ith
at
least
on
e p
eak
valu
e b
etw
een
0.7
5
-1
.0 o
f th
e
amp
litu
de
of@
an
d
the o
ther
-o
n re
vers
al
-b
etw
een
0.5
0
-1
. 0
of ®
. ·P
art
iall
y r
ev
ors
ed
cy
cle
s· are
cy
cle
s w
ith
on
e p
eak
am
pli
tud
e eq
ual
to a
t le
ast
0.1
5 o
f ®
and
th
o o
ther
0.5
0 o
r le
ss o
f ®
.
* 7
5\
of
max
imum
am
pli
tud
e o
f d
efo
rmat
ion
.
I I-'
N
1.0 I
Tab
le
AB
(c
on
t'd
.)
Data
o
n
Num
ber
and
R
ela
tiv
e M
ag
nit
ud
e o
f C
ycle
s P
reced
ing
F
irst
Larg
e-A
mp
litu
de
Resp
on
se
Peak
B
ase
d
on
N
od
al
Ro
tati
on
s
at
2n
d F
loo
r L
ev
el
40
-Sto
ry Is
ola
ted
S
tru
ctu
ral
Wall
s -
10
-sec.
Du
rati
on
In
pu
t M
oti
on
s
®
®
---I
®
No.
o
f Y
ield
t'
irst
1 .. "1
C9
0
IIm
pU t
uu
e In
tcll
:Jit
y
l\iI
\l'li
lu<
le
oC
L.II
:<Je
lit
Run
t'
un
dil
men
tal
Lev
el,
F
acto
r,
f n
esp
on
sc
Tim
e to
O
isp
lst.
E
arth
qu
ilk
o
POilk
$
Max
imum
P
reced
ing
--
No.
P
eri
od
, '1'
1 M
y/l
06
5
1
..
(in
te
rms
of
Ois
pls
t.
Max
. 11
@
f x
SI r
o!.
Co
rrcs
pd
g.
Am
pli
tud
e (i
n
tern
lll
(in
-kip
s) +
In
pu
t V
alu
e at
'l'm
xd
of
Yie
ld
ISW
-(s
ec. )
F
irat
Yie
ld)
Am
pli
tud
e)
40
50
2
.0
2.0
E
C-E
1
.5
5.Q
3
.4
2.9
0
.52
40
09
2
.4
1.0
E
C-E
1
.5
5.7
2
.1
0.2
0
.04
40
23
2
.4
1.0
S
l 1
.5
6.3
*
2.1
0
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0.0
6
40
42
2
.4
1.0
P
.D.
1.5
5
.2*
3
.1
0.5
0
.10
40
20
2
.4
1.5
E
C-E
1
.5
6.0
*
2.1
0
.3
0.0
5
40
27
2
.4
1.5
S
l 1
.5
5.B
*
2.5
0
.4
0.0
7
40
41
2
.4
1.5
P
.D.
1.5
3
.8
8.B
2
.5
0.6
6
40
04
2
.4
2.0
E
C-E
1
.5
5.4
3
.B
3.0
0
.56
40
47
2
.4
2.0
P
.D.
1.5
3
.2
8.3
2
.0
0.6
3
40
12
3
.0
1.0
E
C-E
1
.5
4.6
2
.2
0.1
0
.02
4
03
1
3.0
1
.0
Sl
1.5
6
.7
4.2
3
.2
0.4
8
40
38
3
.0
1.0
P
.D.
1.5
3
.3
8.5
2
.4
0.7
3
40
05
3
.0
1.5
E
C-E
1
.5
5.8
2
.2
0.2
0
.03
40
32
3
.0
1.5
S
l 1
.5
5.4
4
.2
1.8
0
.33
40
37
3
.0
1.5
P
.D.
1.5
2
.1
8.9
1
.4
0.6
7
40
03
3
.0
2.0
E
C-E
1
.5
3.3
2
.1
1.0
0
.30
4
04
8
3.0
2
.0
P.D
. 1
.5
2.0
8
.9
1.1
0
.55
~.
-'---_
. --
--.-
-----
----
---
+
1 in
.-k
ip
a 0
.11
1
kN.m
.
$ eq
ual
to calc
ula
ted
max
imum
re
spo
nse
p
eak
, ex
cep
t w
her
e n
ote
d.
wit
h
amp
litu
de
eq
ual
to a
t le
ast
0.8
5 o
f th
at
of ®
.
No.
o
f ®
Cy
cle
s P
l'c.:
.ks
bet
wee
n
O-s
ec.
lind
Tm
xd
of
Fu
lly
P
art
iall
y
am
pli
tud
e
Rev
erse
d
Rev
erse
d
to®
•
Cy
cles
C
ycle
s
1 0
~
12
0 0
!:! 0
0
!:! 0
0
~ 0
0 1
0 0
1 1
0 1
0 ~
2 1
0
!:! a
a 1
0 ~
1 a
k :2
!:! a
0 1
a k :2
2 k 2
!:! ~
a 0
2 !:!
a
e "F
ull
y revers~d
cy
cle
s"
are
co
mp
lete
cy
cle
s (+
an
d -)
w
ith
at
least
on
e p
eak
v
alu
e
bet
wee
n
0.7
5
-1
.0 o
f th
e
am
pli
tud
e
ofQ
Dan
d
the o
ther
-o
n re
vers
al
-b
etw
een
0
.50
-
1. a
of ®
. "P
art
iall
y r
ev
ers
ed
cy
cle
s"
are
cy
cle
s w
it.h
on
e p
eak
am
pli
tud
e eq
ual
to a
t le
ast
0.7
5 o
f@an
d
the o
ther
0.5
0 o
r le
ss
Of@
)o
* 75
1 o
f m
axim
um
amp
litu
de
of
uefo
rmati
on
.
i I I , i I I
