mathematical modelling of hysteresis loops for … · 2009. 7. 16. · 3.2 skeleton curve 3.3...
TRANSCRIPT
.1
REPORT NO.
UCB/EERC-78/11
JUNE 1978
PB 298274
EARTHQUAKE ENGINEERING RESEARCH CENTER
MATHEMATICAL MODELLING OF HYSTERESIS LOOPS FOR REINFORCED CONCRETE COLUMNS
by
SHINSUKE NAKATA
TERRY SPROUL
JOSEPH PENZIEN
Report to the National Science Foundation
COLLEGE OF ENGINEERING
UNIVERSITY OF CALIFORNIA . Berkeley, California
BIBLIOGRAPHIC DATA ~ort No. ·---r2• Ij.;.Reci~"en~ry~·· 'i'I-~4' .' ~.~E~T~~~~~~ __ -J~ __________ N_S_F~/_RA __ -_7_80_6_3_2 _______ ~ ______ L-______________ tllJ~~I3~--~~~~~~~--~~-~--~----4. TIde: and Subtitle .~. RUo'!: Dat'e·
~1athematical Modelling of Hysteresis Loops for Reinforced Concrete Columns 6.
June 1978
7. Author(s) Shinsuke Nakata, Terry Sproul, Joseph Penzien
9. Performing Organiz"tion Name and Address Earthquake Engineering Research Center University of California, Richmond Field Station 47th and Hoffman Blvd. Richmond, California 94804
12. Sponsoring Organization Name and Address
National Science Foundation 1800 G. Street, N.W. Washington, D.C. 20550
J 5. Supplementary Notes
16. Abstracts
8. Ptrforming Organization Repr.
NOUCB/EERC-78/11 10. Project/Task/Work Unit No.
11. Contract/Grant No.
ENV76-04263
13. Type of Report & Period Cpvered
14.
The objective of this research is to estimate lateral force-deflection curves for reinforced concrete columns subjected to cyclic transverse loads and constant axial loads. These curves are determined in relation to particular column parameters such as shearspan ratio, longitudinal and horizontal reinforcement, and axial force.
The data for this project were obtained from a series of tests reported by Atalay and Penzien and a series of tests made in Japan. 104 specimens are selected from the latter test series, with shear span ratios ranging from 1.0 to 3.0.
Summary equations are developed by statistical methods. This new model takes into account more parameters than previous models. The hysteresis loops generated from these equations are in better agreement with the test data than has been the case with previous models. In particular the new model is compared with one developed previously by Atalay
and Penzien.
17b. Identifiers/Open-Ended Terms
17c. COSA TI Field/Group
Release Unlimited
19. Security Class (This 121. No. of Pages Report) c;-
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PagUNCLASSIFIED II7ofi/krf!v1
18. Av"ibbility Statement
THIS FORM MAY I:lE REP RODUCED USC6M"'· DC 8265· P 74
MATHEMATICAL MODELLING OF HYSTERESIS LOOPS FOR REINFORCED CONCRETE COLUMNS
by
Shinsuke Nakata
Terry Sproul
Joseph Penzien
Report to the National Science Foundation
Report No. UCB/EERC-78/ll Earthquake Engineering Research Center
College of Engineering University of California
Berkeley, California
June 1978
/Q-
ABSTRACT
The objective of this research is to estimate lateral force
deflection curves for reinforced concrete columns subjected to cyclic
transverse loads and constant axial loads. These curves are determined
in relation to particular column parameters such as shear-span ratio,
longitudinal and horizontal reinforcement, and axial force.
The data for this project were obtained from a series of tests
reported by Atalay and Penzien and a series of tests made in Japan.
104 specimens are selected from the latter test series, with shear
span ratios ranging from 1.0 to 3.0.
Summary equations are developed by statistical methods. This
new model takes into account more parameters than previous models.
The hysteresis loops generated from these equations are in better
agreement with the test data than has been the case with previous
models. In particular the new model is compared with one developed
previously by Atalay and Penzien.
il
ACKNOWLEDGEMENTS
The authors express their sincere thanks and appreciation to
W. B. Wagy for his assistance in the preparation of this report, to
G. Feazell and L. Rambrau for drafting the figures, and to S. Edwards
for typing the final manuscript. The financial support of the
National Science Foundation under Grant No. ENV-76-04263 is gratefully
acknowledged.
iii
TABLE OF CONTENTS
ABSTRACT • • .•
ACKNOWLEDGEMENTS
TABLE OF CONTENTS
LIST OF FIGURES
1. INTRODUCTION
2. TEST DATA
2.1
2.2
2.3
2.4
The Test Project
Selection of Test Specimens •
Data Digitization From Graphs • .
Data Reduction
3. EMPIRICAL EQUATIONS OF HYSTERESIS LOOPS ••••
3.1 Outline of Estimated Hysteresis Loops •
4.
3.2 Skeleton Curve
3.3 Definition of the Hysteresis Loop • •
ESTIMATED HYSTERESIS LOOPS • • • •
4.1
4.2
Method for Drawing Hysteresis Loops • .
Comparison with a Mathematical Model
5. CONCLUSIONS AND RECOMMENDATIONS
REFERENCES • • • • • • • • • • • • •
v
Preceding page blank
Page
i
iii
v
vii
1
3
3
4
5
5
6
6
7
12
12
12
16
17
19
Figure
2.1
2.2
2.3
2.4
2.5a
2.5b
2.5c
2.6
2.7
3.1
3.2
3.3a
3.3b
3.3c
3.3d
3.4a
3.4b
3.4c
3.5
3.6a
3.6b
LIST OF FIGURES
specimen Details • •
Loading Apparatus
Cyclic Loading System
Examples of Crack Patterns
Parameter Distribution: aid vs Pt
Parameter Distribution: aid vs Pw
Parameter Distribution: aid vs Plbdf' c
Proc~dure of A-D Conversion
Data Reduction . . . . . . . . . . . Empirical Skeleton Curve • •
Empirical Hysteresis Loop
Average Value in each Parameter Domain of Qyt/Qyc . . . . . . . . . . . . . .. . . . . . .
Comparison Between Calculated Value and Test Value of Bending Yield Shear Force Q
y
Comparison Between Calculated Value and Test Value of Bending Yield Shear Force aQy • • •
Comparison Between Calcula.ted Value and Test Value of Bending Yield Shear Force D7 • Q .
y
Average Value of D6 in Each Parameter Domain
Comparison Between Calculated Value and Test Value of Yield Deflection D6 • • • • •
Comparison Between Sugano's Calculated Value and Test Value of Yield Deflection • .
Guide for the Data Distribution Diagrams •
Average Value in Each Parameter Domain for D7 (Envelope curve) • • • • • • • • • • •
Average Value in Each Parameter Domain for D7 (3 Cyclell Cycle) • • • . • • •
Preceding page blank vii
21
22
23
24
26
27
28
29
30
31
31
32
33
34
35
36
37
38
39
40
41
LIST OF FIGURES (cant. )
Figure Page
3.6c Average Value in Each Parameter Domain for D7 (10 Cycle/l Cycle) · · · · · · · · · · · · · · 42
3.7a Average Value in Each Parameter Domain for Dl (Amplitude) · · · · · · · · · · · · · · · 43
3.7b Average Value in Each Parameter Domain for Dl (3 Cycle/l Cycle) · · · · · · · · · · · · · · 44
3.7c Average Value in Each Parameter Domain for Dl (10 Cycle/l Cycle) · · · · · · · · · · · · · · 45
3.Ba Average Value in Each Parameter Domain for D2 (Amplitude) • · · · · · · · · · · · · · · · · · 46
3.Bb Average Value in Each Parameter Domain for D2 (3 Cycle/l Cycle) · · · · · · · · · · · · · · 47
3.Bc Average Value in Each Parameter Domain for D2 (10 Cycle/l Cycle) · · · · · · · · · · · · · · 4B
3.9a Average Value in Each Parameter Domain for D3 (Amplitude) • · · · · · · · · 0 0 · · 0 0 0 0 49 0
3.9b Average Value in Each Parameter Domain for D3 (3 Cycle/l Cycle) 0 · 0 0 0 · · 0 · 0 0 0 · · 50
3 09c Average Value in Each Parameter Domain for D3 (10 Cycle/l Cycle) · · · 0 0 0 0 0 0 0 0 0 · 0 51
3.10a Average Value in Each Parameter Domain for D5 (Amplitude) • · · · · 0 · 0 0 0 · 0 0 0 · 0 · · 52
3.10b Average Value in Each Parameter Domain for D5 (3 Cycle/l Cycle) · 0 · 0 0 0 0 · 0 0 0 0 · · 53
3 o l0c Average Value in Each Parameter Domain for D5 (10 Cycle/l Cycle) · · · 0 · 0 · · · 0 0 0 0 · 54
30lla Average Value in Each Parameter Domain for DB (Amplitude) · · · · 0 0 · 0 0 0 0 0 0 · 0 55
3.11b Average Value in Each Parameter Domain for DB (3 Cycle/l Cycle) 0 0 · 0 · 0 · · 0 0 0 · · 0 56
3.11c Average Value in Each Parameter Domain for D8 (10 Cycle/l Cycle) · · · · · · · · · · 0 · · · 57
3.l2a Average Value in Each Parameter Domain for D9 (Amplitude) 0 · · 0 · 0 0 · · 0 58
viii
LIST OF FIGURES (cant. )
Figur~ Page
3.12b Average Value in Each Parameter Domain for D9 (3 Cyclell Cycle) . . . . · · · · · · · · · · · · · · · 59
3.l2c Average Value in Each Parameter Domain for D9 (10 Cyclell Cycle) . . . · · · · · · · · · · · · · · · 60
4.1 Estimated Hysteresis Loop · · · · · · · 61
4.2 Hysteresis Loops: Case 1 (aid = 1. 0) . 62
4.3 Hysteresis Loops: Case 2 (aid = 1. 0) · · · · 63
4.4 Hysteresis Loops: Case 3 (aid = 1. 5) · · · · 64
4.5 Hysteresis Loops: Case 4 (aid = 1. 5) 65
4.6 Hysteresis Loops: Case 5 (aid = 2.0) · · · · 66
4.7 Hysteresis Loops: Case 6 (aid = 2.0) · · · · · · · · · 67
4.8 Hysteresis Loops: Case 7 (aid = 2.5) 68
4.9 Hysteresis Loops: Case 8 (aid = 2.5) 69
4.10 Hysteresis Loops: Case 9 (aid 3.0) · · · · 70
4.11 Hysteresis Loops: Case 10 (aid = 3.0) · · · · 71
4.12 Penzien-Atalay Model · · · · · · · · 72
4.13 Comparison of Stiffness (Dl) · · · · · · · · · · · 73
4.14 Comparison of Stiffness (D2) · · · · · · · · 74
4.15 Comparison of Stiffness (D3) · · · · · · · · 75
ix
1
1. INTRODUCTION
The objective of the research presented in this report was to
establish lateral force-deflection curves for reinforced concrete
columns subjected to cyclic transverse loads and constant axial loads,
for particular column parameters such as shear span ratio, ratio of
longitudinal and horizontal reinforcement, and axial force.
Several researchers, including Penzien and Atalay, have
previously developed mathematical models of the restoring force
.. f . f (1-14) character~st~cs 0 re~n orced concrete members. These models
do not apply, however, for all cases involving different modes of
failure. To develop a more general model by statistical methods, it
is necessary to increase the number of structural parameters included
in the model. Up to now empirical expressions for only a few types
(15-17) . of strength and the st~ffness at bending yield for uni-
directional loading have been developed as mathematical models based
on member parameters.
Recently, digital test data became available for lateral load-
deflection relationships for short columns. These had been developed
systematically in Japan. This digital information is used in the
following to predict the shape of hysteresis loops by statistical
procedures.
Finally, the predicted hysteresis loops are used to discuss the
adaptability of the Fenzien-Atalay model for different combinations of
parameters.
3
2. TEST DATA
2.1 The Test Project
Many structures with short columns have suffered serious
damage in recent earthquakes in many parts of the world. (18) In
1972 a large five-year test project was started in Japan to establish
new earthquake resistant design methods for such structures. In that
project, test data were gathered from about 300 columns subjected to
cyclic transverse loads under constant axial loads.
Short columns have been adopted in this program with shear span
ratios of 1.0, 1.5, 2.0, 2.5, and 3.0 taken as standard. A satis-
factory method for calculating horizontal reinforcement for ductile
short columns has not yet been established. In this program, the
(19) shear reinforcement ratio, p , was obtained from Arakawa's formula ,
w
in which the mean shear stress at flexural yield strength is used.
Tentatively, some test specimens with a shear reinforcement ratio
equal to half that described above were also adopted. The shape of
the hoops is mainly square with 135 0 hooks.
Figure 2.1 shows the typical specimen details for all the tests,
the scale of the cross section, and the covering and anchoring of the
main reinforcement. Figure 2.2 shows the loading apparatus. With
this system the test specimen is subjected to antisymmetric moment and
constant axial load without the top and bottom of the column rotating.
Figure 2.3 shows the system of cyclic loading controlled by the
deflection of the top relative to the bottom of the column. Each
amplitude is based on the deflection, 0 , at flexural yield, which is y
obtained from a loading test for each specimen. Figure 2.4 shows
crack patterns developing during the test procedure.
Preceding page b'an~
4
One characteristic of the results is that some specimens showed
bond failure prior to or after flexural yielding. This is rare among
simple supported systems. The typical failure modes that were
observed are as follows:
1) Shear failure prior to flexural yielding
2) Bond failure prior to flexural yielding
3) Shear failure after flexural yielding
4) Bond failure after flexural yielding
5)· Steel buckling after flexural yielding
6) Compressive failure of concrete after flexural yielding.
Most specimens failed in cases 2, 3, 4, and 5, and the latter included
24 percent of the specimens.
2.2 Selection of Test Specimens
The test specimens were selected from more than 250 specimens
that had already been published. Specimens that had failed in shear
or bond at small amplitudes during the loading procedure were excluded.
Among the remaining specimens there were many whose graphs are not
clear enough to be digitized to computer cards. The number of
specimens suitable for the statistical procedure was 104, and the
parametric distributions of these are shown in Figs. 2.5a, b, and c.
The shear span ratio, aid, was either 1.0, 1.5, 2.0, 2.5, or 3.0, and
the majority of the specimens had aid = 2.0.
The columns were subjected to constant axial stress, P/bd,
(ranging from 21 kg/cm2 to 70 kg/cm2
) during the loading. Figure 2.5a
shows the dimensionless ratio P/bdf' , axial stress divided by the c
, concrete compressive strength, f. The compressive strength of the
c
concrete used in these specimens ranges from 153 kg/cm2 to 453 kg/cm2
.
5
The longitudinal tensile reinforcement ratio, p , is the same as the t
compressive reinforcement ratio in the cross-section of each specimen,
and their values are mainly 0.4 percent, 0.6 percent, and 0.95 percent
as shown in Fig. 2.5b. The value of the shear reinforcement ratio is
distributed between 0.09 percent and 2.44 percent (see Fig. 2.5c).
None of the specimens failed in shear before flexural yield.
2.3 Data Digitization from Graphs
Figure 2.6 shows the outline of the data digitization. After
the selection of specimens had been made, the graphs of the force-
deflection relationships were enlarged to approximately four times
their original size. Then from the enlarged graphs the first, third,
and tenth cycles at 10 , 20 , 30 and 40 were reduced to digitized y y y y
form. The accuracy of the digitizer is 0.001 inches and that of the
operator is a minimum of 0.005 inches. Hence the error should be less
than 0.01 percent for the enlarged graphs.
The digitized data were stored on computer cards; 104 specimens
occupying approximately 16,000 cards. (These cards are now stored on
one 1,200 ft reel of tape.)
2.4 Data Reduction
The lateral force-deflection data of each hysteresis loop
(more than 20 points in one loop) were replaced by slopes, deflections,
and shear forces at special points of the loop for use in the
statistical procedure.
The reduced data set consists of 20 points for each specimen in
each cycle as shown in Fig. 2.7. Points 1 to 10 are in the region of
positive loading, and points 11 to 20 are in the region of negative
loading. Points 1 to 5 and 11 to 15 are the slopes of the curve
6
(in ton/rom). Slopes 1, 5, 11, and 15 are calculated from the original
data by taking pairs of points nearest to the 0 axis. Slopes 2 and
12 are the stiffness when the deflection is zero; they are obtained
from the two points nearest the P axis. Slopes 3, 4, 13, and 14 are,
respectively, the stiffnesses at loading and unloading for maximum
deflection in each cycle. Deflections 6 and 16 are the maximum
deflections, and deflections 9 and 19 are the remaining deflections
when the load is zero. Shear forces 8 and 18 are the loads when the
loop crosses the load axis; shear forces 7 and 17 are the loads at
maximum deflection.
Point 10 is the area of the loop on the positive load side, and
point 20 is the corresponding area on the negative side. After
checking data at loading and unloading in each of the regions defined
above, the set 21 to 30 was computed as shown in Fig. 2.7. Points 21
to 25 are average dimensionless stiffness ratios based on the "peak to
peak" stiffness, 27/26: In this way about eighty digital figures
(40 points) in one hysteresis loop were reduced to ten digital data.
3. EMPIRICAL EQUATIONS OF HYSTERESIS LOOPS
3.1 Outline of Estimated Hysteresis Loops
In this section, the authors are searching for empirical
equations Dl, D2, D3, ••• D9 which are developed from the test data
(20) 21, 22, 23, ••• 29 by statistical processes. The skeleton
curve is defined as shown in Fig. 3.1. The shear force Q , the y
deflection 0 (D6) at flexural yield and the envelope curve after y
flexural yielding are obtained experimentally as estimated equations.
The curve from the origin to the yield point is assumed to be parabolic.
7
This curve opens downwards and the maximum value is Q. As a second y
step, a hysteresis loop is defined in terms of six elements as shown
in Fig. 3.2. The six empirical equations are Dl, D2, D3, D5, DB, and
D9, and cubic equations based on the test data are used between each
adjacent pair of elements. The peaks of one loop are defined by the
skeleton curve D7, based on the effect of cyclic loads with fixed
amplitudes. The first cycle at a given amplitude is defined by
Dl (amp) to D9 (amp). All subsequent cycles at that amplitude are
defined by Dl (cycle) to D9 (cycle) where "cycle" is the current
number of repetitions. It should be noted that the first cycle at a
given amplitude should be treated as the last cycle of the previous
amplitude until the deflection exceeds the previous amplitude. The
location of Dl is the start of any given cycle (loop).
3.2 Skeleton Curve
The calculated shear force, Q ,at flexural yielding, which is yc
based on plastic reinforced concrete theory (16) , does not always agree
with the test value, Qyt' especially for short columns. Figure 3.3a
shows the average values of Q t/Q for each combination of parameters. y yc
The notation for this figure is shown in Fig. 3.5. These kinds of
graphs, shown many times in the next section, are always for the same
combination of parameters. In the top diagram, the test specimens are
separated into domains according to their shear span ratio 1.0 and 1.5;
2.0; 2.5 and 3.0. In the second diagram the three groups are each
divided into two domains determined by a shear reinforcement ratio
< 1.2 percent or ~ 1.2 percent. Similarly, the third diagram is the
distribution of longitudinal reinforcement, and the fourth one is the
distribution of axial stress divided by concrete strength.
S
Figure 3.3b shows the comparison between the experimental
values Qyt and calculated values Q used so far. In the next curve, yc
Fig. 3.3c, the calculated value has been corrected to a Q ,where a yc
is obtained by assuming a linear relation between the four test para-
meters and the method of least squares is applied to obtain the
coefficients.
, a 1.4lS - 0.105 aid - 12.49 Pt - 7.37 P - 0.464 P/bdf • w c
Equation 3.1, represented as 07, is obtained from an analysis
of the data distributions in Fig. 3.4a.
07 (yield) = O.SOI + (0.623 - 29.07 Pt - 5.623 Pw - 1.11 P/bdf~)/(a/d) ••••• (3.1)
Then the ordinate of Fig. 3.3d has been corrected to 07(yie1d)· Q • yc
A comparison of the three diagrams, Figs. 3.3b, c, and d, indicates
that Fig. 3.3d gives the best estimate for shear force at flexural
yielding.
Figure 3.4a shows the average rotational angle, 0 /h, at y
flexural yielding for each parameter combination, where 0 is the y
deflection at flexural yielding, and h is the clear span of the column.
An analysis of the significance of the parameters in this diagram
indicates that 0 /h is a linear combination of the parameters, aid, y
Pw' and Pt' From the method of least squares,
06 = 0y/h = 0.005 - 0.00124 aid + 0.63 Pt - 0.056 Pw' (3.2)
Figure 3.4b shows the comparison of the experimental results with
Eq. (3.2). Although the accuracy is not satisfactory in this diagram,
the error is less than in Fig. 3.4c in which a comparison is made
9
between the test results and an empirical equation developed by
(16 ) Sugano • Hence Eq. (3.2) is adopted to estimate 0 /h.
y
Next, the envelope curves after flexural yielding are defined.
Figure 3.6a is the distribution of average ratios of the shear force
at first cycle in each amplitude to the shear force at flexural yield,
Qyt' The following estimated equation, D7,of the envelope curve is
obtained by the method of least squares:
D7(envelope) = 1.0577 + (a/d - 3.0) (3.777 Pt - 0.0221 P/bdf~) amp
•.... (3.3)
where amp is the dimensionless amplitude, % ; 0 is calculated for y y
each specimen from Eq. 3.2.
Figures 3.6b and 3.6c are the shear force reduction ratios of
the third cycle to the first cycle and the tenth cycle to the first
cycle for each amplitude. From these diagrams, Eq. 3.4 is obtained as
an estimate of the effect of cyclic loads on shear force reduction:
D7(cycle) 1.046 - 0.00554 aid - 0.0345 cycle/(a/d) ,
+ (Pt - 0.004) (-0.013 + 2.569 P/bdfc - 5.98 amp)
•••.. (3.4)
These two equations demonstrate the dependence of some parameters in
D7(cycle) on other parameters.
Table 3.1 summarizes the process by which the equations used to
estimate skeleton curves are obtained from the effect of cyclic loads
with fixed amplitude. If an arbitary shear force is needed, it is
obtained as follows:
Q = D7(amp) • D7(cycle) • Q yc
Ele
men
t
D7
(yie
ld)
Q y
D6 O/h
D7
(en
vel
op
e)
= D
7 (a
mp)
TAB
LE
3.1
ESTI
MA
TED
EQ
UA
TIO
NS
FOR
SK
ELET
ON
CU
RVE
Incli
nati
on
of
Eff
ecti
ve P
aram
eter
R
emar
ks
As
aid
in
cre
ase
s,
D7
(yie
ld)
decre
ase
s
Pt
incre
ase
s,
decre
ase
s R
est
rain
ed
by
aid
P in
cre
ase
s,
decre
ase
s R
est
rain
ed
by
aid
w
P
/bd
f'
incre
ase
s,
decre
ase
s R
est
rain
ed
by
aid
c
D7
(yie
ld)
= 0
.80
1
+
(0.6
23
-
29
.07
Pt
-5
.62
3p
-
1.1
1P
/bd
f')/
(a/d
) w
c
As
aid
in
cre
ase
s,
D6
(yie
ld)
decre
ase
s
Pt
incre
ase
s,
incre
ase
s
Pw
in
cre
ase
s,
decre
ase
s
D6
(yie
ld)
= 0
.00
5
-0
.00
12
4a/d
+ 0
.63
Pt
-0
.05
6p w
As
Pt
incre
ase
s,
D7
(en
vel
op
e)
decre
ase
s R
est
rain
ed
by
aid
, am
p
P/b
df'
in
cre
ase
s,
incre
ase
s R
est
rain
ed
by
am
p c
D7
(en
vel
op
e)
= 1
.05
77
+
(a
/d-3
) (3
.77
7p
-
0.0
22
1P
/bd
f')a
mp
t
c
f-J
o
TAB
LE
3.1
(c
on
tin
ued
)
Ele
men
t In
cli
nati
on
of
Eff
ecti
ve P
aram
eter
D7
(cy
cle)
A
s aid
in
cre
ase
s,
D7
(cy
c1e)
d
ecre
ase
s
Pt
incre
ase
s,
decre
ase
s
P/b
df'
in
cre
ase
s,
incre
ase
s c
amp
incre
ase
s,
decre
ase
s
cy
cle
in
cre
ase
s,
decre
ase
s
D7
(cy
cle)
=
1
.04
55
-0
.00
55
a/d
+
(Pt
-0
.00
4)
(-0
.01
32
+
2. 5
69
P/b
df'
-
5. 9
8am
p)
c
Rem
arks
Rest
rain
ed
by
Pt
Rest
rain
ed
by
Pt
Rest
rain
ed
by
aid
-0
.03
45
cy
cle
/(a/d
) ~-
-
I-'
I-'
12
3.3 Definition of the Hysteresis Loop
Using the test data, the elements Dl to D9 (shown in Fig. 3.2)
used to characterize the shape of the hysteresis loop, are now defined.
A hysteresis loop is defined by pairs of equations. Each pair consists
of one equation for amplitude, and the other for cyclic loading with
fixed amplitude. The exception is the element D3. Half of the test
data on D3 were negative or zero in the first cycle for each amplitude
and positive in the third and tenth cycles. Because of this distribu-
tion of data, the estimated equation for D3 was separated with regard
to amplitude and the loading cycles.
Applying the same techniques used in Section 3.2, these
estimated equations Dl, D2, •.. D9 are summarized in Table 3.2,
which also shows the trend of the parameters with the elements,
(e.g., Dl(amp) increases as aid increases). In each case a pair of
equations is used as follows: using Dl as an example, the first cycle
at a given amplitude would be described by Dl(amp). All subsequent
cycles at that deflection would be described by Dl(amp) • Dl(cycle).
4. ESTIMATED HYSTERESIS LOOPS
4.1 Method for Drawing Hysteresis Loops
The hysteresis loops are drawn using cubic equations. First,
as shown in Fig. 4.la, the initial curve OA is a parabolic equation
whose maximum value is at O. In the cyclic hysteresis loop, as shown y
in Fig. 4.lb, the half cycle consists of three sections -- RANGE 1,
RANGE 2, and RANGE 3; the first two are cubic polynomials and the third
is a parabola. The boundary conditions for these have already been
calculated in Section 3. Some examples of estimated hysteresis loops
TAB
LE
3.2
ESTI
MA
TED
EQ
UA
TIO
NS
Incli
nati
on
of
Eff
ecti
ve P
ara
mete
r R
emar
ks
D1
As
aid
in
cre
ase
s,
D1(
amp)
in
cre
ase
s
Pw
incre
ase
s,
decre
ase
s R
est
rain
ed
by
aid
Pt
incre
ase
s,
decre
ase
s R
est
rain
ed
by
aid
,
P/b
df
incre
ase
s,
incre
ase
s R
est
rain
ed
by
aid
c
amp
incre
ase
s,
decre
ase
s R
est
rain
ed
by
aid
D1(
amp)
=
1. 3
54
+
(3.5
-
a/d
) (0
.54
2
-5
.12
6 P
-
49
.9 P
t +
0.5
1 P
/bd
f'
-0
.15
3
amp)
w
c
As
amp
incre
ase
s,
D1
(cy
c1e)
in
cre
ase
s R
est
rain
ed
by
Pt
cy
cle
in
cre
ase
s in
cre
ase
s L
og
arit
hm
D1
(cy
c1e)
=
0.6
67
+
8.9
3
amp
(pt
+ 0
.00
5)
D2
As
Pt
incre
ase
s,
D2(
amp)
d
ecre
ase
s R
est
rain
ed
by
aid
Pw
incre
ase
s,
decre
ase
s R
est
rain
ed
by
aid
amp
incre
ase
s,
decre
ase
s R
est
rain
ed
by
aid
D2(
amp)
=
1
.48
1 +
(a
/d -
3.0
) (4
1.0
8 P
t -
10
.09
Pw
+ 0
.07
am
p)
As
cy
cle
in
cre
ase
s,
D2
(cy
c1e)
d
ecre
ase
s
amp
incre
ase
s,
incre
ase
s
D2
(cy
c1e)
=
0.8
44
-
0.0
31
cy
cle
+
0.0
31
am
p
I
I--'
W
D3
D5
D8
TAB
LE
3.2
(c
on
tin
ued
)
Incli
nati
on
of
Eff
ecti
ve
Par
amet
er
Rem
arks
As
cy
cle
in
cre
ase
s,
D3(
amp,
cy
cle
) in
cre
ase
s L
og
ari
thn
Pt
incre
ase
s,
incre
ase
s R
est
rain
ed
by
aid
P/b
df'
in
cre
ase
s,
decre
ase
s R
est
rain
ed
by
aid
c
amp
incre
ase
s,
incre
ase
s R
est
rain
ed
by
aid
As
aid
in
cre
ase
s,
D5
(am
p)
incre
ase
s
Pt
incre
ase
s,
decre
ase
s R
est
rain
ed
by
aid
amp
incre
ase
s,
incre
ase
s R
est
rain
ed
by
aid
D5(
amp)
=
1.0
54
+
(a
/d -
3) (
0.0
21
+
12
.12
8 P
t +
0.0
39
am
p)
As
cy
cle
in
cre
ase
s,
D5
(cy
c1e)
in
cre
ase
s R
est
rain
ed
by
aid
amp
incre
ase
s,
incre
ase
s R
est
rain
ed
by
aid
D5
(cy
c1e)
=
0
.97
2
+
(3.5
-
a/d
) (-
0.1
14
+
0.0
14
cy
cle
+
0.0
5
amp)
As
p ....
incre
ase
s,
D8(
amp)
d
ecre
ase
s R
est
rain
ed
by
aid
....
amp
incre
ase
s,
chan
ges
R
est
rain
ed
by
aid
D8(
amp)
=
0.2
39
+
5.8
8
(a/d
-3)
P
t +
0.0
14
4
amp
(a/d
-2
.3)
As
cy
cle
in
cre
ase
s,
D8
(cy
cle)
d
ecre
ase
s
amp
decre
ase
s,
incre
ase
s R
est
rain
ed
by
Pt
D8
(cy
cle)
=
0.8
42
+
0.0
04
5
cy
cle
+ 1
3.5
59
(P
t -
0.0
02
) am
p
I--' 01'>
D9
As
Pt
aid
D9(
amp)
As
cy
cle
amp
~-
-
TAB
LE
3.2
(c
on
tin
ued
)
Incli
nati
on
of
Eff
ecti
ve P
ara
mete
r R
emar
ks
incre
ase
s,
D9(
amp)
in
cre
ase
s R
est
rain
ed
by
am
p
incre
ase
s,
incre
ase
s R
est
rain
ed
by
am
p
=
0.1
65
6
+ {
6.7
8
(Pt
-0
.00
2)
+ 0
.01
84
aid
}
amp
incre
ase
s,
D9
(cy
cle)
d
ecre
ase
s
incre
ase
s,
incre
ase
s -------~----
--
~
---------
, I i I i I
!-'
U1
16
(CASE 1, CASE 2, ••• CASE 10) are shown in Figs. 4.2 to Fig. 4.11.
These are compared with the test results and also with a mathematical
. (14) model developed by PenZlen and Atalay for long columns. The
graphs show that the "estimated model" agrees reasonably well with the
test results.
In these figures, the three loops correspond to the first,
third, and tenth cycles of each amplitude. CASE 1: small shear span
ratio (aid = 1.0), small shear reinforcement (p = 0.21); the shape w
of hysteresis loops obtained from test data is that of the hard spring
type even for the initial amplitude. For such a combination of para-
meters, there is a rapid reduction of shear force. The predicted
hysteresis loops demonstrate these results reasonably well. CASES 3
and 4: aid = 1.5 (Figs. 4.4 and 4.5). The different longitudinal
reinforcements of these two cases changes the shapes of the loops.
The estimated hysteresis loops also demonstrate this delicate
difference.
Again for CASE 5 and CASE 6, with different longitudinal
reinforcements, the test results show some differences; such as in the
shear reduction by cyclic loads and in the residual deflections when
shear force is zero.
These figures show that the estimated hysteresis loops agree
reasonably well with the test data. However, the mathematical model
obtained from the test data for long columns (aid 5.5) does not
agree as well as for columns whose shear span ratio is less than 3.0.
4.2 Comparison with a Mathematical Model
It is of some interest at this stage to compare the preceding
results with the Penzien-Atalay model (14) of which Fig. 4.12 shows a
17
typical half cycle. Both ends of the half cycle are restrained by an
empirical skeleton curve which includes the effect of cyclic loads.
Figures 4.13, 4.14, and 4.15 show comparisons of the estimated
stiffness and the stiffness from the mathematical model for the stiff-
nesses 01, 02, and 03, respectively, (for the case that the amplitude
is 1.0 0). The stiffnesses are divided by K. and shown as Y J
dimensionless values.
These graphs indicate that the differences between the mathe-
matical model and the estimated equation (which agrees well with the
behavior of the test data) reduce as the shear span becomes large.
5. CONCLUSIONS AND RECOMMENDATIONS
The proposed method of predicting hysteresis loops for rein-
forced concrete columns involves using test data statistically. The
estimated hysteresis loops are obtained by a series of simple,
statistical procedures and agree reasonably well with the test data
for the following:
1) Change in shear force for a given amplitude and number of cyclic loads.
2) Shape of the hysteresis loops.
3) Shear force and deflection at bending yield for short columns.
It is important to note, however, that this evaluation is based
upon test data for columns which never failed in shear or bond before
flexural failure. There are no test data for loops in these cases.
The comparison of the Penzien-Atalay mathematical model based
on test data for long columns and this estimated model obtained from
18
shorter column data shows emphatically that short columns (shear span
ratio less than 3.0) are not adequately described by the mathematical
model.
For a complete estimation of the load deflection relationship,
we recommend that cyclic loading tests of longer columns (aid = 3.5,
4.0 and 5.0) be developed systematically.
It should be noted that the estimated equations presented herein
are developed only for this particular set of test data. Further work
is needed in order that these equations may be applied to the more
general case of nonrepetitive cyclic loading.
REFERENCES
1. Ramberg, W., and Osgood, W. R., "Description of Stress-Strain Curves by Three Parameters," NACA TN 902, July 1943.
19
2. Jennings, P.C., "Response of Yielding Structures to Statistically Generated Ground'Motion," III W.C.E.E., New Zealand, 1965.
3. Iwan, W.D., "The Distributed-Element Concept of Hysteretic Modeling and its Application to Transient Response Problems," IV W.C.E.E., Santiago, Chile, 1969.
4. Clough, R.W., and Johnston, S.B., "Effect of Stiffness Degradation on Earthquake Ductility Requirements," Proceedings of Japan Earthquake Engineering Symposium, Tokyo, October 1966.
5. Liu, Shih-Chi, "Earthquake Response Statistics of Nonlinear Structures," ASCE Proceedings, Journal of Engineering Mechanics Division, Vol. 95, EM2, April 1969.
6. Geel, S.C., "Inelastic Behavior of Multistory Building Frames Subjected to Earthquake Motion," University of Michigan, 1967. (Thesis) •
7. Shiga, T., and Ogawa, J., "The Experimental Study on the Dynamic Behavior of Reinforced Concrete Frames," Proceedings IV World Conference on Earthquake Engineering, B-2, pp. 165-176, Santiago, Chile, 1969.
8. Takeda, T., Sozen, M.A., and Nielsen, N.N., "Reinforced Concrete Response to Simulated Earthquakes," Proceedings ASCE Vol. 96 (ST12), Journal of the Structural Div., December 1970.
9. Kent, D.C., "Inelastic Behavior of Reinforced Concrete Members with Cyclic Loading," Ph.D. Thesis, Univ. of Canterbury, Christchurch, New Zealand, 1969.
10. Otani, S., and Sozen, M.A., "Behavior of Multistory Reinforced Concrete Frames During Earthquakes," Civil Engineering Studies, Structural Research Series No. 392, Univ. of Illinois, Urbana, November 1972.
11. Bertero, V.V., "Effects of Generalized Excitations on the Nonlinear Behavior of Reinforced Concrete Structures," Proceedings of the International Conference on Planning and Design of Tall Buildings, IABSE-ASCE, Vol. III, pp. 431-453, Lehigh Univ., Bethlehem, Pennsylvania, August 1972.
12. Bertero, V.V., Bresler, B., and Liao, H.M., "Stiffness Degradation of Reinforced Concrete Members Subjected to Cyclic Flexural Moments," Report No. EERC 69-12, Univ. of California, Berkeley, December 1969.
20
13. Celebi, M., and penzien, J., "Experimental Investiga,tion into the. Seismic Behavior of Critical Regions of Reinforced Concrete Components as Influenced by Moment and Shear," Report No. EERC 73-4, Univ. of California, Berkeley, January 1973.
14. Atalay, M.B., and Penzien, J., "The Seismic Behavior of Critical Regions of Reinforced Concrete Components as Influenced by Moment, Shear and Axial Force," Report No. EERC 75-19, Univ. of California, Berkeley, December 1975.
15. Wight, J.K., and Sozen, M.A., "Shear Strength Decay in Reinforced Concrete Columns Subjected to Large Deflection Reversals," Civil Engineering Studies, Structural Research Series No. 403, Univ. of Illinois, Urbana, August 1973.
16. Sugano, S., and Koreishi, 1., "An Empirical Evaluation of Inelastic Behavior of Structural Elements in Reinforced Concrete Frames Subjected to Lateral Forces," Proceedings of the Fifth World Conference on Earthquake Engineering, Vol. I, Rome, 1974.
17. Hirosawa, M., "Synthetic Research on preventing Reinforced Concrete Columns from Total Collapse (in Japanese) ," Building Research Institute, Japan, BRI Research Paper, 1972.
18. Building Research Institute, Japan, Committee on Reinforced Concrete Structures in Building, "The Experimental Study on the Behavior of the Reinforced Concrete Columns under Cyclic Loading," (AR-l Series, AR-2 Series, LM-2 Series, AF Series, WS Series, LS Series, Pilot Series, FC Series, DCW-l Series, DCW-2 Series, SE Series), 1972-1976.
19. The 1971 Architectural Inst. of Japan Standard for Structural Design of Reinforced Concrete Construction.
20. Brownlee, K.A., "Statistical Theory and Methodology in Science and Engineering," John Wiley & Sons, Inc., 1965.
,~
150
, \,10
0
10 10
0 5
00
100
f 15
0 if
L- F
15
00
--
I I
50
0
·1--5
00
·1--5
00
---1
---
------
----
---c
----
----------
2-9<
1>@
6
8.3
------
---
----
------~9
4>-O
-@ 45
.5 =
====
= f:
-.-
---
-----
'" I
~
r ,
'"' ~3
-DI3
---
------
~-----
1----
---
r------
f------
---
---
------
1-----------
---r-----
c-------
---
Fig
. 2
.1
Sp
ecim
en D
eta
ils
(in
mm
)
35
*D ~
.I
0( 18
0
25
0
tv
.....
65
0
55
0
5,4
50
65
0
65
0
d I
t-"
OIL
JAC
K F
OR
AX
IAL
LOAD
OIL
JA
CK
FO
R H
OR
IZO
NTA
L LO
AD
Fig
. 2
.2
Lo
ad
ing
A
pp
ara
tus
(in
rom
)
N
N
+8
!
CY
CL
ES
AT
38
! I
I (P
5,-
PSO
i
(P1
03
)
68
y{P
91
92
) \
I ~ C
YC
LES
AT
4' 8
y \
(P7,-
Pao
i -I ~
O 1"
'"' 1
\
I)
n {}
{} I}
n I} {} I} I
• I
• I
• I ••••••••••• I
• I'
I •
I \
I •
I \
I •
I •
, • ,
• I
• I
• ,
" \,
\ ,
\ ,
\ ,
\ ,
\ ,
• ,
\ ,
\ ,
\ I \,
\
, \,
\ ,
'I
().(Y
tY
1:)(){Y
t)ty() (}
ViY
{
i ,iii,ii,\,' ,(,
• ,1
i,
1 ,~
1
-8
38
y(P
SI)
J
;-
8 8
y( P
IO 1
,10
2)
P y:
LOA
D W
HE
N T
EN
SIL
E R
EIN
FO
RC
EM
EN
T Y
IEL
DS
AT
TE
ST
8 y:
ME
AS
UR
ED
HO
RIZ
ON
TA
L D
ISP
LA
CE
ME
NT
AT
P =
Py
Fig
. 2
.3
Cy
cli
c
Lo
ad
ing
S
yst
em
N
W
24
I
Fig. 2.4 Examples of Crack Patterns
25
D, INDICATES FREQUENCY EQUALS 1
0 INDICATES FREQUENCY EQUALS 2
0 INDICATES FREQUENCY EQUALS 3
'V INDICATES FREQUENCY EQUALS 4
0 INDICATES FREQUENCY EQUALS 5
Q INDICATES FREQUENCY EQUALS 6
0 INDICATES FREQUENCY EQUALS 7
0 INDICATES FREQUENCY EQUALS 8
LJ INDICATES FREQUENCY EQUALS 9
0 INDICATES FREQUENCY EQUALS 10
0 INDICATES FREQUENCY EQUALS 11
0.0152
0.0121
0.0091
0.0061
0.0030
o 0.5
26
2<>
2<>
7n
70
30
4V' V'4
2<> 2<>
IA 2~11 05 1/\ 2<>
IA 2<> I)"" 1.110 ~ --"""'LJi -2<> 7A
2<>
2<> 03
4V' 011 AI
1.1 1.7 2.3 2.9 3.5 aid
Fig. 2.Sa Parameter Distribution: aid vs Pt
0.0268
0.0215
0.0161
0.0107
0.0054
o 0.5
1.6
16
16
1.6
16
~2 16
1.6
r.6
.6
.6 I< .6
~ .6
16
2<>
Tg
2<>
1.6
2"",
30
16
30
16
16
1.6
1.1
Fig. 2.Sb
1.6
1.6
1.6
1.6 1.6
1.6 1.6
~1,2 IV
<>2 .61 61
AI <>2 61
l{l .61
1&2 1 ~ 1,1,2
r: 1,4
~ 61
6 2~!.2 1 < ~ ~ 61 .6
'-
1.7 2.3 2.9 aid
Parameter Distribution: aid vs p w
27
3.5
28
0.4053
0.2999
0.1945
0.0892
-0.0162
-0.1216 0.5
~I
~I
4\7 2<>
4\7
30
2<>
1.1
Fig. 2.Sc
\74
\74
03 ~I
\74
u5
06 07
03 03 4~1
~I
05 06 03
05
30
1.7 2.3 aid
Parameter Distribution: aid vs P/bdf' c
~I
05
~1,3
~I 07
2.9 3.5
HYSTERESIS DIAGRAMS
DATA CARDS FOR
COMPUTER
29
(ORIGINAL DATA)
(MAGNIFYING GRAPH)
(A-D CONVERSION)
104 SPECS (16000 CARDS)
Fig. 2.6 Procedure of A-D Conversion
30
@= @= @= @= @= @= @= @= @
-@ =
I@) I I
p
@
(0) STEP 1
Cb} STEP 2
Fig. 2.7 Data ~eduction
-8 y
Q
-----4----I---J..--.1..-..--------:3~8 I I I I
CUBIC I EQUATION
I I
Fig. 3.1 Empirical Skeleton Curve
QIQe
Fig. 3.2 Empirical Hysteresis Loop
31
32
1.5
1.0
0.5 aid =
1.5 1.0.1.5
........... ' ....... 1.0
0.5
1.5
1.0
0.5 P t
1.5
1.0
0.5 •
~ 1.2%
~ , 1\./ -
L M
\ \ \
-...... ......
> 1.2%
/-A
flJ
S L M
\ "
, \
\ It
2.0
--- 1-_-.
~ 1.2% > 1.2%
.,. ,,- "" ~ .. -- .,'
S L M S L M
1-1 , .. • • ~ • fI"
P Ibdf SM SML ML SML ML L SML ML ML ML L c
-. ~
3.0
",'" -. r
S L M S
.. .. •
ML ML L
Fig. 3.3a Average Value in each Parameter Domain of Q t /Q y yc
CJ)
Z
~ Z
Z 0 t-« ....J ::> U ....J « u
24
20
16
12
8
4 4
6
M 6
8 12 16 20
TEST VALUE IN TONS
Fig. 3.3b Comparison between Calculated Value and Test Value of Bending Yield Shear Force Q
y
33
24
34
en z ~ Z
Z 0 I-« --' ::::> u --' « u
24
~ 20
~
16
M
12 ~
8
4 ~------~------~------~--------~------~ 4 8 12 16 20
TEST VALUE IN TONS
Fig. 3.3c Comparison between Calculated Value and Test Value of Bending Yield Shear Force aQ
y
24
en z ~ Z
Z 0 t-<t --1 ::J U --1 <t U
35
24 r-------~----__ ~----__ ------~------__
20
16 ~
12
8
4 ~------~------~--------~------~------~ 4 8 12 16 20 24
TEST VALUE IN TONS
Fig. 3.3d Comparison between Calculated Value and Test Value of Bending Yield Shear Force D7 • Q
y
36
0.02 r------~----_r__----_,__----~----....,
0.01
o aid =
0.02
0.01
o Pw
0.02
0.01
o
1.0,1.5
a A
~ 1.2% > 1.2%
A A
A A A A
Pt L M S L M S
0.02
A
0.01 AA A A
A A A A A
A A
o
2.0
A A
~1.2% > 1.2%
A a A
A A
L M S L M
A A ~ -
A A
A AA A A
P/bdf' SM SML ML SML ML L SML ML ML ML L c
-
2.5,3.0
~
A A
L M S
A ~
AA A
ML ML L
Fig. 3.4a Average Value of D6 in each Parameter Domain
20r-----~------~----~------~----~
16 ::?! ~
z z 12 0 I-<I: ...J
8 ::::> u ...J <I: u
4
o ~ ____ ~ ______ ~ ____ ~~ ____ _L ____ __J
o 4 8 12 16 20 TEST VALUE IN MM
Fig. 3.4b Comparison between Calculated Value and Test Value of Yield Deflection D6
37
38
20r------r------~----~------~----~
16 ~ ~
Z
z 12 0 .... « -I
8 :::J U -I « u
4
4 8 12 16 20 TEST VALUE IN MM
Fig. 3.4c Comparison between Sugano's Calculated Value and Test Value of Yield Deflection
Fig.
Y: @ to @ ; Test Data/(@ / @) X: Shear Span Ratio (a/d)
Y: Same as above
X: Shear Reinforcement Ratio (p ) w
Y: Same as above
X: Longitudinal Reinforcement Ratio
S: Pt < 0.4% -
M: 0.4% < Pt < 0.8%
L: 0.8% < Pt
Y: Same as above
X: Axial Force/Concrete Strength;
S: - 0.11 < P/bdf' < 0.02 c
M: 0 < P/bdf' < 0.15 c
L: 0.15 < P/bdf' < 0.40 c
~.: 1 0 amp = 1.0 Y
0: 2 0 amp 2.0 y
0: 3 0 amp = 3.0 .y
\7: 4 0 amp 4.0 y
(Pt)
3.5 Guide for the Data Distribution Diagrams
39
40
1.50 ,------~----.,...._----...,_----_,_----_..,
0.501-------11-------1------1-----+-----1
o aid = 1.0,1.5 2.0 2.5,3.0
1.50
1.00 ~ ~ ~ til V V ... ~
V V
0.50
o Pw ~ 1.2 % >1.2% ~ 1.2% >1.2%
1.50~--------~--------~--------~----------T---------~
o V
0.501-------11-------1--1-----1-----+------1
0 Pt
1.50
1.00
0.50
0 P/bdf'
c
L M S L M S L M S L M L M
8
0 V V V V V V 0 V
V
SM SML ML SML ML L SML ML ML ML L ML ML
Fig. 3.6a Average Value in each Parameter Domain for D7 (Envelope Curve)
S
L
1.00
0.80
0.60
0.40 aid = 1,00
1.0,1.5
~ ~ 0.80
0.60
0.40 Pw ~ 1.2% > 1.2%
1.00
0.80
~ II e ~ A ~
~ 0.60
0.40 Pt L M S L M S
1.00
o,eo
0.60
.~ it A <>9 ~ A ~8 e <> It. 0
~o v v
A
I~
0.40
2.0
0 ~ 0 'V
~1.2% > 1.2%
§ a & ~ A
<> 'V ~ ..... ~
v
L M S L M
B I~ tM ig ~ A ~
<'7 0 0 o 'V v
~ 'il
P!bdt~ SM SML ML SML ML L SML ML ML ML L
~
~
2.5,3.0
8 I ~
A
"
L M S
~H Ie IS2I
A
"
ML ML L
Fig. 3.6b Average Value in each Parameter Domain for D7 (3 cycle!l cycle)
41
42
1.50 r-----..,...-------r--------r-----,.---------,
1.001------+-----+-----+-----ooooofo--'o-----I
0.50 \-----+-----+-----+------+------1
o aid = 1.0, 1.5
1.50
1.00
@ @ 0.50
o Pw S 1.2% > 1.2 %
1.50
0.50
1.00
~ @ e @ ~ 6 a
o Pt L M S L M S
1.50
1.00
0.50
6 ~ ij@) 6~ 6~ t<> 6 0 Til 6~ ~ .... ~ Til
y ..... <> ('
o
2.0
@ ~ Til
S 1.2% >1.2%
6 ~ II ~ H
<> 0
~ V
L M S L M
A.
~ 6$ 3~ .e ~~ 9 60
AVO ~ 0 ~
lSI Til
P/bdf' SM SML ML SML ML L SML ML ML ML L c
2.5,3.0
~ 0
II) ~
n
L M S
,
~. $1 ~ 0
"
ML ML L
Fig. 3.6c Average Value in each Parameter Domain for D7 (10 cycle/l cycle)
4.00
2.00 l.
o aid = 1.0,1.5
4.00
2.00
o Pw
4.00
2.00
o A B
A <>
~
~1.2%
A
A <> <> ~ ~
Pt L M S 4.00
A
2.00 AA
7S"
° A<> <>'i1 A A<> ~ ~ ~~~ o
A <> ~
>1.2%
A * <> ° A S 0
L M S
AA <>
AA <>0
~~ ~
A
* °
-.....
2.0 2.5,3.0
A A <>
" a' ~1.2% > 1.2 %
A
0 ~ A
A & $ * I <> 0 <> 0 c;t ~ V
L M S L M L M S
A I
"Pil 1\ A
<>A O~ i <>
A & :1 ~~ <>A A<> <>A II AO<> °0 8<) <>'i1~ 0 I i 0 i i !
P/bdf' SM SML ML SML ML L SML ML ML ML L ML ML L c
Fig. 3.7a Average Value in each Parameter Domain for 01 (Amplitude)
43
44
1.75
1.25
0.75
0.25 aid =
1.75
1.25
0.75
0.25 Pw
1.75
1.25
0.75
0.25
'\l 1"'1
~
~1.2%
u '\l '\l
<> ~ <> !
l:J,.
Pt L M S
t
1.0,1.5
g
<> l:J,.
>1.2%
l!5 '\l
A. n
8 l:J,. A <> V
L M S
~ 1>..
2.0 2.5,3.0
'\l '\l
~.
~ 6
~ 1.2% >\,2%
.... v
'\l l:J,. '\l
~ <> , sa '"' A 0
2 g a X ~ c <> <>
L M S L M L M S 1.75r---------~--------~--------~----------r_------~
1.25~~------~--~----+_----~--+_--------~~------~
<>
0.25~----~--~---X----~--------~--------~--------~
P/bdf' SM SML ML SML ML L SML ML ML ML L c
ML ML L
Fig. 3.7b Average Value in each Parameter Domain for Dl (3 cycle/l cycle)
4.00
2.00
o aid =
4.00 1.0.1.5
2.00
g lS2I
~ ~
o Pw S1.2% >1.2%
4.00
2.00 ~
V ~
<) i ~ <> 0 0 A 6 ~ <>
o Pt L M S L M S
4.00
0
V 2.00 ~
8 V Vo 0"1 g
~
<>ij~ ~ <)<)~ <)
6~ 6 66 1;9 o
2.0
v
V
~ ~
S 1.2% > 1.2%
V
V
V 0 @ i ~ t ~ <>
L M S L M
V V
V V
0 0 &~~ ~~ ~§ 8~ t <> V
P/bdf' SM SML ML SML ML L SML ML ML ML L c
..,
-v
2.5.3.0
V
8 9 • L M S
V
QIj ~ • ML ML L
Fig. 3.7c Average Value in each Parameter Domain for D1 (10 cycle/l cycle)
45
46
4.00
2.00
o aid = 400
1.0,1.5
2.00
o Pw
4.00
2.00
o
r--~
A <> Q
A <> ~
~1.2%
A
~ ~
~
Pt L M S
4.00 -
2.00 Ag
V
A A~~ ~ ~<> <>~O DGJ " V o
A <> fJ
>1.2%
~ 8 <> A
0 A <> ~ fJ
L M S
A
8 A<> A A 0
AA<> <>~ a~O @
2.0
A <> A
~ <> ~
~ 1.2% > 1.2%
A ~ • <> A 0 A <> ~ @ ~
L M S L M
A
AA ~~ ~
+ AA <><> .~
0 ~e<> ~O OV~ V V
P/bdf~ SM SML ML SML ML L SML ML ML ML L
~
2.5,3.0
6 ~ 8 ~ A
L M S
i8 ;~ ~ A
ML ML L
Fig. 3.8a Average Value in each Parameter Domain for D2 (Amplitude)
1.75
1.25
0.75
0.25 aid = 1.75
1.25
0.75
0.25 Pw
1.75
1.25
0.75
0.25
v
0
~
t
~ .
1.0,1.5
v l!1 -..... 2 ~
::S 1.2% >1.2 %
g ~ V -~ W b
~
<> g & 6
Pt L M S L M S
~
'"
2.0 2.5,3.0
0 -6 R
::S1.2% > 1.2%
V ~ B 0 Y .... u -i ~
~ X * ~ <> <>
L M S L M L M S
1.75 r-------r-----~----_r_----_._----_
1.25
0.75
0.25 P/bdf'
c
V 6 V
0 0
'il o
~ 0
* 0 <> &6 6 <> <>
6 V
SM SML ML SML ML L SML ML ML ML L ML
Fig. 3.8b Average Value in each Parameter Domain for D2 (3 cycle/l cycle)
ML
B <>
L
47
48
3.00
2.00
1.00
o aid =
3.00
2.00
1.00
o
i
Pw S 1.2 %
~
1.0, 1.5
~
2.0 2.5,3.0
'" 0 i " ~ V
>1.2% ~1.2% >1.2%
3.00 ,,---_._ .. -I
2.00
\l 8 1.00 ...... \1
o· ~ ~ 0
@I ~ g ~ 0 ~ II
~ 8 ~ 0 0 ¢ 11 \l
o Pt L M S L M S L M S L M L M S
3.00 ,
2.00 \l
1.00
oV 8 \l \l
<> = \1 ~ \l ~ v
o~~ u ~ ,v ~i ~@ 9~ 11
~~ 9.~ ~~ e~ ~ ~. ~ ~ 69 0
11 11 t::,O V o P/bdf' SM SML ML SML ML L SML ML ML ML L ML ML L
c
Fig. 3.8c Average Value in each Parameter Domain for D2 (10 cycle/l cycle)
2.00 r-----__,r__---__,.----__y"------r------,
1.00...-----4------+-------+-----...-----t
o
-1.00 L....-____ -'--____ -L., ____ --L. _____ '---___ ---'
aid =
2.00
1.00
o
-1.00
~ v
Pw ~ 1.2% 2.00
1.00 V
o g
8 V'
-1.00
1.0,1.5
V ~ ..,
> 1.2%
~ V n
9 IQ • b
Pt L M S L M S
2.0 2.5,3.0
! ! '0;11'
~ 1.2% > 1.2%
V V
~ • ~ V A A b b - n .., u V <> - ~ V
L M S L M L M S 2.00 ~------__,r__------__,.--------__y"-------__r--------_,
1.00
0
-1.00 P/bdf'
c
<>V 8b b
<> <> V
b
SM SML ML SML ML L SML ML ML ML L ML ML
Fig. 3.9a Average Value in each Parameter Domain for D3 (Amplitude)
<>
L
49
50
2.50
1.50
-0.50 ~
-0.50 a/d = 1.0,1.5 2.0 2.5,3.0
2.50
1.50
0.50
-0.50 Pw
2.50
1.50
0.50
-0.50 Pt
2.50
1.50
0.50
-'0.50 P/bdf' c
v 8
~1.2_%
i V
8 ',<
$
'L M S
X
SM SML ML
Fig. 3.9b
V V 0 i 8 0
> 1.2% "::'1.2% > 1.2%
-, , ..
v , g V
~ V R 8 g " V A ¢ ~
£» $ "~, ~' ., ~ L M S L M S L M L M S
V
V 0 <>
g~
0
SML ML L SML ML ML ML L ML ML L
Average Value in each Parameter Domain for D3 (3 cycle/l cycle)
4.00
2.00
o aid = 1.0,1.5
4.00
2.00
o Pw
4.00
2.00
o
~
~ 1.2%
X V 0
& e Pt L M S
4.00
A~ .... \J
~<> 0 0 6 V 6 ~~ ~
o ~
ij 6
>1.2%
~ 6 g
6
~ L M S
V
A. go 9
/:l.O ~ 6~
V 6 e
=--- t-- ..,.
2.0 2.5,3.0
V V
a ~
~ 1.2% > 1.2%
v
V @ i1 V 6 i 8 (» I:l. Q
$ ~ -~ ..,
L M S L M L M S
V
V ~
v 6Vg V 0 V 0
~fd 86 a~ @$ 8 .e. @6 Q
V Q 0 @ ~
P/bdf' SM SML ML SML ML L SML ML ML ML L ML ML L c
Fig. 3.9c Average Value in each Parameter Domain for D3 (10 cycle/l cycle)
51
52
1.50
1.00
0.50
o a/d :"'
1.50
1.00
0.50
1.00
0.50
o
~
g
--~~
1.0,1.5
~ ~
0
~ V .....
S 1.2% >1.2%
A
A
~
0 0 Jr ~ 0
0 n ~ 0 0 ....
~ ..,
--- -
~
S 1.2,%
.... a v e 0 ~
" 0
Pt L M S L M S L M S
~ .. -I tr'""
2.0 2.5,3.0
v ~
0
>1.2 %
v v X b .....
2S v 0 ~ 0 e @ v
L M L M S 1.50 r-----T-----......-rA------r--v---~----.....,
~
~ .... v V.~ b :,~ I. 00 1-:~~V--~-=--~r"'I. 'v~-----+rr.-:---.-~-.J;IVLf--~-A---:;--+--fiJIIllUr--n-... --'o.-f
gOo A~O ¢v V~o ~~ ¢ ~~ 0g 0 ~ ~ 8 ~ 'A ~ 0 1lIl.A J8I U 0
0.50 f--ilQt--i-1!!t-v....:O~¢~'""U~-9....1¥1---&t ..,-....::::::.----+-----+-------1
V o
P/bdf' SM SML ML SML ML L SML ML ML ML L c
ML ML L
Fig. 3.l0a Average Value in each Parameter Domain for D5 (Amplitude)
3.00
2.00
1
1.00 -o aid = 1.0,1.5 2.0 2.5,3.0
3.00
2.00
1.00 s ~ ~ ~ .... ~ v
o Pw .~ 1.2 % >1.2 % ~ 1.2 % > 1.2%
3.00
2.00
1.00 8 v
~ v
~ fl fl ~ Ii) S2 ~ g A n - SZ ..... ...
~ ... v ~ 0 fl I:l Q v ~ ~ i JIll W
o Pt L M S L M S L M S L M L M S
3.00~--------~--------~--------~----------~------~
2.00r-~~----~--------+---------~--------~--------~
o P/bdf' SM SML ML SML ML L SML ML ML ML L
c ML ML L
Fig. 3.10b Average Value in each Parameter Domain for D5 (3 cycle/l cycle)
53
54
6.00
4.00
2.00
o a/d ::::
6.00
4.00
2.00
o
'V
~
PV1 .::. 1.2 % 6.00
4.00
2.00
~ V
8 o
8
Pt L M S
6.00
4.00
'V 'V
o "
1.0,1.5
'V
~
> 1.2 %
" 0
§ 0 0 ~
L M S
" ~
2.00
!~ g§~ ~~ ...... 0
0
A~~ C~ ~ o
2.0
'V @ 8 ~
< 1.2% > 1.2%
T"7
V 0 @ 8 ~ , C
., L M S L M
'V .... 'V
.@lvU ,~ A~.e- .~ i6 •
P/bdf' SM SML ML SML ML L SML ML ML ML L c
...
2.5,3.0
lj
~ I II
L M S
. -=
ge IIi II
ML ML L
Fig. 3.10c Average Value in each Parameter Domain for DS (10 cycle/l cycle)
0.60
0.40
0.20
o aid =
0.60
0.40
0.20
o Pw
0.60
0.40
0.20
o
A
0 ~
~ 1.2%
II ~
0
~ ~
1.0,1.5
A
<>
" > 1.2%
~
A V A ~
II A 0 0 ~ sa
Pt L M 5 L M 5
~ ~
2.0 2.5,3
A
81 • ~ 1.2% >1.2%
~ V 8 i A ~ •
b e '9 .... • 0 ~
L M 5 L M L M S 0.60~------~--------~--------~--------~--------
0040
0.20
0 P/bdf' c
A AV
AA
eO A~b ~ t~ 00
~ 9 v 0 0 ~~ 0
SM SML ML SML ML L SML ML ML ML L ML ML
Fig. 3.lla Average Value in each Parameter Domain for 08 (Amplitude)
e
L
55
56
3.00
2.00
1.00
o a/d =
3.00
2.00
.1.06
o Pw
3.00
2.00
1.00
o
V ,....
~
!!: 1.2%
8 V
<> ~ A
,Iz..
1.0,1.5
v
Ii
~
>1.2%
V
~ V ,., ,.... e
~ <;;7
A A A
Pt L M S L M S
..Q
-"
2.0 2.5,3.0
~ V f'i
A A
!!:1.2% > 1.2%
V V V B .,
i 0 a II f"II A .... Z A .u
A" A ... A A
L M S L M L M S 3.00~------~~------~~-------,--------~--------~
2.00
1.00
0 P/bdf
, c
V
0 V V V V
~ B ~o
<>A A<> A
SM' SML ML SML ML L SML ML ML ML L ML ML
Fig. 3.llb Average Value in each Parameter Domain for DB (3 cycle/l cycle)
L
4.00
2.00
o aid =
4.00
2.00
o Pw
4.00
2.00
o
V
8 6
~ 1.2%
V V
0 0
<> 2 6
~
1.0,1.5
'0
0
&
>1.2%
V
V 0 'iJ 0 0 Q
8 g 6 6
P t L M S L M S
.... 'Y -y ...
2.0 2.5,3.0
V V
& 0 6
~1.2 % >1.2%
V V
~ ij ~ 0 I@
0 ~ I) & 6 6 ~ 6. 6.
L M S L M L M S 4.00 r--------,r--------.-------r----~----__.
'iJ
V V
V n 0 In 2.00~--~~--~--------~--V------4---------~--------~
8 0 V 0 V V
o
<>0 o~ ;9 <> ~ o§ Q <>80 ~~ o~ ~@ 6~ ~gi 66 6~~ 86. 6 6.~~ 6 6
P/bdf' SM SML ML SML ML L SML ML ML ML L c
ML ML L
Fig. 3.11c Average Value in each Parameter Domain for D8 (10 cycle/l cycle)
57
58
1.50
0.50 .S1
-~ ~ o aid = 1.0,1.5 2.0 2.5,3.0
1.00
0.50 v
V V 0 9 ~ 8 <> 6
6 6
< 1.2% > 1.2 % ~1.2% < 1.2%
0.50 V V
§ V .:;;J u
6 V V 0 v 0 0
0 0 <> 0 6 <> 6 i ~ ij <> <> <> <> V 6 S
6 6 6 6 B 6 ~
o Pt L M S L M S L M S L M L M S
1.00
V V
0.50
0 Zro
V V ~<> U R .... tr'I ~. C.
Vv V o V -V <>ec ;,V V <> ¢v
A g~g t, ~ 0 <>0 0<> 6 0 6 ij <> <>@
~8 6~ 6 . ~A V 6 6<> S
66 6A Hi ~ 6
o P/bdf' SM SML ML SML ML L SML ML ML ML L
c ML ML L
Fig. 3.l2a Average Value in each Parameter Domain for D9 (Amplitude)
1.50
1.00
0.50
o aid = 1.50
1.00
0.50
o Pw
1.50
1.00
0.50
o
/.ijj
e
~'f'"'
1.0,1.5
'il -<> 0 6 6
~ 1.2% >1.2 %
~ 9 0
u .. e- 'il V <> 6 0 6 0 6 6
Pt L M S L M S
--E)
r----:: 2.0 2.5,3.0
.., ~ v
~ 6
~ 1.2% >1.2%
0
.., X ~
g 0 A \l - ....
6 v ~ 0 0 6 -or
<> <> @ 6 <> 6
6 6 6
L M S L M L M S 1.50,..------r------or------r------------.
1.00
0 P/bdf'
c
6 6 6
6
SM SML ML SML ML L SML ML ML ML L ML ML
Fig. 3.l2b Average Value in each Parameter Domain for D9 (3 cycle/l cycle)
@ 6
L
59
60
1.50
1.00
0.50
o a/d = 1.50
1.00
0.50
1.00
0.50
o
v ~
~
<>
A
~ 1.2%
V
" ~ -~
<> A
----I:'""
tr---
1.0,1.5
n
0 <>
A
>1.2%
V 0
A
~ V <> 0
V & A 0
A A
Pt L M S L M S 1.50
1.00
V 0 <> V
88 V V oV 0 0 0 A
0.50 <> 0
98 vi v<> !
<> &0 AOO V A A 0 A
A A 0 A A
o A
-........, ---2.0
0 ~
<> A
A
~ 1.2% >1.2%
0 V
IS2I ~ a <>
~ <>
~
6 <> A A
A
L M S L M
e 0 <> 0 V
V ~6A Vv
fJ 00 <>
r. ~ 0 0<> ~A V<>
... OA
0 A AA A A
P/bdf' SM SML ML SML ML L SML ML ML ML L c
f:::::::::.....
::;: ~
2.5,3.0
I¥' v
8 0 0 A <> 0
A A
L M S
0
0 vv v
V 0 0 0 00
&A OA 0
A A
ML ML L
Fig. 3.l2c Average Value in each Parameter Domain for D9 (10 cycle/l cycle)
Q
A
07 (ESTIMATED EQUATION)
PARABOLIC EQUATION
o ------------~~--~----------~~8
By
( a) PRIMARY CURVE
Q 03
RANGE 2 04 RANGE I
------~~----~------~~----~8
( b) HYSTERESIS LOOP
Fig. 4.1 Estimated Hysteresis Loop
61
62
10Yt-__ lOY 20Y 30Y -tOY
MEASURED
<tOY 30Y 3DY iDY
ATALAY
1.3r----.-----r----.-----.---~r_--~----_r--~
w u 0.6~--~----_+----_+----~~~~~~~~~~--~ 0::
f2 0:: 0 « w :I:
Cf) _ 0.6 F-----b?..::::.....--¥::~'--__tfi'---t---iES TI MA TED __ -+-__ -;
-1.3 -4 -3 -2 -I 0 1 2 3 4
DEFLECTION IN 8 y ,
a/d = 1.0 Pt = 0.38 Pw = 0.21 P/bd = 0 f 190 c
Fig. 4.2 Comparison of Hysteresis Loops: Case 1
/-----+- +--.. -t--------J iOY 20Y 30Y iOY
MEASURED
ATALAY
1
1.3~----~-----r----~------~----~----~----~----~
w u 0.6 ~----+-----~-----+------~HL~~~~~~~~~~~ 0::
f2 0:: 0 « w ::t:
(/) - o. 6 1----::::o.-s.,~=---,~6+_~~s._~_,p_H_~---.'- TIMATED ____ ~----~
-1.3 L-____ ~ ____ ~~ ____ ~ ____ _L ____ ~ ______ ~ ____ _L ____ ~
-4 -3 -2 -I 0 I DEFLECTION IN 8
y
2 3 4
,
63
aid 1.0 Pt = 0.34 P = 0.36 w
p/bd 26.3 f = 274 c
Fig. 4.3 Comparison of Hysteresis Loops: Case.2
64
MEASURED
ATALAY
1.3~~--~~--~----~----~----~-----.r-----.-----.
w ~----4-----~-----4------~~~~~~~~~~~~~ u 0.6 0::
~ 0:: 0 <l: W J: (/) - 0.6 ESIH~ATED
-1.3 -4 -3 -2 -I 0 2 3
DEFLECTION IN <5 y
aid 1.5 Pt 0.41 Pw = 1.02 P/bd = 30
Fig. 4.4 Comparison of Hysteresis Loops: Case 3
4
I
f = 240 c
65
4 Y
MEASURED
40Y 30Y ZOY 30Y 40Y
ATALAY
1.3r-----~----~------~----~----~------~----_r----~
w u O.6~----+_----~----_+------~_r~*_~~~~~~--~~ a:: f2 a:: 0 <t W J: en _ O. 6 ~=---~=_=--___Ioo~,.....:;..--_ffP.,,&_--~----- .. ES TI MA TED ___ -+-___ --1
-1.3 -4 -3 -2 -I 0 1 2 3 4
DEFLECTION IN 6 y ,
a/d = 1.5 Pt 1.24 Pw := 2.12 P/bd 30 f 207 c
Fig. 4.5 Comparison of Hysteresis Loops: Case 4
66
'lOY lOY 30Y <tOY
MEASURED
ATALAY
1.3~----~----~------.------r----~r-----.------.-----.
w u 0.6~----+-----~----~-----+~~~~~~~~~~~~ 0:::
f2 0::: 0 « w ::I: en ~ 0.6 I--__ ~d:_.....:;::~~~~:;..<::J~~'--+_----,L.
- I. 3 -4 -3 -2 -I 0 1
DEFLECTION IN <5 y
aid = 2.0 Pt 0.34 Pw = 0.71
2
P/bd 52.5
Fig. 4.6 Comparison of Hysteresis Loops: Case 5 .
3 4
I
f = c 245
4 lDY 4DY
MEASURED
ATALAY
1.3 ~----~------~----~------~------~----~------~----~
~ 0.6~----~-----+------~----~~~~~~~~~~~-=~~ a:: f2 a:: 0 « w :r: (f) _ 0.6 ESTIMATED
-1.3 -4 -3 -2 -I 0 1 2
DEFLECTION IN 0 y
aid = 2.0 Pt = 0.95 Pw = 1.27 p/bd 26.3
Fig. 4.7 Comparison of Hysteresis Loops: Case 6
3 4
f 245 c
67
68
., OY 30Y 'tOY
MEASURED
'tOY 30Y -tOY
ATALAY
1.3r-----.-----.-----~----_r----~----~~----~--~
w U 0.6~----~----~----_4------~_#~~~~~~~~~~~ 0::
l:2 0:: 0 « w I (/) _ 0.6 h~~_I_=~1f:::...,...:F~~~~~:;L__+-----!ESTI MA TED --__ -I-____ ~
- 1.3 -4 -3 -2 -I 0 1 2 3 4
DEFLECTION IN 0 y
1
aid 2.5 Pt = 0.61 Pw = 0.36 P/bd 26.3 f 205 c
Fig. 4.8 Comparison of Hysteresis Loops: Case 7
69
i0Y
MEASURED
i0Y iOY
ATALAY
1 .3r-----.-----.-----~----~----~----~------~--~
w u 0.6 r-----+-----~----_+------~~~~~~~~~~ __ ~~ a:: ~ a:: 0 « w J: (f) _ 0.6 ESTIMATED
-1.3 --4 -3 -2 -I 0 2
DEFLECTION IN 0 y
aid 2.5 Pt 0.61 Pw =' 0.77 P/bd ::: 52.5
Fig. 4.9 Comparison of Rystcresis Loops: Case 8
3 4
I
207 f = c
70
iOY ZOY 30Y iOY
MEASURED
1.3 r------.------~----~------~----~------~----__ ----~
-1.3 -4 -3 -2
aid = 3.0 0.34
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p = 0.28 w
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2
52.5
:'ig. 4.10 Comparison of Hysteresis Loops: Case' 9
3 4
f~ = 193
71
30Y ~OY
MEASURED
ATALAY
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w u a::: 0.6
0 lL..
a::: 0 <{ W I (f)
- 0.6
- 1.3 -4 -3 -2 -I 0 1 2 3 4
DEFLECTION IN 0 y
aid 3.0 0.96 P/bd I
Pt Pw == 0.60 26.3 f 189 c
Fig. 4.11 Comparison of Hysteresis Loops: Case 10
72
where
A = {- 0.17 + (0.27 + 0.3 P/bdf') amp - (0.02 + 0.04 P/bdf') amp2} D7 J c c
B = (0.245 - 0.284 P/bdf' - 1.712 p ) lamp - 1 • D7 Jew
and CpJ is the value of 0 that yields a zero value of FJ(O).
Fig. 4.12 Penzien-Ata1ay ~ode1
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1
77
EARTHQUAKE ENGINEERING RESEARCH CENTER REPORTS
NOTE: Numbers in parenthesis are Accession Numbers assigned by the National Technical Information Service; these are followed by a price code. Copies of the reports may be ordered from the National Technical Information Service, $285 Port Royal Road, 'Springfield, Virginia, 22161. Accession Numbers should be quoted on orders for reports (PB------) and remittance must accompany each order. Reports without this information were not available at time of printing. Upon request, EERC will mail inquirers this information when it becomes available.
EERC 67-1
EERC 68-1
EERC 68-2
EERC 68-3
EERC 68-4
EERC 68-5
EERC 69-1
EERC 69-2
EERC 69-3
EERC 69-4
EERC 69-5
EERC 69-6
EERC 69-7
EERC 69-8
"Feasibility Study Large-Scale Earthquake Simulator Facility," by J. Penzien, J.G. Bouwkamp, R.W. Clough and D. Rea - 1967 (PB 187 905)A07
Unassigned
"Inelastic Behavior of Beam-to-Co1umn Subassemblages Under Repeated Loading," by V. V. Bertero - 1968 (PB 184 888)A05
"A Graphical Method for Solving the Wave Reflection-Refraction Problem," by H.D. McNiven and Y. Hengi - 196B (PB 187 943)A03
"Dynamic Properties of McKinley School Buildings," by D. Rea, J .G. Bouwkamp and R.W. Clough -1968 {PB 187 902)A07
"Characteristics of Rock Motions During Earthquakes," by H.B. Seed, LM. Idriss and F.W. Kiefer -196B (PB 188 338) A03
"Earthquake Engineering Research at Berkeley," - 1969 (PB lB7 906)All
"Nonlinear Seismic Response of Earth Structures," by M. Dibaj and J. PE;lnzien - 1969 (PB 187 904)AOB
"Probabilistic Study of the Behavior of Structures During Earthquakes," by R. Ruiz and J. Penzien - 1969 (PB 187 886)A06
"Numerical Solution of Boundary Value Problems in Structural Mechanics by Reduction to an Initial Value Formulation," by N. Distefano and J. Schujman - 1969 {PB 187 942)A02
"Dynamic Programming and the Solution of the Biharmonic Equation," by N. Distefano -1969 (PB 187 94l)A03
"Stochastic Analysis of Offshore Tower Structures,"by A.K. Malhotra and J. Penzien - 1969 (PB 187 903)A09
"Rock Motion Accelerograms for High Magnitude Earthquakes," by H.B. Seed and I.M. Idriss - 1969 (PB 187 940)A02
"Structural Dynamics Testing Facilities at the University of California, Berkeley," by R.M. Stephen, J.G. Bouwkamp, R.W. Clough and J. Penzien -1969 {PB 189 ll1)A04
EERC 69-.9 '. "Seismic Response of Soil Deposits Underlain by Sloping Rock Boundaries," by H. Dezfulian and H.B. Seed 1969 (PB 189 114)A03
EERC 69-10 "Dynamic Stress Analysis of Axisymmetric Structures Under Arbitrary Loading," by S. Ghosh and E.L. Wilson 1969 {PB 189 026)AIO
EERC 69-11 "Seismic Behavior of Multistory Frames Designed by Different Philosophies," by J.C. Anderson and V. V. Bertero - 1969 (PB 190 662)A10
EERC 69-12 "Stiffness Degradation of Reinforcing Concrete Members Subjected to Cyclic Flexural ~ments," by V.V. Bertero, B. Bresler and H. Ming Liao -1969 (PB 202 942)A07
EERC 69-13 "Response of Non-Uniform Soil Deposits to Travelling Seismic Waves," by H. Dezfulian and H.B. Seed-1969 (PB 191 023)A03
EERC 69.-14 "Damping Capacity of a Model Steel Structure," by D. Rea, R.W. Clough and J.G.Bouwkamp-1969 (PB190663)A06
EERC 69-15 "Influence of Local Soil Conditions on Building Damage Potential during Earthquakes," by H.B. Seed and I •. M. Idriss - 1969 (PB 191 036)A03
EERC 69-16 "The Behavior of Sands Under Seismic Loading Conditions," by M.L.Silver and H.B. Seed - 1969 (AD 714 9S2)A07
EERC 70-1 "Earthquake Response of Gravity Dams," by A.K. Chopra -1970 (AD 709 640)A03
EERC 70-2 "Relationships between Soil Conditions and Building Damage in the Caracas Earthquake ot July 29, 1967," by H.B. Seed, LM. Idriss and H. Dezfulian - 1970 (PB 195 762)A05
EERC 70-3 "Cyclic Loading of Full Size Steel Connections," by E.P. Popov and R.M. Stephen -1970 (PS 213 545)A04
EERC 70-4 "Seismic Analysis of the Charaima Building, Caraba1leda, Venezuela," by Subcommittee of the SEAONC Research Committee: v.v" Bertero, P.F. Fratessa, S.A. Mahin, J.H. Sexton, A.C. Scordelis, E.L. Wilson, L.A. Wyllie, H.B. Seed and J. Penzien, Chairman-1970 {PB 201 455)A06
Preceding page blank
78
EERC 70-5 "A Computer Program for Earthquake /illalysis of Dams," by A.K. Chopra and P. Chakrabarti - 1970 (AD 723 994)A05
EERC 70-6 "The Propagation of Love Waves Across Non-Horizontally Layered Structures," by J. Lysmer and L.A. Drake 1970 (PB 197 896)A03
EERC 70-7 "Influence of Base Rock Ch<lracteristics on Ground Response," by J. Lysmer, H.B. Seed and p.B., Schnabel 1970 (pB 197 897}A03
EERC 70-8 "Applicability of Laboratory Test Procedures for Measuring Soil Liquefaction Characteristics under Cyclic Loading," by H.B. Seed and w.n. Peacock - 1970 (pB 198 016}A03
EERC 70-9 "A Simplified Procedure for Evaluating Soil Liquefaction Potential," by II.B. Seed and I.M. Idriss - 1970 (pB 198 009)A03
EERC 70-10 "Soil Moduli and Damping Factors for Dynamic Response Analysis," by H.B. Seed and I,M. Idriss -1970 (pa 197 869)A03
r.r:!~C 71-1 "Koyna Earthquake of December 11, 1967 and the Performance of Koyna Dam," by A.K. Chopra and P. Chakrabarti 1971 (AD 731 4961AO&
EERC 71-2 "Preliminary In-Situ Measurements of Anelastic Absorption in Soils Using a Prototype Earthquake S~ulator," by R.D. Borcherdt and P.W. Rodgers - 1971 (PB 201 454}A03
EERC 71-3 "Static and Dvnamic lInalvsis of Inelastic Frame Structures," by F,L. Porter and G.H. Powell-1971 (PB 210 135) A06
EERC 71-4 "Research Needs in Limit Design of Reinforced Concrete Structures," by V. V. Bertero -1971 (PB 202 943)A04
EERC 71-5 "Dynamic Behavior of a High-Rise Diagonally Braced Steel Building," by D. Rea, A.A. Shah and;; .G. Bo'..lwJ~a .. 1p 1971 (PB 203 S84)A06
EERC 71-6 "Dynamic Stress lInalysis of Porous Elastic Solids Saturated with Compressible Fluids," by J. Ghaboussi and E. L. Wilson - 1971 (pB 211 396)A06
EERC 71-7 "Inelastic Behavior of Steel Beam-to-Column Subassemblages," by H. Krawinkler, V.V. Bertero and E.P. Popov 1971 (pB 211 335)A14
EERC 71-8 "Modification of Seismograph Records for Effects of Local Soil Conditions," by P. Schnabel, H.B. Seed and J. Lysmer - 1971 (PB 214 450}A03
EERC 72-1 "Static and Earthquake Analysis of Three Dimensional Frame and Shear Wall Buildin9s," by E.L. Wilson anli H. H. Dovey - 1972 (pB 212 904)A05
EERC 72-2 "Accelerations in Rock for Earthquakes in the Western United States," by p.B. Schnabel and H.B. Seed -1972 (pB 213 100)A03
EERC 72-3 "Elastic-Plastic Earthquake Response of Soil-Building Systems," by T. Minami -1972 (PB 214 868)A08
EERC 72-4 "Stochastic Inelastic Response of Offshore Towers to Strong Motion Earthquakes," by M.K. Kaul-1972 (1'13 215 713)A05
EERC 72-5 "Cyclic Behavior of Three Reinforced Concrete Flexural Members with High Shear," by E.P. Popov, V.V. Bertero and H •. Krawinkler - 1972 (pB 214 555)A05
EERC 72-6 "Earthquake Response of Gravity Dams Including Reservoir Interaction Effects," by P. Chakrabarti and A.K. Chopra - 1972 (AD 762 330)A08
EERC 72-7 "Dynamic Properties of Pine Flat Dam," by D. Rea, C. Y. Liaw and A.K. Chopra -1972 (AD 763 928)AOS
EERC 72-8 "Three Dimensional Analysis of Building Systems," by E.L. Wilson and H.H. Dovey -1972 (PB 222 438)A06
EERC 72-9 "Rate of Loading Effects on Uncracked and Repaired Reinforced Concrete Members," by S. Mahin, V.V. Bertero,
D. Rea and M. Atalay - 1972 (pB 224 520)A08
EERC 72-10 "Computer Program for Static and Dynamic Analysis of Linear Structural Systems," by E.L. Wilson, K.-J. Bathe, J. E. Peterson and H. H,Dovey - 1972 (pB 220 437)A04
EERC 72-11 "Literature Survey - Seismic Effects on Highway Bridges," by T. Iwasaki, J. Penzien and R.W. Clough -1972 (pB 215 6l3)A19
EERC 72-12 "SHAKE-A Computer Program for Earthquake Response Analysis of Horizontally Layered Sites," by P.B. Schnabel and J. Lysmer - 1972 (PB 220 207)A06
EERC 73-1 "Optimal Seismic Design of Multistory Frames," by v. V. Bertero and H. Kamil - 1973
EERC 73-2 !'Analysis of the Slides in the San Fernando Dams During the Earthquake of February 9, 1971." by H.B. Seed, K.L. Lee, I.M. Idriss and F. Makdisi -1973 (PB 223 402)A14
79
EERC 73-3 "Computer Aided Ultimate Load Design of Unbraced Multistory Steel Frames," by M.B. El-Hafez and G.H. Powell 1973 (PB 248 3l5)A09
EERC 73-4 "Experimental Investigation into the Seismic Behavior of Critical Re0ions of Reinforced Concrete Components as Influenced by Moment and Shear," by M. Celebi and J. Penzien - 1973 (PB 215 884)A09
EERC 73-5 "Hysteretic Behavior of Epoxy-Repaired Reinforced Concrete Beams," by M. Celebi and J. Penzien - 1973 (PB 239 568) A03
EERC 73-6 "General Purpose Computer Program for Inelastic Dynamic Response of Plane Structures," by A. Kanaan and G.H. Powell - 1973 (PB 221 260)A08
EERC 73-7 "A Computer Program for Earthquake Analysis of Gravity Dams Including Reservoir Interaction," by P. Chakrabarti and A.K. Chopra -1973 (AD 766 271)A04
EERC 73-8 "Behavior of Reinforced Concrete Deep Beam-Column Subassemblages Under Cyclic Loads," by o. Kiistii and J.G. Bouwkamp -1973 (PB 246 ll7)A12
EERC 73-9 "Earthquake Analysis of Structure-Foundation Systems," by A.K. Vaish and A.K. Chopra -1973 (AD 766 272)A07
EERC 73-10 "Deconvolution of Seismic Response for Linear Systems," by R.B. Reimer -1973 (PB 227 l79)A08
EERC 73-11 "SAP IV: A Structural Analysis Program for Static and Dynamic Response of Linear Systems," by K.-J. Bathe, E.L. Wilson and F.E. Peterson -1973 (PB 221 967)A09
EERC 73-12 "Analytical Investigations of the Seismic Response of Long, Multiple Span Highway Bridges," by W.S. Tseng and J. Penzien - 1973 (PB 227 8l6)AlO
EERC 73-13 "Earthquake Analysis of Multi-Story Buildings Including Foundation Interaction," by A.K. Chopra and J.A. GutiF:rrez -1973 (PB 222 970)A03
EERC 73-14 "ADAP: A Computer Program for Static and Dynamic Analysis of Arch Dams," by R.W. Clough, J.M. Raphael and S. Mojtahedi -1973 (PB 223 763)A09
EERC 73-15 "Cyclic Plastic Analysis of Structural Steel Joints," by R.B. Pinkney and R.W. Clough-l973 (PB226 B43)AOB
EERC 73-16 "QI.'AD-4: A Computer Program for Evaluating the Seismic Response of Soil Structures by Variable Damping Finite Element Procedures," by I.M. Idriss, J. Lysmer, R. Hwang and H.B. Seed -1973 (PB 229 424)AOS
EERC 73-17 "Dynamic '.<'havior of a Multi-Story Pyramid Shaped Building," by R.M. Stephen, J.P. Hollings and J.G. Bouwkamp - 1973 (PB 240 7lB)A06
EERC 73-1B "Effect of Different Types of Reinforcing On Seismic Behavior of Short Concrete Columns," by V.V. Bertero, J. Hollings, O. Kustu, R.M. Stephen and J.G. Bouwkamp -1973
EERC 73-19 "Olive View Medical Center Materials Studies, Phase I," by B. Bresler and V.V. Bertero -1973 (PB 235 9B6)A06
EERC 73-20 "Linear and Nonlinear Seismic Analysis Computer Programs for Long Multiple-Span Highway Bridges," by W.S. Tseng and J. Penzien -1973
EERC 73-21 "Constitutive Models for Cyclic Plastic Deformation of Engineering Materials," by J.M. Kelly and P.P. Gillis 1973 (PB 226 024)A03
EERC 73-22 "DRAIN - 2D User's Guide," by G.H. Powell - 1973 (PB 227 016)A05
EERC 73-23 "Earthquake Engineering at Berkeley - 1973," (PB 226 033)All
EERC 73-24 Unassigned
EERC 73-25 "Earthquake Response of Axisymmetric Tower Structures Surrounded by Water," by C.Y. Liaw and A.K. Chopra 1973 (AD 773 052)A09
EERC 73-26 "Investigation of the Failures of the Olive View Stairtowers During the San Fernando Earthquake and Their Implications on Seismic Design," by V.V. Bertero and R.G. Collins -1973 (PB 235 l06)A13
EERC 73-27 "Further Studies on Seismic Behavior of Steel Beam-Column Subassemblages," by V.V. Bertero, H. Krawinkler and E.P. Popov-1973 (PB 234 l72)A06
EERC 74-1 "Seismic Risk Analysis," by C.S. Oliveira - 1974 (PB 235 920)A06
EERC 74-2 "Settlement and Liquefaction of Sands Under Multi-Directional Shaking," by R. Pyke, C.K. Chan and H.B. Seed 1974
EERC 74-3 "Optimum Design of Earthquake Resistant Shear Buildings," by D. Ray, K.S. Pister and A.K. Chopra -1974 (PB 231 l72)A06
EERC 74-4 "LUSH - A Computer Program for Complex Response Analysis of Soil-Structure Systems," by J. Lysmer, T. Udaka, H.B. Seed and R. Hwang - 1974 (PB 236 796)A05
EERC 74-5
80
"Sensitivity Analysis for Hysteretic Dynamic Systems: Applications to Earthquake Engineering," by D. Ray 1974 (PB 233 2l3}A06
EERC 74-6 "Soil Structure Interaction Analyses for Evaluating Seismic Response," by H.B. Seed, J. Lysmer and R. Hwang 1974 (PB 236 5l9}A04
E~RC 74-7 Unassigned
EERC 74-8 "Shaking Table Tests of a Steel Frame - A Progress Report," by R.W. Clough and D. Tang-1974 (PB 240 S('9}A03
EERC 74-9 "Hysteretic Behavior of Reinforced Concrete Flexural Members with Special Web Reinforcement," by V.V. Bertero, E.P. Popov and T.Y. Wang - 1974 (PB 236 797)A07
EERC 74-10 "Applications of Reliability-Based, Global Cost Optimization to Design of Earthquake Resistant Structures," by E. Vitiello and K.S. Pister -1974 (PB 237 231)A06
EERC 74-11 "Liquefaction of Gravelly Soils Under Cyclic Loading Conditions," by R.T. Wong, H.B. Seed and C.K. Chan 1974 (PB 242 042)A03
EERC 74-12 "Site-Dependent Spectra for Earthquake-Resistant Design," by H.B. Seed, C. Ugas and J. Lysmer -1974 (PB 240 9~3)A03
EERC 74-13 "Earthquake Simulator Study of a Reinforced Concrete Frame," by P. Hidalgo and R.W. Clough -1974 (PB 241 9 t 4}A13
EERC 74-14 "Nonlinear Earthquake Response of Concrete Gravity Dams," by N. Pal - 1974 (AD/A 006 583}A06
EERC 74-15 "Modeling and Identification in Nonlinear Structural Dynamics - I. One Degree of Freedom Models," by N. Distefano and A. Rath - 1974 (PB 241 548)A06
EERC 75-1 "Determination of Seismic Design Criteria for the Dumbarton Bridge Replacement Structure, Vol. I: Description, Theory and Analytical Modeling of Bridge and Parameters," by F. Baron and S.-H. Pang -1975 (PB 259407)A15
EERC 75-2 "Determination of Seismic Design Criteria for the Dumbarton Bridge Replacement Structure, Vol. II: Numerical Studies and Establishment of Seismic Design Criteria," by F. Baron and S. -H. Pang - 1975 (PB 259 408) All (For set of EERC 75-1 and 75-2 (PB 259 406})
EERC 75-3 "Seismic Risk Analysis for a Site and a Metropolitan Area," by C.S. Oliveira -1975 (PB 248 l34)A09
EERC 75-4 "Analytical Investigations of Seismic Response of Short, Single or Multiple-Span Highway Bridges," by M.-C. Chen and J. Penzien-1975 (PB 241 454)A09
EERC 75-5 "An Evaluation of Some Methods for Predicting Seismic Behavior of Reinforced Concrete Buildings," by S.A.
EERC 75-6
Mahin and V.V. Bertero -1975 (PB 246 306}A16
"Earthquake Simulator Study of a Steel Frame Structure, Vol. I: Experimental Results," by R.W. Clough and D.T. Tang - 1975 (PB 243 981)A13
EERC 75-7 "Dynamic Properties of San Bernardino Intake Tower," by D. Rea, C.-Y. Liaw and A.K. Chopra -1975 (AD/A008406) AD5
EERC 75-8 "Seismic Studies of the Articulation for the Dumbarton Bridge Replacement Structure, Vol. I: DescriptiOn, Theory and Analytical Modeling of Bridge Components," by F. Baron and R.E. Harnati -1975 (PB 251 539)A07
EERC 75-9 "Seismic Studies of the Articulation for the Dumbarton Bridge Replacement Structure, Vol. 2: Numerical Studies of Steel and Concrete Girder Alternates," by F. Baron and R.E. Hamati -1975 (PB 251 540)A10
EERC 75-10 "Static and Dynamic Analysis of Nonlinear Structures," by D.P. Mondkar and G.H. Powell -1975 (PB 242 434)A08
EERC 75-11 "Hysteretic Behavior of Steel Columns," by E. P. Popov, V. V. Bertero and S. Chandramouli - 1975 (PB 252 365) All
EERC 75-12 "Earthquake Engineering Research Center Library Printed Catalog," - 1975 (PB 243 711) A26
EERC 75-13 "Three Dimensional Analysis of Building Systems (Extended Version)," by E.L. Wilson, J.P. Hollings and H.H. Dovey - 1975 (PB 243 989)A07
EERC 75-14 "Determination of Soil Liquefaction Characteristics by Large-Scale Laboratory Tests," by P. De Alba, C.K. Chan and H.B. Seed - 1975 (NUREG 0027)A08
EERC 75-15 "A Literature Survey - Compressive, Tensile, Bond and Shear Strength of Masonry," by R.L. Mayes and R.W. Clough -1975 (PB 246 292)A10
EERC 75-16 "Hysteretic Behavior of Ductile Moment Resisting Reinforced Concrete Frame Components," by V.V. Bertero and E.P. Popov -1975 (PB 246 388)AD5
EERC 75-17 "Relationships Between Maximum Acceleration, Maximum Velocity, Distance from Source, Local Site Conditions for Moderately Strong Earthquakes," by H.B. Seed, R. Murarka, J. Lysmer and I.M. Idriss -1975 (PB 248 172)A03
EERC 75-18 "The Effects of Method of Sample Preparation on the Cyclic Stress-Strain Behavior of Sands," by J. Mulilis, c. K. Chan and H. B. Seed - 1975 (Summarized in EERC 75-28)
81
EERC 75-19 "The Seismic Behavior of Critical Regions of Reinforced Concrete Components as Influenced by Moment, Shear and Axial Force," by M.B. Atalay and J. Penzien -1975 (PB 258 842)All
EERC 75-20 "Dynamic Properties of an Eleven Story Masonry Building," by R.~!. Stephen, J.P. Hollings, J.G. Bouwkamp and D. Jurukovski - 1975 (PB 246 945)A04
EERC 75-21 "State-of-the-Art in Seismic Strength of Masonry - An Evaluation and Review," by R. L. Mayes and R.W. Clough 1975 (PB 249 040)A07
EERC 75-22 "Frequency Dependent Stiffness Matrices for Viscoelastic Half-Plane Foundations," by A.K. Chopra, P. Chakrabarti and G. Dasgupta - 1975 (PB 248 121)A07
EERC 75-23 "Hysteretic Behavior of Reinforced Concrete Framed Walls," by T.Y. Wong, V.V. Bertero and E.P. Popov-1975
EERC 75-24 "Testing Facility for Subassemblages of Frame-Wall Structural Systems," by V.V. Bertero, E.P. Popov and T. Endo-1975
EERC 75-25 "Influence of Seismic History on the Liquefaction Characteristics of Sands.," by H.B. Seed, K. Meri and C.K. Chan -1975 (Summarized in EERC 75-28)
EERC 75-26 "The Generation and Dissipation of Pore Water Pressures during Soil Liquefaction," by H.B. Seed, P.P. Martin and J. Lysmer - 1975 (PB 252 648)A03
EERC 75-27 "Identification of Research Needs for Improving Aseismic Design of Building Structures," by V.V. Bertero 1975 (PB 248 l36)A05
EERC 75-28 "Evaluation of Soil Liquefaction Potential during Earthquakes," by H .B. Seed, 1. Arango and C.K. Chan - 1975 (NUREG 0026)A13
EERC 75-29 "Representation of Irregular Stress Time Histories by Equivalent Uniform Stress Series in Liquefaction Analyses," by H.B. Seed, I.M. Idriss, F. Makdisi and N. Banerjee -1975 (PB 252 635)A03
EERC 75-30 "FLUSH - A Computer Program for Approximate 3-D Analysis of Soil-Structure Interaction Problems," by J. Lysmer, T. Udaka, C.-F. Tsai and H.B. Seed - 1975 (PB 259 332)A07
EERC 75-31 "ALUSH - A Computer Program for Seismic Response Analysis of Axisymmetric Soil-Structure Systems," by E. Berger, J. Lysmer and H.B. Seed -1975
EERC 75-32 "TRIP and TRAVEL - Computer Programs for Soil-Structure Interaction Analysis with Horizontally Travelling Waves," by T. Udaka, cT. Lvsmer ilnd H.B. Seed-1975
EERC 75-33 "Predicting the Performance of Structures in Regions of High Seismicity," by J. Penzien -1975 (PB 248 130)A03
EERC 75-34 "Efficient Finite Element Analysis of Seismic Structure - Soil - Direction," by J. Lysmer, H.B. Seed, T. Udaka, R.N. Hwang and C.-F. Tsai -1975 (PB 253 570)A03
EERC 75-35 "The Dynamic Behavior of a First Story Girder of a Three-Story Steel Frame Subjected to Earthquake ~ading," by R. w. Clough and L.-Y. Li - 1975 (PB 248 841)A05
EERC 75-36 "Earthquake Simulator Study of a Steel Frame Structure, Volume II-Analytical Results," by D.T. Tang-1975 (PB 252 926)AIO
EERC 75-37 "ANSR-I General Purpose Computer Program for Analysis of Non-Linear Structural Response," by D.P. Mondkar and G.H. Powell - 1975 (PB 252 386)A08
EERC 75-38 "Nonlinear Response Spectra for Probabilistic Seismic Design and Damage Assessment of Reinforced Concrete Structures." by M. Murakami and J. Penzien - 1975 (PB 259 530)A05
EERC 75-39 "Study of a Method of Feasible Directions for Optimal Elastic Design of Frame Structures Subjected to Earthquake Loading," by N.D. Walker and K.S. Pister-1975 (PB 257 781)A06
EERC 75-40 "An Alternative Representation of the Elastic-Viscoelastic Analogy," by G. Dasgupta and J.L. Sackman-1975 (PB 252 173)A03
EERC 75-41 "Effect of Multi-Directional Shaking on Liquefaction of Sands," by H.B. Seed, R. Pyke and G.R. Martin -1975 (PB 258 781)A03
EERC 76-1 "Strength and Ductility Evaluation of Existing Low-Rise Reinforced Concrete Buildings - Screening Method," by T. Okada and B. Bresler -1976 (PB 257 906)All
EERC 76-2 "Experimental and Analytical Studies on the Hysteretic Behavior of Reinforced Concrete Rectangular and T-Beams," by S.-Y.M. Ma, E.P. Popov and V.V. Bertero-1976 (PB 260 843)A12
EERC 76-3 "Dynamic Behavior of a Multistory Triangular-Shaped Building," by J. Petrovski, R.M. Stephen. E. GartenbaUIII and J.G. Bouwkamp -1976 (PB 273 279)A07
EERC 76-4 "Earthquake Induced Deformations of Earth Dams," by N. Serff, H.B. Seed, F.r. Makdisi & C.-Y. Chang - l,976 (PB 292 065)A08
82
EERC 76-5 "Analysis and Design of Tube-Type Tall Buildinci Structures," by H. de Clercq and G.H. Powell - 1976 (PB 252220) AIO
EERC 76-6 "Time and Frequency Domain Analysis of Three-Dimensional Ground Motions, San Fernando Earthquake," by T. Kubo and J. Penzien (PB 260 556)All
EERC 76-7 "Expected Performance of Uniform Building Code Design Masonry Structures," by R.L. Mayes, Y. Ornote, S.W. Chen and R.W. Clough - 1976 (PB 270 098)A05
EERC 76-8 "Cyclic Shear Tests of Masonry Piers, Volume 1 - Test Results," by R.L. Mayes, Y. Omote, R.W. Clough - 1976 (PB 264 424)A06
EERC 76-9 "A Substructure Method for Earthquake Analysis of Structure - Soil Interaction," by J.A. Gutierrez and A.K. Chopra - 1976 (PB 257 783)A08
EERC 76-10 "Stabilization of Potentially Liquefiable Sand Deposits using Gravel Drain Systems," by H.B. Seed and J.R. Booker- 1976 (PB 258 820)A04
EERC 76-11 "Influence of Design and Analysis Assumptions on Computed Inelastic Response of Moderately Tall Frames," by G.H. Powell and D.G. Row - 1976 (PB 271 409)A06
EERC 76-12 "Sensitivity Analysis for Hysteretic Dynamic Systems: Theory and Applications," by D. Ray, K.S. Pister and E. Polak - 1976 (PB 262 859)A04
EERC 76-13 "Coupled Lateral Torsional Response of Buildings to Ground Shaking," by C.L. Kan and A.K. Chopra -1976 (PB 257 907)A09
EERC 76-14 "seismic Analyses of the Ban= de America," by V.V. Bertero, S.A. Mahin and J.A. Hollings - 1976
EERC 76-15 "Reinforced Concrete Frame 2: Seismic Testing and Analytical Correlation," by R.W. Clough and J. Gidwani - 1976 (PB 261 323)A08
EERC 76-16 "Cyclic Shear Tests of Masonry Piers, Volume 2 - Analysis of Test Results," by R.L. Mayes, Y. Ornate and R.W. Clough - 1976
EERC 76-17 "Structural Steel Bracing Systems: Behavior Under Cyclic Loading," by E.P. Popov, K. Takanashi and C.W. Roeder - 1976 (PB 260 7l5)A05
EERC 76-18
EERC 76-19
EERC 76-20
EERC 76-21
EERC 76-22
EERC 76-23
EERC 76-24
EERC 76-25
EERC 76-26
EERC 76-27
EERC 76-28
EERC 76-29
EERC 76-30
EERC 76-31
EERC 76-32
"Experimental Model Studies on seismic Response of High Curved OVercrossings," by D. Williams and W.G. Godden - 1976 (PB 269 548)A08
"Effects of Non-Uniform Seismic Disturbances on the Durnbarton Bridge Replacement Structure," by F. Baron and R.E. Hamati - 1976 (PB 282 98l}A16
"Investigation of the Inelastic Characteristics of a Single Story Steel Structure Using System Identification and Shaking Table Experiments," by V.C. Matzen and H.D. McNiven - 1976 (PB 258 453)A07
"Capacity of Columns with Splice Imperfections," by E.P. Popov, R.M. Stephen and R. Philbrick - 1976 (PB 260 378)A04
"Response of the Olive View Hospital Main Building during the San Fernando Earthquake," by S. A. Mahin, V.V. Bertero, A.K. Chopra and R. Collins - 1976 (PB 271 425}A14
"A Study on the Major Factors Influencing the Strength of Masonry Prisms," by N.M. Mostaghel, R.L. Mayes, R. W. Clough and S.W. Chen - 1976 (Not published)
"GADFLEA - A Computer Program for the Analysis of Pore Pressure Generation and Dissipation during cyclic or Earthquake Loading," by J.R. Booker, M.S. Rahman and H.B. Seed - 1976 (PB 263 947)A04
"Seismic Safety Evaluation of a RIC School Building," by B. Bresler and J. Axley - 1976
"Correlative Investigations on Theoretical and Experimental Dynamic Behavior of a Model Bridge Structure," by K. Kawashima and J. Penzien - 1976 (PB 263 388)All
"Earthquake Response of Coupled Shear Wall Buildings," by T. Srichatrapimuk - 1976 (PB 265 157)A07
"Tensile Capacity of Partial Penetration Welds," by E.P. Popov and R.M. Stephen - 1976 (PB 262 899}A03
"Analysis and Design of Numerical Integration Methods in Structural Dynamics," by H.M. Hilber - 1976 (PB 264 4l0}A06
"Contribution of a Floor System to the Dynamic Characteristics of Reinforced Concrete Buildings," by L.E. Malik and V.V. Bertero - 1976 (PB 272 247)A13
"The Effects of Seismic Disturbances on the Golden Gate Bridge," by F. Baron, M. Arikan and R.E. Harnati _ 1976 (PB 272 279}A09
"Infilled Frames in Earthquake Resistant Construction," by R.E. Klingner and V.V. Bertero - 1976 (PB 265 892)A13
83
UCB/EERC-77/01 "PLUSH - A Computer Program for Probabilistic Finite Element Analysis of Seismic SOil-Structure Interaction," by M.P. Rome Organista, J. Lysmer and H.B. Seed - 1977
UCB/EERC-77/02 "Soil-Structure Interaction Effects at the Humboldt Bay Power Plant in the Ferndale Earthquake of June 7, 1975," by J.E. Valera, H.B. Seed, C.F. Tsai and J. Lysmer - 1977 (PB 265 795)A04
UCB/EERC-77/03 "Influence of Sample Disturbance on Sand Response to Cyclic Loading," by K. Mori, H.B. Seed and C.K. Chan - 1977 (PB 267 352)A04
UCB/EERC-77/04 "Seismological Studies of Strong Motion Records," by J. Shoja-Taheri - 1977 (PB 269 655)AIO
UCB/EERC-77/05 "Testing Facility for Coupled-Shear Walls," by L. Li-Hyung, V.V. Bertero and E.P. Popov - 1977
UCB/EERC-77/06 "Developing Methodologies for Evaluating the Earthquake Safety of Existing Buildings," by No.1 -B. Bresler; No.2 - B. Bresler, T. Okada and D. zisling; No.3 - T. Okada and B. Bresler; No.4 - V.V. Bertero and B. Bresler - 1977 (PB 267 354)A08
UC8/EERC-77/07 "A Literature Survey - Transverse Strength of Masonry Walls," by Y. ornote, R.L. Mayes, S.W. Chen and R.W. Clough - 1977 (PB 277 933)A07
UCB/EERC-77/08 "DRAIN-TABS: A Computer Program for Inelastic Earthquake Response of Three Dimensional Buildings," by R. Guendelman-Israel and G.H. Powell - 1977 (PB 270 693)A07
UCB/EERC-77/09 "SUBWALL: A Special Purpose Finite Element Computer Program for Practical Elastic Analysis and Design of Structural Walls with Substructure Option," by D.Q. Le, H. Peterson and E.P. Popov - 1977 (PS 270 567)A05
UCB/EERC-77/l0 "Experimental Evaluation of Seismic Design Methods for Broad cylindrical Tanks," by D.P. Clough (PS 272 280)A13
UCB/EERC-77/ll "Earthquake Engineering Research at Berkeley - 1976," - 1977 (PB 273 507)A09
UCB/EERC-77/12 "Automated Design of Earthquake Resistant Multistory Steel Building Frames," by N.D. Walker, Jr. - 1977 (PS 276 526)A09
UCB/EERC-77/13 "Concrete Confined by Rectangular Hoops Subjected to Axial Loads," by J. Vallenas, V.V. Bertero and E.P. Popov - 1977 (PB 275 165)A06
UCS/EERC-77/l4 "Seismic Strain Induced in the Ground During Earthquakes," by Y. Sugimura - 1977 (PS 284 201)A04
UCB/EERC-77/l5 "Bond Deterioration under Generalized Loading," by V.V. Bertero, E.P. Popov and S. Viwathanatepa - 1977
UCB/EERC-77/l6 "Computer Aided Optimum Design of Ductile Reinforced Concrete Moment Resisting Frames," by S.W. Zagajeski and V.V. Bertero - 1977 (PS 280 137)A07
UCB/EERC-77/l7 "Earthquake Simulation Testing of a Stepping Frame with Energy-Absorbing Devices," by J.M. Kelly and D.F. Tsztoo - 1977 (PB 273 506)A04
UCB/EERC-77/18 "Inelastic Behavior of ECcentrically Braced Steel Frames under Cyclic Loadings," by C.W. Roeder and E.P. Popov - 1977 (PB 275 526)A15
UCB/EERC-77/l9 "A Simplified Procedure for Estimating Earthquake-Induced Deformations in Dams and Embankments," by F.I. Makdisi and H.B. Seed - 1977 (PB 276 820)A04
UCB/EERC-77/20 "The Performance of Earth Dams during Earthquakes," by H.B. Seed, F.I. Makdisi and P. de Alba - 1977 (PB 276 821)A04
UCB/EERC-77/21 "Dynamic Plastic Analysis Using Stress Resultant Finite Element Formulation," by P. Lukkunapvasit and J.M. Kelly - 1977 (PB 275 453)A04
UCB/EERC-77/22 "Preliminary Experimental Study of Seismic Uplift of a Steel Frame," by R.W. Clough and A.A. Huckelbridge 1977 (PB 278 769)A08
UCB/EERC-77/23 "Earthquake Simulator Tests of a Nine-Story Steel Frame with Columns Allowed to Uplift," by A.A. Huckelbridge - 1977 (PB 277 944)A09
UCB/EERC-77/24 "Nonlinear Soil-Structure Interaction of Skew Highway Bridges," by M.-C. Chen and J. Penzien - 1977 (PB 276 176)A07
UCB/EERC-77/25 "Seismic Analysis of an Offshore Structure Supported on Pile Foundations," by D.D.-N. Liou and J. Penzien 1977 (PB 283 180)A06
UCB/EERC-77/26 "Dynamic Stiffness Matrices for Homogeneous Viscoelastic Half-Planes," by G. Dasgupta and A.K. Chopra -1977 (PB 279 654)A06
UCB/EERC-77/27 "A Practical Soft Story Earthquake Isolation System," by J.M. Kelly, J.H. Eidinger and C.J. Derham -1977 (PB 276 814)A07
UCB/EERC-77/28 "Seismic Safety of Existing Buildings and Incentives for Hazard Hitigation in San Francisco: An Exploratory Study," by A.J. Meltsner - 1977 (PB 281 970)A05
UCB/EERC-77/29 "Dynamic Analysis of Electrohydraulic Shaking Tables," by D. Rea, S. Abedi-Hayati and Y. Takahashi 1977 (PB 282 569)A04
UCB/EERC-77/30 "An Approach for Improving Seismic - Resistant Behavior of Reinforced Concrete Interior Joints," by B. Galunic, V.V. Bertero and E.P. Popov - 1977 (PB 290 870)A06
84
lie 'B/EERC-78/0l
U<:B/EERC-78/02
UCB/EERC-78/03
UCB/EERC-78/04
UCB/EERC-78/0S
UCB/EERC-78/06
UCB/EERC-78/07
l:CBiEERC-78/08
CCB/EERC-78/09
UCB/EERC-78/l0
\XB/EERC-78/11
"The Development of Energy-Absorping Devices for Aseismic Base Isolation systems," by J.M. Kelly and D.F. Tsztoo - 197B (PB 284 978)A04
"Effect of Tensile Prestrain on the Cyclic Response of Structural Steel Connections, by J.G. Bouwkamp and A. Mukhopadhyay - 1978
"Experimental Results of an Earthquake Isolation System using Natural Rubber Bearings," by J.M. Eidinger and J.M. Kelly - 1978 (PB 281 686)A04
"Seismic Behavior of Tall Liquid Storage Tanks," by A. Niwa - 1978 (PB 284 017) A14
"Hysteretic Behavior of Reinforced Concrete Columns Subjected to High Axial and Cyclic Shear Forces," by S.W. Zagajeski, V.V. Bertero and J.G. Bouwkamp - 1978 (PB 283 858)A13
"Inelastic Beam-Column Elements for the ANSR-I Program," by A. Riahi, D.G. Ilow and G.H. Pow~ll - 1978
"Studies of Structural Response to Earthquake Ground t10tion," by O.A. Lopez and A.K. Chopra - 1978 (PB 282 790)A05
"A Laboratory Study of the Fluid-Structure Interaction of Submerged Tanks and Caissons in Earthquakes," by R.C. Byrd - 1978 (PB 284 957)A08
"Model for Evaluating Damageability of Structures," by I. Sakamoto and B. Bresler - 1978
"Seisnlic Performance of Nonstructural and Secondary Structural Elements," by r. Sakamoto - 1978
"Mathematical nodelling of Hysteresis Loops for Reinforced Concrete Columns," by S. Nakata, T. Sproul and J. Penzien - 1978